end Bounty

/- One-file Erdős 1062(ii) proof candidate.
The submission body is independent of local modules and data files. -/

/- Component PolicyCombinatorialFrontFast; SHA256 9f1109298a4d819400a9ca244751c04849e7fee75492eae7fa39e0a2f8219316. -/
section PolicySubmissionPart0
/- Ordinary combinatorial front: compact finite base, normalization, depth-5 closure, and both input families. -/

/- Frozen source PolicyBaseExactCompact; SHA256 e2225388355ddc67c206ff2e1867c675da6447335cd4360f12ac0457d05386a2. -/
section PolicyCombinatorialFront_PolicyBaseExactCompact
/- One-file proof candidate assembled from the actual local import graph.
A complete ordinary-kernel check and target axiom audit are still required. -/

/- Component Solution; SHA256 dd1b2e49c0e97dfe5eb14a613957f604da4aacacc129697486e6add57caf69ab -/
section SubmissionComponent_Solution
/- Combinatorial and arithmetic lemmas for Erdős 1062(ii). -/

open Filter
open scoped Topology

namespace Bounty

def forkFree_iff (A : Set ℕ) :
    Erdos1062.ForkFree A ↔
      ∀ a b c, a ∈ A → b ∈ A → c ∈ A →
        a ≠ b → a ≠ c → a ∣ b → a ∣ c → b = c := by
  simp only [Erdos1062.ForkFree, Set.Subsingleton, Set.mem_ofPred_eq,
    Set.mem_sdiff, Set.mem_singleton_iff]
  aesop

def forkFree_mono {A B : Set ℕ} (hAB : A ⊆ B)
    (hB : Erdos1062.ForkFree B) : Erdos1062.ForkFree A := by
  rw [forkFree_iff] at *
  exact fun a b c ha hb hc hab hac habd hacd =>
    hB a b c (hAB ha) (hAB hb) (hAB hc) hab hac habd hacd

def forkFree_empty : Erdos1062.ForkFree ∅ := by
  simp [Erdos1062.ForkFree]

def exists_maximizer (n : ℕ) :
    ∃ A ⊆ Set.Icc 1 n, Erdos1062.ForkFree A ∧ A.ncard = Erdos1062.f n := by
  classical
  exact Nat.findGreatest_spec
    (P := fun k => ∃ A ⊆ Set.Icc 1 n, Erdos1062.ForkFree A ∧ A.ncard = k)
    (m := 0) (Nat.zero_le n)
    ⟨∅, Set.empty_subset _, forkFree_empty, by simp⟩

def card_le_f {n : ℕ} {A : Set ℕ} (hA : A ⊆ Set.Icc 1 n)
    (hfork : Erdos1062.ForkFree A) : A.ncard ≤ Erdos1062.f n := by
  classical
  apply Nat.le_findGreatest
  · calc
      A.ncard ≤ (Set.Icc 1 n).ncard := Set.ncard_le_ncard hA
      _ = n := by simp
  · exact ⟨A, hA, hfork, rfl⟩

def window_multiple {A : Set ℕ} {P : ℕ → Prop} {r a b : ℕ}
    (hpos : ∀ x ∈ A, 0 < x)
    (hwindow : ∀ x ∈ A,
      (P x ∧ r < 4 * x ∧ x ≤ r) ∨ (¬P x ∧ r < 6 * x ∧ 2 * x ≤ r))
    (hdouble : ∀ x ∈ A, P (2 * x) ↔ ¬P x)
    (htriple : ∀ x ∈ A, P (3 * x) ↔ P x)
    (hfour : ∀ x ∈ A, P (4 * x) ↔ P x)
    (hfive : ∀ x ∈ A, 5 * x ∉ A)
    (ha : a ∈ A) (hb : b ∈ A) (hne : a ≠ b) (hdvd : a ∣ b) :
    (P a ∧ b = 3 * a) ∨ (¬P a ∧ b = 2 * a) := by
  have ha0 := hpos a ha
  have haw := hwindow a ha
  have hbw := hwindow b hb
  have halow : r < 6 * a := by rcases haw with h | h <;> omega
  have hbhigh : b ≤ r := by rcases hbw with h | h <;> omega
  obtain ⟨k, rfl⟩ := hdvd
  have hk : k < 6 := by
    by_contra h
    have hle : 6 ≤ k := by omega
    have hm := Nat.mul_le_mul_left a hle
    omega
  interval_cases k
  · simp_all
  · simp_all
  · have hp := hdouble a ha
    have haw := hwindow a ha
    have hbw := hwindow (a * 2) hb
    simp only [Nat.mul_comm a 2] at *
    rcases haw with h | h
    · rcases hbw with hb' | hb'
      · exact False.elim (hp.mp hb'.1 h.1)
      · omega
    · exact Or.inr ⟨h.1, trivial⟩
  · have hp := htriple a ha
    have haw := hwindow a ha
    have hbw := hwindow (a * 3) hb
    simp only [Nat.mul_comm a 3] at *
    rcases haw with h | h
    · exact Or.inl ⟨h.1, trivial⟩
    · rcases hbw with hb' | hb'
      · exact False.elim (h.1 (hp.mp hb'.1))
      · omega
  · have hp := hfour a ha
    have haw := hwindow a ha
    have hbw := hwindow (a * 4) hb
    simp only [Nat.mul_comm a 4] at *
    rcases haw with h | h
    · omega
    · rcases hbw with hb' | hb'
      · exact False.elim (h.1 (hp.mp hb'.1))
      · omega
  · exact False.elim (hfive a ha (by simpa [Nat.mul_comm] using hb))

def forkFree_window {A : Set ℕ} {P : ℕ → Prop} {r : ℕ}
    (hpos : ∀ x ∈ A, 0 < x)
    (hwindow : ∀ x ∈ A,
      (P x ∧ r < 4 * x ∧ x ≤ r) ∨ (¬P x ∧ r < 6 * x ∧ 2 * x ≤ r))
    (hdouble : ∀ x ∈ A, P (2 * x) ↔ ¬P x)
    (htriple : ∀ x ∈ A, P (3 * x) ↔ P x)
    (hfour : ∀ x ∈ A, P (4 * x) ↔ P x)
    (hfive : ∀ x ∈ A, 5 * x ∉ A) :
    Erdos1062.ForkFree A := by
  rw [forkFree_iff]
  intro a b c ha hb hc hab hac habd hacd
  have h₁ := window_multiple hpos hwindow hdouble htriple hfour hfive ha hb hab habd
  have h₂ := window_multiple hpos hwindow hdouble htriple hfour hfive ha hc hac hacd
  aesop

def Smooth23 (n : ℕ) : Prop := ∃ a b : ℕ, n = 2 ^ a * 3 ^ b

def smooth23_pos {n : ℕ} (hn : Smooth23 n) : 0 < n := by
  obtain ⟨a, b, rfl⟩ := hn
  positivity

def smooth23_not_dvd_five {n : ℕ} (hn : Smooth23 n) : ¬5 ∣ n := by
  obtain ⟨a, b, rfl⟩ := hn
  intro h
  have hp : Nat.Prime 5 := by decide
  rcases hp.dvd_mul.mp h with h | h
  · have h' := hp.dvd_of_dvd_pow h
    norm_num at h'
  · have h' := hp.dvd_of_dvd_pow h
    norm_num at h'

def factorization_two_double {n : ℕ} (hn : 0 < n) :
    (2 * n).factorization 2 = 1 + n.factorization 2 := by
  rw [Nat.factorization_mul (by decide) (Nat.ne_of_gt hn), Finsupp.add_apply]
  rw [Nat.prime_two.factorization_self]

def factorization_two_triple {n : ℕ} (hn : 0 < n) :
    (3 * n).factorization 2 = n.factorization 2 := by
  rw [Nat.factorization_mul (by decide) (Nat.ne_of_gt hn), Finsupp.add_apply]
  have h : (3 : ℕ).factorization 2 = 0 :=
    Nat.factorization_eq_zero_of_not_dvd (by decide)
  omega

def factorization_two_four {n : ℕ} (hn : 0 < n) :
    (4 * n).factorization 2 = 2 + n.factorization 2 := by
  rw [Nat.factorization_mul (by decide) (Nat.ne_of_gt hn), Finsupp.add_apply]
  have h : (4 : ℕ).factorization 2 = 2 := by
    change (2 ^ 2).factorization 2 = 2
    exact Nat.factorization_pow_self Nat.prime_two
  omega

def cutoffWindow (p r : ℕ) : Set ℕ :=
  {n | Smooth23 n ∧
    ((n.factorization 2 % 2 = p ∧ r < 4 * n ∧ n ≤ r) ∨
      (n.factorization 2 % 2 ≠ p ∧ r < 6 * n ∧ 2 * n ≤ r))}

def cutoffWindow_forkFree {p : ℕ} (hp : p < 2) (r : ℕ) :
    Erdos1062.ForkFree (cutoffWindow p r) := by
  apply forkFree_window (P := fun n => n.factorization 2 % 2 = p) (r := r)
  · intro n hn
    exact smooth23_pos hn.1
  · intro n hn
    exact hn.2
  · intro n hn
    rw [factorization_two_double (smooth23_pos hn.1)]
    omega
  · intro n hn
    rw [factorization_two_triple (smooth23_pos hn.1)]
  · intro n hn
    rw [factorization_two_four (smooth23_pos hn.1)]
    omega
  · intro n _ h
    exact smooth23_not_dvd_five h.1 (dvd_mul_right 5 n)

def cutoffWindow_subset (p r : ℕ) : cutoffWindow p r ⊆ Set.Icc 1 r := by
  intro n hn
  have hpos := smooth23_pos hn.1
  have hwin := hn.2
  constructor
  · omega
  · rcases hwin with h | h <;> omega

def cutoffWindow_finite (p r : ℕ) : (cutoffWindow p r).Finite :=
  (Set.finite_Icc 1 r).subset (cutoffWindow_subset p r)

def cutoffWindow_disjoint {p q r s : ℕ}
    (hcutoff : (if p = q then 4 else 6) * s ≤ r) :
    Disjoint (cutoffWindow p r) (cutoffWindow q s) := by
  apply Set.disjoint_left.mpr
  intro n hn hm
  have h₁ := hn.2
  have h₂ := hm.2
  by_cases hpq : p = q
  · simp only [hpq, if_true] at hcutoff
    subst q
    rcases h₁ with h₁ | h₁ <;> rcases h₂ with h₂ | h₂ <;> omega
  · simp only [hpq, if_false] at hcutoff
    rcases h₁ with h₁ | h₁ <;> rcases h₂ with h₂ | h₂ <;> omega

def cutoffWindow_lower {p r n : ℕ} (hn : n ∈ cutoffWindow p r) :
    r < 6 * n := by
  have hpos := smooth23_pos hn.1
  rcases hn.2 with h | h <;> omega

def coefficient4 (n : ℕ) : ℤ :=
  let x := 4 ^ n
  let y := 3 ^ Nat.log 3 x
  if 15 * x < 16 * y then 78
  else if 9 * x < 10 * y then 30
  else if 3 * x < 4 * y then -30
  else if 2 * x < 3 * y then 30
  else if x < 2 * y then 0
  else if 3 * x < 8 * y then -60
  else -12

def coefficient3 (n : ℕ) : ℤ :=
  let x := 3 ^ n
  let y := 4 ^ Nat.log 4 x
  if 3 * x < 4 * y then 30
  else if 5 * x < 8 * y then 35
  else if 3 * x < 5 * y then 29
  else if x < 2 * y then 24
  else -60

def coefficient4_bound (n : ℕ) : |(coefficient4 n : ℝ)| ≤ 78 := by
  unfold coefficient4
  dsimp only
  split_ifs <;> norm_num

def coefficient3_bound (n : ℕ) : |(coefficient3 n : ℝ)| ≤ 60 := by
  unfold coefficient3
  dsimp only
  split_ifs <;> norm_num

def weighted_summable {a : ℕ → ℝ} {b M : ℝ} (hb : 1 < b)
    (ha : ∀ n, |a n| ≤ M) : Summable (fun n => a n / b ^ n) := by
  have hb0 : 0 < b := lt_trans zero_lt_one hb
  have hgeo := (summable_geometric_of_lt_one (inv_nonneg.mpr hb0.le)
    (inv_lt_one_of_one_lt₀ hb)).mul_left M
  apply hgeo.of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_div, abs_of_pos (pow_pos hb0 n),
    div_eq_mul_inv, ← inv_pow]
  exact mul_le_mul_of_nonneg_right (ha n) (pow_nonneg (inv_nonneg.mpr hb0.le) n)

def coefficient4_summable :
    Summable (fun n => (coefficient4 n : ℝ) / (4 : ℝ) ^ n) :=
  weighted_summable (by norm_num) coefficient4_bound

noncomputable def explicitDensity : ℝ :=
  (32 + (∑' n, (coefficient4 n : ℝ) / (4 : ℝ) ^ n) +
    (∑' n, (coefficient3 n : ℝ) / (3 : ℝ) ^ n)) / 0xb4

def weighted_shift_identity {a : ℕ → ℝ} {b M : ℝ} (hb : 1 < b)
    (ha : ∀ n, |a n| ≤ M) (q : ℕ) :
    (b ^ q - 1) * (∑' n, a n / b ^ n) =
      b ^ q * (∑ n ∈ Finset.range q, a n / b ^ n) +
        (∑' n, (a (n + q) - a n) / b ^ n) := by
  have hb0 : b ≠ 0 := ne_of_gt (lt_trans zero_lt_one hb)
  have h₁ := weighted_summable hb ha
  have h₂ := weighted_summable hb (fun n => ha (n + q))
  have hsplit := h₁.sum_add_tsum_nat_add q
  have htail :
      b ^ q * (∑' n, a (n + q) / b ^ (n + q)) =
        ∑' n, a (n + q) / b ^ n := by
    rw [← tsum_mul_left]
    apply tsum_congr
    intro n
    rw [pow_add]
    field_simp
  have hscaled := congrArg (fun x : ℝ => b ^ q * x) hsplit
  rw [mul_add, htail] at hscaled
  have hdiff :
      (∑' n, (a (n + q) - a n) / b ^ n) =
        (∑' n, a (n + q) / b ^ n) - (∑' n, a n / b ^ n) := by
    simp only [sub_div]
    exact h₂.tsum_sub h₁
  rw [hdiff]
  nlinarith

def integerPrefix (a : ℕ → ℤ) (b q : ℕ) : ℤ :=
  ∑ n ∈ Finset.range q, a n * (b : ℤ) ^ (q - n)

def integerPrefix_cast (a : ℕ → ℤ) {b : ℕ} (hb : 0 < b) (q : ℕ) :
    (integerPrefix a b q : ℝ) =
      (b : ℝ) ^ q * (∑ n ∈ Finset.range q, (a n : ℝ) / (b : ℝ) ^ n) := by
  unfold integerPrefix
  push_cast
  rw [Finset.mul_sum]
  apply Finset.sum_congr rfl
  intro n hn
  have hle : n ≤ q := Nat.le_of_lt (Finset.mem_range.mp hn)
  have hb0 : (b : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hb)
  have hp : (b : ℝ) ^ q = (b : ℝ) ^ n * (b : ℝ) ^ (q - n) := by
    rw [← pow_add, Nat.add_sub_of_le hle]
  rw [hp]
  field_simp

def integer_weighted_shift {a : ℕ → ℤ} {b : ℕ} {M : ℝ}
    (hb : 1 < b) (ha : ∀ n, |(a n : ℝ)| ≤ M) (q : ℕ) :
    ((b : ℝ) ^ q - 1) * (∑' n, (a n : ℝ) / (b : ℝ) ^ n) =
      (integerPrefix a b q : ℝ) +
        (∑' n, ((a (n + q) - a n : ℤ) : ℝ) / (b : ℝ) ^ n) := by
  rw [integerPrefix_cast a (by omega) q]
  push_cast
  exact weighted_shift_identity (by exact_mod_cast hb) ha q

def irrational_log_four_div_log_three :
    Irrational (Real.log 4 / Real.log 3) := by
  rintro ⟨q, hq⟩
  have hlog4 : 0 < Real.log 4 := Real.log_pos (by norm_num)
  have hlog3 : 0 < Real.log 3 := Real.log_pos (by norm_num)
  have hqpos : 0 < q := by
    have hreal : (0 : ℝ) < q := by
      rw [hq]
      exact div_pos hlog4 hlog3
    exact_mod_cast hreal
  have hnum : 0 < q.num := Rat.num_pos.mpr hqpos
  have habsI : (q.num.natAbs : ℤ) = q.num := by
    rw [Int.natCast_natAbs, abs_of_pos hnum]
  have habs : (q.num.natAbs : ℝ) = (q.num : ℝ) := by
    simpa only [Int.cast_natCast] using congrArg (fun z : ℤ => (z : ℝ)) habsI
  have hden : (q.den : ℝ) ≠ 0 := by
    exact_mod_cast q.den_nz
  have hratio :
      Real.log 4 / Real.log 3 = (q.num : ℝ) / (q.den : ℝ) := by
    rw [← hq, Rat.cast_def]
  have hcross := (div_eq_div_iff (ne_of_gt hlog3) hden).mp hratio
  have hlogs : Real.log ((4 : ℝ) ^ q.den) = Real.log ((3 : ℝ) ^ q.num.natAbs) := by
    rw [Real.log_pow, Real.log_pow, habs]
    nlinarith
  have hrealpow : (4 : ℝ) ^ q.den = (3 : ℝ) ^ q.num.natAbs :=
    Real.log_injOn_pos (by exact pow_pos (by norm_num : (0 : ℝ) < 4) q.den)
      (by exact pow_pos (by norm_num : (0 : ℝ) < 3) q.num.natAbs) hlogs
  have hpow : (4 : ℕ) ^ q.den = (3 : ℕ) ^ q.num.natAbs := by
    exact_mod_cast hrealpow
  have hdiv : 2 ∣ (4 : ℕ) ^ q.den := by
    obtain ⟨k, hk⟩ := Nat.exists_eq_succ_of_ne_zero q.den_nz
    rw [hk, pow_succ]
    exact ⟨2 * 4 ^ k, by ring⟩
  rw [hpow] at hdiv
  have hbad := Nat.prime_two.dvd_of_dvd_pow hdiv
  norm_num at hbad

end Bounty

end SubmissionComponent_Solution

/- Component GridWork; SHA256 f152ca58e05da7e36dc3f63f1fb16436c60d2532669012b1b49e753b86708bb9 -/
section SubmissionComponent_GridWork
/- A row-counting proof of the two-dimensional fork-free bound. -/

namespace Bounty

def GridForkFree (A : Finset (ℕ × ℕ)) : Prop :=
  ∀ a ∈ A, ∀ b ∈ A, ∀ c ∈ A, a ≠ b → a ≠ c →
    a.1 ≤ b.1 → a.2 ≤ b.2 → a.1 ≤ c.1 → a.2 ≤ c.2 → b = c

def gridRow (A : Finset (ℕ × ℕ)) (y : ℕ) : Finset (ℕ × ℕ) :=
  A.filter (fun a => a.2 = y)

def gridRow_card_le_two {A : Finset (ℕ × ℕ)} (hA : GridForkFree A) (y : ℕ) :
    (gridRow A y).card ≤ 2 := by
  classical
  by_cases hr : (gridRow A y).Nonempty
  · let X := (gridRow A y).image Prod.fst
    have hX : X.Nonempty := hr.image Prod.fst
    obtain ⟨a, ha, hamin⟩ := Finset.mem_image.mp (Finset.min'_mem X hX)
    have hay : a.2 = y := (Finset.mem_filter.mp ha).2
    have hamin' : ∀ b ∈ gridRow A y, a.1 ≤ b.1 := by
      intro b hb
      rw [hamin]
      exact Finset.min'_le X b.1 (Finset.mem_image_of_mem Prod.fst hb)
    have he : ((gridRow A y).erase a).card ≤ 1 := by
      apply Finset.card_le_one.mpr
      intro b hb c hc
      obtain ⟨hba, hbr⟩ := Finset.mem_erase.mp hb
      obtain ⟨hca, hcr⟩ := Finset.mem_erase.mp hc
      have hby : b.2 = y := (Finset.mem_filter.mp hbr).2
      have hcy : c.2 = y := (Finset.mem_filter.mp hcr).2
      exact hA a (Finset.mem_filter.mp ha).1 b (Finset.mem_filter.mp hbr).1
        c (Finset.mem_filter.mp hcr).1 hba.symm hca.symm
        (hamin' b hbr) (by omega) (hamin' c hcr) (by omega)
    have hcard := Finset.card_erase_add_one ha
    omega
  · have hempty : gridRow A y = ∅ := Finset.not_nonempty_iff_eq_empty.mp hr
    simp [hempty]

def grid_forbidden_upper {A : Finset (ℕ × ℕ)} (hA : GridForkFree A)
    {a b c : ℕ × ℕ} (ha : a ∈ A) (hb : b ∈ A) (hc : c ∈ A)
    (habrow : a.2 = b.2) (habcol : a.1 < b.1)
    (haccol : a.1 ≤ c.1) (hacrow : a.2 < c.2) : False := by
  have hab : a ≠ b := by
    intro h
    subst b
    omega
  have hac : a ≠ c := by
    intro h
    subst c
    omega
  have hbc := hA a ha b hb c hc hab hac habcol.le
    (by omega) haccol hacrow.le
  have := congrArg Prod.snd hbc
  omega

def grid_above_pair_left {A : Finset (ℕ × ℕ)} (hA : GridForkFree A)
    {a b c : ℕ × ℕ} (ha : a ∈ A) (hb : b ∈ A) (hc : c ∈ A)
    (hab : a ≠ b) (habrow : a.2 = b.2) (hacrow : a.2 < c.2) :
    c.1 < a.1 ∧ c.1 < b.1 := by
  have habcol : a.1 ≠ b.1 := by
    intro h
    exact hab (Prod.ext h habrow)
  by_cases hlt : a.1 < b.1
  · have h : c.1 < a.1 := by
      by_contra hh
      exact grid_forbidden_upper hA ha hb hc habrow hlt (by omega) hacrow
    omega
  · have h : c.1 < b.1 := by
      by_contra hh
      exact grid_forbidden_upper hA hb ha hc habrow.symm (by omega) (by omega) (by omega)
    omega

def gridRows (A : Finset (ℕ × ℕ)) : Finset ℕ := A.image Prod.snd

def gridDoubleRows (A : Finset (ℕ × ℕ)) : Finset ℕ :=
  (gridRows A).filter (fun y => (gridRow A y).card = 2)

def gridDoubles (A : Finset (ℕ × ℕ)) : Finset (ℕ × ℕ) :=
  A.filter (fun a => (gridRow A a.2).card = 2)

def gridDoubles_fst_injective {A : Finset (ℕ × ℕ)} (hA : GridForkFree A) :
    Set.InjOn Prod.fst (gridDoubles A : Set (ℕ × ℕ)) := by
  intro a ha b hb hfst
  have haA := (Finset.mem_filter.mp ha).1
  have hbA := (Finset.mem_filter.mp hb).1
  by_cases hrow : a.2 = b.2
  · exact Prod.ext hfst hrow
  · by_cases hlt : a.2 < b.2
    · have hcard := (Finset.mem_filter.mp ha).2
      obtain ⟨c, hc, hca⟩ := Finset.exists_mem_ne (show 1 < (gridRow A a.2).card by omega) a
      have hcA := (Finset.mem_filter.mp hc).1
      have hcy := (Finset.mem_filter.mp hc).2
      have h := grid_above_pair_left hA haA hcA hbA hca.symm (by omega) hlt
      omega
    · have hcard := (Finset.mem_filter.mp hb).2
      obtain ⟨c, hc, hcb⟩ := Finset.exists_mem_ne (show 1 < (gridRow A b.2).card by omega) b
      have hcA := (Finset.mem_filter.mp hc).1
      have hcy := (Finset.mem_filter.mp hc).2
      have h := grid_above_pair_left hA hbA hcA haA hcb.symm (by omega) (by omega)
      omega

def grid_card_decomposition {A : Finset (ℕ × ℕ)} (hA : GridForkFree A) :
    A.card = (gridRows A).card + (gridDoubleRows A).card := by
  have hcard : A.card = ∑ y ∈ gridRows A, (gridRow A y).card := by
    simpa [gridRows, gridRow] using Finset.card_eq_sum_card_image Prod.snd A
  rw [hcard]
  calc
    (∑ y ∈ gridRows A, (gridRow A y).card) =
        ∑ y ∈ gridRows A, (1 + if (gridRow A y).card = 2 then 1 else 0) := by
      apply Finset.sum_congr rfl
      intro y hy
      have hupper := gridRow_card_le_two hA y
      have hlower : 0 < (gridRow A y).card := by
        obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hy
        apply Finset.card_pos.mpr
        exact ⟨a, Finset.mem_filter.mpr ⟨ha, rfl⟩⟩
      split_ifs <;> omega
    _ = (gridRows A).card + (gridDoubleRows A).card := by
      simp [Finset.sum_add_distrib, gridDoubleRows]

def gridDoubles_card (A : Finset (ℕ × ℕ)) :
    (gridDoubles A).card = 2 * (gridDoubleRows A).card := by
  have hfilter :
      A.filter (fun a => a.2 ∈ gridDoubleRows A) = gridDoubles A := by
    ext a
    simp only [Finset.mem_filter, gridDoubleRows, gridDoubles]
    constructor
    · intro h
      exact ⟨h.1, h.2.2⟩
    · intro h
      exact ⟨h.1, Finset.mem_image_of_mem Prod.snd h.1, h.2⟩
  have hsum := Finset.sum_card_fiberwise_eq_card_filter A (gridDoubleRows A) Prod.snd
  rw [hfilter] at hsum
  calc
    (gridDoubles A).card = ∑ y ∈ gridDoubleRows A, (gridRow A y).card := hsum.symm
    _ = ∑ _y ∈ gridDoubleRows A, 2 := by
      apply Finset.sum_congr rfl
      intro y hy
      exact (Finset.mem_filter.mp hy).2
    _ = 2 * (gridDoubleRows A).card := by simp [Nat.mul_comm]

def grid_card_bound {A : Finset (ℕ × ℕ)} {W H : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < W) (hH : ∀ a ∈ A, a.2 < H) :
    A.card ≤ H + W / 2 := by
  have hrows : (gridRows A).card ≤ H := by
    calc
      (gridRows A).card ≤ (Finset.range H).card := by
        apply Finset.card_le_card
        intro y hy
        obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hy
        exact Finset.mem_range.mpr (hH a ha)
      _ = H := Finset.card_range H
  have hdoubles : (gridDoubles A).card ≤ W := by
    calc
      (gridDoubles A).card = ((gridDoubles A).image Prod.fst).card :=
        (Finset.card_image_iff.mpr (gridDoubles_fst_injective hA)).symm
      _ ≤ (Finset.range W).card := by
        apply Finset.card_le_card
        intro x hx
        obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hx
        exact Finset.mem_range.mpr (hW a (Finset.mem_filter.mp ha).1)
      _ = W := Finset.card_range W
  rw [gridDoubles_card] at hdoubles
  rw [grid_card_decomposition hA]
  omega

end Bounty

end SubmissionComponent_GridWork

/- Component GridBoundary; SHA256 bb520fd269023ebb862cba3aee015678bb7acc03206e3afe7e4920bd975172a2 -/
section SubmissionComponent_GridBoundary
/- Equality cases for the row-counting bound. -/

namespace Bounty

def gridRows_card_le {A : Finset (ℕ × ℕ)} {H : ℕ}
    (hH : ∀ a ∈ A, a.2 < H) : (gridRows A).card ≤ H := by
  calc
    (gridRows A).card ≤ (Finset.range H).card := by
      apply Finset.card_le_card
      intro y hy
      obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hy
      exact Finset.mem_range.mpr (hH a ha)
    _ = H := Finset.card_range H

def gridDoubles_card_le {A : Finset (ℕ × ℕ)} {W : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < W) :
    (gridDoubles A).card ≤ W := by
  calc
    (gridDoubles A).card = ((gridDoubles A).image Prod.fst).card :=
      (Finset.card_image_iff.mpr (gridDoubles_fst_injective hA)).symm
    _ ≤ (Finset.range W).card := by
      apply Finset.card_le_card
      intro x hx
      obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hx
      exact Finset.mem_range.mpr (hW a (Finset.mem_filter.mp ha).1)
    _ = W := Finset.card_range W

def grid_saturated_counts {A : Finset (ℕ × ℕ)} {W H : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < W) (hH : ∀ a ∈ A, a.2 < H)
    (hcard : A.card = H + W / 2) :
    (gridRows A).card = H ∧ (gridDoubleRows A).card = W / 2 := by
  have hr := gridRows_card_le hH
  have hd := gridDoubles_card_le hA hW
  rw [gridDoubles_card] at hd
  have hsum := grid_card_decomposition hA
  omega

def grid_saturated_rows {A : Finset (ℕ × ℕ)} {W H : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < W) (hH : ∀ a ∈ A, a.2 < H)
    (hcard : A.card = H + W / 2) : gridRows A = Finset.range H := by
  apply Finset.eq_of_subset_of_card_le
  · intro y hy
    obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hy
    exact Finset.mem_range.mpr (hH a ha)
  · simp only [Finset.card_range, (grid_saturated_counts hA hW hH hcard).1]
    exact le_rfl

def grid_saturated_even_columns {A : Finset (ℕ × ℕ)} {k H : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < 2 * k) (hH : ∀ a ∈ A, a.2 < H)
    (hcard : A.card = H + k) :
    (gridDoubles A).image Prod.fst = Finset.range (2 * k) := by
  apply Finset.eq_of_subset_of_card_le
  · intro x hx
    obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hx
    exact Finset.mem_range.mpr (hW a (Finset.mem_filter.mp ha).1)
  · have hd := (grid_saturated_counts hA hW hH (by omega)).2
    rw [Finset.card_range, Finset.card_image_iff.mpr (gridDoubles_fst_injective hA),
      gridDoubles_card]
    omega

def grid_point_below_double {A : Finset (ℕ × ℕ)} (hA : GridForkFree A)
    {a c : ℕ × ℕ} (ha : a ∈ gridDoubles A) (hc : c ∈ A) (hrow : a.2 < c.2) :
    c.1 < a.1 := by
  have hcard := (Finset.mem_filter.mp ha).2
  obtain ⟨b, hb, hba⟩ := Finset.exists_mem_ne (show 1 < (gridRow A a.2).card by omega) a
  exact (grid_above_pair_left hA (Finset.mem_filter.mp ha).1
    (Finset.mem_filter.mp hb).1 hc hba.symm
    (by simpa using (Finset.mem_filter.mp hb).2.symm) hrow).1

def grid_top_double_of_saturated_even {A : Finset (ℕ × ℕ)} {k h : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < 2 * k)
    (hH : ∀ a ∈ A, a.2 < h + 1) (hcard : A.card = h + 1 + k) :
    (gridRow A h).card = 2 := by
  have hrows := grid_saturated_rows hA hW hH (by omega)
  have hmem : h ∈ gridRows A := by rw [hrows]; exact Finset.mem_range.mpr (by omega)
  obtain ⟨c, hc, hch⟩ := Finset.mem_image.mp hmem
  have hk : 0 < k := by have := hW c hc; omega
  have hcols := grid_saturated_even_columns hA hW hH hcard
  have hzero : 0 ∈ (gridDoubles A).image Prod.fst := by
    rw [hcols]
    exact Finset.mem_range.mpr (by omega)
  obtain ⟨a, ha, ha0⟩ := Finset.mem_image.mp hzero
  have hah := hH a (Finset.mem_filter.mp ha).1
  have hay : a.2 = h := by
    by_contra hh
    have := grid_point_below_double hA ha hc (by omega)
    omega
  simpa [hay] using (Finset.mem_filter.mp ha).2

def grid_bound_top_single {A : Finset (ℕ × ℕ)} {k h : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < 2 * k)
    (hH : ∀ a ∈ A, a.2 < h + 1)
    (htop : ∀ a ∈ A, a.2 = h → a.1 = 0) : A.card ≤ h + k := by
  have hbound := grid_card_bound hA hW hH
  by_contra hc
  have hcard : A.card = h + 1 + k := by omega
  have htwo := grid_top_double_of_saturated_even hA hW hH hcard
  have hone : (gridRow A h).card ≤ 1 := by
    apply Finset.card_le_one.mpr
    intro a ha b hb
    obtain ⟨haA, hay⟩ := Finset.mem_filter.mp ha
    obtain ⟨hbA, hby⟩ := Finset.mem_filter.mp hb
    exact Prod.ext (by rw [htop a haA hay, htop b hbA hby]) (by omega)
  omega

def grid_top_pair_of_saturated_even {A : Finset (ℕ × ℕ)} {k h : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < 2 * k)
    (hH : ∀ a ∈ A, a.2 < h + 1)
    (htop : ∀ a ∈ A, a.2 = h → a.1 < 2)
    (hcard : A.card = h + 1 + k) : (0, h) ∈ A ∧ (1, h) ∈ A := by
  have htwo := grid_top_double_of_saturated_even hA hW hH hcard
  have heq : gridRow A h = ({(0, h), (1, h)} : Finset (ℕ × ℕ)) := by
    apply Finset.eq_of_subset_of_card_le
    · intro a ha
      obtain ⟨haA, hay⟩ := Finset.mem_filter.mp ha
      have hax := htop a haA hay
      have hx : a.1 = 0 ∨ a.1 = 1 := by omega
      rcases hx with hx | hx
      · have he : a = (0, h) := Prod.ext hx hay
        simp [he]
      · have he : a = (1, h) := Prod.ext hx hay
        simp [he]
    · rw [htwo]
      simp
  constructor
  · have hm : (0, h) ∈ gridRow A h := by rw [heq]; simp
    exact (Finset.mem_filter.mp hm).1
  · have hm : (1, h) ∈ gridRow A h := by rw [heq]; simp
    exact (Finset.mem_filter.mp hm).1

end Bounty

end SubmissionComponent_GridBoundary

/- Component GridOdd; SHA256 5aaeb15303e19575a7f83d8109895c72326b34c1b82994a81331e1a67dca4683 -/
section SubmissionComponent_GridOdd
/- Rigidity in odd-width grids with a single available top cell. -/

namespace Bounty

def grid_double_row_mem {A : Finset (ℕ × ℕ)} {a b : ℕ × ℕ}
    (ha : a ∈ gridDoubles A) (hb : b ∈ A) (hrow : b.2 = a.2) :
    b ∈ gridDoubles A := by
  apply Finset.mem_filter.mpr
  exact ⟨hb, by rw [hrow]; exact (Finset.mem_filter.mp ha).2⟩

def grid_double_zero_excluded {A : Finset (ℕ × ℕ)} {h : ℕ}
    (hA : GridForkFree A) (hH : ∀ a ∈ A, a.2 < h + 1)
    (htop : ∀ a ∈ A, a.2 = h → a.1 = 0) (hmem : h ∈ gridRows A) :
    ∀ a ∈ gridDoubles A, a.1 ≠ 0 := by
  intro a ha ha0
  obtain ⟨c, hc, hch⟩ := Finset.mem_image.mp hmem
  have hah := hH a (Finset.mem_filter.mp ha).1
  by_cases hay : a.2 = h
  · have hcard := (Finset.mem_filter.mp ha).2
    obtain ⟨b, hb, hba⟩ := Finset.exists_mem_ne (show 1 < (gridRow A a.2).card by omega) a
    obtain ⟨hbA, hby⟩ := Finset.mem_filter.mp hb
    have hb0 := htop b hbA (by omega)
    exact hba (Prod.ext (by omega) hby)
  · have := grid_point_below_double hA ha hc (by omega)
    omega

def grid_saturated_odd_columns {A : Finset (ℕ × ℕ)} {k h : ℕ}
    (hA : GridForkFree A) (hW : ∀ a ∈ A, a.1 < 2 * k + 1)
    (hH : ∀ a ∈ A, a.2 < h + 1)
    (htop : ∀ a ∈ A, a.2 = h → a.1 = 0)
    (hcard : A.card = h + 1 + k) :
    (gridDoubles A).image Prod.fst = Finset.Icc 1 (2 * k) := by
  have hrows := grid_saturated_rows hA hW hH (by omega)
  have hmem : h ∈ gridRows A := by rw [hrows]; exact Finset.mem_range.mpr (by omega)
  have hnonzero := grid_double_zero_excluded hA hH htop hmem
  apply Finset.eq_of_subset_of_card_le
  · intro x hx
    obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hx
    have haW := hW a (Finset.mem_filter.mp ha).1
    have ha0 := hnonzero a ha
    exact Finset.mem_Icc.mpr ⟨by omega, by omega⟩
  · have hd := (grid_saturated_counts hA hW hH (by omega)).2
    rw [Finset.card_image_iff.mpr (gridDoubles_fst_injective hA), gridDoubles_card]
    simp only [Nat.card_Icc]
    omega

def grid_double_one_two_same_row {A : Finset (ℕ × ℕ)}
    (hA : GridForkFree A) (hnozero : ∀ a ∈ gridDoubles A, a.1 ≠ 0)
    {a b : ℕ × ℕ} (ha : a ∈ gridDoubles A) (hb : b ∈ gridDoubles A)
    (ha1 : a.1 = 1) (hb2 : b.1 = 2) : a.2 = b.2 := by
  by_contra hne
  by_cases hlt : a.2 < b.2
  · have := grid_point_below_double hA ha (Finset.mem_filter.mp hb).1 hlt
    omega
  · have hcard := (Finset.mem_filter.mp ha).2
    obtain ⟨c, hc, hca⟩ := Finset.exists_mem_ne (show 1 < (gridRow A a.2).card by omega) a
    obtain ⟨hcA, hcy⟩ := Finset.mem_filter.mp hc
    have hcD := grid_double_row_mem ha hcA hcy
    have hc0 := hnozero c hcD
    have hc2 := grid_point_below_double hA hb hcA (by omega)
    exact hca (Prod.ext (by omega) hcy)

def grid_three_in_column_forbidden {A : Finset (ℕ × ℕ)}
    (hA : GridForkFree A) {x y z w : ℕ}
    (hy : (x, y) ∈ A) (hz : (x, z) ∈ A) (hw : (x, w) ∈ A)
    (hyz : y < z) (hzw : z < w) : False := by
  have hh := hA (x, y) hy (x, z) hz (x, w) hw
    (by intro he; have := congrArg Prod.snd he; simpa using hyz.ne this)
    (by intro he; have := congrArg Prod.snd he; omega)
    le_rfl hyz.le le_rfl (by omega)
  have := congrArg Prod.snd hh
  omega

def grid_odd_forced_pair {A : Finset (ℕ × ℕ)} {k b : ℕ}
    (hk : 0 < k) (hA : GridForkFree A)
    (hW : ∀ a ∈ A, a.1 < 2 * k + 1) (hH : ∀ a ∈ A, a.2 < b + 3)
    (htop : ∀ a ∈ A, a.2 = b + 2 → a.1 = 0)
    (hsecond : ∀ a ∈ A, a.1 = 2 → a.2 ≤ b)
    (hcard : A.card = b + 3 + k) : (1, b) ∈ A ∧ (2, b) ∈ A := by
  have hH' : ∀ a ∈ A, a.2 < (b + 2) + 1 := by intro a ha; have := hH a ha; omega
  have hrows := grid_saturated_rows hA hW hH (by omega)
  have hmem : b + 2 ∈ gridRows A := by
    rw [hrows]
    exact Finset.mem_range.mpr (by omega)
  have hnozero := grid_double_zero_excluded hA hH' htop hmem
  have hcols := grid_saturated_odd_columns hA hW hH' htop (by omega)
  have h1 : 1 ∈ (gridDoubles A).image Prod.fst := by
    rw [hcols]
    exact Finset.mem_Icc.mpr ⟨by omega, by omega⟩
  have h2 : 2 ∈ (gridDoubles A).image Prod.fst := by
    rw [hcols]
    exact Finset.mem_Icc.mpr ⟨by omega, by omega⟩
  obtain ⟨a, ha, ha1⟩ := Finset.mem_image.mp h1
  obtain ⟨c, hc, hc2⟩ := Finset.mem_image.mp h2
  have hrow := grid_double_one_two_same_row hA hnozero ha hc ha1 hc2
  have hcb := hsecond c (Finset.mem_filter.mp hc).1 hc2
  have hab : a.2 = b := by
    by_contra hne
    have hablt : a.2 < b := by omega
    have hzero : ∀ y, b ≤ y → y < b + 3 → (0, y) ∈ A := by
      intro y hby hyH
      have hy : y ∈ gridRows A := by rw [hrows]; exact Finset.mem_range.mpr hyH
      obtain ⟨d, hd, hdy⟩ := Finset.mem_image.mp hy
      have hdx := grid_point_below_double hA ha hd (by omega)
      have he : d = (0, y) := Prod.ext (by omega) hdy
      rwa [← he]
    exact grid_three_in_column_forbidden hA
      (hzero b (by omega) (by omega)) (hzero (b + 1) (by omega) (by omega))
      (hzero (b + 2) (by omega) (by omega)) (by omega) (by omega)
  constructor
  · have he : a = (1, b) := Prod.ext ha1 hab
    exact he ▸ (Finset.mem_filter.mp ha).1
  · have he : c = (2, b) := Prod.ext hc2 (by omega)
    exact he ▸ (Finset.mem_filter.mp hc).1

end Bounty

end SubmissionComponent_GridOdd

/- Component GridBridge; SHA256 f53cd8833bdeabaa4ab47df355c2739ef8bd82171dac1a5979bbeb05511b8711 -/
section SubmissionComponent_GridBridge
/- Divisibility among two-prime smooth numbers is product order on a grid. -/

namespace Bounty

def gridValue (a : ℕ × ℕ) : ℕ := 2 ^ a.1 * 3 ^ a.2

def gridValue_pos (a : ℕ × ℕ) : 0 < gridValue a := by
  unfold gridValue
  positivity

def gridValue_factorization_two (a : ℕ × ℕ) :
    (gridValue a).factorization 2 = a.1 := by
  unfold gridValue
  rw [Nat.factorization_mul (by positivity) (by positivity), Finsupp.add_apply,
    Nat.factorization_pow_self Nat.prime_two]
  have h : (3 ^ a.2).factorization 2 = 0 := by
    apply Nat.factorization_eq_zero_of_not_dvd
    intro hd
    have := Nat.prime_two.dvd_of_dvd_pow hd
    norm_num at this
  omega

def gridValue_factorization_three (a : ℕ × ℕ) :
    (gridValue a).factorization 3 = a.2 := by
  unfold gridValue
  rw [Nat.factorization_mul (by positivity) (by positivity), Finsupp.add_apply,
    Nat.factorization_pow_self Nat.prime_three]
  have h : (2 ^ a.1).factorization 3 = 0 := by
    apply Nat.factorization_eq_zero_of_not_dvd
    intro hd
    have := Nat.prime_three.dvd_of_dvd_pow hd
    norm_num at this
  omega

def gridValue_injective : Function.Injective gridValue := by
  intro a b hab
  apply Prod.ext
  · have := congrArg (fun n : ℕ => n.factorization 2) hab
    simpa only [gridValue_factorization_two] using this
  · have := congrArg (fun n : ℕ => n.factorization 3) hab
    simpa only [gridValue_factorization_three] using this

def gridValue_dvd_iff (a b : ℕ × ℕ) :
    gridValue a ∣ gridValue b ↔ a.1 ≤ b.1 ∧ a.2 ≤ b.2 := by
  constructor
  · intro h
    have hf := (Nat.factorization_le_iff_dvd (ne_of_gt (gridValue_pos a))
      (ne_of_gt (gridValue_pos b))).mpr h
    constructor
    · simpa only [gridValue_factorization_two] using hf 2
    · simpa only [gridValue_factorization_three] using hf 3
  · rintro ⟨h₁, h₂⟩
    exact mul_dvd_mul (pow_dvd_pow 2 h₁) (pow_dvd_pow 3 h₂)

def gridForkFree_iff {A : Finset (ℕ × ℕ)} :
    GridForkFree A ↔ Erdos1062.ForkFree (gridValue '' (A : Set (ℕ × ℕ))) := by
  rw [forkFree_iff]
  constructor
  · intro hA x y z hx hy hz hxy hxz hdivy hdivz
    obtain ⟨a, ha, rfl⟩ := hx
    obtain ⟨b, hb, rfl⟩ := hy
    obtain ⟨c, hc, rfl⟩ := hz
    obtain ⟨hy₁, hy₂⟩ := (gridValue_dvd_iff a b).mp hdivy
    obtain ⟨hz₁, hz₂⟩ := (gridValue_dvd_iff a c).mp hdivz
    have hab : a ≠ b := by intro he; exact hxy (congrArg gridValue he)
    have hac : a ≠ c := by intro he; exact hxz (congrArg gridValue he)
    exact congrArg gridValue (hA a ha b hb c hc hab hac hy₁ hy₂ hz₁ hz₂)
  · intro hA a ha b hb c hc hab hac hy₁ hy₂ hz₁ hz₂
    apply gridValue_injective
    exact hA (gridValue a) (gridValue b) (gridValue c)
      ⟨a, ha, rfl⟩ ⟨b, hb, rfl⟩ ⟨c, hc, rfl⟩ (fun he => hab (gridValue_injective he))
      (fun he => hac (gridValue_injective he))
      ((gridValue_dvd_iff a b).mpr ⟨hy₁, hy₂⟩)
      ((gridValue_dvd_iff a c).mpr ⟨hz₁, hz₂⟩)

def gridCoordinates (n : ℕ) : ℕ × ℕ := (n.factorization 2, n.factorization 3)

def gridCoordinates_value (a : ℕ × ℕ) : gridCoordinates (gridValue a) = a := by
  apply Prod.ext
  · exact gridValue_factorization_two a
  · exact gridValue_factorization_three a

def gridValue_log_bounds {a : ℕ × ℕ} {n : ℕ} (h : gridValue a ≤ n) :
    a.1 ≤ Nat.log 2 n ∧ a.2 ≤ Nat.log 3 n := by
  have hn : n ≠ 0 := by have := gridValue_pos a; omega
  constructor
  · apply (Nat.le_log_iff_pow_le (by norm_num) hn).mpr
    have hp : 1 ≤ (3 : ℕ) ^ a.2 := Nat.one_le_iff_ne_zero.mpr (by positivity)
    exact (by unfold gridValue at h; nlinarith : 2 ^ a.1 ≤ n)
  · apply (Nat.le_log_iff_pow_le (by norm_num) hn).mpr
    have hp : 1 ≤ (2 : ℕ) ^ a.1 := Nat.one_le_iff_ne_zero.mpr (by positivity)
    exact (by unfold gridValue at h; nlinarith : 3 ^ a.2 ≤ n)

end Bounty

end SubmissionComponent_GridBridge

/- Component FiveLoss; SHA256 6f0b67fcd12a16d548f86ae1f479385c0fd472ad713c8542f1851c7b1dbeedf2 -/
section SubmissionComponent_FiveLoss
/- Equality in adjacent powers-of-five components forces a forbidden fork. -/

namespace Bounty

def forkFree_not_double_five {S : Set ℕ} (hS : Erdos1062.ForkFree S)
    {a : ℕ} (ha : 0 < a) (haS : a ∈ S) (h2 : 2 * a ∈ S) (h5 : 5 * a ∈ S) : False := by
  have hh := (forkFree_iff S).mp hS a (2 * a) (5 * a) haS h2 h5
    (by omega) (by omega) (by exact ⟨2, by ring⟩) (by exact ⟨5, by ring⟩)
  omega

def grid_five_layer_loss {A B : Finset (ℕ × ℕ)} {S : Set ℕ} {k j b : ℕ}
    (hk : 0 < k) (hA : GridForkFree A) (hB : GridForkFree B)
    (hWA : ∀ a ∈ A, a.1 < 2 * k + 1) (hHA : ∀ a ∈ A, a.2 < b + 3)
    (htopA : ∀ a ∈ A, a.2 = b + 2 → a.1 = 0)
    (hsecondA : ∀ a ∈ A, a.1 = 2 → a.2 ≤ b)
    (hWB : ∀ a ∈ B, a.1 < 2 * j) (hHB : ∀ a ∈ B, a.2 < b + 1)
    (htopB : ∀ a ∈ B, a.2 = b → a.1 < 2)
    (hAS : ∀ a ∈ A, gridValue a ∈ S)
    (hBS : ∀ a ∈ B, 5 * gridValue a ∈ S)
    (hS : Erdos1062.ForkFree S) :
    A.card + B.card + 1 ≤ (b + 3 + k) + (b + 1 + j) := by
  have hAbasic := grid_card_bound hA hWA hHA
  have hBbasic := grid_card_bound hB hWB hHB
  by_contra hlt
  have hAc : A.card = b + 3 + k := by omega
  have hBc : B.card = b + 1 + j := by omega
  obtain ⟨ha1, ha2⟩ := grid_odd_forced_pair hk hA hWA hHA htopA hsecondA hAc
  obtain ⟨_, hb1⟩ := grid_top_pair_of_saturated_even hB hWB hHB htopB hBc
  have h1 : 2 * 3 ^ b ∈ S := by simpa [gridValue] using hAS (1, b) ha1
  have h2 : 2 * (2 * 3 ^ b) ∈ S := by
    have hh := hAS (2, b) ha2
    norm_num [gridValue] at hh
    convert hh using 1
    ring
  have h5 : 5 * (2 * 3 ^ b) ∈ S := by simpa [gridValue] using hBS (1, b) hb1
  exact forkFree_not_double_five hS (by positivity) h1 h2 h5

end Bounty

end SubmissionComponent_FiveLoss

/- Component SmoothRank; SHA256 34273eadda8c4afb918793f21e0088eb02d207953335e532c5eb54ef49396c9e -/
section SubmissionComponent_SmoothRank
/- The sharp upper bound in a two-prime divisibility component. -/

namespace Bounty

def smoothRankBound (n : ℕ) : ℕ :=
  if n = 0 then 0 else
    Nat.log 3 n + 1 + Nat.log 2 n / 2 +
      if Nat.log 2 n % 2 = 1 ∧ 2 * 3 ^ Nat.log 3 n ≤ n then 1 else 0

def grid_natural_sharp_bound {A : Finset (ℕ × ℕ)} {n : ℕ}
    (hn : 0 < n) (hA : GridForkFree A) (hbound : ∀ a ∈ A, gridValue a ≤ n) :
    A.card ≤ smoothRankBound n := by
  have hW : ∀ a ∈ A, a.1 < Nat.log 2 n + 1 := by
    intro a ha
    exact Nat.lt_succ_of_le (gridValue_log_bounds (hbound a ha)).1
  have hH : ∀ a ∈ A, a.2 < Nat.log 3 n + 1 := by
    intro a ha
    exact Nat.lt_succ_of_le (gridValue_log_bounds (hbound a ha)).2
  have hbasic := grid_card_bound hA hW hH
  unfold smoothRankBound
  rw [if_neg (by omega : n ≠ 0)]
  by_cases hpar : Nat.log 2 n % 2 = 1
  · by_cases htop : 2 * 3 ^ Nat.log 3 n ≤ n
    · rw [if_pos ⟨hpar, htop⟩]
      omega
    · rw [if_neg (by simp [htop])]
      have hWeven : ∀ a ∈ A, a.1 < 2 * ((Nat.log 2 n + 1) / 2) := by
        intro a ha
        have := hW a ha
        omega
      have hsingle : ∀ a ∈ A, a.2 = Nat.log 3 n → a.1 = 0 := by
        intro a ha hay
        by_contra hax
        have hpow : 2 ≤ (2 : ℕ) ^ a.1 := by
          calc
            2 = (2 : ℕ) ^ 1 := by norm_num
            _ ≤ 2 ^ a.1 := Nat.pow_le_pow_right (by norm_num) (by omega)
        have hb := hbound a ha
        unfold gridValue at hb
        rw [hay] at hb
        apply htop
        nlinarith
      have hh := grid_bound_top_single hA hWeven hH hsingle
      omega
  · rw [if_neg (by simp [hpar])]
    omega

end Bounty

end SubmissionComponent_SmoothRank

/- Component WindowCount; SHA256 58f33d4b9f803b7a0322843468c1288acc1863366d0070e366ddb3418be4416f -/
section SubmissionComponent_WindowCount
/- Explicit finite witnesses for the two-prime rank bound. -/

namespace Bounty

def log_scaled_bounds {b d n : ℕ} (hb : 1 < b) (hd : 0 < d) (hdn : d ≤ n) :
    d * b ^ Nat.log b (n / d) ≤ n ∧
      n < b * (d * b ^ Nat.log b (n / d)) := by
  have hquot : n / d ≠ 0 := by have := Nat.div_pos hdn hd; omega
  have hlo := Nat.pow_log_le_self b hquot
  have hhi := Nat.lt_pow_succ_log_self hb (n / d)
  constructor
  · have hh := (Nat.le_div_iff_mul_le hd).mp hlo
    simpa [Nat.mul_comm] using hh
  · have hh := (Nat.div_lt_iff_lt_mul hd).mp hhi
    simpa [pow_succ, Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using hh

def two_pow_even (j : ℕ) : (2 : ℕ) ^ (2 * j) = 4 ^ j := by
  rw [pow_mul]
  norm_num

def two_pow_odd (j : ℕ) : (2 : ℕ) ^ (2 * j + 1) = 2 * 4 ^ j := by
  rw [pow_add, two_pow_even]
  simp [Nat.mul_comm]

def window0Primary (n i : ℕ) : ℕ × ℕ := (2 * Nat.log 4 (n / 3 ^ i), i)
def window0Secondary (n j : ℕ) : ℕ × ℕ := (2 * j + 1, Nat.log 3 (n / 4 ^ (j + 1)))

def window0Grid (n : ℕ) : Finset (ℕ × ℕ) :=
  ((Finset.range (Nat.log 3 n + 1)).image (window0Primary n)) ∪
  ((Finset.range (Nat.log 4 n)).image (window0Secondary n))

def window0Primary_injective (n : ℕ) : Function.Injective (window0Primary n) := by
  intro a b hab
  exact congrArg Prod.snd hab

def window0Secondary_injective (n : ℕ) : Function.Injective (window0Secondary n) := by
  intro a b hab
  have hh := congrArg Prod.fst hab
  dsimp [window0Secondary] at hh
  omega

def window0Grid_card (n : ℕ) :
    (window0Grid n).card = Nat.log 3 n + 1 + Nat.log 4 n := by
  unfold window0Grid
  rw [Finset.card_union_of_disjoint]
  · rw [Finset.card_image_of_injective _ (window0Primary_injective n),
      Finset.card_image_of_injective _ (window0Secondary_injective n)]
    simp
  · apply Finset.disjoint_left.mpr
    intro a ha hb
    obtain ⟨i, hi, hia⟩ := Finset.mem_image.mp ha
    obtain ⟨j, hj, hja⟩ := Finset.mem_image.mp hb
    have hh := congrArg Prod.fst (hia.trans hja.symm)
    dsimp [window0Primary, window0Secondary] at hh
    omega

def window0Primary_mem {n i : ℕ} (hn : 0 < n) (hi : i ≤ Nat.log 3 n) :
    gridValue (window0Primary n i) ∈ cutoffWindow 0 n := by
  have hd : 0 < (3 : ℕ) ^ i := by positivity
  have hdn : (3 : ℕ) ^ i ≤ n :=
    (Nat.le_log_iff_pow_le (by norm_num) (by omega : n ≠ 0)).mp hi
  have hh := log_scaled_bounds (by norm_num : 1 < (4 : ℕ)) hd hdn
  have hvalue : gridValue (window0Primary n i) = 3 ^ i * 4 ^ Nat.log 4 (n / 3 ^ i) := by
    simp [gridValue, window0Primary, two_pow_even, Nat.mul_comm]
  constructor
  · exact ⟨(window0Primary n i).1, (window0Primary n i).2, rfl⟩
  · left
    constructor
    · rw [gridValue_factorization_two]
      simp [window0Primary]
    · rw [hvalue]
      exact ⟨hh.2, hh.1⟩

def window0Secondary_mem {n j : ℕ} (hn : 0 < n) (hj : j < Nat.log 4 n) :
    gridValue (window0Secondary n j) ∈ cutoffWindow 0 n := by
  have hd : 0 < (4 : ℕ) ^ (j + 1) := by positivity
  have hdn : (4 : ℕ) ^ (j + 1) ≤ n :=
    (Nat.le_log_iff_pow_le (by norm_num) (by omega : n ≠ 0)).mp (by omega)
  have hh := log_scaled_bounds (by norm_num : 1 < (3 : ℕ)) hd hdn
  have hvalue : 2 * gridValue (window0Secondary n j) =
      4 ^ (j + 1) * 3 ^ Nat.log 3 (n / 4 ^ (j + 1)) := by
    dsimp only [gridValue, window0Secondary]
    rw [two_pow_odd, pow_succ]
    ring
  constructor
  · exact ⟨(window0Secondary n j).1, (window0Secondary n j).2, rfl⟩
  · right
    constructor
    · rw [gridValue_factorization_two]
      simp [window0Secondary]
    · rw [← hvalue] at hh
      constructor <;> omega

def window0Grid_subset {n : ℕ} (hn : 0 < n) :
    ∀ a ∈ window0Grid n, gridValue a ∈ cutoffWindow 0 n := by
  intro a ha
  rcases Finset.mem_union.mp ha with ha | ha
  · obtain ⟨i, hi, rfl⟩ := Finset.mem_image.mp ha
    exact window0Primary_mem hn (by have := Finset.mem_range.mp hi; omega)
  · obtain ⟨j, hj, rfl⟩ := Finset.mem_image.mp ha
    exact window0Secondary_mem hn (Finset.mem_range.mp hj)

def window0Witness (n : ℕ) : Finset ℕ := (window0Grid n).image gridValue

def window0Witness_card (n : ℕ) :
    (window0Witness n).card = Nat.log 3 n + 1 + Nat.log 4 n := by
  rw [window0Witness, Finset.card_image_of_injective _ gridValue_injective, window0Grid_card]

def window0Witness_subset {n : ℕ} (hn : 0 < n) :
    (window0Witness n : Set ℕ) ⊆ cutoffWindow 0 n := by
  intro x hx
  obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hx
  exact window0Grid_subset hn a ha

end Bounty

end SubmissionComponent_WindowCount

/- Component FiveInterval; SHA256 cd96d816231a581130f9eb75453fd8593b7f671da1d2b7ef59a996b917986353 -/
section SubmissionComponent_FiveInterval
/- The powers-of-five loss on its exact arithmetic interval. -/

namespace Bounty

def badWindow (n : ℕ) : Prop :=
  ∃ j b : ℕ, 4 ^ j ≤ n ∧ 4 * n < 5 * 4 ^ j ∧
    10 * 3 ^ b ≤ n ∧ n < 12 * 3 ^ b

def gridValue_column_lt {a : ℕ × ℕ} {q n W : ℕ}
    (_hq : 0 < q) (hbound : q * gridValue a ≤ n) (hlt : n < q * 2 ^ W) : a.1 < W := by
  by_contra hh
  have hpow : (2 : ℕ) ^ W ≤ 2 ^ a.1 := Nat.pow_le_pow_right (by norm_num) (by omega)
  have h3 : 0 < (3 : ℕ) ^ a.2 := by positivity
  unfold gridValue at hbound
  have hmul : q * 2 ^ W ≤ q * 2 ^ a.1 := Nat.mul_le_mul_left _ hpow
  have hh : q * 2 ^ a.1 ≤ q * (2 ^ a.1 * 3 ^ a.2) := by nlinarith
  omega

def gridValue_row_lt {a : ℕ × ℕ} {q n H : ℕ}
    (_hq : 0 < q) (hbound : q * gridValue a ≤ n) (hlt : n < q * 3 ^ H) : a.2 < H := by
  by_contra hh
  have hpow : (3 : ℕ) ^ H ≤ 3 ^ a.2 := Nat.pow_le_pow_right (by norm_num) (by omega)
  have h2 : 0 < (2 : ℕ) ^ a.1 := by positivity
  unfold gridValue at hbound
  have hmul : q * 3 ^ H ≤ q * 3 ^ a.2 := Nat.mul_le_mul_left _ hpow
  have hh : q * 3 ^ a.2 ≤ q * (2 ^ a.1 * 3 ^ a.2) := by nlinarith
  omega

def badWindow_grid_bounds {n j b : ℕ}
    (h4 : 4 * n < 5 * 4 ^ j) (h3lo : 10 * 3 ^ b ≤ n) (h3hi : n < 12 * 3 ^ b) :
    0 < j ∧
    (∀ a : ℕ × ℕ, gridValue a ≤ n →
      a.1 < 2 * j + 1 ∧ a.2 < b + 3 ∧
      (a.2 = b + 2 → a.1 = 0) ∧ (a.1 = 2 → a.2 ≤ b)) ∧
    (∀ a : ℕ × ℕ, 5 * gridValue a ≤ n →
      a.1 < 2 * (j - 1) ∧ a.2 < b + 1 ∧ (a.2 = b → a.1 < 2)) := by
  have h3pos : 0 < (3 : ℕ) ^ b := by positivity
  have hj : 0 < j := by
    by_contra hh
    have he : j = 0 := by omega
    simp only [he, pow_zero] at h4
    omega
  refine ⟨hj, ?_, ?_⟩
  · intro a ha
    have ha1 : 1 * gridValue a ≤ n := by simpa using ha
    constructor
    · apply gridValue_column_lt (by norm_num : 0 < (1 : ℕ)) ha1
      rw [one_mul, two_pow_odd]
      omega
    constructor
    · apply gridValue_row_lt (by norm_num : 0 < (1 : ℕ)) ha1
      rw [one_mul, pow_add]
      norm_num
      omega
    constructor
    · intro hay
      have hbase : (2 : ℕ) ^ a.1 * (9 * 3 ^ b) ≤ n := by
        simpa [gridValue, hay, pow_add, Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using ha
      by_contra hax
      have hx : 2 ≤ (2 : ℕ) ^ a.1 := by
        have hh := Nat.pow_le_pow_right (n := 2) (by norm_num) (show 1 ≤ a.1 by omega)
        simpa using hh
      nlinarith
    · intro hax
      by_contra hby
      have hy : 3 ^ (b + 1) ≤ (3 : ℕ) ^ a.2 :=
        Nat.pow_le_pow_right (by norm_num) (by omega)
      rw [pow_succ] at hy
      have hbase : 4 * 3 ^ a.2 ≤ n := by simpa [gridValue, hax] using ha
      omega
  · intro a ha
    constructor
    · apply gridValue_column_lt (by norm_num : 0 < (5 : ℕ)) ha
      rw [two_pow_even]
      have hj' : j = (j - 1) + 1 := by omega
      have hpow : (4 : ℕ) ^ j = 4 * 4 ^ (j - 1) := by
        calc
          (4 : ℕ) ^ j = 4 ^ ((j - 1) + 1) := by rw [← hj']
          _ = 4 * 4 ^ (j - 1) := by rw [pow_succ]; ring
      rw [hpow] at h4
      omega
    constructor
    · apply gridValue_row_lt (by norm_num : 0 < (5 : ℕ)) ha
      rw [pow_succ]
      omega
    · intro hay
      by_contra hax
      have hx : 4 ≤ (2 : ℕ) ^ a.1 := by
        have hh := Nat.pow_le_pow_right (n := 2) (by norm_num) (show 2 ≤ a.1 by omega)
        simpa using hh
      have hbase : 5 * (2 ^ a.1 * 3 ^ b) ≤ n := by simpa [gridValue, hay] using ha
      nlinarith

def badWindow_five_layer_loss {n j b : ℕ} {A B : Finset (ℕ × ℕ)} {S : Set ℕ}
    (h4 : 4 * n < 5 * 4 ^ j) (h3lo : 10 * 3 ^ b ≤ n) (h3hi : n < 12 * 3 ^ b)
    (hA : GridForkFree A) (hB : GridForkFree B)
    (hAn : ∀ a ∈ A, gridValue a ≤ n) (hBn : ∀ a ∈ B, 5 * gridValue a ≤ n)
    (hAS : ∀ a ∈ A, gridValue a ∈ S) (hBS : ∀ a ∈ B, 5 * gridValue a ∈ S)
    (hS : Erdos1062.ForkFree S) :
    A.card + B.card + 1 ≤ (b + 3 + j) + (b + 1 + (j - 1)) := by
  obtain ⟨hj, hAb, hBb⟩ := badWindow_grid_bounds h4 h3lo h3hi
  exact grid_five_layer_loss hj hA hB
    (fun a ha => (hAb a (hAn a ha)).1)
    (fun a ha => (hAb a (hAn a ha)).2.1)
    (fun a ha => (hAb a (hAn a ha)).2.2.1)
    (fun a ha => (hAb a (hAn a ha)).2.2.2)
    (fun a ha => (hBb a (hBn a ha)).1)
    (fun a ha => (hBb a (hBn a ha)).2.1)
    (fun a ha => (hBb a (hBn a ha)).2.2) hAS hBS hS

end Bounty

end SubmissionComponent_FiveInterval

/- Component BadRank; SHA256 b6f86ea82ba214bc4e38e5a034b96a5a21963b27d80507a593dfac1a5180bb25 -/
section SubmissionComponent_BadRank
/- Exact component ranks in the obstruction window and disjointness of losses. -/

namespace Bounty

def badWindow_rank_values {n j b : ℕ}
    (h4lo : 4 ^ j ≤ n) (h4hi : 4 * n < 5 * 4 ^ j)
    (h3lo : 10 * 3 ^ b ≤ n) (h3hi : n < 12 * 3 ^ b) :
    smoothRankBound n = b + 3 + j ∧ smoothRankBound (n / 5) = b + 1 + (j - 1) := by
  have h3pos : 0 < (3 : ℕ) ^ b := by positivity
  have hn : n ≠ 0 := by omega
  have hn5 : n / 5 ≠ 0 := by omega
  have hj2 : 2 ≤ j := by
    by_contra hbad
    have hj : j = 0 ∨ j = 1 := by omega
    rcases hj with rfl | rfl <;> norm_num at h4hi <;> omega
  have hlog2 : Nat.log 2 n = 2 * j := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · rwa [two_pow_even]
    · rw [two_pow_odd]
      omega
  have hlog3 : Nat.log 3 n = b + 2 := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · rw [pow_add]
      norm_num
      omega
    · rw [show b + 2 + 1 = b + 3 by omega, pow_add]
      norm_num
      omega
  have hj' : j = (j - 2) + 2 := by omega
  have h4pow : (4 : ℕ) ^ j = 16 * 4 ^ (j - 2) := by
    calc
      (4 : ℕ) ^ j = 4 ^ ((j - 2) + 2) := by rw [← hj']
      _ = 16 * 4 ^ (j - 2) := by rw [pow_add]; ring
  have hlog2half : Nat.log 2 (n / 5) = 2 * (j - 2) + 1 := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · rw [two_pow_odd]
      apply (Nat.le_div_iff_mul_le (by norm_num : 0 < (5 : ℕ))).mpr
      rw [h4pow] at h4lo
      omega
    · apply (Nat.div_lt_iff_lt_mul (by norm_num : 0 < (5 : ℕ))).mpr
      rw [pow_succ, two_pow_odd]
      rw [h4pow] at h4hi
      omega
  have hlog3half : Nat.log 3 (n / 5) = b := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · omega
    · rw [pow_succ]
      omega
  have htophalf : 2 * 3 ^ Nat.log 3 (n / 5) ≤ n / 5 := by
    rw [hlog3half]
    omega
  constructor
  · simp [smoothRankBound, hn, hlog2, hlog3]
  · simp only [smoothRankBound, hn5, ↓reduceIte, hlog2half, hlog3half]
    have hpar : (2 * (j - 2) + 1) % 2 = 1 := by omega
    rw [if_pos ⟨hpar, by simpa [hlog3half] using htophalf⟩]
    omega

def badWindow_not_div_five {n : ℕ} (hn : badWindow n) : ¬badWindow (n / 5) := by
  rintro ⟨j, b, hjlo, hjhi, _, _⟩
  obtain ⟨k, c, hklo, hkhi, _, _⟩ := hn
  have hpowpos : 0 < (4 : ℕ) ^ j := by positivity
  have hkj : j + 2 ≤ k := by
    by_contra hh
    have hp : (4 : ℕ) ^ k ≤ 4 ^ (j + 1) :=
      Nat.pow_le_pow_right (by norm_num) (by omega)
    rw [pow_succ] at hp
    omega
  have hp : (4 : ℕ) ^ (j + 2) ≤ 4 ^ k := Nat.pow_le_pow_right (by norm_num) hkj
  rw [pow_add] at hp
  norm_num at hp
  omega

def badWindow_rank_loss {n : ℕ} {A B : Finset (ℕ × ℕ)} {S : Set ℕ}
    (hn : badWindow n) (hA : GridForkFree A) (hB : GridForkFree B)
    (hAn : ∀ a ∈ A, gridValue a ≤ n) (hBn : ∀ a ∈ B, 5 * gridValue a ≤ n)
    (hAS : ∀ a ∈ A, gridValue a ∈ S) (hBS : ∀ a ∈ B, 5 * gridValue a ∈ S)
    (hS : Erdos1062.ForkFree S) :
    A.card + B.card + 1 ≤ smoothRankBound n + smoothRankBound (n / 5) := by
  obtain ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩ := hn
  obtain ⟨hr1, hr2⟩ := badWindow_rank_values h4lo h4hi h3lo h3hi
  rw [hr1, hr2]
  exact badWindow_five_layer_loss h4hi h3lo h3hi hA hB hAn hBn hAS hBS hS

end Bounty

end SubmissionComponent_BadRank

/- Component Core23; SHA256 103b078245eb4cd986fff5b29b6f4a857f44b4c96ccb11a574d1e6fa5dc1f7ed -/
section SubmissionComponent_Core23
/- Canonical decomposition into a coprime-to-six core and a two-prime component. -/

namespace Bounty

def core23 (n : ℕ) : ℕ := ordCompl[3] (ordCompl[2] n)

def core23_pos {n : ℕ} (hn : 0 < n) : 0 < core23 n := by
  apply Nat.ordCompl_pos 3
  exact ne_of_gt (Nat.ordCompl_pos 2 (ne_of_gt hn))

def core23_le (n : ℕ) : core23 n ≤ n :=
  (Nat.ordCompl_le (ordCompl[2] n) 3).trans (Nat.ordCompl_le n 2)

def core23_decomposition (n : ℕ) : core23 n * gridValue (gridCoordinates n) = n := by
  have h3 : (ordCompl[2] n).factorization 3 = n.factorization 3 := by
    rw [Nat.factorization_ordCompl]
    simp
  have he2 := Nat.ordProj_mul_ordCompl_eq_self n 2
  have he3 := Nat.ordProj_mul_ordCompl_eq_self (ordCompl[2] n) 3
  rw [h3] at he3
  change core23 n * (2 ^ n.factorization 2 * 3 ^ n.factorization 3) = n
  calc
    core23 n * (2 ^ n.factorization 2 * 3 ^ n.factorization 3) =
        2 ^ n.factorization 2 * (3 ^ n.factorization 3 * core23 n) := by ring
    _ = n := by
      have hh : 3 ^ n.factorization 3 * core23 n = ordCompl[2] n := by
        simpa only [core23, h3] using he3
      rw [hh]
      exact he2

def core23_not_dvd_two {n : ℕ} (hn : 0 < n) : ¬2 ∣ core23 n := by
  intro hd
  exact Nat.not_dvd_ordCompl Nat.prime_two (ne_of_gt hn)
    (hd.trans (Nat.ordCompl_dvd (ordCompl[2] n) 3))

def core23_not_dvd_three {n : ℕ} (hn : 0 < n) : ¬3 ∣ core23 n :=
  Nat.not_dvd_ordCompl Nat.prime_three (ne_of_gt (Nat.ordCompl_pos 2 (ne_of_gt hn)))

def core23_coprime {n : ℕ} (hn : 0 < n) : (core23 n).Coprime 6 := by
  have h2 : Nat.Coprime 2 (core23 n) :=
    (Nat.prime_two.coprime_iff_not_dvd).mpr (core23_not_dvd_two hn)
  have h3 : Nat.Coprime 3 (core23 n) :=
    (Nat.prime_three.coprime_iff_not_dvd).mpr (core23_not_dvd_three hn)
  simpa using (h2.mul_left h3).symm

def core23_gridValue (a : ℕ × ℕ) : core23 (gridValue a) = 1 := by
  have hh := core23_decomposition (gridValue a)
  rw [gridCoordinates_value] at hh
  have hp := gridValue_pos a
  nlinarith

def core23_mul (m n : ℕ) : core23 (m * n) = core23 m * core23 n := by
  simp only [core23, Nat.ordCompl_mul]

def core23_eq_self {q : ℕ} (hq : q.Coprime 6) : core23 q = q := by
  have h2 : ¬2 ∣ q := by
    intro hd
    have hg := Nat.eq_one_of_dvd_coprimes hq hd (by norm_num : 2 ∣ 6)
    norm_num at hg
  have h3 : ¬3 ∣ q := by
    intro hd
    have hg := Nat.eq_one_of_dvd_coprimes hq hd (by norm_num : 3 ∣ 6)
    norm_num at hg
  unfold core23
  rw [(Nat.ordCompl_eq_self_iff_zero_or_not_dvd q Nat.prime_two).mpr (Or.inr h2)]
  exact (Nat.ordCompl_eq_self_iff_zero_or_not_dvd q Nat.prime_three).mpr (Or.inr h3)

def core23_coordinates_injective :
    Function.Injective (fun n => (core23 n, gridCoordinates n)) := by
  intro m n he
  have hc := congrArg Prod.fst he
  have hg := congrArg Prod.snd he
  dsimp only at hc hg
  calc
    m = core23 m * gridValue (gridCoordinates m) := (core23_decomposition m).symm
    _ = core23 n * gridValue (gridCoordinates n) := by rw [hc, hg]
    _ = n := core23_decomposition n

end Bounty

end SubmissionComponent_Core23

/- Component ComponentSum; SHA256 1267861b451434ccab5de81dd48d55fd7cba530d0429d8d0cab53d29994fa22a -/
section SubmissionComponent_ComponentSum
/- Decomposing a finite fork-free set into its coprime-to-six components. -/

namespace Bounty

def forkFree_scale_iff {q : ℕ} (hq : 0 < q) (S : Set ℕ) :
    Erdos1062.ForkFree ((fun m => q * m) '' S) ↔ Erdos1062.ForkFree S := by
  rw [forkFree_iff, forkFree_iff]
  have hi : Function.Injective (fun m : ℕ => q * m) := by
    intro a b hab
    dsimp only at hab
    exact Nat.eq_of_mul_eq_mul_left hq hab
  constructor
  · intro hh a b c ha hb hc hab hac hdab hdac
    apply hi
    exact hh (q * a) (q * b) (q * c) ⟨a, ha, rfl⟩ ⟨b, hb, rfl⟩ ⟨c, hc, rfl⟩
      (fun he => hab (hi he)) (fun he => hac (hi he))
      (Nat.mul_dvd_mul_left q hdab) (Nat.mul_dvd_mul_left q hdac)
  · intro hh a b c ha hb hc hab hac hdab hdac
    obtain ⟨x, hx, rfl⟩ := ha
    obtain ⟨y, hy, rfl⟩ := hb
    obtain ⟨z, hz, rfl⟩ := hc
    have hxy : x ≠ y := by intro he; exact hab (congrArg (fun m => q * m) he)
    have hxz : x ≠ z := by intro he; exact hac (congrArg (fun m => q * m) he)
    apply congrArg (fun m => q * m)
    exact hh x y z hx hy hz hxy hxz
      ((Nat.mul_dvd_mul_iff_left hq).mp hdab) ((Nat.mul_dvd_mul_iff_left hq).mp hdac)

def coreFiber (A : Finset ℕ) (q : ℕ) : Finset ℕ := A.filter (fun n => core23 n = q)
def componentGrid (A : Finset ℕ) (q : ℕ) : Finset (ℕ × ℕ) :=
  (coreFiber A q).image gridCoordinates

def componentGrid_card (A : Finset ℕ) (q : ℕ) :
    (componentGrid A q).card = (coreFiber A q).card := by
  apply Finset.card_image_iff.mpr
  intro m hm n hn hcoords
  have hmcore := (Finset.mem_filter.mp hm).2
  have hncore := (Finset.mem_filter.mp hn).2
  apply core23_coordinates_injective
  change (core23 m, gridCoordinates m) = (core23 n, gridCoordinates n)
  exact Prod.ext (hmcore.trans hncore.symm) hcoords

def componentGrid_scaled_mem {A : Finset ℕ} {q : ℕ} {a : ℕ × ℕ}
    (ha : a ∈ componentGrid A q) : q * gridValue a ∈ A := by
  obtain ⟨n, hn, rfl⟩ := Finset.mem_image.mp ha
  obtain ⟨hnA, hncore⟩ := Finset.mem_filter.mp hn
  have hh := core23_decomposition n
  rw [hncore] at hh
  rwa [hh]

def componentGrid_bound {A : Finset ℕ} {q n : ℕ}
    (hbound : ∀ m ∈ A, m ≤ n) :
    ∀ a ∈ componentGrid A q, q * gridValue a ≤ n := by
  intro a ha
  exact hbound _ (componentGrid_scaled_mem ha)

def componentGrid_forkFree {A : Finset ℕ} {q : ℕ}
    (hq : 0 < q) (hA : Erdos1062.ForkFree (A : Set ℕ)) :
    GridForkFree (componentGrid A q) := by
  apply gridForkFree_iff.mpr
  apply (forkFree_scale_iff hq _).mp
  apply forkFree_mono _ hA
  rintro x ⟨y, ⟨a, ha, rfl⟩, rfl⟩
  exact componentGrid_scaled_mem ha

def coprimeCores (n : ℕ) : Finset ℕ := (Finset.Icc 1 n).filter (fun q => q.Coprime 6)

def core23_mem_coprimeCores {A : Finset ℕ} {n m : ℕ}
    (hA : ∀ a ∈ A, 1 ≤ a ∧ a ≤ n) (hm : m ∈ A) : core23 m ∈ coprimeCores n := by
  have hmb := hA m hm
  apply Finset.mem_filter.mpr
  constructor
  · exact Finset.mem_Icc.mpr ⟨core23_pos (by omega), (core23_le m).trans hmb.2⟩
  · exact core23_coprime (by omega)

def card_eq_sum_components {A : Finset ℕ} {n : ℕ}
    (hA : ∀ a ∈ A, 1 ≤ a ∧ a ≤ n) :
    A.card = ∑ q ∈ coprimeCores n, (componentGrid A q).card := by
  simp only [componentGrid_card]
  have hh := Finset.sum_card_fiberwise_eq_card_filter A (coprimeCores n) core23
  have he : A.filter (fun a => core23 a ∈ coprimeCores n) = A := by
    apply Finset.filter_eq_self.mpr
    intro a ha
    exact core23_mem_coprimeCores hA ha
  rw [he] at hh
  exact hh.symm

def componentGrid_rank_bound {A : Finset ℕ} {n q : ℕ}
    (hbound : ∀ m ∈ A, m ≤ n) (hA : Erdos1062.ForkFree (A : Set ℕ)) (hq : 0 < q) :
    (componentGrid A q).card ≤ smoothRankBound (n / q) := by
  have hbd : ∀ a ∈ componentGrid A q, gridValue a ≤ n / q := by
    intro a ha
    apply (Nat.le_div_iff_mul_le hq).mpr
    simpa [Nat.mul_comm] using componentGrid_bound hbound a ha
  by_cases hnq : n / q = 0
  · have he : componentGrid A q = ∅ := by
      apply Finset.eq_empty_iff_forall_notMem.mpr
      intro a ha
      have hp := gridValue_pos a
      have hh := hbd a ha
      omega
    simp [he]
  · exact grid_natural_sharp_bound (Nat.pos_of_ne_zero hnq) (componentGrid_forkFree hq hA) hbd

end Bounty

end SubmissionComponent_ComponentSum

/- Component MatchingLoss; SHA256 3cef6769bb02764c68ead0a6f082283dd18b9268f21f3a7499abb7e4616e73ae -/
section SubmissionComponent_MatchingLoss
/- Summing disjoint losses in a finite family of components. -/

namespace Bounty

def sum_matching_losses {ι : Type*} [DecidableEq ι]
    (Q E : Finset ι) (g : ι → ι) (a r : ι → ℕ)
    (hEQ : E ⊆ Q) (hgQ : E.image g ⊆ Q)
    (hginj : Set.InjOn g (E : Set ι)) (hdisj : Disjoint E (E.image g))
    (hbound : ∀ i ∈ Q, a i ≤ r i)
    (hloss : ∀ i ∈ E, a i + a (g i) + 1 ≤ r i + r (g i)) :
    (∑ i ∈ Q, a i) + E.card ≤ ∑ i ∈ Q, r i := by
  let d : ι → ℕ := fun i => r i - a i
  have hdecomp : ∀ i ∈ Q, a i + d i = r i := by
    intro i hi
    exact Nat.add_sub_of_le (hbound i hi)
  have hedge : ∀ i ∈ E, 1 ≤ d i + d (g i) := by
    intro i hi
    have hh := hloss i hi
    have hiQ := hEQ hi
    have hgiQ := hgQ (Finset.mem_image_of_mem g hi)
    have hd1 := hdecomp i hiQ
    have hd2 := hdecomp (g i) hgiQ
    omega
  have hcard : E.card ≤ ∑ i ∈ E, (d i + d (g i)) := by
    calc
      E.card = ∑ _i ∈ E, 1 := by simp
      _ ≤ ∑ i ∈ E, (d i + d (g i)) := Finset.sum_le_sum hedge
  have hsum : (∑ i ∈ E, (d i + d (g i))) = ∑ i ∈ E ∪ E.image g, d i := by
    rw [Finset.sum_add_distrib, Finset.sum_union hdisj, Finset.sum_image]
    exact fun i hi j hj hij => hginj hi hj hij
  rw [hsum] at hcard
  have hdQ : (∑ i ∈ E ∪ E.image g, d i) ≤ ∑ i ∈ Q, d i := by
    apply Finset.sum_le_sum_of_subset_of_nonneg
    · exact Finset.union_subset hEQ hgQ
    · intro i _ _
      exact Nat.zero_le _
  have hwhole : (∑ i ∈ Q, a i) + (∑ i ∈ Q, d i) = ∑ i ∈ Q, r i := by
    rw [← Finset.sum_add_distrib]
    exact Finset.sum_congr rfl hdecomp
  omega

end Bounty

end SubmissionComponent_MatchingLoss

/- Component GlobalUpper; SHA256 dc239b5528393e265c4b58f66e52be64cf3971a8d022da7680ca03028464dc43 -/
section SubmissionComponent_GlobalUpper
/- The global upper bound, including every disjoint powers-of-five loss. -/

namespace Bounty

def badWindow_ge_ten {n : ℕ} (hn : badWindow n) : 10 ≤ n := by
  obtain ⟨j, b, _, _, h3lo, _⟩ := hn
  have hp : 0 < (3 : ℕ) ^ b := by positivity
  omega

def componentGrid_five_loss {A : Finset ℕ} {n q : ℕ}
    (hbound : ∀ m ∈ A, m ≤ n) (hA : Erdos1062.ForkFree (A : Set ℕ)) (hq : 0 < q)
    (hbad : badWindow (n / q)) :
    (componentGrid A q).card + (componentGrid A (5 * q)).card + 1 ≤
      smoothRankBound (n / q) + smoothRankBound (n / (5 * q)) := by
  let S : Set ℕ := {m | q * m ∈ A}
  have hS : Erdos1062.ForkFree S := by
    apply (forkFree_scale_iff hq S).mp
    apply forkFree_mono _ hA
    rintro m ⟨a, ha, rfl⟩
    exact ha
  have hAn : ∀ a ∈ componentGrid A q, gridValue a ≤ n / q := by
    intro a ha
    apply (Nat.le_div_iff_mul_le hq).mpr
    simpa [Nat.mul_comm] using componentGrid_bound hbound a ha
  have hBn : ∀ a ∈ componentGrid A (5 * q), 5 * gridValue a ≤ n / q := by
    intro a ha
    apply (Nat.le_div_iff_mul_le hq).mpr
    simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using componentGrid_bound hbound a ha
  have hAS : ∀ a ∈ componentGrid A q, gridValue a ∈ S := by
    intro a ha
    exact componentGrid_scaled_mem ha
  have hBS : ∀ a ∈ componentGrid A (5 * q), 5 * gridValue a ∈ S := by
    intro a ha
    change q * (5 * gridValue a) ∈ A
    simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using componentGrid_scaled_mem ha
  have hh := badWindow_rank_loss hbad (componentGrid_forkFree hq hA)
    (componentGrid_forkFree (by omega : 0 < 5 * q) hA) hAn hBn hAS hBS hS
  simpa only [Nat.div_div_eq_div_mul, Nat.mul_comm q 5] using hh

noncomputable def lossCores (n : ℕ) : Finset ℕ :=
  open scoped Classical in (coprimeCores n).filter (fun q => badWindow (n / q))

def lossCores_subset (n : ℕ) : lossCores n ⊆ coprimeCores n := by
  classical
  exact Finset.filter_subset _ _

def lossCores_five_subset (n : ℕ) :
    (lossCores n).image (fun q => 5 * q) ⊆ coprimeCores n := by
  classical
  intro x hx
  obtain ⟨q, hq, rfl⟩ := Finset.mem_image.mp hx
  obtain ⟨hqQ, hbad⟩ := Finset.mem_filter.mp hq
  obtain ⟨hqI, hq6⟩ := Finset.mem_filter.mp hqQ
  obtain ⟨hq1, hqn⟩ := Finset.mem_Icc.mp hqI
  have hten := badWindow_ge_ten hbad
  have hle : 5 * q ≤ n := (Nat.le_div_iff_mul_le hq1).mp (by omega)
  apply Finset.mem_filter.mpr
  constructor
  · exact Finset.mem_Icc.mpr ⟨by omega, hle⟩
  · exact (Nat.coprime_mul_iff_left).mpr ⟨by norm_num, hq6⟩

def lossCores_disjoint (n : ℕ) :
    Disjoint (lossCores n) ((lossCores n).image (fun q => 5 * q)) := by
  classical
  apply Finset.disjoint_left.mpr
  intro x hx hy
  obtain ⟨q, hq, rfl⟩ := Finset.mem_image.mp hy
  have hbad := (Finset.mem_filter.mp hq).2
  have hbad' := (Finset.mem_filter.mp hx).2
  apply badWindow_not_div_five hbad
  simpa only [Nat.div_div_eq_div_mul, Nat.mul_comm q 5] using hbad'

def forkFree_card_with_losses {A : Finset ℕ} {n : ℕ}
    (hbound : ∀ m ∈ A, 1 ≤ m ∧ m ≤ n) (hA : Erdos1062.ForkFree (A : Set ℕ)) :
    A.card + (lossCores n).card ≤ ∑ q ∈ coprimeCores n, smoothRankBound (n / q) := by
  classical
  rw [card_eq_sum_components hbound]
  have hi : Set.InjOn (fun q : ℕ => 5 * q) (lossCores n : Set ℕ) := by
    intro q hq r hr he
    dsimp only at he
    omega
  apply sum_matching_losses (coprimeCores n) (lossCores n) (fun q => 5 * q)
    (fun q => (componentGrid A q).card) (fun q => smoothRankBound (n / q))
    (lossCores_subset n) (lossCores_five_subset n) hi (lossCores_disjoint n)
  · intro q hq
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
    exact componentGrid_rank_bound (fun m hm => (hbound m hm).2) hA hqpos
  · intro q hq
    obtain ⟨hqQ, hbad⟩ := Finset.mem_filter.mp hq
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hqQ).1).1
    exact componentGrid_five_loss (fun m hm => (hbound m hm).2) hA hqpos hbad

noncomputable def globalUpper (n : ℕ) : ℕ :=
  (∑ q ∈ coprimeCores n, smoothRankBound (n / q)) - (lossCores n).card

def f_le_globalUpper (n : ℕ) : Erdos1062.f n ≤ globalUpper n := by
  classical
  obtain ⟨A, hAb, hAf, hAc⟩ := exists_maximizer n
  have hfin : A.Finite := (Set.finite_Icc 1 n).subset hAb
  let T := hfin.toFinset
  have hT : (T : Set ℕ) = A := Set.Finite.coe_toFinset _
  have hbound : ∀ m ∈ T, 1 ≤ m ∧ m ≤ n := by
    intro m hm
    have hmA : m ∈ A := by rwa [← hT]
    exact hAb hmA
  have hfree : Erdos1062.ForkFree (T : Set ℕ) := by rwa [hT]
  have hh := forkFree_card_with_losses hbound hfree
  have hc : T.card = Erdos1062.f n := by
    rw [← Set.ncard_coe_finset, hT, hAc]
  rw [hc] at hh
  unfold globalUpper
  omega

end Bounty

end SubmissionComponent_GlobalUpper

/- Component WindowExact; SHA256 7c1db549ba2a17e00ad4334fbee770863cdc4286251a8486ec2c0c60d3d8f68f -/
section SubmissionComponent_WindowExact
/- Each cutoff window is exactly its explicit witness. -/

namespace Bounty

def log_scaled_eq {b d n k : ℕ} (hd : 0 < d)
    (hlo : d * b ^ k ≤ n) (hhi : n < b * (d * b ^ k)) :
    Nat.log b (n / d) = k := by
  apply Nat.log_eq_of_pow_le_of_lt_pow
  · apply (Nat.le_div_iff_mul_le hd).mpr
    simpa [Nat.mul_comm] using hlo
  · apply (Nat.div_lt_iff_lt_mul hd).mpr
    simpa [pow_succ, Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using hhi

def cutoffWindow0_grid_mem {n a b : ℕ}
    (hm : gridValue (a, b) ∈ cutoffWindow 0 n) : (a, b) ∈ window0Grid n := by
  have hn : 0 < n := by
    have hp := gridValue_pos (a, b)
    have hh := (cutoffWindow_subset 0 n hm).2
    omega
  have hbounds := gridValue_log_bounds (cutoffWindow_subset 0 n hm).2
  rcases hm.2 with hm | hm
  · rw [gridValue_factorization_two] at hm
    change a % 2 = 0 ∧ n < 4 * (2 ^ a * 3 ^ b) ∧ 2 ^ a * 3 ^ b ≤ n at hm
    have ha : a = 2 * (a / 2) := by omega
    have hpow : (2 : ℕ) ^ a = 4 ^ (a / 2) := by
      calc
        (2 : ℕ) ^ a = 2 ^ (2 * (a / 2)) := by rw [← ha]
        _ = 4 ^ (a / 2) := two_pow_even _
    have hlog : Nat.log 4 (n / 3 ^ b) = a / 2 := by
      apply log_scaled_eq (by positivity)
      · rw [hpow] at hm
        nlinarith [hm.2.2]
      · rw [hpow] at hm
        nlinarith [hm.2.1]
    apply Finset.mem_union_left
    apply Finset.mem_image.mpr
    refine ⟨b, Finset.mem_range.mpr (by omega), ?_⟩
    apply Prod.ext
    · dsimp [window0Primary]
      omega
    · rfl
  · rw [gridValue_factorization_two] at hm
    change a % 2 ≠ 0 ∧ n < 6 * (2 ^ a * 3 ^ b) ∧ 2 * (2 ^ a * 3 ^ b) ≤ n at hm
    have ha : a = 2 * (a / 2) + 1 := by omega
    have hpow : (2 : ℕ) ^ a = 2 * 4 ^ (a / 2) := by
      calc
        (2 : ℕ) ^ a = 2 ^ (2 * (a / 2) + 1) := by rw [← ha]
        _ = 2 * 4 ^ (a / 2) := two_pow_odd _
    have hvalue : 2 * (2 ^ a * 3 ^ b) = 4 ^ (a / 2 + 1) * 3 ^ b := by
      rw [hpow, pow_succ]
      ring
    have hlog : Nat.log 3 (n / 4 ^ (a / 2 + 1)) = b := by
      apply log_scaled_eq (by positivity)
      · rw [← hvalue]
        exact hm.2.2
      · rw [← hvalue]
        omega
    have hj : a / 2 < Nat.log 4 n := by
      have hp : 0 < (3 : ℕ) ^ b := by positivity
      have hh : (4 : ℕ) ^ (a / 2 + 1) ≤ n := by
        rw [hvalue] at hm
        nlinarith [hm.2.2]
      have := (Nat.le_log_iff_pow_le (by norm_num : 1 < (4 : ℕ)) (by omega : n ≠ 0)).mpr hh
      omega
    apply Finset.mem_union_right
    apply Finset.mem_image.mpr
    refine ⟨a / 2, Finset.mem_range.mpr hj, ?_⟩
    apply Prod.ext
    · dsimp [window0Secondary]
      omega
    · exact hlog

def cutoffWindow0_eq {n : ℕ} (hn : 0 < n) :
    cutoffWindow 0 n = (window0Witness n : Set ℕ) := by
  apply Set.Subset.antisymm
  · intro m hm
    obtain ⟨a, b, he⟩ := hm.1
    have he' : m = gridValue (a, b) := he
    rw [he'] at hm ⊢
    exact Finset.mem_image_of_mem _ (cutoffWindow0_grid_mem hm)
  · exact window0Witness_subset hn

def cutoffWindow0_ncard {n : ℕ} (hn : 0 < n) :
    (cutoffWindow 0 n).ncard = Nat.log 3 n + 1 + Nat.log 4 n := by
  rw [cutoffWindow0_eq hn, Set.ncard_coe_finset, window0Witness_card]

end Bounty

end SubmissionComponent_WindowExact

/- Component WindowCountOne; SHA256 f7fe9933c5b7f1a612fa7f98d6b23aef403bd701a01ae219e695e60056ee5b7b -/
section SubmissionComponent_WindowCountOne
/- The other parity of the cutoff construction and exact component rank. -/

namespace Bounty

def window1Witness (n : ℕ) : Finset ℕ :=
  insert (3 ^ Nat.log 3 (n / 2)) ((window0Witness (n / 2)).image (fun m => 2 * m))

def window1Witness_card (n : ℕ) :
    (window1Witness n).card = Nat.log 3 (n / 2) + Nat.log 4 (n / 2) + 2 := by
  have hnot : 3 ^ Nat.log 3 (n / 2) ∉
      (window0Witness (n / 2)).image (fun m => 2 * m) := by
    intro hh
    obtain ⟨m, hm, he⟩ := Finset.mem_image.mp hh
    have hd : 2 ∣ 3 ^ Nat.log 3 (n / 2) := ⟨m, he.symm⟩
    have := Nat.prime_two.dvd_of_dvd_pow hd
    norm_num at this
  have hi : Function.Injective (fun m : ℕ => 2 * m) := by
    intro a b hab
    dsimp only at hab
    omega
  rw [window1Witness, Finset.card_insert_of_notMem hnot,
    Finset.card_image_of_injective _ hi, window0Witness_card]
  omega

def window1_base_mem {n : ℕ} (hn : 2 ≤ n) :
    3 ^ Nat.log 3 (n / 2) ∈ cutoffWindow 1 n := by
  have hn' : n / 2 ≠ 0 := by omega
  have hlo := Nat.pow_log_le_self 3 hn'
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < (3 : ℕ)) (n / 2)
  rw [pow_succ] at hhi
  have hpow : (3 ^ Nat.log 3 (n / 2)).factorization 2 = 0 := by
    have hh := gridValue_factorization_two (0, Nat.log 3 (n / 2))
    simpa [gridValue] using hh
  constructor
  · exact ⟨0, Nat.log 3 (n / 2), by simp⟩
  · right
    exact ⟨by omega, by omega, by omega⟩

def window1_double_mem {n m : ℕ} (hm : m ∈ cutoffWindow 0 (n / 2)) :
    2 * m ∈ cutoffWindow 1 n := by
  have hmpos := smooth23_pos hm.1
  have hfactor := factorization_two_double hmpos
  constructor
  · obtain ⟨a, b, he⟩ := hm.1
    exact ⟨a + 1, b, by rw [he, pow_succ]; ring⟩
  · rcases hm.2 with hm | hm
    · left
      exact ⟨by omega, by omega, by omega⟩
    · right
      exact ⟨by omega, by omega, by omega⟩

def window1Witness_subset {n : ℕ} (hn : 2 ≤ n) :
    (window1Witness n : Set ℕ) ⊆ cutoffWindow 1 n := by
  intro m hm
  rcases Finset.mem_insert.mp hm with rfl | hm
  · exact window1_base_mem hn
  · obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hm
    exact window1_double_mem (window0Witness_subset (by omega : 0 < n / 2) ha)

def log_four_eq (n : ℕ) : Nat.log 4 n = Nat.log 2 n / 2 := by
  exact Nat.log_pow_left 2 2 n

def log_three_half {n : ℕ} (_hn : 0 < n)
    (htop : 2 * 3 ^ Nat.log 3 n ≤ n) : Nat.log 3 (n / 2) = Nat.log 3 n := by
  have hp : 0 < (3 : ℕ) ^ Nat.log 3 n := by positivity
  have hn2 : n / 2 ≠ 0 := by omega
  apply le_antisymm
  · apply Nat.log_mono_right
    exact Nat.div_le_self n 2
  · apply (Nat.le_log_iff_pow_le (by norm_num) hn2).mpr
    omega

def log_four_half_odd {n : ℕ} (hpar : Nat.log 2 n % 2 = 1) :
    Nat.log 4 (n / 2) = Nat.log 4 n := by
  rw [log_four_eq, log_four_eq, Nat.log_div_base]
  omega

end Bounty

end SubmissionComponent_WindowCountOne

/- Component WindowExactOne; SHA256 e41d375d05a6e50965b8238113172fa9284275332240b2f251738df55ef0ae51 -/
section SubmissionComponent_WindowExactOne
/- Exact cardinalities and lower-endpoint cases of both cutoff windows. -/

namespace Bounty

def cutoffWindow1_half {n m : ℕ} (hs : Smooth23 m)
    (hm : 2 * m ∈ cutoffWindow 1 n) : m ∈ cutoffWindow 0 (n / 2) := by
  have hfactor := factorization_two_double (smooth23_pos hs)
  constructor
  · exact hs
  · rcases hm.2 with hm | hm
    · left
      exact ⟨by omega, by omega, by omega⟩
    · right
      exact ⟨by omega, by omega, by omega⟩

def cutoffWindow1_eq {n : ℕ} (hn : 2 ≤ n) :
    cutoffWindow 1 n = (window1Witness n : Set ℕ) := by
  apply Set.Subset.antisymm
  · intro m hm
    obtain ⟨a, b, he⟩ := hm.1
    have he' : m = gridValue (a, b) := he
    rw [he'] at hm ⊢
    by_cases ha : a = 0
    · have hmem : 3 ^ b ∈ cutoffWindow 1 n := by
        simpa [ha, gridValue] using hm
      have hfactor : (3 ^ b).factorization 2 = 0 := by
        simpa [gridValue] using gridValue_factorization_two (0, b)
      have hwindow : n < 6 * 3 ^ b ∧ 2 * 3 ^ b ≤ n := by
        rcases hmem.2 with h | h
        · omega
        · exact h.2
      have hlog : Nat.log 3 (n / 2) = b := by
        apply Nat.log_eq_of_pow_le_of_lt_pow
        · omega
        · rw [pow_succ]
          omega
      change gridValue (a, b) ∈ window1Witness n
      have hvalue : gridValue (a, b) = 3 ^ Nat.log 3 (n / 2) := by
        simp [gridValue, ha, hlog]
      rw [hvalue]
      exact Finset.mem_insert_self _ _
    · have ha' : a = (a - 1) + 1 := by omega
      have hvalue : gridValue (a, b) = 2 * gridValue (a - 1, b) := by
        change 2 ^ a * 3 ^ b = 2 * (2 ^ (a - 1) * 3 ^ b)
        conv_lhs => rw [ha', pow_succ]
        ring
      rw [hvalue] at hm ⊢
      have hs : Smooth23 (gridValue (a - 1, b)) := ⟨a - 1, b, rfl⟩
      have hhalf := cutoffWindow1_half hs hm
      rw [cutoffWindow0_eq (by omega : 0 < n / 2)] at hhalf
      apply Finset.mem_insert_of_mem
      exact Finset.mem_image_of_mem _ hhalf
  · exact window1Witness_subset hn

def cutoffWindow1_ncard {n : ℕ} (hn : 2 ≤ n) :
    (cutoffWindow 1 n).ncard = Nat.log 3 (n / 2) + Nat.log 4 (n / 2) + 2 := by
  rw [cutoffWindow1_eq hn, Set.ncard_coe_finset, window1Witness_card]

def cutoffWindow_zero (p : ℕ) : cutoffWindow p 0 = ∅ := by
  apply Set.eq_empty_iff_forall_notMem.mpr
  intro m hm
  have hh := cutoffWindow_subset p 0 hm
  have := hh.1
  have := hh.2
  omega

def cutoffWindow1_one : cutoffWindow 1 1 = ∅ := by
  apply Set.eq_empty_iff_forall_notMem.mpr
  intro m hm
  have hbound := cutoffWindow_subset 1 1 hm
  have hm1 : m = 1 := by have := hbound.1; have := hbound.2; omega
  subst m
  have hfactor : (1 : ℕ).factorization 2 = 0 := by simp
  rcases hm.2 with hh | hh <;> omega

def cutoffCount (p n : ℕ) : ℕ :=
  if p = 0 then
    if n = 0 then 0 else Nat.log 3 n + 1 + Nat.log 4 n
  else
    if n < 2 then 0 else Nat.log 3 (n / 2) + Nat.log 4 (n / 2) + 2

def cutoffWindow_ncard {p : ℕ} (hp : p < 2) (n : ℕ) :
    (cutoffWindow p n).ncard = cutoffCount p n := by
  by_cases hp0 : p = 0
  · subst p
    by_cases hn : n = 0
    · subst n
      simp [cutoffCount, cutoffWindow_zero]
    · rw [cutoffWindow0_ncard (by omega)]
      simp [cutoffCount, hn]
  · have hp1 : p = 1 := by omega
    subst p
    by_cases hn : n < 2
    · have he : n = 0 ∨ n = 1 := by omega
      rcases he with rfl | rfl <;> simp [cutoffWindow_zero, cutoffWindow1_one, cutoffCount]
    · rw [cutoffWindow1_ncard (by omega)]
      simp [cutoffCount, hn]

def cutoffCount_mono (p : ℕ) : Monotone (cutoffCount p) := by
  intro n m hnm
  have h3 := Nat.log_mono_right (b := 3) hnm
  have h4 := Nat.log_mono_right (b := 4) hnm
  have hhalf : n / 2 ≤ m / 2 := Nat.div_le_div_right hnm
  have h3half := Nat.log_mono_right (b := 3) hhalf
  have h4half := Nat.log_mono_right (b := 4) hhalf
  unfold cutoffCount
  split_ifs <;> omega

end Bounty

end SubmissionComponent_WindowExactOne

/- Component GlobalWindow; SHA256 a7b66394c6115a86e778d7fc92d0e6bee6f5ffa829a479daa37161887b5349d6 -/
section SubmissionComponent_GlobalWindow
/- A local-to-global criterion for the cutoff construction. -/

namespace Bounty

def core23_small_multiplier {a b n : ℕ}
    (_ha : 0 < a) (hb : 0 < b) (hlow : n < 8 * a) (hhigh : b ≤ n)
    (hab : a ∣ b) (hne : a ≠ b) (h5 : b ≠ 5 * a) (h7 : b ≠ 7 * a) :
    core23 b = core23 a := by
  obtain ⟨k, rfl⟩ := hab
  have hk : k < 8 := by nlinarith
  have hk0 : 0 < k := by nlinarith
  have hk1 : k ≠ 1 := by intro he; simp [he] at hne
  have hk5 : k ≠ 5 := by intro he; apply h5; rw [he]; ring
  have hk7 : k ≠ 7 := by intro he; apply h7; rw [he]; ring
  have hs : Smooth23 k := by
    have hc : k = 2 ∨ k = 3 ∨ k = 4 ∨ k = 6 := by omega
    rcases hc with rfl | rfl | rfl | rfl
    · exact ⟨1, 0, by norm_num⟩
    · exact ⟨0, 1, by norm_num⟩
    · exact ⟨2, 0, by norm_num⟩
    · exact ⟨1, 1, by norm_num⟩
  obtain ⟨x, y, he⟩ := hs
  have hcore : core23 k = 1 := by
    rw [he]
    exact core23_gridValue (x, y)
  rw [core23_mul, hcore, mul_one]

def forkFree_of_components_above_eighth {S : Set ℕ} {n : ℕ}
    (hbound : ∀ a ∈ S, 0 < a ∧ n < 8 * a ∧ a ≤ n)
    (h5 : ∀ a ∈ S, 5 * a ∉ S) (h7 : ∀ a ∈ S, 7 * a ∉ S)
    (hcomponents : ∀ q, Erdos1062.ForkFree (S ∩ {a | core23 a = q})) :
    Erdos1062.ForkFree S := by
  rw [forkFree_iff]
  intro a b c ha hb hc hab hac hdab hdac
  have habcore : core23 b = core23 a := by
    exact core23_small_multiplier (hbound a ha).1 (hbound b hb).1 (hbound a ha).2.1
      (hbound b hb).2.2 hdab hab (by intro he; exact h5 a ha (he ▸ hb))
      (by intro he; exact h7 a ha (he ▸ hb))
  have haccore : core23 c = core23 a := by
    exact core23_small_multiplier (hbound a ha).1 (hbound c hc).1 (hbound a ha).2.1
      (hbound c hc).2.2 hdac hac (by intro he; exact h5 a ha (he ▸ hc))
      (by intro he; exact h7 a ha (he ▸ hc))
  exact (forkFree_iff _).mp (hcomponents (core23 a)) a b c
    ⟨ha, rfl⟩ ⟨hb, habcore⟩ ⟨hc, haccore⟩ hab hac hdab hdac

end Bounty

end SubmissionComponent_GlobalWindow

/- Component SelectedFamily; SHA256 24f7ad88a998e9eac12aa46e63b7af28a81b696f27571d0aa2f32b30cfc6d7c2 -/
section SubmissionComponent_SelectedFamily
/- Assembling compatible cutoff windows in disjoint arithmetic components. -/

namespace Bounty

noncomputable def scaledCutoff (q p r : ℕ) : Finset ℕ :=
  (cutoffWindow_finite p r).toFinset.image (fun s => q * s)

noncomputable def selectedFamily (Q : Finset ℕ) (p r : ℕ → ℕ) : Finset ℕ :=
  Q.biUnion (fun q => scaledCutoff q (p q) (r q))

def mem_scaledCutoff {a q p r : ℕ} :
    a ∈ scaledCutoff q p r ↔ ∃ s ∈ cutoffWindow p r, a = q * s := by
  simp [scaledCutoff, eq_comm]

def mem_selectedFamily {a : ℕ} {Q : Finset ℕ} {p r : ℕ → ℕ} :
    a ∈ selectedFamily Q p r ↔
      ∃ q ∈ Q, ∃ s ∈ cutoffWindow (p q) (r q), a = q * s := by
  simp only [selectedFamily, Finset.mem_biUnion, mem_scaledCutoff]

def smooth23_core {s : ℕ} (hs : Smooth23 s) : core23 s = 1 := by
  obtain ⟨a, b, rfl⟩ := hs
  exact core23_gridValue (a, b)

def scaledCutoff_core {a q p r : ℕ} (hq : q.Coprime 6)
    (ha : a ∈ scaledCutoff q p r) : core23 a = q := by
  obtain ⟨s, hs, rfl⟩ := mem_scaledCutoff.mp ha
  rw [core23_mul, core23_eq_self hq, smooth23_core hs.1, mul_one]

def scaledCutoff_card {q p r : ℕ} (hq : 0 < q) (hp : p < 2) :
    (scaledCutoff q p r).card = cutoffCount p r := by
  have hi : Function.Injective (fun s : ℕ => q * s) := by
    intro a b hab
    exact Nat.eq_of_mul_eq_mul_left hq hab
  rw [scaledCutoff, Finset.card_image_of_injective _ hi,
    ← Set.ncard_eq_toFinset_card (cutoffWindow p r) (cutoffWindow_finite p r), cutoffWindow_ncard hp]

def scaledCutoff_forkFree {q p r : ℕ} (hq : 0 < q) (hp : p < 2) :
    Erdos1062.ForkFree (scaledCutoff q p r : Set ℕ) := by
  have he : (scaledCutoff q p r : Set ℕ) = (fun s => q * s) '' cutoffWindow p r := by
    ext a
    simp only [Finset.mem_coe, mem_scaledCutoff, Set.mem_image]
    constructor
    · rintro ⟨s, hs, he⟩
      exact ⟨s, hs, he.symm⟩
    · rintro ⟨s, hs, he⟩
      exact ⟨s, hs, he.symm⟩
  rw [he]
  exact (forkFree_scale_iff hq _).mpr (cutoffWindow_forkFree hp r)

def selectedFamily_card {Q : Finset ℕ} {p r : ℕ → ℕ}
    (hQ : ∀ q ∈ Q, 0 < q ∧ q.Coprime 6) (hp : ∀ q ∈ Q, p q < 2) :
    (selectedFamily Q p r).card = ∑ q ∈ Q, cutoffCount (p q) (r q) := by
  have hd : ∀ q ∈ Q, ∀ t ∈ Q, q ≠ t →
      Disjoint (scaledCutoff q (p q) (r q)) (scaledCutoff t (p t) (r t)) := by
    intro q hq t ht hne
    apply Finset.disjoint_left.mpr
    intro a ha hb
    exact hne ((scaledCutoff_core (hQ q hq).2 ha).symm.trans (scaledCutoff_core (hQ t ht).2 hb))
  rw [selectedFamily, Finset.card_biUnion hd]
  apply Finset.sum_congr rfl
  intro q hq
  exact scaledCutoff_card (hQ q hq).1 (hp q hq)

def selectedFamily_components {Q : Finset ℕ} {p r : ℕ → ℕ}
    (hQ : ∀ q ∈ Q, 0 < q ∧ q.Coprime 6) (hp : ∀ q ∈ Q, p q < 2) (q : ℕ) :
    Erdos1062.ForkFree ((selectedFamily Q p r : Set ℕ) ∩ {a | core23 a = q}) := by
  by_cases hqQ : q ∈ Q
  · apply forkFree_mono _ (scaledCutoff_forkFree (r := r q) (hQ q hqQ).1 (hp q hqQ))
    intro a ha
    obtain ⟨t, ht, s, hs, he⟩ := mem_selectedFamily.mp ha.1
    have hmem : a ∈ scaledCutoff t (p t) (r t) := mem_scaledCutoff.mpr ⟨s, hs, he⟩
    have hcore := scaledCutoff_core (hQ t ht).2 hmem
    have htq : t = q := hcore.symm.trans ha.2
    rwa [htq] at hmem
  · have he : ((selectedFamily Q p r : Set ℕ) ∩ {a | core23 a = q}) = ∅ := by
      apply Set.eq_empty_iff_forall_notMem.mpr
      intro a ha
      obtain ⟨t, ht, s, hs, he⟩ := mem_selectedFamily.mp ha.1
      have hmem : a ∈ scaledCutoff t (p t) (r t) := mem_scaledCutoff.mpr ⟨s, hs, he⟩
      have hcore := scaledCutoff_core (hQ t ht).2 hmem
      have htq : t = q := hcore.symm.trans ha.2
      exact hqQ (htq ▸ ht)
    rw [he]
    exact forkFree_empty

def selectedFamily_exclude_multiple {Q : Finset ℕ} {p r : ℕ → ℕ} {d : ℕ}
    (hQ : ∀ q ∈ Q, 0 < q ∧ q.Coprime 6) (hd : 0 < d) (hd6 : d.Coprime 6)
    (hdisj : ∀ q ∈ Q, d * q ∈ Q →
      Disjoint (cutoffWindow (p q) (r q)) (cutoffWindow (p (d * q)) (r (d * q)))) :
    ∀ a ∈ selectedFamily Q p r, d * a ∉ selectedFamily Q p r := by
  intro a ha hb
  obtain ⟨q, hq, s, hs, has⟩ := mem_selectedFamily.mp ha
  obtain ⟨t, ht, u, hu, hbu⟩ := mem_selectedFamily.mp hb
  have hcorea : core23 a = q :=
    scaledCutoff_core (hQ q hq).2 (mem_scaledCutoff.mpr ⟨s, hs, has⟩)
  have hcoreb : core23 (d * a) = t :=
    scaledCutoff_core (hQ t ht).2 (mem_scaledCutoff.mpr ⟨u, hu, hbu⟩)
  have htq : t = d * q := by
    rw [core23_mul, core23_eq_self hd6, hcorea] at hcoreb
    exact hcoreb.symm
  have hsu : s = u := by
    apply Nat.eq_of_mul_eq_mul_left (mul_pos hd (hQ q hq).1)
    calc
      (d * q) * s = d * (q * s) := by ring
      _ = d * a := by rw [has]
      _ = t * u := hbu
      _ = (d * q) * u := by rw [htq]
  have hD := hdisj q hq (htq ▸ ht)
  have hu' : s ∈ cutoffWindow (p (d * q)) (r (d * q)) := by
    rw [hsu]
    rwa [htq] at hu
  exact Set.disjoint_left.mp hD hs hu'

def selectedFamily_forkFree {Q : Finset ℕ} {p r : ℕ → ℕ} {n : ℕ}
    (hQ : ∀ q ∈ Q, 0 < q ∧ q.Coprime 6) (hp : ∀ q ∈ Q, p q < 2)
    (hcut : ∀ q ∈ Q, q * r q ≤ n)
    (hlow : ∀ q ∈ Q, ∀ s ∈ cutoffWindow (p q) (r q), n < 8 * (q * s))
    (h5 : ∀ q ∈ Q, 5 * q ∈ Q →
      (if p q = p (5 * q) then 4 else 6) * r (5 * q) ≤ r q)
    (h7 : ∀ q ∈ Q, 7 * q ∈ Q →
      (if p q = p (7 * q) then 4 else 6) * r (7 * q) ≤ r q) :
    Erdos1062.ForkFree (selectedFamily Q p r : Set ℕ) := by
  apply forkFree_of_components_above_eighth
  · intro a ha
    obtain ⟨q, hq, s, hs, rfl⟩ := mem_selectedFamily.mp ha
    refine ⟨mul_pos (hQ q hq).1 (smooth23_pos hs.1), hlow q hq s hs, ?_⟩
    have hsr := (cutoffWindow_subset (p q) (r q) hs).2
    exact (Nat.mul_le_mul_left q hsr).trans (hcut q hq)
  · exact selectedFamily_exclude_multiple hQ (by norm_num : 0 < (5 : ℕ)) (by norm_num)
      (fun q hq ht => cutoffWindow_disjoint (h5 q hq ht))
  · exact selectedFamily_exclude_multiple hQ (by norm_num : 0 < (7 : ℕ)) (by norm_num)
      (fun q hq ht => cutoffWindow_disjoint (h7 q hq ht))
  · exact selectedFamily_components hQ hp

end Bounty

end SubmissionComponent_SelectedFamily

/- Component CutoffCertificate; SHA256 c10fb000d64bdd10e74f201284ed9e9f3922358a9af8997fb0a9338b14a450eb -/
section SubmissionComponent_CutoffCertificate
/- The precise certificate needed to attain the global upper bound. -/

namespace Bounty

noncomputable def lossChildren (n : ℕ) : Finset ℕ :=
  (lossCores n).image (fun q => 5 * q)

noncomputable def componentQuota (n q : ℕ) : ℕ :=
  open scoped Classical in smoothRankBound (n / q) - if q ∈ lossChildren n then 1 else 0

def smoothRankBound_pos {n : ℕ} (hn : 0 < n) : 0 < smoothRankBound n := by
  unfold smoothRankBound
  rw [if_neg (ne_of_gt hn)]
  omega

def lossChildren_rank_pos {n q : ℕ} (hq : q ∈ lossChildren n) :
    0 < smoothRankBound (n / q) := by
  classical
  obtain ⟨t, ht, rfl⟩ := Finset.mem_image.mp hq
  have hbad := (Finset.mem_filter.mp ht).2
  have hten := badWindow_ge_ten hbad
  have hn : 0 < n / (5 * t) := by
    rw [Nat.mul_comm 5 t, ← Nat.div_div_eq_div_mul]
    omega
  exact smoothRankBound_pos hn

def componentQuota_sum (n : ℕ) :
    (∑ q ∈ coprimeCores n, componentQuota n q) = globalUpper n := by
  classical
  have hsubset : lossChildren n ⊆ coprimeCores n := lossCores_five_subset n
  have hfilter : (coprimeCores n).filter (fun q => q ∈ lossChildren n) = lossChildren n := by
    ext q
    simp only [Finset.mem_filter]
    exact ⟨fun h => h.2, fun h => ⟨hsubset h, h⟩⟩
  have hsum : (∑ q ∈ coprimeCores n, if q ∈ lossChildren n then 1 else 0) =
      (lossChildren n).card := by
    rw [Finset.sum_boole, hfilter]
    norm_cast
  have hcard : (lossChildren n).card = (lossCores n).card := by
    apply Finset.card_image_of_injective
    intro a b hab
    dsimp only at hab
    omega
  unfold componentQuota globalUpper
  rw [Finset.sum_tsub_distrib, hsum, hcard]
  intro q hq
  split_ifs with hh
  · exact lossChildren_rank_pos hh
  · exact Nat.zero_le _

structure CutoffCertificate (n : ℕ) where
  parity : ℕ → ℕ
  cutoff : ℕ → ℕ
  parity_lt : ∀ q ∈ coprimeCores n, parity q < 2
  cutoff_bound : ∀ q ∈ coprimeCores n, q * cutoff q ≤ n
  lower_bound : ∀ q ∈ coprimeCores n, ∀ s ∈ cutoffWindow (parity q) (cutoff q),
    n < 8 * (q * s)
  compatible_five : ∀ q ∈ coprimeCores n, 5 * q ∈ coprimeCores n →
    (if parity q = parity (5 * q) then 4 else 6) * cutoff (5 * q) ≤ cutoff q
  compatible_seven : ∀ q ∈ coprimeCores n, 7 * q ∈ coprimeCores n →
    (if parity q = parity (7 * q) then 4 else 6) * cutoff (7 * q) ≤ cutoff q
  quota : ∀ q ∈ coprimeCores n, cutoffCount (parity q) (cutoff q) = componentQuota n q

def cutoffCertificate_witness {n : ℕ} (C : CutoffCertificate n) :
    ∃ A : Finset ℕ, (∀ m ∈ A, 1 ≤ m ∧ m ≤ n) ∧
      Erdos1062.ForkFree (A : Set ℕ) ∧ A.card = globalUpper n := by
  have hQ : ∀ q ∈ coprimeCores n, 0 < q ∧ q.Coprime 6 := by
    intro q hq
    obtain ⟨hqI, hq6⟩ := Finset.mem_filter.mp hq
    exact ⟨(Finset.mem_Icc.mp hqI).1, hq6⟩
  refine ⟨selectedFamily (coprimeCores n) C.parity C.cutoff, ?_, ?_, ?_⟩
  · intro m hm
    obtain ⟨q, hq, s, hs, rfl⟩ := mem_selectedFamily.mp hm
    constructor
    · exact mul_pos (hQ q hq).1 (smooth23_pos hs.1)
    · exact (Nat.mul_le_mul_left q (cutoffWindow_subset _ _ hs).2).trans (C.cutoff_bound q hq)
  · exact selectedFamily_forkFree hQ C.parity_lt C.cutoff_bound C.lower_bound
      C.compatible_five C.compatible_seven
  · rw [selectedFamily_card hQ C.parity_lt]
    calc
      (∑ q ∈ coprimeCores n, cutoffCount (C.parity q) (C.cutoff q)) =
          ∑ q ∈ coprimeCores n, componentQuota n q := Finset.sum_congr rfl C.quota
      _ = globalUpper n := componentQuota_sum n

def f_eq_globalUpper_of_certificate {n : ℕ} (C : CutoffCertificate n) :
    Erdos1062.f n = globalUpper n := by
  apply le_antisymm (f_le_globalUpper n)
  obtain ⟨A, hbound, hfree, hcard⟩ := cutoffCertificate_witness C
  rw [← hcard, ← Set.ncard_coe_finset]
  apply card_le_f _ hfree
  intro m hm
  exact hbound m hm

end Bounty

end SubmissionComponent_CutoffCertificate

/- Component QuotaIdentity; SHA256 dbd6804f74b09f50a215146d881d7238a4c9fbb7ebd802a406146a78919c99b9 -/
section SubmissionComponent_QuotaIdentity
/- The component quota is the type-dependent quota of the rational recursion. -/

namespace Bounty

def lossChildren_iff {n q : ℕ} (hq : q ∈ coprimeCores n) :
    q ∈ lossChildren n ↔ 5 ∣ q ∧ badWindow (n / (q / 5)) := by
  classical
  constructor
  · intro hh
    obtain ⟨t, ht, rfl⟩ := Finset.mem_image.mp hh
    constructor
    · exact dvd_mul_right 5 t
    · simpa using (Finset.mem_filter.mp ht).2
  · rintro ⟨⟨t, rfl⟩, hbad⟩
    have htQ : t ∈ coprimeCores n := by
      obtain ⟨hqI, hq6⟩ := Finset.mem_filter.mp hq
      obtain ⟨hqpos, hqn⟩ := Finset.mem_Icc.mp hqI
      apply Finset.mem_filter.mpr
      exact ⟨Finset.mem_Icc.mpr ⟨by omega, by omega⟩, (Nat.coprime_mul_iff_left.mp hq6).2⟩
    apply Finset.mem_image_of_mem
    apply Finset.mem_filter.mpr
    exact ⟨htQ, by simpa using hbad⟩

def quotient_ge_one_of_core_mem {n q : ℕ} (hq : q ∈ coprimeCores n) :
    1 ≤ (n : ℚ) / q := by
  obtain ⟨hqI, _⟩ := Finset.mem_filter.mp hq
  obtain ⟨hqpos, hqn⟩ := Finset.mem_Icc.mp hqI
  apply (le_div_iff₀ (by exact_mod_cast hqpos : (0 : ℚ) < q)).mpr
  simpa using (show (q : ℚ) ≤ n by exact_mod_cast hqn)

def rational_scaled_quotient (n q d : ℕ) :
    (n : ℚ) / (d * q : ℕ) = ((n : ℚ) / q) / d := by
  rw [div_div]
  congr 1
  push_cast
  ring

def floor_five_quotient {n q : ℕ} (hq : 0 < q) (h5 : 5 ∣ q) :
    ⌊5 * ((n : ℚ) / q)⌋₊ = n / (q / 5) := by
  obtain ⟨t, rfl⟩ := h5
  have ht : (t : ℚ) ≠ 0 := by exact_mod_cast (by omega : t ≠ 0)
  have he : 5 * ((n : ℚ) / (5 * t : ℕ)) = (n : ℚ) / t := by
    push_cast
    field_simp
  rw [he, Nat.floor_div_eq_div]
  simp

noncomputable def rationalQuota (eps : Bool) (u : ℚ) : ℕ :=
  open scoped Classical in smoothRankBound ⌊u⌋₊ -
    if eps = true ∧ badWindow ⌊5 * u⌋₊ then 1 else 0

def componentQuota_eq_rationalQuota {n q : ℕ} (hq : q ∈ coprimeCores n) :
    componentQuota n q = rationalQuota (decide (5 ∣ q)) ((n : ℚ) / q) := by
  classical
  have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
  unfold componentQuota rationalQuota
  rw [Nat.floor_div_eq_div]
  by_cases h5 : 5 ∣ q
  · rw [floor_five_quotient hqpos h5]
    simp [lossChildren_iff hq, h5]
  · simp [lossChildren_iff hq, h5]

end Bounty

end SubmissionComponent_QuotaIdentity

/- Component ComputableWindow; SHA256 f52220eca8eacfad95e815a69b744ca4fc7b894f14bf7a4c259862092a3d5b5b -/
section SubmissionComponent_ComputableWindow
/- A finite decision procedure for the obstruction window. -/

namespace Bounty

def badWindow_iff_bounded (n : ℕ) :
    badWindow n ↔ ∃ j ∈ Finset.range (Nat.log 4 n + 1),
      ∃ b ∈ Finset.range (Nat.log 3 n + 1),
        4 ^ j ≤ n ∧ 4 * n < 5 * 4 ^ j ∧ 10 * 3 ^ b ≤ n ∧ n < 12 * 3 ^ b := by
  constructor
  · intro hn
    have hn0 : n ≠ 0 := by have := badWindow_ge_ten hn; omega
    obtain ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩ := hn
    have hj : j ≤ Nat.log 4 n := (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr h4lo
    have hb : b ≤ Nat.log 3 n :=
      (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr (by omega)
    exact ⟨j, Finset.mem_range.mpr (by omega), b, Finset.mem_range.mpr (by omega),
      h4lo, h4hi, h3lo, h3hi⟩
  · rintro ⟨j, _, b, _, h4lo, h4hi, h3lo, h3hi⟩
    exact ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩

def badWindow_decidable (n : ℕ) : Decidable (badWindow n) :=
  decidable_of_iff
    (∃ j ∈ Finset.range (Nat.log 4 n + 1), ∃ b ∈ Finset.range (Nat.log 3 n + 1),
      4 ^ j ≤ n ∧ 4 * n < 5 * 4 ^ j ∧ 10 * 3 ^ b ≤ n ∧ n < 12 * 3 ^ b)
    (badWindow_iff_bounded n).symm

def quotaValue (eps : Bool) (u : ℚ) : ℕ :=
  letI := badWindow_decidable
  smoothRankBound ⌊u⌋₊ - if eps = true ∧ badWindow ⌊5 * u⌋₊ then 1 else 0

def quotaValue_eq (eps : Bool) (u : ℚ) : quotaValue eps u = rationalQuota eps u := by
  unfold quotaValue rationalQuota
  by_cases hh : eps = true ∧ badWindow ⌊5 * u⌋₊ <;> simp [hh]

end Bounty

end SubmissionComponent_ComputableWindow

/- Component RationalWindow; SHA256 fc6f9921cfc61e6dd3b976f94a8b5eb3871e61cd7531794cdd557224d3edd899 -/
section SubmissionComponent_RationalWindow
/- Rational cutoffs retain the strict endpoints required by the construction. -/

namespace Bounty

def rationalWindow (p : ℕ) (r : ℚ) : Set ℕ := cutoffWindow p ⌊r⌋₊

def rationalWindow_lower {p n : ℕ} {r : ℚ} (hn : n ∈ rationalWindow p r) :
    r < 6 * (n : ℚ) := by
  have hh : ⌊r⌋₊ < 6 * n := cutoffWindow_lower hn
  have hlt := Nat.lt_of_floor_lt hh
  exact_mod_cast hlt

def rationalWindow_eighth {p n : ℕ} {r u : ℚ}
    (hn : n ∈ rationalWindow p r) (hru : 3 * u ≤ 4 * r) : u < 8 * (n : ℚ) := by
  have hh := rationalWindow_lower hn
  linarith

def floor_scaled_le {r s : ℚ} (hs : 0 ≤ s) {d : ℕ} (hd : (d : ℚ) * s ≤ r) :
    d * ⌊s⌋₊ ≤ ⌊r⌋₊ := by
  have hr : 0 ≤ r := (mul_nonneg (Nat.cast_nonneg d) hs).trans hd
  apply (Nat.le_floor_iff hr).mpr
  push_cast
  exact (mul_le_mul_of_nonneg_left (Nat.floor_le hs) (Nat.cast_nonneg d)).trans hd

def rationalWindow_scaled_eighth {n q s p : ℕ} {r : ℚ} (hq : 0 < q)
    (hcut : 3 * ((n : ℚ) / q) ≤ 4 * r) (hs : s ∈ rationalWindow p r) : n < 8 * (q * s) := by
  have hsq := rationalWindow_eighth hs hcut
  have hmul := (div_lt_iff₀ (by exact_mod_cast hq : (0 : ℚ) < q)).mp hsq
  exact_mod_cast (by nlinarith : (n : ℚ) < 8 * ((q : ℚ) * s))

end Bounty

end SubmissionComponent_RationalWindow

/- Component CutoffLevels; SHA256 d5fec12465da57274832497430fd6445c0531c87ef263e82a296f7c981d1adc1 -/
section SubmissionComponent_CutoffLevels
/- Exact half-open intervals on which a cutoff window has prescribed size. -/

namespace Bounty

def cutoffCount_unbounded (p k : ℕ) : ∃ r, k ≤ cutoffCount p r := by
  by_cases hp : p = 0
  · refine ⟨3 ^ k, ?_⟩
    have hn : (3 : ℕ) ^ k ≠ 0 := by positivity
    simp only [cutoffCount, hp, ↓reduceIte, hn, Nat.log_pow (by norm_num : 1 < (3 : ℕ))]
    omega
  · refine ⟨2 * 3 ^ k, ?_⟩
    have hk : 0 < (3 : ℕ) ^ k := by positivity
    have hn : ¬2 * 3 ^ k < 2 := by omega
    have hdiv : (2 * 3 ^ k : ℕ) / 2 = 3 ^ k := by omega
    simp only [cutoffCount, hp, ↓reduceIte, hn, hdiv,
      Nat.log_pow (by norm_num : 1 < (3 : ℕ))]
    omega

noncomputable def lowerCutoff (p k : ℕ) : ℕ := Nat.find (cutoffCount_unbounded p k)

def lowerCutoff_spec (p k : ℕ) : k ≤ cutoffCount p (lowerCutoff p k) :=
  Nat.find_spec (cutoffCount_unbounded p k)

def lowerCutoff_le_iff (p k r : ℕ) : lowerCutoff p k ≤ r ↔ k ≤ cutoffCount p r := by
  constructor
  · intro hh
    exact (lowerCutoff_spec p k).trans (cutoffCount_mono p hh)
  · intro hh
    exact Nat.find_min' (cutoffCount_unbounded p k) hh

def lt_lowerCutoff_iff (p k r : ℕ) : r < lowerCutoff p k ↔ cutoffCount p r < k := by
  have hh := lowerCutoff_le_iff p k r
  omega

def cutoffCount_level_iff (p k r : ℕ) :
    cutoffCount p r = k ↔ lowerCutoff p k ≤ r ∧ r < lowerCutoff p (k + 1) := by
  rw [lowerCutoff_le_iff, lt_lowerCutoff_iff]
  omega

def cutoffCount_floor_level_iff (p k : ℕ) {r : ℚ} (hr : 0 ≤ r) :
    cutoffCount p ⌊r⌋₊ = k ↔ (lowerCutoff p k : ℚ) ≤ r ∧ r < lowerCutoff p (k + 1) := by
  rw [cutoffCount_level_iff, Nat.le_floor_iff hr, Nat.floor_lt hr]

end Bounty

end SubmissionComponent_CutoffLevels

/- Component CutoffRecursion; SHA256 08fe00aa39b943b9462552b350e5ad8b75eeb4b09779eaa98722b584170efac6 -/
section SubmissionComponent_CutoffRecursion
/- The candidate cutoff recursion; universal availability is still to be proved. -/

namespace Bounty

noncomputable def cutoffTrial (u : ℚ) (k p : ℕ) (c5 c7 : ℕ × ℚ) : ℚ :=
  max (max (3 * u / 4) (lowerCutoff p k : ℚ))
    (max ((if p = c5.1 then 4 else 6) * c5.2) ((if p = c7.1 then 4 else 6) * c7.2))

def cutoffAvailable (u : ℚ) (k p : ℕ) (c5 c7 : ℕ × ℚ) : Prop :=
  cutoffTrial u k p c5 c7 ≤ u ∧ cutoffTrial u k p c5 c7 < lowerCutoff p (k + 1)

noncomputable def cutoffAvailable_decidable (u : ℚ) (k p : ℕ) (c5 c7 : ℕ × ℚ) :
    Decidable (cutoffAvailable u k p c5 c7) := by
  unfold cutoffAvailable
  infer_instance

noncomputable def cutoffCandidate (eps : Bool) (u : ℚ) (c5 c7 : ℕ × ℚ) : ℕ × ℚ :=
  letI := cutoffAvailable_decidable
  let k := quotaValue eps u
  let preferred := Nat.log 2 ⌊u⌋₊ % 2
  let p := if cutoffAvailable u k preferred c5 c7 then preferred else 1 - preferred
  (p, cutoffTrial u k p c5 c7)

def floor_div_lt_floor {u : ℚ} {d : ℕ} (hu : 1 ≤ u) (hd : 1 < d) :
    ⌊u / d⌋₊ < ⌊u⌋₊ := by
  rw [Nat.floor_div_natCast]
  apply Nat.div_lt_self
  · exact (Nat.le_floor_iff (by linarith : 0 ≤ u)).mpr hu
  · exact hd

noncomputable def cutoffState (eps : Bool) (u : ℚ) : ℕ × ℚ :=
  if hu : u < 1 then (0, 0) else
    cutoffCandidate eps u (cutoffState true (u / 5)) (cutoffState eps (u / 7))
termination_by ⌊u⌋₊
decreasing_by
  · exact floor_div_lt_floor (d := 5) (by linarith) (by norm_num)
  · exact floor_div_lt_floor (d := 7) (by linarith) (by norm_num)

def cutoffTrial_bounds (u : ℚ) (k p : ℕ) (c5 c7 : ℕ × ℚ) :
    3 * u / 4 ≤ cutoffTrial u k p c5 c7 ∧
    (lowerCutoff p k : ℚ) ≤ cutoffTrial u k p c5 c7 ∧
    (if p = c5.1 then 4 else 6) * c5.2 ≤ cutoffTrial u k p c5 c7 ∧
    (if p = c7.1 then 4 else 6) * c7.2 ≤ cutoffTrial u k p c5 c7 := by
  unfold cutoffTrial
  exact ⟨(le_max_left _ _).trans (le_max_left _ _),
    (le_max_right _ _).trans (le_max_left _ _),
    (le_max_left _ _).trans (le_max_right _ _),
    (le_max_right _ _).trans (le_max_right _ _)⟩

def cutoffTrial_size {u : ℚ} {k p : ℕ} {c5 c7 : ℕ × ℚ}
    (hu : 0 ≤ u) (hvalid : cutoffAvailable u k p c5 c7) :
    cutoffCount p ⌊cutoffTrial u k p c5 c7⌋₊ = k := by
  have hh := cutoffTrial_bounds u k p c5 c7
  have hr : 0 ≤ cutoffTrial u k p c5 c7 := by linarith [hh.1]
  apply (cutoffCount_floor_level_iff p k hr).mpr
  exact ⟨hh.2.1, hvalid.2⟩

def cutoffCandidate_parity (eps : Bool) (u : ℚ) (c5 c7 : ℕ × ℚ) :
    (cutoffCandidate eps u c5 c7).1 < 2 := by
  unfold cutoffCandidate
  dsimp only
  split_ifs <;> omega

def cutoffCandidate_eq_trial (eps : Bool) (u : ℚ) (c5 c7 : ℕ × ℚ) :
    (cutoffCandidate eps u c5 c7).2 =
      cutoffTrial u (quotaValue eps u) (cutoffCandidate eps u c5 c7).1 c5 c7 := by
  unfold cutoffCandidate
  dsimp only

def cutoffState_of_small {eps : Bool} {u : ℚ} (hu : u < 1) : cutoffState eps u = (0, 0) := by
  rw [cutoffState, dif_pos hu]

def cutoffState_of_large {eps : Bool} {u : ℚ} (hu : 1 ≤ u) :
    cutoffState eps u = cutoffCandidate eps u (cutoffState true (u / 5)) (cutoffState eps (u / 7)) := by
  rw [cutoffState, dif_neg (by linarith)]

def cutoffState_parity (eps : Bool) (u : ℚ) : (cutoffState eps u).1 < 2 := by
  by_cases hu : u < 1
  · rw [cutoffState_of_small hu]
    norm_num
  · rw [cutoffState_of_large (le_of_not_gt hu)]
    exact cutoffCandidate_parity _ _ _ _

end Bounty

end SubmissionComponent_CutoffRecursion

/- Component CutoffBase; SHA256 92ba667e4f197efc465542c84024b066863a3afc820f9c082bf897aee13ad6d6 -/
section SubmissionComponent_CutoffBase
/- Initial rational intervals on which trial availability can be proved directly. -/

namespace Bounty

def lowerCutoff_eq_of_step {p k r : ℕ} (hr : 0 < r)
    (hlo : k ≤ cutoffCount p r) (hprev : cutoffCount p (r - 1) < k) :
    lowerCutoff p k = r := by
  have hh := (lowerCutoff_le_iff p k r).mpr hlo
  have hp := (lt_lowerCutoff_iff p k (r - 1)).mpr hprev
  omega

def badWindow_ge_270 {n : ℕ} (hn : badWindow n) : 0x10e ≤ n := by
  obtain ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩ := hn
  by_contra hsmall
  have hj : j < 5 := by
    by_contra hh
    have hp : (4 : ℕ) ^ 5 ≤ 4 ^ j := Nat.pow_le_pow_right (by norm_num) (by omega)
    norm_num at hp
    omega
  have hb : b < 3 := by
    by_contra hh
    have hp : (3 : ℕ) ^ 3 ≤ 3 ^ b := Nat.pow_le_pow_right (by norm_num) (by omega)
    norm_num at hp
    omega
  interval_cases j <;> interval_cases b <;> norm_num at * <;> omega

end Bounty

end SubmissionComponent_CutoffBase

/- Component BaseStates; SHA256 16daa0038fe381a7831ec0be6b457ec5de7a0046266e1219618ef2c8e4ae7eaf -/
section SubmissionComponent_BaseStates
/- Explicit initial values of the candidate recursion. -/

namespace Bounty

end Bounty

end SubmissionComponent_BaseStates

/- Component BaseSixteen; SHA256 3a10dc0f3b114809e15c19ac9f757b1bc903b853edd8462f5c7150f8864e81f9 -/
section SubmissionComponent_BaseSixteen
/- Trial availability throughout the initial interval below sixteen. -/

namespace Bounty

end Bounty

end SubmissionComponent_BaseSixteen

/- Component WindowLogBounds; SHA256 d22a772f9048d9d734776debabd97a8b2218845f4718da76f7a8e2f27f37f76d -/
section SubmissionComponent_WindowLogBounds
/- Canonical obstruction indices and logarithms on rational verification intervals. -/

namespace Bounty

def badWindow_log_indices {n j b : ℕ}
    (h4lo : 4 ^ j ≤ n) (h4hi : 4 * n < 5 * 4 ^ j)
    (h3lo : 10 * 3 ^ b ≤ n) (h3hi : n < 12 * 3 ^ b) :
    Nat.log 4 n = j ∧ Nat.log 3 n = b + 2 := by
  constructor
  · apply Nat.log_eq_of_pow_le_of_lt_pow h4lo
    rw [pow_succ]
    omega
  · apply Nat.log_eq_of_pow_le_of_lt_pow
    · rw [pow_add]
      norm_num
      omega
    · rw [show b + 2 + 1 = b + 3 by omega, pow_add]
      norm_num
      omega

def badWindow_iff_canonical (n : ℕ) :
    badWindow n ↔
      4 ^ Nat.log 4 n ≤ n ∧ 4 * n < 5 * 4 ^ Nat.log 4 n ∧
      10 * 3 ^ (Nat.log 3 n - 2) ≤ n ∧ n < 12 * 3 ^ (Nat.log 3 n - 2) := by
  constructor
  · rintro ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩
    obtain ⟨hj, hb⟩ := badWindow_log_indices h4lo h4hi h3lo h3hi
    rw [hj, hb, Nat.add_sub_cancel]
    exact ⟨h4lo, h4hi, h3lo, h3hi⟩
  · intro hh
    exact ⟨Nat.log 4 n, Nat.log 3 n - 2, hh⟩

def log_floor_of_bounds {u : ℚ} {b k : ℕ} (hu : 0 ≤ u)
    (hlo : ((b ^ k : ℕ) : ℚ) ≤ u) (hhi : u < ((b ^ (k + 1) : ℕ) : ℚ)) :
    Nat.log b ⌊u⌋₊ = k := by
  apply Nat.log_eq_of_pow_le_of_lt_pow
  · exact (Nat.le_floor_iff hu).mpr hlo
  · exact (Nat.floor_lt hu).mpr hhi

def smoothRank_floor_of_indices {u : ℚ} {a b : ℕ} (hu : 1 ≤ u)
    (ha : Nat.log 2 ⌊u⌋₊ = a) (hb : Nat.log 3 ⌊u⌋₊ = b) :
    smoothRankBound ⌊u⌋₊ = b + 1 + a / 2 +
      if a % 2 = 1 ∧ ((2 * 3 ^ b : ℕ) : ℚ) ≤ u then 1 else 0 := by
  have hu0 : 0 ≤ u := by linarith
  have hn : ⌊u⌋₊ ≠ 0 := by
    have hh : 1 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
    omega
  unfold smoothRankBound
  rw [if_neg hn, ha, hb]
  simp only [Nat.le_floor_iff hu0]

end Bounty

end SubmissionComponent_WindowLogBounds

/- Component CutoffTable; SHA256 f573fc818b82ce302cb6a099e022c9f4e1ce81c04db88879700fcc8673c0f4ea -/
section SubmissionComponent_CutoffTable
/- Rational interval tables and a checked route from their recursion equations to states. -/

namespace Bounty

structure CutoffPiece where
  lo : ℚ
  hi : ℚ
  parity : ℕ
  slope : ℚ
  intercept : ℚ

def CutoffPiece.value (row : CutoffPiece) (u : ℚ) : ℕ × ℚ :=
  (row.parity, row.slope * u + row.intercept)

def cutoffTableEval : List CutoffPiece → ℚ → ℕ × ℚ
  | [], _ => (0, 0)
  | row :: rows, u => if u < row.hi then row.value u else cutoffTableEval rows u

def cutoffTableSpan : ℚ → ℚ → List CutoffPiece → Prop
  | lo, hi, [] => lo = hi
  | lo, hi, row :: rows =>
      row.lo = lo ∧ row.lo < row.hi ∧ cutoffTableSpan row.hi hi rows

def cutoffTableEval_eq_of_mem {rows : List CutoffPiece} {row : CutoffPiece} {u : ℚ}
    (horder : rows.Pairwise (fun x y => x.hi ≤ y.lo)) (hmem : row ∈ rows)
    (hlo : row.lo ≤ u) (hhi : u < row.hi) :
    cutoffTableEval rows u = row.value u := by
  induction rows with
  | nil => simp at hmem
  | cons first rest ih =>
      obtain ⟨hfirst, hrest⟩ := List.pairwise_cons.mp horder
      rcases List.mem_cons.mp hmem with heq | hmem
      · subst row
        simp [cutoffTableEval, hhi]
      · have hnot : ¬u < first.hi := not_lt_of_ge ((hfirst row hmem).trans hlo)
        rw [cutoffTableEval, if_neg hnot]
        exact ih hrest hmem

def cutoffTableSpan_lower {rows : List CutoffPiece} {lo hi : ℚ}
    (hspan : cutoffTableSpan lo hi rows) {row : CutoffPiece} (hmem : row ∈ rows) :
    lo ≤ row.lo := by
  induction rows generalizing lo with
  | nil => simp at hmem
  | cons first rest ih =>
      obtain ⟨heq, hlt, hrest⟩ := hspan
      rcases List.mem_cons.mp hmem with hr | hmem
      · subst row
        exact heq.ge
      · exact (heq ▸ hlt.le).trans (ih hrest hmem)

def cutoffTableSpan_ordered {rows : List CutoffPiece} {lo hi : ℚ}
    (hspan : cutoffTableSpan lo hi rows) :
    rows.Pairwise (fun x y => x.hi ≤ y.lo) := by
  induction rows generalizing lo with
  | nil => simp
  | cons row rest ih =>
      obtain ⟨_, _, hrest⟩ := hspan
      apply List.pairwise_cons.mpr
      exact ⟨fun _ hmem => cutoffTableSpan_lower hrest hmem, ih hrest⟩

def cutoffState_eq_table {limit : ℚ} (rows : Bool → List CutoffPiece)
    (hsmall : ∀ eps u, u < 1 → cutoffTableEval (rows eps) u = (0, 0))
    (hstep : ∀ eps u, 1 ≤ u → u < limit →
      cutoffCandidate eps u (cutoffTableEval (rows true) (u / 5))
        (cutoffTableEval (rows eps) (u / 7)) = cutoffTableEval (rows eps) u) :
    ∀ eps u, u < limit → cutoffState eps u = cutoffTableEval (rows eps) u := by
  have hall : ∀ m : ℕ, ∀ eps u, ⌊u⌋₊ = m → u < limit →
      cutoffState eps u = cutoffTableEval (rows eps) u := by
    intro m
    induction m using Nat.strong_induction_on with
    | h m ih =>
        intro eps u hm hlim
        by_cases hu : u < 1
        · rw [cutoffState_of_small hu, hsmall eps u hu]
        · have hu1 : 1 ≤ u := le_of_not_gt hu
          have h5lt : ⌊u / 5⌋₊ < m := by
            rw [← hm]
            exact floor_div_lt_floor hu1 (by norm_num : 1 < (5 : ℕ))
          have h7lt : ⌊u / 7⌋₊ < m := by
            rw [← hm]
            exact floor_div_lt_floor hu1 (by norm_num : 1 < (7 : ℕ))
          have h5 := ih _ h5lt true (u / 5) rfl (by linarith : u / 5 < limit)
          have h7 := ih _ h7lt eps (u / 7) rfl (by linarith : u / 7 < limit)
          rw [cutoffState_of_large hu1, h5, h7]
          exact hstep eps u hu1 hlim
  intro eps u hlim
  exact hall ⌊u⌋₊ eps u rfl hlim

def cutoffTrial_eq_of_bounds {u r : ℚ} {k p : ℕ} {c5 c7 : ℕ × ℚ}
    (hbase : 3 * u / 4 ≤ r) (hlevel : (lowerCutoff p k : ℚ) ≤ r)
    (hfive : (if p = c5.1 then 4 else 6) * c5.2 ≤ r)
    (hseven : (if p = c7.1 then 4 else 6) * c7.2 ≤ r)
    (heq : r = 3 * u / 4 ∨ r = (lowerCutoff p k : ℚ) ∨
      r = (if p = c5.1 then 4 else 6) * c5.2 ∨
      r = (if p = c7.1 then 4 else 6) * c7.2) :
    cutoffTrial u k p c5 c7 = r := by
  apply le_antisymm
  · exact max_le (max_le hbase hlevel) (max_le hfive hseven)
  · have hb := cutoffTrial_bounds u k p c5 c7
    rcases heq with heq | heq | heq | heq
    · exact heq ▸ hb.1
    · exact heq ▸ hb.2.1
    · exact heq ▸ hb.2.2.1
    · exact heq ▸ hb.2.2.2

def cutoffCandidate_eq_preferred {eps : Bool} {u : ℚ} {k p : ℕ} {c5 c7 : ℕ × ℚ}
    (hq : quotaValue eps u = k) (hp : Nat.log 2 ⌊u⌋₊ % 2 = p)
    (ha : cutoffAvailable u k p c5 c7) :
    cutoffCandidate eps u c5 c7 = (p, cutoffTrial u k p c5 c7) := by
  simp [cutoffCandidate, hq, hp, ha]

def cutoffCandidate_eq_alternate {eps : Bool} {u : ℚ} {k p : ℕ} {c5 c7 : ℕ × ℚ}
    (hq : quotaValue eps u = k) (hp : Nat.log 2 ⌊u⌋₊ % 2 = p)
    (ha : ¬cutoffAvailable u k p c5 c7) :
    cutoffCandidate eps u c5 c7 = (1 - p, cutoffTrial u k (1 - p) c5 c7) := by
  simp [cutoffCandidate, hq, hp, ha]

end Bounty

end SubmissionComponent_CutoffTable

/- Component BaseTableData; SHA256 8fcfeb97c99481d4991146d5419e8d046b51401696241edc194c6f4608e898d6 -/
section SubmissionComponent_BaseTableData
/- Candidate base-table data, with kernel proofs of ordering and cutoff thresholds. -/


namespace Bounty

def basePieces0 : List CutoffPiece :=
  [⟨0, 1, 0, 0, 0⟩,
   ⟨1, (4 / 3), 0, 0, 1⟩,
   ⟨(4 / 3), 2, 0, (3 / 4), 0⟩,
   ⟨2, (8 / 3), 1, 0, 2⟩,
   ⟨(8 / 3), 4, 1, (3 / 4), 0⟩,
   ⟨4, (16 / 3), 0, 0, 4⟩,
   ⟨(16 / 3), 8, 0, (3 / 4), 0⟩,
   ⟨8, (80 / 9), 1, 0, 8⟩,
   ⟨(80 / 9), 10, 1, (9 / 10), 0⟩,
   ⟨10, (32 / 3), 1, 0, 8⟩,
   ⟨(32 / 3), 16, 1, (3 / 4), 0⟩,
   ⟨16, (0xa0 / 9), 0, 0, 16⟩,
   ⟨(0xa0 / 9), 20, 0, (9 / 10), 0⟩,
   ⟨20, (64 / 3), 0, 0, 16⟩,
   ⟨(64 / 3), 27, 0, (3 / 4), 0⟩,
   ⟨27, 32, 0, 0, 27⟩,
   ⟨32, (0x140 / 9), 1, 0, 32⟩,
   ⟨(0x140 / 9), 40, 1, (9 / 10), 0⟩,
   ⟨40, (0x80 / 3), 1, 0, 32⟩,
   ⟨(0x80 / 3), 54, 1, (3 / 4), 0⟩,
   ⟨54, 64, 1, 0, 54⟩,
   ⟨64, (0x280 / 9), 0, 0, 64⟩,
   ⟨(0x280 / 9), 80, 0, (9 / 10), 0⟩,
   ⟨80, 81, 0, 0, 64⟩,
   ⟨81, 0x6c, 0, 0, 81⟩,
   ⟨0x6c, 0x80, 0, (3 / 4), 0⟩,
   ⟨0x80, 0x87, 1, 0, 0x80⟩,
   ⟨0x87, 0x90, 0, 0, 0x6c⟩,
   ⟨0x90, 0xa0, 0, (3 / 4), 0⟩,
   ⟨0xa0, 0xa2, 1, 0, 0x80⟩,
   ⟨0xa2, 0xd8, 1, 0, 0xa2⟩,
   ⟨0xd8, 0x100, 1, (3 / 4), 0⟩,
   ⟨0x100, (0xa00 / 9), 0, 0, 0x100⟩,
   ⟨(0xa00 / 9), 0x140, 0, (9 / 10), 0⟩,
   ⟨0x140, (0x400 / 3), 0, 0, 0x100⟩,
   ⟨(0x400 / 3), 0x17a, 0, (3 / 4), 0⟩,
   ⟨0x17a, 0x1b0, 0, 0, 0x144⟩,
   ⟨0x1b0, 0x200, 0, (3 / 4), 0⟩,
   ⟨0x200, (0x1400 / 9), 1, 0, 0x200⟩,
   ⟨(0x1400 / 9), 0x280, 1, (9 / 10), 0⟩,
   ⟨0x280, 0x2a3, 1, 0, 0x200⟩,
   ⟨0x2a3, 0x2d0, 1, 0, 0x288⟩,
   ⟨0x2d0, 0x320, 1, (9 / 10), 0⟩,
   ⟨0x320, 0x32a, 1, (3 / 4), 0⟩,
   ⟨0x32a, 0x360, 1, 0, 0x288⟩,
   ⟨0x360, 0x400, 1, (3 / 4), 0⟩,
   ⟨0x400, (0x2800 / 9), 0, 0, 0x400⟩,
   ⟨(0x2800 / 9), 0x500, 0, (9 / 10), 0⟩,
   ⟨0x500, (0x1000 / 3), 0, 0, 0x400⟩,
   ⟨(0x1000 / 3), 0x800, 0, (3 / 4), 0⟩,
   ⟨0x800, (0x5000 / 9), 1, 0, 0x800⟩,
   ⟨(0x5000 / 9), 0xa00, 1, (9 / 10), 0⟩,
   ⟨0xa00, (0x2000 / 3), 1, 0, 0x800⟩,
   ⟨(0x2000 / 3), 0xd2f, 1, (3 / 4), 0⟩,
   ⟨0xd2f, 0xd80, 1, 0, 0xa20⟩,
   ⟨0xd80, 0x1000, 1, (3 / 4), 0⟩,
   ⟨0x1000, (0xa000 / 9), 0, 0, 0x1000⟩,
   ⟨(0xa000 / 9), 0x1400, 0, (9 / 10), 0⟩,
   ⟨0x1400, (0x23000 / 27), 0, 0, 0x1000⟩,
   ⟨(0x23000 / 27), 0x15e0, 0, (27 / 35), 0⟩,
   ⟨0x15e0, 0x19a1, 0, (3 / 4), 0⟩,
   ⟨0x19a1, 0x2000, 0, 0, 0x19a1⟩,
   ⟨0x2000, (0x14000 / 9), 1, 0, 0x2000⟩,
   ⟨(0x14000 / 9), 0x2800, 1, (9 / 10), 0⟩,
   ⟨0x2800, (0x8000 / 3), 1, 0, 0x2000⟩,
   ⟨(0x8000 / 3), 0x3342, 1, (3 / 4), 0⟩,
   ⟨0x3342, 0x4000, 1, 0, 0x3342⟩,
   ⟨0x4000, (0x28000 / 9), 0, 0, 0x4000⟩,
   ⟨(0x28000 / 9), 0x4ce3, 0, (9 / 10), 0⟩,
   ⟨0x4ce3, 0x6684, 0, 0, 0x4ce3⟩,
   ⟨0x6684, 0x8000, 0, (3 / 4), 0⟩,
   ⟨0x8000, 0x8025, 1, 0, 0x8000⟩,
   ⟨0x8025, 0x88b0, 0, 0, 0x6684⟩,
   ⟨0x88b0, 0x99c6, 0, (3 / 4), 0⟩,
   ⟨0x99c6, 0xcd08, 1, 0, 0x99c6⟩,
   ⟨0xcd08, 0x10000, 1, (3 / 4), 0⟩,
   ⟨0x10000, (0xa0000 / 9), 0, 0, 0x10000⟩,
   ⟨(0xa0000 / 9), 0x1338c, 0, (9 / 10), 0⟩,
   ⟨0x1338c, 0x14000, 0, 0, 0x1338c⟩,
   ⟨0x14000, (0x40000 / 3), 0, 0, 0x10000⟩,
   ⟨(0x40000 / 3), 0x166ce, 0, (3 / 4), 0⟩,
   ⟨0x166ce, 0x19a10, 0, 0, 0x1338c⟩,
   ⟨0x19a10, 0x20000, 0, (3 / 4), 0⟩,
   ⟨0x20000, (0x140000 / 9), 1, 0, 0x20000⟩,
   ⟨(0x140000 / 9), 0x28000, 1, (9 / 10), 0⟩,
   ⟨0x28000, 0x280b9, 1, 0, 0x20000⟩,
   ⟨0x280b9, 0x2ab70, 1, 0, 0x26718⟩,
   ⟨0x2ab70, 0x300de, 1, (9 / 10), 0⟩,
   ⟨0x300de, 0x33420, 1, 0, 0x26718⟩,
   ⟨0x33420, 0x40000, 1, (3 / 4), 0⟩,
   ⟨0x40000, (0x280000 / 9), 0, 0, 0x40000⟩,
   ⟨(0x280000 / 9), 0x50000, 0, (9 / 10), 0⟩,
   ⟨0x50000, (0x100000 / 3), 0, 0, 0x40000⟩,
   ⟨(0x100000 / 3), 0x601bc, 0, (3 / 4), 0⟩,
   ⟨0x601bc, 0x64000, 0, 0, 0x4ce30⟩,
   ⟨0x64000, 0x80000, 0, (3 / 4), 0⟩,
   ⟨0x80000, (0x500000 / 9), 1, 0, 0x80000⟩,
   ⟨(0x500000 / 9), 0xa0000, 1, (9 / 10), 0⟩,
   ⟨0xa0000, (0x200000 / 3), 1, 0, 0x80000⟩,
   ⟨(0x200000 / 3), 0xc839d, 1, (3 / 4), 0⟩,
   ⟨0xc839d, 0xcd080, 1, 0, 0x99c60⟩,
   ⟨0xcd080, 0x100000, 1, (3 / 4), 0⟩,
   ⟨0x100000, (0xa00000 / 9), 0, 0, 0x100000⟩,
   ⟨(0xa00000 / 9), 0x140000, 0, (9 / 10), 0⟩,
   ⟨0x140000, (0x2300000 / 27), 0, 0, 0x100000⟩,
   ⟨(0x2300000 / 27), 0x150612, 0, (27 / 35), 0⟩,
   ⟨0x150612, (0x400000 / 3), 0, 0, 0x100000⟩,
   ⟨(0x400000 / 3), 0x1853d3, 0, (3 / 4), 0⟩,
   ⟨0x1853d3, 0x1921ee, 0, 0, 0x1853d3⟩]

def basePieces1 : List CutoffPiece :=
  [⟨0, 1, 0, 0, 0⟩,
   ⟨1, (4 / 3), 0, 0, 1⟩,
   ⟨(4 / 3), 2, 0, (3 / 4), 0⟩,
   ⟨2, (8 / 3), 1, 0, 2⟩,
   ⟨(8 / 3), 4, 1, (3 / 4), 0⟩,
   ⟨4, (16 / 3), 0, 0, 4⟩,
   ⟨(16 / 3), 8, 0, (3 / 4), 0⟩,
   ⟨8, (80 / 9), 1, 0, 8⟩,
   ⟨(80 / 9), 10, 1, (9 / 10), 0⟩,
   ⟨10, (32 / 3), 1, 0, 8⟩,
   ⟨(32 / 3), 16, 1, (3 / 4), 0⟩,
   ⟨16, (0xa0 / 9), 0, 0, 16⟩,
   ⟨(0xa0 / 9), 20, 0, (9 / 10), 0⟩,
   ⟨20, (64 / 3), 0, 0, 16⟩,
   ⟨(64 / 3), 27, 0, (3 / 4), 0⟩,
   ⟨27, 32, 0, 0, 27⟩,
   ⟨32, (0x140 / 9), 1, 0, 32⟩,
   ⟨(0x140 / 9), 40, 1, (9 / 10), 0⟩,
   ⟨40, (0x80 / 3), 1, 0, 32⟩,
   ⟨(0x80 / 3), 64, 1, (3 / 4), 0⟩,
   ⟨64, (0x280 / 9), 0, 0, 64⟩,
   ⟨(0x280 / 9), 80, 0, (9 / 10), 0⟩,
   ⟨80, 81, 0, 0, 64⟩,
   ⟨81, 0x6c, 0, 0, 81⟩,
   ⟨0x6c, 0x80, 0, (3 / 4), 0⟩,
   ⟨0x80, 0x87, 1, 0, 0x80⟩,
   ⟨0x87, 0x90, 0, 0, 0x6c⟩,
   ⟨0x90, 0xa0, 0, (3 / 4), 0⟩,
   ⟨0xa0, 0xa2, 1, 0, 0x80⟩,
   ⟨0xa2, 0xd8, 1, 0, 0xa2⟩,
   ⟨0xd8, 0x100, 1, (3 / 4), 0⟩,
   ⟨0x100, (0xa00 / 9), 0, 0, 0x100⟩,
   ⟨(0xa00 / 9), 0x140, 0, (9 / 10), 0⟩,
   ⟨0x140, (0x400 / 3), 0, 0, 0x100⟩,
   ⟨(0x400 / 3), 0x195, 0, (3 / 4), 0⟩,
   ⟨0x195, 0x1b0, 0, 0, 0x144⟩,
   ⟨0x1b0, 0x200, 0, (3 / 4), 0⟩,
   ⟨0x200, (0x1400 / 9), 1, 0, 0x200⟩,
   ⟨(0x1400 / 9), 0x280, 1, (9 / 10), 0⟩,
   ⟨0x280, 0x2a3, 1, 0, 0x200⟩,
   ⟨0x2a3, 0x2d0, 1, 0, 0x288⟩,
   ⟨0x2d0, 0x320, 1, (9 / 10), 0⟩,
   ⟨0x320, 0x32a, 1, (3 / 4), 0⟩,
   ⟨0x32a, 0x360, 1, 0, 0x288⟩,
   ⟨0x360, 0x400, 1, (3 / 4), 0⟩,
   ⟨0x400, (0x2800 / 9), 0, 0, 0x400⟩,
   ⟨(0x2800 / 9), 0x500, 0, (9 / 10), 0⟩,
   ⟨0x500, (0x1000 / 3), 0, 0, 0x400⟩,
   ⟨(0x1000 / 3), 0x800, 0, (3 / 4), 0⟩,
   ⟨0x800, (0x5000 / 9), 1, 0, 0x800⟩,
   ⟨(0x5000 / 9), 0xa00, 1, (9 / 10), 0⟩,
   ⟨0xa00, (0x2000 / 3), 1, 0, 0x800⟩,
   ⟨(0x2000 / 3), 0xd2f, 1, (3 / 4), 0⟩,
   ⟨0xd2f, 0xd80, 1, 0, 0xa20⟩,
   ⟨0xd80, 0x1000, 1, (3 / 4), 0⟩,
   ⟨0x1000, (0xa000 / 9), 0, 0, 0x1000⟩,
   ⟨(0xa000 / 9), 0x1400, 0, (9 / 10), 0⟩,
   ⟨0x1400, (0x23000 / 27), 0, 0, 0x1000⟩,
   ⟨(0x23000 / 27), 0x15e0, 0, (27 / 35), 0⟩,
   ⟨0x15e0, 0x19a1, 0, (3 / 4), 0⟩,
   ⟨0x19a1, 0x2000, 0, 0, 0x19a1⟩,
   ⟨0x2000, (0x14000 / 9), 1, 0, 0x2000⟩,
   ⟨(0x14000 / 9), 0x2800, 1, (9 / 10), 0⟩,
   ⟨0x2800, (0x8000 / 3), 1, 0, 0x2000⟩,
   ⟨(0x8000 / 3), (0x1338c / 5), 1, (3 / 4), 0⟩,
   ⟨(0x1338c / 5), 0x4000, 1, 0, 0x3342⟩,
   ⟨0x4000, (0x28000 / 9), 0, 0, 0x4000⟩,
   ⟨(0x28000 / 9), 0x4ce3, 0, (9 / 10), 0⟩,
   ⟨0x4ce3, 0x6684, 0, 0, 0x4ce3⟩,
   ⟨0x6684, 0x8000, 0, (3 / 4), 0⟩,
   ⟨0x8000, 0x8025, 1, 0, 0x8000⟩,
   ⟨0x8025, 0x88b0, 0, 0, 0x6684⟩,
   ⟨0x88b0, 0x99c6, 0, (3 / 4), 0⟩,
   ⟨0x99c6, 0xcd08, 1, 0, 0x99c6⟩,
   ⟨0xcd08, 0x10000, 1, (3 / 4), 0⟩,
   ⟨0x10000, (0xa0000 / 9), 0, 0, 0x10000⟩,
   ⟨(0xa0000 / 9), 0x1338c, 0, (9 / 10), 0⟩,
   ⟨0x1338c, 0x14000, 0, 0, 0x1338c⟩,
   ⟨0x14000, (0x40000 / 3), 0, 0, 0x10000⟩,
   ⟨(0x40000 / 3), 0x1806f, 0, (3 / 4), 0⟩,
   ⟨0x1806f, 0x19a10, 0, 0, 0x1338c⟩,
   ⟨0x19a10, 0x20000, 0, (3 / 4), 0⟩,
   ⟨0x20000, (0x140000 / 9), 1, 0, 0x20000⟩,
   ⟨(0x140000 / 9), 0x28000, 1, (9 / 10), 0⟩,
   ⟨0x28000, 0x280b9, 1, 0, 0x20000⟩,
   ⟨0x280b9, 0x2ab70, 1, 0, 0x26718⟩,
   ⟨0x2ab70, 0x300de, 1, (9 / 10), 0⟩,
   ⟨0x300de, 0x33420, 1, 0, 0x26718⟩,
   ⟨0x33420, 0x40000, 1, (3 / 4), 0⟩,
   ⟨0x40000, (0x280000 / 9), 0, 0, 0x40000⟩,
   ⟨(0x280000 / 9), 0x50000, 0, (9 / 10), 0⟩,
   ⟨0x50000, (0x100000 / 3), 0, 0, 0x40000⟩,
   ⟨(0x100000 / 3), 0x601bc, 0, (3 / 4), 0⟩,
   ⟨0x601bc, 0x64000, 0, 0, 0x4ce30⟩,
   ⟨0x64000, 0x80000, 0, (3 / 4), 0⟩,
   ⟨0x80000, (0x500000 / 9), 1, 0, 0x80000⟩,
   ⟨(0x500000 / 9), 0xa0000, 1, (9 / 10), 0⟩,
   ⟨0xa0000, (0x200000 / 3), 1, 0, 0x80000⟩,
   ⟨(0x200000 / 3), 0xc839d, 1, (3 / 4), 0⟩,
   ⟨0xc839d, 0xcd080, 1, 0, 0x99c60⟩,
   ⟨0xcd080, 0x100000, 1, (3 / 4), 0⟩,
   ⟨0x100000, (0xa00000 / 9), 0, 0, 0x100000⟩,
   ⟨(0xa00000 / 9), 0x140000, 0, (9 / 10), 0⟩,
   ⟨0x140000, (0x2300000 / 27), 0, 0, 0x100000⟩,
   ⟨(0x2300000 / 27), 0x150612, 0, (27 / 35), 0⟩,
   ⟨0x150612, (0x400000 / 3), 0, 0, 0x100000⟩,
   ⟨(0x400000 / 3), 0x1853d3, 0, (3 / 4), 0⟩,
   ⟨0x1853d3, 0x1921ee, 0, 0, 0x1853d3⟩]

def basePieces (eps : Bool) : List CutoffPiece :=
  if eps then basePieces1 else basePieces0

def basePieces0_span : cutoffTableSpan 0 0x1921ee basePieces0 := by
  unfold basePieces0
  repeat' apply And.intro
  all_goals norm_num [cutoffTableSpan]

def basePieces0_ordered : basePieces0.Pairwise (fun x y => x.hi ≤ y.lo) :=
  cutoffTableSpan_ordered basePieces0_span

def baseTable_eval_0_0 {u : ℚ} (hlo : 0 ≤ u) (hhi : u < 1) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0, 1, 0, 0, 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_1 {u : ℚ} (hlo : 1 ≤ u) (hhi : u < (4 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 1) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨1, (4 / 3), 0, 0, 1⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 1) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_2 {u : ℚ} (hlo : (4 / 3) ≤ u) (hhi : u < 2) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(4 / 3), 2, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 2) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_3 {u : ℚ} (hlo : 2 ≤ u) (hhi : u < (8 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 2) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨2, (8 / 3), 1, 0, 2⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 3) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_4 {u : ℚ} (hlo : (8 / 3) ≤ u) (hhi : u < 4) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(8 / 3), 4, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 4) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_5 {u : ℚ} (hlo : 4 ≤ u) (hhi : u < (16 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 4) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨4, (16 / 3), 0, 0, 4⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 5) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_6 {u : ℚ} (hlo : (16 / 3) ≤ u) (hhi : u < 8) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(16 / 3), 8, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 6) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_7 {u : ℚ} (hlo : 8 ≤ u) (hhi : u < (80 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 8) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨8, (80 / 9), 1, 0, 8⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 7) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_8 {u : ℚ} (hlo : (80 / 9) ≤ u) (hhi : u < 10) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(80 / 9), 10, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 8) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_9 {u : ℚ} (hlo : 10 ≤ u) (hhi : u < (32 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 8) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨10, (32 / 3), 1, 0, 8⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 9) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_10 {u : ℚ} (hlo : (32 / 3) ≤ u) (hhi : u < 16) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(32 / 3), 16, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 10) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_11 {u : ℚ} (hlo : 16 ≤ u) (hhi : u < (0xa0 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 16) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨16, (0xa0 / 9), 0, 0, 16⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 11) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_12 {u : ℚ} (hlo : (0xa0 / 9) ≤ u) (hhi : u < 20) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0xa0 / 9), 20, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 12) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_13 {u : ℚ} (hlo : 20 ≤ u) (hhi : u < (64 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 16) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨20, (64 / 3), 0, 0, 16⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 13) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_14 {u : ℚ} (hlo : (64 / 3) ≤ u) (hhi : u < 27) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(64 / 3), 27, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 14) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_15 {u : ℚ} (hlo : 27 ≤ u) (hhi : u < 32) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 27) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨27, 32, 0, 0, 27⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 15) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_16 {u : ℚ} (hlo : 32 ≤ u) (hhi : u < (0x140 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 32) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨32, (0x140 / 9), 1, 0, 32⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 16) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_17 {u : ℚ} (hlo : (0x140 / 9) ≤ u) (hhi : u < 40) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x140 / 9), 40, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 17) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_18 {u : ℚ} (hlo : 40 ≤ u) (hhi : u < (0x80 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 32) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨40, (0x80 / 3), 1, 0, 32⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 18) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_19 {u : ℚ} (hlo : (0x80 / 3) ≤ u) (hhi : u < 54) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x80 / 3), 54, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 19) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_20 {u : ℚ} (hlo : 54 ≤ u) (hhi : u < 64) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 54) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨54, 64, 1, 0, 54⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 20) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_21 {u : ℚ} (hlo : 64 ≤ u) (hhi : u < (0x280 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 64) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨64, (0x280 / 9), 0, 0, 64⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 21) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_22 {u : ℚ} (hlo : (0x280 / 9) ≤ u) (hhi : u < 80) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x280 / 9), 80, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 22) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_23 {u : ℚ} (hlo : 80 ≤ u) (hhi : u < 81) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 64) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨80, 81, 0, 0, 64⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 23) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_24 {u : ℚ} (hlo : 81 ≤ u) (hhi : u < 0x6c) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 81) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨81, 0x6c, 0, 0, 81⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 24) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_25 {u : ℚ} (hlo : 0x6c ≤ u) (hhi : u < 0x80) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x6c, 0x80, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 25) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_26 {u : ℚ} (hlo : 0x80 ≤ u) (hhi : u < 0x87) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x80) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x80, 0x87, 1, 0, 0x80⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 26) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_27 {u : ℚ} (hlo : 0x87 ≤ u) (hhi : u < 0x90) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x6c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x87, 0x90, 0, 0, 0x6c⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 27) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_28 {u : ℚ} (hlo : 0x90 ≤ u) (hhi : u < 0xa0) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x90, 0xa0, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 28) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_29 {u : ℚ} (hlo : 0xa0 ≤ u) (hhi : u < 0xa2) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x80) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xa0, 0xa2, 1, 0, 0x80⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 29) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_30 {u : ℚ} (hlo : 0xa2 ≤ u) (hhi : u < 0xd8) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0xa2) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xa2, 0xd8, 1, 0, 0xa2⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 30) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_31 {u : ℚ} (hlo : 0xd8 ≤ u) (hhi : u < 0x100) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xd8, 0x100, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 31) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_32 {u : ℚ} (hlo : 0x100 ≤ u) (hhi : u < (0xa00 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x100) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x100, (0xa00 / 9), 0, 0, 0x100⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 32) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_33 {u : ℚ} (hlo : (0xa00 / 9) ≤ u) (hhi : u < 0x140) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0xa00 / 9), 0x140, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 33) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_34 {u : ℚ} (hlo : 0x140 ≤ u) (hhi : u < (0x400 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x100) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x140, (0x400 / 3), 0, 0, 0x100⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 34) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_35 {u : ℚ} (hlo : (0x400 / 3) ≤ u) (hhi : u < 0x17a) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x400 / 3), 0x17a, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 35) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_36 {u : ℚ} (hlo : 0x17a ≤ u) (hhi : u < 0x1b0) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x144) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x17a, 0x1b0, 0, 0, 0x144⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 36) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_37 {u : ℚ} (hlo : 0x1b0 ≤ u) (hhi : u < 0x200) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x1b0, 0x200, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 37) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_38 {u : ℚ} (hlo : 0x200 ≤ u) (hhi : u < (0x1400 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x200) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x200, (0x1400 / 9), 1, 0, 0x200⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 38) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_39 {u : ℚ} (hlo : (0x1400 / 9) ≤ u) (hhi : u < 0x280) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x1400 / 9), 0x280, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 39) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_40 {u : ℚ} (hlo : 0x280 ≤ u) (hhi : u < 0x2a3) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x200) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x280, 0x2a3, 1, 0, 0x200⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 40) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_41 {u : ℚ} (hlo : 0x2a3 ≤ u) (hhi : u < 0x2d0) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x288) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x2a3, 0x2d0, 1, 0, 0x288⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 41) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_42 {u : ℚ} (hlo : 0x2d0 ≤ u) (hhi : u < 0x320) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x2d0, 0x320, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 42) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_43 {u : ℚ} (hlo : 0x320 ≤ u) (hhi : u < 0x32a) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x320, 0x32a, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 43) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_44 {u : ℚ} (hlo : 0x32a ≤ u) (hhi : u < 0x360) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x288) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x32a, 0x360, 1, 0, 0x288⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 44) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_45 {u : ℚ} (hlo : 0x360 ≤ u) (hhi : u < 0x400) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x360, 0x400, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 45) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_46 {u : ℚ} (hlo : 0x400 ≤ u) (hhi : u < (0x2800 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x400) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x400, (0x2800 / 9), 0, 0, 0x400⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 46) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_47 {u : ℚ} (hlo : (0x2800 / 9) ≤ u) (hhi : u < 0x500) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x2800 / 9), 0x500, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 47) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_48 {u : ℚ} (hlo : 0x500 ≤ u) (hhi : u < (0x1000 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x400) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x500, (0x1000 / 3), 0, 0, 0x400⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 48) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_49 {u : ℚ} (hlo : (0x1000 / 3) ≤ u) (hhi : u < 0x800) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x1000 / 3), 0x800, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 49) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_50 {u : ℚ} (hlo : 0x800 ≤ u) (hhi : u < (0x5000 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x800) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x800, (0x5000 / 9), 1, 0, 0x800⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 50) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_51 {u : ℚ} (hlo : (0x5000 / 9) ≤ u) (hhi : u < 0xa00) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x5000 / 9), 0xa00, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 51) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_52 {u : ℚ} (hlo : 0xa00 ≤ u) (hhi : u < (0x2000 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x800) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xa00, (0x2000 / 3), 1, 0, 0x800⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 52) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_53 {u : ℚ} (hlo : (0x2000 / 3) ≤ u) (hhi : u < 0xd2f) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x2000 / 3), 0xd2f, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 53) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_54 {u : ℚ} (hlo : 0xd2f ≤ u) (hhi : u < 0xd80) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0xa20) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xd2f, 0xd80, 1, 0, 0xa20⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 54) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_55 {u : ℚ} (hlo : 0xd80 ≤ u) (hhi : u < 0x1000) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xd80, 0x1000, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 55) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_56 {u : ℚ} (hlo : 0x1000 ≤ u) (hhi : u < (0xa000 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x1000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x1000, (0xa000 / 9), 0, 0, 0x1000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 56) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_57 {u : ℚ} (hlo : (0xa000 / 9) ≤ u) (hhi : u < 0x1400) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0xa000 / 9), 0x1400, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 57) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_58 {u : ℚ} (hlo : 0x1400 ≤ u) (hhi : u < (0x23000 / 27)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x1000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x1400, (0x23000 / 27), 0, 0, 0x1000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 58) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_59 {u : ℚ} (hlo : (0x23000 / 27) ≤ u) (hhi : u < 0x15e0) :
    cutoffTableEval (basePieces false) u = (0, (27 / 35) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x23000 / 27), 0x15e0, 0, (27 / 35), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 59) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_60 {u : ℚ} (hlo : 0x15e0 ≤ u) (hhi : u < 0x19a1) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x15e0, 0x19a1, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 60) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_61 {u : ℚ} (hlo : 0x19a1 ≤ u) (hhi : u < 0x2000) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x19a1) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x19a1, 0x2000, 0, 0, 0x19a1⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 61) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_62 {u : ℚ} (hlo : 0x2000 ≤ u) (hhi : u < (0x14000 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x2000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x2000, (0x14000 / 9), 1, 0, 0x2000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 62) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_63 {u : ℚ} (hlo : (0x14000 / 9) ≤ u) (hhi : u < 0x2800) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x14000 / 9), 0x2800, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 63) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_64 {u : ℚ} (hlo : 0x2800 ≤ u) (hhi : u < (0x8000 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x2000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x2800, (0x8000 / 3), 1, 0, 0x2000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 64) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_65 {u : ℚ} (hlo : (0x8000 / 3) ≤ u) (hhi : u < 0x3342) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x8000 / 3), 0x3342, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 65) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_66 {u : ℚ} (hlo : 0x3342 ≤ u) (hhi : u < 0x4000) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x3342) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x3342, 0x4000, 1, 0, 0x3342⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 66) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_67 {u : ℚ} (hlo : 0x4000 ≤ u) (hhi : u < (0x28000 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x4000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x4000, (0x28000 / 9), 0, 0, 0x4000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 67) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_68 {u : ℚ} (hlo : (0x28000 / 9) ≤ u) (hhi : u < 0x4ce3) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x28000 / 9), 0x4ce3, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 68) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_69 {u : ℚ} (hlo : 0x4ce3 ≤ u) (hhi : u < 0x6684) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x4ce3) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x4ce3, 0x6684, 0, 0, 0x4ce3⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 69) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_70 {u : ℚ} (hlo : 0x6684 ≤ u) (hhi : u < 0x8000) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x6684, 0x8000, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 70) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_71 {u : ℚ} (hlo : 0x8000 ≤ u) (hhi : u < 0x8025) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x8000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x8000, 0x8025, 1, 0, 0x8000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 71) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_72 {u : ℚ} (hlo : 0x8025 ≤ u) (hhi : u < 0x88b0) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x6684) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x8025, 0x88b0, 0, 0, 0x6684⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 72) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_73 {u : ℚ} (hlo : 0x88b0 ≤ u) (hhi : u < 0x99c6) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x88b0, 0x99c6, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 73) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_74 {u : ℚ} (hlo : 0x99c6 ≤ u) (hhi : u < 0xcd08) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x99c6) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x99c6, 0xcd08, 1, 0, 0x99c6⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 74) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_75 {u : ℚ} (hlo : 0xcd08 ≤ u) (hhi : u < 0x10000) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xcd08, 0x10000, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 75) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_76 {u : ℚ} (hlo : 0x10000 ≤ u) (hhi : u < (0xa0000 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x10000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x10000, (0xa0000 / 9), 0, 0, 0x10000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 76) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_77 {u : ℚ} (hlo : (0xa0000 / 9) ≤ u) (hhi : u < 0x1338c) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0xa0000 / 9), 0x1338c, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 77) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_78 {u : ℚ} (hlo : 0x1338c ≤ u) (hhi : u < 0x14000) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x1338c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x1338c, 0x14000, 0, 0, 0x1338c⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 78) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_79 {u : ℚ} (hlo : 0x14000 ≤ u) (hhi : u < (0x40000 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x10000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x14000, (0x40000 / 3), 0, 0, 0x10000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 79) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_80 {u : ℚ} (hlo : (0x40000 / 3) ≤ u) (hhi : u < 0x166ce) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x40000 / 3), 0x166ce, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 80) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_81 {u : ℚ} (hlo : 0x166ce ≤ u) (hhi : u < 0x19a10) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x1338c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x166ce, 0x19a10, 0, 0, 0x1338c⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 81) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_82 {u : ℚ} (hlo : 0x19a10 ≤ u) (hhi : u < 0x20000) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x19a10, 0x20000, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 82) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_83 {u : ℚ} (hlo : 0x20000 ≤ u) (hhi : u < (0x140000 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x20000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x20000, (0x140000 / 9), 1, 0, 0x20000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 83) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_84 {u : ℚ} (hlo : (0x140000 / 9) ≤ u) (hhi : u < 0x28000) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x140000 / 9), 0x28000, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 84) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_85 {u : ℚ} (hlo : 0x28000 ≤ u) (hhi : u < 0x280b9) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x20000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x28000, 0x280b9, 1, 0, 0x20000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 85) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_86 {u : ℚ} (hlo : 0x280b9 ≤ u) (hhi : u < 0x2ab70) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x26718) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x280b9, 0x2ab70, 1, 0, 0x26718⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 86) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_87 {u : ℚ} (hlo : 0x2ab70 ≤ u) (hhi : u < 0x300de) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x2ab70, 0x300de, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 87) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_88 {u : ℚ} (hlo : 0x300de ≤ u) (hhi : u < 0x33420) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x26718) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x300de, 0x33420, 1, 0, 0x26718⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 88) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_89 {u : ℚ} (hlo : 0x33420 ≤ u) (hhi : u < 0x40000) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x33420, 0x40000, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 89) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_90 {u : ℚ} (hlo : 0x40000 ≤ u) (hhi : u < (0x280000 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x40000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x40000, (0x280000 / 9), 0, 0, 0x40000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 90) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_91 {u : ℚ} (hlo : (0x280000 / 9) ≤ u) (hhi : u < 0x50000) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x280000 / 9), 0x50000, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 91) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_92 {u : ℚ} (hlo : 0x50000 ≤ u) (hhi : u < (0x100000 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x40000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x50000, (0x100000 / 3), 0, 0, 0x40000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 92) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_93 {u : ℚ} (hlo : (0x100000 / 3) ≤ u) (hhi : u < 0x601bc) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x100000 / 3), 0x601bc, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 93) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_94 {u : ℚ} (hlo : 0x601bc ≤ u) (hhi : u < 0x64000) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x4ce30) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x601bc, 0x64000, 0, 0, 0x4ce30⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 94) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_95 {u : ℚ} (hlo : 0x64000 ≤ u) (hhi : u < 0x80000) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x64000, 0x80000, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 95) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_96 {u : ℚ} (hlo : 0x80000 ≤ u) (hhi : u < (0x500000 / 9)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x80000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x80000, (0x500000 / 9), 1, 0, 0x80000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 96) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_97 {u : ℚ} (hlo : (0x500000 / 9) ≤ u) (hhi : u < 0xa0000) :
    cutoffTableEval (basePieces false) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x500000 / 9), 0xa0000, 1, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 97) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_98 {u : ℚ} (hlo : 0xa0000 ≤ u) (hhi : u < (0x200000 / 3)) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x80000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xa0000, (0x200000 / 3), 1, 0, 0x80000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 98) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_99 {u : ℚ} (hlo : (0x200000 / 3) ≤ u) (hhi : u < 0xc839d) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x200000 / 3), 0xc839d, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 99) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_100 {u : ℚ} (hlo : 0xc839d ≤ u) (hhi : u < 0xcd080) :
    cutoffTableEval (basePieces false) u = (1, 0 * (u) + 0x99c60) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xc839d, 0xcd080, 1, 0, 0x99c60⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x64) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_101 {u : ℚ} (hlo : 0xcd080 ≤ u) (hhi : u < 0x100000) :
    cutoffTableEval (basePieces false) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0xcd080, 0x100000, 1, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x65) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_102 {u : ℚ} (hlo : 0x100000 ≤ u) (hhi : u < (0xa00000 / 9)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x100000, (0xa00000 / 9), 0, 0, 0x100000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x66) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_103 {u : ℚ} (hlo : (0xa00000 / 9) ≤ u) (hhi : u < 0x140000) :
    cutoffTableEval (basePieces false) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0xa00000 / 9), 0x140000, 0, (9 / 10), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x67) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_104 {u : ℚ} (hlo : 0x140000 ≤ u) (hhi : u < (0x2300000 / 27)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x140000, (0x2300000 / 27), 0, 0, 0x100000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x68) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_105 {u : ℚ} (hlo : (0x2300000 / 27) ≤ u) (hhi : u < 0x150612) :
    cutoffTableEval (basePieces false) u = (0, (27 / 35) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x2300000 / 27), 0x150612, 0, (27 / 35), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x69) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_106 {u : ℚ} (hlo : 0x150612 ≤ u) (hhi : u < (0x400000 / 3)) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x150612, (0x400000 / 3), 0, 0, 0x100000⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x6a) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_107 {u : ℚ} (hlo : (0x400000 / 3) ≤ u) (hhi : u < 0x1853d3) :
    cutoffTableEval (basePieces false) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨(0x400000 / 3), 0x1853d3, 0, (3 / 4), 0⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x6b) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_0_108 {u : ℚ} (hlo : 0x1853d3 ≤ u) (hhi : u < 0x1921ee) :
    cutoffTableEval (basePieces false) u = (0, 0 * (u) + 0x1853d3) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces0) (row := ⟨0x1853d3, 0x1921ee, 0, 0, 0x1853d3⟩)
    basePieces0_ordered (List.mem_of_getElem? (i := 0x6c) (by rfl)) hlo hhi
  exact hh

def basePieces1_span : cutoffTableSpan 0 0x1921ee basePieces1 := by
  unfold basePieces1
  repeat' apply And.intro
  all_goals norm_num [cutoffTableSpan]

def basePieces1_ordered : basePieces1.Pairwise (fun x y => x.hi ≤ y.lo) :=
  cutoffTableSpan_ordered basePieces1_span

def baseTable_eval_1_0 {u : ℚ} (hlo : 0 ≤ u) (hhi : u < 1) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0, 1, 0, 0, 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_1 {u : ℚ} (hlo : 1 ≤ u) (hhi : u < (4 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 1) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨1, (4 / 3), 0, 0, 1⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 1) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_2 {u : ℚ} (hlo : (4 / 3) ≤ u) (hhi : u < 2) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(4 / 3), 2, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 2) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_3 {u : ℚ} (hlo : 2 ≤ u) (hhi : u < (8 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 2) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨2, (8 / 3), 1, 0, 2⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 3) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_4 {u : ℚ} (hlo : (8 / 3) ≤ u) (hhi : u < 4) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(8 / 3), 4, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 4) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_5 {u : ℚ} (hlo : 4 ≤ u) (hhi : u < (16 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 4) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨4, (16 / 3), 0, 0, 4⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 5) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_6 {u : ℚ} (hlo : (16 / 3) ≤ u) (hhi : u < 8) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(16 / 3), 8, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 6) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_7 {u : ℚ} (hlo : 8 ≤ u) (hhi : u < (80 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 8) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨8, (80 / 9), 1, 0, 8⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 7) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_8 {u : ℚ} (hlo : (80 / 9) ≤ u) (hhi : u < 10) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(80 / 9), 10, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 8) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_9 {u : ℚ} (hlo : 10 ≤ u) (hhi : u < (32 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 8) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨10, (32 / 3), 1, 0, 8⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 9) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_10 {u : ℚ} (hlo : (32 / 3) ≤ u) (hhi : u < 16) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(32 / 3), 16, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 10) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_11 {u : ℚ} (hlo : 16 ≤ u) (hhi : u < (0xa0 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 16) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨16, (0xa0 / 9), 0, 0, 16⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 11) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_12 {u : ℚ} (hlo : (0xa0 / 9) ≤ u) (hhi : u < 20) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0xa0 / 9), 20, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 12) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_13 {u : ℚ} (hlo : 20 ≤ u) (hhi : u < (64 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 16) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨20, (64 / 3), 0, 0, 16⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 13) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_14 {u : ℚ} (hlo : (64 / 3) ≤ u) (hhi : u < 27) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(64 / 3), 27, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 14) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_15 {u : ℚ} (hlo : 27 ≤ u) (hhi : u < 32) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 27) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨27, 32, 0, 0, 27⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 15) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_16 {u : ℚ} (hlo : 32 ≤ u) (hhi : u < (0x140 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 32) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨32, (0x140 / 9), 1, 0, 32⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 16) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_17 {u : ℚ} (hlo : (0x140 / 9) ≤ u) (hhi : u < 40) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x140 / 9), 40, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 17) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_18 {u : ℚ} (hlo : 40 ≤ u) (hhi : u < (0x80 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 32) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨40, (0x80 / 3), 1, 0, 32⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 18) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_19 {u : ℚ} (hlo : (0x80 / 3) ≤ u) (hhi : u < 64) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x80 / 3), 64, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 19) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_20 {u : ℚ} (hlo : 64 ≤ u) (hhi : u < (0x280 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 64) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨64, (0x280 / 9), 0, 0, 64⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 20) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_21 {u : ℚ} (hlo : (0x280 / 9) ≤ u) (hhi : u < 80) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x280 / 9), 80, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 21) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_22 {u : ℚ} (hlo : 80 ≤ u) (hhi : u < 81) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 64) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨80, 81, 0, 0, 64⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 22) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_23 {u : ℚ} (hlo : 81 ≤ u) (hhi : u < 0x6c) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 81) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨81, 0x6c, 0, 0, 81⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 23) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_24 {u : ℚ} (hlo : 0x6c ≤ u) (hhi : u < 0x80) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x6c, 0x80, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 24) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_25 {u : ℚ} (hlo : 0x80 ≤ u) (hhi : u < 0x87) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x80) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x80, 0x87, 1, 0, 0x80⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 25) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_26 {u : ℚ} (hlo : 0x87 ≤ u) (hhi : u < 0x90) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x6c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x87, 0x90, 0, 0, 0x6c⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 26) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_27 {u : ℚ} (hlo : 0x90 ≤ u) (hhi : u < 0xa0) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x90, 0xa0, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 27) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_28 {u : ℚ} (hlo : 0xa0 ≤ u) (hhi : u < 0xa2) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x80) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xa0, 0xa2, 1, 0, 0x80⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 28) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_29 {u : ℚ} (hlo : 0xa2 ≤ u) (hhi : u < 0xd8) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0xa2) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xa2, 0xd8, 1, 0, 0xa2⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 29) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_30 {u : ℚ} (hlo : 0xd8 ≤ u) (hhi : u < 0x100) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xd8, 0x100, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 30) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_31 {u : ℚ} (hlo : 0x100 ≤ u) (hhi : u < (0xa00 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x100) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x100, (0xa00 / 9), 0, 0, 0x100⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 31) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_32 {u : ℚ} (hlo : (0xa00 / 9) ≤ u) (hhi : u < 0x140) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0xa00 / 9), 0x140, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 32) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_33 {u : ℚ} (hlo : 0x140 ≤ u) (hhi : u < (0x400 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x100) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x140, (0x400 / 3), 0, 0, 0x100⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 33) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_34 {u : ℚ} (hlo : (0x400 / 3) ≤ u) (hhi : u < 0x195) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x400 / 3), 0x195, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 34) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_35 {u : ℚ} (hlo : 0x195 ≤ u) (hhi : u < 0x1b0) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x144) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x195, 0x1b0, 0, 0, 0x144⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 35) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_36 {u : ℚ} (hlo : 0x1b0 ≤ u) (hhi : u < 0x200) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1b0, 0x200, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 36) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_37 {u : ℚ} (hlo : 0x200 ≤ u) (hhi : u < (0x1400 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x200) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x200, (0x1400 / 9), 1, 0, 0x200⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 37) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_38 {u : ℚ} (hlo : (0x1400 / 9) ≤ u) (hhi : u < 0x280) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x1400 / 9), 0x280, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 38) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_39 {u : ℚ} (hlo : 0x280 ≤ u) (hhi : u < 0x2a3) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x200) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x280, 0x2a3, 1, 0, 0x200⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 39) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_40 {u : ℚ} (hlo : 0x2a3 ≤ u) (hhi : u < 0x2d0) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x288) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x2a3, 0x2d0, 1, 0, 0x288⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 40) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_41 {u : ℚ} (hlo : 0x2d0 ≤ u) (hhi : u < 0x320) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x2d0, 0x320, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 41) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_42 {u : ℚ} (hlo : 0x320 ≤ u) (hhi : u < 0x32a) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x320, 0x32a, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 42) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_43 {u : ℚ} (hlo : 0x32a ≤ u) (hhi : u < 0x360) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x288) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x32a, 0x360, 1, 0, 0x288⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 43) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_44 {u : ℚ} (hlo : 0x360 ≤ u) (hhi : u < 0x400) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x360, 0x400, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 44) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_45 {u : ℚ} (hlo : 0x400 ≤ u) (hhi : u < (0x2800 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x400) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x400, (0x2800 / 9), 0, 0, 0x400⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 45) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_46 {u : ℚ} (hlo : (0x2800 / 9) ≤ u) (hhi : u < 0x500) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x2800 / 9), 0x500, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 46) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_47 {u : ℚ} (hlo : 0x500 ≤ u) (hhi : u < (0x1000 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x400) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x500, (0x1000 / 3), 0, 0, 0x400⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 47) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_48 {u : ℚ} (hlo : (0x1000 / 3) ≤ u) (hhi : u < 0x800) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x1000 / 3), 0x800, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 48) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_49 {u : ℚ} (hlo : 0x800 ≤ u) (hhi : u < (0x5000 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x800) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x800, (0x5000 / 9), 1, 0, 0x800⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 49) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_50 {u : ℚ} (hlo : (0x5000 / 9) ≤ u) (hhi : u < 0xa00) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x5000 / 9), 0xa00, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 50) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_51 {u : ℚ} (hlo : 0xa00 ≤ u) (hhi : u < (0x2000 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x800) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xa00, (0x2000 / 3), 1, 0, 0x800⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 51) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_52 {u : ℚ} (hlo : (0x2000 / 3) ≤ u) (hhi : u < 0xd2f) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x2000 / 3), 0xd2f, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 52) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_53 {u : ℚ} (hlo : 0xd2f ≤ u) (hhi : u < 0xd80) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0xa20) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xd2f, 0xd80, 1, 0, 0xa20⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 53) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_54 {u : ℚ} (hlo : 0xd80 ≤ u) (hhi : u < 0x1000) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xd80, 0x1000, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 54) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_55 {u : ℚ} (hlo : 0x1000 ≤ u) (hhi : u < (0xa000 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x1000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1000, (0xa000 / 9), 0, 0, 0x1000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 55) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_56 {u : ℚ} (hlo : (0xa000 / 9) ≤ u) (hhi : u < 0x1400) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0xa000 / 9), 0x1400, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 56) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_57 {u : ℚ} (hlo : 0x1400 ≤ u) (hhi : u < (0x23000 / 27)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x1000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1400, (0x23000 / 27), 0, 0, 0x1000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 57) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_58 {u : ℚ} (hlo : (0x23000 / 27) ≤ u) (hhi : u < 0x15e0) :
    cutoffTableEval (basePieces true) u = (0, (27 / 35) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x23000 / 27), 0x15e0, 0, (27 / 35), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 58) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_59 {u : ℚ} (hlo : 0x15e0 ≤ u) (hhi : u < 0x19a1) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x15e0, 0x19a1, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 59) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_60 {u : ℚ} (hlo : 0x19a1 ≤ u) (hhi : u < 0x2000) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x19a1) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x19a1, 0x2000, 0, 0, 0x19a1⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 60) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_61 {u : ℚ} (hlo : 0x2000 ≤ u) (hhi : u < (0x14000 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x2000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x2000, (0x14000 / 9), 1, 0, 0x2000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 61) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_62 {u : ℚ} (hlo : (0x14000 / 9) ≤ u) (hhi : u < 0x2800) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x14000 / 9), 0x2800, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 62) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_63 {u : ℚ} (hlo : 0x2800 ≤ u) (hhi : u < (0x8000 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x2000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x2800, (0x8000 / 3), 1, 0, 0x2000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 63) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_64 {u : ℚ} (hlo : (0x8000 / 3) ≤ u) (hhi : u < (0x1338c / 5)) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x8000 / 3), (0x1338c / 5), 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 64) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_65 {u : ℚ} (hlo : (0x1338c / 5) ≤ u) (hhi : u < 0x4000) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x3342) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x1338c / 5), 0x4000, 1, 0, 0x3342⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 65) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_66 {u : ℚ} (hlo : 0x4000 ≤ u) (hhi : u < (0x28000 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x4000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x4000, (0x28000 / 9), 0, 0, 0x4000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 66) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_67 {u : ℚ} (hlo : (0x28000 / 9) ≤ u) (hhi : u < 0x4ce3) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x28000 / 9), 0x4ce3, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 67) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_68 {u : ℚ} (hlo : 0x4ce3 ≤ u) (hhi : u < 0x6684) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x4ce3) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x4ce3, 0x6684, 0, 0, 0x4ce3⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 68) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_69 {u : ℚ} (hlo : 0x6684 ≤ u) (hhi : u < 0x8000) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x6684, 0x8000, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 69) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_70 {u : ℚ} (hlo : 0x8000 ≤ u) (hhi : u < 0x8025) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x8000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x8000, 0x8025, 1, 0, 0x8000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 70) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_71 {u : ℚ} (hlo : 0x8025 ≤ u) (hhi : u < 0x88b0) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x6684) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x8025, 0x88b0, 0, 0, 0x6684⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 71) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_72 {u : ℚ} (hlo : 0x88b0 ≤ u) (hhi : u < 0x99c6) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x88b0, 0x99c6, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 72) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_73 {u : ℚ} (hlo : 0x99c6 ≤ u) (hhi : u < 0xcd08) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x99c6) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x99c6, 0xcd08, 1, 0, 0x99c6⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 73) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_74 {u : ℚ} (hlo : 0xcd08 ≤ u) (hhi : u < 0x10000) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xcd08, 0x10000, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 74) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_75 {u : ℚ} (hlo : 0x10000 ≤ u) (hhi : u < (0xa0000 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x10000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x10000, (0xa0000 / 9), 0, 0, 0x10000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 75) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_76 {u : ℚ} (hlo : (0xa0000 / 9) ≤ u) (hhi : u < 0x1338c) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0xa0000 / 9), 0x1338c, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 76) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_77 {u : ℚ} (hlo : 0x1338c ≤ u) (hhi : u < 0x14000) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x1338c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1338c, 0x14000, 0, 0, 0x1338c⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 77) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_78 {u : ℚ} (hlo : 0x14000 ≤ u) (hhi : u < (0x40000 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x10000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x14000, (0x40000 / 3), 0, 0, 0x10000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 78) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_79 {u : ℚ} (hlo : (0x40000 / 3) ≤ u) (hhi : u < 0x1806f) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x40000 / 3), 0x1806f, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 79) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_80 {u : ℚ} (hlo : 0x1806f ≤ u) (hhi : u < 0x19a10) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x1338c) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1806f, 0x19a10, 0, 0, 0x1338c⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 80) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_81 {u : ℚ} (hlo : 0x19a10 ≤ u) (hhi : u < 0x20000) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x19a10, 0x20000, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 81) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_82 {u : ℚ} (hlo : 0x20000 ≤ u) (hhi : u < (0x140000 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x20000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x20000, (0x140000 / 9), 1, 0, 0x20000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 82) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_83 {u : ℚ} (hlo : (0x140000 / 9) ≤ u) (hhi : u < 0x28000) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x140000 / 9), 0x28000, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 83) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_84 {u : ℚ} (hlo : 0x28000 ≤ u) (hhi : u < 0x280b9) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x20000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x28000, 0x280b9, 1, 0, 0x20000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 84) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_85 {u : ℚ} (hlo : 0x280b9 ≤ u) (hhi : u < 0x2ab70) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x26718) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x280b9, 0x2ab70, 1, 0, 0x26718⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 85) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_86 {u : ℚ} (hlo : 0x2ab70 ≤ u) (hhi : u < 0x300de) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x2ab70, 0x300de, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 86) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_87 {u : ℚ} (hlo : 0x300de ≤ u) (hhi : u < 0x33420) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x26718) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x300de, 0x33420, 1, 0, 0x26718⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 87) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_88 {u : ℚ} (hlo : 0x33420 ≤ u) (hhi : u < 0x40000) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x33420, 0x40000, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 88) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_89 {u : ℚ} (hlo : 0x40000 ≤ u) (hhi : u < (0x280000 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x40000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x40000, (0x280000 / 9), 0, 0, 0x40000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 89) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_90 {u : ℚ} (hlo : (0x280000 / 9) ≤ u) (hhi : u < 0x50000) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x280000 / 9), 0x50000, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 90) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_91 {u : ℚ} (hlo : 0x50000 ≤ u) (hhi : u < (0x100000 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x40000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x50000, (0x100000 / 3), 0, 0, 0x40000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 91) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_92 {u : ℚ} (hlo : (0x100000 / 3) ≤ u) (hhi : u < 0x601bc) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x100000 / 3), 0x601bc, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 92) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_93 {u : ℚ} (hlo : 0x601bc ≤ u) (hhi : u < 0x64000) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x4ce30) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x601bc, 0x64000, 0, 0, 0x4ce30⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 93) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_94 {u : ℚ} (hlo : 0x64000 ≤ u) (hhi : u < 0x80000) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x64000, 0x80000, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 94) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_95 {u : ℚ} (hlo : 0x80000 ≤ u) (hhi : u < (0x500000 / 9)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x80000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x80000, (0x500000 / 9), 1, 0, 0x80000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 95) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_96 {u : ℚ} (hlo : (0x500000 / 9) ≤ u) (hhi : u < 0xa0000) :
    cutoffTableEval (basePieces true) u = (1, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x500000 / 9), 0xa0000, 1, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 96) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_97 {u : ℚ} (hlo : 0xa0000 ≤ u) (hhi : u < (0x200000 / 3)) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x80000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xa0000, (0x200000 / 3), 1, 0, 0x80000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 97) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_98 {u : ℚ} (hlo : (0x200000 / 3) ≤ u) (hhi : u < 0xc839d) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x200000 / 3), 0xc839d, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 98) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_99 {u : ℚ} (hlo : 0xc839d ≤ u) (hhi : u < 0xcd080) :
    cutoffTableEval (basePieces true) u = (1, 0 * (u) + 0x99c60) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xc839d, 0xcd080, 1, 0, 0x99c60⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 99) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_100 {u : ℚ} (hlo : 0xcd080 ≤ u) (hhi : u < 0x100000) :
    cutoffTableEval (basePieces true) u = (1, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0xcd080, 0x100000, 1, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x64) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_101 {u : ℚ} (hlo : 0x100000 ≤ u) (hhi : u < (0xa00000 / 9)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x100000, (0xa00000 / 9), 0, 0, 0x100000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x65) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_102 {u : ℚ} (hlo : (0xa00000 / 9) ≤ u) (hhi : u < 0x140000) :
    cutoffTableEval (basePieces true) u = (0, (9 / 10) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0xa00000 / 9), 0x140000, 0, (9 / 10), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x66) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_103 {u : ℚ} (hlo : 0x140000 ≤ u) (hhi : u < (0x2300000 / 27)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x140000, (0x2300000 / 27), 0, 0, 0x100000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x67) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_104 {u : ℚ} (hlo : (0x2300000 / 27) ≤ u) (hhi : u < 0x150612) :
    cutoffTableEval (basePieces true) u = (0, (27 / 35) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x2300000 / 27), 0x150612, 0, (27 / 35), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x68) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_105 {u : ℚ} (hlo : 0x150612 ≤ u) (hhi : u < (0x400000 / 3)) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x100000) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x150612, (0x400000 / 3), 0, 0, 0x100000⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x69) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_106 {u : ℚ} (hlo : (0x400000 / 3) ≤ u) (hhi : u < 0x1853d3) :
    cutoffTableEval (basePieces true) u = (0, (3 / 4) * (u) + 0) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨(0x400000 / 3), 0x1853d3, 0, (3 / 4), 0⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x6a) (by rfl)) hlo hhi
  exact hh

def baseTable_eval_1_107 {u : ℚ} (hlo : 0x1853d3 ≤ u) (hhi : u < 0x1921ee) :
    cutoffTableEval (basePieces true) u = (0, 0 * (u) + 0x1853d3) := by
  have hh := cutoffTableEval_eq_of_mem (rows := basePieces1) (row := ⟨0x1853d3, 0x1921ee, 0, 0, 0x1853d3⟩)
    basePieces1_ordered (List.mem_of_getElem? (i := 0x6b) (by rfl)) hlo hhi
  exact hh

def baseTable_small (eps : Bool) (u : ℚ) (hu : u < 1) :
    cutoffTableEval (basePieces eps) u = (0, 0) := by
  cases eps <;> simp [basePieces, basePieces0, basePieces1, cutoffTableEval, CutoffPiece.value, hu]

def baseLower_0_1 : lowerCutoff 0 1 = 1 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_2 : lowerCutoff 0 2 = 3 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_3 : lowerCutoff 0 3 = 4 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_4 : lowerCutoff 0 4 = 9 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_5 : lowerCutoff 0 5 = 16 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_6 : lowerCutoff 0 6 = 27 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_7 : lowerCutoff 0 7 = 64 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_8 : lowerCutoff 0 8 = 81 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_9 : lowerCutoff 0 9 = 0xf3 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_10 : lowerCutoff 0 10 = 0x100 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_11 : lowerCutoff 0 11 = 0x2d9 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_12 : lowerCutoff 0 12 = 0x400 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_13 : lowerCutoff 0 13 = 0x88b :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_14 : lowerCutoff 0 14 = 0x1000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_15 : lowerCutoff 0 15 = 0x19a1 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_16 : lowerCutoff 0 16 = 0x4000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_17 : lowerCutoff 0 17 = 0x4ce3 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_18 : lowerCutoff 0 18 = 0xe6a9 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_19 : lowerCutoff 0 19 = 0x10000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_20 : lowerCutoff 0 20 = 0x2b3fb :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_21 : lowerCutoff 0 21 = 0x40000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_22 : lowerCutoff 0 22 = 0x81bf1 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_23 : lowerCutoff 0 23 = 0x100000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_24 : lowerCutoff 0 24 = 0x1853d3 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_0_25 : lowerCutoff 0 25 = 0x400000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_2 : lowerCutoff 1 2 = 2 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_3 : lowerCutoff 1 3 = 6 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_4 : lowerCutoff 1 4 = 8 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_5 : lowerCutoff 1 5 = 18 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_6 : lowerCutoff 1 6 = 32 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_7 : lowerCutoff 1 7 = 54 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_8 : lowerCutoff 1 8 = 0x80 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_9 : lowerCutoff 1 9 = 0xa2 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_10 : lowerCutoff 1 10 = 0x1e6 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_11 : lowerCutoff 1 11 = 0x200 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_12 : lowerCutoff 1 12 = 0x5b2 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_13 : lowerCutoff 1 13 = 0x800 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_14 : lowerCutoff 1 14 = 0x1116 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_15 : lowerCutoff 1 15 = 0x2000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_16 : lowerCutoff 1 16 = 0x3342 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_17 : lowerCutoff 1 17 = 0x8000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_18 : lowerCutoff 1 18 = 0x99c6 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_19 : lowerCutoff 1 19 = 0x1cd52 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_20 : lowerCutoff 1 20 = 0x20000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_21 : lowerCutoff 1 21 = 0x567f6 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_22 : lowerCutoff 1 22 = 0x80000 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseLower_1_23 : lowerCutoff 1 23 = 0x1037e2 :=
  lowerCutoff_eq_of_step (by decide) (by decide) (by decide)

def baseStepValid (eps : Bool) (u : ℚ) : Prop :=
  cutoffCandidate eps u (cutoffTableEval (basePieces true) (u / 5))
      (cutoffTableEval (basePieces eps) (u / 7)) = cutoffTableEval (basePieces eps) u ∧
  cutoffAvailable u (quotaValue eps u) (cutoffTableEval (basePieces eps) u).1
    (cutoffTableEval (basePieces true) (u / 5)) (cutoffTableEval (basePieces eps) (u / 7))

end Bounty

end SubmissionComponent_BaseTableData

/- Component BaseIntervalArithmetic; SHA256 7553e19db62313e1f2bc843865d3a34593cca755ddb9daca4960e95c6a26bd48 -/
section SubmissionComponent_BaseIntervalArithmetic

/- Finite endpoint certificates for the repeated arithmetic in the base intervals. -/

namespace Bounty

abbrev intervalAffineLE (lo hi a b c d : ℚ) : Prop :=
  a * lo + b ≤ c * lo + d ∧ a * hi + b ≤ c * hi + d

abbrev intervalAffineLT (lo hi a b c d : ℚ) : Prop :=
  a * lo + b < c * lo + d ∧ a * hi + b ≤ c * hi + d

def intervalAffineLE_sound {lo hi a b c d u : ℚ}
    (h : intervalAffineLE lo hi a b c d) (hlo : lo ≤ u) (hhi : u ≤ hi) :
    a * u + b ≤ c * u + d := by
  rcases h with ⟨hl, hh⟩
  by_cases hac : a ≤ c
  · have := mul_nonpos_of_nonpos_of_nonneg (sub_nonpos.mpr hac) (sub_nonneg.mpr hlo)
    nlinarith
  · have := mul_nonneg (sub_nonneg.mpr (le_of_not_ge hac)) (sub_nonneg.mpr hhi)
    nlinarith

def intervalAffineLT_sound {lo hi a b c d u : ℚ}
    (h : intervalAffineLT lo hi a b c d) (hlo : lo ≤ u) (hhi : u < hi) :
    a * u + b < c * u + d := by
  rcases h with ⟨hl, hh⟩
  by_cases hac : a ≤ c
  · have := mul_nonpos_of_nonpos_of_nonneg (sub_nonpos.mpr hac) (sub_nonneg.mpr hlo)
    nlinarith
  · have := mul_pos (sub_pos.mpr (lt_of_not_ge hac)) (sub_pos.mpr hhi)
    nlinarith

abbrev compactRankConditions (lo hi : ℚ) (a b rank : ℕ) : Prop :=
  1 ≤ lo ∧ (2 ^ a : ℕ) ≤ lo ∧ hi ≤ (2 ^ (a + 1) : ℕ) ∧
  (3 ^ b : ℕ) ≤ lo ∧ hi ≤ (3 ^ (b + 1) : ℕ) ∧
  ((a % 2 = 1 ∧ (2 * 3 ^ b : ℕ) ≤ lo ∧ rank = b + 1 + a / 2 + 1) ∨
   ((a % 2 ≠ 1 ∨ hi ≤ (2 * 3 ^ b : ℕ)) ∧ rank = b + 1 + a / 2))

def compactRankConditions_sound {lo hi u : ℚ} {a b rank : ℕ}
    (h : compactRankConditions lo hi a b rank) (hlo : lo ≤ u) (hhi : u < hi) :
    Nat.log 2 ⌊u⌋₊ = a ∧ smoothRankBound ⌊u⌋₊ = rank := by
  rcases h with ⟨h1, h2l, h2h, h3l, h3h, hx⟩
  have hu : 1 ≤ u := h1.trans hlo
  have hu0 : 0 ≤ u := by linarith
  have ha := log_floor_of_bounds hu0 (h2l.trans hlo) (hhi.trans_le h2h)
  have hb := log_floor_of_bounds hu0 (h3l.trans hlo) (hhi.trans_le h3h)
  refine ⟨ha, ?_⟩
  rw [smoothRank_floor_of_indices hu ha hb]
  rcases hx with ⟨hodd, hcut, hr⟩ | ⟨hcut, hr⟩
  · rw [if_pos ⟨hodd, hcut.trans hlo⟩, hr]
  · rw [if_neg (by
      intro hc
      rcases hcut with heven | hcut
      · exact heven hc.1
      · exact (not_le_of_gt (hhi.trans_le hcut)) hc.2), hr, Nat.add_zero]

abbrev compactBadConditions (lo hi : ℚ) (j b low high : ℕ) (bad : Bool) : Prop :=
  (low : ℚ) ≤ 5 * lo ∧ 5 * hi ≤ high ∧
  4 ^ j ≤ low ∧ high ≤ 4 ^ (j + 1) ∧ 3 ^ b ≤ low ∧ high ≤ 3 ^ (b + 1) ∧
  if bad then
    4 * (high - 1) < 5 * 4 ^ j ∧ 10 * 3 ^ (b - 2) ≤ low ∧ high ≤ 12 * 3 ^ (b - 2)
  else
    5 * 4 ^ j ≤ 4 * low ∨ high ≤ 10 * 3 ^ (b - 2) ∨ 12 * 3 ^ (b - 2) ≤ low

def compactBadConditions_sound {lo hi u : ℚ} {j b low high : ℕ} {bad : Bool}
    (h : compactBadConditions lo hi j b low high bad) (hu : 0 ≤ u)
    (hlo : lo ≤ u) (hhi : u < hi) : badWindow ⌊5 * u⌋₊ ↔ bad = true := by
  rcases h with ⟨hlo5, hhi5, h4lo, h4hi, h3lo, h3hi, hb⟩
  have hu5 : 0 ≤ 5 * u := by positivity
  have hnlo : low ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff hu5).mpr (by linarith)
  have hnhi : ⌊5 * u⌋₊ < high := (Nat.floor_lt hu5).mpr (by linarith)
  have hj : Nat.log 4 ⌊5 * u⌋₊ = j :=
    Nat.log_eq_of_pow_le_of_lt_pow (h4lo.trans hnlo) (hnhi.trans_le h4hi)
  have hc : Nat.log 3 ⌊5 * u⌋₊ = b :=
    Nat.log_eq_of_pow_le_of_lt_pow (h3lo.trans hnlo) (hnhi.trans_le h3hi)
  rw [badWindow_iff_canonical, hj, hc]
  cases bad with
  | false =>
    simp only [Bool.false_eq_true, ↓reduceIte, iff_false] at hb ⊢
    intro hbad
    rcases hbad with ⟨_, hn4, hn3l, hn3h⟩
    rcases hb with hb | hb | hb <;> omega
  | true =>
    simp only [↓reduceIte] at hb
    simp only [iff_true]
    omega

abbrev compactQuotaConditions (eps : Bool) (lo hi : ℚ) (a b rank quota j c low high : ℕ)
    (bad : Bool) : Prop :=
  compactRankConditions lo hi a b rank ∧
  if eps then compactBadConditions lo hi j c low high bad ∧
    quota = rank - if bad then 1 else 0
  else quota = rank

def compactQuotaConditions_sound {eps : Bool} {lo hi u : ℚ}
    {a b rank quota j c low high : ℕ} {bad : Bool}
    (h : compactQuotaConditions eps lo hi a b rank quota j c low high bad)
    (hlo : lo ≤ u) (hhi : u < hi) :
    Nat.log 2 ⌊u⌋₊ = a ∧ quotaValue eps u = quota := by
  obtain ⟨ha, hrank⟩ := compactRankConditions_sound h.1 hlo hhi
  refine ⟨ha, ?_⟩
  have hu : 0 ≤ u := by have := h.1.1; linarith
  cases eps with
  | false =>
    have hq : quota = rank := h.2
    simp [quotaValue, hrank, hq]
  | true =>
    have hb := compactBadConditions_sound h.2.1 hu hlo hhi
    have hq : quota = rank - if bad then 1 else 0 := h.2.2
    simp only [quotaValue, hrank, true_and, hb, ← hq]


end Bounty

end SubmissionComponent_BaseIntervalArithmetic

/- Component BaseIntervalCutoff; SHA256 e7c7ee03ca5ad20713a0fbdb69658ee2d84715448053f98d30d7c59f9d3dde41 -/
section SubmissionComponent_BaseIntervalCutoff

/- A single ordinary proof turns finite affine endpoint checks into a valid base interval. -/

namespace Bounty

structure CompactQuotaData where
  logTwo : ℕ
  logThree : ℕ
  rank : ℕ
  quota : ℕ
  logFourFive : ℕ
  logThreeFive : ℕ
  lowFive : ℕ
  highFive : ℕ
  bad : Bool

abbrev compactQuotaDataConditions (eps : Bool) (lo hi : ℚ) (d : CompactQuotaData) : Prop :=
  compactQuotaConditions eps lo hi d.logTwo d.logThree d.rank d.quota
    d.logFourFive d.logThreeFive d.lowFive d.highFive d.bad

abbrev compactTrialConditions (lo hi : ℚ) (p p5 p7 level next : ℕ)
    (s t s5 t5 s7 t7 : ℚ) : Prop :=
  intervalAffineLE lo hi (3 / 4) 0 s t ∧
  intervalAffineLE lo hi 0 level s t ∧
  intervalAffineLE lo hi ((if p = p5 then 4 else 6) * s5 / 5)
    ((if p = p5 then 4 else 6) * t5) s t ∧
  intervalAffineLE lo hi ((if p = p7 then 4 else 6) * s7 / 7)
    ((if p = p7 then 4 else 6) * t7) s t ∧
  ((s = 3 / 4 ∧ t = 0) ∨ (s = 0 ∧ t = level) ∨
    (s = (if p = p5 then 4 else 6) * s5 / 5 ∧ t = (if p = p5 then 4 else 6) * t5) ∨
    (s = (if p = p7 then 4 else 6) * s7 / 7 ∧ t = (if p = p7 then 4 else 6) * t7)) ∧
  intervalAffineLE lo hi s t 1 0 ∧ intervalAffineLT lo hi s t 0 next

def compactTrialConditions_sound {lo hi u s t s5 t5 s7 t7 : ℚ}
    {p p5 p7 k level next : ℕ}
    (hlo : lo ≤ u) (hhi : u < hi)
    (hlevel : lowerCutoff p k = level) (hnext : lowerCutoff p (k + 1) = next)
    (h : compactTrialConditions lo hi p p5 p7 level next s t s5 t5 s7 t7) :
    cutoffTrial u k p (p5, s5 * (u / 5) + t5) (p7, s7 * (u / 7) + t7) = s * u + t ∧
    cutoffAvailable u k p (p5, s5 * (u / 5) + t5) (p7, s7 * (u / 7) + t7) := by
  rcases h with ⟨hbase, hlev, hfive, hseven, heq, hself, hupper⟩
  have ht : cutoffTrial u k p (p5, s5 * (u / 5) + t5)
      (p7, s7 * (u / 7) + t7) = s * u + t := by
    apply cutoffTrial_eq_of_bounds
    · have := intervalAffineLE_sound hbase hlo hhi.le
      linarith
    · rw [hlevel]
      simpa only [zero_mul, zero_add] using intervalAffineLE_sound hlev hlo hhi.le
    · have := intervalAffineLE_sound hfive hlo hhi.le
      dsimp at this ⊢
      convert this using 1 <;> ring
    · have := intervalAffineLE_sound hseven hlo hhi.le
      dsimp at this ⊢
      convert this using 1 <;> ring
    · rcases heq with ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩
      · exact Or.inl (by ring)
      · exact Or.inr (Or.inl (by rw [hlevel]; ring))
      · exact Or.inr (Or.inr (Or.inl (by dsimp; ring)))
      · exact Or.inr (Or.inr (Or.inr (by dsimp; ring)))
  refine ⟨ht, ?_⟩
  unfold cutoffAvailable
  rw [ht, hnext]
  constructor
  · simpa only [one_mul, add_zero] using intervalAffineLE_sound hself hlo hhi.le
  · simpa only [zero_mul, zero_add] using intervalAffineLT_sound hupper hlo hhi

def compactBaseInterval_preferred (d : CompactQuotaData)
    {eps : Bool} {lo hi u s t s5 t5 s7 t7 : ℚ} {p p5 p7 level next : ℕ}
    (hlo : lo ≤ u) (hhi : u < hi)
    (hp : cutoffTableEval (basePieces eps) u = (p, s * u + t))
    (h5 : cutoffTableEval (basePieces true) (u / 5) = (p5, s5 * (u / 5) + t5))
    (h7 : cutoffTableEval (basePieces eps) (u / 7) = (p7, s7 * (u / 7) + t7))
    (hlevel : lowerCutoff p d.quota = level)
    (hnext : lowerCutoff p (d.quota + 1) = next)
    (hquota : compactQuotaDataConditions eps lo hi d)
    (hpar : d.logTwo % 2 = p)
    (htrial : compactTrialConditions lo hi p p5 p7 level next s t s5 t5 s7 t7) :
    baseStepValid eps u := by
  obtain ⟨hlog, hq⟩ := compactQuotaConditions_sound hquota hlo hhi
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = p := by rw [hlog]; exact hpar
  obtain ⟨ht, hav⟩ := compactTrialConditions_sound hlo hhi hlevel hnext htrial
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_preferred hq hpreferred hav, ht]
  · simpa only [hq] using hav


end Bounty

end SubmissionComponent_BaseIntervalCutoff

/- Component PolicyBaseIntervalsCompact; SHA256 a8bddfd75ebc14e9afb6194b944e9d20e96dabd19ded50b8bffa8fcd91896d6e -/
section SubmissionComponent_PolicyBaseIntervalsCompact

namespace Bounty

def baseIvlLo {L lo u : ℚ} (h : lo ≤ L) (hu : L ≤ u) : lo ≤ u := le_trans h hu

def baseIvlHi {H hi u : ℚ} (h : H ≤ hi) (hu : u < H) : u < hi := lt_of_lt_of_le hu h

def baseIvlLo5 {L lo u : ℚ} (h : lo * 5 ≤ L) (hu : L ≤ u) : lo ≤ u / 5 :=
  (le_div_iff₀ (by norm_num)).2 (le_trans h hu)

def baseIvlHi5 {H hi u : ℚ} (h : H ≤ hi * 5) (hu : u < H) : u / 5 < hi :=
  (div_lt_iff₀ (by norm_num)).2 (lt_of_lt_of_le hu h)

def baseIvlLo7 {L lo u : ℚ} (h : lo * 7 ≤ L) (hu : L ≤ u) : lo ≤ u / 7 :=
  (le_div_iff₀ (by norm_num)).2 (le_trans h hu)

def baseIvlHi7 {H hi u : ℚ} (h : H ≤ hi * 7) (hu : u < H) : u / 7 < hi :=
  (div_lt_iff₀ (by norm_num)).2 (lt_of_lt_of_le hu h)

def baseInterval_0_0 {u : ℚ} (hlo : 1 ≤ u) (hhi : u < (4 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_1 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_0_1 {u : ℚ} (hlo : (4 / 3) ≤ u) (hhi : u < (9 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_2 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_0_2 {u : ℚ} (hlo : (9 / 5) ≤ u) (hhi : u < 2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_2 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_0_3 {u : ℚ} (hlo : 2 ≤ u) (hhi : u < (12 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_3 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_0_4 {u : ℚ} (hlo : (12 / 5) ≤ u) (hhi : u < (8 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_3 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_0_5 {u : ℚ} (hlo : (8 / 3) ≤ u) (hhi : u < 3) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_0_6 {u : ℚ} (hlo : 3 ≤ u) (hhi : u < (16 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 1, 2, 2, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_0_7 {u : ℚ} (hlo : (16 / 5) ≤ u) (hhi : u < 4) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 1, 2, 2, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_0_8 {u : ℚ} (hlo : 4 ≤ u) (hhi : u < 5) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_5 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_9 {u : ℚ} (hlo : 5 ≤ u) (hhi : u < (16 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_5 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_10 {u : ℚ} (hlo : (16 / 3) ≤ u) (hhi : u < (27 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_11 {u : ℚ} (hlo : (27 / 5) ≤ u) (hhi : u < 6) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_12 {u : ℚ} (hlo : 6 ≤ u) (hhi : u < (20 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_13 {u : ℚ} (hlo : (20 / 3) ≤ u) (hhi : u < 7) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_14 {u : ℚ} (hlo : 7 ≤ u) (hhi : u < (36 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_15 {u : ℚ} (hlo : (36 / 5) ≤ u) (hhi : u < 8) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_0_16 {u : ℚ} (hlo : 8 ≤ u) (hhi : u < (80 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_7 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 1, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_17 {u : ℚ} (hlo : (80 / 9) ≤ u) (hhi : u < 9) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 1, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_18 {u : ℚ} (hlo : 9 ≤ u) (hhi : u < (28 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_19 {u : ℚ} (hlo : (28 / 3) ≤ u) (hhi : u < 10) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_20 {u : ℚ} (hlo : 10 ≤ u) (hhi : u < (32 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_9 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_21 {u : ℚ} (hlo : (32 / 3) ≤ u) (hhi : u < (64 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_22 {u : ℚ} (hlo : (64 / 5) ≤ u) (hhi : u < (40 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_23 {u : ℚ} (hlo : (40 / 3) ≤ u) (hhi : u < 14) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_24 {u : ℚ} (hlo : 14 ≤ u) (hhi : u < 16) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_0_25 {u : ℚ} (hlo : 16 ≤ u) (hhi : u < (81 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_11 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_26 {u : ℚ} (hlo : (81 / 5) ≤ u) (hhi : u < (0xa0 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_11 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_27 {u : ℚ} (hlo : (0xa0 / 9) ≤ u) (hhi : u < 18) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_28 {u : ℚ} (hlo : 18 ≤ u) (hhi : u < (56 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_29 {u : ℚ} (hlo : (56 / 3) ≤ u) (hhi : u < 20) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_30 {u : ℚ} (hlo : 20 ≤ u) (hhi : u < (64 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_13 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_31 {u : ℚ} (hlo : (64 / 3) ≤ u) (hhi : u < (0x6c / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_32 {u : ℚ} (hlo : (0x6c / 5) ≤ u) (hhi : u < (80 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_33 {u : ℚ} (hlo : (80 / 3) ≤ u) (hhi : u < 27) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_0_34 {u : ℚ} (hlo : 27 ≤ u) (hhi : u < 28) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_15 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_6 baseLower_0_7
  all_goals decide +kernel


def baseInterval_0_35 {u : ℚ} (hlo : 28 ≤ u) (hhi : u < 32) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_15 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_6 baseLower_0_7
  all_goals decide +kernel


def baseInterval_0_36 {u : ℚ} (hlo : 32 ≤ u) (hhi : u < (0x140 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_16 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_37 {u : ℚ} (hlo : (0x140 / 9) ≤ u) (hhi : u < (0x70 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_17 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_38 {u : ℚ} (hlo : (0x70 / 3) ≤ u) (hhi : u < 40) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_17 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_39 {u : ℚ} (hlo : 40 ≤ u) (hhi : u < (0x80 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_18 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_7 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_40 {u : ℚ} (hlo : (0x80 / 3) ≤ u) (hhi : u < (0x190 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_7 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_41 {u : ℚ} (hlo : (0x190 / 9) ≤ u) (hhi : u < (0xf3 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_8 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_42 {u : ℚ} (hlo : (0xf3 / 5) ≤ u) (hhi : u < 50) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_8 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_43 {u : ℚ} (hlo : 50 ≤ u) (hhi : u < (0x100 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_9 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_44 {u : ℚ} (hlo : (0x100 / 5) ≤ u) (hhi : u < (0xa0 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_9 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_45 {u : ℚ} (hlo : (0xa0 / 3) ≤ u) (hhi : u < 54) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_0_46 {u : ℚ} (hlo : 54 ≤ u) (hhi : u < 56) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_7 baseLower_1_8
  all_goals decide +kernel


def baseInterval_0_47 {u : ℚ} (hlo : 56 ≤ u) (hhi : u < (0x230 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_7 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_7 baseLower_1_8
  all_goals decide +kernel


def baseInterval_0_48 {u : ℚ} (hlo : (0x230 / 9) ≤ u) (hhi : u < 64) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_7 baseLower_1_8
  all_goals decide +kernel


def baseInterval_0_49 {u : ℚ} (hlo : 64 ≤ u) (hhi : u < (0x144 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_21 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_50 {u : ℚ} (hlo : (0x144 / 5) ≤ u) (hhi : u < 70) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_21 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_51 {u : ℚ} (hlo : 70 ≤ u) (hhi : u < (0x280 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_21 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_9 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_52 {u : ℚ} (hlo : (0x280 / 9) ≤ u) (hhi : u < (0xe0 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_22 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_9 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_53 {u : ℚ} (hlo : (0xe0 / 3) ≤ u) (hhi : u < 80) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_22 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_54 {u : ℚ} (hlo : 80 ≤ u) (hhi : u < 81) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_23 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_11 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_0_55 {u : ℚ} (hlo : 81 ≤ u) (hhi : u < (0x320 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_11 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_56 {u : ℚ} (hlo : (0x320 / 9) ≤ u) (hhi : u < 0x64) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_12 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_57 {u : ℚ} (hlo : 0x64 ≤ u) (hhi : u < (0x140 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_13 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_58 {u : ℚ} (hlo : (0x140 / 3) ≤ u) (hhi : u < 0x6c) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_59 {u : ℚ} (hlo : 0x6c ≤ u) (hhi : u < 0x70) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_25 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_60 {u : ℚ} (hlo : 0x70 ≤ u) (hhi : u < (0x460 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_25 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_11 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_61 {u : ℚ} (hlo : (0x460 / 9) ≤ u) (hhi : u < 0x80) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_25 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_0_62 {u : ℚ} (hlo : 0x80 ≤ u) (hhi : u < 0x87) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_26 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_8 baseLower_1_9
  all_goals decide +kernel


def baseInterval_0_63 {u : ℚ} (hlo : 0x87 ≤ u) (hhi : u < 0x8c) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_27 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 8 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) = 0 * u + 0x6c := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_64 {u : ℚ} (hlo : 0x8c ≤ u) (hhi : u < 0x90) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_27 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 8 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = 0 * u + 0x6c := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_65 {u : ℚ} (hlo : 0x90 ≤ u) (hhi : u < (0x2d9 / 5)) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_28 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 8 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_66 {u : ℚ} (hlo : (0x2d9 / 5) ≤ u) (hhi : u < (0x1c0 / 3)) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_28 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 8 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_67 {u : ℚ} (hlo : (0x1c0 / 3) ≤ u) (hhi : u < 0xa0) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_28 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 8 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_68 {u : ℚ} (hlo : 0xa0 ≤ u) (hhi : u < 0xa2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_16 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 8, 8, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_8 baseLower_1_9
  all_goals decide +kernel


def baseInterval_0_69 {u : ℚ} (hlo : 0xa2 ≤ u) (hhi : u < (0x640 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_16 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_70 {u : ℚ} (hlo : (0x640 / 9) ≤ u) (hhi : u < 0xbd) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_71 {u : ℚ} (hlo : 0xbd ≤ u) (hhi : u < (0x3cc / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_72 {u : ℚ} (hlo : (0x3cc / 5) ≤ u) (hhi : u < 0xc8) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_73 {u : ℚ} (hlo : 0xc8 ≤ u) (hhi : u < (0x400 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_18 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_74 {u : ℚ} (hlo : (0x400 / 5) ≤ u) (hhi : u < (0x280 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_18 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_75 {u : ℚ} (hlo : (0x280 / 3) ≤ u) (hhi : u < 0xd8) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_76 {u : ℚ} (hlo : 0xd8 ≤ u) (hhi : u < 0xe0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_77 {u : ℚ} (hlo : 0xe0 ≤ u) (hhi : u < 0xf3) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_16 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_78 {u : ℚ} (hlo : 0xf3 ≤ u) (hhi : u < (0x8c0 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_16 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 5, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_79 {u : ℚ} (hlo : (0x8c0 / 9) ≤ u) (hhi : u < 0x100) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_17 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 5, 9, 9, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_0_80 {u : ℚ} (hlo : 0x100 ≤ u) (hhi : u < 0x118) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_32 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_17 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_81 {u : ℚ} (hlo : 0x118 ≤ u) (hhi : u < (0xa00 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_32 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_18 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_82 {u : ℚ} (hlo : (0xa00 / 9) ≤ u) (hhi : u < (0x380 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_33 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_18 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_83 {u : ℚ} (hlo : (0x380 / 3) ≤ u) (hhi : u < 0x140) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_33 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_84 {u : ℚ} (hlo : 0x140 ≤ u) (hhi : u < (0x400 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_34 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_20 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_85 {u : ℚ} (hlo : (0x400 / 3) ≤ u) (hhi : u < (0xc80 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_35 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_20 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_86 {u : ℚ} (hlo : (0xc80 / 9) ≤ u) (hhi : u < 0x17a) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_35 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_21 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_87 {u : ℚ} (hlo : 0x17a ≤ u) (hhi : u < 0x190) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_21 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_88 {u : ℚ} (hlo : 0x190 ≤ u) (hhi : u < 0x195) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_22 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_89 {u : ℚ} (hlo : 0x195 ≤ u) (hhi : u < 0x1b0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_90 {u : ℚ} (hlo : 0x1b0 ≤ u) (hhi : u < (0x88b / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_91 {u : ℚ} (hlo : (0x88b / 5) ≤ u) (hhi : u < 0x1c0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_92 {u : ℚ} (hlo : 0x1c0 ≤ u) (hhi : u < 0x1e6) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_21 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_93 {u : ℚ} (hlo : 0x1e6 ≤ u) (hhi : u < (0x1180 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_21 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_94 {u : ℚ} (hlo : (0x1180 / 9) ≤ u) (hhi : u < 0x200) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_22 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_0_95 {u : ℚ} (hlo : 0x200 ≤ u) (hhi : u < 0x21c) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_22 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_96 {u : ℚ} (hlo : 0x21c ≤ u) (hhi : u < 0x230) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_22 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_97 {u : ℚ} (hlo : 0x230 ≤ u) (hhi : u < 0x237) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_98 {u : ℚ} (hlo : 0x237 ≤ u) (hhi : u < (0x1400 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_99 {u : ℚ} (hlo : (0x1400 / 9) ≤ u) (hhi : u < (0xb64 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_39 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_100 {u : ℚ} (hlo : (0xb64 / 5) ≤ u) (hhi : u < 0x280) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_39 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_101 {u : ℚ} (hlo : 0x280 ≤ u) (hhi : u < 0x2a3) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_40 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_25 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_102 {u : ℚ} (hlo : 0x2a3 ≤ u) (hhi : u < 0x2d0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_41 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_26 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_103 {u : ℚ} (hlo : 0x2d0 ≤ u) (hhi : u < 0x2d9) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_42 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_104 {u : ℚ} (hlo : 0x2d9 ≤ u) (hhi : u < 0x2f4) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_42 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_105 {u : ℚ} (hlo : 0x2f4 ≤ u) (hhi : u < 0x320) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_42 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_106 {u : ℚ} (hlo : 0x320 ≤ u) (hhi : u < 0x32a) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_43 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_28 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_107 {u : ℚ} (hlo : 0x32a ≤ u) (hhi : u < (0x1000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_108 {u : ℚ} (hlo : (0x1000 / 5) ≤ u) (hhi : u < 0x360) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_109 {u : ℚ} (hlo : 0x360 ≤ u) (hhi : u < 0x380) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_110 {u : ℚ} (hlo : 0x380 ≤ u) (hhi : u < 0x3b1) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_26 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_111 {u : ℚ} (hlo : 0x3b1 ≤ u) (hhi : u < 0x3f0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_27 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_112 {u : ℚ} (hlo : 0x3f0 ≤ u) (hhi : u < 0x400) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_28 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_0_113 {u : ℚ} (hlo : 0x400 ≤ u) (hhi : u < 0x438) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_46 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_28 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_114 {u : ℚ} (hlo : 0x438 ≤ u) (hhi : u < 0x460) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_46 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_28 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_115 {u : ℚ} (hlo : 0x460 ≤ u) (hhi : u < 0x46e) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_46 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_116 {u : ℚ} (hlo : 0x46e ≤ u) (hhi : u < (0x2800 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_46 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_117 {u : ℚ} (hlo : (0x2800 / 9) ≤ u) (hhi : u < 0x500) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_47 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_118 {u : ℚ} (hlo : 0x500 ≤ u) (hhi : u < (0x19a1 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_119 {u : ℚ} (hlo : (0x19a1 / 5) ≤ u) (hhi : u < (0x1000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_120 {u : ℚ} (hlo : (0x1000 / 3) ≤ u) (hhi : u < (0x3200 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_121 {u : ℚ} (hlo : (0x3200 / 9) ≤ u) (hhi : u < 0x5b2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_122 {u : ℚ} (hlo : 0x5b2 ≤ u) (hhi : u < 0x5e8) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_123 {u : ℚ} (hlo : 0x5e8 ≤ u) (hhi : u < 0x640) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_31 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_124 {u : ℚ} (hlo : 0x640 ≤ u) (hhi : u < (0x1400 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_33 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_31 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_125 {u : ℚ} (hlo : (0x1400 / 3) ≤ u) (hhi : u < (0x222c / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_31 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_126 {u : ℚ} (hlo : (0x222c / 5) ≤ u) (hhi : u < 0x700) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_31 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_127 {u : ℚ} (hlo : 0x700 ≤ u) (hhi : u < (0x4600 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_128 {u : ℚ} (hlo : (0x4600 / 9) ≤ u) (hhi : u < 0x7e9) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_129 {u : ℚ} (hlo : 0x7e9 ≤ u) (hhi : u < 0x800) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_35 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_0_130 {u : ℚ} (hlo : 0x800 ≤ u) (hhi : u < 0x870) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_35 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 6, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_131 {u : ℚ} (hlo : 0x870 ≤ u) (hhi : u < 0x88b) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 6, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_132 {u : ℚ} (hlo : 0x88b ≤ u) (hhi : u < 0x8c0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_133 {u : ℚ} (hlo : 0x8c0 ≤ u) (hhi : u < (0x5000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_34 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_134 {u : ℚ} (hlo : (0x5000 / 9) ≤ u) (hhi : u < (0x1c00 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_51 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_34 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_135 {u : ℚ} (hlo : (0x1c00 / 3) ≤ u) (hhi : u < 0xa00) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_51 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_35 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_136 {u : ℚ} (hlo : 0xa00 ≤ u) (hhi : u < 0xa56) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_35 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_137 {u : ℚ} (hlo : 0xa56 ≤ u) (hhi : u < (0x2000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_138 {u : ℚ} (hlo : (0x2000 / 3) ≤ u) (hhi : u < (0x6400 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_139 {u : ℚ} (hlo : (0x6400 / 9) ≤ u) (hhi : u < 0xbd0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_38 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_140 {u : ℚ} (hlo : 0xbd0 ≤ u) (hhi : u < 0xc80) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_38 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_141 {u : ℚ} (hlo : 0xc80 ≤ u) (hhi : u < (0x4000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_39 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_142 {u : ℚ} (hlo : (0x4000 / 5) ≤ u) (hhi : u < 0xd2f) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_39 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_143 {u : ℚ} (hlo : 0xd2f ≤ u) (hhi : u < 0xd80) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_144 {u : ℚ} (hlo : 0xd80 ≤ u) (hhi : u < 0xe00) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_145 {u : ℚ} (hlo : 0xe00 ≤ u) (hhi : u < 0xe10) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_146 {u : ℚ} (hlo : 0xe10 ≤ u) (hhi : u < (0x4ce3 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_147 {u : ℚ} (hlo : (0x4ce3 / 5) ≤ u) (hhi : u < (0x8c00 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_148 {u : ℚ} (hlo : (0x8c00 / 9) ≤ u) (hhi : u < 0xfa0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_149 {u : ℚ} (hlo : 0xfa0 ≤ u) (hhi : u < 0xfd2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_42 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_150 {u : ℚ} (hlo : 0xfd2 ≤ u) (hhi : u < 0x1000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_43 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_0_151 {u : ℚ} (hlo : 0x1000 ≤ u) (hhi : u < 0x10e0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_43 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_152 {u : ℚ} (hlo : 0x10e0 ≤ u) (hhi : u < 0x1116) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_153 {u : ℚ} (hlo : 0x1116 ≤ u) (hhi : u < 0x1180) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_154 {u : ℚ} (hlo : 0x1180 ≤ u) (hhi : u < (0xa000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_40 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_155 {u : ℚ} (hlo : (0xa000 / 9) ≤ u) (hhi : u < 0x1275) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_57 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_40 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_156 {u : ℚ} (hlo : 0x1275 ≤ u) (hhi : u < 0x13b0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_57 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_41 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_157 {u : ℚ} (hlo : 0x13b0 ≤ u) (hhi : u < 0x1400) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_57 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_42 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_158 {u : ℚ} (hlo : 0x1400 ≤ u) (hhi : u < (0x6684 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_58 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_42 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_159 {u : ℚ} (hlo : (0x6684 / 5) ≤ u) (hhi : u < (0x23000 / 27)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_58 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_42 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_160 {u : ℚ} (hlo : (0x23000 / 27) ≤ u) (hhi : u < 0x15e0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_42 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_161 {u : ℚ} (hlo : 0x15e0 ≤ u) (hhi : u < 0x1626) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_43 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_162 {u : ℚ} (hlo : 0x1626 ≤ u) (hhi : u < (0xc800 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_163 {u : ℚ} (hlo : (0xc800 / 9) ≤ u) (hhi : u < 0x17a0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_46 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_164 {u : ℚ} (hlo : 0x17a0 ≤ u) (hhi : u < 0x1900) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_46 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_45 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_165 {u : ℚ} (hlo : 0x1900 ≤ u) (hhi : u < 0x19a1) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_47 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_45 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_0_166 {u : ℚ} (hlo : 0x19a1 ≤ u) (hhi : u < (0x5000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_47 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_45 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_0_167 {u : ℚ} (hlo : (0x5000 / 3) ≤ u) (hhi : u < 0x1c00) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_45 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_0_168 {u : ℚ} (hlo : 0x1c00 ≤ u) (hhi : u < (0x11800 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_46 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_0_169 {u : ℚ} (hlo : (0x11800 / 9) ≤ u) (hhi : u < 0x2000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_47 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_0_170 {u : ℚ} (hlo : 0x2000 ≤ u) (hhi : u < 0x2300) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_62 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_47 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_171 {u : ℚ} (hlo : 0x2300 ≤ u) (hhi : u < (0x14000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_62 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_172 {u : ℚ} (hlo : (0x14000 / 9) ≤ u) (hhi : u < (0x7000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_63 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_173 {u : ℚ} (hlo : (0x7000 / 3) ≤ u) (hhi : u < 0x2800) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_63 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_174 {u : ℚ} (hlo : 0x2800 ≤ u) (hhi : u < (0x8000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_49 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_175 {u : ℚ} (hlo : (0x8000 / 3) ≤ u) (hhi : u < (0x19000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_49 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_176 {u : ℚ} (hlo : (0x19000 / 9) ≤ u) (hhi : u < (0xe6a9 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_50 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_177 {u : ℚ} (hlo : (0xe6a9 / 5) ≤ u) (hhi : u < 0x3200) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_50 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_178 {u : ℚ} (hlo : 0x3200 ≤ u) (hhi : u < (0x10000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_179 {u : ℚ} (hlo : (0x10000 / 5) ≤ u) (hhi : u < 0x3342) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_0_180 {u : ℚ} (hlo : 0x3342 ≤ u) (hhi : u < (0xa000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_0_181 {u : ℚ} (hlo : (0xa000 / 3) ≤ u) (hhi : u < 0x3800) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_0_182 {u : ℚ} (hlo : 0x3800 ≤ u) (hhi : u < (0x1338c / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_0_183 {u : ℚ} (hlo : (0x1338c / 5) ≤ u) (hhi : u < (0x23000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_0_184 {u : ℚ} (hlo : (0x23000 / 9) ≤ u) (hhi : u < 0x4000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_0_185 {u : ℚ} (hlo : 0x4000 ≤ u) (hhi : u < 0x41eb) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_186 {u : ℚ} (hlo : 0x41eb ≤ u) (hhi : u < 0x4380) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_53 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_187 {u : ℚ} (hlo : 0x4380 ≤ u) (hhi : u < 0x4600) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_188 {u : ℚ} (hlo : 0x4600 ≤ u) (hhi : u < (0x28000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_189 {u : ℚ} (hlo : (0x28000 / 9) ≤ u) (hhi : u < (0xe000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_190 {u : ℚ} (hlo : (0xe000 / 3) ≤ u) (hhi : u < 0x4ce3) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_53 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_0_191 {u : ℚ} (hlo : 0x4ce3 ≤ u) (hhi : u < 0x5000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_53 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_192 {u : ℚ} (hlo : 0x5000 ≤ u) (hhi : u < (0x32000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_55 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_53 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_193 {u : ℚ} (hlo : (0x32000 / 9) ≤ u) (hhi : u < 0x5c49) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_53 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_194 {u : ℚ} (hlo : 0x5c49 ≤ u) (hhi : u < 0x5e80) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_195 {u : ℚ} (hlo : 0x5e80 ≤ u) (hhi : u < 0x6400) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_196 {u : ℚ} (hlo : 0x6400 ≤ u) (hhi : u < 0x6684) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_57 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_197 {u : ℚ} (hlo : 0x6684 ≤ u) (hhi : u < (0xaf000 / 27)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_57 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_198 {u : ℚ} (hlo : (0xaf000 / 27) ≤ u) (hhi : u < 0x6d60) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_58 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_199 {u : ℚ} (hlo : 0x6d60 ≤ u) (hhi : u < 0x7000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_200 {u : ℚ} (hlo : 0x7000 ≤ u) (hhi : u < (0x46000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_201 {u : ℚ} (hlo : (0x46000 / 9) ≤ u) (hhi : u < 0x8000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_0_202 {u : ℚ} (hlo : 0x8000 ≤ u) (hhi : u < 0x8025) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_71 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 17, 17, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_17 baseLower_1_18
  all_goals decide +kernel


def baseInterval_0_203 {u : ℚ} (hlo : 0x8025 ≤ u) (hhi : u < 0x88b0) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = 0 * u + 0x6684 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_204 {u : ℚ} (hlo : 0x88b0 ≤ u) (hhi : u < (0x2b3fb / 5)) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_205 {u : ℚ} (hlo : (0x2b3fb / 5) ≤ u) (hhi : u < 0x8c00) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_206 {u : ℚ} (hlo : 0x8c00 ≤ u) (hhi : u < (0xf5000 / 27)) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_58 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_207 {u : ℚ} (hlo : (0xf5000 / 27) ≤ u) (hhi : u < 0x9920) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_59 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_208 {u : ℚ} (hlo : 0x9920 ≤ u) (hhi : u < 0x99c6) :
    baseStepValid false u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_0_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hquota : quotaValue false u = 17 := by
    simp [quotaValue, hrank]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_0_209 {u : ℚ} (hlo : 0x99c6 ≤ u) (hhi : u < 0xa000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_210 {u : ℚ} (hlo : 0xa000 ≤ u) (hhi : u < (0x64000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_61 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_211 {u : ℚ} (hlo : (0x64000 / 9) ≤ u) (hhi : u < 0xb367) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_212 {u : ℚ} (hlo : 0xb367 ≤ u) (hhi : u < (0x39aa4 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_213 {u : ℚ} (hlo : (0x39aa4 / 5) ≤ u) (hhi : u < 0xc800) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_214 {u : ℚ} (hlo : 0xc800 ≤ u) (hhi : u < (0x40000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_215 {u : ℚ} (hlo : (0x40000 / 5) ≤ u) (hhi : u < 0xcd08) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_216 {u : ℚ} (hlo : 0xcd08 ≤ u) (hhi : u < (0x28000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_217 {u : ℚ} (hlo : (0x28000 / 3) ≤ u) (hhi : u < 0xe000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_218 {u : ℚ} (hlo : 0xe000 ≤ u) (hhi : u < 0xe6a9) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_62 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_219 {u : ℚ} (hlo : 0xe6a9 ≤ u) (hhi : u < (0x8c000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_62 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 10, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_220 {u : ℚ} (hlo : (0x8c000 / 9) ≤ u) (hhi : u < 0x10000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_63 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 10, 18, 18, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_0_221 {u : ℚ} (hlo : 0x10000 ≤ u) (hhi : u < 0x11800) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_76 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_63 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_222 {u : ℚ} (hlo : 0x11800 ≤ u) (hhi : u < (0xa0000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_76 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_223 {u : ℚ} (hlo : (0xa0000 / 9) ≤ u) (hhi : u < (0x38000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_77 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_224 {u : ℚ} (hlo : (0x38000 / 3) ≤ u) (hhi : u < 0x1338c) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_77 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_225 {u : ℚ} (hlo : 0x1338c ≤ u) (hhi : u < 0x14000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_78 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_65 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_226 {u : ℚ} (hlo : 0x14000 ≤ u) (hhi : u < (0x40000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_79 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_66 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_227 {u : ℚ} (hlo : (0x40000 / 3) ≤ u) (hhi : u < (0xc8000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_80 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_66 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_228 {u : ℚ} (hlo : (0xc8000 / 9) ≤ u) (hhi : u < 0x166ce) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_80 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_67 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_229 {u : ℚ} (hlo : 0x166ce ≤ u) (hhi : u < 0x1806f) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_67 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_230 {u : ℚ} (hlo : 0x1806f ≤ u) (hhi : u < 0x19a10) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_231 {u : ℚ} (hlo : 0x19a10 ≤ u) (hhi : u < (0x81bf1 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_232 {u : ℚ} (hlo : (0x81bf1 / 5) ≤ u) (hhi : u < 0x1c000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_233 {u : ℚ} (hlo : 0x1c000 ≤ u) (hhi : u < 0x1cd52) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_67 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_234 {u : ℚ} (hlo : 0x1cd52 ≤ u) (hhi : u < (0x118000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_67 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_235 {u : ℚ} (hlo : (0x118000 / 9) ≤ u) (hhi : u < 0x20000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_0_236 {u : ℚ} (hlo : 0x20000 ≤ u) (hhi : u < 0x20094) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_83 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_237 {u : ℚ} (hlo : 0x20094 ≤ u) (hhi : u < 0x21a35) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_83 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_238 {u : ℚ} (hlo : 0x21a35 ≤ u) (hhi : u < (0xacfec / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_83 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_239 {u : ℚ} (hlo : (0xacfec / 5) ≤ u) (hhi : u < (0x140000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_83 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_240 {u : ℚ} (hlo : (0x140000 / 9) ≤ u) (hhi : u < 0x28000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_84 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_241 {u : ℚ} (hlo : 0x28000 ≤ u) (hhi : u < 0x280b9) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_85 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_70 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_242 {u : ℚ} (hlo : 0x280b9 ≤ u) (hhi : u < 0x2ab70) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_86 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_71 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_243 {u : ℚ} (hlo : 0x2ab70 ≤ u) (hhi : u < 0x2b3fb) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_87 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_244 {u : ℚ} (hlo : 0x2b3fb ≤ u) (hhi : u < 0x2cd9c) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_87 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_245 {u : ℚ} (hlo : 0x2cd9c ≤ u) (hhi : u < 0x300de) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_87 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_70 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_246 {u : ℚ} (hlo : 0x300de ≤ u) (hhi : u < (0x100000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_70 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_247 {u : ℚ} (hlo : (0x100000 / 5) ≤ u) (hhi : u < 0x33420) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_70 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_248 {u : ℚ} (hlo : 0x33420 ≤ u) (hhi : u < 0x38000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_70 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_249 {u : ℚ} (hlo : 0x38000 ≤ u) (hhi : u < 0x38103) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_71 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_250 {u : ℚ} (hlo : 0x38103 ≤ u) (hhi : u < 0x3bcd0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_72 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_251 {u : ℚ} (hlo : 0x3bcd0 ≤ u) (hhi : u < 0x40000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_0_252 {u : ℚ} (hlo : 0x40000 ≤ u) (hhi : u < 0x40128) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_90 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_253 {u : ℚ} (hlo : 0x40128 ≤ u) (hhi : u < 0x4346a) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_90 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_254 {u : ℚ} (hlo : 0x4346a ≤ u) (hhi : u < (0x280000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_90 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_255 {u : ℚ} (hlo : (0x280000 / 9) ≤ u) (hhi : u < (0x1853d3 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_91 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_256 {u : ℚ} (hlo : (0x1853d3 / 5) ≤ u) (hhi : u < 0x50000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_91 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_257 {u : ℚ} (hlo : 0x50000 ≤ u) (hhi : u < (0x100000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_92 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_258 {u : ℚ} (hlo : (0x100000 / 3) ≤ u) (hhi : u < 0x567f6) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_93 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_259 {u : ℚ} (hlo : 0x567f6 ≤ u) (hhi : u < (0x320000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_93 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_260 {u : ℚ} (hlo : (0x320000 / 9) ≤ u) (hhi : u < 0x59b38) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_93 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_76 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_261 {u : ℚ} (hlo : 0x59b38 ≤ u) (hhi : u < 0x601bc) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_93 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_76 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_262 {u : ℚ} (hlo : 0x601bc ≤ u) (hhi : u < 0x64000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_77 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_263 {u : ℚ} (hlo : 0x64000 ≤ u) (hhi : u < (0x206fc4 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_78 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_264 {u : ℚ} (hlo : (0x206fc4 / 5) ≤ u) (hhi : u < (0x140000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_78 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_265 {u : ℚ} (hlo : (0x140000 / 3) ≤ u) (hhi : u < 0x70000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_79 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_266 {u : ℚ} (hlo : 0x70000 ≤ u) (hhi : u < 0x7822b) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_79 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_267 {u : ℚ} (hlo : 0x7822b ≤ u) (hhi : u < (0x460000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_268 {u : ℚ} (hlo : (0x460000 / 9) ≤ u) (hhi : u < 0x80000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_77 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_0_269 {u : ℚ} (hlo : 0x80000 ≤ u) (hhi : u < 0x80250) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_77 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 11, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_270 {u : ℚ} (hlo : 0x80250 ≤ u) (hhi : u < 0x81bf1) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_77 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 11, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_271 {u : ℚ} (hlo : 0x81bf1 ≤ u) (hhi : u < 0x868d4) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_77 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_272 {u : ℚ} (hlo : 0x868d4 ≤ u) (hhi : u < 0x8c000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_78 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_273 {u : ℚ} (hlo : 0x8c000 ≤ u) (hhi : u < (0x500000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_79 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_274 {u : ℚ} (hlo : (0x500000 / 9) ≤ u) (hhi : u < (0x1c0000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_97 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_79 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_275 {u : ℚ} (hlo : (0x1c0000 / 3) ≤ u) (hhi : u < 0x9cfa2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_97 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_80 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_276 {u : ℚ} (hlo : 0x9cfa2 ≤ u) (hhi : u < 0xa0000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_97 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_277 {u : ℚ} (hlo : 0xa0000 ≤ u) (hhi : u < (0x200000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_98 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_82 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_278 {u : ℚ} (hlo : (0x200000 / 3) ≤ u) (hhi : u < (0x640000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_82 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_279 {u : ℚ} (hlo : (0x640000 / 9) ≤ u) (hhi : u < 0xb3670) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_83 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_280 {u : ℚ} (hlo : 0xb3670 ≤ u) (hhi : u < 0xc8000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_83 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_281 {u : ℚ} (hlo : 0xc8000 ≤ u) (hhi : u < 0xc839d) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_84 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_282 {u : ℚ} (hlo : 0xc839d ≤ u) (hhi : u < (0x400000 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_283 {u : ℚ} (hlo : (0x400000 / 5) ≤ u) (hhi : u < 0xcd080) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_284 {u : ℚ} (hlo : 0xcd080 ≤ u) (hhi : u < 0xd5930) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_285 {u : ℚ} (hlo : 0xd5930 ≤ u) (hhi : u < 0xe0000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_286 {u : ℚ} (hlo : 0xe0000 ≤ u) (hhi : u < (0x48fb79 / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_287 {u : ℚ} (hlo : (0x48fb79 / 5) ≤ u) (hhi : u < 0xf0456) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_288 {u : ℚ} (hlo : 0xf0456 ≤ u) (hhi : u < (0x8c0000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_289 {u : ℚ} (hlo : (0x8c0000 / 9) ≤ u) (hhi : u < 0x100000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_84 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_0_290 {u : ℚ} (hlo : 0x100000 ≤ u) (hhi : u < 0x1004a0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_84 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_291 {u : ℚ} (hlo : 0x1004a0 ≤ u) (hhi : u < 0x1037e2) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_84 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_292 {u : ℚ} (hlo : 0x1037e2 ≤ u) (hhi : u < 0x118000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_84 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_293 {u : ℚ} (hlo : 0x118000 ≤ u) (hhi : u < 0x11850f) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_85 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_294 {u : ℚ} (hlo : 0x11850f ≤ u) (hhi : u < (0xa00000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_295 {u : ℚ} (hlo : (0xa00000 / 9) ≤ u) (hhi : u < 0x12b010) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_103 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_296 {u : ℚ} (hlo : 0x12b010 ≤ u) (hhi : u < (0x614f4c / 5)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_103 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_297 {u : ℚ} (hlo : (0x614f4c / 5) ≤ u) (hhi : u < 0x140000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_103 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_298 {u : ℚ} (hlo : 0x140000 ≤ u) (hhi : u < (0x2300000 / 27)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_104 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_299 {u : ℚ} (hlo : (0x2300000 / 27) ≤ u) (hhi : u < 0x150612) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_105 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_300 {u : ℚ} (hlo : 0x150612 ≤ u) (hhi : u < (0x400000 / 3)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_106 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_301 {u : ℚ} (hlo : (0x400000 / 3) ≤ u) (hhi : u < (0xc80000 / 9)) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_107 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_302 {u : ℚ} (hlo : (0xc80000 / 9) ≤ u) (hhi : u < 0x166ce0) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_107 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_303 {u : ℚ} (hlo : 0x166ce0 ≤ u) (hhi : u < 0x1853d3) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_107 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_89 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_0_304 {u : ℚ} (hlo : 0x1853d3 ≤ u) (hhi : u < 0x190000) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_108 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_89 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 13, 24, 24, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_24 baseLower_0_25
  all_goals decide +kernel


def baseInterval_0_305 {u : ℚ} (hlo : 0x190000 ≤ u) (hhi : u < 0x1921ee) :
    baseStepValid false u := by
  have hp := baseTable_eval_0_108 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_91 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_0_89 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 13, 24, 24, 0, 0, 0, 0, false⟩ hlo hhi hp h5 h7
    baseLower_0_24 baseLower_0_25
  all_goals decide +kernel


def baseInterval_1_0 {u : ℚ} (hlo : 1 ≤ u) (hhi : u < (4 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_1 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 1, 1, 5, 7, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_1_1 {u : ℚ} (hlo : (4 / 3) ≤ u) (hhi : u < (9 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_2 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 1, 1, 6, 9, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_1_2 {u : ℚ} (hlo : (9 / 5) ≤ u) (hhi : u < 2) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_2 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨0, 0, 1, 1, 1, 2, 9, 10, false⟩ hlo hhi hp h5 h7
    baseLower_0_1 baseLower_0_2
  all_goals decide +kernel


def baseInterval_1_3 {u : ℚ} (hlo : 2 ≤ u) (hhi : u < (12 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_3 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 1, 2, 10, 12, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_1_4 {u : ℚ} (hlo : (12 / 5) ≤ u) (hhi : u < (8 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_3 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 1, 2, 12, 14, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_1_5 {u : ℚ} (hlo : (8 / 3) ≤ u) (hhi : u < 3) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 0, 2, 2, 1, 2, 13, 15, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_1_6 {u : ℚ} (hlo : 3 ≤ u) (hhi : u < (16 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 1, 2, 2, 1, 2, 15, 16, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_1_7 {u : ℚ} (hlo : (16 / 5) ≤ u) (hhi : u < 4) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_4 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨1, 1, 2, 2, 2, 2, 16, 20, false⟩ hlo hhi hp h5 h7
    baseLower_1_2 baseLower_1_3
  all_goals decide +kernel


def baseInterval_1_8 {u : ℚ} (hlo : 4 ≤ u) (hhi : u < 5) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_5 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_0 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 2, 20, 25, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_9 {u : ℚ} (hlo : 5 ≤ u) (hhi : u < (16 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_5 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 2, 25, 27, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_10 {u : ℚ} (hlo : (16 / 3) ≤ u) (hhi : u < (27 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 2, 26, 27, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_11 {u : ℚ} (hlo : (27 / 5) ≤ u) (hhi : u < 6) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 3, 27, 30, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_12 {u : ℚ} (hlo : 6 ≤ u) (hhi : u < (20 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_1 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 3, 30, 34, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_13 {u : ℚ} (hlo : (20 / 3) ≤ u) (hhi : u < 7) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_0 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 3, 33, 35, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_14 {u : ℚ} (hlo : 7 ≤ u) (hhi : u < (36 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 3, 35, 36, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_15 {u : ℚ} (hlo : (36 / 5) ≤ u) (hhi : u < 8) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_6 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨2, 1, 3, 3, 2, 3, 36, 40, false⟩ hlo hhi hp h5 h7
    baseLower_0_3 baseLower_0_4
  all_goals decide +kernel


def baseInterval_1_16 {u : ℚ} (hlo : 8 ≤ u) (hhi : u < (80 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_7 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 1, 4, 4, 2, 3, 40, 45, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_17 {u : ℚ} (hlo : (80 / 9) ≤ u) (hhi : u < 9) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 1, 4, 4, 2, 3, 44, 45, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_18 {u : ℚ} (hlo : 9 ≤ u) (hhi : u < (28 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_1 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 2, 3, 45, 47, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_19 {u : ℚ} (hlo : (28 / 3) ≤ u) (hhi : u < 10) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_8 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_2 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 2, 3, 46, 50, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_20 {u : ℚ} (hlo : 10 ≤ u) (hhi : u < (32 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_9 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 2, 3, 50, 54, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_21 {u : ℚ} (hlo : (32 / 3) ≤ u) (hhi : u < (64 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 2, 3, 53, 64, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_22 {u : ℚ} (hlo : (64 / 5) ≤ u) (hhi : u < (40 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_3 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 3, 3, 64, 67, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_23 {u : ℚ} (hlo : (40 / 3) ≤ u) (hhi : u < 14) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_2 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 3, 3, 66, 70, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_24 {u : ℚ} (hlo : 14 ≤ u) (hhi : u < 16) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_10 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨3, 2, 4, 4, 3, 3, 70, 80, false⟩ hlo hhi hp h5 h7
    baseLower_1_4 baseLower_1_5
  all_goals decide +kernel


def baseInterval_1_25 {u : ℚ} (hlo : 16 ≤ u) (hhi : u < (81 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_11 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 3, 80, 81, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_26 {u : ℚ} (hlo : (81 / 5) ≤ u) (hhi : u < (0xa0 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_11 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 81, 89, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_27 {u : ℚ} (hlo : (0xa0 / 9) ≤ u) (hhi : u < 18) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 88, 90, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_28 {u : ℚ} (hlo : 18 ≤ u) (hhi : u < (56 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_3 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 90, 94, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_29 {u : ℚ} (hlo : (56 / 3) ≤ u) (hhi : u < 20) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_12 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_4 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 93, 0x64, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_30 {u : ℚ} (hlo : 20 ≤ u) (hhi : u < (64 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_13 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 0x64, 0x6b, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_31 {u : ℚ} (hlo : (64 / 3) ≤ u) (hhi : u < (0x6c / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 0x6a, 0x6c, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_32 {u : ℚ} (hlo : (0x6c / 5) ≤ u) (hhi : u < (80 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_5 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 0x6c, 0x86, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_33 {u : ℚ} (hlo : (80 / 3) ≤ u) (hhi : u < 27) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_14 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 2, 5, 5, 3, 4, 0x85, 0x87, false⟩ hlo hhi hp h5 h7
    baseLower_0_5 baseLower_0_6
  all_goals decide +kernel


def baseInterval_1_34 {u : ℚ} (hlo : 27 ≤ u) (hhi : u < 28) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_15 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_4 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 3, 6, 6, 3, 4, 0x87, 0x8c, false⟩ hlo hhi hp h5 h7
    baseLower_0_6 baseLower_0_7
  all_goals decide +kernel


def baseInterval_1_35 {u : ℚ} (hlo : 28 ≤ u) (hhi : u < 32) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_15 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨4, 3, 6, 6, 3, 4, 0x8c, 0xa0, false⟩ hlo hhi hp h5 h7
    baseLower_0_6 baseLower_0_7
  all_goals decide +kernel


def baseInterval_1_36 {u : ℚ} (hlo : 32 ≤ u) (hhi : u < (0x140 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_16 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xa0, 0xb2, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_37 {u : ℚ} (hlo : (0x140 / 9) ≤ u) (hhi : u < (0x70 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_17 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_5 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xb1, 0xbb, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_38 {u : ℚ} (hlo : (0x70 / 3) ≤ u) (hhi : u < 40) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_17 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_6 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xba, 0xc8, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_39 {u : ℚ} (hlo : 40 ≤ u) (hhi : u < (0x80 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_18 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_7 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xc8, 0xd6, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_40 {u : ℚ} (hlo : (0x80 / 3) ≤ u) (hhi : u < (0x190 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_7 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xd5, 0xdf, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_41 {u : ℚ} (hlo : (0x190 / 9) ≤ u) (hhi : u < (0xf3 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_8 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 4, 0xde, 0xf3, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_42 {u : ℚ} (hlo : (0xf3 / 5) ≤ u) (hhi : u < 50) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_8 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 5, 0xf3, 0xfa, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_43 {u : ℚ} (hlo : 50 ≤ u) (hhi : u < (0x100 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_9 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 3, 5, 0xfa, 0x100, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_44 {u : ℚ} (hlo : (0x100 / 5) ≤ u) (hhi : u < (0xa0 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_9 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 4, 5, 0x100, 0x10b, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_45 {u : ℚ} (hlo : (0xa0 / 3) ≤ u) (hhi : u < 54) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 6, 6, 4, 5, 0x10a, 0x10e, false⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_46 {u : ℚ} (hlo : 54 ≤ u) (hhi : u < 56) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_6 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 6, 4, 5, 0x10e, 0x118, true⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_47 {u : ℚ} (hlo : 56 ≤ u) (hhi : u < (0x230 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_7 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 6, 4, 5, 0x118, 0x138, true⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_48 {u : ℚ} (hlo : (0x230 / 9) ≤ u) (hhi : u < 64) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_19 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨5, 3, 7, 6, 4, 5, 0x137, 0x140, true⟩ hlo hhi hp h5 h7
    baseLower_1_6 baseLower_1_7
  all_goals decide +kernel


def baseInterval_1_49 {u : ℚ} (hlo : 64 ≤ u) (hhi : u < (0x144 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x140, 0x144, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_50 {u : ℚ} (hlo : (0x144 / 5) ≤ u) (hhi : u < 70) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_8 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x144, 0x15e, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_51 {u : ℚ} (hlo : 70 ≤ u) (hhi : u < (0x280 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_20 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_9 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x15e, 0x164, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_52 {u : ℚ} (hlo : (0x280 / 9) ≤ u) (hhi : u < (0xe0 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_21 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_9 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x163, 0x176, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_53 {u : ℚ} (hlo : (0xe0 / 3) ≤ u) (hhi : u < 80) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_21 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_10 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x175, 0x190, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_54 {u : ℚ} (hlo : 80 ≤ u) (hhi : u < 81) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_22 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_11 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 3, 7, 7, 4, 5, 0x190, 0x195, false⟩ hlo hhi hp h5 h7
    baseLower_0_7 baseLower_0_8
  all_goals decide +kernel


def baseInterval_1_55 {u : ℚ} (hlo : 81 ≤ u) (hhi : u < (0x320 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_23 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_11 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x195, 0x1bd, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_56 {u : ℚ} (hlo : (0x320 / 9) ≤ u) (hhi : u < 0x64) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_23 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_12 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x1bc, 0x1f4, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_57 {u : ℚ} (hlo : 0x64 ≤ u) (hhi : u < (0x140 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_23 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_13 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x1f4, 0x216, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_58 {u : ℚ} (hlo : (0x140 / 3) ≤ u) (hhi : u < 0x6c) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_23 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x215, 0x21c, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_59 {u : ℚ} (hlo : 0x6c ≤ u) (hhi : u < 0x70) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_10 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x21c, 0x230, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_60 {u : ℚ} (hlo : 0x70 ≤ u) (hhi : u < (0x460 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_11 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x230, 0x26f, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_61 {u : ℚ} (hlo : (0x460 / 9) ≤ u) (hhi : u < 0x80) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_24 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨6, 4, 8, 8, 4, 5, 0x26e, 0x280, false⟩ hlo hhi hp h5 h7
    baseLower_0_8 baseLower_0_9
  all_goals decide +kernel


def baseInterval_1_62 {u : ℚ} (hlo : 0x80 ≤ u) (hhi : u < 0x87) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_25 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_14 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 8, 8, 4, 5, 0x280, 0x2a3, false⟩ hlo hhi hp h5 h7
    baseLower_1_8 baseLower_1_9
  all_goals decide +kernel


def baseInterval_1_63 {u : ℚ} (hlo : 0x87 ≤ u) (hhi : u < 0x8c) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_26 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_12 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 5 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2a3 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2bc := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 8 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) = 0 * u + 0x6c := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_64 {u : ℚ} (hlo : 0x8c ≤ u) (hhi : u < 0x90) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_26 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 5 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2bc ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2d0 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 8 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = 0 * u + 0x6c := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_65 {u : ℚ} (hlo : 0x90 ≤ u) (hhi : u < (0x2d9 / 5)) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_27 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 5 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2d0 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2d9 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 8 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_66 {u : ℚ} (hlo : (0x2d9 / 5) ≤ u) (hhi : u < (0x1c0 / 3)) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_27 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_13 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 6 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2d9 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2eb := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 8 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, 0 * (u / 7) + 16)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_67 {u : ℚ} (hlo : (0x1c0 / 3) ≤ u) (hhi : u < 0xa0) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_27 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_15 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 7 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 8 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0xa2 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 4 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 6 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2ea ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x320 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 8 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 8 0 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_8] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 8 0 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_9]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 8 1 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 8 1 (0, 0 * (u / 5) + 27) (0, (3 / 4) * (u / 7) + 0)
    rw [baseLower_1_8] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_9] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_68 {u : ℚ} (hlo : 0xa0 ≤ u) (hhi : u < 0xa2) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_28 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_16 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 8, 8, 4, 6, 0x320, 0x32a, false⟩ hlo hhi hp h5 h7
    baseLower_1_8 baseLower_1_9
  all_goals decide +kernel


def baseInterval_1_69 {u : ℚ} (hlo : 0xa2 ≤ u) (hhi : u < (0x640 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_16 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 4, 6, 0x32a, 0x379, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_70 {u : ℚ} (hlo : (0x640 / 9) ≤ u) (hhi : u < 0xbd) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_14 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 4, 6, 0x378, 0x3b1, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_71 {u : ℚ} (hlo : 0xbd ≤ u) (hhi : u < (0x3cc / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 4, 6, 0x3b1, 0x3cc, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_72 {u : ℚ} (hlo : (0x3cc / 5) ≤ u) (hhi : u < 0xc8) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_17 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 4, 6, 0x3cc, 0x3e8, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_73 {u : ℚ} (hlo : 0xc8 ≤ u) (hhi : u < (0x400 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_18 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 4, 6, 0x3e8, 0x400, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_74 {u : ℚ} (hlo : (0x400 / 5) ≤ u) (hhi : u < (0x280 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_18 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 5, 6, 0x400, 0x42b, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_75 {u : ℚ} (hlo : (0x280 / 3) ≤ u) (hhi : u < 0xd8) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_29 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 5, 6, 0x42a, 0x438, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_76 {u : ℚ} (hlo : 0xd8 ≤ u) (hhi : u < 0xe0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_15 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 5, 6, 0x438, 0x460, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_77 {u : ℚ} (hlo : 0xe0 ≤ u) (hhi : u < 0xf3) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_16 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 4, 9, 9, 5, 6, 0x460, 0x4bf, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_78 {u : ℚ} (hlo : 0xf3 ≤ u) (hhi : u < (0x8c0 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_16 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 5, 9, 9, 5, 6, 0x4bf, 0x4dd, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_79 {u : ℚ} (hlo : (0x8c0 / 9) ≤ u) (hhi : u < 0x100) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_30 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_17 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨7, 5, 9, 9, 5, 6, 0x4dc, 0x500, false⟩ hlo hhi hp h5 h7
    baseLower_1_9 baseLower_1_10
  all_goals decide +kernel


def baseInterval_1_80 {u : ℚ} (hlo : 0x100 ≤ u) (hhi : u < 0x118) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_17 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x500, 0x578, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_81 {u : ℚ} (hlo : 0x118 ≤ u) (hhi : u < (0xa00 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_31 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_18 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x578, 0x58f, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_82 {u : ℚ} (hlo : (0xa00 / 9) ≤ u) (hhi : u < (0x380 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_32 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_18 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x58e, 0x5d6, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_83 {u : ℚ} (hlo : (0x380 / 3) ≤ u) (hhi : u < 0x140) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_32 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_19 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x5d5, 0x640, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_84 {u : ℚ} (hlo : 0x140 ≤ u) (hhi : u < (0x400 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_33 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_20 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x640, 0x6ab, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_85 {u : ℚ} (hlo : (0x400 / 3) ≤ u) (hhi : u < (0xc80 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_34 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_20 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x6aa, 0x6f2, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_86 {u : ℚ} (hlo : (0xc80 / 9) ≤ u) (hhi : u < 0x190) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_34 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_21 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x6f1, 0x7d0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_87 {u : ℚ} (hlo : 0x190 ≤ u) (hhi : u < 0x195) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_34 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_22 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x7d0, 0x7e9, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_88 {u : ℚ} (hlo : 0x195 ≤ u) (hhi : u < 0x1b0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_35 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x7e9, 0x870, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_89 {u : ℚ} (hlo : 0x1b0 ≤ u) (hhi : u < (0x88b / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 6, 0x870, 0x88b, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_90 {u : ℚ} (hlo : (0x88b / 5) ≤ u) (hhi : u < 0x1c0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_19 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 7, 0x88b, 0x8c0, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_91 {u : ℚ} (hlo : 0x1c0 ≤ u) (hhi : u < 0x1e6) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 7, 0x8c0, 0x97e, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_92 {u : ℚ} (hlo : 0x1e6 ≤ u) (hhi : u < (0x1180 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_20 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 7, 0x97e, 0x9b9, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_93 {u : ℚ} (hlo : (0x1180 / 9) ≤ u) (hhi : u < 0x200) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_36 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_21 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨8, 5, 10, 10, 5, 7, 0x9b8, 0xa00, false⟩ hlo hhi hp h5 h7
    baseLower_0_10 baseLower_0_11
  all_goals decide +kernel


def baseInterval_1_94 {u : ℚ} (hlo : 0x200 ≤ u) (hhi : u < 0x21c) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_23 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_21 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xa00, 0xa8c, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_95 {u : ℚ} (hlo : 0x21c ≤ u) (hhi : u < 0x230) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_21 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xa8c, 0xaf0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_96 {u : ℚ} (hlo : 0x230 ≤ u) (hhi : u < 0x237) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_22 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xaf0, 0xb13, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_97 {u : ℚ} (hlo : 0x237 ≤ u) (hhi : u < (0x1400 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_37 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xb13, 0xb1d, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_98 {u : ℚ} (hlo : (0x1400 / 9) ≤ u) (hhi : u < (0xb64 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xb1c, 0xb64, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_99 {u : ℚ} (hlo : (0xb64 / 5) ≤ u) (hhi : u < 0x280) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_38 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_24 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xb64, 0xc80, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_100 {u : ℚ} (hlo : 0x280 ≤ u) (hhi : u < 0x2a3) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_39 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_25 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xc80, 0xd2f, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_101 {u : ℚ} (hlo : 0x2a3 ≤ u) (hhi : u < 0x2d0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_40 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_26 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xd2f, 0xe10, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_102 {u : ℚ} (hlo : 0x2d0 ≤ u) (hhi : u < 0x2d9) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_41 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 5, 11, 11, 5, 7, 0xe10, 0xe3d, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_103 {u : ℚ} (hlo : 0x2d9 ≤ u) (hhi : u < 0x2f4) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_41 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_23 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 5, 7, 0xe3d, 0xec4, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_104 {u : ℚ} (hlo : 0x2f4 ≤ u) (hhi : u < 0x320) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_41 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_27 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 5, 7, 0xec4, 0xfa0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_105 {u : ℚ} (hlo : 0x320 ≤ u) (hhi : u < 0x32a) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_42 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_28 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 5, 7, 0xfa0, 0xfd2, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_106 {u : ℚ} (hlo : 0x32a ≤ u) (hhi : u < (0x1000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_43 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 5, 7, 0xfd2, 0x1000, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_107 {u : ℚ} (hlo : (0x1000 / 5) ≤ u) (hhi : u < 0x360) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_43 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 6, 7, 0x1000, 0x10e0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_108 {u : ℚ} (hlo : 0x360 ≤ u) (hhi : u < 0x380) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_24 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 6, 7, 0x10e0, 0x1180, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_109 {u : ℚ} (hlo : 0x380 ≤ u) (hhi : u < 0x3b1) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_25 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 6, 7, 0x1180, 0x1275, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_110 {u : ℚ} (hlo : 0x3b1 ≤ u) (hhi : u < 0x3f0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_26 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 6, 7, 0x1275, 0x13b0, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_111 {u : ℚ} (hlo : 0x3f0 ≤ u) (hhi : u < 0x400) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_44 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_27 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨9, 6, 11, 11, 6, 7, 0x13b0, 0x1400, false⟩ hlo hhi hp h5 h7
    baseLower_1_11 baseLower_1_12
  all_goals decide +kernel


def baseInterval_1_112 {u : ℚ} (hlo : 0x400 ≤ u) (hhi : u < 0x438) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_29 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_27 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x1400, 0x1518, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_113 {u : ℚ} (hlo : 0x438 ≤ u) (hhi : u < 0x460) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_27 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x1518, 0x15e0, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_114 {u : ℚ} (hlo : 0x460 ≤ u) (hhi : u < 0x46e) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_28 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x15e0, 0x1626, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_115 {u : ℚ} (hlo : 0x46e ≤ u) (hhi : u < (0x2800 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_45 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x1626, 0x1639, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_116 {u : ℚ} (hlo : (0x2800 / 9) ≤ u) (hhi : u < 0x500) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_46 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_30 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x1638, 0x1900, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_117 {u : ℚ} (hlo : 0x500 ≤ u) (hhi : u < (0x19a1 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_47 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 7, 0x1900, 0x19a1, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_118 {u : ℚ} (hlo : (0x19a1 / 5) ≤ u) (hhi : u < (0x1000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_47 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x19a1, 0x1aab, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_119 {u : ℚ} (hlo : (0x1000 / 3) ≤ u) (hhi : u < (0x3200 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_31 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x1aaa, 0x1bc8, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_120 {u : ℚ} (hlo : (0x3200 / 9) ≤ u) (hhi : u < 0x5b2) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x1bc7, 0x1c7a, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_121 {u : ℚ} (hlo : 0x5b2 ≤ u) (hhi : u < 0x5e8) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_29 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x1c7a, 0x1d88, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_122 {u : ℚ} (hlo : 0x5e8 ≤ u) (hhi : u < 0x640) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_32 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x1d88, 0x1f40, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_123 {u : ℚ} (hlo : 0x640 ≤ u) (hhi : u < (0x1400 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_33 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x1f40, 0x2156, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_124 {u : ℚ} (hlo : (0x1400 / 3) ≤ u) (hhi : u < (0x222c / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x2155, 0x222c, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_125 {u : ℚ} (hlo : (0x222c / 5) ≤ u) (hhi : u < 0x700) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_30 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x222c, 0x2300, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_126 {u : ℚ} (hlo : 0x700 ≤ u) (hhi : u < (0x4600 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_31 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x2300, 0x26e4, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_127 {u : ℚ} (hlo : (0x4600 / 9) ≤ u) (hhi : u < 0x7e9) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_34 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x26e3, 0x278d, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_128 {u : ℚ} (hlo : 0x7e9 ≤ u) (hhi : u < 0x800) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_48 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_35 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨10, 6, 12, 12, 6, 8, 0x278d, 0x2800, false⟩ hlo hhi hp h5 h7
    baseLower_0_12 baseLower_0_13
  all_goals decide +kernel


def baseInterval_1_129 {u : ℚ} (hlo : 0x800 ≤ u) (hhi : u < 0x870) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_35 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 6, 13, 13, 6, 8, 0x2800, 0x2a30, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_130 {u : ℚ} (hlo : 0x870 ≤ u) (hhi : u < 0x88b) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 6, 13, 13, 6, 8, 0x2a30, 0x2ab7, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_131 {u : ℚ} (hlo : 0x88b ≤ u) (hhi : u < 0x8c0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_32 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x2ab7, 0x2bc0, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_132 {u : ℚ} (hlo : 0x8c0 ≤ u) (hhi : u < (0x5000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_49 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x2bc0, 0x2c72, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_133 {u : ℚ} (hlo : (0x5000 / 9) ≤ u) (hhi : u < (0x1c00 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_33 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x2c71, 0x2eab, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_134 {u : ℚ} (hlo : (0x1c00 / 3) ≤ u) (hhi : u < 0xa00) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_50 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_36 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_34 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x2eaa, 0x3200, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_135 {u : ℚ} (hlo : 0xa00 ≤ u) (hhi : u < (0x2000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_51 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_34 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x3200, 0x3556, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_136 {u : ℚ} (hlo : (0x2000 / 3) ≤ u) (hhi : u < 0xb13) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_34 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x3555, 0x375f, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_137 {u : ℚ} (hlo : 0xb13 ≤ u) (hhi : u < (0x6400 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_37 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_35 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x375f, 0x378f, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_138 {u : ℚ} (hlo : (0x6400 / 9) ≤ u) (hhi : u < 0xbd0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_38 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_35 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x378e, 0x3b10, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_139 {u : ℚ} (hlo : 0xbd0 ≤ u) (hhi : u < 0xc80) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_38 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x3b10, 0x3e80, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_140 {u : ℚ} (hlo : 0xc80 ≤ u) (hhi : u < (0x4000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_39 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 6, 8, 0x3e80, 0x4000, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_141 {u : ℚ} (hlo : (0x4000 / 5) ≤ u) (hhi : u < 0xd2f) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_52 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_39 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 8, 0x4000, 0x41eb, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_142 {u : ℚ} (hlo : 0xd2f ≤ u) (hhi : u < 0xd80) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_53 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 8, 0x41eb, 0x4380, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_143 {u : ℚ} (hlo : 0xd80 ≤ u) (hhi : u < 0xe00) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_36 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 8, 0x4380, 0x4600, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_144 {u : ℚ} (hlo : 0xe00 ≤ u) (hhi : u < 0xe10) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_40 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 8, 0x4600, 0x4650, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_145 {u : ℚ} (hlo : 0xe10 ≤ u) (hhi : u < (0x4ce3 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 8, 0x4650, 0x4ce3, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_146 {u : ℚ} (hlo : (0x4ce3 / 5) ≤ u) (hhi : u < (0x8c00 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_37 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 9, 0x4ce3, 0x4dc8, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_147 {u : ℚ} (hlo : (0x8c00 / 9) ≤ u) (hhi : u < 0xfa0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_41 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 9, 0x4dc7, 0x4e20, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_148 {u : ℚ} (hlo : 0xfa0 ≤ u) (hhi : u < 0xfd2) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_42 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 9, 0x4e20, 0x4f1a, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_149 {u : ℚ} (hlo : 0xfd2 ≤ u) (hhi : u < 0x1000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_54 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_43 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨11, 7, 13, 13, 7, 9, 0x4f1a, 0x5000, false⟩ hlo hhi hp h5 h7
    baseLower_1_13 baseLower_1_14
  all_goals decide +kernel


def baseInterval_1_150 {u : ℚ} (hlo : 0x1000 ≤ u) (hhi : u < 0x10e0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_43 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x5000, 0x5460, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_151 {u : ℚ} (hlo : 0x10e0 ≤ u) (hhi : u < 0x1116) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x5460, 0x556e, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_152 {u : ℚ} (hlo : 0x1116 ≤ u) (hhi : u < 0x1180) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_38 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x556e, 0x5780, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_153 {u : ℚ} (hlo : 0x1180 ≤ u) (hhi : u < (0xa000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_55 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x5780, 0x58e4, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_154 {u : ℚ} (hlo : (0xa000 / 9) ≤ u) (hhi : u < 0x1275) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_39 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x58e3, 0x5c49, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_155 {u : ℚ} (hlo : 0x1275 ≤ u) (hhi : u < 0x13b0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_40 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x5c49, 0x6270, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_156 {u : ℚ} (hlo : 0x13b0 ≤ u) (hhi : u < 0x1400) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_56 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_44 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_41 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6270, 0x6400, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_157 {u : ℚ} (hlo : 0x1400 ≤ u) (hhi : u < (0x6684 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_57 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_41 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6400, 0x6684, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_158 {u : ℚ} (hlo : (0x6684 / 5) ≤ u) (hhi : u < (0x23000 / 27)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_57 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_41 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6684, 0x67b5, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_159 {u : ℚ} (hlo : (0x23000 / 27) ≤ u) (hhi : u < 0x15e0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_58 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_41 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x67b4, 0x6d60, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_160 {u : ℚ} (hlo : 0x15e0 ≤ u) (hhi : u < 0x1626) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_42 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6d60, 0x6ebe, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_161 {u : ℚ} (hlo : 0x1626 ≤ u) (hhi : u < (0xc800 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_45 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_43 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6ebe, 0x6f1d, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_162 {u : ℚ} (hlo : (0xc800 / 9) ≤ u) (hhi : u < 0x17a0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_46 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_43 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x6f1c, 0x7620, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_163 {u : ℚ} (hlo : 0x17a0 ≤ u) (hhi : u < 0x1900) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_46 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x7620, 0x7d00, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_164 {u : ℚ} (hlo : 0x1900 ≤ u) (hhi : u < 0x19a1) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_59 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_47 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 7, 14, 14, 7, 9, 0x7d00, 0x8025, false⟩ hlo hhi hp h5 h7
    baseLower_0_14 baseLower_0_15
  all_goals decide +kernel


def baseInterval_1_165 {u : ℚ} (hlo : 0x19a1 ≤ u) (hhi : u < (0x5000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_47 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 7, 9, 0x8025, 0x8556, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_1_166 {u : ℚ} (hlo : (0x5000 / 3) ≤ u) (hhi : u < 0x1c00) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_44 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 7, 9, 0x8555, 0x8c00, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_1_167 {u : ℚ} (hlo : 0x1c00 ≤ u) (hhi : u < (0x11800 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_45 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 7, 9, 0x8c00, 0x9b8f, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_1_168 {u : ℚ} (hlo : (0x11800 / 9) ≤ u) (hhi : u < 0x2000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_60 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_46 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨12, 8, 15, 15, 7, 9, 0x9b8e, 0xa000, false⟩ hlo hhi hp h5 h7
    baseLower_0_15 baseLower_0_16
  all_goals decide +kernel


def baseInterval_1_169 {u : ℚ} (hlo : 0x2000 ≤ u) (hhi : u < 0x2300) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_46 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xa000, 0xaf00, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_170 {u : ℚ} (hlo : 0x2300 ≤ u) (hhi : u < (0x14000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_61 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_47 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xaf00, 0xb1c8, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_171 {u : ℚ} (hlo : (0x14000 / 9) ≤ u) (hhi : u < (0x7000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_62 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_47 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xb1c7, 0xbaab, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_172 {u : ℚ} (hlo : (0x7000 / 3) ≤ u) (hhi : u < 0x2800) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_62 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_48 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xbaaa, 0xc800, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_173 {u : ℚ} (hlo : 0x2800 ≤ u) (hhi : u < (0x8000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_63 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_49 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xc800, 0xd556, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_174 {u : ℚ} (hlo : (0x8000 / 3) ≤ u) (hhi : u < (0x19000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_49 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xd555, 0xde39, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_175 {u : ℚ} (hlo : (0x19000 / 9) ≤ u) (hhi : u < (0xe6a9 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_50 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 9, 0xde38, 0xe6a9, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_176 {u : ℚ} (hlo : (0xe6a9 / 5) ≤ u) (hhi : u < 0x3200) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_50 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 10, 0xe6a9, 0xfa00, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_177 {u : ℚ} (hlo : 0x3200 ≤ u) (hhi : u < (0x10000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 7, 10, 0xfa00, 0x10000, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_178 {u : ℚ} (hlo : (0x10000 / 5) ≤ u) (hhi : u < 0x3342) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 15, 15, 8, 10, 0x10000, 0x1004a, false⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_179 {u : ℚ} (hlo : 0x3342 ≤ u) (hhi : u < (0xa000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_51 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 15, 8, 10, 0x1004a, 0x10aab, true⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_180 {u : ℚ} (hlo : (0xa000 / 3) ≤ u) (hhi : u < 0x3800) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_48 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 15, 8, 10, 0x10aaa, 0x11800, true⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_181 {u : ℚ} (hlo : 0x3800 ≤ u) (hhi : u < (0x1338c / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_64 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 15, 8, 10, 0x11800, 0x1338c, true⟩ hlo hhi hp h5 h7
    baseLower_1_15 baseLower_1_16
  all_goals decide +kernel


def baseInterval_1_182 {u : ℚ} (hlo : (0x1338c / 5) ≤ u) (hhi : u < (0x23000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_49 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 8, 10, 0x1338c, 0x1371d, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_1_183 {u : ℚ} (hlo : (0x23000 / 9) ≤ u) (hhi : u < 0x4000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_65 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨13, 8, 16, 16, 8, 10, 0x1371c, 0x14000, false⟩ hlo hhi hp h5 h7
    baseLower_1_16 baseLower_1_17
  all_goals decide +kernel


def baseInterval_1_184 {u : ℚ} (hlo : 0x4000 ≤ u) (hhi : u < 0x41eb) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_52 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x14000, 0x14997, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_185 {u : ℚ} (hlo : 0x41eb ≤ u) (hhi : u < 0x4380) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_53 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x14997, 0x15180, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_186 {u : ℚ} (hlo : 0x4380 ≤ u) (hhi : u < 0x4600) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_50 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x15180, 0x15e00, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_187 {u : ℚ} (hlo : 0x4600 ≤ u) (hhi : u < (0x28000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_66 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x15e00, 0x1638f, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_188 {u : ℚ} (hlo : (0x28000 / 9) ≤ u) (hhi : u < (0xe000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_51 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x1638e, 0x17556, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_189 {u : ℚ} (hlo : (0xe000 / 3) ≤ u) (hhi : u < 0x4ce3) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_67 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 8, 16, 16, 8, 10, 0x17555, 0x1806f, false⟩ hlo hhi hp h5 h7
    baseLower_0_16 baseLower_0_17
  all_goals decide +kernel


def baseInterval_1_190 {u : ℚ} (hlo : 0x4ce3 ≤ u) (hhi : u < 0x5000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_54 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x1806f, 0x19000, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_191 {u : ℚ} (hlo : 0x5000 ≤ u) (hhi : u < (0x32000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_55 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x19000, 0x1bc72, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_192 {u : ℚ} (hlo : (0x32000 / 9) ≤ u) (hhi : u < 0x5c49) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_52 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x1bc71, 0x1cd6d, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_193 {u : ℚ} (hlo : 0x5c49 ≤ u) (hhi : u < 0x5e80) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_53 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x1cd6d, 0x1d880, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_194 {u : ℚ} (hlo : 0x5e80 ≤ u) (hhi : u < 0x6400) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_56 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x1d880, 0x1f400, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_195 {u : ℚ} (hlo : 0x6400 ≤ u) (hhi : u < 0x6684) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_68 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_57 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x1f400, 0x20094, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_196 {u : ℚ} (hlo : 0x6684 ≤ u) (hhi : u < (0xaf000 / 27)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_57 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x20094, 0x20685, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_197 {u : ℚ} (hlo : (0xaf000 / 27) ≤ u) (hhi : u < 0x6d60) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_58 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x20684, 0x222e0, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_198 {u : ℚ} (hlo : 0x6d60 ≤ u) (hhi : u < 0x7000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_54 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x222e0, 0x23000, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_199 {u : ℚ} (hlo : 0x7000 ≤ u) (hhi : u < (0x46000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_55 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x23000, 0x26e39, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_200 {u : ℚ} (hlo : (0x46000 / 9) ≤ u) (hhi : u < 0x8000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_69 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨14, 9, 17, 17, 8, 10, 0x26e38, 0x28000, false⟩ hlo hhi hp h5 h7
    baseLower_0_17 baseLower_0_18
  all_goals decide +kernel


def baseInterval_1_201 {u : ℚ} (hlo : 0x8000 ≤ u) (hhi : u < 0x8025) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_70 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_59 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 17, 17, 8, 10, 0x28000, 0x280b9, false⟩ hlo hhi hp h5 h7
    baseLower_1_17 baseLower_1_18
  all_goals decide +kernel


def baseInterval_1_202 {u : ℚ} (hlo : 0x8025 ≤ u) (hhi : u < 0x88b0) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_71 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 10 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x280b9 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2ab70 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = 0 * u + 0x6684 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inr (Or.inr (Or.inl (by norm_num <;> ring)))
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_203 {u : ℚ} (hlo : 0x88b0 ≤ u) (hhi : u < (0x2b3fb / 5)) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 10 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2ab70 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2b3fb := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_204 {u : ℚ} (hlo : (0x2b3fb / 5) ≤ u) (hhi : u < 0x8c00) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_56 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 11 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2b3fb ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2bc00 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (9 / 10) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_205 {u : ℚ} (hlo : 0x8c00 ≤ u) (hhi : u < (0xf5000 / 27)) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_57 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 11 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2bc00 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2d5ee := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, 0 * (u / 7) + 0x1000)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_206 {u : ℚ} (hlo : (0xf5000 / 27) ≤ u) (hhi : u < 0x9920) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_58 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 11 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2d5ed ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x2fda0 := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (27 / 35) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_207 {u : ℚ} (hlo : 0x9920 ≤ u) (hhi : u < 0x99c6) :
    baseStepValid true u := by
  have hu : 1 ≤ u := by linarith
  have hp := baseTable_eval_1_72 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_59 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  have hl2 : Nat.log 2 ⌊u⌋₊ = 15 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hl3 : Nat.log 3 ⌊u⌋₊ = 9 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hpreferred : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by rw [hl2]
  have hrank : smoothRankBound ⌊u⌋₊ = 17 := by
    rw [smoothRank_floor_of_indices hu hl2 hl3]
    have hd : ¬(0x99c6 : ℚ) ≤ u := by linarith
    norm_num [hd]
  have hb4 : Nat.log 4 ⌊5 * u⌋₊ = 8 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hb3 : Nat.log 3 ⌊5 * u⌋₊ = 11 := log_floor_of_bounds (by linarith)
    (by norm_num <;> linarith) (by norm_num <;> linarith)
  have hfl : 0x2fda0 ≤ ⌊5 * u⌋₊ := (Nat.le_floor_iff (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hfh : ⌊5 * u⌋₊ < 0x300de := (Nat.floor_lt (by linarith : 0 ≤ 5 * u)).mpr (by norm_num <;> linarith)
  have hbad : ¬badWindow ⌊5 * u⌋₊ := by
    rw [badWindow_iff_canonical, hb4, hb3]
    norm_num
    omega
  have hquota : quotaValue true u = 17 := by
    simp [quotaValue, hrank, hbad]
  have ht : cutoffTrial u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) = (3 / 4) * u + 0 := by
    apply cutoffTrial_eq_of_bounds
    · linarith
    · rw [baseLower_0_17] <;> norm_num <;> linarith
    · norm_num <;> linarith
    · norm_num <;> linarith
    · exact Or.inl (by norm_num <;> ring)
  have hav : cutoffAvailable u 17 0 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) := by
    unfold cutoffAvailable
    rw [ht, baseLower_0_18]
    constructor <;> norm_num <;> linarith
  have hnot : ¬cutoffAvailable u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0) := by
    intro hv
    obtain ⟨hb, hl, hc5, hc7⟩ := cutoffTrial_bounds u 17 1 (0, 0 * (u / 5) + 0x19a1) (0, (3 / 4) * (u / 7) + 0)
    rw [baseLower_1_17] at hl
    unfold cutoffAvailable at hv
    rw [baseLower_1_18] at hv
    norm_num at hl hc5 hc7 hv
    linarith only [hlo, hhi, hb, hl, hc5, hc7, hv.1, hv.2]
  unfold baseStepValid
  rw [hp, h5, h7]
  constructor
  · rw [cutoffCandidate_eq_alternate hquota hpreferred hnot]
    norm_num only [Nat.reduceSub]
    rw [ht]
  · simpa only [hquota] using hav


def baseInterval_1_208 {u : ℚ} (hlo : 0x99c6 ≤ u) (hhi : u < 0xa000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_60 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_59 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x300de, 0x32000, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_209 {u : ℚ} (hlo : 0xa000 ≤ u) (hhi : u < (0x64000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_61 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_59 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x32000, 0x378e4, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_210 {u : ℚ} (hlo : (0x64000 / 9) ≤ u) (hhi : u < 0xb367) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_59 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x378e3, 0x38103, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_211 {u : ℚ} (hlo : 0xb367 ≤ u) (hhi : u < (0x39aa4 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x38103, 0x39aa4, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_212 {u : ℚ} (hlo : (0x39aa4 / 5) ≤ u) (hhi : u < 0xc800) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_62 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x39aa4, 0x3e800, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_213 {u : ℚ} (hlo : 0xc800 ≤ u) (hhi : u < (0x40000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 8, 11, 0x3e800, 0x40000, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_214 {u : ℚ} (hlo : (0x40000 / 5) ≤ u) (hhi : u < 0xcd08) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_73 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 9, 11, 0x40000, 0x40128, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_215 {u : ℚ} (hlo : 0xcd08 ≤ u) (hhi : u < (0x28000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_63 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 9, 11, 0x40128, 0x42aab, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_216 {u : ℚ} (hlo : (0x28000 / 3) ≤ u) (hhi : u < 0xe000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_60 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 9, 11, 0x42aaa, 0x46000, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_217 {u : ℚ} (hlo : 0xe000 ≤ u) (hhi : u < 0xe6a9) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 9, 18, 18, 9, 11, 0x46000, 0x4814d, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_218 {u : ℚ} (hlo : 0xe6a9 ≤ u) (hhi : u < (0x8c000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_61 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 10, 18, 18, 9, 11, 0x4814d, 0x4dc72, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_219 {u : ℚ} (hlo : (0x8c000 / 9) ≤ u) (hhi : u < 0x10000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_74 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_62 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨15, 10, 18, 18, 9, 11, 0x4dc71, 0x50000, false⟩ hlo hhi hp h5 h7
    baseLower_1_18 baseLower_1_19
  all_goals decide +kernel


def baseInterval_1_220 {u : ℚ} (hlo : 0x10000 ≤ u) (hhi : u < 0x11800) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_62 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x50000, 0x57800, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_221 {u : ℚ} (hlo : 0x11800 ≤ u) (hhi : u < (0xa0000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_75 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_63 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x57800, 0x58e39, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_222 {u : ℚ} (hlo : (0xa0000 / 9) ≤ u) (hhi : u < (0x38000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_76 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_63 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x58e38, 0x5d556, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_223 {u : ℚ} (hlo : (0x38000 / 3) ≤ u) (hhi : u < 0x1338c) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_76 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_64 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x5d555, 0x601bc, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_224 {u : ℚ} (hlo : 0x1338c ≤ u) (hhi : u < 0x14000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_77 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_65 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x601bc, 0x64000, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_225 {u : ℚ} (hlo : 0x14000 ≤ u) (hhi : u < (0x40000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_78 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_66 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x64000, 0x6aaab, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_226 {u : ℚ} (hlo : (0x40000 / 3) ≤ u) (hhi : u < (0xc8000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_79 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_66 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x6aaaa, 0x6f1c8, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_227 {u : ℚ} (hlo : (0xc8000 / 9) ≤ u) (hhi : u < 0x1806f) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_79 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_67 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x6f1c7, 0x7822b, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_228 {u : ℚ} (hlo : 0x1806f ≤ u) (hhi : u < 0x19a10) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_80 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x7822b, 0x80250, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_229 {u : ℚ} (hlo : 0x19a10 ≤ u) (hhi : u < (0x81bf1 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 11, 0x80250, 0x81bf1, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_230 {u : ℚ} (hlo : (0x81bf1 / 5) ≤ u) (hhi : u < (0x868d4 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_64 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 12, 0x81bf1, 0x868d4, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_231 {u : ℚ} (hlo : (0x868d4 / 5) ≤ u) (hhi : u < 0x1c000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_65 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 12, 0x868d4, 0x8c000, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_232 {u : ℚ} (hlo : 0x1c000 ≤ u) (hhi : u < 0x1cd52) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 12, 0x8c000, 0x9029a, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_233 {u : ℚ} (hlo : 0x1cd52 ≤ u) (hhi : u < (0x118000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_66 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 12, 0x9029a, 0x9b8e4, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_234 {u : ℚ} (hlo : (0x118000 / 9) ≤ u) (hhi : u < 0x20000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_81 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_67 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨16, 10, 19, 19, 9, 12, 0x9b8e3, 0xa0000, false⟩ hlo hhi hp h5 h7
    baseLower_0_19 baseLower_0_20
  all_goals decide +kernel


def baseInterval_1_235 {u : ℚ} (hlo : 0x20000 ≤ u) (hhi : u < 0x20094) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_68 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_67 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xa0000, 0xa02e4, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_236 {u : ℚ} (hlo : 0x20094 ≤ u) (hhi : u < 0x21a35) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_67 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xa02e4, 0xa8309, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_237 {u : ℚ} (hlo : 0x21a35 ≤ u) (hhi : u < (0xacfec / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xa8309, 0xacfec, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_238 {u : ℚ} (hlo : (0xacfec / 5) ≤ u) (hhi : u < (0x140000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_82 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xacfec, 0xb1c72, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_239 {u : ℚ} (hlo : (0x140000 / 9) ≤ u) (hhi : u < 0x28000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_83 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_69 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xb1c71, 0xc8000, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_240 {u : ℚ} (hlo : 0x28000 ≤ u) (hhi : u < 0x280b9) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_84 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_70 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xc8000, 0xc839d, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_241 {u : ℚ} (hlo : 0x280b9 ≤ u) (hhi : u < 0x2ab70) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_85 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_71 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xc839d, 0xd5930, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_242 {u : ℚ} (hlo : 0x2ab70 ≤ u) (hhi : u < 0x2b3fb) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_86 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 10, 20, 20, 9, 12, 0xd5930, 0xd83e7, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_243 {u : ℚ} (hlo : 0x2b3fb ≤ u) (hhi : u < 0x2cd9c) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_86 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_68 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 9, 12, 0xd83e7, 0xe040c, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_244 {u : ℚ} (hlo : 0x2cd9c ≤ u) (hhi : u < 0x300de) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_86 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_72 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 9, 12, 0xe040c, 0xf0456, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_245 {u : ℚ} (hlo : 0x300de ≤ u) (hhi : u < (0x100000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_87 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 9, 12, 0xf0456, 0x100000, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_246 {u : ℚ} (hlo : (0x100000 / 5) ≤ u) (hhi : u < 0x33420) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_87 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 10, 12, 0x100000, 0x1004a0, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_247 {u : ℚ} (hlo : 0x33420 ≤ u) (hhi : u < 0x38000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_69 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 10, 12, 0x1004a0, 0x118000, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_248 {u : ℚ} (hlo : 0x38000 ≤ u) (hhi : u < 0x38103) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_70 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 10, 12, 0x118000, 0x11850f, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_249 {u : ℚ} (hlo : 0x38103 ≤ u) (hhi : u < 0x3bcd0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_71 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 10, 12, 0x11850f, 0x12b010, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_250 {u : ℚ} (hlo : 0x3bcd0 ≤ u) (hhi : u < 0x40000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_88 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_72 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨17, 11, 20, 20, 10, 12, 0x12b010, 0x140000, false⟩ hlo hhi hp h5 h7
    baseLower_1_20 baseLower_1_21
  all_goals decide +kernel


def baseInterval_1_251 {u : ℚ} (hlo : 0x40000 ≤ u) (hhi : u < 0x40128) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_73 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_72 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 12, 0x140000, 0x1405c8, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_252 {u : ℚ} (hlo : 0x40128 ≤ u) (hhi : u < 0x4346a) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_72 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 12, 0x1405c8, 0x150612, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_253 {u : ℚ} (hlo : 0x4346a ≤ u) (hhi : u < (0x280000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_89 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 12, 0x150612, 0x1638e4, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_254 {u : ℚ} (hlo : (0x280000 / 9) ≤ u) (hhi : u < (0x1853d3 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_90 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 12, 0x1638e3, 0x1853d3, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_255 {u : ℚ} (hlo : (0x1853d3 / 5) ≤ u) (hhi : u < 0x50000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_90 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_74 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1853d3, 0x190000, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_256 {u : ℚ} (hlo : 0x50000 ≤ u) (hhi : u < (0x100000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_91 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x190000, 0x1aaaab, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_257 {u : ℚ} (hlo : (0x100000 / 3) ≤ u) (hhi : u < 0x567f6) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_92 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1aaaaa, 0x1b07ce, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_258 {u : ℚ} (hlo : 0x567f6 ≤ u) (hhi : u < (0x320000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_92 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_75 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1b07ce, 0x1bc71d, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_259 {u : ℚ} (hlo : (0x320000 / 9) ≤ u) (hhi : u < 0x59b38) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_92 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_76 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_73 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1bc71c, 0x1c0818, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_260 {u : ℚ} (hlo : 0x59b38 ≤ u) (hhi : u < 0x601bc) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_92 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_76 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1c0818, 0x1e08ac, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_261 {u : ℚ} (hlo : 0x601bc ≤ u) (hhi : u < 0x64000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_93 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_77 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1e08ac, 0x1f4000, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_262 {u : ℚ} (hlo : 0x64000 ≤ u) (hhi : u < (0x206fc4 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_78 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x1f4000, 0x206fc4, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_263 {u : ℚ} (hlo : (0x206fc4 / 5) ≤ u) (hhi : u < (0x140000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_78 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x206fc4, 0x215556, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_264 {u : ℚ} (hlo : (0x140000 / 3) ≤ u) (hhi : u < 0x70000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_79 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_74 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x215555, 0x230000, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_265 {u : ℚ} (hlo : 0x70000 ≤ u) (hhi : u < 0x7822b) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_79 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x230000, 0x258ad7, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_266 {u : ℚ} (hlo : 0x7822b ≤ u) (hhi : u < (0x460000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_75 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x258ad7, 0x26e38f, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_267 {u : ℚ} (hlo : (0x460000 / 9) ≤ u) (hhi : u < 0x80000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_94 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨18, 11, 21, 21, 10, 13, 0x26e38e, 0x280000, false⟩ hlo hhi hp h5 h7
    baseLower_0_21 baseLower_0_22
  all_goals decide +kernel


def baseInterval_1_268 {u : ℚ} (hlo : 0x80000 ≤ u) (hhi : u < 0x80250) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_80 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 11, 22, 22, 10, 13, 0x280000, 0x280b90, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_269 {u : ℚ} (hlo : 0x80250 ≤ u) (hhi : u < 0x81bf1) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 11, 22, 22, 10, 13, 0x280b90, 0x288bb5, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_270 {u : ℚ} (hlo : 0x81bf1 ≤ u) (hhi : u < 0x868d4) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_76 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x288bb5, 0x2a0c24, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_271 {u : ℚ} (hlo : 0x868d4 ≤ u) (hhi : u < 0x8c000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_77 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x2a0c24, 0x2bc000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_272 {u : ℚ} (hlo : 0x8c000 ≤ u) (hhi : u < (0x500000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_95 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_78 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x2bc000, 0x2c71c8, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_273 {u : ℚ} (hlo : (0x500000 / 9) ≤ u) (hhi : u < (0x1c0000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_78 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x2c71c7, 0x2eaaab, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_274 {u : ℚ} (hlo : (0x1c0000 / 3) ≤ u) (hhi : u < 0xa0000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_96 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_81 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_79 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x2eaaaa, 0x320000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_275 {u : ℚ} (hlo : 0xa0000 ≤ u) (hhi : u < 0xa8309) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_97 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_82 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_79 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x320000, 0x348f2d, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_276 {u : ℚ} (hlo : 0xa8309 ≤ u) (hhi : u < (0x200000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_97 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_82 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_80 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x348f2d, 0x355556, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_277 {u : ℚ} (hlo : (0x200000 / 3) ≤ u) (hhi : u < (0x640000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_98 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_82 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_80 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x355555, 0x378e39, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_278 {u : ℚ} (hlo : (0x640000 / 9) ≤ u) (hhi : u < 0xb3670) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_98 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_83 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_80 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x378e38, 0x381030, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_279 {u : ℚ} (hlo : 0xb3670 ≤ u) (hhi : u < 0xc8000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_98 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_83 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x381030, 0x3e8000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_280 {u : ℚ} (hlo : 0xc8000 ≤ u) (hhi : u < 0xc839d) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_98 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_84 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x3e8000, 0x3e9211, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_281 {u : ℚ} (hlo : 0xc839d ≤ u) (hhi : u < (0x400000 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 10, 13, 0x3e9211, 0x400000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_282 {u : ℚ} (hlo : (0x400000 / 5) ≤ u) (hhi : u < 0xcd080) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_99 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 13, 0x400000, 0x401280, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_283 {u : ℚ} (hlo : 0xcd080 ≤ u) (hhi : u < 0xd5930) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_85 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 13, 0x401280, 0x42bdf0, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_284 {u : ℚ} (hlo : 0xd5930 ≤ u) (hhi : u < 0xe0000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_81 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 13, 0x42bdf0, 0x460000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_285 {u : ℚ} (hlo : 0xe0000 ≤ u) (hhi : u < (0x48fb79 / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 13, 0x460000, 0x48fb79, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_286 {u : ℚ} (hlo : (0x48fb79 / 5) ≤ u) (hhi : u < 0xf0456) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_86 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 14, 0x48fb79, 0x4b15ae, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_287 {u : ℚ} (hlo : 0xf0456 ≤ u) (hhi : u < (0x8c0000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_82 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 14, 0x4b15ae, 0x4dc71d, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_288 {u : ℚ} (hlo : (0x8c0000 / 9) ≤ u) (hhi : u < 0x100000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_100 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨19, 12, 22, 22, 11, 14, 0x4dc71c, 0x500000, false⟩ hlo hhi hp h5 h7
    baseLower_1_22 baseLower_1_23
  all_goals decide +kernel


def baseInterval_1_289 {u : ℚ} (hlo : 0x100000 ≤ u) (hhi : u < 0x1004a0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_87 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x500000, 0x501720, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_290 {u : ℚ} (hlo : 0x1004a0 ≤ u) (hhi : u < 0x1037e2) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x501720, 0x51176a, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_291 {u : ℚ} (hlo : 0x1037e2 ≤ u) (hhi : u < 0x118000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_83 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x51176a, 0x578000, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_292 {u : ℚ} (hlo : 0x118000 ≤ u) (hhi : u < 0x11850f) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_84 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x578000, 0x57994b, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_293 {u : ℚ} (hlo : 0x11850f ≤ u) (hhi : u < (0xa00000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_101 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_85 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x57994b, 0x58e38f, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_294 {u : ℚ} (hlo : (0xa00000 / 9) ≤ u) (hhi : u < 0x12b010) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_85 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x58e38e, 0x5d7050, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_295 {u : ℚ} (hlo : 0x12b010 ≤ u) (hhi : u < (0x614f4c / 5)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x5d7050, 0x614f4c, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_296 {u : ℚ} (hlo : (0x614f4c / 5) ≤ u) (hhi : u < 0x140000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_102 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_88 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x614f4c, 0x640000, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_297 {u : ℚ} (hlo : 0x140000 ≤ u) (hhi : u < (0x2300000 / 27)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_103 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x640000, 0x67b426, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_298 {u : ℚ} (hlo : (0x2300000 / 27) ≤ u) (hhi : u < 0x150612) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_104 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_86 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x67b425, 0x691e5a, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_299 {u : ℚ} (hlo : 0x150612 ≤ u) (hhi : u < (0x400000 / 3)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_105 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x691e5a, 0x6aaaab, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_300 {u : ℚ} (hlo : (0x400000 / 3) ≤ u) (hhi : u < (0xc80000 / 9)) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_106 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_89 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x6aaaaa, 0x6f1c72, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_301 {u : ℚ} (hlo : (0xc80000 / 9) ≤ u) (hhi : u < 0x166ce0) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_106 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_87 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x6f1c71, 0x702060, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_302 {u : ℚ} (hlo : 0x166ce0 ≤ u) (hhi : u < 0x1853d3) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_106 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 12, 23, 23, 11, 14, 0x702060, 0x79a31f, false⟩ hlo hhi hp h5 h7
    baseLower_0_23 baseLower_0_24
  all_goals decide +kernel


def baseInterval_1_303 {u : ℚ} (hlo : 0x1853d3 ≤ u) (hhi : u < 0x190000) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_107 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_90 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 13, 24, 24, 11, 14, 0x79a31f, 0x7d0000, false⟩ hlo hhi hp h5 h7
    baseLower_0_24 baseLower_0_25
  all_goals decide +kernel


def baseInterval_1_304 {u : ℚ} (hlo : 0x190000 ≤ u) (hhi : u < 0x1921ee) :
    baseStepValid true u := by
  have hp := baseTable_eval_1_107 (u := u) (baseIvlLo (by decide +kernel) hlo) (baseIvlHi (by decide +kernel) hhi)
  have h5 := baseTable_eval_1_91 (u := u / 5) (baseIvlLo5 (by decide +kernel) hlo) (baseIvlHi5 (by decide +kernel) hhi)
  have h7 := baseTable_eval_1_88 (u := u / 7) (baseIvlLo7 (by decide +kernel) hlo) (baseIvlHi7 (by decide +kernel) hhi)
  apply compactBaseInterval_preferred ⟨20, 13, 24, 24, 11, 14, 0x7d0000, 0x7da9a6, false⟩ hlo hhi hp h5 h7
    baseLower_0_24 baseLower_0_25
  all_goals decide +kernel


def baseStepValid_0_below_limit {u : ℚ} (hlo : 1 ≤ u) (hhi : u < 0x1921ee) :
    baseStepValid false u := by
  by_cases hcut153 : u < 0x1116
  · by_cases hcut76 : u < 0xd8
    · by_cases hcut38 : u < (0x70 / 3)
      · by_cases hcut19 : u < (28 / 3)
        · by_cases hcut9 : u < 5
          · by_cases hcut4 : u < (12 / 5)
            · by_cases hcut2 : u < (9 / 5)
              · by_cases hcut1 : u < (4 / 3)
                · exact baseInterval_0_0 hlo hcut1
                · exact baseInterval_0_1 (le_of_not_gt hcut1) hcut2
              · by_cases hcut3 : u < 2
                · exact baseInterval_0_2 (le_of_not_gt hcut2) hcut3
                · exact baseInterval_0_3 (le_of_not_gt hcut3) hcut4
            · by_cases hcut6 : u < 3
              · by_cases hcut5 : u < (8 / 3)
                · exact baseInterval_0_4 (le_of_not_gt hcut4) hcut5
                · exact baseInterval_0_5 (le_of_not_gt hcut5) hcut6
              · by_cases hcut7 : u < (16 / 5)
                · exact baseInterval_0_6 (le_of_not_gt hcut6) hcut7
                · by_cases hcut8 : u < 4
                  · exact baseInterval_0_7 (le_of_not_gt hcut7) hcut8
                  · exact baseInterval_0_8 (le_of_not_gt hcut8) hcut9
          · by_cases hcut14 : u < 7
            · by_cases hcut11 : u < (27 / 5)
              · by_cases hcut10 : u < (16 / 3)
                · exact baseInterval_0_9 (le_of_not_gt hcut9) hcut10
                · exact baseInterval_0_10 (le_of_not_gt hcut10) hcut11
              · by_cases hcut12 : u < 6
                · exact baseInterval_0_11 (le_of_not_gt hcut11) hcut12
                · by_cases hcut13 : u < (20 / 3)
                  · exact baseInterval_0_12 (le_of_not_gt hcut12) hcut13
                  · exact baseInterval_0_13 (le_of_not_gt hcut13) hcut14
            · by_cases hcut16 : u < 8
              · by_cases hcut15 : u < (36 / 5)
                · exact baseInterval_0_14 (le_of_not_gt hcut14) hcut15
                · exact baseInterval_0_15 (le_of_not_gt hcut15) hcut16
              · by_cases hcut17 : u < (80 / 9)
                · exact baseInterval_0_16 (le_of_not_gt hcut16) hcut17
                · by_cases hcut18 : u < 9
                  · exact baseInterval_0_17 (le_of_not_gt hcut17) hcut18
                  · exact baseInterval_0_18 (le_of_not_gt hcut18) hcut19
        · by_cases hcut28 : u < 18
          · by_cases hcut23 : u < (40 / 3)
            · by_cases hcut21 : u < (32 / 3)
              · by_cases hcut20 : u < 10
                · exact baseInterval_0_19 (le_of_not_gt hcut19) hcut20
                · exact baseInterval_0_20 (le_of_not_gt hcut20) hcut21
              · by_cases hcut22 : u < (64 / 5)
                · exact baseInterval_0_21 (le_of_not_gt hcut21) hcut22
                · exact baseInterval_0_22 (le_of_not_gt hcut22) hcut23
            · by_cases hcut25 : u < 16
              · by_cases hcut24 : u < 14
                · exact baseInterval_0_23 (le_of_not_gt hcut23) hcut24
                · exact baseInterval_0_24 (le_of_not_gt hcut24) hcut25
              · by_cases hcut26 : u < (81 / 5)
                · exact baseInterval_0_25 (le_of_not_gt hcut25) hcut26
                · by_cases hcut27 : u < (0xa0 / 9)
                  · exact baseInterval_0_26 (le_of_not_gt hcut26) hcut27
                  · exact baseInterval_0_27 (le_of_not_gt hcut27) hcut28
          · by_cases hcut33 : u < (80 / 3)
            · by_cases hcut30 : u < 20
              · by_cases hcut29 : u < (56 / 3)
                · exact baseInterval_0_28 (le_of_not_gt hcut28) hcut29
                · exact baseInterval_0_29 (le_of_not_gt hcut29) hcut30
              · by_cases hcut31 : u < (64 / 3)
                · exact baseInterval_0_30 (le_of_not_gt hcut30) hcut31
                · by_cases hcut32 : u < (0x6c / 5)
                  · exact baseInterval_0_31 (le_of_not_gt hcut31) hcut32
                  · exact baseInterval_0_32 (le_of_not_gt hcut32) hcut33
            · by_cases hcut35 : u < 28
              · by_cases hcut34 : u < 27
                · exact baseInterval_0_33 (le_of_not_gt hcut33) hcut34
                · exact baseInterval_0_34 (le_of_not_gt hcut34) hcut35
              · by_cases hcut36 : u < 32
                · exact baseInterval_0_35 (le_of_not_gt hcut35) hcut36
                · by_cases hcut37 : u < (0x140 / 9)
                  · exact baseInterval_0_36 (le_of_not_gt hcut36) hcut37
                  · exact baseInterval_0_37 (le_of_not_gt hcut37) hcut38
      · by_cases hcut57 : u < 0x64
        · by_cases hcut47 : u < 56
          · by_cases hcut42 : u < (0xf3 / 5)
            · by_cases hcut40 : u < (0x80 / 3)
              · by_cases hcut39 : u < 40
                · exact baseInterval_0_38 (le_of_not_gt hcut38) hcut39
                · exact baseInterval_0_39 (le_of_not_gt hcut39) hcut40
              · by_cases hcut41 : u < (0x190 / 9)
                · exact baseInterval_0_40 (le_of_not_gt hcut40) hcut41
                · exact baseInterval_0_41 (le_of_not_gt hcut41) hcut42
            · by_cases hcut44 : u < (0x100 / 5)
              · by_cases hcut43 : u < 50
                · exact baseInterval_0_42 (le_of_not_gt hcut42) hcut43
                · exact baseInterval_0_43 (le_of_not_gt hcut43) hcut44
              · by_cases hcut45 : u < (0xa0 / 3)
                · exact baseInterval_0_44 (le_of_not_gt hcut44) hcut45
                · by_cases hcut46 : u < 54
                  · exact baseInterval_0_45 (le_of_not_gt hcut45) hcut46
                  · exact baseInterval_0_46 (le_of_not_gt hcut46) hcut47
          · by_cases hcut52 : u < (0x280 / 9)
            · by_cases hcut49 : u < 64
              · by_cases hcut48 : u < (0x230 / 9)
                · exact baseInterval_0_47 (le_of_not_gt hcut47) hcut48
                · exact baseInterval_0_48 (le_of_not_gt hcut48) hcut49
              · by_cases hcut50 : u < (0x144 / 5)
                · exact baseInterval_0_49 (le_of_not_gt hcut49) hcut50
                · by_cases hcut51 : u < 70
                  · exact baseInterval_0_50 (le_of_not_gt hcut50) hcut51
                  · exact baseInterval_0_51 (le_of_not_gt hcut51) hcut52
            · by_cases hcut54 : u < 80
              · by_cases hcut53 : u < (0xe0 / 3)
                · exact baseInterval_0_52 (le_of_not_gt hcut52) hcut53
                · exact baseInterval_0_53 (le_of_not_gt hcut53) hcut54
              · by_cases hcut55 : u < 81
                · exact baseInterval_0_54 (le_of_not_gt hcut54) hcut55
                · by_cases hcut56 : u < (0x320 / 9)
                  · exact baseInterval_0_55 (le_of_not_gt hcut55) hcut56
                  · exact baseInterval_0_56 (le_of_not_gt hcut56) hcut57
        · by_cases hcut66 : u < (0x2d9 / 5)
          · by_cases hcut61 : u < (0x460 / 9)
            · by_cases hcut59 : u < 0x6c
              · by_cases hcut58 : u < (0x140 / 3)
                · exact baseInterval_0_57 (le_of_not_gt hcut57) hcut58
                · exact baseInterval_0_58 (le_of_not_gt hcut58) hcut59
              · by_cases hcut60 : u < 0x70
                · exact baseInterval_0_59 (le_of_not_gt hcut59) hcut60
                · exact baseInterval_0_60 (le_of_not_gt hcut60) hcut61
            · by_cases hcut63 : u < 0x87
              · by_cases hcut62 : u < 0x80
                · exact baseInterval_0_61 (le_of_not_gt hcut61) hcut62
                · exact baseInterval_0_62 (le_of_not_gt hcut62) hcut63
              · by_cases hcut64 : u < 0x8c
                · exact baseInterval_0_63 (le_of_not_gt hcut63) hcut64
                · by_cases hcut65 : u < 0x90
                  · exact baseInterval_0_64 (le_of_not_gt hcut64) hcut65
                  · exact baseInterval_0_65 (le_of_not_gt hcut65) hcut66
          · by_cases hcut71 : u < 0xbd
            · by_cases hcut68 : u < 0xa0
              · by_cases hcut67 : u < (0x1c0 / 3)
                · exact baseInterval_0_66 (le_of_not_gt hcut66) hcut67
                · exact baseInterval_0_67 (le_of_not_gt hcut67) hcut68
              · by_cases hcut69 : u < 0xa2
                · exact baseInterval_0_68 (le_of_not_gt hcut68) hcut69
                · by_cases hcut70 : u < (0x640 / 9)
                  · exact baseInterval_0_69 (le_of_not_gt hcut69) hcut70
                  · exact baseInterval_0_70 (le_of_not_gt hcut70) hcut71
            · by_cases hcut73 : u < 0xc8
              · by_cases hcut72 : u < (0x3cc / 5)
                · exact baseInterval_0_71 (le_of_not_gt hcut71) hcut72
                · exact baseInterval_0_72 (le_of_not_gt hcut72) hcut73
              · by_cases hcut74 : u < (0x400 / 5)
                · exact baseInterval_0_73 (le_of_not_gt hcut73) hcut74
                · by_cases hcut75 : u < (0x280 / 3)
                  · exact baseInterval_0_74 (le_of_not_gt hcut74) hcut75
                  · exact baseInterval_0_75 (le_of_not_gt hcut75) hcut76
    · by_cases hcut114 : u < 0x438
      · by_cases hcut95 : u < 0x200
        · by_cases hcut85 : u < (0x400 / 3)
          · by_cases hcut80 : u < 0x100
            · by_cases hcut78 : u < 0xf3
              · by_cases hcut77 : u < 0xe0
                · exact baseInterval_0_76 (le_of_not_gt hcut76) hcut77
                · exact baseInterval_0_77 (le_of_not_gt hcut77) hcut78
              · by_cases hcut79 : u < (0x8c0 / 9)
                · exact baseInterval_0_78 (le_of_not_gt hcut78) hcut79
                · exact baseInterval_0_79 (le_of_not_gt hcut79) hcut80
            · by_cases hcut82 : u < (0xa00 / 9)
              · by_cases hcut81 : u < 0x118
                · exact baseInterval_0_80 (le_of_not_gt hcut80) hcut81
                · exact baseInterval_0_81 (le_of_not_gt hcut81) hcut82
              · by_cases hcut83 : u < (0x380 / 3)
                · exact baseInterval_0_82 (le_of_not_gt hcut82) hcut83
                · by_cases hcut84 : u < 0x140
                  · exact baseInterval_0_83 (le_of_not_gt hcut83) hcut84
                  · exact baseInterval_0_84 (le_of_not_gt hcut84) hcut85
          · by_cases hcut90 : u < 0x1b0
            · by_cases hcut87 : u < 0x17a
              · by_cases hcut86 : u < (0xc80 / 9)
                · exact baseInterval_0_85 (le_of_not_gt hcut85) hcut86
                · exact baseInterval_0_86 (le_of_not_gt hcut86) hcut87
              · by_cases hcut88 : u < 0x190
                · exact baseInterval_0_87 (le_of_not_gt hcut87) hcut88
                · by_cases hcut89 : u < 0x195
                  · exact baseInterval_0_88 (le_of_not_gt hcut88) hcut89
                  · exact baseInterval_0_89 (le_of_not_gt hcut89) hcut90
            · by_cases hcut92 : u < 0x1c0
              · by_cases hcut91 : u < (0x88b / 5)
                · exact baseInterval_0_90 (le_of_not_gt hcut90) hcut91
                · exact baseInterval_0_91 (le_of_not_gt hcut91) hcut92
              · by_cases hcut93 : u < 0x1e6
                · exact baseInterval_0_92 (le_of_not_gt hcut92) hcut93
                · by_cases hcut94 : u < (0x1180 / 9)
                  · exact baseInterval_0_93 (le_of_not_gt hcut93) hcut94
                  · exact baseInterval_0_94 (le_of_not_gt hcut94) hcut95
        · by_cases hcut104 : u < 0x2d9
          · by_cases hcut99 : u < (0x1400 / 9)
            · by_cases hcut97 : u < 0x230
              · by_cases hcut96 : u < 0x21c
                · exact baseInterval_0_95 (le_of_not_gt hcut95) hcut96
                · exact baseInterval_0_96 (le_of_not_gt hcut96) hcut97
              · by_cases hcut98 : u < 0x237
                · exact baseInterval_0_97 (le_of_not_gt hcut97) hcut98
                · exact baseInterval_0_98 (le_of_not_gt hcut98) hcut99
            · by_cases hcut101 : u < 0x280
              · by_cases hcut100 : u < (0xb64 / 5)
                · exact baseInterval_0_99 (le_of_not_gt hcut99) hcut100
                · exact baseInterval_0_100 (le_of_not_gt hcut100) hcut101
              · by_cases hcut102 : u < 0x2a3
                · exact baseInterval_0_101 (le_of_not_gt hcut101) hcut102
                · by_cases hcut103 : u < 0x2d0
                  · exact baseInterval_0_102 (le_of_not_gt hcut102) hcut103
                  · exact baseInterval_0_103 (le_of_not_gt hcut103) hcut104
          · by_cases hcut109 : u < 0x360
            · by_cases hcut106 : u < 0x320
              · by_cases hcut105 : u < 0x2f4
                · exact baseInterval_0_104 (le_of_not_gt hcut104) hcut105
                · exact baseInterval_0_105 (le_of_not_gt hcut105) hcut106
              · by_cases hcut107 : u < 0x32a
                · exact baseInterval_0_106 (le_of_not_gt hcut106) hcut107
                · by_cases hcut108 : u < (0x1000 / 5)
                  · exact baseInterval_0_107 (le_of_not_gt hcut107) hcut108
                  · exact baseInterval_0_108 (le_of_not_gt hcut108) hcut109
            · by_cases hcut111 : u < 0x3b1
              · by_cases hcut110 : u < 0x380
                · exact baseInterval_0_109 (le_of_not_gt hcut109) hcut110
                · exact baseInterval_0_110 (le_of_not_gt hcut110) hcut111
              · by_cases hcut112 : u < 0x3f0
                · exact baseInterval_0_111 (le_of_not_gt hcut111) hcut112
                · by_cases hcut113 : u < 0x400
                  · exact baseInterval_0_112 (le_of_not_gt hcut112) hcut113
                  · exact baseInterval_0_113 (le_of_not_gt hcut113) hcut114
      · by_cases hcut133 : u < 0x8c0
        · by_cases hcut123 : u < 0x5e8
          · by_cases hcut118 : u < 0x500
            · by_cases hcut116 : u < 0x46e
              · by_cases hcut115 : u < 0x460
                · exact baseInterval_0_114 (le_of_not_gt hcut114) hcut115
                · exact baseInterval_0_115 (le_of_not_gt hcut115) hcut116
              · by_cases hcut117 : u < (0x2800 / 9)
                · exact baseInterval_0_116 (le_of_not_gt hcut116) hcut117
                · exact baseInterval_0_117 (le_of_not_gt hcut117) hcut118
            · by_cases hcut120 : u < (0x1000 / 3)
              · by_cases hcut119 : u < (0x19a1 / 5)
                · exact baseInterval_0_118 (le_of_not_gt hcut118) hcut119
                · exact baseInterval_0_119 (le_of_not_gt hcut119) hcut120
              · by_cases hcut121 : u < (0x3200 / 9)
                · exact baseInterval_0_120 (le_of_not_gt hcut120) hcut121
                · by_cases hcut122 : u < 0x5b2
                  · exact baseInterval_0_121 (le_of_not_gt hcut121) hcut122
                  · exact baseInterval_0_122 (le_of_not_gt hcut122) hcut123
          · by_cases hcut128 : u < (0x4600 / 9)
            · by_cases hcut125 : u < (0x1400 / 3)
              · by_cases hcut124 : u < 0x640
                · exact baseInterval_0_123 (le_of_not_gt hcut123) hcut124
                · exact baseInterval_0_124 (le_of_not_gt hcut124) hcut125
              · by_cases hcut126 : u < (0x222c / 5)
                · exact baseInterval_0_125 (le_of_not_gt hcut125) hcut126
                · by_cases hcut127 : u < 0x700
                  · exact baseInterval_0_126 (le_of_not_gt hcut126) hcut127
                  · exact baseInterval_0_127 (le_of_not_gt hcut127) hcut128
            · by_cases hcut130 : u < 0x800
              · by_cases hcut129 : u < 0x7e9
                · exact baseInterval_0_128 (le_of_not_gt hcut128) hcut129
                · exact baseInterval_0_129 (le_of_not_gt hcut129) hcut130
              · by_cases hcut131 : u < 0x870
                · exact baseInterval_0_130 (le_of_not_gt hcut130) hcut131
                · by_cases hcut132 : u < 0x88b
                  · exact baseInterval_0_131 (le_of_not_gt hcut131) hcut132
                  · exact baseInterval_0_132 (le_of_not_gt hcut132) hcut133
        · by_cases hcut143 : u < 0xd2f
          · by_cases hcut138 : u < (0x2000 / 3)
            · by_cases hcut135 : u < (0x1c00 / 3)
              · by_cases hcut134 : u < (0x5000 / 9)
                · exact baseInterval_0_133 (le_of_not_gt hcut133) hcut134
                · exact baseInterval_0_134 (le_of_not_gt hcut134) hcut135
              · by_cases hcut136 : u < 0xa00
                · exact baseInterval_0_135 (le_of_not_gt hcut135) hcut136
                · by_cases hcut137 : u < 0xa56
                  · exact baseInterval_0_136 (le_of_not_gt hcut136) hcut137
                  · exact baseInterval_0_137 (le_of_not_gt hcut137) hcut138
            · by_cases hcut140 : u < 0xbd0
              · by_cases hcut139 : u < (0x6400 / 9)
                · exact baseInterval_0_138 (le_of_not_gt hcut138) hcut139
                · exact baseInterval_0_139 (le_of_not_gt hcut139) hcut140
              · by_cases hcut141 : u < 0xc80
                · exact baseInterval_0_140 (le_of_not_gt hcut140) hcut141
                · by_cases hcut142 : u < (0x4000 / 5)
                  · exact baseInterval_0_141 (le_of_not_gt hcut141) hcut142
                  · exact baseInterval_0_142 (le_of_not_gt hcut142) hcut143
          · by_cases hcut148 : u < (0x8c00 / 9)
            · by_cases hcut145 : u < 0xe00
              · by_cases hcut144 : u < 0xd80
                · exact baseInterval_0_143 (le_of_not_gt hcut143) hcut144
                · exact baseInterval_0_144 (le_of_not_gt hcut144) hcut145
              · by_cases hcut146 : u < 0xe10
                · exact baseInterval_0_145 (le_of_not_gt hcut145) hcut146
                · by_cases hcut147 : u < (0x4ce3 / 5)
                  · exact baseInterval_0_146 (le_of_not_gt hcut146) hcut147
                  · exact baseInterval_0_147 (le_of_not_gt hcut147) hcut148
            · by_cases hcut150 : u < 0xfd2
              · by_cases hcut149 : u < 0xfa0
                · exact baseInterval_0_148 (le_of_not_gt hcut148) hcut149
                · exact baseInterval_0_149 (le_of_not_gt hcut149) hcut150
              · by_cases hcut151 : u < 0x1000
                · exact baseInterval_0_150 (le_of_not_gt hcut150) hcut151
                · by_cases hcut152 : u < 0x10e0
                  · exact baseInterval_0_151 (le_of_not_gt hcut151) hcut152
                  · exact baseInterval_0_152 (le_of_not_gt hcut152) hcut153
  · by_cases hcut229 : u < 0x166ce
    · by_cases hcut191 : u < 0x4ce3
      · by_cases hcut172 : u < (0x14000 / 9)
        · by_cases hcut162 : u < 0x1626
          · by_cases hcut157 : u < 0x13b0
            · by_cases hcut155 : u < (0xa000 / 9)
              · by_cases hcut154 : u < 0x1180
                · exact baseInterval_0_153 (le_of_not_gt hcut153) hcut154
                · exact baseInterval_0_154 (le_of_not_gt hcut154) hcut155
              · by_cases hcut156 : u < 0x1275
                · exact baseInterval_0_155 (le_of_not_gt hcut155) hcut156
                · exact baseInterval_0_156 (le_of_not_gt hcut156) hcut157
            · by_cases hcut159 : u < (0x6684 / 5)
              · by_cases hcut158 : u < 0x1400
                · exact baseInterval_0_157 (le_of_not_gt hcut157) hcut158
                · exact baseInterval_0_158 (le_of_not_gt hcut158) hcut159
              · by_cases hcut160 : u < (0x23000 / 27)
                · exact baseInterval_0_159 (le_of_not_gt hcut159) hcut160
                · by_cases hcut161 : u < 0x15e0
                  · exact baseInterval_0_160 (le_of_not_gt hcut160) hcut161
                  · exact baseInterval_0_161 (le_of_not_gt hcut161) hcut162
          · by_cases hcut167 : u < (0x5000 / 3)
            · by_cases hcut164 : u < 0x17a0
              · by_cases hcut163 : u < (0xc800 / 9)
                · exact baseInterval_0_162 (le_of_not_gt hcut162) hcut163
                · exact baseInterval_0_163 (le_of_not_gt hcut163) hcut164
              · by_cases hcut165 : u < 0x1900
                · exact baseInterval_0_164 (le_of_not_gt hcut164) hcut165
                · by_cases hcut166 : u < 0x19a1
                  · exact baseInterval_0_165 (le_of_not_gt hcut165) hcut166
                  · exact baseInterval_0_166 (le_of_not_gt hcut166) hcut167
            · by_cases hcut169 : u < (0x11800 / 9)
              · by_cases hcut168 : u < 0x1c00
                · exact baseInterval_0_167 (le_of_not_gt hcut167) hcut168
                · exact baseInterval_0_168 (le_of_not_gt hcut168) hcut169
              · by_cases hcut170 : u < 0x2000
                · exact baseInterval_0_169 (le_of_not_gt hcut169) hcut170
                · by_cases hcut171 : u < 0x2300
                  · exact baseInterval_0_170 (le_of_not_gt hcut170) hcut171
                  · exact baseInterval_0_171 (le_of_not_gt hcut171) hcut172
        · by_cases hcut181 : u < (0xa000 / 3)
          · by_cases hcut176 : u < (0x19000 / 9)
            · by_cases hcut174 : u < 0x2800
              · by_cases hcut173 : u < (0x7000 / 3)
                · exact baseInterval_0_172 (le_of_not_gt hcut172) hcut173
                · exact baseInterval_0_173 (le_of_not_gt hcut173) hcut174
              · by_cases hcut175 : u < (0x8000 / 3)
                · exact baseInterval_0_174 (le_of_not_gt hcut174) hcut175
                · exact baseInterval_0_175 (le_of_not_gt hcut175) hcut176
            · by_cases hcut178 : u < 0x3200
              · by_cases hcut177 : u < (0xe6a9 / 5)
                · exact baseInterval_0_176 (le_of_not_gt hcut176) hcut177
                · exact baseInterval_0_177 (le_of_not_gt hcut177) hcut178
              · by_cases hcut179 : u < (0x10000 / 5)
                · exact baseInterval_0_178 (le_of_not_gt hcut178) hcut179
                · by_cases hcut180 : u < 0x3342
                  · exact baseInterval_0_179 (le_of_not_gt hcut179) hcut180
                  · exact baseInterval_0_180 (le_of_not_gt hcut180) hcut181
          · by_cases hcut186 : u < 0x41eb
            · by_cases hcut183 : u < (0x1338c / 5)
              · by_cases hcut182 : u < 0x3800
                · exact baseInterval_0_181 (le_of_not_gt hcut181) hcut182
                · exact baseInterval_0_182 (le_of_not_gt hcut182) hcut183
              · by_cases hcut184 : u < (0x23000 / 9)
                · exact baseInterval_0_183 (le_of_not_gt hcut183) hcut184
                · by_cases hcut185 : u < 0x4000
                  · exact baseInterval_0_184 (le_of_not_gt hcut184) hcut185
                  · exact baseInterval_0_185 (le_of_not_gt hcut185) hcut186
            · by_cases hcut188 : u < 0x4600
              · by_cases hcut187 : u < 0x4380
                · exact baseInterval_0_186 (le_of_not_gt hcut186) hcut187
                · exact baseInterval_0_187 (le_of_not_gt hcut187) hcut188
              · by_cases hcut189 : u < (0x28000 / 9)
                · exact baseInterval_0_188 (le_of_not_gt hcut188) hcut189
                · by_cases hcut190 : u < (0xe000 / 3)
                  · exact baseInterval_0_189 (le_of_not_gt hcut189) hcut190
                  · exact baseInterval_0_190 (le_of_not_gt hcut190) hcut191
      · by_cases hcut210 : u < 0xa000
        · by_cases hcut200 : u < 0x7000
          · by_cases hcut195 : u < 0x5e80
            · by_cases hcut193 : u < (0x32000 / 9)
              · by_cases hcut192 : u < 0x5000
                · exact baseInterval_0_191 (le_of_not_gt hcut191) hcut192
                · exact baseInterval_0_192 (le_of_not_gt hcut192) hcut193
              · by_cases hcut194 : u < 0x5c49
                · exact baseInterval_0_193 (le_of_not_gt hcut193) hcut194
                · exact baseInterval_0_194 (le_of_not_gt hcut194) hcut195
            · by_cases hcut197 : u < 0x6684
              · by_cases hcut196 : u < 0x6400
                · exact baseInterval_0_195 (le_of_not_gt hcut195) hcut196
                · exact baseInterval_0_196 (le_of_not_gt hcut196) hcut197
              · by_cases hcut198 : u < (0xaf000 / 27)
                · exact baseInterval_0_197 (le_of_not_gt hcut197) hcut198
                · by_cases hcut199 : u < 0x6d60
                  · exact baseInterval_0_198 (le_of_not_gt hcut198) hcut199
                  · exact baseInterval_0_199 (le_of_not_gt hcut199) hcut200
          · by_cases hcut205 : u < (0x2b3fb / 5)
            · by_cases hcut202 : u < 0x8000
              · by_cases hcut201 : u < (0x46000 / 9)
                · exact baseInterval_0_200 (le_of_not_gt hcut200) hcut201
                · exact baseInterval_0_201 (le_of_not_gt hcut201) hcut202
              · by_cases hcut203 : u < 0x8025
                · exact baseInterval_0_202 (le_of_not_gt hcut202) hcut203
                · by_cases hcut204 : u < 0x88b0
                  · exact baseInterval_0_203 (le_of_not_gt hcut203) hcut204
                  · exact baseInterval_0_204 (le_of_not_gt hcut204) hcut205
            · by_cases hcut207 : u < (0xf5000 / 27)
              · by_cases hcut206 : u < 0x8c00
                · exact baseInterval_0_205 (le_of_not_gt hcut205) hcut206
                · exact baseInterval_0_206 (le_of_not_gt hcut206) hcut207
              · by_cases hcut208 : u < 0x9920
                · exact baseInterval_0_207 (le_of_not_gt hcut207) hcut208
                · by_cases hcut209 : u < 0x99c6
                  · exact baseInterval_0_208 (le_of_not_gt hcut208) hcut209
                  · exact baseInterval_0_209 (le_of_not_gt hcut209) hcut210
        · by_cases hcut219 : u < 0xe6a9
          · by_cases hcut214 : u < 0xc800
            · by_cases hcut212 : u < 0xb367
              · by_cases hcut211 : u < (0x64000 / 9)
                · exact baseInterval_0_210 (le_of_not_gt hcut210) hcut211
                · exact baseInterval_0_211 (le_of_not_gt hcut211) hcut212
              · by_cases hcut213 : u < (0x39aa4 / 5)
                · exact baseInterval_0_212 (le_of_not_gt hcut212) hcut213
                · exact baseInterval_0_213 (le_of_not_gt hcut213) hcut214
            · by_cases hcut216 : u < 0xcd08
              · by_cases hcut215 : u < (0x40000 / 5)
                · exact baseInterval_0_214 (le_of_not_gt hcut214) hcut215
                · exact baseInterval_0_215 (le_of_not_gt hcut215) hcut216
              · by_cases hcut217 : u < (0x28000 / 3)
                · exact baseInterval_0_216 (le_of_not_gt hcut216) hcut217
                · by_cases hcut218 : u < 0xe000
                  · exact baseInterval_0_217 (le_of_not_gt hcut217) hcut218
                  · exact baseInterval_0_218 (le_of_not_gt hcut218) hcut219
          · by_cases hcut224 : u < (0x38000 / 3)
            · by_cases hcut221 : u < 0x10000
              · by_cases hcut220 : u < (0x8c000 / 9)
                · exact baseInterval_0_219 (le_of_not_gt hcut219) hcut220
                · exact baseInterval_0_220 (le_of_not_gt hcut220) hcut221
              · by_cases hcut222 : u < 0x11800
                · exact baseInterval_0_221 (le_of_not_gt hcut221) hcut222
                · by_cases hcut223 : u < (0xa0000 / 9)
                  · exact baseInterval_0_222 (le_of_not_gt hcut222) hcut223
                  · exact baseInterval_0_223 (le_of_not_gt hcut223) hcut224
            · by_cases hcut226 : u < 0x14000
              · by_cases hcut225 : u < 0x1338c
                · exact baseInterval_0_224 (le_of_not_gt hcut224) hcut225
                · exact baseInterval_0_225 (le_of_not_gt hcut225) hcut226
              · by_cases hcut227 : u < (0x40000 / 3)
                · exact baseInterval_0_226 (le_of_not_gt hcut226) hcut227
                · by_cases hcut228 : u < (0xc8000 / 9)
                  · exact baseInterval_0_227 (le_of_not_gt hcut227) hcut228
                  · exact baseInterval_0_228 (le_of_not_gt hcut228) hcut229
    · by_cases hcut267 : u < 0x7822b
      · by_cases hcut248 : u < 0x33420
        · by_cases hcut238 : u < 0x21a35
          · by_cases hcut233 : u < 0x1c000
            · by_cases hcut231 : u < 0x19a10
              · by_cases hcut230 : u < 0x1806f
                · exact baseInterval_0_229 (le_of_not_gt hcut229) hcut230
                · exact baseInterval_0_230 (le_of_not_gt hcut230) hcut231
              · by_cases hcut232 : u < (0x81bf1 / 5)
                · exact baseInterval_0_231 (le_of_not_gt hcut231) hcut232
                · exact baseInterval_0_232 (le_of_not_gt hcut232) hcut233
            · by_cases hcut235 : u < (0x118000 / 9)
              · by_cases hcut234 : u < 0x1cd52
                · exact baseInterval_0_233 (le_of_not_gt hcut233) hcut234
                · exact baseInterval_0_234 (le_of_not_gt hcut234) hcut235
              · by_cases hcut236 : u < 0x20000
                · exact baseInterval_0_235 (le_of_not_gt hcut235) hcut236
                · by_cases hcut237 : u < 0x20094
                  · exact baseInterval_0_236 (le_of_not_gt hcut236) hcut237
                  · exact baseInterval_0_237 (le_of_not_gt hcut237) hcut238
          · by_cases hcut243 : u < 0x2ab70
            · by_cases hcut240 : u < (0x140000 / 9)
              · by_cases hcut239 : u < (0xacfec / 5)
                · exact baseInterval_0_238 (le_of_not_gt hcut238) hcut239
                · exact baseInterval_0_239 (le_of_not_gt hcut239) hcut240
              · by_cases hcut241 : u < 0x28000
                · exact baseInterval_0_240 (le_of_not_gt hcut240) hcut241
                · by_cases hcut242 : u < 0x280b9
                  · exact baseInterval_0_241 (le_of_not_gt hcut241) hcut242
                  · exact baseInterval_0_242 (le_of_not_gt hcut242) hcut243
            · by_cases hcut245 : u < 0x2cd9c
              · by_cases hcut244 : u < 0x2b3fb
                · exact baseInterval_0_243 (le_of_not_gt hcut243) hcut244
                · exact baseInterval_0_244 (le_of_not_gt hcut244) hcut245
              · by_cases hcut246 : u < 0x300de
                · exact baseInterval_0_245 (le_of_not_gt hcut245) hcut246
                · by_cases hcut247 : u < (0x100000 / 5)
                  · exact baseInterval_0_246 (le_of_not_gt hcut246) hcut247
                  · exact baseInterval_0_247 (le_of_not_gt hcut247) hcut248
        · by_cases hcut257 : u < 0x50000
          · by_cases hcut252 : u < 0x40000
            · by_cases hcut250 : u < 0x38103
              · by_cases hcut249 : u < 0x38000
                · exact baseInterval_0_248 (le_of_not_gt hcut248) hcut249
                · exact baseInterval_0_249 (le_of_not_gt hcut249) hcut250
              · by_cases hcut251 : u < 0x3bcd0
                · exact baseInterval_0_250 (le_of_not_gt hcut250) hcut251
                · exact baseInterval_0_251 (le_of_not_gt hcut251) hcut252
            · by_cases hcut254 : u < 0x4346a
              · by_cases hcut253 : u < 0x40128
                · exact baseInterval_0_252 (le_of_not_gt hcut252) hcut253
                · exact baseInterval_0_253 (le_of_not_gt hcut253) hcut254
              · by_cases hcut255 : u < (0x280000 / 9)
                · exact baseInterval_0_254 (le_of_not_gt hcut254) hcut255
                · by_cases hcut256 : u < (0x1853d3 / 5)
                  · exact baseInterval_0_255 (le_of_not_gt hcut255) hcut256
                  · exact baseInterval_0_256 (le_of_not_gt hcut256) hcut257
          · by_cases hcut262 : u < 0x601bc
            · by_cases hcut259 : u < 0x567f6
              · by_cases hcut258 : u < (0x100000 / 3)
                · exact baseInterval_0_257 (le_of_not_gt hcut257) hcut258
                · exact baseInterval_0_258 (le_of_not_gt hcut258) hcut259
              · by_cases hcut260 : u < (0x320000 / 9)
                · exact baseInterval_0_259 (le_of_not_gt hcut259) hcut260
                · by_cases hcut261 : u < 0x59b38
                  · exact baseInterval_0_260 (le_of_not_gt hcut260) hcut261
                  · exact baseInterval_0_261 (le_of_not_gt hcut261) hcut262
            · by_cases hcut264 : u < (0x206fc4 / 5)
              · by_cases hcut263 : u < 0x64000
                · exact baseInterval_0_262 (le_of_not_gt hcut262) hcut263
                · exact baseInterval_0_263 (le_of_not_gt hcut263) hcut264
              · by_cases hcut265 : u < (0x140000 / 3)
                · exact baseInterval_0_264 (le_of_not_gt hcut264) hcut265
                · by_cases hcut266 : u < 0x70000
                  · exact baseInterval_0_265 (le_of_not_gt hcut265) hcut266
                  · exact baseInterval_0_266 (le_of_not_gt hcut266) hcut267
      · by_cases hcut286 : u < 0xe0000
        · by_cases hcut276 : u < 0x9cfa2
          · by_cases hcut271 : u < 0x81bf1
            · by_cases hcut269 : u < 0x80000
              · by_cases hcut268 : u < (0x460000 / 9)
                · exact baseInterval_0_267 (le_of_not_gt hcut267) hcut268
                · exact baseInterval_0_268 (le_of_not_gt hcut268) hcut269
              · by_cases hcut270 : u < 0x80250
                · exact baseInterval_0_269 (le_of_not_gt hcut269) hcut270
                · exact baseInterval_0_270 (le_of_not_gt hcut270) hcut271
            · by_cases hcut273 : u < 0x8c000
              · by_cases hcut272 : u < 0x868d4
                · exact baseInterval_0_271 (le_of_not_gt hcut271) hcut272
                · exact baseInterval_0_272 (le_of_not_gt hcut272) hcut273
              · by_cases hcut274 : u < (0x500000 / 9)
                · exact baseInterval_0_273 (le_of_not_gt hcut273) hcut274
                · by_cases hcut275 : u < (0x1c0000 / 3)
                  · exact baseInterval_0_274 (le_of_not_gt hcut274) hcut275
                  · exact baseInterval_0_275 (le_of_not_gt hcut275) hcut276
          · by_cases hcut281 : u < 0xc8000
            · by_cases hcut278 : u < (0x200000 / 3)
              · by_cases hcut277 : u < 0xa0000
                · exact baseInterval_0_276 (le_of_not_gt hcut276) hcut277
                · exact baseInterval_0_277 (le_of_not_gt hcut277) hcut278
              · by_cases hcut279 : u < (0x640000 / 9)
                · exact baseInterval_0_278 (le_of_not_gt hcut278) hcut279
                · by_cases hcut280 : u < 0xb3670
                  · exact baseInterval_0_279 (le_of_not_gt hcut279) hcut280
                  · exact baseInterval_0_280 (le_of_not_gt hcut280) hcut281
            · by_cases hcut283 : u < (0x400000 / 5)
              · by_cases hcut282 : u < 0xc839d
                · exact baseInterval_0_281 (le_of_not_gt hcut281) hcut282
                · exact baseInterval_0_282 (le_of_not_gt hcut282) hcut283
              · by_cases hcut284 : u < 0xcd080
                · exact baseInterval_0_283 (le_of_not_gt hcut283) hcut284
                · by_cases hcut285 : u < 0xd5930
                  · exact baseInterval_0_284 (le_of_not_gt hcut284) hcut285
                  · exact baseInterval_0_285 (le_of_not_gt hcut285) hcut286
        · by_cases hcut296 : u < 0x12b010
          · by_cases hcut291 : u < 0x1004a0
            · by_cases hcut288 : u < 0xf0456
              · by_cases hcut287 : u < (0x48fb79 / 5)
                · exact baseInterval_0_286 (le_of_not_gt hcut286) hcut287
                · exact baseInterval_0_287 (le_of_not_gt hcut287) hcut288
              · by_cases hcut289 : u < (0x8c0000 / 9)
                · exact baseInterval_0_288 (le_of_not_gt hcut288) hcut289
                · by_cases hcut290 : u < 0x100000
                  · exact baseInterval_0_289 (le_of_not_gt hcut289) hcut290
                  · exact baseInterval_0_290 (le_of_not_gt hcut290) hcut291
            · by_cases hcut293 : u < 0x118000
              · by_cases hcut292 : u < 0x1037e2
                · exact baseInterval_0_291 (le_of_not_gt hcut291) hcut292
                · exact baseInterval_0_292 (le_of_not_gt hcut292) hcut293
              · by_cases hcut294 : u < 0x11850f
                · exact baseInterval_0_293 (le_of_not_gt hcut293) hcut294
                · by_cases hcut295 : u < (0xa00000 / 9)
                  · exact baseInterval_0_294 (le_of_not_gt hcut294) hcut295
                  · exact baseInterval_0_295 (le_of_not_gt hcut295) hcut296
          · by_cases hcut301 : u < (0x400000 / 3)
            · by_cases hcut298 : u < 0x140000
              · by_cases hcut297 : u < (0x614f4c / 5)
                · exact baseInterval_0_296 (le_of_not_gt hcut296) hcut297
                · exact baseInterval_0_297 (le_of_not_gt hcut297) hcut298
              · by_cases hcut299 : u < (0x2300000 / 27)
                · exact baseInterval_0_298 (le_of_not_gt hcut298) hcut299
                · by_cases hcut300 : u < 0x150612
                  · exact baseInterval_0_299 (le_of_not_gt hcut299) hcut300
                  · exact baseInterval_0_300 (le_of_not_gt hcut300) hcut301
            · by_cases hcut303 : u < 0x166ce0
              · by_cases hcut302 : u < (0xc80000 / 9)
                · exact baseInterval_0_301 (le_of_not_gt hcut301) hcut302
                · exact baseInterval_0_302 (le_of_not_gt hcut302) hcut303
              · by_cases hcut304 : u < 0x1853d3
                · exact baseInterval_0_303 (le_of_not_gt hcut303) hcut304
                · by_cases hcut305 : u < 0x190000
                  · exact baseInterval_0_304 (le_of_not_gt hcut304) hcut305
                  · exact baseInterval_0_305 (le_of_not_gt hcut305) hhi

def baseStepValid_1_below_limit {u : ℚ} (hlo : 1 ≤ u) (hhi : u < 0x1921ee) :
    baseStepValid true u := by
  by_cases hcut152 : u < 0x1116
  · by_cases hcut76 : u < 0xd8
    · by_cases hcut38 : u < (0x70 / 3)
      · by_cases hcut19 : u < (28 / 3)
        · by_cases hcut9 : u < 5
          · by_cases hcut4 : u < (12 / 5)
            · by_cases hcut2 : u < (9 / 5)
              · by_cases hcut1 : u < (4 / 3)
                · exact baseInterval_1_0 hlo hcut1
                · exact baseInterval_1_1 (le_of_not_gt hcut1) hcut2
              · by_cases hcut3 : u < 2
                · exact baseInterval_1_2 (le_of_not_gt hcut2) hcut3
                · exact baseInterval_1_3 (le_of_not_gt hcut3) hcut4
            · by_cases hcut6 : u < 3
              · by_cases hcut5 : u < (8 / 3)
                · exact baseInterval_1_4 (le_of_not_gt hcut4) hcut5
                · exact baseInterval_1_5 (le_of_not_gt hcut5) hcut6
              · by_cases hcut7 : u < (16 / 5)
                · exact baseInterval_1_6 (le_of_not_gt hcut6) hcut7
                · by_cases hcut8 : u < 4
                  · exact baseInterval_1_7 (le_of_not_gt hcut7) hcut8
                  · exact baseInterval_1_8 (le_of_not_gt hcut8) hcut9
          · by_cases hcut14 : u < 7
            · by_cases hcut11 : u < (27 / 5)
              · by_cases hcut10 : u < (16 / 3)
                · exact baseInterval_1_9 (le_of_not_gt hcut9) hcut10
                · exact baseInterval_1_10 (le_of_not_gt hcut10) hcut11
              · by_cases hcut12 : u < 6
                · exact baseInterval_1_11 (le_of_not_gt hcut11) hcut12
                · by_cases hcut13 : u < (20 / 3)
                  · exact baseInterval_1_12 (le_of_not_gt hcut12) hcut13
                  · exact baseInterval_1_13 (le_of_not_gt hcut13) hcut14
            · by_cases hcut16 : u < 8
              · by_cases hcut15 : u < (36 / 5)
                · exact baseInterval_1_14 (le_of_not_gt hcut14) hcut15
                · exact baseInterval_1_15 (le_of_not_gt hcut15) hcut16
              · by_cases hcut17 : u < (80 / 9)
                · exact baseInterval_1_16 (le_of_not_gt hcut16) hcut17
                · by_cases hcut18 : u < 9
                  · exact baseInterval_1_17 (le_of_not_gt hcut17) hcut18
                  · exact baseInterval_1_18 (le_of_not_gt hcut18) hcut19
        · by_cases hcut28 : u < 18
          · by_cases hcut23 : u < (40 / 3)
            · by_cases hcut21 : u < (32 / 3)
              · by_cases hcut20 : u < 10
                · exact baseInterval_1_19 (le_of_not_gt hcut19) hcut20
                · exact baseInterval_1_20 (le_of_not_gt hcut20) hcut21
              · by_cases hcut22 : u < (64 / 5)
                · exact baseInterval_1_21 (le_of_not_gt hcut21) hcut22
                · exact baseInterval_1_22 (le_of_not_gt hcut22) hcut23
            · by_cases hcut25 : u < 16
              · by_cases hcut24 : u < 14
                · exact baseInterval_1_23 (le_of_not_gt hcut23) hcut24
                · exact baseInterval_1_24 (le_of_not_gt hcut24) hcut25
              · by_cases hcut26 : u < (81 / 5)
                · exact baseInterval_1_25 (le_of_not_gt hcut25) hcut26
                · by_cases hcut27 : u < (0xa0 / 9)
                  · exact baseInterval_1_26 (le_of_not_gt hcut26) hcut27
                  · exact baseInterval_1_27 (le_of_not_gt hcut27) hcut28
          · by_cases hcut33 : u < (80 / 3)
            · by_cases hcut30 : u < 20
              · by_cases hcut29 : u < (56 / 3)
                · exact baseInterval_1_28 (le_of_not_gt hcut28) hcut29
                · exact baseInterval_1_29 (le_of_not_gt hcut29) hcut30
              · by_cases hcut31 : u < (64 / 3)
                · exact baseInterval_1_30 (le_of_not_gt hcut30) hcut31
                · by_cases hcut32 : u < (0x6c / 5)
                  · exact baseInterval_1_31 (le_of_not_gt hcut31) hcut32
                  · exact baseInterval_1_32 (le_of_not_gt hcut32) hcut33
            · by_cases hcut35 : u < 28
              · by_cases hcut34 : u < 27
                · exact baseInterval_1_33 (le_of_not_gt hcut33) hcut34
                · exact baseInterval_1_34 (le_of_not_gt hcut34) hcut35
              · by_cases hcut36 : u < 32
                · exact baseInterval_1_35 (le_of_not_gt hcut35) hcut36
                · by_cases hcut37 : u < (0x140 / 9)
                  · exact baseInterval_1_36 (le_of_not_gt hcut36) hcut37
                  · exact baseInterval_1_37 (le_of_not_gt hcut37) hcut38
      · by_cases hcut57 : u < 0x64
        · by_cases hcut47 : u < 56
          · by_cases hcut42 : u < (0xf3 / 5)
            · by_cases hcut40 : u < (0x80 / 3)
              · by_cases hcut39 : u < 40
                · exact baseInterval_1_38 (le_of_not_gt hcut38) hcut39
                · exact baseInterval_1_39 (le_of_not_gt hcut39) hcut40
              · by_cases hcut41 : u < (0x190 / 9)
                · exact baseInterval_1_40 (le_of_not_gt hcut40) hcut41
                · exact baseInterval_1_41 (le_of_not_gt hcut41) hcut42
            · by_cases hcut44 : u < (0x100 / 5)
              · by_cases hcut43 : u < 50
                · exact baseInterval_1_42 (le_of_not_gt hcut42) hcut43
                · exact baseInterval_1_43 (le_of_not_gt hcut43) hcut44
              · by_cases hcut45 : u < (0xa0 / 3)
                · exact baseInterval_1_44 (le_of_not_gt hcut44) hcut45
                · by_cases hcut46 : u < 54
                  · exact baseInterval_1_45 (le_of_not_gt hcut45) hcut46
                  · exact baseInterval_1_46 (le_of_not_gt hcut46) hcut47
          · by_cases hcut52 : u < (0x280 / 9)
            · by_cases hcut49 : u < 64
              · by_cases hcut48 : u < (0x230 / 9)
                · exact baseInterval_1_47 (le_of_not_gt hcut47) hcut48
                · exact baseInterval_1_48 (le_of_not_gt hcut48) hcut49
              · by_cases hcut50 : u < (0x144 / 5)
                · exact baseInterval_1_49 (le_of_not_gt hcut49) hcut50
                · by_cases hcut51 : u < 70
                  · exact baseInterval_1_50 (le_of_not_gt hcut50) hcut51
                  · exact baseInterval_1_51 (le_of_not_gt hcut51) hcut52
            · by_cases hcut54 : u < 80
              · by_cases hcut53 : u < (0xe0 / 3)
                · exact baseInterval_1_52 (le_of_not_gt hcut52) hcut53
                · exact baseInterval_1_53 (le_of_not_gt hcut53) hcut54
              · by_cases hcut55 : u < 81
                · exact baseInterval_1_54 (le_of_not_gt hcut54) hcut55
                · by_cases hcut56 : u < (0x320 / 9)
                  · exact baseInterval_1_55 (le_of_not_gt hcut55) hcut56
                  · exact baseInterval_1_56 (le_of_not_gt hcut56) hcut57
        · by_cases hcut66 : u < (0x2d9 / 5)
          · by_cases hcut61 : u < (0x460 / 9)
            · by_cases hcut59 : u < 0x6c
              · by_cases hcut58 : u < (0x140 / 3)
                · exact baseInterval_1_57 (le_of_not_gt hcut57) hcut58
                · exact baseInterval_1_58 (le_of_not_gt hcut58) hcut59
              · by_cases hcut60 : u < 0x70
                · exact baseInterval_1_59 (le_of_not_gt hcut59) hcut60
                · exact baseInterval_1_60 (le_of_not_gt hcut60) hcut61
            · by_cases hcut63 : u < 0x87
              · by_cases hcut62 : u < 0x80
                · exact baseInterval_1_61 (le_of_not_gt hcut61) hcut62
                · exact baseInterval_1_62 (le_of_not_gt hcut62) hcut63
              · by_cases hcut64 : u < 0x8c
                · exact baseInterval_1_63 (le_of_not_gt hcut63) hcut64
                · by_cases hcut65 : u < 0x90
                  · exact baseInterval_1_64 (le_of_not_gt hcut64) hcut65
                  · exact baseInterval_1_65 (le_of_not_gt hcut65) hcut66
          · by_cases hcut71 : u < 0xbd
            · by_cases hcut68 : u < 0xa0
              · by_cases hcut67 : u < (0x1c0 / 3)
                · exact baseInterval_1_66 (le_of_not_gt hcut66) hcut67
                · exact baseInterval_1_67 (le_of_not_gt hcut67) hcut68
              · by_cases hcut69 : u < 0xa2
                · exact baseInterval_1_68 (le_of_not_gt hcut68) hcut69
                · by_cases hcut70 : u < (0x640 / 9)
                  · exact baseInterval_1_69 (le_of_not_gt hcut69) hcut70
                  · exact baseInterval_1_70 (le_of_not_gt hcut70) hcut71
            · by_cases hcut73 : u < 0xc8
              · by_cases hcut72 : u < (0x3cc / 5)
                · exact baseInterval_1_71 (le_of_not_gt hcut71) hcut72
                · exact baseInterval_1_72 (le_of_not_gt hcut72) hcut73
              · by_cases hcut74 : u < (0x400 / 5)
                · exact baseInterval_1_73 (le_of_not_gt hcut73) hcut74
                · by_cases hcut75 : u < (0x280 / 3)
                  · exact baseInterval_1_74 (le_of_not_gt hcut74) hcut75
                  · exact baseInterval_1_75 (le_of_not_gt hcut75) hcut76
    · by_cases hcut114 : u < 0x460
      · by_cases hcut95 : u < 0x21c
        · by_cases hcut85 : u < (0x400 / 3)
          · by_cases hcut80 : u < 0x100
            · by_cases hcut78 : u < 0xf3
              · by_cases hcut77 : u < 0xe0
                · exact baseInterval_1_76 (le_of_not_gt hcut76) hcut77
                · exact baseInterval_1_77 (le_of_not_gt hcut77) hcut78
              · by_cases hcut79 : u < (0x8c0 / 9)
                · exact baseInterval_1_78 (le_of_not_gt hcut78) hcut79
                · exact baseInterval_1_79 (le_of_not_gt hcut79) hcut80
            · by_cases hcut82 : u < (0xa00 / 9)
              · by_cases hcut81 : u < 0x118
                · exact baseInterval_1_80 (le_of_not_gt hcut80) hcut81
                · exact baseInterval_1_81 (le_of_not_gt hcut81) hcut82
              · by_cases hcut83 : u < (0x380 / 3)
                · exact baseInterval_1_82 (le_of_not_gt hcut82) hcut83
                · by_cases hcut84 : u < 0x140
                  · exact baseInterval_1_83 (le_of_not_gt hcut83) hcut84
                  · exact baseInterval_1_84 (le_of_not_gt hcut84) hcut85
          · by_cases hcut90 : u < (0x88b / 5)
            · by_cases hcut87 : u < 0x190
              · by_cases hcut86 : u < (0xc80 / 9)
                · exact baseInterval_1_85 (le_of_not_gt hcut85) hcut86
                · exact baseInterval_1_86 (le_of_not_gt hcut86) hcut87
              · by_cases hcut88 : u < 0x195
                · exact baseInterval_1_87 (le_of_not_gt hcut87) hcut88
                · by_cases hcut89 : u < 0x1b0
                  · exact baseInterval_1_88 (le_of_not_gt hcut88) hcut89
                  · exact baseInterval_1_89 (le_of_not_gt hcut89) hcut90
            · by_cases hcut92 : u < 0x1e6
              · by_cases hcut91 : u < 0x1c0
                · exact baseInterval_1_90 (le_of_not_gt hcut90) hcut91
                · exact baseInterval_1_91 (le_of_not_gt hcut91) hcut92
              · by_cases hcut93 : u < (0x1180 / 9)
                · exact baseInterval_1_92 (le_of_not_gt hcut92) hcut93
                · by_cases hcut94 : u < 0x200
                  · exact baseInterval_1_93 (le_of_not_gt hcut93) hcut94
                  · exact baseInterval_1_94 (le_of_not_gt hcut94) hcut95
        · by_cases hcut104 : u < 0x2f4
          · by_cases hcut99 : u < (0xb64 / 5)
            · by_cases hcut97 : u < 0x237
              · by_cases hcut96 : u < 0x230
                · exact baseInterval_1_95 (le_of_not_gt hcut95) hcut96
                · exact baseInterval_1_96 (le_of_not_gt hcut96) hcut97
              · by_cases hcut98 : u < (0x1400 / 9)
                · exact baseInterval_1_97 (le_of_not_gt hcut97) hcut98
                · exact baseInterval_1_98 (le_of_not_gt hcut98) hcut99
            · by_cases hcut101 : u < 0x2a3
              · by_cases hcut100 : u < 0x280
                · exact baseInterval_1_99 (le_of_not_gt hcut99) hcut100
                · exact baseInterval_1_100 (le_of_not_gt hcut100) hcut101
              · by_cases hcut102 : u < 0x2d0
                · exact baseInterval_1_101 (le_of_not_gt hcut101) hcut102
                · by_cases hcut103 : u < 0x2d9
                  · exact baseInterval_1_102 (le_of_not_gt hcut102) hcut103
                  · exact baseInterval_1_103 (le_of_not_gt hcut103) hcut104
          · by_cases hcut109 : u < 0x380
            · by_cases hcut106 : u < 0x32a
              · by_cases hcut105 : u < 0x320
                · exact baseInterval_1_104 (le_of_not_gt hcut104) hcut105
                · exact baseInterval_1_105 (le_of_not_gt hcut105) hcut106
              · by_cases hcut107 : u < (0x1000 / 5)
                · exact baseInterval_1_106 (le_of_not_gt hcut106) hcut107
                · by_cases hcut108 : u < 0x360
                  · exact baseInterval_1_107 (le_of_not_gt hcut107) hcut108
                  · exact baseInterval_1_108 (le_of_not_gt hcut108) hcut109
            · by_cases hcut111 : u < 0x3f0
              · by_cases hcut110 : u < 0x3b1
                · exact baseInterval_1_109 (le_of_not_gt hcut109) hcut110
                · exact baseInterval_1_110 (le_of_not_gt hcut110) hcut111
              · by_cases hcut112 : u < 0x400
                · exact baseInterval_1_111 (le_of_not_gt hcut111) hcut112
                · by_cases hcut113 : u < 0x438
                  · exact baseInterval_1_112 (le_of_not_gt hcut112) hcut113
                  · exact baseInterval_1_113 (le_of_not_gt hcut113) hcut114
      · by_cases hcut133 : u < (0x5000 / 9)
        · by_cases hcut123 : u < 0x640
          · by_cases hcut118 : u < (0x19a1 / 5)
            · by_cases hcut116 : u < (0x2800 / 9)
              · by_cases hcut115 : u < 0x46e
                · exact baseInterval_1_114 (le_of_not_gt hcut114) hcut115
                · exact baseInterval_1_115 (le_of_not_gt hcut115) hcut116
              · by_cases hcut117 : u < 0x500
                · exact baseInterval_1_116 (le_of_not_gt hcut116) hcut117
                · exact baseInterval_1_117 (le_of_not_gt hcut117) hcut118
            · by_cases hcut120 : u < (0x3200 / 9)
              · by_cases hcut119 : u < (0x1000 / 3)
                · exact baseInterval_1_118 (le_of_not_gt hcut118) hcut119
                · exact baseInterval_1_119 (le_of_not_gt hcut119) hcut120
              · by_cases hcut121 : u < 0x5b2
                · exact baseInterval_1_120 (le_of_not_gt hcut120) hcut121
                · by_cases hcut122 : u < 0x5e8
                  · exact baseInterval_1_121 (le_of_not_gt hcut121) hcut122
                  · exact baseInterval_1_122 (le_of_not_gt hcut122) hcut123
          · by_cases hcut128 : u < 0x7e9
            · by_cases hcut125 : u < (0x222c / 5)
              · by_cases hcut124 : u < (0x1400 / 3)
                · exact baseInterval_1_123 (le_of_not_gt hcut123) hcut124
                · exact baseInterval_1_124 (le_of_not_gt hcut124) hcut125
              · by_cases hcut126 : u < 0x700
                · exact baseInterval_1_125 (le_of_not_gt hcut125) hcut126
                · by_cases hcut127 : u < (0x4600 / 9)
                  · exact baseInterval_1_126 (le_of_not_gt hcut126) hcut127
                  · exact baseInterval_1_127 (le_of_not_gt hcut127) hcut128
            · by_cases hcut130 : u < 0x870
              · by_cases hcut129 : u < 0x800
                · exact baseInterval_1_128 (le_of_not_gt hcut128) hcut129
                · exact baseInterval_1_129 (le_of_not_gt hcut129) hcut130
              · by_cases hcut131 : u < 0x88b
                · exact baseInterval_1_130 (le_of_not_gt hcut130) hcut131
                · by_cases hcut132 : u < 0x8c0
                  · exact baseInterval_1_131 (le_of_not_gt hcut131) hcut132
                  · exact baseInterval_1_132 (le_of_not_gt hcut132) hcut133
        · by_cases hcut142 : u < 0xd2f
          · by_cases hcut137 : u < 0xb13
            · by_cases hcut135 : u < 0xa00
              · by_cases hcut134 : u < (0x1c00 / 3)
                · exact baseInterval_1_133 (le_of_not_gt hcut133) hcut134
                · exact baseInterval_1_134 (le_of_not_gt hcut134) hcut135
              · by_cases hcut136 : u < (0x2000 / 3)
                · exact baseInterval_1_135 (le_of_not_gt hcut135) hcut136
                · exact baseInterval_1_136 (le_of_not_gt hcut136) hcut137
            · by_cases hcut139 : u < 0xbd0
              · by_cases hcut138 : u < (0x6400 / 9)
                · exact baseInterval_1_137 (le_of_not_gt hcut137) hcut138
                · exact baseInterval_1_138 (le_of_not_gt hcut138) hcut139
              · by_cases hcut140 : u < 0xc80
                · exact baseInterval_1_139 (le_of_not_gt hcut139) hcut140
                · by_cases hcut141 : u < (0x4000 / 5)
                  · exact baseInterval_1_140 (le_of_not_gt hcut140) hcut141
                  · exact baseInterval_1_141 (le_of_not_gt hcut141) hcut142
          · by_cases hcut147 : u < (0x8c00 / 9)
            · by_cases hcut144 : u < 0xe00
              · by_cases hcut143 : u < 0xd80
                · exact baseInterval_1_142 (le_of_not_gt hcut142) hcut143
                · exact baseInterval_1_143 (le_of_not_gt hcut143) hcut144
              · by_cases hcut145 : u < 0xe10
                · exact baseInterval_1_144 (le_of_not_gt hcut144) hcut145
                · by_cases hcut146 : u < (0x4ce3 / 5)
                  · exact baseInterval_1_145 (le_of_not_gt hcut145) hcut146
                  · exact baseInterval_1_146 (le_of_not_gt hcut146) hcut147
            · by_cases hcut149 : u < 0xfd2
              · by_cases hcut148 : u < 0xfa0
                · exact baseInterval_1_147 (le_of_not_gt hcut147) hcut148
                · exact baseInterval_1_148 (le_of_not_gt hcut148) hcut149
              · by_cases hcut150 : u < 0x1000
                · exact baseInterval_1_149 (le_of_not_gt hcut149) hcut150
                · by_cases hcut151 : u < 0x10e0
                  · exact baseInterval_1_150 (le_of_not_gt hcut150) hcut151
                  · exact baseInterval_1_151 (le_of_not_gt hcut151) hcut152
  · by_cases hcut228 : u < 0x1806f
    · by_cases hcut190 : u < 0x4ce3
      · by_cases hcut171 : u < (0x14000 / 9)
        · by_cases hcut161 : u < 0x1626
          · by_cases hcut156 : u < 0x13b0
            · by_cases hcut154 : u < (0xa000 / 9)
              · by_cases hcut153 : u < 0x1180
                · exact baseInterval_1_152 (le_of_not_gt hcut152) hcut153
                · exact baseInterval_1_153 (le_of_not_gt hcut153) hcut154
              · by_cases hcut155 : u < 0x1275
                · exact baseInterval_1_154 (le_of_not_gt hcut154) hcut155
                · exact baseInterval_1_155 (le_of_not_gt hcut155) hcut156
            · by_cases hcut158 : u < (0x6684 / 5)
              · by_cases hcut157 : u < 0x1400
                · exact baseInterval_1_156 (le_of_not_gt hcut156) hcut157
                · exact baseInterval_1_157 (le_of_not_gt hcut157) hcut158
              · by_cases hcut159 : u < (0x23000 / 27)
                · exact baseInterval_1_158 (le_of_not_gt hcut158) hcut159
                · by_cases hcut160 : u < 0x15e0
                  · exact baseInterval_1_159 (le_of_not_gt hcut159) hcut160
                  · exact baseInterval_1_160 (le_of_not_gt hcut160) hcut161
          · by_cases hcut166 : u < (0x5000 / 3)
            · by_cases hcut163 : u < 0x17a0
              · by_cases hcut162 : u < (0xc800 / 9)
                · exact baseInterval_1_161 (le_of_not_gt hcut161) hcut162
                · exact baseInterval_1_162 (le_of_not_gt hcut162) hcut163
              · by_cases hcut164 : u < 0x1900
                · exact baseInterval_1_163 (le_of_not_gt hcut163) hcut164
                · by_cases hcut165 : u < 0x19a1
                  · exact baseInterval_1_164 (le_of_not_gt hcut164) hcut165
                  · exact baseInterval_1_165 (le_of_not_gt hcut165) hcut166
            · by_cases hcut168 : u < (0x11800 / 9)
              · by_cases hcut167 : u < 0x1c00
                · exact baseInterval_1_166 (le_of_not_gt hcut166) hcut167
                · exact baseInterval_1_167 (le_of_not_gt hcut167) hcut168
              · by_cases hcut169 : u < 0x2000
                · exact baseInterval_1_168 (le_of_not_gt hcut168) hcut169
                · by_cases hcut170 : u < 0x2300
                  · exact baseInterval_1_169 (le_of_not_gt hcut169) hcut170
                  · exact baseInterval_1_170 (le_of_not_gt hcut170) hcut171
        · by_cases hcut180 : u < (0xa000 / 3)
          · by_cases hcut175 : u < (0x19000 / 9)
            · by_cases hcut173 : u < 0x2800
              · by_cases hcut172 : u < (0x7000 / 3)
                · exact baseInterval_1_171 (le_of_not_gt hcut171) hcut172
                · exact baseInterval_1_172 (le_of_not_gt hcut172) hcut173
              · by_cases hcut174 : u < (0x8000 / 3)
                · exact baseInterval_1_173 (le_of_not_gt hcut173) hcut174
                · exact baseInterval_1_174 (le_of_not_gt hcut174) hcut175
            · by_cases hcut177 : u < 0x3200
              · by_cases hcut176 : u < (0xe6a9 / 5)
                · exact baseInterval_1_175 (le_of_not_gt hcut175) hcut176
                · exact baseInterval_1_176 (le_of_not_gt hcut176) hcut177
              · by_cases hcut178 : u < (0x10000 / 5)
                · exact baseInterval_1_177 (le_of_not_gt hcut177) hcut178
                · by_cases hcut179 : u < 0x3342
                  · exact baseInterval_1_178 (le_of_not_gt hcut178) hcut179
                  · exact baseInterval_1_179 (le_of_not_gt hcut179) hcut180
          · by_cases hcut185 : u < 0x41eb
            · by_cases hcut182 : u < (0x1338c / 5)
              · by_cases hcut181 : u < 0x3800
                · exact baseInterval_1_180 (le_of_not_gt hcut180) hcut181
                · exact baseInterval_1_181 (le_of_not_gt hcut181) hcut182
              · by_cases hcut183 : u < (0x23000 / 9)
                · exact baseInterval_1_182 (le_of_not_gt hcut182) hcut183
                · by_cases hcut184 : u < 0x4000
                  · exact baseInterval_1_183 (le_of_not_gt hcut183) hcut184
                  · exact baseInterval_1_184 (le_of_not_gt hcut184) hcut185
            · by_cases hcut187 : u < 0x4600
              · by_cases hcut186 : u < 0x4380
                · exact baseInterval_1_185 (le_of_not_gt hcut185) hcut186
                · exact baseInterval_1_186 (le_of_not_gt hcut186) hcut187
              · by_cases hcut188 : u < (0x28000 / 9)
                · exact baseInterval_1_187 (le_of_not_gt hcut187) hcut188
                · by_cases hcut189 : u < (0xe000 / 3)
                  · exact baseInterval_1_188 (le_of_not_gt hcut188) hcut189
                  · exact baseInterval_1_189 (le_of_not_gt hcut189) hcut190
      · by_cases hcut209 : u < 0xa000
        · by_cases hcut199 : u < 0x7000
          · by_cases hcut194 : u < 0x5e80
            · by_cases hcut192 : u < (0x32000 / 9)
              · by_cases hcut191 : u < 0x5000
                · exact baseInterval_1_190 (le_of_not_gt hcut190) hcut191
                · exact baseInterval_1_191 (le_of_not_gt hcut191) hcut192
              · by_cases hcut193 : u < 0x5c49
                · exact baseInterval_1_192 (le_of_not_gt hcut192) hcut193
                · exact baseInterval_1_193 (le_of_not_gt hcut193) hcut194
            · by_cases hcut196 : u < 0x6684
              · by_cases hcut195 : u < 0x6400
                · exact baseInterval_1_194 (le_of_not_gt hcut194) hcut195
                · exact baseInterval_1_195 (le_of_not_gt hcut195) hcut196
              · by_cases hcut197 : u < (0xaf000 / 27)
                · exact baseInterval_1_196 (le_of_not_gt hcut196) hcut197
                · by_cases hcut198 : u < 0x6d60
                  · exact baseInterval_1_197 (le_of_not_gt hcut197) hcut198
                  · exact baseInterval_1_198 (le_of_not_gt hcut198) hcut199
          · by_cases hcut204 : u < (0x2b3fb / 5)
            · by_cases hcut201 : u < 0x8000
              · by_cases hcut200 : u < (0x46000 / 9)
                · exact baseInterval_1_199 (le_of_not_gt hcut199) hcut200
                · exact baseInterval_1_200 (le_of_not_gt hcut200) hcut201
              · by_cases hcut202 : u < 0x8025
                · exact baseInterval_1_201 (le_of_not_gt hcut201) hcut202
                · by_cases hcut203 : u < 0x88b0
                  · exact baseInterval_1_202 (le_of_not_gt hcut202) hcut203
                  · exact baseInterval_1_203 (le_of_not_gt hcut203) hcut204
            · by_cases hcut206 : u < (0xf5000 / 27)
              · by_cases hcut205 : u < 0x8c00
                · exact baseInterval_1_204 (le_of_not_gt hcut204) hcut205
                · exact baseInterval_1_205 (le_of_not_gt hcut205) hcut206
              · by_cases hcut207 : u < 0x9920
                · exact baseInterval_1_206 (le_of_not_gt hcut206) hcut207
                · by_cases hcut208 : u < 0x99c6
                  · exact baseInterval_1_207 (le_of_not_gt hcut207) hcut208
                  · exact baseInterval_1_208 (le_of_not_gt hcut208) hcut209
        · by_cases hcut218 : u < 0xe6a9
          · by_cases hcut213 : u < 0xc800
            · by_cases hcut211 : u < 0xb367
              · by_cases hcut210 : u < (0x64000 / 9)
                · exact baseInterval_1_209 (le_of_not_gt hcut209) hcut210
                · exact baseInterval_1_210 (le_of_not_gt hcut210) hcut211
              · by_cases hcut212 : u < (0x39aa4 / 5)
                · exact baseInterval_1_211 (le_of_not_gt hcut211) hcut212
                · exact baseInterval_1_212 (le_of_not_gt hcut212) hcut213
            · by_cases hcut215 : u < 0xcd08
              · by_cases hcut214 : u < (0x40000 / 5)
                · exact baseInterval_1_213 (le_of_not_gt hcut213) hcut214
                · exact baseInterval_1_214 (le_of_not_gt hcut214) hcut215
              · by_cases hcut216 : u < (0x28000 / 3)
                · exact baseInterval_1_215 (le_of_not_gt hcut215) hcut216
                · by_cases hcut217 : u < 0xe000
                  · exact baseInterval_1_216 (le_of_not_gt hcut216) hcut217
                  · exact baseInterval_1_217 (le_of_not_gt hcut217) hcut218
          · by_cases hcut223 : u < (0x38000 / 3)
            · by_cases hcut220 : u < 0x10000
              · by_cases hcut219 : u < (0x8c000 / 9)
                · exact baseInterval_1_218 (le_of_not_gt hcut218) hcut219
                · exact baseInterval_1_219 (le_of_not_gt hcut219) hcut220
              · by_cases hcut221 : u < 0x11800
                · exact baseInterval_1_220 (le_of_not_gt hcut220) hcut221
                · by_cases hcut222 : u < (0xa0000 / 9)
                  · exact baseInterval_1_221 (le_of_not_gt hcut221) hcut222
                  · exact baseInterval_1_222 (le_of_not_gt hcut222) hcut223
            · by_cases hcut225 : u < 0x14000
              · by_cases hcut224 : u < 0x1338c
                · exact baseInterval_1_223 (le_of_not_gt hcut223) hcut224
                · exact baseInterval_1_224 (le_of_not_gt hcut224) hcut225
              · by_cases hcut226 : u < (0x40000 / 3)
                · exact baseInterval_1_225 (le_of_not_gt hcut225) hcut226
                · by_cases hcut227 : u < (0xc8000 / 9)
                  · exact baseInterval_1_226 (le_of_not_gt hcut226) hcut227
                  · exact baseInterval_1_227 (le_of_not_gt hcut227) hcut228
    · by_cases hcut266 : u < 0x7822b
      · by_cases hcut247 : u < 0x33420
        · by_cases hcut237 : u < 0x21a35
          · by_cases hcut232 : u < 0x1c000
            · by_cases hcut230 : u < (0x81bf1 / 5)
              · by_cases hcut229 : u < 0x19a10
                · exact baseInterval_1_228 (le_of_not_gt hcut228) hcut229
                · exact baseInterval_1_229 (le_of_not_gt hcut229) hcut230
              · by_cases hcut231 : u < (0x868d4 / 5)
                · exact baseInterval_1_230 (le_of_not_gt hcut230) hcut231
                · exact baseInterval_1_231 (le_of_not_gt hcut231) hcut232
            · by_cases hcut234 : u < (0x118000 / 9)
              · by_cases hcut233 : u < 0x1cd52
                · exact baseInterval_1_232 (le_of_not_gt hcut232) hcut233
                · exact baseInterval_1_233 (le_of_not_gt hcut233) hcut234
              · by_cases hcut235 : u < 0x20000
                · exact baseInterval_1_234 (le_of_not_gt hcut234) hcut235
                · by_cases hcut236 : u < 0x20094
                  · exact baseInterval_1_235 (le_of_not_gt hcut235) hcut236
                  · exact baseInterval_1_236 (le_of_not_gt hcut236) hcut237
          · by_cases hcut242 : u < 0x2ab70
            · by_cases hcut239 : u < (0x140000 / 9)
              · by_cases hcut238 : u < (0xacfec / 5)
                · exact baseInterval_1_237 (le_of_not_gt hcut237) hcut238
                · exact baseInterval_1_238 (le_of_not_gt hcut238) hcut239
              · by_cases hcut240 : u < 0x28000
                · exact baseInterval_1_239 (le_of_not_gt hcut239) hcut240
                · by_cases hcut241 : u < 0x280b9
                  · exact baseInterval_1_240 (le_of_not_gt hcut240) hcut241
                  · exact baseInterval_1_241 (le_of_not_gt hcut241) hcut242
            · by_cases hcut244 : u < 0x2cd9c
              · by_cases hcut243 : u < 0x2b3fb
                · exact baseInterval_1_242 (le_of_not_gt hcut242) hcut243
                · exact baseInterval_1_243 (le_of_not_gt hcut243) hcut244
              · by_cases hcut245 : u < 0x300de
                · exact baseInterval_1_244 (le_of_not_gt hcut244) hcut245
                · by_cases hcut246 : u < (0x100000 / 5)
                  · exact baseInterval_1_245 (le_of_not_gt hcut245) hcut246
                  · exact baseInterval_1_246 (le_of_not_gt hcut246) hcut247
        · by_cases hcut256 : u < 0x50000
          · by_cases hcut251 : u < 0x40000
            · by_cases hcut249 : u < 0x38103
              · by_cases hcut248 : u < 0x38000
                · exact baseInterval_1_247 (le_of_not_gt hcut247) hcut248
                · exact baseInterval_1_248 (le_of_not_gt hcut248) hcut249
              · by_cases hcut250 : u < 0x3bcd0
                · exact baseInterval_1_249 (le_of_not_gt hcut249) hcut250
                · exact baseInterval_1_250 (le_of_not_gt hcut250) hcut251
            · by_cases hcut253 : u < 0x4346a
              · by_cases hcut252 : u < 0x40128
                · exact baseInterval_1_251 (le_of_not_gt hcut251) hcut252
                · exact baseInterval_1_252 (le_of_not_gt hcut252) hcut253
              · by_cases hcut254 : u < (0x280000 / 9)
                · exact baseInterval_1_253 (le_of_not_gt hcut253) hcut254
                · by_cases hcut255 : u < (0x1853d3 / 5)
                  · exact baseInterval_1_254 (le_of_not_gt hcut254) hcut255
                  · exact baseInterval_1_255 (le_of_not_gt hcut255) hcut256
          · by_cases hcut261 : u < 0x601bc
            · by_cases hcut258 : u < 0x567f6
              · by_cases hcut257 : u < (0x100000 / 3)
                · exact baseInterval_1_256 (le_of_not_gt hcut256) hcut257
                · exact baseInterval_1_257 (le_of_not_gt hcut257) hcut258
              · by_cases hcut259 : u < (0x320000 / 9)
                · exact baseInterval_1_258 (le_of_not_gt hcut258) hcut259
                · by_cases hcut260 : u < 0x59b38
                  · exact baseInterval_1_259 (le_of_not_gt hcut259) hcut260
                  · exact baseInterval_1_260 (le_of_not_gt hcut260) hcut261
            · by_cases hcut263 : u < (0x206fc4 / 5)
              · by_cases hcut262 : u < 0x64000
                · exact baseInterval_1_261 (le_of_not_gt hcut261) hcut262
                · exact baseInterval_1_262 (le_of_not_gt hcut262) hcut263
              · by_cases hcut264 : u < (0x140000 / 3)
                · exact baseInterval_1_263 (le_of_not_gt hcut263) hcut264
                · by_cases hcut265 : u < 0x70000
                  · exact baseInterval_1_264 (le_of_not_gt hcut264) hcut265
                  · exact baseInterval_1_265 (le_of_not_gt hcut265) hcut266
      · by_cases hcut285 : u < 0xe0000
        · by_cases hcut275 : u < 0xa0000
          · by_cases hcut270 : u < 0x81bf1
            · by_cases hcut268 : u < 0x80000
              · by_cases hcut267 : u < (0x460000 / 9)
                · exact baseInterval_1_266 (le_of_not_gt hcut266) hcut267
                · exact baseInterval_1_267 (le_of_not_gt hcut267) hcut268
              · by_cases hcut269 : u < 0x80250
                · exact baseInterval_1_268 (le_of_not_gt hcut268) hcut269
                · exact baseInterval_1_269 (le_of_not_gt hcut269) hcut270
            · by_cases hcut272 : u < 0x8c000
              · by_cases hcut271 : u < 0x868d4
                · exact baseInterval_1_270 (le_of_not_gt hcut270) hcut271
                · exact baseInterval_1_271 (le_of_not_gt hcut271) hcut272
              · by_cases hcut273 : u < (0x500000 / 9)
                · exact baseInterval_1_272 (le_of_not_gt hcut272) hcut273
                · by_cases hcut274 : u < (0x1c0000 / 3)
                  · exact baseInterval_1_273 (le_of_not_gt hcut273) hcut274
                  · exact baseInterval_1_274 (le_of_not_gt hcut274) hcut275
          · by_cases hcut280 : u < 0xc8000
            · by_cases hcut277 : u < (0x200000 / 3)
              · by_cases hcut276 : u < 0xa8309
                · exact baseInterval_1_275 (le_of_not_gt hcut275) hcut276
                · exact baseInterval_1_276 (le_of_not_gt hcut276) hcut277
              · by_cases hcut278 : u < (0x640000 / 9)
                · exact baseInterval_1_277 (le_of_not_gt hcut277) hcut278
                · by_cases hcut279 : u < 0xb3670
                  · exact baseInterval_1_278 (le_of_not_gt hcut278) hcut279
                  · exact baseInterval_1_279 (le_of_not_gt hcut279) hcut280
            · by_cases hcut282 : u < (0x400000 / 5)
              · by_cases hcut281 : u < 0xc839d
                · exact baseInterval_1_280 (le_of_not_gt hcut280) hcut281
                · exact baseInterval_1_281 (le_of_not_gt hcut281) hcut282
              · by_cases hcut283 : u < 0xcd080
                · exact baseInterval_1_282 (le_of_not_gt hcut282) hcut283
                · by_cases hcut284 : u < 0xd5930
                  · exact baseInterval_1_283 (le_of_not_gt hcut283) hcut284
                  · exact baseInterval_1_284 (le_of_not_gt hcut284) hcut285
        · by_cases hcut295 : u < 0x12b010
          · by_cases hcut290 : u < 0x1004a0
            · by_cases hcut287 : u < 0xf0456
              · by_cases hcut286 : u < (0x48fb79 / 5)
                · exact baseInterval_1_285 (le_of_not_gt hcut285) hcut286
                · exact baseInterval_1_286 (le_of_not_gt hcut286) hcut287
              · by_cases hcut288 : u < (0x8c0000 / 9)
                · exact baseInterval_1_287 (le_of_not_gt hcut287) hcut288
                · by_cases hcut289 : u < 0x100000
                  · exact baseInterval_1_288 (le_of_not_gt hcut288) hcut289
                  · exact baseInterval_1_289 (le_of_not_gt hcut289) hcut290
            · by_cases hcut292 : u < 0x118000
              · by_cases hcut291 : u < 0x1037e2
                · exact baseInterval_1_290 (le_of_not_gt hcut290) hcut291
                · exact baseInterval_1_291 (le_of_not_gt hcut291) hcut292
              · by_cases hcut293 : u < 0x11850f
                · exact baseInterval_1_292 (le_of_not_gt hcut292) hcut293
                · by_cases hcut294 : u < (0xa00000 / 9)
                  · exact baseInterval_1_293 (le_of_not_gt hcut293) hcut294
                  · exact baseInterval_1_294 (le_of_not_gt hcut294) hcut295
          · by_cases hcut300 : u < (0x400000 / 3)
            · by_cases hcut297 : u < 0x140000
              · by_cases hcut296 : u < (0x614f4c / 5)
                · exact baseInterval_1_295 (le_of_not_gt hcut295) hcut296
                · exact baseInterval_1_296 (le_of_not_gt hcut296) hcut297
              · by_cases hcut298 : u < (0x2300000 / 27)
                · exact baseInterval_1_297 (le_of_not_gt hcut297) hcut298
                · by_cases hcut299 : u < 0x150612
                  · exact baseInterval_1_298 (le_of_not_gt hcut298) hcut299
                  · exact baseInterval_1_299 (le_of_not_gt hcut299) hcut300
            · by_cases hcut302 : u < 0x166ce0
              · by_cases hcut301 : u < (0xc80000 / 9)
                · exact baseInterval_1_300 (le_of_not_gt hcut300) hcut301
                · exact baseInterval_1_301 (le_of_not_gt hcut301) hcut302
              · by_cases hcut303 : u < 0x1853d3
                · exact baseInterval_1_302 (le_of_not_gt hcut302) hcut303
                · by_cases hcut304 : u < 0x190000
                  · exact baseInterval_1_303 (le_of_not_gt hcut303) hcut304
                  · exact baseInterval_1_304 (le_of_not_gt hcut304) hhi

def baseStepValid_below_limit (eps : Bool) {u : ℚ} (hlo : 1 ≤ u) (hhi : u < 0x1921ee) :
    baseStepValid eps u := by
  cases eps
  · exact baseStepValid_0_below_limit hlo hhi
  · exact baseStepValid_1_below_limit hlo hhi

def cutoffState_eq_base (eps : Bool) (u : ℚ) (hu : u < 0x1921ee) :
    cutoffState eps u = cutoffTableEval (basePieces eps) u := by
  apply cutoffState_eq_table basePieces baseTable_small _ eps u hu
  intro e v hvlo hvhi
  exact (baseStepValid_below_limit e hvlo hvhi).1

def cutoffAvailability_below_base (eps : Bool) {u : ℚ}
    (hlo : 1 ≤ u) (hhi : u < 0x1921ee) :
    cutoffAvailable u (quotaValue eps u) 0 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) ∨
    cutoffAvailable u (quotaValue eps u) 1 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) := by
  have hv := (baseStepValid_below_limit eps hlo hhi).2
  have hp := cutoffState_eq_base eps u hhi
  have h5 := cutoffState_eq_base true (u / 5) (by linarith)
  have h7 := cutoffState_eq_base eps (u / 7) (by linarith)
  rw [← hp, ← h5, ← h7] at hv
  have hpar := cutoffState_parity eps u
  have hcases : (cutoffState eps u).1 = 0 ∨ (cutoffState eps u).1 = 1 := by omega
  rcases hcases with hzero | hone
  · exact Or.inl (by simpa only [hzero] using hv)
  · exact Or.inr (by simpa only [hone] using hv)


end Bounty



end SubmissionComponent_PolicyBaseIntervalsCompact


/- Component RationalCertificate; SHA256 4bf290ccbdabe7b223ee62ecbc320e7beb70013a61188aa52647bbbf8aabd452 -/
section SubmissionComponent_RationalCertificate
/- Rational certificates give natural cutoff certificates without rounding gaps. -/

namespace Bounty

structure RationalCutoffCertificate (n : ℕ) where
  parity : ℕ → ℕ
  cutoff : ℕ → ℚ
  parity_lt : ∀ q ∈ coprimeCores n, parity q < 2
  cutoff_nonneg : ∀ q ∈ coprimeCores n, 0 ≤ cutoff q
  cutoff_bound : ∀ q ∈ coprimeCores n, cutoff q ≤ (n : ℚ) / q
  lower_bound : ∀ q ∈ coprimeCores n, 3 * ((n : ℚ) / q) ≤ 4 * cutoff q
  compatible_five : ∀ q ∈ coprimeCores n, 5 * q ∈ coprimeCores n →
    (if parity q = parity (5 * q) then 4 else 6) * cutoff (5 * q) ≤ cutoff q
  compatible_seven : ∀ q ∈ coprimeCores n, 7 * q ∈ coprimeCores n →
    (if parity q = parity (7 * q) then 4 else 6) * cutoff (7 * q) ≤ cutoff q
  quota : ∀ q ∈ coprimeCores n, cutoffCount (parity q) ⌊cutoff q⌋₊ = componentQuota n q

noncomputable def RationalCutoffCertificate.toNatural {n : ℕ} (C : RationalCutoffCertificate n) :
    CutoffCertificate n where
  parity := C.parity
  cutoff := fun q => ⌊C.cutoff q⌋₊
  parity_lt := C.parity_lt
  cutoff_bound := by
    intro q hq
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
    have hh := (Nat.floor_le (C.cutoff_nonneg q hq)).trans (C.cutoff_bound q hq)
    have hmul := (le_div_iff₀ (by exact_mod_cast hqpos : (0 : ℚ) < q)).mp hh
    exact_mod_cast (by nlinarith : (q : ℚ) * ⌊C.cutoff q⌋₊ ≤ n)
  lower_bound := by
    intro q hq s hs
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
    exact rationalWindow_scaled_eighth hqpos (C.lower_bound q hq) hs
  compatible_five := by
    intro q hq ht
    have hh := C.compatible_five q hq ht
    by_cases he : C.parity q = C.parity (5 * q)
    · simp only [he, ↓reduceIte] at hh ⊢
      exact floor_scaled_le (C.cutoff_nonneg (5 * q) ht) hh
    · simp only [he, ↓reduceIte] at hh ⊢
      exact floor_scaled_le (C.cutoff_nonneg (5 * q) ht) hh
  compatible_seven := by
    intro q hq ht
    have hh := C.compatible_seven q hq ht
    by_cases he : C.parity q = C.parity (7 * q)
    · simp only [he, ↓reduceIte] at hh ⊢
      exact floor_scaled_le (C.cutoff_nonneg (7 * q) ht) hh
    · simp only [he, ↓reduceIte] at hh ⊢
      exact floor_scaled_le (C.cutoff_nonneg (7 * q) ht) hh
  quota := C.quota

def f_eq_globalUpper_of_rational_certificate {n : ℕ} (C : RationalCutoffCertificate n) :
    Erdos1062.f n = globalUpper n := f_eq_globalUpper_of_certificate C.toNatural

end Bounty

end SubmissionComponent_RationalCertificate

/- Component RationalSystem; SHA256 b7de74307a5b0cd6cb43eb087dd137f3c1721f930d55f988aa2b75dce23b693e -/
section SubmissionComponent_RationalSystem
/- A universal two-type cutoff system suffices for every extremal problem size. -/

namespace Bounty

structure RationalCutoffSystem where
  parity : Bool → ℚ → ℕ
  cutoff : Bool → ℚ → ℚ
  parity_lt : ∀ eps u, 1 ≤ u → parity eps u < 2
  cutoff_nonneg : ∀ eps u, 1 ≤ u → 0 ≤ cutoff eps u
  cutoff_bound : ∀ eps u, 1 ≤ u → cutoff eps u ≤ u
  lower_bound : ∀ eps u, 1 ≤ u → 3 * u ≤ 4 * cutoff eps u
  compatible_five : ∀ eps u, 5 ≤ u →
    (if parity eps u = parity true (u / 5) then 4 else 6) * cutoff true (u / 5) ≤ cutoff eps u
  compatible_seven : ∀ eps u, 7 ≤ u →
    (if parity eps u = parity eps (u / 7) then 4 else 6) * cutoff eps (u / 7) ≤ cutoff eps u
  quota : ∀ eps u, 1 ≤ u → cutoffCount (parity eps u) ⌊cutoff eps u⌋₊ = rationalQuota eps u

noncomputable def RationalCutoffSystem.toCertificate (S : RationalCutoffSystem) (n : ℕ) :
    RationalCutoffCertificate n where
  parity := fun q => S.parity (decide (5 ∣ q)) ((n : ℚ) / q)
  cutoff := fun q => S.cutoff (decide (5 ∣ q)) ((n : ℚ) / q)
  parity_lt := fun q hq => S.parity_lt _ _ (quotient_ge_one_of_core_mem hq)
  cutoff_nonneg := fun q hq => S.cutoff_nonneg _ _ (quotient_ge_one_of_core_mem hq)
  cutoff_bound := fun q hq => S.cutoff_bound _ _ (quotient_ge_one_of_core_mem hq)
  lower_bound := fun q hq => S.lower_bound _ _ (quotient_ge_one_of_core_mem hq)
  compatible_five := by
    intro q hq ht
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
    have h5qn := (Finset.mem_Icc.mp (Finset.mem_filter.mp ht).1).2
    have hu : (5 : ℚ) ≤ (n : ℚ) / q := by
      apply (le_div_iff₀ (by exact_mod_cast hqpos : (0 : ℚ) < q)).mpr
      exact_mod_cast h5qn
    have hflag : decide (5 ∣ 5 * q) = true := by simp
    have hh := S.compatible_five (decide (5 ∣ q)) ((n : ℚ) / q) hu
    simpa only [rational_scaled_quotient, hflag, Nat.cast_ofNat] using hh
  compatible_seven := by
    intro q hq ht
    have hqpos := (Finset.mem_Icc.mp (Finset.mem_filter.mp hq).1).1
    have h7qn := (Finset.mem_Icc.mp (Finset.mem_filter.mp ht).1).2
    have hu : (7 : ℚ) ≤ (n : ℚ) / q := by
      apply (le_div_iff₀ (by exact_mod_cast hqpos : (0 : ℚ) < q)).mpr
      exact_mod_cast h7qn
    have hd : (5 ∣ 7 * q) ↔ 5 ∣ q := by
      rw [(show Nat.Prime 5 by decide).dvd_mul]
      norm_num
    have hflag : decide (5 ∣ 7 * q) = decide (5 ∣ q) := by simp only [hd]
    have hh := S.compatible_seven (decide (5 ∣ q)) ((n : ℚ) / q) hu
    simpa only [rational_scaled_quotient, hflag, Nat.cast_ofNat] using hh
  quota := by
    intro q hq
    rw [componentQuota_eq_rationalQuota hq]
    exact S.quota _ _ (quotient_ge_one_of_core_mem hq)

def f_eq_globalUpper_of_system (S : RationalCutoffSystem) (n : ℕ) :
    Erdos1062.f n = globalUpper n :=
  f_eq_globalUpper_of_rational_certificate (S.toCertificate n)

end Bounty

end SubmissionComponent_RationalSystem

/- Component CutoffValidity; SHA256 b76b811b8d2e4c826d143b84e416baa04e731af2cecbbf989464d59f3d674bd1 -/
section SubmissionComponent_CutoffValidity
/- Universal trial availability is the remaining combinatorial construction obligation. -/

namespace Bounty

def cutoffCandidate_available {eps : Bool} {u : ℚ} {c5 c7 : ℕ × ℚ}
    (h : cutoffAvailable u (quotaValue eps u) 0 c5 c7 ∨
      cutoffAvailable u (quotaValue eps u) 1 c5 c7) :
    cutoffAvailable u (quotaValue eps u) (cutoffCandidate eps u c5 c7).1 c5 c7 := by
  unfold cutoffCandidate
  dsimp only
  by_cases hp0 : Nat.log 2 ⌊u⌋₊ % 2 = 0
  · rw [hp0]
    split_ifs with hh
    · exact hh
    · simpa using h.resolve_left hh
  · have hp1 : Nat.log 2 ⌊u⌋₊ % 2 = 1 := by omega
    rw [hp1]
    split_ifs with hh
    · exact hh
    · simpa using h.resolve_right hh

def cutoffState_eq_trial {eps : Bool} {u : ℚ} (hu : 1 ≤ u) :
    (cutoffState eps u).2 = cutoffTrial u (quotaValue eps u) (cutoffState eps u).1
      (cutoffState true (u / 5)) (cutoffState eps (u / 7)) := by
  simpa only [cutoffState_of_large hu] using
    cutoffCandidate_eq_trial eps u (cutoffState true (u / 5)) (cutoffState eps (u / 7))

def cutoffState_bounds {eps : Bool} {u : ℚ} (hu : 1 ≤ u) :
    3 * u / 4 ≤ (cutoffState eps u).2 ∧
    (lowerCutoff (cutoffState eps u).1 (quotaValue eps u) : ℚ) ≤ (cutoffState eps u).2 ∧
    (if (cutoffState eps u).1 = (cutoffState true (u / 5)).1 then 4 else 6) *
      (cutoffState true (u / 5)).2 ≤ (cutoffState eps u).2 ∧
    (if (cutoffState eps u).1 = (cutoffState eps (u / 7)).1 then 4 else 6) *
      (cutoffState eps (u / 7)).2 ≤ (cutoffState eps u).2 := by
  have hh := cutoffTrial_bounds u (quotaValue eps u) (cutoffState eps u).1
    (cutoffState true (u / 5)) (cutoffState eps (u / 7))
  rwa [← cutoffState_eq_trial hu] at hh

def CutoffAvailability : Prop :=
  ∀ eps u, 1 ≤ u →
    cutoffAvailable u (quotaValue eps u) 0 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) ∨
    cutoffAvailable u (quotaValue eps u) 1 (cutoffState true (u / 5)) (cutoffState eps (u / 7))

def cutoffState_available (H : CutoffAvailability) {eps : Bool} {u : ℚ} (hu : 1 ≤ u) :
    cutoffAvailable u (quotaValue eps u) (cutoffState eps u).1
      (cutoffState true (u / 5)) (cutoffState eps (u / 7)) := by
  simpa only [cutoffState_of_large hu] using cutoffCandidate_available (H eps u hu)

noncomputable def cutoffSystemOfAvailability (H : CutoffAvailability) : RationalCutoffSystem where
  parity := fun eps u => (cutoffState eps u).1
  cutoff := fun eps u => (cutoffState eps u).2
  parity_lt := fun eps u _ => cutoffState_parity eps u
  cutoff_nonneg := by
    intro eps u hu
    have hh := (cutoffState_bounds (eps := eps) hu).1
    linarith
  cutoff_bound := by
    intro eps u hu
    have hh := (cutoffState_available H (eps := eps) hu).1
    rwa [← cutoffState_eq_trial hu] at hh
  lower_bound := by
    intro eps u hu
    have hh := (cutoffState_bounds (eps := eps) hu).1
    linarith
  compatible_five := by
    intro eps u hu
    exact (cutoffState_bounds (eps := eps) (by linarith : 1 ≤ u)).2.2.1
  compatible_seven := by
    intro eps u hu
    exact (cutoffState_bounds (eps := eps) (by linarith : 1 ≤ u)).2.2.2
  quota := by
    intro eps u hu
    have hh := cutoffTrial_size (by linarith : 0 ≤ u) (cutoffState_available H (eps := eps) hu)
    rw [← cutoffState_eq_trial hu] at hh
    rwa [quotaValue_eq] at hh

def f_eq_globalUpper_of_availability (H : CutoffAvailability) (n : ℕ) :
    Erdos1062.f n = globalUpper n := f_eq_globalUpper_of_system (cutoffSystemOfAvailability H) n

end Bounty

end SubmissionComponent_CutoffValidity

/- Component LocalCutoffCertificate; SHA256 36d38defe29cad748866a71ca0c76260923f99bf4676c3fe0a146c9c68e057ce -/
section SubmissionComponent_LocalCutoffCertificate
/- Availability on a bounded rational interval suffices for all smaller extremal problems. -/

namespace Bounty

def CutoffAvailabilityBelow (limit : ℚ) : Prop :=
  ∀ eps u, 1 ≤ u → u < limit →
    cutoffAvailable u (quotaValue eps u) 0 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) ∨
    cutoffAvailable u (quotaValue eps u) 1 (cutoffState true (u / 5)) (cutoffState eps (u / 7))

end Bounty

end SubmissionComponent_LocalCutoffCertificate

/- Component BaseExact; SHA256 53c2821bff560ca19580f278c1d0d10265cb800b1b19e5030fd626325654654c -/
section SubmissionComponent_BaseExact
/- The exact extremal formula throughout the verified finite base range. -/

namespace Bounty

def cutoffAvailabilityBelow_base : CutoffAvailabilityBelow 0x1921ee := by
  intro eps u hlo hhi
  exact cutoffAvailability_below_base eps hlo hhi

end Bounty

end SubmissionComponent_BaseExact


end PolicyCombinatorialFront_PolicyBaseExactCompact

/- Frozen source PolicyClosureInputMath; SHA256 e628d9bcd519a9a1c50759276dd0f324c0c5ce733c98d201f338862911126baf. -/
section PolicyCombinatorialFront_PolicyClosureInputMath
/- One-file proof candidate assembled from the actual local import graph.
A complete ordinary-kernel check and target axiom audit are still required. -/

/- Component NormalizedCounts; SHA256 cc30e10e0045906b45078bdb26cb5ee7dbf0f1a8355fd72b97ec0e3cb126c06f -/
section SubmissionComponent_NormalizedCounts
/- The two cutoff deficits, in the form used by the normalized closure. -/

namespace Bounty

def log_four_half_even {n : ℕ} (hn : 2 ≤ n)
    (hpar : Nat.log 2 n % 2 = 0) :
    Nat.log 4 (n / 2) + 1 = Nat.log 4 n := by
  have hlog : 1 ≤ Nat.log 2 n :=
    (Nat.le_log_iff_pow_le (by norm_num) (by omega : n ≠ 0)).mpr (by simpa using hn)
  rw [log_four_eq, log_four_eq, Nat.log_div_base]
  omega

def log_three_half_below {n : ℕ} (hn : 2 ≤ n)
    (htop : ¬2 * 3 ^ Nat.log 3 n ≤ n) :
    Nat.log 3 (n / 2) + 1 = Nat.log 3 n := by
  have hlog : 1 ≤ Nat.log 3 n := by
    by_contra hh
    have hz : Nat.log 3 n = 0 := by omega
    simp only [hz, pow_zero, mul_one] at htop
    omega
  have hb : Nat.log 3 n - 1 + 1 = Nat.log 3 n := by omega
  have hp := Nat.pow_log_le_self 3 (by omega : n ≠ 0)
  have hp' : 3 ^ (Nat.log 3 n - 1) * 3 ≤ n := by
    simpa only [← pow_succ, hb] using hp
  have he : Nat.log 3 (n / 2) = Nat.log 3 n - 1 := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · omega
    · rw [hb]
      omega
  omega

def log_two_odd_iff_four_threshold {n : ℕ} (hn : 0 < n) :
    Nat.log 2 n % 2 = 1 ↔ 2 * 4 ^ Nat.log 4 n ≤ n := by
  have power (j : ℕ) : (2 : ℕ) ^ (2 * j + 1) = 2 * 4 ^ j := by
    rw [pow_succ, pow_mul]
    norm_num
    omega
  have hlo := Nat.pow_log_le_self 2 (by omega : n ≠ 0)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < (2 : ℕ)) n
  rw [log_four_eq]
  by_cases hp : Nat.log 2 n % 2 = 1
  · have he : Nat.log 2 n = 2 * (Nat.log 2 n / 2) + 1 := by omega
    rw [he, power] at hlo
    exact iff_of_true hp hlo
  · have he : Nat.log 2 n + 1 = 2 * (Nat.log 2 n / 2) + 1 := by omega
    rw [Nat.succ_eq_add_one, he, power] at hhi
    exact iff_of_false hp (by omega)

def cutoffCount_zero_deficit {n : ℕ} (hn : 0 < n) :
    cutoffCount 0 n +
      (if Nat.log 2 n % 2 = 1 ∧ 2 * 3 ^ Nat.log 3 n ≤ n then 1 else 0) =
      smoothRankBound n := by
  simp [cutoffCount, smoothRankBound, Nat.ne_of_gt hn, log_four_eq]

def cutoffCount_one_deficit {n : ℕ} (hn : 2 ≤ n) :
    cutoffCount 1 n +
      (if ¬Nat.log 2 n % 2 = 1 ∧ ¬2 * 3 ^ Nat.log 3 n ≤ n then 1 else 0) =
      smoothRankBound n := by
  have hc : cutoffCount 1 n = Nat.log 3 (n / 2) + Nat.log 4 (n / 2) + 2 := by
    simp [cutoffCount, show ¬n < 2 by omega]
  have hr : smoothRankBound n = Nat.log 3 n + 1 + Nat.log 4 n +
      (if Nat.log 2 n % 2 = 1 ∧ 2 * 3 ^ Nat.log 3 n ≤ n then 1 else 0) := by
    simp [smoothRankBound, show n ≠ 0 by omega, log_four_eq]
  rw [hc, hr]
  by_cases hp : Nat.log 2 n % 2 = 1
  · have h4 := log_four_half_odd hp
    by_cases hd : 2 * 3 ^ Nat.log 3 n ≤ n
    · have h3 := log_three_half (by omega : 0 < n) hd
      simp only [hp, hd, and_self, not_true_eq_false, reduceIte]
      omega
    · have h3 := log_three_half_below hn hd
      simp only [hp, hd, and_false, not_true_eq_false, false_and, reduceIte]
      omega
  · have h4 := log_four_half_even hn (by omega)
    by_cases hd : 2 * 3 ^ Nat.log 3 n ≤ n
    · have h3 := log_three_half (by omega : 0 < n) hd
      simp only [hp, hd, false_and, not_true_eq_false, and_false, reduceIte]
      omega
    · have h3 := log_three_half_below hn hd
      simp only [hp, hd, not_false_eq_true, and_self, reduceIte]
      omega

def cutoffCount_zero_floor_deficit {u : ℚ} (hu : 1 ≤ u) :
    cutoffCount 0 ⌊u⌋₊ +
      (if 2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ≤ u ∧
          2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ u then 1 else 0) =
      smoothRankBound ⌊u⌋₊ := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 0 < ⌊u⌋₊ := by
    have hh : 1 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
    omega
  have hh := cutoffCount_zero_deficit hn
  simpa only [log_two_odd_iff_four_threshold hn, Nat.le_floor_iff hu0,
    Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] using hh

def cutoffCount_one_floor_deficit {u : ℚ} (hu : 2 ≤ u) :
    cutoffCount 1 ⌊u⌋₊ +
      (if ¬2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ≤ u ∧
          ¬2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ u then 1 else 0) =
      smoothRankBound ⌊u⌋₊ := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hh := cutoffCount_one_deficit hn
  simpa only [log_two_odd_iff_four_threshold (by omega : 0 < ⌊u⌋₊),
    Nat.le_floor_iff hu0, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] using hh


end Bounty

end SubmissionComponent_NormalizedCounts

/- Component NormalizedLevels; SHA256 ce27accb82b45eddab5f148b265cc2842517defc56d50d7be12768d28eb2a147 -/
section SubmissionComponent_NormalizedLevels
/- Exact threshold locations needed for normalized cutoff trials. -/

namespace Bounty

def lowerCutoff_zero_at_count {n : ℕ} (hn : 0 < n) :
    lowerCutoff 0 (cutoffCount 0 n) =
      max (4 ^ Nat.log 4 n) (3 ^ Nat.log 3 n) := by
  let a := 4 ^ Nat.log 4 n
  let b := 3 ^ Nat.log 3 n
  have ha : a ≤ n := Nat.pow_log_le_self 4 (by omega)
  have hb : b ≤ n := Nat.pow_log_le_self 3 (by omega)
  have hab : max a b ≤ n := max_le ha hb
  have hpos : 0 < max a b := lt_of_lt_of_le (by dsimp [a]; positivity) (le_max_left _ _)
  have h4 : Nat.log 4 (max a b) = Nat.log 4 n := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · exact le_max_left _ _
    · exact lt_of_le_of_lt hab (Nat.lt_pow_succ_log_self (by norm_num) n)
  have h3 : Nat.log 3 (max a b) = Nat.log 3 n := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · exact le_max_right _ _
    · exact lt_of_le_of_lt hab (Nat.lt_pow_succ_log_self (by norm_num) n)
  have hc : cutoffCount 0 (max a b) = cutoffCount 0 n := by
    simp [cutoffCount, Nat.ne_of_gt hn, Nat.ne_of_gt hpos, h4, h3]
  apply le_antisymm
  · exact (lowerCutoff_le_iff _ _ _).mpr (le_of_eq hc.symm)
  · change max a b ≤ lowerCutoff 0 (cutoffCount 0 n)
    by_contra hh
    let r := lowerCutoff 0 (cutoffCount 0 n)
    have hr : r < max a b := by dsimp [r]; omega
    have hrn : r ≤ n := le_trans (Nat.le_of_lt hr) hab
    have hs : cutoffCount 0 n ≤ cutoffCount 0 r := lowerCutoff_spec _ _
    have hrpos : 0 < r := by
      by_contra hh
      have hz : r = 0 := by omega
      simp [cutoffCount, hz, Nat.ne_of_gt hn] at hs
    have h4le := Nat.log_mono_right (b := 4) hrn
    have h3le := Nat.log_mono_right (b := 3) hrn
    have hcount : Nat.log 3 n + 1 + Nat.log 4 n ≤ Nat.log 3 r + 1 + Nat.log 4 r := by
      simpa [cutoffCount, Nat.ne_of_gt hn, Nat.ne_of_gt hrpos] using hs
    have h4eq : Nat.log 4 n = Nat.log 4 r := by omega
    have h3eq : Nat.log 3 n = Nat.log 3 r := by omega
    have har : a ≤ r := by
      dsimp [a]
      rw [h4eq]
      exact Nat.pow_log_le_self _ (by omega)
    have hbr : b ≤ r := by
      dsimp [b]
      rw [h3eq]
      exact Nat.pow_log_le_self _ (by omega)
    have := max_le har hbr
    omega

def lowerCutoff_one_scale {k : ℕ} (hk : 2 ≤ k) :
    lowerCutoff 1 k = 2 * lowerCutoff 0 (k - 1) := by
  have equiv (r : ℕ) : k ≤ cutoffCount 1 r ↔ k - 1 ≤ cutoffCount 0 (r / 2) := by
    by_cases hr : r < 2
    · have hz : r / 2 = 0 := by omega
      simp [cutoffCount, hr, hz]
      omega
    · have hr0 : r / 2 ≠ 0 := by omega
      simp only [cutoffCount, one_ne_zero, reduceIte, hr, hr0]
      omega
  apply le_antisymm
  · apply (lowerCutoff_le_iff _ _ _).mpr
    rw [equiv]
    simpa using lowerCutoff_spec 0 (k - 1)
  · have h := (equiv (lowerCutoff 1 k)).mp (lowerCutoff_spec 1 k)
    have hh := (lowerCutoff_le_iff 0 (k - 1) (lowerCutoff 1 k / 2)).mpr h
    omega

def lowerCutoff_one_at_count {n : ℕ} (hn : 2 ≤ n) :
    lowerCutoff 1 (cutoffCount 1 n) =
      2 * max (4 ^ Nat.log 4 (n / 2)) (3 ^ Nat.log 3 (n / 2)) := by
  have hn0 : n / 2 ≠ 0 := by omega
  have hc : cutoffCount 1 n = cutoffCount 0 (n / 2) + 1 := by
    simp [cutoffCount, show ¬n < 2 by omega, hn0]
    omega
  have hk : 2 ≤ cutoffCount 1 n := by
    simp [cutoffCount, show ¬n < 2 by omega]
  rw [lowerCutoff_one_scale hk, hc, Nat.add_sub_cancel,
    lowerCutoff_zero_at_count (by omega)]


end Bounty

end SubmissionComponent_NormalizedLevels

/- Component NextLevels; SHA256 4dcf40da0403155de833962370e6c5abfcbcc143216e485e8a680c6339e02016 -/
section SubmissionComponent_NextLevels
/- The next cutoff level occurs at the first subsequent power threshold. -/

namespace Bounty

end Bounty

end SubmissionComponent_NextLevels

/- Component PreviousLevels; SHA256 9d2bcf6dd070c4d44702e2d8c626018e68ce2d18f724987a42bfb234449da2f9 -/
section SubmissionComponent_PreviousLevels
/- The preceding cutoff level, separated according to its last threshold. -/

namespace Bounty

def lowerCutoff_zero_previous_four {n : ℕ} (hn : 0 < n)
    (horder : 3 ^ Nat.log 3 n < 4 ^ Nat.log 4 n) :
    lowerCutoff 0 (cutoffCount 0 n - 1) =
      max (4 ^ (Nat.log 4 n - 1)) (3 ^ Nat.log 3 n) := by
  have hj : 0 < Nat.log 4 n := by
    by_contra hh
    have hz : Nat.log 4 n = 0 := by omega
    have hp : 0 < (3 : ℕ) ^ Nat.log 3 n := by positivity
    simp only [hz, pow_zero] at horder
    omega
  have hs : Nat.log 4 n - 1 + 1 = Nat.log 4 n := by omega
  have hp : 4 ^ (Nat.log 4 n - 1) * 4 = 4 ^ Nat.log 4 n := by
    rw [← pow_succ, hs]
  have hp0 : 0 < (4 : ℕ) ^ (Nat.log 4 n - 1) := by positivity
  let m := 4 ^ Nat.log 4 n - 1
  have hm : 0 < m := by dsimp [m]; omega
  have hmn : m ≤ n := by
    have hh := Nat.pow_log_le_self 4 (Nat.ne_of_gt hn)
    dsimp [m]
    omega
  have h4 : Nat.log 4 m = Nat.log 4 n - 1 := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · dsimp [m]
      omega
    · rw [hs]
      dsimp [m]
      omega
  have h3 : Nat.log 3 m = Nat.log 3 n := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · dsimp [m]
      omega
    · exact lt_of_le_of_lt hmn (Nat.lt_pow_succ_log_self (by norm_num) n)
  have hc : cutoffCount 0 m = cutoffCount 0 n - 1 := by
    simp [cutoffCount, Nat.ne_of_gt hn, Nat.ne_of_gt hm, h4, h3]
    omega
  rw [← hc, lowerCutoff_zero_at_count hm, h4, h3]

def lowerCutoff_zero_previous_three {n : ℕ} (hn : 0 < n)
    (horder : 4 ^ Nat.log 4 n < 3 ^ Nat.log 3 n) :
    lowerCutoff 0 (cutoffCount 0 n - 1) =
      max (4 ^ Nat.log 4 n) (3 ^ (Nat.log 3 n - 1)) := by
  have hj : 0 < Nat.log 3 n := by
    by_contra hh
    have hz : Nat.log 3 n = 0 := by omega
    have hp : 0 < (4 : ℕ) ^ Nat.log 4 n := by positivity
    simp only [hz, pow_zero] at horder
    omega
  have hs : Nat.log 3 n - 1 + 1 = Nat.log 3 n := by omega
  have hp : 3 ^ (Nat.log 3 n - 1) * 3 = 3 ^ Nat.log 3 n := by
    rw [← pow_succ, hs]
  have hp0 : 0 < (3 : ℕ) ^ (Nat.log 3 n - 1) := by positivity
  let m := 3 ^ Nat.log 3 n - 1
  have hm : 0 < m := by dsimp [m]; omega
  have hmn : m ≤ n := by
    have hh := Nat.pow_log_le_self 3 (Nat.ne_of_gt hn)
    dsimp [m]
    omega
  have h3 : Nat.log 3 m = Nat.log 3 n - 1 := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · dsimp [m]
      omega
    · rw [hs]
      dsimp [m]
      omega
  have h4 : Nat.log 4 m = Nat.log 4 n := by
    apply Nat.log_eq_of_pow_le_of_lt_pow
    · dsimp [m]
      omega
    · exact lt_of_le_of_lt hmn (Nat.lt_pow_succ_log_self (by norm_num) n)
  have hc : cutoffCount 0 m = cutoffCount 0 n - 1 := by
    simp [cutoffCount, Nat.ne_of_gt hn, Nat.ne_of_gt hm, h4, h3]
    omega
  rw [← hc, lowerCutoff_zero_at_count hm, h4, h3]


end Bounty

end SubmissionComponent_PreviousLevels

/- Component PreviousParity; SHA256 724a9e910d2bead52a554109c5b06d03566ad461af430e783840df3d7bc11ff1 -/
section SubmissionComponent_PreviousParity
/- Previous levels for the odd cutoff parity. -/

namespace Bounty

def cutoffCount_one_ge_three {n : ℕ} (hn : 6 ≤ n) :
    3 ≤ cutoffCount 1 n := by
  have hh : 3 ≤ n / 2 := by omega
  have hlog : 1 ≤ Nat.log 3 (n / 2) :=
    (Nat.le_log_iff_pow_le (by norm_num) (by omega : n / 2 ≠ 0)).mpr (by simpa using hh)
  simp [cutoffCount, show ¬n < 2 by omega]
  omega

end Bounty

end SubmissionComponent_PreviousParity

/- Component NormalizedPowers; SHA256 bbf6d8dbfec9260fcd9572e2f3463dfb90b21c7f47ef43df17af024e2907ebba -/
section SubmissionComponent_NormalizedPowers
/- Power normalization and the two possible power bins after scaling. -/

namespace Bounty

def power_floor_nat_bounds {b : ℕ} (hb : 1 < b) {u : ℚ} (hu : 1 ≤ u) :
    ((b ^ Nat.log b ⌊u⌋₊ : ℕ) : ℚ) ≤ u ∧
      u < ((b ^ (Nat.log b ⌊u⌋₊ + 1) : ℕ) : ℚ) := by
  have hu0 : 0 ≤ u := by linarith
  have hn : ⌊u⌋₊ ≠ 0 := by
    have hh : 1 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
    omega
  constructor
  · exact (Nat.le_floor_iff hu0).mp (Nat.pow_log_le_self b hn)
  · exact (Nat.floor_lt hu0).mp (Nat.lt_pow_succ_log_self hb _)

def normalized_power_bounds {b : ℕ} (hb : 1 < b) {u : ℚ} (hu : 1 ≤ u) :
    1 / (b : ℚ) < (b : ℚ) ^ Nat.log b ⌊u⌋₊ / u ∧
      (b : ℚ) ^ Nat.log b ⌊u⌋₊ / u ≤ 1 := by
  have hu0 : 0 < u := by linarith
  have hb0 : (0 : ℚ) < b := by exact_mod_cast (by omega : 0 < b)
  have hh := power_floor_nat_bounds hb hu
  constructor
  · rw [div_lt_div_iff₀ hb0 hu0, one_mul]
    simpa only [Nat.cast_pow, Nat.cast_mul, pow_succ] using hh.2
  · apply (div_le_one hu0).mpr
    simpa only [Nat.cast_pow] using hh.1

def power_floor_two_bins {b j : ℕ} {u : ℚ} (hu : 0 ≤ u)
    (hlo : (b : ℚ) ^ j ≤ u) (hhi : u < (b : ℚ) ^ (j + 2)) :
    (b : ℚ) ^ Nat.log b ⌊u⌋₊ =
      if (b : ℚ) ^ (j + 1) ≤ u then (b : ℚ) ^ (j + 1) else (b : ℚ) ^ j := by
  by_cases hm : (b : ℚ) ^ (j + 1) ≤ u
  · have he : Nat.log b ⌊u⌋₊ = j + 1 :=
      log_floor_of_bounds hu (by simpa only [Nat.cast_pow] using hm)
        (by simpa only [Nat.cast_pow, Nat.add_assoc] using hhi)
    simp [hm, he]
  · have he : Nat.log b ⌊u⌋₊ = j :=
      log_floor_of_bounds hu (by simpa only [Nat.cast_pow] using hlo)
        (by simpa only [Nat.cast_pow] using (lt_of_not_ge hm))
    simp [hm, he]

def scaled_power_two_bins {b k : ℕ} (hb : 1 < b) (hk : 0 < k)
    {u d : ℚ} (hu : 1 ≤ u) (hd : 0 < d)
    (hdlo : (b : ℚ) ^ (k - 1) < d) (hdhi : d ≤ (b : ℚ) ^ k)
    (hindex : k ≤ Nat.log b ⌊u⌋₊) :
    (b : ℚ) ^ Nat.log b ⌊u / d⌋₊ =
      if (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 1) ≤ u / d
      then (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 1)
      else (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) := by
  have hb0 : (0 : ℚ) < b := by exact_mod_cast (by omega : 0 < b)
  have hroot := power_floor_nat_bounds hb hu
  have hloRoot : (b : ℚ) ^ Nat.log b ⌊u⌋₊ ≤ u := by
    simpa only [Nat.cast_pow] using hroot.1
  have hhiRoot : u < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + 1) := by
    simpa only [Nat.cast_pow] using hroot.2
  have hproduct : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) * (b : ℚ) ^ k =
      (b : ℚ) ^ Nat.log b ⌊u⌋₊ := by
    rw [← pow_add, Nat.sub_add_cancel hindex]
  have hproductHi : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 2) * (b : ℚ) ^ (k - 1) =
      (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + 1) := by
    rw [← pow_add]
    congr 1
    omega
  have hlo : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) ≤ u / d := by
    apply (le_div_iff₀ hd).mpr
    calc
      (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) * d ≤
          (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) * (b : ℚ) ^ k :=
        mul_le_mul_of_nonneg_left hdhi (le_of_lt (pow_pos hb0 _))
      _ = (b : ℚ) ^ Nat.log b ⌊u⌋₊ := hproduct
      _ ≤ u := hloRoot
  have hhi : u / d < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 2) := by
    apply (div_lt_iff₀ hd).mpr
    calc
      u < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + 1) := hhiRoot
      _ = (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 2) * (b : ℚ) ^ (k - 1) := hproductHi.symm
      _ < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 2) * d :=
        mul_lt_mul_of_pos_left hdlo (pow_pos hb0 _)
  exact power_floor_two_bins (div_nonneg (by linarith) (le_of_lt hd)) hlo hhi


end Bounty

end SubmissionComponent_NormalizedPowers

/- Component PowerScales; SHA256 cd806089de0e99effeaf86cbc602fed15b71ff13aee9d2146fccbdee3b709891 -/
section SubmissionComponent_PowerScales
/- The two power bins under multiplication, including the factor-five loss window. -/

namespace Bounty

def multiplied_power_two_bins {b k : ℕ} (hb : 1 < b)
    {u d : ℚ} (hu : 1 ≤ u)
    (hdlo : (b : ℚ) ^ k ≤ d) (hdhi : d < (b : ℚ) ^ (k + 1)) :
    (b : ℚ) ^ Nat.log b ⌊d * u⌋₊ =
      if (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 1) ≤ d * u
      then (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 1)
      else (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k) := by
  have hb0 : (0 : ℚ) < b := by exact_mod_cast (by omega : 0 < b)
  have hd0 : 0 < d := lt_of_lt_of_le (pow_pos hb0 _) hdlo
  have hu0 : 0 < u := by linarith
  have hroot := power_floor_nat_bounds hb hu
  have hloRoot : (b : ℚ) ^ Nat.log b ⌊u⌋₊ ≤ u := by
    simpa only [Nat.cast_pow] using hroot.1
  have hhiRoot : u < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + 1) := by
    simpa only [Nat.cast_pow] using hroot.2
  have hlo : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k) ≤ d * u := by
    rw [pow_add, mul_comm d u]
    exact mul_le_mul hloRoot hdlo (le_of_lt (pow_pos hb0 _)) (le_of_lt hu0)
  have hhi : d * u < (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 2) := by
    calc
      d * u < (b : ℚ) ^ (k + 1) * u := mul_lt_mul_of_pos_right hdhi hu0
      _ < (b : ℚ) ^ (k + 1) * (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + 1) :=
        mul_lt_mul_of_pos_left hhiRoot (pow_pos hb0 _)
      _ = (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 2) := by
        rw [← pow_add]
        congr 1
        omega
  exact power_floor_two_bins (le_of_lt (mul_pos hd0 hu0)) hlo hhi

def multiplied_power_normalized {b k : ℕ} (hb : 1 < b)
    {u d : ℚ} (hu : 1 ≤ u)
    (hdlo : (b : ℚ) ^ k ≤ d) (hdhi : d < (b : ℚ) ^ (k + 1)) :
    (b : ℚ) ^ Nat.log b ⌊d * u⌋₊ / u =
      if (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 1) / u ≤ d
      then (b : ℚ) ^ Nat.log b ⌊u⌋₊ / u * (b : ℚ) ^ (k + 1)
      else (b : ℚ) ^ Nat.log b ⌊u⌋₊ / u * (b : ℚ) ^ k := by
  have hu0 : 0 < u := by linarith
  rw [multiplied_power_two_bins hb hu hdlo hdhi]
  simp only [div_le_iff₀ hu0]
  split_ifs <;> simp only [pow_add] <;> ring


end Bounty

end SubmissionComponent_PowerScales

/- Component NormalizedLoss; SHA256 235c33ee30f7895b5b2820014e03a4e286c8aff6edc667644ee38e57dcab9736 -/
section SubmissionComponent_NormalizedLoss
/- Exact rational endpoints for the powers-of-five obstruction window. -/

namespace Bounty

def badWindow_floor_iff_powers {u : ℚ} (hu : 10 ≤ u) :
    badWindow ⌊u⌋₊ ↔
      4 * u < 5 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ∧
      10 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ 9 * u ∧
      3 * u < 4 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 10 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hn0 : ⌊u⌋₊ ≠ 0 := by omega
  have ha : 1 ≤ Nat.log 4 ⌊u⌋₊ :=
    (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr (by norm_num; omega)
  have hb : 2 ≤ Nat.log 3 ⌊u⌋₊ :=
    (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr (by norm_num; omega)
  have hp4 : (4 : ℕ) ^ Nat.log 4 ⌊u⌋₊ = 4 * 4 ^ (Nat.log 4 ⌊u⌋₊ - 1) := by
    calc
      4 ^ Nat.log 4 ⌊u⌋₊ = 4 ^ (Nat.log 4 ⌊u⌋₊ - 1 + 1) := by congr 1; omega
      _ = 4 * 4 ^ (Nat.log 4 ⌊u⌋₊ - 1) := by rw [pow_succ, Nat.mul_comm]
  have hp3 : (3 : ℕ) ^ Nat.log 3 ⌊u⌋₊ = 9 * 3 ^ (Nat.log 3 ⌊u⌋₊ - 2) := by
    calc
      3 ^ Nat.log 3 ⌊u⌋₊ = 3 ^ (Nat.log 3 ⌊u⌋₊ - 2 + 2) := by congr 1; omega
      _ = 9 * 3 ^ (Nat.log 3 ⌊u⌋₊ - 2) := by rw [pow_add]; norm_num; omega
  have hp4q : (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ = 4 * 4 ^ (Nat.log 4 ⌊u⌋₊ - 1) := by
    exact_mod_cast hp4
  have hp3q : (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ = 9 * 3 ^ (Nat.log 3 ⌊u⌋₊ - 2) := by
    exact_mod_cast hp3
  rw [badWindow_iff_canonical]
  constructor
  · rintro ⟨_, h4, h3lo, h3hi⟩
    have h4' : ⌊u⌋₊ < 5 * 4 ^ (Nat.log 4 ⌊u⌋₊ - 1) := by omega
    have h4q : u < 5 * (4 : ℚ) ^ (Nat.log 4 ⌊u⌋₊ - 1) := by
      exact_mod_cast (Nat.floor_lt hu0).mp h4'
    have h3loq : 10 * (3 : ℚ) ^ (Nat.log 3 ⌊u⌋₊ - 2) ≤ u := by
      exact_mod_cast (Nat.le_floor_iff hu0).mp h3lo
    have h3hiq : u < 12 * (3 : ℚ) ^ (Nat.log 3 ⌊u⌋₊ - 2) := by
      exact_mod_cast (Nat.floor_lt hu0).mp h3hi
    exact ⟨by nlinarith [hp4q], by nlinarith [hp3q], by nlinarith [hp3q]⟩
  · rintro ⟨h4, h3lo, h3hi⟩
    have h4q : u < 5 * (4 : ℚ) ^ (Nat.log 4 ⌊u⌋₊ - 1) := by nlinarith [hp4q]
    have h3loq : 10 * (3 : ℚ) ^ (Nat.log 3 ⌊u⌋₊ - 2) ≤ u := by nlinarith [hp3q]
    have h3hiq : u < 12 * (3 : ℚ) ^ (Nat.log 3 ⌊u⌋₊ - 2) := by nlinarith [hp3q]
    have h4' : ⌊u⌋₊ < 5 * 4 ^ (Nat.log 4 ⌊u⌋₊ - 1) :=
      (Nat.floor_lt hu0).mpr (by exact_mod_cast h4q)
    have h3lo' : 10 * 3 ^ (Nat.log 3 ⌊u⌋₊ - 2) ≤ ⌊u⌋₊ :=
      (Nat.le_floor_iff hu0).mpr (by exact_mod_cast h3loq)
    have h3hi' : ⌊u⌋₊ < 12 * 3 ^ (Nat.log 3 ⌊u⌋₊ - 2) :=
      (Nat.floor_lt hu0).mpr (by exact_mod_cast h3hiq)
    exact ⟨Nat.pow_log_le_self 4 hn0, by omega, h3lo', h3hi'⟩

def badWindow_floor_scaled_iff {u v : ℚ} (hu : 0 < u) (hv : 10 ≤ v * u) :
    badWindow ⌊v * u⌋₊ ↔
      4 * v < 5 * ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ∧
      10 * ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) ≤ 9 * v ∧
      3 * v < 4 * ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) := by
  rw [badWindow_floor_iff_powers hv]
  have h4 : (4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u * u = (4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ :=
    div_mul_cancel₀ _ (ne_of_gt hu)
  have h3 : (3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u * u = (3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ :=
    div_mul_cancel₀ _ (ne_of_gt hu)
  constructor <;> rintro ⟨h₁, h₂, h₃⟩
  · exact ⟨by nlinarith, by nlinarith, by nlinarith⟩
  · exact ⟨by nlinarith, by nlinarith, by nlinarith⟩


end Bounty

end SubmissionComponent_NormalizedLoss

/- Component ParityPowers; SHA256 fbe6af3f90e0826256f98d1a27476a9363ba98f71ea23b68fb55ef4a28132dab -/
section SubmissionComponent_ParityPowers
/- The latest odd-parity thresholds in terms of the two unscaled powers. -/

namespace Bounty

def log_powers_distinct {n : ℕ} (hn : 3 ≤ n) :
    4 ^ Nat.log 4 n ≠ 3 ^ Nat.log 3 n := by
  intro he
  have hc : Nat.Coprime (4 ^ Nat.log 4 n) (3 ^ Nat.log 3 n) :=
    (by norm_num : Nat.Coprime 4 3).pow _ _
  rw [he, Nat.coprime_self] at hc
  have hlog : 1 ≤ Nat.log 3 n :=
    (Nat.le_log_iff_pow_le (by norm_num) (by omega : n ≠ 0)).mpr (by simpa using hn)
  have hh : 1 < 3 ^ Nat.log 3 n := Nat.one_lt_pow (by omega) (by norm_num)
  omega

def double_four_power_half {n : ℕ} (hn : 2 ≤ n) :
    2 * (4 : ℚ) ^ Nat.log 4 (n / 2) =
      if 2 * 4 ^ Nat.log 4 n ≤ n
      then 2 * (4 : ℚ) ^ Nat.log 4 n else (4 : ℚ) ^ Nat.log 4 n / 2 := by
  by_cases hp : 2 * 4 ^ Nat.log 4 n ≤ n
  · have hp' := (log_two_odd_iff_four_threshold (by omega : 0 < n)).mpr hp
    have hh := log_four_half_odd hp'
    simp [hp, hh]
  · have hp' : Nat.log 2 n % 2 = 0 := by
      have hnot : ¬Nat.log 2 n % 2 = 1 :=
        mt (log_two_odd_iff_four_threshold (by omega : 0 < n)).mp hp
      omega
    have hh := log_four_half_even hn hp'
    have he : (4 : ℚ) ^ Nat.log 4 n = 4 * (4 : ℚ) ^ Nat.log 4 (n / 2) := by
      rw [← hh, pow_succ]
      ring
    simp only [hp, if_false, he]
    ring

def double_three_power_half {n : ℕ} (hn : 2 ≤ n) :
    2 * (3 : ℚ) ^ Nat.log 3 (n / 2) =
      if 2 * 3 ^ Nat.log 3 n ≤ n
      then 2 * (3 : ℚ) ^ Nat.log 3 n else 2 * (3 : ℚ) ^ Nat.log 3 n / 3 := by
  by_cases hd : 2 * 3 ^ Nat.log 3 n ≤ n
  · have hh := log_three_half (by omega : 0 < n) hd
    simp [hd, hh]
  · have hh := log_three_half_below hn hd
    have he : (3 : ℚ) ^ Nat.log 3 n = 3 * (3 : ℚ) ^ Nat.log 3 (n / 2) := by
      rw [← hh, pow_succ]
      ring
    simp only [hd, if_false, he]
    ring

def double_four_power_half_floor {u : ℚ} (hu : 2 ≤ u) :
    2 * (4 : ℚ) ^ Nat.log 4 ⌊u / 2⌋₊ =
      if 2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ≤ u
      then 2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ else (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / 2 := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hh := double_four_power_half hn
  have hfloor : ⌊u / 2⌋₊ = ⌊u⌋₊ / 2 := Nat.floor_div_natCast u 2
  simpa only [hfloor,
    Nat.le_floor_iff hu0, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] using hh

def double_three_power_half_floor {u : ℚ} (hu : 2 ≤ u) :
    2 * (3 : ℚ) ^ Nat.log 3 ⌊u / 2⌋₊ =
      if 2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ u
      then 2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ else 2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / 3 := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hh := double_three_power_half hn
  have hfloor : ⌊u / 2⌋₊ = ⌊u⌋₊ / 2 := Nat.floor_div_natCast u 2
  simpa only [hfloor,
    Nat.le_floor_iff hu0, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] using hh


end Bounty

end SubmissionComponent_ParityPowers

/- Component ProfileLevels; SHA256 5b94fd28810ff485629b707cf8d64beb0bfca2c5fc4868c19a45d69834f5fbe2 -/
section SubmissionComponent_ProfileLevels
/- The current and preceding cutoff levels as rational threshold profiles. -/

namespace Bounty

def cutoffPowerFour (p n : ℕ) : ℚ :=
  if p = 0 then 4 ^ Nat.log 4 n else 2 * 4 ^ Nat.log 4 (n / 2)

def cutoffPowerThree (p n : ℕ) : ℚ :=
  if p = 0 then 3 ^ Nat.log 3 n else 2 * 3 ^ Nat.log 3 (n / 2)

def rational_power_pred {b k : ℕ} (hb : 0 < b) (hk : 0 < k) :
    (b : ℚ) ^ (k - 1) = (b : ℚ) ^ k / b := by
  have hb0 : (b : ℚ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hb)
  apply (eq_div_iff hb0).mpr
  rw [← pow_succ, show k - 1 + 1 = k by omega]

def lowerCutoff_zero_previous_rational {n : ℕ} (hn : 3 ≤ n) :
    (lowerCutoff 0 (cutoffCount 0 n - 1) : ℚ) =
      if (4 : ℚ) ^ Nat.log 4 n > (3 : ℚ) ^ Nat.log 3 n
      then max ((4 : ℚ) ^ Nat.log 4 n / 4) ((3 : ℚ) ^ Nat.log 3 n)
      else max ((4 : ℚ) ^ Nat.log 4 n) ((3 : ℚ) ^ Nat.log 3 n / 3) := by
  by_cases hh : (3 : ℕ) ^ Nat.log 3 n < 4 ^ Nat.log 4 n
  · have hhq : (3 : ℚ) ^ Nat.log 3 n < 4 ^ Nat.log 4 n := by exact_mod_cast hh
    have hj : 0 < Nat.log 4 n := by
      have hp : 0 < (3 : ℕ) ^ Nat.log 3 n := by positivity
      by_contra he
      have hz : Nat.log 4 n = 0 := by omega
      simp only [hz, pow_zero] at hh
      omega
    rw [if_pos hhq, lowerCutoff_zero_previous_four (by omega) hh]
    simp only [Nat.cast_max, Nat.cast_pow, Nat.cast_ofNat]
    have he : (4 : ℚ) ^ (Nat.log 4 n - 1) = (4 : ℚ) ^ Nat.log 4 n / 4 := by
      simpa only [Nat.cast_ofNat] using rational_power_pred (by norm_num : 0 < (4 : ℕ)) hj
    rw [he]
  · have hneq := log_powers_distinct hn
    have hh' : (4 : ℕ) ^ Nat.log 4 n < 3 ^ Nat.log 3 n := by omega
    have hhq : ¬(3 : ℚ) ^ Nat.log 3 n < 4 ^ Nat.log 4 n := by exact_mod_cast hh
    have hj : 0 < Nat.log 3 n := by
      have hp : 0 < (4 : ℕ) ^ Nat.log 4 n := by positivity
      by_contra he
      have hz : Nat.log 3 n = 0 := by omega
      simp only [hz, pow_zero] at hh'
      omega
    rw [if_neg hhq, lowerCutoff_zero_previous_three (by omega) hh']
    simp only [Nat.cast_max, Nat.cast_pow, Nat.cast_ofNat]
    have he : (3 : ℚ) ^ (Nat.log 3 n - 1) = (3 : ℚ) ^ Nat.log 3 n / 3 := by
      simpa only [Nat.cast_ofNat] using rational_power_pred (by norm_num : 0 < (3 : ℕ)) hj
    rw [he]

def lowerCutoff_at_count_profile {p n : ℕ} (hp : p < 2) (hn : 2 ≤ n) :
    (lowerCutoff p (cutoffCount p n) : ℚ) =
      max (cutoffPowerFour p n) (cutoffPowerThree p n) := by
  have hp' : p = 0 ∨ p = 1 := by omega
  rcases hp' with rfl | rfl
  · rw [lowerCutoff_zero_at_count (by omega)]
    simp only [cutoffPowerFour, cutoffPowerThree, ↓reduceIte, Nat.cast_max,
      Nat.cast_pow, Nat.cast_ofNat]
  · rw [lowerCutoff_one_at_count hn]
    simp only [cutoffPowerFour, cutoffPowerThree, show ¬(1 : ℕ) = 0 by omega,
      if_false, Nat.cast_mul, Nat.cast_max, Nat.cast_pow, Nat.cast_ofNat]
    exact mul_max_of_nonneg _ _ (by norm_num : (0 : ℚ) ≤ 2)

def lowerCutoff_previous_profile {p n : ℕ} (hp : p < 2) (hn : 6 ≤ n) :
    (lowerCutoff p (cutoffCount p n - 1) : ℚ) =
      if cutoffPowerFour p n > cutoffPowerThree p n
      then max (cutoffPowerFour p n / 4) (cutoffPowerThree p n)
      else max (cutoffPowerFour p n) (cutoffPowerThree p n / 3) := by
  have hp' : p = 0 ∨ p = 1 := by omega
  rcases hp' with rfl | rfl
  · simpa only [cutoffPowerFour, cutoffPowerThree, ↓reduceIte] using
      lowerCutoff_zero_previous_rational (by omega : 3 ≤ n)
  · have hcp := cutoffCount_one_ge_three hn
    have hc : cutoffCount 1 n = cutoffCount 0 (n / 2) + 1 := by
      simp [cutoffCount, show ¬n < 2 by omega, show n / 2 ≠ 0 by omega]
      omega
    have he : cutoffCount 1 n - 1 - 1 = cutoffCount 0 (n / 2) - 1 := by omega
    rw [lowerCutoff_one_scale (by omega : 2 ≤ cutoffCount 1 n - 1), he]
    simp only [Nat.cast_mul, Nat.cast_ofNat, cutoffPowerFour, cutoffPowerThree,
      show ¬(1 : ℕ) = 0 by omega, if_false]
    rw [lowerCutoff_zero_previous_rational (by omega : 3 ≤ n / 2)]
    have heq : 2 * (4 : ℚ) ^ Nat.log 4 (n / 2) > 2 * (3 : ℚ) ^ Nat.log 3 (n / 2) ↔
        (4 : ℚ) ^ Nat.log 4 (n / 2) > (3 : ℚ) ^ Nat.log 3 (n / 2) := by
      constructor <;> intro hh <;> linarith
    simp only [heq]
    split_ifs <;> rw [mul_max_of_nonneg _ _ (by norm_num : (0 : ℚ) ≤ 2)] <;>
      congr 1 <;> ring


end Bounty

end SubmissionComponent_ProfileLevels

/- Component ProfileQuota; SHA256 8e275e2f296b96cb3e20e0b237940f5fb7776c4858cb3c640c640c3a750b05f8 -/
section SubmissionComponent_ProfileQuota
/- The signed difference between a quota loss and a cutoff parity deficit. -/

namespace Bounty

def quotaLossValue (eps : Bool) (u : ℚ) : ℕ :=
  letI := badWindow_decidable ⌊5 * u⌋₊
  if eps = true ∧ badWindow ⌊5 * u⌋₊ then 1 else 0

def cutoffDeficit (p : ℕ) (u : ℚ) : ℕ :=
  if p = 0 then
    if 2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ≤ u ∧ 2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ u then 1 else 0
  else
    if ¬2 * (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ ≤ u ∧ ¬2 * (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ ≤ u then 1 else 0

def cutoffDelta (eps : Bool) (p : ℕ) (u : ℚ) : ℤ :=
  (quotaLossValue eps u : ℤ) - (cutoffDeficit p u : ℤ)

def quotaLossValue_le_one (eps : Bool) (u : ℚ) : quotaLossValue eps u ≤ 1 := by
  unfold quotaLossValue
  split_ifs <;> omega

def cutoffDeficit_le_one (p : ℕ) (u : ℚ) : cutoffDeficit p u ≤ 1 := by
  unfold cutoffDeficit
  split_ifs <;> omega

def cutoffCount_add_deficit {p : ℕ} (hp : p < 2) {u : ℚ} (hu : 2 ≤ u) :
    cutoffCount p ⌊u⌋₊ + cutoffDeficit p u = smoothRankBound ⌊u⌋₊ := by
  have hp' : p = 0 ∨ p = 1 := by omega
  rcases hp' with rfl | rfl
  · simpa only [cutoffDeficit, ↓reduceIte] using cutoffCount_zero_floor_deficit (by linarith : 1 ≤ u)
  · simpa only [cutoffDeficit, show ¬(1 : ℕ) = 0 by omega, ↓reduceIte] using cutoffCount_one_floor_deficit hu

def quotaLossValue_one_ge_fifty_four {eps : Bool} {u : ℚ} (hu : 0 ≤ u)
    (hloss : quotaLossValue eps u = 1) : 54 ≤ u := by
  have hb : badWindow ⌊5 * u⌋₊ := by
    unfold quotaLossValue at hloss
    split_ifs at hloss with hh
    · exact hh.2
  have hh : (0x10e : ℚ) ≤ 5 * u :=
    (Nat.le_floor_iff (by positivity : 0 ≤ 5 * u)).mp (badWindow_ge_270 hb)
  linarith

def cutoffDelta_bounds (eps : Bool) (p : ℕ) (u : ℚ) :
    -1 ≤ cutoffDelta eps p u ∧ cutoffDelta eps p u ≤ 1 := by
  have hl := quotaLossValue_le_one eps u
  have hd := cutoffDeficit_le_one p u
  unfold cutoffDelta
  omega

def quotaValue_cast_eq_count_sub_delta {eps : Bool} {p : ℕ} (hp : p < 2)
    {u : ℚ} (hu : 2 ≤ u) :
    (quotaValue eps u : ℤ) = (cutoffCount p ⌊u⌋₊ : ℤ) - cutoffDelta eps p u := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 0 < ⌊u⌋₊ := by
    have hh : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
    omega
  have hr := smoothRankBound_pos hn
  have hl := quotaLossValue_le_one eps u
  have hc := cutoffCount_add_deficit hp hu
  have hdef : quotaValue eps u = smoothRankBound ⌊u⌋₊ - quotaLossValue eps u := rfl
  rw [hdef]
  unfold cutoffDelta
  omega

def cutoffDelta_one_ge_fifty_four {eps : Bool} {p : ℕ} {u : ℚ} (hu : 0 ≤ u)
    (hd : cutoffDelta eps p u = 1) : 54 ≤ u := by
  have hl := quotaLossValue_le_one eps u
  have hdef := cutoffDeficit_le_one p u
  have he : quotaLossValue eps u = 1 := by unfold cutoffDelta at hd; omega
  exact quotaLossValue_one_ge_fifty_four hu he


end Bounty

end SubmissionComponent_ProfileQuota

/- Component ProfileValidity; SHA256 4024ca34b3c981b4b47947e205aab2bac69f07f4defc22eef7a3db38aba97ff4 -/
section SubmissionComponent_ProfileValidity
/- The rational closure profile is exactly the cutoff quota condition. -/

namespace Bounty

def cutoffProfileLower (eps : Bool) (p : ℕ) (u : ℚ) : ℚ :=
  if cutoffDelta eps p u = 0 then max (cutoffPowerFour p ⌊u⌋₊) (cutoffPowerThree p ⌊u⌋₊)
  else if cutoffPowerFour p ⌊u⌋₊ > cutoffPowerThree p ⌊u⌋₊
    then max (cutoffPowerFour p ⌊u⌋₊ / 4) (cutoffPowerThree p ⌊u⌋₊)
    else max (cutoffPowerFour p ⌊u⌋₊) (cutoffPowerThree p ⌊u⌋₊ / 3)

def cutoffProfileValid (eps : Bool) (p : ℕ) (u r : ℚ) : Prop :=
  0 ≤ cutoffDelta eps p u ∧ cutoffProfileLower eps p u ≤ r ∧
    if cutoffDelta eps p u = 0 then r ≤ u
    else r < max (cutoffPowerFour p ⌊u⌋₊) (cutoffPowerThree p ⌊u⌋₊)

def lowerCutoff_quota_profile {eps : Bool} {p : ℕ} (hp : p < 2)
    {u : ℚ} (hu : 2 ≤ u) (hd : 0 ≤ cutoffDelta eps p u) :
    (lowerCutoff p (quotaValue eps u) : ℚ) = cutoffProfileLower eps p u := by
  have hh := quotaValue_cast_eq_count_sub_delta (eps := eps) hp hu
  have hdhi := (cutoffDelta_bounds eps p u).2
  have hu0 : 0 ≤ u := by linarith
  by_cases hz : cutoffDelta eps p u = 0
  · have hq : quotaValue eps u = cutoffCount p ⌊u⌋₊ := by omega
    have hn : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
    rw [hq, lowerCutoff_at_count_profile hp hn]
    simp [cutoffProfileLower, hz]
  · have hd1 : cutoffDelta eps p u = 1 := by omega
    have hu54 := cutoffDelta_one_ge_fifty_four hu0 hd1
    have hn : 6 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr (by norm_num; linarith)
    have hq : quotaValue eps u = cutoffCount p ⌊u⌋₊ - 1 := by omega
    rw [hq, lowerCutoff_previous_profile hp hn]
    simp [cutoffProfileLower, hz]

def cutoffProfileValid_iff {eps : Bool} {p : ℕ} (hp : p < 2)
    {u r : ℚ} (hu : 2 ≤ u) (hr : 0 ≤ r) :
    cutoffProfileValid eps p u r ↔
      r ≤ u ∧ cutoffCount p ⌊r⌋₊ = quotaValue eps u := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 2 ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hbounds := (cutoffCount_floor_level_iff p (cutoffCount p ⌊u⌋₊) hu0).mp rfl
  have hcast := quotaValue_cast_eq_count_sub_delta (eps := eps) hp hu
  have hdelta := cutoffDelta_bounds eps p u
  have casesDelta : cutoffDelta eps p u = -1 ∨ cutoffDelta eps p u = 0 ∨ cutoffDelta eps p u = 1 := by omega
  rcases casesDelta with hneg | hz | hone
  · apply iff_of_false
    · intro hv
      have := hv.1
      omega
    · rintro ⟨hru, hsize⟩
      have hm := cutoffCount_mono p (Nat.floor_mono hru)
      omega
  · have hd : 0 ≤ cutoffDelta eps p u := by omega
    have hq : quotaValue eps u = cutoffCount p ⌊u⌋₊ := by omega
    have hlo := lowerCutoff_quota_profile (eps := eps) hp hu hd
    constructor
    · intro hv
      have hru : r ≤ u := by simpa only [hz, ↓reduceIte] using hv.2.2
      refine ⟨hru, (cutoffCount_floor_level_iff p (quotaValue eps u) hr).mpr ?_⟩
      constructor
      · simpa only [hlo] using hv.2.1
      · rw [hq]
        exact hru.trans_lt hbounds.2
    · rintro ⟨hru, hsize⟩
      have hb := (cutoffCount_floor_level_iff p (quotaValue eps u) hr).mp hsize
      refine ⟨hd, ?_, ?_⟩
      · simpa only [hlo] using hb.1
      · simpa only [hz, ↓reduceIte] using hru
  · have hd : 0 ≤ cutoffDelta eps p u := by omega
    have hz : cutoffDelta eps p u ≠ 0 := by omega
    have hq : quotaValue eps u + 1 = cutoffCount p ⌊u⌋₊ := by omega
    have hlo := lowerCutoff_quota_profile (eps := eps) hp hu hd
    have hhi : (lowerCutoff p (quotaValue eps u + 1) : ℚ) =
        max (cutoffPowerFour p ⌊u⌋₊) (cutoffPowerThree p ⌊u⌋₊) := by
      rw [hq, lowerCutoff_at_count_profile hp hn]
    constructor
    · intro hv
      have hrhi : r < (lowerCutoff p (quotaValue eps u + 1) : ℚ) := by
        simpa only [hz, ↓reduceIte, hhi] using hv.2.2
      have hru : r ≤ u := by
        rw [hq] at hrhi
        exact (hrhi.trans_le hbounds.1).le
      refine ⟨hru, (cutoffCount_floor_level_iff p (quotaValue eps u) hr).mpr ?_⟩
      exact ⟨by simpa only [hlo] using hv.2.1, hrhi⟩
    · rintro ⟨_, hsize⟩
      have hb := (cutoffCount_floor_level_iff p (quotaValue eps u) hr).mp hsize
      refine ⟨hd, ?_, ?_⟩
      · simpa only [hlo] using hb.1
      · simpa only [hz, ↓reduceIte, hhi] using hb.2


end Bounty

end SubmissionComponent_ProfileValidity

/- Component ProfileTrial; SHA256 8ee28eb10e5bc33de807f03b4b6265c7e3ba75ae33b57f2ad7e40f72827c3b3e -/
section SubmissionComponent_ProfileTrial
/- Equivalence between the actual recursive trial and its rational profile. -/

namespace Bounty

def cutoffProfileTrial (eps : Bool) (u : ℚ) (p : ℕ) (c5 c7 : ℕ × ℚ) : ℚ :=
  max (max (3 * u / 4) (cutoffProfileLower eps p u))
    (max ((if p = c5.1 then 4 else 6) * c5.2) ((if p = c7.1 then 4 else 6) * c7.2))

def cutoffProfileTrial_bounds (eps : Bool) (u : ℚ) (p : ℕ) (c5 c7 : ℕ × ℚ) :
    3 * u / 4 ≤ cutoffProfileTrial eps u p c5 c7 ∧
    cutoffProfileLower eps p u ≤ cutoffProfileTrial eps u p c5 c7 ∧
    (if p = c5.1 then 4 else 6) * c5.2 ≤ cutoffProfileTrial eps u p c5 c7 ∧
    (if p = c7.1 then 4 else 6) * c7.2 ≤ cutoffProfileTrial eps u p c5 c7 := by
  unfold cutoffProfileTrial
  exact ⟨(le_max_left _ _).trans (le_max_left _ _),
    (le_max_right _ _).trans (le_max_left _ _),
    (le_max_left _ _).trans (le_max_right _ _),
    (le_max_right _ _).trans (le_max_right _ _)⟩

def cutoffTrial_eq_profile {eps : Bool} {u : ℚ} {p : ℕ} (hp : p < 2)
    (hu : 2 ≤ u) (hd : 0 ≤ cutoffDelta eps p u) (c5 c7 : ℕ × ℚ) :
    cutoffTrial u (quotaValue eps u) p c5 c7 = cutoffProfileTrial eps u p c5 c7 := by
  unfold cutoffTrial cutoffProfileTrial
  rw [lowerCutoff_quota_profile hp hu hd]

def cutoffAvailable_delta_nonneg {eps : Bool} {u : ℚ} {p : ℕ} {c5 c7 : ℕ × ℚ}
    (hp : p < 2) (hu : 2 ≤ u) (ha : cutoffAvailable u (quotaValue eps u) p c5 c7) :
    0 ≤ cutoffDelta eps p u := by
  have hsize := cutoffTrial_size (by linarith : 0 ≤ u) ha
  have hm := cutoffCount_mono p (Nat.floor_mono ha.1)
  have hc := quotaValue_cast_eq_count_sub_delta (eps := eps) hp hu
  omega

def cutoffAvailable_iff_profile {eps : Bool} {u : ℚ} {p : ℕ} {c5 c7 : ℕ × ℚ}
    (hp : p < 2) (hu : 2 ≤ u) :
    cutoffAvailable u (quotaValue eps u) p c5 c7 ↔
      cutoffProfileValid eps p u (cutoffProfileTrial eps u p c5 c7) := by
  have hb := cutoffProfileTrial_bounds eps u p c5 c7
  have hr : 0 ≤ cutoffProfileTrial eps u p c5 c7 := by linarith [hb.1]
  constructor
  · intro ha
    have hd := cutoffAvailable_delta_nonneg hp hu ha
    have he := cutoffTrial_eq_profile hp hu hd c5 c7
    apply (cutoffProfileValid_iff hp hu hr).mpr
    constructor
    · simpa only [he] using ha.1
    · simpa only [he] using cutoffTrial_size (by linarith : 0 ≤ u) ha
  · intro hv
    have he := cutoffTrial_eq_profile hp hu hv.1 c5 c7
    have hh := (cutoffProfileValid_iff hp hu hr).mp hv
    have hlevel := (cutoffCount_floor_level_iff p (quotaValue eps u) hr).mp hh.2
    unfold cutoffAvailable
    rw [he]
    exact ⟨hh.1, hlevel.2⟩


end Bounty

end SubmissionComponent_ProfileTrial

/- Component DivisionPowers; SHA256 237fd97e9899f0cd27dac4ac1f01dfa4194ee8c9fb5f05cb309986c25a0b5fab -/
section SubmissionComponent_DivisionPowers
/- Child powers divided by the root input, in the closure's rational coordinates. -/

namespace Bounty

def divided_power_normalized {b k : ℕ} (hb : 1 < b) (hk : 0 < k)
    {u d : ℚ} (hu : 1 ≤ u) (hd : 0 < d)
    (hdlo : (b : ℚ) ^ (k - 1) < d) (hdhi : d ≤ (b : ℚ) ^ k)
    (hindex : k ≤ Nat.log b ⌊u⌋₊) :
    (b : ℚ) ^ Nat.log b ⌊u / d⌋₊ / u =
      if (b : ℚ) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k ≤ 1 / d
      then (b : ℚ) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k
      else ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k := by
  have hu0 : 0 < u := by linarith
  have hb0 : (0 : ℚ) < b := by exact_mod_cast (by omega : 0 < b)
  have hp : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) * (b : ℚ) ^ k =
      (b : ℚ) ^ Nat.log b ⌊u⌋₊ := by
    rw [← pow_add, Nat.sub_add_cancel hindex]
  have hsmall : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) / u =
      ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k := by
    apply (eq_div_iff (ne_of_gt (pow_pos hb0 _))).mpr
    rw [div_mul_eq_mul_div, hp]
  have hbig : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 1) / u =
      (b : ℚ) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k := by
    rw [pow_succ]
    calc
      (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) * b / u =
          b * ((b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k) / u) := by ring
      _ = b * (((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k) := by rw [hsmall]
      _ = (b : ℚ) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k := by ring
  have hcond : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ - k + 1) ≤ u / d ↔
      (b : ℚ) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) / (b : ℚ) ^ k ≤ 1 / d := by
    rw [← hbig, le_div_iff₀ hd, div_le_div_iff₀ hu0 hd, one_mul]
  rw [scaled_power_two_bins hb hk hu hd hdlo hdhi hindex]
  simp only [hcond]
  split_ifs <;> simp only [hsmall, hbig]

def multiplied_power_normalized_linear {b k : ℕ} (hb : 1 < b)
    {u d : ℚ} (hu : 1 ≤ u)
    (hdlo : (b : ℚ) ^ k ≤ d) (hdhi : d < (b : ℚ) ^ (k + 1)) :
    (b : ℚ) ^ Nat.log b ⌊d * u⌋₊ / u =
      if (b : ℚ) ^ (k + 1) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) ≤ d
      then (b : ℚ) ^ (k + 1) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u)
      else (b : ℚ) ^ k * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) := by
  have hh := multiplied_power_normalized hb hu hdlo hdhi
  have he : (b : ℚ) ^ (Nat.log b ⌊u⌋₊ + k + 1) / u =
      (b : ℚ) ^ (k + 1) * ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) := by
    rw [show Nat.log b ⌊u⌋₊ + k + 1 = Nat.log b ⌊u⌋₊ + (k + 1) by omega, pow_add]
    ring
  simpa only [he, mul_comm] using hh


end Bounty

end SubmissionComponent_DivisionPowers

/- Component ProfileScaling; SHA256 87a4be247874c01ebe3a829c380e270bfcc4c325f14e0e84b4a98a93c6012850 -/
section SubmissionComponent_ProfileScaling
/- Normalizing the cutoff profile by a positive root input. -/

namespace Bounty

def normalizedParityFour (p : ℕ) (v a : ℚ) : ℚ :=
  if p = 0 then a else if 2 * a ≤ v then 2 * a else a / 2

def normalizedParityThree (p : ℕ) (v b : ℚ) : ℚ :=
  if p = 0 then b else if 2 * b ≤ v then 2 * b else 2 * b / 3

def normalizedProfileLower (delta : ℤ) (a b : ℚ) : ℚ :=
  if delta = 0 then max a b else if a > b then max (a / 4) b else max a (b / 3)

def normalizedProfileValid (delta : ℤ) (v a b r : ℚ) : Prop :=
  0 ≤ delta ∧ normalizedProfileLower delta a b ≤ r ∧
    if delta = 0 then r ≤ v else r < max a b

def cutoffPowerFour_normalized (p : ℕ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffPowerFour p ⌊v * u⌋₊ / u =
      normalizedParityFour p v ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) := by
  by_cases hp : p = 0
  · simp [cutoffPowerFour, normalizedParityFour, hp]
  · have hh := double_four_power_half_floor hv
    have hfloor : ⌊v * u / 2⌋₊ = ⌊v * u⌋₊ / 2 := Nat.floor_div_natCast (v * u) 2
    rw [hfloor] at hh
    have hc : 2 * ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ≤ v ↔
        2 * (4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ ≤ v * u := by
      rw [← mul_div_assoc, div_le_iff₀ hu]
    simp only [cutoffPowerFour, normalizedParityFour, hp, ↓reduceIte, hh, hc]
    split_ifs <;> ring

def cutoffPowerThree_normalized (p : ℕ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffPowerThree p ⌊v * u⌋₊ / u =
      normalizedParityThree p v ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) := by
  by_cases hp : p = 0
  · simp [cutoffPowerThree, normalizedParityThree, hp]
  · have hh := double_three_power_half_floor hv
    have hfloor : ⌊v * u / 2⌋₊ = ⌊v * u⌋₊ / 2 := Nat.floor_div_natCast (v * u) 2
    rw [hfloor] at hh
    have hc : 2 * ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) ≤ v ↔
        2 * (3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ ≤ v * u := by
      rw [← mul_div_assoc, div_le_iff₀ hu]
    simp only [cutoffPowerThree, normalizedParityThree, hp, ↓reduceIte, hh, hc]
    split_ifs <;> ring

def normalizedProfileLower_scale (delta : ℤ) (a b : ℚ) {u : ℚ} (hu : 0 < u) :
    normalizedProfileLower delta a b / u = normalizedProfileLower delta (a / u) (b / u) := by
  unfold normalizedProfileLower
  simp only [div_lt_div_iff_of_pos_right hu]
  split_ifs <;> rw [← max_div_div_right hu.le] <;> congr 1 <;> ring

def cutoffProfileLower_normalized (eps : Bool) (p : ℕ) {u v : ℚ} (hu : 0 < u)
    (hv : 2 ≤ v * u) :
    cutoffProfileLower eps p (v * u) / u =
      normalizedProfileLower (cutoffDelta eps p (v * u))
        (normalizedParityFour p v ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u))
        (normalizedParityThree p v ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)) := by
  change normalizedProfileLower (cutoffDelta eps p (v * u))
    (cutoffPowerFour p ⌊v * u⌋₊) (cutoffPowerThree p ⌊v * u⌋₊) / u = _
  rw [normalizedProfileLower_scale _ _ _ hu,
    cutoffPowerFour_normalized p hu hv, cutoffPowerThree_normalized p hu hv]

def normalizedProfileValid_scale (delta : ℤ) (v a b r : ℚ) {u : ℚ} (hu : 0 < u) :
    (0 ≤ delta ∧ normalizedProfileLower delta a b ≤ r * u ∧
      if delta = 0 then r * u ≤ v * u else r * u < max a b) ↔
      normalizedProfileValid delta v (a / u) (b / u) r := by
  unfold normalizedProfileValid
  rw [← normalizedProfileLower_scale _ _ _ hu, ← div_le_iff₀ hu]
  simp only [mul_le_mul_iff_left₀ hu, max_div_div_right hu.le, lt_div_iff₀ hu]

def cutoffProfileValid_normalized (eps : Bool) (p : ℕ) {u v r : ℚ} (hu : 0 < u)
    (hv : 2 ≤ v * u) :
    cutoffProfileValid eps p (v * u) (r * u) ↔
      normalizedProfileValid (cutoffDelta eps p (v * u)) v
        (normalizedParityFour p v ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u))
        (normalizedParityThree p v ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)) r := by
  change (0 ≤ cutoffDelta eps p (v * u) ∧
    normalizedProfileLower (cutoffDelta eps p (v * u))
      (cutoffPowerFour p ⌊v * u⌋₊) (cutoffPowerThree p ⌊v * u⌋₊) ≤ r * u ∧
      if cutoffDelta eps p (v * u) = 0 then r * u ≤ v * u
      else r * u < max (cutoffPowerFour p ⌊v * u⌋₊) (cutoffPowerThree p ⌊v * u⌋₊)) ↔ _
  rw [normalizedProfileValid_scale _ _ _ _ _ hu,
    cutoffPowerFour_normalized p hu hv, cutoffPowerThree_normalized p hu hv]


end Bounty

end SubmissionComponent_ProfileScaling

/- Component QuotaScaling; SHA256 1171240a9ff518c1440f9bf2a22494e770c83914d55a498c64974d1f3ff8eaea -/
section SubmissionComponent_QuotaScaling
/- The normalized loss and deficit formulas used by the closure certificate. -/

namespace Bounty

def normalizedDeficit (p : ℕ) (v a b : ℚ) : ℕ :=
  if p = 0 then if 2 * a ≤ v ∧ 2 * b ≤ v then 1 else 0
  else if ¬2 * a ≤ v ∧ ¬2 * b ≤ v then 1 else 0

def normalizedLossValue (eps : Bool) (v a b : ℚ) : ℕ :=
  if eps = true ∧ 5 * v < (5 / 4 : ℚ) * a ∧ (10 / 9 : ℚ) * b ≤ 5 * v ∧
    5 * v < (4 / 3 : ℚ) * b then 1 else 0

def normalizedDelta (eps : Bool) (p : ℕ) (v a b a5 b5 : ℚ) : ℤ :=
  (normalizedLossValue eps v a5 b5 : ℤ) - (normalizedDeficit p v a b : ℤ)

def cutoffDeficit_normalized (p : ℕ) {u v : ℚ} (hu : 0 < u) :
    cutoffDeficit p (v * u) = normalizedDeficit p v
      ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) := by
  have h4 : 2 * ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ≤ v ↔
      2 * (4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ ≤ v * u := by
    rw [← mul_div_assoc, div_le_iff₀ hu]
  have h3 : 2 * ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u) ≤ v ↔
      2 * (3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ ≤ v * u := by
    rw [← mul_div_assoc, div_le_iff₀ hu]
  simp only [cutoffDeficit, normalizedDeficit, h4, h3]

def quotaLossValue_normalized (eps : Bool) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    quotaLossValue eps (v * u) = normalizedLossValue eps v
      ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u)
      ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) := by
  have hh := badWindow_floor_scaled_iff (u := u) (v := 5 * v) hu (by nlinarith : 10 ≤ (5 * v) * u)
  have hb : badWindow ⌊5 * (v * u)⌋₊ ↔
      4 * (5 * v) < 5 * ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ∧
      10 * ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) ≤ 9 * (5 * v) ∧
      3 * (5 * v) < 4 * ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) := by
    simpa only [mul_assoc] using hh
  have hb' : badWindow ⌊5 * (v * u)⌋₊ ↔
      5 * v < (5 / 4 : ℚ) * ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ∧
      (10 / 9 : ℚ) * ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) ≤ 5 * v ∧
      5 * v < (4 / 3 : ℚ) * ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) := by
    rw [hb]
    constructor <;> rintro ⟨h₁, h₂, h₃⟩ <;>
      exact ⟨by linarith, by linarith, by linarith⟩
  simp only [quotaLossValue, normalizedLossValue, hb']

def cutoffDelta_normalized (eps : Bool) (p : ℕ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffDelta eps p (v * u) = normalizedDelta eps p v
      ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
      ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u)
      ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) := by
  unfold cutoffDelta normalizedDelta
  rw [quotaLossValue_normalized eps hu hv, cutoffDeficit_normalized p hu]


end Bounty

end SubmissionComponent_QuotaScaling

/- Component TrialScaling; SHA256 2502d94740d81774eb053d76bb047ef55c61b1d3745b12bba6ad4a61585b1f1a -/
section SubmissionComponent_TrialScaling
/- The entire recursive trial expressed in normalized coordinates. -/

namespace Bounty

def normalizedProfileTrial (delta : ℤ) (v a b : ℚ) (p p5 p7 : ℕ) (r5 r7 : ℚ) : ℚ :=
  max (max (3 * v / 4) (normalizedProfileLower delta a b))
    (max ((if p = p5 then 4 else 6) * r5) ((if p = p7 then 4 else 6) * r7))

def cutoffProfileTrial_normalized (eps : Bool) (p p5 p7 : ℕ) (r5 r7 : ℚ)
    {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffProfileTrial eps (v * u) p (p5, r5 * u) (p7, r7 * u) / u =
      normalizedProfileTrial (cutoffDelta eps p (v * u)) v
        (normalizedParityFour p v ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u))
        (normalizedParityThree p v ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)) p p5 p7 r5 r7 := by
  have hscale (a b : ℚ) : a * (b * u) / u = a * b := by
    field_simp
  have hbase : 3 * (v * u) / 4 / u = 3 * v / 4 := by
    field_simp
  unfold cutoffProfileTrial normalizedProfileTrial
  simp only [← max_div_div_right hu.le, hscale, hbase]
  rw [cutoffProfileLower_normalized eps p hu hv]

def cutoffAvailable_iff_normalized {eps : Bool} {p : ℕ} (hp : p < 2)
    (p5 p7 : ℕ) (r5 r7 : ℚ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    let a := normalizedParityFour p v ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u)
    let b := normalizedParityThree p v ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
    let delta := cutoffDelta eps p (v * u)
    cutoffAvailable (v * u) (quotaValue eps (v * u)) p (p5, r5 * u) (p7, r7 * u) ↔
      normalizedProfileValid delta v a b (normalizedProfileTrial delta v a b p p5 p7 r5 r7) := by
  dsimp only
  rw [cutoffAvailable_iff_profile hp hv]
  have htrial := cutoffProfileTrial_normalized eps p p5 p7 r5 r7 hu hv
  have he := (div_eq_iff (ne_of_gt hu)).mp htrial
  rw [he, cutoffProfileValid_normalized eps p hu hv]


end Bounty

end SubmissionComponent_TrialScaling

/- Component CandidateChoice; SHA256 3f26e35fb12df49b94cf7eb63aa2071314b6a73aa47fa0904ec45b133b93035f -/
section SubmissionComponent_CandidateChoice
/- Explicit phase and value choices made by the recursive candidate. -/

namespace Bounty

def preferred_phase_normalized {u v : ℚ} (hu : 0 < u) (hv : 1 ≤ v * u) :
    Nat.log 2 ⌊v * u⌋₊ % 2 = 1 ↔
      2 * ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ≤ v := by
  have hv0 : 0 ≤ v * u := by linarith
  have hn : 0 < ⌊v * u⌋₊ := by
    have hh : 1 ≤ ⌊v * u⌋₊ := (Nat.le_floor_iff hv0).mpr hv
    omega
  rw [log_two_odd_iff_four_threshold hn, Nat.le_floor_iff hv0]
  simp only [Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat]
  rw [← mul_div_assoc, div_le_iff₀ hu]

def cutoffCandidate_phase_one_iff (eps : Bool) (u : ℚ) (c5 c7 : ℕ × ℚ) :
    (cutoffCandidate eps u c5 c7).1 = 1 ↔
      if Nat.log 2 ⌊u⌋₊ % 2 = 1 then cutoffAvailable u (quotaValue eps u) 1 c5 c7
      else ¬cutoffAvailable u (quotaValue eps u) 0 c5 c7 := by
  by_cases hp : Nat.log 2 ⌊u⌋₊ % 2 = 1
  · by_cases ha : cutoffAvailable u (quotaValue eps u) 1 c5 c7 <;>
      simp [cutoffCandidate, hp, ha]
  · have hp0 : Nat.log 2 ⌊u⌋₊ % 2 = 0 := by omega
    by_cases ha : cutoffAvailable u (quotaValue eps u) 0 c5 c7 <;>
      simp [cutoffCandidate, hp0, ha]

def cutoffCandidate_value_profile {eps : Bool} {u : ℚ} {c5 c7 : ℕ × ℚ} (hu : 2 ≤ u)
    (ha : cutoffAvailable u (quotaValue eps u) 0 c5 c7 ∨
      cutoffAvailable u (quotaValue eps u) 1 c5 c7) :
    (cutoffCandidate eps u c5 c7).2 =
      if (cutoffCandidate eps u c5 c7).1 = 1
      then cutoffProfileTrial eps u 1 c5 c7 else cutoffProfileTrial eps u 0 c5 c7 := by
  have hp := cutoffCandidate_parity eps u c5 c7
  have hc := cutoffCandidate_available ha
  have hd := cutoffAvailable_delta_nonneg hp hu hc
  have he := cutoffTrial_eq_profile hp hu hd c5 c7
  rw [cutoffCandidate_eq_trial, he]
  by_cases hphase : (cutoffCandidate eps u c5 c7).1 = 1
  · simp only [hphase, ↓reduceIte]
  · have hzero : (cutoffCandidate eps u c5 c7).1 = 0 := by omega
    simp only [hzero, show ¬(0 : ℕ) = 1 by omega, ↓reduceIte]


end Bounty

end SubmissionComponent_CandidateChoice

/- Component NormalizedStep; SHA256 eb69d34d60eb3cf1306faf2e54db3172effdbc39537fc290f3c55a93d36bbac9 -/
section SubmissionComponent_NormalizedStep
/- The normalized state and trial predicates appearing in the closure inputs. -/

namespace Bounty

def normalizedStateValid (eps : Bool) (p : ℕ) (v a b a5 b5 r : ℚ) : Prop :=
  normalizedProfileValid (normalizedDelta eps p v a b a5 b5) v
    (normalizedParityFour p v a) (normalizedParityThree p v b) r

def normalizedTrialValue (eps : Bool) (p p5 p7 : ℕ) (v a b a5 b5 r5 r7 : ℚ) : ℚ :=
  normalizedProfileTrial (normalizedDelta eps p v a b a5 b5) v
    (normalizedParityFour p v a) (normalizedParityThree p v b) p p5 p7 r5 r7

def normalizedTrialAvailable (eps : Bool) (p p5 p7 : ℕ) (v a b a5 b5 r5 r7 : ℚ) : Prop :=
  normalizedStateValid eps p v a b a5 b5 (normalizedTrialValue eps p p5 p7 v a b a5 b5 r5 r7)

def cutoffProfileValid_iff_normalizedState (eps : Bool) (p : ℕ) {u v r : ℚ}
    (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffProfileValid eps p (v * u) (r * u) ↔
      normalizedStateValid eps p v
        ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
        ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) r := by
  rw [cutoffProfileValid_normalized eps p hu hv]
  unfold normalizedStateValid
  rw [cutoffDelta_normalized eps p hu hv]

def cutoffAvailable_iff_normalizedTrial {eps : Bool} {p : ℕ} (hp : p < 2)
    (p5 p7 : ℕ) (r5 r7 : ℚ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffAvailable (v * u) (quotaValue eps (v * u)) p (p5, r5 * u) (p7, r7 * u) ↔
      normalizedTrialAvailable eps p p5 p7 v
        ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
        ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u) r5 r7 := by
  have hh := cutoffAvailable_iff_normalized (eps := eps) hp p5 p7 r5 r7 hu hv
  dsimp only at hh
  unfold normalizedTrialAvailable normalizedStateValid normalizedTrialValue
  simpa only [cutoffDelta_normalized eps p hu hv] using hh

end Bounty

end SubmissionComponent_NormalizedStep

/- Component ClosureRootBounds; SHA256 946665fa0be10ef0d2dbbf96fcff337840818a19d06dd563fb04e426192563b7 -/
section SubmissionComponent_ClosureRootBounds
/- Uniform root and descendant bounds for the seven-step closure. -/

namespace Bounty

def closure_root_log_bounds {u : ℚ} (hu : 0x1921ee ≤ u) :
    10 ≤ Nat.log 4 ⌊u⌋₊ ∧ 13 ≤ Nat.log 3 ⌊u⌋₊ := by
  have hu0 : 0 ≤ u := by linarith
  have hn : 0x1921ee ≤ ⌊u⌋₊ := (Nat.le_floor_iff hu0).mpr hu
  have hn0 : ⌊u⌋₊ ≠ 0 := by omega
  constructor
  · apply (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr
    norm_num
    omega
  · apply (Nat.le_log_iff_pow_le (by norm_num) hn0).mpr
    norm_num
    omega

end Bounty

end SubmissionComponent_ClosureRootBounds

/- Component PowerCoordinates; SHA256 4bac70d657eb28cbe06f1080612987f6be0999d40af2c9a5d0dde1acce7ee6e5 -/
section SubmissionComponent_PowerCoordinates
/- A common two-bin coordinate for the finite normalized closure. -/

namespace Bounty

def normalizedPowerCoordinate (b : ℕ) (scale v x : ℚ) : ℚ :=
  if (b : ℚ) * scale * x ≤ v then (b : ℚ) * scale * x else scale * x

def normalizedPower_divided_coordinate {b k : ℕ} (hb : 1 < b) (hk : 0 < k)
    {u d : ℚ} (hu : 1 ≤ u) (hd : 0 < d)
    (hdlo : (b : ℚ) ^ (k - 1) < d) (hdhi : d ≤ (b : ℚ) ^ k)
    (hindex : k ≤ Nat.log b ⌊u⌋₊) :
    (b : ℚ) ^ Nat.log b ⌊u / d⌋₊ / u =
      normalizedPowerCoordinate b (1 / (b : ℚ) ^ k) (1 / d)
        ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) := by
  simpa only [normalizedPowerCoordinate, div_eq_mul_inv, one_mul, mul_one,
    mul_assoc, mul_left_comm, mul_comm] using
    divided_power_normalized hb hk hu hd hdlo hdhi hindex

def normalizedPower_multiplied_coordinate {b k : ℕ} (hb : 1 < b)
    {u d : ℚ} (hu : 1 ≤ u)
    (hdlo : (b : ℚ) ^ k ≤ d) (hdhi : d < (b : ℚ) ^ (k + 1)) :
    (b : ℚ) ^ Nat.log b ⌊d * u⌋₊ / u =
      normalizedPowerCoordinate b ((b : ℚ) ^ k) d ((b : ℚ) ^ Nat.log b ⌊u⌋₊ / u) := by
  simpa only [normalizedPowerCoordinate, pow_succ, mul_assoc, mul_left_comm, mul_comm] using
    multiplied_power_normalized_linear hb hu hdlo hdhi


end Bounty

end SubmissionComponent_PowerCoordinates

/- Component ClosurePowerCoordinates; SHA256 79e763138951fe9dd640f969282bca0b0f575b56fdc4db5bde1b507650e959fe -/
section SubmissionComponent_ClosurePowerCoordinates
/- Exact power coordinates for the seven-step closure. -/

namespace Bounty

def closurePower4_node_0_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 : ℚ) (1 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 4) (k := 0)
    (u := u) (d := (1 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 : ℚ) (1 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 3) (k := 0)
    (u := u) (d := (1 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (4 : ℚ) (5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 4) (k := 1)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (3 : ℚ) (5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 3) (k := 1)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 16 : ℚ) (1 / 7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 2)
    (u := u) (d := (7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 7 : ℚ) * u = u / (7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 9 : ℚ) (1 / 7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 2)
    (u := u) (d := (7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 7 : ℚ) * u = u / (7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 4 : ℚ) (5 / 7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 1 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 1)
    (u := u) (d := (7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 7 : ℚ) * u = u / (7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 3 : ℚ) (5 / 7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 1 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 1)
    (u := u) (d := (7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 7 : ℚ) * u = u / (7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 16 : ℚ) (1 / 5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 2)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 5 : ℚ) * u = u / (5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 9 : ℚ) (1 / 5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 2)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 5 : ℚ) * u = u / (5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 : ℚ) (1 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 4) (k := 0)
    (u := u) (d := (1 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 : ℚ) (1 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hh := normalizedPower_multiplied_coordinate (b := 3) (k := 0)
    (u := u) (d := (1 : ℚ)) (by norm_num) (by linarith : 1 ≤ u)
    (by norm_num) (by norm_num)
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 49 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (49 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 49 : ℚ) * u = u / (49 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 81 : ℚ) (1 / 49 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 4)
    (u := u) (d := (49 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 49 : ℚ) * u = u / (49 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 16 : ℚ) (5 / 49 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 2)
    (u := u) (d := (49 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 49 : ℚ) * u = u / (49 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 27 : ℚ) (5 / 49 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 3)
    (u := u) (d := (49 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 49 : ℚ) * u = u / (49 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 35 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 35 : ℚ) * u = u / (35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 81 : ℚ) (1 / 35 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 4)
    (u := u) (d := (35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 35 : ℚ) * u = u / (35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 16 : ℚ) (1 / 7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 2)
    (u := u) (d := (7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 7 : ℚ) * u = u / (7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 9 : ℚ) (1 / 7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 2)
    (u := u) (d := (7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 7 : ℚ) * u = u / (7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 25 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 25 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (25 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 25 : ℚ) * u = u / (25 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 25 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 27 : ℚ) (1 / 25 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 3)
    (u := u) (d := (25 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 25 : ℚ) * u = u / (25 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 16 : ℚ) (1 / 5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 2)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 5 : ℚ) * u = u / (5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 9 : ℚ) (1 / 5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 2 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 2)
    (u := u) (d := (5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 5 : ℚ) * u = u / (5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x157 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x157 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x157 : ℚ) * u = u / (0x157 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0x157 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0x157 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x157 : ℚ) * u = u / (0x157 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (5 / 0x157 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0x157 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x157 : ℚ) * u = u / (0x157 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 81 : ℚ) (5 / 0x157 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 4)
    (u := u) (d := (0x157 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x157 : ℚ) * u = u / (0x157 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xf5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0xf5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0xf5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xf5 : ℚ) * u = u / (0xf5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xf5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0xf5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0xf5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xf5 : ℚ) * u = u / (0xf5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 49 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (49 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 49 : ℚ) * u = u / (49 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 49 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 81 : ℚ) (1 / 49 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 4)
    (u := u) (d := (49 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 49 : ℚ) * u = u / (49 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xaf : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0xaf : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0xaf : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xaf : ℚ) * u = u / (0xaf : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xaf : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xf3 : ℚ) (1 / 0xaf : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 5)
    (u := u) (d := (0xaf : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xaf : ℚ) * u = u / (0xaf : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 35 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 35 : ℚ) * u = u / (35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 81 : ℚ) (1 / 35 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 4)
    (u := u) (d := (35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 35 : ℚ) * u = u / (35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_3_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x7d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0x7d : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0x7d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x7d : ℚ) * u = u / (0x7d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_3_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x7d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xf3 : ℚ) (1 / 0x7d : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 5)
    (u := u) (d := (0x7d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x7d : ℚ) * u = u / (0x7d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_3_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 25 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 64 : ℚ) (1 / 25 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 3)
    (u := u) (d := (25 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 25 : ℚ) * u = u / (25 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_3_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 25 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 27 : ℚ) (1 / 25 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 3 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 3)
    (u := u) (d := (25 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 25 : ℚ) * u = u / (25 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x961 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x961 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x961 : ℚ) * u = u / (0x961 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x961 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x961 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x961 : ℚ) * u = u / (0x961 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (5 / 0x961 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x961 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x961 : ℚ) * u = u / (0x961 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (5 / 0x961 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0x961 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x961 : ℚ) * u = u / (0x961 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x6b3 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x6b3 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x6b3 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6b3 : ℚ) * u = u / (0x6b3 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x6b3 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x6b3 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x6b3 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6b3 : ℚ) * u = u / (0x6b3 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x157 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x157 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x157 : ℚ) * u = u / (0x157 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x157 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0x157 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0x157 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x157 : ℚ) * u = u / (0x157 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x4c9 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x4c9 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x4c9 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4c9 : ℚ) * u = u / (0x4c9 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x4c9 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x4c9 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x4c9 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4c9 : ℚ) * u = u / (0x4c9 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xf5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0xf5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0xf5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xf5 : ℚ) * u = u / (0xf5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xf5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0xf5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0xf5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xf5 : ℚ) * u = u / (0xf5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_3_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x36b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x36b : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x36b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x36b : ℚ) * u = u / (0x36b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_3_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x36b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x36b : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x36b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x36b : ℚ) * u = u / (0x36b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_3_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xaf : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0xaf : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0xaf : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xaf : ℚ) * u = u / (0xaf : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_3_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xaf : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xf3 : ℚ) (1 / 0xaf : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 5)
    (u := u) (d := (0xaf : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xaf : ℚ) * u = u / (0xaf : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_4_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x271 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x271 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x271 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x271 : ℚ) * u = u / (0x271 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_4_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x271 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0x271 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0x271 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x271 : ℚ) * u = u / (0x271 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_4_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x7d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100 : ℚ) (1 / 0x7d : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 4 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 4)
    (u := u) (d := (0x7d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x7d : ℚ) * u = u / (0x7d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_4_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x7d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xf3 : ℚ) (1 / 0x7d : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 5)
    (u := u) (d := (0x7d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x7d : ℚ) * u = u / (0x7d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x41a7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x41a7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x41a7 : ℚ) * u = u / (0x41a7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x41a7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x41a7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x41a7 : ℚ) * u = u / (0x41a7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (5 / 0x41a7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x41a7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x41a7 : ℚ) * u = u / (0x41a7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (5 / 0x41a7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x41a7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x41a7 : ℚ) * u = u / (0x41a7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x2ee5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x2ee5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x2ee5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x2ee5 : ℚ) * u = u / (0x2ee5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x2ee5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x2ee5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x2ee5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x2ee5 : ℚ) * u = u / (0x2ee5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x961 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x961 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x961 : ℚ) * u = u / (0x961 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x961 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x961 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x961 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x961 : ℚ) * u = u / (0x961 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x217f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x217f : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x217f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x217f : ℚ) * u = u / (0x217f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x217f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x217f : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x217f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x217f : ℚ) * u = u / (0x217f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x6b3 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x6b3 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x6b3 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6b3 : ℚ) * u = u / (0x6b3 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x6b3 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x6b3 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x6b3 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6b3 : ℚ) * u = u / (0x6b3 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_3_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x17ed : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x17ed : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x17ed : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x17ed : ℚ) * u = u / (0x17ed : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_3_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x17ed : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x17ed : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x17ed : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x17ed : ℚ) * u = u / (0x17ed : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_3_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x4c9 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0x4c9 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0x4c9 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4c9 : ℚ) * u = u / (0x4c9 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_3_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x4c9 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x4c9 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x4c9 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4c9 : ℚ) * u = u / (0x4c9 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_4_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1117 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x1117 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x1117 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1117 : ℚ) * u = u / (0x1117 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_4_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1117 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x1117 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x1117 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1117 : ℚ) * u = u / (0x1117 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_4_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x36b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x36b : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x36b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x36b : ℚ) * u = u / (0x36b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_4_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x36b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x88b : ℚ) (1 / 0x36b : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 7)
    (u := u) (d := (0x36b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x36b : ℚ) * u = u / (0x36b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_5_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xc35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0xc35 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0xc35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc35 : ℚ) * u = u / (0xc35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_5_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xc35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0xc35 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0xc35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc35 : ℚ) * u = u / (0xc35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_5_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x271 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x400 : ℚ) (1 / 0x271 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 5 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 5)
    (u := u) (d := (0x271 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x271 : ℚ) * u = u / (0x271 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_5_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x271 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2d9 : ℚ) (1 / 0x271 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 6)
    (u := u) (d := (0x271 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x271 : ℚ) * u = u / (0x271 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x1cb91 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x1cb91 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1cb91 : ℚ) * u = u / (0x1cb91 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x1cb91 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x1cb91 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1cb91 : ℚ) * u = u / (0x1cb91 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (5 / 0x1cb91 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x1cb91 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x1cb91 : ℚ) * u = u / (0x1cb91 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (5 / 0x1cb91 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0x1cb91 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0x1cb91 : ℚ) * u = u / (0x1cb91 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x14843 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x14843 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x14843 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x14843 : ℚ) * u = u / (0x14843 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x14843 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x14843 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x14843 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x14843 : ℚ) * u = u / (0x14843 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x41a7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x41a7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x41a7 : ℚ) * u = u / (0x41a7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x41a7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x41a7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x41a7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x41a7 : ℚ) * u = u / (0x41a7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xea79 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0xea79 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0xea79 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xea79 : ℚ) * u = u / (0xea79 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xea79 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0xea79 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0xea79 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xea79 : ℚ) * u = u / (0xea79 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x2ee5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x2ee5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x2ee5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x2ee5 : ℚ) * u = u / (0x2ee5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x2ee5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x2ee5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x2ee5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x2ee5 : ℚ) * u = u / (0x2ee5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_3_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xa77b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0xa77b : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0xa77b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xa77b : ℚ) * u = u / (0xa77b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_3_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xa77b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0xa77b : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0xa77b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xa77b : ℚ) * u = u / (0xa77b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_3_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x217f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x217f : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x217f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x217f : ℚ) * u = u / (0x217f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_3_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x217f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x217f : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x217f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x217f : ℚ) * u = u / (0x217f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_4_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x77a1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x77a1 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x77a1 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x77a1 : ℚ) * u = u / (0x77a1 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_4_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x77a1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0x77a1 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0x77a1 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x77a1 : ℚ) * u = u / (0x77a1 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_4_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x17ed : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x17ed : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x17ed : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x17ed : ℚ) * u = u / (0x17ed : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_4_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x17ed : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x17ed : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x17ed : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x17ed : ℚ) * u = u / (0x17ed : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_5_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x5573 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x5573 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x5573 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x5573 : ℚ) * u = u / (0x5573 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_5_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x5573 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0x5573 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0x5573 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x5573 : ℚ) * u = u / (0x5573 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_5_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1117 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x1117 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x1117 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1117 : ℚ) * u = u / (0x1117 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_5_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1117 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0x1117 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0x1117 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1117 : ℚ) * u = u / (0x1117 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_6_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x3d09 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x3d09 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x3d09 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x3d09 : ℚ) * u = u / (0x3d09 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_6_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x3d09 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x3d09 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x3d09 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x3d09 : ℚ) * u = u / (0x3d09 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_6_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xc35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x1000 : ℚ) (1 / 0xc35 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 6 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 6)
    (u := u) (d := (0xc35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc35 : ℚ) * u = u / (0xc35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_6_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xc35 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x19a1 : ℚ) (1 / 0xc35 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 8)
    (u := u) (d := (0xc35 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc35 : ℚ) * u = u / (0xc35 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_0_7 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xc90f7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100000 : ℚ) (1 / 0xc90f7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 10)
    (u := u) (d := (0xc90f7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc90f7 : ℚ) * u = u / (0xc90f7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_0_7 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xc90f7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x1853d3 : ℚ) (1 / 0xc90f7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 13 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 13)
    (u := u) (d := (0xc90f7 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xc90f7 : ℚ) * u = u / (0xc90f7 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_0_7 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(5 / 0xc90f7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (5 / 0xc90f7 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0xc90f7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0xc90f7 : ℚ) * u = u / (0xc90f7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_0_7 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(5 / 0xc90f7 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (5 / 0xc90f7 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0xc90f7 / 5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (5 / 0xc90f7 : ℚ) * u = u / (0xc90f7 / 5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_1_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x8f9d5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100000 : ℚ) (1 / 0x8f9d5 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 10)
    (u := u) (d := (0x8f9d5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x8f9d5 : ℚ) * u = u / (0x8f9d5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_1_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x8f9d5 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x1853d3 : ℚ) (1 / 0x8f9d5 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 13 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 13)
    (u := u) (d := (0x8f9d5 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x8f9d5 : ℚ) * u = u / (0x8f9d5 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_1_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x1cb91 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x1cb91 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1cb91 : ℚ) * u = u / (0x1cb91 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_1_6 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1cb91 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x1cb91 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x1cb91 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1cb91 : ℚ) * u = u / (0x1cb91 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_2_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x6694f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100000 : ℚ) (1 / 0x6694f : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 10)
    (u := u) (d := (0x6694f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6694f : ℚ) * u = u / (0x6694f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_2_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x6694f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x81bf1 : ℚ) (1 / 0x6694f : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 12 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 12)
    (u := u) (d := (0x6694f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x6694f : ℚ) * u = u / (0x6694f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_2_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x14843 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x14843 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x14843 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x14843 : ℚ) * u = u / (0x14843 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_2_5 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x14843 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x14843 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x14843 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x14843 : ℚ) * u = u / (0x14843 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_3_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x4945d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x100000 : ℚ) (1 / 0x4945d : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 10)
    (u := u) (d := (0x4945d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4945d : ℚ) * u = u / (0x4945d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_3_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x4945d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x81bf1 : ℚ) (1 / 0x4945d : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 12 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 12)
    (u := u) (d := (0x4945d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x4945d : ℚ) * u = u / (0x4945d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_3_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xea79 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0xea79 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0xea79 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xea79 : ℚ) * u = u / (0xea79 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_3_4 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xea79 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0xea79 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0xea79 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xea79 : ℚ) * u = u / (0xea79 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_4_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x34567 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x34567 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x34567 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x34567 : ℚ) * u = u / (0x34567 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_4_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x34567 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x81bf1 : ℚ) (1 / 0x34567 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 12 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 12)
    (u := u) (d := (0x34567 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x34567 : ℚ) * u = u / (0x34567 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_4_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0xa77b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0xa77b : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0xa77b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xa77b : ℚ) * u = u / (0xa77b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_4_3 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0xa77b : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0xa77b : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0xa77b : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0xa77b : ℚ) * u = u / (0xa77b : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_5_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x25625 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x25625 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x25625 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x25625 : ℚ) * u = u / (0x25625 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_5_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x25625 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x25625 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x25625 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x25625 : ℚ) * u = u / (0x25625 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_5_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x77a1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x77a1 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x77a1 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x77a1 : ℚ) * u = u / (0x77a1 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_5_2 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x77a1 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0x77a1 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0x77a1 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x77a1 : ℚ) * u = u / (0x77a1 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_6_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1ab3f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x1ab3f : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x1ab3f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1ab3f : ℚ) * u = u / (0x1ab3f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_6_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1ab3f : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x1ab3f : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x1ab3f : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1ab3f : ℚ) * u = u / (0x1ab3f : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_6_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x5573 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x10000 : ℚ) (1 / 0x5573 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 8 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 8)
    (u := u) (d := (0x5573 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x5573 : ℚ) * u = u / (0x5573 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_6_1 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x5573 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0xe6a9 : ℚ) (1 / 0x5573 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 10 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 10)
    (u := u) (d := (0x5573 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x5573 : ℚ) * u = u / (0x5573 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_node_7_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x1312d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x40000 : ℚ) (1 / 0x1312d : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 9)
    (u := u) (d := (0x1312d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1312d : ℚ) * u = u / (0x1312d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_node_7_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x1312d : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x2b3fb : ℚ) (1 / 0x1312d : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 11 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 11)
    (u := u) (d := (0x1312d : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x1312d : ℚ) * u = u / (0x1312d : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower4_loss_7_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (4 : ℚ) ^ Nat.log 4 ⌊(1 / 0x3d09 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 4 (1 / 0x4000 : ℚ) (1 / 0x3d09 : ℚ)
        ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  have hindex : 7 ≤ Nat.log 4 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).1
    omega
  have hh := normalizedPower_divided_coordinate (b := 4) (k := 7)
    (u := u) (d := (0x3d09 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x3d09 : ℚ) * u = u / (0x3d09 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


def closurePower3_loss_7_0 {u : ℚ} (hu : 0x1921ee ≤ u) :
    (3 : ℚ) ^ Nat.log 3 ⌊(1 / 0x3d09 : ℚ) * u⌋₊ / u =
      normalizedPowerCoordinate 3 (1 / 0x4ce3 : ℚ) (1 / 0x3d09 : ℚ)
        ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  have hindex : 9 ≤ Nat.log 3 ⌊u⌋₊ := by
    have hh := (closure_root_log_bounds hu).2
    omega
  have hh := normalizedPower_divided_coordinate (b := 3) (k := 9)
    (u := u) (d := (0x3d09 : ℚ)) (by norm_num) (by norm_num)
    (by linarith : 1 ≤ u) (by norm_num) (by norm_num) (by norm_num) hindex
  have harg : (1 / 0x3d09 : ℚ) * u = u / (0x3d09 : ℚ) := by norm_num; ring
  rw [harg]
  convert hh using 1 <;> norm_num [normalizedPowerCoordinate]


end Bounty

end SubmissionComponent_ClosurePowerCoordinates

/- Component ClosureRaw; SHA256 12759138e6cb4fdbcd4dcb33a6d9b8e411399dd8973691bd7f11c644cb8968f1 -/
section SubmissionComponent_ClosureRaw
/- A typed finite closure formula. No contradiction theorem is asserted here. -/

namespace Bounty

noncomputable def closurePhase (p : Prop) : ℕ := by
  classical
  exact if p then 1 else 0

def closurePhase_of_nat {p : ℕ} (hp : p < 2) : closurePhase (p = 1) = p := by
  classical
  by_cases hh : p = 1
  · simp [closurePhase, hh]
  · have hz : p = 0 := by omega
    simp [closurePhase, hz]

structure ClosureNode where
  i : ℕ
  j : ℕ
  v : ℚ
  scale4 : ℚ
  scale3 : ℚ
  lossScale4 : ℚ
  lossScale3 : ℚ
  child5 : ℕ
  child7 : ℕ
  leaf : Bool

def closureNode : ℕ → ClosureNode
  | 0 => ⟨0, 0, 1, 1, 1, 4, 3, 2, 1, false⟩
  | 1 => ⟨0, 1, (1 / 7), (1 / 16), (1 / 9), (1 / 4), (1 / 3), 4, 3, false⟩
  | 2 => ⟨1, 0, (1 / 5), (1 / 16), (1 / 9), 1, 1, 5, 4, false⟩
  | 3 => ⟨0, 2, (1 / 49), (1 / 64), (1 / 81), (1 / 16), (1 / 27), 7, 6, false⟩
  | 4 => ⟨1, 1, (1 / 35), (1 / 64), (1 / 81), (1 / 16), (1 / 9), 8, 7, false⟩
  | 5 => ⟨2, 0, (1 / 25), (1 / 64), (1 / 27), (1 / 16), (1 / 9), 9, 8, false⟩
  | 6 => ⟨0, 3, (1 / 0x157), (1 / 0x400), (1 / 0x2d9), (1 / 0x100), (1 / 81), 11, 10, false⟩
  | 7 => ⟨1, 2, (1 / 0xf5), (1 / 0x100), (1 / 0x2d9), (1 / 64), (1 / 81), 12, 11, false⟩
  | 8 => ⟨2, 1, (1 / 0xaf), (1 / 0x100), (1 / 0xf3), (1 / 64), (1 / 81), 13, 12, false⟩
  | 9 => ⟨3, 0, (1 / 0x7d), (1 / 0x100), (1 / 0xf3), (1 / 64), (1 / 27), 14, 13, false⟩
  | 10 => ⟨0, 4, (1 / 0x961), (1 / 0x1000), (1 / 0x19a1), (1 / 0x400), (1 / 0x2d9), 16, 15, false⟩
  | 11 => ⟨1, 3, (1 / 0x6b3), (1 / 0x1000), (1 / 0x88b), (1 / 0x400), (1 / 0x2d9), 17, 16, false⟩
  | 12 => ⟨2, 2, (1 / 0x4c9), (1 / 0x1000), (1 / 0x88b), (1 / 0x100), (1 / 0x2d9), 18, 17, false⟩
  | 13 => ⟨3, 1, (1 / 0x36b), (1 / 0x400), (1 / 0x88b), (1 / 0x100), (1 / 0xf3), 19, 18, false⟩
  | 14 => ⟨4, 0, (1 / 0x271), (1 / 0x400), (1 / 0x2d9), (1 / 0x100), (1 / 0xf3), 20, 19, false⟩
  | 15 => ⟨0, 5, (1 / 0x41a7), (1 / 0x10000), (1 / 0x4ce3), (1 / 0x1000), (1 / 0x19a1), 22, 21, false⟩
  | 16 => ⟨1, 4, (1 / 0x2ee5), (1 / 0x4000), (1 / 0x4ce3), (1 / 0x1000), (1 / 0x19a1), 23, 22, false⟩
  | 17 => ⟨2, 3, (1 / 0x217f), (1 / 0x4000), (1 / 0x4ce3), (1 / 0x1000), (1 / 0x88b), 24, 23, false⟩
  | 18 => ⟨3, 2, (1 / 0x17ed), (1 / 0x4000), (1 / 0x19a1), (1 / 0x1000), (1 / 0x88b), 25, 24, false⟩
  | 19 => ⟨4, 1, (1 / 0x1117), (1 / 0x4000), (1 / 0x19a1), (1 / 0x400), (1 / 0x88b), 26, 25, false⟩
  | 20 => ⟨5, 0, (1 / 0xc35), (1 / 0x1000), (1 / 0x19a1), (1 / 0x400), (1 / 0x2d9), 27, 26, false⟩
  | 21 => ⟨0, 6, (1 / 0x1cb91), (1 / 0x40000), (1 / 0x2b3fb), (1 / 0x10000), (1 / 0xe6a9), 29, 28, false⟩
  | 22 => ⟨1, 5, (1 / 0x14843), (1 / 0x40000), (1 / 0x2b3fb), (1 / 0x10000), (1 / 0x4ce3), 30, 29, false⟩
  | 23 => ⟨2, 4, (1 / 0xea79), (1 / 0x10000), (1 / 0x2b3fb), (1 / 0x4000), (1 / 0x4ce3), 31, 30, false⟩
  | 24 => ⟨3, 3, (1 / 0xa77b), (1 / 0x10000), (1 / 0xe6a9), (1 / 0x4000), (1 / 0x4ce3), 32, 31, false⟩
  | 25 => ⟨4, 2, (1 / 0x77a1), (1 / 0x10000), (1 / 0xe6a9), (1 / 0x4000), (1 / 0x19a1), 33, 32, false⟩
  | 26 => ⟨5, 1, (1 / 0x5573), (1 / 0x10000), (1 / 0xe6a9), (1 / 0x4000), (1 / 0x19a1), 34, 33, false⟩
  | 27 => ⟨6, 0, (1 / 0x3d09), (1 / 0x4000), (1 / 0x4ce3), (1 / 0x1000), (1 / 0x19a1), 35, 34, false⟩
  | 28 => ⟨0, 7, (1 / 0xc90f7), (1 / 0x100000), (1 / 0x1853d3), (1 / 0x40000), (1 / 0x2b3fb), 37, 36, true⟩
  | 29 => ⟨1, 6, (1 / 0x8f9d5), (1 / 0x100000), (1 / 0x1853d3), (1 / 0x40000), (1 / 0x2b3fb), 38, 37, true⟩
  | 30 => ⟨2, 5, (1 / 0x6694f), (1 / 0x100000), (1 / 0x81bf1), (1 / 0x40000), (1 / 0x2b3fb), 39, 38, true⟩
  | 31 => ⟨3, 4, (1 / 0x4945d), (1 / 0x100000), (1 / 0x81bf1), (1 / 0x10000), (1 / 0x2b3fb), 40, 39, true⟩
  | 32 => ⟨4, 3, (1 / 0x34567), (1 / 0x40000), (1 / 0x81bf1), (1 / 0x10000), (1 / 0xe6a9), 41, 40, true⟩
  | 33 => ⟨5, 2, (1 / 0x25625), (1 / 0x40000), (1 / 0x2b3fb), (1 / 0x10000), (1 / 0xe6a9), 42, 41, true⟩
  | 34 => ⟨6, 1, (1 / 0x1ab3f), (1 / 0x40000), (1 / 0x2b3fb), (1 / 0x10000), (1 / 0xe6a9), 43, 42, true⟩
  | 35 => ⟨7, 0, (1 / 0x1312d), (1 / 0x40000), (1 / 0x2b3fb), (1 / 0x4000), (1 / 0x4ce3), 44, 43, true⟩
  | _ => ⟨0, 0, 0, 0, 0, 0, 0, 0, 0, false⟩

def closureNodeType (eps : Bool) (k : ℕ) : Bool := if (closureNode k).i = 0 then eps else true

def closureNodeFour (k : ℕ) (X : ℚ) : ℚ :=
  normalizedPowerCoordinate 4 (closureNode k).scale4 (closureNode k).v X

def closureNodeThree (k : ℕ) (Y : ℚ) : ℚ :=
  normalizedPowerCoordinate 3 (closureNode k).scale3 (closureNode k).v Y

def closureLossFour (k : ℕ) (X : ℚ) : ℚ :=
  normalizedPowerCoordinate 4 (closureNode k).lossScale4 (5 * (closureNode k).v) X

def closureLossThree (k : ℕ) (Y : ℚ) : ℚ :=
  normalizedPowerCoordinate 3 (closureNode k).lossScale3 (5 * (closureNode k).v) Y

noncomputable def closureNodeTrial (eps : Bool) (k phase : ℕ) (X Y : ℚ)
    (p : ℕ → Prop) (r : ℕ → ℚ) : ℚ :=
  normalizedTrialValue (closureNodeType eps k) phase
    (closurePhase (p (closureNode k).child5)) (closurePhase (p (closureNode k).child7))
    (closureNode k).v (closureNodeFour k X) (closureNodeThree k Y)
    (closureLossFour k X) (closureLossThree k Y) (r (closureNode k).child5) (r (closureNode k).child7)

noncomputable def closureNodeAvailable (eps : Bool) (k phase : ℕ) (X Y : ℚ)
    (p : ℕ → Prop) (r : ℕ → ℚ) : Prop :=
  normalizedStateValid (closureNodeType eps k) phase (closureNode k).v
    (closureNodeFour k X) (closureNodeThree k Y) (closureLossFour k X) (closureLossThree k Y)
    (closureNodeTrial eps k phase X Y p r)

noncomputable def closureNodeConstraint (eps : Bool) (k : ℕ) (X Y : ℚ)
    (p : ℕ → Prop) (r : ℕ → ℚ) : Prop := by
  classical
  exact if k = 0 then
    ¬closureNodeAvailable eps k 0 X Y p r ∧ ¬closureNodeAvailable eps k 1 X Y p r
  else if (closureNode k).leaf then
    3 * (closureNode k).v / 4 ≤ r k ∧
    if p k then normalizedStateValid (closureNodeType eps k) 1 (closureNode k).v
      (closureNodeFour k X) (closureNodeThree k Y) (closureLossFour k X) (closureLossThree k Y) (r k)
    else normalizedStateValid (closureNodeType eps k) 0 (closureNode k).v
      (closureNodeFour k X) (closureNodeThree k Y) (closureLossFour k X) (closureLossThree k Y) (r k)
  else
    (closureNodeAvailable eps k 0 X Y p r ∨ closureNodeAvailable eps k 1 X Y p r) ∧
    (p k ↔ if 2 * closureNodeFour k X ≤ (closureNode k).v
      then closureNodeAvailable eps k 1 X Y p r else ¬closureNodeAvailable eps k 0 X Y p r) ∧
    r k = if p k then closureNodeTrial eps k 1 X Y p r else closureNodeTrial eps k 0 X Y p r

noncomputable def ClosureRawHypothesis (eps : Bool) (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Prop :=
  1 / 4 < X ∧ X ≤ 1 ∧ 1 / 3 < Y ∧ Y ≤ 1 ∧ ∀ k < 36, closureNodeConstraint eps k X Y p r


end Bounty

end SubmissionComponent_ClosureRaw

/- Component ClosureInputNormalization; SHA256 b800ebbc61da502ecbc26db0dc08d07df642e49a4410f2421c92966d5572b8c5 -/
section SubmissionComponent_ClosureInputNormalization
/- Normal forms shared by the mathematical definitions and finite inputs. -/

namespace Bounty

def closureGamma_zero (P : Prop) [Decidable P] (r : ℚ) :
    (if (0 : ℕ) = closurePhase P then 4 else 6) * r =
      if (P ↔ False) then 4 * r else 6 * r := by
  classical
  by_cases hp : P <;> simp [closurePhase, hp]

def closureGamma_one (P : Prop) [Decidable P] (r : ℚ) :
    (if (1 : ℕ) = closurePhase P then 4 else 6) * r =
      if (P ↔ True) then 4 * r else 6 * r := by
  classical
  by_cases hp : P <;> simp [closurePhase, hp]

def closureIndicator_cast (P : Prop) [Decidable P] :
    Int.ofNat (if P then (1 : ℕ) else 0) = if P then (1 : ℤ) else 0 := by
  by_cases hp : P <;> simp [hp]

def closureIndicator_natCast (P : Prop) [Decidable P] :
    (Nat.cast (if P then (1 : ℕ) else 0) : ℤ) = if P then (1 : ℤ) else 0 := by
  exact closureIndicator_cast P

def closureCap_simplify (P : Prop) [Decidable P] (r v m : ℚ) :
    (if P then r ≤ (if P then v else m) else r < (if P then v else m)) ↔
      if P then r ≤ v else r < m := by
  by_cases hp : P <;> simp [hp]

def normalizedProfileTrial_left (delta : ℤ) (v a b : ℚ)
    (p p5 p7 : ℕ) (r5 r7 : ℚ) :
    normalizedProfileTrial delta v a b p p5 p7 r5 r7 =
      max (max (max (3 * v / 4) (normalizedProfileLower delta a b))
        ((if p = p5 then 4 else 6) * r5)) ((if p = p7 then 4 else 6) * r7) := by
  unfold normalizedProfileTrial
  simp only [max_assoc]


end Bounty

end SubmissionComponent_ClosureInputNormalization


end PolicyCombinatorialFront_PolicyClosureInputMath

/- Frozen source ClosureRawDepth5Policy; SHA256 cdf58e7d4efa59a34a6df9cf802df23f66f0b327b2463a31d9ceb6bf9663e065. -/
section PolicyCombinatorialFront_ClosureRawDepth5Policy

/- Depth-5 finite closure.

The generator `build_closure_1062.py` finds the closure already contradictory at
depth 5 (cells `5^i * 7^j`, `i + j ≤ 5`): 21 nodes instead of 36, with a Z3 proof
and certificate pipeline roughly half the size.

The depth-5 cells are exactly the first 21 nodes of `closureNode`, and the
depth-4 nodes 10..14 already have the depth-5 nodes 15..20 as children, so no
renumbering is needed: nodes 15..20 simply become leaves.

`closureRawHypothesis5_of_raw` shows every model of the depth-7 hypothesis is a
model of the depth-5 one, so the existing mathematical proof of
`ClosureRawHypothesis` is reused unchanged. -/

namespace Bounty

/-- `closureNodeConstraint` with the depth-5 nodes `15 ≤ k` treated as leaves. -/
noncomputable def closureNodeConstraint5 (eps : Bool) (k : ℕ) (X Y : ℚ)
    (p : ℕ → Prop) (r : ℕ → ℚ) : Prop := by
  classical
  exact if k = 0 then
    ¬closureNodeAvailable eps k 0 X Y p r ∧ ¬closureNodeAvailable eps k 1 X Y p r
  else if 15 ≤ k then
    3 * (closureNode k).v / 4 ≤ r k ∧
    if p k then normalizedStateValid (closureNodeType eps k) 1 (closureNode k).v
      (closureNodeFour k X) (closureNodeThree k Y) (closureLossFour k X) (closureLossThree k Y) (r k)
    else normalizedStateValid (closureNodeType eps k) 0 (closureNode k).v
      (closureNodeFour k X) (closureNodeThree k Y) (closureLossFour k X) (closureLossThree k Y) (r k)
  else
    (closureNodeAvailable eps k 0 X Y p r ∨ closureNodeAvailable eps k 1 X Y p r) ∧
    (p k ↔ if 2 * closureNodeFour k X ≤ (closureNode k).v
      then closureNodeAvailable eps k 1 X Y p r else ¬closureNodeAvailable eps k 0 X Y p r) ∧
    r k = if p k then closureNodeTrial eps k 1 X Y p r else closureNodeTrial eps k 0 X Y p r

noncomputable def ClosureRawHypothesis5 (eps : Bool) (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Prop :=
  1 / 4 < X ∧ X ≤ 1 ∧ 1 / 3 < Y ∧ Y ≤ 1 ∧ ∀ k < 21, closureNodeConstraint5 eps k X Y p r

/-- Every trial value dominates `3v/4`: it is a `max` whose innermost left term is `3v/4`. -/
def closureNodeTrial_ge (eps : Bool) (k phase : ℕ) (X Y : ℚ)
    (p : ℕ → Prop) (r : ℕ → ℚ) :
    3 * (closureNode k).v / 4 ≤ closureNodeTrial eps k phase X Y p r := by
  unfold closureNodeTrial normalizedTrialValue normalizedProfileTrial
  exact le_trans (le_max_left _ _) (le_max_left _ _)

/-- None of the first 28 nodes is a depth-7 leaf. -/
def closureNode_leaf_false (k : ℕ) (hk : k < 28) : (closureNode k).leaf = false := by
  interval_cases k <;> rfl

/-- The depth-7 hypothesis implies the depth-5 hypothesis on the same `p`, `r`. -/
def closureRawHypothesis5_of_raw (eps : Bool) (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis eps X Y p r) : ClosureRawHypothesis5 eps X Y p r := by
  classical
  obtain ⟨h1, h2, h3, h4, hall⟩ := h
  refine ⟨h1, h2, h3, h4, fun k hk => ?_⟩
  have hc := hall k (by omega)
  have hleaf := closureNode_leaf_false k (by omega)
  unfold closureNodeConstraint at hc
  unfold closureNodeConstraint5
  by_cases hk0 : k = 0
  · simpa only [hk0, if_true] using hc
  · rw [if_neg hk0] at hc ⊢
    rw [if_neg (by simp [hleaf])] at hc
    by_cases h15 : 15 ≤ k
    · rw [if_pos h15]
      obtain ⟨hor, hp, hr⟩ := hc
      refine ⟨?_, ?_⟩
      · rw [hr]
        split_ifs
        · exact closureNodeTrial_ge eps k 1 X Y p r
        · exact closureNodeTrial_ge eps k 0 X Y p r
      · by_cases hpk : p k
        · rw [if_pos hpk, hr, if_pos hpk]
          show closureNodeAvailable eps k 1 X Y p r
          split_ifs at hp with hC
          · exact hp.mp hpk
          · exact hor.resolve_left (hp.mp hpk)
        · rw [if_neg hpk, hr, if_neg hpk]
          show closureNodeAvailable eps k 0 X Y p r
          split_ifs at hp with hC
          · exact hor.resolve_right (fun h1 => hpk (hp.mpr h1))
          · exact not_not.mp (fun h0 => hpk (hp.mpr h0))
    · rw [if_neg h15]
      exact hc

end Bounty


end PolicyCombinatorialFront_ClosureRawDepth5Policy

/- Frozen source PolicyClosureInputsSelectivePair; SHA256 65a19e816381cbe450b02db974663a94b5adfc5a3591eef5bd8925734d75fbe7. -/
section PolicyCombinatorialFront_PolicyClosureInputsSelectivePair

/- Ordinary shared formulas with checked selective numeric annotations. -/

namespace SelectiveSharedInputs

noncomputable def q0 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (5 / 0x41a7) <
      (5 / 4) *
        if (5 / 0x41a7) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X

noncomputable def q1 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 0x41a7) ≥
      (10 / 9) *
        if (5 / 0x41a7) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q2 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 0x41a7) <
      (4 / 3) *
        if (5 / 0x41a7) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q3 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x41a7) ≥
          2 *
            if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4
            else (1 / 0x10000) * X) ∧
      ¬(1 / 0x41a7) ≥
          2 *
            if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q4 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x41a7) ≥
          2 *
            if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4
            else (1 / 0x10000) * X then
      2 *
        if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X
    else
      (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) /
        2

noncomputable def q5 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x41a7) ≥
          2 *
            if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3
            else (1 / 0x4ce3) * Y then
      2 *
        if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y
    else
      (2 *
          if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3
          else (1 / 0x4ce3) * Y) /
        3

noncomputable def q6 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then 1
            else 0) -
            if SelectiveSharedInputs.q3 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q4 X ≥ SelectiveSharedInputs.q5 Y then SelectiveSharedInputs.q4 X
      else SelectiveSharedInputs.q5 Y
    else
      if SelectiveSharedInputs.q4 X > SelectiveSharedInputs.q5 Y then
        if SelectiveSharedInputs.q4 X / 4 ≥ SelectiveSharedInputs.q5 Y then SelectiveSharedInputs.q4 X / 4
        else SelectiveSharedInputs.q5 Y
      else
        if SelectiveSharedInputs.q4 X ≥ SelectiveSharedInputs.q5 Y / 3 then SelectiveSharedInputs.q4 X
        else SelectiveSharedInputs.q5 Y / 3

noncomputable def q7 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then 1
            else 0) -
            if SelectiveSharedInputs.q3 X Y then 1 else 0) =
          (0 : ℤ) then
      r (15 : ℕ) ≤
        if
            ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q3 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x41a7)
        else
          if SelectiveSharedInputs.q4 X ≥ SelectiveSharedInputs.q5 Y then SelectiveSharedInputs.q4 X
          else SelectiveSharedInputs.q5 Y
    else
      r (15 : ℕ) <
        if
            ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q3 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x41a7)
        else
          if SelectiveSharedInputs.q4 X ≥ SelectiveSharedInputs.q5 Y then SelectiveSharedInputs.q4 X
          else SelectiveSharedInputs.q5 Y

noncomputable def q8 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x41a7) ≥
        2 *
          if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4
          else (1 / 0x10000) * X) ∧
      (1 / 0x41a7) ≥
        2 *
          if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q9 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) ≥
      if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q10 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q9 X Y then
      if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X
    else if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q11 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) >
      if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q12 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) /
        4 ≥
      if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q13 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q12 X Y then
      (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) /
        4
    else if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q14 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X) ≥
      (if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q15 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q14 X Y then
      if (1 / 0x41a7) ≥ (1 / 0x10000) * X * 4 then (1 / 0x10000) * X * 4 else (1 / 0x10000) * X
    else
      (if (1 / 0x41a7) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q16 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then 1
            else 0) -
            if SelectiveSharedInputs.q8 X Y then 1 else 0) =
          (0 : ℤ) then
      r (15 : ℕ) ≤
        if
            ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q8 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x41a7)
        else SelectiveSharedInputs.q10 X Y
    else
      r (15 : ℕ) <
        if
            ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q8 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x41a7)
        else SelectiveSharedInputs.q10 X Y

noncomputable def q17 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then 1
          else 0) -
          if SelectiveSharedInputs.q8 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (r (15 : ℕ) ≥
          if
              ((if False ∧ SelectiveSharedInputs.q0 X ∧ SelectiveSharedInputs.q1 Y ∧ SelectiveSharedInputs.q2 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q8 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q10 X Y
          else
            if SelectiveSharedInputs.q11 X Y then SelectiveSharedInputs.q13 X Y else SelectiveSharedInputs.q15 X Y) ∧
        SelectiveSharedInputs.q16 X Y r

noncomputable def q18 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x961) <
      (5 / 4) *
        if (1 / 0x961) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X

noncomputable def q19 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x961) ≥
      (10 / 9) *
        if (1 / 0x961) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q20 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x961) <
      (4 / 3) *
        if (1 / 0x961) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q21 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x2ee5) ≥
          2 *
            if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X) ∧
      ¬(1 / 0x2ee5) ≥
          2 *
            if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q22 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x2ee5) ≥
          2 *
            if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X then
      2 *
        if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        2

noncomputable def q23 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x2ee5) ≥
          2 *
            if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3
            else (1 / 0x4ce3) * Y then
      2 *
        if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y
    else
      (2 *
          if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3
          else (1 / 0x4ce3) * Y) /
        3

noncomputable def q24 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q21 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q22 X ≥ SelectiveSharedInputs.q23 Y then SelectiveSharedInputs.q22 X
      else SelectiveSharedInputs.q23 Y
    else
      if SelectiveSharedInputs.q22 X > SelectiveSharedInputs.q23 Y then
        if SelectiveSharedInputs.q22 X / 4 ≥ SelectiveSharedInputs.q23 Y then
          SelectiveSharedInputs.q22 X / 4
        else SelectiveSharedInputs.q23 Y
      else
        if SelectiveSharedInputs.q22 X ≥ SelectiveSharedInputs.q23 Y / 3 then SelectiveSharedInputs.q22 X
        else SelectiveSharedInputs.q23 Y / 3

noncomputable def q25 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q21 X Y then 1 else 0) =
          (0 : ℤ) then
      r (16 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q21 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x2ee5)
        else
          if SelectiveSharedInputs.q22 X ≥ SelectiveSharedInputs.q23 Y then SelectiveSharedInputs.q22 X
          else SelectiveSharedInputs.q23 Y
    else
      r (16 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q21 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x2ee5)
        else
          if SelectiveSharedInputs.q22 X ≥ SelectiveSharedInputs.q23 Y then SelectiveSharedInputs.q22 X
          else SelectiveSharedInputs.q23 Y

noncomputable def q26 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x2ee5) ≥
        2 *
          if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
          else (1 / 0x4000) * X) ∧
      (1 / 0x2ee5) ≥
        2 *
          if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q27 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q28 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q27 X Y then
      if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q29 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) >
      if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q30 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4 ≥
      if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q31 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q30 X Y then
      (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4
    else if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q32 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      (if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q33 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q32 X Y then
      if (1 / 0x2ee5) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x2ee5) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q34 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q26 X Y then 1 else 0) =
          (0 : ℤ) then
      r (16 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q26 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x2ee5)
        else SelectiveSharedInputs.q28 X Y
    else
      r (16 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q26 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x2ee5)
        else SelectiveSharedInputs.q28 X Y

noncomputable def q35 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then 1
          else 0) -
          if SelectiveSharedInputs.q26 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (r (16 : ℕ) ≥
          if
              ((if True ∧ SelectiveSharedInputs.q18 X ∧ SelectiveSharedInputs.q19 Y ∧ SelectiveSharedInputs.q20 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q26 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q28 X Y
          else
            if SelectiveSharedInputs.q29 X Y then SelectiveSharedInputs.q31 X Y else SelectiveSharedInputs.q33 X Y) ∧
        SelectiveSharedInputs.q34 X Y r

noncomputable def q36 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x6b3) <
      (5 / 4) *
        if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X

noncomputable def q37 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x6b3) ≥
      (10 / 9) *
        if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q38 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x6b3) <
      (4 / 3) *
        if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q39 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x217f) ≥
          2 *
            if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X) ∧
      ¬(1 / 0x217f) ≥
          2 *
            if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q40 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x217f) ≥
          2 *
            if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X then
      2 *
        if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        2

noncomputable def q41 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x217f) ≥
          2 *
            if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3
            else (1 / 0x4ce3) * Y then
      2 *
        if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y
    else
      (2 *
          if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q42 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q36 X ∧ SelectiveSharedInputs.q37 Y ∧ SelectiveSharedInputs.q38 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q39 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q40 X ≥ SelectiveSharedInputs.q41 Y then SelectiveSharedInputs.q40 X
      else SelectiveSharedInputs.q41 Y
    else
      if SelectiveSharedInputs.q40 X > SelectiveSharedInputs.q41 Y then
        if SelectiveSharedInputs.q40 X / 4 ≥ SelectiveSharedInputs.q41 Y then
          SelectiveSharedInputs.q40 X / 4
        else SelectiveSharedInputs.q41 Y
      else
        if SelectiveSharedInputs.q40 X ≥ SelectiveSharedInputs.q41 Y / 3 then SelectiveSharedInputs.q40 X
        else SelectiveSharedInputs.q41 Y / 3

noncomputable def q43 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q36 X ∧ SelectiveSharedInputs.q37 Y ∧ SelectiveSharedInputs.q38 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q39 X Y then 1 else 0) =
          (0 : ℤ) then
      r (17 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q36 X ∧ SelectiveSharedInputs.q37 Y ∧ SelectiveSharedInputs.q38 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q39 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x217f)
        else
          if SelectiveSharedInputs.q40 X ≥ SelectiveSharedInputs.q41 Y then SelectiveSharedInputs.q40 X
          else SelectiveSharedInputs.q41 Y
    else
      r (17 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q36 X ∧ SelectiveSharedInputs.q37 Y ∧ SelectiveSharedInputs.q38 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q39 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x217f)
        else
          if SelectiveSharedInputs.q40 X ≥ SelectiveSharedInputs.q41 Y then SelectiveSharedInputs.q40 X
          else SelectiveSharedInputs.q41 Y

noncomputable def q44 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x217f) ≥
        2 *
          if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ∧
      (1 / 0x217f) ≥
        2 *
          if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q45 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q46 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q45 X Y then
      if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q47 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) >
      if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q48 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4 ≥
      if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q49 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q48 X Y then
      (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4
    else if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y

noncomputable def q50 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      (if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q51 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q50 X Y then
      if (1 / 0x217f) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x217f) ≥ (1 / 0x4ce3) * Y * 3 then (1 / 0x4ce3) * Y * 3 else (1 / 0x4ce3) * Y) /
        3

noncomputable def q54 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x4c9) <
      (5 / 4) *
        if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X

noncomputable def q55 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x4c9) ≥
      (10 / 9) *
        if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q56 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x4c9) <
      (4 / 3) *
        if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q57 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x17ed) ≥
          2 *
            if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X) ∧
      ¬(1 / 0x17ed) ≥
          2 *
            if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q58 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x17ed) ≥
          2 *
            if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X then
      2 *
        if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        2

noncomputable def q59 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x17ed) ≥
          2 *
            if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3
            else (1 / 0x19a1) * Y then
      2 * if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y
    else
      (2 *
          if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q60 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q57 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q58 X ≥ SelectiveSharedInputs.q59 Y then SelectiveSharedInputs.q58 X
      else SelectiveSharedInputs.q59 Y
    else
      if SelectiveSharedInputs.q58 X > SelectiveSharedInputs.q59 Y then
        if SelectiveSharedInputs.q58 X / 4 ≥ SelectiveSharedInputs.q59 Y then
          SelectiveSharedInputs.q58 X / 4
        else SelectiveSharedInputs.q59 Y
      else
        if SelectiveSharedInputs.q58 X ≥ SelectiveSharedInputs.q59 Y / 3 then SelectiveSharedInputs.q58 X
        else SelectiveSharedInputs.q59 Y / 3

noncomputable def q61 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q57 X Y then 1 else 0) =
          (0 : ℤ) then
      r (18 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q57 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x17ed)
        else
          if SelectiveSharedInputs.q58 X ≥ SelectiveSharedInputs.q59 Y then SelectiveSharedInputs.q58 X
          else SelectiveSharedInputs.q59 Y
    else
      r (18 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q57 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x17ed)
        else
          if SelectiveSharedInputs.q58 X ≥ SelectiveSharedInputs.q59 Y then SelectiveSharedInputs.q58 X
          else SelectiveSharedInputs.q59 Y

noncomputable def q62 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x17ed) ≥
        2 *
          if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ∧
      (1 / 0x17ed) ≥
        2 *
          if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q63 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q64 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q63 X Y then
      if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q65 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) >
      if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q66 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4 ≥
      if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q67 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q66 X Y then
      (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4
    else if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q68 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      (if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q69 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q68 X Y then
      if (1 / 0x17ed) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x17ed) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q70 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q62 X Y then 1 else 0) =
          (0 : ℤ) then
      r (18 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q62 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x17ed)
        else SelectiveSharedInputs.q64 X Y
    else
      r (18 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q62 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x17ed)
        else SelectiveSharedInputs.q64 X Y

noncomputable def q71 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then 1
          else 0) -
          if SelectiveSharedInputs.q62 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (r (18 : ℕ) ≥
          if
              ((if True ∧ SelectiveSharedInputs.q54 X ∧ SelectiveSharedInputs.q55 Y ∧ SelectiveSharedInputs.q56 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q62 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q64 X Y
          else
            if SelectiveSharedInputs.q65 X Y then SelectiveSharedInputs.q67 X Y else SelectiveSharedInputs.q69 X Y) ∧
        SelectiveSharedInputs.q70 X Y r

noncomputable def q72 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x36b) <
      (5 / 4) *
        if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X

noncomputable def q73 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x36b) ≥
      (10 / 9) *
        if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q74 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x36b) <
      (4 / 3) *
        if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q75 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x1117) ≥
          2 *
            if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X) ∧
      ¬(1 / 0x1117) ≥
          2 *
            if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q76 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x1117) ≥
          2 *
            if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4
            else (1 / 0x4000) * X then
      2 *
        if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        2

noncomputable def q77 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x1117) ≥
          2 *
            if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3
            else (1 / 0x19a1) * Y then
      2 * if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y
    else
      (2 *
          if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q78 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q75 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q76 X ≥ SelectiveSharedInputs.q77 Y then SelectiveSharedInputs.q76 X
      else SelectiveSharedInputs.q77 Y
    else
      if SelectiveSharedInputs.q76 X > SelectiveSharedInputs.q77 Y then
        if SelectiveSharedInputs.q76 X / 4 ≥ SelectiveSharedInputs.q77 Y then
          SelectiveSharedInputs.q76 X / 4
        else SelectiveSharedInputs.q77 Y
      else
        if SelectiveSharedInputs.q76 X ≥ SelectiveSharedInputs.q77 Y / 3 then SelectiveSharedInputs.q76 X
        else SelectiveSharedInputs.q77 Y / 3

noncomputable def q79 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q75 X Y then 1 else 0) =
          (0 : ℤ) then
      r (19 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q75 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x1117)
        else
          if SelectiveSharedInputs.q76 X ≥ SelectiveSharedInputs.q77 Y then SelectiveSharedInputs.q76 X
          else SelectiveSharedInputs.q77 Y
    else
      r (19 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q75 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x1117)
        else
          if SelectiveSharedInputs.q76 X ≥ SelectiveSharedInputs.q77 Y then SelectiveSharedInputs.q76 X
          else SelectiveSharedInputs.q77 Y

noncomputable def q80 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x1117) ≥
        2 *
          if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ∧
      (1 / 0x1117) ≥
        2 *
          if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q81 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q82 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q81 X Y then
      if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q83 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) >
      if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q84 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4 ≥
      if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q85 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q84 X Y then
      (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) /
        4
    else if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q86 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X) ≥
      (if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q87 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q86 X Y then
      if (1 / 0x1117) ≥ (1 / 0x4000) * X * 4 then (1 / 0x4000) * X * 4 else (1 / 0x4000) * X
    else
      (if (1 / 0x1117) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q88 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q80 X Y then 1 else 0) =
          (0 : ℤ) then
      r (19 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q80 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x1117)
        else SelectiveSharedInputs.q82 X Y
    else
      r (19 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q80 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x1117)
        else SelectiveSharedInputs.q82 X Y

noncomputable def q89 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then 1
          else 0) -
          if SelectiveSharedInputs.q80 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (r (19 : ℕ) ≥
          if
              ((if True ∧ SelectiveSharedInputs.q72 X ∧ SelectiveSharedInputs.q73 Y ∧ SelectiveSharedInputs.q74 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q80 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q82 X Y
          else
            if SelectiveSharedInputs.q83 X Y then SelectiveSharedInputs.q85 X Y else SelectiveSharedInputs.q87 X Y) ∧
        SelectiveSharedInputs.q88 X Y r

noncomputable def q90 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x271) <
      (5 / 4) *
        if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X

noncomputable def q91 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x271) ≥
      (10 / 9) *
        if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q92 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x271) <
      (4 / 3) * if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q93 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0xc35) ≥
          2 *
            if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      ¬(1 / 0xc35) ≥
          2 *
            if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q94 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0xc35) ≥
          2 *
            if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4
            else (1 / 0x1000) * X then
      2 * if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        2

noncomputable def q95 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0xc35) ≥
          2 *
            if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3
            else (1 / 0x19a1) * Y then
      2 * if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y
    else
      (2 *
          if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q96 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q93 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q94 X ≥ SelectiveSharedInputs.q95 Y then SelectiveSharedInputs.q94 X
      else SelectiveSharedInputs.q95 Y
    else
      if SelectiveSharedInputs.q94 X > SelectiveSharedInputs.q95 Y then
        if SelectiveSharedInputs.q94 X / 4 ≥ SelectiveSharedInputs.q95 Y then
          SelectiveSharedInputs.q94 X / 4
        else SelectiveSharedInputs.q95 Y
      else
        if SelectiveSharedInputs.q94 X ≥ SelectiveSharedInputs.q95 Y / 3 then SelectiveSharedInputs.q94 X
        else SelectiveSharedInputs.q95 Y / 3

noncomputable def q97 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q93 X Y then 1 else 0) =
          (0 : ℤ) then
      r (20 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q93 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xc35)
        else
          if SelectiveSharedInputs.q94 X ≥ SelectiveSharedInputs.q95 Y then SelectiveSharedInputs.q94 X
          else SelectiveSharedInputs.q95 Y
    else
      r (20 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q93 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xc35)
        else
          if SelectiveSharedInputs.q94 X ≥ SelectiveSharedInputs.q95 Y then SelectiveSharedInputs.q94 X
          else SelectiveSharedInputs.q95 Y

noncomputable def q98 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0xc35) ≥
        2 *
          if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      (1 / 0xc35) ≥
        2 *
          if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q99 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q100 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q99 X Y then
      if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q101 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) >
      if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q102 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4 ≥
      if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q103 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q102 X Y then
      (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4
    else if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y

noncomputable def q104 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      (if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q105 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q104 X Y then
      if (1 / 0xc35) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0xc35) ≥ (1 / 0x19a1) * Y * 3 then (1 / 0x19a1) * Y * 3 else (1 / 0x19a1) * Y) /
        3

noncomputable def q106 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    if
        ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q98 X Y then 1 else 0) =
          (0 : ℤ) then
      r (20 : ℕ) ≤
        if
            ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q98 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xc35)
        else SelectiveSharedInputs.q100 X Y
    else
      r (20 : ℕ) <
        if
            ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q98 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xc35)
        else SelectiveSharedInputs.q100 X Y

noncomputable def q107 : ℚ → ℚ → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y r =>
    ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then 1
          else 0) -
          if SelectiveSharedInputs.q98 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (r (20 : ℕ) ≥
          if
              ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q98 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q100 X Y
          else
            if SelectiveSharedInputs.q101 X Y then SelectiveSharedInputs.q103 X Y
            else SelectiveSharedInputs.q105 X Y) ∧
        SelectiveSharedInputs.q106 X Y r

noncomputable def q133 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x157) <
      (5 / 4) *
        if (1 / 0x157) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X

noncomputable def q134 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x157) ≥
      (10 / 9) *
        if (1 / 0x157) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q135 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x157) <
      (4 / 3) * if (1 / 0x157) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q136 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x6b3) ≥
        2 *
          if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      (1 / 0x6b3) ≥
        2 *
          if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q137 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q138 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q137 X Y then
      if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q139 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) >
      if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q140 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4 ≥
      if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q141 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q140 X Y then
      (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4
    else if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q142 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      (if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q143 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q142 X Y then
      if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q144 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x1acc) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q136 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q138 X Y
          else
            if SelectiveSharedInputs.q139 X Y then SelectiveSharedInputs.q141 X Y
            else SelectiveSharedInputs.q143 X Y then
      (3 / 0x1acc)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q136 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q138 X Y
      else if SelectiveSharedInputs.q139 X Y then SelectiveSharedInputs.q141 X Y else SelectiveSharedInputs.q143 X Y

noncomputable def q145 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q144 X Y ≥ if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
        SelectiveSharedInputs.q144 X Y
      else if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)) ≥
      if p (16 : ℕ) ↔ False then 4 * r (16 : ℕ) else 6 * r (16 : ℕ)

noncomputable def q146 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q145 X Y p r then
      if SelectiveSharedInputs.q144 X Y ≥ if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
        SelectiveSharedInputs.q144 X Y
      else if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)
    else if p (16 : ℕ) ↔ False then 4 * r (16 : ℕ) else 6 * r (16 : ℕ)

noncomputable def q147 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q136 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q146 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q136 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x6b3)
        else SelectiveSharedInputs.q138 X Y
    else
      SelectiveSharedInputs.q146 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q136 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x6b3)
        else SelectiveSharedInputs.q138 X Y

noncomputable def q148 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then 1
          else 0) -
          if SelectiveSharedInputs.q136 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q146 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q136 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q138 X Y
          else
            if SelectiveSharedInputs.q139 X Y then SelectiveSharedInputs.q141 X Y
            else SelectiveSharedInputs.q143 X Y) ∧
        SelectiveSharedInputs.q147 X Y p r

noncomputable def q149 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x6b3) ≥
          2 *
            if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      ¬(1 / 0x6b3) ≥
          2 *
            if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q150 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x6b3) ≥
          2 *
            if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4
            else (1 / 0x1000) * X then
      2 * if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0x6b3) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        2

noncomputable def q151 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x6b3) ≥
          2 *
            if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3
            else (1 / 0x88b) * Y then
      2 * if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y
    else
      (2 *
          if (1 / 0x6b3) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q152 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q149 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q150 X ≥ SelectiveSharedInputs.q151 Y then SelectiveSharedInputs.q150 X
      else SelectiveSharedInputs.q151 Y
    else
      if SelectiveSharedInputs.q150 X > SelectiveSharedInputs.q151 Y then
        if SelectiveSharedInputs.q150 X / 4 ≥ SelectiveSharedInputs.q151 Y then
          SelectiveSharedInputs.q150 X / 4
        else SelectiveSharedInputs.q151 Y
      else
        if SelectiveSharedInputs.q150 X ≥ SelectiveSharedInputs.q151 Y / 3 then SelectiveSharedInputs.q150 X
        else SelectiveSharedInputs.q151 Y / 3

noncomputable def q153 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x1acc) ≥ SelectiveSharedInputs.q152 X Y then (3 / 0x1acc) else SelectiveSharedInputs.q152 X Y) ≥
          if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
      if (3 / 0x1acc) ≥ SelectiveSharedInputs.q152 X Y then (3 / 0x1acc) else SelectiveSharedInputs.q152 X Y
    else if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)

noncomputable def q154 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q153 X Y p r ≥
            if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ) then
        SelectiveSharedInputs.q153 X Y p r
      else if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q149 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x6b3)
      else
        if SelectiveSharedInputs.q150 X ≥ SelectiveSharedInputs.q151 Y then SelectiveSharedInputs.q150 X
        else SelectiveSharedInputs.q151 Y

noncomputable def q155 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q153 X Y p r ≥
            if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ) then
        SelectiveSharedInputs.q153 X Y p r
      else if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q149 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x6b3)
      else
        if SelectiveSharedInputs.q150 X ≥ SelectiveSharedInputs.q151 Y then SelectiveSharedInputs.q150 X
        else SelectiveSharedInputs.q151 Y

noncomputable def q156 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then 1
          else 0) -
          if SelectiveSharedInputs.q149 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q153 X Y p r ≥
                if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ) then
            SelectiveSharedInputs.q153 X Y p r
          else if p (16 : ℕ) ↔ True then 4 * r (16 : ℕ) else 6 * r (16 : ℕ)) ≥
          SelectiveSharedInputs.q152 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q133 X ∧ SelectiveSharedInputs.q134 Y ∧ SelectiveSharedInputs.q135 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q149 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q154 X Y p r
        else SelectiveSharedInputs.q155 X Y p r

noncomputable def q158 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0xf5) <
      (5 / 4) * if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X

noncomputable def q159 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0xf5) ≥
      (10 / 9) *
        if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q160 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0xf5) <
      (4 / 3) * if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q161 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x4c9) ≥
        2 *
          if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      (1 / 0x4c9) ≥
        2 *
          if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q162 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q163 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q162 X Y then
      if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q164 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) >
      if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q165 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4 ≥
      if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q166 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q165 X Y then
      (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        4
    else if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q167 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ≥
      (if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q168 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q167 X Y then
      if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q169 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x1324) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q161 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q163 X Y
          else
            if SelectiveSharedInputs.q164 X Y then SelectiveSharedInputs.q166 X Y
            else SelectiveSharedInputs.q168 X Y then
      (3 / 0x1324)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q161 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q163 X Y
      else if SelectiveSharedInputs.q164 X Y then SelectiveSharedInputs.q166 X Y else SelectiveSharedInputs.q168 X Y

noncomputable def q170 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q169 X Y ≥ if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
        SelectiveSharedInputs.q169 X Y
      else if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)) ≥
      if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)

noncomputable def q171 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q170 X Y p r then
      if SelectiveSharedInputs.q169 X Y ≥ if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
        SelectiveSharedInputs.q169 X Y
      else if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)
    else if p (17 : ℕ) ↔ False then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)

noncomputable def q172 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q161 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q171 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q161 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x4c9)
        else SelectiveSharedInputs.q163 X Y
    else
      SelectiveSharedInputs.q171 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q161 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x4c9)
        else SelectiveSharedInputs.q163 X Y

noncomputable def q173 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then 1
          else 0) -
          if SelectiveSharedInputs.q161 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q171 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q161 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q163 X Y
          else
            if SelectiveSharedInputs.q164 X Y then SelectiveSharedInputs.q166 X Y
            else SelectiveSharedInputs.q168 X Y) ∧
        SelectiveSharedInputs.q172 X Y p r

noncomputable def q174 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x4c9) ≥
          2 *
            if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) ∧
      ¬(1 / 0x4c9) ≥
          2 *
            if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q175 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x4c9) ≥
          2 *
            if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4
            else (1 / 0x1000) * X then
      2 * if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X
    else
      (if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4 else (1 / 0x1000) * X) /
        2

noncomputable def q176 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x4c9) ≥
          2 *
            if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3
            else (1 / 0x88b) * Y then
      2 * if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y
    else
      (2 *
          if (1 / 0x4c9) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q177 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q174 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q175 X ≥ SelectiveSharedInputs.q176 Y then SelectiveSharedInputs.q175 X
      else SelectiveSharedInputs.q176 Y
    else
      if SelectiveSharedInputs.q175 X > SelectiveSharedInputs.q176 Y then
        if SelectiveSharedInputs.q175 X / 4 ≥ SelectiveSharedInputs.q176 Y then
          SelectiveSharedInputs.q175 X / 4
        else SelectiveSharedInputs.q176 Y
      else
        if SelectiveSharedInputs.q175 X ≥ SelectiveSharedInputs.q176 Y / 3 then SelectiveSharedInputs.q175 X
        else SelectiveSharedInputs.q176 Y / 3

noncomputable def q178 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x1324) ≥ SelectiveSharedInputs.q177 X Y then (3 / 0x1324) else SelectiveSharedInputs.q177 X Y) ≥
          if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
      if (3 / 0x1324) ≥ SelectiveSharedInputs.q177 X Y then (3 / 0x1324) else SelectiveSharedInputs.q177 X Y
    else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)

noncomputable def q179 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q178 X Y p r ≥
            if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
        SelectiveSharedInputs.q178 X Y p r
      else if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q174 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x4c9)
      else
        if SelectiveSharedInputs.q175 X ≥ SelectiveSharedInputs.q176 Y then SelectiveSharedInputs.q175 X
        else SelectiveSharedInputs.q176 Y

noncomputable def q180 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q178 X Y p r ≥
            if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
        SelectiveSharedInputs.q178 X Y p r
      else if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q174 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x4c9)
      else
        if SelectiveSharedInputs.q175 X ≥ SelectiveSharedInputs.q176 Y then SelectiveSharedInputs.q175 X
        else SelectiveSharedInputs.q176 Y

noncomputable def q181 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then 1
          else 0) -
          if SelectiveSharedInputs.q174 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q178 X Y p r ≥
                if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
            SelectiveSharedInputs.q178 X Y p r
          else if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)) ≥
          SelectiveSharedInputs.q177 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q158 X ∧ SelectiveSharedInputs.q159 Y ∧ SelectiveSharedInputs.q160 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q174 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q179 X Y p r
        else SelectiveSharedInputs.q180 X Y p r

noncomputable def q182 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0x4c9) ≥
          2 *
            if (1 / 0x4c9) ≥ (1 / 0x1000) * X * 4 then (1 / 0x1000) * X * 4
            else (1 / 0x1000) * X then
      SelectiveSharedInputs.q181 X Y p r
    else ¬SelectiveSharedInputs.q173 X Y p r

noncomputable def q183 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0xaf) <
      (5 / 4) * if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X

noncomputable def q184 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0xaf) ≥
      (10 / 9) *
        if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q185 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0xaf) <
      (4 / 3) * if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q186 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x36b) ≥
        2 *
          if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ∧
      (1 / 0x36b) ≥
        2 *
          if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q187 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ≥
      if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q188 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q187 X Y then
      if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q189 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) >
      if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q190 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        4 ≥
      if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q191 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q190 X Y then
      (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        4
    else if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q192 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ≥
      (if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q193 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q192 X Y then
      if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else
      (if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q194 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0xdac) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q186 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q188 X Y
          else
            if SelectiveSharedInputs.q189 X Y then SelectiveSharedInputs.q191 X Y
            else SelectiveSharedInputs.q193 X Y then
      (3 / 0xdac)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q186 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q188 X Y
      else if SelectiveSharedInputs.q189 X Y then SelectiveSharedInputs.q191 X Y else SelectiveSharedInputs.q193 X Y

noncomputable def q195 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q194 X Y ≥ if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
        SelectiveSharedInputs.q194 X Y
      else if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)) ≥
      if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)

noncomputable def q196 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q195 X Y p r then
      if SelectiveSharedInputs.q194 X Y ≥ if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
        SelectiveSharedInputs.q194 X Y
      else if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)
    else if p (18 : ℕ) ↔ False then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)

noncomputable def q197 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q186 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q196 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q186 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x36b)
        else SelectiveSharedInputs.q188 X Y
    else
      SelectiveSharedInputs.q196 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q186 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x36b)
        else SelectiveSharedInputs.q188 X Y

noncomputable def q198 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then 1
          else 0) -
          if SelectiveSharedInputs.q186 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q196 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q186 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q188 X Y
          else
            if SelectiveSharedInputs.q189 X Y then SelectiveSharedInputs.q191 X Y
            else SelectiveSharedInputs.q193 X Y) ∧
        SelectiveSharedInputs.q197 X Y p r

noncomputable def q199 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x36b) ≥
          2 *
            if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ∧
      ¬(1 / 0x36b) ≥
          2 *
            if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y

noncomputable def q200 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x36b) ≥
          2 *
            if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X then
      2 * if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else
      (if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        2

noncomputable def q201 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x36b) ≥
          2 *
            if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y then
      2 * if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y
    else
      (2 *
          if (1 / 0x36b) ≥ (1 / 0x88b) * Y * 3 then (1 / 0x88b) * Y * 3 else (1 / 0x88b) * Y) /
        3

noncomputable def q202 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q199 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q200 X ≥ SelectiveSharedInputs.q201 Y then SelectiveSharedInputs.q200 X
      else SelectiveSharedInputs.q201 Y
    else
      if SelectiveSharedInputs.q200 X > SelectiveSharedInputs.q201 Y then
        if SelectiveSharedInputs.q200 X / 4 ≥ SelectiveSharedInputs.q201 Y then
          SelectiveSharedInputs.q200 X / 4
        else SelectiveSharedInputs.q201 Y
      else
        if SelectiveSharedInputs.q200 X ≥ SelectiveSharedInputs.q201 Y / 3 then SelectiveSharedInputs.q200 X
        else SelectiveSharedInputs.q201 Y / 3

noncomputable def q203 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0xdac) ≥ SelectiveSharedInputs.q202 X Y then (3 / 0xdac) else SelectiveSharedInputs.q202 X Y) ≥
          if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
      if (3 / 0xdac) ≥ SelectiveSharedInputs.q202 X Y then (3 / 0xdac) else SelectiveSharedInputs.q202 X Y
    else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)

noncomputable def q204 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q203 X Y p r ≥
            if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
        SelectiveSharedInputs.q203 X Y p r
      else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q199 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x36b)
      else
        if SelectiveSharedInputs.q200 X ≥ SelectiveSharedInputs.q201 Y then SelectiveSharedInputs.q200 X
        else SelectiveSharedInputs.q201 Y

noncomputable def q205 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q203 X Y p r ≥
            if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
        SelectiveSharedInputs.q203 X Y p r
      else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q199 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x36b)
      else
        if SelectiveSharedInputs.q200 X ≥ SelectiveSharedInputs.q201 Y then SelectiveSharedInputs.q200 X
        else SelectiveSharedInputs.q201 Y

noncomputable def q206 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then 1
          else 0) -
          if SelectiveSharedInputs.q199 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q203 X Y p r ≥
                if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
            SelectiveSharedInputs.q203 X Y p r
          else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)) ≥
          SelectiveSharedInputs.q202 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q183 X ∧ SelectiveSharedInputs.q184 Y ∧ SelectiveSharedInputs.q185 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q199 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q204 X Y p r
        else SelectiveSharedInputs.q205 X Y p r

noncomputable def q207 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0x36b) ≥
          2 *
            if (1 / 0x36b) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X then
      SelectiveSharedInputs.q206 X Y p r
    else ¬SelectiveSharedInputs.q198 X Y p r

noncomputable def q208 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 0x7d) <
      (5 / 4) * if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X

noncomputable def q209 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x7d) ≥
      (10 / 9) *
        if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q210 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 0x7d) <
      (4 / 3) * if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q211 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x271) ≥
        2 *
          if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ∧
      (1 / 0x271) ≥
        2 * if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q212 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ≥
      if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q213 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q212 X Y then
      if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q214 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) >
      if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q215 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        4 ≥
      if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q216 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q215 X Y then
      (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        4
    else if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q217 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ≥
      (if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) / 3

noncomputable def q218 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q217 X Y then
      if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else
      (if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) / 3

noncomputable def q219 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x9c4) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q211 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q213 X Y
          else
            if SelectiveSharedInputs.q214 X Y then SelectiveSharedInputs.q216 X Y
            else SelectiveSharedInputs.q218 X Y then
      (3 / 0x9c4)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q211 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q213 X Y
      else if SelectiveSharedInputs.q214 X Y then SelectiveSharedInputs.q216 X Y else SelectiveSharedInputs.q218 X Y

noncomputable def q220 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q219 X Y ≥ if p (20 : ℕ) ↔ False then 4 * r (20 : ℕ) else 6 * r (20 : ℕ) then
        SelectiveSharedInputs.q219 X Y
      else if p (20 : ℕ) ↔ False then 4 * r (20 : ℕ) else 6 * r (20 : ℕ)) ≥
      if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)

noncomputable def q221 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q220 X Y p r then
      if SelectiveSharedInputs.q219 X Y ≥ if p (20 : ℕ) ↔ False then 4 * r (20 : ℕ) else 6 * r (20 : ℕ) then
        SelectiveSharedInputs.q219 X Y
      else if p (20 : ℕ) ↔ False then 4 * r (20 : ℕ) else 6 * r (20 : ℕ)
    else if p (19 : ℕ) ↔ False then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)

noncomputable def q222 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q211 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q221 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q211 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x271)
        else SelectiveSharedInputs.q213 X Y
    else
      SelectiveSharedInputs.q221 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q211 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x271)
        else SelectiveSharedInputs.q213 X Y

noncomputable def q223 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then 1
          else 0) -
          if SelectiveSharedInputs.q211 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q221 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q211 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q213 X Y
          else
            if SelectiveSharedInputs.q214 X Y then SelectiveSharedInputs.q216 X Y
            else SelectiveSharedInputs.q218 X Y) ∧
        SelectiveSharedInputs.q222 X Y p r

noncomputable def q224 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x271) ≥
          2 *
            if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) ∧
      ¬(1 / 0x271) ≥
          2 * if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q225 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x271) ≥
          2 *
            if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X then
      2 * if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X
    else
      (if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X) /
        2

noncomputable def q226 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x271) ≥
          2 *
            if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y then
      2 * if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y
    else
      (2 * if (1 / 0x271) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) /
        3

noncomputable def q227 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q224 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q225 X ≥ SelectiveSharedInputs.q226 Y then SelectiveSharedInputs.q225 X
      else SelectiveSharedInputs.q226 Y
    else
      if SelectiveSharedInputs.q225 X > SelectiveSharedInputs.q226 Y then
        if SelectiveSharedInputs.q225 X / 4 ≥ SelectiveSharedInputs.q226 Y then
          SelectiveSharedInputs.q225 X / 4
        else SelectiveSharedInputs.q226 Y
      else
        if SelectiveSharedInputs.q225 X ≥ SelectiveSharedInputs.q226 Y / 3 then SelectiveSharedInputs.q225 X
        else SelectiveSharedInputs.q226 Y / 3

noncomputable def q228 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x9c4) ≥ SelectiveSharedInputs.q227 X Y then (3 / 0x9c4) else SelectiveSharedInputs.q227 X Y) ≥
          if p (20 : ℕ) ↔ True then 4 * r (20 : ℕ) else 6 * r (20 : ℕ) then
      if (3 / 0x9c4) ≥ SelectiveSharedInputs.q227 X Y then (3 / 0x9c4) else SelectiveSharedInputs.q227 X Y
    else if p (20 : ℕ) ↔ True then 4 * r (20 : ℕ) else 6 * r (20 : ℕ)

noncomputable def q229 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q228 X Y p r ≥
            if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
        SelectiveSharedInputs.q228 X Y p r
      else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q224 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x271)
      else
        if SelectiveSharedInputs.q225 X ≥ SelectiveSharedInputs.q226 Y then SelectiveSharedInputs.q225 X
        else SelectiveSharedInputs.q226 Y

noncomputable def q230 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q228 X Y p r ≥
            if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
        SelectiveSharedInputs.q228 X Y p r
      else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q224 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x271)
      else
        if SelectiveSharedInputs.q225 X ≥ SelectiveSharedInputs.q226 Y then SelectiveSharedInputs.q225 X
        else SelectiveSharedInputs.q226 Y

noncomputable def q231 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then 1
          else 0) -
          if SelectiveSharedInputs.q224 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q228 X Y p r ≥
                if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
            SelectiveSharedInputs.q228 X Y p r
          else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)) ≥
          SelectiveSharedInputs.q227 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q208 X ∧ SelectiveSharedInputs.q209 Y ∧ SelectiveSharedInputs.q210 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q224 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q229 X Y p r
        else SelectiveSharedInputs.q230 X Y p r

noncomputable def q232 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0x271) ≥
          2 *
            if (1 / 0x271) ≥ (1 / 0x400) * X * 4 then (1 / 0x400) * X * 4 else (1 / 0x400) * X then
      SelectiveSharedInputs.q231 X Y p r
    else ¬SelectiveSharedInputs.q223 X Y p r

noncomputable def q258 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 49) <
      (5 / 4) * if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X

noncomputable def q259 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 49) ≥
      (10 / 9) * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q260 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 49) <
      (4 / 3) * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q261 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0xf5) ≥
        2 *
          if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      (1 / 0xf5) ≥
        2 * if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q262 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q263 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q262 X Y then
      if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q264 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) >
      if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q265 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4 ≥
      if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q266 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q265 X Y then
      (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4
    else if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q267 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      (if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) / 3

noncomputable def q268 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q267 X Y then
      if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) / 3

noncomputable def q269 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x3d4) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q261 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q263 X Y
          else
            if SelectiveSharedInputs.q264 X Y then SelectiveSharedInputs.q266 X Y
            else SelectiveSharedInputs.q268 X Y then
      (3 / 0x3d4)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q261 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q263 X Y
      else if SelectiveSharedInputs.q264 X Y then SelectiveSharedInputs.q266 X Y else SelectiveSharedInputs.q268 X Y

noncomputable def q270 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q269 X Y ≥ if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
        SelectiveSharedInputs.q269 X Y
      else if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)) ≥
      if p (11 : ℕ) ↔ False then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)

noncomputable def q271 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q270 X Y p r then
      if SelectiveSharedInputs.q269 X Y ≥ if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
        SelectiveSharedInputs.q269 X Y
      else if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)
    else if p (11 : ℕ) ↔ False then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)

noncomputable def q272 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q261 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q271 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q261 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xf5)
        else SelectiveSharedInputs.q263 X Y
    else
      SelectiveSharedInputs.q271 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q261 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xf5)
        else SelectiveSharedInputs.q263 X Y

noncomputable def q273 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then 1
          else 0) -
          if SelectiveSharedInputs.q261 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q271 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q261 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q263 X Y
          else
            if SelectiveSharedInputs.q264 X Y then SelectiveSharedInputs.q266 X Y
            else SelectiveSharedInputs.q268 X Y) ∧
        SelectiveSharedInputs.q272 X Y p r

noncomputable def q274 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0xf5) ≥
          2 *
            if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      ¬(1 / 0xf5) ≥
          2 * if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y

noncomputable def q275 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0xf5) ≥
          2 *
            if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      2 * if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 2

noncomputable def q276 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0xf5) ≥
          2 *
            if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y then
      2 * if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y
    else
      (2 * if (1 / 0xf5) ≥ (1 / 0x2d9) * Y * 3 then (1 / 0x2d9) * Y * 3 else (1 / 0x2d9) * Y) /
        3

noncomputable def q277 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q274 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q275 X ≥ SelectiveSharedInputs.q276 Y then SelectiveSharedInputs.q275 X
      else SelectiveSharedInputs.q276 Y
    else
      if SelectiveSharedInputs.q275 X > SelectiveSharedInputs.q276 Y then
        if SelectiveSharedInputs.q275 X / 4 ≥ SelectiveSharedInputs.q276 Y then
          SelectiveSharedInputs.q275 X / 4
        else SelectiveSharedInputs.q276 Y
      else
        if SelectiveSharedInputs.q275 X ≥ SelectiveSharedInputs.q276 Y / 3 then SelectiveSharedInputs.q275 X
        else SelectiveSharedInputs.q276 Y / 3

noncomputable def q278 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x3d4) ≥ SelectiveSharedInputs.q277 X Y then (3 / 0x3d4) else SelectiveSharedInputs.q277 X Y) ≥
          if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
      if (3 / 0x3d4) ≥ SelectiveSharedInputs.q277 X Y then (3 / 0x3d4) else SelectiveSharedInputs.q277 X Y
    else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)

noncomputable def q279 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q278 X Y p r ≥
            if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ) then
        SelectiveSharedInputs.q278 X Y p r
      else if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q274 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0xf5)
      else
        if SelectiveSharedInputs.q275 X ≥ SelectiveSharedInputs.q276 Y then SelectiveSharedInputs.q275 X
        else SelectiveSharedInputs.q276 Y

noncomputable def q280 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q278 X Y p r ≥
            if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ) then
        SelectiveSharedInputs.q278 X Y p r
      else if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q274 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0xf5)
      else
        if SelectiveSharedInputs.q275 X ≥ SelectiveSharedInputs.q276 Y then SelectiveSharedInputs.q275 X
        else SelectiveSharedInputs.q276 Y

noncomputable def q281 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then 1
          else 0) -
          if SelectiveSharedInputs.q274 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q278 X Y p r ≥
                if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ) then
            SelectiveSharedInputs.q278 X Y p r
          else if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)) ≥
          SelectiveSharedInputs.q277 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q258 X ∧ SelectiveSharedInputs.q259 Y ∧ SelectiveSharedInputs.q260 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q274 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q279 X Y p r
        else SelectiveSharedInputs.q280 X Y p r

noncomputable def q282 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0xf5) ≥
          2 *
            if (1 / 0xf5) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      SelectiveSharedInputs.q281 X Y p r
    else ¬SelectiveSharedInputs.q273 X Y p r

noncomputable def q283 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 35) <
      (5 / 4) * if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X

noncomputable def q284 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 35) ≥
      (10 / 9) * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q285 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 35) <
      (4 / 3) * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q286 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0xaf) ≥
        2 *
          if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      (1 / 0xaf) ≥
        2 * if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q287 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q288 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q287 X Y then
      if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q289 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) >
      if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q290 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4 ≥
      if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q291 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q290 X Y then
      (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4
    else if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q292 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      (if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) / 3

noncomputable def q293 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q292 X Y then
      if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) / 3

noncomputable def q294 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x2bc) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q286 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q288 X Y
          else
            if SelectiveSharedInputs.q289 X Y then SelectiveSharedInputs.q291 X Y
            else SelectiveSharedInputs.q293 X Y then
      (3 / 0x2bc)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q286 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q288 X Y
      else if SelectiveSharedInputs.q289 X Y then SelectiveSharedInputs.q291 X Y else SelectiveSharedInputs.q293 X Y

noncomputable def q295 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q294 X Y ≥ if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
        SelectiveSharedInputs.q294 X Y
      else if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)) ≥
      if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)

noncomputable def q296 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q295 X Y p r then
      if SelectiveSharedInputs.q294 X Y ≥ if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
        SelectiveSharedInputs.q294 X Y
      else if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)
    else if p (12 : ℕ) ↔ False then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)

noncomputable def q297 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q286 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q296 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q286 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xaf)
        else SelectiveSharedInputs.q288 X Y
    else
      SelectiveSharedInputs.q296 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q286 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0xaf)
        else SelectiveSharedInputs.q288 X Y

noncomputable def q298 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then 1
          else 0) -
          if SelectiveSharedInputs.q286 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q296 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q286 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q288 X Y
          else
            if SelectiveSharedInputs.q289 X Y then SelectiveSharedInputs.q291 X Y
            else SelectiveSharedInputs.q293 X Y) ∧
        SelectiveSharedInputs.q297 X Y p r

noncomputable def q299 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0xaf) ≥
          2 *
            if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      ¬(1 / 0xaf) ≥
          2 * if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q300 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0xaf) ≥
          2 *
            if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      2 * if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 2

noncomputable def q301 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0xaf) ≥
          2 *
            if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y then
      2 * if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y
    else
      (2 * if (1 / 0xaf) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) /
        3

noncomputable def q302 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q299 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q300 X ≥ SelectiveSharedInputs.q301 Y then SelectiveSharedInputs.q300 X
      else SelectiveSharedInputs.q301 Y
    else
      if SelectiveSharedInputs.q300 X > SelectiveSharedInputs.q301 Y then
        if SelectiveSharedInputs.q300 X / 4 ≥ SelectiveSharedInputs.q301 Y then
          SelectiveSharedInputs.q300 X / 4
        else SelectiveSharedInputs.q301 Y
      else
        if SelectiveSharedInputs.q300 X ≥ SelectiveSharedInputs.q301 Y / 3 then SelectiveSharedInputs.q300 X
        else SelectiveSharedInputs.q301 Y / 3

noncomputable def q303 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x2bc) ≥ SelectiveSharedInputs.q302 X Y then (3 / 0x2bc) else SelectiveSharedInputs.q302 X Y) ≥
          if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
      if (3 / 0x2bc) ≥ SelectiveSharedInputs.q302 X Y then (3 / 0x2bc) else SelectiveSharedInputs.q302 X Y
    else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)

noncomputable def q304 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q303 X Y p r ≥
            if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
        SelectiveSharedInputs.q303 X Y p r
      else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q299 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0xaf)
      else
        if SelectiveSharedInputs.q300 X ≥ SelectiveSharedInputs.q301 Y then SelectiveSharedInputs.q300 X
        else SelectiveSharedInputs.q301 Y

noncomputable def q305 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q303 X Y p r ≥
            if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
        SelectiveSharedInputs.q303 X Y p r
      else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q299 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0xaf)
      else
        if SelectiveSharedInputs.q300 X ≥ SelectiveSharedInputs.q301 Y then SelectiveSharedInputs.q300 X
        else SelectiveSharedInputs.q301 Y

noncomputable def q306 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then 1
          else 0) -
          if SelectiveSharedInputs.q299 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q303 X Y p r ≥
                if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
            SelectiveSharedInputs.q303 X Y p r
          else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)) ≥
          SelectiveSharedInputs.q302 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q283 X ∧ SelectiveSharedInputs.q284 Y ∧ SelectiveSharedInputs.q285 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q299 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q304 X Y p r
        else SelectiveSharedInputs.q305 X Y p r

noncomputable def q307 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0xaf) ≥
          2 *
            if (1 / 0xaf) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      SelectiveSharedInputs.q306 X Y p r
    else ¬SelectiveSharedInputs.q298 X Y p r

noncomputable def q308 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 25) <
      (5 / 4) * if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X

noncomputable def q309 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 25) ≥
      (10 / 9) * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q310 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 25) <
      (4 / 3) * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q311 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 0x7d) ≥
        2 *
          if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      (1 / 0x7d) ≥
        2 * if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q312 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q313 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q312 X Y then
      if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q314 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) >
      if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q315 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4 ≥
      if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q316 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q315 X Y then
      (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 4
    else if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q317 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ≥
      (if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) / 3

noncomputable def q318 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q317 X Y then
      if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) / 3

noncomputable def q319 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x1f4) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q311 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q313 X Y
          else
            if SelectiveSharedInputs.q314 X Y then SelectiveSharedInputs.q316 X Y
            else SelectiveSharedInputs.q318 X Y then
      (3 / 0x1f4)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q311 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q313 X Y
      else if SelectiveSharedInputs.q314 X Y then SelectiveSharedInputs.q316 X Y else SelectiveSharedInputs.q318 X Y

noncomputable def q320 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q319 X Y ≥ if p (14 : ℕ) ↔ False then 4 * r (14 : ℕ) else 6 * r (14 : ℕ) then
        SelectiveSharedInputs.q319 X Y
      else if p (14 : ℕ) ↔ False then 4 * r (14 : ℕ) else 6 * r (14 : ℕ)) ≥
      if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)

noncomputable def q321 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q320 X Y p r then
      if SelectiveSharedInputs.q319 X Y ≥ if p (14 : ℕ) ↔ False then 4 * r (14 : ℕ) else 6 * r (14 : ℕ) then
        SelectiveSharedInputs.q319 X Y
      else if p (14 : ℕ) ↔ False then 4 * r (14 : ℕ) else 6 * r (14 : ℕ)
    else if p (13 : ℕ) ↔ False then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)

noncomputable def q322 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q311 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q321 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q311 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x7d)
        else SelectiveSharedInputs.q313 X Y
    else
      SelectiveSharedInputs.q321 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q311 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 0x7d)
        else SelectiveSharedInputs.q313 X Y

noncomputable def q323 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then 1
          else 0) -
          if SelectiveSharedInputs.q311 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q321 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q311 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q313 X Y
          else
            if SelectiveSharedInputs.q314 X Y then SelectiveSharedInputs.q316 X Y
            else SelectiveSharedInputs.q318 X Y) ∧
        SelectiveSharedInputs.q322 X Y p r

noncomputable def q324 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 0x7d) ≥
          2 *
            if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) ∧
      ¬(1 / 0x7d) ≥
          2 * if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y

noncomputable def q325 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 0x7d) ≥
          2 *
            if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      2 * if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X
    else
      (if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X) / 2

noncomputable def q326 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 0x7d) ≥
          2 *
            if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y then
      2 * if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y
    else
      (2 * if (1 / 0x7d) ≥ (1 / 0xf3) * Y * 3 then (1 / 0xf3) * Y * 3 else (1 / 0xf3) * Y) /
        3

noncomputable def q327 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q324 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q325 X ≥ SelectiveSharedInputs.q326 Y then SelectiveSharedInputs.q325 X
      else SelectiveSharedInputs.q326 Y
    else
      if SelectiveSharedInputs.q325 X > SelectiveSharedInputs.q326 Y then
        if SelectiveSharedInputs.q325 X / 4 ≥ SelectiveSharedInputs.q326 Y then
          SelectiveSharedInputs.q325 X / 4
        else SelectiveSharedInputs.q326 Y
      else
        if SelectiveSharedInputs.q325 X ≥ SelectiveSharedInputs.q326 Y / 3 then SelectiveSharedInputs.q325 X
        else SelectiveSharedInputs.q326 Y / 3

noncomputable def q328 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x1f4) ≥ SelectiveSharedInputs.q327 X Y then (3 / 0x1f4) else SelectiveSharedInputs.q327 X Y) ≥
          if p (14 : ℕ) ↔ True then 4 * r (14 : ℕ) else 6 * r (14 : ℕ) then
      if (3 / 0x1f4) ≥ SelectiveSharedInputs.q327 X Y then (3 / 0x1f4) else SelectiveSharedInputs.q327 X Y
    else if p (14 : ℕ) ↔ True then 4 * r (14 : ℕ) else 6 * r (14 : ℕ)

noncomputable def q329 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q328 X Y p r ≥
            if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
        SelectiveSharedInputs.q328 X Y p r
      else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q324 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x7d)
      else
        if SelectiveSharedInputs.q325 X ≥ SelectiveSharedInputs.q326 Y then SelectiveSharedInputs.q325 X
        else SelectiveSharedInputs.q326 Y

noncomputable def q330 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if
          SelectiveSharedInputs.q328 X Y p r ≥
            if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
        SelectiveSharedInputs.q328 X Y p r
      else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q324 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 0x7d)
      else
        if SelectiveSharedInputs.q325 X ≥ SelectiveSharedInputs.q326 Y then SelectiveSharedInputs.q325 X
        else SelectiveSharedInputs.q326 Y

noncomputable def q331 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then 1
          else 0) -
          if SelectiveSharedInputs.q324 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if
              SelectiveSharedInputs.q328 X Y p r ≥
                if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
            SelectiveSharedInputs.q328 X Y p r
          else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)) ≥
          SelectiveSharedInputs.q327 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q308 X ∧ SelectiveSharedInputs.q309 Y ∧ SelectiveSharedInputs.q310 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q324 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q329 X Y p r
        else SelectiveSharedInputs.q330 X Y p r

noncomputable def q332 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 0x7d) ≥
          2 *
            if (1 / 0x7d) ≥ (1 / 0x100) * X * 4 then (1 / 0x100) * X * 4 else (1 / 0x100) * X then
      SelectiveSharedInputs.q331 X Y p r
    else ¬SelectiveSharedInputs.q323 X Y p r

noncomputable def q333 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (5 / 49) <
      (5 / 4) * if (5 / 49) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X

noncomputable def q334 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 49) ≥
      (10 / 9) * if (5 / 49) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q335 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 49) <
      (4 / 3) * if (5 / 49) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q336 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 49) ≥
        2 * if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      (1 / 49) ≥
        2 * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q337 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q338 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q337 X Y then
      if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q339 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) >
      if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q340 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4 ≥
      if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q341 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q340 X Y then
      (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4
    else if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q342 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      (if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) / 3

noncomputable def q343 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q342 X Y then
      if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) / 3

noncomputable def q344 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0xc4) ≥
          if
              ((if
                      False ∧
                        SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q336 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q338 X Y
          else
            if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y
            else SelectiveSharedInputs.q343 X Y then
      (3 / 0xc4)
    else
      if
          ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q336 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q338 X Y
      else if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y else SelectiveSharedInputs.q343 X Y

noncomputable def q345 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q344 X Y ≥ if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q344 X Y
      else if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)) ≥
      if p (6 : ℕ) ↔ False then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)

noncomputable def q346 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q345 X Y p r then
      if SelectiveSharedInputs.q344 X Y ≥ if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q344 X Y
      else if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)
    else if p (6 : ℕ) ↔ False then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)

noncomputable def q347 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q336 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q346 X Y p r ≤
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q336 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 49)
        else SelectiveSharedInputs.q338 X Y
    else
      SelectiveSharedInputs.q346 X Y p r <
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q336 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 49)
        else SelectiveSharedInputs.q338 X Y

noncomputable def q348 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
            1
          else 0) -
          if SelectiveSharedInputs.q336 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q346 X Y p r ≥
          if
              ((if
                      False ∧
                        SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q336 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q338 X Y
          else
            if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y
            else SelectiveSharedInputs.q343 X Y) ∧
        SelectiveSharedInputs.q347 X Y p r

noncomputable def q349 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 49) ≥
          2 * if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      ¬(1 / 49) ≥
          2 * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q350 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 49) ≥
          2 *
            if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X then
      2 * if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 49) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 2

noncomputable def q351 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 49) ≥
          2 *
            if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y then
      2 * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y
    else
      (2 * if (1 / 49) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) /
        3

noncomputable def q352 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q349 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
      else SelectiveSharedInputs.q351 Y
    else
      if SelectiveSharedInputs.q350 X > SelectiveSharedInputs.q351 Y then
        if SelectiveSharedInputs.q350 X / 4 ≥ SelectiveSharedInputs.q351 Y then
          SelectiveSharedInputs.q350 X / 4
        else SelectiveSharedInputs.q351 Y
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y / 3 then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y / 3

noncomputable def q353 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0xc4) ≥ SelectiveSharedInputs.q352 X Y then (3 / 0xc4) else SelectiveSharedInputs.q352 X Y) ≥
          if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
      if (3 / 0xc4) ≥ SelectiveSharedInputs.q352 X Y then (3 / 0xc4) else SelectiveSharedInputs.q352 X Y
    else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)

noncomputable def q354 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q353 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
        SelectiveSharedInputs.q353 X Y p r
      else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) ≤
      if
          ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q349 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 49)
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y

noncomputable def q355 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q353 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
        SelectiveSharedInputs.q353 X Y p r
      else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) <
      if
          ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q349 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 49)
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y

noncomputable def q356 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if False ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
            1
          else 0) -
          if SelectiveSharedInputs.q349 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q353 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
            SelectiveSharedInputs.q353 X Y p r
          else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) ≥
          SelectiveSharedInputs.q352 X Y ∧
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q349 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q354 X Y p r
        else SelectiveSharedInputs.q355 X Y p r

noncomputable def q358 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 7) <
      (5 / 4) * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X

noncomputable def q359 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 7) ≥
      (10 / 9) * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q360 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 7) <
      (4 / 3) * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q361 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 35) ≥
        2 * if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      (1 / 35) ≥
        2 * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q362 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q363 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q362 X Y then
      if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q364 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) >
      if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q365 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4 ≥
      if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q366 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q365 X Y then
      (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4
    else if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q367 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      (if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) / 3

noncomputable def q368 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q367 X Y then
      if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) / 3

noncomputable def q369 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x8c) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q361 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q363 X Y
          else
            if SelectiveSharedInputs.q364 X Y then SelectiveSharedInputs.q366 X Y
            else SelectiveSharedInputs.q368 X Y then
      (3 / 0x8c)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q361 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q363 X Y
      else if SelectiveSharedInputs.q364 X Y then SelectiveSharedInputs.q366 X Y else SelectiveSharedInputs.q368 X Y

noncomputable def q370 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q369 X Y ≥ if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
        SelectiveSharedInputs.q369 X Y
      else if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)) ≥
      if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)

noncomputable def q371 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q370 X Y p r then
      if SelectiveSharedInputs.q369 X Y ≥ if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
        SelectiveSharedInputs.q369 X Y
      else if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)
    else if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)

noncomputable def q372 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q361 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q371 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q361 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 35)
        else SelectiveSharedInputs.q363 X Y
    else
      SelectiveSharedInputs.q371 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q361 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 35)
        else SelectiveSharedInputs.q363 X Y

noncomputable def q373 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then 1
          else 0) -
          if SelectiveSharedInputs.q361 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q371 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q361 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q363 X Y
          else
            if SelectiveSharedInputs.q364 X Y then SelectiveSharedInputs.q366 X Y
            else SelectiveSharedInputs.q368 X Y) ∧
        SelectiveSharedInputs.q372 X Y p r

noncomputable def q374 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 35) ≥
          2 * if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      ¬(1 / 35) ≥
          2 * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y

noncomputable def q375 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 35) ≥
          2 *
            if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X then
      2 * if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 2

noncomputable def q376 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 35) ≥
          2 *
            if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y then
      2 * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y
    else
      (2 * if (1 / 35) ≥ (1 / 81) * Y * 3 then (1 / 81) * Y * 3 else (1 / 81) * Y) /
        3

noncomputable def q377 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q374 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q375 X ≥ SelectiveSharedInputs.q376 Y then SelectiveSharedInputs.q375 X
      else SelectiveSharedInputs.q376 Y
    else
      if SelectiveSharedInputs.q375 X > SelectiveSharedInputs.q376 Y then
        if SelectiveSharedInputs.q375 X / 4 ≥ SelectiveSharedInputs.q376 Y then
          SelectiveSharedInputs.q375 X / 4
        else SelectiveSharedInputs.q376 Y
      else
        if SelectiveSharedInputs.q375 X ≥ SelectiveSharedInputs.q376 Y / 3 then SelectiveSharedInputs.q375 X
        else SelectiveSharedInputs.q376 Y / 3

noncomputable def q378 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x8c) ≥ SelectiveSharedInputs.q377 X Y then (3 / 0x8c) else SelectiveSharedInputs.q377 X Y) ≥
          if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
      if (3 / 0x8c) ≥ SelectiveSharedInputs.q377 X Y then (3 / 0x8c) else SelectiveSharedInputs.q377 X Y
    else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)

noncomputable def q379 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q378 X Y p r ≥ if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q378 X Y p r
      else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q374 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 35)
      else
        if SelectiveSharedInputs.q375 X ≥ SelectiveSharedInputs.q376 Y then SelectiveSharedInputs.q375 X
        else SelectiveSharedInputs.q376 Y

noncomputable def q380 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q378 X Y p r ≥ if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q378 X Y p r
      else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q374 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 35)
      else
        if SelectiveSharedInputs.q375 X ≥ SelectiveSharedInputs.q376 Y then SelectiveSharedInputs.q375 X
        else SelectiveSharedInputs.q376 Y

noncomputable def q381 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then 1
          else 0) -
          if SelectiveSharedInputs.q374 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q378 X Y p r ≥ if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
            SelectiveSharedInputs.q378 X Y p r
          else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)) ≥
          SelectiveSharedInputs.q377 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q358 X ∧ SelectiveSharedInputs.q359 Y ∧ SelectiveSharedInputs.q360 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q374 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q379 X Y p r
        else SelectiveSharedInputs.q380 X Y p r

noncomputable def q382 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 35) ≥
          2 *
            if (1 / 35) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X then
      SelectiveSharedInputs.q381 X Y p r
    else ¬SelectiveSharedInputs.q373 X Y p r

noncomputable def q383 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (1 / 5) <
      (5 / 4) * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X

noncomputable def q384 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 5) ≥
      (10 / 9) * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q385 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (1 / 5) <
      (4 / 3) * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q386 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 25) ≥
        2 * if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      (1 / 25) ≥
        2 * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q387 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q388 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q387 X Y then
      if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q389 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) >
      if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q390 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4 ≥
      if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q391 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q390 X Y then
      (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 4
    else if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q392 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ≥
      (if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y) / 3

noncomputable def q393 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q392 X Y then
      if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y) / 3

noncomputable def q394 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0x64) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q386 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q388 X Y
          else
            if SelectiveSharedInputs.q389 X Y then SelectiveSharedInputs.q391 X Y
            else SelectiveSharedInputs.q393 X Y then
      (3 / 0x64)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q386 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q388 X Y
      else if SelectiveSharedInputs.q389 X Y then SelectiveSharedInputs.q391 X Y else SelectiveSharedInputs.q393 X Y

noncomputable def q395 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q394 X Y ≥ if p (9 : ℕ) ↔ False then 4 * r (9 : ℕ) else 6 * r (9 : ℕ) then
        SelectiveSharedInputs.q394 X Y
      else if p (9 : ℕ) ↔ False then 4 * r (9 : ℕ) else 6 * r (9 : ℕ)) ≥
      if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)

noncomputable def q396 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q395 X Y p r then
      if SelectiveSharedInputs.q394 X Y ≥ if p (9 : ℕ) ↔ False then 4 * r (9 : ℕ) else 6 * r (9 : ℕ) then
        SelectiveSharedInputs.q394 X Y
      else if p (9 : ℕ) ↔ False then 4 * r (9 : ℕ) else 6 * r (9 : ℕ)
    else if p (8 : ℕ) ↔ False then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)

noncomputable def q397 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q386 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q396 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q386 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 25)
        else SelectiveSharedInputs.q388 X Y
    else
      SelectiveSharedInputs.q396 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q386 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 25)
        else SelectiveSharedInputs.q388 X Y

noncomputable def q398 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then 1
          else 0) -
          if SelectiveSharedInputs.q386 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q396 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q386 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q388 X Y
          else
            if SelectiveSharedInputs.q389 X Y then SelectiveSharedInputs.q391 X Y
            else SelectiveSharedInputs.q393 X Y) ∧
        SelectiveSharedInputs.q397 X Y p r

noncomputable def q399 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 25) ≥
          2 * if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) ∧
      ¬(1 / 25) ≥
          2 * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y

noncomputable def q400 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 25) ≥
          2 *
            if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X then
      2 * if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X
    else (if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X) / 2

noncomputable def q401 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 25) ≥
          2 *
            if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y then
      2 * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y
    else
      (2 * if (1 / 25) ≥ (1 / 27) * Y * 3 then (1 / 27) * Y * 3 else (1 / 27) * Y) /
        3

noncomputable def q402 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q399 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q400 X ≥ SelectiveSharedInputs.q401 Y then SelectiveSharedInputs.q400 X
      else SelectiveSharedInputs.q401 Y
    else
      if SelectiveSharedInputs.q400 X > SelectiveSharedInputs.q401 Y then
        if SelectiveSharedInputs.q400 X / 4 ≥ SelectiveSharedInputs.q401 Y then
          SelectiveSharedInputs.q400 X / 4
        else SelectiveSharedInputs.q401 Y
      else
        if SelectiveSharedInputs.q400 X ≥ SelectiveSharedInputs.q401 Y / 3 then SelectiveSharedInputs.q400 X
        else SelectiveSharedInputs.q401 Y / 3

noncomputable def q403 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0x64) ≥ SelectiveSharedInputs.q402 X Y then (3 / 0x64) else SelectiveSharedInputs.q402 X Y) ≥
          if p (9 : ℕ) ↔ True then 4 * r (9 : ℕ) else 6 * r (9 : ℕ) then
      if (3 / 0x64) ≥ SelectiveSharedInputs.q402 X Y then (3 / 0x64) else SelectiveSharedInputs.q402 X Y
    else if p (9 : ℕ) ↔ True then 4 * r (9 : ℕ) else 6 * r (9 : ℕ)

noncomputable def q404 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q403 X Y p r ≥ if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
        SelectiveSharedInputs.q403 X Y p r
      else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q399 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 25)
      else
        if SelectiveSharedInputs.q400 X ≥ SelectiveSharedInputs.q401 Y then SelectiveSharedInputs.q400 X
        else SelectiveSharedInputs.q401 Y

noncomputable def q405 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q403 X Y p r ≥ if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
        SelectiveSharedInputs.q403 X Y p r
      else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q399 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 25)
      else
        if SelectiveSharedInputs.q400 X ≥ SelectiveSharedInputs.q401 Y then SelectiveSharedInputs.q400 X
        else SelectiveSharedInputs.q401 Y

noncomputable def q406 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then 1
          else 0) -
          if SelectiveSharedInputs.q399 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q403 X Y p r ≥ if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
            SelectiveSharedInputs.q403 X Y p r
          else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)) ≥
          SelectiveSharedInputs.q402 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q383 X ∧ SelectiveSharedInputs.q384 Y ∧ SelectiveSharedInputs.q385 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q399 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q404 X Y p r
        else SelectiveSharedInputs.q405 X Y p r

noncomputable def q407 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 25) ≥
          2 *
            if (1 / 25) ≥ (1 / 64) * X * 4 then (1 / 64) * X * 4 else (1 / 64) * X then
      SelectiveSharedInputs.q406 X Y p r
    else ¬SelectiveSharedInputs.q398 X Y p r

noncomputable def q408 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    (5 / 7) <
      (5 / 4) * if (5 / 7) ≥ (1 / 4) * X * 4 then (1 / 4) * X * 4 else (1 / 4) * X

noncomputable def q409 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 7) ≥
      (10 / 9) * if (5 / 7) ≥ (1 / 3) * Y * 3 then (1 / 3) * Y * 3 else (1 / 3) * Y

noncomputable def q410 : ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    (5 / 7) <
      (4 / 3) * if (5 / 7) ≥ (1 / 3) * Y * 3 then (1 / 3) * Y * 3 else (1 / 3) * Y

noncomputable def q411 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 7) ≥
        2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ∧
      (1 / 7) ≥
        2 * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q412 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ≥
      if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q413 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q412 X Y then
      if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q414 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) >
      if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q415 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 4 ≥
      if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q416 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q415 X Y then
      (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 4
    else if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q417 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ≥
      (if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q418 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q417 X Y then
      if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else (if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q419 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 28) ≥
          if
              ((if
                      False ∧
                        SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q411 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q413 X Y
          else
            if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y
            else SelectiveSharedInputs.q418 X Y then
      (3 / 28)
    else
      if
          ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q411 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q413 X Y
      else if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y else SelectiveSharedInputs.q418 X Y

noncomputable def q420 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q419 X Y ≥ if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q419 X Y
      else if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)) ≥
      if p (3 : ℕ) ↔ False then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)

noncomputable def q421 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q420 X Y p r then
      if SelectiveSharedInputs.q419 X Y ≥ if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q419 X Y
      else if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)
    else if p (3 : ℕ) ↔ False then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)

noncomputable def q422 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q411 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q421 X Y p r ≤
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q411 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 7)
        else SelectiveSharedInputs.q413 X Y
    else
      SelectiveSharedInputs.q421 X Y p r <
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q411 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 7)
        else SelectiveSharedInputs.q413 X Y

noncomputable def q423 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
            1
          else 0) -
          if SelectiveSharedInputs.q411 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q421 X Y p r ≥
          if
              ((if
                      False ∧
                        SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q411 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q413 X Y
          else
            if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y
            else SelectiveSharedInputs.q418 X Y) ∧
        SelectiveSharedInputs.q422 X Y p r

noncomputable def q424 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ∧
      ¬(1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q425 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X then
      2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else (if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 2

noncomputable def q426 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y then
      2 * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y
    else
      (2 * if (1 / 7) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q427 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q424 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
      else SelectiveSharedInputs.q426 Y
    else
      if SelectiveSharedInputs.q425 X > SelectiveSharedInputs.q426 Y then
        if SelectiveSharedInputs.q425 X / 4 ≥ SelectiveSharedInputs.q426 Y then
          SelectiveSharedInputs.q425 X / 4
        else SelectiveSharedInputs.q426 Y
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y / 3 then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y / 3

noncomputable def q428 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 28) ≥ SelectiveSharedInputs.q427 X Y then (3 / 28) else SelectiveSharedInputs.q427 X Y) ≥
          if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
      if (3 / 28) ≥ SelectiveSharedInputs.q427 X Y then (3 / 28) else SelectiveSharedInputs.q427 X Y
    else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)

noncomputable def q429 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q428 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
        SelectiveSharedInputs.q428 X Y p r
      else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) ≤
      if
          ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q424 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 7)
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y

noncomputable def q430 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q428 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
        SelectiveSharedInputs.q428 X Y p r
      else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) <
      if
          ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q424 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 7)
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y

noncomputable def q431 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if False ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
            1
          else 0) -
          if SelectiveSharedInputs.q424 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q428 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
            SelectiveSharedInputs.q428 X Y p r
          else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) ≥
          SelectiveSharedInputs.q427 X Y ∧
        if
            ((if
                    False ∧
                      SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q424 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q429 X Y p r
        else SelectiveSharedInputs.q430 X Y p r

noncomputable def q432 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X then
      SelectiveSharedInputs.q431 X Y p r
    else ¬SelectiveSharedInputs.q423 X Y p r

noncomputable def q433 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    True ∧
      (1 < (5 / 4) * if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) ∧
        (1 ≥ (10 / 9) * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y) ∧
          1 < (4 / 3) * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q434 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    ((1 / 5) ≥
        2 * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ∧
      (1 / 5) ≥
        2 * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q435 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ≥
      if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q436 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q435 X Y then
      if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q437 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) >
      if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q438 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 4 ≥
      if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q439 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q438 X Y then
      (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 4
    else if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q440 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ≥
      (if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q441 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q440 X Y then
      if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else (if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q442 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 20) ≥
          if
              ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q434 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q436 X Y
          else
            if SelectiveSharedInputs.q437 X Y then SelectiveSharedInputs.q439 X Y
            else SelectiveSharedInputs.q441 X Y then
      (3 / 20)
    else
      if
          ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
              if SelectiveSharedInputs.q434 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q436 X Y
      else if SelectiveSharedInputs.q437 X Y then SelectiveSharedInputs.q439 X Y else SelectiveSharedInputs.q441 X Y

noncomputable def q443 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q442 X Y ≥ if p (5 : ℕ) ↔ False then 4 * r (5 : ℕ) else 6 * r (5 : ℕ) then
        SelectiveSharedInputs.q442 X Y
      else if p (5 : ℕ) ↔ False then 4 * r (5 : ℕ) else 6 * r (5 : ℕ)) ≥
      if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)

noncomputable def q444 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q443 X Y p r then
      if SelectiveSharedInputs.q442 X Y ≥ if p (5 : ℕ) ↔ False then 4 * r (5 : ℕ) else 6 * r (5 : ℕ) then
        SelectiveSharedInputs.q442 X Y
      else if p (5 : ℕ) ↔ False then 4 * r (5 : ℕ) else 6 * r (5 : ℕ)
    else if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)

noncomputable def q445 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
            if SelectiveSharedInputs.q434 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q444 X Y p r ≤
        if
            ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
                if SelectiveSharedInputs.q434 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 5)
        else SelectiveSharedInputs.q436 X Y
    else
      SelectiveSharedInputs.q444 X Y p r <
        if
            ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
                if SelectiveSharedInputs.q434 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 5)
        else SelectiveSharedInputs.q436 X Y

noncomputable def q446 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
          if SelectiveSharedInputs.q434 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q444 X Y p r ≥
          if
              ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q434 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q436 X Y
          else
            if SelectiveSharedInputs.q437 X Y then SelectiveSharedInputs.q439 X Y
            else SelectiveSharedInputs.q441 X Y) ∧
        SelectiveSharedInputs.q445 X Y p r

noncomputable def q447 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬(1 / 5) ≥
          2 * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) ∧
      ¬(1 / 5) ≥
          2 * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y

noncomputable def q448 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if
        (1 / 5) ≥
          2 * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X then
      2 * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X
    else (if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X) / 2

noncomputable def q449 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if
        (1 / 5) ≥
          2 * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y then
      2 * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y
    else
      (2 * if (1 / 5) ≥ (1 / 9) * Y * 3 then (1 / 9) * Y * 3 else (1 / 9) * Y) / 3

noncomputable def q450 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
            if SelectiveSharedInputs.q447 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q448 X ≥ SelectiveSharedInputs.q449 Y then SelectiveSharedInputs.q448 X
      else SelectiveSharedInputs.q449 Y
    else
      if SelectiveSharedInputs.q448 X > SelectiveSharedInputs.q449 Y then
        if SelectiveSharedInputs.q448 X / 4 ≥ SelectiveSharedInputs.q449 Y then
          SelectiveSharedInputs.q448 X / 4
        else SelectiveSharedInputs.q449 Y
      else
        if SelectiveSharedInputs.q448 X ≥ SelectiveSharedInputs.q449 Y / 3 then SelectiveSharedInputs.q448 X
        else SelectiveSharedInputs.q449 Y / 3

noncomputable def q451 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 20) ≥ SelectiveSharedInputs.q450 X Y then (3 / 20) else SelectiveSharedInputs.q450 X Y) ≥
          if p (5 : ℕ) ↔ True then 4 * r (5 : ℕ) else 6 * r (5 : ℕ) then
      if (3 / 20) ≥ SelectiveSharedInputs.q450 X Y then (3 / 20) else SelectiveSharedInputs.q450 X Y
    else if p (5 : ℕ) ↔ True then 4 * r (5 : ℕ) else 6 * r (5 : ℕ)

noncomputable def q452 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q451 X Y p r ≥ if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q451 X Y p r
      else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)) ≤
      if
          ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
              if SelectiveSharedInputs.q447 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 5)
      else
        if SelectiveSharedInputs.q448 X ≥ SelectiveSharedInputs.q449 Y then SelectiveSharedInputs.q448 X
        else SelectiveSharedInputs.q449 Y

noncomputable def q453 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q451 X Y p r ≥ if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q451 X Y p r
      else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)) <
      if
          ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
              if SelectiveSharedInputs.q447 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 5)
      else
        if SelectiveSharedInputs.q448 X ≥ SelectiveSharedInputs.q449 Y then SelectiveSharedInputs.q448 X
        else SelectiveSharedInputs.q449 Y

noncomputable def q454 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
          if SelectiveSharedInputs.q447 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q451 X Y p r ≥ if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
            SelectiveSharedInputs.q451 X Y p r
          else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)) ≥
          SelectiveSharedInputs.q450 X Y ∧
        if
            ((if SelectiveSharedInputs.q433 X Y then 1 else 0) -
                if SelectiveSharedInputs.q447 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q452 X Y p r
        else SelectiveSharedInputs.q453 X Y p r

noncomputable def q455 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 5) ≥
          2 * if (1 / 5) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X then
      SelectiveSharedInputs.q454 X Y p r
    else ¬SelectiveSharedInputs.q446 X Y p r

noncomputable def q456 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    False ∧
      (5 < (5 / 4) * if 5 ≥ 4 * X * 4 then 4 * X * 4 else 4 * X) ∧
        (5 ≥ (10 / 9) * if 5 ≥ 3 * Y * 3 then 3 * Y * 3 else 3 * Y) ∧
          5 < (4 / 3) * if 5 ≥ 3 * Y * 3 then 3 * Y * 3 else 3 * Y

noncomputable def q457 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (1 ≥ 2 * if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) ∧
      1 ≥ 2 * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q458 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) ≥
      if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q459 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q458 X Y then if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X
    else if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q460 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) >
      if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q461 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) / 4 ≥
      if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q462 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q461 X Y then
      (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) / 4
    else if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q463 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) ≥
      (if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y) / 3

noncomputable def q464 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if SelectiveSharedInputs.q463 X Y then if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X
    else (if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y) / 3

noncomputable def q465 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 4) ≥
          if
              ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q457 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q459 X Y
          else
            if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y
            else SelectiveSharedInputs.q464 X Y then
      (3 / 4)
    else
      if
          ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
              if SelectiveSharedInputs.q457 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q459 X Y
      else if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y else SelectiveSharedInputs.q464 X Y

noncomputable def q466 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q465 X Y ≥ if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
        SelectiveSharedInputs.q465 X Y
      else if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)) ≥
      if p (1 : ℕ) ↔ False then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)

noncomputable def q467 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q466 X Y p r then
      if SelectiveSharedInputs.q465 X Y ≥ if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
        SelectiveSharedInputs.q465 X Y
      else if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)
    else if p (1 : ℕ) ↔ False then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)

noncomputable def q468 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
            if SelectiveSharedInputs.q457 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q467 X Y p r ≤
        if
            ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
                if SelectiveSharedInputs.q457 X Y then 1 else 0) =
              (0 : ℤ) then
          1
        else SelectiveSharedInputs.q459 X Y
    else
      SelectiveSharedInputs.q467 X Y p r <
        if
            ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
                if SelectiveSharedInputs.q457 X Y then 1 else 0) =
              (0 : ℤ) then
          1
        else SelectiveSharedInputs.q459 X Y

noncomputable def q469 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
          if SelectiveSharedInputs.q457 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q467 X Y p r ≥
          if
              ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q457 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q459 X Y
          else
            if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y
            else SelectiveSharedInputs.q464 X Y) ∧
        SelectiveSharedInputs.q468 X Y p r

noncomputable def q470 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    (¬1 ≥ 2 * if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) ∧
      ¬1 ≥ 2 * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y

noncomputable def q471 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X =>
    if 1 ≥ 2 * if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X then
      2 * if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X
    else (if 1 ≥ 1 * X * 4 then 1 * X * 4 else 1 * X) / 2

noncomputable def q472 : ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun Y =>
    if 1 ≥ 2 * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y then
      2 * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y
    else (2 * if 1 ≥ 1 * Y * 3 then 1 * Y * 3 else 1 * Y) / 3

noncomputable def q473 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
            if SelectiveSharedInputs.q470 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
      else SelectiveSharedInputs.q472 Y
    else
      if SelectiveSharedInputs.q471 X > SelectiveSharedInputs.q472 Y then
        if SelectiveSharedInputs.q471 X / 4 ≥ SelectiveSharedInputs.q472 Y then
          SelectiveSharedInputs.q471 X / 4
        else SelectiveSharedInputs.q472 Y
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y / 3 then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y / 3

noncomputable def q474 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 4) ≥ SelectiveSharedInputs.q473 X Y then (3 / 4) else SelectiveSharedInputs.q473 X Y) ≥
          if p (2 : ℕ) ↔ True then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
      if (3 / 4) ≥ SelectiveSharedInputs.q473 X Y then (3 / 4) else SelectiveSharedInputs.q473 X Y
    else if p (2 : ℕ) ↔ True then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)

noncomputable def q475 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q474 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
        SelectiveSharedInputs.q474 X Y p r
      else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) ≤
      if
          ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
              if SelectiveSharedInputs.q470 X Y then 1 else 0) =
            (0 : ℤ) then
        1
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y

noncomputable def q476 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q474 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
        SelectiveSharedInputs.q474 X Y p r
      else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) <
      if
          ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
              if SelectiveSharedInputs.q470 X Y then 1 else 0) =
            (0 : ℤ) then
        1
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y

noncomputable def q477 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
          if SelectiveSharedInputs.q470 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q474 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
            SelectiveSharedInputs.q474 X Y p r
          else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) ≥
          SelectiveSharedInputs.q473 X Y ∧
        if
            ((if SelectiveSharedInputs.q456 X Y then 1 else 0) -
                if SelectiveSharedInputs.q470 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q475 X Y p r
        else SelectiveSharedInputs.q476 X Y p r

noncomputable def q504 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 0xc4) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q336 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q338 X Y
          else
            if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y
            else SelectiveSharedInputs.q343 X Y then
      (3 / 0xc4)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q336 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q338 X Y
      else if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y else SelectiveSharedInputs.q343 X Y

noncomputable def q505 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q504 X Y ≥ if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q504 X Y
      else if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)) ≥
      if p (6 : ℕ) ↔ False then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)

noncomputable def q506 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q505 X Y p r then
      if SelectiveSharedInputs.q504 X Y ≥ if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
        SelectiveSharedInputs.q504 X Y
      else if p (7 : ℕ) ↔ False then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)
    else if p (6 : ℕ) ↔ False then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)

noncomputable def q507 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q336 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q506 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q336 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 49)
        else SelectiveSharedInputs.q338 X Y
    else
      SelectiveSharedInputs.q506 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q336 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 49)
        else SelectiveSharedInputs.q338 X Y

noncomputable def q508 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then 1
          else 0) -
          if SelectiveSharedInputs.q336 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q506 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q336 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q338 X Y
          else
            if SelectiveSharedInputs.q339 X Y then SelectiveSharedInputs.q341 X Y
            else SelectiveSharedInputs.q343 X Y) ∧
        SelectiveSharedInputs.q507 X Y p r

noncomputable def q509 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q349 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
      else SelectiveSharedInputs.q351 Y
    else
      if SelectiveSharedInputs.q350 X > SelectiveSharedInputs.q351 Y then
        if SelectiveSharedInputs.q350 X / 4 ≥ SelectiveSharedInputs.q351 Y then
          SelectiveSharedInputs.q350 X / 4
        else SelectiveSharedInputs.q351 Y
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y / 3 then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y / 3

noncomputable def q510 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 0xc4) ≥ SelectiveSharedInputs.q509 X Y then (3 / 0xc4) else SelectiveSharedInputs.q509 X Y) ≥
          if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
      if (3 / 0xc4) ≥ SelectiveSharedInputs.q509 X Y then (3 / 0xc4) else SelectiveSharedInputs.q509 X Y
    else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)

noncomputable def q511 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q510 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
        SelectiveSharedInputs.q510 X Y p r
      else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q349 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 49)
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y

noncomputable def q512 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q510 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
        SelectiveSharedInputs.q510 X Y p r
      else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q349 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 49)
      else
        if SelectiveSharedInputs.q350 X ≥ SelectiveSharedInputs.q351 Y then SelectiveSharedInputs.q350 X
        else SelectiveSharedInputs.q351 Y

noncomputable def q513 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then 1
          else 0) -
          if SelectiveSharedInputs.q349 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q510 X Y p r ≥ if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ) then
            SelectiveSharedInputs.q510 X Y p r
          else if p (6 : ℕ) ↔ True then 4 * r (6 : ℕ) else 6 * r (6 : ℕ)) ≥
          SelectiveSharedInputs.q509 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q333 X ∧ SelectiveSharedInputs.q334 Y ∧ SelectiveSharedInputs.q335 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q349 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q511 X Y p r
        else SelectiveSharedInputs.q512 X Y p r

noncomputable def q515 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 28) ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q411 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q413 X Y
          else
            if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y
            else SelectiveSharedInputs.q418 X Y then
      (3 / 28)
    else
      if
          ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q411 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q413 X Y
      else if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y else SelectiveSharedInputs.q418 X Y

noncomputable def q516 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q515 X Y ≥ if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q515 X Y
      else if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)) ≥
      if p (3 : ℕ) ↔ False then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)

noncomputable def q517 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q516 X Y p r then
      if SelectiveSharedInputs.q515 X Y ≥ if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
        SelectiveSharedInputs.q515 X Y
      else if p (4 : ℕ) ↔ False then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)
    else if p (3 : ℕ) ↔ False then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)

noncomputable def q518 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q411 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q517 X Y p r ≤
        if
            ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q411 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 7)
        else SelectiveSharedInputs.q413 X Y
    else
      SelectiveSharedInputs.q517 X Y p r <
        if
            ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q411 X Y then 1 else 0) =
              (0 : ℤ) then
          (1 / 7)
        else SelectiveSharedInputs.q413 X Y

noncomputable def q519 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then 1
          else 0) -
          if SelectiveSharedInputs.q411 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q517 X Y p r ≥
          if
              ((if
                      True ∧
                        SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                    1
                  else 0) -
                  if SelectiveSharedInputs.q411 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q413 X Y
          else
            if SelectiveSharedInputs.q414 X Y then SelectiveSharedInputs.q416 X Y
            else SelectiveSharedInputs.q418 X Y) ∧
        SelectiveSharedInputs.q518 X Y p r

noncomputable def q520 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
              1
            else 0) -
            if SelectiveSharedInputs.q424 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
      else SelectiveSharedInputs.q426 Y
    else
      if SelectiveSharedInputs.q425 X > SelectiveSharedInputs.q426 Y then
        if SelectiveSharedInputs.q425 X / 4 ≥ SelectiveSharedInputs.q426 Y then
          SelectiveSharedInputs.q425 X / 4
        else SelectiveSharedInputs.q426 Y
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y / 3 then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y / 3

noncomputable def q521 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 28) ≥ SelectiveSharedInputs.q520 X Y then (3 / 28) else SelectiveSharedInputs.q520 X Y) ≥
          if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
      if (3 / 28) ≥ SelectiveSharedInputs.q520 X Y then (3 / 28) else SelectiveSharedInputs.q520 X Y
    else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)

noncomputable def q522 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q521 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
        SelectiveSharedInputs.q521 X Y p r
      else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) ≤
      if
          ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q424 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 7)
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y

noncomputable def q523 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q521 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
        SelectiveSharedInputs.q521 X Y p r
      else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) <
      if
          ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                1
              else 0) -
              if SelectiveSharedInputs.q424 X Y then 1 else 0) =
            (0 : ℤ) then
        (1 / 7)
      else
        if SelectiveSharedInputs.q425 X ≥ SelectiveSharedInputs.q426 Y then SelectiveSharedInputs.q425 X
        else SelectiveSharedInputs.q426 Y

noncomputable def q524 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then 1
          else 0) -
          if SelectiveSharedInputs.q424 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q521 X Y p r ≥ if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
            SelectiveSharedInputs.q521 X Y p r
          else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)) ≥
          SelectiveSharedInputs.q520 X Y ∧
        if
            ((if True ∧ SelectiveSharedInputs.q408 X ∧ SelectiveSharedInputs.q409 Y ∧ SelectiveSharedInputs.q410 Y then
                  1
                else 0) -
                if SelectiveSharedInputs.q424 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q522 X Y p r
        else SelectiveSharedInputs.q523 X Y p r

noncomputable def q525 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (1 / 7) ≥
          2 * if (1 / 7) ≥ (1 / 16) * X * 4 then (1 / 16) * X * 4 else (1 / 16) * X then
      SelectiveSharedInputs.q524 X Y p r
    else ¬SelectiveSharedInputs.q519 X Y p r

noncomputable def q526 : ℚ → ℚ → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    True ∧
      (5 < (5 / 4) * if 5 ≥ 4 * X * 4 then 4 * X * 4 else 4 * X) ∧
        (5 ≥ (10 / 9) * if 5 ≥ 3 * Y * 3 then 3 * Y * 3 else 3 * Y) ∧
          5 < (4 / 3) * if 5 ≥ 3 * Y * 3 then 3 * Y * 3 else 3 * Y

noncomputable def q527 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        (3 / 4) ≥
          if
              ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q457 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q459 X Y
          else
            if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y
            else SelectiveSharedInputs.q464 X Y then
      (3 / 4)
    else
      if
          ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
              if SelectiveSharedInputs.q457 X Y then 1 else 0) =
            (0 : ℤ) then
        SelectiveSharedInputs.q459 X Y
      else if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y else SelectiveSharedInputs.q464 X Y

noncomputable def q528 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q527 X Y ≥ if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
        SelectiveSharedInputs.q527 X Y
      else if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)) ≥
      if p (1 : ℕ) ↔ False then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)

noncomputable def q529 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if SelectiveSharedInputs.q528 X Y p r then
      if SelectiveSharedInputs.q527 X Y ≥ if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
        SelectiveSharedInputs.q527 X Y
      else if p (2 : ℕ) ↔ False then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)
    else if p (1 : ℕ) ↔ False then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)

noncomputable def q530 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
            if SelectiveSharedInputs.q457 X Y then 1 else 0) =
          (0 : ℤ) then
      SelectiveSharedInputs.q529 X Y p r ≤
        if
            ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
                if SelectiveSharedInputs.q457 X Y then 1 else 0) =
              (0 : ℤ) then
          1
        else SelectiveSharedInputs.q459 X Y
    else
      SelectiveSharedInputs.q529 X Y p r <
        if
            ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
                if SelectiveSharedInputs.q457 X Y then 1 else 0) =
              (0 : ℤ) then
          1
        else SelectiveSharedInputs.q459 X Y

noncomputable def q531 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
          if SelectiveSharedInputs.q457 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (SelectiveSharedInputs.q529 X Y p r ≥
          if
              ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
                  if SelectiveSharedInputs.q457 X Y then 1 else 0) =
                (0 : ℤ) then
            SelectiveSharedInputs.q459 X Y
          else
            if SelectiveSharedInputs.q460 X Y then SelectiveSharedInputs.q462 X Y
            else SelectiveSharedInputs.q464 X Y) ∧
        SelectiveSharedInputs.q530 X Y p r

noncomputable def q532 : ℚ → ℚ → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y =>
    if
        ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
            if SelectiveSharedInputs.q470 X Y then 1 else 0) =
          (0 : ℤ) then
      if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
      else SelectiveSharedInputs.q472 Y
    else
      if SelectiveSharedInputs.q471 X > SelectiveSharedInputs.q472 Y then
        if SelectiveSharedInputs.q471 X / 4 ≥ SelectiveSharedInputs.q472 Y then
          SelectiveSharedInputs.q471 X / 4
        else SelectiveSharedInputs.q472 Y
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y / 3 then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y / 3

noncomputable def q533 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → ℚ := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if
        (if (3 / 4) ≥ SelectiveSharedInputs.q532 X Y then (3 / 4) else SelectiveSharedInputs.q532 X Y) ≥
          if p (2 : ℕ) ↔ True then 4 * r (2 : ℕ) else 6 * r (2 : ℕ) then
      if (3 / 4) ≥ SelectiveSharedInputs.q532 X Y then (3 / 4) else SelectiveSharedInputs.q532 X Y
    else if p (2 : ℕ) ↔ True then 4 * r (2 : ℕ) else 6 * r (2 : ℕ)

noncomputable def q534 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q533 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
        SelectiveSharedInputs.q533 X Y p r
      else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) ≤
      if
          ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
              if SelectiveSharedInputs.q470 X Y then 1 else 0) =
            (0 : ℤ) then
        1
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y

noncomputable def q535 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    (if SelectiveSharedInputs.q533 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
        SelectiveSharedInputs.q533 X Y p r
      else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) <
      if
          ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
              if SelectiveSharedInputs.q470 X Y then 1 else 0) =
            (0 : ℤ) then
        1
      else
        if SelectiveSharedInputs.q471 X ≥ SelectiveSharedInputs.q472 Y then SelectiveSharedInputs.q471 X
        else SelectiveSharedInputs.q472 Y

noncomputable def q536 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
          if SelectiveSharedInputs.q470 X Y then 1 else 0) ≥
        (0 : ℤ) ∧
      (if SelectiveSharedInputs.q533 X Y p r ≥ if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ) then
            SelectiveSharedInputs.q533 X Y p r
          else if p (1 : ℕ) ↔ True then 4 * r (1 : ℕ) else 6 * r (1 : ℕ)) ≥
          SelectiveSharedInputs.q532 X Y ∧
        if
            ((if SelectiveSharedInputs.q526 X Y then 1 else 0) -
                if SelectiveSharedInputs.q470 X Y then 1 else 0) =
              (0 : ℤ) then
          SelectiveSharedInputs.q534 X Y p r
        else SelectiveSharedInputs.q535 X Y p r

end SelectiveSharedInputs

namespace ClosureOriginalInputs0
open Bounty

noncomputable def input_0 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => (1 / 4) < X

noncomputable def input_1 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => X ≤ 1

noncomputable def input_2 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => (1 / 3) < Y

noncomputable def input_3 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => Y ≤ 1

noncomputable def input_15 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if p (20 : ℕ) then
      ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then 1
            else 0) -
            if SelectiveSharedInputs.q93 X Y then 1 else 0) ≥
          (0 : ℤ) ∧
        r (20 : ℕ) ≥ SelectiveSharedInputs.q96 X Y ∧ SelectiveSharedInputs.q97 X Y r
    else SelectiveSharedInputs.q107 X Y r

noncomputable def input_22 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q173 X Y p r ∨ SelectiveSharedInputs.q181 X Y p r

noncomputable def input_23 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (12 : ℕ) ↔ SelectiveSharedInputs.q182 X Y p r

noncomputable def input_24 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (12 : ℕ) =
      if p (12 : ℕ) then
        if
            SelectiveSharedInputs.q178 X Y p r ≥
              if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ) then
          SelectiveSharedInputs.q178 X Y p r
        else if p (17 : ℕ) ↔ True then 4 * r (17 : ℕ) else 6 * r (17 : ℕ)
      else SelectiveSharedInputs.q171 X Y p r

noncomputable def input_25 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q198 X Y p r ∨ SelectiveSharedInputs.q206 X Y p r

noncomputable def input_26 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (13 : ℕ) ↔ SelectiveSharedInputs.q207 X Y p r

noncomputable def input_27 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (13 : ℕ) =
      if p (13 : ℕ) then
        if
            SelectiveSharedInputs.q203 X Y p r ≥
              if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
          SelectiveSharedInputs.q203 X Y p r
        else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)
      else SelectiveSharedInputs.q196 X Y p r

noncomputable def input_28 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q223 X Y p r ∨ SelectiveSharedInputs.q231 X Y p r

noncomputable def input_29 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (14 : ℕ) ↔ SelectiveSharedInputs.q232 X Y p r

noncomputable def input_30 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (14 : ℕ) =
      if p (14 : ℕ) then
        if
            SelectiveSharedInputs.q228 X Y p r ≥
              if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
          SelectiveSharedInputs.q228 X Y p r
        else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)
      else SelectiveSharedInputs.q221 X Y p r

noncomputable def input_34 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q273 X Y p r ∨ SelectiveSharedInputs.q281 X Y p r

noncomputable def input_35 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (7 : ℕ) ↔ SelectiveSharedInputs.q282 X Y p r

noncomputable def input_36 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (7 : ℕ) =
      if p (7 : ℕ) then
        if
            SelectiveSharedInputs.q278 X Y p r ≥
              if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ) then
          SelectiveSharedInputs.q278 X Y p r
        else if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)
      else SelectiveSharedInputs.q271 X Y p r

noncomputable def input_37 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q298 X Y p r ∨ SelectiveSharedInputs.q306 X Y p r

noncomputable def input_38 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (8 : ℕ) ↔ SelectiveSharedInputs.q307 X Y p r

noncomputable def input_39 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (8 : ℕ) =
      if p (8 : ℕ) then
        if
            SelectiveSharedInputs.q303 X Y p r ≥
              if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
          SelectiveSharedInputs.q303 X Y p r
        else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)
      else SelectiveSharedInputs.q296 X Y p r

noncomputable def input_40 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q323 X Y p r ∨ SelectiveSharedInputs.q331 X Y p r

noncomputable def input_41 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (9 : ℕ) ↔ SelectiveSharedInputs.q332 X Y p r

noncomputable def input_42 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (9 : ℕ) =
      if p (9 : ℕ) then
        if
            SelectiveSharedInputs.q328 X Y p r ≥
              if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
          SelectiveSharedInputs.q328 X Y p r
        else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)
      else SelectiveSharedInputs.q321 X Y p r

noncomputable def input_46 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q373 X Y p r ∨ SelectiveSharedInputs.q381 X Y p r

noncomputable def input_47 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (4 : ℕ) ↔ SelectiveSharedInputs.q382 X Y p r

noncomputable def input_48 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (4 : ℕ) =
      if p (4 : ℕ) then
        if
            SelectiveSharedInputs.q378 X Y p r ≥
              if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
          SelectiveSharedInputs.q378 X Y p r
        else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)
      else SelectiveSharedInputs.q371 X Y p r

noncomputable def input_49 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q398 X Y p r ∨ SelectiveSharedInputs.q406 X Y p r

noncomputable def input_50 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (5 : ℕ) ↔ SelectiveSharedInputs.q407 X Y p r

noncomputable def input_51 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (5 : ℕ) =
      if p (5 : ℕ) then
        if
            SelectiveSharedInputs.q403 X Y p r ≥
              if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
          SelectiveSharedInputs.q403 X Y p r
        else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)
      else SelectiveSharedInputs.q396 X Y p r

noncomputable def input_52 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q423 X Y p r ∨ SelectiveSharedInputs.q431 X Y p r

noncomputable def input_53 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (1 : ℕ) ↔ SelectiveSharedInputs.q432 X Y p r

noncomputable def input_54 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (1 : ℕ) =
      if p (1 : ℕ) then
        if
            SelectiveSharedInputs.q428 X Y p r ≥
              if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
          SelectiveSharedInputs.q428 X Y p r
        else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)
      else SelectiveSharedInputs.q421 X Y p r

noncomputable def input_55 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q446 X Y p r ∨ SelectiveSharedInputs.q454 X Y p r

noncomputable def input_56 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (2 : ℕ) ↔ SelectiveSharedInputs.q455 X Y p r

noncomputable def input_57 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (2 : ℕ) =
      if p (2 : ℕ) then
        if
            SelectiveSharedInputs.q451 X Y p r ≥
              if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
          SelectiveSharedInputs.q451 X Y p r
        else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)
      else SelectiveSharedInputs.q444 X Y p r

noncomputable def input_58 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => ¬SelectiveSharedInputs.q469 X Y p r ∧ ¬SelectiveSharedInputs.q477 X Y p r

def raw_input_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_0 X Y p r := by
  classical

  exact h.1

def raw_input_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_1 X Y p r := by
  classical

  exact h.2.1

def raw_input_2 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_2 X Y p r := by
  classical

  exact h.2.2.1

def raw_input_3 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_3 X Y p r := by
  classical

  exact h.2.2.2.1

def raw_input_15 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_15 X Y p r := by
  classical

  have hn := h.2.2.2.2 20 (by norm_num)
  have hs := hn.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_15
  dsimp only [SelectiveSharedInputs.q90, SelectiveSharedInputs.q91, SelectiveSharedInputs.q92, SelectiveSharedInputs.q93, SelectiveSharedInputs.q94, SelectiveSharedInputs.q95, SelectiveSharedInputs.q96, SelectiveSharedInputs.q97, SelectiveSharedInputs.q98, SelectiveSharedInputs.q99, SelectiveSharedInputs.q100, SelectiveSharedInputs.q101, SelectiveSharedInputs.q102, SelectiveSharedInputs.q103, SelectiveSharedInputs.q104, SelectiveSharedInputs.q105, SelectiveSharedInputs.q106, SelectiveSharedInputs.q107]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_22 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_22 X Y p r := by
  classical

  have hn := h.2.2.2.2 12 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_22
  dsimp only [SelectiveSharedInputs.q158, SelectiveSharedInputs.q159, SelectiveSharedInputs.q160, SelectiveSharedInputs.q161, SelectiveSharedInputs.q162, SelectiveSharedInputs.q163, SelectiveSharedInputs.q164, SelectiveSharedInputs.q165, SelectiveSharedInputs.q166, SelectiveSharedInputs.q167, SelectiveSharedInputs.q168, SelectiveSharedInputs.q169, SelectiveSharedInputs.q170, SelectiveSharedInputs.q171, SelectiveSharedInputs.q172, SelectiveSharedInputs.q173, SelectiveSharedInputs.q174, SelectiveSharedInputs.q175, SelectiveSharedInputs.q176, SelectiveSharedInputs.q177, SelectiveSharedInputs.q178, SelectiveSharedInputs.q179, SelectiveSharedInputs.q180, SelectiveSharedInputs.q181]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_23 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_23 X Y p r := by
  classical

  have hn := h.2.2.2.2 12 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_23
  dsimp only [SelectiveSharedInputs.q158, SelectiveSharedInputs.q159, SelectiveSharedInputs.q160, SelectiveSharedInputs.q161, SelectiveSharedInputs.q162, SelectiveSharedInputs.q163, SelectiveSharedInputs.q164, SelectiveSharedInputs.q165, SelectiveSharedInputs.q166, SelectiveSharedInputs.q167, SelectiveSharedInputs.q168, SelectiveSharedInputs.q169, SelectiveSharedInputs.q170, SelectiveSharedInputs.q171, SelectiveSharedInputs.q172, SelectiveSharedInputs.q173, SelectiveSharedInputs.q174, SelectiveSharedInputs.q175, SelectiveSharedInputs.q176, SelectiveSharedInputs.q177, SelectiveSharedInputs.q178, SelectiveSharedInputs.q179, SelectiveSharedInputs.q180, SelectiveSharedInputs.q181, SelectiveSharedInputs.q182]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_24 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_24 X Y p r := by
  classical

  have hn := h.2.2.2.2 12 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_24
  dsimp only [SelectiveSharedInputs.q158, SelectiveSharedInputs.q159, SelectiveSharedInputs.q160, SelectiveSharedInputs.q161, SelectiveSharedInputs.q162, SelectiveSharedInputs.q163, SelectiveSharedInputs.q164, SelectiveSharedInputs.q165, SelectiveSharedInputs.q166, SelectiveSharedInputs.q167, SelectiveSharedInputs.q168, SelectiveSharedInputs.q169, SelectiveSharedInputs.q170, SelectiveSharedInputs.q171, SelectiveSharedInputs.q174, SelectiveSharedInputs.q175, SelectiveSharedInputs.q176, SelectiveSharedInputs.q177, SelectiveSharedInputs.q178]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_25 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_25 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_25
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q197, SelectiveSharedInputs.q198, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203, SelectiveSharedInputs.q204, SelectiveSharedInputs.q205, SelectiveSharedInputs.q206]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_26 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_26 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_26
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q197, SelectiveSharedInputs.q198, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203, SelectiveSharedInputs.q204, SelectiveSharedInputs.q205, SelectiveSharedInputs.q206, SelectiveSharedInputs.q207]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_27 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_27 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_27
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_28 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_28 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_28
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q222, SelectiveSharedInputs.q223, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228, SelectiveSharedInputs.q229, SelectiveSharedInputs.q230, SelectiveSharedInputs.q231]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_29 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_29 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_29
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q222, SelectiveSharedInputs.q223, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228, SelectiveSharedInputs.q229, SelectiveSharedInputs.q230, SelectiveSharedInputs.q231, SelectiveSharedInputs.q232]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_30 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_30 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_30
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_34 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_34 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_34
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q272, SelectiveSharedInputs.q273, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278, SelectiveSharedInputs.q279, SelectiveSharedInputs.q280, SelectiveSharedInputs.q281]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_35 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_35 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_35
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q272, SelectiveSharedInputs.q273, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278, SelectiveSharedInputs.q279, SelectiveSharedInputs.q280, SelectiveSharedInputs.q281, SelectiveSharedInputs.q282]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_36 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_36 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_36
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_37 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_37 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_37
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q297, SelectiveSharedInputs.q298, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303, SelectiveSharedInputs.q304, SelectiveSharedInputs.q305, SelectiveSharedInputs.q306]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_38 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_38 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_38
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q297, SelectiveSharedInputs.q298, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303, SelectiveSharedInputs.q304, SelectiveSharedInputs.q305, SelectiveSharedInputs.q306, SelectiveSharedInputs.q307]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_39 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_39 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_39
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_40 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_40 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_40
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q322, SelectiveSharedInputs.q323, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328, SelectiveSharedInputs.q329, SelectiveSharedInputs.q330, SelectiveSharedInputs.q331]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_41 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_41 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_41
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q322, SelectiveSharedInputs.q323, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328, SelectiveSharedInputs.q329, SelectiveSharedInputs.q330, SelectiveSharedInputs.q331, SelectiveSharedInputs.q332]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_42 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_42 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_42
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_46 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_46 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_46
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q372, SelectiveSharedInputs.q373, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378, SelectiveSharedInputs.q379, SelectiveSharedInputs.q380, SelectiveSharedInputs.q381]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_47 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_47 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_47
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q372, SelectiveSharedInputs.q373, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378, SelectiveSharedInputs.q379, SelectiveSharedInputs.q380, SelectiveSharedInputs.q381, SelectiveSharedInputs.q382]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_48 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_48 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_48
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_49 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_49 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_49
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q397, SelectiveSharedInputs.q398, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403, SelectiveSharedInputs.q404, SelectiveSharedInputs.q405, SelectiveSharedInputs.q406]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_50 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_50 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_50
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q397, SelectiveSharedInputs.q398, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403, SelectiveSharedInputs.q404, SelectiveSharedInputs.q405, SelectiveSharedInputs.q406, SelectiveSharedInputs.q407]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_51 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_51 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_51
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_52 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_52 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_52
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q419, SelectiveSharedInputs.q420, SelectiveSharedInputs.q421, SelectiveSharedInputs.q422, SelectiveSharedInputs.q423, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q427, SelectiveSharedInputs.q428, SelectiveSharedInputs.q429, SelectiveSharedInputs.q430, SelectiveSharedInputs.q431]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_53 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_53 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_53
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q419, SelectiveSharedInputs.q420, SelectiveSharedInputs.q421, SelectiveSharedInputs.q422, SelectiveSharedInputs.q423, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q427, SelectiveSharedInputs.q428, SelectiveSharedInputs.q429, SelectiveSharedInputs.q430, SelectiveSharedInputs.q431, SelectiveSharedInputs.q432]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_54 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_54 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_54
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q419, SelectiveSharedInputs.q420, SelectiveSharedInputs.q421, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q427, SelectiveSharedInputs.q428]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_55 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_55 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_55
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q445, SelectiveSharedInputs.q446, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451, SelectiveSharedInputs.q452, SelectiveSharedInputs.q453, SelectiveSharedInputs.q454]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_56 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_56 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_56
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q445, SelectiveSharedInputs.q446, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451, SelectiveSharedInputs.q452, SelectiveSharedInputs.q453, SelectiveSharedInputs.q454, SelectiveSharedInputs.q455]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_57 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_57 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_57
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_58 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 false X Y p r) : input_58 X Y p r := by
  classical

  have hn := h.2.2.2.2 0 (by norm_num)
  have hs := hn
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_58
  dsimp only [SelectiveSharedInputs.q456, SelectiveSharedInputs.q457, SelectiveSharedInputs.q458, SelectiveSharedInputs.q459, SelectiveSharedInputs.q460, SelectiveSharedInputs.q461, SelectiveSharedInputs.q462, SelectiveSharedInputs.q463, SelectiveSharedInputs.q464, SelectiveSharedInputs.q465, SelectiveSharedInputs.q466, SelectiveSharedInputs.q467, SelectiveSharedInputs.q468, SelectiveSharedInputs.q469, SelectiveSharedInputs.q470, SelectiveSharedInputs.q471, SelectiveSharedInputs.q472, SelectiveSharedInputs.q473, SelectiveSharedInputs.q474, SelectiveSharedInputs.q475, SelectiveSharedInputs.q476, SelectiveSharedInputs.q477]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

end ClosureOriginalInputs0

namespace ClosureOriginalInputs1
open Bounty

noncomputable def input_0 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => (1 / 4) < X

noncomputable def input_1 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => X ≤ 1

noncomputable def input_2 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => (1 / 3) < Y

noncomputable def input_3 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => Y ≤ 1

noncomputable def input_14 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => (3 / 0x30d4) ≤ r (20 : ℕ)

noncomputable def input_15 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    if p (20 : ℕ) then
      ((if True ∧ SelectiveSharedInputs.q90 X ∧ SelectiveSharedInputs.q91 Y ∧ SelectiveSharedInputs.q92 Y then 1
            else 0) -
            if SelectiveSharedInputs.q93 X Y then 1 else 0) ≥
          (0 : ℤ) ∧
        r (20 : ℕ) ≥ SelectiveSharedInputs.q96 X Y ∧ SelectiveSharedInputs.q97 X Y r
    else SelectiveSharedInputs.q107 X Y r

noncomputable def input_25 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q198 X Y p r ∨ SelectiveSharedInputs.q206 X Y p r

noncomputable def input_26 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (13 : ℕ) ↔ SelectiveSharedInputs.q207 X Y p r

noncomputable def input_27 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (13 : ℕ) =
      if p (13 : ℕ) then
        if
            SelectiveSharedInputs.q203 X Y p r ≥
              if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ) then
          SelectiveSharedInputs.q203 X Y p r
        else if p (18 : ℕ) ↔ True then 4 * r (18 : ℕ) else 6 * r (18 : ℕ)
      else SelectiveSharedInputs.q196 X Y p r

noncomputable def input_28 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q223 X Y p r ∨ SelectiveSharedInputs.q231 X Y p r

noncomputable def input_29 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (14 : ℕ) ↔ SelectiveSharedInputs.q232 X Y p r

noncomputable def input_30 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (14 : ℕ) =
      if p (14 : ℕ) then
        if
            SelectiveSharedInputs.q228 X Y p r ≥
              if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ) then
          SelectiveSharedInputs.q228 X Y p r
        else if p (19 : ℕ) ↔ True then 4 * r (19 : ℕ) else 6 * r (19 : ℕ)
      else SelectiveSharedInputs.q221 X Y p r

noncomputable def input_34 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q273 X Y p r ∨ SelectiveSharedInputs.q281 X Y p r

noncomputable def input_35 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (7 : ℕ) ↔ SelectiveSharedInputs.q282 X Y p r

noncomputable def input_36 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (7 : ℕ) =
      if p (7 : ℕ) then
        if
            SelectiveSharedInputs.q278 X Y p r ≥
              if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ) then
          SelectiveSharedInputs.q278 X Y p r
        else if p (11 : ℕ) ↔ True then 4 * r (11 : ℕ) else 6 * r (11 : ℕ)
      else SelectiveSharedInputs.q271 X Y p r

noncomputable def input_37 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q298 X Y p r ∨ SelectiveSharedInputs.q306 X Y p r

noncomputable def input_38 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (8 : ℕ) ↔ SelectiveSharedInputs.q307 X Y p r

noncomputable def input_39 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (8 : ℕ) =
      if p (8 : ℕ) then
        if
            SelectiveSharedInputs.q303 X Y p r ≥
              if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ) then
          SelectiveSharedInputs.q303 X Y p r
        else if p (12 : ℕ) ↔ True then 4 * r (12 : ℕ) else 6 * r (12 : ℕ)
      else SelectiveSharedInputs.q296 X Y p r

noncomputable def input_40 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q323 X Y p r ∨ SelectiveSharedInputs.q331 X Y p r

noncomputable def input_41 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (9 : ℕ) ↔ SelectiveSharedInputs.q332 X Y p r

noncomputable def input_42 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (9 : ℕ) =
      if p (9 : ℕ) then
        if
            SelectiveSharedInputs.q328 X Y p r ≥
              if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ) then
          SelectiveSharedInputs.q328 X Y p r
        else if p (13 : ℕ) ↔ True then 4 * r (13 : ℕ) else 6 * r (13 : ℕ)
      else SelectiveSharedInputs.q321 X Y p r

noncomputable def input_46 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q373 X Y p r ∨ SelectiveSharedInputs.q381 X Y p r

noncomputable def input_47 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (4 : ℕ) ↔ SelectiveSharedInputs.q382 X Y p r

noncomputable def input_48 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (4 : ℕ) =
      if p (4 : ℕ) then
        if
            SelectiveSharedInputs.q378 X Y p r ≥
              if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ) then
          SelectiveSharedInputs.q378 X Y p r
        else if p (7 : ℕ) ↔ True then 4 * r (7 : ℕ) else 6 * r (7 : ℕ)
      else SelectiveSharedInputs.q371 X Y p r

noncomputable def input_49 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q398 X Y p r ∨ SelectiveSharedInputs.q406 X Y p r

noncomputable def input_50 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (5 : ℕ) ↔ SelectiveSharedInputs.q407 X Y p r

noncomputable def input_51 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (5 : ℕ) =
      if p (5 : ℕ) then
        if
            SelectiveSharedInputs.q403 X Y p r ≥
              if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ) then
          SelectiveSharedInputs.q403 X Y p r
        else if p (8 : ℕ) ↔ True then 4 * r (8 : ℕ) else 6 * r (8 : ℕ)
      else SelectiveSharedInputs.q396 X Y p r

noncomputable def input_52 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q519 X Y p r ∨ SelectiveSharedInputs.q524 X Y p r

noncomputable def input_53 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (1 : ℕ) ↔ SelectiveSharedInputs.q525 X Y p r

noncomputable def input_54 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (1 : ℕ) =
      if p (1 : ℕ) then
        if
            SelectiveSharedInputs.q521 X Y p r ≥
              if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ) then
          SelectiveSharedInputs.q521 X Y p r
        else if p (3 : ℕ) ↔ True then 4 * r (3 : ℕ) else 6 * r (3 : ℕ)
      else SelectiveSharedInputs.q517 X Y p r

noncomputable def input_55 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => SelectiveSharedInputs.q446 X Y p r ∨ SelectiveSharedInputs.q454 X Y p r

noncomputable def input_56 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => p (2 : ℕ) ↔ SelectiveSharedInputs.q455 X Y p r

noncomputable def input_57 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r =>
    r (2 : ℕ) =
      if p (2 : ℕ) then
        if
            SelectiveSharedInputs.q451 X Y p r ≥
              if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ) then
          SelectiveSharedInputs.q451 X Y p r
        else if p (4 : ℕ) ↔ True then 4 * r (4 : ℕ) else 6 * r (4 : ℕ)
      else SelectiveSharedInputs.q444 X Y p r

noncomputable def input_58 : ℚ → ℚ → (ℕ → Prop) → (ℕ → ℚ) → Prop := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact fun X Y p r => ¬SelectiveSharedInputs.q531 X Y p r ∧ ¬SelectiveSharedInputs.q536 X Y p r

def raw_input_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_0 X Y p r := by
  classical

  exact h.1

def raw_input_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_1 X Y p r := by
  classical

  exact h.2.1

def raw_input_2 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_2 X Y p r := by
  classical

  exact h.2.2.1

def raw_input_3 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_3 X Y p r := by
  classical

  exact h.2.2.2.1

def raw_input_14 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_14 X Y p r := by
  classical

  have hn := h.2.2.2.2 20 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_14
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_15 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_15 X Y p r := by
  classical

  have hn := h.2.2.2.2 20 (by norm_num)
  have hs := hn.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_15
  dsimp only [SelectiveSharedInputs.q90, SelectiveSharedInputs.q91, SelectiveSharedInputs.q92, SelectiveSharedInputs.q93, SelectiveSharedInputs.q94, SelectiveSharedInputs.q95, SelectiveSharedInputs.q96, SelectiveSharedInputs.q97, SelectiveSharedInputs.q98, SelectiveSharedInputs.q99, SelectiveSharedInputs.q100, SelectiveSharedInputs.q101, SelectiveSharedInputs.q102, SelectiveSharedInputs.q103, SelectiveSharedInputs.q104, SelectiveSharedInputs.q105, SelectiveSharedInputs.q106, SelectiveSharedInputs.q107]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_25 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_25 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_25
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q197, SelectiveSharedInputs.q198, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203, SelectiveSharedInputs.q204, SelectiveSharedInputs.q205, SelectiveSharedInputs.q206]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_26 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_26 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_26
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q197, SelectiveSharedInputs.q198, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203, SelectiveSharedInputs.q204, SelectiveSharedInputs.q205, SelectiveSharedInputs.q206, SelectiveSharedInputs.q207]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_27 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_27 X Y p r := by
  classical

  have hn := h.2.2.2.2 13 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_27
  dsimp only [SelectiveSharedInputs.q183, SelectiveSharedInputs.q184, SelectiveSharedInputs.q185, SelectiveSharedInputs.q186, SelectiveSharedInputs.q187, SelectiveSharedInputs.q188, SelectiveSharedInputs.q189, SelectiveSharedInputs.q190, SelectiveSharedInputs.q191, SelectiveSharedInputs.q192, SelectiveSharedInputs.q193, SelectiveSharedInputs.q194, SelectiveSharedInputs.q195, SelectiveSharedInputs.q196, SelectiveSharedInputs.q199, SelectiveSharedInputs.q200, SelectiveSharedInputs.q201, SelectiveSharedInputs.q202, SelectiveSharedInputs.q203]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_28 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_28 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_28
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q222, SelectiveSharedInputs.q223, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228, SelectiveSharedInputs.q229, SelectiveSharedInputs.q230, SelectiveSharedInputs.q231]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_29 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_29 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_29
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q222, SelectiveSharedInputs.q223, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228, SelectiveSharedInputs.q229, SelectiveSharedInputs.q230, SelectiveSharedInputs.q231, SelectiveSharedInputs.q232]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_30 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_30 X Y p r := by
  classical

  have hn := h.2.2.2.2 14 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_30
  dsimp only [SelectiveSharedInputs.q208, SelectiveSharedInputs.q209, SelectiveSharedInputs.q210, SelectiveSharedInputs.q211, SelectiveSharedInputs.q212, SelectiveSharedInputs.q213, SelectiveSharedInputs.q214, SelectiveSharedInputs.q215, SelectiveSharedInputs.q216, SelectiveSharedInputs.q217, SelectiveSharedInputs.q218, SelectiveSharedInputs.q219, SelectiveSharedInputs.q220, SelectiveSharedInputs.q221, SelectiveSharedInputs.q224, SelectiveSharedInputs.q225, SelectiveSharedInputs.q226, SelectiveSharedInputs.q227, SelectiveSharedInputs.q228]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_34 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_34 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_34
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q272, SelectiveSharedInputs.q273, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278, SelectiveSharedInputs.q279, SelectiveSharedInputs.q280, SelectiveSharedInputs.q281]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_35 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_35 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_35
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q272, SelectiveSharedInputs.q273, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278, SelectiveSharedInputs.q279, SelectiveSharedInputs.q280, SelectiveSharedInputs.q281, SelectiveSharedInputs.q282]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_36 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_36 X Y p r := by
  classical

  have hn := h.2.2.2.2 7 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_36
  dsimp only [SelectiveSharedInputs.q258, SelectiveSharedInputs.q259, SelectiveSharedInputs.q260, SelectiveSharedInputs.q261, SelectiveSharedInputs.q262, SelectiveSharedInputs.q263, SelectiveSharedInputs.q264, SelectiveSharedInputs.q265, SelectiveSharedInputs.q266, SelectiveSharedInputs.q267, SelectiveSharedInputs.q268, SelectiveSharedInputs.q269, SelectiveSharedInputs.q270, SelectiveSharedInputs.q271, SelectiveSharedInputs.q274, SelectiveSharedInputs.q275, SelectiveSharedInputs.q276, SelectiveSharedInputs.q277, SelectiveSharedInputs.q278]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_37 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_37 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_37
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q297, SelectiveSharedInputs.q298, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303, SelectiveSharedInputs.q304, SelectiveSharedInputs.q305, SelectiveSharedInputs.q306]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_38 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_38 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_38
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q297, SelectiveSharedInputs.q298, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303, SelectiveSharedInputs.q304, SelectiveSharedInputs.q305, SelectiveSharedInputs.q306, SelectiveSharedInputs.q307]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_39 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_39 X Y p r := by
  classical

  have hn := h.2.2.2.2 8 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_39
  dsimp only [SelectiveSharedInputs.q283, SelectiveSharedInputs.q284, SelectiveSharedInputs.q285, SelectiveSharedInputs.q286, SelectiveSharedInputs.q287, SelectiveSharedInputs.q288, SelectiveSharedInputs.q289, SelectiveSharedInputs.q290, SelectiveSharedInputs.q291, SelectiveSharedInputs.q292, SelectiveSharedInputs.q293, SelectiveSharedInputs.q294, SelectiveSharedInputs.q295, SelectiveSharedInputs.q296, SelectiveSharedInputs.q299, SelectiveSharedInputs.q300, SelectiveSharedInputs.q301, SelectiveSharedInputs.q302, SelectiveSharedInputs.q303]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_40 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_40 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_40
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q322, SelectiveSharedInputs.q323, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328, SelectiveSharedInputs.q329, SelectiveSharedInputs.q330, SelectiveSharedInputs.q331]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_41 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_41 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_41
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q322, SelectiveSharedInputs.q323, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328, SelectiveSharedInputs.q329, SelectiveSharedInputs.q330, SelectiveSharedInputs.q331, SelectiveSharedInputs.q332]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_42 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_42 X Y p r := by
  classical

  have hn := h.2.2.2.2 9 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_42
  dsimp only [SelectiveSharedInputs.q308, SelectiveSharedInputs.q309, SelectiveSharedInputs.q310, SelectiveSharedInputs.q311, SelectiveSharedInputs.q312, SelectiveSharedInputs.q313, SelectiveSharedInputs.q314, SelectiveSharedInputs.q315, SelectiveSharedInputs.q316, SelectiveSharedInputs.q317, SelectiveSharedInputs.q318, SelectiveSharedInputs.q319, SelectiveSharedInputs.q320, SelectiveSharedInputs.q321, SelectiveSharedInputs.q324, SelectiveSharedInputs.q325, SelectiveSharedInputs.q326, SelectiveSharedInputs.q327, SelectiveSharedInputs.q328]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_46 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_46 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_46
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q372, SelectiveSharedInputs.q373, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378, SelectiveSharedInputs.q379, SelectiveSharedInputs.q380, SelectiveSharedInputs.q381]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_47 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_47 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_47
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q372, SelectiveSharedInputs.q373, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378, SelectiveSharedInputs.q379, SelectiveSharedInputs.q380, SelectiveSharedInputs.q381, SelectiveSharedInputs.q382]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_48 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_48 X Y p r := by
  classical

  have hn := h.2.2.2.2 4 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_48
  dsimp only [SelectiveSharedInputs.q358, SelectiveSharedInputs.q359, SelectiveSharedInputs.q360, SelectiveSharedInputs.q361, SelectiveSharedInputs.q362, SelectiveSharedInputs.q363, SelectiveSharedInputs.q364, SelectiveSharedInputs.q365, SelectiveSharedInputs.q366, SelectiveSharedInputs.q367, SelectiveSharedInputs.q368, SelectiveSharedInputs.q369, SelectiveSharedInputs.q370, SelectiveSharedInputs.q371, SelectiveSharedInputs.q374, SelectiveSharedInputs.q375, SelectiveSharedInputs.q376, SelectiveSharedInputs.q377, SelectiveSharedInputs.q378]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_49 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_49 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_49
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q397, SelectiveSharedInputs.q398, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403, SelectiveSharedInputs.q404, SelectiveSharedInputs.q405, SelectiveSharedInputs.q406]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_50 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_50 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_50
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q397, SelectiveSharedInputs.q398, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403, SelectiveSharedInputs.q404, SelectiveSharedInputs.q405, SelectiveSharedInputs.q406, SelectiveSharedInputs.q407]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_51 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_51 X Y p r := by
  classical

  have hn := h.2.2.2.2 5 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_51
  dsimp only [SelectiveSharedInputs.q383, SelectiveSharedInputs.q384, SelectiveSharedInputs.q385, SelectiveSharedInputs.q386, SelectiveSharedInputs.q387, SelectiveSharedInputs.q388, SelectiveSharedInputs.q389, SelectiveSharedInputs.q390, SelectiveSharedInputs.q391, SelectiveSharedInputs.q392, SelectiveSharedInputs.q393, SelectiveSharedInputs.q394, SelectiveSharedInputs.q395, SelectiveSharedInputs.q396, SelectiveSharedInputs.q399, SelectiveSharedInputs.q400, SelectiveSharedInputs.q401, SelectiveSharedInputs.q402, SelectiveSharedInputs.q403]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_52 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_52 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_52
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q515, SelectiveSharedInputs.q516, SelectiveSharedInputs.q517, SelectiveSharedInputs.q518, SelectiveSharedInputs.q519, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q520, SelectiveSharedInputs.q521, SelectiveSharedInputs.q522, SelectiveSharedInputs.q523, SelectiveSharedInputs.q524]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_53 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_53 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_53
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q515, SelectiveSharedInputs.q516, SelectiveSharedInputs.q517, SelectiveSharedInputs.q518, SelectiveSharedInputs.q519, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q520, SelectiveSharedInputs.q521, SelectiveSharedInputs.q522, SelectiveSharedInputs.q523, SelectiveSharedInputs.q524, SelectiveSharedInputs.q525]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_54 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_54 X Y p r := by
  classical

  have hn := h.2.2.2.2 1 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_54
  dsimp only [SelectiveSharedInputs.q408, SelectiveSharedInputs.q409, SelectiveSharedInputs.q410, SelectiveSharedInputs.q411, SelectiveSharedInputs.q412, SelectiveSharedInputs.q413, SelectiveSharedInputs.q414, SelectiveSharedInputs.q415, SelectiveSharedInputs.q416, SelectiveSharedInputs.q417, SelectiveSharedInputs.q418, SelectiveSharedInputs.q515, SelectiveSharedInputs.q516, SelectiveSharedInputs.q517, SelectiveSharedInputs.q424, SelectiveSharedInputs.q425, SelectiveSharedInputs.q426, SelectiveSharedInputs.q520, SelectiveSharedInputs.q521]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_55 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_55 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_55
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q445, SelectiveSharedInputs.q446, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451, SelectiveSharedInputs.q452, SelectiveSharedInputs.q453, SelectiveSharedInputs.q454]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_56 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_56 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.2.1
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_56
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q445, SelectiveSharedInputs.q446, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451, SelectiveSharedInputs.q452, SelectiveSharedInputs.q453, SelectiveSharedInputs.q454, SelectiveSharedInputs.q455]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_57 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_57 X Y p r := by
  classical

  have hn := h.2.2.2.2 2 (by norm_num)
  have hs := hn.2.2
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_57
  dsimp only [SelectiveSharedInputs.q433, SelectiveSharedInputs.q434, SelectiveSharedInputs.q435, SelectiveSharedInputs.q436, SelectiveSharedInputs.q437, SelectiveSharedInputs.q438, SelectiveSharedInputs.q439, SelectiveSharedInputs.q440, SelectiveSharedInputs.q441, SelectiveSharedInputs.q442, SelectiveSharedInputs.q443, SelectiveSharedInputs.q444, SelectiveSharedInputs.q447, SelectiveSharedInputs.q448, SelectiveSharedInputs.q449, SelectiveSharedInputs.q450, SelectiveSharedInputs.q451]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

def raw_input_58 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ)
    (h : ClosureRawHypothesis5 true X Y p r) : input_58 X Y p r := by
  classical

  have hn := h.2.2.2.2 0 (by norm_num)
  have hs := hn
  simp only [closureNodeConstraint5, closureNodeAvailable, closureNodeTrial,
    closureNodeType, closureNodeFour, closureNodeThree, closureLossFour, closureLossThree,
    closureNode, normalizedStateValid, normalizedTrialValue, normalizedProfileTrial_left,
    normalizedProfileValid, normalizedProfileLower, normalizedDelta, normalizedLossValue,
    normalizedDeficit, normalizedParityFour, normalizedParityThree, normalizedPowerCoordinate,
    closureGamma_zero, closureGamma_one, closureIndicator_cast, closureIndicator_natCast, max_def',
    ↓reduceIte, Nat.reduceEqDiff, Bool.false_eq_true, Bool.true_eq_false,
    iff_true, iff_false, ite_not, true_and, false_and, Nat.reduceLeDiff] at hs
  unfold input_58
  dsimp only [SelectiveSharedInputs.q526, SelectiveSharedInputs.q457, SelectiveSharedInputs.q458, SelectiveSharedInputs.q459, SelectiveSharedInputs.q460, SelectiveSharedInputs.q461, SelectiveSharedInputs.q462, SelectiveSharedInputs.q463, SelectiveSharedInputs.q464, SelectiveSharedInputs.q527, SelectiveSharedInputs.q528, SelectiveSharedInputs.q529, SelectiveSharedInputs.q530, SelectiveSharedInputs.q531, SelectiveSharedInputs.q470, SelectiveSharedInputs.q471, SelectiveSharedInputs.q472, SelectiveSharedInputs.q532, SelectiveSharedInputs.q533, SelectiveSharedInputs.q534, SelectiveSharedInputs.q535, SelectiveSharedInputs.q536]
  norm_num only [closureIndicator_cast, closureIndicator_natCast, mul_assoc, mul_comm, mul_left_comm, div_eq_mul_inv,
    one_mul, mul_one, iff_true, iff_false, ite_not, true_and, false_and,
    ite_true, ite_false, closureCap_simplify] at hs ⊢
  exact hs

end ClosureOriginalInputs1









end PolicyCombinatorialFront_PolicyClosureInputsSelectivePair

end PolicySubmissionPart0

/- Component ClosureSemantics; SHA256 e1a16bfa77026db4e832a66d12e20301386e1e9ab7eacf1955630edd6e7c254e. -/
section PolicySubmissionPart1
/- Typed interpretation of a finite arithmetic and Boolean expression DAG. -/
namespace ClosureSemantics

structure Value where
  b : Bool
  z : Int
  q : Rat

def zeroValue : Value := ⟨false, 0, 0⟩
def boolValue (b : Bool) : Value := ⟨b, 0, 0⟩
def intValue (z : Int) : Value := ⟨false, z, 0⟩
def ratValue (q : Rat) : Value := ⟨false, 0, q⟩

abbrev Valuation := Nat → Value

inductive Op where
  | input : Nat → Op
  | qConst : Rat → Op
  | zConst : Int → Op
  | bConst : Bool → Op
  | alias | bNot | bOr | bAnd | bEq | ite
  | qEq | zEq | qLe | zLe | qLt | zLt
  | qAdd | zAdd | qMul | zMul | qNeg | zNeg | qSub | zSub | qDiv

structure Node where
  op : Op
  children : List Nat

def evalOp (input : Valuation) : Op → List Value → Value
  | .input k, _ => input k
  | .qConst c, _ => ratValue c
  | .zConst c, _ => intValue c
  | .bConst c, _ => boolValue c
  | .alias, [a] => a
  | .bNot, [a] => boolValue (!a.b)
  | .bOr, xs => boolValue ((xs.map Value.b).any id)
  | .bAnd, xs => boolValue ((xs.map Value.b).all id)
  | .bEq, [a, b] => boolValue (a.b == b.b)
  | .ite, [c, a, b] => if c.b then a else b
  | .qEq, [a, b] => boolValue (decide (a.q = b.q))
  | .zEq, [a, b] => boolValue (decide (a.z = b.z))
  | .qLe, [a, b] => boolValue (decide (a.q ≤ b.q))
  | .zLe, [a, b] => boolValue (decide (a.z ≤ b.z))
  | .qLt, [a, b] => boolValue (decide (a.q < b.q))
  | .zLt, [a, b] => boolValue (decide (a.z < b.z))
  | .qAdd, a :: rest => ratValue ((rest.map Value.q).foldl (· + ·) a.q)
  | .zAdd, a :: rest => intValue ((rest.map Value.z).foldl (· + ·) a.z)
  | .qMul, a :: rest => ratValue ((rest.map Value.q).foldl (· * ·) a.q)
  | .zMul, a :: rest => intValue ((rest.map Value.z).foldl (· * ·) a.z)
  | .qAdd, [] => ratValue 0
  | .zAdd, [] => intValue 0
  | .qMul, [] => ratValue 1
  | .zMul, [] => intValue 1
  | .qNeg, [a] => ratValue (-a.q)
  | .zNeg, [a] => intValue (-a.z)
  | .qSub, a :: rest => ratValue ((rest.map Value.q).foldl (· - ·) a.q)
  | .zSub, a :: rest => intValue ((rest.map Value.z).foldl (· - ·) a.z)
  | .qDiv, [a, b] => ratValue (a.q / b.q)
  | _, _ => zeroValue

def evalNode (input values : Valuation) (node : Node) : Value :=
  evalOp input node.op (node.children.map values)

def evalNode_congr (input values other : Valuation) (node : Node)
    (h : ∀ j ∈ node.children, values j = other j) :
    evalNode input values node = evalNode input other node := by
  unfold evalNode
  congr 1
  exact List.map_congr_left h

def interpret (program : Nat → Node) (input : Valuation) : Valuation :=
  Nat.lt_wfRel.wf.fix fun i previous =>
    evalNode input (fun j => if h : j < i then previous j h else zeroValue) (program i)

def interpret_eq (program : Nat → Node) (input : Valuation) (i : Nat)
    (h : ∀ j ∈ (program i).children, j < i) :
    interpret program input i = evalNode input (interpret program input) (program i) := by
  rw [interpret, WellFounded.fix_eq]
  apply evalNode_congr
  intro j hj
  rw [dif_pos (h j hj)]

def Equations (program : Nat → Node) (input values : Valuation) : Prop :=
  ∀ i, values i = evalNode input values (program i)

def interpret_equations (program : Nat → Node) (input : Valuation)
    (h : ∀ i, ∀ j ∈ (program i).children, j < i) :
    Equations program input (interpret program input) := by
  intro i
  exact interpret_eq program input i (h i)

end ClosureSemantics

end PolicySubmissionPart1

/- Component PolicyLRATDirect; SHA256 37d7c27b1ff433e53e758a9ad45ecd8daeefdb13a1e07648e90ae75a365de8ec. -/
section PolicySubmissionPart2
/- Trusted list LRAT checker with directly constructed clauses; no hash-map parser. -/

namespace Bounty
open Std.Sat Std.Tactic.BVDecide.LRAT Std.Tactic.BVDecide.LRAT.Internal

end Bounty

end PolicySubmissionPart2

/- Component PolicyLRATList; SHA256 b1512bf254baf600e187f39000a1e6c91327a13c2dfa60c86b4709aa613492a7. -/
section PolicySubmissionPart3
/- Transparent list-based LRAT inputs, retaining the trusted checker and its soundness. -/

namespace Bounty
open Std.Sat Std.Tactic.BVDecide.LRAT Std.Tactic.BVDecide.LRAT.Internal

end Bounty

end PolicySubmissionPart3

/- Component PolicyLRATSemantics; SHA256 99246fc0f7154a56586c35576a362be2d7249e5f09c14d0d7e7d33ac47795384. -/
section PolicySubmissionPart4
/- Propositional semantics of the transparent signed-clause input representation. -/

namespace Bounty
open Std.Sat Std.Tactic.BVDecide.LRAT Std.Tactic.BVDecide.LRAT.Internal

def policySignedHolds (P : Nat → Prop) (z : Int) : Prop :=
  if 0 < z then P z.natAbs else ¬ P z.natAbs

def policySignedClauseHolds (P : Nat → Prop) (c : List Int) : Prop :=
  ∃ z ∈ c, policySignedHolds P z

end Bounty

end PolicySubmissionPart4

/- Component ClosureCircuit; SHA256 9543e2ea042f895ae0affd1cbff0a127734830a60c82caefd6802586b4e7ecdf. -/
section PolicySubmissionPart5
/- Ordinary Tseitin-clause soundness for Boolean gates and typed DAG nodes. -/

namespace ClosureCircuit
open Bounty

inductive Gate where
  | fixedValue : Bool → Gate
  | neg : Nat → Gate
  | disj : List Nat → Gate
  | conj : List Nat → Gate
  | iff : Nat → Nat → Gate
  | alias : Nat → Gate
  | ite : Nat → Nat → Nat → Gate

def Gate.inputs : Gate → List Nat
  | .fixedValue _ => []
  | .neg a | .alias a => [a]
  | .disj xs | .conj xs => xs
  | .iff a b => [a, b]
  | .ite c a b => [c, a, b]

def Gate.eval (B : Nat → Bool) : Gate → Bool
  | .fixedValue b => b
  | .neg a => !B a
  | .disj xs => xs.any B
  | .conj xs => xs.all B
  | .iff a b => B a == B b
  | .alias a => B a
  | .ite c a b => if B c then B a else B b

def Gate.clauses (v : Nat) : Gate → List (List Int)
  | .fixedValue true => [[v]]
  | .fixedValue false => [[-(v : Int)]]
  | .neg a => [[v, a], [-(v : Int), -(a : Int)]]
  | .disj xs => (-(v : Int) :: xs.map (fun (a : Nat) => (a : Int))) ::
      xs.map (fun (a : Nat) => [(v : Int), -(a : Int)])
  | .conj xs => ((v : Int) :: xs.map (fun (a : Nat) => -(a : Int))) ::
      xs.map (fun (a : Nat) => [-(v : Int), (a : Int)])
  | .iff a b => [[-(v : Int), -(a : Int), b], [-(v : Int), a, -(b : Int)],
      [v, a, b], [v, -(a : Int), -(b : Int)]]
  | .alias a => [[-(v : Int), a], [v, -(a : Int)]]
  | .ite c a b => [[-(c : Int), -(a : Int), v], [-(c : Int), a, -(v : Int)],
      [c, -(b : Int), v], [c, b, -(v : Int)]]

def Holds (B : Nat → Bool) (clause : List Int) : Prop :=
  policySignedClauseHolds (fun i => B i = true) clause

def signed_pos (B : Nat → Bool) {a : Nat} (ha : 0 < a) :
    policySignedHolds (fun i => B i = true) (a : Int) ↔ B a = true := by
  simp [policySignedHolds, Nat.ne_of_gt ha]

def signed_neg (B : Nat → Bool) (a : Nat) :
    policySignedHolds (fun i => B i = true) (-(a : Int)) ↔ B a = false := by
  cases hb : B a <;> simp [policySignedHolds, hb]

def holds_nil (B : Nat → Bool) : ¬ Holds B [] := by
  simp [Holds, policySignedClauseHolds]

def holds_cons (B : Nat → Bool) (z : Int) (zs : List Int) :
    Holds B (z :: zs) ↔ policySignedHolds (fun i => B i = true) z ∨ Holds B zs := by
  simp [Holds, policySignedClauseHolds]

def holds_map_pos (B : Nat → Bool) (xs : List Nat)
    (hpos : ∀ a ∈ xs, 0 < a) :
    Holds B (xs.map (fun (a : Nat) => (a : Int))) ↔ ∃ a ∈ xs, B a = true := by
  change (∃ z ∈ xs.map (fun (a : Nat) => (a : Int)),
    policySignedHolds (fun i => B i = true) z) ↔ _
  constructor
  · rintro ⟨z, hz, hv⟩
    obtain ⟨a, ha, rfl⟩ : ∃ a ∈ xs, (a : Int) = z := List.mem_map.mp hz
    exact ⟨a, ha, (signed_pos B (hpos a ha)).mp hv⟩
  · rintro ⟨a, ha, hv⟩
    exact ⟨(a : Int), List.mem_map.mpr ⟨a, ha, rfl⟩, (signed_pos B (hpos a ha)).mpr hv⟩

def holds_map_neg (B : Nat → Bool) (xs : List Nat) :
    Holds B (xs.map (fun (a : Nat) => -(a : Int))) ↔ ∃ a ∈ xs, B a = false := by
  change (∃ z ∈ xs.map (fun (a : Nat) => -(a : Int)),
    policySignedHolds (fun i => B i = true) z) ↔ _
  constructor
  · rintro ⟨z, hz, hv⟩
    obtain ⟨a, ha, rfl⟩ : ∃ a ∈ xs, -(a : Int) = z := List.mem_map.mp hz
    exact ⟨a, ha, (signed_neg B a).mp hv⟩
  · rintro ⟨a, ha, hv⟩
    exact ⟨-(a : Int), List.mem_map.mpr ⟨a, ha, rfl⟩, (signed_neg B a).mpr hv⟩

def gate_clauses_sound (B : Nat → Bool) (g : Gate) (v : Nat)
    (hv : 0 < v) (hp : ∀ a ∈ g.inputs, 0 < a) (he : B v = g.eval B) :
    ∀ clause ∈ g.clauses v, Holds B clause := by
  cases g with
  | fixedValue b =>
    cases b <;> simp [Gate.clauses, Gate.eval, holds_cons, holds_nil, signed_pos B hv,
      signed_neg, he]
  | neg a =>
    have ha : 0 < a := hp a (by simp [Gate.inputs])
    simp only [Gate.clauses, List.mem_cons, List.not_mem_nil, or_false]
    intro clause hc
    rcases hc with rfl | rfl <;>
      simp only [holds_cons, holds_nil, signed_pos B hv, signed_pos B ha, signed_neg,
        or_false] <;>
      cases h1 : B v <;> cases h2 : B a <;> simp_all [Gate.eval]
  | «alias» a =>
    have ha : 0 < a := hp a (by simp [Gate.inputs])
    simp only [Gate.clauses, List.mem_cons, List.not_mem_nil, or_false]
    intro clause hc
    rcases hc with rfl | rfl <;>
      simp only [holds_cons, holds_nil, signed_pos B hv, signed_pos B ha, signed_neg,
        or_false] <;>
      cases h1 : B v <;> cases h2 : B a <;> simp_all [Gate.eval]
  | iff a b =>
    have ha : 0 < a := hp a (by simp [Gate.inputs])
    have hb : 0 < b := hp b (by simp [Gate.inputs])
    simp only [Gate.clauses, List.mem_cons, List.not_mem_nil, or_false]
    intro clause hc
    rcases hc with rfl | rfl | rfl | rfl <;>
      simp only [holds_cons, holds_nil, signed_pos B hv, signed_pos B ha, signed_pos B hb,
        signed_neg, or_false] <;>
      cases h1 : B v <;> cases h2 : B a <;> cases h3 : B b <;> simp_all [Gate.eval]
  | ite c a b =>
    have hc : 0 < c := hp c (by simp [Gate.inputs])
    have ha : 0 < a := hp a (by simp [Gate.inputs])
    have hb : 0 < b := hp b (by simp [Gate.inputs])
    simp only [Gate.clauses, List.mem_cons, List.not_mem_nil, or_false]
    intro clause hcl
    rcases hcl with rfl | rfl | rfl | rfl <;>
      simp only [holds_cons, holds_nil, signed_pos B hv, signed_pos B ha, signed_pos B hb,
        signed_pos B hc, signed_neg, or_false] <;>
      cases h1 : B v <;> cases h2 : B c <;> cases h3 : B a <;> cases h4 : B b <;>
        simp_all [Gate.eval]
  | disj xs =>
    change B v = xs.any B at he
    intro clause hc
    rcases List.mem_cons.mp hc with rfl | hc
    · rw [holds_cons, signed_neg, holds_map_pos B xs hp]
      cases h : B v with
      | false => exact Or.inl rfl
      | true =>
        right
        exact List.any_eq_true.mp (by simpa only [h] using he.symm)
    · obtain ⟨a, ha, rfl⟩ := List.mem_map.mp hc
      simp only [holds_cons, holds_nil, signed_pos B hv, signed_neg, or_false]
      cases h : B a with
      | false => exact Or.inr rfl
      | true =>
        left
        exact he.trans (List.any_eq_true.mpr ⟨a, ha, h⟩)
  | conj xs =>
    change B v = xs.all B at he
    intro clause hc
    rcases List.mem_cons.mp hc with rfl | hc
    · rw [holds_cons, signed_pos B hv, holds_map_neg]
      cases h : B v with
      | true => exact Or.inl rfl
      | false =>
        right
        obtain ⟨a, ha, hn⟩ := List.all_eq_false.mp (by simpa only [h] using he.symm)
        exact ⟨a, ha, by cases hb : B a <;> simp_all⟩
    · obtain ⟨a, ha, rfl⟩ := List.mem_map.mp hc
      simp only [holds_cons, holds_nil, signed_neg, signed_pos B (hp a ha), or_false]
      cases h : B v with
      | false => exact Or.inl rfl
      | true =>
        right
        exact List.all_eq_true.mp (by simpa only [h] using he.symm) a ha

def Gate.toNode : Gate → ClosureSemantics.Node
  | .fixedValue b => ⟨.bConst b, []⟩
  | .neg a => ⟨.bNot, [a]⟩
  | .disj xs => ⟨.bOr, xs⟩
  | .conj xs => ⟨.bAnd, xs⟩
  | .iff a b => ⟨.bEq, [a, b]⟩
  | .alias a => ⟨.alias, [a]⟩
  | .ite c a b => ⟨.ite, [c, a, b]⟩

def evalNode_toNode (input values : ClosureSemantics.Valuation) (g : Gate) :
    (ClosureSemantics.evalNode input values g.toNode).b = g.eval (fun i => (values i).b) := by
  cases g <;>
    simp [Gate.toNode, Gate.eval, ClosureSemantics.evalNode, ClosureSemantics.evalOp,
      ClosureSemantics.boolValue, List.map_map, List.any_map, List.all_map, Function.comp_def]
  split_ifs <;> rfl

def Gate.rename (σ : Nat → Nat) : Gate → Gate
  | .fixedValue b => .fixedValue b
  | .neg a => .neg (σ a)
  | .disj xs => .disj (xs.map σ)
  | .conj xs => .conj (xs.map σ)
  | .iff a b => .iff (σ a) (σ b)
  | .alias a => .alias (σ a)
  | .ite c a b => .ite (σ c) (σ a) (σ b)

def Gate.inputs_rename (σ : Nat → Nat) (g : Gate) :
    (g.rename σ).inputs = g.inputs.map σ := by
  cases g <;> rfl

def Gate.eval_rename (B : Nat → Bool) (σ : Nat → Nat) (g : Gate) :
    (g.rename σ).eval B = g.eval (fun i => B (σ i)) := by
  cases g <;> simp [Gate.rename, Gate.eval, List.any_map, List.all_map, Function.comp_def]

def Gate.eval_congr (g : Gate) (B C : Nat → Bool)
    (h : ∀ i ∈ g.inputs, B i = C i) : g.eval B = g.eval C := by
  cases g with
  | fixedValue b => rfl
  | neg a => simp only [Gate.eval, h a (by simp [Gate.inputs])]
  | «alias» a => exact h a (by simp [Gate.inputs])
  | iff a b =>
    simp only [Gate.eval, h a (by simp [Gate.inputs]), h b (by simp [Gate.inputs])]
  | ite c a b =>
    simp only [Gate.eval, h c (by simp [Gate.inputs]), h a (by simp [Gate.inputs]),
      h b (by simp [Gate.inputs])]
  | disj xs =>
    have hm : xs.map B = xs.map C := List.map_congr_left h
    simpa [Gate.eval, List.any_map] using congrArg (fun l : List Bool => l.any id) hm
  | conj xs =>
    have hm : xs.map B = xs.map C := List.map_congr_left h
    simpa [Gate.eval, List.all_map] using congrArg (fun l : List Bool => l.all id) hm

def node_clauses_sound (input values : ClosureSemantics.Valuation)
    (B : Nat → Bool) (σ : Nat → Nat) (g : Gate) (out : Nat)
    (he : values out = ClosureSemantics.evalNode input values g.toNode)
    (hout : B (σ out) = (values out).b)
    (hinputs : ∀ a ∈ g.inputs, B (σ a) = (values a).b)
    (hpos_out : 0 < σ out) (hpos_inputs : ∀ a ∈ g.inputs, 0 < σ a) :
    ∀ clause ∈ (g.rename σ).clauses (σ out), Holds B clause := by
  apply gate_clauses_sound B (g.rename σ) (σ out) hpos_out
  · intro a ha
    rw [Gate.inputs_rename] at ha
    obtain ⟨j, hj, rfl⟩ := List.mem_map.mp ha
    exact hpos_inputs j hj
  · rw [Gate.eval_rename, hout]
    calc
      (values out).b = (ClosureSemantics.evalNode input values g.toNode).b :=
        congrArg ClosureSemantics.Value.b he
      _ = g.eval (fun i => (values i).b) := evalNode_toNode input values g
      _ = g.eval (fun i => B (σ i)) := (Gate.eval_congr g _ _ hinputs).symm

end ClosureCircuit

end PolicySubmissionPart5

/- Component ClosureCircuitCheck; SHA256 5b2ebec0cdd5335935033a5233c80f9ae3d0d76c440a686f60b381c5ecd6f9c2. -/
section PolicySubmissionPart6
/- Checked membership of actual clauses among a typed node's Tseitin clauses. -/
namespace ClosureCircuit
open ClosureSemantics Bounty

def gateOf : (node : Node) → Option {g : Gate // node = g.toNode}
  | ⟨.bConst b, []⟩ => some ⟨.fixedValue b, rfl⟩
  | ⟨.bNot, [a]⟩ => some ⟨.neg a, rfl⟩
  | ⟨.bOr, xs⟩ => some ⟨.disj xs, rfl⟩
  | ⟨.bAnd, xs⟩ => some ⟨.conj xs, rfl⟩
  | ⟨.bEq, [a, b]⟩ => some ⟨.iff a b, rfl⟩
  | ⟨.alias, [a]⟩ => some ⟨.alias a, rfl⟩
  | ⟨.ite, [c, a, b]⟩ => some ⟨.ite c a b, rfl⟩
  | _ => none

def clauseSubset (source target : List Int) : Bool :=
  source.all (fun lit => decide (lit ∈ target))

def clauseSubset_sound (P : Nat → Prop) (source target : List Int)
    (hc : clauseSubset source target = true) (hs : policySignedClauseHolds P source) :
    policySignedClauseHolds P target := by
  obtain ⟨lit, hlit, hv⟩ := hs
  have hm : ∀ z ∈ source, z ∈ target := by simpa [clauseSubset] using hc
  exact ⟨lit, hm lit hlit, hv⟩

def checkGateClause (program : Nat → Node) (out : Nat) (clause : List Int) : Bool :=
  match gateOf (program out) with
  | none => false
  | some g => ((g.val.rename Nat.succ).clauses (out + 1)).any (fun c => clauseSubset c clause)

def checkGateClause_sound (program : Nat → Node) (input values : Valuation)
    (he : Equations program input values) (out : Nat) (clause : List Int)
    (hc : checkGateClause program out clause = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) clause := by
  cases hg : gateOf (program out) with
  | none => simp [checkGateClause, hg] at hc
  | some g =>
    have hmem : ∃ c ∈ (g.val.rename Nat.succ).clauses (out + 1), clauseSubset c clause = true := by
      simpa only [checkGateClause, hg, List.any_eq_true] using hc
    obtain ⟨c, hcm, hsub⟩ := hmem
    apply clauseSubset_sound _ c clause hsub
    apply node_clauses_sound input values (fun v => (values (v - 1)).b) Nat.succ g.val out
      _ _ _ (Nat.succ_pos _) (fun _ _ => Nat.succ_pos _) c hcm
    · rw [← g.property]
      exact he out
    · simp
    · intro a ha
      simp

def checkCircuitEntry (program : Nat → Node) (clauses : Nat → List Int) : List Nat → Bool
  | [clauseId, out] => checkGateClause program out (clauses clauseId)
  | _ => false

def checkCircuitEntry_sound (program : Nat → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : Nat → List Int)
    (entry : List Nat) (hc : checkCircuitEntry program clauses entry = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) (clauses (entry.headD 0)) := by
  cases entry with
  | nil => simp [checkCircuitEntry] at hc
  | cons clauseId rest =>
    cases rest with
    | nil => simp [checkCircuitEntry] at hc
    | cons out tail =>
      cases tail with
      | cons a as => simp [checkCircuitEntry] at hc
      | nil => exact checkGateClause_sound program input values he out (clauses clauseId) hc

end ClosureCircuit

end PolicySubmissionPart6

/- Component ClosureCircuitBlock; SHA256 8ce5aaa2c9bc1a33c0ca7f1c101abea44ce96741ee35c3b4e773cc7c8ddf0f83. -/
section PolicySubmissionPart7
namespace ClosureCircuit
open ClosureSemantics Bounty

def checkCircuitBlock (program : ℕ → Node) (clauses : ℕ → List ℤ)
    (records : ℕ → List ℕ) (start count : ℕ) : Bool :=
  (List.range count).all fun i => checkCircuitEntry program clauses (records (start + i))

def checkCircuitBlock_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : ℕ → List ℤ) (records : ℕ → List ℕ)
    (start count : ℕ) (hc : checkCircuitBlock program clauses records start count = true)
    (i : ℕ) (hi : i < count) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (clauses ((records (start + i)).headD 0)) := by
  have h : ∀ j ∈ List.range count,
      checkCircuitEntry program clauses (records (start + j)) = true := by
    simpa only [checkCircuitBlock, List.all_eq_true] using hc
  exact checkCircuitEntry_sound program input values he clauses (records (start + i))
    (h i (List.mem_range.mpr hi))

end ClosureCircuit

end PolicySubmissionPart7

/- Component PolicyLinearCertificate; SHA256 cf77a260405b54f95bd0f1310c3ffdf7b90b25d5e0e8eb394123a4f5a147618d. -/
section PolicySubmissionPart8
/- A sparse affine linear certificate checker, with ordinary kernel soundness. -/

namespace ClosureLinear

abbrev Coefficients := List (ℕ × ℚ)

def evalCoefficients (x : ℕ → ℚ) : Coefficients → ℚ
  | [] => 0
  | (i, q) :: xs => q * x i + evalCoefficients x xs

def insertCoefficient (a : ℕ × ℚ) : Coefficients → Coefficients
  | [] => [a]
  | b :: bs =>
    if a.1 = b.1 then (a.1, a.2 + b.2) :: bs
    else b :: insertCoefficient a bs

def addCoefficients : Coefficients → Coefficients → Coefficients
  | [], ys => ys
  | a :: xs, ys => insertCoefficient a (addCoefficients xs ys)

def scaleCoefficients (q : ℚ) (xs : Coefficients) : Coefficients :=
  xs.map fun a => (a.1, q * a.2)

def eval_insertCoefficient (x : ℕ → ℚ) (a : ℕ × ℚ) (xs : Coefficients) :
    evalCoefficients x (insertCoefficient a xs) = a.2 * x a.1 + evalCoefficients x xs := by
  induction xs with
  | nil => simp [insertCoefficient, evalCoefficients]
  | cons b bs ih =>
    simp only [insertCoefficient]
    split_ifs with h
    · simp only [evalCoefficients, h]
      ring
    · simp only [evalCoefficients, ih]
      ring

def eval_addCoefficients (x : ℕ → ℚ) (xs ys : Coefficients) :
    evalCoefficients x (addCoefficients xs ys) = evalCoefficients x xs + evalCoefficients x ys := by
  induction xs with
  | nil => simp [addCoefficients, evalCoefficients]
  | cons a xs ih =>
    simp only [addCoefficients, eval_insertCoefficient, ih, evalCoefficients]
    ring

def eval_scaleCoefficients (x : ℕ → ℚ) (q : ℚ) (xs : Coefficients) :
    evalCoefficients x (scaleCoefficients q xs) = q * evalCoefficients x xs := by
  induction xs with
  | nil => simp [scaleCoefficients, evalCoefficients]
  | cons a xs ih =>
    simp only [scaleCoefficients, List.map_cons, evalCoefficients] at *
    rw [ih]
    ring

structure Affine where
  coefficients : Coefficients
  fixedValue : ℚ

def Affine.eval (f : Affine) (x : ℕ → ℚ) : ℚ :=
  f.fixedValue + evalCoefficients x f.coefficients

def Affine.zero : Affine := ⟨[], 0⟩

def Affine.add (f g : Affine) : Affine :=
  ⟨addCoefficients f.coefficients g.coefficients, f.fixedValue + g.fixedValue⟩

def Affine.scale (q : ℚ) (f : Affine) : Affine :=
  ⟨scaleCoefficients q f.coefficients, q * f.fixedValue⟩

def Affine.eval_zero (x : ℕ → ℚ) : Affine.zero.eval x = 0 := by
  simp [Affine.zero, Affine.eval, evalCoefficients]

def Affine.eval_add (f g : Affine) (x : ℕ → ℚ) :
    (f.add g).eval x = f.eval x + g.eval x := by
  simp only [Affine.add, Affine.eval, eval_addCoefficients]
  ring

def Affine.eval_scale (q : ℚ) (f : Affine) (x : ℕ → ℚ) :
    (f.scale q).eval x = q * f.eval x := by
  simp only [Affine.scale, Affine.eval, eval_scaleCoefficients]
  ring

structure Row where
  form : Affine
  strict : Bool

def Row.Holds (r : Row) (x : ℕ → ℚ) : Prop :=
  if r.strict then 0 < r.form.eval x else 0 ≤ r.form.eval x

def Row.nonneg (r : Row) (x : ℕ → ℚ) (h : r.Holds x) : 0 ≤ r.form.eval x := by
  cases hs : r.strict <;> simp [Row.Holds, hs] at h
  · exact h
  · exact le_of_lt h

def weightedSum : List (ℕ × Row) → Affine
  | [] => Affine.zero
  | (w, r) :: xs => (r.form.scale w).add (weightedSum xs)

def hasStrict (xs : List (ℕ × Row)) : Bool :=
  xs.any fun a => decide (0 < a.1) && a.2.strict

def weightedSum_nonneg (xs : List (ℕ × Row)) (x : ℕ → ℚ)
    (h : ∀ a ∈ xs, a.2.Holds x) : 0 ≤ (weightedSum xs).eval x := by
  induction xs with
  | nil => simp [weightedSum, Affine.eval_zero]
  | cons a xs ih =>
    have ha := (a.2.nonneg x (h a (List.mem_cons_self ..)))
    have hr := ih (fun b hb => h b (List.mem_cons_of_mem _ hb))
    simpa [weightedSum, Affine.eval_add, Affine.eval_scale] using
      add_nonneg (mul_nonneg (Nat.cast_nonneg a.1) ha) hr

def weightedSum_pos (xs : List (ℕ × Row)) (x : ℕ → ℚ)
    (h : ∀ a ∈ xs, a.2.Holds x) (hs : hasStrict xs = true) :
    0 < (weightedSum xs).eval x := by
  induction xs with
  | nil => simp [hasStrict] at hs
  | cons a xs ih =>
    have ha := h a (List.mem_cons_self ..)
    have hr : ∀ b ∈ xs, b.2.Holds x := fun b hb => h b (List.mem_cons_of_mem _ hb)
    have split : (0 < a.1 ∧ a.2.strict = true) ∨ hasStrict xs = true := by
      simpa [hasStrict, Bool.or_eq_true, Bool.and_eq_true] using hs
    rcases split with hfirst | hrest
    · have hp : 0 < a.2.form.eval x := by simpa [Row.Holds, hfirst.2] using ha
      have hw : (0 : ℚ) < a.1 := by exact_mod_cast hfirst.1
      simpa [weightedSum, Affine.eval_add, Affine.eval_scale] using
        add_pos_of_pos_of_nonneg (mul_pos hw hp) (weightedSum_nonneg xs x hr)
    · have hp := ih hr hrest
      simpa [weightedSum, Affine.eval_add, Affine.eval_scale] using
        add_pos_of_nonneg_of_pos (mul_nonneg (Nat.cast_nonneg a.1) (a.2.nonneg x ha)) hp

def zeroCoefficients (xs : Coefficients) : Bool :=
  xs.all fun a => decide (a.2 = 0)

def evalCoefficients_eq_zero (x : ℕ → ℚ) (xs : Coefficients)
    (h : zeroCoefficients xs = true) : evalCoefficients x xs = 0 := by
  induction xs with
  | nil => rfl
  | cons a xs ih =>
    have hh : a.2 = 0 ∧ zeroCoefficients xs = true := by
      simpa [zeroCoefficients, Bool.and_eq_true] using h
    simp [evalCoefficients, hh.1, ih hh.2]

def check (xs : List (ℕ × Row)) : Bool :=
  let total := weightedSum xs
  zeroCoefficients total.coefficients && decide (total.fixedValue ≤ 0) &&
    (decide (total.fixedValue < 0) || hasStrict xs)

def check_sound (xs : List (ℕ × Row)) (x : ℕ → ℚ)
    (h : ∀ a ∈ xs, a.2.Holds x) (hc : check xs = true) : False := by
  have hparts : (zeroCoefficients (weightedSum xs).coefficients = true ∧
      (weightedSum xs).fixedValue ≤ 0) ∧
      ((weightedSum xs).fixedValue < 0 ∨ hasStrict xs = true) := by
    simpa [check, Bool.and_eq_true, Bool.or_eq_true] using hc
  have heval : (weightedSum xs).eval x = (weightedSum xs).fixedValue := by
    simp [Affine.eval, evalCoefficients_eq_zero x _ hparts.1.1]
  rcases hparts.2 with hnegative | hstrict
  · have hn := weightedSum_nonneg xs x h
    rw [heval] at hn
    exact (not_lt_of_ge hn) hnegative
  · have hp := weightedSum_pos xs x h hstrict
    rw [heval] at hp
    exact (not_lt_of_ge hparts.1.2) hp

end ClosureLinear

end PolicySubmissionPart8

/- Component PolicyLinearNormalization; SHA256 178c2708a3e3cf82eaa9b66fe146cea89e82a9599bee362a6d8c010f14b5c387. -/
section PolicySubmissionPart9
/- Verified arithmetic normalization used by reflected linear certificates. -/

namespace ClosureLinear
open ClosureSemantics

def Affine.const (q : ℚ) : Affine := ⟨[], q⟩
def Affine.variable (i : ℕ) : Affine := ⟨[(i, 1)], 0⟩
def Affine.neg (f : Affine) : Affine := f.scale (-1)
def Affine.sub (f g : Affine) : Affine := f.add g.neg

def Affine.eval_const (q : ℚ) (x : ℕ → ℚ) : (Affine.const q).eval x = q := by
  simp [Affine.const, Affine.eval, evalCoefficients]

def Affine.eval_variable (i : ℕ) (x : ℕ → ℚ) : (Affine.variable i).eval x = x i := by
  simp [Affine.variable, Affine.eval, evalCoefficients]

def Affine.eval_neg (f : Affine) (x : ℕ → ℚ) : f.neg.eval x = -f.eval x := by
  simp [Affine.neg, Affine.eval_scale]

def Affine.eval_sub (f g : Affine) (x : ℕ → ℚ) : (f.sub g).eval x = f.eval x - g.eval x := by
  simp [Affine.sub, Affine.eval_add, Affine.eval_neg, sub_eq_add_neg]

def Affine.eval_of_zeroCoefficients (f : Affine) (x : ℕ → ℚ)
    (h : zeroCoefficients f.coefficients = true) : f.eval x = f.fixedValue := by
  simp [Affine.eval, evalCoefficients_eq_zero x _ h]

def Affine.mul? (f g : Affine) : Option Affine :=
  if zeroCoefficients f.coefficients then some (g.scale f.fixedValue)
  else if zeroCoefficients g.coefficients then some (f.scale g.fixedValue)
  else none

def Affine.div? (f g : Affine) : Option Affine :=
  if zeroCoefficients g.coefficients then some (f.scale g.fixedValue⁻¹) else none

def Affine.mul?_sound (f g out : Affine) (x : ℕ → ℚ) (h : f.mul? g = some out) :
    out.eval x = f.eval x * g.eval x := by
  unfold Affine.mul? at h
  split_ifs at h with hf hg
  · cases h
    rw [Affine.eval_scale, Affine.eval_of_zeroCoefficients f x hf]
  · cases h
    rw [Affine.eval_scale, Affine.eval_of_zeroCoefficients g x hg]
    ring

def Affine.div?_sound (f g out : Affine) (x : ℕ → ℚ) (h : f.div? g = some out) :
    out.eval x = f.eval x / g.eval x := by
  unfold Affine.div? at h
  split_ifs at h with hg
  · cases h
    rw [Affine.eval_scale, Affine.eval_of_zeroCoefficients g x hg]
    simp [div_eq_mul_inv, mul_comm]

def foldAdd (f : Affine) : List Affine → Affine
  | [] => f
  | g :: gs => foldAdd (f.add g) gs

def foldSub (f : Affine) : List Affine → Affine
  | [] => f
  | g :: gs => foldSub (f.sub g) gs

def foldMul (f : Affine) : List Affine → Option Affine
  | [] => some f
  | g :: gs => do
    let product ← f.mul? g
    foldMul product gs

def eval_foldAdd (f : Affine) (fs : List Affine) (x : ℕ → ℚ) :
    (foldAdd f fs).eval x = (fs.map (fun g => g.eval x)).foldl (· + ·) (f.eval x) := by
  induction fs generalizing f with
  | nil => rfl
  | cons g gs ih => simp [foldAdd, ih, Affine.eval_add]

def eval_foldSub (f : Affine) (fs : List Affine) (x : ℕ → ℚ) :
    (foldSub f fs).eval x = (fs.map (fun g => g.eval x)).foldl (· - ·) (f.eval x) := by
  induction fs generalizing f with
  | nil => rfl
  | cons g gs ih => simp [foldSub, ih, Affine.eval_sub]

def eval_foldMul (f out : Affine) (fs : List Affine) (x : ℕ → ℚ)
    (h : foldMul f fs = some out) :
    out.eval x = (fs.map (fun g => g.eval x)).foldl (· * ·) (f.eval x) := by
  induction fs generalizing f with
  | nil => simpa [foldMul] using (congrArg (fun a => a.map (fun g => g.eval x)) h).symm
  | cons g gs ih =>
    cases hm : f.mul? g with
    | none => simp [foldMul, hm] at h
    | some product =>
      have hr : foldMul product gs = some out := by simpa [foldMul, hm] using h
      rw [ih product hr]
      simp [Affine.mul?_sound f g product x hm]

def normalizeOp : Op → List Affine → Option Affine
  | .qConst q, _ => some (Affine.const q)
  | .zConst z, _ => some (Affine.const z)
  | .qAdd, [] | .zAdd, [] => some (Affine.const 0)
  | .qMul, [] | .zMul, [] => some (Affine.const 1)
  | .qAdd, f :: fs | .zAdd, f :: fs => some (foldAdd f fs)
  | .qSub, f :: fs | .zSub, f :: fs => some (foldSub f fs)
  | .qMul, f :: fs | .zMul, f :: fs => foldMul f fs
  | .qNeg, [f] | .zNeg, [f] => some f.neg
  | .qDiv, [f, g] => f.div? g
  | _, _ => none

def evalNumbers : Op → List ℚ → Option ℚ
  | .qConst q, _ => some q
  | .zConst z, _ => some z
  | .qAdd, [] | .zAdd, [] => some 0
  | .qMul, [] | .zMul, [] => some 1
  | .qAdd, q :: qs | .zAdd, q :: qs => some (qs.foldl (· + ·) q)
  | .qSub, q :: qs | .zSub, q :: qs => some (qs.foldl (· - ·) q)
  | .qMul, q :: qs | .zMul, q :: qs => some (qs.foldl (· * ·) q)
  | .qNeg, [q] | .zNeg, [q] => some (-q)
  | .qDiv, [q, r] => some (q / r)
  | _, _ => none

def normalizeOp_sound (op : Op) (fs : List Affine) (out : Affine) (x : ℕ → ℚ)
    (h : normalizeOp op fs = some out) :
    evalNumbers op (fs.map fun f => f.eval x) = some (out.eval x) := by
  fun_cases normalizeOp op fs <;>
    simp only [normalizeOp, evalNumbers, List.map_nil, List.map_cons, Option.some.injEq] at h ⊢
  all_goals first
    | (cases h <;> simp [Affine.eval_const, Affine.eval_neg, eval_foldAdd, eval_foldSub])
    | exact (eval_foldMul _ _ _ x h).symm
    | exact (Affine.div?_sound _ _ _ x h).symm

def rationalOp : Op → Bool
  | .qConst _ | .qAdd | .qSub | .qMul | .qNeg | .qDiv => true
  | _ => false

def integerOp : Op → Bool
  | .zConst _ | .zAdd | .zSub | .zMul | .zNeg => true
  | _ => false

def intCast_foldl_add (xs : List ℤ) (a : ℤ) :
    ((xs.foldl (· + ·) a : ℤ) : ℚ) =
      (xs.map fun z => (z : ℚ)).foldl (· + ·) (a : ℚ) := by
  induction xs generalizing a with
  | nil => rfl
  | cons z zs ih => simpa using ih (a + z)

def intCast_foldl_sub (xs : List ℤ) (a : ℤ) :
    ((xs.foldl (· - ·) a : ℤ) : ℚ) =
      (xs.map fun z => (z : ℚ)).foldl (· - ·) (a : ℚ) := by
  induction xs generalizing a with
  | nil => rfl
  | cons z zs ih => simpa using ih (a - z)

def intCast_foldl_mul (xs : List ℤ) (a : ℤ) :
    ((xs.foldl (· * ·) a : ℤ) : ℚ) =
      (xs.map fun z => (z : ℚ)).foldl (· * ·) (a : ℚ) := by
  induction xs generalizing a with
  | nil => rfl
  | cons z zs ih => simpa using ih (a * z)

def evalNumbers_rational (input : Valuation) (op : Op) (vs : List Value) (q : ℚ)
    (ho : rationalOp op = true) (h : evalNumbers op (vs.map Value.q) = some q) :
    (evalOp input op vs).q = q := by
  fun_cases evalOp input op vs <;>
    simp_all [rationalOp, evalOp, evalNumbers, ratValue, zeroValue]
  cases op <;> simp_all [rationalOp]
  all_goals cases vs with
    | nil => simp_all [evalNumbers]
    | cons a rest =>
      cases rest with
      | nil => simp_all [evalNumbers]
      | cons b tail => cases tail <;> simp_all [evalNumbers]

def evalNumbers_integer (input : Valuation) (op : Op) (vs : List Value) (q : ℚ)
    (ho : integerOp op = true)
    (h : evalNumbers op (vs.map fun v => (v.z : ℚ)) = some q) :
    ((evalOp input op vs).z : ℚ) = q := by
  fun_cases evalOp input op vs <;>
    simp_all [integerOp, evalOp, evalNumbers, intValue, zeroValue,
      intCast_foldl_add, intCast_foldl_sub, intCast_foldl_mul, List.map_map]
  all_goals first
    | (rw [List.flatMap_map, ← List.map_eq_flatMap]; exact h)
    | skip
  cases op <;> simp_all [integerOp]
  all_goals cases vs with
    | nil => simp_all [evalNumbers]
    | cons a rest =>
      cases rest with
      | nil => simp_all [evalNumbers]
      | cons b tail => cases tail <;> simp_all [evalNumbers]

def normalizeOp_rational_sound (input : Valuation) (op : Op)
    (fs : List Affine) (vs : List Value) (out : Affine) (x : ℕ → ℚ)
    (hvals : fs.map (fun f => f.eval x) = vs.map Value.q)
    (ho : rationalOp op = true) (h : normalizeOp op fs = some out) :
    out.eval x = (evalOp input op vs).q := by
  have hn := normalizeOp_sound op fs out x h
  rw [hvals] at hn
  exact (evalNumbers_rational input op vs _ ho hn).symm

def normalizeOp_integer_sound (input : Valuation) (op : Op)
    (fs : List Affine) (vs : List Value) (out : Affine) (x : ℕ → ℚ)
    (hvals : fs.map (fun f => f.eval x) = vs.map fun v => (v.z : ℚ))
    (ho : integerOp op = true) (h : normalizeOp op fs = some out) :
    out.eval x = ((evalOp input op vs).z : ℚ) := by
  have hn := normalizeOp_sound op fs out x h
  rw [hvals] at hn
  exact (evalNumbers_integer input op vs _ ho hn).symm

end ClosureLinear

end PolicySubmissionPart9

/- Component PolicyLinearDAG; SHA256 1f375409245a24265a43b10cca7e09610d1b0626a446f54083e3cdc44b8e343a. -/
section PolicySubmissionPart10
/- Checked affine normalization of finite arithmetic fragments of an expression DAG. -/
namespace ClosureLinear
open ClosureSemantics

def collect {α β : Type} (f : α → Option β) : List α → Option (List β)
  | [] => some []
  | a :: as => do
    let b ← f a
    let bs ← collect f as
    pure (b :: bs)

def collect_sound {α β γ : Type} (f : α → Option β) (g : β → γ) (e : α → γ)
    (h : ∀ a b, f a = some b → g b = e a) (as : List α) (bs : List β)
    (hc : collect f as = some bs) : bs.map g = as.map e := by
  induction as generalizing bs with
  | nil => simpa [collect] using hc.symm
  | cons a as ih =>
    cases ha : f a with
    | none => simp [collect, ha] at hc
    | some b =>
      cases hr : collect f as with
      | none => simp [collect, ha, hr] at hc
      | some rest =>
        have hb : b :: rest = bs := by simpa [collect, ha, hr] using hc
        subst bs
        simp only [List.map_cons, h a b ha, ih rest hr]

def closedOp : Op → Bool
  | .input _ => false
  | _ => true

def evalOp_closed (op : Op) (vs : List Value) (input : Valuation)
    (h : closedOp op = true) :
    evalOp (fun _ => zeroValue) op vs = evalOp input op vs := by
  cases op <;> simp_all [closedOp]
  all_goals cases vs with
    | nil => rfl
    | cons a rest =>
      cases rest with
      | nil => rfl
      | cons b tail =>
        cases tail with
        | nil => rfl
        | cons c more => cases more <;> rfl

def closedNode (program : ℕ → Node) : ℕ → ℕ → Option Value
  | 0, _ => none
  | fuel + 1, i =>
    if closedOp (program i).op then do
      let children ← collect (closedNode program fuel) (program i).children
      pure (evalOp (fun _ => zeroValue) (program i).op children)
    else none

def closedNode_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (fuel i : ℕ) (v : Value)
    (h : closedNode program fuel i = some v) : v = values i := by
  induction fuel generalizing i v with
  | zero => simp [closedNode] at h
  | succ fuel ih =>
    simp only [closedNode] at h
    split at h
    next hop =>
      cases hc : collect (closedNode program fuel) (program i).children with
      | none => simp [hc] at h
      | some children =>
        have hv : evalOp (fun _ => zeroValue) (program i).op children = v := by
          simpa [hc] using h
        subst v
        have hchildren := collect_sound (closedNode program fuel) id values
          (fun j w hw => ih j w hw) _ children hc
        simp only [List.map_id_fun, id_eq] at hchildren
        rw [hchildren, evalOp_closed _ _ input hop, he i]
        rfl
    next => simp_all

def numericValue (integer : Bool) (v : Value) : ℚ :=
  if integer then (v.z : ℚ) else v.q

def numericOp (integer : Bool) (op : Op) : Bool :=
  if integer then integerOp op else rationalOp op

def normalizeOp_numeric_sound (integer : Bool) (input : Valuation) (op : Op)
    (fs : List Affine) (vs : List Value) (out : Affine) (x : ℕ → ℚ)
    (hvals : fs.map (fun f => f.eval x) = vs.map (numericValue integer))
    (ho : numericOp integer op = true) (h : normalizeOp op fs = some out) :
    out.eval x = numericValue integer (evalOp input op vs) := by
  cases integer with
  | false => exact normalizeOp_rational_sound input op fs vs out x hvals ho h
  | true => exact normalizeOp_integer_sound input op fs vs out x hvals ho h

def normalizeTerm (program : ℕ → Node) (cut : ℕ → Option ℕ) (integer : Bool) :
    ℕ → ℕ → Option Affine
  | 0, _ => none
  | fuel + 1, i =>
    match cut i with
    | some j => some (Affine.variable j)
    | none =>
      if numericOp integer (program i).op then do
        let fs ← collect (normalizeTerm program cut integer fuel) (program i).children
        normalizeOp (program i).op fs
      else do
        let v ← closedNode program (fuel + 1) i
        pure (Affine.const (numericValue integer v))

def normalizeTerm_sound (program : ℕ → Node) (cut : ℕ → Option ℕ)
    (integer : Bool) (input values : Valuation) (x : ℕ → ℚ)
    (he : Equations program input values)
    (hcut : ∀ i j, cut i = some j → x j = numericValue integer (values i))
    (fuel i : ℕ) (out : Affine)
    (h : normalizeTerm program cut integer fuel i = some out) :
    out.eval x = numericValue integer (values i) := by
  induction fuel generalizing i out with
  | zero => simp [normalizeTerm] at h
  | succ fuel ih =>
    cases hc : cut i with
    | some j =>
      have hout : Affine.variable j = out := by simpa [normalizeTerm, hc] using h
      subst out
      exact (Affine.eval_variable j x).trans (hcut i j hc)
    | none =>
      simp only [normalizeTerm, hc] at h
      split at h
      next hop =>
        cases hfs : collect (normalizeTerm program cut integer fuel) (program i).children with
        | none => simp [hfs] at h
        | some fs =>
          have hn : normalizeOp (program i).op fs = some out := by simpa [hfs] using h
          have hchildren := collect_sound (normalizeTerm program cut integer fuel)
            (fun f => f.eval x) (fun j => numericValue integer (values j))
            (fun j f hf => ih j f hf) _ fs hfs
          have hv : fs.map (fun f => f.eval x) =
              ((program i).children.map values).map (numericValue integer) := by
            simpa only [List.map_map, Function.comp_def] using hchildren
          rw [he i]
          exact normalizeOp_numeric_sound integer input (program i).op fs
            ((program i).children.map values) out x hv hop hn
      next =>
        cases hv : closedNode program (fuel + 1) i with
        | none => simp [hv] at h
        | some v =>
          have hout : Affine.const (numericValue integer v) = out := by simpa [hv] using h
          subst out
          rw [Affine.eval_const, closedNode_sound program input values he _ i v hv]

end ClosureLinear

end PolicySubmissionPart10

/- Component PolicyLinearAtoms; SHA256 3c7cf73f4f3438eb44bfe2443706923a599b27209e7a39ea406262cfc30ab545. -/
section PolicySubmissionPart11
/- Sound conversion of rational and integer comparisons into affine inequalities. -/
namespace ClosureLinear
open ClosureSemantics

abbrev Branches := List (List Row)

def Branches.Holds (bs : Branches) (x : ℕ → ℚ) : Prop :=
  ∃ rows ∈ bs, ∀ r ∈ rows, r.Holds x

def makeRow (integer strict : Bool) (f : Affine) : Row :=
  if integer && strict then ⟨f.sub (Affine.const 1), false⟩ else ⟨f, strict⟩

def makeRow_sound (integer strict : Bool) (f : Affine) (x : ℕ → ℚ)
    (hi : integer = true → ∃ z : ℤ, f.eval x = z)
    (h : if strict then 0 < f.eval x else 0 ≤ f.eval x) :
    (makeRow integer strict f).Holds x := by
  cases integer with
  | false => exact h
  | true =>
    cases strict with
    | false => exact h
    | true =>
      obtain ⟨z, hz⟩ := hi rfl
      have hpos : (0 : ℚ) < z := by simpa [hz] using h
      have hzpos : 0 < z := by exact_mod_cast hpos
      have hone : (1 : ℚ) ≤ z := by exact_mod_cast (show (1 : ℤ) ≤ z by omega)
      simpa [makeRow, Row.Holds, Affine.eval_sub, Affine.eval_const, hz] using sub_nonneg.mpr hone

inductive Comparison where
  | eq | le | lt

def Comparison.eval : Comparison → ℚ → ℚ → Bool
  | .eq, a, b => decide (a = b)
  | .le, a, b => decide (a ≤ b)
  | .lt, a, b => decide (a < b)

def atomBranches (integer : Bool) : Comparison → Bool → Affine → Affine → Branches
  | .eq, true, f, g => [[makeRow integer false (f.sub g), makeRow integer false (g.sub f)]]
  | .eq, false, f, g => [[makeRow integer true (f.sub g)], [makeRow integer true (g.sub f)]]
  | .le, true, f, g => [[makeRow integer false (g.sub f)]]
  | .le, false, f, g => [[makeRow integer true (f.sub g)]]
  | .lt, true, f, g => [[makeRow integer true (g.sub f)]]
  | .lt, false, f, g => [[makeRow integer false (f.sub g)]]

def atomBranches_sound (integer : Bool) (cmp : Comparison) (positive : Bool)
    (f g : Affine) (x : ℕ → ℚ)
    (hi : integer = true → (∃ a : ℤ, f.eval x = a) ∧ (∃ b : ℤ, g.eval x = b))
    (h : cmp.eval (f.eval x) (g.eval x) = positive) :
    (atomBranches integer cmp positive f g).Holds x := by
  have hfg : integer = true → ∃ z : ℤ, (f.sub g).eval x = z := by
    intro he
    obtain ⟨⟨a, ha⟩, ⟨b, hb⟩⟩ := hi he
    exact ⟨a - b, by simp [Affine.eval_sub, ha, hb]⟩
  have hgf : integer = true → ∃ z : ℤ, (g.sub f).eval x = z := by
    intro he
    obtain ⟨⟨a, ha⟩, ⟨b, hb⟩⟩ := hi he
    exact ⟨b - a, by simp [Affine.eval_sub, ha, hb]⟩
  cases cmp <;> cases positive <;>
    simp only [Comparison.eval, decide_eq_true_eq, decide_eq_false_iff_not] at h <;>
    simp only [atomBranches, Branches.Holds, List.mem_cons, List.not_mem_nil,
      or_false, exists_eq_or_imp, exists_eq_left, forall_eq_or_imp, forall_eq] at ⊢
  · rcases lt_or_gt_of_ne h with hlt | hgt
    · right
      exact makeRow_sound integer true (g.sub f) x hgf (by simpa [Affine.eval_sub] using sub_pos.mpr hlt)
    · left
      exact makeRow_sound integer true (f.sub g) x hfg (by simpa [Affine.eval_sub] using sub_pos.mpr hgt)
  · constructor
    · exact makeRow_sound integer false (f.sub g) x hfg (by simp [Affine.eval_sub, h])
    · exact makeRow_sound integer false (g.sub f) x hgf (by simp [Affine.eval_sub, h])
  · exact makeRow_sound integer true (f.sub g) x hfg
      (by simpa [Affine.eval_sub] using sub_pos.mpr (lt_of_not_ge h))
  · exact makeRow_sound integer false (g.sub f) x hgf
      (by simpa [Affine.eval_sub] using sub_nonneg.mpr h)
  · exact makeRow_sound integer false (f.sub g) x hfg
      (by simpa [Affine.eval_sub] using sub_nonneg.mpr (le_of_not_gt h))
  · exact makeRow_sound integer true (g.sub f) x hgf
      (by simpa [Affine.eval_sub] using sub_pos.mpr h)

def comparisonOp (integer : Bool) (cmp : Comparison) : Op :=
  match integer, cmp with
  | false, .eq => .qEq
  | false, .le => .qLe
  | false, .lt => .qLt
  | true, .eq => .zEq
  | true, .le => .zLe
  | true, .lt => .zLt

def comparisonOp_eval (integer : Bool) (cmp : Comparison) (input : Valuation)
    (a b : Value) :
    (evalOp input (comparisonOp integer cmp) [a, b]).b =
      cmp.eval (numericValue integer a) (numericValue integer b) := by
  cases integer <;> cases cmp <;>
    simp [comparisonOp, evalOp, boolValue, Comparison.eval, numericValue]

def atomBranches_values (integer : Bool) (cmp : Comparison) (positive : Bool)
    (f g : Affine) (x : ℕ → ℚ) (input : Valuation) (a b : Value)
    (hf : f.eval x = numericValue integer a) (hg : g.eval x = numericValue integer b)
    (h : (evalOp input (comparisonOp integer cmp) [a, b]).b = positive) :
    (atomBranches integer cmp positive f g).Holds x := by
  apply atomBranches_sound integer cmp positive f g x
  · intro hi
    subst integer
    exact ⟨⟨a.z, hf⟩, ⟨b.z, hg⟩⟩
  · rw [hf, hg]
    exact (comparisonOp_eval integer cmp input a b).symm.trans h

end ClosureLinear

end PolicySubmissionPart11

/- Component PolicyLinearBranches; SHA256 4c96643afb5a2de47b6c62823b8a60cfa81b6365fef5a092b748b42281c94e60. -/
section PolicySubmissionPart12
/- Boolean branch operations used in checked linear sequents. -/
namespace ClosureLinear

def collect_members {α β : Type} (f : α → Option β) (as : List α) (bs : List β)
    (hc : collect f as = some bs) :
    (∀ a ∈ as, ∃ b ∈ bs, f a = some b) ∧
      (∀ b ∈ bs, ∃ a ∈ as, f a = some b) := by
  induction as generalizing bs with
  | nil =>
    have hb : bs = [] := by simpa [collect] using hc.symm
    subst bs
    simp
  | cons a as ih =>
    cases ha : f a with
    | none => simp [collect, ha] at hc
    | some b =>
      cases hr : collect f as with
      | none => simp [collect, ha, hr] at hc
      | some rest =>
        have hb : b :: rest = bs := by simpa [collect, ha, hr] using hc
        subst bs
        obtain ⟨hin, hout⟩ := ih rest hr
        constructor
        · intro c hm
          rcases List.mem_cons.mp hm with rfl | hm
          · exact ⟨b, List.mem_cons_self .., ha⟩
          · obtain ⟨d, hd, hfd⟩ := hin c hm
            exact ⟨d, List.mem_cons_of_mem _ hd, hfd⟩
        · intro d hm
          rcases List.mem_cons.mp hm with rfl | hm
          · exact ⟨a, List.mem_cons_self .., ha⟩
          · obtain ⟨c, hc, hfc⟩ := hout d hm
            exact ⟨c, List.mem_cons_of_mem _ hc, hfc⟩

def crossBranches (a b : Branches) : Branches :=
  a.flatMap fun xs => b.map fun ys => xs ++ ys

def crossBranches_sound (a b : Branches) (x : ℕ → ℚ)
    (ha : a.Holds x) (hb : b.Holds x) : (crossBranches a b).Holds x := by
  obtain ⟨xs, hxs, hx⟩ := ha
  obtain ⟨ys, hys, hy⟩ := hb
  refine ⟨xs ++ ys, ?_, ?_⟩
  · exact List.mem_flatMap.mpr ⟨xs, hxs, List.mem_map.mpr ⟨ys, hys, rfl⟩⟩
  · intro r hr
    rcases List.mem_append.mp hr with hr | hr
    · exact hx r hr
    · exact hy r hr

def allBranches : List Branches → Branches
  | [] => [[]]
  | bs :: rest => crossBranches bs (allBranches rest)

def allBranches_sound (bs : List Branches) (x : ℕ → ℚ)
    (h : ∀ b ∈ bs, b.Holds x) : (allBranches bs).Holds x := by
  induction bs with
  | nil => exact ⟨[], List.mem_cons_self .., by simp⟩
  | cons b bs ih =>
    exact crossBranches_sound b (allBranches bs) x
      (h b (List.mem_cons_self ..)) (ih (fun c hc => h c (List.mem_cons_of_mem _ hc)))

def anyBranches_sound (bs : List Branches) (x : ℕ → ℚ)
    (h : ∃ b ∈ bs, b.Holds x) : Branches.Holds bs.flatten x := by
  obtain ⟨b, hb, rows, hr, hrows⟩ := h
  exact ⟨rows, List.mem_flatten.mpr ⟨b, hb, hr⟩, hrows⟩

def combineBranches (conjunction : Bool) (bs : List Branches) : Branches :=
  if conjunction then allBranches bs else bs.flatten

def combineBranches_sound (conjunction : Bool) (bs : List Branches) (x : ℕ → ℚ)
    (h : if conjunction then ∀ b ∈ bs, b.Holds x else ∃ b ∈ bs, b.Holds x) :
    (combineBranches conjunction bs).Holds x := by
  cases conjunction with
  | false => exact anyBranches_sound bs x h
  | true => exact allBranches_sound bs x h

def combine_collect_sound (conjunction : Bool) {α : Type} (f : α → Option Branches)
    (values : α → Prop) (as : List α) (bs : List Branches) (x : ℕ → ℚ)
    (hf : ∀ a b, f a = some b → values a → b.Holds x)
    (hc : collect f as = some bs)
    (h : if conjunction then ∀ a ∈ as, values a else ∃ a ∈ as, values a) :
    (combineBranches conjunction bs).Holds x := by
  obtain ⟨hin, hout⟩ := collect_members f as bs hc
  apply combineBranches_sound
  cases conjunction with
  | false =>
    obtain ⟨a, ha, hval⟩ := h
    obtain ⟨b, hb, hfb⟩ := hin a ha
    exact ⟨b, hb, hf a b hfb hval⟩
  | true =>
    intro b hb
    obtain ⟨a, ha, hfa⟩ := hout b hb
    exact hf a b hfa (h a ha)

end ClosureLinear

end PolicySubmissionPart12

/- Component PolicyLinearFormula; SHA256 26271c067cc0506a5457180f6b9108c21705aec0858414f2180b044640791ce2. -/
section PolicySubmissionPart13
/- Verified extraction of linear contradiction branches from Boolean DAG nodes. -/
namespace ClosureLinear
open ClosureSemantics

inductive FormulaRule where
  | fixedValue : Bool → FormulaRule
  | same : ℕ → FormulaRule
  | neg : ℕ → FormulaRule
  | combine : Bool → List ℕ → FormulaRule
  | atom : Comparison → ℕ → ℕ → FormulaRule
  | reject

def comparisonOf (integer : Bool) : Op → Option Comparison
  | .qEq => if integer then none else some .eq
  | .qLe => if integer then none else some .le
  | .qLt => if integer then none else some .lt
  | .zEq => if integer then some .eq else none
  | .zLe => if integer then some .le else none
  | .zLt => if integer then some .lt else none
  | _ => none

def comparisonOf_eq (integer : Bool) (op : Op) (cmp : Comparison)
    (h : comparisonOf integer op = some cmp) : op = comparisonOp integer cmp := by
  cases integer <;> cases op <;> simp_all [comparisonOf, comparisonOp]
  all_goals subst cmp; rfl

def parseFormula (integer : Bool) (node : Node) : FormulaRule :=
  match node.op, node.children with
  | .bConst b, _ => .fixedValue b
  | .alias, [j] => .same j
  | .bNot, [j] => .neg j
  | .bAnd, js => .combine true js
  | .bOr, js => .combine false js
  | op, js =>
    match comparisonOf integer op, js with
    | some cmp, [a, b] => .atom cmp a b
    | _, _ => .reject

def FormulaRule.Holds (integer : Bool) (input values : Valuation) (positive : Bool) :
    FormulaRule → Prop
  | .fixedValue b => b = positive
  | .same j => (values j).b = positive
  | .neg j => (values j).b = !positive
  | .combine conjunction js =>
    if conjunction == positive then ∀ j ∈ js, (values j).b = positive
    else ∃ j ∈ js, (values j).b = positive
  | .atom cmp a b => (evalOp input (comparisonOp integer cmp) [values a, values b]).b = positive
  | .reject => True

def parseFormula_sound (integer : Bool) (input values : Valuation)
    (node : Node) (positive : Bool) (h : (evalNode input values node).b = positive) :
    (parseFormula integer node).Holds integer input values positive := by
  fun_cases parseFormula integer node <;>
    simp_all [FormulaRule.Holds, evalNode, evalOp, boolValue]
  · cases positive <;> simp_all
  · cases positive <;> simp_all
  · rename_i cmp a b _ _ _ hc _
    rw [← comparisonOf_eq integer node.op cmp hc]
    exact h

def normalizeFormula (program : ℕ → Node) (cut : ℕ → Option ℕ) (integer : Bool) :
    ℕ → ℕ → Bool → Option Branches
  | 0, _, _ => none
  | fuel + 1, i, positive =>
    match parseFormula integer (program i) with
    | .fixedValue b =>
      some (if b == positive then [[]] else [[makeRow false false (Affine.const (-1))]])
    | .same j => normalizeFormula program cut integer fuel j positive
    | .neg j => normalizeFormula program cut integer fuel j (!positive)
    | .combine conjunction js => do
      let bs ← collect (fun j => normalizeFormula program cut integer fuel j positive) js
      pure (combineBranches (conjunction == positive) bs)
    | .atom cmp a b => do
      let f ← normalizeTerm program cut integer fuel a
      let g ← normalizeTerm program cut integer fuel b
      pure (atomBranches integer cmp positive f g)
    | .reject => none

def normalizeFormula_sound (program : ℕ → Node) (cut : ℕ → Option ℕ)
    (integer : Bool) (input values : Valuation) (x : ℕ → ℚ)
    (he : Equations program input values)
    (hcut : ∀ i j, cut i = some j → x j = numericValue integer (values i))
    (fuel i : ℕ) (positive : Bool) (bs : Branches)
    (hn : normalizeFormula program cut integer fuel i positive = some bs)
    (h : (values i).b = positive) : bs.Holds x := by
  induction fuel generalizing i positive bs with
  | zero => simp [normalizeFormula] at hn
  | succ fuel ih =>
    have hv : (evalNode input values (program i)).b = positive := by rw [← he i]; exact h
    have hs := parseFormula_sound integer input values (program i) positive hv
    simp only [normalizeFormula] at hn
    cases hr : parseFormula integer (program i) with
    | fixedValue b =>
      rw [hr] at hn hs
      have hb : b = positive := hs
      subst b
      have hbs : [[]] = bs := by simpa using hn
      subst bs
      exact ⟨[], List.mem_cons_self .., by simp⟩
    | same j =>
      rw [hr] at hn hs
      exact ih j positive bs hn hs
    | neg j =>
      rw [hr] at hn hs
      exact ih j (!positive) bs hn hs
    | combine conjunction js =>
      rw [hr] at hn hs
      cases hc : collect (fun j => normalizeFormula program cut integer fuel j positive) js with
      | none => simp [hc] at hn
      | some children =>
        have hbs : combineBranches (conjunction == positive) children = bs := by
          simpa [hc] using hn
        subst bs
        exact combine_collect_sound (conjunction == positive)
          (fun j => normalizeFormula program cut integer fuel j positive)
          (fun j => (values j).b = positive) js children x
          (fun j b hj hv => ih j positive b hj hv) hc hs
    | atom cmp a b =>
      rw [hr] at hn hs
      cases hf : normalizeTerm program cut integer fuel a with
      | none => simp [hf] at hn
      | some f =>
        cases hg : normalizeTerm program cut integer fuel b with
        | none => simp [hf, hg] at hn
        | some g =>
          have hbs : atomBranches integer cmp positive f g = bs := by simpa [hf, hg] using hn
          subst bs
          exact atomBranches_values integer cmp positive f g x input (values a) (values b)
            (normalizeTerm_sound program cut integer input values x he hcut fuel a f hf)
            (normalizeTerm_sound program cut integer input values x he hcut fuel b g hg) hs
    | reject => simp [hr] at hn

end ClosureLinear

end PolicySubmissionPart13

/- Component PolicyLinearSequent; SHA256 175452e3dd63ee58637954deb45cb870dbd185e315751127df0ad92a239e7f7e. -/
section PolicySubmissionPart14
/- A sound, computational checker for arithmetic implication leaves. -/
namespace ClosureLinear
open ClosureSemantics

def selectRows (rows : List Row) (weights : List (ℕ × ℕ)) : Option (List (ℕ × Row)) :=
  collect (fun iw => rows[iw.1]?.map (fun r => (iw.2, r))) weights

def selectRows_sound (rows : List Row) (weights : List (ℕ × ℕ))
    (selected : List (ℕ × Row)) (x : ℕ → ℚ)
    (hs : selectRows rows weights = some selected) (h : ∀ r ∈ rows, r.Holds x) :
    ∀ a ∈ selected, a.2.Holds x := by
  intro a ha
  obtain ⟨iw, _, hw⟩ := (collect_members _ weights selected hs).2 a ha
  cases hr : rows[iw.1]? with
  | none => simp [hr] at hw
  | some r =>
    have heq : (iw.2, r) = a := by simpa [hr] using hw
    subst a
    exact h r (List.mem_of_getElem? hr)

def checkBranch (rows : List Row) (weights : List (ℕ × ℕ)) : Bool :=
  match selectRows rows weights with
  | some selected => check selected
  | none => false

def checkBranch_sound (rows : List Row) (weights : List (ℕ × ℕ)) (x : ℕ → ℚ)
    (hc : checkBranch rows weights = true) (h : ∀ r ∈ rows, r.Holds x) : False := by
  cases hs : selectRows rows weights with
  | none => simp [checkBranch, hs] at hc
  | some selected =>
    exact check_sound selected x (selectRows_sound rows weights selected x hs h)
      (by simpa [checkBranch, hs] using hc)

def checkBranches : Branches → List (List (ℕ × ℕ)) → Bool
  | [], [] => true
  | rows :: bs, weights :: cs => checkBranch rows weights && checkBranches bs cs
  | _, _ => false

def checkBranches_sound (bs : Branches) (certs : List (List (ℕ × ℕ))) (x : ℕ → ℚ)
    (hc : checkBranches bs certs = true) (h : bs.Holds x) : False := by
  induction bs generalizing certs with
  | nil => obtain ⟨rows, hr, _⟩ := h; simp at hr
  | cons rows bs ih =>
    cases certs with
    | nil => simp [checkBranches] at hc
    | cons weights cs =>
      have hp : checkBranch rows weights = true ∧ checkBranches bs cs = true := by
        simpa [checkBranches, Bool.and_eq_true] using hc
      obtain ⟨rs, hrs, hrows⟩ := h
      rcases List.mem_cons.mp hrs with rfl | hrs
      · exact checkBranch_sound rs weights x hp.1 hrows
      · exact ih cs hp.2 ⟨rs, hrs, hrows⟩

def normalizeSequent (program : ℕ → Node) (cut : ℕ → Option ℕ) (integer : Bool)
    (fuel : ℕ) (signed : List (ℕ × Bool)) : Option Branches := do
  let bs ← collect (fun ib => normalizeFormula program cut integer fuel ib.1 ib.2) signed
  pure (allBranches bs)

def normalizeSequent_sound (program : ℕ → Node) (cut : ℕ → Option ℕ)
    (integer : Bool) (input values : Valuation) (x : ℕ → ℚ)
    (he : Equations program input values)
    (hcut : ∀ i j, cut i = some j → x j = numericValue integer (values i))
    (fuel : ℕ) (signed : List (ℕ × Bool)) (bs : Branches)
    (hn : normalizeSequent program cut integer fuel signed = some bs)
    (h : ∀ ib ∈ signed, (values ib.1).b = ib.2) : bs.Holds x := by
  cases hc : collect (fun ib => normalizeFormula program cut integer fuel ib.1 ib.2) signed with
  | none => simp [normalizeSequent, hc] at hn
  | some children =>
    have hbs : allBranches children = bs := by simpa [normalizeSequent, hc] using hn
    subst bs
    exact combine_collect_sound true
      (fun ib : ℕ × Bool => normalizeFormula program cut integer fuel ib.1 ib.2)
      (fun ib : ℕ × Bool => (values ib.1).b = ib.2) signed children x
      (fun ib b hb hv => normalizeFormula_sound program cut integer input values x
        he hcut fuel ib.1 ib.2 b hb hv) hc h

def checkSequent (program : ℕ → Node) (cut : ℕ → Option ℕ) (integer : Bool)
    (fuel : ℕ) (signed : List (ℕ × Bool)) (certs : List (List (ℕ × ℕ))) : Bool :=
  match normalizeSequent program cut integer fuel signed with
  | some bs => checkBranches bs certs
  | none => false

def checkSequent_sound (program : ℕ → Node) (cut : ℕ → Option ℕ)
    (integer : Bool) (input values : Valuation) (x : ℕ → ℚ)
    (he : Equations program input values)
    (hcut : ∀ i j, cut i = some j → x j = numericValue integer (values i))
    (fuel : ℕ) (signed : List (ℕ × Bool)) (certs : List (List (ℕ × ℕ)))
    (hc : checkSequent program cut integer fuel signed certs = true)
    (h : ∀ ib ∈ signed, (values ib.1).b = ib.2) : False := by
  cases hn : normalizeSequent program cut integer fuel signed with
  | none => simp [checkSequent, hn] at hc
  | some bs =>
    exact checkBranches_sound bs certs x (by simpa [checkSequent, hn] using hc)
      (normalizeSequent_sound program cut integer input values x he hcut fuel signed bs hn h)

def cutIndex : List ℕ → ℕ → Option ℕ
  | [], _ => none
  | a :: as, i => if i = a then some 0 else (cutIndex as i).map Nat.succ

def cutIndex_get (ids : List ℕ) (i j : ℕ) (h : cutIndex ids i = some j) :
    ids[j]? = some i := by
  induction ids generalizing j with
  | nil => simp [cutIndex] at h
  | cons a as ih =>
    by_cases hi : i = a
    · have hj : j = 0 := by simpa [cutIndex, hi] using h.symm
      subst j
      simp [hi]
    · cases hc : cutIndex as i with
      | none => simp [cutIndex, hi, hc] at h
      | some k =>
        have hj : k + 1 = j := by simpa [cutIndex, hi, hc] using h
        subst j
        simpa using ih k hc

def checkSequent_of_cuts (program : ℕ → Node) (ids : List ℕ) (integer : Bool)
    (input values : Valuation) (he : Equations program input values)
    (fuel : ℕ) (signed : List (ℕ × Bool)) (certs : List (List (ℕ × ℕ)))
    (hc : checkSequent program (cutIndex ids) integer fuel signed certs = true)
    (h : ∀ ib ∈ signed, (values ib.1).b = ib.2) : False := by
  apply checkSequent_sound program (cutIndex ids) integer input values
    (fun j => numericValue integer (values (ids[j]?.getD 0))) he _ fuel signed certs hc h
  intro i j hj
  rw [cutIndex_get ids i j hj]
  rfl

def checkImplication (program : ℕ → Node) (ids : List ℕ) (integer : Bool)
    (fuel : ℕ) (premises : List ℕ) (conclusion : ℕ) (certs : List (List (ℕ × ℕ))) : Bool :=
  checkSequent program (cutIndex ids) integer fuel
    (premises.map (fun i => (i, true)) ++ [(conclusion, false)]) certs

def checkImplication_sound (program : ℕ → Node) (ids : List ℕ) (integer : Bool)
    (input values : Valuation) (he : Equations program input values)
    (fuel : ℕ) (premises : List ℕ) (conclusion : ℕ) (certs : List (List (ℕ × ℕ)))
    (hc : checkImplication program ids integer fuel premises conclusion certs = true)
    (h : ∀ i ∈ premises, (values i).b = true) : (values conclusion).b = true := by
  cases hconclusion : (values conclusion).b with
  | true => rfl
  | false =>
    apply False.elim
    apply checkSequent_of_cuts program ids integer input values he fuel _ certs hc
    intro ib hib
    rcases List.mem_append.mp hib with hp | heq
    · obtain ⟨i, hi, rfl⟩ := List.mem_map.mp hp
      exact h i hi
    · have hi : ib = (conclusion, false) := by simpa using heq
      subst ib
      exact hconclusion

end ClosureLinear

end PolicySubmissionPart14

/- Component ClosurePattern; SHA256 a786e2a8c781ead32f67dfb7c900933fe95e93bd08a45ed6fef7e064b80fe035. -/
section PolicySubmissionPart15
/- A total matcher for finite expression schemas, with kernel soundness. -/
namespace ClosurePattern
open ClosureSemantics

inductive Pattern where
  | hole : Nat → Pattern
  | node : Op → List Pattern → Pattern

def eval (env : Valuation) : Pattern → Value
  | .hole k => env k
  | .node op children => evalOp (fun _ => zeroValue) op (children.map (eval env))

def sameOp : Op → Op → Bool
  | .input a, .input b => a == b
  | .qConst a, .qConst b => a == b
  | .zConst a, .zConst b => a == b
  | .bConst a, .bConst b => a == b
  | .alias, .alias | .bNot, .bNot | .bOr, .bOr | .bAnd, .bAnd
  | .bEq, .bEq | .ite, .ite | .qEq, .qEq | .zEq, .zEq
  | .qLe, .qLe | .zLe, .zLe | .qLt, .qLt | .zLt, .zLt
  | .qAdd, .qAdd | .zAdd, .zAdd | .qMul, .qMul | .zMul, .zMul
  | .qNeg, .qNeg | .zNeg, .zNeg | .qSub, .qSub | .zSub, .zSub
  | .qDiv, .qDiv => true
  | _, _ => false

def sameOp_sound (a b : Op) (h : sameOp a b = true) : a = b := by
  cases a <;> cases b <;> simp_all [sameOp]

def allPairs (f : α → β → Bool) : List α → List β → Bool
  | [], [] => true
  | a :: as, b :: bs => f a b && allPairs f as bs
  | _, _ => false

def allPairs_map_eq (f : α → β → Bool) (left : α → γ) (right : β → γ)
    (h : ∀ a b, f a b = true → left a = right b)
    (as : List α) (bs : List β) (hc : allPairs f as bs = true) :
    as.map left = bs.map right := by
  induction as generalizing bs with
  | nil => cases bs <;> simp_all [allPairs]
  | cons a as ih =>
    cases bs with
    | nil => simp [allPairs] at hc
    | cons b bs =>
      have hh : f a b = true ∧ allPairs f as bs = true := by
        simpa [allPairs, Bool.and_eq_true] using hc
      simp only [List.map_cons, h a b hh.1, ih bs hh.2]

def check (program : Nat → Node) (cut : Nat → Option Nat) :
    Nat → Pattern → Nat → Bool
  | 0, _, _ => false
  | _ + 1, .hole k, i => cut i == some k
  | fuel + 1, .node op children, i =>
      ClosureLinear.closedOp op && sameOp op (program i).op &&
        allPairs (check program cut fuel) children (program i).children

def check_sound (program : Nat → Node) (cut : Nat → Option Nat)
    (input values env : Valuation) (he : Equations program input values)
    (hcut : ∀ i j, cut i = some j → env j = values i)
    (fuel : Nat) (pattern : Pattern) (i : Nat)
    (hc : check program cut fuel pattern i = true) : eval env pattern = values i := by
  induction fuel generalizing pattern i with
  | zero => simp [check] at hc
  | succ fuel ih =>
    cases pattern with
    | hole k =>
      simp only [eval]
      apply hcut i k
      simpa [check, beq_iff_eq] using hc
    | node op children =>
      have hh : (ClosureLinear.closedOp op = true ∧ sameOp op (program i).op = true) ∧
          allPairs (check program cut fuel) children (program i).children = true := by
        simpa only [check, Bool.and_eq_true] using hc
      have hop := sameOp_sound op (program i).op hh.1.2
      have hchildren := allPairs_map_eq (check program cut fuel) (eval env) values
        (fun p j hp => ih p j hp) children (program i).children hh.2
      simp only [eval, hchildren]
      rw [ClosureLinear.evalOp_closed _ _ input hh.1.1, hop, he i]
      rfl

def environment (ids : List Nat) (values : Valuation) : Valuation :=
  fun j => values (ids[j]?.getD 0)

def check_of_cuts (program : Nat → Node) (ids : List Nat)
    (input values : Valuation) (he : Equations program input values)
    (fuel : Nat) (pattern : Pattern) (i : Nat)
    (hc : check program (ClosureLinear.cutIndex ids) fuel pattern i = true) :
    eval (environment ids values) pattern = values i := by
  apply check_sound program (ClosureLinear.cutIndex ids) input values (environment ids values)
    he _ fuel pattern i hc
  intro k j hj
  simp only [environment, ClosureLinear.cutIndex_get ids k j hj]
  rfl

end ClosurePattern

end PolicySubmissionPart15

/- Component ClosureSchema; SHA256 813f5d94ac9b3da1870e09109161da29971933311616dd09775ec803969d51d9. -/
section PolicySubmissionPart16
/- Ordinary proved expression schemas and checked instantiation in a DAG. -/
namespace ClosurePattern
open ClosureSemantics

structure Schema where
  definitions : List (Nat × Pattern)
  premises : List Pattern
  conclusion : Pattern

def Schema.Valid (s : Schema) : Prop :=
  ∀ env : Valuation,
    (∀ d ∈ s.definitions, env d.1 = eval env d.2) →
    (∀ p ∈ s.premises, (eval env p).b = true) →
    (eval env s.conclusion).b = true

def checkSchema (program : Nat → Node) (ids : List Nat) (fuel : Nat)
    (s : Schema) (premises : List Nat) (conclusion : Nat) : Bool :=
  s.definitions.all (fun d => check program (ClosureLinear.cutIndex ids) fuel
    d.2 (ids[d.1]?.getD 0)) &&
  allPairs (check program (ClosureLinear.cutIndex ids) fuel) s.premises premises &&
  check program (ClosureLinear.cutIndex ids) fuel s.conclusion conclusion

def checkSchema_sound (program : Nat → Node) (ids : List Nat)
    (input values : Valuation) (he : Equations program input values)
    (fuel : Nat) (s : Schema) (premises : List Nat) (conclusion : Nat)
    (hv : s.Valid) (hc : checkSchema program ids fuel s premises conclusion = true)
    (hp : ∀ i ∈ premises, (values i).b = true) : (values conclusion).b = true := by
  have hh : (s.definitions.all (fun d => check program (ClosureLinear.cutIndex ids) fuel
        d.2 (ids[d.1]?.getD 0)) = true ∧
      allPairs (check program (ClosureLinear.cutIndex ids) fuel) s.premises premises = true) ∧
      check program (ClosureLinear.cutIndex ids) fuel s.conclusion conclusion = true := by
    simpa only [checkSchema, Bool.and_eq_true] using hc
  have hd : ∀ d ∈ s.definitions, environment ids values d.1 =
      eval (environment ids values) d.2 := by
    intro d hdm
    exact (check_of_cuts program ids input values he fuel d.2 _
      (List.all_eq_true.mp hh.1.1 d hdm)).symm
  have hmaps : s.premises.map (eval (environment ids values)) = premises.map values := by
    exact allPairs_map_eq (check program (ClosureLinear.cutIndex ids) fuel)
      (eval (environment ids values)) values
      (fun p i h => check_of_cuts program ids input values he fuel p i h)
      s.premises premises hh.1.2
  have hps : ∀ p ∈ s.premises, (eval (environment ids values) p).b = true := by
    intro p hpm
    have hm : eval (environment ids values) p ∈ premises.map values := by
      rw [← hmaps]
      exact List.mem_map.mpr ⟨p, hpm, rfl⟩
    obtain ⟨i, hi, heq⟩ := List.mem_map.mp hm
    rw [← heq]
    exact hp i hi
  have hout := hv (environment ids values) hd hps
  rw [check_of_cuts program ids input values he fuel s.conclusion conclusion hh.2] at hout
  exact hout

end ClosurePattern

end PolicySubmissionPart16

/- Component ClosureRewriteParametricCompact; SHA256 6bcd83c7277875574280a06b56029b5a6a07acbe04924865c42af66c93072a43. -/
section PolicySubmissionPart17
namespace ClosureRewriteParametric
open ClosurePattern ClosureSemantics

abbrev x0 : Pattern := .hole 0

abbrev x1 : Pattern := .hole 1

abbrev x2 : Pattern := .hole 2

abbrev x3 : Pattern := .hole 3

abbrev x4 : Pattern := .hole 4

abbrev x5 : Pattern := .hole 5

abbrev x6 : Pattern := .hole 6

abbrev x7 : Pattern := .hole 7

abbrev qc (n : Int) (d : Nat) : Pattern := .node (.qConst ((n : Rat) / (d : Rat))) []

abbrev zc (n : Int) : Pattern := .node (.zConst n) []

abbrev bt : Pattern := .node (.bConst true) []

abbrev bf : Pattern := .node (.bConst false) []

abbrev alias1 (a : Pattern) : Pattern := .node .alias [a]

abbrev bAnd2 (a b : Pattern) : Pattern := .node .bAnd [a, b]

abbrev bAnd3 (a b c : Pattern) : Pattern := .node .bAnd [a, b, c]

abbrev bAndn (xs : List Pattern) : Pattern := .node .bAnd xs

abbrev bEq2 (a b : Pattern) : Pattern := .node .bEq [a, b]

abbrev bNot1 (a : Pattern) : Pattern := .node .bNot [a]

abbrev bOr2 (a b : Pattern) : Pattern := .node .bOr [a, b]

abbrev bOr3 (a b c : Pattern) : Pattern := .node .bOr [a, b, c]

abbrev bOrn (xs : List Pattern) : Pattern := .node .bOr xs

abbrev ite3 (a b c : Pattern) : Pattern := .node .ite [a, b, c]

abbrev qAdd2 (a b : Pattern) : Pattern := .node .qAdd [a, b]

abbrev qDiv2 (a b : Pattern) : Pattern := .node .qDiv [a, b]

abbrev qEq2 (a b : Pattern) : Pattern := .node .qEq [a, b]

abbrev qLe2 (a b : Pattern) : Pattern := .node .qLe [a, b]

abbrev qLt2 (a b : Pattern) : Pattern := .node .qLt [a, b]

abbrev qMul2 (a b : Pattern) : Pattern := .node .qMul [a, b]

abbrev zAdd2 (a b : Pattern) : Pattern := .node .zAdd [a, b]

abbrev zAdd3 (a b c : Pattern) : Pattern := .node .zAdd [a, b, c]

abbrev zEq2 (a b : Pattern) : Pattern := .node .zEq [a, b]

abbrev zLe2 (a b : Pattern) : Pattern := .node .zLe [a, b]

abbrev zMul2 (a b : Pattern) : Pattern := .node .zMul [a, b]

abbrev zSub2 (a b : Pattern) : Pattern := .node .zSub [a, b]

def schema0 : Schema := ⟨[], [], (bOr2 x0 (zEq2 (zc (0)) (ite3 x0 (zc (1)) (zc (0)))))⟩

def schema0_valid : schema0.Valid := by
  intro env hd hp
  norm_num [schema0, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema1 : Schema := ⟨[], [], (bOr3 (bEq2 x0 x1) (bNot1 x0) (bNot1 x1))⟩

def schema1_valid : schema1.Valid := by
  intro env hd hp
  norm_num [schema1, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema2 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 (qDiv2 (qc (1) 1) x1) x0)) (qLt2 (alias1 (qDiv2 (qc (1) 1) x1)) (alias1 x0)))⟩

def schema2_valid : schema2.Valid := by
  intro env hd hp
  norm_num [schema2, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema3 : Schema := ⟨[], [], (bEq2 (qLt2 (alias1 (qDiv2 (qc (1) 1) x1)) x0) (bNot1 (qLe2 x0 (alias1 (qDiv2 (qc (1) 1) x1)))))⟩

def schema3_valid : schema3.Valid := by
  intro env hd hp
  norm_num [schema3, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema4 : Schema := ⟨[], [(bEq2 x0 x1)], (bEq2 (bEq2 x2 x0) (bEq2 x2 x1))⟩

def schema4_valid : schema4.Valid := by
  intro env hd hp
  norm_num [schema4, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema5 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (bNot1 x1)) (bNot1 (bEq2 x1 x0)))⟩

def schema5_valid : schema5.Valid := by
  intro env hd hp
  norm_num [schema5, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema6 : Schema := ⟨[], [(bEq2 x0 x1), (bEq2 x1 x2)], (bEq2 x0 x2)⟩

def schema6_valid : schema6.Valid := by
  intro env hd hp
  norm_num [schema6, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema7 : Schema := ⟨[], [x0, (bEq2 x0 x1)], x1⟩

def schema7_valid : schema7.Valid := by
  intro env hd hp
  norm_num [schema7, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema8 : Schema := ⟨[], [], (bEq2 (bEq2 (qLe2 x0 (alias1 (qDiv2 (qc (1) 1) x2))) x1) (bEq2 (qLe2 (qc (0) 1) (qAdd2 (alias1 (qDiv2 (qc (1) 1) x2)) (qMul2 (qc (-1) 1) x0))) x1))⟩

def schema8_valid : schema8.Valid := by
  intro env hd hp
  norm_num [schema8, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema9 : Schema := ⟨[], [(bEq2 x0 x1)], (bEq2 (bNot1 x0) (bNot1 x1))⟩

def schema9_valid : schema9.Valid := by
  intro env hd hp
  norm_num [schema9, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema10 : Schema := ⟨[], [], (qEq2 (alias1 (qMul2 (qDiv2 (qc (1) 1) x1) x0)) (qMul2 (alias1 (qDiv2 (qc (1) 1) x1)) x0))⟩

def schema10_valid : schema10.Valid := by
  intro env hd hp
  norm_num [schema10, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema11 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qMul2 (alias1 (qDiv2 (qc (1) 1) x2)) x1)) (qEq2 x0 (qMul2 x1 (alias1 (qDiv2 (qc (1) 1) x2)))))⟩

def schema11_valid : schema11.Valid := by
  intro env hd hp
  norm_num [schema11, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema12 : Schema := ⟨[], [], (bEq2 (qEq2 x0 x1) (qEq2 (qAdd2 x0 (qMul2 (qc (-1) 1) x1)) (qc (0) 1)))⟩

def schema12_valid : schema12.Valid := by
  intro env hd hp
  norm_num [schema12, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema13 : Schema := ⟨[], [], (bEq2 (qEq2 (qc (0) 1) x0) (qEq2 x0 (qc (0) 1)))⟩

def schema13_valid : schema13.Valid := by
  intro env hd hp
  norm_num [schema13, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema14 : Schema := ⟨[], [(bEq2 x0 x1)], (bEq2 x1 x0)⟩

def schema14_valid : schema14.Valid := by
  intro env hd hp
  norm_num [schema14, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema15 : Schema := ⟨[], [], (qEq2 (alias1 (qDiv2 (qc (1) 1) x0)) (qDiv2 (qc (1) 1) x0))⟩

def schema15_valid : schema15.Valid := by
  intro env hd hp
  norm_num [schema15, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema16 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (16) 1))) (qDiv2 (qc (1) 1) (qc (16) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (16) 1))) (qc (1) 16)))⟩

def schema16_valid : schema16.Valid := by
  intro env hd hp
  norm_num [schema16, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema17 : Schema := ⟨[], [(qEq2 (alias1 (qDiv2 (qc (1) 1) x0)) (qDiv2 (qc (1) 1) x0)), (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) x0)) (qDiv2 (qc (1) 1) x0)) (qEq2 (alias1 (qDiv2 (qc (1) 1) x0)) x1))], (qEq2 (alias1 (qDiv2 (qc (1) 1) x0)) x1)⟩

def schema17_valid : schema17.Valid := by
  intro env hd hp
  norm_num [schema17, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema18 : Schema := ⟨[], [], (qEq2 (alias1 (qMul2 x0 x1)) (qMul2 (alias1 x0) x1))⟩

def schema18_valid : schema18.Valid := by
  intro env hd hp
  norm_num [schema18, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema19 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qMul2 x1 x2)) (qEq2 x0 (qMul2 x2 x1)))⟩

def schema19_valid : schema19.Valid := by
  intro env hd hp
  norm_num [schema19, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema20 : Schema := ⟨[], [], (bEq2 (qEq2 x0 x1) (qEq2 (qAdd2 x1 (qMul2 (qc (-1) 1) x0)) (qc (0) 1)))⟩

def schema20_valid : schema20.Valid := by
  intro env hd hp
  norm_num [schema20, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema21 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x10000) 1))) (qDiv2 (qc (1) 1) (qc (0x10000) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x10000) 1))) (qc (1) 0x10000)))⟩

def schema21_valid : schema21.Valid := by
  intro env hd hp
  norm_num [schema21, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema22 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x41a7) 1))) (qDiv2 (qc (1) 1) (qc (0x41a7) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x41a7) 1))) (qc (1) 0x41a7)))⟩

def schema22_valid : schema22.Valid := by
  intro env hd hp
  norm_num [schema22, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema23 : Schema := ⟨[], [], (bOr2 (bNot1 x0) (qEq2 (alias1 (qDiv2 (qc (1) 1) x2)) (ite3 x0 (alias1 (qDiv2 (qc (1) 1) x2)) x1)))⟩

def schema23_valid : schema23.Valid := by
  intro env hd hp
  norm_num [schema23, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema24 : Schema := ⟨[], [], (bEq2 (alias1 (zEq2 x0 (zc (0)))) (zEq2 (alias1 x0) (zc (0))))⟩

def schema24_valid : schema24.Valid := by
  intro env hd hp
  norm_num [schema24, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema25 : Schema := ⟨[], [], (zEq2 (alias1 (zSub2 x0 x1)) (zSub2 (alias1 x0) (alias1 x1)))⟩

def schema25_valid : schema25.Valid := by
  intro env hd hp
  norm_num [schema25, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema26 : Schema := ⟨[], [], (bEq2 (zEq2 x0 (zSub2 x1 x2)) (zEq2 x0 (zAdd2 x1 (zMul2 (zc (-1)) x2))))⟩

def schema26_valid : schema26.Valid := by
  intro env hd hp
  norm_num [schema26, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema27 : Schema := ⟨[], [], (bEq2 (zEq2 x0 (zAdd2 x1 x2)) (zEq2 (zAdd3 x1 x2 (zMul2 (zc (-1)) x0)) (zc (0))))⟩

def schema27_valid : schema27.Valid := by
  intro env hd hp
  norm_num [schema27, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema28 : Schema := ⟨[], [], (bEq2 (zEq2 (zc (0)) x0) (zEq2 x0 (zc (0))))⟩

def schema28_valid : schema28.Valid := by
  intro env hd hp
  norm_num [schema28, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema29 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 (qDiv2 (qc (1) 1) x1))) (qLe2 (alias1 x0) (alias1 (qDiv2 (qc (1) 1) x1))))⟩

def schema29_valid : schema29.Valid := by
  intro env hd hp
  norm_num [schema29, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema30 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 (alias1 (qDiv2 (qc (1) 1) x2)))) (bEq2 x0 (qLe2 (qc (0) 1) (qAdd2 (alias1 (qDiv2 (qc (1) 1) x2)) (qMul2 (qc (-1) 1) x1)))))⟩

def schema30_valid : schema30.Valid := by
  intro env hd hp
  norm_num [schema30, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema31 : Schema := ⟨[], [], (bOr2 (bNot1 x0) (qEq2 x1 (ite3 x0 x1 x2)))⟩

def schema31_valid : schema31.Valid := by
  intro env hd hp
  norm_num [schema31, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema32 : Schema := ⟨[], [], (bOr2 x0 (qEq2 x1 (ite3 x0 x2 x1)))⟩

def schema32_valid : schema32.Valid := by
  intro env hd hp
  norm_num [schema32, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema33 : Schema := ⟨[], [], (bEq2 (alias1 (bEq2 x0 x1)) (bEq2 x0 (alias1 x1)))⟩

def schema33_valid : schema33.Valid := by
  intro env hd hp
  norm_num [schema33, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema34 : Schema := ⟨[], [], (bEq2 (alias1 (ite3 x0 x1 x2)) (ite3 (alias1 x0) (alias1 x1) (alias1 x2)))⟩

def schema34_valid : schema34.Valid := by
  intro env hd hp
  norm_num [schema34, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema35 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 x0 x1)) (qLt2 (alias1 x0) (alias1 x1)))⟩

def schema35_valid : schema35.Valid := by
  intro env hd hp
  norm_num [schema35, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema36 : Schema := ⟨[], [], (bEq2 (qLt2 x0 x1) (bNot1 (qLe2 x1 x0)))⟩

def schema36_valid : schema36.Valid := by
  intro env hd hp
  norm_num [schema36, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema37 : Schema := ⟨[], [], (bEq2 (bEq2 (qLe2 x0 x1) x2) (bEq2 (qLe2 (qc (0) 1) (qAdd2 x1 (qMul2 (qc (-1) 1) x0))) x2))⟩

def schema37_valid : schema37.Valid := by
  intro env hd hp
  norm_num [schema37, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema38 : Schema := ⟨[], [], (bOr3 (bNot1 (ite3 x0 x1 x2)) x0 x2)⟩

def schema38_valid : schema38.Valid := by
  intro env hd hp
  norm_num [schema38, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema39 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 x1)) (qLe2 (alias1 x0) (alias1 x1)))⟩

def schema39_valid : schema39.Valid := by
  intro env hd hp
  norm_num [schema39, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema40 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 x2)) (bEq2 x0 (qLe2 (qAdd2 x1 (qMul2 (qc (-1) 1) x2)) (qc (0) 1))))⟩

def schema40_valid : schema40.Valid := by
  intro env hd hp
  norm_num [schema40, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema41 : Schema := ⟨[], [], (qEq2 (alias1 x0) x0)⟩

def schema41_valid : schema41.Valid := by
  intro env hd hp
  norm_num [schema41, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema42 : Schema := ⟨[], [], (bEq2 (alias1 x0) x0)⟩

def schema42_valid : schema42.Valid := by
  intro env hd hp
  norm_num [schema42, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema43 : Schema := ⟨[], [], (bEq2 (bEq2 x0 bf) (bNot1 x0))⟩

def schema43_valid : schema43.Valid := by
  intro env hd hp
  norm_num [schema43, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema44 : Schema := ⟨[], [], (qEq2 (alias1 (ite3 x0 x1 x2)) (ite3 (alias1 x0) (alias1 x1) (alias1 x2)))⟩

def schema44_valid : schema44.Valid := by
  intro env hd hp
  norm_num [schema44, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema45 : Schema := ⟨[], [(qEq2 x0 x1)], (bEq2 (qEq2 x2 x0) (qEq2 x2 x1))⟩

def schema45_valid : schema45.Valid := by
  intro env hd hp
  norm_num [schema45, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema46 : Schema := ⟨[], [], (bEq2 (alias1 (qEq2 x0 x1)) (qEq2 x0 (alias1 x1)))⟩

def schema46_valid : schema46.Valid := by
  intro env hd hp
  norm_num [schema46, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema47 : Schema := ⟨[], [], (qEq2 (alias1 (ite3 x0 x1 x2)) (ite3 x0 (alias1 x1) (alias1 x2)))⟩

def schema47_valid : schema47.Valid := by
  intro env hd hp
  norm_num [schema47, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema48 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x1 x2)], (qEq2 x0 x2)⟩

def schema48_valid : schema48.Valid := by
  intro env hd hp
  norm_num [schema48, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema49 : Schema := ⟨[], [(qEq2 x0 x1)], (bEq2 (qEq2 x0 x2) (qEq2 x1 x2))⟩

def schema49_valid : schema49.Valid := by
  intro env hd hp
  norm_num [schema49, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema50 : Schema := ⟨[], [], (bEq2 (qEq2 x0 x1) (qEq2 x1 x0))⟩

def schema50_valid : schema50.Valid := by
  intro env hd hp
  norm_num [schema50, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema51 : Schema := ⟨[], [], (qEq2 (alias1 (qMul2 x1 x0)) (qMul2 x1 (alias1 x0)))⟩

def schema51_valid : schema51.Valid := by
  intro env hd hp
  norm_num [schema51, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema52 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 (qDiv2 x1 x2))) (qLe2 (alias1 x0) (alias1 (qDiv2 x1 x2))))⟩

def schema52_valid : schema52.Valid := by
  intro env hd hp
  norm_num [schema52, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema53 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 (alias1 (qDiv2 x2 x3)))) (bEq2 x0 (qLe2 (qc (0) 1) (qAdd2 (alias1 (qDiv2 x2 x3)) (qMul2 (qc (-1) 1) x1)))))⟩

def schema53_valid : schema53.Valid := by
  intro env hd hp
  norm_num [schema53, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema54 : Schema := ⟨[], [], (bOr2 x0 (qEq2 x1 (ite3 x0 (alias1 (qDiv2 x2 x3)) x1)))⟩

def schema54_valid : schema54.Valid := by
  intro env hd hp
  norm_num [schema54, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema55 : Schema := ⟨[], [], (qEq2 (alias1 (ite3 x0 (qDiv2 x2 x3) x1)) (ite3 (alias1 x0) (alias1 (qDiv2 x2 x3)) (alias1 x1)))⟩

def schema55_valid : schema55.Valid := by
  intro env hd hp
  norm_num [schema55, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema56 : Schema := ⟨[], [], (bOr2 (bNot1 x0) (qEq2 (alias1 (qDiv2 x2 x3)) (ite3 x0 (alias1 (qDiv2 x2 x3)) x1)))⟩

def schema56_valid : schema56.Valid := by
  intro env hd hp
  norm_num [schema56, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema57 : Schema := ⟨[], [(qEq2 x0 x1)], (bEq2 (qEq2 (alias1 (qDiv2 x2 x3)) x0) (qEq2 (alias1 (qDiv2 x2 x3)) x1))⟩

def schema57_valid : schema57.Valid := by
  intro env hd hp
  norm_num [schema57, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema58 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (64) 1))) (qDiv2 (qc (1) 1) (qc (64) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (64) 1))) (qc (1) 64)))⟩

def schema58_valid : schema58.Valid := by
  intro env hd hp
  norm_num [schema58, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema59 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qMul2 (qc (1) 1) x1)) (qEq2 x0 x1))⟩

def schema59_valid : schema59.Valid := by
  intro env hd hp
  norm_num [schema59, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema60 : Schema := ⟨[], [(qEq2 x0 x1)], (qEq2 x1 x0)⟩

def schema60_valid : schema60.Valid := by
  intro env hd hp
  norm_num [schema60, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema61 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (35) 1))) (qDiv2 (qc (1) 1) (qc (35) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (35) 1))) (qc (1) 35)))⟩

def schema61_valid : schema61.Valid := by
  intro env hd hp
  norm_num [schema61, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema62 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 (qc (1) 1))) (qLe2 (alias1 x0) (qc (1) 1)))⟩

def schema62_valid : schema62.Valid := by
  intro env hd hp
  norm_num [schema62, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema63 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 (qc (1) 1))) (bEq2 x0 (qLe2 x1 (qc (1) 1))))⟩

def schema63_valid : schema63.Valid := by
  intro env hd hp
  norm_num [schema63, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema64 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 (qDiv2 (qc (1) 1) x1) x0)) (qLt2 (alias1 (qDiv2 (qc (1) 1) x1)) x0))⟩

def schema64_valid : schema64.Valid := by
  intro env hd hp
  norm_num [schema64, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema65 : Schema := ⟨[], [], (bEq2 (bEq2 (qLe2 x0 (alias1 (qDiv2 (qc (1) 1) x2))) x1) (bEq2 (qLe2 (qAdd2 x0 (qMul2 (qc (-1) 1) (alias1 (qDiv2 (qc (1) 1) x2)))) (qc (0) 1)) x1))⟩

def schema65_valid : schema65.Valid := by
  intro env hd hp
  norm_num [schema65, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema66 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (4) 1))) (qDiv2 (qc (1) 1) (qc (4) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (4) 1))) (qc (1) 4)))⟩

def schema66_valid : schema66.Valid := by
  intro env hd hp
  norm_num [schema66, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema67 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 (alias1 (qDiv2 (qc (1) 1) x2)))) (bEq2 x0 (qLe2 (qAdd2 x1 (qMul2 (qc (-1) 1) (alias1 (qDiv2 (qc (1) 1) x2)))) (qc (0) 1))))⟩

def schema67_valid : schema67.Valid := by
  intro env hd hp
  norm_num [schema67, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema68 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (81) 1))) (qDiv2 (qc (1) 1) (qc (81) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (81) 1))) (qc (1) 81)))⟩

def schema68_valid : schema68.Valid := by
  intro env hd hp
  norm_num [schema68, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema69 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x1 x0)) (qLe2 (alias1 x1) (alias1 x0)))⟩

def schema69_valid : schema69.Valid := by
  intro env hd hp
  norm_num [schema69, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema70 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x2 x1)) (bEq2 x0 (qLe2 (qc (0) 1) (qAdd2 x1 (qMul2 (qc (-1) 1) x2)))))⟩

def schema70_valid : schema70.Valid := by
  intro env hd hp
  norm_num [schema70, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema71 : Schema := ⟨[], [], (bOr2 x0 (qEq2 x1 (ite3 x0 (alias1 (qDiv2 (qc (1) 1) x2)) x1)))⟩

def schema71_valid : schema71.Valid := by
  intro env hd hp
  norm_num [schema71, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema72 : Schema := ⟨[], [], (qEq2 (alias1 (ite3 x0 (qDiv2 (qc (1) 1) x2) x1)) (ite3 (alias1 x0) (alias1 (qDiv2 (qc (1) 1) x2)) (alias1 x1)))⟩

def schema72_valid : schema72.Valid := by
  intro env hd hp
  norm_num [schema72, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema73 : Schema := ⟨[], [(qEq2 x0 x1)], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) x2)) x0) (qEq2 (alias1 (qDiv2 (qc (1) 1) x2)) x1))⟩

def schema73_valid : schema73.Valid := by
  intro env hd hp
  norm_num [schema73, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema74 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x1 x2), (qEq2 x2 x3)], (qEq2 x0 x3)⟩

def schema74_valid : schema74.Valid := by
  intro env hd hp
  norm_num [schema74, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema75 : Schema := ⟨[], [], (bOr3 x0 (bNot1 x1) (bNot1 (bEq2 x0 x1)))⟩

def schema75_valid : schema75.Valid := by
  intro env hd hp
  norm_num [schema75, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema76 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x2 x1)) (bEq2 x0 (qLe2 (qAdd2 x2 (qMul2 (qc (-1) 1) x1)) (qc (0) 1))))⟩

def schema76_valid : schema76.Valid := by
  intro env hd hp
  norm_num [schema76, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema77 : Schema := ⟨[], [], (bEq2 (alias1 (bAnd3 x0 x1 x2)) (bAnd3 (alias1 x0) (alias1 x1) (alias1 x2)))⟩

def schema77_valid : schema77.Valid := by
  intro env hd hp
  norm_num [schema77, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema78 : Schema := ⟨[], [], (bEq2 (bAnd3 x0 x1 x2) (bNot1 (bOr3 (bNot1 x0) (bNot1 x1) (bNot1 x2))))⟩

def schema78_valid : schema78.Valid := by
  intro env hd hp
  norm_num [schema78, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema79 : Schema := ⟨[], [], (bEq2 (alias1 (bAndn [bf, x0, x1, x2])) (bAndn [bf, (alias1 x0), (alias1 x1), (alias1 x2)]))⟩

def schema79_valid : schema79.Valid := by
  intro env hd hp
  norm_num [schema79, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema80 : Schema := ⟨[], [], (bEq2 (bAndn [bf, x0, x1, x2]) bf)⟩

def schema80_valid : schema80.Valid := by
  intro env hd hp
  norm_num [schema80, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema81 : Schema := ⟨[], [(bEq2 x0 bf)], (bEq2 (bEq2 x1 x0) (bEq2 x1 bf))⟩

def schema81_valid : schema81.Valid := by
  intro env hd hp
  norm_num [schema81, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema82 : Schema := ⟨[], [], (zEq2 (alias1 (ite3 x0 (zc (1)) (zc (0)))) (ite3 (alias1 x0) (zc (1)) (zc (0))))⟩

def schema82_valid : schema82.Valid := by
  intro env hd hp
  norm_num [schema82, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema83 : Schema := ⟨[], [(zEq2 x0 x1)], (zEq2 x1 x0)⟩

def schema83_valid : schema83.Valid := by
  intro env hd hp
  norm_num [schema83, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema84 : Schema := ⟨[], [(zEq2 (zc (0)) x0), (zEq2 x0 x1)], (zEq2 (zc (0)) x1)⟩

def schema84_valid : schema84.Valid := by
  intro env hd hp
  norm_num [schema84, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema85 : Schema := ⟨[], [], (bOr2 (bNot1 x0) (zEq2 (zc (1)) (ite3 x0 (zc (1)) (zc (0)))))⟩

def schema85_valid : schema85.Valid := by
  intro env hd hp
  norm_num [schema85, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema86 : Schema := ⟨[], [(zEq2 x0 x1)], (bEq2 (zEq2 (zc (0)) x0) (zEq2 (zc (0)) x1))⟩

def schema86_valid : schema86.Valid := by
  intro env hd hp
  norm_num [schema86, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema87 : Schema := ⟨[], [(zEq2 (zc (1)) x0), (zEq2 x0 x1)], (zEq2 (zc (1)) x1)⟩

def schema87_valid : schema87.Valid := by
  intro env hd hp
  norm_num [schema87, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema88 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (7) 1))) (qDiv2 (qc (1) 1) (qc (7) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (7) 1))) (qc (1) 7)))⟩

def schema88_valid : schema88.Valid := by
  intro env hd hp
  norm_num [schema88, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema89 : Schema := ⟨[], [], (bOr3 (bNot1 (ite3 x0 x1 x2)) (bNot1 x0) x1)⟩

def schema89_valid : schema89.Valid := by
  intro env hd hp
  norm_num [schema89, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema90 : Schema := ⟨[], [], (bEq2 (alias1 (zLe2 (zc (0)) x0)) (zLe2 (zc (0)) (alias1 x0)))⟩

def schema90_valid : schema90.Valid := by
  intro env hd hp
  norm_num [schema90, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema91 : Schema := ⟨[], [], (bEq2 (alias1 (bOr2 x0 x1)) (bOr2 (alias1 x0) (alias1 x1)))⟩

def schema91_valid : schema91.Valid := by
  intro env hd hp
  norm_num [schema91, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema92 : Schema := ⟨[], [], (bEq2 (alias1 (bAnd2 x0 x1)) (bAnd2 (alias1 x0) (alias1 x1)))⟩

def schema92_valid : schema92.Valid := by
  intro env hd hp
  norm_num [schema92, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema93 : Schema := ⟨[], [], (bEq2 (bAnd2 x0 x1) (bNot1 (bOr2 (bNot1 x0) (bNot1 x1))))⟩

def schema93_valid : schema93.Valid := by
  intro env hd hp
  norm_num [schema93, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema94 : Schema := ⟨[], [], (bEq2 (alias1 (bNot1 x0)) (bNot1 (alias1 x0)))⟩

def schema94_valid : schema94.Valid := by
  intro env hd hp
  norm_num [schema94, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema95 : Schema := ⟨[], [], (bOr2 (bNot1 x0) (qEq2 (qc (1) 1) (ite3 x0 (qc (1) 1) x1)))⟩

def schema95_valid : schema95.Valid := by
  intro env hd hp
  norm_num [schema95, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema96 : Schema := ⟨[], [], (qEq2 (alias1 (ite3 x0 (qc (1) 1) x1)) (ite3 (alias1 x0) (qc (1) 1) (alias1 x1)))⟩

def schema96_valid : schema96.Valid := by
  intro env hd hp
  norm_num [schema96, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema97 : Schema := ⟨[], [(qEq2 x0 x1)], (bEq2 (qEq2 (qc (1) 1) x0) (qEq2 (qc (1) 1) x1))⟩

def schema97_valid : schema97.Valid := by
  intro env hd hp
  norm_num [schema97, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema98 : Schema := ⟨[], [], (qEq2 (alias1 (qDiv2 x0 x1)) (qDiv2 x0 x1))⟩

def schema98_valid : schema98.Valid := by
  intro env hd hp
  norm_num [schema98, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema99 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (4) 1))) (qDiv2 (qc (3) 1) (qc (4) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (4) 1))) (qc (3) 4)))⟩

def schema99_valid : schema99.Valid := by
  intro env hd hp
  norm_num [schema99, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema100 : Schema := ⟨[], [(qEq2 (alias1 (qDiv2 x0 x1)) (qDiv2 x0 x1)), (bEq2 (qEq2 (alias1 (qDiv2 x0 x1)) (qDiv2 x0 x1)) (qEq2 (alias1 (qDiv2 x0 x1)) x2))], (qEq2 (alias1 (qDiv2 x0 x1)) x2)⟩

def schema100_valid : schema100.Valid := by
  intro env hd hp
  norm_num [schema100, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema101 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (3) 1))) (qDiv2 (qc (1) 1) (qc (3) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (3) 1))) (qc (1) 3)))⟩

def schema101_valid : schema101.Valid := by
  intro env hd hp
  norm_num [schema101, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema102 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (5) 1))) (qDiv2 (qc (1) 1) (qc (5) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (5) 1))) (qc (1) 5)))⟩

def schema102_valid : schema102.Valid := by
  intro env hd hp
  norm_num [schema102, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema103 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x2 x3)], (bEq2 (qEq2 x0 x2) (qEq2 x1 x3))⟩

def schema103_valid : schema103.Valid := by
  intro env hd hp
  norm_num [schema103, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema104 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (9) 1))) (qDiv2 (qc (1) 1) (qc (9) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (9) 1))) (qc (1) 9)))⟩

def schema104_valid : schema104.Valid := by
  intro env hd hp
  norm_num [schema104, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema105 : Schema := ⟨[], [(zEq2 x0 x1)], (bEq2 (zEq2 (zc (1)) x0) (zEq2 (zc (1)) x1))⟩

def schema105_valid : schema105.Valid := by
  intro env hd hp
  norm_num [schema105, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema106 : Schema := ⟨[], [], (qEq2 (alias1 (qDiv2 x0 x1)) (qDiv2 (alias1 x0) x1))⟩

def schema106_valid : schema106.Valid := by
  intro env hd hp
  norm_num [schema106, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema107 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qDiv2 x1 (qc (2) 1))) (qEq2 x0 (qMul2 (qc (1) 2) x1)))⟩

def schema107_valid : schema107.Valid := by
  intro env hd hp
  norm_num [schema107, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema108 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (bEq2 x1 bt)) (bEq2 x0 x1))⟩

def schema108_valid : schema108.Valid := by
  intro env hd hp
  norm_num [schema108, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema109 : Schema := ⟨[], [(qEq2 (alias1 (qDiv2 x2 x3)) x0), (qEq2 x0 x1)], (qEq2 (alias1 (qDiv2 x2 x3)) x1)⟩

def schema109_valid : schema109.Valid := by
  intro env hd hp
  norm_num [schema109, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema110 : Schema := ⟨[], [], (bOr3 (bNot1 (bOr2 x0 x1)) x0 x1)⟩

def schema110_valid : schema110.Valid := by
  intro env hd hp
  norm_num [schema110, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema111 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qDiv2 x1 (qc (3) 1))) (qEq2 x0 (qMul2 (qc (1) 3) x1)))⟩

def schema111_valid : schema111.Valid := by
  intro env hd hp
  norm_num [schema111, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema112 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x8c) 1))) (qDiv2 (qc (3) 1) (qc (0x8c) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x8c) 1))) (qc (3) 0x8c)))⟩

def schema112_valid : schema112.Valid := by
  intro env hd hp
  norm_num [schema112, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema113 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x100) 1))) (qDiv2 (qc (1) 1) (qc (0x100) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x100) 1))) (qc (1) 0x100)))⟩

def schema113_valid : schema113.Valid := by
  intro env hd hp
  norm_num [schema113, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema114 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x2d9) 1))) (qDiv2 (qc (1) 1) (qc (0x2d9) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x2d9) 1))) (qc (1) 0x2d9)))⟩

def schema114_valid : schema114.Valid := by
  intro env hd hp
  norm_num [schema114, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema115 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (27) 1))) (qDiv2 (qc (1) 1) (qc (27) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (27) 1))) (qc (1) 27)))⟩

def schema115_valid : schema115.Valid := by
  intro env hd hp
  norm_num [schema115, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema116 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (25) 1))) (qDiv2 (qc (1) 1) (qc (25) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (25) 1))) (qc (1) 25)))⟩

def schema116_valid : schema116.Valid := by
  intro env hd hp
  norm_num [schema116, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema117 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xf5) 1))) (qDiv2 (qc (1) 1) (qc (0xf5) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xf5) 1))) (qc (1) 0xf5)))⟩

def schema117_valid : schema117.Valid := by
  intro env hd hp
  norm_num [schema117, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema118 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x36b) 1))) (qDiv2 (qc (1) 1) (qc (0x36b) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x36b) 1))) (qc (1) 0x36b)))⟩

def schema118_valid : schema118.Valid := by
  intro env hd hp
  norm_num [schema118, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema119 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (20) 1))) (qDiv2 (qc (3) 1) (qc (20) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (20) 1))) (qc (3) 20)))⟩

def schema119_valid : schema119.Valid := by
  intro env hd hp
  norm_num [schema119, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema120 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x2bc) 1))) (qDiv2 (qc (3) 1) (qc (0x2bc) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x2bc) 1))) (qc (3) 0x2bc)))⟩

def schema120_valid : schema120.Valid := by
  intro env hd hp
  norm_num [schema120, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema121 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x217f) 1))) (qDiv2 (qc (1) 1) (qc (0x217f) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x217f) 1))) (qc (1) 0x217f)))⟩

def schema121_valid : schema121.Valid := by
  intro env hd hp
  norm_num [schema121, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema122 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4000) 1))) (qDiv2 (qc (1) 1) (qc (0x4000) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4000) 1))) (qc (1) 0x4000)))⟩

def schema122_valid : schema122.Valid := by
  intro env hd hp
  norm_num [schema122, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema123 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0xdac) 1))) (qDiv2 (qc (3) 1) (qc (0xdac) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0xdac) 1))) (qc (3) 0xdac)))⟩

def schema123_valid : schema123.Valid := by
  intro env hd hp
  norm_num [schema123, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema124 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xaf) 1))) (qDiv2 (qc (1) 1) (qc (0xaf) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xaf) 1))) (qc (1) 0xaf)))⟩

def schema124_valid : schema124.Valid := by
  intro env hd hp
  norm_num [schema124, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema125 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x2ee5) 1))) (qDiv2 (qc (1) 1) (qc (0x2ee5) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x2ee5) 1))) (qc (1) 0x2ee5)))⟩

def schema125_valid : schema125.Valid := by
  intro env hd hp
  norm_num [schema125, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema126 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x400) 1))) (qDiv2 (qc (1) 1) (qc (0x400) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x400) 1))) (qc (1) 0x400)))⟩

def schema126_valid : schema126.Valid := by
  intro env hd hp
  norm_num [schema126, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema127 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x7d) 1))) (qDiv2 (qc (1) 1) (qc (0x7d) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x7d) 1))) (qc (1) 0x7d)))⟩

def schema127_valid : schema127.Valid := by
  intro env hd hp
  norm_num [schema127, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema128 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4c9) 1))) (qDiv2 (qc (1) 1) (qc (0x4c9) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4c9) 1))) (qc (1) 0x4c9)))⟩

def schema128_valid : schema128.Valid := by
  intro env hd hp
  norm_num [schema128, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema129 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4ce3) 1))) (qDiv2 (qc (1) 1) (qc (0x4ce3) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x4ce3) 1))) (qc (1) 0x4ce3)))⟩

def schema129_valid : schema129.Valid := by
  intro env hd hp
  norm_num [schema129, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema130 : Schema := ⟨[], [(zEq2 (zc (0)) x0)], (zEq2 x0 (zc (0)))⟩

def schema130_valid : schema130.Valid := by
  intro env hd hp
  norm_num [schema130, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema131 : Schema := ⟨[], [(zEq2 x0 x1), (zEq2 x1 (zc (0))), (zEq2 (zc (0)) x2)], (zEq2 x0 x2)⟩

def schema131_valid : schema131.Valid := by
  intro env hd hp
  norm_num [schema131, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema132 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (49) 1))) (qDiv2 (qc (1) 1) (qc (49) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (49) 1))) (qc (1) 49)))⟩

def schema132_valid : schema132.Valid := by
  intro env hd hp
  norm_num [schema132, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema133 : Schema := ⟨[], [], (bEq2 (zEq2 x0 (zc (1))) (zEq2 (zc (1)) x0))⟩

def schema133_valid : schema133.Valid := by
  intro env hd hp
  norm_num [schema133, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema134 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 x1 x0)) (qLt2 (alias1 x1) (alias1 x0)))⟩

def schema134_valid : schema134.Valid := by
  intro env hd hp
  norm_num [schema134, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema135 : Schema := ⟨[], [], (bEq2 (qLt2 x1 x0) (bNot1 (qLe2 x0 x1)))⟩

def schema135_valid : schema135.Valid := by
  intro env hd hp
  norm_num [schema135, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema136 : Schema := ⟨[], [], (bEq2 (bEq2 (qLe2 x0 x1) x2) (bEq2 (qLe2 (qAdd2 x0 (qMul2 (qc (-1) 1) x1)) (qc (0) 1)) x2))⟩

def schema136_valid : schema136.Valid := by
  intro env hd hp
  norm_num [schema136, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema137 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qDiv2 x1 (qc (4) 1))) (qEq2 x0 (qMul2 (qc (1) 4) x1)))⟩

def schema137_valid : schema137.Valid := by
  intro env hd hp
  norm_num [schema137, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema138 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x1f4) 1))) (qDiv2 (qc (3) 1) (qc (0x1f4) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x1f4) 1))) (qc (3) 0x1f4)))⟩

def schema138_valid : schema138.Valid := by
  intro env hd hp
  norm_num [schema138, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema139 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x271) 1))) (qDiv2 (qc (1) 1) (qc (0x271) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x271) 1))) (qc (1) 0x271)))⟩

def schema139_valid : schema139.Valid := by
  intro env hd hp
  norm_num [schema139, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema140 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xf3) 1))) (qDiv2 (qc (1) 1) (qc (0xf3) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xf3) 1))) (qc (1) 0xf3)))⟩

def schema140_valid : schema140.Valid := by
  intro env hd hp
  norm_num [schema140, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema141 : Schema := ⟨[], [], (qEq2 (alias1 (qMul2 (qDiv2 x1 x2) x0)) (qMul2 (alias1 (qDiv2 x1 x2)) (alias1 x0)))⟩

def schema141_valid : schema141.Valid := by
  intro env hd hp
  norm_num [schema141, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema142 : Schema := ⟨[], [], (bEq2 (qEq2 x0 (qMul2 (alias1 (qDiv2 x2 x3)) x1)) (qEq2 x0 (qMul2 x1 (alias1 (qDiv2 x2 x3)))))⟩

def schema142_valid : schema142.Valid := by
  intro env hd hp
  norm_num [schema142, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema143 : Schema := ⟨[], [], (qEq2 (qMul2 x0 (alias1 (qDiv2 x1 x2))) (qMul2 (alias1 (qDiv2 x1 x2)) x0))⟩

def schema143_valid : schema143.Valid := by
  intro env hd hp
  norm_num [schema143, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema144 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (4) 1))) (qDiv2 (qc (5) 1) (qc (4) 1))) (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (4) 1))) (qc (5) 4)))⟩

def schema144_valid : schema144.Valid := by
  intro env hd hp
  norm_num [schema144, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema145 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x1 x2), (qEq2 x2 x3), (qEq2 x3 x4)], (qEq2 x0 x4)⟩

def schema145_valid : schema145.Valid := by
  intro env hd hp
  norm_num [schema145, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema146 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x64) 1))) (qDiv2 (qc (3) 1) (qc (0x64) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x64) 1))) (qc (3) 0x64)))⟩

def schema146_valid : schema146.Valid := by
  intro env hd hp
  norm_num [schema146, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema147 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x961) 1))) (qDiv2 (qc (1) 1) (qc (0x961) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x961) 1))) (qc (1) 0x961)))⟩

def schema147_valid : schema147.Valid := by
  intro env hd hp
  norm_num [schema147, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema148 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x1000) 1))) (qDiv2 (qc (1) 1) (qc (0x1000) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x1000) 1))) (qc (1) 0x1000)))⟩

def schema148_valid : schema148.Valid := by
  intro env hd hp
  norm_num [schema148, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema149 : Schema := ⟨[], [(zEq2 x0 x1)], (bEq2 (zEq2 x0 (zc (0))) (zEq2 x1 (zc (0))))⟩

def schema149_valid : schema149.Valid := by
  intro env hd hp
  norm_num [schema149, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema150 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x9c4) 1))) (qDiv2 (qc (3) 1) (qc (0x9c4) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x9c4) 1))) (qc (3) 0x9c4)))⟩

def schema150_valid : schema150.Valid := by
  intro env hd hp
  norm_num [schema150, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema151 : Schema := ⟨[], [], (bEq2 (alias1 (ite3 x0 x1 x2)) (ite3 x0 (alias1 x1) (alias1 x2)))⟩

def schema151_valid : schema151.Valid := by
  intro env hd hp
  norm_num [schema151, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema152 : Schema := ⟨[], [], (bOr2 x0 (qEq2 x1 (ite3 x0 (qc (1) 1) x1)))⟩

def schema152_valid : schema152.Valid := by
  intro env hd hp
  norm_num [schema152, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema153 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x1117) 1))) (qDiv2 (qc (1) 1) (qc (0x1117) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x1117) 1))) (qc (1) 0x1117)))⟩

def schema153_valid : schema153.Valid := by
  intro env hd hp
  norm_num [schema153, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema154 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x19a1) 1))) (qDiv2 (qc (1) 1) (qc (0x19a1) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x19a1) 1))) (qc (1) 0x19a1)))⟩

def schema154_valid : schema154.Valid := by
  intro env hd hp
  norm_num [schema154, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema155 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x88b) 1))) (qDiv2 (qc (1) 1) (qc (0x88b) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x88b) 1))) (qc (1) 0x88b)))⟩

def schema155_valid : schema155.Valid := by
  intro env hd hp
  norm_num [schema155, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema156 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x6b3) 1))) (qDiv2 (qc (1) 1) (qc (0x6b3) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x6b3) 1))) (qc (1) 0x6b3)))⟩

def schema156_valid : schema156.Valid := by
  intro env hd hp
  norm_num [schema156, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema157 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xc35) 1))) (qDiv2 (qc (1) 1) (qc (0xc35) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0xc35) 1))) (qc (1) 0xc35)))⟩

def schema157_valid : schema157.Valid := by
  intro env hd hp
  norm_num [schema157, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema158 : Schema := ⟨[], [(zEq2 (zc (1)) x0)], (zEq2 x0 (zc (1)))⟩

def schema158_valid : schema158.Valid := by
  intro env hd hp
  norm_num [schema158, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema159 : Schema := ⟨[], [(zEq2 (zc (0)) x0), (zEq2 x1 (zc (1)))], (bEq2 (zEq2 (zc (0)) x1) (zEq2 x0 (zc (1))))⟩

def schema159_valid : schema159.Valid := by
  intro env hd hp
  norm_num [schema159, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema160 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (4) 1) (qc (3) 1))) (qDiv2 (qc (4) 1) (qc (3) 1))) (qEq2 (alias1 (qDiv2 (qc (4) 1) (qc (3) 1))) (qc (4) 3)))⟩

def schema160_valid : schema160.Valid := by
  intro env hd hp
  norm_num [schema160, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema161 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x1 x2), (qEq2 x2 x3), (qEq2 x3 x4), (qEq2 x4 x5)], (qEq2 x0 x5)⟩

def schema161_valid : schema161.Valid := by
  intro env hd hp
  norm_num [schema161, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema162 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 x1)) (qLe2 x0 (alias1 x1)))⟩

def schema162_valid : schema162.Valid := by
  intro env hd hp
  norm_num [schema162, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema163 : Schema := ⟨[], [], (bOrn [(bNot1 (bOr3 x0 x1 x2)), x0, x1, x2])⟩

def schema163_valid : schema163.Valid := by
  intro env hd hp
  norm_num [schema163, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema164 : Schema := ⟨[], [(zEq2 x0 x1), (zEq2 x1 (zc (0)))], (zEq2 x0 (zc (0)))⟩

def schema164_valid : schema164.Valid := by
  intro env hd hp
  norm_num [schema164, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema165 : Schema := ⟨[], [(qEq2 x0 x1), (qEq2 x1 x2), (qEq2 x2 x3), (qEq2 x3 x4), (qEq2 x4 x5), (qEq2 x5 x6)], (qEq2 x0 x6)⟩

def schema165_valid : schema165.Valid := by
  intro env hd hp
  norm_num [schema165, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema166 : Schema := ⟨[], [(zEq2 x0 x1), (zEq2 x1 x2)], (zEq2 x0 x2)⟩

def schema166_valid : schema166.Valid := by
  intro env hd hp
  norm_num [schema166, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema167 : Schema := ⟨[], [], (bEq2 (zEq2 x0 (zc (0))) (zEq2 (zc (0)) x0))⟩

def schema167_valid : schema167.Valid := by
  intro env hd hp
  norm_num [schema167, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema168 : Schema := ⟨[], [], (bEq2 (alias1 (bAndn [bt, x0, x1, x2])) (bAndn [bt, (alias1 x0), (alias1 x1), (alias1 x2)]))⟩

def schema168_valid : schema168.Valid := by
  intro env hd hp
  norm_num [schema168, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema169 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (bAndn [bt, x1, x2, x3])) (bEq2 x0 (bAnd3 x1 x2 x3)))⟩

def schema169_valid : schema169.Valid := by
  intro env hd hp
  norm_num [schema169, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema170 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 (qc (1) 1) x0)) (qLt2 (qc (1) 1) (alias1 x0)))⟩

def schema170_valid : schema170.Valid := by
  intro env hd hp
  norm_num [schema170, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema171 : Schema := ⟨[], [], (bEq2 (qLt2 (qc (1) 1) x0) (bNot1 (qLe2 x0 (qc (1) 1))))⟩

def schema171_valid : schema171.Valid := by
  intro env hd hp
  norm_num [schema171, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema172 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (10) 1) (qc (9) 1))) (qDiv2 (qc (10) 1) (qc (9) 1))) (qEq2 (alias1 (qDiv2 (qc (10) 1) (qc (9) 1))) (qc (10) 9)))⟩

def schema172_valid : schema172.Valid := by
  intro env hd hp
  norm_num [schema172, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema173 : Schema := ⟨[], [(qEq2 (alias1 (qDiv2 (qc (1) 1) x2)) x0), (qEq2 x0 x1)], (qEq2 (alias1 (qDiv2 (qc (1) 1) x2)) x1)⟩

def schema173_valid : schema173.Valid := by
  intro env hd hp
  norm_num [schema173, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema174 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (28) 1))) (qDiv2 (qc (3) 1) (qc (28) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (28) 1))) (qc (3) 28)))⟩

def schema174_valid : schema174.Valid := by
  intro env hd hp
  norm_num [schema174, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema175 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (0x41a7) 1))) (qDiv2 (qc (5) 1) (qc (0x41a7) 1))) (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (0x41a7) 1))) (qc (5) 0x41a7)))⟩

def schema175_valid : schema175.Valid := by
  intro env hd hp
  norm_num [schema175, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema176 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x157) 1))) (qDiv2 (qc (1) 1) (qc (0x157) 1))) (qEq2 (alias1 (qDiv2 (qc (1) 1) (qc (0x157) 1))) (qc (1) 0x157)))⟩

def schema176_valid : schema176.Valid := by
  intro env hd hp
  norm_num [schema176, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema177 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (0x961) 1))) (qDiv2 (qc (5) 1) (qc (0x961) 1))) (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (0x961) 1))) (qc (5) 0x961)))⟩

def schema177_valid : schema177.Valid := by
  intro env hd hp
  norm_num [schema177, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema178 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 (qDiv2 x1 x2) x0)) (qLt2 (alias1 (qDiv2 x1 x2)) (alias1 x0)))⟩

def schema178_valid : schema178.Valid := by
  intro env hd hp
  norm_num [schema178, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema179 : Schema := ⟨[], [], (bEq2 (qLt2 (alias1 (qDiv2 x1 x2)) x0) (bNot1 (qLe2 x0 (alias1 (qDiv2 x1 x2)))))⟩

def schema179_valid : schema179.Valid := by
  intro env hd hp
  norm_num [schema179, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema180 : Schema := ⟨[], [], (bEq2 (bEq2 (qLe2 x0 (alias1 (qDiv2 x2 x3))) x1) (bEq2 (qLe2 (qc (0) 1) (qAdd2 (alias1 (qDiv2 x2 x3)) (qMul2 (qc (-1) 1) x0))) x1))⟩

def schema180_valid : schema180.Valid := by
  intro env hd hp
  norm_num [schema180, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema181 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (7) 1))) (qDiv2 (qc (5) 1) (qc (7) 1))) (qEq2 (alias1 (qDiv2 (qc (5) 1) (qc (7) 1))) (qc (5) 7)))⟩

def schema181_valid : schema181.Valid := by
  intro env hd hp
  norm_num [schema181, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema182 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 x1 x0)) (qLt2 x1 (alias1 x0)))⟩

def schema182_valid : schema182.Valid := by
  intro env hd hp
  norm_num [schema182, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema183 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 x0 x1)) (qLe2 (alias1 x0) x1))⟩

def schema183_valid : schema183.Valid := by
  intro env hd hp
  norm_num [schema183, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema184 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 x1 x2)) (bEq2 x0 (qLe2 x1 x2)))⟩

def schema184_valid : schema184.Valid := by
  intro env hd hp
  norm_num [schema184, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema185 : Schema := ⟨[], [], (bEq2 (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x30d4) 1))) (qDiv2 (qc (3) 1) (qc (0x30d4) 1))) (qEq2 (alias1 (qDiv2 (qc (3) 1) (qc (0x30d4) 1))) (qc (3) 0x30d4)))⟩

def schema185_valid : schema185.Valid := by
  intro env hd hp
  norm_num [schema185, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema186 : Schema := ⟨[], [], (bEq2 (alias1 (qLe2 (qDiv2 x1 x2) x0)) (qLe2 (alias1 (qDiv2 x1 x2)) x0))⟩

def schema186_valid : schema186.Valid := by
  intro env hd hp
  norm_num [schema186, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema187 : Schema := ⟨[], [], (bEq2 (bEq2 x0 (qLe2 (alias1 (qDiv2 x2 x3)) x1)) (bEq2 x0 (qLe2 (qc (0) 1) (qAdd2 x1 (qMul2 (qc (-1) 1) (alias1 (qDiv2 x2 x3)))))))⟩

def schema187_valid : schema187.Valid := by
  intro env hd hp
  norm_num [schema187, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema188 : Schema := ⟨[], [], (bEq2 (alias1 (qLt2 x0 x1)) (qLt2 x0 (alias1 x1)))⟩

def schema188_valid : schema188.Valid := by
  intro env hd hp
  norm_num [schema188, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

def schema189 : Schema := ⟨[], [(zEq2 x0 (zc (0)))], (zEq2 (zc (0)) x0)⟩

def schema189_valid : schema189.Valid := by
  intro env hd hp
  norm_num [schema189, eval, evalOp, boolValue, intValue, ratValue, zeroValue] at hd hp ⊢ <;>
    grind (config := { splits := 64, ematch := 0, gen := 0 })

end ClosureRewriteParametric

end PolicySubmissionPart17

/- Component CompactNatData; SHA256 2ab9f722c7bce53f25abfeb5db53bc4cd7258217f43b0aed46de4c663a2ba4f8. -/
section PolicySubmissionPart18
/- Packed base-64 digits of finite numerical certificate data. -/
namespace CompactNatData

def step (state : List Nat × Nat × Nat) (d : Nat) : List Nat × Nat × Nat :=
  let value := state.2.1 + d % 32 * state.2.2
  if d < 32 then (value :: state.1, 0, 1)
  else (state.1, value, state.2.2 * 32)

def read : Nat → Nat → (List Nat × Nat × Nat) → (List Nat × Nat × Nat)
  | 0, _, state => state
  | fuel + 1, packed, state => read fuel (packed / 64) (step state (packed % 64))

def decode (digits packed : Nat) : List Nat :=
  (read digits packed ([], 0, 1)).1.reverse

end CompactNatData

end PolicySubmissionPart18

/- Component PackedNatTable; SHA256 4dbc0fd1f62f91219e64063380c873d611f8bd540bba3156d774d7ec2687dc0a. -/
section PolicySubmissionPart19
/- Random access to finite packed numerical records using balanced tables. -/
namespace PackedNatTable

inductive Table (α : Type) where
  | leaf : Array α → Table α
  | branch : Nat → Table α → Table α → Table α

def Table.get (fallback : α) : Table α → Nat → α
  | .leaf xs, i => xs[i]?.getD fallback
  | .branch cutoff left right, i =>
      if i < cutoff then left.get fallback i else right.get fallback (i - cutoff)

structure Block where
  offsets : Nat
  data : Nat

def emptyBlock : Block := ⟨0, 0⟩

def Block.start (b : Block) (i : Nat) : Nat :=
  (b.offsets >>> (13 * i)) &&& 0x1fff

def Block.get (b : Block) (i : Nat) : List Nat :=
  let first := b.start i
  let count := b.start (i + 1) - first
  let packed := (b.data >>> (6 * first)) &&& ((1 <<< (6 * count)) - 1)
  CompactNatData.decode count packed

def records (t : Table Block) (i : Nat) : List Nat :=
  (t.get emptyBlock (i / 32)).get (i % 32)

end PackedNatTable

end PolicySubmissionPart19

/- Component PackedTableAll; SHA256 9c01cd09571cad070d9e1d6443d53b7794fed50f43d7a2fa1b7fd48859621c7c. -/
section PolicySubmissionPart20
namespace PackedNatTable

def Table.All (P : α → Prop) : Table α → Prop
  | .leaf xs => ∀ a ∈ xs, P a
  | .branch _ left right => left.All P ∧ right.All P

def Table.get_all (P : α → Prop) (fallback : α) (hf : P fallback)
    (t : Table α) (ht : t.All P) (i : Nat) : P (t.get fallback i) := by
  induction t generalizing i with
  | leaf xs =>
    cases he : xs[i]? with
    | none => simpa only [Table.get, he, Option.getD_none] using hf
    | some a =>
      simpa only [Table.get, he, Option.getD_some] using ht a (Array.mem_of_getElem? he)
  | branch cutoff left right ihl ihr =>
    obtain ⟨hl, hr⟩ := ht
    by_cases hi : i < cutoff
    · simpa only [Table.get, hi, ↓reduceIte] using ihl hl i
    · simpa only [Table.get, hi, ↓reduceIte] using ihr hr (i - cutoff)

end PackedNatTable

end PolicySubmissionPart20

/- Component ClosureSchemaParametricRegistry; SHA256 0dc7118a6102a6013eced625d3ebf736d4cb3fe5bc7c02a35a71c392bd03a4c1. -/
section PolicySubmissionPart21
namespace ClosureRewriteParametric
open ClosurePattern ClosureSemantics PackedNatTable

def fallback : Schema := ⟨[], [], .node (.bConst true) []⟩

def fallback_valid : fallback.Valid := by
  simp [Schema.Valid, fallback, eval, evalOp, boolValue]

def tableLLLL : Table Schema := .leaf #[schema0, schema1, schema2, schema3, schema4, schema5, schema6, schema7, schema8, schema9, schema10]

def tableLLLL_valid : tableLLLL.All Schema.Valid := by
  simp [Table.All, tableLLLL, schema0_valid, schema1_valid, schema2_valid, schema3_valid, schema4_valid, schema5_valid, schema6_valid, schema7_valid, schema8_valid, schema9_valid, schema10_valid]

def tableLLLR : Table Schema := .leaf #[schema11, schema12, schema13, schema14, schema15, schema16, schema17, schema18, schema19, schema20, schema21, schema22]

def tableLLLR_valid : tableLLLR.All Schema.Valid := by
  simp [Table.All, tableLLLR, schema11_valid, schema12_valid, schema13_valid, schema14_valid, schema15_valid, schema16_valid, schema17_valid, schema18_valid, schema19_valid, schema20_valid, schema21_valid, schema22_valid]

def tableLLL : Table Schema := .branch 11 tableLLLL tableLLLR

def tableLLL_valid : tableLLL.All Schema.Valid := ⟨tableLLLL_valid, tableLLLR_valid⟩

def tableLLRL : Table Schema := .leaf #[schema23, schema24, schema25, schema26, schema27, schema28, schema29, schema30, schema31, schema32, schema33, schema34]

def tableLLRL_valid : tableLLRL.All Schema.Valid := by
  simp [Table.All, tableLLRL, schema23_valid, schema24_valid, schema25_valid, schema26_valid, schema27_valid, schema28_valid, schema29_valid, schema30_valid, schema31_valid, schema32_valid, schema33_valid, schema34_valid]

def tableLLRR : Table Schema := .leaf #[schema35, schema36, schema37, schema38, schema39, schema40, schema41, schema42, schema43, schema44, schema45, schema46]

def tableLLRR_valid : tableLLRR.All Schema.Valid := by
  simp [Table.All, tableLLRR, schema35_valid, schema36_valid, schema37_valid, schema38_valid, schema39_valid, schema40_valid, schema41_valid, schema42_valid, schema43_valid, schema44_valid, schema45_valid, schema46_valid]

def tableLLR : Table Schema := .branch 12 tableLLRL tableLLRR

def tableLLR_valid : tableLLR.All Schema.Valid := ⟨tableLLRL_valid, tableLLRR_valid⟩

def tableLL : Table Schema := .branch 23 tableLLL tableLLR

def tableLL_valid : tableLL.All Schema.Valid := ⟨tableLLL_valid, tableLLR_valid⟩

def tableLRLL : Table Schema := .leaf #[schema47, schema48, schema49, schema50, schema51, schema52, schema53, schema54, schema55, schema56, schema57, schema58]

def tableLRLL_valid : tableLRLL.All Schema.Valid := by
  simp [Table.All, tableLRLL, schema47_valid, schema48_valid, schema49_valid, schema50_valid, schema51_valid, schema52_valid, schema53_valid, schema54_valid, schema55_valid, schema56_valid, schema57_valid, schema58_valid]

def tableLRLR : Table Schema := .leaf #[schema59, schema60, schema61, schema62, schema63, schema64, schema65, schema66, schema67, schema68, schema69, schema70]

def tableLRLR_valid : tableLRLR.All Schema.Valid := by
  simp [Table.All, tableLRLR, schema59_valid, schema60_valid, schema61_valid, schema62_valid, schema63_valid, schema64_valid, schema65_valid, schema66_valid, schema67_valid, schema68_valid, schema69_valid, schema70_valid]

def tableLRL : Table Schema := .branch 12 tableLRLL tableLRLR

def tableLRL_valid : tableLRL.All Schema.Valid := ⟨tableLRLL_valid, tableLRLR_valid⟩

def tableLRRL : Table Schema := .leaf #[schema71, schema72, schema73, schema74, schema75, schema76, schema77, schema78, schema79, schema80, schema81, schema82]

def tableLRRL_valid : tableLRRL.All Schema.Valid := by
  simp [Table.All, tableLRRL, schema71_valid, schema72_valid, schema73_valid, schema74_valid, schema75_valid, schema76_valid, schema77_valid, schema78_valid, schema79_valid, schema80_valid, schema81_valid, schema82_valid]

def tableLRRR : Table Schema := .leaf #[schema83, schema84, schema85, schema86, schema87, schema88, schema89, schema90, schema91, schema92, schema93, schema94]

def tableLRRR_valid : tableLRRR.All Schema.Valid := by
  simp [Table.All, tableLRRR, schema83_valid, schema84_valid, schema85_valid, schema86_valid, schema87_valid, schema88_valid, schema89_valid, schema90_valid, schema91_valid, schema92_valid, schema93_valid, schema94_valid]

def tableLRR : Table Schema := .branch 12 tableLRRL tableLRRR

def tableLRR_valid : tableLRR.All Schema.Valid := ⟨tableLRRL_valid, tableLRRR_valid⟩

def tableLR : Table Schema := .branch 24 tableLRL tableLRR

def tableLR_valid : tableLR.All Schema.Valid := ⟨tableLRL_valid, tableLRR_valid⟩

def tableL : Table Schema := .branch 47 tableLL tableLR

def tableL_valid : tableL.All Schema.Valid := ⟨tableLL_valid, tableLR_valid⟩

def tableRLLL : Table Schema := .leaf #[schema95, schema96, schema97, schema98, schema99, schema100, schema101, schema102, schema103, schema104, schema105]

def tableRLLL_valid : tableRLLL.All Schema.Valid := by
  simp [Table.All, tableRLLL, schema95_valid, schema96_valid, schema97_valid, schema98_valid, schema99_valid, schema100_valid, schema101_valid, schema102_valid, schema103_valid, schema104_valid, schema105_valid]

def tableRLLR : Table Schema := .leaf #[schema106, schema107, schema108, schema109, schema110, schema111, schema112, schema113, schema114, schema115, schema116, schema117]

def tableRLLR_valid : tableRLLR.All Schema.Valid := by
  simp [Table.All, tableRLLR, schema106_valid, schema107_valid, schema108_valid, schema109_valid, schema110_valid, schema111_valid, schema112_valid, schema113_valid, schema114_valid, schema115_valid, schema116_valid, schema117_valid]

def tableRLL : Table Schema := .branch 11 tableRLLL tableRLLR

def tableRLL_valid : tableRLL.All Schema.Valid := ⟨tableRLLL_valid, tableRLLR_valid⟩

def tableRLRL : Table Schema := .leaf #[schema118, schema119, schema120, schema121, schema122, schema123, schema124, schema125, schema126, schema127, schema128, schema129]

def tableRLRL_valid : tableRLRL.All Schema.Valid := by
  simp [Table.All, tableRLRL, schema118_valid, schema119_valid, schema120_valid, schema121_valid, schema122_valid, schema123_valid, schema124_valid, schema125_valid, schema126_valid, schema127_valid, schema128_valid, schema129_valid]

def tableRLRR : Table Schema := .leaf #[schema130, schema131, schema132, schema133, schema134, schema135, schema136, schema137, schema138, schema139, schema140, schema141]

def tableRLRR_valid : tableRLRR.All Schema.Valid := by
  simp [Table.All, tableRLRR, schema130_valid, schema131_valid, schema132_valid, schema133_valid, schema134_valid, schema135_valid, schema136_valid, schema137_valid, schema138_valid, schema139_valid, schema140_valid, schema141_valid]

def tableRLR : Table Schema := .branch 12 tableRLRL tableRLRR

def tableRLR_valid : tableRLR.All Schema.Valid := ⟨tableRLRL_valid, tableRLRR_valid⟩

def tableRL : Table Schema := .branch 23 tableRLL tableRLR

def tableRL_valid : tableRL.All Schema.Valid := ⟨tableRLL_valid, tableRLR_valid⟩

def tableRRLL : Table Schema := .leaf #[schema142, schema143, schema144, schema145, schema146, schema147, schema148, schema149, schema150, schema151, schema152, schema153]

def tableRRLL_valid : tableRRLL.All Schema.Valid := by
  simp [Table.All, tableRRLL, schema142_valid, schema143_valid, schema144_valid, schema145_valid, schema146_valid, schema147_valid, schema148_valid, schema149_valid, schema150_valid, schema151_valid, schema152_valid, schema153_valid]

def tableRRLR : Table Schema := .leaf #[schema154, schema155, schema156, schema157, schema158, schema159, schema160, schema161, schema162, schema163, schema164, schema165]

def tableRRLR_valid : tableRRLR.All Schema.Valid := by
  simp [Table.All, tableRRLR, schema154_valid, schema155_valid, schema156_valid, schema157_valid, schema158_valid, schema159_valid, schema160_valid, schema161_valid, schema162_valid, schema163_valid, schema164_valid, schema165_valid]

def tableRRL : Table Schema := .branch 12 tableRRLL tableRRLR

def tableRRL_valid : tableRRL.All Schema.Valid := ⟨tableRRLL_valid, tableRRLR_valid⟩

def tableRRRL : Table Schema := .leaf #[schema166, schema167, schema168, schema169, schema170, schema171, schema172, schema173, schema174, schema175, schema176, schema177]

def tableRRRL_valid : tableRRRL.All Schema.Valid := by
  simp [Table.All, tableRRRL, schema166_valid, schema167_valid, schema168_valid, schema169_valid, schema170_valid, schema171_valid, schema172_valid, schema173_valid, schema174_valid, schema175_valid, schema176_valid, schema177_valid]

def tableRRRR : Table Schema := .leaf #[schema178, schema179, schema180, schema181, schema182, schema183, schema184, schema185, schema186, schema187, schema188, schema189]

def tableRRRR_valid : tableRRRR.All Schema.Valid := by
  simp [Table.All, tableRRRR, schema178_valid, schema179_valid, schema180_valid, schema181_valid, schema182_valid, schema183_valid, schema184_valid, schema185_valid, schema186_valid, schema187_valid, schema188_valid, schema189_valid]

def tableRRR : Table Schema := .branch 12 tableRRRL tableRRRR

def tableRRR_valid : tableRRR.All Schema.Valid := ⟨tableRRRL_valid, tableRRRR_valid⟩

def tableRR : Table Schema := .branch 24 tableRRL tableRRR

def tableRR_valid : tableRR.All Schema.Valid := ⟨tableRRL_valid, tableRRR_valid⟩

def tableR : Table Schema := .branch 47 tableRL tableRR

def tableR_valid : tableR.All Schema.Valid := ⟨tableRL_valid, tableRR_valid⟩

def table : Table Schema := .branch 95 tableL tableR

def table_valid : table.All Schema.Valid := ⟨tableL_valid, tableR_valid⟩

def schema (i : Nat) : Schema := table.get fallback i

def schema_valid (i : Nat) : (schema i).Valid :=
  Table.get_all Schema.Valid fallback fallback_valid table table_valid i

end ClosureRewriteParametric

end PolicySubmissionPart21

/- Component PolicyLinearClause; SHA256 ed38b741d2cf872a03c0e92ffd071c2fac5ec580ae6dba84d77409a7803affbc. -/
section PolicySubmissionPart22
/- Arithmetic implication certificates imply the actual signed SAT clauses. -/
namespace ClosureLinear
open ClosureSemantics Bounty

def implicationIncluded (premises : List ℕ) (conclusion : ℕ) (clause : List ℤ) : Bool :=
  decide (((conclusion + 1 : ℕ) : ℤ) ∈ clause) &&
    premises.all (fun i => decide (-((i + 1 : ℕ) : ℤ) ∈ clause))

def dense_positive_holds (values : Valuation) (i : ℕ) (h : (values i).b = true) :
    policySignedHolds (fun v => (values (v - 1)).b = true) ((i + 1 : ℕ) : ℤ) := by
  have hp : (0 : ℤ) < ((i + 1 : ℕ) : ℤ) := by omega
  simpa only [policySignedHolds, if_pos hp, Int.natAbs_natCast, Nat.add_sub_cancel] using h

def dense_negative_holds (values : Valuation) (i : ℕ) (h : (values i).b ≠ true) :
    policySignedHolds (fun v => (values (v - 1)).b = true) (-((i + 1 : ℕ) : ℤ)) := by
  have hp : ¬(0 : ℤ) < -((i + 1 : ℕ) : ℤ) := by omega
  simpa only [policySignedHolds, if_neg hp, Int.natAbs_neg, Int.natAbs_natCast,
    Nat.add_sub_cancel] using h

def implicationIncluded_sound (values : Valuation) (premises : List ℕ)
    (conclusion : ℕ) (clause : List ℤ)
    (hc : implicationIncluded premises conclusion clause = true)
    (h : (∀ i ∈ premises, (values i).b = true) → (values conclusion).b = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) clause := by
  classical
  have hp : (((conclusion + 1 : ℕ) : ℤ) ∈ clause) ∧
      ∀ i ∈ premises, -((i + 1 : ℕ) : ℤ) ∈ clause := by
    simpa [implicationIncluded, Bool.and_eq_true] using hc
  by_cases hm : ∀ i ∈ premises, (values i).b = true
  · exact ⟨_, hp.1, dense_positive_holds values conclusion (h hm)⟩
  · push Not at hm
    obtain ⟨i, hi, hv⟩ := hm
    exact ⟨_, hp.2 i hi, dense_negative_holds values i hv⟩

def checkImplicationClause (program : ℕ → Node) (ids : List ℕ) (integer : Bool)
    (fuel : ℕ) (premises : List ℕ) (conclusion : ℕ) (certs : List (List (ℕ × ℕ)))
    (clause : List ℤ) : Bool :=
  implicationIncluded premises conclusion clause &&
    checkImplication program ids integer fuel premises conclusion certs

def checkImplicationClause_sound (program : ℕ → Node) (ids : List ℕ) (integer : Bool)
    (input values : Valuation) (he : Equations program input values)
    (fuel : ℕ) (premises : List ℕ) (conclusion : ℕ) (certs : List (List (ℕ × ℕ)))
    (clause : List ℤ)
    (hc : checkImplicationClause program ids integer fuel premises conclusion certs clause = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) clause := by
  have hp : implicationIncluded premises conclusion clause = true ∧
      checkImplication program ids integer fuel premises conclusion certs = true := by
    simpa [checkImplicationClause, Bool.and_eq_true] using hc
  exact implicationIncluded_sound values premises conclusion clause hp.1
    (checkImplication_sound program ids integer input values he fuel premises conclusion certs hp.2)

end ClosureLinear

end PolicySubmissionPart22

/- Component PolicyLinearRecords; SHA256 3015b3ca06db8cd233f235e499a16993dae4a4e9e4896b710e8d43364ef16b85. -/
section PolicySubmissionPart23
/- Untrusted numerical records and bounded batches of arithmetic certificates. -/
namespace ClosureLinear
open ClosureSemantics Bounty

structure ArithmeticCertificate where
  integer : Bool
  fuel : ℕ
  conclusion : ℕ
  cuts : List ℕ
  premises : List ℕ
  weights : List (List (ℕ × ℕ))

def readNatList : List ℕ → Option (List ℕ × List ℕ)
  | [] => none
  | n :: xs => if n ≤ xs.length then some (xs.take n, xs.drop n) else none

def readWeightPairs : ℕ → List ℕ → Option (List (ℕ × ℕ) × List ℕ)
  | 0, xs => some ([], xs)
  | n + 1, i :: w :: xs => do
    let (rest, tail) ← readWeightPairs n xs
    pure ((i, w) :: rest, tail)
  | _, _ => none

def readWeightBranches : ℕ → List ℕ → Option (List (List (ℕ × ℕ)) × List ℕ)
  | 0, xs => some ([], xs)
  | n + 1, count :: xs => do
    let (weights, tail) ← readWeightPairs count xs
    let (rest, tail) ← readWeightBranches n tail
    pure (weights :: rest, tail)
  | _, _ => none

def decodeArithmeticCertificate : List ℕ → Option ArithmeticCertificate
  | mode :: fuel :: conclusion :: xs => do
    let (cuts, xs) ← readNatList xs
    let (premises, xs) ← readNatList xs
    match xs with
    | count :: xs =>
      let (weights, tail) ← readWeightBranches count xs
      match tail with
      | [] => pure ⟨mode == 1, fuel, conclusion, cuts, premises, weights⟩
      | _ => none
    | [] => none
  | _ => none

def checkArithmeticRecord (program : ℕ → Node) (clause : List ℤ) (record : List ℕ) : Bool :=
  match decodeArithmeticCertificate record with
  | none => false
  | some cert => checkImplicationClause program cert.cuts cert.integer cert.fuel
      cert.premises cert.conclusion cert.weights clause

def checkArithmeticRecord_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (clause : List ℤ) (record : List ℕ)
    (hc : checkArithmeticRecord program clause record = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) clause := by
  cases hd : decodeArithmeticCertificate record with
  | none => simp [checkArithmeticRecord, hd] at hc
  | some cert =>
    exact checkImplicationClause_sound program cert.cuts cert.integer input values he
      cert.fuel cert.premises cert.conclusion cert.weights clause
      (by simpa [checkArithmeticRecord, hd] using hc)

def checkArithmeticEntry (program : ℕ → Node) (clauses : ℕ → List ℤ) : List ℕ → Bool
  | [] => false
  | clauseId :: record => checkArithmeticRecord program (clauses clauseId) record

def checkArithmeticEntry_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : ℕ → List ℤ) (entry : List ℕ)
    (hc : checkArithmeticEntry program clauses entry = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) (clauses (entry.headD 0)) := by
  cases entry with
  | nil => simp [checkArithmeticEntry] at hc
  | cons clauseId record =>
    exact checkArithmeticRecord_sound program input values he (clauses clauseId) record hc

def checkArithmeticBlock (program : ℕ → Node) (clauses : ℕ → List ℤ)
    (records : ℕ → List ℕ) (start count : ℕ) : Bool :=
  (List.range count).all fun i => checkArithmeticEntry program clauses (records (start + i))

def checkArithmeticBlock_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : ℕ → List ℤ) (records : ℕ → List ℕ)
    (start count : ℕ) (hc : checkArithmeticBlock program clauses records start count = true)
    (i : ℕ) (hi : i < count) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (clauses ((records (start + i)).headD 0)) := by
  have h : ∀ j ∈ List.range count,
      checkArithmeticEntry program clauses (records (start + j)) = true := by
    simpa only [checkArithmeticBlock, List.all_eq_true] using hc
  exact checkArithmeticEntry_sound program input values he clauses (records (start + i))
    (h i (List.mem_range.mpr hi))

end ClosureLinear

end PolicySubmissionPart23

/- Component ClosureSchemaParametricRecords; SHA256 3c51ab537365a243c9a9ae846878c9d35657109bf657203fff54f634968efa3f. -/
section PolicySubmissionPart24
namespace ClosurePattern
open ClosureSemantics Bounty

structure SchemaCertificate where
  schemaIndex : Nat
  fuel : Nat
  conclusion : Nat
  cuts : List Nat
  premises : List Nat

def decodeSchemaCertificate : List Nat → Option SchemaCertificate
  | schemaIndex :: fuel :: conclusion :: xs => do
      let (cuts, xs) ← ClosureLinear.readNatList xs
      let (premises, tail) ← ClosureLinear.readNatList xs
      match tail with
      | [] => pure ⟨schemaIndex, fuel, conclusion, cuts, premises⟩
      | _ => none
  | _ => none

def checkSchemaRecord (program : Nat → Node) (clause : List Int) (record : List Nat) : Bool :=
  match decodeSchemaCertificate record with
  | none => false
  | some cert =>
      ClosureLinear.implicationIncluded cert.premises cert.conclusion clause &&
      checkSchema program cert.cuts cert.fuel (ClosureRewriteParametric.schema cert.schemaIndex)
        cert.premises cert.conclusion

def checkSchemaRecord_sound (program : Nat → Node) (input values : Valuation)
    (he : Equations program input values) (clause : List Int) (record : List Nat)
    (hc : checkSchemaRecord program clause record = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) clause := by
  cases hd : decodeSchemaCertificate record with
  | none => simp [checkSchemaRecord, hd] at hc
  | some cert =>
    have hh : ClosureLinear.implicationIncluded cert.premises cert.conclusion clause = true ∧
        checkSchema program cert.cuts cert.fuel (ClosureRewriteParametric.schema cert.schemaIndex)
          cert.premises cert.conclusion = true := by
      simpa [checkSchemaRecord, hd, Bool.and_eq_true] using hc
    exact ClosureLinear.implicationIncluded_sound values cert.premises cert.conclusion clause hh.1
      (checkSchema_sound program cert.cuts input values he cert.fuel
        (ClosureRewriteParametric.schema cert.schemaIndex) cert.premises cert.conclusion
        (ClosureRewriteParametric.schema_valid cert.schemaIndex) hh.2)

def checkSchemaEntry (program : Nat → Node) (clauses : Nat → List Int) : List Nat → Bool
  | [] => false
  | clauseId :: record => checkSchemaRecord program (clauses clauseId) record

def checkSchemaEntry_sound (program : Nat → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : Nat → List Int) (entry : List Nat)
    (hc : checkSchemaEntry program clauses entry = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true) (clauses (entry.headD 0)) := by
  cases entry with
  | nil => simp [checkSchemaEntry] at hc
  | cons clauseId record => exact checkSchemaRecord_sound program input values he _ record hc

def checkSchemaBlock (program : Nat → Node) (clauses : Nat → List Int)
    (records : Nat → List Nat) (start count : Nat) : Bool :=
  (List.range count).all fun i => checkSchemaEntry program clauses (records (start + i))

def checkSchemaBlock_sound (program : Nat → Node) (input values : Valuation)
    (he : Equations program input values) (clauses : Nat → List Int) (records : Nat → List Nat)
    (start count : Nat) (hc : checkSchemaBlock program clauses records start count = true)
    (i : Nat) (hi : i < count) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (clauses ((records (start + i)).headD 0)) := by
  have h : ∀ j ∈ List.range count,
      checkSchemaEntry program clauses (records (start + j)) = true := by
    simpa only [checkSchemaBlock, List.all_eq_true] using hc
  exact checkSchemaEntry_sound program input values he clauses (records (start + i))
    (h i (List.mem_range.mpr hi))

end ClosurePattern

end PolicySubmissionPart24

/- Component PolicyInitialParametricData; SHA256 490025abab2651d5acd7ec2dd9fae3628428058da7a231380f5f297a0796b7f4. -/
section PolicySubmissionPart25
namespace PolicyCircuitPacked0
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x6102e01640ac0530280134094047022010407c03b01c00d406402f01600a404c023010007403401700a004401c00b0040014004000, 0x18fc0607fd7ded9e76f75cf9c73d6dcf5a73a65bdd86f65dbd966f555ad546b54dabd267a459e506763d8c8e5f1357acc4332d0cca3fe24ff883fd1ced86226146f840f90c2f42401⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x6ba82801aea07f06ba41f81ae807d06ba01f01ae707b06b9c1e81aba07906a981e01aa607706a801d81a6a075069a81d01a67073068f01c81a240710688c1c01a2306f067d81b819f606d067881b019bc06b066a81a819aa0690669c1a019a70670659819819650650658c1901963063064881881922061⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x72ec3801cba0bf072e82f81cb70bd072dc2f01cb70bb072b02e81cac0b9071d82e01c760b7071d42d81c750b5071d02d01c730b3071cc2c81c730b1071c82c01c720af071982b81c660ad070c82b01c320ab070c82a81c2c0a9070b02a01be70a706df42981b7d0a506cb82901b2b0a306cac2881b200a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x7ac04801e7c0ff079f03f81e760fd0798c3f01e630fb079883e81e620f9078fc3e01e3f0f7078c83d81df90f5077e43d01de80f3076d03c81d790f1075e43c01d760ef075d83b81d350ed074cc3b01d330eb074c83a81d320e9074943a01cf10e7073c43981ceb0e5073ac3901cbb0e3072ec3881cbb0e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x7fdc5801ff513f07fc84f81ff113d07fbc4f01feb13b07fac4e81fea13907f804e01fa613707e984d81fa513507e904d01fa313307ddc4c81f7113107cf84c01f3e12f07c944b81f2512d07c904b01f2412b07c844a81f2112907bd84a01ee012707b804981ebf12507af84901ebe12307af44881ebd121⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa3e068028f617f0a3cc5f828f117d0a3b85f028ea17b0a3a05e828e21790a3805e028bd1770a2e45d828b71750a2c05d028ad1730a2ac5c828a91710a2885c028a016f0a1f45b8287916d0a1dc5b0286e16b0a1b45a8286a1690a0fc5a028251670a084598282016507ff45901ffc16307fec5881ff8161⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa7e478029f51bf0a7c86f829ee1bd0a7ac6f029e91bb0a7906e829e11b90a6ec6e029a41b70a6846d8297e1b50a5f46d0297b1b30a5e46c829771b10a5d06c0296f1af0a5b46b829651ad0a5906b029621ab0a4ec6a829371a90a4cc6a029311a70a4b869829251a50a48c69029211a30a3f468828fa1a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa9e08802a771ff0a9d87f82a751fd0a9d47f02a751fb0a9cc7e82a701f90a9bc7e02a6c1f70a9847d82a601f50a8fc7d02a3e1f30a8f47c82a3d1f10a8dc7c02a311ef0a8c07b82a301ed0a8bc7b02a2e1eb0a8b87a82a2d1e90a8b47a02a251e70a88479829ff1e50a7fc79029fe1e30a7f878829fd1e1⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xadd49802b6823f0ad8c8f82b3b23d0ace48f02b3323b0acc88e82b2e2390acb48e02b2c2370aca08d82b262350ac908d02b202330abf88c82af72310abd48c02af122f0abbc8b82ab522d0aac48b02aaf22b0aabc8a82aaa2290aaa88a02aa82270aaa08982aa62250aa8c8902a7e2230a9f48882a7d221⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb190a802c6027f0b0e89f82c3827d0b0d89f02c3227b0b0b09e82c2c2790b0989e02c232770affc9d82bf82750afd49d02bf32730afc49c82bed2710afac9c02be926f0af989b82be426d0af8c9b02bbf26b0aef89a82bbc2690aee09a02bb22670aeb49982bab2650ae909902ba22630adf89882b7c261⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb4d8b802d312bf0b4c0af82d302bd0b4b0af02d2a2bb0b49cae82d232b90b3fcae02cfc2b70b3e4ad82cf72b50b3d0ad02cf02b30b3b8ac82ce62b10b394ac02ce32af0b380ab82cbc2ad0b2e8ab02cb42ab0b2c8aa82cb02a90b2b0aa02cab2a70b2a0a982c7c2a50b1eca902c722a30b1b0a882c692a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb7ecc802df92ff0b7e0bf82df42fd0b7ccbf02df12fb0b7b8be82ded2f90b7a4be02de82f70b798bd82de42f50b6f4bd02dba2f30b6dcbc82db52f10b6c8bc02db02ef0b6a8bb82da62ed0b690bb02da12eb0b5f4ba82d7b2e90b5ccba02d702e70b5b8b982d6c2e50b584b902d602e30b4f4b882d3b2e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xbad8d802eb533f0baaccf82eaa33d0ba9ccf02ea533b0ba8cce82ea13390ba80ce02e773370b9d0cd82e743350b9c4cd02e6f3330b9accc82e693310b8e8cc02e3932f0b8e0cb82e3632d0b8c8cb02e2d32b0b8b0ca82e2c3290b8acca02e283270b898c982e243250b888c902e213230b880c882dfe321⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xbde0e802f7437f0bdccdf82f7237d0bdc0df02f6f37b0bdb4de82f6a3790bda0de02f643770bd8cdd82f3e3750bcecdd02f373730bcd0dc82f303710bcbcdc02f2136f0bbf8db82efc36d0bbe0db02ef536b0bbc4da82eef3690bba8da02ee63670bb90d982ebe3650baf4d902ebc3630baecd882eb7361⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xe1f8f80387b3bf0e1e8ef8387a3bd0e1e8ef038793bb0e1e0ee838683b90e188ee0383d3b70e0eced838393b50e0dced038333b30e0b4ec838243b10e080ec02fff3af0bff8eb82ffd3ad0bfd8eb02ff13ab0bfbcea82fea3a90bfa0ea02fae3a70be8ce982fa23a50bdfce902f7e3a30bdf0e882f7b3a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xe6c908039b13ff0e6bcff839ad3fd0e6a4ff039a33fb0e684fe839783f90e5d0fe039723f70e5bcfd8396e3f50e5a4fd039673f30e590fc8393d3f10e4d0fc039313ef0e488fb838ff3ed0e3e4fb038f33eb0e380fa838bb3e90e2e0fa038b43e70e2acf9838a73e50e294f9038a53e30e280f8838a03e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xeafd1803abd43f0eadd0f83ab643d0eac90f03ab143b0eac10e83aad4390eaa10e03aa64370ea890d83aa04350e9b90d03a6c4330e9a90c83a674310e9950c03a6142f0e8fd0b83a3942d0e8cd0b039f642b0e7d50a839f44290e7bd0a039e84270e79109839bf4250e6e909039b94230e6dd08839b6421⟩
]

def tableLLL : Table Block := .branch 8 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xefa52803be747f0ef8d1f83be147d0eefd1f03bbb47b0eee51e83bb54790eec51e03bad4770eea91d83ba84750ede51d03b744730eda91c83b684710ed951c03b3446f0ecc11b83b2946d0ec9d1b03b2646b0ec951a83b244690ec851a03afb4670ebcd1983af14650ebbd1903aeb4630eba51883ae5461⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf2bd3803cab4bf0f29d2f83ca64bd0f2912f03c7d4bb0f1f12e83c774b90f1c52e03c704b70f1b52d83c694b50f19d2d03c3f4b30f0f92c83c3d4b10f0f12c03c3b4af0f0e52b83c374ad0f0cd2b03c314ab0f0bd2a83c2d4a90f0a92a03c254a70f08d2983bfd4a50eff12903bfa4a30efcd2883bee4a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf6914803da14ff0f5fd3f83d7e4fd0f5dd3f03d704fb0f5993e83d3d4f90f4ed3e03d394f70f4d93d83d344f50f4c93d03d2b4f30f4a53c83d264f10f4913c03d204ef0f3f93b83cfd4ed0f3d53b03cf44eb0f3c53a83cef4e90f3b93a03ce54e70f38d3983cbd4e50f2e13903cb64e30f2d13883cb34e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf9f55803e7a53f0f9d54f83e7053d0f9bd4f03e6f53b0f9a54e83e675390f9854e03e3a5370f8e54d83e375350f8d54d03e325330f8b94c83e2c5310f8994c03e2452f0f8894b83dfe52d0f7f54b03dfa52b0f7b94a83ded5290f7914a03dbe5270f6ed4983db65250f6c94903daf5230f6b14883da8521⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xfce96803f3957f0fcd15f83f3157d0fcbd5f03f2d57b0fcb15e83f2a5790fca15e03f255770fc8d5d83f215750fbf95d03ef45730fbcd5c83eef5710fbb95c03eec56f0fba95b83ee956d0fb915b03ee156b0fafd5a83eb95690fadd5a03eb55670fac95983eb05650fab55903ea95630fa9d5883ea1561⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xffa97803fe85bf0ff956f83fe45bd0ff916f03fe15bb0ff816e83fba5b90fee56e03fb85b70fed96d83fb05b50fead6d03faa5b30fea96c83fa75b10fe996c03fa45af0fe816b83f7e5ad0fdf16b03f795ab0fdd56a83f735a90fdb56a03f6a5a70fda16983f675a50fd8d6903f625a30fcf96883f3c5a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x121b9880486e5ff121b57f8486c5fd121a57f048645fb1218d7e848635f9121817e0483f5f7120ed7d8483a5f5120dd7d0482c5f3120ad7c8482a5f1120a57c048265ef120957b848245ed120917b048245eb120917a83fff5e90fff97a03ffc5e70ffe57983ff55e50ffcd7903fee5e30ffb57883feb5e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x124d1980492e63f124b18f8492963d1249d8f0492563b124858e848ff639123ed8e048f3637123b58d848ed635123a18d048e7633123818c848bb631122bd8c048ac62f122b18b848ab62d122a98b048aa62b122a58a848a9629122998a048a4627121ed898487a625121e58904876623121d18884873621⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x12885a804a2067f128819f849ff67d127fd9f049fe67b127ed9e849f9679127dd9e049f5677127cd9d849f1675127ad9d049e9673127819c849bc671126e99c049b866f126d99b849b366d126b99b049ac66b126959a849a4669125fd9a04979667125e19984973665125c99904960663124ed9884937661⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x12bf1b804afb6bf12be9af84af76bd12bcdaf04ae26bb12afdae84abd6b912aedae04ab76b712ad5ad84ab16b512abdad04aad6b312ab1ac84aa36b112a8dac04a796af129d9ab84a746ad129c9ab04a716ab129b5aa84a696a912995aa04a616a7128f1a984a376a5128d9a904a366a312889a884a216a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x12ed5c804bb36ff12ec9bf84bae6fd12eadbf04ba86fb12e89be84b7e6f912df5be04b7a6f712de5bd84b786f512dd1bd04b716f312db9bc84b686f112d99bc04b636ef12cfdbb84b3d6ed12cddbb04b326eb12cbdba84b2d6e912ca1ba04b236e712c89b984b226e512c81b904aff6e312bf5b884afd6e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x13181d804c3f73f130fdcf84c3e73d130f9cf04c3d73b130f5ce84c3c739130ddce04c31737130b9cd84c2d735130a1cd04c247331308dcc84c2273112ffdcc04bfd72f12fe9cb84bf972d12fd1cb04bf272b12fc1ca84bed72912fadca04be772712f99c984bbf72512ef5c904bbc72312ee1c884bb7721⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x133d1e804cf277f133bddf84ced77d133b1df04cea77b133a1de84ce677913391de04ce2777132fddd84cba775132e1dd04cb2773132c5dc84caf771132a1dc04ca476f13285db84ca076d131fddb04c7576b131a9da84c697691318dda04c6276713181d984c6076513181d904c6076313181d884c60761⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x136f5f804dbc7bf136ddef84db47bd136b9ef04dad7bb136a5ee84da77b9135ddee04d767b7135cded84d727b5135c5ed04d6f7b3135a5ec84d647b113585ec04d3d7af134f1eb84d3b7ad134e5eb04d357ab134d1ea84d2f7a9134b1ea04d2b7a7134a1e984d247a513489e904cf87a3133dde884cf67a1⟩,
  ⟨0xa104d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x4ee3060804ebe7ff13af1ff84eba7fd13addff04eb37fb13ac5fe84eac7f913981fe04e3f7f7138f1fd84e387f5138d1fd04e347f3138cdfc84e307f1138b9fc04e2b7ef138a5fb84e277ed13895fb04e237eb137f1fa84dfb7e9137ddfa04df37e7137c9f984df07e5137adf904de87e313791f884de37e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x13ee8186013ee8183f13ed8183e13ec4183d13ec0183c13ec0183b13ea0183a13e90183913dfc183813df4183713da0183613d98183513d88183413d80183313cec183213cdc183113cd0183013cc8182f13cb4182e13ca4182d13c90182c13c88182b13bfc182a13bec182913be4182813bd0182713bc8182613bc0182513bb4182413bac182313ba4182213b941821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x161fc18a0161f8187f161f8187e161f4187d161e4187c161c4187b161c0187a161b41879161881878161841877161801876160c81875160c018741609c187316094187216090187116088187016084186f13ff0186e13ff0186d13fec186c13fe8186b13fe0186a13fcc186913fc4186813fc0186713fb8186613f98186513f88186413ef8186313ef0186213ee81861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x164f818e0164e018bf164e018be164d818bd164d418bc164d018bb164a418ba1649c18b91649818b81648418b7163f818b6163f018b5163d818b4163d418b3163cc18b2163c418b1163bc18b0163ac18af163a418ae1639418ad1638c18ac1638018ab162f018aa162e818a9162d418a8162cc18a7162c018a6162b818a5162a418a41629018a31628c18a21628c18a1⟩
]

def tableLLR : Table Block := .branch 9 tableLLRL tableLLRR

def tableLL : Table Block := .branch 17 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x168a81920168a018ff167e818fe167e018fd167d818fc167d418fb167d018fa167b818f9167ac18f8167a418f71679418f61678c18f5166fc18f4166f818f3166ec18f2166d818f1166cc18f0166c818ef166c418ee166c018ed1669c18ec1669418eb1668818ea165f818e9165f018e8165d818e7165d018e6165b818e5165a418e41659018e31658c18e21658c18e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x16b94196016b94193f16b90193e16b80193d16af8193c16aec193b16ae4193a16ad4193916ad0193816acc193716acc193616a9c193516a94193416a8c1933169fc1932169f41931169e81930169e0192f169dc192e169cc192d169c8192c169b8192b169ac192a169a01929169981928169881927169841926168e01925168d81924168cc1923168c01922168b81921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x16e9019a016e84197f16dfc197e16df0197d16dec197c16dec197b16de8197a16ddc197916dc4197816dbc197716da4197616d90197516d88197416cf0197316cdc197216cc4197116cbc197016cb0196f16ca4196e16c94196d16c90196c16bfc196b16bec196a16be4196916bd4196816bd0196716bc8196616bc4196516bbc196416bb4196316ba8196216ba41961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1719019e01718819bf170fc19be170ec19bd170e419bc170c819bb170bc19ba170b419b9170ac19b81709c19b71709419b61708419b516ff819b416fec19b316fe419b216fdc19b116fd019b016fc819af16fbc19ae16fac19ad16fa419ac16f8c19ab16f8019aa16ef819a916ef019a816ee019a716ed819a616ec819a516eb419a416eac19a316ea419a216ea019a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x174cc1a20174c019ff174b819fe174b019fd174a419fc1749c19fb1749419fa1748819f9173f019f8173bc19f7173b419f6173a819f51739819f41739019f3172f419f2172f019f1172dc19f0172c419ef172b819ee172b019ed172a019ec1729c19eb1729419ea171fc19e9171f419e8171e819e7171d819e6171d019e5171b819e4171ac19e3171a419e21719c19e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x178901a60177f81a3f177f41a3e177f01a3d177e01a3c177dc1a3b177d01a3a177c01a39177b01a38177a41a37177981a36177901a35176f81a34176ec1a33176dc1a32176dc1a31176c81a30176c41a2f176b81a2e1768c1a2d176881a2c175e01a2b175cc1a2a175c41a29175bc1a28175b01a27175a81a261758c1a25175841a24174f81a23174f01a22174e81a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x17ca41aa017c8c1a7f17c8c1a7e17bfc1a7d17bf41a7c17bf01a7b17bc81a7a17bb01a7917bb01a7817b9c1a7717b9c1a7617adc1a7517ac81a7417abc1a7317ab01a7217ab01a7117ab01a7017ab01a6f17aac1a6e17aac1a6d17aa81a6c17aa41a6b179e41a6a179cc1a69179b81a68179b01a67179a41a66179941a65179881a64178f41a63178c01a62178981a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x17fd01ae017fcc1abf17fb01abe17fac1abd17f9c1abc17f981abb17f8c1aba17f841ab917efc1ab817ef81ab717ee41ab617ed81ab517ecc1ab417ec01ab317eb81ab217eb41ab117e801ab017ddc1aaf17dd41aae17dcc1aad17dc01aac17db81aab17da81aaa17da01aa917cf81aa817cf41aa717cec1aa617ce81aa517ce01aa417cd01aa317cc81aa217cb41aa1⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a28c1b201a1fc1aff1a1f41afe1a1e41afd1a1cc1afc1a1c81afb1a1c41afa1a1c01af91a1b41af81a1ac1af71a1a41af61a1941af51a1901af41a18c1af31a1841af21a1801af11a0f41af01a0ec1aef1a0dc1aee1a0d81aed1a0c81aec1a0c81aeb1a0c41aea1a0b81ae91a0b01ae81a0a41ae71a09c1ae61a08c1ae51a0881ae41a0841ae31a0841ae217fe01ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a4c41b601a4b01b3f1a4981b3e1a4901b3d1a3f81b3c1a3f41b3b1a3f01b3a1a3ec1b391a3ec1b381a3e81b371a3d81b361a3d41b351a3c41b341a3c01b331a3b81b321a3a41b311a39c1b301a3941b2f1a2f81b2e1a2f41b2d1a2f01b2c1a2e81b2b1a2e01b2a1a2dc1b291a2d41b281a2d01b271a2c01b261a2bc1b251a2b41b241a2a41b231a2901b221a28c1b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a8c01ba01a8b81b7f1a8ac1b7e1a8a41b7d1a8941b7c1a8901b7b1a7f81b7a1a7f01b791a7e41b781a7d41b771a7bc1b761a7a81b751a7941b741a78c1b731a6f41b721a6e41b711a6dc1b701a6d81b6f1a5f41b6e1a5f01b6d1a5e81b6c1a5d81b6b1a5c41b6a1a5bc1b691a5b41b681a5a81b671a5a01b661a5881b651a4f41b641a4f01b631a4e01b621a4dc1b61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1abbc1be01abb01bbf1aba01bbe1ab981bbd1ab841bbc1aaf81bbb1aaf01bba1aae81bb91aadc1bb81aad41bb71aac81bb61aab81bb51aab01bb41aa9c1bb31aa941bb21aa881bb11a9f81bb01a9f01baf1a9d41bae1a9bc1bad1a9b41bac1a9ac1bab1a99c1baa1a9941ba91a9841ba81a8fc1ba71a8ec1ba61a8e41ba51a8dc1ba41a8d81ba31a8d41ba21a8c41ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1aeec1c201aed81bff1aed01bfe1aecc1bfd1aeb81bfc1aea41bfb1ae981bfa1ae901bf91adfc1bf81adf81bf71adf81bf61adf41bf51adf01bf41ade41bf31ade41bf21ade01bf11adc41bf01adbc1bef1ada81bee1ada41bed1ad841bec1acd41beb1accc1bea1acc81be91acb41be81aca81be71aca01be61ac941be51ac8c1be41abf41be31abcc1be21abc41be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b1b81c601b1b01c3f1b1ac1c3e1b1981c3d1b1901c3c1b1881c3b1b1801c3a1b0ec1c391b0e81c381b0e01c371b0d41c361b0bc1c351b0b81c341b0a81c331b0a41c321b09c1c311b0901c301b0801c2f1aff81c2e1afe41c2d1afe01c2c1afd81c2b1afd41c2a1afcc1c291afc41c281afc01c271afb81c261afb41c251af981c241af901c231af841c221aef41c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b4c81ca01b4c41c7f1b4c01c7e1b4b01c7d1b4ac1c7c1b4a41c7b1b49c1c7a1b4901c791b4881c781b3f81c771b3f41c761b3dc1c751b3d01c741b3901c731b2fc1c721b2ec1c711b2dc1c701b2cc1c6f1b2c01c6e1b2b01c6d1b2b01c6c1b2ac1c6b1b2a81c6a1b2981c691b2981c681b2941c671b28c1c661b2801c651b1f41c641b1e81c631b1d01c621b1c41c61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b79c1ce01b7981cbf1b7881cbe1b7841cbd1b6fc1cbc1b6f01cbb1b6e81cba1b6d81cb91b6d41cb81b6d01cb71b6bc1cb61b6ac1cb51b6a41cb41b6981cb31b6901cb21b6881cb11b5f81cb01b5f01caf1b5e81cae1b5e41cad1b5e01cac1b5d01cab1b5c41caa1b5b81ca91b5b01ca81b5a01ca71b59c1ca61b5801ca51b4f01ca41b4e41ca31b4d81ca21b4d01ca1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1baf01d201bab41cff1baa41cfe1baa01cfd1b9ec1cfc1b9d41cfb1b9d41cfa1b9c01cf91b9b81cf81b9b01cf71b9a41cf61b99c1cf51b9981cf41b9881cf31b9841cf21b8ec1cf11b8e01cf01b8d81cef1b8c81cee1b8c41ced1b8a41cec1b89c1ceb1b8981cea1b8941ce91b8801ce81b7ec1ce71b7dc1ce61b7d01ce51b7b01ce41b7a81ce31b7a01ce21b7a01ce1⟩
]

def tableLRL : Table Block := .branch 8 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1e1901d601e0fc1d3f1e0fc1d3e1e0e81d3d1e0e81d3c1e0d41d3b1e0bc1d3a1e0a81d391e0801d381bffc1d371bff81d361bff41d351bff41d341bff41d331bff01d321bff01d311bfec1d301bfac1d2f1bf941d2e1bdb41d2d1bda41d2c1bda01d2b1bd8c1d2a1bcf01d291bcec1d281bce01d271bcd81d261bcd01d251bccc1d241bcbc1d231bcb01d221bb841d21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1e8841da01e8841d7f1e8801d7e1e7fc1d7d1e7ec1d7c1e7e01d7b1e7d01d7a1e7c41d791e7b41d781e7a81d771e7941d761e7841d751e7801d741e6fc1d731e6e81d721e6d41d711e6b41d701e6a41d6f1e69c1d6e1e6881d6d1e6841d6c1e5f01d6b1e5e01d6a1e5d41d691e5cc1d681e5bc1d671e5b81d661e3dc1d651e1fc1d641e1f41d631e1ec1d621e1c81d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1eaf41de01eaf01dbf1eae41dbe1eae41dbd1eae01dbc1ead41dbb1eacc1dba1eac41db91eabc1db81eaa41db71eaa01db61ea981db51ea8c1db41ea841db31e9f41db21e9f01db11e9d41db01e9c81daf1e9b81dae1e9a01dad1e99c1dac1e9901dab1e8f81daa1e8f01da91e8e41da81e8dc1da71e8cc1da61e8bc1da51e8b81da41e8a41da31e8941da21e88c1da1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1edec1e201edd41dff1edc81dfe1edc01dfd1edb01dfc1eda01dfb1ed901dfa1ed841df91ecf81df81ecf01df71ece01df61ecdc1df51ecd81df41ecd41df31ecb81df21ecb41df11eca01df01ec9c1def1ec941dee1ec881ded1ebf01dec1ebe01deb1ebe01dea1ebdc1de91ebd81de81ebcc1de71ebc81de61ebc41de51ebb01de41eb981de31eb901de21eaf81de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f0e41e601f0e41e3f1f0c81e3e1f0c41e3d1f0bc1e3c1f0b81e3b1f0ac1e3a1f08c1e391f0801e381eff01e371efec1e361efd01e351efc01e341efbc1e331efa41e321ef9c1e311ef981e301ef881e2f1ef841e2e1eef01e2d1eee81e2c1eee41e2b1eed41e2a1eec81e291eebc1e281eeb41e271eeac1e261eea81e251eea41e241ee941e231ee901e221edfc1e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f3a41ea01f3981e7f1f3901e7e1f3801e7d1f2f81e7c1f2e81e7b1f2d81e7a1f2d01e791f2c41e781f2b01e771f2a81e761f2a01e751f2941e741f28c1e731f2881e721f1f81e711f1f81e701f1ec1e6f1f1e81e6e1f1e41e6d1f1dc1e6c1f1d81e6b1f1cc1e6a1f1c41e691f1bc1e681f1b81e671f1a81e661f1a41e651f1981e641f1901e631f1841e621f0fc1e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f6f81ee01f6e41ebf1f6d01ebe1f6c41ebd1f5e81ebc1f5e41ebb1f5dc1eba1f5cc1eb91f5c81eb81f5c01eb71f5b01eb61f5b01eb51f5a81eb41f5881eb31f5801eb21f4f81eb11f4e81eb01f4e01eaf1f4d01eae1f4c81ead1f4ac1eac1f4881eab1f4841eaa1f3f41ea91f3f01ea81f3e81ea71f3d81ea61f3d01ea51f3cc1ea41f3c41ea31f3b41ea21f3ac1ea1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1fa9c1f201fa941eff1fa8c1efe1f9fc1efd1f9f41efc1f9e01efb1f9d41efa1f9d01ef91f9c81ef81f9b81ef71f9b01ef61f9881ef51f9841ef41f8f41ef31f8ec1ef21f8e01ef11f8d01ef01f8c81eef1f8b41eee1f8ac1eed1f8a01eec1f8901eeb1f8881eea1f7f41ee91f7e81ee81f7e01ee71f7d81ee61f7c81ee51f7a01ee41f79c1ee31f78c1ee21f7801ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1fec01f601feb81f3f1fea81f3e1fea01f3d1fdf01f3c1fde81f3b1fdbc1f3a1fdb41f391fd901f381fd881f371fcfc1f361fcec1f351fce41f341fcd01f331fcc81f321fcc01f311fcb01f301fcac1f2f1fc9c1f2e1fc901f2d1fc841f2c1fbfc1f2b1fbec1f2a1fbe81f291fbc41f281fbbc1f271fba41f261fb9c1f251fb8c1f241fb841f231faec1f221fae41f21⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2238c1fa0223841f7f222ec1f7e222e41f7d222d81f7c222c41f7b222bc1f7a222841f79221a01f78221881f77220f41f76220cc1f75220c41f74220c41f73220b41f72220b01f71220ac1f70220a41f6f220a01f6e220801f6d1ffec1f6c1ffe81f6b1ffdc1f6a1ffd41f691ffb81f681ffb41f671ffa41f661ff9c1f651ff981f641fef01f631fee81f621fee01f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x228941fe0227f81fbf227941fbe2278c1fbd226fc1fbc226e41fbb226d41fba226c81fb9225ac1fb8225981fb7225881fb6224fc1fb5224ec1fb4224e81fb3224d01fb2224cc1fb1224bc1fb0224ac1faf224a41fae224801fad223fc1fac223f81fab223f01faa223e81fa9223dc1fa8223d41fa7223d01fa6223c81fa5223bc1fa4223b41fa3223ac1fa2223a01fa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x22bc8282022bbc1fff22bac1ffe22ba41ffd22b981ffc22b881ffb22b801ffa22aec1ff922ae41ff822ad81ff722ac81ff622ac01ff522aa41ff422a981ff322a901ff222a881ff1229f81ff0229ac1fef229a01fee2299c1fed229941fec229881feb229841fea228fc1fe9228fc1fe8228e01fe7228e01fe6228dc1fe5228c81fe4228c01fe3228b41fe2228ac1fe1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x22eb4286022ea4283f22e9c283e22dfc283d22df4283c22df0283b22dec283a22de4283922de0283822ddc283722dd0283622dcc283522dc4283422dbc283322db4283222da8283122d94283022d8c282f22cf4282e22cec282d22ce0282c22ccc282b22cc4282a22c98282922c98282822c8c282722bfc282622bf8282522bf4282422be0282322bd8282222bd02821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2329c28a023298287f23284287e231fc287d231f0287c231dc287b231d4287a231bc2879231b42878231a828772318c2876230f02875230dc2874230d42873230c82872230c42871230b02870230a0286f2308c286e22fbc286d22fac286c22fa4286b22f98286a22f88286922f80286822ef8286722ef4286622eec286522ee4286422ed4286322ec4286222ec02861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x235bc28e0235a828bf2359828be2359428bd2358828bc2358028bb234e828ba234d828b9234cc28b8234c428b7234c028b6234a028b5234a028b42349428b32348c28b2233fc28b1233f428b0233e028af233c828ae233c828ad232f028ac232ec28ab232ec28aa232e828a9232dc28a8232d428a7232c428a6232bc28a5232b828a4232b028a3232ac28a2232a428a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x239b42920239a428ff2399828fe2399028fd238f028fc238e428fb238e028fa238dc28f9238cc28f8238c828f7238bc28f6237d828f5237d428f4237c028f3237ac28f22379c28f12378c28f02378828ef2378428ee2378028ed2378028ec236d028eb236c028ea236b428e9236b028e8236a028e72369428e62368c28e52368828e4235e828e3235dc28e2235c428e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x23e88296023df4293f23ddc293e23dc4293d23d94293c23cdc293b23cac293a23c9c293923bec293823be4293723bd4293623bcc293523bb8293423bb0293323ba4293223b94293123b8c293023af0292f23aec292e23ae0292d23ad8292c23ad4292b23ac0292a23abc292923aac292823a802927239fc2926239ec2925239e82924239e02923239d02922239b82921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2628829a0261fc297f261e8297e261e0297d261c4297c261c0297b261ac297a261ac2979261982978261942977261802976260f42975260ec297426090297326080297223fec297123fec297023fe4296f23fd0296e23fc8296d23efc296c23ee8296b23ed8296a23ed8296923ed4296823ed4296723ed4296623ecc296523ec8296423ebc296323e90296223e8c2961⟩
]

def tableLRR : Table Block := .branch 9 tableLRRL tableLRRR

def tableLR : Table Block := .branch 17 tableLRL tableLRR

def tableL : Table Block := .branch 35 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x264c829e0264c429bf264b029be264ac29bd264a429bc264a029bb2649c29ba2649429b92648c29b82648829b7263f829b6263f029b5263e829b4263dc29b3263d829b2263c829b12639c29b02638829af262fc29ae262f429ad262d029ac262cc29ab262c429aa262c029a9262bc29a8262b829a7262b429a6262a029a5262a029a42629829a32629429a22629029a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x267e42a20267d029ff267c829fe2678829fd266fc29fc266e829fb266e029fa266d829f9266c429f8266bc29f7266a829f6266a429f52669829f42668c29f32668829f2265fc29f1265ec29f0265e429ef265c029ee265bc29ed265bc29ec265b829eb265b829ea265b429e9265b429e8265b029e7265a829e62659029e52658829e4264e429e3264d029e2264cc29e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x26ae42a6026ae02a3f26ac02a3e26ab02a3d26a9c2a3c26a9c2a3b26a882a3a269f82a39269ec2a38269e42a37269c82a36269b42a35269a42a34269a02a332699c2a322699c2a31269982a302698c2a2f269842a2e269802a2d268f82a2c268f42a2b268f02a2a268ec2a29268a82a28268982a272688c2a262688c2a25268882a24268802a23267f82a22267f02a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x26ee42aa026edc2a7f26ed82a7e26ec42a7d26eb42a7c26eb02a7b26eac2a7a26e9c2a7926de42a7826dd42a7726dbc2a7626db42a7526da82a7426d982a7326d902a7226cfc2a7126ce42a7026cd02a6f26cac2a6e26ca82a6d26ca82a6c26c942a6b26c902a6a26c842a6926bd42a6826bcc2a6726bc42a6626ba82a6526b982a6426b942a6326af82a6226ae82a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x272942ae02728c2abf271e82abe271d02abd271c02abc271c02abb271bc2aba271b82ab9271a42ab8271942ab7271882ab6270d42ab5270c02ab4270bc2ab3270ac2ab22709c2ab1270902ab0270882aaf26ff82aae26ff02aad26fd82aac26fc82aab26fc42aaa26fc02aa926fac2aa826f982aa726f902aa626f8c2aa526f842aa426f802aa326ef82aa226ef42aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x275942b20275902aff274f42afe274e82afd274d82afc274c82afb274b82afa274b42af92749c2af8274982af7274882af6274842af5273f82af4273f02af3273e82af2273e42af1273d42af0273b02aef273a82aee273a02aed273902aec273882aeb273802aea272f42ae9272ec2ae8272e82ae7272d82ae6272d42ae5272cc2ae4272bc2ae3272a82ae2272a42ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x278842b60277f42b3f277f02b3e277e42b3d277dc2b3c277cc2b3b277c02b3a277b82b39277b02b38277a82b37277902b362778c2b35277802b34276f82b33276ec2b32276e42b31276d42b30276d02b2f276b02b2e276a42b2d2769c2b2c276942b2b276842b2a275fc2b29275ec2b28275e42b27275dc2b26275c42b25275c02b24275b82b23275ac2b22275a42b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x27b942ba027b902b7f27b882b7e27afc2b7d27af42b7c27af02b7b27ae82b7a27aa82b7927a902b7827a902b7727a802b76279e42b75279e02b74279d82b73279d02b72279c42b71279bc2b70279b02b6f279a42b6e279902b6d278f82b6c278f02b6b278d82b6a278d42b69278d02b68278cc2b67278bc2b66278b82b65278b42b64278942b632788c2b62278882b61⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x27fbc2be027fac2bbf27fa42bbe27f982bbd27f902bbc27ef02bbb27ec42bba27eac2bb927e9c2bb827e8c2bb727df42bb627dec2bb527de82bb427dc82bb327db82bb227db82bb127db42bb027db02baf27da42bae27da02bad27d9c2bac27d942bab27d802baa27cf02ba927cf02ba827cc02ba727cac2ba627ca02ba527c8c2ba427bd42ba327bc82ba227bbc2ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2a3f42c202a3dc2bff2a3bc2bfe2a3a42bfd2a3a42bfc2a3902bfb2a3902bfa2a2e82bf92a2d02bf82a2bc2bf72a2b02bf62a2a42bf52a2a42bf42a2a42bf32a2a42bf22a2a02bf12a2a02bf02a29c2bef2a2982bee2a2982bed2a1d82bec2a1c02beb2a1ac2bea2a1a42be92a1942be82a0fc2be72a0ec2be62a0e02be527fe82be427fdc2be327fd42be227fc42be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2a7d02c602a7c82c3f2a7c42c3e2a78c2c3d2a7802c3c2a6fc2c3b2a6ec2c3a2a6e02c392a6d82c382a6d42c372a6a02c362a68c2c352a6802c342a5f02c332a5ec2c322a5e02c312a5cc2c302a5bc2c2f2a5b82c2e2a5a82c2d2a5a42c2c2a59c2c2b2a5902c2a2a5882c292a4f82c282a4f42c272a4d42c262a4b02c252a4a02c242a4982c232a4902c222a4802c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2aabc2ca02aaac2c7f2aaa82c7e2aa942c7d2aa8c2c7c2aa882c7b2a9f82c7a2a9f42c792a9e82c782a9e02c772a9d82c762a9d42c752a9c42c742a9b42c732a9ac2c722a9a42c712a99c2c702a99c2c6f2a9842c6e2a9802c6d2a8f82c6c2a8ec2c6b2a8e42c6a2a8d42c692a8d02c682a8cc2c672a8b42c662a8a82c652a8982c642a8842c632a7f42c622a7e42c61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2acfc2ce02acf82cbf2ace82cbe2ace42cbd2ace42cbc2acd02cbb2acc82cba2acc02cb92acb42cb82aca82cb72ac982cb62ac882cb52ac842cb42abf82cb32abf02cb22abe42cb12abe02cb02abdc2caf2abd82cae2abc82cad2abc82cac2abc42cab2abb82caa2abb02ca92aba02ca82ab8c2ca72ab882ca62aaf82ca52aaf02ca42aadc2ca32aad42ca22aac82ca1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b0882d202b0842cff2afec2cfe2afd82cfd2afb02cfc2af942cfb2af942cfa2af902cf92af902cf82af8c2cf72af882cf62af842cf52af842cf42aee42cf32aed02cf22aed02cf12aec02cf02aeac2cef2aea42cee2ae9c2ced2adf82cec2adf82ceb2adec2cea2add82ce92add42ce82add42ce72adcc2ce62adc82ce52adbc2ce42adb82ce32adac2ce22ad802ce1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b3f82d602b3f02d3f2b3ec2d3e2b3d82d3d2b3d02d3c2b3c02d3b2b3b82d3a2b3942d392b3802d382b2fc2d372b2d42d362b1f82d352b1ec2d342b1e82d332b1e82d322b1e42d312b1e02d302b1d42d2f2b1c42d2e2b1bc2d2d2b1b02d2c2b19c2d2b2b1942d2a2b0e82d292b0e82d282b0d02d272b0c82d262b0a42d252b0a02d242b0982d232b0942d222b0902d21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b7a82da02b79c2d7f2b7942d7e2b7902d7d2b6fc2d7c2b6f02d7b2b6e82d7a2b6e02d792b6d42d782b6cc2d772b6c02d762b6b02d752b6a82d742b6842d732b5fc2d722b5f02d712b5e02d702b5d82d6f2b5bc2d6e2b5b42d6d2b5a42d6c2b59c2d6b2b5842d6a2b4f02d692b4ec2d682b4c42d672b4b82d662b4b42d652b4a02d642b4882d632b4882d622b4842d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2bb942de02baf82dbf2baf42dbe2bae82dbd2babc2dbc2b9c02dbb2b9bc2dba2b9b82db92b9ac2db82b9982db72b9902db62b9842db52b8fc2db42b8f02db32b8dc2db22b8d42db12b8bc2db02b8b42daf2b8ac2dae2b8a82dad2b8a02dac2b8882dab2b7f82daa2b7e42da92b7dc2da82b7d02da72b7c02da62b7bc2da52b7b82da42b7b82da32b7b42da22b7b42da1⟩
]

def tableRLL : Table Block := .branch 8 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2bebc2e202be8c2dff2bddc2dfe2bdd02dfd2bdbc2dfc2bdb42dfb2bda02dfa2bd9c2df92bd9c2df82bd902df72bd8c2df62bd802df52bcfc2df42bcf82df32bcdc2df22bcd42df12bcb42df02bcac2def2bca82dee2bca42ded2bc982dec2bc942deb2bc902dea2bc882de92bbf42de82bbe82de72bbe02de62bbd82de52bbcc2de42bbc42de32bbac2de22bb9c2de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2e2a02e602e2982e3f2e2802e3e2e2802e3d2e1f82e3c2e1f02e3b2e1e82e3a2e1e02e392e1b82e382e1a42e372e1a42e362e1a02e352e1842e342e1802e332e0f82e322e0e42e312e0cc2e302e0bc2e2f2e0b82e2e2e0a02e2d2e0882e2c2bffc2e2b2bff42e2a2bfcc2e292bfac2e282bfa42e272bf9c2e262bf882e252bf842e242bef42e232bef02e222bee82e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2e5d42ea02e5c02e7f2e5bc2e7e2e5942e7d2e58c2e7c2e5802e7b2e4fc2e7a2e4e82e792e4e02e782e4d82e772e4c82e762e4ac2e752e4a42e742e4942e732e48c2e722e3d42e712e3cc2e702e3ac2e6f2e3ac2e6e2e3a02e6d2e3902e6c2e38c2e6b2e2ec2e6a2e2e82e692e2e42e682e2dc2e672e2d82e662e2d42e652e2cc2e642e2b82e632e2b02e622e2a82e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2ecc42ee02ecb82ebf2ecb42ebe2ecac2ebd2ec9c2ebc2ec942ebb2ec842eba2eb842eb92eb802eb82eae82eb72ead82eb62ead02eb52eaa02eb42ea9c2eb32ea8c2eb22ea802eb12e9dc2eb02e9c82eaf2e9ac2eae2e9a42ead2e9982eac2e7fc2eab2e7e82eaa2e7e02ea92e7d42ea82e7bc2ea72e7b02ea62e6c82ea52e5e82ea42e5e82ea32e5e42ea22e5e02ea1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2f2842f202f1f82eff2f1f02efe2f1e82efd2f1c82efc2f1c02efb2f1b82efa2f1a82ef92f1a02ef82f1942ef72f1842ef62f0fc2ef52f0cc2ef42f0c82ef32eff42ef22eee42ef12eee02ef02eed82eef2eebc2eee2eea42eed2eea02eec2ee982eeb2ee902eea2edcc2ee92ed9c2ee82ed8c2ee72ed882ee62ed842ee52ecf02ee42ece02ee32ecd42ee22ecc82ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2f58c2f602f4e82f3f2f4e02f3e2f4dc2f3d2f4d42f3c2f4cc2f3b2f4c02f3a2f4b42f392f4ac2f382f4a42f372f4942f362f4882f352f3fc2f342f3ec2f332f3d02f322f3cc2f312f3c02f302f3b02f2f2f3a02f2e2f3982f2d2f38c2f2c2f3842f2b2f2f42f2a2f2f02f292f2ec2f282f2e02f272f2cc2f262f2c42f252f2bc2f242f2b02f232f2a02f222f2982f21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2faec2fa02fa9c2f7f2fa982f7e2fa942f7d2fa882f7c2fa842f7b2f9ec2f7a2f9b02f792f9a82f782f9a42f772f9842f762f6fc2f752f6f42f742f6f02f732f6ec2f722f6d82f712f6d42f702f6b02f6f2f6882f6e2f6802f6d2f5fc2f6c2f5e42f6b2f5d42f6a2f5d02f692f5cc2f682f5cc2f672f5c82f662f5b82f652f5b82f642f5ac2f632f5a42f622f5942f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x328b42fe0328ac2fbf328942fbe323c42fbd323bc2fbc323b82fbb323b02fba323a42fb92fedc2fb82fed42fb72fecc2fb62feb42fb52feb02fb42fea42fb32fe9c2fb22fe902fb12fe882fb02fdf82faf2fdf42fae2fddc2fad2fdd02fac2fbf42fab2fbf02faa2fbe42fa92fbdc2fa82fbcc2fa72fbc82fa62fbb82fa52fbb42fa42fb982fa32fb8c2fa22fb842fa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x331a43820330f82fff32ffc2ffe32ff82ffd32ff42ffc32fe82ffb32fe42ffa32fdc2ff932fc02ff832eec2ff732edc2ff632eb82ff532ea02ff432ea02ff332e9c2ff232ddc2ff132dc42ff032cd42fef32ccc2fee32cbc2fed32cb42fec32bd42feb32bd42fea32af42fe932aec2fe832adc2fe732ad42fe632ab02fe5329c42fe4329bc2fe3329b42fe23298c2fe1⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x334e83860334c0383f334b0383e33494383d333fc383c333f4383b333e4383a333e03839333cc3838333c83837333c03836333b43835333b03834333a83833333a43832333a03831333843830332fc382f332ec382e332dc382d332d8382c332c4382b332b8382a332ac3829332a83828332a03827332983826332803825331f03824331e83823331b43822331b03821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x339bc38a0339a0387f3399c387e33990387d33988387c338a4387b33898387a338903879338883878338803877337f43876337f03875337e83874337dc3873337cc3872337c43871337b03870337a4386f3379c386e33794386d33784386c336fc386b336f0386a336e03869336d83868336ac3867336a438663369c3865335fc3864335e43863335843862334fc3861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x33c9838e033c9438bf33c9038be33c8438bd33c8038bc33bfc38bb33bf838ba33bec38b933bd838b833bb838b733ba438b633ba038b533ba038b433b9038b333b8838b233ae838b133ae038b033adc38af33ad838ae33ad838ad33ad438ac33ad038ab33ac438aa33ac038a933ab838a833ab038a733aa838a633a9c38a533a8838a433a8038a3339d438a2339d038a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x360ac39203609838ff33fd038fe33f8038fd33ee438fc33ed838fb33ed438fa33ecc38f933ec038f833eac38f733ea438f633e8c38f533df438f433df038f333de438f233de038f133ddc38f033dd438ef33dc438ee33dbc38ed33da838ec33d9438eb33d9038ea33d9038e933cf438e833cf038e733ce438e633cd438e533ccc38e433ca838e333ca438e233ca038e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x367c0396036798393f36794393e36788393d366dc393c365e0393b365dc393a365d83939365cc3938365c83937365c03936365a43935364d43934364c43933363f03932361f83931361e43930361c0392f36194392e36194392d3618c392c3618c392b3618c392a361883929361883928361843927361803926360e43925360cc3924360cc3923360c83922360bc3921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x36be039a036bc8397f36bc0397e36bb4397d36ba4397c36b9c397b36af4397a36aec397936ad4397836abc397736aa4397636a8c397536a843974369ec3973369a43972369a0397136994397036990396f3698c396e36988396d368f4396c368e8396b368d8396a368c03969368a83968368a039673689039663688c3965367f83964367f03963367d83962367c83961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x36f9c39e036f8c39bf36f8439be36ee839bd36ed439bc36ebc39bb36eb439ba36ea439b936e9439b836e8839b736df839b636df439b536dd839b436dcc39b336dc439b236db439b136db039b036dac39af36da039ae36d8839ad36cf039ac36ce839ab36cd839aa36cc839a936cb439a836ca839a736ca039a636c9839a536c8c39a436c8439a336bf839a236be839a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x373983a203738c39ff372fc39fe372f439fd372d439fc372cc39fb372c839fa372c439f9372bc39f8372b839f7371bc39f6371b839f5371b039f4371a439f33719039f23718839f1370f439f0370e039ef370d439ee3709839ed3709039ec3708839eb36ff839ea36ff839e936ff439e836fec39e736fdc39e636fd439e536fc439e436fbc39e336fb039e236fa439e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x377b03a60377a83a3f377a03a3e377903a3d377843a3c376f83a3b376f03a3a376e83a39376dc3a38376cc3a37376c43a36375ec3a35375a43a34375943a33375903a323758c3a31374f83a30374e83a2f374e03a2e374d43a2d374c83a2c374c03a2b374b83a2a374b03a29374ac3a28374a83a27373f83a26373f03a25373e43a24373d03a23373c83a223739c3a21⟩
]

def tableRLR : Table Block := .branch 9 tableRLRL tableRLRR

def tableRL : Table Block := .branch 17 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3a2b83aa03a2a43a7f3a2903a7e3a2903a7d3a28c3a7c37cd43a7b37ccc3a7a37cbc3a7937cb43a7837ca03a7737c903a7637c8c3a7537c843a7437be03a7337ba83a7237af43a7137ae03a7037aac3a6f37a983a6e37a883a6d379d83a6c379c43a6b379b03a6a378cc3a69378c43a68378b43a67378943a66378883a65377f83a64377e03a63377cc3a62377c03a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3ac843ae03abf03abf3abec3abe3abec3abd3abe43abc3ab803abb3aafc3aba3aaf03ab93aae03ab83aad43ab73aad03ab63aac83ab53a7dc3ab43a7b43ab33a6f43ab23a6c43ab13a5d43ab03a5883aaf3a4fc3aae3a4a03aad3a4883aac3a3f03aab3a3e03aaa3a3dc3aa93a3d83aa83a3cc3aa73a3bc3aa63a3b43aa53a3ac3aa43a39c3aa33a3943aa23a2d03aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3b0f83b203b0ec3aff3b0d43afe3b0c43afd3b0a43afc3b0943afb3affc3afa3afe43af93afdc3af83afc43af73afb43af63af9c3af53af943af43af8c3af33aefc3af23aee43af13aed03af03aec43aef3aeac3aee3aea03aed3ae903aec3ae883aeb3ae843aea3ade43ae93add43ae83adc03ae73adb83ae63acfc3ae53acb83ae43acb43ae33ac903ae23ac903ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3b7b43b603b6d03b3f3b6c83b3e3b6983b3d3b6803b3c3b5fc3b3b3b4b43b3a3b4ac3b393b4a03b383b48c3b373b4843b363b3d83b353b3d43b343b3c83b333b3b83b323b3b03b313b3903b303b3883b2f3b3843b2e3b3803b2d3b2f83b2c3b2943b2b3b2903b2a3b2883b293b1fc3b283b1e83b273b1e03b263b1bc3b253b1b43b243b19c3b233b18c3b223b0fc3b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3badc3ba03baa43b7f3ba943b7e3ba883b7d3b9f43b7c3b9f43b7b3b9e43b7a3b9e03b793b9d43b783b9a83b773b9a43b763b9a03b753b8f43b743b8ec3b733b8e03b723b8dc3b713b8d03b703b8c83b6f3b8c03b6e3b8b43b6d3b89c3b6c3b8943b6b3b88c3b6a3b8843b693b8803b683b7f43b673b7f03b663b7e03b653b7d03b643b7cc3b633b7c43b623b7bc3b61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3e39c3be03e2903bbf3e28c3bbe3e1cc3bbd3e1bc3bbc3e1943bbb3e0e83bba3e0d03bb93bf983bb83bf943bb73bf8c3bb63bf883bb53bef03bb43be9c3bb33be943bb23be883bb13bdf83bb03bdf03baf3bdc03bae3bcc03bad3bc803bac3bbf03bab3bbec3baa3bbd43ba93bbc43ba83bbbc3ba73bbac3ba63bb983ba53bb903ba43bb8c3ba33bafc3ba23baec3ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3e9a83c203e9a43bff3e9903bfe3e9803bfd3e6d03bfc3e6943bfb3e6803bfa3e5fc3bf93e5cc3bf83e5c43bf73e5ac3bf63e5a43bf53e5983bf43e5843bf33e4fc3bf23e4e43bf13e4e03bf03e4d83bef3e4bc3bee3e4a03bed3e4983bec3e3f43beb3e3f03bea3e3ec3be93e3e03be83e3d83be73e3d43be63e3cc3be53e3c83be43e3c03be33e3bc3be23e3a43be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3eee03c603eedc3c3f3eed83c3e3eec43c3d3eeb83c3c3ecf43c3b3ecf03c3a3ec843c393ebf43c383ebf03c373ebdc3c363ebd03c353ebbc3c343eaf83c333eaf43c323eaec3c313ead83c303eac83c2f3eac43c2e3eaac3c2d3ea9c3c2c3ea943c2b3ea943c2a3ea943c293ea903c283e9f83c273e9f43c263e9e43c253e9c83c243e9c43c233e9b83c223e9b03c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3fce43ca03fccc3c7f3fcc83c7e3fcbc3c7d3fcb03c7c3fb9c3c7b3fb983c7a3fae83c793f9f43c783f9e83c773f9ac3c763f99c3c753f89c3c743f8883c733f7f43c723f7e43c713f7e03c703f7dc3c6f3f7d83c6e3f7cc3c6d3f7c43c6c3f7b43c6b3f4803c6a3f1e83c693f1e43c683f1dc3c673f0a43c663f0903c653f0843c643efcc3c633efa83c623eef83c61⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x423c03ce0423ac3cbf423943cbe423943cbd423843cbc4228c3cbb421f43cba421dc3cb9421d83cb8421cc3cb7421c03cb6421a83cb54219c3cb4421943cb3420bc3cb2420ac3cb1420a83cb0420a43caf420a03cae3fff83cad3fff43cac3ffe03cab3ffc83caa3ffc03ca93ffb03ca83ffac3ca73ff8c3ca63ff843ca53fef43ca43feec3ca33fdd83ca23fcf83ca1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x42a903d20429fc3cff429dc3cfe429cc3cfd429cc3cfc429c83cfb429b43cfa428e43cf9428c43cf8428883cf7428803cf6427fc3cf5427f03cf4427dc3cf3427b83cf2427a03cf1427a03cf04279c3cef427903cee427803ced426f43cec426ec3ceb426e43cea426dc3ce9425c83ce8424b83ce7424983ce64248c3ce5423f43ce4423e03ce3423d83ce2423c83ce1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x461f83d60461e43d3f461d03d3e461c83d3d461b83d3c461b03d3b461a03d3a461903d39460fc3d38460f03d37460dc3d36460d83d35460d43d34460d03d33460c03d32460bc3d31460903d3043ff83d2f43c9c3d2e42eb83d2d42bcc3d2c42bbc3d2b42bac3d2a42b983d2942b8c3d2842ae83d2742ad83d2642acc3d2542ac03d2442ab83d2342ab03d2242aa03d21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x469d43da0469d03d7f469c43d7e469c03d7d467f83d7c467e83d7b467c83d7a467c03d79467903d78466f83d77466f03d76466e83d75466d43d74466bc3d73465883d72465803d71464e43d70464dc3d6f464d83d6e464c43d6d464bc3d6c464b43d6b464a83d6a464943d69464803d68463c43d67463c03d66463843d65463803d64462e03d63462dc3d62462d83d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x474b83de0474b03dbf474a03dbe4748c3dbd473f43dbc473f03dbb473e43dba473dc3db9473cc3db8473c03db7473ac3db6473a03db5473983db4473903db3470e03db2470dc3db1470d83db0470cc3daf470c83dae470c03dad470b83dac470b43dab470a43daa470a03da946fbc3da846fb03da746fa83da646cb03da546bb43da446bb03da346b943da246b883da1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x47af83e2047af03dff47ae43dfe47ad43dfd47acc3dfc47ab83dfb47aa03dfa47a9c3df947a883df847a843df7479e43df6479dc3df5479d83df4478f83df3477f03df2477d83df1477cc3df0477b43def477ac3dee476c83ded476bc3dec476b83deb4769c3dea476983de9476903de8476843de7475fc3de6475b43de5474d83de4474d43de3474d03de2474c83de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x47fb03e6047fa83e3f47fa03e3e47f983e3d47f943e3c47ef83e3b47eec3e3a47edc3e3947ed83e3847ed03e3747ebc3e3647ea43e3547e943e3447e883e3347e803e3247dfc3e3147ddc3e3047dd43e2f47dc43e2e47dbc3e2d47da43e2c47d8c3e2b47cf03e2a47cec3e2947cdc3e2847cd83e2747cd03e2647cc83e2547cbc3e2447bb83e2347bb43e2247b883e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4aa803ea04a9f83e7f4a9f43e7e4a9f03e7d4a9e43e7c4a9dc3e7b4a9d83e7a4a9c43e794a9b83e784a9b03e774a9a43e764a9883e754a8f03e744a8d43e734a8cc3e724a8ac3e714a8a43e704a8a03e6f4a89c3e6e4a8903e6d4a8843e6c4a7d83e6b4a5cc3e6a4a5c83e694a5ac3e684a0b43e674a0a43e664a0a03e654a09c3e644a0943e6347fc03e6247fb43e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4b0943ee04b0843ebf4affc3ebe4aff43ebd4afe43ebc4afd83ebb4add03eba4adcc3eb94adc43eb84adb03eb74ad8c3eb64ad843eb54acf83eb44ac843eb34ac803eb24abe83eb14abe03eb04abd83eaf4abcc3eae4abb83ead4abb03eac4ab983eab4ab803eaa4aafc3ea94aaf03ea84aad43ea74aad03ea64aac43ea54aab43ea44aaac3ea34aa883ea24aa843ea1⟩
]

def tableRRL : Table Block := .branch 9 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4e0a43f204e0a03eff4e0943efe4bfe83efd4bfe43efc4bfdc3efb4bfcc3efa4bfc83ef94bfb43ef84bfb03ef74bef43ef64beec3ef54bee83ef44bed43ef34bec03ef24beac3ef14bea03ef04bde03eef4bdc83eee4bb983eed4b1d03eec4b1c83eeb4b1c43eea4b1a43ee94b1a03ee84b0ec3ee74b0e03ee64b0dc3ee54b0bc3ee44b0ac3ee34b0a83ee24b0a03ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4f8903f604f8803f3f4f7f83f3e4f7e03f3d4f7dc3f3c4f7d03f3b4f7a43f3a4f6a83f394f6a43f384f6a03f374f6943f364f6903f354f6883f344f5fc3f334f5f83f324f5f03f314f5d43f304f5c43f2f4f5b43f2e4f5b03f2d4f5a03f2c4f3e43f2b4f3b43f2a4f3b03f294f3943f284f19c3f274e3903f264e3883f254e2fc3f244e2ec3f234e2e43f224e2d03f21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x52d983fa052d903f7f52cfc3f7e52cf43f7d52cb03f7c52cac3f7b52ca83f7a52ca03f79526803f78525e83f77525c83f76524943f754fe803f744fab43f734faa43f724faa03f714fa983f704fa903f6f4fa883f6e4f9f43f6d4f9ac3f6c4f9a03f6b4f99c3f6a4f9943f694f98c3f684f9843f674f8f83f664f8e43f654f8dc3f644f8c43f634f8b03f624f8a83f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x533e03fe0533d83fbf532fc3fbe532e03fbd532d43fbc532d43fbb532c03fba532b03fb9532a03fb8532903fb7532883fb6531f83fb5531e03fb4531b83fb3531a83fb25319c3fb1531903fb052ff43faf52fa03fae52f9c3fad52f943fac52f8c3fab52eb43faa52e9c3fa952dfc3fa852df43fa752df03fa652de03fa552dd83fa452dcc3fa352dbc3fa252db43fa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x53b98482053aec3fff53ad43ffe53ad03ffd53ab83ffc53aac3ffb539f83ffa539e03ff9539d43ff8539cc3ff7539b83ff6539a83ff5538d43ff4538cc3ff35389c3ff2537cc3ff1537bc3ff0537b83fef5379c3fee537983fed537803fec536883feb536803fea535e83fe9535e43fe8535a43fe7535a03fe65358c3fe5535803fe4534f83fe3533f43fe2533f03fe1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x576cc4860576bc483f576ac483e576a8483d576a0483c57680483b575fc483a575ec4839575804838574fc4837574d44836574cc4835574c84834574c44833573ec4832573e04831573dc4830573cc482f573c8482e573bc482d573b4482c57394482b571e4482a571d44829571804828570f0482756f98482656f94482553ec8482453ea0482353e84482253bc04821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x57bc848a057bc4487f57ae0487e579e8487d579dc487c579d8487b57990487a579844879578fc4878578f84877578e84876578dc4875578cc4874578b04873578a84872578a0487157898487057894486f577f8486e577e4486d577d4486c577b8486b577b4486a577b048695778c4868577884867577844866576ec4865576e84864576e44863576d84862576d44861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5a59048e05a4f848bf5a4f448be5a2c848bd5a2c448bc5a2b848bb5a0e848ba5a0e448b95a0d848b85a0a848b75a0a448b65a0a048b557fe048b457fd848b357fcc48b257fbc48b157fb448b057fa048af57f8848ae57ef448ad57eb848ac57eb048ab57eac48aa57cf848a957cf448a857cec48a757cac48a657bf848a557bf048a457bdc48a357bd448a257bd048a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5acec49205ace448ff5acb848fe5acac48fd5ac8048fc5abfc48fb5abe848fa5abe048f95aaf048f85aad048f75aab848f65aaac48f55aaa848f45aaa048f35aa9448f25aa8048f15a9ec48f05a9c448ef5a98448ee5a7b848ed5a78848ec5a78448eb5a69848ea5a69448e95a68c48e85a5e448e75a5dc48e65a5d048e55a5c048e45a5b848e35a5a448e25a59448e1⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5b4e449605b4b0493f5b4a8493e5b49c493d5b498493c5b494493b5b490493a5b48449395b3f849385b3f449375b29849365b1d849355b1c049345b0e849335b09449325afcc49315afc849305afbc492f5afa8492e5aee8492d5aed8492c5aed4492b5aecc492a5aeb849295aeb449285ae9849275add049265adc049255adbc49245adb449235ada049225ad904921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5fde449a05fddc497f5fa8c497e5f9e8497d5f9e4497c5f9c4497b5e8dc497a5e8d449795e8d049785e8c049775e8b849765e8b049755e89449745e88c49735e88849725e7e049715e2f849705b880496f5b7f8496e5b7f0496d5b7ec496c5b7e8496b5b7d8496a5b7cc49695b7bc49685b7a449675b79449665b78c49655b78049645b6e849635b5c049625b5bc4961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x628e049e0628dc49bf628d449be628d049bd6268049bc625e849bb625dc49ba625a049b96258c49b8624f449b7624ec49b6624dc49b5624cc49b4624c449b3624bc49b2624ac49b1624a449b0623f449af623c449ae620a449ad620a049ac5feec49ab5fee449aa5fecc49a95febc49a85feb449a75fea449a65fe9449a55fe9049a45fe8849a35fe8049a25fdec49a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x63cd04a2063ca449ff63bac49fe63ba849fd63ba049fc63b9049fb62dac49fa62ccc49f962c8449f862c8049f762bf449f662bec49f562be049f462bc849f362bb849f262bb049f162b9849f062b8849ef62b8049ee62ae849ed62ae449ec62ad849eb62aac49ea629b049e9629ac49e8629a849e76299c49e66299849e56299049e46298849e36298049e2628e849e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x668c44a60668b84a3f668b44a3e668884a3d667fc4a3c667f04a3b666984a3a666904a39665f84a38665e84a37665e04a36665c84a35665c44a34665b84a336658c4a32664944a31664904a30663cc4a2f663c44a2e662ac4a2d662944a2c661f84a2b661f04a2a63f884a2963f844a2863db04a2763da84a2663d904a2563d804a2463cf84a2363ce04a2263cdc4a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x670fc4aa0670f84a7f670f44a7e670ec4a7d670e44a7c670e04a7b670d04a7a670c44a79670bc4a78670a44a77670944a766708c4a7566ff44a7466ff04a7366fe44a7266fb84a7166ed04a7066ecc4a6f66ec04a6e66ebc4a6d66db44a6c66dac4a6b66d944a6a66d844a6966cfc4a6866ce44a6766ce04a6666cd44a6566ca84a64669a44a63668ec4a62668d44a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x6a9ec4ae06a9e84abf676844abe675fc4abd675e44abc675d44abb675cc4aba675b04ab9675a84ab8675884ab7673d84ab6673cc4ab5673c44ab4673bc4ab3673b04ab2673a84ab1673984ab0673904aaf672f44aae672e44aad672e04aac672c84aab672c04aaa672a84aa9672984aa8672904aa7671f44aa6671ec4aa5671cc4aa4671b44aa3671ac4aa2671944aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x6bed04b206bec04aff6beb44afe6bdf04afd6bde84afc6bddc4afb6bdcc4afa6bdc44af96bd904af86bd884af76bcfc4af66bcec4af56bce44af46bcb04af36bcac4af26bca04af16bbf44af06bbe84aef6bbe44aee6bbc04aed6bbb84aec6bba04aeb6bb904aea6bb884ae96bad04ae86adcc4ae76adc84ae66adb04ae56ac984ae46ac944ae36ac804ae26aaf44ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x764f44b60764f44b3f764f44b3e6fed84b3d6f9f04b3c6f9c44b3b6f9c44b3a6f9c44b396f9c44b386f9c44b376f9c44b366f6e44b356f6dc4b346f6c44b336f6b44b326f6ac4b316f6944b306f6904b2f6f6844b2e6f5d84b2d6f4e84b2c6f4e44b2b6bfc84b2a6bfc44b296bfb44b286bfa84b276bfa44b266bf984b256bf804b246bef04b236bee44b226bed44b21⟩
]

def tableRRR : Table Block := .branch 9 tableRRRL tableRRRR

def tableRR : Table Block := .branch 18 tableRRL tableRRR

def tableR : Table Block := .branch 35 tableRL tableRR

def table : Table Block := .branch 70 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table i

end PolicyCircuitPacked0


namespace PolicyRewriteParametricPacked0
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x10807f03c41bc0d106082c014408f03e018c0a603d016807401a000, 0xa2b46404b74001b350428ac14f12dcc28a104287f0a1d820a2883384b710028750428a110d12dc000a1cc28710828a018c12dbc006cd430a1c430a1f472c4b6e001b350c20a1ec6284b6d0a1b010a0f4286708286e10912dac006ff41ffc0a0e030a1b08204b6a0a1a428660828680a19428610c286a0c612da400a1881ffc08286914512da02864041ffc0a18c28600c286610412d9c006ff428380828641c312d98006ff41c2108286118212d94007ff0283c08283f10112d90007fe0107fec5004b63⟩,
  ⟨0xe306b83181780b1053826c11007b035816809a03a016807401a000, 0xbf04293b15812eac04829340a4c830a4dc75c4baa0000a4946584ba801204292414f12e9c00028fa19512e9000710428f914f12e8c28f20428f00a39c20a3cc3384ba10028e60428f210d12e8000a38c28e40828f119412dfc00428b10a39030a3b854c4b7e0010730828ec15212df428e10428bf0a2d820a3883384b7b0028b50428e110d12de800a2cc28b10828e018c12de400710c28b10c28bd1cb12de000710c20a2ec6284b77⟩,
  ⟨0x11108003bc1be0cb05d029812407f03701840a804101a008401c000, 0xa8e429f3082a66141904be1001c6f071b420a98c506312f8000a8f42a3c082a6110112efc0072e81cb7070bc30a8c4506212ef80072ec1cb9082a25141844bbc0029fa0a7cc1cb90c29fd141804bbb0029e50a79829e30c29eb141804bb80029e60a79429e30c29e915f12edc04829b70a69030a7848784bb60120a00829bf19d12ed400a5f810a6845004bb40a5e010a5d8296c0829790ce12ec800a5ac10a5e04704bb10029690a59829380c297719b12ec000a5a029660a4e030a5d06684baf002f81b820a5c45644bae⟩,
  ⟨0x11c08783fc1e20de068830416609f04581e80cc05301f809802c000, 0x2afc042b2510d12fd00077a42afa082b2419412fcc0077a410ac84406912fc82af6042af40abb820abdc3384bf0002aed042af610d12fbc007dcc2aeb082af519412fb8007dcc10abc8406912fb40071c41c70070e030aaa8506212fac00a8e429f30a9d030aa8c706812fa40071bc1c6d082aa11419c4be8002a3d0a9d02a730c2a77141984be70a9b810a8f82a69082a7010912f9800a8f429f30a8e430a9b8706512f942a6b0a9a020a9a82a670a98c30a9b03184be4002a640a8f420a9ac5144be30a99810a8f42a650a98830a9a04104be2⟩,
  ⟨0x13f09304541fc0e406802fc15809504081a00b004201a0098026000, 0x2b730adc820a7f02b710a7d030add03184c260029f30a7ec20adcc4072130942b700429f30a7ec1cbd0c2b72101c44c240adb82b670829fb0ad981cbd0c2b700c1c04c23001c6d072c41cb90c2b6e141bc4c22001cbe072f420ada0506e130802b62042b310ac9c20ad8c3384bff0ad8010abe82b300a79830ad88406d12ff80077a81de9077a030ad80506c12ff42b3a0ace020ace42b370acd430acec3184bfc001cb90acb420ace85144bfb0acd810acb42a21077a030ace04104bfa001cb9042b36101ac4bf9001de8042b35101a84bf8002b2f0abe82b2d0c2b3215f12fdc2b25042b230abf420ac983384bf5⟩,
  ⟨0x11a08784081de0d906302cc13808903b018c0a6040019808c026000, 0xafd4607a130ec0063b810afd053c4c3a0afb010afa82be5082bed0ce130dc2be0041182bba0ab9440afb06079130d800460ae9c2bac102beb1c1e04c350af8810aeec2bbd082be4109130cc2be0042ba70aee82ae50c2be2101b44c32001181f6e07dbc40af806077130c400460ae9c2bac102bbc1c1d84c2f001182ba70aeb040aee08075130b8004607db830aed86074130b42ba3042ba10adec20ae903384c2c002b7a042ba310d130ac00addc2b78082ba2194130a80070066cc20adfc5073130a42b740429fc0a7d020add43384c27⟩,
  ⟨0x105076037018c0ba056827411807e035017c0a403f017807401c000, 0x2ca70b29020b2982ca30b1fc30b2a03184c70002ca00b1e020b29c5144c6f0b28810b1e02ca10b1f830b2904104c6e0010c20b28870c4c6d0010c20b1fc60a0131b000b1e02c77082c7c101131a800b1982c65082c72141fc4c69001e69042c70141f84c68002c660aff42c650c2c69141804c670000b0e8607d131940066c010b0e453c4c640019b00ade02a2d0c2c3221e131880066c01c2e082c3019d131842c250430aff420aff8307c1318000c2bfd082c26141ec4c3f001e68042c24101a44c3e⟩,
  ⟨0x10607c83a41b00ca0580270110075034016008e039017008c020000, 0x2cec042cf810d1329000b3a82bf9082cf718c1328c0063b830afe430b3d072c4ca20018ee0c20b3c86284ca10b3a42c68082c3c0b19c2bfd0c2c3f0c1c04c7f0b39c10b19c2c3c082ce90c1f04c7e001e68079a41e6a0c2ce7141b04c7d0b39010b3882cb9082ce50ce131ec00b2e010b3904344c7a002cb60b19820b38c6504c790010aff42c660c2ce0153131e00041e68082cbe152131dc0002cb4182884c75001042cb314f131d02caa042c790b29420b2b04244c720010b1e030c2caa242844c71⟩,
  ⟨0x11207f03a81ae0c3059027c124082038818c0b004b01b808c026000, 0xb6fc10b6cc2dbe082de10c1f04cbd0019b7066cc1c390c2dbf141b04cbc002d210add82da90c2db515f132e400b4842b760b6a430b6c070a6132e00066dc19b3082dae142944cb70b69410b68c2d7a082da60ce132d800b5e410b6944344cb5002d770b4e020b6906304cb4001828202d380c2da11cb132cc0060a08082d7f18a132c80002d70182904caf001828042d6f14f132b800b4802d380b4ac30b4ec5060132a80066c02d200b4ac30b4d890a3132a40066c0182b082d3419d132a02cf8042cf60b3b420b3e43384ca5⟩,
  ⟨0x15209f84a022810107503581860b004c81e40ca05201d809c028000, 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⟩,
  ⟨0x13108e84281e60e006682d814408f04101c80c404e01d00a802e000, 0xbae02aeb0badc30baec50601349c2ea6042ea40b3ec20ba9c3384d250b9f410b3e82e340add830ba98406d1349000afe42cfa0b8a830ba9457c4d230b9fc10b8d42e37082ea1109134842e7d042bf90b8d02b760c2e7f101b44d200018f0063c419b20c2e7d141b04cff0b9c010b9b82e68082e710ce133f000b99c10b9c04344cfb002e640b99420b9bc6504cfa001c019b7082e6c141cc4cf9002cfa0afe42e2a0c2e36141804cf50019b00b3e82e2a0c2e322428c4cf40019b0063c420b8c06744cf30b89410b88c2d22082e260ce133c82df5042d200b4e42d210c2e25101b44cf1⟩,
  ⟨0x13109004341ec0e306602e014809003f81b80b6042019007001c000, 0xaba42f61082f64142ac4d3c0bcf410bbb82ef7082f3e0ce134ec2f38042eeb0bbb42ef60c2f3d101b44d3a0bce810bcd82efd082f3b0ce134e02f38042eec0bbb42ef60c2f3a101b44d37001f7a07dd81f7b0c2f38141b04d36002eeb0bbb02ee90c2f37141804d35002eec0bbac2ee90c2f341c2984d34001f7a07dd820bcc850a5134cc00bc9c2ee9082f30142ac4d32002eec0bbac2ee90c2eef15f134b42ee50bb8c20bb902ee20bb8030bb983184d2c001f230badc20bb945144d2b0bb8410badc2ebd07dc430bb8c4104d2a001f23042ee1101ac4d29001f71042ee0101a84d28⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0x13008f842c1f40e906a82f015809604101b80b404901c0094022000, 0x1e3b078e420e0c45067135b800bfe42ef60bfb430e0907068135b4007df81f7c0838221419c4d6c002ffc0bfb420e08050ab135ac007e801f7f07d8c30bfc45062135a82fe90bf9c20bfa02fe60bf8c30bfa83184d69002f7f0be8820bfa45144d680bf9410be882fa00bf8830bf9c4104d67002f7d0bdc42f7a0c2fe5182b84d66001fa107df41f610c2fe3142b44d65002ba70bbd82f710c2f781c2b04d63001f6e07df020bdd850a51358800bc8c2f71082f74142ac4d61002ae60ab942f610c2f6d15f134fc00ab982ae50bd8430bda070a6134f8007dd01f70082f66142944d3d⟩,
  ⟨0x13409084442080f1070832016e0a004301c80c204d01e00a0028000, 0x39320e4dc39390c396419a136840076d41daf0839611591368000e3fc10e4c45004d7f001bfd0e3bc38780c38f921e135f8006ff41db00838f719d135f438eb0e3a820e2e838e90e2cc30e3b03184d7c0038b20e2e420e3ac4072135ec38e80438b20e2e41e650c38ea101c44d7a0e39838bf0838b90e2f81e650c38e80c1c04d79001df3078e41e610c38e6141bc4d78001e660799420e380506e135d800e0a038b20798430e2ec5060135d400798c1e610838ab141844d72001e62078fc1db10c38a0141884d71001e3d078f01e200c383d141884d700038290e0a038260c38331c1a04d6f⟩,
  ⟨0x11f08603e01d40dc06282c414608a03e01a00a80400198080026000, 0x39b50439300e4cc20e6dc4244db70e6cc10e4bc39320839b5102d84db6001db40439b3142c84db50038ff0439b1142d44db30e69c39770839370e5d820e5c430b4136bc39a50439760e4dc20e69c30b3136b80076b810e69450b2136b439a20e68020e684397f0e5f430e68c3184dac0039750439a2101ac4dab0e5f810e5d4397c0839a0102c44daa00397b0e5e839790c397e102c04da9001dad076ac1da50c397d142bc4da80039750439781401369c39680439660e4f020e5a43384da400393b04396811c1368c00e4e039370e4e430e59c66c4da2⟩,
  ⟨0x11108303e41cc0d906482e414c09604481d80be04b01c00ac028000, 0x3a6e182e04deb001bfd043a6d14f137a83a66043a640e8f820e99c3384de8003a3d043a6610d1379c00e8f03a2f083a651941379800700709c20e988507313794006ff43a2f0e3ec30e8e48784de3001bfd076c820e8dc6744de20039390439f611c1378439f30439e70e7a820e7d44244de00e7c4106ff439e60e7a430e7cc60a9136fc006ff41dbc076e830e7c460a8136f8006ff439e50e6f030e7a075c4dbc001db60439bf158136ec39b80e6c020e4c8392f0839ac0c2dc4db90e6cc10e4bc39320839b80c2cc4db8⟩,
  ⟨0x11708503e81d80d906102b812a08503781840a60400168080020000, 0xeb9c10ebc04344dfe001f780eaac20ebbc6504dfd001f78043aec101a44dfc0eb9010ead43aac083ae50ce137e83ae2043aab0ead02eec0c3ae4101b44df9001f7907de01f770c3ae2141b04df80eaf83abc083abd0eaec3ab90c3abf0c6137dc0079843ab1083abe145137d83aba043ab10e29c1f770c3abc104137d400798410eae8406b137d0007ddc10eae4406a137cc00eacc3aab0eac430ead857c4df20ea9c10ea943a7f083aa80ce137c000e9f810ea9c4344def003a7d0e3bc20ea986504dee001c01c20083aa3141cc4ded⟩,
  ⟨0x12508c04201f40e706802f015209603f81b80b404c01c0090026000, 0xeedc10ef804344e34001f790eacc20eefc6504e33001f79043bbc101a44e320eed010eec03ba9083bb50ce138c03bb2041bfd0eebc38290c3bb4182a44e2f001bfd078981e200c3bb2182a04e2e001bfd0eeb838350c3bb11d7138b43ba7043b690ed9020eea03384e2b0eb8810eacc3ab40bbb030ee9c406d138a80078fc1df9083b79142ec4e28003aab0eacc3ab10c3b6a141804e27001db6043b29142e84e25003b230ebe439bc0c3b26142e44e240039e90e2c83af90c3b211c1a04e23001df5077cc20ebfc5067138883af0043aee0eba020ebc43384dff⟩,
  ⟨0x12208603ec1d40dd06502f415409704381e80ce04e01e8098026000, 0xf19010f0d03c3e0f18430f1984104e69003c3a0f0e020f19060bd139a00077ec1dfa083c62142f04e67003c34043c37140139983c2e043c2c0f08820f0bc3384e64003c21043c2e11c1398c00effc39370efc030f0b466c4e62003bfe0e4dc3bf00c3c2a19a139840077f41daf083c27159139800077f810efcc5604e3d0efb410efa03be2083bee0ce138ec3bec0efac20efa03bea0ef8830efb43184e3a0038280e2e420efb04072138e438e80438280e2e41e650c3beb101c44e380038b20e0a01e610c3be915f138dc3be0043bbe0eee020ef843384e35⟩,
  ⟨0x12408883e81cc0d305f82b813a08903e01a40aa04701b80a4020000, 0xf2c810bdb02f6e083cb4109139f03cb0042ae50bdac2eeb0c3cb2101b44e7b001f7407dc01f750c3cb0141b04e7a0f2b810f2a83ca5083caf0ce139e43cac043ca90bfe420f2b840e1139e0007d941f63083cac143804e77003ca80bfb020f2ac50bf139d80077dc1df6076e830f1f45062139cc00efc010f1f04704e720f1d810f0d83c30083c770ce139c03c74043c350eff820f1d840b6139bc0077f010f1d050b2139b800e1e03c38083c71145139b40076c410f1bc50be139b03c680f19820f19c3c650f18830f1a43184e6b003c3c0f0d020f1a05144e6a⟩,
  ⟨0x11408003b41b40cf06102bc13608703a01980b004b01f00ac028000, 0x1e71079ac1f640c3d71141b04eb90af8810aeec2bbd083d700ce13ae03cb2042f6c0bdb820f5983384eb70000f4f460e313ad40046083d3c143884eb4003cfa0b0f03cf90c3d2015f13aa400b0f03cfa0f3e430f3f4506013aa000e1e438680e1e030f3d4506613a9c39b50439300e4cc20f3d03384ea6003c34043cf1142d44ea5001dfe043ce5142e84ea2003cba043ce311c13a84007d8010f2f45604ea00f2dc10f2d42ef0083cb80ce139fc3cb0042ae60bdac2eeb0c3cb7101b44e7e002ae50ab982f610c3cb6141804e7d⟩,
  ⟨0x13209104442060ef06e83381800ac04c82180de04f01d809c028000, 0x3dea0f7a420f7b84044eec003db80f6dc20f790507f13bac0079bc10f788507e13ba800f6e03da60f6dc30f6ec506013ba43dae0480f69820f69c307c13b9c0203da6083daf141ec4ee6001e6e043dad101a44ee50f2b010f2a42ff9083da50c1f04ee30f5f410f3fc3d21083d7f10913b843d7c043d210f3fc20f5f43384ee00f5ec10b0f02ba70f3ec30f5f0406d13afc3d7a0f5d83d730c2ba70f5d43ca80f3ec40f5ec30aa13af83d78043d750ae9c20f5e8307c13af4007db41f6507d8c30f5e0506c13af000f5d03ca80bfb030f5dc57c4ebb0f5c410f3ec3ca8083d730c1f04eba⟩,
  ⟨0x10807a038019a0c0058027c12208603d81a00b003f017806401a000, 0xf8ec10f6e43cfa083e3d0c1f04f21001e6e079bc1e700c3e3b141b04f200f8d810f8d03e2b083e370ce13bf400f8a810f8d84344efc003e280f6e020f8d46504efb0060f6983db80c3e3215313be80181e6e083e3015213be40003e26183944ef7006043e2514f13bd83dfc043deb0f7dc20f7f84244ef40060f7a880c3dfc242844ef30f7e43df6083df80f7d43df10c3dfa0c613bc800f7c83dea083df914513bc43df4043dea0f7cc3df00c3df610413bc00188083df41c313bbc0188083df1182804eee⟩,
  ⟨0x11007d83a41b00c605d82c013a09004001c40ca05101f80c4034000, 0xfbc01443ee70faec30fbc860a913ce00441ea407a8830fbc060a813cdc0443ee60fb9430fbb075c4f350110fb983ee50c3ee91c29c4f340000fae460e613cc804410fae053c4f310fac410fabc3ea6083eb20ce13cbc00fa9410fac44344f2e003ea30f9dc20fac06304f2d01e203e770c3ead1cb13cb00788083eab18a13cac00f9a83e770f9a030f9e8506013ca00443e6a0f9a030f9d490a313c9c0441c25083e7319d13c983d7b043cfa0ae9c3cfb0c3e61101b44f240f8f43dba083cfa0f6e43da60c3db10c1c04f22⟩,
  ⟨0x13609404541fc0ea06b830c16009c04882180d205501d809c026000, 0x106cdc20fddc5484f6f0fd9810fcec3f3d083f6810913db03f64043f360fcdc3ef60c3f66101b44f6b001b3706ce01ce10c3f64141b04f6a0028710fcd83f350c3f3c15f13da000fcd828710fcd430fce4506013d9c00f9ec3ef60fbd430fcbc57c4f65003ef60f9ec3ef50c3f2c141804f640000fc9460e813d8407810fc9053c4f600fbf43efc083ebb0fb9c3e7b0fb9840fbf840e713cf83ef0043ee70faec20fbf4307c13cf43efb0fbe020f9ec3ef70fb9830fbf0307013cf03efa043ef70f9ec20fbec307c13cec0073981ce207a8c30fbe0506c13ce83ef2043eeb0fbb420fbd04244f39⟩
]

def tableLLL : Table Block := .branch 12 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0x13e093844c1f80e906b02fc13e08b03c81ac0b00410170084022000, 0xfef410f9dc3e780f9ec30fefc406d13e840070901c250739430fef4506c13e803fb5043e7b0faec3ef70c3fba101b44f7f0fedc10fcb83f30083fb910913df83fb6043f300fcb820fedc3384f7d0fed410fbd83ebb0fbdc30fed8406d13df03efd0fba03fb40c3ebb0fb9c3ee60fbdc40fed430aa13dec3ef8043ef70fb9820fed0307c13de80443f360fcd430fec090a313de40441b38083fae19d13de03fa5043f380fda420fe9c4244f770fd9010a1c43f370fbd830fe94406d13dd83f7d043f7b0fdc820fdf83384f73003f71043f7d10d13dc800fdbc3f36083f7c19413dc400428710fcd830fde454c4f70⟩,
  ⟨0x11f08483e01ce0d706182c013a09004001bc0c204e01b8090026000, 0x4831044823120c0482d0c483310413ed400faec29ec084831141904fb4001eb907adc2120b8506313ecc01208c482808482c10113ec801208c48220fb94312098506613ec43fbf043e790f9f020fffc3384faf0fff410ffec3ff2083ffe0ce13eb800ffc410fff44344fad003fef0f9a820fff06504fac0060f9dc3e6a0c3ff915313eac0181c24083ff715213ea83fec043fe70ffa420ffb84244fa80fef410f9a83e780f9ec30ffb0406d13e9c00f9dc3e6a0f9a030ffa057c4fa5003e6e0f9a020ff9450ab13e903fbf043e790f9f020ff844244fa2⟩,
  ⟨0x13409304542020f006b831c16209d04481d40c205001e80a4020000, 0x1f72044922101a44fea001f2507c8c2123cc506113f98007c901f21079e43123a0506213f94007c841ebd0848e0142ec4fe31229448a30848a412288487f0c48a60c613f880121dc48790848a514513f8448a1044879121ec487e0c48a310413f800121b04875121cc31228460ae13efc007af01eb8079fc3121fc50ad13ef8007aec1eba07a883121b8506213ef400faec29ec120883121a4706813ef0007ae41eb70848671419c4fbb120e41120a4483408483b10913ee401208c29ec0faec3120e4706513ee04836120cc2120d44832120b83120dc3184fb700482f1208c2120d85144fb6⟩,
  ⟨0x13709184541f80eb06a02e814c09504081b80ae0430180074020000, 0x3c74043c350eff82125f840e913ffc007d801125cc50ba13ff4496b125a82124e84969124d43125b03184ffb0029ec124e42125ac407213fe849680429ec124e41f270c496a101c44ff912598493f084939124f81f270c49680c1c04ff8001eb707bec1f230c4966141bc4ff7001f2807c9c212580506e13fd40124e029ec07c8c3124ec506013fd0493304492d124a02124d03384ff2124c410bae02eb90ab983124cc406d13fc4007dcc1f7207dc43124c4506c13fc000abac2eb80badc3124b857c4fef1249811249048fe0849270ce13fb40123f41124984344fec001f720bae02124946504feb⟩,
  ⟨0x11f08903ec1ce0d906002c813c08a03b01a40ac04901b008c026000, 0x127ec1127f85005838127bc49bf0849a6126f82126e430b4160c449ed0449be126982127bc30b3160c0007ce01127b450b2160bc49ea127a02127a449e7127943127ac318582e0049bd0449ea101ac582d127981126f449e40849e8102c4582c0049e31278849e10c49e6102c0582b001f3707cd41f2f0c49e5142bc582a0049bd0449e0140160a449b70449b5126ac2126e033858270049aa0449b711c160980126a049a60f2e83126d866c58250049a7126983cba0c49b319a16090007cfc1f390849b01591608c497e043cf00f3b42125fc3385820⟩,
  ⟨0x14209104381f40e606902f815609804081b80b0045019007c01c000, 0x12bc44aee12ba83129984aed12b9c4ab9104af20c2a8586d12bbc112bb44a66084af10c1f0586c001fb807ec01faa0c4aef141b0586b12ba0112ae44ae7084aea0c1f0586a001fae07eb01faf0c4ae8141b05869004a3f12ae04ab60c4abd141805867004ab8128fc4ab60c4abb15f161984aae044a70129a0212abc338586412aa41129984a6f1299c312ab8406d1618c4aab044a73129d4212ab4424586212aa41046129bc4a67104aab181e45861001181fb907ee8412aa46077161800046129984a6e104a741c1e0583e001184a66129b84129c47076160f40128d04a21084a3c141fc583a001f3c044a3a141f85839⟩,
  ⟨0x12208783e01c80d306282c813e09204101c40c204d01e00b802e000, 0x12e9c112df04b73084ba80ce162884ba5043aab12dec4b720c4ba7101b458a1001f7907de01fe00c4ba5141b058a0001e6112de4212e8850ec161fc007f80112e84406a161f800eacc3aab12de4312df457c587d12d9c112d944b3c084b680ce161e8012cec112d9c4345879004b3912ca8212d986505878002c3c12ca8212d8c50eb161dc0070079ac212d8450ea161d80128f84b2a127fc312cb45060161c80128f849ff084b28141fc5871001f3a044b26141f8587012bc81128fc4a6612ae4312bdc406d161bc4af2044ab8129984ab90c4af3101b4586e⟩,
  ⟨0x14109504582060ec06c03141620a004781f00ca05201d809c028000, 0x4bf6044b6c12fb84a7a0c4bfe101b458b5004a6712db04be00c4bfd1418058b412fe0112fbc4bf1084bfa109162cc4bf6044a6712fb84a7a0c4bf8101b458b2001fbd07eec1fbe0c4bf6141b058b1004b6c1299c4be00c4bf015f162bc012db04a6712f80312fac70a6162b8007ef41fbb084be91429458ad004be312f80212f9c50ab162b04bbe044bb112ea8212efc33858ab12ee4112dc84bb0129ec312ef8406d162a84bbb044bb412ed8212ef442458a912ee41129e84bb0129ec312eec406d162a0007f841fbf07f88312ee4506c1629c012dc84a7a12ebc312ed457c58a5004a7a12dc84baf0c4bb21418058a4⟩,
  ⟨0x138094046c2140f906c831416409f04401d00b604701a0090026000, 0x1fa707ce42132f056458ee001fa8044ca8158163ac012b9c4aeb084ca4142fc58ea003c3b0f0e42131d450ee163a038e90e39838bf0c38b20e2e438be0799440e2cc30aa1639c38ba0438b90e2c820e3a4307c1639838ec0438ba0e2cc2131a842458e4131841130d84c38084c631091638c4ba5043ab312dec4b720c4c61101b458e2003aab0eacc4b790c4c371418058bf130c84a73081184a67129bc4129d450ed162f44aa9044a6f1299c2130c8307c162f00046129984a6e104c28201d458b9001181fb90c4c26181d058b8004b34129b821309050ab162dc4bfe044bfc12db4212ffc33858b6⟩,
  ⟨0x11808283c41c60d206102d013608b03a81900a60460198098026000, 0x134cc1133c44ce5084d340ce1648c4d31044cf0132cc2134cc40b616488007e981134c450b2164840128d44a21084d2f142ac5920004a21133d42134b051458ff001f3d044d2a142f858fe1348c4d21084d22134804cfd0c4d240c6163f40133dc4cef084d23145163f04cff044cef133e44cfc0c4d21104163ec0133d44cf3084cff182f458fa001fa507e902133f450bc163e40133bc1133c850058f81338c1133844cb7084ce40ce163c80132d811338c47058f1004cb4126984ca50c4ce219b163c00132cc49a6132943132fc66858ef⟩,
  ⟨0x12f08d841c1ec0dd06682dc14608f03d819c0ac045019007801a000, 0x4bf6044bee129e82136e4307c164d00129984a7b135c03136d070ac164c8007ee41fe3084db2142945931136a04da6084da7136944da20c4da90c6164c00135cc4d76084da8145164bc4da4044d76135d04da10c4da6104164b801359c4d70135b831369060ae164b4007fa01fe407ea431368850ad164b0007f9c1fe607ea83135a45062164ac0129fc4a7b134e83135847068164a8007f941fe3084d3f1419c5929004aa2134e82134f450ab164a04d38044ca3131f82134e43385927134d81132884a7f084d38103845926001fb007ea82134d850e0164940132941134d44705924⟩,
  ⟨0x145097046c2080f006e832816609f04601f80d405902400b8034000, 0x4dfd044a3e12cac4a3f0c4e24101b4596a004b2a128f849ff0c4e2315f165a44dfd044b2a12cac4a3f0c4dff101b45968001fab07ce81f3b0c4dfd141b05967004aec12b9c4aeb0c4dfc15f165984dfa044df6137c42137ec3385965137e01128d04df512ae03137e8406d16590007eb41f3c07cf43137e0506c1658c0137d04a34128843137dc57c5962001fa8044deb142e8593f004b72129e84baf0c4de81c298593d001fe107efc21379850a5164f00137804baf084de4142ac593b136f84bb1084a7b12ec04b720c4baa0c1c0593a12ee4112ec04a7b084dbe0c1f05939136e44bfc084a7a12fb84b6c0c4b6d0c1c05935⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0x106079037c1a40c2059027c124082038818c0a604501a0098026000, 0x4a34137d04a210c4ef21418059a213ba8113ba04ee2084eeb0ce16680013b84113ba8434597f004ebf128d0213ba4650597e001c01e71084ee6141cc597d13aec113ae44eb0084ebc0ce165e8013abc113aec4345979004ead0b480213ae865059780060b4e02d200c4eb7153165dc018182a084eb5152165d80127fc4cf3084e60145165cc007cec1138f850be165c8007c8c4e2f084e38143b05971001fbc044e37101a85970002aeb0bae04e2f0c4e3315f165bc4e24044e2212980213894338596b⟩,
  ⟨0x11808203cc1be0cc05f82bc14208d03d019c0b404a01c80a802e000, 0x4fa2124e04fac0c4fb61c1a059b7001efd07bec213ed05067166d800bae02aeb138bc313dfc5060166d04f67044f6513cfc213da033859b2004f3e044f6710d166c40071a04f3c084f66194166c00071a0113d8c4069166bc013cb84f2f13cb0313cd05060166b0013cbc4f2e13cb0313cc857c59ab13c8c113c844ef8084f240ce166a8013bdc113c8c43459a9004ef5137d0213c8865059a8004a34137d0213bfc50ef1669c0181f3c084efd143a859a613bcc113bc44eec084ef40ce166904df8044df4137d44ab80c4ef3101b459a3⟩,
  ⟨0x14209604602080f006e831016609c04481d80be04b01c008c022000, 0x160b41122a85828160a83160bc41059e8004ffa1608c58210c582d182b859e7001f2007bf01ee30c582b142b459e6001eff07bf81ee40c4ffc1418859e513fdc113fc84fef084ff80ce167904ff613fd4213fc84ff413fbc313fdc31859e3004938124e4213fd84072167884968044938124e41f270c4ff5101c459e10029ec124e01f230c4ff315f167804fed044e32138a8213fb833859be13fac10bae04e3112db0313fb4406d166f4007dcc1f7207ef0313fac506c166f04fe5044fe113e8c213f9833859bb13f8c1444fe013e88313f9460a9166e80441eea07b90313f8c60a8166e40444fbf13ee0313f8875c59b8⟩,
  ⟨0x12408a040c1e80e0067830415c09a04081c40b604a01c80a4020000, 0x58b6162ac21638c65059fc005876162ac21638050ef167ec0181e7a0858be143a859fa005876162ac587e0c58ae1418059f6011161d8587e0c58a921e167d40441e7a0858a719d167d0586f04583f161a82161c442459f2004fb9124e04fa20c586f1c19459f1161b0586908586b161a058640c586d0c6167c00161944fb908586c145167bc5867044fb91619858630c5869104167b8013e8849380858671419059ed001efd07bec2161905063167b0013ee4583e085862101167ac5831160bc2160c0582e160ac3160c831859ea005825122a82160c451459e9⟩,
  ⟨0x13809084041da0d906282c813c08b03a018009a040018008001a000, 0x164c411648c4fa2164903164c8406d168c45930164bc592e0c4fa213f804fbf164904164c430aa168c04fe3044fe013e882164c0307c168bc592c04592413efc2164b8307c168b8007ba01ee607ba43164b0506c168b40161dc5923164883164a457c5a2c005923161dc59220c5926141805a2b163ec1162b458af0858fc0ce168a458f90458ab162b058770c58fb101b45a28001ee7079e81e7b0c58f9141b05a27163c01163b858e80858f10ce1688c01639c1163c04345a220058e6161d82163bc6505a21001c01ce60858ec141cc5a201639011638858b90858e50ce167f80162e011639043459fd⟩,
  ⟨0x12308803fc1d80d506082b814209104001c00b804b01e8098026000, 0x165ac593f122a43166d857c5a65005962122a42166cc50ab1699059af04596d165bc2166c44245a63166b41165ac596c1648c3166bc406d16988007b941e78079e43166b4506c1698459a60459a4165ec21669c3385a6000597a0459a610d168fc0165e0596b0859a5194168f800fbd8596b0859a2143ac5a3d001c01ce20859a0143a85a3c00593f165ac48a90c596e141805a38011164fc48a90c596921e168dc0441e7808596719d168d8593104587713e8859240c5936101b45a34164cc1164a0592a085935109168cc593204592a164a02164cc3385a32⟩,
  ⟨0x12108704041e20e306602e414408f03e01a80ae04a01d00a802e000, 0x5a2f045a2d1689c2168c03385a7a005a26045a2f10d169e40077a82b2f085a2e194169e00077a81168ac4069169dc4feb042aeb138c44b6c0c59fc101b45a75167e41167dc58780859fa0ce169d058f9045876162b058770c59f9101b45a730058ab161d8587e0c59f815f169c858fb0458ad162bc2167d44245a7001113efc4fb80c59ee1c29c5a6f167a81167a059e20859eb0ce169b40167841167a84345a6c0059e0164fc2167a46505a6b001c01ce20859e6141cc5a6a166f41166d459b70859bf109169a059ad04593f165b059230c59bd101b45a67⟩,
  ⟨0x13309004301f60ea06f834016c0a204681e80c404d01c008c022000, 0x16ab85a6c16ab4316af857c5ab0005aae169b05aad0c5ab91c2985aaf001c6907194216adc50a516ab8016ac45aad085ab5142ac5aad00016a9c60f016ab00070d86085aa6143885aab16a805a7e085a6c169a45a3b0c5a790c1c05aa8169d01169a45a6c085aa00c1f05aa7001c36185a3b168e44169fc707616a985a76045a6a169b42169e04245aa4169d01070d86169a45a6c105a76181e45aa3001c36181c63071904169d0607716a880070d86168ec5a39105a6b1c1e05aa0001c36185a3b168e44169988075169fc0070d860718c3169906074169f80168f85a39085a62142ac5a7d⟩,
  ⟨0x145099046c20e0f306f833817a0aa04801f00d205201f00ac028000, 0x5b36045b3016cac216cdc3385ae516cd0116bf05afd0a7cc316cd8406d16b90006e801c6b071b0316cd0506c16b8c0168c45afc16be8316cc4506016b88016bf05a3116be8316ca470ac16b80006e801c6b085b27142945abf005b2116be8216c9450ab16af8016bf05a3116be8316bfc57c5abd16bd85abd085a3116af05a6c0c5abf0c1c05aba16b98116af05a31085af60c1f05ab916bcc116bb85af0085af510916ae05ae6045aae16af05a310c5af3101b45ab7005a6c16ab85aad0c5aef141805ab516ba0116af45abf085aea10916ad05ae6045a6c16af05a310c5ae8101b45ab3001c69071941c6a0c5ae6141b05ab2⟩,
  ⟨0x11e08583e01c20ce05b828c11e07c034817009803e015807801c000, 0x5bb916ebc5bb70c5bbc15f16be45baa045b7e16dd8216eac3385af616e94116ce05b7d16bf0316ea8406d16bd45ba7045ba016e88216ea44245af416e94116d945b7d16bf0316e9c406d16bcc006dfc1b7e06df4316e94506c16bc8016ce05b6516dec316e84506016bc0016d945b3816dec316dfc57c5aef16dc0116db85b68085b710ce16bb4016d9c116dc04345aec001b7f16d94216dbc6505aeb001b7f045b6c101a45aea16d8c116d845b3b085b640ce16ba4016ce8116d8c4345ae8001b7e16ce0216d886505ae7001b7e045b3f101a45ae6⟩,
  ⟨0xf807603641980bc056027c116078036818409c0410188084028000, 0xeb01171a853c5b311718c1171845c38085c640ce16cbc0170dc11718c4345b2e005c35170cc2171886305b2d00eb08170cc3170fc72c5b2c00eb08085c3d18a16cac016ec05c28170983170b4506016ca00170a05bb0170983170ac57c5b2700016fec60f116c9005bd045bfa14f16c8c5bf3045bf116fa0216fd03385b21005be7045bf310d16c80016f945bb9085bf218c16bfc05bd0c5bb90c5bef1cb16bf805bd0c216fb46285afd005baf16ee45bb70c5bbe141805afa⟩,
  ⟨0x10807c039c1b20c60578278116078035016408c0390148060016000, 0x5ce0172f82173b46305b65001a76205cbe0c5cea1cb16d900069d88085ce818a16d8c5cbb045cb0172c82172f44245b61172e41171c05caf170a03172ec406d16d8003ae3af5e50c5cb9141b05b3f005c33171c05ca00c5cb115f16cf405bb171c05ca00c5cac2428c5b3c016ecebc2172a86745b3b005ca4172802172a050ab16ce85c7e045c7c171cc2171fc3385b39005c72045c7e10d16ce00171bc5c70085c7d19416cdc0185c33171c03171e854c5b360063ae085c7815216cd40005c6b183c85b32⟩,
  ⟨0xe806b831816c0ab04f825010e07c037817009e03f017008001a000, 0x5bff175d42176a0506416df80064fc193d085da51418c5b7d005da0175dc21768c4045b7c000175cc60f516dec05bb045d7214f16de80005d3e183d05b74001a70045d3d14f16dcc0005d30183cc5b70001a76045d2f14f16dbc5d26045d24173ec21749c3385b6c005cfa045d2610d16dac0173dc5cf8085d2519416da80185cbe173e031748854c5b69006069e02174805485b68173b81173b05ce3085cef0ce16d9c0173881173b84345b66⟩
]

def tableLLR : Table Block := .branch 12 tableLLRL tableLLRR

def tableLL : Table Block := .branch 25 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0x12f08f84241f60ed06c831816009d04581dc0cc05301f809802c000, 0x66a45b7b085e2514516ec85e21045b7b177f81b7d0c5e2310416ec40066a4117884406b16ec0006df4117880406a16ebc0177e45d75066a43177f0506016eb85df3045def177a02177d03385bab177c415bb177b85bff0c5df3182a45baa016ec192a064a03177c460a816ea405bb177b45db50c5df01d716ea0016ffc5d75176d8317790706816e980064fc193d085de21419c5ba5176c01176845dab085db210916e8c0176805d7516ffc3176c0706516e885dad176a82176b05da9176943176b83185ba1005da6176802176b45145ba0176a01176805da7176903176a84105b7f⟩,
  ⟨0x15b0a384c02320f9072834817c0ac04c82000de05801f00a8032000, 0x65841960064a03179b8506216f8c5e64045bb016ffc5c290c5e69101b45be2179901170a05bff170a4317994406d16f845e63179845e600c5bff177b85ded170a441799030aa16f805df1045dee16ffc21798c307c16efc05bb177b45db50c5e621c29c5bbe178f81170a45ded085e600c1f05bbd0179978819290c5e3e141b05bbc178f01177ec5df6085e3d0ce16eec5e3b178e82177ec5e39177d83178f03185bba005d75177e82178ec407216ee45e38045d75177e819ad0c5e3a101c45bb8178d85e2f085dfa178b819ad0c5e380c1c05bb700193d0668419a90c5e36141bc5bb60019ae066b42178c0506e16ed05e251788c2178905e22178803178983185bb3⟩,
  ⟨0x13109184401f20e506902ec15209b04401c40bc04701b0094022000, 0x67dc117dac406916fe45f3c045f3717ce4217cf84245bf70ad8010acbc2b300a798317cf0406d16fd800abe82b2f0acb4317ce0506016fd05f31045afe168c8217cc83385bf216cd01168c45afd0a7cc317cc4406d16fc405bb16ebc5bb70c5f2921e16fbc05bb5e0085f2719d16fb85efe045bbb16ec4217bfc3385bed17be4116ebc5bba16ec0317bf8406d16fb05efb045bbd16efc217bf44245beb17be4116ee45bba16ec0317bec406d16fa805bf5e05e10c5ef9141b05be90019ab066a4217bc8506116f9c0066a819a7063fc317b9c506216f9800669c1963085eb7142ec5be4⟩,
  ⟨0x12908c03f81d40d706002b0132085039016c08e03c0180074020000, 0x17fc05fba085ff4142ac5c2e17fb45fbd08493817ef05fb40c5fb50c1c05c2d17fa0117ef04938085fed0c1f05c2c17fa8117f805fe2085fec109170ac5fe8045fbb17ef049380c5fea101b45c2a001e3307be41efa0c5fe8141b05c29005fb417eec5fba0c5fe115f1709c017eec5fb417ee8317ef85060170985fac044f3313cd8217eb84245c2317ea8113cbc4f3013cd4317eb0406d170880067e419f5067e8317ea8506c170840005f77183d85bff00bc8117dd853c5bfe17dbc117db45f67085f700ce16ff0017d98117dbc4345bfb0019f717d90217db86505bfa⟩,
  ⟨0x12a08b84301fa0ea06b830015809904101b80b604701b0094022000, 0x167f0113df84f7908687310917194000686d183dc5c63001ea01821a1b050e217188683504682b1a0b421a1943385c3f1a18811a0e8683c086864109170f46833045ffc1a0a85fbb0c6862101b45c3c005ffb17ff05ffa0c683b141805c3a1a0d411a0ac682d086837109170e46833045ffb1a0a85fbb0c6835101b45c38001ef707bd41ef80c6833141b05c37005ffc17fec5ffa0c682c15f170d4017ff05ffb17fe831a09c70a6170d0007bdc1ef5086825142945c33005fff17fe821a08c50ab170c8017ed05fbb17ee8317fe070ac170c00078cc1ef9085ff6142945c2f⟩,
  ⟨0x13109184401fa0e606d83301760a804801ec0d005101e009c024000, 0x67d811a480406a171f001a3dc4f6d73c0c68fa141805c7b1a3bc113cc45faf0868f1109171e45faa044f2e13cc04f350c68ef101b45c780001a3a460f8171d800679860868e8143885c750068a21a1f821a2f850ab171c868bb0468b91a2d821a2f03385c701a2c4107a8061a2ac5ffb1068bb181e45c6f001ea018687a1a1f841a2e87078171b868b30468ac1a2b821a2d44245c6c1a2c411a1e868ab17fec31a2cc406d171ac007a80607bcc1ef41068b1181dc5c6a001ea018687a1a1f841a2b47076171a0007a8061a1e8687e1068a9201d45c67001ea0181ef30c68a7181d05c66⟩,
  ⟨0x13208f84301ea0e206582e815209604101cc0be04b019008c01a000, 0x692917d9068fb0c69b915f172c4697b0469361a5e021a5f44245caf1a5cc11a4cc69351a59031a5ec406d172b8697504696e1a5a421a5d83385cab1a5cc11a4d069351a59031a5d4406d172a806ec6e86ed0c6973141b05ca900693b1a4c821a5c450ab172a001a4cc69341a4c831a5bc57c5ca70069331a4d069320c69621c2985ca501bb1ba021a58050a51729001a4d069331a4c831a4dc50601728c017d9069291a3ec31a4b050601728469251a48c21a49069221a48031a4983185ca001cf068fb086925145171fc69210468fb1a3f419f60c6923104171f8073c046921101ac5c7d⟩,
  ⟨0x12b08d84341f40e306782f014a09103f01a80b204801a0094024000, 0x67e06929086a65194173980067e011a9884069173946a3a046a381a7e021a8ec3385ce31a8c811a7dc6a2c0a7e831a8e8406d17388013dc869f71a7fc31a8e45060173846a34046a2d1a8bc21a8d84245cbf1a8c8113dc86a2c0a7e831a8d0406d172f8006fa01caf072c031a8c8506c172f401a7dc4f721a7fc31a8b857c5cbb0069f713dc869ff0c6a291c2b05cba001be8072bc21a89c50a5172e401a88469ff086a25142ac5cb80069e71a79869e40c69f51c2985cb601cc1cb821a7cc50a5172d401a79c69e61a79031a7a857c5cb4004f6d1a3ddcf031a6f457c5cb2⟩,
  ⟨0xe906f034817e0b205102441080710320150088037016008001a000, 0x6abe183e85cfa004a811aaf453c5cf91aad811aad06aab086ab70ce173dc01aaa811aad84345cf6006aa81a9c421aad46505cf50011a9d86a710c6ab2153173d00044b021aac05485cf31aa9811aa906a7b086aa70ce173c401a9e811aa984345cf0006a781a9d821aa946305cef004a831a9d831aa8872c5cee004a83086aa018a173b40006a6f183e45ceb0078011a9b853c5cea1a99811a9906a3e086a670ce173a001a8f411a9984345ce7⟩,
  ⟨0x13b09404441f40da06302c813c08a03b818c09e03c017807c01c000, 0x6b67046b651acc421ada03385d301ad8011acbc6af91acc031ad9c406d174bc6b60046af51abe46b300c6b61101b45d2e1acfc6b3c1ace431abe46b3b1acd86b30106b600c2a85d2d1acf411acec6af9086b3f0c1f05d2c0019b0072801c7a0c6b3d182a05d2b1acdc11acc06b36086b390c1f05d2a001c7e071f01c7f0c6b37141b05d29006b2f1abd46b2e0c6b3515f174a001abd46b2f1acb831acc850601749c00ade06b200a8b431ac8c5060174906af0046aee1ab9421abc43385d21006ae4046af010d1748001ab882cfa086aef194173fc0042bf90b3e831abb054c5cfe001063c021aba85485cfd⟩,
  ⟨0x12608983f01d20dc06602ec15809904101b80b604a01b809c026000, 0xb7dc10b4e82d3c086bed0ce175986bb0046b721ade86b2f0c6be7101b45d651af9411af8c6bba086be60ce1759001aee411af944345d63006bb71adc821af906505d62002e651adc821af8450ef175840181c30086bbf143a85d601aec811aea06baa086bb4109174f46bb0042e651ade86b2f0c6bb2101b45d3c001c7d070c01c310c6bb0141b05d3b006b720b9946b790c6ba915f174e400b9cc6b79086ba6142ac5d380019b00b9946b790c6ba421e174dc0066c01c30086ba219d174d800b9946b721ade431adf05060174d46b68046b311ad9421ada84245d31⟩,
  ⟨0x13008e84281e60e006682d814408f04101c80c205101f009c028000, 0x1b0b411ac886b24086c6c0ce1768c6c39046c341b0d821b0ec4245d7c1b0ac10ade06b211abd431b0e4406d175ec01ac802b780a8b431b0d457c5d791b0b411ac886b24086c2f109175dc6c2b046b201ac846af50c6c2d101b45d76001c7b070b81c2f0c6c2b141b05d751b0a011b0986bfd086c290ce175cc01aff011b0a04345d72006bfa1ac8021b09c6505d71002b761ac8021b09050eb175c00070066cc21b08850ea175bc6bf7046bf21afd021afe44245d6d1acf41066c06b3b1abe431afdc60a9175b00066c06b361ace831afcc75c5d6a0019b01acd86b3a0c6bf01c29c5d69⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0x13f097045c1fa0e906c031016209a04301d40ce05301c8094022000, 0x13da46cbd086cef101c85dba1b3b0113da46cbd069b431b3b84071176e46cea1b38c21b2f46ce2069b431b3b03070176e00067f41a61069a431b3a8506f176dc0069b81a6d086ce4141b85db5006cbc13da41a690c6cbf141805db41b2d811b2a46ca2086cb70ce176c86cb4044f3c1b2a04f710c6cb6101b45db1001c680719c1cac0c6cb4141b05db0001a691b29821b2c050ec176bc0072b011b2bc406a176b801b29c4f3c1b29831b2a85060176b46ca113cc4213cd44f3013cb8317ebc3070176ac5faa044f3013cd421b284307c176a8013cbc4f2e13cb031b1e870a61769c0067e419f5086c78142945da6⟩,
  ⟨0x13609284481fc0ef06f032c1680a004681d80c404f01d80a8032000, 0x19b1cc9ccc31b5d4506c177bc01b4dc6d3d1b58431b5c457c5ded006d371b4f46d610c6d6c1c2b05dec019b1cc821b5a850a5177ac01b5906d61086d68142ac5dea1b4d411b4cc6cf3086d360ce177a06d2d046cf21b4944f690c6d35101b45de7004f351b3c86cf80c6d34141805de61b4bc11b4986d28086d31109177906d2d044f351b4944f690c6d2f101b45de3001939067ec19fc0c6d2d141b05de2006cf213cd46cf80c6d2715f1778001b3c84f351b3e031b48870ac176fc0064e419fb086d20142945dbe006cfa1b3e021b3f850ab176f46cef1b3b821b2f86ced1b2e031b3c03185dbb⟩,
  ⟨0x13308e04201ea0de06502dc14609204081d80d005501f00a802e000, 0x6de3044f711b6f44f720c6deb101b45e24006dac13dc46db00c6dea141805e231b79411b6f86de0086de7109178846de3046dac1b6f44f720c6de5101b45e20001cad072ac1cae0c6de3141b05dff004f711b6b06db00c6dbf15f177f4013dc46dac1b6c031b6e870a6177f00072b41cab086db8142945dfb006db21b6c021b6d850ab177e80006da6183ec5df801ae46086da5143885df71b5f411b5ec6d38086d7e0ce177d46d75046d371b5bc68f70c6d7d101b45df4006d3d1b4dc6d610c6d7c141805df31b5dc11b5c06d72086d79109177c46d75046d3d1b5bc68f70c6d77101b45df0⟩,
  ⟨0x13c09284441fc0e706a830415a09d04601e40c404f01c009c026000, 0x1b98c11b8ac6e391a79831b9bc406d178e406b9186e2b1b8a841b9b87076178e06e65046e3a1b8f021b99c4245e361b98c16b9186e391a79841b9946079178d406b919cb1cb441b98c6077178d006b9186e2b1b8a841b8ec7078178c806b9186e2b1b8a841b8d88075178c406b919cb031b8d06074178c001b8b86e2a086e32142ac5e2f1b8a011a7a46df3086e290ce178b86e220469e61a7a06d3d0c6e28101b45e2d1b89011b7e86dfc086e26109178b06e220469e71a7a06d3d0c6e24101b45e2b01cc1cb9cc431b888506c178a801a79869e71a79031b7ec5060178a06deb046de91b6a021b7b03385e25⟩,
  ⟨0x14409804742080f306e832816609f04601cc0c404c0198088026000, 0x69641bca86f300c6f33141805e6f1bb8011a3e468f4086ee10ce179b46ebf1baf821a3e46ebd1a3d031bb803185e6c004f6d1a3e021bafc4072179ac6ea3044f6d1a3e1d8031baf84071179a86eac0469b81a6d421bab43385e681baa8117d90692a13cbc31bab0406d1799c0067e019f7067d831baa8506c179986ea70469bc1a6f821baa44245e651ba986ea50869bc1ba9069be0c6ea70c61799001a3dc68f8086ea6101c85e631ba8c11a3dc68f87600c6ea5101c45e621ba846e7a0868f81b9e5d8031ba8c30701798406f073473c0c6ea1141bc5e6001d85d8021b9ec506e178f86e6f046e6d1b9a021b9c03385e3a⟩,
  ⟨0x13708f04341ec0e306902f815a09904281d80ca05201d8090026000, 0x78751e1d021e1c478731e1ac31e1d83185ea3006cbc1b2f421e1d4407217a886cec046cbc1b2f41a6d0c7874101c45ea1004f691b2f01a690c787215f17a800069ac1a69087864141845e7e001a6a0699c19bf0c783a141885e7d001a670688c21e0bc50bb179ec01bff06feb1bfec31bffc5066179e801bca869641bcc031bdb470ac179e006286ee086f6b142945e77006f651bcc021bda450ab179d86f62046f321bcac21bd8c3385e751bcf411bca86f3113db431bd88406d179d06f3d0469641bcc44f6d0c6f3f101b45e73018a1bb9bbc31bcf4506c179c801bca869641bcc031bcd857c5e70⟩,
  ⟨0x12d08c84141e80e306802e414809103c819009e03a014005c018000, 0x1e6d879b71e6d031e7e0506017aec01e6dc79b61e6d031e79470a617adc0068f41a3b0879e3142945eb60079bd1e6d021e78450ab17ad401e6dc79b61e6d031e6e857c5eb41e5f811e5a0797613cb831e6a8406d17ac800679861e5a079671079a91c1d85eb11e68011e5dc79790879a210917abc797e0419e618797613cb841e680607917ab80067986067cc19f410797e181dc5ead0019e61879681e59c41e5e0707817aac00679861e5a07967107973201d45eaa0019e61819f30c7971181d05ea900796b1e59c21e5bc50ab17aa0000787f183f05ea6019fc11e1f853c5ea5⟩,
  ⟨0x13d09584682060f006c831416209d04601ec0d005501f00ac028000, 0x67986068e431e9fc607417bc401e9e47a76087a7d142ac5ef01e98411e7ac7a271b2f031e9a4406d17bb87a63047a3d1e8e021e9903385eeb1e98411e8987a271b2f031e98c406d17ba80065f41a3f0698031e984506c17ba401e7ac7a261e89031e8f8506017ba001e89879eb1e89031e8cc70ac17b980065f41a3f087a31142945ee5007a2b1e89021e8bc50ab17b9001e89879eb1e89031e8a457c5ee31e88811e6e479ec087a230ce17b8879fc0479b61e6e079eb0c7a22101b45ee11e7f811e7dc79f9087a2010917afc79fc0479b71e6e079eb0c79fe101b45ebe001a3d068ec1a3e0c79fc141b05ebd⟩,
  ⟨0x143098046420a0ec06e03181700aa04b020c0d805701f80a802a000, 0x7aeb047abb1ead021ebb03385f241eba4113cf07aba16ab831ebac406d17c8c0071a01c670719831eba4506c17c887ae51eb8c21eb907ae21eb8031eb983185f21001a691eae421eb945145f201eb8411eae46cb30719831eb8c4105eff001a69047ae1101ac5efe001c66047ae0101a85efd006ca713cf07ab90c7abc141805efc1eac811eac07a6d087ab30ce17be87aaa047a6c1ea9079b60c7ab2101b45ef90019e6187a6c1e9d841eac4707617be07aaa0419e6187aa41e6d841eab0607917bd80067986068e41a3a107aaa181dc5ef50019e6187a6c1e9d841ea98707817bcc00679861e9b07a76107aa1201d45ef2⟩,
  ⟨0x13609284401f60e906c031415809b04201c40bc0470198088028000, 0x1deb0779c21ede450a517ce0007a8061ecc47b30107b611c1e05f35001ea0187b311ecc041ecf0807517cd0007a80607ab431ece8607417ccc01ecd07b30087b38142ac5f321ecb011ec907b26087b2e10917cc47b2b1eca821ec907b291ec9831ecb03185f300029fa0a7ec21ecac407217cbc2b700429fa0a7ec1cbd0c7b2a101c45f2e0029f30a7e81cb90c7b2515f17cb07b21047af51ebc021ec883385f2b1ebfc10acbc7af417ed031ec84406d17ca80077a81de9078c831ebfc506c17ca40072e47af3087afc143b05f28001e32047afb101a85f27002afa0acbc7af30c7af6141805f26⟩,
  ⟨0x143099047c2100f506f032816e0a304801e40cc05301e00a0028000, 0x1efb07bb6087bf0142ac5f6c1efa011eee07bb1087be90ce17dac7be3047bb01eedc38b20c7be8101b45f6a1ef9411eeec7bbd087be710917da47be3047b6a1eedc38b20c7be5101b45f68001df1077b41df20c7be3141b05f67007bb01eda87bb60c7bbc15f17d9401eda87bb01eed831eee4506017d907bae047bac1edac21eebc3385f621ee9811eda47b7d1eda831eeb8406d17d8400a7987b691edc431eeb457c5f601eea011edf87ba0087baa10917cf87ba60429e61edf47b6a0c7ba8101b45f3d001deb0779c1dec0c7ba6141b05f3c007b690a7987b710c7b7f141805f3a0029e61eda47b710c7b7b1c2985f39⟩,
  ⟨0x13d095044c1fe0ec06c031c16809d04181bc0b604701b0094022000, 0x7c6d047c631f19421f1bc4245fa11f1ac11ed887c620a79431f1b4406d17e80007acc1eaf07ad031f1ac506c17dfc01f0d07b621f0cc31f19057c5f7d007c341ed887c330c7c3f1c2985f7c001eb307abc21f0f450a517dec7c300429e81f0b421f0c84245f7a1f09810a79429e70a7b031f0c0406d17de47c280a7a820a7b029e70a79830a7b4307017dd87c260429e70a7b021f0a0307c17dd40077ac1eb507ad831f098506c17dd000a79829e50a78c31f08070ac17dc80077ac1eb5087bfe142945f71007bf80a78c21eff050ab17dc001eec07b6a1eed831efd070a617db80077c41ded087bf2142945f6d⟩,
  ⟨0x138095846c21a0fa071834017a0a604881f80cc05101f00ac028000, 0x7cbc047ce510d17ee000719c6ca7087ce419417edc00719c11f384406917ed87cb9047cb51f2c021f2e83385fb41b2d011b29c6ca813dc431f2e4406d17ecc013cf06ca71b29831f2d857c5fb21f2ac11f2a47ca4087cac0ce17ec07c7f047b311ecfc7b620c7cab101b45faf001ea0187b311ecc041f2a8707617eb87ca1047b601ed8c21f28c4245fac1f1fc107a8061ecfc7b62107ca1181e45fab001ea0181ead07ab841f1fc607717ea87c6d047c631f19421f1ec3385fa61f1e011f1c07c72087c7a10917e947c6b047c341f18829e50c7c78101b45fa4007b621f0d07c330c7c71141805fa2⟩
]

def tableLRL : Table Block := .branch 12 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0x12208583d81c80d306402f015209c04601f40d405201e80a0026000, 0x1f3f811f3b87cef1b6b031f5ec406d17fc80070d861f3b87cec107d77201d45fef001c36181ca90c7d75181d05fee007d6f1f3b021f5cc50ab17fb40007d62183f45feb004a011f58453c5fea1f4e411f4dc7d31087d3a0ce17fa001f4c011f4e44345fe7007d2d1f4b821f4e06505fe6001c04bc21f4d4507317f947d20047cf01f3d421f4884245fe21f3f81070d861f3bc6dac107d20181e45fe1001c36181ca9072a841f3f8607717f800070d861f3b87cec107cf31c1d85fbd001c36187cee1f3b041f3c4707817ef07ce5047ce31f2f421f3983385fb9⟩,
  ⟨0x10107703841a20c105a028412808403981980b604f01c009c026000, 0x7e3c047e3a1f8c421f8f4338682a007e30047e3c10d1a0a401f8b87dbb087e3b18c1a0a002f40c7dbb0c7e381cb1a09c02f40c21f8d862868261f8b011f8a87e21087e2d0ce1a09001f88011f8b04346823007dfe1f6e821f8ac65068220011f6ec7dba0c7e281531a084004bd821f89854868200001f7e860fe17ff402f4047df914f17ff07de9047dbb1f6f07de10c7deb101b45ff900bd8bdcbe031f7a4506c17fe001f6e87dbb1f6e031f780506017fd801f6ec7dba1f6e031f6f857c5ff5⟩,
  ⟨0x10607c83a01aa0c805c02a412c08903c81a40ac04901c80a802e000, 0x12074087efd19d1a18c01fbdc7ef5087efb142ac68621fba011fb987ee0087ee90ce1a18001fafc11fba0434683f007ebc1faf421fb9c650683e001c01d821fb9050731a0f47ea4047ea21f9f021fa943386838007e7b047ea410d1a0dc01f9e44a3e087ea31941a0d80070079ac21fa8050731a0d47e73047e711f9ac21f9d03386832007e6a047e7310d1a0c401f9a47e65087e721941a0c000702f9087e6f141cc682f1f98011f6f47dee087e621091a0b47de9047dba1f6f07de10c7e60101b4682c⟩,
  ⟨0x10207783881a40c4058829012808303b01ac0be04c01a8090022000, 0x1febc11feb47fa7087fb00ce1a1ec01fe9811febc434687a0019371fe8421feb86506879001937047fab101a468781fd8c11fd847f38087f640ce1a1c801fcdc11fd8c4346871007f3616ebc21fd88650687000116ee45baf0c7f3f1531a1bc0056fc21fcf4548686e0001fcd060ff1a1b00763047f3314f1a1ac7f2a047f231fc9421fcb042468691fca010a3907f220a49c31fca8406d1a1a000730740750c7f28141b068670028b10a3907ef50c7f2415f1a19404828e41fbd431fbfc8786864⟩,
  ⟨0x100079838019a0bf059028c124083035016c08a038015005c018000, 0x88ad0488ba11c1a2c40222ac88aa222983222e466c68b00088a8222a888a60c88b619a1a2bc05f25ec0888b31591a2b806370488a1142e868ac019d98c822218850bb1a2a806796765ee0c882c1418868a9019e99e022208050611a29c7ff61ffd021ffd47ff31ffc031ffdc31868a6019e07fe8087ff61451a2947ff2047fe81ffc419360c7ff41041a2900678047ff2101ac68a3001936047ff0101a868a2007fea1fe847fe80c7fed15f1a2840007fbc18480687e0098811feec53c687d⟩,
  ⟨0x11207f03c41c20d405d82ac12a08403a819c0a804701a0084026000, 0x224dc1223e088bc088939103a468e4018d41224dc50b21a38c0220a088fb0889341451a38805ee048932142f868e1224a889280889292249c89230c892b0c61a3800223fc88f608892a1451a2fc89260488f62249489220c89281041a2f80223f488fb088926182f468bd018d18cc22248c50bc1a2f00223d81223e850b51a2ec88ec0488ea223802223b433868b80088bf0488ec11c1a2dc0222f488aa221fc3223ac66c68b60088bc222a8887f0c88e819a1a2d406365ec0888e51591a2d088ba0488b8222b82222ec33868b2⟩,
  ⟨0x13108f84442000ec06e831016609d04201cc0c805101f009c026000, 0x2622288488280c8a2b21e1a3d802625ed088a2919d1a3d4063062f5f70c89e51418868f4007fb21fdf489b10c89bf1c1a068f3018b98b02226f450671a3c88976225d42225948974225803225dc31868f1007f7d225902225d840721a3c08973047f7d225919f03225d440711a3bc8971225a8222590896967c0c89730c1c068ee018b19c19e03225c4506f1a3b4067d67c08896b141b868eb0089631fdf59e032259850601a3a8893e047fec1ff942224fc33868e8224f011fe847feb1b3c83224f8406d1a39c0064e01937064d83224f0506c1a39889390488f9223cc2224e833868e5⟩,
  ⟨0xee06d833817c0ae0508238102071030014c09003c0178088022000, 0x22ba8122ba08abf088aeb0ce1a4b8022af8122ba8434692d008abc22aa8222ba4630692c001e8822aa8322b9872c692b001e88088ae418a1a4a88aba048ab822abc222aec3386928008aae048aba10d1a49c022aac8aac088ab91941a4980188aaa22ab0322ad854c692500607c088ab41521a4900008aa6184846921001e8122a9453c6920008a68048a6b1401a3f4007b881228e056068fa004faf13eb02228c850ab1a3e400b6f02e2a088a2d142ac68f7⟩,
  ⟨0x11708203c41c20ce06082b813608b03e81a80ac04801a808801c000, 0x22cfc8b2c228d4322db466c6966008b3e22cb08a350c8b6a19a1a594007b841e77088b671591a5908b3c048b3a22cc0222cf43386962008b2f048b3c11c1a584022cb48b2c22c90322cec66c6960008a6322cb08b240c8b3819a1a4fc0079f41e77088b351591a4f80079f8122c9850ba1a4f08b22048a6a22990222c8c338693b22c801229a48a63088b22102d8693a001e7c048b20142c869390ffb010ff9c3fe9088aff0ce1a4e08afc0449fd127c0222bf8424693722be81127f049a7088afc102d86936001f3e048afa142c86935⟩,
  ⟨0x10607b03a41b60cd05f82b013808e03a819409e03e016808001a000, 0x1923063f422319c564697d008c31048c371401a5ec0230c41230d450b51a5e80065a01230b050ba1a5e400649012308c50ba1a5e05b36045b3016cac222ef842469740048a922de0222ec45146971001e79048baf142f8697022ea08ba6088ba722e948ba20c8ba90c61a5bc022df08b74088ba81451a5b88ba4048b7422df88ba10c8ba61041a5b4022de88b78088ba4182f4696c001ebf07af8222e8850bc1a5ac022dd0122ddc500696a22db8122db08b62088b6f0ce1a5a0022d84122db84706967⟩,
  ⟨0x11408283e01ca0d105f02a813808903e01a40ac0460198098026000, 0x16ec18fe088cf619d1a6bc0232dc1232e850069ae232b41230d08ca8088caf1091a6b48ca3048c33230e02232b440e91a6b08ca5048c36230e422329c42469aa2328c1230cc8c38088ca5102d869a9001966048ca3142c869a8232801231f88c74088ca10ce1a69c0231cc12328047069a6008c71230f48c2a0c8c7f19b1a6940230e08c3d230a83231f066869a4001967063f42231e456469a3231b81231b08c62088c6f0ce1a6840231841231b847069a0008c3f230f48c210c8c6d19b1a5fc0230f88c3d230843231a8668697e⟩,
  ⟨0x12a08b84141e40de06502cc13e08b03c01940a203e0188084024000, 0x16ec1970065a83236a460a81a79805bb235ec8d7f0c8da51d71a79005bb235ec8d7f0c8da21c29c69e3235f01234b88d7b088d7e0c1f069e200196e065b0196f0c8d7c141b069e1235c812359c8d68234b43235d0406d1a6fc0065ac18fe063fc3235c8506c1a6f80233b88d6717aa43235c450601a6f402359c8cee17aa43235a857c69bb008d2c234b48d2b0c8d3315f1a6dc0234b48d2c234ac3234c050601a6d88d24048d22233f022349433869b5008cfb048d2410d1a6d00233e88cee088d231941a6cc00705e2088d20141cc69b2016ec8cee17aa43233e087869b0⟩,
  ⟨0x13d096047021c0fb072034017a0ab04e022c0e805d01e80a402c000, 0x65941964088e3f142f069f7008cbb238b82238cc51469f6001921048e31142f869f5237d01237a88dec088df61091a7d08df2048dbc237a48d2c0c8df4101b469f300196d0648019210c8df2141b069f2008db5236f08cbb0c8deb15f1a7c005bb236f08cbb0c8de721e1a7bc05bb0648022379467469ee008dbf232ec22378c50ab1a7b48daf048d2c234d08d2e0c8db4101b469ec236bc1234b48d34234b83236c0406d1a7ac8dae236848d7e0c8d34236808d7b234b84236bc30aa1a7a88da9048da0234d02236b8307c1a7a48dab048da4236982236b442469e8236a415bb236808d340c8dab182a469e7⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0x11408203d81c60d006182d814a09203f01c00c605001b809c022000, 0x5ea9238d8223af05146a2b0018ff048eba142f86a2a23ad0123aa88eac088eb61091a8a08eb3048eac23aa8223ad03386a27008c2a048eb311c1a8980065a0123ab85606a25008eac235fc223ac050ab1a8908e7e048e73239d4223a804246a22239f01239c08c3d088e7e102d86a210018fc048e7c142c86a20008e6e048e741401a7f88cad048c34232a02239a433869fc239948e63088e64239888e3f0c8e660c61a7ec0238e48c31088e651451a7e88e61048c31238e88e3e0c8e631041a7e40238b88e36088e61182f469f8⟩,
  ⟨0x11208083b81b60c705c829811e07c037817c0a003d018008001e000, 0x19a306684223dec50671a9805efb045bbd16efc223dc43386a3f23d901232e48cb4088f650ce1a8f48f3d048cb8230f8223d9040b61a8f0006488123cf450b21a8ec8f36048d6923590223cdc3386a3a235c81233b88d68234b4323cd8406d1a8e48efa048ef823bc8223bec3386a36008ef1048efa10d1a8d4023bc08dbc088ef91941a8d000705e6088ef6141cc6a3323bb4123bac8ee2088eee0ce1a8c4023b84123bb44346a30008ebf2359c223bb06506a2f005bb02359c223ba450eb1a8b800705e2088ee7143a86a2d⟩,
  ⟨0x13b09384501f60ea069830015809904281b00b804601a8090028000, 0x173e05cbe260d43260ec50601a9d08ff8048ff322ed0223fe43386a7123fdc8ff6088ff323fd48bb40c8ff80c61a9c00177e45dfa088ff7101c86a6f178e01177e45dfa066b4323fd840711a9b80175d45df9066a4323fd057c6a6d0019a506690196a0c8fbf141886a6b23ec4123e848fac088fb31091a9a4023e805df9234d0323ec470651a9a08fae23eac223eb48faa23e98323ebc3186a67008fa723e80223eb85146a6623ea4123e808fa823e94323eac4106a65008d34177e4223ea450641a99000668c19a1088fa61418c6a63008fa023dfc223e904046a62008d34177e48f730c8f7d1c1a06a61⟩,
  ⟨0x12708b03f41da0d706182bc14208e04081b80b604b01f00ac028000, 0x72dc1c730898e7142ec6aa7262f898bc0898bd262ec98b80c98bf0c61aa980262c42a2e0898be1451aa9498ba042a2e262d098b70c98bc1041aa900262bc98ad262943262e860ae1aa8c0072d81cb2071e43262e050ad1aa880071e01262a050ba1aa8498a30498a1261dc2262903386aa00098760498a311c1a9fc0261cc1ff3261d032628866c6a7e00987207fcc98740c987f19a1a9f40071dc1c2d08987c1591a9f00070d01261ac5606a79261901260e8983c0898661091a9e09862045cbe260dc982b0c9864101b46a77001a78069e41a7a0c9862141b06a76⟩,
  ⟨0x12508883d01b60cd05c829412a08803b81900a003d014806c01c000, 0x9966049937126982265a040e91aaf49938264d449ed0c9937126f849a60c99660c48c6abc2658c996108996226580993e0c99640c61aaec0264d812658c406b1aae8993f049936264f422658440b11aae40264f0993b264e83264fc40b01aae0006a067703264f850af1aadc0264d81264e45006ab6126fc1126f81264d431221aad4992a0498f9264902264b04246ab2263fc1263e0987208992a103a46ab1264841263ec98f00899231091aab898ff0498f8261c822648440b61aab40071d81263fc50b21aab00263d81263f05006aaa0098f60498fa142d46aa9⟩,
  ⟨0x10a07b839c1b20ce06082c014009204101d00b604b01a8090026000, 0x99ed07fcc1fec0c99f919a1abc40070cc1c2d0899f61591abc00264dc12679c41251abb800099ba184906aeb0018ec0499b914f1aba800b4bc2d2b0899b1142ac6ae8006b79265b42266a85146ae7001c310499a8142f86ae6002a2d265ac22668c5146ae5001c2f0499a1142f86ae4265e89978089979265dc99730c997b0c61ab8c0265bc98f608997a1451ab8899760498f6265d499720c99781041ab840265b4996b089976182f46ae0001c75071d02265cc50bc1aafc9968049967264b82265a84246abe⟩,
  ⟨0x11b08403c41ba0c905c82a012a08203a818809c0400198080026000, 0x9a71049a65268fc2269c83386b24269bc10b3e89a642609c3269c4406d1ac8c0063c018f1069c83269bc506c1ac880069c02cfa269883269b490a31ac840069c018f1089a6b19d1ac80023ffc9a62089a69142ac6aff002bf90b3e89a620c9a6615f1abf89a3c04986a07fb42268f84246afc001fec049a3c11c1abec9a3a049a25267fc2268ec3386af9268e012689099ed089a3a102d86af8001c32049a38142c86af7009a23049a261401abd899fd0499fb267c42267f83386af40099f00499fd11c1abcc0267b81ff307fb03267f066c6af2⟩,
  ⟨0x12b08b84101e00d706382c414008f03e01a00a80400178078020000, 0x66dc1c3c070f4326cc4506c1ace89b23049af526bf8226c944246b38009aeb0b4842b760c9b231c4a06b3726c809afd089aff26bf09af80c9b210c61acd8026be49aeb089b201451acd49afb049aeb26be89af70c9afd1041acd000b4842b76089afb1449c6b330019b7066cc226be051261acc8026bb49aec26bac326bcc57c6b31001c61070f81c3b0c9aef141b06b30002dbe26b9c2a730c9aea141806b2f005a3b0a7cc2ab10c9abe1c2b06b2d001c63071b4226af050a51acb0026ad82ab1089aba142ac6b2b001c34049aa7142e86b2800996b0a8b4226a884046b27⟩,
  ⟨0x11b08383d01c00d206202c413a08903b01a40b204801c8094028000, 0x9bba041ff907fcc226efc40e91adcc9bbc041ffa07fd0226ef84246b7226ee8107fe41ff3089bbc102d86b71001c2c049bba142c86b70001ff8049bb9142d46b6f264a81263e49924089bb10ce1adb49b7e049ae8168ec226e80307c1ada40071881c3a070e0326df8506c1ada09b6e049b6c26d8c226dbc3386b63009b62049b6e10d1ad88026d849b2f089b6d1941ad8400add89b2f089b6a144a46b60001066cc226da050ea1acfc00b4849b2f26cb8326cfc70ac1acf40066dc1c3c089b3d142946b3c009b2f0b4849b2e0c9b34141806b3b⟩,
  ⟨0x12808b84001cc0d206082b413408d03e81bc0b604a01c8098026000, 0x9c25270b422718040721aea49c3d049c25270b41b310c9c3f101c46ba8270ec9c34089c2d270cc1b310c9c3d0c1c06ba7001ae106c941b2d0c9c3b141bc6ba6001b3206cc42270d4506e1ae900270b09c2506cb43270bc50601ae8c9c23049c2126fec2270903386ba1009bfa049c2310d1ae8000749c9bf8089c221941adfc00749c126ffc40691adf8026fa09be726f94326fd870a61adf0006af41ab9089bf4142946b7b009bee26f94226fc850ab1ade8026fa09be726f94326fac57c6b79169d81169a85a6d089be30ce1addc9bbf049bb826ed4226f803386b74⟩,
  ⟨0x13e09384502020ea06b030815c09d04501cc0be04e02000b0032000, 0x272dc1272989cb1271fc32738c406d1aef002718c9ca62729032738857c6bbb272e41272c89cb4089cbb1091aee49cb7049c63272c49c7f0c9cb9101b46bb8001d6c075a81d6d0c9cb7141b06bb7009ca62718c9ca40c9cb3141806bb5009c63272989ca40c9caf1c2986bb4001d6c075a82272b450a51aecc9c79049c6d271902271e83386bb2271dc126fe09c6c2718c3271e4406d1aec400749c1d26075ac3271dc506c1aec0006cb49c6a089c74143b06baf001d6b049c73101a86bae009c6b26fe09c6a0c9c6e141806bad271841270b89c26089c620ce1aeac9c60270fc2270b89c3e270983271843186baa⟩,
  ⟨0x12a08a84001d60d906402d014609203f81a00a80410168088026000, 0x1aaa181ab706ae04275c860771afcc006aa86274d09d3e109d6e1c1e06bf1001aaa189d34274f84275a480751afc0006aa8606adc32759c60741afbc0275849d3e089d65142ac6bee004f71271fc9cf60c9d321c2b06beb001cad075b82274c050a51afa80274a89cf6089d2e142ac6be9274941273ec9cfd089d271091afa09d23049c7f273dc9c7b0c9d25101b46be7001cad075b81d6f0c9d23141b06be6004f71271fc9cf60c9cfc15f1af900271fc4f71273d83273e450601af8c0009cec184a86be1001aaa182273ac50e21af809ce3049ce1272f02273903386bbd⟩,
  ⟨0x13408e84241e40de06582dc14c09504101d40ca05702200b4030000, 0x27794113cbc9dbc270943277b4406d1b0a00276b84f2f276b43277b050601b09c9de5049dae276f09c250c9de7101b46c250019f906afc1ae00c9de5141b06c24004f2f276b89dad0c9dbe15f1b088013cbc9dae276b43276e470ac1b0840067e41abf089db7142946c20009db1276b42276d450ab1affc9da6049da4275f822769c3386bfd009d7d049da610d1aff0007ac89cee089da51941afec007ac812768840691afe89d7a049d78274d42275ec3386bf8275c81274d09d6c26f9c3275e8406d1afdc006aa86274d09d3e109d791c1d86bf6275c8106aa86275b09be7109d74181e46bf4⟩
]

def tableLRR : Table Block := .branch 13 tableLRRL tableLRRR

def tableLR : Table Block := .branch 25 tableLRL tableLRR

def tableL : Table Block := .branch 50 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0x13809204441fc0e506a82fc1620a304781f00ca05201d809c026000, 0x9e6a16ab89e700c9e76141806c3e005aae279a89e700c9e7415f1b0f40279846b361ace832799057c6c3b278f49e3b089e3c278e89e380c9e3e0c61b0e80075e09e2f089e3d1451b0e49e39049e2f278d41eb00c9e3b1041b0e00075e01278e4406b1b0dc007ac01278e0406a1b0d80278c09cee278bc3278cc50601b0d49e24049bea277bc2278943386c32277f8126f9c9be9276b8327890406d1b0c49e20049df6277e02278884246c2f277f8126fa09be9276b8327880406d1b0b8006af41ab906af83277f8506c1b0b4026f9c9be826f943277dc50601b0ac9ded049deb276a02277b83386c29⟩,
  ⟨0x143098048c22c0ff07403201680a004681e80cc05502100ac028000, 0x7b2c047b241ec98227d943386c77008c21049f3011c1b1d4006490127cac5606c7427bb811abd47cee1acc0327bc8406d1b1c09eee046b2f1f3b86b300c9eef101b46c6f27bb49e631ace431f3b89e621acd86b30109eee0c2a86c6e27bac1279887cee089eed0c1f06c6d001ca8072801c7a0c9eeb141b06c6c1af9c11adec6b73089ee51091b1ac6de5046dbe1b780227ae83386c68005aae279a89e700c9eaa1c2b06c65001c69074a8227aa050a51b1909e7f049e73279ac227a803386c63279e81279a89e72279943279fc406d1b1889e7a045aae279c89e650c9e7c101b46c61001c69074a81d2b0c9e7a141b06c60⟩,
  ⟨0x12208703f41d40dd06682fc15c09b04201c40b40460198088028000, 0x9eac27994a8370ca8651c1a06cb5001d2e074b022a18c50671b2d09ff6049ff427fb8227fdc3386cb2009fed049ff610d1b2c4007ac49e30089ff51941b2c0007ac4127fc840691b2bc012be049ff089fbc142ac6ca827e98127dac9f66089fa70ce1b28c9fa0045b6527da869f70c9fa6101b46ca227e88127df09f79089fa30ce1b2849fa0045b3827da869f70c9fa2101b46ca0001b7f06df81be70c9fa0141b06c7f005b6516ce09f690c9f7d15f1b1f80066a49f69089f72143b06c7b001be7049f71101a86c7a005b3816d949f690c9f6c141806c79⟩,
  ⟨0x136091043c1f00e406882f415809b04401c40ba04a01c8094028000, 0xa9302a4dca9360ca973141806cee2a5b412a598a96808a96f1091b3b4a96b04a9302a594a9310ca96d101b46cec001b2106bfc1b220ca96b141b06ceb00a9372a4c0a9360ca96715f1b3a402a4dca9302a4d832a58870a61b3a0006c841aff08a960142946ce700a93a2a4d822a4f850ab1b398a8fc04a8f627f9422a3f43386cbf2a3e81278c09e311f0d032a3f0406d1b2f8007ac81eb107ac032a3e8506c1b2f40273b89e30278bc32a3dc57c6cbc001d7a075e022a3bc50611b2e80075e41d76073b832a39050621b2e40075d81d3208a8b4142ec6cb7001d30074bc1cf70ca86b141886cb6⟩,
  ⟨0x15009e84a422c0ff076034c1840ab04881f40d805801f00a802e000, 0x9e65271ec1d780ca9f415f1b4900271ac9bf82a78032a78c50601b488a9b7049e32278b022a6e03386d202a3e81273b89e311f0d032a6dc406d1b3fca9b404a97f2a68422a6d84246cfe2a6cca9b208a97f2a6c4a9a10ca9b40c61b3f4027994a97e08a9b3101c86cfc2a6c0127994a97e075f032a6c840711b3eca9ae2a69c22a5f8a9a6075f032a6c030701b3e80074b01d70075e032a6b8506f1b3e40075f41d7c08a9a8141b86cf7009c7b279941d780ca9a0141806cf52a5f4a96608a9312a594a9300ca9680c1c06cf32a5ac12a594a93108a97d0c1f06cf22a5e812a5c8a97408a97c1091b3c4a96b04a9372a594a9310ca97a101b46cf0⟩,
  ⟨0x14b09c04842180f406f832816a0a304901fc0d005402080a002e000, 0xaa6a04aa682a89422a9ac3386d382a98812a890aa3c2a4c032a9a8406d1b4dc006aa862a890aa2e10aa691c1d86d362a988106aa862a8f0a93010aa64181e46d34001aaa181afd06bf842a98860771b4cc006aa862a890aa2e10aa3e1c1e06d31001aaa18aa242a8b842a8e480751b4c0006aa8606bf432a8dc60741b4bc02a8c4aa2e08aa35142ac6d2e2a7f012a788a9ba08a9fd0ce1b4aca9fa049bf82a784a9b90ca9fc101b46d2a001d27074981d250ca9fa141b06d292a7e012a7cca9f008a9f90ce1b4a0a9f72a7d822a7cca9f52a7c032a7e03186d27009c7b2a5f822a7dc40721b498a9b0049c7b2a5f81d7c0ca9f6101c46d25⟩,
  ⟨0x13d09604642000ef06c03141620a004781f00ca05201d809c028000, 0x74a01d2408aae6142946d6c2aaec12aad8aab108aabc0ce1b5acaaba2aae422aad8aab82aac432aaec3186d6a009c2c270b422aae840721b5a49c3d049c2c270b41b310caab9101c46d68009c25270b01b2d0caab715f1b59c01e6dca9312a9c832aabc70ac1b5900068f41b2308aaad142946d6300aaa72a9c822aaac50ab1b588aaa404aa742a9b022aa943386d612a9fc11e6dcaa73270b032aa90406d1b580aaa104aa772a9e422aa8c4246d3f2a9fc12a4c4aa73270b032aa84406d1b4f80068f41b2306c9032a9fc506c1b4f401e6dca9312a9c832a9e057c6d3b00a9311e6dcaa720caa75141806d3a⟩,
  ⟨0x13c095846c2100f106f032c1680a104501dc0cc05301e00a0028000, 0x1cb3072c422ad8850631b68802ace0ab3c08ab601011b684ab3304ab312acb022acd03386d7f1eba411b29c7aba16ab832accc406d1b5f8013cf06ca71eae432acc857c6d7d2aca410a7a829ed08ab2a0ce1b5ec7c260429e60a79c29ec0cab29101b46d7a2abd412abacaaed08ab260ce1b5e0aaf304aabf2aba89e6a0cab23101b46d7600a9b92aafcaabd0caafc15f1b5d002ab84aabd08aaf9142ac6d732abd412abacaaed08aaf71091b5c8aaf304a9b92aba89e6a0caaf5101b46d71001d28074901d290caaf3141b06d7000aabf2a6e4aabd0caaec141806d6e00a9b92aafcaabd0caae81c2986d6d⟩,
  ⟨0x12508884001d80db068031016009c04581dc0c805001b809c022000, 0x6ca81b2606bb432b0b450ad1b6e0006cac1ae708abfb142ec6db6001b2e06cac1aa30cabe5141886db5001b2f06cb422aee450611b6cc000abab184ac6db000e9812aea853c6daf001cb5072d01c7a0cab7e141886dad006af90a7e8ab370cab7b1c1a06dac001cb3072c422ade450671b6ac02ace0ab371ace832adcc50b91b6a8ab6d04ab3d2ada022adbc4246da800ab380a7e86af90cab6d1c1946da72ada8ab6708ab692ad98ab620cab6b0c61b69802ad8cab3808ab6a1451b694ab6504ab382ad90ab610cab671041b69001abe429fa08ab65141906da3⟩,
  ⟨0x11208283d41cc0d406282dc14809704201c40c205301d00a8028000, 0xacec04acf510d1b7ac02b3acacbb08acf41941b7a8007076608acf1141cc6de901d8cacbb2af8432b3948786de701d8c1aa208ace319d1b79802b1e812b1f850b51b794ac7004ac6e2b19022b1c43386de300ac6304ac7011c1b78802b184ac3f2b0e032b1bc66c6de100ac602b0fcac380cac6c19a1b780006bac1aa108ac691591b6fc006bb012b0e850ba1b6f4ac332b0c422b0c8ac302b0b432b0d03186dbc00ac272af8822b0cc5146dbb2b0bc12af88ac292b0b032b0c44106dba00ac252b08cac210cac2f182b86db9⟩,
  ⟨0x10f07f83bc1c40cf06102c814609104101bc0b004701a0098026000, 0x2b5c8ad7008ad7f18c1b7f806a520ad700cad7c1cb1b7f406a52022b5e86286dfc2b5b812b5b0ad6608ad6f0ce1b7e802b59412b5b84346df900ad642b4dc22b5b46506df8001c1da822b5a850731b7dc07632b4dcad2e0cad6121e1b7d4076306a9022b4fc6746df42b4b012b480acfa08ad2d0ce1b7ccad2a045baf2b3fcace70cad2c101b46df2016fd781d9432b4a8506c1b7c4076316ebcacfd0cad282428c6df001d8d78022b4986746def005bb916ebcacfd0cad2115f1b7b8acf504acf32b3b422b3d83386dec⟩,
  ⟨0x105079036c1940b7054826010a07a037016c09c03e016808001a000, 0xadfd04ade92b78c22b7f83386e362b7ec12b688ade82b58c32b7f4406d1b8d406a76a87690cadfb141b06e3401d8cada22b79832b7d090a31b8c007636a808adf219d1b8bc02b7b0ade608adf0142ac6e2e00ad702b688ade60cadea15f1b8b4000adbc184b06e2901a9412b6ec53c6e282b6d012b6c8ada908adb50ce1b89802b6a012b6d04346e2500ada62b68822b6cc6506e240062b5c0ada20cadb01531b88c019a9c22b6b85486e222b68012b5f8ad7508ada10ce1b88002b5d012b6804346dff⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0x11a08383b81bc0c805c02a013008b03c01ac0b004501a808801c000, 0x1a702b9bcaea90caebc2081b9b4aeb92bad822bae0aeb52bac432bae83186e6c00aeb22b9bc22bae45146e6b2bad012b9bcaeb32bac032bad84106e6a001a702baa422bad070c6e69001a70069d022bac46086e6800ae6f2bab022babc4046e6700ae6b04ae6e1401b998ae6004ae3e2b8d022b9843386e6100ae3304ae6011c1b98002b8c4ac3f2b88c32b8fc66c6e3f00ae302b0fcae230cae3c19a1b8f8006a9c1aa108ae391591b8f4ae2104ac7d2b1dc22b8883386e392b7fc12b1f0ac6008ae21103a46e38001aea04adff142c86e37⟩,
  ⟨0x11108003cc1c00cc05f02cc14c09304301b40ba04601b008c026000, 0x6a941aa308af30142f06ea100af2604af291401ba80af2104ae6d2b8b022bc883386e7e2bbfc12b9b0ac3f08af21102d86e7d001aa004aeff142c86e7c0002bbe861301b9e8005108aef9143886e792bbc812bbbcaee408aef30ce1b9dc02bb8c12bbc84346e762bbc0aeee08aeef2bba0aeea0caef10c61b9d402bb88aea908aef01941b9d0aeed04aea92bb88aee90caeee101b46e730014498270caeed184bc6e720014498272baa442bbac712e1b9c40051069cc32bba0612d1b9c0aebc04aead2badc22baf84246e6e⟩,
  ⟨0x1560a104b82100eb06882f415409604281c80bc05001b809c022000, 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⟩,
  ⟨0x15e0a384cc23e105078835c1860af04e02200ea05e02500dc040000, 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⟩,
  ⟨0x10807d83a01a80c6059829813208603901900a004301b008c026000, 0x8a3504b8bb11c1bc94b8b804b8ab2e2c822e2e84246f242e1d4122dd48b3e08b8b8103a46f23008b7404b8ac142d46eff2e29412e1fcb87b08b8a60ce1bbf0022c9012e2944706efb001e7e04b8a01581bbe8b877048b7622dc022e1e03386ef62e1d4122dd48b3e08b877102d86ef5001ee004b875142c86ef426bbc126bb89ae708b8710c1f06ef300987404b86e11c1bbc80071e012e1a45606ef1001a70173e098350cb83921e1bbac0069c01a7908b83719d1bba8b82d04affc2bff822e0bc4246ee9⟩,
  ⟨0x11808083b81ae0c3057827012208203781880a404401b0088022000, 0x2e5b01278c0b96117ff032e5dc406d1bcf0b96e04b9642e59822e5c04246f3a2e5b01273b8b96117ff032e5b8406d1bce4007ac81eb107bd832e5b0506c1bce00278c09cee2e4fc32e59450601bcdc0273b89e302e4fc32e58c57c6f360002e4e861321bcd40073d4608b939143886f342e4a812e4a0b92208b92b0ce1bcc402e48412e4a84346f30001d26271ac22e4a46506f2f001d2604b926101a46f2e001ee204b8eb142e86f2a00687a124e058230cb8e81c2b06f28001ef307bec22e39850a51bc9c02e380582308b8e4142ac6f26⟩,
  ⟨0x13809204582060ec06c031415e09c04501dc0c004c01c0090026000, 0x2bcec12bc9cae3008bb30103a46f7500af2604bb27142d46f732eafc12ead4bab008bae11091bdbcadfb04ad702b7a0ad630cbabf101b46f6e00ada22b5c0ade60cbab6141806f6c2ea9812e9fcbaa108baa81091bda8baa405d8cba7c2e3e432ea9860a91bda4076306ab81aac0cbaa4182a06f6801d8cba782e6bc32ea8075c6f662e9d812e9a8ba6508ba770ce1bd94ad2a045bb92b3fcace70cba76101b46f64005baf16ee4acfd0cba6b141806f62001ae506b901aac0cb9fa141886f6000b8f927094b9b00cb9f51c1a06f3f001ae306b8422e7cc50671bcf8b97704b9622e5c422e5e44246f3d⟩,
  ⟨0x13d09604802060f006e830015809804201cc0c004b01c80a0026000, 0x4bc392f0ec32f19454c6fa70015c22f18c5486fa62eed4aff708bb392ee8098272bed442eff440e71be8cbbb704bba32edc822eee44246fa22eed812edc8bba308bbb70ce1be84bbb52bfb422ece4bba0260acafb510bbb61039c6fa02eecc12ee80bb3908bbb50c1f06f7f001d21073e41cf70cbbb3141b06f7e00982b2609cafe30cbbaf1c2986f7d001a7b069cc22eeb450a51bdf002edf0afb52a0d832ee9057c6f7b001cf518bb392ecdc42ed9c80751bde80073d460748832ed9460741bde402ecfcbb3708bb63142ac6f78001cf518bb392ecdc42ecf070781bddcbb3004bb262eca822ecc84246f76⟩,
  ⟨0xef06e03241720a804a82200f006902e814808e03c0180074020000, 0xf9dc3e6a2f2e832f39857c6fbc001bfd0f9a8bcba0cbce121e1beec006ff41c2508bcbf19d1bee802f2dcbcba08bcbd142ac6fb92f2c012f2b8bca508bcb10ce1bedc02f29012f2c04346fb600bca22f0e422f2bc6306fb50150cbc390cbcac1cb1bed0054308bcaa18a1becc000bc7e184d06fb001504bc7d14f1bebc000bc72184cc6fad003e812f1c453c6fac2f1a412f19cbc3e08bc6a0ce1bea802f0f412f1a44346fa900bc3a2f0ec22f1a06506fa8⟩,
  ⟨0x12608783f01ca0d105e82b413808903e01b00b804801a807801c000, 0x2f5f010a1c4bd310a28c32f6b8406d1bff4bd7e04bd322f3dc22f6804246ff72f5f010fcd8bd310a28c32f5f8406d1bfd8006cdc1b3806ffc32f5f0506c1bfd4006ff43f362f4bc32f5e490a31bfd0006ff41b3808bd7719d1bfcc02f5c4bd2f08bd75142ac6ff22f5a812f5a0bd6208bd6b0ce1bfc402f58412f5a84346ff000bd3e2f4fc22f5a46506fef001c01a7308bd66141cc6fee003f360a1c4bd2f0cbd35141806fea0028710fcd8bd2f0cbd3315f1bfa4afa2043ef61ecc43ef70cbd25101b46fe30038fb0f0e822f3d05146fe0001db304bcf2142f86fbf⟩,
  ⟨0x144098047c2180ef06a830415c09a04301cc0c404f01f00ac028000, 0x6cf22fadcbeb60cbee11c2987839001939064d422fafc50a51e0e02dec042de50b79c22fa9c338783426e80bea4085a3b26ba02b760b6f842fa9440e71e0c8bea30b6fc20add82db30b6f832fa9030701e0c42db4042db30add822fa8c307c1e0c0bea104b867261a822fa88338782f2fa801261d01fec08bea1104d4782e00a8a82a29ca8a60cbe7b14198782c009ae70b6f82a730cbe6c15f1e0a800a9f02a7408be61142ac78270fd9810fcec3f3d08bdbf0ce1e09000fea43f3508bdbd142ac78232f6d012f394bce708bdb61091e080bdb2043e6a2f3903a240cbdb4101b46fff001c24070941c260cbdb2141b06ffe⟩,
  ⟨0x141097046c2080f006c831416409e04681f00ca05101f009c026000, 0x8afc0449fd127c02323b833878722fed812fed0bf7308bfb70ce1e1b8bfae04bf722fe945d750cbfb6101b4786d00bee72fdc8bf780cbfb514180786c2feb812fb9cbfa5175d432fec0406d1e1a80061bc193b064f032feb8506c1e1a402fdc8bee72fde032fe9c57c786700bf722fb9cbf780cbfa21c2b0786600186f064ec22fe8050a51e19402fde8bf7808bf7e142ac78642fbbc11b3c8bee42fb9c32fbf8406d1e18402fadc6cf22fad832fbdc50601e0fcbef104bee52fba022fbcc424783e2fbbc12fadcbee42fb9c32fbc4406d1e0f40064e41935064e832fbbc506c1e0f001b3c8beb72fad832fb9857c783a⟩,
  ⟨0xf807283601920bc054827011807e03981940a404501a8098026000, 0x32cd0132cc8cb2c08cb350ce1e2a0032cac132cd043478a701ea8cb2908cb331941e29807aa04cb30101a478a532af0132ae8cab408cabd0ce1e28c032acc132af043478a2001abb32ac4232aec65078a1001abb04cab8101a478a0000329c461361e1f40779182329c050e21e1f0ca2c04ca2a328902328b4338787900ca2304ca2c10d1e1e0032880ca2108ca2b1941e1dc00703b108ca28141cc7876137fc112cb04b2e08c8f10ce1e1d04bf8044bef12fc42323bc3387873⟩
]

def tableRLL : Table Block := .branch 12 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0x11508283b81bc0cb05e02a412e07e037016009203b0158078022000, 0x331dccc3808cca51941e2eccca204cc38331dccc7e0ccca3101b478ba00144cc700ccca2184bc78b900144cc70330e0433280712e1e2e000513a90ccc7d184b478b7331ac1330f0cc6608cc6d1091e2d403a632ff8cc380ccc6b2081e2d0cc683319423319ccc64331803331a431878b300cc6132ff82331a051478b23318c132ff8cc62330fc33319441078b100e98cc3808cc631c31e2c003a63aa08cc601821e2bc032ff8cc3b08cc3e1011e2b8032fe8132ff450078ad01080132fc050ba1e2ac04333fd3a50ccbae144dc78a9⟩,
  ⟨0x13a09484582100f406e832816e0a004001bc0b604a01c8098032000, 0xbd8bdcea03334a4506c1e3d803a61f6e8ccfa0ccd252428c78f500e98bdc23348c67478f4007dba1f6ecccfa0cccfd1418078f33339410f3e82ff90f3ec3333a8406d1e3b0cce7043cff332f42333a042478ea333981332f43cff08cce70ce1e3a4cce5042c3c0bfe43cfb0ccce6101b478e80f694cce00f5cc30bfe43ca90f2a03cfb10cce50c2a878e7003ca80bfb023338451381e39400f3e82c3c0f3e43332ec70a61e38c0079c41e6b08ccb91429478e200ccb30f3e42332dc50ab1e384cca704cca4331e42332a033878be00cc7804cca710d1e2f4cca53328c233290cc7d331fc33329831878bc⟩,
  ⟨0xfa077838c1a00c3059828812a08a03f01b00bc04b01b80a802e000, 0x337a4613a1e4a4006004cde814f1e4a0cde004cdbe336d4233784338792600cdb404cde010d1e4940336c8cdad08cdbf1941e490018cdb1336b43336f054c792300606208cdba1521e488000cdab184e4792000c901336a853c78ff00ee0cd74335843335fc87878fd00ee0f842335f467478fc334bc132ff0cbf608cd300ce1e3eccd2d04cbfb32fd42334bc40b61e3e803b604cd2d142c878f9334ac1333f0ccf708cd2c0ce1e3e0cd29047dbb333eccc700ccd2b101b478f7⟩,
  ⟨0x12708a04041e20e306402d013a088039818009a03a016807401a000, 0x339f0ce7a339c8333aa866c796400ce7b339e8ce720ccea719a1e58c0073c81cec08cea41591e5880073cc1339d450ba1e580ce702ecec2073d462aafcbb3a10bb34143b4793d339a412ece8aabf08ce700c1f0793c339a412ece4bb3a2aafc3339ac406d1e4e80073d46074881d2310ce69181dc7939001cf518bb392ecdc43398870761e4dc7c300429e81f0b42338a433879362f6d012f394bce708ce260ce1e4d4cdfb04cdf9337c02337f0338793000cdef04cdfb10d1e4bc0337b4cdb108cdfa18c1e4b8006020cdb10ccdf71cb1e4b40060202337d4628792c⟩,
  ⟨0x11608283d01cc0d305f82c413c08e03a819409e03e016808001a000, 0xcf2733c94233cc060bd1e5dc0074d01d3308cf2d142f0797600cf2004cf24142d4797533bd4133acccead08cef60ce1e5cccef304ceb2339ec233bd440b61e5c80073c4133bcc50b21e5c40069c0bd3f2a298333bb8878796f001a70073b4233bb0674796e33b8ccee108cee233b80cebd0ccee40c61e5b4033adcceb108cee31451e5b0cebf04ceb133ae4cebc0ccee11041e5ac033ad4a8a608cebf182f4796a001cf0073b8233af450bc1e5a4033ac4133ad0500796833aac133aa4ce7f08ceac0ce1e5980339f8133aac4707965⟩,
  ⟨0x11308003b01bc0ce06002b414009004001b40ba04d01f809802c000, 0xcfa204cf2333bf4233e8c33879a833e80133c88cef708cfa2103a479a7001d3504cfa0142c879a600a8a633c94233df451479a5001cee04cf7b142f879a433dd8133dd0cf6e08cf770ce1e68c033db4133dd843479a200cf6c33d80233dd465079a1001c01a7b08cf72141cc79a0001a7033d80ceb50ccf6a21e1e5f80069c01cef08cf6819d1e5f4033ad4cf2708cf3d1451e5f00073c0133cec50be1e5eccf3433cc8233ccccf3133cb4333cd4318797a00cf2933c80233cd0514797933cc0133c80cf2f33cb0333cc84107978⟩,
  ⟨0xfd077837c1a40c5058828812208203901900ac04301b008c020000, 0x67f6a308d9b91821e6f40365dcd9b408d9b71011e6f00365cc1365d850079bb01adc1365a450ba1e6e40067e019f7068f0336294506c1e6e0073a6f608d87e142ec79b601cf5ce9ac833619450621e6d4073e73c08d8391418479b301cf0d82608d82f143b079b2001a3c04d82e101a879b1001d3704cfb9142e879af33ed0133ec8cfa808cfb50ce1e6b8033e9c133ed047079ad00cfa4339e8cfa50ccfb319b1e6b0033bdcce7a33e94333ec066879ab001d36073b0233eb456479aa⟩,
  ⟨0x12708c84141e40e506602f014a09504101cc0c004e01a809401e000, 0x67f5e008da2e19d1e7c0016ebc5bb9368943368a050601e7bcd9fd04d9fa367bc2367f833879ec00d9ee04d9fd10d1e7acd9fb367e42367e8d9f3367d43367f031879ea00d9ed366c42367ec65079e9367e01366c4d9ed367d03367e4406d1e7a00051367a43367e0612f1e79c0051367a4d9b110d9f61c4b879e600145a883367cc612d1e794d9e404d9b5366fc23679842479e3019fcd977366c433679082079e236784d9be08d9e0366f4d9b90cd9e20c61e7840366e8d97708d9e11451e780d9bc04d977366ecd9b80cd9be1041e6fc067f366c42366f070c79be⟩,
  ⟨0x10f08103c81c60d106182c013c09004101bc0b604e01d8090026000, 0x36acc136af04347a2100dab236a90236aec6507a20001c0bf4236ae050731e7fc02f236a90da690cdaaf21e1e7f802f26b308daad19d1e7f47deb047dbf1f788236a8c33879fc00bc87e6536180336a8487879fb00bc9ac42369fc67479fa00da6404da68142d479f9368e41365d4d96f08da3a0ce1e7dcda3704d974365b82368e440b61e7d806af04da37142c879f5368d413689cda2208da360ce1e7d0da33045bb936898d9e90cda35101b479f3016fd781a843368cc506c1e7c8067f16ebcda250cda302428c79f1⟩,
  ⟨0xf7073036418a0ba057026c11c07e037018409c0410188080026000, 0x488aac36cdc336d888787a3601207d08db6019d1e8d4022ab08aaa36cdc336ce850601e8d0000db2a184ec7a31006d0136ca453c7a3036c88136c80daf708db230ce1e8b8036bd8136c884347a2d00daf436b88236c846307a2c006d0836b88336bf872c7a2b006d0808dafc18a1e8a8daf104daef36b98236bc83387a2800dae504daf110d1e89c036b8cdabe08daf01941e898018dae236af8336bb454c7a250061b608daeb1521e890dabc04daba36ad0236af43387a22⟩,
  ⟨0x12b08c04041e00dd06782ec15009104001b40ac045019007c022000, 0xdbb904dbac36e90236ee83387a6736edc122aa8dbab36e8c336ee4406d1e998007c07d1330cdbb7141b07a65004a08aac36ea8336ed490a31e990012807d08dbb319d1e98c022ab08aaa36ea8336eb450601e988dba104db3936cc4236e883387a6036dfc122aa8db3836cc0336e84406d1e8fc007c07d07e0cdb7f141b07a3e36df0136dd4db7708db7e1091e8f4db7a04dabe36dd0dab10cdb7c101b47a3c006d86dcbf0336de8506c1e8ec036b88dabe36da8336dd857c7a3a00bc8dabe36da8336dc490a31e8e402f21b708db6f19d1e8e0036d9cdb6a08db6d142ac7a37⟩,
  ⟨0x10607983981a60c0059027c11607e035817809c03f016007c01e000, 0x371b41371acdc6108dc6e0ce1ea880371801371b44707aa100dc3e365b8d9670cdc6c19b1ea800368ecd96e3659c3371a46687a7f01ad9ac02371985647a7e370f013699cda6108dc3d0ce1e9f0dc3a04da66368ec2370f040e91e9ec06b504dc3a142c87a7a36ff0136fe8dbf408dbfd0ce1e9d0036fcc136ff04347a7300dbf20a6dc236fec6507a72001c01fc236fe050731e9c4dbe804dbe636f80236fa43387a6c00dbbf04dbe810d1e9ac036ef0dbbd08dbe71941e9a8007013408dbe4141cc7a69⟩,
  ⟨0x11408183c01ba0ca05e82a812e08903e01b00be04601b008001e000, 0xdd61374e423759450ab1eae40374ecdd33374e43374f857c7ab82aa8412a9dcaa7908dd2a0ce1eac4dcfd04dcfb373c42373f83387ab000dcf004dcfd11c1eabc0373b8d96e371dc3373f066c7aae00dca5365b8dc770cdcf919a1eab406fa6b008dcf61591eab006f904dcea142c87aaa00da69372c023739c5147aa901ad013739450be1eaa0dcbe372f02372f4dcbb372e03372fc3187aa700dcb2372a82372f85147aa6372e81372a8dcb4372dc3372f04107aa500dcb0372b82372e860bd1ea9006f86f708dcb8142f07aa3⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0x11a08303c81be0c805a02a413a08903b01a40b204801c8094022000, 0x377e81374f0ddf908ddfc0c1f07aee001af206bc01af30cddfa141b07aed377dc13778cddbd08ddf80ce1ebb0ddf504ddad37788dd3b0cddf7101b47aeb001af106a901aa50cddf5141b07aea000377b0613c1eba001ae04ddeb14f1eb9c02b4dcddad2b4b833779050601eb94ddbb04ddb9376c02376f03387ae300ddaf04ddbb10d1eb880376b0ddad08ddba1941eb8402b4dcddad08ddb7143bc7ae000606a902376d450ea1eafc006bbc1aa206a8c3375d8506c1eaf00374ecdd33374e43375a470a61eaec006bc81af008dd67142947aba⟩,
  ⟨0x12208804081e20e006602e8158099041018809c03a0168080026000, 0xe98def937bdc337ca08787b2200e99dc4237c986747b2100df2037bdc237c9050ab1ec80037a90de7e08deea142ac7afe005c70170ccdeb20cdeb8141807afc00e98ca21379f8337aac8787afb00e99dcc237aa46747afa2a99012a8f4aa3f08de760ce1ebe4de7004dd332a890dd3c0cde71101b47af8379bcde21377f032a890de20377e4dd3c10de700c2a87af7379b4137880aa2408de6f0c1f07af6001afc06bd01aee0cde6d141b07af500ac3804de6c11c1ebd002b88c1378c44707af2001aec04de251581ebc00377fcddf9377f433788857c7aef⟩,
  ⟨0x10d07d038c19e0bf058827411407d036817c0a003f016007c01e000, 0xe92104e8f53a3b823a4883387b363a3fc13a384e8f42a4dc33a484406d1ecd4006af01abb06c8033a3fc506c1ecd007fc3a3cc23a3f050ec1eccc006c8013a3ec406a1ecc8032ac4e8e13a3cc33a3d850601ecc4e8ec04e8ea3a39023a3b43387b3000e8e304e8ec10d1ecbc006af0e8e108e8eb1941ecb8006af013a3a040691ecb407fe7fc08e8b4141847b2a01ff5fe9dc833a2a450621eca4df3404df3237cb0237cd43387b2700df2b04df3410d1ec98037ca8def908df331941ec9400703a908df30141cc7b24⟩,
  ⟨0x12b08d04181e40e106682e814809103f81b00b204201a809c028000, 0x3ae3af3b00ceb2a141b07b6a001b2906ca01aee0ceb24141887b6900e8bb270b0eabd0ceb211c1a07b68001b2706c9423abfc50671ed9c03aaf8eabd377f433abe450b91ed98eabb04eab73aacc23aaf03387b653aae417633aad8e8bb0ceabb182a47b6401d8c1af406bb833aae460a81ed8c0763377e4ddfd0ceab81d71ed889e20049df6277e023aac83387b602779c1276f49dbf08e9f70ce1ecfc6eaa0469291a4a84f2f0ce9f3101b47b3e001aa804e9bd1581ecf0006aa013a6c450ba1ece89d74049d6d275bc23a5d43387b38001abc06aec1aba0ce938141b07b37⟩,
  ⟨0x12c09084542040f4070833816e0a404881e80cc04c01d80a802e000, 0x3af9c613d1edf803b804ebe614f1edf403b8336b4ebb00cebbf2428c7b7b00ee018c23aef46747b7a00cdb1336b4ebb00cebb415f1ede4eba704eba33ae8023aea03387b783a3fc132ac4e8f42a4dc33ae9c406d1eddc03a384cab13a3cc33ae9057c7b763ade013add0eb6f08eb790ce1edd0e93804e8e13a4a89be80ceb78101b47b7300cab13a384e9280ceb75141807b723ad94eb3e08eb383acf418200ceb670c1c07b7001ec1fd1ff033ad94506f1edbc006084182008eb3f141b87b6d3acb0137adcdeb908eb2e1091edb0eb2a045c3337ad0c92b0ceb2c101b47b6b⟩,
  ⟨0x11608383d01ba0ce05d82b813408803d019c0b404a01d80a0022000, 0x1c0eec23b1a850731eebcec6204ec303b0a023b18c3387bae3b18012f0e4ec2f3b09c33b188406d1eeb405d83ba0cec60141b07bac00ee0bc3b3b0b833b0ec90a31eea803b86023b0e46747ba900bc3b2f0e4ec2e0cec31141807ba800ee0ebfa334fc33b0948787ba700ee0ef023b08c6747ba63afe013afd8ebf008ebf90ce1ee9403afbc13afe04347ba400ebee335d023afdc6507ba3001c0f8023afd050731ee88ebec04ebb33aea823afb43387ba13afa81336b4ebb23aea433afb0406d1ee8000620633bf0cebea141b07b7f⟩,
  ⟨0x10d07e83c01ae0c7058828012207e038817809603d0180074020000, 0x334fcecbd08ecf61451ef8003bd04ecf4142f87bbf3b3b4eceb08ecec3b3a8ece70cecee0c61eef803b384ecb908eced1451eef4ece904ecb93b38cece60ceceb1041eef003b2fcecbd08ece9182f47bbb00f8cef823b39c50bc1eee8eca304eca13b1dc23b2903387bb900ec7604eca311c1eee003b1d0cbf532fb833b28866c7bb700cd3132fd4cbee0cec7f19a1eed803ff3b708ec7c1591eed403fe04ec70142c87bb33b1b813b1b0ec6608ec6f0ce1eec803b19413b1b84347bb100ec643afe823b1b46507bb0⟩,
  ⟨0x10e07d039c1ac0c905b028811e081037818409c041017006c01a000, 0x33e80133c88cef708ee33102d87bfb261901260e8983c08ee320ce1efe8033d8cceb508ee2d142ac7bf700cf2004ee271401efd8edfb04edee3b7d423b7f44247bf333bcc133ac8ce7b08edfb103a47bf233bd4133acccead08edf41091efc0033ac413b7bc50b51efb803a6171c0deb20ceda621e1efa403a63af08eda419d1efa0ed2c04ed2a3b48023b4b43387be700ecff04ed2c11c1ef9803b3f4cbf53b29833b4ac66c7be500ecb432fd4eca60ced2819a1ef9003e53b708ed251591ef8c03e404ecf9142c87be1⟩,
  ⟨0x12f08d84201e80e006602e014a09103c01a00a40410180080026000, 0x74f01cef073c033bb80506c1f0bc03baf0cf6033ad433bafc57c7c2e3bac813ba9cee6208eeb40c1f07c2c001a70074fc1d390ceeb2182a07c2b001d3d074ec1d3e0ceead141b07c2a001a703ba98ee3a0ceea91c29c7c293b9dc13b99cee7208ee791091f09c03b9989c7b3b98833b9dc70651f098ee743b9c423b9ccee703b9b033b9d43187c2500ee6d3b99823b9d05147c243b9bc13b998ee6e3b9ac33b9c44107c2300ee62271ec23b9bc50641f0880075c81d7008ee6c1418c7c2100ee663b99423b9a84047c20001d3704ee3d1581effcee3304ee263b88823b8d03387bfc⟩,
  ⟨0x12e08b04041dc0e1068830016009c04401cc0c205001d80a802e000, 0x3befc1073d463bbcc9ca610efe1181e47c63001cf5181d68075a443befc60771f188efa604efa43bdec23be9c3387c6100ef7a04efa610d1f18003bde0ef7408efa51941f0fc02609cef7408efa2143ac7c3e001c01a7308efa0143a87c3d3bcfc13bcf4eef208ef610c1f07c3a001d67074fc1d390cef3f141b07c39001cf518eef23bbc043bc8080751f0e00073d46075a033bbf860741f0dc03bbe0eef008eefc142ac7c36001cf518eef23bbc043bbd470781f0d40272a09ca408eee6142ac7c323bb8813baf8eeb608eee30ce1f0c4eee004cf603baf4eea00ceee2101b47c30⟩,
  ⟨0x12008683e41d80d306182b413808d03f81b00b204101a009c026000, 0x3e4b813e3e8f8f408f92f0ce1f1e4f92c04f8f93e3a823e4b840e91f1e0077504f92c142c87c773e49cf92508f9263e490f9200cf9280c61f1d803e3f0f8f708f9271451f1d4f92304f8f73e488f8ff0cf9251041f1d00379f8def708f923182f47c7301dd1dc823e48050bc1f1c803e3dc13e3ec50b51f1c4afe004afb92beec23e1cc3387c6b3e1b812ececbb3408f86f0ce1f1a8ce69041cf518bb3a2aafc43e1b860791f1a40339c813e0e84707c67001cf304f8341581f19803baaceea03baa833bf9450601f194efe104eef43bba823bf883387c64⟩,
  ⟨0x12a08b041c1f60e806d832016a0a704a01ec0d005402080a0022000, 0xfa663e8f4fa650cfa69141807cac01fe9ed823e69450bb1f2a4077704f9731581f2a0f96a04f9683e4f823e5ac3387ca700f93d04f96a11c1f29803e4e8f8e53e4ec33e5a466c7ca500f8ea3e394f93b0cf96619a1f290077677008f9631591f28cf93704f8eb2659c23e4e44247ca13e4d8f93408f8eb3e4c499670cf9370c61f280f93504f9313e3ac23e4d83387c7f3e4b013e3e4f8ea08f935102d87c7e3e4cc12659cf93108f9340ce1f1f499e73e4c822659c99e53e4c433e4cc3187c7c3e4c0993808f8f9264dc23e4c8413f1f1ecf8fa04f8f904f9300c4f87c7a⟩,
  ⟨0x13109004341f40e306882f415a09c04401d00ca05201d8090026000, 0x3ebe4faf308fafd142ac7cbf0069333e8f8faf30cfaf715f1f2f8faee04faaa3eaf023ebbc3387cbd3eba4177918faa93e99843ebb860791f2f0077919e99e9c43eba460771f2ec077918faa83ea9843ead880751f2e4077919e9833ead060741f2e003eab8faa608fab2142ac7cb701de463eaa0faa610faab1c1e07cb600fa3d3e998fa650cfaa41c2987cb401eb1ea023ea8850a51f2ccfa7804fa683e8fc23e9e43387cb23e9cc13e8f4fa673e8f833e9e0406d1f2c4fa7304fa663e99cfa3e0cfa75101b47cb001eb1ea1eb433e9cc506c1f2bc03e8f4fa663e99433e9b057c7cad⟩
]

def tableRLR : Table Block := .branch 13 tableRLRL tableRLRR

def tableRL : Table Block := .branch 25 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0x12408803e41ca0d105f02a813a09004181bc0bc04b01a008c01e000, 0x1d74075cc1d390cfc29141887cf13f09413bdd0fc223baac33f09c406d1f3c00074e81ced073b833f094506c1f3bc02f4fcef742a29833f09050601f3b8fbf204fbb03e39823efcc3387cec3efb413eebcf8e508fbf2102d87ceb01dbc13efb450b21f3a803e4ec13efa84707ce900fbae04fbb11401f39cfb6704fb643ed9823eda4307c1f39803b13a977c0cfb67141b07ce53ecec13ebd8fb3608fb3d1091f390fb3104fa3e3ebd4eb370cfb3b101b47ce301bb1eb9ebc33ecc4506c1f38801a4ccfa3e3ebcc33ec8470ac1f38406ec7ae08faff142947ce0⟩,
  ⟨0x12a08b84281ee0e406682e814e09403e81b00b204b01d009c026000, 0x6b8bc3b3fcb833fce490a31f4a001ae6023fcdc6747d2700bc392f0ecff2e0cff3215f1f498fee5049cf8273c423fb9c4247d252748c113dc49cf7271ec33fb94406d1f490ce6b04ce613398c23f9f43387d222ac8c12abecaafd08fe670ce1f3fcfe2104fdf53f7b023f8883387cfd3f7fc122ab0fdf43f6e833f884406d1f3f0007c07d1e70cfdff141b07cfb007808aac3f7c833f7f490a31f3e801e007d08fdfb19d1f3e402f0c0fdf208fdf9142ac7cf8008aaa22ab0fdf20cfdf615f1f3dc0331c0c92b3ed8c33f1e850601f3cc0324accc703ed8c33f1e457c7cf2⟩,
  ⟨0x11908383e01ce0d405e82b013408c03c01940b004801c809801e000, 0x67f3fedc6ffb0d082f21e1f4f0067f066f82420b46747d3b0108271bfec2420ac50ab1f4e8fffc04ffef3ffa823fff43387d383ffe811a9d8ffee1f4b033fff0406d1f4dc012c12d12e0cfffa141b07d36004a06a713ffb433ffe08787d35004a04b423ffd86747d34006a711a9d8ffed0cfff0141807d333ff8813ff80ffba08ffe30ce1f4c403fee413ff884347d3000ffb63fedc23ff846507d2f001c1a8823fef850731f4b8ff3d04ff313fcac23fcf83387d2b3fcec12f0ecff303fbdc33fcf4406d1f4a805d81b00cff3b141b07d29⟩,
  ⟨0x11808283c81c20ce05d82b813c08f03e81b80b60440198084026000, 0x109e113efc4fb80d09e415f1f5dc5fea045fe017f882426ec3387d7500bd6d2a2982425c850ab1f5c87ca1047b601ed8c2424b83387d70423dc1423d508ef0908f80ce1f5ac0423b81423dc4347d6a0108ed422982423d86507d69001c1aa82423cc50731f5a0067f4229908bd0d08eb21e1f598067f067802423a46747d65422881421c908690908a30ce1f59108a004ada2421c508680d08a2101b47d6301a9daa1aa4342280506c1f588067f2b689086f0d087d21e1f584067f6a809087b19d1f58002b5c0ada2421bc3421cc57c7d3f⟩,
  ⟨0x13709004341f40e306802fc16209e04581dc0c605001c8094022000, 0x7aff042afa1ebd05fb40d0ab9101b47db2002b2f0abe87af30d0ab615f1f6c50aab045fbd17ed4242ab03387dae17fa0117ed05fbc124e0342aac406d1f6b4b8bb048a36228f4242aa03387daa001d782e4fc2429dc50ec1f69c007bd81429d8406a1f6987c78047c701f1c82429c83387da5272e41272c89cb4090a6d0ce1f68d0a2b0509e21a1e82428b4307c1f680007bc81eea07b903428ac506c1f5fd09fe0509f6427e02428804247d7d2f6c810f9dcbce40e8903427f8406d1f5f000f9a83e772f2e83427dc50601f5e80161dc5923164883427b870a61f5e4007ba01ee60909ec142947d78⟩,
  ⟨0x11f08403d41d00d806482d813e08e03d81a00b404601a0098026000, 0x11865046a76460c90f340d187d101b47df0461cc1461c5186b0918740ce1f7b40461a81461cc4347dec01186943bfc2461c86507deb001c078c2461bc50731f7a91867051863460f82461a03387de84619411a9c5183243cd034619c406d1f79c012c12d1e20d1865141b07de6006a761a9c518310d186415f1f79401e01a9c518310d183c2428c7de4007804b42460e86747de3006a711a9d918310d1834141807de2007810eff43c9c3460908787de0007807902460886747dbf1a2cc11a2b068ae090aef0ce1f6ed0ab9050ab542abc242ae83387db3⟩,
  ⟨0x140096046c1fc0e406802f415209c04481c80be04b01d0098026000, 0x4ab8128fc4ab60d19b51c2987e26001fae07eb02466cc50a51f894de6f465f022a890de20374ccddf911197d1039c7e24465ecddfa08dd33374f0ddf90d197c0c1c07e23374f41374f0dd3309197b0c1f07e22464fc1464e119350919600ce1f880adff04ac7c2b1802464fc40b61f7fc02b1e81464e45007dfe464c01464b919290919310ce1f7f0dd7604acbb375c8dd330d1930101b47dfb00dd6b2b2ecabe10d192f15f1f7e802a8909c2c2b08c34649470ac1f7e0006bf41b25091923142947df700d9e9421a118bd0d18e0141807df41e6a811e6a079a30918b71091f7c9187d051833460b82461f83387df1⟩,
  ⟨0x1580a284c823610807a837817c0aa04b020c0de05d02500dc040000, 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⟩,
  ⟨0x12408883f81d40dd06903141700a504901ec0ce04d01c8098026000, 0xbc392f0ed1cf80d1cfc15f1f9d91cef051c35470bc2473c03387e74473b41470d088aa091cef102d87e73017ac1473b450b21f9c80011ce8185807e700060424739c50e21f9bc0470cc1470d85007e6d3a7cc11a4ac692d091c2e1091f9ad1c27051be946fac2470a44247e6a4228012b5c10871421a034709c406d1f9a402b688ad70421bc346fa850601f99d1b2e1a8b420a7e86a2c13dc831a8bc30701f9906a32046a2c0a7e8246cb8307c1f98c7d20047cf01f3d4246cb03387e621f5ec11f3c87d27091aed1091f9842e7f042e350b8dc246b883387e3d⟩,
  ⟨0x11a08583dc1c80ce05e02ac13008503c01a00b2046017808001a000, 0x1bc9bc02477c450671faac0476c11daf475b43477ac50b91faa91da5051da04768824769c4247ea8475c012f2475b85a210d1da5182a47ea700bc91d69475b434768475c7ea500bc9af5aec3475c060a81fa906d2f046d261b4a02474d83387ea3474cc1474c51d2b091d340ce1fa800474a81474cc4347e7f011d29228842474c86507e7e001c09942474bc50731f9f51d27051cfb473c82474a03387e7b4749412f0ed1cfa473c434749c406d1f9e805d82640d1d25141b07e7900988bc3b473e034748c90a31f9e00262602474846747e77⟩,
  ⟨0x14a09d04a423410707a03741940b705001d00c004c01c8094028000, 0x11eaf479cc247af06507ee0002d21479cc247ae450ef1fafc01819b7091eb7143a87ebe47a981479d51ea3091ea81091faed1ea5051ea3479d4247a983387eba479f81479cc5a3b479d0347a94406d1fae51ea0051e782f9a0247a884247eb8479fc12f9a11e78091ea00ce1fadd1e7e042b76168ed1e740d1e7f101b47eb626e809ae92e1c51e7d479f05168ec9ae826b9c9aee26bb51e74191e7e0c5847eb5479e81479d09aed091e7c0c1f07eb4001c3f066cc1c600d1e7a141b07eb3011e730add91e720d1e7915f1fac800add91e73479c83479d850601fac406f46f36bb0d1df6141887ead005a2113db51daf0d1df31c1a07eac⟩,
  ⟨0x11d08503dc1d40da06582e415609b04701ec0d6057020008001a000, 0x36b88dabe47e84347e9457c7ef947dd8147dd11f6e091f770ce1fbd8047db4147dd84347ef5011f6c47cfc247dd46507ef4001c09a4247dc850731fbcc026247cfd1f360d1f6921e1fbc402625ef091f6719d1fbc0047cd888fd091f3c1451fbbc05f0051f3a142f87eee4709c146fa51beb091f340ce1fbb4026bac9af4091eee1011fb9c026bb09aed26bac347bb450601fb991ee1042d21168ec2db30d1ee2101b47ee526e80be6b0b7843168ec9ae80b6f82db3111ee10c2a87ee447af4147aed1eb2091ebe0ce1fb88047ac4147af44347ee1⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0x11508103bc1b20c805d82a012808703d01b80b8049019008401c000, 0x1197d04dd343788424a5c43387f354a0b0147ee91fb509282d0ce1fcc1282a049891fb91fec834a0b060a91fcbc02625f95f70d282a182a07f2e0088a605282911c1fcb52824051fef47fa424a0943387f284a088147fb888a8092824102d87f27017c414a08850b21fc98047fb4147fc05007f25017cc147ef85607f21009891fb8226c0347eec75c7f2047ecc147e911f7e091fb40ce1fbf91fb104dabe47e8d1f6b0d1fb3101b47efd006d86dc9a0347ec4506c1fbf0026236af91fa10d1faf2428c7efb009886dc247eb46747efa⟩,
  ⟨0x11908303e41cc0d306182c013808e03a819409e03e0168080026000, 0x12a6d052a6b4a98424a9b83387f65012a60052a6d11c1fd9004a8f92a3d4a7d034a9b066c7f630129ff4a8f529f40d2a6919a1fd8800678c19bd092a661591fd852a3b052a264a88024a8f03387f604a8e414a89529ff092a3b102d87f3f0019e2052a39142c87f3e4a8d12a32092a334a8c52a2e0d2a350c61fcf404a8a12a24092a341451fcf12a30052a244a8a92a2d0d2a321041fcec0422f46ffb092a30182f47f3a0019e1066fc24a8b850bc1fce404a89014a89c5007f380019e40529f61581fcdd297104de21374d024a5cc4247f36⟩,
  ⟨0x11608183c01c00cd05c82ac13608d03e81bc0ac046018007c01c000, 0x12ae74a8f52ae80d2af619b1fddc04a9bd2a3d4aba034abcc6687f76001a27066f424abc05647f754ab9414a9ed2a75092ae60ce1fdcd2ae3052a7a4a9bc24ab9440e91fdc800689814ab8c50b21fdc40422f52a7f092ae01451fdc000678414aaf850be1fdbc01bfed2a7d092ab51451fdb80066fc14aacc50be1fdb52aac4aaa824aaad2aa94aa9434aab43187f6c012aa14a9e024aab05147f6b4aaa014a9e12aa74aa9034aaa84107f6a012a7f4a9f424aaa060bd1fda40068941a24092aa5142f07f68012a78052a7c142d47f67⟩,
  ⟨0x11708203c41bc0cb05c0294122083038018809c03b017008001a000, 0x8d74048d70235ac24b1a44247fab1a8e811a8e069f8092c381091fea4b86e04b867269e824b0bc4247fa817cf0117cdc5f39092c280ce1fe989a3c04986a07fb424b0943387fa54aff814aff12bf8092bff0ce1fe8c9a38049a24267b424aff840e91fe8802688c14aff450b51fe84b86e04b867269e824afd83387fa00019e4052b74142e87f7f001a210688019e80d2b63141887f7d019fc19ea067a034ac9060a81fdf004a7d014ac844707f7b001a28052afa142e87f7a4abdc14abd52aeb092af80ce1fde404aba814abdc4707f78⟩,
  ⟨0x15009204401f80e806a030415a09904301cc0b804801a8094028000, 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⟩,
  ⟨0x12c08e042c1f80e906a82f015809604281d00c805001e80a802e000, 0x138b54bedc24e3886507ff10058774bedc24e2fc50ef1ffc00181ee80938bd143a87fef4e09c14bfe138220938291091ffa804bf8858771648c34e09c71281ffa538244e08424e08d38204bff034e0943187fe8012ffd4bf8824e0905147fe74bffc14bf892ffe4bfec34e0844107fe60058771648c24bffc51271ff94007ba01ee6092ffc144987fe4012fe2463bc24bfe84047fe3012fe34bef92fe20d2ff7141807fe24bfc414bee52fee092ff31091ff852feb052fbc426f024bfb44247fe04bfa81426f12fbc092feb0ce1fefd2fe90459231a1e92fb80d2fea101b47fbe⟩,
  ⟨0x11408203b81be0d106082d015009604181b00b2046019808001a000, 0x13dec4f6a424f7cc51488274f7b814f6a53ded4f7a834f7c04108826006b93de3093dee1c32209401ae1b2093deb1822209004f6a53de6093de91012208c04f69414f6a05008822008a014f5d45607fff007813d6e42d9c34f5c475c7ffe4f59c14b1cd2c70093d680ce1fff0d8a5046929360a079b70d3d67101b47ffb16bcc116bb85af0093cf90ce1ffe87aac047aa51ea9c24f3b03387ff8279f01279d49e77093ce50ce1ffdc7a69047a281e99824f19c3387ff64e38c14e38538b80938e40ce1ffcc04e2dc14e38c4347ff2⟩,
  ⟨0x12508904101e20dd06802f416009704381c00c004d01f00ac032000, 0x4f8c93da04f5c834f8f8668883a0089c6fc24f8ec56488394f8c014f69d3da1093e310ce220dd3e2e053da64f68024f8c040b6220d801be053e2e142c888354f8ac14f8a13dfd093e2c0ce220cc04f7f014f8ac43488324f8a53e27093e284f8853e230d3e2a0c6220c404f7ed3de3093e29194220c13e26053de34f7ed3e220d3e27101b4882f00144fef70d3e26184bc882e00144fef74f78c44f890712e220b400511b10d3e21184b4882c4f7d814f79d3df1093df8109220a801ae4f6a53de30d3df6208220a53df34f7c024f7c93def4f7ac34f7d03188828⟩,
  ⟨0x11c08483c81be0cc05c828c12408503901780a20400198080026000, 0x52c9c10bae82eb4094b280ce221dc4931042aeb0bae42ae60d4b27101b488762f6b812f4d0bd3609497a0ce221d09bbc041ffa07fd02525c833888704fab014f5c13d6b093ead0ce221b13eaa047813d6f42dc834fab060a9221ac01e022c22a0d3eaa182a0886a013d72053ea911c221a53ea1053e6a4f99024fa8833888634f9fc14f9a53e32093ea1102d888620089814f9fc50b22218401a9d11831093e7d142ac8860013e68053e6b140220fd3e62053e604f8d824f98c338883d013e35053e6211c220f004f8cd3da04f5c834f98466c883b⟩,
  ⟨0x13009084401d40d606102d014008d04001c00be05001e8098026000, 0x10bce8c2531f05162222d402b2f8abe1094c64142ac88b23bad0eea85309ceeaf10ee623ba9ceea63bab0eea014eea10c4c488b03bab413bab0eea6094c270c1f088af52fa8152fa4ce7a094bed102d888ad001ceb054bea142c888ac00cf603baf0ceb50d4b7f1418088a752ddc152dd54b6c094b780ce22294052dac152ddc43488a4014b693baf0252dd865088a300cf603baf0252dcc50ef222880181cef094b71143a888a152d94152d8d4b3e094b660ce221fcfc2504bd3f3f088eeab0d4b65101b4887e00ef742f4fca8a60d4b6415f221f4b82d04affc2bff8252cf4338887c⟩,
  ⟨0x12e08a84181e20e406b831015609a04181c00be04c01b0094026000, 0x536854d7f094da0535f94d7c0d4da20c6223c003a5535d425368451488ef535f41535d4cbaa7a90d4d7f104223b803a5054d7d101ac88ed01ea41535f0406a223b14d67054d3f535842535a442488eb535994d65094d3f535914d610d4d670c6223a803acdceb38094d66101c888e93ad9c13acdceb38060803535944071223a0032ab4eb377fc0d4d601418088e600e8be3aaf42533f450ab223914caf054cab531a42532c033888bb532b413b8532a94c680d4caf182a488ba00ee10910883532b460a8222e403b8532a54ca00d4cac1d7222e00531a0e8d4c740d4c7e1c1a088b6⟩,
  ⟨0x153099848021a0f607183401720a804a01dc0c605201c0090022000, 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⟩,
  ⟨0x13e09584602020f006e032416c0a204881f80ce05402080b802e000, 0x2fec012fe98bfa8095be50ce224f4befe04bef62fbe0253ec8338893b53e994fa308ce7b33e9423b8f03164224e0cead04ce7b054fa60c488893753e88133e94ce7b094fa30c2cc893600ef393ba98ee3a0d4fa115f224d14bed054bec52f88253bc0338893300ee62271ecee7c0d4ebb1c1a08931001d72075c0253ae45067224c14eb3054ead53aa8253ad0338892f3bac81069c0eea73b988353acc60a9224b80069c0eea63b8e8353ab875c892d539f413babd4e6f094e7e109224b14e7c054e6f3babc2539f4338892b539dc13ba80eef23bab03539f0406d224a94e7704eeab3bbc8eeac0d4e78101b48929⟩
]

def tableRRL : Table Block := .branch 12 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0x12a08b83e81c00cd05c82b013c08b038817409403a016006c01c000, 0x576e010fba03ee0095dba109226a83ef0576dc20fb9c3ebb0fb983e7b115db81039c89a90fed03efa083ee60fbdc3e7b0d5db70c1c089a8576a41575e95d7c095dab1092268cdcea04dcab372942576a440e92268806fb055da0142e8897f00dcaa055d7b142d4897d125b01124e84935095d60109225e55d36164b02161dc592413efc3574dc3070225d45925045924161dc2574d8307c225d0b8bb048a36228f42573ec424896d00587e22de82573cc514896b001e7b055cf1142f8896a0058a2161f82573b450ab225a403e6055ce5142e8896800ecb9055c75142d48965⟩,
  ⟨0x11408003cc1ce0d406082b814208e03d01b40c204e01b8090026000, 0x370e8136998da3b095efb102d889e800da64055ef71402279c06b7055eb8158227909d25049cfb273f42579e833889e1271841270b89c26095e7710922780fa7504fa6b3e9b42578fc33889be00cbee055e3e11c226f55e39055e2b5789c2578e833889bb3b1c01334f0cd31095e39102d889ba00cd3a055e2c140226d80420055dfe158226cd5df8055df4577ac2577e433889b2536e8132ca54d763e8f43577e0406d226c403b5a4cb29535d43577d457c89b0010c50c10883577b85062226bc3ef2043eeb0fbb42576ec33889ab⟩,
  ⟨0x120089840c1e40e306782f815409604181bc0b604701a0080026000, 0x15feb055ff710d227f4057fa95fb0095ff6194227f000fbd95fb0095ff3144a489fb00107388257fc450ea227e800f9ed5fb057ebc357fa070ac227e00073981ea6095fe61429489f7015fb00f9ed5faf0d5fbd1418089f6001ce607a981ea70d5fb4141b089f5015fa657e955fa40d5fae15f227d0057e955fa657e90357eac5060227cc007aac1ea807a94357ea0506c227c95fa204af722bdc4257e8c307c227c55f3c055c74571d8257cf842489f03b3e413b2e8ecb4095f3c103a489ef00d967055efe11c227ad5efb055ef657bcc257bf033889e9⟩,
  ⟨0x15d0a504d823a10d07b83981aa0c2054826010204f01d809c026000, 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⟩,
  ⟨0x11f08603e41cc0cd05b028c12c08603a81980a4041018007401a000, 0x169e004eea83ba8425a7884248a6b0fe9410fce03f690969a50ce2299d69a2055dbf0fbe825a68c4248a645a09969a1095dbf5a0903efa0d69a20c62298caf75043e7b0fbd83ef70d69a1101b48a625a5e015a5d9696d0969790ce228fc05a5b015a5e04348a3e01696b57ff425a5dc6508a3d003e7b57ff425a5d050ef228f00181ce6096972143a88a3b015ffd0fbd95ffc0d69691c2988a39001ea90738825a59c50a5228e005a5855ffc096965142ac8a37015ffd0fbd95ffc0d693e15f228d8033584ecbf0968b2145228c003e20568b0142f88a2f⟩,
  ⟨0x16a0ab851024e10d07c83981a60b604e01fc0be045018807401a000, 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⟩,
  ⟨0x1720af852c27412908a84081dc0d105582600f606102700dc040000, 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⟩,
  ⟨0x148091043c1f00e4069830015a09604181b40b604701b0094022000, 0x26e80be6b0b7842dff105a3b26ba02dbe0b6cc2d21149ae40c4c48af55b2941169f85a79096ca60ce22bcc5a74045a3b169a45a6c0d6ca5101b48af2010d3213da52b3d0d6c761c1a08af00019ff067f425b1d0506722bbd6c39042db42f9a025b0e84248aed5b0e012f9a02db4096c390ce22bb11ee1042b76168ec2db30d6c38101b48aeb5afc415afa56beb096bf310922ba52b24059fd29f1434c835afc460a922ba0067f467d519f90d6bea1d722b9801f3b829fa262b435aee870ac22b940072a41cb1096bb8142948ae4011b2a262b425aed850ab22b8c0262c098ae2629835aecc516322b8801b7c8ab37096bae142ac8ae1⟩,
  ⟨0x147099848c1e20dd06602e414a08c03f01a80a00420170084026000, 0x6b9196dab5b79045b7bc807522cc006b919b9835b7b4607422cbcafa157e896a6657eb56d7d57ec861ecc4af722bdc55fa757e955fb10f9ec72bd88316522cb55fb4055fb157e9425b5f4307c22cb002bd983ef5096d70142ac8b295b4e015b4a56d23096d390ce22c956d2f056d2822cb025b4e040e922c916d345b4cc25b4ad6d322e1fc35b4d43188b23016d28056d341059c8b225b4c415b4a08b24096d33104d48b215b4bd6d2e096d2822cb08b240d6d310c5988b20001e76056d2f142c88aff5b4b4122c908b2c096d2e0c2cc8afe016d26056d2c14022bf405b49815b4a850b522bf04bbb044bb412ed825b3f83388afa⟩,
  ⟨0x1630a784f024611007e035818a0a804701ec0c805001e8098028000, 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⟩,
  ⟨0x12c08c84101e80e706802f015e09c04401ec0d005101e80a802e000, 0x5fea010a4d8292d097fa90ce22e9d7fa60520a4d429280d7fa8182a48ba60120e30e10d7fa6182a08ba5002938057fa511c22e917f7e264e020a5989937097f780c2d08b7e5fdf01264dc2966097f7e0c2cc8b7d001ac15fdf050b222df17f760429a00a5e825fddc3388b7a5fdd010a5fc2968097f76102d88b79002f415fdd050b222de17e78057e705f9c825f9e84248b754bde810afe52f6f4bd9835f9e0406d22dd000b3e82bf94bdb435f9c4506022dcc5fac044f3313cd825e8dc3388b70138901138884a60097a3510922db97a315b4a4222cb16d28096d230c2dc8b6c⟩,
  ⟨0x11a08603e01ca0d806402e414c09304001cc0b404a019808c020000, 0xc9018c2625846748bbd00cdad336c589380d893b141808bbc624c01624b989280989310ce22ee806249c1624c04348bb9018926624842624bc6508bb8001c0cb02624b0507322edc01e04f5b90b670d88fd1c29c8bb5225dc122594896009882910922ec97fba057fb75feb025feec3388bb0017fab057fba10d22ebd7fb85fed825fedd7fb05fec835fee43188bae017faa0a0e025fee06508bad5fed410a0e17faa5fec435fed8406d22eb000510a28c35fed4612f22eac00510a28c2838117fb31c4b88baa001441c200d7fb0184b48ba9⟩,
  ⟨0x12308803dc1ce0d106082c414209404081b40be04e01d8090026000, 0x66c18a6b62a94362ae08208bfb62ad58ab2098ab462ac58aad0d8ab60c622fe8062ab98a6b098ab514522fe58ab0058a6b62abd8aac0d8ab210422fe00066c18aa5098ab01c322fdc0066c019b4098aad18222fd80629ad8aa8098aab10122fd406299c1629a85008bf4628fc1628e58a36098a600ce22fc52a39052a254a7fc2628fc40e922fc004a8901628e850b522fb802b4e8ad2e098977142ac8be46259c1624e989320989680ce22f85896504cdb1624e589250d8967101b48be00018818ccac362594506c22efc0324336b589380d89632428c8bbe⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0x12508903ec1dc0db06402d014c09304301b40ba04601b008c026000, 0x18b32058afc62bdc262ccc3388c30271dc1271ac9c6c2718c362cc8406d230bc052fa0162c845008c2d009bf8271ac9c6a0d8afd15f230ad8af1058a696298c262bc83388c2962bbc1629a12a3d098af1102d88c280019bc058aef142c88c2762bb4162ba98abf098aee0ce23094062af8162bb44348c2462bad8ae9098aea62b8d8ae50d8aec0c62308c062af58aa5098aeb194230898ae8058aa562af58ae40d8ae9101b48c21001442b760d8ae8184bc8c20001442b7662a94462b98712e22ffc0051066cc362b8c612d22ff98ab8058aa962acc262ae84248bfc⟩,
  ⟨0x13a095044c2060f007083381780a304981f40dc060028010c04c000, 0x18f3b63c8c263da46508c6f63d98163c8d8f3b63d88363d9c406d231b800512b39c363d98612f231b400512b39d8f23118f641c4b88c6c00145d98363d84612d231ad8f36058f2763cc4263ce04248c6901d8d8eea63c8c363cd88208c6863ccd8f30098f3263cbd8f2b0d8f340c62319c063cb18eea098f33145231998f2e058eea63cb58f2a0d8f3010423194076363c8c263cb870c8c6401d8dd9c263cac6088c63018eea63c98263ca44048c6200f8f7058ee414023180afa12bdd821ecc4af720fbd83ee61189a01039c8c3e2eed4bba32e090afea10bb392ee80afb52bf90982b14bb720c4c48c3c⟩,
  ⟨0x12a08b841c1e80e106402e014409204101c80be04c01c8098032000, 0x1452f66664f44665f8712e232b80051063cc3665ec612d232b59970059961665ac2665c84248caa0018ec66491993d0d9970208232a5996d665a82665b19969665943665b83188ca8019966664902665b45148ca7665a01664919967665903665a84108ca60018ec664f42665a070c8ca50018ec063d02665946088ca40199246658026658c4048ca3662a813babceea10998ab109231f16afd04eea13babc2662a83388c7b1bb8011a3e468f4098fe2109231d18f6b058f6863cf4263db03388c72018f3c058f6b10d231c58f6963d9c263da18f6163d8c363da83188c70⟩,
  ⟨0x13d094846820c0f3070030c15e09504081c00ba05001b809c020000, 0x3f6e90f346688c3668ec70a62338801e81e3099a39142948ce1010f343f6e99a230d9a31141808ce0668b01623f19a20099a2e109232f99a2b059a20623f02668b03388cbd668a99a29090b724f5bcfdba4f5b84668ac40e7232f13eaa053d6f42dc82668a8307c232ed9a286689423f6e99a244f5b83668a43070232e99a27059a243f6e82668a0307c232e401e81e322b0d9a25141b08cb86669416668999770999a60ce232d00665d81666944348cb36668d99a10999a2665ed997d0d99a40c6232c80665d5993d0999a3194232c599a005993d665d5997c0d99a1101b48cb0001452f660d99a0184bc8caf⟩,
  ⟨0x12808d84081e40db06582e015009504101a40b2043019808c026000, 0x19b3d059b6c10d233dd9b6a66da0266da59b6266d90366dac3188cf6019b3c66c90266da86508cf566d9c166c919b3c66d8c366da0406d233d001810e890366d9c612f233cc01810e8919b24119b651c4b88cf2006041c270d9b62184b48cf166cdc166ca19b32099b39109233bc006ff4282066c90366cdc8208cee66cd19b31099b3366cc19b2c0d9b350c6233b4066cb42820099b34145233b19b2f04282066cb99b2b0d9b31104233ac006ff59b24099b2f1c3233a8006ff41c2a099b2c182233a400a0819b27099b2a101233a17a29056d2b5e8842669a43388ce5⟩,
  ⟨0x12208a83f01d80d506282c814408f03f01940aa03f018808c026000, 0x19c21059c3010d234a99c2e670b02670b59c26670a03670bc3188d29019c2066fa02670b86508d28670ac166fa19c206709c3670b0406d2349c01810f9ec3670ac612f2349801810f9ed9be8119c291c4b88d25006041ce60d9c26184b48d2466fec166fb19bf6099bfd109234880459bb366fa0366fec8208d2166fe19bf5099bf766fd19bf00d9bf90c623480066fc59bb3099bf8145233fd9bf3059bb366fc99bef0d9bf5104233f80459be8099bf31c3233f40441ce9099bf0182233f0066ecd9beb099bee101233ed9b6c059b6966cf8266db43388cf8⟩,
  ⟨0x132091043c1fe0e606b03001640a404581ec0ca05101d0098026000, 0x1442c3c0d9cac184bc8d3c001442c3c671c44672a8712e234ec0051079ac36729c612d234e99c7c671e82671ed9c79671d83671f43188d38019c72670e02671f05148d37671e01670e19c77671d43671e84108d36019c71059c78145ac8d35001e6c059c76145a88d34671b19c6a099c6b671a59c640d9c6d0c6234cc0670f96d26099c6c145234c99c68056d266719d9c630d9c6a104234c40670f19c3a670e03671a060ae234c00670f19c3a670e16d26119c65145a48d2f001e75079cc1e6d0d9c62145a08d2e2ecc012ec98bb2a099c340ce234b59c30059c2d670882670c43388d2b⟩,
  ⟨0x11007e03a01ba0d005e82c014009003f81c40c004d020009c02e000, 0x4bf9414bf912fbe099d300c1f08d704bed014278909e1099d2f0c1f08d6f000673cc616c235b4079d099cf2143888d6c673ac1673a59ce3099cec0ce235a80673881673ac4348d69019ce0672d02673a86508d6801e741e710d9ce7184b48d67019cb4670e82672f4507f235940079c81672ec507e235900672d59c3a099cb9142ac8d63672c41672b99ca3099cb20ce235840672881672c44348d60672bd9cad099cae6729d9ca90d9cb00c6234fc0672819c71099caf194234f99cac059c71672819ca80d9cad101b48d3d⟩,
  ⟨0x14409884782220f807403441820ae04f02140ea05f028810c058000, 0x1e1d811e1c4786b09aa7b1092369d9da0059d7d675c82676843388da0019d71059da010d235fd9d7e675f02675f59d76675e03675fc3188d7e019d6f675802675f86508d7d675ec1675819d6f675dc3675f0406d235f001810f3e83675ec612f235ec01810f3e99d60119d791c4b88d7a006041e710d9d76184b48d79675ad9d69099d6a675a19d650d9d6c0c6235dc0675859c3c099d6b145235d99d67059c3c675999d640d9d69104235d406758016759c516b235d00079d0167594516a235cd9d31052fb74bee0687a0d2ff1101b48d724befd9d304bf999d2f428ac54bee12fbe4bf9109e142788687a199d310c5848d71⟩,
  ⟨0x1530a004cc23410a079838c1a00c0056826810e06e02e8118028000, 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⟩,
  ⟨0x11008003bc1be0cc05f82bc13c08f03e01ac0a40420160078020000, 0x1af6c6bdb426bde86508dfa0028a36bdb426bddc50eb237e400700708026bdd450ea237e1af6305af616bce026bd903388df601af3705af6310d237d406bcd1af3509af62194237d000e8bdaf3509af3f143bc8df3006076c826bcf450ea237c9af2a05aefc6bc9426bcb04248df001166ebdaebe0daf2a208237bdaf276bc9026bc99af236bbfc36bca03188dee01af2066ebc26bc9c5148ded6bc88166ebdaf216bbf836bc904108dec0116baf826bc8870c8deb0110738c26bbfc6088dea019baf6bbc826bbf44048de9⟩,
  ⟨0x12a08d04101ea0e706b831016209a04301c80be04801a008001a000, 0x1bd79470dc26f6805148e386f5ec1470ddbd7a6f5dc36f5f44108e37016edbd7009bd7b1c3238d805bb5e309bd78182238d40470ddbd7309bd76101238d06cf0046cbe1b2e026f4e84248e326bfc016bfb1afe809aff10ce238adafee05af356bfadaf660daff0101b48e2a001e23076c81db30dafee141b08e29003a2f6bcd438fb0dafed141808e286becc16beb1afae09afb510923885afb105af6d6bea5af650dafb3101b48e20001e21076c01db10dafb1141b08dff0038ef6bdb438780dafad141808dfd6bdec16bde5af7009af7c0ce237f006bdbc16bdec4348dfb⟩,
  ⟨0xe306802f416009704381c00c004d01f00ac032000, 0x6f3f046f351bcdc26f9f03388e666f6e016f6d5bdaa09bdb90ce2399006f6a416f6e04348e636f6d9bdb409bdb56f6b9bdb00dbdb70c62398806f6a1bd7009bdb619423985bdb305bd706f6a1bdaf0dbdb4101b48e60001445bb00dbdb3184bc8e3f001445bb06f5c046f6c4712e238f800515e20dbdae184b48e3d6f68c16f5d1bd7e09bda5109238ec05bb470ddbd700dbda3208238e9bda06f5f426f5fdbd7c6f5e036f6843188e39⟩
]

def tableRRR : Table Block := .branch 13 tableRRRL tableRRRR

def tableRR : Table Block := .branch 25 tableRRL tableRRR

def tableR : Table Block := .branch 51 tableRL tableRR

def table : Table Block := .branch 0x65 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table (32 * (i / 16) + i % 16)

end PolicyRewriteParametricPacked0


namespace PolicyCircuitPacked1
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x6c033818c0be05b02b814c09e04b023810c07e03b01c00d406402f01600a404c023010007403401700a004401c00b0040014004000, 0x66f018019bc7c19ab7819aa7419aa7019a76c19a76819646419636019635c19225818fc55ff547ef4ded9276f45cf5073d3dce8e6f735bd8c6f62dad4a6af251e484321cff463fd14ff043bd0ced42401⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x71d82801c7507f071d01f81c7407d071cc1f01c7307b071981e81c66079070c81e01c32077070b01d81b7d07506cbc1d01b2e07306cac1c81b2b07106ba81c01ae806f06ba01b81ae706d06b9c1b01aba06b06a981a81aa0069069a81a01a6a0670699c1981a3c065068901901a230630688c18819e2061⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x78c83801dfc0bf077f02f81dfb0bd077e82f01dfa0bb077e42e81de80b9076d02e01db40b7076b82d81d790b5075e42d01d760b3075d82c81d350b1074cc2c01d330af074c82b81d320ad074942b01ceb0ab073ac2a81cbb0a9072e82a01cba0a7072dc2981cb70a5072d82901cac0a3072b02881c760a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x7ce04801f380ff07ce03f81f250fd07c943f01f250fb07c903e81f240f907c843e01f210f707c803d81ee00f507b803d01ebf0f307af83c81ebd0f107af43c01ebc0ef07ac03b81eb00ed079f03b01e7c0eb079d83a81e630e90798c3a01e630e7079883981e620e5078fc3901e3f0e3078f83881e320e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa1c4580286e13f0a1b04f8286813d0a19c4f0286213b0a0f84e8283b1390a0e04e028361370a0c84d828311350a0c04d028231330a0844c81ffd13107fec4c01ff012f07fb04b81feb12d07fac4b01fea12b07f804a81fa612907e984a01fa512707e904981fa312507ddc4901f7112307cf84881f3e121⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa4dc680293317f0a4bc5f8292e17d0a4b45f0292b17b0a49c5e829231790a4885e029201770a3cc5d828ec1750a3a05d028e81730a39c5c828e61710a3945c028e116f0a3805b828bf16d0a2ec5b028b816b0a2e05a828ac1690a2a85a028a81670a1f4598287b1650a1e459028751630a1d05882872161⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xa8887802a201bf0a7f06f829fb1bd0a7e86f029ec1bb0a79c6e829e71b90a7886e029e21b70a7806d829e01b50a6f46d029b71b30a6c86c829a81b10a6946c029a51af0a6946b829a41ad0a68c6b029a31ab0a5cc6a8296d1a90a5a06a029661a70a59069829631a50a58c69029601a30a4e868829381a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xabb48802ae71ff0ab8c7f82ae21fd0ab847f02abf1fb0aaf87e82abd1f90aaf47e02ab81f70aadc7d82ab41f50aaa47d02aa81f30aa9c7c82aa01f10a9f87c02a7a1ef0a9e07b82a6a1ed0a9947b02a631eb0a8fc7a82a361e90a8d07a02a321e70a8bc7982a2d1e50a8b07902a281e30a89c7882a251e1⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xafcc9802bee23f0afac8f82be923d0af988f02be423b0af808e82bbf2390aef88e02bb72370aecc8d82bb02350aeac8d02baa2330ae948c82ba42310adf08c02b7a22f0ade48b82b7422d0adc48b02b6d22b0ada08a82b672290ad9c8a02b632270ad888982b3b2250ac848902aff2230abe48882af3221⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb2b4a802caa27f0b2a09f82ca627d0b2889f02c7f27b0b1f09e82c7c2790b1e89e02c782770b1d49d82c712750b1bc9d02c6a2730b1a49c82c672710b1949c02c6226f0b1809b82c3e26d0b0cc9b02c3226b0b0b89a82c2a2690b0a09a02c252670b08c9982c212650aff89902bfa2630afe09882bf4261⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb5d8b802d742bf0b5c8af82d6f2bd0b5b4af02d6a2bb0b598ae82d642b90b4fcae02d392b70b4dcad82d342b50b4c0ad02d2e2b30b490ac82d222b10b480ac02cff2af0b3ecab82cf92ad0b3d8ab02cf62ab0b3ccaa82cf12a90b3b4aa02ceb2a70b2f8a982cbd2a50b2eca902cb82a30b2d0a882cb22a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xb9a8c802e682ff0b988bf82e602fd0b8f8bf02e3a2fb0b8e4be82e362f90b8a8be02e292f70b880bd82dfa2f50b7dcbd02df22f30b7b8bc82dea2f10b79cbc02de32ef0b780bb82dbe2ed0b6e4bb02db62eb0b6ccba82db12e90b6b8ba02daa2e70b6a0b982da32e50b684b902d7e2e30b5f0b882d7a2e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xbcc0d802f2e33f0bca8cf82f2933d0bc88cf02eff33b0bbf0ce82efa3390bbe0ce02ef53370bbb8cd82eed3350bba4cd02ee63330bb8ccc82ee13310baf4cc02ebc32f0baeccb82eaf32d0bab4cb02eab32b0baa4ca82ea63290ba90ca02ea03270b9f8c982e763250b9d4c902e733230b9c4c882e6e321⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xbfd8e802ff237f0bfc4df82ff037d0bfa0df02fe737b0bf90de82fe33790bf84de02fbe3770bee4dd82fb73750bed4dd02fae3730beb4dc82fac3710bea8dc02fa736f0bdf4db82f7c36d0bde0db02f7636b0bdccda82f713690bdacda02f633670bd84d982f3f3650bce4d902f383630bcd4d882f33361⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xe3c4f8038eb3bf0e39cef838e63bd0e38cef038e23bb0e2f8ee838bd3b90e2ecee038b93b70e2e0ed838b43b50e2c8ed038ad3b30e2a4ec838a53b10e290ec0387e3af0e1f0eb838623ad0e0dceb038363ab0e0ccea838323a90e0c4ea0382f3a70e0a4e9838263a50e088e902ffb3a30bfe8e882ffa3a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xe6e508039b83ff0e6c4ff839ab3fd0e6acff039a43fb0e688fe839a23f90e5b0fe039693f70e5a0fd839673f50e58cfd039623f30e580fc8393f3f10e4f4fc0393b3ef0e4e8fb839363ed0e4d0fb039323eb0e4bcfa8392a3e90e4a0fa039213e70e3f0f9838fa3e50e3e4f9038f63e30e3ccf8838f23e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xeab11803aaa43f0ea990f83aa443d0e9f10f03a7a43b0e9dd0e83a734390e9c50e03a6b4370e9a50d83a674350e9910d03a614330e8fd0c83a3d4310e8e10c03a3742f0e8d10b83a2842d0e89d0b039ff42b0e7f50a839fa4290e7d90a039f44270e7b109839ea4250e7a109039e44230e6f908839be421⟩
]

def tableLLL : Table Block := .branch 8 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xeddd2803b7347f0edc91f83b6047d0ecfd1f03b3d47b0ecf11e83b394790ecd91e03b334770ecb11d83b2b4750ec9d1d03b244730ec851c83aff4710ebed1c03afa46f0ebe51b83af146d0ebbd1b03aee46b0eba51a83ae64690eb8d1a03abe4670eaed1983ab94650eadd1903ab44630eac91883ab1461⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf1c53803c6f4bf0f1b92f83c6c4bd0f1ad2f03c674bb0f1912e83c3c4b90f0d92e03c324b70f0c52d83c2c4b50f0a12d03c254b30f08d2c83c214b10efe92c03bf84af0efd52b83bf14ad0efbd2b03be84ab0ef992a83be44a90eed12a03bb34a70eeb92983ba44a50ee8d2903b7f4a30edf12883b794a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf4914803d234ff0f3f93f83cf84fd0f3d13f03cf24fb0f3b93e83ced4f90f3b13e03cec4f70f3ad3d83ce84f50f3a13d03ce74f30f3953c83ce14f10f2fd3c03cb94ef0f2d93b83cb44ed0f2c93b03cad4eb0f2b53a83cab4e90f2ad3a03cab4e70f2a53983ca84e50f2953903c7a4e30f1e53883c784e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xf8a15803e2653f0f7fd4f83dfd53d0f7f14f03df953b0f7dd4e83df55390f7d14e03dee5370f7a54d83de95350f69d4d03da25330f6854c83da15310f6814c03d7d52f0f5f54b83d7852d0f5d94b03d7452b0f5c14a83d6e5290f5b54a03d6b5270f5a94983d685250f5954903d645230f5894883d26521⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0xfba56803ee357f0faf55f83eba57d0fad55f03eb157b0fab95e83eab5790faa55e03ea75770fa8d5d83ea15750f9fd5d03e7b5730f9dd5c83e765710f9d55c03e7556f0f9d15b83e7256d0f9b95b03e6d56b0f9b55a83e6c5690f9a15a03e605670f8f95983e3a5650f8e15903e315630f8bd5883e2c561⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x120817803fe65bf0ff956f83fe25bd0fedd6f03fb65bb0fed16e83fa45b90fde56e03f755b70fdbd6d83f6e5b50fdb16d03f6b5b30fd916c83f635b10fd816c03f3a5af0fcd16b83f325ad0fcbd6b03f2b5ab0fca56a83f245a90fbfd6a03efd5a70fbe96983ef65a50fbd16903ef25a30fbbd6883eeb5a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x123e588048f75ff123d57f848f35fd123c17f048ec5fb123a97e848e75f91238d7e048e15f7122f17d848ba5f5122d97d048b45f3122b97c848ac5f1122a57c048a55ef1228d7b848795ed121d97b048745eb121c97a8486d5e9121ad7a048695e71219579848635e512185790483d5e31209578848215e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x127e198049f663f127cd8f849ef63d127b58f049e563b1278d8e849e0639126f18e049ba637126c58d849af635126b18d049a8633126998c849a0631125f98c0497b62f125dd8b8497562d125818b0493f62b124e98a84936629124c58a0492f627124b5898492a6251249d89049256231248d88848fb621⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x12ce5a804b3767f12cad9f84b2567d12c8d9f04b2167b12bf99e84aee67912a8d9e04aa0677129f19d84a7b675129d19d04a72673129c19c84a6e671129ad9c04a6566f129899b84a6066d128f99b04a3a66b128d19a84a34669128b99a04a2b667128a59984a286651288999049ff663127f598849fb661⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x12fb1b804be96bf12f99af84be46bd12ef1af04bbb6bb12ee1ae84bb76b912ed9ae04bb56b712ed5ad84bb36b512ebdad04bae6b312eb5ac84bac6b112eb1ac04ba96af12e99ab84ba46ad12e81ab04b7e6ab12de1aa84b756a912dcdaa04b6e6a712dada984b696a512d95a904b636a312cf9a884b3b6a1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x133adc804ce96ff1338dbf84cbf6fd132f5bf04cb56fb132d1be84cb16f913299be04c6b6f7131a9bd84c676f513199bd04c656f313189bc84c616f113181bc04c396ef130ddbb84c346ed130bdbb04c2d6eb13099ba84c236e913089ba04c206e712fe5b984bf56e512fd1b904bf26e312fc5b884bef6e1⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x136edd804db973f136ddcf84db573d136c9cf04dad73b136adce84da1739135f1ce04d76737135d1cd84d6f735135b5cd04d6b733135a1cc84d63731134f5cc04d3a72f134d5cb84d3372d134adcb04d2972b134a1ca84d277291348dca04d2272713481c984cf7725133d1c904cf2723133c1c884ced721⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x139e5e804e7577f139cddf84e6b77d1399ddf04e6577b1398dde84e3f779138f5de04e39777138dddd84e2f775138a9dd04e29773138a5dc84e2577113891dc04dff76f137f9db84df976d137e1db04df576b137c5da84def7691379dda04de576713791d984de376513785d904de0763136fdd884dbc761⟩,
  ⟨0xa004d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x13d9df804f667bf13d89ef84f3f7bd13ccdef04f317bb13cb9ee84f2a7b913ca1ee04f207b713bf9ed84ef97b513bdded04ef47b313bc9ec84ef07b113bb1ec04eea7af13b99eb84ee17ad13afdeb04ebc7ab13ae1ea84eb67a913ab1ea04ea97a713a9de984ea57a5139fde904e7f7a3139f9e884e7c7a1⟩,
  ⟨0xa104d825812208c04382080fa07803981b80d206402f81680aa050025811808203c01b80c805a0280118078032014007802800a000, 0x586006080583d7ff160f1ff8583a7fd160ddff058357fb160c9fe8582d7f9160adfe058237f716085fd84ff87f513fd1fd04ff27f313fc9fc84fed7f113fb5fc04fe37ef13ef9fb84fb47ed13ec5fb04fb17eb13ec5fa84fb17e913ec1fa04fb07e713e81f984f7c7e513dd5f904f737e313dc9f884f6e7e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1659c186016594183f164ec183e164d4183d164d4183c164c0183b164bc183a164a018391648c1838163d41837163cc18361638c1835162fc1834162e01833162d41832162d01831162c81830162bc182f162a8182e162a0182d16288182c161e0182b161d8182a161d81829161c81828161c01827161a01826161981825161941824161901823161881822161841821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1688418a0167f4187f167e4187e167dc187d167d0187c167d0187b167b8187a167a41879167a018781679018771678c1876167801875166f81874166ec1873166ec1872166e81871166d81870166cc186f166c4186e166b8186d166a8186c166a0186b16684186a166801869165f81868165e81867165d41866165d01865165c41864165bc1863165b01862165a41861⟩
]

def tableLLR : Table Block := .branch 8 tableLLRL tableLLRR

def tableLL : Table Block := .branch 17 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x16ad818e016acc18bf16ac018be16ab818bd16ab418bc16aa018bb16a9018ba16a8818b916a8018b8169f418b7169ec18b6169e018b5169d018b4169c818b3169b018b2169a418b11699c18b01698818af168f418ae168f018ad168f018ac168e018ab168dc18aa168dc18a9168d818a8168c818a7168bc18a6168b018a5168a818a4168a018a31689c18a21688818a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x16da4192016da018ff16d8018fe16cf018fd16ce018fc16cd818fb16cd018fa16ccc18f916cc818f816cb418f716cac18f616c9c18f516c9418f416c8418f316bfc18f216bf818f116bf418f016be018ef16bdc18ee16bcc18ed16bc818ec16bc018eb16bb818ea16bb418e916ba818e816b9018e716b8818e616b8018e516afc18e416af818e316ae018e216adc18e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x170b81960170a4193f17084193e16ff4193d16fe8193c16fe0193b16fd0193a16fc8193916f9c193816f8c193716f88193616f84193516eec193416ee8193316ed8193216ed4193116ec0193016eb8192f16eb4192e16ea0192d16e94192c16e88192b16e80192a16df8192916df4192816df0192716de0192616ddc192516dd0192416dc8192316dbc192216db41921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x173a819a017398197f17394197e17390197d17380197c172e4197b172d4197a172c41979172c01978172bc1977172ac1976172a81975172a019741729819731728c1972172881971171f81970171f4196f171e4196e171d8196d171c8196c171b4196b171b0196a171981969171901968171881967170ec1966170e81965170e01964170d41963170cc1962170bc1961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x176b019e0176a019bf1769c19be1769019bd1768819bc175f819bb175e419ba175e019b9175e019b8175d419b7175cc19b6175c019b51759019b41758419b3174f819b2174f019b1174ec19b0174dc19af174d819ae174c819ad174bc19ac174a819ab1749819aa1749419a91749019a81748019a7173f019a6173e419a5173c819a4173c419a3173bc19a2173b019a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x179e01a20179cc19ff179c019fe179bc19fd179b419fc1799c19fb1798c19fa1798c19f91798819f81798419f7178f019f6178ec19f5178e019f4178ac19f31789819f21788819f11788419f0177fc19ef177c019ee177b819ed177a819ec177a419eb177a019ea1778019e9176f819e8176e819e7176e019e6176c819e5176c019e4176b819e3176b819e2176b419e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x17d8c1a6017d841a3f17cfc1a3e17cf41a3d17cdc1a3c17cd01a3b17cc81a3a17cc01a3917cb41a3817cac1a3717ca01a3617c901a3517c881a3417bec1a3317be41a3217bd41a3117bcc1a3017bac1a2f17b9c1a2e17b981a2d17b941a2c17aec1a2b17ae41a2a17ac01a2917abc1a2817ab81a2717ab41a2617ab01a2517aa41a2417aa01a2317a9c1a2217a941a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a0c01aa01a0a81a7f1a0981a7e1a0941a7d1a0901a7c1a08c1a7b17fec1a7a17fe41a7917fd81a7817fd01a7717fc81a7617fc41a7517fac1a7417fa81a7317f901a7217f881a7117f801a7017ee81a6f17ee41a6e17edc1a6d17ecc1a6c17eb41a6b17ea81a6a17ea01a6917e941a6817e881a6717df41a6617de41a6517de01a6417dd41a6317db41a6217dac1a61⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a3b41ae01a3b01abf1a3ac1abe1a3a01abd1a39c1abc1a3881abb1a3841aba1a2fc1ab91a2f41ab81a2ec1ab71a2e01ab61a2d01ab51a2c81ab41a2b01ab31a29c1ab21a2981ab11a2881ab01a2841aaf1a1f01aae1a1ec1aad1a1dc1aac1a1d01aab1a1c81aaa1a1c01aa91a1b41aa81a1ac1aa71a1a01aa61a1901aa51a1881aa41a0e01aa31a0d81aa21a0c81aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1a7a01b201a7941aff1a7801afe1a6fc1afd1a6f01afc1a6e41afb1a6e01afa1a6d41af91a6a81af81a6a41af71a6a01af61a6941af51a6901af41a68c1af31a68c1af21a68c1af11a6841af01a6801aef1a5fc1aee1a5e81aed1a5e01aec1a5c81aeb1a5b81aea1a5b01ae91a5a01ae81a5941ae71a58c1ae61a5841ae51a4ec1ae41a4e81ae31a4dc1ae21a4b01ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1aae81b601aae41b3f1aae01b3e1aac81b3d1aac41b3c1a9f41b3b1a9b41b3a1a9a41b391a99c1b381a99c1b371a9881b361a9801b351a9801b341a8e01b331a8cc1b321a8a41b311a8981b301a8981b2f1a8941b2e1a8881b2d1a8801b2c1a7dc1b2b1a7d81b2a1a7d41b291a7d41b281a7c81b271a7c01b261a7bc1b251a7a81b241a7a81b231a7a41b221a7a01b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b1d41ba01b1cc1b7f1b1c81b7e1b1b81b7d1b1b41b7c1b19c1b7b1b1881b7a1b0fc1b791b0f41b781b0ec1b771b0dc1b761b0d41b751b0c81b741b0c01b731b0bc1b721b0ac1b711b0a81b701b0a01b6f1b0981b6e1b08c1b6d1b0801b6c1aff01b6b1afd41b6a1ae841b691adfc1b681adf41b671add81b661aca81b651aca41b641ab8c1b631ab881b621aaf81b61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b4b41be01b4b41bbf1b4ac1bbe1b4a41bbd1b4981bbc1b4941bbb1b4881bba1b3dc1bb91b3d81bb81b3d41bb71b3c01bb61b3ac1bb51b3a81bb41b3a81bb31b3941bb21b3901bb11b3881bb01b2f81baf1b2f01bae1b2dc1bad1b2cc1bac1b2c01bab1b2bc1baa1b2ac1ba91b2a81ba81b2a01ba71b2981ba61b2941ba51b2881ba41b1ec1ba31b1e81ba21b1dc1ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1b7dc1c201b7d81bff1b7d01bfe1b7cc1bfd1b7c41bfc1b7c01bfb1b7a81bfa1b6f41bf91b6e01bf81b6d41bf71b6c41bf61b6bc1bf51b6a41bf41b69c1bf31b6841bf21b6801bf11b5f01bf01b5ec1bef1b5e81bee1b5d81bed1b5ac1bec1b5a41beb1b5801bea1b4f81be91b4f41be81b4ec1be71b4e81be61b4d41be51b4d41be41b4d01be31b4cc1be21b4b41be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1baf81c601bae81c3f1bae41c3e1bad01c3d1bac01c3c1bab01c3b1baac1c3a1ba941c391ba8c1c381ba881c371b9f81c361b9f41c351b9ec1c341b9e41c331b9e01c321b9d01c311b9c41c301b9b01c2f1b9b01c2e1b9ac1c2d1b9981c2c1b9881c2b1b9841c2a1b8ec1c291b8e41c281b8a41c271b8a01c261b8941c251b8901c241b88c1c231b8841c221b7ec1c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1bfdc1ca01bfd01c7f1bfcc1c7e1bfc81c7d1bfbc1c7c1bfb41c7b1bfac1c7a1bfa01c791bf8c1c781bf841c771bee41c761bee01c751bedc1c741bec81c731bcf01c721bce01c711bcdc1c701bcd01c6f1bcc01c6e1bcbc1c6d1bcb81c6c1bca81c6b1bc8c1c6a1bbe81c691bbe41c681bbd01c671bbc81c661bbb81c651bbb01c641bb881c631bb841c621bb801c61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1e3d01ce01e3c81cbf1e3c41cbe1e3bc1cbd1e3b01cbc1e3ac1cbb1e3901cba1e3841cb91e2f81cb81e2dc1cb71e2c01cb61e1f81cb51e1f01cb41e1ec1cb31e1c81cb21e1bc1cb11e1ac1cb01e1941caf1e1841cae1e0ec1cad1e0ec1cac1e0e81cab1e0e01caa1e0dc1ca91e0c41ca81e0c01ca71e0b81ca61e0941ca51e08c1ca41bfec1ca31bfe41ca21bfe01ca1⟩
]

def tableLRL : Table Block := .branch 8 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1e7881d201e7841cff1e7801cfe1e6fc1cfd1e6f41cfc1e6f01cfb1e6e01cfa1e6dc1cf91e6d41cf81e6cc1cf71e6c81cf61e6b81cf51e6ac1cf41e6a41cf31e6881cf21e5fc1cf11e5f81cf01e5f41cef1e5e81cee1e5e41ced1e5bc1cec1e5a81ceb1e5a01cea1e5801ce91e4f81ce81e4f01ce71e4d41ce61e4cc1ce51e4c01ce41e4b01ce31e4a81ce21e3e01ce1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1eaa41d601ea901d3f1ea881d3e1ea841d3d1ea801d3c1e9f81d3b1e9e81d3a1e9d01d391e9c81d381e9b81d371e9b01d361e9941d351e98c1d341e8fc1d331e8f41d321e8d01d311e8c81d301e8bc1d2f1e8b41d2e1e8a01d2d1e8901d2c1e88c1d2b1e8801d2a1e7fc1d291e7f41d281e7e81d271e7d81d261e7cc1d251e7b81d241e7a81d231e7a41d221e7981d21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1ede41da01ede01d7f1edcc1d7e1edc01d7d1edb81d7c1edb01d7b1eda81d7a1ed9c1d791ed801d781ecfc1d771ecec1d761ece01d751ecd41d741eccc1d731ecbc1d721ecb81d711ec941d701ec8c1d6f1ec801d6e1ebe41d6d1ebe01d6c1ebd01d6b1ebc81d6a1ebbc1d691ebb41d681eba41d671eba01d661eaf81d651eae81d641eacc1d631eac41d621eabc1d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f0f01de01f0ec1dbf1f0e81dbe1f0e41dbd1f0cc1dbc1f0c01dbb1f0a01dba1f08c1db91f0841db81f0801db71eff81db61efe01db51efd01db41efd01db31efcc1db21efc81db11efb81db01efb41daf1ef801dae1eef41dad1eee01dac1eedc1dab1eec81daa1eec41da91eeb41da81eeb01da71ee9c1da61ee941da51ee841da41edfc1da31edf81da21edf01da1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f4841e201f4801dff1f3fc1dfe1f3f41dfd1f3ec1dfc1f3e01dfb1f3dc1dfa1f3d41df91f3cc1df81f3c41df71f3b81df61f3a41df51f39c1df41f3801df31f2ec1df21f2e01df11f2d41df01f2cc1def1f2b81dee1f2a01ded1f29c1dec1f2941deb1f28c1dea1f1f41de91f1e41de81f1dc1de71f1c81de61f1b81de51f1b01de41f1901de31f0fc1de21f0f81de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1f7b01e601f7b01e3f1f7a81e3e1f7a41e3d1f7a01e3c1f7981e3b1f7881e3a1f7801e391f6dc1e381f6d81e371f6c81e361f6c41e351f6c01e341f6901e331f68c1e321f6801e311f5d41e301f5d01e2f1f5cc1e2e1f5bc1e2d1f59c1e2c1f5841e2b1f5841e2a1f4fc1e291f4f41e281f4ec1e271f4d41e261f4d01e251f4c41e241f4b41e231f4ac1e221f48c1e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1fb941ea01faf41e7f1fae41e7e1fadc1e7d1fadc1e7c1fac81e7b1fac81e7a1fac01e791faa01e781fa8c1e771f9e41e761f9e01e751f9dc1e741f9d81e731f9d81e721f9d81e711f9d41e701f9d41e6f1f9941e6e1f8fc1e6d1f8e81e6c1f8e01e6b1f8d41e6a1f8bc1e691f8b01e681f8a81e671f8981e661f8941e651f8881e641f7dc1e631f7d81e621f7d41e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x1fec81ee01fec41ebf1feb01ebe1feac1ebd1fe9c1ebc1fe981ebb1fe8c1eba1fe841eb91fdfc1eb81fde01eb71fdd81eb61fdcc1eb51fdc41eb41fdb81eb31fdb01eb21fda01eb11fd901eb01fcfc1eaf1fce01eae1fcc81ead1fcb81eac1fcb81eab1fcb41eaa1fca41ea91fca01ea81fca01ea71fc9c1ea61fc901ea51fbd41ea41fbc01ea31fbb01ea21fb981ea1⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x221d01f20221c41eff221b81efe2219c1efd221941efc2218c1efb221881efa221841ef9220dc1ef8220c81ef7220c41ef6220b81ef5220b01ef4220ac1ef3220981ef22208c1ef1220841ef01fffc1eef1fff81eee1ffe81eed1ffe41eec1ffdc1eeb1ffd41eea1ffc81ee91ffb81ee81ffb01ee71ff9c1ee61ff881ee51fef41ee41fedc1ee31fedc1ee21fecc1ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x224e81f60224e01f3f224d41f3e224c01f3d224b81f3c224901f3b224901f3a223f81f39223f01f38223d01f37223cc1f36223c41f35223c01f34223bc1f33223b41f32223b01f31223801f30222f81f2f222f41f2e222e01f2d222d81f2c222d41f2b222c81f2a222c01f29222b41f28222a41f272229c1f26222881f25222801f24221fc1f23221ec1f22221dc1f21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x228f01fa0228e41f7f228d41f7e228cc1f7d228c81f7c228bc1f7b228b41f7a2289c1f792288c1f78228841f77227e81f76227e01f75227d01f74227c01f73227b41f72227b01f71227981f70227901f6f226f81f6e226e81f6d226e01f6c226c81f6b226c41f6a226b81f692268c1f68225b01f67225901f662258c1f65225881f64224fc1f63224f81f62224f01f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x22bf81fe022bec1fbf22be41fbe22bd41fbd22bd01fbc22bb41fbb22ba81fba22b981fb922b841fb822afc1fb722af41fb622ae01fb522ad01fb422acc1fb322ac81fb222ac41fb122ab41fb022ab01faf22aa81fae22aa41fad22a9c1fac22a941fab22a901faa22a841fa9229e81fa8229dc1fa7229d01fa6229c01fa5229ac1fa4229a81fa3229981fa2228f81fa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x22ebc282022eb41fff22ea81ffe22e941ffd22e901ffc22df81ffb22df01ffa22de81ff922de01ff822ddc1ff722dd81ff622dc81ff522dc41ff422db81ff322db01ff222da01ff122d8c1ff022d881fef22cf81fee22cf01fed22ce41fec22cdc1feb22cd41fea22cc41fe922cbc1fe822cac1fe722ca41fe622c9c1fe522c981fe422c941fe322c841fe222c801fe1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x231a0286023194283f2318c283e230fc283d230f8283c230f4283b230f4283a230f02839230dc2838230cc2837230bc2836230ac28352309428342308c283322ff4283222ff0283122fe4283022fe0282f22fdc282e22fcc282d22fc4282c22fb4282b22fb0282a22f9c282922f8c282822f88282722ef0282622ee0282522ee0282422edc282322ed0282222ec82821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x234b428a0233e8287f233d8287e233d0287d233c4287c233bc287b233b0287a233a028792339c2878233982877232f42876232e42875232e02874232dc2873232c42872232c02871232b02870232ac286f232a0286e23298286d23290286c2328c286b231fc286a231f02869231e02868231d82867231d02866231cc2865231c82864231b82863231b42862231a82861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x23be028e023bdc28bf23bd828be23ab428bd23aa828bc23aa828bb239c428ba239c028b92399828b8238fc28b7238f828b6238f028b5238e028b4238c028b3238b828b2238b028b1238a828b0237bc28af237a828ae237a028ad2379028ac2378828ab236f828aa2368028a9235fc28a8235b828a7235a428a62359c28a52359028a4234f828a3234e428a2234c828a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x23ef8292023ef428ff23ef028fe23ee428fd23ee028fc23edc28fb23ed428fa23ec028f923eac28f823ea428f723e9c28f623e9028f523df428f423dd028f323da028f223d9428f123d8828f023d8028ef23cf828ee23cf428ed23cec28ec23ce428eb23cd828ea23cd028e923cc428e823cb028e723ca828e623c8c28e523c8828e423bfc28e323bf428e223be428e1⟩
]

def tableLRR : Table Block := .branch 8 tableLRRL tableLRRR

def tableLR : Table Block := .branch 17 tableLRL tableLRR

def tableL : Table Block := .branch 34 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x262ec2960262e0293f262d4293e262c4293d262bc293c262b4293b262ac293a262a82939262842938261f42937261dc2936261d02935261b02934261a829332619c29322618c2931261882930260e0292f260d4292e260cc292d23ffc292c23ff8292b23ff0292a23fd8292923fd4292823fc8292723fb8292623fb0292523f90292423f88292323f84292223f802921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x266ec29a0266e4297f266cc297e266b8297d266ac297c266a4297b2669c297a266902979266882978265f82977265f02976265c82975265b82974265b42973264e42972264cc2971264cc2970264c8296f264c4296e264c0296d264b8296c264b0296b264a8296a263d42969263c82968263c42967263bc2966263b42965263ac2964263a029632638c2962263842961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x26ab029e026a9829bf26a8829be26a8429bd269ec29bc269dc29bb269d429ba269cc29b9269bc29b8269b429b7269a029b62698c29b52698429b4268f829b3268e829b2268e029b1268c029b0268b029af268ac29ae2689829ad2688c29ac2688429ab267fc29aa267f029a9267ec29a8267d829a7267d029a6267c829a5267b829a4267a029a32679c29a22678029a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x26da82a2026da029ff26d9829fe26d8c29fd26d8829fc26d8029fb26cf429fa26ce429f926cdc29f826cc829f726cc029f626cb429f526ca429f426c9c29f326bf429f226be829f126be029f026bd829ef26bc429ee26bbc29ed26bb429ec26ba029eb26b9829ea26b8c29e926b8829e826b8029e726af429e626ae429e526adc29e426acc29e326ac029e226ab829e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2729c2a602728c2a3f272842a3e271e02a3d271902a3c270bc2a3b270b42a3a270a82a39270a02a38270942a37270842a3626ffc2a3526fe82a3426fdc2a3326fd02a3226fc82a3126fc02a3026fb02a2f26fa82a2e26f9c2a2d26f8c2a2c26f842a2b26ee82a2a26ed42a2926ec42a2826ec02a2726e9c2a2626e942a2526e8c2a2426de42a2326de02a2226dcc2a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x277f42aa0277e02a7f277dc2a7e277d02a7d277a02a7c276f42a7b276f02a7a276d42a79276cc2a78276b82a77276b42a762769c2a75276942a74276882a73275f82a72275f02a71275e02a70275cc2a6f275b82a6e275802a6d274fc2a6c274d42a6b274cc2a6a274b42a69274ac2a682749c2a67274942a66274882a65273f02a64272b42a63272b02a62272a82a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x27c982ae027c8c2abf27c802abe27bd02abd27bc42abc27bb42abb27bac2aba27b902ab927b8c2ab827b882ab727af42ab627aec2ab527ae02ab427acc2ab327ac42ab2279b82ab1279ac2ab0279a82aaf279a82aae279a42aad2799c2aac279902aab279882aaa278fc2aa9278e82aa8278e02aa7278b02aa6278a82aa52789c2aa4278982aa3278942aa22788c2aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x27fdc2b2027fd82aff27fbc2afe27fa82afd27f942afc27f882afb27ef02afa27edc2af927ed82af827ed82af727ec42af627eb42af527eac2af427ea42af327e9c2af227e942af127dfc2af027df42aef27df02aee27dec2aed27ddc2aec27db02aeb27d9c2aea27d982ae927d842ae827cf42ae727cec2ae627cdc2ae527cc82ae427cb02ae327cac2ae227ca42ae1⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2a58c2b602a5882b3f2a4f42b3e2a4dc2b3d2a4d02b3c2a4c82b3b2a4b42b3a2a4b02b392a4b02b382a4a82b372a4982b362a4902b352a4882b342a4802b332a3b02b322a3902b312a3842b302a3802b2f2a2e02b2e2a2c02b2d2a2b42b2c2a2a02b2b2a29c2b2a2a1e42b292a1d42b282a1d02b272a1cc2b262a1c02b252a1bc2b242a1b82b232a1a82b222a08c2b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2a8902ba02a8802b7f2a7f82b7e2a7ec2b7d2a7e42b7c2a7dc2b7b2a7d82b7a2a7c42b792a7c02b782a7b42b772a7a82b762a7a02b752a7982b742a78c2b732a6fc2b722a6f42b712a6e02b702a6d02b6f2a6cc2b6e2a6ac2b6d2a6ac2b6c2a6902b6b2a6842b6a2a6802b692a5f82b682a5f42b672a5ec2b662a5d82b652a5cc2b642a5bc2b632a5a82b622a5a42b61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2acf42be02ace42bbf2acdc2bbe2ac882bbd2ac802bbc2abec2bbb2abdc2bba2abc42bb92abbc2bb82aba42bb72aba02bb62ab942bb52ab902bb42ab8c2bb32ab882bb22aad02bb12aa982bb02aa942baf2a9f82bae2a9f02bad2a9ec2bac2a99c2bab2a9942baa2a9882ba92a9842ba82a8f82ba72a8cc2ba62a8c82ba52a8bc2ba42a8b82ba32a8a42ba22a8a02ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b0fc2c202b0dc2bff2b0d82bfe2b0d02bfd2b0c82bfc2b0b42bfb2b0ac2bfa2b0882bf92b0842bf82b0842bf72b0802bf62aff82bf52aff42bf42afe82bf32afdc2bf22afd82bf12afcc2bf02afc82bef2afbc2bee2afb82bed2af842bec2aef82beb2aed02bea2aec82be92aebc2be82aea02be72adc42be62adc02be52adb02be42ada42be32ad802be22acfc2be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b49c2c602b48c2c3f2b4882c3e2b4802c3d2b3f02c3c2b3dc2c3b2b3d82c3a2b3d42c392b3c82c382b3b42c372b3a82c362b3982c352b3902c342b3842c332b2f42c322b2ec2c312b2d82c302b2cc2c2f2b2b02c2e2b2a82c2d2b2a02c2c2b2842c2b2b1fc2c2a2b1f42c292b1e82c282b1e02c272b1d82c262b1c82c252b1c02c242b1ac2c232b1942c222b1802c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2b8942ca02b88c2c7f2b8882c7e2b7dc2c7d2b7cc2c7c2b7c42c7b2b7c42c7a2b7b02c792b7b02c782b78c2c772b6f82c762b6d02c752b6c82c742b6bc2c732b6bc2c722b6bc2c712b6b82c702b6b82c6f2b6b42c6e2b5f42c6d2b5c82c6c2b5bc2c6b2b5b82c6a2b5b02c692b5a42c682b5902c672b5882c662b4c82c652b4c02c642b4b42c632b4ac2c622b4a02c61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2bcc82ce02bcc42cbf2bcbc2cbe2bca82cbd2bca02cbc2bc9c2cbb2bc842cba2bc802cb92bbf82cb82bbec2cb72bbe42cb62bbd02cb52bbc42cb42bbac2cb32bb9c2cb22bb882cb12bb842cb02baf42caf2bad42cae2bac42cad2ba842cac2b9fc2cab2b9f82caa2b9ac2ca92b9a02ca82b9982ca72b9942ca62b9802ca52b8fc2ca42b8b82ca32b8b02ca22b8a02ca1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2e1e02d202e1d42cff2e1cc2cfe2e1c82cfd2e1bc2cfc2e1b82cfb2e0bc2cfa2e0a82cf92e0a02cf82e0942cf72bffc2cf62bff42cf52bf902cf42becc2cf32beb82cf22bea82cf12be9c2cf02be842cef2bdfc2cee2bde42ced2bde02cec2bdd02ceb2bdcc2cea2bdcc2ce92bdc82ce82bdc42ce72bda82ce62bd942ce52bd8c2ce42bcfc2ce32bcf42ce22bcd82ce1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2e6882d602e6842d3f2e6802d3e2e5f82d3d2e5f42d3c2e5ec2d3b2e5dc2d3a2e5d02d392e5982d382e5902d372e4f82d362e4f42d352e4f02d342e4ec2d332e4dc2d322e4d82d312e4d42d302e4bc2d2f2e4a02d2e2e4982d2d2e4882d2c2e4802d2b2e3c42d2a2e3b42d292e3ac2d282e3a82d272e3a02d262e2942d252e2882d242e1f82d232e1f42d222e1f02d21⟩
]

def tableRLL : Table Block := .branch 8 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2e9b82da02e98c2d7f2e9882d7e2e9842d7d2e8f02d7c2e8d82d7b2e8982d7a2e8842d792e7f82d782e7ec2d772e7d42d762e7cc2d752e7c82d742e7b82d732e7b02d722e7ac2d712e7a42d702e7942d6f2e78c2d6e2e6f42d6d2e6e42d6c2e6e02d6b2e6d42d6a2e6cc2d692e6c82d682e6c82d672e6bc2d662e6ac2d652e6a82d642e6a42d632e6a42d622e6882d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2ecd82de02ecc02dbf2ecbc2dbe2ec982dbd2ec802dbc2ec802dbb2ebec2dba2ebec2db92ebe82db82ebc42db72ebac2db62eb982db52eb8c2db42eb802db32eb802db22eb802db12eb802db02eafc2daf2eafc2dae2eaf82dad2eaf42dac2eaf42dab2eab42daa2ea9c2da92ea882da82ea802da72e9f02da62e9e42da52e9e42da42e9d42da32e9c82da22e9c42da1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2effc2e202eff42dff2eff02dfe2efe82dfd2efdc2dfc2efcc2dfb2efc82dfa2efc42df92efbc2df82efa82df72ef942df62ef902df52eefc2df42eef02df32eee82df22eedc2df12eec82df02eec42def2eeb42dee2ee842ded2ee802dec2edf82deb2ede42dea2edd02de92edcc2de82edc02de72edbc2de62ed8c2de52ed842de42ed802de32ecf02de22ece82de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2f4802e602f3f02e3f2f3e82e3e2f3d82e3d2f3c42e3c2f3bc2e3b2f3b42e3a2f3a02e392f3882e382f3882e372f3842e362f2ec2e352f2d82e342f2d02e332f2cc2e322f2a42e312f1d42e302f1c02e2f2f1b82e2e2f1b02e2d2f1a82e2c2f1902e2b2f0fc2e2a2f0f42e292f0f42e282f0e02e272f0dc2e262f0d02e252f0a42e242f0a02e232f09c2e222f08c2e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2f8c02ea02f8b42e7f2f8a42e7e2f89c2e7d2f8842e7c2f8802e7b2f7e42e7a2f7a42e792f6d82e782f6cc2e772f6c42e762f6bc2e752f6b82e742f6a42e732f69c2e722f68c2e712f6842e702f5cc2e6f2f5c82e6e2f5b82e6d2f5ac2e6c2f5a42e6b2f5942e6a2f5882e692f5802e682f4f82e672f4ec2e662f4dc2e652f4d42e642f4c02e632f4ac2e622f4982e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x2fcc42ee02fcbc2ebf2fc942ebe2fc882ebd2fc802ebc2fbf82ebb2fbf02eba2fbd82eb92fbb82eb82fbac2eb72fb982eb62fb902eb52fb882eb42faf42eb32faf02eb22fae82eb12fab42eb02fa9c2eaf2fa8c2eae2f9f42ead2f9f02eac2f9dc2eab2f9c82eaa2f9b42ea92f99c2ea82f9942ea72f98c2ea62f9882ea52f9842ea42f9802ea32f8e42ea22f8c82ea1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x321f42f20321ec2eff321d82efe321a82efd321a02efc321942efb321842efa320fc2ef9320e82ef8320dc2ef7320d42ef6320cc2ef5320c02ef4320b82ef3320a02ef2320902ef1320882ef02fff82eef2ffe82eee2ffdc2eed2ffd42eec2ffc02eeb2ffb02eea2ffac2ee92ffa02ee82fef42ee72fdf82ee62fdf42ee52fdf02ee42fddc2ee32fd9c2ee22fcd02ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x326a02f603268c2f3f326882f3e325f82f3d325f02f3c325d82f3b325c82f3a325c02f393259c2f38325942f37325842f36324fc2f35324e02f34324d82f33324c02f32323e02f31323dc2f30323d42f2f323d02f2e323cc2f2d323c82f2c323c42f2b323bc2f2a323ac2f29323a82f283239c2f27322cc2f26322b42f25322b42f24322982f23322902f22322842f21⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x32afc2fa032ad02f7f32ac42f7e32ab82f7d32ab42f7c32aac2f7b329f02f7a329902f79328e82f78328d42f77328ac2f76328902f753288c2f743288c2f73328882f72328882f71328842f70328802f6f327e02f6e327c82f6d327c02f6c327ac2f6b327a82f6a327902f69327882f68326fc2f67326ec2f66326e42f65326d02f64326c42f63326ac2f62326a42f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x32ea82fe032e9c2fbf32df02fbe32dec2fbd32de82fbc32dd02fbb32dcc2fba32dc82fb932dc82fb832db82fb732da82fb632da42fb532d9c2fb432d902fb332d882fb232d842fb132cf02fb032ce82faf32cd82fae32cd02fad32cac2fac32c942fab32bf82faa32bf42fa932be42fa832bd02fa732bc82fa632ba42fa532ba02fa432b9c2fa332b942fa232b902fa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x332803820331f02fff331ec2ffe331d82ffd331c82ffc331b42ffb331b02ffa3319c2ff9331942ff8331842ff7330f42ff6330dc2ff5330d42ff4330bc2ff3330b82ff2330a82ff1330a02ff0330902fef330802fee32ff82fed32fec2fec32fd82feb32fd02fea32fa02fe932ef02fe832ef02fe732ee42fe632ed02fe532ecc2fe432ec42fe332ebc2fe232eac2fe1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x335b43860335a4383f335a0383e33580383d334f8383c334f0383b334d4383a334cc3839334bc3838334b43837334a03836334983835333f03834333ec3833333dc3832333d03831333c03830333a8382f33398382e33384382d332ec382c332dc382b332d4382a332c83829332c43828332b43827332a03826332983825332903824332883823332883822332843821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3398438a033980387f338f0387e338ec387d338e4387c338d8387b338d0387a338c03879338bc3878338a83877338943876338883875337b03874337a03873337943872337883871337803870336f0386f336ec386e336d4386d336cc386c336bc386b336b4386a3369c38693369438683368c3867336803866335e43865335e03864335d03863335c83862335bc3861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3618438e0360e038bf360dc38be360dc38bd360d838bc360c038bb3608438ba3608038b933ff038b833f9838b733f8438b633efc38b533eec38b433ee438b333ec438b233ea838b133e9c38b033e9438af33e8438ae33e8038ad33cbc38ac33cb838ab339f438aa339dc38a9339d438a8339cc38a7339b438a6339b038a5339a838a43399c38a33399438a23398c38a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x364f03920364c438ff363d838fe363d438fd363c838fc363c438fb363c038fa363b438f9363b038f8363a838f7363a038f63639838f5362fc38f4362f438f3362d438f2362cc38f1362c838f0362c438ef362b838ee362b438ed362ac38ec362a438eb362a038ea3628438e9361f838e8361ec38e7361dc38e6361d038e5361a838e43619c38e33619038e23618c38e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x368ac396036898393f36884393e367f8393d367f0393c367d8393b367bc393a367b43939367ac3938367a83937367a43936367943935367903934366fc3933366f03932366e83931366d83930366d4392f366b4392e366a8392d3669c392c36694392b365fc392a365f43929365e43928365d03927365c83926365b03925365a03924365983923365803922364fc3921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x36bd039a036bc0397f36bb8397e36ba4397d36b9c397c36b90397b36afc397a36af8397936ad4397836ad0397736abc397636aac397536aa8397436a9c397336a8c397236a843971369e03970369dc396f369d8396e369d0396d369cc396c369c8396b369bc396a369b43969369b039683699c3967369803966368dc3965368cc3964368c43963368b83962368b03961⟩
]

def tableRLR : Table Block := .branch 8 tableRLRL tableRLRR

def tableRL : Table Block := .branch 17 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x370e039e0370c839bf370b839be370b439bd370b039bc370a439bb370a439ba370a039b93709439b83708439b736ff839b636ff439b536fec39b436fe839b336fe039b236fd839b136fc039b036f8839af36f8439ae36ef039ad36edc39ac36ed039ab36dd439aa36cd839a936cd439a836ccc39a736cc039a636cb439a536c9839a436c8839a336c8439a236bd839a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3a5d43a203a59c39ff3a58c39fe3a58439fd3a4e039fc3a4d039fb3a39c39fa3a38839f93a2e839f83a2e039f73a29839f63a1c039f53a1b839f43a1ac39f33a19c39f23a19439f13a18039f03a0f039ef3a0dc39ee3a0d039ed3a0a039ec37fd839eb37fd839ea37fac39e937fa439e837f8c39e737efc39e637ee839e53719039e43718839e3370f839e2370f039e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3acf03a603ac843a3f3abd43a3e3abd03a3d3abb03a3c3abac3a3b3aba43a3a3aaf43a393a9f43a383a9d83a373a9d03a363a9cc3a353a9a43a343a9a03a333a9883a323a9803a313a8e83a303a8e43a2f3a8e03a2e3a8d43a2d3a8d43a2c3a8d03a2b3a8cc3a2a3a8b43a293a8b03a283a8a03a273a7fc3a263a6bc3a253a6a83a243a6803a233a5f83a223a5e03a21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3b4f43aa03b4f03a7f3b4e03a7e3b4c83a7d3b4983a7c3b3a43a7b3b3a03a7a3b2e83a793b2d83a783b2d43a773b2a43a763b2a03a753b2983a743b1fc3a733b1f43a723b1f03a713b1f03a703b1ec3a6f3b1d03a6e3b1c03a6d3b1bc3a6c3add83a6b3add43a6a3adcc3a693adc83a683adc03a673adb83a663adb43a653adac3a643ada83a633ad9c3a623ad843a61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3bcf83ae03bcf43abf3bcec3abe3bce83abd3bcbc3abc3bcb83abb3bbe03aba3bbd83ab93bbd43ab83bb983ab73bb943ab63bb843ab53baf43ab43b8803ab33b7e43ab23b7cc3ab13b7bc3ab03b7ac3aaf3b7a83aae3b6803aad3b5fc3aac3b5f03aab3b5e43aaa3b5d83aa93b5d43aa83b5c83aa73b5b43aa63b5983aa53b5943aa43b5903aa33b58c3aa23b4f83aa1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3e9ec3b203e9e83aff3e9e03afe3e9d43afd3e9c43afc3e9bc3afb3e9a83afa3e9a03af93e99c3af83e1fc3af73e1f43af63e1dc3af53e1c03af43e1b83af33e1a03af23e1903af13e1883af03bef43aef3beec3aee3bedc3aed3bed43aec3bec43aeb3beb43aea3bea83ae93be943ae83bdfc3ae73bdd43ae63bdd03ae53bd943ae43bd883ae33bd803ae23bcfc3ae1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x3efe03b603efb43b3f3ef943b3e3ef903b3d3ef883b3c3ef843b3b3eee43b3a3eed83b393eec43b383eec03b373eeb03b363eea83b353eea43b343ee903b333ee883b323edfc3b313edec3b303ede43b2f3edbc3b2e3eda03b2d3ed843b2c3ec903b2b3ec803b2a3ebec3b293ebe03b283ebd83b273ebd03b263ebcc3b253ebc83b243ebc03b233ebbc3b223e9fc3b21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x423ec3ba0423d43b7f420a83b7e420a43b7d420a03b7c420943b7b3fffc3b7a3fff03b793fed83b783fec03b773febc3b763feb03b753fe983b743fcc83b733fcc43b723fcb43b713fca83b703f8f83b6f3f8f03b6e3f8ec3b6d3f7983b6c3f0f03b6b3f0e83b6a3f0d83b693f0cc3b683f0c03b673f0b83b663f0a03b653f0903b643f0883b633eff03b623efec3b61⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x429983be0429903bbf428f03bbe428e03bbd428d43bbc428c43bbb428bc3bba428ac3bb9428a03bb8428983bb7428903bb6428803bb5427f83bb4427dc3bb3427c83bb2427c43bb1427bc3bb0427b83baf426c03bae426ac3bad426ac3bac426a83bab4268c3baa426843ba9425e43ba8425e03ba7425d83ba6425d43ba5425d03ba4425c83ba3425c43ba2424dc3ba1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x42d943c2042d8c3bff42d843bfe42d803bfd42cf03bfc42cec3bfb42ce43bfa42cb03bf942ca03bf842c9c3bf742c803bf642bfc3bf542bec3bf442be83bf342be03bf242bd83bf142b983bf042ae43bef42ad03bee42ac03bed42ab83bec42aa43beb42a9c3bea42a943be942a8c3be842a883be7429f43be6429e03be5429d03be4429bc3be3429a43be24299c3be1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x433943c60432fc3c3f432ec3c3e432e43c3d432bc3c3c432ac3c3b432a83c3a4329c3c39431f03c38430f43c37430f03c36430ec3c35430e03c34430dc3c33430d43c3242fbc3c3142fa83c3042f803c2f42ee43c2e42ee03c2d42ee03c2c42edc3c2b42eb43c2a42ea03c2942e883c2842e843c2742dfc3c2642ddc3c2542dcc3c2442dc83c2342db43c2242d983c21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x43ce03ca043cdc3c7f43cbc3c7e43ca83c7d43c983c7c43c943c7b43c8c3c7a43c803c7943bf43c7843aec3c7743ae83c7643ad43c75437b43c74437a43c73437a03c72437883c71436fc3c70436a03c6f435f83c6e435e83c6d435b43c6c435a83c6b434d03c6a434c03c69434ac3c684349c3c67434903c66433fc3c65433b83c64433b03c63433a43c624339c3c61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4688c3ce0468883cbf465ac3cbe464f43cbd463e43cbc463d43cbb463c83cba463bc3cb9462ec3cb8461803cb7460ec3cb6460c03cb5460bc3cb4460843cb343ff43cb243fd83cb143fd03cb043fc43caf43fb03cae43fa83cad43f943cac43ed03cab43ec03caa43eb03ca943ea83ca843e9c3ca743e983ca643df43ca543de43ca443dd43ca343cf83ca243ce43ca1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x476ac3d20474fc3cff474dc3cfe474ac3cfd473d03cfc473bc3cfb473b03cfa473883cf9473803cf846ee43cf746eb83cf646cc03cf546cb43cf446bf03cf346bd43cf246bd03cf146aac3cf046aa43cef4699c3cee469983ced468fc3cec468f43ceb468ec3cea468e83ce9468d83ce8468d43ce7468cc3ce6468c03ce5468b83ce4468a03ce3468a03ce24689c3ce1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4a3883d604a3803d3f4a2e83d3e47e883d3d47da43d3c47ca03d3b47c943d3a47c8c3d3947c843d3847b803d3747aec3d3647ae43d3547ad83d3447ac03d3347ab83d3247ab43d31479b83d30479a43d2f4799c3d2e479983d2d479903d2c4798c3d2b478ec3d2a478e43d29478dc3d28478a83d27478a03d26478983d25478883d24478803d23477c83d22476d83d21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4adf43da04ade83d7f4adc43d7e4adbc3d7d4adac3d7c4ada43d7b4acf83d7a4ace03d794acc43d784acbc3d774acb43d764ac903d754ac883d744abfc3d734abf43d724abf03d714abe03d704abd43d6f4abc83d6e4abc03d6d4abb03d6c4abac3d6b4ab8c3d6a4aad03d694aac83d684a4c03d674a4a83d664a4983d654a3c83d644a3c03d634a3b43d624a39c3d61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4b5c03de04b5b83dbf4b5a83dbe4b5a43dbd4b5843dbc4b4f83dbb4b4ec3dba4b2943db94b2843db84b1fc3db74b1f03db64b1d43db54b1cc3db44b0f43db34b0e43db24b0cc3db14b0b43db04afb83daf4afb03dae4afa43dad4af943dac4af8c3dab4af883daa4aee43da94aecc3da84aebc3da74aeb83da64aea83da54aea43da44ae903da34ae883da24adfc3da1⟩
]

def tableRRL : Table Block := .branch 8 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4b89c3e204b8903dff4b8883dfe4b7fc3dfd4b7f43dfc4b7e43dfb4b7e03dfa4b7c43df94b7b43df84b7a83df74b7a03df64b7983df54b7983df44b7943df34b7903df24b7803df14b6f43df04b6e83def4b6e03dee4b6d03ded4b6cc3dec4b6c83deb4b6b03dea4b6a03de94b6943de84b68c3de74b6843de64b5fc3de54b5e43de44b5e03de34b5d43de24b5cc3de1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4bea43e604be9c3e3f4be903e3e4be8c3e3d4be883e3c4bdfc3e3b4bdbc3e3a4bdb83e394bda83e384bd9c3e374bcbc3e364bca83e354bca03e344bc883e334bbf83e324bbf03e314bbd83e304bbd43e2f4bbc83e2e4bb9c3e2d4baa03e2c4ba9c3e2b4ba983e2a4ba8c3e294ba883e284ba843e274b8dc3e264b8d83e254b8c83e244b8c03e234b8b83e224b8a03e21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4e28c3ea04e2843e7f4e1f43e7e4e1ec3e7d4e1c83e7c4e1b03e7b4e1943e7a4e1903e794e1803e784e0fc3e774e0ec3e764e0e43e754e0c03e744e0bc3e734e0b83e724e0b03e714e0b03e704e0ac3e6f4e0a83e6e4e09c3e6d4e0943e6c4e0903e6b4e0883e6a4e0843e694bfe03e684befc3e674bee03e664bec83e654bec83e644bec43e634bec03e624beb43e61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4e5c03ee04e5bc3ebf4e5b43ebe4e5ac3ebd4e5a43ebc4e5983ebb4e5843eba4e4fc3eb94e4e43eb84e4d43eb74e4d03eb64e4c83eb54e4b83eb44e4b03eb34e4a03eb24e4883eb14e3f03eb04e3e83eaf4e3d83eae4e3c83ead4e3b83eac4e3a03eab4e3843eaa4e3803ea94e2f03ea84e2e83ea74e2d43ea64e2bc3ea54e2b83ea44e2ac3ea34e2a43ea24e2a03ea1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4ebb03f204ebac3eff4eb943efe4eb8c3efd4eb803efc4eaf03efb4eae83efa4eac83ef94eab43ef84eab03ef74ea9c3ef64e9f43ef54e9e83ef44e9943ef34e9903ef24e9803ef14e8f43ef04e8843eef4e7f43eee4e7f03eed4e7dc3eec4e7d43eeb4e7bc3eea4e7ac3ee94e7a43ee84e78c3ee74e7883ee64e6fc3ee54e6d03ee44e5d43ee34e5d03ee24e5cc3ee1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4efac3f604efa43f3f4ef9c3f3e4ef943f3d4ef8c3f3c4ef803f3b4eeec3f3a4eee43f394eed03f384edfc3f374edf03f364edec3f354ede43f344edd83f334edd43f324edcc3f314edb03f304eda03f2f4ed903f2e4ed883f2d4ed843f2c4ece43f2b4ece43f2a4ecc83f294ecb83f284eca03f274ec9c3f264ec903f254ebfc3f244ebf83f234ebd83f224ebbc3f21⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4f9e83fa04f9e03f7f4f9d83f7e4f9c83f7d4f9a83f7c4f2d03f7b4f1e03f7a4f1d83f794f1cc3f784f1b43f774f1ac3f764f1a83f754f19c3f744f1983f734f18c3f724f0e03f714f0dc3f704f0d83f6f4f0cc3f6e4f0c83f6d4f0b83f6c4f0a03f6b4f09c3f6a4f0843f694effc3f684efe43f674efe03f664efd43f654efcc3f644efc83f634efc03f624efb03f61⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x4fec03fe04febc3fbf4feb03fbe4fe843fbd4fd883fbc4fd843fbb4fd803fba4fcf43fb94fcf03fb84fce83fb74fcdc3fb64fcc03fb54fcbc3fb44fcb03fb34fcac3fb24fca43fb14fc8c3fb04fbf43faf4fbf03fae4fbcc3fad4fbc03fac4fbbc3fab4fbb43faa4fbac3fa94fba43fa84fb9c3fa74fb983fa64faf83fa54fa943fa44fa843fa34fa803fa24f9ec3fa1⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x52aa84820529cc3fff529c03ffe529883ffd528fc3ffc528f43ffb528ec3ffa528e83ff9528cc3ff8528b43ff7528ac3ff6528a03ff5528843ff4527983ff3527943ff2527883ff1526b43ff0526a83fef5269c3fee521d83fed4fff03fec4ffe83feb4ffe03fea4ffd43fe94ffc03fe84ffb83fe74ffa43fe64ff903fe54ff883fe44fef03fe34fee03fe24fed83fe1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5319448605318c483f530fc483e530c4483d530b4483c530b0483b530a8483a5309c483953094483853084483752fe4483652fe0483552fd4483452fcc483352fc4483252fac483152fa4483052eec482f52edc482e52ed8482d52ecc482c52eb4482b52e98482a52e90482952e8c482852e84482752df4482652dec482552de8482452dc4482352db8482252cdc4821⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x56ef448a056ee8487f56ee0487e56ed8487d560ac487c53bd0487b53bcc487a53bc0487953ae0487853ad84877539e44876539cc4875539c44874539904873538c84872538c44871538b84870534bc486f534b4486e534a8486d534a0486c5349c486b53494486a5348c4869533884868533844867532e04866531ec4865531c04864531b04863531a448625319c4861⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x578c848e0578bc48bf5789048be5788c48bd5788848bc577ec48bb577d848ba577c848b9577bc48b8576f848b7576e448b6576e048b5576bc48b45768c48b3573f848b2573f048b1573e048b0573d848af573c848ae573c048ad5739848ac5739048ab5738448aa572f448a9572ec48a85718448a7570f448a6570d448a5570c448a4570c048a356f8c48a256efc48a1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x5a8ec49205a8e048ff5a8cc48fe5a6b048fd5a69448fc5a1a848fb57f9c48fa57edc48f957db048f857c8848f757bf848f657bf048f557be448f457bcc48f357bc448f257bb848f157ba448f057b9448ef57b9448ee57b9048ed57b8448ec57afc48eb57af848ea57adc48e9579b848e85799c48e75799448e65798c48e5578f448e4578dc48e3578dc48e2578cc48e1⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x635b849606359c493f63594493e63590493d63584493c62bf0493b62bd4493a62bd0493962b88493862b84493762afc49365fb9049355f8c849345f3d449335e7ac49325e7a849315e79049305b2f4492f5b2d0492e5b2cc492d5b2c8492c5b29c492b5b298492a5b28849295b0c449285b0bc49275b0b049265b09449255b08049245affc49235afd849225a9884921⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x677b449a0677b0497f677a4497e67790497d674ec497c674dc497b673ec497a673ec4979673ec4978673dc4977670e0497666fe0497566dc4497466bb4497366ba84972666844971637e04970637dc496f637d8496e637d0496d637bc496c637b4496b6379c496a6378c4969637844968636ec4967636e84966636dc4965636b04964636904963636804962635e84961⟩,
  ⟨0xc005d02d015c0a8051027012c09004502100fc07803901b00cc06002d015009c04802100f006c030015009003c018009003000c000, 0x6ecc049e06eaf449bf6e29849be6e29449bd6b1d449bc6b1a849bb6aa8c49ba6a4cc49b96a1f849b86a1f449b76a1ec49b66a1e849b567fe049b467ec449b367eb049b267eac49b167cb849b067c9049af67c8049ae67bdc49ad67b8449ac67aa849ab67a9049aa67a8849a967a8049a8679f049a7679e849a6679d049a5679c049a4679b849a3679ac49a2678d449a1⟩,
  ⟨0xc000, 0x6ed8049e1⟩
]

def tableRRR : Table Block := .branch 8 tableRRRL tableRRRR

def tableRR : Table Block := .branch 17 tableRRL tableRRR

def tableR : Table Block := .branch 34 tableRL tableRR

def table : Table Block := .branch 68 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table i

end PolicyCircuitPacked1


namespace PolicyRewriteParametricPacked1
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x11f08583e01c20ce05d829412407f0360170096038015806c01a000, 0x28640428390a0f020a1d8307c127d0287304286b0a1b420a1d442449f30a19010a0ac28390a0f030a1cc406d127c800460a0ac282910286c1c1d849f00a19810a0e8283d082868109127bc28640411828390a0f040a1986079127b8004607ee41fba102864181dc49ed00118282b0a0a440a0ec7078127ac00460a0ac2829102836201d449ea001181fb90c2834181d049e900282e0a0a420a0c850ab127a0282204282007fe820a08c33849e7001ff904282210d12798007de01ff708282119412794007de0107ff84069127900077f8107fc056049e2⟩,
  ⟨0x12108703ec1c40d105d028011807b035017009203e0188098032000, 0xa4901ff70a39830a49c57c4a2a0a3fc10a39028be0829200ce128a028fe0a3f420a39028fc0a2f830a3fc3184a270028a30a38c20a3f840721289828fb0428a30a38c1e650c28fd101c44a250a3e428f20828e30a3c41e650c28fb0c1c04a24001df3078e41e610c28f9141bc4a23001e660799420a3cc506e1288400798428e60828ec143b04a20001fe00428eb101a849ff0028e20a28c1e610c28e515f127f800028ac182e049fc001bfd0428ab14f127ec000287d1838c49f90011820a1f050e2127e028760a0e820460a0f0283910283d143b449f5⟩,
  ⟨0x134090043c1fc0ed06c83201680a004781f00ca05101f00ac028000, 0x29f50a0f029f40c2a201c2984a3d001fbd07eec20a7f850a5128f000a7e029f40829fc142ac4a3b001e630798420a7b05061128e40079881e3f076c430a7885062128e00078fc1df90829b7142ec4a36001e3d078f01e200c2968141884a350028250a28c29380c29601c1a04a34001e3b078e420a4f85067128cc29360429320a4b020a4dc3384a320a4d0106ff429310a09430a4d860a9128c4006ff41e260788030a4d060a8128c0006ff4293007fb030a4cc75c4a2f0a4a810a498292108292b0ce128b42928041ff70a494287f0c292a101b44a2c001f7907de01fe00c2928141b04a2b⟩,
  ⟨0x135091045420a0f7072032c1740a304781f00ca05101f009c026000, 0x2a7f042a7d0a9dc20aa803384a72002a76042a7f10d129c4007de42924082a7e194129c0007de410a9ec4069129bc2a69042a640a8f820a9a83384a6d0a9a02a67082a640a9982a3e0c2a690c6129b000a38828e3082a68101c84a6b0a3ec10a38828e30799430a99c4071129a800a28c28e20798430a9945060129a42a35042a330a8b820a8d83384a660a8a410a7d42a230a2b830a8d4406d1299400a0f029f50a7d030a8d05060129902a2b042a240a89820a8b44244a620a8a410a0f02a230a2b830a8ac406d12984007ef41fbb07ef830a8a4506c1298000a7d4283c0a7d030a89457c4a3e⟩,
  ⟨0x13a09304482020e706982fc15809804281c40b00480190084020000, 0x1df7077d81dba0c2b21141884aa4002a6d0a3882abc0c2af31c1a04aa2001df5077cc20abc4506712a842aea0ab98206ff42a6d0ab9430ab80516d12a802ae8042ae50a9b420aba8307c129fc006ff41dbc076e830aba060a8129f8006ff42ae40aaec30ab9c75c4a7d002aa50aaf02abb0c2abf141984a7b0aad810aa982ab1082ab8109129e800aa9428e20a9b430aad87065129e42ab30aac020aac82aaf0aaac30aad03184a78002aac0aa9420aacc5144a770aab810aa942aad0aaa830aac04104a76002a6d0a38820aab85064129d40077d41df3082aab1418c4a74002aa50aa9020aaa44044a73⟩,
  ⟨0x142099048421c0fb072034417c0a704381cc0be04c01c0090028000, 0x1bfd0709420af886744ab7002bbc0aee020af8050ab12ad82ba9042b780ae9820aeac4244ab30aea010ae982b78082ba90ce12ac82ba1042b760a9b42b770c2ba8101b44ab10ae8c10adec2b70082ba510912ac02ba2042b700adec20ae8c3384aaf0ae8410adbc2a6d0addc30ae88406d12ab82aea0ae802b7f0c2a6d0ab942ae40addc40ae8430aa12ab42b7d042b770ab9020adfc307c12ab000709c1c20076ec30adf4506c12aac00add82b6f0add430adf057c4aaa002b6f0add82b750c2b79141804aa9001bfd0acfc2b3d0c2b6d2428c4aa7001bfd06ce020adac6744aa6002b3f0acf82b3d0c2b62141804aa5⟩,
  ⟨0x11b08383f01e20de06382cc14009304181c80c805101d0098026000, 0x6ff42ae40aaec30b19c70a712bb80002c62183a04aec01e042c6114f12bac2c29042c270aec820b0a83384ae70afc010aec42be70add830b0a4406d12b9800aee42bb10aee030b0a0506012b942c22042c200afdc20b08c3384ae3002bf6042c2210d12b8800afd42bb9082c2119412b840182bb10aee430aff854c4ae00060709020aff05484abf0afc810afa02bea082bf410912af42bf0042bb90af9c2b760c2bf2101b44abc001c24070941c260c2bf0141b04abb002bb10aee42bb80c2be915f12ae4006ff42bb90aee030af908784ab8⟩,
  ⟨0xfb075836c1900bb055826811808203a81880aa04501b00a802e000, 0xb3982ce7082cf119412c9800700708020b3b8507312c942cbc042cba0b2c420b2f43384b22002cb0042cbc10d12c8400b2b82b3e082cbb18c12c80006cd430acf830b2e072c4aff001b350c20b2d86284afe0000b2a86404afb001b35042ca914f12be82c79042c770b1b820b1e83384af6002c6d042c7910d12bd400b1ac2bb1082c7818c12bd007880aec430b1d472c4af301e2020b1cc6284af20b1a010ab982ae0082c6a10912bc02ae8041bfd0ab942a6d0c2c68182a44aef⟩,
  ⟨0x11308183c81cc0d306302d814e09b04401c40bc04b01a008001a000, 0xb5802d3a082d6d19412cf00042d280b4e830b5a854c4b3b0015c20b5a05484b3a0b4e010b4d82d2d082d390ce12ce000b4b010b4e04344b37002d2a0b4a020b4dc6304b360150c2d280c2d341cb12cd40543082d3218a12cd02d23042d210b0b420b4903384b310b3f010acfc2b600adbc30b48c406d12cc000acf82b3f0acf430b48857c4b2f0b3f810ad842c7e082d2010912cb82cfc042b3e0ad802b6f0c2cfe101b44b2d001b3706ce01bff0c2cfc141b04b2c0b3c810b3c02cea082cf30ce12ca000b3a410b3c84344b27⟩,
  ⟨0xf206f033017a0af04e02240f806c02d8134084037016008001a000, 0x2df40b7842df30c2df7141804b760b7a410c2de1082de20c1f04b740030b78420b7a8507b12dcc0079a010b7a0406912dc82cfe042b610b1f820b6d83384b6d0b6c810b6c02da7082db30ce12db000b69810b6c84344b6b002da40acfc20b6c46504b6a0010acf82b3f0c2dae15312da40041b37082dac15212da00002d7e184d04b64015042d7d14f12d8c0002d76184cc4b61003e410b5d453c4b600b5b810b5b02d63082d6f0ce12cf800b58810b5b84344b3d⟩,
  ⟨0xfc077837c19c0c005a82a812e087037017809003c017807c01c000, 0x2e66042e7210d12ea400b9902df4082e7119412ea00042de10b7d030b9b854c4ba7001079a020b9b05484ba60000b98860a212e9000410b98453c4ba30b8e010b89c2e33082e3a10912e840042e260c30b8e090a112e802e350b8c820b8d02e310b8b430b8d83184b7f002e2e0b89820b8d45144b7e0b8c010b8982e2f0b8b030b8c84104b7d0010c20b8c070c4b7c0010c20b8b460a012dec00b8982e25082e2a10112de400b7d02df3082e20141fc4b78001e69042dfe141f84b77⟩,
  ⟨0x12e08d040c1de0dc06402dc14c09504101d40ca05501d809c026000, 0x2eb50bad82eb40c2efa141804be30bbbc10bad42ee40bb9c30bbc4406d12f840078cc1e31078d030bbbc506c12f8000bad82eb50bad030bb9857c4bbe002eb60bad42eb40c2ee11c2984bbd001e33078c420bafc50a512ef000bae42eb4082ebd142ac4bbb002b660acf420babc50ab12ee02ea5042ea30b9f420ba983384bb4002e7c042ea510d12ecc00b9e82dba082ea419412ec80070079ac20ba84507312ec42e790b7d820b7b02df50b78430b7b4307012ebc2e77042df50b7b020b9e4307c12eb80079a01e69079a830b9dc506c12eb42e72042e700b99c20b9cc3384baa⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0x14509684602060ee06e032416409e04381cc0c004c01d80a802e000, 0x2f7e041db8182f740bad440be80607912fe00076e06078bc1e30102f7e181dc4bf7001db8182f660bd9040bdd8707812fd40076e060bd982f64102f71201d44bf4001db8181e2f0c2f6f181d04bf30bd8810bd802efe082f630ce12fc82f3a042efd0bcc428a30c2f62101b44bf1002ee70bbf42f230c2f61141804bf00bce810bb9c2f310a28c30bcf0406d12fb80078dc1e35078e030bce8506c12fb400bbf42ee70bc8c30bccc57c4beb002efd0bb9c2f230c2f2e1c2984bea001e37078d420bcb050a512fa400bc982f23082f2a142ac4be80bbec10bbe42ef4082efc0ce12f942eef042eb60bb902ee70c2efb101b44be4⟩,
  ⟨0x12908b04081e20e006602ec15409704001b00c205201f80b002a000, 0x38250438210bf9820e0983384c2d0e08c10e0802a6b083825103844c2c001fb007ea820e08c50e0130ac00bffc2ff8083822142fc4c2a002a6b0a9c42fef0c2ff61c1a04c29001fe507f8c20bfd05067130a000abe02fef082ff2142ac4c270bf8810bef42fbf082fe41091309429280429240a494287f0c2fe2101b44c24001ff70a49028e60c2fbe141804c220000bee4616e130840076e06082fb8143884c200be8010bdd42f77082fae0ce12ff42fab042fa60bea020beb44244bfc0bdf810bd982f740bad430beac406d12fec0076e060bd982f64102fa71c1d84bf9⟩,
  ⟨0x144098846820c0f306f831416209d04601ec0c405201e00a0028000, 0xe38410e2e838bc0838e31091318438bf0428ae0e2d82a710c38e1101b44c60001fe107efc1fe20c38bf141b04c3f00287f0a2b838b50c38bb15f130f400a2b8287f0e2d430e2e05060130f038af0a8cc20a2b82a230a7d430a8b83070130e82a29042a230a2b820e2bc307c130e400a0ac2a710e0c030e2a470ac130dc007ee41fe30838a7142944c360038a10e0c020e29450ab130d4387d0e1ec20e1f0387a0e1dc30e1f83184c340038330e0d820e1f45144c330e1e410e0d838340e1d830e1ec4104c320038280e0c0382e0c3879182b84c31001fe807f901fa90c3877142b44c30001fe707f981faa0c3829141884c2e⟩,
  ⟨0x11608103d01c20d406082b813c09004181d40c805001f80b8028000, 0xe4dc10e3dc38fd083939103a44c75001f38043937142c84c740e4cc10e4c439270839340ce131c800e49810e4cc4704c710039240e3f438ee0c393219b131c000e48c38fd0e3b830e4bc6684c6f001fa707ce420e4b05644c6e0038f60438fc142d44c6b0038f60438f9140131a8007ea010e3c450ba131a400e3bc382e0838f3142ac4c6800287f0a2b838b50c38eb1c2984c66001fe107efc20e3a450a51319400a2cc38b50838e7142ac4c640e39038b7082a710e2d8287f0c38b10c1c04c630e2fc10e2d82a710838e40c1f04c62⟩,
  ⟨0x10407883901a80c305a82a813a08a03d01980aa04701d009c026000, 0xe7f810e7f039f30839ff0ce132a800e7c810e7f84344ca90039ef0e7c020e7f46504ca80060e7b839f00c39fa1531329c0181a780839f81521329800039ec183d04ca4001a700439eb14f1328c0069c039b50e6cc30e7908784ca1001a70073bc20e7886744ca00039b50e6d039b30c39b8141804c7f002dba0e68820e6c4507f131f8007ce810e6bc507e131f400e5a410e5b05004c7c0e58410e3e0393c083963109131e839370438f70e3f420e58440b6131e439390438fb0e3f820e4ec4244c76⟩,
  ⟨0xf5074036018e0b9057028c13008b03c01a009e03f0148074020000, 0xe9bc10e9ec4344cbf003a6d0e7b820e9e86304cbe001a762039ee0c3a771cb132f40069d88083a7518a132f00003a6b183944cba006043a6a14f132e40003a61183cc4cb6001a76043a6014f132d43a36043a250e8c420e8e04244cb30060e89080c3a36242844cb20e8cc3a30083a320e8bc3a2b0c3a340c6132c400e8b03a24083a33145132c03a2e043a240e8b43a2a0c3a30104132bc0188083a2e1c3132b80188083a2b182804cad003a240e88c20e8a04044cab⟩,
  ⟨0x12908a83f81d40d706182c814208e03d01980a6040019808c026000, 0xebcc3af40ebc830eccc5060133d03b2d043af30ec883b250c3b2f101b44cf3001d6c075a81d6d0c3b2d141b04cf2003af40ebcc3af20c3b2415f133c000ebd03af30ebc830ebfc70a6133bc0075b01d6a083afd142944cee003af70ebc820ebec50ab133b400eb903aeb0eba830ebc457c4cec003aeb0eb903aea0c3aee141804ceb0039f00e7b83ab30c3ab9141804ce80039ee0e7c03ab30c3ab715f1339c3aab043aa90ea8c20eab03384ce5003aa2043aab10d1339000ea8439b5083aaa1941338c0070069ec20ea9c5073133883a7b043a790e9c020e9f03384ce0⟩,
  ⟨0x14809a048020c0f206f032816e09f04501d40c004e01e80a8026000, 0xeee410eec43abf083bbb0c1f04d29001a70074fc1d390c3bb9182a04d280eedc3bb5083aeb0ebb03bb00c3bb80c1c04d270ebc010ebb03aeb083bb70c1f04d26001d3d074ec1d3e0c3bb5141b04d25001a700eec03baf0c3bb31c29c4d240ee8810edec3b7d083ba4109134883ba0041cf5183b7a0ebcc40ee886079134840073d46075a01d69103ba0181dc4d20001cf5183b610edb040edf07078133f80073d460ed843b6c103b77201d44cfd001cf5181d680c3b75181d04cfc003b6f0edb020edcc50ab133ec3b3e043b320ecec20ed804244cf90ecb410ebd03b220ec9430ecf8406d133e03b2f043b230ec9820ecd83384cf5⟩,
  ⟨0x10807883741920b5052024c1000750348158092039014006801e000, 0xf1a010f0a43c2a0f0e030f1a8406d134f80072b41d6e075bc30f1a0506c134f400ec943c290f09c30f1905060134ec00f0a43b250f09c30f0d870ac134e40072b41d6e083c34142944d38003c2e0f09c20f0c850ab134dc00f0a43b250f09c30f0b057c4d360000f0946120134d40261043c2414f134d03bf9043bf70efb820efe83384d32003bed043bf910d134c400efac3bbd083bf818c134c00063b830eef430efd472c4d2f0018ee0c20efcc6284d2e0000efa06132134b00073d46083be7143884d2b⟩,
  ⟨0x11a08683f41da0e206a830815c09504281bc0bc04d01e80a8026000, 0x3cbd043ce610d135c800f2e83cbb083ce5194135c40070069cc20f3885073135c00003cb6181e84d6d0018ee043cb514f135b03ca7043c770f28820f2a44244d6a003c760f0e03abf0c3ca71c1944d690f2903ca1083ca30f2803c7c0c3ca50c6135a000f1f43c76083ca41451359c3c7f043c760f1f83c7b0c3ca11041359800eafc3c38083c7f141904d65001d72075c020f1f050631359000f1d83c75083c7a1011358c3c70043c2b0f1b420f1c43384d620f1a010ec943c2a0f0e030f1c0406d135843c6a043c630f19420f1b04244d3f⟩,
  ⟨0x11808583e41d60e006a830815609804281b80b404701a0090026000, 0x1fa8043de9158136a40442b3f0f5fc30f69c90a3136a00441b38083da519d1369c0003d78183984da5011043d7714f136903d6c043d670f5a420f5b84244da10eee41069c03bb10eafc30f5b060a9136800069c03bb00eebc30f5a075c4d7e0f48810f3dc3cf9083d24109135ec3d20043cbb0f3d83aeb0c3d22101b44d7a001d3a073b41cee0c3d20141b04d79003cf50f2ec3ce80c3cf815f135dc0069c03cbb0f3a030f3c88784d76001a70073b420f3c06744d75003cea0f3a020f3b850ab135d03ce6043ce40f2f820f39c3384d73⟩,
  ⟨0x10607d03a41b60ca05b829012e08703b81900ae04701b80a802e000, 0xc8c10fa8853c4de2003e340f9b420f9ec507f13780007cf010f9e4507e136fc00f9cc3e6d083e77142ac4dbe003e6f0f8d03e6d0c3e7215f136f43e3f043e3d0f8dc20f9803384dbb003e36043e3f10d136e800f8cc3e34083e3e194136e40070079c420f8ec5073136e03e30043e2e0f89420f8c43384db6003e24043e3010d136d400f8883e20083e2f18c136d00060203e200c3e2c1cb136cc00602020f8a86284db20f7cc10e2dc38b1083df5109136b038bf04287f0e2d82a710c3df3101b44dab⟩
]

def tableLLL : Table Block := .branch 12 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0xfb073834c1820b205202441080740318154088036011005c016000, 0x3f20043eb80f8c820fc88307c137e00079b81e6f079c030fc80506c137dc3efc0480fabc20fbd4307c137d40203eaf083efd141ec4df4001e6e043efb101a44df30fbcc10fbc43ee8083ef40ce137c400fb9c10fbcc4344df0003ee50fadc20fbc86504def0060fabc3eb70c3eef153137b80181e6e083eed152137b400fadc3eb6083ee3141fc4deb001e6f043ee1141f84dea003eb70fabc3eb60c3eba141804de90000faac613a137980060043eaa14f137940003ea3184e44de3⟩,
  ⟨0x12f08d841c1e60df06582dc14c09303e01a00aa04801c009c034000, 0x3fa0043f7e0a0ac20fe88307c138b0007ee01fb007ea830fe80506c138ac3f7a043f770bffc20fdf0307c138a8007eb81fac07ebc30fde8506c138a400fd943e660fdb430fde45060138a000f9983f650fdb430fdd470a61389c007eb81fac083f73142944e260fce410f9c43e67083f3a0ce1388c3f37043e340f9c03e660c3f39101b44e22001fad07cf01f3d0c3f37141b04e210fccc10fcc43f28083f340ce1388000fc9c10fccc4344dff003f250f98420fcc86504dfe0060f8803e610c3f2f153137f401818820fcb45484dfc0fc883eb9083e320fae03eaf0c3eb00c1c04df9⟩,
  ⟨0x147099847c2160f8072032c1760a504a020c0e605f02580dc040000, 0xbffc3f7d0bfe03120805060138f03ffc043fb20fdf420fff8307c138ec007edc1fb407ec430fff0506c138e83fe4043fb50fefc20ff984244e39003fb00f9983f650c3fe41c4a04e380ff843fbe083fe00fef43fb90c3fe20c6138dc00fee83fb0083fe1145138d83fbc043fb00feec3fb80c3fbe104138d400f9983f65083fbc1449c4e34001fae07eb020fee45126138cc00fec03f68083fb7101138c800fec43fac0fec030fed05060138c43fad043faa0feb020febc307c138c0007ed41fac07ed830feb4506c138bc3fa3043e660a0ac3f770c3fa4101b44e2e0fe883f7f0fdf030a0ac3f7e0bffc3f77103fa30c2a84e2d⟩,
  ⟨0xee07083381820b10508238102071030815009203d0190098026000, 0x607c0848e5152139d448bb0448b9122cc2122f03384e730048b20448bb10d139c80122bc48b00848ba194139c400700709c2122dc5073139c048ad0448ab122882122b83384e6e0048a10448ad10d139b40121fc487e0848ac18c139b0007a20487e0c48a91cb139ac007a2021229c6284e6a000121d861211399c007a04487514f13998000486d183f44e640049c1121b053c4e63003e660fd943f6d0c482515f138f800fdf42fff0bfe031208457c4e3d⟩,
  ⟨0xf0070034c1800b3051824810a071033016409c0410170084022000, 0x6cc8125c03126b072c4eb1006cc80849aa18a13ac0497f04497d125d02126803384eae00497304497f10d13ab40125c4496c08497e19413ab00184970125b03125ec54c4eab0061b508497915213aa80124f04933124ec3124fc506013aa00004931185bc4ea6012442124c050e213a940004927182904ea200182804492614f13a8448eb0448e9123802123b03384e790048bf0448eb10d139e00122f4487a0848ea194139dc018487e121e831239c54c4e76⟩,
  ⟨0xf8072836819c0bb057027811a07f036017c09e03e0180074020000, 0x49b5127984a2a0c4a2e15f13b9800049ff184ec4ee3006cc1127f853c4ee2127dc1127d449ec0849f80ce13b800127ac1127dc4344ebf0049e9127982127d86504ebe006126d449e60c49f315313af4018182a0849f115213af049e40449e2126e42127943384eba0049b80449e410d13ae40126d849b50849e318c13ae00060a08126d431278072c4eb7001828202126f86284eb6126c01126b849a50849b10ce13ad00126901126c04344eb30049a2125c02126bc6304eb2⟩,
  ⟨0xdf06903081640a704d023c106072032014c09003c0188090020000, 0x12d84112da84344f21004b3f129dc212da46504f2001e741e710c4b66184b44eff00012cec616c13bf0079d084b3a143884efb00012c9460f613be002f1044b2414f13bdc0129dc4a76084aa0141fc4ef3001e72044a7e141f84ef2004a78129d82129f050ab13bc40004a72183e44ef0006fc1129c453c4eef00012988607d13bac0066c011298453c4eea0019b0127984a2a0c4a3a2428c4ee80019b0060ac2128e06744ee7⟩,
  ⟨0x11708503f01c60d305e82b013608803c019c0a804701b809c026000, 0x74dc112fe45604f38004bbb044bec142d44f3512f944be3084be412f884bbf0c4be60c613cd0012ee04bbb084be514513ccc4be1044bbb12ee44bbe0c4be310413cc8012eb04bb5084be1182f44f31001c31070bc212efc50bc13cc00066c04b7a12eb0312ecc8784f2f0019b0070c0212ec46744f2e004ba812eb0212ebc50ab13cb44ba5044ba312df4212e983384f2b004b7c044ba510d13ca8012de44b7a084ba419413ca40070066dc212e84507313ca001279849b5128a8312dcc506013c944b6a044b6812d88212dac3384f22⟩,
  ⟨0x11508103c81be0ce05a829411e081039818c0ac04301b008c020000, 0x181132e44ca0104ce31c4b84f6d006041ce60c4ce0184b44f6c132cc1132904cae084cb510913da80444c6a132803132cc8204f69132c04cad084caf132b04ca80c4cb10c613da00132a44c6a084cb014513d9c4cab044c6a132a84ca70c4cad10413d980444ca0084cab1c313d940441ce9084ca818213d900131a84ca3084ca610113d8c0131881131945004f62130e01130d84c2c084c390ce13cfc0130ac1130e04704f3e004c291309c4c240c4c3719b13cf40130a04c27130903130d06684f3c001cf2073b02130c45644f3b⟩,
  ⟨0x11208103b01b60ca05e82a812c08803e81c00ba05001b809c020000, 0x4d28134902134d05144fa2134c01134904d2a134b43134c84104fa10039b30f3a02134c060bd13e800073c01cee084d2e142f04f7f004d24044d2714013df84cff044c64130fc2134803384f7c133f411318c4c27084cff102d84f7b001ceb044cfd142c84f7a000133d0616013ddc0181084cf3143884f76133a811339c4cbc084ceb0ce13dcc0132ec1133a84344f72133a04ce6084ce7133804ce20c4ce90c613dc40132e84ca0084ce819413dc04ce5044ca0132e84ce10c4ce6101b44f6f006044cb90c4ce5184bc4f6e⟩,
  ⟨0x11a08383e81ce0d406202c413a08f03e01940a204701e00a4032000, 0x136d81136d04daa084db70ce13ee80136a41136d84704fb9004da71309c4bf60c4db519b13ee00136984c2712fd83136c86684fb7001d36073b02136bc5644fb6136801134984d21084da10ce13ed04d7e044d25130a021368040b613ecc0073c41135f850b213ec84d7b043ab80eae82135f03384fb0135e410e7b83ab50e9f43135ec406d13ebc0069e01a79069e83135e4506c13eb80004d6f19613ea40481135b853c4fa8001a700e7c03ab30c4d6321e13e980069c01a79084d6119d13e944d34134c82134cc4d31134b83134d43184fa3⟩,
  ⟨0x11108203c41c80d406202c014008c03e01b80aa045017807801a000, 0x63b011399853c4fef138f81138f04e36084e3f0ce13fb40138d41138f84344fec004e32138cc2138f46504feb001c018f3084e3a141cc4fea001a70138844e200c4e2f2428c4fe8001a70063c42138b46744fe7004e210eef44e200c4e24141804fe6003ce8137802137e45144fe3001cee044df7142f84fe2137c04dee084def137b44dea0c4df10c613f840137904dbc084df014513f804dec044dbc137984de90c4dee10413efc0137884de0084dec182f44fbe001d34074cc2137a850bc13ef40136f01136fc5004fbc⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0xea06e833417c0ab04f02380fc071033016808e03a0150064016000, 0x4ee8044ef110d16094013b9c4ee2084ef019416090007012e084eed141cc582313b80113af84eb5084ee10ce16084013ad0113b804345820004eb213ab4213afc6304fff004a4313ab4313af072c4ffe004a43084eba18a13ff40004ea9183e84ffa004a4113aa053c4ff9139f41139ec4e72084e7e0ce13fd80139c41139f44344ff5004e6f138842139f06504ff40010eef44e210c4e7915313fcc00418f0084e7715213fc80004e67184904ff0⟩,
  ⟨0x12308803f01dc0db06202c013a08603a818409c0410188080026000, 0x4f71044dbe136e0213dc8338583d13dbc1136f44da6084f71102d8583c001d35044f6f142c8583b13db411388c4dfd084f6e0ce160e84f6b043bbd138883bbe0c4f6d101b458390018f0063c41a720c4f6b141b0583813d94113cf84f60084f67109160dc4f63044ead13cec4eae0c4f65101b45836004ac4b04b4313d8c506c160d4013c904ead13ce4313cfc5060160cc4f32044f3013c9c213ccc3385832004f26044f3210d160c4013c8c4f24084f31194160c00044ead13c90313cb854c582f00112b084f2c152160b84ef1044eef13ba4213bc83385826⟩,
  ⟨0x11608403bc1be0c905c029c13408703d019c0a8044019807c01c000, 0x1aea04587f142c85872161c4586f085870161b8586b0c58720c6161c4016194583d085871145161c0586d04583d1619c586a0c586f104161bc01618c586108586d182f4586e001ae906ba02161ac50bc161b40160f4116180500586c160d81160d0582a0858370ce161a80160a41160d847058690058261609058270c583519b161a001609458241609c3160c86685867001aeb06a842160bc5645866001d7a075e0213fe05061161880075e41d76073b8313fb45062161840075d81d32084fe3142ec583f001d37044f75142e8583e⟩,
  ⟨0x10f07d83a41b60d006082c013808b03e81a80ba04a01b809c028000, 0xaee42bb1165c03165f850601629c0442bb9165c03165e890a3162980441c2508597819d162940005969184a858a3001aaa182165a050e216288006cbc1b2d08593b14184587f001b2e06cac1aa30c593014188587e001b2b06b9c2164a050bb161f0006aa01162e050ba161ec58b30458b11629c2162d0338587a0058a60458b311c161e401628c5824162903162c866c5878004fff1609058a40c58af19a161dc006a9c1aa10858ac159161d858a104583f160e42162883385874161fc1160f858250858a1102d85873⟩,
  ⟨0x11a08483ec1d00d406082a812c08303901900a003d018008001e000, 0x11168c05a370c5a6221e162fc0441e78085a6019d162f80166d05a241688c3168a857c58bb005a24166d05a230c5a271418058ba167f01167e059bf0859fd0ce162e059fa0459a2166f059b40c59fc101b458b7001ee7079e81e7b0c59fa141b058b60059a41668859bb0c59f915f162d404459a2166ec3167b887858b3011079e82167b067458b20059a21669059bb0c59be1418058b0166c81166c059a70859b30ce162b80166981166c843458ad0059a3166902166c465058ac0059a2166902166b850ef162ac0181e7a0859ac143a858aa⟩,
  ⟨0x13208f84201e80e106502dc14008c03c81940a404501a8090028000, 0x16af41169985a68085abf109163cc5abb045a64169945a240c5abd101b458f2001ee5079e01e790c5abb141b058f116ad41169fc5aaf085ab7109163c05aaa042b3e169f85a6d0c5ab5101b458ef16ab0116a845aa3085aae109163b45aaa042b3f169f85a6d0c5aac101b458ec001b3706ce01ce10c5aaa141b058eb002b3e0acfc3d7f0c5aa215f163a400acfc2b3e0f5fc316a805060163a05a7c045a7a169c42169f433858e7005a70045a7c10d163980169b85a64085a7b194163940169b45a64085a78143ac58e4001c01ce2085a76143a858e3005a30169905a370c5a671418058e0⟩,
  ⟨0x14a099848021a0f606b030815e09a04401dc0ca05101e80a8026000, 0x16be81166d059f016894316bfc406d164945afc045a29168ac216bf8424592416bec1168ac5a29085afc0ce1648c5afa045a24167c05a250c5afb101b4592216be45aec16ba43167c05aeb16b985a25105afa0c2a8592116bd0116bac59f0085af90c1f0592016bd8116bbc5af1085af8109163fc5af405116bac59f00c5af6182a458fe01107ba81ee40c5af4182a058fd01116b985aea0c5af01d7163ec0445ae616ba8316bb470a7163e85ae7045a2516b98216ba4307c163e4007ba01ee607ba4316b9c506c163e05ae3045ae1168c4216b9033858f716aec1168c05a6516890316b8c406d163d80169905a30168dc316b8857c58f5⟩,
  ⟨0x12e08d841c1ec0e506902ec15009503f01a80ae04a01d00a802e000, 0x5b3916d885b610c5b7215f164e4016ce45b6216d84316db470ac164e00068f41b23085b6b142945937005b6516d84216da450ab164d85b37045b35165ac216ce0338593416cbc10aee4597c132e4316cdc406d164cc00aec42bb9165c0316cd857c593216cc41165f4597f085b33109164c05b2f042bb1165f04cb90c5b31101b4592f001c24070941ce50c5b2f141b0592e16cb0116ca85b24085b2d0ce164b0016c8c116cb0434592b005b2216688216cac650592a001c01ce6085b28141cc592916c801166f459b5085b210ce1649c59fa0459a4166f059b40c5b20101b45926⟩,
  ⟨0x145098848021e0f5070833816e0a304801f00d205201f00ac028000, 0x16e8c5baa16ea4316f9c70a6165b4006c841aff085be514294596c005bbf16ea4216f8c50ab165ac5bbc16eb0216d885bab16e8c316e903070165a85bb7045bab16d88216ef0307c165a45bb9045baf16ec4216eec424596816edc116ea85bab16d88316ee4406d1659c006c841aff06c88316edc506c16598016e8c5baa16ea4316ec057c5964005baa16e8c5ba90c5bad14180596316e84116dfc5b3b085ba20ce165845b79045b3916dc05b3a0c5ba1101b45960005b6216ce45b610c5ba014180593f16dec116dc45b73085b7d109164f45b79045b6216dc05b3a0c5b7b101b4593c001a3d06c8c1b240c5b79141b0593b⟩,
  ⟨0x12908a84041e00dd06302c813608703a018009e03e015807801c000, 0x1719c5c68171943171d85060166880171a05c67171943171c870a6166840074a01d24085c701429459a01718c1171845bfc085c640ce165fc5c3c042eb6170d85bfb0c5c63101b4597e005c220bad85c2c0c5c6214180597d170f01170885c3616fec3170f8406d165f00078cc1ef907be83170f0506c165ec00bad85c22170b03170e057c5979002eb6170885c2c0c5c331c2b05978001e3307be42170c450a5165dc0170945c2c085c2f142ac597616fe4116fdc5bf1085bfa0ce165cc016fc0116fe44345972001d2716fb8216fe06505971001d27045bf5101a45970⟩,
  ⟨0x149097846c20c0ee06c831015e09d04601ec0d005101f00ac028000, 0x5cfa173e0216ea85ced172cc3172d03070166e45cf3045ced16ea82173e8307c166e0006aa86172cc5ce3105cf91c1d859b7173cc106aa86173b45baa105cf5181e459b6001aaa181afd06bf84173cc6077166d4006aa86172cc5ce3105cef1c1e059b3001aaa185cb31738c4173a88075166c8006aa8606bf43173a06074166c40172f05ce3085ce6142ac59b0005c6b171942172c450ab166ac5ca1045c75171e02172bc33859aa171fc11719c5c74171dc3172b0406d166a40171a05c67171943172a057c59a7172841171d45c78085ca3109166985c7f045c68171d05c770c5ca1101b459a5001d28074901d290c5c7f141b059a4⟩,
  ⟨0x13c09284481fe0e806a030015809b04401c40ba04901a8090026000, 0x176a41175b85da0170883176c4406d167c0016fa85d6e175d03176c057c59ef176ac1176845da3085dad109167b45da9045bea176805c220c5dab101b459ec001ef707bd41ef80c5da9141b059eb005d6e16fa85d740c5da21418059e9005bea175b85d740c5d7e1c29859e8001ef707bd42175f050a51679c5d3a045d2e174c42174f042459e2174e01173f45cfe174c03174e8406d167840071a41d2a074ac3174e0506c167800171dc5cfd173ec3174bc5060166f80173f45c77173ec3174a870ac166f40071a41d2a085d281429459bc005d22173ec21749850ab166ec0173f45c77173ec31748057c59ba⟩,
  ⟨0x13608e84301ea0db06382d814609003c81940a203e0188084026000, 0x178d85e35085e25178d05e200c5e370c616894016ce85e24085e36101c85a24178cc116ce85e2406cc43178d440711688c5e31178a82178905e2906cc43178cc307016888006b841b2506cb43178c4506f16884006cc81b31085e2b141b859ff005e2316ce81b2d0c5e2615f167f85dfe045ded1779c2177fc33859fc177f0116fb85dec171a03177f8406d167ec00749c1d26074943177f0506c167e80177ac5bee177a83177b85060167e45dbf045dbd176dc21778033859f6005db6045dbf10d167d4007ac85be9085dbe194167d0007ac81176ec4069167cc5db1045daf175bc2176c833859f1⟩
]

def tableLLR : Table Block := .branch 12 tableLLRL tableLLRR

def tableLL : Table Block := .branch 24 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0x13909584601fe0ee06b82f415209804201c40b404601a809c026000, 0x17aa0117ab050b5168e05ea4045e72179b8217a943385a3717a8c5ea2085e7217a845e6e0c5ea40c6168d80174c05e71085ea3101c85a3517a801174c05e71075f0317a884071168d05e7e179dc2179c45e76075f0317a803070168cc0074b01d70075e03179f8506f168c80075f41d7c085e78141b85a30003c38174c01d780c5e73141805a2f179b01179805e3a085e6d0ce168b45e6a045be9178fc5bea0c5e6c101b45a2c001eb207ac41ef60c5e6a141b05a2b001d78178f421799c50ec168a8007bd8117998406a168a40178f85be9178f43179845060168a05e37045e25178802178e03385a26⟩,
  ⟨0x10c07f83bc1be0d205f82c814409304081c80c204801c0088022000, 0x5f20045f2c10d169a8017bf85efc085f2b18c169a406a5205efc0c5f281cb169a006a520217c986285a6717be8117be05ef2085efb0ce16994017bc4117be84345a64005ef017b80217be46505a63001c1da8217bd8507316988076317b805ead0c5eeb21e16980076306a90217ba46745a3f005ee317ab4217b9c50ab168f85eba17ae0217ae45eb717acc317aec3185a3d005eaf17aa0217ae85145a3c17ad8117aa05eb517ac8317ae04105a3b005ead161d8217ad860bd168e8006a941aa3085eb3142f05a39⟩,
  ⟨0x12708803ec1cc0d105f82b012407e0358160082036015007c026000, 0x5fbb045f6617ed45c670c5fbd101b45aa3001cf5181d220748c417eec607716a880073d4617d985fa9105fb71c1d85aa0001cf5185f6617ea4417ecc8075169fc0073d4607488317ec46074169f85cac045ca7172a4217e883385a7b17e805cff085d30173f85c770c5d3d0c1c05a7a174e01173f85d30085fa00c1f05a79174e81174b85d31085f790ce169e05f74043ab60eac0217dd43385a77135e410e7c03ab50e9f4317dd0406d169d80005f61183fc5a7201d8c117d8053c5a7100017cd0612c169b806a5045f3314f169b45f2c045f2a17c84217cb43385a6b⟩,
  ⟨0x11308183cc1cc0d306302d814e09504301d40c404e02000b402a000, 0x1a0f8683908686b18c16af405bd0c68390c68681cb16af005bd0c21a1986285abb1a0dc11a0d4682f0868380ce16ae401a0b811a0dc4345ab800682d17ffc21a0d86505ab7001c1d9821a0cc507316ad8076317ffc58760c682a21e16ad0076306a8821a0a06745ab3006822161d821a09850ab16ac85fe9045eab16080217fa83385aab17f9c117aa84fff085fe9103a45aaa001aa6045fe7142c85aa917f8c117f845fa4085fe40ce16a9c5fbb041cf5185fb51719c417f8c607916a980073d4617d985fa9105fe21c1e05aa5⟩,
  ⟨0x10207a83881960ba05382681140790360164096037016008001a000, 0x68e80468eb14016bd068e60468a01a1e821a39c3385af31a39011a0e4687f1a0b031a398406d16bc805bf5e07650c68e4141b05af11a2f011a2e868b10868bd0ce16bb801a2c011a2f04345aed0068ae1a1f821a2ec6505aec0011a0e4687e0c68b815316bac0056fc21a2d85485aea01d8c687e1a1f431a2b090a316ba007635e00868aa19d16b9c01a1f868391a1f431a284506016b980006874183c45ae2016f411a1cc53c5ae11a1b011a1a8686108686d0ce16afc01a18011a1b04345abe⟩,
  ⟨0x12008383dc1c00d005e82b414409504101bc0ac0460180080020000, 0x1a5dc69750869761a5bc69710c69780c616c9c01a5a4692608697719416c9869740469261a5a469700c6975101b45b25001443bbe0c6974184bc5b24001443bbe1a49841a5c8712e16c8c0051069cc31a5bc612d16c880006965184c05aff0014421a59050e216bf8693904692a1a4d021a4ec4245afc001a701a3b069260c693920816bec69361a4cc21a4d469321a4b831a4dc3185afa00692f1a3b021a4d85145af91a4c411a3b069301a4b431a4cc4105af8001a701a49821a4c470c5af7001a70069d021a4b86085af60068ec1a4a421a4b04045af5⟩,
  ⟨0x12608904041dc0da06082c413608a03c81a40aa042017008001a000, 0x59f016fec69a10c69e51c1a05b3a001efd07bec21a78c506716ce469b70469a71a6c821a6e44245b370069a216fec59f00c69b71c1945b361a6d069b10869b31a6c069ac0c69b50c616cd401a6b469a20869b414516cd069af0469a21a6b869ab0c69b110416ccc0167c05bfb0869af141905b32001efd07bec21a6b0506316cc401a68869a60869aa10116cc001a68869a116ba831a694506616cbc697e0468ea17fcc21a5fc3385b2d1a5f011a3a4582408697e102d85b2c001aa004697c142c85b2b1a5e411a5d8696b08697a0ce16ca401a5a811a5e44345b28⟩,
  ⟨0x13509084381f40e706983081620a004601ec0c405201e00a0028000, 0xb7b03e321ade431ae84506016dbc00f8c82dec1ade431adfc57c5b6e001e71079ac1f640c6b7b141b05b6d006ae61ab9c6ae00c6b7615f16db001a9e46a781aadc31aaf8706816da8007df81f7c086abc1419c5b69006a7c1aadc21aae850ab16da0007c941f23086a6d141845b64001f2407c841e790c6a62141885b63001f2107af421a8e050bb16d846a211a7fc21a88069fe1a7ec31a8883185b600069f31a7d421a8845145b3f1a7f411a7d469f71a7e831a7fc4105b3e0069e81a7c469ef0c69fd182b85b3d001f2007bf01ee30c69fb142b45b3c001eff07bf81ee40c69ea141885b3b⟩,
  ⟨0x135091043c1f60e706a030415409704201c40bc04a01c80a0028000, 0x5ab5045a7f16abc21b1ec3385ba7004cb9169b46c6f0c6c7515f16e900169b44cb91b1bc31b1c8506016e8c01a9fc6c381b0d831b0f4506016dfc01b0e06a7f1b0d831b0ec57c5b7e1b0b811b09c6c29086c3010916df06c2c046a741b0906a7f0c6c2e101b45b7b001181f6e07dbc41b0b0607716de800461a9d06c22106c281c1d85b78001186a741b08841b098707816ddc6bff046bfb1aac021b0803385b761aff411afe86a79086bff103845b75001f6507d8c21aff450e016dd001ab9c6ae0086bfc142fc5b731ae9011aba06a74086ba60c1f05b71001f6d07d941f630c6ba4141b05b70⟩,
  ⟨0x136092844820a0f5073834017209904281c80ba04b01d00a0028000, 0x1eb907adc21b3b8506716eec6ce3046ce11b2ec21b3903385bba006cba046ce310d16ee4007dc86cb8086ce219416ee0007dc811b2fc406916edc6cb2044cb91b18c6c700c6cb7101b45bb41b2c81169b46c631b1c031b2cc406d16ecc6cb11b2906ca10c6c631b28c6c7e1b1c041b2c830aa16ec86cac046ca31b18c21b2c4307c16ec46cae046ca71b2a421b2c04245bb01b2b01446ca31b18c31b2b860a916ebc0441ea407a8831b2b060a816eb80446c7e1b28831b2a075c5bac0111b1f86ca20c6ca51c29c5bab1b1fc11b1c06c7e086ca10c1f05baa001ce6073881ea30c6c7f141b05ba9⟩,
  ⟨0x13808f843c1f20e506882f415809904281b00b804601a8090028000, 0x1b5a86d68086d691b59c6d640c6d6b0c616fb001b4f86a29086d6a14516fac6d66046a291b5846d630c6d6810416fa801b4cc6d3c1b4e831b59860ae16fa4007af01eb8079fc31b59050ad16fa0007aec1eba07a8831b4d4506216f9c01b3a46ce5086d2b142ac5be61b49011b3d06cff086d2610916f9001b3cc6ce71b18c31b490706516f8c6d211b3f821b4806cfd1b3e431b4883185be2006cfa1b3cc21b4845145be11b3f011b3cc6cfb1b3e031b3f84105be0006c631b39c21b3f0506416efc007ae41eb7086cf91418c5bbe006cf31b3c821b3dc4045bbd006c631b39c6ce50c6cf01c1a05bbc⟩,
  ⟨0x14009384581fe0e5068830015809904101b80aa0450178084026000, 0x1b7a06de7086db71b7986db00c6de90c616ffc01b39c6db6086de8101c85bfe1b79411b39c6db607c9c31b79c407116ff46de31b6f021b6d86dbb07c9c31b794307016ff0007adc1efb07c8c31b78c506f16fec007ca01f27086dbd141b85bf9005bfb1b39c1f230c6db8141805bf81b6b811b5fc6d75086daf0ce16fd86dac046cb81b5f86c380c6dae101b45bf5001f7307dc81f710c6dac141b05bf41b6a06da6086da71b6946da30c6da90c616fcc007c8c6d7b086da814516fc86da4046d7b1a9a41f710c6da610416fc4007c8c11b690406b16fc0007dc411b68c406a16fbc01b5f46cb81b5ec31b68057c5bee⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0x140096046020e0f606e833416e0a304781ec0d005101f009c026000, 0x6aa31b9bc6e750c6e78141805c33006a741a9e06e220c6e661c2b05c30001f6e07df021b99050a5170bc01b8f86e22086e62142ac5c2e1b8e86e38086e391b8dc6e340c6e3b0c6170b401b8946e28086e3a145170b06e36046e281b8986e330c6e38104170ac01b7e86e221b88031b8d860ae170a8007e841f7d07d8431b8d050ad170a4007e801f7f07d8c31b7ec5062170a06df5046c3a1b7c821b7dc4245c271b7b411a9fc6c391aa8c31b7d4406d170986def046c3c1b0f821b7c44245c241b7b411b0e06c391aa8c31b7bc406d1708c007dd01f7007dd431b7b4506c170886de9046db71b6c021b7a83385c20⟩,
  ⟨0x13009004401f40e7069830816209d04601ec0d005101f009c026000, 0x6ee9168c021bbc86505c68001c01ce2086eef141cc5c671b0b010461b0906a7f106ee5181e45c651b7bc11b0f06c3e086ee20ce1719001b0e06a7f1b0d831baf870a617184007dd01f70086ebc142945c60006eb61b0d821bae850ab170fc01b9bc6aa31b9d431bac070a6170f4007de81f76086eae142945c3c006ea81b9d421bab050ab170ec6ea4046e771b9c021ba943385c3a1b9fc11b9bc6e761a9e031ba90406d170e46ea1046e7a1b9f021ba8c4245c381b9fc11aa8c6e761a9e031ba84406d170dc007de81f7607dec31b9fc506c170d801b9bc6aa31b9d431b9ec57c5c34⟩,
  ⟨0x11308003cc1c00cd05e82bc13c08b03c01940aa044018808001a000, 0x6fec046fea1bf8021bfb43385ca0006fbf046fec11c171fc01bef438fd1bed031bfac66c5c7e006fbc0e3f46fb40c6fe819a171f4007cfc1f39086fe5159171f0007d8011bedc50ba171e801bed46e20086fb9142ac5c7916ab0116a845aa3086fb20ce171e06df5046c3a1b7c821bcf03385c77001186a741b08841bcd08075171cc004607db831bcc86074171c801bcb06c22086f30142ac5c711b0b811b09c6c29086f230ce171bc00f5f03d7f086efa142ac5c6d1bbcc11bbc46eeb086ef40ce171a801bba811bbcc4345c69⟩,
  ⟨0x12b08b84101e00dc06402d014609003e01b80aa045017807801a000, 0x69c078661e1a831e1c870a7172d001e1b078661e1a831e1bc57c5cb31e19c11e18c78660878690c1f05cb2001a7b069cc1cf80c7867141b05cb1003bbe0e9f478390c7865141805cb0003a7d0eef878390c78611c2985caf001a7b069cc21e0fc50a5172b8782d046ff61bfc421e0b83385cab1e0ac11bfd46fbc08782d102d85caa001f3e04782b142c85ca91e09078220878231e0846ffe0c78250c6172a001bfe06ff40878241451729c7820046ff41bfe86ffd0c78221041729800f9b439a2087820182f45ca5001f3d07cec21bff850bc1729001bfd011bfdc5005ca3⟩,
  ⟨0x1840ac051026211e083839c1a60bf04c82140e405f02400a0028000, 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⟩,
  ⟨0x10807a03841ac0c705a029c12e08603b81900ae0440168080026000, 0x1689811689459b40879720c1f05cfa00796c16b985aea0c796f15f173e40007960183dc5cf7001ea01821e4fc50e2173d879340479321e4a421e4d43385cf400792804793410d173cc01e49c78f5087933194173c80166d078f5087930143bc5cf100607ba021e4b850ea173c001e3d45a241e3cc31e3e057c5cee004bf60478f211c173b478f00478e01e2f421e3c43385cec1e1d81069c078701e1cc31e3c060a9173ac01309011e3bc4705cea001cf30478e4158173a00069c078661e1a831e38475c5ce7⟩,
  ⟨0x15a0a184c023010307703641900b505102140e405f02100b8034000, 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⟩,
  ⟨0x1540a084b822e104078836817409d04181bc0b804b01b0090026000, 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⟩,
  ⟨0x11808283b81b60c7059828811e07c037817c0a203e0188084026000, 0x1eaf411eae47a2e087abe0ce176805e6a045e3e178fc5bea0c7abd101b45d7f005be9178f85e3d0c7aba15f175f80075d01d73074e431eacc5062175f400eafc3c380f2b031eabc7068175ec0075c81d70087aad1419c5d7a176ac1176845da3087aa40ce175e47a73047a711e9ac21e9d03385d75007a6a047a7310d175d0007dcc6d7d087a72194175cc007dcc11e9bc4069175c87a64047a621e8f021e9943385d70007a3b047a6410d175bc007ac45e3e087a63194175b8007ac411e9804069175b479be0479b11e6a821e8904245d63⟩,
  ⟨0x141097045c2040ea06a830015609904401d00ba04901b0088022000, 0x7b6d047b6b1ed9821edb83385db51ed8411eca07b361ece431edb4406d176d0006aa861eca07b27107b6c1c1d85db31ed84106aa861ecd87b39107b63181e45db1001aaa181ab706ae041ed846077176c0006aa861eca07b27107b381c1e05dae001aaa187b281ec9c41eccc8075176b4006aa8606adc31ecc46074176b001ecac7b27087b2f142ac5dab007ae21eb847ae00c7b25141805da91ebe811eb887af01788c31ebf0406d1769c0067e41abf06b8031ebe8506c1769801eb847ae21eb8031ebc857c5da4007ae11eb887ae00c7aed1c2b05da30019f906afc21ebac50a51768801eb947ae0087ae9142ac5da1⟩,
  ⟨0x144098047c2160fa07003301720a204701e80ce05401d80a8026000, 0x5deb16fb87bef0c7bf2141805dec007bb61ee8021ef8050ab177a401ee887b391ee8031eef470a61779c006af41ab9087bbb142945de61eecc7ba4087ae21ee8c7b390c7b7d0c1c05de51eeb811ee8c7ae2087bb30c1f05de41eec011ee987ba8087bb21091778c7bae047ba21ee8c7ae20c7bb0101b45de2001abd06ae41abe0c7bae141b05de1007b391ee887ba00c7ba7141805dbf007ba21ece47ba00c7ba515f176f87b77047b6f1edc421ede44245dbc1edd87b75087b6f1edd07b710c7b770c6176ec00f0e05e71087b76101c85dba17a8010f0e05e71075f031edd44071176e40174c03c38075e031edc057c5db7⟩,
  ⟨0x130090041c1ee0e1069831416409904401c40ba04a019807c01c000, 0x6041e710c7c7a184b45e231f1b47c6b087c6c1f1a87c670c7c6e0c61788001f18c7c3d087c6d145177fc7c69047c3d1f1a07c660c7c6b104177f801f18811f1a4516b177f40079d011f19c516a177f07c27047c221effc21f0a03385df71f0987c25087c221f0907bff0c7c270c6177d801788c5e24087c26101c85df5178cc11788c5e2406cc431f0944071177d0016ce85e2306cb431f08c5060177cc7bfd047bf11efb021eff83385df11efec116fb87bf00ebd031eff4406d177c000749c1d26075ac31efec506c177bc006cb47bef087bf8143b05dee001d6b047bf7101a85ded⟩
]

def tableLRL : Table Block := .branch 12 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0x13208f843c2020e806c030815c09704181c00c604a01d008c026000, 0x7ce11f2f07ce30c7cee19a178d8007b841e77087ceb159178d401f29c11f2ec50b5178c87cb41f2c821f2cc7cb11f2b431f2d43185e31007c3f1f29c21f2d05145e301f2c011f29c7c601f2b031f2c84105e2f007c3d129d87c3a0c7cb0182b85e2e007c3d129d87c3a1f29c41f2b85169178b40079d41e73079b431f2ac5168178b07ca4047ca11f1d821f2943385e2a007c75047ca410d178a47ca21f28021f2847c7a1f1f031f28c3185e28007c731f18821f2886505e271f1fc11f1887c731f1ec31f280406d1789801810f8c831f1fc612f1789401810f8c87c62107c7d1c4b85e24⟩,
  ⟨0x11508083d01c20cd05f82bc14208803c01880a20400198080026000, 0x16b98796c16ba831f59c5060179a0007b8811f5845605e671f4e811f3e87cf4087d3b0ce179947d38047cf91f38421f4e840b617990007b8011f4e050b21798c0168dc7cfc087d35145179880079e411f4cc50be179847d2c1f4a821f4ac7d291f49831f4b43185e60007d201f3e021f4b05145e3f1f4a011f3e07d221f49431f4a84105e3e007cfe1f3f021f4a060bd178f4007afc1ebe087d26142f05e3c007cf8047cfb140178ec7cf2047cf01f39821f3cc3385e39007ce5047cf211c178e001f3887cbc1f38c31f3c466c5e37⟩,
  ⟨0x12908b04081e80e106a030015a09904001c00b404901c00a0028000, 0x7db5047cba1f2f421f6dc4245e791f6cc11f2e47cbc087db5103a45e78001e76047db3142c85e771f6c011f5807d3c087db10ce179d401f38c11f6c04705e74001eef07b981ef00c7da8141b05e731f68811f5c87d7d087da4109179c801f5a059b41689031f6887128179c47d7f1f5f021f5f87d7b1f5dc31f6803185e70007d781f5a021f5fc5145e6f1f5e811f5a07d791f5d831f5f04105e6e0059b41689021f5e85127179b4007ba01ee6087d77144985e6c007d681f5c421f5d44045e6b007d691f5a87d680c7d6f141805e6a001ef107bb81eeb0c7d6c141b05e69⟩,
  ⟨0x12308783ec1ce0d606182bc12c086038017c09c03e015807801c000, 0x1f9d47e6512ed431f9e0506617ab00072d41cb4071e831f8e8506217aac01f7c07def1f7a831f8d4706817aa80072cc1cb1087e331419c5ea91f89011f7d07dff087e2610917a9c01f7ac7def1f7c031f890706517a987e211f7f821f8807dfd1f7e431f8883185ea5007dfa1f7ac21f8845145ea41f7f011f7ac7dfb1f7e031f7f84105ea3007df01f7bc21f7f0506417a880072cc1cb1087df91418c5ea1007deb1f7cc21f7dc4045ea01f79c11f7947dbf087de80ce179fc01f6f811f79c4345e7e001de91f6f021f7986505e7d001de9047de3101a45e7c⟩,
  ⟨0x139093043c1f60ea06e032416009f04401b80b404901b0094022000, 0x7f37047f2c1fc8c21fce03385ee31fcd411f6f07f2b0bad831fcdc406d17b880077a81de9078c831fcd4506c17b840072e47f28087f32143b05ee0001e32047f31101a85ebf007f2a1f6f07f280c7f2d15f17af87f201fbfc21fbbc7efe1fb9c31fc843185ebc007def1fbb821fc80407217aec7efd047def1fbb81cbd0c7eff101c45eba1fbec7ef4087eee1fbcc1cbd0c7efd0c1c05eb9001c6d072c41cb90c7efb141bc5eb8001cbe072f421fbd4506e17ad801fbb47def072e431fbc057c5eb5001cbb072e421faf4506117ac00072e81cb7070bc31fac8506217abc0072dc1c73087ea8142ec5ead⟩,
  ⟨0x14c09e04942240ff07403201680a104501d80c604f01d809c026000, 0x19b0070b821feec6745ef81feb811fd987df01fdd031fecc406d17bdc7fb0047f771fd8021fec84245ef61febc11fd807f77087fb00ce17bd47fae047f391f7c07f740c7faf101b45ef41feb47f7e1fdf031f7c07f7d1fde47f74107fae0c2a85ef31fea011fdf47df0087fad0c1f05ef21fea811fe807fa2087fac10917bc47fa80419b01fdf47df00c7faa182a45ef00019b0072801c7a0c7fa8182a05eef0019b01fde47de90c7fa11d717bb40066c07f791f7a431fdfc70a717bb07f7a047f741fde421fdf0307c17bac0071f81c7c071fc31fde8506c17ba801fd987f391fdc831fde0506017ba401fce47f661fdc831fdd857c5ee8⟩,
  ⟨0x12b08b841c1e80dd06502cc13e08c03c01940b004801b809c026000, 0x66c04e211ffec3220dc90a317cb00066c018f108883519d17cac882d047ffd1ffe02220b83385f2a220a010eef47ffc124f03220b4406d17ca4882a048820220882220b04245f28220a01138847ffc124f03220a8406d17c9c0063c018f1066c83220a0506c17c9800eef44e211ffec32208457c5f24004e210eef47ffb0c7ffe141805f231ffd811ffd07feb087ff70ce17c8401ffa811ffd84345f20007fe81fefc21ffd46505eff00493c1fefc21ffc850eb17bf80070066cc21ffc050ea17bf401fd947fbf12ed431ff88506017be80066c07f6512ed431fef48785ef9⟩,
  ⟨0x13008e84402000ef070033416c0a204781ec0d005101f00ac028000, 0x222c41222bc88a60888b20ce17d880222941222c44345f610088a3221bc2222c06505f60004b7a221bc2222b450ef17cfc0181c300888ab143a85f3e221f81221e87f3a0888a010917cec887c044b7a221d47f390c887e101b45f3a001c7d070c01c310c887c141b05f3900886f12de84bac0c887b15f17ce0012de8886f12eb03221dc506017cdc88660488641fd9c22219c3385f33220f811fd947fe01fd98322198406d17cc801fefc7f6512ed432219457c5f312218011ff847fe308886210917cbc883e047fbf1ff807f660c8860101b45f2e001c7b070b81c2f0c883e141b05f2d⟩,
  ⟨0x13d09504682180f307183341720a504901ec0d005101e80a802e000, 0x12fb48929224883224d46685f75001c33070b42224c85645f74001c34048924142e85f72223f488fb0888fc223e888f70c88fe0c617dc40223c87e790888fd14517dc088f9047e79223d088f60c88fb10417dbc0223c088ee223b03223e460ae17db80071c81c6e070d43223dc50ad17db488bf044b7212dd02223803385f6b222e81126d44a2c124cc3222fc406d17da888bc044a2d1289c2222f84245f69222e81127984a2c124cc3222f0406d17da00060a8182b066d83222e8506c17d9c88b4048876221c02222e03385f65222d01221d888700888b610917d90887c04886f221d47f390c88b4101b45f63⟩,
  ⟨0x11f08403e01ca0d506102bc12c08603801800a00400198080026000, 0x89e004897d226d489bc0c89e1101b45fa7001442b6f0c89e0184bc5fa6001442b6f225f44226f8712e17e940051070803226ec612d17e9089b00489a1226ac2226c84245fa2001bfd2258c897d0c89b020817e8489ad226a82226b089a9226943226b83185fa00089a62258c2226b45145f7f226a012258c89a7226903226a84105f7e001bfd225f42226a070c5f7d001bfd070842226946085f7c0089632268022268c4045f7b00893f04896214017de88939048937224b42224e83385f7800892c04893911c17ddc0224a88929224883224e066c5f76⟩,
  ⟨0x12308603f01d20d906002c013408c03f01ac0ae04901b00a4020000, 0x8a290489ee227f48a250c8a2a101b45fb9001442dec0c8a29184bc5fb8001442dec227b842289c712e17edc0051079ac322890612d17ed889f9227dc2227e089f6227cc3227e83185fb40089ef1f0e82227e45145fb3227d411f0e889f4227c83227dc4105fb20089ee0489f5145ac5fb1001e6c0489f3145a85fb0227ac122584893b0889ec0ce17ebc89e9048960224a42227ac40b617eb80070b01227a450b217eb489e50489e2226dc2227983385fab0089b60489e510d17ea889e32278422278889bb226f43227903185fa90089b5225f422278c6505fa8⟩,
  ⟨0x14009684582040ef06d830816209a04381d00ba04901b00a4020000, 0x22a801229f48a76088aa10ce17fb88a7e048a75229f07def0c8aa0101b45fed001be8072bc1cb00c8a7e141b05fec1fc8411fbbc7ee7088a6b10917fa401f6f07f2a1fca0322998506017fa08a61229802228f48a3f228e83229883185fe7005bfb1b6d8222984407217f986de5045bfb1b6d81f270c8a60101c45fe5006ce716fec1f230c8a3e15f17f908a38048a34228c42228e43385fe21b6b011b5f46d7e1b0e03228e0406d17f8401b2e06d7d1b5ec3228d4506017f808a2e048a2b228802228bc3385fbd0089ff048a2e10d17ef08a2c228a82228ac8a24228983228b43185fbb0089fd227b82228b06505fba⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0x12e08d840c1dc0d906202c814209604381cc0c405101f009c028000, 0x22c90122bf48aff088b261091a08c8b22041c36188afc22b90422c9060791a0880070d86072a41caa108b22181dc6821001c36188ae322bb8422bf8707817ffc0070d8622b8c8aee108af9201d45ffe001c36181ca90c8af7181d05ffd008af122bb8222bd450ab17ff00008ae1183c05ffa001c3618222b8050e217fe40229d48a71229ec322ae070ac17fd8006fa01caf088ab6142945ff5008ab0229ec222ad050ab17fd08aab048aa622aa0222ab44245ff3229f81229c48a7c1f7bc322aac406d17fc80229d48a71229ec322a9c57c5ff0008a71229d48a7b0c8aa4141805fef⟩,
  ⟨0x13108f041c1e80e106502d814408e03e81a80ba04d01f80b002a000, 0x8b7b048b7922ce0222df0338683822dcc122b908b6a229c4322dec406d1a0dc00f0a48ae422cf4322de857c683622dd4122dac8b6d088b771091a0d08b73043c2922da88a710c8b75101b46833001cad072ac1cae0c8b73141b06832008ae40f0a48b3d0c8b6c141806830003c2922b908b3d0c8b681c298682f001cad072ac222d9850a51a0b88b36048b3422cb8222cdc338682c008b2d048b3610d1a0ac0077a87f2a088b351941a0a80077a8122cc840691a0a48b2a048b2822b94222cac338682722c88122b8c8afc22b90322ca8406d1a0980070d8622b8c8aee108b291c1d86825⟩,
  ⟨0x13109184401fa0e606902f815609404001b40b804e01d80a0022000, 0x77a0122ffc406a1a1b001fca87dbc22fe0322ff057c686b22fc0122fac8ba9088bf10ce1a1a48bee048ba822fa86ce70c8bf0101b46868001deb07ad41eb60c8bee141b06867008be922ea08be80c8bec14180686622f98122ed88bae088be70ce1a1948be4046cb822ed429f50c8be6101b46864001f7307dc81fbc0c8be4141b068631b7a411b6dc6db0088be31091a188007c8c8bb3088bbc143b06861001fbc048bbb101a86860006d7d1b2e08bb30c8bb715f1a0fc8ba3048a65229b0222e94424683c1fcd411fca87f2b0bad8322e8c406d1a0ec022d848b3d088b7e142ac6839⟩,
  ⟨0x144096846020a0ed06c030c15c09c04581e00c204d01a009001c000, 0x231bc1230c08c66230c43231dc406d1a1fc007a806230c08c38108c761c1d8687e231c412319c8c69088c731091a1f08c6f041ea0188c66230c44231c460791a1ec007a80607ab41eae108c6f181dc687a001ea0188c30230e04231a070781a1e0007a806230c08c38108c63201d46877001ea0181ead0c8c61181d06876008c3b230e02230fc50ab1a1d48c2a048bfb22fc82230ac3386873230a011f6f08bfa22ea03230a8406d1a1c80077a81de9077a03230a0506c1a1c48c242308822308c8c2122ffc3230943186870001cb922fe0223090514686f23080122fe07eb9077a0323088410686e001cb9048c20101ac686d⟩,
  ⟨0x13d09304481fc0ed06e032016e0a604601e00ca04e01d009c026000, 0x8c28047f2a22fe88ba80c8cf9101b468b4007dbc1fca88bf80c8cf61418068b3008ba822fa48be80c8cec1c2b068b0001deb07ad42233a850a51a2bc0230b88be8088ce8142ac68ae008c7a230c48ca00c8cbd1c29868ac001eb307abc2232ec50a51a2ac0232d48ca0088cb9142ac68aa232c88ca2088be9232848c7a0c8c7b0c1c068a9232b41232848be9088cb20c1f068a8232bc1232948ca7088cb11091a29c8cad048c31232848be90c8caf101b468a6001eb307abc1eb40c8cad141b068a5008c7a230c48ca00c8ca615f1a28c0230c48c7a2328032328c50601a2888c77048c75230c82231e033868a0⟩,
  ⟨0x12b08b84101e20de06883041620a004681d00c604c01c0090026000, 0x66dc19b3070e43238c4506c1a3a80124cc493c124ec3238b857c68e9008e21238988e250c8e2c15f1a3a08de9048de7237842237a833868e6008de0048de910d1a3940236fc7f65088de81941a3900070066cc22379450731a38c0220c07ffb088da0142ac68e0235b41235a08d63088d6e0ce1a2fc8d6c235ac2235a08d6a2358c3235b431868be007eed1fbb82235b040721a2f47efd047eed1fbb81cbd0c8d6b101c468bc007def1fbb41cb90c8d691418068bb0049341fbb488ee0c8d3e1c2b068b9001c63071b42234f050a51a2e08cf9048cf5233c02233e833868b5⟩,
  ⟨0x137095045c2080f407383581860b004e82280e605c01e00a0028000, 0x23ca0123cd447068fe008f25224a48f260c8f3419b1a3f4023c90892923c98323cc466868fc001c77070b4223cb856468fb001c34048ef71581a3dc023bd48e25088ef9142ac68f6222f01128b44a27088e710ce1a3d0882a048820220882239c033868f3238f41124f84935088e3f1091a3c88e3c044935124f82238f433868f1238dc1124cc4934124f43238f0406d1a3c08e3704493c124d0493d0c8e38101b468ef238d88e2b238cc3124d08e2723898493d108e370c2a868ee238d012389c4934088e360c1f068ed001c62070e81c380c8e34141b068ec238c41124f48e26088e330c1f068eb⟩,
  ⟨0x10f07b03981a00bf057028411c07a03601840aa0420170084026000, 0x8fed23fac223fb08fea23f9c323fb83186934008fe123ee4223fb4514693323fa4123ee48fe323f98323fac4106932008fbf23ef4223fa460bd1a4c40071d41c74088fe7142f06930008fb9048fbc1401a4bc8fb4044beb12fb8223ed4338692d23ec8112fa84bed088fb4103a4692c001c32048fb2142c8692b00023eac613c1a4a401ad048faa14f1a4a08f73048f3f23bf0223dd03386925227a41225808929088f73103a46924008f26048f6511c1a4880224fc123d8050b51a4848f35048f3323ca4223cd833868ff⟩,
  ⟨0x11008003cc1cc0d305e02a412a08403981800a6040016007801c000, 0x7c3a227bc2262d4404696d007ca70498b11401a5b00079f81262845606969261d81260c898340898770ce1a5948bee048be922fa86ce70c9876101b46964231c412319c8c690898740ce1a58c0230c06ce71b4f032619c70ac1a580007ab41eb708986514294693f00983f1b4f022618c50ab1a4f8022ea08be922fa03260cc57c693c008922048fff11c1a4ec8ffb048fbb23ed8223ff0338693923fe4123ee88f24088ffb102d86938001c76048ff9142c86937004bb523ef4223fd85146936001c2f048ff4142f86935⟩,
  ⟨0x10f08003b41be0cc05f82b013008a03e81a80ba04a01b809c028000, 0x705e208997f141cc69a91bb9411b0946c3108996d0ce1a6980079f81264cc50ba1a6906cae046ca71b2a42264c833869a200987e04993111c1a68499290498f4263b82264a8338697c2649c1263cc98bc089929102d8697b001e7c049927142c8697a0098f20498f51401a5e498ec0498ea263802263b433869770098bf0498ec11c1a5d80262f47cbc261f83263ac66c69750098bc1f2f0987e0c98e819a1a5d00079f41e770898e51591a5cc98ba0498b0262b02262ec33869711f6cc11f2e47cbc0898ba102d86970⟩,
  ⟨0x11508203cc1c00c905b028c11807b033815408e03c0180074020000, 0x73981ce2089a2e1429469e0009a281b1bc2268b050ab1a6fc9a200499fe266b422688433869bd267e011a1f899f0265e0326880406d1a6f001a0e4687e267983267fc57c69bb267e81267c499f30899fc1091a6e899f8046839267c099780c99fa101b469b9016fd7817843267e0506c1a6e001a1f86839267983267c850601a6d805bb1a1f899e60c99ee21e1a6d405bb5e00899ec19d1a6d000099ab183d469af016ec1266a853c69ae2668c126684997b0899a40ce1a6b00265e812668c43469ab009979265d022668865069aa⟩,
  ⟨0xf807703881a20c4059828011a080038018409c0410188084028000, 0x26ac065469f3001c4126abc53c69f2012269e09a760c9aa621e1a7c00481d0226a9067469ef009a7e269d8226a8850ab1a7b80268c89a78269d83269ec57c69ed269d01269c89a6c089a750ce1a7b00269ac1269d043469eb009a6a269902269cc65069ea001c01d82269c050731a7a49a62049a60268dc22698c33869e7009a36049a6210d1a7980268d09a32089a6118c1a79400710c9a320c9a3e1cb1a79000710c2268f062869e3004cb9169b46c6f0c9a301c29869e1⟩,
  ⟨0xe706b832816e0aa04d02240f8071032816809c03b017007801a000, 0x2f30c9b220c9b3d1cb1a8b802f30c226cec6286a2d26cc4126cbc9b26089b320ce1a8ac026c94126cc44346a2a009b2326bf8226cc06506a2900126c889afe0c9b2d1531a8a0004bd4226cac5486a2700026be860fe1a89002f3049af914f1a88c0009af1185c06a21013ec126bc053c6a2026b84126afc9ab6089ae20ce1a7e8026ad4126b8443469f9009ab4269e0226b8065069f8001268c89a780c9abd1531a7dc0041cc226aec54869f6⟩
]

def tableLRR : Table Block := .branch 12 tableLRRL tableLRRR

def tableLR : Table Block := .branch 24 tableLRL tableLRR

def tableL : Table Block := .branch 49 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0x12b08f04381fa0f006c82e414a09103f01ac0b00410180074020000, 0x26efc126fac4346a68009bbc26ef4226fa86506a6700626eec9bbd0c9be71531a998018eb4226f945486a6526ee41169b48c301b1c0326ee8406d1a98c9bb826ed06ca10c8c3026ecc6c7e1b1c0426ee430aa1a9889bb6049bb3230c0226ee0307c1a984007ab01ea407a88326ed8506c1a980026ec86c7e1b288326ed457c6a3f16cc41165f4597f089bb10ce1a8f89b77049a7a26db8226de44246a3926dd41269e09a79269a4326ddc406d1a8e000730740750c9b75141b06a3726d84126cfc9b36089b620ce1a8c4026cd4126d844346a30009b3326c88226d806306a2f⟩,
  ⟨0xfb075036c1900bb0558268114077032015c08e037015007c026000, 0xf8d03e6f089d22143bc6aa000607cf022748050ea1a9fc9cab049ca9272802272b03386a7e009c7f049cab10d1a9f40271f49c79089caa1941a9f000b7b09c79089ca7143ac6a7b001c01e6b089ca5143a86a7a170f81170dc5c39089c640ce1a9d89c29049c2726ff82270a83386a73009bfd049c2910d1a9c8026fec9bbb089c2818c1a9c403ab209bbb0c9c251cb1a9c003ab2022708c6286a6f00026fd060f21a9b003ab049bf314f1a9ac9beb049be926f80226fb03386a69⟩,
  ⟨0x12308783f01ca0d105f02c414209004081b80b60440180074020000, 0xb6e89c790e6883276cc50601aad09dac049d72275d02276b84246ab3276a810b6e89d710fd943276b0406d1aac8007eac1f3a07cec3276a8506c1aac49da6049da4275ec22769c3386ab0009d7a049da610d1aabc0275e43fa9089da51941aab800f9983fa9089da2143bc6aad00607eb822768050ea1aab00271e42dba0e6883275cc57c6aa9003fa90fd943fa80c9d6015f1aaa03f37043e6f0f9c03e660c9d2f101b46aa5003e340f9bc3e6d0c9d2b141806aa4274981274909cfb089d270ce1aa8c0273e81274984346aa2009cf80f9bc2274946506aa1⟩,
  ⟨0x123088040c1e00dd066830016409f04581c80c404c01d80a802e000, 0x9e63049e61278dc2279903386ae8009e36049e6311c1ab9c0278d09e21278b432798866c6ae6009e32278849e2d0c9e3f19a1ab940076d41daf089e3c1591ab900278981278b05006ae2009e26049e2a142d46ae1277d81277a09df1089df81091aafc00bfe42a710a9ac3277d870651aaf89df3277c02277c89def277ac3277d03186abd009dec0bfe42277cc5146abc277b810bfe49ded277a83277c04106abb002a6b0a9c42277b850641aae8007f941fe3089deb1418c6ab9276d01276c89d6d089db50ce1aad89daa049c79275c43f650c9db4101b46ab5⟩,
  ⟨0x10807a83841a60c605c02ac13a08a03e81a80ae047018007001c000, 0x27cc410e5ac3966089f320ce1ac849f2f04396a0e48c227cc440b61ac80007e98127cbc50b21abfc007fb4127c984706afb001dae049ef9142c86af9009e2d049eed11c1abd80077f8127b9050ba1abd49ebc049eba27ac0227af43386af3009eaf049ebc11c1abc8027ab49e2107fb4327aec66c6af1009e65278841fed0c9eb819a1abc00077f41daf089eb51591abbc9eac279b42279949e6c089e660c2dc6aed27aa81279b09e65089eac0c2cc6aec001dfc049eaa142c86aeb009e6a049e6e142d46aea⟩,
  ⟨0x141098047421a0fa076838019a0ba05382400fa06a029809c026000, 0xbffc2ff8089fea144e06b3b001bfd0b39c29a30c9fbc21e1ace0006ff41db0089fba19d1acdc287304286b0a1b4227ec43386b36006fb4049fa911c1accc00e3b8127dfc4706b2f274bc1274a89d2c089f7d0ce1acb89f65049f3c27d88227d9c4246b2b27d90127d889f3c089f650ce1aca89f3e043fa90a0ac3faa0c9f64101b46b2927d8010feac4822089f611091aca09f3f0448220feac227d803386b2727cf810fd94282b0fea8327cfc406d1ac983fa20fffc3ffe0fecc3faf14282b0fdf83f7d0fec83fac0fea8627cf831611ac9400fd943fa90fea0327cf450601ac902a2b042a240a898227cdc3386b22⟩,
  ⟨0x134090043c2020ee06d03301720a604902100e206102a00a0028000, 0x2b760adbc2b750ca93d1c2986b7a001c270708022a4ec50a51ade4007b8812a4b050ba1add8a92504a9212a48c22a4983386b741f4e011f3e47ce108a925103a46b73007cf804a922142d46b720a19810a0e8283d08a8e10ce1adb8a8b704a8722a1b422a2e03386b6c2a2d412a1c49e3208a8b7102d86b6b001db404a8b5142c86b6a001bfd122c0a8740ca8ad21e1ada0006ff41db208a8ab19d1ad9c02a1c012a1cc5006b6627fac9fe90fdf0482427fc450a9ac38200bffc3f770fd943e66189fed0c5846b3e0fd9810f9983f65089ff10c1f06b3d0e08c10e0802a6b089feb0c1f06b3c⟩,
  ⟨0x12b08d84281f60e806882f415409604481ec0ce05402080a002e000, 0x2a6e4a96c08a9e61941aec00122c0a96c08a9e3143bc6baf006076c822a78450ea1aeb8a9b704a9752a5b822a6e03386bac2a6d412a5b0a9742a5b432a6dc406d1aeac00788c1db2076cc32a6d4506c1aea8a9b204a97a2a68822a6d04246ba92a2d412a1c49e3208a9b2103a46ba8001db604a9ab1581ae9c02a1c012a5ec50b51ae8c0122c0a96c2a1d032a5d850601ae88a96804a93f0ae9822a5a84246ba02a59c10ae98a93f08a9680ce1adfca9662a59420ae98a9642a4fc32a59c3186b7e002b760a9b422a59840721adf42b70042b760a9b42b6f0ca965101c46b7c⟩,
  ⟨0x12e08d04041e20db06502e415209603f81ac0b404701a008001a000, 0x29620a28c28250caa601c1946be42a8f4aa3a08aa3c2a8e4aa350caa3e0c61af8c02a8d8296208aa3d1451af88aa380429622a8dcaa340caa3a1041af8400a09428a308aa38141906be0001e3b078e422a8d450631aefc00a588a9e908aa331011aef8aa2d04aa272a7fc22a8b83386bbd2a8ac10b39caa262a7cc32a8b4406d1aef00078841db0076c432a8ac506c1aeec00b3d429a308aa29142ac6bba00aa250b39c29a30caa2815f1aee402a5b4a9f32a7c832a7e457c6bb600a9f32a5b4a9f20ca9f6141806bb52a79c12a794a9bc08a9e80ce1aec802a6ec12a79c4346bb1⟩,
  ⟨0x13209204441fc0ea06b030c15e0a204581dc0c604f01d809c026000, 0x1f7704aaeb101a86bfa00292407fdcaae40caae815f1afe4aab3049e292788822aad03386bf527be41278a09e2108aab3103a46bf427be41278a09e2108aaae102d86bf32aa9012a9f4aa7a08aaa50ce1afc49eaa049e6c2799422aa9040b61afc00279a812a9f85006bef27bb0aa76089e2d07fb4207fb831641afb4aa75041fed278b422a9d830b31afb0aa6804a9f40a4c022a9c0307c1afa829340429310a09422a9b0307c1afa40078901e220789432a9a0506c1afa0006ff4293007fb032a99c70a71af9c00a588293807fb032a99450661af98aa6004aa312a8ec22a9884246be5⟩,
  ⟨0x13108d04241ea0e206a831416c09f04581e00c204d01a009001c000, 0xab6d04487e2ad94ab300cab6f101b46c2f001f01f44c832adb4506c1b0b80121e8487e2ad8c32ada450601b0b0ab3e04ab3c2acd822acfc3386c2b00ab3504ab3e10d1b0a802acd0ab2c08ab3d1941b0a4007013308ab3a141cc6c282abd010a490aae61b9bc32ac94406d1b094007fdc29242ab9032ac8850601b090aaf604aae72ab8422abdc3386c212abd0107fdcaae61b9bc32abd8406d1b080007de41f7807ddc32abd0506c1affcaaf02abb822abbcaaed2abac32abc43186bfe001e612ab9022abc05146bfd2abb012ab9028e107ddc32abb84106bfc001e6104aaec101ac6bfb⟩,
  ⟨0x11b08583d41c80d306002b013208503b81a40ac04901b008c026000, 0x2b084abbd08ac2c1451b184ac2804abbd2b09cac240cac2a1041b18002affcabfd08ac28182f46c3f001a250689022b09450bc1b0f8abf904abf82afd422afe83386c3d23ec8112fa84bed08abf9102d86c3c2afc412af80abeb08abf31091b0e8abe604abbf2aed822afc440e91b0e400689812af9850b21b0dc02aef412af8450b51b0d8abb304abb12ae9c22aed03386c3500aba604abb311c1b0d002ae8caba22ae9032aec866c6c3300aba02ae88aba40cabaf19a1b0c800678c19bd08abac1591b0c4ab6f04ab682ada822adc44246c30⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0xf3071834818a0ba057028c12e08403b819c0b004601b809c032000, 0x2b2dcacb108ace41941b1e00185efc2b2c432b38454c6c770066a708acbf1521b1d8000acac183f06c72019fc12b2ac53c6c710002b284613d1b1bc03b704aca014f1b1b8ac7704ac752b1bc22b1e03386c6b00ac6e04ac7710d1b1a802b1b4ac3b08ac761941b1a400706aa08ac73141cc6c68019fcac3b2b0c432b1948786c66019fc19e008ac6319d1b19402b0c4abff08ac371451b19000678412b0d450be1b18cac2c2b0a822b0acac292b09432b0b43186c62⟩,
  ⟨0x12208784081de0dc06602e414408f03e01940a8040017008001a000, 0x2b5b412b5acad6108ad6e0ce1b2c002b58012b5b44706caf00ad3d2ae88ad3e0cad6c19b1b2b802aed8aba22b4f832b5a46686cad001a27066f422b5985646cac2b4b012b4a8acb208ad2d0ce1b2a0ad2404acb12b3f8ac6c0cad2c101b46ca7005efc2b2c4acf40cad2b15f1b298ad2604acff2b48422b4a04246ca52b490117bf0acfe2b1b032b498406d1b29006a76a86a90cad24141b06ca300acb117bf0acf40cad20141806ca1019fcacb12b3d032b3f08786ca0019fdaa022b3e86746c7f2b39412b38cacba08ace60ce1b1e802b2e412b3944346c79⟩,
  ⟨0x12a08b84241ec0e206802f415209603f81ac0b0044019807c01c000, 0x19fc687e2baf032bb9c90a31b3a0067f5e008aee519d1b39c067f067a819e80caeab182a06ce62ba9412b9f0aea408aea70c1f06ce501aa9a8819e90caea5141b06ce400ac6c2b9ecae7a0caea115f1b38c02b9ecac6c2b9e832b9f850601b388ae6404ae242b89c22b9984246ce02b98812b7fcae202b89832b990406d1b2fc0071a41c65071a832b988506c1b2f80173f4adff2b7f832b89457c6cb800adff173f4adfe0cae22141806cb7001a6b069a422b7dc50611b2d40069a81a67066fc32b7b050621b2d000699c1a2308ade3142ec6cb2001a2804ad72142e86cb1⟩,
  ⟨0x12908b04241f20eb06c031c16809d04501dc0c004f01e0098028000, 0xaf6404af622bcf022bd943386cfc00af3b04af6410d1b3ec00719caf3908af631941b3e800719c12bd8040691b3e4ad2604acff2b48422bcd83386cf700acf12b3d022bcc850ab1b3d8af3004af2e2bca422bcc43386cf52bc9011a1f8aee92b9ec32bcc0406d1b3d001a0e4687e2baf032bcbc57c6cf32bc9812bba8aeec08af281091b3c8af240468392bba4ae7b0caf26101b46cf1016fd781a8432bc90506c1b3c0aeff04aefa2bbf022bc844246cef2baac167f2baa4ae700caeff182a46cee019fcaea42baa032bbec75c6cec00687e1a0e4aebc0caeeb141806ce9⟩,
  ⟨0x14009384581fe0e5068830015809904101b80aa0450178084026000, 0x2bef8afbd08afad2bef0afa80cafbf0c61b4c402b9b0afac08afbe101c86d302beec12b9b0afac069b432bef440711b4bcafb92bec822beb0afb1069b432beec30701b4b80067f41a61069a432bee4506f1b4b40069b81a6d08afb3141b86d2b00afab2b9b01a690cafae141806d2a2be9812bddcaf7008afa70ce1b4a0afa404af392bdd85cfd0cafa6101b46d27001c680719c1c660cafa4141b06d262be80af7e08af7f2bdf4af7b0cafa10c61b4940069a4af7308afa01451b490af7c04af732b7cc1c660caf7e1041b48c0069a412bdf0406b1b48800719812bdec406a1b48402bdd4af392bdcc32bde057c6d20⟩,
  ⟨0x135092845c2080f106c831015e09d04601dc0c804d01c8094028000, 0x6dfcb8f908b9261941b59c006dfc12e48c40691b59802e3b8ae262e3b032e3c457c6d642e39c12e1dcb87108b8e80ce1b588b8e5041c3618b8762b7fc42e39c60791b5840070d860718c1c6410b8e5181dc6d60001c361849342e1d042e28880751b4f00070d860718c32e28060741b4ec02e1e8b87408b87e142ac6d3a001c361849342e1d042e1e070781b4e4b86d04ae212b99c22e1bc4246d372b9881173f4ae202b89832e1b4406d1b4d80068841a20067a032e0a850621b4d402b9c0ae6c2bf8432e09470681b4d00067fc19fd08b8231419c6d3300afe22bf84aea80caffd142e46d32⟩,
  ⟨0x12508b84101e00df06702ec14808f03b01980a004201a008001a000, 0x6df812e79840691b688ae6404ae242b89c22e6e43386d7f005cfd2b7fcadfe0cb9af1c2986d7b001c690719422e6b450a51b5e802e69cadfe08b9ab142ac6d792e5fc12e5e8b97c08b9a11091b5d8b8e50449342e1d8adff0cb97f101b46d75001c361849342e1d042e5ec70761b5ccb9652e58c22e590b9622e58032e5983186d710019a92e4dc22e5945146d702e58412e4dcb93d06df432e58c4106d6f0019a904b961101ac6d6e001b7d04b960101a86d6d00b9382e3e4b9370cb93b141806d6c2e49c12e494b8ff08b9280ce1b5a402e3f812e49c4346d68⟩,
  ⟨0x13a09304541f80eb06a02e814c09504081b80ae0430180074020000, 0xb96a2e5a4ba340cba3c1c1a06db600193f064f422e8e850671b6d4ba312e8c022e880ba2f2e7f032e8c83186db400b9692e7fc22e8c440721b6ccba2e04b9692e7fc19ad0cba30101c46db22e8b0ba2508b9ff2e89019ad0cba2e0c1c06db100193d0668419a90cba2c141bc6db00019ae066b422e898506e1b6b802e3d8b969066a432e88450601b6b4b9fa04b9f42e7c422e7ec3386dab2e7e012e4e0b9392e3b832e7e8406d1b6a8006dfc1b7e06df432e7e0506c1b6a402e3e4b9382e4dc32e7d457c6da82e7a812e7a0b9e208b9eb0ce1b69402e78412e7a84346da4001b7e2e4e022e7a46506da3⟩,
  ⟨0x12e08d841c1e80e206882f415809804281c40b00480190084020000, 0xbb31265e0bb3d0cbb6315f1b7b00265e0bb312ecf432ed8050601b7ac05bb2ecdcba780cbb3c1c29c6dea016ecbb372e9e032ece875c6de90019ab066a422ec9850611b7900066a819a7063fc32ebec50621b78c00669c196308baeb142ec6de10019610658019280cbaa2141886de02e9c012e980ba6b08ba721091b6f802e8fcb9692e5a832e9c070651b6f4ba6d2e9a822e9b0ba692e99432e9b83186dbc00ba662e8fc22e9b45146dbb2e9a012e8fcba672e99032e9a84106dba00b96a2e5a422e9a050641b6e40064fc193d08ba651418c6db800ba3f2e8f822e98c4046db7⟩,
  ⟨0x14409884782200fd07383501820aa04b82100da04d01c8098024000, 0x9bbb26ef4bba90cbbba15f1b7fc05bb26ef4bba90cbbb72428c6dfe016eceb822eed46746dfd2edfc12ece4bb7c08bba11091b7f0bb69056ecbb382e5a832edfc60a91b7ecbb7204bb3f2ecc822edd04246df72edc412ecc8bb3f08bb720ce1b7d8bb6c04bb312e5a8bb3e0cbb71101b46df52edb812ed88bb6408bb701091b7d0bb6d04bb642ed8822edb83386df32edb01265e0b96a2ecf832edb4406d1b7c8bb6b2ececbb680cb96a2ece0bb372ecf842edb030aa1b7c4bb6904bb382e5a822edac307c1b7c005bb064a819280cbb69182a06def2ed9812ecf8bb3708bb680c1f06dee0179978819290cbb66141b06ded⟩,
  ⟨0x13508f84381fa0ed06d030c15e09b04401c40ba04c01d80a0022000, 0xbc2e04bc252f0b4bc2a0cbc301041b8cc02e3c8b8f608bc2e141906e320019a30668422f0ac50631b8c402f094bc2408bc291011b8c0bc2204bbfe2efec22f08c3386e2f2f08012e3b8b8ef1fbb432f088406d1b8b8006e801c6b071b032f080506c1b8b402b898b8ee2e3b032effc50601b8b0bbf904b93a2e4d022efe83386e2a2e7e012e3e4b9392e3b832efe4406d1b8a402e3b8ae262e3b032efdc70ac1b8a0006e801c6b08bbf5142946e2700b9bc2e3b022efcc50ab1b898bbe304bbb92eeec22ef944246e232ef84126ef4bbaa2ecc432ef8c406d1b88803ad3ae5e50cbbe1141b06e21⟩,
  ⟨0x13909384602080f106c031c16009d04481d40c205001e80a4020000, 0x5bb265d0babd0cbce821e1b99405bb063f822f3986746e640099742f2f8babd0cbce1141806e632f2e812f2d4bcb208bcbb0ce1b988bcb92f2e022f2d4bcb72f2c832f2e83186e6100b8f62e7fc22f2e440721b980ba2e04b8f62e7fc19ad0cbcb8101c46e3f00b9692e3d819a90cbcb615f1b8f802eafcbabe2eaf432f2a450661b8f000669419a4065a832f1c050621b8ec02e3c8b8f62f0f032f1a870681b8e400668c19a108bc681419c6e382f0d812f098bc3108bc381091b8dc02f094b8f62e3c832f0d870651b8d8bc332f0c022f0c8bc2f2f0ac32f0d03186e3500bc2c2f09422f0cc5146e34⟩
]

def tableRLL : Table Block := .branch 12 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0x11107e83a81a80c1057827011207c036016c098038013005c018000, 0x65b8196c065bc32f5dc506c1b9ecbd7104bd6a2f5b022f5cc4246e7a2f5bc15bb2f59cb8f20cbd71182a46e79016ec1970065a832f5bc60a81b9e005bb2f598bc3b0cbd6b1d71b9d805bb2f598bc3b0cbd691c29c6e752f4fc12f4f4bd3408bd600ce1b9cc02f4cc12f4fc4346e7200bd312f4a022f4f86506e7100bcf32f4a022f4ec50ef1b9c0018192008bd39143a86e6f00bcf32f4a0bcfb0cbd2b141806e6c016ecbcf32f3ec32f4988786e6b016ec192008bd2419d1b9a8000bcf1184ac6e6800e9412f3c053c6e67⟩,
  ⟨0x11908303e41d20d806482d813e08e03d019c0a6040019808c028000, 0xbe3104be2f2f89822f8c83386eb000be2504be3110d1babc02f88cbcbe08be301941bab80265e0bcbe08be2d143ac6ead001c178822f8ac50ea1bab0bdff04bdf82f7e822f8844246eaa2f7f4126c88bdf52f6ec32f7fc406d1baa402f52f63a70cbdfd141b06ea8009afe26c88bdf30cbdf9141806ea700bcf42f5d4bd740cbdb115f1ba9002f5d4bcf42f5d032f6b850601ba8cbda804bda62f68022f6a43386ea100bd7f04bda810d1ba8002f5f8bcf308bda71941b9fc00705e608bda4141cc6e7e2f5bc12f59cb8f208bd7c0c1f06e7c⟩,
  ⟨0x1530a284b823610407803741940b305002240ec05f02580d0028000, 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⟩,
  ⟨0x12908c840c1e20df06782f012c08903b017c09a03f01a0098026000, 0x2ff80bf7d08bfe71451bca4bfe204bf7d2ff84bfbe0cbfe41041bca0006ff512fedc32ff8871731bc9c006ff510769032fefc61721bc9802fdf4bfba08bfbd1011bc9438e10438ba0e2f022fddc3386f2327fac9fe90fdf03f78102a6b0e0802fff0fddc3e66149fed0c4c46f20004bbb04bf341401bbdcbf2e04b8f02e3a422fcbc3386ef62f08012b898b8ef1fbb432fcb8406d1bbd4012713c904f390cbefc21e1bbc0012712c08befa19d1bbbc000bee6185c46eec003e5108bee5143886eeb2f9f812f380be6b08bebd1091bba403a526bf8bdf30cbead2428c6ee6⟩,
  ⟨0x12108a84281f60e806d830816409b04581e00d005402080b8032000, 0x4308c86318a1bcf8000c837185d46f3b001bfd442320d850e21bce8c82f04c82c320842320c03386f3800c82004c82f10d1bcdcc82d320ac2320b0c8253209c3320b83186f3600bfff2fedc2320b46506f35320a812fedcbfff320983320ac406d1bcd000512ffe03320a8612f1bccc00512ffe0bfb710c8281c4b86f32001441da30cc825184b46f3100bff12ffc8bfef0cbff7141806f2e00bff22ffc4bfef0cbff515f1bcb4bfea04bfbb2ff9422ffb04246f2c001bfd44bf7d2fedc42ffa881741bcacbfe72ff9022ff98bfe32fefc32ffa03186f2a⟩,
  ⟨0x11b08403c41bc0ca05c829813208903c01a80a603f016007c01e000, 0xc8e904bff4321c82323ac4246f71321b412ffc4bff32ffe03323a4406d1bdc05af6045aef16bc423239c3386f6f0059b4168905a230cc8b31c2986f6e001ee807b982322c450a51bdb4c8a504c8a3321e82322983386f6c00c87904c8a510d1bdac0321dcbff108c8a41941bda8004bff22ffc433228454c6f69001076802321fc5486f68321b412ffc8bff32ffe03321bc406d1bd940076801da1076883321b4506c1bd90c86904c867320f82321a83386f6200c83d04c86910d1bd840320ecbff208c86818c1bd8000432ffc833219472c6f3f⟩,
  ⟨0x11e08283d41bc0ce05d82ac13008b03d81b40a8044017007c020000, 0x325ecc97908c97a325ccc9750cc97c0c61bea00325b0c92c08c97b1941be9cc97804c92c325b0c9740cc979101b46fa600604c9680cc978184bc6fa500604c968324b04325d8712e1be90018107ccc3325cc612d1be8cc96604c964324f823259c3386fa100c93d04c96610d1be80007cc0c93b08c9651941bdfc007cc013258840691bdf8c937324d42324d8c934324c83324e03186f7c00c92d323dc2324dc5146f7b324cc1323dcc92f324c43324d44106f7a011324b02324cc51271bde40441f3608c932145d86f7800c8f7324b42324c04046f77⟩,
  ⟨0x11508203d41c40cf05c029012208403a018c0aa04301a008001a000, 0x73d73a6b20cca24141886fbe01cf9cf02327e050611bef039610438f80e4f02327ac3386fba327a413269cc9a108c9ea0ce1bee4c9e704c93b32698c9680cc9e9101b46fb8001f3007cc41f320cc9e7141b06fb73278c132784c9b808c9e40ce1bed80326dc13278c4346fb500c9b5326942327886506fb4006324ecc9a50cc9bf1531becc0181f3008c9bd1521bec8044c9a5326903326c451781bebc0441f3108c9af145dc6fae00c9a5324ecc9a40cc9a8141806fad325f41325e8c96f08c97e0ce1bea80325b81325f44346fa9⟩,
  ⟨0x10907d03a01b40ca05e829012807e0368178096037015007001e000, 0x702fc08cb37141cc6ff100bc4cb2132be0332cac8786fef00bc5acc232ca46746fee00caf832b98232bf85146fed01ad0132bf050be1bfb0caf332bc4232bc8caf032bb0332bd03186feb00cae832ac0232bcc5146fea32bbc132ac0caee32bac332bc44106fe900cae632b90232bbc60bd1bfa006f86f708caec142f06fe732af8132acccaaa08cabf0ce1bf98cab904cab232a8c232af840e91bf9406f904cab9142c86fe400cab004cab4142d46fe301bec1329f050ba1bf84073a6f608ca3a142ec6fbf⟩,
  ⟨0x12108703e81c20d105d82a813208903a81880a80430180074020000, 0xcba904cb7932e90232eac424782300cb711fbb4cb750ccba91c194782232e98cba308cba532e88cb7e0ccba70c61e084032dfccb7108cba61451e080cba104cb7132e80cb7d0ccba31041bffc032dd47eed08cba1141906ffe001c6f071b4232df850631bff4032dc4cb7808cb7c1011bff0032dc4cb7023894332dd050661bfec02f1125b0cb630ccb6e2428c6ffa00bc46d8232db06746ff9004afd32d8c232da850ab1bfe00125c0496c32d8c332d9c57c6ff732cec132ce4cb3308cb3c0ce1bfd0032cc8132cec4346ff300cb3132c84232ce86506ff2⟩,
  ⟨0x12008503f41de0dc06482f015209604401d40bc04d01c8094028000, 0x330c81330a4c9f4067d83330d0410783601cf01330c8406b1e0d40067d81330c4406a1e0d00330accc22330a43330b857c783332ffc132ff4cbf308cc200ce1e0c4032fc8132ffc470783000cbf032a84ca7a0ccbfe19b1e0bc032a8ccaa1329e8332fec668782e01be9ac0232fe0564782d32f9c132d98cb6008cbe80ce1e0accbe504496c32d94cb2d0ccbe7101b4782a006d46d8bec332f94506c1e0a40071c41c70070e0332ef050621e0a0032dd47eed32dc0332ee470681e09c0071bc1c6d08cbb71419c782600cb7132dc08e250ccbb1142e47825⟩,
  ⟨0x146099048421c0f6070833816e0a204681e00cc05301e00a001e000, 0xcc22330acccb20cccb514180786b00cc6b331982332a050ab1e1a0cca504cca3331802332983387867331f41067986331d0cc3f10cca5181e478660019e618cc683319843329070781e194cc7f04cc75331dc2332844247863331f41331a0cc74330fc3331fc406d1e1880067986067cc19f410cc7d181dc78610019e618cc68331984331d870761e0fc0067986331a0cc6610cc72201d4783e0019e61819f30ccc70181d0783d330f01330b4cc2308cc3d0ce1e0eccc3a04cc22330b07ae10ccc3c101b4783a0019f8067dc19f60ccc3a141b07839330d8cc3408cc35330cccc310ccc370c61e0e0073c330a42330d85147837⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0x12008883f81e20e1069830015209504081b40b8049019007801c000, 0x19e6182334fc50e21e280cd3404cd32334b02334d4338787e00cd2b04cd3410d1e1f40067e0cc2b08cd331941e1f00067e01334c040691e1ec016ce4cce7333943334a057c7878333f4116ce4ccf2333d43333fc406d1e1d80068f41a3b068f83333f4506c1e1d403339c5b39333943333d050601e1cc016ce4cce7333943333c070a61e1c80068f41a3b08ccee142947871333801332d0ccac08cce10ce1e1c0ccbe04cc2b332cc5b390ccce0101b4786f0019f8067dc1a3c0cccbe141b0786e01cf0ccb208ccbb143b0786d001a3c04ccba101a8786c⟩,
  ⟨0x11d08603ec1d00db06582f415409303f81a00a80410168070016000, 0x67e419f508cdbe1429478b400cce3336e42336f050ab1e2cccdb404cdb2336b02336d433878b200cdab04cdb410d1e2c40067dccc2208cdb31941e2c00067dc1336c040691e2bccda604cda4335fc23369c33878ac335e813358ccd702beac333698406d1e2ac0333d4cd633358833369450601e2a8cd7a04ccf5335c0afab0ccd7c101b478a800197d068fc1a600ccd7a141b078a700cd63333d4cd620ccd7215f1e29403358cccf5335883335b470ac1e2900065f41a3f08cd6b1429478a300cd65335882335a450ab1e288000cd60183e078a1⟩,
  ⟨0x142095845c2000ec06c830815c09b04201c00ba04901c009c028000, 0x339b811eb84cde3337983339d8406d1e3ac0330fc7ae1336e43339d450601e3a8ce6e04cc3f3378ccde60cce70101b478e80019f9067d419fa0cce6e141b078e733990133988ce2108ce650ce1e390ce3d04ce20338dcae6c0cce64101b478e300cde633880ce2d0cce631418078e2338fc1338e0ce3a08ce611091e384ce3d04cde6338dcae6c0cce3f101b478e0001939067ec19fc0cce3d141b078bf00ce2033798ce2d0cce3915f1e2f4033880cde6338b43338d070ac1e2f00064e419fb08ce321429478bb00ce27338b42338c050ab1e2e801eb84cc3f336e433379457c78b6007ae1330fccdb90ccde01c29878b5⟩,
  ⟨0x12108503d81ca0d205d82a812e08a03d01ac0b004501b8098026000, 0x8be4046d7d22ed429f50cd87a101b4792d006cb81b5f48bb30cd87714180792c0059e7166ec2360e050ab1e490cfff04cfa933eb023608442478ff33ff410f984cfa833eac333ffc406d1e3f800620630ff0ccffd141b078fd33f80133ef8cfb808cfe10ce1e3e8033edc133f8043478f900cfb633ec8233efc65078f8001c0480233ef050731e3dc00f8803e6133df8333ea857c78f4003e43e6133df8333e9490a31e3cc00f906308cfa319d1e3c8017bb8cf7e08cfa1142ac78f12e5fc12e5e8b97c08cf2f0ce1e3c0ce7604ce74339982339dc33878ec⟩,
  ⟨0x11308183cc1c60d606182bc14208803c01880a20400198098026000, 0x66c0d92b08d9361c31e5880066c019b408d9331821e5840363c4d92e08d9311011e5800363b41363c0500793f363941362c0d8aa08d8e60ce1e4f0d8e304d8af2ae8023639440b61e4ec00678813638c50b21e4e8d8be362f02362f4d8bb362e03362fc318793900d8b2362b82362f85147938362e81362b8d8b4362dc3362f0410793700ac312b6b42362e860bd1e4d800678419bf08d8b8142f0793500d8ae04d8b11401e4d000679013628456079312e1b412b884ae6708d87e0ce1e4c0d87a04d876361cc2361ec338792e⟩,
  ⟨0x12d08d04181f00e506c02fc15e09804401d40ca05201f809802c000, 0xd97804d8ef363a42365e43387974365d81363b8aba208d978102d879730019bc04d976142c87972365cc1365c0d96508d9740ce1e5c00365901365cc434796f365c4d96f08d970365a4d96b0cd9720c61e5b803658cd92b08d9711941e5b4d96e04d92b3658cd96a0cd96f101b4796c00144493c0cd96e184bc796b00144493c364ac4365b0712e1e5a80051066cc3365a4612d1e5a4d93e04d92f364e423658042479670019b0363c4d92b0cd93e2081e598d93b364e02364e8d937364cc3364f0318796500d934363c42364ec5147964364d81363c4d935364c83364e04107963⟩,
  ⟨0x12c08c04141e20e006682d814408f03c01900a203d016006c01a000, 0x1939064d4193a0cda28141b079aa00ce20367c4d9f00cda2115f1e6a0033880d9f1367c03367f070a61e69c0064e4193508d9fa1429479a6367b81367b0d9a908d9ef0ce1e694d9e604d9a8366f4b9690cd9ee101b479a400d9af366a0d9ae0cd9ed1418079a3367a01366f8d9e008d9ea1091e684d9e604d9af366f4b9690cd9e8101b479a000186f064ec193c0cd9e6141b0797f00d9a8366bcd9ae0cd9bf15f1e5f40366a0d9af366b83366e870ac1e5f00061bc193b08d9b814294797b00d9b2366b82366d850ab1e5e80067901365fc50ba1e5dc02ae901365f44707976⟩,
  ⟨0x12708c041c1ee0e9068030015409904401e80d805201f00a802e000, 0x67f066f8236b8867479e000bbb02eea4236ad450ab1e6fc02f3ecda7508daab1451e6f0006484136aa450be1e6ecdaa236a80236a84da7f369ec336a8c31879ba00da77369b8236a8851479b9369f81369b8da7d369e8336a8041079b800da75369cc2369f860bd1e6dc006594196408da7b142f079b600da6e04da72142d479b500196804da60142e879b3368d0da3208d9af367fcce200cda2d0c1c079b0368a01367fcd9af08da340c1f079af00d9f133880d9f00cda331418079ae368a8136880da2208da2c1091e6b0da2804d9f1367fcd9af0cda2a101b479ab⟩,
  ⟨0x14709984801dc0da06302cc13808903c01940a203e0188084024000, 0x66c01c3a070e0336ee060a81e7e00066c08e2623894336edc75c79f71e5d87d6636da87d6e36d8078f71879621e5b4796c1f5ac7d6a1e3d85a241c79f50c59479f41f5b011f5ac796c08db6a0c1f079f31f6a011e3d87d6a08db600c1f079f236cd0136cbcdb3108db361091e7c4a9b50448b02a5d0a96d0cdb34101b479f000a96c122c0a8740cdb3015f1e7b80123b8a87408db2d142ac79ed1affc11afec6ab008db221091e7b06b7b046b7a1ab9c236c80307c1e7acdaf504daf336bb4236bd833879e800daec04daf510d1e79c036bacdaba08daf41941e79800706a208daf1141cc79e5019fcdaba2b6b4336b9087879e1⟩,
  ⟨0x11f08784041dc0d706182c814809003e81a40b604d01e00a002e000, 0x71a0af7508dc621941e8b00071a01370fc40691e8acdc3704dc2b370902370e03387a29370d412bdd4dc2a0f0a43370dc406d1e8a00071a01c67072b03370d4506c1e89c0069a4dc2908dc32143b07a26001cac04dc31101a87a2500af392bdd4dc290cdc2c141807a2436ff0136fd4dbf708dbfe1091e8888ff9048fba23c90236ff040e91e884023ee4136fd850b51e7fc0071e0136fc050ba1e7f80234dc88ee08dbe2142ac79fc0088f1223bc88ed0cdbe11458c79fb00cbae32dc0236ef050ab1e7e8dbb80419b036ed4cb750cdbba182a479f9⟩,
  ⟨0x13609284582060f006c831816609c03e01a00a804201a008001a000, 0x39b50e6d023a1ac50ef1e9900181cef08e869143a87a633a0d812b9f4e82408e8371091e8f4e83504e8242b9f423a0d83387a3c3a0c412b1b0cc682b9f033a0d4406d1e8ece83304aea03a0a423a0d04247a3a3a0c813a0a4aea008e8330ce1e8e4e83104ae7b331a0ae7c0ce832101b47a383a0c0e82d2ba9c3331a0e82c2ba90ae7c10e8310c2a87a373a0b813a0b0cc6808e8300c1f07a360019f2067a819e80ce82e141b07a3500e949bbd37ef0337fa48787a3100e94eb8237f9c6747a30009bbd26eecdfbc0cdfbf141807a2f3718c137184dc3b08dc640ce1e8b80370e813718c4347a2d⟩,
  ⟨0x145099046c2100f4070832816c09904281c40ae0430180074020000, 0xea2b048ca2231ec23a8b44247a7d232b41231e88ca122fa433a8ac406d1e9f03d6c043d670f5a423a6a83387a790eed410ebb03bb008e9a20c1f07a783a5f410e6dce97408e97e0ce1e9d8e97b0439b40e6d83ae40ce97d101b47a75001d3c073bc1cf00ce97b141b07a743a384e8be083b613a2d03ae40eec043a38840e71e9b8e8bf04e8b40ed8423a384307c1e9b400759c1d3f074e433a2fc506c1e9b0e8bd0eed420eb903aec0eec033a2f830701e9ac3aed043aec0eb9023a2f4307c1e9a803a2cc3bb00eebc33a2e057c7a693a1bc13a1b4e86408e8700ce1e99c03a18c13a1bc4347a6600e8610e6d023a1b86507a65⟩,
  ⟨0x12d09004341e00dc06482ec15a09a04181bc0ac0460180088028000, 0x7d8013ac845607ab21e6ec11e6d079b608eaf50ce1eac479761e7c821e588796d168905ae610eaf41039c7ab0135f81134944c2808eaed103a47aaf0ecf810ecc83b3b08eabd0ce1eab40073cc13a9d850ba1eab001349013a9cc50b51eaacea6704ea373a8c823a9a03387aa93a994116fa4ea36231e833a99c406d1eaa0007ac81eb107ac033a994506c1ea9cea613a8fc23a980ea3e3a8f033a9883187aa6001d783a8d423a9845147aa53a8f413a8d44ff407ac033a8fc4107aa4001d7804ea3d101ac7aa3001eb004ea3c101a87aa2005e3e16fa4ea350cea38141807aa1⟩
]

def tableRLR : Table Block := .branch 12 tableRLRL tableRLRR

def tableRL : Table Block := .branch 24 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0x12508903f81da0dc06482e014e09304001b40b404701a0080022000, 0x6cb7046c6c1b1c423b39c3387aeb00796216fec69f10cecba1c2b07ae9001ef307bec23b2e050a51eba003b2c869f108ecb6142ac7ae7229881228f48a3a08eca91091eb940175a469a108eca6142ac7ae400a92b1a7bc23b1f450ab1eb8801a7a469f21a7c033b1ec51631eb846ea1046e7a1b9f023b1d03387ae00afc810afa02bea08ec700ce1eafcab2504ab212abf023add84247abc0a3fc10a39028be08eb731091eaec03a0acaea42baa033adc057c7aba00ac6c2b9ecae7a0ceb671c2987ab601aa9a8823ad9450a51ead40165cc597008eb3c142ac7ab3⟩,
  ⟨0x11d08503cc1be0cc05e02a013008a03b819c0b20460198080026000, 0xedff04edee3b7a423b8803387b213b7f410eef4eded138c433b7fc406d1ec800063c018f1063c833b7f4506c1ebfc0063b04e213b7b033b7e48787afe0018ec063c423b7dc6747afd004e210eef4edec0cedef141807afc00adad2aff423b6805147afa0019bf04ed7e142f87af91fea811fe807fa208ed790ce1ebe0012eb08fbf08ed761451ebdc0070c413b5d050be1ebd88d6d048d682358c23b5984247af323ffc123bd48f2008ed640ce1ebc8ed3c048f6423bd423b4f84247af0001c7804ed321581ebb4ece7046c711b1b023b3a44247aec⟩,
  ⟨0x16009d04982260ff07603541820ae04d021c0e805d02500dc040000, 0x3bd98ef3c238cc493e10cb7536ed48e26124f4493314ef610c4c47b3636ee0136ed4cb7508ef660c1f07b3536ee8136ed8dbb108ef601091eccc0066c08e262389433bcf470a71ecc4ef2d04eef73bbe823bcbc4247b2f3bcac13bbc8eef33bbe433bcb4406d1ecb80077ac1de7077b033bcac506c1ecb4022ea0eef23bbc433bbe057c7b2c00eef222ea0eef10ceef5141807b2b3bb9010ebb43ae508eee61091eca8eee3043ae50ebb423bb903387b293baf810eb903abf0ebb033bb8c406d1eca0eee0043af00eea823bb844247b273bafc10eea83af008eee00ce1ec98eebe043aeb0eafc3aec0ceebf101b47b250eeec3bb23a68830eafc3bb10eec03aec10eebe0c2a87b24⟩,
  ⟨0x11d08803dc1ce0d006002b413a08a03e81b40be04b01c80a802e000, 0x3e18013e1bc4347b6b3e1b4f86b08f86c3e194f8670cf86e0c61eda803e0f8f83b08f86d1941eda4f86a04f83b3e0f8f8660cf86b101b47b6800144efab0cf86a184bc7b6700144efab3e0ec43e1a0712e1ed98005107cb433e194612d1ed94efbc04efba3bed023bef43387b6300efb304efbc10d1ed88007ca8efa708efbb1941ed84007ca813bee040691ed8003bdf4efa73bdec33bea850601ecf4044ef7d3bdec33be9451781ecf00441f2b08efa3145dc7b3b3bdcc13bbd0ef3008ef751091ece4ef2b048ba83bbcceef90cef73101b47b38⟩,
  ⟨0x12008683e81da0dd06602f8156094040019c0ae041019008c026000, 0x3abd011e7d4796e08fa7e0ce1ee80fa7904fa773e9b823e9e83387b7d00fa6d04fa7910d1edf003e9acef7d08fa781941edec004efa73bdf433e9d454c7b7a00107ca823e9cc5487b793e99813bea4efac08fa681091edd8fa6404efa73bea0efab0cfa66101b47b75001f2a07cac1f2c0cfa64141b07b743e1f8f87c08f87d3e1ecf8790cf87f0c61edc803e0f0c8f308f87e1451edc4f87a04c8f33e0f4f8780cf87c1041edc0044f83b08f87a1449c7b6f01107cb823e1e451761edb80323ccf83c08f8771011edb4f86f04f86c3e18423e1c03387b6c⟩,
  ⟨0x13408e84241ec0e906c83201700a504901ec0b604801a8084026000, 0x2a8ac12a894aa262a7cc33eebc406d1eef400b39caa250a68c33eeb050601eef0fba304fba13ede023ee903387bba00fb7704fba310d1eee403edd4aa2508fba21941eee000adbcaa2508fb7f143ac7bb7001c01c2008fb7d143a87bb63edc012a7d4a9ef08fb721091eed0fb6f04a9ef2a7d423edc03387bb33edb812a5b428252a7d033edbc406d1eec8aa6c2a998aa700c28250a4c429302a7d043edb830aa1eec42f3c042f320bcd023ed843387baf3ebfc13ebe8faf108fb200ce1eeac782b046ff51bef023ebfc40e91eea801bfd013ebec50b51eea4fa7e04796e1e7d423e9fc4247ba1⟩,
  ⟨0x12a08b841c1e80e306502e814809604401e00ca04e01e80a8026000, 0x1445a6d3ef9c43f0a0712e1efc400510738833f094612d1efc0fbfa04fbeb3efd423eff04247bee01113198fbe70cfbfa2081efb4fbf73efd023efd8fbf33efbc33efe03187bec00fbf01319823efdc5147beb3efc8113198fbf13efb833efd04107bea0113ef9c23efc870c7be90110738c23efbc6087be8004c663efa823efb44047be73ef8c13eed4fbe008fbe51091ef944f6b044e21138883bbe0cfbe3101b47be4004e281388023eee450ab1ef8800eef44e211388033eed857c7be13edb812a7cc28252a7d033eec4406d1ef80fbaf04fbab3eea023eec03387bbe⟩,
  ⟨0x13b092044c1fe0ec06a830815609704181c00ba05001b809c020000, 0xff2e049b223fc98fefa0cff30101b47c2500bd4bd8bdc33fcb8506c1f090026bf89b223fc9033fca850601f088fe3d04fc393f0c823f8f83387c203f8e013bbe4fc380a38833f8f4406d1effcfe3a04fc3b3f0f423f8f04247bfe3f8e013f0dcfc380a38833f8e8406d1eff40077c41ded077c833f8e0506c1eff003bbe4fc373f0d433f0f050601efe803f0dceef93f0d433f0e857c7bf93f0bc13f0b0fc2108fc300ce1efdc03f08013f0bc4347bf63f0b4fc2b08fc2c3f094fc270cfc2e0c61efd403effcfbe708fc2d1941efd0fc2a04fbe73effcfc260cfc2b101b47bf3001445a6d0cfc2a184bc7bf2⟩,
  ⟨0x13008f842c1ee0de06702e014809003e81ac0ba04901c0090026000, 0x1b2706c942427d450671f0f40426a509a84269c3427bc50b91f0f0006ca41b2806bb83426ac50621f0ed09a242680242685097f425f034268c3187c3a010977163cc2426885147c39425f81163cd0979425ec3426804107c38010975425cd09710d097e182b87c37001b2a06c981aed0d097c142b47c363ef8c13eed4fbe00909370ce1f0d002f126bf8ff240d08fb21e1f0c802f12f60908f919d1f0c4022ea0eef23bbc434209470a61f0b80077ac1de7090823142947c2d00fc373bbe4fc350cffac1c2987c28001df1077b423fea850a51f09cff3004ff293fcac23fcc84247c26⟩,
  ⟨0x12108503e41ca0d106102bc13008403a01980a403f0190088028000, 0x10a7f050a6a429d90a600d0aa1101b47c7101eb1ea1eb43429fc506c1f1c00428fd0a6a429a03429e050601f1b80429a90a3f429a03429d070a61f1b407ac7a8090a72142947c6c428ec1428b90a27090a3c0ce1f1a90a390509fa428b45ba30d0a3b101b47c69001abc06aec1b200d0a39141b07c6801ff10a2c090a35143b07c67001b20050a34101a87c6600e9b8427e90a2c0d0a2f141807c654289414288d09fd090a260ce1f18c0427f01428944347c62001abc427e82428906507c61001abc050a21101a47c600109b216ce909a80d09f71c1a07c3e⟩,
  ⟨0x13f094045c2080f106c031c16009604281d00c205001e8098026000, 0x10afc050a6042bcce9b20d0afe101b47ca501bb1eb9ebc342bf0506c1f290042bb10a6042bc8342be057c7ca242b94142acd0aad090ae60ce1f2850ae442b8c242acd0ae242ab4342b943187ca000e9b242ac8242b9040721f1fd0ae104e9b242ac818200d0ae3101c47c7e42afd0ab8090ab242adc18200d0ae10c1c07c7d01ec1fd1ff0342afc506f1f1f00060841820090ab9141b87c7a010ab13a6c9ff0342ad050601f1e40429b50a68090aa9142ac7c7642a98142a910a65090aa70ce1f1d50a7f050a3f429d90a600d0aa6101b47c74010a6a428fd0a680d0aa515f1f1cd0aa1050a77429e4242a8c4247c72⟩,
  ⟨0x13009084381ee0e3069830815e09804081bc0b60470198090026000, 0x1ff9ff0242eb450611f2e50ba0045bac16e90242e884247cb716edc116e8c5bab16d88342e80406d1f2d80779190b2e42cf4442ddc80751f2d0077919e98342dd460741f2cc042dbd0b3d090b73142ac7cb242db0142cfd0b3a090b6d0ce1f2c50b67050b2e42cf90a3f0d0b6c101b47cb042d9c1779190b3e428fc442da460791f2bc077919e99e9c442d9c60771f2b80779190b2e42cf4442d8c70781f2b00779190b2e42cf4442d8070761f2ac042bb10a6042bc8342cb070ac1f2a406ec7ae090b2a142947ca8010b2442bc8242ca050ab1f29d0afe050af742be4242c804247ca6⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0x11708383c01c00cd05f02ac132080038016809603d0168080022000, 0x432d90c76090ce41941f3b90ce1050c76432d90cbd0d0ce2101b47ced00144682c0d0ce1184bc7cec00144682c431d84432fc712e1f3ac00517660d0cbc184b47cea432a41431e90ca4090cab1091f39c0763430f10c760d0ca92081f3990ca64328c2432950ca2431f834329c3187ce5010c7f430f02432985147ce4432841430f10ca0431f434328c4107ce301d8d0c76090ca11c31f3880763767090c7e1821f3840430f10c79090c7c1011f3800430e01430ec5007cbf01fe9ed8242fbc50bb1f2f007fd7fa7720d0bb9141887cbb⟩,
  ⟨0x13e09384441fa0ea06b030815e09d04501cc0be04c01c8098032000, 0x1a39011a1f8687f1a0b034369c406d1f4890d7405d8d0d32426c834368860a91f4840432c10d37434f43435f850601f480076306bd01aee0d0d74182a07cff435c41435ad0d31090d730c1f07cfe001af206bc01af30d0d71141b07cfd010d37432c10d3d0d0d6d15f1f3f00763434c509a70d0d341d71f3ed0d2a050d26433ac2434ac3387cf9434a0117ffd0cf6432c03434a8406d1f3e0006bbc1aa206a8c3434a0506c1f3dc0433d45fff161d834349c57c7cf60068391a1f8687d0d0d2415f1f3d50ce6050ce3432e024339c3387cf1010cb7050ce610d1f3c10ce44338824338d0cbc432f83433943187cef⟩,
  ⟨0x11408303cc1b80cb05c02a8132086039018409c03a0168080026000, 0x13ecbd8243cf06747d3443cb8143c890efc090f2f0ce1f4cd0f2c049bbd43c850eec0d0f2e101b47d3200eb4eb9484343cb0506c1f4c404fb26ef50eff0d0f2a2428c7d30013eceb8243ca06747d2f009bf943bfc243c9850ab1f4b8026eec9bbd43bfc343c8c57c7d2d00bdbb37df90eb70d0eba141807d2c00eb4eb8ebc3439e8506c1f4ad0dec050c3a430d02437b43387d2a437a81430e50c33090dec102d87d2901dbc1437a850b21f4a001609c1437a04707d26001aec050de21581f4950da7050d23433f82436a03387d23⟩,
  ⟨0x10b07e83a81ba0ca05b82a412c08203a81a00b804901a8090026000, 0x43eb414608450b51f5a10ff5050ff343fa4243fd83387d67010fe8050ff511c1f598043f990c3343de8343fd066c7d65010fa8430cd0f7a0d0ff119a1f5900776770090fee1591f58d0fe4050faf43ea4243f943387d6143f88143eb90fa8090fe4102d87d6001dd4143f8850b21f4fc043eb4143ec05007d3e01ddc143df45607d3b010f7643dc10f740d0f7915f1f4e90f71050eb843dc0243dcc307c1f4e403b03a877c0d0f71141b07d3800bd4bd93f4343d80506c1f4d804fb26bf90f330d0f3e2428c7d35⟩,
  ⟨0x13a093044c1f80eb06c031416e0a404801e40b204501a009c028000, 0xacb117bf11a240d1a3d141807d7d468e41468c91a34091a3b1091f5f11a3704acb1468c45eef0d1a39101b47d7b01a9daa1da43468dc506c1f5e8017bf0acb1468903468cc57c7d7801d8cacb1468903468b890a31f5dc07636a8091a2c19d1f5d87afc047af11ebcc2464f43387d74001abc06aec1aba0d1929141b07d73460fc137df90b2e43ae0346180406d1f5bd183e43de10f730d0b2e43ddd0f7043ae04460fc30aa1f5b9183c050f7742cb82460f8307c1f5b407a577d77b0d183c141b07d6c010f7a05183b11c1f5ad182e051820460a42460c04247d6a43f88143eb90fa809182e103a47d69⟩,
  ⟨0x1590a304bc21e0fb073835016e0a404881e80ce05001e80a802e000, 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⟩,
  ⟨0x135091045420c0f9073034c1800ad04b01d80c605001e80a8026000, 0x11e27051e25477fc2478a03387df0011dfe051e2710d1f7bc07aa477e42478986507dee01ea814788c40691f7b4dbfc04dbf536fdc2476d83387dea27dfc10f79c9f76091dab0ce1f7a51d3e046b7e1addc2474fc4247de7474f411addc6b7e091d3e0ce1f7991d3c042dec1a9d06b7a0d1d3d101b47de51ae986b7536c8031a9d06ae81ab9c6b7a111d3c0c2a87de43e99813bea4efac091d370ce1f78c04738c7f791f7a43474ac57c7de0473b811fddd1cbe091cef1091f6f91ced051cbe1fddc2473b83387dbd473a411fce48ae31fdd03473b4406d1f6f11ceb047f75473842473b04247dbb⟩,
  ⟨0x11108183c01c60d306202ac13408b04001c80c204d01f00a802e000, 0x2f16b10928eb19d1f8b528e10528bf4a2e424a3883387e2c0128b80528e110d1f8ac04a2d928b00928e01941f8a800702f80928bd141cc7e2947ea11fa1091f7b47e81d80347ea830701f8a006f073473c0d1fa8141bc7e2701d85d80247e88506e1f8940011f25184d87e2201de46091f24143887e2101bd1bcdaec347aec50621f7fc0479c51e70479ac347ad870681f7f806f26f0091eb41419c7dfd011e6c479ad1e6a0d1eae142e47dfc479881173e05cb4091e641091f7e05cf3045cb3173b45baa0d1e62101b47df7⟩,
  ⟨0x12808a04001da0d606282c813c08f03f01940a803e0158080024000, 0x4abe414abcd0ab1092b250c1f07e63012abf4ab952ae40d2b24141807e624abec14abd12af6092afd1091f9812af9052abf4abcd0ab10d2afb101b47e3f01cc1fc9fcc34abe4506c1f8f804ab952abf4ab9034abd457c7e3c012ae54aafd2ae40d2af01c2b07e3b01cc1fc824abb850a51f8e804aba12ae4092aec142ac7e394aadd2ab6092ab34aad52aad0d2ab80c61f8dc0479c11f7b092ab7101c87e3647ea81479c11f7b7600d2ab6101c47e35011f3b479c1cf034aad050601f8d0001292a183ec7e3101ae46092929143887e3000bc528b03288034a3b48787e2e⟩,
  ⟨0x12208403d01c20ca05c829412407f039018c0ac04301980a0034000, 0x4aec12ba1092abf4ae812b780d2b790c1c07e794aeac14ae812abf092bb00c1f07e784aeb414ae8d2ba5092baf1091f9dd2bab052b744ae812abf0d2bad101b47e7601fc1fb9fc434aeac506c1f9d404ade12b744adf834ae9050601f9cc04add12b784adf834ae8857c7e724adc014adb92b68092b710ce1f9c004ad9c14adc04347e6f01ead2b65092b6f1941f9b807ab052b6c101a47e6d00e8063a24accc44acf8917b1f9a803a018e8834acf0617a1f9a40012b31185e47e6800e806092b30143887e674ac952b23090ab14abcd2ae50d2afe0c1c07e64⟩,
  ⟨0x141094045c2000ed06c831416809b04501cc0c204e01b808c01e000, 0x12c784b1dc24b1d12c764b1bc34b1e43187eb000afab2beb024b1e040721fabcafbb04afab2beb01a6d0d2c77101c47eae00ae6c2beac1a690d2c7515f1fab4006b941ae406ab034b0f450621faa404ac985e234b0b034b0e470681faa0006b8c1ae1092c371419c7ea74afc52bf0092bed4afbd2bea0d2bf20c61fa98042ac50ab2092bf1101c87ea542b84142ac50ab20608034afc040711fa9003a6c90ab17fc0d2bee15f1fa8d2be8052be44af8424afa43387ea1464a41427e918fb1ee8834afa0406d1fa8003a6e109fa463e434af9450601f9fc04add12b784adf834aee470a61f9ec07f07ee092bb7142947e7a⟩,
  ⟨0x13208f842c1f80eb06c030415a09604281c80bc04f01f00ac028000, 0x10aec4b6a52dad0d2dbd15f1fb98042bb12da94b6b434b6e070a61fb9406ec6e8092db6142947ee4012db04b6b424b6d050ab1fb8d2da2052da04b4f424b68c3387ee14b5e814b4f12d71479c034b688406d1fb8004b58d2d3c4b58834b68450601fafd2d7a052d634b5c51e700d2d7c101b47ebd018a1bb9bbc34b5e8506c1faf004b4f12d634b58834b5cc57c7eba012d3c4b58d2d620d2d6e1c2b07eb9018a1bb824b5b050a51fae004b5992d62092d6a142ac7eb74b29014b2812c7b092ca50ce1fad0afa404af752bdd85cfd0d2ca4101b47eb300af392bdd4af730d2ca1141807eb2⟩
]

def tableRRL : Table Block := .branch 12 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0x13c09484581fe0eb06a030815c09a04501e40cc04f01d80a0022000, 0x4aae014aacd2aad092e371091fbf12e31052e2f4b7b024b8c83387efa4b8a414b7ad2e204b6a434b8c4406d1fbe406b9192deb4b7c844b8c070761fbe12e2905ae464b8812da9112e2b181e47ef601ae466e66e7112e29181dc7ef501ae464b7ad2df2112e221c1e07ef301ae464b7ad2df2112dfd201d47ef201ae466e60d2dfb181d07ef1012df54b7c824b7e450ab1fbc12de9052de74b69024b7a83387eee4b784142bb12dbb4b58c34b7a4406d1fbb404b6a50aec4b6b434b7a050601fbb12de3052dbc4b6f824b7944247eea4b78414b6a52dbb4b58c34b78c406d1fba406ec6e86ed0d2de1141b07ee8⟩,
  ⟨0x11d08803dc1ce0d006002b413c08b03c81800a003a015807401a000, 0x4bbe814bca44347f2e4bc9d2f25092f264bbfd2f210d2f280c61fcb404bbe52ee1092f271941fcb12f24052ee14bbe52f200d2f25101b47f2b00144ae7b0d2f24184bc7f2a00144ae7b4bb8444bc88712e1fca400516a20d2eff184b47f284bbd014bb952eef092ef61091fc98067f4ba9d2ee10d2ef42081fc952ef14bbb824bbc12eed4bba434bbc83187f24012eea4ba9c24bbc45147f234bbb014ba9d2eeb4bba034bbb84107f22019fd2ee1092eec1c31fc84067f6a3092ee91821fc8004ba9d2ee4092ee71011fbfc04ba8c14ba985007efe⟩,
  ⟨0x11208083c81c80d706302d815209504101b00b204701a0080026000, 0x1382d4e0ac24e0d860bd1fd9c03e23bd093833142f07f6601382605382a142d47f6500f9414bfe050ba1fd8804323fc3a40d2fb8144dc7f6000e912fa4092fad143b07f3f01fbc14beb0406a1fcf80477e52b654be9034be9c50601fcf52f6d052f664bda024bdbc4247f3a4bdac17634bd8d2b260d2f6d182a47f3901d8c1aae06ab034bdac60a81fce007634659d19650d2f671d71fcd92f2e052ea54ba8024bcbc3387f334bcb014ba90caa1092f2e102d87f3201abc14bcb050b21fcc52f29052f264bbec24bca83387f2f⟩,
  ⟨0x11708003bc1b80ce05d82a013608b03e01a80b804c01f809802c000, 0x138b7043e614e2b138740d38b9101b47f7a0018818cef834e2dc506c1fde403b70f98538aa0d38b52428c7f7800edc18c24e2cc6747f77003e200f98538aa0d38ae15f1fdd938a20538a04e1e824e28c3387f730138790538a210d1fdc804e1e138680938a11941fdc400703bf09387e141cc7f7000edd38684e0fc34e1c88787f6e00edcf8024e1c06747f6d01383f4e0b424e1945147f6c00f8414e18c50be1fdad383a4e0e024e0e538374e0cc34e0ec3187f6a01382f4e09824e0e85147f694e0d814e09938354e0c834e0e04107f68⟩,
  ⟨0x10907e03a41b80cc05e82a812608403881900a003e0180080026000, 0x3e3053936142c87fad4e4cc14e4c5392b0939340ce1feb004e4a814e4cc4347fab0139294e39024e4c86507faa001c0ee824e4bc50731fea539270538f94e3c424e4a03387fa74e49410b4a138f84e3c034e49c406d1fe9805d83b90d3925141b07fa500edc2d3a4e3dc34e48890a31fe8c03b76024e4806747fa2002d3a0b4a138f70d38fa141807fa100edd38e44e2ec34e3b88787f7f00edceec24e3b06747f7e0138bb4e0ac24e3845147f7d00ef014e2fc50be1fdf138b90538ad4e29c24e2e83387f7b⟩,
  ⟨0x11908303d01b60cb05a829813008803d81a00b604801a809c028000, 0x139e10539b24e6f024e78c4247fbf00e9539744e6b834e7848207fbe4e6f939bb0939bd4e6e939b60d39bf0c61fef404e6dd39740939be1451fef139b90539744e6e139b50d39bb1041feec03a54e6b824e6e470c7fba00e94ea424e6d86087fb90139744e6c424e6d04047fb80139700539731401fedd396a0539684e4f824e5ac3387fb501393d05396a11c1fed004e4ed393a4bfd834e5a466c7fb3012ffd4e4e92ff60d396619a1fec803e43b60939631591fec539380538294e08c24e4e43387faf4e4d814e0a12ffd093938103a47fae⟩,
  ⟨0x12408984041dc0d706302cc13e09203f81c80b2049019008801e000, 0xbc5af5aec34e98460a81ffcc02f14e8d51e6a0d3a3d1d71ffc53a20052fa64be8424e8843387ff04e7f814ad952fa54add034e880406d1ffbc07ab7aa7ef0d39fe141b07fee4e7ec14e5c9396c0939fc0ce1ffb139f90539714e4e824e7ec40b61ffac03b50539f9142c87fea4e7d814e7cd39e80939f70ce1ffa004e79c14e7d84347fe74e7d139f20939f34e7b139ee0d39f50c61ff9804e79939ae0939f41941ff9539f10539ae4e79939ed0d39f2101b47fe400144bdbb0d39f1184bc7fe300144bdbb4e6b844e7bc712e1ff8800513a80d39ec184b47fe1⟩,
  ⟨0x13b097047821a0fe07583601820ae04d82100c805001e00a402c000, 0x4eae014eb904348826013ab64eacc24eb8c6508825005ee04eacc24eb8050ef220900181aa4093abe143a888234eaac1435f53aa8093aad109220813aaa053aa8435f424eaac3387fff4ea901434dc5cb3435ac34eaa8406d1fff93aa6050d6c4e9ec24ea9c4247ffd4ea9414e9ed0d6c093aa60ce1fff13aa4050cb0172cd0d6b0d3aa5101b47ffb4ea8d3aa0435cc3172cd3a7f434c50d6b113aa40c2a87ffa4ea8414e9fc5cb3093aa30c1f07ff9001afc06bd01aee0d3aa1141b07ff816dec116dc45b73093a7a0ce1ffd93a63053a3c4e8f824e9944247ff54e98412f14e8e51e710d3a63182a47ff4⟩,
  ⟨0x11b08704041ea0e306a830815c09d04481e00ca05201d809c026000, 0x3fd053bb1142c8883f013b7c053b7f140220f803ff053b6c158220ec03b74ed953b630d3b681d7220e8006bb014ece450ba220e05cf5045cee173c024ecc83388835005cb316ce909730d3b2e1c2b08834001afd06c9424ecb050a5220cc0425d90974425c834ec905163220c80427ad09a8093aff142ac8831013a7e434c509a70d3afe15f220c13af5053aee4eba824ebd8338882f4ebcc14eacd3aed434dc34ebd4406d220b8006bc41aa406a9434ebcc506c220b4017b813ab317ab434ebbc5060220a93ae4053ae24eae424eb943388827⟩,
  ⟨0x11308203bc1c40d506102bc13208803d81a00b604801a809c028000, 0x3a44efd024f08051488764eff014efd12fb47a90d3bfe104221d403a4053bfc101ac887401ea414efec406a221cc04ad951df94efd034efe057c88724efbc14ed9d3b60093bf00ce221c13bed04edd3b66477cc34efbc60a9221bc03b74234210d3bed182a0886e013b69053bec11c221b53be4053be24eee024ef943388867013bb7053be411c2219804eed5393a4eda434ef8c66c8865013b774e4e93b690d3be019a2219003fe3b6093bbd1592218d3bb3053b7e4ede024eed033888614eec414edf53b77093bb3102d88860⟩,
  ⟨0x132091843c1f80e9068030015409a04581ec0ce05402080a8032000, 0x10b8e8824f1c45162222a804f0c13c2f4ed8c34f1ac50b9222a53c65053c354f18024f19c42488a7013c303a2477cc34f1947065222993c624f0fc24f1853c3e4f0e834f18c31888a5013c3b4f0c024f18851488a44f0f414f0c13c3c4f0e434f0fc41088a3011df33a2093c3d1419088a2010b8e8824f0e8517c2228404f0c13c34093c381012228004f0c13c2f4ed8c34f0cc5066221fd0afe050af742be424f0b8338887e4f09814efdd3bf1093c270ce221e93c24051df94efd90a6a0d3c26101b4887901eadea9ea434f090506c221e13c204eff824effd3bfd4efec34f0843188877⟩,
  ⟨0x10a07b03a01b00ca05b829012c08903b01880aa0480188090026000, 0x4fcd01369c0da65093f36103a488ea001966053f34142c888e900babd369cc24fcc051488e80018ff053f2e142f888e72ef8c12eee4bbbb093f2b0ce223980127121e8ab630d3f232428c88e30049c1f424fc8467488e20058a4053ef011c222f93eee053eec4fba024fbbc33888bd17f9c117aa84fff093eee102d888bc005ea8053eed140222ec006aa014faf856088b8460fc12f6ed0b2e43ae034fa94406d222dc0777053e6a142e888af010c10bd08434f1e05062222b00477cce893c2f0d3c731c1a088ab⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0x12808783fc1d00d806282d414408f03b01980a00400180080026000, 0x4ff853fbf093fe04fee53fbb0d3fe20c6223f004fecd3f7b093fe1194223ed3fbe053f7b4fecd3fba0d3fbf101b488fa001444e310d3fbe184bc88f9001444e314fdec44fef0712e223e00051063cc34fee4612d223dd3fae053f7f4fea424fec042488f50018ec4fd853f7b0d3fae208223d13fab4fea024fea93fa74fe8c34feb031888f3013fa44fd8424feac51488f24fe9814fd853fa54fe8834fea041088f10018ec4fdec24fe9870c88f00018ec063d024fe8c60888ef013f614fdf824fe8440488ee013f3d053f60140223b53f3604da71369ac24fcdc33888eb⟩,
  ⟨0x10c07f83b01b00cb05f02ac13008b03c01940aa042017008001a000, 0x1adc15279850ba224bd49e10549ac52698252788338892e526fc1526ad49a50949e1102d8892d01ad41526fc50b2224b00526a81526b4500892b338fc1338e0ce3a093ffc0ce224a53ff9053ff74ffb424ffe83388928013fec053ff911c2249c04ffa93f38368f834ffe066c892600da654fce0da3e0d3ff519a2249400659c18fd093ff2159224913fe8053f3f4fce424ffa433889224ff9814fcf93f38093fe8102d889210018fc053fe6142c889204ff8c14ff813fb5093fe40ce223f804fed014ff8c43488fd⟩,
  ⟨0x11407e83b41be0cc05c02a812e08403681800a804101a008401c000, 0x3a9941178f8ea36231e8352ee8406d225c000e6cc4de2094bb7145225bc0073c0152ed450be225b94bac054ba552e80252eb4338896d13dbc1136f44da6094bac103a4896c004dbc054ba6142d4896b005be9178f8ea350d4b7d15f225a50b69050b6242d90252cdc3388962474f010f8c86a741ade83529c0406d224f405278c152988470893a01adc1528cc5608935528b01528a94a20094a2d0ce224d00527fc1528b047089330149fd32a8549e30d4a2b19b224c8052694caa15278c3528a0668893101ad9ac02528945648930⟩,
  ⟨0x13d08e84241ec0e206802f015209704181d00c605001e8098026000, 0x14c79531914c760d4bff531854c60530a04531e830aa226994c77054c6152ffc2531e4307c2269404fb06180183e0d4c77182a089a4531d01530a14c60094c760c1f089a3014893f8183f0d4c74141b089a2010eeb43bb14c260d4c6714180897f013ed4c60530f835319470a7225f804fb531814c3e0d4c631d7225f4043bb10eeb530983530c470a6225f005224fe094c2f14294897b010ef1530982530b450ab225e8043bb10eeb530983530a857c897952fdc152fc94bed094bf9109225dd0f60049afe43cd10eeb0d4bf7101b48976009b2226bf90f330d4bf315f225d14bba054b7c52de4252eec3388971⟩,
  ⟨0x12c08c84201f00ea06e832816e0a304a82140ee06602980b402e000, 0xaf752bce4dc290d5bbf15f227b002bb80aebc09582b142ac89e6005ead1618c253bd051489e4001aa5054ef2142f889e3014e73054eb814022788c86f04bff62ffe4253ad833889e1539e01539d54e70094e790ce227814e76054e745399c2539e040b6226fc0064881539d850b2226f80166ec7cfe094e32145226e80079ec1538c050be226e4026c850f33094d2d142ac89b45338c1531894ce0094d2a0ce226c54c79531914c76530a4452ffd4c61531814c2843bac5530803131226ad4c77053ed4c6152ffc35338c60a9226a94c7a050eec52ffd4c280d4c7b101b489a7⟩,
  ⟨0x14c09c84881ec0e206783081640a404881e80ce05402080a802e000, 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⟩,
  ⟨0x12908d84201e80e006782f015008f03f81a40b004701b8090026000, 0x6f9c157ba0406a2299402e3e4b93857b80357b9057c8a64001d30074bc1cf70d5e67141888a3f007873174c15e360d5e631c1a08a3d001d2e074b02579845067228f15e31055e21578b02578cc4248a3b015e20174c078730d5e311c1948a3a578b95e2b095e2d578a95e260d5e2f0c6228e405789d5e20095e2e145228e15e29055e20578a15e250d5e2b104228dc01e1cc5d30095e29141908a36001d2e074b02578985063228d40578815dff095e24101228d0ea2b048ca2231ec2577bc3388a321f58011f38c11f4f0317d228c55db7055dae576d02576e44248a2d⟩,
  ⟨0x1600a684d82320ff075835c1800a004681e80c605001c8094022000, 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⟩,
  ⟨0x12d08d04181e60e006682e815a09a04681e80ce05702500e4026000, 0x18ae0049e6d27998262b884248aee27aa81279b09e65098ae0103a48aed436881434cd0d2e0979eb10922b808caf048ca52329c25b2f43388abd1f4e811f3e87cf4096cb410922af099fa0499f1267cc25b2c83388abb016bf3056ca711c22ae56c30056c2e5b09025b0c43388ab5016c23056c3011c22ad005b0853f385afcc35b0bc66c8ab3014e674fce16bf30d6c2c19a22ac800648c18fd096c2915922ac400649015afd85608aaf0068a51a1f425a69450ab22a809bb826ed06ca11b1d04230c09bb31b1f86c70169b45268883131229f95fe6046c7157f8c257f9c4248a7d⟩,
  ⟨0x11f08783f01d20d006002a813408a03d01b00b604801a0098026000, 0x181066dc363790612d22c998db9058daa636d02636ec4248b240019b0363d58da60d8db920822c8d8db6636cc2636d58db2636b83636dc3188b22018daf363d42636d85148b21636c41363d58db0636b43636cc4108b200019b0636982636c470c8aff0019b0066e82636b86088afe00d8f5636a42636b04048afd00d8ae058da0142d48afb00ac3e2b0c42635e850ab22be98d6d058d666358c2635b83388af9161fc1160f85825098d6d103a48af800583d058d67142d48af72aab81278acaaa9098afc10922bc46ea4046e771b9c0262bd44248af0⟩,
  ⟨0x12808a84081de0dc06482ec15409704181c00c604a01d008c026000, 0xbbc410bb942ee8099c380ce22ced2d7c052d724b5d0266fe03388b3a333fc1333ccccf6099b710ce22ce4cd7c04cd71335cc266bb43388b384b8ac14b8852e23099aea0ce22cdc00649016668450ba22cd8036af4adad098df8142ac8b33637d41635fd8da1098df710922cc8d8e304d8af2ae802637d440e922cc58dee058deb637802637bc3388b2d018dbf058dee10d22cb18dec637a82637ad8de4637983637b43188b2b018dbe636982637b06508b2a637a41636998dbe637943637a8406d22ca40181124cc3637a4612f22ca00181124cd8da6118de71c4b88b27⟩,
  ⟨0x13a09384502020ef07003341800b005002340ec06302800e404c000, 0x2e8c812e880b9fc099fac10922e988b24048afd22bfc267cb83388ba422dd4122dac8b6d099f200ce22e840459e76323d4367aa8517822dd40441f34099ea8145dc8b7467a841679fd9e79099ea20ce22dcc0679e0167a844348b72019e75679d8267a806508b7101e741f330d9e7d184b48b70679cc1679bd9e6a099e740ce22db8c9e704c9a532698c9680d9e73101b48b6d00c93b32694c9a40d9e7015f22db19deb059de3677942677b44248b643a5ec10e6d439b60eb903677ac406d22d8c00e6d039b50e6cc36779057c8b610eeec3bb23a6883aed103abf0eec43bb00ebb03ae4143ae50c4c48b60⟩,
  ⟨0x6902fc15e09c04481d80c605001c8098026000, 0x3abb413a9c8eae809bb300ce22f8002affcac3109babd10122ef0afbf04afad2bea026e2984248bb86b1d0123d848f6409ac7510922ed48f65048f6423d8426b1d03388bb423d94123d908f6109ac6a10922ecda932047b241ebfc26a4cc3388bae1ebe811eb847af01788c36a4c8406d22eb52bf2052bed4afa826a1f84248bac4b1e414b1d12c6f09a87b10922eac5fbd045fb617ee0267fe03388ba9⟩
]

def tableRRR : Table Block := .branch 12 tableRRRL tableRRRR

def tableRR : Table Block := .branch 24 tableRRL tableRRR

def tableR : Table Block := .branch 49 tableRL tableRR

def table : Table Block := .branch 98 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table (32 * (i / 16) + i % 16)

end PolicyRewriteParametricPacked1

end PolicySubmissionPart25

/- Component ClosureProgram; SHA256 ccc83efd3f39b3af359c3e2b79d8bf1099c1ba872c816d046800b14491d4526c. -/
section PolicySubmissionPart26
/- A total DAG program with backward references, for arbitrary decoded data. -/
namespace ClosureSemantics

def boundedNode (i : Nat) (node : Node) : Node :=
  ⟨node.op, node.children.filter (fun j => decide (j < i))⟩

def boundedProgram (raw : Nat → Node) (i : Nat) : Node := boundedNode i (raw i)

def boundedProgram_children (raw : Nat → Node) (i j : Nat)
    (h : j ∈ (boundedProgram raw i).children) : j < i := by
  have hh : j ∈ (raw i).children ∧ decide (j < i) = true := by
    simpa only [boundedProgram, boundedNode, List.mem_filter] using h
  exact of_decide_eq_true hh.2

def programModel (raw : Nat → Node) (input : Valuation) : Valuation :=
  interpret (boundedProgram raw) input

def programModel_equations (raw : Nat → Node) (input : Valuation) :
    Equations (boundedProgram raw) input (programModel raw input) := by
  exact interpret_equations (boundedProgram raw) input
    (fun i j h => boundedProgram_children raw i j h)

def boundedProgram_eq (raw : Nat → Node) (i : Nat)
    (h : ∀ j ∈ (raw i).children, j < i) : boundedProgram raw i = raw i := by
  unfold boundedProgram boundedNode
  have hh : (raw i).children.filter (fun j => decide (j < i)) = (raw i).children := by
    apply List.filter_eq_self.mpr
    intro j hj
    exact decide_eq_true (h j hj)
  rw [hh]

end ClosureSemantics

end PolicySubmissionPart26

/- Component ClosurePackedProgram; SHA256 968044345330c011b1c6e55075d6d865bd5d48b86e1f663877c1f945ac329c7f. -/
section PolicySubmissionPart27
/- Typed expression nodes decoded from finite numerical records. -/
namespace ClosurePackedProgram
open ClosureSemantics

def signed (n : Nat) : Int :=
  if n % 2 = 0 then Int.ofNat (n / 2) else -(Int.ofNat (n / 2)) - 1

def decodeNode (i : Nat) : List Nat → Node
  | [] => ⟨.bConst false, []⟩
  | 0 :: _ => ⟨.bConst false, []⟩
  | 1 :: _ => ⟨.bConst true, []⟩
  | 2 :: k :: _ => ⟨.input k, []⟩
  | 3 :: num :: den :: _ => ⟨.qConst ((signed num : Rat) / (den : Rat)), []⟩
  | 4 :: n :: _ => ⟨.zConst (signed n), []⟩
  | op :: args =>
      let children := args.map (fun d => i - d)
      let tag := match op with
        | 5 => Op.alias | 6 => Op.bNot | 7 => Op.bOr | 8 => Op.bAnd
        | 9 => Op.bEq | 10 => Op.ite | 11 => Op.qEq | 12 => Op.zEq
        | 13 => Op.qLe | 14 => Op.zLe | 15 => Op.qLt | 16 => Op.zLt
        | 17 => Op.qAdd | 18 => Op.zAdd | 19 => Op.qMul | 20 => Op.zMul
        | 21 => Op.qNeg | 22 => Op.zNeg | 23 => Op.qSub | 24 => Op.zSub
        | 25 => Op.qDiv | _ => Op.bConst false
      ⟨tag, children⟩

def raw (t : PackedNatTable.Table PackedNatTable.Block) (i : Nat) : Node :=
  decodeNode i (PackedNatTable.records t i)

end ClosurePackedProgram

end PolicySubmissionPart27

/- Component ClosureFixedWidthProgram; SHA256 2bcad5c1fc11db1c8f491f610a7d042edf5f71cea5d3b1344d488811f63e40c5. -/
section PolicySubmissionPart28
/- Direct bit-field decoding of typed expression nodes. -/
namespace ClosureFixedWidthProgram
open ClosureSemantics PackedNatTable

def children (i width : Nat) : Nat → Nat → List Nat
  | 0, _ => []
  | count + 1, packed =>
      (i - (packed &&& ((1 <<< width) - 1))) ::
        children i width count (packed >>> width)

def decodeNode (i bits packed : Nat) : Node :=
  let op := packed &&& 31
  let payload := packed >>> 5
  if op = 0 then ⟨.bConst false, []⟩
  else if op = 1 then ⟨.bConst true, []⟩
  else if op = 2 then ⟨.input payload, []⟩
  else if op = 3 then
    ⟨.qConst ((ClosurePackedProgram.signed (payload &&& 0xffffff) : Rat) /
      ((payload >>> 24) : Rat)), []⟩
  else if op = 4 then ⟨.zConst (ClosurePackedProgram.signed payload), []⟩
  else
    let width := (payload &&& 15) + 1
    let args := children i width ((bits - 9) / width) (payload >>> 4)
    let tag := match op with
      | 5 => Op.alias | 6 => Op.bNot | 7 => Op.bOr | 8 => Op.bAnd
      | 9 => Op.bEq | 10 => Op.ite | 11 => Op.qEq | 12 => Op.zEq
      | 13 => Op.qLe | 14 => Op.zLe | 15 => Op.qLt | 16 => Op.zLt
      | 17 => Op.qAdd | 18 => Op.zAdd | 19 => Op.qMul | 20 => Op.zMul
      | 21 => Op.qNeg | 22 => Op.zNeg | 23 => Op.qSub | 24 => Op.zSub
      | 25 => Op.qDiv | _ => Op.bConst false
    ⟨tag, args⟩

def getNode (b : Block) (slot i : Nat) : Node :=
  let first := b.start slot
  let bits := b.start (slot + 1) - first
  let packed := (b.data >>> first) &&& ((1 <<< bits) - 1)
  decodeNode i bits packed

def raw (t : Table Block) (i : Nat) : Node :=
  getNode (t.get emptyBlock (i / 32)) (i % 32) i

end ClosureFixedWidthProgram

end PolicySubmissionPart28

/- Component ClosureFixedWidthData0; SHA256 38a2d11023fa6d09068e8af5e0647998eee35eb99b2724c4db0057720d155337. -/
section PolicySubmissionPart29
namespace ClosureFixedWidthData0
open PackedNatTable
def tableLLLLLL : Table Block := .leaf #[
  ⟨0x32818d8b985622a01488a084e626012688e840a1f20f286c02f61760b505742a214208683f01de0e306a027c12008303b81a806a000, 0x61c8000008000090c0000040000506326f3ca7c8ab126dc293a05261b264000004008000731a6587200000201069c300000100000a18100985a84471640000040834e07446d6178111e590000010000061d44d61780130e400000400002060000020000043⟩,
  ⟨0x2bf1580a7c51427513008ac44221010087c83c61ce0dc86902de13a092845821e10807583601920b4050824810607002e812806a000, 0x722af136ee0acf405660f6b90000010099c61c0d226d3ca7c8ab126e60acf005660e4b900000102000018000008000020ddbd72d8a8244091fb4406e8f84a714eb9a051a794f9154428de8527a0a4c185720000020066843⟩,
  ⟨0x288139896048622b10987f03ca1ca0d986783181770b3053c27a12e08b84201ec0e906a02f414a09203f81b00b20410180098026000, 0x715c63902aa7255404b644045445029acf03319a5d28aaa501668cf9a8ce4a2b135509b66076ce449469367066cd64f5092b45a3746a8829b21945158926742460728e0dd317c0514346881a414686093⟩,
  ⟨0x2ef1700b2455629413e8920486237115087840e1d20da067030816d0ab04ec24810f07e838819a0b604d82180de05a01f80a802a000, 0x184f03a9a79b2816501c8cd03edb200000200258430a2130b51880ef6c80000080bb940c097c8ca09648808a08a058d9e071334bfcd556002cd19b3519c941680aab3055b894b66808155033ab722f6cdd2abe4b4155591ab7409580e6ae⟩,
  ⟨0x2f416d8b1855e29814089b84a024111b889841e1f10ed074037e1a80cc86282e215809f84281e20bc04f02140e805d02600d402e000, 0x990a7c8f69ab68e6cef04cc03b99c19a6366d02ca389103689b40e569d8ae05942ab33606813681c0d3e45549363005e71202f3018b7c8000008040000c0625f200000200bb943b56c0b284df4d0346f0771a7026d038da77ef016505bacd⟩,
  ⟨0x2c11530a444f025d12408bc4341ff0f507443701a30c105b42aa13d094044c1f00e306702f014e09603e81ac0b804301a008802a000, 0x1600aaaf055b6e52f9a0205540ceadb92b7cd52abe4a4155511ab62409d80310ee06d5c434380ba9c855012d910115114172af0785697222aad81568cf9a8ce4a2b135509b6841df391251a4da3067cd64f5092b45a3746a⟩,
  ⟨0x3321888bb05b62c21588a6051227812f891845a1f80f4874035e1960be852027812f09184281aa0b704f821c0e005901f009c024000, 0x2cacc05d40418bcac81e3781da3cf04da0376f3e455226dd10179e700bcc0755f200000200222c3309e037cf3bab9017500dc3b4073df2000002001acc3482616a5100e23e4000004042fe0604bd06504b244045045029ecf03399a5f46aaa601668cd9a8ce4a⟩,
  ⟨0x2c01558a6450827312d092047222010887fc3e41dd0e206bc32c17d0b2054c26412308c84201de0ce05a82ac138083032813806a000, 0x19f3519c945626aa136fa83be7224a349bee0cf9ac9ea12568b46e8d5da14f91ed3560873e70c09d80384ee1f3c606080ba8e2440d226d01b979d65580ba81aa9db03424d01b479d7ac059406ab340785f20000020085fc3⟩,
  ⟨0x3131838bb056e29914089a44a423b11008243e81e20e386c832e17c0b3853026e11c08383b81aa0c004f82280e405a02280c002a000, 0x271006311900000100bf681812f3d9412c9101141140a733c0cd6697b1aaa96059a3366a339282c01555e0ab616298cd0102aa06756c345719aa557c9482aaa2356ee813b00771dc0d2b8dadb0175390aa025b22022a2282e15e0eead2e04555a82ad⟩,
  ⟨0x33e1918c485dc2df16a8b1055228513509804a223610a87f03c21ac0c4057c29c133091041c1d20d206182a0108069027006401a000, 0x312870f9e2211100c28e2440d226d00c2627168a80614068a43606849a018244e9e9805d4034aed00cc632000002005fb438140c030a010307b5740d1bc070489c09b4030b89d3a40594168b34c27806251387434030a00c321a0191c640000040026486984c2d⟩,
  ⟨0x2d015d8a8051627012d890044a2100f6075c37e1a70c905f42c414d09c0498222100072834c1880a904d02200f606602580d8036000, 0x6756d745719aa557c9482aaa2356cb4050c00cb21c0d2b8954ac030a7215404b64404544505a2bc1cd5a5c08aab1055a33e6a33928ac4d5426da281e3391251a4da381a33593d424ad168dd1aa7a0a8c8f69aa220e8cc4c050c⟩,
  ⟨0x3361928c285d22d015f8a9052a286135894046a2000f286c03481970c585c027611d08283b41ac0bf05202340f006602580d8036000, 0x304da01afc4e9e9805d4134aed1837806cd13e4554936ec0189dcc031300dd632000002001000300dce32000002000dac3502616a91006d1190000010088b81812f2d9412c9101141140a533c0c96697b1aaa8e059a3366a339282c01555e0ab6b6298cd0102aa⟩,
  ⟨0x30f17a0b885a62b81548a5c51427512d091445420f0fa078c37e1b00d306542f415609d84c4244107073033416407d02c80b0036000, 0x6640f19c8928d26e6c0d19ac9ea12568b46e8d591054647b4d56507466ce0286006cd0e1f3c592ca01851c4881a44da01aec4ed56900c280d6886c0d0934035889fdfd00ba807e5da01c2c640000040088b8756ab80614010181e13081e3780eb113⟩,
  ⟨0x2ed16a8af454c28f13a097449023610d88183d61d00dd86803161700ad850024a110076035c17e0a704901f40c404d01c0098022000, 0x12c9101141140a733c0cd6697b1aaa96059a3366a339282c01555e0ab75e298cd0102aa06756ec45719aa557c9482aaa2356e04050c00e021c0d2b8bf5fc030a7215404b64404544505c2bc1dd5a5c08aab5055a33e6a33928ac4d5426d⟩
]

def tableLLLLLR : Table Block := .leaf #[
  ⟨0x36f1aa0d2867632017e0b8458c291136890045e21410187a03b21c80d686482ee14209984601f40e3064024c10e07a037014c03c000, 0x1b790d81a1268075913e270c030a00f0a1a01ecc640000040061a87aad580614010182ebb081e3780f5913c1368076713e455226de480627c600c4c03cd8c8000008002d90cc278076d13a7480b280d1668078f190000010004e21aa130b558803bc8c8000008030d40c0979eca⟩,
  ⟨0x2c91528a404f026012588d84362060f8877c3941b90cf06302fa1620a9850426811f08203bc1a80b904f02340d205a02800fc048000, 0x1d2e980614e42a8096c8808a88a0b85783bab4b811556a0ab467cd467251589aa84dbed03c67224a349bef03466b27a8495a2d1ba3579415191ed356e41d19dd80a1801dd4387cf1b8dc8061471220691368076313df6f4030a⟩,
  ⟨0x30f17f0b8c5a42b714c8a084e625611a88703fe1e10e486c43341830b4054427812a08783e81ba0c205682400f606002580c002a000, 0xd1bc07f689c09b403fd89cd980594165b34c27803024ce868005d4033eed66e049c812f3d9412c9101141140a733c0cd6697b1aaa96059a3366a339282c01555e0ab6030a6734040aa819d5b0285739aa557c9482aaa2356f54050c00f521c0d2b8⟩,
  ⟨0x3931c20dc86ae3221828ba05a62c21568a6c4ee25c11f886c4001e30e4069031216e0a884702020f2067030414c08b0380154062000, 0x624d2e12b8e01898000008000060dc58ea6715385292e135689b466cd4672500b7001856dc030d8b5b29cec4040185007610d8bdb39cecb5d0fd6ec4030ad86b21bff024300189672000002009610300ff21c7963f5fb00c29c51aa00c3747f489ea0030dd2fca27f4fa806140080603c2128⟩,
  ⟨0x2ca15c8a7051427b12f093c47a23010a87e03ba1c00d186182e214a09e84b823e10407603741a00ac04c821c0f006902600bc024000, 0x284db2c00f39c8928d26cb4034e6b27a8495a2d073c9552806539073c955123af39898029600312cb81c17111c4800ca98514a9aa53022c6a808be8a509ee2d0d734390a0c11ab125524d6c551b00f338d64199c63194a5724a⟩,
  ⟨0x2d915e0a604fa26011588784061f70f5073037a1b10ce06042d215a0a684a423010607c83781820af051021c0d805101e009c02a000, 0xcd7338441c030a00c1a1a00cf9390000010002ae1b0af33455517138a4084a6caa54c5840cea70458150117914a13dc5a15f986e14366d5092b45b3d00aa9f096a52a12568b69ac1557b3db090b90555c02ad19f3519c945626a⟩,
  ⟨0x3861ba8d8069c32a1878bc859c2b314b09ec4ae23c10f880839a1b00d085e82da15209a84681fa0d605282500ee06602480a001e000, 0x344da3366a3392805cb00c2b940186d28e0ce7800200c2803bf86d2ce34e78bbd87ef388018570f770d9980496003464e400000400d660600cc72e3cb130cc400ca9c51bd00c35b296e67bb00c35b8966672dcb800ca80100c0783a50346f00e5d99c09b40199267696602ea05b276984f⟩,
  ⟨0x2cd15d8ab051e280137098448c22910707c43a81b70d105ec2dc15f0a804e0240111082038019e0b104d02200f206a02780c802a000, 0x191251a4daf0069cd64f5092b45a0dd6aaab20b6720dd6aaa8679673440052c0068797035ae285a18019530a24534aa6097c8808b48a509ee2d0af6c2f0a1b36ea040594074b35624aa49ad8abb06789baf50cce91752525c26a⟩,
  ⟨0x2f716d0af451026b11b08a441c2020fa875c3901bc0d3863c2ee1680ad84dc24c108078837c1a40b704d01fc0d405502180b803a000, 0x5b800ccc01b7a720000020004003006dc9c8000008000f50d85789a2aa8c89c520424c654ea63020655384be44045c45284f71684ffe19850c9b730202ca03959aa12568b659815549cfd4a42d0155660ab467cd467251589aa84db5d00f39⟩,
  ⟨0x3891b70d4465a31217a8b6856c29b13f098445820f10007643981b10ca05e42b813508203cc1ac0c505402100d205801d80b003a000, 0x1da00c36f875673d4010061401e9c36fa75a73d5e8c3fa1d400c2ba7cf86d94024b001bc272000002004c903006c7971e58b16c600654e28e68061ae357f33e58061ae457b33afec0006540080603ce5281e3780760ccf04da00d91338c45c030a04c5a1a306f006cf99f22aa49b6f80333⟩,
  ⟨0x2dc1650af454428513509344602130ff075c3941bb0d606502f816d0b004f025610d07b03901aa0c605582380e205c02580d8048000, 0x5092b45a0dd6aab160b6720dd6aaaea7d673760052c006eb97035ae2e9ba8019530a24534aa6097c8808b48a509ee2d0afac2f0a1b36e8040594073b35624aa49ad8abd0cb89bcf82ccef5792525c26ad1368cd9a8ce4a0176c030a⟩,
  ⟨0x2bb14309e44bc252122889c43020c0fb877c38e1b80d586102e615509f04b023e104073833016e0a204801ec0d404d01d80b001e000, 0x8000af0d85789a2aa8d89c520424c654ea63420655384be44045c45284f716827078332a1936e8040594073b35424ad16cb302aaaca0a9485a02aacc1568cf9a8ce4a2b135509b71e01e7391251a4dc80069cd64f⟩,
  ⟨0x3941bb8d7067031d1800b8c55c291141096c49c23310b07ec3bc1b70c305d42b0147095046c2140ed06802cc0fc06f02900d003a000, 0xd79e69cf97c30ff0790030af1f7e1b970092c007549c800000800dac0c01cae5c796329ca8019538a3c20186bad91ccfbe0186bb190ccf23c900195002018176b4a078de01e4b33c136803964cf915489b742006679f80333007469c8000008000f30cc2780397ccf1e202ca03859a00e8139⟩,
  ⟨0x2fc1708b1054e28a13a8938482232111882c3e61e40eb86cc3441840b6856c29813d09104141d00d306102b413607702e00fc036000, 0x6eb555a740b39d400296003a7cb81ad71a6e9c00ca9851229a55304be44045a45284f716857fe17850d9b740202ca039d9ab125524d6c55fc97c4dfbda667acbf1292e135689b466cd4672500bd601857a8030dd71e59cf90040185007c70d⟩,
  ⟨0x2a914e09f84de26312708d843c20f101076c3941ac0ca860c2ec15b09f048c21c0f907383481820a4049020c0cc05702280e003a000, 0xe290212632a7531c1032a9c25f22022e229427b8b41388c19950c9b740202ca039d9aa12568b659815562d0f4a42d0155660ab467cd467251589aa84dbc100f39c8928d26f08034e6b27a8495a2d06eb555bd05b39⟩
]

def tableLLLLL : Table Block := .branch 14 tableLLLLLL tableLLLLLR

def tableLLLLRL : Table Block := .leaf #[
  ⟨0x38b1b70d4c65e31417b8b6854a28813c894848a22a10687c83aa1ae0be85b029e13e090840c1d80dd060027c10c06901a009c018000, 0x77cfb4e7ebed87fb3e801857cfd70de380496003da4e4000004004e20600f172e3cb1c4f1400ca9c51ed00c35e2e0e67eb00c35e8e0667c1f0800ca80100c07cda50346f00f8599c09b401e32678f1016505c2cd309e00f2733c7c6017500e2bb401e92720000020001f43615e268aaa3a2⟩,
  ⟨0x3011730b2455828f13d094c48c23711408403f01e90ee06d43481860b7857429c13f09104141d00d306102b413607702e00fc036000, 0xdd6aabae85673d80052c007af97035ae3adeb8019530a24534aa6097c8808b48a509ee2d0560b05e54366dc8080b280e366ac4954935b15410c7cce07f2667dcc09292e135689b466cd4672500bf601857e8030def1f19cfc0040185007df0d⟩,
  ⟨0x2a914e09f84de26312708d843c20f101076c3941ac0ca860c2ec15b09f048c21c0f907383481820a4049020c0cc05702280e003a000, 0xe290212632a7531e1032a9c25f22022e229427b8b4138bc19950c9b720202ca038d9aa12568b65981556ed154a42d0155660ab467cd467251589aa84dbf100f39c8928d26fc8034e6b27a8495a2d06eb555ed05b39⟩,
  ⟨0x3821b38d286562f616c8b2854629613d89784862260ff872837219c0c585b82be14e09784401e20bc05682400d805101a009c018000, 0x3439d86fe2024b000c17ac80000080055c0c01fba5c7963ecfb4019538a3360186b29f34cf320186b2df24cfe6f9c019500100602e0152078de01fd133c136803f7ccf915489b602801a9c0200353003026b20000020001443309e00fe53393494030a00c921ac47e539615e268aaa3e2⟩,
  ⟨0x2fc1768b785862ab14e0a3c4d625a12408e445420f0f8074437e1b00d086182ce148099848821a0fb06b82f013a07902f00fc048000, 0xa14d4a98116254045e45284f7168677a1b850f9b5624aa49ad8ab79f8899bb865538446fa92b125524d6c5556f944caac2ca9c1c2b1492e135689b466cd4672500b5201856a0030d83e68eb3a2010061401d0c36109a4ace8f3f0fcf688030a⟩,
  ⟨0x2eb1638ad854829713e097c49a24011288203da1d80e186c433818b0b6056829612c08e842c1fc0e306202a411406b02600dc01a000, 0x57c61b850d9b5424ad16cf402aaf85e694a8495a2da6a0555eeb05290b80555b82ad19f3519c945626aa136c4900f59c8928d26c4b00d59ac9ea12568b41cb15544106359072c555054e3d660b802a600182d4e06f5c41482a00694c28⟩,
  ⟨0x3401928c185b82a714b09dc4cc24711488484021e20e9871034a1860b384c82260de06882d815409d03f81c00c804f01a007001a000, 0xd18061a6722754e284510034a00200c03c03a40f1bc01c52a9e09b400c59a9edd80594275b3460de0063054f915524d8e0006a71b400d4c00c6fac8000008000400c00c6dac8000008000310d85799a2aa8789c52042526552a61c206753822c0a808bc8a509ee2d⟩,
  ⟨0x36a1a30cd462e3001770b7c5a02b314a09d44c024f11d08a04081e90e5069831616c0a884b42240f306a027c10007102380e803e000, 0x2bc30bc286cdbb81016501dacd5892a926b62a5725c9995b92d5390c57a925c26ad1368cd9a8ce4a016bc030ad70061b224d4d67500200c2803a786c8b35559d4e961fa4d400615a7d1c362d804a6001903590000010007a818018b14e3cb115a2b801a538a34a018699a8a153⟩,
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c01a007001a000, 0x28495a2d966055510cc25242d0155660ab467cd467251589aa84db2bc03d67224a349b2c403566b27a8495a2d06eb55529c16d641bad5547b393598fa00a980063e5381ad711ea3d801a530a24534aa6097c8808b48a509ee2d⟩,
  ⟨0x32f18a0bd459629614289984aa23610a87f03da1ce0d806642f414509c0474222104073035c1960b604f02180ee06a02300d402e000, 0x67c030d3392baa72c258801a500100601e31d2068de00e5954e04da0065cd4f373005d40b96ed309e0066054f1e202ca03859a00668d640000040001186c2bc4d1554444e290212632a753101032a9c25f22022e229427b8b427e70cc2864dba81016501d2cd⟩,
  ⟨0x36a1a30cd462e3001770b7c5a02b314a09d44c024f11d08a04081e90e5069831616c0a884b42240f306a027c10007102380e803e000, 0x2bbf0bc286cdb901016501c6cd5892a926b62a562bc999579ed539cc56a925c26ad1368cd9a8ce4a016bc030ad70061b3a4d2d67480200c2803a386ceb35559d4e861fa0d400615a7cfc365d804a60019c35900000100057818019714e3cb12da5b801a538a342018699696153⟩,
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c01a007001a000, 0x28495a2d966055528cc05242d0155660ab467cd467251589aa84db43c03d67224a349b44403566b27a8495a2d06eb55541c16d641bad554db393599ba00a980066e5381ad7136a6d801a530a24534aa6097c8808b48a509ee2d⟩,
  ⟨0x3131810b8c5a42b31520a4c4e825511b08043e41d30d906642f414509c0474222104073035c1960b604f02180ee06a02300d402e000, 0xf1bc01d16a9e09b400d1da9f22a9136d3300353a60006a60069bd640000040000d86613c00d20a9e1e100ba80705da00698d640000040000c86c2bc4d15544c4e290212632a753121032a9c25f22022e229427b8b427e30cc2864db901016501c6cd⟩,
  ⟨0x3991c38de06d234c1968c385f22e81698b0453a28213188fc4482050f5071835618c0b684e023210a070034c17009903f017c06a000, 0xb125524d6c54ae641332b756aa7528af524b84d5a26d19b3519c9402d780615ae00c36a69a9acea00401850074f0da9e6aab3a9d2c3f49a800c2b4fa386d1f0094c003516b20000020007d030034729c79628d51b0034a714684030d335452a79f00c34ce512a9d14a2a006940040180b98f48⟩
]

def tableLLLLRR : Table Block := .leaf #[
  ⟨0x2dc1608ab052e285138097c48022e10f88003e21df0e906dc33017d0af04fc24010b070835018a0b604f02180ee06a02300d402e000, 0xb40555982ad19f3519c945626aa136d7300f59c8928d26d7500d59ac9ea12568b41bad5556b05b5906eb5554fce4d66a0802a6001a814e06b5c53ea7e00694c28914d2a9825f22022d229427b8b42bbf0bc286cdba01016501cecd⟩,
  ⟨0x2f11690ad053a28c136897849e23010887c837a19e0c885d82d415d09f84c024810f07b837c1a00c304f82380e005902380e803e000, 0x6c054f36502ca13919a306f00361ea7c8aa926d9700353b28006a6006cb56400000400008064a2c1d6585789a2aa8a89c520424c654ea62820655384be44045c45284f71684fc619850c9b740202ca039d9aa12568b659815550730949⟩,
  ⟨0x3aa1c68db869e33a1948c506042de1618a9050026512308ac40e1ec0e686b82f215a0a584842280f906d02fc14007602080c0022000, 0xf2e0e663c6ded4ed68f4a49709ab44da3366a33928054500c2a880186db027f599f008030a00cf61b6c8a05667f3b87cea7c01854f6730db0401298006d45640000040006206006bfd38f2c57dafc00694e289d8061a4c2bbd4e720186932aeb53aef5e000d280080300f64e903c6f0075e6a7826d⟩,
  ⟨0x2c915b8aa051227a134096c480221103079c3901a90ca05a82ba14e09f84902180fd07803301760a904d022c0dc04f018007801e000, 0x191251a4dbb801ab3593d424ad1683962aaba40c6b20e58aaad3163acda80054c00369e9c0deb8b4b69800d29851429a953022c4a808bc8a509ee2d0cd74370a1f36ac4954935b152b9c4cccaddc3a9db32bd495892a926b62a⟩,
  ⟨0x2cc15a8a584c225411c88b44402020f9879c3a41b70cf864030615f0a704f025e11407a838c1ac0bb04e02040d805702280c003e000, 0x39d9a006ff5640000040000386c2bccd1554244e290212932a953081033a9c116054045e45284f716857061b850d9b5424ad16cf402aaae461a92a12568b69a815556e23d490b80555b82ad19f3519c945626aa136dda00f59⟩,
  ⟨0x3ab1c60da069a32e1898bbc5a82b514b098448423310487f03c21c20d386202bc12908c03e41d00c905d02a411406b02600f403c000, 0x61929159a3808030a00d1a1b86ca4d66914487d0e8e018551a850dbd60129800708d640000040004606006f4538f2c5e6bce00694e28a00061a4e6f054e7c018693bbbd53bc178400d280080301564e903a6f00778aa7626d0037a6a7c8aa04db7fc00d4efe001a9de5c0759309e006f6d4f4e802ca⟩,
  ⟨0x2f61748b3855e29413a895846e2220fc07ac3b81cd0da867431c1810ae853025c11708283d81ce0ca05582300ee06602880fc036000, 0x345a0dd6aab1b82dac8375aaac165a2b38340153000e0ca7035ae30560b0034a61448a6954c12f910116914a13dc5a15af05e14366dda080b280ec66ac4954935b151f7f64cc7d626a9e161fb492e135689b466cd4672500a9c0185534030d⟩,
  ⟨0x29b14709cc4ce25a11e08b444220c0fa077039a1c00ce062c2da1560a204dc2380fd07103341700a604882000c204f0200084024000, 0x30af1345550b138a408498ca9d4c2840caa7097c8808b88a509ee2d09e08330a1936e9040594074335424ad16cb302aaba648e921680aab3055a33e6a33928ac4d5426dc7e01eb391251a4dc8201ab3593d424a⟩,
  ⟨0x3b91cf0dfc6b63401908c185c42c71540a244a823511307f03de1d40da86682f615108e042c1d80db05e027810e07802c80e003e000, 0x14c00c373c143acd08040185006830dcf4522b3479fc3e7d4600c2a8b3d86e4a0094c0039c2b2000002000190300391e9c796322e460034a7144fc030d2698fea73d00c349d63da9e3fc800069400401807be5481a37803c83538136801c9153c5840b282e066984f00393ea7979402ea01c976e4fcc159⟩,
  ⟨0x2ef16e8b4056a29613d897047a21e104877c3a41c30da06703081750b4051026611507f03b01ba0ce05782400e205c02580d8048000, 0x28495a2d06eb555a5816d641bad5566a2cf59cd800a9800735d381ad719a735001a530a24534aa6097c8808b48a509ee2d0ad742f0a1b36e3040594071335624aa49ad8a87b44ba98f5d0b53cea3e2925c26ad1368cd9a8ce4a01534030a⟩,
  ⟨0x2a814489f04c225512408a843620f0fd07883941bb0d706282f215b0a204c824a10a07583401760a604a01fc0dc04f01e80b801e000, 0x185abab2c2bc4d1554344e290212632a7530c1032a9c25f22022e229427b8b427810cc2864db8c1016501c4cd5092b45b2cc0aab1911ea485a02aacc1568cf9a8ce4a2b135509b74f007ace4494693750006acd64f⟩,
  ⟨0x3781af8d0064e3061768b3855e27a12d89304442150fe07743881a50bd851826a11608283981ae0c605382200f205a02580f803e000, 0x1d876edd1bd59ddd677eaee00bab6f51dbab40253000ed3ac80000080001c0c00eaaa71e58d51aa400d29c51aa02ed197a8aa7a602ed1a1a82a7a8b51801a50010060275f52078de00f5254f04da00755d4f915489b760801a9ebed7f53389e0075854f91568b760001a9ebdd7d53⟩,
  ⟨0x2eb1660adc51a280138898848e22f110084c3e41e10e787003621920b9855028413309204141cc0c7059028411807a02c8100042000, 0x1da54e06f5c6d0da200694c28a14d4a98116254045e45284f7168cfb8dba87cdab125524d6c543da5a54c7aeeea9ede1f1495892a926b62a11b2baa62337454f6c08fa49709ab44da3366a339280b8c05d5c402eddb636ab3b20402ea⟩,
  ⟨0x2d315c0a80522284130093c47a23010a87d83c81d70de067430416d0ac051826212008083bc1c00c1059028012607802c80f803e000, 0x22c0a808bc8a509ee2d0ac74370a1b36a8495a2d9e80555a7490525424ad16d3502aad322e6921700aab7055a33e6a33928ac4d5426de0a01eb391251a4de0e01ab3593d424ad1683962aadfa0c6b20e58aab68901aced30054c⟩,
  ⟨0x35519b0c9c5fa2f016b8ae053e28012b08844041e30e2069432c1770ac04e42340fb076033415c08f041019c0b604e018008402a000, 0x789538f2c710e2200694e28db01768d4e1553d901768d6e1153e15c2c00d2800803013af6900079ad3c01f0ca9f330034d003c4ea7c8ab98001a6f2900353e4dcbaa600796d3c00f18a9f22ae540069bca000d4f92f28a9b0af33455505138a4084a4caa54c1040cea7⟩
]

def tableLLLLR : Table Block := .branch 14 tableLLLLRL tableLLLLRR

def tableLLLL : Table Block := .branch 29 tableLLLLL tableLLLLR

def tableLLLRLL : Table Block := .leaf #[
  ⟨0x32318a0c145da2d51630ae45302871348948480231111080c3c81c50d8067c3141780ab84f823e0fe072831815a08c039815006a000, 0x48a6954c12f910116914a13dc5a2bf22eea1b36ec040594075b35624aa49ad8a84b516a9895ea153e80262925c26ad1368cd9a8ce4a02e901757400bb7a18e3acf10100ba80785dbd14725678f7ddfbdc402eae1dd76f150094c003ceeb20000020000503⟩,
  ⟨0x2e716c0b2c54e29613c098449e24211388203da1d80e186c433818b0b6056829612c08e842c1fc0e306202a411406b02600dc01a000, 0x284f71684e3a19850c9b740202ca039d9aa12568b65981556fd17d490b40555982ad19f3519c945626aa136f6900f59c8928d26f6b00d59ac9ea12568b41bad5576105b5906eb555cd481d679b802a6001e6d4e06b5c734e6a00694c28⟩,
  ⟨0x36319c8cb061a2ee1678ac050c251119084c3e81d50e3069c3101690a504ac2380fd06f02fc16409704581f80c005102280c0030000, 0x772ee600694e28f3a0069a1afb654fcd801a686fed553ed9db400d2800803013e2290007c353c01f6ea9f840034d003dd6a7c8abc0801a6f8b00353f11e2aa6007bf53c00f7aa9f22aef60069be2800d4fc3f89a9b0af13455507138a408498ca9d4c1840caa7097c8808b88a⟩,
  ⟨0x3141838b745982ba1558a704fa25e11f88b443c20f0f8074436419d0c605dc2ca14409584301dc0d705c028410606c02680b801e000, 0x716819f7c06e943e6d5892a926b62a1295f6a624fdbd4fd3896a4ac4954935b1502caef53057ec6a7e8417524b84d5a26d19b3519c94050202ea800176fa40f359f0080b280f766fa60f959f7d59fd3d016579e6cdeec00e99e87ce56400f74a71e58⟩,
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c021009c01e000, 0x28495a2daab0555d8c2cd242e4155700ab467cd467251589aa84dbf3c03d67224a349bf4403566b27a8495a2d072c555f1c18d641cb15579b14159f3a00a98007ce5381bd71e6bcd801a530a285352a6818116154045e45284f⟩,
  ⟨0x29e14a0a084f026612c88e84201fe0f887483901a90cb86142f615c0a904cc228102076838c1900b005082500d405902380e803e000, 0x206fac1606fd415c4e007e6d33e67cd0034af641584ff2401d3a06003f1e99e6829748f03004f874e81be0802a7001f814cec4141a15103022c0a808bc8a509ee2d02bf940dd286cdaa12568b68a415576717f49⟩,
  ⟨0x27512d093c47422d0fc07a43b81c90ca06042dc15b0a704f426012308a04041e00e306b030c15c09b033015c09403f0170070024000, 0x1102129e13420aa645a000002000000330a2c3385e4a00000200000238624b99a1df043f8a4a0d2e29d331a49559132869a14b8a43244cde9a0304480701202fc7521b13e99a13589a4ba4781beb05⟩,
  ⟨0x22810988183f21e80eb86d83521960c605e42d415709b048c2200fb077037c1a20c0059828812608903a01940a004101b8098022000, 0x90a55d0a5853366b1a35c1b8045cd84fd1a36060ed1661443d49800c185ce9c92d3525cd253d0a4e24c10dea69f14949a4c24c0d58aa93492152a9309303651b419553146f⟩,
  ⟨0x27412e894048623211088003e61de0ea06fc36019b0bd05942a0141097047c2200f3073034c1920b604081b00b2044018808001e000, 0x882997429614cd9ac68d70ae0117361387eab60607b55985107d59800c285ce082cb03d653c8e8ea37624d249ad81a95b09f0346c0c1b22c00004000000860d6ad0d1220dab390e4b86692b349849⟩,
  ⟨0x298131893847e22a10d88303d61de0e486fc3541750b2054c28812d090044c2040f1068030c1580a204581f80ce052018808001e000, 0x41a70000021c27d94f239152b7624d249847027b5b09e50d5b03031aac040000000008786692b349849aa2997429614d49ac60d70d403573613ce06cd8180cc65b8c40ce69c1859404a18ae786692b349849⟩,
  ⟨0x22f10f08443f81f20f0875c36c1a10c905fc2ce1520a404cc24c10f07e03c81c20d706002cc138087039018c0a8033013005c01a000, 0x2e99fc5227667818a4d303436000db20e6ca611c384586e345418d9606831b2b89c0f5669a2918197cd70301e0cd71881e4d381ab2c28d97624d249855006b5b09dc26c0cc2b⟩,
  ⟨0x294133894848a22410d07e43d01d70e4069c33418d0bd05a42ac14509c045c21a0ec06d031c1740a504f02240ee06d0260108042000, 0x892893001b5430d9584f11e0296e81804a236d9a6692c34984988900bb650a5c521da3270e41ca3228f0c27881003b740c0030ff6c2a94a434a30d212aca921e2ca5d23c0c0170ed6e81a1d0026dc0110e76c⟩,
  ⟨0x22610987f03c81da0e386b832e17e0b4855828a138094847021e10007683781a60c2058828812a08a03c81b00c404d02180b8042000, 0x3b44e00ecd08f087818374480dfbb40db6880e0bce25ecb2821f34cfe295c92e29a3318493c5139927048f1a5e4d0d89eccd09a44d2e2781a20ecb03445595c4e0031276c⟩,
  ⟨0x26812588e043620a0f187403821a80c585c82d014b09c04a42200ff073037019a0bb055026c11807f036816c09203f0168068016000, 0x6a694d4725006a4938c9ac08006a29555325308fba02ed0069a9881efbce060069795d8d25308e03aced1a3881ec3ce063c9795828c19dc259a4771595095fb82e420b036360a8ea1f224e09⟩
]

def tableLLLRLR : Table Block := .leaf #[
  ⟨0x21110307e43cc1cb0db066c3101730b3056829213c095048021a0fe075836018a0b8053826010e07a032816c0980420178074014000, 0x1899853764940301868342c4030389dd525a1233d19b11964cfe292f91e060cd12d8aab592d6f25bfa4bc66da33fe49a533f8a460ccf03644981aa792c288f5449a06⟩,
  ⟨0x20e0fe07c83c21c60d706883201840b6058829413709204442080f5073835018e0b6053827411807d03601740a603e0178068016000, 0xba4781864d32110c34fe2a1f11a9647a46d1028781b01122b0492e372594d0f429389314340a89f14949a4c24c0d8a6934925469309303625ab4e24937abdb13e26⟩,
  ⟨0x2010f907843a41c70dc06803221860bd05b42b414909a04a822e10d07d039c1b40c205c029413608803a81800a604201980a002e000, 0x6125e4d39927049c499256886c4f89a119c539149704cf4266781b2392c0d9d4972543f8a4371a1e06a89130362d258ad0e554a79334519f224e091d34a79acd⟩,
  ⟨0x27612d894446c2190ff07ac3a01bd0d6066c31c1730b4053428012508d84001ca0ca05c02b8126086035816408e036014806801a000, 0x76486c0c01b142c01a4e6201b244e9192806bd0d8b52326692834b8a6b20785e09df81e16c2701d561b03006a70b00eea2201aac4f7105818034e86b8c4035089eca0bb582e699fc52b925c53466⟩,
  ⟨0x28c13d896847a23011088504101fb0f107143501810b2055428412a08b84341f40eb06802f414409803f81b80ba05001a80a801a000, 0x907347c8c439c10d124fe295892e29c46714cb053a495aba53568112901f3b0064e0367529308e1ba2c361a2aa592c0d52c94c23806e10d0c122a3b944e06a10d75c99a4a0d2e29b401e178269801e56c27⟩,
  ⟨0x27b135097448423810e88403ea1e20e086b432817b0b1052426011308403bc1bc0cf06102c014c09703d019c0ba04a01b8090032000, 0x439ad84e03d14360600e8216e3100e8a27d549400661ee738e8b8372e9b8c074db813a406f9d37d6ceb2d75395e09b30875cc9a6f23f8a4ba47818c24803a54af4892c0da2c979244c7689c122174eb⟩,
  ⟨0x24a11b88b442c2030f8076038e1b80d686703161790b7858028a13808e84282000ed07183201760a004681c80aa0440198098016000, 0x2a143c0de0b32c30438688b9b1c8a8c33e449c1234697e3697c8f031c4900eda1ac31046e22716496068764b036bc030d61898f63138664bab00c34d68fa6326692834b8a74c0785e09⟩,
  ⟨0x25f12a88d04422060fc87783941bb0d5066c31816d0b0054428e13a08283c41c00d105f02ac13c083038019809a03e018808802e000, 0x40c0033f76bb564a01f0c3586244f1c4ec4d14f23c49b7624d249b0a01a96c278c9b0330ac00010000000875fe8b06695c921f21e1c45b89f9a0186ff29181a005dd671260cde9270486f6cb⟩,
  ⟨0x2c31570a444f426712c092445421d10608083e21bc0d0864830e16c0aa84c424e10e08203a41a40be058829010606602b80f0036000, 0x712ae030065b380b46f192ec49a49352008d2d84fe66d81874d600004600000430441a0f91270480607090f5d9a0101c060f03017fba60600fbe1b400b469bd16852c29a02008b5db803cacc23f9c030d0019feb880fd313⟩,
  ⟨0x278134892047222a10f885040e1f20ea86d032e1820b885882ae146092844c2120fa06c833417c0a904701ec0d005901e009c014000, 0x3c934760156fb492d89f13626614d1a5961c0065a003467710061e99d1959624cf9127048d9a68bc026da5c23c0c79268ac016db48c611c1ad5750212aafd92df725308f040032d0655880b054ce06⟩,
  ⟨0x277131093445821f10107e03b61ce0d886403021720a8851026212708a037c1a40c305a828812a08403a81ac0b404b01d00ac042000, 0x13caac1e1574b80c173613c8001cb6060063e95b0c431902660b34ab73d893492694407ed6c27e8d1b030768b0000040000021d0a4e24c90d12a27c5252693093036a9a4d24959a4c24c0c01947b6d⟩,
  ⟨0x28713d097448823a11088343f81eb0ee06fc3641a50c705dc2ac149096048820a0ee06882c013208e03b81a00ae04601b806801a000, 0x389c0198e5b0606f181b1405d78268b86692b34984996c0a95d0a585227d32c0f965d37041dcd84f2a0072d8180194a56079b4401952660f94cf739b099782604b65f6a6c334959a4c24c8e054ae852c29⟩,
  ⟨0x25b11f08ac44220e0fd87b83ac1c20d8868832e1860b6856c2a214209284501ee0ed06c833c16409704401ac0b803f01a80a0028000, 0x3424b74648c0db222c3043b0ac39722b475162ccf9127048c9a62c4dda5e23c0c6926740065a3c712167699c0d6d68b03003374b6dc808898470066b969a5100e6d99c0cc2bb5545ceb45⟩,
  ⟨0x2b414f89f84e225412508b44301fb0ed074036619a0c585e82d615c09e84c024211708503541820b204882100ae04d016008801a000, 0x6755d5b00adcd84f508072d81801a7e560c2b1006a199807557dce060069a96987f3c4f23c49b7624d249d4c01a96c278c9b0330ac0001440000087a828bf926a74016cfe29001a9b003b3c0d5320056981aa5ecae27⟩,
  ⟨0x2751320940488227108080c3cc1cb0e0869833217e0ad053427412b09004441ec0de06a030415a08c03e81b00b604c017808802a000, 0x1826b98945846b040196cec2d17138035f4b77d2288c0dbd9042dc4e018f42ca51d0542a4cdb421f224e0934931726434361a1e06a85132c28b7c0226e7a14d86692b349849aa00a95d0a58524d0ab⟩
]

def tableLLLRL : Table Block := .branch 14 tableLLLRLL tableLLLRLR

def tableLLLRRL : Table Block := .leaf #[
  ⟨0x289139099449022d11188203e21e10e506fc3501950c385d02c2146095847021e10007a83681860b904f020c0d404f0200070016000, 0xb3f32dc4e00dc52df11ee2303784f30b037193798d76db2704dce8cb0f513f437b889df513d70ec2fac0d859c498337a49c1208e8c2f00163c0dce6fc2c03ae8381eebac03b1839a4b0236b5f0a3e35e09⟩,
  ⟨0x2a414b89a84c023f11a888040a1fb0f0073c3681900bd85b02c215209b84702240fd079837c16c0a704b01f40c804d01a009002a000, 0xf14800d8c801d9e06b17002b4c0d62b658e8060f035863d0b1c33806390b8da68150adc853e449c1271260e958683906a781b0095303638a280817fc039ec5344b9a100dd20506e903e18ed506ebf8c6e8920eea7⟩,
  ⟨0x2a21468a084ce25012088a84222020f8875037a1b30cb05ec2d41590a604bc24811308303a41be0c205a826010806302100c0042000, 0x2aa1538245387858182c9f14cee0326c005cfda9878cf8d81f2ddc098f030038c4b4192a88c99a4a0d2e29c4c0795e098735b09c03c3e5b0300386cadc6200e1f33a2b450a3af4b9a300cd39e4d06fc9363600b67⟩,
  ⟨0x30517b0ba85ae2ba1558a404d825912308ac4422060f587783a21c60d486142d0105079838419c0bc05182280ea05c020809001e000, 0xd89f91bda9300becca4c23807df0bf7004050ae9a4bd3497ba0183c0deef4c2f69fb83d0a5853899f790253affb0060f1f3f1298f6070042a00803011e38fe4f2d836120d2c49b9f06cc03748165ba41e94e6194eb00e1e0f93b112d06954d6a6⟩,
  ⟨0x25512108e044a2160fc87a03961c10d8067431c1710aa04dc25a11008083d01c40cf05e02c813e08e04081c80ca05802580e803a000, 0x69a46063c516611f600065a3e7100f6299c0c386beea4a611f590065a00c1b3101f5b99c0c02c152b348ee2b2a12bb292f6b2581bae92d599fc52b125c53066714ad9a404ec253d781329⟩,
  ⟨0x28413a898049623010e88283fe1ea0ea870035619c0c885f02ce14c0a104b422810707e83801860b904e02240d806202280a803a000, 0xad4d3e0a9be654b28e6a7f15124ea2704d712ac1b94f4d4ab36c53e449c120d2a99a5568244ea78187955224d467c3340db78032d05e2498c0c00ed92d0ed220cedd3381b680065a09ddc45c4fb28032d⟩,
  ⟨0x28513989a44ac24911f88ac42c2070fe07b43a41b70d6866030a1700b3052427811f07c03ac19c0bf05a029411006102b80e804e000, 0x5c23c0dfe496ccd03419a2ea429f224e0934923ff74341c0353c0d782a9fd24b302a78184392656e270064795c8b230152a93347e0449f224e0934932047f2d0063a00e4f0347200ca7ec928031b83b27⟩,
  ⟨0x1e00e906fc3641a30cb06242f41690ad053c28012f090044420c0fa07683681920ba058027411c08303b81a00a8042019807c014000, 0xca1af944f8a5724b8a6ccc612628d3d927049e49af345a496c4f89a119c53f1c9604ce611e06f824ad89f135231849805455491cc24c00a2bb891e06⟩,
  ⟨0x234115085c41a1f00eb86e834c1910c205dc2c415509d04c023611108103b81b40c605c82a813a08e03f81a80aa04a01a806801a000, 0x8185144c0df08032d018578803f1cce1dd144a4cf466a330bc29fc52087b29e060b454c0cd8aa175161751624d17c52b925c532a98c24cd22a650d53824185532e342a2852c29⟩,
  ⟨0x23310f085040a1fb0f3873c3861b90d086342f21680ac853827a12c08b84341fc0e106a02dc14608f04281c40bc04f02200c4030000, 0xc199e06c893034fda2d02243c2340c1889153e68b4568b1a67c8938246cd2f06d13833c0c7927f10065ae31007f399ceea2cefa2c0d3aa8a8c21f224e090d5121116ed08e687⟩,
  ⟨0x1fb0f8877438a1b90d7865c30616f0af054428413509404642100f9077037c18e0b8056828412808003781680a003c019007801a000, 0x40d46e8b50890f08d03064245517a2d67a2e699fc52b925c534663092f269cc93824e24c92b443627c4d08ce29a1345c133d0999e06a154581a91d1694cfe29⟩,
  ⟨0x27e12f892c48222d10707f43a61c40d286182ce15d09f04a822e10807b83a81aa0cb05e02c813c08903a81ac09803b017006401e000, 0xd3aa5d38a2c0d4d68a0069d51c60d601c28d38a518478780069a00698d4401c3ea9c0c0069752eafd166a43fe49a533f8a460ccf03644981a92d16848cf49a8d03007a4949a533f8a460ccf036449⟩,
  ⟨0x27f135895047a23310f88283f61f00ed86f03421970c1058c28812508883c81be0cc05c8298126074034816008e038015806401e000, 0x5aba2c602c703058f035a8a291f29f224e0907f54c6000f4d043e54f0303daa400c57a68018b751003166a767e8a3be29d375344cb289889121ba26f04580fa874bc13b06b9934de47f149748f031849⟩,
  ⟨0x275134091c47a21c10507b43b21bc0d4066c2f41700a784ec25010706d03241780ad050024c1080730320164094033012006401a000, 0xc27c71003b740c0038df6c2e14801fce6970e8a037e334b9145613e34001dba06001c66b65bda286487001c63b66316318085ab34cfe295c92e29a3318497934e649c1271244cc643627c4d08ce29⟩,
  ⟨0x2ea1648aa052e25e12508d84442150fa071c3661a60c285ec2b413909384741f80f206882c013e08e03f81780a20440198088022000, 0x32bc02ad395c005691834800801001e565a2f7516f7d16fa515c4e0039156cc89c8a001b55e7a2b09f218072dd0300d6425b007b20edc5d23c0c0299016e81b1f804adc0238fb6cd334961a4c24e3c805db2852e291a36559c860d9d278⟩
]

def tableLLLRRR : Table Block := .leaf #[
  ⟨0x271132096847222510807ec3dc1d70e006c033218e0bb858829612a08e83f01e40d105e02b81320780318160086036013806801a000, 0x162981b2c0112d980a8b6e2a7a8153d99a349660186c98cc68b09938262416645f29c0cf63820e525b184e0799456e8180eb282d9002a7d2181b14e05b9376ec11566093ee5678a5624b8a70cce29⟩,
  ⟨0x29113909a049223911108043dc1de0e386c033e1920c085d82ca15a0a584b021a0ee07203141620a2041816408a0380148070014000, 0x4e5e546060292ea979d8c064b1c18f336dc1da26731a69a649998c91a34e99b24d3826e0d7098c238019a74d00335ea200e6ad4e06003352977d28a611c00cd1a58019a002a958268b066bc8fe292e91e06⟩,
  ⟨0x2c815f0a7c51c26d12a08ec45822110407a43901be0d286182ce14809a049c2100f3074835018a0b605382200bc04a02000b003e000, 0x81800d03a5e89c40633b2e7413ce7089e73e449c120338e9a0001e9a020732e78180661d20067bd3400cfba88019f353c7b457138019e54d80858c0d08cab3c8ee12cc238019874b00330801d2b7ed1606c4f457138019cb4d⟩,
  ⟨0x2bf1500a1c4cc25111e08b44302030f6075437c1a70c806142dc15f0a8050424411507b03b019a09804381d80d204a01f80b003e000, 0x1a494bce0178a7d686dcffd9520e0a9c94d8dea9bb054ce64cb9b419606cb1e74f65ce5ccbc12b2632e3536c49a493cbe8bd2d84f45401d360600344e9600000e00000439334941a5c5342403d2f049a68b613d050074d⟩,
  ⟨0x29e1478a084ec26912708bc4201e60e386e034e1920bf05d02c015309a046421e0f4070030415009704301e40b404f01b00a4014000, 0x1624b8a7119c53140542489da3a4da20114900f8dc00d1c03636a498471a358c99aacd51606b3545713801a694de480e2303780030bb2745a5e0069abbeef19334941a5c534a803d2f04836a3ad84f49801d3606⟩,
  ⟨0x2c815c8a78506279132096848c2060fd87b03b41b90d1060c2e41610aa04d425410b07f037c1aa0b604b81e00ca05202380b001a000, 0x389295964341cc353c0d884a981b41d14008022f800f2bd1f1358a683c185ef5d2da064b1c2555ca6c99a4a0d2e29aa601e97826da021a5b09c01d4fa6c0c006a6d2c00dafa881ba9f53cc112fc2270483bed0b0219028fe29⟩,
  ⟨0x22e11088484021f20f387603801b10d3066831a1790b4054c292135095845c1fc0f1068031815a0a304781b80c80430178068016000, 0x28cc6125e4d39927049c494ae4886c4f89a119c53a6e8b826713a33c0da628b0369aa2f002b9fc5203bc06e781b7009d3036b0a286d100b9e06010ba87568ca2f0429f224e09⟩,
  ⟨0x2d315c0aa453028b13c89bc4c025612108784281f90ea86c433e1840b0050422e0fc06c030415409d03f01840ae03a014807001a000, 0x6185709fc932a67f149ec8f03544981b4bd171c2200c1e06c60820f88bbde60e01bd5e20f78835d6e507b75d2e3072dfa368e5bb46167a396acb072cd90a90703658f56b32dc4e006c65362114e630347028caf34cfe295c92e29⟩,
  ⟨0x2e116a0ad455428b13f097c4aa23610b87e03ce1d60e586c032a1760a604e025610c076838c1880af04d01fc0c805702500fc048000, 0xe29b8601e9782711889a5b09c01dbfa6c0c006ded2c00e1ea8883b7f53c534a59a70480f930b00ee20e006dd52c00db93754ad9145713801b634d3836d6a3031c0b674b91f54bd1aa7183283e306307a14b0a7130ab1109c38b00307⟩,
  ⟨0x2ec1668ae454e29d13e09c84a223010a88203c81da0df86d43281800a504e425011908403b41a40b705402240d404b0208088022000, 0x3562a9c068a5d23c0c017b9d6e81b730026dc011b976c02f8a0fe290080fc10781805de84c0db880036cde545eb1e3e67a2dc1f18d2b66988923269f16461601d141f1fe0859847b960069a00760544ee5cda9c0c76b5ed2e4cd25069⟩,
  ⟨0x29e1488a184ea26812f092848022c10f87f83a21bd0d8063c30a1640a9850826611208283e01ca0ca05b827011e06e032010c03e000, 0x2ccd09a44d2e2781b8fd1606e3d45713800ef4db37a37a4006d5c628ac27014de5b740c025bc76cd334961a4c24eef805db2852e290e51809b8c483746022df18613801eebdba06001dd5b6004056a89010ab354⟩,
  ⟨0x272128891c45c21710107843981ab0cb06042ec1610a304e4258121083038818e0b4051825810e07a036817809603c018808001e000, 0x6eeb9cf035cd6ba65c46483529f8340f2dc0eca7e0b037b74f0aa609953825fd9581afbc1e852c29c4df30bc242bf200c1c2bf584d2087cd33f8a5724b8a68cc6124f144e649c123c6979343627⟩,
  ⟨0x34318e0c485ea2eb1650ad850a26812588b841e1f20ef870836e19a0c485e02da15009984481ca0d105c02b811a07001f809801a000, 0x201ce727818029c65303717000db35d5161d98e9ebc24f740072900ae7948035ac9d554efa580352ca6a79354d524a704d4b72cae94d29269c1201ca72b0065593800f255ac007924976d5a8e8ba602e7818933916d6eb58d2781cce3324793d95839ef6c1cfe29⟩,
  ⟨0x31c17e8bc45c42d51558a5c50624811788383ce1cc0da869431c16d0af055026611c08903c41a80c705002580f205c02580a801a000, 0x918e9748c611d8560062f802a5749a2ed5a2cbf202033e20727c6e073e2efdbb9e3c8f63a93f87c909f7898fe98c06931c16f912d9491e0606fe41b67002c78181b38fadc3748d27f1480236489278186a90e532147d27813480471adb0059d64fe29⟩,
  ⟨0x3c01d90e8c7283751b40d2467e3201758b3055a28e12488b03ba17c0b885902b013908e03f41bc0bf05002040c405501b00b001a000, 0xaa1b624d249df533a96c270073329b030019954b00000400000618019614795d9ea9a0365b51f1bb60060169db924e035c727c1ad6a6c0200c04c664ec1662ad55340040100363147c4d666c466079c69a00e27276219be9a0064551e43e6da6cbecd94d00319a8f18f3553584f19b345360697519696c27⟩
]

def tableLLLRR : Table Block := .branch 15 tableLLLRRL tableLLLRRR

def tableLLLR : Table Block := .branch 29 tableLLLRL tableLLLRR

def tableLLL : Table Block := .branch 58 tableLLLL tableLLLR

def tableLLRLLL : Table Block := .leaf #[
  ⟨0x3441978c806162f616b8ae055a28e138896846621f10407f43cc1c70d406502ee15a09e84a821a0fa06d82f8142091039012001a000, 0x7d54fea6fbc54f7eaa67a040a5cf300b4bc1200e78d2c01b064e07732c011b6c995707a2eb70cbc12db4b2e69cd5a48019934998946bbef293e4394c9c01cce539e49801c9a4f96c9a9f324a3df17d4a401cd2533d8d4e97cd1d7fd395f1474a81200402a964f666⟩,
  ⟨0x2bf15a8a9850a279135095c47e22b10b88203d21d80dc86bc33018b0bf057427c12f08803bc1a00c605282440e806702400a403e000, 0x40c7927b74016db48c611c3445cc22457a9a2fa7a29847003aea9a3c710b3af2a7035716cba14b0a7b18022d7e7c03d2cc23801d614d001ec2b8803d6553818007afed7e628b660f92b713801d514d9e6122a3034f908d4b⟩,
  ⟨0x24811d88b043c20b0ff07b43bc1d40e186d03461940c505a42b4139095046c22010507c038c1880a304201bc0bc04f02200cc024000, 0xa149c49921a2544f8a4a4d2612606d5349a492b349849818033baada7927ba002adf6925b13e26c4cc29ee1b2ece0034d001ee0b8801da153edfb2c499f224e091b34f70804db4b847⟩,
  ⟨0x2fb14d0a284e226612688f844e2080fb87983ae1b80d586783121740a9851824e11d07f03c41a40b1051024c0e4065029012006a000, 0x77aa8200008926c8ca5b851edb1a8d11d78250a85d7ea980d163efd09d4dc334959a4c24ef90154ba14b0a49e5560f0abf09049b9b09f79003a6c0c0077852d8620c77954c10bc0ae7b126924f7f00fdad84fd1a36060ed160000060000043⟩,
  ⟨0x2d015f8a8052c287139097c4a423a112885040a1fa0f487603861b90d5062c2fc15f0a504d425611607c836815209204081a009e000, 0x1838803e4f53818d25c6ad943243b0ac2e822a4cecb1a67c8938246cd2f06d13833c0c792789801a6b8c400f15a9c65d96496cb03461d9401eda4eecf85d37adcbf6adda4e071b269dcd4cc4e961a5748f04080449ecb956e327⟩,
  ⟨0x2c115b8a60506264127890046221010187b83c81cf0cd06242f01690a504f426011d08503a41b80bd059825010606402180b803e000, 0x103001e874d07258801e8b53802b2ec49a4931f005b6b613d61ab606069558000028000010f0cd256693093cd00552e852c294d5161a22fd08022e6c27e5a00e9b03001e574b1e38801e5b53001f3bb9c9fd94c23801e4b4d⟩,
  ⟨0x27111e08a44281fd0f3074438c1b30cc060c2dc15f0a9050c27012508904201e20e406683041640a504501d40c005301a007c02a000, 0x120000043f591312cab82599700232c3fd578243245f8084aa914b2c19594e24c19bd24e094d51710a1e06250996c2709019748c611d8560f812aa08acb04765713801e914d1a758c0c2caab⟩,
  ⟨0x26a125890445821f10808103ea1d60d6065c3041750ab050426e12208a84081e80e106302e015009904101cc0c804301b007c02a000, 0x14f88a9c0d38eab613ca4ba46308e007b3d2fb30010054a9feb2c9a595c4e007bc53767163036ad2ad84f7c22f08695d0e0856a9e08692c63c8e222b37624d249981042b5b09e00366c0c0fcab⟩,
  ⟨0x2a214189c84c225211988984322040f787383821a20cc05e42d814d09604342000e106102e013208803d81a80be04a01f80c0022000, 0x3c57a4a6e19a4acd26127d000aa5d0a58524c4ab06155fdabc2dcd84fe6401d3606003e5e96c31035e66a6efdf5d73f2603a9ae27003e469a033bd54606067de2963469c335c9a7049b72ae131847003e1a9a3471⟩,
  ⟨0x29f14309ec4c4243115084c3f81ec0ea86f834e1900b9058c29c13f09a047c20c0eb070833015a09404081c80ba04801d80b403e000, 0x5351ba704d2d13ac00fc1a6ced8bc7d60648190c994c6931d931a4327d5e65eebacbea480b1ff5311ba9f224e0907954d11bbb410f253c0c0eaa9f5c0069b3864f10f513729ad7152b46a7613d10d543001f1347⟩,
  ⟨0x2aa1488a004de26012088d044e20e0fa875038e1a80cf05fc2e4153099048c22e10807b83b41a80bb05102240d005701b00a8022000, 0x30f19d386692b349849fc002a9742961484e73ac0735d7fe017f73613fd90074d81800fd7a5b0c4637d9a985c7f4dccc24e235649f133c0d5d7eeb01bf73d7debac0af9cf6a037ae7b6731100c2b9f1180691d34ee6⟩,
  ⟨0x27212f88f845621e10788043dc1e10e8070436e1a40ca86102ea16b0a604ec23810d08003d41cc0c7054021c0fa05c02380c8032000, 0x3743c0180bdb65343d0a4e24c50d02a27c52526930930344a8934925e693093037231694d1b348b2e434f6c4f06684d892400feda68abe375103a10173c0c02053eea8a8b2c545968cbdce7f44e7⟩,
  ⟨0x22e10f881c3f01ed0f0875037e1ae0cc863c2f41700ad851827211e08a03fc1ea0e006582e81560a004581b00b405001d80b0016000, 0xe24c92b443627c4d08ce298dcb2e099e84ccf0346ed96068f4b2dc2a9fc520d81a9e06a8254c0d1a16598d53e419f224e09065548cbe754d3d91e0616154c0a61fb71c73c26⟩,
  ⟨0x2050fd87983961c10d6065c31417d0b9057c28e13409104582080f8076036819e0c00558258102070031815008e03a0158068016000, 0x10346e595390153c0c8c4a73e153d0a585389b4b44ab8143a76897b91f118aa47c46c463511e13362a8c7b2c64d96442cb9a67f14ae49714d198c24bc9a7324e09⟩
]

def tableLLRLLR : Table Block := .leaf #[
  ⟨0x27a138093c45c20d0f9075c36c1a70cb06242e816a0ad854427810f08103e01ae0c405b827c12a0820368160092038015806401e000, 0x206001863b5800c65dc5492196e6019341e4f4f8680547b59ff24d299fc523066781b224c0d1d7650018ed002b3c19a060068eab4e8a87f14870343c0dc0a2638acad5aa7fc932a67f149ec8f035449⟩,
  ⟨0x31917c0b8c5b22c41518a104ae24211188643f01e70eb072c35818b0af04fc240113079034c1920aa04c82200f605a02780b8042000, 0x32316b916b2c0d22765001918b3801f5d4b7ad001916b548ed9768801a3c0cf5321d6bc734b59a704d38e574b53990db3a9c486299d9c00d30a3d34a6b4b713800c385b791d32a8c0dc8a9852e4cd25069714c34803daf04c682955ad84e0070cb6d⟩,
  ⟨0x3041738b2855a29a13e898049e23c10e88403cc1dc0de86cc32015708904001da0da06382d012a074034816008e038015806401e000, 0x94a4f94c9d28ca401ab2535349a49b265361593298133cad2600b3f68fe2900200e7dd1e060053e69303095e1098e4ba4f592d538b399c108000a59c9659f1106c4d132ba26224486a89f7a0429601f2436bc13b06b9934de47f149748f031849⟩,
  ⟨0x32b1840b605862b61498a244cc25512208d44242050fc076c3941ad0ce063c2d816209f84b42180eb06b0304134090036813003e000, 0x61658c858c2c80038a945b2b09e15c015c740c0138566334cd2586930930a8005e32852e2900678964d9c8019da591278613800e1418e81800309ec6150a44df04574001821ba4945964b6ca0980331c9e0684b09a71d27e0156793e489009b3c8593147⟩,
  ⟨0x2fe1748b7057228913a095c48c22310807b43b01b50d406142f61580a184e024611608383e81da0e005e826811204c01b808801a000, 0x2592cae27000c343190cf8680007152bb65a6009938c19e196031c707a8701843271c0d2a786380ab1cc27015c3171d0300a61878ca51566093e75678a5624b8a70cce2986b802b130d600162460d2001001000e1a98894cb2ca6d9654acae27⟩,
  ⟨0x22010587d83c61d40e486d832617b0b8857827612608984081ea0e606c833017a0aa04d82400fe06e02f814808e036014807c014000, 0x953b2cc25951b43e449c121ca26232005c6847643c0c1aa2622a001c6cbc5965043e699fc52b925c53466309278a27324e091e34bc9a1b13d99a13489a5c4f034b259606⟩,
  ⟨0x2b114e09ec4dc24d11c088c42c1f50eb073035a1a00c085d42d015709684602120e806c82e015c0a104601dc0d004701c005c01a000, 0x12b565001923b6b8c4006496e72b16595bb2b89c006476da037b4d460601dd9e96c27009d969708ce271a35809ec2006952a965308e0032236d34a2007227738198572996594db29847001909b69a5100390bb9c0cc2b⟩,
  ⟨0x29414509d44cc25712408cc4302030fc87903aa1b40cf85f82e815f0a504d424411408083d81c20d3059027c0fc05b02880c0042000, 0x81b81956791dc25984707b5583d06aa98ab2c0d30f65308e0032736d0745881649ddce06ab155cefaa5e99521ba27286c5913825a8957043000c965b43f48805c975cc00b144c6c0d24e0036d38a200325373⟩,
  ⟨0x26712c892c47e23011008444041df0e506dc3521960c185b02aa14a09984902240fd07403541940b905202600ee06001f80c8022000, 0x690d0435237ca6aec6d94d929a2f005ac6ceeaa43744e50d8b226b744cc32cb961197824149659e4b3912a652cb343651c517827c4d732f65a4600194ab681a0d100b94cb9b89c00651adbd071⟩,
  ⟨0x32518c0bdc5da2cc15f8a784fe24a11688384081e30e206dc32c17f0ba857828a13808b84081d20da06782d8126072034013c020000, 0xc27003983b6c0c0033036b6188084c1dcfbe801a98000010000010c01bfa4ff217fd3606001979b6841f8b51713800cbb5b770668c0dbc232c0639cec2b016d8c754dfd944625cf91270480c3ba630a067c680864239e060a83748210620bf8c390a7d6c6⟩,
  ⟨0x2b41550a244f825d11988a44282050f2071434819a0bd85982b2138090845c2000eb069830c16a0a404982100c605602480d8046000, 0x81aa74016d2e270031c6971a238002a540d3b365308e0033396d0031aea200733d7381800c68a5ce8d95c4f32a0036dd40da3037302cb9cfb286e243d663610d86692b34984998a00ab5d0a58529c22c3745c5c0f0999⟩,
  ⟨0x29013e89a84b624e11f88d04362020fc077c3a41b90d6868031a16c0ab852825211008303b41980b9053026c11006902d012c054000, 0xab912da224e24c19bd24e09099e75cd00b9e069b9c75b09c1269d708ce270fd163d2c02ea9edb2b89c0066cadb2034f181a3c61d735c1256dab112ba22704aa68bafa02e8f6926124cf08045a400d7900f47⟩,
  ⟨0x26512708dc44820d0fe87b03be1ce0e186a833e1920b8859c29c141094041c1f40e906d033c17c0a504982240f407002780d802a000, 0x1481b241516487a871d41972d8c3069a334b9a704845e3ae13309e7602b6db035be53adc4e0390eb42c70e75699a30cf9127048c9a704f1da5f23c0ca926060019c8b680ddbc40d672ae740565⟩,
  ⟨0x3071798b8c5b02cb1550a2c50226212588b04041e90e806dc33c1850ba05a42a012f08b03d41b80cd06102a411006702e811001e000, 0x5c8a35163426713800d005b432cc7a8c0c19a62d2c0de6385b9874bbf835e40d1d2f71cf96fee7ebe375a46db9c079dd3bee684c03c8e79f10e1b6bbecb9c1ddb61cee9b6e7c8938240761d306e1bf6d016fd673c0cdda8e9bd030c00c6da3eea6⟩,
  ⟨0x4c325c92588ea4402000fa47b23991bd0d4064c30716e8af051e24f11c08643c81a40ac84e824c0db06202d014808503a019c0ac000, 0x40c0ff91f62f0feffdcf810610fa1fd47c4580c7c8c11fb4703bd93a18d5520e8be1ec3ea8f07effd1e0f5fe813478350720bd1e10418a3c1f82f05a8f6220f167072b10077b3df816c3b809077a3fde8cb82904a8e3aef88b31df471dd520750b2be1471da0aea38e91637be8e006eb526e7d1a51d441cc02857009a381e6c9d4c6dcc6a754f6923469c335c9a64d80114c37801003a7947⟩
]

def tableLLRLL : Table Block := .branch 14 tableLLRLLL tableLLRLLR

def tableLLRLRL : Table Block := .leaf #[
  ⟨0x30617c8b985962b814e8a404da26312008703f61da0e286cc3521860be056426c11d08803bc1ca0cc061027c11407d02d00a8032000, 0x1c521ca3013978906e8c0465630c27001c8b31d0300064558c0080b21120109aeba000cd6dd2a32ca5d23c0c00b911e3a0691080271c0089106301785cfe290103df73c0c05bae981a432001c653ed95c4e001921e2c1b724206be2b59cdf802e7⟩,
  ⟨0x27e13789904a6242119889843620a0fe87cc3bc1d40df86c831e15f0a504d424c11707a038417c0b104702100c205001f80c001a000, 0x3324e091e34bc9a1b13d99a13489a5c4f0355859606aafb2b89c003244c6490e488001c5554d961214f0298e23c8f80318e0c90f23c009e3984e01491d63a0600948e319a6692c34984991a002f19429⟩,
  ⟨0x29214189a048823a10f88283e61dc0e886d833e18a0ba85a82aa13a08b03ec1dc0e106b02ec12e07c034816009603c0178088026000, 0xd24d7ec70d00d68070781ab20184d5a596dd664d5b4c9c1254abc2e7c864df1aa62b9538261f95910c7c1ef10fc741c318c83d0a585389b10158484f0e018384f0f099410f9a67f14ae49714d198c249e289⟩,
  ⟨0x25f129091844e2080ef07483661a10c905f42d015e0a604fc26a12008b04041e40e506983241740ae04c81ec0dc04a01a8068016000, 0x30a691801ef3a4ef2de147de00040151e11b77803a4aa48e6126b36cae6247818a847b3340d5996581ab96cb711fc525c23c0d512611aafeca0728263d998020a9cc2aaf2cb5f0441f224e09⟩,
  ⟨0x2a714609c44ac23b10d07e43bc1b50d586282ea1660ad851825611008303cc1d20c8056828012208403b019c0a804101b009401a000, 0x4ab4b11d1c3a16078341c031183d60087db730380dcf9f75c2f2830078dcf0355d8ccdb48954f9127048312a72dab86821c0a78185e44c0d5620036dc7e9623e295c92e298218c24c5e8980d1382470d3a8cd11429⟩,
  ⟨0x2ca1578a9051226e12e893048222610587c03981b70ce06482ee15e0a284e022e10d07a037c1880b5055023c0e805002300ac042000, 0x2e77184e09b977a178e5dc1e94d29269c1203d042c03f583807c50b00f87e90ab27b2e38030781b33dd85d041b9e7905cfe29019c3f73c0d367ae9e3b538223507c893824031784eae670d0080e2b07818051384c0c00358b6d⟩,
  ⟨0x3371960c3c5d02cb1570a3c50027112808984381fb0f7073c3441980c185d82aa13609604341e40d105b026c10006502400b4024000, 0x626878ab949530e803272a61d94c390c49fde80ba3da49849367601169003ee403d1e06b91005b4b89c00fbaa5cd33dc8015aa06b33b2b89c006bcada4afda546062bdeca9601adc1c566bb6dbc08ac1f0d8d83f940709017921200c0727bbf921601b9426e906⟩,
  ⟨0x2ff1730b545882a7140097c48c22510607a43b41d00d6868031e1850b1052425010d079038c1b20bc04c02380da05001b806801a000, 0x7c693a6e0d2f46931e3b9398d1d16727c4c6c173e56139f270701ce037ae70634c2b19891e060704c1f18c27c67340c0dc981e3ba3b5cfc9cfd8e700f060ee9e242e923c0cf4c132bbf6b40307818006c2adaf240b31b0ac7395d1149e852c29⟩,
  ⟨0x3291830b945882b31510a4c4e426512c08dc42c1f30f3071437619a0c685b029212808383e81b20bc059025410407002a80e803a000, 0x4e5997e4c006522cf2932ab6dc334959a4c24d9f0055ae852c290098d6b5800c6adae69c8bcc9b09ecdc00edb03000d9adad86319d66f7345acd1f2600312367892b30b6b89c006cbadb043e13181a077ba561e227d506f486e121af4426027a257009fd2b⟩,
  ⟨0x2cd1600a9c51c26b12f08f4466212102879038a1b40d286202e21640a184982380ff07703741a00af052021c0f405902780b8042000, 0xc29098a7580c4bae6ec268ccb09c00ed7edb03000daedad8621056bf734c31d6a706695c9200ce327f9f596e27001b54b6c163d4c6068507895c99a4a0d2e29b4d007b5e0901e5295b09c00ed26db03000da3dad86249969373⟩,
  ⟨0x2cf1570a344d8257124089c42c1f50f5877038e1b60d386603161790b2053c28a13008a836818a0a804581b80be04e01e80b801a000, 0xdc25ac0075dae200370d73d74b29847001b7fb68d1c400ee06e7031e4be9ab28c19dc259a4771595095d2d65e99b2c0dd25657347a0e8b420008c544c9e3eacd09883298ac4194881154a7c53619a4acd26126d9802ad7429⟩,
  ⟨0x31717f0b745a02af1470a104c624211988483e21e40e186b83321780aa84d023c0fd07503241680a304902140c805901c00ac014000, 0xd839c2b694ed6e27001ba1b68ed5285c60620da4eb5800dcedb4d28d5e5cfdcc006e6adae31001b9cb9eb1d97592cb72a0036d000c03f2200372f7381ee14006e46da1b244006e4ee7d59659334941a5c5371400f6bc13af600f6b613801dc35b606⟩,
  ⟨0x2d015d8ab452a28913f89a84aa240117888042a2040f387543961bc0cd85f82e815f09f04741f80ed06602b4118082031813805a000, 0xc75b2dd0d10890f08d030f11ab16acb8e9658a33e449c1230690473b969748f031849bb4001b68139b4c606c4eb2dd8000db400710ee266376573308e0037596d00326ea200775d7381800c98a5e22d970f82c6ce15787a16167⟩,
  ⟨0x2e116a0ae455e29a14809ec4c024f11f08bc4402030f107143601a60c285b02a614809583481820b305102340f006d02c0124054000, 0x1e290640d4f034412a606c7ab2c10bca79634ac1a62249c49d735b95800c4b59f59d6a57302a7818d5f1a2d7c9b8e9dbe374e0936a3f9581f544dc00805380060749f71cdd436fb9a31552244a9c121c2ab388e0065b52c00cb50114a⟩,
  ⟨0x30f17c0b5c56c289136091445020b0f206f432c1790b605742a014309a045c2100fd070032014209603c81a00a604901a00a802a000, 0x4602c9050c03b69db46059ced62fcebacfe7f5927ec7ceeae4fe7f8f27f2fdc93f95edf8727f33c7f124fe5799e1c9fc40324fe295c92e29933184901bc494d649c1200f832981d288ee40100a4f89bbd00a538267a1333c0d90f6581b27acb30aa7⟩
]

def tableLLRLRR : Table Block := .leaf #[
  ⟨0x2c615e0a9c530277134091c47a23010d881836a1580a284e025211b08403ec1d40db06882e815609404281ec0bc047015006c016000, 0x206d03b29847001c21b69a51003c23b9c0cc2bccfb2e7e59415cbccae4138aee362ce5e40ac02c09a5705751af6794d0f429389314340a89f14949a4c24c0d442b24d24829ec930930371a31cb40cb648c3c5cbdb13c863426⟩,
  ⟨0x2c11570a6c4f026b125090043e2120f887483661920c285902a214709a04842280fc073835818e0bc05582300f40700308100042000, 0x9a22c3345d15c04f99613801e205b606001c3eb5b0c4033102e6082ab54c00c6ba3e1ca3cdb5c4e00386f6db9923036088b0c10ec2b0d9c8ace4b2c599f224e091934d1b0214d2f11e06349200384f6d00345aa201585373⟩,
  ⟨0x29213c89bc4ac24111608844141fd0f7077c38019f0c705b42b814b09f04742240fd078033c18a0a404781b00b604a01d806801a000, 0x2e921e3035da33aedbd53758a9c12b6132d84f1a9b453001a5d4752fc59b68d19f15c02edb26692834b8a714c01ed78246d956c27003c4fb6c0c00389b6b9c15894ae86d93c334959a4c24e238055ae852c29⟩,
  ⟨0x27d134095446821b10187d83c61d50e106bc33c1910c005bc2ac13d092042c2000e706e831016e0a804e02340ec05802180b8042000, 0x1acf650cd0e0039056dd71978c7c143d9983b44cd0d2d22731448d1a70cd72698a34e786baf3ac1d75f60ebaf0a75e0908ad75c0d900eeb613ca4ba46308e06732e68104cad1db2e8cd95c4e0038cb6d⟩,
  ⟨0x33f18e0c3c5dc2e41618ad852a27612a88d842a2060f2875836a1ab0cb05dc2d414009584301fa0f206982d01140800308100042000, 0x523ca9399613801e515b606001ca0b5b0c403b28ae75099054f2703c6da00681d1d41326ada611c007262da79440bb26ae7035822ac00c65a3b0ac0080d8c74ad46b28088b747c89382400c5ea4d7b00f4d00200e2b51e0600316a9200390f6d0035daa200391373⟩,
  ⟨0x26a12d893847a23211288103de1e50e706bc33417b0a8850825a11e08483f81ce0cc05e82bc14209204081c00c20400198098026000, 0xf24c99a18d3099c4e00397f6da3a58c0d51c32c00c87a3d3b2ac0148ba382f00322a8f8298185531a9a281538250ca65c142b076c4f343590d5a9b0cd2566930939520156ba14b0a5364586a8b⟩,
  ⟨0x32017f8b785862a813189284622180ff87b83aa1c40d486602fa1620a804d423410507a038c1ac0b5055024c10c06502d80e8046000, 0xce4001b68a4750dc6893f84cfa87093b937f11438199eb3e101ba40b05d20372e7abc175dd3980695d34ee6960060f40e63d4aa0e01964261d062fc5a0f2612c1fdfd5326692834b8a733401ed782434765b09f32400edb03000e63dae0816895aa96193⟩,
  ⟨0x2ed1718b0856a29413f89a84aa24211088503e61d20e4069c3241810b8058c28413708b04241d00de05e82700f605a02680b002c000, 0x103000e81db5c62003a0b73ef8b2f81d97bd6ca1821f3f0046dae27cfa001b6e0f001dc606c1f001b5f735964cd25069714e79003daf04f10dbe5ad84e0079dd6d8180073b2d6003c3971b76ceeb9800e74db5c620039d7738c7e1671b85⟩,
  ⟨0x23611088303fe1de0e486fc35819b0c705f42e41610ab051c24c11307903a01aa0c0059828011007b035016c0a003f017006401e000, 0x1994eac6ab713e90800db4c81630337c8b1a34e99b24d3826e0d7098c23e8b000db43648801e8c5ce060cd17e0f657138608b73e08af334719f224e091b34cc1b44e4cf032e49⟩,
  ⟨0x2a014489f04ce24c11f88b843e21410187b83b21cf0e006d832a1800af852826a11408503a41900b905502240f806702e8120026000, 0x9ccd96e27071559d81eaae334699f224e091a34d442b44e0cf032c498180074dada0c8b1001d38b9f92d97c8ecb8aba636d8180074bedb78177571d8934927cbc0b2d6c27a8356c0c0d0ab00008c0000061d2e8b⟩,
  ⟨0x25d12708dc4322040fd07943aa1c00d286382fe1730b2055429613408f84282000df06602ec15c09d04901ec0e006102000ac014000, 0x611c0ed6581d80d95f796581bd3acb918d3baa78e6714f94d32cc24e235649c48f035f44cb06253a502ae06d51001b6aba911a34e19ae4d382455565c26308fa900036d076588286a55ce06⟩,
  ⟨0x2ad14609fc4bc25411988483e21dc0e586e835e18e0bd858c2a013d098043c1dc0e406182c014209604281b80b204f01f00d0026000, 0x1fc200f6b613ec1001db606001d80b5800fee5c400760ae7fb565c734b59a70480be50dae5843ba374386e879d116e27d73001b6e4b808dc606c9800fb5a2087c89382474d3d453344eccf03149a606d66001b6fc891⟩,
  ⟨0x2a214a8a004ca25b12308e44302030fc87903b41b90d4061c2ec1650ac04dc25810b07f03741a60b204881c00b604a01c80b0016000, 0x1c4e0ccab6250955037ff595c4e003b3d6d1a058c0dd3cab818007666da3c71036d9bb9c99a4a0d2e29d93007b5e09fed007b5b09f63c00edb03000ec6dac007fa2e2003b1f73fe6b2c99a4a0d2e29d86007b5e09⟩,
  ⟨0x25312108cc44821510207bc3b21cf0dc86a831217a0ac853c28412c08b03fc1d40c905b028c12808703c01b40ac04301c8088026000, 0x7b1acf23b84b308e386b1b3354beb0b034bdb0a611c0076eada694400f6f2e70330ae5dd85977e1669a63838a9c0cb6c6db56a2594449c498337a49c12224b2e0143c0d18eb2ce238f68b⟩,
  ⟨0x2ad14b8a204ea26612b88d044e21410507dc3841b10d006442e01630ab050c26010d080037c1aa0b405182080be04901e006c014000, 0x1160c29e474651bb126924cc7002d8b613d068d81832458000800000010f0cd256693093bac0156ba14b0a535458688baf4802326c27dcf003b6c0c003b9b6b1e38800ee7dcc0035e2c9cc1b0ae27001dc7b6f41c606⟩
]

def tableLLRLR : Table Block := .branch 15 tableLLRLRL tableLLRLRR

def tableLLRL : Table Block := .branch 29 tableLLRLL tableLLRLR

def tableLLRRLL : Table Block := .leaf #[
  ⟨0x29c14789f84da24a11e88704241f10f1070433c1880b9059428813309484602120fa07583581760a504d82140ec055020007c02a000, 0x614cd9ac68d761400464d84fbfe0076d8180077f6d661440077fee6001b06e4e88f85a22e15c4e003bed6de838c0dec6b3c8ee12cc2383d2ac1e43554c8b0b0345f70a611c0077a6da0e6b1003debb9c0c0e0ab⟩,
  ⟨0x2a514a0a0c4e825312308e44502170fa079c38c1bc0cd86382da15709a049422410307a03441880b105382500be04e01e80b801a000, 0x186692b349849e2100ab5d0a5853526b1835d8c404993613801f0d5b606001e18b5b8c400786ae7461c28072c53933c8e8ca37624d249a2e805b16c27a0d1b030648b0002d90000021e19a4acd2612781802ad7429⟩,
  ⟨0x26112588d444821710307ec3c81d90e506a43281730b4854828a13008a84201ee0e806e83301720a404d022c10206002680b002c000, 0x1128c2c49b0a3469c335c9a7048aa2cb84c611c0078eeda0cab104ce3db9c0d29132dc4e0c0abf1f3d55c668d33e449c1234694651a27067819624c0dc520036d0cd22003c57739b2e166b785⟩,
  ⟨0x2d21578a8850227712b09244502120f787883821aa0d006242e815d0a604ec25810b07f03c41c00cf056027c0fc0740298110046000, 0x2cf2021c9b09c00f98adb03000f305adc62003cc57389fe14033671c9b89c00796ada830b4606d57d960e2a743759786692b349849e5100ab5d0a5853366b1a35d97c01193613801f255b606001e48b59851001e4ab98006cb193⟩,
  ⟨0x29e1478a004ba25012088dc4501f30f4872036a19f0c805ec2d815d09d04b423010e07c831015e08e03e81b00ba03c0178088022000, 0x3624d2498b6002716c27ec9b031a4b0000190000021c0c003cf76de0523163c29e4723356ec49a49315801862d84f706ad8181b156000036000004306553f368135b70cd256693093cd20156ba14b0a6a4d6306b⟩,
  ⟨0x31416a8b285702a7143098c48423810b87f83d01d90e5069c3341830bc858825a11807b83901a20ba052825810207202d80e8042000, 0x9f0040408ad00e0f89a0906ab73750000db40031edc88027515ce06001e9cb6da00bc643185d89349267ac071c5b09f78366c0c076b2c0003d400000860e0a7e90031b6860878d51a4a931c1d153b29b5cd537a980ef63f438385b40621ce113d0b6d⟩,
  ⟨0x23311488603ee1eb0eb06f434a19b0c185b42ae14409b84a023410907e03ac1b80d206082c814209204401bc0c0047019009c02c000, 0x40c3069ec2027b6e2303629cb665db92050f035c224548db0b24dc2cb887a149c49821bd4d3e292934984981ad4d26924a4d261260611c7769a49c50f778d919e130d1a643f85⟩,
  ⟨0x2f31678ae452c27312e08b042c2010fb875033c18d0be05c42b014709704341ee0ea06482c014c08d03a819c0ac04701e00ac024000, 0x50c020283c8d70c14291a624003233c3818ccb02280064638a91c617d054f0301064538b0edd06e3807c1f14d29669c1207e4eb1a3380d73ac06b465d5263c2b89c007b42dbd152f181ba69dd710bd0f1434499f224e091c34f1163b4b847⟩,
  ⟨0x28813e898849a23811188383ee1d40e486d834a1960c485dc2da15e09d849423610507d037c17c0a304b021c0f406e0308118046000, 0xc131518c2e789530cca9802548322a721f65807a4978bc13c422e64d3791fc525d23c0c6124003242c5c9030b0348f70b098034783f770ab5b6980a83f8a5624b8a7919c5204a3c24007144c4c50c28b89⟩,
  ⟨0x29314209b04ba25212308e44462120fe87cc3ba1d30de869833217b0b885682a013a08683ec1c00c505982600fa06202380c0036000, 0x1c499256886c4f89a119c53296c2e099e84ccf034a5f0b034abb0b6c2b1fc5206c8363c0d5c132606945614dc01d514e0f48834a63f0900c66131b8346a31098bc6613258dc2e483585819ac7cf4558ce2f0b⟩,
  ⟨0x2040f4875038c1b70d3066430e17d0b7059029c136096046420e0fb07783741a40c3056825c102070031815008e03a0158068016000, 0x526054e9caa98a1bf24ca99fc527b23c0d512606946e155b0a1e064650e5523e236231a88f099b154a070b283c2cb2b0b9a67f14ae49714d198c24bc9a7324e09⟩,
  ⟨0x27612d890044a2130fc07b43a41af0d0063c30416d0b1855029413408203dc1da0ca05c82b012e08d03d019009e03a016808002a000, 0x35da484e8f5b0900e76139f8367b3909c139fd4c2c0152afc3fe49a533f8a460ccf03644981a54985000ca980058783340c006951e2794cfe291c333c0db0a265378566c53b35a9e852c29c4d22aa9⟩,
  ⟨0x3681a38ce065831d1800bd85aa2b414989c848a2240fe87803861920be85a829e12e08883d81ce0dc060829810407802e80f0042000, 0x3eef88b99849c46ac93288032781bacf82ad6003c1767e07e08b5f0474ad9f81fa5380ace491d3f67014049264f404292984e7f948032300507c9f812cd2149803e4838f2fb8db60a33a4e08d941f224e0900ec21345dbc340203d6c1e0600eb212003ecf6d00d0222363ed373⟩,
  ⟨0x3391928c445e02d11580a744f826d12f08ec45c21110387a836a1a40c986182ca15a09b84a82120ff06f02ec134084031810003e000, 0x103e8d04a8df440036d57503ea2003f416d0d922855f4573d8934926c862b6c5b09c03ad25b03003594ac000dac000008726692834b8a7e4801ed7826568007c5b09c00fe3adb03000fc65ac0032afc8800fc75ce55b85f88001b68fe24eb91001f86b680180951⟩
]

def tableLLRRLR : Table Block := .leaf #[
  ⟨0x34e1a10ccc64430d17b8b845a82b314a0a284d6255124089c4101fe0ef870035818d0c1058c13408d04001c40c404e01d80a0028000, 0x2918c238c9ae048d5062c2c1830ae27fbd001b6c0e0075181b9e801a5c3070ae27001fb7b6c398875181a1d441a580186f49875468730da938261d435a58008010018026401f1002803003b27e3fb43804004805005d9eccd8668d4d229a1551abf93587268134681746⟩,
  ⟨0x28f137098448022a10a07f83d61dc0e886f83521910c385d02d414909b04541ec0e506c031c17809d04902140c804501d807001e000, 0xff25b5c62003fcd73842e1610d858416151f43e449c121e225a855a11e90f030b08981bf54006da1da4404ff5ee7d5408d2c64d3666a834e09019d4297099c4ff940036d836026a30374a00f4b613ca4b⟩,
  ⟨0x23210787e83e01d90e206c433c1860ba85a02ae14c09b84b023e0fe074837c1940bd055024810a07403281680920380118064014000, 0x2008001c6e112c6068281960c2a787917a821ed97a1c64d3666a834e0927855c26713ffa800db615163036492adc4e1822dcf822bccd1c67c8938246cd3306d13933c0cb92606⟩,
  ⟨0x2b91578a6451e26c12e891c47a21a10387903861a00c085b42b213a08b84201f20d606482e81600a3037016008a036014806001a000, 0x103432b0b0340840038da4a30c7c2c0d01d000e34314880ee03f93001ec6b3c065d8f8d0031e6931d28d1d68c0062051c8cb014c6ec49a4930eb00362d84f19360661580000a0000030e1cb85c691279264cd0c6984ce27⟩,
  ⟨0x24f11d087c4222020f987803961b60d6065430c1790b5057c29013509584502060f006a831016a0aa04c82100e406802c80d8046000, 0x50a9da06053ed0d9925524876873b355c00a9e06b6c19671260cde9270486accba050f035328cb1f338648b46535551667c89382464d3018ad2f11e063492001813e343b48801a05393⟩,
  ⟨0x3961c38df06cc3431968c285d62bb1528a184f82590ce06402ee1630a204cc2200ff06e033417c09b04701fc0ea0680198074018000, 0x1b13e26a70e180034e0c4ce170a001a6f61c00ccca5932c0034dcc5538f0b31800d1e06263d35316168156158160df2e6200215c165a5416616215a91816b67a4601a174cdfa34de141499c7300060a58d1a3893760a993d8934926702006c5b09dc26c0cc2b0002bc0000061cdef0a3469e46⟩,
  ⟨0x27e136896c4a224010e88383d61df0e8070c36819e0c405c82ca142094847c2000ed07002fc15209804581f00de06202a8118046000, 0x2f0da5e23c0c3469000c2031a714400d082c9e231a47715ce2aa96616a4f85a92e15c4f075000e375819e3034fe0094b0c50ec2b01e60f754e470b5667f14ac49714c199c53792400938bc4ce2800b89⟩,
  ⟨0x24e12208b843e2100fd87a03bc1c90db06943281890bb058429213b09404542100e5069032016a0ab04401d40a403c0158070022000, 0x206ba7614c24cca694354cc287819495567821f60d2f869c13e7a2c2814f40fd0f54306e87ce916e2784880071a6ba46062d5170342300038d0cd2200184764ea6d858b33e449c123c69⟩,
  ⟨0x2ef1728b08556294138890445420f0fa07a83961bc0d686282fa16a0b0053c23410907c03a41bc0cd055026011c07f02e00e402c000, 0x40c067a9f62c0e063e4cacb03054ff0e05fa9f017b0e06db1c9d3485c70030781aa3131a5ec49a49376400962d84f01a36061e3580222e0000030fb8d31867c89382468d3758003e34be47818e2480061518d000dd4f2200185564eea585⟩,
  ⟨0x2a31468a0c4c0253118084440e1e60e806f435c1a30c906042d81620a8851c248115079038c1ac0c4057026011c0780348118046000, 0x4abf0b034388a8d8d713c3800038da8800ea3037ff000dae61f854490f9127048f9a72cda27a67818acd30300061a58d38a200486a64cd23b8aca84aaabe16ab18581aaa785308e001863e34003541c881a619393⟩,
  ⟨0x2a114b89d04a222e10c88103e21dc0e706fc3641a30cc05d42c415809a84a02120df06903041640a704b01dc0ca05b026010803e000, 0x10300062078b000d09722093882e4e30d52144a90e90e642abe218e24c19bd24e0900340631740a1e0680a957716e2700356e96056ad00da5619a2ccf9127048c1a6aa00fa69788f03284981a1cc001c6d4d01351⟩,
  ⟨0x2e31600acc520286131895046220e0fc07883b01b50d406142de1600a884b824211208403ec18c0b004f823810205e02980c0046000, 0x64f001193613c4880078d818003120c59851000c48b26001c9ae4f15985c556160688c80071ac31005446f278a4c2ec49a49384d00362d84f1936066158010bf8000010f08f859334941a5c53109003e2f04d0a81338b613c4140078d⟩,
  ⟨0x2b01508a484de262126890c45c1f90f4075c3901a50cc062c2ec1630a004cc220106071835816609003f81b80be03c0178088022000, 0xd89349271a4026c5b09e40d5b030312ac010000000008786692b34984989c802b174296149302ac3f45e53803393613800e2658d818003130c5b0c4031132c9804b28f93c334959a4c24c4a40158ba14b0a66cd6346b⟩,
  ⟨0x3631a00c4060c2e31610a7c51226612288884181eb0e5069c32c1850bb054c28c13908c03dc1a80c705202680ee06a023809002a000, 0x3dd60d1877b8bdd20cf87818003161c6800fb9dc4003163c9cc9b0a0018aee34007efee20018afe4e67385040e6cb3800f82d9de0d157c6e19a4acd261262a600ac5d0a5852013de36b001ef0b5e5a1ee193613c5300078d81800314ac5b0c5dd314cc9bda72c3933c8e452ad⟩,
  ⟨0x28813989a04a624410b88043e01e50eb07003661a00ca06142f01600a504d024e104078839c1a80c7052024410e076029811802c000, 0x98455e090a4559c4b005f93001b54d830a726bc13c92e6ad8561393e8ba46308ec2b0ec48a9a8e1669f8571380062e38d8d923034288b71380062d98d81923037a1ac003076c3b0ac002fc983a62a68b85⟩
]

def tableLLRRL : Table Block := .branch 14 tableLLRRLL tableLLRRLR

def tableLLRRRL : Table Block := .leaf #[
  ⟨0x2a114b89d84d425d126087c4121fa0eb872034a19b0c305c02a212e08e83e81ca0ca05e82b814008d03d01c00b604801d80a002a000, 0x103745802da6119c4e326b008e95001b54ea30a611c00319cc69851013467b2703480aae6eb850039828e6618cae3464ce0018c9e373796318e0a9fccc6127086b8d122b22606b165587489f333b289c35133a0ab⟩,
  ⟨0x31c1838b905ae2b41550a1c4f425711b08543e41e10ea070c3701a10cb06242cc14509d84682120e806382680f206a02f813805a000, 0x6d55e761d7399613800e3838d8180031bfc5b0c404d1c1c9f5956bdcc007d4ecf1ba7a863464d3666a834e092d0597099c4e0018d963405fa9ee30301df52dac70ce01dd476be9300eb3803f49006d9fa48022cf9127048c9a7ee7a72da003d1a00767⟩,
  ⟨0x2c61518a644ec269123088c4282080fc87883b01b70d506242f216209a84942080e306702ec15a09804181c80c2052017808802a000, 0x71e4c6c0c0018f162d86207b8f264e088862c99849c46ac93e80b1e0607bfecb5b09c15ffaad75d8d52b31c1cfbb4006cf018dea3ea769001f69b4f745983d43d10dadaa9b3454e19a4acd2612639000ac5d0a58524dcab⟩,
  ⟨0x2f61698ae853228c13e89c44c424911f88703f21d60da86482b2148097847820a0fa070834017e0ae04f81f00de06202480c001a000, 0x24080d5c6815339c4c0695cf466309388d59268005cf0302860bd8b000c3fb0e09382e62c007beecf1f780be37c3fbbc004256cf30e6018a74c639a2e25d38262a59d706e6c334959a4c24c7ac0158ba14b0a4260dd60304ebce8c12f32c27⟩,
  ⟨0x3871b20d6467431717c0ba45bc2bf15009d84d824d115082c3d81c90d8065c2e815b09d045c21a0ea06482a010e06e02580c8032000, 0x48904dd8d84c0075351e4426a3c6808d5d47c89382400eaca4ea9d514d00200f54d1e06003aa29200190c6353cea4a8801d234790a9a4b1b6682e701c87383264258da8aa74801fd7d9c00301fc3c0d20d7d5e37c142aece0a3f4167f5e03cb380f439c1d3208c680fbb9fe3e5da03a8e7⟩,
  ⟨0x3311870bbc57e2a914e09e44de24c11c88984361fc0f3070c3681a50c1054829012508c84281d60c1055825411006502d80f003a000, 0x1a9b61c00eb5a59ad0003534c554ef0ac2715c48ff1b031abea578bab912da2270480cd474ba9561aa52007c3da498493403004e24003525001e1e06a91801b1348c611c00eada5eac00200a95420c2cfeb0ac279148a931b03691d4d4bd59ac69600ce127⟩,
  ⟨0x29513b09904b424b12088783fe1e90ee06e43341900b8856c290135091043c1e00cd06102c414009104201c80d005901b008002c000, 0x1ba806d34bc47819424c0d25f000e3770807a8d5f30ae2792d80071bb2c01d4606d94006975d9c2e668996113112243644ec40214b007d4ff1782760d73269bc8fe292e91e063092001a9b62ea698581aa6385⟩,
  ⟨0x29813a896848823710a07e43de1d20de069c32417f0b5057029613e09684882060f8075832017c09f04901cc09203c0158070022000, 0x94200071bbe00c46e1785713ca000038ddd00e230344200caeed7858c3548512a43c439d0aaf8861834d19a5cd3824046e4a5c26613c9bcdbf8d81b6fef3a5b89c00ef1a5813de0036958668b33e449c123069⟩,
  ⟨0x24311688604061f00ed873437c1b10d1065c2f41670ae850026612008403ec1d40db06802fc15809a04802040ee0540218080014000, 0x5d970b306a90a5548768732455fd0c71260cde9270480d1f4aea143c0d1d82b2b7138668bc49c8ad334619f224e091934b248d2f91e065493034a240038d1c38801651793b8761606⟩,
  ⟨0x2a114a0a044ae24a11c88a843e20e0f787743a61c40dd065c2f41640ad04dc23010207a83481900a904d022c0d005b026010806a000, 0xe270c917cb00880da5619a2ccf9127048c1a405f26a69788f0328498180032b7c6e6402cc69058581a566001c6f1a00351a40e1584f2af38b63606e2dc5e97b126924ddac00d8b613c64d819856001b5800000c3⟩,
  ⟨0x2e61618a9853827f13109144502010fa07443681aa0c685a828e132093044c1f60e606882f813e09104101d40cc05b01e00a403e000, 0x25c8001c68b90bcc60617e15958030bc9e1284e5706429278220b84e4ee2796d80071a29c1f3181856836572d7000e342ef1f7c8833aa711b9243e37143c81aa428d521d21c06738a5f90c71260cde92704806e634ba050f0372e0294b⟩,
  ⟨0x27b132090446e21a10687d83b01cb0dd06ac34018f0bc058c2b214a0a0047420c0e306682dc13407d03781780a204001a806001a000, 0x1c0d111c4c1f270346c2ecadc4e06db2c75a1ecae334699f224e091a34d410cd13833c0cb12606000cbcf1a0673440032f5c9ddff0b77dc282d104a61f056531430c9a6ccd5069c130d0cb2b84ce27⟩,
  ⟨0x28313a099c4aa24b11e08644061f90f1869832c1830b8056c290137094044c1fc0f106702ec16209404181d80ca05a01e80c8046000, 0x5e47f149748f031849000de6b17798c2c0d795c28004004003b06e1e1b1a52935472607e54c91268334ae4906453a912adc4f310000e359f48c0d2103b2b1a34e19ae4d38240a8f657098c23cc140038d⟩,
  ⟨0x33618c8bf05ba2c014e8a304f626e125890043a2100f6878c38019d0bd059028e12a08f84001c60d005982580f205c01c80b8022000, 0x2e600a5200dd529f60b969600dcf273d64d031b26692834b8a6678007c5e09bf5801f16c2799c000f1b03000666d8b000df9b2200199c64efc9859e27594ce93bca704ac0f774b0066a94cd9269ae6994cd4014a40199e5366d992b165de8f17826c9022573269⟩,
  ⟨0x2d71668ac054628e14109d44c424711888904021e40ed06f43661900b985882a214409084581e60e606182e412c07302800e803a000, 0x40d758612b6138972ae119c4e1ba2d6a8155603b0ae279ad00071b6d8253181adf04257034d540038db582198c99a4a0d2e299a8001f17826ffc007c5b09e698003c6c0c0019a562c0037f9c8800669993bfbe16edba25373dd929⟩
]

def tableLLRRRR : Table Block := .leaf #[
  ⟨0x2a11480a144cc25b12708ac4182020f187583721ad0d0063c2d01520a284882060f906d031015e08c03c81980ae04a01d80c0026000, 0x15069c12033f852e13389e6fe001c6feb5eb5181bf52f3a5b09c04bc65708ce27183580f768032ac10e15c4f373000e37ef803a8c0df7800d2f105850775380e26db8dab912da224e24c19bd24e09026ee95c0287⟩,
  ⟨0x29814389b04ba25012288d04221f60e986f43561a10c905f02cc15009004341fc0f3070030c1560a104702100c2044018807801a000, 0x1d34822c50f6c4f46684d0269000ce7b1a01ae4440033a0c9da4f0ae923c0cd8aad1b85b46e16d4d8503d5a180f9874790f91270487689c182096847943c0c2ba26069c500071b7f83531c45130ba2464d3666⟩,
  ⟨0x22e11208383f21e80ec873837219e0c485fc2d415b0a004c424c11307803741a00c1059828012608203981a40ac04701a0094036000, 0x206b5c6169394fb067c8938241a15222be43460ccf030d22a6353440bea7894d0983743ced002f8d94d0f429389314340a89f14949a4c24c0d32a24d248a289309303590150d⟩,
  ⟨0x21310087dc3be1c90d9868832a1860bc85b02ba14c09e84c824610b07e03c41ca0d806102c413809203e01c80b804701d007c02a000, 0x3848f030642455b4b0b71cc2e699fc52b925c534663092f269cc93824e24c92b443627c4d08ce29b6261704cf4266781ad8b8581adb985c4553f8a41bc353c0d684a9⟩,
  ⟨0x2190fb07843a81bc0d9067c32a17f0b5053c28213209084502040f8074837c1920ae0520244104075034017009603c018009402c000, 0x7b7b6261154fe290fc68781ba244c0d6edc2b3629eb05853e90df92654cfe293d91e06a893035b970b0980a9e06fa90fb91e852c29a463934b627e4684d4926dfb85⟩,
  ⟨0x2a914d09dc4d425b128891041e1f90f4075c3901b70ce06042cc15709a04441dc0e4060829812e08603c819c0ba04e02200b8014000, 0x149271fc006c5b09dc26c0cc2b0000af0000021e3e30b8c695b34c4491934f5fad0b00f7e0fd4eac2cc23d0500038d000dc07221d1a0b64e060e7dbfb1612ebc1ff24ca99fc527b23c0d512606b7b61413ce00c1e06⟩,
  ⟨0x2b11520a545142771320968476228104877c39c1bf0da068c3081720b4056426c12908303c01cc0d0063028c10806102580a001e000, 0x1066f493824d945d42878180b485a58608700320e972080600ea54619f224e091a348078fb4d2f91e063892001a19635862477a1a64ea738581aa698581a856001c68018e351000d0b72752ec2800684f8d8a0978ec49⟩,
  ⟨0x29013d896049223410c880c3f21e30e806bc30416f0b0054827e130093044420c0f706a030416e09403f81b80b604301a808801e000, 0x7c5880128cf93308e0f2ab0780d55563c2c0d560c2c71260028eab3920000c74d9e419318498a1a0344d24781ab9157098c23d1400098d0f50f03000689b8d8dd58ef9a45d43d43c43d90c1ca1d77459c49⟩,
  ⟨0x2a314009d44c824111708844201ff0fa074437c1a60c986002e8151098048c2000df06a82c813e09004281d00ba04801f00b4046000, 0x425c0b98b84da267a4080371a1da1e8cdee696e34e0900dc23b175e21e34da1c3b43df08b846000d1d71bd5609971713d1c80038dea8012b8c0d08200862d1143e449c123c69842d9a27867818a8d30300068cb8d⟩,
  ⟨0x2ab15009fc4e826712208e843220c0f6870c36c1a50cb062c2f415b0a304f025a123080038417c0a804901bc09803d0170064014000, 0x609008930b5c26613d28089f8d81a4ad15ed6e270031569603a2a00fa5719a34cf9127048d1a627008a689c19e0658930300069218d003122a2001a4964ef6b85bd9e16916001c6816a62d9130933a9a60d53491e06⟩,
  ⟨0x2c615a8aac51027912b091c47422810907f03e41dc0c885f82d61550a304c42240f3071034c17c0a904e01e40b40500178078022000, 0xacd30300069858d38a2004a6264cd23b8aca84abdd616f778581af6d850020080180400bf528f3c49a8d9343130d4a9bc0acc0063451e35469a6c19a572483129d28156e27a5580071b1680ed460693501bb58c1a68cd2e69⟩,
  ⟨0x27e13889884ae242118889c4241fd0f4074c3701ae0c585e02d2146099844020c0f306e8310142082037016c098041018007c014000, 0x20cde92704c88aae04cf031d12ac1914efc0ab66153aac40a781a9b0001c693691308f4d5000e343948800e9af938183645df330a037ce705dd33b1a007ead27b4d191243e449c123e69cb3689e99e06⟩,
  ⟨0x26e12b090c460223100079c3ba1c00db064c2f41670ac053427812708904201ee0ed06502dc15009503e819c0ba047019007401e000, 0x234d21c3a43dae8b713d4000038ded1478c0d5e0252b81a9f6001c6f4153c51043e449c123a6994a5689d99e062934c0d4f0000e37844898470f5161e0d15849c2c0d7e4c2af52a6959531431c49⟩,
  ⟨0x2a414989d04c425812488fc4381fd0ed07103741970bc05a428c13708a04281e60dd06702fc15409704681c00ba04c01d80c0026000, 0x1934cdc0254d2f91e065493030006a3d8d00335aa200ba9064f0398581aa32001c68049a351308f516000e34c288166a319381ab8165e04f0a6126253421aa64143c0d650772bd3d0f8e696b34e0906ac595d7687⟩,
  ⟨0x2ba1498a1c4c825711b08243e61e60e186883301770b1053427412508b84201f60ec070832816e0ad04702040c40380158068016000, 0x1c300293d23001306989713800cdfdae6f8c4c006d5733c2b89ea78001c6c03cdd5c6068069b8b5cc1aa4295521da1cc9157e431c498337a49c121ba32ea143c0c1c672d2dc4e00671d2c0c4e201d4ad334619f224e09⟩
]

def tableLLRRR : Table Block := .branch 15 tableLLRRRL tableLLRRRR

def tableLLRR : Table Block := .branch 29 tableLLRRL tableLLRRR

def tableLLR : Table Block := .branch 59 tableLLRL tableLLRR

def tableLL : Table Block := .branch 0x75 tableLLL tableLLR

def tableLRLLLL : Table Block := .leaf #[
  ⟨0x3261838b905aa2c615189cc4d224611d08b44141da0e206ac34217e09f0494228101077038c1840a504c02240f80700318118046000, 0x5daba5dc9400f87b4930926cd2008c48006e42003c3c0d71f002e26119c4e0019f362e7cb3fa000e2acc385cc0173c0c59c9f0e2c5009fbc22858e51c0605d328e6c45130ba2704807c0ddac0ac564fe295892e29e46714e1e04ca461d73bc4dce800f89⟩,
  ⟨0x2f81670b045602a114b0a144cc25112388e045c20b0f6072436619d0b805842a814309a04942040e106b82d012206e0188078016000, 0x1d5e407d2b8cd1a67c89382468d35cc045344e0cf032c49818003579c6801adb51000d5ef27644c2d90b0a17e183121673c932668634f449309348fa4762e224006cf035232e538b000d2130f489a4562c6600b305adcab0f26a259144e09⟩,
  ⟨0x2da1648a984ec26512b092c47421710287ec3d81c90d3067030c1770aa051424411808583d41be0d005682380d606102100b003e000, 0x78ce001a6c62e9ae01400662a28cf9127048c1a401f4d2c69748f031849000d6671b42a00564606b62e14c23d6500038d34a2003acb64e06615daf70b6c2c29847ac600071a006c054400758ec9c0c006bed2eca785713801af54b⟩,
  ⟨0x29b13c09b849623e11488744201ff0f2073838219e0bd85c429c13809184381f60e606c031c1740a904f022c10007302800b4046000, 0x462806b9181a316033c5b09c4c55708ce2718358f682aab72615c4f5b9000e362fc003c8c0d17f000e2edbf8590354851aa43b439f1aaf8861934d99aa0d38253c45c26713d6a00038d00ad3732303005a9b58b⟩,
  ⟨0x2d21638a9050225112388904341f70ea06c433c18f0c205c42b414209c04942360f807082f815609804381e80d205e01d80c0046000, 0x3048006a3789a8c545f1a001001d4670f03000aa2f8981abba001c68006a2391a88d77f268fa1f224e090f1131d0b3423d21e0616113030006ba38d0305a201aae9e4f1144c2e891934d99aa0d3824019191c5c26713d7140038d⟩,
  ⟨0x30617b8bb05b62c41578a9452c28c134894845e21910187d03bc1bb0d606882fe16c0b104fc2380f9077032c15007802a80c801e000, 0x3224e091a34fa10cd13833c0cb12606000d7f31a07a3440035fec9db070b6bfc29849a94e1aa50003c4d24781aa43528c5d048781abde001c6d46aa4991a8e548717826a3f51ac58036a43870048032a4187000d4570f5e7a8963401151ec3e449⟩,
  ⟨0x280133895848222610988103ee1e60ed87383561960c605a42ac1430990494228109073036c19c0ab04902200ca05801f8078022000, 0xa09d75cbb9a6714f14ada9ed8449e49933431a613389ec34001c6fd02c606aa6807b161f21ddc458c9a6ccd5069c12009aa362e13389ec1a001c698c2bc606aa0020f16e27018175874007bab8cd1a67⟩,
  ⟨0x31e17d8bc459c2ab14409dc4cc24710e87f83be1d20d7864030c1650a204bc2180fb076034c1740ad04501c40ce04e01a8090016000, 0x7644c6c0c001b2162c003835c89052c8993a534a49a602c12a3c0a8090468e00605d1e06c0ea5b89c003638c6eb38175181aa7d026d6003fc369fdeb34c12177878334ae4901ba73d55c3adc4f62c000e3686d5e3035159bac067dd344e6a19e74e09⟩,
  ⟨0x34519d0c746222f01678b0053a27c12c893c45c22310a08143ec1d50d406483101720aa84c82220a004681f00d605e01d80c001a000, 0x18240feca5708c0032736793a961b69847000d97b1a0032bd711d5d98327031d4caddae131e477096611c00655ad60032aa0076ac12e1606c1161401e2a4e39db27e36ad0e82ce6a7354349a63e0016772a0482b878964d26692834b8a6c90007c5e09c1d106b16c27⟩,
  ⟨0x42d20f105080e3d21de0eac73438d1b50d7c69c34118f0c505e22e41608aac510272132890845e22510405f41ca0400190084026000, 0xe136066158017728000010fc25859334941a5c5367c003e2f04c39ad84f678001e3606000d9db16e31000d9e327dfec28007cbb93efee15c4e001b37e365b48c0ddd8332b3624cf267ad0c6a2342953e00336280530e6c399dccf1a16d43684aa78004654362004f0e6c299d24e6676d0a6a1342153a0013299b0c02587ca1870d314341689⟩,
  ⟨0x30b17e0b645742a314609f84ce25012088d843e1fe0f0075837e1b50c905c429c14409084301d20c605382100c204e01f80c001a000, 0x6aa6000da8f1a042a4545aca64c968c98a18743638898c7c8938240c964ccd0235b40838ec781814564c0c001b4a634006652e203fb4b64e06b4800cf1a0c4a7b4700831b68d000e3400d71a8806ad1f93000da2b1b54a47624d249f0c001b16c27⟩,
  ⟨0x2da1658af055e29d14389c44ce25111b08a843a2080f987403761980c485e82ae14a09d84c42440ed06502ac110072014007001c000, 0x1c259a4771595095d65c2f58f0b0375830a085929e11b8cc0eca7e375680aed6f8d07f538102d6b8dd8934927b38009c5b09df26c0c692c005fb400000876ac000e3400d95a88006d5d93ec9e16742001001000c00987846ca1b686⟩,
  ⟨0x28112f08ec45821b10607f43b41cd0df06d034e1720ae053c25811908783f01d60de06683081620a604b81d00c604001b009c022000, 0x25b7464c047efdc99e478936ec49a493d8400362d84f1936066158002000000010fafd85713db580038d65923033688b1a34e99b24d382760d7098c23db2c0038d1a38800ed9b93818f25f5a30a3067⟩,
  ⟨0x2bc1538a6050e276133891046e22a10a88003ba1d00d6868c30016b0a4049422810307a03441880b705102340d405d01d00c001a000, 0x7953daa6c334959a4c24dbfc0158ba14b0a49f1560f6abf89008b26c27001dbe31b030006ded8b075588006df19300dfc2f2786692b349849b77802b17429614936aac1b157f0401564d84f6e8001e3606000db9b16c31⟩
]

def tableLRLLLR : Table Block := .leaf #[
  ⟨0x2f01718b0056c293143098c48022b10407c43c81d30e106d43241870bb05a428c13c08c84281ce0c405182000d405301e009c02e000, 0x613dc8c0078d818003721c5b0c5c39723c9d477e139306653dc7004f8d03bd8fa669334941a5c53716003e2f04b51ad84f712001e3606000dc43170944091ef9c98006e1b8d001a27b88006e1f93dea6140da63dfb6cd07354c4634364c9⟩,
  ⟨0x34619c8c586002dd15d0a5c4e825111d08ac4402090f407283801a90c3059429c12108b83d01c20be04f81f80da05c02780b0042000, 0x1c62001ba3e4fe4d85b6afcb326001b79e1ede973fc68006e0587b9edc0f1a23f31f224e0903f1934a60f36d020fcb1e0603e192001b9a63413e93ae20f531c00773c092cf030196e5f8d0f50e01eb96e3400f94a3d233cadb64cd25069714dc9c00f8bc1200fc456b⟩,
  ⟨0x2d61638af055628813b09b04ba25311808343ee1e50ec872834e1840bd055c268111077032c1740a904e01e40dc05d02800b4046000, 0x3224e091834dbfae318d2f11e065093030006eb98db88dbe323f40c2e288fc8d1a980036f0c3dbcade38d818003753c6803eddf91000dd471a001b83e46dc7753c9c99a4a0d2e29ba5801f178261cd6c27001dd1f1b030006e8b8b⟩,
  ⟨0x2e916e0aec534277135091c47a21a0fc875838e1b80ca86202f216f0b104b422e10807d83b01c20be05582840fc0710270078022000, 0xc290089cfb5800ce75aff369c3c9b09eefe003c6c0c001bbee2e05c006e29bdfcae4f624d249df7801b16c27709b0330ac0001f40000087be9c29c498337a49c12006b80e2f6143c0d6feb90e2dc4e001b8fe2ee6371e006e2b0cd1667⟩,
  ⟨0x3141788b38570297140097c47822510a08183e61e60ee06e43301750b104fc25811908603a418c0bc04c82100c205001f80c001a000, 0xf20f22001bd3e4f96385c10533b3cd92c70019d1b3a74af3d8d0d318e3e698a1a0e44d19a06bcb80071a0033c571011de67261b21c02f793c687a87ff91ae27000de3f1a03fbac64606b905d5b160e2a7011dd531786692b349849bc3002b17429⟩,
  ⟨0x3131780b6c5982bd14d0a344f827213188b84161fe0ed871435e19e0c686002ba15209784881fe0f506902bc11806902e00e4046000, 0x5f100038d2e158ec49a493eb800562d84e706d818e258002648000010c0037bac6b8c40037bcc9f3130beaec2c99a4a0d2e29bd9001f1782766800ac5b09c0077aec6c0c001bd662c003b2fc88012f5d93000dea71ac312a85eaf27b2ac2de940038d⟩,
  ⟨0x2c815f0aa0526289133094045a22010888103f01e90ec06d433e17c0a604a423410507503501940b404f82540ec036015007401e000, 0x81b987853c133c0c001e61e2798185008f3070fe295c92e29e4630925669000ed7313cb9c36d6801189003f2dc0038700372db12611c1ad560d41aab6a58581b6a5858c153c0d5cc1252c00802006012b551e11b4cdd4340a6⟩,
  ⟨0x2000f407783961bc0d7868832c1850bb05a42bc14d09b848822c10507c03981b80c905d029011c0780358160092038015806401e000, 0xb3028781a8a43ee47a14b0a6918f8d2d89f0cd09a84d3d01c2c5099f11964cfe292f91e060c912d8ab9a385e69e17a3585d3332a87fc932a67f149ec8f035449⟩,
  ⟨0x2000f5075c38c1b90d506743201810b605742a413d09404642140ff075036019c0b8057026011c0780348160096039017808002c000, 0xe94616d043e699fc52b925c5346630923dca9cc938241ad52f36686c4f429a134c0aa4ba4781b9ef8581b9f38581ba2185fc932a67f149ec8f03544981b9d385⟩,
  ⟨0x2e41660aa450c27012f893847e21a10688003de1de0e686f035e18a0c0056c29812908303c01960b504801e80ce05a02100e004a000, 0x8aa9200fdedf28001bdb653a8d85d334961a4c24c056005eb2852e291f364d1c874d95078613c046001eba060006021d636320035e9728003bd2653abd858070001d7755b0b00d0003aeea9e14bc43f8a423d21e060e512000c027ae⟩,
  ⟨0x29c1478a144de265127890843a1ea0f007283761b10c605fc2ea1500a304842200ff078032c17c0b104e02240e806102a00bc04a000, 0x713c0dd69c2c0dd68c2b89c001813759025c0980016aa06eb0e17923c0c00bc08fac713c0d0218029ae818012810b5da6692c34984980f400bd650a5c520d0ac4f1240ccac46930c27000e035d740c000c067ac⟩,
  ⟨0x244115884840e1e80ec070c35c1a30c705d42d015b0a784f025610a078836418c0b9054026c11c07f03601740a204601a8098022000, 0xbab374d95cba7048b1c554bb6c69e154c132a704bfdab06e39cf429614c2306e8989730ac400b9c521dd309250f7721fc525069714c998d248a289309388d82474d37922c84cf4269⟩,
  ⟨0x2a314409e44dc26312b090043a20a0fb87903a21b80ca86282f21680ac853027413009083f81d00de064029411805c02300b4046000, 0x3b6050f6c4f89b1330a7b558506de27b1b89a265744c44890d513ee20eb007f5df1782760d73269bc8fe292e91e063092001eb762fad98581bad385000f5bb0e03d0eb0738007ad98aeb9e178805cf03038fac98b⟩,
  ⟨0x22d10f084c4041e70e306f034618b0bf85b42c214909f849c2220fb074036c1980be055827811a07e03a018c0a804301a00a801e000, 0x19127048e1a6151f8680fe0239e06fa08749fc543e2352c8f48da2050f03602245770b0bdd9c2ca687a149c498a1a0544f8a4a4d2612606c5349a492a34984981a08ef869c49⟩,
  ⟨0x25512208cc43420d0ff07c43c81d50de06b43441890b8854028a12c08d84181f80e606e03181660a604702100e206702880d8036000, 0x16ce6b773740639fc52b925c5326630920dc8e9ac938240785d303a511ba0204e7c4dba04e9c133d0999e06eefe1606efb616e543f8a4351a1e069891303774b0a0f81c1e042883c041307⟩
]

def tableLRLLL : Table Block := .branch 14 tableLRLLLL tableLRLLLR

def tableLRLLRL : Table Block := .leaf #[
  ⟨0x3b01d30e046b833b1970c045ee2d61660a9c52226412188584021e00de86682d41530a204e423c103072836c18409f0420184096000, 0x81a0f100275c00441e1ac005d44b3f8a400400f50acf030016a05a60683a4001d666cf0ba8fa71a7567002d47b3ea0800ea359f50acc0031836746a63d31b606b0261ec01605b01e1c47b63e449c120180c266e07868107d98f0300feba40038e9c68066511000e3af27e14c288200200b4311e1f147⟩,
  ⟨0x2be1538a104c224011788884262060fc87a83b21ca0df86b831617c0b805942ac133093040419c0b805582180f805702080bc04a000, 0x2104d28006297878a6648b1b9fc02167cd33f8a5724b8a68cc6125f4d39927048d1a59e70e8c43627e4684d49259db0ddc3b89c00183f75907e41fa000eab3d985613800707ceba0600060f7d6679b0a5d23c0c005c1e7ae⟩,
  ⟨0x2de15d8aa050a26012788f845e20c0ff87c83c21d00d586782f61710a7050423c107071032c1780ab04e02340d005b026010806a000, 0x3944c586891000e51b2600ec2a9b3c334959a4c24e4f40158ba14b0a6a4d6306b8534009d9b09f26c003c6c0c001c9a62dc62001c9b64e10fd280030a2ece10ed29e478936ec49a493085000dab613c64d8198560099c60000043⟩,
  ⟨0x34118f0bec5ca2c215b8a504e626011e88a040a1e40e086782f61580a704ac22c0f3071034418409f04902140e405f01d00b4014000, 0x11968cc62400308dc4c2030d07f84662704c1fa1678cff900bb387087cae00671a0cca7013e56b1a003c2367cac384b1a00195061f2ad29dc680064858781b2a6001c6830ac45a3955c9e19a4acd2612729a00ac5d0a58529da2c3a45c2b60126cd84e003ca363606⟩,
  ⟨0x2fe16d8b145682a314a09bc4c425512108c443c2070fd07543961a60cb85d02a213b08c03d41d00b8057022c0cc05001c808802e000, 0x38f8ca68f70ba6692c34984985b400bd650a5c5219a3268e418a338886c309c00385975d0300030b1eb1b19002b1cf94035639b29a55c2c5622a987002c55b0fe29000800e2a987818003153c480030ac6bb48d85bf659362f32704d7bacc⟩,
  ⟨0x2b61548a7851a28013b09804ac24011988383b61c50dc064c3121640a9850826610e08083d01b60c8057827011e06a03000ec046000, 0x2ccd09a44d2e2781b4b78581b4b58571380030c4eb21888624001d569530ac278614014d740c0094307acd334961a4c24c2fe005eb2852e290194762789201927623498613c2ee001eba060006175d6045549022f1f394⟩,
  ⟨0x2d21578a384f226e12688a84361f80ea86c83501850b1055429013d08d03a818e0b4051825810e07a036817809603c018808001e000, 0x19979c4c6800e295a7136cd09800713ecec4dcdfe34c23e6f40038d000f42b22addcdfe4e0656df41f1601a8c261e852c29c4d18000be2402b17f000e1c02b184c4d2087cd33f8a5724b8a68cc6124f144e649c123c6979343627⟩,
  ⟨0x3041718b5858e2ba1568a784fa26e131890845a2000fa87503841b80d106603041780b103f81e40e606d03381560880328110042000, 0xaaf00cb3f8a5724b8a64cc612401aabed3592704800d565a5a28d15480020056784d550003692e91e06e94e1606e95e1606ea1614f82001001632da9000300861e11a11a11b9199079cac6b2d33938dce45c2f1a0039ff67680671b1a00399b67⟩,
  ⟨0x31717a0b785902bb14b0a304ce25112108744201eb0dc06b83301830bb056c2a213c08b84041dc0e206082d010e07d02e00dc042000, 0x72f194ecde17b418561380070f76ba0600061ecd675c70a711c00387a758e2700061e8d643cd0f38005aa81bad78516453f8a410e253c0c0c2a900061ded7758b0bec21f118016b4ecfe29001003ad1b3c0c0035a16900061d5d775f70b59b59367⟩,
  ⟨0x2d61638a8852a288139898049623611488103f41d50de86682ee1520a084c02420fc077838819a0bc053825811206402d00d4046000, 0xc24c422005eb2852e290715627a9206f5640dae184e001c413ae818001881f58115924028cc5e5003398aca44060096bb4cd2586930930ff8017aca14b8a41a159367206656449e184f0fb8007ae81800187d7585429007f2f394⟩,
  ⟨0x29714609f44b825211e08bc4141d70e086b034417d0b3052027012908d042c1ec0eb06f02e415e08a03a81980a20460188088022000, 0x426e49200361d6781bbb58571380031166b222b88b0001d577570b302a7818036889f580e8b1c0d004c78cc6814c7127a53722aa613309c032887b5d03006110e6b01b553829afb1538270ad593a9b4cd25869⟩,
  ⟨0x2d51640a945362781338908442212103879838a1980c705b429412908303c019e0be058828812a08803c81a00b204e01e807001a000, 0xc27d31800f1b0300074c38bc13899551256cc022caacf912704800d96da70d001eda00200764b67818006ca6d2001d2b6340070bee2001d2c64fbe185b24010b3e699fc52b925c534663092fe69cc9382470d200f633686c4f266⟩,
  ⟨0x2a4140898047a22810287d83a61c20cf865430816e0b0854828c137095046c20a0ef06c82e015609d04981c00be04e0208078026000, 0xea131a00f8bb71000ea0b1a0dcb10076a1326611c003a7ec68d9c4007a80c9c0c306bee8e1584f292f118d23b8ae71577870bddec2f7730a00997167613dd0d0369ad9658d9334941a5c53a67003e2f049a48b⟩,
  ⟨0x282136095c49823711088503e21dc0e906f435819b0c805ec2b414909e046420c0fc0748320166086038017c0aa0400118058014000, 0x3c2b850f055e09b8155f82f0ae27000ea7b1b0d8b181a2a9574a694934e092a555800db459e24d6e27000ea4f1b2324606f11160036b76707b5580081d5afdabbf9859133c0cbecab0ec4443c99a11a06⟩,
  ⟨0x2b814a89d04a223b11608243f41d70e686d83401890ba059029e13a09184381fe0f207183601860ae052020c0ec05502480f005a000, 0xeb131a00393b71000eb1b27e5cc29847000eaff1a6144099ac1c9c0d280b2fc51853d15920faa980c6ffc54f7f2a5dc165f472ace24c19bd24e0927555d20a9e06032c85b5b09c01320ed708ce27389600b8fe0036a⟩
]

def tableLRLLRR : Table Block := .leaf #[
  ⟨0x2b014d89d84d224611e08644181e90e306d43501970c605d42d415d09d049c23a10607683701760a204982200de04e016808c014000, 0x6a55c5f00116e584e003d70e3606000eb7f16c31011eb872601b9fbe4c64d3666a834e09139997099c4e001d6a636d248c0d80832c063dce3c6b140d8e750446b9f224e09018a74e518045b4040e21cf0301433a606⟩,
  ⟨0x28e139898047822110788143f01eb0f0872c3641a50cc06342e815309d04902160ea06a830014e09204181c80c2052017808802a000, 0x30e84c10888601003078580e12e123c0cc27a3340de72c283dd39e852c29c4d6a06e902b5017380da3a7cd3852eb1739516d839f50d52168a901ae73bf9aaed53619a4acd261275d000ac5d0a58524d6ab⟩,
  ⟨0x2aa14e8a3050226612d094045621e0fc87bc3941bb0cb06242c813109384441f00ee06482c012a07a03681780a204401a8068016000, 0x30cd7269c120c8fc3211a068c3012fd7309e30a046b5d0302311846b0e2380071836b1c4e000c60bac8c0e304000b55037acb0a03c2e781a2fe044f5dc5b8e770c56131707c1fc52b925c5306630920888c27b24e09⟩,
  ⟨0x2e41608a8052628613d896845a20c0ef87383821b00cf86182f21580a704d4256106072830015a09e04801f40e406502000d8022000, 0x6c7c71f2609182b67a14b0a7136058225a410f040006ce08581f696141880b8838c9a6ccd5069793482c9b9fc52020722e78180a3dd303463e0a16b3e84405ce0a0463bac8790e7126c86a951309984f18b824dae8181248c57583469⟩,
  ⟨0x30d1790b3855a29c14589e84da24a11f88984321f60f6072436018b0a9050426012107f03c41c80cb059023410005d02980c0046000, 0x6791c1ccd2237c1ddb7805cf86e69334941a5c53b5d003e2f04834d3ad84e003dace3606000ed5f172802f135a2340d988f068622e1359f0cd256693093b5000562e852c2909c17580e03ae336365b72c27001ed271b03000768f8b61882e769393⟩,
  ⟨0x3911bf0dcc6b032b1890c005ca2b814f8a184d6247116081c3f01ee0e486b834817f0b204fc23c0f106b02c412c07102b00ec02e000, 0xd822704d16ff0c13d0fdc4db380f23a617068538e1227989227367f3ee74f6f93a67d3883cf66f3683806670704ea366d652478181718d8f593e00c1e0605ba360d7006d10705a635dd703961d59c1c70e40c2ce019941c1688d675c01a841e35705475c58b4c1ee06883dbcce6583f2cec7⟩,
  ⟨0x34f1960c6c6183011780b3c57a2b31520a044c025612008283d21c80d985d02be14a09c84bc2140e9067028410c06b02380b0026000, 0x2b7498d8a33e449c123069126cc1b69748f031849dcd80071a23d9797181bddf850281d360889c1f74b752d2003bbd69dd4b300404034b8121f07c2bb36ebd9bf5cd0303191be6bb1f8426cf4ca541c41f1f066ecf51a6426975084c13308d83e2719098b8873c5c89⟩,
  ⟨0x26412488d043e2040fa87803781980c705a82ae14a09d84b423410d07e03b41c60d206182c814609903c01a4090039017008c02c000, 0x4fc2123d6a70aa53c80d2a7954d236a71345805070c46403078182c238bc2a5343d0a4e24c50d02a27c525269309303629a4d24951a4c24c0d99c2676d38922639996f6c4f89b1330a7df785⟩,
  ⟨0x44120f0fec7b03a81c90cec63c3011790b54568293139097c47c229103075836a1880b384e82320ec06582780e205601d80b8014000, 0x1be4000e34003984c8b5a77cd93c6d67c800387a19618422212d6d884d3a2f58c3c4a034a4058925311240188a539f99f76b001cf6b3e7ce7d5ae1a93000f1d5a78cacce34f9361dc67f25678e1f21f3becf90d9dd8ff67c9fc7db3e4164f63e59f23327ecf93d93391767c9acabb3e4ce5564459f26b273222cff5f9c1c1bf383f8a4020bf8c1e06⟩,
  ⟨0x36219f8c786282f31720b0c56c295134097849023b10c07dc3da1cc0e1067c32016d0ab84d02220ee06c02a012406f02600b4014000, 0x3808001c68096e05c606011dbeb59c47003dbcb5b89c007682d7b73b3e0056a81bdb785713efe00038d006d9ab8c0c00bb316b81b7e6001c69c51000efd727ed0c280077df8d000e63f22001df8e4fda985c98643000387c9161844392dc3ca188a38700713e8e001a1c61e06⟩,
  ⟨0x3331930c545e42e115f0ac451828212e88b44141f40e886ec3301820af854824411807a834010c078032815008e036015806001a000, 0x38a468d800ae2564860d8009e2466184e001c819ae818001902b58001001f10f24001dc7653bf985000ee3329dfbc2f10c00387e21e1800baf7c3f8a4002003d7ae1e06000ebe3131feb87dacc78806c00202450061fc86e41163269b33541a704aee8b84ce27⟩,
  ⟨0x25612388e845a21e0fd87b03c21be0d3065c3021760a9850825a123086840c1da0de06882fc16a0a804181e40c605202080c801a000, 0x1724b8a68cc612400fb4dc4e649c12001da56250a9221b13ed1f0d89b68a002c4e899c4eccf0377e70b0377ef0b711fc525c23c0ce29004e41ad740de0cc2e99a4b0d26126414002f59429⟩,
  ⟨0x3af1cc0e1c6f436b1a30ce46282e116b8b0455e2a514009d84a222c0f105c41e60e406983181680aa04d82440f604b020807801a000, 0x79accb133e998e2380072276b1c4e000c89bac912e44c000b550379030a5d23c0c020c88dae81a44400ff5c01f4887ac97ae49a11132ddb0e1f6c3925979421f24932c97a6c5b0fb60c924bc610d92361e4cae5e7b15c3fe499533f8a4f64781aa24c0de0dc2ed5b61e001c3c0db54d86e1f34cfe29⟩,
  ⟨0x2e71610ac44e025912108ac43c1f90e306bc31417d0b3857029e12a09003ec1d00d906582e014a09a04681a00bc0390150078016000, 0x491e0016a460d20008004001c91ba891cb4b23a69647ed2b89c00191af5923548d6000eaa46bd2c8d09dbeb184f3b8c3426613a7952326ba064f22462d66fa873c9324344c890d90f09984e02a48b5ae8180529163587127918d144e09⟩,
  ⟨0x25811a887440c1f90f4076c39c1bf0d4066431a1820b6857828612e090845c2020f707083381860b004581a00b604c01f80c804a000, 0xa6ecb1309250f1c731fc525069714c998d248282c9309388d8241f5537923b08153f40aa5c4f0379e30b0379df0a1da261307489004247bd6003e7c18cf14ac49714e199c532480015a9⟩
]

def tableLRLLR : Table Block := .branch 15 tableLRLLRL tableLRLLRR

def tableLRLL : Table Block := .branch 29 tableLRLLL tableLRLLR

def tableLRLRLL : Table Block := .leaf #[
  ⟨0x3581a70cac6102e516b0b1c54429514309f04de23a11188003a01a00cb05cc2a012f09104542140e905e026c0f006b02f014c060000, 0x81b986001c680074bb91004f31727b126924c0d80036ad84ee136066158000188000010e066d2c52748f87d20452348d87573800b33987818003cb3c68e0389f9101fb13b3d0a585389ac2c06ed203561c00367019b0db4806b77187a14b0a7136ea802d8900aeecc00387⟩,
  ⟨0x36119e0cac63430b1730b645982a9143098c48023310708103be1af0c605a42a613c09284381ee0e006482c811a06802280d0046000, 0x949a5acd334961a4c24c99c005eb2852e29000f43318009e82648003d0ac60023a0598613c98c001eba0600064c4d60004005cfdc9740f89194000f11f29edac2ef86c9f71193eb7b2774264c1dac9800992075b264b9013b5925c00d9ac9b180170e3867ed36e94400387⟩,
  ⟨0x29b13c097c49c22b10c08143f41e50e206cc34c1970c505f42dc15d0a7050c26410f08003d01d20da05b82a810a05201e00bc014000, 0x46354b8b01ee74f9b981e5d2fc4f2c89aed138254ad596bc02167cd33f8a5724b8a68cc6125f4d39927048d1a56a7bffc43627e4684d4925695bf0c3b89c00193635926bc9b0000eabde385613c9a800a6ba06⟩,
  ⟨0x3541998c6861a2e816f0ae453c27912b08983ec1d30d186402fa1720ab84f025a12208883b81940c005282600ea04501d8094014000, 0xc88a8f73e6e0b9d84f2878211ae8181069437580180c1e50b040b5dc01df7e1f7d7c00df761f82bc02e0061f82fc18c3f05b82fc15c3cda8964913824172885cb81907c89382464d2e96d58634032903c1e069401612e27000eaaf17b2bd55000b15037fc30b1700c1e06⟩,
  ⟨0x4091f30f5c7983a91c30d5869832918f8bf05b2275132896448622c103878837a1a20bf85c828413808a836016a08503100c8032000, 0x8e0761f224e09000f02f13c68820634002003e04e1e06001701f130374ec0038de2fc0eb22001eb3f02f805c3e00100670f498d08dd5bc301bcc7017e522d700c3290eb9d5a94835d0508c1fab5bfcc3f8a4003d58dfd61e06eabefe313bfddfa6fdb7df87df86fcb0fbefdf8efbb0e097e1661c12dc2b041e1e5a49cf9316e7⟩,
  ⟨0x2b61560a64514277134097847622a10387c83c21be0d8868832c18b0bd05ac2aa13f09484181f20c905982901340770280118046000, 0x2069951269245144984981b5f1bc3c68e9a7783af6c7d9099e84d3d59d6063584f312f11b048c1adb157d330bf4ec2fd430a001e1be1d856001d4570d715f45c2d24781a093ae3c5803fa01b27818003d46c6c1135bf91⟩,
  ⟨0x2c21598aa052e274131096048e22410087783a41c30d0065430015009d049021e0d606402f813607a033816809603e016808001e000, 0x3224e091f3480376378d2f11e061b34f5f40038d000ec5b22007ebfe4f918e23800f6258bc120caabd8780040058afb9e17ee38585f55db1801a0e800d9ee86818003d6ec6e1fb76dc79343d0a4e24f99b94d3e2929349849⟩,
  ⟨0x34419c8c585e62d01588a384de23611508703fa1da0db86502e215b0a504e425410707d03b41b40c705102540e406802280d0022000, 0xc12056851e2f678056c5ecec0598bc6d8e29343d321e1c03633a3b24800de780159e11bc860039528fd9932ae37b30648c6b8c366987000ecd713a6cc3619a4acd26127b2200ac5d0a58528d22c3945cb4cdf8ee584e003ec563606000f623178271df5ed4f271667⟩,
  ⟨0x3a31c90dbc6b23361958c205ca2c01578a9450025312388e843e2120fb874836219f0c705a429c12908803b419409a03500e8046000, 0x3d1a4003de9c4f78f0dde2ef462704f787bcf8c000f7530eeefcb59ac9133c0cef14b53ac00a68056383d23419a9b5884c19a935e83cb44eedeb8040a4dcf858347b99dd7967b5c01a241e59c065b5cf38ee7e5b71c70fcb6e3861f96bc6fd3be1c2ddcace59e1f847cb5e5961eed864c2940b18b⟩,
  ⟨0x2e115f0ac451c28413088f84362050f9078c3b01c70db068432e1860be056429412708c042c1f20e2065830415408703200d0022000, 0x1f78003e2d84fde2001e3606000f78316001fb9e44003de2c9fdc70a8921f224e091f34e59b44f4cf03159a606000f74f1a7144009dd5c99a4771595095045e9608ed2c0d043e947ff084c3c2da173898620200207871fec2cf0f7069⟩,
  ⟨0x2d015e8aa850a27a134896049223c11508804221ec0ea872c36819d0bc059c26811d08703ac18c0a304c81d00ba04c01d80b8016000, 0xe51398a2c010823357827a0d73269bc8fe292e91e063092000c107ab82074b0340fda5820f4c000c105a719358010000c101aa821f4a611c003defc6800303c6c4007df1c9c0c000c0ebab82934b26692834b8a7bcc007c5e09⟩,
  ⟨0x2f016d0adc52827112d892046a22a10b87c83c61d40d885f82e814f0a184d023e10407703601920a604881b80c804f01c8098026000, 0xfc8e14003e23c68007f0391000f89727f8bc2d9a89655138257445c152003e9ed24c249fc4002712000c14a001e9e06828c006d4d23184707555e8084aafd2e17eff85308fe0d000e341bd62003f07e4e0606c55fddf0bca2267b44c8489⟩,
  ⟨0x25c11c88984382090fd07b43bc1d30e006b434618e0be85a029a13c09684882220fc07503801a20ae04c820c0f206302c80d8046000, 0xf2200071bec24606ed91671260cde927049b08ba050f032b8aac7cce0deabb8b35551667c89382464d2352ad2f11e063492001f16e3610563f9cc2c0df97c2c0de27000e343e488007c5393⟩,
  ⟨0x2cb15a0aa852628613889944b023510287bc3c41bf0ce06482de14c095845420c0f7069031416c0ac04f81a80a6042019808001a000, 0x4380d181a13e65b09c4f15708ce27000cb1f172c601c000715fc7c2b89fcb2001c680de5859181806d2c0c5f9540038d85a001b8fc730bb126924c2400036ad84f1936066158000fa0000030e11ad2c19a572487a8786d16e27⟩
]

def tableLRLRLR : Table Block := .leaf #[
  ⟨0x2a514109ac4c223e11488683ee1e80e286ec34418b0bc05a42bc14b094044020c0f3074831814608c03d81b80ba05201d80c0046000, 0xbf4464e146d2c0de81000e344d962611fcfc001c698510587a0327035700bae13dd2a3a87c8938243a4481425bd8d08f0878185644c0de6f000e340932d8c8cd22cb1934d99aa0d382464865c26713f9940038d⟩,
  ⟨0x26712e88e842e1f40ef872836e1a20ca06142f01690af051426412808784081d60cd06002bc14009504201b40b605102100e002a000, 0x40c001f51e2c003f6bc8813bd4b9398354852aa43b439922afc863893066f4938241b2dd750a1e06c84a75b89c0c865988e3995a668c33e449c12326982499a5f23c0ca92606000fa1b1a0f6b1⟩,
  ⟨0x2d215c8ab053626b12f093447c23311107fc3d41e00e8871c3481810af051c26012308003741a60b004f823810205e02980c0046000, 0x36845d6e271f35cd3401c00fc5719a34cf9127048d1a4011347c689c19e065893037ad80038d000cd0722001f5c64e16fd2c2dba5713fac00038d0614cef2303030e6738b9334941a5c53ea9003e2f04fdc00a98b613fa940078d⟩,
  ⟨0x2a514d09fc4e826712208a443e2040f4873836618f0c1057c28813a08f84281ea0e205f82c414009304101dc0bc053023008c014000, 0x18262a3085c26713fb800038d15c4a23030aa210b00c4a0f0d8742e0f0f83c0e0d0e83b89fdae001c688a1511818430885cc1aa4295521fa1c01f35cc5fd0c3269b33541a70484f03ae13389fd8e001c6ec89bc606⟩,
  ⟨0x2f41738b605962be1588a804fa25a12588fc4502030fa076c3741a40c705d42d614a08482e815209804281cc0b003d0178078022000, 0xf14ac49714c199c52b6690027f2713fc8004e25b13f2340bba6001605cd4984701a475d180813abf7f85fdfe167805cf0347c04f5ac002000d6eb85fb4e0008004bd5add50bee9e65cd94e60dd131c8305a37098d056131430c9a6ccd5069⟩,
  ⟨0x2cd15d0aac53c28f14209c44bc25411888883fe1f20f086c434e1900c185802a214709c048422e0f406882b812e07602a80a0022000, 0xca224e24c19bd24e094551710a1e0600947a716711c0071e7c5b89c64d71e4004000b1503414ba5713fc4c0038deca303624b82834b037c340038d000c76722001f87e4e099d2800e99d9c007636d6003b19b116a83674b5667⟩,
  ⟨0x48723e91708764312080fbc79439716c08303ee1e20eb07303521940b8853825611408083c81ce0d4058826411e07c02c80d8026000, 0x40d1e1b9f6b89f001b3c0d1dbbcd6bc7ac7cb4940111869c9ff88bc9fbd3be5c0040030025856bbaf95e077035e4cf96aedcdc000b877cb0004004003b0a5771f29c0de063c96416f95aed4dbc00987902b34fed9a11a06f9b00071a1d6b1000fcd31a00185d644003f36c9c17da54690f9127048708900ec7e71a11d50f0306889f9400071a0018fa64402ff2ac9d5a89⟩,
  ⟨0x6e235f9ac0d4a68232f98bcc4a6022ef96f0b324c0258123c8dc44d216102c7d43df1df0bc843216705402700f60660288110042000, 0x11178c3e449c120018bb626357173c68004007173c3c0c0018b9624003f5cc6c48a34d919deb9970e02215300840036327a1b5a9f675fae15becb85538d0dea01543787a0c6017ddeb4ee40095a777c04ad2023bbd69900ddeb5c7f825daf04824c7edac00829ce10d7b802d628af83ea002bc2079c80627060177d4e1c00629be10487abda015b13d7bdf4e014e0fbce002f38200b3ea30f21d79bd7ba7035ec7d3d898534fa6001707f83c8e5c3c871e6d5ed9c057ad1c96257d33e95151c1ee0e8a6400387a46001db1b4ed4d9b6b2cce27000fd1b1b167ba371⟩,
  ⟨0x5122300e8472c3801ae8b485902a5141097c48022c10d88383fa1ec0e486f03181820af85542601060708308146079037812801a000, 0x218efddb2ebdba770006b12800b8adc55b11c38617387863494dfb965c7b6cedc00b624000f1578a962287042e30f09a16386750fe031b0c22c9412e0e1c92000c371d3262b862e1e06000fdf71a0018f9645d3ff7fc980180b49805461934d99aa0d2f269002c2eb0fe29000800e171878180050b6c4c0d3ae0b11acb0001400d1c5869d6b58012ab51e25442a3c3f0055528f034eaa2c0ebb8f305725100070f266⟩,
  ⟨0x3c81d28dd46c433f1980c986062ca1600a744f425512308dc4241df0ea86c03481970ba051025a11a08803b41980a903c8150042000, 0x860805b0e00f86000570e1821c025224c5d247819d85221c58009ee9e375bd9e06000fe6f1a01f90ee462eb001f4f6926124c3940046a40018b9c003d3c0d172800ba9846713800640d8b902c8480038a870b4b00a1e06757c8071743f44369f477a9b0fe91f46fa970ef4b4293a77a561487a874e00bd4f67⟩,
  ⟨0x5772ab14cca204e02378ff87b63c51ca8dfc6b833915d8a9450826111f08a03201600a084781f60cb05b02840fc04e01e80b0042000, 0x43475559dd53666c3d982dbd87b2cd97edbb87e3f0892cc3699b2ed9810d965fc3a1ac44765fb2e5982d3165eb30e1c00346cc4d19f0d671000d90f0f467c35246d0989b3d5a131365ab2cda46c52001b2c08710c9657c3da9b0c0031296744afed71a001b10e26ba586b45cf9b909c83b299714cbd0a3887f315d9d87851156ec9f8700353a8e54ffd7e34a83080c39554a8107fc3c2e2a5b8152ec4863e1dd863e986361e9cd2d269c1202dd936b⟩,
  ⟨0x3f11e70ca463630d1810bd05a22ac14d8a284fa25a12788a843a1fa0f807343501850b20504268111078039818a0a40408110042000, 0xafff263415600100172d00076bc0565a0a82f6847e6a72f0f543650d09a086fef00071a0694279b19334941a5c53fd9003e2f04c1420716ad84e003feae3606000ff4f16000c139b106e7f5726003371674db7f3f1ae27000ff371b3a41af7181a744356d60033ad674ed7f231b0b8e4cf369dc787e423ab30fd570e567⟩,
  ⟨0x21e10287b43c21cf0e186ac3421890b9056c29013b09604782160fe07683781a80c305a028c12808a038818809203a017809002e000, 0x33821d27f150f88d4b23d23688143c0d8089150c469619fd2ca687a149c498a1a0544f8a4a4d2612606c5349a492a34984981b8aedda7126e781ded89f13626614c2e1a5⟩,
  ⟨0x23411188504121fa0f1074c3901bc0d7866030e1720b4054428e13008e84401f00ee06d83441740a104401bc0c005502200ac014000, 0x7934e649c127126495a21b13e26846714c349a5c133d0999e0686974b034379a5b950fe290d468781a6244c0d0cc6943f5dcfac50e7d50973e449c123869d6fd7680e80239e06⟩,
  ⟨0x20a0fe87c83ba1c20d6867c32017f0b905802ac14709e849821c104078837c1a60c705a82a8136084036815808a038014807001e000, 0x185389a45552a4c0a9d395531437e499533f8a4f64781aa24c0d0cde955b0a1e064650e5523e236231a88f099b15431fa586474b0ec69734cfe295c92e29a331849⟩
]

def tableLRLRL : Table Block := .branch 14 tableLRLRLL tableLRLRLR

def tableLRLRRL : Table Block := .leaf #[
  ⟨0x3541978a6850226812e88f042e1e40e486b831217a0b4857028e13d097049021a0da066830c13c08d04001ac0c204e01b808801a000, 0x2962064d682568269496e9a0104041ae78a4bae090e369e601dd20d2ee9c122d34cd6b05aa1c1d382d30e002c9a700d860f65b342c00a86f74ff92694cfe2918333c0d91260686cb4a000c36800169e0cd03000d0d8ea794cfe291c333c0db0a261a9d2b3629d9ad4f429⟩,
  ⟨0x50627a93809ac4c725e926090e46222590d08544051fc0f4c7783a518109dc3be1d20aa051c27611807a835015e08e0348110042000, 0x3e0da27067819624c0c000c0ffad19388003040ece316d2c629a581a07900075ae31000607bd9c61da58c474a001ae1eb8aa0bd0ebba8a09e295004a2e9a049e9e0ba092b8a5d3294fd440015c4ae1c004c3c170123713ba5d29ba86001c55dc46e1a003c3d198002002b87f506e93711a52416811f87b3342300060bf8783041871a0035c5672b7e06ad6800d1fd9ca3d81a35a000c0cfad577e51b220034b567⟩,
  ⟨0x24c11887f83d21da0e686f03621a40bf85a82c014b09c04942240fa075837819e0c4058827812808103a018409203c0158070022000, 0xe6a160cc85071036aac615679264cd0c6984ce278270001d6c8fac6068dd5587a876ed1776a1e76621ce24c19bd24e093691760a1e06be116e270d916eabd15c668d33e449c123469⟩,
  ⟨0x2c415a8a404e624e122089c4201f50ed071c3721a60c986002ca14009a848822210207a838c1b20ca052823810806d02a012804a000, 0x308f0618003ad006e5988007062ece06006e295c4a3a5e671a13c5e5c243444d90d59a26824486289d604e160094429abc130422e64d3791fc525d23c0c6124001882f57104e9606881b4b9402e781819c881756000c411a7⟩,
  ⟨0x2e71618ac453828713e099c4ac24511b089c4141ef0e906d43561860b4857029a14009a049c2140e5060026411a06802d80f802e000, 0x6e803cf83eee0d1b6a96a254e0966155cb1a560d31124e24d741bcac03df8386b5c4aeb40064f03056b11a6ac0ab7e4fe295892e29e46714db204ca42d8898f53131000fa9006d600a4f48c00246afa9713803754aee9ad8019544b7a5⟩,
  ⟨0x2cd1580a8c50c25f129090446422710b07e43ce1dd0e7071033e1820ae851827811707d03ac18c0b704902200e205a01f80b4036000, 0x47d752b7138035c4ac18adc0e95699a30cf9127048c9a6b104a5a5f23c0ca9260600060f6d680355cc400b83e3671c86960683c4001d6809534c4c23c1dc000eb4c2880ef0786ce06ea05971c3e9403d784f3e0dd38300ba107⟩,
  ⟨0x2af1490a1c4f425511e08c842a2080f7878c3ac1b50c405c42c413d08e03dc1da0cc05b828811e07a03601740a004101b0074014000, 0x1999cae13389e12100075a1b54f181b2d2a256c2704a675c23389c007176d78b81440036a8ebb4a611e11500075a0038b1710c8a117d9c0c6418ab6b98354852aa43b439922afc863893066f4938241a49d750a1e06⟩,
  ⟨0x29d14309f04ca25412188d04462060f4873037e19a0ba85ac28c133092046420c0e5066830c1600a6040818009a03a0148070016000, 0x116de96068b534b6c695a34c4491834e99a5cac01d1e4fa4e952b713800309ceb40258f0b6303068b1e06ad1e43e449c121da242ef1d6da11e50f030ae8981a12c00075a1698df71cc5130c22464d3666a834e09⟩,
  ⟨0x284133897448022d10d081c3de1e10e8070c3641a70c505fc2e414d09804982120f806f82f815a09e04982080d205702680f8032000, 0x8f82098c0d2983d2b0f90f1e22c5d43d83c43dd0c3269b33541a70481324cae13389e15500075b1712d3181a43252563e67019275c88586baa2ccf9127048c9a41a31da5e23c0c6924001851b5b0802f1⟩,
  ⟨0x36e1b10d5c6903231798ba45782a51470978442210100878037e1b20c685a82c013d08d03d41a00ad03e81a80b604e01e80c804a000, 0x391a1352493aae181d6800e002001c3c0c002005fff6a8d0f4b1a1e95cc344561c61dcc1018a2230df0f06695c9200386967c37f4ab5b89c00185d35b43f7a3e4606a1f3d171707c83f62609d82835304fc139a90c7e5a30e18ecb3e8a30f9da24f24c99a18d3099c4f0b28003ad⟩,
  ⟨0x2b01530a1c4cc24511b08ac42c1f10e206e833218b0af04f425411d08704001da0e0067830016c0a304a020c0e806a02280d001e000, 0x81812d6fa4811f65d9fb28022cf9127048312a503f82fb5a003d8a0076781bb0c07ad3d4300e7e100cd9fb0005acf29a1e852712628681513e292934984981a05449a492e34984981a0a940ab5a346940a20a7d7b627⟩,
  ⟨0x3851b40d6469033b1948c7c6203061778b2057c299141070c3701a20be857026e12808c83d01ce0d8067030411807502b00dc054000, 0x679f27fc932a67f149ec8f03544981a447d2807e300327818001911f5322269414683152a87b2948109bd852000450409fca63106e31ad3c2682261a1b400075a0035e97100261b6d9ec49a493401800dab613b84d8198560004e200000439ff74b5d2b951c14d72a3f8a400827ae147⟩,
  ⟨0x2030f907943a61c90dd06c03321810bb85902aa14809d84bc23c10f08103dc1cc0cf05d02b813a09003f01d00c205201d809001a000, 0x4a99fc527b23c0d51260691b74b66050f0351487dc8f429614d231f1a5b13e19a13509a6485d2c5099f11964cfe292f91e060c912d8aa455d2c8afa5927b4ba66⟩,
  ⟨0x22c10a88083ea1dd0e987003361840b885802a614409b84a823610607b83b01ae0c2059829013208403901a00a2047018009801e000, 0x937b4a5e21fc5211e90f030728900069ecd74959a5b410f9a67f14ae49714d198c248f72a7324e0906b54bcd9a1b13d0a684d302a92e91e0691ef4b0348fba581a494d2fe49⟩,
  ⟨0x2d215d8ab851225612608d444c21c0fb87a83c01bb0d886302f616a0ad84d825211c08483e01ca0d4063828813007303080f002e000, 0x24d7d2b89c001a84759507d4200016aa0693434b491e06005ea0bd6389e060052a08d740d5028025aed334961a4c24d402005eb2852e290cd1936720c519127861380074fceba0600069f7d6150a400542f7b4000617ada496ba5⟩
]

def tableLRLRRR : Table Block := .leaf #[
  ⟨0x257120086c3f41d50df069c33418d0c085b82bc14009484441fc0f1070034c18c0b7052025411207e03681780920380158084014000, 0x1fcc90006243d6800d685c400189176728ce94df963d0a585308c1ba27a318af302c729c99309250f7721fc525069714c998d248a289309388d82474d37922c84cf4269713c0d26c69606⟩,
  ⟨0x2f11608adc54028d141898046022310a88103e61e60e086d83461960b8859c28412f085039418409d04301cc0c8059020007c014000, 0x14a6a58000b15034db1a59050f03004e9578b97b800400587e33650d26692834b8a6258001f57824d645b09e254000f5b0300031296ae0148800951dece24f00075a001a4d644001894767360e951143e449c120304e9ad5007b689e19e06⟩,
  ⟨0x2ce15d8a6850a27b13509144481ff0f407443881b70d5865031216b0aa04f425411708603dc1ac0c705e02ac11005b02880c0046000, 0x3144d88803db44f0cf030e9a400189ff5a003619710006281d9caa7a5aa218f429614c2301a2c9c4d3c10163ce02c995274b36a259244e092e355d6b00659f224e091934abe296d8d001ad1007b3c0d5a000b6971380069638b⟩,
  ⟨0x2ca15d8a5851227c135896846a22810187e43a81c50d005ec2c814d09e04ac23c0f9077036c19c0a904f81e80d20440168068016000, 0xc24c5460056ae852c299b358d1aeab1002366c27000e29cd6c0c000c535ab30a2000c539b30006aaad9ced7a59da74b26692834b8a6291001f57824d345b09e28d000f5b030003145eaf44e2000d4e9b39be74a88a1f224e09⟩,
  ⟨0x2dc1668ae055229a13a89a04a624911a07fc3dc1dd0e706a433818f0bf05b429013b08b04301ce0da05a82400d605e01c8088022000, 0x3c8e45aadd893492679500ab56c27a0356c0c0ccab0000f30000021e19a4acd261262b7002b57429614ce9ac70d7563803bb3613c560001eb60600062aed5b0c40058ac36600b5581b38aa8001d6b0c40208ab3673bd6970cd25669⟩,
  ⟨0x29613e89a84ae24c11a88483f61d60e0867031617c0b8858027e12a090043c20a0e005f82c813a08203c01840980420158078020000, 0x30f7dd9baa269a44e09276197b1600761c0c363c5ba0226b41b54e01745b7ad8f33e449c123869b6402fb689d19e062834c0d1688003adb3b029b8b89c19d57c4c12aa069cf74b002a781a02165b09f8868cc6⟩,
  ⟨0x2eb16e0adc55429d14509c44bc24511c084c4121e40e186782f21620aa84c024c10107783941800b5054020c0f205401e8090016000, 0x1849abc400bd650a5c521c23027ede41b23023e5f0c27aba4003d740c000d5cfac0102f479001f135ed000189ab692e4e9584e077d5c3ae8180edab7f585f23c0c00355b9ae84cc27ab64003d740c000d5afac96ef4b978ae9c4ca74e09⟩,
  ⟨0x2d31630ae454c29113f08f445c22110b08143e61e90e907203621a70c8060c2bc12b08a03cc1d00dc05b82900fe06c0238088022000, 0x50a5c52192266f4d018224007002400bab0750d89f4cd09ac4d25d23c0d2fa6960697d34b034bf5a571380035806b2affac00001d54bd7a504299d53c26c46005eafad706287004aaf8d706e87abd8104d755ea0096bb4cd25869⟩,
  ⟨0x26a12e893848022f11108444041f80f1875037e1b00d3060c2dc14b09984a022a0f006682a012207e035817809a0400198090022000, 0x28527126086f534f8a4a4d2612606a05549a490a654984981a97c009c68312a400f4bcc7fc2243c26f0512000c663ad000d2df22000c667b398574b99a1df043f8a4a0d2e29d331a49559132869⟩,
  ⟨0x2d215b89f84de25c12688f843220c0fc87bc3b81a70cb06142ec1650a004c424011308303c41a40bf059023410605e02580b002a000, 0xa760863ab2e3e0781959cf23a368dd8934926b65006356c27b0d1b030688b00000400000a1fa1a4f8d2b92460d31aa0019abd093686ba14b8a418556023b154cdf45b09c0038d2f5b0300031a4eaf2148f5b00353ad374b824a7⟩,
  ⟨0x27412e892846e22c10987e03ce1da0e586f83621a20c886082ee1660a584f026012508b03ec1dc0c904b01fc0d005e01c8088016000, 0xf06d8fbb226ba44e09148b764302107cd33f8a5724b8a68cc6125f4d39927048d1a603ae843627e4684d4925f33583b89c001ad6f595ad56b6000eaa640d2e302c7818073ad5b59daab26a7564e09⟩,
  ⟨0x61c2fd9608ad854929992b082e3821af8cf06322f61698a8c51824211a88484061f80ea86c83041780aa84c021a0f0073030c024000, 0xde2eb5b488d3e3484bebb73cd1f000303a69f8b586000e2c7138a9c32fa6d3c40e0ddab480d1f347ae2d38aba75f49a7781bdbb468fda3d4e21a3c7165c54d3b766df03477037347cbe8b4789c3b4ece29e9f84fc4fc4f1038a18be1ff0fb16001e2561c003c4dc58007899c4dc548cba5b9c97e58826e2000e1e4cc008e10e1f224e09000f0db13c34e37e34002003e0e61e06000f0cb12000c717ade33f0bf239100327819c23c67c5862b14a0bd504caca021f34420e80da62271864a0fe9f0f06⟩,
  ⟨0x3681ae8cf863e3151790b54564295144096048223410787c03cc1c70d4060c2c812708d84441d80df05d026c12207202780b0016000, 0xc120224952e47001a3c0c48faa3e2c01efe4e003aa2e2c01f0a4ec2b000d5087818a95734ae2700063b8d6c85f975181a427c9a5801f65471ec23b3d6804f7947a9a800400447dc3c2340c3dbc75dad71380031d66b63cfbba8c0d1e3dcd2c043c49c4b8c78978be3000fb5e09⟩,
  ⟨0x32618e0bdc5b02b314a09a846a22010087883701a90ce061c2f21640a784c02220f2070830816a09604501fc0d8042015807001e000, 0x2061fde205d5801db7471b62203d5ffcdb147da5fef6bd1c02fd1ff32aa8f442a9fe008a97fbc0952c0080294d47994d26606d54e90ccd8a9ad854ca20314bfc406297f840452c60ce01befd2d84e013f0d2e11b048608bfb3f7400d2a56bd29c498337a49⟩,
  ⟨0x34c1938c285da2cc1548a184ee26c12588a03f01ee0e586a831216a0ab852426c10c07f83a01a60c405782680f606602b812804a000, 0x347e404d68032bc9e599625ad270df67d4f13330f58440261f224e09001802b4d60ab3d8d000d5fcfff8781aafa7fec4c013fd5a5fe6006d33040e51c3044c90d17a240081897b47a334640c907854c0a67f754ecf2a65c821a5df02af053389c0018f9b5a3fc440fb1⟩
]

def tableLRLRR : Table Block := .branch 15 tableLRLRRL tableLRLRRR

def tableLRLR : Table Block := .branch 29 tableLRLRL tableLRLRR

def tableLRL : Table Block := .branch 59 tableLRLL tableLRLR

def tableLRRLLL : Table Block := .leaf #[
  ⟨0x53c28b94289ca4db25b12548e044f217108c80437b1ae0ce46342f51690acc520283129892444c21c0fb84e01620980328118042000, 0xb048abbd6309ec102ae75d03156f6076b0006c56cf606162daea88a82b4d40d43da704d4054bdb07861b847661384cc519f5ab40996327d3ecfd8349b8b9b1317b2b61d2e1af1b13576d0b6962403ef4a4801652787f148004007291c3c0c002947e2606afe87f3d60734d5329f908f0eb0a3209a690e196e2599d9a337cadda71b0daa528f11fc095a2d58b3a2f228ff4f04e2e99a59c03143b4e94f4c51e16c1ab74e003a3d67⟩,
  ⟨0x3861b18c986062d31590a8c52c28513a09a44b823711688203ce1d20e3869830216009d84681ea0d4057827811a06a02e80b4046000, 0x312d425c8e18f0b585cc2b61f105863c3e17f103862c3da2d9f5a4f24f19b58d2346784cc272adac28d740c55a584dac001aa0b4d4d59a13000d4ed9caafb0835c00351b672a5ac1fd6000d53d9caa8b0735c00356f67b068ab8d75b9a5a8d2005e6d61fc52001001f3630f0300079b789⟩,
  ⟨0x4031ef0ee47343751aa0cbc6302f31670abc518267122087c3f81cc0d486702d816209f843c1d80dd06902bc11805c02900bc04a000, 0xaa52326b646300075a00f3c54400191875a0039dd710006463d9ce2da5917466fd6800322e6b5cd64ba880068b187515a459d680068cb87518e457d6f09f0d987e1361af0d3875a761bb0fe29000ad330d98781969786ac4e1bf0d1862c380230cd87c893824003863c4ef368578d000800f0c38781800585fc4c0d2228003ad⟩,
  ⟨0x35019c8c506062de1678b0053628e13f89d44d023310e07f43b01b30cb05c42a812f08f04342000db06802ac13c079037812804a000, 0x94a74a000c907ad1a38867b242ecf624d249988c006d5b09dc26c0cc2b0000640000061cc3ba500374e8e2ea48edad52b2475d680388c9c30f91cf5a00e3f270c76471d6c99a4a0d2e2991b4007d5e09980065bd5b09c00391a75b030003233eac00197ef6232ac8d3b3⟩,
  ⟨0x2cc15e0ab453c25412208d444c21810287e83da1c80d2866c2f01670ad052427c11b088040c1bc0bb05882380fe06002980d0014000, 0x90c6fd4d7a980037f200163b4027878ec6a94c7926c86a9913099c4e000c933ada5b168f230352d4b438b1934d99aa0d38240174b0c5c2671380032476b695663ac8c0d4aa31c62ce23803c6d4b713801b254bc676440152a06⟩,
  ⟨0x32d18e0c346062e41698ad054a29914709fc4b424811f08bc4302010f5072c3741ab0c3054c26c11708003d81ae03f0180080020000, 0x5c693093036d70c74d1a34861dab4f6c4fc8d09a92480b125d6b5d247819b154ed9a59db34b3c1e942b6c7a3c29a672487d739f69c3ea9cf43e6d3803f249df3e9da5d002c7819f669aa5800499200ac7a8026ff4002001801000a006c3caa688c68ac690c6⟩,
  ⟨0x243116085c4141ef0f2874038c1af0cc06042e41670a904cc22a10b07a039819c0c0054825811207a036016409803b016008801e000, 0x4f6da5b0553f8a41a8353c0d404a981a792d2a4f2c7f0218f912704831aa43ceeda681e60d8f03713ec9f21ba1d21fa86da598f29a1e852712628681513e292934984981a05449a49⟩,
  ⟨0x32718d0bf45e22e41638a8051227c12b88e84602130b70544288135094046c2180ef07003541700a003c81b80a20400158084014000, 0x309c04ade5708ce270067895cef598032a9f334ae2700064fcd693939cc60626e71958b443d620b28c01540b394402901400b184919961f240324fe295c92e29933184901b2094d649c1200e3b2981d288c640100a4f89b1900a538267a1333c0d3cfe9606⟩,
  ⟨0x33a18c8c085e62c61588a9852627c134895849222c10c87f03861b80d586182ca13808d83e01d60c605182640ec069022009c03a000, 0xf6cad6077b1cd258026d7836da838557827e145cfd5a593512c8a274cc00d7329ace4c0256f27d7e0b5001002b3c26c33058b289eb75ecabece553af455d67006ae938aaeea38b7138003286eb457f74ec8c0c2beba662dc4e000ca11ad2a2bb98c0c53d732b⟩,
  ⟨0x2ce15e8ac052628013a89604662160f7874836a1a80c185982b813f095045420c0f106e030c15409b04701fc0e805b02100e002e000, 0x2bcd36660067994ce72684c00ced270a5653ed6cd938c9e689ae70938033849e6da9656e270006538d6d1f514c606ab6a095f7a2a41b5537a9aeb1535daa9d13075e806bace24c19bd24e0908cb75e380b9e060c8db4b581a8c7⟩,
  ⟨0x2db1620ad455429313b096049c23711308604021f00ec86f033e1780b4054426811708283ec1ac0cc05382280da054019808001a000, 0x16c4c7c8938240e364e296c4b4091bac78187df648c1a6286216993e46903619385d9f2bc285795803419e927a8c6b4c5936506b2bb2452959788f0300072a76b6069530001d6d477fcc6c2bfa57d06ae7db00e7b3c9a890c113666⟩,
  ⟨0x3b11c60dc469833d1910bf85ce2dd1630ab454628412e893848223010988203f61d60e6069c3141770ae04dc22807c02f810804a000, 0xcb09ad00c2e220024b0db3308e018442c030701c2a717d2c0d38a697e005cf034352034b9ae8fa1a4e7926ccd4c699a00193c2661384f96b06ba0609ead5ed600302ca60093007f50707fed5ad6633b383871a109704f8589063032b36a0c1064e2e874787a59079389b9249c01c4e4e18a4acbad⟩,
  ⟨0x278132896848e23010787b839a1c20d886102da1560a604ac23c10f08183d01ce0d806082a812608003881980aa03a012806c014000, 0x1cd178262145ce77a59b0010b5cd78025ac00e6bad782470d73560020056a9ceb4b39c696060199a7b5b09e525e231a47715ce2a9cbb4b39569672fd2a2287c89382478d31105c344f0cf03151a606⟩,
  ⟨0x3161860bac5ac2b5144099c4a4244117886840a1fa0f2872834c18b0be05c42ac135088841c1d80e205e82cc12407302c00e4054000, 0x2069d39d7b683a2a6756746de059398003670319ccb48332a6a8652554c89aa7c55578253e9560bf5c1c0e0af541c11ed83e449c1201f5426716706da0101fa20f0300bcd098189ba96b35b030164df5ac00da9a380fdd0b0036b28e692c021ebb554a⟩
]

def tableLRRLLR : Table Block := .leaf #[
  ⟨0x2b014d8a184e224c12008ac4382070f9074436018f0c205b428012908903ec1b40b9056027412007f03901840a4048019809001e000, 0x9f954f7caa78e953280b76ac7e4607454f0a6df354e5b2a67bc0ead73dc0096b0039edb5e090321960033d40056a9dcb4b3b8696242658134efd9c0f6776cf4293893e66e534f8a4a4d2612606e85549a490b8549849⟩,
  ⟨0x34b1a08c7061e2ea1698ab852e28012d88e84121fd0f9075c3781970ba057427011707903881960bb05202340d805502280b802e000, 0x40c000cc07ab7188003302ecee03d2800370cecee02d281a4c700065fcd683cd07dc621004021da4fc8d898037c83dfafb0d97d4001d6d37598791036d8e000cbe5ad06fa01b881b242331e8b180c364db635a84c98365933fc0b76b0345934d8d4a83267d164e7a8cb⟩,
  ⟨0x2ca15d8ab050e27a13589844a821f104078c3a01ab0ce06342d015b0a6050826a100074836018e0b804982180f206802b80c804a000, 0x3624d249b89c006d5b09e326c0cc2b0010000000021dc43a5986c001d687491002661dd9ec49a4936db000dab613b84d8198560012c20000043b6c34b86692b349849983000ad5d0a5853526b1835dc42004ecd84f3028007ad⟩,
  ⟨0x33d1970c245ee2ed16f0b1c54c29c13b89483ea1bc0d7067c31c17d0b7052427812f08d04141c00d305702900fe06a0228080022000, 0x69266487cd35a6b23c0d0926854d28014c559e06000663cd6bccd3206c68b400898410816812c2dacf45816a00200567ea1bb53619a4acd26126633002b574296149392ac1c5577230025b361380073166b606000662ad5835ac400198b366005dc7fb33c8f126d⟩,
  ⟨0x3de1ea0ec46002bf1590a344d025e11c885040e1fa0f7872832e1720b2856828613408783b018e0bd04c022c0d00380158068016000, 0x206876fc23162fa0e56341352d1998e54e9dac98e808d00e818d03a7803e0613cb4004d3b89e65f00075b31abdc7b181a6347b875702e43f7a7a14b0a71343ed02c6a605787d8001d3c0ad0faea584f89a15bd318479940001d68007e81918596652d9c0d0b1be7bab7138007e778bf96fce80158a9335419f224e09⟩,
  ⟨0x3cf1dc0e4c6dc3571a00c6c5ec2d11638a8852626e13088f84162010f506e834617e0b3854027211407882f813607802a8120046000, 0x5065a52a5ee6ed9c456000e9e656d34453a6000615ad3c2b733f6b665200074f034ca7332eace238007331eadc4e001f7e62e6607bec002d540d448697378058f6661c0ee6380df338eb40dd63dfbccd030d8f3368089ad47ee7970ee830d153e769c00fef7c4fbe85c389f848b8712e270006666d6c3bbe1591⟩,
  ⟨0x2d51630abc54827f137896849624011588183d61e10e6070833a17a0aa852c24c10307903841a80af052024c10c06102b80c804a000, 0x16a9964764e0900ae679d5c163115a9f224e0906854cd40f906b410e653c0c148a981a69600075a001f8d6466999a63670300033496b4019818c8c99a4a0d2e299a34007d5e098735b09c0039a275b030003343eadc62000cd13b3⟩,
  ⟨0x46121f106c7d63c81d38c105ee2d81598a70518275135091444820f10007ac38c1b10c6050825610e07682c011a06a02f80f002e000, 0x1f42fa26255c7f49c3fc495c5f48c3fcbbe7d8700e9bbb3be3023100025593abaf5d3ab52e692467b58149a7c335071454797289d0d381dcc9e0c6dfb59382406e873b56137ebf6707954f6a6eb854cd645626b41a54f3580055adea6a44c05eaa200ee1e93764d7a0dc9eb1fd42ce02b7a9f525eb187ea400130e003c7161e1300071c5879a998e0d68190c9⟩,
  ⟨0x2f416c8b1c54c29814389d84ce24211a88a041a1f20e687003361910b6056c26c12508b042c1e00cf05e82cc13007302900b4036000, 0x858060f0f837a5000d9f086c334959a4c24cdba0056ae852c290450216019fc2eef22bb372c27000e6d6d6c0c000cda9abc13895cd24fece2ccf9127048066b09133addb69788f0300663099b24001d6800d6c5c412d9b2f672d8349e5907⟩,
  ⟨0x3af1a90b9c5ba2b81488a004de26011d88b84422060f587183721940c505942a812f08a04141f40df05f0268120075035811804a000, 0x4bc669b9a7200127d4a6ce9e5e234d8d3800055a14fa54d8d3c0d380c929ad10b270664f86692b3498499bf000ad5d0a5852089242c032385de18583ee584e001cdebad8180019bcf57a2712c0600cd98223907c893824031984d8008bdb402038bc1e060145613030003373eb4006beae20884dd3b3⟩,
  ⟨0x6253031770b7a5932b49528a404ff26910bc8183e91e30c8c4e424f10f87e838e1a20be85b82c813f08904201c60be0458198066000, 0x1b977c51f7bef2dc947de7c128fbcb81ee1a3ef3debb868fbc767d1f6a6f0d9d476d5823b3b6a411366d9c59c5dd23ec77d23ed76f1b4f5c1589f563559cd3d642b3389ad2d67b175a4ad1e2d89b76da3e877c23e976e1b4b5c057701659544d3b134edac7ceef7c7d0edbb3ccda52e00bb78b2aaa1e9c61353fc38c1461153ec394232fde9cb0128425fad380032fa69c9c3913757491e066836572d5800ccece8d9e06000670ad6b4112b76c65e997ae5eed3cbbb2f769e5e397725edd38007300b34da7⟩,
  ⟨0x5c42d99640afc5742b2956ca6c51527f139c96e47a2320db44d025c11d88703ee1d20d785fc29e10e074831016208c033811804a000, 0x1934801e9d98d2f91e06549303000339f6b7e58006e3561696abcd2800975186ac3aea0002ba7c34e1f29f861d5c6c99914ae056a645f000956927207ff776240878417916dad8bb1c2f4e3ab0d9132215bead448bc000aad04e38ffceebc80ef07af20b9036d4c5d0e15a78467f182cb4801fdf479cc87edd6ce62ac06b61390dec3c2621370ddc3808d37fa2bc3c882011137cd1569e460918b5201548bda7ee9132c748cdab9636470d5d8c18dda4c6ac5ed25864ea9ac⟩,
  ⟨0x28a13e89b04c225411788304041df0e5069c32817c0b5857829a142098849822e0f206f82e816009d04301e40d00380158068016000, 0x24cd0c6984ce279d80001d68042a1191818023506c5830a9c025504c5f2487c6e2871a34e99b24d3826e0d7098c23cea2000eb4344880073a9ece060c517566695c4e3c6ba79003401d8ad334619f224e09⟩,
  ⟨0x27f12d094047222c10c88043e81e30ea07243701a50c806182ee16d0a404dc2240fb072035418c0a104a02140f606e01c808801e000, 0x913c46ce068c6d96e270e516ec3d15c668d33e449c1234699211a27067819624c0c000cee9ad1c3880033bb6ceaf9d2d5efa5d8934926b01001b56c278c9b0330ac000f50000018757de973c449e49⟩,
  ⟨0x28b13a09884b024911f88684061ec0ef86e832e18d0b5054c28413308f04241f80d706202e814609204281d00d205202380e0026000, 0x581acd2f11e065093034f3e000eb678768d639a5713cf36000eb71f8003c8c0d8fe000e2eb83d2c19a572483229d48956e279e44001d6b3e9181a91d658d1a70cd7269c122a6b2e1318479e18001d687c91⟩
]

def tableLRRLL : Table Block := .branch 14 tableLRRLLL tableLRRLLR

def tableLRRLRL : Table Block := .leaf #[
  ⟨0x2ae14489e84da23d113087040a1d50e006ac3301830ba85902ae14609d846021a10006d82e015c08b03f019c09203c0158070022000, 0x12d99f2366611d8572d6000800f1559069606ac6f4be58c90e4730f206a90a35487a873e255f50c3269b33541a70480272338b84ce279ec0001d6e4440c79181b226061c5b89c0df6593bc35958668b33e449c123069⟩,
  ⟨0x2ce1618ab8546296138893848822110707ac3b81b70d205fc2ea1620a584a822a0f406782f015a0a204881b80b204f01f00d001e000, 0x304c47aae13389e7e000075a00897a64606004cbcb161f21c0352f0c598479f64001d687091000e7dbd9c0c1aa2eb30d2800c23da610acc003c2f6738527d0d6a2287c89382478d200b9706344f0cf03151a60600067c6d69a51⟩,
  ⟨0x28f14109b44a424511a08944342090fa07883b01c90df866830e1700b3050424011307703341860a004481d00b20440178078022000, 0x389c1bd56b5c6aab0cd1667c89382460d3420ad2f11e065093034fee000eb7ea48d6a1a581a7f300075bc6e03d71713cfe0000eb78d000ee303643c0038baec34b2d8a7864ad4ea4ea9993548c9a6ccd5069⟩,
  ⟨0x29114209cc4c825912408bc43421010087dc3a41b90ca05f42cc15c09b84781f20e406782f014e09904501f40dc06302000b4046000, 0x1c668d33e449c123469b8087689c19e06589303000340d6b406c9e2000d039b3ade74b5bbe9606a050001d680d63c4052a05b67206a90a3548748732255f50c71260cde92704801b2558ba050f03649c0638b⟩,
  ⟨0x3121778b3056c2050f7077839c1bb0d606803221800bb057c29413709204302040dd06502ec15c09f04a01f40d406002380e8042000, 0x351fa56c580072eb89cb76199846269f1a60adc757b888bf944e5127b8199e65db4e075327eb1b2b1ab7449849c46ac93026781bba06583029e1e45ea087b65e8781a83100075beca44e24c19bd24e090dad9760a1e0668c175b89c06fdd61d7c1eea⟩,
  ⟨0x43a218102c7f83d71e40eec7523921bd8dc46b433918b0bcc5a02ad145099c4882210ff076439e1aa0c3858820a08c02e0118046000, 0x2060006863d69c510012865d99a477159509564be96c98d2c0d649e94fd6522cff5ecee61fde50fbc3fb8fdcb8987cfb930fe7ef40627efdf71c4c3ec00b87000d0c70f433a19634001963b4f03509a000eb4003a98c8a85d427ecdee5946e51c628dc7e5d9b4ecc63dc928d334c463b8fac514a37a7000e4e72f187d2c61b4c3940c4ea432e78b⟩,
  ⟨0x2a41468a0c4d826112a08bc4342100fe87b83921ba0ca862c2fc1670a804ac2100e3066029c12c07f03601740a4041018006c022000, 0xb2f34b035981a584ce27000687fd68d0ac6063fd16611c001a1eb5a6944003a1f3670330aeca4d2d94fa5a1cc001d680074bb910006875d9dd75a5a1bc001d6e89c6ca8d2a2487c8938247cd3966d13d33c0c5669⟩,
  ⟨0x25412488e842a2060fb879439c1b70d206643101710ab052c27c11908203e81ca0d806182dc15409703e01940a804501b00a402e000, 0x84d89268a201035a611cf25e2895669696cd4d28e08bc13c26bb32b4a0eaca9e13389c001a2575ae70b1819dd956c2713455c23389c3945b1802aab2f74a30677096691dc565425596ba5⟩,
  ⟨0x22f10c080c3e81df0e506cc3381910bd05942b4145097046c21c0ff07883781a20c0058829c12808503a01940b6044019807001a000, 0x4e6ec907054e4a6c6f54dd82a653365c970cbc12da3b2f67157825ad15754b31e5343d0a4e24c50d02a27c52526930930344a8934925e693093034c9acd1b34cb94cf6c4f066⟩,
  ⟨0x2eb16d0b2457429514409ec4c824d114086c3ec1ec0e386e832a1700a904ec24810d07b03ac1a80bd04f82200e204c01e809802e000, 0x619a4acd261268e1002b5742961489d4cb03a59787880ffb9613800746d6b60600068d8d5b0c4062a36b6603c43e1b3ab7b8b1ebcc64cbacc99bd19733932f04f094cbd5c98f9b4f16381e2c7d9b597280d3ccc7fd4c068327953389ec9⟩,
  ⟨0x2e01678af855a29c14689a04b624e11a88703ee1ea0e286ec32c1890b204fc25c11d08803ac1c00cf061027412606e03080f004a000, 0x91734a39b0cd25669309347f8015aba14b0a4263dd6031cebc43c014dcb09e8f8000f5b03000347b6ad862043d1f1b3003620ed9c99a4a0d2e29a3bc007d5e098735b09e8eb000f5b030003474eadc62000d1d7b3b53b4a03ae1a1b3⟩,
  ⟨0x3001798b805a22c615b8a7850c27c134894841a1ff0f887883a61ae0d0864030c1770a104bc21410006d83081560860398138052000, 0x93359087c893824d248ad53b4311a1e06805136a4e9426400400b19803acf043490db126924daec005ead84f266d818f258004e20000030c384380334876b606000690cd6c980bc6d6bd2812f484eb43e43803f483eb4098a41b5b4402050ce7⟩,
  ⟨0x34218e8bf05d62da1668aa053a27813589184782170f9073436c1910b6051c26011d084038c1a80af04d01d40d605802080d0042000, 0x1a5135b18c01b719334941a5c5349f800fabc135fe800fab613800749deb6060006939d580035fc6c4001a4ef675fb69693500075a000da9fb10006937d9dab3a50fd0f04cada4bc584d69847000692dd68312c4003a4bf670307e8bb5574ae270f117603614ea⟩,
  ⟨0x36d1a90cec66231a1838bf45d0237115086c41c2010f687803a61c50db86883261860b0853825a10807182f813207402780f002e000, 0xf81aaad8ed2c0d6c5e970143c0ccecab0010029764ba00300400500600700800900a00b00cb3e19ae53719b8cd39e8da66d33450df436add9a3534998001a5435bc5244006db6ce5b7529bad20b294cd6d296409eb48afa52b5a443d293ad0006948d687e91000694ad9dadda5⟩,
  ⟨0x2e51600ab8548295138092c44c20f10287b83ba1cc0df866831e16a0ae84e025c10907202fc15009b03b01840ae042019809002a000, 0x3dfb9ad2f91e0638934c00003ad0006fd7d880034c16cef9fd2c0d7ce6964cd25069714d2ee003eaf04db8c003ead84e001d2e7ad818001a5c756000db83b10006973d9db7fa571380034b66b652163034832acf23b84b308e0faab⟩
]

def tableLRRLRR : Table Block := .leaf #[
  ⟨0x21010087d83ce1cf0e006d435219c0c285d02be15509f04d023a10c07f83a81c00d106382c013008c04101a80a603c0158070022000, 0xcc93824e24c92b443627c4d08ce29beeb4b8267a1333c0d7dde9606bf2b4b4a67f148c199e06c893035f5da598448784681830122afaad2df79a58c33e449c123469⟩,
  ⟨0x26412c891846822a10988243e41e80e886b02f21660ab851827212408d042c2020ea06902ec16207e033815809203a0168080022000, 0x84d70a24ba4781afc9d2c0d7e5e9606bf5b4a007e023a7003b01000334fd521ff24d299fc523066781b224c0d7dc69681121f005d340c0008023801eaafb4d2e699fc52b925c534663092f269⟩,
  ⟨0x28113b89804a622e0fd87903ae1b20d4060c2d81590a604d0254117079036c1900b7055026c11c081039017c0a0045019007401c000, 0x1036067a571380038e7eb31cec73c001d56049a5613e396001eba0600071c9d6603da52f10fe2908f487818394480038e16bafeed2da087cd33f8a5724b8a68cc6124ff44e649c121e225e6cd0d89f286⟩,
  ⟨0x28c135894c49023510807bc3941b30d0063430016f0b1055428c13309104542100f5070033411807d03801940a804201c008402e000, 0x785bb7fc2243c26f0512000d401ad001856b880035016cf04ed2e66877c10fe292834b8a74cc69255644ca1a6852e290c91337a680c1120038012005e321a86c4fa6684d62692e91e06c0b74b03605ba5⟩,
  ⟨0x2de1648aa852a288131896446822110107743701930b7052c24c10f07d03b41bc0d005f82c814209204401cc0c804f02000d802a000, 0x19d57b740754c69556c27000ea20d6c0c000d43dabf852201f6b54f23698f75b50d0003ad98ea818d8800350c6b4003357c8800350d6cf067d2e0929e8527126086f534f8a4a4d2612606a05549a490a654984981a174026da0c4a9⟩,
  ⟨0x2f51700b5856228c13e89c849a2280fa87ac38c1bc0cb85c82ca14008d84441d80cb05e82bc14209003f81c00be03a015806801a000, 0x1502a781a664a1075600447c7a7c8938240018f835341e47bdad00040038f7b4f0300051ee6a6060006a38d6c6ff41b6c5c4f51a8003ad99563d5d8c0d32a47a7ab0420f153d50d543590de8693e34ae491834d4520066af424da1ae852e29⟩,
  ⟨0x3b11c80e106ee3541920c345ec2ec1648ac851a26812e89204462170f907343501970b9053427e11a07a8340156086037812804a000, 0x116000b6984671380067438b9d04e840038ac2cb4b180b1e06023ce7316b6db1e352009f531fc004fa984c0c8a7008aa56d6d23436f209ea640c904f5201bc84fa71e33806f5286b401d8fbb5394347540056a63e8002b52004c7cfa999b23ead5800320f6a6419d349d6016e9c00199d74f20bc831ab⟩,
  ⟨0x2f416e8b40556278137095c49023e10c88304041dd0e986b832e17e0b2856828212e08d84401f20d605302140ec06b02d00dc014000, 0xc30b4ae270007271d664df9380005aa81b09cd2f247818006c9af58e2781b267000f5d0300039336bb092d2cd4a3a64e65d38264a61d958225f444e091d659731a21ae1e62931921a61e2dc022cf9127048c9a517d3a8c6800c59001d9e06⟩,
  ⟨0x22b10e08443fc1ed0ea872c3701ae0c485f02ae14009484441fc0f1070034c18c0b7052025411207e03681780920380158084014000, 0x6449c121e22660da11e90f030b089818001aa735ae310006a9ed9e1a7a5c36b4b09250f7721fc525069714c998d248a289309388d82474d37922c84cf4269713c0d85fe9606⟩,
  ⟨0x31e1878ba85ba2d015f8ab851227c12b893445021b0fb07443741950c4058c29813d09704241f80ed071835814208a02b80d0026000, 0xc24d5860056ae852c299e358e9af2d3002366c27aaf0003d6c0c000d575ab618800d55e6cc001cb3367957e96ab500075ac31002aab7d9e555a5d8934927145001b56c27709b0330ac00445c000008789fe944288519355d3cc3a6a98715d9e6b3a3e87⟩,
  ⟨0x2da15a8a4050227012f894045621e10887f03ce1c20da864030c1610a704a42080f5072035418c0a104a02140f606e01c8088022000, 0x2bab935b0f48003a7b54d86692b349849ab7800ad5d0a58524caab06455e5d80096cd84e001d5afad818001ab57561f244001ab5f66005e5cbb33c8f126dd89349272c7001b56c278c9b0330ac0066840000087960e970cd25669⟩,
  ⟨0x4031ec8ee075239e1be8d7065e3251820be85aa2b413d896845a20c0f586f83221700a184581e20cc05a82580ee06202680e802a000, 0x57db0161e8e0115d967c893824006ba6d37eab036d001003ae7b3c0c0055cb6981aafa00075b7dcaf771ae9ae0ae2adbb3d7cd74d9eb96be2ba2cf5f162367b0fb10b3d87587d86d9ec2abdebd6cf7755eb67aebbb9af4b3d76d77d7959d4fca88752000d435a9a8774d27e50d2656835a383ea9fff95a18a1eae6004b5a0d4a7⟩,
  ⟨0x34c1938c545e02cb15a0a744f826f12108e042e20d0f407443481830b204fc25c12108804141c80d9066029c11007e02e80f803e000, 0x7312d6150a4005d52db40006a95da5993a5b33b4a00b61367f14800801d83d9e06002b05b4c0c000e60daeb2ff4b60f6015f3679d1596b5801b3547ac4c691d68c9a6ccd5069c12b1f3956b84ce27ac2c001d6e89b195181a71162ad6006c5d1ec3d88a5d81b1147⟩,
  ⟨0x29514309ec4d424911d08b44442130f907a03a21c40cf85b02aa14809184641e80e3069030c13c09104201c40c004d01e00bc014000, 0x19927048e1a401ec5ad0d89e4cd09b924800d85d9e06b3974ae270007326d6664b9930003aab3834ac27cc88014d740c0096641acd334961a4c24e638005eb2852e290d11936720c9191278613e628001eba06⟩,
  ⟨0x2d31620ae852a28813f096449e22a10987f83d21de0e486a830015f09f04bc24810307002cc152088033815809203a0168080022000, 0x5247818006cd4758e27818003cd3b5d036696000ebace1d2d31aa62a1538261e1593067151e5ecc09c3474bef71b3a61591d9f224e09001b26b4f35c9998d0014bdb1eb3c0c97764569b21010b3e699fc52b925c534663092fe69⟩
]

def tableLRRLR : Table Block := .branch 15 tableLRRLRL tableLRRLRR

def tableLRRL : Table Block := .branch 29 tableLRRLL tableLRRLR

def tableLRRRLL : Table Block := .leaf #[
  ⟨0x24e11b88a843a2120fd877438c1ae0cd86382fa1700b18550282132093046c2140fb07303541900be053827410c07902a008402e000, 0xc4a63d0a585389a29464938a058e4a2326124a1eee43f8a4a0d2e299331a4914512612711b048e9a6f2459099e84d2e2781acf3d2c0d679695c4e000e6afaccd57356000b550359d7a5⟩,
  ⟨0x2fa16c8b3057e2b4149899848a23711308544101e30ec07143701930c485902a612e08b84201fa0e6061829413608402f80f002e000, 0xeade6cf429614e26b6f036b481adba000d9c0d2dced3543499a4a0d2e29ae64007d5e0934916c27ae54003d6c0c000d727abc1389f439be6cc45563e449c12069b27a26007c68107418f03019ec90006b88d68007a1d910006b8ad9da63a5⟩,
  ⟨0x2a314c8a084e626612a092847a21810707dc3cc1d50e306843281870bb057429813309304041ee0d205882300ea05001c808802e000, 0x40d696e96e23f8a4b847819c52009e757ae81ad3ed2e99a4b0d261273a5002f594297148d1b02a51e4306c55927c309c003ce775d0300039cdeb0040e35e4000d63fb4b4bb4a026d63bb48d0192fe2b2704be92cc⟩,
  ⟨0x33a1970c885fa2da15a8a404da24811288003d21c80d385e82b214c09e84c024611407983901b20b805001cc0d004701b008402e000, 0x291b118001af8b5b721e2c646be06c6b5b5ef8003ad001ee0b22000d7bbad000fbdf22000d7bfb3c17f4a51b57567bbdbbfb3dde5df5ddd9ee90032cfe295c92e299331849006ba4b4d649c12003743693a6288b99001002b3e26b9d002b4e899c4eccf035a57a5⟩,
  ⟨0x3061708b485822b414f8a5450c27c13288c844e21d0fc078437c1af0d005ec29614108e043c1d80bc059026c11408002e8060018000, 0xac20f4ff92694cfe2918333c0d912606c1e34a000e0f400169f1340c000e0efa9c1d34bb94005e1ed24c249bbc8008d48007720007c3c0d837800ba971380078cb8bdbff1900058a81aeead2c099e06b96717f1600200400600957767846a46⟩,
  ⟨0x21f10a88183f81e50e6870c36019d0c8060c2ee1640ac850426011908203bc1c40cd06002cc14009303d81c40bc05402280b802e000, 0x40d512606c2874ba5850f0361287b210f429614c2306489c4d01050fe269c2eb4a498671eb33d9984a4cf466a3316e87f14847543c0c29a26066c55842e97087d2e19da5⟩,
  ⟨0x26a12d893447422d10e08344061f20f187483861b90cb061c2c81550a504fc26411b07b034c16009904101dc0a803f018007c024000, 0xe24c50d02a27c525269309303629a4d24951a4c24c0dbdc02f634e2481737b58f6c4f89b1330a70b4d280a56186b76d9b6ec4813b6d5878afd92fa23270480f6edd8b85453fe499533f8a4f647⟩,
  ⟨0x25412508cc4522120ff87c83b41d00de86cc3381850b7055c29013d09604241d60e106502c814c09404401c00cc04e01b808001a000, 0x81b0e9d2c0d880696e543f8a4351a1e06989130361b9a51fe98fe5431fc0963e449c12386903cefdf1a0798463c0dc44324fe2a1f11a9647a46d1028781b01122b0ccd2e1cba594d0f429⟩,
  ⟨0x26112508ec46021910207983b61c40d906a03221870b8059829e12208583f81de0e206a831815e0a004a81f80cc04801e809802a000, 0x1b7b26b24e0903b192d1468ce04131e136802c92e91e06c4834b036245a581b139d2da484903059f20c63f8a5724b8a64cc612436864d649c12072b26074a22c8104c7c4d84132704cf42667⟩,
  ⟨0x28513d09a44ae24d11b08b042a20b0fa079c38418f0bc05ac28c13c08b84001da0e006402f8156086037817008a038014807001e000, 0x109ac4d25d23c0d8b6e9606c5b74b0362e7a57138003a446b3487d220001d562c9a5613e908001eba060007482d662bda52ed0fe2908f28781838448003a3debb150d2d5e87e4318fe295c92e299331849⟩,
  ⟨0x2aa14a8a184e226212c08d44401fd0f2876838e1a20bf856828613008e84401fe0f207283581860b2052826010a07002e807001a000, 0x281552692429952612606c5100271a0c4a9003e2831ff0890f09bc144800365ceb400389bc8800365decf18ed2e66877c10fe292834b8a74cc69255644ca1a6852e290c91337a680c1120038012005e893a86c4fa66⟩,
  ⟨0x29a14609ec4d425b125089442c2050fc07ac3ac1b50d0064c2dc16409f84b02160e6061827810e07203281580900370150064014000, 0x2686f4349f1a57248c1a6cdf003357a126d0d74297148322ae64c02ee6344ab613800766b6b6060006cd4d5f029100498cb98003668eb4003f12c88003669ecf1a7d2e0929e8527126086f534f8a4a4d2612606⟩,
  ⟨0x2f71768b2057c29914109ac4a8249119087c4182010f6072435419b0c805fc2b813209404241fa0f0066827410c0730348118062000, 0x40da788007ae818001d3c35d8e2e975e564e4d4c9c138f4b328f44ba689c126d4abad212a70f2a40451f224e091934e357e7d8d00329001d1e069440169308ce27000fcbb17f2df9b8007158e26970143c0c019f94e2c2b54f5ad6c0085927⟩,
  ⟨0x2b114b09c448223710a07c03ba1d00df86c834a1960c285d82d415f0a704cc23c10d07903a01a20c404f81b00c404b01e00c801a000, 0x18fc2603e58675a001b0404770f03584c23789084401307ab90fe292834b8a64cc6924bcd2612711b048d9a40b0e8449099e04d20180c1e06c7574ae2700074fbd669f3a7d0005aa81b1cfd2f247818006d3d758e27⟩
]

def tableLRRRLR : Table Block := .leaf #[
  ⟨0x2ef1650acc544291142097c4a824111a083c40a1e00e786a832617e0b7859029e12a08784141e00e606082700ee06001e8068016000, 0x1d6a46cf487d2c99a4a0d2e29b4fc007d5e0935116c27000ed3bd6c0c000da73abe1388003a916cf3d4d2913a9f224e0906454c0980046b410e253c0c140a9818001b4b35a000c08db10006d2ed9e3e3a5b30d9931360d09161f224e09⟩,
  ⟨0x2f21728b6058a2b21468a004b625111608643e81cf0dc069c32c1870b1055429013709304041e80cf062828012606e02480c801a000, 0x2852c294ed161d22f573002366c27b578003d6c0c000dab9ab0d122000dabdb3000756cd9e93da5c334959a4c24daa80056ae852c299e358e9af564002366c27000ed4dd6c0c000da97ab618800d6a6ecc001d57767a46694001b51b5ac31⟩,
  ⟨0x3311860b705a42af1518a584e624311608743f01d50d8069830616c09e04b423c10b07e03b41900bb054027811605602280d004a000, 0x1690a8a7ad000c3400078781a19c005c4c23389c00344fc5d13a898001c56ab3a5308f6bd0003ad000d12b22001daf9b3818003447c5eaa3a5000812218187b54c791d1946ec49a493a5a002dab613d068d81832458004458000010f0cd2566930936b28015ab⟩,
  ⟨0x28913a09944b024911f089c4202060f787883961ad0d0063c3001750b3050425e12508b03fc1b80d205682580e204e0158070022000, 0x13deab3893066f49382436965d802c781b35965b89c0d765d2ac2995266a833e449c1269260ae01435a6b23c0d092742ed2800a8758781ad8c00075a0643460a5b63b6743686ae1e1aa008c3e449c123269⟩,
  ⟨0x31d1880bac5a82af14509dc4c8259123088c4282090fc075434a19b0bc05b02be13c08603d41cc0c104f01e40de04c01a8080016000, 0xe310006dc7d9ea91a500675acd9db8000a6b6ce44b6a89c12ca22e8d0008c3e449c123269b9bd21b1a001a31800f0f03518400b8984671380069058ba40d1fc0038ad4df4a611c001b6b75a001a3ee44003b6bf670300068f58bd4bf4b8d2a9a3054e09⟩,
  ⟨0x3071710b2c5742a914e09dc4d824711d08544161e60e086703121640a784c424611907a03441800af05101f40e406102a00bc04a000, 0xd76f26b6d24d3499a4a0d2e29b77c007d5e09001ad21d5b09c003b76f5b0300036eceaed1b0007620316b85b30c10e008dbabad52a53818e098f24340c000dba1ad0065d3f2326692834b8a6dcb001f578261cd6c27b71c003d6c0c000db8bab⟩,
  ⟨0x34a1928c005ce2ce1618aa850e27212688d043620c0fe879839a1be0da066c3041780a984e81f20ec06f8318142088031812804a000, 0x178b5e368081daefb4fcf674fafdba704fa7fbb01a514ac3831a9edfc00935a2d6ae7168373e649549207431d76bdd7491e06bdac7580e339e060006df0d6d5d43c4001000ad2f03074f06683300d8b9edea02cb5a0318e70236de8d680cdb9ede602735b6f28141ad⟩,
  ⟨0x3251800b945b02b41550a3c50a26012488b84121d60df86883301730b0854027e13008583f81e20d605d828010a0780298124048000, 0x46c25ac02f720fe290080fb50781805d884c0db058003accaf34a01e7c1c00184d756000c2680e96ab2b0d2c7400c9e0608ee130d5e1e0da6692c349849d7f800bd650a5c5201c0c30137989006ff0c855de30c27000f5f6d740c000ebe9ac0080ae512⟩,
  ⟨0x272131895849223a113886041a1fc0f5877039e1c40d986983381850bd85902ae13207f83a01b60b6056021c0e005e02a00bc04a000, 0x1724b8a68cc6124f144e649c123c6979343627b334269134b89e06cb634b0365afa57138003b0feb361ed87c001d565a3a56138007b0deba060007619d66597a52e91e06002f615d740db098013ae⟩,
  ⟨0x2db15b0a94528285130094c48c22f10a07fc3c81d70d906a030615f09d04542000eb070032c1600a304b022c0e004c018807801a000, 0x3a3b296bb4cd258693093b270017aca14b8a40c166027931207f560c38f186138007b236ba060007644d600405c28900716e46d0029b71f693c2a982654e097e5560627f07a14b0a7134ec2b0909ce8030709cea132821f34cfe29⟩,
  ⟨0x3561988c886222fc1728b6c5882b714909c44ce24611788383d21c60d186082ba13c08d83e81c60cc060829011a07a02a8100036000, 0x4ba2366611c68d63266ac4a74b03624da5713800373e6b761c00ee3036c8000daf123d2800eb959cd86b9db5a00181461e05302ac6800ef2d9cdfab9cb5aa4fbaf67525d39b3ea8ea9da6cd464d3b0c9c12295232b9b19921921f656004f5c0f6a7d95003cd7007a107⟩,
  ⟨0x2e315f0ac451826712308844201ff0fa077c37819b0c5057429c12908d03d41d60d806082b813e09404181c00b605102000d8022000, 0x37526ad8620095d4db33156524d9800e0a59cc15ba7f5bac695c34e0912355c4aee8f87001cd3b38c1ac01f15f346d4611ee9500075a614401bba5f67036428bc4f34a88a1f224e091e34cd68d13c33c0c5469818001ba1b5a3a71⟩,
  ⟨0x2b514f0a504fa26c12d893044e21a10687f03d61c60dc86503141650ac04cc2380f7073035418c0a104a021c0e806101e00bc014000, 0x10093460684419786692b349849baf800ad5d0a5853526b1835ed9c61eee584e001dd6fad818001bad756e310006eb7d9e2b9a530d67ccd9e19a4acd26126ead002b57429614a748b0e517b4998b9b9613dd4c001eb606⟩,
  ⟨0x2d515f0ad053a28613d899049a23a113887040a1e20e8870033e1950b8055428c13708904141ec0ec06f82a812607202f80c804a000, 0x18c1e9606c63f4a0f032f04de02cbc6174bbaa269a44e09276997225002e1c6ccfb86d001c05b3c0c000dda9adc502623b126924ec380036ad84ee136066158003598000010f616d2800e2b59c364580ae25e2a5a9c4e000dd8bad⟩,
  ⟨0x37e1ac8ce06463021708b0055e28a134892044e2020f086f03361760aa84c02060f906a02bc13c09103e01c80c2057019008c024000, 0xd00dbcf5800383369bf0b35f7e0c5a6fb802ed37da005691934edd65f66b2faf052d99ef8276cc12cf6b66dd067a6b80073bacfb7299dfae001c0db4edc6606eb0006f5ece5f16dc5acb6d001003b3c0db6f19e7ae33cb6ddd62e19fc5227467818a0d3036dac675eb0c238c1acf64a⟩
]

def tableLRRRL : Table Block := .branch 14 tableLRRRLL tableLRRRLR

def tableLRRRRL : Table Block := .leaf #[
  ⟨0x3851ad8d1067431517b0b44574299144099c4a022b10907b43a81b30c9061c2cc15109203ac19408503b81a00b404701e00bc014000, 0x1adf1f001a56715a5818001bc875a006f7544001bc8f679a1e97a13a1ad354e6e17e19b481eac701daf19d680c339c083bc5f5b3b28e9e2c094b5f15817daf04816f14dae989520418079e76701fc02c01cf2b380ae78d9f3cc006fff000076cf3431c49ba1ac544c26613edea6816ba06⟩,
  ⟨0x3061708b0056628e134897c47422b10307e43a81a10cb86002c2157099044c20c0f5073036c1940a904b82340fc05901c00b003e000, 0x1bd135a049b357171380037a0eb46cf852363030d9d0a36ace2380070a26adc4e000c24bab8506124000b55036b05a5d860068f030d8908feaf17801a3c99a28cf9127048d9a761191eda5d23c0c7924001bca75ac83aff71846713801d714b⟩,
  ⟨0x30016f8ae855629e14609d44bc25411e88a84402010e206d834a1940c485a827412c08b83f01ce0c805d82580ee06d02700a4014000, 0x1dbbb8800b7b3eccd23b8aca84ace734b9e469606cf174b40a1e06077bf296007000d81002987821ba4d31a69c120bf7b52c0035fe014e1e0867ad53c8ed8a706753829ccf4b71380037a5eb774e64a8c0dbaf3152c001bd1f5a09f74d4606⟩,
  ⟨0x2f71690acc51c27f12d09144402160fb871c36c1a50cc05cc2d01550a4048c2320f407182f815609c04882000be04a02000bc04a000, 0x37c26b400e5ba88c3f7c36ccc2380037c06b4185623915f05b381b9001ea5ce6c02c54dc3c99a4a0d2e29bddc007d5e0935d16c27000ef73d6c0c000dee3abd1388ab5bad6cd1243e449c123e69dc100cb689e99e062b34c0c000decbad⟩,
  ⟨0x2fe1778b9458c2b714c09e84de25812088c043220e0fb876037219a0bd853828211c07e83cc1a80b5053026c0f805d01980a4014000, 0xc24c0d9c042534d24882cdd4f03f4131e1301f8c9ceff4bae69f81d978242fa65f3be274be75ce29600789d1c00f10a5b87ef5388da9c4e000df23ad0e3cd2a303070e654b0118b28f912704801c5349cc389a9a00401e27a3c0c00b12d2606⟩,
  ⟨0x2c11510a0c4ec25712188904321fa0f7874035619e0bc85682a013108383f41a60bc051825810e079034016c09403b0188080022000, 0x754d1f4f74ea5d19800e97a4e9aa3699d2d49c13a634ad2e13001d2347bee868ed6b89efb800075ba33a154606d1bd029606399001a3c0c05800f30a567aba5128e73d0a4e24c10dea69f14949a4c24c0d6a6934925269⟩,
  ⟨0x31817c8b245782ab14e0a4450025d125890446422810187803921aa0c585f82be14b09604842040f706c02cc12806a0258098026000, 0x3a7e97f1734f0037158668b33e449c12306934c7c471a5e23c0ca12606bf60001d69a47e1791cffb4b9df3852737e76a4e19800e68a4e6aa3669ccf49c139ab44d2e13001cc547bf2c660d6846cd14708411733d1c00e69a3df8e3406b623448a089⟩,
  ⟨0x3511990c445742a114809dc4d824d0fe07a03b01b90d286182e214e0a084701f20ef06602ec15c09d04901cc0d005b01b00b001a000, 0x7c0d1c1c396ad74220039e0009e96b2ea61c0611d33ee69e8374e0913be8696092002b9d2ca004ef567f3946f4c6003a6a93a4e8db140a52c1814e012f94e2dc4f7f98003ad35ffc9b23031afbe498b1834d19a5cd3824046b9a5c26613dfd034ceb606d69a8696e27⟩,
  ⟨0x21f10908143ec1e50eb072c3781a40ca86282fc1710ad052426812a08984241e40db06702c014c08f04281b80be05302200ac042000, 0x38a68cc6125e4d39927049c499256886c4f89a119c53a1ce9704cf4266781b43ad2c0da28e96f8563f8a40dd06c781ad8264c0da16e94c24e235649c30173c0c1cfcb96b⟩,
  ⟨0x28b134090c4401fb0f207443841b10d2063c30a1760b6055428012908f83e81d20dc06503001620a704801bc0ca044016807001e000, 0xf1a591c10c001d680064a3910007045d9e5a9a59a90ff92694cfe2918333c0d912606d14f4b42467d1534d03000fa296a654cfe293d91e06a893036893a513ce0173c0c02239aead11b4b9a67f14ae49⟩,
  ⟨0x3411900bec5d82dd15c0a144f625612508f44542000f4877036e1960c605ac2b414909e045c2180e706d02d415608603080f004a000, 0x17fd16bd208007d3da49849397d8011a9000747e000f4f0368f8002ea6119c4e1a22c09f230034acbcf4ae27c158001d6fec007dc606fd700db5c99a4a0d2e29c13c007d5e09cc30007d5b09f04b000f5b030003824eac001cc1f62000e097b3cc174a000e08bad⟩,
  ⟨0x31d1868ba058629e14589e04da24a11288604121fc0f8078c3981a70c1053c25411d07f03501940b305302040bc0540188078016000, 0x1058c8dee107adc208b7bd6a345840eb71044bee89c1200e95862c00fd26f4fe295892e29c46714c112c90103336d4e66a003ea4006d248001d3800ba48ea5c4e0079d52c14f390054a81b32ed2b89c001c1af5b29939a6460694d9ccb1746a259344e09⟩,
  ⟨0x4b924c11ac8944291fe0f3c75c3811aa0b8c58029d14388d845421d10987b83961b60c985b829612608183781760340140070020000, 0x17d978f67bc3bebbc6b3df5df459efaef9ecf7d57cd7cb67be2bebbe8b3dfbdf4d9ef22fdafa2cf7937977cb67003ae7c026e3e00a2f7f290006c3c81a41189000c87b131fbc3000801001dcd807dedd9f91a8cd030003849eb641ce0ac8dcad98003215c3a425847eb40031f9c3a41b846eb40031b7c3a36b845eb40131acc3979a00080040019c58c9b0008002e951a7a46a46a4680c6⟩,
  ⟨0x4091ee0f487623901b78d086122f41698ab851a28012989244501fb0ec06d43241620a084c824e10607182d815808b0408170072000, 0x239f7e76781873703ad207f77767eefbd8b3f775ebdead9fbbfa5c007be2cfb6b66db4001b39d6fc556bb72ef5acfe29001dc9bd4b3c0db917a569bd7bd0bcab3cb863bb87918c8d70f22c91161e45122b910e1c022f2acf912704800de3da6585233c6800801de2d9e06002bc3b4c0d8538003ad95cc8b72378f77d78177567⟩,
  ⟨0x49623a915082e3f61e30e6471e36a1a38c9061c2e91620a7c442216105079438419d0bd055426411107802bc11c06102000b801a000, 0x3a6321ad778d7856b742e63ef1cb95c3dcadc359f31b42c001e1c138006f9acf0361ba5f16b643121ac4800645b8990561a06781a75303440cda90012064d3813c9e24f22798005cf398360d000b0f09a91a05fc34f5a001fe761dfcfc3475a00191161d220c33f5a04b904e1ef22eaed3d0175f6b39b8b7d5ddee0ad3dbdde659edaedeaf2ece003bbd69e9418746fd6cfe29⟩
]

def tableLRRRRR : Table Block := .leaf #[
  ⟨0x3231880bac5bc2b91578a284f225412188d04522180fb87943b61ca0d286102be1530a2048c1ec0df06402c414e0840318108042000, 0x6e8be474eb7dcb09c003c4075b03000387feaf04e2758dd95b38b33e449c123a6900be70b69788f030c9a70f400075a003cd77100170f6d9d231847001e67b5f330008015ab3b8d2e76da5b0058f0349c1cc38bbeeb8db4df75ceda6e72fb6d371d7d969⟩,
  ⟨0x2c715c0ab851a27c12d88b841a2000f887943b41c90dd068c3181750b3051426c12b084036c18809104181c80c20520168080026000, 0x184981ba6bb5ada3869ed4e98b78055e9800d9c026f4ad2c27989788d8246cd6d8ab3ddd2e7bfa5cf874ba92c00717ecee12f04800652f8b001bf2c5bb567a7a5391e7ab00074f843619a4acd26127108002b57429614a308b⟩,
  ⟨0x2c114d0a0c4d825b12508fc44c2090f306d833a1930b8053426c11f07e03c41b40c7053026411407d036017c09c03f01a8088026000, 0x805314ab3d5d2e7aba59534a41a70481ff3ac0196a4e001ce562c4bb9c912ce2bd405cf0303e338d8b92d497313363b2634c64811a5778bc1310e32f794580ddf259e8527127ccdca69f14949a4c24c0d22a24d248a089⟩,
  ⟨0x286138893845422010287dc3a01b50d1065430c1780b2856028e138097046c2180fb076038817e0ae04581f00e006502b00c4014000, 0x189521239b9634031f01c1e068e87a13d430393d833278d05a0f29a1e852712628681513e292934984981a05449a492e34984981a6ba10ec68d1a421935bc7b627e4684d4924105c51f5a01cc800c9e06⟩,
  ⟨0x3381948c105da2e31660ac452025d12308944361f60ea872c35418d0b8054c28012308c03dc1ac0b505401ec0e205001a8068016000, 0x3092000eb3dabd6734b036b33a500d2a0e0030996b000484bd67355ae3e96118006cf03108faca6ae1c8006cf0348cc84dae418ee531d481290063494c6d268d63394e092368ffb5fc27c159c0a7e0acfe29001027f80b3c0c04beff6911c960f240441f224e09⟩,
  ⟨0x3301800bac5b02bb14d094047e22e10987bc3a81b90d6061c2c815a09b84701ee0e406882f815608a03281680920380148070014000, 0xa7869444c18706c54cfb269f02b94c4b935d9d10e886d2653ad23b87a534a49a65d6783cb6cd29838065b079554e16e270007197d6cf142a19181a78e14ec58069307052b192d6e268995d13112243544c2d8085ac00fd69f5782760d73269bc8fe292e91e06⟩,
  ⟨0x30517b0bac5b42bb1530a7051628112e08f443020b0f607083701a10c905b429c12908f84001d20d806482b811406f02700b4046000, 0x19127048e9a794f0fa689d99e062934c0d8de0003ad003c26a2391637db3713801e0d4be03c140152a06dfc74a611c001c6cf5a00780544003c6d76703001dfb4bdfa74b0a699c9376a9c1e9975a941c034d838a7c395ae18c006cf0344a50df8b⟩,
  ⟨0x31917d0bc05962ac14389c04be24e12088704221f20f2870036c1910b9053427012308c040c1c00d106102741200710338120026000, 0xbb05260600071e2d6801e935100071e4d9f03da59334941a5c538ed800fabc1201ba052d84e001e3afad818001c75757ce800d44025e6fb671b4a966254e0962155d46802587d893492780d1ccf56c27e6200e9b03001e5f4b000c350000021a2087⟩,
  ⟨0x2f41738b485662a21498a204ee25612208e84562060f287643981ab0bf059c2b013308903b41c60c205582300fa07202980d0014000, 0xb3303da9c1e76aa6c519f224e091b34bb2dfedb4ba47818f24e3f2000eb40fafe2e308ce27001bf7b5dfb5fa000dab834d2984700071f1d6800df95c4003c7cf6703000df7daf82cd2808ecf47c89382400f64a4f4f0114d00200fb151e06⟩,
  ⟨0x32418b8bd85aa2b41498a184c225711908143c01bb0ce05f42e41530a104c42480ff07a037c1a40ad05181f80d20440188078026000, 0x714800c285b0026122e400309d6c7aa846bc309c003e8335d030003d056b000400a106e4423e31db41e8f18dda79cf2d49f2be6e93827ca79fa6499a4a0d2e29c844007d5e091b055b09c003c8375b030003905eaea056200ef3e9b3dcd132d22704c728b⟩,
  ⟨0x3051770b9059a2c014d89a04a224410f88543e01d90e386f433018e0b48510246116074837c17c0b404781e00c605202080c801a000, 0x1c3e69606e1ff4ae270007a2ed6745bd170003aae1d74ac27000fa2ad740c000f451ace1bf4a5d23c0c005f449ae81ba2200275c0047443ac0058a9b3f8a400400e29ecf03001452da606e868001d670c1a5856b3699a4b0d26127a14002f59429⟩,
  ⟨0x27412388883fa1e80e987203661940c385e82de150093041c1e80e306b031c1740ad04f022c0f8071030013c080033014005c014000, 0x100288ab900718ebed0029c75b693c2a982654e097e55601afb147a14b0a7137d402f4902bf4c00d1c0afd3a4d2087cd33f8a5724b8a68cc6124f144e649c123c6979343627b334269134b89e06⟩,
  ⟨0x33c1988c405de2d01518a304fe25a11c88bc41c1f70f206fc3541850b204fc25c11d08703a41b80cf05c025c10406102a00bc04a000, 0xc1200720d6b0018f5b3801fd34b0017e88f7b57159a5713800393eeb63f9f92e30347ebf15ae6c66486487e994013d703da9fa6300f35c003131672267a61d7699a4b0d26127a5d002f594297148182cc009891b903fab00c223ef0c27000fa55d740c000f4a7ac⟩,
  ⟨0x3551a58c986022bc1590a344d824711a088442c1f50ea071436c1910b2056826a12608283601820b7050024c0dc04d0218088022000, 0x1030003951eb648c43e76254f4150e600332b6781b29f00075a00393d710f4f2a1d9d58895d11382402a4dad71d201967b49309276c10027520031ca0116781b8e8001b52611c00648ad60032420076adb7b4b036d71a571380039456b4c1e46ee30349248cdaf14d29669⟩,
  ⟨0x43920e0ffc7d83cf1e20e9c7043611a00c7c5fc2dd15c0a6c4ec25911e085c3e81d30db068c30c0c7055026c120073027009c03a000, 0x16f5c129006d294d9b26b32d194c26006ce93859995f6b65b4b5acf32732d69a29a5cb4d22d2e5ac006172cf95c1143ad0074593e56c1a36b739d525200e6f27cacc334d6e57935387a3e9a8b3803bdca77593271c4ca52b495b4abcb19c149534aa25552ac38c1b425612b200ac3811bac9f224e090077294a1ff249eb40100f7093c0c016dd29⟩
]

def tableLRRRR : Table Block := .branch 15 tableLRRRRL tableLRRRRR

def tableLRRR : Table Block := .branch 29 tableLRRRL tableLRRRR

def tableLRR : Table Block := .branch 59 tableLRRL tableLRRR

def tableLR : Table Block := .branch 0x76 tableLRL tableLRR

def tableL : Table Block := .branch 0xeb tableLL tableLR

def tableRLLLLL : Table Block := .leaf #[
  ⟨0x3d81d98e386fe3721b08d4068a3381898c245c82c51588a9850e26212188783fe1da0e686a033c17909c03dc1d80cb0530214042000, 0xeb487cdd70f99d68eb0f24f19b58d3426784cc271ef3acbd740c3dd7593ac003e9a93e828d09800fa3a38f6bd61eb800f95a38f39d616b000fada38f5dd5feb984fd5e8e4bae818723eaef594b52d7e4bc9a3fa73bce44f3c7099cd3c26001f08b3e5909caeb6663c76cf612db9a5b92e69747118e970f2b92bd69⟩,
  ⟨0x3821b80d986b23341950c4c6082e51630a84526280136892842e1f80e986d031416b0a084882060d905d025411006302c80d0014000, 0xb847819c53d778eafac81b481d2dea6f400568e007a751fae91d3f5d74349c896c5136f6b7c624f1da64476ed3801ec3471d8b2f4d6f56f7347ed1d57dc51fc27b6a3f83f6bdca8fe0fc0d1fc477aa3f87ef3dfa8e007c3d1c784eb6758c271e37ad7d740c3c5f5abacf9a00401d1e06⟩,
  ⟨0x266125890444c20f0fe07bc3c01d20df86c83421920c405dc2d01570a404f823610c074836819e0c405b82800f6058019807001a000, 0x1994153c0cb831aab489d2ca687a149c498a1a0544f8a4a4d2612606c5349a492a34984981a9e400bc69c49004d3c31ed89f13626614e8e5a5000730ad680069d391000730cd9e8e1a5b88fe29⟩,
  ⟨0x2e81638aa04f626412a88c04221ec0f1070c36019b0c805ec2d01550a204e425411507f039c1a40c504901ec0dc04901a00a802e000, 0x1809b3801f7d4b0017bd808b56981a5308e000e67fad003ee6a200c6683b38180b7b6a5d1a89c8d55e092f055c568b811167e6bc12792f048d5a586974acd2837a9d856000c966016eab4a7d2b89c001cca75b006b181be145e947a5⟩,
  ⟨0x3181868bf05b62c615e0aac54227c12d88d844e2060ec87083701a10c905b429812708e83e81ae0c104f01b80b0042018808002a000, 0xc123c69eea00bb689e19e062a34c0c000e6bbad001ee4b880099afeccc23800f70dac007b8000ed5a6569606d31f4a611f35300075a003db571549b355d9c0d52476be2c00350cc4d41f0c002a91e1ea38001a9161ea3b86a82e1b54d29869c121c0ab⟩,
  ⟨0x25011d88b04161fc0f8879039a1be0d606542fc16d0b1054427413008c84301ea0e906e032c160099046019c0ac04c01c808801e000, 0xad559a4b045783753a4bc13a2bd3cb4a792f144ad3cf4ba7ae94ecd782644d7a75e96063b1196c2709099708ce2718358ff02aad38f4ae27000736bd6f99c60688517a6f6951143e449⟩,
  ⟨0x30c1738b6856a2ab14309e44a822f10507f43b01c10ce05ec2ac14108e04141c80d706482d014c09103e01a40b604801a8080016000, 0xee3d7b8dcb09c003ce8b5b0300039d06ad862002e745b35ec6a20d980039ce6b5862035673db3d46b4b9cc0003ad001d97b8b7c19cd6cc1814e000e729ad718da2f03504a7e334d0c0cca9fa19e955323aa90d9138435ea89a5913832abbc455e09⟩,
  ⟨0x33f18e0c0c524281138097c4a022b10f08443f41e30df06c43181820ae854025610605e02b814009204081c00c203c0178088022000, 0x1b2b338b40c473ded402801301900c4002fe9032e1e09cd86692b349849cef400ad5d0a5852269b2c0d265f79a049ee584e001e76dad818001ced356c31012f3b6d981196666cef460530008008007879a1ac86ca1b0cd2566930939d48015aba14b0a674d6386b⟩,
  ⟨0x3351958c485f62e21698b0c5702a113e09944b023f10d07d43841b10d1065c2fc1650a9852426010b079038419004a01c8088016000, 0x1035f59bb40e864d8de3bdb13e563426c605939ee0021adbd858fa66019d73e7b004d6b655b5f774e7eecab4bee69e28cf91270480d1ba686b1da5d23c0c033ee900073cdd6c7ce3c671cd2d36e70535ef007201a00d8005fe171506561e51cde373276f764e09⟩,
  ⟨0x34e1a20c7c5fc2d91548a384da24a11e88344061e00eb06c426611e08483b81a60c0059829012c08303b01940ac04c01a809801e000, 0x206d00d04cd6800c7cd9c8f7d0075b3e39ff041b0e088e426398412ce005a0161fc52001001d0030f03000a7fd8981bbe5238358001001044c1a77e90238122e857fcc3c1c59a302cd2679425e32584ca687a149c498a1a0544f8a4a4d2612606dc1592692416c649849⟩,
  ⟨0x5e12ea16bcb185822af94f89a64842058fa87aa3c71d20dd05d22c61528a1047e21e10907c43c41c10cf05ec29612808283540e2000, 0xe270007423d6ccb8b459181a66e5a0c5aa571559eab93df14e83899ccb3ded045d39abf55c2088b579ce3a739bd0433891cc9aae8f793de94e6d3800f50da7a6acd84341620b589c196029a6d87734b89e07ae1ea703dd3986d587b9d06f0e01282fe1fa6fa52d3d27d3569e32e23e34e65e7bb3800f3cda791801b9e2d351240079dad3820c0e62f03ee8dc5b97702c001c3e06703b8b73d60570ee79c0a39230ed480013d7a9a0f63e59bd930ed47000bd7699ef62e56f2c9ec787⟩,
  ⟨0x48222e911884e4041ea0e9c72c3871be0d7467832a1900c045b82c8153883c28412f09104442000e106682b813408603180f803e000, 0x3c32000759c41e9682506a4d62eb0387ac3d62ab018748ebbc48cb3c499f224e0900322a92a396116d2e11e0600321a93a1b0a2dad90946b2ab24b5c9924db77fa7eab69f20add56cab6c2d2517c3a4c6905a24a56d55a056e15b056ca9f87c78a2c0b4002493669c3044d99abcd3d2690036ce936aa8d6a6d9526d751ad9d1800333dc3a675a13eb400da8a3da4b4b4b⟩,
  ⟨0x30b1760b685962ac14f89e848e23d113085c41a1e80ec873c3541980c705a42be13a08a83f81e20cc061027410c06502c00ac042000, 0x541a1148e891f124d3aa09477138003e276b3c4cf134002d540dc61696923c0c0057891ac348f03000fe22eb8ba47818004f1075d03787e0016b8001f0fb59c5a69584fe1d8007ae818001f0e759c5ae94016f1acfe29001003bc4b3c0c00378769⟩,
  ⟨0x2ef1728b0054a28013489104422120f7876838a1a20bf857026e11207f83b01c20cc051023c104071032015c0900370140070022000, 0x40c000f8e3ac043e164000e7ebb4e3934a01867e7b4000dfc3136a980597f0c4d62aa44a952003bf6e26fd8002c4deb4003890063c64d678c800beb37544d3489c129c4aca9344c04d1e6e43f8a4a0d2e299331a492d349849c46c123269⟩
]

def tableRLLLLR : Table Block := .leaf #[
  ⟨0x2fa1718ae451e27b12e08c841a1da0e586f83581a20ca85c02cc14f0a104742260ee06e833017a09804581f80da05802380c804a000, 0x38e9d2c88a8d1ea8e006a3479a3c79a34768e9478e11d639d1c471e2f74e2387178234e9ee23f8a4b847819c53e42802fac81b8f5d2b09c013f2075d030023e3feb34cd258693093e3d8017aca14b8a468d857eb2183671eae184e001f8e7ae⟩,
  ⟨0x279132093c46e22c10c881c3fa1e60ee07143761a40c285982b214c0a084881f00d906602f415809f046820c0e806a02980a403e000, 0xc0a968a34482243c26e05125d23c0dc81e9606e4174b037239a591e0528f23c09d1e852c29c4c00e45d264500e0034791203693866fc932a67f149ec8f03544981b8c8d2c8f0060068f0348d00347⟩,
  ⟨0x26712a091447621e10587b83be1d20e386d83221740a784e024a11808003d81c60c8058826810e074033816009603e0178068016000, 0xa8893093036ca054b43044811b1cbdb13e99a13589a4001d36b5a00ebb3100074dcd9f241a52e10fe2908ec87818354482178aae45f4bc8be962f43f5887f14ae49714c998c248d1aa6b24e09⟩,
  ⟨0x25612488c843620a0fa87803961bc0d886702fe1640ad051427412708103cc1aa0b7054825811207a036016409803b016008801e000, 0x1857ca8697951d2ef19e334ce7e0a722f53e449c120d8a908f7e96821d4a78183a1530983b43e9e800deb645323b8098e86e0163fd0d29a1e852712628681513e292934984981ac5449a49⟩,
  ⟨0x25d129890046c2110ff076438c1b30d106543081790b3056c29c12908c04381fa0f0070835418c0b505002240e406301f00bc014000, 0x1030b289818001d4875a1aa4401dd48f67a8a2619448c9a6ccd5069c12caa2e13389f51500075bd27181bdcd6c27949748c611c6cd74246ae57b4bcac694c23ea10000eb4d288007a856ce06⟩,
  ⟨0x2ca15b8aa053c27d139893845a2080fa87983b61ca0d486503141790b7852825210407a835014e09004301bc0b404b02000b4030000, 0xf748c2478180db0ded7036a7e000eb40070d2e20196a83b34450f9127048f1a70b802eda27867818a8d3030003a99eb40070a2e20026a6bb3308e00384b6b001c24003b57305a581b97fd291029f224e090f512dc8ad08f687⟩,
  ⟨0x292140897048e23d11608883fa1d80e586d03021770b0053427c12908a03fc1e00e306a03241640a104b82000da05a02380bc04a000, 0x70d203049d7ad13a33c0c506981b55e00075a02bc9cbb171381b0cb9388057000b55037349a50d5133a9a2594e9caa9912549c498337a49c12821b2e04cf03403ccb0fd0fbe22ebc43c69b43c0daa28003ad⟩,
  ⟨0x2ad1518a084e626412788e84362080ff07843a01c30d9069c31417f0b9053425011e07c83981820ae04b02300ce0500158068016000, 0x103056689dace24cca694554c2aa9e01024a5cc28781bff1e2563269b33541a704839fd4ae13389f57300075a00549f5b18183f493e3561ba1c01493db56fa21d6e9a1e06d5a8001d681ccd10fb356cd9c799f224e09⟩,
  ⟨0x3561988c345d02c31560a6852026b13088f042e1f60e486dc34818b0b9059c29c13509303d81ce0dc06782e012e06a0298118042000, 0x1f64b580101566240afea2db40007515da73c3a52e91e06056bd8bd740dec482b1ae055fd88d600168bd9c54800745acf53834d889be0c75de82baf0481ddbac07f1ce692c0093e607d629d25e09d15f3d3a5001d1ab5e8cdba000dab9e7d2b89c001d61b5a15ba2b71⟩,
  ⟨0x31917a0b8857a2b01458a044b823811308703ee1ea0e286e43581870aa04f423010707b039c1840b505402340e405701e00bc014000, 0xbd7b67aebb41bdb105cf5cc27f6bc176d740c0ba7b5bac0080a590794c1a06f6a013ad7309c004f69f5908ce270007da3d67b45ed18003aae87f4a0097b41aed334961a4c24fb38005eb2852e2900da21809b0448036686022bd186138007eca6ba06⟩,
  ⟨0x3b41cb8b2c5762ac14689c84a623411387f43e61d40dc867831617d0b5057c28812908703cc1b00b405101d40d004d014005c014000, 0xad24b95800432401934964bc004c8c646b225916319b56b22a28014ec3d8635ea6bb7776939b22c26e65c8a3840b9547f1480107d7228f0303cb8f49c688e1222c64243744f50dcb2270487b110c9f816133f9cc26713e8480a73079a00671079ac18037a9d0320f06600d160fedb028dae3833b89e06⟩,
  ⟨0x2e21688b0856a2aa14c8a3050426b130892847a2180f2873836e1ad0c4059c28c13908604081c20d005f82d012e07402b809c014000, 0x1e4d0d89eccd09a44d2e2781ba40d2c0dd1fe95c4e000fbcfacf79bde7000755d1ce9620163c0c02a7bc5aca2ea2cb396851659fc5200259d45567818b328a6d32a694834e0900eba958006b7d870064f958939ec75bcc549400c9e06⟩,
  ⟨0x2a814189e44a823310907e43d81cb0dd067c3141750b5054c26812708d043c1e00c60538250106076033816809a03e0158070022000, 0xf624d6c0db110003addb0c0cb8ed8605dae565dcec27094c08b5ca398b3c183cd0aa609553824ff76601ad7347a14b0a7136b502f4902bad000d1c0aeb4a4d2087cd33f8a5724b8a68cc6124f144e649c123c69⟩,
  ⟨0x31b1830bac5a02b514d0a044cc241113082c3e01d70d9066c2ec16b0a6049c21c0f506e02ec15009904701d40a803f01a8070014000, 0x6bd59959f784ffbef09fea32128bfe4262809d201fd427e2b02275888fcc33e3f8867dfe10c019473fc4c04aeb80c263fc4804b6ba13001deb47d8cc6f3d687d439e9c51d2274ce9c1adbfb5aa487c893824068dd382bb756d15d33c0c073ee92f11e06⟩,
  ⟨0x3cd1de0eac74038f1b70d3464030917d0b5456828f142899049a22e10687b039e1b00a9852424811a07a83481620900378138042000, 0x1aa694c34e093b35800ca8d9c0064dad600326b2a16aebe34a611f65b00075a00326371000f65dd9c0c00325d6bebc34bbf360d277df742d7bedbeb6b017af93803e11473088001195acee0010daed3c0db270e09ad81b64c00075bfa15cce4769b602cfaffbd569de9d7eb4ef5ef55af78b688006cfbd1bd36b⟩
]

def tableRLLLL : Table Block := .branch 14 tableRLLLLL tableRLLLLR

def tableRLLLRL : Table Block := .leaf #[
  ⟨0x31d1890c045d82da1680afc53428513c89a84aa23a11188303fe1da0da86ac30c1650a204d425410907202dc15a08c0338108042000, 0x182470d2558ad2e91e0618348003b3f6b64156348c611c1915718212abb14d2f621a5713ecea000eb6383007b6303470400e6ae83a832ce01141967c89382400682ad330846f9ad001003a07b3c0c00340d69d9a0001d6cb451bbec632a332d310119167⟩,
  ⟨0x30617e0b6457029513a09844622220fe87a838a1bb0d306543081750a8050c26c12508a03bc1c40bd059823810205c022808001e000, 0x206015fe671600352767001fe5f16003537670dd16016fca2a6714611c001da735a19a44022da7b67034082af0cd256693093b4a0015aba14b0a6a4d6306bf9e9fc9dcb09c003da375b030003b45eadc62000ed1bb3ec974afe0da15b38a33e449⟩,
  ⟨0x35f19d0cb46102f11660ad453c27912a09244482030f106d433c17d0b905441e80e406a830815e09e04882000ea06002a8120046000, 0x3b626adc62000ed8db3f7cf4a000fd57b3f7cb4b3223263cd0113571e6000babc12001c795ab001a6db3800c505ac00627e9c2d5da36962740f2d78240ea26ed76a8118a00080ccfc10005a7acc6c94d78225f6448c9a6ccd5069c125e2ab84ce2700076a6d6802ff3791⟩,
  ⟨0x30f17d0b5c5902bd1560a1c4ae24d11508743f41ca0e006a43341750a904b424610007b034415809b04501f40b004d01e00bc014000, 0x172aae1d600cc3e449c1232699749daed680061cc007c3c0d0e7002e25c4e001ed4e2fb55da800162a06f82f4a611c001db575a001ed1e44014db5f6703004bb418b818001db3f5a0064b83b19334941a5c53b65000fabc130e6b6138007b636b606⟩,
  ⟨0x5b32cf9600ac254028f8fac7ae3c31d70e345682a014609dc4c4241110080c3c81c30d7852c26c11107f03640a40420188078016000, 0x741a3740eeb49ee9cfe92fc7bb96b7e2dceb5b79dbcdfac0008008f74c7a001df25b4cda792e3695b5ada36d436adb58daa6d49c148be7dec3c4ba354aa373ad9b6db65ed6001001000db512576d03689b437c46d23695b4eda66d1b678009878df468f746d77b36c559b737742d7d31cff6bfe6fb94c0f5f749e6de6bb5f5fa37e70683a3b6cbc932f727b8c3834a9f6ed00ab5a1d21f6eb005f5a32b346d1e8c7a40008caa001003630de9fa31a01cd66a259544e09⟩,
  ⟨0x4fa25811648704151f28f0873e3621ab0ccc6202ed1650a9c50827712908bc44a2020ef86e836018b0b4044415a088032810803e000, 0x3fa30669bae9c207b87fe87f2e0cb374d37c0f30f835839698ba80530f174009c6270e0128ba61c01114ac3c61800200c8b8e1f11a27a009c4c5d00138900445cf131438bbe2e285141c5c5022838b713ee28000eb632313ec8c0d19389e62c003178c3ee1e88f6b606dc35112d6d6aab59891aefee34af7d593436cf0fa561ae7ede4cedb2bea5c3f0ff8a0003a9aaf37e31755d6f162eaba773c5801eed49⟩,
  ⟨0x4bb245919888242a2028f807ac3b11ba0d4c6643111790b34554287132090443c1fb0ec06a030a16209f84801fa0cd05501b4094000, 0x634b1ab8e5c3b01328c69c001882353100e98003881b4f3dcca2fa781a202dcf75a38eff4ea2253387740ea8b4f6df545a7b2970ace0079951f7371fd35b5cd193626baa32cc48caeba989da1d793173789bbe2f001827c5ca3704187946592703f87c0fd77f17b41af4e2e317187c5b3386349199dcab0e32f1995ca70f1aa8d4e2e0d2019fea468b0f17a18b61c6efa71fe94a0afdf87⟩,
  ⟨0x3d41e18e786fa3581a08c705f22d415e8ab854429314209c44ce24211488403ee1d60d88470220104070832c1500920368120046000, 0x3838eec6000eb400687ee2000eecbb3fa8b4a000eebfad000c57b22000eec3b3fa9b4a692791b424ba498050f0348ca06eeac0761cfb5b6eba2db73e8d0ed39c0f6dd435ac315e94ffe30c2000800521b00cf21bf483a7c46c46000e3d7138eec363b71e989c7861b748028f5bba38003ad91540ced8e35b1cd87⟩,
  ⟨0x3511980c746142ff1750b2c5782b115009f44a624911508743f41ca0e006a433018e0b5832016e0aa04e823c10807902a00bc04a000, 0x494836b9b512c9227049722ae6f80ca3e449c123269458c5ef1a0066d007a3c0d36402d25c4e0018bb62e2ef17500162a06fafb4b4267818029170c5800200100060020042002800c4c1407e05f0051a7b673519b4cdb4342684dbb40015ad0017767d6c0c000eecbad⟩,
  ⟨0x3021678ae0556286130895c46421b10307c43ac1bd0d206442fc1730af04f425c12308903c41880ba04c82300d603e01a0074014000, 0x18e1e40fd5755da57138003bd0eb6404000f63034806000eafaacd2f2ba9fca94e4aa141fdbe1d2a1e8e79b512c92270497a2ae2f8032cf9127048c9a6316932da00317200f6781a2e0016d2e27001a47b5d215230015aa06fb2b4bf0a1e06⟩,
  ⟨0x2eb1700b3c58429d14989b84c223c11288003da1c80da868831e1840b8856428412b08e043c2000f506802ac14207c02b80c801a000, 0x6098735b09c003df075b030003bdfeadc62000ef83b3ebe74a576ff4db3e551320f002babdd517a222c7945e090c5161b0915d5fe97abdd29c498337a49c120044823ab8e10001d3c0d2074719ab00063f1d380071c56ac00190474ec2b⟩,
  ⟨0x3621a58c9862630017a8b4055a29e1498a084ba22d11188003e81e70e1063c2f01530a4849018e0b905782280f205402180c804a000, 0x23a865c2ac009e9e6e44b6489c1200642ddabd3800230f9127048c9a615a9b135a001d35800f0f0369a400b89846713800335ceae6b89af4001d57ebfa58468001d3c0d0af4d69ab00040022baa12884a63a7d3dd0d030003be5eb478e20166f9bb39334941a5c53be2800fab⟩,
  ⟨0x3431960c386082ed1718af854e282135896c490235115084c3c01bb0d606842f815709204681ea0eb06302840f806701a0074014000, 0x67a4cd020e931e06054193030003bffeb40e1688097c00ece30163ca635a289855138247da65c0bc5890015a70022415d3e449c12000c825a98f50035d68002001c821a7818002903b53030003bf66b402e8f3b62000c7e1a706d5580020164811aaebdf4bb0a1e06⟩,
  ⟨0x3131780b7c5a02c515a0a3c4f427012f895446020b0ff076c3561a10c505ec2ac13308704101c20ca05482100da048018808802e000, 0x2a3cf878f33e449c1238699009578d689d19e062834c0c000f035ad55b63fcd8b89c003570c5d606ade002c540de73694c238003c096b400356ac88007c0a6ce06000d59f17e6f694006c92cfc059677ad03298fc048097ad115d8f91270481a8c9⟩
]

def tableRLLLRR : Table Block := .leaf #[
  ⟨0x2cd15d0a8851627e12c890847021f10707f43dc1c90de06bc33c18d0b3056426812a08283e01a60bc04b82000d20440188078026000, 0x1ba2ed80a2bb7cd2b89c001e1035b089346068b1075e19a4acd26127839002b57429614d49ac60d70124004f6584e001f065ad818001e0c356e310007832d9f677a50007147d9f6cda503158fc1480bfadd45130ca2704bf08b⟩,
  ⟨0x2a914f0a144dc26112b092044621210087d039e1c40d786882fa1730a704f422c10507b03ac1b40b5051826411006301f006401a000, 0x182482c5d6129b1d84f09ac86e17804dd6c99a4a0d2e29e168007d5e091ad55b09f856000f5b030003c2a6af04e2011601ef4e2ccf9127048e1a6430008b5a5e23c0c30690007849d68003215ec401ce12f6708ce27⟩,
  ⟨0x4312080ffc7dc3e11de0ec47403931b70d9067e3321868bd859e2aa14289804762160f185a826e10406f82e812a06202780a802a000, 0x19375719334941a5c53c40000fabc130e6b613f0f8001eb606000787ad5b8c4001e1f367f04e9408d4061e9cd8d3646a51439b134f175c5dda98be62e6d3c5f117769e2f48bde2edd3b5a708dac249090f658355e14a6de9d4dab049236d3d822a6cb9b7a713520d4d3800305769e0b482bf5a25dc22cddae9c33438029c33eb6989530d0a9⟩,
  ⟨0x3ca1df8e686ea34219c0c4c5dc2c915209c449c21b0fc07203461920c285d02c61570a2047c2240ed065030013a08202f80bc04a000, 0x30480033986a67489cbb5a0008007394e9e06000672cd48003c4f6b67039d0f62e04cdf5a770226f96fc34fc08e0361f5ff9a2f580d3c8170db876a4c8130d987004613fd38d1a70cd72691d33c2306a87005b88fd6b89c001e2375a12f947646060974a3316018b41c22728ac58477632001c3c0c000f10bad⟩,
  ⟨0x40f1f50f147763961b88cf86322e61688ab853a28c134897c4742150f807843a41ad0d0064430e17a0a284b82120ac02080d001e000, 0x3c626b689eb16f6303514562ceae8f9a3ef53205481947569d449a3db4eccabde15c369f6a6cd5e9002e1c70cfda6d96180070f03716c000eb4001aa8362004f171b3d8934927e50001b56c27709b0330ac00055c0000087f25697b38a8bb4f35d4db68ba361b0aa8005a79ae66da45cf5bc6c3215400074f266002272ed3e449⟩,
  ⟨0x3a31cb0e146f436d1a40c8c6322f41688ab051225911a08a840a1e00dd86b034217c0ab84902340f5075831814207c02b809001a000, 0x499a18d3099c4fc700003ad4a471c3d8c0d9fa6383ab000ca770e949637fab94f4a4b0f29894eca470fc6c5835ad81b8d600075a943f15bb10022c6dd3e449c12000d8d5a9b1a2cb4d68002001d8d1a7818002b19b53030003c65eb6cabb18b62000da11a70006d04d58003681da15aae5bf4ae27⟩,
  ⟨0x42620e0fe47b43bb1ce0dc869e30e15f8ad055029d13c094c45c2090f907743701ad0c4058c27c11907a025c11807e02c80d001e000, 0x206d6c16b316006d6d1ed4daaa5da3b5547b3f68ad4d1c00f857c38004001800948c69c0010009816000e917d3e26a4684dc7c28d7ad646b8f7d6800345d69e8d9e3d75b00069b2ad534698057abc12014d1a3abb21ed2bd5d90d642eaec31b0cf5200a585fa70004002b0531440054020d3c268a1928ae3a35a000e7c7a7cf938e6d69e49⟩,
  ⟨0x48122e10dc8083c31ba0d4465c31f1880bac5762b1146099c48420f0e705fc2b812c077839418009d04481e80da05c028811003e000, 0xd2d3a7a59f923d6e23b49f3451a7c4731dda4f5a27d3e23748163b949e344da7a44d26313a24a4d61ed24c249e701497d48007441496c3c0dd3da929a98c02302d4a52da7ce9f4bc4a574f8d3cbf54b6c66ed0d69da2697e5a25a5b2336d3eb675b789001972355587001171c011aa9c3c0dc870003add7616db236e68c79264cd0c6984ce27e418001d6db4b5d51⟩,
  ⟨0x5f82f395b8a3e4c225a128c92446d21d10547e03e51ec0ecc71c3841af8ce862a2f016588a02ee15209683e81aa0be04c81d009e000, 0x80735994951daee961dfc4024d9294a869e99b000ac93b63b850d3f09f6495334000db1bc03e9fa86b534a51a78578f974f1ef70ad1f269c0018f7f4f1f0efb7ab84ce270007937d6ca0dbebec606a5ef7d5d580031eee9e4a8e4cb5b4bbd2dfa9a5ba976d4c3b165b251f49c255f87de0117e85f9d6b1c073a7875ecb5a44128ea4dd2aec3eb007bf3efcdb58a038d3c0570196a6031b5af4f016c0616b569e02500074f013e9aca9b2e353659d971a9b2decb2d4c05f0e7520f49758f1a7⟩,
  ⟨0x81a4011fccf9c7a93c21de8eaa7303859b6cda26ac3449990c7e58e2b49518a424ee26592a087a38c1668aa83660ae04c0208066000, 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⟩,
  ⟨0x275131094c49023511008444061f80f2874c3921b10d3863c30a16d0a304401fe0f006f834817a0b3052026810407002c0138030000, 0x7fa27324e090f112f36686c4f943426b85125d23c0d01eb8b03407ce2c0d021f8a003e06171c00740c10019c7ea33fe49a533f8a460ccf03644981a034f169447816dc681800080028169ca80cbc5⟩,
  ⟨0x28413889884b023110f07dc3d01db0e806fc3341730a704d824211508103d41ba0d306002c4132081034815808a038014807001e000, 0x1591261260681e2002b9a1922400440efe7b627f33426d1348003ccd6b4000c0e9e88003cce6ce04df16284cf88c5d21fc5211e10f0306e896c5502438b02438b02778b2821f34cfe295c92e29a331849⟩,
  ⟨0x24311b089041a1f60f607543801af0d006543001590a204e824a11607d83b01c20ce054825811207a036016409803b016008801e000, 0x38aca84afceb4bf9d69606fce74b49ca7d833e449c120daa9004504279a306678186a553429a705f53cea684c1ba1f9b0005f5b29a1e852712628681513e292934984981b05449a49⟩,
  ⟨0x2b91550a0c4ec26312c89204262020f887883ae1c60cf86343061740a784a02060eb0708324174095042017c0aa046017807801e000, 0x1492609a0012e5b09e0346c0c3c6b0085fc0000061f71a630cf9127048d1a60940007e697c8f031c4900079d4d680018247d100079d6d9c122e2c0d047b8a611f9cd00075a3471000f9cfd9c0c792ff3fd28c19dc259a47⟩,
  ⟨0x31a17a8b405862b61538a5850a27812989204462160f8879c38419d0bc054c27c12d08e043c1d40df05d02b411007e02c80d001e000, 0x3a0400075b1300077b1613f19b353499a4a0d2e29e7f0007d5e09fdc8038d5b09f9f8000f5b030003cfb6ac001fdb76201973f1b300079f3d6cf8ac64cd25069714f3dc003eaf04feca015ead84e001f3d5ad818001e7a356000fec1b100979ead9ec49⟩
]

def tableRLLLR : Table Block := .branch 14 tableRLLLRL tableRLLLRR

def tableRLLL : Table Block := .branch 29 tableRLLLL tableRLLLR

def tableRLLRLL : Table Block := .leaf #[
  ⟨0x35319e0c846263021788b9057e2b41478a084ba25311708243c81cf0d506142a412d08403e41d80db068030c13c079037812804a000, 0x61b8cb641c14fe43499a4a0d2e29e878007d5e09f67e24dd5b09fa1a000f5b030003d0c6ac001f66b63123f435b306c53f428016eb624588f74f122447911fe9c001862f4f1367421ad3c932668634c267138003d056b626288eb63034f6111c6ac00188e74f11ac46dab⟩,
  ⟨0x29514309ec4ac24111b88484061ec0ef87383601a60c786082ba13809704241e40dd06702f814e09c04781a80c00490190088016000, 0x1e9270480111506afd054f03453a03beace2383eacb7138c9af90804ca81bf48d2b89fa3600075b1490007b181a291000757fa1e9673d4e71275b1b50564c26613f45601ceb606c3a19606f3270b1b05d64e09⟩,
  ⟨0x2d615e8a6051c27512f093c46c22910807bc3ca1ce0dc86502fa158099848022210607983681840b805282000ce042017807001a000, 0x689e2001f4cfb3818067dd7fd9e94e2381ce3adc4e0336eb999a027540dfd6e941fd4e02074afad037d8e03074abad9feba54d6a3487c89382438448ec3bb423aa1e060d113d258003ad018278802fd26ecead44b28893893066⟩,
  ⟨0x2b51530a444ec25f12408ec42c1fb0f8873034e1820ae851826a12708a040c1f00eb06302b414608a03c81b00b605001f80d004a000, 0x611c18d5710212abf6ed2fed9a57138003d3f6b63a1d88c0d0f98037ab0007a7ad68003775ec4001e9f367ec9e9460d394360e891e33c267138003d386b432b9e30306d63ac68d3a66c934e09d835c26308e000f4cbad⟩,
  ⟨0x32518c0bcc5d22c414f89e84aa24811188303fa1d80d9863830815f0a804ac23810f06e03141760a404b81c80ae04d014006c018000, 0xc27000faa3d6c0c000f543ab0007fb5d88009d51ecc001ea7b5ac31a083aa0d9ff61a5308e000f533ad000681cd8802dd4dece060052819d59e47000e817d59847615d0280008007aafe034b037ef7a57138003d45eb6540988c0d100000fab613ca4ba46⟩,
  ⟨0x31417f8bd45bc2c915d0a9453428510c08243f21ea0ef07443861b10d185f82c2157099042c1cc0c104e02100e606202a80c004a000, 0xb7558c0d059b2c1ad536a9aca953826df1560080401808064b80280c0381127c14d998dfa9a91a4cd84354e0db437566000eb43aa9663030003d586b4001c1abe88003d576b4001901362000f561b382ebc59334941a5c53d53800fabc13fdd0015ab⟩,
  ⟨0x3801b40d7868c32117e0b9459c2b71538a4050a2600d086503021710ad053427c12f08503f41dc0e406a82800f606e02480c804a000, 0x83ffc581a107714001eb875a0a453a7b1c971936f1b240d464d66355a6c9c1202bc4a3ab00a00210088001007c01e008f17409e0020c63715f00774fa660cd13118d0c93278cdb126924ffea004ead84ef93606349600264800000c30007acad6b0c4039eb3367ff6695c4e000f58bad⟩,
  ⟨0x22d10c082c3fe1ec0ef871c37a1aa0cd860c2d61530a004bc24411308303e41d40cf06002d413408503b01900b203e0160088014000, 0x142467a3362317487f14847843c0c1ba25b154213e2c213e2c224e2ca087cd33f8a5724b8a68cc61240f8d84e649c1201c5425e6cd0d89f0f0684d8500c24ba4781a0fef1606⟩,
  ⟨0x28a13789944a024511908343f41ed0ef074037a1b00cf864030c1730b2054428413808883f81ae0c805d02bc13c07902900b402a000, 0x10ea53c0c1d0a984c1ba1fb1f005f5b29a1e852712628681513e292934984981b45449a491611261260684c0002b9a1a224004425ee7b6278a1a13789a4001ec275a000612c744001ec2f6708838b58667⟩,
  ⟨0x2cd1618ac053e292134094046222210b88203c61b90d7864030c16e0af84e82360f6076033416a0a404781e80d605602380f004e000, 0x1035488b1d33b0ac00c7f0174a84cfc58de0228f9127049c49a8b4479d68018d400e8f034680054981a133714c238003d99eb400c71a88007d9aece060031ba9709578bc6679d233e34a9f053117a9f224e0906c54801f84ebcd⟩,
  ⟨0x3061770b845782a514d8a104e626212988b844221410087b838e1ba0ca862c2cc15909a043c2040dd05c02b811206a02280e0026000, 0x214df15c4e000f6c5adb4cda3035962cbc334959a4c24f6b60056ae852c294e5161c22e1b58495ecb09c003ed535b030003da96ad862008f6a9b3123b46ad9b89c001ed375a23cc43bb181848b886f560063951c46f886756e270007b46d6d0c91⟩,
  ⟨0x2ac14f8a304f2252122888042c1f10f206fc3341820ba854027e135092045420c0f707303441720af04b82200c60540178094030000, 0x614a6a8b0d1170db000476584e001f6ffad818001edf756c310037b7fd980038feece158f15c4e000f6efade838c0dec6b3c8ee12cc238e1ac6ccd50a638b0342a2e298470007b6ad69a51000fb6cd9c0cc2b851dc5⟩,
  ⟨0x30a1758b0455428b13a096c47822810b880c3d81dc0e286b832c18a0be05c02c815809984381d20c404f81e80c605202080c801a000, 0x26a06fa386b9a61ba8e07631c30ce0a594e0c7abde3380199949987461f33cb0a3019ec9a2c6a139922a631ca7291e91ba86c46c46c460007b90d6800353a6c4015ee4b67dc68083adee3005ad68003dc5eb6ca568e19a4acd26127b86002b57429⟩,
  ⟨0x2ba1548a70516280133897049e22a10287ec3ac1bd0cc05fc2e013d09604842240fa075834818a0ae04802180dc06101e008c032000, 0x64d3666a834e090bba75c267138003ddeeb40b5aabf63030169556eac06d9ce001d557ab01be739a4b0012aa802f354706bc13892e16b714e2381c0badc4e06432ff4704ca81a168715c4e000f751ada04278c0d3e80eb⟩
]

def tableRLLRLR : Table Block := .leaf #[
  ⟨0x2e916f8b2054627e12c890845621410207b43c41cb0da06943341850b6053828812d08303ec1c80bf04d02140dc06002480c8032000, 0x10301eec90007be2d6800356a6c407cef9367e77b277786481d0c9d4c6d39d9382757465cd5ac7c8938241ad52df4ced0321431e068c9d93af60f9fa9f1301f6c7ef3407cd6f798043eb66795207532748633a593a0c3270069d77e20eb⟩,
  ⟨0x34e1a20c7c5f42eb1700b3c554277136892047822f105075c37e1a80cf05e428812b08903e41dc0d505e022c0e806502d010c03c000, 0x206022aaedd5d5d200469f224e091934d5e35746b4001ab90003d3c0d571000ba9846713800356eeaeadcab84001d5432fe2e502c781807aab635624c2e835a4747a7a974d6d7ba6bab1d3826b6fdd64150e78c50561c2e7388fac7c8938240fb64d5b20416b4083f0c7⟩,
  ⟨0x2d115c0a8c51c270130091c46822710e08343d01d70e306e43281890b8058c27c13408783e81a60c2058829811a07c02b812804a000, 0x107eae9c2b54d57aa40e44ec7f0c6abad7493487613c26e54de0d002bad9334941a5c53e0b000fabc120d60eb613f824001eb6060007c10d5de0ac404ac3f9e9d29a524d38244e45d63e670046af2d5b89c001f01b5a03bd5dfb1⟩,
  ⟨0x529285137498c4ab25092087a23ac1c38dc05622a614d0a384d224410f87e83aa1b00c583301740a904801fc0d005702180c8032000, 0x61bd2d0dbdd4006d5fba6971c0183c0c7221952c005001959e56fb2dacb143deafaf2f30614186b26f4f5f5cf3da70006793d4cf1da60004002b25c181cbbd59a56eabe70f6b2c1cb58182000f4f89a11b118001f0db5a7b35d03b10007c34d6cf4a7b2ec40019e274f3c3f863ad07729d7d382fe0bc02f20ac02ee00082ea0bd65961e7e5c995b02eda7a6c1be9cc03d0e9ea736d02c7e373553a36d399a71dcfed08e9⟩,
  ⟨0x5692a314849fc4ce25591ec8ac4231f98bf05ca2cf139081c3f81df0dd065c1e80e706b031c1780ab04501e00dc05f01d006401a000, 0x1d3e627c6300075bb4fdbce474e5a27d4c61f523aa8c3ea53521aa7c3b533f7669da98fbadaa3d3ea57445a8dc3acc6f76f25b97b3a27283bf50fe45f09183be46000c6ae0013468ca7281ba78d3f4dee1c359e3a5886df1825f0200169f490b3c34b00dba303be00001d3c26e280193f8a81c56b6c2ed7ec3e657979f248e83f2478434bd400c87e527d8003a79334519f224e091b34fbf21fdb4ba47818f248003e246b50dfde6e308ce27⟩,
  ⟨0x3ea1ec8ed870c3631a00c405da2c61518a644e42510fd07b43b81cd0d5061c2f415509904a020a0e005e826811608002e80e8014000, 0x1e8d3a5ed24e1f4bba48d2561f4bba59c3e9834a587d2fe9474ad87000e97f0e6972235f334ca001c3c0c69d62347300337fecfa3eea0f500003a1bd44e1e8cd06695c92001d1d61dbb9a33c5b89fc7100075adddd18646066fb68bb17e369be5add426a030e008d4161f224e09000ea0313e76dbf634002003d3ee1e06⟩,
  ⟨0x5372190c7c5fc2dd15e09944a0241119887841a1fc0f687203761ae0ce86302ca15809984a42080f506802ac10c06102480e0022000, 0x34fa0030010004b32ccdab32ecdbbadaeb6348ee62300b8782ff8c025feac00e9da7c0014007002199566d199666d9d6c75ada46730d804c3bd7fd5fed803bfd1800d3f14ede5a78a770ed7c51c3f6b0008008006004d2138670fe4966b14d1436eb59b0cd256693093e4b8015aba14b0a630d6366b894e3c77b2c27f240003d6c0c000f91dab84a278beb4fb30007c8bd68003e0f6c4001f2376710ef8a3867350311d39d7069⟩,
  ⟨0x7152ec1714aec551296141c9c44d5258122c8f8471226109c7e83ea1e28e806f63561988c305422280d086583161660a084701ee000, 0xd3387b7a8e8ab0e29be51cebc0239afbb18d8745efa5f8002c6bc16eb466220c12e02afaa887fa7fee4ce6231ab05aad14e63e9c400c15353650e0afab005b1e8d3e6b600b69f4cc00a66f1a7002337fd3e449c12000e6fba9cecf37ad68002001e6f5a7818001cde752000f967adcdab3aed880039bde9fcb0cde35b28c572ba7d31353f000f2e6e5fc004d5934fa61ea7c00165cbcbf592e001eac7a7d30b53d00074e5cb9397db258002d58b4f09a1379539b06b7ca8cd8f5b5c6c187a7ae35f37d3b4fc0038012005336cccc3370eb73adad24398ac0361e2bfeb00b7fb3005a7⟩,
  ⟨0x49b24611f48d845a22110e08404071fe0f8c7963c11ce0e0c6c03531970c245fe2da15388f04322040ef84101c20bc03d8160066000, 0x384b308e306b3d92a004f16068023c5039a75e09980175c00be2c0d425a015ab019173824e0118b713f9a8000eb6845131b630350882626afc113b9237cd3f3439b54af6a40c79603b1bf7a7fafb7eb0e0fca700ffcccd6bb2900c3b26eb9e74956e5a4b9b6733b692733987fbe5f2bbcf1ba7cee67830f6645995a963be0157d64443d3fd63b27876147be0d3d99cc2877bfa7⟩,
  ⟨0x2d51528a344ea26012908f44502030ef074c35c19b0c805f42bc13f09004542080da06102a813a08e04101cc0cc05701f809c01e000, 0x181b000b1500bf8b00b78a0dea99a192b9536a2a9a1c0014d5d0de00deaf048033436eaf3045e0975d173a40752e74004a58039cf4bc12346b9c80040152a00ff1600ef1584f292f118d23b8ae7154015e2c011e2c016e29e47⟩,
  ⟨0x2ef16a0b2856a2ab143098c47c22b10e87e03c21d00db867831217a0b285402560ff07883901aa0c0058827010e0640208078026000, 0x21c4a781828153030003e906b4003051c88037e916cec143e90c2c64a86c7032193aae6d44774a369ba41f553fa9bef153dfaa9a2140cfd5818009c8363f10d066a94c0e8a9894d0e6a9ca054c0ec0458b81d00131600381ce2f0487c8b⟩,
  ⟨0x3e21de8e606ca32414789e04dc24911c089c4301f30f307643881af0c405ec2ac14c09384501de0d005582300ce05202180e0046000, 0x3d44afa35a24e57a1a7128849baf3f4f3433f4b2f6cd6fa715d000300c0068a898001a22a08da2244e0d3d129a681bd3d14ff5b86692b349849f4e400ad5d0a5852466ab07255c5490a4fd96138007e996b6060007d30d5c42911487649d98019df47f4b04edd68019f547f4a84fbd6913a9f224e0906454c15c0458d⟩,
  ⟨0x43b217106c8143e31eb0ec474e3821ba8d4065630617c8b5055e2a514009a44882210cd063c29c12908203b41ac0b1046019c014000, 0x30a530458f9ae2bdac07ecb09c003f57f5b030003eaeead8620047abfb3b003b27d9fab35f4eb5c4e000faafad9b10003d8c0d3808003abfcb34b37ccdcba900267270ede8f4939f73c116d4e1e8000cee75e8e9e13379bd23e7d8dcce9fd4d739f5a000ce45a99c774d38f69ab4ead43520025699a7e92fa4dd48002eff29f2295d68a25469e06⟩,
  ⟨0x3451970c9061a2fc1788b885962be1548a7452026b11c08843dc1cb0d4060c2bc13909784281ca0c003f81c40c605202080c801a000, 0x1fac69606fd734a726bc13c92ff55d2b09c4a55708ce270006c05d5d8080128003aafd3f4b5f437eaf1869fc3be31c4f9b3c6389f252c82d5800764769e7179c7353037ade000eb71d39c6f6200a57fda7b0280019b60002d3c90d343619a4acd26127d66002b57429⟩,
  ⟨0x2cb1530a044b8237114080c3b21cb0d3064c30c1770b5056429813b096048821e10007783801ac0b105001ec0cc057019008c024000, 0x116176a4007b0675360c000da9b05c002d49849b0aec41d5cf700200a8f54358516216af3343d0a4e24f99b94d3e292934984981a05449a492e34984981ac19b0cf5a3469b0c6c17d7c1099f924fb10275eb4c238c1acf64a⟩
]

def tableRLLRL : Table Block := .branch 14 tableRLLRLL tableRLLRLR

def tableRLLRRL : Table Block := .leaf #[
  ⟨0x65c32918b4c1c5ef29812dc7d43ba1ca8dc06962ee15689784021a40cb85d02ca14208f84201f20e2065829810606002a80c801a000, 0x81aa2818475600708d1f0760fa5cee9d48f525a4ce3e9a30c21a038cfc738df57338d5105a79d77163b8600709f8ae198432757d3bce7085f521a2ebd0ba4be8bf70bbd09d47bd0f8f93d0d70c69fcfbe7af32e1ec3479ef536213cf7a90042c3bd3e496f38800ae1c5853392e9f24a79c272479b74ee1b584e001ce46f38e9dc35b098002b15272279c34ee1a584b62300c2000bcdfa7a330007cdf89e54c038f37627cda037c481b4c9c94cc6cb26c3064ceb0019eafd47ea4c5fa8c0498bc12022f50e2c001b06353266⟩,
  ⟨0x3931b00d486823301888bc85ce2da15a8a5851826d12708903d61e00e986b83161810af04fc2380fd06982d012a07602b812804a000, 0x537a0008b3da7ea1a4cd2506900366a8f672da52e13389c001f7735b77ad854606c4f6ba975e6cb51ec6578b2b47001138ff358db3c267138003ee9eb4b85b3dc8c0c5c3d9de2c00dbba396e36738bb676e28f6bed95b7a3808c4d49c4a01e9389b0bd2f12e15a5b89c001f71b5b5148c27b1⟩,
  ⟨0x3d51e50ee474e39d1c28dec6c63591a08cd061a2d715f8ac851628112d08d443c1b309d0498226105079021c0e605e02780e804a000, 0x109ac4d25d23c0d0cc78b034331e2c0d0ccf8ae27000317a399179e2f40001e54328e2b09e2f225c7e740c97162f1730001b603536c16986259d3110d9d2c153403a9cad38c493a5a2193a502a480680114e4e9eeed183d44fd0dee22461f9d191079d145a500069c4d3e45a3032aa67534d22a6395535250c65ab⟩,
  ⟨0x2b314f0a3c4f426b13088f04522040f6078439c1a90c2057c28e13409084502060f6074836818e0b60548270112074030807001a000, 0x482aa4d248512a4c24c0d7fc8013ad0f912003dfefafd8448784da0a24001f8675a000dfe5b10007e1bd9c348e2d66877c10fe292834b8a74cc69255644ca1a6852e290c91337a680c112001c004800b8b53c86c4fa66⟩,
  ⟨0x2b71530a0c4f026b123088442e1f20e786a83321880bd855829613809584181f80d7062027c10e07203281580900370150064014000, 0x4b9a4003060c3c26713fc80000eb50c7943b630321912866ac0030bcc3a17d2856ae4cd25069714fc6e003eaf049be8b6138007f19eb6060007e31d5e4291c108001d9c621e2d8929e8527126086f534f8a4a4d2612606⟩,
  ⟨0x3151740b7857a2b014689744a623b116081c3c81bf0da86482f41630a605042380f9075035418c0b7048020c0e0066029807801a000, 0x356c00f6781ab28016d2e27000e18317861c2f800b15034554e29847f96c001d680070b591000fe5dd9c0c001c2be2e2a67170db64dac0c9c1202ccc47ac83700e30e791c8855bb126924c63f003dcb613f068d8183a458000018000040c60d3466⟩,
  ⟨0x33b1960c885fa2ca15f8a704d824711107f43cc1d50e206dc3241870b10554260126080837016a0a204782100e205002080d804a000, 0x724781b19c4533578cc000287ae9f1343ce1cf87876c3ca1cd870007e7dd6e32a8a36c6c0eb043532c8e9a4cd25069714fcec003eaf04800d2c76ad84ff390007ad818001f9c3572c40003b100311967a766a259544e095d11757601967c89382464d3357b0cbad⟩,
  ⟨0x2d41630acc53028b13c09a84ae24411988944242010ee06dc3581870bc051425a11c08884001d00de05c82b010e07b037012c030000, 0x9219f143ad002a7d3307a89c21afc44eec891f34c50d072277cd38d90025abc6c4004d5e09000b1afd59c4b00171ae0007550d4b8a766bc13226b8699c581b1a69f1b56c2700127c4d5c23389c003151c5a2a13e00003aa8689c5⟩,
  ⟨0x2f51730b5458c2bc14b8a184c225212308ec4582070f6078838e1af0cb85c829a11a08783e81aa0b0050825410c06102b80c804a000, 0x6924b8d2612606ccbb1dad68d1a71d8ccb35ed89f91a135249bc63eb9d687302a781810a455435ce2c35ce2de5763ae9e782c7274f3c080038e469e1303129c001fabb5b8e34fcfb1309388d59271c000074f0363838e16ad84e0096381ab⟩,
  ⟨0x3151818ba056a29813a894848a21510587a038619e0c786102de14a08b84341d00da05f826810e07a035817409403d0160074026000, 0x1f5837bfe9070aa91fea94b4f56c112793349930e02993261fc52001013c98b0f0300964c389008ef38d3de6e00469f224e0906254e3df9a1eb4001bcc8003d3c0d798003da9ea19cb1953de5a00b69e5343d0a4e24c50d02a27c52526930930340a89⟩,
  ⟨0x31917b0b6c5562a014909b44b824b11e085c4141fd0f0070c33818f0b5058027612a08283d01ca0da05f828011c084034811004a000, 0x122000261c093283800643c002c3c26ca1beff04b75b86692b349849fbec00ad5d0a5852044112b0060795c7102451d96138007f7a6b6060007ef2d5e09c5222f2f7671667c89382403fd849fbdbd4d2f11e0600fe613f738003ad003b66a20fafdd3b3⟩,
  ⟨0x40e1f58f1874237c1b88d3067e31a1870bfc5e42bf1538a3c3d81de0e506943001630a204942100eb06702c4128077036812004a000, 0x302e007c4e4460056ae1cf8743570e78011abc12003439bab6138009ec16ae918c23b0ac001f5f8002d54114e2c112e2841400783fa000e3be0eb800552ff8ab2a48429a7821b84d18001a3434ff8951a3ad9022f94f0346d4be04b32970000d298a40694c5904cae2481e5600c11278160695c0d53d0409ab000f6530ff82bb25ad⟩,
  ⟨0x30817d0ba45b02c91520a5c51427513008e44582070fe87603961a60c085c0296126074837018a0b6054025410407802980c0046000, 0x921b0cd256693093fa00015aba14b0a4995560c8ab8ea0f357b2c27000ff39d6c0c000fe6fab618803bf9cecfccee13f6634670007f32d6e46000cec7046001004000b0fa6687834c612648688d122822606c8a0010d5800703389933002303189⟩,
  ⟨0x4c6254926892046d22810b480c3fb1ef0ee46f036d1ab0cc46182dc15b8a104be21e0fc875035e17c0a4849018e0a203e8160066000, 0x29fa526126063aa4a4f1a00cf5299489d4b1f390020149e134ec00ca7f5b0c535a0b5d59439f8003a784c06831c001fd5f5b56404a7b137ac9c46098787fa1e4d3c3fb0f1c3f3a700c2202d3f8956c1ebdf0fc69e1e0f1b34feda79d3abf2d3c97d3f93be59f92da7f2c61dc00074fe72fb61abf10e2861cbc01bf0ab247d3f8530ffea7c6487ff530ff78c7a9c91bc8ed5e485e1f3075a7⟩,
  ⟨0x3f11ec8ed074e39a1c70da46bc32b1830bb85922ae136894045620c0f6872034a0d805d827812208203a018c0ac04501b00b001e000, 0x112c38b3908011a7a14b0a61180019c775389a71b0008001d3ce34000ea6253716adcab7b53a9d5c2529409a41a3aba34e00d4b270a8ff76d6e98d3549003a5a8e34a7ee7ad3ac42770eb924e1d3d5503be216c25b25674be2183043ab0e2315f7905a7ca01593d060949e8527126086f534f8a4a4d2612606a0005949a49⟩
]

def tableRLLRRR : Table Block := .leaf #[
  ⟨0x2e716e8ae855a2a214a09bc49822710b08143f01d30e406d43501830bc855028611c08203c41c40d7062027c114080037812804a000, 0x40c01393062d84f09b286fe7c001d680064b7910037fa1d9c99a4a0d2e29fe64007d5e0934d16c27fe54003d6c0c000ff27abd13880018ef9d38d05c54450f912704862899f54007d689e19e061d348003fc3eb40019f4362000ff13b3⟩,
  ⟨0x30317c8b505942a313f096444c20e0f4877c3741a70ca06242e81630aa052427011307f03d01c60d905a0244108061018809c01e000, 0x40c0014e1da981a3d7a796e6000338369c001a02756000d011384eaa26ff1680200074f0350074026aed044bea89c1274cab8f33e449c1238699fed26ed689d19e062834c0dfd60003ad60ac9a322e27000c99b17261932800b15034699e2e247⟩,
  ⟨0x32318b0c1c5f42ed16f0b3457c2b315109f44dc26212b89204462160f786e43421940b6858c27811707802f416608c0328100066000, 0x78a5724b8a68cc6125f4d39927048d1a40609fbb50d89f91a1352490162760d3b89c000c7c2e647c18f8400079513f38ac274f471efb9d0327a18f79cc0006799d3a79a8f75ce00066e8000f4f03279e8f6fce4f3b1edb98002ce25a7f148002001ce21a7⟩,
  ⟨0x5fe2c293f89ba4bc24d91d88a242c2038f8877a3981b98d3867a2a8102855027e12a08f83e81ca0c005281f80d605802680a0022000, 0x1522a2c36a5f3576ddf35b4385edf4ea90af6db5279a9b6e79aba1bd15f1a869efc8032d37f016d690b5bf7b4fb33207eafd98f60357ecc6371abc6dfd97d5e3711ffeafe5f903b57f2f7a01abf6662efd5c53c000e9eadcca89af51450ed2da14c685b67798fe630fc3a7da57428da4f04edb36341c1360a9f31bcc5a6334f7eeed29a13ed25826ed991a06099054798be625317a7e3354e5baa704806341c6aed99533df803da700fde0e9ef23ecf3b9644d7689c1200a4f75acd6418f9a67⟩,
  ⟨0x69033c1944c5c5fe2ed9714a284ef26c92d091e46a223909080233414f89e04a621d0ee071820e0f6073831012807102600bc04a000, 0x8595c58046467b9b13a89fe1e26d13989f61e260001c3c4c30dd0ded79208c504896b932e88bbee1c1bb828cc46d5a7000638fd4f7eb0cefcc71fa98e39df8d4c73aefc6b3c29e13c6784bc278cf08f7d718ef73a10e9441bb06f073cedc406adbab6ed9b336dba30b6e5a76db20346dd74606dd33656db5b6f6dc1b71d3c30541d7c783abee8d3a0e959ef0c0f8e000d9ed5ad41d1a7f4de1b06983520d5835b6e7dabf067f383cdfc1a36add10a0d7d3c29a6724def66438798d5ef264187000cc6f0e98ee4a9abf440193c0c99be4a3ab⟩,
  ⟨0x24811e08c44401f00ec070035a1a00c405c02b014509c04a423610807d83a81b60d106002c414009104381900aa032011806001a000, 0xa46c12306b000c7240058a85c5c585c1c50e90ee2b10708a85bdc585b5c594d0f429389314340a89f14949a4c24c0d8a693492546930930346ae3678d38931b18d4e3db13e26c4cc29⟩,
  ⟨0x31b17c0ab853028713b099c480233113084c4001d90e606943361740b184f825611c08883f81b60c605e02ac14207a02b80c0046000, 0x47b00478bf030f20002ea600d61e39b86c334959a4c24c05e0015cba14b0a51b458748b90dc4767b2c270007015f9b03000180abcbd138a3a7cb76cd1343e449c12182263ac00ec689f19e062c34c0c0006024f340031d0c880078097d3613801239b8b⟩,
  ⟨0x59f2be15bca9052528d93e09a24201fe8cf86362f81640a9451e26c0dd86b83461800ac84c821e10006e82e812e0740288118046000, 0x46f7c118b713c0820003cd8fef817230347ffc078b80fc6d1f9a7601f81b820017b8cbb6fb993b1dd3d6e371e4a409a7f3f01770e75f3c3cceda405b810013b8bb3f6edaee60ec61f7c8cce9c0b7191c4c62a32389ec4f983cf587000c797131dec30032327873adde1700051fbdbec002dc419f476bb72967511e2d3d19b1300063778780e046f39b01bc8d5f340031f4c4e0a6017c7cf131f2017627f0202ec5c61230b8b8c200b317824055182c5c7b40578b⟩,
  ⟨0x6853301950c8a63830297b4baa5862b994908ca3521978c645ec2d10e6062c2d0138097041c1c80c1057028412007f02e0118046000, 0x25e95aba46308ec2b0006f46000b5509d78b09cf8a1f9343acfeee7a000e9fe99371e99e20f648e30fa1a79025a62f5b3773a51b73bd33aeabf5adbfacfaf4e68f9f4fba75d174a2e1e7036c654cedb4c2d5542c59f537f4dfce9cbd4b49191f2bc78dfb69c00321ec4c6c70d1b090ee278ccf8874e7ebbb4bd48c7c1ba4bb4f0aeb7e2f1bb7e8dfae7cba7033ad243b4b8d52ee37a7dcbf748c85f71ad3cc1400787da70007c258781a0478001e6e9d6bb991007ed570e1ea1f4cd6c695a34800638b898dfe1802f1c3c38007c1f87⟩,
  ⟨0x3821ba8d8069632418b8bc05cc2bf1590a2c4cc24110d08343cc1c10db86482da16009d84581e20d005982300de05201a80a801a000, 0x18524c8ab06355c8d65e9bd96138003817fcd818000c0bde5b0c400e40bfe9de8dceaecc001bcbb4f02e1793735c4e000605b736a23005b630354c000a6ac00185c753a660032170d4c2de005ea6a5b003b5701e64b67ca70f93e5187645270072893e4992caf240225782406c8a56c27⟩,
  ⟨0x7ef3eb9f28f467993b91d4ce8c71f38a9be0da26b934e19fcc9859b26e103c6a02830d402fc15809d04401cc0ca05402180d001a000, 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⟩,
  ⟨0x2c314e09d44ba24a11b88b04321f80f387683961be0d886883221820bb8598282132093046c2180e706d02cc0fa06502c00c404e000, 0x2b80f1d4003f01dfa911038bcb226bb44e09a691917602167cd33f8a5724b8a68cc6125f4d39927048d1a48b0b44b50d89f91a135249229ecf3d3b89c000c8d9e648d891b2000795108b8ac2791aa000f9d03000191a7cc⟩,
  ⟨0x2c31558a8451227c12a887c42a1fd0f7079037a1b00d305fc2ea14e09b049422810506f03441880af04f02240e806702000d801e000, 0x443ae2c0d10e78ae270003243f9924364870002e540d10cb8bc91e06000d242798e2781a4828003e740c000648273a2147174cd25869309323f8005f32852e29074564d1c81c959310b8613c8f60007ce818000c8f4e63632⟩,
  ⟨0x2e316c0adc514269127089c4041cf0d506743201850b004b42100f006e834017e0b20528258106074034017409803d014005c014000, 0x6268fd01fb480f480000d9c0763fed2019d41e09f850ae692a56a269c94e2546d43d380356ae69e852c29c4d69f002da90056d5700074e00a5aada9849287bb90fe292834b8a64cc692451449849c46c123a69bc9164267a134b89e06⟩,
  ⟨0x3101758b1857228613e095c46021f10707fc3b01cb0df06b432c1850b7058427413008483ac1880ac04281c00b605001d806801a000, 0xb66ad96d3800b6cc69fc5200080076cb69e060006d95d480119299ced334961a4c24c9480017cca14b8a468d82aa34860d902936184e000e4a073a06000324fb98041cd6900018185d488c1c500710303a98d6a9ab054e09a7456011c82d9e852c29⟩
]

def tableRLLRR : Table Block := .branch 15 tableRLLRRL tableRLLRRR

def tableRLLR : Table Block := .branch 29 tableRLLRL tableRLLRR

def tableRLL : Table Block := .branch 58 tableRLLL tableRLLR

def tableRLRLLL : Table Block := .leaf #[
  ⟨0x2bf1588a1c4de25012188d044e21610487e03d21df0e706fc35c19f0ca85c02c213c08903cc1b60bc04e81f80e605401d80a8022000, 0x590c05400ca5a5449de2813e0f47a149c49f33729a7c525269309303529a4d24941a4c24c0daf28df9ad309237d6bc7af005bd800d1c00ef5a4c488e2d2ea5349deb4a697bd04ad2f04893de54b018774c6b9a3219d306e6⟩,
  ⟨0x2ec16b8b345762ad1518a2c4fc26f131094048c23911788203e01cb0d4059c26e12d083038417809504301e40ce05d0270108054000, 0x73123c0c5423ed0d0344bce2c19af23f8a4ba4781ac530300be930bce8999c5c1f1b5dd3ede400787e0c40038fddb13d3ebc8005b12c3c0c00060c8737047935f62000d6b1a7831aad5b9b711fc525c23c0d512611a24ff1400ca700547⟩,
  ⟨0x3cf1ab0c1c5ec2d11620ad455029b146099c4a824911208243ac1b10cc85d028211c074835818e0bc05582180e206702b013004a000, 0x70befcef78914e000404f804785569ede002780220006de3d3edb9addc007f4fe295c92e2983318490062dd6d4dc689c12000dba7a9c5885516e88028000e9edd0004f533b450f691001ba7b55ad2100334f690da2fa7b476d20b45b4e8821f224e091d34ec3b68f6b44eccf03149a606834c00079bb0b5a31b1⟩,
  ⟨0x50b27e13b49904a124a11b48c643c20b8fc872a3701ac8bf052221810607d83d61c60cf85e028a12007d835816208c033817406c000, 0x76495892000c9e7a749f1274398c27939c94379d03250b9399cc92f1dcfd4c978ee7ea5aa5fb4f00cacd2b3524cf4e000c9e9a993bb4cd51000a0018009804f8c1a7f407c7b0009aa1000c004c0234fe8078f4000b5400010007803d857a7846d50e1b137b3560aeae0e834a2e6b4ec839fcdfab9bd600234f2f1fddba9fc13eedd4fdd9f81ea7f64fc1f57fb1fe23ab000bee8d3c0d0719f72f35f5438608189c7⟩,
  ⟨0x55228e13dc95049b23b11007f63d61df8e686ce3401850b9456427c12b891046c21110207c43981a70c1057426c088031813004e000, 0x116e349e8aadc7002a277d3800316d66c1a4e7e25a78334b272d4e9d16bc0fe6933c745ad03f5a4c3f8fe3800388fea70ffd3622b885e9f111c45310ad3c1f944fbcd7126aa9607071e50f942f4f2874a15284e9d829c0f94a0fc7779e4d4d486a898a1a4b900074f6665450e00fd905a7c9bf271d48039936e9e5d693a75308612edf2555a9b8c002e00555a23ee26036ad0d21c42174a07c7000642dd4c855a69400001d3a51393a9ce⟩,
  ⟨0x5922b59510a424f126092788dc44920b0fbc7723961b88d886b03331720b6856628e103878837a1a60b985002360e8053816004a000, 0x1a6a4224e6ad298447cdb08582b0f60fb04d82f0f619b0dd85f0f617b12e1ec27616b1261d626c6ef4eb12e374b11e9e34d162fe396298d3258bb8e001b1761d62bc6ab57491e06b5671a7d5dcbc000e4d15e45ff9a781a1090001e6daa38d1ec406f01380ebf043042f51dfe9e2ae2e8d3e953173e9c0019df7533bc69a2e4d29a67cd3c5c7a52cd55a7cf873d7d3e7bb9f067ada7c3ba2e0d28a781d3e1db3c045bfa50e5b3a7cbdf0ec9ec34fa2f68c1a9⟩,
  ⟨0x5bd2d01634b0456529f1474a1c4e726c12c494e49a24111a888a41e1fc8e385f224b0c706042e80ed06b032c17e09a039813804e000, 0xfd929f8e4d09801fa64e0f9a120737e7fa9ece611c000c23de69a51000708ffa70330ae390f1639bf14001b4e34eb4da11af34011b4a34f185b662b28000a0020012b0f69d64d00180046cc164f593164e000c0088c2b4e592cb26164d46125938001000500066cbe0880007e3964a2c965931184164d000200105790002365d043c00371e8cd466591caef0004002592164a5926305000f4f70c69b1372300036a569d6a8c228e680036aae9d6a94226e6ad0d844bcd⟩,
  ⟨0x3761a78cc060c2e71640ae455c28f135090046c217106879838e1bd0cb05dc2b014909d04741f40eb07082f813208e0388128046000, 0x213207cce680cfab4701002fea51c06f9ea3808fa747c89382400fd0a48f9b7f06b400803f9d47818017cca4c0c000612bf37dd7c7a8c0d09503c873400f86a3f8bf0f4dcc92a92401fca4e3efe2862f923c0c3f5e26e2c001a5874f89801f5e4e0f62123f34000c246e68fb388f91⟩,
  ⟨0x2e11610abc54a28613c8968460223109080c3f01e70e406d835819d0c985b029a12608704101ba0d0054822810006102480a803e000, 0x1bfad2ea143c0dfcbdd52dc4e007dc52c0b7b701d4ad334619f224e091934fb10214d2f91e06549303000184e7cd003eaea2002613af4e3b17160684dc1e979ae2784d800079be8c01d4606fb4006971d6f8be97eb52613001f9f47⟩,
  ⟨0x30e17f8bd05d22dc1620a744f026712b092c46820f0ee06dc32415f0a384e02220ec06282ec12c08103601640880360138068016000, 0x1b13e26c4cc298f0fc500030a7f9a031d42db1f734b71a70485c6cb107eaacd3d35a20f5557a70006a21d380034d86ac001a6beaa8d54795e2984700030a4b9a000d357b100b30a53a70300af4d46ae40d52146a90ed0e644abea18e24c19bd24e09⟩,
  ⟨0x2b11538a684ca24d114080c3ec1c30dc86502f81720ad050825411708503ec1da0da06682f015a0a3049020c0e406302c80d004a000, 0x10330ac017ed0000018726fb8b557d55ba7001eaadd3f8a40010016aabd3c0c001d555a9d1028781b01122a3cff163dc7165343d0a4e24c50d02a27c525269309303629a4d24951a4c24c0d50f80dfad3892036d43baf⟩,
  ⟨0x2d51620ae85442951370934486222105078c3ac1af0cb86182ea1660ad852824611108383e01a20aa04181e40c2052021807001e000, 0x1707181a3fa715c4f0b80000f3625800ee303455800dae3f9f1616d8001e6b0c57b542dde9c7ece2ee9a62ccf9127048c9a64e70011e69788f031a4900030b3b9a00064e4f44005c2d0e9c0d27178bb126924c9c4000dcb613c64d⟩,
  ⟨0x2e916f8ae052226a12a890045a21810507e43d81db0e806bc3481970b8052c28211c08583981660a204982200ee05202000d804e000, 0x10300018607cb0003205ba200a6182f4e30d52144a90ed0e7c2abe21864d3666a834e090098c5b5c26713c2f40003cd22aaf84d8c0c45fdf05ab1e3380037c06aef7f004800cd54519f224e091834801b7bd6b4ba47818c24800185cbcd⟩,
  ⟨0x3701b30d3c68a31e17c8b705962c114e096c49e24010d87f83ae1b00c585a82aa13408f83f81a20bc055826811a06602d80d004e000, 0x81816d64c0d2c3d57ef30001a9af4fb0ec52b9133c0d5b28719ab0004002999ea7dd3d237ca60db2664d3803b9c9c1bc4316e68001862bcdad70384d8800c6fda635ecd18d1b7678dab300146bd9e30400635acf185669334941a5c530c24003f2f04c81b005fcb613c3050007cd⟩
]

def tableRLRLLR : Table Block := .leaf #[
  ⟨0x3a61cd8e086ba34b1a08ca06022f015e8a5850e278128886c4221ea0ef07443581790b08548290123055027c11c06702100ac03c000, 0x30480c63a410aaaeb5a5c23c0c0310e9867c02839b0ce6ad3aac6ad1b4f2078003f1ed24c2498d2e002392000640d0003e3c0d2060002f26119c4e000d6c7abad8ab8b0007551a3f8b891e06b90ab5ed5c8095b397dc00082015b2d6c800169e137ab98000c329e6b6c95acec42f163f8a4083dec7⟩,
  ⟨0x3d71e50e8c6fc3741a78cf865a32217e8b6054a290135897846e212104078c3841a10c0057c27410707102bc110052018808001e000, 0x389c000c363e6824f5d66c60604a2baad5e39a5acd382402bb9c7575c28057a70092b8400ab4e0caa7009ebb2d5b89c000c356e6b7235d7ec606b9a2badd5cfa4fb5a67d67ced33e8005690019f1b4d58d562eaeb37ab5eb5dd3d6ad5b6e9eb59ad56b6cd3ab5e905bc756bb20b15b471e44063dcf22e68933e449⟩,
  ⟨0x49023591188423fa1f48f087623a01bd8d206462fe1658a984fe25a12808a44081d10b3053c2700cd05e02ac140085038012c030000, 0xad66b60d656bf5ac6b0001acf34f2dbd59ef3870ceacfa5b6f3ae0d2f469ac6eb06d3d635582d60fa7ac6ab16d3d63b587e9eb1cac3ab13d3800358e69d58ccb64e65640000e9e0656652d87981d8d571a70eb43b0aadf4e014d5f555b4890619028802369e13d64bc82c9abdc02630bc1419114043ad5f4f8a694b34e0901cc6160c2a70006bb1d580035d80161aa90c3c5⟩,
  ⟨0x4171ff8f6878e3b41d48e586f236a1af8d3864e30017b0b645982a5137899449a23e10b87c03921bf0cc06001d60c602680e803a000, 0x4748e2b183e4869ecd44b2a89c12ba22e0d0324f9127048c9a5371413be68030400f2781a0701652e27000304db9706da09a8002e540d1cef8a611c000c390e680018261d100070e4ba7030001825bcb8e67c5b0cf71173a9d0aed5ba63e8afa29defaa94d383f15f969c05eac4a460312815c0006aa4ab3b4fdbc9865f1653e20c929⟩,
  ⟨0x40a1fd8f8c7ac3b11d28e5871235619f0c986022e012588f846220c0f387082e61680ad84d021e105070035815e09c03a813804e000, 0x3925c46de2b09c004dd675748c611d856000eeaa0016aa234716233714001dff74f5e55e76befc76e1a9906f500398d60007c30000b391d3f99bccdb9c0011a9dd28008d4800fba4ea738bdb6ea5eefac001d3c267138001875fcdce27792d8c0d9c6ef21ab818000c3aae693c91875000679a00061d3f34000c141e880018753d3⟩,
  ⟨0x2f71740b785722a6140895c49222a10b877839e1c20d9869432417f0ba854025e121080037c17409904701b40bc04c01a0070016000, 0x184981b7c6ddeb5a1d227778df135e007c4802a3dd0c05bc4d265543d8d00080400159e1537998c24e50d81a245744c0d9da002fab001b10b4c10c01f61f69b0e00eb4e75e008eaec1c012d782400ac16d6792f144a88ebc588efc53935e09⟩,
  ⟨0x2ce1538a004b624a11c88a84061f60f4876038e1a00c985b02c413b097041c1de0c8054827011a07f03701840a004101b8088026000, 0x220237c7e6c4030003cd003f7e6d8e19a4acd261261ff000ae5d0a5853526b1835cc136f23d9613800387efcd818000c3f5e5b8c4000c3f7e9c4a1e2b789837dd3025e6a8f42938930437a9a7c525269309303402aa4d248bc89⟩,
  ⟨0x3b31ce0ddc6a43471980c645f42d015d8a9052a27013189384362110fc876036e1920c2857827212f085035c16406302c013004a000, 0x78d6c9e01cb5dd5f00c0066af048ab0cbaf599615fe551c2b7c90814707e53d2a6cb388e001effbab713832aaf7fa0090002d540d130b8aea16a369b4ab51b4f09bbd4eadc4e0006207f373e90073630367da00d6acac7cf93784d3ef07e3269c001df8b748dd48002d3c26846880cdf439a000ef8da7⟩,
  ⟨0x3841bb8d7868a31e1888ba85c02b91560a144c024911107f43b017b0b3055c29813908a03e41de0da06182b011607401d80b802e000, 0x61484c3bac0619d73159c12f6584e000e21ff3606000310f796c3100ff10ffa7c0f7aabb303958e000621c73741201ef620187003a702247e1d03802de038b74d3e2fa9f224e090f51201f7029ad06c694f0354caa507364f23ec9b64038b5e126cb00107cb677d4b3f19a67964ecf2c9⟩,
  ⟨0x33c18b8c0057e2ac14289c84be25411d885840e1fc0f587103221870b1055425c0f8077035817a0b304601cc0ca05402180d001a000, 0x723cd4e46ba67709de2660343bd38688788c002eb9b36a259244e090bb875cf2e00669f224e091934a79f83e5cd0006792001f4f034f22002ea5c4e00060f6f2e0ea41ec0005ca81a3fa7169c05cf0300a883cfcba3be73c90d86692b349849888c002b97429⟩,
  ⟨0x3601a40c846282f91660ad053228f135093c45420b0f606042e81630aa052427011908383f41d80c5053026811606c0308108030000, 0x96fdc600092df792e2700ea6163513ca0036a932bc5d18060f03621a0d26aebf5c84d98625e6ae74cbca5ce80254bec4fafe135bb2cb48e6db00074f2668a33e449c123a69c373869a5d23c0c3269000311b79b33f0b547118d238039b34bc120065552e6b6100034a9311c5⟩,
  ⟨0x28d13d89c44b224f11b88b442a1ee0ef87383821af0d2865831817409f04d01fc0e606702f41600a104a021c0f4069021006c018000, 0x5d23c0d2d4f8b034b55e2c0d2d838a00325cbf1ff24ca99fc527b23c0d5126069689c500072e38000f1e060002000a5c672a5a0f165ab716accfe295892e2983338a568d200124cf7264ce8008e4b627c46⟩,
  ⟨0x28c13f896044420a0fe87583981a50c685e82da1550a584e02220f907303541900b9056027c12007d037018c0a003b0160078026000, 0x71380019963cc996132c4000f2a5d771584f32b4001f3a06000332af992ea38a5e21fc5211e90f0307289000332939d2de38b6821f34cfe295c92e29a3318493f1139927048728979b343627b21a1350289⟩,
  ⟨0x28413c899847e21a0f9876c3901b50d4065c31417d0b7056c29413d09804742100f5058028412808903c01980b804401d0088030000, 0x84de0a24000c4e2e68003695ec4000c4e4e9cbd4e2e66877c10fe292834b8a74cc69255644ca1a6852e290c91337a680c112001c004800b98e5c86c4fa6684d62692e91e06976fc581a5dbf16069773c5⟩,
  ⟨0x29b13a09944a824711d08944001ed0f006e435e1880ba854027612e08f84442000f3071034c1920b4052824010207702900f4030000, 0x45040019cbd093686ba14b8a4181570dc0d51b337916c27000713ef9b03000189f3cbc0522350c363b3c1253d0a4e24c10dea69f14949a4c24c0d40aa9349214ca93093035a64004eb418952003da61aff84487⟩
]

def tableRLRLL : Table Block := .branch 14 tableRLRLLL tableRLRLLR

def tableRLRLRL : Table Block := .leaf #[
  ⟨0x2af14f0a3c4f426912e094847423010c082c3c81ae0d206302fa1730a604fc26a10e082037418a0ae04b82300ea0420188080022000, 0xe9a6f2459099e84d2e2781a5fff16069805c571380019a13cc9a0f342000172a0697b9c5e48f0300069a07cc713c0d33fc001f3a06000333fb9d2f4b8b4253264cf64e099139993b6db6a013e9fd0d27c695c923069⟩,
  ⟨0x2ce1620a7451426311e08643e41da0e386e035a19a0ba85742a614009b043c1d40c3055824c1000730310154090039013005c016000, 0x2060003150f9710a440024d2ce980018a81cd000ea272200062a174e6107151e43e449c121da26e8f00235a11e50f030ae89818000c533e68003744ec4000c535e9cc12e2c24943ddc87f14941a5c53266349228a24c24e23609⟩,
  ⟨0x2fa1698aec55029514509d44a824511d08a44081d70e686b03401930b8050025011508583a016a0a804b82180f205202380d004e000, 0xc568e9cc4ae2cdc896c913824c8957e2401167c89382464d3758b551ad001f0d003b3c0de1600b69846713800753d8bd4eea840038a986dc58850f03004b5338ba268001006f4fa669334941a5c531524003f2f049ae8b61380038a8bcd⟩,
  ⟨0x32318a0c285ca2a814f09dc4a422b10d08243f81d50e506dc3541830bc854828211a08103ac1b80d105d02540ee06d02b013004a000, 0x5247818012d1b357f01f70800403787818000c57fe68003a346c4006c581e9c99a4a0d2e298af2001f97824d445b09c001c575e6c0c00062b9f2f84e200066ae74e62c71445363e449c12068326ec200235a041ce63c0c0a6326060003159b9a000dd79b1⟩,
  ⟨0x34c1998c686022f41668b0c53827b12a08b44281fb0f8075c3881b10d306442bc139095047c21c0e905b02b010e07a02a8088030000, 0x9e87900f73b25399f0c270007363b9d0300019b19cc0102e17900e78a21d4011b143fa90d00e97f8574e097e897651c896cd13824c8d573fb5c7d77369eed700334f9127048c9a6ee4d1df5a000dda4003e9e06bb78005d4b89c001d1cb57a3668e20016aa0698ddc5⟩,
  ⟨0x3471930bfc5bc2c91540a1c4b425011488203f21ee0e686b02fe1750aa0528246102073833018209c04581e80d205a0198098032000, 0xd9dd9e2e18b39e6800da35a6cfacc0096896700db3ab380480659cd9e068b782cff9a01167767c893824006ce2d366d6af6d001003b36b3c0c0056696981a2d90001e6d8d5a8dc6692f84cba6709c12096e47dabf673699a4b0d261266cb000be650a5c5203e0ec⟩,
  ⟨0x3141768b54560289135090c46022110b080c3cc1d10e386d83581850b4050426811708584001c60bc05202300de05201f80b0042000, 0x317a3a72b8b8a32f7dfbb38bc20d439a0072651c326c5dfe6a2687c8938243044f46074b44f8cf03161a606000317579a00f3b31000f175fa6c270139a95d236090066995803cb0052a9595c59591c50071493cc7324af8b9354887c4d67b67f69⟩,
  ⟨0x3011670ac454028f14209bc4a023d10988103f41e50cb062c2fa1690a104b423810b07e03541900bb05502640e406501f00d001a000, 0x143424d975869c22dd24f2a694834e090f355801d07470e9160673c681a5724781ad5956000f9260010006011e9f13550de6a8c00062fa7360416386692b3498498bde002b97429614d49ac60d737fc33376584e000e2f4736060003179b96e31⟩,
  ⟨0x3f71e90f1473c3791b78d286523081738b0853a29213689304322010e7070c36c18f0b50580276116078833016a07402b80e803a000, 0x32ade53ecdc4e00063117371053a136303621c7416ae0d803ed30b801f6900e85bb4e2147346af109001357824002c41f56003ce96b0004e73ca075524638a000d2c187b69e13389c000c611e6e1e872f6c606c3f4e5cd587d187069f101c47f52000e21ba9c4234d4aabed2fc485bfa7f3c3f94f9f50cafcfa8657e70712b⟩,
  ⟨0x3751a70ca45b42cb1550a244d025a12488e842a1f40f3870033e1950ba058c2a414308e043c2040e1060026411806502d80d004e000, 0x9ce232273402cca334f4c73f84fd1000389269ea537398105a7a24082d203fd1169da1a0cd2b924001c96b4fca3ca56b71380018c6fcde6de4fb8c0dd2fc9b6bc334959a4c24c6300015cba14b0a402791ad6003c8b6b9c2c6577b2c27000718a79b0300018c4fcb6188e3e8c53d3⟩,
  ⟨0x59b2ba159ca8051d28993c09964a423e915885e40a1f18ef072a36e19c0c845f82d715b0a544e824411187d83a21ac076808002a000, 0x46643511cd71380018cc5cdd433fa723036a15fcf8be42790bd4aa4e8d09c9549b19f79319f152672633d8002e480035256a6723467ae646798d0dcc8cfd1a17991a1233ef30000a91e8cf7c7a4874c21771f9a7c497127d4c334465a7a77ab2d7d39d376bfe6feb5c9b87e4de51b3f24f2672859e72e9cc352002ce59a7219799986a2668ea521a9107000286e00032166994ca4b4e43273310d3cccfd49c35020d8002784c36e00110b14c9e523a784dc0b66⟩,
  ⟨0x42d2040f8c70c3751af8cf06322e916e8ae851427d12b08cc4522060f287103461800ae84e824810106f02ec0bc05202380c804e000, 0x17aa003fa7007afafd3b2e600d003779751ccd52e9c6cd3006c3401401589004c01312001d5065bb0f08d94fcb661f29794ecb5e1dc4e000633c737539021c8c0da9b80fe2fc68052d3e4002969013f1fb4ea5dff18bd4b615f16001c2ce270a986000e89b0f853c2a62c00fa8ec38002001000778b519c00269f91b137e5d9a132f908ccbcd⟩,
  ⟨0x4182030ff07aa3cb1d20df46b834f1910c605ee2ed1630ab851a26811a88743f81f20e686a030e1680a484901fe0cc053820809e000, 0x2e91e0600173a439d034e8e0013ce00113a379800ba2567f14800801e8859e06002d0eb4c0d3a18000f326d571400738ece000eb11ab0007587342355368b8b76200367818cf9d60f57b6df633a9ee5ee7b4c788eb498e91de937dc5f93a9bccefcdd3dea77995f99a7be16f6ed3def4d3c69d965bde5a77d3b2ec00f5e63474b551a7⟩,
  ⟨0x2a714b0a244f826d12d092447822f10e081c3e81af0d0064c3101770b2856c286139090845c1fe0f206582540fa07002480fc030000, 0x141a5c53a663492ab22650d3429714864899bd3406089000e0024005ce5be43627d33426b1349748f034df0e2c0d37c38b034df6e2b89c000ce9ae64e999d34000795379f8ac2700073a5b9d0300019d29cc9bc3c5⟩,
  ⟨0x2b61478a144bc24b11308444081f50f387583921b80d4867c31417b0b3055c29a12a08a83c81b40cf05e02540e404b019808001a000, 0x1c6e4e6c0c000637172f01489f091cd6cf0494f42938930437a9a7c525269309303502aa4d248532a4c24c0d807004e3418952007c02e3fe1121e137828900031b2f9a001c00644000c6cde9ce11e2e66877c10fe29⟩
]

def tableRLRLRR : Table Block := .leaf #[
  ⟨0x2df1690b1455c29714009a44b823511588103cc1bf0cc06002d21520a384c01fa0ec06d833017609404281d00ce05a022808001a000, 0x50a5c52075b304dc6901d2cc1169b0c279dd6000f9d0300019dd3cc020aab48031466dea00018cd9d49c17c5a12993267b2704c89ccc3e1a0ba009f4fe8693e34ae491834c6ed0019cbd093686ba14b8a4181571d09f17b337916c27⟩,
  ⟨0x2d61608a704d224811b88a843620e10087c83c21d20e386d832a1860bd05bc2c013f099042c1aa0bd05802240fe05802380d804e000, 0x16b559b04965ba72c9b6082cb34f76a02167cd33f8a5724b8a68cc6125f4d39927048d1a6f86eaad0d89f91a135249bdbba4b3b89c000cefde64efc9dfa000795388b8ac279df200539d0300129defccd334961a4c24cef30017cc⟩,
  ⟨0x37b1b18cf06422fa1698ae052227912e08fc42a1fd0f807243541a00c0858028e12e09184081d20d405682600e20580188078016000, 0x4e10e2c743038bcd00f3a0f1d040e7f363a00001e6807b91100031d0ba7385b8a00feb27007d6958017ab2129530b78ae2700031cdf9b3167fd46069993f6978d296367a29d74ce50ba70484decc5ae5a3dd20c6a7006b3c6b9c0dea700613c639c0304e79e2c020f9dec226fd44e09⟩,
  ⟨0x4111f60f3476038f1c10d6c66c32c1838ba05922aa14b09dc49a1e10e785b82b414d0a084d025011c07d835015a08602f80e004e000, 0x17d685fdabf4cbf69600def272fb90bb5b89c000c75fe6df4c4846c606be94906d5f990074987000a930e3c8d27c851a1b410a3c3286b03e8f270018080080140300700327e8f83830013160080180400a01a5a51e6051b8cd88de66a46c46001caab3c74b1957cd8e9432b79a00063a4f34001ce44e8c7470003cd193880018e93d3⟩,
  ⟨0x3841b68d3c66e32d18a8c005ec2df1620acc544297141099449022110487d03d41cd08003b41860af04801f40bc03f0170088022000, 0x31d9606303654e59e2c0d395b8bc02a7819cc0658e7f307a534a49a70487daac0196a4e00c272b0061296655393b8b982a78183483a561f4dd18000de3400f004000e557801108ae011803e0108f51a7fc24c04a29001a3c4ea300189f49c0a4cc062752626b00a48d9a711968d32869⟩,
  ⟨0x4412070f9c6f830316f0b1c54427212a88e04221f90f507803861510a384802060f0070835818a0ae04c823c0fc07402680d801e000, 0x1df9f7cddf269e3d18ee0e69cd3310eff7d799d51df76f5fa739a2620dfeb63febc8ea7efb77aed38003bf2ea77ddd372468a8e9c4a1cbb13561c019f64e00cd72b0066a9f25539c78b491e06052669582480088000402335c788f800378f0300018f27cd0326298a2287c89382478d3405b344f0cf03151a60600031e239a065344002478ae99847⟩,
  ⟨0x7d53e21edcf447983c39df4eac73e3979c78e186f43751b48d7a6b234e9a14ce465f32a18fc9f64c51b187c833c17d06f00c004a000, 0xba67f1489d99e062934c0d3eb0000f3274d714c238c1acf64a9d0dc581a7497143cd57827105573a238bcba26db44e0956d558aeb60b4a84939ebe49800eae85d7ba0f01cd4ebfddfd35a050dc9d013c12a3f7c9efa1d43b3932e3c5136b3ee4c78e2ba582c2a106b7b1f45316a73b7c8f11f543a3be07f4f00155cfbaf51ce6e015d7ea30d1cd0efe10773930e38ae860aea83dade47d04c589ce9f23379588f8a1cddefbfa68008ae79d7a0e727008ebf11860e6777ee83b5c97f1dc9740031d82eb4c76ff1c01bb9ecf00040012b9b515c8c247323bf475e2ebe508b71e00000015735018d456a3081cc6efcdd783af8422bc7c4ddf8f745a7⟩,
  ⟨0x34c1928c485d62c415b8a4050c25f12708f445c2070fd07b43b41bd0d506343001590a784a02020da059826c11207f02c013804e000, 0x9fa400679c19a1e7e80014e703259f9fce61380149f9bce8180094fcbe6699a4b0d261267e3800be650a5c521ca3009c66641ba3008c5e70c2700073eff9d0300019f7bcc00402c4a6400423a0f50000c740ea4ea9e29748f03000b9f6dce81a7da0009e700089f67cc⟩,
  ⟨0x26511f088441c1fd0f807843a81c70dc069432c18b0bd05a42b414d0a104c424811a08103e01c00d305601d80bc03d018807801e000, 0xadce00c9c15b9e534821f34cfe295c92e29a3318493c5139927048f1a5e4d0d89eccd09a44d2e2781a768716069da7c571380019fb5cc9fb33f68000f2a764f1410a42d4fc8d9449a1531e47⟩,
  ⟨0x28513a097c4aa23d119886c4041f30f407643641910c385b82c814c09984682020f606e831815209403f81d00be04201a80a003a000, 0x1e2671d333c0d3ba38b034efbe2ea8439f224e0938933c5806b73407400dcf0367013a6069dc1c5979074e7c83af3961d78255b31d74653242dd424f842a982f54e097ff560357649e852c29c4d7402f29⟩,
  ⟨0x2cf1590a8c52826d12308f042a2080f386e83601980bf85d42a013308603ec1dc0df069031416c09904501fc0c404a01d80a003a000, 0x78005c9ed24c2499a6200239200f7803c9e069e70001792e27001da1b5ab1ed00015aa069a53c5ee0173c0dadd1b37abe97b193f49d874327cd33f8a5724b8a68cc612407e7653992704803cd4a5145221b13f2f26c4dca80529⟩,
  ⟨0x3b21c88df06d22fe1738b6c56c29f144098c4602090fc079c3b81bb0d105f429412908f83e81b20ba04f82000ea05602180c004a000, 0x7c16d3e0f664c90e2a4000390a8c9c00169566d869f520d36230003a76ea74e6d369d3a6d3474e2d3e99ba6869c3a790b236b39b2a694834e09003daab580ce39c001c6ab5604fe35204deab68c006cf031b498d36af6c005ecf732e7526311184de32234bc1243ef0d2e4c44ae289c120056b93ab⟩,
  ⟨0x894436a18107282f4041fecfa87bc3ca9cc8d805c72670f187463311880bec530244118080034618e0b4851023e0ad02500d802a000, 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⟩,
  ⟨0x5b62c795e8aa652c283938893a45c2068ee47282f51670a9c50025b11a08343cc16d073037016a09404181c80c603c0178088022000, 0x24520d15e683129c011c8a2e6c8cc5919c7c536becd3c4491136a623ec55c7e20afab8eeddfea5f9e7e7fa7fcfbf3bfd45dbaa3974efcf5fb743d28536f9278ffc07f05a9918aa565b4c000a628c341067f48c38f3adb0f8f22fd24672645f48b8e4c8b74915c908f6489d4c8b658f7cc9176b1eb98b1e645d733690000b13ea524cf633f0b4c2bd34fb47800389ee2714a419ea67d9696579e9e060003223b9a01fa2971c334959a4c24c8890015cba14b0a6a4d6306b⟩,
  ⟨0x47c238118c87c40b1f98f3068a33a1968c605e22cc1528a6c4e826512688984021da0e105b82520da05c829010606202080b0042000, 0x84671380039016af201c808001d54e5ee2c8bf001bcdd023407d69105e0004008c5ac002000f4f89a4cd7cf66917400079a000e3f5b1000922f3a7030001916dcd84a339478a0006459f34001ea7762000645af4e724f15bcb44583796d07c56d71e22b8ad96f2a2e3b8f8ad3594642981e00fe9c0072a2d394766d1a006b3e46e8a59c0072d2d395f6684c00396367⟩
]

def tableRLRLR : Table Block := .branch 15 tableRLRLRL tableRLRLRR

def tableRLRL : Table Block := .branch 29 tableRLRLL tableRLRLR

def tableRLRRLL : Table Block := .leaf #[
  ⟨0x36b1af0cdc63e2fa1698ab85121e60ec071c3721a60c986002ea1680a084702240ed06e033c17c0b3050025411006102b80c804a000, 0x30c59aac8e7e9ca24e2d91565ae9d5d74906e3d66159269ef8b77f34e4eb684fa136b86010804083ee31400095dc5ede9fa861934e10d74227cf438748784ce27000323539a00de427b181801dc847563069a334b9a704af08b84cc27002123279b0300279046ad84e002640dab⟩,
  ⟨0x4d625012588de46521f10b48463fc1b60d846ac32f18e0bd459c2a714788ec3bc17307d03b41ac0c705c0244108075035817004e000, 0x8003883bc7818001441be4c0c40ae48073604cf03000991abcb0002000a2e710127faafe758f13d30001dc784d898000c8f9e6d4891000323df9a0006467744000c8f9e9ca2ae2b35a68800011a1f4ab5e3e87da1ee87e001f2fd9ace9f4c5d0f743cd0f8002e5f7358d3e8dba626879a1de87a000f2f99abe9e8cd9aae9b624d249945a002796c27ec9b031a4b00001c0000061c8e50003cd⟩,
  ⟨0x30517a0b945b42c915a0a88530289131093448223410f88103d81d90e786a830615c0a484f825610406e829c11e06802c813804e000, 0x11467c8938246cd3f58ad2e91e063c92000648e7366e56308ce2706455c7a82aa9497c5e050f03670a00feac00ac427e4801d884fcbe15178247a4580018889c70003110b960006220c44ae54a41e280088845c7c893824000c41fe4c8dd8839cd⟩,
  ⟨0x3721af8d506763181848bf85da2c814c0a384d625e11c88183f81e40e6870c33c12c08383d019a0ba05382700ee06a02980f004e000, 0x19244e090b9275c22801987c89382464d28497651ad000c21400f8781a108005c4b89c001ec8f57d9ff6440016aa069d9fc5ea058f030105d8eeadcc5c00a7fa4f595cc646037357c7c50c95ad387687925c00db9baaa269944e09004f39cd5e9980c063c18acd06853c925005fcd⟩,
  ⟨0x47c21b90047b43a41af8ce86262ec1638a804f6254117886038818e0ba857026e11e08784101d60c6052826c10407802880b0026000, 0x8c6b18d9ecc4005e3c6ef800901ff8efc2a03f71df84c07d7cc1c77e0eff4a000c6ece3fc69f27ea6010c012e5c020803fcb0007e0ad3c95b7c11cd0007dfcd3c9597bfbcd0007f0dd4fe03a68c4effddec54628805fc73ce7189d90171e8485cf191ce9002b298d38448b9f224e09018e74a1459476b4040e31cf0301453a606929000079a849e511b18c7e73cda89⟩,
  ⟨0x4ee27212fc93447522710607a638e1b38cc461c2f815989b848e22f0fc87483741af0c40584274113076031413c08603080f002e000, 0x206594e2ffd5cb3f2d0ea400196774f26012cdf35542c17a7337c7550905e611d399ae3abe18c770071914f1e327464de3c64c8c9ad9878e001b15626c41866cbd19263254adbe3c8858c91192641d71c000c613e4c5fae346468c8af6a38e00063b871e16bf1b13476d8613c700030b278f25ba163f3631a462ee4c62d8c67c9000318c78f25aa406f3644671bf16fcf353f9afe79a90007f42d4fe7ba6⟩,
  ⟨0x3851b10cfc65832217f8ae855829b14509ec4a824711d085c3e81cd0e0066431e1680ad84d021a0e606182c814607e02c813004a000, 0x1f3561ecc3662c5d428781acf765fc5c1f14b8c0004ae971e286c334959a4c24c99a0015cba14b0a4013656c58006cab8ba3547843b2c270007264f9b0300019323cb618964e9327d33c130aa7a600064c6f36c9f64bc8c19a572480034ac69d3a18c1356e27930c00079aaf5c603b1⟩,
  ⟨0x46e22590a077a3ad1cf0dec6d836119f0c6c5d62e115f0ad051a26a10d88403da1c60b4854828c12f08d03cc1a00a9043018c066000, 0x2bef5e8c3fa27d0f87b77800158065e9000a3ca00334f058dd298011652c3e449c12001b27e26d17654c6800400764dc3c0c002b25e2606000326db9b603b42e456079710007001566ad3c26000d98b0e597e4d8f34001580c0029700003599b4f5e069a91aba0d303429c01349abe6800614d87214926a79b5b4b6561fce3e6bc3f9c3cd5e69c3bcd54ba3ccfa7⟩,
  ⟨0x4091f10eec72c36f1ae0d1864630016e8b3055228212f88f04321f40e0867831a1660ad84e02040ea06f82f015e08803f015c02c000, 0xaf624f27364f196bbe680035d469d5ddc9e1e687089b6f61adba017c4db7001989005db6f134469000db6713471c005f30015e2ec67ae3c5b8cf167adf18f355349a779a69a378db4fe69f32e1c6cd2000e8dff33048007d618ca37946f4000f2a5bef17137a5eddf87613d1b73d55ce818f5451b5e64bac000b5e4af669ebdb86⟩,
  ⟨0x58d2ad14cca1c4e925b124c8c643320810047ec3d31d70df86e835118a0bc45821e60db064c2c613008683a80aa04801e80c804e000, 0x14ec3c7af1de9cf7251f1e753db4f4e9dee9a7af4ef72bdd14f569ec15e44c3f8fec13e43c3f8dfc83e33c3c3b7c7387c893824003e36c4d7b0b50eb40030e8f1a61e06873f8cb13e2ef1878e3c5587b6878bb0f403b67f8b70eb863db0b67b63b30c5c1b1fcca7200500132a64a7a0210088f5ee9edc56f1b6761edc96e5c3db8edc96e2c3c9a726cca67a7b60daef16008b6261e532925800100080255b74003951400494db4f066c4d89b132b8193cbcd⟩,
  ⟨0x3e91ec0f2477c3ad1c30dd06d435b19a0c346062eb1620a744ec24f11408643e41cf0d406782f61630a004641e80c104e019804a000, 0x11467c89382460d2004e83c734ba47818c24ca1c0003cd001741cfa3035024e2ca1833a9cd295d285f9b2858000f34a56ce30e899bf9429cd308e0006509734003f79c880039429d3818003f76c5d019e28006a0f872a09282f9b3d75089a79f127ada10f4e01257fda75824c4465b571d10bc44110db0474f4ecbc7da7⟩,
  ⟨0x4111f80f246683111750b1c56228e0f5877839e1c00d8868832617e0b4857829213808a839419a0bf04c01cc0b604f02280c0030000, 0x3bab671ba7290f9a00d000e00441d0004b3fe00500170758033a7000e31f0e84325207340039ebc4e7930c029cf4e1c0140004002838800367e400400140068394013d3f99a25344a6b54d0a9a2534e2aa449953824395563067000fe6316001fcb802b1541178bb4300019459cd54320bdd8c42243c2340c3c46aa061c5a07dc5⟩,
  ⟨0x5832a994c0a004dd24710fc8664121f58f1873e2fc1780b8c58029d13d095c468211103079436a19d0c285902860f404b820402c000, 0x6417703920c3e77f24387c80e77b24187024e4a30f2dcf5700130004d0ee9c00168725b800979fdd3c23000c23d9c425ca5ce680034a4e9d4a34a5ae69b7c6ddb8ec0008004d0b4a7e00fc1feb16b67ba7e46d33278ec6b894f658d7136344f5e277a7b6fc5ef480098b001ef4717824006852d7bce000800b1533cb8b33c38b42141f6ba0ea0fb59b5c00138cc6d5d2a7a736b65080005c6536aa952d3d8930d0762c3800080192963406d9569ec3d86⟩,
  ⟨0x3321878bb058a2b41518a584de26411e88c04121ff0ec06c43141790b4056429c13d08b04101f40eb06202740ec05e02a00f002e000, 0x320f908c580071dd87950463b39b26692834b8a653f0007e5e099d985fbb96c2794f4000f9b03000194f1cb00033b1fa25fa253d74fb8d31867c89382468d34320003f34be47818e24800194d9cd0003430fa2000653774e86171606a17dc50006954d4d299a6⟩
]

def tableRLRRLR : Table Block := .leaf #[
  ⟨0x3941c38d886763141708b5455c2a113f092c4662260ff87703a41af0c605d828c130086837419c0c1058028412406f02c013804e000, 0x714c1e8004ea5079cef4e4cef3000fc900060f1000b4f48c001287a725c4e001c0762d80d84b4001d54eece2b89e54c0001e6d5e30139181ab27807c58006b1f89ac361aaf7570ac561eb1386ab7d6070f56bab756030e79264cd0c69e892612721b90cc5f202c7818c854ea1e580019d49c7⟩,
  ⟨0x32517f0b645882af1520a044e026212789084662240fe87c03b21cf0dc060c2ec14f09604881fa0da05b82400b40350140064018000, 0x56c256273661c02b74f6cca996c54e0901256f7163e698a1a0e44d19b624d249a222013f96c279a0d9b030196cb0030d40000061b89e5588001e6ecbb0459181a14b608356001c10e1f03b81ec5d101303dc7302f4400c0ef1c00a83eb4fe295892e29e46⟩,
  ⟨0x4c4257122c8cc4411ef0f4c7783af1c40d8c6b23341888bb857c2a614a8a2c4cc1df0a504f426210e08183801720960378120046000, 0xa63e18015553c4c19aaabeae0cc5563566e10b25800138dc82ca77ff1f1358b4c9713800195b9cd580e0c6d8c0cb014189ab000d90b0e001aa662c00354bb20e2a795f1744cf032b4b05eeac09a828e17a85dc098025da8e0008003d3813305142f204d42ec04b812cd46800200169eccdc8d582ac2626130006b13872b192b2b9a001abee1cac24ac8e68001958fcd56560b1d88006b6587⟩,
  ⟨0x5ec2e39688ade53c28b94009b64a824191788564161ea8ec06fa3581928c0059a2ac14489984a014b09c04542140e705a01cc0c6000, 0x988261cd3d27948be9e93ba45a915d3d22d48d5227a70006a15d4d3e5a6a8229fed3d409503d3fba7a7c0e99d38005489e9ce950006912d3f4b59a90da43e911a42b4f3b95223a7a3da771a4434f403cc21a768f6806983f4ecd75213a766219ada4234f96996d69ebb74330e001ebc627ae18666a7b453948e4f7428095974c0965b066466e4400903140b203120bf02d1c0ad3eaa89adf0057178240275bcc5d4d3320b567a7864a6400006a68d3e4631b899e0871cd05b80012ca1c7⟩,
  ⟨0x46e23090f88363f81ea8f2474c3831b00cf46342f71750b0c540296139896047a20a0f2870033617609383981860a003e8160066000, 0x24cd75b007626fdc00ec48036fdb89000deaf1388c005bd5626f52004c4df16fd78bbccdfc316001ba7e1efd17e9c5b89c000cb17e6deeefe39181af7b7efc5dcee109b7dca13390b87b78f69ef1c9d074f3914e6fa99d0673fd4ce7d3a06a6b0e9cce5149cd2b11d3ce653adca27593e9f04d810c3e90b84189e09f0831340fd215aca42681ed65235476d27da7⟩,
  ⟨0x42520b8f9c7a23ae1cf8e506e234c18e0c485de2de1668aa452e27412208843f81ed0f186f822010507c834815a0a303e0154060000, 0x12430007087821c3e0870c018c1061f224e09000e07712c1b5a3bad000804f03787818025819c4d39a5a4d201b5dc20f3383055b06d87c18855706b87000e0cf0ec037973abc48f033051e5b6ac0009aa8000c6a9807ba689028e051800101459e9bc784d48d2cac000f35822f2c763034b28303fcd00032c9f9ab2752fbb1bd8804400387⟩,
  ⟨0x5db2e89708b705912b61514a5a515271128491e3871640ac851e27412888b84121e40df867030e16c09e04641b008902c810c026000, 0x40cb1260600032d879a000d229b100032d8fa7389b8b38938a050cd6ad93e9c00101d66b402834f1a832b5b004660dd3c0a78000045d94c3881719ef06b4409126b402e405c0016a561e3cf013bfcac0bb2000335982de0b835860b8b5a0c380061a7d6561831f75fc4e3b09090c1dd771217abae62418480ef590194075ac80e6031d660b004f8798c53a5296a7c15e13305387011e1070e0bf30fb018b0c5a705f587c61ca03061874e001c3c85f30f85ec35d47091879c386a89⟩,
  ⟨0x33118e0c1c5a82c715009ec4e224c10387e43d01d70e406843281870ba058427412d08303f01aa0c404e81d80ca05602580e802a000, 0xcea706555804949b004baa71380019701cdb3ec021d8c0d682003fab879c98e4000801be3c10d86692b34984996ee002b97429614a2c8b0d5174e1d47576584e000e5b87360600032dbb97c27151c9121fa72dad32ff3634cf9127048d1a691a00235a27067⟩,
  ⟨0x3aa1cb8dc869a32a1838b8857a28a13388604041f50f1073c37c1b10d005ec2e014d095041c1a80c905e02540e006602080d001e000, 0x39e44da54010eaed296a4f57a93d44e2f51201ec5cca3329e9da8399474ed414ca0d3fe9c01ba87c3cd020008005464da2ba7d4461a8cdbaa269a448e9a7ccdd8690046d1ad5e09007e9eb17a79d3c62f4efa78c5800333a5a11a784ce2700032e2f9b683527db181ad0fa4f356c27001293ad5d0a6⟩,
  ⟨0x67332718a4c3c5f92e916b4b0c56129713ec9ac4a323691208463fe1eb8f3474c3851af0ce46242ed0a784a02060d005582180c6000, 0x46fbeef6a7dd4f77b53098001f76f4f2f01eec734001f72f4f2ef9ee4f37d18f4874fe8bfa41e8b69fd14f407cffd3f9fbe54e9fca5f3f3ca8d380065ff1426f8f22d48b9a90012468d3800322be9d22acbb4e6c0c918a5d973400620ecf2ec0444737895b5034f2aee559f1c1c8b52b4ecad9e020f112f0005500b980c8030805540b8818342fc7140ee480f1513e9a480189cd85f906c900e200804b689f4e1ff4d0fe3d3994117cc5eda078d3b1a4bdac0efa78221ffed63ffb043eb01178a6c3a6ed4d16b47c01543f74de3c7⟩,
  ⟨0x3f41ee0f1073e3921af8d1c6743131770b9057e29a1458a004b623610187e43a81ca0d185f827a116078832814a0800378160066000, 0x9ee3c59ee7c50007d28d3b0ac001f43bd26d54f68e2b89c000cbdde6c8d5ef7ec60691a7dedd58011e5fe9f224e090007cbcd4fa772326b4001000fcbad3c0c0017971a981a5e80001e6fa6322f6c7cbcf2cfcb5f2bb4e91225e6f37ab3c0eb4e90725e5f3400191834f230c8c5ad1833f983a6b187ddbd3d8cf6307bb5a7⟩,
  ⟨0x26911b087840c1f30f2874838a1b60d4866031617a0b5858429c13f09604742260ee06e82e0146092035817809e04301c009c030000, 0x1f0b80020016aa7c97167c8717bb45d10dc9a1e8527127ccdca69f14949a4c24c0d32a24d248a2893093037c09f1e6b474d3f1d7c05afb2133d09a65f62c91e6b09e625e236091835b62a9edfc5⟩,
  ⟨0x2cb15e8ab053628c132896049623811287f83e21ca0e006643101610a8050426c12508003b81c80d3056021c0c0054022808002a000, 0x610d86692b3498499840002b97429614a348b0e51750d5f3376584e000e60cf36060003305f9782717cc1278ba71667c8938247cd2006fc47ad2f11e061b34cc0c0003cd0007e1ed88007981dd3e46388e001fc35abc120c2ab⟩,
  ⟨0x48c240916889a42620e0fd479c3a71c78cb05ec2e61608aa853e27a12988b84121880bc05a028611007c83501920a403f8168066000, 0xc1340c0003f2d84e000e620f3606000330ff960006815f44000cc41e9d029e2c4720110f604c51bd1b491bc7000311c4036f1ee31800192a75325269a13000325369d2524c34e680cd25869c06792134e91fe234007e00026265e88bd770005c7cac6c4c6c907d16d3e4899207a2ba7a52d9325d0097abc12024c971abf8ec049d5fc74011eae05c0b97e3a597e8b0003a7⟩,
  ⟨0x2e716d8b3057e28f13b897c4a022910d07cc3d21dc0e206b031217a0b7857827610b08083781a40c305b02180dc05602280d004e000, 0x52318476158007b2e002c551c0e2d1c5e29847000331779a6944001cc5fe9c0cc2ba34bc5a377c59e880230f9127048d1a7b113dbc68006798003c3c0d3ca003626918c23b0ac0033d400162a8d7f168ed7164cd25069714cc45000fcb⟩
]

def tableRLRRL : Table Block := .branch 14 tableRLRRLL tableRLRRLR

def tableRLRRRL : Table Block := .leaf #[
  ⟨0x2f01600aac51027912908bc4101fe0ed871836219c0c385c82ce15409e04902180fb07703741a40bf05a029c10005d02980c0046000, 0x1a4ff8077870755380de8178b308e0006640734003408c880279905d381804b405c5c4caa626557132ab844558702af0486a8b0f448aa3abc5a3a7c51934d99aa0d38259545c26713800198d5cd007767f2303003fb3b8b6138013b378b⟩,
  ⟨0x2b71550a0c4d6244116086c3e81dd0df86c03421940c185c82d015309f04a42280ff075035c1920b605181cc0ca05402180e0046000, 0x38c4000cca7e9d205e280018b79d3a461c519338001993dcd84a9a30c38163f2a63093a66c334959a606f625595d2a5ce953cb6a9e5d55e0e2af0143f10c1da1f194580067f4021c3cd0dae696c34e09eef55cffc07987⟩,
  ⟨0x2e716c0ac4538275135895048623211287f83e61e00e986b034417b0b7051c24010f07f03bc1900bb057027411806502c00c404e000, 0x18470003330f9a0c0b1009d3317a7034c3acb9334941a5c5332ec003f2f049f28b6138003996fcd818000ccb5e5b0c4009ccb7e99552a93bd3c334959a4c24ccae0015cba14b0a6a4d6306ba97c0027b2c270007329f9b030001994bcb⟩,
  ⟨0x2871390950488233111085c4001ed0ea871c36819f0c905ac2ac14c09a849022a10a07c83581880ba05582100c205502400cc030000, 0x3b2aa4401f2c788c6d834be1a70498d6cb1610ef0dd0f043062874f955b89c000ccd7e6abb2c606c2d1971467c8938246cd3e05017e34ba47818f2480019997cd00bf8032308ce2706555c9302aaa4a9c5⟩,
  ⟨0x3721ac8cc864a2fe17a0b34580299139099447c22510d88083981a90c986082ec1650ac84c821e0df05e026411806502100e002a000, 0x6e9d753b8ad3f6584e000e680f3606000333ff96c3101673407a656821bff4dc4e000667d735eebde3035056bae1c8808c0029c7000d5c31356ac30e1a7919acd3c8d0fd4a6a71fc35566c3d583c33565c38006acb87ab17e9316e27000333a79b587fd0e4606ac37e7f1733ca9⟩,
  ⟨0x33b1918bf05c62cb1590a744ec25d12208ac4241f90f006f434818b0bd04d4248111080039c15409904581e80d205a0198098032000, 0x5301e2cd230003cdc70178d270e2db1f39f9d1530ee405a71e9aedd3754ae9b9027480d1ba6e6e1d76f82ebad6825f0e3f94e9019874c939a1d715a7000202a78f24e60e51388e6c3187482900035a200161ec1cd243619a4acd26126684000ae5d0a58521376eb⟩,
  ⟨0x2a214989b049223f11388603e21e20dd86c43401880bd8550286139094046c21810007883801960b304d82300ca0560178094030000, 0xc2480019a87cd9bb8027230352b6e298479a7c00079a6144007cd40e9c0da26ba569c5713cd370003cde938c0dee6b613ca4ba46308e366ba123552a2e2d2a0e298479a5400079a6944001cd2ce9c0cc2ba531c5⟩,
  ⟨0x2db15a0aa850625c11a88744101f30f0072c37a1ac0cf863830616e0b1855825e10c081037c19c0ab03d81a80b605001f8070014000, 0x39ac9cd818000cd62e58001a29fd100033593a745378b206a90a354876873e255f10c3269b33541a7049342ae13389e6a90001e6805671391818045387c58f19c003385c5ce1002600cc54519f224e091834803a6ff8d2e91e06⟩,
  ⟨0x30b17a0b585982b51558a104da25611f88a04302010fb077c3a01a90c105e02a213608d83d019a0bc04a82100e606601f80d001a000, 0x57c0cd020ebb1e06055593034d7f0003cd8569a35e73266d664818cc990c68f15938264d265fea6000335d79a013295bf4606000335cb9a059ac44033083cd6f0263cd000335bb9a3c714bab35c3a726692834b8a66b40007e5e09a2a8001f96c27⟩,
  ⟨0x2fc1790b3457429f13d89a84ba24e12088d044e2180f887283761b00cc05c42b213208d83941a40c805081900ac048018808802e000, 0x81a60c059f561821c036585d90820e855599fc52b125c53066714de490009461f934618002f25b13e26a5b7c600034b6b9346078a000696c71c0eb65806a00dd4b5b9590a1e0600cf4b3f9600100100666bd87e21a88611718f91270481b2c9⟩,
  ⟨0x290136897849e23a11188304041dd0e406cc33c1890b8052427c12908c04241f80ea070034415409204401c00c205402280e802a000, 0x9cccf470f992552483629d06165d102c781a626017b57858a9aef54d412a41b5532652eb00514beb97826621573269bc8fe292e91e0630920006978f2e977f1606a5d9c53893066f493824006983f57982a7⟩,
  ⟨0x5752b41514a2a4f0265929890245c21b90407d63c61d08de86aa3221778af052e27212688a04061de0e386882fa156097842010e000, 0x1a66d25be170ef7fd253e130f739658da9b9cb2c6d4dce3963ea72c6b9c3539628005a90006e6ed4d5c9658dcccb173f4d667af9f9eb33f2cf5b5957199ed73ae68fc2f4f7325ccff8569fec5edd4008d3fd89ff07e07a7082ffded4fd97fef6a7fddfb2b53ff17dfbabff87fe0d5fe21f85e9ff0ad37e13f97e9e61d987f533724000f34000d30be880a69b97d37adef865f11af577c38f86df0f5245e3faddf10fc45f0d7c31f0cfc3bf0ddeada7⟩,
  ⟨0x5ab2c21584a7851927912b48b24231fe0f187203691998c305ac2b11520a5c51826711a083c3d81c90cb06302ca13e01b00a002e000, 0x4e043829cd000f0330ee075005ab000efd70f3800dfb736238c9de957a57938e578e4eecabc88e08c738e164231a4906e3a7aa9339c792049ea64cdf1e4ccc9d99329c7932b265f8f26524cb4993e3c91692ffc7928f24564bf71dfc1879b4f429614e268789fbed4bf790f08003a77ef21ead4feeff6f87b3fda9b0fab60002001e9e06abb0d71b9cd716aebf31c9ab933a4cef645f1dbe407db2000400100036766001196c1a508c3e2a857bcf1fc86c37364f5a6⟩,
  ⟨0x3de1dc8e486da3461970c245f82d51658a9050225a11b881c3ae1b20bf856824e11808583e81de0e205d825811806702200b8046000, 0x243d0007520006711f34001b1e7620006712f4ea33f1643890db4ec2737c958339d031be2ac15cc000ef470e6f6ab047337b5bd2c3ef677a3bd0c3ef477a7bcec3b7a71c8e9dbd28e41bbdd3b8631c769dc2d70c238dd39e49e336b1a613389e7060001e6b839405ec6067076809d5800783589e0961a13000782f87⟩,
  ⟨0x2fa1638ad854a29813889984a624610f88543dc1db0db06443081750b38558292138094847c1f40eb06302dc15a08803180f8016000, 0x1ef38184021d3c99a4a0d2e299c80001f97824de45b09c001ce3ce6c0c000671d72f0148cb908056ce44f004b4f42938930437a9a7c525269309303488e002ea4d248005222ea4c24c0d6400013ad0006441d4800f63f6be43e0004002d3c26⟩
]

def tableRLRRRR : Table Block := .leaf #[
  ⟨0x4bc258126886e41f1fd0f4c6e035a19a8c405d22dc1678b1053a26712008643c61bc0c4859027e13207f83d41a00ab03c014c060000, 0xa46dd5e18002800184bf1bd20c3cfc5e3c1fce36ac8a9bea5a77564ee715632acb1bc212d8001846fc7ba761b55954cf4fa5e6975a7697508db8f429614e268464d2df92d2d61188001e3b4b58463c983f108c38f08a60fbc22fe3c291853bc7dae70b4dbf34f25cc96ba770624b7d3f8a4001705a4b5d3c0ce0a4969a9c6560cdd3c18d8ca4199a7c651ba3d3ee8fe1d87dcfee8be1b87⟩,
  ⟨0x7ea3e91eacddc69a2ee9624a2e4f026492888f645421690887f63d41cf0ddc68230b1730b0451c25b11b080c3bc1b90b28408102000, 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⟩,
  ⟨0x4d82659290934473227109c8043cf1d50e146dc3471900ba858e2a4137099047a218100877035219f0bc054c2580d805101ec04e000, 0x613a079ad25ce81903bd690e6000303369d037d68ee640df033e9e06e819a065d3ee80f9b69f73f90eb4f21ce9a5b5af9fe3cb6a9b4bc796d335b682cf1f24d928c4800f249870002edea8c371e0632413a4b9a000fbada9f74f4c001fba9a7edd7b76000b4f034e8c7ddbcd0007efed3ce8a7dffcd96b6fb90ac8158e7297c796b4e099c1071e5acbda3e3af0401752d61ff1c090e380018c15c9⟩,
  ⟨0x4f226592908fe4492110fec7c63bc1ca8db868e32018b0bbc5782a5141078c31e16a0ac852c27412d07d02e412806f03100bc04a000, 0x23d24769e5c7540019c7acaab3bd4c7537290b9438f1dba3b8724000c779e4c771e347708ef1c98ee31e739600123baf1c000c767e3ceb98eefcd81a75bc770e68002efcd78ba7af0b4c49dc9c61d61a28bb55b4849a102804f3e9b2e15900195be3a07c97090d117b5195ae3fb3167de9c78d30437e9a68cdf7ffe08ca769fefe6653f0365374f124c48ba7820a247d3f8a40018202245d3c0d03f4489a9⟩,
  ⟨0x62f3129818bf85d52a2929892a48422e909c8103e31df0e647183591a78ca861630116e08e431017e0ab84c81bc07b03200c404e000, 0x40c00a5f52606ad9e943b9812dd2c304a7095212a02531e9d4b1354db8e12d92c284a60950129c25484a53d389622a9af1f94d29a69088554cb8e1106a98843de38018774710fa56bd5ca3128b69c4b0945b4fe2900044ae94534f030959289ea653001a3c0cce74ac5ab677c3eb48c9d8695d65780d50498928400268eb4ecef07d4918bb0b2ba4aee1a9892e24c4940000b473a781a7660001e6bd15029ec4001426e482a45ece73f1c00080c384da90508bd1ce6e3d0c5a6accc001000f4f034ec55677cd⟩,
  ⟨0x4352090ff47b43b31c70dec6d03351890b7c5aa2ae145899047e20c0f3870831e16a0a184d821e10506f02b814807d02b00dc054000, 0x19f2cfa62626d52001e72e1eb779ce6e7490e009e9e6f44ba489497e11a75074e003ea661c001c92245ed3c0d3be4ea3f34003d22c3cef73a47cd916a46fd3c8ad22cc8dda791ba46cd3c8e7232e9e4729192469d3800323969d237d6dee6309d23c56dce740c91dab6d733982001001e1e06adae945b9c9456b6b73002cc2a3f8a40080398147⟩,
  ⟨0x6793379920c4a6002a194789ba49c23b91807be3cb1ac8c8c6082dd15c086440a1e20df86702f2156063024c11007b02a00bc04a000, 0x1034f2307fbcd000ea330ecc95af1ab589c813199e1e9807e94cfd4944bf28e62ad1e1622a6ce3e17b85fea4571f01056fc2bf4fb13ac44b125581a70007130d4e251a65682ae1a15f057c0ab400042ac9b86e3c02a3533753fc6bb92df1ed509bcba3f8eba5cd775336e380191f470a013c579b743dd13a942601371272a5b909b21368f6825bc000355a78f0ee8c43fc7a62725c00ac4e61401589004e613139e0cc262eab104e309aa96c8f6484d209a611012daf1d9d884a0001d3c2671380019e11cd675a697d8c0ccec4d2bab⟩,
  ⟨0x45621790287c63c01d98e0c6f23561978c605fe2ab14909ec4ac2230ea06843241840b985502941250720338156088032811802c000, 0x2b99a11ae7000309e69eb98213de7001613b87f14800400709bc3c0c001855e26b9522b0e6454ba6999b74a14c96312fde2d5a20ce380c5b9e0d1d3465b19869e32f8c9a32cd3ff21fc47f0ffc660fda77f8a50510334e6126086f334c0800347819a56b61356fed800327f080ba7ccde188a390dc4e51f34b89ccf6697120120051ffaa00100161f33f86⟩,
  ⟨0x4222048fd079e3be1d68e206c63301858b905a22c715009b44c623c10a87c83841b40ab852827a118079833817a096038813004e000, 0x8309cf39ea9897c009d3cb1a560d31ad449fa78952248d3c4a7123c499a70006253d3a250ae93cca850f032258ae8dcc850c001000f4f0357434593ce45915d0b98002860e1c02800186061ea864270001893000283a90acd3d19a8cd15c8023a98ac8010d4c5620016a478d35cdd1587322af8af35915a4577ac8aea2b3d62245ae67ce⟩,
  ⟨0x4182038fb07b43bf1d68e206ca33218d0c2c5c82c114d0a404da25511708243c81cd0d404f42521190818378172094037812804a000, 0x7f35806cf09b4c1ad16684d8e0c000c9f5a7000f67f16000bb3d27ceaaad7714c23cf7a0003cd000f66b22000e7be74e06000f65f17569b8b0034204f1c408a99b4e000d4cfa9a98b4c202d4cba7ff1ffcb0004002ff08003b90f4f44a8d618df16c3410703b6a6082b1635362bc103a981ae080d4d8ad6b56b2d62b5a7596b45ac3ac⟩,
  ⟨0x2e016a8b0855a29814709f44e624c11b88404061ee0f1075c3681990c085a4288121077035818e0a004681980b80490188078016000, 0xc1218226d395a27c67818b0d30300019f3bcd0675880079f3fd36138922ae91b048007a2f8b0600955570f8b57078a000cc0ba7000f44b16000ba23303eaaada714c23cf8d0003cd0dd22000e7c7f4e060d11756b38b14a251044e09⟩,
  ⟨0x3131760b7c59c28d14009cc4ca24010d87d83d61da0e486882d815409e04bc23c11108103cc1d00c305a027010806c023808801e000, 0xf9f91d3f335f19c001000ac3a000f4fc668335d0d61b000da90016c35d4800bd22eaf049f9afb0d6000644bf2e44b00010005caa115c5a111c5613b41ae0cc791dc25e090006c17d5b62aa0f7c5a0fbc5a0ffc5b04ac11d5d821608ead1343e449⟩,
  ⟨0x3071790af054828c13b894048423111008443d41dd0e806ec34c17f0b9052c28211a08483881a20c205b82900fa06b030813804e000, 0x3caac000c8880005caa169c5a165c5d7455c3830003c7c21b0cd2566930933f6800572e852c2922255830aaebf7c87aecb09c001cfd3e6c0c00067e8f2f04e321d26ce74e2ccf91270486e89002b22ab9a5e23c0c19a267e30001e68001914bd1⟩,
  ⟨0x32f1840bc05922ae1508a4850a274133895848e23d113085c4001f10f387003521820af050c23c10c073833014e08002c80c8016000, 0x1a011d3ac67c54ad32477a6589e41e8527127ccdca69f14949a4c24c0d3c2b24d24829ac930930348d39131cd032593225a468f3c8f2b00c1c8d2a8480036336a6530604a2c65d4c9c05090006c63d4c88e9193cb911ae9cb97223000272c001c88be5e09⟩,
  ⟨0x3381898c105f22d415689e84e024b11207f43c81cb0e0069c30816b0a204b423810b07e03541900bb05502640e406501f00d001a000, 0x2268bd3e449c12000cd13a9acf002639a000800734369e060006685d48001a039cd012159cfa32312e9918975e09878f758287b2f8ba080758001a029cdf041a386692b349849a01e002b97429614d49ac60d7607d2b8f6584e000e804736060003401b96e31⟩
]

def tableRLRRR : Table Block := .branch 15 tableRLRRRL tableRLRRRR

def tableRLRR : Table Block := .branch 29 tableRLRRL tableRLRRR

def tableRLR : Table Block := .branch 59 tableRLRL tableRLRR

def tableRL : Table Block := .branch 0x75 tableRLL tableRLR

def tableRRLLLL : Table Block := .leaf #[
  ⟨0x3f01ee0f2075a39b1c80dd469c31b1880bd459c2a914e0a3c50825f116081c3ec1e50ed07043381870aa050426e11e02180cc04a000, 0xb5146b574600dc613688342600dba0f40f8309f36b23180c001d3c26b78060e05be81d735df596cf4f429614e2696b9df1d4bbe12d70003a777be5add4ca9a520d38240e6dd6000cb51a706a5580532c9cb4daab850f034a933acef181604ae60004035000232570f3241cccfa688813f0d992679e3c163490d346cd17a7⟩,
  ⟨0x4d426192d095248a232914c89242a2018f7876e3a31c20d8466230e1748b1053e27a12a88c04161e4093836016a090035811803e000, 0x8b33e449c120070ad2461387835a5e23c0c00708d2682e0001e680030edec4306d05ee9e0da3607c1947819c0d30f032819c0c70e60b81761e16cb58f536b542bda9947f3c4d4ca3f9e2ea6518cf13539e1ca2fa9ce12516d4d83c4a2dcc0308965c012808e68d0a95268f485d58e689a4309d46be3b6b6d34c1f56bcb76da7d63eaeb133ecb57dab9f61abfd5800336ae9e82326d6e6801b5f49⟩,
  ⟨0x54f294143c9fc46e223908874236e19f0c645e82cf154098c36a1820ba058c2a414308e043c2040e3062027412006902f80e004e000, 0xa2a111d39d0173d0b9899e392e0c9006e402d4892453c030e6a9f1d9e6c204e3bd8554569d14d94562672538da4ccd50911ee4af8f1ccb123a4c69f9c9168c47e1f13bc5cf53f907dffabfc7ff04d5a2959c09c78836d2492e12ce3e3b2da0c7a06b802780b89a91221d64eaa7e4526d24b8f6d7d6b6000e9f086c334959a4c24d0700015cba14b0a404620a5801c3f4bb10a87cfb2c27000741a79b030001a0cfcbc138a1ed9c65d3⟩,
  ⟨0x45821a90387d22e115e09dc4cc255123087c4242050f6074c35819f0bc05b828e13608783d81ce0dc06182700f607102c013804e000, 0xd94ed27128b024c871edd08c5b4e7d7607c9406457c19255c3864a38eaafe90a285bd0cf2199833c26730cd086fb8f15ebdc9a7201f23e15420019e3e19a4acd2612684d800ae5d0a5852116ceb01b575d8ab92edd96138003a129cd818000d092e5e89c64b849abe9845739f224e0901ab74c9300153cd0103a973c0c054ee9818000d086e680019255d1⟩,
  ⟨0x5bd2ce15d4a9c52b284139492247222f10ec8304021ef8ef073238f1b40d0461628a12287c43981a50b7856026210a07182f012a000, 0x370167a1862e079b43085c1f37a9bd3ec4f643a858bec7f54716b3390f52ce5922075ff8e0078e5278cd1b9c7d7cc38007afd89ebb61ba85d3cc59b63bd3890014db30f0350b40003cd9fbeecf7a3351a783cb39e3c4f187b536062724d849ec7242e27a71e25681f887b2093f8f12b00fbc3d892d6093b8fbda6e8bac0005258f8eb218000c962e3d90fa6923924b793240e4a571c05dc939e481e39291c9017b251f935f68d7c35e8d7e35e5800ecc0dc15c5d7e3a7⟩,
  ⟨0x56029d94589e64ce25491d87723961b30d0c64030a1738b1056e28713e896847621e0f5874037418408c839818a06802e00e4046000, 0x89b2264d5c4d6853eae1510a6c5c4c28536ae25a89874f12b44b313069cf4cb342632d15c1706218d890536c10c0ad050d6b24c38fab8daae1f569ab7daa61f63bb23c4800791d89d9261b83fc19c3f11383b87f148007885c1bc3c0dc40e0d62712626a4d6d5c4a63ec6391eedd38069f07f2ce1a48f91b931c1c750c542fb7e855163823e8891b4fed8e53d92e69c022deacee80d9e0e84172a0008dcda7c46000f68313d99c37663b3f89⟩,
  ⟨0x4b624010ec7d83db1e50e9470035b1a70c9c6042f816989d84d8245110074432817e0af854823e0fc06c82d8126070028811003e000, 0x7c9566881c7001d2555d1b343fe3c363ce9462a00635bda794349c1a42659a8b52000cd37a79a77a3ed5b89e87d8001e6cdc9d1dec6069b8fa39d5c34dce3c61414a0002d69e9e06000343d79b1d8745db151585785162e2142ab4fcc634d0004d518785661800e99a4c99a2674320008d3f2f4d2d89e639a8b13cc6002e24009cc5c4801798989005a7a92e29899a26ed5801d3749⟩,
  ⟨0x4c625091f08aa4011ee0edc7203691920c646102e115e09ec4d225a12688f04562210fe075c36418d0b4050c25010d079035415c000, 0x175ab075356002e9a9938e05df96df364bd016202c6aaef8f6cc82dda9eea4173d5c9fe02e9cb93fa059f96aada4bab7c80003c784c3267000344679bdd0826db1aad0001001c159d3d9e0c61270cd66692a34c0ddcd025dab03a2aabd48251555ea6aaa049f53dcb0253abb5d415fd5d7e4f0b00ca20f259342d569064eaac808bc9da20b3694b95375e0aeabeb0dba1b29191223192afc7⟩,
  ⟨0x6e435e9a58bee5d228a94288f446321e101876438b1b20c7c5f82cc14c89d84a623011288183be1d20d586202fc15b09b01e404a000, 0x68f5333f9364ca667f300094be69c2b15d5651cd61309122be55f3248e3800b835e9cc234abc97c9384e2b9aca59abe00040080617915ab2878f898000ce1197c522ae2b898449abb2ae964ff1ece6d3513c6635cd932a5fde08a71e089c5131ace3638c3cf1e2601877e4c4cb30efc95abc1e64004c989e3f573c0f87eb3756fc0d871856d44001b4e00af03627c05e07c5f807c018b84c006ffd1c302512ee6b89c000d12ce6f88fbf79181bc45df9c5efab2c5e9da31a5ec82feb03437f86ec02d324e11a202c39bf2e7538f1329585c97f02d0ab038e007d583a9⟩,
  ⟨0x7293899b48d5e6903389948c5e6102e79700b1a54c29b129871e36a1a28c805f62d81588a3042618309f03e41a409c03a813804e000, 0x1b7cc36aaceda5b1401ae9fc79e2ec4e4206f49c8e0de920db23527cafe2dc5e3205f4776b462fd53c001d3dea6aa73a07ab1f4f6c000563dd8003a7f17e1a67b4db79af8c976715458a30ba009e69b71d1413572593cb2898ac20ce3c6817fc3b7862a596355d531e87a70f52e80d1b9876ee3bca9311ea5e5398735330dbca5a99868002d48007ca189b27c98679930c4b4bac18a878d1ec39fbb5d478e8daddbad3cdad9ae4c94e7104580003a8da9588c99fe3c4f05620367468171c6cd447446d104938f2d2a674f1e5a4cce855e9c7999ed2eb93333da5df26668b4bae4b4b999a1c9⟩,
  ⟨0x7fe3e59e98ee674e3949c08db665a2e514e89ae4b023d11548603cd1cb8dd067c2f916b0acc5181de0a704601a60a003d8190046000, 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⟩,
  ⟨0x5df2af151ca284c022e90d88003d91d18db468c3371960c145bc2a814f09dc46420b0ea867c2f416309e04541be0ba049817406c000, 0x326a83fd08c47eab26b0002f2f9da4f1fcd5d314a3d279877a792e74c122a2ab0a6381c792e49bae981ab098a88c6ff8f26064c1f1e4c0498292ffc730ad26178ee0c0c2ac984e3c989930525ef8e03964c071f224e09000325f7934315e1073400080e092f7c781806fc979e4c98092ef25e64b971e4d3c980e3c97c934d25ff8f267e522c9a6e381c76b6ea6d6bd345a68b45c7710d16938eb4e5c42c5a3e3daa56acea5bf5c95ae3b7ea92b2df578edf9e2b1f1dbf345620663c7⟩,
  ⟨0x59e2b59510a1c4db25b129c93847722810748263ee1d68e206aa32217e8b2854a2600fe87603821910bd85582040f806882400d6000, 0x3596d04f59ad3d0d06b1bc7a19ed631ac571f58cd65b588d3a8a1ac769f224e09000758bd4d0dd76d3cd000544bd6274f032895ac3ea7583d61758dd5ff4f81c6b07a7c04b037d60b4f80e7fbf81be9fe9ac0e34f80c7d3381be9ffd9ff6f533aa9ff1c8b768b1c7a12b3a40423c1db479b42638e000f8b3a9f1534d8747ede1ef0f87ac30007fe8e9df698001108342007ec71e06a35101239bda6644c7ec7edfa7f393cd1d3e4d7da5644800164d9e5f9fada7⟩,
  ⟨0x4051f78f307523841af8cb06423141768b2057c29914509f44d826112a08b44101fe0ec86d832215008e83e01dc0c705001a804a000, 0x110dc3443001589004c42f13289aa0fab944959dd5c9f60008019a784ce27000347739abb1ca1bb1819762942f5679264cd0c6984ce270003474f9abad7b6bb1819759f6cf56001a7861d0f8f6c757d3d47d4ad2927fa7e9e63e9000b4e0017fa9a781a8e48001e6a450a2b9d185708f9217bf1e15b952847c70bdb8fa0a6b37a7⟩
]

def tableRRLLLR : Table Block := .leaf #[
  ⟨0x47123391007f63c81d88e286c633c1978c205fc2d915c0a5c4ec24910608043e81cd0d306702ea14e08c039417c09703a0110022000, 0x10352032f15cd9df64b50969c4ffe3d5e9a5c0003a7abc34d3c9d578f267a2aaf1e4aaf09e89c96138917a3f7cd81bc6b245f560031bd678e0915b5c66c7059e35e33237ece987000c5911b18784ce27000347c79a23ee683f460611f534179623b6682f1c47488ec9a09c79eceb6a23ab4e0006265f1e264d1e9e6d65eb4d87aced65ab4b8794094d1004f4e3669⟩,
  ⟨0x67332818809b84b91fe0f9477c38e1bd8db06c233e18b8bfc5ea2d215e0a944ea252111074c36018d0b5051c2480f4074831813e000, 0x42861078784d42821058721364c35eb5a53e289aeb164c7b8559deb19565cf18e29c83331845cc2771266484de44c2ae70afc700f5e9f0e4265c2ac27524230ab0498bc87116ee14c985bd692165c703398f487802673613753e84b61f2843e449c1200184be24bd0c68ae6868343c0c012849e26125868715930a4a9a422f0f08dbac61e119757850e1d43a94afab200ad795d3d3e406989a9b80d312033a9b6269e55cbc4d71ab9789a1a5e3c0038784c001ae3e1cbaa5206e6b83a000309688fb4291122c00c044e3c6c1fafc7⟩,
  ⟨0xac054da9a146a9ff4e626952de81c3e69970c8e63730817a4b845ad2cf162488a43b20a0fb478c3a513088e842618303d8158046000, 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⟩,
  ⟨0x7963921bf4dd4678337191cc285d329293c896246220e8ee86902d61588a384882210ff076c36c1910af04ac2100d8042017406c000, 0x251b46a38d31241649ec903948dc7915122ab93d4c99d98aebf94b8000523a4aba02d7c781a92fabfae682d34183879a7ee40168a0bdc3bd3a11810462095417034ab164a4096a1567b48f28de78f1f13c768e269d5bf204e477c5934f6d0e7a77c3da7f6d2e9d23aac1c587b08c78f3ca923a468a64ecbfed5e071d7fd3275577e91ce344cf297607c75ff2c9d12394f288d10aef997cf1d2a891c74f99d95361e8fbfb2044d4e40ff87036d84713179b08e26c21178c4fcd9f34e9fe6cf9a34ff35fccff3369fe63f9afe69d3c30c08f87863c36e1858770f709cdc3e88df70f5c7002f436b8ef922a9c71df23d5377c81c7⟩,
  ⟨0x3cc1b48d4468c31f17c0b4457c2ab1480a0c4bc24d11408043b81d10d6061c2c4153096047c1f00c205c028010207702800c404e000, 0x8baa00040014957917719ff8f09bf8d898000ca1de3d280943dcda4ff1e3b9b68225f544807a309b33001572b6a648d2000dca9a9b4ca002b98004f21bacc12003f207ace40b90ad67213c80eb0e238003b4bdcc7138001b4bbccb4b7697000172a06a6a1c58160068f0338f7b4afcc00300e8f035a5371e9ce⟩,
  ⟨0x76f3a51c94e106e135d1a4ccdc65131a1834bcc5bf2cc15c4a94514276931890a3411950b6c5502360cb85fc27409b042017406c000, 0x7c1620ea6c400f7f537c5d92b587d2cb392f4aa5b072e5afbd29e5de261ece9fd8ac24fef7cb27055d2d57920f5a5aaf241584b54e4cb3d96b1cb96992d2f96bc0a59e71d7842f019677c700032c7b8f4a4e58e735997cac399cf25b4f1b463624f619ec9450d1deb29333306658ca532b1655f265deef3ddc000d221e55132b0495d2c5f8f914699fc5e665994665b2a8d3b28e080dcdda7655b18c4a9f32ab6553264de48f1e31832ab953ac8741ea3dd77bb32208000b21ee3ccc0e345b307a20f4a36f71cb1780015ccb29ad3d3c9269255258a4944684e3dcd5a600111e5f8f22fa45a71e45d48bd9167c7⟩,
  ⟨0x45b21a108482a3ee1eb0ef872e3861af8ce865632017d8b5054229713909a048221a1010704338169083038417809703d011c018000, 0x424b8041cb8850f08c0006119726116f1a11771a95f0001e68e9c6121d2c0e98011321e9f224e090006640d4c725000fcd000400398fb4f03000531e6a606a56400079b1c78000f46bb2f1663498da63898c74f34ccc65a79a6263198c34f0c1218442ff067cc602b65f1c00cb123536238017a9b1182c1d4d8004ca43df011ec44d3fd000dd173fc327c46⟩,
  ⟨0x2e41678af052a28713c09ac4b8251115085c41a1e60ea87003141790b5057c29c12708a842c1f80d5057021c0fa06502c00c4014000, 0xa05487287001900fb97a431c498337a49c12001a131f2fa143c0d0980014f2c7cce0ceab004d00c8006f2a2ccf9127048c9a60168021e69788f031a4900034b379a000601474400dd2cfe9c0d5df78ae27a58e00079a002a01174606⟩,
  ⟨0x44b21d10ac8424021f88f487863b71d60e746ec34c1a10c606002e81618a884241df0dd068c30015b094040c1a00a003d812002a000, 0x171a4c24c0d78354d3468d3a9eef53db13f23426a492176297d73401e9a0034781800802d314ab083c5b083c514778c6d3fe92855a441bc7259f8b2c0d988add84a1f0d29dcff1ccfcee79477d380030346a605fd320cf7eb879366677d3ccbb26c4ceda797765dbd3c0942117ae3a7a0c51168678750c666ed3a816a184cdba799ae66f99a34f086a9⟩,
  ⟨0x27f13a897449023b11008584021f70ef87003421920c385c82a612908f84001e40c8054825811207a036016409803b016008801e000, 0x40d622b8b58aa7f1483486a781a70953035866e2823bf147bee0228f9127048312a75f5f5a6801be400e8f035f003d49ea180e6ad03347bda05a8f29a1e852712628681513e292934984981a05449a49⟩,
  ⟨0x2020f987883aa1c30dc86a83401880b805982a613b095047421c10107a03941a80c505d02ac12608403c81b40c004801b8088030000, 0x3f24ca99fc527b23c0d512606b10bc598c28781a2143d8a6e2e699fc52b925c534663092f269cc93824e24c92b443627c4d08ce29b0e5c5c133d0999e06b0e7c5⟩,
  ⟨0x24410e88143e41e50e6870c3601890b8857829a140098849022e10807a83981b60c8059829012c08b03c01980b804401d0088030000, 0x36d4b9963db8a5e21fc5211e90f030728900036d2f9d63a38b6821f34cfe295c92e29a3318493ed139927048708979b343627aa1a134c2892e91e06b16fc581ac5cf1606b1a1c5⟩,
  ⟨0x28813a89a04ae24a11e88b843620a0fe87c03ba1c80da85c02c21540a484e024c11c08203e81c40d806002cc11805601f00c4014000, 0x7c10fe292834b8a74cc69255644ca1a6852e290c91337a680c112001c004800bb633c86c4fa6684d62692e91e06b20bc581ac82f1606b20fc57138001b6b1ccb6af6d60000f2ac7e71584f6d50001f3a06⟩,
  ⟨0x2b61518a584de26511f08ac40c1f10f2075438e1b60d4866031217f0b5056c28c13709684281ea0d205d02bc13807502900ac026000, 0xde45b09c001d3a2e6c0c00069d072f014895d582c6cf0494f42938930437a9a7c525269309303502aa4d248532a4c24c0dae4004e3418952007d7163fe1121e137828900034e279a001d6ee44000d38be9d922e2e6687⟩,
  ⟨0x31d1738b7458a2b61560a144f026e12388f442c1fe0f3874038a1ae0c685b027e11e06e83301760ac04d81d00ca05402380e804a000, 0x16ecadd98002e540d65438bc91e06000d6ebb98e2781add50003e740c0006dd4f3aca3716a4e64cda6c9c13329332b8ebcad34d75df67a67a6aaeeb3d6d81459e980a604ada009f4fe8693e34ae491834d3ab0019cbd093686ba14b8a41815782f95e3b3⟩
]

def tableRRLLL : Table Block := .branch 14 tableRRLLLL tableRRLLLR

def tableRRLLRL : Table Block := .leaf #[
  ⟨0x3531960c2c5c82bd1540a4c51027312007fc3b81b70c9057c26a12208a84101ee0ea06d83281760af052024c0e806202980d004e000, 0x1b7a5cc010280790086a6add400514d57a90b6a96a054e09664560dd92fc8e23a71bae5f85cf4710d3ed436a58984e7c7dd3c272e3269dc5e84e1c63d3f0df100268f3721fc525069714c998d24969a4c24e236091934f05f0348e891f124efeef3477138001b769cc⟩,
  ⟨0x2ba1558a6851a278137097c4aa23d10387f03e41cb0d986502ea1560a60494228103079038c1780af05102240e005701f00c4014000, 0x3f24d299fc523066781b224c0d65078a0006ca18002e3e26818000d940e4d93de2801cc747ccfb56978b000d1e060da564db972ae6d334961a4c24dbdc0017cca14b8a4063dd8130ef2018d7617c2be184e000edea73a06⟩,
  ⟨0x63830897a8b0e51524a108872433517a0b3c538277122087c3b41770af852826e12408883c81900b5054024010c07303480fc04e000, 0x90c06d7797106220bf2e63e175f903f336a3a5c3fbe3cc7b2ebcbf6e40f4cd98e950feb8ef310171d0f3a1e1214cd9352d25f03c75efe0bbde61d0efa5a2be017cd71c16faf8311eaf30a87752d05efcbdfc17771f14b5e088a25e03cc1965f4f8a52f03e6027eda7f2ffc83d3f97d31bbbeda792d24bcd3c961259c977a7f2ed6f7d3d03ba0ed31a2a5771c000d0e6982141d681d4c67e3cba4e340eaa79f44ec4890f513bbb4052c717c000f472d50fe2908e6878185144c0c0046f7bea5594ce2800ab299c7⟩,
  ⟨0x76139d1c10d9c65c3149810b865742a0948894246021d90207a437e15189f048c1d40d686182be13808883a818609c03a813804e000, 0x130fe62ef1e61d4c3e98b9c7987733ce62cf1c4c3511490e93149793a65e8933c7994e713f3934f80f0729a9076301eece3b34d383af80ee013d9bf667a7c0697e2075b4e75aee51e625c4925e4025fe886c86d4caed1678e17d79bbd72df69a78436113d5e12bd7183aba799211e1e3c4f1e3af47864ca45e5c2ea71e3b047c0767c5dc6676475d991d4b99e6c5104a20f219d7cac439e3af9488d9c75f27119a235f1cbb747bd9058ecee3aec461886dc7b87600079333de211f2e67b43fee5cd1d90d1cb87e71eb7930fea3dbf263db43f9e4c86487f3cb91032eaf97119e21c72e22343f6e5c861880dcb⟩,
  ⟨0xb925b5ad1166eb10576ab8d580ab35522a61512a64518a8654029174721d18af63921bd8c0855c28913208f43f80f4041013004e000, 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⟩,
  ⟨0x2b715509dc4be24711c08a44342090fb877c3aa1bd0d4067431417209f84c424010f08003641980bf05602640e406501f00d001a000, 0x30ac001a9b8002d558dbe2d8d9e29e477096611c60d67b2558d2e2c0d635b8a1c0abc13e0a2ec67f15f41a918001d3c90d86692b349849a8de002b97429614a6a8b0d117721152af6584e000ea34736060003519b96c31⟩,
  ⟨0x32218c0bcc5bc2b914489984822080fd07b43bc1d00de86a834017d0ae053c25c10d075032415009d03e01a40bc04d020006c01e000, 0x206b0cea8ed6834aa6a8cb0c75e026f3e80070e026f3ee2400f80274f39600201000567ea1b0cc6126a86a0d1229a2606fb4004f1600338369c33005ce05a66fc02ad3f63006e2e6e66ead73720256bc1202136f6b82117825b8d6c270012a72d5d231847⟩,
  ⟨0x2fc1768b185722ac14b8a084b624e11388743ec1e90e1066c30c15f09e03fc1b80b9056027412007f03901840a4048019809001e000, 0x3093530c00572e852c2927e5583eaaee69ac4eecb09c001d4bce6c0c0006a5d72d86200daa5e74d623cdd2e983029c000d4b5e6fe0c065914f08078b5de8fc3fa3bd218701bfa3b0f4293893e66e534f8a4a4d2612606bc5549a490ad549849⟩,
  ⟨0x4cf236109c7a638e1c10d6c64a2fe16b8ac053028012c888c3e01cb0cc055c27012808483a81a60c305602540e40510180088022000, 0x49239b352175ec880049705c7304c000dec84b69e3ccb492432e026cc4b7de380016a4d2168c1771e118a21cba4e3982928852e8f8e00065ebf1ea6e4bd4e68001839bc98391c68393c683cb076f8f07860f241dae3fb07379df79a7f5e7d6fd3faebebc7adda79bc2aa5f5d9fa0d3801b9949f0c60ef72e937283b5240ef64f16370dcc9dbbd93f9d03962d6de7dad33e33ed69921b0cd25669⟩,
  ⟨0x8b84399fc8fba6e42ee14f493c3e11dd0e106ba34517b0ba45882a714009844782170f9072c35c13c08b83c01920a204281ec0a8000, 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⟩,
  ⟨0x4152018fe47d43c31d00e5070e3741a20cb06122d9161896049823611588583de1ca0dd86502e214a0a0047420a0d50658290102000, 0x5d23c0c7924000d521e6804f4b3918467138668b00969540038ab467c500148e30f232000c8df0f233c3000200100060022aed53172afa7e46d82e1a134b1d9aa890001e6fadc003ec4c23d50f0003cd000d5fb22000ea88f4e06000d5ef17688f8b093000800f0f0355072137cdabb5ac3171989e9fbd407a7af4f846b08d5883fc7⟩,
  ⟨0x2b21518a404f6266129892444c21510407dc3d81c90df06c43141670ae84e824e10407883641980c204d82180be04e01f80d0046000, 0x275356e8712554c81aa68143c0d26201a62c64d3666a834e0900ec97717099c4f54d8000f34017a6ec8c0d257d3662c334380574d58b1550ec0d10fa6681aa960001e6830ac4927552ee9c519f224e091b34e9780378d⟩,
  ⟨0x41c2028fb87923b21d28e006d234418f8be85aa2b014589a048e224100877838e1a40c085d82be12c08a03bc1940a5024009401e000, 0xbc159212eb27e9c5c33560ab325c53414fd33ab034d93f4bd04fabfa58052d5fd2bf4d6afe9af99f57f335eb3abbd616f9d5dc061e38bdeb04ab4c3b009589024c3af12049876e2e40565d6500098b001d64f178240c4658002ac87931aab4cdc5a0555bbd5d0293d8eae806568756019006601aab4f549f311a7000c9a713249c31c49⟩,
  ⟨0x3811b80d6c68632b18e0bd45cc2bf15a8aa0520278134890843e1f80f7072c36618e08383c41c60c205a82380d606101f009c02e000, 0x366ba1235596ce2d966e29847aafe00079a6944001d581e9c0cc2bb2bdc5b2bfc5308e0006abbf34003ccbc88003aaf3d3818003cc8c5d954e28043e5be9e7ce000532d000be9f016c05daaef9b0d3d71b0de43002f065a5c4f55ac000f340bb714c8c0c05eb8962c0db64e0635fb4c9⟩,
  ⟨0x24311c88904181f70f407743941b50ce864c3001760a784f022a10207783781a20c005a828812e08a0318148090037015006c01e000, 0x40d082abb325c522053e449c121ea25b915a11ed0f030b289818000d598e686a91003b566ba7a8a2619448c9a6ccd5069c12caa2e13389eac60001e6f49c606f735b09e525d231847⟩
]

def tableRRLLRR : Table Block := .leaf #[
  ⟨0x2d015d8ab453828f13f09cc4bc253123087c3f41f00e586e832a1620a8850826e12608083bc1ca0d6057823810806c02e80d804e000, 0x3e255f10c3269b33541a70493e2ae13389eadd8001e6802b711ec60600dae21d58f19c001b87f5770f00260066aa28cf9127048c1a400eb8675a5d23c0c6124000d5ace6c1f804dc606b329c5308f569c000f34c288023ab53d3⟩,
  ⟨0x2a014989f84e826312c88c84342050fc87bc3b41c20d5066431417f0b8056428813a09584842120d604a82140f605401e80a0026000, 0xf1489d99e062934c0d7734000f32ceff17c48cf08d030e11aacdcf16ceaf17a0cf9127049c49c3659a3266781ba24c0d66bf8a0015c5c001e9c001b8b6e79000b4f518d0355c90003cda739a3206a90a35487687⟩,
  ⟨0x30e16c0b0056628c141096c494239115080c3ec1e90eb07143641a10ca05b42c613c095040c1b80c4056026812006902f80e0022000, 0x2ef95df30003cab419c5613ddef002bce818009ddede6699a4b0d26126ef4800be650a5c521d2326ce41c23224f0c27000777879d030001bbbfcc2a148008d563ea0001aac5d4b3dfc5b3e9c52e91e060017775f9d035dd50013ce0011775398ba67⟩,
  ⟨0x2ec1708b405862b91508a5c4fe27212588543fa1f00e486fc3301830bc058c2ac14709d04b42400f906903040f806402600d004e000, 0x84d2269713c0d68938b035a24e2b89c000de0ae65e09bc1400079568778ac270057781b9d030029bc09cca51566093e75678a5624b8a70cce29bc30002b93785c00172460d200040010003bc2bc8b427c5b429c5b437c57138001bbe7cc⟩,
  ⟨0x240114085c4041f80f0075837c1a70cd05f02e415b0a884e425810507d83501820b0051825010e07a035816009203e016807001a000, 0xb445c5c13389d19e06b43fc581ad10f16a0563f8a40d206c781a80264c0d68df8ac27009178939d030046bc45cc9410f9a67f14ae49714d198c249e289cc9382478d2f2686c4f666⟩,
  ⟨0x21a10187943b01ba0d1064c3041750b18564294140094044020c0f306d832817a0ae050825010a0740328168096033012006401a000, 0x2342638188098fc6602361b2ad0af17f24ca99fc527b23c0d512606b41fc51cc2878183143da0ce2e699fc52b925c534663092f269cc93824e24a572443627c4d08ce29⟩,
  ⟨0x2eb1620ad0502266125890044a20c0f486e434218c0b9859828a13b09104241f60dd06782e815a0a004a82000ca05001c808802e000, 0x69bce7cc9cc60086ee301934f0e02c24090d84e0901c32160342e7000f74716001ee8028f1569d78bceea79e3773f8a40670d5cf034d1a3a65235d314301a6418f0431f5a9e852c29c4d216a92a6054e4caa9a531932e8b2704caf0cc⟩,
  ⟨0x2c01588a9052e28813889884ae240115884040a1ee0ee07483741b00cc06382ec1610a184b021c0f0065826010206a02600d402e000, 0x5c92e2993318490d31935927048192c968a3472084a784d140b24ba4781ad27f1606b4a3c581ad35715ff54ef389e639f90c73d1d2b1d6ef36c7bbb402bd3ddd80350055a7ae199216b3273e9c8c7db958fb32636381c0c7⟩,
  ⟨0x2e316c8ac8550281138097c4a022910e083c3f81e30e806dc3541830bc854826210a071832c1700ab04982240ec04f01b809001a000, 0x40c0052f5973a06bd5e004b9da6692c349849bd56002f994297148648c09cd790608c08cb7c309c001dea3e740c0006f50f30040b19e40026b12f50000d624ea5a89e297687f14847943c0c1c224000de97e75a81e2d5e8788318fe29⟩,
  ⟨0x26e12a88d04362030f8078c3a41c50dc06a432c1870bd85c02be15009d84a823a11307d83c41b20cc05281bc0ca04d01f00d001a000, 0x31459d22b8a02e714c474c24943ddc87f14941a5c53266349228a24c24e236091d34de48b2133d09a5c4f035aace2c0d6aaf8ae2700037aef997ae6f5d0002e540d6a938b491e06002f7ad798e27⟩,
  ⟨0x30b1720b3053228b13d09a44b8235115085c4141e30ec86c834217a0b0854828e12e08583a81c00c705001f40ac03e0128060016000, 0x1ae11d3b2f3c53917faf00074f543499a4a0d2e29adfa001f97824d245b09eb7c8003e6c0c0006b7bf2f04e23906f7074c2355cf91270480e9ba7c8a007c68081e839e0601cf748001add9cd000f903220006b7774ed787146b29cf429614e26⟩,
  ⟨0x3451920c445d42c714b8a204f626a12f89484562040fd074c3601890b30564290137095040c1f00e706d02cc152082039813004a000, 0x23bb9670e50e006ab91736b2338ec3ce22b2138dc39e49933431a613389eb8d0001e6938baa77d18189c65539e5800670987270354df9735d000e1f4cd26692834b8a6b878007e5e096a35b09eb858003e6c0c0006b84f2e128937cbde5d300035c1b9a000f49bb1⟩,
  ⟨0x32418c8c185f22d21640a8452026912708fc4682190fb07483901ad0c3058c27812408483f01de0e4064829411407703200c404e000, 0xc126922d84f5d04001f360600035cff9782711d1b7ca3a6088dc1f224e0900c6613e8d003e3402038b41e0600c56120006b9a734003e88c88001ae6dd3b66dc5304420f429614e2685972125b858060e5a8542654448e0870084001ed0b4f03000cae4bcd⟩,
  ⟨0x3441978c385da2c81538a004be23e10e88483e21e70e106cc3481950b704e024011607f03b41a80bb058025c0c805602280d004e000, 0xb7ab35bcdc4da6e22de2d37f816f7abb81b7ab5c97216f7cb001b7bb3dbbdbc5aeddc026d782401edd6d7035fce0036acf23b84b308e00064cff2c000c99e0007cab5bdc581ad6df1699cd1104e9818774e09809c760003d4b9cdda7aa1a4cd25069714d745000fcb⟩,
  ⟨0x36c1a28ce06222ea16a8ab851226812e08ec4341f30e6064c2fc1690ac052826e12408c84301ca0be05a02340f406c02c8118042000, 0x35e1396c3100615e1ba7265284e74c19d4e0006bbff3700c00b36200374569846003ba1b4dd00015a4000c8aee38b98914dcb00101fb9a002b3db7d9ae52cc3069fa1bc7449ba8984ce2700035dbb9abfee4dc746065ff526db9618a2668694112f8a26ff5004f5600371569⟩
]

def tableRRLLR : Table Block := .branch 15 tableRRLLRL tableRRLLRR

def tableRRLL : Table Block := .branch 29 tableRRLLL tableRRLLR

def tableRRLRLL : Table Block := .leaf #[
  ⟨0x3d91d90e2c7003591a60c946362f41668a9853627412688a04021da0d2058c21e101078037c1a00a904e023c0f406501f00c4014000, 0x15c52fc973ab8c3b27e6609764b5c5b98c27ae297e379d035712bf17ccadfb5bdf935bdab7e72704d6f5ae19cc536b3ad38f488aee9a78074f4a78ea6ca02171e442bd3e7ff9c7b379e39f49b82ed3c8863c70b37400e0bb5e3c90d86692b349849af1a002b9742961493c2ac1dd577e764cdf6584e000ebc373606⟩,
  ⟨0x4041e70e246c831f1870bf45dc2dd15b0a9c52c28913e095445c2070fd074c3921a20bd855025a10607d835015a09c03a813804e000, 0xa03ae8a1d8871e80e3bb6744eec3f8f4eb7cdda7af80e8958a05751e3fa1a4f8d2b92460d35ef000672f424da1ae852e2900035eeb96d1c2bc774c00357b8e5b09c001d7b3e6c0c0006bd8f2ebd90001e8d78768d3d3ae795ccf935ccab9df2704d731ae7dcbae595c97923667bf2d5c779c0006b83f1eb8cdf94e70001ae27c7⟩,
  ⟨0x496238912882e40d1f40e9c70434f1720b605942be1588a9052e27012688983e61cc0cb05bc29012107d034c176098038813804e000, 0x1fc4f53010416cf340010b3bf11d3c0c1677e1fa9fc5bf0dfc3ff09d3fe4df8b69ff12fc97f15d3fe4a00080040018008002fe45a7c46a21b11a4cd466e330001afabcda7df4e722767abe9f37f16fc63f1bd3c0097e37c77e230021f8d71c000d7cfe68003824bd1af9a00079a0006f64744000d7cfe9de7ee2800701d87af91003f9a001a6ae1ca69d7c6e6c10b8277c7⟩,
  ⟨0x3eb1e20e7471037e1ab8c846203031790b9858629c14789a048a23b10a07cc3a01a90b98540256114078832814a07201f8068016000, 0x58040003cd8e6712f3a3682a781a2489d65e58a3370fd016b8e3269b33541a6118003e9bc39e98aff3cd713d7f70003cdead547b230345782a39cb001fbab3bedea358bbdd63edf8e3ec6f750fb6e3f7a3bd5890007f68d4fec7a6000f7930f5facef1737ff2fc5f4fff8fe2df8a69ff1ffc63f12d385a7f8b69f224e09⟩,
  ⟨0x42d20e10348063f01f08f407823b71c80dfc6b034919e8cc86462fc1750b805a22b91508a242e41670ae04d42240eb01e80c804e000, 0x526930930340a8934925c693093035f1800a5cd1a348050be2dcf6c4fc8d09a9248049b02bcd7491e066c557b0f8b7b0f8b7b438a00de18f000789ea00d801980082bc40004a7194e43d9c3a96024d18a9ef6578001af1e1362605ad602f9a001a9661ca955809e694dd005f0c62021800189de00c00168002006200bb8f09a1358055849cd⟩,
  ⟨0x4211f58e5c51e27813088f84361f80ea872033018e0b5855027a12e09184381ce0c905f82a013408203a017409403d017008001a000, 0x149129bdd4f6e3d4a3a8d1490e9bd54f5e3806a007800ee29495172a305850b0b006986a43b6603e80353e0546fa7d793bde3c106c90501920019dd61e77dda3c5ce6e733870154e670fe2900080a272f8781804d396c4a4d4c7d2218f912704831aa40345f2ee681c80d8f03623ec9f21ba1d21fa86bc598f29a1e852712628681513e29⟩,
  ⟨0x91b46b22090be83c40b9f90f7a72d3831b40c6260a2ea163cad44bc252123090043b1ec0ce46242eb153072c34816e042017404e000, 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⟩,
  ⟨0x3731a00cd862230517c0b4c54028813c894845a2060fe075c38c1b50d406042ec1650ac04c424e100078832816408b03300fc04e000, 0x36e78007a781adcd00175308ce270006dc9d5db916e60003aabe1bc5308f61ec000f34001b71362003ec3ef4e060036dc1d5c99a4a0d2e29b0e6001f97825acd6c27b0de000f9b030001b0dbcba4a2000702b74ef7cf14000d869e680036dfec4000d86be9def4e2c697763fc7⟩,
  ⟨0x74138e1bd4d9c68d33b9948c566062e995fca7c4db23c0fdc7d03c91c40d605cc2740db83ac1760a804a82280ea05002080d804a000, 0x1a866483a9a2b1452396c83208571f68900069b2d6bf4fc1ac30003cd6e9dd25589ee6ebb1b1569f61bd75f629d3cbc0a25ad724a754874e38ed59fdbf41cd069c3b4b3fa3f3f401a90ab99fe3db8a3c3cfb35da880026847c7b712787680252137d98ed40000b422e3daa6d63b0a8f5d8357e3580d83a7d5f1a2cd81877d8b4838794cfff7d8f6e12469f1df63520d9ffc3ca0fa89663b707c73576fb169065563a6693ff6661d4af1e4e7d40b315b82e39aba36ed482e7fe5333aac45985f6254ae3e9e3c9a6615b81e39a1b57268ac3d9c896d513824c81576ea0011a7c89382464d36ee5ba7ad⟩,
  ⟨0x5e72b3140c9bc4b924311848a043f20d0fd47a03ab1ca0d7868e32218b8c285c62be15a0a3c4941e70ba85082360e505f022004a000, 0x3e4380f33da77e4d0199eeff3a3d5f1e7b35155b44ce389311b2cbe3f9c54aee9eaf1cb274f578001596469eb33abbb4fe6692e348003584e9eb0bfe2b57586d5f5a70006b0fd4d60fa60002ab9e87771eb09d3000357269e13389ec590001e6d60dfc06c606ac1ff7ed5cf515642867de64f1ed084bff528e2924528513fe3da0f97fca51a6760a48149f44fb8e322e917fd0e9e83e5098e39fae718f0ab78f2fc6880f1e6104c4c6a39c7a17b43a53033837718b455f8f9216a1ba9⟩,
  ⟨0x90246622950c080c3eb1e44e2067b333190cc3c5eb2d315489de47d2058db06302a613808e83cc1bf0c4854c25810506f02a00e4000, 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⟩,
  ⟨0x4d726312848d644820c0fd479c3bf1da8e386d636119d0c5c5ce2c4138098c4ac22f10407c03cc1bf0cc05c4276114076822808a000, 0x349a6117f47b4e82f22841813e3e06302987c0be04f02587000e03f0e6053076f32923c0c605f075732e70001c3c0c6053073f3aec1759c3dd72ebf758c3dd7eea7870ea2000400139bbaf95c7a33519a2058004e3800187bbc98775c681ac768001e6c4da87b7d1879b0f0f8f0f261e643c2e3d8e925b3cdb1d06c379b06528a03250720cd121aae71e88ecc8a997f22ff8f303a88e48be2a69c7⟩,
  ⟨0x2cc15f8ac053a28c13f89c84be24a11b87c83c61d60e586e835019e0c305f02c815a0a104d421c0d806002cc11808202d80e0022000, 0xd331a49559132869a14b8a43244cde9a0304480070012002f05ef21b13e99a13589a4ba4781ae2a71606b8a9c581ae2b715c4e000707e73307de0fc0003cab897c5613e0f83011ce818c0360f6e6000700187300383d39d4e69⟩,
  ⟨0x2b114509dc4a023b117087c4222000f987883a61c90da06943201810bb854027611407e03c41bc0b704801a40a203e015807801a000, 0x6ca272f0148d7a76bf9d3c1253d0a4e24c10dea69f14949a4c24c0d40aa9349214ca930930357460013cd062548007ae89cff8448784de0a24000d92de68001ae7fd1000364bfa771c78b99a1df043f8a4a0d2e29⟩
]

def tableRRLRLR : Table Block := .leaf #[
  ⟨0x3861b08cb86122e416b8ac051628112e08983a41af0c605d42bc153098047c21c0ff077031c1700a704d02340f005101f00c4014000, 0x3b6fed574fda6f6dddaa69c001ed3b4fda876a3ab7138001b2bfcded4fb4ed8c0ddaa7699ab00d3070d0adf1c0342c765d4b07090ad71c0e134ac381c36fd879f259322732704811f0a58cf4349f1a57248c1a6ca7800ce5e849b435d0a5c520c0ab6c075ebba66f22d84e000eca373606⟩,
  ⟨0x55c29b94b4a104e325f12648e844f22290807f63d61e18ec0640281138098c4a41b30d3854c1e00e305e02c811607e02b8108042000, 0xa55fd4c0d4a15605ab9554005d4d5fc002ea4004abf75349f55fbaba4f6842d5c0d49dd607ab0006a98d3d07d54deaf9744db68969a69b599c3b37e6571088deb4b937b809c769a23f219c3337d656f0889eb434d24daae4db8e3269b33541a5caa338266f23f11a668e48699ccace10f0001e3c2333776562d65a10e33c3e3b3766560d65610b421b6785c7613ae4dc2b7ce819725e159e6309c7cd6157e67cd59be57e66cfec5f3b67⟩,
  ⟨0x4d525f92608c441d1fc0f4c75c3691a98cf062e2f216e8a2442e2000fa87403521820ae84d81ea0d406482e012206c02b812804a000, 0x136bc300078af9c7000cb2fa2bdf1cddc935c379915eb8f0e9c403a987a6201d4c4010f46a4000acb98aec000b8f365c343f5a69f7a13bd3953f77e69c7ed4eeca0001c34b00051d7f8f17821a53a5c00020008bb53b27e3f0b9a6c4c000ea57a7b324d4b39b6644019f34001ed3b4eed32cc7f37474a42b2f7254b4f2a60236784c30670003662b9b4a45613b1d6133f19a556000f532b00007a9⟩,
  ⟨0x56429f94689ea4a622490f484c4051f80f907463821ad8d1063a2ea14d89d846a2100ee871833e16908303841940a303f0164046000, 0xb9926dbd3801773069ee57b93b4e73d4dbc0015cc937a69e5cc39e66dd0006e639bcf4fc8d52b324007fd6d3fd766a469bb4e73971aea2d3ff8026d9f0d3ae5ce70198c7c34aba5f9d38a9d2332c69e6579817da79c52607d3953532b69ca9940535d999574f388cf9fa700067109f3b4f3df6993b34587e3a1e18611161b8e6f5d0f0430759910c1a2c2f1c00185b7530b36989b24582e3c4071056a6204882b566ef89b0c57fe380066e189⟩,
  ⟨0x84a40a9fb8fbe7c73d01e44ed47523959c18dbe6c73411904b6257b29b148497c4791b88d286462d410407e02d01560978240102000, 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⟩,
  ⟨0x31c1890bb45c02bb1578a884fa24a11908943fc1d90e786a82d215e0a984b020a0f4071828812a08803d01ac0b8035014006401e000, 0x81802abd4756c270012f4fd5c23389c001bd23577a3de96000eab0cbf15c4e0006cfd73401fbd0f6303003d7a0eaf7240004002004f4f09a130018b3e7cd002767cb9a3667fc3680020010007419e9eccda66821b624d249bfb2002396c27789b03184b⟩,
  ⟨0x28913f896049c22710007bc3c41cd0e186c83501810b4856829a13b091842c2020e906b033016e084038817809e04201980a0026000, 0x103000bc423ce81b1078009e70008c41dcc5e33f8a44f0cf03151a606c40e000799802f8a691dc5654255ff9e2e000e2c0d80038be0a1e06c7555ee7600c8055a7ab912da224e24c19bd24e0926d55c8287⟩,
  ⟨0x3351780b605802a814d89d047c22610c87c83d01c10d8067c3201690ae053c27812b08c041c1f40d3064828812006902100a8024000, 0x40010003c49fc8c07fc5c081c5c087c57138001c45bccc45988b4000f2b01c71584e0057114f3a060027889f99a6692c349849c446002f994297148748c9b390708c893c309f10d8003e740c000710cf30a85200236677a80006cce75300df17010714ba47⟩,
  ⟨0x28313a09a44b024711c08ac44020f10107e03c01d60df06c431415409e04bc2100fe06b830816e0a204a82180f206c02f80e0022000, 0x6649c123c6979343627b334269134b89e06c0a1c581b028715c4e0007122733121e2440003cac093c5613e2400057ce818014e23ee6528ab3049f3ab3c52b125c53866714e2520015c9c4a2000b923069⟩,
  ⟨0x2b21508a4050625c12888f846220a10007643901a10c705fc2e816109e049023410707002ec12807c034816009603c0178088026000, 0x24cd25069714da81000fcbc126922d84f69f4001f3606000369ef97827101418993a68ea1f224e090ed13a32000fad08f08781837448001b4e1cd000745fd88001b4e5d3c0c9c59410f9a67f14ae49714d198c249e289⟩,
  ⟨0x35c1a80d0465031d1820b8c5962b314d0a0c4b824510f081c3c01c90d9069c3201770aa051427412107e033018409f043010401c000, 0xe46388e0792ebc12031aebc6010275623ce2e08be2c1be3a40ca638073c511ce037d8f8a180397380eb63806cc509ce8afd92fa232704bdd6cc8e9074e80012987c8938240645d3a3e5fb5ad000e7ec11f8781b3f408dc4d64239d64dd9c8425aff0b8e04d7f84000e9ea86⟩,
  ⟨0x33f18d0c2c6002ef1650a5c51a26812e093c4541f70ef874038c1a10a6850826a10e07483081620a204b82180da05b0288100032000, 0x695200469f224e091934e961a606b4001d290003d3c0da51000ba98467138003a5e6af4bbd2e4001d56257e2e247818017d2df56000406459f55990000b8f09b0cc0006d58f34001d2cb620046d59f4e28cf9127048f1a43345da5d23c0c346900036a9b9b960ef1⟩,
  ⟨0x2bb1588a284ee25e12788d843a2020f4877036a19c0c905e42c815a0a084b02220fc073833816a09c04881e00be046019808002a000, 0x40d6b8c01f735724480e93a7e531ee8ba740f1d3001f42f24f5d6e27b5b400079bf676f181be8e5d7802a781becd9d70eca7aa0d54e0daa7c7255f7e039f02e1d3e170ebc136ddcebf1b775f8153ae6e44b6489c1264eab⟩,
  ⟨0x63c31097e8bae5b02cf1620afc55729814249f84c625e12549164642170fa472a314178890c32a12305c027410806b02800b0036000, 0xfee0e6807178f380039b1c3e2ef3365ce2a11f3438681b17599b0e719afc5d5cc000b1d9b8fe290002000e3b271e0600051d8b930362e33351cc571d5f19c1171d5c6d7c56e34e0878eae32be23719704168cf8f68c95c5d7c354d2dc6085c381f7e1bc75f5c06712eeddddc0fc21f8e7469705c39243ed07e50fa110ae3bbb6776f77807e3113f22823f057051d19872244278e44208a0113e1f8a3f0048c5ddfe3b2fc89ef41289ff769ddaa20fa702c2e0fb826e912db7492a1f0b098060f07d073660a2a7⟩,
  ⟨0x71234899a8c0e55923f116486833b17d0bbc5902a112e08bc4482050ef072c3741930c105c4294114078833813c07b02a00c404e000, 0x28e3c3d1a6fad2355df5a285108e1638f087e110f1dc51ce748715503c65f352ae3ce73577633129b25338b44aa2069d9c21743b372138f39c95dd4f6019874d8e99bda2451014eca7a9c21a842c8762e41f1f6fe18e353b7f0c71a9198139bc65d2bb79ebb4ebc0039ec3112a875699a53609ea0a1f6d10dc80e3f55dd9df55a001e9e130001a53fc7b2df6c679b4c5445b57eab9b5c70018b1631b3c260038ba8f068f18173bd7448e19ccfee2ffe75c1a5e8d267ae38a71ccf5471333afc7cf5679b0f9edcefe1f3d99decf1e1c0039ecc399e9c5edcccf800070f0319f1c5e7cc⟩
]

def tableRRLRL : Table Block := .branch 14 tableRRLRLL tableRRLRLR

def tableRRLRRL : Table Block := .leaf #[
  ⟨0x6983399840b3c51d23f11c489842720c10347d03c31c80e186c233a18a8bb855a28812a88b83f61d80e1066c2ac0f305701ec0a8000, 0x472b1d3abe600093b9dbd7b69c55adc757ca000e77337ae6d3707bd56af1d5f2369b00053b95bd6b69a83dcab538eaf8db4d3c7778bc000677237ac6d3307b5569f1f0cd5955651a70022b28d3e449c12000d64da9c81f2c4d68002001d647a7818001ac8b536cd4000f37201caff636ccd94ff3768b43e10d4abbf4f6a25c09a7b50ed44b80f4f2e092e8f1f965e50f8f4d38007d6589f57e19e9b5c8ee3cecea7062db1a6271dda4533a9d9a31c5d5d3abbe38c609d9877654a2f1cc1db55a5f4d3d22c5105c7ad88f0ad11589f5ae09c7⟩,
  ⟨0x3a71cb0e246f836d1a40cdc65431d17c0b8c57c27912308ec42c2040fd07883b01c00db06782f215409784281ae0b2046813004e000, 0x141a5c538663492004cb5ba98434d0a5c52000cb53a98ac3400032d3ea4003000800158bef912d0800200169e134b46000ea4ba4781afe071606bf81c581afe17166bd9c0b4f37d4da1a7b0a66ebd3cddd37269e6ed9b8e6e8d3cda7376e9e6f79b2f4f379cdeb35b4df7a700066fad3a6fbc667ce⟩,
  ⟨0x2d41568a8c4f826912208bc44421310287d03ce1d60e386f43501990c205d42d614409784201e00e506902ac10805d02280c801a000, 0x76e139b030001b705cbc0523c9a7075b3bd253d0a4e24c10dea69f14949a4c24c0d38aa9349214aa930930343ff0013cd06154800787fbcff0448784dd0a24000db6be6800187f1d100036db7a77f738b8921e5af003f4fe29⟩,
  ⟨0x5702a59498a1e4ca242913c7f63b61b10cec5d823e0ed86d832216c0a384881fa0ec06d833017609404281d00ce05a022808001a000, 0x953a547d580036d7ea6dacd3153a88e2bf10a9c71d7decbfcbf7ee9d38ee9cd7de4b3de3cbfa97e230c1d395fbde39f263e014fbdd5371cf929eff20434fb9d52f1e9f6a3aee3bdfef7ef1911d75a29a7714eae7961e4f3da7a0a5508b83bb8a7e4b722e7e71dbfb53931270b6ae9f88aa2e395452bae9f304cc3f533a8ce09a99d426fdd4cea1389eb3678009f4fe8693e34ae491834db8d0019cbd093686ba14b8a418157c20f277b337916c27⟩,
  ⟨0x39e1b40d0c6583071710b2c54c27012f893847e21810587f83b21b40c686002b214f094046c1e80cd05e02b411006302b00bc014000, 0x26105fe37531c70006da5d4db3da6b676da4d48003293ea6520d32aaf7f0e9caab448d5fc1c7c334959a4c24dbb90015cba14b0a4009956756000cab1abc792ba2fb2c2700076ecb9b030001b761cb618a551b765d35d095323a706695c92000dd39a7952e54cd5b89c000dba7e6ca9b2a4ec606⟩,
  ⟨0x5d02ce9640ad255f29c140897a46921b103c6e034d1940c045b429513f08303ea1d20d686202c613e08583a018209a03200f404a000, 0x9d0e7349ccf4ec274c858f479d032640c79fcc721a2baacf871ec6bb90c15d367bf8f1442c6b390b15d167bb8f6f795cd2dc69ecf63ffbe3a99515548b82bbcb90871d046c5704d9eaa859c787ac41b132dda20da9897a8faf8f41057e8f1e82000011934bf438f6b86986422ecf1938000681f4c315f0fc7b6974dd2ae96624c94b6cf536d91927a9b6caf42d65b617c0e9edacb6bef80d38007a4787b7953b8b9b3070e8af1ce7acc1b3a29c700032db7932da38d1ecd3c5a7⟩,
  ⟨0x57329e94589de4ca25191f08aa41f1d68ddc5b02a514909fc4b422710107743a01c30dc064c2c013b084038c16008b032016004a000, 0x393289502c3f8f129e25671d42a44a6e3d0d320a69e2348ad2e38ad1a8a3c78945683b8f27f2250da0de3b90a9f4150cd4db91d35c5712a78e93f62543398e3ae0d536a2b2918057997250e4208e8c49db417c7af3e636b2774f88225f744cbf764d69e5fab2665e5d3cbf12f9e9e5f6b3434f429614e26b3225f2d4cbe36658003a797c2ccad4cbdd2f84bd7a797d25ecd3cbe72f5cbd5a700065e7d3a5f0c7afcca46aefac8aaef34f3a24e6ba7⟩,
  ⟨0x76b3a21c84df46ca35399dcc0a5f02e69674ada4ec262923c8943f61c98c8457c29d115881039c1980a2038418c0b404c81f80c6000, 0x4844366fc7000ecf70e6cfb20873b513abcda0e1f573f42c3ed0f571f41c3cbc798f731c8000cc7a98e285978f3ff6650c6a6b0ea0550bea670ea06f9dea5f0e8d625f92325a70d565456e377aaa17c7048b3fc78f51c4122234be3ae2aa8e0090d1a571edab2e29a8de09091a4f1c6cedb555c5151b8120a348e38d9cb6a8b89ea3682409ea48d1f8f51b0c1ccf95a948e5025f5f1e6adcaece26004d740301a915035e17bba1e3a2b58295c75c448ad20a4f1e0a481ff0443c75c4005660a401fe0441c7b698b87c0ac414703fa087f8e01f8427d306f47be1321fc427e1f88482110432086171a3913a9efc7⟩,
  ⟨0x66031c9848bd65c42c715a4a8851f27d135496048923210c48183e71e00e646e431e17c8b5055e28a13288f84321f20ca847012a000, 0x6af971139adaa6029f2e6ffc052e5b8688081c770cf00ea01ff1f682712753b4b39e7a9da57870d4f0dfb4a6a786ee18353c2fed25a9809ada5397c246d17a7e11ee4bda2b4fc34b9d7a973ab868d4d9ce70d7cbb4aafcab976660e1e71dcafa927786ce106d20f1e868a4275347dd213a9493e836d4d25941b6a7082c45758e0ee01c71c00180674e806ae14f37850d8c11098037838f0b74fc27f09db17d0668844019c1bf859a7e13b84dd8ba832441e31a802f836f0af4fc26f099b16d062883463300526ffc1af855a7⟩,
  ⟨0x7873aa1a5ccc86473151834bb458b26e90447d43871b50d0c64c2ff14687f43b01b10c5059428011d07c034415808703100f4014000, 0x5d266a94e63a773227f21716aa1e1a28bd7dba4923a2452b0808cbd4b5e3dbd2173d06da7b6ae594dcf72ca6e4b9a529e7c187abbe9e0c84f3a0c2e213576d3d2ff6cf93016657ccb0997332e21488b2c731495378f4bf9b3dcc04995d32be65c4cb785202cae9e455d7731295338f52b1446f1dc348afe6f7c2c694a7cc75e3803f549c1f5dc57e6803ef49c1eddc55e6b6676ce8f159b2e38619508daf78ed999b39bc5570f4d96dc304a83b25cdaf38fc4c6d5bab80cafd239769cacabf2dc59dadf52e81ed6fa9e8173fb12e7eed6ba9b560db3797c2d000da700136abd38003ac169f6acdab756000eaca001e9e06⟩,
  ⟨0x3711a60c9461a2fa1698b1856a2a814d8a304ca25412388e84261fe0eb86482b8151095046021c0f607603501940b20458198066000, 0xff99b10003721fa780a78b8921e0b6000fe3f8a4a0d2e29c331a490013059f930869a14b8a4000c163e4c561a0000c161e480060010002b20af220af00010005c784d0574000f24ba4781b006f1606c01bc581b007f160fdb5d2e3f1f9c7c69f8fbe3df8f6d3f3dfd15f1e9a7⟩,
  ⟨0x29914609fc4d424511908943fc1f40e686e832a1800b985902ac14509c049c23010e07c83a81aa0c605e025c10405d02280e804e000, 0x14297148302af95b645b666f22d84e000ee4f73606000372739780a4590fe553677a4a7a149c49821bd4d3e292934984981a71552692429552612606ff4c009d6830aa4007ff475fe0890f09ba1448001b90bcd⟩,
  ⟨0x41f20a8fc07c23bc1d68e8c6f83571980bf45e42cd15309fc4b024010d879432216a0a183f81ae0b004481e00ce0580238080022000, 0x40dcd5800ba934920017353a93093034e450013cd00079a5d480079c87cfe688001000b4f09b9a10007520006e5c734000ce3ee88001b975d3bf25c5e67399ad3a1187383785b8ee701637a117bc2ad8738f1468fc8f1e2ae9f90e3c55c3b367b68fc7f1cfcfc81ee3ca4e1dc3c78325065393e8693e34ae491834dca70019cbd093686b⟩,
  ⟨0x2ff16e0ad44e826a121887841a1fc0f6877036a1a60ca86202f616609f84b023e0f8077031c16808d034016c09803e016808001e000, 0x6ca787b9c6880f9b0a3800305a0055a781ae700001e6c68f3106c7d0d27c695c923069b9b4003397a126d0d74297148302acf5340e4e99bc8b6138003b9a3cd818000dccfe5e029181ba7a7fa7cd98025a7a149c49821bd4d3e2929349849⟩,
  ⟨0x36b1a30c145f02e716c0b3457429514189e44cc23f10d08343f81bb0d7067431216a0a584982020dc05b82b011205601f00bc04a000, 0x42d200169e1680006e2f85bb4f2668a33e449c121b22618498fb5a5d23c0c19224000dcf9e6cc4b0bfec7ccd5c6700076fd8334015d3c19874d32468d2400652405c8fa4c6b0b2deae62f596f573170009ab000e62dd5e09000d95f1731542e0000eab1fc717923c0d1a74c4dab⟩
]

def tableRRLRRR : Table Block := .leaf #[
  ⟨0x5ea2ef9738b4e5962b01544a5451b27a13a89ba4c525691a08283b119f8a4449823710807a43901a10bd054c2580e705881b004e000, 0x3049d1ac000dc79e38c9ac0045c64b8efca308f7478000f34d288003ba41d381985793a78b93a78b19c3004adb194adc78ce51ab96d8466fc011c78ce31ab56d7da0e8cdd801f8e3ac633846ac5b5d6836336e006e3ccbc16d535b66b7cd699ae135ba6b44d679acd28f38f5692675993f0003c7aa3b308298105c91053020f9305153d69153b020793020054e7260208a9be4e4f9153bcca105566c752cce2e3d59aa1c333878f566687036ec99c1c7a05f337eacc1955e3d0e41d19c7⟩,
  ⟨0x33d1980c245fe2d81658a904fa26a12b893047221210187e03a21aa0ba05a828611c085835418c09f04801a40be05201d0088022000, 0xc270007750f9b030001ba83cb6188027ba87d3b9055967a746a259344e095c917179ae48f1f224e090003723f93734a2f9f34000c5e1b919c781a2efdc8be48001b915c7193580088bdb722394611ee968001e69a51000774bfa70330af27d71727d71714d29669⟩,
  ⟨0x3a11900b3057c2ad14e0a344cc25912608dc4441fb0f7071c37a1960c4858827611407f83a81860b205082480d605e02880f004e000, 0x17641f1214d58c228726ec75c68971dc7426a00050e43fc7b6e9c78a1b0cd256693093757800572e852c2927455839aaf2a25cedecb09eeab8003e6c0c0006eaaf2d86200b2eabf4ee7353d5e9dd510003cdd285883a29c018dd4ee6e19a4acd26126ea5000ae5d0a58524deab06e55e55ab913d9⟩,
  ⟨0x3e91ef8ee074a37e1ab8d2867632d18e0c3c5fc2ef1728af855e28813c89bc4902210fd07103721920b5851023a10506f02dc102000, 0x1030001bb07cbc05236260fa9f4eecd0012e3d0a4e24c10dea69f14949a4c24c0d7648002f24d248002bb21c93093035d770013cd0003763392001eebaf3eec480010005c784d7620000f24000dd6ce68001bae1d1000375bba77deb8b760eec0f1e5ccda4ee3cb98b49aab0f8ef8950e55d8f8c24535aec8bfb5b8d3c7⟩,
  ⟨0x3791b70d2c6482f41750b1c57a296137892044220a0f1873034a18e0b3849822a10407a839017a0ae04e824010606e02380d004e000, 0x1824003d05c4cc483a07cd000800fa0787818005d01c4c0c0006ecef34e70cc42e880019863c7bb3530bf9a061b1c0225d98e681aac7bb2c015b9a075b1c0345d94e6c3f005942ca013e9fd0d27c695c923069bb1c003397a126d0d74297148302acfad589fe99bc8b6138003bb0bcd⟩,
  ⟨0x42f20f10448083e11e60ea46c833a1978c305f42f016c0b3856c2ac14a08c44141e30de065c2e012b06b833014a07e02b80c801e000, 0x421a6852e29000cfd31315868000cfcb120018004000acac1c88ac0040151e134fb8003892e91e06bed3c581afb4f1606bed7c58cc054910c2a21897caf9cf8e00065e7f1eed8cbd0e69d108ebbcb80ae02ad58006982bc700052f7e5df2506e3800197bd6a965dea505e3e2600032fab8f76a65f5f36ed44c0de6fd43f506ac011d08c3e449⟩,
  ⟨0x29914209dc4d025a12488f045621c10907f43dc1d90e507003321860af851c278129081036c16809c04481a80ba04c01f80c8046000, 0x15a4a7a149c49821bd4d3e292934984981a31552692428552612606ad8c00279a1ea24003d6c4e7e82243c26c85120006ee8734000d6bfe88001bba5d3beffc5a490f19007d1fc525069714e198d2480267f189⟩,
  ⟨0x3f31e90f0076c39e1ca0df06e435a1830a8c46220c0f2864430016f0b0053c25011908403ec1dc0d9059027c12406b03080e804e000, 0x5cc800da4ba4781af73f1606bdcfc581af75f160305655b2675ff2a4d71e02fdab9aca964cabfdd499e3be19ad18e00aa4ebb845a7b7d778fc45711da9023377e39a897008b21c9ad12009f8fe8693e34ae491834ddf20019cbd093686ba14b8a4181567efab6674cde45b09c001dde9e6c0c0006ef3f2f0148d6c53f6fd3⟩,
  ⟨0x2d115e0abc54029314309dc4c425512488d841e1f70f206f434a1880b3856829213c09784801fe0f007183581920a804981c805a000, 0x139aa7f14ae49714c198c24850aa5c5348c1f2240026635e7f04143ec289cc6400079b7c178b3add287ba9011b3f8a4a4d2e29c331c49002ba3b49a4993350a5c5200373d6979b34000dce5a40028007001396a39173400400367⟩,
  ⟨0x2e11648ac8546298140896847e23511008583de1d70d8067c31c17f0b7051c27012708d04341f40d306002cc11808202d813804e000, 0x199038a22231f224e09030593996800373410ff53c0c17aa981b32a8001e6df22e2d68a0039c7f4349f1a57248c1a6f19800ce5e849c435d0a5c521c22dd73dc2ce99ec8b613de2a0007cd818000de28e5b0c40085e2ae9dc2475bfd3⟩,
  ⟨0x3321930bfc5b02cb15209f44e624c10587f03d21da0e5869032e1840bd05a426812308904141bc0d306002cc11808202d813804e000, 0x2118000d6d4e3de62ada5cd713de600003cd344947dfa3031aa1a3ebcb8b0417b88b8022d39e474591bb126924e6530027cb613c468d8187cd600001200002839334941a5c537938003f2f049e68b6138003bc95cd818000de48e5b0c4006de4ae9d7e60003d3⟩,
  ⟨0x4f0255915c8603fa1c40d846743131760b1453c279123088c3f81d90da06442dc14b09c04541e40e306c02d411c05e02a00c404e000, 0xb31b32d83195180e39616b31932d4318d17fe3d17fa2ebc7a2f745fa8ba71de05007e45ca894ab89062dada5c7762d07c792ec5a0f9725d8841f1e4c1f0761fc98362ec3b9399a5d87733b6cec474fdb576d7d8869f547aa0c49ab99cafcbd596ab3172d74b5babd4e005713ab400ae27566002c486689d59eacb16008d59e1f224e09000eac3134808d57734002003d5761e060016ab313030006bccbcd⟩,
  ⟨0x2d71640adc520281138098c4ac24310e08243f81d50e5869032e1700a484c024611408383e81d60d206282e414007902c00fc030000, 0x2e491834dea20019cbd093886ba14b8a43845a06eb07bd33d916c27bd32000f9b030001bd2fcb6188010bd33d3b06a819ba7241ae7f14ae49714c198c2481463a5c5348c0312e900099a939f0e0402e7860174e6a10003cdbed9c5⟩,
  ⟨0x87e42ba0c90167f33b19d64e6470d3641a8ccfc6672c6142c9143dc18f894c43a1ab0c30584278115078032c10c04501a0088022000, 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⟩,
  ⟨0x3791a90ce865031e17b8bb458c29f1470a044d8262128891c4402080fc87503421890bf859c2ac14c093825c11808103a813804e000, 0x73697332bdf14ba47818005e6cee740d9b30004f3800466cbe62e99fc5227667818a4d30366c40003ccca89c5308e000e855ab0007429000f5594f38b03653ce2d099e06002f423d5800100468a8c012000c0004c378001ce4be3e26c4d08d2dcef63f36f630001e68003cae3d1⟩
]

def tableRRLRR : Table Block := .branch 15 tableRRLRRL tableRRLRRR

def tableRRLR : Table Block := .branch 29 tableRRLRL tableRRLRR

def tableRRL : Table Block := .branch 59 tableRRLL tableRRLR

def tableRRRLLL : Table Block := .leaf #[
  ⟨0x28813a89a04ae24a11e88b843620a0fe87c03ba1c80da85c02c21540a484e024c11c08203e81c40d806002cc11805601f00c4014000, 0x7c10fe292834b8a74cc69255644ca1a6852e290c91337a680c112001c004800bcd33c86c4fa6684d62692e91e06cb15c581b2c571606cb19c57138001cdb1cccdaf9b60000f2b2c0f1584f9b50001f3a06⟩,
  ⟨0x2d31648a8851e26812f08dc4241fd0f807843a61c20da869032a18b0bb059c2a414309c84481fa0d605f02cc14007902900ac026000, 0x40c0006f91f2f6148c85b77b7d3818000df1fe6dfffb54ec70494f42938930437a9a7c525269309303502aa4d248532a4c24c0d48a8004f3418952001e91473fe1121e137828900037c279a0006911f44000df0be9e5a7e2e6687⟩,
  ⟨0x4051ef0f447543a01bc8db068a31e1888ba858a2bb14b09c44981fd0cd04a022e10607b839817e0b004f824810a07002480d004e000, 0x19cbda97f6584e000efa17360600037d0396c315fbf7d0ba6d4a2ae074dc4e0006f9df36fbcbf6f63036db97eceac001bf6f4f7eb5fafab00b0016bfc28370fdb4e00ac00aafef506d20101faf1c01500145fdca0d4868480307e9c7f4349f1a57248c1a6f97000ce5e849b435d0a5c520c6ab77c5218ba6342ab6138003be4bcd⟩,
  ⟨0x3661ae0cf465c30f1800bd859e2b0144897c4a8235107079c3801a80c485902620fe07583741940bc055826811606402b812804a000, 0x2068200169269240140ea4984981a3f60009e680181549000f1fab9f01c00802a3c2680c006920006fac734000c7e5e88001beb5d3c787c5802ffe8fa92dfa7a743bf524bf4b4e87759657e8e9c3744e50d8b226486c334959a4c24df490015cba14b0a4009bf9f56000dfcdab⟩,
  ⟨0x4ca244915886240c1e58e286e633d16d09a03ce1980c385d82d214209b849022e0f007302fc158087034016c09803e016808001e000, 0x36e200df556c16f4f819607f49fe9f029dae353831ee47aba4f3668c0bf03cd3e09b81d800381469f033d3532250fedc6b8f4c85b32302b72c2a1f9b8cf1e990366360544461cb0287d6e31c722074c7db313029222ee57d43e3717e3c7bc14c4697d1b0043a79334941a5c537dd4003f2f049bc8b6138003bee3cd818000df6fe5e0291f39613fd9c1802547a149c49821bd4d3e2929349849⟩,
  ⟨0x32e18d8c306022f016f8b405862b81538a6852027813709584922220f6075038e1a00cb05bc2ae13e09284682020da04c81d0082000, 0xf144e649c123c6979343627b334269134b89e06cc4dc581b314f15c4e00073c1f333c167830003cacc09c56138003ceffce818000e77de665fee2d4d1ba68aa1d3826869dd920d9822f1f55ac112f8edafb4f7fcee51a9d560039db934faabd2a001c6dc7a7⟩,
  ⟨0x2c915e0abc52c27d132092c47c217106879838a19e0bb858829a14209684381fe0f407082f0124088034815808a038014807001e000, 0x142971480f6bb02779e403d6ec31dc7c309c001e7abe740c00073d4f30040b5de40392f96f500155f2cea5112a619d5382609959d280cd1f224e090dd13a830e93ad003d140a51e06e8604e932821f34cfe295c92e29a331849⟩,
  ⟨0x36f1b28cbc62e2ff16c0b2c5782af1518a504da246117081c3a21aa0c185a029a14209384381f60d405f82600fe05802380d804e000, 0x40c0004001668de5663ee2e653e2cc84cd15c7f14ae49714f231849000531fb920007245f2734171b244cc7be4cc7acd0000078f31e733ff24086cc70e3c1e01097fc1a13825fd0f85fcf93a43243e7bb0027ce07c53e7b9007bce01e57380e6cf6fced334961a4c24e7b30017cc⟩,
  ⟨0x2000f787883a61c60dc86a832e1880be85a82aa14609c04b423410807f03981b80c405d028811e08003781880a004601b80b402a000, 0xcd33f8a5724b8a68cc6124fd44e649c121d225e6cd0d89ee8684d50a24ba4781b33371606ccd1c581b33bf15b643fe499533f8a4f64781aa24c0d99078a9a267⟩,
  ⟨0x29c1488a004e225c12588f846821c10907e83da1c60c806182dc15f0aa84b8242117078039817e0a704a021c0de06502900ac026000, 0xc123a69bc9164267a134b89e06cd53c581b356715c4e000740473340368070005ca81b350f17923c0c001b401731c4f0367fe0007ce818000e7fde76697e297887f14847a43c0c1ca24000e7f5e7668fe2da087⟩,
  ⟨0x2d71580a244e225812488f844a2000ef87543781950b8052426211808583f81e60da05c8280110075034015c09403d017006c018000, 0x19e5dd10003811fa79b5b8a1152e7c893824069dd3aca000fad0103a473c0c0346e9000380e79a000eb1fb1000380efa79b278a353ce7a14b0a7134c8b3a4566405ce2930e9849287bb90fe292834b8a64cc692451449849c46⟩,
  ⟨0x31b1850b8c59c2c41598aa450425b127089c3e21e70e786f036418b0aa852027412908c042c1c80d906302e4124088030813804e000, 0xe1a5add4f4de689d19e062834c0d8178000f35ad54f47e8b89c000cf45e5cf3f9e88000b950366ede2c8287818009cf3fe580019202000b8fc66ca1a4cd25069714e04e000fcbc126b22d84f8128001f3606000381239700a440026831e9e0450003cd⟩,
  ⟨0x2ce1608ad053a282135894048621c10907ac38e1a00bc858829614009484402060f6075834816209804281c80ce0520158068016000, 0x2852e2903f19809cf4480fa661cb39186138003d0d7ce818000e869e60040597890073bfdbd400d77fb3a992f326ee364e09b99d98adb4e7a14b0a7136aa93a5475405cea1a8e9bc5130b227049f3aaef3c000ae3c799f224e09⟩,
  ⟨0x3a11cb0dc46943171868ba056a290135891846a22810b88183ca1da0dc86502de14a09283c81b40bf05a82400d205802380d804e000, 0x1824001887b5327719b67340013eb2218d3c0c7d54435a9004e21c87ff4f0fe4435a9882221ad4c433103ea478d32668d34e39a779801ed7824017792d79aec40babcd7220cd580030f6e9c001880b56000c4030feeab2a27179e0183c0c6ede6abab9a4f34a79304e6d334961a4c24e8730017cc⟩
]

def tableRRRLLR : Table Block := .leaf #[
  ⟨0x2d11600aac54228913f899c4ac24911b88b443c2140fe076039c1aa0c905dc2d015d0a7049c2060f906f035017808902400d001e000, 0x18267a1333c0d9c8b8b03672de2ca99fc527b23c0d512606ce2bc506f9c0307818020bf342b389717da0883e449c1271240f7675be6807d00383c0de60142606ce13c5000b2d888a74e000e5ad96bc451a79bb463ec621dd3e449⟩,
  ⟨0x3dd1dc0e4c71036319f0c2c5e62db146099c48421b0f286bc2b613407f03b41c00d106202dc15008f04001d40b804401a8090032000, 0x16b35b7fabb5a0004d5e09000ad66d580036ddeaedba0004002d56258e2e256e2da5fe76306d260daffa70006cfcd3dabd6afeae957d209e3d1c9a55d48238f48da956d207e3cc20a467307e7f84155e380f3ceffc701e59df807871f34cfe295c92e29a33184907eb74e649c1203d0e98a14886c4fcae6c4dc604e9⟩,
  ⟨0x3ff1f90f747903a11ca0db46c633c1958c105c22ba1548a6851e27c12b8914476228100877036a1a70cb051c1b806302b012804a000, 0x30a4895560c8abd236b747b2c27000783ff9b030001c1fbcbe138adcbbd91d3000dda30f83e4bb4f362ccf91270487089005adcfd69788f0306889c1e000079a000db95b1002183cba70436799e4d0f3ec0030012d8ed3fa22ba6499fe7d0004001db1ba7f44174b933bcf9610c001000ad8cd3f19b91ad555747536b12ba3a9⟩,
  ⟨0x5bd2cb15c4a984da259926c8523a81c18d7865630616f8ae850e1f70e806742f016109003ec1b00a504d02300ca05402180d001a000, 0xe9ca29af1e09382974f05277d9a77c35145207120967cb8ba0a02bf1c000cd0fe4cd09e32d1a826ee981d441ef295a508278eb46609b3a5f35ae7bc66b3cad1750fc7e97ba35d3aba9b01e9ed26574f602d3eab9725e9ebdb4a0be3fa4fef369ee77e963b6ad3a08a7ca0ec71d2bc12e5a22f1cd73b3c72e3df244a65c793e2db6f48f4f6da8003a7b69b4d6b1fa4127adb67a7f47c004d38012edb870007d1d000b4f09b686c2145dfb9b86692b349849c20c002b97429⟩,
  ⟨0x67430897b0b9257528193d899e4a824091688a04291f98f3074a36f1a40b5852222e0ed06f433016209e84581e20b003e816004a000, 0x2028586c802bca9794b450b8f240001fa700776570f90cc00147760edcf3338f6af2c56e43200031dd43b6bccbe3d99af49543be38004bd73c700077aeb8e00061d071e06c2737adb9b7a3126fd435e3d4347459c787cb0f07977a261f75432e3e1343b0dcd792967147fb1d82a8b0a0fc15471f21247652f9345cf8f908e3b217c8b13d6ab68b971cbe3a7f0b55962769e8f1f2ecb24f2c9d4bda788f4964952ef1e5f7686f4eea624c9f1e899697f4fb7cedf544c34bda70a0658d0a034ff807d63a7fbffeb0facb4ff7ffdfba7⟩,
  ⟨0x7a23bd9bacd106342eb96c8afe55a293936094a49823991388524041ef8ee072636e1a38c885fa2d614109844741b908d03e4198000, 0x2aa454fce5e5e284d240cc15233763b655222cfacf2be3b375054708a47dfe038cbc3c77dd72839299a5c6c8a7c7c28e0d0f11963740c3f99d3e131e55e9f09bc25fcaad3801de4669fe96f10bc10d3fd2be20eba7ec1781fa7f034001f16b4f466eff706ed4f81b8376a706df033538360005a90007c0ad4becb85b5cbc1a3bfed4e0d1e28ea616bbc51e5e081e196ac001c1934f853585df3721f3ed64b62947accf71fb43192d2a0864277263bf4d690eec002a87951a66a88f3538f6b12c5ac77d9ad01dd4004d0f1a34ad50de69f1fb6cceecfdb467468567b33e0d141a38772c86f1de880a961c200cf2aaa3559d7a245c7⟩,
  ⟨0x4171f90f347503951c10d4868633618a8bd059e2aa14389c84c025611788203c61b00be85cc29812507f035c1960a403e8158066000, 0x45f4008ea40108be75276945f9ab9910f2621c01508a07361cf24d198027076d383801169d110ecad5c5d60756ae106001c3e0c598f647818003e174e68ec3955bcb41f22edd381a283dc5d9a78bb80010acb4f03616e0003cd1d452a9fa21e66a8171c000d4eee4e230005a9ffc9a9fc00139353f49767265d6002c4d1332878003a7⟩,
  ⟨0x9484549fb0e045dc2e896a8b0655e29593a896e47622890e87f23d41d68cb060e2e81628abc51425410f07282ce0f505080f804a000, 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⟩,
  ⟨0x5732b49508a424fa26212b091648122d0f6476437c18c8c0c5da2d715a0a9c4ee26d125089c4001ca0d386001e00ab042017404e000, 0x40da6c4e8773000665ace000658c72c000cb171363cad0fdc59ef001b3c0c27ca589f2f04880050009491cc294a687637308b8e633261271e60f18cb9847c700033022e2ebb180004735b8f892c362230d9d1c367b332987f1480073d5992c3c0d9e8cc8e2732198cc39d2fd151c73a5da29ce9571f71bb95c4c4627537c9abbb77254355b26bcfb713ac8bdc4f3fadc7c1237bf6f516071e3e074c0e1c7c3a581cb8f11e70e8e071e3e1d23f6bc7⟩,
  ⟨0x4262028f8877e39c1c48d8867e31c17c8ba05822b014f897847620b0f4071432a1720a584a023c0f706802b410c06502c00ac042000, 0x9286ad6020e90627a3e01fc4f478005890f513a734e8ef33a39d29c67487a518ce93f483183a673999a7239d92698b34fbfce51a21fb27e9f947cb7c3f27f945cb6c3f2db96987e5df2b70fcbae5672c70e001e5d61ce5be9bee672f800387818e5fe9bbe669bb3403ce000f0b30fa6e0e16f380166eacfe290010039b8b3c0c00536d69⟩,
  ⟨0x4a223d91588984272000f6c7503811ba0d946b034c19f8c685e62cc14b09bc49422509604881f60d6058829810205a01a8080016000, 0xe204e6d0d73456c606a1aa688d5e2001459cda0fe897d3d07d44b0017a7507da52f8fe295892e29c46714d11f41c6a54476770e4e76f506dc9506ba508000f1d41a6941e4cf673daea40039ec74e7f08f631ec5904b6576b11ca2bbc1ea2c0c43db6c3f897b0ee4a26cf0003c78193f5e1eee6d04000269e7f99f0b4f098001a0834ea0770f4f349e3d7ff4f5cca996a54e09⟩,
  ⟨0x623251924c7e83d11dd8e6870a3641988c685f62dc14d89f045a21f106079c3881910b9052020e0fb06d02d412005d02880c801a000, 0x5f0495a37de0036806eb992ee100009a4054b0a95db1c36406c7f2c2a7859ff83df262ec50f0a1794bf6e82cc8a8e4e3d7631ff494ba7be2cc7a8e231727fdadcf1ef74fd5c7000f69313d9fc3000d0f5a6782cc03b43967a06c0079f474f30ae9a93534a4d2da69499f34003a05e5f1d3d32a574997be7cba05400198734f5434dc89a1f052ad5edfca538b14625ea98bf4f43a9451e8a50da4f47a1e66790006882d3f23005cd5da66926de3573488a43ab99d0001a1bf4f08c0068851c51d9a3756e27⟩,
  ⟨0x68032818b4c145fd2f81794b845922b794fca384ec2649288926489231112c88241a1fb8f5077c3811b60d586401cd02e00e402c000, 0xd2b74a348387d2a693f0fa52e9261e852c29c4dd1fd2762749bd1f000e1f499d1ec4e92b499a47c3e94349187d27e91f48d87000e90f0e6933513732923c0c69a7511f300fe63c0c699b51073946bf07c38007e0389f7e618002a320017c130f46766f6ae197c55fb689a3c7be132b5afbe8072b99cee240031a4554baa971b1eb6456c892c3e7881ffd3dfc63005118a1c94c8a3a78f7c2256adf7c00e37335dc400053488a97152db63c6c88d90e5874f0f3ff87bf4c5f8a221437298edd2599551d1c781740c312001c8962721b86⟩,
  ⟨0x59f2ca95b8a9652427f933094e47422790a88364111f60e9c73a3761a88ca84081eb0e5061426210a079037c1980a903b014c046000, 0x40d898cabdf340035acc3e2612b5bcd56562b3d3ab28ab7c565a78aca2b7d3c55d158c56da700062b6d3c567a8a6ae923c0d1646a23ab00036ba6b1822b7e3c0d8954000f362b7d43762eef25a371d7d90a4c95ff73dc04db66d9e72aa19542b66631d2d9ba546a026148b2ce14893bb2bfbdc7851c73d2e52f5a404c5cf4775e75b78e025ee79bbae013075b38e000665e72664df1af444cec89d7c738b0fcfdb5eee70e9f9c3d2ac3f3779c1d29c3e95fa5387⟩,
  ⟨0x3a61c18db86c83531a48c885fe2f21678a7c52a27d139894048621c0fc87bc3981a50c005b42740f9077832014208e03d8158066000, 0x3a29d47c689d19e062834c0c000713ff37a81d0ec8b89c003d0cc5f4fba16002c540da4e78b032ab7a0f8b7138001c4ebcd554f4df23032aa3a6b8b69435c0f8fa4fc5d3a72590e001693b173e9c001d26f49c8b9b4f030017c4d7cdac868b2b8f17225b044ab19e3969c00757fc38002ac578e1a7⟩
]

def tableRRRLL : Table Block := .branch 14 tableRRRLLL tableRRRLLR

def tableRRRLRL : Table Block := .leaf #[
  ⟨0x2bc1508a504fe27112e091c46421f0fe079c3b41c50d8063c2dc15509e04c4230105071033c16e0a204b81d00c603c0158070022000, 0x601c94fc6606f54d90cadca9b5454d812a43244f57d5a58b06854d19899d53310a9acd01cb5d6606b5af5759d7aa32ebc122fa6eb0e10e015ea9e2e1543b1f443e8919f13753ba378bb133e2890017cd8f33e449c123869⟩,
  ⟨0x84940b1ffcfb07b33b71c68daa6b033e96c4af655429693dc98248b22308fc3401790a904ac1ea0d006282c011206602680f0036000, 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⟩,
  ⟨0x5bf2a694a09b248a22b910c83c4071f10eec72836d19d0be45c42bd145095c46420d0ed06d432015d0a484201c60b0045816004a000, 0x2beb7312e6219c3ad0225439c0f8f68bdca3a94a7d7b6b7b2be9cd7b4f9c25a4dcd62f6b73269c001b476e95d3f9aa300038b26a715fd35a4572569c56c62dbe680019f1fc79f218b679b957e5999bde9f2aecb2ee83cdeb4f65069b2bdcaff4f95e657d95de9f2c7cb032b9d3d79d98e6a79c5e6b74fcd9f389cd669f30d1e6b4e0016575a71e58001cae74fe5e8d95fe56d95c6563a7b4b32b8d3d9df695e56fa7cc572bdd3e57398a6579a7ba47a43cc534e0016629a7⟩,
  ⟨0x5862af94e8a2a4f025791f070636d1ae0d2c64c3171790b3458029913a09a848a22210607a438c1a30bf044c1fa0e706880c804a000, 0x291c4fbde5da9d7366a6cc5b9af536a6dd03acb8412bdb47ae6bd3dc4a95e27b5a7580a006168e33a174f610d421b00142576000400aba6744e6001601ce71de3cdb30d4a6949348003c2f69f7530003c38e9d2cbe17b56e2700038bd79a9acf0b7b181935ee167560019b3e266af869ab4d9b133659aae266cb358c5e0da9abeafa54e77c001000adf54aa0003d3cb3b0d36fc34d6f0cafb8952398c5a0ace29d320001083c107f38371eccd97ae5e1a9⟩,
  ⟨0x51124f91e08483ee1e48e586e234c19a8cac60c1fe0f5876038a1b20d386002b214a09d84501bc0d4056828412806d01b807c014000, 0x2545f57d676791b5926ddb6616e3d6bbae0fcb92aa66e64abe614a6c7c73370a786ae171f164c5ab4f8b062c78b4e9c001c5a74f8b370cfabb4058f0362d9c326ad98f3c8267a80c2400080025840cef096b002f0040007339c228e80a800c169bf1f4d9370d2693512c8a2704800ba48fcbd378001f8f6926124e79b0011c90003a6e0001f1e06d36c00179308ce2700033f0b973f067ea8001e56793e2d60a9e06⟩,
  ⟨0x60f2f41740b5256429f94a0a064be21710347f03e31b88cec62c2e315f0a2c4b023310006fc33416709a043c1b80b703f00a802a000, 0x1c691d3c9f7c5b7cefff3a6f89e12599f85e2fc70007639d4ec67a6f27bcbed3a1b6434b4092f7371e2d05e73b72b3d090d211672271408db96f1c0068cad345966a2fb32bea57d7407e810113422c7676f8edca280f67b6e3ea1db6ae9d48fd4376d4d3ee5db67e9f72ddb3b6ccd3edafb686d95a7b1276ced3d98d6246d9ba7db536cbdb376c7d3edc9b6a69f6d0db8f6d3d3edbdb706dc7a7dd1f6e3d3edb3ba36dc5a77317513d3801001f244fdd9c00080021c8f80804fd71f8eecdc7966⟩,
  ⟨0x3781ac8cc86102e91520a644e824d11408443d81b60d606142bc14d09e04b42380f507303541900bb055020c0e406501f00d001a000, 0x36c2920082e29f3ed680a00347b5a02a92f876d01800981fbc784c000fc6fa7c6bafbf79a000fcada9f8e74df1c7caba9000503f196971e0600038d5f9a004ae23747d0d27c695c923069c6a2003397a12750d74297148c9ae002dbf0e9c39ad84e000f1a47360600038d1b96e31⟩,
  ⟨0x3a61cc8e206ee3501a18c706242eb16f0adc53e2780e506942e413c08e83f81e20e206a831016e0a604b82340dc05f02000c404e000, 0x1853526b1835eb96bd1bd96138003c6ffcd818000e37de5b8c4000e37fe9e492e2de85b929d3b4375b29a0964dbb7776e3f13e5c0a94dcc361e9371f5a7f4974fad31581e9269ee91dd757a31c7b816ea8f6f80dd1e8527127ccdca69f14949a4c24c0d6d802d24d24802b69493093035c550045cd⟩,
  ⟨0x3301848bd859e2be1568a784ee26a12e893047621410387803ac1af0d105ec2c613c08b83c01920bc04a81f40ca05402180d001a000, 0xc74800079a18a4400c63a6e9e19a4acd261271cf000ae5d0a5853526b1835eb84c6e3d96138003c72fcd818000e395e5b8c4000e397e9e4ace2e369b429d30007d14d3e38fc6cbcdc71c00079ae3100038e43a7928b8b928f8b86692b349849c70c002b97429⟩,
  ⟨0x3331860ae055a29e13b898049622410887f83de1e20e987203661a00cb06042b414709003e41860b4055020c0e206602c00c4014000, 0x63c40091cd00031ed9e9180028fa1c784d9a98000e3c0e6b38ad106853e3bd0053cd8b512c8224e24c19bd24e0922c55c428781a985560006fcaf1c7f458001bf1fc700037d6f960072fad5f91e56247818010df57e59588f09b286c74e00079a0012fa974606⟩,
  ⟨0x4f0265929890245c2148edc66c2e215089f04ae23010487d83ca1d40e486c831617409f04b424610c07c83980f607003280f802e000, 0x7b3fd3f689da2eaece6ed3f53dad769fa9ed27140eb534eea11d41c36059ceb39967433aae3ba837512ea09d452ce559ceb39a1aff1df61bf257d34d3b60b571ff24fa23e99fca34ff0f5f97a9f8cafd1d4c00c5fa1c95f9f002f9374a1e54d29069c120e432c000df72e381aecb00ad7b72fb872a44cf0342a6cbced124ba1fddbf432ae0000400200f2cbbd3c2684c00931e3f371e30007e6818ec7⟩,
  ⟨0x6503159798b8259a2ba9508a525102220fc07923931b60cd85e22ca14288883601a40bf856826a110082838015a09503e8160066000, 0x8f2a3c3d5a766827d32c11dd71f5198f8f530b55bf671f81cd0a34fc0e7037a13e9f9385d3c1c6e984670626654beb90016c571a4f93b95a06ea81682baa27dc5c74ebc9d826543eb86aebc79aaab9c38ed8326aa1303e3add3c309c77392b74b0c1f1dce42dc1c304b7478f06620ccf1c001cc5d59eced7f8e000a62e2cf575b6d289daf71c000cc5b2b1eb3d1d6d34a176bbc7846edd3b67d4f725db56afb91001356001f721abc12000f69babee34001000b55a07f8ba0778bda4f691abed27b44d3f691da1f685a7⟩,
  ⟨0x4c324111bc8c244e21d90a08063dc1da8e386ce3401978c205c62be14b89c04922220f786b82be14009b04441c20ba02400c404e000, 0x4c9e92dfb1b5ede9c3744e50d8b226e944a2c89d9db6a9d5caee6d41cb9b578ec3974c0297f72e97ee3d1e5e3d09965cb1d34b66f9b4dcbd9bad57d5ecdbb32eae572ad3be5cda25135cb9b42b0ff974bd940d72c70ef86fd79d38e1b43d7c35ebc69e87b1c32879f867d77d3f140034781ad4ca24b5600492000070eda531cef2c000e19446fb19b0001beee47cbc78e174d03123dc80bcd⟩,
  ⟨0x5872bc15b4aac53128f94549fc4d7259122c8f64641c48d9066231e16e8af053227812288803da16c0b104ec22c0f106601e0066000, 0x6449c1206d324058ef935a5e23c0c06b32721e8001e68003defec4029643fe9d2634ca2c7c679713ee3dbda199912cbae6534d2af14e0a6d6d80476331966f8ff7a0019a7fbcd9fc002f4f50c9bef167ea79900274f55801167ab32adb0e00d55d67cb9b54ecbb34f97665d1a7cbaf2e7cb9b4e00991d1000175a6c0130dcb51165c9c781b2158aa2e6eb631e0ea63c0d6c353aa26b61abb172f8e1eb4ccd45a31c7809afa8ac5c2d17e3a4b9ec757b9a7⟩,
  ⟨0x5d12d5133c8d844520f0fdc7a03a91c10d8c6002d913b08103061750b2054c28811d088040c1d80d505702840f407002480e0022000, 0x1064df0971ea061201b8c152e2a6054b926491212a5f8a9a890552dea5b4608e3d40ba96f52fea5c45f3a81fc71ef72b1b9247c2562f248f94ac5e64aed95b7cc95b52bb3992b66561732624c0a3a081aeff73b2be9a0aea867c799f800138f33eddaaba2a68bcd9b0001f1e67d3b547452d175b35e3980005c799f2ed4d710ba2868b8d9ab1cb8001e3e10d86692b349849c8a2002b9742961488cacb039197b199df876584e000f225736060003912397827177d5884fa71667⟩
]

def tableRRRLRR : Table Block := .leaf #[
  ⟨0x3641970c686082f61718b405822ae14689b849622e10987c839e1ae0c4859828e12008283e81be0bc050824810e07a0310114030000, 0xfc0040403fa41e1451bdf586d21a6944a2489e892182250eb04ad70e409d2fe141ffc5d7409cac03ed84e06a1adad819f39c5e05dfbdaf9be7c8756431f81e2e18418a5d35b3dd5cb00f5a1309803de848017e618b027c616e92f04e8af58f71401aa25600254f8af6ad639c5⟩,
  ⟨0x3a91c10d0466c31f1860b945802a814909fc4d825912308843f81d70e306e83521980b9853825610807282d410a07b02a00bc04a000, 0x7fbf649731eac000423785034f89a13ed3074870003927f9b131bda5b1a07087f69e1ad444cea899091219a262607b2f5712fc4bdab84c212fd58f1a711974d388698961ec3d5c254f616ac003ec3c3fb03d838bf5bfaf30feb3f5b7aef0feb4000800f0f0364883d69cd7aee250d5c0d126bd73ab⟩,
  ⟨0x47d2330fec6e835d1a30c8c6002df1640a844fc25911a08944341f50e7066c32216c0a284781ee0ed06302a411806b01f00c4014000, 0x10aee98229737c022000a53c095cc97d38450fd839bc010a7f4000ca7612b192da7860f4d4ecb27f04300c5fe044878b056c91b3819ac7c97600079a00cfbee4601980574e004402fa7c893824001805753aec0026734001000e012d3c0c000c023a9000392c39a00075d5f4402364b2e9c0c7fc364df3807ba2537380d292e6c7db3971172e3e59d84fb250ff8f3a06⟩,
  ⟨0x46622090707ee3d21cf8c605ea29e1498a144bc24d11e08b440c1f90f6071c34417b0b7051c27a1160848388176098038812804a000, 0x1f18958356000cacba77b9a55ed5ca832b369e5579502565d3803c1229966129bb1c0020512139cab1a70027b930e251ec6000450e00202ae1e13510d9368f73f370cd256693093935800572e852c29002623fd5800311f6af65e267becb09c001e4cfe6c0c0007266f2d86288df267f4d33a5b4de98007dc587c9907b8f9a0007263f3623688cb62000c2c9a9⟩,
  ⟨0x4f52759328980499239112c84841a1fa8f387523841a88c786162f816a8afc4fc27313108ec4301c40b083bc0dc06302b00bc014000, 0x1030016d9da606000394079a35faba5f46ba55740e5d7407027cb81acefe0bb578292835f1e24186f34f0ddc4b5a7890625888ff4e145c32802ae9e5444ce289000fbeb13ef6c300a0000caa50c7e9e130d99c004e4efe6fc640cd879b20004814b80043e2fc79b1e004414b370000067c5b8f363800802956dfe000b2161f15e3cd8d001e0a5115436fe000390acf8a71e13389f2738001e6be272b16c606⟩,
  ⟨0x50626f92e092246a21a103c7b835b1a30c845f42d31560a144aa24b11207f43b41c40ce85d829e11907182c011e08003a815005a000, 0x25734898e4c89795cbc990b12b9393b442572730b9dcaeb95cfc7f6afda1d3fb4fed57b41a732d463b4c7398e4adca0004010d661e3edfd9ad0eb417570a16b82f2eb82572ce5d72b7b4fcbacb759ef8f8dd000e4f30f0365143271cd949f5a2b8f94bcaa61f2a7860003590b8f943eb20734ba15653e3d6492e83594b8f592eb20d650e38015f31fde1a7008dbab3e449c12003b6f69aea236d39a002007b6b67⟩,
  ⟨0x4f626792a08e444b20a8fc079e3aa1c28d806963241770ae052228213b89404521f30f487082fa15609003a818608d033013804e000, 0x32a2511ee6d18da35bc7a30f46328d671e8b8d173e3d170a2e545bf8e521c8cba9a42a49b49491231ea63ef918f591ee8003a7a3eb30a3aa2dfc747b028e68b771e8b9d16ca2cbc7189145ab8f9127048001a2cfc9a5e340879a0004621d165e3c0c310a8b1f268b55161a2c745738f46528b571e8b35193a2d3c7a2e545d28c9f1e4ce4a0fe3c5c29431282b8e0006577726574f1a5764898e4caec9133c9⟩,
  ⟨0x6062f096e8b1a5832ae14b0a0a4de25b92488d644420e8fe86b632b16b899438c1b10ce05ec2b413908c03c41980a7041016c04a000, 0x3896e1e7575e96bd272f7c80077decf0365601be7cd6fa6615bc787aca4660f935db0cc1f24cc1576be4fa286f7ea6bb58defe48deeaed5c97bcf5dab96043cbe61eed7cdf9ac459169f5fb2b66be16fe671e5731e3fcdbe8ff14c3d15a9bee8e480025140e3d1599bece1bd3bf2391000744ff8e8e40000a43a00048ee91e5d13ea33d569e8cdf1e902cd25d66c47a5ab4e2052cda70fc00ad20034af69da7230fb9861ec7fbac911e3fcd647f72236b05295190e38a4e14a3463f8e000db37a7⟩,
  ⟨0x4d026212848e245b21c10207ca3b51c90d8867e3181798ab850e26411a087440c1df0d486082f015107e837017609a03a813804e000, 0x84691ac5f71200191a000b0f17bc345ea48f898bce4da2ef878bbc60f0f1738bb460b0f184bf461e3077e78c0e1c0037edc3e579300bcdb079954d3d66b583a3804ccd71e30d198ae3e6332eb87cc5e5d330f87ec1593d82b256b25784e5ac169607182f8f184c000f1e06af015ee3975cac0380dfc8c2037c38fbfe0dd69dff06eb4836eff5a6d5bf7df575d4ab99f2eb4a1986e5b897af61cb⟩,
  ⟨0x2a114489d84d225a12608e445821b10608083e21e20e887083701950c3058c2a814909f04c42320f206782a012006d01e806801a000, 0x1acb38b29a1e852712628681513e292934984981b14d26924a8d2612606c38002f1a712401386ec7b627c4d899853abf78a00072c6f34003867c88001cb1fd3d5f7c58c0c9830f25fc9d46030e00691ce1e852c29⟩,
  ⟨0x2df1690a88530275131094448423711208043de1e50e907103581a10c605942b013108604081ba0ce05481d80bc05201d00c0030000, 0x78a400201d93ce1e0600dc9e31396a1f20cf91270486e89018e25b1a7b23c0c59a264868b5e8784c0cea7cb66009f9ae27000396c79a012edcdb1818024db9356611c001db8b56000edc2003eab59871691b440a1e06c0448ad62bc5⟩,
  ⟨0x32a18a8c005ea2e016a8b2054227c139093448021b10788083ba1aa0c906142bc13909784281ee0e806983201620a303e0118046000, 0x39e957c9cabc1266eab84ce270003977b9a0295d03b1818051b9ff56c270012e7dd5c23389c001b9db5773adcf2000eab5adf15c4e00072e9734046b9c76303008b737eac3f44c2a681e54e093f01978431836d61fc7306bac38c1a71e4fb27bc3807e4f787⟩,
  ⟨0x3681a80d0466e3101818be45a42c81508a244cc259114887c3f81d50de86682b210a06d033018409b04401dc0d205602280b802e000, 0xd6ddc5a48f030006dbe1cc713c0c000f6f6f3a06dbd400079dad938a00596b61fc52001001cb530f0300065a7890003b78f9dad738b2d096661ee86cd4be534b274f742e6a3f4f7ca496469c00390000161fa8681b2f6803de6f6c891f34c50d072277cd374932ee3b658182c7⟩,
  ⟨0x2aa13a094448823711608243b21b60cf062c2fc16d0b0054c28813109104582160fa075835818a0b805702581180740338100014000, 0xedbe12d3293c700c657b0f429614e26cab005312013cac80070e012cac626124a1eee43f8a4a0d2e299331a4914512612711b048e9a6f2459099e84d2e2781b5bb71606d6ebc57138001dbedccdbe9b7d400172a06⟩,
  ⟨0x3521a10c746182fb1760b145702ab14a09c44b4237115080c3f21d20d105ec2a813f095047c2140e506102d415009d03d012804e000, 0x27b1b3a34aeb4fa6692c349849dc5a002f994297148190cc004cb632406333007d2d6cc309c001ee25e740c0007711f30002002968e4801fe5a7ea0037cb4dd4c2a54d37aa704d19ab2ec3b69f4e023cf1e1e852c29c4d9da00fe2403d9de000e1c03b9ddc4e12e3295c7⟩
]

def tableRRRLR : Table Block := .branch 15 tableRRRLRL tableRRRLRR

def tableRRRL : Table Block := .branch 29 tableRRRLL tableRRRLR

def tableRRRRLL : Table Block := .leaf #[
  ⟨0x69e32c96aca904f425010f46e232c1828b88576294130893c46822210988103ba1b80ce864c2dc14709003e41a40ab042013804e000, 0x2506c8b492fd9a3b8f677168dd9e61c203846cc436fdb5eae35ae830952e38c8f83db66d1fe5d987d2a9c7b3b566191442287ac75c79ab9a5494ced9857f93c79ab7a5454ce5984bde2ff238ee5214cdd983bde106fe0a23fc7ad635aeab5956b4ad672fc78f2fc01f8a6d607a9c7677b2fbf8fd5eea7e273196190e5e631c2dfcb82b000106d34fb183006e309b9c1b324aa49000339978f1de477babc48060f03482f1dd6aef3dbf93e4de808005c9800379ff930006f96f2ef96df29e5dedabe4fc7bdb25f42f9371ef935f29e5df324d31c7⟩,
  ⟨0xbe75baac8557ca014d6a6192dc91a484230d1588794319b14d5c66932318c0c1a5dd2e39680af24351ff8f244921e60ba04bc17a000, 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⟩,
  ⟨0x5cc2e11674b1c5692ad1540a5250426e92a893e47a22990b080a3ed1e40e846d63461898b3857029112d88943fc1c809483cc198000, 0x81a8a70017526924002a29752612606b0f000279a000d143a9000f61db9f44f000200169e13513a000ea4000e698e68001b0e3d100039a6ba7af378b44c5125a765f73fbb8e827679fa225e3c43711669e221886a22bd3a09a00024586555f1e247864bfb103b8f3ce6f72c301e3c8efbdc974a78f3cba7f2f1e7f1cf2d9fc9c7cb197a7e78c5ecb6e4574ac14bd9da9afd10978f74a81984424e3cc309dddc7cb137a72f643fee9e2b35edb8fd9d774ed74a014a33e5cfd1c7⟩,
  ⟨0x3031698ac051a26a121887841a1fc0f6877036a1a60ca86202f616609f84b023e0f8077031c16808d034016c09803e016808001e000, 0x4572373156c3fd722b589fb0c56b120018dae1c8d966c0e6e622013e9fd0d27c695c923069cd74003397a126d0d74297148302ae1b758ffe99bc8b6138003cd63cd818000e6afe5e0291b1f10d9fa74578025a7a149c49821bd4d3e2929349849⟩,
  ⟨0x57d2ab14cca5250627193009363ed1e30e7c6d23331860b5852226e12588a03f01ee0e386802f215209584101dc0a902a812804e000, 0x19b90000f36eb174fc8c0d759ba6e2c00374dc3dd2ae978bf167c50d3d738ae655ceab99df36ad0d8ebc009b4fbae6d5a2b8e0006b1f71eb2866dbe6df339f0e60538e5c661a9171be3e1e10011c73cd58780003f1cf34985fc3be001b8e004b8f61c003711c3dc76e3d8b000dbd000787818b85e6d0e6971abf5fcba2ab19778f40a0a1d71cc075f56e4df7ebeadc9a1be188ada0d49eec00138e4569069845c9eea000f8f09800315dc3915bcd8bcd⟩,
  ⟨0x3521a20ce465c3191790b2c5742a914d09cc4cc25911b084c3d81df0dc06b830e17a0a984b02120d9066029410407802a80c001a000, 0x3286c4d89a089539c0020673737f843ee6e19a4acd2612737d800ae5d0a5852009bbe62c00377bc5eee16a15d96138003cde9cd818000e6f2e5b0c4bba66f4e9b503bae5d3ba8dd5b0f74dba85d570ee2700039baf9b772bb764606bb9ddb316000f8c7a7bb4ddab16e27⟩,
  ⟨0x6c234d9a0ccc463b30a1778b505812ad14d4a3c4d925911f08503b61d08e486fa36e1768b605922b4147897046e21a0fd85ac17a000, 0xe728e9edbee2c1941859e9d2d3a7e4b3729ecdc70966cdc67b2f1e7ab4f57a729c700034e838f4e7b38e734001f27b53e4c69953e2a7e9f8ce24f8f330a594f1ec044cc19651c77b78db4d9769cdc8d11c7892d3ee2598be7e643ef825eb371c1c953a29b3c5536a9a248bd619f66f9e5f0258e69658c86b8e0cca9a14d3caa9d31fc85d3e98de422db1a7d31b4c4d3815f749c04415a380039f5400142053211891000120e23d58e38d5700053ea400204096421121c0019bda8386f55f8e3558000cfa808110708001000308365b099079bd9890dc7⟩,
  ⟨0x30217a8b385862b015189f04e424b11c084c3e41e50eb072036e1aa0cc862830015f0a804bc240116077833814e07a037813804e000, 0x1c539d0c003f2f049bc8b6138003ce7fcd818000e73de5e0291e81690dd9c2480959e8527126086f534f8a4a4d2612606841005b49a4900283fb4984981ad238009e6800c1dda4003da45e7c1c00080159e1341b800da4000e726e68001b481d1⟩,
  ⟨0x37e1b68d7069a32618c8c305f62ea1618ad851e28512f09444542030fb073c3581a20bf859c2680ef06602940fc0570238088022000, 0x30cd2566930939d8400572e852c299f358f1af7bb5096ecb09c001e75ae6c0c00073ac72d862001f3ad74e847e522e9b89c000e753e6d21c0079181a940001c5ec0be2a9022ece741a7a03a52002ec339fe3800690f87290b9d2f9a0006b5df1eb5ce749e6ed6372ac010e9e4cd25069⟩,
  ⟨0x28c13c89b04ba24f11e08bc43c20f10287d03ca1d40e286ec3281850af053c28813909604501da0de05c82b013206602e011001c000, 0x94d0f429389314340a89f14949a4c24c0d8a69349254693093033a40a161cd389342b9d1f73db13e26c4cc29d859c5cedc59eb9a711c003e8db56e270ed17d1980340016aa06d845c5a13217c8000f1e486⟩,
  ⟨0x3921b40d4c67c3231820b9458c29f13c095446c2110ee07343841a30c0058428413708c03cc19c0c3057026c11c07602f011804e000, 0x31805406d4773a55e7a29f2cf153f07c4749e1f8b2938af8752686ba90fe5d0d6522dcbb5300b70f89b0ed1c006a41f4e0040162404d47ad4d89b8500ba4d3900178be09c1697c1004d2f04807e054be964008d5f4b0012eaf04c62aac3943b8ac22d22b61ff17620f1400efaa388c8cf0bcd⟩,
  ⟨0x75538f9b2ccd06142e01628a8a526278132494443f1e68de468626812c08c44141e70e106742f015109604141bc0bb042815406c000, 0x157d87b95ac0e3cbb6682ad050e4fb466e3c4bb976b1e0e27eb5238df1c7998b44725da3aabd249c7a237a48e5d9baaab733c7a2356073248f1ccb0b858c9217e438fe87cc51f2475117a2a9c700039d238f9eeb3a3736d85995570a786db48e6548e3db0a32a9a46dc2961b5caa1712b8f92264365810a29f94d78f4446887d122e3b0a6616e31d9a039e6c0f4b4163007580ec90f602ac05d812b021c7d6c6000354338f5436a87734c7524bc4d041d3d6ae81fa01f57d33f42bab52af439f974ab529bab835742e39743aa874f2e545243c3de4b2d66e6df8f6b101b49230e0e31951c01bd0d80c63c7⟩,
  ⟨0x7683a19c98e026f23739b28d4a672334190cc385d72c19508a4250c27b936098848e23691205ea2bf0db851416a0aa04981b006c000, 0xc21020fd5c64fb49f07d082b4f91270480305ca7082c1fb5a000e0f0102e9e06c1d8207d4d1356a77c792d4391472253f4e3c9691c894630721d3f3e3aba63e3f347de169c0063c6d31d7668eeb300199d4999346a7af41d29def1ff3132ece004435fa7191eaecf3694e037e6e00140033bc991a9213654c5777b056e1a2f38e01197dcf9d5ba4b74a1c072fab8e00140025847e3e6d07d813805f9a80030009234a50e600f97d12fb0f0c8e016e90f9cdba3e520e3cdfe9c000008001bebf7e690d5b8f37f70a35f379bfe00040013ebe7e670d578f09af9fd367c7434dcdb5d75e7d1be71ebcf23f21569c7⟩,
  ⟨0x38d1c10dc467c3261870b785982bf1580a9052a28813c8984492231107079c3681970bd0574270113069028811e07202f810804a000, 0x182470d743900020016ab690f1768ff14b2600196f61e7d06613ca4bc46348ee2b9c55b4578bb4478bb45b8afe996061e84b0242e3eaa41040483a70261594c190aca61482e538490489abc244218d58419aa6610011de9f5f600111d61e14930030cca604934070c4a61780a538428477ab⟩
]

def tableRRRRLR : Table Block := .leaf #[
  ⟨0x3f51e70efc75435b1a68d0463c30f1760b2454827f12d093c4742070f7875c3681a60c1858027a10a071830013a092037812804a000, 0x8f41474e3533b129f58116d40010009300d3ed0dc8c00195ae26453008e56989959808b134e20049aba70c004d580074e16af048302ac001a6fc002d56d31e2ed2fe2800660d89aa18029305c4cc1002789982005b160a36ada97669c000cf57e3cafa57f8b95f004b178240212bcc5d0ee0086ae876001356001d0ebab⟩,
  ⟨0x37d1b70cec6382e9152094048423111008443d41dd0e806ec34c17f0b9052c28211a08483881a20c205b82880fa06b030813004a000, 0x18a9b5a30091322d3dec00947e9545eb000f4f9e05d2a05ea0005c7cf00e94d2fe85e90003c7c21b0cd256693093a0e800572e852c292365583aaaf827a9dfecb09c001e833e6c0c0007418f2f04e2a7672fe74e2ccf912704835aa4029a26b5a5e23c0c0cea9d04c00079a000d12bb1⟩,
  ⟨0x35919b0c445bc29914409dc4d024111a089c4201f90e9071433c1940b6857026a12008884181e20cc058829c12408803080f002a000, 0x1331999e2626e006f4f1368bec00d69d13605f5848c00678f86692b349849d0ba002b97429614888ccb031597c1b546476584e000f42b736060003a15397a271518585b7a647ca7c8938241ed534fb8073ad043e54f0305baa6060003a1239a000d3e3b10065a12ba7682a7⟩,
  ⟨0x5ed2c814949fc4f125d92c491446d22810ac7f03951af8ca45c825412288e044e21c10787a03821b70c805c4294123076826406c000, 0x12e5cb3e844c57c854ca7ba742a259e0f0a2bd42203e24d2f4ea2e27d9f1fc52000545b4fb1e3c0ca2d67d7f270fe025387f0129b0cc37ed3b91d7905865a7391aa596cb52f1f5548b0c78f244ce3c030be3af1d06c5040b8ebc701b0c2818203c762f860c9f8d32937230ffc84d609add929c73c932668634c267138001d0dfcdaf3d54efa30357a0aa73cb0035828e158aa9bf2e8e269cce3d1c3d39794eb8f09e2e0641d18352c5638f09dee05c1d0835112358abf1f5799d3c7061c7⟩,
  ⟨0x3971b80d9867e32c1838b885aa2c615c0a9c53428913d09c049623c10b88203fc1d70d9062c2b014d09404041b40b304d81d809e000, 0x3d149cd818000e8a2e5e0291a442a72d9c7aa00969e8527126086f534f8a4a4d26126068f34005d49a49000a3cbd4984981a86d8009e680031e3ea4003d0d9e7c7880008005a784d1e18003a90003a22f9a000686a744000e88de9ef77e2c77d1de69e8125022e3cb992d021148554a7da7⟩,
  ⟨0x3c11d80e7c72037f1ac0d2467032b18f0c345cc2d51640a8452e27013188f04481fd0eb04a02220de04081c00be052015808001a000, 0x1e8693e34ae491834e8c00019cbd093a86ba14b8a464d629da66574e1cd6c27d16e000f9b030001d16bcb7188001d16fd3d723c5998229b7a7482e5bd71e874439558ce000411ca0cb38ff430886b10a2aca1c7a30f4c253705001169c4a5e09c480a08464000874f26692834b8a74540007e5e0937916c27⟩,
  ⟨0x4241fe8f1c72237e1b68d706a233e18e8bf05aa29f14909ac4c223a10087d83c61bc0ca85b82c813d08e03d41ba06b02c013804e000, 0xa310b3278e80f68c3acc8e3e8e1968da1cb8f15a1ed8d2b469c1249a2faf3a2ece003d936700030b2b963b1a1648ec8e5309f46b8008e6c0c002e162f2fba000401c03acf8983c43801dd1a3cd0003a3439a001215ff46060003a3379a003de7710003a33fa7ba778a7264e8b0001b4587240e498002e3f7326818000e8c6e68012b499d1⟩,
  ⟨0x4392090fb47c63be1cc8dd069e3381898bb85be2d515809f44e624c11388083ec1d10d506742ec14f0a284781f20d2056822004a000, 0x7482736e57860763035cad0bfeac00186034f0be42fbab00060aed4c155a60006145d3c1530a46ae923c0d726c377ab0006e4900174f030001d1ebcdb9221b7d880031c6e9e11800185ff4e86c7478735c4e00074777351b857d2e8c0c8deebe872c0018d974e8d8abe772ea17a8cb4fe3678d3a7888e5ea529adc0b5fe4296f8f6819593a7⟩,
  ⟨0x34919a0c7c5f42d51580a8852228212e88e04562040ef875436019f0c705fc2b014b09f04641e80cd060026411e06802d80d001a000, 0x14c6a98a854dcef0686ae19f85bb570cf433babda1a0cd2b9240018ffb4f0c0c305ab7138001d233cd864a17fd8c0d0ca42fbabc334959a4c24e9120015cba14b0a400985db56000c2ebabe2448f77b2c270007a42f9b030001d213cb618a16ed217d347ad8887a6e27⟩,
  ⟨0x3491910c546102e315f0a5c51426312c88c844a1fe0eb871836e1920b68580272114085039419c0be05382480fa058019809001e000, 0x1a51000572e852c2900261cdd580030e66af89523cfecb09c001e93de6c0c000749df2d862871749ef4d1e45fbbe9c19a5724800320ce9e1bf870356e270003a4cb9b0f9c37bb181a1f286ef56061326231a1c164e782a6fc9530bb43d9ab0006e7ad3d0a606454d4a6⟩,
  ⟨0x53828993b895a49a24391448183b81cb8da860e295138092c44c1ff0e486902fe15a08a84281fc0f206582980fe058018808001e000, 0xd6d8906d3b0dddb969c65b0004002f5674f22c9a159358df7af619638f6379ebdbd7a0cafc7b1baf5e8b3e3d790cadc7984655b3b274c1b2a59cb3cbd767aee455054858dae396787aeaf5d88a9d673151f63678fea8fa9fa7ec87b1ed3d06741569c004d5e4e38005b364001b8f33c0015a745de639d3801126a69c000d9ae0004000f8f89b11a11aaed694ce68003323e9d324694ae6a66fd293cdd290ba679b86692b349849⟩,
  ⟨0x41c1fb8f4875a3881b18cc063630c1808bc05922ae1520a3c50424f12188784221de0ea06bc2f81640a6049c1cc0b004581d0082000, 0x1f061c6d4c38a3e06a61c59337592664389ac870a1c8d3c37d0e0c38fa7d8853e449c123e695d9fc1db9a0e21a9e06bcb54d19800986f4001d3e23000b0a8e9fc5200080070a7e9e06000614ed48002001436faae06bc5e06bc5852a148d3a3268c9421601169e7ce000889e9c7000684dd4d08fa60017d5dd6e34f3916b6e0027ab9a7⟩,
  ⟨0x4202098fb07c43bd1ad0d3868831d1860b9458029914089c84c623c117888042c2090ea06f032e16409f84981fe0c904400ac02e000, 0x613e9a30013cd818009c907572922135a0570006000652d71e11a060003a6779a7a710003a66f9a000e475b10003a677a7bc578bb126924ef1e000dcb613c64d81985600359800000c3de31c587264d0d3c34b0d34391a701121d4d3d0513a696f2404e3a3fea5ba900f8e0018fa602043a1a7000647500087d200fe1cfd3faca3434da6⟩,
  ⟨0x2db1640acc5502931370924448219104075437a1a50ca06282ca1540a284e025211d08904041e40da06102a811607c02f8108030000, 0x3b689add55e096e955e4c800deaf263001356001e4c5abc123e6b000725f000b55bcef8bbce78b746b81801ec96b563467dc96c27989788d82468d6d8ab79671779771779871400c06a3b84b007ff93803fecac00bfc8054ade47c5⟩,
  ⟨0x35f1a20ce46482ff16c0acc50026b12b09044381f70e9071c36417f0b3853c27411908583f41c40c5054022c0dc05101a0084026000, 0x66084a7c4db84a9c9f0001d3e9e064f9cdc9e440bd3840593c0815a75fb54e7daa7ac95393d006babc9e4004d5800793c6af048352af2750004002d56f58e2ef56e2cd22ac10b06d4f2436d0de416427f70b25215fed29f841494fe20a4a413fc252187e72b0c113d4371e89⟩
]

def tableRRRRL : Table Block := .branch 14 tableRRRRLL tableRRRRLR

def tableRRRRRL : Table Block := .leaf #[
  ⟨0x2b214689ec4e225c11a88403d21da0e2868032217a0b5054c27812508c04241f60ea06e833017a0b304e02340f006902f80e804a000, 0x30ca935a5e23c0c0dca9d40000079a000e53fb10055a80ba7529a4a54eac0da8ac7894c0613268b1a84164c09ec988498f42938930437a9a7c525269309303410ac9349217ea9309303650f945eb41ed53944e50baf⟩,
  ⟨0x2f51758b1855029c14909ac4a823d10b07c43a61ae0d0063c2fc16f0a404ec25c11908203741a00a904f81e00ce040017808002a000, 0x1036587963eac082d8c7a4681b50f8004e6fdeec903998e000750e734082caff632bce463e310000e9f086c334959a4c24ea140015cba14b0a48f5560f8abe452cacfb2c270007a8379b030001d417cbc138b2adcfadd38b33e449c120e4a9⟩,
  ⟨0x4192060fb47863821ad8cd861e2e81608aa450c27912488fc4381f50eb072433e1950bb05b028a13007e82b812e080034811004a000, 0x1e6602b26a8e0440a499a3baa382088a425a69f5200001e68007788ec4000ea3ee68001e31bd10003a903a7c55f8a005eeb61fc52001001f7530f030007baf89e4461107980164851fc5200401c8ea3c0c00a4652606e4385b4b9866aa7002f19b00d34e005633527c49bc019e9f98664f30cc90bc993963811fab8f8202979600003a7⟩,
  ⟨0x3d91e08ed071a36a1b00cf464a31017d8b6056a296137897846e22610a87c83841a30c2056827611407a83ac18809d03d014c060000, 0x1bed78ae27d4c400079bc9a001e4606e9f000717c04f8b732a9ba754dbfc8cf8c2335bfb1800611d1f9230424e70e19c22df244e75c1a5e8d2449f02e1c891e0421661e24444a3c4b87b478950f220d1c00c4aa38447e477cc8a00068f03044fe471cc2d21c8df9c001b31e1f91a9664e7000bbcf870070007bcd87⟩,
  ⟨0x27212f892847622e10f88503e21de0ea06c43481910bc85b02b614c0a084c823e10d08183d01b80ca05e82cc11807b02a0128046000, 0x3643972aace24c19bd24e0900375771770a1e06ead005f16e270d517aa2915266b833e449c126925d4469cc8f035249df7dc56791e8cd036a6a0003cd1b388004d4d9d381b5330001e6f27800391⟩,
  ⟨0x2c215c0a944fc25912308cc44421510207e43c81d90e606943001760a8850823a11007f83301840aa04e81d80c205702100a802a000, 0x2060d912000755173703e006b6388225f7448c9a6ccd5069c125ecab84ce27d52e00079a017606db1818030c0d356711c003c0cb56e271935e05e0040005aa81b7eff15c4faa2c000f3620d6303480aaf7ee71670d5214ca9⟩,
  ⟨0x55729394749f44f0264929880e3f01ef8f387563881ac0cd461c2eb1708ae852a1c906f833c1880b405201f40d405b02800f4030000, 0x4007e52c3c0c002f28626060003ab039bdfef34644f1a02d4617c004191680110025348835c9e5fe3f412c79634ac1a7beb6f3c3dbdadd987b7adbaede187000dbd70e5bcb952732df2001c3c0c5beb950f333e3ba2f4e0008b7a1e27058ec2c4001b2205e3e0010002cd150d58794b8e0004b799e26058c77018580002643ebc7800180049a28f3103559e51e3e663626dac6dcc6d556c0f39a8e21f224e090e91200fe08dad08ee87⟩,
  ⟨0x59c2b49510a5a50e25d124c8603be1cb8dd069a30817f0b5c51026f132890037e19c0b604bc2320f606782a81060600288118046000, 0xbc02ec9bde34e000d4c7a9a97b4db692b51f19931e5922ec79e9c1f1e9c10008e380069a8524558f2b1e3c661c7000b350648a3fc463c8c78b197f1e22da1dbe380071d987d5b463ab9b34f4000e3330f05c781b56bea68e6b1c78ede3bb0dd38f3a7950173c0c04c5f4bab05d0c3480120025004d34d83669e73e3cf2c023870014f2802187000cf2675200fc3f82f0c001f2861f5661e4de6800392069f565323ee68023caf87c893824003e54c4f9bbca58d⟩,
  ⟨0x3d61e28ed875639a1c38dc86d03591a78ca06362f416e0b1056a28e13f896049c23f11388003e61cc0da06702ae0f405000f404a000, 0x234cf9127048d1a5104689c19e065893030001d5f7cd6188009d5fbd3daa3c5da97c5308fabd4000f34c288008d5efd381b125ed45e2eaef0003cd7188001d5e3d3da7bc5da7dc55d44747812fdca9e3aea196d0747412f136db951c796ce74718c705d304bbc796cc746d8c685d210f609738f0d578d7655ef3a7⟩,
  ⟨0x27e13a09704a422b10207d439c1bf0cc06382f21610a604dc24810f08083c01c60d206382c814e09a03981800ac04301b009401a000, 0x206dafbc581b5908001e68004bb7fd1308fac78000f34c288024d641d381a20557b5e38b386a90a65487e873e555fd0c3269b33541a7049322ae13389f5860001e6e269181bd145b89c7cd7673d15c66⟩,
  ⟨0x3591828a8852e28713008e444820f0fe079c3b21ca0de86b834618e0bd85c429413908903701960bc05882800f206702e813804e000, 0x17186e2a00020007c09f8e58c142f162e0002000ae3071e1352630001d681cd00a53a1fa3206a90a3548708732255f10c71260cde927048deaae6143c0c00eaee8f2c78ce0006ee7f2eee700160019ca8a33e449c123069002377279a5d23c0c6124000eb26e6dd8e0019d1⟩,
  ⟨0x3471900c585de2dd15b0a3c4ee25f126890c4382120f587103661a60c8861c2ec16c0a284b423c0f706082a413e08703b01b008a000, 0x3e6a5ce818000f350e6150a4004756a750000ead3ea6dcfe2edd4e29748f03000be691ce81b9a30009e70008e68bcc5d33f8a44eccf03149a606e67c000799b6ff8a611c000ce95e580019d28000f95b6d78b036db5e2c099e0600b53a3b9600138140003bb4bc7⟩,
  ⟨0x2f216e8b405822b41538a684e624c11d87d83bc1c60d706842f4144096047c1f00ee06382d814a09603781880aa042018807801a000, 0xf9d59e295892e29c3338a79c4800ae4f3880005c9183480010004000f9c37236f9f176fa7176fbf15c4e00079b27339b1f3640003cadbd9c5613f360002bce818009f35ee6699a4b0d261279ad000be650a5c521d2326ce41c23224f0c27⟩,
  ⟨0x2b114f0a3c508273131094c48c23b11508744261fb0f887643981a50b7855c28413309103ec1d00c105602140f00510238080016000, 0x78a27324e091e34bc9a1b13d99a13489a5c4f036e0ce2c0db8338ae270003ce0f99ce0b9c18001e56e05e2f6529fa530c19f9be8031e707a870061cdef9c0d2a7e6f200ab9cc270057cddf9d030029e6ebcca5156609⟩,
  ⟨0x2b61538a384da26312509004501f20ed87103721a00c485d02be15409e8468216100076831812c08c034815808a038014807001e000, 0xe24ebec3b4074c0dcf0368813a606dc1dc500f9c282f0ef1fb6f64eeeac9c12db9aebd18593844a986f54e094159994ad00de1f224e090e5133bdca567340034a800b61e06a530057134821f34cfe295c92e29a331849⟩
]

def tableRRRRRR : Table Block := .leaf #[
  ⟨0x22c10e88303fa1f20f1872c3781b10d2866030016f0ad054027012e08b04141f00e306c83281800a804b81d80d804b0198068016000, 0x3092f269cc93824e24c92b443627c4d08ce29dc4fc5c133d0999e06dc51c581b721f1694cfe2918333c0d912606dc37c5e23386c080b9e06010b80756e17e2ec0439f224e09⟩,
  ⟨0x2030fa07a43ac1c10d906903321860ba05a82a4148098049821c0ff077038419e0c505b02b012807c039017c08e036014806801a000, 0x6649c121c225e6cd0d89ea8684d30a24ba4781b71171606dc49c581b71ef17f24ca99fc527b23c0d512606dc29c51cc2878183143ee11e2e699fc52b925c53466⟩,
  ⟨0x2b51520a544dc26112a09044502150fe07bc3901be0cb85d829e12808803f41e00d806702ec12807c034816009603c0178088026000, 0x58693093d040005f32852e290c9181382f20c118117ef86138003e811ce818000f406e600815d3c8004eb8aea0001d713d4dcbbc52f10fe2908f48781839448001e7f9cedcabc5b410f9a67f14ae49714d198c249f689⟩,
  ⟨0x26312b091447022b10e08243f41ee0f187483861ae0ce864030c16e0b2053027e11807103601800b105382000e606902100e0022000, 0x78a4a0d2e299331a4914512612711b048e9a6f2459099e84d2e2781b74071606dcffc57138001e841cce83dd07c00172a06dcf1c5e48f030017e835cc713c0dd05800a73a060025d0579da669⟩,
  ⟨0x3261780b2c54828b13e09c44b023110808183da1c60cf85e02c014709d04b4244109074033c1780a304b02240fc06502200ac026000, 0x1407cfa15029c70006814d3a811d3cbcb08c773e449c12038ae99f4a001f9a020784e78180705d2000762cf34000cfa0e88001d8b7d3dd95c520bc73d0a585389adc71d2376e02e71ab674e22871ab673d0a585389ac459d22b6202e714b074c24943ddc87⟩,
  ⟨0x33d1838b0853628b13a09744a423b10b081c3e81e60e9871836a1a40cb85c02ca1520a284782280ed06d02cc14c07f02c013804e000, 0x11d06502b033e3bf9f8e81281181971ea465494e3f363559ec99d51938266e9660003f7869e25306689ba1ad244f19a4cd25069714ec73000fcbc126da2d84fb1bc001f36060003b1b79750a45463f456e9b89f6348001e6a8c3d3d7d181946169e9e5cfa2502bc7⟩,
  ⟨0x3771b68d546963331930bfc5922b115209f44e624c11a08884301f10f387003321740b384d025410507d835017809703900fc04e000, 0x40dcf4f8b0373d6e2b89c000f48de6748ce91a000795cf338ac270007d2279d030001e90fcce78dc52e91e060017d20f9d0374810013ce0011d20398002e331a7f148002001e32da7818002c653530374790003cce76fc50007186d3800386beac001c35b18ed573a3e2ca066069c7⟩,
  ⟨0x2b6147897046a20e0fc87903b21c40cf864830a17a0aa84881fa0ea06c833017a0b00518250102072033815808a036014807801a000, 0xf4b2e600020014c3db20071b0dba800a761af527855304ca9c12fcaac0063186d3d0a585389b182005752009e302000e9c013c607532821f34cfe295c92e29a3318493c5139927048f1a5e4d0d89eccd09a44d2e27⟩,
  ⟨0x3541978c285f62f01658a904e226712108743f01db0e806cc3381890b1053424c11508203d419c0c105a02740f006301f00c4014000, 0xc8031fcd3854b8ff69f224e0900071fcd4f42f0549cd00042a0c7e74f03053d8fc6a4208c4b35214fe25daba785295e091429c95cb88c90c10fd308008f381e54fd30001d73b4cd258693093d2f0005f32852e29030598004cc4bb207f560061311ee184e000fa5a73a06⟩,
  ⟨0x3dc1d48e106be33a1958c705ea2c215c0a444d825b12508943e41cd0cd05d429c13f09a84382020ea07002e412808702a012804a000, 0xd6783210b874f99d667ba9ca572a6d4e73395469ed24c249e4a4ca9792000e72b95269e06e892ca8b92127e519a7a734b49a718a97934f8e063132f1e9e5e897934f2f3cbc72f169c001977f4e9793a70f33123c0c97e3a6f73184f2f169a064be9d36b9d32466e9a7f14800332366e5a781a644cdc7539b866d5a7⟩,
  ⟨0x5602ab14cca5250226d926888c3e31b88d3064a2fe16d8ae052626c11b084c3ba1980c7059c2680e006a02bc11007b02a00bc04a000, 0x8180058a2c4c0c0007690f34c34430be8ee7ac463106f0be9db9e188b31051ca4f0b71db9d988a31031ca21779e15e3b73a31126202393c2ee6dce78538f124b119a9860a8917970c10c4b72f13b89cc5f817c238988fde11d4eaa16de1c785cdaa81b77f1c009e0dc380026fbd83af8f968c000b7ddc1d5c781b6879e08e6bc09bed8005a73c06f6f1bed55dd0003c78460007f17d3ed0a7e37cd713ed080003cd16c7fd1d8c0c2db7f9fab⟩,
  ⟨0x4b024992248c443d20b0fe47cc3c91d10db064e2d3138094c46c219102077c3741950b7051c25010106e02dc12808503d015c060000, 0xb8b94c0c00076a1734001d797620e1b6a274f810064fc2c9b08c3e53577c1ae71eaef34aa06b7c7abbafd39a54835ae3d5dc7e9ad2a363d0359e3d5db7e98d29c56a6c7906b1c7c4c3194e2618ca71200a520dea9d75f5d3d5ebac2f1eaf5d5d6f3571cc82f0f2c2f04731e5801bab47da5a175b9bae67fedabd72f5a2d5802315387c8938240038a6c4c3113149cd000800f14987⟩,
  ⟨0x4ac23b0f2074636d1940b504e225411b88684121f80f4870836a1a80c585b828e13a08984241c40d105502340fc07302b00c4014000, 0xb302af0ecc271eede0699b49396f0ed2ab8f572333d2c56d8ac6aefc7d5d641ad38391ac080f1b8e0e42b01b4cf078bc7071f5809a673f730789c7071d5805a66bf72d93e0f0f8fe177727007ca93f97e64b70cd256693093b55c00572e852c290239a95803cccafab3b5f2ecb09c001ed50e6c0c00076a772f44e2d7b3333f4c08e4a4f912704803c7ca75eb0e375a00807c6c9e06⟩,
  ⟨0x82c3fc9f50f2674e37d1a98d0265c30b970cb2054b27b9340970491236111c8043bd18f094845a2160f786e430616c093831013e000, 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⟩,
  ⟨0x24a11b488c41f1fc0f0873a37616b8a8449a1f90cb05c418609c03a813804e000, 0x372f4137931a1a826f26de39543e3d297a52bc75ccab99304871cf76f8b74f72af841f1eef55de3bbdb7792ef34fe07c55c20b64a4f21e3acff44cd2f238ef34567f487444cb2f1f8f3a4edf5c4347a124f0b8f3a4adf544337a104f06476f1f170e8bb4e8f5e218bd069b524efcd941c4b27828e8b2c3cdabe38f6dda31c7c25a3d3b8ed236746f1e5cbcbbde3cb0f9429c7⟩
]

def tableRRRRR : Table Block := .branch 15 tableRRRRRL tableRRRRRR

def tableRRRR : Table Block := .branch 29 tableRRRRL tableRRRRR

def tableRRR : Table Block := .branch 59 tableRRRL tableRRRR

def tableRR : Table Block := .branch 0x76 tableRRL tableRRR

def tableR : Table Block := .branch 0xeb tableRL tableRR

def table : Table Block := .branch 0x1d7 tableL tableR

def program : Nat → ClosureSemantics.Node := ClosureFixedWidthProgram.raw table
end ClosureFixedWidthData0

end PolicySubmissionPart29

/- Component ClosureFixedWidthData1; SHA256 d3d27c0d6cbcdf064cde992107a4e922ac3e24f67165c541779425ad553968a2. -/
section PolicySubmissionPart30
namespace ClosureFixedWidthData1
open PackedNatTable
def tableLLLLLL : Table Block := .leaf #[
  ⟨0x32818d8b985622a01488a084e626012688e840a1f20f286c02f61760b505742a214208683f01de0e306a027c12008303b81a806a000, 0x61c8000008000090c0000040000506326f3ca7c8ab126dc293a05261b264000004008000731a6587200000201069c300000100000a18500985a84471640000040834e07446d6178111e590000010000061d44d61780130e400000400002060000020000043⟩,
  ⟨0x2bf1580a7c51427513008ac44221010087c83c61ce0dc86902de13a092845821e10807583601920b4050824810607002e812806a000, 0x722af136ee0acf405660f6b90000010099c61c0d226d3ca7c8ab126e60acf005660e4b900000102000018000008000020ddbd72d8a8244091fb4406e8f84a714eb9a051a794f9154428de8527a0a4c185720000020066843⟩,
  ⟨0x288139896048622b10987f03ca1ca0d986783181770b3053c27a12e08b84201ec0e906a02f414a09203f81b00b20410180098026000, 0x715c63902aa7255404b644045445029acf03319a5d28aaa501668cf9a8ce4a2b135509b66076ce449469367066cd64f5092b45a3746a8829b21945158926742460728e0dd317c0514346881a414686093⟩,
  ⟨0x3011750b6c5882a614789e0486237115087840e1d20da067030816d0ab04ec24810f07e838819a0b604d82180de05a01f80a802a000, 0x16e334c2781d2d3cb900b280e36681f4d90000010012c21a2130b51880ef6c80000080bb940c097c8ca09648808a08a058d9e071334bfcd556002cd19b3519c941680aab3055b894b66808155033ab722f6cdd2abe4b4155591ab7409580e6ae⟩,
  ⟨0x2fe1748b405762a414689d84c624511b08b04362040f3073c38a1b40ce86382fe1660a684d01fe0e6058824c0dc05d02300d403c000, 0x6e8d53014f91ed356c1cd9dc0998076b38334c6bd80594712206d13681c8d3af580b2855566c0d026d037da7c8aa926c580bce2005e60314f9000001008000180c43e4000004017728766d016501061fab2068de0edb4e04da07134ef5d02ca⟩,
  ⟨0x2be1560a444f826312408cc4342050f507543781a30c705b42b0140094044c1fc0e306702e414e09204081a00ac047017007c01a000, 0xce4a0b00555782adb6297cd0102aa06756dc15be6a955f2520aaa88d5b1004ec018777036ae2161805d4e42a8096c8808a88a0b85783bab4b911556a0ab467cd467251589aa84db400ef9c8928d26d1033e6b27a8495a2d⟩,
  ⟨0x3591920c0c5b42c91580a7c50c277133093446821b0f3075c37c19d0c205ac26c12a08e84441f00c305282340ea05e02380b002a000, 0x20085fc3b1b20175008185e6ba078de0766f3c13680dd3cf915489b74005e79a02f301d47c80000080088b0cc2780debcee6e005d4036eed01ce7c8000008006b30d20985a9440386f9000001010bf81812f3d9412c9101141140a733c0cd6697d1aaa96059a3366a⟩,
  ⟨0x2a014589d84c824f11f08944262040f587703941bd0d4063c2f41610a404bc23c0fd07703901a60ba04c82000ec06702700c0032000, 0xd41568cf9a8ce4a2b135509b7d01df391251a4df6067cd64f5092b45a3746aec0a7c8f69ab0039f38404ec01c1770f9e2ff0005d4712206913680dc3ceaea805d40d52ed81a12680d9bcebd602ca03559a03c0f9⟩,
  ⟨0x30b17f0bc85ae2a214209b04a823d113082c3e81df0e686c833a1820b3854826e12208383c81b20c005582280ea05d02280c0036000, 0x30b538803178c800000805fb40c0979eca09648808a08a05399e066b34bd8d554b02cd19b3519c941600aaaf055b0a14c66808155033ab6182b8cd52abe4a4155511ab77009d803b6ee0695c6ced00ba9c855012d910115114170af0775697022aa⟩,
  ⟨0x35019a8c686122e516b0b305762a013e09844ae24811688303e61d80d185fc2a414109304541f40dc06282d813607702e0104018000, 0x8900a180188c387cf10f8800614712206913680611138ac50030a0344e1b03424d00c0e274f4c02ea01a5768066119000001002fda1c0604018500406078ec2068de0381c4e04da018544e9d202ca0b459a613c031189c36180185006170d00c8a3200000200132434c2⟩,
  ⟨0x2d015a8a8050a27012a890044a20a0fa87443781a40c605dc2c414709904742160f607283281700a904701fc0da06002580c0036000, 0xa0205540ceadae0ae3354aaf9290555446ad9600a180195c381a571299500614e42a8096c8808a88a0b457839ab4b81155620ab467cd467251589aa84db4403c67224a349b4603466b27a8495a2d1ba354f015191ed354401d19⟩,
  ⟨0x33618d8c285de2ce15a8a9051227a135894046a21a0f2872832a1890be05c02aa12008103a81a40bb05202240e405d02580c0036000, 0x75789e09b4035e89d3d300ba82695da306f00d9627c8aa926dd40313b90062601ba464000004002000601b9464000004001b586a04c2d52200d9e320000020111703025e5b2825922022822814a678192cd2f635551c0b3466cd4672505802aabc156d685319⟩,
  ⟨0x30517a0b6458e2b814e8a384f826f12d08fc45420f0fa07643901a40ca862c2f415f09d848022c107076032c16409703100f8022000, 0x1426dcc01e3391251a4dcd01a33593d424ad168dd1ab200a8c8f69aac80e8cd98050c00d961c3e78b1d90030a389103489b4035c89da6d0018501acf0d81a126806af13fbfa017500fcbb403848c8000008011170eab5600c28020303dc6103c6f⟩
]

def tableLLLLLR : Table Block := .leaf #[
  ⟨0x2fa16e0b1055829513f098c49823711288283ea1da0df86a831e17a0af852825e11407f836c18c0ae04b02040d805101e009c02a000, 0x979eca09648808a08a05399e066b34bd8d554b02cd19b3519c941600aaaf055bae14c66808155033ab7602b8cd52abe4a4155511ab7000286006ff0e0695c5f6fc0185390aa025b22022a2282e15e0eead2e04555a82ad19f3519c945626a⟩,
  ⟨0x3751a88cd865831d1810b785862a8139893c4442110fb07943941bb0d5063c2e815909204541f40dc06282a80ea06902e014006a000, 0x1bdde0061406ddc3606849a01d5c4f87c200c2803c186807b11900000100186a1ea7540185004060be2c2078de03d5c4f04da01d944f915489b7900189f14031300f3232000002000b643309e01dac4e9d202ca03459a01e34640000040013886a84c2d56200eee3200000200c3503⟩,
  ⟨0x2ba1528a044d825411e089c4241f70f107343761a60ca85e82d015909f04bc23a11007d83801960b004a81e80d204501b00b0036000, 0x1a571d1e900614e42a8096c8808a88a0b85783bab4b811556a0ab467cd467251589aa84dbec03c67224a349bee03466b27a8495a2d1ba3579015191ed356e01d19dd00a1801dcc387cf1b7dc0061471220691368076113⟩,
  ⟨0x32b17d0ba459c2bd1510a104da25e120888040e1ea0e606d03381850b7054c27812708a83e81ca0c805682600f606602580d8036000, 0x20180f07ca068de03fac4e04da01fe44e6cc02ca0b2d9a613c0180e67434002ea019f76b3701ce40979eca09648808a08a05399e066b34bd8d554b02cd19b3519c941600aaaf055b0105339a0205540cead8102b9cd52abe4a4155511ab7a80286007a70e⟩,
  ⟨0x3651ab0d106522f416b8af056e2a214889f04d424611588383d41cf0d9065c2e615809e84801d60d0060827412007502d00fc048000, 0x1c934b84ae38062600000200001837163a99807850901709ab44da3366a3392805b800c2b6e0186c58d94e7620200c2803b086c5cd9ce765ae87eb76201856c3590dff0121800c4939000001004b081807f70e3cb1f9fd00614e28d50061ba3f9c4f500186e97e313f9fd0030a⟩,
  ⟨0x2d015f8a88520281132095448623610d87f83c61c60d486302ee1500a184d024a10a07783801a60af04e02280f606c02780c802a000, 0xa136cb003ce7224a349b2d00d39ac9ea12568b41d33554a019ce41d3355448ec4e62600a5800c4b2e0715c447120032a61454a6ad4c08b22a010a055284f71686f9c1d850628d5892a926b62a8d80799c6b20ccc088ca525026a⟩,
  ⟨0x2db15f0a684fe262116888040a1f90f6073837e1b30cf060c2d615c0a784ac23410807d83801860b105202240d805101e009c02a000, 0x335cce130800c280307868033e4e4000004000ab86c2bccd15545c4e290212a32a953161033a9c116054045e45284f716857e81b850d9b5424ad16cf402aa9665a94a8495a2da6b05552abdb290ba0555c82ad19f3519c945626a⟩,
  ⟨0x3861ba8d8069c32a1878bc859c2b314b09ec4ae23c10f880839a1b00d085e82da15209a84681fa0d605282500ee06602480a001e000, 0x344da3366a3392805cc00c2b960186d28e14e7820200c2803c086d2ce3ce78dbe87ef78a0185713790d9980496003464e400000400d660600cc72e3cb130cc400ca9c51be00c35b396e67bc00c35b9966672dcb800ca80100c079de50346f00e5d99c09b401992676b6802ea05b376984f⟩,
  ⟨0x2cb15c8aa851a27e136097c48822710607bc3a41b50d005e42d815d0a704d823c10f081037819a0af04c02180ee06802680c002a000, 0x644946936bc01a73593d424ad168375aaaac82d9c8375aaaa19e69cd10014b001a1e5c0d6b8a168600654c28914d2a9825f22022d229427b8b42bdc0bc286cdba81016501d2cd5892a926b62aec99e26ec5433334756125c26a⟩,
  ⟨0x2fa16e8b0051626e11c88b04222050fc07683961bf0d506482f416b0af04dc24c108078837c1a40b704d01fc0d405502180b803a000, 0x2dc0066600dbd3900000100020018036e4e40000040007a86c2bc4d1554644e290212632a753181032a9c25f22022e229427b8b41380019950c9b730202ca03959aa12568b659815556efdca42d0155660ab467cd467251589aa84db5d00f39⟩,
  ⟨0x3891b70d4465a31217a8b6856c29b13f098445820f10007643981b10ca05e42b813508203cc1ac0c505402100d205801d80b003a000, 0x1db00c36f875a73d5010061401ea436fa75e73d6e943fa3d500c2ba9d086d94024b001bc272000002004c903006c7971e58b16c600654e28e70061ae3d7f33e60061ae4d7b33afec0006540080603db7281e3780760ccf04da00d91338cc60030a04c5e1a306f006cf99f22aa49b6f80333⟩,
  ⟨0x2da1640aec540283134092c45c2110fe07543901b90d506482f416b0af04e825210b07a03881a60c405482300e205c02580d8048000, 0x1424ad168375aaac582d9c8375aaaba9f69cdd8014b001bae5c0d6b8ba6ea00654c28914d2a9825f22022d229427b8b42bec0bc286cdba01016501cecd5892a926b62af4b2e26f460b3366796125c26ad1368cd9a8ce4a01770030a⟩,
  ⟨0x2bb14309e44bc252122889c43020c0fb877c38e1b80d586102e615509f04b023e104073833016e0a204801ec0d404d01d80b001e000, 0x8000af0d85789a2aa8d89c520424c654ea63420655384be44045c45284f716827080332a1936e8040594073b35424ad16cb302aac6e0b9485a02aacc1568cf9a8ce4a2b135509b71e01e7391251a4dc80069cd64f⟩,
  ⟨0x3941bb8d7067031d1800b8c55c291141096c49c23310b07ec3bc1b70c305d42b0147095046c2140ed06802cc0fc06f02900d003a000, 0xd79e79cf9bc50ff0f94030af27821b970092c007549c800000800dac0c01cae5c796329ca8019538a3c40186baf91ccfc00186bb390ccf23c900195002018179fca078de01e4b33c136803964cf915489b742006679f80333007469c8000008000f30cc2780397ccf1e202ca03859a00e8139⟩
]

def tableLLLLL : Table Block := .branch 13 tableLLLLLL tableLLLLLR

def tableLLLLRL : Table Block := .leaf #[
  ⟨0x2fd1710b1455028b13b093c48423311208303e81e50ec06c43401820b5856429413b090040c1d00d306102b413607702e00fc036000, 0xdd6aab4e81a73a80052c0074f97035ae34dd38019530a24534aa6097c8808b48a509ee2d0560005e54366dd0080b280e766ac4954935b157f65f137f36999cc3f3092e135689b466cd4672500bd801857ac030dd71e69cf94040185007c90d⟩,
  ⟨0x2a914e09f84de26312708d843c20f101076c3941ac0ca860c2ec15b09f048c21c0f907383481820a4049020c0cc05702280e003a000, 0xe290212632a7531c1032a9c25f22022e229427b8b41389019950c9b740202ca039d9aa12568b65981556ff0fca42d0155660ab467cd467251589aa84dbc100f39c8928d26f08034e6b27a8495a2d06eb555bd05b39⟩,
  ⟨0x38b1b70d4c65e31417b8b6854a28813c894848a22a10687c83aa1ae0be85b029e13e090840c1d80dd060027c10c06901a009c018000, 0x77cfbce7edee87fb7ea01857d3d90de380496003da4e4000004004e20600f172e3cb1c4f1400ca9c51ee00c35e3e0e67ec00c35e9e0667c1f0800ca80100c07e7e50346f00f8599c09b401e32678f1016505c2cd309e00f2733c7c6017500e2bb401e92720000020001f43615e268aaa3a2⟩,
  ⟨0x3011730b2455828f13d094c48c23711408403f01e90ee06d43481860b7857429c13f09104141d00d306102b413607702e00fc036000, 0xdd6aabae85a73d80052c007af97035ae3adeb8019530a24534aa6097c8808b48a509ee2d0560c05e54366dc8080b280e366ac4954935b15412c7cce08f2666c840b292e135689b466cd4672500bf801857ec030def1f29cfc4040185007e10d⟩,
  ⟨0x2a914e09f84de26312708d843c20f101076c3941ac0ca860c2ec15b09f048c21c0f907383481820a4049020c0cc05702280e003a000, 0xe290212632a7531e1032a9c25f22022e229427b8b4138c019950c9b720202ca038d9aa12568b65981557bf15ca42d0155660ab467cd467251589aa84dbf100f39c8928d26fc8034e6b27a8495a2d06eb555ed05b39⟩,
  ⟨0x3821b38d286562f616c8b2854629613d89784862260ff872837219c0c585b82be14e09784401e20bc05682400d805101a009c018000, 0x3439d86fe2024b000c17ac80000080055c0c01fba5c7963ecfb4019538a3360186b29f34cf320186b2df24cfe6f9c019500100602e0152078de01fd133c136803f7ccf915489b602801a9c0200353003026b20000020001443309e00fe53393494030a00c921ac47e539615e268aaa3e2⟩,
  ⟨0x2f41728b585762a314a0a1c4c625212008c44442070f407343761ac0ce86082c6148099848821a0fb06b82f013a07902f00fc048000, 0xa14d4a98116254045e45284f7168677a1b850f9b5624aa49ad8ab79f8899bb86553fcefa12b125524d6c5556f944caac2ca9fceb1092e135689b466cd4672500b5201856a0030d83e68eb3a2010061401d0c36109a4ace8f3f0fcf688030a⟩,
  ⟨0x2ef1658ae855029b140098449e24211388203da1d80e186c433818b0b6056829612c08e842c1fc0e306202a411406b02600dc01a000, 0x57c61b850d9b5424ad16cf402aa89479a92a12568b69a8155446305490b80555b82ad19f3519c945626aa136c4900f59c8928d26c4b00d59ac9ea12568b41cb15544106359072c555054e3d660b802a600182d4e06f5c41482a00694c28⟩,
  ⟨0x3401928c185b82a714b09dc4cc24711488484021e20e9871034a1860b384c82260de06882d815409d03f81c00c804f01a007001a000, 0xd18061a6722754e284510034a00200c03c6ca40f1bc01c52a9e09b400c59a9edd80594275b3460de0063054f915524d8e0006a71b400d4c00c6fac8000008000400c00c6dac8000008000310d85799a2aa8789c52042526552a61c206753822c0a808bc8a509ee2d⟩,
  ⟨0x3681a20ccc62a2fe1760b7459c2b114909d44c024f11d08a04081e90e5069831616c0a884b42240f306a027c10007102380e803e000, 0xaf0c2f0a1b36ee040594076b35624aa49ad8a95c9726656e4b54e5d57a525c26ad1368cd9a8ce4a016bc030ad70061b224d4d67500200c2803a786c8b35559d4e961fa4d400615a7d1c362d804a6001903590000010007a818018b14e3cb115a2b801a538a34a018699a8a153⟩,
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c01a007001a000, 0x28495a2d96605552b0c25242d0155660ab467cd467251589aa84db2bc03d67224a349b2c403566b27a8495a2d06eb55529c16d641bad5547b393598fa00a980063e5381ad711ea3d801a530a24534aa6097c8808b48a509ee2d⟩,
  ⟨0x32f18a0bd459629614289984aa23610a87f03da1ce0d806642f414509c0474222104073035c1960b604f02180ee06a02300d402e000, 0x67c030d3392baa72c258801a500100601e6652068de00e5954e04da0065cd4f373005d40b96ed309e0066054f1e202ca03859a00668d640000040001186c2bc4d1554444e290212632a753101032a9c25f22022e229427b8b427e70cc2864dba81016501d2cd⟩,
  ⟨0x3681a20ccc62a2fe1760b7459c2b114909d44c024f11d08a04081e90e5069831616c0a884b42240f306a027c10007102380e803e000, 0xaefc2f0a1b36e4040594071b35624aa49ad8a958af26655e7b54ebd56a525c26ad1368cd9a8ce4a016bc030ad70061b3a4d2d67480200c2803a386ceb35559d4e861fa0d400615a7cfc365d804a60019c35900000100057818019714e3cb12da5b801a538a342018699696153⟩
]

def tableLLLLRR : Table Block := .leaf #[
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c01a007001a000, 0x28495a2d9660555430c05242d0155660ab467cd467251589aa84db43c03d67224a349b44403566b27a8495a2d06eb55541c16d641bad554db393599ba00a980066e5381ad7136a6d801a530a24534aa6097c8808b48a509ee2d⟩,
  ⟨0x3131810b8c5a42b31520a4c4e825511b08043e41d30d906642f414509c0474222104073035c1960b604f02180ee06a02300d402e000, 0xf1bc01d16a9e09b400d1da9f22a9136d3300353a60006a60069bd640000040000d86613c00d20a9e1e100ba80705da00698d640000040000c86c2bc4d15544c4e290212632a753121032a9c25f22022e229427b8b427e30cc2864db901016501c6cd⟩,
  ⟨0x3971c28dd86ce34a1958c385f22e81698b0453a28213188fc4482050f5071835618c0b684e023210a070034c17009903f017c06a000, 0x2c4954935b152b9904ccadd5aa9e42af4a4b84d5a26d19b3519c9402d780615ae00c36a69a9acea00401850074f0da9e6aab3a9d2c3f49a800c2b4fa386d1f0094c003516b20000020007d030034729c79628d51b0034a714684030d335452a79f00c34ce512a9d14a2a006940040180ba6148⟩,
  ⟨0x2dc1608ab052e285138097c48022e10f88003e21df0e906dc33017d0af04fc24010b070835018a0b604f02180ee06a02300d402e000, 0xb40555982ad19f3519c945626aa136d7300f59c8928d26d7500d59ac9ea12568b41bad5556b05b5906eb5554fce4d66a0802a6001a814e06b5c53ea7e00694c28914d2a9825f22022d229427b8b42bbf0bc286cdba01016501cecd⟩,
  ⟨0x2f11690ad053a28c136897849e23010887c837a19e0c885d82d415d09f84c024810f07b837c1a00c304f82380e005902380e803e000, 0x6c054f36502ca13919a306f00361ea7c8aa926d9700353b28006a6006cb56400000400008064a2c1d6585789a2aa8a89c520424c654ea62820655384be44045c45284f71684fc619850c9b740202ca039d9aa12568b659815557030949⟩,
  ⟨0x3a81c58db069e33a1948c506042de1618a9050026512308ac40e1ec0e686b82f215a0a584842280f906d02fc14007602080c0022000, 0x3cb83998f1b7b53e10f4949709ab44da3366a33928054500c2a880186db027f599f008030a00cf61b6c8a05667f3b87cea7c01854f6730db0401298006d45640000040006206006bfd38f2c57dafc00694e289d8061a4c2bbd4e720186932aeb53aef5e000d280080300f64e903c6f0075e6a7826d⟩,
  ⟨0x2c715a8a9850e278133096447c21f102079438c1a70c905a02b614c09e84882140fb07703281720a704c02240d804d018007801e000, 0x644946936ee006acd64f5092b45a0e58aaae9031ac83962aab4c58eb36a00153000da7a7037ae2d2da60034a61450a6a54c08b12a022f229427b8b4335d0dc287cdab125524d6c54ae713332b770ea7c52bd295892a926b62a⟩,
  ⟨0x2cc15a8a584c225411c88b44402020f9879c3a41b70cf864030615f0a704f025e11407a838c1ac0bb04e02040d805702280c003e000, 0x39d9a006ff5640000040000386c2bccd1554244e290212932a953081033a9c116054045e45284f716857061b850d9b5424ad16cf402aabb661a92a12568b69a81555d723d490b80555b82ad19f3519c945626aa136dda00f59⟩,
  ⟨0x3ab1c60da069a32e1898bbc5a82b514b098448423310487f03c21c20d386202bc12908c03e41d00c905d02a411406b02600f403c000, 0x61929159a3808030a00d1a1b86ca4d66914487d0e8e018551a850dbd60129800708d640000040004606006f4538f2c5e6bce00694e28a00061a4e6f054e7c018693bbbd53bc178400d28008030157f2903a6f00778aa7626d0037a6a7c8aa04db7fc00d4efe001a9de5c0759309e006f6d4f4e802ca⟩,
  ⟨0x2f41738b3055a292139895046a2200fb07a43b41cb0d9866c31817f0ad852825811508183d01ca0c805482300ee06602880fc036000, 0xd168375aaac6e0b6b20dd6aab05968ace0d0054c0038329c0d6b8c1582c00d29851229a55304be44045a45284f716856bc17850d9b768202ca03b19ab125524d6c547dfd9331f589aa7f69fb292e135689b466cd4672500a9c0185534030d⟩,
  ⟨0x29b14709cc4ce25a11e08b444220c0fa077039a1c00ce062c2da1560a204dc2380fd07103341700a604882000c204f0200084024000, 0x30af1345550b138a408498ca9d4c2840caa7097c8808b88a509ee2d09e08330a1936e9040594074335424ad16cb302aac7848e921680aab3055a33e6a33928ac4d5426dc7e01eb391251a4dc8201ab3593d424a⟩,
  ⟨0x3b91cf0dfc6b63401908c185c42c71540a244a823511307f03de1d40da86682f615108e042c1d80db05e027810e07802c80e003e000, 0x14c00c373c143acd08040185006830dcf4522b3479fc3e7d4600c2a8b3d86e4a0094c0039c2b2000002000190300391e9c796322e460034a7144fc030d2698fea73d00c349d63da9e3fc800069400401807cb7481a37803c83538136801c9153c5840b282e066984f00393ea7979402ea01c976e4fcc159⟩,
  ⟨0x2ef16e8b4056a29613d897047a21e104877c3a41c30da06703081750b4051026611507f03b01ba0ce05782400e205c02580d8048000, 0x28495a2d06eb555a5816d641bad5566a2cf59cd800a9800735d381ad719a735001a530a24534aa6097c8808b48a509ee2d0ad742f0a1b36e3040594071335624aa49ad8a87b44ba98f5d0b538983e2925c26ad1368cd9a8ce4a01534030a⟩,
  ⟨0x2a814489f04c225512408a843620f0fd07883941bb0d706282f215b0a204c824a10a07583401760a604a01fc0dc04f01e80b801e000, 0x185abab2c2bc4d1554344e290212632a7530c1032a9c25f22022e229427b8b427810cc2864db8c1016501c4cd5092b45b2cc0aab4d91ea485a02aacc1568cf9a8ce4a2b135509b74f007ace4494693750006acd64f⟩
]

def tableLLLLR : Table Block := .branch 13 tableLLLLRL tableLLLLRR

def tableLLLL : Table Block := .branch 27 tableLLLLL tableLLLLR

def tableLLLRLL : Table Block := .leaf #[
  ⟨0x3781af8d0064e3061768b3855e27a12d89304442150fe07743881a50bd851826a11608283981ae0c605382200f205a02580f803e000, 0x1d876edd1bd59ddd677eaee00bab6f51dbab40253000ed3ac80000080001c0c00eaaa71e58d51aa400d29c51aa02ed197a8aa7a602ed1a1a82a7a8b51801a50010060275f52078de00f5254f04da00755d4f915489b760801a9ebed7f53389e0075854f91568b760001a9ebdd7d53⟩,
  ⟨0x2eb1660adc51a280138898848e22f110084c3e41e10e787003621920b9855028413309204141cc0c7059028411807a02c8100042000, 0x1da54e06f5c6d0da200694c28a14d4a98116254045e45284f7168cfb8dba87cdab125524d6c543da5a54c7aeeea9cb51f1495892a926b62a11b2baa62337454e5788fa49709ab44da3366a339280b8c05d5c402eddb636ab3b20402ea⟩,
  ⟨0x2d315c0a80522284130093c47a23010a87d83c81d70de067430416d0ac051826212008083bc1c00c1059028012607802c80f803e000, 0x22c0a808bc8a509ee2d0ac74370a1b36a8495a2d9e80555c1890525424ad16d3502aae042e6921700aab7055a33e6a33928ac4d5426de0a01eb391251a4de0e01ab3593d424ad1683962aadfa0c6b20e58aab68901aced30054c⟩,
  ⟨0x35519b0c9c5fa2f016b8ae053e28012b08844041e30e2069432c1770ac04e42340fb076033415c08f041019c0b604e018008402a000, 0x789538f2c710e2200694e28db01768d4e1553d901768d6e1153e15c2c00d2800803013c9a900079ad3c01f0ca9f330034d003c4ea7c8ab98001a6f2900353e4dcbaa600796d3c00f18a9f22ae540069bca000d4f92f28a9b0af33455505138a4084a4caa54c1040cea7⟩,
  ⟨0x32318a0c145da2d51630ae45302871348948480231111080c3c81c50d8067c3141780ab84f823e0fe072831815a08c039815006a000, 0x48a6954c12f910116914a13dc5a2bf22eea1b36ec040594075b35624aa49ad8a84b516a9895ea153a2e262925c26ad1368cd9a8ce4a02e901757400bb7a18e3acf10100ba80785dbd14725678f7ddfbdc402eae1dd76f150094c003ceeb20000020000503⟩,
  ⟨0x2e716c0b2c54e29613c098449e24211388203da1d80e186c433818b0b6056829612c08e842c1fc0e306202a411406b02600dc01a000, 0x284f71684e3a19850c9b740202ca039d9aa12568b659815576617d490b40555982ad19f3519c945626aa136f6900f59c8928d26f6b00d59ac9ea12568b41bad5576105b5906eb555cd481d679b802a6001e6d4e06b5c734e6a00694c28⟩,
  ⟨0x36319c8cb061a2ee1678ac050c251119084c3e81d50e3069c3101690a504ac2380fd06f02fc16409704581f80c005102280c0030000, 0x772ee600694e28f3a0069a1afb654fcd801a686fed553ed9db400d2800803013e2290007c353c01f6ea9f840034d003dd6a7c8abc0801a6f8b00353f11e2aa6007bf53c00f7aa9f22aef60069be2800d4fc3f89a9b0af13455507138a408498ca9d4c1840caa7097c8808b88a⟩,
  ⟨0x3141838b745982ba1558a704fa25e11f88b443c20f0f8074436419d0c605dc2ca14409584301dc0d705c028410606c02680b801e000, 0x716819f7c06e943e6d5892a926b62a1295f6a624fdbd4ebf096a4ac4954935b1502caef53057ec6a75e017524b84d5a26d19b3519c94050202ea800176fa40f359f0080b280f766fa60f959f7d59fd3d016579e6cdeec00e99e87ce56400f74a71e58⟩,
  ⟨0x2cb15c8ab052227212b890845a21b10307d43ac1c40da865830e1750b4053425c11307a035416c0a103b81a80b604c021009c01e000, 0x28495a2daab0555f302cd242e4155700ab467cd467251589aa84dbf3c03d67224a349bf4403566b27a8495a2d072c555f1c18d641cb15579b14159f3a00a98007ce5381bd71e6bcd801a530a285352a6818116154045e45284f⟩,
  ⟨0x28a13f89a04b624c12108cc43820f100072c32c1850bc05982b814d0a18490226102076838c1900b005082500d405902380e803e000, 0x304c60ecb613be4d818d258182d1619fea500000100000118000008000000d60cfe292f11e065093037c10034cef72f63941a15103022c0a808bc8a509ee2d02bf940dd286cdaa12568b68a41557d017f49⟩,
  ⟨0x2040f787943a41c20da868831417d0b605742a4141098046c22210207c03941b00c505b029812e08403b81900a60400178078022000, 0xe959c0c19a2e0b15c4e1822dcf822bccd1c67c8938246cd3306d13933c0cb926060e51ae310d92792974316f528668d71886093ea72c0d259334941a5c536e6b⟩,
  ⟨0x24011808844241f90f6075c39a1b80c185c02c21540a184e025611608083dc1c40cd05c029411a07c03781780a604201b80a0026000, 0xbcc5d893492668c9d6c27c0356c0c0dcab0000040000061eba8b3c932668634c26713f60ab509163032312ac18d4e940abe490f8dc50e3469d33649a704dc1ae131847b015686c91⟩,
  ⟨0x29314489b849a24111a08984302080f8875837e1b50cf062c2e815f0a404e025211a07e83c01b20cf05c020c0d805702280b802e000, 0x40c1b9cc2c48d168cf48d466aa1ae86a0c6c4059a0198c4495f69c0c06f3364448dc02cd0745881b2d3dec5d89349264d11e56c2707159b030186cb0000070000021d002cdf8158caa0a066b340ca688194d3⟩
]

def tableLLLRLR : Table Block := .leaf #[
  ⟨0x25d12408d444420d0f9079c3a81c30da069c32a18b0be058429e14509984602120fa07082f416609804701f40dc05901a808c022000, 0xdc2a9d09121fa279655618ab42f04d908b9934de47f149748f03184900d36174b82c0d4882d340f07b49309262c15d201a480e0f0351c050981a19ca611c18556011050a156f82d020d2267⟩,
  ⟨0x26f132095447821e10a07f43e61e10e806fc36819b0c605cc2a414009784582180f3071034418c0af04d02040c004f01c00b802a000, 0x609389330b4ed035c1b1e06aa0993035f20b6a694a34e09038f759847018e7580c6d2bab1505a3734300b9e06878875d29a524d38241c96583029c063dd6031c3eeacb72c102c78190a29d7138a9⟩,
  ⟨0x1fe0f887903aa1c40da86a83361830ba05a42ba15009f04b423010e07e03c81c00cf06102c014c09704681ec0c605901c009801e000, 0x1c534663092f269cc93824e24c92b443627c4d08ce29ca41704cf4266781b2b0581b5d059533f8a4f64781aa24c0d8882b6c143c0c02176eeac2c16e0863e449⟩,
  ⟨0x1fc0f3873037c1af0cf06442fe1750b3057029412f09284482060f607483741980bd058829812e08503981a40a203f016807001e000, 0x66c53d60b0a7d21bf24ca99fc527b23c0d512606dac16130153c0df521f723d0a585348c72696c4fc8d09a924f3e0ae123c0c190915a282fca0b9a67f14ae49⟩,
  ⟨0x24f12208cc4342050fd87b03c41c70d7064c30216f0a304b423c10d08003b81c80d506582e413008e03981780a20390178070024000, 0x6091a34f0843b44e0cf032c4981803038680edbc4030089c620b1682b24c504639c4a45cff92654cfe293d91e06a8930371a0a131002e78180fc684c22a9fc521f8d0f037448981b7b05⟩,
  ⟨0x29f14a89e84c624511508183da1cc0d586683161760b1855827612208c03fc1e00e306a032416009704681d00ce04e016808001e000, 0x40cbcfcc2ebbd63b9acf18e3afd41c73f91941ee2cdcf5f6f64e788c4b073c19a572483029e1e45b89e380186e08dbc606c019759c498337a49c120d76ebb70173c0d71d4eb71380f43ac3b9c3dd5c668d33e449⟩,
  ⟨0x2cb15d0ab4524287136097c48823a10f88103d21ce0da866831016d0a904dc248103078838019e0c005782580f206002880d8036000, 0x141a5c534803c2f04e096f0b61380e890d818034285806fb1158cfe26019fc3407d1e2019e44e9d0500cee1a0195c44033889c712500192cb6d1a0b8c695b34c4491934e261bac018124f8384eb308f2d00c3403fc88afa5513⟩,
  ⟨0x23210d08403f01e50e906fc3641a30ca86082ea1640aa852c27412b08d042c2020e806c83001620a604d82380f606002380b0022000, 0x3440a1e06c0448a99a4b40c965343d0a4e24c50d02a27c525269309303629a4d24951a4c24c0dd43eed38923bd0ef6c4f89b1330a64e928069f0d15e1788069b0d80af6232669⟩,
  ⟨0x28113708ec45621b10587f03e41d70e0069431a17c0b6858829e134091046020a0ea06e832017a0a804c81f80b404701d0094036000, 0x143c96004608311b53c9635a634f6370a681b060186818cd125e0227995d0f1267c893824354490e1d0d2e11e060c5137714c37ccde8aabc121f6ab308e01b142c03610542a8892c19b2054f030ceb90b⟩,
  ⟨0x27a133094847e1fe0f707343681a70cc062c2fc16f0ab051c27812308583a81be0c605a828012c08303c81980a2044014807c014000, 0x203d1603d179e92df92110f8090ebb9f5b1b92f755cf9e18e7f14ae49714c998c248365ba6b24e0901c874c0e94462008139f1362013a704cf4266781a9492c0d57c968154fe290660d4f034812a606⟩,
  ⟨0x23110d083c3f01eb0ed073837e1b20ce86282ee16a0a784d825811308003bc1c00d506202a412e08d03e01840a4037015807001e000, 0x16c432f0486b2cb613a61ae918c23b0ac608d5d7c96da92b89c03be86c201bc606830175f5f258b33e449c123c69d302e1a5e23c0c3469d88061a714741ae89e231a47715ce2a⟩,
  ⟨0x26412d092c48222610587c03ba1ca0dd86803221760b6056428c13508d04041d20dc06682fc15809904781d80c605602180c002e000, 0x819624c0c01f3c3403d788807c913f524be9494c23807c30d30a21eef44e06e0517e6c9464ce01ed4368061e3d3850f86630932434468914113034c883ac3444c9991344c8e89940a75dbb8cb⟩,
  ⟨0x24d12008cc43c2090f4076c37c1b40cb86102c61520a284d025211408483f01c20ce06202bc14409103c81b00b604c02080c002a000, 0x14296149122ac18d573ea05573613c0801cb6060060295f02910249efb98c9a6ccd5069c124f4ab84ce2700fe21b89a4606d1155b89c7cd7673d15c668d33e449c123469ee8221a27067⟩,
  ⟨0x2bd1570a9052e26212708fc43c2110f207683721af0cd062c2dc15709d04c0232104074835017e0aa04a82180d604e01e80b003a000, 0x11936066158000048000010e0c517f24d07802d9fc5200341a0076781a82c00ad303504d94c238030e4b40f1688c10ccce06bdb99784ca7b2f954fc06a90b75483829e0d957829803bd83c00df4b70cd256693093058152b⟩
]

def tableLLLRL : Table Block := .branch 13 tableLLLRLL tableLLLRLR

def tableLLLRRL : Table Block := .leaf #[
  ⟨0x2a314c8a004a624211988884222020f287603961b40ce85f02de1520a404ac2280f706b02f415809303d01a80b604a01d80b001a000, 0x40d1f40eb008086f0d83cb39aa53619a4acd261264202a5742961489c6cb03899745402f73613c7601cb606006399581b8d10063699808511dcc0725d386e6c2c874b3e639f9b18f23c49b7624d24983c01a96c27⟩,
  ⟨0x29e14a09fc4dc25d12708c44482170ff07943881b70cd06402e615a09e847021a0fc076837817e0b2051826411805702180d8032000, 0x206a59b2e19a4acd261266502a5742961484dcbac06e1d74a402573613cbc01cb6060065c9580d93c40196666017497733c8f126dd893492659806a5b09e326c0cc2b0000100000021cada2b89c019325a6344f1⟩,
  ⟨0x29b14509c44cc24d11d08744181ff0f807983921ac0cd86282fa1600aa851026e11a08803cc1cc0c905b025410c06502c00ac042000, 0x6f39b7501d38277335d61821e850465b54e6d13eca681801a025a064e1319334941a5c533d80f2bc130e6b6138073bcb6060067595b8c4019ca67cbc942de8dae7f92697c016cfe29001a5d003b3c0d4b600569⟩,
  ⟨0x2a914f8a084ea25812188b843a20c0fe87803a61c60da86903061760ac853c26412308303941a00bb05102480ee06002480c002e000, 0x10355200cb5c6200d4d33a21b2d415970cd256693093508152ba14b0a66cd6346ba8e008b9b09e9a00e5b030034c4acc288034accc006a1ee74e765a71b280da3a7fb1aaa7f83f706c905d99203bee7e1e2758182c9⟩,
  ⟨0x2ad14f0a3c4dc261126090845a1f80f487683721ac0cc863c2f814709b049422c0f9076037c19c0bd04e023c0e406802580f8042000, 0x1b126924d5381a5ad84f906ad8181c1560020000000043d89349268ec06ad6c27c0d1b0306c8b0009610000021e19a4acd26126b702a57429614cf9ac78d754c03f73613807584b606006ae95b0c407aae6603153f73⟩,
  ⟨0x2c91560a544f026e12688e844a2100fb87703861b30d106443041650ac052c26011507a039c1940c005182580f2058020809002a000, 0x17507b2d03418e28dd12d81ab6c006dba049419d4f47aad39c673a626b0901c774d363619a4acd26126db02a574296148265d0b00cb61759425b73613da801cb606006d295b0c526b3e6624d5877303c58e3959b2d3c8e46ead⟩,
  ⟨0x29214389d84aa24311c88a84121fd0f7076c3861b00ce86382e21600a184e425011508403ec1b40bd05702440e005302480a002a000, 0x3048d9a6bf4026da5c23c0c7926be4016db48c611c3545d0224579725f264a611c01bf25a3e7100ef999c0c386bf064b429614d730045afc001e56611c01bc65a0035c57100eee99c0c0035bf6bee64a0f8a7⟩,
  ⟨0x25a12388f44541f50f407643961b80d586683161810b805842a014109b845820e0e606b832017a0b205282400e605201a808001e000, 0x3a346c0c1da2c0000100000087429389324344a89f14949a4c24c0daa6934925669309303006585db4f24d848055bed24b627c4d89985360565c400196800d80dc401c3667601658933e449⟩,
  ⟨0x2a614489fc4c425511c085c4001f50ef073c37019b0c505e42d414d0a004cc23c109074036c17c0b404b82280da04c01e80b801a000, 0x3d2a5b03003a44ad86230e8b3304eb0ab9cd88cbc130a5b2fd5301a4c7cfc4f96e19a4acd261273b02a5742961493caac1e15765409573613e6801cb6060073295b0c431cbe6608764773d8934926c7c07ed6c27⟩,
  ⟨0x3001778b785922bf1580a9851227c12f892c46e2230ef06dc3381810ae84b02260f606f830816209403d81a80b204c017809001a000, 0x1b34cc1b44e4cf032e4981801d925ae310076199c43a2c44a2c40a2cecedbb2eb3b14749c765d622939d757078a6ce0fa789eca0e3943c89a512701857390dabcb40dd63eaa2d4b46ccfa98192da86c73c99a4a0d2e29d380795e090f9d96c27⟩,
  ⟨0x23411508343f21e80ec871035e1a20c285c02cc1530a104d424811908403f41dc0d105f028412e084038018c0a00380158068016000, 0x81b3b0065719a8b06695c920cca756355b89f820065a640b1819be458d1a74cd9269c13706b84c611f770065a1b24403dd267030668b8a5457138608b73e08af334719f224e09⟩,
  ⟨0x25612408dc45421910707c43cc1d90de067c32a1780b5855827612e08e84382060f206e832c1820b2054022c0f005b02380e803a000, 0x3c861934d99aa0d382409d5e57099c4fd10032dd042f98c0da885b2b713835aad4a8e55699a30cf9127048c9a64395a5f23c0ca92606007919687c9101f8e99c6ba2b89f8c0065b9580731⟩,
  ⟨0x24911f089c43820d0f807743801b60cf86482fe1670ad052427412f08f04341f00ee06f83541700ab04701e80cc05201e80a002a000, 0x182456965c26308fe30032d0d522327873381b11265b89c3045b9f045799a38cf9127048d9a660da27267819724c0c00f692d718803d8cce4bd16665164a51650d52148a90f90e7c6ab⟩,
  ⟨0x2ae14889d04ae23a10e88383fe1e00e986f836819f0b5053426011b08003b41bc0d206182d015409303f01a40be0420178078022000, 0x3a0d6e5600ef127d635995803bec9f85f9a5bb126924cff0674b613e21ab60606f5580000e0000030c01a6a4fee5372d9dd53c7338a7be512612711ab24e24781b9a265831a9d281570379e00cb55d488d1a70cd7269⟩
]

def tableLLLRRR : Table Block := .leaf #[
  ⟨0x3571a18cdc65031b1880bec5ce2d315b0a9c53828d138092447e222107074c31c13f08c03ec1a80b705682300a204201b009c014000, 0x42fa2c233627d336261b235412a2c2ea2cfc0449f224e093493645852d0067900e4f034f000ca604d172b9da719cf2993e553ace7384e59449f299d2729be519c72793e419464d27c9b2293e4b90e4127af00193c0c5777cd6bc226d9a26ac824e612711ab24d3e00c9e06⟩,
  ⟨0x26012b090846622810e08343f21e70ec071035e1a50c986182f81680af052827212c08b84341f80e8056826010a07a02e813805a000, 0x81a2dd15b13e26a4630930be8aa923984985b4573123c0c5423d19a068594581a22d17d4cfe291d333c0de2698414503744d0a8a0324f00aa927d1382403b6256791c007006d60038000116a⟩,
  ⟨0x1ed0f007443881b50d306442f81710ae050426812708c84181f20ea06e83401820b0050825810e076033816009a04101a008001e000, 0x1e295c92e29954c612669153286a9c120c2a9ba6a151429614e50d7ca27c52b925c5366630931469ec93824f24fd1a2d24b627c4d08ce2986f458133c247⟩,
  ⟨0x2f916e0b2457e2a014989d04d025b11e08483fc1f10e9072035217f0b004ac24210207283401820b605082080ce05d02400f803e000, 0x4e5d2b9050f0332b81d4b6138048194b8467138018314b82f02000d2a39d1584f179905360664104a9707807803a3c016994b83803400bf3a3c0d15c00d3719ff662474a7c8938241dd52c561dd3410f553c0c166a981a26001a6b0e86b51⟩,
  ⟨0x2b21540a1c4e626612288e445820b0ef07283661a60c405f82ce15d09e04a02220f2071836018a0a603e01c80a60360138068016000, 0x206001c52b64e4a2b09c01313ed908ce27001c4bb6625625800daa6f5142e763f8a4083cac781816364c0c0038856e94d45b7798f0600bd1f224e090d11306a14d3400c130254781a09010a4e66074ace24c19bd24e09⟩,
  ⟨0x26b12f08f44662120ff87c43bc1d30df06c031e17e0b6857827a13009184381f60e806b832815209f03f01a40ac04901a80b8042000, 0x309c0871c6dd0300fe37db03c44fd0deda2704c0d2b2c86c68012b7699a4b0d2612719002ed94297148302b1304907c8c8e3c309f17000edd03000e2d5b04a4e571a518692f28a9184e0078a96e⟩,
  ⟨0x22210a88183f21ec0ee87283761b00cf86382fe1720b3855829213f095848421a10006f82c813c08b040818009603e0178080016000, 0x3c52b925c53466309278a27324e091e34bc9a1b13d99a13489a5c4f034eaa2c0d3a68ae27001c7eb663ee3f000daa71d166143c0c0478f36c07653f998e24d4a6a4554c26⟩,
  ⟨0x25712688f043a2100f887743a21c20da869832417e0b5053c280135092040c1be0d505d029c13408d04081b80ac04b01c0090022000, 0x40c36690033a29ac3100d396a7ea68b88c691dc5738ab335171c51731d17ec1083e449c123a69cce1f4b6807e20b83c0df004c278643d0a585308c2ca26e1121e1358289a4f45a410f9a67⟩,
  ⟨0x281138097c4a0231112085c40c1f50ea071c35019e0bf85c82a613f08f04281f60ec066830015e0a504a017c09c03f01a008c024000, 0x186692b349849a0e02a97429614d49ac60d79e201373613d000074d81800cfea5b8c400cfba9fb7a2800e74dcfdb517624d249f7404696c273f36c0c3a6b0000190000021c619f224e091f34be1b4be47⟩,
  ⟨0x25512408e445e2220f687643981bd0d7867031e17e0b785942a814509a04942360fa07583281760ac050825811207402a80d002a000, 0xc278c9b0330ac00006c0000087f8e8b429389324344a89f14949a4c24c0daa69349256693093030066825b4f24e810055bed24b627c4d8998539f765a1c0069a0039f57100342ea79f365⟩,
  ⟨0x2c21558a304ee26612a891844e21a10687d83be1be0d886483101690a904cc22410307a034c18c0b105382480ba04e01e80b803e000, 0xcf68801a9153802b2e19a4acd26126a200aa5d0a585226432c0c765e9600d5cd84e00e9ed36060034ee96060b4400d38a9809e92dcf624d249d2302ab5b09e80d5b030332ac00000c0000086791e24dbb126924fe900d4b⟩,
  ⟨0x279132896047222210c08043e41db0e706dc33218f0bd059c2ba14609c84b023810b07d03b419c0c3056027c10007602b810003e000, 0x1ab68ae270035a29a7b7346063bb196711c1ea65b89c0e665e7ca09950340cd964143c0c4f032d84fc66e0c69334941a5c5355003d2f0486e4cb613d500074d81800d4ea5e702d1004d11b9d4b0034d⟩,
  ⟨0x24911d08bc43c20d0fc07b83be1d50db06a43141760b10538282132093045c20c0f106e832417809d04702100ea06102b80e003e000, 0x19127048d9a660da27267819724c0c006c1535c62006bfd4f6451764d1762d1584f292e918c238c9ae048d5b428bb328ae270035ce9bd94606c497b1e8b03001adb4d018778801ad553⟩,
  ⟨0x24211a889042a20b0fb07843ae1b80d186402fa1650a804f425811f087040c1e40e706c02e414c08703e81a80ac04901b0078022000, 0x34cd8669a48f032d3aae2094f035a30034d3e358c2689f510faecd0e0c2a7879163469d33649a704dc1ae131847b2a0069a1b24401d92a9c0c19a2f6bd15c4e1822dcf822bccd1c67⟩
]

def tableLLLRR : Table Block := .branch 14 tableLLLRRL tableLLLRRR

def tableLLLR : Table Block := .branch 27 tableLLLRL tableLLLRR

def tableLLL : Table Block := .branch 54 tableLLLL tableLLLR

def tableLLRLLL : Table Block := .leaf #[
  ⟨0x24811a88ac4282070fa077039e1be0d786903261800b705902aa14b09604741fc0ea070030416409e04781c00c204201c008c01e000, 0xa850f034a2acb7138668bcc9c8ad334619f224e091934b268d2f91e06549303001b754d38a2032dbd4f81d1606b6a0069b494799514c23db10034d30a20c6d754e06bc155ef9a29849⟩,
  ⟨0x26712408cc43c20b0fa07a43a41bb0d206643041760b3856827212508884101ca0ce06202b4130083038016c09a03e018808802e000, 0x1bd3538abb2cb6d964a44fc14cbc1223d32f68865ecd6cbc13a42b2e918c23b0ac07dc09d5cc68bcda8ae270037629bb30b4606d77d97386a90a6548768732555fd0c71260cde92704869acb⟩,
  ⟨0x2f215e8a7850226212688f045621c0fe87c03c61d00de867031e1700b3051c26811507a037c1a00c1051025410007603080b001a000, 0x1324000008782400d3401d8e620070354f366cb86692b349849c0402a97429614a6e8b0d917bde01173613dfb0074d81800df9a5860910037daa6003bd17397bb2ec49a493dc41fd2d84fe86ad8181ed560000c800000c30037b29ae31⟩,
  ⟨0x26912f890045a22310207ac3981b80d2865831617a0b0853028413109384201de0e0063829812408803a01940ac035014006401e000, 0x1036290034d25123036260034d019578801c4753ed1454410f9127048e9a63829da27667818a4d3036190034d850478984701867580c281babde51606eb145d8934927388026d6c277c9b031a4b⟩,
  ⟨0x23611388744081f50ee07343841b70d506582ee15e0a7850025611608183e41c00d106202d415409704301f00d205602180c0030000, 0xc24c0c4bbced3893b846ef6c4f89b1330a7c151400e40a6ea0e3c4d24cea612654ca1aa68143c0c2b50eb3893066f493827d045c899e066f1161ea1f3a45d348784f287904a87⟩,
  ⟨0x27e13a095449022910a87d03ca1ce0df86c031e1820b5858429411507a03a81980b8052826011207b034016c09403b0188080022000, 0x2060039a696e3100399aa7fba8a0f9c55733c8e237337624d2499e606bb5b09f48366c0c073b2c0001000000086330002e7818b81fccaf334594d0f429389314340a89f14949a4c24c0d8a6934925469⟩,
  ⟨0x25d129090c44820f0f807983961bc0d486442fa1700af854028a13408c841c1fa0ee072031415409604281d00ce04801e80b003e000, 0x1098c23801d114d06158910d0b5381a1c1e8598470f1161db915f6e8b8668b33e449c123069ca8521a5e23c0ca126060039d69a0dc7c47fd5164cd25069714e6f00f4bc130e6b613e6b0074d⟩,
  ⟨0x2aa14c8a284d625e12888f044e2060fc87683a01b10d206142d8137093045c2040ef071030c1600a604581c00aa04401b8098036000, 0xacd261275400aa5d0a58524caab06455f3405d5e584e00f50d3606003a7e96c3103ba72a76602f30000020000021c19a5724832a9ed745b89c00e95a6ba89181a3812858073d07d5e7e1a3469c335c9a70482a2b0b⟩,
  ⟨0x2cd15c0a7c52a27612b88e045221a0fc87b03ba1d30e306442f81630a504ec25e12008283ec1c00c705601ec0d205802380c0022000, 0x10bd65c00173c0db1c00d3400d1ca8809d8953d893492615c01ad6c27709b0330ac00001400000870a36501af73da583b4c24e235649a48060f0352b9f0b01d473b5b9b0b58010203d773cd60d4ce6c2730186c7089ab29b8669⟩,
  ⟨0x21a10687f83da1dc0e7870836219c0c6855028a13a09704842180fd07583841980c2056828c11c07d037018c0a80350118064014000, 0x34cc6926b0d32869a14b8a460d37be68389201201601bd8d686c4f89a119c53d4d65e48e5d23c0dd476581ba92cb03756d9720cf9127049c490274969a7b23c0d512606⟩,
  ⟨0x35619b8c606182ed1670abc52027112a08d44302050f406a03281750b0850824a118078839c1940c004f82300d603e015807801a000, 0xed1a3ecfe134da46003b0e8fb1378d3755705a6801db747db1c0e9a00d3527557c069a00d4729a764d4e545290035eabbd76aeb47b0b460039ba939a68d6e94e51c05bd64fe2900403bce4f0300578ca606eba279b606a87001eb8b675bf5c009da9f043f8a4a0d2e29⟩,
  ⟨0x29e1468a004c225612288e043220f0f8078c3881b00c785ec2d41590a504ac23c11108003bc19c0c105102600f206a02580a802a000, 0xa0d2e29e5001e978261cd6c27007c929b03001e454b718801e3f53ef145001ee3b9fe1a2e19a4acd261278c80aa5d0a5853366b1a35f808045cd84e00f8953606003c4296614400f0da9800f7d5cfb82cbdbd65⟩,
  ⟨0x28d14189c047622a10d88403fe1de0e486fc35c1a40c185d02c214909a84ac22e108074835816e0ad04d02180ce05a01d8098022000, 0x1030788b0011170000021c799f224e091c34f9c0125b44e8cf03141a606f3301fb698470f5161e0d15d8a8b03790a29847003cda9a1b24401f33a9c0c19a2fac51798001a6b8c400f2da9ecf597bfacb2669⟩
]

def tableLLRLLR : Table Block := .leaf #[
  ⟨0x28513989a44b4239116887841a1f80f1873837e1a00c885c82d015309f04bc23010907d03641980b505582500be0500208080026000, 0x5c23c0c7927d70016db48c611c68d72246a828b2c13594c23801ebf4d30a2103ae54e06f8155c10d94f238898cdd8934927ca4126d6c278e0d9b03018acb0019a10000021ec49a493b7c0416b6138fc8d⟩,
  ⟨0x2b41528a6051626a12488e84361fa0ed874436019f0c705fc2c01530a304cc2400ff079034c1920aa04e81f80ba04c01e80c8042000, 0x8d4d429614fba016dae1340b2d6611fc2001a6800fb85c414781a9c0c04dedb6bc334959a4c24f7c0154ba14b0a5374586c8bf6601db9b09fba803a6c0c007b9d2d86203fb854c05bd7ee71267c8938246cd3ec00136d⟩,
  ⟨0x2a614d8a284f225a11d889041a2020f587503881b30d1064c2e81670ad050c25810b07f037c1aa0b605482280d205801c808802e000, 0x3135239a7dcc007d3d37c7875a8f3d2c9d1c9938273f16581c6c7e0c6c334959a4c24f9c0154ba14b0a44ed6581d8cbf8608cb9b09fca803a6c0c007c9d2d862197c854c217dfee63c67017e3a9bc1532f04a8dccb⟩,
  ⟨0x2c215289f84d424d12108944281fb0ed07243741af0d0061c2ea16b0ae054827c12c091040c1f20da06182a812c08503d8170022000, 0x1f025600f7fe34abf2d17bd0165782403eee563867019275c889053ab20cf9127049c490d8c769ec8f03544981bef514bc4781801fb5a6c0decc00d37f0268c000bafecd1604cf037970f94b00389b1480201800e8f54e6⟩,
  ⟨0x26812b892046e22810f08143e81db0e006d033e1900c085bc2b614709c04b424010c07b83701900b404f82480fa06802480a803e000, 0xf5349a492d34984981ad0d5da326933b27783704a7c4616d5498473c978a257fda2fffa2ba4bc13a2bfeb450665583284aafe945fe54506454f198d8d53118a9f7003297edc0252f04802f6b4b⟩,
  ⟨0x27b132093448422d10a07ec3cc1cf0d8866831a1780b0853026612008a84081d20c8059827810e07203281580900370150064014000, 0x4184cb82b197826afd57aa54ebd40e758b1a9d45063a79e898e0a8325c53146ab0335930c0ab20cb75fc88bc122ea2c071dd78c0204ea819b2c0bd94bc465a5fa9e8527126086f534f8a4a4d2612606⟩,
  ⟨0x35f1798b1c56e29613a894048222a10d080c3d81d50df069431c1770b4854827611a08483e41c40cb05602540fc06702e80f803e000, 0x4250040183b6a325c20445424a394ea140fc63d263025408dac1da042d6600f8c4c7b14c0693278b1b85e64dddec9b80992076b27b16dd7a35b1c0ed64ed0c6b632759964c0081d5ac60d32d8d283b24349648628114bc33d9606bb1e6df65c0dfdc2ed2c21406a380181147⟩,
  ⟨0x2eb1640ac8522284131893847e22e10f88403de1e20e987243781870b9058c2a8133093045c21a10006582d813607a0308100042000, 0x4206f93801616120006dac31015845b9ffed94f23c49b7624d249ffa006b5b09e326c0cc2b004ce30000021ffa597624d249fa4006b5b09dc26c0cc2b002ee50000021fcf594031f83c178905b40669ce13705b6d0037ca8ebe70576d⟩,
  ⟨0x2b41538a184c625212088d04262080fb87a83921bf0cf06442e015b09c049c22c10707303641980bb055021c0f405902780b8042000, 0x6188124345cc03f057c9c99a4a0d2e29864007b5e098735b09c00e182db03000c2f5adc620030b77397eb29a6603f93c334959a4c24c2b0055ae852c299a358c9ae07c017c9b09c00e13edb03000c26dadc6200309573⟩,
  ⟨0x3121788b605842a714609ac4ac23510d07e43cc1c50d7065c2da15e0aa04cc22410107803841800b305302440f805902600ac042000, 0x622adbf002f18356147f48838065507885127b683b29e20c0deda01afc1e204582da1a21c0561feda06531e64b66e6b00200e8f9a9a06001879b680e434dc70cd2566930930e80156ba14b0a49b1560d6ab82f009b26c2786d003b6c0c0030d76b⟩,
  ⟨0x28d13f09b44b0243117087c3fc1ef0e7071036e1a20c685f82de14c09f84b024411106e03341780ad04f01f40e006102b812802a000, 0x611c6cd74246abc9b2d41594c23800c525b4d28801c50dce06615d38d96ef2cbb126924c1f40278b6138e28d8187cd600834e00001433c8f126dd89349271f401ad6c278c9b0330ac00014400000878ef65⟩,
  ⟨0x29514209d44a824711d08a44301f50f4071c37a19c0c785b8296136096042c1dc0d906402e415c09d04501e00dc05d01e00b4018000, 0x566930931900156ba14b0a678d63a6b859002326c270038c1b6c0c00317f6b61880345e5cc0030abc9fedd96068b9001b6d6200cc7f5acb1667c89382474d2ba234bc4781864d200315d6d38a201d15773a46⟩,
  ⟨0x2ee16e8b3055229c13d89c44a024311107fc3d41c90d6062c2f41690ad04e425811f08603e41ac0c905402780fa06a0248098022000, 0x268d6326b86a817726c270038e6b6c0c0031c96b718800c70dcc0ad0cec9e65d9400637eda00ded310368dcb9e19a4acd2612636402ad7429614a768b0e9170c100464d84f1a40076d818006342d61a244006336e600185d64ffb6cb8669⟩,
  ⟨0x2bc1568a284fa26812f09244282030f9078c3841b50d4065c30c1630ab04d425610a07e837017209804081b00b604a01d806801a000, 0xa49302a01ee2d84fd86ad8181e5560011160000043c334959a4c24c800055ae852c299c358d9ae1d401bc9b09e3e400edb03000c7bdad8620091e97300a438f271e60036d8c05a39b765c334959a4c24c768055ae852c29⟩
]

def tableLLRLL : Table Block := .branch 13 tableLLRLLL tableLLRLLR

def tableLLRLRL : Table Block := .leaf #[
  ⟨0x275131096048e2120ff87c03ca1d40df86a834018f0c2859029e12e08c84301ee0dc06902f415009e04381880a804501a809801e000, 0x101a36061e358000118000010d1143e449c123c692315689e19e062a34c0d23a0036d06b58800c8d5cf0facae2706755ef304aa81b0d2cb082a781ba21658105601b1fa86c14d818c791c44066ec49⟩,
  ⟨0x2bb1580a7c4f826a130094448e22410787e83ca1d80e486e832e18a0bc85bc2c012b08b03d41a80bb04d02100da04c01e80b801a000, 0x6091834c4f400d8d2f11e0650930344e00038da05b2d01d963054f666d89349260a200bc5b09ce4db031e4b00217f000002183f29c0fe4d6db2680036d01ee78800c98dce08d85032d8f25e0996dd893492714004ad6c27⟩,
  ⟨0x2c51560a2c50226812c890046621a0fc87bc3b21c80db86a831217e0b6858027e13508a04141c40cc05582380da058020808001e000, 0x35ef1016968b9c0c2958eb388e0754eb71380d63ae9eac09d50340bb0b26692834b8a657001ed7825acd6c27958003b6c0c0032ad6ba4a200188ce4e04185001952b6803a5cc400653ee7cab6503f58e0fd29b6d8b33e449⟩,
  ⟨0x2ad13c09b849a23410987f43c81d50e506d43301770b6855028e13b096044c1e40e506202ac14208803b81a80b204e01d80c0042000, 0x6d6000004381a620006da03a0f1001985b9c0230b9646e7c89382418553bd1932d01c61e73c0d883ae9613d2350a601b973cbc05d5b5c4f2ec0036d0cbe78c0c4178eb1a34e19ae4d38259b45c26308f2d60036d⟩,
  ⟨0x29513c09a44b024911d085c4141fb0f8879035e1990c205d42c014909a04582180eb06d031c16409103c01a40b4037015006401e000, 0x146817333c8f126dd89349262f6006c5b09e326c0cc2b0000090000141c5d70a0d4a9e94dcd2a992c18f786a702423b1e0602d997b68d19d704683ea9c0fa64eda15b0e7d893492602400ac5b09e0cdb031c4b⟩,
  ⟨0x2e71630af053628e136896046a22810387b03c41c70d706542f815b0a104a42200f9074035c1940a904f021c0f405902780b8042000, 0x1ce55b6060019c8b5b8c4006716e775565093462726e270019c2b6c55c31181a42df8580d4b9e9b75d73f4ce79b9ea573ce1939c0641cf233cede8f58f26692834b8a66cc01ed78243ef65b09c00e6bedb03000cd6dad8620d335573⟩,
  ⟨0x21810487d83c81d50e006b83481970c506002d615a0a5850026211808303f01da0d806582f416609203c81a00ae04a014807801a000, 0x309324a2152473093793657091e06613d99a06bc6b2dc19f224e093493822ced3991e06a49377765713cd0d03000ce9db432e1e326692834b8a673801ed78261cd6c27⟩,
  ⟨0x2b014689a849623e10a08283d61e10df06a43381920b785902ae134095041c1e40e5061024810a072032815809203c0168070016000, 0x8e900271c0088e8e3002c2ea3f8a400803859478180142aa4c0d1ca000e32d7ecae2781a38c006c7426613800e3898e8180031c2c65ed595c4e0018dfe3237b1be007e2b8ccd821fc52b925c5306630932e698334e09⟩,
  ⟨0x2aa14389bc4c825a11b88504061f20f187003661a60ca86102e61620aa84c8250105079835016a0a004582040bc04901b80b4014000, 0x311f2c6072243e2681a3dc014c7004a3db8ed334961a4c24c7a40178ca14b8a47cd936721d36449e184e0038f0e3a06000c77f185429006b115400361ea972d65b9bb2c0d1d8000e3ae46ca5d23c0c00b8ea63a06⟩,
  ⟨0x25812288c844a21410387e83d61d80e386e835a19a0c285c826a12608c84381fa0eb07083301840ad051823810205e0170064014000, 0xacd0ef821fc525069714e998d24aac899434d0a5c52192266f4d01822400e009005c88710d89f4cd09ac4d25d23c0d7816581af02cb035e1595c4e0018fbe323ed1f7000e2aedecb891e06⟩,
  ⟨0x274133891847821b10407ec3cc1d00dd86b833e1910c005cc2c41530a484d024a11008083dc1b40c7055024810e07402980d802a000, 0x613801d34db606001a67b5e8291619df9d9646185b1253d0a4e24c10dea69f14949a4c24c0d20aa93492144a930930373004cb43e4480fcb4bf61121e1368289001a4eb6803c8cc400692ee77af65⟩,
  ⟨0x2a21458a004d225412508a44101e70ec071436c1a70c205dc2c815a0a384481ea0d806382d814e09603a81980aa04801d809802a000, 0x2de064e09b5d9980f2a7818006a16da0031517101fa82b99e474791bb126924c92c0378b613e468d81837458000018000040c01ee64fddf752df4349f1a57248c1a69c8032d7a126d0d74297148312ae60e6340ab⟩,
  ⟨0x2c714e8a4c4e825311a08543e81d50e206dc35019b0c705fc2dc15f0aa050c24811508483f81de0d006182800e005b02200e802e000, 0x100752e8f03001a9549001aa7b6daab83510034fe8f548a7b6db8a0428f9a67f14ae49714d198c24be9a7324e091a34dba84b486c4fc8d09a924daf8294771380064b38c92c49640038ac13b2e902c78180f3254c661b8c9⟩,
  ⟨0x2f01728b3055a28e137899048a22410187883821b00cf86383001710b104fc26412308c84281aa0cb05502340ee05802480f803e000, 0xc12736cec5015c28f58ab2526b1d61a4e09ac95f2971b64f76700f8dbb3800c5f59e2feb02da3267ae36d899ea86d89349264fe009c5b09fb26c0c692c01069c000008703000d595b64800663276c2808aa147c89382400d4ea4dc6b614d⟩
]

def tableLLRLRR : Table Block := .leaf #[
  ⟨0x3171850b9c56e2a214a89c84d024511a088c4281f10f2075c37c1a50c605cc2cc14309c84581ea0d605b828811206602780b002a000, 0x389c0032b1c64ac2562001c5623d9584e014956e3a060094aaf19a6692c349849953802f1942971480edbb02725e403b2ec08c77c309c00729fc740c00194ee30040b09e434b2355000e45aa61859406e1cf29705ce380c163ca541758e80ed93d7ea9⟩,
  ⟨0x24e117889440c1e70e406ec35c1a30c2056827612808b84281f60ee070834817e0b00528250106074033817009603e01a007c02a000, 0x28f001a3c0d47e9052e49459a381a90f47a14b0a71348302f4902b20800d1c0ac8da4d2087cd33f8a5724b8a68cc6124f144e649c123c6979343627b334269134b89e06c4eb2c0d89b65⟩,
  ⟨0x2a714b0a144f025712608ec45c20d10187883aa1b40cf85f02ce1560a384f025610c07d03c01be0be057823810407302a00a802a000, 0x499a4a0d2e29b27007b5e098735b09c00ec8edb03000d90dadc6200363d73d6eb280065c593e9eb2c599f224e091d34e320174d2f11e061934d89800db4e28b165885ce918c23801a4d4ba4a0040152ba42cbb9d65⟩,
  ⟨0x2cd15f0ab453828d136097c4a423d11408143f01d70e686b033e17e0ad84e82360fa078033c1780ad04f01f40e006102b812802a000, 0x1ba9b0cd25669309368c0156ba14b0a49dd560ecab99a956726c27b3f003b6c0c00367b6b618817d9d5ccaa532ec9800d9cdb400d50a880dd9b5ce06001b35b6d5291d8934927ae401ad6c278c9b0330ac0000c40000087d6765⟩,
  ⟨0x2bb1560a2c4fc271130093c45821f0ff07d03a61c40d186002be152098846c20a0f6072835818e0a404b82200fc07101e009801c000, 0x1849b6900ab5d0a58533c6b1d35cd5802f93613db1001db606001b60b59e51001b5db9804269f93001b5cb6b8c4006d66e72c0c2cb0b0a791e24dbb126924caf800d8b613c64d819856008000000004395c61437121e486⟩,
  ⟨0x2f616a8b0053e27a137097c48021f10407c43a01b90cc061c2ec1690a404f425811f07f03d01a60c4050825c0ec05901c0088022000, 0x2e2805eda0d0a7029b88b6812e0a8b1f11a953001b154758bb83b681a8c7ab599b7000916d03758f6fc0bd6d9334941a5c536f400f6bc12d66b613801dbb5b606001b74b5d25100cccdf2703000db85b401cfa620036db73969e170cd25669⟩,
  ⟨0x29914509cc4cc25311a88ac42a2080f3874038c1af0cf06342fc15d0a8050c26412107f03c41a00c605282600ee06101f00d0026000, 0x711c1d165b89c3845ce2e0995034c330ae27ba2001b6c724d181a31065e19a4acd26126e6c02ad7429614d49ac60d738a01f64d84f7280076d818006e4ad6e31001b8fb9cbe30a0369c164e06b8c031b686c87⟩,
  ⟨0x26e12e892047c22910f88283de1e20df06d033218f0bd058429013d092042c1e40e706402a412c08303a019c0b004d01b008402e000, 0x304ce2746781b41ecb03684d97700583f8a403b601c1e06da00a130368dd976b51d3a7b2e9c13a5d2ecb1ab74d5583a7048a9b9b4b0893ba8f56a2594449c498337a49c1222ab2e1054f0352a6cb⟩,
  ⟨0x21010307cc3c81d70e506f835a19e0c9061c2f016309c84bc20a0f006f83481860b6054826811207a0378180090039017008802a000, 0x81bca43ee47a14b0a6918e4d2d89f91a135249d42b2803ad60068f030010235a695a2f65cd33f8a5724b8a68cc6125e4d39927049c494ae4886c4f89a119c53a1565⟩,
  ⟨0x23e114885840e1f60f487503941bb0d8867030e1720b4051c264125086840c1e00e606882f012408303901940a604901d00c0036000, 0x3ae2cb3521ff24d299fc523066781b224c0da7765a1233e9e59a06007d3ab4c02a9fc521f0d0f037048981b4c6cac54a70535d40bd1ff24ca99fc527b23c0d512606d2ab2c0602a7⟩,
  ⟨0x2e31600a404f626e125890443c1fb0f507643941a70cd06342f816b0ad052427811908783b01b40bb053021c0e405d02800b4046000, 0x67e58c9f8cfc80038aeb3b2b09e7dc016c740c0149f66327d6011c7699a4b0d261267ce00bc650a5c52346cac390c1b268f0c279ef800f1d0300067bb8c2e94800f86aa74dd9400f84aa74d597b0ecac27001cf5b1d0300067a98c⟩,
  ⟨0x1f40ef873037e1b20d3064c2f61700ae852026a12408b84201f60ee06f833017a0b205082401020740348160096041016008801a000, 0x87a5670c87a14b0a61185944dc2243c26b0513de765a410f9a67f14ae49714d198c249e289cc9382478d2f2686c4f66684d2269713c0dd756581bae6cae27⟩,
  ⟨0x27c133897449023911608684202030f007583821b00cf86402da1600a9850825611a08183d81a60c905302200d205401a8080016000, 0xef9b2c0ddf765b88fe292e11e06714804e8558e81bc32cba6692c349849a12002f194297148d1b0549690c1b26476c309c00741cc740c001a0d63008384d2003f0ea9df965089f06a94c6a98a854e09⟩,
  ⟨0x21f10a08043d21d60e206e033418e0b80594294135090043c2040f307303641940b9055027c12007803481780a4045018007c014000, 0x626c29129d050e8ca25dc47a460304231e9180c104c784c085faabb9acbdd165cd33f8a5724b8a68cc6125e4d39927049c494ae6886c4f89a119c53df965d13389d99e06⟩
]

def tableLLRLR : Table Block := .branch 14 tableLLRLRL tableLLRLRR

def tableLLRL : Table Block := .branch 27 tableLLRLL tableLLRLR

def tableLLRRLL : Table Block := .leaf #[
  ⟨0x22d10e083c3f41f00f0875c3841950c405f82ba14a09e8494236108079837819e0be058827c12a08603e019c098042016806801a000, 0x14a67f148c199e06c89303784d94007c2c00acf06681801bc22d3a2a1fc521c0d0f036c289f00b2b35a9ff24ca99fc527b23c0d512606efab2a5102a78190814eefa1e852c29⟩,
  ⟨0x2cf1570a744f824f11f08bc4482130f907803ac1c70d306142f61660ac84e022e10d076037419c0ad050024410e07a02280c001e000, 0x1335775ac78ce0035d96baebae300cb54519f224e091834b0356f5b4ba47818c24e5f000db57e2b66e303725d95c4e0039736d235ad4b8c0c4a55a56bd8934927d7401ad6c278c9b0330ac0007d00000187eaf6500af14b3fe49⟩,
  ⟨0x29e14589f84d625311f08bc41c1fb0ed074037a1a80cb86182ee1560a484f025611a07b83a81920bf04f02440e005b01e009c014000, 0x17d45b89c3945e341456d0594c23800e725b43448801e70dce060c517ad965c334959a4c24e6d8055ae852c29a9358c1ae98a009ccb09c00f352db03000e695adc6200399f73d5db2801f3d53d88b2c8e00c9e06⟩,
  ⟨0x29a14109d44c424f12208bc4382070fc87603861b90cc05e42b0143099048c23010507303501940b904c01e40b004b01f0074014000, 0x2cda1e0cde2a249d44e097a65586a8773655d50c003a036d12158c0c0039fd6d003906a20039f773d73b2c599f224e090c5138e814d34bc4781874d20039e56d0038d6a20479df73933389c0073b6daafa4606⟩,
  ⟨0x27912d092047c22f10707bc39c1c40d786802fe1700a7851426811f08903c41bc0d406082d014a09904501d40b4045018007c02a000, 0x19b807d34bc47818d24800e935b400e69a8804e91dce06ddeb29847001d20b6985100fd1db9c0da26bdd8b2b89c007466dbc4a4606d9d16c27949748c611c1c95788212ab67acbb3565c133c0c858ab⟩,
  ⟨0x2a71430964490237114081c3f41ed0ed071c3481970bb05b029613e08e83f81d20dc05d82a013c08903b01a40a203c0158070022000, 0xdd0daee82e7d9fed586692b349849d4500ab5d0a585299a2c3245d41401199613801e9f5b606001d3cb5b0c402f4e6e60074f54fb2ecae27001d36b6dcc9181a411561821d8561ab915b7f658b33e449c123269⟩,
  ⟨0x2a114609f44d025d12308a04302090fd07b03b21ce0e086802fe1750aa050c26c12508d041c1f80ed06602ac11408002f810003e000, 0xeca9e14dbeaa9c12dabb2f38104c796c6b54c7926e86b1913099c4e003abb6d00cbb3b8c0c0457636b1a34e19ae4d38259d45c26308e003aa56d001ba7b880c6a7dce06016ba4b5801d0547003ba2b5801d0347⟩,
  ⟨0x29313e09944aa23e11388383ea1e60ec872837e1a60c6860c2c815709c04b023e11007303441740af04c020c0d805501f009c020000, 0x7ff2c903c993d18dcf8b2787264c53abae2439d671260cde9270484c23ae0005cf03081d814b613804d7d4b8467139c4b00bae800d2b81aca0f232f04e202cbdfcb2f218c7a60d920a93240ca63bca2cb96c6⟩,
  ⟨0x2d41598a90506279136095848022710707d43a81c30d506643001750ac04ec25411908603ac1c00c705d026411e06e02a80c8032000, 0xdaa001b69a51003da7b9c0cc2b80ae160f985ed037481763a40795ce1b37796be67300e9ba755cda9a4e9c1269e6d2b26f1393c99a4a0d2e29d95007b5e0906c675b09c00f646db03000ec7dae7805e2329aa964eb291d34756e9⟩,
  ⟨0x23110e08383fa1f00ef87503821b60d486202ea16b0ac052c27412208a84101ea0ea06c83181620a704c02380da05c01d809401e000, 0x7ccabfa1864d3666a834e094fd17099c4fb820036dc4d23036628b7138f9aeee7a2b8cd1a67c89382468d288a344e0cf032c4981b6c0006da3671001dadb9c07f0b01dc29847⟩,
  ⟨0x26412188c041e1fa0f487703961c00d586803261720ae854c27c131091045820e0f6070832c16a0a804381c80d005301e80a0026000, 0x1deab68689101ade7b9f48aac64d3666a834e0933555c26713eef800db702563035e3aad84f292e918c238c9ae048d504bc2c11f0ae27dd2001b6c61ac60688155c10b0b386a90a65487e87⟩,
  ⟨0x2bb14d09e44de24e11c88a042e20a0f4877837a1b00c786142c814309104341d80df05f02a4128081039019c0a803f0138074014000, 0xd54dc400f822e703000d535afa02cb26692834b8a780801ed7827db801ed6c27dfe003b6c0c003bf96b001f69b8800efcdcfd9ecbbf00036d718800efadcf9cecbd2f6547d0f912704878896a156847a43c0c2c22606⟩,
  ⟨0x273133095c498237112086840e1fa0f386e835a19c0c686082e615209e84cc24410d07d83b81c80c305902a010e06602280c0042000, 0x419bd24e091a155cc28781bd745b89c3545d6000a0055aa4cdd067c893824d2480755d5b464ccf03409a7a4acb8b23d19a06e13001b6ca9c606e10001b6800d575c4007836e7d1365308fc160036d⟩
]

def tableLLRRLR : Table Block := .leaf #[
  ⟨0x26b12d093c48021f10607ac3c21ce0dc869832a1800b785802aa1440998478228105072035c16c0a104602080da05802180c001e000, 0x5c1ae131847e47001b686691003e44b9c0c1822feb6ca18a1c74d79be6a8d33e449c123669873689c19e063c92003c6d6d718800f19dcfe82cbf476581be72cb406a90a75486c8700bacbb59c49⟩,
  ⟨0x288133893048422110307943ac1b50d306142f61620a604dc23810d07d03ac1be0d006082dc14408d03c01b809a03a0148070016000, 0xe6a001b6823791181800799eda01dcc4401f992e6611f98c006da6144233982e7034500bae1ad850ad53c80d8a7954d7d224c24e235649c48f032512ac1894e9c0ab81b940006daaea4468d3a66c934e09⟩,
  ⟨0x24f11c08684081fa0f287303721a40ca86202f216e0aa850827011d08803d41a20c4059829013208a03781680a003f014805c014000, 0x190cb031c1b2a0a98581bfc2cb601aeb0d90e5caab3893066f4938241aa5d730a1e065373a16e2700f32161ae582a15266e833e449c1269278a14868c999e068134c3970b8b23c99a06⟩,
  ⟨0x24e11b88b442c2050fc079c3b81c90df06bc31c17b0ad054027a12708a04041dc0d606182d015209804081b00c4051023809801e000, 0x66868c0c37332c68d3a66c934e09d2117098c23f50000db43748801f4edce060d117004c28688784516b8a1cea821d1043e449c123a69a0299a27667818a4d303746800db6384689847⟩,
  ⟨0x2b31510a4c51027712f093048423310907e43de1da0e686b03261890b8056c27411907c035416809904401e40c805802180b8042000, 0x4519f224e09183486e8bb4ba47818c24800f615b72c21e30379e595c4fd7a0036dae0378c0d5a02ebf39b2800f5c5b4067fc2e2003d6d6d086c46723d680036ddbab62232699d4d18aa78461a454c62aa5c4fd560036d⟩,
  ⟨0x2b31510a544e826912408ec4342100f7873835a18c0b98578292136090844c2040f507203641800b5054021c0dc06402580e8042000, 0x141a5c53dd000f6bc13f121e56b613f72001db606001ee2b5800fc25c43b3b7ee7dbe0036daae578c61aa4289521da1cf8557c430c9a6ccd5069c12138eeb84ce27ed1001b6e16dbc606c1d9758f19c075dd7ac2418ea⟩,
  ⟨0x26912b090c47021f10708043e41e50ec072c3741970ba05942b214309004441f00d706082ac13008e03a817409e0400188080022000, 0x1892263744e0910d475d599fc52b125c53066714ad9a400906fc4c1b8013896c4fc8d163c300162c589308e03feebfe01027541970b065c2d428781affe5d653948f1436ea6e14deae6e14d2669⟩,
  ⟨0x2be14d0a144e025512588c041e1fc0f487583861a80c285e82d21580a484f025412008883b81b00ce05c029411405a02200b4046000, 0x26c010142bf36cbf4f65978060f034c2630bdf5e2953e268995d13112243544de8210b007c60b1782760d73269bc8fe292e91e0630920018bce2e2ef8581a2e9850d90e01b5c2c00216a8bbe2a34585ae058f03059a2df8b⟩,
  ⟨0x2c015a8a9052628413b89944b624c114884c4121f30e806dc30e16e0b2050425c11b08803d41a40c305a024c0c605901b00a8036000, 0xc13b06b9934de47f149748f031849000c1ef17079c2c0d076c280060f78701a2758285233079c54180b9e0604f41cb1736a259244e0905d0217071003e1ed24c249fb0009b480060da003c3c0d06b003626918c238066f0b⟩,
  ⟨0x2aa14a09b44b424d11e08bc44421310107cc3ce1dc0e586b83321880b5858429613e08d83ac1c20cb05c02200ea06202780f0046000, 0x277785043260264f5721fc525069714c998d24979a4c24e236091b3480b8e4a2484cf02690071793c0d208c2b89c00371fc65c76e3c002c540d202c2e8b26032815a11d87bcd132b226224486889b11075803e1098b⟩,
  ⟨0x2ba14c89d84c024a11c88a04361fa0f7877039e1ae0d2060c2e014d09b84581ea0e2069832016a0a404602080de06502200dc02c000, 0x7e26e6001bbb64e86f85a1ae164cd25069714fc1803daf049ac8b613801fbfdb606001f7db5c0291000dd03273c5c2fbc800db7346132e28fa1f224e090f113306d08f4878185844c0c003edd6d718800fb5dce43985⟩,
  ⟨0x2b91560a5c51a278121888841e1ee0ef873037a1ae0c585f82d61610a704642100f7074031c1740ad04e022c0d005b01d00c001e000, 0xc27fc356c0c0faab00007d0000021800fd2db43d48814fd15ccf23a328dd893492689a016c5b09e8346c0c1922c0003cc000008786692b349849f9500ab5d0a5853366b1a35ddf401193613fc7001db606001f8cb59851⟩,
  ⟨0x3781aa0c9c63a2fc1748b2055a2a3141099c48c225102078c39c1ba0c685e02ae13608a83d01a60b204881ec0ba05002080c8046000, 0x10227b079e01c037883c0df8e0036d0d522327f8973944ae13037e1000db6461088d32d2fda697a992d2a354ad67001a57b4d2cd9a8bd1800541eb4acf4a366001a69b3d357dbdb40069eacff6b4f76dfb4001b6800d35dc4007ec6e7124c28105098f466d54db126924cff00838b⟩,
  ⟨0x2ab14e0a3c50027512d091c47a22210887f039e1be0d786903261720b0055828e12608283ec1ca0d805b825811806b02d00fc036000, 0x1c498337a49c1206da42fc143c0db11942c78ce0e0ab02fa2d00cb54519f224e091834d140155b4ba47818c24800febdb409288ee303451b0ae27fd2001b680650f5c60619da1cb5e319ef37b84810159c83cc2850b⟩
]

def tableLLRRL : Table Block := .branch 13 tableLLRRLL tableLLRRLR

def tableLLRRRL : Table Block := .leaf #[
  ⟨0x34f19c8c706122fd1770b2c55c28b134096c47022e10587e43de1cc0d7869430412b08c03ec1bc0d305b01e40d405502100bc01c000, 0x4af70a1145487f8a4d48c791c7ed7cdc7003f749c7df7cbc70fcaf958e613df207e38e8187df7c6c61f48f030fa6f878ef5c0193c0c3e6be063000e10b0240ed0003134c3fa726fa89f9493df4ca70493bf44b020a00103c44bb0fe29a00d522fa24384380651cdaf286⟩,
  ⟨0x30016e8ae854828113a094447622a10c88303d21de0e586f83361910b7057427412408383e01da0d005b824010c06902f80f0046000, 0xc0a726001c0de4ea7f85000c09f1ac3100740932753ac2c99a4a0d2e29810001f17824d445b09c00701cc6c0c00180d62f84e2001beee4e8cd85023d593e449c1200fa529a8087680201fa12781802f3a5303000601b8d01a278800601593⟩,
  ⟨0x29213b8984496236116085c4041f40f287483861b40c886102e21670aa047c21c0fd077032c17c0b1050023c0d805f01e00c801e000, 0x2604255557b0b498c2c00a9e06ba15583ba9f8863c8e8ca37624d249aaa805b16c27a0d1b030648b0001000000021e19a4acd2612606a00ac5d0a58533c6b1d35e08801193613c0b80078d81800302cc59e51⟩,
  ⟨0x2a614889b84ba24c11e886841a2000f6876836e1aa0c385f42b414d095041c1ec0e706e032c1640a004b02140c4053018009002a000, 0x1f54e03e834e370cd25669309306500562e852c294e5161c22f0a803cc9b09e0bc003c6c0c00182e62d86201182ce4c06b84dc9c599f224e091d34f505bb4bc4781864d3050000e34e28839209b93a46308e0ceab⟩,
  ⟨0x29d14709ec4d425d12808f44502150ec07243781b10d0063830816e0b2053828812e09083f819c0b8051823810606c02100d0036000, 0x69255644ca1a6852e290c91337a680c112007004802f0cf886c4fa6684d62692e91e06998e1606998e160699be15c4e001c1ee3307983d000e2a65185b6754cd62a704a5b0cb0033a67f51fa8601c473b16030d⟩,
  ⟨0x28c12b890445821f10808083e21e40e987103741a50cb06042e41680a384c82220f9077036c17009703a0178096038015806801a000, 0x400000a1e22b0b824a7a149c49821bd4d3e292934984981a81552692429952612606bb5009b68312a401eecedff0890f09bc14480061298d001baeb88006123939a96173343be087f14941a5c53a66⟩,
  ⟨0x28e13a89704a223210888003de1e00e786b033a18c0bf85c82ba13c09384681ee0ed06502d412808503a01940ac033013005c01a000, 0x33155d2a996e9c1214e5c5328600cacfe8693e34ae491834c3040198bd093686ba14b8a41ad560255a5731a955b09c0070b8c6c0c00185b62e30563596017733c8f126dd8934927120006c5b09e326c0cc2b⟩,
  ⟨0x288135897446c21910307e43d41dc0e486f035619c0c905fc2e015f0a8051825211807d83b01c00d5063028c0f807202580d403e000, 0x8d81e94f50c0e6de0cc9e3305a4f29a1e852712628681513e292934984981a05449a492e34984981ad2f765a3469f6ed097b627e4684d492443d0d1c6807ad803278180100b5995450f0b143c28c994d47⟩,
  ⟨0x24311a088c4282090fd07883a61c80de06bc3321880b985a42a614909984782220f6076035c19a0b704d01f40dc06302700c4014000, 0x18497934e649c127126495a21b13e26846714c5d30b8267a1333c0d175c2c0d18cc2d62a9fc520d21a9e069c254c0d168c28471f49e3d0224f9127048312a7f2b9e5a00c7001c9e06⟩,
  ⟨0x23511007d83ce1d60e486dc35a19e0ca05f82c61590a304dc25411d08884001e20e506d032c16a08e042017408e036014806801a000, 0xc54a70530180bd1ff24ca99fc527b23c0d5126068ca616030153c0de521f723d0a585348c72696c4fc8d09a924c6b30a01fe200c9e0600411fbe55181c2e699fc52b925c53466⟩,
  ⟨0x29c143098c4b223611488183e01da0db86582e615d0a504ec25411d08403f81de0e506782e814809a03b81880aa03d019808002c000, 0x8c7e1400b93ec6c0d147000e35c620018a264e2f7858be614003142c6800f255c400313fc9c61b0b3521ff24d299fc523066781b224c0d1a5c2d0919e34d8681800f1a4c4c02a9fc521f0d0f037048981a33785⟩,
  ⟨0x2d115e0ab454429313f09984b824911988304041df0df06ac34217e0ab852c27c131091845c1e80e5061027c12006d02b80d0046000, 0x1110a7c893824d24c51ab43d1a1e06e0513198c2e9014a988781800315fc680f520dc68143c0c017ca862c221cc8543d23599b8cd44342300062a98d34a200f8a8e4c003151c69c51000c53b2718dc2800629b8d1d38800629593⟩,
  ⟨0x25b12888f845e21c106880c3c41d10d806843281890bc055426812508c04241e60dd06382d815209403f01a00b204c02080b002c000, 0x40d32a24d248a289309303533f46db474d3d174cb6f6c4f46684d02698be80071b43fd0b71348ee2b9c551c4c2c7030b1c5c28d19dc564306a8e1616373856c4fa66c4c3646a8d0e1637b85⟩,
  ⟨0x28913c09a44bc24d11608684201ff0ee06ec33018c0be85702a213c08783e41c60d005e82a013c07d035017409c040016808001e000, 0x11667c8938247cd201b5136d2f11e061b34c6880038d001a84b8801e33f93e46388e0075016bc120c6aba7d001002b5479f0b1e5c286e87ef917b02a78181529dad729a1e852712628681513e2929349849⟩
]

def tableLLRRRR : Table Block := .leaf #[
  ⟨0x2c715d0a6451a28213588f845021e0fe879839e1b80d686582ea1540a304d424811507903941b00c5059023c10405f02a80c8042000, 0x309c013b4ad708d8240d465d54767000daa42b8581820fb2ed6069b1e6ce65ce8ccbc1312632ea7c112d753c0436bc21b0cd2566930931b600562e852c29469161ca2f34aebaccb09c0071afc6c0c0018d6e2f04e3d69d0973⟩,
  ⟨0x2e91690ac452026f132093444020a0fa07743941bb0d806742f81640ad051c27812508103ac1ba0c6058826011a07402980c8042000, 0xa3b327bc81e2d7de20096b003ef0b5e0903b996003dda0056a91761645985d5a1968e21f224e090e513dcb57f6d08ee878187544c2603698e05a8eb6340c164d10c4e0327f495324bcebc12b920ebab105cb5d580045ac60ce00d55d6b⟩,
  ⟨0x3291880c145d82d31580a004de24e11688303e61d50e006bc32c17d0ae051426a11e08383b81b20c405782380da04801e009c02e000, 0x95ee9c120788eb01997380073f78b049e7e81358a97730a8be0b9e145301cf09437ee7be3d73917bb18e0f6a98373411d3a4e605d3e061076b039593898d8723271e064db3e3ae0c5539e2a9c3254f7d03fdafbe40aed7700ad56c7e4606a54f8637752c9⟩,
  ⟨0x2c515d8a8852628413a897047622510d88143f01d50d906a030a1760b4856829e13608e844c1f40eb06903141440720340148032000, 0x1036d833acf23b84b308e03b6eb01da037549930b0349870ae27000c87f1a0d3904e4606069481f1671260cde927048466baf2405cf03656abace2381e9badc4e0018fde2c1a11fa00162a06929e147a7eceded329cf600ae9⟩,
  ⟨0x2fe1768b5c5882b914d0a344d424b120888842a1f60f5077437c1940bf05bc2ca14608e04481de0d0063028c10405f02480f0032000, 0x3c4d72fac2dc287c4d3b27e525c4e0019226340a50ba8c0c04e84d2d84e01283d2e119c4e007ec52febd030034a976616923c0c027e9d2c00fb000b47818003234c6804f9f51818003231c6800dba5c400322ec9cb2b0ae27000c8b31bb810f1⟩,
  ⟨0x2a714209dc4a824a11388103c21cb0db068c32817f0b6055c284133093045c2180f7071036016e0aa04481f40e006101a0078016000, 0x4ab400f8b613800e4d18d818003266c5800655191000c98f272a6c2d732a43f44c2a681e54f7e89be255dc72ace24c19bd24e0926955ca0a9e06026b98b5b09c012e5ad708ce27389600b7240036a9806147145e09⟩,
  ⟨0x23d11608744181fd0f9877039a1b60d386703221840b7052c27412b090043c1f00e606e033415409303e81cc0ba04c01d80b8016000, 0x18a693492546930930313aecd3893548b3db13e26c4cc2998c61401527dc6c599f224e091934ca0ccd2f11e063493274000e3620168cc430b034c2f0b26692834b8a64d8007c5e09⟩,
  ⟨0x24311908744261fd0f987743981bf0d5068031e1850b7856827e12108183e41b60c6055827010e07403381600940370150064014000, 0x6099e84ccf034d130b034d6f0b8a67f148d199e068234c0d337c2896a9ec78353ab94098e7268163c0c6944b65053a9e006653c2a681753ca687a149c498a1a0544f8a4a4d2612606⟩,
  ⟨0x3071780b485782b214e0a344d4253118089841a1ea0dd067c2f615109b04481ee0ea06d83381820b204b82200fa0620250098036000, 0x1cecb03981b2a6158581a61585308e0019626340e068827e5839381a7575d6193998e1c3253300c5e1f579283e3b5591839a4b326aa8faad341f53a5d241f440c83f8a5724b8a64cc61240d9e84d649c1201cdc26074a232e010141f1365c0509⟩,
  ⟨0x3051798ba45b42b71508a5c50225e123885c4101e50e1067c32a1720af853028212808283e01d20dc068030c15008503100c801e000, 0x5d23c0c6124003355c5cd4f0b034d430a0019aae1c0f06581bc9b7353c5184796f80071a0019a66440d72dcc9c0c0699a4e2f5044bf289c121d68eb0084d230fe295892e29c46714e7015090cdcc4f1331200462400f33f000e1c00d33ec49847⟩,
  ⟨0x3081768b805782b214b8a0445421910507e43c01c50dd868030e1760ae854826e0e006782f015209604181b009203e016807001a000, 0x830160fe2900c10070781b320184cce70a5e29bb06b437a0010d5e1f91cc612771cdb606e9d70060f036bf670b01d274ea39b4f45d3825a9aa85975400219e0d806826d387ca736a68996513112243744ff20cb007cd7b1782760d73269bc8fe29⟩,
  ⟨0x25f12a88c842e20a0fd87b83c01d10df06ac34018f0bb85a82ba151098043c1c40d605a828c12807e034817c09a04001b008002c000, 0x40d329000e37ade988f8a5724b8a6086309317a260344e091c34e6334450a585348c007de369ef0eeeb3f7700080159e11bbb400ed2a92398499a3615cc48f031508f46681a68b8581a6bf85⟩,
  ⟨0x2a814589e04dc25112208a443a2100ff876c38a1b80ca85e82e015509f848822c10a080037417409704101cc0d005301c0074026000, 0x260795d428781a047e656c27027de1708ce27183581fe601854deb0ae2799f00071beb01c4606fc00617375c284501a1e11a11a0699a87971b3340f0e366661e7c6912a9f224e0906254fafdf0d043814f030bc89⟩,
  ⟨0x2b414c8a284fe264123888c4321fe0fa07443681990bb056c290139097046c1fc0e606e032417e09c03f81700920360138068016000, 0x45260f9127048068d098714396804074483c0c02a142606000cd871a4f42d3100cd60f35e099e366d2753a3887c8938243944c140f4b423ba1e06155130300066a78d0060498805e6a193ab912da224e24c19bd24e09⟩
]

def tableLLRRR : Table Block := .branch 14 tableLLRRRL tableLLRRRR

def tableLLRR : Table Block := .branch 27 tableLLRRL tableLLRRR

def tableLLR : Table Block := .branch 55 tableLLRL tableLLRR

def tableLL : Table Block := .branch 0x6d tableLLL tableLLR

def tableLRLLLL : Table Block := .leaf #[
  ⟨0x3801ba8d4865e30c1758af853e26f132094045a21c10587f83b61d00d886903021770aa04d42240bb05002380e605601f809002e000, 0x84c2439c4e36710001c6890a12191cbecbcb3e5c65ee5dd9c02635a380061b4002c3c26cb7469c018bf1b26692834b8a66f8007c5e0900d97e96c279bc000f1b0300066ed8bca2006a263cd9ce4c0ce2059f28868ca2226c3806ab09b0c1ac154848791149dbc563d128d09e3336dac7⟩,
  ⟨0x46422090988283f91f00f147423961bd8d6067a32e1918c205ca2c115b8a7052426f12608c43ce190096046c1e209403c8170016000, 0xe3cea727c200c1f8d065560a132f34e70765e0e0a06e5a0f098038583ce843078d0464e0f91270480721099c389771a0101e3a0f0300b1909818003397c6895a70391316020e24d11e8278477406c3893047809d11d19c280b87337892c47223b04e000680987b27328dcda9fe8e00999046c47049034247567bd5f2131b00b27233089237001cc5002b3c26⟩,
  ⟨0x32017c8b7056a2a214289884a224011888384021f40ec86f833618e0b5858427c12d08603c41c40d705e02640ea06b0280118046000, 0x978410064f2e881290065d96e4f2dc9a7f0f64f11c00ce1f0cd2566930933c100562e852c290476e1601ed42f756c9fccb09c0073bac6c0c0019dc62f44e3933d0d730474e0f912704807a10985d073b1a0101f3a0f0300b99098180033acc6800616991⟩,
  ⟨0x2ff1690ac452027a130895046622910808183c61cd0c1859028e12a08e84382020f007183481860b904e02340e006102b80e803a000, 0x8017b15c802bd72e8003eb774a1ee14176dcfe290103d973c0c05aee9818003ba8c750d30b135138034850b450c3e8fd23499bc5393cde2949e8527127ccdca69f14949a4c24c0d3300b293492014c92930930351544cb4019825343d112f⟩,
  ⟨0x2b81568a704f626c130095448c22510c07d438a1af0d006582e61600ab04cc244111081037c1a40c505902440fc05d02800b4046000, 0xc123469cd0f3bb43627e4684d492732bcd2cee27000ef2719bc8de4800715456c2d24781802bbc4c60768781b782012c7699a4b0d2612777a00bc650a5c5219a30027da6e418a30023d9ef0c27dda800f1d0300077678c⟩,
  ⟨0x29e14789b84b825212188e444621110387903b41b70cb05d42ac14c095846020a0fa072831012e076032816009203c017808001e000, 0xe24f20770db4f64781aa24c0d5a1c29788f03000e8438d81a83e001c6f6af1adc7b578d2d71a000d1e06469ed2b5f7089bf1138256bd599af9b967cd3cd6cdbb3e6d80859f34cfe295c92e29a3318497d34e649⟩,
  ⟨0x278133894846222210a08043dc1db0e8070436e1960c005bc2bc13109104441fe0e906f83241740af05002280f20580158068016000, 0xcf3583229c06b97ed67926e86b19136322e4845e09cc9703000f7bdaeb4b8518338d9ac02bd5801ad4611c60d67b2556af0b0356cf0af12f04c24bad6e1470ce003dcf6bee6e4500ab56419f224e09⟩,
  ⟨0x32f1900c585ea2cb1600ad052227012d88e042e1f40e386a43101710ad051424c10707e03741840b405082480fa06802b8108042000, 0x62478180abe0ed600657002a3c26846a3200071a009efd710625380068c38d001f18b880868bd93c16db003fb39e86f58fce7e296b2b0192ae0327fa95329c1552e5301fa5e0903b29297a02aa9ee860c913a29b34552864a9f2348382a7c1003ad601bcc56b⟩,
  ⟨0x3051780b985aa2cb1540a244cc25711c08383f01ee0ec06dc3481910c0057c27810f082838817e0aa04e82080f006302c80d8042000, 0x27867818a8d303000690d8d003ddaa2004a41e4cc23801ee74b003dc801d2aa0d8581aa0785a7ba74b4d228984d13ac69001a4eb3a99b8818e001a66003b3c0ca66e1ee394cbc3cc60bf29fc52087e29e060ba54c0dc3552f6301d94e061f0d6b⟩,
  ⟨0x3031700b4c5882ba15689e04c42050fb87a43b01c70dc065431017b0b4055426412508103e01aa0c405182000ba04a01d80c003e000, 0x557800d8b613c64d81985600002800000c3aac615e8647a4cc00400a874076cf143450d86692b349849a4e802b17429614a348b0e517c873dce6584e003a4b63606000d25317e2717b3f62b9d244ee58da481cd31a88a1f224e091e34f7c0174d⟩,
  ⟨0x30b17b8b605882a514309d44d025712308cc4502150fb075c39a1ae0c785c028c13007b83ac1ae0cd05502640ec05701a007801e000, 0x7b9a3001f7b49ea346ea1ef293eefa7d2464d3666a834bc9a68945e093c917f7fa6d2fef7ada5c0c03bee52c00f41a3801e914b003d1fa1d2aa7585004001a30002b3d237d0a340c001a59634f4e2001a5863400fd0a8800695b93a97e17624d249⟩,
  ⟨0x2c51590a7c52028313a09a449423711688384021ec0f0074c37c1a30c686002ba14809f047c22a0f206e82e813608703400f8054000, 0x157225b4449c498337a49c1202715d2e0143c0d8a01ed2d84e276ab846713837aaeedc155556f0ae27a6c00071a354b181b0e028a5c0d4d3000e341b962618a6864c00e15a4df5a3002c1f47c120070751f05518087c000347⟩,
  ⟨0x38f1bc0d686863241828b9858e2a814489fc4c0223102079438c1960b6053425c11a07d834416c09303f01bc0c805101d007c02a000, 0x5a9cc7133a2b1df4c64ff609949097fd693df402527f8004a4803fdf490abfca9703053fe34b2184958eee78ac3fe8f0f49fdde3297fb7f652e4a442a3cbe1fcdc29f2d47f8df2292007edd27c5d18bafd4a3fcd2e9f4e8e01bec1c2fd4f3c6fec29f224e090d5132a0b341e9353c0dca2a9⟩
]

def tableLRLLLR : Table Block := .leaf #[
  ⟨0x3961c48d986b833918b0bcc5a02ad145099c48822510107d43a41b30d486282ea15209404741f80e906302940d005302200b401e000, 0x184e003a94e3606000d49f16001ae5644bf9524c9d491dcb8da9180071aefeb2de46a42001c69c5eb1d910039428e64ea8f635c4e001a8e63792df2a8c0dc92f852c1d94e045a8be37db86400347c4d00afc96b0c90e001a8963418e00ae2010220c99c0c18707954e4a6b6bd8e82d2e63e6a6⟩,
  ⟨0x35f1a30c9c60826b12e893c480232112085440c1f50f2075c3681a90c305e42ac14c09484181c60c005182000de05e02880b8046000, 0x52d33b400e8ea39a32a918d0012514003f03ee002fd9003004005006007b3cd0d44350a6fa1be86814d129a4cd25069714d4f000f8bc1357c13962d84e003a9c63606000d4db16001abbe444d9533c98006a678d9c26a989c7ea638d9334941a5c5352d003e2f04d73cc058b⟩,
  ⟨0x4c621690587fe3de1d88e486e63521988c905ee2ed1660aac514275133096c4742190ff07d03a61a60c8859017e0a001a0094032000, 0xff4df3a8fff00940a0090ff00a40750465aecf402b2424f64cb431fd9d8de59d8face0071c51f1d63ba5cce4cd59fc2a66acfe29001f08998b3c0de0d32f69f04039b381c78e59f7254f912704800f80da7fb7cd2da0e4229e06030efdb4f7e78977d59fbeecddf5ee5df1673e3362e89fe200d00e00c3f700b00a00300f3e2b3e81d0749012035fabf700301d2c008d0547d94d08c0348e7⟩,
  ⟨0x271129090446822310c07e43dc1df0de06a430c17c0ae854027e12708d04241f40ef06f03341700ae04f82540e406502100b002c000, 0x19f00f52c68d3866b934e090159de97098c23d6080038d0d122672abfe4e06ce004696e271f35bdd045799a38cf9127048d9a624da27267819724c0d570000e35c62001ab6e4f00785c3461700185⟩,
  ⟨0x2df1680ab451826912f88f845021b0fd07343801af0d006543081630a7051026a12b084039c1880ae04c01e40c804f021007c014000, 0x1847ad480071a0031f771001d69b2703000c7c5af08185713800c7adac03a3d003ed5c668d33e449c1234698ee008b689c19e065893030006b2d8d0018e8b88006b2793c18e1705f85d0605a960caa752355b89eb1a001c69902c606⟩,
  ⟨0x26a12d894447423010687d83ce1da0e486e835618a0b8859c28812308103c41c40cd05c02ac110073034815808a0380138070016000, 0x2123c0d6d232e06ae300071b5d0b44f24c99a18d3d124c24fce341dae6c05cf033e66deb8b0019bcb3b3f7cbdae0cd2b9241954eac6ab713d6d00038d32058c0cdf22c68d3a66c934e09b835c26⟩,
  ⟨0x26212a890846622810a87f83cc1dc0e4869832216e0ab851827212808e84181f60ee06582d015409304201d40cc05101b008002c000, 0x24cc8ea1f224e090ed1304c33423c21e060dd12001af0e341f162012aef64f890658c9a6ccd5069c122f632e13389ebac001c6e710d181b306659e477096611c1ad560d41aab0cb8581b0c585⟩,
  ⟨0x3321878bf05d22de15d8a6051227a12b889c43a1fa0f707843801930be85b02c413f08503fc1e80d1057022c0d005302280c0036000, 0xdf986ec5c9a8964513824017087c5e1b400f87b4930926e98008c480070d2003c3c0d867002e26119c4e0030076b802705001b55d130b026781a0f07fec5801005c2869d1e13626000d7cf1a072c2b646be2001c6c1c0fef9106654fd0cf4aa90a153900c0a7⟩,
  ⟨0x3041790ba05a42bd1598a744f825911c088c4282090f407143741990bb0554268113079037417c0ad04e02340fc05f01e0074014000, 0x2e11e06b7461739acd035bb70a00312967b11a2571a0032d769881b31c4784c0032cf67b0ea5971b098006542cf61a5cb6363ce2eace30f1f7671878bcb3800c9ada64b6cc3c79451e58d2b0698892712780f00a580070ed87dfdbfe9790a1e06⟩,
  ⟨0x29013f89c84ca25211888784221ee0f207043681910b8055426411f089040c1ec0e906d03241780b004f81f00ce05801a807c014000, 0xc435d0a5c521d22ef8fca6e67c22d84f643001e3606000d90716c3100958fb27e437b77300d9e0e165b1e6366d43f8a5724b8a60cc6124b4d2e29a461a348013c4d8f82133f249f1180071b6eec2bb891e06⟩,
  ⟨0x34f1960c885fe2e916e0ae451227b133096449023b117087c4141f50f4076c39819f0c8054c27012308681d00c605202180c801e000, 0xfc678e818003e31c65c970ae27000f8bb19e2cf16804b1514321c29fc525069714d998d24e252a7011534297149c4902fd16032b41849016b450061e3ac405502a706954dc470b796a149f42206b62169f021820b29e33803d67f4349f1a57248c1a6c9800cc5e849⟩,
  ⟨0x2b81570a6051c27813589204302020fa87483901a50ca060c2e81510a204dc24c11308103c41c80c105b82500fe05c023008c01a000, 0x81ae3f8581ae3d857138007c9b8cf2679340038ab8c61584fe4900ae3a06009f91f19a6692c349849f21802f194297148d1b150490c1b278f0c27f1d800f1d030007c738c1393900063c594b80e140031e0ca5c030ac27⟩,
  ⟨0x25912608a443e1fc0f3874838e1b20c886102ee16c0a584781fa0ea06c833017a0b00518250102072033815808a036014807801a000, 0xc27f3880ef1d0300e7cdf8c9e154c132a704bfbab006a5fecf429614e2697b017b480acbd000d9c0565ead34821f34cfe295c92e29a3318493c5139927048f1a5e4d0d89eccd09a44d2e27⟩,
  ⟨0x2b21518a6450c277132095449622a10c87e03d21dc0e8870033a17c0b685782a613609384441f60e506202a411007b0270110046000, 0xc24c0d52a24d248a6893093034f24da5b47cd33653c56f6c4f86684d4269b5e00071b3b3359713c8ee12f04803004adb155ce70b73bc2dcf70a00327b67fcfea1600b26f67f14800801c9ad9e06001937b4f9cc07b8c⟩
]

def tableLRLLL : Table Block := .branch 13 tableLRLLLL tableLRLLLR

def tableLRLLRL : Table Block := .leaf #[
  ⟨0x4a6241918087a4271a08aa43f01e50e706f834e19c0c285d42c014b098048420c0eb06502a413c081037016c09c03f0188078022000, 0x36eac58006feb91000db9f277f3c295e49f101f2bc45e15cf43d30badd96c2c600d28fc034058d06006870e3ef2c606962ee1a40d0163834659e0cfab9b0f30a0038bcb3ab1a3467dc33cb1633e45f3c417c331679864c07cb27e31bdf864e09f5dd99cd8dae2a9c3454807b309a14c27ec427ae2684ce390fdae718952d78265207a57de22e5343d0a4e24c50d02a27c525269⟩,
  ⟨0x25f12608f445421b10888003de1de0e7870836e1a60c185d82a613d09384542160fc07303401740a904c022c0d005d01d00b4014000, 0x50a89349229224c24c0d746d1e34c49bdb13d99a13489a40036fec6b8c40036fbc9e2770b89ec2ba48f03362ac4b61712d85c57e164cd25069714dbc000f8bc137fa003e2d84e003b7663606⟩,
  ⟨0x23110d88183f21de0ea06fc36a19f0c505e42d415f0a504d424011608083c81ae0c805e82a810e07403381600940370150064014000, 0x18e6c2e42a9fc520e01a9e06b8254c0d8c2c2d4729f60cf912704834aa628d5a3066781869553229a306053c6a684c1ba1ee28017c6ca687a149c498a1a0544f8a4a4d2612606⟩,
  ⟨0x22310b88183ee1eb0f0074437618e0c2055c282130091845020e0fa07583681960c0058826411407f03981980a003f0150080014000, 0x5231c9a5b13f23426a493906c2801eb1800d9e06001011d61b5636f0b9a67f14ae49714d198c24bc9a7324e09389324ad10d89f1342338a719d85c133d0999e06c67e1606⟩,
  ⟨0x23811188644142000f5075437e1b50c905f42e01580a704ec26211b08303641940b9056026812008103b818408c03c014806801a000, 0x18333c0d912606c7fe16848cf900c340c007c7f6260154fe290f868781b8244c0d8f5c2b1529c0a75e005ecff92654cfe293d91e06a8930363bb0b0180a9e06f290fb91e852c29⟩,
  ⟨0x2d81628ab051227e136897049a240117089042a1f20ee07483781a90c8058029413b08c03d41a40c805282100c6040016807801a000, 0xe1131e20eb007e4831782760d73269bc8fe292e91e063092001c8be2f22b8581b225850dd0e0300eb00081ff22b8aca0614c23ddd80038d000e4372207abb9e4e0603c642b1648129967001968b3a596edf8d9a90ff92694cfe29⟩,
  ⟨0x2e11690abc51c26b130890045421710207e43ac1c10d9068c3001650ad84e0252110077836419e0b905602240cc05c01c8098026000, 0x611c0037a9c6800ef1dc40077a6c9c0c003bc16bcade16ac44ae889c1200aa1fe2fb314f6926124e1fc01389077214f0364d400d89308e0360eb01af037562830b0361db0ae27000de471b42e054e4606a16829f17b9a265a44c4489⟩,
  ⟨0x28d13a099447022710e08343ee1e80ea872036e19f0ca85fc2e414f09b04b0226104070834815e0a504c02080d805f01e008c032000, 0x3ace73496009d5c1a96a3835e09c497979c29c471f916e271f35edc24540d973c2b89c0037bbc6df04bc606bd07759847000dedb1a69440077b3c9c0cc2bcb561732f857138006f5d8db10978c0d600eeb⟩,
  ⟨0x2fa1720b0c5682a9144099c47423010787b03961a80c985f82e015b0a304b422810307b03941b40c105b02a410c06502d80e8042000, 0x334985008e08b3e449c12003c0d69ecb035b6800801f01d9e06001e02b48006fc38d001ec6b880befbd9399e54838aa748667054dec2a77869d7ba20eb1934d99aa0d38242f61d7099c4e001be863434fad6e303069759dac06d5ce007d636b⟩,
  ⟨0x2f61750b7457428a13a094c49222610a88103ea1d20e286e034a1920b7858827e13508904141c40bf059023c0f407002d80e805a000, 0x2119c4e00191062e43ecfb000e2b65385f26001b3c0cf5c90de2f0cd2566930937ff00562e852c294c91618a2ff7ef53ccb09c0077f8c6c0c001bfb62d86200abf9e4de99158c9b89c0037f1c6f832c606f4455800f06d9d856002077c176a⟩,
  ⟨0x29214389c04a424211988784201fd0f7078c3a01af0cb86342f415709b048c2200ff07903841ac0b505502740f405902780b8042000, 0x304bef0cb0360131f631b553030aa78864650f91270487489f05d13b6847443c0c1b227036001c6f7fe875c6d144c2a891934d99aa0d3824033db2d7099c4e001c08637ccb40ee3037b3680dad84e0099ff6b⟩,
  ⟨0x34f1a18ca863e3061728b1054627612a891843220c0f4874038c1ad0cb85d82a612607683701960b204c82080c204a01d009402a000, 0x52302523a70483d1bac007992ce00bd016be71e62b3f35738730d9c0079aece792c01b9ef9a6d4e27000e0fb1b2c06f181a5c05d79f2c2800f9359de8d838c6f31801033d9c00798819800acf18e686734431b9e000dd20bfb2400793ecf13fb2fc3181f953018dffaa9⟩,
  ⟨0x3081738b18562290142899048622e10687e03d41d50e306d43481950b905942b014509904342000dd06982c014608002e80f0032000, 0xeadeabb4800fab5a7d42cde9feab69c13e9df8f6b094f51b3d112a7d482e6ce0caa9fa19e9153029b0cd25669309385a00562e852c294f5161e22e0443a4372c27001e14f1b0300070a38b618805709d93744cc7b26003d0967c263a171a034ae9⟩,
  ⟨0x30317b0b9c5b42cd15f0a8c528289137096446a22a10787f43e61dd0e986f436619d0c1059c286116074833815408702b80e8042000, 0x78a5724b8a64cc61240d4184d649c12019f425a28d13a0080a0f09a7401849748f0368fb0b0369030b03695f0b359941e6b3183cd2612f838a074909959c4afa484c6cf2f8b41e252e8ac1c227a0bc3844b41410bc3e7884c9f1c9dd3d59d5d69⟩
]

def tableLRLLRR : Table Block := .leaf #[
  ⟨0x2c91598a9850227712909044602210fe07bc3c41cf0df06ac31417d0ac053825211a07b835017c0ab04f02180f806902200b8036000, 0x1a93c2b09e07000535d0300250376b34cd2586930930350017aca14b8a432464d1c830467520045e184e001c0c5ae818001818358d8c8013409ca3a7681194d3e614bb43f8a423ca1e060e112000c0adaed37616af43d141907⟩,
  ⟨0x292137893046c223108080c3e41e50ec072436c1a50cc062c2f01630a8043c2000f3074035c18a0bb052826c10a07b0328160066000, 0x38bbc8800719193d5e6173343be087f14941a5c53a663492ab22650d3429714864899bd3406089001c009002e09ed43627d33426b1349748f036a730b036a730b036a870ae270006074d640e703a0003aa⟩,
  ⟨0x28513c09ac4ac233110084c3e01e60e186c031a1780b5857029c13d098047c220106078838819a0be05a02440f805902080d8046000, 0x14297148302ad07d72dc99bc8b613800f1c98d8180038e2c5e0291b9320df27824a7a149c49821bd4d3e292934984981a81552692429952612606c6100271a0c4a9003e3031ff0890f09bc14480071978d⟩,
  ⟨0x2e416b8ad0522274133896049623e117884840a1f90ee06dc3201730a704e025011107d03bc1b00a804281d00c60540218080022000, 0x618804321193b08a17f277101b27f14ae49714c198c248056e4a5c5348c00db32900120f2d7dae0100327b580194c1de000eb738585d4c6a32d932a832704c9c0cc6b7360ed5987b38009f0fe8693e34ae491834e3b40198bd093686b⟩,
  ⟨0x3021708b0854228213c095448823510b07b039a1ae0c8861c2d014509a048c22810307003441800b3053024c0e005d02800b4046000, 0x2c91926d6007fad1d91ec8ad701800d1e0658fe64f170a699c9396ff751f2d7edcab4700396a8f95b2bd2feb0064f036f9ca94b92a00730fe8693e34ae491834e4580198bd093886ba14b8a43845a19ec33933d916c27c86800f1b0300072178b⟩,
  ⟨0x3771b60d3c67c3291898c185c62c815f0a8451628112f090c45a2200fe87683a01ad0c906002dc14b08d84001ca040017807801e000, 0x60900a4f958c1adec4d5aebc2b89f288001c6f3c071181a4700657b4dc2c0d93e000e37920188eb8b0ae27c9d00071b5d70d264606aeb068b1601e1c277706df41b59e19fc3866359c19ec38073d07cd66e16da96f2439d300f313e0da19b54ea931c9f5a4d1879634ac1a62249c49⟩,
  ⟨0x24c11f88c044c2190f207383761ac0d086382f21610ab851027411708203841a40c605b829013407d03801740a003f0170088022000, 0x613c64d81985600011800000c3da1e151e43e449c121da264815a11e50f030ae8981b2b6001c68749100ee56326612711ab24dc28781a5905e56c275551746679338e99e91ad0d27469⟩,
  ⟨0x27a132896048622810d88283f61f00ef87303741b00d0865c2e816109f04a023c0fb074036416c0a704201e80da05702080c8046000, 0x1b9556e2706355b311caad334619f224e091934f268d2f91e0654930300072f98d0d92200ccbce4f6498581b2ee001c692291308f974000e34d28800f2e393819857b19c2ec6b0bb126924ed2400d8b⟩,
  ⟨0x294138899c4a224411088284001e90ec071c3741970c605a42b813909784301d20c60588270112074033015c09403b0180074014000, 0x9cb66a727036d3f0ae27cd300071b31b34606ced19726692834b8a733e007c5e09d54082316c27ccd800f1b0300073338b000ea8f22202ccb64e60d5214aa90ed0e64aabf218e24c19bd24e093791750a1e06⟩,
  ⟨0x2a414789d04cc25111e08a44242040f987983aa1ca0d886983321760a9852424c11507903081620a204b82180c605102380e002a000, 0xa253b60c2a7e21a40d52146a90f10e3eab2fa861934d99aa0d38242609d7099c4f9bb000e340c33a6c8c0c07c9d262c7cce0019d162e742046006e2a2ccf9127048c9a408339cc69788f031a49000e6b31a0f8b1⟩,
  ⟨0x3081728b1056a2a6141895849822910e07f43a61c90d986983061600ab04cc24c10307203681760a504401d40b804b0190084018000, 0x38667ab1b16a01767b49309273fe008c4800c58803d9e06d2a801712e27003dfa97c63be802a540d9f7c2b89c0039dcc6e368ef19181b1b2776c5b89c0039d7c6ef90075181bb1001a5eb770a00cb9279024c0330e99f734f4bba64dcc0d0a9e46⟩,
  ⟨0x2fc16c8aa450c27912e08d4456215103078c38c1a30cc85f02ce1520a384a023810d07c037418e0b104f022c10005d01f00a803e000, 0xd8b801f12006dd280070e005dd2625c4e00e3f2b9c31e00a55036c430a611c003a01c68038ccc40599fec9c0c1562d2ba06548b3aa704804f0f4ba46308e0c6ab8810955a94c2ea4b0b98a261844e09007e3bf160078952785d1a13001e1f47⟩,
  ⟨0x2ab14c8a3c50027612988d04221fb0f607243741970c686002d41540a5049c2200ed06d031c1780a504101d40cc0590268100046000, 0x17c8f032a49818003a26c6801b0351004e88f27acac29847d1080071a6944007a1ec9c0cc2bd616175878581b432001c6818ad1011e85b2798225f844e091d019600fdd761fc52b125c5388ce29aa009948a9f63189⟩,
  ⟨0x28513c095448023610f88243dc1d90e206c433818e0be85c02be1540a084d8252106073837417c0b104901a00b604a01d80c003e000, 0xe27d2480071b886b181a90165eb9f0b0d8a42660d5214aa90f90e7caabf21864d3666a834e094f917099c4fa37000e340bd92a8c0c062c852dc4e006c752c0b58d01d4ad334619f224e091934d870214d⟩
]

def tableLRLLR : Table Block := .branch 14 tableLRLLRL tableLRLLRR

def tableLRLL : Table Block := .branch 27 tableLRLLL tableLRLLR

def tableLRLRLL : Table Block := .leaf #[
  ⟨0x28212488d844e21c10487c83b41d00de86cc3201790ab04fc25c12108804141dc0e306b02cc13c09403e81c00b604f02100c402c000, 0x146dfb154b5ece8f21f224e090ed1325033423ca1e0615d130300074c18d030da2019d2ee4f491658c9a6ccd5069c1233232e13389f4aa001c6fbc2c606bcd996c2713455c23389c60d63e00aab5d985⟩,
  ⟨0x38b1ba8c786223001618ac854228412e891845221c0fc87703a41b50ce05e42c01510a304b42280f3074834814a084037813805a000, 0x718b0a391cc3055400209f04b61e8cd60e61c40273306093c3d29a524d23fe3f271fb1e1ea4e07f31c7bbae56e27000e9fb1a3f5d131818a8b9a5603c0e7070e9e71abd0ae7c8938240609d30142ed01598073c0d63f32415ee10b76ce0038cf69c42b362e63159f173132cf8a58b789767⟩,
  ⟨0x33718d0c2c6002e31600a6451e27212788b04121fa0f7874835e1a40c3859028612008983c019a0c3050024c108078034811802c000, 0x111849f224e090062e948cba40f8d004038ae4f03003154a7544001c68006405911946a7f26711e1300347c9f53828dc6c260069693ea663778d001f5ab3bd6f52f8d713ea540038d8f90027230347cc00f8b613ca4ba46308e0018f7e2e3dc00100162b8c985⟩,
  ⟨0x2e01668af055629c13c89b04be24a11a88404061e00eb06cc34c1830b0053c27c12f08f04041bc0c105a02440dc06402080b003a000, 0xabe4d86692b349849d63002b1742961493c2ac1dd5715aa435b9613eafc0078d818003abdc5b0c4061abac9c84ef2793b634ad1a62248c1a73dcf256001e2861f3acee56e27000eac71a010e246460619b711b160e2a9b14d1945d27⟩,
  ⟨0x295138093445421b10707d83c01ca0de06a433818d0c005bc2c41510a104e024e11808383e01dc0cb05e026411407d033811004e000, 0x921c55fb3000c9230fae8922e34d23b8ac22ba2b97185e5d6168869d10f4293893e66e534f8a4a4d2612606a5349a492834984981a46b22cc6984991548cf1f689d853ca8c2eb364418d00ac693d5c00d8b27⟩,
  ⟨0x2ee1658af854e28413689784a623c10c87ec3e21da0db86503121720b2050423c10707a038c1a40c5051025c0f406d025010003a000, 0x24d807ec5d9980ca63812f60f8d11dd8f91270481f2c903bc9931a041f263c0c07ab275fc001c6810a4bf91c13bcc32e486000c4e70faf889be340d963e2b269334941a5c53af2003e2f0480da04ad84faee001e3606000ebb3178600331⟩,
  ⟨0x2e91630ac051a26a12c893047622a10387903b21b60c986202ca15b09c04541e40e506b03281760ac04d02100dc05902700e4046000, 0x1944e265018693fca231328793f6246cd3a66ca34cd9a650727ac5ca0801f8bc1200d94062c01b276c5e0993a002f170349ee4e78b000c9bb0f270938e2d84f292e918c239e4bc512b9d985e76e143a95782680557cdfc2c9b40518b⟩,
  ⟨0x3791ab0ccc64c30317b8bb05aa2a514789e44c424b11908843fc1e10d206042e214e09584201ae0cb05d02a412e08403080f801c000, 0x1951e4400fb48c9b09c0092a0c5d2360903819600194e000b15d18c2f45b0a07931ed5b65add93aea1cd22a9126272ecc25207005e027243b87000ca6313498c05194be2652c050c4ca580a18b01020304b673d234839a01cd2f8306887d9700071b28b94364402528c000e1ea86⟩,
  ⟨0x2ff1780b345802b314f0a244c825711a08a840e1f40e886b83161750b104fc2380f906b030015a09e04982000ba04801f00b4046000, 0x1849db4802b174296149122ac18d571a9a58db9613800f6c58d818003b60c5d829196058bb27976192e1c00319cc4c67b0d9149a5bd2cfc3800658187967cb071a00191ce1e5978644d0f91270486089954803b1a27c67818b0d30300076978d⟩,
  ⟨0x34519c0c4c6122e41668b0054429814089dc4a424511107fc3ea1d20da86482f21680a784d82260fc076835817e0680228088022000, 0xc278d482f5d740c179c6a1ac0bd98fe29020fa31e0605c993034690179eb1c4fb7e000e365b603bc8c0d2dc01ce2cfcdc24f2d90766240795d3cee6e6e474f1f2ba65aa0e8c581b0c9cd4ccabb26b316481101e203f01e80fa4bf87963822b172c601562f0cd25669⟩,
  ⟨0x33e18c8c285f82d715d0a5451626612088c043e2100f587783a21c00d186482ea1680a184e42280ed06502d012207b02a012804a000, 0x2ff8dcf59029ba868dc11afd700386c9e36d0c3b5d0346d60096b80138dab5da6692c3498498d9800bd650a5c52346c02b06990c1b009c1270c27000e35ed740c000c6b9ac00403bfe64001b82e53a9d85000dc0f29d4dc2d2c008072781a3540bff5c17f46a7ac⟩,
  ⟨0x3ae1c68df06c634017b0b4c54624c11f08c044420d0fc07943a41b50cc05ec2d4145094042c1dc0db05b024410405d026010803a000, 0x3a007edcff8e601db73837378f8d95b85201295bd958e1c19f1e5c38f8419d1e4c3800400400301c4714041878a1b486f21b85552a6ea90c1138849b0f03e538701729c3402948c9a637f0c33598584b2cc842496047904b03e43c6f400feba379008b5c6126377007b59626781801b8dd35800de927⟩,
  ⟨0x3771b08d5c6823341878b7058c2b11538a084be23c11888383a21c00d784f825a11e08783a81ba0ce06202d410007602980c0032000, 0x76ab0b0376a70ae2700063aed6475b1d70003aaed1e172054f0300a51d4eb23cf1eac4c7a63cd89c131e88f2e307f60aa0af4b370e3267ae368fe00ff2bb00082fe5952c9005e1f15cdb126924c5f8004ead84fd936063496000d660000043818003bcec6cc40003918bcf4bd204e7⟩
]

def tableLRLRLR : Table Block := .leaf #[
  ⟨0x26412588d04221fc0f3877038a1a20ca86202fa15a095041c1e80e306b031c1740ad04f022c0f8071030013c080033014005c014000, 0x8a7f74e74ec7030c83b0f342a982554e093fd59801a91161e852c29c4d21e00be2402b21d000e1c02b21dc4d2087cd33f8a5724b8a68cc6124f144e649c123c6979343627b334269134b89e06⟩,
  ⟨0x4322078fb876a3941b38d106423141788b4058c2a514409ac4421fe0f6072435c1930a484e023a0fa06f828811207002f8118046000, 0x3854001c6ca61075c662660260a5f2cf6272fd67b1297d97bb3874784b8d0f770931ae27000f08b1b28845b7181a6b48aed600c4d278a2299594936322e811908a70e0019bd6271b060c64de7139a5341e66d485cc180020a491a86630f9ce67d4061336c083e2e5d2d85c8c01cd3010c9e1c073dcf999aeb907300d639f8180adc6863649787⟩,
  ⟨0x3b11c60dd86aa3321828b9056e28a13a898048622610487dc38c1ba0ce85d82aa13808a84081be0be057829010606201a80ac014000, 0x12090003ace806140067cecfc4750be367567d66bacf35934f679a39ab9a6b3cd24ceccbd9e39553244a905a4d93c1706ca40188253fd8300311824fec9e91a1482a4f0842704c9e71890ed600cc527e1b09831a1aa1f868013c68044c659f224e09001989b4cde90a5b400400e61ecf030014c2da606⟩,
  ⟨0x3861ae0ce462c3001778b7857629e13d89704642130fa07283561860bc855029412508984241c80da05a82400de06201a80ac014000, 0x802c07520105f7328001bede53a3f85fb34d71a61e636ac3803abc9c6b1c62c6e3b6c547c74d85b2d1f1d635a3dfbc6747bf58cb0551c00e0aa38bef211eb184f2108be5ae8185f0907f585d23c0c005c839ae81a41a00275c0044833ac005a03b3f8a400400e806cf030014ffda606⟩,
  ⟨0x2c815b8aa053a28c13589704a024511b08544101e30d8066831a1680af04e4250117084038c1ac0c905a025410006102a00bc04a000, 0x7d34e649c123469fa0f64b43627e4684d4927e4bd7acee270006447d6488d2238003aae9b61584e00a4887ae818012910759a6692c34984990f400bd650a5c520d2ac01382aa40ceac011822b0c27000e435d740c000c867ac⟩,
  ⟨0x3241808b785a82b114809bc49822910407ec39c1c40d186082d615609884701ee0e205e82a812e08c03b815808a038014807001e000, 0xe5500071ab64ac6646065b1d62b1600367767aa0b33b580066d7879b94db31a09b3fb67f14800825cfdd9e0604a9f9b4d24d25da694b64830a9e46200cf5c0daa7918002ed703fa9c62f917b5dcb226bb44e0952b567b780859f34cfe295c92e29a331849⟩,
  ⟨0x3fd1f60f7c7783b21c78e006b63441908c505e22da1618a9843620a0fc87a038e170086037013e08e03c81a00b604a01c806001a000, 0xd66b613f3200078d818003cc6c5d2510006489d9c3ada5000f30b1ae31000f2ff2701b6961d7d29334449c0149b07cd2b3a2960010014e216c6003c3ccb9a59cd28e6a9caa8b4a6ac00bd297caad7969387e943e516deb5f5ab2d796bb875afc51123d875af449e28691dc38c99eb9ecc3269b33541a5e4d36d35516b84ce27⟩,
  ⟨0x2fd16d0adc50e27b134091446421d0fd07643981c10d9869030216009e84cc22410307a033c1840af05282480ba04c01d80b8016000, 0x1e7563747b461c8809b47c001c3d2307e8701073971a1921e54d5a001e7163401f2f6e2c27c4dc431847e6e00071a0039257100bf367270300ae47daf624d24987b8017d5b09c7546c0c19a2c0003d4000008726692834b8a7998007c5e09⟩,
  ⟨0x29013e897048e236114886041a1f60f587783761b10c805fc2bc131090044420c0f706b03101740ab05082280f607102700b4014000, 0xe10e01d9816b226538c1a68cd2e69c1222032e13309fa0001fc6c0c0779b56b1c33800e6c5af35f2c802ad59067c893824e2481c656db4f64781aa24c0d102e97123c0c001e7763724c0bee3a43000e1e06⟩,
  ⟨0x3101818bd85ca2d41578a884fe275129090c4401fb0f2073435819d0c905c429c12108b83d81d80c905302640ec05502580a802a000, 0xa14b0a66cd6346b9460008d9b09fa48003c6c0c001e9162cc288007a3f930006511d9c9c3a5937f4a0115c567c893824006b7ed2fe095a63400400eb76cf0300156dda606000f44f1b28f7ed645c4e001e88634baff5ee3031797eadaf40d52166a9⟩,
  ⟨0x2d61660aa450c26312a091c45821510587d03c61d20e2868832e1860bc855829812908d03d41bc0d405882380d605402180c8046000, 0x206000f5271a00194c644009d46c99847615ce086aa94134b034a03a59334941a5c53d3d003e2f04b61ad84e003e9ce3606000f4df17894400193eb67279e9606000f4cb1a001940e44003d2fc9c9dba5c334959a4c24f4ac0158b⟩,
  ⟨0x2d51590a94530283137092447821910787b03b21b40d286403021720a68500256121086035c16809103f01bc0c8053018006c022000, 0x1d6a00562e852c2922455831aae559012366c27001f58f1b030007ac38bc85220214aa7b33c8e47eadd893492651d00f356c27e8356c0c0f0ab0100000000021f5500038db12c7132288a1f224e091e34ca780178d13c33c0c5469⟩,
  ⟨0x2e115f0a9c53028713c09a448823711408784221dc0e286d834e1820ba85982b814f08d040c1c00bd04d01dc0a803f018808001e000, 0x15ec4e4e408d29e478936ec49a493202800dab613c64d81985600080000000438fff4bb126924c5e80036ad84ee136066158000ab8000010e2eed2db1404187000d8a70f645b156340031dec3c77fae18d06653e90d86692b349849⟩,
  ⟨0x2ee1658af856229e14589984b223611608243ec1d30d7067431817d0ad053428012f08f03e41d80c905f827011e06c02380c001a000, 0x3b5400ac5d0a58529d22c3945cb2e013ecd84e003ed1e3606000f6871619a44003d9ec980412c86cf0cd256693093d9a00562e852c299e358e9ae589002366c27ec9800f1b030007b238b618801bb1d930006582d9c81ba5ec600071ac31⟩
]

def tableLRLRL : Table Block := .branch 13 tableLRLRLL tableLRLRLR

def tableLRLRRL : Table Block := .leaf #[
  ⟨0x2b91570a844fc26512d890846222110507fc3cc1db0e606a432416f0b2853026a11c07c83901820ac04b82180c6040018808001e000, 0x1099c4e001ee463432a9e30348d43ac68d3f98df44b2704be463ae131847000f6f71a07cb4410fdbac9c0d0aeceb03dd8ee734eb0156b3f0e0c6a701276d31a0f6a7f7c568f99fb60010c68006f4d87894d86692b349849⟩,
  ⟨0x39a1c68da86a632e18b8bd85aa2b81568a404de24e110882c3d01d20ca85c82be15009e84a81f40ee06a82c813207602f80f0032000, 0x1c62001ef464e40fd280032eb6ce40ed286c5d35a4f26ea6d7e400b2bc1201f8d2b001b8fb3800dcb5ac006e56e46d5e86c2c44a2298988ee1a6a8a58054031f0faf300e61c3244c0a6fc5129c21c142001d7761f9180669cfdd104de3406b5ce0aeee7e340ec63f7340db8dee600431b3202e7⟩,
  ⟨0x2c215c0a5450025d11c08b84161f40f2875038a1b60c886102ea16b0af04a4224101078038417c0b1052024c10405d02800b4046000, 0x206000f827160c4b1000f81b260074be7b381bc08001c6f936d13c8f126dd8934926427001b56c278c9b0330ac000b640000087210e970cd256693093df400562e852c29a9358c1ae5de002766c27001f7b71b030007bd78b⟩,
  ⟨0x3ad1b40d585f22ef1660aac52c27512408cc4241ef0e606c433e17c0b3851026611007683701960bc04c82300fe06a02a80c0046000, 0x1e7d6960031d376d67f141aa5c007ce7cec5b45bc5bacf03241bc4d8d001e55b4f1c59800b93ecfc92003c9d67e4ab3000ddcd9fc3ebbac6f87a2438d00ff613ff83539c02d8706e53f86405f8d1e33803fc2f8dacd804b0f86692b349849f09002b17429614934aac1a1572fd002bb3613f82c0078d⟩,
  ⟨0x510281938097a49a24691a88a84312070fac74237e1b40d146442ff16e0ae452c27312808c441c1ef0b704f82020de05d827008a000, 0x6188017c9193da8deb726001f23e35863695f2264fcdd85000d8d70e001f21637c55691c8d9bec39618b19da4f0e001b18e26cc186b2fd8c31362fb2f626d17664c5da2accb8bb125a2f1366eb45e26d1566dc4dc174598b00316e8fe3422ce3406d0da3fa3478df0fa28bcfa18058bc6b0dcd59dac0418fe6e1dabe417898ff330f00b806e2759a698c5c5a8514b22f8bf082712d6adc05f0f727e7f1d56997b567⟩,
  ⟨0x30116f0b2457e29c1450a004ba25311808343d41c70d2065c2e815e0970480224101078038417c0b1052024c10405d02800b4046000, 0x1674b9ce345f8cf030016ce5892f91e06001f9931b0379880038d000dcc32366af2fe4ecd372ec5d99acd387613d996ccd8bb3361bc8200100161e486b21b0cd256693093e5400562e852c299d358e1ae6146d6372c27001f9371b030007c978b⟩,
  ⟨0x34018d8c385d62e115f0ac451c26b12d092447421710507f43b41b70c906142c415809a84881fe0dc05c82580e605001e80b8046000, 0x99e576bdcb09fd10003c6c0c001f4362d86374af41e4eec9953c9e19a4acd26127cfe00ac5d0a5852008b4362c003685c5ccdcb656e584e003f3c63606000f9db1750a46d89b4dc9f9cc0038db9f5ce32200cb3ce1ecf0014c4804ecef8964d0f9127048006ced89⟩,
  ⟨0x3751af8cbc64a30215c0a204ca24f11d08b84361f80ea86c83461970c405cc2d214609184001860b405182481060600298118046000, 0x16d7c35bffd20001c3c0c035f53e36ed1e8db71dbe409b870265d9c08387000ddc713767c3037a9e1183943806bd3f8d000ddaf0fe9dbb4634c24e23564998153c0d766baee2c00375ec3dd6aeb78b01d8006eac030c3c0a6c334959a4c24fa3c0158ba14b0a4013752c58006ea38b⟩,
  ⟨0x3811ae0d3c65832217f8bb05922bc14c89d84d8249113080c3a61c60d186642ec1530a204e422c0f306182e412c08c0348118046000, 0x135caf33b9613800fd918d818003ec6c5e4291bc9e65326e27f6100071a07cdee64606b87ef6b16001cf7e1c003bd8c581e37af9efc5309fd74074c6c0d70803a62c0116e4c3e449c12001b70e26e076dfc680040076dfc3c0c002b6ee2606000fabb1a001b7ee46db1eabc9db5400387⟩,
  ⟨0x36a19d0bf45d02cf14289ec4b023510287c03b61c60d186282f616209f84b023c10b08003741840b405182481060600298118046000, 0x3806086e81e1f804085e81015b0e250a7a02e73effc002082e7f814f0f03008fdc98ddfee8530fa0bdfe684f0fce6a7a0354853aa4003a11c390ccbae25300c7b9fdb4090c687289da1b5844e0900cdc97173580a9e286c334959a4c24fb3c0158ba14b0a40116f8c58006def8b⟩,
  ⟨0x4021c88c806242e21660aa453828d14009bc4c425112108e042a2060f187503941a70c2058426210e075832014a06802280c0046000, 0x360bd8301b800bb0b80e377f60b0fd8201b0007b03d84c069bbbb0d87ba18003b04d8161f60586d80804f0f4293893e66e534f8a4a4d2612606d7c0017126924005af6c4984981bb77dc1c680075e589edff6e71faf000100070faef000e27ae1ef2c6fbc40038deb7dd0322047bd8825bdad87bd8022b0e0e8a9f335eb7a0787⟩,
  ⟨0x3601a98d0065a31c1848bf05ae2cd1540a404da24a11288384021dc0e906b432c1870b105542600fd079837019e0aa05001ec0c8000, 0x7148628c4f1243e6c4e930c279bb0003d740c000cdd5ac08aa920046a4f28002d496526e600075d01ee9584f3718007ae8180019b875901be94e23800736f6b1c4e000cdbbac9b6e6dc000b55034071a5613cdb0001eba0600066d6d64065a5d837610070003c079bc3b0787⟩,
  ⟨0x26912c092c47c22f10e08344021f60f287583821b00d186643041780b0855025e0fc079036c19c0a904f81e80c605202080c801a000, 0x5069714c998d248a289309388d82474d37922c84cf4269713c0d01b6960680d74ae270006701d64dff3800005aa81a02ed2b09c0039bf35d03000337d6b2028d2e99a4b0d261266f4002f59429⟩,
  ⟨0x31e17c8b505862b215189f84e226412088a840e1f00f186f836818f0b8853825611608583d81a60c605c82b811605b01c008001a000, 0x27327dcb5cfb8ce63acd334961a4c24ce5a005eb2852e29000fdab1826ab48003f68c62fa6d86138007392eba060006723d6010539a5f61d66650051acbca4f02b304bd2ab0035e86c3d0a585389bcd0016c48057d02001c38053d0189849287bb90fe29⟩
]

def tableLRLRRR : Table Block := .leaf #[
  ⟨0x31a1818bb05b22b414e8a484f626412688d84221fc0eb86c83361760af855027a11808403ec1b00b505401e00dc04b01c80bc014000, 0x3a1364f304c90c5133a780e9ace7b9998278f86677d6ccd5d998067b1e74901435c0c6a79d18024d700c13a2eb80d96380b53a1eb80e064c26037d9339f80bfacb6c6c337af3d7187003faeb0fe290008017d7187818007eb7c49748f033ee939a6ba06⟩,
  ⟨0x490236912884e4041eb8f347503831b00cf464e2d01618a804fa27212788b04361f80ea86c831e13806a02c40b404c01e008c020000, 0xbcedf5313f93bea62c0037d5c3df4afa78bbc5001003b3c0d3b6178bae2f1276bd67a47d2789000fa1f13e82c30332fe80013c2025dcd7879336bb35cf89d736baf138275cbb0cc66e5014f87a673785014b87000f9f30fe7afcae3711fe82c3fcd400bec5002015be4f87f967cd0009ec40018157e4d87fcc00a313ebf029809c002002f6161e486e0c6817a7606689eac6⟩,
  ⟨0x3c11cf0e486ee35c1a90cb46402fb1788b3055227911e08643ec1d30d805982b614a093841018e0b105102541080730348118046000, 0x18d8004e2711a633384c825f0781a78d6cf75cc279e2db4ad740cda44f13acc676eeb0f8cac66eee70e159005e046f4987bcce03f137c4c07e2701d7c3c4fe92f878bc02844400c17bfd061e130c99c003fb6c6fe7afc391bd385d800e001c3dea70c61268cd26692834c0df97bece2ef0979ec4df56f3d89⟩,
  ⟨0x4bd25992408da45e22990c081a3dd1e98ec06b231c17c8b2454c28313008f44341f50e906b43301730a904b42180e70620180046000, 0x1037fa7b9d8deb47c030f9127048007e2f89feaf5cb1a001eb1fbef0f037587e27893e2bab021b8a206c60d70e10c09bf4db05587c14609b0f822c13e0970ffa4fd36271d2038c4e3a000f89db02feb18001d9361db499e7f5c001da1e1db449e775c0e2a99e6cbf4d6000dead9cbea9e675c0037c9672f96797d77490f6787c11609018a0fa01af49318b87c47001c2cffb3c3e36001389⟩,
  ⟨0x4192040fd47c43c71de8e686ee3541a48ce862a2f21610ad452426f132090443c1fb0ec06d432412107f036c170095039013c060000, 0x1a869a91123a2262c0183c0decfc2ae2f06600ac4e1000178984c791e00000075be7ec67647094001c1de1e4cd84cc65e2c00382ac4c26000e0db13ec2c63e2fd83835c5fb037d78b000efcb0fbe9df562dd7f8b503282d80c80eb0901f630ff22f8fe1fd11e7ac3f9e7d4387dc9ee371211bf1ee1c009dd4c3fd1603470008c07ad587⟩,
  ⟨0x4d024991248183cf1dd0e5c6e83511970c245b22ac13e099c4a423d10d07dc3a81b10c705ac290125081037c15e07f0348118060000, 0xc0100a038a139c3e00404e1c40e804e30f81bc00073c26f870115fff035c24c3b102a702c020c4807f02b89c3761c30e001c0a61e02107835bd3900f04bf0e1de35fa5d07c08009b0d38782354d122a639d53805bfc62709f868c4e13b01389c04613713807c02e2700984bc4e1930978bc02618b13861c01e270b97efc3804fa52010c3f4a000211ec3dfff0c001e0de2780186f42f49023587⟩,
  ⟨0x3aa1cc8e286fe36e1a58cf065e32418a8bc85d02d11620a7c4d825511d08c04161ee0e7871434017d08c83f81b60ab037012c060000, 0x1fcd39927048e1a400ff78c43627933426e492001face1e0685874ae270006805d650094028003aa85734b1c00c1e06046e800d660a0149c0156ca3c0d01a0003adb80d29322efec7a02901ea0a30afa05f0f40ec41c27f87dc3875831d87cc384f4300036c3d61c2798efc3e105907c2d060c05787⟩,
  ⟨0x2ef16a0b1c5742af14a09c04aa240115888040a1e20d906a030616009d84602120fe075831812c08c034815808a038014807001e000, 0x4b85707a14b0a71309a550994898030794096135cca996a54e091250e18003f40e1c0037d4bf261e068171e7cd68006ff98781697fdd6df8003387c8938243744c08cbfd6b40037db00a61e06bec804f132821f34cfe295c92e29a331849⟩,
  ⟨0x4cb23d11948ae43620a8fd07a63b21c88df86d43491960c2c5cc2c51520a0c4c424110e07dc3b41b50c9058829a12a02880f8032000, 0x4ef800a1ba1a80151159e822cd34350f80a5a687a886d344002569011a1fb4a02d0fdb286e87ad818a2600d19002752d3ff805290019d2b4d0881ff6b0ff6836d88274276ca12a0bb6505508db0006816ce503507dae282683dd7003f849c3f5a0f35800297ee1d38800197e61e716cc25197961d9d8f3a1c80ef1d0134ca7ebc56e743b58c0c5fdc3add60008cf30f27c9a044811f53dc64e7⟩,
  ⟨0x3831b00cf465c3231800b7455a2a3140096c4702150f8073c35c18d0c0054c29212808183d019e0c005a029412c08c0338118042000, 0x7ba7de18b0047b930f9127048007dcd89f75fb931a001001fb7f0f030007dc58900060a1d6fb07dcd91000fb370f04f3d8badf49d55b3fd17cf59c017e82cfe29001003f9eb3c0c003f3b6928a285ed71c4728a285dd75247c467493112606288a857d6000cffd9ca08a1575802d41767⟩,
  ⟨0x3701a58c9c63a2f816f8ae854228012808dc44c1f60f3870836618e0c205dc2c014908c83d81d20c605182000e204e01e00bc04a000, 0x6b6893d7006a7b083c0c0d7d11fae01827381134476b2260dcf110502e70417f680ff870182738c9ac011864040628c23800305eeb4d28800705d6ce06615c353a586a74bedf0057b970e001f71e268cc009f71627dc2008c4fb80005893893eeefbbe2ca847c3340d0558017ad⟩,
  ⟨0x2fe1788b3058429d14809ac49023310f084c3fc1eb0ee872835e1940b8859026812a083836819c0bc05682200c60540250094014000, 0x184e001c1d3ad818001839f56c3100ba0e4d9e22776993aa354c54aa704c342ac3144e50d88227856384f0ac9090b0fdd30fe29000857fee5878182bff70c480405bc03c1e11b8906308f44d0369ae0712899d752478181b0a25b593e00c1e06⟩,
  ⟨0x32e1858bf85b22b41550a144f026912e893846e21910107ac3b81d20d68508270113077039017e0ae04e82380d205c02780e804a000, 0x19e98c5b89c00184235b07b0013b181a0f5001f56c27949748c611c0c865c70209950f8e961edd2d24781a0ea010b56026804a0134022000800afc9e9e0600060f7d6c1ca01f6c60682960f4d6e19a4acd261260f0002b5742961493b2ac1d55746d3121b9⟩,
  ⟨0x36a1ae8d3067a3331870bfc5b42cb1608a704ee25211b88803f61be0d8067c31c1830b8052c2300f3068027410c07702900bc014000, 0x3c52526930930340f2002ea4d24800503bea4c24c0d069c223ad0006073d4c21f068ebc1a4253c0e1a681bc028d4809fd33a6c000e1e486f734b71a7049708b7a52047d38264f49c08da7000602bd38007d418b0005e9f810f55102694c2380030876b4003e9bc8801d085ece06⟩
]

def tableLRLRR : Table Block := .branch 14 tableLRLRRL tableLRLRRR

def tableLRLR : Table Block := .branch 27 tableLRLRL tableLRLRR

def tableLRL : Table Block := .branch 55 tableLRLL tableLRLR

def tableLRRLLL : Table Block := .leaf #[
  ⟨0x3f91e90ed472037f1ba8d405e62e716d8ad852226c12388903e81cf0c005c42b813708903f41e40cd054020c0a003b017007c022000, 0x10a40d05c9c018524e108d221ac9133c0c10ad21bac06d41b60004002852c1cbd3c2342304530a4eb214808a358107d20faea41820ed7071bf9f870328717f9d87828003cd5c116d45bd70000c287a7d94d98ea9849e09bd5807104deaf7d957824034826356000c277a78256096d5c10709cc103a74ba53d0a4e24c10dea69⟩,
  ⟨0x4cc24590f07be3d51d80e2c6402fb16b0a9845a2100f987603961b00c985d82c815a09a84a820a0ec06382d014609203680e803a000, 0x385dfe3000e01bd39c2cff10004fe1c035a73855fe10005fc28064dc5d3c0c000c2cdad3852163d8c1260fb88f4c75c16ad5ac2dba707ba169d483f30b4ea7dbf8e805b61e0b16ac5ede07441d200240b485a74f294972992a5194807c90983301fc90901a4494c8602ca4b84781824aa47b5d898248a473590602e7a468246d749687b834bd1a4213819b4e10940ca0ffe9e1283a4f0ac0f27⟩,
  ⟨0x3901b58d1867831717b0b4455828713a09844ac235108080c3e81e70ed87383521840af84b020e0fa06a82881300810380198082000, 0x618ad69c7107d6c60639360f8d5800f2559ce4886175a718c4b1a738c20c5d3da0897d51382403b916d6007c4a5a7f14ac49714e2338a610c002753085c36ba986d0007d4800d1248003a70016248d4b89c00185c35707142de0016aa0686b74b0267818e3285ab570013fc80021c31a7⟩,
  ⟨0x4112000fbc7c43bd1d90e8472836f1b28d0065e30a1728b0853a28613088f84322020d585a82360cc05f82b813a07802280c801a000, 0x126692834b8a61a7001f57825b8d6c27868c003d6c0c000c343ab813880094b26ce19e00075a001caa644001866f6747ee94001866b5a001cb4644001865f6747c6960530282566b9f23ae56c3a050813c1f672ae9d02783e800284a1026d3c1f281e2098000c24fa7d33529a524d200fc247a7007a122006b4e1f21c01b83f756e27⟩,
  ⟨0x2d51528a5050c27312f094448a23b10b08243c81c10db865030a1780b48578296138097042c1f80d906602a40f206f02c006c01c000, 0x183200fe1e30e3669ba1aca44d0229d84f08d03004b0e16b5c4f0e00003ad011e5eb2303008b2f18b3893066f4938251d45e428781803596cc59c47001e5ab16e27000e5b317967cb5800b15035223a5c0a800400585bc3f19a286⟩,
  ⟨0x2fc1648afc550296146099c4ba23810987f03ae1c60da86983021740b3855828a13409184581e20e706102c011a07602980f002e000, 0xa6ca9b3000b550349afa52e91e0600129add740d4d58005ae00069aad6499fa5a6a0011d7699a4b0d261269a4002f594297148d1b2ace4306cb93c309e99c000f5d0300034cd6b0b852000f50f29270694007d41ca49cba5a650001d749bba5⟩,
  ⟨0x29814089dc4c023d11388604121e40e086dc32417f0b8058829e13c09884901fe0f5068030416a0a204b82100e606602b80c804a000, 0x93eb4b0349f3a5000e03713810c354493092c075397acc0200070f0330114e46b37d439e49921a264486c8784cc27005e9c1d740c00ad37fac3893c8c68a27049e08cb133e998e2380074daeb1c4e000d369ac⟩,
  ⟨0x24911c084c40c1e10e506cc3401930c305e82ce15c0a204c4234102076838019e0c205a829812208203b01ac0ac047016005c014000, 0x3c690006229d6b8c4001889b6729de966dad2e9087a14b0a61183644e26a0828798513298696124a1f2394fe292834b8a64cc69242b152612711b048342a6f244c102a794154b89e06⟩,
  ⟨0x2da1668ae856029d134091444020f0ff07c43981c10d706842f81720a684e822a0fe07a033c158087038017409c043018007c014000, 0x184f71a36060d51600186a0000043000cae30e95cc489ad9334941a5c53120000fabc126c22d84f11e0007ad81800188eb5720a44001a7f7673716960688d4001d68007611910006232d9d09fa54490f91270486489873689e99e06⟩,
  ⟨0x30917c0b4c58c2a114b89c84ca24010d88383d21d60e606dc3401850bc05a42b414b09304642080fa07282c011606802180d004a000, 0x3c6ba9612e2d9b09e267000f5b030003132ead862003c4c5b34b6ea51d9b89e26000075b11a460698155ce13a5066094f466c14db126924ce16018ead84e1dead8181b55600015e00000438940001d6800659191005e24dd9ec49a4934340033ab⟩,
  ⟨0x2bb14c09a04ae24811e88b842e2050fd87b03c41cb0d406782f216209c04b42300f306702e414408f04081c00be0500158078022000, 0x66078b98100b40158ac833e449c127126fa8669ec8f03544981a72bd2e7d00038781800189f35a62b34400f250a347c4c0faa700fa277d6804f13b6b41894f3d1b343a43c90d86692b34984989b800ad5d0a58533e6b⟩,
  ⟨0x32e1858bd05a22b814a89f04b223610987e83aa1b00c605d42bc14509004241e80df06602dc14009104201d40d405301f00d0022000, 0x3e1dca4b2da5063f86f297142e906262c3138770e905be2bb138ad05b627158002c480da3a6a6962af59534016bac3436e090703558f5b533407e5ce07d4535adc9018fd86a90ba5486c8733955c43cc73893066f49382435865fc0a9e0602acc17163867⟩,
  ⟨0x26912e894047222810988243e41e80e8870836a1a30cc86302ce15d0a304d4248115078038c1ac0c5056026c1040750280118042000, 0x108ce29965b4ba26713b33c0d2c9e960696574b711fc525c23c0ce29004ea84d740d2d36974cd25869309353f0017aca14b8a468d815caf2183667f1be184e001d4edae818001a9d3580207bcf2⟩
]

def tableLRRLLR : Table Block := .leaf #[
  ⟨0x1fa0f8076c3981bf0d9069832a1860bc85b82be148098049022410807803641840b1052025411007b036016c0980410190068016000, 0x20684a53ee47a14b0a6918ecd2d89e4cd09b924cba3a5b04687a467091e060c848a96934b2f769734cfe295c92e29a3318497934e649c1271252b9a21b13e26⟩,
  ⟨0x239111082c3f01e90ec072c36c1ac0ce864c2f81670a8051824210c07f839c1ba0ca06002a412808503a019c0aa04b01e00c8036000, 0x126d6964d4d2cd487fc934a67f148c199e06c893034b93a5a1233cb95a681800797235308aa7f1487e343c0dd12260696ff4b632a7fc932a67f149ec8f03544981a5b9d2c6602a7⟩,
  ⟨0x3731a90c946362f614f8a4c50e27a137098c47c2190fa074c35c18d0b4051c24c11707903841780b205082280fa06e031014c060000, 0x1ddbd9c00656002acf031765193eb40020020018012a2c005c3d23523699b11b1346404386b49e68c7f5a000c63dad87d00cb8800318e6b40066dae20084633b30019b1b3cd94d9db4c23800318b6b46ce2001c627b381860d726de9584f292e918c2380069098ba4180040058a⟩,
  ⟨0x34a19f0cbc6282f016c8b0856a29013a89ac4a024611088183c21ca0d286002b614409b84481de0e506102bc14008b04001ac042000, 0x2918c23806230b88004050a9fe74b328e95c4e000c687ad0342e2303016130b8180018cfb5a018c4440018cef67318e9633a00075a000cc03b10006337d9cc5fa5713800319aeb40414acc8c0c021a5562c3e44c2a681d54e0989c55801c01200aa8e002f0e0193e767⟩,
  ⟨0x27512908b444620c0fc875037e1a40cb86082e81610a704f425e11c08583e01ca0da06382e012807d03601840a0039017807001e000, 0x1990e441448da367035037a50e10e000c6cbada1e58ad182a7d330302a7086bfd13eb2247cd314341c89df34fa48be91178245b459c4b02cbc030a99834a766bc13226b996b4b0348e8b613ca4b⟩,
  ⟨0x2e616b8b0056c29b14709cc4c824f118889442e1fc0f086f035a1880b2850026c113081037c15e09e04782100e605001f00d004a000, 0x2b24cb02c7818996285b09c636085e2a6bb053c402098f88db43425e50700c820e08f46fbad308e000c6f7ad000cd5b22019c6f1b3818063353c58f99c003351c5cd4265600dc54599f224e091934852a64d8d2f11e0634931b58003ad⟩,
  ⟨0x2f51740b0c572294137892846620e0fb87703821af0ca05c02be15009d84602160e606182e412c08303a81880ae040014806c018000, 0xc27000e3a9d6c0c000c74fab0006574d880031d26ce572d2c746000eb736b68c562f0900d0a130a834863f078dc823d078334ae490725380966a18b71380031cbeb403b34dc8c0c04e9a5e2c3b44f50dcd227049b92cb1b418f0431849c46⟩,
  ⟨0x3391968c8060e2e215e8a284ca25612188ac42820a0f987883b01b50af054828813409184081be0ba05482100e606202a80c004a000, 0x188ce29ca0a7481932cb6a6595002352003cd22000e9c0069a4352611c3e4587a3454b1ba581a58dd2d099e06a99805f16099ad5000400400300261f11aa86fac6817304ac8359eb48e6fc380031d9eb478e2a94c761b39334941a5c531d6800fabc132bc800fab⟩,
  ⟨0x2ba1538a5050226812188e044e21610387e83d01de0e786a83261890b90534268101075034418e0a204781f00e204e014807001a000, 0x25744c44890d5136020eb003e6aed5e09d835cc9a6f23f8a4ba47818c248003352eae6a3d2c0d3506940019a974e0342eb02800019a8f553556966c05cf03013934deaef044bec89c1200eaa3e2c0109a6b4fe295892e29⟩,
  ⟨0x25a12188d44281fd0f5077439c1c00d6868031e1800bb058c2a814309a04a822210007383601980c105902340d806202080a8026000, 0x339e64f50c390832e7c8598f29a1e852712628681513e292934984981a05449a492e34984981b06f5da3469bbbf77b627e4684d492404f8fc75a073a02e7818040a6dd5370e966e1d2e2689⟩,
  ⟨0x25e128891046a21a10588003ca1cd0d486783061720ae854c27813208d84181f20de06a02fc16a09e04381c00c205602080a0014000, 0x1c53266309206a4426b24e0900d161303a511410080a0f89a820284e099e84ccf034e27a581a72ad2d62a9fc520d21a9e069c254c0d3836951ef63ee10c7c89382418953a5aced03a41b1e06⟩,
  ⟨0x3b21c78de86e035f1aa8cc061a30016f8abc54a28e13989a44901f90ef07303621700a584601fa0d905f028c0fe05b01b807001e000, 0x15cbbabc689d19e062834c0c000c88baddd12b7f22e27001addb5ee895b8002c540d308696440183c0c2655af6b04581199c1c11a58af4e0183c265b069641a1208b2c4e040ce07a70502702d3827f3808271a7accfe0f3bac4fa0f58a9c1eb15283d5ea35083d92a55583d32ad5483d301907f14ae49⟩,
  ⟨0x46721b901c76039b1b58cec6162c114f0a444dc25f11e08643ec1d50d286082aa14b093040c1a60bd04682080c203c0158070022000, 0x6d34006014c38008027b5ac3ea4d121bc8da580058bd8796fb3321752289dc3b12b52091ac380452d5bc4c3a139117bc3ddfa6570e001de0e260cc007de0627224800777d89ddb6eff17bb5ddee2e53e526d7b4c44880070fbbbdd962c00653c00ecf0312b322b6b5395bb7c580074fe00fc3eebf0db4300080370f0980064d6ce491489fad8f33e449c123869⟩,
  ⟨0x3ce1d48e106be33a1968c205e22cc15e8a9850226211e889842e1fc0ec070436e1a00c285ec2b414509804942140da05501e80ae000, 0x1922b56000cd7fb10012487d98003243eb58620064909b39aeb4b2418003ad84a33dae9400192035a007e0d4400191f7673d7e94c23806d50b00da4070a9abb4b034c81a5ac0060f0367e0b1daf7c55386ca9c122fb342c559b5116ae1f6a3b5f014e1c050953da861d309bc8c3a5c4009b4ed4b224f79787⟩
]

def tableLRRLL : Table Block := .branch 13 tableLRRLLL tableLRRLLR

def tableLRRLRL : Table Block := .leaf #[
  ⟨0x31c1868c045d42c515b0a8450c26f12c09144762260da86a433618d0bf85d42a012f08503941800af04f02440d806101e00bc014000, 0x6c4fc8d3ea6980059f4f52611c1855700212aa6dad2cdb5a5d050f034cdaaed1c1790bd000400400300200170fc8d543610da4340c000c931ad9f701eb8c92c000eb40019ef762009c927b39334941a5c53248000fabc133620015ab61380072466b606⟩,
  ⟨0x33a1958c686202ed16a0ac4530277136892044a20c0f3870833a1780a984d021e10206e831815e09e04882080ea06802d812804a000, 0x2b24c099e060def0a316030ee7042709b16ff08e77b7e8373c0d2608003ad0d37087220304e792f81a3d6c97a000eb40019f9362003c975b300064bad6803ff75192e0001d6b8c400192d767405e9680cd2d599fc52b125c53066714ad9a40049b93533718013a9⟩,
  ⟨0x2f81698af056428d139097c48822910707a83c01bb0d006582e21560a384f02420fe06d034016a0ab04301ac0a4041014006c018000, 0x64ead6e48cd181a4e700075bd236c466943f4bab09026c20e10ea41c180fe9c1e06937c1abd680b970781a4dc071f5a08e941f224e0900f3e121cdb27e340203e6c1e060172e130300032696b641c78880c9ba635cd1220e7f331849c46⟩,
  ⟨0x30816a8af856828f13f09b44c424911207c43b41c30d8069831a16b0ae853827c12f08f04342000db06802ac13c079037812804a000, 0x158089a0db55300b1e06014e82fd5d39a5a4d38257e29d6030505da7017e82d016b4e06bb1eddc65d028781a0d65d61a086443c10de29a031bd53499a4a0d2e2993cc007d5e099ca004ed5b09c00393bf5b030003276eac0019c8f6202449d5b3⟩,
  ⟨0x288138893046a22610d88303ea1d70e686d83581950c105bc2b814909904342040f107003441880b205402640e805d02980f002e000, 0xa1fb4a0394a53ade0218f9127049c49dfc19a0758363c0da4132606a1d34b79a265644c44890d11398832c00fa1075782760d73269bc8fe292e91e063092000d071aba0db4b035067a50006838d381aecb⟩,
  ⟨0x23911208243dc1e20e5070034a18e0bb856428012d09004442060f007183481860b905402641100790378160092032011806001a000, 0x2d6a7a9f114f4821a9e11b830a1e066a50555458696523639f92898f102ee794d0f429389314340a89f14949a4c24c0d8a69349254693093037df8cd3893ebdb3db13e26c4cc29⟩,
  ⟨0x20e0fb87803921b80d5867031e1820b985882a614809c848422410707d83b81ae0c6058829c12008603781780a203c019008402e000, 0x2895d2d12fa5a37b4b9a67f14ae49714d198c24bc9a7324e09389324ad10d89f1342338a68aad2e099e84ccf035157a581a8c2d2ea99fc523666781a48d303513da5⟩,
  ⟨0x20d0fe07bc3b41d00de869832217c0b785882ae14209384482080f5072035c18a0bb05602881160730348158088038016006801e000, 0x1ca67f148e199e06d8513457e959b14ecd6a7a14b0a71348aaa5498153a72aa6286fc932a67f149ec8f03544981a8a1d2ab6143c0c8ca1caa47c46c463511e13362a⟩,
  ⟨0x32618a8ba05a22ba1558a504e624611788883fa1e40ed07043541890b4050c2200eb06e032c17c0a904f824010c06f01e00bc04a000, 0x78d601b1cc0036aa4534a07231dc2581bcc70018e6b5800c728305aa90dd2b89c00196835bd206f181ba005d7555e962e6272ce0031836722fa599d68162050d189a7002a8c3d3fe49a533f8a460ccf03644981a8b8d2800345d0005a783340c003516fa9⟩,
  ⟨0x29b14309ac4c224010988203ea1d00d7865030c1710b1853827612a08e84301f60e006282e814208e04181c80d004701d006401a000, 0x4c1aa61e0183c0c2252136b8df00110cb3c260d10e000cb87ad10c8ffb8a5202a7d218185534432702a7f2448d9a74cd94699b34c081d0b8084e1782447fdd71522f04c79ae060fa8ecb5b09c0123aad708ce27⟩,
  ⟨0x30417b8b485622a714409dc4b024711c08b44381fb0f4877c39c1a90c505942b214c096840c1d80dd05c02640e806a025807801e000, 0x71380032f4eb4062002e30304affd4b1d3380fff94b8b33e449c1238699217f7b69788f030c1a65db00075a007f954491b97636708ce27003fc297fbff6801a555c9a5308e000cba5ad003faea201a4b9fb3818197e8a5c73018089d9cc24cea6⟩,
  ⟨0x2ae14989e04ba253119085c3f81e10e9071c35818f0b5858428c12108883c01aa0c5058028811a07f035017009603e0168088016000, 0x39383e3f210bb80060f037470c6daecd6084d7ecb098de320f9127048071309bb986968062d8783c0d15c2c24114a49f4f858d22427f6700cfa0f5d8d440a9d21819553d433922a7e861934d99aa0d3824bd065c26⟩,
  ⟨0x22c11008583fc1e70e806f43601a10c986002e61620a9852427012908c04241fe0e406a82e81560a004a82200e204c01d80b0042000, 0x84681b01122a958d2d2e3a594d0f429389314340a89f14949a4c24c0d8a693492546930930365b350d389398ca43db13e26c4cc29a5034a0c6cc1fad8534ce49c12323d276b⟩,
  ⟨0x282134894446022510607ec3cc1dc0e286ec3481910c205b02c414f0a284b82260f806e83381860b204b81cc0d204e01b00a8024000, 0x785d303a511b20204e7c4dba04e9c133d0999e06a5d74b035319a5b950fe290d468781a6244c0d4b46941fb583ed05107d98260f9127048e1a76bb1868075c0483c0dac04427c72a1f11b861a1e1447⟩
]

def tableLRRLRR : Table Block := .leaf #[
  ⟨0x34518c0c0458827a134896049223a10f88103d21ce0e2067c3081600a3849821a0f406982c8122078035817009e0420198068016000, 0x33562056aa6cf4b8581a187383e387c2b8d086861cd0f861e58d2b06988927127c358858077307ab77e17c900c1e060772985d5b5f69076b6cd9f07efcd73e9776639fbf71cfd7f8e7eafbd973f673ecb9fabb361cfc818e7f14ae49714c998c2483723a6b24e09⟩,
  ⟨0x2f21668ab050e27d133095c4642230ff07d03ce1d00dc86a83361760b485682a014308703dc1ac0c705e028410005302480a001a000, 0x19a2b5a00339771002a687d9c0d4fd694c2380033426b4d288007340ece06615d38da5a7cf4bb126924d9540036ad84f1936066158001388000010eca4d2cd908359f224e0900c26133653636d0019ad101b3c0d35620b6900c120ec2b⟩,
  ⟨0x29b14509ec4ac24911e08a442c1f10f206fc36a1900c1857827212c08383d01d40d706202dc13e08803b81a00ba04c015806401e000, 0x159a4c24cd500056ae852c294c91618a2ee92009772c27000e6a1d6c0c000cd3fab618801534e6cc01e85b366e27000669ad6dcc9181b04458608761586ce4553b7a58b33e449c1232699d0010b69788f031a49⟩,
  ⟨0x2e11650a9452427512f091c46022510907d03ba1c60db86a83361900b9855829812b08903c41b00cb04f021c0f405501c00b8022000, 0x1080b4412dba3b67caa264a056571cab2e30465838acbc1218a2e10104caa8274b502e94e24c19bd24e090223d95c7200c9e0623a9f9b580c639c00e7ded6031ce7615800cfa0465aa9f6d2b89c0019abf5b1805f3181a2f0b6578669⟩,
  ⟨0x2f51758b1856e29213d895847e21a10187d83a21b40d5063430016d0af853024a0f4073035c18c0b5054020c0f006102a00bc04a000, 0x1030003374eae92880037566ced13d28003372eb40ef6880033716ceb26d2b89c0019b835b3083f3181a6007656c27d6d17b4357487008039624e00804764af27921bb53499a4a0d2e299b44007d5e090d4596c27000e6cdd6c0c000cd97ab⟩,
  ⟨0x2dc1668b0855a29a14809bc4c023f11908443c81da0e186d83221700b3051427611607a83401720a204882000e604e02180c804a000, 0xf4938248895700a1e0601f978b59c47003976b5b89c0065e2d72e72ee0056a81ad2cd2b89e6fc00075a00d2e57181804e5c2d7034dee000eb40065a6e2007cde9b303f18ff7f3364cd25069714cdde003eaf04b59ad84f3758007ad⟩,
  ⟨0x2e91680b1455829514289b84ae23a111884c3dc1d50d8067c31c17f0ad053428012708703a41b80b705682200f6056018807001a000, 0x12b26e9c132952eb0325932d8d2a43263c964d4c314af8e165c16300033906b406d9e202f4e3bb3c334959a4c24ce340056ae852c2909ae7580d6baeeda294b72c27000e713d6c0c000ce23ab618814d3876cca4b81cf6739aab3893066⟩,
  ⟨0x2fa1708b2056e2aa14c8a384ea26a12e88e042e20d0f6074436018f0b1051426412808783581900b804f82180da05402180a8022000, 0x537dd3bc26e91934d99aa0d38276a11d7099c4e000ce83ad022a81b8c0c0fd4ff6b00f3e0e1a54fb6ba5d1d3b386652e0e959eb918e4f80a1e0676cd75800d2700115ad9e8869cc6b203748158ba406a5cf3762ebaa7340b4ba40651d32ce6⟩,
  ⟨0x3661a78cb86323081678ab050e26a128890044e20e0fa877035e1980c585d02ca15a0a184882080fa07182f813a07803080f004a000, 0x2d4bd2cdd974d9c1c553f8e616c032a7b2e6b38006e11875c26764d690d71c9c0611d35ce6ad8374c1563a67ab5d73b38eba759ae2dcb3d6b0c993308b4c7c8938240d8648704e65b4083aac78180d464cea2000eb400671ee206d4e9db303218e02bce9bad03898e031ce97ad⟩,
  ⟨0x35619a8c845fc2ef1720b0453c26e13209044381f90f407783721940b7857829a12008b03c41a00ab04e02340d005b026010806a000, 0x2904006cf07a8c008df1e1f224e09000ef8713f53dfae34002003def61e06000ef7712000cf01addf7fd3b23046781a77c00075a000c9adb12eba779d98e19f78db5334ea0056781a77500075a0033d7710026772d9ec49a4936a8800dab613c64d8198560012c20000143⟩,
  ⟨0x4aa244917085e41f1fe0f5c76838f1b70d2c65030514389cc4be24b11708443c21c00c9859828a122079030813e07a02680b001a000, 0x29e0142cf4ef3d409f670019fa0c3b3da63000798587bdb5cd4d7000799d87bdadccfd74cf2b659feb2524c3fc5938b872ce76e70e5dbf479654002479cc70008006604c3d9aa35bca35cfa364d8fca71ec96539882398c870f56062f67aafa94316b3d5703098ad9c05e822cfc22503e1f843c0550361f818014e10e1f869be4c3c95200269e97273c00ecf3833a7678420068f666⟩,
  ⟨0x7f43ee9f4cf7879d3841a04cda5ca2d294e898243a1e78e0068631e16a0a144cc24110f07e438c1b10d386082be11e07d82b00ba000, 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⟩,
  ⟨0x2d61608ac053028d13d095449022310607d43c41c10da068c32c1890bd056429013b09704341f00d704b01a40bc03d0158084014000, 0x18952f06ff8448784de0a240019f975ae3100067e2d9d227a5a45f4b8921e33403ecfe292834b8a70cc6924026322d30869a14b8a4006312d3158680018c2b4800c00400157dbea22fc00400acf09a2f8006d25d23c0d47a69606⟩,
  ⟨0x24411088483da1dc0db86b433c1870bb059c2b014b09c848821610107503541900b9055826811a07c036818c09c03f015006c022000, 0x3dd8726611c001a0235a3471000e805d9c0c792e935d28c19dc259a4771595095499696930d2c0d496e970494f42938930437a9a7c525269309303502aa4d248532a4c24c0d526d⟩
]

def tableLRRLR : Table Block := .branch 14 tableLRRLRL tableLRRLRR

def tableLRRL : Table Block := .branch 27 tableLRRLL tableLRRLR

def tableLRRRLL : Table Block := .leaf #[
  ⟨0x2f51758b1856228c133890843a20e0ff876839a1b80d706642c81530a104cc2440fd07703741a00c3057022c0ec06902200e802a000, 0x1030003414eac1ad62000d04db39467018d9800327e69e4fd945f5bb126924d2ae0206ad84ff06ad8181f15600000e0000143f4349f1a57248c1a6817003357a126d0d74297148382aeed000ec98d72ad84e001d01dad818001a03357402b1⟩,
  ⟨0x2ce15b8a4850a26012b08c44481ff0ed07343501910c385c02b614c09b84b022e100078838019e0c004d823810206c02b80c804a000, 0xce65e07a0266cd84e001d08fad818001a11756c31011e842d9808b81b6cdc4e000d081ad730da3033a82cb07754f4a6e7654e09eb55581a4c7b94d86692b349849a0c800ad5d0a58524e4ab07155e03f2906cd84f4158007ad⟩,
  ⟨0x3bb1cc0dd46a432217f8b70572294138890443c1fb0f6078437c19b0b5858427c13408783141740ac04381d80ca056018809002e000, 0x6e2f6b78bdc56dbb17b0500b61f6a3b5c9cfe1e739b5ac4ed536b589000ed630f431b6c7adda480430fafed7e9fd30e00eda4e1c011b51c3e449c12001da7627699b7cc68004007b4cc3c0c002da562606466e856d6cecc0034d300101c30f09a686a149b3ad6e19a4acd2612684e002b57429614899ecb⟩,
  ⟨0x47c23391088023ce1e18e787183821b58d846943401948c105a223c10e87a83521790b2055027a10006e82e812e07402880b8046000, 0x8ac3400032046a4006002000ac1b751201000200169e134808000ea4ba4781a8e0d2c0d47069606a3934a45c47aba790048b322ef4f09e816f1e611230014cd4a7ccdeb37c2e8fa7e49c7a8e447b6a72fc69db242239b5297df4f3d5a7a824b0e0f0a9ecc6eadd933d1a78808011d87d7b6be31201f9d4e1f5d0004c4ed6c00b890026d6b12001dab6261300076ab89⟩,
  ⟨0x2a814f09e44a822f10c080c3ec1e70ed07343801ad0cf062c2cc14e0a184c02160f407082f015e09e04882100ea05001f80c804a000, 0x818001a2a756000d21bb100068a6d9d217a588b53f8a5624b8a60cce292f51311243b44800b8406bf01121e135c289c1f0001d6d1eda5a490f208001fa7f14941a5c538663492004c81da98434d0a5c52000c815a9⟩,
  ⟨0x2da1660aec55429b14509944ac24511c08ac42c1f30ef07443581a20be85c029612808183c819a0b6052825010e06202b80c804a000, 0x2886f4349f1a57248c1a68c5003357a12710d7429714834aafcb800cc98f3aad84e001d179ad818001a2eb56c3100868b7d98013ca99300068b6d68f9c4001a2cf6748ae964cd25069714d15e003eaf04d224003ead84e001d157ad⟩,
  ⟨0x2bb1570a6c51026312b08c444e2020fa87403561960b885802a214609a84401fc0f407283001680a504801d40bc04701a00a802a000, 0x30a539458708bc358041d9b09e8e5000f5b030003471ead862008d1c1b300eb0cfd983aa9e8de00db5b1267c8938246cd385e8013ad2e11e063c9385c800bada46308e0d8abac1095549a696932d2e0287819999560e6a7⟩,
  ⟨0x36b1af0d3467c32d1900c2c6022f21740b4457e2a814f09e44c423f10d0684234105070032c16c0ab04b01c40c605202080c801a000, 0x719b68cff92694cfe2918333c0d912606b55f4b0a23dab1a6818001b55b536a9e9400343fc3d1f4a25eb40024ee1bf779cd8281d39bf09fdb4e000a76e3a637ecf39304e3a6b7df3fae9fc6ecd227c8e7a9a6354c542a704c3faae06700074fb43619a4acd261268ec002b57429⟩,
  ⟨0x2050fb07943b01c60de06b434618c0ba05a82ae14809d84b824411108103d41d40d906102b414209004181c40ce05402280b802e000, 0x1f92654cfe293d91e06a893035afba5b3028781a8a43ee47a14b0a6918f8d2d89f0cd09a84d36cae96284cf88cb267f1497c8f03066896c556b2e96d67d2db5da5⟩,
  ⟨0x23911608504141f70e906ec3501950c405e42d815f0a804ec25812108603dc1c40d706102c014c08f04281b80c804d01c007401c000, 0x1e2908f287818384480038876badbfd2d5e87c310fe295c92e2993318491b154d649c120dca968a3468919e13540aa4ba4781ad8fd2c0d6c8e9606b6a34ad44a7841654f0a9be86⟩,
  ⟨0x2c51590a7c52028413889984a6240119088c3fc1f10e6066431e1780b3857029e12a09003ec1d20df05d02c011606602780a8026000, 0x15622574449c49e4635d13824f646442879a18e2380078946b1c4e000e24facc497126000b55035bafa58133c2661380138906ba06001f11ed61748f03000988d6ba06c460002d7000388beb2dc9d2e22a000ebadf1d297687⟩,
  ⟨0x25a126890046822110b07f83d61d40de069c3341890be05bc2c014b09e04c024a11208183ac1b00cb06082a8140089033010c026000, 0x2852c298460d91389a820a1e6144dc49a584928798e53f8a4a0d2e299331a490a0549849c46c121e226f24684143e4289713c0d6f769606b7b74bf8efc5e1fef3f89c3fde3f11f85c3eb887⟩,
  ⟨0x30716d0b3457e2ae14e8a404d626012689004362110f6076436818f0b5051425c11b08604041dc0c905a02a813207402780a8026000, 0xeee00159f8cd943499a4a0d2e29a690007d5e0935916c27a680003d6c0c000d33dab8052200262c3b3a66c001d68003071ec4001a66367808e951143e449c1218a2600e001f5a2786781874d2000d31fad0006009d880034c66cee2ed2e9087⟩
]

def tableLRRRLR : Table Block := .leaf #[
  ⟨0x3441908c405da2de1688b1856a29013689204622040fd073436c19f0bd05ac2c014f09503dc1da0c805d82580c605902100bc04a000, 0x929002b1a3a6900449431ed89e8cd09a04d2000d387ad000c92b22000d381b3ae1b4a007d5e0036781800400bab6d55c0696b80d2c06200669f224e091934c06307feb400180b0007d3c0d015800ba9713800307d6ae0f583e4002d540d8146964143c0c009c1e9ab⟩,
  ⟨0x26712d08a84401fd0f4075c3901bd0d406142e61690aa051423010d07d03541840b5053026010a078033816009c03b0160064014000, 0x78a400202c8b6e1e0601545b31341aa7c833e449c120cea9010c9a71a7b23c0c2c6a9894c043d8e03d6784c1ba1e9d9005f5b29a1e852712628681513e292934984981a65449a4914512612606⟩,
  ⟨0x37f1b70d7c67432d1900c1c5dc2d515e0abc51428012d88e842a1f00e886b032616e0a484a820a0ee06b833016a0900358118046000, 0x161a4c24e3a0005eb2852e2901c07604dc3c806f9d9696cf861380078e46ba0600071c6d6008158bc80b795bf68056caddb4131fd2920554007a9a99874812f000ea6000025b53d544ad271bd025f592213260c764e09816196000d3dfad00b60d4d8d3dae80eb62e316fc380ba2df87⟩,
  ⟨0x2e11650acc54028d141097c47422d10f084440a1f80ee86e032616009d84b0236106077839419c0bf04d022c0cc05c01c8088022000, 0x1695696d37d2ea0897e51382401d4b9c5802173ee9fc52b125c5388ce298f82a1208f5a39a9b46c008d4800f73a0003a7001ae73d498471b358d19aad13d2c0d689e94c2380035096b4c28a949507ece06a51000717685e9719cda669⟩,
  ⟨0x264129892046a22a10e87e03ca1db0e406d434818c0bd85b02c215009e84ac242112076837016e0a004b01fc0e004b01e005c01a000, 0xa834e094f917099c4f5228003adbc5230361e8b0c10e3a6b659c8a8c33e449c12346989d1a5f23c0c7124001a8db5a38710006a33d9da6ba581ad32d29847a8bc001d69a51000ea2cd9c0cc2b⟩,
  ⟨0x2d71660aa4508275133090441c2040ef874c38c1af0c885e82d614609784282000dd06402f014e08c03f01a40a8041016007801a000, 0x609005f31717760800fa7b4930926d3e002352000dd7a001e9e06baec005d4c23389c0c965c8a2059569b694c23d4b6000eb40c468b96b52c6ce06e598107160d4a9e460a353b60c4a7e21a60d5214aa90f50e7caabf21864d3666⟩,
  ⟨0x2c21588a9852a28a13d895846620e10207843941b90cb05982aa14609d84a820e0f5075837016e0a4046820c0d806201e8098026000, 0x324d3826e0d7098c23d50a000eb4003ce0c880075416ce06000f377176ab6947cce001e6d62f9b200b006e2a2ccf9127048c9a400dcd4c69788f031a490006a74d6e8291b5334b035a8fa5818001a9bb5b761b46ad44b2889⟩,
  ⟨0x30b1730b645842b815089b048e22810187b03b61ca0de866031a1680ad84d825810707102f415409504001cc09c03b018807801a000, 0x5b70040ead84ffc1b360603f59600057800000c3aa90001d6801d9b510006aa1d9dae7a59334941a5c5354e800fabc136cc010bab613d532001eb6060006a97d580036c9ec407faa53674ba2c1894eac0ab713d520000eb59d48c0cdda2c68d3a66⟩,
  ⟨0x272129890846a22410c87e83de1e00dd86902fe1750ab052426811908603ec1d80e106802ec15209f04802180c204c01a807801e000, 0x37a01ca58d1a70cd7269c1202b77d2e131847ab08001d68182d11baaabfd9c0dba01f52dc4e0f8ab37b3955a668c33e449c123269d475697c8f032a4981aab000075b602b1b79b4b6c1697624d249⟩,
  ⟨0x2fe1798b905822a314c8a084d622a10e88383fa1ec0ef86e835e18a0be856029c129082037c17409904401e40c804f0210074014000, 0x3049a4905f55f31a07c0363c0ddc0b26ddfd2800200100eb79e69f8cdea9a4cd25069714d5ba003eaf04dbb20676ad84e001d5b3ad818001ab5f56000dba9b10322ad4d9800356a6b40c62bae306695c920c6a752155b89eacd00075acf24606⟩,
  ⟨0x3821b18d5069232a1858b845ae2b81570a244d423510b07b03841a30bc855026a12608083a01860b905002240f8063019809801e000, 0x46eea3e449c1200775d27e78d3a6801007ba68f03002dcf4981ab0100075bf2066d4775ee2dc9b7a8fc3f75d1f73f0edd547de7de38751fa1f0fa3eefe85c3a8e000d5f3adf8001ea2611c001abdb5a0396f1000eaf3d9c0c0390ebb7af4ae2701c575d60818800ac5499be8863e449⟩,
  ⟨0x273132096447422710e87f83e21dc0e086d03461940c485e82ca1500a304dc24010e08103e01a60c9052024410805f02000d802e000, 0x7a49c1201bf8d2e6143c0dfb81a52dc4e0e4ab5f12955266d833e449c126926b455a3066781b924dc23a53591f91a06ac5001cd6c0d5890003ade9922e27ac3c001d6fd60075181bea801a5dccfa5⟩,
  ⟨0x31817c8b505762a013d896845a2030f8077438c1a30cb05fc2de1580a684d823e115078038c17c09b04881b80b2044018807001a000, 0x3f0a8f5a49019ad01a173a8a3d0d0462b46d6c33393d9e195c99c92cfcbf94722a3c46891411206e31c0a35d3c5d1980ca64cd634c92c9c132e432c14563c0d59b0083ad713d668000eb407f5c7c8c0c040ae2e2e40d52146a90d90e5c4ab3893066⟩,
  ⟨0x2ad1510a544fc25912308cc45020f0ff07b03ae1cd0d4060c2e41650a8051826a12b08303dc1ac0a904902200e205a02800bc03e000, 0x189985371c6940c4ad9f5b992263844e0910c275e29a4a8478a4b340d993116bae22d3325d62e19fc5227467818a0d303663c456eb0c23800c97dac0064b800ed571be9606b8ef4bec0b1e060ac928b5d6637c4f8d49⟩
]

def tableLRRRL : Table Block := .branch 13 tableLRRRLL tableLRRRLR

def tableLRRRRL : Table Block := .leaf #[
  ⟨0x24d12108c44241f10f3873836c1aa0c785d02d414f09c049423010907d83a01b60ca05d82c414009104001c40ce04801c8068016000, 0x18246cd239fd9534078c11cf037083ba4dc221e9184c4253b3882a7819706f555c9fa594d0f429389314340a89f14949a4c24c0d8a693492546930930379919d4d3892333cbd3db13e26⟩,
  ⟨0x3881bd8d5869633a1968c205fc2d91650a9451c28412f88e842a1fe0ef870033612208904041c00bf05902140f605a02080a001e000, 0x714d752003eaf04b61ad84e001d74bad818001ae8f578944001cd9b679ab696060006b9ed68003076ec4001ae6f679a869769ed5a4801da3471b62b98d6917e3be007040980020015fe045e69e831a71cd1a119d670148ceb3f8a400404a332cf03008465da43ba9cfd24ce7e80973e449⟩,
  ⟨0x37f1ae0d1464430f17e0bc45b82a9134090c46822910c07cc3801b60c886142f015309004241f40f0065826c12206c0238088022000, 0x714400389ccff4b073e27e1eb044be889c12748ab1dfa1101dc34e3bea0d10878edfa7843c008d3e449c1232698436378d680030850007a781a10800175308ce27000636ed5c6db1b88003aacdb34b491e06004a369d58004027597c3c0c000d75fad0006365d8801b5d66ce4cd25069⟩,
  ⟨0x34a19e8c6061a2fc1778b2858029b146099c48421d0fc07843a41ad0c4058c2b213408e84401d60b805582200f206e02f80e8014000, 0x1c535f4800fabc12d46b613d7ca001eb6060006be3d5c251002f3a6d980035f06b4001a4e762000d7bbb3c6bf4a611ebdb00075a000c95db1000ebd8d9c0c000c957abcd2f4ae2700064a8d5c9912538015aa933708c01187c893824d24d24f250eb4003c1e001e1e06⟩,
  ⟨0x2ff1750b7c5942b514e8a304fa26612088d041e1ea0f006ec34817f0b4054428213608f83e818e0bd04c021c0c403d0178088022000, 0x6d9aa704eb92ad5bd4f3c450f06695c9206531c04c8ef756e27b000001d680a51dd6c60601763b8d581b0c7afec059d68596c7031993058d0980c363d7ea023eb40010052141d3c0c00c57e5ad1d33801d5f86b68817e098f343699a4cd25069⟩,
  ⟨0x4ca22f90407723961b30ccc6202e01650a9c4781e50e906fc3341790aa04fc23c10f08103c41cc0d905a023c10a060024809001e000, 0x8c01ea3a0003160ea6043d3d3bd94005ac1b1cf87a5a7f62d8300140780450f470e3d1f8a61c79a3d0f89e1e19f8a71f33d3800be7d87f978007e7b87f98618469f36c3a87f1812090883462318820a5a7000a3f8f99e0f47e000b0f18c9b239313410b4e9c0066d6ce4db5835adae453cf181359cf24c99a18d3099c4e000d825ad00e2506d8c0c01cca09ab03158e01d4a05ab07454eea6⟩,
  ⟨0x44d214101c70034d19e0cb46102d51590a3c500276128884040c1e10de066430616009804681ee0d2063029c126088034811004a000, 0x1a0914f7ac91793db4a8ce83d46726f7d6894cf924ef1c124ba7ad0e53fb2e74f0a699c9365b24cba7497ecb549934e00193261e4c3979c5d24781ab3e65db5729a8002928d673a781ac3b00075b59cb2e5b1000c99313242c3487a47f878e2487647d87800e180036fdc3d866b7f6b791800fbca4fb5a3426003ee68f6169221ad0038968f6158f29ad⟩,
  ⟨0x2d61638ae855a29e14689f84e626212088c844c21b10607ac3bc1b90c305bc2c413d09984381c80da05a82400de06201a80ac014000, 0x1724b8a68cc6125f4d39927048d1a691a62ad0d89f91a135249a3e980b3b89c001d08f59a116846000eaaf6cd2b09ca8cd07f5d031515a0eeb000cb800747818a83d06b5c5416833ac0058fdb3f8a400400e3eecf0300147cda606⟩,
  ⟨0x2dd1650ad4544261129091447422910b88343ec1ec0ea872c3681a70c1053c27012b08303f01ae0b604881f80d606001f807801a000, 0x192266f4d018224007002400bd1b350d89f4cd09ac4d25d23c0d7cd69606be6b4b035f39a57138003a216b3441d108001d55f23a5613e87c554eba062a9f43cd6000d5059caa1d0eb5dcb226bb44e09014aa3b64ca80859f34cfe29⟩,
  ⟨0x26e130093c48423111108604061f40ef874038c1a10c6059c29e14409884301ce0c2055826010a078033816809a03e015806801a000, 0x2086f534f8a4a4d2612606a05549a490a654984981a38500275a0c4a9001e383d7fc2243c26f0512000d933ad000637ed8800364b6cefb7d2e66877c10fe292834b8a74cc69255644ca1a6852e29⟩,
  ⟨0x2f616a8aac52827d12c08dc4402090ff07743701a70cb061c2ec1510a104c424811708103741940bd04c02380d2056018807001e000, 0x1e22c2d34b8b5d2da3feeec903498e57ce91daeaf906fb3d094c9933d93824122bd2d91d8804fa7f4349f1a57248c1a6cbb003357a126d0d74297148302adc0c903b666f22d84e001d965ad818001b2c35780a46407701767824a7a149c49⟩,
  ⟨0x3831bb0d9469a3401978c8062a3041798b785a82c515d8a5850a26012488c844a2000ef875436819d0c1022c0f006502200dc014000, 0x389c7cd7573d15c668d33e449c1234698f3689c19e0658930359ba000eb464e2000d9b5b3c0d34b819695c4f66b8003ad81b003b8c0d0400036bc2674bd9d641c0b402cd7900f6800139e23c2a8a14f0440c36100089b004f013b27e57a0d3dc326e0a4c0f716967f1480083cc5959e06⟩,
  ⟨0x289132896048e23811688704021ec0f1074c3921a40cb85c82b6144097846820e0f2072034c18c0b505502240fc07102600ac042000, 0x1ff0703e15c668d33e449c123469047e61a27067819624c0c000d9ffad61883e567e6cf05cd2e0ada598354852aa43f439f22afe861934d99aa0d38240260f6d7099c4f6770003ad832013b8c0d06e0236b⟩,
  ⟨0x2b014589d04aa23410387d83d41d90e686e033a1860b8855028e12208283ec1bc0cd06002bc14808f04201dc0a403d0198078022000, 0x74f2d760eda5dd1b928f05e42b6782f82e214b38e1a7919acd3c8d130a77a15d4f14ab2c18d4e09c252b713da36000eb43f83e630307d06cac64d3666a834e0927955c26713da20000eb744d6303668aadc4e3e6b⟩
]

def tableLRRRRR : Table Block := .leaf #[
  ⟨0x29314009c44ca25a12488e844a21410387f43cc1dc0e286e03261600ab04fc26012608083d01d40c505d82580fe06002980a403e000, 0xa289309388d82474d37922c84cf4269713c0d84869606c23f4ae270007505d66a07a820005aa81b088d2f247818006d3ff58e2781b4fb000f5d030003a7d6bb07ed2805ddd47f14801007bb28f03001dd749⟩,
  ⟨0x3511a38c986022e015d8a9050626212088883f01d90d3066c30e1620a184781fe0f20728368176091039016808e03a014807001e000, 0x103000d48da4001b5a35a003685710006d65d9e0f9a5bb9789b3dd75d85a6e7aedecfdb3c6d1fc1f6bf1947009de28e000c9a800169e136d2a35ab63b9eb400e8ea3dab2347eb40c6d2a3d0a585389b66814a4813d9a0068e04b66526124a1eee43f8a4a0d2e299331a49⟩,
  ⟨0x36b1a40cf86322d81618a804fa25a12608ec45421d0fc07b43b41cd0d406782f21660a084d822a0f006782a811207a037813805a000, 0x680800387819c44aa47576ba0003286191fa7cc9b340f290d8781db53f0f03a000e1f4869334941a5c536bf000fabc126ba2d84f6bd0007ad818001b5e35710a44a30d4ef670980067f2cf6b993f3ad0019ddb3dae24edeb4022a4ecf912704800d4ada6d1c01eda00200751d67⟩,
  ⟨0x4ad2280fcc7a03ab1bc0d4c6402b51500a4450a276132896c46c2150f8072c3301650ad84d82220ec06d831414407f02e00e4046000, 0x8308032638da8600434d5a7b43c018b5080074181a69d380822078988d905ed3c43311aa0bba787ea1fcd4d978d28d9cda7304505a32bccab0006d3c94a74f83166309388d592644cf0319c92a0eac00756ece66dca7fab947cd5ad39a8b28f1ab3a79478011000b4f0300036caeb4cd994e7634633321a71934ef230dbc700462400fbc6c4f12b7938b000f0c713b86c3706778d8b⟩,
  ⟨0x4f726b133094e4862148f686fa32e1848bc85b62b614189184121fc0ec87303521860b1850023a112077832812e0800348118046000, 0x1666da6060006dc8d6e86664dc5c597162b44bd88c8d6a1b4f6e75a2c64656877b0e9ed154fdd293ad08c8bb7374e654a7ec9495682667e9c001a90b5351ee9aa3ed354b7528e9ea57a96aa50d3e4080096dac5ee1c003901001db8f0fe66000e3fb13066003e3f7138fc003627212006c5e3fadff8bb800013178240056fec580030696ae0d10004002d55c71a5b8db4a001b7761eded6f8c5dbdb2558b⟩,
  ⟨0x41e1f70ef873e3751b20d4c6903291830b8455c2a113e09c849a228101878836417f08a04241fc0d905a024c10807902c00dc014000, 0x80442cab7e1c8192d421661e06c2da3c088190b28f4a694934e0900708e96001966e1c001931f56967c98c9686a984f6ef07e1ad81841c930b56004d723a7ae4c65ed380366759e11f283e2ce1eaf19a61c58d380035e280a000144cd128801da784d09add3331b5b6e9570fad008cd4b3e449c120039a369ccfd15b6800801e67d9e06⟩,
  ⟨0x4242070ffc7e43e31ec0f2c74c39c1bb8d5065e30c17f8b3c58a2a213e896846e2070f206d030816109884041c00b30480180046000, 0x912618e24c19bd24c26613a4ebae6eba0649cf5cbd6000642587486f5c9d60016da987f1480040076d2c3c0c001b68e25269d70b5d6cfb65e1ea01581c3d59e9ff580c3dacaaf387b58d5e2aef87abc55f2aeb879a8a4c70e9309a824830e92f9a7a42b0f2132f1677f2908977b3caf2aeb879a4caeeae987ab855caae956dc390b6ae187⟩,
  ⟨0x37b1ab0d2464831a17a8b4055629814289e84aa23011088483da1ba0d8062c2fe1720a8849021a10006d82e015c08903200c4046000, 0x5fee5356ad84f7140007ad818001b89b56000dfe5b12992e23d9d1a8964d1382400ba03357875800fa7b4930926fc5002352000e1ce001e9e06c394005d4c23389c00695ad74ab4e20036abef74ae27b848001d6d19d4a39181a7fb293f57207ab01a7903800155ff4f243000645389⟩,
  ⟨0x33018e8c205fc2ef1728b0056628e13b89804a222c10e87e03dc1e10e506cc34817f0ad04d425610607782480be04e01e80c0016000, 0x4451a27067819624c0c000dc8bad61880157216cf075d2e0dfa5308f71f8003ad34a2001dc79b3819857833e97068d298470006e37d68003185ec4003b8d3670300031846af05dd2c8a387ea6385879620b77e9d71a257b0fcd3c99a4a0d2e29b8b0007d5e09⟩,
  ⟨0x25f12408e445e20e102077c37c1990c205bc2b814709c84a023610a07f83b01c20d4057827012407f039018409203c0158070022000, 0x6147a5848f03012cf75ae06b994001d6800cf5dc4021b98b67386a90a65487e873e655fd0c3269b33541a704a7e8b84ce27b958001d6e269181b3145b89c7cd7773d15c668d33e449c123469⟩,
  ⟨0x27c132093c47422710307dc3d41db0e806ec35019e0c485f02d213c097847821e10407983481800b605382740f005702000d8022000, 0xbea08788354850aa43943805d06dace24c19bd24e091bf55d028781bc5156e270c91740402201b6ac334599f224e091834805cfe5b4bc47819424c0c000dce1ad9ea005b8e145a581ae6c00075b0271⟩,
  ⟨0x2a2145897848e23011288383fe1da0d386403001680ae054827a12608783f81de0e406982f01540a004881b00aa04b01a007c026000, 0x30d2d28064e1005d9fa856484e8c9c120f9b2ce2380031bc6ac0018ddc008d561cba5d2c6884487846818788d58626970e0d2c519f224e091834e3b6cd2e91e0630937488003adb759a3036171a506554e236e287⟩,
  ⟨0x2050f6878c3a01b90d4066c31817f0b9058c2a414309c04a422210207b83ac1bc0c705b028412e08003b017c09803f0138074014000, 0x39850f0306287c3234b9a67f14ae49714d198c24bc9a7324e09389324ad10d89f1342338a70ded2e099e84ccf0361bfa581b0fad2d0a87f14864343c0d0122606⟩,
  ⟨0x1fe0f387503861b60d3866831a17e0b585702a213e094846821810107703701a40bb0588268120079035016409803a018008402e000, 0x310cd2da087cd33f8a5724b8a68cc6124fb44e649c121c225e6cd0d89ea8684d30a24ba4781b0d9d2c0d86de9606c3d34bf92654cfe293d91e06a893036197a5⟩
]

def tableLRRRR : Table Block := .branch 14 tableLRRRRL tableLRRRRR

def tableLRRR : Table Block := .branch 27 tableLRRRL tableLRRRR

def tableLRR : Table Block := .branch 55 tableLRRL tableLRRR

def tableLR : Table Block := .branch 0x6e tableLRL tableLRR

def tableL : Table Block := .branch 0xdb tableLL tableLR

def tableRLLLLL : Table Block := .leaf #[
  ⟨0x2b11520a5c50826f12e086c4181ff0fa078c3a21c70d8069831e1850b7058427810907903941800b604881e80ce05a02100e004a000, 0x1429714864899bd3406089001c009002f6ead43627d33426b1349748f0362a3a581b151d2c0d8a9e95c4e000ed81acdaff6c00007558a469584fb5e0007ae818001daeb598a1694bc43f8a423d21e060e512000ed67ae⟩,
  ⟨0x23d117088041e2020f887883b01c30da067c3201860ba858029e13409484581e20e405f82a012207e035817809a0400198090022000, 0x7126086f534f8a4a4d2612606a45549a490a754984981aa4da0c6a97837c0084a784df0a24001bc635ae310006f15d9e2dfa5c5d74b99a1df043f8a4a0d2e29d331a49559132869⟩,
  ⟨0x2e415f8a684ea264129891046620e0ff87b83c21d40df867030e17a0aa852c24c111077035c1900b904a021c0e806a02b808801a000, 0x6f4ad680036d06c4013bd1f67e8693e34ae491834de860066af424da1ae852e2906955fa50011931a755b09c003bceb5b03000379c6ae10562001f46e4f190d2ec49a4938c9803dab613f068d8183a458000188000050f1494f429⟩,
  ⟨0x2a114509cc4b825111d089c4282090fa079c3a41bb0d5066c32017f0ad052027c12f08503941b20cc05381d00ba04e022007c014000, 0x18c6e97bf164f0ecc9c13bfab331344cae89c128daabb33038a9d94b66c519f224e091b34808d6d86b4ba47818f2480037ab6b6c8501076308ce270006da9d5db516d38003aac6b34b491e060062da4d583a29e06⟩,
  ⟨0x25712208dc44c21910607f43d41db0e787103661a40c785f82e21670a8051825e12207e83281800a904d02400d605e02a00bc04a000, 0x5dc87f14941a5c53266349228a24c24e236091d34de48b2133d09a5c4f03633fa581b19ed2b89c001dcff59b9eee7c0016aa06c65f4b491e06001b739d6389e06000f736d740db998003ae⟩,
  ⟨0x2bd14c0a344f426d12408f84322080f187303721aa0cf86302ce1520a404dc2240ed06402c413c09104201e00ca05a02100bc030000, 0x17d5000fabc1269a2d84f7d30007ad818001be9357a2710007767d9e63fa54450f9127048628991c4007d689e19e061d3480037cc6b400191b362000df2bb3c78f4ba421e852c298460d91389a820a1e6144e3b3a5849287⟩,
  ⟨0x3291820bb45c62be14e89e04c225012088d844a2000f707903a61ae0c485902b014b09303cc1b80cd054020c0bc054017807801a000, 0xef1fb3d7bb4b0300037e3eb4006546e2000df89b3d01b4b1667c89382470d324a4d9dad2f11e061834df76000eb40019b27632475f71b3846713800336b6ae6d59b10001d56667a5308f7d90003ad00066d1d8801f7d7ece0600366ced5c99a4a0d2e29⟩,
  ⟨0x34819d8c605d02d11600ad852626011d88583cc1db0e4068c2fc1660ad8534250105070033c17c0b104602040e006301f00d001e000, 0x71380064078b90148000038ad8374b42678180371fec5c06a94d3c1ba79966069d3ccb335169c0031dc00c61f1306287bf74012d6dfb8002eb422a21e13790c000dfb1ad000c7c722006dfabb39334941a5c537e9000fabc12d86b61380077e76b6060006fccd5e251⟩,
  ⟨0x4af24611a48884211ff0f6c7703931b18d3467c3281828b885b02b313907042200eb06f033417c0b305101fc0da06302a00bc018000, 0x6fb77b789dd6ef6b1350fb7b5abddb6fb313be9df66277d1ba9c4eea37d589a86a052d5801f7d0001c3ef230c612776f86ddb000f12002ddae2606812aa12d5d543005421d89be9dab76adaa8b6ad5aac6acd2b06ae1d0371bdea06ad34ed5b356b5453568d5bb566957b564f4fb8dce813571a79514001d3c99a28cf9127048d9a52f9209c69748f031e490006fedd6c80d2ef91846⟩,
  ⟨0x3d61ce8dc06ca3521968c305e82e71630a9450826312108844001e10eb06dc32c1690a9052024e11a07a83501940a903b0118046000, 0x32a401f6c57d2ce003950be76784c1921c001c09b5abe39bf71854287b336610095a736404ad20239b169cc300ab4e698055a402734ad2bd39ab6bbd001297824015e6a5800e64dac007323312d598ce96065e1cceb5b89c001c04b5abbbbb571819773762d755ad2c0df7e9f7e7bed00661f78dbbbc4ef737dd89⟩,
  ⟨0x32518b0c2c5f42d51600ad854e29d13c094c45c217100076c36c1a50ca06142c01530a304841f80d70650294136076034811003e000, 0x19127048d1a6ad100235a27067819624c0c000e085ad0006acbd8800381fecf190d2e31da50006b3ed3d67f81e6b70cd25669309381c0015aba14b0a4009ad5b56000d6ababe08ab53dcb09c003c0c75b030003817ead8635a76059b3ad32afcd9ce5bff47⟩,
  ⟨0x3ed1e40e8c6fc3591930c705ee2d21568a204f624811888303fa1f20e686a02ea16b0a304f022e0f206682a01060760288078022000, 0x5d57dababeaa8ed5d5f3578eac013abb74e007802557669e06aae2af5d5800354269c003aa1f56000d50fa76158003542550baac6b34a00455d1a7c893824001ab9753571d5d5ad0004003ab8f4f030005570ea6060007054d6800356eec6ae3c14766000d57fa7aaf3050d6b89c001ab635600755ae007eab8cd1a67⟩,
  ⟨0x25f12708fc46a22210988003e21e70e106c431817d0b805942a812f090044420c0f3072033416c09f04a81c00be05202080c0016000, 0x149a4c24c0d42a24d248a48930930356275866b478d35855623af6c4f66684d2269c1ec028d69e4770978243945b62ac7134b8e36971c8d2c0d562d5f7ab1b34e99b28d33669ab0000dd5e09⟩
]

def tableRLLLLR : Table Block := .leaf #[
  ⟨0x38c1b38bf050627613509784a424210e87e03a61be0cc85d029e13f095046c20c0f1066029c138085039017409403d017008001a000, 0x2aafcd38004001b70a0025466002800da700040026e10003a8c8004a878005d3c99a11a11a11a9b1b0a2acdb5b53e6143adabc30a0d6836a9c001c27b5b572d64fb170055c863cd630342a7953713aa66dd535900071abac7c048d5e098c7997de22fd594f29a1e852712628681513e29⟩,
  ⟨0x3b11c60d9c6843371890bb45742ad144098c4b223411288583e21e40ea872c3781870b104f42301010750314140094037812804a000, 0x15c06195ad002abe7d4d7cc004ea704d7cb5abeae609ad9f4f30dcc115b369dc4e000e185ad01bebe2d8c0d5a857c1abd8934927781002756c277c9b031a4b0017ed0000021e16c000eb4001a62762000e167b3dde34a066b1c001c2c75b57c5683b18460006abfd3d58157d6b4001ab8f4f57be157ad⟩,
  ⟨0x46b22310e482840a1f28f007363841af8ce865a3081788b6856e292136892042a1f00de86602e60fa076031c14407d02c00cc04a000, 0x6708003ead84e001e1d1ad818001c39b56000e6ffb100070e3d9e6fba5c389af0d6e1c2000eb5c62000e1bdb3d4074ba81694003b08c3b60d86deb4001accf4f59be1b3ad6e1aaf9aa034edca5501a76e05b93a9ff4f510d447a900caa1fd38002dd78060016d4ba01c00c801769f886a88405fd4d6aa02fea405ead535359156afababcab56d5ed0c000d6dfa7⟩,
  ⟨0x47822990b88123e61e08c404d625c127890846a22810d88343fe1f00e5869830215c09b84481da0c805282000be04e01e80c0016000, 0x645ad3c8b722e6b5b60c4235a001d9f61db41c41b5b55680c0001800800500040048010003000e002d64da7000800800605fdf000100bc005003001c010009c3d4a6833419a8cd866d336d0db4340a66de70fad6b61387ceb40018bef4f17e61efadc3d8001d68003a756c4017c3cf66000e1e7add89803f22000e1e3ad011a7bb8c99a4a0d2e29c3b0007d5e09⟩,
  ⟨0x5cd2e0166caec55128f14489da4e025d92208e246022b10c47ce3dc1e78ea870e3711a70cac5f62e51600a6c39c11d04b0060018000, 0xe2994a8009d4ca538e6ea71cc001f52000ca4e00169e918004c98752e27000632ed5c65b0fc0003aac7174ba2678196d88ca756001d94000b64fe87c3c2683337ef88ceb40036d1c4db2b0d6c9b68626d6b6c6c3dac6d696c5c3db2b0d8890003ad5ace31dd880200098008007801c009002355c002803580ea01f5535598e9c010003c013004400c0038012000c06aaadeb3000374f55b000600880d2006001a0010017597e9c00200b00601a37d2067008002800587846a46⟩,
  ⟨0x39a1c28dec6c835a1a18c806262e316c8ad8558295138092c4301f30e0066c2d013507a034415c09b04401f40b40350140064018000, 0x4e8cf036559a581b2aed2f34000b87f14800799c003c3c0dccc00162606cb034a000cd51a79ab7906d64add55ecac1a7957a545d3ca832aeca89a7950b276d3ca8393aca75a794e1ea2ce7f4eda0bd42da14a6fa7dbcedef1201bdbbe1ed144c2a89c1200fb75e2c00a94c34fe295892e29e46⟩,
  ⟨0x3af1be0d5c66430d17f0bcc59c2a913b09b048e23d10c07cc36418d0ad04d425011908603fc1e00cb05e02c411807402080d8022000, 0x575b5d8574da7002eb99d3d7855e5ea4008968b4f91270480032cfea6b40aedf5a00080072cee9e06000a59bd4c0d8af0003adace6bb1d8cb292cb4b3b2c7e9e74e96774f2ccce9b2ce69e57800334fe295c92e299331849001a574d4d649c12000cae3a93a608895b4001000b4f89a56d000b538267⟩,
  ⟨0x4502158fe07a63a01b68d2864a3021690ab4514267121083c3b81c70dc06a43281890be055c29a12808183b018e09403080f004a000, 0x805200dd3c0270064017a7a9264cad3ac65013bbe1a780c5e83814b4e001c3461f184714b5be22fb0e1fc3de21fb061e07081b74fc9fe50e278ffcc6c4d64b2dbe9dc1eac925b6d3cb68000cb63a79d6b31c49f14dd8aa984cc279d8b93ed740d3b07279ac00066e5d4cdc1a696965a7d3cb492d34b47a7969a5af96874e000d77fa9ae6f4d5d8d74fa7⟩,
  ⟨0x55e29e94689ea4c22088fb07ac3b11c60dfc6e43671a10c3c5d42c515109c846222710107743881ab09903541600a30380198082000, 0x3d73992e3b8a2c3e1d3cd93b74f273a79927669f40ea7eea06907aa67b0e1c615175c658135e1cad374e000d565a98e8e191d0aac753673d4d3a7a14b0a71354cb6726a6ce2a990001d3d9c55326a6ce1b37f4f2f999be1e5692f899b61ea594ba92bc000b4f03632c000eb40e1981b6203b6e7e0dc76db1b4b753bd4b553cf02f53e56c669e9e7a7c700ec02e05da79b4e8dec045a7f1480028ddc041a78191b9808753752bbe8fcfd499a7⟩,
  ⟨0x3fc1e48efc7343751a80cac60c2e11650a9c522247111082c39c1ad0c906142d414509d047c1f40d906502fc13c07d028011804a000, 0x4003c0db4f03000381aea71c700075b84d8009b1c714001d680038056c4001c70b67969694003039c4c0d30c41da3b421885de7fc380038aa6a714ed31899e954734b361c68f8decf970341f8cc01d1c1f1b7064b5b09803a583e3680d1eb40239a6cf912704800f35da79a7de2da002007cc96781800799ed2000e357ad⟩,
  ⟨0x3381908c306042dd1680aac4f026b12d092c48022f10507d43d61dc0e906b43101630a604d420a0f806982b811206402a812804a000, 0xcbf34b202a7818025c0b756e27000702bd5801d815001faae334699f224e091a34e0480046b44e0cf032c49818001c7675a000e03db100071d6d9e5d5a5cba34a400000c12b0fc6600070a8d3e14b8e8eb703dc0ef4e0046077a7c893824001c0e7538af0013ad⟩,
  ⟨0x3161840bec5ac2b114d0a3c4f026c12388503de1e20de866031c1690a2047c1f40eb05c02a413c09103d01ac0b2042015806801e000, 0x2286933001b822ea4045c1175710832f048e84cba464557042d3a2bc8aa6083a700f3200d6b89f1fe00075a01d6079b1818039c0eb56000e119a7000f08ad5800384969cd258009843e121aa7497827457981e94f25e2895982697306d29c9af04f24b⟩,
  ⟨0x2e416a8b2c54c29113608f045a20a0fa877837a1ae0cf86383041710b1052c26812708103ac1c20ca05a829812207c0328138066000, 0x30930360cf8376b41e55383660cbaf000c5e400587d94c0358bc6271d14e0ee31f904d094f429ad530c9a6118e0d3d1240c463b484cb713e42c000eb693f68c0d45eb2c1a953629aba553454a998a997206b1c39425380020016097a7⟩,
  ⟨0x3fd1ed0ed470436c1958c185a62ae13d896048421f0e1067c2d814709103f41e60ce055827811e081038018c0a404301c809002a000, 0x11b4dd161c002853f4e8d800030a769e36386854a149852e144d3c2ed0a969e14e85d6151d3c2870a2e9e1428512141d3d7bc00387af7e1bdf1efac488d223b08d54e1a9eb82469e30b17ec5df273c4c0cda7c11b048d4800782269c001a6ff4f03646f8206b402518ac3d0a4e24c10dea69f14949a4c24c0df8aa9349217aa9⟩
]

def tableRLLLL : Table Block := .branch 13 tableRLLLLL tableRLLLLR

def tableRLLLRL : Table Block := .leaf #[
  ⟨0x52e284935896246221e90b88463fe1ec8e987383771b68d206462c614b0a004ba23a105072434c1900b584e017e08c0348118046000, 0x162080674eb0e2c3f00c69e582579f4efe92c288f3ca88ea369c00885ab4f91270480030b3ea645c76d75a00080070b2e9e06000a163d4c0d92e8003ad914ddafd8bf8d0af2c108edca70e9d69c0031d18e261ebbd86fd9febf0f603fd8e1eb6f602fd861dfc047a1d348e874e001c97627257868d9a186d3c2cd1b2c30ba7471d5fd47215fb859e15385391d0d3c2cd26b4303a7dd3d73f13ba2ae7626bcbbdec66f76bc98c⟩,
  ⟨0x47d22d112c88041d1fd0f2878039d1bc0d546302f51628a104be23a11488103be1ba0ca85c029613408783a816e08703e8160066000, 0x8d6661f224e09000eb2b13ad5d71634002003d63e1e06000eb1b12000e505add6d6b4323c61b58f57fdff87b1758d713c5ff7e80470eff22d5c007c061a78114010d4801f0226a788d2000c085a99502814d5ca7f024eae53e80ef57016404fab000603cd4c06fa680da03bd4aabd019e9d55a5576032d3d56c002003c3c0d936aab7ada022534d5bfdcb4e406da7⟩,
  ⟨0x3cf1d50e1c6e234e1958c205ca2c214e89e84da23d11988403c01bd0d806342d414709b044c1c60cd05502500e205f0290120046000, 0x6554d816b4003728c4dbe70d6f8b93e26e4d6f7c4e862e298cb89e85f1800185161e8aae9ab5d6f2dc561fc52001b786e230f035bbb75389004803f5e387000ebbf13e660076bbb13aed006e275d8002c48d9a75e3b9ac5eb735d2001c3eb2b0c001d6ce275a386d686b63125423e19a06ca3000bd6eb9f5b58b⟩,
  ⟨0x52e29194009a04ad245119c88841f20910147f43d51d10df46b431d17d0b5454a28212908bc41419f093040c1da0ca05380b8046000, 0x3133fb2183898603fc00038785fbfbf1201cd9061eaf97cfc3ebdf5f3895b628e1d3d0a585389a8dd5b5752b69d1b8000e9d6d3a39b536d2b6861edf36fbb87e8530e001d09e1da25ea075c4acb8a5c330e00fde1e1c03000ede161c003ae7c3e568d72eb56f3a6916f16c200073e4e8d3d3ade4725d346b78360e0031f2546969c003802c4dff70d724b97e27441706c3addab75ae5ad81533c0009c8d466e9e136af757f89⟩,
  ⟨0x3561a48cf06603131840b845882ad14e0a2c500263123087c4041dd0e7071033e1920c385d029e12a083831814207e01e806801a000, 0x2852c298460076f94e26db4020064fb600329d4cb4b4e696934e09cab3e95e0b9549f20c1329938039249c326a7ab57891e060cde9e7d5b09e1367b26cb50001d686474f16c6f0f589c3d38540f2d7874669ce7aa7074ee78c2161d6b95bd96b4a8ab4f0c57fae1e852c29⟩,
  ⟨0x3171820be45a82b31530a5450c27b135091446622910d07d43a01c40db86482be14809184641e80cf06002d414807f026010803a000, 0x46c89c120084fd9ab001b87b3c99a28cf9127048d9a67d69fd75a5d23c0c7924001cbf75b3e0cfa3b18467138003688eaed109fb0001d56cf5a59dd8001d3c0d3ec5a19ab9ef800dd3e449c123a699f127d1d680033dc8011a781a7b7002753b981127⟩,
  ⟨0x3341878bc05c62b91578a4050c26112508d844a21410287803a61c60d386202d214a09e846021c0e905f82680ea05801d80c0026000, 0x23af2d600591f47f148010072368f030029174981baeb000759ab66961b51b4cd258693093d728017aca14b8a400c30a6009851520030ba98eb61356184e001f5bbae818001eb6f5800401421a9084f7426d03a6ba0f69cff3329e639e94e09e5fa2965e489⟩,
  ⟨0x28f13e09944a824711c08ac43c20f0ff07bc3c81d30db069c3361900c085902ae13207f83a01b60b6056021c0e005e02a00bc04a000, 0x5348ccc418f9a67f14ae49714d198c24be9a7324e091a34f642dca1b13f23426a493d50a7277138003d7feb3afeebfc001d56b03a56138007d7deba060007af9d66af7a52e91e06002faf5d740dd798013ae⟩,
  ⟨0x36419f8c685ea2c21558a504ea25011e88604061de0e686f035a1880bd85b82b213a09284181f20d406502940f60560188078016000, 0xb656defd4dbff6f96ac2c6b7ef4f65c8002160e9ed8ed34276c90031c68e2397657ae0c10fd948023ae06e53f64e017ebb4cd258693093d918017aca14b8a41d958026335481d1580963256184e001f637ae818001ec67580040145fa9005b7616d001ebb0769cb226bb44e09⟩,
  ⟨0x3b11d10df46d834719e8cb062a30817c8bb45bc2bb14589d04ba23810a879438418f0c2858027a11a0738308156086030812804a000, 0x611c001ce275a3671000f386d9c0c306bd2334ac27949748c611c0039acc5e6ac002002c56917a5d2174b1e6bfe7a7b187fcb0f62f2f47fc70fff0001e1c00158b6220d3c0cff766ebadb6217af136ce2f5e26cc40a82e05d380037006a6df8d35bef6ffea6dfeb7db536fd69acbcb65b536f85b2da9⟩,
  ⟨0x3811b68d3065230617b8bb459029814709a448823710907bc3ca1c20d7868431c1830b804141f20ed070835015e094037812804a000, 0x17268d374b9967000e2630e5c7c4b62e923c0c4f255fbabc6c800536987818001ce875a4efd5f3b171380039cf6b402d9cac8c0c017ce462c3444dd0d69a2704e248bc838001000b337000c2c300134f08d88d88d0660007390d68079b11004738dd983219c6eb4001ce335b930000fb1⟩,
  ⟨0x480238913086a42b20a0d5469632618089e84ca25512008c841a1ea0db861c2e81660a985002360f60630294130073027011003e000, 0x3093dd68003add0cb4b03685fa57a06e577a0de8289ba26c7a11e7f833e27e7ac00017a034f036786000eb518fc47762016805c177b12391d21384f366c6017e9c19153018dfc6a9fa182eaadd34f8664e661c018aaac9cbd3e19002a9cac3866898219f244c5c89ac358a3d5d619585eaf11385d4e1e1e7c5746d6e2700073afd693db5886c60627b2b0ed5801b9d49⟩,
  ⟨0x2cc1538a404fe26e13088f046220c0ff87683a01ab0c305842a412d08e03dc1da0de06382d815209403e81b00ba0520208070014000, 0x73e9d9f575a59334941a5c539f2800fabc13a270023ab61380079f0eb60600073dfd58003a24ec400bcf7366611c001cf6f5a3071000f3d8d9c0c692f43ed28f99d85637a6ad0f74b1467c89382460d3dd8800bad2e91e06⟩
]

def tableRLLLRR : Table Block := .leaf #[
  ⟨0x2dd1628ad054a29a14489d84c825a12588984262090f9078c3a81af0d1064430e1760a084702160e606782a813a078030812804a000, 0x18eb1151467c89382460d389a34ba47818c248003a00eb5b348c0dc78697624d249e3e800ed5b09cf0db030d1ac004c9000001879fa8003ad1b3880039f96cf8e5d280039f8eb5c62000e7ddb3e37f4bc766973ec00075a000e28db1⟩,
  ⟨0x26f12508944361f60ef873037a1b10d1064430e1720af852826e11f088841c1c40d106202cc15009304401ec0ac04101b8090026000, 0x9a14ecc0538e0367037816000eb748dd2e3489309388d592644cf036392ac3f43a782ac5e43e03d43e50d0368300146b464d3666a834e0926555c26713e820000eb607563037f68b1e338728b⟩,
  ⟨0x2b51530a6451a28012f89304562060ec86e032c1860bb05982ac14509a04942280ef070033c1840b505201fc0dc06101e00c801a000, 0xb125c53c8ce2901ebc8b4f4489001bc6b4803be13ebef0c068006cf7860356908864ca1e531a6b1a8b1b0b1bd0d27c695c923069d0dc00cd5e849c435d0a5c52386b8e2005bd9bd1ad84e001e85dad818001d0b356c31⟩,
  ⟨0x2db1660ad453c29413e89c04b222610c88203f21ee0ef86e835019e0c785e02b414e0a2047c1f40ed064028c13207402780b801a000, 0x724be5974bcc0b1e06e9f596e2703ed9758800f40056aa4cd7067c893824d2480e95856b4e64781a924f2ada5020f1b1e91a060007455d6d5d6035ec5c4fa290003ad017aafed8c0c02ed5f9aba69c37cd3de7de4d9ef34092cfe29⟩,
  ⟨0x28913f896846a22210a87f43e61e00eb06c43341890bd85882aa14009584181e60e506902fc14c08d04101ac0b804a0198070016000, 0x10378a2004eb8008f143585d21fc5211e10f030ac8981bc49000759cc1697c4cf14300c439f0cd604a906153802d5936ac3144cd0d28225f144c108bae0411d782417f659e4b3912b962d2f2d7a53935e09⟩,
  ⟨0x261128090c46822710d082c3f01e90ef07343781ad0d006543081770b68558298135094040c1a00b9056021c0fa05802080bc04a000, 0x19a67f14ae49714d198c249e289cc9382478d2f2686c4f66684d2269713c0dccf69606e67b4ae270007c5dd678b9e2e8003aae65f4ac27000fc59d740c000f8aface6474a5d23c0c005f8a7ae⟩,
  ⟨0x33c18b8c285fa2e616a8af855229c13b89b449023910a07bc3b01c30d7068c31c1690a2047c1d80c705c02b413407502100e0026000, 0xf24800bd650a5c52063b3268e4062b3362170c27000fc8ad740c000f911ac6c6401f6063b400bf030da738ba5b2654cb5aa704c952b2b44ad5353501d7fba7afeeb55d3d66d5fd56a9a7ad84019d3e449c121ba26ea9ad835a000d6b800a69e06ad68013d4ca087⟩,
  ⟨0x29114209d44c425112208dc44820f0fe06ec35819f0ca060c2e21670a8051825e12508704041b80a904902140c0056018808001e000, 0x1a663492ab22650d3429714864899bd3406089001c009002fcc6d43627d33426b1349748f0373cba581b9e5d2c0dcf3e95c4e000f939acf26fc9c000755cee69584fe4c0029ae818012f25b59a6692c349849⟩,
  ⟨0x29a13a898847a22810d88303fc1ed0f0073c3801b60d086482fa16e0b2050425c10b07983a01aa0b004681a00a203e015807801a000, 0x1d42b5780a44f6caa9767624a7a149c49821bd4d3e292934984981a41552692428952612606c1d80271a1f22400f839c7ec2243c26d0512000e9e7ad000e0d322000e9e1b3e7f34b59a1df043f8a4a0d2e29⟩,
  ⟨0x2c515b0aa052e28c13f89684a022b10a08103f01d30de065c30015b0a304842140f3074034415c09d04601fc0b404f01e00bc014000, 0x7126086f534c2661380d3e776ba06019fcecd601a6c99ac6a46f39c091d701bac7f39405ed7019ac7017fce3d703da9c046f38b592a23261c964e098565999bf010e1e4cd25069714ea20003eaf049bc8b6138007a866b606⟩,
  ⟨0x3a21be8d606122ac14489e04ce25811988984321fe0f186f836218c0c105742a012b08303ac18c0ab04c81f80e605801f809801a000, 0x20868127530484093a9aa56094871a0a67a2b4f54a41270e2cf51052bd13a76787a2b0f86692b349849d50800ad5d0a585209bbc2c037685fa620b5ecd84fa9d8007ad818001d4e756c3105bf536d982c9e956cc035583ea680ab6b4035b84d7a0d5dad42704d72b30bada674874eb9c0685cf866⟩,
  ⟨0x37d1b60d6c69832718d0c345dc2cf1550a744f026e12488e04262020f987a03921a40c906202d214408f83e81cc0c7051014c060000, 0x186692b349849d59c00ad5d0a5852023dad2c00fb4a5faad429ee584e001eac1ad818001d57b578271a137235d9c599f224e09003eaa923d450f1ad2f11e06003e9a93aa98003ad0006873d88f45aa86cfd151bcf7a1a39b8741469c79482ae1cbaa6a03bd3fa67d2187f4c7a3fd1d87⟩,
  ⟨0x4a624a918887a40a1f28f007203811ae0d186422fc1768b8c57c29914789a846e22d104078c36018b0a703fc144094037812804a000, 0x178d372861750c269e18986174f0c443090c1e9c00186034f0c2fa9dacaf0d6fc00f87388fea5c337aeaef61b0f7c3eb52004e1eba7a48f03432bea2eb218100074f034325ea16ba17f00055d4d3c0de9fe1ddae0f4640ad387ce1e84813a7b3e28b5d3fd4ef3f83f001e1e8067d4979e60f8002d3d00afa8d038bceb07a000e9f886000688dd3eadb4456b4001a2674fab5d135ad⟩,
  ⟨0x54d28d13d498449d247120c8bc4392030ff07ae3cd1d40e0c68431d1750a6c46020b0d7050c24010a04f81e80c603e0158078022000, 0x18ed001990ce9f218c83b4f90a642f906e9c008d3b74f9127048003a756a7555c7cb5a0008007a7469e06000b4e6d4c0dacf0003add4f71ecd8e9d5a70e9c7a6e69f4ddd37f4fa6e69bda6de9f532d4d3535d4db53bd3e823215451974e348721fc535a7690a1ebd3c527145485174d681f14c69e292897a289909ee99d03a297d3800684f89a10e1a25c896e286909228f90f624ad380030ca6a618fd3432a006e9c3144c19a8cdec69⟩
]

def tableRLLLR : Table Block := .branch 13 tableRLLLRL tableRLLLRR

def tableRLLL : Table Block := .branch 27 tableRLLLL tableRLLLR

def tableRLLRLL : Table Block := .leaf #[
  ⟨0x4a024991c089a42820d8fd87d83c71dd0e546e034b1940c145de2cc1548a1046a2100f586e030a16009d84201aa0b003e812804a000, 0x61480269738b000d2e317ec6681bb96138007ae2eb60600075c3d5b0c54b1d70367a035e4bb300075bfd6d2ca95d91000d30b134bcc352ee98389a6052eb13ad4a975abd3ff4d0d56b55553134fa84a987a7d4254c2d3ea10a60a933a7525f5bdd41b4fab1a97fa7d53750fd3ea17aa66a1da7d433516d40b4fa8069fda7d3eb4ffd3f74fa7de9e9a76e9f20dc83f52006e435a7⟩,
  ⟨0x3c71de0eb47103631ac0ccc6002db15b0a444d82010ef06ec3301870bc055427e11a07b83901b40b704381e40c605202080c801a000, 0x426c48e0036bd1ad0006adcd3e26aa6eadad3d59f54d55b3a7d78c001d6dff156b6c4001ab474f569d5a9ab59456505a8b5812166d64d5cf4f4a5a6c6269b54d8c4d35e9b3898534ce49000d33b134c6c30003a84e9e98b4c6c5d828781a9ab4c3c58006bd14c4c3c90d4c2c3619a4acd261275cc002b57429⟩,
  ⟨0x3161788b3057e2b01510a44508273132096846a22610087c83d01c30cf05e428c13b08b03c41980a704801ac0b804f01f00bc04a000, 0x28d29587675eb8025a7a149c49821bd4d3e292934984981abcf0017526924002af3752612606bcfc009d680035e4ea4007bcf75f5e3000200169e13578a000ea4001d7d75a000de71b100075f2d9ef09a5af02bbad39849f33719a6923c0d80155bfab⟩,
  ⟨0x2d81598aa4508275133095c4742130fe07c83b61be0da063c2c41510a004c42400fb076036c19c0c1056021c0e806702100e0026000, 0xd3fc008d8c0dadd800dab3c8ee12cc23803504ac01a7c03956e4da581b723d2d2600c9e06d6c0299d5f77bddf13c1fd0d27c695c923069d85c00cd5e849b435d0a5c520c0ab95a28d9d99bc8b6138007b076b606000760cd5e0291⟩,
  ⟨0x32c1838bc059629813989904a223911108604021f20e686e832a18b0bc059c2ac14909204641e80e706102e012606e02480c804a000, 0x7751d4f091a6dd3c008d4800fc230003a7001b845d498470dd161b0d15ba3e9606dd1f4a611c001d8fb5a1824401ad8ef670361a8b9334941a5c53b1b000fabc13b9d000fab6138007b196b6060007630d58003b9aec4001d8b767b99e95c4e000ec57ad⟩,
  ⟨0x25912608b440c1fa0f587783981c20d786142dc1610a704fc25c12108784141ec0ec06a830016c09103d01540900390160080022000, 0x1466013eca920470a00c9f11af23f8a4ba478183044801f34dfa95c2f6974cccaa1ff24ca99fc527b23c0d512606e14b4a78267818001e14b53c27e94011e1434fe295c92e29e4630925669⟩,
  ⟨0x2ff1790b8c5aa2c415b8a9852e28d137097c48023111388203d21ca0d006542ec15109904341ec0d705c02380de06202a8124054000, 0x50a4e24c10dea69f14949a4c24c0de1002d24d24802f05493093037690134d003dfa9201fb3d3fbd8010054784dde800d24001d9df5a007b1544001d9d367c64697baf73a380bf5747f54e2c0551c037b6a3d0a585308dec80652400fb100547⟩,
  ⟨0x31d17c0b145762a414a8a2c4cc236116081c3c41bd0d6066c31817b0ab051c26c12908e041c1c40cf061027412606e02d80d803e000, 0xe35fabc6c31ae000b550371ffa5a48f0300318d4eac003b4e01661e0600076a1d680038d2ec4013da7b67e8693e34ae491834ed340066af424da1ae852e2906155d8620046ccdf45b09c003da475b030003b47eaf214880036156cf8e3d2f8c02547⟩,
  ⟨0x2fa1708af055629c13f896047621610387f43b01b30d486102be14c09c84b823210607b83b01b60b6050825c10c07c02b80c801a000, 0x21ea1d63875c9da78534ce49f03cf93f8ddff9d27007c99387975dbeae923c0d5d25769abae24001d3c0db5e8003adae16bb0d8de28985913824fb1568821f224e091d348f3f8dc6b44eccf03149a606dab8001d680038d96c4798daaf66e27⟩,
  ⟨0x2fa16a8ad854629013e89a849222410c88203ee1e80ed872437e1b00c585d02d415309704341b40c305b02440d806201e8090016000, 0x2edbab5bd75d851f5344cb289889121ba262a8042d6007f1bdabc13b06b9934de47f149748f03184900078d5d5f1a7a581b8d0d28003c6ae9c00626ed644d0003c69eab8dad2b89f6d100075a449f197b1818894e327572712e9889274e09⟩,
  ⟨0x3691a50cfc6402fb16e0b2057a29e13c89b048e22610e07ec3d81cd0e0066c2d015e0a384d825810706a02bc0ec06b02f80e802a000, 0x61a51e13001eb3471d5b707d680185b498554684c0061551c42fdc0b5ae270007700d6c653af5c6068cb75cb59c47007d6a96e270006bddd58eaf5ee0005aa81b93bd2c099e062306bd7d5d74e0019177a7aee03fcd39f500080145cd9e134230003b76eb48b7af43620d4a7⟩,
  ⟨0x33f1900c145d42d115f8a98536276132891044a2110fe07a43b41c50d906442e014f09d04641f00d706602ac0fc07102900f803e000, 0x39da5d4786416130485c2407f9d300837ffeba7048201b5b6afddcce911d5670030ae9309a8d5caa90fd130a9a07953dfa2639c086d71cd0ed6b0018e3b4c39d980061eecf0e50e76b87201bb5e09019870b5b9b800c6cd9fccc007afd27abd1bab75ea4c3701347⟩,
  ⟨0x53628894109be4ba258122c8fc45922691008423ee1eb8ee87603911af0bcc4f420f0cb059828612007e8378172094037812804a000, 0x587ce6b62e270007748d687739cbec6060f23395d5b09c004ce4f5708ce270035fa962bee71e000eab84dd2f5a00c9e0677d5e696b478a05a4869f5d05a375b25e875b162635d3d3eb9eb462e6dad8af41ad8312fae969f5b0d7a17355e7d896d6bf4b3d3eb5faf3ae69ad8af3cc4aeb5da5969ed1252b29d61ca7368ac4da24a7189b44000b120069b527576d5bf57aba8adbabd5d356cd5eb7c29beaf55714c353ab40a61a9⟩
]

def tableRLLRLR : Table Block := .leaf #[
  ⟨0x3c11b20d346502f5130092c47022910b07b03841b40cf86442f81710aa052426c111082037c1740a704c02340f405502000d804a000, 0xebf60d3af1ebca5976c37a7d9374db32ecb7a7d987664d96b4e1940652cc9ebfbaef4eed1128d29b842f47a7aa55487c89814dfea26abd8eac7470034a2aed1ee8606254f50ce42a9c120dfbb2b84c1e21f7570f235b6660007375d3e6ed9d26b51143e449c121922739f16375a2786781878d2000ee97ad⟩,
  ⟨0x47e22d91448584091f20f347503991c70df46b032518d8bd85d22c41488a1c4e025312488903fe1940a284481da0d605a824009e000, 0xba01c5c0dbc40003ad000e7eb22000ef0bb3f80b4b86a8019a7c89382464d38bd69b7ad00070d0001f4f0362e8002ea5c4e000e9adabd39f4d5000b55037c95a5e2c0193c0c1c669a1ab894f073d3acffb87ee19b8ac4a4b3dae67a7dc1a251dc5167eda934eb1c0341baf69c001db6353b6969a74a752d3b4fae59a7c1acb30760369cd3baff8356bc8597ec39a7⟩,
  ⟨0x3311860b9c584271133096c46c21110387883821ae0cd86302fe1700b2854827e135089040c1c00d305802000ec05f02900b4014000, 0x1721dc8ba9001ae35d3dc2372069c004008da8d4b7f801acf09a13003bbd26b6e2ede8f5b036f42000eb781c06ee356a2594449c498337a49c128a22e0143c0c011d04e2ce23800f40f8b71380074138bd0268200058a81be0dd2b89f78d00075a006d01e4606⟩,
  ⟨0x3c01cd8de06a62f61708b445782a714809e44d025a12388d041e1ea0e286a03161800b184f82320f606c833c154095045819808a000, 0xd1537cad68007b9787df21dc8d68056000dc5400c86e400169f856cd298d760a97ec53cd8ec98d31923e699a1a4e44b6289b9a4e24d5dcd172ceaef03382b57e80692bf3c3e95e090f3cd95ea20d0beada16d43f57a2601162f5d0064f035cba1e3eac74ccf03001bbd6eb785009ed600a6dc6adc0401567⟩,
  ⟨0x38a1be8d2868031b1660b0453827713609444582110f687483801b50cd05d42b414b0a0049420c0e206c02f416608e037812804a000, 0x3c52000ae45b2be9e065c83656d4ef09b2fe1d4000ef2da784c000ee99a7df8f7d1d6c2600ee20fbf0036dad086fa0e0c07ef60e01dfc27710684c01de41f7d9113b5a08dc41f224e0900ed613140d95340203d9c1e06016c613030003be7eb4c944aa88003a0569f407df335a000e8afa7⟩,
  ⟨0x4111f90f3475438b1b30d046382f71690ab4510277133096446822910c082c3cc1dc0db86a830a16e0a484c81c60a203e812804a000, 0x647524001e0275be09245e4400c81a3f00c23f6b780576235bc020003ad0006fbed88023c00ecc001e0075a0065d9fb19334941a5c53bfe000fabc130e6b613eff0001eb60600077f6d5b8c4001dfcf67f80694001fedf67f7fe95877dc2378ed9a57b7d3ee0fb9eb0c1b8fe9d881dcdb4ec3eb101b9ae9f65bd95f4eb926cb3a7⟩,
  ⟨0x3b11bf0d9c6ac34c1938af05602a014a0a204c623e10c87d03c81bf0aa051827012a08583f81e60d4057824010207602b80d0014000, 0xef1fc19eab910d2c099e06d1d5728d580020206faa0010007ad18009a7846b2c6a46c460007820d6e8dab90ec4001d12b4fa27f03bada0c6d1eb81bd6ed62bb729e40008004001ed69a7a21a886b21a48c94a4f99a130018ef47e048475d680892147c89382400c92a49243c758d00200e45d1e06⟩,
  ⟨0x4ca252923890045b21b10948284071f10f5c7643a51c00dd86a232c1838b8857a2980ec87383521840b082c013e07a037812804a000, 0x1d30353a4f69a0860007847d6e96e1026c64cd25069714f084003eaf04f28a0ff6ad84e001f07dad818001e0f356000f281b107e3839d98003a57e9f4ade0e35a00e692fa7007d78a00797fd5bf76afd6d3788df98015014713a834b4f098001d2d34fa597067ad016f6db0e00d2f0a00ced54bfc2df000c2a13ad780200076f07a7a534e8fc002eaf048007a3e6ac001de4b4e000ef21ab⟩,
  ⟨0x32618b8c105de2dd15c0a4c500256126089c4201eb0ec07143741a30bf05bc2c815309703ec1e20cc05f82680ce05d02300bc04a000, 0x2353457269d7b365a0c000c2f7a7e19617cd68f08700218bc8d1e06017b861d681d2c701ab85fd6cda89649138245ea65de3600669f224e091934de4b808eb4001bc58007d3c0d78f800ba971380038066af007c02c002d540dfaee9648163c0c02d600dab⟩,
  ⟨0x43c20b90347d03c51db0eac72436d19e8ccc62027b134095449422510007c43c41bd0c506002b614f0a104941fc0e70690320146000, 0x3bc6fcfd8c0c7785f9bab86b03df0f91270480faba6efe6beb5a00186883cb0f03433c1e389b3e6cfa2aaf716dbdc7addf1b821d7f7276d3c9a896451382400bd3cf57d3c800fa7b4930927956002352000f4ea001e9e06e9cc005d4c23389c018be571748600cab94ed2ce0a9e06d39022ad5ee05b718002b996bd23ccf01a0010006002727fa7⟩,
  ⟨0x48523010b48463fe1ec8e987063501998c505ea2cb15609e44de24a11588303da18208b84181ea0d4057828c10406102b80c804a000, 0x260ec2fabbcb8001114f4f030003c53eb44bcd84f622280fa78d269f5d7b5fc4ecb99a54909a7adec294c82909498970fa8f1122543da380389d470006dea12734f030895c4deb400ca2a3cac9474d94f1e28ec84b210cad162380e632dbe269d7cedcb770ee0e04411f136eed3e99a4b0d2003dcb673b8afd7d5e230657725a400bb8ecf031de7c46eb5c4e000f117ad⟩,
  ⟨0x3b51c80e046ec35119e0c245fc2d91638af454c29c14289ec4c823f106079c3681810ae04a42080d106002c411805901f0064014000, 0x35899a9ac93824001b12752d1468b108001000b4f09ac450007525d23c0dd95e9606ecb74b037689a5b0dac3dd3d87963bd86ba7b0e2c48d3d86f623d863a7b0e2c76b0cb4f61b5829a7b066c35b04f4f60d5373a7b0669b8b04b4f0a699c93953826fa704c72a604db4e019b41c133d86b57491e06⟩,
  ⟨0x28e13d89b04c423d11508143ec1e90ef07343501830af051c26412608984181dc0e4068830815609403e81a808a038014807001e000, 0x5644984981ab42002b5a19224008ad035ed89fccd09b44d2000f1c1ad0006b3ad88003c6eecfb4bd2c5099f118b943f8a423ba1e060d912d8abb40d2f681a5ed674b17a1ec4d00334fe295c92e299331849⟩,
  ⟨0x288131896446820f0f5074c37c1ad0cf064c2fc1590a204e824a11607d83b01c20ce054825811207a036016409803b016008801e000, 0xe428003d6c0c000f211ab0007ba0d88003c82ecfb9ed2d2729f60cf912704836aa4022ad6b5a306678186a553429a705f53cea684c1ba1f8f6005f5b29a1e852712628681513e292934984981b05449a49⟩
]

def tableRLLRL : Table Block := .branch 13 tableRLLRLL tableRLLRLR

def tableRLLRRL : Table Block := .leaf #[
  ⟨0x31f1840b8c57c2ab14c0a344d0251116087441c1e90db06b030e17b0b7056c25c11708503941800b604882000de06201e80c801a000, 0x7aafa50007929d680954df6c6ae44b6889c1200656adabf4734de8d800fa7b4930927b94002352000fa2e001e9e06f454005d4c23389c3445809c1a800dabb8cd2b89f91500075b596001fb181ab4400375726692834b8a790e001f57827ba5001f56c27⟩,
  ⟨0x26912b092c47c21910307f03d21d60e286b433818d0c105c42bc14c0a104cc21c0fd06c030416e0a0048821c0f006e02480f002e000, 0x9fa2e13389f94700075ba8a4606cbd161821c74d6cbb9151867c89382468d323a34be47818e248003c9c6b474e2000f26bb3f57b4b037ab7a5848f035c4b81b92e00075ae31000792bd9faa5a5⟩,
  ⟨0x2a21488a004e226412909204722140fe87cc3b81b70cb058c29813f08d04401d60d606502d413408c03b818809e03a0148070016000, 0x360d73269bc8fe292e91e063092000fab1abf55b4b037aa7a50007d58d3800c40dac8800007d56d57abba561390cbcad6b60621efd4dd58332a79182894ed030a9f68688354850aa43c439d2aac64d3666a834e09⟩,
  ⟨0x2d31630adc55828b13c09b849a24011488744201ff0f0872837a1980bb85b429813509584181ca0c004e82280ee06402880c0016000, 0x419bd24e090098aab5c428781a29c166d6c27095d9708ce27183587a60595ed1e95c4fcbd8003ad886003b8c0d1360036bf8034b0372ea000eb6200126e3cb98003ad4ce6e2b2399a265844c44890d9131200216b003fd61d5e09⟩,
  ⟨0x2b51510a284e626212c090446e21210187b03c41bd0d706242c814308f041c1e80e506d031c16009804701ec0e204c01a808801e000, 0x18a2e080a2bdd6d2c099e06f63197037346000eb6928fbb9a581b99f00075a6944073e67367cce0003ad0019d2b88003cccecfdc8d2a3687c8938243844e93acd08ec878185444c0dcc78003adc45da357225b4449c49⟩,
  ⟨0x26912908b43f41e50eb87103581990c505fc2d815709f84d4244118079838019a0ba055827811e08403581680a0037015006401a000, 0x15fc69abdfafc34f5edd7bd5f7e9c18553c432f2873ab08746d0f912704870897a656847643c0c2a2260600079bad6ff0919b912d9224e24c19bd24e09098875f099e06850e75b09d30d708ce27⟩,
  ⟨0x2a81498a1c4ec26912b893447422b10a07f43cc1d90e006c43401930c085dc2d015e0a384982380f7070024410407203080f004a000, 0x8a133e232c99fc525f23c0c19225b157bb5a5f7734bf11e974cc1976e7fc932a67f149ec8f03544981bdccd281d900b9e060007dccd4fb93a50004002000c0d9f72b4fa29ae31a95cc000d7fba9afd74d5fa57f9a9⟩,
  ⟨0x1f60f3876039a1b80d3067030a17b0b2056828613409184582080fa07583841940b2054025410c079036018009e04001980a002e000, 0x1b13d0a684d302a92e91e06f8034b037c05a581be19d2fe499533f8a4f64781aa24c0def9696cc0a1e06a290fb91e852c29a463e34b627c33426a134fc15a5⟩,
  ⟨0x29414509cc4d225212288783d01d10e2067432616c0aa850826a11d08984001b20c2057827812208203a81a00b204401a80a802a000, 0x81be72d2c0df3a695c4e00060f6f320f641ed0003caf9a74ac2783d2000f9d03000183cfccf98f4a5e21fc5211e90f0307289000307839df18e96d043e699fc52b925c5346630923dca9cc938241ad52f3668⟩,
  ⟨0x2b114609dc4a423a11788703ee1d20d686583061700b1854828a138094845820a0f807583601860b0035817009e044019808402e000, 0x15700013ad06254800f56f6bfe1121e13782890007a44d6800356cec4001e90767f47e973343be087f14941a5c53a663492ab22650d3429714864899bd3406089000e0024005c217e43627d33426b1349748f037ce5a5⟩,
  ⟨0x2e01698af853228413b894849022310707a43881a90c2057c27412307f03641880b7054026811207c03581700a403d0170064014000, 0x7148342ae9bfa9476634cab6138007d32eb6060007a63d5c00ac6a4aa6e367d300003adc081223d2f0003ad0006a53d88003d2decfce0d2800351fe9fa59a9035b824a7a149c49821bd4d3e292934984981a81552692429952612606⟩,
  ⟨0x31f18a8bc05c62be1548a7c51426512c089441c1e90db05d42d415f09d04b42100fe06c82c014409404181c80c6052016807801a000, 0x40d5395481ab7138003d43eb6a1963035222ac001b90b4ec2b0006a77b90355e83696a72b8f34f53754e371de9c001a9bc00200774f09b1374f40a96b584e00df4f1ad81801ba9b35602054e62e7a21aa86f4349f1a57248c1a7a6e003357a126d0d7429⟩,
  ⟨0x36b1aa0cbc63030b1730b2c5822a614789d04ca24a11287c83b61c60de065c2c81580a184c024a110075831814207c02b812804a000, 0x19ed1001faa8d9fa55a5713f54c000eb78e0388c0dc600c2fd25d28079f07709601d341c001acd356000d6660e5eabd1dd2c20a9e0606f2b2fd5d4aa0008039a7e468055493e89c12970ab0006e4fd38021543eac031ea435a000d485a7a912a45d5b89c001ea335b5335485b1⟩,
  ⟨0x25712108b44302090fc07ac3b41c90d7064c31016d0ac053427012108b83f01de0d805d02b413808d04101c40b404801f00bc04a000, 0x4e12a41854e94cab854c3869e336d9a6b0d3e50642fc82485e091178a17110abc12340abb6058f03770bd0b71381b8cb296c732b4cd1867c89382464d3547334be47819524c0c000f557ad⟩
]

def tableRLLRRR : Table Block := .leaf #[
  ⟨0x2f416c8ad453c28e13b897849c23d11608743f01eb0ef071c3601890be055c29a12808d83d81a20ba05181f80ce05001d809801e000, 0xe09420e768da960e071b272b1b26264c280b9eeb1b0cd256693093d700015aba14b0a44dd6581b8cb8540ab13b2c27000fad9d6c0c000f5afab61880abd6a6ceabdd0e7672a2b26249648003545ea6a85d36f7ec7d7054dfa2a40ec63d6a6⟩,
  ⟨0x31f1870bf45dc2c715d0ab452827b1310924478215105879038619e0bc858829213009284301e60ce05482300fe05802700c404e000, 0x699a4b0d26126167800be650a5c5203daec09e57900f5bb0238df0c2700070b1f9d030001858bcc0102de7901c9b376d0001d9b769f8a697674dd3a5b0e9c13a3aeec967d73801157dea5da9aa174e02c3f27f1480201c3b278180286e530342b35db3cc⟩,
  ⟨0x262127890846222410b88203ea1e60ed073c37c1af0cd06242f81720ad854427412d083034018c0af05002580de06202c00c404e000, 0x2ee43f8a4a0d2e299331a4914512612711b048e9a6f2459099e84d2e2781bf37d2c0df9b695c4e000616ff3216ec2de0005ca81bf2fd2d24781800bc2d9e6389e0600290b5b9d0342d30025ce⟩,
  ⟨0x30016e0b0456029f14a09cc4a4225102078438c1bc0cc85e02ae14809e84b02120dc06902c413c09104201e00ca05a02100bc030000, 0x195a8030718da6134e696934e09b5db7cb5da75aed9ed52d36d72ce0036af675acf56717cd00c1e065baf55b176ea2dd67b7500db3e449c123a69a61add31a0036e00116781adb8026d3a421e852c298460d91389a820a1e6144fedba5849287⟩,
  ⟨0x2ed1718b5055e28c14009cc4a422210587c03cc1c50d9867030a17a0b1850023a10e08183a018a09504581a009a040019809c024000, 0x1031e490007b68d6ae4690391846713800dcddad73547d000e2bf9bd2f14030781871ae5ad746834d8ec98d31938262e166509bc0b87a3980370f912704806eb09a6fd1cb1a001a3700230f0351b02e3891c5c20f429614c2303a2a6d706⟩,
  ⟨0x2ce15b0a9453627813489784a424611087f83b21b40c886082ba14e094847c2240fa07103401860b904a01c40c005102300d4024000, 0x207f71684cf030043b3f8b6c4f89a91b918001ee0b5a001efa64400aedff67dbf8003ad002765b22611c001edf35a6944003ede7670330ae075716076f14a847c3340ddb90017ad5d4522f171467c8938246cd34865d1e34ba47⟩,
  ⟨0x3101768b785a62c214f89bc4ca24211b08a440c1d60df06ac34217e0b5856029a13808a84181f60ea063825c11a06a02e80e8014000, 0xf0f00230f9127048c9a7c63e1dc68007c32003c3c0de17002e26119c4e001f09e2fc25e16000e2a08b7176143c0c025f0762e6d44b2489c125c0abec880330f9127048c9a7c3bdaac68007b18007c3c0dd8b002e25c4e001ed2e2fb4dda400162a06⟩,
  ⟨0x2d71610ae054e29d13b097849e23e11608544161f40ee87483761a40ba057429a13608f83f81d20c605182380d6046019808002a000, 0x9d99e062934c0d0e38000f32001f14c238c1acf64affc74b037ff3a5076d97826c8165ffe7a5a0981203d7870301931d8d19fb25f456481f5f65afda157dcb5e5e2c0794ccc5f692afc474b0c5f20ca2ae9e6e44b6489c1266aab⟩,
  ⟨0x2a414b8a204f626e12f893847e23411188183ee1eb0f007443701ab0c2053826c12908103e01a20b905382740ec06c022807801a000, 0xf14ae49714d198c24be9a7324e091a3496b00ca1b13f23426a4935b22e771380018745cc87430e88000f2a00c71584e000e1cf73a0600030e7399004b8a5d23c0c002e1cc73a06872c00279c00221caf3174cfe29⟩,
  ⟨0x2e816d8b4057c2b11450a004b223e10b88183ea1e60df86c834a1900ba858028a138088841c1c00bc04b81c80be04c02080b8022000, 0x613e26f3c1984e07a21e7f3a0603cd0f379801e9c1c0ef43cbe6699a4b0d261261e3000be650a5c520ecac04f72240e8ac12f6a30c2700070efb9d0300018779cc0080bab1200b7765da003dbb26d39644d7689c134d2320c0424f9a67⟩,
  ⟨0x2dc15f8a8852e27a131893045e21d10907d439c1bb0d686682fe1700b1854828e13a08984241c40cd05f02c813e07803180f004e000, 0xa44c795d2033caf048cb474af0596494aac70060494ffa0d098018064e080a1f47383a44f10dbca27f64c839c49f33729a613309e1ef8043e740c01061eef301f953c29a1183b43c3d70039ce07953c3d50075ce06d53803287a9cc⟩,
  ⟨0x30d17f8bb05be2ce15f8ad454829514209d44d624a11d88684162000fa87a03a01ab0c30584278117079034416008b0250100032000, 0x114340a89f14949a4c24c0d8a69349254693093035b15b0db4e24dafdb05bdb13e26c4cc2980b3c52d5fc37d6e4693e16a72339f23533e3e465a9c893232d66463911eb3a80016cf177d4f67000ead3d38c734525d9e000e9e068842aba39b998ee9⟩,
  ⟨0x2af14d0a404f026e12b090c46c21e10a08043ee1df0df06742f816d0b1054426010307c83601800b404981c80d0047017807001e000, 0x50999e068119c581a051f16c543f8a4341a1e069091303407fe28075bed9edf009acf6f601367c8938246cd36f56f76d001b76004b3c0d6e800f69e18887a461a93027381c880b9e06170190754070e2ca687a149c49⟩,
  ⟨0x37019d0c4c60c2e515c0ab852e276136091c44c1c90df06742f015309704442080f5074036c1980af05002540f006001c80b8022000, 0xd020c000f1c002c082e4b89c006e92d67037460056a81bf1fd2dc8000d9e069ad0b9ed5802f3859e68b00058c7632268ad99b4f89800795ace72bf8f9ad39abc7bd697b3b20e9e8c0324fe295c92e29933184901a8894d649c1200d0b2981d288a040100a4f89a8100a538267⟩
]

def tableRLLRR : Table Block := .branch 14 tableRLLRRL tableRLLRRR

def tableRLLR : Table Block := .branch 27 tableRLLRL tableRLLRR

def tableRLL : Table Block := .branch 54 tableRLLL tableRLLR

def tableRLRLLL : Table Block := .leaf #[
  ⟨0x3731a70ca46082df15e0a9850625311708744182010f0071c3481740a9852424c11308003d41a00a904e0234100074033812804a000, 0x174538269cbb09ac74f3954e59a963be737d380062e9898b361a46d1b7c3c6f646b1b6c39751391e9e54d29069c120077816b01dd738006c4f8b07058981b98aba9001b3c0cbbab11e2ed044bea89c120074d8fab001f02338fe295892e29c46714ed404ca4369fc9f53f93000fa9⟩,
  ⟨0x2d91678aa852e28913b098c47c23310707a43881b80d486102f216809a847822210207b039c1b40cb05a027410c07902a00bc04a000, 0x1034e6d6596ac3c44c10cfda274e44ce62008eaf04801f397eaed47003f576a3000dabc46348e001da87abc12326bb502ca3000755fb0e9584f292f118d23b8ae7157eb3a5fd434bface95c4e000f95dad9c66d33d8c0d38c5a63ab⟩,
  ⟨0x26712108bc44421310287c83ca1d40e286ec3501990c305dc2da14809b84482060f6075836816a09004081c80ce05402280b802e000, 0x2fe756b65343d0a4e24c50d02a27c52526930930354a89349229a24c24c0d6b0d989ad1f34d9856afebdb13e19a13509a7cd400075b6985979b13c8ee12f0487c8b6c55fb6e97f6fd2fee3a5⟩,
  ⟨0x30817f0b645682a914a09bc49422510c88103e81dd0e306842f81570a604dc2080ed06b030415809d04901f40b003d0198078026000, 0x818001f4275b6b2b559b184c0f8a70007d05d6cee1676ec6c0175298fc8c0eea998c696d992d65326ce60133576728009ab000ece4d5e0906c5580036708005aafe674bfcbe9689d56476a7c8938241e15366cdaedad043d94f0307a2a61306e87⟩,
  ⟨0x3141808bb85b62b61538a6851628012d892047c21910607a436c1a90cc06242fc16d0a404d825811d08983b81920b104602080ba000, 0xf0d122ea24394380176d06ace24c19bd24e09001ada8d5e028781ada56b0f56e27000eb07176cab580006eab0cd1667c89382460d36d63575ad2f11e065093037a22000eb6cc26ad363056f8b6b48003a781ad92b6175766400a4004800392c4eeba7⟩,
  ⟨0x34e1a08ca86262ec16f8ae856028b13d095447c22f11208343d01ca0e006a433e17a0aa84c023610c07c83981660a904201b409e000, 0x185222932c0d165c5365b9bd96138007ea2eb6060007d43d5e89c6dc7e0476622531f224e09031d93692808bad020e2b1e06050d93030003e9beb4001b47f6201f7a69b3e4153faa69d51238a1c001b3b4044d3c0de97004dad87b98efa16d63d9d0039005393c4f2ba7⟩,
  ⟨0x39c1bb8d486823301908bf05de2e21608a804f226c12388f44301f70e906b43101630a104741f00d304902200c605202080c801a000, 0x7261d3fad3bbf6b70cd256693093eb28015aba14b0a402348ed6003a456b8a9edfc7b2c27000fd5ed6c0c000fab9abd1b001b8efd7c156cf6d5db5f52000eda7a7f55f6d0d6e301fed9cc739d2b4f3d7cf65a9000ed0dd38002d6ada0400de9e06f542d2ad6e19a4acd26127d4c002b57429⟩,
  ⟨0x5d62ca962cac853f28d14409d24c424f91f88ba43c20d8fd878639e1998bc857e24611087f039219609c84501c20ae0448158066000, 0x1e3a9dc9e4034f03455171f5cee399dc1d3f1ae000e9e0671ed15379d70568cba7cfe9b4cd3ee9ee5da76a366ecfb37b2d69d95d9ab4c068d85e9e033d405526d3abf74e7e9e9f0d8efa94ae32c21dacec25d3e8d512735f8c9a69dafb80bea38d3d055c04d503419405d60f53db8cc69f19ac65f4f8cd632da7c667195c6534f8c8ee018cbe9e9e7a9f2c19a7a2029f7934f97165bda7cb872ddcb734fc45ede196d69f816e2434fc41f02bc47e9f3eb9f7c4c044d7ca3aba7⟩,
  ⟨0x7913b61d50e6670e321175ca3043d20d10106fa2f6170099c4301f30e706a43081730b104f424c10106d02dc10805102000c404e000, 0xfb53b38979c5001d36b3fb4e6856b55888cff6e6034086808ca6193432906540ca76f8e32aa00771cd0033fcd01dcbccfea204d02d3ed3990fe469dc99fa0003003163844e71ebb8d7d913c01a7b1bf9030068005776b69bd7ea3d689cbb213f3f21ec8cfb9277ff4e001e746279c386f2e2c6cf418002e400017d7df69877f34e000802de5bed47c7ffa0b635ed2eefde9fb9b86f2d7913da878fdb1a7c17f06bccdd3f225b50782baf9f1f9a7763758dd4eb17ac6ea758cd62b53c8f3bada7c534a59a4001e38f53c6f698001e3534ee3762adf3000bdcec3f1de40cf20fa7e415dce000f4f4467a48f0338fd8aa9cc⟩,
  ⟨0x34a1a00c7462230416f8ab052828113b89484061f50f0075836218c0bd85a82ba138096847021e0ea07002ec15c089038812804a000, 0x206eca80171308ce27000726ed5e4db91b0003aa89b1c5b850f030031934eaee0700100010008d6cd3cd0d9f966818001f6f35a0066915b19334941a5c53edb800fabc130e6b6138007ed9eb6060007db1d5b8c4001f6bb6713038a00122b974c001f6b35a000e4a7b1⟩,
  ⟨0x3441918c585e22d01630a9451026512508e04361fe0f8873035219f0be056c29012308703a41ac0c305c028c1000710330154060000, 0xe21287b5b89c001f7a35ba11c3d7181b41f872d600cfd271405bf71601a4c268b060062193a89124adc4e000fbbbad67edbdb230333f2de98bd68d77b486c87f75c02cd683229fdd500975b37225b244e0932855f67001187c89382464d3a4de47bad000f65c00787⟩,
  ⟨0x44220e8fe07a63c81d68de86c434a1978c505e02cb13e09844a823910f07e43bc18f0ae05042380ec06c82d81260660298108042000, 0x2e9004fb577478009ab000ee8ed5e0900cea1774580020016aa054f16053f14032b83cce6b0b8a4a80307ba16de8d5db7607e5c9e09bd0d1a700cce1306603cca13310342686604ff57469f42edb403d413eb922861d3db66077d0c1a700cda0e09d5bbbab70cd931a0587c4d1370b11b62ee1428dc5800f0ae7f59e8a93471a7438546d7c444616b⟩,
  ⟨0x3661ad8d1864230f1828bc05962a614089cc4c023310787f43a01c20d386542f415f09d047c2220f606d82d81360800328100036000, 0x3048332a4024babb5a5e23c0c0c4a9f890001d68003754ec401ef88767e4363a87a5c74091a83806951983dbe0c01b8c6aa7079a18035084d220d47a7c269d4684dbfe0a4eac036984cd0c12b4426ce1184d0fc0a1eae934684d628d09a2d5e136fb02b7abb7d4152d5d6a7b0b⟩
]

def tableRLRLLR : Table Block := .leaf #[
  ⟨0x33418c8bf85c62be14c89d049e23410c881c3d81b90d5867431817b0b6051c27412d08c040c1b80cf05502800f606a022808001e000, 0xc6e4e138cc4c27119184dd9a0ca6aeecca2cf577175d97abb804007d3c502d0700cd6131a8304e6707b7f0001000b4f143650d86692b349849f8e400ad5d0a5852464ab07155c6285c3bd96138007f196b6060007e30d5e89c6e17ec1f67f16dd13ad8b33e449⟩,
  ⟨0x5552a594989ca4d9266926890a45221690207f63d61d88e9c7042b514809744702050e906b42f415509a03cc19c0b30478170036000, 0x10349f7362eaf3b60010001000b4f48dc8d303cc62000e9eec2cdaa9e763a47e9c001f98b5b273cd7bb17138003f2feb676293c363034ec32776acd5b3578d4f3568d593574d5ce1f0d5f36d8db4df94db7e00f4fcd1731ba7e68798ce62f4fccf6e41a7e67771f32ef4fccdf33bccc69f9a1e6674fcd07331ccbe9fe5300075babc973715aab4c939c82ddd3eb8c09f69e7d3483cea7b3383dd3d060822da7b826e9d052a8b6d3e531d09⟩,
  ⟨0x3e61e28e9072236c1a38cd06022f71690a4450c27312708a44222040ef86e832a1740a784a820a0e006a82c011605802000d8022000, 0x2ffc086d37fc005690fd1336b4dc7ab9b56518d58f6870006f0b941f4f037d04010eb6505996f57200074f09832438003f3f6b65039b336309850f6669a78010d4cd6e0086a400f9adb537cc015699ad800ad4801335aea65069ad7572828009abc120014a07ab00066acd58003355cef7aa8037c581a4fe9aef572267⟩,
  ⟨0x47622890b080e3e21de8e2870035b19d0c646082e314a09bc4942250f907343501830af052c26c10907f836816a0900358118042000, 0x1119b39f5367059cfa9b39acdfd4dad16716ac003b38f4e000c2b9586e9e06fa8ed62d6d65d675a6e90006cf5af66a63a78b3d6275d45a8b0aafe21a78552b5dd3c2a766369d279bc8b4f43f24f1790e9e6ed00f3533768079a99bce529d5804d3bfe9e7a43873a9c04400701ecf037d2200a6b66b42fdb533669809a9300e6ccd4800d365ea66db9b37577e204369⟩,
  ⟨0x4021ee8ee07263821b88d9067e3341918c585e22e71610ad452027812888e43d41a90c205e02a614408f83e81aa0a203e812804a000, 0x11fb2766000fd93ad003379bd8c99a4a0d2e29fb10007d5e098735b09fec0000f5b030003f5f6adc62000fd77b38a49c5000319ffa7148f8b6afd76b6b1d65bbf8e9ecc9b32ecdfb4934e000da45a9e46001ad21d4d4490006d1fd4f775bca6afbb9b5c75766bda60000e9f791eedf5765fd9b200569c001b4634ff55da9bad⟩,
  ⟨0x57428493a098a44c21490187c23be1cc8dd86a231e17c8b1852626e11d88583c61a20be84f02120ff06d031c14406102b012804a000, 0x7a3401777b401cf3661a17d1b4fa8b2d169fa2259f0ef4500296c38033e6b3e870cf3bd5a7ef676d713db4ef5e27e4978b356001eade1fee275675b0df870e262f8d4034f17be9ff17169e2f4d41f4f179ea0c61069e2f18bce2eed3c5ef177e9e2f68bba2edd3a1a718be9fa0b7c4febfd3fd7dd053e25d0ce9df15df9353d0bbe45f5e7411a7002e37f00074f03000ff696b432438027f686b6cb00004002b5bf4f09a11becc00075a000ef81b1⟩,
  ⟨0x3d01d58e106be33a18a8bd85bc2b914b09c449422510687b83921a40bf85c02ca15409783f01e40cd06082d011e05c02200bc04a000, 0x7f0ad580018669d10013f07d98b27f83eb4001fc1b5b73c00d46197f14001fc0f5a003e68647f0100075a0006299f44001fbfb6713978a006dc51c5b6fbf35bb59eeb7a7df28008d3e449c123269df277cad68003be28007a781b7c300175308ce2700077e5d5efc9be18003aa8ab3c584153c0c0196fc1ab⟩,
  ⟨0x38a1bf0dc869a3281818b7857229413787883aa1c80dd86b433e1910c185d42a012b083039c1840b1050024c0dc06301e00bc014000, 0x391a118001fca35b8610999b100070c6d3e187f92eb4001c51f4f8a2fe47ad0033152d3a52b15f1080080100180200280300380459e0cd066833590d643610d943750c3027e31adc55ff17d6e28bf8b6b400e0ca38c1bf8a6b64cd25069714fe20003eaf04c3390015cb6138007f866b606⟩,
  ⟨0x34e19f8cb063a3131810bc45c02d11620ae455028313b094447222110788143ec1de0e306b831212c09083f01ae0b204d81d8016000, 0xd248a4893093035d1b478d3126f6c4f66684d22690007f3fd6b8c4001fcf3670eff8b0f038ae923c0cd8aa1dc7161dc7161e7f1401dc5d74e0045de025b8c7a00a0013a784c000e16ba7c31ff30d68003867ea70abd361558676a400118d84b0000aee9000c00dd3e26⟩,
  ⟨0x23210e88403ea1eb0eb073036819f0c705fc2e815f0a504d425611608383b01ba0d205f826810e07a035817409403d0160074026000, 0x32154fe290700d4f035c12a60687c9c5a8e53ec19f224e0906954c51ab460ccf030d2aa6453460c0a78d4d0983743feaa00beb65343d0a4e24c50d02a27c52526930930350a89⟩,
  ⟨0x3ad1bc0d4c65c3071688ab84fc25b11c08203b01a80c285e02d215c0a7850023a10e081838019009804681a80b204401d0088030000, 0x138800000c30007f89d68097b01ec4b3ec3e0e3967c87be5a238f671b44e1ece9670b4461eceb66dc3d9d6cd987b3a59aecd587b2ad952ce587b3359d2ce387b3300330fe295c92e299331849003598b135927048006cbf8981d288b2d800400587c4d65b00162704cf4266781a1f8f16068811c5⟩,
  ⟨0x3151790b3458029b14189ac4b424911d08544101fb0f507643641a50c005d82a214408f841c1c40bf04d022c0f805502400a403e000, 0x1b3ce27fa900075ae310007fa6d9c407e2c40ee2e19a4acd26127fa1002b57429614d49ac60d71d8440bf6584ffcd0007ad818001fe6356e310007f95d9c40ce2901fc7cecc0034fbc3a9f9fc96b7624d249879417bb96c27bd800e9b03001bd54b⟩,
  ⟨0x35e1aa0cf06323041670b04538275135891046622410087783a21ac0c485fc2b413709084581e60ce05582200f206e02580e8014000, 0x2068839c5000db270e0c2ab0116008220ff29c4e000ff89ad00391063a303001b882dcb8334ae49000d5770f55fad862dc4e000ff77adab0d6b723036428ad5eac00355fc4d55f0d09800355cc3aab3fd9eb6d0367dc38022cff87c89382400367dc4bc1b4002003b3d61e06⟩,
  ⟨0x270132896048e23b116087c4141f20ed072c34c1970b905a02a613b09404542040ef06d02cc15009704301dc0d405802700fc030000, 0x84cc274d35d2318476158c91aa228716227714c23ffc0000eb4c288073feeece06dc155c451e2e668996113112243644e082ac007c42ae5e09d835cc9a6f23f8a4ba47818c2480018843cb883fc5⟩
]

def tableRLRLL : Table Block := .branch 13 tableRLRLLL tableRLRLLR

def tableRLRLRL : Table Block := .leaf #[
  ⟨0x27312608dc42c1f90f607783961bd0d5065c3001690af051c27012608703d81ce0dc06782dc15009603f01980aa04a01c808402e000, 0x400a0003cdae658ba1d8129c22e7d0f4668a183844f90ddba26dc44db38cbb41197824158659e4bc512a236716238f15d25e09d15c45fe29e4bc512a230716231714f0d782684d711638b034610cb⟩,
  ⟨0x36d19e8c685ee2c71578a8052c27311b08ac43a1f60e986b033618a0bd855028e13a09284401d20dc05a82ac10807702800ac026000, 0x1699b415a9f0e001b51e1c00369cc58006d376a4c5449be2e24781802f697c58006cf206f00161e13590d007c000f34003692c880118039d3c334959a4c24c0190015cba14b0a49cd560e4ab90060023b2c278024000f9b0300018021cb618802b801bd30007addd9c480e287e87⟩,
  ⟨0x2b71548a58512278134897c490239111084c4121f20ed871036a1a50cd060c2b8145097046c2100fd074030c1480900368128046000, 0x450d02a27c525269309303530ac934920a8b24c24c0ccf23340cd64e262cf6c4f298d09a40164c0380003cd3571a30a2b1e4d44b2289c125ccabd5f96a2d3801f4f49f3b463ceda7f0e001b4761cb47c02ce6da0ed5187⟩,
  ⟨0x35c19a8ca863230c1728b6c5682a7140096446c22710207ac3761a30ca06282e212708e04401d20d005482400d2056017807001e000, 0x80d4001f97825f4d6c270007019b9b03000180c9cb618800780c3d311b9209ba6001b9a61dc258006ea78701c875831c003751c544ffe2e247819f70dd600101b5ab9162002c3c26e46000301539a037cf100ef0147a60370e7017301439a1ba1c00bc04ee6ca687a149c49⟩,
  ⟨0x30116d0b0456e29e14889e04ce24e11c88904322000f987983a21be0cb85d02ca15a09b84481c40d805a82380d2056017807801a000, 0x10228000f36adf5e303713dbad84f1516eb8b7343c539ea9553252a9c124748eb613e19a3becc1b21e03d0017e68022e9b87c89382400376bc4ede000d6b4002003ba461e06000dd9f120006038f3400edbaf621b21e037001be6c99a4a0d2e29⟩,
  ⟨0x2b81508a4850e27612e88fc46a21e109080c3d41df0e3069431a17c0b584b824211408283d819e0c205982a413406501f009401a000, 0xb8218f9127048d9a72e69da06b8363c0d543b27118d2381ca3af0480d23ae470805d5143f8a3467eb3680040f16f000161f8cd266d89349262978008e5b09de26c0c612c0036b000001860006047736bc05e3149f8ae27⟩,
  ⟨0x2fa1708b3856a29414189d04d225811f88b44462140f6875035a1950c585cc2cc13f094047820a0c8059829011e07a030812004e000, 0xf61d61821c06f1d776181cea8c33e449c12346907b67697c8f031c49817c00079a0362f1000302efa714af8b034528e2b89c000c0b7e6e4b6d181b6565d770a04904012478706a54d8a6ae954d152a68ad1d74220eb001921b3891f8157cd⟩,
  ⟨0x34a1988c405f22de1618aa04ea267127089c41c1e70e706fc36819b0c105842ae13e09a04341e80e306802a410c05601e8090016000, 0x25539ce8b289ae703198e4a8642e16f985c2a030bd8c4001003f4f24300df39c061c0e1e680e7b9c06840dfe6847e39f224e0901f974fffbbb4040fddcf03017aba606000303579b8df2f1f37307a8781a2006f9b91e4a0e1d09d91d4a061c064dcfb5b6ebda0575e09⟩,
  ⟨0x34b1920c5c6142f316e0ad455028113b89404722140fe87b83ae1c00d286282de15409c84782060e806682c810a06a02780d0032000, 0x410a0015cba14b0a444c658196cb91f204abb2c270007040f9b0300018203cb8805a20927bb1b303d993aa99a7564f466c9aa8ce16f48e426091c84c6e0709a8c0e16448c424df1884c5cdd098bbe217162a42cd3068a28a0ee989425e51284c45e30988bde17fdf0eb⟩,
  ⟨0x3491980c906162f21700b5855e29f14209a449c1ff0f987603681930b6055427c13108503bc1ca0ca05282380fa064018808001e000, 0x344e9e4606a174d002ba4b847818033c124e6e56319e2d0b93d1a172641c2c16c03f8001de5c0d1d3c231226d072211e6b07001892b3c11a1121cd037d8f46eb2dc4f0458000f366e5a88c0d6e2c42c15fd97f4e06e326c5cd60b6e9d96c15b01674f86692b349849⟩,
  ⟨0x3541968c485de2b21470a084e226211f889042e1f00ea872c36019f0c705fc2b014b09f048c2100e106a02b414607c0378120046000, 0x829401db9b66b742c32b7c5c3800af7019407ce1c03939341f11a0cd2b9240037bfc3c6a370b713c13f0003cd90c6223034c22d0bc334959a4c24c1380015cba14b0a4130f858061d0b92445e9fb2c278262000f9b030001825fcb61881078259d35e83bfcd985e2efb87⟩,
  ⟨0x36e1ab0c4457a2a814b0a044e025f12808fc4441fb0ef073c3501810ad054025211007b83981960b005182200da05202180a0014000, 0x22b6f159dcc5c20007158b8ecee00008002000717078f01b66eec1a142cd8c695b34c4491934c4acd4ac000c5b8e3b3111cacc23c15c0003cd000316c3a2087e0acf4e06043b16b79747f0e901fd74fc39b430683806cf09933022cd09b281e136401424d24dab510bec041b1e06⟩,
  ⟨0x27a138093c48023311208643f01e50ed86e835a19a0c105d42c81550a504e425011308483e81e00c905e02540fa06502d80d004e000, 0x20682d019b59c498337a49c1200d0516bb050f0341280bdadc4e1aa2dd47a2b8cd1a67c89382468d3d06d13833c0cb1260682e600079ac31000f05c3a717578b15c78b03416d0003cd618880f82d5d3⟩,
  ⟨0x30717b0b9c5b82cb1520a4851027912908ac4081fa0f1074c38819d0c806042ee16a09a84741ec0d105502480e205c02480f002a000, 0x4599f224e091934c7d90023cd2f11e06349200060d1734000c7d4e8800b833fd381a3e8717624d2498f9e001b96c278c9b0330ac00c35000001871f278a00060ca734001c8a76200060c8f4e211f160d004ad60c0a787916e27831800079b036b1⟩
]

def tableRLRLRR : Table Block := .leaf #[
  ⟨0x3691af8d1c67431317e0bc85b62c314e0a244c424a11187f03d61da0e686983361740b3850026c10f074030415208202e80d8022000, 0x10345cde2b89e0e38001e6d506d181ad0165c5cae2c1c20003cd0c52200060dff4e2e2714000c1bee680528b65d19334941a5c5306e4003f2f04c5e1000fcb613c1b50007cd818000c1b3e580018bb9d1000306c3a7176b8b06bc000f36bcf22a76306b4000f3401aca7b63ba69⟩,
  ⟨0x242119889042a2050fb078c3a81c90db068431217f0b6051426411b08503f41d80e106502fc16408b03a01a80a6044019809802a000, 0x2c5374a6ed4d4d8d22991b43e449c121ca25e895a11d90f0306a89000307779bcca47890658c9a6ccd5069c122f632e13389e0e98001e6e126d181b311659c473f35b89c64d79046a⟩,
  ⟨0x30f1800bd85a22c214e8a38506278135894c4581f30f107443841b30c905c42a013b09884281f20ea06482700fa05c02380f4030000, 0x184981b2fa01df5a7124075cbe35ed89f13626614c491e280548401cd0190170188dcb3cb1a560d31124e24c4f44edac00635acf1371396be4153c0c22662f572e14d339255b633ecead919cad1670035b28ead31d56bfc153c0d60f91cfab29ca47⟩,
  ⟨0x2b213f89d44a0239111082c3f81f10f006ec33a1930be05902b012e08203e81a00b8052826011207b034016c09403b0188080022000, 0x1004b5bfd3c0c0086b7da91de98fe5331fc0963e449c1236690243313d681e6118f03710ec9370887a460095940151c0cd6a003478180b801ad14a8951c594d0f429389314340a89f14949a4c24c0d8a6934925469⟩,
  ⟨0x5c62dc9648ade5652a014bca3c50f27f136c97049524411848744302048cb85862ad14b899042a1d40c9851023e0c202b80c801a000, 0x1c4f0924000f37d2fe88c8c0d9df3d0dabb634ad1a62248c1a7cd7e6ac58007e8587f3479a716e27000308f79a5df2282746063cc9140b97141538723e07254fe41335aa580004e3e8ca11f142ad2b3e1a1171dde50005f177c54002e3e5873d3d1670d69ec31881a6b0c11a7d357f8bc5966dfb60b4f6bf6f5b36f5b03a7b5fa6ddb602d7dd3dafba494db96bfdaf9a7939da7ed3cdb5820e086547151374c69ece1f302f38b3a64e5c35764fd3eb87ae0e9c014d7074fe29⟩,
  ⟨0x2cf1620ad451c27b12a092846e21f10908043c01d30e106cc3501970bf05a42be1500a3047c2240eb06982ec15409903b0118046000, 0x426308f09a0000f343548800384cbd38183245c6c6e2b89c7cd7e01c1eeae334699f224e091a3484753b44e0cf032c49818000c255e6b0c4071c252e9c6b9e2c6b5e2d29a524d3e8ffa861fd1df4ff44e1c003e8ec3fa2bd178b⟩,
  ⟨0x29414389f44ac23911788203ea1e80e0869033417d0b28548286136092846821a0e6065830414c09103b018c09603a0168070022000, 0x83340d0a20000f36e0092630342850003cdf1922e27850400079b6d0073181ad9006571d1f8b9e224f24c99a18d3099c4f09dc000f34210688c0c118242c1894e128142f9243e371438d1a74cd9269c13706b⟩,
  ⟨0x26e12989244582140fc874837a1a80ca86002e21640aa852825a11a08803cc1cc0d105b02a413008903f01bc0b404501d80a8024000, 0x2a00388c0db68032b8f29c500d360e052a152f3650d52148a90d90e5c6ab3893066f49382406bda5730a1e06bcc3695b89c1d156c6652aa4cdd067c893824d24da92b464ccf03409a6377714e647⟩,
  ⟨0x271131894848a23411488304021f40e686c835018b0bf05b42aa14809b84a023a10c07d83981b80cd061827011606402600d004e000, 0x1f430c9a6ccd5069c1204f152b84ce27858400079b6709c4606e101195b89c7cd7573d15c668d33e449c1234698f3689c19e0658930342b10003cd19388001855dd38e6bc58e67c5713c2ab0003cd⟩,
  ⟨0x2b01530a4450827112208dc44c21710607ec3b41c80df06bc34a17e0b7852026012607f83a81a40c504f01f40e605201e80a002a000, 0x81bb5556e270cd172de02401d6ad334619f224e0919348064b4db4be47819524c0c000616df34e28896285b1d38ec1c581a16b0001e6cc0ac63b0f15c4f0b48000f3408a56ae303010cac5ae60d5214aa90fd0e7c8ab⟩,
  ⟨0x28b13f09b44bc25312108944262090fd07c03921ac0c285b42bc13709404041ee0e206502d414008d036017809e04201980a0026000, 0x699a30cf9127048c9a67903e5a5f23c0ca9260600030c039a00ce73100110bf7a71e2f8a611e17d8001e69851004b0be3a703460aae3c2f1660d5214aa90ed0e0192f76bfa18e24c19bd24e091be55d4287⟩,
  ⟨0x2e516d8af856829c14909ac49c22710607e83561950c285c02b6148099849422810707b03ac1a80c905e02540f006e028811004e000, 0x103536014a6068f1fc581a1928001e6803bfcc4068c322e98079309e1c1965000040026516022d3e3130de58d306a90a55487c873e455f90c3269b33541a7048980cb84ce27862200079a0bd09318183aa0a56e27006809582b3f81d2a⟩,
  ⟨0x2df14f0a3450227412b88c043e2100fe87803a61ac0c786142d01590a604f426411908303f01be0ce05882280da05e029811004e000, 0x4098cb7acf4015e9c70d3c8d066abc1f938375703d278334ae490e90e0856b2b713c33f0003cd06eb298c0c755612b3893066f4938241b95d710a1e0638b8f958e19c01e3657c654a054aaa20224f9127049c49a8387968034e80727⟩,
  ⟨0x29e14589f84da260129891046222010988183e61de0e586182ee16a0af853827813208d04401f00ee06b032414406c02a00c404e000, 0x1f043f8a4a0d2e29d331a49559132869a14b8a43244cde9a0304480070012002e5a1721b13e99a13589a4ba4781a3fef16068ffbc581a401f15c4e000658c73258bcb180003ca8fe9c5d0000070f0319ff9627cc⟩
]

def tableRLRLR : Table Block := .branch 14 tableRLRLRL tableRLRLRR

def tableRLRL : Table Block := .branch 27 tableRLRLL tableRLRLR

def tableRLRRLL : Table Block := .leaf #[
  ⟨0x2bc1548a704ea26b12208c44181f70f5076c39a1bc0d7867831e1850b8058429813d09984381f20d405e02c413c07702900ac026000, 0x37916c2700070e239b030001870dcbc052301f65b7b3c1253d0a4e24c10dea69f14949a4c24c0d40aa9349214ca930930342a0004eb418952003c29daff8448784de0a24000c36fe680030a4ec4000c36ce9c81ee2e6687⟩,
  ⟨0x35f1aa8cc05c22c21570a2c4cc24110f08444081f90eb069830615e0a384c024a10206e83301760ac04d81d00ca05402380e804a000, 0x40c10c685faba14e65fc9d226fc8f74e0070dd270a519c49201c4c8031e8ea4326996b4fa33d4be1e852c29c4da72d17e2745da92000e1f45ba91c4cf9908fe9e7ca64c99cc9c12048d25e32015009f4fe8693e34ae491834c3910019cbd093686ba14b8a418157971408bb3⟩,
  ⟨0x3671a10c6c6102d51620ad8546290139890046a22810087703a41ad0cf06443041770ad04f426610e077832815608c02c813004a000, 0x3a2669e1e4b44de6ff289ce105cb08cf4e3469b21aa944a28898c41495845b9bf0003a784ce2700030efb9a115e74db181822ace935671260cde9270481112cae210064f030445a24eac00efca38007a23eac00f00a3801dfb4b1bf34441bfb54e2700030eb39a10ce863b1⟩,
  ⟨0x3021750b645942b91560a5c51a27e13a097049423211407c83b41c20cd86302fa15609004581de0e306b02e411e07702d0140066000, 0x24fcf17a8cff92694cfe2918333c0d9126069387c5a511e50871a060002000a50772a4dff164ea7165058007e3da4984931f74004724000ca070007c781a5028005e4c23389c018865688266001a547d5e2c1800c9e068361c95e711a0e846fa7⟩,
  ⟨0x23611608143da1da0e686d43561980b8856428c13509404642180ff078037419c0c3058026c11807e039818009c0440160088014000, 0x20697a200079d28678a5e21fc5211e90f030728900032f2b9d28478b6821f34cfe295c92e29a3318493f9139927048768979b343627c21a13582892e91e0693d1c581a4f571606⟩,
  ⟨0x26412608d044221410187d83d21da0e386e03581a10c806042d815b0a7051025812208503f41ac0a004b01f80de06501f00c404e000, 0x947dc5849287bb90fe292834b8a64cc692451449849c46c123a69bc9164267a134b89e069457c581a517715c4e00065eef325edcbdc0005ca81a511f16923c0c001a5ebf31c4f03000397a9ce⟩,
  ⟨0x2ea16f8b3057e298147099c4a822d10307843741a20c786002ea16209e84a023c10d073030413408203781880aa04901b00ac026000, 0x3049ac8b613c4470007cd818000c445e5c029100093023a71108000f34001f45762000621ff4e52af151143e449c1218a26208001f5a2786781874d2000621b734001880f620006219f4e5247174843d0a585308c1b22713504143cc289⟩,
  ⟨0x2f616f8b5056c29f14389d04c2256120887041a2020f8873033218f0b5057427010507d838c1a00c605081c40c805602280d004e000, 0xd464e26a4080b1e88164ca7fe2cda8964913824b8d571158019a7c89382464d3115fa63ad0006226001f4f03444a002ea5c4e000fa59abf533d2b000b55034a6ce2c8287818013f49b57464000800b0fc66ca1a4cd25069714c44b000fcb⟩,
  ⟨0x33c18a8b945b62b81560a7c4f0242115086c3e81cd0d306702ea15d0a504ec26011d07c038c1b20c805081f00aa03d0130064018000, 0x44b107979a001863000f0f03431000b89846713800183e3cb83e10778000f2a54f714c23c4800003cd000307b3a2000e23ef4e06000307a7972a5b8a88a1f224e090c513122000fad13c33c0c3a69000311cb9a000c47fb1000311bfa72a278b60431e852c29846⟩,
  ⟨0x2d71668a9852e27012488c44301ff0fa076c3981bb0d506742ec16b0ab0524244118078837016a0a204782100e204e0158070022000, 0x40c0006638f31b1900a68035d4013d0067a92b138b2d20e98f9574e098e99765ca69334941a5c531270003f2f048d5aad84f1260001f36060003125b97282b100333167a777a25d644e096d517d0f865e1e196008c3e449c123269⟩,
  ⟨0x2de14c8a284fa272130893c48a22d111882c4021e90ee06d42fe1670ad04cc25210207883801a20aa04e82400ee06602680d004e000, 0x38009001732bf90d89f4cd09ac4d25d23c0d2b938b034ae4e2c0d2bab8ae27000332179932126428001e54adbe2b09e6408014e740c004a63ff334cd25869309331ec005f32852e2901af764d1c806b5d94a10f8613800398e7ce⟩,
  ⟨0x27c13589704a423d11708644142000ee872034a18d0c105bc29012507f03981a60c0059828812a08803c81980aa04801d80a0026000, 0x2934984981a81552692429952612606f3680271a0c4a9003f9af1ff0890f09bc144800189b9cd000f99b22000626cf4e582f173343be087f14941a5c53a663492ab22650d3429714864899bd3406089⟩,
  ⟨0x29714609bc4ba246117889041a1ea0ec87203721a80c085c82c21540a384c821a0fa0768318178095041017409003b016007801a000, 0x6094e74a95c1a0d4253264cf64e09917d99d5c013e1fd0d27c695c92306989fc003397a126d0d74297148302af44f784b666f22d84e000e27af3606000313cf9780a45e0bd12367824a7a149c49821bd4d3e29⟩
]

def tableRLRRLR : Table Block := .leaf #[
  ⟨0x33f19a8c405e22cc1568a784d625812688f04481f70f6077c3701970c685b02be13e09904942040d205d02b410c06302c80d8036000, 0x40c2f6f749ab0037428e001f745ab0037c68e692c004ee7c5efd50e08bc13c26b9371c5596d79001b3c2671380018a39cd5ded96b8c0cbbbb296b6138026c95ae119c4e001dbe62f6f6d8e000e2a4d5f15c4e0006288734ba5b77c8c0c5d1dbae2e813b84cea7f09⟩,
  ⟨0x3821aa8cf463c3141778b2854a28413a89a84aa23210287ec3b41a70b3050421c0f9073036018a0b204981d00ca05802480f803e000, 0x6abb1e2d51f0b8b88000d1e06dba0aebd5ef0fbc4ea67fb16ef4fb2a06367c8938241b952dbadd3e340076400b2cf036c78155a67f23638caad39b633f89b1a654e9fbb16e2b4edc27760dc4e9ea8d521e227c86eed13ae226fb01fa5df501b4b3893066f493824045f0a5da200347⟩,
  ⟨0x37e1b68d7066a3281808bdc5a02c314e09d449c22d10a88103ba1b80d0064c30816f0a704b42460fe06e82f01360760288118042000, 0x270d6366b9aaed7f7b2c270007159b9b0300018ac9cb61880048ac3d36bed00c7a600062b0736ad8006e31f8b8a3267000315739bb7b1573b1a1c287e331849a8fb3547001da400aa36d3036dea558eaea3402ed35340176900aa99b4ede254ceaf6f0001357824002dbbb5600355f6b⟩,
  ⟨0x3c61cc8de06c634e1938c485862b91490a044e0265122087c3f41c70d1063c2b814909f84781ba08e04001c80c2050020806801a000, 0x323724b2dece07d92167bc653839a9e2c3002be687f29c8332c44001a0ef71cd3c0d160832df3720d2f669c1200d5b96b213b60ed3ec1db11e9f60ad837622d38003b1169c3b458035b06ec41aab850f0356980bdaf70d000aa1f000f4fb8610d2000d43c00169e486aa1b0cd25669309315b400572e852c29⟩,
  ⟨0x47d22c10cc81c4011e70f1073e37a1a38c685ea2c2140897046e2040f187503921a80c1855829812b09083e81aa09c03d8138042000, 0x1bedefa7a9d6bb5b0d3eb5867669fc52000eb5467569e06d6a4ce8d4f24a670e9f9243380cdfd3e7067266ed9f7dd003f4fbee001dbdf69f7bddf6c00ddc9f4fb916e49a9dcd7725d3ee57b9a6e49a7008cdcb3e449c120039b369dfc7738d6800801e6bd9e06002cd5b4c0d1644000f377e8dccb6399d9a19a599767cb3cceb3e5b659666d9f24724f2decf92797167⟩,
  ⟨0x3201898bb056c29e14889a84c0239110883c40a1de0ea06b430c1750b4054c292138097041c1de0e005d82200e006602700bc04a000, 0x71380019b23cc9b213644000f2a5dff1584f3634001f3a060003362f992ee78a5d23c0c002e6c3f3a069b0a00279c00226c273174cfe2913b33c0c526981a6be8001e64baae298470006380d580031bf8007aa9745c581a5d171755001a3c0c356c6f3ab⟩,
  ⟨0x29313f098c49c23311307fc3ea1ce0d5060c2b814909b04ac2300fd076037c1a00c305b029c12c08703e01ac0a004101a80a8036000, 0x3b2b013448903a2b04b428c309e6d68003e740c00066d5f3002029ec48016c154ea001e82a7d4e59135da2704d348cba8420f9a67f14ae49714d198c24be9a7324e091a34e9ad5086c4fc8d09a924e7ac507⟩,
  ⟨0x33c1980c8c60c2df15c0a084b624e11788143f61e30e206e83321820b5858028212a08b83c01b60b404c81c80c2050020806801a000, 0xc46714c5204ca41144a33e4ca32000fc9000d30d8000f1c002cc35e4b89c00efea5c51dfa00a95034a2be2ef80034781b31dbe2d7424b2644f64e0908fbea9709db24324380139b7bce0705380319b77ce00cea0e05326dcf3b4cd25869309336d4005f32852e29⟩,
  ⟨0x2ef1700b3c5802b614789f84ae24811e08c44441fb0ee874c36a19d0c2859026e11a08383a81860a204781f00e2050014807001a000, 0x1a492e34984981a62c8728e68d1a43934c57e7b627e4684d492438fc61fe683e0058f030105b99530038b30038b92b92f696c14b2c89b3803a3ca724936759849f36ce72f93b8664759ed044bea89c1201d9b56b001f30ff8fe295892e29⟩,
  ⟨0x287137899449a238115884040c1f10f3873c3601910c105dc2c413b088841c1d00da05c826810e07a035817409403d0160074026000, 0x4c32e2c0d30f78b58aa7f1483486a781a70953034c25e2823e7f47e7c0228f9127048312a439ecc6ee6801e7200e8f0373703d49ea18721c65cfcd00b51e5343d0a4e24c50d02a27c52526930930340a89⟩,
  ⟨0x35b19d0c345cc2b014889a848621c0fc87483741990b904f025611e08784081ea0e606482e815e09203d01ac0b004d018007c014000, 0x640e4c59f21320325ece3226530f1c6444a601927c70031c28f19942547363321574e680018cc7cd000ffb722000633074e52ff15d1f532ce0a0a647f1c140cc8e04ffc7cd33f8a5724b8a68cc6124079ea539927048033bca6285221b13ce926c4d3900529c133d0999e06⟩,
  ⟨0x2c01588a8c520283139098c4b224611b889842e20d0f6076c3741ab0cf064c30815d09e04a824011107c83841920a8043816805a000, 0x389314340a89f14949a4c24c0d12a24d24979a4c24c0da4403d6d1b3480e6905bdb13c19a136249000319df9a02ba35717491e066c5529bf8b29bf8b2a238b91990967c8cc83b3e45e41640d9f18ec87226cf8fb91791167⟩,
  ⟨0x2c715c0a4450e27a131092841a1fe0f7873835a1a00b985a4290133091044c2100f306902f416609e04781d00ca05a023808001a000, 0x1a5100071aa3a70330ae55e71655e716b8600100156bb0ffa9bf5364ee4dd9c0b726ecfe2900102bc99b3c0c053931699ce53ec19f224e090665481b69d5b460ccf030d12a6153400baa7814d0983743c68d002fcd94d0f429⟩,
  ⟨0x2e316c8b0456828d13b09b04aa24411988903fa1f00f1874037a1960c485882b013109203f41ac0c505a02a413007703300d804e000, 0x40d2b738ae2700031b1f9b95034606c8799786692b3498498d80002b97429614a708b0dd173a00feaf6584e000e35cf360600031adf96c3100211ad3a67f3a00cf4f14d29669c12746b001ccfb38c9ac011fcb666e28c2380018d57cd⟩
]

def tableRLRRL : Table Block := .branch 13 tableRLRRLL tableRLRRLR

def tableRLRRRL : Table Block := .leaf #[
  ⟨0x2c515c8a484de24811b88403ee1e20ea871c36c1a50cd060c2e015f0aa050c27212208583f01ca0c004681d40cc05702400cc030000, 0x148c0006374f34003724c8801c8dcdd31e3380018dcbcd8319788e119f4cd2434d9a6a0d38245fd65ae28baf35e09d835c0ddc632c0e663b84b03118e000c0bdab000605d018b552b8f8a791dc2598470675583306aa95bfc5⟩,
  ⟨0x3981c60dac68831d1780b9857e29813b894044021110107b43a81ca0d286503061780b185002200ef06602701080750358120016000, 0xe46001c0bb3ced01819ce9da0303b9d7500020076781a7660cede70cec9d97cc001afdb3ceca19c7ceb9c007c13b8730935a9aa0d533202e781809a8217578e696b34e0916b55dcb5793875df5cb179187001bc4b38006e5d8b000dcb578b8a960bc5c48f03008ae538b000800ae48089c3c26⟩,
  ⟨0x3d21d88e706c634218a8ba058a29513a097c4582150fe078c3841ad0cd061c2e815b0a704b424610a0800364128073017008801a000, 0x235eb0ad31ad66ac8abfac1abbb3d6bd6459eb12b5ab1ecf5a56cb5ad67b142b5b0eacdb13ab570e003b9369dc3b353ae5e1017ba7b749937ca4ebbd4b75800e05da7016cd04226c8449ea8905a773f8a4040e95cf030151ba6069db233eb9800801a0195ff7ff67008bfeb3800801005e01da059f11acdacd466⟩,
  ⟨0x4372090e1c6f436d1b08d0864230016c8ae052226a12288903fa1d80db865831215c0a904c42200e305b025410c07b02d00dc014000, 0x1b630326ad99a82b41620a7f4482ab24b94c002002c3e19a0cd08c007dcd1deeb68eda003b27671b411d0b9a003b37671b451d039a000639ff34da4816362003c19671c1f1cf39b4f92c8ba70d6aa1b3db4569d9fc520036cd5a36781ad96b3ed3a9359567d48ac9ac7b3d69565d62d9c022b26cf912704800d635a6ca0d94c6800801d6259e06⟩,
  ⟨0x3b71d68e3070435b1958c686122ec16c8af052a27a12d893844e2060fe076c36c19f0b6052c25411f07f02f4138069024006c014000, 0x40c0055736981a797bb18e615fcafd670c3e39a5acd200f2d29e464cb0f0527583815724e01b041caedaea5b89e3ae0001e6f12ad5dc606e245a9b58003da66a7801d33b5df873b5ba786a865b4c32434da704c31c4cdaebfca82361dfb5b4e00d2db69afeaa062f9f4f7b57d967be3bd9bebb3e899e06⟩,
  ⟨0x4c624992248c843f2060c546002df15f09f445c223101076c37c1ab0ce06342d014109a04342060dc06502cc15208202d80e805a000, 0x1fd0a5dbd3c0dfa04bb5a997165d1d3cb87618cbd9a73b20e8cb0c391edd0b78f167c86b21a486a5eae5da0005fde2198868ec174f78366995c23b4e0f611da400297597a7371f4e000cba92eaaf4c6e369e13000e0f59c6f1477de6f93e5ca68d44f6495892000f04ba770453cff98c2776d73cf79d033b699e77cc2a11fb0fd340d3cddd90739d8fcf36e6002d5ed9fc5200200757767⟩,
  ⟨0x64d31317c0bb05cb2d21668ae655b29c1454a144e7261127492048323c114c8403fb1eb0e8c6fc32f17e0b6c11206402a812804a000, 0x67b97327b8cf720003ca9643c5613cf6e0007ce818000cf6ce64b1be2e9b34cd89d32e9af138274c9a6fc65581014e9da5f88d74f429614e2688ada5bd4b4b51180003a7696622fd4c3610d96a7db5b202475d3c8e9671e9ee5fc1f455cb189dbad3ecbd524d87ba78bf8a5b39e20358276d5235ac65526efa06273abc25f5e1565f289e993580d88dad140c98444d8dd9253622649ec90dc520ed31d2eb0edc94b74d6f3421d843a08752f6c00302d505a90c54fd238ffa3cbc1a7c893824001977b53fad7e8dad⟩,
  ⟨0x286139893044e2000f407543841b50d2065c31417b0b4055c29413d09504542040bd057028412c08503981a40a2047017809401a000, 0x3c14480018f93cd0007c9dd880018f8dd3968fc5ccd0ef821fc525069714e998d24aac899434d0a5c52192266f4d018224003800900173e7390d89f4cd09ac4d25d23c0d2cab8b034b2ae2c0d2cb38ae27⟩,
  ⟨0x27f138097c4a4245118082c3f01eb0e206e83261800ad851827212a08e042c1fc0ed06f035017e0b004d823010405d024008c016000, 0x6849b435d0a5c520c0abdcf3cc9d99bc8b61380038fc5cd818000c7e0e5e0291f30b735d9e0929e8527126086f534f8a4a4d2612606a05549a490a654984981bca400275a0c4a9001fca2d7fc2243c26⟩,
  ⟨0x3951990c345b42b71508a404fe27012488f045e20c0fa874835e1a20bd85c429412c082837818e0b005282380d205802380e004e000, 0x71b0e2d3f8037d91584fd9f1fe81997b4f32e7d0132ee9f9c5ce4c4eb730da6692c3498499f94002f9942971480075ad8c136da4001d6a633598059cc309c001cfc2e740c00067e0730082a8d2359b0da7a86b161b475284a64c99ec9c13227333ca5009f4fe8693e34ae491834c7eb0019cb⟩,
  ⟨0x3801b98d3068431b1860b945b62b414789a04a024110d07d439c1c40cf861c2c013b09604842200eb05c02b811207d038012c030000, 0x61380039053cd818000c827e5d25100193faba70300019047cd0006c56d880019041d39b15c5308e000640f734001fd8b62000e40df4e060007f5fd5cf36e2c6315893c7b124008d3e449c123269b11ff5cd680036220007a781ac4200175308ce270007f52d5fea3faa8003aa9e53c5⟩,
  ⟨0x40f1ee0f1470835f19d0c5451c27a13209044341f50e106b433c1790b2053c28812f08e03d41c80bd04001c80c20500218070022000, 0x32e8c8b3a7941b4d22cc9d9263c9eba793ea4f2d4ca0127beae4ff93fb56e57395f246c91600080044768dbd29769f73d1bc6186000f43f0e7436420735ca0fed74ee23b93ffda69c189537a9bfb1005f4f05aa9b1f54e09ade5587687906a00639a3867906600379a001e49f0ec01f879a1a4cd25069714c82d000fcbc12d66b⟩,
  ⟨0x3e71eb0f1c77a3aa1cd8e206f236f1a70cf463830d1800bd45c82bd14e09d44ba23011307e43c21c90d406041e20b0037812804a000, 0x149a4c24c0d32a24d248a28930930345e0055b474d20111756f6c4f46684d02690003216f9a0031697100032163a732df8a0070bc0036781800400a172d532c78b32c78a0031216790a2223b9a933d2eb9cbb001c23e529d000d0dd52c738f2674bad23049f9a7917e5d593ba4fbd3ca1b27c6a661593f75730a4a09ab⟩,
  ⟨0x2eb1620ae852627612c88c841e1ec0ef86bc34a1820b6857029a14209684301f40f006d8330144097042017409403d017008001a000, 0x50533e7dce818f9e5051e66bdb04a401d724f221447ef37ea3f4fc380bbe9f87f148004059f4dc3c0c02afa66268354f9067c89382419d520431a76d3d91e0616354c4a6043fc00f51e1306e8790e2005f9b29a1e852712628681513e29⟩
]

def tableRLRRRR : Table Block := .leaf #[
  ⟨0x3361918c546042ef16f0b445802b514f0a4c50c25f11d08c04161ea0e286482e216409b84b421810206d82ac14207a02980d001a000, 0x3744ed0dab226b9448c9a6ccd5069c1226532e13389c000c89fe6808bf8cec6060113f17d5800c0bd9c001fc575644ffe284506a801627ecfe2900100389db3c0c0051376981a82d1f4de67a14002003c3c0d415cfa5738fa4d056e6001a65470a7b415798c27⟩,
  ⟨0x3681958c285ee2e31620a9450826d12608ac42c1e90ef074837a1960c4858828213708b04241c40c105b82580e605d02400cc028000, 0x43a7afbeb402bc380c414da43144fe0a37df0214901ff7a920d904f6bd6a996003193670288c7b58b0a9c0061a400acf89a11a046cd22ec00ef35c4e000645cf3417e376e30302f46ddadc4e000645a73416a29ee30302cc52dac003f5ac4fd470d344a986554801ac149ab746⟩,
  ⟨0x30b17c0b545882b71540a6c51c27f137097c4a8243110084440a1fa0f587203761940af051827211208403841920a803d813805a000, 0x5348cfef00430f9a67f14ae49714d198c24be9a7324e091a34fd6ffa7886c4fc8d09a924fd4ff5b877138001a13fcca13d427c000f2a6baf1584f426c001f3a06000342679935bf8b32d2d76796799596ab3cb9cbaccad9e5d665acf2df2e932b67⟩,
  ⟨0x3ab1bd8d5065a30e17d0b6c56229014089d84aa23410387f43b81d20d586302d2139080037c1a40a504d81e80e00490188078016000, 0x4005fbec9001b88f9d4007111efa800707d26f651b02dfba3e01c097ea8e01132d67c89382400664ed3388c136d001003991b3c0c00531f6981a47d0001e6f9fc0751ff126270ffe14c4261b0f3233113153096700598ab3f8a400400e622cf030014c35a606000342df9d36338bcb226bb44e09⟩,
  ⟨0x3601a68c9861e2e81668b0c53827512a091c4342100f7879437c18b0bd051c26c12508b03bc1c40d5060027411006502c00c404e000, 0xf90e007e878f380d6638057a1dfced810d4f0350ec006dce006b43af9800b3db67f14800801cf5d9e060029e9b4c0d4390017732010270c7bfd3e4b9a00e26d2005d3e99a4b0d2612686e800be650a5c520c8ac004ff17240c4ac01fff0f30c27a1aa000f9d030001a1a7cc⟩,
  ⟨0x50b274130493446422090447f63c81d18df06ae3241808b6854827f12488903fe1da0da8608298137082037414e08002c811804e000, 0x6409879292480b9b03353cd71c0df40cc4f33c7001572b0f13a000d7270f13bc360890ce44bda7b0421b7d3c00d581dc7b037e2dd3d6d96067c59a79adcd4b0f0b2162971e16313564379c7dea3770d4c1fc8ca6def78fbdd6edda7ddb776fd4eeddbb66a7760ddbb4fbadeebfbb6e9c000c0006b39c7a88b3531f4b66a6ba757fd1e038eaff55aec77fe3c2685703c757f719238f1522400de0a39fdfa1e7ce⟩,
  ⟨0x40b1fd0fa47b43c91d10e4c7043751b40d5c66432118a0bb45c62bc1578a204e024b10c07d439c1890b3050c1de08c03b014c060000, 0x7a1a4f8d2b92460d3259800672f424ea1ae852e291935ff82ec56ce1cd6c27000725779b03000192b7cb718800192b1d3a199c57607fb8d9cbabef2b7dda7000ef730e6f764aa7363f528a74f511fb78f1498a661e27978ac3c7e7514800093d2c7eae3c7e6514600053d227a38fd3c7bc3e1a41120ac4c7da41d878ff47d641b87⟩,
  ⟨0x3661aa8d1866a30e17f8bb85c22d41618a7851a28012c893c4502190fa07703a41ab0c3057c28e0fd075035c16008b02c013804e000, 0xf8d2b92460d3261c00672f424da1ae852e291e35fe3c0046cdb0d6c27000725fb9b03000192f9cbc4a2000fe2fb3954bc5818000c977e680030caec4000c974e9ca9de2e6643e8001ec2801b0f194983543c970002dcd9f10003d3cf853e18005a7818000c96ce680128d8bd1⟩,
  ⟨0x39a1c80dac68c3211770b244fe27412988b04321f20e586903261820b9853027e13209084401d20dc05a82ac10807702800a4022000, 0x2068720035d680030ee6a4033871b5f0ec805c000e9e1d900bb52264ce2bf5000202dc3c26ff3ff5b480019343cd0d122009a4cf74c000c46ce3c46d8925cdc334959a4c24c9990015cba14b0a668d6326ba3031227a6c279324000f9b0300019321cb7188001931bd3890545eba72aef8be869⟩,
  ⟨0x36f1a40c485de2ca15c8abc514257125890043a2070f006ec32c16f0a4048c1fc0d906602f416009f04902040e406802180d001e000, 0x18aa960fc731532c18c52f1c0038a3c3b14dd4f6ae04cf035effd4deac001000bad7d3f23626000e28b1389dc30001937dcdbd7fa94d880037bae9d7b9c9bbe6afa1857dc7b652f66d3c3d90f569e1ea00ff4f4293893e66e534f8a4a4d26126068788005d49a49000a1e0d49849⟩,
  ⟨0x4af24511507883ad1cc0e0c6b834f1a10cdc6202da1598a384ce2310ee871836a1a40be851c2280ef05e025c0e006502c00c404e000, 0x5b2cbd569dc3640b538cfc754fe00051342d366ff4f319c47c0b49235c7b35f4d13ea97a154bef78a0dc7a14b0a71344fc7de7c97de51404000f1df78c500e4c4c1f6569e1b3c35de3c36386cd0d738ef7f5f7600017f930d9f8ff8669b60d2f8697dd70d8f8efbaa1b13ed5e3fdcdf747dc7a7fbb3ee4d3fdd7f71fdc5a70007edfd3bee8a333cc84cc277df9465b9d033efaa329cc⟩,
  ⟨0x3c51d68e306ee3661a28ce064e31b1850bfc5e02c91540a0c4ec24f11508803f61ac0ca851825e11807a8378172094037812804a000, 0x1371b8a003cdb69e68b36419fa04006cf4661b34e232d1a6131e47000b27ff9a003cb967397ac74d5b89e4fd8001e69cf5638ec6063a0ac6fd5af60001db4c000dafba7b6774cbd72f3800080056d0e9f34bd35ab3a6000decb136cb69ad95b67f536ca5b4ba9b692d93d4db396c96a6da3ce23596d16709ac⟩,
  ⟨0x3801bb0d786723061728b005622a7141090446e2100f587283761b00cf85f82a214709304641f00cb06082a413407302900ac042000, 0x81a700716c243a774e74bd84674e69c007a72ce74cd87faba48f031d5761e6ac01c00066b63a974f030001943fcd3a92c38d8f4d00659f224e091934f51f515b4007a5401ecf0374d002da5c4e003d3d6be9ce9d002b540d379f8a611c000ca0fe6800f4c5c4001ca0ce9c0c003d2b6b⟩,
  ⟨0x2fe1778b7059c2bb1540a4c4fc27312f092447c2290f407703a01c60cf85e82a614608f83f81e80d305f027411c07f038012c030000, 0x3b5306a89ba1ad444cea89ef255f4c2af04adc2ad6b957826c5156000d8720010009a7a46c46818000ca3ae680596626c475d4a38e6b89c000ca36e681475f5c606029ebcb5830a9c07baead6791dc2598470006cb8d5800365b8007aa9c01c5⟩
]

def tableRLRRR : Table Block := .branch 14 tableRLRRRL tableRLRRRR

def tableRLRR : Table Block := .branch 27 tableRLRRL tableRLRRR

def tableRLR : Table Block := .branch 55 tableRLRL tableRLRR

def tableRL : Table Block := .branch 0x6d tableRLL tableRLR

def tableRRLLLL : Table Block := .leaf #[
  ⟨0x34d1940c545dc2d71600a7c51426912909204421fc0f5876839a1a60cd86282fa1560a604942300f106c82c80c605401e80b802e000, 0x1fdc0065a70cd0f29a000a7362c264c188c9001eddb4f6bd980afb6ecf08131e06000329839a00659d5b19334941a5c53296c003f2f04c39ad84e000e52bf36060003295796e310003294ba738c78a3b6a90b74c013b12eca20004016d3c0a6030993ca99c4164c06ec9⟩,
  ⟨0x36119d0c546162e415f8ab853a290134897849a24010c883c3d01db0da06702ea1600a484e42360ee05681e80d605b02200bc04a000, 0x12a28007f340028c034f030001950fcd0032d11d8c99a4a0d2e299504001f978261cd6c27000729fb9b03000194f9cb718800194f3d39cb5c51e0548f7a7ef6a7034d93418ceaa3863f7701c814d9c06d9c1ecc400e34f636598601be9cc24c2634106c9cc153c0c030d9edab⟩,
  ⟨0x3c31da0e646ea35d1a28ca864030516f0adc520269121086c3ec1d10dd06542c413d08e04141dc0d505f025c10405b02880a8022000, 0x184700c76171c0080a152f578b2f4f8b0400c1e069545e16ac5e5547255c5caa8e4ab19954fc957192a9f98ae4a553732552ab91e65b1f65eea7d63e14b5750369aceb3bef4e77a59d477d69c092c6774fe220136755a193143b1c1a1dce06f31e548805ce683229e5478056e6c0d2a3403ff36523dd23c67⟩,
  ⟨0x30317a8b6856628e134896048e23810888103ee1e40e886a833a1760b6051426810d07e03b41c40d1056026812007f02c00cc018000, 0x710c019c41c09ccac8e68003154e9e2aa8b975b86692b3498499584002b97429614a308b0dd174ab0098f4d84f2aec001f360600032ae797827102574a9ba71667c89382474d31688017ad2f11e0619348001955dcd00062ccd880059557d3a46⟩,
  ⟨0x34018f8c485e22d01578a284ca24010d88283c61d20e086c831617e0b8858029e12808d83d01d40c305b023c0ee05001d8098036000, 0x2f79b4b8a4063dc6d6003eed69f6f016b5d9fed7eeac0148ffb56009da8babb510012d58e99c0074ae0e6e19a4acd2612656e000ae5d0a5853526b1835d2cb1ec3d9613cad50007cd818000cad3e5b8c4000cad0e9cea3e28f598f51d3ae554c952a70488ea50b⟩,
  ⟨0x3a41c08dd06ca3571a30ce46503191878bb05ba2ba1558a844f825911a08103f21d60d786282c614b094041c1380860328110042000, 0x86f004b0f42938930437a9a7c525269309303435800b89349200286a624c24c0ddc90013ad000c34312003f721af86680040058784d0cc000e24000caf6e68003dc5ec4000caf3e9cf3be2c31e18b87fc5f15b39efa075800203dc7ca7c886d9a7d8361be3c01ad200bf1d6900e454f17e61e536b⟩,
  ⟨0x4db25b12447c639e1a50c9c6042cf15509dc48821f10908143f41d50d105f427011308103c41c80bd059027c12406b03080e804e000, 0x47436fc69e377b8ff4e9075c6423a883e8e4e9f0339cf46ef2cc60a39da6e3c9d8922d228d9e1f1c986c8a24ffd24564ebf1fe9df51c4e93bf0169f49cf807487d3e93fa4be9f49ed25b495d3e92da4c6927a7d25be39d3d0a585389be2cd24b53a48fc68000e9f490f8cf528dc60f21b391f4dc7eda0021d3c99a4a0d2e299626001f97824de45b09c001cb0fe6c0c0006586f2f0148bb918151d3⟩,
  ⟨0x3981b98d3067232e18d8bd05c62d21638ad851e25912088c84502010fa07a83861b80d586102f415309d841418009b02380c404e000, 0x695dd4d3120015cc0d11309833448006a61dcc94349c1a704979b0000d308e65307a6100007953ac78b491e0600134c0f98e2781a9800006e74266138003a5fdce818000d2fce64ea4e2c4359bfacf378e4c5d40444349bf9c7001275bd38001500d10c898a8002e3f46f0d0327f29657cd⟩,
  ⟨0x4392120ffc7e03e11eb0f047383871998c386022dc15a8a404d224411a88a840a1e00d6868c2fc15709902c414607e02c80d001e000, 0xd8a9938e601d43627a54d09a7055326ecbeda78e553ae30845c004a45ccb6be3c6bb1b06a74cc000c633a796bc8c6b9a000c667a746692d739a00446c1a7c8938240018d7b531bb46b7ad00040038d6f4f0300031ad6a4000cb53e6c61f1b8ec5733ae1f488d0875cb1800196b4f8bf8f04352c00046a696c0027534b00011a9001e95fd4e449⟩,
  ⟨0x34e1938c7061e2e816f0adc53e26c12a88c0446216105879836618e0b4851023a0f606882a810a074033816009603e0178068016000, 0x29a90006e74266138003a6a1ce818000d34ee6529be280020c6de59a7bbb34dfa97851a7a14b0a7137849fa7ea7f4df08c001d3fe9be11ea7f4cfd2b4fd8647fba757ab224b8f0bb615ef1e95a7c674eb90e465f1e60c00434f9a67f14ae49714d198c248f7aa7324e09⟩,
  ⟨0x3a01be8d9c6a232e1838b8853a27812988b84121e40ea86c03121620a7851026210a07c83a01ba0cc05281bc0ae04801f005c014000, 0xfcd713f2fc37ccb0c001f9161cf96d36fe653574e0e9d441287f9ce0f6538f599e9f7a9bd28009d4de940056a6f450027520045e89a9e892000de85a9a6ca002f994d91a9bf303444c260cd12001a9b073250d27069c125e6c00034d6b994d669ad0001e552a8e2d247818004d355e6389e06⟩,
  ⟨0x3ef1f00f5876a3a61c28dd86d83471930c045a82c91540a044b823510e87f0322118087039c18409d04702040e006502c00c404e000, 0x184981a1c8016d2692400a1c2d2612606a678009d6800c365a4007a6735f0d20020056784d0d00036900032ef79a000d32fb100032eeba7418b8b0c70c367816489a226620f000a983a3cb4f02c113244c057910700034c151e3a781a5da8001e6916d10e6c69d081574e7126ccd4a6984cc27a6eca7839d0329dea6e9cc⟩,
  ⟨0x2b81548a7c4f026b13088e845e2220fd87c43941b20c685f02d615e09b84b023210c072836c1680a103d016409803d0178078022000, 0xa48f030009a761cc713c0d4eb400373a13309c001d3abe740c00069d4f3291571696500874f26692834b8a65ed0007e5e0937916c2700072f5b9b03000197a9cbc0522a66e0b7f4e1e804acf42938930437a9a7c525269⟩
]

def tableRRLLLR : Table Block := .leaf #[
  ⟨0x26f130095448421b0f707903861b00cf86483061760b4856828e13809684702160fc07783901a60c605e029013408203a8138030000, 0x6449c121ba2626d0d4ce6800e9e80a59e06d3b013b4ca087cd33f8a5724b8a68cc6124f144e649c123c6979343627b334269134b89e06a4b3c581a92e715c4e00069daf329da53b50003caa46fc5⟩,
  ⟨0x39c1c78da06b234e19f8c605c42d81588a644b024911207fc3b41b50d205fc2b0133080037418e0b205382480d605602080d8042000, 0x93340b80011c7c893824d24c3f48171cd000302cc001f1e0681640007934e1b8b50a8003060492ba7c94d5178019a9a8ec00dd4d45e0066a400ba8bb5344690006a2cd4d3e10059cc923a8b0d3d153246d15fa7000fa4f0fea3c30392a613038aa401253d9e64f12a6199538260b559a8403367⟩,
  ⟨0x28f134097846e21f10907ac3c21ba0d106542dc13809584602160fc07783881a60c2058829812e084039018c0960390178088030000, 0x54120007ce818000d410e653a4e2b09c001d40ee740c0006a067329c2f15c4e0006a04f32a03d408001fcae3336087f14ae49714c198c24cb9a60cd3824c24a24885491cc24d374e2ba48f03389e06a717c5⟩,
  ⟨0x23a116888042a2000f2874037a1ac0cf86403061760b3855028a13a09484602120fc07883801a60c9058829c11e08202d809401a000, 0x2852c29c4ddaaa94fa054e9f4a99410f9a67f14ae49714d198c249e289cc9382478d2f2686c4f66684d2269713c0d4ec78b0353b4e2b89c000d416e65415a82c0007954eab8ac27⟩,
  ⟨0x2f51740b0451627313308fc46a20e0fe87b03ba1b60d4867031617a0b4855028e12008b03bc1ba0b604f01dc0be04a01a80a802a000, 0xe2700035147995142a288001e553f7e2b09ea268013e740c0046a25f334cd258693093511c005f32852e291a36559c860d9912b8613d43f0007ce818000d43de6170a400063f37529e771401547e4ea53dfe2cf0aa609953825f9558c7ea7⟩,
  ⟨0x28613d89a048221a0f9876c3901b50d4065c31417d0b7056c29413d09804742100f5058028412808903c01980b804401d0088030000, 0x21378289000332a39a0006500f44000cca5e9d41de2e66877c10fe292834b8a74cc69255644ca1a6852e290c91337a680c112001c004800ba8f7c86c4fa6684d62692e91e06a801c581aa0071606a805c5⟩,
  ⟨0x29014089c04c625612088704121fc0ea872c3481910b6055027e13209184542080f7073035c19a0b8054825010a07b02a00fc030000, 0xd093686ba14b8a418557e0e0011b337d16c270007330b9b0300019981cbc8522000f82bb3a86dc5c1253d0a4e24c10dea69f14949a4c24c0d40aa9349214ca93093034a080013cd062548007940dcff84487⟩,
  ⟨0x33018c0bc45bc2cb1600aac50827513509644641fc0f9072c37e1b20c5855427a12e09203f41d00de05b82400d205802380e004e000, 0xa859c5014f2173a937225b244e0932855ca3b0011c7c89382464d328ea51df34000ca360007c781a51a0005e4c23389c000ca47e5ca469468000795514b8b491e060031290b960d8a7818000ccd2e68001947dd10027333fa7e8693e34ae491834cccb0019cb⟩,
  ⟨0x3401998c305ca2cc1608aa051e27612e88d841e1e80e786a032e1700af853827e11808583f81da0d406182a813a076036011404e000, 0x614d4d10103cca9a0025b98ff2aecc12fb2aec94927648c9bb00631ce0236a64f3aa640016e70015a98fce01b57380b6a98bce1e33800fa987ced334961a4c24d4bf0017cca14b8a468d81506f2183657c0be184f52dc001f3a06000352d798041fc69000190bdd4⟩,
  ⟨0x3e31ec0edc7243711a80c8c6162e615989904822110fb07b038e1a20be856026610e07a83901960c005382580fa06402580c8032000, 0x609004a33b5c74a227e9c00773ece00300d6b001805df0b551b4e2dfb57f0e9efd6bf66fe0d3aaf778ec6f17ebaae7a7ab9a02b0e7e2ab920270f6900c1e06289a384d5c772084ea63cb042b531dc8213a904223b8d481ff1dbea40749d3aae6d4d174e09d3d0766639a361dd3180ee9068b7482c23a60c11d30404e9⟩,
  ⟨0x35a19a8c386082df15d0a544e026311808604161e40df86d43201810b9058c2a413d092846c2060f606782a814007b0318108042000, 0x1ac9362004e6a474e060046b21d58003593e9c003ac7f56000d651a7615800358e564daaa053c571380019a7fcd8a70008d8c0d14d800dab3c8ee12cc238d1ac64cd540778b03501ae2b89c000cd32e6c51e001ec6068a38001d5d017e2808c0cda68da066d746a00d6b⟩,
  ⟨0x2a514b0a044e6262128890843620e10087b03b21b20d285f82e814d0a004641e40e505f02ac14208e03e81c00be05402080d804e000, 0x13a9a65953243619a4acd261266b2000ae5d0a58524c0ab0fd17553959cf6584e000e6aef36060003356f96c3100313563a6acca41474dc4e00066ab7359448c0dd922c68d3866b934e0966117098c2380019a97cd⟩,
  ⟨0x3f91e90f1473c3941b68d8067232117d0b8c5982bc1528a384d224410f87e83aa1ca0d286002b614408f83b010207202680e0026000, 0x1553d52276584e000e6c4736060003361b96e310003360fa741b78aa8f2373f4e949648186c98ac6890993061b262db01175716d4451ab000622ad3c44d113eae22601075782403f88935710f0005a98858001d3c42da68872221d3c43110dc441a7294a2090006af729463c706eb4f829aafc008f4ed54a9abc0021d386e89⟩,
  ⟨0x2e11670aec55829f1480a144dc25d12988b84121e40df86b02f216c0a284c8250111083838017609404181c80c603c0178088022000, 0x136a2592449c498337a49c1223b32f84cf0300e701e6ac001ab0f4e001c075ab0006ac6d38748b0066037ab1354e270003366b9a6b24606d251970300019b2bcd000602fd880659b25d3c334959a4c24cd8f0015cba14b0a6a4d6306b⟩
]

def tableRRLLL : Table Block := .branch 13 tableRRLLLL tableRRLLLR

def tableRRLLRL : Table Block := .leaf #[
  ⟨0x3e11e70e9c7183711b20cf466630c17d8ba858628d139095c4662180f8879037a1b30c6059c2b014d099042c1b00ce0548088022000, 0x19a1c0c3d591e70167f099f01212c2702ab56379d030153ab17ccc834bd9a61280196e3819c849e06578f9dc8c1eff8f83dfb1d8b83807170702f7560b98c27ab0005db9d030174aafdccb02818ad3e449c1201c3c262c02c1ae68003602830ba781ac14060f52b0380020010303573c80876d1dc983de9eb1cd58e6⟩,
  ⟨0x51a27b934898a49e23c91bc8904231fe0f5c76036b1a30cbc5f221e10387d035e18a0b184f824e11d07b034415809503700e004e000, 0x3fd2c3bfa9522eadc4e00066f3f3743ca90b630347d05481cb000742ad3b4289bc5cd0007456d3b46a9bc1cd1ebf13421373463e38003b15ea75aed30f0e89503c3f8f114a2c980017c58f209bda37b2000409656a926401e250d5638a71e183d348f26889e88a18260005e3cc4a002e9d11bc51de380030ebea61d2d340d3748000f36224c27762000c463a7873f4d0c6d10cf1d109431a4431c71833d59302b7ce⟩,
  ⟨0x3131760b6458c2b51540a5c51826712e093c4502030fc875038e1a20cb06242f014509684781ee0e806082dc12407a0348160066000, 0x1b9c13d3cc5130c22464d3666a834e090032391d5c26713ce000003cd00363d6d8c0d1c5c7a9ab61380091e96ae119c4e326b00223ce00075543478a611e6fa0001e69851470137c7a70346fc000eae865f1694d29269abb9fd8d3bfa3576bfafa7⟩,
  ⟨0x3b11ce8dd869e2f21740b04500270132096446820d0ff075c36419b0bb057c274107078037419c0c3058022c0e606902b013004a000, 0x17aa8d1fe63fdf24001c7f7e3c522000d4e08d4c52516de9e068ffb38979a000800557ed64da786c6a4684c000e8f9a768f5387f9be299a704e1de680031c76a6389d347111c6ea6389d300051d469e3a100063a7d3c745a647d0f912704878898fa0022d6847a43c0c2c22606000338339a000c7c5b1⟩,
  ⟨0x41b1fa0f347503811b00d2067232a1818bd85c62d91640a4c504271131095c48c21f106880c3e81cd0d305fc2ce15d0a282d4120000, 0x59c93d39c9200079b21c4865b19c8e00079b7e600371a59fc5d8934926a650012e5b09e0346c0c3c6b00445c0000061f71a630cf9127048d1a6a5f0007e697c8f031c49000338cf9a0006a5cf44000ce30e9d4b8e2c0d52d38a3b582f58cc70bd48a6153b11af452f20538f19d467ba91da817a42f40cc59024a9d08d6a2960003c7⟩,
  ⟨0x3e71e40ed072236a1a28c7857628813b89a04862100f587183661a90c2050c25c12108a040c1e40e505f02cc11807f02c013804e000, 0x194b4994546000f52b0e755a733f34001fe0f4efe12732f340070cfe90968b3d1675130e3d556006cac9a78534ce49912e561d3c8952b0488ba7000644ad3c88d223eae6143c0dc774889ab0006aa10008003d3f4a59b8cde669334941a5c533948003f2f04d2da0017cb613ce4e0007cd818000ce4ce58001a5abd1⟩,
  ⟨0x3c91d30e547083771a80d1463c3111750b80572292135891843e20c0fd871433c1860af855425c10906b02c411807f02c00c404e000, 0x1e14f0b62e4cd25069714ce86000fcbc133fcdfc772d84e000e7417360600033a039600067f7745fc44e7de98003fb8e9e73e3fc7e6c1689af34c29c900d17bf8e0006226f2622471a401c3e3e3c0d58f213573bf78e1e74fc397eefc3c69c001e1cf4fc3afef5ab71380019cddcd91dafddfa30348ec7eebcb⟩,
  ⟨0x4ca25e12a48984362100eb86d23241738b6456c2a013e8968466210101077c3781950b9053c25810506f02dc15808902980ec046000, 0x3c86c750e000fdde00121d58df3ccda789f61a29f8621cefbb23fbb1370008782a475f1ceec3eeb21cd23ab8f1fd4efe313591d3c7000f8fbc0fe31c3c10c001f17627c4d86f12f8b713e2cf126264931e27e58007c6d89821801fe35c4f8d001d8991d6788797e27f12627c67e24c4f8dbc3d8b9248787f97248c00272c001c922e5e09000f86f17247c0008002e54fe1e2cfdfe28007c1b87⟩,
  ⟨0x33017d0bb05bc2bb14a0a0c4e426311e08bc44420d0fc074438819d0c985b02b613408683f01da0e2066829812808a03a813804e000, 0x9038000400171e686da18003e97c3cec63d31cdc334959a4c24cec20015cba14b0a48c9560e2abad63251fb2c2700073aef9b0300019d73cbd138c9419721d39d6c77d79b1667c8938241995200924a1734bc47818189533ab4000f34000c93de8801e9d55d3⟩,
  ⟨0x65f32418dcc205eb2d5164cb085772b31554a96526280937096e49223691208423eb1cb8d4860628212607682d015d09c044404e000, 0x715da6193380019dd1cde8e7a67d8f3cc000800fc06e9f82cd31849a33499a4a0d3037465d2feaf7fbe77753d2df3bba9e773a5ad4f45dd2d6ac001e9734fd2c74b3ab6f8522ff8edf064a048bee3a20689eac2b5e3134e3e3c4f4440ad2f2838f1f3a493e6baf88134bbd384ec86c4f3960d8b21a7af5167d90c71deaac59e6249c7778b3d0deb1c1af79c70d81ebc71d90ac808614ec85de2e04e90003c784c000e961a7695b3b379aff82321274c63c4000c8873f1362bc0160a7f321178b0c28cf13850ae3c903920bc9⟩,
  ⟨0x68632f98e8bba5d12e316ecb2856d2a314849f44d716f8b2056e29213689203e81ea0e186782f215209684201c20ab0430140016000, 0x44f0ae6f3ccef869f9e40004002000de6277b74fc8d09a133aa19e09cd9e0600079aea8e033f44001ff1f4f3c02024f34093e3fc3b9ba9320e6edcdc3da5737af021edbbda78336f8bdfa7c2bb46c08d3a62ac67488f072dc000bc52394a142de4f438e76f90de641b15300004e6f0f27b7bae3fdfba69573010dfd4e9f4b4d2b752001e3d7a776ed0e221b9800169a3c781a77b31e7e6e5340016a4001caab535aedc47f3388ecaa759c456551ac70cd08078ee19610003d6e3f0cbc31e9dcec418a7477c70003119a0f50002e3e26⟩,
  ⟨0x29113b09b04ae23f119880039a1c30c805e02ca1580a484ec25011b08503ec1e20e006883001620a704001c409403b0180094030000, 0xce229e06947549b8443d230009d778005a70067aef00074f03002e000f5dbaaa10fc594d0f429389314340a89f14949a4c24c0d8a6934925469309303407775a9cd3892eb4a03af3db13e26c4cc29a0e1c5⟩,
  ⟨0x5ba2c394909de4e425f926077a3a91cf0de46a432b13d08ac3b81d20d5861828211e07d83b817c0b404881f00ce05202180e004e000, 0x382fe0d3855d3841d083918e8864c88102cfc724b06e0e166a3c2600075d5d3b5d29e8bcd30980018eb80023fb4dde1c047028ebeb8d43801224b18126e0c34fafa8d89800191a74f3d0123573679fa52ee68df66ec1ffe37e475208e475086d2580090570fc1569c16bdb7c00243090bfd382d5b6f21aa000a17da781a79d3785e6806bd6869e45cc9590064e8578fdefef6e1c029dedc3f8a4002012ef5e1e0600877ab1275ca7b6653d84a9f224e091b34baed8121cd⟩,
  ⟨0x480238919c8843f31f48f0873a3761a88cb05f22c61508a284ca23210687f83e61ce0d485d82d814709e84581e20b0045816004a000, 0xa48f036c51562eaeaccab36aca000760cd3c0c00067b2f34001ab0762d88e7b174c145d83b4fc18f067a7e0c3832e0bf4fc1df069c16e9c001d7b753ae569b5e0d75b4faee6bbfaeae9c008e0bb4f9127048003c15ea785cd7a35a0008007c14e9e06000b827d4c0d3d44000f377dcd78b63c15f045c12703ba7e15b82bd3f04fc2af055a7e0cf835e1574fc1af0ada7⟩
]

def tableRRLLRR : Table Block := .leaf #[
  ⟨0x3ea1cd8e186e234c17c0bac5b42c915f0a644e423c11488103ee1d00d586842f815509804842240eb05c02b810e07a02a8088030000, 0x1126e22aa93abc3644d3c2daa5a81520086c8ba72244e2195478001a565c7e33639a5acd3824014d907574ab000a71c00752ab0027c70cd0e00855f3ab71380019ef7cd005eaf6d8c0db1c55e9ab6c693ddf9b5670017a7b49309268c08008e48003565000fa781a94e0005e4b89c001ab2f57574d5940016aa06a2f3c5⟩,
  ⟨0x78d3ab9c0cdbc6b934a19bcc946092fa9784b625902b79528a344f9272130c94447f22e10b07b037518187b03aa1b004c81d0082000, 0x11a359e94706e3b4af8d1917519e8c709e3cc8c230ea6658118b5332308c3a91182645d488b73226a40018b506801b474f9de8d9fa8d7fa797c05f0f5254f569a79a91b494fb302eaefeca67809e1c006a06d34eb66a74a80b4d3fd39da7024a77c5e0455078b7925c12fd18747c910916f4c40f0383c747c7108d8e02de8881c07038e8f8a21131bf5bceb79a20681bfe3804f47f88b04639074f70cc31cc81d074e47f60139c3d0e2b91931a080df800170a1c7dba34c02aefb9a78b5ae18dc3ba2be18de443a463467f18e0012c02610371c501d2c3a623f947f0e1378fb1d6c79a944a388cd91b4e893f117578ec8ba7⟩,
  ⟨0x5f72e916acb0c52928213748f44552110ff47b03931b80d2464430c1738b0851e26a12288783ee1d00c585182200dd05c021406c000, 0x7c6ff2b6a64563e58e5fca1f27eaf27df9cbe80f9bbe71f9bf4fe1e6639a7910cb6438ecc61f35bc3979831a41f37f1c08496d34f604892b2e9e9f49c707353a543839a98d5f1ac2350a5d0e3f04b82f898e3ed2b3971c7a38a72f81986972eb43d3cbf72e569e5fa9725c0cd3b827a4fea748d7027531c30e04f24e04470be4a5f38e17cb8d4697d0e0334a2e3a5f38d44d231a50f1e3509c0e4bdbc797a749f97cb4f2f94bd7a797c65ea97a74f645e9f76455909644e9d9e9ab668d1dc7⟩,
  ⟨0x85f40f1fe4fac7b13bf1d38bba5c72d215fcab452728113749704851f30e0c6da2ec117882036818f0bc054c25810506f02dc0c6000, 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⟩,
  ⟨0x3fa1f68f787a23c01d98e887263891bc0da46b034919f8c606122e21590a3c4ee25211687e83941b30c805ac28c13c08a83c0066000, 0x28527127ccdca69f14949a4c24c0d4a69349250693093034599858bcd30930b0e2cbf3c005d8d000e1c003d8cc4d0a8e28003ed569f218c86756003e5d000169fb0c006000e1f214d375fc00789f6d4003d48005eda6a6066ba7162b9796d3b01a77182e35635c42ca00b90ea595d049c5996915e6a1c47ce3fe35ae93d97a7⟩,
  ⟨0x34d1930bfc5e82e11558a4c4f626612988f846021b10307843781b10c6059427c11708603ec18a0ad04a82180f206102480c4046000, 0x10bc800272c001c2f1e5e090e51600061770002e550d1e2d0cfe2835a9e74458392a60863f154e072a7602003b5791f801babc12005e47bab8b6a00339716d000272c001c5b3e5e091835c5b00002000b95430b8b43038a691dc56115d1542e38b42eb8b443004fb3d87⟩,
  ⟨0x3be1da0e346f83551a00cc464c3131760b505942b71568a184be238112885c36817e0b9857026a10e05f82c414a096038813004e000, 0x2060003412797a2718bc72c5fa6444a7c8938243f44c30a003bcd08fa878185b44c0c000681ef34000c304e88016a075d38850f54345b27bb0001c00428bb6c25c78b620005b08f1e13018cc7000340d39ad83e2e7f440010008003f748044d3e90dc8dca9b24f0033539276641a9cc7c00ad4c2f3003bcb⟩,
  ⟨0x30a1798b3057e298147099c4ac22f10f083c4081ed0e306d03541930b6051423c10e07b83981aa0c604f824810a07002d80d004e000, 0xd765d85d8663d96138003a0cfcd818000d065e5e09c6195cd3ce9c599f224e09033592012e2fd734bc478180c964d05a0003cd000317d7a2011682bf4e2b19fc463e19a4acd26126829000ae5d0a5852454ab06955d83c8bd3d96138003a097cd⟩,
  ⟨0x4bb257121c8fa45622490888143e31df0e646e835d19c0c845f82f11660a942fe16809903fc17c09704481e00ce058018809002e000, 0x309e8448003e6c0c0006843f2dc62000684274ec17f152744b53e9e5a8004e9e98500234f4a68003a7a60f4c000d309a9a5f34d4bdd307a984c000d301a752fd41e79a91599c8a8fb7d150d5a283bf1f8e88ecdd9dfc18b8312f89def0000164a2c02e0c633b6e3e487a6671eced26c7f1f3b3cd0b38ed3e7659a0e5439c6e9e39f8001e3e10d86692b349849a0dc002b9742961488b0cb⟩,
  ⟨0x36019d8cbc6403131700b2056024d12088d445221c0fa87383761940c2857828c11f07d034c1760aa04c82280c605602480e004e000, 0x1337bd5d23184761580039bb8005aab0a5c5b0c3c581e80004001000300084ee78f08d08d48d066a13c584f9b4274000f3478488001a137cd38a2000684c74ec21714000d097e680039b3ec4000d094e9d840e2e19a4acd26126848000ae5d0a5853526b1835d87a49e1d9⟩,
  ⟨0x2c014689fc4dc25d127089c43420d0fd079c3801b30c606082b614e09384001e60cc05b82b413008903e01b40c404f01e00c801a000, 0xcbdc00100cf4f243619a4acd26126862800ae5d0a58529ea2c3c45d8856719d96138003a17dcd818000d0bce5b0c400ad0b9e9b385943dd37138001a16fcd85158c0d01eab3893066f4938253b45dc287818018cdf756c27⟩,
  ⟨0x51d24e106c7f03d11cd8e106ba3481918c506122f41668a6852026b12b08bc4101e50d906342b413307e835814004c01c80a802a000, 0x1421d1a45083687d4215eafc1715eb1c788d503a8b8c8f84561c84287c14464e3e0b304d8781d860ab8e2d060759829e381bac700bd43939bbf2a9cebc03ed3e449c120f6a98c5ccebf9a000e75401ce9e06cea4037d4836a9e86c8043e6803ca1b1cd01cd9370f9f3d5f69f569f3a3cfab4f9d1662b9f4e9e041b3a0e3b2ff8104ce7f8f0192044f1e03f40638111c7824000b4017002f27cbc70e513329a56152168a7⟩,
  ⟨0x8c8451a23108e78a3b29cf8e106d230a9750b865b22c695a0a6a4f426792a893a476228911c8442b111086f825c0cb06002640e4000, 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⟩,
  ⟨0x5e02cf95e8aa654829d94509da4d623990047b83b51c10d6c66830d16b8a9048220b0db86042bc13908a03c41980a503f013804e000, 0x81e12bd983cf5d3f9bde76ea659fbcf7e5c267138001a24bcd798b2cefa3e6c69903f4b9f40f6c4e2750d38ae3a07d7658ecb503d31379d412e7b8f6dae863a787f2a65b8ef6b8e55d3be9e739b852e3c86e6c9fc7901b21d78f21aa4064874e3d9914c759a9a787eb0e7cfff3bd37797001f8f008e00e4015e3bbc984c4ef45854c25be3be8084a67fef8fff6005e25ff6eebf52ff8775da9ff7800b12000f759a986367fbb970c6a0f272c423ff3ff861c000c1e6e3c314a217cd⟩
]

def tableRRLLR : Table Block := .branch 14 tableRRLLRL tableRRLLRR

def tableRRLL : Table Block := .branch 27 tableRRLLL tableRRLLR

def tableRRLRLL : Table Block := .leaf #[
  ⟨0x4302048fe07a239b1c70df46d835f19c0cb463830f1740b7856e2a8140896846620c0fa073c35417708a03781720a203e8160066000, 0x3abf452b9a3867001b45239b3a78e850001e3e99a4cd25069714d142000fcbc12d46b613d13e0007cd818000d13ce5c2513aa363ffa6000689cf34000cb32e88001a26dd3ac7dc5a8f2a34d4d3b551b69e9e0a766a35d3c2421f963f34116c2440459c782f0f444116f1c001f31f53e6269822af32b4fe867a1da7f42bd08d3fa09e84fa0fa7⟩,
  ⟨0x7693921bc4d4465d3049758b5e5882b09500a144c524f11dc88233918a0bbc5902a513908543a81be0cb849414807f02e0118046000, 0x8d7a3b5b96771b9c78d9f57ee59b4f7206d6e31d8c79678e9e222406c87dcf11b8ea6d1e5946e07944f2d38fe59d367e2869e7723475e380018a21c7b25514479c5db3db67797cf77a06671de5ea90b7bbb032f8f081a10271e104c1fde3c20883f908078e53756d22da383c505acb2041a253a53b6905ba0b440bb2df1a3814948358f0df8fdc97717a90007ba7d3bba5a2b1cda56526b123670ea3502e9e0afb67ad9d535fc310cbf4ea268003a34f77da7b63e1a7d0a9c9e39d142c6c55254e4022e8331095b8e744cb1a954884c1098a0cb822d538fc7005a9c6d3800714789c5061b148013c380073ab87⟩,
  ⟨0x6703309958c5e6082e91720b425972b8152ca544c7227111083a3fc1e78e7c6f034217e8b5854025b11b083c35814f07202fc0a8000, 0xc893824000c520e4c27977e9cd0002000e28f71e0600051473930351820003cdf007beed88026e659d039a07d1fa482040015578e3c0e503e000303fc10103f41047e8e9e06a2f83fa79bf27ec967f5bf92f63b3bd76986f61c38f5f8a1dc71e9c3d7a286f1e285c50d8a2b141b8f141e284f1e28345088a0bc7691052b20e23bdde3e90fffae9e43136a7e3d43c5c9ce5b63c8365b7419c7b936db61908643b92b9f9d3dc996da8c85724f3f0320dc9ba7e7dee46d3dc93723dc977220c8031fdc95a78f16e3be3b639687453c7⟩,
  ⟨0x55b2a0146ca18501278132492c48c233916c89c4332000fa079e3c51d50d586622ec16b05942a812d07b834817609603f816804e000, 0x32250b982c008d3e449c1232698dea982b9a000cc0c001e9e069810005d4c23389c031b8582353018003aab2a3c5c40173c0d028b42c179c1e027b66ecd0a2f1f4b9a8634e0bc4dd8800197b9c79f7e197e941a52cf50771a5341e601e91c3ea30bc535bba825d078a0ee976d43ee546a3f37c1428452f28001436caeeb8f78e6144514cf8f14b8510c532e38003defea7bdad3001bdeee9fbdad377efdf6e9fbf3efdbbecd380088a47c7⟩,
  ⟨0x284138897848c239114086441c1fd0f5076039c1bd0cb061c2c01540a284d023e10707783901aa0ae04f81e00dc0490188078016000, 0x94d1629a1d01921e4cd1667c89382474d2ba234bc4781864d200068df734e28800ea377d3a46308e366ba12355525e2d517e2c26308f46cc000f34c28a4b5a361d381a4b300075754438b37225b244e09⟩,
  ⟨0x36d1ad0d4065630617b8bb058e2a2137899448023610787a834a19a0b204f42300f307103541880b904a02240f805502100e0026000, 0x110a1e0600eb525d5801161fe9f224e090006c3cd4ea41623eb4001000ec3ad3c0c0015871a9818000d1dee6d81ba8d6c5a7e80019150b3938f09a399aa4f80bbc7a3b200079a00e6a2bb1936c01fd58c9a6ccd5069c1200d49adab84ce27a39e00079bdba46069340015d586087⟩,
  ⟨0x3971c68d986b83351870ba45b82a914f89e84e024911888303ee1ea0e286e032216c0b104f42300f306702a4124087038012c030000, 0x40c002ece8f3a06b39e00279c0022ce7730005b30b4fe290004003b3034f03000565f6a606b38e00079955bf8a008596da706353f198005b14352e27a3f000079a01dd8b7b1818047b1675761d0017a9b11800bd48015622ea4043b1235708232f048280cb0006c4bd580036255953aaaa9dc5⟩,
  ⟨0x3941c50d8c68431b1770b8c58429b13a093446a2140f987303761aa0cd85d02ce15a0a384982260f207282f816808d03000e4024000, 0x81a37f0009e6800d3c5a4003c6fce7d3a80080159e1353a000da4000d223e680018defd100034883a7566f8b4df4db67001a79b38a7ab3cbced334961a4c24d9e10017cca14b8a43846004d395c83646370d385e184f6764001f3a060003675f980020054d772001f3603a81b6a6bff50ba47⟩,
  ⟨0x2a714209cc4c4253121086c4181fb0f707843981a50c906142bc15409684681e60d206282d815009704501e40d406001f80c001e000, 0x6d0404f87f4349f1a57248c1a6922800ce5e849b435d0a5c520c0ab8fb88a7ba66f22d84e000e91e73606000348eb9780a4514bc7d5e9d4300959e8527126086f534f8a4a4d2612606a7e005b49a49002a7cb49849⟩,
  ⟨0x50a26a123c8d44452100fec7ac3b11b60ce46282ef16c0acc51c277120882c3e018d09c84501de0d80608288108078031813804e000, 0x2903c45aa40bc78a8f24d5ad3d022e3f02dc0c6a7bfe1c8353dff0e43a9f000720d48e3fdffea4724efff58ab9500db6118a79c7eee086ed8374f8e763a3a90007bdfd4f7b3a6d57f561d48003ac1ea7552d349266b30d5ef8eab3a4e7be3ae3eed7b07076271c41db1499853c86e78e71c0a4c429d076088538ea57436fa7000651dd4ca2fa6a7319201b8ad1c0c904c7846aa8b303ea9c01f5a14e70719b427ce⟩,
  ⟨0x56f2a513ec9ca4d826292d091e47823090f082a4091fe0f5476438b1b20d5c66032617f8b6856628313c89484561b908d01ec08a000, 0x1b18ce9c00100080198c79f5ed3fd570d46681912be690006391d4c717a68e3b4c000c6fda74713692799c8dc66b48c8c4f9c001fb461ed219f69e72389b487ce613da41470fce8191c2da3fe6000318169d17fda3ce67d48002003c3c0d68e51c3f391c35a38e623cf6e7c6814d0438a2340f3b7b8ebad575b2eb7a43cbd30d44af495e9a6934d1cf1d7a62eb45d6abd20d44521d5d6c6930d1c2eb7e3cf0734a150238edce9c4f1a4f9e0dc7⟩,
  ⟨0x3851af0cdc65a3061770b7c570282135097449c241117889443020e0f3873c30a1760b3854828e13a08984241c40bd053015c082000, 0x63bff44001d2a8e9c0c00063be72ea55f14c2380018ef3cb00031de000572aa5e7160cd791fc525d23c0d62981ad3123b0e654b9e28040051f6c006009f0e7126253422aa613309d1945a5ae740c8c9ad2c7300018c7b5318c6980050074001007231cd3fcb70c0018036fb04635a7⟩,
  ⟨0x4111f70f2c7703ae1c38dd86ca3561a38c906022de1668b0c53822a10f084840c1f90e906ac30815d09b043c1d80c904c80d804e000, 0x1d2be1f4b3c9cc5d428781a79f1c99e5cb1a560d31124e24efbb7db8b000f1df0fbebdf662e04cf031be9a96fcb0002e3b9bc500020006001279571e11b11b91b0cd4ad8000f34000d4b0e89be1a567d300034acf9b3c8ce42f469588001e6801f7bb91e3369030fa39e32e8ff0e6918d219a45481b3c72a24f1cc238001a557cd⟩
]

def tableRRLRLR : Table Block := .leaf #[
  ⟨0x25512388a44282010fa07943ae1c40db869832e18d0bd05ac2b414b0a0847821a0ea06d833c1880b504701cc0d204e01b007801e000, 0x1d431c90658fbaca794d0f429389314340a89f14949a4c24c0d02a24d24971a4c24c0dc06019e3468d2031e0263db13f23426a492008a9697343e0153c0c085b2aaa68f16a68f17324aa49⟩,
  ⟨0x3711b10d6066632417f8bc05cc2c114e09dc4d025112308843f41c70b9853825211c074837c1740a304601f40e405d01d007c02a000, 0x61260691b4005d49a49000a46bd4984981a4c993475a000c8cfa9933e4c7d7b62791934d09a46200075291b297e736460918645ed3b92d6f933da40219a87e3c84521069c02990834fe290004027907b4f03004b20eea51c263c110c7c89382418952048e0de341f0353c0dd3ca9⟩,
  ⟨0x5b127290a078a3ac1c98de86c635319e0cc46342d514f89e84aa2220f786f03321690a10430170093037016c09c03f0188078022000, 0xce6e94855f649147ff8051009e6012bdc8d8350a86011496b8ebdc980430045ee0bdc58039b053689429e96c9b073611c7a9887ff0050009c49113e5f8f5318e9b68c74c5daba40fc64ff637ef6c9c13f7d32c034247f9f1d52ef8e019e7c6a467e3b97923369dcbc91974ee5dc8c8e5969e43e80d1cb9d3b95f01b3971a7e58f31b0fcb4e5873170e72dea8af1ce5b55143983c700ba016c02d005c9f07c791da482d3c90200b69e5343d0a4e24c50d02a27c525269⟩,
  ⟨0x30e17d8ba05a02bd1550a6c4e826111d08c043a2050f9078c3b01c70db068432e1860be055428c11f088040c1e20d906082dc13e000, 0x34b45d388784f6870ed0f6ba2cc23d3440003cd0d122000e9a0f4e060c51760a38a8921f224e091f34e59b44f4cf03159a606a66a00079a6944002d332e99a477159509562038b60678b035816e2c01f8c12d9e609ec12e8f75074a1be43bd8457c7⟩,
  ⟨0x24d11d08ac44020f0ff07a43be1ce0e2067431c1670ac052c27212108483fc1ce0d806482d014a09b04301cc0d20420168070016000, 0x8921f224e091f34e59b44f4cf03159a606a6c200079a6944002d35ee99a47715950955be78b5a438b03568de29849954d206a9a48f032722af8243c0d4d3c000f34c8163ae696c34e09⟩,
  ⟨0x2db15c0ab851628112d08dc44821510007ac3ac1c70dd06ac34017b0b5058027612808a84081d40e005c825010a07b02b013004a000, 0x15e1c7918180b50e1c5c0d4e18000f340a5f97c886a89994d0aca74e454c692a4e24c19bd24e09007eefad5c099e06bbdc01dd587e87d6d174e21e13da1e06a6e400079b76e802db1848f035dda00a6ae06a6d800079b76b8023b1⟩,
  ⟨0x2c61570a6c518281137092c46622910b08303ca1c20cd86202ea1660ac852827e12808a842c1d00db05c02b013e07c02600d004e000, 0x2b83f151c43e449c121ca27f6f0fec6847743c0c2aa260600034e839a001fd8e4487bd39de9d5c896d11271260cde9270489d2cb8050f03019bf4d8b6138013f498b84671380061d18b873fe800038ab0f3c5713d38b0003cd⟩,
  ⟨0x2c215b8aa850626c131092c47c22d0fd07b43b81cd0e106c431817a0b805842ae13008f841c1de0e006b02c414e08002d80d004e000, 0x213389e9e40001e6e824d181b59065b89c78d748a001a0076ab4cd1867c89382464d2003d21dad2f91e065493030001a76fcdb138d6efe2d6ebe2c247818057a40f570353af0003cd013e900d8d3ad0003cd618a8fda755d3⟩,
  ⟨0x3311910bf45ac2af144098447422910c082c3c81d90d906942fc1740a684981fe0ea06f032c16609e04481d80a2040019808802e000, 0x1ea98001bd7b4f4fa17aff357a953e7e6d3e65ec1cd00034f979a028ac4ef464cd25069714d3e0000fcbc135cec01a72d84f4f70001f360600034f6b960006b9b74401753d7e9832aa711bd443ebb343c41aa4285521ea1c00ea48b563269b33541a70489e2cb⟩,
  ⟨0x2fb1750b745902be1578a9451a27b131896446421a0f987903aa1ae0bc05b828e13b09604541ee0df06382c014c0810120060018000, 0x5299fc523066781b224c0d62fb8b0a23d8bfe340c0006c5ef26c5d716c5d8007e3da4984935cd0004f24000d8b70007c781ac5a8006e4d231847032d9728082655751e2d72be2c402c781a9410117572a700020010006002370da7c46c46c46⟩,
  ⟨0x23b11708704242030fc87843921bf0d606743201830bb85982ae14a09f84b822c0e606d03241780aa05002340ba045016808001e000, 0x78a4f64781aa24c0d638f8b66050f0351487dc8f429614d231f1a5b13e19a13509a6c7df14011f80000e1f11960cfe292f11e060c9120010017de715632f8b63378bc66da33fe49⟩,
  ⟨0x25812008d84461fc0f2074437c1b10d106543101790b20554294135090042c2000eb06c833c16e0ad04a822c0e605e0170080022000, 0x8f28781838448001b81fceb249c5abd0f7621fc52b925c532663092360a9ac938241b552d1468c1233c26a41549748f0358f4e2c0d63db8b03590de2b30a9c041f9600c61fe86fc932a67⟩,
  ⟨0x32e1838bf45ac2c314e09e44d825d12788f8462220108881c3c81d50d9068c3321740a884b01f80f1067029c10405b021808001a000, 0x1d46ae6c0c0006a3472f0148b7a3877bd3fc7004b0f42938930437a9a7c5252693093037e1800b893492002fc2624c24c0dbcc8013ad000fe0312003ef2faffbe80040058784df7c000e24000d451e68003bc96c4000d44ee9d960e2fddfee3872ed0fe29⟩,
  ⟨0x3121808bc05c22ba1568a8051626812988c04461fc0f9072c3361740a684d41fe0ee06e833817a09604381d80d205c023808001a000, 0x34cd258693093713c005f32852e2907e560027f8f9207c560023f8b986138003b88fce818000dc45e60004005fc0c900359fddd400033fb7a965638b3725bc88027e3fa1a4f8d2b92460d351cc00672f424da1ae852e2906055c3c46f55d337916c27⟩
]

def tableRRLRL : Table Block := .branch 13 tableRRLRLL tableRRLRLR

def tableRRLRRL : Table Block := .leaf #[
  ⟨0x276131895049023d115086c4061f00f187643821b70cf86383021700b2054c28413709203f418e0af05002580de06202c00c404e000, 0x57449849c46c1219a26f24444143c0289713c0d66078b035980e2c099e4cd6267a4694349c1a7048ba8c0003717b997172e2e8001e55973e2f24781800bdc59e6389e06b8aa00539d030012b8a9ce⟩,
  ⟨0x33017d0b885922bf14c09fc4cc25b11b08984021f20f387083361680af04e422810707d03bc194097039016808e03a014807001e000, 0x3160006cc3f2acc77178c05cf030187b2ffcbd6d074e7eaba704819d50a6afd31838780a34f91270480030136a675b0386e680021c14047a7818380808b5200d4043a7a14b0a713403800b6a40158070001d3802900dea6124a1fae43f8a4a0d2e299331a49⟩,
  ⟨0x3fa1ea8f207763b01c58d6066630e17487843941a50c905fc2d815909f045c2180fb075036c19c0bc059028c0f806402d0108036000, 0x4a81474f429614e268130046d4808b0260003a7011204bd481f9742e9c0fcc10b4ef95dbfd523800800004fdb264101e803d50da82554acd256e4ae4bad8ae71eff8f027e9b45629174f89a265744c44890d5139b0842c007d992e5e09d835cc9a6f23f8a4ba47818c248001b313cbb30fc581acc2714000d989e3807190b⟩,
  ⟨0x5812bb9550a8a53628793a09aa4cb25211408343f71ea0ec471c33a1968c285ce2c41508a2c4d024110d07cc28a12007d80f804e000, 0x1034e64d898bcc92a924000c5ade38f8d8b35cb9050f031a608b2fcb000f154a2a9c4be37b1c7347712f4debf1f48da5fc4ea8f4c58bd51691f17a6cd2161c7d200018a991534de971e0cda56d2ce274ada5cc5e9574838b000e97313a57c300074a187349d53cf9a0006a79734d244586e8ad70700c19f0d910b0992ff0c0a3e743979778f6b38f37af285a7def258dd3a7ae97bc09ac000b8069773259e4d1099d92d149117caf1e189d32f1086ddc7⟩,
  ⟨0x2e81680b1855c29d14709f44e025b128890847022010707d83d81b60cf06182be1500a084681c80da059829c13007902780dc03e000, 0xb6f9c581adc5f17a8cff92694cfe2918333c0d912606b6abc5a511edd171a060002000add072ada8f16db3716dce8007e3da49849365ec004f24000db990007c781adcb8006e4d231847003b2a97b2400802a55998e2d972e2ec400347⟩,
  ⟨0x24811d88504141e30e586e03561930c485d829e137092044c20c0f7075037419c0bb056028411c07903501700a203e0160088014000, 0x613dd110007ce818000dd0fe65bb9e297887f14847a43c0c1ca24000dd08e75ba3e2da087cd33f8a5724b8a68cc6124fe44e649c121da25e6cd0d89f08684d60a24ba4781adbd71606⟩,
  ⟨0x29c13a897449423711508644181ff0f807743981bf0d9067c314177099048c22c10b07d03a01bc0c605e029013408203a8138030000, 0x355a7a76f978b99a1df043f8a4a0d2e29d331a49559132869a14b8a43244cde9a0304480070012002ee9ff21b13e99a13589a4ba4781ade471606b791c581ade5715c4e0006e8af32e8a5d150003cab77fc5⟩,
  ⟨0x2e91610ab4540279137892046a20e0f3870035619e0c786042e01630a9050c27212408a84001e20e706002ac10806c030813804e000, 0x11384f02f4c68156c270007561f9b030001ab0bcbd052277fa26d74eac10001e6c35276cdd1c1253d0a4e24c10dea69f14949a4c24c0d40aa9349214ca93093034bed0013cd06254800797d7cff8448784de0a24000d56ce6800197cdd1⟩,
  ⟨0x2ff1780b245782af14c0a044d4253123087c42a1ee0e806a430416a0a984f026211a06302e014e09604381d809e040017808802a000, 0x1849bae2002f9942971481cecc137da4072b3045d6c309c001dd69e740c0006eb3f30082b0d200bd4443a80006887f52e007169cd64cca4c9c132e8b3034f8001842877c001571e686f4349f1a57248c1a6ac8000ce5e849b435d0a5c520c4ab⟩,
  ⟨0x276135097c49823d112884840a1fb0f187643821b00d1864830c1750b2056428c11f07483441840b804882100f40530248088022000, 0x311b0486689bc9111050f00a25c4f035c29e2c0d70b38b02679335899e91a50d27069c122ea30000dd80e65d7ebafe000795706f8bc91e06002f75ef98e2781aebb8014e740c004aebb73b4cd25869⟩,
  ⟨0x33e18b8bc05922b11480a044ec25511708043ee1d60d786202c2149094046c21c10307102d412807c034817009603e018808801e000, 0x2af50001e6800194b5d10003579fa7715b8a0113ed67c8938240067d2d33ad4003f3400400e7c6cf03000cf85a4000d5dee680019d61d10003576fa771278a0353d767a14b0a7134f300b5a4056798006ce0293cb69849287eb90fe292834b8a64cc692457449849⟩,
  ⟨0x34b1930c5c6182fb16a0a8452e27213288f84101fe0f3074c3921a20b784b824211308103c41c80bd059027c12406b03080e804e000, 0x713800669f224e091934ced994efcd0007897001f4f03715e002ea5c4e000653972e5544a710005ca81ae377166143c0c005253672c002e320003d38003c63f07400169f8cd943499a4a0d2e29abe6001f97824d645b09eaf78003e6c0c0006af6f2e01488004bb61d3⟩,
  ⟨0x36418f8c405f62f01678af456629b14889e44de25711b080037e1700aa84e825e10c07d836819a0c005a82500ce046019808002a000, 0xe0024005de0fe43627a98b3426a96001b49748f035d3ce2c0d74f38b035d42e2d4654759dcadcce991f7c7f6f97b5d1c7ca0d3e8dfedeaf69a38793fa788c2e130a8842704842694f8bd673029d1259e852c29c4d43e09f6904ea1f001b3826d0f5a66d44b2489c125c8ab⟩,
  ⟨0x2ac14d8a3050426d12f092447423010587d83a21b90d7066c2e814f09404401fa0ea06e833017e0b205182080e206402b80d8042000, 0x2934984981a81552692429952612606e9d8009d68312a4007e9d35ff0890f09bc1448001ac79cd0007a6fd88001ac73d3babbc5ccd0ef821fc525069714e998d24805550da650d3429714800d4eda66f4d000353769⟩
]

def tableRRLRRR : Table Block := .leaf #[
  ⟨0x35a1a80ca46282ed16f0adc52026912f88e044020f0f406c831a17e0b9859027a10a080036c1a20b903a017409003b016007801a000, 0x206000359a797702b1000f16fba6611c000d665e68001a7a3d10007598ba7030001a79dcbbb0bc51c338001a797cba7954ee000572aee000234f9127049c4975194ecf9a000ddb6001e9e06bb64002d4c0d75e78addfc000d3a9ac71c7d8c34d824a7a149c49821bd4d3e29⟩,
  ⟨0x33f1980c985fe2ea1618ae452426b123071433c18b0be05a42bc14b09b04a022e10607b839817e0b004f824810a07002480d004e000, 0x624781801453e3e5839a9c014d3e1e5c0c0006b4273401053dee8ddb71be69e4afd6f389272c41ccbcfd29c1084038f0a8107ff1c3d44c0a6ff113827db4583f29e886f4349f1a57248c1a6b3a000ce5e849b435d0a5c520ecab8b8a003ba6368ab6138003acd7cd⟩,
  ⟨0x44721e90588123e21ec0ec473236319e0bdc5a02a9141096c46820d0f306fc3301730a604941fc0d7058022c0cc03f015006c01e000, 0x40d79c4002f3984e000ef3873a06000379bb9979af8b36526f54d95e3cd6e8641c78a4938a2a484b57e3af2a971bc7806c2c1b9300d8583f2601c0b06e48b05806fc9161500df9935997daf1e6b2c066e3cd6400b9c7df637dad4c02d4a3bc9805a95639300bd2abf252ab402ee4cc02805dcc32e251ad3f34a02a69e9f28053e3db82a4c24e235649⟩,
  ⟨0x4011fa8e8471236619f8c605c429d14989b048a2200fd87583621a20be855826211e08984001b20b204582000b204a0200064018000, 0x148d3c7c0009279ad6049eb8f3e4b8c001940e1c94156c6e69284ad8bcd98113c6ab55f1dbf84fbb0002e0578f0356c19e37cd9b62b3478f6ae8013a9b5bc00ad4daba004ea4008b57353d124001b56b537a0a7e5733aeab4434e18a2613060899f8b79f798001a7e1f267e10005e4e099f82003399891e06001379d798c27846⟩,
  ⟨0x5df2b693ec9a849e23b914087e4352070d446883381920c6061a2e615f8a604e224a11187f03aa1ae0bc04cc25010106d02540e4000, 0x26450fc81f9532225e7838d1fbf8e990932241c54c86e7f9322a646e3c7f3b2a1c78fe5653e3f6f1c000c7eae3c7ee8fdfcbe133c0d22be3f672c000c1a100041f68001a5e429f4d9d20ce14f9000920b78fa66846ba746e46c4d20c6b6df34000c885e3c88aadb3cd000322538f2246b6bf34000d6d6e6c8a18fbfd100031c138f1c0ab69f3638c80028df7c78e3000066d9c6fae3c2600030ad38f1c6eb677357a14c119d715ad38e00793ce1eb59000324f6bd01c1500019e11c7⟩,
  ⟨0x98c467a0fcf047783a89ac8d506813259818ba05a92c114f49d24c4247119c7543561798ba058629c13a862c2f4169074030c120000, 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⟩,
  ⟨0x5b82c895a8a8653729414049964b324d911c7323741aa8cc05d62b51530a3c4d422910f08443d41e00dc86502c212b08202fc0d6000, 0xae5400079a0006ab4744002d727e9d2318470003559397558c0008002e5583ae2d838e2c26d7798bdbe12ec26fe3d6bbad7b074e1cfba352a73076dbbecf75af2562f38fc5ef177a7037cbe8e00bd5bda7a86a1ca6a9a3cf6e3d43479ea34d38e79276a6d36d4a0036a768e348fac200074f09984eeab6f6ef3a0675577b6f99d4a7521a7ea4fa8fea3b4f28824f63a8ce3cc889439c773b4f3d1ddc58a9e3b9d979e6e4e5ddbd8a8e3f76d9f377b76987271cec79e5a7⟩,
  ⟨0x35c19b8c105be2ba14a89b84761fa0f6076c3941bb0ca061c2f41670aa04b42400f9077832016e09003f81c00ca054016806c022000, 0x957369fd3cab7b4f4a4da70006524d3caaf2ac6ac00194cb4e94c2ba2f376e7e844002d3edcdd0872e0000e9f086c334959a4c24d73e0015cba14b0a5184586e8bbe5b55ffb2c2700075cdf9b030001ae6bcbc138d579a819d38b33e449c123a69001755b79a5e23c0c3269⟩,
  ⟨0x499231903c7763961b88d3064a2d11600abc540279136097c4742150f707843741b00c4859027a11806b832014607e02b80c004a000, 0x9586a60201fe38018aab0ddfd2b72569e38017aaaeddfaacca568e3cabb2bfea656d95ff532bf4ad9a9ab5557d79600492a23779aaa4958f8f86692b349849aebe002b9742961480112c36ac0019617577d26accf6584e000ebac7360600035d5b972bf0003b1ab274893a72a9cad7a70006533954b6a7d3d8a69554009d4cb1b2afeaeac6a55fe5d58c0053cbc12013cab9ab⟩,
  ⟨0x45322490a883a40e2010fcc7c03c81d80e6070e37d1af0c3c5642a714d8a384ce24811087f03aa1bd0cc05c429412307e02dc0c6000, 0x40d38c03d2d84f292e918c238628b80448ab341c5b339c58133c0d36005d2c002000f5d281d0004d380020016ba1ae8c0e6001e9f134234998000d778e6cce0095100035ddb9a000cfc1b100035dcfa7663f8a000cf9ba74f9d5dc79b5dc0263734000d603e3d76eac69cd7474808aa61d58fe3d4c26f04006eaada021e3d4c16f02006aaad47bd4041c7⟩,
  ⟨0x3861af8d406863321938c685e62ce1620a7c4f42550f906002e215209d04b423410c07c83981aa0c805b829810e06802480a803e000, 0x2bd51f6fe69e49933431a613389c000d7a4e6c2cf0b0ec60685fe15fd580030b069e15c857757589d567000248188f86c9d71eb1328fd3e680004f9b290040f7c7b94c0368151e3c0a1eccc1ca266869611378a2468d3866b934c51a67500da5ce99d94b9d73b2973ac0552f048089d34b⟩,
  ⟨0x3831b58d8467432d1830be85da2dc1530a384fe25812488884302070f7872832e1720a684f826610e07482d815808703000ec046000, 0x5a07e2c0c007265672d84e001265572e119c4e326b00113298000f2acfff14c23d7bf0003cd30a20046bde74e06f135d9f9e2c2f10b869e17785be172d3d20948169c008a40b4f91270480034806a6978001b5a000800747ee9e0600068fcd4d7ae0003cda5c0001d8d9e7e28007edd87⟩,
  ⟨0x2ba1538a484fa27212e89384362080fe87a83a41ad0c4058c2b014708a03f01c80da05a82a013208d03f01bc0ba0450168070022000, 0x29644facaafc11578242e956692c004a50e94ad50e68bc1310a2ed0e71683e00435741e8009ab000e83cd5e091c35d0720008005aab437c5b433c581802aa0d756c27949748c611cf25e2895683f8b68478a766bc13226b⟩,
  ⟨0x3531960c5c5e02cb1580a8c4fc25911a087c4101e30df06642e814f095040c1ea0e7069030c15c09904201d40c004b01a0084026000, 0x213ab015cd07253d8080003cd012a866d8fd802a7a3341d0016ea610800b752016420fa907854c20fa68418037d4806d082ea4051841756000d2bda7005e95ad5802b4b069c18f1f8253ed0d24303d2a725363caa78c1520d2a9ad4d550a99e954c258cb0d9138435ea89⟩
]

def tableRRLRR : Table Block := .branch 14 tableRRLRRL tableRRLRRR

def tableRRLR : Table Block := .branch 27 tableRRLRL tableRRLRR

def tableRRL : Table Block := .branch 55 tableRRLL tableRRLR

def tableRRRLLL : Table Block := .leaf #[
  ⟨0x3281808ba85b62d015c8a484e826a12989244441fb0ea071c36019f0c806142dc14909b84b42300f1066029412c07f02c00c404a000, 0x51134beba623431f224e090395933424035f34083c6c781816164c0c0006c10734000cd03e88064b03bd3f333f88c78b33e449c1206032403ea1db5a5e23c0c0f8a9b02600079a000d0e3b100716043a7c2980c663d80e0003cd00a133c7a308c000c279a7⟩,
  ⟨0x3b01c58e046b43331860b5850426912908b442c1ff0f7876038219a0b984f425811b08603941b00cb05a02740ec06902100e0022000, 0xa154d4c0c0006c2473544bcd2be8cd104ac7c74ab1343d2b171e687804c009a028144af1dce5dd78af32c072a28357c7332c0f664ed636ceac9e9ad93347c038f2e68f0078e5a1309a0800678f86692b349849b06a002b9742961488f0cb03dd97807d447f6584e000ec1773606000360b397a271⟩,
  ⟨0x4112030fdc7a03b11d30e646e43681a08c885de29213688e842a1f00f186c034c1810ae04dc2400fb064028c12808903200f4014000, 0x1098f24a532c063ccbb60068f09984e94d3016f3a064a6580af997c2f1d1c5cca3d05d0d3d1cc05d8bae2f7812f469e9e589a34b4f461cb11468e9e9aba69f4f2975353a7f148003296534fa781a52aa69b534b58bb1a794a8001d3ca55a694c29b5d3ca59297d369a7002215bd3e449c12000c2b1a99a62a2b39a00080070ab69e06⟩,
  ⟨0x39b1c10d6c6683011658aec554299145098c4ac249118085c3e01e30de06c83161740a684a02120ea06582b011a07e02f80e0022000, 0x6147ba66b6a9e8e5cd6c4321cb038e1c901ab4ea3ba69d8001e3f263619a4acd26126c40800ae5d0a5852114aeb01a475e0709ac1d96138003b0f5cd818000d878e5e602d19ab5553fa72a88043a9bc602a9378c05d26f15fea4dfd013490117f293d12400dfaa4e0364a6fccc06aa3df983069⟩,
  ⟨0x30f1740b7856e29f12808dc43c2050f6077838a1b80d4867031617e0b685782a813b096044c2080fa06982e812607202c80c8032000, 0x3c0e7ce818000e071e66058e2c3d008143712d04ba3a7adce74e3e73a727ddd7a7a4eba21b484dcf4293893e66e534f8a4a4d2612606c905749a4902c7749849819478cd76e680e1ba66ba28efe7e08100b9f0005d362340237361f0dd32186e9⟩,
  ⟨0x24611a88a043220c0ff87c03ba1ce0e186c83421920c285e82d215c0a904e8260118085839015c09604381f40ac04901f806001a000, 0x334cfe295c92e29a3318493c5139927048f1a5e4d0d89eccd09a44d2e2781b03671606c0e7c57138001c0fbccc0f981f4000f2b032f16923c0c002703c731c4f036075000dce84cc27⟩,
  ⟨0x4aa2148edc6c63511960c4c5d82c71580a2c46e1f60ef872036219a0ba853827211207e83a01ba0c8053826811a08203080d0026000, 0x319ac1ab50c95650c5814e54955dcf8e18c91502c19b50a862abb9014de3d796029818c50e3229fe3ca20c0a1529da701b873d8e40173cd0006222d4c43fa604f65fed3a967000404f26d5a954e3d2cc00082772f269e5a7d37368c9e8d193cc23265a4009b598284012f301c152008f0507326855304aa9c12fd8ac01a829b3d0a585389a09405ed202b04800367015828b4d2087⟩,
  ⟨0x3401988c285fa2f016e8b28546296137899447c231105078c3a41c10db066c2ec16509784801f20ea06182e413c086035811004a000, 0x3093642400572e852c294dd161b22f064cde8ecb09c001d902e6c0c0006c8072d862003ec7ef4e6f0d262e9e29a52cd3824077785800330ae9c60d6001e6ec2613e51847000363d39a61440b858f1e9c0d6e00c2ed877140364838001b1dbcdc865aaa3ecb44e9a7⟩,
  ⟨0x32918d0bcc5cc2d91630acc51827f12c093844e21a0f987303761aa0cf86102be15008e84401d20ce06202a41220500188088022000, 0x6126c94800ae5d0a58529b22c3545e113531fd96138003b245cd818000d920e5b0c4007591de9a988a7dbd3b534a51a70480f4d0b000698cd39e4b001a981a62b54e27000364539b9f01c4606cf006176cb78b1036ec7bb252efa733d98e8f029b0cd25669⟩,
  ⟨0x3761b08ce864a2fe16b8af052a28613c89a04ba25011488083f01d10d606142c012a08283d81d40db06002d812206c0238088022000, 0x1a54f65240157341d94f651c01a734000d946e6f4787119b7c001b8e79264cd0c6984ce27000364fb9a012e70ff46060373387796000cca9a70087386f97bbaef3da76ee93fe1bcef1fde107034e612711ab24ef003078181bda66f56000d341a70062999d5ccae0dbe9f0cd25669⟩,
  ⟨0x5a02c4954ca1c48d1fe8f1c74036a16d0a9c4cc24b11808543ec1db0e006c434c18b0b80530284127073035c1100710308070018000, 0xe8df4cf1fe314d881e3bc7ea57318a2bdbf1ec5c382eadcb2082c8037d5578b65c38f62ddc16d6e4903f63fdbea45dc578965bf8f5fbebfbd7fde3d268affbc7afd5499ebfe71dcdfa5d159256bf80e357eb4406f83688d71fe0c9a2c6b6d3801ff05839235ae9f8de084f43c109eff3e127a75d52fd1d885853a907c89382403d684f53c70d0083f9f078181bd2848003efe8d4e0ebe9fd53000b33d0086352ccb7a70379935d8c99de70100010005c7b0c6a46⟩,
  ⟨0x5f22d69618ac253c283134093445521810247c43ca1d18db46aa2e315e0a544dc238108876c34a17e0a4040c1b80a603080f004a000, 0x2325443d8c13450b8f18da22c71f14bc62753cfe7057a9b1712dda319f1ec91463290a3c78c89180de4d71de68c6307c5d17eb8e000f9b5a779b166079a000632272631ef1a315c63ae3c6278c5518e78f18fb8c8ea9d0758ccb1554b31e48d968e3cec89f4dc7b01d6023936296bf1f1ec5257e2afc1c7715d5f978e8635c56d7e4e3d7e9afc55f738e4096bf071d3d49024afbfc7afcd5f76befd7d9e3d807afcdc7afc5601abf2f1dc66b984790943d38e000f477a9e8d34dd19f475a9⟩,
  ⟨0x5902b49510a6e510274937c97048221e8e006b63281718af04b224811b88403d21b30c805a42b415009484181f80d5057016804e000, 0x366cf8f0bfc301ab7138001b34fcdabe8e3bba30355f371d9cb8cc71889d0071e331462173fe89738f64f2c9f39fe8c40f2da22e5a13a3ed63413082242a24dc7f1b754ad3f799e366a93a7a11cf1adde5b548e3d0806a8fc714190665908bd827dfd08e38f2c695834d2699dcdc7a3f06aab8e6a8e8fb9aa9e3800754987354d49a797491e0635b3499b96001d6261e06b31e00079a6b12931745aa43e737ddef5ce76d71feeeee1fe41d3d11038f5c7⟩
]

def tableRRRLLR : Table Block := .leaf #[
  ⟨0x2ed16e0b345862b01508a384fe27512808fc43420b0ff07cc3c41bb0d6067432416d0af051825c11608283b81920a403e8160066000, 0x526930930350a89349229224c24c0dc857189ad1e34f185c846bdb13d99a13489a6cddabf4e69e477097824001863b56d8aad4ef16d4ff16d50f1474d30c369a185003352005c309a971ed644f97c7af15dabaf938aad3d7c15f1f153a7⟩,
  ⟨0x3931c48d8867a3161828bdc5a428313c89484222050f007443581870b104f423010d07c031415a095041017409403d017008001a000, 0x40c0006cf4f34001e3ab62004ecf374f84cf2430007623e9c001f2c2412e61ac1ad3c0d6785626f3403c00061bab0634fc8c000c36fa9d14c019c36da986d4032d4f1b90d8eaf8db001356001f1b5abc120c2ab00078d7000b556afb8b6af38bde22ec09005b4f29a1e852712628681513e29⟩,
  ⟨0x4df24d10647302db13c09b44902210fd07a43b01c90d106543101730af04dc25410307c834818209a04381e00da05a01a8074026000, 0x21e943dd22da15371e01c42f381aab19d0f6d9a243d122d78f00dd0f3c6b5b343035163342f243a7c7a5900009e8eba1d79a890d90f0a1e443cc879635a5829e3d2c700035fd5d0e3d1c003bc7c4c000c881a7b40691079b68092227370cd25669309367f800572e852c29227558332af0f43941ecb09c001d9f7e6c0c0006cfaf2f44e2e4eea61f4d1f43e449c121e2278f0006b5a11e90f030b089⟩,
  ⟨0x44e21390688083fa1e98ec070035d1950c145a429113d88b043e21410487f43ac1af0c5058c28411b06d022c10007302600ac042000, 0x8ad61f3e6309e2ab868188ab61efe744db5738789944d757187d5c6ad30f7d76cd5891e9f122bf134f7dee2437e1e9c0012f23667beaf4fa63c35ef20008004001df1fa7933626c4d08d68617a2f357ab5a17e680037c469d7c35a15e6800e0b59c60a5a13e6800594e6d2260369c001ca6cc7bda40c05d3c267138001b41dcdc03cdfb8c0d8399bb6b⟩,
  ⟨0x3c61da8e386fe36e1b08d5068631c1858bf85ae2cd1530a5c4e026611f88603e21d90ca057826e11007482d81260630200064014000, 0x60d3692400672f424da1ae852e291d35cfe0a9f7d36b35b09c001da40e6c0c0006d1f72e928d4f49fb3d3818000da3ae68001aaa9d1000368dfa773bb8ac1e2893d1bb7e4dc760e546e853d71df35d18be3d18a7e37c97e35462793855e20a8ab69e2b7157c3c56a2ad155c380062a58722af87db99891e06⟩,
  ⟨0x49d248116888442a20d90307fa3ec1ed0f087703a01c88e186f236119d0c105d82d41568a184a019308903ac12e064018808001e000, 0xc2b0003520000172adeff16deef14f23b84b308e306b3d92adeb71606b7b5c574978274576f4f8a0006a8972ea8880010005cab7a5c5b7a1c5000318878f187630f72c1afba1f94fbc7490545128ec3f2a75cd6692cc153a47ad32a6800cdbefe3d143a3aefca654c8018b3db67bedf771e8d8bf3be4b08d7ead450254b8016e3e0e5844e125a7c22ca93fd534fe8693e34ae49⟩,
  ⟨0x3d51d70e1c6a232a17a0abc4b624c10587f03dc1df0e886f83561a10bd055429012307f035c1600a503f01ac0c004f021006c01e000, 0x6507f2402955a4e7ca0c009a00078f2830026f2654b3c650099c70016aa28001466be3800a551200063350003e3d2a6aa1c0010020002d3d8a6da18c24d10d31a245244c0d2b2400972c001a9f753666002aa7cd4d4f6004ea6562000ce5c63d0025cbc12004231df2e0845e096e35b09c0025484e5d231847⟩,
  ⟨0x3231678b0c55a29e1488a004ea24e12088684201e90e106a830615c09a84382020f2072835018e0b605382740ec06702000c404e000, 0x100052aca742133be3e234ccf0c7926ccd4c69c4d89b2749f3984f89aa74973a069d2189a398000654ff26514718000ca1ce3ca27c4c9cc943f28778f287402f71e8527127ccdca69f14949a4c24c0d2854002f24d2480029427c930930355a600a9cd⟩,
  ⟨0x69c33a9940c3a5ea2e29648ad653527812ac8f04371f40ce84dc20b0fc079c3ac1af0bc850c2380e605f826011207f02c00c404e000, 0x5ce18a4f997385cd9a7b9bee6bb9ab4fc546fd573469f86de2ab4fc4d70d9c54e9dc23d394e3cb0a7bca2eff8f2c268c1bde4177dc79611460a3508bbde3d583ef11779a7ab03de1f6f4bbbd3d57fef07b7926a1775a78e58ec7c1db5937b274f8085dbd31da6242a1edfd71c5db90fb176a2edac9b472b076b64e5d8f5311150d4c71f00f1e71b4e8c00272b0c6234e7ae3dd687b834bd1a6745ce76e3ce8a9ceb39d38f3a1a7444e83e3ce8c9d09c79d173a0e74171c000ce7fe3ce88c4f5cca48f034e9ec4efcc954a00078f034e9bc4e9ce⟩,
  ⟨0x3551a10c6c5ec2e916d0b305762ae14e8a3850825f12808ac4382120f5871833e16c0b084f022a0ee06382bc11407d02b013004a000, 0x180a46925d086e9dcce00969e8527126086f534f8a4a4d2612606b97c005d49a49000ae5dd4984981a8e00009e6800372cea4003d1bee7dcac0008005a784d72a8003a900036b539a00068dcf44000dad1e9ddece2dca172769d84ee40f14bf3a0672038a5798000dcd7a7⟩,
  ⟨0x3df1dc0e446d43341778a6c4ec243117087c4141fb0eb06c42fc1570a304d424c115077037c19c0c105a027c0f006502c00c404e000, 0x5b0a0831cd9d912ebf8f3b6a5d871e76ccbaf1f19c789cf44cdee9a899e3c4e6a264f749e992898e3db05c1669ed99b60782bd383aaa77536da2a71536dc9b7069eeabdb8b4f718dd55b70e9c013d280e3fa1a4f8d2b92460d36bd800672f424da1ae852e2906055d08da4a5d337916c2700076bb79b030001b5d7cb⟩,
  ⟨0x3f51f40f0476e3901bf8d6067e3301928c305ca2c415d0a8452e27012488883ba1b80c985b828e12007c83a018209a039813004a000, 0xc2700076ca79b030001b64fcbd138d5ddabebd308bd73e449c120374e9aa6e02e39a020770e78180ad9d3030001b637cd000354c7a202c6d8c74c04ac6fe0140ac778e04bd637a902c6b1bd4d6340586a6a9580b3e5d52a0155cb00031bdf935ce6015b1bdb931bd40567265ae80ace5d5c50165cbab8802cf96000d61fa7⟩,
  ⟨0x69e3429978c986423149808bb65b42d19628a124791fc0a1c4a220c0eb072c36418b0b204041960ba05482680e606602c810004e000, 0x7cdd203c6b00f34bc4781807bdd36d14000f34000d5fce880ebb685d3eb7373f539d2b7d4917cad254a70f5bb29f9e96ff8f3876dd8c9519f9cf956a483fea4adc96fb8f2746d6949d0b51e95b6c96bfe97359c77c1514785a53e5f9c2e955dff447ac086d4e4acdd3b9fb36f22a277e00ba5b7695b29613bd0b4d96a3ae6cd08be3d22d5b7501bf8f48b2915adb980ddc796c72e04000f1e1300deb9c000db37e6cb84019dd101652df12a7ce0f7fc12e078f2ded2a70019e3e19a4acd26126d98000ae5d0a5852118aeb01c475e31aabc7d9⟩,
  ⟨0x4cb24f11e488c4051f00eb46582eb13508943fc1c80d0864c3041710b104ec25c12108403bc1900bb04a02280c60520158068016000, 0x440464c4dd9c899b24b4e4399131648e9ec8fb246c93b2334f64fd91ba7b27ac8cb22f4f6bf65082dc245fab31117e22fa4639c7126fc90cf8fcb5d3dbd479fb4cfa99d53b7b3bf4f0ad2af1ebaf533979f8f47f8f2c42c3cf1df3a8abd96a3c7b0ee00078f843619a4acd26126dac800ae5d0a585211fceb01fd75e348aad7d96138003b6a5cd818000db50e5e09c6ab2d827e9c599f224e09⟩
]

def tableRRRLL : Table Block := .branch 13 tableRRRLLL tableRRRLLR

def tableRRRLRL : Table Block := .leaf #[
  ⟨0x68632f98e0c225ee2e39680b2256a2a19470a244eb26992c09124441878ba856e29213688e842a1f00de856820c0e5060013805a000, 0xe015e8867cb711d300036e239b8ae33d644c62db86e6b101b70bcd308e0006dc1f34000d455e88003b701d3818000d452e5e1b9e2800715b8731576df39ad0162ae3fad521dc7a33349ae97fcbc1b62f6c56028b89d804b3ce5e8ad352b7d94d5863a53cfb3ef67d05a25d16e3d801449e9ebffa24a894d3d7ff5fde9ec02afd34f600d7e75fc69ec09238f4f4295941a7b216851b27f4e2341445ac9d59a32876bf1f1c467d7df5938a22964bf1e32232ed364cd92ba71198b25d64ca887afb822d845af1e2d227ecf0ff16713d67⟩,
  ⟨0x2991478a004ec25e12308e846021b10187ac3b41cb0e006bc3101760b6057426c10f08283b41b80cb05f025c11806502c00c404e000, 0x103644981b0eff1621121e11a061e23561dbe2e1e9e2c519f224e091834801ec447cd2e91e0630936e60000f3400b621ee8c0d873f8b26692834b8a6dc88007e5e09c0341a0b96c2700076e379b030001b717cb⟩,
  ⟨0x2cf1540a044ae24c11288343cc1b00cf86483061760b4856827612c09084081d40db06382f013a08c03b81b40aa04b019808802a000, 0x6adc0adc9c0aa00139200755802a3c260003892f9381478a1aab124f1c354e2480d4fc7cd33f8a5724b8a68cc612403ea2a4e649c120074fd26285221b13e9ca3626d3400a938267a1333c0d87b38b0361f7e2d299fc5230667⟩,
  ⟨0x2d91648ae454428b14009a44a822d0fb877c39e1be0d8868032a1700b2856026210e082037c19c0ad04001840a804501c00b003e000, 0x1918d918da42b2426864e09079d960fea7000352db960006a5a8041e56227e2dd630c9a6ccd5069c12004c4c9ab84ce27b7b000079b8fe6c9646068978d90d58f99c00763ad7b1ad8a01b6a015ad28fe295892e29e46714eae00d49⟩,
  ⟨0x44021b103c7d43c31cf0de46863361878ba05bc2b71550a0c4bc25411788283ca1c00d586842f4153096042c1c80cc0538080020000, 0x81800d5603e580033c569c001d601e580033cce9c0019e73569e6eaff2797e5389c000dc02e68011a55dd181800852ace5b89c000dbfde68019409ec606002e811d5d01a557e9e8fb2abb4f2194903a9aacb340c0006dfa734001d5ede8dbf20003cd0018b2b88001b7dfd3c1adc5075f12fd383a58a480020e9800400180089d50091a7c8c6dec6⟩,
  ⟨0x34819f0c9862a30417b8b4058a29e14889a84c023910907ac3941a30bf05a426611c0848388176096038817009a0400188098026000, 0x81b078f164cd25069714dc25000fcbc137e0441872d84e000ee10f36060003707f960006fbe7444155c1ce9800c20d9c4215c1be680413db6a65094e00069400024e3cf3da6bc5134b093d672e960a7b1e580293cd6a40239ebf5711aab3893066f4938251d45dc287⟩,
  ⟨0x2d01628ae052226e132090445c20b0fe07c83be1d50d7066c2e815c0a484e825e11e07d83981b80cb060826811606402a8120030000, 0x84ce27b89000079a00bce4e4606005671f161da1c02f9c5c5c247818b545c0d70f8000f3432488001b877d3c205c54450f9127048f1a40179b8c689e19e062a34c0c0006e18f34d2899b1b85dd3308ec2bcd700040078ac1edc5⟩,
  ⟨0x26812088dc43020b0fb076c39c1bd0d7068c32417d0b585842a414809084381ec0de06582f014e09203b818809a03c0178078026000, 0xf4371a7a70379f05b4b713835aacda8e55699a30cf9127048c9a641d5a5f23c0ca92606b8b400079bd0a470c2f1708ef143544d0a68d653c54a9de86853a322a6341523269b33541a704fe08b⟩,
  ⟨0x2e61608ab0544293144898847a2160ff07983b81b50c805a42b014909a047c2240eb06c033815e09e04882000ea05602580f002a000, 0x289d00235a27067819624c0c0006e42f34001a25f620006e4174f0a7f170a6f1606b8fe00079a000d123b100a571f3a706695c920c6a752155b89ee3b8001e6b3c9181bd581ca58d1a70cd7269c1202bd352e131847b8d800079a0e0b1⟩,
  ⟨0x2bb14d09ec4dc24711008583de1de0e786e834e19a0b985782a813d097048422410707803741a60ae05081f009203c0158070022000, 0xc5459feffe0a5b89c000dca7e6803cc2bfd18183ede15de5c19a572483029e1e45b89ee4f0001e6c0dac606e0659671260cde9270486d6cbb050f0300d14536adc4e000d149ab003a8a3003f55c668d33e449c123469⟩,
  ⟨0x47f2158f2070635e19b8c485d6279133085c4181fb0ea070c3681930b9059427c11d08983b81b60ca05c82a0112068029812004e000, 0x2e2a48c4237446f6187e3dae179be0b117a1bfdf05c1c755209bdecf0aeffe38003e06e9ee633c0ae68003deee9ee623bdee6dadb5e7a9bcacee2efb05c9643f8f8dc98001668d9a2000b211d3c26cd735cbe11b5cd8334ae490018c4b3c63463dadc4e0006e5c736432312e303640e4616ae0b44d79a648d23a69fcff9a9600317f698b9b34260018bcb388ffb957cd⟩,
  ⟨0x47b22d11248704131f00eec72c36319f0c5c5e42e81608a784ee25210f87b03921990bb04d425410707002e412808702a012804a000, 0x16411d9ee0d2f469bea3779d3df4fbbc2a9fa7be9efa3d3df557ce69efa9be6efa0d380037d4e9d7d364a9e65f5a000e9e065f5d929b991aa8cc626d7a3652e3deffb2ae9f64ebdfb654d3eca5bb5a2e7a78cd45d30f1998b9c5cb0f1918b7e1d19d2b2efa100074f8980034dac3e49a29b7cec932bea39c563eefba7f148002562eef7a7818ac3ddeb53bbceeeba7⟩,
  ⟨0x3641988c646022f41728b645942bd1570a584fc26612c88c841a2030ef06ec2c815a09983d81a60c405a82680f606002b00c404e000, 0xcdc8001000b55867f8b86778ac27949788c691dc5738ab0caf170c8f170cb715c4e0006e7ef359fe95df630334092baeac0079eac3d15c26210e000ba8b4a787818cf35cf6e6d20a8a800a09761c013a0ac3e6495492019541c8f7e3a5d9c030781a3761f8357031a16b9d7cd⟩,
  ⟨0x3c51d80e2c6cc34119b0c845dc2d615f0a6c51a26a12388903e81df0df06a030a16209f84701f20d805b82b01160660208070022000, 0x184ea99690029d5cb460026ac003968b5782419556000cb3e0016ab0db7170da714003004c4e90c019801e26004018c4e89c0378b011400000387ff5b3000ffeda700b86c023ff3137e200e626ffe01cc4806effd89000f77f0ffddfdf6bfee010b5e0900efecb5e6ee0076af376001356001e6ebabc12346b⟩
]

def tableRRRLRR : Table Block := .leaf #[
  ⟨0x3691a90cac63c2f71768b1856a28e13e89b84c624e114885c41a1f80e886b030a1760b084ac1cc0db05c02440a804501c809002a000, 0x60b2f29ea5c4ecb09c001dd47e6c0c0006ea2f2f04e296fad0e74e2ccf91270483baa4035ce9b5a5e23c0c0e6a9ba7400079a000e743b1005f74dfa77a9a9b94e000aa5d1a35e3a4a6000352e4d1a71e13000602b8722fb74c79a00100100da02987894dc8c0e4a9a54d462a9⟩,
  ⟨0x34d1930c645e42e81608ac0512272131896048621e10187e43c81da0d986382ce1520a183bc19409704481e00ce058018809002e000, 0x195659e976584e000eeb4736060003759b97a271679960d3a6220b1f224e0907e54cbb401e6b410fc53c0c174a9818000dd5ae680032ea6c401add57e9e00a9f45354da004f69b92d79a55e3cb5c00169f3aa96b4001d3e10d86692b349849ba9c002b974296148884cb⟩,
  ⟨0x48223c11448583eb1e30e4c6c033b1840b8c57829713208fc4341e70e106742f015108d83e01a60a004781f80de04801d80b802e000, 0x206bb1200079b9641f33b1eb0bac4eb33abdd3e40dd6169f1f5c817ac1d3e403919e40ba7ca8b205d3e3f9950e409a70007ad4d3e54875abceeddbaa2d3f6ebd50d56fa7edd7b71d3f727db569fb92eda7b6ed3f72fdc5e9c361c8af4f95d6579a903658ff38e06c71fd81b0e3e99f4d389ebdc01ad3f5ed2728033a7c334959a4c24dd6f0015cba14b0a4449658190cb⟩,
  ⟨0x42420a90287ce3c41ca0e286ce35d19b0c4c5ac2b114609644682010e706a43081630a704e42300eb06302dc15808703100bc04a000, 0xc893824003074c4c1e60e38d000800e0e587818005070c4c0c0006ed17360b1073c88e13503a827c561c21acc774f91f75c9a7eb7f23deb8f4fd6a75ada7eb4fad5eb4b4fd6af5bfd6869f30ccc1f53992001fa7001fa6b4fcf59be86cdf11f3567f84f87f99b38011d6869f224e090007acdd4f3707cfeb4001000facbd3c0c0017593a9⟩,
  ⟨0x55029c1474a1c50327a134c95e4a524512008d044516a0afc53427912b08cc4242070f307043381690a884b82160b702a0128046000, 0xc597c5eb8220f9127049c491d6a86b6807a40383c0dd00142606c54dc511cebff0f59fdeea40d40772e1413f680eac4f61ff458380018118e8f5b242618b5ae54766355d5b75c203fc10c81d4aa8bc7874b3667799f6a7efbf02d23af841625f95082c5fe4802daf04801fe3dac001c9934e000e4c5ab0007261c98f55823f8b01080962400900ec38002208f01f58e1000de38001208d01f18e031c10019c781aed61018e680220ef87⟩,
  ⟨0x2cc14c8a0849e243118088c4162010f706ec3461900b785882a614609c84a82120fa077833817208c040818009c0440160088014000, 0xa59a969a5b34f48ce98028a5a8001d3e2316e87f14847543c0c1a2240010086974d562c5e2c5e879c400cb3f8a5724b8a64cc612401a702d3592704800cdeda5a28d13720020056784d372003692e91e06c565c581b15a71606⟩,
  ⟨0x4f5270135895e48a23491208363f81eb8ec86aa2dc1608a8051626a11e88a03961be0cc85d029e12a0818378172094036813004a000, 0x17ca981af040001e6958b50aec77e7bd14f3da06b679ec034033b3ed1368d89014971b3d2d54b369c00925cc920a355b4fa60b4e00412e448fd1a8d76369cd945303a7fafde120034e969a6db352dd3559e95e96a9a6cf4dd6600e000124628cd25ae97ad3c99a928a5d753490d2e9a9a480002d480034b96a72dd291fe6523d4b8eb2934a5c3594b7d267accb6e25d79c0032df67cb6825c39d4b552dba7⟩,
  ⟨0x65e32a18b4c2a4d11c68d206422fa16209fc4c823d10c082c3b01ce0d485d82be14109183f81ba0aa04a81f80de06402680a0014000, 0x206cbe200079991cb8a20bd4f541406d4ea6a609e828200d4ea98ac33e841c697712f4c84227c7aa1595a0ccd3a56d03d78f04fdb5329a8531f04f04328069754a56141408e33bb877a60210be3c81e8ad0266952b550aafa0f8f69c542a52b44c03c7b4a3694f936ac2d59f26958d5138c83c7a5614a52a894640e3806830761df979f9d4c900a9a7f1480034c800a5a781a98f01435202c533601c69d8ca63b461258f1e5c463d406006e9eb0ab8ed3500801656f69eb3acc222b1f224e090309925675437ad020e031e06⟩,
  ⟨0x36519f0c745ec2e516a0b1453c29114209c44a023d10d08343cc1dc0da86202c213a08984041ee0d0063027c0f005b027009c03a000, 0x19848008f38006406ce240b30873b4cd2586930939830005f32852e290e5180131f5720dd1925f47c66184e000f30273a060003980b980020051e772002166afa84962cd575092be5fee71748f03000bcbf7ce81b2fc8009e70008cbf1cc0168e93f8a40100e8c93c0c0151529⟩,
  ⟨0x4ab24411f88b643c213100c7bc3bf1d00df468e3221778b2852e27212688683ea1c20c0857026a11006d031414406c0178084026000, 0x41822699181a0f3132c58018b74989761a25a45ac4f3939da69e1cc36a4c3587149ae2d71f13706535d1defe3bbc5aaa69ddeb7787553d3e9dba98e9f4ecd4c1ac0d3e9d9a7469f4fed3874fa7ee9c1a72e9f508d3db4fa832b92d85e9f505d40d5c86c2b4e000e8ada7cc38d15f9c228d0ffa7a63b4c1db6af1e8855201a933e1d354c0e111c7c7934000403c906c3dd0dc4306087⟩,
  ⟨0x7f83e89e6ceca73e38b9bc0b3a5852b69518a3e4e926112307f835d19c0c4c5dc2c713984f824e11007682a010a06201f80d004e000, 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⟩,
  ⟨0x6df35c1a80c7a52628d13d49a049d23c11448583f91e30e846dc32916a8af84fa23c11287bc3901a10c4836c18609c03a813804e000, 0x1bd53d3cd07c597389c09f81cd3a004b5f7b8e3eaac1454809f76d4dcd48002463b075052f525ae86a54102758ce643f18dc02ff271e91a23f88ef4f16a447ba75db62d388f34e000c51ba7459d99ab9d1644589a78b1e2c38b0b4f1b7c6a716069f76a92f74f1a56ed325e69e04b2d9f5d82000b8e95ae04aad9e5d8000078f058e9b6f189220b38b674f1238003b7845b1a782cf4d72b676e59ade3ce513a01c7000364df9364c78c003aa3500019a492542691c94baf9474ae6e15607e3ca18e334e7ac8fc7ac08c4cb8f0da1d167261ba3a33e4ba3286e7c9⟩,
  ⟨0x3661ac8cc86503011770b1c54027912908e84262060fb87a43b01cb0dd06ac34217a0b5851026a12b082037416c08003a813804e000, 0x184e000ef64f360600037b1f97c0a440024e1ce98001bd89cd000370c3a20006f60f4f34e716bf58012e3d0a4e24c10dea69f14949a4c24c0d5f8c002f24d248002afc3c9309303562a0013cd00035f7792001eb1473ebed00010005c784d5f64000f24000deace68001ac47d1⟩,
  ⟨0x31417f8b605922be1568a184a024610f884c40c1df0d486442fc1740a684e02040f407183481860b204581f00d605e02880f002a000, 0x32955c1ff0011c7c89382464d35976e20734000c1fa0007c781a0fc0005e4c23389c000dc4ce5dc4bb8720007959ae78b80a1e060033711f9615aa70003063801671e686f4349f1a57248c1a6f69000ce5e849b435d0a5c520c8ab9c46002fa6344ab⟩
]

def tableRRRLR : Table Block := .branch 14 tableRRRLRL tableRRRLRR

def tableRRRL : Table Block := .branch 27 tableRRRLL tableRRRLR

def tableRRRRLL : Table Block := .leaf #[
  ⟨0x7393891a44c7a5e92c314c898044e22210746fc2fd12f08643e81dc0c4050c26812708b042c1fc0d705802980fe0580188078016000, 0x131d44c471c8090974970e85ae5945690bef6ee7b8e40444b9cb865598ab878f2fee6cccc049b652eff8f2f3e5fd4d98980736c65df71e5c1bea87cb551fe0f971c0012060997a3cb206ecdae99c5c71e5736b615e0001970303725d0f1e06be0332fb9b664a4df5301936726ea4dfc9bb9b5336e660571e4dd49be9b5126ca6dc4c09937340cf8f30224df5990937b26e66d3c9bc9b6f26e297ff1e7a2584fb14966438e000dc79a9b433c69e8284f2c2658a1b31bc742773d015c62e53e39e49933431a613389c000def3e6aea0b425d181acc0da10e58001b417c7b41b683b9737225b244e09⟩,
  ⟨0x6072d215f4aac52f2841384974493236111483c39d1778b2054227a12988b042a1d00d486082ba13808883a818609c03a813804e000, 0x433f1e8f0e1aa95b11eb901c7873d19f7930ea233e72633dc3a7e4c36f874dc98cf51a63991a4234bf3234b468fe6439686f5c790890b278f210ca9571ed4a4b3ea305723abf0d6a6973b70e38e54a966bb7a165f8860259ed6a5b87f72368c0df90e3ccbd000bc999bab2c392b2be66e726a5b4cdfe580018417c9b2b34d47c597abf2d7cedc77cc5082392f9ae104727e6ab2a353653fcd3a9a95d75479752b692572ee9a5d1ee5d1d7baabcba3ad471797758eeb172d65041ffe4d4a789e1cb⟩,
  ⟨0x6563179890c266062ef9754b5c5a12bd1588a7652a28c93d09ba4b824992188be43a218102c76e2fa14b88d038419b0ab02640a8000, 0x2fa50007e5e098735b09efa30003e6c0c0006fa272dc620006fa0f4efd1715b46d5a1e9d29a524d2000ece1a9d9ab4c000eccfa7d9a766ad5b89ef9c0001e6ed07b33ec606da0b665d5db2fbccd6cbaf68dad4e3886b922820bca9ecbb184016cb6049570bbb615e21fcf71ebc95b2c83ff5e1eed7d789e3bf23af0d5e22bc4c1feb657c77e455e16bc3c15daf1107f6d9571ebffb342e3b34e811b7212bbdf1c414902784e52e72ed3ddaa7f1e209abc10ef7afdd81ab8f07e6289c3d78ff9c783f1144a0ac43d68ff7c7⟩,
  ⟨0x6002ec9650afa54728893a89a43bb1d88e2868a2f11650a8c5162640e2863c2d014308f043c2080df05c02140f6056017807801a000, 0xa95c419b8e4196a5680019609c7ba7b4d2ca258e4b14e38e3f20c563c78e0006a2e726a2b71a5f0c3781f015592118000184f30242ba761cb10bf7776ef057b81e5b609082eb7d8e3c0d9d5af15f3444c408d892702cb8e225e046564f892502c78f0eed8ac71c000c3d5e4c3b2e3439f8d69c9bba822404491b0a8172df3eba2ddd7af5f389b8ea622b6f5f46e3bfb5b035c7db5f6d3d38011b6ae9f224e0900076d3d4e7360023cd0004003db434f030003b67ea7399000de6c99a4a0d2e29⟩,
  ⟨0x6c53311874a844d022790e48464181f88f2874637e1a58ca06022da15b8a404d224210f87e03a21aa0c1853425411403a813804e000, 0x11cb221ad67ba832843e30771e306c72b8868848b8e001684cc56f62e17816beecbf78a02ffa8440de028ca845948b371c8b2c56ea1300012329916962dfc722d00004001509722c91948001c56de3c67b0dd3bc36260003296b8f7e0652df36fc015c3e6b031164e9d814605e2c8d3800778387bef86eff9a6036783727019813c498129e09c99e066047933c0800172400380fc4e73d9e03cc9e014c97994d92992732991d363e6000f813d3b778f801000e1f0038620d0ff42ef58867af870ad25eec2b3bbd182af8f0005ffc71c005db7ae3c28d20cfc7⟩,
  ⟨0x61030097d8bca5c42d79694b2858a2b19508a3650c27592f894c49c24211747f438819a0c345ae2470ea85501e20e706001ec04e000, 0xc89382478d3be00176d13c33c0c5469818000dfa2e6800ef55c40025f9fe99847001de7b5800ef3001dab16c71606c5abc58c1f1847931dca132c73a8886847630e71e3b8c1c484c91ce6221211c8c37c78ee0845a131c1c38c35c78c74e8f78f18e5d7d3a3ce3c89b831c0011fd4c735887d185ea115684e3c89a0006fea2b41c18d8e69227b8f22663b180027f4f5a0a0c64733913bc78ec51da6b4080017f4d224b8f035f8ebba3cd911f1cbe3acc188e3c88e8e5d1d620c3c614e3c5d38babc9⟩,
  ⟨0x2d01578a9450824f11e08b44302030f7077c3a41c30dc065c30c17c0ad852026a12208504001b20c605b82b411808202d80e8026000, 0xe13003b6c0c003c236b0003d4000006186a899d4d12ca74e554c892a4e24c19bd24e09020c08b5c099e06c0501eb587e87df1175e21e34da1e06bf6800079a7ba46123c0d7f7bf36b81afd70001e6800efb5c45fbdfabe9a2287⟩,
  ⟨0x71c36b9a0cc226012ed16ccb2056b29c14449d44d32560cec6301c50d005ec2ac13108d03dc1c20cb054020c0f205202180d001a000, 0x94129bc930e63e3e3aeea3d08986d378ca08e3aee61e8c00069611de55db8bb778fad8c000652df1e52cdfe5e6e1f00eb89e1b4055d3908dc3600a9a7bc14014f8f7825fa171ff41d30050bc45c711b2435c7d3d89e87e4c7463bfc8e57fe6013aa362ba056bec714184c6a9bcae235a01fcc4cb0657969d37e11ae38172c2f8787e0c73e3bec486573cad7402c50ec8b84c70c183c6a7bcaa235201ec554989560c2f2c3a6dacc11f638f5af5711a70f0ab89d4d6bf5c4ea4001eb3f53d65e9800305cc4c15f0d058c3000e0af870007b29d3c0d7f3c82af37624d249c674385796c27⟩,
  ⟨0x58f2b81524a264ec25b124c8c643c20a8ec87503811620ac453c27912308843f813f099847420e0fb07302fc16408b0320168066000, 0x1b5749b4416b079e16a65f48001e385a897d1c921c12f4087271e2010e4c3c36e1ff0e3c3d020a045c90007407b8f444e888890c0002e22e8d371e06a0737fff9a92cc48fcb9821f60020004a0df00146571070000c4bebc789512482266d89b934f36ecdaf371e9c0019b7b4f3705e2bab12312e4487a0001000483640019955000865a106c0005e3d2345e70d98fc342348dd9a889dff1e6b89c000dfefe6d2065e17d181a90f2f09e5cc152504c05a7⟩,
  ⟨0x3da1d98df46e634c1858b9856628c13288f842e1f80e106e032216a09283f81e20e206a831016e0a604b82340dc05f02000c404e000, 0x28c7d079e68001a0ccbb8f8f0350655dc3c9bb76edfbb9aed9d3a20576ee9d0f14406edcd385a29811c90b9b302393301c2e6726d6c4be9e5dc4b7b4ba0ca0006d9b71e06c03800079ae2a2119f45e57aa3497f56b0b8e16ea5fd71e8527127ccdca69f14949a4c24c0d6c402d24d24802b5f493093035ac3b445cd⟩,
  ⟨0x62830917bcbb25852b11530a524d5259110086a42a2018f7074c30713b89483fc1d70d805e82a611d07b033c13206601f80c004a000, 0xc77618003e53c4f9430cf5a9ec6493169ec00278e001f05e27c0d8600378270ed31249680052a2cd3cb8e005efde1c000d153a2a2d57c0013560a369c784d09b01f1e02e69df5c07bcd6ab4d56e94671cd64c4e6238c164ea0653b6a7f43ba2a6551d4e391c50b25502e9dad1d31dcf5324d73d3f9e3cb6b2dbea52aa0ee5421b531e8e8f1c0235144e3d4575dd9c7a8acbbad774f1eaa35b50e3d545b69e59578f5516aa1f1e5ddaef2e3aeee9774bbc78f7735ddf77169e835aee8e3e449c12000ddcba9⟩,
  ⟨0x499246119487c42d20f0fe47ac3c91d10dfc6ea35217f0b6456828d11c88b042c1f30e806b43141670a884a820a0d205782640a8000, 0xc3132f381a3a6c292d9c74e0cd2b92400194e74f973cba62dc4e00070317372f5971c8c0d994cb7e2c002b8b79fe2661ccfdf1d56ec1e352000ca3ba74dd3816f9ae2cc000cfed000467df8f066cc5e1b2eb992c4e60732589cc8e603139aecc1e2f35b987c5e62f0c0007028f359a7e5bb63340ceaecf569c0038f4c4e3bf0c000933f2754c88bc7000299f5340a753c889c7⟩,
  ⟨0x4231f80f2c7683811ae0cdc6082e91670a9c53028913208fc4542200fd869c288133091044c1d80df06902bc11806502c00c404e000, 0x44991adc49ba700065ffd4cbf5a68d60f34892b4f1dd4771ab8eea3b1d3c7731d8475fa7c9e561201c8c1f040818fe6e6495492000ca67a7674399bd5d60a9e066753998d5802071a54032bff1a16e3801f71a3402ebfed5c5342bc7c334959a4c24e0740015cba14b0a4013981c580073018bd0bcc2afb2c27000781b79b030001c0d7cb⟩
]

def tableRRRRLR : Table Block := .leaf #[
  ⟨0x6182fa9738b4e5842b094f0a0c4f025e91e08483d01d48e086b63161610a3c4d823c0fb868c28013208d03cc17a098038813004a000, 0xc93f0e4987054f362a9a11fe38e3b73389dc96e6712c104239a722c3153c000f1f727866db78f084674ed6fcf9dcb31c9f5c73e752cc1adf115dc9f3c730b86174f9ca160965fc796292c3f932c3a589f2684d05f0e3d45aa8614252a0b71ea2cd42fa863424ea0af1de958fa5e81d3fa5fd3187f4b7a5fd2b87000600121dc3041e3800200070ede1c9b040e3aaaa0002000a1db4392607fc7921acfef1a6124c5be3cc209847316b8e000e055a7c11cbf7b9b1f147b3a9a2248f6f971ae449da7⟩,
  ⟨0xaf75692ae952aa70525a8994029bc3da9dc0dc064130d172cb4c59c2ba92e081437a18b8ad052a281100076436418b0b204b822e000, 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⟩,
  ⟨0x26712108bc44421310287c83ca1d40e286ec3501990c305dc2da14609a84381fe0f2073835815e0a004882180c205201d0088014000, 0x592a00b69e5343d0a4e24c50d02a27c52526930930350a89349229224c24c0d5e2167973478d2b3c2bc373db13d99a13489a706a2c80e69e477097824001b18b56d8ab2e1f172e2f172e3f1606⟩,
  ⟨0x34819c8c4860a2f81718b3854e29a13989a448423310608083b61b60c785a024e11b08303dc1c40cd054024c0fc07302f00ac026000, 0x3093842400572e852c2923d5583e2af479d7b1ecb09c001e102e6c0c000708072e928d7abb79dd3818000e0fce680036896c4018e0f9e9e0f950a7cdb2a400100baca3d3f23035aa71536152a69bd52014d909aba0455873aaf048302ac024b410001d565e2e2f788b⟩,
  ⟨0x2eb1630a8451427312e094447423010587f83de1e30ea06b42ee15f0a384e822a10607883881ae0c204e82080f00630180088022000, 0x5a8202e6aed4000f356068b1ec5a65d914cbc1222bb2e06b4c0007d5b09e525d23184700035f2b975f240008002e56615e2e613e2b09c02bb4bf575a999a94f912704833aa6d2901275a0a92a9e064e3548024000d971a7a21b0cd25669⟩,
  ⟨0x48322e106c7ec3a71c80d3c65431b17b0b4457c2b014e8a284ca240118082c3cc1c10ce05dc2a412d084031c172094037812804a000, 0x4cd699bbc9009ece301fecfad3809f44ee9c025b38403a01f6cf8d3d6b4c7b37c023b3d8015d3800367a6a6653004b679ea6cf20093521ea27e86f7113bea26d4a008356000d9a9a9d0c6019ecd3d4d9a40336a6d4501a35765d599fa9b316ccfd4d99d6626a6d4ab32b576a4d99fabb388001b32ecdcd3e10c01d5991a901aacc8d4d98e034ea6d43b2fb5765e80b9ab⟩,
  ⟨0x3eb1e20e7c6d836119e0c545e02bd1578a7851a27e12b892847a22610887a83ba1b60d606142f015109504541dc0c905100fc030000, 0x1c2d5cdb5d80a0d88003cf5dacfa784c000d9ffa75ae385979b6b18005a7b58856d00074f243619a4acd261270af000ae5d0a585226032c1fd57a5356b876584e000f0abf36060003855796c310071854ba6b5a6f15f4c1b94e00070a8736d5c00d3633366b9f71edfa4d3399aeb43d6875f06e3800199bdc999afc6⟩,
  ⟨0x8023e61ed0f547923b69d18e426fc36b98e0c225ea2e29678aee55029494089984a5237906c53626511787a830e0bb0248090032000, 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⟩,
  ⟨0x35719f8be854c29514209d449c24111a088441c1e70ed06cc3521820b8852826e12808e84301ca0d006302d415608402e80d804e000, 0x6358e2c47724dd5bd800d71e23b126d87d35bd400cf1f0cd256693093869000572e852c29461161ba2f4c749fbecb09c001e19de6c0c00070cdf2f44e327d6e34f4d1143e449c123c6993c6002f9a27867818a8d3030001c31fcd00032777a200130c674cc23800193b5cb⟩,
  ⟨0x35a19a8bc053823910a081c3f01ea0ec87303761ac0d106443041710b1056026212007c831817409504301dc0ca04d01a808002a000, 0x1a8d7356bc76b2c58ba5e7bc75e39595ec5cd8b85e79c75e3758eab2b58b8b16ebcef8e0095e73a7a149c49821bd4d3e292934984981bd4d26924b4d26126069429281f9a3269940b284b9e000de5000169f118005bc9f52611cf25e28958d838b8d8b8a1c6abc13082ab⟩,
  ⟨0xc9d633afd577eb7a54fa9f14cc9b842b1db0e4e71c37e9b58d5e67931a1654aa04ed23d90247103340b4832814607c02a80c0016000, 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⟩,
  ⟨0x42020b0fbc7ca3be1cb8e186f23641ad0d2467e3181800bc459429413e09c84b424b11207f43ac1cc0d286342cc141085813804e000, 0x818005e9d1e740da73c004f3800469cee62e99fc5227667818a4d30369c70003ccd35dc5308e0006ba672c000d74b0007cad345c581b4d3714c23e1f60003cd00035d17a2000f0f9f4e0600035d0b97a63b8b14193b271d1519d8f4e426e8f0b9aee3840484940da821838c18a1e426aad65a42c23ee66a25df1e15dc2b4e488818153c7⟩,
  ⟨0x36619f8c605ea2e01658b0055629614189704762140f987303761aa0cd85d02ce15a0a384982260f207282f816808d03000e4024000, 0x1ae22ae6e2290003cd01a465323ad6a9ab454e09a7355c8eaa432438013d3d3ce00196fb38978d3cfce001b70b38b79d3cbced334961a4c24e9e10017cca14b8a43846004db8dc836464b65b7de184fa764001f3a060003a75f980020056d572001f7603a82596ebff50ba47⟩,
  ⟨0x88c440a1ad08881f3fc1e90e826ed2dc13ec9a84ad1f08e706cc33f18c0bc459426712d88d041a1e60df84f812007b016008402c000, 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⟩
]

def tableRRRRL : Table Block := .branch 13 tableRRRRLL tableRRRRLR

def tableRRRRRL : Table Block := .leaf #[
  ⟨0x6ac3429978c6e6102f49708b545832ba1570a6a50e273933c950483236111c5ca2370bd055426410f076035414a08f0360154060000, 0xc4d400079a0006069744003e267e98001c4cfcd000368d7a2000713274f4d6f171318001e6c251d36fc5000389839a00074ef744000e25de9e9a8e2c5728573c70006dd9d4dba5a6b746dd8d4d1eb64d72d085aa135224456c671cab44c85752d8213702c95c36b76a49260d2b55af3aa4fd60d58cdb54cb8e11ba15a03d4093515e4882561674098625c95cb59e3846d8566e80e5ac03d3c3101265c95457822075856d9371c00d84634e00acdae1f3459b4c3e6cf32b87866b4d99accf80070f98ec300073398986b74d0d63337a9000800b35987⟩,
  ⟨0x53328f14509fe48d22b90d884a4141f68edc72435f19f0c745e02cf1540a6c4e826a12188083f01d104682040ea06802d813804e000, 0x4e0a9e06ae75598829e0aec2a0ffc63683fcecdb8eb8c48a6d90ce3efc00759fa8d33a69b210b7a78eb752c83ade8e39bbf6f369cddeb794d9bd3eef6ee59f787756cfbc1ba9bb367001de8b38de6d485cc6138dffd481ce8186feea3ee65bda6f380036f2e9e06d47638b79d0b8e19ac2e4a27d03180008002000600100029241afd8ebd6d9a4fdaa0434e0e2dcd385840b15038f48d88d066b33699b1360001e68006d3d5d1⟩,
  ⟨0x29e14489fc4ce25411e88c84362040f687583961b80ce86142da13d09984301ec0e506c030c17209604001c40c805201d0088030000, 0x3e09530369f0e2fee89925d97824ac765c22ccb8211960e032f048648bf410955a7d78ba7c78a001001d8630f031627d4c3ceb09e1970cfe2913a33c0d58b004626b1586348ee2b2a12b4ed7174f0f1606d3cbc5⟩,
  ⟨0x239117087c40e1f80f687843a81bc0d586583181740b5054828213409104602120ff07383301840a704781e00d205e02780a0014000, 0x1824e24c92b443627c4d08ce29d411c5c133d0999e06d413c581b50c71654cfe293d91e06a8930369fce29b482a781812e85569f9e2c510c7c893824e248049d459cd03001b1e06⟩,
  ⟨0x276131894448e22f11288344061eb0e206382f616c0ad853827212f09004581fc0e6067031011c076032816009203c017808001e000, 0x2e1449748f036a17e2c0da8678b036a24e2800fd4bfc7001da97800671faa43fe49a533f8a460ccf03644981b50371681121f529f1a0600020047528f2b50171734cfe295c92e29a3318497934e649⟩,
  ⟨0x6c33561a14cd865c32293506a81c50d786643121730a8050c226109073034c1840b5053026411807d035016c0a003d0140064016000, 0x1dcc900038c279b40d6f1d6c6cba98f09f213ed98b2a9a000c00246275d92001630dda8ca22f5e50ca20095012c026096a587fa82d5062de3e237c0b9c784f709f2cc5154c0004000e3132ec80009186ad45d116af26650c04a0095012e4b4ec3f5415a82f14c6de36236c0b7c784f509eecc4954b0002000a312aec700071866d455115af24650a0ab809301280258969587da829505a2985bc5c46b816b8f6b8c358130d7d8d547c357fc03587f148006bfa018c3c0d5fb00be26d043e699fc52b925c5346630927fa27324e090f112f36686c4f943426⟩,
  ⟨0x33018f8c386062ea1638a804d425211c88bc4101f70f3076c3881a10bd051025811d07b033c15009e03b81980ae04c01a8070014000, 0xa534a49a70481e33ac0036fac38001831dcb00030634b7cf2b53d716e005cf0300bf8313cbd534a61a70483fecb000dbc70e0006bd6f2c000d7ac2df1cad4e3c5308e000718b734000d7a8e88077c627d381803ad7a5e5c519f224e0903c992e158ed2e91e06⟩,
  ⟨0x2da1668af055a2a31490a0c4e426312c890046221810487f83e61e60e7069c2e212c08a84101e60e806782d811e05902000d801e000, 0x3c525269309303629a4d24951a4c24c0dc148ed389345bcef6c4f89b1330a7546f1719c8031e6ac2f831ace838e0006326cf8b60c5c7ce134d2a694834e0903ce7580d2b9c000daffe580a2b5fc0293958e02e78180645afbe5c4a6⟩,
  ⟨0x2e215d8a50514272131895045a220108881c3f41c50d686802f21600ab04f424810b07402e014a09804001a00a003d0180084026000, 0xeae9e8800bc6d1d381b572f17624d249d5c8001b96c278c9b0330ac02ee500000187ab7b8ae2700038d739bfb7cf181bf2f1d6039ae7c8c975d93819587060d934193870e90ee2b10708ad543c5d53bc594d0f429389314340a89⟩,
  ⟨0x2fe16b8acc55228e13a89804a223c11188283fe1e60e887183621980bb857c28e0e406a031816a0a404a82280f205202000d804e000, 0x3584812de680652c983c0d27644271f15ce0d6a9b54d654a9f4e575f997baf0496f8baee11578242b15603bceb01dd02756ac8e2eac6e2d7f2000319122d20002022fc7c0c6ca1b74d31667c89382464d3abb8008f34bc47818d248001c6d7cd⟩,
  ⟨0x3821ad8cd061a2f81748b785922ae1498a244e826a12188a04021ec0ee86e83481810b5855426410f04701fc0e204e0198090032000, 0xa4de7ae9e3a90129cd027f8ea39a45ea7c8938241b153061543410ea53c0c150a9818000e39ee6806011100478e6fa7002a7894c001b61e26d7d86000d74f1370dc3572b0d751baa624129682c3c65fb01b16fc00080022bb4024009971fe53550c0fdb85e265cce83e449c120398e9⟩,
  ⟨0x3f61e78ea07363741ac8d3c66831b1850bc459c2b512187083521550a384e425011708403841a80c705902740ec06902100e0022000, 0x53e3c9e9c232bd33d37138001c78fcdaf28e230358d430b01a274ceb986681ce001bcae1e6e71d65e49e1f000583f6057ad9a6177e39791787a00120fd45ea02bb6ccf0bb71c4ea5cf1b44000c1f8000400778f143450d86692b349849c76a002b9742961491caac1e157ae7c0a7f6584e000f1d77360600038eb397e271⟩,
  ⟨0x40a1f18ef072a36e1a38c805f22d215588e44241dc0da85fc2d815e0a584f425811b08603941b00cb05902640e406501f00d001a000, 0x23d04d3fe4cd3e8f3fc99af51e7f9935f8698f266bf0d32e4cd801a63c91a6135ff9373d26bff32a19d474e3db578dee6882a7a54f2c2714dd38f6a3ad2471ed46daa0b48fc7b72c00db8f6e561188035e386e89e21b7644c90d86692b349849c7aa002b9742961484d7bac06b9d7aefe11cf6584e000f1e77360600038f3396c31⟩,
  ⟨0x3741a68d0c6383091710aec540279136097449e23e11888804222070f0074435419b0c885a828611c073036c16808d03300fc04e000, 0x7902b9b030001c811cbd05238916cd1f4f2028001e6e7f471196a0004b8f42938930437a9a7c5252693093034b48000bc93492000a5a3724c24c0d8f98004f34000cb42e48007c7c9cf967e000400171e134b3e0003c900038fbf9a00071eff44000e3ece9e5d7e2cb39966fc7⟩
]

def tableRRRRRR : Table Block := .leaf #[
  ⟨0x33818f8c386062ea1618aa051a27212f895447422d10307ac3c21c60b9043c2020f006f834017e09804481e00d605e024808801a000, 0x1fd74fcb9a1300fd39f21301c0e680735077ae5e1796c2c2fa143c0dbcdfc2dc4f9078000f37718088c0db7bf42c00101aa03578824015f1c00081a9035509b7104002ae3cd0de8693e34ae491834e4130019cbd093686ba14b8a41895766ab12674c68156c27⟩,
  ⟨0x44b1e50ed47283731b10d046402f91690a34500274132896c46820f0f4070c32015d09c04141bc0cb058025410e06c02880d8036000, 0x1aab6131d7321a632af71e44d47f1e4fecc017b256900bd93b4d61a402f646d3b2001569baa8bebf99b0297d7730002db325f4f31838ee29a468893032faed80bcc0006f9dd3afa6d807ccbe9af9ed3df4b7cedf39a7be76f9fbe6b4e9785f3fa73ded2efbe7b4f0a24017f1f02448065707c9e52172434bc1d09c683a120dc6427918e85f1df90b⟩,
  ⟨0x46c22f91308724122028f787a83ad1d00de46a434518f0be45de2ca15e8ab854429313608d843c2060b385002500e305e021808a000, 0x614a6a8b0d117b16e090f6584e000f232f36060003918f96c31001b9183a7046b09cf4dc4e000722f737a29002763037450003ead84f292e918c238001843fcb843c000400172b3aef173adf1527d9c0f45d89f51c5e9c107178de09099de39e3800180fbc980f1c6b78b1d972c661a6e3dbc411e3c75cc76f0c47871c9c954a745135fb4e54a04e40d7da02dc7⟩,
  ⟨0x2ef1650a8c4f825512508e44061eb0e9870836e1920b5851826e12808c84201ec0de06a02f015209e04581cc0ca05402180d001a000, 0x68ec006ea60a1b473e5c1420009cb000705079782478d6000609f0002e56789e2e787e2d49af04800fa34eac000c12be3e8cda33eacf23b84b308e306b3d92b3bdf1606ceffc51fd17827a145e778e2c90d86692b349849c8d8002b97429⟩,
  ⟨0x3801bb0d3c67c3171810bcc5d02d31560a50514277136891843e1f80f2875c30615e0a484e824a11007583180e406502b80c804a000, 0x818000e4a9e5e89c61385f77e991229f224e0906154c15c003fcd08fe878185d44c0c000724ef34000c156e88018c935d39850f7430009822f77a610fba62e3e910020ea41e953e29bbe553c74a9e97c03dd5e8f600ceae087c21700020009d2d71e0cd3430003a3c6a7ccc00768efa9⟩,
  ⟨0x31f1880bfc5b02c915c0aac53c28d133095449022110b87c03c21ba0c985b028a12d07b83981aa0c604f824810a07002d80d004e000, 0x2e491834e4c80019cbd093686ba14b8a470d76c8da90f4da8d6c27c97e000f9b030001c97bcb84a2d46ad8e74c000e4bae68001b31dd1000392dfa7a0d38b1e1211e8019e3e19a4acd26127259000ae5d0a5852458ab06b55ec9c84edd96138003c957cd⟩,
  ⟨0x47322610947de3aa1c38d8867a31817a8b4055628c12587f03e41cb0d3063c2d414709204542140e7060024010c0630180088022000, 0x1af99125c96553227b93717a3ff5297e38fedaa7152915df71cf97931c3da4cbe46a6d385f2352be3da6fa9be3000b12000da6ba9ed221ead5804fc94786fe1c0000a863d3c37d0df8002df150c5a781b26d87dfe68003b656a76c3d37c9ce9369fa53d25c38073a4f87c893824003d25c4d9a70037cd000805fa458781802bd21c4fc898fc0003a79a1bd0d27c69⟩,
  ⟨0x64531117f4bb45862a093b496e4a624912188ce44420a0fcc7983a91c30b9c5b82d1146099447c1f90e906702cc13f08c029802c000, 0x674edfe2672676ff53fc2fdee26a1c625eb5039912bc971ea1ada80affb990f8f50d2d3fd7fcb78d990b8f649ef48d849e38f19fa751a91805e97a39d76f95873ac9d72f9387001af1b3e4fc15dfcdbda5edb12006bd961eb06da73a05f029a0ec00010004e56dca4cfc8e3e26c4d582ab735a70afdbc7c9ea1a2f9b93d0bd57368f3d385a3e14e7b8f4e668d5f1e9cc51b9a355c7b2d766029b8f1e402dc65e3c47e9147c9687d3ea5a242b1f9f5758aeaf971da1e80019f50d11c27babf4563d3eaab1571ecfb86⟩,
  ⟨0x5db2e81714b3c5912b51514a7651628393889aa4b023e91cc8b644e21390087f03d315e0a98506276134897847620b0f40714210000, 0x426c4d94a1313735c4e0007293736626839b63034c4b0726ace2380070716adc4e000c149ab837e0a3000b55036b0fe2b89c000e51ae6cc3504f6c606986609cd5d7f0a4d4cb3e7ead62a00020607182953392576c5e4e0d627ac531bbe42ede4ea953c7ba861b1878eac3d0a585389b1cd8c0c4e2fb1ca001c3e2fb1db89c5ee2e70f2486d86c97f936f5876b0fc6e5a2f7214ed4315199a13c765895f95dcc86884f747669079383c588e8c8d1d2c706a99097c1eb23531b09fc7⟩,
  ⟨0x3b11ce0ddc6a431f1880bec5da2d81618a784f224611d88b040e1e00e586e03541970c2057c274117080837817609804681a808a000, 0x13b4a98429f99d5c2120156ac0090006644d3cea606d54d10c9d8a9ad254c18cfc8eae0c5008b56000800531e69f1346a600060bfd3a0bcca77cd8db5486a89ba1ad444cea8998dc017d5cc6cfc1eac003f87c4fe030c001fc1e1fefff80c5fdfc0238bc1200ffbee2c00498a74e00064eb0e610005c7⟩,
  ⟨0x6e634919acc6a60e2f39688a424eb22d8c985fe2d81588a284c623c0f4068c3241830af04dc25410306e034815608603780a802a000, 0x2c03b94c7374e731e89f1e1af434ae3c35d86930d2f8f0d761adf1f15ee6a3e3e2bca7ef49672ebf1ec72583e0dc2f6f68b545bfa86162a38ecf32cef59f3e3b31bb0781b7cef8ac9eb14c8de9edde37be3957e92ed6d89df786de4290e249ac3e2d0736328328efb31aa56b524b15c50208e757a6734f71e79fe362e4d7bfc6d9c9c6d75efb938daec4b72f1c05895e5b323c695c77354e6f2e044a05af75c786463a3e5022656e3c19a5724800306869d06962b0e5b89c000e553e6a0d4c55bd181906ae2abe580030696a60cad3000f1d070c5d32571c8a152dd0a9⟩,
  ⟨0x89a439a130ff07a43be9d58e5e7083709ae8d2666c322983cafe4c223710e07c83bd1cb0dbc5a027c12c890c41a18c067817406c000, 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⟩,
  ⟨0x76439e9be0da26ac34a99b8c8e6202fc9748b565842ae94f0a4e50224090787d03c11cd0dcc6983251800b285461d707e02a008a000, 0x799196ab9af87a53f3cb982c9c7c34b0aab8e000dc39a9b8534d83e28d4727090d1a8e4e120a345c9a343847f93468708ff328dce118e66117c23bcccc2117ef8e0035dd69aebb36851a2f6a6ec2be0fcc19905320b96f46a5780ef8e18c53edafb3b5cc5bcdaa2f1e7bce2ee6657c79e5cc1bb933cb983ef26798307ce4b07b9e5fc961813cbf983d4e0d7a79ee5217981171f301586ee3b3219380ccda2831b9c8a0f523e83d2fa92dd24fe68255990e3b320937eccd62829b9b8a0cd1d283cafa82dd04fe1a39d049a91dc79743413282456cbb31dc7a0972e81a395048a08f5b2b8f5112a1a5295cbfbc7⟩,
  ⟨0x13288f84101e10dd064c2d814508783a816e07202f012804a000, 0x119f22bcf1e33dc5788aa9c78cf719e78ec0a7096725818612ce4b02fc25dc94e277cfb8f7ccc00266efe3f983e7169fcd9f303ce1d38001abec000b063f1f3051b3ad1b2a6c7a74e000f98fa7⟩
]

def tableRRRRR : Table Block := .branch 14 tableRRRRRL tableRRRRRR

def tableRRRR : Table Block := .branch 27 tableRRRRL tableRRRRR

def tableRRR : Table Block := .branch 55 tableRRRL tableRRRR

def tableRR : Table Block := .branch 0x6e tableRRL tableRRR

def tableR : Table Block := .branch 0xdb tableRL tableRR

def table : Table Block := .branch 0x1b7 tableL tableR

def program : Nat → ClosureSemantics.Node := ClosureFixedWidthProgram.raw table
end ClosureFixedWidthData1

end PolicySubmissionPart30

/- Component PolicyFixedClauseData; SHA256 4d19e49c906a9c4b07ae987f5cab505e65280dc38230312979ca26ccb69c050f. -/
section PolicySubmissionPart31
/- Direct fixed-width signed-literal records, validated by the consuming checkers. -/

namespace Bounty

def policyFixedLiterals (width : Nat) : Nat → Nat → List Int
  | 0, _ => []
  | count + 1, packed =>
      let code := packed &&& ((1 <<< width) - 1)
      let lit : Int := if code % 2 = 0 then (code / 2 : Nat) else -(code / 2 : Int)
      lit :: policyFixedLiterals width count (packed >>> width)

def policyFixedClauseDatabase (width : Nat)
    (t : PackedNatTable.Table PackedNatTable.Block) (i : Nat) : List Int :=
  let b := t.get PackedNatTable.emptyBlock (i / 32)
  let first := b.start (i % 32)
  let count := b.start (i % 32 + 1) - first
  policyFixedLiterals width count (b.data >>> (width * first))

end Bounty

end PolicySubmissionPart31

/- Component PolicyCompactCore; SHA256 fa5c14e806285d04f3ebe136805a99c10d1ee8d6c84012bc168fa07d5e2208a9. -/
section PolicySubmissionPart32
/- Fixed16-bit compact clauses and positive maps to the dense semantic variables. -/

namespace Bounty

def policyFixedCompact0ClauseTable : PackedNatTable.Table PackedNatTable.Block :=

(.branch 0x93 (
(.branch 73 (
(.branch 36 (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3f01e80ec07203601a00c806002e01600a804e025011808403c01c00d006002c014009004001c00c005002000c0040018004000000, 0x6e006a0068006b006400670062004800610057006100600056005a005d0058004800540057004e0057005200510055004a004d0048004d0044004700400030004300390041003a003d0036003900320035002c002f0028002b0026002b001e0025001c0025002000230018001b00120015000e0011000c0008000b0007⟩, ⟨0x45021010007c03c01d00e006a03301880bc05a02b0148098048022010007403401800b005002401000700300140080030010004000, 0xc000bd00bf00be00b000af00bd00bc00ae00b800bb00b400bb0006006d00b700b000b300ae00b300aa00ad009d00a900a8009c00a000a5005e000d00a3009e0092009a009d0096009d0098005e00060006005f009900920095008e0091007f008d008c007e00860089008400890080008300770081007c007f007a007f007600790074007900700073⟩, ⟨0x4d025812408e045021810007a03b01c80dc06a03301880bc056028012808803e01d00d806002c01400880380160090038014004000, 0xeb00ff00fe00ea00f800fb00f600fb00f200fb00f4000d00a700a6000d00f500ee00f100ec00f100db00ef00ee00da00d900ed00e800eb00de00eb00ea00df00e500e900e600e000e900e800e000e700e200a60006000600a700e300da00dd00d800dd00dc00d900db00d400d700d200d7008a000d00d100ce008a00060006008b00cf00bb00cd00c600c900c200c9006c000d00c500bc00c1⟩, ⟨0x49023811408604001e80ec07203701a80c806002e01580a404e025011808403e01d00d806402e014009004001c00c0048018006000, 0x144014701420147013e0141013c0124013b013c01250137012f013b013a012e013401370130013700fc000d0133012c012f0128012f000600fd012b012401270115012301220114011c011f011a011f01160119010901170116010801120115010e0115000600cb0111010a010d0108010d010401070102010700fe00d80101010000d800ff00fa00d90101010000d900fb⟩]) (
(.branch 2 (
.leaf #[⟨0x49023810c08203f01e80ec07203601a00c806002e01600a404c024011007c03801a00c005802801100780340160090038014006000, 0x18d018f018801840180018b0187018901830185017c017f0170017f017b017d0178000d013901740177017201770167017501650173016f017100060139016d0006015f016b0166016901640169016001420163015c01430163014f01610160014e015a015d0156015d0120000d01590152015501500155014501530143015101500142014c014f0148014f00060121014b⟩, ⟨0x55029814009a04a023811408403f01e00e406e03401880b8058029013008c04001e00d806402c012008003801800a0040014006000, 0x211021301fa0209020f02080205020b02040203020701fe01fc020101fb01fd01e401f301f901f201ef01f501ee01ed01f101e801e601eb01e501e701e001d601e301d401dd01df01d801d601db01d501d701bc01cb01d101ca01c701cd01c601c501c901c001be01c301bd01bf01b801b101bb01a501b901b001ab01b501a601a4019c01a9019501a3019f01a1019e00d5019b019d019a00d301960194019900d601950190018e0193⟩]) (
.leaf #[⟨0x55029814009c04b024011808604001f00ec07203601a00c405c02b014009804402000f006c030016009804401c00b0048018006000, 0x2910293028c028a028f0289028b0284027c02870280027e0283027d027f02760279027b02740273027702720009026e026c0271000a026d02680266026b02650267024e025d0263025c0259025f02580257025b025202500255024f0251024a02460242024d0249024b024502470236023f0241023a0238023d02370239023202300235022f023102200229022b02240222022702210223021c0212021f02100219021b021402120217⟩, ⟨0x520270130092046021810407c03c01c80d406603101700b0054028012808803e01d00d806402e015009004001a00a0040018006000, 0x2d602d002b402d902d502d702d002b402d502d202d102d502d402d102d302d000e102cc02c502cf02b702cd02c402bf02c902ba02b802b602bd02b502bb02b302b902b602b402b202b400e700e602b502a702b1029c02ad02af02ac02a602ab02ac02a702a902aa00ff02a800fb00fa02a902a600d900d802a7029e02a302a500fd02a100fc029d029f029c00fd029f029c01010100029d029800fc029b029402920297⟩, ⟨0x520278130092047022010407e03d01d00e006a03201780b4054027012008804001e00e006802e014009004001a00a0040014004000, 0x34203410345031c0329033f0334032f0339032d0335032c032400fc03280326032b03250327012a03250320031e0323031d031f030a0315031b031403130317030e030c0311030b030d02f603010307030002ff030302fa02f802fd02f702f900ea02f300e402f102ee00df00de02ef02ea02d502ed02d402eb02ed02ea00e900e802eb02dc02b202e902de02e302e502df02e102d202dd02df02dc02d302df02d102db⟩]))))) (
(.branch 4 (
.leaf #[⟨0x5602a014409c04c024811808604001e80ec07003501900c005a02a013809404402000e806c030015009004001c00b0040014006000, 0x3cf03d103c003c903cb03c403c203c703c103c303ba03bd03bf02a603b903bb03b802a703bb03b403b303b703ae03ac03b103ab03ad03a4039a03a7039803a103a3039c039a039f0399039b0388039103970390036c0393038c038a038f0389038b0384037d038703770385037c0366037f037b037d0376036a0379037003730375036e036b0371036b036d036803660352035d0363035c035b035f03560354035903530355029002990351⟩, ⟨0x5602a014409c04c025011c08a04202000f407403701a00c806002d015009c04802200f807003401700a804801c00c0048018006000, 0x459045b045204570459045604530459045304550450044e044a0448044d04470449044204400445043f044104280437043d043604330439043204310435042c042a042f0429042b03dd0423040c041b0421041a0417041d0416041504190410040e0413040d040f04000409040b0404040204070401040303fc03f503ff03e703fd03f403ef03f903ea03e803e603ed03e503eb03de03e103e303dc03d703df03d803d603db03d203d003d5⟩, ⟨0x55029014009a04b024011408604001f00ec07003601980c405c02c014809804602000e8068030015009003c01a00b0040018006000, 0x4da046704dd046104db04d204a704d504a104d304a404a104cf04c604bf04c904b904c704be044e04c104bd04bf04b802da04bb04b402d004b704a904af04a804a604ab04a504a704a0049e04a30497049f0498049b049d0496047f04990480048f0495048e048b0491048a0489048d04840482048704810483047a0470047d046e04770479047204700475046f04710004046d04680466046b046504670460045204630458045d045f⟩, ⟨0x520280138098049023010c08003e01d80e406e03401880b805802a013809404401f00e806802e015009804001a00b0040014004000, 0x5430545054003cc053e0364043e0537053d053604fa0539053203540535052e050b05310505052f05260512052905230525052405220510051b0521051a0519051d051405120517051105130002050f050a03a8050d0509050b050404f8050704fc0501050304fd04ff04f804ad04fd04ac04f904fd04f904fb04f604ac044604ef04f504ee045404f1044b04ed04de04e704eb04e6049604e904e204e004e504df04e1⟩]) (
(.branch 2 (
.leaf #[⟨0x56029014009a04a024011408604001e00e806e03401880b8054028012808c04001e00d806402c014008803c01a00b0040014006000, 0x5bc05b8058205bf05bb05bd05b8058105bb05b4058605b705b305b505ae05ac05b105a105ad05a205a905ab05a405a002f405a705a305a505700565059f05780593059b0592056005950588058f0591058a05840560058d0589058b057c057a057f0579057b05740572057705710573056c056a056f0569056b05640562056705610563055a0555055f054f055b05490553015f0551054e0548015e054a0548054d016a0549054403080547⟩, ⟨0x520280134094047022810c08203f01e00e807003501900bc058028013008c04201f00e006402c014009003c01a0090038014006000, 0x6170619061406120617061006130617061606110613013a06150612012501360611060e01310606060b060d060a01350605060905fa0605060705fe0601060305fc05fb05ff05f005f705f905f205ee05e405f505f105f305e405ed05f105ed05ef05e305eb05ca05e705e905e605e305e505dc05d705e105d305dd017e05d505d205d005ce016e05d105cc05c805c605cf05cb05cd05b905c905c505c705ba05c105c3⟩]) (
.leaf #[⟨0x56029814009c04b024011808604001f00e807003501900bc05a02b014009804802100f006c030015009804001c00b0040014004000, 0x6a4065206a706a0069e06a3069d069f0698065e069b068e068906930683068f068406820687067e067c0681067b067d06740670066e067706730675065c0667066d066606630669066206610665065d065f0659065b06540650065706510653012606510648064b064d064606130649063406330637062e01380631062a0628062d06270629061e06230625013906210138061b061f061a0139061f061a0617061d0616061b061d061a013d⟩, ⟨0x55029814009a04b024811808804101f00ec07203601980c405c02b014009804602000e8068030015009004001a00a0040014006000, 0x71f0727071e07160138071a0718071d07170719016c0717071207100715070f071106fa0705070b07040703070706fe06fc070106fb06fd06ee06f706f906f206f006f506ef06f106dc06e706ed06e606e506e906e006de06e306dd06df06d606d906db06d4064f06d706ba066f06d306ce06c506d106c106cf06c606c406c906c006be06c306b906bf06b806bb06bd06b4067806b706a106b506ae065b06b1065506af0678065a06a9⟩, ⟨0x5802a814c0a004d025012008a04201f80f407403701a00c405c02c01500a004a02300f807403401700a004401c00b0040018006000, 0x79e079c07a1079b079d078807930799079207910795078c078a078f0789078b0776077f0787077e06080781077a0778077d07770779076007690775076c076f0771075e0610076d07680716076b07640762076707610763012e075f075c012d06720759075b075801290754074a06be075707530755074a06b90753074c074f0751070c074b074d074406f007470732073d0743073c073b073f07360734073907330735070e071b073107260721072b⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x56029814009c04b024011408403f01e80e806e03501980c405c02b014809c04802100f8070032016009804401a00b0048018006000, 0x81805ea081b081407480817081308150644057a08110752075d080f07ae07b3080d07d407df080b08020801080507ff080307fe07e2061207f807f307fd07ed07f907dd07f107eb07ef07ec07ea07dc07e807e407eb07e707e907e307e507de07dc07e107d807d607db07d507d707be07cd07d307cc07c907cf07c807c707cb07c207c007c507bf07c107ba07b607b207bd07b907bb07b507b7060407af07b1079a07a307ad07a2062007a5⟩, ⟨0x5b02c81580a8051027012c090045021810007a03a01b80d006202e01580a404c02200f807003201700a004401c00b0040014006000, 0x89d089f08980859089b08550899088a05ea088d037a0377088505b205af08830876087f0881087a0878087d087708790872038a08750862037c0871086c05b4086f08680572086b086403ac0867085e03d00861085a0858085d085408520857084d0853084e084c0851061806140612084b065806550849084407f008470840083c0843083f084107b8060f083b08320837083905e2083308350568082b0831082a05a0082d082605b5082905af0827081208190821⟩, ⟨0x5802a81480a004d025012008a04202000f407403701a00c405e02c014809c04802200f806c032016009804001a00b0040014006000, 0x92609180929091e09230925091f09210918091d091f091c0919091f0919091b0914056a0917089c084f091308c3090d090808a8090b08f209010907090008fd090308fc08fb08ff08f608f408f908f308f508e608ef08f108ea08e808ed08e708e908e208db08e508cd08e308da08d508df08d008ce08cc08d308cb08d108c408c708c908c208bd08c508be08bc08c108b808b608bb08b508b708b008af08b308aa08a808ad08a708a908a0089e08a3⟩, ⟨0x540288138098049023811008403f01e00e406e03401880bc05802a013809404401f00e806c030015009804001a00a0038014004000, 0x9ac09aa09af09a609a409a909a309a5099e099c09a1097b099d097e097a099b0998097e0994098a0997098809910993098c098a098f0989098b0958096309870976096f097909690977096e09540971096d096f09680966096b09610967096209600965095c095a095f0959095b09560954094809510953094c094a094f0949094b0932094109470940093d0943093c093b093f09360934093909330935092e092c0931092b092d⟩]) (
(.branch 2 (
.leaf #[⟨0x55029013809804a023811408403f01e80e806e03501900bc05802a013809004201e00d806002c013008803801800a0038014004000, 0xa1a091a0a1d0a16092009180a19091d0a170a16091c0a12092d0a1509270a130958097f0a0b0a0609a50a09099f0a0709a2099f0a0309f609fb09fd09f709f909aa09f509f709f409ab09f709f009cb09f309ad09f109d009ba09ed09e801be09eb09d209e109e709e009dd09e309dc09db09df09d609d409d909d309d509cc09ca09cf09c909cb09c409b909c709b309c509bb09bf09ba09b809bd09b709b909b209b009b509ab09b1⟩, ⟨0x5702a01480a004d025812008a04302000f407603801a00c806002d014809c04802100f006c030015009003c01800a0038014004000, 0xa460a770a7b0a770a790a76014d0a6e0a730a750a6f0a710a420a690a6f0a680a430a6f0a6c0a680a680a4c0a6b0a640a5d0a670a4f0a650a5c0a570a610a520a500a4e0a550a450a530a4d0a510a4e0a4c0a440a480a4409600a4b0a470a490a4409600a470a4609600a450a4209610a470a4609610a43092a09270a410a2a0a390a3f0a380a350a3b0a340a330a370a2e0a2c0a310a2b0a2d0a260a210a290a1b0a270a200a0c0a230a1f0a21⟩]) (
.leaf #[⟨0x51027012c092046021810007c03b01c00d406402f01680a804e025011007c03a01b00c805c02a01200800380160090038014006000, 0xad005520ad30acc0aca0acf0ac90acb0ab60ac10ac70ac00abf0ac30aba0ab80abd0ab70ab90ab2094a0ab50aac0aaf0ab1015e0aa90aad0aa8015f0aad0aa80a9f0aab01620aa90aa20aa50aa70a9a0a860aa30a990aa10a9e0a980a9d0a9e0a990a9b0a9c01610a9a015d015c0a9b0a98014301420a990a920a8d0a970a890a930a850a8b0a880a860a84014e0a870a810a830a7d0a7f0a7c01490a760a470a7b⟩, ⟨0x55029814409e04d025012008a04201f80f007403701a80c805e02d015009c04802100f806c032016009804401c00c0048018006000, 0xb550b570b560b540b54016501640b550b500b4e0b5301680b4f0b4a0b3c0b4d0b460b1e0b490b420b080b450b3e0b3c0b410b3b0b3d0b300b2b0b350b250b310b260b240b290b200b1e0b230b1d0b1f0b060b150b1b0b140b110b170b100b0f0b130b0a0b080b0d0b070b090b020af408360b050b010b03083e08450aff0af80af20afb08370af905c40af30af70af30af50ae40ae30ae70ade015e0ae10ada03640add0ac80ad10ad9⟩, ⟨0x500270130092046021810407c03b01c80d806803101700b0054028012808c04001e00d806002c01300880380180090030010004000, 0xb6b0bd50b910bd30ba00bad0bcf0bb40bb10bcd0bb80bb60bbb0bb50bb70bb00ba80bb30bac0baa0baf0ba90bab0ba40ba20ba70ba10ba30b6e0b790b9f0b980b850b9b0b7f0b990b8d0b8f0b8e0b8c0b860b840b890b830b850b7e0b7c0b810b770b7d0b780b760b7b0b720b700b750b6f0b710b6a0b680b6d0b670b690b5e0b630b650b5f0b610b580b5d0b5f0b5c0b590b5f0b590b5b0b58016701660b59⟩]))))) (
(.branch 4 (
.leaf #[⟨0x520280134094048022810807e03c01d00e006a03301800b8056028012808804001d00d006002a01200800340140080030010004000, 0xc3f0c450c400c3e0c430c3a0c380c3d0c370c390c180c250c330c280c2b0c2d01380c210c290c240c220c270c210c230c2001790c1c0c1a0c1f0c190c1b0c140c120c170c110c130bfa0c090c0f0c080c050c0b0c040c030c070bfe0bfc0c010bfb0bfd0bf608780bf90bee0bec0bf10beb0bed0be60b540be90bde0be30be50bdf0be10b540bd10bdf0bd00b550bdf0bdc0b5c0bbd0bdb0bd10bd90bd80bd00b8b0bd7⟩, ⟨0x54029014009c04c025012008a04201f80f407403701980c405c02b014009404602000f006c032016009004001a00a0040014006000, 0x62b0cab0caa062a0c3b0ca90ca80c3a0ca30ca70ca60ca20ca20ca00ca50c9c0c200c9f0c340b840c990c960c920c920b700c950c880c8f0c910c8a0bf40b760c8d0c890c8b0bf20b770c890c100c810c870c800c5c0c830c7c0c730c7f0c6d0c7d0c740c720c770c710c730c6c0c6a0c6f0c5d0c6b0c600c670c690c620c5e0c5c0c650c610c630c360c410c5b0c540c4d0c570c470c550c4c0b8a0c4f0c4b0c4d0c460c440c49⟩, ⟨0x5702a01480a004d025011c08a04201f80f007203701980c405e02c014809c04802200f006c03201600a004802000e0060028010000, 0xd000cfe0d0301760cff0ccb0cfd0cf80cee0cfb0cf40cd80cf70cf00cee0cf30ced0cef0cd60ce50ceb0ce40ce10ce70ce00cdf0ce30cda0cd80cdd0cd70cd90cd20cce0cca0cd50cd10cd30ccd0ccf0bc20cc70cc90cc20cc00cc50bc30cc10cbc0b900cbf0cbb0cbd07ee07e807e40cb90cb406290cb7062f0cb50cb00ca10cb30c9d0cb10cac07550cac0cab0cac0b8d0cac0ca90cac0ca70cac06bf0caa0ca80ca60bd20b8c075406be0cad⟩, ⟨0x5702a014809e04c025011c08a04202000f007403801b00cc06002d014809c04802100f006c02e014009003c01800a0038010004000, 0xd720c380d750d6e0d6c0d660d690d6b0d4a0d630d670d640d620d5c0d570d610d550d5d0d540d520d50017a0d530d4e0d4c0d480d510d430d4f0d4b0d4d0d470d490d420d410d450d400bc30d350d360d3d0d3f0d380d340b8e0d3b0d370d390d340b8d0d370cba0cc30d330cc60ccb0d2d0cec0d010d2b0bdc0b600b580d250d200d1f0d230d1d0d210d1c0d080b580d160d110d1b0d0f0d170d0e0d0c0cfe0d0a0d060d0d0d090d0b0d050d07⟩]) (
(.branch 2 (
.leaf #[⟨0x5b02c01540a404f026012808e04402100fc07803901b00cc06202e01600a404c023010007403401700a004801e00c0048014006000, 0xde603c20de90dd00ddf0de50dde0ddb0de10dda0dd90ddd0dd40dd20dd70dd10dd30dcc04820dcf0dc80dc70dcb0dc50dc90dc40d040b540dbe0dc10dc30db6015f0dbf015e0db70dbf0dba0db80dbd0db70db90db20db00db50daf0db10daa0c120dad0c720b920da90b660da10da70da00b560da30cc00bc40d9b0d8a0d910d990d900b5a0d930d8c0bbc0d8f0d8b0d8d0cfc0cd00d890d460cd10d870d7c0d830d850d7e0d7a0c3e0d810d7d0d7f0d6c0c4c0d77⟩, ⟨0x5702a014409e04c024811808804101f00ec07003501980c005c02b014009804802100f006c030016009804001a00b0040014004000, 0xe760e670e730e6a0e6f0e710e6b0e6d0e660e690e6b0e680e670e6b0e600e5e0e630e5d0e5f0e580db60e5b0e540e520e570e380e430e490e420e410e450e3c0e3a0e3f0e390e3b0e340e320e370e310e330e2c0e240e2f0e280e260e2b0e250e270e2204560e0c0e1b0e210e1a0e170e1d0e160e150e190e100e0e0e130e0d0e0f0dfc0e050e0b0e040b580e070e000dfe0e030dfd0dff0dea0df50dfb0df40df30df70dee0dec0df10deb0ded⟩]) (
.leaf #[⟨0x53028813c09804a023811408403e01e00e806e03501900b805802a014009404402000f006c030015009804001a00a0040018006000, 0xee0014501440ee10edc0eda0edf0ed90edb0ed40ecd0ed70ebf0ed50ecc0ec70ed10ec20ec00ebe0ec50e750ec30ebd0ec10eb60eb10ebb0eaf0eb70eae0eac0a9a0eaa0ea60ea00ead0ea90eab0ea50ea70ea401570e9e0e770ea30e760e9f0ea30e9f0ea10e9e015b0e8c0e930e9d0e9205500e950e8e0e640e910e8d0e8f0dae0dbb0e8b0e5c0e7d0e850e7c0e780e7f0e7a0e600e730e790e740e720e770e660e730e77⟩, ⟨0x55029814409c04b024811808804101f00f007203701a00c405c02b014009804602000e8068030015009004001a00a0040014004000, 0xf410f610f600f400f360f410f5f0f5a0f4b0f5d0f470f5b0f460f440f490f3f0f450f400f3e0f430f3a0f380f3d0f370f390ef20eef0f350f2e0ee40f2a09340f2d0f260f160f290f140f1f0f250f1e0f1d0f210f180f160f1b0f150f170efe0f0d0f130f0c0f090f0f0f080f070f0b0f020f000f050eff0f010efa0a200efd0ef60ef40ef90ef30ef50eee0ee00ef10ee60eeb0eed0ee70ee90ee00ee50ee70ee40ee10ee70ee10ee3⟩, ⟨0x5802b014c0a004e025812408c04302000f407603801b00cc06002c015009c04a02200f807003201700a004401c00b0048018006000, 0xfdb0fdd0ed80fcd0fd30fcc0ee20fcf0edd0fcb0fc60ef50fc90eef0fc70f500e720fc50fb20fbd0fc30fbc0fbb0fbf0fb60fb40fb90fb30fb50fae0fa70fb10fa30faf0fa80fa60fab0fa20aa00fa50f9e0f6a0a980fa10f9e0f660f9a0f750f9d0f710f9b0f800f8f0f950f8e0f8b0f910f8a0f890f8d0f840f820f870f810f830f7a09d40f7d0f760f740f790f700a980f730f680f6d0f6f0f690f6b0a980f670f690f660a990f690f620f4a0f65⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5602a014409e04c025011c08604101f00ec07003501980c005a02b014009804802100f8070034017009804401c00b0048018006000, 0x105a105610561054105910531055104e104c1051103d104d10421049104b10441040103c104710431045103c103f1043103e103d1043102c103510371030102e1033102d102f10260ff81029102210201025101f1021101a100f101d1009101b101410101010100e1013100d100f10081006100b0ff910070ffc100310050ffe0ffa0ff810010ffd0fff0ff40fdc0ff70ff00fee0ff30fed0fef0fda0fe50feb0fe40fe30fe70fde0fdc0fe1⟩, ⟨0x520278130094048023010c08203e01d80e406c03301880b8056028013008c03e01d00d006002c01300880380180090038010004000, 0x10d010c810d310cc10ca10cf10c910cb10c800cf00ce10c910c410c210c710c110c310b010b710bd10b610b510b910b110b310a210a910af10a810a710ab10a310a51090109910a11098107c109b109410921097109110931086108d108f10881084107c108b108710891080107e1083107d107f107a0ff01074106f107710691075106e10641071106d106f1068103c106b10661064106010551063104f10611057105b⟩, ⟨0x56029814009a04b024011808604001f00ec07203601980c005c02b014009404402000e806c030015009804001c00b0040014006000, 0x1154115111571150114f1153114a1148114d11471149114211401145113f1141113a1132113d11361134113911331135112e112c1131112b112d1126111c1129111a11231125111e111c1121111b111d1104111311191112110f1115110e110d111111081106110b11051107110010fe110310fd10ff10f810f010fb10f410f210f710f110f310ec10ea10ef10e910eb10e410a410e710c010cd10e310dc10d510df10d110dd10d410be10d7⟩, ⟨0x5802a81480a004d025011c08804201f80f007203601a00c405e02c014809c04802000f0070032016009804001c00b0040014006000, 0x11d211db11dd11d611d411d911d311d511ce11a811d111bc11c711cd11c611c311c911c211c111c511bd11bf11a611b511bb11b411b111b711b011af11b311aa11a811ad11a711a911a2119911a5119511a3119a1198119d119411921197118311931188118f1191118a11861182118d1189118b11861184116c117b1181117a1177117d1176117511791170116e1173116d116f1168115e116b115c116511671160115e1163115d115f11461155115b⟩]) (
(.branch 2 (
.leaf #[⟨0x5802b014c0a004d025812008a04202000f807603801a80c805e02c015009c04602100f807003201700a004401c00b0040014006000, 0x8b125f125c10c8008a1258008a125b125412101257125312551240124912511248123e124b12441242124712411243122d123f1238123b123d1236122f1239123212021235122c12121231122e122d123112281221122b121512291220121b122512161214120e121912131217120d120f12001209120b1204120212071201120311fc11be11ff11f811e611fb11f4116e11f711f0114811f311e411ed11ef11e811e611eb11e511e711de11d411e1⟩, ⟨0x56029814009a04a024011408403f01e00e406c03301880b8056028012808c04201f00e806c03201600a004401c00b0040014004000, 0x10f012bd12bf12bc10f112bf10e810f512bb12b410ff12b710f912b512aa12ad12af008a12a712ab12a6008b12ab12a6129d12a9129c12a712a912a012a312a51298129412a11297129f129a1296129d129c1296129b12981297129d129c12971299129a008d008c129b0088129912960075007e12951292007b1230128f1291128e007d112a1137128d113e113b128b1282122c128512521259127d126e126d127112661261126b125d1267⟩]) (
.leaf #[⟨0x53028813809804a023811408404001e80e807003501980c005c02c014809804802100f006c03201600a004401e00c0048018006000, 0x134113431338132d133b132713391332132e132e132c1331132b132d132613241329131f13251320131e1323131a1318131d13171319131213101315130f1311130a0e33130d0e2d130b0e4f130512f412fd12ff12f812f612fb12f512f712e212ed12f312ec12eb12ef12e612e412e912e312e512da12d512dd12cf12db12d4103812d712d312d512ce032412d1103a029212cd0fec108112cb12c410b212c712be12c112c3⟩, ⟨0x53028813c09a04a024011808604001e80ec07003501980c405c02c0148098048022010007403601800b004c01e00d005001c008000, 0x13a713a913a413a213a0139e139a0e53139d0e59139b0e55139913940e8e1397138813911393138c138a138f1389138b1360135d138713821379138513731383137e137a137a1378137d137713791372134a1375136e13631371135d136f136513691368136413641362136713611363135c135a135f134b135b1350135713591352134e134a135513511353134a134d1351134c134b13511340134713491342133e131e1345⟩, ⟨0x530280134096049023811008404001e80e807003501980c405c02b014809404602000e8068030015009804001c00b0040018006000, 0x140c13f8140f14061401140b13fb140713f913ff005f13fd13fa13f8005e13f80099009813f913f4005e13f713f00e4c13f313ef13f113ea131113ed0e2913eb131313e713d813e113e313dc13da13df13d913db13d413ae13a613d713d413aa13c613cd13d313cc13a813cf13c8139e13cb13c713c913c213bb13c513b513c313ba13a213bd13b913bb13b413a613b713ac13b113b313ad13af13a613ab13ad13aa13a713ad⟩]))))) (
(.branch 4 (
.leaf #[⟨0x5702a014809e04b024811c08804201f80f007203701a00c405c02b014809804802100f006802e014009004001a00b0040018006000, 0x148c148a148f147d148b1480148714891482147e147c148514811483147a147814741472147714711473146a146d146f14601469146b14641462146714611463145c145a145f145613fc1459145213fe1455144e13001451144d144f14481443144b14191449144214281445142c14351441143814221416143b1434141c14371430142e1433142d142f142a142814201425142714211423141e141714211417141d14181416141b141214101415⟩, ⟨0x56029814009c04b024011408604001e80e806e03501900bc058029013809404401f00e806802e014009003c01800a0038014004000, 0x1510150f1513150a1508150d15071509150214f8150514f614ff150114fa14f814fd14f714f914e014ef14f514ee14eb14f114ea14e914ed14e414e214e714e114e314ca14d914df14d814d514db14d414d314d714ce14cc14d114cb14cd14c814c614ba14c314c514be14bc14c114bb14bd14a814b314b914b214b114b514ac14aa14af14a914ab147014a114a714a0147c14a31475149f149a1493149d148d149b14921478149514911493⟩, ⟨0x5702a014409e04c024811408404001e80e807003501980c405c02b014009404602000e806c030015009804001c00b0048018006000, 0x159204481595158e158515911581158f1586158415891580157415831578156e0524157f1576157b157d15771579156e052315770522156f1577156f15751570156e1573156e00db00da156f156a1568156d15640dd21567156015561563155c1557155f153d155d153215431555154215401545153b1541153c153a153f15361534153915331535152e152c1531152b152d152602a6152915241522151c042a151f15061515151b151415111517⟩, ⟨0x5702a014409c04b024011408404001e80e806e03501980c005a02a013809404402000e806c030016009804401c00b0040014004000, 0x152a152716071602044016051592044a160115fc14cc15ff15f814bc15fb15f414e215f715f015eb15f315e715f115ea152015ed15e602b015e915e2152d15e5152715e3152f15dd15c615d515db15d415d115d715d015cf15d315ca15c815cd15c715c915c215bd15c515b715c315bc152215bf15bb15bd15b615b415b9154b15b5154c154a15b3156115b10464046115af159615a515ab15a415a115a715a0159f15a3159a1598159d15971599⟩]) (
(.branch 2 (
.leaf #[⟨0x56029814409e04c025011c08a04201f00f007203701a00c405c02b014809804602000f006c03201700a004801e00c0048018006000, 0x16841679168716731685167e167a167a1678167d16771679167216701675166316711666166d166f166816641662166b16671669165e165c1661165b165d164c164b164f164600a616491642164016451622162d163f00a71639163216351637162a00a7163300a6162b1633162b1631162c162a162f162a00f500f4162b16261624162916231625161c1310161f16180e32161b1612161516170e2416111613160c0e3a160f16081508160b⟩, ⟨0x54029013c09a04a024011408203f01e00e806e03501900bc05a02a013809404402000e8068030015008803c01a00a0040014004000, 0x16f3170116f816dc16fb16f716f916f216f016f516e116f116e616ed16ef16e816e416e016eb16e716e916e216e116e716de16dc16d816d616db16d516d716c816d116d316cc16ca16cf16c916cb169216c116c716c0169e16c3169716bf16ba16b316bd16af16bb16b2169a16b516ae16ac16b1169f16ad16a216a916ab16a416a0169e16a716a316a5169c169a16961694169916931695165a168b1691168a1662168d165f1689⟩]) (
.leaf #[⟨0x540288138098049023811408403f01e00e806e03501980c005a02b014009004401f00e8068030015009003c01a00a0038014006000, 0x144c1453177f1776145b17791457177717681767176b170f17651764170e1754175d1763175c1730175f17581756175b1755175717501745175317411751174a17461746174417491740173e17431731173f1734173b173d17361732173017391735173717101465172f1715172b1726171d172917191727171e171c172117181460171b1714171217171711171316d41707170d170616e0170916d91705170416d8170016f91703⟩, ⟨0x55029013c098049023811008203f01d80e406c03301800b805802a014009804601f00e8068030015009804001c00b0040018006000, 0xa617d717db17d600a717db17d617c717d917c617d717d917c317d517ce17d117d317cc17c017cf009c17cd17c817c417c217cb17c717c917c417c217c717c617c217c517c617c117c317c400a900a817c517c2009300a417c117be00a117b417bb17bd17b617b2179417b917b517b7178c179717b117a817a417a417a217a717a117a3179c179a179f1795179b1796179417991790178e1793178d178f13ee13f5178b178013f01783⟩, ⟨0x5702a81480a004d025012008a04302000f407203701a00c405e02c014809804602100f006c032016009004001c00b0040018006000, 0x1864184c1860185918631855186118581850185b1854182e185718521850184c184a184f1849184b184417e01847183a18411843183c1838182e183f183b183d1836182f183b183218301835182f1831182a13da182d182417fc18271820181e1823181a1811181d180d181b181218101815180c180a180f17fd180b180018071809180217fe17fc18051801180317f8161c17ec17f517f717f017ee17f317ed17ef17e2163817e517da17dd17df⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x530280138098049023811008203f01e00e806e03501900b805802a013809404402000e806802e015009804001800a0038014004000, 0x18da18d818dd18d800e300e218d918d418d218d718d118d3189c18c918cf18c818a818cb18a118c718be18a418c118bd18bf18b818b618bb18a918b718ac18b318b518ae18aa18a818b118ad18af18a618a418a0189e18a3189d189f1896187e1899189518971882188b1893188a186a188d188618841889188318851880187e1874187b187d18761872186a187918751877186e186c1871186b186d184818331869184d1865⟩, ⟨0x54028813c09804a023811408404001e80e406e03401900bc05a02a014009404401f00e006402e014009003c01a00a0038014006000, 0x194c1949194f1949194b19441942194719411943193c193a193f1939193b193419321937192319331928192f1931192a19261922192d1929192b19241923192919251927191e19151921190f191f19140fd6191719131915190e02a0191118f418fd190d19021905190718fa00fd190300fc18fb190318fb190118fc18fa18ff013218fb18f617fa18f918f518f718d018db18f318e818e318ed18df18e918d918e118de18d800a6⟩, ⟨0x56029814009c04b024811c08804101e80ec07003401900bc05802a014009404402000e8068030015009004001a00b0048018006000, 0x19cc19cb19cf19c619c119c9028119c719c019ba19c319bf19c119bc19ba19b2028a19b519a819af19b119aa19a6027c19ad19a919ab199c19a319a5199e199a197a19a1199d199f1972197d199919921987199519831993198c198819881986198b198219801985197b1981197c197a197f197619741979197319751940196b1971196a194a196d1945196919641959196719551965195e195a195a1958195d195419481957194e19511953⟩, ⟨0x530280134094048022810807e03d01d00dc06803201780b4056029013008c04201f00e006802e014009004001a00b0040018006000, 0x1a2c1a371a3d1a361a351a391a301a2e1a331a2d1a2f1a1c1a251a2b1a2416301a271a201a1e1a231a1d1a1f1a0c1a151a1b1a1419221a171a101a0e1a131a0d1a0f1a08193b1a0b19351a09193d1a031a02193c19da19d71a0119fc19f319ff19ed19fd19f819f419f419f219f719f119f319ec19ca19ef19e819dd19eb19d719e919e219de19de19dc19e119db19dd19d619d419d919cb19d519ce19d119d319ca19cd19cf⟩]) (
(.branch 2 (
.leaf #[⟨0x54029013c09804a023811008003e01e00e807003501900bc05a02a013809004401f00e0068030015009004001c00b0040018006000, 0x1ab91abb1ab41a821ab71aae1a701ab11a911aa91a941a541aa71a9c1aa31aa51a9e1a9a1a441aa11a9d1a9f1a9a1a981a951a971a961a941a901a681a931a801a891a8b1a841a821a871a811a831a6e1a791a7f1a781a771a7b1a721a701a751a6f1a711a6a1a681a6d1a641a551a671a491a651a571a5f1a5a102e1a5d1a561a541a591a531a551a4d1a511a4c1a441a4f1a481a461a4b1a451a471a4016f81a4316d60e4e1a3f⟩, ⟨0x5702a014409c04c024811c08804101f00f007203701a00c405c02b014809804602000e806c030015009004001a00b0040018006000, 0x1b341b3f1b451b3e1b3d1b411b381b361b3b1b351b371b301b001b331b1b1b2f1b1c1b271b2d1b261b251b291b201b1e1b231b1d1b1f1b161ad31b191abd1b171afe1b0d1b131b0c1b091b0f1b081b071b0b1b021b001b051aff1b011ae81af71afd1af61af31af91af21af11af51aec1aea1aef1ae91aeb1ae41ada1ae71ad81ae11ae31adc1ada1adf1ad91adb1ad41ad21ad71acc1ac81ac81ac61acb1ac51ac71ac01ab81ac31abc1aba1abf⟩]) (
.leaf #[⟨0x5902b014c0a204e025812008a04201f80f007203701a00c405e02c015009c04802200f806c03201600a004401c00b0048018006000, 0x1bd01bcf1bd31bca1bc81bcd1bc71bc916780e4a1bc11bbc11061bbf1bb61b9e1bb91bb21b921bb51b9c1bab1bb11baa1ba71bad1ba61ba51ba91ba01b9e1ba31b9d1b9f1b901b991b9b1b941b921b971b911b931b8c1b851b8f1b811b8d1b841b661b871b801b7e1b831b711b7f1b741b7b1b7d1b761b721b701b791b751b771b6c02221b6f1b6a1b681b541b5f1b651b5e1b5d1b611b581b561b5b1b551b571b5001fc1b531b4c01e61b4f1b4612f61b49⟩, ⟨0x520280134094047022010807e03d01d00dc06a03301880bc058029013809404401f00e8068030015009004001a00b0040014006000, 0x1c411c431c2a1c391c3f1c381c351c3b1c341c331c371c2e1c2c1c311c2b1c2d1c221c211c251c20003b1c1a1c1d1c1f1c181c0e1c1b00381c191c111c171c161c101c131c151c101c051c131c0e1c0d1c11003c1c0f1c0c00311c061c091c0b1c04003f1c0700421c051bfe1bf91c031bf71bff1bf61bee003e1bf21bf01bf51bef1bf11bea1bc41bed1be91beb1bda1be31be51bde1bdc1be11bdb1bdd1bc61bd11bd7⟩, ⟨0x55029814009c04b024011808604001e80e806e03501900bc05a02a013809404401f00e806c030016009804401c00c0048018006000, 0x1c271cc51cb61cc11cc31cc000371cba1cbd1cbf1be61cb51cbb1cb31cb91cb41cb31cb71ca41ca31ca71c9e003e1ca11c9a1bc21c9d1be81bf31c991c231c931c5e1c691c911c881c871c8b1c851c891c841c6c1c0c1c7e1c791c831c771c7f1c761c741c641c721c6e1c751c711c731c6d1c6f1c681c661c6b1c651c671c601c561c631c5f1c611c5a1c581c5d1c571c591c401c4f1c551c4e1c4b1c511c4a1c491c4d1c441c421c47⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x5902b81500a204e025812408c04302000f407603801a80c806002d01500a004a02300f807403601900b004c02200d0050018006000, 0x1d3a1d381d221d311d371d301d2d1d331d2c1d2b1d2f1d261d241d291d231d251d0c1d1b1d211d1a1d171d1d1d161d151d191d101d0e1d131d0d1d0f1d081cfe1d0b1cfc1d051d071d001cfe1d031cfd1cff1cf80a2c1cfb1cf41cf21cf701461cf31cee1cec1cf11ceb1ced1ce61ce21cde1ce91ce51ce71ce11ce31ce21ce00e721cd91cdd1cd80e731cdd1cd91cdb1cd40e6c0e661cd71cd013ba1cd304fe04f804f61ccf1cc81ccb1ccd1cc61c0d1cc9⟩, ⟨0x56029814409e04c024811c08a04302000f807603901b00cc06002d01580a004a02200f807403401700a004401c00c0048018006000, 0x1dae1da91db31da51daf1d951da71da41da21d941da01d9c1da31d9f1da11d9b1d9d1d9a01511d961d941d9901541d951d901d8e1d931d8d1d8f1d761d851d8b1d841d811d871d801d7f1d831d7a1d781d7d1d771d791d601d6f1d751d6e1d6b1d711d6a1d691d6d1d641d621d671d611d630a7c1d5d1d5f1d5c0a7d1d5f1cea1cf51d5b0a1e0a1b1d551d500b3d1d530b511d511d481d241d4b1d441d0e1d471d400dec1d431d3c08b61d3f⟩]) (
.leaf #[⟨0x530288138096048022810c08003d01d00e006a03201780b4056028013008c04201f00e806c030015009004001a00a0040014006000, 0x1df51e2b1e101e1f1e251e1e1e1b1e211e1a1e191e1d1e141e121e171e111e131dfe1e091e0f1e081e051e0b1e041e031e071dff1e011dfa1df81dfd1df41dec1df71df01dee1df31ded1def00821ded1de81ddf1deb1de31de71de212931de51de000871dde00851dd91ddd1dcd1ddb1dd00fb41dd31dcc0fee1dcf1dc810931dcb10991dc91dc410921dc71dc01dbe1dc31dbd1dbf1db81db71dbb1db51db91db41d9a0a98⟩, ⟨0x4f026012408e045021810007c03b01c80d806803201780b0052027012008403c01c00d006002a013008803c01800a0040014006000, 0x1e8c129e1e8f1e881e7e1e8b1e871e891e7b1e851e821e801e7a1e781e7d1e771e791e721e701e751e6b1e711e6c1e6a1e6f1e4f1e691e681e4e1e561e611e671e601e5f1e631e5a1e581e5d1e571e591e501e531e5512961e4f1e511e4e12971e511e4b1e4d1e4a007700761e4b1e461e441e4900781e451e411e431de91e3f1e3a1e311e3d1df11e3b1e331e371e321e301e351e2f1e311e2a1df91e2d⟩, ⟨0x56029814009c04b024011808804101f80f007203701a00c405c02a014009404602100f006c030016009804001c00b0040018006000, 0x1e2e1df11f0b1f041eff1f091efd1f051efc1efa1dec1ef81ef61efb1eeb1ef91ef51ef71ef01eef1ef31eed1ef11eec1eea1e4a1ee61edd1ee91ed91ee71ede1edc1ee11ed81e4c1edb1ece1ed51ed71ed01ecc1e4a1ed31ecf1ed11eca1e4b1ecf1ecb1ecd1ecc1eca1e9e1e6d1ec91e761e731ec71ebe1eb71ec11eb31ebf1eb61e801eb91eb21eb01eb51eab1eb11eac1eaa1eaf1ea21ea01ea51e9f1ea11e9612961e991e921e901e95⟩]))) (
(.branch 2 (
.leaf #[⟨0x5902b014c0a004d025011c08804101f00ec07203601980c005a02b014009804602000f0068030014008803c01a00b0040014006000, 0x1f861f891f8b1f841f831f8710fc10f91f811e401e471f7f1e861e8d1f791f721e001f751f6e1e421f711f5c1f671f6d1f661f651f691f601f5e1f631f5d1f5f1f461f551f5b1f541f511f571f501f4f1f531f4a1f481f4d1f471f491f421f411f451f3f1f431f3e1ef412961f3a1f2f1f3d1f2b1f3b1f321f2e1eaa1f351f311f331f2a1f1e1e3e1f2d1f261f171f291f131f271f191f211f1d1f1f1f181f161f1b1f121f101f1500721f111f0c1e361f0f⟩, ⟨0x540288138098049023811008203e01e00e406e03401880bc05a02b014009404602000e806802e015009804001a00b0040010004000, 0x1ff41ff31ff71fee1fec1ff11feb1fed1fe601821fe901811fe702d01fe31fe51fe202d11fe51fde1fd51fe11fcf1fdf1fd61fd41fd91fd31fd51fce1fcc1fd11dd404a61fc71fc41fc209f51fc11fc009f41dbc1fb51fbf1fb4125e1fb71dc11fb31fac1de11fb11f8c1f841faf1f8e1eaa1fad1f821eab1fad1faa1f951faa1f931f941f921fab1fa61f9f1fa91f911fa71f9e1f991fa31f941f921f901f971f8f1f951f8d1f93⟩]) (
.leaf #[⟨0x520278130094047022810808003d01d80e006a03201800b8058029013008c04201f00e006002c014009004001a00a0040018006000, 0x205a2058205d20542049205720332055204e202c2051204b204f204a2048204d204720492042203b204520372043203a202c203d2036202e2039203220302035202f203100f0202f202a202820222025202702f202a82023201c201720212013201d201120152012201002a8200e200a20022011200d200f200c00f92009200b200800f720002005200720042001200720012003200000f31fea1ff91fff1ff81ff51ffb⟩, ⟨0x510270130092047022010407e03b01c80d806803101700b0052026012008403e01c00d006002c014009003c01800a0038010004000, 0x20c820c620cb20c520c720be20b020c120bc20ba20ae20b720b920b220b020b520af20b10e22045a045220ad20aa20a820a420a320a720a120a520a02084156e209c209b209f2099209d2098208002a62092208d2097208b2093208a2088202e208820832086208220892085208720862084208400ef00ee208520812083207c2059207f2072206d20772067207320682066206b2060205e20630b212061205b205f⟩, ⟨0x5902b014c0a004d025011808604101f00ec07003401900bc058029013809004401f00e806802e015009004001c00b0048018006000, 0x2f0212d2131212820c6212b211a2004212502ee01872123018602ef21232098208202b02121203a2028211f2119211b21141fec211720f6210121132104210b210d210620fc1fc421092105210720fc1fc321051fc220fd2105210020fe210320fd20ff20f81fc820fb20f720f920f21fe720f51fe320f31fe2018120f120da20e520ef20e320e920e420e220e720e200dd00dc20e320de20dc20e120db20dd20c420d320d920d220cf20d520ce20cd20d1⟩]))))))))))) (
(.branch 37 (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5702a014809e04b024811c08804101f00ec07003501900c005a02a013809404602100f0070032016009804401c00b0048018004000, 0x21ac21a621af21ab21ad2046203321a921a221a0211821a5200521a3211d21a1212620dc219f21921b84219921941b562197217c218b2191218a2187218d2186218521892180217e2183217d217f21762179217b2174216d21772170216c21732151216b21672169216821662162215b216521532163215a2155215f215221502146214c214a214f2147214b214202d02145213e213a2141213d213f2130213721392132212e02f0213521312133⟩, ⟨0x5802b014c0a004d025012008a04202000f407403801a80c806002d015009c04a02200f007003201600a004401c00b0040014006000, 0x222e222c220e22192229221e22212223221600cb221f00ca2217221f2217221d22182216221b221222102215220f221121ee21f7220d21fe21fd220100cb21fb21f600ca21f921f221f021f521ef21f121dc21e721ed21e621e521e921e021de21e321dd21df21d221d921db21d421d021c621d721d321d521ce21c721d321ca21c821cd21c721c91dd8105421c5100c100921c31dd6100e21c121aa21b121bf21b8018f21bb019721b921b001a221b3⟩, ⟨0x53028813c09804a023810c08203e01e00e806e03501900c005a02a013809004401f00e006402e014009003c01a00a0038014004000, 0x22af22b122a822a622a222a022a5229f22a12294229b229d229622922274229922952297228e22832291227d228f2288228422842282228722812283227c227a227f2275227b2276227422792270226e227322602269226b2264226222672261226322502259225f22582232225b22542252225722512253224c2245224f223f224d2244222c224722432245223e223022412236223b223d2237223922342231223722312233⟩, ⟨0x55029814009c04b024011808604001f00f007203701a00c805e02b014809804802100f006c032016009804401c00c004801c008000, 0x232c232823282326232b23252327232021c62323231c231a231f2319231b22e423112317231022ec231322e9230f230823042304230223072301230322fc22fa22ff22ed22fb22f022f722f922f222ee22ec22f522f122f322e822e622eb22e522e722d222dd22e322dc22db22df22d622d422d922d322d5229e22cb22d122ca22aa22cd22a322c922c022a622c322bf22c122ba22b822bd22ab22b922ae22b522b722b022ac22aa22b3⟩]) (
(.branch 2 (
.leaf #[⟨0x520280134096048023010c08003d01d00dc06803201780b0054027012808c04001d00d806402e014008803c01800a0038014004000, 0x157123a1239c239a239f2399239b23941aac23972393239516f616f3239123862389238b236a238523872384236b23872362236f23832378235e237b237723792372236a2375236e236c2371236b236d236623642369236323652360235e235a15b4235d2354234f2359234923552343234d0121234b234823420120234423422347014a2343233e226c2341233d233f231821cb233b231d233723322327233523212333⟩, ⟨0x5a02b81500a404f025812008a04201f80f007203701a00c405c02c014809c04802200f807003401800a804801c00c0048018006000, 0x240819f2240b2404240224072401240323fc19c023ff0be00bd80b5423fb23f61b3623f923f21e5823f523c823d123f123de23e523ed23e423d423e723e023dc23e323df23e123d623d923db23ce008b23d7008a23cf23d723cf23d523d023ce23d300d023cf23ca23be23cd23c923cb1912190f23c723c0147223c5124523c323c2124423b823b523bd122c23b923bb23b423b21de623b723b123b314920e5023af2392154323ad2398153d23ab23a0156923a3⟩]) (
.leaf #[⟨0x530280134094047022010407e03c01c80dc06803101700ac052027012808c04201f00e8068030015009004001a00b0040014004000, 0x2454234c2457244e245124530120244b244f244a0121244f244a243f244d243e244b244d243f2449244224452447243a2436244324392441243c2438243f243e2438243d243a2439243f243e2439243b243c01230122243d011e243b2438010901082439011424372434010f24262431243324300113242a242d242f238e2425242b2423242924242423242724092421240c2417241d2416241524192410240e2413240d240f⟩, ⟨0x56029814409c04c024811c08804101f80f007203601980c405c02b014009804602100f0070032015009804401e00c0048018006000, 0x24da222a24dd24d924db24d424d224d7011024d324ce24cc24d124cb24cd233c234524c924c224af24c524ab24c324b424b324b724ae241e24b124aa012024ad24a4249d24a7249924a5249e249c24a124982476249b2494248d249724872495248c2472248f248b248d24862484248924772485247a24812483247c24782476247f247b247d2474247224632471246c138a246f2468193a246b24641a0e2467245e19dc246124002455245d⟩, ⟨0x540280138096048023011008203f01e00e806e03401900bc05802a014009404602000f006c02e015009004001a00b0048018006000, 0x255625522530255925552557252825332551254a253f254d2539254b254425402540253e2543253d253f25382536253b25312537253225302535252c252a252f2529252b24f225212527252024fe252324f7251f251e24f6251624fa2519251525172510250e251324ff250f2504250b250d2506250224fe250925052507250024ff250524fc24fa24f624f424f924f324f524f0236624ca24d524ef24d824df24e924de234a24e1⟩]))))) (
(.branch 4 (
.leaf #[⟨0x54029014009a04a023811008203f01e00e406e03401900bc056029013009004402000e806c030015009804001c00b0040014006000, 0x25c925cd25c525c725c2154a25c525c4154b25c125b025b925bf25b818e025bb25b425b225b725b125b30288028525af2584258125ab25a625a225a225a025a5259f25a1259a2574259d2596257a2572259925772597259225872595258125932589258d258c258825882586258b258525872580257225832578257d257f2579257b25762573257925732575255e25672571256621fa2569256225602565255f25612554255b255d⟩, ⟨0x5702a814809e04d025011c08804101f80f407603901b00cc06002e01580a004c023010007403601800a804401c00b0048018004000, 0x261c00c326162619261b2614260c261700ba2615260226112613261026032613260e260a26112610260b260d00cc260f00c8260d260a00af00ae260b26042607260900ca26032605260200cb26051537260125f225fb25fd25f625f425f925f325f5200c25c525f125c4200d25f125e825ed25ef25e925eb25c0170f25e9170e25c125e925c625c015b425e725c8170e25e525e025d925e325cb25e125d825d325dd25ce25cc25ca25d125c325cf⟩, ⟨0x50026812c090045021010007a03b01c00d806603101780b4054028013008c04001d00d006002a01200780340160080030010004000, 0x268c2674268f268b268d2676268126872680267f2683267a2678267d26772679266c26712673266d266f266a260b266d260b266926642662266726612663266000c100c02661265c2656265f265b265d26572659263e264d2653264c2649264f26482647264b264226402645263f2641261c263b263d263a261d263d2634262f2639262b26352629262d262a2628260c26252627262400c726212623261d261f⟩, ⟨0x5602a014409e04c024811808804101f00ec07003601980c005a02a014009404401f00e8068030015009804401c00b0040014004000, 0x270b270d270626da27092705270726fe26f4270126f226fb26fd26f626f426f926f326f526dc26eb26f126ea26e726ed26e626e526e926e026de26e326dd26df26c426d326d926d226cf26d526ce26cd26d126c826c626cb26c526c726b226bd26c326bc26bb26bf26b626b426b926b326b526aa26af26b126ab26ad26a826a526ab26a526a726a400b1268a269526a32698269b269d26901bbb26991bba2691269926942692269726912693⟩]) (
(.branch 2 (
.leaf #[⟨0x5802a814c0a004c025012008a04302000f407403701a00c405e02c015009804802200f8070032016009803c01a00a0038014006000, 0x27882781278b277527892780277b2785277627742772277927712773277000ab276c276a276f00ac276b2764274a276727602742276327482757275d275627532759275227512755274c274a274f2749274b27442742274727412743273c27382734273f273b273d27372739265a266527332704270f272d272426c62727272026de27232716271d271f27182714270a271b27172719270a271327172712270b27172713271527142712270e270c2711⟩, ⟨0x56029814009a04b024011808604001e80ec07203601980c005c02c014809804602100f0070032016009804001c00b0040014004000, 0x27e6097f280909a20963280127f8096627fb27ed27f727ee27f327f527ef27f1097a27ed27ef27ec097b27ef27e8246227eb27e727e9263b27e527c0276827e327be27c727e127d627d127db27cd27d727c527cf27cc27ca27c426a6266827cb27c627c427c900b227c527c0275e27c327bf27c12740276d27bd27b427aa27b727a827b127b327ac27aa27af27a927ab278c279f27a7279e279727a32796279527992790278e2793278d278f⟩]) (
.leaf #[⟨0x5702a014409c04b024811808604001e80e807003501900bc058029013009004401f00e8068030015009004001a00b0040018006000, 0x2872287b28810960287b287d287a0961287d28762874287928732875286e1cec28711d8c1d97286d285e21192865154a285f2863285e154b2863285f28612150047e285d28581aea285b285425f42857284e2851285311e21fcd284f284a283f284d2839284b282728472840283e2843283d283f283820fc283b2832282a282a2820282d28262824282928212825281c2815281f280f281d2814238c281728132815280e24282811280a1fd4280d⟩, ⟨0x5802a814c0a004d025812408c04302080f807603801a80cc06002d015009c04802000f006c030016009804401c00c0048018006000, 0x28f628f128f928ed28f728ec28e428ef28e828e628eb28e528e7015828e528d828e128e328dc28da28df28d928db28d422d428d728c028cb28d128ca28c928cd28c428c228c728c128c328b8137828bb28b4136228b70ea41ce528b31ce40ea528b328a828af28b128aa28a60ea828ad28a928ab1cd81cdf28a528a0289528a3288b28a1289a288e289d2897289b28962894289928932895288e1d8e2891288a1da6288d28861d78288928821d622885⟩, ⟨0x55029814009c04b024011408404001e80e806e03401900bc058029013008c04001e00e006402e014008803c01800a0040014006000, 0x29632967296229602965295f2961295a27ce295d0f7e0e5e295929542678295729502941295329472951294a2706294d2946270a2949294229402945293c2935293f2931293d293428bc29372930290e2933291c2925292f2928268c292b2924269029272920291e2923291d291f291a00b5290c29172919291600b929102913291528be290b29112909290f290a2909290d28d32907290628d2290228fb290528e9290328fc28fa28ff⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x55029013c09a04a023811408403f01e00e406e03501900bc05802a013809004201f00e8068030015008803c0180090038014004000, 0x29d829e129e329dc29da29df29d929db29ca29d329d529ce29cc29d129cb29cd29b429c329c929c229bf29c529be29bd29c129b829b629bb29b529b729b229ac29ae28da29b12990298d29ab29a6298b29a9298d29a72988298d29a32998299b299d2994282129992995299729912993298c2428298f2989298b297e298529872980297c29722983297f2981297a2973297f29762974297929732975296f2971296a2961296d295b296b⟩, ⟨0x5702a014409e04c024811c08804101f00ec07003601980c005c02b014009804602100f0068030015009804401c00b0040014006000, 0x2a5406fc2a572a5001d22a532a4f2a512a4a2a422a4d2a462a442a492a432a452a3e29b62a412a3a29cc2a3d2a3629ea2a392a2c099f2a352a302a2e2a332a2d2a2f2a282a262a2b2a222a212a252a1f2a232a1e07e6064e2a1a2a182a1d2a172a192a122a102a152a052a112a062a0d2a0f2a082a042a022a0b2a072a092a002a052a072a022a0029fe29d629e829f729fd29f629f329f929f229f129f529ec29ea29ef29e929eb29e429da29e7⟩, ⟨0x5c02c81580a6050026812408c04302080f407403601980c005a02b014009404402000e806402e014008803c01a00b0040014004000, 0x4bc04b92ac12aa004be2abf2aa62aad2abd1fe2285f2ab7285e1fe32ab52448243c24382ab12aac02da2aaf2aa82aa42aab2aa72aa902e602e002d22aa309b609b32a9f1fc009f809aa2a9d09d009b82a9b2a8c20f82a992a942a192a972a132a952a882a5a2a8b2a8410fe2a872a802a272a832a472a812a722a792a7b2a742a702a422a772a732a752a422a6f2a732a6e2a432a732a702a6e2a6b2a6d2a6c2a6a2a582a632a692a622a612a652a5c2a5a2a5f2a592a5b⟩, ⟨0x54028813c098049023010c08203e01d80e406e03401900bc05a02a013009004201f00e8068030015009004001c00b0040018006000, 0x2b3a2b392b3d2b352b370bea0be72b330c700c6d2b310b3a0b512b2f2b2a17ee2b2d2b282b262af22b1f2b252b1e2afa2b212af72b1d2b162b122b122b102b152b0f2b112b0a2b082b0d2afb2b092afe2b052b072b002afc2afa2b032aff2b012af62af42af92af32af52aee2aea2aea2ae82aed2ae72ae92ae22ac22ae52ade2ad32ae12acf2adf2ad52ad92ad42ad22ad72ace2acc2ad12ac32acd2ac62ac92acb2ac42ac32ac7⟩]) (
(.branch 2 (
.leaf #[⟨0x530278134096048023010c08203e01e00e806e03401880bc05a02b014009404402000f0070032016009804401c00b0040018006000, 0x2bac2baa2ba82baf2ba72ba92ba600192ba22ba02ba5001a2ba12b9c2b9a2b9f2b992b9b2b942b912b972b9200292b9000272b8a2b8d2b8f2b8800162b8b2b8600172b8b002a2b8900222b872b8400212b722b7d2b832b7c2b7b2b7f2b762b742b792b732b752b6f2b712b702b6e2b562b612b672b602b5f2b632b5a2b582b5d2b572b592b522b482b552b462b4f2b512b4a2b482b4d2b472b492b422b362b452b342b3b2b41⟩, ⟨0x5702a014409c04b024011408604101f00f007203601980c405c02b014009404201f00e0068030016009804001a00a0040014006000, 0x2b982ba32c3b2c1e2c272c352c2a2c2d2c2f25fe2c252c2b2c262c242c292c202bc22c232c1f2c212c192c1d2c182bea2c1b2c112c172bc608142c152c102bfc2c132be8084f2c0f2bed2c0d08982bfd2c0b2c0005e22c032bfc2bc42bff2bf22bf92bfb2bf42bf0084c2bf72bf32bf52bec2bea2bef2be92beb2be62bc62be42bc42bc82bdb2be32bda2bd32bdf2bd22bd12bd52bcc2bca2bcf2bc92bcb2bbe2bb72bc12bab2bbf2bb62bb12bbb⟩]) (
.leaf #[⟨0x5602a014409e04c024811808604001e80ec07003501900bc05a02a013809004401f00e006402c01400880380180090030010004000, 0x2cb42cb02cb02cae2cb32cad2caf2ca829722cab19be02812ca52a162a132ca32c9e2c4c2ca12c9a2c802c9d2c962c5a2c992c942c562c7e2c8d2c932c8c2c892c8f2c882c872c8b2c822c802c852c7f2c812c7a2c702c7d2c6e2c772c792c722c702c752c6f2c712c582c672c6d2c662c632c692c622c612c652c5c2c5a2c5f2c592c5b2c4a2c532c552c4e2c4c2c512c4b2c4d2c442c472c492c422c412c452c40001f2c3e001d00242c3d⟩, ⟨0x510278130094048022810c08203e01d80e406c03301800b8058029013009004402000e806c030016009804001a00a0040014006000, 0x2d2201172d1e2d1c2d212d1b2d1d01182d1b2d162d102d192d152d172d112d132cdc2ce72d0d2d002d052d072d012d0324382a6b2d012a6a24392d012cfa2cf52cff2cf12cfb2ce52cf32cf02cee2ce42cec24402cef2ceb2ced2cec2cea2cea010b2ce62ce42ce9010c2ce52ce02cde2ce32cdd2cdf2cc62cd52cdb2cd42cd12cd72cd02ccf2cd32cca2cc82ccd2cc72cc92cc024352cc52cc12cc32cba29702cbd⟩, ⟨0x54029013c09a04a024011408403f01e00e806e03401900bc05a02a013809004401f00e806802e014009003c01800a0038010004000, 0xa22d8f2b6e253e2d8d2d8a011d2d862d852d892d84011b2d6e2d7d2d832d7c2d792d7f2d782d772d7b2d722d702d752d6f2d712d142d1f2d6d2d642d632d672d612d652d602d2224382d5e2d422d4c2d572d5d2d562d552d592d502d4e2d532d4d2d4f2d442d492d4b2d452d472cea2d432d452d422ceb2d452d3e2d3d2d412d3b2d3f2d3a2d262cea2d342d2f2d392d2d2d352d2c2d2a2d1a2d282d242d2b2d272d292d232d25⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x530280138096047022810c08003e01d80e406c03401900c005a02a014009404401f00e006402e015009804401c00b0040018006000, 0x2de22ddb2de52dcf2de32dda2dd52ddf2dd02dce2dcc2dd32dcb2dcd2dca00452dc62dc42dc900462dc52dc02dbe2dc32dbd2dbf2db82db52dbb2db600552db4004f2db2005b2daa2dad2daf2da82da02dab00562da92d962da52da72da42d972da72da22d9e2da52da42d9e2da32da42d9f2da12da2006100602da3005c2da12d9e00492d982d9b2d9d005e2d972d992d96005f2d992d9600632d902d932d95005e2d8f2d91⟩, ⟨0x5702a014409c04b024811808604101f00ec07003501900c005a02b014809804802200f8070032016009804001c00b0040014004000, 0x2e542e632e692e622e5f2e652e5e2e5d2e612e582e562e5b2e552e572e462e4d2e532e4c2e4b2e4f2e472e492e402e432e452e3e2e352e411ac41ac12e3d2e362e392e3b1b1a2d9f2e372e34004b2e302e2e2e332e2d2e2f004c2e2d2e282e222e2b2e272e292e232e252dbc2dc72e212e042e0d2e1b2e102e132e152b262e0b2e112e0c2e0a2e0f2e062de62e092e052e072de82dfb2e032dfa2df32dff2df22df12df52dec2dea2def2de92deb⟩]) (
.leaf #[⟨0x5802a814c0a004d025011c08804201f80f007403701a80c805c02c014809c04802100f006c032016009804001c00b0040014004000, 0x2eea2ee82eed2ee72ee92eca2ed52ee32ed82edb2edd1d382ed32ed92ed42ed22ed72ece2ecc2ed12ecb2ecd2e902e9b2ec92ec02ebb2ec32eb72ec12eb62eb42eb92ea92eb52eaa2eb12eb32eac2ea82ea62eaf2eab2ead2ea82ea52eab2ea62ea42e9e2ea12ea320a82e992e9f2e9a2e982e9d2e942e922e972e912e932e8c2e822e8f2e802e892e8b2e842e822e872e812e832e6a2e792e7f2e782e752e7b2e742e732e772e6e2e6c2e712e6b2e6d⟩, ⟨0x55029013c09a04b024011408604101f80f407403701a00c405e02c014809804602000e806c032016009804001c00b0040018006000, 0x2f682f522e342f622f5d2f672f592f632f4d2f5b2f582f562f4c2f542f502f572f532f552f4f2f512f4e00592db92f492f322f412f472f402f3d2f432f3c2f3b2f3f2f362f342f392f332f352e262e312f312f282f042f2b2f162e922f272f222e482f252f1e2e6c2f212f1a2e562f1d02752f152f1402742f022f0d2f132f0c2f0b2f0f2f062f042f092f032f052efe2ee82f012ee42ecc2efd2efa2ef82ee62ef12ef72ef02eef2ef3⟩, ⟨0x5902b01500a204e026012408c04302000f807603801a00c805e02c015009c04a02200f8070032016009804001a00a0038014004000, 0x2fe42fe22fe72fe12fe32fdc26a42fdf2fd82fd62fdb2fd52fd72fbe2fcd2fd32fcc2fc92fcf2fc82fc72fcb2fc22fc02fc52fbf2fc12fba26b42fbd2fae2fb52fb72fb02fac2fa22fb32faf2fb12fa22fab2faf2fa62fa42fa92fa32fa52f9e2f9c2fa12f9b2f9d2f9625162f992f9222622f952f8e248c2f912b6a249c2f8d2b6c25602f8b253c25392f892f722f812f872f802f7d2f832f7c2f7b2f7f2f762f742f792f732f752f6c2f6b2f6f2f692f6d⟩]))) (
(.branch 2 (
.leaf #[⟨0x5a02b81500a204f026012408c04402080f407603901b80cc06002d01500a004c0230100074034017009804001a00b0040014006000, 0x306a3069306d3068304030673068304130653066006f3052305d3063305c305b305f305630543059305330553048304f3051304a30463040304d3049304b30463044304130433030302a3024303f303a3038303d3034303230373028302d302f3029302b302530272514251130232f9a2fa730213006300b3019301426403017301027353013300c300a27e4300f2ffe300730093002300030052fff30012fd42fdd2ff92ff02fe22ff32fee2fec2fe02fe92feb⟩, ⟨0x5702a814809e04b024811808604001e80ec07003501900bc058029013809404602000e8068030015009804401c00b0040018006000, 0x30d530d730cc307530d5307430cd30d530d030cc300030d330cf30d130ce2fff30cd30bc30c330cb30c2300030c530be307630c130bd30bf2324232130bb230022fd30b930b214aa30b52908301130b1273a291b30af22be22bb30ad30aa30a630a8307400b630a3308a309130a130963099309b308e006d3097308f30953090308e309300c4308f308b308d307830833089308230813085307c307a307f3079307b306e30713073006c306b306f⟩]) (
.leaf #[⟨0x5802a814809e04d025011c08804101f80f007203601a00c405c02b014809c04802100f007003201600a004401c00b0048018006000, 0x31563159315b3154314f31573150314e3153314b314d31443147314931422c3f31453134313b3141313a3139313d31353137310e311731333122312b312d31263124312931233125311c311f31213112311b311d31163114311931133115310f311131003107310d31063094310931022b6831053101310330f430f930ff30f830a230fb30f530f730f0307a30f330e830e730eb30e2303930e5303530e3262430cf30dd30ce262530dd30d430d930db⟩, ⟨0x55029013c098049023811008203e01d80e406c03401880b805802a013809004402000f006c030015009004001a00a0040014006000, 0x31de2c2031e131da305431dd31d431d731d931d0303331d531d231d031b831c731cd31c631c331c931c231c131c531bc31ba31bf31b931bb31b231b131b531af31b331ae31942c3e31a831a331ad319f31a9319331a1319e319c3192319a3196319d3199319b319531972b95318f31783187318d318631833189318231813185317c317a317f3179317b3168316f3175316e316d31713169316b314a3151316731553161315c3124315f⟩, ⟨0x5a02b81500a404f026012408e04402000f807803901b80d006202e01580a004802100f0070030016009804401c00b0048018006000, 0x325632243259325232503255324f3251322e3224324d324a3225324d3246323f324932313247323e323932433234323232303237322f3235322d323332243229322b3225322732082d0e3223321e2d7032213206320f321d1fd21fcf321932142d4e32172d5e2d462cea3213320e2d1a3211320a3208320d32073209320231fe2cc232053202320031fa31f331fd31e731fb31f431f231f731ee2cdf31f12ce731ef31ea2cde31ed31e62cf231e931e22cc831e5⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5802b014c0a004d024811808604101f00f007203701a00c405c02b014809804802100e806c030016009804401a00b0040014004000, 0x2f9732e132dc24f432df2812280f32db296e297732d932d229961fca32d532cc31ff32d1242232cd32cf325b32cb325e325a32c9325f32c7327c328932c5326932bf32a832b732bd32b632b332b932b232b132b532ac32aa32af32a932ab32a0329a32a33299329b328e329532973290328c32843293328f329132883286328b328532873280327e3283327d327f327822382230327b327622543264326d3275326c2cec326f32683266326b32653267⟩, ⟨0x55029013c09a04b024011408604001f00ec07003501900c005a02b014009404402000e806802e015009004001a00b0038014004000, 0x33683366336b336233603365335f3361335c006933563359335b335430643357006a3355334c33513353334d334f3332334133473340333d3343333c333b333f33363334333933333335332e207d333132eb332f32ea3321332b32fa3305331d3312330d3317330b3313330a330833003042302633093304330233073301330332fc32f432ff32fb32fd32f632ee32f932f532f732f032ec32ea32f332ef32f132e632e432e932e332e5⟩, ⟨0x520280138096049023011008203d01d80e006c03301800b8058029012808c04001e00e006802e014008803c01800a0038014004000, 0x334b33e533e133e333dc33da33df006633db33ce33cb33d133b933cf33be33c533c733c033bc33b433c333bf33c133b833b633bb33b533b733a8339533b333aa33a433ad33a933ab33a533a7339a33a133a3339c33983390339f339b339d33943392339733913393338e3387338e336733863366338f3388338b338d33663385338933863384335e33693383337a337633763374337933733375336e336c33713367336d⟩, ⟨0x5a02b81500a4050026812c09004502100fc07803901b00cc05e02d015009c04a022010007403401700a804801e00c0048018008000, 0x344831cf3451344c344a344f3449344b34453447343e226f34412277343f162412de343b2cac2ca934393430299234373432298a3435259e259b342f342a340c342d340a34173429341a34213423341c341229b2341f341b341d341229ad341b34163414341934133415340e340c3411340b340d2f182eba340933d433d2340734023400340533d33401324c2d8b33ff33f6243833f933f232a633f532e233dd33f13350334933eb32e733e933e433e2334833e7⟩]) (
(.branch 2 (
.leaf #[⟨0x5902b014c0a004e025812008a04302000f807803901b00cc05e02d01500a004a02200f807003201600a004401c00b0048018006000, 0x34c234c534c734bc34c134c334c034bd34c334bd34bf34a034a934bb34b034b334b534ac34a534b134ae34ac34a834a634ab34a534a734a134a3349c2e06349f34983460349b348e349534973490348c17c23493348f3491348a17c3348f348c348a34721a8e3489347034793487347c347f348121663477347d34783476347b34721ab2347534713473345e3469346f34683467346b346234603465345f346134463442345d3444344d345b345034533455⟩, ⟨0x5c02c81580a6050026812808e04402080f807803901b00cc06002d01580a004a023010007403601700a004401c00b0040014004000, 0x353413183537352e3531353328e40121352f012028e5352f19f019ed352d2242223f352b352424ae3529352013c83523351606de35193512350b351535073513350c350a350f35062a0435093500350335050f3e34fd350134fc0f3f350134fd34ff34f80e7834fb34f434f234f734f134f3132a132734ef28d2132c34ed34ea2cba2d022a6c243834e91938193534e734e21bdc34e534de34ca34e134da34a234dd34c834d334d934d234d134d534cc34ca34cf34c934cb⟩]) (
.leaf #[⟨0x56029814009a04a024011408404001e80ec07003601980c005c02b014009804802100f006c030016009804001a00b0040014004000, 0x35aa358c35ad359835a335a935a235a135a5359c359a359f3599359b358a358f3597358e35803591358b358d3582358735893583358514c6357b3583357b3581357c357a357f3576356a357935753577356e35713573356c3569356f3568001335633565355c1f5e355f13b813b5355b352628f03559351a2a2635571d9135553544354d3553354c1900354f35483546354b35453547354018f6354313161321353f1cde1cd9353b1cdf3539⟩, ⟨0x5602a014409e04c025011c08804101f80f007203601980c005a02a013809404401f00e006802e015009804001c00b0040014006000, 0x35bd3637362e361736313613362f3620361e3623361d361f361235c03615360e360c361113761373360b34f9360934f00f47360735f80d8c360335fc35ff360135fa0ba935fd35ee35e235f135e035e735ed35e6266035e935e2265435e535e135e335d035d935df35d8266835db35d435d235d735d135d335c835cd35cf35c935cb35c335c735c234fc35c535bb35c135bc35ba35bf181013e435b935b4181f35b7182535b53574357d35b1⟩, ⟨0x54029013c098049023011008203f01e00e406c03301880bc05a02a014009404602000f006c03201600a004401c00b0040018006000, 0x36a536a73688369536a33698369b369d369032a5369936943692369736913693368c368a368f3689368b3660366b3687367e367436813672367b367d36763674367936733675366f3671366e002d366a3668366d002e366936643662366736613663365c1411365f140d365d36583651365b364b3659365236503655364f3651364a34a4364d1a521a4936471a501a693643363e27e83641363c1a1005080505363b3636360d3639⟩]))))) (
(.branch 4 (
.leaf #[⟨0x5702a014409c04c024811808804101f80f007403701a00c405c02b014009004402000e8068030015009004001c00b0048018006000, 0x371e371b3721371a3719371d37143712371737113713370c3702370f37083703370b36e9370936fe2aa9370136ef36ff36ee36ec36f136e736ed36e836e636eb36e2365036e5361635b236e136d22db736df36d836db36dd130236d136d936d436d036be36d736d336d536d00053164012e036cf36ca36c536cd36c136cb36c40fd836c736c036be36c336bb36bf005036bb1676167336b91cc736b736a436af36b536ae36ad36b136a836a636ab⟩, ⟨0x5a02c01540a204f026012408c04402080f807603801b00cc06202e01580a004c023010007403601800b004c02000d0048018006000, 0x3795379737901c2c3793378c37881cc4378f378b378d1cb23785378737801cb83783377c1bd8377f377b377d375e37693779376e377137733764376d376f37683766376b376537673760375c3763375f3761374a3755375b375437533757374e374c3751374b374d374437473749374237393745373e373d3741373b373f373a37381c7037380033364e364b37373732360c3735372e350a3731216a2152214a372d36f62146372b213c04e737293710371f3725⟩, ⟨0x53028813c09804a023811408604001e80e807003501900c005c02b014009404602100f006c03201700a004401c00b0040014006000, 0x380f3811380e009f380a3808380d38073809380237fc38053801380337fd37ff37ea37f537fb37f437f137f737f037ef37f337eb37ed37c837cf37e937de37d937e337d537df37cd37d737d437d237cc34be17d437d337ce37cc37d1009437cd37c937cb361c37c137c337bc2f9d37bf300337bd37b837b6377a378137b53784378937af37961c2837ad37a8366237ab3794379f37a7379e379c37a10034379d37983796379b⟩, ⟨0x55029013c09804a023811008404001f00ec07203601980c405c02b014009404402000e8068030015009004001a00a0040014004000, 0x388220de38853876387b3881387a20e8387d387738792118285f3875386a3869386f386b386d3868009738653867385e386138633860009b385c361d385f37c037c5385937c73857385217bf3855383c384b3851384a3847384d3846384538493840383e3843383d383f3800380b383b383238313835382f3833382e381234bc382a3829382d3827382b3826380e17c23820381b38253819382138183816380638143810381738133815⟩]) (
(.branch 2 (
.leaf #[⟨0x5802b014c09e04d025011c08a04202000f407603801a80c805e02d015009c04602000e806c030016009804001c00b0048018006000, 0x38f3390738fe38f9390338f438f235c638f738d738f538d838d638f138ec38e938ef38c938ed38e434f338e738cf38e538ce38cc38d138c738cd38c838c638cb38c20e7238c50f6038b738c138b838b638bb38b538b738ac38af38b1386438ab38ad1c161c141c0438a938a22d8e38a5389e389a38a1389d389f38961e9138991e973897204e202a389538901473389314a138912860211b388f3883388d38823878388b12d212cf388901801fe33887⟩, ⟨0x5802a814c0a004e025811c08a04302000f807603901a80cc06202e01580a004c023010007403401700a004401c00b0040018006000, 0x397a3978397d397739793972396b3975395f3973396a3965396f3960395e395c3963395b395d395a000f395639543959001039553950394e3953394d394f394839443940394b39473949394339453562393d393f39383564393b39343566393739333935389c38a33931106c1069392d38a6106e392b18bc18b939292376237339271894186f3925390e391d3923391c3919391f39183917391b391239103915390f3911390a38e8390d390638ff3909⟩]) (
.leaf #[⟨0x5c02c815c0a80520278130092046021810007a03a01b80d006202e01580a004802100f807003401700a004401c00c0048018006000, 0x39f6244039f939f339f5283c283939f139e939ef085803cc39ed39e8089e39eb0542054b39e739e0357639e32a4e2a4b39df018c019739dd3560119839db0ebc0e6839d93932393939d7393c394139d139cc39b039cf39c8399a39cb39c4394e39c739ae39b939c33584357a14c839bd39b839b639bb001439b739b239b039b539af39b1399839a739ad39a639a339a939a239a139a5399c399a399f3999399b394c3957399739763989399139883981398d3980397f3983⟩, ⟨0x5702a014409c04c025011c08804202000f407403701a00c805e02b014009804802100f8070032016009804401c00b0040014006000, 0x3a80252a3a833a7c35d23a7f3a52308c3a7b3a593a793a783a583a4a3a6f3a773a6e3a683a713a4f3a6d3a653a693a5a3a653a673a5e3a613a633a5c3a5b3a5f3a4e3a4c3a513a4b3a4d3a4633603a492688266e260a3a453a3a22443a3d01063a333a2d3a313a2c3a2a3a2f3a293a2b3a24327e3a273a2039f43a233a1c2cea3a1f3a1839fe3a1b3a173a193a003a0f3a153a0e3a0b3a113a0a3a093a0d3a043a023a073a013a0339f239f739fd⟩, ⟨0x5e02d81600aa0520280134094047022010407c03a01a80c805e02c01500a004a02200f807403601800a804c02000d0050018006000, 0x3b0c3b0f3b113afc324b3b0d3b003b053b0b3b0432263b073b013b0332c63ae73afb32983aed3af53aec32ca3aef3ae83ae63aeb3a163a1d3ae5284628333ae13ad835ca26203adb262c26262622261e3ad73ac23ac93ad53ac8334e3acb3ac43aba3ac73ac33ac53abd3ac13abc33aa3abf3ab633743ab93aae3aa93ab33aa53aaf3aa33aa73aa43aa200163a9e3a953aa13a913a9f3a943a543a973a90006c3a933a8c30f63a8f30d630cc30a83a8b3a5830be3a893a84389e3a87⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5b02c01540a6051027012c090045021810007a03b01c00d406603001680ac050024010807803601800a804801e00c0048018006000, 0x3a5633ca3b773b723b673b753b633b733b693b6f2f4a2db33b6d3b683b663b6b3b622f5a3b653b5e0adb3b610adf3b5f3b560eda3b593b4e092e3b553b4f3b533b4e092c3b511cda35393b4d3b48343235381ce03b473b423b413b453b3f3b433b3e1d9e0ee00f2e0ee80ee03b3d31902b853b3b3b363b343b393b3031a03b333b2c314c3b2f3b28316a3b2b1236120c3b272b0e2b0b3b252ae62ae33b233a3e22823b213af032263b193a283a373b153afc322c3b13⟩, ⟨0x5802b014c0a004d025812008c04302000f407403701a00c405e02b014809804602000e8068030016009004001a00a0040014004000, 0x3be53be736ba3bdd3bdf2280227d3bdb3bd621f13bd921f73bd73bd23bd03bd53bcf3bd13372336f3bcd3ba63bab3bcb3bb23bbb3bc93bc231103bc53bbe31363bc13bba2c3c3bbd3bb63bb43bb93bb33bb53bae3baa318e3bb13bad3baf3a643ba73ba93b963b9f3ba53b9e3aa63ba13a662b933b9d3b983a6a3b9b3b973b993b942a303b903b8c27f63b933b8f3b91096c09693b8b3b86095b3b8909633b873b78095a3b813b7c096e3b7f3b7a3b78⟩, ⟨0x5802a814c0a004e025812008c04302000f407603801a80c805e02d015009c04802100f807003201700a804801e00c0048018008000, 0x3c6e3c423c713c3f3c6f3c6a3c693c6d3c673c6b3c6631982c403c623c5b3c653c533c633c5a3c553c5f3c523c083b8e3c4e27e93c513b8d3c4f3c263c353c3b3c343c313c373c303c2f3c333c2a3c283c2d3c273c293c203c233c253c1e3c173c213c183c163c1d3c123c103c153c093c113c0c3c083c0f3c003b353c033b313c013b373bfd3b16291e3bfb3bdc3be33bf93bea3bf13bf73bf02e2c3bf33bec3be03bef3beb3bed3be63be22f483be9⟩, ⟨0x5a02b81500a204e026012408c04302000f407603801a80cc06002d015809c04802100f807403401700a004401c00b0048018004000, 0x3c0409603cef38b434f93ced360838b73ceb3ce233f33ce533f73ce33cbe3aed3cdf3cc63afe3cdb3cd624da3cd90f5a34f33cd53cbe32573cd13cca3cc63cc63b023cc93cc23cc03cc53cbf3cc13cac2a2f3cbd27e63c133cb53c0d3cad3c523c103b903ca9334a335d3ca73ca232513ca532573ca3287b3c9d09c809ad3c9b3c4e09993c993c7e3c8d3c933c8c3c893c8f3c883c873c8b3c823c803c853c7f3c813c743c7b3c7d3c763c723c3e3c793c753c77⟩]) (
(.branch 2 (
.leaf #[⟨0x5e02d81600ac054028813c09a04a024011408403f01e00e406c03401880b8056027012808003801900b004c01e00d0040018006000, 0x3d523d4a3d553d4e3d4c3d513d4b3d4d01403d4b3d463b4a3d493d453d473d413d430c4a0c473d3f3b7d3d3d101e10273d3b3d323d353d373d30385d3d3304d22aa93d2f3d2610203d293d223d1b3d253d173d233d1c3d1a3d1f3d16361e3d193d0c3d133d153d0e364420083d113d0d3d0f2014200e200a20023d0b25ea25c017643d0915ba15b73d073d0215bc3d053cf83cff3d013cfa3c9e0a803cfd3cf93cfb0a8a0a820a7e0a783cf728773cf52892288b3cf33554289a3cf1⟩, ⟨0x5a02b81500a204f026012408c04402080f807603801a80cc06002c014809804802100f8070032016009804401c00c0050018006000, 0x264026f3ddf3dd63dce3dd93dd23dcf3dd53dcb3dd33dca38aa3dcd0e300e2d3dc93dc40b693dc70da13dc53dbe3d463dc13c9c3dad3dbd287a3d533db93db00cbc3db33dac3d403daf3dab3dad3da60b683da90a700a6c0a423da53d743d9b3da13d9a3d7e3d9d3d983d783d943d8d3d973d893d953d8c3d703d8f3d883d7c3d8b3d823d853d873d7c3d813d833d7d3d7f3d783d763d7b3d753d773d72143027f627f0097a3d6d3d6809a43d6b3d443d4f3d67⟩]) (
.leaf #[⟨0x5a02c01540a6050026812408c04302000f407403801a80c805e02d015009c04802200f807003201600a004401c00b0040014004000, 0x3e653e673e6038703e633e5f3e612a2c27f93e5d3e58233e3e5b270226ac26a43e573e3c3e473e553e4a3e4d3e4f2c563e453e4b3e463e443e493e403e3e3e433e3d3e3f3e2a3e353e3b3e343e333e373e2e3e2c3e313e2b3e2d3e2435623e273e20213e3e233e1c1c9b3e1f1c9f3e1d3e003e133e1b3e123e0b3e173e0a3e093e0d3e043e023e073e013e03022e023b3dff023e02433df93df43de23df73df002663df33dec02503def3de43de23de73de13de3⟩, ⟨0x5902a814c0a204e025812008a04201f80f007203701a00c405c02b014009804602100f0068030016009804401c00c0048018006000, 0x3ee43ee23ee03ee73edf3ee13ede0065332e32ee3edd332033003edb3ed622523ed93ec23ecb3ed53a363a323ed13a423a2a3ecf3eca221c3ecd3ec63ec43ec93ec33ec53e763e813ec13ea03eb33ebb3eb23eab3eb73eaa3ea93ead3ea43ea23ea73ea13ea33e9c3e953e9f3e893e9d3e943e8f3e993e8a3e883e863e8d3e853e873e84008f3e803e7e3e8300903e7f3e7a3e783e7d3e773e793e7237ec3e753e643e6b3e713e6a37d63e6d3e663e5e3e69⟩, ⟨0x5902b01500a204e026012408c04302000f807603901b00c806002e01580a004a02200f806c030016009804001a00a0040014006000, 0x3f843f713f873e253f853f703f683f733f6c39343f6f3f6a3f683f4c3f5f3f673f5e3f573f633f563f553f593f503f4e3f533f4d3f4f3f483f413f4b3f353f493f403f3b3f453f363f343f323f393f313f333f3000713f2c3e2c3f2f3f283e3e3f2b32c632513f273f20359a3f233f1c37ca3f1f386c385637c43f1b3f1613f13f1913f53f173efa3f0d3f153f0c3f053f113f043f033f073efe3efc3f013efb3efd3ef63eef3ef93ee33ef73eee3ee93ef3⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x57029814409e04d025812008a04201f80f007403701a80c805c02c01500a004c023010007403401800a804c02000c0048018006000, 0x4012400e400a401540114013400d400f4009400b4008013f295e295b40073fe83ffb40033ffa3ff33fff3ff23ff13ff53fec3fea3fef3fe93feb3fe43fdd3fe73fd13fe53fdc3fd73fe13fd23fd03fce3fd53fcd3fcf3fcc01053fc93fcb3fc801033fac3fbf3fc73fbe3fb73fc33fb63fb53fb93fb03fae3fb33fad3faf3fa83fa13fab3f953fa93fa03f9b3fa53f963f9401a03f993daa3d533f933f8c3f8f3f913f8a3f753f8d3f783f743f89⟩, ⟨0x5802b014c0a004d025012008a04302000f407403701a80c805e02c015009c04602100f006c030015009804001c00b0040018006000, 0x17e340b5409840ab40b340aa40a340af40a240a140a5409c409a409f4099409b4092408d4097408b4093408a40884010407e407440814072407b407d407640744079407340754060406b4071406a4069406d406440624067406140634056405d405f40584054400c405b405740594038404b4053404a4043404f404240414045403c403a403f4039403b4032402d4037402b4033402a402840084022401b402740174023401a4019401d401640143d4a⟩]) (
.leaf #[⟨0x5a02b81500a204e025812008c04302000f407403801a80cc06002c015009c04802100f006c03201700a004801e00c0050018006000, 0x4144413e414741400612414341284137413d413641334139413241314135412c412a412f4129412b4110411f4125411e411b4121411a4119411d41144112411741114113410c4105410f40fb410d410440ff410940fa40f23fca40fd40f540f940f4293440f740d640e940f140e840e140ed40e040df40e340da40d840dd40d740d93e7b40d540d030bf40d330c340d140043f7040cf40ca0f6140cd40bf40cb40be35c634fe40c140b838b640bd40b417e140b7⟩, ⟨0x5802b014c0a004d025812408e04502180f407403701a00c405e02c015009c04602000f006c030015009004001a00a0040014004000, 0x41b41c0f1c161c0e41b541b0023041b317a0179d41af41ac2b7141ac307541ac32e141ac3a7941ac248d3a7832e030742b70248c41ad419041a341ab41a2419b41a7419a4199419d41944192419741914193418c4185418f4179418d4184417f4189417a41783670417d417416414177164741754164415441734162416941714168064e416b4164415c416741634165415e4144416141584112415b415641264150412a4153414c4145414f4141414d⟩, ⟨0x270130094048023010808003e01e00e807003601a00c806002c01500a004c024011007803801600a004001c00c005002000c004000, 0x20a02060202020001f801f701f601f401f001ec01ea01e201de01dc01da01d001cf01ce01cc01c801c401c201ba01b701b601b401af01b301b201ae01ad01ac01aa01a801980192018a41b41c17⟩]))) (
(.branch 2 (
.leaf #[⟨0x22010808003e01e00e807003601a00c806002e01600a804c024011008003c01c00d006002c014009004001c00c005002000c002000, 0x2bc02ae02a202a4029a0296028e02860282027a02780270026a026202610260025e025a02560254024c0240023c0234022a02280226021e021a02180216020e020d020c⟩, ⟨0x2b014809c04c023011008003e01e00e807003401900c005c02c0140098048022010007803801a00c00580240100050020008002000, 0x33e033d033c033b033a0338033303370336033203310330032e032a0322031a03190318031603120310030603050304030202fe02fc02ec02e802e402e202d802ce02cb02ca02c802c302c702c602c202c102c002be⟩]) (
.leaf #[⟨0x2e01680b005602a01480a004e023010807c03c01d00d806403001700b0054028012008804001e00e00600240100060018008002000, 0x3b603b203b003a603a203a0039e00060369036f038d03960395039403810392038e03860383038203810380037e037803740372036203610360035e035a03580350034f034e034b034d034c034a0349034803430347034603400344⟩, ⟨0x2d01500a004e022010007c03c01d00e006c03401900c005802a012008803c01c00d006002c014009004001c00c005002000c004000, 0x3ce03d90427042604250424042203af03e9040504110420041f041e041c041804140412040a0408040603fe03fb03fa03f803f303f703f603f203f103f003ee03e403ec03e203e003da03d403ca03c803c603be03bc03aa03b5⟩, ⟨0x26012809004402100e807003601a00c805c02c01500a004c024011008003c01c00d006002c014009004001c00a0040018008002000, 0x4ba04b604b204b104b004ae0443045104ad04aa04a2049c049a0494049304920490048c04880486047c047804760474046c046a0462045e045c044c0444043c043b043a043804340430042e⟩]))))))))))))) (
(.branch 73 (
(.branch 36 (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3a01c80e005e02d01600ac054029014009c04c025012008804001f00d806403001700a804c02401000700300100060020008002000, 0x52a05280006000503c504690473047b0485051505250520051f051e051c05180516050e050c05060502050004f404f304f204d704f004ec0451045704e304ea04cd04e804e404dc04d904d804d704d604d404d104d004cf04ce04cd04cc04b304b504cb04ca04c304c804c504c404c304c204c0⟩, ⟨0x3201880c005e02e01600a804e025011808804202000f807803001700b0054028011008003801a00c00580280100060028010004000, 0x5b005aa05a805a6059e059d059c0597058602f5056d059a059905980597059605940590058e058c00060367057d058305850587057e0576056e0566055e0559055d055c0558055705560554054c0546053c053b053a052b053805340530052d052c052b⟩, ⟨0x28013809804a022010807c03801b00d006403001700b0054028013009004402000f0070034014009003801800a0040018008002000, 0x656064c064a0642063f06410640063e063b063a063506390638063206360630062c06220624061c060c0602060005f805f605f405e805e005db05df05de05da05d905d805d605d405c205c005be05b6⟩, ⟨0x3101780b805a02c01580a804e025011808404001f00f007403001700a004802200e006802c014009004001c00c0040018008002000, 0x6cc06cb06ca06c806c206bc06b6069c06a506b306b206ab06b006ad06ac06ab06aa06a806a606a2000606710679067f0699069a067a068506970696069506940692068d06910690068c068b068a0688068606800676066c066b066a066806640660⟩]) (
(.branch 2 (
.leaf #[⟨0x29013809804a024011808403e01e00d806803001700b0054028012008804001e00e0068030016009004001c00c005002000c004000, 0x74207410740073e073a07380730072f072e072d072c072a0725072907280724072307220720071c0714070a0709070807060702070006f806f606f406ec06eb06ea06e806e406e206da06d806d206d006cd⟩, ⟨0x3b01d00e407002e01600a40500260128090044021010007c03c01c00d006403001700a804c024011008003c01c00d006002c002000, 0x7c407bc07b0000605ef05fd0645074507490765077b078d079f07ac07ab07aa07a707a907a807a6063b07a407a007980797079607940790078e078607850784078307820780077c077407730772072d076e0770076a0766075a07560750074e000605ef062b064506c7070d07130737074507490746⟩]) (
.leaf #[⟨0x2f01680ac0540280130094046021010007c03c01d00e006c02e01500980480220100068030014009004001c00c0040018008002000, 0x830082f082e0823082c082808250824082308220820081f081e081d081c081a08160810080e080c07b4067f07c307d9080a08090808080708060804080007fc07f707fb07fa07f607f507f407f207e007da07d207d107d007ce07ca07c6⟩, ⟨0x3f01e80e406e03601a80cc064030017009c04c025012008c04402100b804c024011008003c01c00d00600280120080018008002000, 0x894089308920889088b08910890088f088e088c0888088708860884038308820825000605ef07490869086d0873087b0880087e087c08740870086e0006000305ef0749085b085f086308650869086d0580036705750587086a08660860085c08560850084a084806ad084608420006067f07b907c3083d083a08380834⟩, ⟨0x2d014009c04a024011808804202000f807803a01b00d005c02c0140098048022010007803801a00c00500240100070028010004000, 0x90c08cf08eb08f70909090a090609050904090208fe08fa08f808f008ee08ec08e408e108e008de08d908dd08dc08d808d708d608d408ca08d208c808c608c008ba08a608b108b208ae08ac08a4081d08a2089a089708960895⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3501a00c405e02c01500a404e025012008c044021010007c03c01d00d806803201800b805802a014009804802200f003000c002000, 0x98e098609830985098409730982097d09810980097f097c097809750974097309720970096a0964095e09520950094e0946094509440942093e093a0938093009280924092209160912089305ec0005074908630869086d08a108ab08b908b408bf09110910090f090e⟩, ⟨0x3501980c405e02d014809c04c025011808404001f00e807003601a00c806002e0150098048022010007803801a00c0018008002000, 0xa0a0a010a080a050a040a030a020a010a000963098509ff09fe097d09fc09fa09f209ef09ee09c109ec09ea09e609e509e409e209de09da09d809ce09c609c309c209c109c009bc09b409ae09a809a0099a00060005092f0937094d0957095d098d0995099609920990⟩, ⟨0x3201880c005e02e01680b00540290130094046022010808003e01a00c005802a014009804802200f006803001600a002800c002000, 0xa8e0a8c0a7a0a740a720a6a0a660a630a620a600a5b0a5f0a5e0a5a0a590a580a560a540a4a0006095709a709bb09f50a400a110a3e0a3d0a3c0a3a0a360a320a300a280a250a240a0f0a220a1c0a180006091d0957095d0a0d0a140a110a100a0f0a0e⟩, ⟨0x3601a00cc064027012008c04201e00e807003601a00c805c02a014009804802000f007003401800b0050024010007003000c004000, 0xafc08070afa0af60006036505ef07490869091509550a690ab30abb0acd0af00aed0aef0aee0aec0aeb0aea0ae50ae90ae80ae20ae60ae00adc0ad80ad70ad60ad50ad40ad20ace0ac60ac50ac40ac20abe0abc0ab40aae0ab00aaa0aa40aa60a960a910a950a940a900a8f⟩]) (
(.branch 2 (
.leaf #[⟨0x2e01680b005602a01480a004e026011008404001f00d806802e01500a004402000e006803001600a004001c00c005002000c004000, 0xb880b800b7a0b740b6c0b640b620b520af20b430b470b4b0b4c0b480b440b000b0b0b210b3f0b400b1c0b270b390b380b370b360b340b2f0b330b320b2e0b2d0b2c0b2a0b280b220b1a0b190b180b160b120b0e0b0c0b040afe0afd⟩, ⟨0x2c01580a80520280138094048023011008404001f00f007403801b00c805c026011008003801a00c0058028012007002800c002000, 0xc2c0c2a0c260c1e0c160c0e0c0d0c0c0c0a0c060c020c000bf80bf00be80be40be20bce0bcb0bcc0bcb0bca0bc10bc50bc90bc80bc70bc60bc00bbf0bbe0bba0bb20bae0ba60b9e0b9d0b9c0b950b9a0b970b960b950b94⟩]) (
.leaf #[⟨0x3001780ac0500260128090046022010807c03a01c00d006002e01600a8050026012008003801800a004802000e006002800c002000, 0xc9e00060bf30c350c970b820b7f0c9b0c9a0b950c980c940c900c8e0c8c0c860c850c840c790c820c7e0c7b0c7a0c790c780c760c6e0c680c660c640c5a0c590c580c510c560c530c520c510c500c4e0c480c420c3c0c320c310c300c2f0c2e⟩, ⟨0x43021010407c03d01d80e807203801a00cc06402e01680ac054029014009c04c025012008c04402100e806c02200f006802c002000, 0xd220d1e0d1a0d150d190d180d140d130d120d100d020cd00b470cf50cf90cfa0cf60ccc0b210cdb0cf10cf20cea0ce90ce80ce60ce20cde0cdc0cd40cc80cc40cbe0cb8062606350639063d063c062f000605fd07370745077b079f0b8f0b910c1d0c3b0cb606430cb20caf0cae0c2f0006062b06c7070d0745078d0b8f0b910c3b0ca30ca4⟩, ⟨0x3901c00d006603201880b805802b015009004201f00d006403001500a0048022010007803801a00c005002000e0060020008002000, 0xd8600060d6f0d730d7b0d840d820d800c360c410d790d780c510d760d7400060c150c5f0c930d650d6d0c100c810d710d700c7900060c750c930d650d6d0d6a0d680d600d5b0d5f0d5e0d5a0d590d580d560d440d3e0d3c0d3a0d320d310d300d2f0d2e0d2c0d2a0d290d280d270d260d24⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x260128090046022010807c03c01d00e006c03401900c005c02c01500a004c024011007803401800a004802000c0040018008002000, 0xdf80df60df20df00de80de40de30de20de00ddc0dd80dd60dce0dca0dc60dc20dc00dbc0db40dac0da80da60da50da40d9d0da20d9e0d9d0d9c0d9a0d980d970d960d950d940d920d8e0d88⟩, ⟨0x290140098048023010807c03c01d00e006c03401900c005802a0140098048022010007803401800b0050024010006002000c004000, 0xe900e8a0e890e880e870e860e840e830e820e810e800e7e0e700e6e0e620e5a0e560e480e470e460e440e400e3e0e360e2e0e2a0e200e1f0e1e0e1c0e180e140e120e0a0e090e080d950e060e020dfa0df9⟩, ⟨0x2c01580a40500270130094048023011008404001f00f007003601800b8054028013009003c01c00c0058028012007002000c002000, 0xf1a0f120f110f100f0e0f0a0f060f040efc0ef80ef00eec0eea0ede0ed60ed30ed20ed00ecb0ecf0ece0eca0ec90ec80ec60ec40eba0eb50eb90eb80eb40eb30eb20eb00ea20e9c0e9b0e9a0e970e990e980e960aeb0e94⟩, ⟨0x3601a80d006603201880c005e02e01680b0056029013809404601f00e806c03401900c005c02a013009001c00c0050018008002000, 0xf920f900f8c0f880f860f7c0f780f720f6e0f6c0f640f5e0f550f5c0f590f580f570f560f550f540f4f0f510f530f520e810f4e0f4d0f4c0f480f420f3c0f340f330f320f310f30000608cf08eb098d09950a2f0ab30ee50efb0f270f2b0f2c0f280f240f230f220f200f1c⟩]) (
(.branch 2 (
.leaf #[⟨0x3201880c005e02e01680ac054029014009c04a023010808003801a00c8050024011008003c01c00c0050024010007002800c004000, 0x1004100210000ff60ff20fea0fe90fe80fe60fe20fe00fd40e870fd20fd10fd00f310fce0fca0e7b0ee50f3b0fc80f330fc400060e7b0f630f670fa90fc20fc10fc00fbe0fba0fb80fb00fad0fac0f970faa0fa40fa00f9c0f990f980f970f960f940f93⟩, ⟨0x3401980c806202e015009c04a023010808003e01d00d806803201800b805802a014009804801c00b004802000e0050018008002000, 0x108c108a1082103e105b10650006103f105710671052104f10791078105d107610731072105d1070106a1062105f105e105d105c10581050104a1048104610361034103200060ffb10151023101e1027102b102a101710281024101c10191018101710161012100a⟩]) (
.leaf #[⟨0x28013809804a024011808804202000f807403601900b805802a014009804802000f007003401600a004802000c0040018008002000, 0x11141110110c110a110210fa10f610ee10e610e210e110e010d910de10db10da10d910d810d610d210ce10c610bc10bb10ba10b810b410ae10ad10ac10aa10a610a0109f109e109d109c109a1096108e⟩, ⟨0x23011008404001f00f007403601a00c806002e01600a8050026012008003c01c00d006002c014009004001c00c005002000c002000, 0x119e119c11961190118e118c1180117f117e117c117811741172116a116611641162115a1159115811561152114e114c1144113c113811301128112411221120111811171116⟩, ⟨0x25011808804202000f807803a01c00d806803201800b805802a014009804802200f007003401800b004802000e0060028010004000, 0x121e121d121c121a1218120a1208120611fe11fa11f611f211ee11ec11ea11e011dc11da11d811d011cc11cb11ca11c811c411c011ba11b911b811b611b211ae11ac11a411a111a0119f⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3901b80d806803301880b805a02b014009c04c025011008403e01e00e8070036011007803401800b00500240100070028010002000, 0x1286124d12841280127f127e127c127b127a127712791278127612751274126f12731272126c1270126a1265126912681264126312621260125a1256105a10111031108510c510e512111233123712451250124f124e124d124c124a1246123c123a1234122a122712261224121f12231222⟩, ⟨0x2e01680b0056029014009c04c025011808404001f00f007003401900c005c02a013008803c01c00d006002c0140090040018008000, 0x12fe12fc12fa12f212f112f012ee12ea12e812dc12d912d8033b12d612d012cc12ca12c912c8109d12c612c212c012ba12b912b812b112b612b312b212b112b012ac12ae12a812a212a41290128c1289128a12891288128112831287⟩, ⟨0x49023811008404001f80f807803a01c80e006e03601a80d006002f01700b40540280130090046022010808003e01e00e0068032000, 0x1386136d1368134d137f138413811380136b137c13741370136d136c136b136a1366135e1358135613540006131b1333133f13481346134413161321133d133c1335133a1337133613351334133013281322131c1314130c13091308130713060006028d02fb03650b8b0b8f0b910dab0e350e3d0e4b0e4d0e4f0e510e550fd70fd90fdf103912df12e112e712f913011303⟩, ⟨0x43021010007e03e01e80f0074038012008c04402100e807003001600a004c024010007003401800b005002400e0060028010006000, 0x1408140414031402140013f613f213ec13e913e8130713e6028d02fb03650b8b0b8f0b910dab0e3d0e4b0e4f0e510e550fd70fdf103912df12e113dd13e513e213e013de000613a113a313d513d60006139f13a513ab13d213d113d013bf13ce13ca13c413c113c013bf13be13bc13b613b213b0139c0fd5139613921390138e134c1369137b⟩]) (
(.branch 2 (
.leaf #[⟨0x2b014809c04c025012008c044021010007c03c01d00e006c03401900b8054028010007003001600a004802000e0060028010006000, 0x149c14991498149714961494148e1488148614841476146e146c1466145e145814541450144a14471446143d14440006141f142b14311440143f143e143d143c143a1436143214261424141a1414140e140a14051409⟩, ⟨0x270130094048023011008404001f00e807003601a00c806002c01500a004c024011008003c01c00c00580280120080030010006000, 0x15161512150e150c1504150014fe14fc14f414f314f214f014ec14e814e614de14dd14dc14da14d614d214d014c414c214c014b814b714b614b414b014ae14a614a514a4149714a2149e147b147f⟩]) (
.leaf #[⟨0x3801b80d806803201880c005e02e01680b005602a01480a004c024011008003801a00c805c02c01500a004c024011002000c002000, 0x159c15941590158d158c158b158a15881582157e157c157a1572156c15661562155e155b155a1559155815531554155315521549154d15511550154f154e1548154715461544153e1538153015280006039d03a504ad0de714bf14c914cf14e514fb1503150b151d151e151a15191518⟩, ⟨0x46022811008604101f80f807a03801b00d0066029013809804a024011808804001e00e807003600e005002000c0040018008002000, 0x15fe15fa15f615f215ef15ee15df15ec15e8000603b915211525153715e415e115e015df15de15dc0003039d03a503a903c5042d1525153715cb15da15d915d815d615d215ce15cc15c415c115c0154f15be15b815b20006000503c5044b0473047b04850515152515611565156b159b052415251561158715ae04d915ac158b15aa15a915a815a615a2159e⟩, ⟨0x3501a00cc06403101700b4056028013809804a024011808403e01e00e807003601a00b8054028013009004402000f0068030002000, 0x166e166c166a16601658165516571656165416531652164d16511650164a164e16481644163e163d163c163b163a16361634162e1628130e0e29162116201307161e161a16161614160e160a160615e116040006039d03a503b903e9040505330de7150b151d16031600⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x2c01580a8052028013809804a024011808804001e00e806803001600a8050026012008804001e00d005802800e0050018008002000, 0x16fc16fa16f416ee16ec16ea16da16d216d016ce16c616c516c416b716c216be169d16a116bc16b916b816b716b616b416b016aa16a816a616981690168f168e1681168c16881665167f16861683168216811680167c1674⟩, ⟨0x5502a014c08403001600a80500270130090044021010007c03c01d00e006803001600a004c02401100800300140080038010004000, 0x1766176a172a0de71413145d147914ad1523160d161916271643167b169b16cd16d9170f174714680de71413145d147914ad1523160d161916271643167b169b16cd16d9170f171f174700061733174b1759176217611760174d175e175a1752174f174e174d174c17481742173c173a1738172e172d172c1723172817251724172317221720171a1716000616dd16e31705170c170b170a16fd1708170416df16e5170216ff16fe16fd⟩, ⟨0x3201880c005e02e01680b0050027013009404602100f807803a01c00d806803001500a004802200f00680300140070030010002000, 0x17dc17de17d817d017d217ca0006179117a917b317bc17ba17b817b017af17ae17ab17ac17ab17aa17a6179e17981792178a178917881785178717861784176f1782177e177d177c177b177a1778177517741771177317721770176f176e1769176d176c⟩, ⟨0x2d01580a4050027013009404802000f807803a01c00d806403001700a804c024011008003c01c00d0050024010007002000c002000, 0x1862185f185e185d185c185a1856184e18460006107b1085109518421840183e1834182c1828181718261822181c18191818181718161814180e1808180618041610161917f917f617f417f217ea17e717e917e817e6165317e4⟩]) (
(.branch 2 (
.leaf #[⟨0x3001700b405802b01500a004c025011008003e01e00e807003601a00c805c02c012008003801a00c00580280120080038014006000, 0x18e618e518e418e218dc18d618ce18cd18cc18c318ca18c618a718ab18c418c318c218c018ba18b418b218b018a2189a188f18980006187318811887189218911890188f188e188c1888187c187a18781870186818671866185d186418371853⟩, ⟨0x2e01580a404e0260128090046022010808003e01e00e807003401700b0050026012008003801a00c00580280120070028010002000, 0x1968194d195f19661963196219611960195c1956195219501946193e19361930192e192c1920191d191c1919191b191a1918034919161910190c190b190a190919081906190418fe18f818f218f118f018ef18ee18ec18e718eb18ea⟩]) (
.leaf #[⟨0x3101800bc05c02d01600a8050027011808003c01d00e006c03401900a8050026012008003801800a004802000e006002800c002000, 0x19e419e019d819d219d019c819c519c419b719c2000619a719b319bd0288028519b919b819b719b619b419b019ae19ac00061977198d199b19a419a219a0199819971996198f199419911990198f198e198a1984197e19781970196f196e1961196c⟩, ⟨0x3a01c80e006e03601a80d006403101800bc05c02c01500a4050026012008c04402000f007402601000600280100060028010004000, 0x1a5c1a581a4e1a4a1a421a3e1a3c1a3b1a3a1a381a341a321a2a1a291a28163b1a261a221a1a1a191a181a051a161a121a0a1a071a061a051a041a02028d06c7070d0745138d195b198919bb19df19cc19e319f5000619cd19df19f91a0019e719fe19fb19fa19e519f619ee19ea19e719e619e5⟩, ⟨0x270130094048023011008403e01e00e807003601a00c805c028013009004402000f007003401800a004802000e006002800c002000, 0x1aee1ae61ae21ae01ade1ad61ad01acf1ace1aca1ac21abe1ab61ab01aaa1a611aa81a971a9b1aa61aa41aa21aa01a921a8a1a881a861a7e1a7d1a7c1a7a1a761a741a6c1a661a631a621a611a60⟩]))))) (
(.branch 4 (
.leaf #[⟨0x2e01680b005602a01480a004e025012008c044021010007803a01c00d8068030016006802c014009004001c00c0040018008002000, 0x1b621b601b5c1b5a1b521b4e1b481b441b431b421b401b3c1b3a1b321b2c1b2b1b2a1b281b241b221b181b151b141acf000603e904051acd1ad51add1ae51aed1b031b121b111b101b0e1b0a1b061b041afc1afb1afa1af81af41af0⟩, ⟨0x2f012008c04402100f807803a01c00d806803201800b8054028013009004402000f0070034016009004001c00c005002000c004000, 0x6161d16651813182b1bc31bc51bcb1bd91bdf1be71be41be21be01bd61bd51bd41bd21bce1bcc1bc01bbe1bb81bb41bb01baf1bae1bac1ba81ba41ba21b9a1b981b961b8e1b8b1b8a1b891b881b861b821b7c1b7a1b781b6e1b641b63⟩, ⟨0x26012808c044021010007c03c01c00d806803201800b8054028013009004402000f007003401800b005001c00c0040018008002000, 0x1c801c7c1c7b1c7a1c781c6a1c621c5c1c541c531c521c501c4c1c481c461c3e1c3d1c3c1c3a1c361c321c301c241c1c1c1e1c121c081c0a1c021bfd1c011c001bfc1bfb1bfa1bf81bf41bec⟩, ⟨0x2b01500a40500270130094048023011008404001f00f007403401900b8050026012008804001e00d00580280100060028010006000, 0x1d021cfa1cf61cf01ce81cdc1cd61cd21cce1ccc1cca1cc21cbe1cbc1cb01cad1caf1cae1cac1cab1caa1ca51ca91ca81ca21ca61ca01c9c1c981c971c961c951c941c901c8f1c8e1c8d1c8c1c8a1c861c821c7d1c81⟩]) (
(.branch 2 (
.leaf #[⟨0x3d01e00ec07403901b80d406803201800b805a022010808003e01e008803c01c00d006002c014008003801800a0040018008002000, 0x1d6c1d681d661d5e1d5a1d591d581d571d561d540a251d521d4f1d4e1d4d1d4c000609090b5d1ab51d011d091d3b1d3d1d411d451d491d4a1d461d421d3e00060937094d098d09950a171a851cf91d011d091d111d271d391d361d351d341d321d2e1d2a1d281d201d1f1d1e1d1c1d181d141d121d0a1d061d04⟩, ⟨0x3801b80d806a03401980c806203000e807003601900c005c02c015009004401e00e0068030016009004001c00c0050020008002000, 0x1e0a1e061e021dfc1df61df21dea1de41dda01c101d901e102b3039d03a5094d09bb0f7b0f9f150b151d16031a5b1dd11dd51dd71dd91dd21dce1dca109f1dc61dc21dba1db61db21dad1db11db01dac1dab1daa1da81d981d921d8a1d891d881d861d821d7e1d7c1d741d731d721d70⟩]) (
.leaf #[⟨0x2c01500a4050027013009404001f00f007403601a00c806002e01600a8050024010007803401600a004001c00c005002000c002000, 0x1e9c1e9b1e9a1e981e941e8e1e8a00061e4f1e7b1e7f1e831e7c1e741e6e1e661e651e641e621e5e1e5c1e541e521e481e3c1e391e381e271e341e2c1e291e281e271e261e241e231e221e201e1c1e181e161e0e1e0d1e0c⟩, ⟨0x2f01700b405802a0138098048023011008404001e00e006c03401900c005c02c014009003801800a004001c00c0050020008002000, 0x1f1a1f141f0e1f0a1e391f081f031f071f061f021f011f001efe1ef21eee1ee81ee51ee41ee31ee21ee01eda1ed61ed41ed21ec81ec51ec61ec51ec41ea91ead1ec31ec21ebb1ec01ebd1ebc1ebb1eba1eb81eb41eae1ea81ea71ea61ea4⟩, ⟨0x3501980b00540280138094046022010807c03c01d00e006c03201800b805802a014009804801a00b004802000e006002800c002000, 0x1f8012b31e8410ed120512bd1e831e931f4b1f7e1f7d1f7c1f7b1f7a1f781f771f761e9b1f741f701f6c1f6b1f6a1f681f641f621f5a1f591f581f561f521f4e1f4c1f441f4000061e831ea31ecb1edf1f3c1f391f381f371f361f301f341f2c1f281f251f241f231f22⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x4b0250124090047023011408804202000fc07c03d01e00bc05a02a014809c04c010007803801800b004001c00a0040018008002000, 0x1ffc1ffa1ff61ff21ff01fe81fe41fe01fdd1fdc1fdb1fda1fd81fd01fc6000601c101d901e1039d03a5094d0f7b11f9150b151d1fc11fc31fbe1fbd1fbc1fb91fbb1fba1fb812751fb61fb201c101d901e102b3039d03a5094d09bb0f7b0f9f10bf123312c5150b151d16031dc51dd11dd51e811f851fb01fae1fa81fa51fa41fa21f9d1fa11fa01f9c1f9b1f9a1f981f961f8a1f88⟩, ⟨0x3101800b80580280128090044021010007c03a01c00d806402e01600a804c022010007803801a00c005802000e005002000c004000, 0x208c207e207b207a207920780b372065206920762071207520742070206f206e206c206a20640b272062205c205620532052203f2050204c204420412040203f203e203c20382034202420262020201b201f201e201a20192018201620061ffe1ffd⟩, ⟨0x3601a80d006603101800a80500260128090046021010007c03c01d00e006c02000f007003401800b0050024010007002000c002000, 0x2108210220fa20f420f120f001841fef2005202b20c920df20ee20ed20ec20eb20ea20e620e020d820d720d620d420d020cc20ca20c200060473047b048509090b5d15651d3d1d4120bd20bf20c020b820b620b420ac20a620a2209e209a20962091209520942090208f208e⟩, ⟨0x3c01d80e807203801b80d803e01d00e006403001600a8050026012008804001e00e006803001600a004802000e0050018008002000, 0x21842182217a21782172216e0006039d03a5044b0473047b048514cf14e514fb1503150b151d156516031ab51d011d091d111d271d3921512169216421612160215e2159215d215c2158215721562154214e214821442140213821362134212a212421222120211e2116211221112110210f210e210c210a⟩]) (
(.branch 2 (
.leaf #[⟨0x52028814009e04e026813009604a024010408003e01e00e807003701b00d406602f01700b405602a01480480220050018008002000, 0x21e821e421e221da21d821d621cc21c421c210190006044b0ffb103120b320bb213b21c021be21bd21bc21b521ba21b721b621b521b421b221ae21a82053211c1fef204b21a721a4219e219c219b219a2198000601e901ff0215021d0225039d03a5042d04430473047b08cf08eb0dcd0dd5159316091b692175218121932195219604ac039d03a503c5042d111f1127123312bd16091ba11bbd2190218f218e218c2188⟩, ⟨0x3001780ac0520270130094046021010007c03c01d00e006803001700b0054028013008803801a00b004001c00c005002000c002000, 0x22660006222f22352255225e225d225c2249225a2256224e224b224a2249224822462240223c223a2228222722262225222422222220221a2214220c220b220a22072209220822062205220421ff2203220221fc220021f821f421ec21eb21ea⟩]) (
.leaf #[⟨0x2b01500a404e026012809004602100f807803601900c005c02c01500a004c02400e0068030016009003801800a0040018008002000, 0x22f422ea22e222e122e022de22da22d822d022cf22ce22c522cc22c822a922ad22c622c522c422c222bc22b622b422b222a40006227122892293229c229a22982290228d228c228b228a2286227e22782272226a2268⟩, ⟨0x3e01e80f007603a01c80d806a03301900c406002f00f007003401700a804c024011008003c01a00b005001c00a0040018008002000, 0x237a237423702368235c2358235323572356235223512350234e23462340233609550a690ab319bb19f521e121f32213222b222d2265226d228522a722d72305233a23392338232f233621cf232d233423312330232f232e232a2322231e231623152314230b2312230e22ef2309230c230b230a230622fe22f822f6⟩, ⟨0x6c03581a80d205e02e81700b605a02c015c0ac05502a014c06803201800b0054029013809804a0230068024010007002800c002000, 0x23e823e623e20006103110e51233147f16dd1a951dc11e811f8523dd23da23d823d223cc23c6191d23c423bc23ba23b623ae000601e901ff0215021d0225028d02fb0365039d03a5042d04430b8b0b8f0b910dab0e510e550fd70fdf1039152f15cb16091a411a6b1aad1b692193219523ac23a923aa23a923a81549235b23a723a623a523a423a215ad239e2396239016ff0006028d02fb03650b8b0b8f0b910dab0e4f0e510e550fd70fdf103911f9160d18d51a211a31235f238d238f0006236123672385238a2388238223812380237d237e237d237c⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x5d02d81640b005702b01540a805302901440a004f02000f807a03c01d80e807203801b80a003a01c00a00280120080030010004000, 0x245c245b245a24592458245624502452244c244424462432242e242c242002fb03650b8b0b8f0b910dab0e5511f9238d238f23fd24052411241f241c241b241a241824142412240a240623fe00060215021d14c714fb150315f515f915fd1b4d1b511b591b671b6b1b6d0006085f08650bd914c714fb150315f515f915fd23f723fa0bda0b5d0b730b8b0b8f0b910b930bb90006000508ab08b90bb90bf50bf70def0e010e1123f823f423f023ef23ee23e923ec23eb23ea23e9⟩, ⟨0x500270130092048023010c08404102000fc07c03a01b80d406603101800bc05a02b01500a405002701300940200040018008002000, 0x24c6245924c424c124c024bd24bf24be24bc24bb24ba24b524b924b824b224b624b024ac000624752479249f248a248724a924a8249124a624a324a2249124a0249a24962493249224912490248e248824822480247e000602fb036509090937098d09950a0d0b5d0b8b0b8f0b910dab0e551cf91d3d1d4123fd245f24632465000602fb03650b8b0b8f0b910dab0e5523fd245f2469246d246e246a24662460⟩]) (
.leaf #[⟨0x3001700b005602a01480a004e025011808803e01d00e006c03401900c005c02c013008803c01c00c004802000c005002000c004000, 0x254c25492548254725462542253a2534252e252625252524251b2522251e24fd2503251c251b251a25182512250c250a250824f82384235f24f124ee24ed24ec24eb24ea24e824e724e624e324e524e424e224bb24e024dc24d624d024c824c7⟩, ⟨0x3501980c406002f01680ac050026011808404001f00f007003401900c005c02c015009804001e00d006002c00e0060028010004000, 0x25be25bd25bc18ef25ba25b625ae25ad25ac19b72596258d25a325aa2591258c259725a725a8258f25a4259c2598259425912590258f258e258a2582257e257c2570256f256e256b256d256c256a2205256825640006252d25452553255c255a25582550254f254e2547⟩, ⟨0x5602a81500a6050027813409804b025012409004702300d004202000f807803a01c00d806803201700b004c024010007803801a000, 0x26462644263c2638263326372636263226312630262e2618261a26122606260815b0044b0473047b0485051509090b5d103114791565156b159b16dd170f1a951d3d1d412600039d03a5042d044310311479152f15cb160916dd170f1a951add1ae51aed1b0325f725ff25fc25fa25f825f025ee25ec25e625e425e225df25de25dc25d725db25da25d625d525d425d225d000060de710111031104114791523160d162716d9170f1a3125b5⟩]))) (
(.branch 2 (
.leaf #[⟨0x25012008c044021010007803a01c00d806803201800b0050026012008804001e00d006002c014009004001c00c0050018008002000, 0x26d626d426d026cc26ca26c226c126c026be26ba26b826b026ae26a226a126a0269f269e269c269a2696268e2686268526842682267e267c267226702666265e265226512650264e264a⟩, ⟨0x3c01d80e807203801b80d806803201880bc05a02c00f807803a01c00d8068032018006803001600a004801c00c005002000c004000, 0x275827542750274e2746273e273227312730272f272e272c272b272a272927280006091d098d09950a2f0ab30f2b1bb326f726ff27152721272527262722271e271c271a27102708000608cf08eb1b9526a926b726c926db26e126f726ff270026fc26fa26f826f026ef26ee26ec26e826e426e226d826d7⟩]) (
.leaf #[⟨0x3101800b805802b01500a4050027012809004202000f007403801b00d006002e014009804402000f0070034012008003800c002000, 0x27c227bc27bb27ba27b927b827b627b227b027ae27a627a527a427a2279d27a127a0279c279b279a279827942792278a278727862784277f27832782277e277d277c277a2778276e273627612765276927662762273a2745274d275f275c275b275a⟩, ⟨0x5802b81580a8052028814009e04e026012008c04501980b803601800a804c024011008003c01c00c005002400c0050018008002000, 0x28282822281e281b281a2819281828162810280c28082807280609ff27f92805280428032802139802fb036509090937095d098d09950a0d0a690b5d0b8b0b8f0b910dab1cf91d3d1d4109580963097f098509ff000601c101d901e102fb036503af03d309a709bb0a510b8b0b8f0b910bd10dab0e550f7b1b392800098527ff27fe097d27fd27fc099f27fa27f427f227ea27e227e027df27de27dd27dc27da27d527d927d827d427d327d227d027c8⟩, ⟨0x45022010c08404001f80f807a03c01b00d006403101780b805a02700c005c02c01500a004c02200f0068030016008003000c002000, 0x288c288828842880287f287e287c287828701ce41cef1d5d1d651d7b1d91286c286b286a28692868286621492864286201861fef2005202d20c920df212c044b0473047b048509090b5d0ff110111031105715651d3d1d41213b285c285a285628522850284c28492848210f284428232842283a2836282328352834282728302823282f282e282b282c⟩]))))))))))) (
(.branch 37 (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x2b01500a404e025012008804001f00f007403801b00d006402e01600a8050026012008804001600a004802000e0050018008002000, 0x2914291229042901290028f328fe28f828f528f428f328f228ee28ea28e228e028de28d628d028cf28ce28cc28c828c628ba28b628b20006132f136513a328a728b028ae28ac28a428a2289f289e2869289c28982890⟩, ⟨0x3101780b805a02c01580a80520280138094046022010808002e01600a0048022010007803401600a004802000c0040018008002000, 0x29a0299f299e299c299a298e2986298429822978296c2969296827dd2964295c2958000600031109111f11271bb326892921295529562952294f294e2729294c29482944293e293b293a2939293829362932292e292d292c269f292a292629222918⟩, ⟨0x3e01e80c806203001780b805a02000f007403801b00d006403001700b0054028013009004001e00e006803001600a0038014006000, 0x2a20000606d506e1074508cf08eb098d09950a2f0f2b2a1b2a1c2a142a0e2a0c2a0a0006022506f30937098d09951cf91d011d091d111d2720a92a0329fc29fb29fa29f829f429f029ee29e629e229e029de29d429d229d029c829c729c629c429c029bc29ba29b029aa283729a129a829a529a429a329a2283129a1⟩, ⟨0x6703281900c4061028011c07203801b00d006603201880c005c02d01600ac054029014009c04c01700b00540280050018008002000, 0x2a922a912a902a8e2a7d2a8a000601d901e1039d03a5042d064706ff074509d709e911e916091fc92a292a5d2a6d00060003039d03a5042d11e928412a5d2a6d000601c101d901e106f30f7b111f112712331bbd1e4f1e5b2a712a852a862a822a7f2a7e2a7d2a7c2a7a2a782a762a682a672a662a642a602a5e2a562a522a4c2a48000601d901e109d109d709e90ab30f670fb729dd29e529ff2a372a3b2a3f2a402a3c2a38000601c101d901e1094d09bb0f7b0f9f14fb150315f515fd1a851dd121672a3428072a322a2a2a24⟩]) (
(.branch 2 (
.leaf #[⟨0x9d04e026813009704b025412809304701c40c406002f81700b205702a814c09404901700b405801a00c803800e005002000c004000, 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⟩, ⟨0x4a024812008e046022811008404102000fc06803201800b805a02000b8054026012007803401800b0050024010007003000c002000, 0x2b5c2b542b502b4e2b4c2b442b402b3f2b3e2b3c2b38000608ab08b90bdd0def11ab11d711df11e311f911fd2b320d9f2b300c7b2b2e1d4f2b2c0006039d03a503c5042d04f7111f1127160917f11ba11bbd2b270006000311011109111f1127112f120523c32b242b232b222b192b202b1c2afd2b172b1a2b192b182b142b0c2b062b042b022af82ad82ac52aef2af02adb2aec⟩]) (
.leaf #[⟨0x37014809c04c023011008003e01e00e807003401900b0054026012008804001e00e0068030016009004001c00c0050018008002000, 0x603af03d31add1ae51b3127ad27b528552bad2bc32bc52bc72bcd2be22be12be02bde2bd92bdd2bdc2bd82bd72bd62bd42bd02bce2bc02bbd2bbc2bba2bb52bb92bb82bb42bb32bb22bb02bae2ba42b9e2b962b8c2b8e2b822b812b802b7e2b7a2b782b662b652b642b622b5e⟩, ⟨0x3801b80d806a03401900c005e02d01580a8052028013809804402100e807003601900b0050024010006001800a0040018008002000, 0x2c522c502c482c462c3a2c392c382c372c362c342c332c322c312c302c2e2c2c2c282c222c1c0b5d1d412be72c1a2c160bd11b392be72c142c122c0e2c052c0c2be52bf12c0a2c092c082c072c062c052c04088908a52c01000600030749085f08652be52c022bfe2bfa2bf82bf62bee⟩, ⟨0x3a01b00c805e02d01600a8052028013809404601600a8050026011008003c01c00d006002c014009004001800a0040018008002000, 0x2ca6236725a32cb10006297b2cb52cbb296e29772cbf2cbe2cb72cbc2cb82cb72cb62cb22caa2ca419c52ca22a9300060745098d09950a2f0f2b2a012c732c7b2c952c972c9b2c9f2ca02c9c2c982c922c912c902c8e2c8a2c862c842c7c2c782c762c742c6c2c6b2c6a2c682c642c602c5e2c54⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3501a00cc06403101800b405802a01480a004e0260120088042014009804801e00e006002c014009004001800a0040018008002000, 0x2d522d4a2d482d402d3c2d382d332d372d362d322d312d302d2e2d202d182d0c2d0b2d0a2d092d08000601d901e1039d03a5042d074509d709e911e916091fc52a6f2d062d042cfe2cf92cfd2cfc2cf82cf72cf62cf42ce82ce22cda2cd92cd82cd62cd22cce2ccc2cc4⟩, ⟨0x25011808804202000f807803a01c00d806803201800b805802a014009804402000f007003401800a004001c00c0050018008002000, 0x2dd82dd72dd62dd42dd22dc82dc22dba2db02dac2dae2da62d9a2d9c2d942d922d8c2d882d822d812d802d7e2d7a2d762d742d6c2d6b2d6a2d692d682d662d622d5c2d5b2d5a2d582d54⟩, ⟨0x3901c00dc06c03401980c806203001700b0056029013809804a0240118088028012008803801a00b00500240100070028010002000, 0x2e4a2e442e422e3c1ad12e3a2e382e322e2a2e202e1f2e1e2e1d2e1c2e1a2e192e182e172e162e142e122e0e2e08000603af03d31109111f112727ad27b52b2b2bc52bc72dd12de72ded2e022e012e002dfe2df92dfd2dfc2df82df72df62df42df02dee2de42de12de02dde2dd92ddd2ddc⟩, ⟨0x26012008c04201f00f007403801b00d006403001700b0054028013009004001e00e0068030016009004001c00c0050020008002000, 0x2ec62ec52ec42ec22ebf2ebe2ebd2ebc2eb82eb22eb02eae2ea22ea02e9c2e962e8e2e8a2e882e862e7e2e7d2e7c2e7a2e762e722e702e682e672e662e642e602e5c2e5a2e522e512e502e4e⟩]) (
(.branch 2 (
.leaf #[⟨0x3401980c806202f01680b005602a01480a004e025012008c044021010007c02200f007003401800b004801c00c005002000c004000, 0x2f3e2f3a2f382f302f2f2f2e2f2d2f2c2f2a2f262f242f202f1c2f122f112f102f0e2f0a2f082f002efc00061a851b471d011d091d272e592e6f2e852e8d2ea72ee52eeb2ef92ef62ef52ef42ef22eee2eec2ee22ee12ee02edf2ede2edc2eda2ed62ed02ec82ec7⟩, ⟨0x260128090046022010808003e01e00e807003601a00c806002c0140098048022010007803801a00c004802000c0050020008002000, 0x2fc62fc42fbc2fb82fb62fb42fb22fa82fa02f982f942f902f8c2f8a2f8825492f862f852f842f822f7e2f7a2f782f702f6e2f6a2f662f612f652f642f602f5f2f5e2f5c2f462f452f442f42⟩]) (
.leaf #[⟨0x3701480a004e026012809004402000e006803201800b805802a014009804402000e006002c014009004001c00c0050018008002000, 0x6114b116111691a851d011d091d111d271d3928552b433031303b303e303c3036302e302c3022251d3020301f301e2ffd3003301d301c301b301a301830163012300e300830042ffc2ffb2ffa2ff82ff72ff62ff52ff42ff22fea2fe82fe62fde2fda2fd22fd12fd02fce2fca⟩, ⟨0x3a01c00d806a03401800bc0560290140098048023011008404001e00e807003601a00c806002e009003801800a0040018008002000, 0x30b8230d30b6177b30b430b02658263b2643276130ae000621d12329233730ac22c730a430a0309f309e309d309c309a3098309230883087308630843080307e30703072306c000601d901e109d709e909f50ab31add1ae51b3128552bc330473057306230613060305e305a30583050304e304c⟩, ⟨0x2b01500a40500270130094048022010007c03c01c00d006403001500a004c024010007003401800b005002400e005002000c004000, 0x312e312c312a31283120311e3118310c310b310a309d3108310430fe30fd30fc30a530fa30f230ee30e930ed30ec30e630ea30e430e130e030df30de30dc30da30d830d230ca30c930c830c730c630c430c030ba2331⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x2a014809804a023011008403e01e00e807003601a00c805c02c01500a004802000f007003401800b005002400e0060028010004000, 0x31b031ac31a731ab31aa31a631a531a431a2318c318b318a318831843180317e31763174317331723170316c31663165316431633162315e315a31583152314831463140313f313e313c3138313231313130312f⟩, ⟨0x3b01d00e407003601a00c804c025012008c04402100f807403801a00c806002e00d006002c014009003801800a0040018008002000, 0x322a32223220321c321b321a2d6932181fdd000609090b5d11cf11d711df11e91d3d1d41280b2d5f3215321632123210320c320431fc31f931f82d0931f631f02d0b31ec31e831e431ce03af03d30bd11b3929dd29e52a372a3f2ff131e031dc31d831d631cc31cb31ca31c831c431c031be31b631b4⟩, ⟨0x2b01500a40500270130090046022010808003e01e00d006402e01500a004c024010007803801a00c005002400c0050018008002000, 0x32b832b432b032ae32a2329e329d329c329632943292328a32820006222d32773279327a32743273327232713270326e326a326232613260325c325832543248324532443242323d32413240323c323b323a32383236⟩, ⟨0x3301880bc05a02a0138094046021010007403801a00c806002e01600a8050026012008003801800b0050024010006002000c002000, 0x332a33293328331933263325332420c3332333222069331f331e3305331c331b331a3319331833163311331533143310330f330e330c330632fe32f832f232e832de32da281b32d832d732d62cb732d432d032ce32c832c432c332c232c132c032bc32bb32ba⟩]) (
(.branch 2 (
.leaf #[⟨0x2c01580a80500260128090046022010808003801b00d006002c0140098048022010007803801a00c00500240100070030014006000, 0x33c233ba33b233b133b033af33ae33ac33a233a0339e339600063363337b3387338c338a338233813380337d337e337d337c33783370336a33643358335a33523346334533443342333e333a33383330332d332c3327332b⟩, ⟨0x2c01500a404e025012008c044021010007c03c01a00c806002e01500a004c024010007003401800b005002000e0050018008002000, 0x342e25a9342c3428342734263425342434223420341e34183410340833e832ed3337334b3406340433fe33fc33fb33fa33f833f433f033ef33ee33ed33ec33ea33e633de33d833d733d633d033cd33cc33c933c833c633c4⟩]) (
.leaf #[⟨0x28013809804a024011808804201f00e807003601a00c806002c01500a004c024011007803401800b005002400e0050020008002000, 0x34aa349e349a3496349434923488348634853484348334823480347e347a3474346e346d346c346a34663464345c345a345934583457345634543452344e3440343d343c228b343a34382cb934363434⟩, ⟨0x3a01c80e006c03401980c806203001780b805802b0138098030016009004402000f006803001600a004802000e0050018008002000, 0x351c35183514351135102a91350e35083504350234fa34f634ee133734ec0006297d2cb134eb34e8052203c5044b0473047b0485051511ab11d711df11e311f911fd156534e61a07000619271a031a1134e434e034dc34d834d734d634d434d034ce34c634c434ba34b934b834b734b634b434b2⟩, ⟨0xaf057027c13c08f0468230104074032018c0a4047022810c08404102000f807803501500a004e01a00c806002c006002000c004000, 0x357000061161116911f111f512331ecb2c732c7b2c952c972c9b2c9f355d3561355e0006114b116111691171119b11ab11d711df11e311f911fd12051ecd1f61355a13c135581bba03af03d30bd11109111f11271b391bb31bb71b4a111f11271add1ae51b311b471b951ba11bbd266b2675267b2859064601c101d901e106f30f7b111f11271b951ba11bbd266b2675267b2a55351b3556000601c101d901e109bb0f7b0fa912f9138d13d51add1ae51aed1b031b4b1dd134f50006029502dd044f094d0de70f7f0fdf1cd5353535413552355135501909354e354a3542353e353d353c13352906094d0f7f1cd5246d28b5352100060ab30abb0b8b0b8f0b910dab0db30e610e650e69353a28a53536000609550a690ab3134f138d139f19bb19f5226d22d7241128fd35323530352c19fb00060de70fd70fdf10391523170f19a719f5222b2255226d228522d729af3281352a224b35283522351e351d⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x3e01e00ec07403801b00d4068033019009804a024011808403e01d00e004401e00e0068030016009003801800a0040018008002000, 0x35ea272f35e835e435de35dd35dc2fb935da35d635ce35cc25fe111f112717f11add1ae51b311ba11bbd285528592b2735c435be35b835b6182935b035af35ae359335ac000603e9040514fb150315f515f915fd356d359d35ab35a835a735a635a435a0359e35963595359435933592359035883586357e35783572⟩, ⟨0x7c03581a00cc05a021010007c03c01d00e006c03201800bc05c02c01580a805202100f805002400e0068030016008002800c004000, 0x60357039d03a503a903af03d3042d0bd1103114791521153716dd1a951b3925cd1926193d363d363a052d2168039d03a503c5042d04f714fb150315f515fd16091a8500060de714791523160d161d16271643167b16d9170f18211b6d1d011d091d451d4920ab26c926e126f726ff34db360f3638363536343633363236293630362d362c362b362a36293628361b362136273626362536243622361a361936183614361000061a851b6d1d111d392f072f152f17360a13811764030f0de70fd71365138d139f15232907353535493606360536040f4f34f9351f3602360035fe35f6301d35f535f42ffb35f335f22fa735f035ec35eb⟩]) (
.leaf #[⟨0x3901c00dc06c03501980c406002f01700b405802a014009c04c025012008c04402100f807403601a00c803c014007002800c002000, 0x36b236b036ac36aa36a236a136a0369f369e369c369a3696368e368636853684368336823680367c367a3678366c3666365e30b7365a3657365634b73654364c0006044b045705150de71031156b159b1a9b239d1a96147916dd1a9936451490148d36493648149736461a6336421aab3640⟩, ⟨0x48023811808a044021010007c03c01d00e006403001780b805a02c011808804202000f807803a01b00c806002e01600a0040004000, 0x371c37183716370e370a370737063705370436f9370036fd36fc36fb36fa36f936f82143219d286736f536f736f436f336f236f036ea36e4000600031109111f112717ff182b2de735b336e036de36dc36da36d636ce36cc36c936c836bd36c636c236bc36b816831c921c451c5b366536b6039d03a503c5042d04f716091bdf29b929dd29e529ed368d36a936b436b3⟩, ⟨0x5c02d81640ae05602a81500a60520238114088043021010408003f01f00f4076032018808c04401500a004c02200d0020008002000, 0x377e3778377737763775377437723770376a3762000608cf08eb1bdf2e852e8d2f1b2f1f3743374f375d375a37593758375637523750374837463740373c373636570006000517ff182b26f726ff27253653373337342a6c039d03a51109111f112711f9150b151d1bb72a892a8d2b292b2b3730000626f726ff272127252b2b2e852e8d2f1b2f1f2fe52fed34af372c372a37283727372604b3219d2aad00060003039d03a503a9042d0ffb10312aa53724372337223720⟩]))) (
(.branch 2 (
.leaf #[⟨0x5602a014c0a004f026813009604a024811c08a038015008003601900b805802a011008003c016009003801800a0040018008002000, 0x37e637e537e437e237dd37e137e037dc37db37da37d837d037c237be37bb37ba35f7000603c50473047b0485091d098d09950a2f0ab30e230f2b156500061bb326f726ff27032725294329cf2c5d2c732c7b2c832fbb37b72a6e01c101d901e103af03d306f30bd10f7b1b39000626432761300d35ef37b437b337b237b137b037ae378a1c291c2f37a937ac37aa1c2636653791379937a637a537a437a337a237a0379a3792378e37863782⟩, ⟨0x34019809804a024011808804001f00f007403801b00c805c02c01500a004c02400f007003001600a004802000c005002000c004000, 0x386e000614bf14c914cf14e514fb150329b929cf29d729dd29e529ed3862385a385838543850384f384e384c384838443842383a383938383837383638343830382c38283824381f38233822381e381d381c381a380c380437fa37f937f837f637f237ee37e837e7⟩]) (
.leaf #[⟨0x3401900c00540280138094048023011008403e01d00d806803201800b805802a014009004401e00d0060028010007002800c004000, 0x38e238e138e038df38de351f38c338d538d938dd38dc38db38da38d438d338d238d038ca38c438c038bf38be38bd38bc360538ba38b238b038ae38a838a438a038981e9d3894389214a5388e2865388a388812d9388620f138843880387f387e20eb387c38742865⟩, ⟨0x52028814009e04d0258124090046022010807002a014009c04c025012008c04401a008803c01c00b005002000e0060028010004000, 0x393e393a39363930392f392e2db1392c1073392a392818c53926237f3924189b376c09090b5d1d3d1d412e592e6f2e852e8d34e3216601d901e1064706ff074509d709e914cf14e514fb15031ab52a29392239213920391e391a39163914390c09be09f50ab30f770f85138d13d534f50006000301c101d901e1094d09cd0f9f1dd1390839053904390238fd3901390038fc38fb38fa38f838f638f038ee38eb38e638e3⟩, ⟨0x3301900c405e02e01680b005602a014009804a01c00d006402c01500980480220100078034018009004001800a0040018008002000, 0x39ba39b439ac39ab39aa39a839a439a0399e39963995399439933992000627ad27b529cf29d72ff134433961397b3990398f398e398c3987398b398a3986398539843982397e397c397439713970396e3969396d396c3968396739663964396239583952394a⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x6203001780ba05b024011408804302080fc07c03c01900b005002600c806002e015009804802200d006002c0140060020008002000, 0x39fc39fb39fa33fb39f839f028490006028d03650de70fd70fdf1039132f137b13951523170f22d7236725a329af2cbb3525352739ee05412bf139ec39ea39e639e539e40ad539e239de2a8f0b5c08ab08b90def2c4f2c572c5d2c732c7b2c830bd6087b0b870b8f0b910b93388c01870191212939dc21b70006114b1161116911711187120529cf2c5d2c732c7b2c8337b739da39d839d639d539d439d339d239d0394239c539c939cd39ce39ca39c639463951399d39b339c239c139c039bf39be39bc⟩, ⟨0x5f02c0124090047022810c08404101900c406002f01700b403601600a004c022010006002c014009004001c00a0040018008002000, 0x32e01bb32b6f2f8f2f9330a93a59000600031109111f11271bb3292129552b6f2f8f2f9f30a932dd3a593a7d3a7e3a7a3a763a753a743a733a723a703a6c1bb32b6b2b6f2b7730a930f1315d3a473a533a553a573a593a5d3a6b3a623a603a503a483a4400060ab30e610e69132f137b21e1226522d72367247324cf24fb25412563258935253527324e3257325f32633a413a40325d3a3c3a383a353a343a302cc131e331f53a2e3a263a223a1e3a1a3a143a133a123a103a0c3a083a06⟩, ⟨0x520268130096048023011407003501980c8062025012008c04401f00f007003601a00c0054028012008804001e00e0068008002000, 0x6247324f725413ad93ada3ad63ad43acf3ad33ad23ad13ad000061b95226523052329247924fb28bd28bf2b5b2b69307d3a8d3ace33d73acd3acc34033aca3ac63ac01bb32b532b6b2b6f30a930f13a533a553a573a593ab73abe3ab83ab43ab23aad3ab13ab03aac3aab3aaa3aa83aa03a9d3a9c3a993a9b3a9a3a9830ef3a963a923a8e3a8a3a8800060e4d0fd912f913031bb330a930b33a593a813a853a863a82⟩, ⟨0x5d02a014c0a204402100e006e03401900c004e026012008c04402100f807403801a00c0058028010007803801800a0040018008000, 0x23c212331237161d16651813182b2aeb2b133b263b242b1b000604570473047b0dcd0dd50de72a3b2c732c7b2c972c9b37b93b222af100060de71479152316d9170f2255229329af32813b2032283b1d3b1f3b1e2cdd3b1c3b1b3b1a2cc12ccb2d0f2d7331e33201320b321f3b183b143a393b123b103b0e3b0a3b093b0832613b063afa3af93af83af73af63af33af43af33af2329f3a413af13aee3aea3ae43ae33ae232713ae03adf3ade3add3adc32d3000624fb2501251f⟩]) (
(.branch 2 (
.leaf #[⟨0xd0067833819a0c1054827013408b03d019c0c806203081800be04b02380cc06203001780b805a02c00f807803a01c00d8038008000, 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⟩, ⟨0x6e03681ac0d406603201880c2052028814009e04e026812c092048023811805802b014809c048021010007c03c0110078034012000, 0x3bd43bcc337f3bca3bac2b9d317d3bb73bc83bc73bc631773bc400061b6d1d011d091d451d4920ab2c432c5d2c732c7b2c83315d3bbf3bc33bc03bbc3bb83bb03ba83ba43ba33ba23ab53ba03b9c3b9a000601c101d901e1098d099509bb0a2f0efb0f2b0f7b29dd29e529ed2a312c732c7b2c952c972c9b2c9f3143315d363f3b293b2d3b923b8a09753b883b853b8409733b833b82097f09ff3b803b7e3b76000614bf14c914cf14e514fb15031add1ae51aed1b0325f725ff3b743b713b702f713b6e2dc12f4b2f7733a60fd912f91303142917a52b4b337733bd⟩]) (
.leaf #[⟨0x6f02f81740b805b02d01640b005702b01540a8053029014409e04d025811c05602a0148094046021010007c03c01d0088010004000, 0x6000301c101d901e108cf08eb098d099509bb0a2f0efb0f2b0f7b3c1f3c2b3c3a3c393c383c363c323c2e3c2c3c243c223c1c3c1a3c143c0e3c0a3c063c053c023bff3bfe31b73bfc2b9d319131bd2faa02250275039d03a5042d111f112711e916091bbd1d011d091d271fc5267b26f726ff27212725294b2e952f292fbb2fc32fd935d53b173bfa3bf83be42dc12f373be13bf63bf53bf42f2d3bf23bee3be83bde0b5c08ab08b90def12f92e3f2e852e8d2f192f1b2f1f2f23091c022502750937094d098d09951cf91d011d091d272e952f293bda228d3bd8220b⟩, ⟨0x8103f81f80fa07c03d81e80f207803b81d80d205b02700d804202000f807403801900c005802a014009003c01c00c002800c004000, 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⟩, ⟨0xb905b02cc1620b0057828413e09d04d025c128090046822c11008604282100ec067032818009a04101f80d405802a0138094030000, 0x3cd032633ccf3cce325d3ccd3ccc3aed3cc83cc4000611ab11d711df11f91ab51d011d091d3b1d451d491fd72d432d513cbc3cbb3cba3cb93cb83cb33cb73cb63c413c453cb43cb13cb33cb228053c053cab3cb03c1b3caf3cae3c1924703b913b953caa3c0b3ca83ca6000601c101d901e1094d0f7b111f112717f11bbd1fc1348b3499349d00061b95267b2713294b2b2b2de72fad2fbb2fc32fd93463348d35d53b173ca43ca1000619bb19df1a113c9f000601c101d901e102f502fb0309036703af03cd03d303e9040509cd0e650ec10f630fa91dd1136809550ab30ec10ef70f030f190f3b132f138d139f3b793c9a09ef3b52000301c101d901e1094d09cd0a171cf93b910ee4000301c101d901e1094d09cd0f1927ed3c983c973c963c4b3c953c9427fd00061b471b9526c926e126f726ff27132e592e6f2e852e8d2ea7000601d901e10937098d099509d109d709e90a0d1cf929dd29e529ff2a372a3b2a3f2c5d2c732c7b2c8337b73c733c83⟩]))))) (
(.branch 4 (
.leaf #[⟨0xa4051827c11807d03e01ec0f407903981c40e006f03181800b605902b014c0a204d025812408a04401c00b005601b0078010004000, 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⟩, ⟨0x8003f81f40f807b03d01e00d2062027010807a03701a80cc04202000f80500240100070034016009004001c00c005002000c004000, 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⟩, ⟨0x7c03701b40d406702d813c08003e01e00ec07203701b00d406803301900c4054028010807403801b00a80340160090030014006000, 0x1a8c14cf14fb15031aaf1ab31ab529dd29e529ed3143315d3b293b2d3da43ca032613da33da2325f3a411fc001d901e10215021d09d709e90ab31b4d1b511b6d1b7332a401d901e109d709e909f50ab329dd29e52a372a3f34e3000601c101d901e109bb0f7b138d192729b929dd29e529ed2a312fe531cf3da03d9f3d9e3d913d9c3d963d933d923d913d903d8e3d8a3d863d843d7a27e628053c053c133c193cab3d6f3d6e3c1b27ec0a4d23fd245f24652a313b7900063b7b3b913d693d6c3d6a1d5c1ce5286f28832887288f0bd40b730b8b0b8f0b910b930ba50bd13d663d653d643d5b3d623d5f3d613d603d5e3d5d3d5c3d593d5b⟩, ⟨0x7703981c00dc06d03601a80d006702f81780b805a02c814808203f01980c4058029013809804802100f8074018008003801800a000, 0x248025302693de53de020693deb3dea3de93de83de63dde3ddd3ddc3ddb3dda0006110112051b951ba11bbb1e6923f33dd83dd43dd13dd038b33dcc1a5e03c50e5117651a411a5b3d03000603c50e350e3d0e4b0e4d0e4f0e510fd912df12e112e712f91301130317653d033dc8130913e603c50e3d0e4b0e4f0e5112df12e113dd13e517653d033dc60da500061ce3288735553dbf3d443d4f3dc33dc23d5b3dc03dbc3dbb3dba3db73db93db83d633db63d5b0006039d03a503af03d3042d11e916091b391fc92777279127ad27b53da73db13db53db40b6b0b910bd13db23dae3da83bce33d533d93ac93ad3⟩]) (
(.branch 2 (
.leaf #[⟨0x51028013c09c04d0260128092048023811808a04401700b003401800b8050026011008003c01c00d00580240100070018008002000, 0x3e503e4e3e4c3e483e423e3a3e393e383e363e323e303e263e2200060473047b092f0937098d09950dcd0dd50ec10edd0f190f3b0ff10ff51023103b1057131b159317fb3e213e1e1cb1000601a701c101d301d901e101e901ff0215021d0225022d023306f3219327ad27b53e053e1a3e193e183e163e113e153e143e103e0f3e0e3e0c3e083e063dfe3dfd3dfc3dfb3dfa3df802443ded3df13df53df63df23dee⟩, ⟨0x8f047023411808a044821810a083041020410007f03f01f40f607903901c40e006f032812c08803c01b00c80620300100010004000, 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⟩]) (
.leaf #[⟨0xc7061830016e0b2050024c0f8070032014c08c04201b00a8052027012808404001f00f007403601900c0028010007002000c002000, 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⟩, ⟨0x5d02e016c0ae05502981480a205001d00c405002600d806403001500a0048022010007803801800b004001c00a0040018008002000, 0x3f2e3f2a37c63e733e7b3f1d3f263f253f243ce13f223f1e3f1a0006000301c101d901e1098d099509cd0f270f2b0fa91b6d1d011d091d491dd12f072f152f1734fd3b4f3b57000609bb09f50a6d23fd245f24652a313b7d000600031add1ae51b312b4b2bc333993abb3f181789000600031109111f11271bb327ad27b529213ee53eff3f143f133f123f103f0b3f0f3f0e3f0a3f093f083f063f023f003ef83ef53ef43ef23eed3ef13ef03eec3eeb3eea3ee83ee63edc3eda⟩, ⟨0x6a032818c0c205e02e01640ae05602a815008c044021810007e03d01e00ec07403901680ac0540270130090046022010807401a000, 0x629ad340f3f6b3f6d3f863f833f823f813f803f7d3f7f3f7e39d33f7c3f773f7b3f7a3f793f763f723f6e0006039d03a503af03d3042d20bf27ad27b52bc52bc73dd73f373f513f663f653f643f623f5d3f613f603f5c3f5b3f5a3f583f543f523866039d03a514cf14e514fb1503150b151d1ab520b321693f4a3f473f463f443f3f3f433f423f3e3f3d3f3c3f3a3f382966273b2761276500060003039d03a5042d134f138d139f2411284128fd2a5d32333a213cc33cd73e281b9526c926e126f726ff27132c732c7b2c9b2c9f3f293f2d⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x8003f81f40f807b03d01d80c806203081780ba05b02d01640b005702a81500a2050027013409804b01e008c0420150018008002000, 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⟩, ⟨0x3401880c005c02d01600ac054027013009004602200f807803801b00d006402e013008804001a00c00500240100070030010006000, 0x404e4049404d404c40484047404640444040403e40364031403540344030402f402e402c40264021402540244020401f401e401c401840062969356629ad340f40054002400140003ffe3ff93ffd3ffc3ff83ff73ff63ff43ff03fee3fe63fe33fe23fe03fdb3fdf⟩, ⟨0x3c01d80e006e03501a00cc06403101700b405602a014809c04201f00e807003601a00c805c02c01500a004c024011008000c002000, 0x40b040ae40a940ad40ac40a840a740a640a440a0409e40964091409540944090408f408e408c38ea40874086351d38d338db40834085408438d9408238c34080407c407a40784070406f406e406c40684066405e405c405a000601c101d901e103af03d3094d0f7b1fc127ad27b54029403d405240514050⟩, ⟨0xdf06f03741b80cf065831c1720ab04f827413809a04c0254128092048823411807403681ac0c404a02400e805202400a0040004000, 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⟩]) (
(.branch 2 (
.leaf #[⟨0x3f01f00f407803a01c80e006e03601a80cc06403101800bc05c02c01580a004e025012008c04401e00e8028010007002000c002000, 0x414841464142413c413b413a413841344130412e4124412341224120411c41184116410e410b410a410841034107410641024101410040fe40fc40f81bbb292930ab40f6000601c101d901e1094d09bb0f7b111f11271b951ba11bbd267527ad27b528bd30a740db40f340f040ef40ee40ec40e740eb40ea40e640e540e4⟩, ⟨0x8e046823011608a044021c10808304082000fe07e03881bc0ba05a02b014808804302080fc07c03d01e00ec04001f0028010004000, 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⟩]) (
.leaf #[⟨0xbf05d82d41580a504f827813a09c04d826812a091045822411007a03781880aa04801d00d806401c00d8064012007003000c004000, 0x39b339cd3940394e29ad342b372f340f3f97393400d835350f7f0457044304ad04ec1cd500eb02d5354135351cd50f7f029502d1124512371011105a1085008a139e13641faa41ac0c9206c70b91070d0b8f0c3b0b8f0b910c3b01390c3b0c1d0b910b8f079f01370b910cac41b4000608ab08b9098d09950ab30ee50f270f2b3b4f405540654077407f00060005092f0937094d098d09953677367f3fd33fed2ea6114b1161116912f92b4b2e852e8d2f1b2f1f303b33993bd3356c14bf14cf14fb15031bdf29b929dd29e529ed32a5356b3f2103b80357039d03a503a903c5042d1bdf29b929dd29e529ed32a5022c0215021d1b4d1b511b671b6d1bdf29b929dd29e529ed32a541b137fe384138533e7b23b01f191f6f1f73000601c101d901e1039d03a506f30ab30e610e690f7b132f137b150b151d22d72a712a8d2ca734313525352741b241ae17ad000611011109111f112712051bdf27ad27b529b929dd29e529ed32a5417b419541aa41a941a841a641a141a541a441a0419f⟩, ⟨0x8103e81f00e806c03301800b605a02c01580a004a0238114086042020810007c03001780a004e01b00d006402e0100068018004000, 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⟩, ⟨0x5e02e814c0a004e025011408403c01b80d806a03401980c806002f01700b405802b01500a404801f00a80500260120058008002000, 0x23370a470dab0e550b8f0bd10b910b8b0365095809601cef1d911ce408360b3c05231ecd2d5f04531fad23dd1dc1147f1eab089c08590893286f1cef1d5d1cde3c9c1d8e20891555155f1525156e23662cba2cb0258825a2129d1298338e32ee10560ff01a101a0314782005212720df285e0184290735490fd725c615b429ad342b340f393415932082212720df20052a04195a19de19ba0a0909f509bb0ef70ec10f3b097e0a990b5d0dab0b8f0bd10b910b8b0e670db613a205b8⟩]))))) (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x8003c81b80d806b03201780ba05c02d81680a004f027012c09404702000ec06c03501900bc056027010806803001700b0008002000, 0x9f509bb09630ec109550ef70f3b3e5d05ef245f074901420a7e09bb09f523fd091509610cca0cee1ac82f542dc13be63a813a5930a92d9e352724fb0e610e69352500cb137a247224f62540387323c123bf1211184d103b12451237106500a718a4187e2ab501842004101003a9153715250a0d091d0fa909cd38c1360713d505ef0749086908a1086d0d4c06c70c3b070d0cee0d6c09550aa80b3c074905ef0645074905ef06450137074905ef064501380749071305ef0645062b012f09550aa805ef074905ec08a10869243e0114230419f428fd0f7f1cd529060ef70a0d091d38c13cd50fa909bb267527610955222b226d222d0a69230519f5228422a6⟩, ⟨0xb805b02d015e0a404d025012408f042821010608103e01e80e207003781ac0bc053027812409004401d80dc05801b00a0048006000, 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⟩]) (
.leaf #[⟨0xce063830c1780b905982c015a0a9054027812c092048021810407c03581a80d206803381840b605702981180700340118044006000, 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⟩, ⟨0xf807783a81ae0cc065832418c0c405a02cc15209904a02180f007303381940c6055029013809203b01800ac050024011808002e000, 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⟩, ⟨0x16b0a684c826212c094049824611908a844c20c10307f03c01c80d205f02b413a09904081a00a805001f80ec072037015807001c000, 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⟩]))) (
(.branch 2 (
.leaf #[⟨0x1980c6061c3061780b4853c27e11c08203e01ee0f607883b01b40c805e829c14609e04582100f407503101600a20380110048018000, 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⟩, ⟨0x1d40e6871435a1a20cc06242fc1630ab054428c13a09b04b024211408504001ea0ed071035418209f04802080ca05a02900b000e000, 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⟩]) (
.leaf #[⟨0x7c03c81d80e606d03281880c206002e01680a604a02300f407803a01900b8054028012008403a019007802c0140060018008002000, 0x12451085008a122e1212123110ed12bd12442aa11e8102b31dc51f85008b1edf1ecb1e9310ed12bd1ec91ec71e8321672aad02f0167a2bc4028d0fd72cec21681ce5015f0a99226d28fd2906222b03650e5525c520df2005044325ff152f0fd7354929071ce503650e55015d0a990e55036528fd2906222b226d0a69015c2bc611011244123123bf103923c10fd7028d1211122d25c5156b03a9154a20df2127156b044e044e04f9044304ad04a1044e028d0100044f20df204b285e200500e0028d044f0100241f238f238d24052a3503650e552809245f23fd22130a6921f30121222c0a9e0e550365015d0e650e610aa90b3c3b4e0954⟩, ⟨0xc806102f01680b3053028813c09d04a024811007f03e01e80dc06c03281600ae04f025010406802e01580a00460210068024006000, 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⟩, ⟨0x6503281940ca06503281940ca06503281900c405e02e81700b0051027812808404001e80e006802e01380880380160070024008000, 0x115242323fd238d238f044f028d13f8015f1413145d0e55036503650e55044300d804ad00eb012102d5044e1413145d0e5503650fd703650e5500d804ad0443152f0fd701212611260a0a69012100ca03650e5523fd2423012003650e5523fd04f71413145d03650e550fd7028d1413145d0fd70e550365028d10392a0400a62169010104f90e55028d0fd7036510391a4125c5156b1a8f1a8d1a9b03a91039028d0fd703650e551a41044304f91039028d0fd71f19147c1039028d0fd723c1008a1e81147f1f85008b⟩]))))))))))))))

def policyFixedCompact0Db : Nat → List Int := policyFixedClauseDatabase 16 policyFixedCompact0ClauseTable

def policyFixedCompact0VariableTable : PackedNatTable.Table Nat :=
(.branch 0x83
  ((.branch 65
  ((.branch 32
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x338033603180312031102f102f002ee02eb02e402130212020101fe01fd01e701e201dd01d601cb01c5010600e500de00d30079005d00410010000a00050000, 0x4a304a2048504820481047f047c047503fd03fc03d603b803af03a8039e039d039c039a037c0377037603750373035b0358035503540352034f0344033a0339, 0x569056805670566055a054905460545054305400535052a05290527051c050905040503050204f604e504e204df04dc04d504ca04c904c704c604a904a604a5, 0x65a0659065706560652064c0639063606350634063306320631062e06260618061506120611060f060c060b060205e705bd058e058d058b058a0580056d056a])
  (.leaf #[0x72d072307220721071f071e071206ff06f906f806e806d706d406d106b906b806b606b5069806950693069206910685067406710670066e066b066a0664065b, 0x7eb07ea07e907e007c607c507c407c307c207b707b1079e079d079b07850784078307810780077607630760075f075e075d075c0750073f073c073b07390736, 0x8370836082e082d082c082a08290828082608240821081f081e081d08050801080007fd07fc07fb07fa07f807f707f607f507f407f207f107f007ef07ee07ed, 0x86908680867086208610860085f085d085c085b08590858085708560850084f084d084c084b084a084908480846084208410840083f083d083c083b08390838])))
  ((.branch 4
  (.leaf #[0x899089708960893089208910890088e088d088c088508840883088208810880087d087c087a087908780877087608750873087208710870086e086d086c086a, 0x8e408e308e108df08db08da08c408c108c008be08bd08bc08bb08ba08b908b808b708b608b408b308b108af08ae08ad08ac08a508a408a308a208a108a0089b, 0x92309210920091f091e091d091c091709110910090f090e090d09050903090108ff08fe08fd08fc08f908f808f508f408f208f108ee08ed08eb08ea08e908e8, 0x97209710970096f096e096a09550951094f094a09480946094509430941093e093d093c0938093709360935093409330930092f092e092c092b092a09280926])
  (.leaf #[0x9a309a209a0099b099a0999099809960995099309920991098e098d098c098b09880987098609850984098309810980097f097e097d09790977097609750974, 0x9df09de09dd09dc09db09d809d609d209d109cd09cc09cb09ca09c609c409c309c209c109bf09be09bd09bc09bb09b509b409b309b209b009ae09a809a709a4, 0xa120a100a0c0a0a0a060a050a040a030a0209ff09fe09fc09f809f709f509f409f309f209f109f009ed09ec09eb09ea09e909e809e609e509e409e309e209e0, 0xa4c0a4b0a4a0a480a470a460a440a420a3f0a3c0a3b0a3a0a390a380a320a300a2c0a2b0a290a280a250a240a230a200a1f0a1e0a1a0a190a180a170a160a15])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0xa7b0a790a780a770a760a740a730a720a700a6f0a6e0a6d0a690a670a660a650a640a630a620a600a5f0a5e0a5c0a5b0a5a0a590a540a530a520a510a500a4f, 0xab50ab30ab20ab00aaf0aae0aad0aac0aab0aa10aa00a9f0a9d0a9c0a9b0a9a0a960a940a910a900a8f0a8c0a8b0a8a0a890a870a860a830a820a7f0a7e0a7c, 0xae80ae70ae60ae50ae40ae30ae10adf0add0adc0ada0ad90ad70ad60ad50ad40ad20ad00ace0aca0ac90ac60ac50ac40ac30ac10ac00abf0abd0abc0abb0aba, 0xb0d0b0c0b0b0b0a0b080b060b050b040b030b020b010b000aff0afe0afd0afb0afa0af90af80af70af50af40af30af20af10af00aef0aee0aed0aec0aea0ae9])
  (.leaf #[0xb4a0b470b460b450b440b430b420b410b400b3f0b3d0b370b360b340b330b310b300b2f0b2e0b2c0b2b0b2a0b290b280b1a0b190b180b170b160b150b120b10, 0xb810b800b7e0b7d0b7c0b7b0b780b770b750b740b710b700b6f0b6e0b6a0b690b660b650b640b630b610b600b5e0b5d0b5c0b5b0b5a0b570b560b550b540b4b, 0xbb40bb30bb20bb10bb00baf0bae0bad0bac0baa0ba80ba60ba40ba30ba20ba10b9e0b9d0b9b0b9a0b980b970b960b940b920b900b8f0b8e0b8a0b880b840b83, 0xc0d0c0c0c060c040c020c000bff0bfe0bfd0bfc0bf60bf10bef0bed0bec0bea0be90be80be70be50be30bce0bc30bc20bbf0bbe0bbd0bbc0bbb0bba0bb80bb6])))
  ((.branch 4
  (.leaf #[0xc6a0c690c680c660c600c5f0c5c0c5b0c5a0c580c570c540c530c4b0c490c470c450c400c3e0c3b0c3a0c390c380c280c220c1d0c1b0c190c170c150c130c11, 0xcb30cb20cb10cb00caf0cae0cad0cac0caa0ca90ca80ca70ca60ca40ca30ca10c9d0c9c0c940c930c910c900c820c7f0c7b0c790c770c730c720c6e0c6c0c6b, 0xce40cdf0cdd0cdc0cda0cd90cd80cd70cd60cd50cd30cd20cd10cd00ccf0cce0ccd0ccc0cc90cc80cc70cc50cc30cc20cc10cc00cbe0cbd0cb80cb70cb50cb4, 0xd410d400d3f0d2e0d2d0d2c0d2b0d2a0d290d270d260d250d240d220d210d200d1f0d1e0d190d170d130d120cf60cf50cf40cf30cf10cef0cee0ceb0ce80ce7])
  (.leaf #[0xd6f0d6e0d6c0d6b0d6a0d690d680d650d640d620d5f0d5e0d5d0d5c0d5a0d590d570d560d550d520d510d500d4f0d4d0d4c0d4a0d480d470d460d450d430d42, 0xdd00dcd0dcc0dca0dc90dc80dc70db90db70db40daa0da90da80da70da50da40d940d900d890d870d860d850d840d810d7f0d7b0d790d740d730d720d710d70, 0xe020dfd0dfc0dfb0dfa0df90df80df30df10dee0ded0dec0deb0de90de80de70de60de30de20de10de00ddf0dde0ddc0ddb0dda0dd90dd80dd50dd40dd20dd1, 0xe2d0e290e280e270e260e240e220e1f0e1e0e1d0e1c0e1b0e1a0e190e180e170e160e140e130e120e110e100e0f0e0e0e0d0e0c0e0a0e090e070e050e040e03])))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0xe6d0e6a0e650e630e620e5d0e5b0e580e570e560e550e540e530e520e500e4f0e4e0e4c0e4b0e4a0e470e460e450e440e3d0e3c0e370e360e340e310e300e2f, 0xe9c0e9b0e9a0e990e980e960e950e940e920e8c0e8b0e8a0e890e880e870e860e850e840e830e820e800e7f0e7e0e7d0e7c0e790e750e740e710e700e6f0e6e, 0xeda0ed70ed60ed50ed20ed10ecf0ece0ecd0ecc0ecb0ec80ec70ec50ec40ec30ec10ec00ebf0ebe0ebd0ebc0ebb0eba0eb80eb70eb60eb30eb10eb00ea60e9d, 0xf120f110f100f0e0f0d0f0c0f0b0f060f050f040f030f020f010efe0efd0efc0efa0ef90ef80ef60ef40ef10eee0eed0eec0eeb0eea0ee40ee20ede0edd0edb])
  (.leaf #[0xf4d0f4c0f4b0f490f480f470f460f410f400f3d0f3c0f3a0f390f350f330f300f2f0f2e0f290f280f270f260f210f1d0f1b0f1a0f190f180f170f160f150f14, 0xf7a0f780f750f740f730f720f700f6f0f6e0f6d0f6c0f6b0f6a0f690f680f650f640f630f610f600f5f0f5e0f590f580f570f560f550f540f520f510f500f4f, 0xfa30fa20fa10f9e0f9d0f9c0f9b0f9a0f990f980f950f940f930f910f900f8f0f8e0f8d0f8c0f8a0f880f870f850f840f830f820f810f800f7e0f7d0f7c0f7b, 0xfd40fd00fce0fcb0fca0fc90fc70fc60fc50fc40fc00fbf0fbe0fbd0fbc0fbb0fb90fb80fb70fb50fb40fb30fb20fae0fad0fac0faa0fa90fa80fa70fa60fa4])))
  ((.branch 4
  (.leaf #[0xffe0ffd0ffc0ffb0ff90ff80ff70ff50ff40ff30ff20fee0fed0fec0feb0fea0fe90fe80fe70fe50fe40fe10fe00fdf0fdd0fdc0fda0fd90fd80fd70fd60fd5, 0x10341033102e102d102c10291027102410231020101f101e101b101a101910171016101510131011100e100c100b100a10091008100610051004100310020fff, 0x108210811080107f107e107b107a10731071106d106810671060105e105b104f104c104b104a104910461045104410431041103f103b103a1039103710361035, 0x10bf10be10b910b810b310b210b110ac10ab10aa10a810a610a0109f109c109b109a10971096109410931091108e108d108c108b108910881087108610851084])
  (.leaf #[0x10f210f110f010ef10ed10eb10ea10e910e810e610e510e010df10dd10dc10db10da10d910d810d710d610d510d310d210d010ce10cd10cc10cb10c510c410c3, 0x1133113211311130112e112d112c112911281125112411211120111c111a11171116111511021101110010ff10fe10fd10fb10f910f810f710f610f510f410f3, 0x1168116511621161115f115e115d115c115b115a115711561155115411511150114f114e114d114c114b11491147114411431142113e11391138113611351134, 0x119e119d119c119711961195119411921191118f118e118d118c11881186118311821180117f117d117c117b117a11781177117311721171116f116e116b116a])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x11cf11ce11cd11cb11ca11c911c811c711c511c211c111be11bd11bc11ba11b911b811b711b411b311b111b011ae11ad11a811a711a611a511a311a211a1119f, 0x11fa11f911f811f611f411f311f211f111f011ef11ed11eb11e911e711e611e511e411e011df11de11dd11dc11db11d911d811d711d611d511d411d311d211d1, 0x1240123f123e1235122a12291223122212211220121f121e121d121c121b12191217121612121211120e120d120c1208120612041203120211ff11fe11fd11fc, 0x126f126d126c126b126a126912681267126612651264126312621261125f125e125c125a125912581257125212511250124f124e124d12481246124412431241])
  (.leaf #[0x12a1129f129d129c129b129a1299129812961295129412931291128f128c128b128a12881284128312821281127f127d12781277127612751274127312721271, 0x12e312e212e112de12dd12dc12db12d912d712d612d412d212ce12cd12cc12c912c812c712c612c412c212b712b612b312b212b112b012af12ae12a912a712a4, 0x1314131313121310130f130e130d130b130a130913081307130513041303130212ff12fd12fc12fb12fa12f812f712f612f312f212f112f012eb12e812e612e4, 0x136d136c136b136a1369136813661365136413631362135e135d135c135b135a13591357135613551353135213511350134c134b1320131f131e131c13181317])))
  ((.branch 4
  (.leaf #[0x13a213a113a0139f139b139a139713961394139313921391138d138c13891384138313821381137f137e137d137b137a1379137813741373137213711370136f, 0x13e213e113de13dc13da13d913d813d613d413d113d013cf13cc13cb13c813c713c413c313bf13be13bd13bc13ba13b813b513b013ac13a813a713a613a513a3, 0x141f141e141214111410140f140d140b14071405140414031402140113fc13fb13fa13f813f713f613f513f313f213f113f013ef13ee13ed13eb13e613e513e3, 0x145914551454145314521450144f144e144d14491447144414431442143f143e143d143c1439143814311430142f142d142c142b142914271424142214211420])
  ((.branch 2
  (.leaf #[0x148214811480147e147d147c147b14791476147514741473147214711470146f146e146c146b146a1469146814651464146314621460145f145e145c145b145a, 0x14b714b614b514b414b314b014ae14ad14a914a714a414a314a2149e149d14981496149514941493149214911490148f148e148c148b14891488148714861485])
  (.leaf #[0x14e914e814e614e514e414e314e214df14de14dd14db14da14d814d614d514d314d214d114d014cf14cd14c714c614c514c414c214c114c014be14bd14bc14bb, 0x15211520151f15191518151715161515151315121510150f150e150d150b150a150915081507150414ff14fc14fa14f914f814f714f614f514f414ee14eb14ea, 0x1551154d154c154a1547154615451544154315421540153f153e153d153c153a15391538153715361534153315321531152e152d152b152a1528152615241522])))))))))))
  ((.branch 33
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x157b157a15791576157515741573157215711570156f156e156d156c156a1569156815661565156415631560155f155e155d155b155915571555155415531552, 0x15b415b115b015af15ae15ac15a915a815a415a315a215a1159f159c159b15971596159415911590158f158e158c158b158915871585158415831582157f157e, 0x15e015df15de15dd15dc15db15d815d715d615d515d215d115cd15cc15cb15ca15c915c815c715c515c415c315c115c015bf15be15bc15bb15ba15b915b715b6, 0x160e160d160c160b160a16071606160516041601160015fe15fd15fb15fa15f915f815f715f615f415f315f215f115ef15ee15ed15eb15ea15e915e815e315e2])
  (.leaf #[0x163e163d163c163a163916381636163516341633162e162d162b162a16291628162716261624162316221621161f161e161d161b161a1619161816121611160f, 0x167c167b166f166e166d166c166a166916681666166516641663165d165c165b165916571656165316511650164e164c164a164816471646164516441640163f, 0x16ac16ab16aa16a916a316a216a116a0169e169d169c169b169a16991696169316921690168f168e168d168c168b168916881687168616851684168216811680, 0x16e616e416e216de16dd16db16da16d716d616d516d216d116d016ce16cd16cc16ca16c816c516c316c216c116c016bb16b816b716b316b216b116b016af16ae])))
  ((.branch 4
  (.leaf #[0x171e171d171c171b171a171817161710170f170c17061705170417031701170016fe16fd16fc16fb16f816f716f616f416f316f116f016ef16ec16eb16e916e8, 0x17831782177f177e177d177c177b177917721770176c17671766175717551752174f174c174b174a174917391733172e172c1729172517241723172217211720, 0x17b717b617b517b417b317b217b017af17ae17ad17ab17aa17a917a817a717a317a1179e179d179c179b179a179917981797179417921791178d178c17891787, 0x17f117ed17ec17eb17ea17e817e717e617e517e317e217e117e017df17de17dd17da17d917d817d617d517d317d217d017cf17ce17cd17cc17ca17c017bd17bb])
  (.leaf #[0x18211820181f181d181c181b181a1817181618151813181218111810180e180d180c180b180918071805180318021801180017ff17fa17f817f617f417f317f2, 0x18511850184f184e184d184c18491847184418431842183f183e183d183c183918381833183218311830182f182d182c182b182a182918281825182418231822, 0x187e187d187c187b187a187918761875187418711870186f186e186d186918681867186618651864185e185d185c185b185a1859185818571856185518541853, 0x18b518b318b118b018af18ae18ad18ac18aa18a918a818a718a218a0189d189c189b189818971896189218911890188e188c188b188618851884188318811880])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x190218ff18fe18fd18fc18fb18f918f818f518f318ef18ed18ea18e918e518e418e318e218df18dd18dc18d918d818d718d618d518bd18bc18bb18ba18b918b6, 0x192c192b192a1927192619251924192219211920191f191e191b191a191919181917191619151914191219111910190f190e190d190b19091907190519041903, 0x195d195c195b195a19591957195619551954195219511950194e194d194c194b1947194619451944194219411940193e193d193c193b19351934192f192e192d, 0x19921991198e198d198c198a1989198819871985198419831982197d197c19781973197219711970196f196e196c196b196a196819671966196519611960195e])
  (.leaf #[0x19c619c419c219bf19be19bd19bc19bb19b919b819b719b419b119b019af19ae19aa19a919a819a719a619a119a0199f199d199c199a19991997199519941993, 0x19f619f519f419f319f219f119f019ee19ed19e719e619e519e419e319e119e019df19dd19dc19db19da19d619d519d419d319d219d019ce19cd19cb19c919c8, 0x1a241a231a221a211a201a1f1a1b1a1a1a191a181a171a151a141a0f1a0e1a0d1a0b1a0a1a091a081a071a061a041a031a021a0019ff19fe19fd19f919f819f7, 0x1a571a561a541a531a501a4f1a4c1a4b1a4a1a491a461a451a441a431a421a411a401a3f1a3d1a3c1a3a1a381a341a331a311a301a2e1a2d1a2c1a2b1a281a26])))
  ((.branch 4
  (.leaf #[0x1a8c1a8b1a8a1a891a881a871a861a841a821a801a7e1a7d1a7c1a7b1a781a771a761a741a731a701a6f1a6e1a6c1a6a1a641a631a601a5f1a5e1a5b1a5a1a59, 0x1aba1ab91ab81ab71ab51ab41ab31ab11ab01aae1aac1aaa1aa81aa71aa61aa51aa11aa01a9f1a9c1a9b1a991a981a961a951a941a931a921a911a901a8f1a8d, 0x1ae51ae31ae21ae11ae01adf1ade1adc1ada1ad81ad61ad51ad41ad31ad21ad01acf1ace1acb1aca1ac91ac81ac61ac51ac41ac31ac21ac11abe1abd1abc1abb, 0x1b181b161b141b121b111b101b0f1b0a1b091b081b071b061b051b041b021b001aff1afd1afb1afa1af71af61af41af31af21aec1aeb1aea1ae91ae81ae71ae6])
  ((.branch 2
  (.leaf #[0x1b4d1b4c1b4a1b491b481b471b461b451b431b411b3b1b3a1b371b351b301b2f1b2e1b2d1b2c1b2b1b291b281b271b261b251b231b221b211b201b1d1b1b1b1a, 0x1be51bad1bab1ba91ba81ba71ba61ba31ba21b9f1b9d1b9c1b9b1b9a1b981b971b961b951b941b931b921b901b8f1b8e1b8c1b8b1b611b601b5f1b5e1b5c1b5b])
  (.leaf #[0x1cac1ca71ca61c771c3f1c3e1c3d1c3c1c3b1c3a1c361c351c341c321c311c2c1c241c221c1f1c1a1c181c151c0f1c0d1c0a1c001bff1bfe1bfd1bfc1bfb1beb, 0x1ce11ce01cdf1cde1cdd1cda1cd91cd51cd41ccd1ccc1cca1cc91cc81cc71cc61cc41cc21cc11cc01cbe1cbc1cbb1cba1cb81cb71cb51cb31cb11caf1cae1cad, 0x1d161d131d111d0f1d0e1d0d1d0c1d091d081d051d041d031d021d011d001cff1cfe1cfc1cfb1cfa1cf81cf71cf41cf31cf11cf01ced1cec1cea1ce91ce51ce3])))))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x1d481d471d461d451d431d411d3f1d3d1d3c1d3b1d3a1d361d351d341d321d311d2e1d2d1d291d281d271d261d241d231d211d1e1d1d1d1c1d1b1d191d181d17, 0x1d761d751d731d721d711d701d6c1d6b1d691d661d651d641d631d611d601d5e1d5d1d5c1d5b1d591d581d571d551d541d531d521d511d501d4f1d4c1d4a1d49, 0x1da81da71da41da31da11da01d9e1d9c1d9a1d981d971d961d951d941d901d8e1d8d1d8c1d8b1d8a1d881d871d861d851d841d821d811d7f1d7c1d7b1d781d77, 0x1dd91dd81dd61dd51dd41dd21dd11dcf1dce1dcd1dcc1dcb1dca1dc91dc81dc61dc51dc41dc31dc11dbf1dbe1dbb1db91db51db41db21db11db01daf1dac1dab])
  (.leaf #[0x1e0d1e0b1e0a1e081e061e031e021e001dfe1dfc1dfb1dfa1df91df41df21df01def1dee1ded1de91de81de71de61de51de31de21de11de01dde1ddc1ddb1dda, 0x1e3a1e391e381e371e361e351e331e321e311e301e2f1e2e1e2d1e2b1e2a1e291e281e261e251e241e231e211e1f1e1d1e191e171e131e121e111e101e0f1e0e, 0x1e691e661e651e641e631e611e601e5f1e5e1e5d1e5a1e591e561e551e541e531e511e501e4c1e4b1e4a1e491e481e471e451e441e431e421e411e3f1e3e1e3b, 0x1e9a1e991e981e971e951e941e931e921e911e8b1e8a1e881e821e811e801e7e1e7d1e7c1e7b1e7a1e791e761e751e741e731e721e711e701e6d1e6c1e6b1e6a])))
  ((.branch 4
  (.leaf #[0x1ede1edd1ed91ed81ed41ed31ed21ed11ed01ebe1ebb1eba1eb91eb71eb51eb31eb21eb11eb01eaf1eac1eab1eaa1ea91ea81ea51ea21ea11ea01e9f1e9e1e9d, 0x1f111f0d1f0c1f0b1f0a1f081f071f061f041f031f021f011efd1efc1efa1ef91ef81ef71ef61ef51ef21ef11eef1eeb1ee91ee81ee71ee61ee31ee21ee01edf, 0x1f421f401f3f1f3e1f3d1f3c1f381f371f351f341f331f321f311f2f1f2e1f2d1f2c1f2b1f281f221f211f201f1d1f1c1f1b1f1a1f181f171f161f141f131f12, 0x1f811f7f1f7d1f7b1f7a1f791f781f751f711f701f6f1f6e1f6c1f691f681f671f661f641f631f621f611f601f5b1f5a1f591f581f4f1f471f461f451f441f43])
  (.leaf #[0x1fba1fb91fb21faf1fae1fad1fac1fa41fa31fa21fa11f9f1f9e1f9d1f9b1f9a1f991f981f941f931f921f911f901f8f1f8c1f8b1f8a1f881f871f861f841f83, 0x1ff51ff41ff21ff01fee1fed1fec1fe91fe81fe71fe61fe51fdf1fdc1fdb1fda1fd91fd81fd71fd51fd01fcf1fce1fcd1fcb1fca1fc91fc81fc71fc41fc01fbc, 0x205b205a2059205820562055205320512050204f204e2049204720412040202820222020201d20132011200d200c200b2009200820001ffe1ffb1ffa1ff71ff6, 0x20892088208620832080207f207e207d207c207b207a20792077207620752074207320722071206f206e206d206c206b206a2068206720652063206220612060])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x20df20dd20d920d520d220d120d020b720b620b520b320b120ab20aa20a720a620a520a220a1209f209e209c209b209a20992097209420932092208f208b208a, 0x21422141213e213d212b212a21282127212621252124212221212120211f211e211d211821172116211221112110210f210d210b21092105210420fe20e520e3, 0x21722171216f216e216b216a21692168216621652164216221612160215f215b215a21592158215621552154215221512150214f214921482146214521442143, 0x21a721a521a421a321a2219d219c219b219a219821972195219321922191219021862185218321822180217f217e217d217c217a217821772176217521742173])
  (.leaf #[0x21d521d421d121d021cf21cd21c921c821c721c621c421c221bf21bd21bc21bb21ba21b921b821b721b621b421b321b221b121b021af21ae21ad21ac21aa21a9, 0x2222221c221b221a221722162215221422122211220c220b22082203220221ef21eb21e921e621e521e421e321e221e121e021df21de21dd21db21da21d921d8, 0x2251224f224e224d224c224b224a22492248224722462245224322412240223f223e223c223b22392237223622352234222f222e222d222c222a222922272223, 0x229d229a2299229622952293229222912290228f228b228822852284228322822280227f227e227d227c2278227622722271225c225b225a2259225722552254])))
  ((.branch 4
  (.leaf #[0x22cc22cb22c922c822c722c522c422c322c222c122bf22be22bc22ba22b922b722b622b422b222b122b022af22ae22ac22aa22a922a622a522a422a222a0229f, 0x231f231c2319231823172316231323122311230f230e22f622f522f422f222f022ef22ed22eb22ea22e722e522e322e222e122e022df22d422d022cf22ce22cd, 0x235823562355235423532350234f234e234d234b234a2340233f233e233c233b233a233923382337233623342333232e232d232c232923262325232423232321, 0x23a523a4239d23972396238b238a23872386237b237a2379237823762375237423732372236e236d236c236b2369236823672365236423632362235c235b235a])
  ((.branch 2
  (.leaf #[0x23f923f823f723f623f423f323f223df23da23d623d523d323d223d123cf23ce23cd23cb23c923c623c423c323c223c123c023bf23bd23bb23b723b623b323b1, 0x2444244324422441243f243e243c243a24392438243724312430242b242a24262425242424222420241f241d241c241b241a2415240f240a2404240023ff23fb])
  (.leaf #[0x247f247e247d247c247b247a247924772476247324722471246724652462245f245e245d245c245a24582454245324512450244f244e244d2448244724462445, 0x24aa24a924a824a624a424a324a224a1249f249e249924982496249524942493249224912490248f248c248b248a248924882487248624852484248324822481, 0x24e124df24de24da24d924d824d724d624d524d124cf24ce24ca24c924c824c624c324c224c124bf24bb24ba24b924b824b624b324b024af24ae24ad24ac24ab])))))))))))))
  ((.branch 66
  ((.branch 33
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x2523252225212520251f251e251d251c251b251a2518250a25062505250325022501250024ff24fe24fd24fc24fb24f924f824f624f424f324f224f124e724e2, 0x256525642561255e255c255a25592558255725562550254f254e254c25472542253e253c253b253a2539253825322531252f252d252b25292528252725262525, 0x25a425a3259f259d25992598259425932591258e258b258a258925852584258325812580257f257d257b257825752574257325722571256f256b256a25692566, 0x25e025df25de25dd25dc25da25d925d825d725d625d525d125ce25cd25cc25cb25c725c025be25b925b525b425b325af25ae25ad25ac25aa25a925a825a625a5])
  (.leaf #[0x261426112610260f260e260b260a26072606260426032602260125ff25fe25fd25fc25fb25f625f425f225f125f025ef25ee25eb25ea25e625e525e425e325e1, 0x2652264f264d264a264926482645264426432642263e263a26392637263426332630262f262e262d262a2629262826252624262226212620261f261d261b2615, 0x267c267b267a2679267826762675267426722670266c266b266a26692668266726642663266226612660265f265d265c265b265a265926572656265526542653, 0x26af26ae26ad26ab26a926a726a526a426a326a2269e269d269c269a26992696269526922690268e268d268c268b2687268626852683268226812680267e267d])))
  ((.branch 4
  (.leaf #[0x26de26dd26db26d926d726d526d426d326d226cd26cc26cb26c926c826c726c626c526c426c226c126c026bf26be26bb26ba26b926b826b726b426b226b126b0, 0x270d270c27052704270327022701270026fe26fd26fc26fb26f926f826f726f626f326f226f026ef26ee26ed26ec26eb26ea26e726e526e426e326e226e026df, 0x273c273a273927382737273627352734273327312730272f272e272c272b2729272827242723271e271d271c271b2719271827162715271427132712270f270e, 0x27982790278b2789278827872783278227752772276f276e276d276b2765276427622761275f275e275d275c275b275a2751274f274a2748274427432740273f])
  (.leaf #[0x27e427e327dc27d127d027cb27ca27c727c627c327c227c027bd27bc27bb27ba27b927b627b227b127ae27ad27ac27ab27a927a827a727a627a527a0279c279b, 0x284928482847284628362830282b282928252823281f281b28182817281627fa27f927f727f627f527f427f227f127f027ef27ee27eb27ea27e927e827e627e5, 0x289e289d289c289b289628952894288c28882887288628852884288328822880287f287d287c287a28772876286f286d286928642863285a28542852284f284c, 0x28d328d228d028ce28c828c728c428c328c228c028bf28bd28bc28bb28ba28b828b728b528b328b228af28ae28ad28ab28aa28a928a828a728a628a428a228a0])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x290e290d290c290a290929062905290128fd28fc28fa28f928f828f728f628f428f328f228f128f028e328e228e028df28de28db28da28d828d728d628d528d4, 0x293a293929382937293629352934293229312930292d292c292b292a2929292829272924292229212920291f291e291d291b2919291729152914291329122911, 0x29682966296329622961295e295d295c295b295a2959295729562955295429522951294f294d294b294a2949294829452944294329422941293f293e293d293c, 0x29942993299229912990298f298d298c298a298929862983298229812980297e297d297c297b297929782977297629752973297229712970296e296d296c296b])
  (.leaf #[0x29cf29cb29ca29c929c829c729c629be29bb29b929b629b529b329b229af29ae29ad29ab29aa29a929a729a529a229a0299f299e299d299c299a299929982997, 0x2a242a1a2a192a142a132a122a112a0f2a0d2a092a082a072a062a052a042a032a022a0129fb29f929f629ec29e529e429e329e229e129d929d729d429d329d0, 0x2a712a702a6f2a6e2a6d2a6a2a652a632a602a5f2a5e2a552a3e2a3d2a3b2a3a2a392a382a372a352a342a322a312a302a2f2a2e2a2c2a2b2a292a272a262a25, 0x2aad2aac2aaa2aa92aa82aa72aa62aa12a9f2a9c2a9b2a9a2a912a8e2a8d2a8c2a8a2a882a862a822a812a802a7e2a7d2a7c2a7b2a7a2a772a762a752a742a73])))
  ((.branch 4
  (.leaf #[0x2ade2adc2adb2ada2ad92ad82ad72ad52ad42ad32ad22ad02acf2ace2acc2acb2aca2ac92ac52ac12ac02abf2abe2abc2abb2aba2ab82ab72ab62ab52aaf2aae, 0x2b0b2b0a2b092b082b062b042b022b012aff2afe2afd2afb2af92af82af72af62af42af22af02aef2aee2aed2aec2aea2ae92ae72ae62ae52ae42ae32ae02adf, 0x2b562b542b512b4f2b4e2b4d2b302b2f2b2e2b2d2b2b2b272b262b252b242b232b222b212b202b1f2b1e2b1c2b1b2b192b172b162b152b142b0f2b0e2b0d2b0c, 0x2b832b822b812b7f2b7d2b7c2b7a2b792b782b772b762b752b732b722b712b702b6f2b6e2b6d2b6b2b6a2b682b672b662b652b642b5e2b5d2b5c2b5a2b592b58])
  ((.branch 2
  (.leaf #[0x2bb62bb52bb42bb32baf2bad2bab2ba82ba72ba62ba42ba32ba22ba02b9f2b9e2b9d2b9b2b972b962b952b942b922b902b8d2b8b2b8a2b892b882b862b852b84, 0x2bff2bfe2bfd2bfc2bf72bf62bf32bed2bec2beb2bea2be92be82be72be52be32be22be12be02bde2bdd2bdc2bdb2bda2bd92bcf2bce2bc32bc22bc12bbf2bb7])
  (.leaf #[0x2c452c402c3f2c3e2c3d2c3c2c3b2c3a2c392c382c372c352c312c2e2c292c282c272c212c202c1f2c1e2c1d2c192c172c132c0f2c0e2c0d2c082c042c022c01, 0x2c7e2c7c2c752c742c732c722c6b2c682c662c642c632c622c612c5b2c5a2c592c582c572c562c552c542c532c522c4e2c4d2c4c2c4b2c4a2c492c482c472c46, 0x2cb52cb42cb22cb02caf2cae2cac2ca72ca52ca42ca32ca22ca02c9f2c9a2c992c982c972c962c952c922c912c902c8b2c8a2c892c882c862c852c842c832c82])))))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x2d482d472d462d442d432d422d402d3f2d372d362d322d2e2d2b2d2a2d292d282d262d252cff2cfa2cf82cf52cf32cef2cec2cd22cd02ccf2cba2cb92cb82cb7, 0x2da12da02d9f2d9c2d9b2d982d972d952d942d922d912d902d8e2d8d2d8c2d8b2d8a2d872d862d852d812d802d612d602d5f2d5a2d592d562d552d542d532d51, 0x2e242e232e212e202e1f2e1e2e132e122e112e102dfd2dd92dd82dd72dd62dd52dd32dcf2dcd2dc92dc82dc72dc62dc52dc42dc32db32db22da72da52da32da2, 0x2e532e512e502e4f2e4e2e4c2e4b2e4a2e482e472e462e452e412e402e3e2e3d2e3c2e3b2e3a2e392e362e322e312e302e2f2e2e2e2d2e2a2e292e282e272e25])
  (.leaf #[0x2e8c2e8b2e8a2e892e882e852e822e812e7f2e7e2e7b2e7a2e782e742e732e722e702e6c2e6b2e682e672e662e652e632e612e5f2e5d2e5c2e5b2e5a2e582e57, 0x2ebe2ebc2eb92eb72eb52eb42eb32eb22eb12eae2ead2eab2eaa2ea92ea82ea62ea52ea42ea32ea22e9a2e992e982e972e962e952e942e932e922e902e8f2e8d, 0x2f462f452f442f432f422f412f402f3b2f2c2f2b2f2a2f292f282f252f212f1c2edf2edd2edc2edb2ed62ed52ed42ed22ece2ecd2ecc2ecb2ec22ec12ec02ebf, 0x2fbc2fbb2fb82fb72fb62fb42fb32f7e2f7d2f7c2f7b2f792f782f772f762f732f722f712f6f2f6e2f6d2f6c2f692f662f652f632f612f5f2f5b2f592f562f47])))
  ((.branch 4
  (.leaf #[0x310c310b310a3108310531043071306f306e306c306b306930682fd72fd62fd52fd42fd32fd02fce2fcd2fcc2fcb2fc92fc82fc72fc62fc42fc22fc02fbe2fbd, 0x319331923190318f318e318d318c3175316731663165315f315d315c315b315a31583157315631553154314c314b31313130312f312e312d312c31233122310d, 0x322c322b322932283227322532233220321e321d321c31ff31fe31fd31fc31fa31f931f831f731f631f031ef31db31d731ce31cc31c831c731b731b131953194, 0x325f325e325b3259325732563255325432513250324e324d324b324a32483247324632453244324332423240323f323d323c323b323a3239323632353233322d])
  (.leaf #[0x329f329a3290328f328d328c328b328932853283327f327d327c327a3279327832773273327232713270326d326c326b326a3269326832673266326532613260, 0x32f032ec32eb32e932e832e732e632e532e432e132e032df32de32dc32db32da32d832d732d632d532d032cb32ca32c932c832c732c632bf32bd32b932b732a1, 0x3330332f332e332b332933283327332633243323332233213315330933063304330333023301330032ff32fd32fc32fb32fa32f932f732f632f532f332f232f1, 0x3364336333623361335f335d335a33583357335633553354335333513350334f334e334d334c334b334a3349334733463344334233413340333f333533343333])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x339c339b339933953394339333923390338d338a338933883387338633853384338333813380337f337e337d337b337a3378337633753373336e336c33693368, 0x33d333d233d033cf33cd33cb33ca33c933c833c333c233c033bd33bc33bb33b933b833b733b633b533b433b233b133b033af33ae33aa33a833a533a433a3339d, 0x34b034af34a934a834953491347c3445343e343c34393430342534233422342134203419341734133412340f340e340b340633f433e033d933d833d633d533d4, 0x34fc34fb34fa34f934f834f634f534f334f234f134f034ef34ec34e634e534e434e234e134e034de34dc34d934d734d634d534b834b734b634b534b334b234b1])
  (.leaf #[0x354735433541353f353b35293528352735253524352335223521351d351c351a351935173516351535133510350e350a35083507350535043503350234fe34fd, 0x3583358235813580357e357d357c357a357935783577357235713570356f356d356c356b3569356835673566355d355c355b355a355835553554354f354d3549, 0x35bc35ba35b835b635b535b335b135af35ad35ac35ab35aa35a835a735a235a0359c359a359935973596359535923591358d358c358a35893588358735863585, 0x35f035ef35ec35eb35e935e835e735e635e435e335e235e135e035db35da35d935d735d535d335cf35cd35cc35ca35c935c835c535c435c235c135bf35be35bd])))
  ((.branch 4
  (.leaf #[0x3629362836263624362336223621361d361c361a361836173615360636053604360336023601360035ff35fe35fd35fc35fb35fa35f835f735f635f535f435f1, 0x3679367836763674367336723671366a3667366636653663365f365e365d365c365a365836553653365236513650364f364e364a3642362f362e362d362c362b, 0x36d036bb36ba36b636a936a736a536a436a336a236a1369e369d369a36993698369736953694369236913690368f368e368d368c368b368a367e367d367c367b, 0x36fd36fc36fa36f836f736f536f336f236f036ef36ec36eb36ea36e936e836e736e436e336e136e036de36dd36dc36db36da36d936d736d636d536d336d236d1])
  ((.branch 2
  (.leaf #[0x376a375d375c375a375837573752374d374b3749374637453742373e373637313730372f372d372c3713371237113710370d370c370a370537033702370136fe, 0x38673866386538643860385e38543852384e3849384738443843383337953794379337923790378f378e378d378c378837863784378337823781378037783777])
  (.leaf #[0x39543953395238f738f338ed38ec38dd38d138b538a2389f389d3898388838823881387f387c387b38783877387638753873386f386e386d386c386b386a3868, 0x39b939b839b539b439b039af39ae39ad39a739a5399f399e399b398e398d398c398a39843981397f397c397b39793960395f395d395c395b3959395839573955, 0x39f839f739f639f439f139f039ed39ec39ea39e739e639e539e439e339e239df39dd39d939d739d439d339d139d039cb39ca39c839c739c439c339c239c139c0])))))))))))
  ((.branch 33
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x3a3a3a393a383a373a303a2f3a2e3a2d3a2c3a2a3a273a263a233a223a203a1f3a1e3a1d3a1b3a193a153a143a113a103a0e3a093a083a053a0339ff39fd39f9, 0x3a833a823a813a803a793a763a753a743a723a6e3a6d3a6c3a6b3a693a673a643a623a613a603a5f3a5e3a5d3a593a513a453a443a433a423a413a3f3a3e3a3c, 0x3afe3afd3afc3afb3af83af73af63af43af33af13af03aef3aee3aed3aec3ad43ad33ad23ad13ac63ac43ac03abf3abe3aba3a8d3a8c3a8b3a8a3a883a873a85, 0x3b333b313b2f3b2c3b2a3b293b283b273b263b253b1d3b1c3b1b3b1a3b183b173b163b143b133b123b103b0f3b0d3b073b063b053b043b033b023b013b003aff])
  (.leaf #[0x3b6b3b6a3b663b653b643b633b623b603b5f3b5e3b5b3b5a3b573b563b543b523b4f3b4d3b4a3b493b483b453b443b423b413b3d3b3c3b393b383b373b353b34, 0x3bdc3bc73bc63bc53bc43bc23bc13bc03bbe3bbd3bbc3bbb3bb73bb33bb03baf3ba13b9f3b903b8f3b803b7e3b7c3b7b3b7a3b793b753b743b713b703b6f3b6e, 0x3c763c753c743c733c723c713c703c6f3c6e3c6d3c6b3c693c683c673c663c443c433c423c333c2f3c2e3c253c243c1a3c143c123be63be53be33be23be13bdf, 0x3ca63ca53ca33ca13ca03c9f3c9e3c993c983c973c963c953c943c933c923c913c903c8f3c8e3c8c3c883c873c863c853c833c803c7d3c7c3c7b3c7a3c783c77])))
  ((.branch 4
  (.leaf #[0x3d353d333d323d313d303d2e3d2d3d2c3d2b3d2a3d293d283d253d243d233d203d1f3cd43cc53cc33cc03cbf3cb33cb23cb13cb03cae3cac3cab3caa3ca93ca8, 0x3d7b3d7a3d773d763d743d733d6f3d6e3d693d5e3d5d3d5c3d5b3d5a3d563d543d523d513d503d4f3d4b3d4a3d473d463d453d443d423d3e3d3d3d3c3d393d38, 0x3e093e073e053e043e033e013e003df33df23ded3dea3dde3dd83dd73dd63dd53dd13dd03dce3da93da73da53da33d9d3d9c3d9b3d973d913d813d7f3d7d3d7c, 0x3f663f653f5a3f3d3f3a3f2b3f2a3f283f273f073f063f023f013eff3efd3efb3ef93ef83ef73ef63ef53ef33ef23ef13ef03eed3eec3e803e3a3e393e383e37])
  (.leaf #[0x3ff63ff23ff03fef3fed3fec3feb3fea3fe33fe23fe13fe03fde3fdd3fdc3fdb3fda3fb63f9e3f9d3f9b3f993f973f933f923f913f8f3f8e3f8c3f8b3f7a3f67, 0x4061405d404340424040403d403b403740364035403340324030402f402a40294027402640254024400f400d400b400a4009400840073ffe3ffd3ffc3ffa3ff8, 0x40e740e640e440e340e040df40dd40dc40db40d940d740b2408e4086408540834082407d407940784077407640754073407240714070406f406b406940654064, 0x414c414b41484144413f413e4137413641334132412d41194113411241114110410d410b410341024101410040ff40fe40fc40fb40f940f740f640ee40ec40e8])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x4414441344114410440f440e4404440243fe43fd43ab438742fc41ce41a7417441734172416f416b41664163415a415941564155415341524150414f414e414d, 0x4460445f445d445844574456444f443e443d443944354434443344324431442f442e442d442c442b44284427442544244423441f441e441c441a441744164415, 0x44d344cf44ce44c444bd44bc44bb44a244a144a0449f4499449844974496449544914490448f448e448d448c448a4489448544834480447f44714470446f4461, 0x456845654562453545344533453245314530452f452e452d4517451544fe44fd44fa44f944f844f644f444f244f144f044ef44ed44e444de44dc44db44da44d5])
  (.leaf #[0x466a46684667466646654664466346184617461646154613461246114610460f460e460d46094608460745ef45ee45ec45eb45ea45e9458e458c458b456d456c, 0x46bf46b046ad469646954694469346924691468f468e468d468c468b46884687468546834681467d467c467b4679467846774676467346724670466f466d466b, 0x47414740473f473e473d473c473a473947384737473647354732471e471a46fc46f646f346f146ed46eb46d246d146cf46ce46c746c646c546c446c346c146c0, 0x479b479a47974796479447924791478f478e476e476d47624761475e475d475c475b4759475847574755475447534752474e474d474847474746474547444742])))
  ((.branch 4
  (.leaf #[0x47d747d647d547d447d347d147cf47cd47c947c747c547c447c247c147c047bf47be47ba47b747b647b547b447b247b147b047af47ae47a947a747a347a2479c, 0x48b348b248b148ab48aa480d480c480a480948084807480648054804480247f047ef47ed47ec47eb47ea47e947e847e747e647e547e447e347de47dc47db47da, 0x49314930492e492d492c492b49294928492649224921491c491b491949154914491349124910490e490b490949084907490649044901490048fd48fb48f648f5, 0x496c496b4966496549634960495f495e495c4955495449534951494d494c494b494a49484945494249414940493f493e493d493c493b49394938493749364935])
  ((.branch 2
  (.leaf #[0x49fe49fd49fc49f949f849f649ed49dd49b449b349b249b149ac49ab49a349a1499e499d498449814980497a49794978497749764975497349724970496e496d, 0x4bcf4bce4bcb4bca4bc84bc74bba4bb84bb64bb24bad4b664a3f4a344a334a324a314a304a2d4a294a284a1b4a184a174a0f4a0b4a0a4a084a054a014a0049ff])
  (.leaf #[0x4c034c014bff4bfc4bfa4bf94bf84bf74bf34bf24bf14bef4bed4bec4beb4bea4be94be84be64be54be24be14bdf4bdd4bdc4bdb4bda4bd94bd64bd54bd44bd0, 0x4eb54eb34eb14eb04ead4eac4eab4ea84ea74e794e6d4e6c4e654e274c644c634c624c614c5f4c5e4c5d4c5b4c5a4c594c584c544c534c094c084c074c054c04, 0x4f014f004eff4efe4efd4ef84ef74ef64ef44ef34ef24ef04eee4eeb4ee94ee84ee74eca4ec94ec84ec74ec54ec44ec34ec24ec14ebf4ebe4ebd4ebc4ebb4eba])))))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x4f3f4f3d4f2b4f2a4f284f274f264f254f244f234f224f214f204f1e4f1d4f1b4f194f184f174f164f114f104f0e4f0c4f0b4f0a4f094f084f074f064f044f03, 0x51a851a651a551a451a3519f519e519d518c518b518a51895188518750c050bf50ba50b250854fc04f4d4f4c4f4a4f494f484f474f464f454f444f434f424f41, 0x520051fd51fc51ed51ec51ea51e851e751e551e451e351e251cd51cc51c751c651bf51be51bd51bc51bb51b851b751b651b551b351b251b151af51ae51ad51ac, 0x525f525e525852555250524f524d524c524b52485247524452425240523e523c523852375234523352325231522f522e522d522a5229522752265224521e5207])
  (.leaf #[0x52e652e552e252e052df52da52c252c152c052bf52bd52bc52ba52b952b552a952a852a752a652a552a352a252a0529f529e529d527d527c5278527752765275, 0x53465343533e533d533c53385337533653355334533353325330532e532d532a5329532853155314531353075306530452fd52fc52f352f252ef52ee52ed52e7, 0x566f566d5665563956385637563556345620561f561c561b55e655e553d253c853c653c353c253c1538653705366535b5359535553545353534e534d534b534a, 0x56d556d456d356d256cf56cb56ca56c956c856c056bf56be56bd56bb56ba56a0569f56975696569556945693569256915690567b567a56785677567356725671])))
  ((.branch 4
  (.leaf #[0x5712570c570b570a570957085707570657055704570356fe56fc56f956f856f556f456ee56ed56ec56eb56e356e256e156e056df56db56da56d956d856d756d6, 0x579c579b578b577e577c577b57775776577557745773577257715770576f576057585757573a573757365724572357215720571f571e571a5719571757145713, 0x57fc57fb57f857f757f657f557f357f257f157ef57ee57ed57ec57e857e657e257e157dd57d457d257cf57ce57cd57cc57cb57ca57c857c457c357c2579e579d, 0x58ad58a958a758a558a458a358a2589e589d585258515850584e581a5819581858165815581458125810580d580a5809580858075806580558035802580157ff])
  (.leaf #[0x59445940593f593e593d593b593a5939593859315926592158ee58e258e158e058d058c658c558c358c258c158b958b858b758b658b458b358b258b058af58ae, 0x59b259b059af59ae59ad59a859a4599b5999598e598b598a59895980597f597d597a59795978595c595759545953594e594d594c594b594a5949594859475945, 0x5a7e5a7d5a465a455a365a345a305a1e5a1a5a195a185a055a0459f359f259f159ef59ee59ec59ea59e959da59d859d659d559d459d359ce59cd59c659c359b4, 0x5ae55ae45ae35ae25ae05adf5ada5ad95abd5ab05aaf5aae5a995a985a955a945a935a915a8f5a8e5a8d5a8c5a8b5a8a5a895a875a865a855a845a835a815a80])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x5d0f5d0e5d0d5d0c5d095d065d055d045d035d025d015cf85cf75c5e5c535b005aff5afe5afd5afc5afb5afa5af95af75af65af55af35af25aef5aed5ae95ae8, 0x5fc95fc85fc65fc55fc45fc35fc25fc15fc05fbf5fbe5fbc5fbb5fba5fb95fb85fb75fb65fb45f435f405f3a5f395f385f335f315f305d175d155d145d115d10, 0x6093609260916090608f608e608c608b608a608960886084607d607c60716068600960085fdb5fda5fd95fd85fd75fd65fd55fd35fd25fd05fcf5fce5fcd5fcc, 0x61276126612561246123612261216120611f611a611961186117611661156114611360c060ba60b960b760a860a760a560a360a1609d609b609a609860976096])
  (.leaf #[0x6171616f616e616d616c616b616a61696168616661656163616261616160615f615a6159615861566155615461526150614d614b614a6149612c612b612a6129, 0x639f639e639d6398639763966394639363926390638e638b638963886387636b636a6368636461ab61aa6193619261816180617d617c617b617a617861776172, 0x64aa64a864a564a364a264a1648564846473647264716470644b644a64456444643e643d643c63e263e163ac63ab63aa63a963a863a763a663a463a363a163a0, 0x650a650965086507650565036502650164ff64fe64fc64fb64c664c564c464c364c264c164c064be64bd64bb64ba64b964b864b764b264b164b064ae64ad64ac])))
  ((.branch 4
  (.leaf #[0x65a965a865a765a565a465a265a165a0659f659e6599659865976595659465936591658f658c658a658965886529651b6519651565146511650e650d650c650b, 0x660f660e660d660c660b660966086606660566046603660265fd65fc65fb65f965f865f765f565f365f065ee65ed65ec65d465d365d065cf65ad65ac65ab65aa, 0x6646664566446643663d663c663b663a6638663666336632662d662c662b662a6628662566246622661f661e661d661c661b661a661966186614661366116610, 0x66756673667266716670666f666e666c666b666a666966676666666566646663665d665b6659665866576656665266516650664f664e664d664c664a66496647])
  ((.branch 2
  (.leaf #[0x697f695d6951694f693b693a66c166c066bf66be66bd66bc66bb66b966b866b666b566b466b366b266ac66ab66aa66a966a766a566a266a166916690668f6676, 0x6b7f6b7d6b7c6b7a6b796b786b736b706b6f6b6e6b6d6b6c6b6b6b6a6b686b676b656b646b636b626b616b5469b369b269ac6986698569846983698269816980])
  (.leaf #[0x6bbf6bbc6bbb6bba6bb96bb76bb66bb56bb36bb26bb16bb06ba96ba46ba36ba26ba16b9f6b9e6b9d6b9b6b9a6b996b986b8c6b8b6b8a6b886b876b866b846b82, 0x6eb86eb66eb56eb46e9a6e996bf26bf16bf06bee6bed6bec6bea6be96be86be66be26be16be06bdf6bdc6bdb6bd96bd86bd56bd46bd36bd16bd06bcf6bcd6bcc, 0x749d6fd66fd56f3c6f316ed96ed86ed76ed66ed56ed46ed36ed16ed06ece6ecd6ecc6ecb6eca6ec56ec46ec36ec16ec06ebf6ebd6ebb]))))))))))))))

def policyFixedCompact0Rename (i : Nat) : Nat :=
  (((policyFixedCompact0VariableTable.get 0 (i / 32)) >>> (16 * (i % 32))) &&& 0xffff).succ

def policyFixedCompact1ClauseTable : PackedNatTable.Table PackedNatTable.Block :=

(.branch 0x8e (
(.branch 71 (
(.branch 35 (
(.branch 17 (
(.branch 8 (
(.branch 4 (
.leaf #[⟨0x3e01e00e406e03501980c405e02d01580a404e025011008003c01c00d006002c014009004001c00d005802400e0050018004000000, 0x620067005a004b00610053005f005e00520058005b0056005b0054004a00500053004e0053004a004d004600490044003e000800070041003c003f0038003b002d00370036002c00300033002e0024002a002d0028002d0024002700200023001f001a001d00120019000e001900140017000f0011000a000d0006⟩, ⟨0x46022010808003e01e00e406c03401900c005a02a0140098048022010007803801a00b805402601100780340140080030010004000, 0xa900b700a700b500b400a600b000b300ac00b300ae007a001e001e007b00af00a800ab00a600ab00a200a5001e005d00a1009c0082009f008f009d0096009900940099009000930083009100900082008c008f0088008f001e0043008b00840087007e00810071007d007c00700074007900340007007700720068006e0071006c00710068006b00640067⟩, ⟨0x47022810808003e01e00e806e03501980c405e02d01580a404e025011808403e01c00d006002a013008803c01a00a0038010004000, 0xfa00ff00fe00fb00fd00fc00f000ef00fb00fa00ee00f600f9001e00c700f500f000f300ee00f300ea00ed00db00e900e800da00e200e500e000e500dc00df00d300dd00dc00d200d800db00d400db001e009b00d700ce00d100cc00d100c400a700cb00b300c900c800b200c200c500ba00c500c000bd00c300be0007007b007a000700bf00b600b900b400b9⟩, ⟨0x4d025812408c04302000f807803a01c00d406603101780b4056029013008c04001e00e006802e014008803c01a00b0048018006000, 0x1400145013e0145013a0116013d013c0116013b01360117013d0127013b013a012601340137012e0137013201310135012a012d0128012d0119012b0117012901240127011c01270122011f0125012000e6001e001e00e701210118011b0116011b01120115010e00ee0111011000ee010f010a00ef011100f9010f010e00f80108010b0100010b0106010301090104000700c700c600070105⟩]) (
.leaf #[⟨0x4f026812808e045021010007a03b01c00d006402f01600a404c024010807c03a01b00c805802801200800380180090030010004000, 0x1a701a901a2017c01a5019e019501a1018f019f01960194019901930195018e018c0191017d018d01820189018b01840180017c018701830185017e017d0183016801730179017201710175016c016a016f0169016b01620165016701020163015e016101520161015d015f010c0007015b0156015901540159014901570147015501510153001e010d014f001e0139014d0148014b0146014b01420145⟩, ⟨0x520278134094048022810807e03d01d00dc06803101700b0054027012808804001e00e006802e014009003c01800a0038014006000, 0x21e021c02210163021d0218017a021b021702190206020d0215020c01ec020f020801c4020b0207020901de01e7020501f601f501f901ee01f101f301ea010d01ef010c01eb01ef01eb01ed015a01eb01e601e401e9010d01e501e001d801e301df01e101dc01d4017b01db01da017a01c801d101d301cc01ca01cf01c901cb01b801c101c301bc01ba01bf01b901bb01b201a901b501a301b301ae01aa01aa01a801ad⟩, ⟨0x540288134096048022810807e03c01c80dc06a03301800b4056028012808804001e00e0068030015009804401c00b0040014006000, 0x25e026502670260025c02580263025f02610258025b025f025202550257010c024f0253024e010d0253024e024302510242024f0251024e01110110024f023f024d02460249024b0244023c024700f802450242023e0241023c023f02430242023d023f0240010f023e00ef00ee023f010a023d023a01010232023702390236010902330235023001620233022801630233022a022d022f01c60229022b022801070216021f0227⟩, ⟨0x56029814409c04c024011808604001e80ec07003401900c005a02a013809404401f00e006802e014008803c01800a0038014004000, 0x2ea02e802ed02d902e902e402a202e702e302e502de02d802bc02e102dd02df02d802bc02dd02da02d902dd02d402cd02d702bf02d502cc02c702d102c202c002be02c502bd02c302bb02c102a602b102b702b002af02b302aa02a802ad02a702a9028c0295029f0294010c02970290028e0293028d028f027c0285028b0284025802870280027e0283027d027f02780271027b026b0279027001d40273026f0271026a0268026d02590269⟩]))) (
(.branch 4 (
.leaf #[⟨0x54028813c09804a023810c08203e01d80e406c03301880b8058029013809004201f00e006802e014009003c01a00a0040018006000, 0x36a0368036d03670369036203600365035103610356035d035f035803540350035b03570359035203510357034c034a034f0349034b0344033a03470340033b03430321034103360319033903270337032603240329031f03250320031e0323031a0318031d03180316030e03130315030f03110304030d030f030c0305030f0305030b030603040309030202a202dc02ff030102fe00f702fc02fa02f402f702f902f202db02f5⟩, ⟨0x55029013c09a04a024011808804101f00ec07003601980c405c02b014009404602100f0070032016009804001a00a0038014004000, 0x3da03e303e503de03dc03e103db03dd03d603d403d903d303d5030d03d103d0030c03ba03c903cf03c803c503cb03c403c303c703be03bc03c103bb03bd03b602e503b902eb03b7032e02d803b303ae03a403b103a203ab03ad03a603a403a903a303a5000403a1039c039a039f0399039b034803910397039003500393038c01ca038f03760385038b0384038103870380037f0383037a0378037d0377037903720369037503630373⟩, ⟨0x55029014009a04a023811008404001e80e806e03401900bc058029013809004402000f006c030015009804401c00b0040014006000, 0x46204600465045f046104480457045d045604530459045204510455044c044a044f0449044b04460444042e043d0443043c0439043f04380437043b043204300435042f043103980427042d0426030a0429042203d5042503070423041a0404041d0345041904150417041604140402040d0413040c040b040f040604040409040304050002040103ea03f903ff03f803f503fb03f403f303f703ee03ec03f103eb03ed03e603dc03e9⟩, ⟨0x5902b81500a204f026012808e04302080f807603801a80cc06002d01580a004a02200f8070032016009804401c00b0040014006000, 0x4f104f304e404ed04ef04e804e604eb04e504e704e004d904e304cb04e104d804d304dd04ce04cc04ca04d104c904cf04c204c504c704c004bb04c304bc04ba04bf04b604b404b904b304b504ae04ad04b104a804a604ab04a504a704a0044a04a3049c0430049f04960460049903d203070495047e048d0493048c0489048f04880487048b048204800485047f0481047a03ec047d0476046c0479046a04730475046e046c0471046b046d045e04670469⟩]) (
(.branch 2 (
.leaf #[⟨0x5a02b814c0a204e026012408c04302080fc07803a01b80d406402e01600a404a02200f8070032016009804401e00c0048018006000, 0x570057705790572056e056c05750571057305680566056b056505670554055d0563055c0530055f05580556055b05550557054e054a054a0548054d05470549054205400545053105410536053d053f053805340530053b0537053905320531053703d003100304052f052a0480052d052604b405290522051205250510051b0521051a0519051d0514051205170511051304c1050b050604a6050904f004ff050504fe04fb050104fa04f904fd04f404f204f7⟩, ⟨0x55028813c098049023811008403f01e00e406c03401880b8058029013009004201f00e006802e014008803801800a0038014004000, 0x5ec05e802fc05ef05eb05ed05e802fb05eb05e402a005e705e305e505de05d905e105d505df05d802b805db05d401ea05d705c805d105d305cc05ca05cf05c905cb05a805a505c705c205bd05c505b905c305bc05b605bf05b8059805bb05b005ac05ac05aa05af05a905ab05a405a205a7059905a3059c059f05a10598059b059d0564059105970590056c05930569058f0588058405840582058705810583057c057a057f056d057b⟩]) (
.leaf #[⟨0x550290138098049023811008403f01e80e806e03501980c005802a013809404602000f006803001600a004401c00b0048018006000, 0x65e066506670660064201d60663065f066106580651065b064b0659065006340653064f0651064a0648064d06430649064406420647063e063c0641063b063d06360634062a06310633062c0628060e062f062b062d0622061d0627061906230160061b061806160614015c061706120610060c061506070613060f0611060b060d060605f9060905e205fd060505fc05fa05ff05f505fb05f805f405f705f805e905f505ea05f105f3⟩, ⟨0x530280134094047022810c08203e01e00e406e03401900c005a02b014009804802100f006c030016009804001c00b0048014006000, 0x6ce06cc06d106c606c906cb06c2049b06c7049a06c306c706c306c506c20147014606c306be06bc06c1015806bd06b8069a06bb06b706b906b206a906b5067506b306ab06af06aa06a806ad06a706a906a2067f06a5067b06a30681069d0684069306990692068f0695068e068d069106880686068b068506870680067e0683067a0678067d0673067906740672067701440673066e066a060a0671066d066f060a0669066d⟩, ⟨0x5802a81480a004d025011c08804201f80f007403701a00c405e02c015009c04602100f006c030015009804001a00b0040014004000, 0x7580757075b075207500755074f075107360745074b0744074107470740073f0743073a0738073d07370739072a07330735072e072c0731072b072d0726071c0729071a07230725071e071c0721071b071d0716070f071907010717070e07090713070407020700070706ff070506e806f706fd06f606f306f906f206f106f506ec06ea06ef06e906eb06dc06e506e706e006de06e306dd06df06d606d906db06cc06d506d706d406cd06d706cd06d3⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x540280138096049023011008403f01e00e806e03501900c005a029013809004201f00e006402e015009004001a00a0040014006000, 0x7d407d007ce07d707d307d507c807c307cb07b707c907c207bc07c507c107c307be07bc07a807a507bb07b6079207b907b007ac07ac07aa07af07a907ab07a407a207a7079307a30798079f07a1079a07960792079d0799079b079407930799078e078c07910787078d07880786078b078207800785077f0781077c077a07760774077907730775076e07660771076a0768076d076707690762074c076507610763074e0759075f⟩, ⟨0x56029814409c04c024811808804101e80ec07003601980c005c02b014009404402000e8068030016009804001a00b0040014006000, 0x864084c086708630865085e085708610853085f085608500859085208380855084e084c08420849084b084408400838084708430845083c083a083f0839083b082c083508370830082e0833082d082f0814082308290822081f0825081e081d082108180816081b08150817080808110813080c080a080f0809080b07f507fb07f607f407f907f007ee07f307ea07e307ed07df07eb07e207cc07e507de07dc07e107cf07dd07d207d907db⟩, ⟨0x55029814009a04b024011008403f01e00e807003601980c005a02b014009404402000e8068030016009804001c00b0038014006000, 0x8c508d308ca08c808cd08c408c208c708b308c308b808bf08c108ba08b608b208bd08b908bb08b208b508b908b408b308b908b608b408b200d300d208b308a008ab08b108aa08a908ad08a408a208a708a108a3089c0892089f08900899089b08940892089708910893086e07f4088f088c07f5088f088a0875088a087308740872088b0886087f088908710887087e087908830874087208700877086f0875086d08730862083d086b⟩, ⟨0x54029013c09a04a023811008203f01e00e406c03301880b8056029013809404401f00e806802e015009004001a00b0048018006000, 0x9330935092e01a809310923092d092801ba092b092201940925091e06500921091a063d091d0645091b063c02a4091705f409130915091205f50915090a090f0911090b090d09060903090b09020907090b09070909090309050904090208f608ff090108fa08f808fd08f708f908f2082e08f508ee08e908f108e308ef08e8077a08eb08e708e908e207fa08e5078f08e108de082a08da08a208dd08d606de08d908d208c908d5⟩]) (
(.branch 2 (
.leaf #[⟨0x5702a014409c04b024811808604001f00ec07003601980bc05a02a013809404402000f007003201700a004401c00c0048018006000, 0x9a409a709a909a2099d09a5099e099c09a109980996099b099509970990098609930984098d098f09880986098b09850987097809810983097c097a097f0979097b096e097509770970096c09620973096f09710962096b096f096a0963096f096c096a096609640969096309650962014901480963095e095c0961095b095d094809530959095209510955094c094a094f0949094b0932094109470940093d0943093c093b093f093609340939⟩, ⟨0x5802a814c0a004c025011c08804101f00ec07203501980c005c02c014809804602000e806c030016009804001c00b0040014004000, 0xa460a3f0a490a330a470a3e0a390a430a340a320a000a370a2d0a350a2e0a2c0a3109f80a130a230a120a080a150a0c0a0f0a110a020a090a0d0a090a0b0a040a0009fe0a070a030a0509fa09f409fd09f909fb091f09f7095a096709f309d809e709ed09e609e309e909e209e109e509dc09da09df09d909db09d409c209d709a309cf09ca09c909cd09c409c209c709c109c309aa09b909bf09b809b509bb09b409b309b709ae09ac09b109ab09ad⟩]) (
.leaf #[⟨0x5902b014c0a004e025812008a04202000f407403701a80c805e02c014809c04802100f007003201600a004401c00b0048018006000, 0xad2094a0ad50ace0ab00ad10aca0a6a0acd0ac80a840aae0abd0ac30abc0ab90abf0ab80ab70abb0ab20ab00ab50aaf0ab10a9c0aa70aad0aa60aa50aa90aa00a9e0aa30a9d0a9f0a860a950a9b0a940a910a970a900a8f0a930a8a0a880a8d0a870a890a800a760a830a740a7d0a7f0a780a760a7b0a750a770a680a710a730a6c0a6a0a6f0a690a6b0a6409340a670a6009da0a630a5c03bc0a5f0a270a5b0a560a0a0a590a1a05fa0a530a4e05f40a51⟩, ⟨0x5802a814809e04d025011c08804101f80f007203601980c405c02b014009404602100f006c032016009804401c00b0040018006000, 0xb600b5d0b630b5c0b5b0b5f0b560b540b590b530b550b3a0b490b4f0b480b450b4b0b440b430b470b3e0b3c0b410b3b0b3d0b220b310b370b300b2d0b330b2c0b2b0b2f0b260b240b290b230b250b0c0b1b0b210b1a0b170b1d0b160b150b190b100b0e0b130b0d0b0f0b050b0b0b060b040b090b000afe0b030afd0aff0af00af90afb0af40af20af70af10af30aec0ae20aef0ae00ae90aeb0ae40ae20ae70ae10ae30ada09960add0ad60a880ad9⟩, ⟨0x5702a814809e04c025012008a04201f80ec07203701a00c405e02c014809804602100f006c030015009804001c00b0040014006000, 0xbdd0bdf0bd80bce0bdb0bcc0bd50bd70bd00bce0bd30bcd0bcf0bca0bc80bc40b0e0bc70bc00b240bc30bb60bbd0bbf0bb80bb40bb20bbb0bb70bb90bb00b9e0ba40bad0baf0ba80ba60bab0ba50ba70ba00b540ba30b9a0b3c0b9d0b8e0b970b990b920b900b950b8f0b910b880b8b0b8d0b7e0b870b890b860b7f0b890b820b800b850b7f0b810b7a0b500b7d0b790b7b0b740b6a0b770b680b710b730b6c0b6a0b6f0b690b6b0b520b610b67⟩]))))) (
(.branch 4 (
.leaf #[⟨0x530288138098049023811008404001f00f007203501980c005c02c015009c04802100f807003401700a004401c00b0048018006000, 0xc390c490c420c3d0c470c3b0c430c3a0c380c3600aa0c390c340c320c370c250c350c310c330c3000a700a60c310c260c2d0c2f0c280c240c220c2b0c270c290c200c250c270c2400a900a80c250c220c200c0e0c190c1f0c180c170c1b0c120c100c150c0f0c110c0a0c080c0d0c070c090c020b7e0c050bfe0b900c010bec0bf70bfd0bf60bf50bf90bf00bee0bf30bed0bef0be80bde0beb0bdc0be50be70be00bde0be3⟩, ⟨0x530280134094048022810c08003c01d00e006c03401880bc05802a013809004201e00e006802c014009003c01800a0040014006000, 0xcca0cc30ccf0cc20cc10cc50cbc0cba0cbf0cb90cbb0cb40cad0cb70ca10cb50cac0ca70cb10ca20ca00c9e0ca50c9d0c9f0c9c00cf0c990c9b0c9800cd0c940c920c9700d00c930c8e0c8a0c910c8d0c8f0c720c810c870c800c7d0c830c7c0c7b0c7f0c760c740c790c730c750c6f0c710c6a0c660c620c6d0c690c6b0c650c6707f40c5f0c610c5a0c560c5d0c590c5b0c530c570c520c500c550c4f0c510c4a0c480c4d⟩, ⟨0x5802b014c0a004d025012008a04201f80f007203601a00c805e02c014809804802200f807003201600a004401c00b0040018006000, 0xd550d570d3e0d4d0d530d4c0d490d4f0d480d470d4b0d420d400d450d3f0d410cf00cf90d3d0772076f0d370d2e03780d310d2a0d200d2d0d1e0d270d290d220d200d250d1f0d210d1c0d1a0d140d170d190d1207670d150d0e07740d110d080d030d0d0cff0d090cf70d010cfe0cfc0cf608c206d20cfd0cf80cf60cfb0cf20c880cf50cf10cf30c8c0c950cef0ce40cda0ce70cd80ce10ce30cdc0cda0cdf0cd90cdb0cd408f80cd70cb80ccb0cd3⟩, ⟨0x520278134096048022810c08003d01d00e006a03301800b4056028012808c04001e00d806002c014008803801800a0040014006000, 0xdc40dc20dc70dc10dc30dbc0dba0dae0db70db90db20db00db50daf0db10d9c0da70dad0da60da50da90da00d9e0da30d9d0d9f0d940d990d9b0d950d970d8a0d930d950d920d8b0d950d8b0d910d8c0d8a0d8f0d8608060d890d850d870d800d7f0d830d7d0d810d7c0d6208b20d760d710d7b0d6d0d770d5d0d6f0d6c0d6a0d5c0d680d640d6b0d670d690d630d650d6200dd0d5e0d5c0d6100de0d5d0d580d560d5b⟩]) (
(.branch 2 (
.leaf #[⟨0x5802b014c0a004d025011c08804201f80f007203601980c005a02a014009804602000e8068030015009003c01a00b0048018006000, 0xe470e530e4a0e2c0e4d0e460e440e490e2e0e3d0e430e3c0e390e3f0e380e370e3b0e320e300e350e2f0e310e280e060e2b0e240dec0e270e2008160e230e1c0db00e1f0e160d9e0e190e040e0f0e150e0e0e0d0e110e080e060e0b0e050e070e020e000dea0df90dff0df80df50dfb0df40df30df70dee0dec0df10deb0ded0de40dda0de70dd80de10de30ddc0dda0ddf0dd90ddb0d930dd70dd60d920dc00dcf0dd50dce0dcb0dd10dca0dc90dcd⟩, ⟨0x55029814009c04b024011408404001e80ec07003601980c005a02a013809004401f00e006402c014009004001c00b0048018006000, 0x920eab0ea60ea40ea90ea30ea50e8a0e990e9f0e980e950e9b0e940e930e970e8e0e8c0e910e8b0e8d0e860e840e890e830e850e7a0e7f0e8100e70e7d00e60e770e7b0e7600e70e7b0e760e6d0e790e6c0e770e790e700e730e750e6e0e680e7100da0e6f0e6a08b20e6d0e6c08b20e6b0e6808b30e6d0e6c08b30e690e6a00e900e80e6b00e40e690e6600e30c680e630e650e6200e10d540d5f0e610d840d8d0e5b0e520e4b0e55⟩]) (
.leaf #[⟨0x510278130092046021810407c03b01c00d806803201780b4054027012008403e01c00d006002c013008803c0180090038014006000, 0xf090f0b0f020f050f07009a0eff0f030efe009b0f030efe0ef70f01009e0eff0ef80efb0efd0ef40ef20ef90ef60ecb0ef500980ef5008e0ef30ef0008d0eec0eeb0eef0eea00890ed40ee30ee90ee20edf0ee50ede0edd0ee10ed80ed60edb0ed50ed70ea20ead0ed30ecb0ecd0eca008300820ecb0ec40ebf0ec90ebb0ec50eab0ebd0eba0eb80eaa0eb60eb20eb90eb50eb70eb10eb30eb000910eac0eaa0eaf⟩, ⟨0x520278130094048023010c08203e01e00e406e03401900c005a02b014009404401f00e8068030015009004001a00b0040018006000, 0xf580f750f7d0f740f600f770f5d0f730f6d0f6f0f6e0f6c0f640f690f6b0f650f670f620f530f650f530f610f5c0f5a0f5f0f590f5b0f540f520f570f52011901180f530f4e0f4c0f510f4b0f4d0f340f430f490f420f3f0f450f3e0f3d0f410f380f360f3b0f350f370f300ce80f330f2f0f310f2a0f1c0f2d0f220f270f290f230f250f200f1d0f230f1d0f1f0f180f160f1b0f150f170f080f110f130f0c0f0a0f0f⟩, ⟨0x530280138096049023011008203e01d80e006a03201800b4056028012808c04001d00d806402e014009003c01a00a0040014004000, 0xfec0fea0fef0fe90feb0fe40fdb0fe70fd50fe50fdc0fda0fdf0fd90fdb0fd409080fd70fd009060fd30fba0fc90fcf0fc80fc50fcb0fc40fc30fc70fbe0fbc0fc10fbb0fbd0fb60fb40fb90fb30fb50fae0fa00fb10fa60fab0fad0fa70fa90fa00fa50fa70fa40fa10fa70fa10fa30fa0011701160fa10f9c0f9a0f9f0f990f9b0f940f920f970f910f930f8c0f8a0f8f0f850f8b0f860f840f890f800f700f830f7f0f81⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x520280134096048022810c08003e01d80e006a03301800b4054028012808c04001e00d806402c01400880380180090038014004000, 0x106b106d106210601065105f10610f141057105d10560f1e10590f19105510500f3110530f2b1051103a1045104b104410431047103e103c1041103b103d0f4a0f5510390f7e0f87103510300f9310330f8d10311024101d102710171025101c0f6c101f101b101d101610141019100f10151010100e10130130100f0f981003100910020fa210050f9d10010ffc0fb50fff0faf0ffd0fb70ff70ff20feb0ff50fd10ff3⟩, ⟨0x55029814009c04b024011408604001e00e806e03401900c005a02a014009404402000e8068030015009804401c00c004801c008000, 0x10ea10e810e210e010e510df10e110cc10d710dd10d610d510d910d010ce10d310cd10cf10c010c710c910c210be109e10c510c110c310bc109f10c110b610ab10b910a710b710b010ac10ac10aa10af10a610a410a9109f10a510a0109e10a3109a1098109d10971099105e108f1095108e106610911063108d1088107d108b107710891082107e107e107c1081107b107d10761074107910671075106a10711073106c10681066106f⟩, ⟨0x55028813c09804a023811408203f01e00e406e03401900bc05a02b014009804602000f006c032016009804001c00b0048018004000, 0x115e115a11541161115d115f1152115b115d11581156114e114c1151114b114d1146111811101149111511471122111f1145113e11341141113d113f11381112113b11361134113011251133111f1131112a112611261124112911231125111e111011211116111b111d111711191114111111171111111310de1109110f110810ec110b110010e8110310ff110110fa10f810fd10ed10f910ee10f510f710f010ec10e610f310ef10f1⟩, ⟨0x530288138098049023011008203e01e00e406e03501900c005a02b014809804802100f0068030015009004001a00a0040014006000, 0x11da11d611d611d411d911d311d511ce11c011d111c611cb11cd11c711c911c011c511c711c411c111c711c111c311bc11ba11bf11b911bb11b011ac11ac11aa11af11a911ab11a4119911a7119311a5119e119a119a1198119d119711991192117c11951188118f1191118a1186117c118d1189118b1184117d11891180117e1183117d117f1176115a1179116e11561171116d116f11681166116b115b1167115c11631165⟩]) (
(.branch 2 (
.leaf #[⟨0x55029013c09a04a023811008203f01e00e406e03401880b8056029013009004201f00e006802e014008803c0180090038014004000, 0x125400e61257125011b61253124f12511234123d124d124212451247123a00e7124300e6123b1243123b1241123c123a123f123610ca1239123512371218121f1233122412231227121e12101221121a11b4121d1219121b1204120d1217009b1211120c120a120f00d6120b120611ee12091205120711f011fb120111fa11f911fd11f411f211f711f111f311b811e711ed11e611c211e911bd11e511e411bc11e011d511e311cf11e1⟩, ⟨0x56029814009c04b024011408604001e80e806e03501900bc05802a013808c04201e00d806402c013008803c01800a0040018006000, 0x12d212db12dd12d612d412d912d312d512cc12c212cf12c012c912cb12c412c212c712c112c312aa12b912bf12b812b512bb12b412b312b712ae12ac12b112ab12ad129812a312a912a212a112a5129c129a129f1299129b128c12931295128e128a12741291128d128f12881275128d1282127d1287127b1283127a1278126c12760ecc127912751277127400851270126e1273126d126f0086126d0e87126b124e12551269125a1259125d⟩]) (
.leaf #[⟨0x56029813c09a04a024011408403f01e80e406e03501900bc05802a013809404401f00e006802e015009004001a00b0040014004000, 0x134e135513571350134c0eca1353134f1351134a0ecb134f134c134a1346133a134913420e8c1345133c133a133f1339133b13341330132e1337133313350ea1132f0e821271132d12fc132113271320130613231301131f131612f4131913151317131013041313130a130d130f13081305130b13051307130012fe130312fd12ff113c113912fb12f612f41196119312f312f012ee0760076b12ed12e6075012e912e2073812e512de1296⟩, ⟨0x5602a014409e04c025011c08804101f00ec07003601980c405c02c014809804802100f006c032016009804001a00b0040014004000, 0x13d6007f13d213d013d5008013d11392139b13cf13c813a013c412d413c713c0136e13c313aa13b913bf13b813b513bb13b413b313b713ae13ac13b113ab13ad13a213a713a913a313a513a0139913a31399139f139a1398139d1394136a139713931395138e138413911382138b138d13861384138913831385136c137b1381137a1377137d1376137513791370136e1373136d136f135813631369136213611365135c135a135f1359135b⟩, ⟨0x5902b01500a204e025812408c04202000f807403801a80c805e02d015009c04802100f006c032016009804001c00b0048018004000, 0x144e14531455144f145111b21427144f143011b2144d14481441144b143314491440143b144514361434143214391429143714311435142c1428100e142f142b142d1428100e142b1426100f142b142a100f14271426013313400ea41425133813d3142314021415141d1414140d1419140c140b140f1406140414091403140513fe13f4140113f213fb13fd13f613f413f913f313f513ee13e713f113db13ef13e613e113eb13dc13da13d813df13d713d9⟩]))))) (
(.branch 4 (
.leaf #[⟨0x4e026012408c04402100fc07a03a01b80d006403001680a8050025011008003a01b00c805802801200800380180090030010004000, 0x14a914ab14a6149314a914a0149614a3149f14a1149414921488148d148f0139148b0138148514891484013914891484147b14871484013d013c1485147e14811483147c1466147f0126147d147a0fa01479147a0fa114671478013b1472146d1477146914731465146b146814661464146601370136146714611463145d145f145c012f1456142b145b142a1457145b145714591456013501341457⟩, ⟨0x55029814009a04b024811808804101f00f007203701a00c805e02d015009c04a02200f807003201600a004401c00c005001c008000, 0x1525152b1526152415291520151c1523151f1521151a151815141512151715111513150c1504150f15081506150b15051507150014fe150314fd14ff14f814f114fb14eb14f914f0149814f314ef14f114ea14e214ed14e614e414e914e314e5149e14d914e114d814b614db14c2149014d714ce14c414d114ca14c814cd14c514c914be14b614c114ba14a414bd14b914bb14b314b714b414a714b314a814af14b114aa14a6149414ad⟩, ⟨0x5702a014009a04a024011408203f01e80e807003501900c005a02a013809404401f00e006802e015009004001a00b0040014006000, 0x15a2153f1573159e1578157215a1157e1574159d15981591159b158315991590158b1595158615841582158915811587157f15851576157b157d15771579157215751577157415731577157201231560156b1571156a1569156d15641562156715611563151e1527155f1530152d155d1554154d155715471555154c1518154f154b154d154615441549153f15451540153e1543011e153f0fe80fd1153915341532153715311533152c152a152f⟩, ⟨0x530288138098049023811008203e01d80e406c03301880b8056029013809004401f00e806802c014009004001a00a0040018006000, 0x15091615160e149a1611160d160f16081513160b150d160915e615ef160315f415f315f715ee013815f115ea15e815ed15e715e915c215cf15e515da15d515df15d315db15d215ca013815ce15cc15d115cb15cd014c15cb15c615c415c915c315c515bc15b715c115b515bd15b415b2147c15b015ac15a615b315af15b115ab15ad15aa011d15a415a315a915a215a515a915a515a715a401251580153e15a31572153f15a3⟩]) (
(.branch 2 (
.leaf #[⟨0x55028813c098049022810c08003d01d80e006c03301880b8056029013809404602000e006802e015009004001800a0040018006000, 0x168816841504168b168716891680151216831676167d167f167816741656167b16771679164e16591673166c1665166f165f166d16641646166716631665165e165c16611657165d16581656165b165216501655164f16511645164d164c1644164a1648163a16411643163c16381620163f163b163d1632162d1637162b1633162a162816260150162916241622161e16271619162516211623161d161f161814b5161b1614160f1617⟩, ⟨0x5a02c01540a6051027012c09004502180fc07a03a01b80d006402f01600a004c0230100074032016009804001a00b0040018006000, 0x14a16fb16f616f016f916f516f716f116f316da16e916ef16e816e516eb16e416e316e716de16dc16e116db16dd16d616d2161c16d916d516d7161c16d116d50fd80fd516cf160c150916cd16ca16c616c614fe16c916bc16c316c516be16ba14e216c116bd16bf16b814e316bd164414f016b714ee14eb16b5090c0906090416b116aa0fda16af169816a316a916a216a116a5169c169a169f1699169b1510150d1695168116931648160e16911686168d168f⟩]) (
.leaf #[⟨0x5902b014c0a004c025011c08804201f80f007203601a00c405c02c014809804602000f0068030015009804001a00b0048018006000, 0xc5e0c63178b1770177517891778177d17851780177c0c701783177f1781173c1779177b1774173e177717711773176c1748176f1752171b17691756172c1759175217491755173517531744173c17471740173e1743173d173f1734172a1737172e17311733172a1725172f1724172b172f172b172d17261722171e172917251727171a12e0171d1719171b16f416fd1717170c170717111703170d16fb17051702170016fa096406c4170116fc16fa16ff⟩, ⟨0x530288138096048023010c08203e01e00e406c03401900b8058029013809004401f00e806c030015009804001a00a0038014004000, 0x180d180f17b817ef180d17e617f1180b180417fd180717f7180517fc17e217ff17fb17fd17f617f417f917ef17f517f017ee17f317ea17e817ed17e717e917e417e217de11c811c017e10f8717dd17d80f8117db101117d917d017c317d317bf17d117be101417c117bc17b617ba17b817aa17b317b517ae17ac17b117ab17ad179417a317a917a2179f17a5179e179d17a117981796179b179517971790178e1793178d178f⟩, ⟨0x5902b01500a404f026012808e04402080fc07803901b00d006202e01600a404c023010807c03801900b005002200e005001c008000, 0x11d211cf188f1843188d1883188b188617ac1889188211ba18851880186a186e1879187f18781877187b187218701875186f1871185818631869186218611865185c185a185f1859185b184e11d41851184a1848184d18471849184217fc1845183e18261841183a17e9183d17f1183b183817ea17c217b6183717dc17c3183510301827182f182518270f90101118230fb20faf181d16ac0fa80fa0181b1816169a1819180c18131815180e17ee17ba1811⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5702a814809e04c024811808804201f80f407403801a80c405e02c014809c04a022010007403601800a004801e00c0048018006000, 0x1903191119061854190919020e7c190518f218fb190118fa18d018fd18f618f418f918f318f518ec18e818e818e618eb18e518e718e018de18e318d118df18d418db18dd18d618d218d018d918d518d718cc18a218cf18c818c618cb18c518c718be18ba18ba18b818bd18b718b918b218b018b518a318b118a618ad18af18a818a418a218ab18a718a91846189b18a1189a1240189d088e0e6718991856086c18971890189318951856088d1891⟩, ⟨0x5602a014809e04c024811808604001f00ec07003501900c005a02a014009004201f00e006402e015009003c01800a0038014006000, 0x19871989198601131982103c1985197e0f161981197a0f30197d1968196f1979196e009a1971196a194c196d1969196b194e19571967195c195f19611954009b195d009a1955195d1955195b1956195419591950194a1953194f195119461940191e1949193e19431945193f1941193c191f193f1936192b1939192719371930192c192c192a192f1926191e1929192219201925191f1921191a1914191d1919191b19161914191019071913⟩, ⟨0x55029014009c04b024811808804101f00ec07003601980c005c02b014809804602100f006c030015009804001a00b0040010004000, 0x1a0c1a081a0f1a0b1a0d1a071a091a021a001a05012c1a0119fc19fa19ff19f919fb19e219f119f719f019ed19f319ec19eb19ef19e619e419e919e319e519de19dc19e119d819d619db19c319d719d019c919d519c519d119c819c719cb19c419c21990011419c319a619b919c119b819b119bd19b019af19b319aa19a819ad19a719a919a217e819a5199c199719a11995199d19941992198c198e198a19881991198d198f0bb3198b⟩, ⟨0x55029014009c04b024011408604001f00f007203601980c405c02a014009804602000e806802e015009003c01a00a0038014006000, 0x1a861a851a8b1a8600c100bc1a851a721a7d1a831a7c1a7b1a7f1a761a741a791a731a751a6e19dd1a7119d91a6f19df1a691a2e1a371a671a361a2f1a651a5e1a571a611a491a5f1a561a511a5b1a4c1a4a1a481a4f1a3f1a4d1a471a4b1a421a3e1a451a3a100e1a3d100e1a371a391a36100f1a391a321a301a351a2f1a3119f81a031a2d1a241a231a271a211a251a201a060fa01a1a1a151a1f1a111a1b1a011a131a101a0e1a00⟩]) (
(.branch 2 (
.leaf #[⟨0x55029014009a04a023811008403f01e00e806c03401880b8056029013809404602000f006c030016009804001c00b0038014006000, 0x1ad01ad51ad700c71ad300c61acd1ad11acc00c71ad11acc1abf1acf1abe1acd1acf00ca1acd1ac61ac91acb1ac41aba1ac700b21ac51ac01abc0c301ac31abf1ac11abc0c301abf1abe0c301abd1abe0c311abb1abc00c900c81abd00c41abb1ab800bb1a8a1ab51ab71ab400c31aae1ab11ab31aa81a871aaf1a851aad1aa81a8c1aab1aa41a9d1aa71a8f1aa51a9c1a971aa11a921a901a8e1a951a891a931a8d1a911a881a841a8b⟩, ⟨0x55029814009c04c024811c08804101f00ec07203601a00c405e02c014809804602000e806803001600a004401e00c0048018006000, 0x1b391b631b561b4b1b591b451b571b501b4c1b4c1b4a1b4f1b491b4b1b441aac1b471b401a841b431b381b301b3b1b341b321b371b311b331b2c1b2a1b2f1b291b2b1b241b221b271b211b231b1c1b1a1b1f1b161b141b191af81b051b131b081b0b1b0d1b0000c71b0900c61b011b091b041b021b071b011b031b00010501041b011afc1afa1aff1af91afb1aea1ae91aed1ae41ad21ae71ae01ade1ae3186a11001add1ad810e01adb⟩]) (
.leaf #[⟨0x5702a814809e04c025011c08a04202000f407403701a80c806002d01580a004a023010007403401700a804801e00c0048018006000, 0x1bd71bd91bd20b7a1bd51b201bcb1bd11bca0c321bcd1b251bc91bc41b751bc71b711bc51bb81bbd1bbf1bb91bbb1bb61b971bb91b901b991bb51bae1ba51bb11b9f1baf1ba61ba41ba91ba31ba51b9e1b9c1ba11b971b9d1b981b961b9b1b920b381b951b911b931b7a1b891b8f1b881b851b8b1b841b831b871b7e1b7c1b811b7b1b7d1b761b741b791b700c301b731b6a1b6d1b6f0c301b691b6b1b680c311b6b1b281b351b671b621b1b1b65⟩, ⟨0x540288138096049023010c08003e01e00e406e03501980c405e02c014809c04802100f8070032016009804401c00b0048018006000, 0x1c4c1c491c4f1c481c471c4b1c421c401c451c3f1c411c1c1c3b1c3d1c3a1c1d1c3d1c341c2f1c391c2b1c351c291c2d1c2a1c281ac41c251c271c2400b11c211c231c1d1c1f1c1c00ad0c060c031c1b1c140b7b1c170b831c151bd61bdf1c0f1c0a1bd91c0d1bdf1c0b1bf21c011c071c001bfd1c031bfc1bfb1bff1bf61bf41bf91bf31bf51bee0c101bf11bea1b151bed1be31beb1be20c341be51bde0c241be11bda1bd81bdd⟩, ⟨0x55029013c09804a023811008203e01e00e406e03501900c005a02a013809004201f00e006802e013008803c01a00a0040014006000, 0x1cd21cd91cdf1cd815ca1cdb1cd4186c1cd71cd31cd51cb61cc91cd11cc81cc11ccd1cc01cbf1cc31cba1cb81cbd1cb71cb91cb01ca91cb51ca71cb11caa1ca41ca61ca419861c3b1ca31c541c5f1ca11c801c931c9b1c921c8b1c971c8a1c891c8d1c841c821c871c811c831c7c1c751c7f1c691c7d1c741c6f1c791c6a1c681c641c6d1c5d1c671c631c651c6200a31c5e1c5c1c6100a41c5d1c581c561c5b1c551c571c3e1c4d1c53⟩]))))) (
(.branch 4 (
.leaf #[⟨0x55029814009804a024011408604001e80ec07003401900bc05a02a014009404602000f006c030015009804401c00b0048018006000, 0x1d4d1d5b1d501d571d591d521d4e1d4c1d551d511d531d4a1d481d441d421d471d411d431d341d3d1d3f1d381d361d3b1d351d371d2a1d311d331d2c1d281d081d2f1d2b1d2d1d081d271d2b1d281d261d221d1d1d251d171d231d1c1cfc1d1f1d1b1d1d1d161d141d191d091d151d0a1d081d131d001d0b1d111d041d021d071d011d031cfe1cfc1cf81cf61cfb1cf21adf1cf51ae51cf31cee1b001cf11ce4148a1ce71ce018521ce3⟩, ⟨0x54028813c09804a023010c08003e01d80e406e03401900bc05802a013809404402000e806802e015009003c01a00a0040014006000, 0x1dce1dcc1dd11dcb1dcd1dc61cf71dc91cef1dc71dc01d9a1d921dc31d8a1db91dbf1db81d941dbb1d8f1db71db21da71db51da11db31dac1da81da81da61dab1da51da71da01d921da31d981d9d1d9f1d991d9b1d961d931d991d931d951d8e1d8c1d911d8b1d8d1d781d831d891d821d811d851d7c1d7a1d7f1d791d7b1d401d711d771d701d4c1d731d451d6f1d6a1d631d6d1d5d1d6b1d621d481d651d611d631d5c1d5a1d5f⟩, ⟨0x54029013c096049023010c08203e01e00e806e03401900bc05802a014009404602000f006c030015009804001a00a0038014004000, 0x1e311e411e361e3d1e3f1e381e341e301e3b1e371e391e301e331e371e321e311e371e331e351e2c1e2a1e2f1e291e2b1e261e241e001e0d1e231e181e131e1d1e111e191e101e0800c61e0c1e0a1e0f1e091e0b00f41e091e041e021e071e011e031dca1df51dff1df31df91df41df21df71dd21ddf1df11de815e91deb15ef1de91de21de51de71dda01391de301381ddb1de31dde1ddc1de11ddb1ddd1dd61dd41dd91dd31dd5⟩, ⟨0x56029814009a04b024011408203f01e00e406a03301800b4056029013009004201f00e006402e014008803c01800a0040014006000, 0x1ea61eaf1eb51eae1e081eb11eaa1ea81ead1ea71ea91ea21d7a1ea51e981e9f1ea11e9a1e261df21e9d1e991e9b1df21e251e991e8e1e951e971e901e8c1e6a1e931e8f1e911e8a1e6b1e8f1e841e791e871e731e851e7e1e7a1e7a1e781e7d1e771e791e721e701e751e6b1e711e6c1e6a1e6f1e661e641e691e631e651e281e5b1e611e5a1e301e5d1e2d1e591e541e491e571e431e551e4e1e4a1e4a1e481e4d1e471e491e421e401e45⟩]) (
(.branch 2 (
.leaf #[⟨0x55029014009a04b024811808604101f00f007203601a00c405c02c015009c04802100f8070030016009804001a00b0040018006000, 0x1ef61f291f2d1f2a1f281f240af21f270adf1f231f220ade0b780b831f211ba21b9f1f1f1f1a1eca1f160aff1f190b071f170afc0b071f131f021eff1f111f031f051efe0b0a1f011efa1ef81efd1ef71ef91edf1ef51ee21eed1ef31eec1eeb1eef1ee61ee41ee91ee31ee51ede0afe1ee11eda1bba1b961edd1eda1bb61ec61ecf1ed91ece00c61ed11eca1ec81ecd1ec71ec91ebe1ec31ec51ebf1ec11eba1ba41ebd1eb60dc21eb9⟩, ⟨0x55029814009c04b024811808604001e80ec07203601980c005a02b014009804802100f8070032016009804401a00b0040018004000, 0x1fa600b51fa21fa01fa500b81fa11f9c1f721f9f1f9b1f9d0c4e0c4b1f991f901f861f931f841f8d1f8f1f881f861f8b1f851f871f821f801f7c1ee41f7f1f321f671f7b1f741f441f771f6e1f6b1f711f6b1f6d1f661c661f691f371f651f3b1f631f5e1c401f611f5b1f5d1f421f511f571f501f4d1f531f4c1f4b1f4f1f461f441f491f431f451f3e1f3a1ca21f411f3d1f3f1f361f341f391f331f351f2e1f2a1ef61f311f2d1f2f⟩]) (
.leaf #[⟨0x5a02b814c0a004d025811c08a04201f80f007203601980c005802a013809404401f00e006402c014008803801800a0038010004000, 0x201c1cb8201f1caa1ca61988201b201619c22019201220102015200f2011200a20062004200d2009200b153e200120031ffc154c1fff1fd61fd31ffb1e461e431ff71ff21dcc1ff51fee1fd81ff11fe41feb1fed1fe61fe215ae1fe91fe51fe71fda1fd81fdd1fd71fd91fd21df81fd51f281f3b1fd11f9c1f581fcf1f9a1fa31fcd1fc41fc31fc71fc11fc51fc01fa60c301fba1fb51fbf1fb11fbb1fa11fb31fb01fae1fa01fac1fa81faf1fab1fad1fa71fa9⟩, ⟨0x5802a814c0a204e025812408c04302000f807603901b00cc06002d015009c04802100f006c030016009804401c00b0040014006000, 0x209220802095206b208f208b208d207e20872089208220802085207f2081206c2077207d2076207520792070206e2073206d206f1fde1e4820691fe1206714fc14e7206520600ba6206315aa2009205f200815ab205f154a1547205d20002005205b2056203c2059205220262055204e20102051203a2045204d204420422047011a2043203e203c2041203b203d2024203320392032202f2035202e202d203120282026202b20252027200e20172023⟩, ⟨0x5702a014009c04b024811808604001f00f007203601980c005c02b013809404402000e806802e015009004001a00a0038014006000, 0x2110211721192112210e2106211521112113210a2108210d2107210920f420ff210520fe20fd210120f820f620fb20f520f720f220f020da20e920ef20e820e520eb20e420e320e720de20dc20e120db20dd20d020d720d920d220ce152420d520d120d320ca20c820cd20c720c9208a20bf20c520be20a220c120ba20b120bd20ab20bb20b220b020b520af20b120aa20a020ad20a420a720a9209e20a120a520a120a3209c209a2096206e2099⟩]))))))))))) (
(.branch 35 (
(.branch 17 (
(.branch 8 (
(.branch 4 (
.leaf #[⟨0x5802a81480a004d025011c08804201f80f007203601a00c405c02b014809804602100f006c032016009804001a00b0040014004000, 0x219c214e219f21982182219b219621682180218f2195218e218b2191218a2189218d21842182218721812183216a2179217f21782175217b217421732177216e216c2171216b216d2164215a2167215821612163215c215a215f2159215b214c215521572150214e2153214d214f2148097a214b21440e3021472142211a212c213b2141213a2137213d2136213521392130212e2133212d212f2128211e212b211c212521272120211e2123211d211f⟩, ⟨0x5902b01500a204e025812008a04201f80f007403801a80c805e02d015009c04802100f807003201600a004401c00b0040018006000, 0x22262224222922232225221c0a54221f10fe10fb221b221421d22217221021fc221321fa2209220f22082205220b22042203220721fe21fc220121fb21fd21f821f621f221e821f521e621ef21f121ea21e821ed21e721e921d021df21e521de21db21e121da21d921dd21d421d221d721d121d320c6152d21cf21c4154421c70f2e0f2b21c321c00f2021bc20f621bf21b820dc21bb21b4212e21b721ae21a521b1210b21af21a621a421a921a0216c21a3⟩, ⟨0x5802a814c0a004d025011c08804101f00f007203601980c005c02b014009804602100f006c032016009804001a00b0048018006000, 0x22b222ab22b522a322b322aa22a522af22a222a005f62298226c229d22662220229b226422912297229006c22293228c226d228f2269228d2272228122872280227d2283227c227b227f22762274227922732275226e226c2271226806c4226b2265226722600a2622630a252261225a223c225d2256095c225922512253224c0962224f223a2245224b2244224122472240223f2243223b223d221d22392222223122372230222d2233222c222b222f⟩, ⟨0x53028813c098049023011008203d01d80e006a03201780b4054028013009004201f00e006402c01300880380160090038010004000, 0x22d1233322c92331232a22fe232d232422d42327232022cd232322cf231f2316023b231d231823142312231b2317231922fc230b2311230a2307230d230623052309230022fe230322fd22ff22f422f222f722f122f322f000ff00fe22f122ec22ea22ef22e922eb22d222e122e722e022dd22e322dc22db22df22d622d422d922d322d522c822c022cb22c422c222c722c122c300ec22c122bc22ba22bf22b922bb22b6229e⟩]) (
.leaf #[⟨0x5c02c815c0a8051027012c092046021810007a03a01b80d006202e01580a004c024010807803801900b004801e00c0048018006000, 0x23a623a223a923a123a3239a05f4239d02f202ba23992394039a2397238c23912393238d238f023e0415238d0414023f238d01a601a3238b238606b82389238206862385237e23472381237a16f6237d237616dc23790912236723752250224d2371225e2252236f236b236d23672369236223582365235e23592361234d235f0a5a0a552357234c0a24234f2348234616d2234b026e026b234506b606bf234322a002fa233d2338027e233b092602702337016423132335⟩, ⟨0x54029013c098049023011008203e01d80e006c03301800b4054027012008403c01b00c805802801200800340160080030010004000, 0x2401240d2402240524072400031f240323fc033a23ff1664149c23fb23f723f9145c23f523f723f4145d23f723f023ea23f323e823e523ef23e923eb23e41a1223e723dc19fa23e323de19e423e12218101c23db0192018f23d923b4232823d723b223bb23d523cc0a9e23cf23c423c923cb23c523c70ac423bf23c523b923c323bf23c123be00f123ba23b823bd00f223b923b422d023b723b323b523b023ae0a5723ad23aa23a6⟩, ⟨0x5602a014409e04c025011c08804202000f807603801a80c806002d01500a004a02200f807003401600a004401c00b0048018008000, 0x24832485247e247c2481247b247d247624742479246f24752470246e2473246a2464246d2469246b2465246724612463244a2459245f24582455245b245424532457244e244c2451244b244d241c242524492440243924432429244102d82321243d232002d9243d24382432243b24342332243724332435242e231e22cc2431242d242f242823c2242b242423be24272420241e2423241d241f2418033b241b24092419240c240a2408240f⟩, ⟨0x5a02b81540a404f026012408c04402080f807803a01b80d406402f01600a404c024010807403401800a804401e00d0050018006000, 0x251c251a251f2519251b250e24e82511250a2508250d25041650250724e224ed250324f824f324fd24f124f924f024e8010c24ec24ea24ef24e924eb014e24e924e424e024e724e324e522b822c524df24c624be24d324c424cb24d124ca22f024cd24c624bc24c924c524c724b2016224b502340230016224b124ac24a524af249924ad24a4249f24a9249a24982462249d0231249b247f24972482248b2495238e0416023e248f248a024c248d248624842489⟩]))) (
(.branch 4 (
.leaf #[⟨0x520278134096048022810c08003e01d80e406e03501900bc05a02a014009804602000f006c030015009804001c00b0040018006000, 0x25982597259b259325992591259525922590257c258a2585258f2583258b2582258025542580257f257e257a2581257d257f2579257b25780073256c25732577256e0c582571256d256f2568255f256b25592569256125652560255e256325582556255b255525572540254b2551254a2547254d25462545254925412543253a2533253d252f253b253225162535252e252c2531252a2514251825232529252225212525⟩, ⟨0x55029014009a04a024011408604101f00ec07003501900bc05a02a014009404402000e8068030015009003c01800a0040014006000, 0x261a25cc261d2619261b261426082617260c26112613260d260f26042609260d2609260b26062604260025ac260325fa25d025fd25e425f325f925f225ef25f525ee25ed25f125e825e625eb25e525e725e025de25e325dd25df25ce25d725d925d225d025d525cf25d125c025c925cb25c425c225c725c125c325bc12ac25bf25aa25b525bb25b425b325b725ae25ac25b125ab25ad25a825a6259e25a325a5259f25a1259c2591259f⟩, ⟨0x55029814009a04b024011408403f01e00e406e03501900bc05802a014009804802100f8070032016009804401c00b0040014004000, 0x267126772672267026752668266d266f007b266b007a266526692664007b2669266426592667265826652667265e26612663265c2652265f0070265d2655265b2656265426592658265426572658265326552656007d007c26572654006900782653264e264d2651264c007526362645264b2644264126472640263f2643263a2638263d26372639263225c22635262e251a263125dc2627262d2626260a26292622261b262526152623⟩, ⟨0x540288138098049023811008403f01e00e806e03401880b8058029013809404602000f006c030016009804401c00b0040014006000, 0x26f426f926ff26f826c426fb26f526f726f026d526f326d126f126e826e326eb26df26e926e226a826e526de26dc26e126bb26dd261a25fe26db26d626d426d926d026c226d326c826cd26cf26c926cb26c626c326c926c326c526ad26c126b326bf26b226b026b526ab26b126ac26aa26af26a226a026a5269f26a1269a267f269d2679269b268c1cf6269526901ade269326841d3626872680267e2683267d267f26782676267b⟩]) (
(.branch 2 (
.leaf #[⟨0x5602a014409e04c025012008a04302000f407203701a00c405c02b014009804602000f007003401700a804801e00c004801c008000, 0x2777277927722688277527712773276c26a1276f2673276d2768006d2758276527672764006f275e2761276327042757275f275a275626dc275d2759275b27482747274b2742007a2745273e26a62741271c2727273d2732272d2737272b2733272a2722007a27262724272927232725272200af00ae2723271e27182721271d271f268e1ec8271b2706271127172710270f2713270a2708270d27072709261826152703260e260826062701⟩, ⟨0x54028813c09804a023811408403f01e80ec07203601980c405c02c015009c04802100f807003401700a804801e00c0040018006000, 0x27fa27f527fd27ef27fb27f427ea27f727f327f527ee277627f127ec27ea27e6277227e927da27d527df27cf27db27c927d3005d27d127ce27c8005c27ca27c827cd00a027c927c427a827c727c327c527c027a427aa27b527bb27b427b327b727ae27ac27b127ab27ad27a0279e27a3279d279f2798268a279b279727992770277b2795278c1f04278f27822789278b278427802776278727832785277e27772783277a2778277d⟩]) (
.leaf #[⟨0x55028813c09a04a023811008203e01d80e006a03301880bc058029013009004401f00e006802e015009804001800a0038010004000, 0x2870286e286c2873286b28712869286f28622865286727e028612863285228512855284c005c284f284827e4284b2838283f2847283e27d22841283a2820283d2839283b27e52837283427e22822282d2833282c282b282f28262824282928232825281d281f267c2679281b281426a0281928162814280e267e2813280f28112810280e2804280b280d28062802267028092805280726702801280528002671280527e727ff27fe27e6⟩, ⟨0x530280134094047022010407c03c01d00dc06803201780b0052026012008804001e00e0068030015009804401c00b0040014006000, 0x20b0209028b728b2208c28b528ac28af28b1005c28a928ad28a8005d28ad28a8289d28ab289c28a928ab006028a9289d28a728a028a328a52898289428a12897289f289a2896289d289c2896289b28982897289d289c28972899289a005f005e289b005a28992896004b004a2897005228952892004f288a288f2891288e00512889288d2888286a288b28602889288b286827e028872882287b2885286d2883287a2875287f⟩, ⟨0x55029014009a04a023011008203f01e80e807003501980c005a02b014009804602100f006c030016009804401c00c0048018006000, 0x293227be29352931293327c227cb292f29222929292b2924281e279c292729232925281c279d292328b32921291e2900291a2911291d290b291b291229102915290f2911290a28fe290d2902290729092903290528fc2901290328fd28ff28f828f328fb28bf28f928f227e228f528ee28d228f128ea28b928ed28c928eb28e228d328e528cf28e328ce28cc28d128c728cd28c828c628cb28c2288828c528be288c28c128ba28b828bd⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5802b014c0a204e025812408c04302000f407403701a00c805c02c014809c04802100f0070032016009804401c00a0040018006000, 0x29a729a929a229a029a5299f29a12992299b299d29962994299929932995298c298f29912896206b298d206a2897298d29882896298b2976297d2987297c27d0297f297827bc297b2977297928a6289a28962975297200572962296f2971296e0059294027a6296d29662969296b27a629612967295f2965295e294229632960295f2963295a2953295d2945295b2952294d2957294829462944294b294329492941294729302937293f2936279c2939⟩, ⟨0x5802a81480a004d025812008a04202000f407603801a80c805e02d01500a004a02200f807003401700a004401c00c0048018006000, 0x2a362a352a392a302a2e2a332a2d2a2f2a282a232a2b2a1f2a292a1e2a1c2a212a1829942a1b2a142a122a172a112a132a0c2a0a2a0f29ef2a0b29f229ee2a0929f62a012a072a0029ff2a0329fa29f829fd29f729f929ea29e329ed29df29eb29e227a429e529de296429e129da295e29dd29d629d429d929d329d529bc29cb29d129ca29c729cd29c629c529c929c029be29c329bd29bf29b829b629bb29b229a629b529ac29af29b129aa29a729ad⟩, ⟨0x5802a814809e04d025812008a04202000f407403801a80cc06002d015009c04802200f8070032016009804401c00b0048018006000, 0x279627a12ab10e4a0de82aad21b221a42aab2aa82a9e2aa626c62aa02aa32aa52a9e0e452aa12a9a2a8c2a9d2a982a962a8a2a932a952a8e2a8c2a912a8b2a8d2a862a5f2a8929892a872a8213ac2a852a7c2a7f2a812a7a2a1d2a7d2a762a222a792a702a672a732a632a712a682a662a6b2a62289e2a652a5e2a422a61299e2a572a5d2a5629a82a5929a32a5529d229f32a532a4e29b72a5129b32a4f2a102a0d2a492a2c2a3b2a412a3a2a372a3d⟩, ⟨0x5602a014409c04b024011408604001e80e807003501900bc05802a013809404401f00e8068030015008803c01a00a0038014004000, 0x2b3b2b3d2b362b342b392b1a2b292b2f2b282b252b2b2b242b232b272b1e2b1c2b212b1b2b1d2b1604e62b192b0a2b132b152b0e2b0c2b112b0b2b0d2aee2b012b092b002af92b052af82af72afb2af22af02af52aef2af12aea2ae82aed2ae72ae92ae22ada2ae52ade2adc2ae12adb2add2ad62acf2ad92ac32ad72ace2ac92ad32ac42ac22ac02ac72abf2ac12abe00eb24da24d42abd064e064b2abb2ab82ab625720c382ab525532ab3⟩]) (
(.branch 2 (
.leaf #[⟨0x5802a814c0a004d025011c08a04201f80f007403701a80c405e02d01580a404e024010007403401800a804801e00c0048018006000, 0x2bb42b942bb72bb32bb52b962ba92bb12ba82ba12bad2ba02b9f2ba32b9a2b982b9d2b972b992b822b8d2b932b8c2b8b2b8f2b862b842b892b832b852b7c2b772b812b712b7d2b722b702b6e2b752b6d2b6f2b6c01432b6a01412b672b692b66013f236a06a82b6523722366066a2b6324da24d62b612b5c2b352b5f2adf2b5d101a10172b592b522b552b570f842b512b532b500f852b532b3a2b492b4f2b482b452b4b2b442b432b472b3e2b3c2b41⟩, ⟨0x55029014009c04b024811808804101f00f007203601980c405e02d01580a004a02200f8070032016009804001c00b0040014006000, 0x2c1e2c1c2c212c1b2c1d2c152c192c142c122c172c112c132c0a2c092c0d2c0800312c022c052c072c002bf82c03002c2c012bfc2bef2bff2bfa2bf62bfd2bfc2bf62bfb2bfa003700362bfb00322bf92bf600252bf02bf32bf52bee00352bf12bea17c22bed06a606752be92bb22bbb2be72bcc2bdb2be12bda2bd72bdd2bd62bd52bd92bd02bce2bd32bcd2bcf2bc82b842bcb2bc22bc52bc72bc02bb92bc32bb92bbf2bba2bb82bbd⟩]) (
.leaf #[⟨0x5702a014009c04c024011808604001e80e406e03401900bc05a02a013809004401f00e006402e014008803c0180090038014006000, 0x2c982c932c9d2c8e2c8c2c8a2c912c812c8f2c892c8d2c842c801ef62c872c832c852c801ef62c832c821ef72c7f2c742c7b2c7d2c762c6c0bca2c792c752c772c702c6e2c732c6d2c6f2c682c522c6b2c672c692c542c5f2c652c5e2c5d2c612c582c562c5b2c552c572c4c2c4f2c512c4a2c412c4d2c462c452c492c432c472c422c402c2c2c3a2c352c3f2c332c3b2c322c302c1a2c2e2c2a2c312c2d2c2f2c292c2b2c28002f2c102c1f2c27⟩, ⟨0x5702a814809e04c025011c08a04202000f407403801a80c806002d01580a004a02200f807403401700a004401e00c0040014004000, 0x2d1a2d162d162d142d192d102d022d132d082d0d2d0f2d092d0b2d062d032d092d032d052cfe2cfc2d012cfb2cfd2cd62ce32cf92cee2ce92cf32ce72cef2ce62cde00342ce22ce02ce52cdf2ce12cda2cd82cdd2cd72cd92cc02ccf2cd52cce2ccb2cd12cca2cc92ccd2cc42cc22cc72cc12cc32c662c712cbf1c242c832cb52c821c252cb52cac2cb12cb32cad2caf2ca42c7f2cad2c842c7e1ef82cab2ca42c882ca72ca02c992ca32c8b2ca1⟩, ⟨0x57029814409c04b024811808604001f00ec07003601980c405c02b014009804602000e8068030015009803c0180090038014004000, 0x2d9a2d962d942d9d2d992d9b2d882d912d932d8c2d8a2d8f2d892d8b2d762d812d872d802d7f2d832d7a2d782d7d2d772d792d722d502d752d6e2d6c2d712d662d622d622d602d652d5f2d612d5a2d4e2d5d2d542d572d592d522d4f2d552d4f2d512d322d3d2d4b2d402d432d4500342d3b2d412d3c2d3a2d3f00762d3b2d362d342d392d332d352d2e2d0a2d022d312cfa2d272d2d2d262d042d292cff2d252d242cfe2d202d152d232d112d21⟩]))))) (
(.branch 4 (
.leaf #[⟨0x54029013c09a04a024011408203f01e80e807003501980c005c02b013809404401f00e006802e014008803c01a00a0040014006000, 0x2e132e212e182e002e1b2e172e192e122e102e152e052e112e062e0d2e0f2e082e042dfe2e0b2e072e092e022e002dfa2df82dfd2df72df92dee2dec2df12deb2ded2de62de42de92dd92de52dda2de12de32ddc2dd82d4c2ddf2ddb2ddd2dc62dd12dd72dd02dcf2dd32dca2dc82dcd2dc72dc92db62dbf2dc52dbe2d942dc12dba2db82dbd2db72db92db02dac2dac2daa2daf2da92dab2da42da22da72d952da32d982d9f2da1⟩, ⟨0x5902a814c0a204e025812008c04302000f407403701a80c805e02d015009804802100f006c030015009804001c00b0048018006000, 0x2e960f660f522e990f632e972e960f622cb60f5a2e952e9025e62e932e8c2e672e8f2e632e8d2e842e662e872e802e6e2e832e6c2e772e7d2e762e752e792e702e6e2e732e6d2e6f2e682e662e6b2e622e602e652e552e612e562e5d2e5f2e582e5412de2e5b2e572e5927f227ef2e532e4e27f42e512e4a2d8a2e4d2e2c2e412e472e402dd82e432e312e3f2e342dec2e392e362e342e302e2e2e332e2d2e2f2df62e252e2b2e242e042e272e202e192e23⟩, ⟨0x530278134096049023811008403f01e80e806e03401900c005a02a013809404402000e006802e014008803801800a0040018006000, 0x2f042f022efc2f072eff2f012efe00652efb2efd2efa00632ef62ef42ef900662ef52ef02eee2ef32eed2eef2ee825422eeb2ec22ecd2ee72edc2ed72ee12ed32edd2ecb2ed52ed22ed02eca265a25942ed12ecc2eca2ecf006a2ecb2ec62ec42ec92ec32ec52ebe2eba2ab22ec12ebd2ebf26ba2eb72eb9269e26732eb52ea82ead2eb32eac1dda2eaf2ea92eab2ea61fee2e9b2ea52ea22e9e2e9e27982ea12e9a29322e9d⟩, ⟨0x5702a014409e04c024811808604101f00f007403701a00c805e02b014809804802100f8070032016009804001a00a0040014006000, 0x2f8c2f8a2f8f2f862f842f892f7b2f852f7e2f812f832f7c2f7b2f7f2f442f732f792f722f4c2f752f492f712f6c2f612f6f2f5d2f6d2f662f622f622f602f652f5c2f5a2f5f2f4d2f5b2f502f572f592f522f4e2f4c2f552f512f532f482f462f4b2f452f472e182df22f432f402cb82ebc27692f3f2eb62ebb2f3d2eec2ef72f3b2f1a2f2d2f352f2c2f252f312f242f232f272f1e2f1c2f212f1b2f1d2f162f0f2f192f032f172f0e2f092f13⟩]) (
(.branch 2 (
.leaf #[⟨0x54028813c098049023011008203d01d00dc06803201780b0054027012008804001e00d806402c014009003c01a00a0038014004000, 0x2ffe2ffc30012ffb2ffd2ff626d42ff92ff226f62ff52fea2fef2ff12feb2fed2fe826552feb291e290428fc2fe72fe229102fe52fde29f82fe12fda2fd92fdd2fd72fdb2fd62fc229a62fd02fcb2fd52fc92fd12fc82fc62fb62fc42fc02fc72fc32fc52fbf2fc12fbe00552fba2fb82fbd2fb72fb92fb22fac2fb52fb12fb32fad2faf2fa829732fab2fa62f9c2fa02f7a2fa32f9c2f9a2f9f2f992f9b2f942f8b2f972f872f95⟩, ⟨0x5902b014c0a204e026012808e045021810007c03c01c80dc06803101680a004802100f007003201700a004401a00b0040018006000, 0x306c306f3071007a3065306d3065306b306630643069306400bf00be30653060305e3063305d305f3043305b3056304d305930473057304f3053304e304c3051304b304d30461fb2304930421ab930451f1c1ec01c2030411c2c1c261c221c1e303f2cae2ca82c7e303d30341ef830373030302e3033302c05583024301f3027301b3025301e30163021301a23c0301d23c623be0ac6301914cb3015301014a1301314d930112ffa3005300b300430033007⟩]) (
.leaf #[⟨0x5702a014409c04c024811c08804201f80f007203601980c005c02b014009404401f00e806c032016009804001c00b0040014006000, 0x310630e431093102080a310530fe07e2310130db30fd30f430f230f730f130f330e230df30ef30e330e530de07fa30e130da07aa30dd30c430d330d930d230cf30d530ce30cd30d130c830c630cb30c530c72e482cfc30c330be30a830c126c030a330bd26be30a930b730a430a230a7174130a130a01740309e30963098309b309d309630913099309230903095308d308f307830833089308230813085307c307a307f3079307b305c30673077⟩, ⟨0x540288138096049023011008203f01e00e806e03401880b805802a013809004402000e806c03001600a004401c00b0040014004000, 0x14b2237f317717fa17f73175182417bf3173316b316f316a3168316d3167316907c007b73165316200d9177e315f3161315e00d5315a0d00315d3134190631593136313f3157314c314731513143314d313d31453142313c00e6313e313c3141313c01210120313d3138312a313b3137313931301e6531331e6d3131312c1e6631260f0a3129312007c2312308e608e3311f31180762311b310a06cf3117310e310c3111310b310d⟩, ⟨0x5c02c81580a60510270130092045021810007c03a01b80cc06202f015009c04802100f007003201700a004801e00d005001c008000, 0x1f6e1f2931cb31c4256e31c71a841f6f31c31b3531c131bc152131bf152731bd31b031b731b931b231ae146031b531b131b331aa1ce131ad1ce531ab14501426120231a923f41a3031a731a223f8145c31a523f531a331a223f4146a1462145e145831a11662165f319f03660363319d31980368319b319425093197250f3195319001e1319301e7319130aa26dc318f317b318d318830a8318b31863182318230a23185317c317f3181317a26ab317d21c00f240f1c3179⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5802a81480a004d025812008c04302000f807603801a80c805e02c014809c04802200f807003201700a004001a00b0040014004000, 0x32381ef6323b32343230323732333235322a3225322d3221322b3220321e32233219321f321a3218321d3214078132170789321508e007ef320f30fa077a320731ec31f5320531fa31fd31ff31f831f331fb31f431f231f731ee0e1a31f131ed31ef31e831e731eb31e531e931e4265425781b481b4531e331de31dd31e131db31df31da1faa0c24305a1f6a1f5c31d931d41ec931d71ecf31d51f3a1f2931d31f621c3a31d131cc1f2b31cf1f6f31cd⟩, ⟨0x5802a814809e04c025011c08804201f80f407203601980c005a02b014009404402000e806c030015009003c01a00a0040014006000, 0x32b632c532cb32c432c132c732c032bf32c332ba32b832bd32b732b932b2326c32b532ae326532b1325f32af32a4329f32a9329b32a5329a327c2b68329d327e3291329932903289329532883287328b328232803285327f3281326a3275327b327432733277326e326c3271326b326d32663264326932633265325e325432613258325b325d325632553259324e322f3251321b324f32463244324932433245323e302f32413035323f302e2cb8323d⟩, ⟨0x5b02b81500a404f026812408c04302000f407403801a80c805e02c015009c04802100f006c030015009804001a00b0040018006000, 0x333e333c0c9a334133383333333b332733393332332e3335333133330dd60d960d8a332d33260d903329247a247733253316331d3323331c023e331f331832fe331b331733193300330f3315330e330b3311330a3309330d330433023307330133032468247132f9246001c632f50580057d32f332e416f232f132da32e932ef32e8170432eb32e432dc32e7234732e332d2067e32e132dc32d432df32db32dd32d616f232d932d532d717d0182732d12b501a4632cd⟩, ⟨0x5702a01480a004d025011c08804101f80f007203601980c405c02b014009404602000e8068030016009804001a00a0040014006000, 0x2ab6339333cb33b733c933c633c233c2322e33c533bc33bf33c133ba321933bd33b6322433b933b2338033b533b033ac33ac337233af33a633a933ab337433a533a733a0339933a3339533a133983390339b33943392339733703379338f33883381338b337d338931ee0dbe3383337c3374337f33783376337b337533773371337333543367336f3366335f336b335e335d336133583356335b33553357335033493353333d335133483343334d⟩]) (
(.branch 2 (
.leaf #[⟨0x530288138098049023010c08003e01d80e006a03301800b8056027012808c04001d00d005c02a013008003801800a0040018006000, 0x343c343a341c3427343700433431342a342d342f00423425342b3426342434293420341e3423341d341f340a3415341b341434133417340e340c3411340b340d3402340734093403340533fa33f3340333fe33f833f2340133f133ff33f533f933da33f533f733f433db33f733f433f133f333ea33e533ef33e133eb33df33e333e033de0ef433db33dd33da009733d733d933d333d533d200953330332733d133ca33cd33cf⟩, ⟨0x56029814409c04b024811c08804001f00ec07203601a00c405e02c014809804602100e806802e014009003c0180090038014004000, 0x34c434c234c734bd34c334be34bc34c134b834b034bb34b734b934b434b234a634ad34af34a834a4348e34ab34a734a934a0349934a3349334a13498348c349b34973499349234903495348f3491346e3477348b347c347b347f347600423479347234703475346f3471346a344a3444346d343e34633469346234463465345e345534613451345f3456345434593450344434533448344d344f3449344b344534473440343a3443343f3441⟩]) (
.leaf #[⟨0x56029814009c04b024011808603f01e80ec07003601980c405c02b014809804602000f006c030015009804401c00a0040014004000, 0x3540353f3543353a3538353d35373539352e135a3531352a3523352d3517352b3522351d3527351835163514351b3513351535120039350e350c3511003a350d35083506350b3505350734fe3501350334fc34f434ff003e34fd34ea34f934fb34f834f234f734f834f334f534f6004534ec34ef34f1004234eb34ed34e6109934e910a134e734e2109a34d834df34e134da34d634bc34dd34d934db34b634bf34d534ca34b234cd34c934cb⟩, ⟨0x5602a014409c04a024011408604101f80f007403701a00c405c02b014009404602000f006c030015009003c01a00a0040018006000, 0x35cf35d135b235bb35cd35be35c535c735c035b621f835c335bf35c135ba35b835bd35b735b935b335b535a935af35aa35a835ad35a535a73504350f35a135563532359b35941331359933f035953597357034383593355e3563359135883578358b357d3587357c357a357f3579357b357433fe35773570355c357335543567356f35660ecc35693562139e3565355f356135583556355b355535573552353435363549355135483541354d⟩, ⟨0x55029814409c04c024811808604101f00ec07003601980c405c02b014009404602000f006c030016009004001a00a0040014006000, 0x36533655364d364f18b618b3364b008a3647363e305e36453640307a364330f80864363d363a003d35a435ab363935e835ed3631362c3629362f3625362d36243604362735093623360c361b3621361a3617361d3616361536193610360e3613360d360f35f63601360b35ff3605360035fe360335fa35f835fd35f735f935f235ee35ec35f535f135f335e035e935eb35e435e235e735e135e335d235d735d935d335d535ce216935d3⟩]))))) (
(.branch 4 (
.leaf #[⟨0x5b02c01540a404f026012408e04402080f807603801a80c805e02c014809804602000e8068030015009804001c00b0040014006000, 0x301414c336cf3262325f36c736aa1aac36c536be36a836c11b6236a336bd31c036a936b736a736a936a236a036a5369c35ae369f30f030df369b23ac0a553699236806683693236c069c3691308e308a368f308c3093368d34703124368918e418e13687366a366736853680366c368336523679367f36783658367b3674366d367736673675366c3650366f366b366d36663664366936593665365e366136633658365b365f365a3659365f365b365d365412d03657⟩, ⟨0x5802a814c0a004d025011c08804202000f407603801a80c405e02d01500a004a022010007403401700a004401c00b0048018006000, 0x3756375537593751375337483747374b37422d343745373e2d7837413732373b373d37363734373937333735372e0029371a372b372d372a002b372437273729371e371937253720371c3718372337173721371b371d36f8107c3715370f3713370e116e3711370a114d370d1177370b3702114c370536fe10aa370136f6109836fd36f2340c36f536e036eb36f136ea36e936ed36e436e236e736e136e336d4345436d7304a304736d32366091336d1⟩, ⟨0x5702a814809e04c025011c08804101f00f007203601a00c405e02c014809c04802000f0070032016009804001c00c0048018006000, 0x37ed37ef37d637e137e737e037df37e337da37d837dd37d737d937cc37cf37d137ca37c937cd37bc37c537c737c037be37c337bd37bf37b4378c37b737b037ae37b337ad37af37a837a137ab379d37a937a0378837a3379c379a379f378d379b3790379737993792378e378c379537913793378a3788377e00343781377a3778377d3774376e3777376c37713773376d376f375f376b376637523769376037633765375e2bf7376137503757375d⟩, ⟨0x5a02b814c0a204e026012408c04302000f807603801a80c805e02c014809804602000e806c030015009004001c00b0040014006000, 0x38723879387b38743870386e387738733875386a3868386d386738693862377838653852385b3861385a2722385d385638543859385338553848266a384b38443842384738380ef13841383a383d383f37d23837383b3836364d3839382c3430382f382837e8382b381a38213827382036463823381c37d4381f381b381d381438173819381237f53815380c3801380f37fd380d3806380238023800380537fc37f437ff37f837f637fb37f537f737f037ee37f3⟩]) (
(.branch 2 (
.leaf #[⟨0x530288138098049022810c08003e01d80e006c03401880bc058029013809004001e00d806402c014008803801800a0038014004000, 0x38ef38f138ea38e838ed38db38e938de38e538e738e038dc38da38e338df38e138d638d438d938d338d5389a38cb38d138ca38a638cd389f38c938c8389e38c438bd38c738b938c538bc38a238bf38b838b638bb38a738b738ac38b338b538ae38aa38a638b138ad38af38a838a738ad38a438a2389e389c38a1389b389d3866389338993892386e3895386b3891388a388638863884388938833885387e387c3881386f387d⟩, ⟨0x55029014009a04b024011408604001e80e806e03401880b8058029013809004001e00e006402e014009003c01a00a0038014006000, 0x3970396e39730040396f396a37ea396d3969396b3964129a396739603959396339553961395837ba395b3954364e3957390a3913395339323945394d3944393d3949393c393b393f39363934393939333935392e39273931391b392f39263921392b391c391a3918391f391739193916002139123910391500223911390c2c0e390f390b390d390637793909377f390738d238ff390538fe38da390138d738fd38f638f238f238f038f5⟩]) (
.leaf #[⟨0x520278130094047022010407e03c01d00dc06a03201780b4056029013809004401f00e8068030015009804001a00a0040018006000, 0x39d639d539d939d039ce39d339cd39cf39c439c739c939c239b939c539be39bd39c139bb39bf39ba39b839a439b8001339b239ad39b739ab39b339aa39a8399839a639a239a939a539a739a139a339a239a0001039a1399c399a399f3999399b3994398c399739933995398e398a3991398d398f39863985398939840015397e39813983397c0008397f397a0009397f001c397d0016397b3974397739790008396f3975⟩, ⟨0x5802a814c0a004d025011c08a04202000f407403701a80c805e02c014809804802100f006c032016009804001a00a0040014006000, 0x3a583a563a5b3a553a573a3e3a4d3a533a4c3a493a4f3a483a473a4b3a423a403a453a3f3a413992399d3a3d3a033a373a243a2f3a353a2e3a2d3a313a283a263a2b3a253a273a0a3a153a233a183a1b3a1d32523a133a193a143a123a173a0e3a0c3a113a0b3a0d3a043a073a093a0239f93a0539fe39fd3a0139fb39ff39fa39f839a039de39e939f739ec39ef39f139e425a739ed39e839e639eb39e539e739e039ca39e339df39e139cc39d739dd⟩, ⟨0x5702a814809e04c024811c08804101f80f007203601980c405c02b014009804602000e806802e015009004001a0090038014004000, 0x3af33af53adc3aeb3af13aea3ae73aed3ae63ae53ae93ae03ade3ae33add3adf3ad63acc3ad93ad23acd3ad535893ad335863abb3acb3aba37063abd107a10773ab93ab43aad3ab73aa93ab53aac37303aaf3aa837203aab396839713aa739873aa13a543a5f3a9f3a7e3a913a993a903a893a953a883a873a8b3a823a803a853a7f3a813a7a3a733a7d3a673a7b3a723a6d3a773a683a663a643a6b3a633a653a62000b3a5e3a5c3a61000c3a5d⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x5c02c81580a60500268128090045021010007a03b01b80d406603001680ac050026011808003a01a00b805402000c0048018006000, 0x3b623b363b653b5e3a563b613b483b573b5d3b563b533b593b523b513b553b4c3b4a3b4f3b493b4b3b343b3f3b473b3e3b3c3b4100183b3d3b383b363b3b3b353b373b303b2c3b283b333b2f3b313b2b3b2d3b1c3b253b273b203b1e3b233b1d3b1f3b1836da3b1b3b173b1933d213333b15133233d33b15116c11693b133b0c3b0f3b1133d63b093b0d3b0a3b0833e233dc33d833d43b07340433fc33f23b053abe33fe3b033af23af93b013af812743afb3af43ada3af7⟩, ⟨0x5b02c01540a404f026012408e04402080f407403701a80c805c02c015009804802100f006c030016009804001c00b0048018006000, 0x3bda34ca3bdd3bd634b83bd93bd034403bd335f0363b3bcf36fa341e3bcd3b9c3bc93bcb3bc8001b3bc23bc53bc736d83b993bc33b9e3b983b1e3bc13ba236d83bbf3bba3bb33bbd3ba53bbb3bb23bad3bb73ba83ba63ba43bab3b9b3ba93ba33ba73b9e3b9a3b1c3ba13b9d3b9f349634933b9736de34983b953b723b7d3b933b883b833b8d3b813b893b803b7800083b7c3b7a3b7f3b793b7b3b7436dc3b773b733b753b163b213b713b243b293b6b3b663b4a3b69⟩, ⟨0x5802b014c09e04d025812008c04302080f807603901b00cc06002d015009c04802100f006c030016009004001a00a0038014006000, 0x3c3b3c4f3c463c413c4b3c3c3c3a3c383c3f3c373c393c3600473c323c303c3500483c313c2c3c2a3c2f3c293c2b2fb02fbb3c273c1e3c1d3c213c1b3c1f3c1a2fbe2896290e290b3c19268e1eca3c173c103c133c150a84252d3c11253e25323c0f3c0a35a63c0d3bec3bf13c093bf83c013c073c00126c3c033bfc3bfa3bff3bf93bfb3bf43bf23bf03bf70eed3bf5364c3bed3bef3be4369d3beb3be63bd43be93be53be73bdb3be33bde37343be1⟩, ⟨0x5a02b81500a204e025811c08a04201f80f007203701a00c805e02c01500a004a02200f807003201600a004401c00b0040014006000, 0x3332332a3cd114b814cf3ccf3cb83cbd3ccd3cc83ca83ccb3cc43c923cc73cc03cbc3ca23cc33cbf3cc137163cb93cbb3ca63cb13cb73cb03cad3cb33cac3cab3caf3ca73ca93ca0372f3ca53ca13ca33c903c973c9f3c963c943c9900263c953c913c933c8c2e2e3c8f2e162e133c8b3c743c833c893c823c7f3c853c7e3c7d3c813c783c763c7b3c753c773c283c333c733c523c653c6d3c643c5d3c693c5c3c5b3c5f3c563c543c593c533c553c4e3c473c51⟩]) (
(.branch 2 (
.leaf #[⟨0x56029814409c04a024011408604001f00ec07203601980c005c02c014809804802100f006c03201600a004401c00c0048018006000, 0x3d3e3d3c3d413d3b3d3d3d303d373d393d323d2835b03d353d313d333d2c3d2a3d2f3d293d2b3d243d223d273d213d233d1c3d0d3d1f3d133d1d3d163d0c3d193d1235d03d153d0e3d0c3d1120133d0b1a333d093ce03ce73d073d003cff3d033cfd3d013cfc0d6606cc3cea3cf53cfb3cf40d6e3cf73cef3cf33cee3cec3cf13ceb3ced3ce631443ce93ce23cde3ce53ce13ce33cda1e643cdd1fe01e783cd934c834c53cd73cd22ffc3cd5⟩, ⟨0x5802b014c0a004c024811c08804101f00ec07203701a00c405e02c015009804602000e8068030015009804001a00b0040018006000, 0x3db33db53dae1da63db13daa1d623dad2aa626ca26c23da93da43da33da73da13da53da012740eb43d943d923d9f2ae62ae33d9d3d8e3d953d9b004c3d933d8f3d913d8a273e3d8d3d863d853d893d833d873d821a0a0f5223f13d8135d435ce21963d7f3d663d3f3d7d3d6e3d223d7b3d763d4c3d793d723d683d753d703d6e3d683d543d6b3d673d693d5235b43d653d4a3d473d633d563d543d4e3d4c3d513d4b3d4d3d463d283d493d423d3a3d45⟩]) (
.leaf #[⟨0x5902b01480a004e026012408e04402080f807803901b00cc06002d01580a004a02200f807403401700a004401c00b0048018006000, 0x3e3a3e353e3f3e303e2e3e2c3e333e2b3e313e293e2f3e263e243e1e12503e21133d3e1d1e621e6d3e1b3e163e0c3e193e123e0d3e153e073e133e06178c3e093e021e2a3e053df03dfb3e013dfa3df93dfd3df43df23df73df13df33dec121a3def3ddc3de53deb3de4195a3de73de03dde3de33ddd3ddf3dd831383ddb3dd411f23dd72dea2de73dd33dce08563dd13dca1d8c3dcd3dc42d6d3dc72d733dc53db23dbb3dc13dba306a3dbd3db63db43db9⟩, ⟨0x5d02d815c0a8050026812808e04402080f807603801a80c806002d015009c04802200f807403401700a004401c00b0040014004000, 0x175d3ea73d0831a21a2e3ea53e9e35603ea313c813a413983ea13e9a3e923e9d31bc3e933e9936a636ab3e9132321eff3e8d1d1a1d173e893e5a3e653e873e6e1d023e833e703e793e813e783e603e7b3e743e723e773e713e733e683e6b3e6d3e60005d3e69005c3e613e693e643e623e673e613e633e5c3e583e5f3e5b3e5d3dc81d1c3e573e2417723e553e4831633e533e283e223e513e4a3e4d3e4f3e223e473e4b3e2a173c3e493e46173d3e493e423e3b3e453e2d3e43⟩, ⟨0x5802a81480a004e025812008c04302080fc07803901b00cc06202e01580a004c023010007403401700a004401e00b0048018006000, 0x3f080ebc3f0b3f043efe3f073f033f053eff3f01233024db3efd3ef816513efb16593ef93ef422eb3ef722f53ef522ed3ef13eec02e43eef3ee82eaa3eeb32e216d03ee73ee235713ee535753ee330421f6c3ee11e761e733edf3eda19fb3edd1a033edb20ae20ab3ed93eae3eb33ed73ece3d903ed53ed03ebe3ed33ebc3ec73ecd3ec63ec33ec93ec23ec13ec53ebd3ebf3eb83eb43eb23ebb3eb73eb928883eaf3eb1172417203ead3ea83ea63eab⟩]))))) (
(.branch 4 (
.leaf #[⟨0x5a02c01540a4050026812c092046022010407c03b01c00d406402e01580a404e024010807803601900b005002200d005001c006000, 0x3f713f7d3f763f743f793f7006d23f733f6b3f6f3f6a36283f6d3f6830a13f6812e130a012e03f691ad93f67054605433f653882387f3f632d5e2d5b3f612da82da53f5f38ee38eb3f5d3eb628933f5b300c2fec26543f593f543f173f573f133f553f193f513f343f473f4f3f463f3f3f4b3f3e3f3d3f413f383f363f3b3f353f373f303f293f333f1d3f313f283f233f2d3f1e3f1c2f003f213f183f163f1b3f122ed43f1525da25a025903f113f023f093f0f⟩, ⟨0x5a02b014c0a204e025812008a04202000f407603801a80c806002d01580a004a02200f8070032016009804401c00b0040018006000, 0x25942592257e3fdf3fda273f3fdd27433fdb1f6c31cd3fd931cc1f6d3fd5177e0c6e3fd318c418cd3fd13fca38293fcd382d3fcb3fc638433fc938493fc7131413113fc53fb03ce23fc33fbe28493fc1284d3fbf1d601d5d3fbd3fba3fb81da41da13fb73fb2185a3fb53fac05e43faf3fa63fa93fab3fa42b6b3fa73f923f9d3fa33f9c3f9b3f9f3f963f943f993f933f953f823f8b3f913f8a2bbe3f8d3f863f843f893f833f853d0a1a683f813f7c3f753f7f⟩, ⟨0x2f01700b405802b01500a4050027013008803e01d00d806403001700a804c024011008003c01c00d00580280120080038018006000, 0x1f001e801e201d201d001ce01c201c001be001e017f019701af0192018f01b701b6019b01b401b101b0019b01ac01a401a0019d019c019b019a01980190018a0188018601780177017601740170016e01663fe22bce3fe53166315b3fe1⟩, ⟨0x2a01480a004e0260128090046022010808003e01e00e806c03201800b8058028012008804001e00d005002400e0040018008002000, 0x272026c0266026402620254025602500248024a0238022e022c022602250224022302220220021a02140213021202110210020e020a02040203020201ff0201020001fe01fd01fc01f701fb01fa01f401f801f2⟩]) (
(.branch 2 (
.leaf #[⟨0x3101780b805a02c01580a4050025012008804202000f807403801b00d006402e014009804402000f005802400e006002800c002000, 0x2f002ef02ee02ec02e602e002d602d302d202d002cb02cf02ce02ca02c902c802c602c402b602b502b402b202ae02ac029e029d029c0299029b029a029801fd02960292001e01dd025d0281028a02890288027502860282027a0277027602750274⟩, ⟨0x3701b00d406603101800bc05c02d01600ac054029013809404602100f807403201700b0054028013009004402000f0028010006000, 0x37e037c037403710370036f036e036c0364035e035c035a034e03460342033f033e033d033c0331033803350334033303320331033002f1032d032f032c032b032a03280322031c0314031203080300001e01cd029102a102a302a502ab02b902f302fd02f802f602e202eb02f1⟩]) (
.leaf #[⟨0x2e01680b005602a01480a004e02600e806c03401900c005c02c014009004402000f007003401800b004801c00c0050018008002000, 0x3f603f203f003e803e403e203e003d8001e000503030345034d038d03a703af03bf03ce03cd03cc03ca03c603c203c003b803b503b402ef03b203b003ac03aa03a803a0039e039603950394036f0392038e038a0389038803860382⟩, ⟨0x3701b00d006603201880c005e02d01600ac054029014009004402000f807403601a00a8050016009004001c00c0050020008002000, 0x464045c045b045a045804540450044e044204410440043e043a04360434041803030353036b042c042b042a041f0428042404210420041f041e04160303031b038d041b041c001e0003038d03d703df03e703ef04070417041204110410040e040a0408040003fe03fd03fc03fa⟩, ⟨0x26011808804001f00f007403801b00d006403001600a8050026012008804001c00c0058028012008003801800a0040018008002000, 0x4dc04d704db04da04d604d504d404d204c804d004c604c404be04b804a404af04b004ac04aa04a2049e049804940421049204910490048e048a04860484047c047804740472047004680466⟩]))))))))))))) (
(.branch 71 (
(.branch 35 (
(.branch 17 (
(.branch 8 (
(.branch 4 (
.leaf #[⟨0x3701b00d406803301900b8046022010808003e01d00e006c03401900b005002600e006802c014009004001c00c005002000c002000, 0x54c0544053e053c053a03d00303031b039d001e038d03d103df03e703ef049b050705230527052b052e052c052805240520051f051e051c0518051604b204bd050f050e050d050c050a04cd04e904f505070508050405030502050004fc04f804f604ee04ec04ea04e204df04de⟩, ⟨0x3101800b4056029013809804a023011008404001f00f007003401900b0050026012008804001e00e006802400e005002000c002000, 0x5ce059a05b105b705c605b505c405c105c005b305be05ba05b405b305b205ae05a605a0059e059605950594058b0592058e056f0589058c058b058a0586057e057805760574056a001e0535054f05590562056105600551055e055a055205510550⟩, ⟨0x2e01680b005602a014809804801f00f007403801900c005802a014009804802000e006803001600a004802000c0040018008002000, 0x6540652064c06460640027c0285063906380275001e01ab01d50629063506320630062e06260621062506240620061f061e061c061a06080604060306020601060005fe05f205f005ee05e605e005dd05dc021105da05d605d205d0⟩, ⟨0x3301900c406002f01700b0054026012808c04202000e006803201800b805802a0140098048022010006002c0140090030010004000, 0x6d006ca06c806c006ba06b406b106b0069f06ae066b0689069b06ac06a406a106a0069f069e069c066b0689069b06980697069606940690068c068a0682067c0676066c0670001e01d70637063f066606640662063a0645065d065c0655065a065706560655⟩]) (
.leaf #[⟨0x25012008c044021010007c03c01d00e006c03401900b8058026012008003c01c00d0060028012008003801800a0040018008002000, 0x74807460742073e073c07340732073007280724072207200718071507140712070d07110710070c070b070a070806fe070606fc06fb06fa06f806f406f006ee06e606e406e206da06d8⟩, ⟨0x2c01580a8052028013808c04201f00f006803001700a8050026012008804001e00e006803001600a004802000c005002000c004000, 0x7e407e007da07d807d6001e079707b107bd07ca07c707c607b307c4001e079507ad07bf07ba07b507b807b407b307b207ae07a607a0079e079c0790078a078407780770076c0764075e075d075c075a07560754074a0749⟩, ⟨0x2c01500a004e026012808404001f00f007403801b00d006002e01600a8050026012008804001c00d005002000e006002800c002000, 0x860085d085c085b085a08580854001e0841084f0851084a08480846083e08360834083208280827082608240820081c081a08120810080e080408030802080007fd07ff07fe078f07fc07f807f207ec07e907e807e707e6⟩, ⟨0x29014009c04c025011808404001f00f007403801b00c806002e01600a8050026012008803c01c00b005002000e006002800c002000, 0x8ea08e408dc08d808d408d108d008cf08ce08cc08c608c008be08bc08b008af08ae08ac08a808a6089e089a089808960888088508840882087d08810880087c087b087a08780876086a08690868085b0866⟩]))) (
(.branch 4 (
.leaf #[⟨0x3201880c005e02e01600ac054029014009804a024011808804202000f807803a01b00c806002e01600a802000e0060028010004000, 0x97409720968096009580957095609540950094e0946094509440942093e093a09380930092a09240920091c091909180655091609140910090e001e03df03e70433044d046f0477047b048308df08f308fb0903090008fe08fc08f408f008ed08ec0803⟩, ⟨0x29014009c04c025012008c04001e00e806002c01500a004c022010007803801a00c0058028012008003801800a0040018008002000, 0x9ea09e809e409e009de09d60994099f09d309d209d109d009ce0703072f09af09c509c009cb09cc09c809c609be09bd09bc09ba09b609b209b009a809a609a0099a0992098e098c098a09820980097e0976⟩, ⟨0x2f01700b405802b01480a004c025011008403e01e00e807003601900c0058024010007803401800b0050024010007002800c004000, 0xa5e0a580a520a500a4c0a4b0a4a0a480a450a440a420a3d0a410a400a3c0a3b0a3a0a380a360a300a2a0a290a280a220a210a200a190a1b0a1f0a1e0a1d0a1c0a180a170a160a140a100a0e0a0609fc09f209f109f009ef09ee09ec09eb⟩, ⟨0x2d011008404001f00f007403601a00c806002e01600a004c024011008003801a00c0058028012008003801800a0040018008002000, 0x1e096b09c50a790a810ac90acb0acf0ad30ad70adb0adc0ad80ad40ad00acc0ac20ac10ac00abe0aba0ab60ab40aac0aab0aaa0aa80aa40aa20a9a0a990a980a960a920a8e0a8c0a820a7e0a7c0a7a0a720a700a6e0a660a62⟩]) (
(.branch 2 (
.leaf #[⟨0x23011008404001f00f007003601a00c806002e01500a004c024011008003801a00c0058028012008003801800a0040018008002000, 0xb640b620b5e0b5a0b580b4e0b4d0b4c0b4a0b460b420b400b360b350b340b320b2e0b2a0b280b200b1f0b1e0b1c0b180b140b120b080b020afa0af80af60aee0aea0ae80ae6⟩, ⟨0x21010007c03c01d00e006c03401900c005c02c01500a004c024011008003c01c00d006002c014009004001c00c005002000c004000, 0xbf40bf20bea0be60be40be20bda0bd60bd40bd20bc60bc20bbe0bbc0bba0bae0bac0baa0ba20b9c0b980b960b940b8c0b8a0b840b7c0b760b720b700b6e0b660b65⟩]) (
.leaf #[⟨0x3a01c00dc06c03501a00cc06403101800bc05c02b01500a004e026012809004601a00c005c02c01500a004c0240050020008002000, 0xc860c850c840c820c7e0c7a0c780c6c0c600c5c0c540c4c0c460c410c450c440c400c3f0c3e0c3c0c2e0c2c0c2a001e00050ae50aed0b930b9b0c0b0c130c230c1e0c1d0c1c0c1a0c160c140c0c0c04001e0ae50aed0b110b270b3f0b570b6d0b750b870bcb0bd10bff0c000bfc0bfb0bfa0bf8⟩, ⟨0x3801b80d806a03301880c004a024011808804202000f007403401900b805802a014009804402000d0060028012008003801800a000, 0xd020cfa0cf40cee0ced0cec0ceb0cea001e000503a703af03bf0ca30cbd0cd50cdd0ce50ce90ce60ce20ce00cde0cd60cd20cd10cd00cce0cc90ccd0ccc0cc80cc70cc60cc40cc00cbe0cb60cb30cb20cb00cab0caf0cae0caa0ca90ca80ca60ca40c960c90001e0c710c770c890c8b⟩, ⟨0x4e026012c094049024011808a044021810808203f01e80f005c02c01500a403801b00d003401800b0050024010007002000c002000, 0xd740d730d720d700d600d5a0d520d510d500d4e0d4a0d460d440d3c0d3b0d3a0d390d38001e06d506e1071f0727073b07530a790a810ac90acb0acf0ad70d0f0d360d350d340d330d32001e0355038d03a703af03bf0a790a810a8b0ab30d1b0d2b0d2f0d300d2c001e06e106ed071f0727073b0a790a810acf0ad70d130d1d0d230d280d260d240d180d160d100d0c0d070d0b0d0a0d060d050d04⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3301900c406002f01700b405802b011808404001f00f007403801b00d006402e01600a8050026012008804001e0060028010002000, 0xdfa0df60df20df00de60de20de00dde001e06e10d930da10db30dbd0dbf0dc50dd40dd30dd20dd00dcc0dc80dc60db80db60db40dac0dab0daa0da80da40da20d9a0d980d8e0d88001e0003080708190895089d08b708d708db0d820d7e0d7a0d750d790d78⟩, ⟨0x3701b00d406603101800b805802b014809c04c025012008804202000f807803a01c00d803001600a004801c00c005002000c002000, 0xe740e640e600e5f0e5e0e5d0e5c0e5a0e590e580e570e560e540e510e500e4f0e4e0e4c0e480e420e410e400e3e0e3a0e360e340e2a0e26001e0895089d0acb0dbb0ddd0de50de90def0e030e090e170e1b0e1d0e210e220e1e0e180e140e130e120e100e0c0e0a0dfe0dfd0dfc⟩, ⟨0x270130094048023011008003e01e00e807003601900b8058026012008003c01c00d0060028012008003801800a0040018008002000, 0xf060f000efa0efc0eee0ee80ee70ee60ee40ee00edc0eda0ed20ed10ed00ecf0ece0ec80ec30ec70ec60ec20ec10ec00ebe0eae0ea80e9e0e9d0e9c0e9a0e960e920e900e880e7e0e800e780e72⟩, ⟨0x260128090046022010808003e01d00d806803201500a004c024011008003801a00c0058028012008003801800a0040018008002000, 0xfac0faa0f9e0f960f8e0f880f820f7c0f7b0f7a0f790f780f760f720f630f6f0f710f6a0f680f5e0f560f500f480f470f460f440f400f3c0f3a0f320f2c0f280f260f1a0f120f100f0e0f04⟩]) (
(.branch 2 (
.leaf #[⟨0x2f01680ac054029014009c04a024011008003e01b00c805c02c014009004401e00d006002c014009003801800a0040018008002000, 0x10261023102210211020101e10181012100c100b100a1008100710060ff9100410000f6f0f950fa50ffe0ffb0ffa0ff90ff80ff40ff10ff00fe10fee0fe60fe30fe20fe10fe00fde0fd60fd20fce0fcd0fcc0fca0fc60fc20fc00fb80fb0⟩, ⟨0x45022010407e03d01e00ec07403901c00dc06c03401900c4052027012809003001600a8050026012008003801800a0040018004000, 0x1090108c10691083108a10871086108510841080107810721070106e1064105c105b105a104d105810540cd50f210f390f4f0f6f0f71103f1052104f104e104d104c001e000503a703af03bf0cd50ce90f390f4f0f6f0f71103f104a104910481046104210401038103710360f791034102b1032102f102e102d102c102b102a100d1011102910281021⟩]) (
.leaf #[⟨0x3101780b405802a01480a004e026012809004001f00e807003601a00c8054028013009003c01a00b004802000e0060028010004000, 0x110e110d110c1105110a110611051104110210fc10f610f410f2001e10e310e710eb10e410dc10db10da10d810d410d2001e109b10b110bf10c810c610c4109610a110bb10ba10b310b810b510b410b310b210ae10a810a2109c1094109310921085⟩, ⟨0x3001780b805a02c01580a804e025012008804202000f807803a01c00c005c028010007803401600a004801c00a0040018008002000, 0x119c11941190118e118c1182114a1177117b117a117311781174117311721170116a116411621160001e114f1155115911501146112b1135001e11271137114711481144112f1142112d1140113a1132112f112e112d112c11281120111c111a⟩, ⟨0x42020810007e03d01d80e80720380130090046022010808003c01c00d806002c01400980480220100078038014006002800c002000, 0x12261220121c12161215121412131212120e1208001e08fb0f0d0f6d107f10ad10cb10d110e91127115711ad11b311b511b711d711ef11f5120011ff11fe11fc11f811f611ec11eb11ea11dd11e811e411c511db11e211df11de11dd11dc11d811d011cc11ca11be001e1187119b11b1001e1185119f11ad11ae11a611a311a211a111a0⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3101800bc05802b01480a004e026012008404001e00d806803201800b8058028012008804001e00e006802c0100070028008002000, 0x1292129012861281128512841280127f127e127c1272126812671266126312651264126212611260125b125f125e1258125c12561252124c124b124a1249124812461244123e1238123212311230122d122f122e122c122b122a1225122912281222⟩, ⟨0x3a01c80e006e03201800b4056029013809404802300a8050026012008804001e00e006002c014009004001c00a0040018008002000, 0x130e130c1302001e113511ad12f112f512fa114311a8118112f912f811a112f211a312ec12eb12ea0d3312e812e4001e049709370989099109dd128b1297129d12af12c512cd12d112d712dc12da12d812ce12ca12c812c612be12bd12bc12ba12b612b212b012a812a712a612a412a0129e1294⟩, ⟨0x43020810007e03e01e80f007403901c00dc06c03501a00cc05e02e01500a4050027012808c04400d00580240100050018008002000, 0x1380137f137e137c13781374137213681367136613641360135e13561354135213320e8f0ea7134713480ea0133d134113431344133e1336132c132b132a13291328001e0463071f0727073b08fb098909910a610a650d0f0f6d10cb10e911b311b711d711f512df12e112ef132613251324131b1322131e12f71309131c131b131a13181312⟩, ⟨0x2f01700b405802a014809804a023011008404001f00e806c03401900c005802a0140098048022010007803801a0040018008002000, 0x13fc13fa13f813f013ed13ec13ea13e513e913e813e413e313e213e013de13d413ce13cd13cc13cb13ca13c613c213be13bd13bc13ba13b613b213b013a813a6139c1396001e000312d7134d135d136b13711387138f1390138c138a1388⟩]) (
(.branch 2 (
.leaf #[⟨0x3501a00c806203001780b805a02c01500a404c025011808804202000f807803801a00c803801800b004001c00a0040018008002000, 0x14741470146f146e146c145a14541452144c144a144714461444143f14431442143e143d143c143a1438142e1424142214211420141f141e001e0003080708190895089d08d713dd13f713ff1407141c141b141a1418141314171416141214111410140e140a14081400⟩, ⟨0x3001780b805a02b01480a004e026012808c04202000f807803801b00d006403001700b0054028013004802000e0060028010006000, 0x150e150a150214fa14f714f614f514f414f214ec14e814e014df14de14dd14dc14da14d614d414d314d214d014cc14c614c014bc14b014ae14ac001e0005099909d5149514971499149b149d14a514a2148c148e148614801482147614711475⟩]) (
.leaf #[⟨0x42020810007e03e01e80ec07403901c00dc06403001700a8050026012008c044021010007803a014009003801a00c0058028002000, 0x158c158a1588157c157a1570156f156e156c15681566001e0f190f21151b151d155e155b155c155b155a153d154115591558155115561553155215511550154e15481542153c153b153a001e000303df03e703ef0cd50fed151b153515380ff109040fdd151b15351536152e15281522001e000503a703af03bf0cd50ce9151b151d1516⟩, ⟨0x3101700b4056028013809804a024011808403e01e00d806803001700b0054028011008003801a00c0058028012007003000c004000, 0x160015fd15ff15fe15fc15fb15fa15f515f915f815f215f615f015ec15e415e315e215e115e015de15d915dd15dc15d815d715d615d415d015c815c015bb15bf15be15ba15b915b815b615a815a0159c159a159715961594158f15931592158e158d⟩, ⟨0x3a01c80e006e03601a80cc06202f01680b005602a01480a0046022010808003a01c00d006403001700a804c0240100070034004000, 0x168a1682167e167c167a1672167116701669166e166b166a1669166816661660165a1654001e163916451647164916421640163e16361631163516341630162f162e162c161a16161613161216051610160a1607160616051604001e08fb14951497149d151515191565157515c715eb16021601⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x4001f80f807a03c01d80e807203701a80c405c02d01600ac054029013808404001f008003801a00c00580280100060018008002000, 0x16ec16ea16e616e216e016d416d816ce0fe316cc1613001e164d16b916c7164c16bb16cb16c816c416c216c016b616b414f7001e000304a904b7149716b316b016ae001e03df03e704330447044d0463046f0477047b048308fb0fa5169d16ab16a816a716a616a416a0169e169614f5169416071692164b16851690168e168c⟩, ⟨0x3901a80cc06402d01580a8050026011008003e01e00e806c03401900c005c02c015009804402000d00600280120080038018004000, 0x1762173b174117611760175f175e175c173b17451757175b175a174b1758175417511750174f174e1739174b174d174c1745174a17461742173a173917381736173217301728171c171617151714171317121710170b170f170e170a17091708170616fe16f806ae16d316df16f116ee16ed⟩, ⟨0x4e026012408e046021810408003401980c806202f01700b405802b01500a4050026012008c044021010007c01c0080030010004000, 0x17ce17cd17cc17c717cb17ca17c917c817c6100b17c517c40f8717c0001e000503a703af03bf0ce90f390f4f103f17af17b717bb17b417b217b017a817a717a617a417a0179c179a1792178a178817871786174b17841782177a1776176e001e0003071f0727073b080708190895089d0a790a810ac90acb0acf0ad70d0f17231718173b174117571761176b176a171f176817671766176517641763⟩, ⟨0x52028013809804a023010c08003e0198094046022010807403801b00d006002c014009004402000f00700340140090038014004000, 0x18301829182e182d182c182b182a18291828100d17bf17cb1822102918211820100b181f181e0f8d0ff608fb09030f950fbf0fdd10e911bd143517af17e3001e000303df03e703ef0f950f9d0fed10e911bd143517af17e31817181c0ffb181a1818001e17bb17e517eb181418121810180a1809180818011806180318021801180017fe17f817f217ec11c411d711e517e017da17d717d617d517d4102917c717d217cf⟩]) (
(.branch 2 (
.leaf #[⟨0x50027013409804b025012408e04602280d406603201880c005e02d01600ac054029014009c04c01b00980480160070028010004000, 0x189e1249189c1898189618941892188e11df18881884001e06e1077b14951497149d1515184b184f185318551857185d186b186d1873187e187d187c187a1876187418681867186618641860185e1850184c1844001e000303df03e703ef0f9d0fed17af17bb1817183f0fa4000303df03e703ef0cd50fed18171840001e0f7110e911bd143517bd17eb001e17b917e31839183c180918361834183318321831⟩, ⟨0x2f01700b405802a0138098048023011007803801a00c806002c01500a004c024011008003001600a004001c00c005002000c004000, 0x19281924191c1912190f190e190b190d190c190a126119081904001e18d318ed18f7190018ff18fe18ef18fc18f818f018ef18ee18ea18e218dc18da18d8001e18a518bf18c918ce18ca18c218c118c018bc18b418ae18ac18aa18a0189f⟩]) (
.leaf #[⟨0x3c01d80e407003701b00d40680290138090046021010007c03a01b00d006403001700b004802200d006002c0100060020008002000, 0x199e199a19991998199619841980197c188c14951497149d15151853186b186d1873188318871978197719761973197519741972122b1970196c196619651964196319621960195e19581952001e1917192d19471948001e19151931193d1944194219181923193b193a193319381935193419331932192e⟩, ⟨0x4202080fc07c03d01e00ec07203801b80d806a03401980c805e02e01600ac054029008803c01c00b005002000e0060028010006000, 0x1a1c1a181a171a161a141a0419fe19f619f519f419f219ee19ea19e819e019da19d419cf19d319d219ce19cd19cc19ca19c6001e03a703af03bf09c50adb0cdd0ce50ce90f5d103f14951497149d151517b71853186b186d18731883199319a319ab19c019bf19be19bc19b719bb19ba19b619b519b419b219ae19ac19a419a0199b199f⟩, ⟨0x3c01d00e407003701b00a004c024011807c03a01c00d806403001500a0048022010007803801a00c00580280100060028010006000, 0x1a821a811a801a7e1a7a1a78001e03a703af08fb099909d50a5d0bb50be10be90bf10f63197b19831a701a6d1a6c1a6b1a6a1a6819e719fd1a331a661a651a641a621a601a5d1a5c1a5a1a551a591a581a541a531a521a501a4e1a441a401a3c1a381a341a2c1a2b1a2a1a291a281a261a221a1e1a191a1d⟩]))))) (
(.branch 4 (
.leaf #[⟨0x29014009c04c023011008003a01c00d806803201800b805802a0140098048022010007803801a00c005002400c0050018008002000, 0x1b0a1b061afe1af61af31af51af41af21af11af01aeb1aef1aee1ae81aec1ae61ae21adc1ada1ad41ad61ace1ac81aca1ac21ab61ab21ab01aaa1aa61aa31aa21aa01a9b1a9f1a9e1a9a1a991a981a961a94⟩, ⟨0x2d01600ac054029014009c04c025011808403e01d00c805c02a013009004402000f006803001600a004802000e0060020008002000, 0x1b8a1b861b821b801b781b721b6e1b6c1b661b5d1b641b611b601b5f1b5e1b5d1b5c1b3f1b411b5b1b5a1b531b581b551b541b531b521b4e1b461b421b3e1b3d1b3c1b3a1b361b2e1b261b1e1b181b121b111b101b0f1b0e1b0c⟩, ⟨0x3201880c005e02e01600a8052028013809804a02000f007003601700a804c024011008003801800a004001c00c005002000c002000, 0x1bfe1bfa1bf81bf01bec1be91be81be71be61be41be01bdc1bd4001e0c211b171b1d1b511bd01bcf1bce1bc11bcc1bc81b2d1b511b691bc61bc31bc21bc11bc01bbe1bbc1bb41bb31bb21bab1bb01bad1bac1bab1baa1ba81ba01b9a1b941b8e1b8d1b8c⟩, ⟨0x44021810408003f01f00f407803a01c80e006e03601a80d006203001700b405802000f007003401800b80280100060020008002000, 0x1c761c721c711c701c6e1c6c1c601c5a1c521c511c501c4e1c4a1c461c441c3c1c381c331c371c361c321c311c301c2e001e0bff11bd17af17e318811a771aa91ad91ae11afd1b4d1c1a1c191c181c111c161c131c121c111c10001e00050ae50aed0b930b9b0ba10c131b1d1b511bd31bdb1bf71c0e1c091c0c1c091c081be71c061c051c041c02⟩]) (
(.branch 2 (
.leaf #[⟨0x4602280e006c03501900c405e02e01680b00560280138094048023010807c03c013008804001a00c00500240100070030010006000, 0x1cd6001e03df03e703ef05070527052b09050cd513f713ff1ca51cbb1cd01ccf1cce1ccc1cc71ccb1cca1cc61cc51cc41cc21cbe1cbc1cb41caf1cb31cb21cae1cad1cac1ca81ca01c9f1c9e1c9d1c9c001e0003038d03d703df03e703ef13f713ff1c6b1c851c9a1c991c981c961c911c951c941c901c8f1c8e1c8c1c881c861c7e1c7b1c7a1c781c731c77⟩, ⟨0x2d01600ac054029014009c04c025010808003e01e00e006803201800b8054026012008804001c00d005002400e006002800c002000, 0x1d5e1d581d561d541d461d3e1d3c1d3a001e1cff1d051d291d321d301d2e1d241d211d201d0d1d1e1d181d121d101d0f1d0e1d0d1d0c1d061cfa1cf41af71cf01cec1ce91ceb1cea1ce815fb1ce61ce21cde1cdd1cdc15e11cda⟩]) (
.leaf #[⟨0x3201880c005e02d015809c04c024011008403c01c00d006403001700b0054028012008804001e00e00600280120060020008002000, 0x1de01dd81dd01dc81dc51dc41b0f001e1da91db71dc11dc21dbe1dbd1dbc1daf1dba1db61d971dad1db41db11db01daf1dae1daa1da21d9e1d9c1d901d881d871d861d841d801d7e1d761d751d741d671d721d6e1d4b1d4f1d6c1d691d681d671d661d64⟩, ⟨0x2f01680b00520270128090046022010808003e01e00e006803201600a804c024011008003c01a00b005002400e0050020008002000, 0x1e5e1e511e5c1e581e351e4f1e561e531e521e511e501e4c1e441e3e1e3c1e3a1e2e1e221e211e201e1f1e1e1e1c1e171e1b1e1a1e161e151e141e121e0e1e061dfe1dfd1dfc1dfb1dfa1df61df01def1dee1ded1dec1dea16011de61de4⟩, ⟨0x2f01680a80520270130094048023011008403e01d00e006c03401900c005c026012008804001a00b004801c00c005002000c004000, 0x1ed81ed71ed61ed31ed51ed41ed21af11ed01ecc1ec41ec21ebc1eb81eb41eb31eb21e1f1eb01eac1ea41ea01e9e1e9c001e1e671e7f1e8d1e961e941e921e621e6d1e891e881e811e861e831e821e811e801e7c1e741e6e1e681e601e5f⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3701a80d006603201880c005e02e01680b0056029013809404602100f806c03201800b0054028013004001800a0040018008002000, 0x1f561f551f541f521f4e1f4a1f481f401f381f2c1f301f261f201c131f1e1bad1f181f151f141f131f121f0f1f101f0f1f0e1efb1f091f0d1f0c1f0b1f0a1f081f071f061f001efc001e04cd04e90895089d0bff0dc50e211b691ebb1ee71ef21ef11ef01eee1eea1ee81ee01edc⟩, ⟨0x29014009c04c025012008c04201f00f007403801900c005802a014009804802000e006803001600a004802000c0040018008002000, 0x1fea1fe81fdc1fd41fd01fce1fcc1fcb1fca1fc91fc81fc61fc21fbe1fb91fbd1fbc1fb81fb71fb61fb41fa41f9e1f981f971f961f951f941f921f8e1f8c1f8a1f7e1f7a1f791f781c9d1f761f701f681f60⟩, ⟨0x3d01e00ec07403801b00d406803301880c005e02e01680b005402800d006403001700b0054028013007002400e0050018008002000, 0x205820542050204c204b204a204920482046204020382037203620342030202c202a2022202120201a6b001e04a904b70a6d0ddd0de50e010e250e290e2d13f713ff1cab201d201e201a20182014200c20021ffe001e1e2d1e7b1fe31fef1e341e4b1e7b1fe31fef1ffa1ff91ff81dfb1ff61e531ff41ff01fec⟩, ⟨0x4001f80f807803a01c80dc06a03401980c8062030011807803a01c00d806803201700b0054028013009004001e00e0038014008000, 0x20d420cc20c420c320c220b720c020bc20b920b820b720b620b420ac20a820a6001e0433044d046f04771387138f13af13c11f252083209d209f001e044704630af5209b20982094208820862084207c207b207a2078207420722068206416972062205e15740cd518871fdb1fdf1fe11ffd205c1553205a2008204f20532057⟩]) (
(.branch 2 (
.leaf #[⟨0x3b01d00b405802b00f007003601a00c806002e01600a8050026012008804001e00d006002c014009003801800a0040018008002000, 0x2152001e046f0477049d04a1082b08310ddd0de50def214321452149214a2146001e097d0d230ddd0de50e250e3320df210f211b2121212921312140213f213e213c213821342132212a212621242122211821162114210c210421032102210020fc20fa20ee20ed20ec20ea20e620e220e020d820d6⟩, ⟨0x4202080fc05602a01480a004c024011808802e01600a8050024011008003c01c00d0058028012008003801800a0040018008002000, 0x21c621c2104f001e000503a703af03bf03df03e7047b04830ce90d2316ab20cf20df20f320f921212129213121a721be21ba21b621b021ad21ac21ab21aa21a8001e049b050705230527215d216521972199219d21a121a2219e219a2194219321922190218c21882186217e217d217c217a217621722170216621622160215e21562154⟩]) (
.leaf #[⟨0x3301900c005e02e01680b005602a00f807403801b00c806002e01600a8050026012008804001c00d006002c014009003800c002000, 0x223e2236223522342232222e222a2228221e001e0bff0cd5159f1aa91ae11b4d1dcf1ea31eab1ffd221a110722162212220e220d220c220a22062202220021f421f021ee21ec21e421e321e221e021dc21d821d621ce21cd21cc153d21c521cb21ca21c921c8⟩, ⟨0x2b01480a004a024011008404001f00f007003401900b8054028012008804001e00e006803001600a004802000c0050018008002000, 0x22b422b122b022ae22a922ad22ac22a822a722a622a4229c229a22962295229422892292228e228b228a228922882286228522842282227e227a22782270226a2262225c2258225409ef224e224a2249224822462242⟩, ⟨0x29014009c04c025012007c03c01d00e006c03401900b805802a014009804801e00d006002c014008003801800a0040018008002000, 0x233e233c233a23362334001e22bd22ed23012315232e232c23262322231c231a2310230f230e230c23082304230222e822f522fb22fa22f922f822f622ee22e622e522e422e222de22da22d822ca22c622be⟩]))))) (
(.branch 4 (
.leaf #[⟨0x4302100f007403801b80d806a03401980c406002f01700b405801f00f007003601a00c005802801200800380100070030010004000, 0x23a823a00a190a57239b239f23a523a409ff239e0601239c2398239623922390238a01b1238823842380237c2378001e0445046f04770497049d04a108190895089d0b931eb71edb237423702255236e23642360235d235c235b235a235123562355235423532352235123500a1f0a2b0a2f0a4d0a4f234e234a23440277234223412340233f⟩, ⟨0x5602a01440a004e026813009604a024812008e045021810808204001f80f407803a01c00dc06c03501a00cc06402300b003400a000, 0x24162415241424112413241224100317240e2406240423fe23fa23f623f223ee23ed23ec1a2923e623e223e023da23d8019d23d623d423d323d223d123d023ce23ca23c823bc23b6001e0ba90d230ddd0de50e250e3320df20f320f921212129213121a723af001e0895089d0bff0dc50ddd0de50def0e211bb72061214523b1001e000502a1094d099909d5225b225f23ab001e000302a104a904b72221222722b7001e02a1049b229922b7⟩, ⟨0x3401980c806002e01680b005602a01480a004e02600c805c02c01500a004c0240100070034016009004001c00c005002000c004000, 0x249e249c24942493249224912490248e248c2488248024782472246c001e01cd02a3054b058505ad05cd0aa123fd2421244f24632465245e245d245c245a245624522450244824472446244524442442243f243e23d1243c243a24362430242a24262422241a2417⟩, ⟨0x4c025812008e045022010c08404101b00b00540280130094046021010007c03801a008803c01a00c0058028010007002000c002000, 0x24fe24fc24f724fb24fa24f624f524f424f224ee24e6001e016d01bd01cd029102a302f31649167516c724e1001e0003038d03d703df03e703ef0aa10ac7240b24de24dd24dc232f24d8232f24d224d024cf24ce22f924cc24c80164232124c324c224c124c022d122d7230123252329232b24bd24bf24ba24b724b8022324b624b424b024ae24ab24aa24a824a324a724a624a224a124a0⟩]) (
(.branch 2 (
.leaf #[⟨0x3401980c806002e01680ac0520280138098048023011008404001e00e006c03401900b805802a014009802400e0060028010004000, 0x258625842576257525741f952570256a25672566255d2562255c255a2550254f254e254c25482544253c25392538253725362534253025282527252625242520251e001e017b01c701cd01d902ab149514972505250b251224ff2510250c250625022501250024ff⟩, ⟨0x4902400e807203801680ac054029014009c04c02500b805802a0140098048022010007003401800b0050024010007003000c004000, 0x2610001e09370989099109dd0adf0af512af12c512cd25db25fb25ff2601260225fc001e0703072f12c512cd259d25af25bd25d325e125e925f825f725f625f425f025ec25ea25e2001e098909910a610a6512c512cd259d25a925af25bd25c525cd25d325d825d625d425ca25c825c625be25ba25b925b825b625b225b025a425a2259a2596258e2589258d258c25882587⟩]) (
.leaf #[⟨0x3101780b805a02c010007c03c01d00e006c03401900c005c02c0140098048022010007803801a00b004802000c0040018008002000, 0x26982697269626942692001e10e711bd17af17e31ea3268126852689268b268d268f26862682267a2674266c266e2666266026622650264a2649264826462642263e263c26342630262c262b262a261f2628262426212620261f261e261c26162612⟩, ⟨0x3901c00a004e025012008c04402100f807803801a00c805c02a014009004001e00e006803001600a004802000c005002000c004000, 0x2720001e10e711bd17af17e31ea325d3268b268d268f26a326a726a92705270b2719271a2716271527142712270e270c27022621270026fe26fd26fc26ed26fa26f226ef26ee26ed26ec26ea26e726e626bd26e426e026da26d826d226ce26cc26bc26b826b726b626b426ae26a4269c2699⟩, ⟨0x3c01980a8052028013809804a024011008003e01e00e807003201800b004c024011008003c01c00c005002400c0050018008002000, 0x1e00050ae50aed0b010b9b0c0b1d392781001e000308190895089d0b391d392781278d278e278a27882786277c2774276e276b276a2697276627622760275c27542751275327522750274f274e2749274d274c2746274a27442740273c273b273a2739273827362731273527342730272f272e272c2728⟩]))))))))))) (
(.branch 35 (
(.branch 17 (
(.branch 8 (
(.branch 4 (
.leaf #[⟨0x3e01e00e407003701b00d406803001680ac0520280138098046022010007c03c01d00e003401600a004802000e006002800c002000, 0x281a269928102801281728182812280c280a2808001e278127eb27ff27fe277f27ed27fc27f927f8279127f627f027e827de27d927dd27dc27d827d727d627d427cc27c6001e10e711bd17af17e31ea32083268d268f27a527a727a927af27bd27bf27ba27b927b827b627b227b027a2279a27942793279227912790⟩, ⟨0x3901c00d806a03201880bc05c02d01600ac054027013009004202000f807803a01c00d006002e01600a80280100070030014008000, 0x2886288428812880287e2879287d287c2878287728762874287228662864285e285b285d285c285a2859285828532857285628502854284e284a284628452844284328422840283c001e1d39208327e127e327e527e7280f281f28212827283228312830282e282a2828001e280328112815⟩, ⟨0x3501a00cc06403001700b4048023010807c03a01b00c805c026011008003801a00c0058028012008003801800a0040018008002000, 0x290c2908290628fa28f728f628d928f4001e000313711387138f20912093283528ef28f028ec28e928e828e728e628dd28e428e128e028df28de28dd28dc28c328d728db28da28d928d828d628d528d428d028ca28c428c028bc28b628b428ae28b028aa28a228a42890⟩, ⟨0x3101780b805a02c01580a8052028013009404402100f807803a01c00d006002e01600a804c02201000780380140060020008002000, 0x29802859297e297a29742970296c296a2968295c2959295829562951295529542950294f294e294c294a293e293d293c293b293a29382934292e292d292c2843292a292829262920209f283528ef291e283528bb2913291c29192918291729162914⟩]) (
.leaf #[⟨0x270130094048022010807c03a01c00d806803201800b0054028013009004402000f007003401800b00500240100070030010002000, 0x2a0229fe29fc29f429e729f029ec29e929e829e729e629e429e029dc29d829d029cf29ce29cc29c829c429c229ba29b429b029ae29a4299c299a29982990298e298a298629852984298129832982⟩, ⟨0x3d01e00ec07403901b80d406803001700b0054029013808c04201f00f007403801b00d006002c01500a004c024011008000c002000, 0x2a6c2a6a2a642a602a5c2a5b2a5a2a4b2a582a5427c129ab29d72a522a472a502a4d2a4c2a4b2a4a2a482a472a4629db29f52a452a4429f12a402a3f2a3e2a3c2a382a342a322a2a2a272a262a252a242a202a1a2a162a0e2a08001e0005209321d521eb21f321ff27c1291329b929c129d729fb2a062a052a04⟩, ⟨0xb2056827812208403c81b80c2054029814409e044021810806a03401980c8048023011008403e00e006803001600a0030010004000, 0x1e02a1095f096b23ab001e01cd03df03e70415041b047b04830bd1215d2165219921a123952ab9001e0acb0bd90ddd0de50def2145215d2165216f21852aa92ab72238018101bd04a904b705150a6d0ddd0de50e250e3322992a9f096c034d038d03a703af03bf09c50aa10ac70ad30adb001e02a102fd08fb091f0f6d11b3156518531dd72339001e09370989099109dd219d21d521eb21f321f921ff25a72633001e037b03a703af08fb098909910a5d0a610a650f211f231f252ab42ab02aaf2aae293b001e000313711387138f2091209327c12a152a312a432aac2aaa001e0a6d0ddd0de50e250e3313711387138f25fb2a832a9f2aa72aa42aa22a9c001e1387138f13c1206b2071208320b3215d2165219921a12a8f2a992a942a922a902a882a75001e046f0477049d04a10af513711387138f2093209b27c128b32a152a312a432a832a842a802a7e2a78208e27c12a152a692a742a6d2a722a6f2a6e2a6d⟩, ⟨0x3c01d80e807203801b80d806a03301900bc05c02c01580a8052028013809804a023011007c03c01c00d806803201800b003000a000, 0x2b262b222b202b182b142b122b102b082b072b062b042aff2b032b022afe2afd2afc2afa2af62af42aec2ae42ae02ad82ad52ad42ad22acd2ad12ad02acc2acb2aca2ac82ac62abc2aba0657001e016d017b01c501c701cd01d902a102a502fd001e02fd091f0927092f221d229f23a00a130a19239b239f⟩]))) (
(.branch 4 (
.leaf #[⟨0x3901c00dc06c03301900c005e02e01680b0056027013008804001e00e006c03401800b805802a014009804802000f0020008002000, 0x2b8e2b8a2b882b802b7b2b7f2b7e2b7a2b792b782b762b742b642b62242c22d122d724d72b6022ce2325232924d52b5e2b5b2b5a2b312b5810232b562b542b4e2b4d2b4c2b4a2b462b422b402b382b322b312b30001e000304e913f713ff2ac52aeb2af32b0f2b172b1f2b2e2b2d2b2c2b2a⟩, ⟨0x3001780b805a02c01580a404e025012008804202000f807803a01c00d8068032018008003801a00a004801c00c005002000c002000, 0x2c062bfe2bf22bf42bec2be806b12be62be52be42be32be22be02bdf2bde2bdc2bd82bd42bd22bca2bc62bc42bbc2bb6001e00050cdd0ce52b732b872b952b9b2bb02baf2bae2bac2ba72bab2baa2ba62ba52ba42ba22b9e2b9c2b922b912b90⟩, ⟨0x2d01580a8052028013809804a024011808803601900c005c02c01500a004c024011007003401600a004801c00a0040018008002000, 0x2c962c952c942c922c902c862c7c2c7a2c782c722c6a001e0bd91f831f892c4b2c532c592c642c632c622c602c5c2c5a2c502c4e2c482c442c3e2c392c3d2c3c2c382c372c362c342c262c252c242c232c222c202c162c0c2c04⟩, ⟨0x2b01500a4050027012808c04401f00f007003601a00c806002c01500a004c024011007803401800b00500240100070028010002000, 0x2d122d0e2d0c2d002cf82cf72cf62cf52cf42cf22ced2cf12cf02cec2ceb2cea2ce82ce42cdc2cd42cd32cd22cd02ccc2cc82cc62cbe2cbd2cbc2cbb2cba2cb42cb22cb02caa2ca62ca22c9f2c9e2c9c2c972c9b2c9a⟩]) (
(.branch 2 (
.leaf #[⟨0x3001780b405802b01500a404a024011808404001f00f007403801a00c005c02c01500a004c01e00e00600280120060020008002000, 0x2d8e2d862d852d842d822d7e2d7c001e2d532d672d6f2d742d702d6a2d692d682d642d5c2d582d562d4a2d492d482d472d462d442d422d3e2d38001e2d172d252d2f2d302d2c2d2b2d2a2d1d2d282d242d072d1b2d222d1f2d1e2d1d2d1c2d18⟩, ⟨0x2a01480a004e026012809004001f00f007403801b00d006002e01600a805002000e006002c014008003801800a0040018008002000, 0x2e1c2e1a2e142e0e2e0c2e0a001e2dfb2dff2e032dfc2df02de82de22de02dde2dd62dd52dd42dd22dce2dcc001e2d972db12dbb2dc42dc32dc22db32dc02dbc2db42db32db22dae2da62da02d9e2d9c2d922d90⟩]) (
.leaf #[⟨0x3001700b005602a014809c04c025012008c044021010007c03c01c00d806802c014009004401c00c00580280120070028010004000, 0x2e8e2e8b2e8a2e892e882e862e822e7c2e7b2e7a2e782e742e722e6a2e642e5e2e5c2e5a2e5227f92e502e4c2df42d172e012e352e462e452e442e3b2e422e3e2d4d2e372e3c2e3b2e3a2e382e322e2a2e292e282e1d2e262e222e1f2e1e2e1d⟩, ⟨0x91048023c11c08c045022410c085041820810208003f81f80fa07b03701b00d406903281880c206002500d404e0260128038002000, 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⟩, ⟨0x3701b00d406803301900c406002f01700b4052027012809003201700b004c024010007803801a00c005002400c0050018008002000, 0x2f682f642f5e2f582f562f542f4a2f422f3e2f3c25522ec72ee92ef12f3a2f392f382f372f36001e000308190895089d0b390b9313f713ff2f052f1f2f342f332f322f302f2b2f2f2f2e2f2a2f292f282f262f222f202f182f152f142f122f0d2f112f102f0c2f0b2f0a2f082f06⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3a01c80e006e03601a80c806202f01700b405802b015008003801900b805802a013008804001e00e00680300140080038010004000, 0x2fe62fe42fe02fdc2fd82fd42fcf2fd32fd22fce2fcd2fcc2fca2fbc2fb42faa001e208327e127e32cff2d8d2dff2e352f632f9d001e2f7d2f8d2fa72f982fa12fa52fa42f912fa22f9e2f962f932f922f912f902f8e2f882f822f802f782f772f762f692f742f702f4f2f672f6e2f6b2f6a2f69⟩, ⟨0x52028814009604a024812008c045022010c07e03801b00d006403001780b805a02b014805c014008003801800a0040018008002000, 0x30483044001e1f1d27eb280f2e9f3040303e303c303a3039303830363032001e0533054b302d1824179117cb1a3b1a433029302b302a1a4130281a6330263023302224453020301c3018301214df300e14c7001e01db036b038d03a703af03bf0a6d0a790a810a850a8b0aa10ab30d2f2421244f2465001e0ba90d230ddd0de50e250e3320df210f21212129213123af300a300930083006300230002ff82ff42ff02fee⟩, ⟨0x540258128090046022010808003e01d00e006e036012005c02c01500a0048022010007803801800a004802000e006002800c002000, 0x1e000313711387138f26d72d2f2d8d30bf30c030bc30bb30ba30b930b830b130b630b530b430b330b230b130b026b930ab30af30ae30ad30ac30a6001e06ed0703071f0727072f073b074d08fb0f6d10cb10e911b311b711d711f512e112ef001e0a790a810acf0ad70d1d0d2321eb21f3221122152a193097309c309a309430883087308630843080307e307630753074307330723070306e306830623058305530541fc93050⟩, ⟨0x4901b80cc06202f01700b40560290140098048023011008404001f00f006c03201800a804c024011007803801a00c0058028012000, 0x1e07bd084d08fb0f0d10d111f51519157518bb18e91915194b194d1e671fef312b3135001e1e7b1e8b312d3132312f312e1e8131283122311e08ed311c07fd311a31163115311431133112311031083104310030f630ee30e930ed30ec30eb30ea30e807fd30e730e6078930e030dc30d830d730d630d430d030cc30ca30c2001e000512af12c512cd25ff2d2f2d8d30a5⟩]) (
(.branch 2 (
.leaf #[⟨0x43020810006a03301880c005a02c01580a805201e00e807003401700a8050024011008003c01a00b005001c00c0040018008002000, 0x319c0371319a001e01cd037b03a703af0703072f0a5d0ac523cd31993196251331920203318e318c31873189318a31843180317e001e037b03a703af0703072f08fb0a5d0f63197f19833178317631741803317217cb182131700d39316c316407c73160315c3158315631553154315331523150314b314f314e314a3149314831463140313a⟩, ⟨0x3d01e00ec07403901c00dc06c03401980c805c02d01580a405002600e807003601900b8048022010007802000c005002000c004000, 0x320031fe31fc31f631f031ea31e631e21b5531e031dc1f5a1c591f471f5931d831d61ed731d21fd131d031ce31cb31c80c591c431f471f591f5f1f731f7531c531c631c231be31bb31ba155f001e10e911bd17eb31af31b831b631b4001e19e719fd20092029203f31a331ac1ced31a831a631a431a0319e166b⟩]) (
.leaf #[⟨0x5f02f01740b805b02d010407e03d01a00bc05a02c01500a4050027012808c044021010007803801a00c00580280100078010004000, 0x327032683260325c325a001e03df03e703ef046f0477049d04a1052b0f9d0fdd14951497149d15151817183f1853186b186d1873188319a3263332533250324d324c3227001e000308190895089d0b390b932f41323132420b071f093239324b324a303932483240303b323c323a3236322c32293228322732263222321c321632133212321132103209320e320d320c320b320a3209320807f70805311d3206001e000307f1080708190895089d08cb08d708db30fb3204320332023201⟩, ⟨0x3601a80b0054029014009c04c025012008804001f00d806002e01500a004c0240100078030016009004001c00c0050018008002000, 0x32cc32520433044d046f047725c5325732b332bb32ca32c932c832c632c232be32bc32b432b032ad32ac32ab32aa236c23732383238732a832a332a732a632a232a132a0329e329c3298329732963294328f32933292328e328d328c328a32863284327a3279327832763272⟩, ⟨0x4d024811c08a044021810408003f01f00f407803a01c00d806403101780b004a024011008003e01a00c806002e0160088010004000, 0x249601db041524873322332133202491331e331a3314331333123310330c3308330632fc32fb32fa32f932f832f732f624b324b924bb32f432f2058d164616531675001e092914951497149b149d150132f032ee32ed32ec171332ea001e16d316df236d32e532e632e032de32d8001e16f32349237732d3001e03a703af03bf0a6d0a790a810a850a8b0ab30cd50d2f21c132d032cf32ce3173⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3b01c80dc06a03401980c806202d01580a804e026012008c044021010007803a01a00c805c02c01500a002400e005002000c004000, 0x338c3385338a33873386338533843382337e337a0c640c8b0d430d59336e336d336c336a3365336933683364336333623360335c335a3352334f334e334c3347334b334a3346334533443342334008b408190895089d08d708db1eb7325732b332bb332f333a333733360e573334332c3328332432f7⟩, ⟨0x5402981480a20500278130096049024011c066031012809004602000f807803a01c00c806002e01600a804c0220100078038004000, 0x341034083406340033f633ee33e933ed33ec33e833e733e633e4001e01cd030d03df03e7047b048306ed0703071f0727072f073b074d08190895089d17231eb7332f33d033370d9201cd030d03df03e7047b048308190895089d08d71eb733ce33cc33c833bb33c733c433c033be33b833a433b133b333b433ae33aa33a833a2339f339e339d339c339a3396001e000301db038d039d03df03e703ef052b247f32ff3305338e338d⟩, ⟨0x2d01600a804e026012809004602200f007403601900c0058028013009004402000f0070030014009004001c00c0050018008002000, 0x3486348434833482347d34813480347a347e34783474001e343d3457346b346c346834673466345b34643460345d345c345b345a34583452344e344c344234363435343434333432342e342c34283422341a3419341834163412⟩, ⟨0x3001780b805a02c01580a8052025011808403a01c00d806803001600a004c024011008003c01c00d00600280100070030014006000, 0x3510350a3500350234fa34ee34f0001e10ad10bd34e334e834e534e410b3001e34b134b534d734e034de34dc34d434d334d234cf34d034cf34ce34cc34c634c034ba34ae34ac34aa34a2349f349e349d349c349a3494348a3489348834853487⟩]) (
(.branch 2 (
.leaf #[⟨0x3801b80d406803301900c405e02d01600ac054025012006803001700a004c022010007803801a00c005002400c0050018008002000, 0x3584358235813580357e35763572356e356d356c356b356a35683564001e134b35533559355d355a001e12d713f713ff34393519352f35333535353b3550354f354e354c3547354b354a3546354535443542353e353c3530352c3529352835263521352535243520351f351e351c351a⟩, ⟨0x3401980c806203001780b805802b00f007403801b00c805c02c01500a004c024011008003801800b0050024010007002800c002000, 0x3606360235fc35f435ea35e635de35dd35dc001e04330447044d0463046f0477215d2165216f21852a192a7b35da35d835d635cc35cb35ca35c935c835c635c435c235bc35ac35a235a0359f359e359d359c359a3598359635923590358f358e13cb358c3585358a⟩]) (
.leaf #[⟨0x2f01680ac0540280130094048023011008404001e00e807003601a00c0050024011008003801800b004802000e0060028010004000, 0x367e367d367c3671367a36763673367236713670366e3668366236603656364a18c3364836443642363c36383637363635df35e536353634363336323630362e362b362a360736263620361f361e361c361836143612360a360936083607⟩, ⟨0x6d03601a80d006603201880c005c02d01640b004901e00ec07003601a00c806202b015007403801a00c0050014006002800c002000, 0x36c036bc36bb36ba36b936b836b136b636b536b436b336b236b136b01b3f36ab36af36ae36ad36ac36a4001e0a790a810acf0ad70ae50aed0b3f0b510b570bff0c210d1d0d231bef001e098909910a610a6512c512cd13c51f231f2525bd25e9365b369e369a080130ed369836973696369536940a21369209f602a102fd0923092709293690001e0463098909910a610a650ae50aed0b3f0b570b870bff12df368e368c368b368a35a3316e0c770c8b177f096a094d099909d512c512cd25bd25d325e926051f3c1c431c5931c53688368618f1368436733682⟩, ⟨0x69034019c0cc06503201740b805a02c012409004702300d806a03301900c406002f01700b0054023010807c03a01900b803c002000, 0x372c3728372637223714371212d7312733fd355d36f936ff3710370c370937081173001e000312d7135d136b13711387138f33fd3559355d36f936ff370337073704370036fc001e12d72633312533fd355d36d536d936db36dd36df36e536f336f736f936fb36f436f036ef36ee36ec36e836e636d636d2305536d02375001e018101bd095f096b2277236336ce36cd36cc36cb36ca36c936c814bf14d5300f36c632ad001e000313f713ff3267326f327d3283001e03a703af046308fb098909910a5d0a610a650f6312df197b198336c4⟩]))))))))) (
(.branch 18 (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0x3601a00cc06403101800bc05c01e00d806803001700b0054028013009004402000e0068030016008003801800a0040018008002000, 0x37a637a537a437a2379e379837963794001e0bd91069109b340f3421343b3473348d34b3371f37313737373f3743377b37863783378537843782374f3780377c377637723770376837643762375c375b375a37583754374e3749374d374c3746374a37443740373c373a3738⟩, ⟨0x3e01e80f005a029014009c048022010007803a01c00d806803201700b0054028013009004402000f0070034012006002000c004000, 0x3822381e001e13c518bb192d340f378937bb37c137cb37d337d537db37e937eb3803001e37f1380738133818381637ec37f9381138103809380e380b380a38093808380437fe37fa37f237e637e537e437e237de37dc37c837d037ce37c637c437c2001e378b378f37b137ac37b537b937b837a537b637b237aa37a7⟩, ⟨0x4d026012408e0460228110086042020810007e03d01d80e807203601a80cc064031010803c01c00d00600240100060028010004000, 0x389438903871388b388e388d388c38883880387a38783876386c38643860385f385e2739385c38583850384d384f384e384c274f384a3846001e03a703af03bf09370989099109dd0adf0af50ce90f5d103f17af17b717bb001e03a703af03bf09370989099109dd0adf0af50d2f0f190f390f4f103f17af17b717bb3840383e383c383438313833383238303483382e382a3826382538243649⟩, ⟨0x3f01f00f407803a0140098048023010007803a01c00d806803201800b8054026012007803401600a004802000e0060028010004000, 0x391e3914390e39083787001e0bff28152ca52cb92d372d632d7b2dad2e9f307d3775384538573863388738a338f339043903390238f9390038fc38dd38f738fa38f938f838f438ec38e638e438e238d838d038cf38ce38c138cc38c838a538ab38c638c338c238c138c038be38ba38b438b238b038a0389838973896388d⟩]) (
(.branch 2 (
.leaf #[⟨0x4c02581280920480238114086042020810006a028013009004601800b0054024011007803801a00c00580240100050020008002000, 0x397839763972396c39663962395f395e395d395c395a395606d4071f0727077708d7096b09c50ad30adb12e312e7001e0b6d0b750bc10bc512af12c512cd1f811f9125fb26072e91395239513950394f394e001e000313711387138f13f713ff25fb26d7391d3937394c394b394a3948394339473946394239413940393e393a39383930392d392c392a3925392939283924392339223920⟩, ⟨0x3401980c806203001700b005602a01480a004e01800b0054028013009004402000f007002c014008003801800a0040018008002000, 0x3a083a063a0039fc39f639f539f439f339f239f039ee39ea39e2001e09370989099109dd21d521eb21f321ff26332997309f39c339cb39d139dc39db39da39d839d439d239c839c639c039bc39b639b139b539b439b039af39ae39ac399e39963990398839803982⟩]) (
.leaf #[⟨0x3601a00cc06002f01680b005602a01480a004c025012008c04402100f807403801a00c806002e01600a00480220040018008002000, 0x3a7c3a793a783a763a713a753a743a703a6f3a6e3a6c3a6a3a603a5a3a523a513a503a4e3a4a3a463a443a3c3a3b3a3a3a393a383a343a333a323a303a2c3a2a3a223a213a203a1f3a1e001e046f0477049d04a10acb0ddd0de50def214526332aa932533a1c3a1a3a163a10⟩, ⟨0x4101f80f407603901b80cc06203001780b4056029014009c04c024011008403a01b00c806001a00b005001c00c0040018008002000, 0x3ad03acf3ace3ac53aca3ac93ac83ac73ac63ac53ac435833abf3ac33ac23ac13ac03abc3ab810873ab63ab33ab23ab13ab03aae3aaa3aa63aa53aa43aa33aa23aa0398b3a433a593a9e3a9d3a9c3a9b3a9a001e000313f713ff215d2165219929972a773a693a833a983a973a963a943a8f3a933a923a8e3a8d3a8c3a8a3a863a84⟩, ⟨0x5402981480a2050027813809a04c023810407e03e01e80f007603a01c00d806a02900f007403800a004001c00c005002000c004000, 0x3b423b403b3a3b323b263b223b1a3b14001e107f10ad114f3b0b001e107f10ad115311573b0b3b1211753b103b0e3b063b043b023b003aff3afe3afd3afc365a0a6d0a790a810a850a8b0ab312af12c512cd12d72e91001e0703072f128912c512cd13c525bd25e9368139653afa3af6001e09370989099109dd0adf0af50f0d1155129d12af12c512cd2e9136513ad73adb3ae13af03aef3aee3aec3ae83ae43ae23ad83ad43ad1⟩]))))) (
(.branch 4 (
.leaf #[⟨0x3d01e00e806002c01580a404e026011808804001f00f007403801a00c005c02c012008804001800b004802000e0060028010004000, 0x3ba03b96349f001e0bd9343b34a534b3371f373137373887389f001e38a338a938c93b943b923b913b903b8f3b8e3b8c3b873b8b3b8a3b863b853b843b823b7e3b763b703b6f3b6e3b6d3b6c3b6a3b2a3a593b633b673b683b643b2e3b393b4d3b5f3b603b5c3b5b3b5a3b583b543b503b4e3b463b453b443b43⟩, ⟨0x46022811008404001f80f807a03c01d00e404e01b00d006403001700b0048022010007803801a00c005002400c0050018008002000, 0x3c0c3c083c063c053c0413293c023bfe3bf63bee3bea36373be8001e000312d7215d216521992a77312533fd355d36df36f336f736f936fb3bd13bd53bd73be212d7312533fd355d36df36f336f736f936fb3bd13bdf3be03bdc3bd83bd23bce362235ef35fb36113bcc3bca3bc63bc43bc03bbe3bbc3bb93bb83bb63bb13bb53bb43bb03baf3bae3bac3baa⟩, ⟨0x4901f00f007603801b80d406803301900c405e02e01580a80500270130094048023010807c03c01d00e0068032012008804001e000, 0x1e000308190895089d0db30dbf13f713ff3c3d3c573c6c3c6b3c6a3c683c633c673c663c623c613c603c5e3c5a3c583c503c4d3c4c3c4a3c453c493c483c443c433c423c403c3e3c343c2e3c263c253c243c233c223c203c1c3c1829193c16001e1aa91ae11b4d1ecb2ca930313c143c123c0e001e0a6d0a790a810a8b21eb21f321ff25152517251d308b34d737373c0b⟩, ⟨0x4902400e406e032012809004001f00f007403801a00c806002e01600a804c022010007803801800a004802000e006002800c002000, 0x3cd0001e06e10895089d08a508b50acb0dc50ddd0de50def0e2121452aa9332b3cce36c9001e2349236b2377237b001e03df03e703ef052b09050cd52151215d21652169216f21853ccc3cbe2c0f3cc53cc93cca3cc63cc23cba3cb63cb53cb43cb23cae3caa3ca43c9e3c9d3c9c3c9b3c9a3c983c8e3c8a2e1f3c883c873c863c843c803c7c3c7a3c723c713c703c6f3c6e⟩]) (
(.branch 2 (
.leaf #[⟨0x5402981480a2050027813809a04c025012008e046022810007c03c01d80e807003601a80d0066032012008c0320130090040002000, 0x3d483d443d403d383d363d343d2e3d263d1e3d1b3d1a35db3d183d143d10001e200720132029203f3d063d053d0431533d023cfe3cfa3cf93cf80e5d3cf63cf03ce83ce4001e08fb0f6d10cb10e911b311d711f517af185d1e4b1e7b3cdb3cdf3cdc001e01cd02a302f317af1e271e4b1e7b33ad33c31e3201cd030d0fdd17af20cb3cd83cd634d1001e0a6d0ddd0de50e010e250e290e2d13711387138f25fb26d7300d3cd33cd4⟩, ⟨0x7603a01cc0e406503081800be053027812c07c03d01700a404e023011008404001b00b005002601200800300140090038018002000, 0x3d983d973d963d8c1b6803df03e7047b048308190895089d08fb09030b390b931f7d0c561c3b1c431c593d883d84365c0a790a810acf0ad70bb112c512cd13c5206125bd25e91a32201323dd23df3d80201323df23f521681387138f13c1215d21652199219d21a125d32fe92ff72fff3d7e001e04a904b713f713ff1cab201d2151215d2165216f21853d0f3d553d6f001e21693d173d713d733d7c3d6d001e35b13d713d773d7a3d783d74001e21693d173d253d573d203d2d3d433d5b3d5f3d6c3d5d3d6a3d643d623d613d603d433d5b3d5f3d5e3d5d3d5c3d5a3d593d58001e21f73d4f3d533d573d50⟩]) (
.leaf #[⟨0x7203881c00de06e03601a80d206803381980c8054029811808a04302080fc07a03c01d80e8072028009804800e0060028010004000, 0x3dfc3df83df63dee3dea3de93de819633de63de23dda3dd63dd22e3d001e07ad07cd080d08410bd926a72cdb2dcb2df3363f3641371f3731377b3c8d3dd0001e07ad07cd080d084d26a72def2df32e492e4b363f36413dcf3dcc3dc63dc33dc22d693dc03dbf3dbe30733dbc3db83db03dac001e08190895089d0a6d0b390ddd0de50e010e250e290e2d1b251d391d4f1f7d36bf1ef403a703af03bf0ae50aed0b3f0b510b570ce90f5d0f71103f10e314351cf91d7d1ecb27eb280f2e9f3da8001e04cd04e91387138f13af13c125d32fe92ff32fff3da63da23d9e3d9c2b333d9a3d99⟩, ⟨0x86042821010608204001fc0f807b03c81e00ee07603a81cc0e206502c015c0aa053028812c09404001a80b005601f009800c002000, 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⟩, ⟨0x6703301840be05d02d81600aa0530288100074035014809004401e00e006803001700a804c024011008003c01c00d0060008002000, 0x3e9c20c6152d153d21c521cb3e983e973e963e953e9421cd3e9036af3e8f3e8e1b3d36c336c21b3531ca31c9001e0cd513c5159f18551fdb1ffd30f9312133fb34393cdb3dd53dd93de13ded3df516b2149114951499149b149d001e0b871bd32f41324728000bff1aa91b4d1cfd1d391da9270b271927e73061307d0c220b931bef2f4132473e8c3e8b3e8a1f093239324b3e881d213e863e853e843e7d3e823e803e7f3e7e3e7d3e7c3e7a3e763e6c3e6a3e663e5e1db61d291d391d49208327a527a727bd28273e593e563e54⟩]))))))) (
(.branch 9 (
(.branch 4 (
.leaf #[⟨0xb805b82b41560a9053828c1440a104e026c13209804b825812a094049820c0e0063029011808a04402180c804601c0078008002000, 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⟩, ⟨0xb105802bc15c0ad05602ac1520a7053029414209d0488234116089042820c10207d03a81a40d0067028011406a023008000c004000, 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⟩, ⟨0x7b03b81d80e4063030817c0ba05b02c816009a03e01e80ec0720350138058028013008003c01a00c0058028012007003000c004000, 0x3f6e350935f136113f6c25a60adf0af525c5001e0a790a810ac90acb0acf0ad7208321eb21f32211221529ab2fdf2fe33f6405533f62388f3f602d6b3f5e2db53f5c38fb3f5a001e049b05070523052712d713711387138f13c92a83001e0433044d046f0477134b1387138f13af13c113c51f25209d352f3e9f3f583f563f533f522ee33f502ebd2ee92ef1209c03df03e703ef046f0477049d04a1052b0af50cd50fdd16ad1817001e0a6d0a790a810a850a8b0ab30ae50aed0b930b9b0ba10cdd0ce51bd33f1f3f393f4e3f4d3f4c3f4a3f453f493f483f443f433f423f403f3c3f3a3f323f2f3f2e3f2c3f273f2b3f2a3f263f25⟩, ⟨0xb104f823c0fe07e03681b00ce06302f814c0a4051027813809a04c025812408e04602280f806401d00e005c016009003801800a000, 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⟩]) (
(.branch 2 (
.leaf #[⟨0x11808704281f00f7074836c19c0cc06282bc15a0ab054826012809303e81ec0f207703a81940c6054029814407e03d0150058028000, 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⟩, ⟨0x90047822411008403f01e80ee07503701a80d206703301940be057028011808a04102000fc07c03d01a00cc04e01900a8018004000, 0x16c600ee250514971495017b24e816482c0f2c2e2bfd2bf62a6929132a492a53208e27c1232922cc22d124da36a636a336ab333f23af1a8836a31d4f039d0d931fac00c50d931d4f36bf0c311d48296327a633c233ac03d0039d03430339034d030303d0039d02dd02fd029102a102b902a502dd02fd029102b902a102a502d902dd02fd029102b902a502a10340036b035302d817e22c7f1abf039d044527ea280e2e9e1e4a2bc00a6d0a790a810a850a8b0ab32b873fe33fe4001e0ae50aed0b010b9b0ba11bd31d3927812bc12bc92bd12e7e049709370989099109dd12af12c512cd25fb26072e692e712e912c182c0b2c0f2cc5001e0bd1134b1387138f13af13c113c5215d2165219921a12ab9352f3e9f3f001333133d13433fe03171⟩]) (
.leaf #[⟨0x8903f01e80e806e035819c0bc05c02c014809804a023010c08203e01c80e006e02f017009804802300f806c0300160070020002000, 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⟩, ⟨0x89043821410808003f81c40d406203001640ac052027813009203f01d00e006602f016009c04801f00d80680320170080038006000, 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⟩, ⟨0x6f034818c0ba05702b01540a404c025812408e046022811008604202080e807202d014809403a01600a804802200f0060018006000, 0x3d002a502a102fd00ee010c24da03d002a502a102fd023f02fd02a502a1017b00ef010d03d002a502a102fd02dd010c063401d408b513a104470ef61347133d33d833f30ecb10ac3b9e36d821693d6e088a2e342f6211ac12f411340777310f08cb211b30df080707d107ac30ff3ded3de11fdb3cdb34393dd91855159f1ffd33fb30f90e6d0d680c8b08b23cdb0f6d11b300e6157420cb159f1ffd0fdd1fdb09031fe124e90d0f161e14b3049a02dd00ee11d606a82ac506c3054a023301c60241023d024202fd02a502a1017b01c7010d03d01e2702dd1e2702dd02d9⟩]))))) (
(.branch 4 (
.leaf #[⟨0xda06a83481a00cf06302f01740b2052828013009204482080f806c03381800aa04c02000e0062028011807c0320130060020008000, 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⟩, ⟨0x9a04a825012208604102000fc07903981c00de06e03681b00d606a03481780b6050027012c09404802300fc06002600c8030002000, 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⟩, ⟨0xc9063030417c0b305702a414409e04d026410207c037017c0a604a01f80e4062029014009404601f00e006002c014009004400c000, 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⟩, ⟨0x8303f01b40d606703081780a80530280128092048023811808a044021810007203401680a804201c009004402000f0050014008000, 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⟩]) (
(.branch 2 (
.leaf #[⟨0xed068031c1540a804f827812809104502080fe06b03401800b80570270134084032015009c04402100c004802200c0050018008000, 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⟩, ⟨0x1820b40568298138094847421c0ff077036c1a00c305f82c413c09d04e026c12e09304702280f8078034816408c0400190070030000, 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⟩]) (
.leaf #[⟨0xf907b03d01d60e607003601a80c8057829412407f03e81e40f006e03101740b4051025810807e03c01d00b40520260118080024000, 0x186a0139096b024200f80a2136cf149714953ccf02a1013902fd091f1bd3186a2e692e85049b1bd3186a2e692e85049b0445146a20133f662cb92ca5268f268d23f5147a20131a0c013706c4069b1bd313a1186a2e6903d00fdd09032e850445067303d001390fdd090305f80a2f22992a9f095f096b2cb9268f268d2ca51ad902dd2e85029102b92e7f225723dd04450f9d23a705f803d002dd01390fdd029102b9090323a705f501102e7f22992a9f095f096b268d2cb92ca5268f1ad922570a0005f803d00fdd0903013900ee05f82e7f010c03d022992a9f095f096b268d2cb92ca51853268f1ad91dd722570a0000ee05f40b510b86183f17bb04470fda17ea142b17db0b511ecb0f5d10e31cf91ef40ce9100e25cd26541f590b39186a28963c2d20910d1d1c591f730c251abc18811ad91b4d1abf1c59186a00b21f3e25cd1f83258126542bf62c0f265700b323dd0f9d02d802a523a7044505f80a002e8502a502d8024e2e7f2257041613a1291327a40fa50d93044434f8003e142b0fed14951853184f1515186d186b1497077708070d0f00e7133d37eb0043008f34f734f534f8350935ec35f135a43be4363725cd1f832bf625812c0f26540b391f2228963c2d20911c590d1d186a198815150ecb142b0807149714952b510fed25cd265428963c2d20910b390d1d1c591f23⟩, ⟨0x1660a5850c24e11208083f01e20e707203881c20df06e833017c0bc04d02400e406602c813c09604501b00d006002400f8044014000, 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⟩, ⟨0x820410208104082041020410007e03e81f00f407703981b40d006302e01680a004c025011c08403601700b4056025011808800e000, 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⟩]))))))))))))))

def policyFixedCompact1Db : Nat → List Int := policyFixedClauseDatabase 16 policyFixedCompact1ClauseTable

def policyFixedCompact1VariableTable : PackedNatTable.Table Nat :=
(.branch 0x80
  ((.branch 64
  ((.branch 32
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x3d603b803af03a8039d039c039a037c037703760375035803550352034f034402390212021101fd01fc01e601e101dd01dc01d501ca01c40010000a00050000, 0x535052a05290527051c050905040503050204e504e204df04dc04db04d504cb04ca04c904c704c604a904a404a304a204850482047f047c047503fd03fc03ef, 0x64c063a0639063606350634063306320626061506120611060f060c060205bd058f058e058d058b058a056d056a056805670566055a05490546054505430540, 0x6fc06fb06fa06f906f806e806d406d306d106ce06c506b906b806b606b50698069506930692069106850674066e066b066a0664065b065a0659065706560654])
  (.leaf #[0x78f07850784078307810780077e076407630760075f075e075d075c075a07500742073f073c073b07390736072d072307220721071f071e071c0712070006ff, 0x80e08090808080308020801080007fe07fd07fc07fb07fa07f007ee07ec07eb07ea07e907e007c607c507c407c307c207b707b1079e079d079b079807970795, 0x83b083a083908380836083508340833083208310830082e082d082c082b082808270826082408220821081e081d081b081a081808160814081208110810080f, 0x87d087b087908730872086f086c086b0868086708660865086408610860085f085e085b0858085708540851084c084b084a08490848084708450842083d083c])))
  ((.branch 4
  (.leaf #[0x8c308b308ad08a808a608a408a308a208a0089e089a089808970896089408930892088f088e088d088c088b088a0888088708860883088208810880087f087e, 0x90f090e090d090c090b0909090809070906090509040902090008fe08fc08fb08fa08f908f808f408ec08ea08e708e208e008dd08d708d508d208c808c508c4, 0x9460945094409420940093f093e093d093b093a09390938093709340930092c092a0929092809270925092409230922091f091e091609150914091309120911, 0x97f0979097809730971096d096c096a0968096709660963096209610960095f095e095d095c095b0958095709560954095309520950094e094b094909480947])
  (.leaf #[0x9c909c809c709c509c409c309c209c109c009bf09bd09bc09bb09ba09b909b809b509b409b309b109b009ad09ab09a809a709a609a309a209a1099d099b0981, 0x9fc09fa09f909f809f709f409f309f209f009ee09ed09eb09ea09e909e809e609e409e209e009df09de09dd09dc09d809d709d609d309d209d009cf09cb09ca, 0xa300a2f0a2e0a2a0a290a280a270a250a240a220a210a200a1f0a1e0a1d0a130a120a110a0e0a0d0a0a0a090a080a070a050a040a030a020a010a0009fe09fd, 0xa5d0a5c0a5b0a5a0a580a570a560a540a530a520a510a4d0a4c0a4a0a490a480a470a460a450a420a410a3f0a3e0a3c0a3a0a390a380a370a350a340a330a31])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0xa970a960a940a930a920a900a8f0a8e0a8d0a840a830a820a810a800a7f0a7e0a7c0a7b0a7a0a790a760a750a730a720a710a700a6e0a6d0a6c0a6b0a6a0a5e, 0xac70ac30ac20ac10ac00abe0abd0abc0abb0aba0ab90ab60ab50ab40ab30ab20ab10aaf0aae0aad0aac0aaa0aa90aa80aa60aa50aa40aa30a9f0a9e0a990a98, 0xaf70af60af30af20af10aee0aed0aea0ae90ae80ae70ae60ae30ae20ae00adf0ade0add0adb0ad90ad80ad60ad30ad20ad10ad00ace0acd0acc0aca0ac90ac8, 0xb300b2e0b2d0b2c0b2a0b290b280b270b220b210b200b1f0b1e0b1d0b1a0b190b180b160b150b140b120b100b0d0b0a0b090b080b070b060b000afe0afa0af9])
  (.leaf #[0xb610b5f0b5d0b5c0b5b0b5a0b590b540b4f0b4d0b4c0b4b0b4a0b490b480b460b450b440b430b410b400b3f0b3e0b3d0b390b370b360b350b340b330b320b31, 0xb930b920b900b8e0b8c0b8a0b890b880b870b830b820b810b7f0b7e0b7c0b7b0b7a0b790b780b770b750b740b710b6f0b6e0b6d0b6c0b690b680b660b650b63, 0xbca0bc90bc70bc60bc40bc00bbe0bbd0bbc0bbb0bb80bb70bb60bb50bb30bb10baf0bab0ba90ba40ba30ba20ba10ba00b9f0b9c0b9a0b990b980b970b950b94, 0xc020c010bfb0bfa0bf90bf80bf60bf40bf20bf10bf00bef0be80be70be60be40be30be20be10be00bde0bdd0bd90bd80bd70bd60bd50bd40bce0bcd0bcc0bcb])))
  ((.branch 4
  (.leaf #[0xc530c520c510c4f0c4d0c4c0c490c470c450c440c430c420c3e0c3d0c3c0c3b0c390c370c220c170c160c130c120c110c100c0f0c0e0c090c080c060c050c03, 0xc7f0c7c0c7b0c7a0c790c780c760c730c720c710c700c6f0c6b0c690c670c660c650c640c630c620c610c5f0c5e0c5d0c5c0c5b0c5a0c590c580c570c550c54, 0xcab0ca90ca80ca70ca60ca30ca20ca10ca00c9f0c9e0c9d0c9c0c9b0c9a0c990c970c960c950c940c930c920c910c8f0c8e0c8c0c8a0c890c880c870c810c80, 0xd040cff0cfe0cfd0cfc0cfa0cf90cf80cf60cf50cf40cf30cec0ceb0cea0ce90ce80ce70ce40ce20cde0cdd0cd90cd80cd70cd30cd10ccf0ccb0cc40cc20cac])
  (.leaf #[0xd350d330d320d310d300d2b0d2a0d290d280d270d260d240d230d210d200d1f0d1e0d1d0d1c0d180d170d160d140d130d120d100d0e0d0b0d080d070d060d05, 0xd650d630d620d5e0d5d0d5b0d5a0d590d580d570d560d540d530d520d510d500d4c0d4b0d4a0d490d470d460d450d440d430d400d3c0d3b0d3a0d390d370d36, 0xd990d980d960d930d920d8f0d8d0d8c0d8b0d8a0d870d860d840d830d810d7f0d7d0d7b0d7a0d790d780d770d720d710d700d6f0d6e0d6d0d6a0d690d680d66, 0xdd70dd50dd40dd30dd20dcf0dce0dcd0dcb0dc40dc30dc20dc00dbf0dbe0dbc0dbb0db90db70db50db30db20db10db00dac0daa0da00d9f0d9e0d9d0d9c0d9b])))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0xe0c0e0b0e080e070e050e040e030e020e010e000dfe0dfa0df90df80df70df50df40df30df10df00def0dee0de80de70de60de50de40de30de10ddb0dd90dd8, 0xe430e410e3f0e3c0e3a0e390e380e370e360e350e310e300e2f0e2e0e2d0e2c0e2b0e2a0e280e270e260e240e230e1e0e1c0e1b0e160e140e120e110e100e0f, 0xe700e6e0e6d0e6c0e6b0e6a0e680e670e660e650e640e620e610e600e5f0e5e0e590e580e560e550e540e530e520e510e4d0e4c0e4b0e490e480e470e450e44, 0xeb70eb60eb50eb40eb30eb00eaf0eae0ead0eac0eab0eaa0ea90ea80ea70ea50ea40ea20ea10e860e850e840e830e820e800e7e0e7d0e7a0e780e770e740e72])
  (.leaf #[0xf0c0f0b0f0a0f080f070f060f050eff0efe0efd0efc0efb0efa0ef90ef80ef70ef60ef50ef40ef30eee0ee90ee70ec70ec50ec20ec10ec00ebf0ebd0ebc0eb8, 0xf410f400f3f0f3e0f3b0f390f370f360f350f340f330f320f310f2e0f2d0f2c0f2b0f280f270f200f1f0f1e0f1d0f1b0f1a0f190f180f170f110f100f0f0f0e, 0xf740f730f720f710f6f0f6e0f6d0f6b0f6a0f690f680f630f610f5d0f5c0f5a0f590f560f550f540f510f500f4e0f4d0f4b0f4a0f490f480f470f460f430f42, 0xfa60fa40fa30fa20fa00f9c0f9a0f990f970f940f930f920f910f8f0f8e0f8d0f8b0f8a0f890f880f840f830f820f800f7f0f7d0f7c0f7b0f7a0f790f760f75])))
  ((.branch 4
  (.leaf #[0xfe00fde0fdc0fd90fd70fd60fd50fd40fd30fd00fcf0fcd0fcb0fc80fc40fc30fc20fc00fbf0fbc0fba0fb90fb80fb50fb30faf0fae0fad0fac0fab0faa0fa9, 0x103610351034103310321031102d102c102b102a10291028102510241023102210211020101d100510041003100110000fff0ffe0ffc0fe60fe50fe40fe20fe1, 0x106a10691067106610651063106210611060105c105b105a105910571056105510541053104e104d104c104b1049104810471045104410431042103d10391038, 0x1096109510911090108f108e108d108c108a1089108710861085108410831082107f107b107a107910781077107610751074107310721070106f106e106c106b])
  (.leaf #[0x10db10da10d910d410d110d010cf10ce10cc10cb10ca10c810c710c610c510c010bf10be10bd10bb10ba10b910b710b610b510b410a0109f109e109b109a1099, 0x110a1109110811071102110110ff10fe10fd10fc10fb10fa10f810f710f610f510f310f210f110ef10ee10ed10ec10e810e510e410e310e210e010df10de10dc, 0x1140113e113c113b113a113911361134113211311130112f112e112d112b112a112911251124112211211120111f111e111d111a111811141112110e110d110b, 0x11ad11ab11aa11a911a811a611a511a411a311a2119e119d119b119a1199119811971196118b118a118511841183118211811180117e117d116e116d11431142])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x11e111df11dc11db11d811d711d611d511d311d111cf11ce11cd11cc11c911c811c611c511c411c311c111c011bf11be11bd11b811b711b511b411b311b211ae, 0x121412131211120f120e120d120c12061205120312021201120011ff11fe11f911f711f511f411f311f211f111f011ef11ee11ec11eb11e911e611e511e411e3, 0x125f125e125d125c12551254125312511250124f124d124b1248124612451244122b122a1227122612251224122212211220121f121b121a1219121812171216, 0x128912881287128612841283128212811280127f127d127a1277127612741273127212711270126f126d126c126b126a12691268126712661265126312621260])
  (.leaf #[0x12ca12c112c012be12bc12bb12b912b612b512b412b312af12ae12ad12ac12ab12aa12a812a712a312a1129d129c129a129912951294129312921290128e128b, 0x12f712f512f112f012ef12ee12ec12ea12e712e512e412e312e212e112e012df12de12dc12db12da12d912d812d712d612d512d412d212d112cf12cd12cc12cb, 0x132e132b132a132713261325132413231322131f131e131d131c131a1319131813171316130f130d130a13091308130513041303130012ff12fe12fd12f912f8, 0x13611360135f135e135c135b135a13581357135613551351134c134b134913481347134613451344133f133e133d133c133b1339133813371335133413331332])))
  ((.branch 4
  (.leaf #[0x13911390138e138d138c138a13891388138713811380137f137e137d1379137813771376137513741373137213711370136f136d136c136b136a136913661365, 0x13f613f413f213ed13eb13e313e113de13d413d113d013c013bc13b513b313b213b113af13ae13ad13ab13a713a613a513a313a213a1139f139e139913931392, 0x142b14281426142514241423142214211420141f141d141c141b141a14191418141714161415141414121411140f140d140c140b140a140314021401140013f8, 0x148f148814861483147514731463145f1458145714551454145314521451144f144e144c144a14491448144714421441143f14381436143214311430142f142d])
  (.leaf #[0x14cd14cc14ca14c914c814c714c114c014bf14be14bd14ba14b814b514b414b314b114b014af14ae14ac14ab14a914a814a714a614a514a4149b149914951490, 0x150014fd14fc14fa14f914f814f714f614f414f314ee14ec14e914e814e714e414e314e214e014df14de14dd14db14da14d914d614d514d314d214d114d014ce, 0x153315321531152c152b152915281527152615221520151d151c151b151815171516151515121511150f150e150c150b150a1509150815071506150315021501, 0x155f155e155d155b1558155715561555155315521550154f154e154d154c154a1548154715441543154215411540153f153d153c153b153a1538153715361534])))))))))
  ((.branch 32
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x15861585158415811580157f157e157d157c157b157a157915781577157615741573157215711570156f156e156d156c156a1569156715641563156215611560, 0x15b615b415b315b215b115af15ad15ab15a915a815a715a615a115a0159f159c159b15981597159615951594159315921591158f158d158c158b158a15881587, 0x15e015df15dc15db15da15d915d715d615d515d415d215d015cf15ce15cd15cc15c915c815c715c515c415c215c115c015bf15be15bd15bc15bb15b915b815b7, 0x161916181617161516131611160f160e160d160c1609160816061601160015fd15fc15fa15f915f815f715f515f415f315f215f115ed15e715e515e315e215e1])
  (.leaf #[0x164a16491648164716461645164316421641163f163e163d163c163916381636163516321630162d162c162b162616251624162316221621161e161c161b161a, 0x167c167b167a1679167816751673167216711670166f166e166c166a166816661665166416631660165f165d165c165916581655165416511650164f164c164b, 0x16b316b216b016af16ad16ab16a916a416a116a0169e169d169c169b169a169816971696169516921691168f168e168a1688168616851684168316821680167f, 0x16df16de16dd16db16da16d916d816d716d416d216d116d016cf16ce16cd16cc16cb16c916c816c716c616c416c316c216c116be16bc16b916b816b716b516b4])))
  ((.branch 4
  (.leaf #[0x17211720171d171c171b171a171817171716171517131711170b170a17071706170517021701170016ff16fe16fc16f016ee16ed16ea16e916e816e716e116e0, 0x175617531750174f174e174d174c174b17491748174717451744174317421740173e173817371734173317321730172f172e172d172c172a1727172617231722, 0x178d178c178b178a1788178717861784178317821781177b177a1779177817761775177417731772176e176b176917671766176517641763175b175a17591758, 0x17c517c417c217c017bd17bc17b917b817b717b517b417ad17ac17ab17aa17a917a317a117a0179f179e179d179c179a1797179617941793179217911790178f])
  (.leaf #[0x17f617f517f417f317f217f117f017ed17eb17ea17e917e717e417e317e217e117e017dd17db17da17d917d817d717d617d317d117cd17cc17ca17c917c817c7, 0x182c182b182a1828182718261824182318221821181c18181817181618151813181218111810180f180a18081806180518041803180217fb17fa17f917f817f7, 0x185d185c185b185a1858185718561854185318521851184c184a184718461845184218411840183d183c183b183a1837183618341833183218311830182f182d, 0x18a718a518a418a318a218a118a0189b189a189918971896189518931891188e188c188b188a186d186c186b186a1868186718661864186218611860185f185e])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x18d118cf18cc18ca18c918c818c718c618c518c418c318c218c118c018bf18be18bc18ba18b918b818b718b618b518b418b218b118af18ae18ad18ac18ab18a8, 0x191319091906190519021901190018ff18fd18fb18f718f618f518f318f218f118f018ef18ea18e918e818e518e318e018df18dc18d918d818d718d518d418d3, 0x19b5198a19891988196319621960195e195c195a1959195819571954195219511950194919461942193e193d193c1937192d192b192919271922192019181916, 0x1a121a111a101a0f1a0e1a0c1a0b1a0a1a091a081a071a061a051a031a021a0019ff19fd19fc19fb19f519c619c419c119c019bf19be19bd19bb19b919b819b6])
  (.leaf #[0x1a421a411a3f1a3b1a3a1a391a371a361a351a341a331a321a311a2f1a2e1a2d1a2c1a291a271a261a221a211a1f1a1e1a1d1a1c1a1b1a1a1a171a161a151a14, 0x1a721a701a6e1a6b1a6a1a691a651a641a631a621a611a5f1a5e1a5d1a5c1a5b1a571a531a521a511a501a4f1a4e1a4c1a4b1a4a1a491a481a471a461a451a44, 0x1aaa1aa91aa81aa61aa41aa01a9e1a9d1a9c1a9b1a9a1a951a941a931a8d1a8b1a8a1a891a861a851a841a821a811a801a7e1a7c1a791a771a761a751a741a73, 0x1ae81ae71ae51ae31add1adc1ad91ad81ad71ad51ad41ad11ad01acf1ace1acc1ac91ac81ac71ac61ac41ac31ac11ac01abf1abc1abb1aba1ab91ab61ab51aab])))
  ((.branch 4
  (.leaf #[0x1b221b211b201b1f1b1b1b1a1b191b181b161b141b091b081b051b041b031b021b011b001afb1afa1af71af61af51af41af31af21af11af01aef1aed1aea1ae9, 0x1b501b4e1b4c1b4b1b4a1b491b451b441b431b421b411b3f1b3e1b3d1b3c1b3b1b3a1b391b381b371b351b341b331b311b301b2c1b2b1b2a1b291b281b261b24, 0x1b8f1b8e1b8d1b8c1b8a1b831b7f1b7a1b791b761b751b741b731b721b711b6f1b6e1b6d1b6c1b6b1b651b621b611b601b5e1b5c1b5a1b591b581b571b541b53, 0x1bf71bf61bf41bf31bf21bf11bef1bee1bed1bec1beb1bea1be81be71be51be31be21be11be01bd91bd81bd71bd61bd51bd21b9c1b981b971b961b941b921b90])
  (.leaf #[0x1c2b1c2a1c291c271c251c241c211c1f1c1b1c1a1c191c181c171c161c151c141c121c111c101c0f1c0e1c0d1c0b1c051c041c031c021c001bfe1bfb1bf91bf8, 0x1c6a1c691c641c621c611c601c5e1c5d1c571c561c511c501c4f1c4e1c4d1c4c1c4a1c401c3f1c3e1c3d1c3c1c3b1c3a1c391c381c361c351c321c311c2f1c2e, 0x1cae1caa1ca81ca71ca51ca01c9f1c9e1c9d1c9c1c9b1c951c941c931c921c901c8f1c8e1c8c1c8b1c8a1c891c781c771c741c731c721c711c701c6f1c6c1c6b, 0x1cd81cd71cd61cd51cd41cd31cd21cd11ccf1cce1ccd1ccb1cca1cc91cc81cc21cc11cbf1cbe1cbd1cbc1cbb1cba1cb91cb81cb71cb61cb41cb31cb21cb11caf])))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x1d071d041d031d001cff1cfd1cfc1cfb1cfa1cf91cf81cf71cf61cf51cf31cf21cf11cee1cea1ce91ce81ce61ce41ce21ce11ce01cdf1cde1cdd1cdc1cdb1cd9, 0x1d341d331d321d311d2f1d2e1d2d1d2c1d2b1d281d261d251d241d231d221d201d1f1d1e1d1d1d1c1d191d181d161d141d131d121d111d0f1d0e1d0d1d0c1d08, 0x1d791d781d771d741d731d721d711d6f1d6d1d6b1d691d681d671d661d601d5e1d5d1d5a1d591d531d511d4f1d4d1d491d441d421d411d401d3f1d3e1d3d1d3a, 0x1dad1dac1dab1daa1da91da71da61da31da11da01d9f1d9e1d9b1d9a1d981d971d951d931d911d8f1d8e1d8d1d8c1d871d851d841d831d821d801d7f1d7c1d7a])
  (.leaf #[0x1dd71dd61dd31dd21dd11dd01dce1dcd1dcc1dcb1dc91dc71dc61dc51dc41dc11dc01dbf1dbe1dbd1dbc1dbb1db91db81db71db61db51db31db21db01daf1dae, 0x1e121e101e0f1e081e071e061e051e031e021e011e001dff1dfe1dfd1dfb1df81df71df41df31df21df11def1dee1ded1dec1de81de61de01ddf1ddd1ddb1dd8, 0x1e441e431e421e411e401e3f1e3d1e3c1e3a1e391e381e371e361e321e311e2e1e2d1e2c1e2b1e291e271e241e231e1f1e1e1e1d1e1c1e1b1e1a1e191e181e13, 0x1e771e761e751e741e731e721e711e701e6e1e6d1e6b1e691e681e671e661e601e5f1e5e1e5b1e5a1e581e551e541e531e521e501e4e1e4d1e4b1e481e471e45])))
  ((.branch 4
  (.leaf #[0x1ea81ea71ea61ea11ea01e9f1e9e1e9d1e9c1e9b1e9a1e981e951e941e931e911e8d1e8c1e8b1e8a1e881e861e831e811e801e7f1e7e1e7d1e7c1e7b1e7a1e78, 0x1ee61ee51ee31ee21ee11ee01edf1ed71ed61ed51ed31ed21ed11ed01ec81ec41ec31ec21ec01ebf1ebe1ebc1eba1eb71eb51eb41eb31eb21eb11eaf1eae1eac, 0x1f361f351f251f1f1f1a1f181f151f131f0f1f0c1f0a1f091f061f051f041f021f011f001efe1efc1ef91ef71ef61ef51ef41ef31eec1eeb1eea1ee91ee81ee7, 0x1f871f861f841f831f811f801f7f1f7d1f7b1f751f741f711f701f6f1f6c1f6b1f681f661f651f641f5d1f5b1f591f571f521f501f481f461f431f391f381f37])
  (.leaf #[0x1fbc1fba1fb81fb71fb61fb51fb31fb21fb11fb01fae1fad1fac1fab1fa81fa71fa41fa31fa11f9f1f9e1f9b1f981f971f951f921f911f8e1f8d1f8c1f891f88, 0x1fed1fec1feb1fe71fe61fe41fe21fe11fdd1fdb1fd71fd61fd31fd21fd11fd01fcf1fce1fcd1fcc1fcb1fca1fc81fc71fc61fc51fc31fc21fc11fc01fbf1fbe, 0x20172015201220112010200e200d200c200b200a20082006200520032002200120001fff1ffe1ffd1ffb1ffa1ff91ff81ff71ff61ff51ff41ff21ff11ff01fee, 0x204d204c204b2049204820472046204220412040203f203e203c203b203a203720362034203320312030202e202d20272026202520242023202220212020201e])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x208d20842083207e207d207c207b2079207720742073207220712070206f206e206d206c2060205f205e205d205c205a2058205620552054205220512050204f, 0x20d220d120d020ce20cd20cc20ca20c820c520c320c220c120ac20a420a320a220a1209f209e209d209c209b209a2099209820972095209420922090208f208e, 0x2104210321022101210020fa20f920f820f720f520f420f320f020ef20ed20ec20eb20e920e620e520e420e320e220e120e020de20dd20db20da20d920d820d7, 0x213421332130212f212d212b212a21262125212221212120211e211d211c211b2119211821152114211321122111210f210e210d210c210b210a210921072106])
  (.leaf #[0x21612160215f215e215d215c2158215621542153215221512150214d214c214b214a21492148214721462145214421412140213e213d213b213a213921372136, 0x21912190218f218e218b218a218921882187218621852184218221812180217f217e217d217b217921772175217421732172216e216d216c216a216921662165, 0x21bc21bb21ba21b921b821b721b621b521b321b221b121b021ae21ad21ac21ab21a821a621a321a221a1219e219d219c219b2199219821972196219521942192, 0x21f121f021ee21ed21ec21eb21e821e721e621e421e321e221dc21db21d821d721d621d421d321d221d121cf21ce21cd21cc21ca21c921c521c421c321be21bd])))
  ((.branch 4
  (.leaf #[0x22232221221f221e221d221c221b22182217221622132212220f220e220b220a22082205220422032202220021ff21fd21fc21fb21f921f821f721f621f321f2, 0x224c224b224a22482247224622452244224322422240223f223e223c223b22382237223622352234223322322231222f222e222d222c222a2229222822272225, 0x229822922291228d228c227a2279227622752274227322712270226f226e226c226a226822672266225d225b22592258225722562255225222512250224f224d, 0x230d230c230b230a230522ef22ea22e922e822e722e522e422e322e222e122de22dd22c022bf22ae22ad22ac22ab22a922a822a722a622a422a3229e229c2299])
  (.leaf #[0x238223812380237f237e237d237c23792378237723762375234d234c234a2331233023272326231f231e231d231c2318231723162314231323112310230f230e, 0x23bd23bc23b423b323a823a723a623a523a423a223a123a0239f239e239d239b239a239923982397239623952394239323912390238e238c238b238a23892383, 0x23ee23ed23ec23eb23e923e723e423e223e123e023df23de23dd23dc23db23d923d823d723d623d523d423d223d023cf23cb23ca23c923c823c723c623c423c3, 0x243d243c243724362434242c242b242a2429242724252423242224212420241a241924182417241524142413241223ff23fe23fc23fb23f923f623f523f423f2])))))))))))
  ((.branch 64
  ((.branch 32
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x2470246f246e246d246c246b246a2468246724652463246224612460245b245a24582457245524512450244f244e244d244c244b244a2449244824462441243f, 0x24c624c424c324c224c124bf24be24bd24bc24bb24b724b224ae24ad249924982493249224912490248f248e248d248c248b248a248924872475247424722471, 0x24fe24fc24fb24fa24f824f624f524f424f324f224f124ee24ec24e824e724e624e324e024df24db24da24d924d824d724d324ce24cd24cb24ca24c924c824c7, 0x25322530252f252e252d252c252825272523252225212520251e251d251c251a2519251825172510250e250c250b250a250925062505250325022501250024ff])
  (.leaf #[0x25612560255f255d255c255b2559255825572556255325522550254f254e254d254c254b254925462544254225412540253f253b253a25372536253525342533, 0x259225912590258f258d258c258b25892588258725862581257d257c257a2579257825772576257525712570256f256e256d256c256825672566256525632562, 0x25c725c625c525c425c325c225c125b925b825b725b525b325b225af25aa25a925a825a725a625a525a325a225a125a0259f259d259c259b2599259825972596, 0x260025ff25fe25fa25f925f725f625f425f325f225f125f025ef25ec25eb25ea25e925e725e625e525e325e225e125e025da25d925d825d625d525d425d125d0])))
  ((.branch 4
  (.leaf #[0x2680267c267b264d264c264b264a26492647264626452643264226412640263c2638263726242613260f260e260d260c260a2609260826072605260426032601, 0x26c226c126c026be26bd26bc26bb26b826b726b526b326b226ae26ad26a0269f269c2695269426932692268f268d268c268b268a268726862685268426822681, 0x270527042703270226fd26f826f726f626f426f326f226f026ee26eb26e826e726e626dd26dc26d926d526d426d326d226ce26cd26cc26ca26c726c626c526c4, 0x27512750274c274a272e272d272b272a27292728272727262724272327222721271f271e271c271a27192718271727132710270e270c270b270a270927072706])
  (.leaf #[0x278f278c278b278a2789278627832780277927742773277227712770276d276c276b27642763276227612760275e275d275c275b275a27582757275527532752, 0x27c827c727c627c527c427bf27be27bd27bc27bb27ba27b727b627ac27ab27a727a627a527a427a327a127a0279f279e279d279c279b279a2798279727922791, 0x2834283328322830282f282e282d282a2829280327f727f627f527f127ef27ed27eb27ea27e927e527e227de27dc27da27d727d627d127cd27cc27cb27ca27c9, 0x289428932892288d288c288b288a28892886288528842883288228812880286c286b286a2864286128602858285728552850284f284d284b2848284728392835])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x28d228cb28c428c328c128c028bf28be28bd28bc28bb28ba28b628b528b328b228af28ae28aa28a928a828a728a628a528a328a228a1289f289d289b28972896, 0x28fd28fb28fa28f928f828f728f628f528f228f128f028ef28ed28ec28ea28e928e828e728e628e528e328e228e128df28de28dd28dc28d828d728d528d428d3, 0x293429332930292c2928292729262925292229212920291e291d291c291a29182915291329122911290f290e290d290b29092908290729042903290028ff28fe, 0x297429712970296f296e296c296b29692968296729652964296329622961295b295429532951294e294b2947294629452944293e293d293c293b293a29362935])
  (.leaf #[0x29b729b129b029af29ad29ac29ab29a929a829a329a0299f299e299d299c299a29992998299729962993298f2985298229812980297f297d297b297a29772976, 0x2a0029ff29fe29fd29fa29f929f829f729f629f529f329f229f129ef29ee29ed29ec29e629e129e029de29dd29d529d429d329d229d129cf29ce29cc29c829c7, 0x2a3a2a392a382a372a362a352a332a322a312a302a2f2a2b2a2a2a252a232a202a1f2a1e2a172a162a152a142a122a112a0d2a0c2a0b2a0a2a082a052a022a01, 0x2a6b2a6a2a692a662a652a642a632a612a602a5f2a5d2a5c2a5b2a5a2a562a552a532a522a4e2a4c2a4b2a4a2a492a482a472a452a412a402a3f2a3e2a3d2a3c])))
  ((.branch 4
  (.leaf #[0x2aa62aa42aa32aa22aa12a922a912a902a8f2a8d2a8c2a8b2a8a2a882a872a862a842a832a822a812a802a7f2a7c2a7a2a772a762a752a742a722a712a6d2a6c, 0x2b082b072b052b042b032b022b012afe2af72af52af32af12aec2aea2ae32ae12ade2ad42ad22acf2ace2acd2abd2ab22ab12aaf2aae2aad2aac2aab2aa92aa8, 0x2b512b4b2b482b472b452b412b402b3f2b3e2b3d2b3a2b332b2f2b2b2b2a2b282b272b262b252b242b222b202b1f2b1c2b152b142b132b112b0e2b0d2b0c2b0b, 0x2b912b902b8f2b8e2b8a2b892b882b872b862b842b812b802b7f2b7e2b7d2b7b2b7a2b792b742b712b702b6d2b6b2b6a2b672b652b622b612b602b5d2b5c2b55])
  (.leaf #[0x2bc92bc72bc62bc42bc12bc02bbf2bbe2bbc2bbb2bb92bb82bb72bb42bb32bb22bb12bb02baa2ba82ba52ba42ba32ba22ba02b9f2b9e2b9d2b9c2b982b962b92, 0x2c3a2c382c372c352c342c332c322c312c2f2c2e2c2d2c0f2c0a2c082c052c032bff2bfd2be42be32be12bdf2bde2bdd2bdb2bd92bd32bd22bcf2bce2bcd2bca, 0x2c8d2c8b2c882c872c862c852c832c822c812c802c7f2c7c2c782c752c712c702c6d2c6c2c6b2c6a2c692c682c672c652c452c442c422c402c3e2c3d2c3c2c3b, 0x2cc22cc12cc02cbf2cbe2cbd2cbc2cbb2cba2cb72cb62cb42cb32cb22caf2cad2ca62ca52ca42ca32ca12ca02c9e2c9d2c9c2c9b2c9a2c972c962c952c942c8f])))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x2cf42cf32cf22cf12cee2cec2ceb2cea2ce92ce82ce62ce52ce42ce32ce22cdf2cdd2cdc2cd92cd82cd52cd42cd32cd22cd12ccf2ccd2ccb2cca2cc92cc82cc7, 0x2d2e2d2d2d2c2d2a2d282d252d232d222d212d202d1f2d1e2d1c2d1a2d162d142d122d112d102d0e2d0c2d062d052d022d012d002cfe2cfd2cfb2cfa2cf82cf5, 0x2d992d962d952d932d902d8f2d8e2d862d842d802d7b2d7a2d712d6b2d692d662d632d602d5f2d5e2d5d2d4d2d472d422d402d3c2d392d382d352d322d312d30, 0x2dcd2dc92dc12dc02dbf2dbe2dbd2db92db82db42db32db22db12db02daf2dae2dad2dac2dab2da92da82da62da52da32da22da12da02d9f2d9d2d9c2d9b2d9a])
  (.leaf #[0x2e032e022e002dff2dfe2dfd2dfc2dfb2dfa2df92df72df52df32df22df12def2dea2de52de42de32de12ddf2dde2ddc2ddb2dda2dd92dd72dd52dd22dd12dd0, 0x2e562e552e542e532e522e492e352e302e2e2e2c2e2a2e282e242e1f2e1d2e1c2e1b2e182e172e162e142e132e122e102e0e2e0b2e092e082e072e062e052e04, 0x2e952e942e902e8f2e8d2e8b2e8a2e862e842e802e7f2e7c2e7b2e7a2e792e762e752e712e702e6f2e6e2e6d2e6c2e682e662e622e612e602e5b2e5a2e592e58, 0x2ec42ec32ec22ec12ec02ebc2eb92eb72eb42eb32eb22eb12eaf2eae2ead2eab2eaa2ea92ea82ea52ea42ea22ea12ea02e9f2e9e2e9d2e9b2e9a2e992e972e96])))
  ((.branch 4
  (.leaf #[0x2f112f102f0f2f0d2f0c2f0b2f092f082f072f062f012f002eff2efd2efb2ef92ef82ef32ee92ee82ed62ed52ed32ed22ed12ed02ecf2ece2ec92ec82ec72ec6, 0x2f4b2f472f462f432f422f3e2f3d2f3c2f3b2f392f372f362f342f322f312f2d2f2c2f272f262f252f242f232f222f212f202f1f2f1d2f192f182f172f152f12, 0x2fbd2fbc2fb72fa72fa62f942f912f8f2f8e2f852f822f802f7e2f7c2f7a2f762f752f6e2f6d2f6b2f6a2f662f652f642f632f622f612f5d2f5c2f5a2f592f4d, 0x300b300a30083007300530043003300230012ffe2ffd2ffa2ff92ff72ff62ff52ff42ff02fef2fec2feb2fea2fe82fe72fe62fe42fe22fdf2fdd2fdc2fdb2fbe])
  (.leaf #[0x303c303b303a303630353033302f302d302a30293028302730253024302330213020301f301e301a30193017301630153014301330123010300f300e300d300c, 0x309730963095309330923090308f308e3078307730753074307330723071306f306b306a3069306730533051304d304b304630453044304330413040303f303d, 0x30c930c830c730c430c330c230c130be30bd30bc30bb30ba30b930b830b630b530b330b230b130b030af30ab30a730a630a530a430a230a130a0309f309e3098, 0x3104310331023101310030f830f630f230f130f030ef30eb30ea30e930e730e430e330e230e130df30de30dd30db30da30d930d830d430d330d130cf30cb30ca])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x3174317331723171316f316c316931683167316631653164315f315e31593154315331513150314e314d314c314b314a3142313c313b3124311a31183115310b, 0x31b031ae31ac31aa31a931a831a731a631a431a331a231a131a0319c319b319a3199319731963195319431933190318b318931853184317e317d317c31793178, 0x31e831e731e531e431e231dc31d931d731d431d331d131d031cf31ce31cb31ca31c931c731c631c531c331c131be31bc31bb31ba31b931b831b431b331b231b1, 0x322432213220321d321c321a321732163215321432123211320f320e320d320a32093208320732043203320031ff31fe31fd31fb31fa31f831f631f531f431f3])
  (.leaf #[0x32553254325232513250324d324c324832473246324532443243324232413240323f323d323c323b323a32383236323532323230322d322c322b322732263225, 0x3290328f328e328d328c32883287328632853283327f327d327c327b327a32773276327432733270326e326a326932663265326432613260325e325b325a3257, 0x32c432c332c232c032bf32bc32ba32b932b832b732b432b332b232b132af32ad32ab32a932a832a732a632a232a0329f329e329d329c329b3295329432933292, 0x3308330533043302330132f632ee32ec32eb32e832e732e532e432e232e032de32dc32db32da32d932d532d432d332d232d032cf32ce32cd32cc32c732c632c5])))
  ((.branch 4
  (.leaf #[0x33333330332e332d332c332b332a332933273326332533243323332233213320331f331d331c331b331a331933183316331433123310330f330e330d330a3309, 0x33e233e133e033df33de33dc33db33da33d933d833d133d033cd33ca33c933c733c533c333c133c033bf33be338f338e338d333d333c333b3337333633353334, 0x3448344734463441343f343e343b343a3437343634343433342a3427342434233422342134203418341734163410340f3401340033ff33fd33fc33e733e633e5, 0x3475347234713470346f346d346c346b346a346934683467346634653463345f345e345d345c345a345834553453345234513450344e344d344c344b344a3449])
  (.leaf #[0x34bf34bd34b934b834b634b434b334b234b134b034af34ae34ac34ab34a934a834a734a634a534a0349f349e349c349b349a34983496349334913490348f3476, 0x34f634f434f034ef34ee34ed34ec34eb34ea34e934e834e634e534e434e334e134df34de34dc34da34d834d634d534d434d334ce34cd34cc34ca34c934c734c5, 0x353335323531352f352e352d352c352b352735263520351f351735143513351235113510350e350d350c350b350a35083506350535033501350034fe34fc34fa, 0x356f356e356d356935683567356635643562355f355e355d355535543550354f354e354b354a354935473543354235413540353e353b35383537353635353534])))))))))
  ((.branch 32
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x35e135dc35da35d835d735d635d435d335d235b535aa35a0359635953594359335923590358f358d358a35863582358135803577357635753574357335713570, 0x361e361d361c361b36183617361536123611360e360d360c360b36093608360736053604360135fe35fd35fc35fb35fa35f935f835f735f635f535f035ef35e2, 0x381b38173816381538143813381238113810380e380d380a38083807380537f637eb37e937e737e337e237df37de37dc37da37d937cd3624362336223621361f, 0x38a0389838973896389438933867386638623861385f385e385d385a385938583857384638453830382f382e382d382b382a382938273826382538243820381c])
  (.leaf #[0x39173915391439133912390e390d390c390b3908390738ff38fe38eb38cf38ce38ca38c238c038bf38be38bd38bb38b838b738b538b438a738a638a338a238a1, 0x39a539a139a0399c398139753974396d396c396b396a39693968395d393d39363934393339323929392839273925392239213920391f391d391c391a39193918, 0x3a693a683a673a5a3a583a563a553a543a533a493a483a463a3f3a3d3a3c3a3b3a343a303a2f3a2c39b639b539b339b239b039ae39ad39ac39ab39aa39a939a7, 0x3af93af73af33af23aef3aee3aec3aeb3aea3ae93ac03abf3abe3abc3ab93ab63ab53ab43ab23aad3aa63aa53aa43aa33a9e3a9d3a9c3a993a983a973a923a86])))
  ((.branch 4
  (.leaf #[0x3b9f3b9e3b9d3b9c3b9b3b9a3b993b963b913b8f3b8e3b8d3b8b3b7b3b783b773b763b753b743b713b663b653b643b633b613b603b5f3b5e3b5d3b003aff3afd, 0x3c213c1d3bdd3bdc3bdb3bda3bd83bd73bd63bd53bd43bd13bd03bcd3bcc3bca3bc93bc53bc33bbf3bbe3bbb3bb83bb53bb43bb33ba63ba53ba43ba23ba13ba0, 0x3d333d313d303d2f3d2e3d2a3d293d283d273d263d243c3f3c3e3c3d3c3c3c3a3c393c373c363c303c2f3c2e3c2d3c2c3c2b3c2a3c283c273c253c243c233c22, 0x3db43db23db03daf3dae3da83da13d843d803d7f3d7b3d7a3d783d773d763d743d733d723d713d703d6f3d6e3d6b3d3f3d3e3d3b3d3a3d393d383d373d353d34])
  (.leaf #[0x3dec3deb3de53de43de33de23de13de03ddd3dd93dd83dd63dd53dd13dd03dcf3dcc3dcb3dca3dc93dc83dc43dc33dc23dc13dbf3dbe3dbd3dbb3dba3db93db8, 0x3e1c3e1b3e1a3e193e163e153e133e123e103e0f3e0e3e0d3e0c3e0b3e0a3e083e073e053e043e033e023e013dfc3dfb3dfa3df83df73df63df43df23def3ded, 0x40033fff3ffe3ffc3ffb3fd63fd53fd03fcf3fce3fcc3fca3fc63fc43f923f913f903f8e3f8d3f8c3f8a3f893f843f7d3f1e3f1d3f1c3f1b3f1a3f183ee63e1e, 0x40ee40ed40eb40d040cb40ca40c840c740c340c240c140c040be40bc40b940b840b740b640b540b440b340b240b14097407b40794075400a4009400840074005])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x412541244123411e411c411b41194118411541144111410f410e410c410b410a4108410741064105410441034101410040ff40fe40fd40f740f540f240f140ef, 0x415941584155415441534150414f414e414d414941484147414641454144414341424141413f413d413c413a4138413741344132412f412e4129412841274126, 0x419f419d419c419b419a419941984194418c418a41884187418641854180417f417e417c417b417a41794178417741764172416a41664165416441634161415f, 0x41ea41e041d941d841d741d641d541cd41cb41c841c741c241c141c041bf41b741b541b341b241b141b041ad41ac41a941a741a641a541a441a341a241a141a0])
  (.leaf #[0x425c425b425a4259425842554253424f424e424b424a424942474246424542434241423e423c423b423a421d421c421b421a4218421742164215421441ef41ed, 0x42ad42ac42aa429d429442934290428f428b428a42884287428642844283427f427e426f426e426d426c426b42694267426642654264426342624261425f425e, 0x4384438343824380437f437d437c4378435b435a4359435743554354433a42ed42ec42ea42e942e842e242e042df42c842c742c242be42bd42ba42b442b342b1, 0x43cd43cc43cb43ca43c943c743c643c543c443c243bd43bb43b943b843b543b443b343b143a0439e439c4399439843974393438f438e438c438a438843864385])))
  ((.branch 4
  (.leaf #[0x4470446f445b4420441f441e441c441b4410440f440e440a4401440043fd43f643f543f443f343f143f043ee43ec43eb43ea43e943e543e443e243d443d043cf, 0x451f451e451d451c451b451a45194517451645154514451345124510450e450c450845074506450445034502450144fe44ab44a5449d44894479447544724471, 0x4673466f466e466d466c466b466a4669466846664665466246614660465f465745d945d845ce4590458f458e458d457c457545744573454b4549452745264523, 0x47184717470d470c470b470a47094708470747064705470347024701470046ff46fc46fb46f846f646f246f146d646cb469f469e469d469c4697468b46814674])
  (.leaf #[0x4787478547844783478247814780477e4760475b4759475647544750474e474d474a472e472d472b472a4729472747264725472447234722471d471b471a4719, 0x495349524951494e4890488f488a48894886488548724870486f486d486b48674866486248614860485f485d485a485947ca47c847c247c147be47a947a84788, 0x498d498c498949854984498349824981497f497e497d497c497b4979497849774975497449724970496e496c496b496a49694964496349624958495749564954, 0x49c449c349c249c149bf49be49bd49bc49ba49b949b749b349b149b049af49ae49ac49ab49aa49a949a849a449a2499e499c49984997499349914990498f498e])))))))
  ((.branch 16
  ((.branch 8
  ((.branch 4
  (.leaf #[0x4a194a174a134a0d4a0c49f249f149f049ee49ed49ec49eb49e949e849e549e449e349e249e149d949d749d349d249d049cf49ce49cd49cb49ca49c949c849c6, 0x4ab24ab04aae4aac4aaa4aa94aa84aa74aa24aa14aa04a9e4a9d4a9b4a9a4a454a444a414a404a3f4a3e4a3c4a3b4a394a384a374a354a344a334a324a304a1d, 0x4ae04adf4add4adc4ada4ad84ad64ad44ad34ad24ad14ad04acd4acc4acb4ac84ac74ac54ac44ac34ac24ac14ac04abf4abc4aba4ab94ab84ab74ab54ab44ab3, 0x4b0f4b0e4b0b4b094b084b074b064b044b034b024b014aff4afd4afb4af94af84af74af64af24af14af04aed4aec4aea4ae94ae84ae74ae64ae54ae44ae34ae1])
  (.leaf #[0x4b824b814b7f4b7e4b7d4b7c4b7b4b764b754b744b724b714b704b6e4b6c4b694b674b664b654b484b474b464b454b434b424b414b404b174b164b124b114b10, 0x4bd24bd14bd04bcd4bcc4bc94bc74bc64bc44bc34bc24bc14bbf4bbe4baf4bae4bad4bab4baa4ba94ba74ba64b8f4b8e4b8c4b8a4b894b884b874b864b854b84, 0x4c244c234c204c1f4c1b4c1a4c194c184c164c134c104c0f4c0e4c0d4c0c4c0b4c0a4c094c074c064c054c044c034c024c014c004bff4bf84bf74bdf4bd84bd6, 0x4c604c5f4c5c4c5b4c5a4c594c574c554c534c4f4c4e4c4d4c4b4c4a4c494c484c474c434c424c414c404c3e4c3d4c3c4c3b4c3a4c374c324c304c2c4c2b4c25])))
  ((.branch 4
  (.leaf #[0x4c9e4c994c984c964c954c944c934c924c914c8f4c8e4c8d4c8c4c8b4c884c874c854c824c804c7c4c7a4c794c774c764c754c724c714c6e4c6c4c684c674c61, 0x4ce84ce34ce24ce14cdf4cde4cdd4cdb4cd94cd64cd44cd34cd24cb54cb44cb34cb24cb04caf4cae4cad4cac4cab4caa4ca94ca84ca64ca54ca34ca14ca04c9f, 0x4d404d3d4d3c4d3a4d254d244d234d214d204d1f4d1d4d1c4d014d004cfe4cfd4cfc4cfb4cf94cf74cf64cf54cf44cf34cf24cf14cef4cee4cec4ceb4cea4ce9, 0x4d754d734d6f4d6e4d6c4d6b4d6a4d654d644d634d624d604d5f4d5e4d5c4d5b4d5a4d594d554d524d514d4d4d4c4d4b4d4a4d494d474d464d454d444d434d41])
  (.leaf #[0x4dbe4dbc4dbb4dba4db94db84db64db54db44db34db24db14dac4daa4da84da74da44da34da24da14da04d994d924d8e4d8c4d884d874d864d844d7f4d7e4d76, 0x4df84df74df54df44df34df24df14df04def4ded4dec4deb4dea4de94de84de74de64de54de44de34de24de04ddf4ddd4ddb4dda4dd94dd84dd44dd34dd14dbf, 0x4e2a4e274e264e254e234e224e214e1f4e1d4e1a4e184e174e164e154e144e134e124e114e104e0f4e0e4e084e074e064e044e014e004dff4dfe4dfc4dfb4df9, 0x4f6b4f6a4f694f684f674f664f654f634f5e4f5c4f454f414f404f3f4f3b4f3a4f394f384f374f364f354f344f324f314f2a4e544e384e364e334e314e2d4e2b])))))
  ((.branch 8
  ((.branch 4
  (.leaf #[0x4fc14fc04fbf4fa24fa14fa04f9f4f9d4f9c4f9b4f9a4f994f974f964f944f904f8f4f8e4f8c4f8b4f894f834f814f7d4f7c4f734f724f704f6f4f6e4f6d4f6c, 0x4ff44ff24ff04fef4fee4fed4fe94fe84fe64fe44fe34fe24fe14fe04fdf4fde4fdc4fdb4fd94fd84fd74fd64fd54fd04fcf4fce4fcc4fcb4fca4fc84fc64fc3, 0x5119511851135111510d510c510b510a5108510751055101510050e650e550e450e250e150df50cd50cc50ca50c750c6503650354ffc4ffa4ff94ff84ff74ff5, 0x51d551d351cd51cc51c651c551c451c351c251c151c051bd51bc51bb51ba51b951b351b151b051ae5197514a5149513351305122511f511e511d511c511b511a])
  (.leaf #[0x5222521f521e5211520f520d520c520b520a520952075206520552045201520051f951f851f751f551f451f351f251f151f051ee51eb51e951db51da51d751d6, 0x528d528a528852875286528552845283528252635262526152605258523b523a52395237523652345230522f522d522c522b5229522852275226522552245223, 0x55e255df55de55dd55dc55da55d955d855d755d655d5540b537453735372537053585356533953385336533553335331533053245320531253115310530e528f, 0x567d567c567b56795678567756765675567256715670566f566656655664566356615660565d565c565b565a5621561d561a56155614561256115610560f55e3])))
  ((.branch 4
  (.leaf #[0x570f570e570d570b570957065704570357025701570056ff56fb56f956f856f656f556f256ef56de56dd56d956d856d756d656d556d056cf56ce56c356c2567e, 0x577857765773577257715770576e576d576c5769576857655764576357615760575f575e575d575a5757572e5727572557235721571d57175716571357125711, 0x5a055a045a0059ff59fe59fd59fb59f659f45922591b591a5918591358cc58c55893582a582957e757e657e557e457d757d657ac57a85782577e577d577c5779, 0x62a0617c61756174616261616160615f5f645f635f125efb5e755ceb5cea5ce45a5d5a545a535a525a475a465a425a415a405a115a105a0f5a0e5a0c5a0b5a09])
  (.leaf #[0x62e662e462e362e262e162e062db62da62d962d762d662d562d362d162ce62cc62cb62ca62c462c362c262c062bf62ba62ae62ad62a762a662a562a462a362a1, 0x66ed66ec66eb66e966e866e666e466e3669b66976696667b6677661865f865b1656d656a64c162f862f762f662f562f462ef62ee62ed62ec62eb62ea62e962e7, 0x67cb678e67846783678067776776677567616756674a674867446743674267416740673f673d673c673b673a6739673467336730672f672e672d672b672a6715, 0x6da06d9f6d906d5d6c466c456a356a346a2a694368936892683e683d683b683a67f867d167cc]))))))))))))

def policyFixedCompact1Rename (i : Nat) : Nat :=
  (((policyFixedCompact1VariableTable.get 0 (i / 32)) >>> (16 * (i % 32))) &&& 0xffff).succ

end Bounty

end PolicySubmissionPart32

/- Component PolicyBitsetRUP; SHA256 3e36aef493889c462d0915c2e758fcfdfddf9fc7592dff332c6d1634f658292e. -/
section PolicySubmissionPart33
/- Signed-clause unit propagation with ordinary natural-number bit masks. -/

namespace Bounty

abbrev PolicyBitState := Nat × Nat

def policyBitValid (P : Nat → Prop) (s : PolicyBitState) : Prop :=
  (∀ i, s.1.testBit i = true → P i) ∧ (∀ i, s.2.testBit i = true → ¬P i)

def policyBitFalse (s : PolicyBitState) (z : Int) : Bool :=
  if 0 < z then s.2.testBit z.natAbs else s.1.testBit z.natAbs

def policyBitAddTrue (s : PolicyBitState) (z : Int) : PolicyBitState :=
  if 0 < z then (s.1 ||| 2 ^ z.natAbs, s.2) else (s.1, s.2 ||| 2 ^ z.natAbs)

def policyBitAddFalse (s : PolicyBitState) (z : Int) : PolicyBitState :=
  if 0 < z then (s.1, s.2 ||| 2 ^ z.natAbs) else (s.1 ||| 2 ^ z.natAbs, s.2)

def policyBitFalse_sound P s z (hv : policyBitValid P s)
    (h : policyBitFalse s z = true) : ¬policySignedHolds P z := by
  by_cases hz : 0 < z
  · simp only [policyBitFalse, policySignedHolds, if_pos hz] at h ⊢
    exact hv.2 _ h
  · simp only [policyBitFalse, policySignedHolds, if_neg hz] at h ⊢
    exact not_not_intro (hv.1 _ h)

def policyBitAddTrue_valid P s z (hv : policyBitValid P s)
    (hz : policySignedHolds P z) : policyBitValid P (policyBitAddTrue s z) := by
  by_cases hp : 0 < z
  · simp only [policySignedHolds, if_pos hp] at hz
    unfold policyBitValid policyBitAddTrue
    rw [if_pos hp]
    refine ⟨?_, hv.2⟩
    intro i hi
    simp only [Nat.testBit_or, Nat.testBit_two_pow, Bool.or_eq_true, decide_eq_true_eq] at hi
    rcases hi with hi | hi
    · exact hv.1 _ hi
    · simpa only [← hi] using hz
  · simp only [policySignedHolds, if_neg hp] at hz
    unfold policyBitValid policyBitAddTrue
    rw [if_neg hp]
    refine ⟨hv.1, ?_⟩
    intro i hi
    simp only [Nat.testBit_or, Nat.testBit_two_pow, Bool.or_eq_true, decide_eq_true_eq] at hi
    rcases hi with hi | hi
    · exact hv.2 _ hi
    · simpa only [← hi] using hz

def policyBitAddFalse_valid P s z (hv : policyBitValid P s)
    (hz : ¬policySignedHolds P z) : policyBitValid P (policyBitAddFalse s z) := by
  classical
  by_cases hp : 0 < z
  · simp only [policySignedHolds, if_pos hp] at hz
    unfold policyBitValid policyBitAddFalse
    rw [if_pos hp]
    refine ⟨hv.1, ?_⟩
    intro i hi
    simp only [Nat.testBit_or, Nat.testBit_two_pow, Bool.or_eq_true, decide_eq_true_eq] at hi
    rcases hi with hi | hi
    · exact hv.2 _ hi
    · simpa only [← hi] using hz
  · simp only [policySignedHolds, if_neg hp, not_not] at hz
    unfold policyBitValid policyBitAddFalse
    rw [if_neg hp]
    refine ⟨?_, hv.2⟩
    intro i hi
    simp only [Nat.testBit_or, Nat.testBit_two_pow, Bool.or_eq_true, decide_eq_true_eq] at hi
    rcases hi with hi | hi
    · exact hv.1 _ hi
    · simpa only [← hi] using hz

def policyBitStart : List Int → PolicyBitState
  | [] => (0, 0)
  | z :: zs => policyBitAddFalse (policyBitStart zs) z

def policyBitStart_valid P c (h : ¬policySignedClauseHolds P c) :
    policyBitValid P (policyBitStart c) := by
  induction c with
  | nil => simp [policyBitStart, policyBitValid]
  | cons z zs ih =>
    apply policyBitAddFalse_valid
    · apply ih
      rintro ⟨w, hw, hp⟩
      exact h ⟨w, List.mem_cons_of_mem _ hw, hp⟩
    · intro hz
      exact h ⟨z, List.mem_cons_self, hz⟩

def policyBitAdvance (db : Nat → List Int) : List Nat → PolicyBitState → Bool
  | [], _ => false
  | h :: hs, s =>
      match (db h).filter (fun z => !policyBitFalse s z) with
      | [] => true
      | [z] => policyBitAdvance db hs (policyBitAddTrue s z)
      | _ => policyBitAdvance db hs s

def policyBitAdvance_sound db hs P s (hv : policyBitValid P s)
    (hc : ∀ i ∈ hs, policySignedClauseHolds P (db i))
    (h : policyBitAdvance db hs s = true) : False := by
  induction hs generalizing s with
  | nil => simp [policyBitAdvance] at h
  | cons i hs ih =>
    have hh : ∀ j ∈ hs, policySignedClauseHolds P (db j) :=
      fun j hj => hc j (List.mem_cons_of_mem _ hj)
    have hex : ∃ z ∈ (db i).filter (fun z => !policyBitFalse s z), policySignedHolds P z := by
      obtain ⟨z, hz, hp⟩ := hc i List.mem_cons_self
      refine ⟨z, List.mem_filter.mpr ⟨hz, ?_⟩, hp⟩
      cases hb : policyBitFalse s z with
      | false => rfl
      | true => exact False.elim (policyBitFalse_sound P s z hv hb hp)
    cases he : (db i).filter (fun z => !policyBitFalse s z) with
    | nil => simp only [he, List.not_mem_nil, false_and, exists_false] at hex
    | cons z zs =>
      cases zs with
      | nil =>
        have hz : policySignedHolds P z := by simpa only [he, List.mem_singleton,
          exists_eq_left] using hex
        exact ih (policyBitAddTrue s z) (policyBitAddTrue_valid P s z hv hz) hh
          (by simpa only [policyBitAdvance, he] using h)
      | cons w ws =>
        exact ih s hv hh (by simpa only [policyBitAdvance, he] using h)

def policyBitRUP (db : Nat → List Int) (c : List Int) (hints : List Nat) : Bool :=
  policyBitAdvance db hints (policyBitStart c)

def policyBitRUP_sound db c hints P
    (hc : ∀ i ∈ hints, policySignedClauseHolds P (db i))
    (h : policyBitRUP db c hints = true) : policySignedClauseHolds P c := by
  classical
  by_contra hn
  exact policyBitAdvance_sound db hints P (policyBitStart c)
    (policyBitStart_valid P c hn) hc h

end Bounty

end PolicySubmissionPart33

/- Component PolicyBitsetComposition; SHA256 8c0f44e6588620fe556ebc89f7b3eba71195198e58de51caca92fbc5672e6554. -/
section PolicySubmissionPart34
/- Well-founded composition of directly checked bitset RUP clauses. -/

namespace Bounty

def policyBitActionGood (db : Nat → List Int) (i : Nat) (hints : List Nat) : Bool :=
  hints.all (fun j => decide (0 < j ∧ j < i)) && policyBitRUP db (db i) hints

def policyBitActionGood_sound db i hints P
    (h : policyBitActionGood db i hints = true)
    (hi : ∀ j, 0 < j → j < i → policySignedClauseHolds P (db j)) :
    policySignedClauseHolds P (db i) := by
  simp only [policyBitActionGood, Bool.and_eq_true, List.all_eq_true,
    decide_eq_true_eq] at h
  exact policyBitRUP_sound db (db i) hints P
    (fun j hj => hi j (h.1 j hj).1 (h.1 j hj).2) h.2

def policyBitGraph_sound (db : Nat → List Int) (initialBound limit : Nat)
    (hints : Nat → List Nat) (P : Nat → Prop)
    (hc : ∀ i, initialBound ≤ i → i < limit → policyBitActionGood db i (hints i) = true)
    (hi : ∀ i, 0 < i → i < initialBound → policySignedClauseHolds P (db i)) :
    ∀ i, 0 < i → i < limit → policySignedClauseHolds P (db i) := by
  intro i
  induction i using Nat.strong_induction_on with
  | h i ih =>
    intro hip hil
    by_cases hlt : i < initialBound
    · exact hi i hip hlt
    apply policyBitActionGood_sound db i (hints i) P (hc i (Nat.le_of_not_gt hlt) hil)
    intro j hj hji
    exact ih j hji hj (lt_trans hji hil)

def policyBitGraph_false (db : Nat → List Int) (initialBound limit root : Nat)
    (hints : Nat → List Nat) (P : Nat → Prop)
    (hc : ∀ i, initialBound ≤ i → i < limit → policyBitActionGood db i (hints i) = true)
    (hi : ∀ i, 0 < i → i < initialBound → policySignedClauseHolds P (db i))
    (hr : 0 < root) (hrl : root < limit) (he : db root = []) : False := by
  have hh := policyBitGraph_sound db initialBound limit hints P hc hi root hr hrl
  rw [he] at hh
  simpa [policySignedClauseHolds] using hh

def policyIntervalJoin (P : Nat → Prop) (a b c : Nat)
    (hl : ∀ i, a ≤ i → i < b → P i)
    (hr : ∀ i, b ≤ i → i < c → P i) :
    ∀ i, a ≤ i → i < c → P i := by
  intro i hia hic
  by_cases hib : i < b
  · exact hl i hia hib
  · exact hr i (Nat.le_of_not_gt hib) hic

end Bounty

end PolicySubmissionPart34

/- Component PolicyRUPBlocks; SHA256 4b281604ceee69ad8abed4e56bc15041643593573b343cc91c3a6e7fce3c3eaf. -/
section PolicySubmissionPart35
/- Finite RUP blocks with an explicit model-preservation theorem. -/

namespace Bounty
open Std.Sat Std.Tactic.BVDecide.LRAT Std.Tactic.BVDecide.LRAT.Internal

end Bounty

end PolicySubmissionPart35

/- Component PolicyRUPBoundary; SHA256 0624fd4b0479c269aaa70229e81f9bb0f7f0a2ce369788d9f2c967cf5b21a234. -/
section PolicySubmissionPart36
/- Signed boundary clauses of a sparse RUP block and explicit variable renaming. -/

namespace Bounty
open Std.Sat Std.Tactic.BVDecide.LRAT Std.Tactic.BVDecide.LRAT.Internal

def policyRenameLiteral (σ : Nat → Nat) (z : Int) : Int :=
  if 0 < z then (σ z.natAbs : Int) else -(σ z.natAbs : Int)

def policySignedHolds_rename (P : Nat → Prop) (σ : Nat → Nat)
    (hσ : ∀ i, 0 < σ i) (z : Int) :
    policySignedHolds P (policyRenameLiteral σ z) ↔
      policySignedHolds (fun i => P (σ i)) z := by
  have hpos : (0 : Int) < (σ z.natAbs : Int) := by exact_mod_cast hσ z.natAbs
  have hn : σ z.natAbs ≠ 0 := Nat.ne_of_gt (hσ z.natAbs)
  by_cases hz : 0 < z
  · simp [policyRenameLiteral, policySignedHolds, hz, hn]
  · simp [policyRenameLiteral, policySignedHolds, hz, hn, not_lt_of_ge (le_of_lt hpos)]

def policySignedClauseHolds_rename (P : Nat → Prop) (σ : Nat → Nat)
    (hσ : ∀ i, 0 < σ i) (cs : List Int) :
    policySignedClauseHolds P (cs.map (policyRenameLiteral σ)) ↔
      policySignedClauseHolds (fun i => P (σ i)) cs := by
  simp only [policySignedClauseHolds, List.mem_map, exists_exists_and_eq_and,
    policySignedHolds_rename P σ hσ]

end Bounty

end PolicySubmissionPart36

/- Component PolicyClauseReindex; SHA256 118589b8c2cd35ae9e899e411a3804d2ba500459d2266275a5473af6154944b5. -/
section PolicySubmissionPart37
/- One shared positive variable renaming for an entire Boolean refutation. -/

namespace Bounty

def policyClauseRename_model (small dense : Nat → List Int) (σ : Nat → Nat)
    (P : Nat → Prop)
    (hσ : ∀ i, 0 < σ i) (i : Nat)
    (hm : (small i).map (policyRenameLiteral σ) = dense i)
    (hi : policySignedClauseHolds P (dense i)) :
    policySignedClauseHolds (fun j => P (σ j)) (small i) := by
  apply (policySignedClauseHolds_rename P σ hσ (small i)).mp
  rwa [hm]

end Bounty

end PolicySubmissionPart37

/- Component PolicyMappedDatabases; SHA256 c8cf262e1f40fd4f208feb1ab02668d8c8b26db280365f6606208b41a1ad1f41. -/
section PolicySubmissionPart38
/- Dense semantic clauses defined directly by the positive compact-variable map. -/
namespace Bounty

def policyMappedDatabase0 (i : Nat) : List Int :=
  (policyFixedCompact0Db i).map (policyRenameLiteral policyFixedCompact0Rename)

def policyMappedDatabase1 (i : Nat) : List Int :=
  (policyFixedCompact1Db i).map (policyRenameLiteral policyFixedCompact1Rename)

def policyMappedDatabase0_model (P : Nat → Prop) (i : Nat)
    (h : policySignedClauseHolds P (policyMappedDatabase0 i)) :
    policySignedClauseHolds (fun v => P (policyFixedCompact0Rename v))
      (policyFixedCompact0Db i) :=
  policyClauseRename_model policyFixedCompact0Db policyMappedDatabase0
    policyFixedCompact0Rename P (fun _ => Nat.succ_pos _) i rfl h

def policyMappedDatabase1_model (P : Nat → Prop) (i : Nat)
    (h : policySignedClauseHolds P (policyMappedDatabase1 i)) :
    policySignedClauseHolds (fun v => P (policyFixedCompact1Rename v))
      (policyFixedCompact1Db i) :=
  policyClauseRename_model policyFixedCompact1Db policyMappedDatabase1
    policyFixedCompact1Rename P (fun _ => Nat.succ_pos _) i rfl h

end Bounty

end PolicySubmissionPart38

/- Component PolicyMappedCircuitChecked0; SHA256 4a6490050d398169f56d49c65a1b8046d0f5cb47a45d53b7e34e28c4d4afb188. -/
section PolicySubmissionPart39
namespace PolicyMappedCircuitChecked0
open ClosureCircuit ClosureSemantics Bounty

def test (start count : Nat) : Bool :=
  checkCircuitBlock (boundedProgram ClosureFixedWidthData0.program)
    policyMappedDatabase0 PolicyCircuitPacked0.records start count

def checked0 : test 0 32 = true := by
  decide +kernel

def checked1 : test 32 32 = true := by
  decide +kernel

def checked2 : test 64 32 = true := by
  decide +kernel

def checked3 : test 96 32 = true := by
  decide +kernel

def checked4 : test 0x80 32 = true := by
  decide +kernel

def checked5 : test 0xa0 32 = true := by
  decide +kernel

def checked6 : test 0xc0 32 = true := by
  decide +kernel

def checked7 : test 0xe0 32 = true := by
  decide +kernel

def checked8 : test 0x100 32 = true := by
  decide +kernel

def checked9 : test 0x120 32 = true := by
  decide +kernel

def checked10 : test 0x140 32 = true := by
  decide +kernel

def checked11 : test 0x160 32 = true := by
  decide +kernel

def checked12 : test 0x180 32 = true := by
  decide +kernel

def checked13 : test 0x1a0 32 = true := by
  decide +kernel

def checked14 : test 0x1c0 32 = true := by
  decide +kernel

def checked15 : test 0x1e0 32 = true := by
  decide +kernel

def checked16 : test 0x200 32 = true := by
  decide +kernel

def checked17 : test 0x220 32 = true := by
  decide +kernel

def checked18 : test 0x240 32 = true := by
  decide +kernel

def checked19 : test 0x260 32 = true := by
  decide +kernel

def checked20 : test 0x280 32 = true := by
  decide +kernel

def checked21 : test 0x2a0 32 = true := by
  decide +kernel

def checked22 : test 0x2c0 32 = true := by
  decide +kernel

def checked23 : test 0x2e0 32 = true := by
  decide +kernel

def checked24 : test 0x300 32 = true := by
  decide +kernel

def checked25 : test 0x320 32 = true := by
  decide +kernel

def checked26 : test 0x340 32 = true := by
  decide +kernel

def checked27 : test 0x360 32 = true := by
  decide +kernel

def checked28 : test 0x380 32 = true := by
  decide +kernel

def checked29 : test 0x3a0 32 = true := by
  decide +kernel

def checked30 : test 0x3c0 32 = true := by
  decide +kernel

def checked31 : test 0x3e0 32 = true := by
  decide +kernel

def checked32 : test 0x400 32 = true := by
  decide +kernel

def checked33 : test 0x420 32 = true := by
  decide +kernel

def checked34 : test 0x440 32 = true := by
  decide +kernel

def checked35 : test 0x460 32 = true := by
  decide +kernel

def checked36 : test 0x480 32 = true := by
  decide +kernel

def checked37 : test 0x4a0 32 = true := by
  decide +kernel

def checked38 : test 0x4c0 32 = true := by
  decide +kernel

def checked39 : test 0x4e0 32 = true := by
  decide +kernel

def checked40 : test 0x500 32 = true := by
  decide +kernel

def checked41 : test 0x520 32 = true := by
  decide +kernel

def checked42 : test 0x540 32 = true := by
  decide +kernel

def checked43 : test 0x560 32 = true := by
  decide +kernel

def checked44 : test 0x580 32 = true := by
  decide +kernel

def checked45 : test 0x5a0 32 = true := by
  decide +kernel

def checked46 : test 0x5c0 32 = true := by
  decide +kernel

def checked47 : test 0x5e0 32 = true := by
  decide +kernel

def checked48 : test 0x600 32 = true := by
  decide +kernel

def checked49 : test 0x620 32 = true := by
  decide +kernel

def checked50 : test 0x640 32 = true := by
  decide +kernel

def checked51 : test 0x660 32 = true := by
  decide +kernel

def checked52 : test 0x680 32 = true := by
  decide +kernel

def checked53 : test 0x6a0 32 = true := by
  decide +kernel

def checked54 : test 0x6c0 32 = true := by
  decide +kernel

def checked55 : test 0x6e0 32 = true := by
  decide +kernel

def checked56 : test 0x700 32 = true := by
  decide +kernel

def checked57 : test 0x720 32 = true := by
  decide +kernel

def checked58 : test 0x740 32 = true := by
  decide +kernel

def checked59 : test 0x760 32 = true := by
  decide +kernel

def checked60 : test 0x780 32 = true := by
  decide +kernel

def checked61 : test 0x7a0 32 = true := by
  decide +kernel

def checked62 : test 0x7c0 32 = true := by
  decide +kernel

def checked63 : test 0x7e0 32 = true := by
  decide +kernel

def checked64 : test 0x800 32 = true := by
  decide +kernel

def checked65 : test 0x820 32 = true := by
  decide +kernel

def checked66 : test 0x840 32 = true := by
  decide +kernel

def checked67 : test 0x860 32 = true := by
  decide +kernel

def checked68 : test 0x880 32 = true := by
  decide +kernel

def checked69 : test 0x8a0 32 = true := by
  decide +kernel

def checked70 : test 0x8c0 32 = true := by
  decide +kernel

def checked71 : test 0x8e0 32 = true := by
  decide +kernel

def checked72 : test 0x900 32 = true := by
  decide +kernel

def checked73 : test 0x920 32 = true := by
  decide +kernel

def checked74 : test 0x940 32 = true := by
  decide +kernel

def checked75 : test 0x960 32 = true := by
  decide +kernel

def checked76 : test 0x980 32 = true := by
  decide +kernel

def checked77 : test 0x9a0 32 = true := by
  decide +kernel

def checked78 : test 0x9c0 32 = true := by
  decide +kernel

def checked79 : test 0x9e0 32 = true := by
  decide +kernel

def checked80 : test 0xa00 32 = true := by
  decide +kernel

def checked81 : test 0xa20 32 = true := by
  decide +kernel

def checked82 : test 0xa40 32 = true := by
  decide +kernel

def checked83 : test 0xa60 32 = true := by
  decide +kernel

def checked84 : test 0xa80 32 = true := by
  decide +kernel

def checked85 : test 0xaa0 32 = true := by
  decide +kernel

def checked86 : test 0xac0 32 = true := by
  decide +kernel

def checked87 : test 0xae0 32 = true := by
  decide +kernel

def checked88 : test 0xb00 32 = true := by
  decide +kernel

def checked89 : test 0xb20 32 = true := by
  decide +kernel

def checked90 : test 0xb40 32 = true := by
  decide +kernel

def checked91 : test 0xb60 32 = true := by
  decide +kernel

def checked92 : test 0xb80 32 = true := by
  decide +kernel

def checked93 : test 0xba0 32 = true := by
  decide +kernel

def checked94 : test 0xbc0 32 = true := by
  decide +kernel

def checked95 : test 0xbe0 32 = true := by
  decide +kernel

def checked96 : test 0xc00 32 = true := by
  decide +kernel

def checked97 : test 0xc20 32 = true := by
  decide +kernel

def checked98 : test 0xc40 32 = true := by
  decide +kernel

def checked99 : test 0xc60 32 = true := by
  decide +kernel

def checked100 : test 0xc80 32 = true := by
  decide +kernel

def checked101 : test 0xca0 32 = true := by
  decide +kernel

def checked102 : test 0xcc0 32 = true := by
  decide +kernel

def checked103 : test 0xce0 32 = true := by
  decide +kernel

def checked104 : test 0xd00 32 = true := by
  decide +kernel

def checked105 : test 0xd20 32 = true := by
  decide +kernel

def checked106 : test 0xd40 32 = true := by
  decide +kernel

def checked107 : test 0xd60 32 = true := by
  decide +kernel

def checked108 : test 0xd80 32 = true := by
  decide +kernel

def checked109 : test 0xda0 32 = true := by
  decide +kernel

def checked110 : test 0xdc0 32 = true := by
  decide +kernel

def checked111 : test 0xde0 32 = true := by
  decide +kernel

def checked112 : test 0xe00 32 = true := by
  decide +kernel

def checked113 : test 0xe20 32 = true := by
  decide +kernel

def checked114 : test 0xe40 32 = true := by
  decide +kernel

def checked115 : test 0xe60 32 = true := by
  decide +kernel

def checked116 : test 0xe80 32 = true := by
  decide +kernel

def checked117 : test 0xea0 32 = true := by
  decide +kernel

def checked118 : test 0xec0 32 = true := by
  decide +kernel

def checked119 : test 0xee0 32 = true := by
  decide +kernel

def checked120 : test 0xf00 32 = true := by
  decide +kernel

def checked121 : test 0xf20 32 = true := by
  decide +kernel

def checked122 : test 0xf40 32 = true := by
  decide +kernel

def checked123 : test 0xf60 32 = true := by
  decide +kernel

def checked124 : test 0xf80 32 = true := by
  decide +kernel

def checked125 : test 0xfa0 32 = true := by
  decide +kernel

def checked126 : test 0xfc0 32 = true := by
  decide +kernel

def checked127 : test 0xfe0 32 = true := by
  decide +kernel

def checked128 : test 0x1000 32 = true := by
  decide +kernel

def checked129 : test 0x1020 32 = true := by
  decide +kernel

def checked130 : test 0x1040 32 = true := by
  decide +kernel

def checked131 : test 0x1060 32 = true := by
  decide +kernel

def checked132 : test 0x1080 32 = true := by
  decide +kernel

def checked133 : test 0x10a0 32 = true := by
  decide +kernel

def checked134 : test 0x10c0 32 = true := by
  decide +kernel

def checked135 : test 0x10e0 32 = true := by
  decide +kernel

def checked136 : test 0x1100 32 = true := by
  decide +kernel

def checked137 : test 0x1120 32 = true := by
  decide +kernel

def checked138 : test 0x1140 32 = true := by
  decide +kernel

def checked139 : test 0x1160 32 = true := by
  decide +kernel

def checked140 : test 0x1180 32 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 96 → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67
  · exact checked68
  · exact checked69
  · exact checked70
  · exact checked71
  · exact checked72
  · exact checked73
  · exact checked74
  · exact checked75
  · exact checked76
  · exact checked77
  · exact checked78
  · exact checked79
  · exact checked80
  · exact checked81
  · exact checked82
  · exact checked83
  · exact checked84
  · exact checked85
  · exact checked86
  · exact checked87
  · exact checked88
  · exact checked89
  · exact checked90
  · exact checked91
  · exact checked92
  · exact checked93
  · exact checked94
  · exact checked95

def checkedRange96 : ∀ i : Nat, 96 ≤ i → i < 0x80 → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked96
  · exact checked97
  · exact checked98
  · exact checked99
  · exact checked100
  · exact checked101
  · exact checked102
  · exact checked103
  · exact checked104
  · exact checked105
  · exact checked106
  · exact checked107
  · exact checked108
  · exact checked109
  · exact checked110
  · exact checked111
  · exact checked112
  · exact checked113
  · exact checked114
  · exact checked115
  · exact checked116
  · exact checked117
  · exact checked118
  · exact checked119
  · exact checked120
  · exact checked121
  · exact checked122
  · exact checked123
  · exact checked124
  · exact checked125
  · exact checked126
  · exact checked127

def checkedRange128 : ∀ i : Nat, 0x80 ≤ i → i < 0x8d → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked128
  · exact checked129
  · exact checked130
  · exact checked131
  · exact checked132
  · exact checked133
  · exact checked134
  · exact checked135
  · exact checked136
  · exact checked137
  · exact checked138
  · exact checked139
  · exact checked140

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 0x8d → test (32 * i) (min 32 (0x11a0 - 32 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 64 0x8d
  (Bounty.policyIntervalJoin _ 0 32 64
  checkedRange0
  checkedRange32)
  (Bounty.policyIntervalJoin _ 64 96 0x8d
  checkedRange64
  (Bounty.policyIntervalJoin _ 96 0x80 0x8d
  checkedRange96
  checkedRange128)))

def checked (i : Fin 0x8d) : test (32 * i.val)
    (min 32 (0x11a0 - 32 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values)
    (i : Nat) (hi : i < 0x11a0) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase0 ((PolicyCircuitPacked0.records i).headD 0)) := by
  have hb : i / 32 < 0x8d := by omega
  have hw : i % 32 < min 32 (0x11a0 - 32 * (i / 32)) := by omega
  have h := checkCircuitBlock_sound (boundedProgram ClosureFixedWidthData0.program) input values he
    policyMappedDatabase0 PolicyCircuitPacked0.records (32 * (i / 32))
    (min 32 (0x11a0 - 32 * (i / 32))) (checked ⟨i / 32, hb⟩) (i % 32) hw
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyMappedCircuitChecked0

end PolicySubmissionPart39

/- Component PolicyMappedRewriteParametricChecked0; SHA256 939851e280be1a1867c2575bacf05df34ecaccd0b77f2104e2e5637f1a51bdfc. -/
section PolicySubmissionPart40
namespace PolicyMappedRewriteParametricChecked0
open ClosurePattern ClosureSemantics Bounty

def test (start count : Nat) : Bool :=
  checkSchemaBlock (boundedProgram ClosureFixedWidthData0.program)
    policyMappedDatabase0 PolicyRewriteParametricPacked0.records start count

def checked0 : test 0 32 = true := by
  decide +kernel

def checked1 : test 32 32 = true := by
  decide +kernel

def checked2 : test 64 32 = true := by
  decide +kernel

def checked3 : test 96 32 = true := by
  decide +kernel

def checked4 : test 0x80 32 = true := by
  decide +kernel

def checked5 : test 0xa0 32 = true := by
  decide +kernel

def checked6 : test 0xc0 32 = true := by
  decide +kernel

def checked7 : test 0xe0 32 = true := by
  decide +kernel

def checked8 : test 0x100 32 = true := by
  decide +kernel

def checked9 : test 0x120 32 = true := by
  decide +kernel

def checked10 : test 0x140 32 = true := by
  decide +kernel

def checked11 : test 0x160 32 = true := by
  decide +kernel

def checked12 : test 0x180 32 = true := by
  decide +kernel

def checked13 : test 0x1a0 32 = true := by
  decide +kernel

def checked14 : test 0x1c0 32 = true := by
  decide +kernel

def checked15 : test 0x1e0 32 = true := by
  decide +kernel

def checked16 : test 0x200 32 = true := by
  decide +kernel

def checked17 : test 0x220 32 = true := by
  decide +kernel

def checked18 : test 0x240 32 = true := by
  decide +kernel

def checked19 : test 0x260 32 = true := by
  decide +kernel

def checked20 : test 0x280 32 = true := by
  decide +kernel

def checked21 : test 0x2a0 32 = true := by
  decide +kernel

def checked22 : test 0x2c0 32 = true := by
  decide +kernel

def checked23 : test 0x2e0 32 = true := by
  decide +kernel

def checked24 : test 0x300 32 = true := by
  decide +kernel

def checked25 : test 0x320 32 = true := by
  decide +kernel

def checked26 : test 0x340 32 = true := by
  decide +kernel

def checked27 : test 0x360 32 = true := by
  decide +kernel

def checked28 : test 0x380 32 = true := by
  decide +kernel

def checked29 : test 0x3a0 32 = true := by
  decide +kernel

def checked30 : test 0x3c0 32 = true := by
  decide +kernel

def checked31 : test 0x3e0 32 = true := by
  decide +kernel

def checked32 : test 0x400 32 = true := by
  decide +kernel

def checked33 : test 0x420 32 = true := by
  decide +kernel

def checked34 : test 0x440 32 = true := by
  decide +kernel

def checked35 : test 0x460 32 = true := by
  decide +kernel

def checked36 : test 0x480 32 = true := by
  decide +kernel

def checked37 : test 0x4a0 32 = true := by
  decide +kernel

def checked38 : test 0x4c0 32 = true := by
  decide +kernel

def checked39 : test 0x4e0 32 = true := by
  decide +kernel

def checked40 : test 0x500 32 = true := by
  decide +kernel

def checked41 : test 0x520 32 = true := by
  decide +kernel

def checked42 : test 0x540 32 = true := by
  decide +kernel

def checked43 : test 0x560 32 = true := by
  decide +kernel

def checked44 : test 0x580 32 = true := by
  decide +kernel

def checked45 : test 0x5a0 32 = true := by
  decide +kernel

def checked46 : test 0x5c0 32 = true := by
  decide +kernel

def checked47 : test 0x5e0 32 = true := by
  decide +kernel

def checked48 : test 0x600 32 = true := by
  decide +kernel

def checked49 : test 0x620 32 = true := by
  decide +kernel

def checked50 : test 0x640 32 = true := by
  decide +kernel

def checked51 : test 0x660 32 = true := by
  decide +kernel

def checked52 : test 0x680 32 = true := by
  decide +kernel

def checked53 : test 0x6a0 32 = true := by
  decide +kernel

def checked54 : test 0x6c0 32 = true := by
  decide +kernel

def checked55 : test 0x6e0 32 = true := by
  decide +kernel

def checked56 : test 0x700 32 = true := by
  decide +kernel

def checked57 : test 0x720 32 = true := by
  decide +kernel

def checked58 : test 0x740 32 = true := by
  decide +kernel

def checked59 : test 0x760 32 = true := by
  decide +kernel

def checked60 : test 0x780 32 = true := by
  decide +kernel

def checked61 : test 0x7a0 32 = true := by
  decide +kernel

def checked62 : test 0x7c0 32 = true := by
  decide +kernel

def checked63 : test 0x7e0 32 = true := by
  decide +kernel

def checked64 : test 0x800 32 = true := by
  decide +kernel

def checked65 : test 0x820 32 = true := by
  decide +kernel

def checked66 : test 0x840 32 = true := by
  decide +kernel

def checked67 : test 0x860 32 = true := by
  decide +kernel

def checked68 : test 0x880 32 = true := by
  decide +kernel

def checked69 : test 0x8a0 32 = true := by
  decide +kernel

def checked70 : test 0x8c0 32 = true := by
  decide +kernel

def checked71 : test 0x8e0 32 = true := by
  decide +kernel

def checked72 : test 0x900 32 = true := by
  decide +kernel

def checked73 : test 0x920 32 = true := by
  decide +kernel

def checked74 : test 0x940 32 = true := by
  decide +kernel

def checked75 : test 0x960 32 = true := by
  decide +kernel

def checked76 : test 0x980 32 = true := by
  decide +kernel

def checked77 : test 0x9a0 32 = true := by
  decide +kernel

def checked78 : test 0x9c0 32 = true := by
  decide +kernel

def checked79 : test 0x9e0 32 = true := by
  decide +kernel

def checked80 : test 0xa00 32 = true := by
  decide +kernel

def checked81 : test 0xa20 32 = true := by
  decide +kernel

def checked82 : test 0xa40 32 = true := by
  decide +kernel

def checked83 : test 0xa60 32 = true := by
  decide +kernel

def checked84 : test 0xa80 32 = true := by
  decide +kernel

def checked85 : test 0xaa0 32 = true := by
  decide +kernel

def checked86 : test 0xac0 32 = true := by
  decide +kernel

def checked87 : test 0xae0 32 = true := by
  decide +kernel

def checked88 : test 0xb00 32 = true := by
  decide +kernel

def checked89 : test 0xb20 32 = true := by
  decide +kernel

def checked90 : test 0xb40 32 = true := by
  decide +kernel

def checked91 : test 0xb60 32 = true := by
  decide +kernel

def checked92 : test 0xb80 32 = true := by
  decide +kernel

def checked93 : test 0xba0 32 = true := by
  decide +kernel

def checked94 : test 0xbc0 32 = true := by
  decide +kernel

def checked95 : test 0xbe0 32 = true := by
  decide +kernel

def checked96 : test 0xc00 32 = true := by
  decide +kernel

def checked97 : test 0xc20 32 = true := by
  decide +kernel

def checked98 : test 0xc40 32 = true := by
  decide +kernel

def checked99 : test 0xc60 32 = true := by
  decide +kernel

def checked100 : test 0xc80 32 = true := by
  decide +kernel

def checked101 : test 0xca0 12 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (32 * i) (min 32 (0xcac - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (32 * i) (min 32 (0xcac - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 96 → test (32 * i) (min 32 (0xcac - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67
  · exact checked68
  · exact checked69
  · exact checked70
  · exact checked71
  · exact checked72
  · exact checked73
  · exact checked74
  · exact checked75
  · exact checked76
  · exact checked77
  · exact checked78
  · exact checked79
  · exact checked80
  · exact checked81
  · exact checked82
  · exact checked83
  · exact checked84
  · exact checked85
  · exact checked86
  · exact checked87
  · exact checked88
  · exact checked89
  · exact checked90
  · exact checked91
  · exact checked92
  · exact checked93
  · exact checked94
  · exact checked95

def checkedRange96 : ∀ i : Nat, 96 ≤ i → i < 0x66 → test (32 * i) (min 32 (0xcac - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked96
  · exact checked97
  · exact checked98
  · exact checked99
  · exact checked100
  · exact checked101

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 0x66 → test (32 * i) (min 32 (0xcac - 32 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 64 0x66
  (Bounty.policyIntervalJoin _ 0 32 64
  checkedRange0
  checkedRange32)
  (Bounty.policyIntervalJoin _ 64 96 0x66
  checkedRange64
  checkedRange96))

def checked (i : Fin 0x66) : test (32 * i.val)
    (min 32 (0xcac - 32 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values)
    (i : Nat) (hi : i < 0xcac) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase0 ((PolicyRewriteParametricPacked0.records i).headD 0)) := by
  have hb : i / 32 < 0x66 := by omega
  have hw : i % 32 < min 32 (0xcac - 32 * (i / 32)) := by omega
  have h := checkSchemaBlock_sound (boundedProgram ClosureFixedWidthData0.program) input values he
    policyMappedDatabase0 PolicyRewriteParametricPacked0.records (32 * (i / 32))
    (min 32 (0xcac - 32 * (i / 32))) (checked ⟨i / 32, hb⟩) (i % 32) hw
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyMappedRewriteParametricChecked0

end PolicySubmissionPart40

/- Component PolicyArithmeticPacked0; SHA256 6a4ce32fc3c2b916dd90f54f2635b2d0b1922464a0bbbf429a1b2a49fd710849. -/
section PolicySubmissionPart41
/- Untrusted packed arithmetic leaves for the shortened Boolean certificate. -/
namespace PolicyArithmeticPacked0
open PackedNatTable

def tableLLL : Table Block := .leaf #[
  ⟨0x13208e04181e60da06102bc14209304281bc0b604d01f80ac030000, 0x420410810029f3072f420a7e46004bba0420400810029ec0a79820a7c86004bb904204008100296804297d14112ecc10810020400a4e029680a59830a5bc7044bad0410400810810020800a4e010a5945044bac0420400810029280429311c012ea410810400029231c012e9810810400028fd1c012e9410810400028f81c012e8810810020400a39028b10828ea1c012df010810420400c28b10828b928012dd810810400028b01c012dd410810400028ab1c012dc810810020400c287108287928012db0108100204007fcc107fdc5044b6204104008108100208007fb0107fc85044b61⟩,
  ⟨0x15509704602140f407303481880b604b82100dc05802100b002c000, 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⟩,
  ⟨0x18b0ba84f424e111075835418409c04301c80c805602000a8028000, 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⟩,
  ⟨0x1910bf05ac2b013108c04141da0d706082800dc05802100b002c000, 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⟩,
  ⟨0x1b40d086202e012608803e81ce0d104381e40c604d01b80a4026000, 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⟩,
  ⟨0x1d20d006482fe1690a984201be0c905a827c11207602780f004c000, 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⟩,
  ⟨0x17c0b7058029a13709484541fe0e904f81e00c804e02000a802c000, 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⟩,
  ⟨0x1960c005a82a814609804241e60dd05b02801180760300128068000, 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⟩,
  ⟨0x1b20ce06182e615d0a3848421c0fb07102f015209603e81940a4000, 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⟩
]

def tableLLR : Table Block := .leaf #[
  ⟨0x1c50d686682a0106078034417c0a804901f00cc05001d009002c000, 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⟩,
  ⟨0x1b90d186342ee1610a704b022c10006702900fc06b02900b0032000, 0x108100204012db02eb8084e2e180165b81081002040129e84b6c084e29180165b41081002040129e84a67084e27180165b0108100204012ae04a34084df3180165841081042040132941137c050459600420410400c1136dc4de1136ec3129e84a7b12dc8340600593e042041081004a7b129e82136f46005938042041081004a7b12dc82136f0600593704404304204104014112f904db6130b04dad12dc051299c4a7b129984a7a12db0540600593604304204104010112fcc4c2c136b44db6104a67129984a7b129e84406005933043042041040101133ac49f6133a43132944cb3126983132c050458f7042040081004cb3044cec141163d81081002040132944cb3126983133a870458f50430420410401011339c49bb132e43132944cb3126983132b850458f4042041081004cb3044ce8141163cc1081042040132944cb3126983132e870458ed⟩,
  ⟨0x15309e849c2220fb072833c1780a604801e80c804e01c00a8028000, 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⟩,
  ⟨0x1a70ca05f82d015209604141de0d906182b412e08103580a802c000, 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⟩,
  ⟨0x1660ac052826c12008503d01bc0c805902440de05902180d402c000, 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⟩,
  ⟨0x12808904101dc0da06602f816009c04401c80b804e02000b002c000, 0x42040081005cf8172f82175b07005b78042041000175a87005b77042040081005c70170cc21758c7005b76042041081008170cc217584a005b75042041000174f07005b72042041000174cc7005b71042041000174b87005b6e042040081008172f82174a4a005b6d042041081008172f8217398a005b62042040081005c28171c02172dc6005b3e042041081005c70170cc2171d87005b34042041000171b87005b33042041000171a47005b30042040081008170cc2170eca005b2a042040081005bff170a02170c86005b29042040081005bff16ec02170946005b26⟩,
  ⟨0x23e11408183e01da0e203d81d00d305e829c12207b017807001c000, 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⟩,
  ⟨0x2140ff077038c1b00cd83c41c60c405282480f806602c00dc02c000, 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⟩,
  ⟨0x1820b605582160f7070834c18a0af04d82340f005702080ac02c000, 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⟩,
  ⟨0x1ec0ec072836819e0bb84b823010505502100dc05802100b002c000, 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⟩
]

def tableLL : Table Block := .branch 9 tableLLL tableLLR

def tableLRL : Table Block := .leaf #[
  ⟨0x19a0c605ac2aa13f08f04201e40dc06302c0134084037016002c000, 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⟩,
  ⟨0x26b12e88ec44a20f0fd05cc1c60c4057026c10a06f02680b002c000, 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⟩,
  ⟨0x1880b9055028212b08a83cc1ba0bc05302400f405802500d0042000, 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⟩,
  ⟨0x1970bb055027c12808903c01b40b805102300d605501f80b002c000, 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⟩,
  ⟨0x1800b9057027c12b08a841c1e20db06682e814808e03c0188098000, 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⟩,
  ⟨0x1620a604f825011207f03c01b40c605801c80bc04801d00b002c000, 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⟩,
  ⟨0x17a0b2053c27812908803dc1c209504381c80b8048019009001c000, 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⟩,
  ⟨0x1bc0d486402ee12a08b04001d40d404381cc0ba04f02080ac030000, 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⟩,
  ⟨0x1d40df06ac32a17f0b4850825811608183a81ae05802100b002c000, 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⟩
]

def tableLRR : Table Block := .leaf #[
  ⟨0x24511608644061ed0d304301ec0bd05202440f606501f0098026000, 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⟩,
  ⟨0x1940bd85a02aa13c09303c01ba0c403d81b40be04c01c8098026000, 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⟩,
  ⟨0x2ad14b8a044d623e11588603e41da0e386c422a0ff05c828c02c000, 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⟩,
  ⟨0x1800b5052426611d08383a41ac0c004f02200e406402100b002c000, 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⟩,
  ⟨0x3941a38cc463630317687f83d01d209184041d60d505f80dc02c000, 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⟩,
  ⟨0x29014109bc4b22430e506d033c1880b9046c19c08802100b002c000, 0x420410002a4a07006ce3042040081007b6204a9261c01b38810810020401ed887b3108a9241801b38410810020400a7947b6208a9201801b38063983463062c62412181c11981461010c108104100e049eaf27fa09fe3175a42ba60abc09ff912a8c9eb127fc04a7e138a04aa413df0e1f0d029e50a7b01f2727ab09e65278c01d7c129ec4a7a129fc4b6c0abacd27fe86006cb3042041081009e30075f0227fc47006cae0420400810029e51f0d0227fac6006cad042040081007c34278c0227fa46006cac0420400810029ec0a794227f906006cab10b40a0891070461050420802010a3f028f71fae87eb81fb887ef01fbb06c3f1b18c6ae01aaec6a741b1847eef3828b10a49c28e40c6a761a9c47ebd1d02001b2a822412018208070462208050832208021c10f4944afd1b18c9fb01a9d06c610f4a06c3f1ab806abb284a3e0b0f02bfd0c6a711a9d86408006ca904704604504404304204104020112a904aa3128d44a6c129f84ae112a9c7129fc4a34129ec4a6612ae04a7a1299c712bfc6006ca70480c60c50c40c308208108020113b904b3612cd44ae113bbc4efa0f6ac3db5289129984ab8137d04a340f3e83da6207407006ca6042041081004a3e0b0f0227ec47006ca5042041081008cee16ec0227eac7006ca40420400810069f716ce0227dec6006c7d⟩,
  ⟨0x25111d88644061ed0e786f034c1850b7856428612108583d40b4000, 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⟩,
  ⟨0x29514089ac4aa23f116084c30810507b838410806e02680b002c000, 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⟩,
  ⟨0x1d20de06582fa16a0a204ac23010005c029011c078019009002c000, 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⟩,
  ⟨0x2c814909703ce1d10dd86b432e1840b703900b0042017807001c000, 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⟩
]

def tableLR : Table Block := .branch 9 tableLRL tableLRR

def tableL : Table Block := .branch 19 tableLL tableLR

def tableRLL : Table Block := .leaf #[
  ⟨0x1630a684dc24211307e839c1a20bb04881f80d605801f8098026000, 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⟩,
  ⟨0x1b90bc058822a10107983941ae0c1059828011a05501f80a4026000, 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⟩,
  ⟨0x29313e899c3fe1c70ba057829013208e030415609d04480b002c000, 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⟩,
  ⟨0x4121fe0f9878a3af1cc8dc8536240116879424010a04b812802c000, 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⟩,
  ⟨0x22e10187b43ae17b0b2854827a12708c842c1ea0ae0500164042000, 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⟩,
  ⟨0x1990a7050025811608103d01cc0d006102b010c07002500dc042000, 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⟩,
  ⟨0x1ea0eb87042ca14f09e049821a0f7072027411407102400a402c000, 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⟩,
  ⟨0x1870b8856c28a13108d84141de0d904401c80b804601c00a802c000, 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⟩,
  ⟨0x15009d04842120fb076835c1820ab04a82080e805e02400c8032000, 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⟩
]

def tableRLR : Table Block := .leaf #[
  ⟨0x1e50e786e43401870bc85ac2aa13f096045c1e20cf05c81980a0000, 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⟩,
  ⟨0x1d40df06a032a1730ae851c26811b06582d414408a03b8190096000, 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⟩,
  ⟨0x17c0b3054025411407e03a418e0b104d82080de05c02200c4036000, 0x4204008100fdba22ab023f7c46007cf604204108100dab136af823f4806007cf50430420410401013e5b8f9603e3b433e4ecf8e53e3a833eef85047cf404204008100eeab3bdd023f0846007ced0410400810810020803e4ec13eee05047ce804204108100fa6604fabe1c01f2e8108104100304fa7d3e9c8fa630cfa663e8f8fa3d0d01801f2d410810420403e8f8fa6608fa711801f2b810810420403e8f8fa3d08fa641801f2ac10810420403e4ecf8ea3e39433e5847047ca204204108100f8ea04f8f61411f1c010410020403e3a813e3cc5047c6f0410400810810020803e3a813e3c05047c6e04204008100f8e504f8e91411f1b410810020402a4c0aa2408f8a31801f1b0108100204104008200982b2609c23e1947007c68⟩,
  ⟨0x1a10a584b023c108079037018c0b004d02100dc05802100b002c000, 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⟩,
  ⟨0x2f114388e844820e0ed06202e411505002280ee06102580d403e000, 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⟩,
  ⟨0x30e17c0ac853828913988a04241fc0d2063826811e06b01fc02c000, 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⟩,
  ⟨0x32518b8c105dc2a913d89943cc1c80bf036c18a09001e0098026000, 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⟩,
  ⟨0x26010487cc3581740af05202640fa072033817609501d009001c000, 0x4d08c04a0602421c810804800804bdad175a4bdab16fa8c8eb1ab9c2bf70afc8c8e916ff45bf81abc87f6e34bd3f2609c2cfa0c2bf916ebc5bb91cbd6e2001fba810810020400e8903e77091f2f1801fba5b2091c918114110308604db2c36c9cdde93708cdc21377bcadf6421d8c8eb2b7e0adbe2b6e4c36b88dabe2b68882b5c05408007ee80a01411028030a00828011410afdc2bf2168fc50aff02cef2f9945aa42030afe45a3b0add84408007ee3042041081011e730b484247ad47007ebd042040081005a3b479cc247ab86007ebc0420410810108682b5c02478f86007eb02201888050442200c88021411e6b118af16fa85367b0796c16ff45bf8203367a45bb91e5a04408007eaf042040081007968367a42477f06007eae042041081004f69069b42476b86007ea9042040081005a21051da41c01fa9810c10810410040488f1470c488e20c887f222f088aa0c893b1411fa88180d0603028082201c2806045044101201474b47fb92f280bc7b2f180bca7473d86c6d0b8a02bf70afc82cef0b0dcd22884bc39473c4bc3b0b3e830afe47474d48007ea1042040081008a21473c42474b87007e7c042041081011cf12f0ec2473dc6007e75042041000473ac7007e71⟩,
  ⟨0x2490fc86cc3181660a9850023410707703581860ad032013802c000, 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⟩,
  ⟨0x278131085c3761a50c7854c23e109079838019a0ba039816808e000, 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⟩
]

def tableRL : Table Block := .branch 9 tableRLL tableRLR

def tableRRL : Table Block := .leaf #[
  ⟨0x1d70d885a82a813e08c04141d80d9059828010e05401f00ac026000, 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⟩,
  ⟨0x2af14c88403f41d40e086b83301820b6037c17c0a804901f0062000, 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⟩,
  ⟨0x2a614808d044220b0fa877c3981800b505502400b204e0218026000, 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⟩,
  ⟨0x30f17c8b8c50e23f10c875437e17509804681a40bc053021c0ba000, 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⟩,
  ⟨0x4bf256115c744345167098c3d61d50df86a42400fa037016c026000, 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⟩,
  ⟨0x2af14c89cc4ba2060f8077438a1af08603c41b60c805901a8088000, 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⟩,
  ⟨0x49223e10d47cc39218289dc4221fb0ea84682080de06582cc0ac000, 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⟩,
  ⟨0x4e223410387943b71d08d3865a2da136890c37615f08c037412c000, 0x4e04d04c04b18a1891881870461856036026010403810abc03d2a0ebd02af92e4c04fab2e3d0b9740bff49ff0175a56ab75aaa54ea30f998f0abac493807c9c5fbb17ff02ff90bbd89e30075f0ee62271ec2eeb0ab98d406008aa418a0490480471861850440431820402812e3c82af90ebd03e6613ead0a300bff43d2a2e4c0a9270abc0b0ab985ffb0bfe42ef60bbac493817eec2aeb07c9c9406008aa32092084070464022012001c1166e88be10a1e050a2bc28aa1a1a83f6c1a2f509bf28593f0c3ef60a1c4687a1648c6408008aa204204008100ee62056aaa1c0229f010810020403b988eeab096aa8180229ec12812422021cf98506dc833e6087045d32174b4cf6333dc0983f173945d6922bd47db322bdc8aef22aa08aa334cf60260ac5cbe208aaa22ab06408008a7a0420410400c1577855de3083e7b1ecc43ef60ca92c180229c4280c0602c11811418041020a0047047f794209c28af0a2a85bfd16fe08ffb165d508640fad8287842198787c343f363fedc30a1c4d9e916ee46408008a6d0cd0cc0cb08a0c90c80470851840c30c2181301376c8dde0464b0bab92b3bcdd62375e87f312b7b14f263fef10828367b0c8eb38ddad2b2ecdd3b374ccad372b58cada22b39cffb7367a45bb92d01c0229b010c1081041004047c2a1f29c7c685a6c040a7947b620a7b07b31110180229a984444043c43843583042c42041d8181c056040700d808100f04593d0b0f82c220aea82af013eac2c630a2bc28aa0abe42aea16180287822f843f6c166e82cb10b1e920ae9c1f270b0f02bfd0abac2ae60ab944fa2124e03ef60a1c45923164fc3390200229a432c12832432031c31020c308304200a0458ea17f9468781618048fa1a1a858bb576c85920162c83ebe2c5fbb17fec4938161d83e7b13e885877162ac3ebb246832180229a01c090c8407405070101c010700070450ff903eb6229f55de10a2bc28aa0a1e03f6c243e6a0f9dc3e7b0c3ef60a1c46574c88008a662080472064044014001811458ea0fad8af660a2bc28aa0a1e03f6c2058760f9ec30fbd828711458a22002299492c320111b0c104900604dae836cb0db272b5dcadbe2b6e47f312b6acdaf91fa98adec36da0c2b5c0836b88ada236af85408008a610a4ad65b9556e540510ce0cd0cc04b0c83070c66201588040e0801381337c8cdb74a5a8cdeb337983fbc0fc9c3f225a589696f0faa08a7d0a2bc28aa0fdd03f7f0fdb8bd2c2f2ccbca02f1ecbd282f4a97336c4cdad57ff43e7b203e6a0f9dc28710fbd83f362f0ec32f0e4d408008a60⟩,
  ⟨0x3db1a18bec5ca2d215f8a744201970b085381e40cc05c81a002c000, 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⟩
]

def tableRRR : Table Block := .leaf #[
  ⟨0x3f01d20d685fe2e916b0a544e625d113878439c161096822c06c000, 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⟩,
  ⟨0x30c1798b3457428513788ec37e16309e04a417009203f81b00ac000, 0x420410810029380a5a029660d7fa01c122e8010c1081041004057f7a0a5f0296e0c29380a5a029660c296314122dfc10810420400a59815fdec5048b7b0461050830810401411fce85be21fcc49faa175c08d281fdc8716ee45bb0233b85baf1101c022ddc10810020404bd982bf9097ea318022dd811811010c1081005042c375ae8c4f781b9d47cfb1f3a861abe429fa13dc86dac107cfd1c022dc863c13813413012c62862412181d81861460c105800e045f6313d845f6113de16ba313db04f3a1b9d44f70168905f7b0b0dc5f6917dd04f7517df50069b44f3c13da44f351abe429fa13cbc5f6476013dc84f71168844f6d35018022dc462c12811c11811461010c608604100a046e750b0dc68e65ae8c4f7817d845f6313dd44f6c1a3b44f612c6af90a7e84f7213dc44f6913cd44f2e13cf01a6d2468ee18022dbc10c1081041004048a3f2e2a57a2f42b8c4228d48b2c22cf83405048b6d042040081008b2c057a3014122da8480d1202c528524520a1d48041431600858012802c12bbf0aef72bab85d3b2bb997a265e89179f70b18c2bf70afc82cef1f9f86c6d260a82c2240aea9129fc4a3f128f82c3c0afe498270b3e82bfd0ca408008b6504304204104010112a904af8129903129fc4a3f128f835e8985008b64042040081004a7f057a2514022d8c108100204022cb015e88c5048b62042041081004a3f128f825e7e06008b6110d04b20a1080872040410802013b0f55c3b1f6c87db31f6c0bca72f280bc7b1a9f46ae01aaecebfd570fcd1f4b87d2c0c6a763afe8ec272f0e471f5948008b3f⟩,
  ⟨0x3ba1c18d3863e2f91718a0c35e1990c185b41a20620260098026000, 0x450440430420410401810baa8486013ebd5db413eac4fa71829ec0faec493807c9c4fa215018022fa421831030c6042005048ab11f6ccdbec36fc06c6136ea0bc301cdbbd36e8c8aaa22ab04407008be80840430420410401412bdbc58f2166c88be11628850f9ec593f0fbd858761101c022f9c10c108104100404ac722b8b8de320cac382b180ac3f0cac3914122f9810810020401f0d09cee09897a18022f9413812c2282252201152101d82040241161f03f270fc8868bd0faa03ea02b6acadbe2b6e458ea2b7b0686a2b5dc7f314bea8f0f9dc58760f9ecada220ad701a1e8587721020022f8c3b1a0591980570560551940644c14864419100643c138634190c0642c190a0641c8c6c184a36148c6c104a36016042d7c0f9984fab0abe43d2a0bff50aad0a7e02af0168a48be522efc3af4429f82d2626b856c240b5c82d6d1adc18936624a8cdf2336a0cdeb3379989246c2ae60bbac2ef60abac1f270acbc1cbd0a7cc5a310bfe4493817ed02d21169b05a3b0b4802d38624948336c5892155020022f88108104204062494cdb109893718022eec108100204062485892509892b1c022ed81081042040168ec2d210988f118022ed065124414013c13813463012c12011c61861461060c2082046011044eb20b5c82d6d13aac587c164807966168dc5aac163a83f270fc885fb8161805a7c16b8d88e8168d43ea00faa06bb5542d38161dc2b2f072f4587617ed04fa2124e05a6c168ec29f3168c43e7b203e770b4842d2045020022ecc43843058202c582028582024582015482010504500904aefc2bbdc283e0e9ad7fae26dcc29300a4b029220a3f028f70a3a428b80a2bc28aa0a29828784428380a4a029270a39028b10a28c30a1c48408008bb10420410810028380a28c25febc9008ba80430420410401015fe8d7fa15fdfc30a4e029680a59830a5845048ba3042040081002966057fa414122e8810810420400a5a015fe885048ba1⟩,
  ⟨0x30116d8a2448622d10387d03bc1860b8057428811007e83a814a000, 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⟩,
  ⟨0x4c825810807b239d1ad8d1466430c166095c40a16d09083680ba000, 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⟩,
  ⟨0x33917689b848e23110f07183601660a003340f606502780a4026000, 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⟩,
  ⟨0x3831870ba052627d13789844961fe0f4070835818608b8404152000, 0x63863413012c12862462061c61411010c104600d045deb1b4a86ca417cb06c70175ec6cba1e5ec79ac1b1fc6daa27ce05dba1a8885dbd3c4f3c066b44f69069b44f3513cb84f7116d944f721a7dc5bff175d4c406008da304304204104010133ee0cfaa52f90333e94cef7339e8333bec5048da25b92c1b72296e4906dc880821810801c11f6ccdbec22bdcdbf036ea08aa822a8c4ebd0b5c82d6d13ac84eab0b4bcd36ef4dba322aa880b4e02d20190200236841081002040675803cfa099d75240235e01081040019cf61c0235b81081040019cf11c0235ac1081042040672d03cfa099ce62402359942452141c5184084042c001c10a2bc28aa165d42c2223fec2c630fad8aefc2bbdd9c72672942878303f360aff59c710b0f030a1c46408008d62042040081019c710b0f02672989008d390430420410401012f0c0fdf0670cc322ab10b723f6e83437f07008d2c042041081019be80f9ec2670949008d2304304204104010107fd89aae26abc307fb099ed07fcc307fb85048cfa0ce0cc0bb90b0bb90a0bb9090bb908105101231b00241473a91ce566ca43a6b66d80fe26667ed0dfc22ac48aa822a8c3ea80fc9c3f221b1851f2e22b85166c90fdba42dc88aac0e8903e77208aaa210200233e4108104204066c903a24099b61240233c12281d890881860830424810402012e0f45c6d171a05c75170e84eb213af44eab0b5c82d6d1aed42e733b5fc2e76385c33202d380b4805c700b9942d211d02002339c15c18160510604013c23813503012c62412021c61811411060c6090012046c701f8cc7dfc1f7dc2bf70afc86af83b6cc7d2a0b3bc7cea37c806ca42aea06c7f1b6a82bfc1b4a82b7d1f5f86cba1e5ec79ac3b6c581f6ec31b6b04f3c13dc84f710afe44f350ade02b761f3b86af513da41a6d13cb8def9331c11408008ce6⟩,
  ⟨0x47b21510107bc38c19c8b985a02b514789e439a195075024804e000, 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⟩,
  ⟨0x33d18b8b1c56229b142875838011908183b41ae0c104d822002c000, 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⟩,
  ⟨0x4511fc8ef46de32116809e44a622d0ce862826811e0640100044000, 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⟩
]

def tableRR : Table Block := .branch 9 tableRRL tableRRR

def tableR : Table Block := .branch 19 tableRL tableRR

def table : Table Block := .branch 38 tableL tableR

def records (i : ℕ) : List ℕ :=
  PackedNatTable.records table (32 * (i / 16) + i % 16)

end PolicyArithmeticPacked0

end PolicySubmissionPart41

/- Component PolicyClosedConstantCache; SHA256 1a86e0331287eb18ba40023f3aa8644583a558d8681972b439a1396ca9fdb6d3. -/
section PolicySubmissionPart42
/- Experimental constant folding for arithmetic certificates.  Cache entries
are checked against the original program.  This proves transfer of Equations,
not syntactic equality between the original and folded programs. -/
namespace PolicyClosedConstantCache
open ClosureLinear ClosureSemantics Bounty

def checkClosedRatValue (program : ℕ → Node) (fuel i : ℕ) (q : ℚ) : Bool :=
  match closedNode program fuel i with
  | none => false
  | some v => decide (v.b = false ∧ v.z = 0 ∧ v.q = q)

def checkClosedRatValue_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (fuel i : ℕ) (q : ℚ)
    (h : checkClosedRatValue program fuel i q = true) : values i = ratValue q := by
  cases hv : closedNode program fuel i with
  | none => simp [checkClosedRatValue, hv] at h
  | some v =>
    have hf : v.b = false ∧ v.z = 0 ∧ v.q = q := by
      simpa [checkClosedRatValue, hv] using h
    have hq : v = ratValue q := by
      cases v with
      | mk b z r => simp_all [ratValue]
    exact (closedNode_sound program input values he fuel i v hv).symm.trans hq

inductive Cache where
  | empty
  | branch (key fuel : ℕ) (value : ℚ) (left right : Cache)

def Cache.lookup : Cache → ℕ → Option ℚ
  | .empty, _ => none
  | .branch key _ q left right, i =>
    if i = key then some q else if i < key then left.lookup i else right.lookup i

def Cache.check (program : ℕ → Node) : Cache → Bool
  | .empty => true
  | .branch key fuel q left right =>
    checkClosedRatValue program fuel key q && (left.check program && right.check program)

def Cache.lookup_sound (program : ℕ → Node) (input values : Valuation)
    (he : Equations program input values) (cache : Cache)
    (hc : cache.check program = true) (i : ℕ) (q : ℚ)
    (hl : cache.lookup i = some q) : values i = ratValue q := by
  induction cache generalizing i q with
  | empty => simp [lookup] at hl
  | branch key fuel value left right ihl ihr =>
    have hh : checkClosedRatValue program fuel key value = true ∧
        left.check program = true ∧ right.check program = true := by
      simpa only [check, Bool.and_eq_true] using hc
    by_cases hi : i = key
    · subst i
      have hq : value = q := by simpa [lookup] using hl
      subst q
      exact checkClosedRatValue_sound program input values he fuel key value hh.1
    · by_cases hlt : i < key
      · exact ihl hh.2.1 i q (by simpa [lookup, hi, hlt] using hl)
      · exact ihr hh.2.2 i q (by simpa [lookup, hi, hlt] using hl)

def aliasOp : Op → Bool
  | .alias => true
  | _ => false

def foldedProgram (program : ℕ → Node) (cache : Cache) (i : ℕ) : Node :=
  if aliasOp (program i).op then
    match cache.lookup i with
    | some q => ⟨.qConst q, []⟩
    | none => program i
  else program i

def foldedProgram_equations (program : ℕ → Node) (cache : Cache)
    (input values : Valuation) (he : Equations program input values)
    (hc : cache.check program = true) :
    Equations (foldedProgram program cache) input values := by
  intro i
  unfold foldedProgram
  split
  next =>
    cases hl : cache.lookup i with
    | none => simpa only [hl] using he i
    | some q =>
      have hv := Cache.lookup_sound program input values he cache hc i q hl
      simpa only [hl, evalNode, evalOp, List.map_nil] using hv
  next => exact he i

end PolicyClosedConstantCache

end PolicySubmissionPart42

/- Component PolicyClosedConstantValues; SHA256 40da54e30f0c713c767a92a5713e6c5c033211dc18793c7ff4514970743381a9. -/
section PolicySubmissionPart43
/- Canonical rational values: no rational division is needed at lookup. -/
namespace PolicyClosedConstantValues

def q0 : ℚ := ⟨1, 3, by decide +kernel, by decide +kernel⟩
def q1 : ℚ := ⟨1, 4, by decide +kernel, by decide +kernel⟩
def q2 : ℚ := ⟨1, 5, by decide +kernel, by decide +kernel⟩
def q3 : ℚ := ⟨1, 7, by decide +kernel, by decide +kernel⟩
def q4 : ℚ := ⟨1, 9, by decide +kernel, by decide +kernel⟩
def q5 : ℚ := ⟨1, 16, by decide +kernel, by decide +kernel⟩
def q6 : ℚ := ⟨1, 25, by decide +kernel, by decide +kernel⟩
def q7 : ℚ := ⟨1, 27, by decide +kernel, by decide +kernel⟩
def q8 : ℚ := ⟨1, 35, by decide +kernel, by decide +kernel⟩
def q9 : ℚ := ⟨1, 49, by decide +kernel, by decide +kernel⟩
def q10 : ℚ := ⟨1, 64, by decide +kernel, by decide +kernel⟩
def q11 : ℚ := ⟨1, 81, by decide +kernel, by decide +kernel⟩
def q12 : ℚ := ⟨1, 0x7d, by decide +kernel, by decide +kernel⟩
def q13 : ℚ := ⟨1, 0xaf, by decide +kernel, by decide +kernel⟩
def q14 : ℚ := ⟨1, 0xf3, by decide +kernel, by decide +kernel⟩
def q15 : ℚ := ⟨1, 0xf5, by decide +kernel, by decide +kernel⟩
def q16 : ℚ := ⟨1, 0x100, by decide +kernel, by decide +kernel⟩
def q17 : ℚ := ⟨1, 0x157, by decide +kernel, by decide +kernel⟩
def q18 : ℚ := ⟨1, 0x271, by decide +kernel, by decide +kernel⟩
def q19 : ℚ := ⟨1, 0x2d9, by decide +kernel, by decide +kernel⟩
def q20 : ℚ := ⟨1, 0x36b, by decide +kernel, by decide +kernel⟩
def q21 : ℚ := ⟨1, 0x400, by decide +kernel, by decide +kernel⟩
def q22 : ℚ := ⟨1, 0x4c9, by decide +kernel, by decide +kernel⟩
def q23 : ℚ := ⟨1, 0x6b3, by decide +kernel, by decide +kernel⟩
def q24 : ℚ := ⟨1, 0x88b, by decide +kernel, by decide +kernel⟩
def q25 : ℚ := ⟨1, 0x961, by decide +kernel, by decide +kernel⟩
def q26 : ℚ := ⟨1, 0xc35, by decide +kernel, by decide +kernel⟩
def q27 : ℚ := ⟨1, 0x1000, by decide +kernel, by decide +kernel⟩
def q28 : ℚ := ⟨1, 0x1117, by decide +kernel, by decide +kernel⟩
def q29 : ℚ := ⟨1, 0x19a1, by decide +kernel, by decide +kernel⟩
def q30 : ℚ := ⟨1, 0x217f, by decide +kernel, by decide +kernel⟩
def q31 : ℚ := ⟨1, 0x2ee5, by decide +kernel, by decide +kernel⟩
def q32 : ℚ := ⟨1, 0x4000, by decide +kernel, by decide +kernel⟩
def q33 : ℚ := ⟨1, 0x41a7, by decide +kernel, by decide +kernel⟩
def q34 : ℚ := ⟨1, 0x4ce3, by decide +kernel, by decide +kernel⟩
def q35 : ℚ := ⟨1, 0x10000, by decide +kernel, by decide +kernel⟩
def q36 : ℚ := ⟨3, 4, by decide +kernel, by decide +kernel⟩
def q37 : ℚ := ⟨3, 20, by decide +kernel, by decide +kernel⟩
def q38 : ℚ := ⟨3, 28, by decide +kernel, by decide +kernel⟩
def q39 : ℚ := ⟨3, 0x64, by decide +kernel, by decide +kernel⟩
def q40 : ℚ := ⟨3, 0x8c, by decide +kernel, by decide +kernel⟩
def q41 : ℚ := ⟨3, 0x1f4, by decide +kernel, by decide +kernel⟩
def q42 : ℚ := ⟨3, 0x2bc, by decide +kernel, by decide +kernel⟩
def q43 : ℚ := ⟨3, 0x9c4, by decide +kernel, by decide +kernel⟩
def q44 : ℚ := ⟨3, 0xdac, by decide +kernel, by decide +kernel⟩
def q45 : ℚ := ⟨3, 0x30d4, by decide +kernel, by decide +kernel⟩
def q46 : ℚ := ⟨4, 3, by decide +kernel, by decide +kernel⟩
def q47 : ℚ := ⟨5, 4, by decide +kernel, by decide +kernel⟩
def q48 : ℚ := ⟨5, 7, by decide +kernel, by decide +kernel⟩
def q49 : ℚ := ⟨5, 0x961, by decide +kernel, by decide +kernel⟩
def q50 : ℚ := ⟨5, 0x41a7, by decide +kernel, by decide +kernel⟩
def q51 : ℚ := ⟨10, 9, by decide +kernel, by decide +kernel⟩

end PolicyClosedConstantValues

end PolicySubmissionPart43

/- Component PolicyClosedConstantData0; SHA256 e644d0d78ba074e905b795b6589e4c525d3029b6cf561fbc6647a657e42506a2. -/
section PolicySubmissionPart44
/- Every cache leaf contains its original node ID, closed-evaluation fuel,
and claimed full rational Value.  The table is untrusted until checked. -/
namespace PolicyClosedConstantData0
open ClosureSemantics PolicyClosedConstantCache

def certificate : Cache :=
  (.branch 0x1abf 3 PolicyClosedConstantValues.q44
  (.branch 0xf42 3 PolicyClosedConstantValues.q4
    (.branch 0x9ee 3 PolicyClosedConstantValues.q10
      (.branch 0x852 3 PolicyClosedConstantValues.q35
        (.branch 0x832 3 PolicyClosedConstantValues.q5
          (.branch 0x816 3 PolicyClosedConstantValues.q3
            .empty
            .empty)
          .empty)
        (.branch 0x9ce 3 PolicyClosedConstantValues.q36
          (.branch 0x87e 3 PolicyClosedConstantValues.q33
            .empty
            .empty)
          .empty))
      (.branch 0xaa9 3 PolicyClosedConstantValues.q11
        (.branch 0xa34 3 PolicyClosedConstantValues.q1
          (.branch 0xa08 3 PolicyClosedConstantValues.q8
            .empty
            .empty)
          .empty)
        (.branch 0xf2b 3 PolicyClosedConstantValues.q2
          (.branch 0xee6 3 PolicyClosedConstantValues.q0
            .empty
            .empty)
          .empty)))
    (.branch 0x165f 3 PolicyClosedConstantValues.q7
      (.branch 0x15e4 3 PolicyClosedConstantValues.q16
        (.branch 0x151a 3 PolicyClosedConstantValues.q40
          (.branch 0x1500 3 PolicyClosedConstantValues.q20
            .empty
            .empty)
          .empty)
        (.branch 0x1641 3 PolicyClosedConstantValues.q15
          (.branch 0x1614 3 PolicyClosedConstantValues.q19
            .empty
            .empty)
          .empty))
      (.branch 0x1862 3 PolicyClosedConstantValues.q42
        (.branch 0x1826 3 PolicyClosedConstantValues.q37
          (.branch 0x1694 3 PolicyClosedConstantValues.q6
            .empty
            .empty)
          .empty)
        (.branch 0x1937 3 PolicyClosedConstantValues.q32
          (.branch 0x1928 3 PolicyClosedConstantValues.q30
            .empty
            .empty)
          .empty))))
  (.branch 0x2c93 3 PolicyClosedConstantValues.q39
    (.branch 0x213f 3 PolicyClosedConstantValues.q34
      (.branch 0x1ef3 3 PolicyClosedConstantValues.q21
        (.branch 0x1e9b 3 PolicyClosedConstantValues.q31
          (.branch 0x1c38 3 PolicyClosedConstantValues.q13
            .empty
            .empty)
          .empty)
        (.branch 0x1fd1 3 PolicyClosedConstantValues.q22
          (.branch 0x1f8d 3 PolicyClosedConstantValues.q12
            .empty
            .empty)
          .empty))
      (.branch 0x29c4 3 PolicyClosedConstantValues.q18
        (.branch 0x2665 3 PolicyClosedConstantValues.q41
          (.branch 0x24d3 3 PolicyClosedConstantValues.q9
            .empty
            .empty)
          .empty)
        (.branch 0x2b61 3 PolicyClosedConstantValues.q47
          (.branch 0x2ab1 3 PolicyClosedConstantValues.q14
            .empty
            .empty)
          .empty)))
    (.branch 0x32e2 3 PolicyClosedConstantValues.q29
      (.branch 0x3125 3 PolicyClosedConstantValues.q43
        (.branch 0x2e37 3 PolicyClosedConstantValues.q27
          (.branch 0x2e2b 3 PolicyClosedConstantValues.q25
            .empty
            .empty)
          .empty)
        (.branch 0x32c4 3 PolicyClosedConstantValues.q28
          (.branch 0x32b3 3 PolicyClosedConstantValues.q26
            .empty
            .empty)
          .empty))
      (.branch 0x4649 3 PolicyClosedConstantValues.q46
        (.branch 0x36e5 3 PolicyClosedConstantValues.q23
          (.branch 0x3573 3 PolicyClosedConstantValues.q24
            .empty
            .empty)
          .empty)
        (.branch 0x665f 3 PolicyClosedConstantValues.q51
          .empty
          .empty)))))

def checked : certificate.check (boundedProgram ClosureFixedWidthData0.program) = true := by
  decide +kernel

def program : ℕ → Node := foldedProgram (boundedProgram ClosureFixedWidthData0.program) certificate

def equations (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values) :
    Equations program input values := by
  exact foldedProgram_equations (boundedProgram ClosureFixedWidthData0.program) certificate input values he checked

end PolicyClosedConstantData0

end PolicySubmissionPart44

/- Component PolicyHotLiteralOverrides; SHA256 cb3ccaa59610572a37eb08df718151020fbbae36bd7c782b955a763666ce3ef8. -/
section PolicySubmissionPart45
/- The first three comparisons avoid evaluating the underlying program on hits.
Only semantic Equations transfer is claimed; the programs need not be equal. -/
namespace PolicyHotLiteralOverrides
open ClosureSemantics

def program (base : ℕ → Node) (zeroId negativeId oneId i : ℕ) : Node :=
  if i = zeroId then ⟨.qConst 0, []⟩
  else if i = negativeId then ⟨.qConst (-1), []⟩
  else if i = oneId then ⟨.qConst 1, []⟩
  else base i

def equations (base : ℕ → Node) (zeroId negativeId oneId : ℕ)
    (input values : Valuation) (he : Equations base input values)
    (hz : values zeroId = ratValue 0)
    (hn : values negativeId = ratValue (-1))
    (ho : values oneId = ratValue 1) :
    Equations (program base zeroId negativeId oneId) input values := by
  intro i
  unfold program
  split_ifs with h0 h1 h2
  · subst i
    exact hz
  · subst i
    exact hn
  · subst i
    exact ho
  · exact he i

end PolicyHotLiteralOverrides

end PolicySubmissionPart45

/- Component PolicyCachedHotLiteralData0; SHA256 5e9d088002bd8e91702216f5936cdad023935344200d73777005217bb07c9aac. -/
section PolicySubmissionPart46
/- Full-Value certificates at the original bounded nodes, each with fuel 1. -/
namespace PolicyCachedHotLiteralData0
open ClosureSemantics PolicyClosedConstantCache

def zeroChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData0.program) 1 0x81b (0) = true := by
  decide +kernel

def negativeChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData0.program) 1 0x817 (-1) = true := by
  decide +kernel

def oneChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData0.program) 1 0 (1) = true := by
  decide +kernel

def program : ℕ → Node :=
  PolicyHotLiteralOverrides.program PolicyClosedConstantData0.program 0x81b 0x817 0

def equations (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values) :
    Equations program input values := by
  exact PolicyHotLiteralOverrides.equations PolicyClosedConstantData0.program 0x81b 0x817 0
    input values (PolicyClosedConstantData0.equations input values he)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData0.program) input values he 1 0x81b (0) zeroChecked)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData0.program) input values he 1 0x817 (-1) negativeChecked)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData0.program) input values he 1 0 (1) oneChecked)

end PolicyCachedHotLiteralData0

end PolicySubmissionPart46

/- Component PolicyCachedHotArithmeticChecked0; SHA256 08d0f731efec008481f7d4699ad83f9959a743a43217e26c01f39384cb3751ce. -/
section PolicySubmissionPart47
/- Every required arithmetic initial clause, checked by ordinary kernel reduction. -/
namespace PolicyCachedHotArithmeticChecked0
open ClosureLinear ClosureSemantics Bounty

def checked0 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0 32 = true := by
  decide +kernel

def checked1 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 32 32 = true := by
  decide +kernel

def checked2 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 64 32 = true := by
  decide +kernel

def checked3 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 96 32 = true := by
  decide +kernel

def checked4 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x80 32 = true := by
  decide +kernel

def checked5 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0xa0 32 = true := by
  decide +kernel

def checked6 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0xc0 32 = true := by
  decide +kernel

def checked7 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0xe0 32 = true := by
  decide +kernel

def checked8 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x100 32 = true := by
  decide +kernel

def checked9 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x120 32 = true := by
  decide +kernel

def checked10 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x140 32 = true := by
  decide +kernel

def checked11 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x160 32 = true := by
  decide +kernel

def checked12 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x180 32 = true := by
  decide +kernel

def checked13 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x1a0 32 = true := by
  decide +kernel

def checked14 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x1c0 32 = true := by
  decide +kernel

def checked15 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x1e0 32 = true := by
  decide +kernel

def checked16 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x200 32 = true := by
  decide +kernel

def checked17 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x220 32 = true := by
  decide +kernel

def checked18 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x240 32 = true := by
  decide +kernel

def checked19 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x260 32 = true := by
  decide +kernel

def checked20 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x280 32 = true := by
  decide +kernel

def checked21 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x2a0 32 = true := by
  decide +kernel

def checked22 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x2c0 32 = true := by
  decide +kernel

def checked23 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x2e0 32 = true := by
  decide +kernel

def checked24 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x300 32 = true := by
  decide +kernel

def checked25 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x320 32 = true := by
  decide +kernel

def checked26 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x340 32 = true := by
  decide +kernel

def checked27 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x360 32 = true := by
  decide +kernel

def checked28 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x380 32 = true := by
  decide +kernel

def checked29 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x3a0 32 = true := by
  decide +kernel

def checked30 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x3c0 32 = true := by
  decide +kernel

def checked31 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x3e0 32 = true := by
  decide +kernel

def checked32 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x400 32 = true := by
  decide +kernel

def checked33 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x420 32 = true := by
  decide +kernel

def checked34 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x440 32 = true := by
  decide +kernel

def checked35 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x460 32 = true := by
  decide +kernel

def checked36 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x480 32 = true := by
  decide +kernel

def checked37 : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records 0x4a0 32 = true := by
  decide +kernel

def checked (i : Fin 38) : checkArithmeticBlock PolicyCachedHotLiteralData0.program
    policyMappedDatabase0 PolicyArithmeticPacked0.records (32 * i.val) (min 32 (0x4c0 - 32 * i.val)) = true := by
  rcases i with ⟨i, hi⟩
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values) (i : ℕ) (hi : i < 0x4c0) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase0 ((PolicyArithmeticPacked0.records i).headD 0)) := by
  have hblock : i / 32 < 38 := by omega
  have hwithin : i % 32 < min 32 (0x4c0 - 32 * (i / 32)) := by omega
  have h := checkArithmeticBlock_sound PolicyCachedHotLiteralData0.program input values
    (PolicyCachedHotLiteralData0.equations input values he)
    policyMappedDatabase0 PolicyArithmeticPacked0.records (32 * (i / 32))
    (min 32 (0x4c0 - 32 * (i / 32))) (checked ⟨i / 32, hblock⟩) (i % 32) hwithin
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyCachedHotArithmeticChecked0

end PolicySubmissionPart47

/- Component ClosureCoverage; SHA256 b473e60bed02be767c987e29a530125bc3626a03bfff8a8487f2a3a54ede15ad. -/
section PolicySubmissionPart48
/- A finite checked dispatch from clause IDs to certified families. -/
namespace ClosureCoverage

def checkEntry (limits : Nat → Nat) (targets : Nat → Nat → Nat)
    (clauseId : Nat) : List Nat → Bool
  | [family, index] => decide (family < 4) && decide (index < limits family) &&
      (targets family index == clauseId)
  | _ => false

def checkEntry_sound (P : Nat → Prop) (limits : Nat → Nat)
    (targets : Nat → Nat → Nat)
    (hs : ∀ k, k < 4 → ∀ i, i < limits k → P (targets k i))
    (clauseId : Nat) (entry : List Nat)
    (hc : checkEntry limits targets clauseId entry = true) : P clauseId := by
  cases entry with
  | nil => simp [checkEntry] at hc
  | cons k rest =>
    cases rest with
    | nil => simp [checkEntry] at hc
    | cons i tail =>
      cases tail with
      | cons a as => simp [checkEntry] at hc
      | nil =>
        have h : (k < 4 ∧ i < limits k) ∧ targets k i = clauseId := by
          simpa only [checkEntry, Bool.and_eq_true, decide_eq_true_eq,
            beq_iff_eq] using hc
        exact h.2 ▸ hs k h.1.1 i h.1.2

def checkBlock (limits : Nat → Nat) (targets : Nat → Nat → Nat)
    (records : Nat → List Nat) (start count : Nat) : Bool :=
  (List.range count).all fun i =>
    checkEntry limits targets (start + i) (records (start + i))

def checkBlock_sound (P : Nat → Prop) (limits : Nat → Nat)
    (targets : Nat → Nat → Nat)
    (hs : ∀ k, k < 4 → ∀ i, i < limits k → P (targets k i))
    (records : Nat → List Nat) (start count : Nat)
    (hc : checkBlock limits targets records start count = true)
    (i : Nat) (hi : i < count) : P (start + i) := by
  have h : ∀ j ∈ List.range count,
      checkEntry limits targets (start + j) (records (start + j)) = true := by
    simpa only [checkBlock, List.all_eq_true] using hc
  exact checkEntry_sound P limits targets hs (start + i) (records (start + i))
    (h i (List.mem_range.mpr hi))

end ClosureCoverage

end PolicySubmissionPart48

/- Component PolicyArithmeticPacked1; SHA256 8de4a616bd78e86ad7d187c52c001d223651c96cd2587b1a606f2c5a8f6ac0d5. -/
section PolicySubmissionPart49
/- Untrusted packed arithmetic leaves for the shortened Boolean certificate. -/
namespace PolicyArithmeticPacked1
open PackedNatTable

def tableLLL : Table Block := .leaf #[
  ⟨0x1930a404d423e10907303401740a704881ec0da05f01f80a402c000, 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⟩,
  ⟨0x15309e84a423610d07b830815c0a004901f00dc05802100b002c000, 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⟩,
  ⟨0x17a0b2054027412608c04081dc0e0069031015c09a03a012c06a000, 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⟩,
  ⟨0x1c10d006282e815109d84941fe0b7050822c0ea05f01c009001c000, 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⟩,
  ⟨0x1960c1857429412408583e01aa0bf05481f80d605502380a4026000, 0x42040081003923043968141131ec10c10810410040439350e3c039290c38ee0e48c38fd0c3960141131e010810420400e3f410e4fc5044c770430420410401010e4d438f00e4a430e3b839230e3f430e4d85044c730420400810038ee0e48c38fd0c392a1c1131b410810420400e3f410e4845044c6c0420410400c10e2b428b40e2cc30a2b82a710a1fc34791801319c10810420400a9c428ae0838be180130f810810420400a9c4287f0838b4180130ec10c10810410040428b10a1c038a20e2b040a0f0282b0a9c428ae111e46004c38042041081002a6b042fe81401309810810020400a1fc2924082fe11801308c1081040002fb71c012ffc1081041003042f7d0be9020bad42f66082f691c012ff810810420400bad42f66082faa18012fe810810420400bad410bdf07004bf6⟩,
  ⟨0x15509f84b02120f306802e814808e03c018809c040019009001c000, 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⟩,
  ⟨0x16608d04301fc0eb06a831c16209b04681fc0d2053018008801c000, 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⟩,
  ⟨0x14809a04341f20e306682fc1620a304681dc0c604d01f80b002c000, 0x42040081003eaf2020fc906004dfa0440c30420c01010fbe43eea0e9a03a26103eb70fabc80c3eff200137d810810420400fabc8083efa180137c810810020400fadc3eaf083eeb1c0137b010810020400f8c83eaf083eb5180137a01081040003eae1c01379c1081040003ea91c0137901081040003ea11c01378410810020400f9983e34083e6c180136f010810420400f8d03e32083e3a1c0136dc1081042040203e20083e28280136c410810020400a0f0282b083dff180136c01081040003dfc1c0136bc10810020400a0f010f7e47004dae042040081002a710a2b820f7dc6004dad042040081002a710a1fc20f7b86004daa⟩,
  ⟨0x13d094844c1fa0ef06c830c15e0a104982140e205b02380b002c000, 0x108100204020487e0848f9280139f410810020400f8d03e320848f71c0139f01081042040121e8487e0848f51c0139ec10810400048f31c0139e81081002040121e8487e0848e31c0139d01081042040122c02b760848b61c0139bc108104204020487e0848a5280139a410810400048791c0139a010810400048741c013994108104000486b1c0139881081002040203e200848652801398410810420400f9843e200848631c0139801081042040202bb1084861280138fc1081002041040082003e660fd9420fdb07004e2504204008100282b0f99820fd906004e24042040081003e610f88020fcac7004dfb⟩
]

def tableLLR : Table Block := .leaf #[
  ⟨0x1620a604e025411408303e01c40ce05d029011c080039019002c000, 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⟩,
  ⟨0x1800b40554284109079837412808603801880a804601c008801c000, 0x4104008108100208012fd811308c5044f39041040081004bed044bf514113cdc108104204012fb4112fc45044f360b11c2c4616214588408114112ea44b7f129904b77124a44924284a3f204b7a124cc49b520447920013cb0108104204012de84933084ba01c013c9c1081002040124cc49b5084b7818013c982c496c76c60450c20411811288449fc1269c4b22125d84afe127b849291249049bb128c84b6d304970125b08126d449e6151e48004f2404204100012db87004f23042041081004a770f8c8212d949004efe04204100012cf87004efd04204100012ce47004efa04204100012cac7004ef904204100012c8c7004ef604204008100496c125c0212bb87004ef5042041081008125c0212a8ca004ef4042041000129c07004eee⟩,
  ⟨0x21a0e305e02c415408403e81c80d104a02180f006a02a0104032000, 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⟩,
  ⟨0x1c50b4855428e13108d841c1f20eb05a827c12207b03280b0032000, 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⟩,
  ⟨0x1660a804a82280fe07403481780ae04a82080d205602000a8028000, 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⟩,
  ⟨0x1da0e206b831a1770b084801a60bd05502100dc05802100b002c000, 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⟩,
  ⟨0x1b30c805b42ae14109704381f00d705a027811007202780e4046000, 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⟩,
  ⟨0x1fe0f5066431617d0b7856c28a12f08c840c1da06302680b002c000, 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⟩,
  ⟨0x1fd0f7878439a1b70c885f82b013f096045011006a02a010402c000, 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⟩
]

def tableLL : Table Block := .branch 9 tableLLL tableLLR

def tableLRL : Table Block := .leaf #[
  ⟨0x1c20d60658300134090842c1f00b9051825410e079032813c072000, 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⟩,
  ⟨0x20c0f0872c2f01620a604d82400f807282c011407402f00a4026000, 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⟩,
  ⟨0x1e60e986b43281740ab050c25a101075823c0f205802100b002c000, 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⟩,
  ⟨0x28213608603761a50c285c82b813b07703801940b204e00c402c000, 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⟩,
  ⟨0x23510f88243e61e50e7855027c12808903f01d20a4038816c040000, 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⟩,
  ⟨0x1d10dd869431e17909004281e80d1057026010406c02600d8046000, 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⟩,
  ⟨0x243116885c4021eb0ea86fc35219309d04502020ee06a830802c000, 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⟩,
  ⟨0x2080f7866427a12708883ec1ca0bd04b82040d605501f80b002c000, 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⟩,
  ⟨0x1c80d9065030216b0ae84e824810e07c038819807e03400a4026000, 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⟩
]

def tableLRR : Table Block := .leaf #[
  ⟨0x18a0ba057829012508783e41b60c8059027010c07002680b002c000, 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⟩,
  ⟨0x1770b2054428613508f84181da0d405e02a413605802100b002c000, 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⟩,
  ⟨0x1e10dd86a031e17c0b485401de0d906302b813607002100b002c000, 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⟩,
  ⟨0x18c0bb05a02b414409804682080bb04e821c0f206b02a8108068000, 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⟩,
  ⟨0x1cb0db868431614009504702100f406f03401840b40360178090000, 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⟩,
  ⟨0x1f30ee871c36219b0c285bc2b210b07a838419a0bf058826c02c000, 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⟩,
  ⟨0x1b10b3054027412208603d81c00b804f82180dc05502100a402c000, 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⟩,
  ⟨0x235111083c3f21e60c705081fc0c204d02100dc05802280b0032000, 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⟩,
  ⟨0x1d80c805e82c814e078036818e0b404e02180d605501f80b0032000, 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⟩,
  ⟨0x1d60e406e834c1900be85a82a813e079837418e0b10318098026000, 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⟩
]

def tableLR : Table Block := .branch 9 tableLRL tableLRR

def tableL : Table Block := .branch 18 tableLL tableLR

def tableRLL : Table Block := .leaf #[
  ⟨0x23210e08183601a20c605cc2ca14f09c83a01a40c403e819c0a2000, 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⟩,
  ⟨0x25b0f5075037c1850a604d824610d07b82040d605502100b002c000, 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⟩,
  ⟨0x1bf0d4864c2fa1670a8840c1da0ca054824c0fa05d01f80a402c000, 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⟩,
  ⟨0x1950c105b02ac140095047020c0f006d02d011c07803280b002c000, 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⟩,
  ⟨0x27211388643921bb0a904f024c100075035015c09804501d002c000, 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⟩,
  ⟨0x39b1c28dbc6b831116b0ab84a620a0d585782160c303b80b002c000, 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⟩,
  ⟨0x1a70c985f429613509084381ec0d005e825c10206b018007001c000, 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⟩,
  ⟨0x1870b8856c28a12508383c41bc0c8057826410605501f80b002c000, 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⟩,
  ⟨0x1930c2857027612508783e41ac0c005502540e405c02300e0046000, 0x108104000ce7d1c01e3b810c108104100404ce6b338a4cc7a0cae6c33798cc3f331a04337d850078ed0420410400c133390ce6c087ae133798cc3f0cce731801e3a4108104204033798cc3f08ce6d1801e3981081042040337987ae108ce6a1801e39410810420402b9b0cde608ce3c1801e2f8108104100304ce2a33890ce280cae6c33798ce200d1e460078b904204108100ae6c3388023389460078b804204008100cde6330fc2337b060078b704204108100cc2276008cdaf1c01e2b8108104100304cda2335e4cd660cafab333d4cd630d1e460078ad04204108100afab3358c23368c60078a904204108100afab333d42335e060078a6042041000334f8700787f04204008100cc2b76008cd2f1c01e1e8108104100304ccfc33494cce90cccf516ce4cce70d1e46007879⟩
]

def tableRLR : Table Block := .leaf #[
  ⟨0x36c1a48ca06242fc131077431417406782100dc05802100b002c000, 0x420410400c1261ac8c2f361a8322ea06ce722fa434791801e4ac108104100304d8642e6f421fbb4ae262e3b833619c600792a042041081007eed2b89823618c6007929042041081007eed2e3b823618460079283e65464c1b7248144140f98d18b18a4871861851840430421810404011e4f4ae2b0f89cae34233b83ead0faa03f2a124b84939221b44929124904a64129a8ae3533cb479a817098ae33175c951fca83e610f88049332049e6126d41cbd2b7fc49340bad87eed2b8985c22175b8f23aa8800792741341020f20e20d04c20b0f9c0a2092ecc084074060f9c0034116ac82cac0b29c2cb3168d479e8322ac532f8848621f0e04864121807c2f0b1902c3f0fab43ea823ab08eaa502b3e168c05a6d168903166d059a20f8808132e42bb10f984c4792001e49823012c588a0490843e60c58801c10b1c0d83712bb45b26133b04b2a0b1902c3f133e84aa21288449fc12bf4d166884cb90aec48125c0496c191e480079250420410810059b4166882360d8600792319509409305004f04e04d18c18b18a049048047484183182181040481129a87c2f121802c640b0fccbe21f0e079ad327bcae33221b44939233b8ae34170984929124904a642b8accf2d2b8d45d72582bb1166884cb91e58859b41279849331fca82eb62049b52b898adff124d07eed072f45c22175b924792001e48812c1283242c460b1047cc01812b3c8d82f17c8c4878121cc48e217cd85f31135ccace91359c48a430acb117bf0487a20487e151e4800792104204108100acb117bf02360c0700792004204008100cfab0f984233ff060078fc04204108100cfb233eac233f9870078fb04204008100cfb233eac233eec70078f604204108100cfab0f984233ec460078f504204008100adff124d0233cb860078ef⟩,
  ⟨0x22e0f4071435e1990bc058829813608803441760a804781f00c8000, 0x480470460440430420401c133190b96f338a0cd3d368c0ce6b3678c99a82e5b4933880cde6330fcd9af2e5a8b969191e460079b20420410400c1368dcd9f436894333880d9af367c434791801e6c41081042040366bcce2008da311801e6b41081042040366bcd9f108da261801e6a4108104100304d9e5366cc22e5a4d9af366a03367ac60079a204204108100b969366bc236790600797e04204108100b969366a02366b4600797904204008100ae6c3379823669c6007978043042041040101363acd8e7362b032ae90aba22ae8032aed450479752202488072a010a8031401413659c4a3f364c069671a5883bf0126d03cb80f2cc528d92b124f03bbd0c44792001e5c41081042040364ac493c08d9682401e5a010810020402ae881363b0504793e04204108100aba42ae80aba20cd8e81c11e4f410810420402ae801362b450479330410400810810020802ae901362a4504793204c10b10a0490486070466041036011002c11e8d8ae341b2f48bb132f9028610a1e8ae351fb904b6d32eb88cee301f270a7d46cb80a0f05bfb0bad8cb751fbb47f2a072f4a0a7e0600792f⟩,
  ⟨0x23e0fa877c3921b60c585e02aa13f06482040d605501f80a4026000, 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⟩,
  ⟨0x1f50f387443761a50c786042dc1580a104b02320e005382440f6000, 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⟩,
  ⟨0x2a412e092443c1e60e986f42f615a0a204b81d80d906182b4046000, 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⟩,
  ⟨0x26b12b88c44362070f884f42080ee06d831416406702880ac026000, 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⟩,
  ⟨0x2030f6875c3821a00b6856826411f08603e41cc0be038016802c000, 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⟩,
  ⟨0x2a0112077837a1a70c885c02b414409703841960a504780f004c000, 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⟩,
  ⟨0x1a90c9854827812608983c01a00bd05382440f605802100b002c000, 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⟩,
  ⟨0x1b00c505d02bc148099047020c0f006b831015806402700ec050000, 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⟩
]

def tableRL : Table Block := .branch 9 tableRLL tableRLR

def tableRRL : Table Block := .leaf #[
  ⟨0x2db1630ac04fa24b0fb878439616f093044c1c40cf04201b8090000, 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⟩,
  ⟨0x28010587d83d01d20de069c3321830a784f019a0b7050822c02c000, 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⟩,
  ⟨0x276130892c46a1d10ad851425e0c104f02200e405d02780b002c000, 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⟩,
  ⟨0x28013688783ac1930be85a81c20c305802680f206302680b002c000, 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⟩,
  ⟨0x2090fb074031a1770b2052c26a0ed06b83040d005201f80b002c000, 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⟩,
  ⟨0x259123088041a1f40f0872436c18b0ad84481960b502100b002c000, 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⟩,
  ⟨0x27512f87382e41640a884ec24a0ff074835011c06b02a80fc032000, 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⟩,
  ⟨0x2000ed070435c1960c0059c25011207f83a416209b02080ac030000, 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⟩,
  ⟨0x2d81610ab050827112d87d43be1990b6855c1f60e506781cc096000, 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⟩
]

def tableRRR : Table Block := .leaf #[
  ⟨0x27911808283c8196097841c1c80ce05c02940fa06a02a00b002c000, 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⟩,
  ⟨0x3581a10cb062c2a114588b442e2010f587602d80d104501d004c000, 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⟩,
  ⟨0x33d1938c505fc2e814d89184601ea0ce055027c0e204780b002c000, 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⟩,
  ⟨0x3b81aa0be058826610f08203e417409d844c16e08e03c0188098000, 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⟩,
  ⟨0x34819a8c885b82b615189ec4c424a0ea05181ea08a02200b8030000, 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⟩,
  ⟨0x46b222907c7b23b31c68d9c6622e816a8afc43a1c40a4832c0a4000, 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⟩,
  ⟨0x3171820b7051227312688e843c1c30bc84781f009e01e0098026000, 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⟩,
  ⟨0x4c82208f3869e2cc15b09104622090f186f42ca14f09c83f8138000, 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⟩,
  ⟨0x6062be14a09a44802260ea067431418089c041e1b40cf041810c000, 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⟩,
  ⟨0x4401da0e205c022e0f104c01c804c000, 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⟩
]

def tableRR : Table Block := .branch 9 tableRRL tableRRR

def tableR : Table Block := .branch 19 tableRL tableRR

def table : Table Block := .branch 37 tableL tableR

def records (i : ℕ) : List ℕ :=
  PackedNatTable.records table (32 * (i / 16) + i % 16)

end PolicyArithmeticPacked1

end PolicySubmissionPart49

/- Component PolicyAssertedData; SHA256 f6b3d68bbeefd61e9a722401d68807b3057edcf204358ee98e5b389df8f7114d. -/
section PolicySubmissionPart50
/- Authoritative asserted clause identifiers and dense alias roots. -/

namespace PolicyAssertedPacked0
def records : Nat → List Nat
  | 0 => [0x11dd, 0x903]
  | 1 => [0x1201, 0x9a4]
  | 2 => [0x122b, 0xa38]
  | 3 => [0x124c, 0xaa1]
  | 4 => [0x1277, 0xb1a]
  | 5 => [0x12a4, 0xbce]
  | 6 => [0x12b3, 0xc49]
  | 7 => [0x12b7, 0xc5c]
  | 8 => [0x1309, 0xdb7]
  | 9 => [0x136d, 0xeea]
  | 10 => [0x13e4, 0x105e]
  | 11 => [0x13e7, 0x1071]
  | 12 => [0x13f6, 0x109c]
  | 13 => [0x15d5, 0x170c]
  | 14 => [0x15e5, 0x1755]
  | 15 => [0x15e8, 0x1770]
  | 16 => [0x16d6, 0x1a60]
  | 17 => [0x171f, 0x1b37]
  | 18 => [0x173c, 0x1c0d]
  | 19 => [0x173f, 0x1c22]
  | 20 => [0x1848, 0x1ffe]
  | 21 => [0x184b, 0x2020]
  | 22 => [0x186c, 0x20a7]
  | 23 => [0x1948, 0x2465]
  | 24 => [0x19c5, 0x2611]
  | 25 => [0x1a58, 0x2852]
  | 26 => [0x1a5b, 0x286d]
  | 27 => [0x1a78, 0x28c4]
  | 28 => [0x1ad4, 0x29d7]
  | 29 => [0x1ad7, 0x29f9]
  | 30 => [0x1c4a, 0x31cc]
  | 31 => [0x1cd4, 0x3417]
  | 32 => [0x1cd7, 0x343c]
  | 33 => [0x1d8b, 0x3852]
  | 34 => [0x1dae, 0x399b]
  | 35 => [0x1e4a, 0x3cc3]
  | _ => []
end PolicyAssertedPacked0

namespace PolicyAssertedPacked1
def records : Nat → List Nat
  | 0 => [0x1102, 0x86f]
  | 1 => [0x1117, 0x8d5]
  | 2 => [0x111a, 0x8ea]
  | 3 => [0x1169, 0xa13]
  | 4 => [0x1183, 0xa5e]
  | 5 => [0x11ba, 0xb06]
  | 6 => [0x120f, 0xc22]
  | 7 => [0x124c, 0xd04]
  | 8 => [0x1420, 0x13e1]
  | 9 => [0x1423, 0x13f6]
  | 10 => [0x143d, 0x1486]
  | 11 => [0x1440, 0x1499]
  | 12 => [0x1500, 0x1707]
  | 13 => [0x1511, 0x1734]
  | 14 => [0x15a2, 0x1916]
  | 15 => [0x15a5, 0x192b]
  | 16 => [0x15fa, 0x1ad9]
  | 17 => [0x174e, 0x1f46]
  | 18 => [0x1751, 0x1f5b]
  | 19 => [0x1757, 0x1f71]
  | 20 => [0x1a53, 0x2ae1]
  | 21 => [0x1a56, 0x2af5]
  | 22 => [0x1a8c, 0x2bcf]
  | 23 => [0x1acf, 0x2d02]
  | 24 => [0x1ae2, 0x2d69]
  | 25 => [0x1ae5, 0x2d84]
  | 26 => [0x1bdd, 0x30f6]
  | 27 => [0x1be0, 0x3118]
  | 28 => [0x1e3b, 0x4155]
  | 29 => [0x1e5a, 0x41cb]
  | 30 => [0x1e5d, 0x41ed]
  | 31 => [0x1f06, 0x47be]
  | 32 => [0x1f2b, 0x4993]
  | 33 => [0x1fa1, 0x4bd6]
  | _ => []
end PolicyAssertedPacked1

end PolicySubmissionPart50

/- Component PolicyInitialCoverageData; SHA256 e0674f908ddeecfe5e6167a8bec57fc569196cf56edfe1206af12529d28c5fd6. -/
section PolicySubmissionPart51
namespace PolicyInitialCoverage0Tail
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x4001f00f007403801b00d006403001700b0054028013009004402000f007003401800b005002401000700300140080030010004000, 0x6015c15815411825014c14814414011421023c13810c23413012c12812410822011c11811411010c1081041001042002⟩,
  ⟨0x4f026012408c04402080f807803a01b80d006202e01580a404c023010007403401800b005002401000700300140080030010004000, 0x1b8106d041b0100306b041a813c2382069041a0106704198106504d0819010630418810610418013022c27c17812827417012422026c16811c2641⟩,
  ⟨0x5c02c81580a6050026812808e04402080f807803901b00cc06002e01580a004a022010007403601800a804801e00c0048018006000, 0xaa042a410a80429c10a60429410a40428c10a20428414c20a0041fc107e041f4148207c041ec107a041e41442078050081dc1076041d41074041cc1072041c41070041bc1⟩,
  ⟨0x5802a814809e04d025812008a04302080f807603801b00cc06002d01580a004a02200f807003201600a004401c00b0040014004000, 0xe20438410e005a099082fc10be058097082f410bc042ec15820ba042e410b8055082dc10b6042d410b4042cc10b2042c415020b0042bc10ae042b410ac042ac1043⟩,
  ⟨0x5a02b81500a204e026012408c04302000f407603801a80cc06002d015009c04802100f0070032016009804001c00b0040018006000, 0x60083ec10fa043e417c20f8043dc10f6043d410f405e083cc10f205d083c410f0043bc10ee043b410ec043ac10830ea043a410e80439c17020e60439416c20e40438c1⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01600a404c023010807803601800a804801e00c0048018006000, 0x1a42131044c0112f044b810680819c212d044b0112b044a81129044a011270449810660819421250449010640830c18c21230448811210418820610848010ff043f810fd043f01⟩,
  ⟨0x5f02e01640ac0530280134094047022010807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5a81169041bc206e085a01167045981165041b4210306c08590116304588116104580113f041ac213e044f4106a084f0113b044e81139044e01137044d81135044d01133044c81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x770868811a104680117f045f8117d041d8217c045ec117a045e41178045dc1176041d42074081cc2072085d41174045cc1172045c41170045bc1071085b8116d045b01070085ac1⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0x5d02d015c0a8051027012c090045021010007a03a01b80d406402f01600a404c023010007403401700a004401c00b0048018006000, 0x6f811bd046f011bb046e811b9046e011b7046d811c31b5046d010780860c6cc11b2046c411b0046bc11ae046b411ac046ac11aa046a411a80469c11a60450c69411a40468c1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x1f6047d411f40428021f3047c8107f087c411f0047bc11ee047b4107e087b0107d081f0207b087ac11ea047a411e80479c11e60479411e40478c107a081e421e20478411e0046fc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0xa6088c0122f048b8122d04294222c048ac122a048a412280489c12260489412240429022230488812210488010a3087fc11fe0428821fd047f011fb047e810a1087e411f8047dc1⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01600a404c023010007403401800a804801e00c0048018006000, 0x99c10ae082b42266042b02265049901263049881261042ac2260048fc123e048f410aa088f0123b048e81239042a42238048dc1203236048d410a8088d01233048c812310429c2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2a304a8812a104a80127f049f8127d049f0127b049e81279042c820b1089e01277042c02276049d41274049cc1272049c41270049bc126e049b4126c042bc226b049a81269049a01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2b604ad412b404acc12b204ac412b004abc12ae04ab410bf08ab012ab042f820bd082f020bb082e820b9082e020b7082d820b508aa812a904aa012a704a9810b4082cc22a504a901⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01600a404c024010807803601800a804801e00c0048018006000, 0xbb810e60839422ed04bb012eb04ba812e90439022e804b9c10e308b9812e504b9012e304b8812e104b8012432bf04af812bd04af010e208aec12ba04ae410e108ae010e008adc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x326043b8232504c90132304c88132104c8012ff04bf810ed08bf412fc043b022fb04be810eb08be412f804bdc12f604bd410ea083a422f404bcc12f2043a022f10439c22f004bbc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x33e04cf4133c04cec133a04ce4133804cdc133604cd41334043d820f508ccc133204cc4133004cbc10f4083cc232e04cb4132c043c8232b04ca810f108ca41328043c020ef08c9c1⟩
]

def tableLLL : Table Block := .branch 8 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x37904de0137704dd8137504dd010fb08dcc137204dc4137004dbc136e04db4136c04dac10fa08da8136904da0136704d981365043e4236404d8c10f808d881361043dc236004cfc1⟩,
  ⟨0x5d02d015c0a8051027012c09004502100fc07a03a01b80d006202e01580a004a02200f8070032016009804401c00b0048018006000, 0xec013af0448423ae0448023ad04eb013ab04ea813a904c0cea013a7043fc23a604e9413a404e8c10fe08e8813a104e80137f043f420fc08b0cdf8137d04a0cdf0137b04de81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x3e4044b423e304f88112c084ac23e104f8013bf044a82129084a0212708498212508ef813bd04ef013bb04ee813b904ee013b704ed8112408ed413b404ecc13b204ec41123084882⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x3fd04ff013fb04fe81134084cc23f904fe013f704fd813f5044c82131084c023f404fcc13f204fc413f004fbc13ee04fb413ec04fac112f08fa813e9044b823e804f9c13e604f941⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x13b090d8113a090d41434044e42138090cc1432050c41430050bc142e050b4142c050ac1137090a81429050a01427050981425050901423050881136090841420044d423ff04ff81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x46c051ac146a051a414680519c14660519414640459421640858c216208584246305188146105180143f04580213f090f8143d044f8243c050ec143a044f42439050e01437044f02⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x16b09298116a0929414a40528c14a2052841169085a0216709280147f04598247e051f4147c051ec147a051e41478051dc1476051d41474051cc1472051c41470051bc146e051b41⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x4be052f414bc052ec1173085c824ba052e414b8052dc14b6045c42170092d414b4052cc14b2052c4116f085b8216d092c014af052b814ad052b014ab052a814a9052a014a7045b02⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x4f7045e824f6053d414f4053cc14f2053c414f0053bc14ee045e424ed045e024ec053ac14ea053a41177085d824e80539c14e60539414e40538c14e2045d424e10538014bf045d02⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x532045fc2531054c0152f054b8152d045f8217d085f0252c054ac152a045ec2529054a015270549815250549015230548815210548014ff053f814fd053f014fb053e814f9053e01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x56a055a415680559c15660469c21a6086942565055901563046902562055841560054fc153e054f4153c054ec153a054e411a3094e01537054d811a20868421a0094d41534054cc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5a30568815a10568011ae086b4257f055f8157d055f011ac095ec157a055e41578046ac2577055d811aa095d41574055cc1572046a42571055c011a8095bc156e055b4156c055ac1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5bb056e815b9056e011b6086d425b7056d815b5056d011b4096cc15b2056c415b0046cc25af056b815ad056b015ab056a811b2086c425a9056a015a7046c025a60569415a4046bc2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5f4057cc15f2057c411bd086f025f0057bc11bb086e825ee057b415ec057ac15ea046e425e9057a011b80979c15e60579415e40578c15e20578415e0056fc15be056f415bc046dc2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x62b058a811e6098a416280589c16260589416240588c16220588411e5087902620057fc11e3097f815fd057f015fb057e811e20878425f9057e011e0086fc25f7057d811be097d41⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x66105980163f058f8163d058f0163b047c021ef087b821ed087b0263a058e411eb087a82638058dc11e9087a02636058d41634058cc1632058c41630058bc162e058b411e7098b01⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x19f0167b059e81679059e01677059d81675059d01673059c81343671059c0166f059b8166d059b0166b047d021f3099a81669059a01667047c826660599411f1099901663059881⟩,
  ⟨0x5e02d81600aa0520278130092046021810007a03a01b80d006202e01580a004a02200f807003201600a004401c00c0048018006000, 0x1fa09ad016b3047e426b205ac416b005abc11f809ab816ad047dc26ac047d826ab05aa811f509aa416a805a9c16a605a9416a405a8c13c36a205a8413836a0059fc167e059f41⟩
]

def tableLLR : Table Block := .branch 9 tableLLRL tableLLRR

def tableLL : Table Block := .branch 17 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x22209bb0122109bac16ea0488026e905ba016e705b9811ff09b9416e405b8c16e2047f826e105b8016bf05af816bd05af016bb05ae811fd09ae416b8047f021fb09adc16b605ad41⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x72305c88172105c8016ff05bf8122b09bf416fc048a826fb05be81229088a026f90489c26f805bdc16f60489826f505bd016f30489426f205bc416f005bbc122409bb816ed0488c2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x23409ce8173905ce0123309cdc173605cd41734048c8273305cc81731048c4273005cbc123009cb8172d048bc222e09cb0172b05ca8172905ca0122d09c9c172605c94122c09c901⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x77305dc8177105dc0123b088e8276f05db8123909db4176c05dac176a05da4123809da0176705d98176505d90123709d8c1762048d8276105d80173f05cf8123509cf4173c05cec1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x7a904994226409ea017a705e98126309e9417a405e8c17a205e84126208984226009e80177f05df8177d05df0177b05de8177905de0177705dd8123f088f82775048f4223c09dd01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x270089bc226e089b427be05ef4126c09ef0126b09eec17ba05ee4126a09ee017b705ed817b505ed0126909ecc17b2049a027b105ec012670899827af05eb817ad05eb017ab05ea81⟩,
  ⟨0x5f02e01640ac0530280134094047022010407e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x1fd017f305fc817f1049e427f005fbc17ee05fb417ec0500dfac17ea049e027e905fa017e705f9817e505f90127709f8c17e2049d8227509f8417e0049d0227309efc1272089c42⟩,
  ⟨0x6d03481940c405e02d01580a404f025811c08804001e00e006a03101680a804e024010807803601800a804801e00c0048018006000, 0x182c04182b04a842060a81060a41060a010609c12a0081826041825049fc20609010608c106088127e08182104182005ffc127d09ff817fd05ff017fb049f027fa05fe417f8049ec27f705fd817f5049e82⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0x7503881bc0d606803281880bc05a02b014c09e04b023811008003c01c00d006002c014009004001d00c805802600f005801c008000, 0x18620510c186104aa822a908aa02061801060fc1060f812a708183d04183c04183b04a982060e81060e41060e01060dc1060d81060d41060d01060cc1060c812a508183104a9022a308183004182f04182e04a882060b41⟩,
  ⟨0x7803a01c80dc06a03401900c005d02c81540a204d024811408203e01d00d806602f015809c04602000e00600280100060020008000, 0x61f014c3061ec1061e81483061e41061e012ae08187704187604187504187404187304187204187104ab42061c01061bc12ac08186e04186d04186c04186b04aac2061a81061a41061a010619c10619810619410619010618c1⟩,
  ⟨0x7603981bc0d606703201800ba05a02b814c09e04b023811008003c01c80d406202d015009804401e00d005c02600f0060020008000, 0x2b80818b20418b10418b004adc2062bc12b608ad422b40818ae0418ad0418ac0418ab04acc2062a81062a412b20818a80418a70418a604ac420629410629010628c10628812b00818a10418a004abc2061fc1061f81061f41⟩,
  ⟨0x7903a81c40da06903281880bc05a02b014c09e04b024011008003c01c00d406202e015809c04601f00d80600280100060020008000, 0x18eb0418ea0418e90418e80418e704afc20639810639410639012be0818e30418e204af42063841063801062fc1062f812bc0818bd04aec22ba0818bc0418bb0418ba0418b904ae42062e01062dc1062d81062d41062d01062cc1⟩,
  ⟨0x7a03b01cc0de06b03381900c005c02c01540a404e025011808403e01d00d806402f015809c04601f00d805c0260100060020008000, 0x649412e508192404192304192204b902064841064801063fc12e308b882063f81063f41063f01063ec1063e81063e41063e01063dc12e10818f60418f50418f40418f30418f20418f10418f004b802063bc1063b81063b41063b01⟩,
  ⟨0x7903a81c40dc06a03301880bc05a02b81500a004c024011408203d01c80d806402e015009804401e00d005802600f0058020008000, 0x193e04193d04bb02064f01064ec1064e81064e41064e012eb08ba82064dc1064d81064d412e908193404193304193204ba02064c41064c01064bc1064b81064b41064b01064ac1064a812e708192904192804b9820649c1064981⟩,
  ⟨0x7503881b80d606703181800ba05902a814409a04a023010807c03b01b80cc05e02c014009004001d00d005c02600f0058020008000, 0x197304bdc22f608197204197104bd422f408197004196f04196e04196d04bcc2065b01065ac1065a812f208196904196804196704bc420659810659410659012f008bbc22ee08196304196204196104bb42065801064fc1⟩,
  ⟨0x7303781b00d206503081780b60570298140098048022810807c03b01c00d006002c014809404201e00d005802400e0058020008000, 0x19a604c9023230819a50419a404c8823210819a30419a204c8020668410668012ff08bf82065fc12fd08bf02065f81065f41065f012fb08197b04197a04be82065e41065e01065dc1065d812f908be02065d41065d01⟩,
  ⟨0x7703981bc0d606703201840bc05b02b814c09e04b024011408203d01c80d406402e015009c04601f00d805c0260100060020008000, 0x19bd0419bc0419bb0419ba04cb4232c08cac232a0819b90419b80419b70419b604ca423280819b50419b40419b30419b204c9c2066c41066c013260819af0419ae0419ad0419ac0419ab04c942066a81066a41066a010669c1⟩
]

def tableLRL : Table Block := .branch 8 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0x7403881b80d4066031817c0b6057029814009a04a023811008003c01c00d006002d014809404401e00d005802600f005801c006000, 0x33908ce02067c41067c013370819ef0419ee0419ed0419ec04cd8233508cd0233308cc82067ac1067a81067a41067a010679c13310819e60419e504cc020679010678c106788132f0819e10419e00419bf0419be04cb82⟩,
  ⟨0x7803a01c00d806803201800ba05a02b014809c04a023010c07e03b01b80cc05e02c014009804401e00e00600280100060020008000, 0x68ac1068a81068a41068a010689c106898133d08cf020689410689010688c106888106884133b081a200419ff0419fe0419fd0419fc04ce82067ec1543067e81067e41503067e01067dc1067d81067d41067d01067cc1067c81⟩,
  ⟨0x7803a01c40dc06a03381900c005c02c81540a204d024811408203d01c80d406202d015809c04602000e00600280100060020008000, 0x6990136308d8820698c136108d80206988106984133f081a60041a3f041a3e041a3d041a3c041a3b041a3a041a39041a38041a37041a360560c1a35041a3404cf82068cc1068c81068c41068c01068bc1068b81068b41068b01⟩,
  ⟨0x7603901b80d4067031817c0b6057029813c096047022010407c03b01c00d406202d014809404201e00d005802400e005001c008000, 0x69e81069e41069e0136d081a77041a76041a75041a74041a73041a72041a71041a7004db0236b08da8236908da02367081a6f041a6e041a6d041a6c041a6b04d982069a81069a41069a010699c106998136508d902069941⟩,
  ⟨0x7803a01c00d806803281840ba05902a814809e04c024011408403e01d00d806402e015009804401f00d805c02600f0058020008000, 0x6ac8106ac4106ac0106abc1375081aae041aad041aac041aab04dd0237308dc8206aa8137108dc0206aa4106aa0106a9c106a98106a94106a90106a8c106a88136f081aa1041aa0041a7f041a7e041a7d04db82069f01069ec1⟩,
  ⟨0x7803a81c40da06903301880be05c02c81540a204d024811408203e01d00d806402e015009c04601f00d805c02600f005801c008000, 0x37d081aea041ae9041ae804df0206b9c137b08de82379081ae6041ae5041ae4041ae3041ae2041ae104de0206b80106afc106af8106af4106af01377081abb041aba041ab9041ab8041ab7041ab6041ab5041ab404dd8206acc1⟩,
  ⟨0x7c03c01d40e206e03501980c405e02d01580a404e025011808403f01d80dc06602f015809c04601f00d805c0260100060020008000, 0x6c9813a1081b2504e80206c90106c8c106c88106c84106c80106bfc106bf8106bf4106bf0106bec106be8137f081af9041af8041af7041af6041af5041af4041af3041af2041af1041af0041aef04df8206bb8106bb4106bb0106bac1⟩,
  ⟨0x7903a81c40dc06a03301880bc05a02b81500a004c024011008203d01c80d406202d015009804401f00d805c02600f0058020008000, 0x1b3f041b3e04ea0206cf4106cf0106cec106ce8106ce413a708e98206ce0106cdc106cd8106cd413a5081b34041b33041b32041b31041b3004e90206cbc106cb813a3081b2d041b2c041b2b041b2a041b2904e88206ca0106c9c1⟩,
  ⟨0x7903a81c40da06903281880be05b02b814c09e04c024011408403e01d00d806402e015809c04802000e00600280100060020008000, 0x1b78041b77041b76041b75041b7404ebc23ae081b73041b72041b71041b7004eb4206dbc13ac08eac206db8106db4106db0106dac106da813aa081b6904ea4206da0106d9c106d98106d94106d90106d8c106d88106d84106d801⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0x7903a81c40da06903281840ba05902a814409a049023010c07e03b01c00d406202d014809804401e00e00600280100060020008000, 0x1bb2041bb1041bb0041baf041bae041bad041bac041bab041baa041ba9041ba8041ba704ed023b3081ba6041ba504ec823b1081ba4041ba3041ba204ec0206e84106e8015c306dfc106df8106df4106df0106dec106de8106de41⟩,
  ⟨0x7903a81c40da06a03301880be05b02b814c09e04c024011008003c01c00d406202e015809c04602000e00600280100060020008000, 0x1beb041bea041be904eec206fa0106f9c13ba081be6041be5041be4041be304ee4206f88106f84106f80106efc106ef813b8081bbd04edc23b6081bbc041bbb04ed4206ee8106ee4106ee0106edc106ed8106ed4106ed0106ecc1⟩,
  ⟨0x7903a81c40dc06a03301880bc05b02b814c09e04b023810c07e03b01b80cc06002c014009004201e00d00580260100060020008000, 0x1c24041c2304f88207088107084107080106ffc13e1081bfe041bfd041bfc041bfb041bfa041bf9041bf8041bf7041bf6041bf504f80206fd0106fcc106fc813bf08ef8206fc4106fc013bd08ef0206fbc106fb8106fb4106fb01⟩,
  ⟨0x7403801b00d006503081740b20550290138096048022010007803801a00c005a029013008c04001c00c005402400f0060020008000, 0x70e01070dc1070d813ee081c35041c34041c33041c3204fb42070c413ec08fac2070c01070bc1070b81070b41070b01070ac13ea081c2a04fa423e808f9c2070a41070a013e608f9423e408f8c20709c1070981070941⟩,
  ⟨0x7803a01c40dc06a03301880be05b02b814c0a004c024011008003c01c00d006002c014809404201d00c805402200f005801c008000, 0x71c413f408fcc2071c01071bc1071b813f2081c6d041c6c041c6b04fc42071a81071a41071a010719c10719810719410719010718c10718813f0081c61041c60041c3f041c3e041c3d041c3c0580c1c3b041c3a04fbc2070e41⟩,
  ⟨0x7803a01c00da06903281840ba05a02b014809c04b023810c08003c01c00d006002d015009804401e00d005802400f005801c008000, 0x72a41072a013fc081ca7041ca6041ca5041ca404fec20728c10728810728413fa081ca0041c7f04fe42071f81071f41071f01071ec13f808fdc2071e81071e41071e01071dc1071d81071d413f6081c74041c7304fd42071c81⟩,
  ⟨0x7703981c00d806803281840ba05902a814409a049023010c07e03b01c00d006002c014809404401e00d005802600f0058020008000, 0x1ce0050942072fc1072f81424081cbd041cbc041cbb041cba041cb9041cb8041cb70508c2422081cb6041cb5050842072d01072cc1072c81420081cb104ffc2072c01072bc1072b813fe081cad041cac04ff42072ac1072a81⟩,
  ⟨0x7503881b40d2066031817c0b605702a014009a049022810807e03c01c00d006002c014009004201e00d005c0280100060020008000, 0x1cf5041cf4041cf3050c0242f081cf2041cf1041cf0050b82073bc142d081cee041ced050b0242b090a82073b01073ac1073a81073a41073a010739c1429090a020739814270909820739410739010738c1073881073841⟩,
  ⟨0x7003681a40ca06102e816c0ae053028813409204502080f807403601900b8056028012808803e01c00c005402400f0060020008000, 0x43c081d27041d26041d25041d2405a0c1d23041d220590c1d21041d20041cff041cfe050ec2073f41073f01073ec1073e8143a090e42438090dc2436090d42073e41434090cc2432090c42073e01073dc1073d81⟩
]

def tableLRR : Table Block := .branch 9 tableLRRL tableLRRR

def tableLR : Table Block := .branch 17 tableLRL tableLRR

def tableL : Table Block := .branch 35 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0x7503881b40d206503081740b2055029813c098048022810407a03901a80c805c02a013008803e01b00b804c01e00c0048018006000, 0x1d3d041d3c041d3b041d3a041d39041d38041d37041d3605b0c1d35051942074d01464081d33041d32041d31041d300518c2074bc1074b81074b41074b01462081d2b041d2a041d29041d28051842460090fc243e090f42⟩,
  ⟨0x7803a01c00d806803281840ba05a02b014809c04b023810c08003c01c00d006002d015009804401e00d005802400e005001c006000, 0x75d41075d01075cc1075c8146d081d71041d70051b02075bc1075b81075b4146b081d6c041d6b051a82075a81075a41075a010759c1469091a020759810759410759010758c1075881075841075801074fc1467081d3e051982⟩,
  ⟨0x7803a81c40da06903301880bc05b02b81500a004d024811408203d01c80d806402e015009804401e00d00580260100060020008000, 0x475081dad041dac041dab051d02076a81076a41473081da8051c820769c1471081da6041da5041da4041da3041da2051c02076841076801075fc1075f81075f41075f01075ec1075e8146f091b82075e41075e01075dc1075d81⟩,
  ⟨0x7703981bc0d806803201800b805802a014809c04a024011008203e01d00d806602f015809c04602000e00600280100060020008000, 0x1de6041de5051e820779010778c1077881077841077801076fc1743076f81076f41703076f01479091e02076ec1076e81477081db9041db8041db7041db6051d82076d41076d01076cc1076c81076c41076c01076bc1076b81⟩,
  ⟨0x7b03b81cc0de06b03381900c005c02c01500a204d024811408203d01c80d406202e015009804401e00d805c02600f0060020008000, 0x1e21041e20041dff041dfe041dfd051fc2077f01077ec1077e81077e4147e081df8041df7041df6041df5041df4041df3041df2041df1051f42077c01077bc1077b81077b4147c081dec041deb041dea051ec2077a41077a010779c1⟩,
  ⟨0x7503881b40d2065031017c0b805802a0140098048022010407c03b01b80cc05e02b014009404401e00d005c02600f005801c006000, 0x1e36041e35041e34041e33052a824a9092a02078c81078c41078c01078bc1078b81078b414a70929824a5081e2c041e2b041e2a041e290529024a3092882078a010789c14a1081e26041e25041e24041e23041e22052802⟩,
  ⟨0x7803a01c40da06903281880bc05a02b814c09e04b023810c07e03b01b80d006002c014009004001c00c005002000d005001c008000, 0x79b814b2081e6d041e6c041e6b052c42079a81079a414b0081e68041e67041e66041e65041e64041e63041e62041e61052bc2079801078fc1078f81078f41078f01078ec1078e81078e41078e014ae092b424ac092ac2078dc1⟩,
  ⟨0x7a03b01c80dc06a03301880be05b02c01500a004c024011408203e01d00d806402e015009804602000e00600280100060020008000, 0x7aa0107a9c107a98107a94107a90107a8c14b8081ea2052dc207a84107a801079fc1079f814b6081e7d052d42079f01079ec1079e81079e41079e01079dc14b4092cc2079d81079d41079d01079cc1079c81079c41079c01079bc1⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0x7403881b40d4067031817c0b605802a814809c04a023010807c03a01b80d006202e015809c04601f00d805c0280100060020008000, 0x4e4081ebc0538c24e2081ebb041eba041eb90538424e0092fc207ae0107adc107ad8107ad4107ad0107acc14be092f424bc092ec24ba081eb2041eb1041eb0041eaf041eae052e4207ab4107ab0107aac107aa8107aa41⟩,
  ⟨0x7703981bc0d606703181800b805802a0140098048022010407c03a01b00c805c02b014009404201e00d005802400e0050018006000, 0x1ef3041ef2041ef1041ef0041eef053b4207bb8107bb4107bb0107bac107ba8107ba4107ba014ec093ac207b9c107b98107b94107b9014ea093a424e8081ee30539c207b88107b84107b80107afc107af8107af414e6093942⟩,
  ⟨0x7703981bc0d6067031817c0b6057029813c096047022010007a03a01b80cc05e02c014009404201d00c805802400e005001c006000, 0x1f2a041f29041f28041f27041f26041f25041f24041f23041f22041f21041f20041eff053d8207bf814f5093d024f3081efd041efc053c8207bec14f1081efa041ef9041ef8053c0207bdc107bd8107bd414ef081ef4053b82⟩,
  ⟨0x7703981bc0d806903281840ba05902b014809c04a023010807e03c01c00d006202d014809804401e00d005802400f0060020008000, 0x1f61041f60053fc24fe081f3f041f3e041f3d041f3c053f4207cec107ce8107ce4107ce0107cdc14fc093ec207cd8107cd414fa081f34041f33053e4207cc8107cc4107cc0107cbc107cb814f8093dc207cb4107cb0107cac1⟩,
  ⟨0x7103681a40ca06102f016c0b0055029013809404602100f807403601900b8054027012008403a01900b004c02000d0050018006000, 0x1f72041f71041f70041f6f054b8252d094b0252b094a8207db8107db4107db0107dac107da8107da4107da0107d9c107d98107d941529094a02527081f64041f6305498252509490252309488207d881521094802⟩,
  ⟨0x7203781ac0ce06302f81700b00540280134094047021810007803801a00c0058029012808803c01b00c005002200e0050018006000, 0x53c081fa4041fa3041fa2041fa1054ec207e80107dfc107df8153a094e42538081f7d054dc207df0107dec107de8107de4107de01536081f77054d4207dd81534094cc207dd41532094c4207dd0107dcc1530094bc2⟩,
  ⟨0x7403801b40d4066031017c0b805802a0140098049022810407a03a01b80d006002c014009404201d00d005802400e005001c008000, 0x7ee015680959c207edc107ed8156609594207ed4107ed0107ecc107ec81564081fb1041fb0041faf0558c256209584207eb8107eb4107eb01560081fab041faa054fc207ea4107ea0107e9c107e98153e094f4207e941⟩,
  ⟨0x7903b01cc0de06b033818c0be05b02b814c0a004c024011008003c01c00d006002c014809404601f00d805c02600f0060020008000, 0x15b4256c081ff2041ff1041ff0041fef041fee041fed041fec041feb055ac207fa8107fa4107fa0107f9c107f98107f94107f90107f8c107f88156a081fe105e0c1fe0041fbf041fbe041fbd041fbc055a4207eec107ee8107ee41⟩,
  ⟨0x7603901b80d6067031817c0b6057029813c09604702180fc07803901b00cc06002d014809804401e00d005802600f0060020008000, 0xa0a010a09c1577082826042825042824042823042822042821042820041fff041ffe041ffd041ffc055d82575095d02573095c82571081ffb055c0207fe8107fe4107fe0107fdc156f081ff6055b8207fd4107fd0107fcc1⟩
]

def tableRLL : Table Block := .branch 8 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0x7403801b40d4066031017c0b605702a0140098048022810807e03c01c00d006002c014009404401e00d005c02600f005801c006000, 0xa0f015a30968820a0ec10a0e815a10828390428380568020a0dc10a0d810a0d4157f095f8257d095f020a0d010a0cc10a0c810a0c410a0c0157b095e820a0bc10a0b8157908282d04282c04282b04282a042829055e02⟩,
  ⟨0x7b03b81d00e006c03401900c005c02c01500a004c024811408203d01d00d806402e015009804401e00d005c02600f005801c006000, 0x2877056a020a1d810a1d410a1d010a1cc10a1c810a1c410a1c010a1bc10a1b810a1b415a708286c04286b04286a0569820a1a410a1a010a19c10a19810a19410a19010a18c10a18815a508286104286004283f04283e04283d056902⟩,
  ⟨0x7a03b01c80dc06a03301880be05b02b81500a004c025011808403e01d80dc06602f015809c04602000e00600280100060020008000, 0xa2c810a2c410a2c010a2bc10a2b810a2b415ab0828ac0428ab0418030a2a810a2a417c30a2a010a29c10a29815aa0828a50428a40428a30428a20428a10428a0056a420a1fc10a1f810a1f410a1f010a1ec10a1e810a1e410a1e01⟩,
  ⟨0x7c03c01d00e006c03401900c005c02c81540a204d024811408203d01c80d406402f015809c04601f00d805c02600f0060020008000, 0xa3b810a3b410a3b010a3ac10a3a810a3a410a3a010a39c15af0828e60428e50428e40428e30428e20428e10428e00428bf0428be056b825ad0828bd0428bc0428bb0428ba0428b90428b80428b70428b6056b020a2d410a2d010a2cc1⟩,
  ⟨0x7b03b81cc0de06b033818c0be05b02b814c09e04b023811008203d01c80d806402e015009804401f00d805c02600f0058020008000, 0x29290429280429270429260429250429240429230429220429210429200428ff0428fe0428fd056d025b30828fc0428fb056c820a3e810a3e410a3e010a3dc10a3d815b10828f50428f40428f30428f20428f1056c020a3c010a3bc1⟩,
  ⟨0x7403801b00d006503081740b2056029814009a04a023010807c03a01b80d006202e015009804401e00d805c02600f005801c006000, 0xa4f410a4f010a4ec15e008293a042939042938056fc25be096f425bc096ec20a4dc10a4d810a4d410a4d015ba096e425b8096dc20a4cc10a4c810a4c410a4c015b608292f04292e04292d04292c04292b04292a056d42⟩,
  ⟨0x7703981bc0d806903281840ba05902a814809e04c024811808603f01d80dc06602f01580a004802000e00600280100060020008000, 0x2974042973057a425e808297204297104297004296f04296e0579c25e60979425e40978c25e208296d04296c04296b04296a0429690429680578420a59c10a59810a59410a59010a58c10a58810a58410a58010a4fc10a4f81⟩,
  ⟨0x7903a81c80dc06b033818c0be05b02b814c09e04b023811008003d01c80d406202d014809404201e00d005802600f0060020008000, 0x29ad057c020a6b015ef0829ab0429aa0429a90429a80429a70429a60429a50429a40429a3057b820a68815ed0829a10429a004297f04297e04297d04297c04297b057b020a5e810a5e415eb082978057a820a5dc10a5d810a5d41⟩,
  ⟨0x7903a81c40da06a033018c0be05c02c01500a004c024011008003c01c00d006002c014809804401e00d805c02600f0058020008000, 0x29e60429e50429e4057d820a78c15f50829e2057d020a78410a78010a6fc10a6f810a6f410a6f010a6ec10a6e810a6e410a6e010a6dc10a6d815f30818430a6d410a6d015f20829b30429b20429b10429b0057c420a6bc10a6b81⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0x7b03b81cc0de06b03401900c005c02c01500a004d024811408203e01d00d806602f015809c04601f00d805c02600f005801c006000, 0x2a21042a200429ff0429fe057e820a7f410a7f010a7ec10a7e810a7e410a7e015f90829f70429f60429f5057e020a7d010a7cc10620c29f20429f10429f00429ef0429ee0429ed0429ec0429eb0429ea0429e90429e80429e7057dc2⟩,
  ⟨0x7e03d01d80e406e03501980c405e02d01580a404e025811c08603f01d80dc06602f01580a004802000e00600280100060020008000, 0xa8fc10a8f810a8f410a8f010a8ec10a8e810a8e410a8e010a8dc10a8d810a8d410a8d015fc082a33042a32042a31042a30042a2f042a2e042a2d042a2c057ec20a8ac10a8a810a8a410a8a010a89c10a89810a89410a89010a88c10a8881⟩,
  ⟨0x7303781ac0d006503081740b2056029813c096048022810407a03a01b00cc05e02c014809804601f00d805c02600f005801c008000, 0x2a72042a71058a42628082a70042a6f042a6e0589c2626082a6d042a6c058942624082a6b042a6a0588c20a9a41622082a68058842620097fc25fe082a67042a66042a65042a64042a63042a62042a61057f420a9801⟩,
  ⟨0x7a03b01c80dc06a03381900c005c02c01500a004c024811808403e01d00d806402f015809c04601f00e00600280100060020008000, 0xaab010aaac10aaa810aaa4162f098b820aaa010aa9c10aa9810aa9410aa9010aa8c162d098b020aa8810aa8410aa8010a9fc10a9f8162b082a7d042a7c042a7b042a7a058a820a9e410a9e010a9dc10a9d810a9d410a9d010a9cc1⟩,
  ⟨0x7a03b01c80dc06a03301880bc05a02b014809c04a023010807c03a01b80d006202e015809c04601f00e00600280100060020008000, 0xab9810ab9410ab9010ab8c10ab8810ab8410ab8010aafc10aaf810aaf410aaf010aaec10aae810aae410aae010aadc1635098d02633098c82631082ab6042ab5042ab4058c020aacc10aac810aac410aac010aabc10aab810aab41⟩,
  ⟨0x7a03b01c80dc06a03301880be05b02b814c09e04c024011008003c01c00d006202d014809804601f00d805c02600f005801c008000, 0xac8010abfc10abf810abf410abf010abec163a082afa042af9042af8042af7058e420abd810abd410abd010abcc10abc810abc41638082af0042aef058dc20630c2aee042aed042aec042aeb042aea042ae9042ae8058d820ab9c1⟩,
  ⟨0x7903b01c80de06b033818c0be05b02b814c0a004d025011808403e01d00d806402f015809c04601f00e00600280100060020008000, 0x198420ace41660082b38042b37042b36042b35042b34042b33042b32058fc263e098f420acc410acc010acbc10acb810acb410acb0163c082b2b042b2a042b29042b28058ec20ac9c10ac9810ac9410ac9010ac8c10ac8810ac841⟩,
  ⟨0x7803a01c00da06a03301880bc05b02b814c09e04b023810c08003c01c00d006002d015009804401e00d005802400e005001c006000, 0xadc410adc01669099a020adbc10adb810adb41667082b6c042b6b042b6a042b69042b68042b670599820ad9810ad9410ad9010ad8c16650999020ad8810ad8410ad8010acfc10acf810acf410acf010acec1663082b3a059882⟩,
  ⟨0x7503881b40d4066031017c0b6057029813c098048022810807c03b01b80d006202e015809c04601f00d80600280100060020008000, 0x2ba6042ba5059d020ae9010ae8c1673082ba2042ba1042ba0042b7f059c820adf81671099c020adf4166f082b7c059b8266d099b0266b082b7b042b7a042b79042b78059a820addc10add810add410add010adcc10adc81⟩
]

def tableRLR : Table Block := .branch 9 tableRLRL tableRLRR

def tableRL : Table Block := .branch 17 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0x6d03481940c405f02e01600aa052027813009204602180fc07603701a00c405a029013008c03e01c00c805402200d0050018006000, 0x2bb3042bb205a9c26a609a9420aec416a409a8c26a209a8426a0099fc267e082bb0042baf042bae059f4267c082bad042bac059ec267a082bab059e42678082baa042ba9042ba8059dc20ae9c1676099d42⟩,
  ⟨0x7703981bc0d606803201800b805902a814409c04b023811008003c01c00d406402e015009804401f00d805c02600f005801c006000, 0x2bea042be9042be805ac020af9c10af9810af9416af082be4042be305ab826ad082be205ab020af8410af8010aefc16ab09aa820aef810aef410aef010aeec16a9082bba042bb9042bb8042bb7042bb6042bb5042bb405aa02⟩,
  ⟨0x7603981c00da069033018c0be05b02b814c09e04b023810c07e03b01b80cc05e02c014809404401e00d005c02600f005801c006000, 0x6ba09ae426b8082c2005adc26b6082bff042bfe042bfd042bfc042bfb042bfa042bf9042bf8042bf7042bf6042bf5042bf4042bf305ad426b4082bf205acc20afc410afc016b2082bef042bee042bed042bec042beb05ac42⟩,
  ⟨0x7803a01c00d806803281840ba05902a814409a04a023010807c03b01b80cc06002c014809404201d00d00580260100060020008000, 0xb0e010b0dc10b0d810b0d416e2082c34042c33042c32042c31042c30042c2f05b8420b0b810b0b410b0b016e0082c2b042c2a05afc20b0a416be082c28042c27042c2605af420b09416bc09aec20b09010b08c10b08810b0841⟩,
  ⟨0x7703981bc0d606803281840ba05902a814409a049022810407a03901b00cc06002c014009004001d00c805402400e0050018006000, 0x2c6f042c6e042c6d05bac26ea082c6c042c6b042c6a042c69042c68042c67042c66042c65042c64042c63042c6205ba426e809b9c20b18410b18010b0fc10b0f816e6082c3d042c3c05b9420b0ec10b0e810b0e416e409b8c2⟩,
  ⟨0x7603901bc0d6067031817c0b605702a014409a049022810407c03a01b00c805c02a013809004201e00d805c02600f0058020008000, 0xb29416f5082ca4042ca3042ca2042ca1042ca0042c7f05bd026f3082c7e042c7d042c7c042c7b05bc820b1e810b1e410b1e010b1dc10b1d816f109bc026ef09bb826ed082c75042c74042c73042c7205bb020b1c410b1c01⟩,
  ⟨0x7503881b40d206503081740b2055028813409204502100fc07803901a80c405a029013008c04001d00c805402200d005001c008000, 0x2cba042cb9042cb8042cb7042cb6042cb5042cb4042cb3042cb2042cb1042cb0042caf05c8026ff09bf826fd082cae042cad042cac042cab05bf026fb09be826f9082caa042ca9042ca8042ca705be026f709bd820b2981⟩,
  ⟨0x7d03c81d40e406e03501980c405e02d01580a404e025811c08603f01d80dc06602f015809c04601f00d805c0280100060020008000, 0x2cf7042cf605c8c20b3d410b3d010b3cc10b3c810b3c410b3c010b3bc10b3b810b3b41722082cec042ceb042cea042ce9042ce8042ce7042ce6042ce5042ce4042ce3042ce2042ce1042ce005c8420b2fc10b2f810b2f410b2f010b2ec1⟩,
  ⟨0x7b03b81cc0de06b033818c0be05b02b814c09e04b023810c08003c01c00d006002c014809404401e00d005c02600f0060020008000, 0x2d32042d31042d30042d2f042d2e042d2d042d2c042d2b042d2a042d29042d28042d27042d26042d2505ca020b49010b48c10b48810b48410b4801727082cff05c9820b3f810b3f41725082cfc042cfb05c9020b3e810b3e410b3e01⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0x7703a01c00d806903281840ba05a02b014809c04b024011008003c01c00d006202e01580a004802000e00600280100060020008000, 0x1cc420b5a410b5a01730082d67042d66042d6505cbc20b59010b58c10b588172e09cb420b58410b58010b4fc10b4f810b4f4172c09cac272a09ca420b4f010b4ec10b4e810b4e410b4e010b4dc10b4d810b4d410b4d010b4cc1⟩,
  ⟨0x7b03b81cc0e006c03401900c005c02c81540a204d025011808403e01d00d806402e015009c04601f00d805c02600f005801c006000, 0x2da4042da305cd820b68810b68410b68010b5fc10b5f81735082d7d042d7c042d7b05cd020b5e810b5e410b5e010b5dc10b5d810b5d410b5d010b5cc1733082d72042d71042d70042d6f042d6e042d6d042d6c042d6b042d6a05cc82⟩,
  ⟨0x6f03601a00c806002e01640ac053028013009004502080f807603801a00c405c02b013808c03e01b00c005402400f0060020008000, 0x1d9c20b6cc10b6c810b6c410b6c0176609d94276409d8c20b6bc10b6b81762082dad05d84276009cfc20b6b0173e09cf4273c082dab042daa042da9042da805cec273a09ce4273809cdc20b69c10b69810b6941⟩,
  ⟨0x7103701ac0d006503101780b4056029013c096047022010407a03a01b00c805e02b013809004201e00d805c0280100060020008000, 0x1dd8277509dd0277309dc820b79010b78c10b78810b7841771082de0042dbf05dc0276f082dbe05db820b6f410b6f0176d082dbb042dba05db0276b09da82769082db905da020b6e010b6dc10b6d810b6d410b6d01⟩,
  ⟨0x7403881b80d406603101780b4057029813c096048022810807e03b01b80cc05e02b013808c03e01b00b805002000d0048018006000, 0x7a209e8420b7e010b7dc10b7d810b7d410b7d017a0082df3042df2042df105dfc277e09df4277c082df0042def042dee042ded042dec042deb042dea042de9042de8042de705dec20b798177a082de505de4277809ddc2⟩,
  ⟨0x7703a01c40dc06a033818c0c005d02c81540a204e025011808603f01d80dc06602f015809c04601f00d805c0280100060020008000, 0x1eac27aa09ea420b8bc17a8082e2e05e9c27a6082e2d042e2c042e2b05e9420b8a810b8a417a4082e28042e27042e26042e25042e24042e23042e22042e21042e20042dff042dfe05e8c20b7f410b7f010b7ec10b7e810b7e41⟩,
  ⟨0x6b03401900c205d02d015c0a8050026812808e04301f80f007203601980c005a029013008803c01a00b004c02000c0048018006000, 0x1f8020b8e817bf082e3905ef827bd09ef020b8e017bb09ee827b9082e37042e3605ee027b709ed827b509ed027b3082e3505ec820b8d010b8cc10b8c810b8c417b109ec020b8c017af09eb827ad09eb02⟩,
  ⟨0x7103681a80cc06202f816c0ae0540288138094047022010007803801a00c005a02a013808c03e01b00b805002200e005801c006000, 0x2e6b05fbc20b9a810b9a417ee082e68042e6705fb427ec09fac20b99817ea09fa420b99410b99010b98c10b98810b98417e809f9c27e6082e60042e3f042e3e042e3d05f9427e409f8c27e2082e3c042e3b05f842⟩,
  ⟨0x7603901bc0d6067031817c0b605802a0140098048022010007803801a00c005a02a013808c04001c00c005002200e005001c008000, 0xba8417f9082ea0042e7f042e7e042e7d042e7c05fe020b9ec10b9e810b9e410b9e010b9dc10b9d810b9d410b9d010b9cc10b9c817f709fd827f5082e7105fd020b9c010b9bc10b9b817f309fc820b9b417f109fc020b9b01⟩
]

def tableRRL : Table Block := .branch 9 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0x7a03b01c80dc06a03301880be05b02b814c09e04c024811808604001e00e006803001600a004802000e00600280100060020008000, 0x608020bae810bae410bae010badc10bad817ff082eb5042eb4042eb3042eb205ff827fd09ff027fb09fe820bac410bac010babc10bab810bab410bab010baac10baa810baa410baa010ba9c10ba9810ba9410ba9010ba8c10ba881⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbbb810bbb410bbb010bbac1060b02060ac2060a820bba810bba410bba010bb9c10bb9810bb9410bb9010bb8c1060a420bb8810bb8410bb801060a020609c20bafc10609820609420609020baf810608c20608820baf410baf010baec1060842⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbbfc1060ec2060e82060e42060e020bbf810bbf410bbf010bbec1060dc20bbe81060d820bbe41060d420bbe010bbdc10bbd810bbd410bbd010bbcc1060d020bbc810bbc410bbc01060cc2060c82060c42060c02060bc2060b82060b420bbbc1⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbcd410bcd010bccc10bcc810bcc410619420bcc010619020618c20618820618420bcbc10618020bcb810bcb41060fc20bcb010bcac1060f820bca810bca410bca01060f420bc9c10bc981060f020bc9410bc9010bc8c10bc8810bc8410bc801⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbda81061c020bda410bda010bd9c1061bc2061b82061b420bd9810bd9410bd9010bd8c10bd8810bd841061b020bd8010bcfc10bcf81061ac20bcf410bcf01061a82061a420bcec1061a020619c20619820bce810bce410bce010bcdc10bcd81⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x61fc2061f820bdec10bde810bde41061f420bde010bddc10bdd81061f02061ec20bdd410bdd010bdcc1061e82061e420bdc81061e020bdc41061dc20bdc010bdbc1061d820bdb810bdb410bdb010bdac1061d42061d02061cc2061c82061c42⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbec810bec410bec010bebc10beb81062a020beb410beb010beac10bea810629c20bea410629820629420bea010629020be9c10be9810be9410be9010be8c10be8810be8410be8010628c20bdfc10bdf810bdf410bdf01062882062842062802⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbf8c10bf8810bf841062dc20bf8010befc10bef810bef410bef010beec10bee810bee410bee01062d82062d420bedc10bed81062d020bed41062cc2062c82062c42062c02062bc2062b82062b42062b02062ac20bed01062a82062a420becc1⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbfc81063a020bfc410639c20bfc010639820639420639020638c2063882063842063802062fc2062f82062f42062f020bfbc10bfb81062ec20bfb41062e820bfb01062e420bfac10bfa810bfa41062e020bfa010bf9c10bf9810bf9410bf901⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x63d42063d02063cc2063c820e09410e0901063c42063c02063bc2063b82063b42063b020e08c1063ac20e08810e08410e08010bffc10bff810bff410bff010bfec1063a820bfe810bfe410bfe010bfdc10bfd810bfd410bfd010bfcc1063a42⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe0f41063f420e0f010e0ec10e0e810e0e410e0e010e0dc10e0d81063f02063ec2063e820e0d410e0d010e0cc10e0c810e0c410e0c010e0bc10e0b81063e42063e020e0b410e0b010e0ac10e0a810e0a410e0a010e09c10e0981063dc2063d82⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe1d810e1d410e1d010e1cc10e1c810e1c410649020648c20e1c010e1bc10e1b810e1b410e1b010e1ac10e1a810e1a410648820e1a010e19c10e19810e19410e19010e18c10e18810e18410648420648020e1801063fc2063f820e0fc10e0f81⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe2cc10e2c810e2c410e2c010e2bc10e2b810e2b410649c20e2b010e2ac10e2a810e2a410e2a010e29c10e29810e29410e29010e28c10e28810e28410649820e28010e1fc10e1f810e1f410e1f010e1ec10e1e810e1e410649420e1e010e1dc1⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe3b810e3b410e3b010e3ac10e3a810e3a410e3a010e39c1064b020e39810e39410e39010e38c10e38810e38410e38010e2fc10e2f81064ac20e2f410e2f01064a820e2ec10e2e810e2e410e2e01064a420e2dc10e2d810e2d41064a020e2d01⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe3e810e3e410e3e01065802064fc2064f82064f42064f02064ec2064e820e3dc1064e420e3d810e3d410e3d010e3cc10e3c81064e02064dc2064d82064d420e3c410e3c01064d02064cc20e3bc1064c82064c42064c02064bc2064b82064b42⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe4d010e4cc10659820e4c810e4c410e4c010e4bc10e4b810e4b410659420e4b010e4ac10e4a810e4a410e4a010659020e49c10e49810e49410e49010e48c10e48810e48410e48010658c20658820658420e3fc10e3f810e3f410e3f010e3ec1⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe59810e59410e59010e58c1065d020e58810e58410e58010e4fc10e4f810e4f410e4f010e4ec1065cc20e4e81065c82065c42065c02065bc2065b82065b420e4e410e4e010e4dc10e4d81065b02065ac2065a82065a42065a020659c20e4d41⟩,
  ⟨0x4001e00e006803001600a004802000e00600280100060020008000, 0x65fc2065f82065f42065f02065ec2065e82065e42065e02065dc2065d820e5ac1065d420e5a810e5a410e5a010e59c1⟩
]

def tableRRR : Table Block := .branch 9 tableRRRL tableRRRR

def tableRR : Table Block := .branch 18 tableRRL tableRRR

def tableR : Table Block := .branch 35 tableRL tableRR

def table : Table Block := .branch 70 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table i

end PolicyInitialCoverage0Tail

namespace PolicyInitialCoverage0
def records (cid : Nat) : List Nat :=
  if cid ≤ 0x11a0 then [0, cid - 1] else PolicyInitialCoverage0Tail.records (cid - 0x11a1)

def limits : Nat → Nat
  | 0 => 0x11a0
  | 1 => 0xcac
  | 2 => 0x4c0
  | 3 => 36
  | _ => 0

def targets : Nat → Nat → Nat
  | 0, i => (PolicyCircuitPacked0.records i).headD 0
  | 1, i => (PolicyRewriteParametricPacked0.records i).headD 0
  | 2, i => (PolicyArithmeticPacked0.records i).headD 0
  | 3, i => (PolicyAssertedPacked0.records i).headD 0
  | _, _ => 0
end PolicyInitialCoverage0

namespace PolicyInitialCoverage1Tail
open PackedNatTable

def tableLLLL : Table Block := .leaf #[
  ⟨0x4001f00f007403801b00d006403001700b0054028013009004402000f007003401800b005002401000700300140080030010004000, 0x6015c15815411825014c11424814411020c24013c13813410823012c12812410422011c11811411010c1081041002001⟩,
  ⟨0x530280134096048022810807e03d01d00dc06a03201780b0052026011808003a01b00c005402401000700300140080030010004000, 0x1c81071049081c0106f041b8106d0420c1b0106b0410c1a81069041a010670419810650419010630480818810610418017c11c27817417016c1681641003⟩,
  ⟨0x5b02c01540a404f026012808e04402080f807603801a80c805e02c014809804602100f006c030015009004001c00b0040014006000, 0x2b410ac042ac10aa042a413820a80429c10a60429410a40428c10a20428410a0041fc107e041f4107c04d081ec107a041e41078041dc13022c2076041d4107404a081cc1⟩,
  ⟨0x5a02b81500a204f026012408c04402080f807603801b00d006202e01580a004a02200f8070032016009804401c00b0040014006000, 0xe70439810e50540839010e30438814c20e10438010bf042f814824420bd042f010bb042e810b9042e010b7042d810b5042d010b3050082c810b1042c010af04f082b81⟩,
  ⟨0x55029013c098049023811408403f01e80ec07203601980c005a02a014009404401f00e806802e015009804401c00b0040018006000, 0x3f010fb043e810f905e09d083e010f705c09b09a083d810f5043d010f3043c816420f1043c010ef058083b810ed0570830d6083b010eb043a815420e9043a01⟩,
  ⟨0x5e02d81600aa0520278130092046021810007a03a01b80d006202e01580a004a02200f8070032016009804001a00a0038014006000, 0x133044c81066084c41130044bc112e044b41065084b0112b044a81129044a010640818c2127044981125044901123044881062081842060084841120043fc10fe05f0840c3f41⟩,
  ⟨0x5f02e01640ac0530280134094048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5a411680459c11660459411640458c1143162045841160044fc106f084f8113d044f0106e081b4206c081ac213b044e81139044e01137044d8106a081a42068084d411340419c2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x17e045f4107a085f0117b045e81179041e42078085e01077081d82075085dc1176045d41174041d02173045c81171041cc2072085c0116f045b8116d045b01071085ac116a041c02⟩
]

def tableLLLR : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x1b5046d010a30828821b3046c811b10428421b0046bc11ae0428021ad046b011ab046a811a9046a0107f0869c11a6041f821a50469011a304688107d081f021a104680117f041ec2⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01600a404e024010807803601800a804801e00c0048018006000, 0x7bc11ee047b410a8087b011eb0429c21ea047a410a6087a011e70479811e50479011e30478811e10460c78011bf046f811bd046f011bb046e811b90429421b8046dc10a4086d81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2280489c12260489412240488c10af088881221042b820ad0888011ff047f810ac087f411fc047ec11fa047e410ab082a821f8047dc11f6047d410a9087d011f3047c811f1047c01⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01600a404c023010007803601800a804801e00c0048018006000, 0x2d82260048fc123e048f4123c042d4223b048e810b4082cc2239048e010b2088dc1236048d41234048cc1232048c411c3230048bc122e048b4122c048ac10b1088a81229042c02⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x278049dc10be089d81275049d01273042f42272049c410bc082ec2270049bc126e049b410ba089b0126b049a81269049a01267042e420b8089981265042dc22640498c1262049841⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2b10439422b004abc12ae0439022ad0438c22ac04aac12aa04aa412a804a9c10e208a9812a504a9012a304a8810e108a8412a004380227f049f8127d049f0127b049e810bf089e41⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2ea04ba410ec08ba010eb083a822e704b9812e5043a422e404b8c12e204b8412e004afc12be04af410e80839c22bc04aec10e608ae812b904ae012b704ad812b504ad012b304ac81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0xf808bf812fd04bf012fb043dc22fa04be412f804bdc10f608bd812f504bd012f304bc810f5083d020f3083c820f108bc412f0043c022ef04bb812ed043bc22ec04bac10ee083b42⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x33604cd4133404ccc133204cc41120083fc233004cbc132e043f8232d04cb0132b043f4232a04ca4132804c9c1326043f0232504c901323043ec20fa08c881321043e4232004bfc1⟩
]

def tableLLL : Table Block := .branch 8 tableLLLL tableLLLR

def tableLLRL : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x12508490212308dc4137004dbc136e04db4136c04dac136a04da4136804d9c136604d94136404d8c136204d84136004cfc133e04cf4133c04cec133a04ce4112208484233804cdc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x3a4044c82131084c0212f084b8212d084b023a304e8813a104e80137f044ac237e04df4137c04dec112a08de8137904de0137704dd81129084a0237504dd0112708dcc1372044982⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x13a08ef013bb04ee813b904ee0113908edc13b604ed413b404ecc113808ec813b104ec013af04eb8113708eb413ac04eac13aa04ea4113608ea0113508e9c13a6044d0213308e941⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x3ef04fb813ed0459c216608fb013eb04594216408fa813e90458c21620858423e804f9c13e604f9413e404580213f084f823e304f88113d08f8413e004efc113c084ec23be04ef41⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x172085c424240508c1422050841420045c0216f08ffc116e085b423fe04ff413fc04fec13fa04fe413f804fdc13f6045b023f504fd013f304fc8116b085a823f1045a4216808fc01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x43e050f4143c050ec1178090e81439050e01177085d82437050d81175085d02435050d01433050c81431050c0142f050b81173090b4142c050ac142a050a414280509c1426050941⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x475051d01473051c81471051c011a1091bc146e051b4146c051ac11a0091a81469051a0117f0919c146605194117e085f4217c085ec24640518c117a091881461045e42460050fc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x4ac052ac14aa052a414a8046a821a90929c14a6046a021a70929414a40528c14a20528411a609280147f04694247e051f4147c051ec11a4091e81479051e011a3086882477051d81⟩
]

def tableLLRR : Table Block := .leaf #[
  ⟨0x5f02e01680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x138812034e10538014bf052f814bd052f014bb052e814b9052e014b7046cc24b6052d414b4052cc14b2052c411b2086c421b0086bc21ae086b421ac092c014af052b814ad046ac2⟩,
  ⟨0x5d02d01600aa0520280134094047022010407c03b01c00d406402f01600a404c023010007403401700a004401c00b0040014006000, 0x6e022c34fa053e412834f8053dc14f6053d414f4053cc14f2046dc24f1053c014ef053b814ed053b014eb053a814e9046d824e80539c14e60539414e4046d421b40890d38c1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x1e2094c0152f054b811e108780252d054b011bf094ac152a054a41528046f825270549811bd0949411bc0949015230548815210548011bb086e824ff053f814fd046e424fc053ec1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x56b055a81569055a015670479c25660559415640558c156205584156004798253f054f8153d054f0153b04794253a054e41538047902537054d81535054d01533054c815310478c2⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5a50569015a3047b425a20568415a0047b0257f055f8157d055f011eb095ec157a055e411ea095e01577055d811e9095d41574055cc1572047a02571055c0156f055b8156d055b01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5be056f415bc056ec15ba056e415b8047d025b7056d815b5056d011f3087c825b3056c815b1056c011f1087c025af056b815ad056b015ab056a815a9056a011ef0969c15a6047b82⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x5f6057d411fc097d015f3057c815f1057c015ef057b815ed057b015eb047ec25ea057a415e80579c11fa087e421f8087dc25e60579415e4047d825e30578815e10578011f5096fc1⟩,
  ⟨0x5f02e01680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x18ac130362a058a41226098a016270589816250489422240989016230588816210488c2620057fc15fe0488825fd057f015fb0488425fa057e415f80488021ff087f821fd097dc1⟩,
  ⟨0x5f02e01640ac0530280134094047022010407c03b01c00d406402f01680a804e024010807803601800a804801e00c0048018006000, 0x8a4266705998166505990166305988166105980163f058f8163d058f0163b058e8163904d0d8e01637048a02636058d41634058cc1632058c41227098c0162f058b8162d058b01⟩
]

def tableLLR : Table Block := .branch 8 tableLLRL tableLLRR

def tableLL : Table Block := .branch 17 tableLLL tableLLR

def tableLRLL : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x233099f4167c059ec1232088c4267a059e41678059dc1676059d41230088bc222e099d01673048b4222c099c81671048ac2670059bc166e059b4166c048a8266b059a81669059a01⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x6b2048f826b105ac016af05ab816ad048f426ac05aac16aa05aa4123c09aa016a705a98123b088e82239088e02237088d826a505a9016a3048d426a205a8416a0048d0267f059f81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2670899826e905ba0126509b9c16e605b9416e405b8c16e205b8416e005afc16be05af416bc04990226309aec16ba05ae416b805adc126209ad816b505ad0126108980223f09acc1⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x72605c94172405c8c172205c84172005bfc16fe049a826fd05bf016fb05be816f905be016f705bd816f5049a426f405bcc16f2049a026f105bc016ef05bb816ed05bb016eb05ba81⟩,
  ⟨0x5e02d81600aa0520278130092046021810007a03a01b80d006202e01580a004a02200f8070032016009804001a00a0040014004000, 0x272089c4273c05cec127009ce8173905ce0126f09cdc173605cd4173405ccc1732049b8273105cc0172f05cb8172d05cb0126d09cac172a05ca4126c089ac23c372805c9c1383⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x77505dd0177305dc8177105dc0176f05db8176d05db0176b049e4227809da8176905da0176705d98176505d90127709d8c176205d841760049d8273f049d4227409cf8173d049cc2⟩,
  ⟨0x5f02e01640ac0530280134094048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x9f427b005ebc17ae05eb417ac05eac14037aa05ea4127c09ea017a705e9817a505e9017a305e8817a105e80127b09dfc177e05df4177c05dec177a05de4127a09de0177705dd81⟩,
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x7eb05fa817e904a8827e805f9c17e605f9417e405f8c17e205f8412a109f8017bf04a80227f09ef817bd05ef017bb05ee817b905ee017b705ed817b505ed0127e09ecc17b205ec41⟩
]

def tableLRLR : Table Block := .leaf #[
  ⟨0x6002e81680ae0540288138096048022810807e03c01c80d806603001680a804e024010807803601800a804801e00c0048018006000, 0x2ae09ffc17fe05ff417fc05fec12ad09fe817f905fe017f704ab022ab08aa827f605fd417f404aa427f304aa027f204a9c22a609fc417f005fbc17ee04a9427ed05fb012a408a8c2⟩,
  ⟨0x7d03c81d40e206d03481940c205d02c81540a204d024811408203d01c80d406202d015009c04601f00d805c02600f005801c006000, 0x183c04183b04183a04183904183804183704183604183504183404183304183204183104183004182f04182e04182d04182c04182b04182a04182904ac422b008182804182704182604182504182404182304182204182104182004abc2⟩,
  ⟨0x7a03b01c80dc06a03301880bc05a02b014c09e04b024011008003c01c00d006202d014809404201d00d005802400f0060020008000, 0x61d81061d41061d01061cc1061c81061c41061c01061bc1061b812b708186d04186c04ad82061ac1061a81061a41061a010619c12b508186604186504186404186304186204ad020618410618012b308ac82060fc1060f81060f41⟩,
  ⟨0x7903a81c40da06903281840ba05902a814409c04b023810c08003d01c80d406202d014809404201d00d005802400f0060020008000, 0x18af0418ae0418ad0418ac0418ab0418aa0418a90418a80418a70418a604af822bd0818a50418a404af022bb0818a30418a20418a10418a004187f04187e04187d04187c04ae82061ec1061e812b908ae02061e41061e01061dc1⟩,
  ⟨0x7103681a40ca06102e81680ac052027012c09004502080f407203501900b8054026011007c03801900b004c02000d005001c006000, 0x18e00418bf0418be0418bd0418bc04bb42062ec1062e81062e412ec08bac22ea0818b80418b70418b60418b504ba42062d01062cc1062c81062c412e808b9c22e608b9422e408b8c22e208b8422e00818b004afc2⟩,
  ⟨0x7703981c00d806803281840ba05902a814809c04b023810c07e03c01c00d006202d014809404201e00d005c02600f0060020008000, 0x18f704bd82063d81063d412f50818f40418f30418f20418f104bd02063c012f30818ef0418ee0418ed04bc82063b01063ac12f10818ea0418e90418e80418e704bc020639812ef0818e50418e404bb820638c1063881063841⟩,
  ⟨0x7703a01c00d806803201800ba05a02b81500a004c024011008003d01c80d406202d014809404401f00d80600280100060020008000, 0xbfc2064b81064b41064b01064ac1064a812fe08bf422fc08bec2064a41064a010649c10649810649412fa0819240419230419220419210419200418ff04be422f80818fe04bdc2063f41063f01063ec1063e81063e41063e01⟩,
  ⟨0x7b03b81cc0de06b033818c0be05c02c01500a004c024011408403e01d00d806402e015009804601f00d805c02600f005801c006000, 0x196904196804196704196604196504196404196304c902065881065841065801064fc1064f8132308c882064f41064f01064ec1064e81064e41064e01064dc132108193604193504193404193304193204193104193004192f04c802⟩,
  ⟨0x7c03c01d00e006c03401900c205e02d01580a404f025811c08603f01d80dc06602f015809c04601f00d805c0260100060020008000, 0x669410669010668c106688106684106680132808c9c2065fc1065f81065f4132608197c04197b04197a04197904197804197704197604197504197404197304197204197104197004196f04196e04c942065b41065b01065ac1065a81⟩
]

def tableLRL : Table Block := .branch 8 tableLRLL tableLRLR

def tableLRRL : Table Block := .leaf #[
  ⟨0x7503881b40d206503101780b40560290138098048022010407c03b01c80d406202f015809c04601f00d80600280100060020008000, 0x19bd0419bc0419bb0419ba04cb42066e41066e01066dc1066d81066d414c3066d01066cc132c08cac232a0920c19b20419b10510c19b00419af0419ae0419ad0419ac04ca42066ac1066a81066a41066a010669c1066981⟩,
  ⟨0x7903a81c40da06903281880be05b02b814c09e04b023810c07e03b01b80cc05e02c014009004001c00c005002200e0058020008000, 0x19f60419f50419f40419f30419f204cd023330819f10419f00419ef0419ee0419ed0419ec0419eb0419ea0419e90419e80419e70419e604cc820679410679010678c106788106784106780133108cc0232f08cb82066fc1066f81⟩,
  ⟨0x7803a01c00d806803281880bc05a02b014809c04b024011408203d01c80d806402e015009804401e00d005802400e005801c006000, 0x68b81068b41068b01068ac133c08cec2068a81068a41068a010689c106898133a08ce42338081a25041a24041a2304cdc2068881068841068801067fc1067f81067f41067f01067ec1067e81067e413360819f80419f704cd42⟩,
  ⟨0x7c03c01d00e006c03401900c005c02c81540a204d024811408403e01d00d806402e015009c04601f00d805c0260100060020008000, 0x69a81069a41069a010699c10699810699410699010698c1360081a62041a61041a60041a3f041a3e04cfc2068f41068f01068ec1068e81068e41068e0133e081a37041a36041a35041a34041a3304cf42068c81068c41068c01068bc1⟩,
  ⟨0x7b03b81cc0e006d03481940c205d02c81540a204d025011808403e01d00d806402e015009c04601f00d805c02600f005801c008000, 0x1aa5041aa404d942364081aa3041aa2041aa1041aa0041a7f041a7e041a7d041a7c04d8c2069ec1069e81069e41069e01069dc1069d81069d41069d01362081a73041a72041a71041a70041a6f041a6e041a6d041a6c04d842069ac1⟩,
  ⟨0x7803a01c40da06903281840bc05a02b014c0a004c024011008003c01c80d406202d014809404401f00d805c02600f005801c008000, 0x6af4136d081abc041abb041aba041ab904db0206ae0106adc136b08da8206ad8106ad4106ad0106acc106ac81369081ab1041ab0041aaf041aae041aad04da02367081aac041aab041aaa041aa9041aa8041aa704d98206a981⟩,
  ⟨0x7803a01c00d806903301880bc05b02b814c09e04b024011008003c01c80d406202d015009804401e00d005c02600f0058020008000, 0x6bd4106bd0106bcc137508dd0206bc8106bc41373081af0041aef041aee041aed04dc8206bb0106bac106ba81371081ae9041ae8041ae704dc0206b98106b94106b90106b8c136f081ae2041ae1041ae004db8206afc106af81⟩,
  ⟨0x7b03c01d00e006c03481940c205d02d01580a404e025011c08603f01d80dc06602f015809c04602000e00600280100060020008000, 0xde8206cc0106cbc106cb81379081b2d041b2c041b2b04de0206ca8106ca4106ca0106c9c1377081b26041b25041b24041b23041b22041b21041b20041aff041afe04dd8206bf4106bf0106bec106be8106be4106be0106bdc106bd81⟩
]

def tableLRRR : Table Block := .leaf #[
  ⟨0x7803a81c40da06903281840ba05a02b014809e04c024011008003d01d00d806402e015809c04601f00d805c02600f0058020008000, 0x3a2081b68041b67041b66041b65041b64041b6304e84206d88106d8413a008dfc206d80106cfc106cf8137e08df4206cf4106cf0106cec137c081b3a041b39041b38041b37041b36041b35041b34041b3304dec206cc8106cc41⟩,
  ⟨0x7903a81c80dc06a03301880bc05b02c01540a204d025011808403e01d00d806402e015009804401e00d005802600f005801c006000, 0x1ba104ea4206e80106dfc106df8106df4106df013a808e9c23a6081b7b041b7a04e94206de4106de0106ddc106dd8106dd4106dd0106dcc106dc8106dc4106dc0106dbc106db8106db413a4081b6c041b6b041b6a041b6904e8c2⟩,
  ⟨0x7803a81c40da06903301880bc05b02b814c09e04b023810c07e03b01b80cc05e02c014009004001d00c805402400f005801c008000, 0x3b1081bb9041bb8041bb704ec0206ed8106ed413af081bb4041bb3041bb2041bb1041bb0041baf041bae041bad041bac041bab041baa04eb8206ea4106ea0106e9c13ad081ba6041ba504eb023ab081ba4041ba304ea8206e881⟩,
  ⟨0x7203701ac0d006503101780b4056029013c09604702180fc07603801a00c005a02a013008803e01c00c005402400f005801c006000, 0x6fac13bf08ef823bd08ef0206fa8106fa4106fa0106f9c13bb081be6041be5041be4041be3041be204ee8206f84106f8013b908ee0206efc106ef813b708ed8206ef413b508ed023b3081bbc041bbb041bba04ec82⟩,
  ⟨0x7503881b40d206603101780b4056029013809604702180fc07803901b00cc05e02b014009004001c00c005402400e005801c008000, 0x1c20041bff041bfe04fa8206ff4106ff0106fec106fe8106fe4106fe013e9081bf7041bf6041bf504fa023e708f9823e5081bf4041bf304f90206fc8106fc4106fc0106fbc13e308f88206fb813e1081bed04f80206fb01⟩,
  ⟨0x7603901b80d606803281880be05b02b814c09e04b024011408203d01d00d806402e015009804401e00d005c02600f005801c006000, 0x70d81070d413f408fcc23f208fc423f0081c34041c33041c32041c31041c3004fbc23ee081c2f041c2e04fb42070b41070b01070ac1070a81070a41070a010709c10709813ec081c25041c24041c23041c22041c2104fac2⟩,
  ⟨0x7303781ac0ce06303001740b4057029813c096048022810807e03c01c00d006002c014009404201d00c805402200e005801c006000, 0x1c69041c68041c67041c6605084242008ffc23fe081c65041c64041c6304ff423fc08fec23fa08fe42071881071841071801070fc1070f813f8081c3d041c3c041c3b041c3a041c3904fdc23f6081c38041c3704fd42⟩,
  ⟨0x7703981bc0d6067031817c0b605702a014409c04a023811008003c01c00d006002d015009804401f00d805c02600f0058020008000, 0x1ca0041c7f041c7e041c7d041c7c041c7b041c7a041c79050a82429090a02071e01427090982071dc1071d81071d41071d01071cc1425090902071c81071c41423081c70041c6f041c6e041c6d041c6c050882071ac1071a81⟩,
  ⟨0x7903a81c80dc06a03301880bc05a02b014c0a004c024011008003c01c00d006002c014009004201e00d00580260100060020008000, 0x1cb9050c42072e01072dc1072d81072d41072d01072cc1072c81430090bc2072c41072c01072bc1072b81072b41072b01072ac1072a81072a41072a010729c142e090b4207298107294142c090ac20729010728c1072881072841⟩
]

def tableLRR : Table Block := .branch 8 tableLRRL tableLRRR

def tableLR : Table Block := .branch 17 tableLRL tableLRR

def tableL : Table Block := .branch 34 tableLL tableLR

def tableRLLL : Table Block := .leaf #[
  ⟨0x7603901b80d406703201840ba05a02b014c0a004c024011408203d01c80d406202e015009804401e00d805c02600f005801c008000, 0x73bc1073b81073b4143b090e82439081cec050e02073ac1437090d82073a81073a41435081ce8041ce7041ce6041ce5041ce4050d020738c1073881073841073801433081cbf041cbe041cbd041cbc041cbb050c82072e81⟩,
  ⟨0x7303801b40d406603101780b405702a0140098048022810807c03b01c00d406202d015009c04601f00d805c02600f005801c008000, 0x11a02467091982074881074841074801073fc1465091902073f81073f41073f01463091882073ec146109180243f081cfa041cf9050f8243d081cf8041cf7041cf6041cf5041cf4041cf3041cf2041cf1050f02073c01⟩,
  ⟨0x7203781ac0ce06302f816c0b0054028013409404602180fc07603701a00c405c02a013808c03e01b00c005002000c0048018006000, 0x476081d34041d33041d32041d31041d30051d42074bc1074b81474091cc2074b41472081d2c041d2b041d2a051c42470091bc2074a4146e081d28041d27041d26051b420749410749010748c146c091ac246a091a42⟩,
  ⟨0x7803a01c00d806803201800b805802a014409c04a023010c08003c01c00d006002c014809404201d00c805402200e0058020008000, 0x75b01075ac1075a81075a41075a010759c107598107594107590147e091f420758c107588147c091ec2075841075801074fc1074f81074f4147a081d3c041d3b041d3a041d39041d38041d37051e42478091dc2074d81074d41⟩,
  ⟨0x7a03b01c80dc06a03301880bc05a02b014c0a004d024811408203e01d00d806402f015809c04802000e00600280100060020008000, 0x769810769410769010768c1076881076841076801075fc1075f814a40928c24a2081d7d041d7c041d7b052842075e81075e41075e014a0081d77041d76051fc2075d41075d01075cc1075c81075c41075c01075bc1075b81075b41⟩,
  ⟨0x7903a81c40da06903281840bc05a02b014c09e04b023810c07e03b01b80cc05e02b014009004001c00c005002200e0050018006000, 0x1dbf041dbe041dbd041dbc041dbb041dba052ac2076e41076e014aa081db7041db6041db5041db4041db3041db2041db1041db0041daf041dae052a42076b41076b01076ac1076a81076a414a80929c2076a010769c14a6092942⟩,
  ⟨0x7503881b40d206603181800ba05902a814409a049023010c08003c01c00d406202d015009c04601f00d805c0280100060020008000, 0x1df4041df3041df2052d824b5092d024b3081df1041df0041def041dee041ded052c824b1092c02077b01077ac14af081dea041de9052b824ad081de8041de7041de6041de5052b020779010778c1077881077841077801⟩,
  ⟨0x7203781ac0ce06303001740b405702a014009804a023010808003c01c00d006002c014009004201e00d805c02600f005801c006000, 0x4e0081e28041e27041e26052fc24be092f424bc092ec20789410789015430788c1078881503078841078801077fc1077f81077f41077f01077ec14ba092e424b8081dfa041df9041df8041df7041df6041df5052dc2⟩
]

def tableRLLR : Table Block := .leaf #[
  ⟨0x7903a81c40dc06b03401900c005c02c01540a204d024811408203d01c80d406202d015009804602000e00600280100060020008000, 0x1e61041e600539c24e6093942078fc1078f81078f41078f014e4081e3b041e3a041e39041e38041e37041e36041e35041e34041e33041e320538c2078c414e2093842078c01078bc1078b81078b41078b01078ac1078a81078a41⟩,
  ⟨0x7903a81c40dc06b03401900c005c02c01540a204d024811408203d01c80d406202d014809c04601f00e00600280100060020008000, 0x1e7b041e7a053b024eb093a82079e41079e01079dc1079d814e9081e75041e74041e73041e72041e71041e70041e6f041e6e041e6d041e6c041e6b0560c1e6a041e69053a02079a010799c10799810799410799010798c1079881⟩,
  ⟨0x7303801b40d206603181800b805802a014409c04a023010c07e03c01c00d006002c014009004201e00d005802400e005801c008000, 0x13e424f8081eae053dc24f6093d4207ab4107ab0107aac14f4093cc207aa8107aa414f2081ea8053c4207a9c107a98107a94107a90107a8c107a8814f0093bc207a84107a801079fc1079f814ee081e7d053b42079f01⟩,
  ⟨0x7a03b01c80de06b033818c0be05b02b814c09e04b023810c07e03b01b80cc06202d014809804401e00d00580260100060020008000, 0x7ba4107ba014fd081ee7041ee6041ee5041ee4041ee3041ee2041ee1041ee0041ebf041ebe041ebd041ebc041ebb041eba041eb90570c1eb8041eb7053f0207ad8107ad4107ad0107acc14fb093e8207ac8107ac4107ac0107abc1⟩,
  ⟨0x7503881b80d406603101780b405702a014409a049022810407a03901a80c405a029012808403a01900a804801e00c0050018004000, 0x1f2005490207bfc107bf8107bf4107bf0107bec1523094882521081efa041ef9041ef8041ef7041ef6041ef5041ef4041ef3041ef2041ef1041ef0041eef041eee041eed041eec0548024ff093f8264307bac107ba81603⟩,
  ⟨0x7b03b81cc0de06b03401900c005d02c81540a204d024811408203d01c80d406202d014809404401e00d005802400e0058020008000, 0x1f3b041f3a041f39041f38054a4207cdc107cd81528081f35041f34041f33041f32041f31041f30041f2f041f2e041f2d041f2c041f2b041f2a041f29041f280549c207c9c107c98107c94107c90107c8c152609494207c88107c841⟩,
  ⟨0x7903a81c40da06903301880bc05a02b014809e04b023811008003c01c00d006002d015009804401e00d805c0260100060020008000, 0x1f74041f73041f72041f71054c0207dc0107dbc107db8107db4107db0152f081f6b041f6a054b8207da4107da0107d9c107d98107d94152d094b0207d90107d8c107d88152b081f61041f60054a8207cfc107cf8107cf4107cf01⟩,
  ⟨0x7903a81c40da06a033018c0be05b02b81500a004c024011008003c01c00d006002c014009004201d00c805402200e005801c006000, 0x1fad041fac041fab054dc207ea81536081fa9041fa8041fa7054d4207e98107e94107e90107e8c107e88107e84107e80107dfc107df8107df4107df0107dec1534081f7a041f79041f78041f77054cc2532081f76041f75054c42⟩,
  ⟨0x6c03481940c405f02e01640ac053028013409204502080f807603801a80c405a02a013808c03e01c00c005402400e005001c008000, 0x56b081fb9055a82569095a02567095982565095902563081fb8041fb7041fb605588256109580253f081fb5041fb4054f8253d081fb3041fb2054f0207ec4153b094e8207ec0107ebc1539094e0207eb81⟩
]

def tableRLL : Table Block := .branch 8 tableRLLL tableRLLR

def tableRLRL : Table Block := .leaf #[
  ⟨0x7903a81c40da069033018c0be05b02c01500a004c024011008003c01c00d406402e015009804401e00d005802400e005001c006000, 0x1ff2041ff1041ff0041fef055c82571081fee041fed055c0207fb0107fac107fa8107fa4107fa0107f9c107f98107f94156f095b8207f90107f8c107f88107f84107f80107efc107ef8107ef4107ef0107eec156d081fba055b02⟩,
  ⟨0x7703981bc0d606703201800b805802a0140098049023010c08003d01c80d406202d014809404201d00c805402400f005801c008000, 0x2829042828042827042826055ec20a09410a09010a08c10a08810a08410a080157a095e42578095dc2576081fff041ffe041ffd041ffc041ffb041ffa041ff9041ff8041ff7041ff6055d42574081ff5041ff4055cc207fcc1⟩,
  ⟨0x7603901c00d806803301880be05b02b814c09e04b023810c07e03b01c00d406202d014809804601f00d805c02600f005801c006000, 0xa18416c30a18010a0fc16830a0f815a108283d04283c04283b04283a04283904283804283704283604283505680257f082834042833042832055f8257d08283104283004282f04282e04282d04282c04282b04282a055f02⟩,
  ⟨0x7c03c01d00e006c03401900c005c02c01500a004d025011808403e01d00dc06602f015809c04601f00d805c02600f005801c006000, 0xa1f410a1f010a1ec10a1e810a1e410a1e010a1dc10a1d810a1d410a1d010a1cc15a50969020a1c810a1c410a1c010a1bc15a308286e04286d04286c04286b04286a042869042868042867042866042865042864042863042862056882⟩,
  ⟨0x7b03b81d00e006c03401940c205d02c81540a204d024811408203e01d00d806402e015009c04601f00d805c02600f0058020008000, 0x28b8056a820a2dc10a2d810a2d415a90828b40428b30428b20428b10428b00428af0428ae0428ad0428ac056a020a2ac10a2a810a2a410a2a010a29c15a70828a60428a50428a40428a30428a20428a10428a00569820a1fc10a1f81⟩,
  ⟨0x7803a01c00da06903281840ba05a02b814c0a004c024011408203d01c80d406202d014809404201e00d805c02600f0058020008000, 0xa3c010a3bc15b20828ee0428ed0428ec0428eb056c425b00828ea056bc20a3a410a3a015ae0828e70428e60428e50428e40428e30428e20428e10428e00428bf056b425ac0828be0428bd0428bc0428bb056ac20a2e810a2e41⟩,
  ⟨0x7803a01c00d806903281840ba05902b014c0a004c024011008003c01c00d006002d015009804401e00d805c0260100060020008000, 0xa4a010a49c10a49815ba082925042924042923042922056e425b8096dc20a48410a48010a3fc10a3f810a3f410a3f010a3ec10a3e815b6096d420a3e410a3e010a3dc15b40828f60428f5056cc20a3d010a3cc10a3c810a3c41⟩,
  ⟨0x7403881b80d4066031017c0b805802a0140098049023010807c03a01b00c805e02c014809404201d00d005802400f0060020008000, 0x5e60979420a4f010a4ec10a4e815e40978c20a4e410a4e010a4dc10a4d815e20978420a4d410a4d010a4cc10a4c810a4c415e0096fc25be08293004292f04292e056f420a4b410a4b015bc096ec20a4ac10a4a810a4a41⟩
]

def tableRLRR : Table Block := .leaf #[
  ⟨0x7203701a80cc06303001700b0054028013009004402000f007203601900b8056027011807c03801900b004c02000d0050018006000, 0xa5b810a5b410a5b015f4097cc20a5ac10a5a810a5a410a5a010a59c10a59810a59410a59010a58c15f2097c420a58810a58415f008296004293f04293e057bc25ee097b425ec097ac25ea097a420a4f415e80979c2⟩,
  ⟨0x7a03b01c80dc06b033818c0be05b02c01540a204d025011808403e01d80dc06602f015809c04601f00d80600280100060020008000, 0xa6a010a69c10a69815fa0829a50429a40429a30429a2057e425f80829a10429a0057dc20a5fc10a5f810a5f415f608297c04297b04297a042979042978042977042976042975057d420a5d010a5cc10a5c810a5c410a5c010a5bc1⟩,
  ⟨0x7803a01c00d806903301880bc05a02b014809c04a023010c07e03c01c80d406202d015009804401e00d805c02600f005801c006000, 0xa78010a6fc10a6f816220988420a6f410a6f010a6ec10a6e810a6e410a6e010a6dc10a6d816200829b5057fc25fe0829b40429b30429b2057f420a6c410a6c010a6bc15fc0829ae0429ad0429ac0429ab0429aa0429a9057ec2⟩,
  ⟨0x7603901bc0d606703201800b805802a0140098049023010807c03a01b00c805e02b013808c03e01c00c805402200d0048018006000, 0xa7d8162c0829f50429f4058ac20a7cc10a7c810a7c410a7c010a7bc10a7b8162a098a420a7b410a7b010a7ac10a7a810a7a416280829e80429e70429e60429e50589c26260829e40429e30429e20429e10589426240988c2⟩,
  ⟨0x7703a01c40dc06b033818c0be05b02b814c09e04b023811008203e01d00d806402e015009804401f00d805c02600f005801c008000, 0x18d42634098cc2632082a2d042a2c042a2b042a2a042a29042a28042a27042a26042a25058c42630098bc20a89010a88c10a88810a88410a88010a7fc10a7f8162e0829fd0429fc0429fb0429fa0429f90429f8058b420a7dc1⟩,
  ⟨0x7303781b00d206603101780b605802a014009a049022810407c03b01c00d406402e015009804401e00d005c02600f005801c006000, 0x2a600598826610998020a8fc10a8f8163f098f820a8f410a8f0163d082a3b042a3a042a39058f0263b098e82639098e020a8e010a8dc10a8d810a8d410a8d010a8cc1637082a32042a31042a30042a2f042a2e058d82⟩,
  ⟨0x7803a01c00d806903301880bc05a02b81500a204d024811808403e01d00d806402f015809c04602000e00600280100060020008000, 0xa9e010a9dc10a9d8166a099a420a9d410a9d010a9cc16680999c2666082a72042a710599420a9c010a9bc10a9b810a9b410a9b01664082a6b042a6a042a690598c20a9a010a99c10a99810a99410a99010a98c10a98810a9841⟩,
  ⟨0x7703981bc0d6067031817c0b805802a0140098048022810807c03a01b80cc06002d014809404201e00d005802400f005801c008000, 0x2aaf042aae042aad042aac042aab042aaa059cc20aaa410aaa010aa9c10aa9810aa941672099c420aa9010aa8c1670082aa2059bc266e082aa1042aa0042a7f059b420a9f810a9f410a9f0166c082a7b042a7a059ac20a9e41⟩,
  ⟨0x7703981bc0d806903281840ba05a02b014809e04b023811008003d01c80d806402e015009804401e00d005802400e0050018006000, 0x2ae6042ae5059f0267b082ae4042ae3042ae2059e820ab8410ab801679082abf042abe059e020aaf41677082abc059d820aaec10aae810aae410aae010aadc10aad810aad410aad010aacc10aac810aac410aac01675099d02⟩
]

def tableRLR : Table Block := .branch 8 tableRLRL tableRLRR

def tableRL : Table Block := .branch 17 tableRLL tableRLR

def tableRRLL : Table Block := .leaf #[
  ⟨0x7a03b01c80de06c03401900c005c02c01540a404e025011808603f01d80dc06602f015809c04601f00d805c02600f0058020008000, 0xac8010abfc16a209a8420abf810abf410abf010abec10abe816a0099fc20abe410abe010abdc167e082af6042af5042af4042af3042af2042af1042af0042aef042aee042aed042aec042aeb042aea042ae9059f420aba010ab9c1⟩,
  ⟨0x7203701a80ce06302f816c0b0054028013009004402080f407203501880b8054027012008403a01900a804801e00c0048018006000, 0xacc810acc416b0082b30042b2f042b2e05abc20acb410acb010acac10aca810aca416ae082b28042b27042b26042b2505ab420ac9016ac09aac26aa082b23042b22042b2105aa426a809a9c26a609a9426a409a8c2⟩,
  ⟨0x7a03b81cc0de06b033818c0c005c02c01540a204d024811408203d01c80d406402e015009804401e00d005802400f005801c008000, 0x6b6082b6c042b6b042b6a042b69042b6805ad420ad9c10ad9816b4082b65042b64042b63042b62042b61042b60042b3f042b3e05acc20acf410acf010acec10ace810ace410ace010acdc10acd816b2082b35042b3405ac420accc1⟩,
  ⟨0x7603901b80d6067031817c0b6057029813c096047022010007a03901a80c805e02b013809004201e00d805c02600f005801c008000, 0xae8810ae8416e0082ba0042b7f042b7e042b7d042b7c042b7b042b7a042b79042b7805afc20addc16be082b76042b7505af426bc082b74042b7305aec26ba09ae426b8082b72042b71042b70042b6f042b6e05adc20adb41⟩,
  ⟨0x7903a81c40da06903281840be05b02b81500a204d024811408203d01c80d406402e015009804601f00d805c02600f0058020008000, 0x2bbc042bbb042bba042bb9042bb8042bb705c0c2bb6042bb505b9426e4082bb4042bb3042bb2042bb1042bb0042baf042bae05b8c20aeb410aeb010aeac16e2082baa042ba9042ba8042ba7042ba6042ba505b8420ae9010ae8c1⟩,
  ⟨0x7603901b80d406703281840ba05b02b81500a004c024811408203d01c80d406202d015009804401f00d805c02600f005801c008000, 0xafd010afcc10afc816eb09e0c2bf1042bf005d0c2bef05ba820afb810afb416e9082bec042beb042bea042be9042be8042be7042be605ba020af9410af9016e7082be3042be2042be1042be0042bbf042bbe05b9820aef41⟩,
  ⟨0x7a03b01c80dc06a03301880bc05b02b814c09e04b023811008203e01d00d806402e015009804401e00d80600280100060020008000, 0xb0b810b0b410b0b010b0ac10b0a810b0a410b0a016f1082c27042c26042c25042c24042c2305bc026ef09bb820b08810b08410b08010affc10aff810aff410aff010afec16ed09bb020afe810afe410afe010afdc10afd810afd41⟩,
  ⟨0x7b03b81cc0de06b03401940c205d02c81540a404e025011808403e01d00d806402e015009804401e00d005802600f0058020008000, 0x2c69042c68042c67042c6605bd826f5082c65042c64042c63042c6205bd020b18410b18010b0fc10b0f810b0f410b0f010b0ec10b0e810b0e410b0e010b0dc10b0d810b0d410b0d010b0cc16f3082c32042c3105bc820b0c010b0bc1⟩
]

def tableRRLR : Table Block := .leaf #[
  ⟨0x7903a81c80dc06a03301880bc05a02b814c09e04b024011008003d01d00dc06602f015809c04601f00d805c02600f005801c006000, 0x2ca205bf420b28410b28010b1fc10b1f810b1f410b1f016fc082c7b042c7a042c7905bec20b1e010b1dc16fa09be426f8082c76042c75042c74042c73042c72042c71042c70042c6f042c6e042c6d042c6c042c6b042c6a05bdc2⟩,
  ⟨0x7203781ac0d006403001700b0054028013009004402080f807603701980bc056027012008403c01b00c005002000d005001c008000, 0x72b082cb405ca820b2cc10b2c810b2c410b2c010b2bc10b2b810b2b410b2b010b2ac172909ca02727082caa042ca9042ca8042ca7042ca605c98272509c90272309c8820b29410b290172109c8026ff09bf820b28c1⟩,
  ⟨0x7203701ac0ce06302f816c0b00550290138094047022010407c03b01c00d006002c014009404401e00d005c02600f005801c006000, 0xb3981739082ce5042ce4042ce3042ce205ce0273709cd820b38410b380173509cd0273309cc8273109cc020b2fc10b2f810b2f410b2f0172f09cb820b2ec10b2e8172d082cb9042cb8042cb7042cb6042cb505cb02⟩,
  ⟨0x7603981bc0d606703201800b805802a014409a049022810407c03b01b80cc06002c014009004001c00c005002000e005001c008000, 0x761082cfd042cfc042cfb05d8020b3e810b3e410b3e010b3dc173f082cf6042cf5042cf4042cf305cf8273d082cf2042cf105cf020b3c010b3bc10b3b810b3b410b3b010b3ac10b3a810b3a417c30b3a0173b09ce820b39c1⟩,
  ⟨0x7703981bc0d606803281880bc05a02b014809c04a023010c07e03b01c00d006002c014009404401e00d005802400f0060020008000, 0x2d34042d33042d3205da4276809d9c20b4c410b4c010b4bc10b4b810b4b410b4b010b4ac1766082d2a042d2905d9420b4a010b49c10b49810b49417640818030b49010b48c10b48810b484176309d8820b48010b3fc10b3f81⟩,
  ⟨0x7703981bc0d606803201800ba05902a814409a04a023810c07e03b01c00d006002c014009404401f00d805c02600f005801c006000, 0x2d6b042d6a042d6905dc820b5a010b59c1771082d66042d65042d64042d6305dc0276f082d62042d61042d6005db820b4fc10b4f810b4f410b4f0176d09db0276b082d3b042d3a042d39042d38042d37042d36042d3505da82⟩,
  ⟨0x7803a01c00d806803281840bc05a02b014809e04b023811008003c01c00d006202d014809404401e00d005802600f005801c006000, 0xb68c10b68810b68410b680177a082d7f05de420b5f810b5f410b5f01778082d7b042d7a05ddc20b5e410b5e010b5dc10b5d81776082d75042d74042d7305dd420b5c810b5c410b5c01774082d6f042d6e042d6d042d6c05dcc2⟩,
  ⟨0x7803a81c40da06903281880be05b02b814c0a004c024811808403e01d00dc06602f015809c04601f00d805c0280100060020008000, 0x610c2dbb042dba042db9042db805e8427a0082db7042db6042db505dfc20b6d0177e09df420b6cc10b6c810b6c4177c082db0042daf042dae042dad042dac042dab042daa042da905dec20b6a010b69c10b69810b69410b6901⟩,
  ⟨0x7a03b01cc0de06b033818c0be05b02b814c09e04b024011408203d01c80d406402e015009804401e00d005802400e005001c008000, 0xb7d417a7082df4042df3042df2042df1042df0042def042dee042ded042dec042deb05e9827a5082dea042de9042de8042de705e9020b79810b79410b79010b78c10b78810b78410b78010b6fc10b6f810b6f417a309e8820b6f01⟩
]

def tableRRL : Table Block := .branch 8 tableRRLL tableRRLR

def tableRRRL : Table Block := .leaf #[
  ⟨0x7b03b81d00e006c03401900c005c02c01500a004d024811408203d01c80d806402e015009804401e00d005c02600f0058020008000, 0x2e3005eb020b8bc10b8b810b8b410b8b010b8ac10b8a810b8a410b8a010b89c17ab082e26042e25042e24042e23042e2205ea820b88410b88010b7fc10b7f810b7f410b7f010b7ec17a9082dfa042df9042df805ea020b7dc10b7d81⟩,
  ⟨0x7b03c01d00e006c03401900c005c02c01500a204d024811408203e01d00d806402e015809c04601f00e00600280100060020008000, 0x1ec420b9ac10b9a810b9a410b9a010b99c10b99810b99410b99010b98c17b0082e62042e61042e60042e3f05ebc20b8f810b8f410b8f010b8ec17ae082e3a042e39042e3805eb420b8dc10b8d810b8d410b8d010b8cc10b8c810b8c41⟩,
  ⟨0x7603901b80d406603181800b805802a814409c04b023810c07e03b01b80cc05e02b013809004201d00d005c02600f005801c006000, 0xba8410ba8010b9fc10b9f817bb09ee820b9f410b9f017b9082e7b05ee027b7082e7a042e79042e78042e77042e76042e75042e74042e73042e7205ed827b5082e7105ed027b3082e70042e6f042e6e042e6d042e6c05ec82⟩,
  ⟨0x7603901b80d406603181800ba05902a814409a049022810407a03901b00c805c02a013008c04001d00d005c02600f005801c006000, 0xbadc10bad810bad410bad017e509f9027e3082eb3042eb2042eb1042eb0042eaf042eae042ead042eac042eab05f8820baa810baa410baa010ba9c17e109f8027bf09ef827bd082ea6042ea5042ea4042ea3042ea205ef02⟩,
  ⟨0x7103701ac0d006403001700b00550290138094047022010407c03b01c00d406202e015809c04601f00d80600280100060020008000, 0x1fd027f309fc820bba010bb9c10bb9810bb9417f109fc020bb9010bb8c17ef09fb827ed09fb027eb09fa827e9082ee205fa027e7082ee1042ee0042ebf042ebe05f9820baf410baf010baec10bae810bae410bae01⟩,
  ⟨0x7b03b81cc0e006c03401900c005c02c01500a004d024811408203d01c80d406202d014809804401e00d005802400e0058020008000, 0x2f23042f2205fe420bc8410bc8010bbfc10bbf810bbf410bbf010bbec10bbe817f8082ef9042ef8042ef7042ef6042ef5042ef4042ef3042ef2042ef105fdc20bbc010bbbc10bbb810bbb410bbb010bbac17f609fd420bba810bba41⟩,
  ⟨0x7a03b01c80dc06a03301880bc05a02b81500a204e025011808403e01d00d806402e015009804401f00d805c02600f005801c008000, 0x609420609020608c20608820bcdc10608420608020bcd817ff09ff827fd09ff020bcd410bcd010bccc10bcc810bcc410bcc010bcbc10bcb810bcb410bcb010bcac17fb082f2a042f29042f28042f27042f26042f2505fe820bc901⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x60c82060c420bda810bda410bda010bd9c10bd9810bd9410bd901060c020bd8c10bd881060bc20bd841060b82060b420bd8010bcfc10bcf810bcf410bcf010bcec10bce81060b020bce41060ac2060a82060a42060a020609c20609820bce01⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbde810bde410bde010bddc10618820618420618020bdd810bdd41060fc2060f82060f42060f020bdd01060ec2060e820bdcc1060e42060e02060dc2060d82060d420bdc810bdc41060d02060cc20bdc010bdbc10bdb810bdb410bdb010bdac1⟩
]

def tableRRRR : Table Block := .leaf #[
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xbeac10bea810bea410bea01061c42061c020be9c10be9810be941061bc2061b82061b420be901061b02061ac2061a82061a420be8c10be8810be8410be8010bdfc1061a020619c20619820619420619020bdf810618c20bdf410bdf010bdec1⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x61fc2061f820bef41061f420bef010beec10bee810bee410bee010bedc10bed810bed410bed010becc1061f020bec810bec41061ec2061e82061e420bec010bebc10beb810beb410beb01061e02061dc2061d82061d42061d02061cc2061c82⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x62a820bfc81062a420bfc410bfc010bfbc10bfb810bfb410bfb010bfac10bfa81062a020629c20629820629420629020bfa410bfa010bf9c10bf9810bf9410628c20bf9010bf8c10bf8810bf8410628820bf8010befc10bef81062842062802⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x62fc20bff41062f82062f420bff010bfec10bfe81062f020bfe41062ec2062e82062e420bfe010bfdc10bfd810bfd410bfd01062e020bfcc1062dc2062d82062d42062d02062cc2062c82062c42062c02062bc2062b82062b42062b02062ac2⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe0ac10e0a810e0a410e0a010e09c1063c420e09810e09410e09010e08c10e0881063c02063bc2063b82063b42063b020e08410e0801063ac20bffc10bff81063a82063a42063a020639c20639820639420639020638c2063882063842063802⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe18410e1801063ec2063e82063e42063e020e0fc10e0f810e0f410e0f010e0ec10e0e81063dc2063d820e0e410e0e010e0dc1063d42063d02063cc20e0d810e0d410e0d010e0cc10e0c810e0c410e0c010e0bc1063c820e0b810e0b410e0b01⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0xe1b41064bc2064b82064b42064b02064ac2064a82064a42064a020649c20649820649420e1b010e1ac10e1a810e1a410e1a010e19c10649020e19810e19410e19010648c2064882064842064802063fc2063f82063f420e18c10e1881063f02⟩,
  ⟨0x8003e01e00e807003601a00c806002e01600a8050026012008804001e00e006803001600a004802000e00600280100060020008000, 0x658820e1e81065842065802064fc20e1e41064f82064f42064f020e1e01064ec2064e820e1dc10e1d810e1d41064e42064e02064dc2064d820e1d010e1cc10e1c810e1c41064d420e1c01064d02064cc20e1bc1064c820e1b81064c42064c02⟩,
  ⟨0x600280100060020008000, 0x65a020659c20659820659420659020658c2⟩
]

def tableRRR : Table Block := .branch 9 tableRRRL tableRRRR

def tableRR : Table Block := .branch 17 tableRRL tableRRR

def tableR : Table Block := .branch 34 tableRL tableRR

def table : Table Block := .branch 68 tableL tableR

def records (i : Nat) : List Nat := PackedNatTable.records table i

end PolicyInitialCoverage1Tail

namespace PolicyInitialCoverage1
def records (cid : Nat) : List Nat :=
  if cid ≤ 0x10e1 then [0, cid - 1] else PolicyInitialCoverage1Tail.records (cid - 0x10e2)

def limits : Nat → Nat
  | 0 => 0x10e1
  | 1 => 0xc3b
  | 2 => 0x4a9
  | 3 => 34
  | _ => 0

def targets : Nat → Nat → Nat
  | 0, i => (PolicyCircuitPacked1.records i).headD 0
  | 1, i => (PolicyRewriteParametricPacked1.records i).headD 0
  | 2, i => (PolicyArithmeticPacked1.records i).headD 0
  | 3, i => (PolicyAssertedPacked1.records i).headD 0
  | _, _ => 0
end PolicyInitialCoverage1

end PolicySubmissionPart51

/- Component PackedNatHead; SHA256 eef459d79e09719dc8d62d18a6f1a4903e0d7d3ae951e2bd312a01e7f9060fc4. -/
section PolicySubmissionPart52
/- Read the first field without decoding the rest of a packed numerical record. -/
namespace CompactNatData

def headAux : Nat → Nat → Nat → Nat → Nat
  | 0, _, _, _ => 0
  | fuel + 1, packed, value, multiplier =>
      let digit := packed % 64
      let next := value + digit % 32 * multiplier
      if digit < 32 then next
      else headAux fuel (packed / 64) next (multiplier * 32)

def head (digits packed : Nat) : Nat := headAux digits packed 0 1

def read_preserves_first (fuel packed value multiplier first : Nat) (xs : List Nat) :
    ((read fuel packed (xs ++ [first], value, multiplier)).1.reverse).headD 0 = first := by
  induction fuel generalizing packed value multiplier xs with
  | zero => simp [read]
  | succ fuel ih =>
    by_cases h : packed % 64 < 32
    · simpa only [read, step, h, ↓reduceIte, List.cons_append] using
        ih (packed / 64) 0 1 ((value + packed % 64 % 32 * multiplier) :: xs)
    · simpa only [read, step, h, ↓reduceIte] using
        ih (packed / 64) (value + packed % 64 % 32 * multiplier) (multiplier * 32) xs

def headAux_eq (fuel packed value multiplier : Nat) :
    headAux fuel packed value multiplier =
      ((read fuel packed ([], value, multiplier)).1.reverse).headD 0 := by
  induction fuel generalizing packed value multiplier with
  | zero => rfl
  | succ fuel ih =>
    by_cases h : packed % 64 < 32
    · simp only [headAux, read, step, h, ↓reduceIte]
      symm
      simpa only [List.nil_append] using
        read_preserves_first fuel (packed / 64) 0 1
          (value + packed % 64 % 32 * multiplier) []
    · simpa only [headAux, read, step, h, ↓reduceIte] using
        ih (packed / 64) (value + packed % 64 % 32 * multiplier) (multiplier * 32)

def head_eq_decode_head (digits packed : Nat) :
    head digits packed = (decode digits packed).headD 0 :=
  headAux_eq digits packed 0 1

end CompactNatData

namespace PackedNatTable

def Block.head (b : Block) (i : Nat) : Nat :=
  let first := b.start i
  let count := b.start (i + 1) - first
  let packed := (b.data >>> (6 * first)) &&& ((1 <<< (6 * count)) - 1)
  CompactNatData.head count packed

def Block.head_eq_get_head (b : Block) (i : Nat) :
    b.head i = (b.get i).headD 0 :=
  CompactNatData.head_eq_decode_head _ _

def recordHead (t : Table Block) (i : Nat) : Nat :=
  (t.get emptyBlock (i / 32)).head (i % 32)

def recordHead_eq (t : Table Block) (i : Nat) :
    recordHead t i = (records t i).headD 0 :=
  Block.head_eq_get_head _ _

def recordHead16 (t : Table Block) (i : Nat) : Nat :=
  recordHead t (32 * (i / 16) + i % 16)

def recordHead16_eq (t : Table Block) (i : Nat) :
    recordHead16 t i = (records t (32 * (i / 16) + i % 16)).headD 0 :=
  recordHead_eq _ _

end PackedNatTable

end PolicySubmissionPart52

/- Component PolicyInitialFastCoverageData; SHA256 7e066da35b905ca0598de0f98f0ae298580a1cbeec91f8236c07a747b57f5c85. -/
section PolicySubmissionPart53
namespace PolicyInitialFastCoverage0
open PackedNatTable

abbrev records := PolicyInitialCoverage0.records
abbrev limits := PolicyInitialCoverage0.limits

def targets : Nat → Nat → Nat
  | 0, i => recordHead PolicyCircuitPacked0.table i
  | 1, i => recordHead16 PolicyRewriteParametricPacked0.table i
  | 2, i => recordHead16 PolicyArithmeticPacked0.table i
  | 3, i => (PolicyAssertedPacked0.records i).headD 0
  | _, _ => 0

def targets_eq (k i : Nat) : targets k i = PolicyInitialCoverage0.targets k i := by
  match k with
  | 0 => exact recordHead_eq PolicyCircuitPacked0.table i
  | 1 => exact recordHead16_eq PolicyRewriteParametricPacked0.table i
  | 2 => exact recordHead16_eq PolicyArithmeticPacked0.table i
  | 3 => rfl
  | k + 4 => rfl

end PolicyInitialFastCoverage0


namespace PolicyInitialFastCoverage1
open PackedNatTable

abbrev records := PolicyInitialCoverage1.records
abbrev limits := PolicyInitialCoverage1.limits

def targets : Nat → Nat → Nat
  | 0, i => recordHead PolicyCircuitPacked1.table i
  | 1, i => recordHead16 PolicyRewriteParametricPacked1.table i
  | 2, i => recordHead16 PolicyArithmeticPacked1.table i
  | 3, i => (PolicyAssertedPacked1.records i).headD 0
  | _, _ => 0

def targets_eq (k i : Nat) : targets k i = PolicyInitialCoverage1.targets k i := by
  match k with
  | 0 => exact recordHead_eq PolicyCircuitPacked1.table i
  | 1 => exact recordHead16_eq PolicyRewriteParametricPacked1.table i
  | 2 => exact recordHead16_eq PolicyArithmeticPacked1.table i
  | 3 => rfl
  | k + 4 => rfl

end PolicyInitialFastCoverage1

end PolicySubmissionPart53

/- Component PolicyInitialFastCoverageChecked0; SHA256 9c3ecf84539503e41282c7d3076d3588a58332ab219a7e580e8312317264a36f. -/
section PolicySubmissionPart54
namespace PolicyInitialFastCoverage0
open ClosureCoverage

def test (start count : Nat) : Bool := checkBlock limits targets records start count

def checked0 : test 1 0x80 = true := by
  decide +kernel

def checked1 : test 0x81 0x80 = true := by
  decide +kernel

def checked2 : test 0x101 0x80 = true := by
  decide +kernel

def checked3 : test 0x181 0x80 = true := by
  decide +kernel

def checked4 : test 0x201 0x80 = true := by
  decide +kernel

def checked5 : test 0x281 0x80 = true := by
  decide +kernel

def checked6 : test 0x301 0x80 = true := by
  decide +kernel

def checked7 : test 0x381 0x80 = true := by
  decide +kernel

def checked8 : test 0x401 0x80 = true := by
  decide +kernel

def checked9 : test 0x481 0x80 = true := by
  decide +kernel

def checked10 : test 0x501 0x80 = true := by
  decide +kernel

def checked11 : test 0x581 0x80 = true := by
  decide +kernel

def checked12 : test 0x601 0x80 = true := by
  decide +kernel

def checked13 : test 0x681 0x80 = true := by
  decide +kernel

def checked14 : test 0x701 0x80 = true := by
  decide +kernel

def checked15 : test 0x781 0x80 = true := by
  decide +kernel

def checked16 : test 0x801 0x80 = true := by
  decide +kernel

def checked17 : test 0x881 0x80 = true := by
  decide +kernel

def checked18 : test 0x901 0x80 = true := by
  decide +kernel

def checked19 : test 0x981 0x80 = true := by
  decide +kernel

def checked20 : test 0xa01 0x80 = true := by
  decide +kernel

def checked21 : test 0xa81 0x80 = true := by
  decide +kernel

def checked22 : test 0xb01 0x80 = true := by
  decide +kernel

def checked23 : test 0xb81 0x80 = true := by
  decide +kernel

def checked24 : test 0xc01 0x80 = true := by
  decide +kernel

def checked25 : test 0xc81 0x80 = true := by
  decide +kernel

def checked26 : test 0xd01 0x80 = true := by
  decide +kernel

def checked27 : test 0xd81 0x80 = true := by
  decide +kernel

def checked28 : test 0xe01 0x80 = true := by
  decide +kernel

def checked29 : test 0xe81 0x80 = true := by
  decide +kernel

def checked30 : test 0xf01 0x80 = true := by
  decide +kernel

def checked31 : test 0xf81 0x80 = true := by
  decide +kernel

def checked32 : test 0x1001 0x80 = true := by
  decide +kernel

def checked33 : test 0x1081 0x80 = true := by
  decide +kernel

def checked34 : test 0x1101 0x80 = true := by
  decide +kernel

def checked35 : test 0x1181 0x80 = true := by
  decide +kernel

def checked36 : test 0x1201 0x80 = true := by
  decide +kernel

def checked37 : test 0x1281 0x80 = true := by
  decide +kernel

def checked38 : test 0x1301 0x80 = true := by
  decide +kernel

def checked39 : test 0x1381 0x80 = true := by
  decide +kernel

def checked40 : test 0x1401 0x80 = true := by
  decide +kernel

def checked41 : test 0x1481 0x80 = true := by
  decide +kernel

def checked42 : test 0x1501 0x80 = true := by
  decide +kernel

def checked43 : test 0x1581 0x80 = true := by
  decide +kernel

def checked44 : test 0x1601 0x80 = true := by
  decide +kernel

def checked45 : test 0x1681 0x80 = true := by
  decide +kernel

def checked46 : test 0x1701 0x80 = true := by
  decide +kernel

def checked47 : test 0x1781 0x80 = true := by
  decide +kernel

def checked48 : test 0x1801 0x80 = true := by
  decide +kernel

def checked49 : test 0x1881 0x80 = true := by
  decide +kernel

def checked50 : test 0x1901 0x80 = true := by
  decide +kernel

def checked51 : test 0x1981 0x80 = true := by
  decide +kernel

def checked52 : test 0x1a01 0x80 = true := by
  decide +kernel

def checked53 : test 0x1a81 0x80 = true := by
  decide +kernel

def checked54 : test 0x1b01 0x80 = true := by
  decide +kernel

def checked55 : test 0x1b81 0x80 = true := by
  decide +kernel

def checked56 : test 0x1c01 0x80 = true := by
  decide +kernel

def checked57 : test 0x1c81 0x80 = true := by
  decide +kernel

def checked58 : test 0x1d01 0x80 = true := by
  decide +kernel

def checked59 : test 0x1d81 0x80 = true := by
  decide +kernel

def checked60 : test 0x1e01 0x80 = true := by
  decide +kernel

def checked61 : test 0x1e81 0x80 = true := by
  decide +kernel

def checked62 : test 0x1f01 0x80 = true := by
  decide +kernel

def checked63 : test 0x1f81 0x80 = true := by
  decide +kernel

def checked64 : test 0x2001 0x80 = true := by
  decide +kernel

def checked65 : test 0x2081 0x80 = true := by
  decide +kernel

def checked66 : test 0x2101 0x80 = true := by
  decide +kernel

def checked67 : test 0x2181 0x80 = true := by
  decide +kernel

def checked68 : test 0x2201 0x80 = true := by
  decide +kernel

def checked69 : test 0x2281 0x80 = true := by
  decide +kernel

def checked70 : test 0x2301 48 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (1 + 0x80 * i) (min 0x80 (0x2330 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (1 + 0x80 * i) (min 0x80 (0x2330 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 71 → test (1 + 0x80 * i) (min 0x80 (0x2330 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67
  · exact checked68
  · exact checked69
  · exact checked70

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 71 → test (1 + 0x80 * i) (min 0x80 (0x2330 - 0x80 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 32 71
  checkedRange0
  (Bounty.policyIntervalJoin _ 32 64 71
  checkedRange32
  checkedRange64))

def checked (i : Fin 71) :
    test (1 + 0x80 * i.val)
      (min 0x80 (0x2330 - 0x80 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def covers (P : Nat → Prop)
    (hs : ∀ k, k < 4 → ∀ i, i < limits k → P (targets k i))
    (cid : Nat) (hp : 0 < cid) (hi : cid < 0x2331) : P cid := by
  have hb : (cid - 1) / 0x80 < 71 := by omega
  have hw : (cid - 1) % 0x80 < min 0x80 (0x2330 - 0x80 * ((cid - 1) / 0x80)) := by omega
  have h := checkBlock_sound P limits targets hs records (1 + 0x80 * ((cid - 1) / 0x80))
    (min 0x80 (0x2330 - 0x80 * ((cid - 1) / 0x80)))
    (checked ⟨(cid - 1) / 0x80, hb⟩) ((cid - 1) % 0x80) hw
  have hid : 1 + 0x80 * ((cid - 1) / 0x80) + (cid - 1) % 0x80 = cid := by omega
  simpa only [hid] using h
def covers_original (P : Nat → Prop)
    (hs : ∀ k, k < 4 → ∀ i, i < PolicyInitialCoverage0.limits k → P (PolicyInitialCoverage0.targets k i))
    (cid : Nat) (hp : 0 < cid) (hi : cid < 0x2331) : P cid := by
  apply covers P ?_ cid hp hi
  intro k hk i hi
  rw [targets_eq]
  exact hs k hk i hi

end PolicyInitialFastCoverage0

end PolicySubmissionPart54

/- Component PolicyFixedHintData; SHA256 c690738d5de43a4cf40d37d29520372e0da72d43be2d02f6ab8ef26571acd008. -/
section PolicySubmissionPart55
/- Direct fixed-width hint IDs, decoded in bounded pieces. -/
namespace Bounty

def policyFixedHintPart : Nat → Nat → List Nat → List Nat
  | 0, _, result => result
  | n + 1, packed, result =>
      policyFixedHintPart n (packed >>> 15) ((packed &&& 0x7fff) :: result)

def policyFixedHintChunks : Nat → Nat → Nat → List Nat → List Nat
  | 0, _, _, result => result
  | fuel + 1, count, packed, result =>
      if count = 0 then result else
      let n := min count 0x200
      let piece := packed &&& ((1 <<< (15 * n)) - 1)
      policyFixedHintChunks fuel (count - n) (packed >>> (15 * n))
        (policyFixedHintPart n piece result)

def policyFixedHintDecode (record : Nat) : List Nat :=
  let count := record &&& 0xfff
  (policyFixedHintChunks (count / 0x200 + 1) count (record >>> 12) []).reverse

end Bounty

end PolicySubmissionPart55

/- Component PolicySharedUnitFixedData; SHA256 3501536e8e2b15531313db07b32b470bb05d3a42d498e425e679046e6d4b365a. -/
section PolicySubmissionPart56
/- The same shared-unit certificate with directly packed fixed-width hint IDs. -/
namespace Bounty

def policySharedUnitFixed0Clauses : PackedNatTable.Table PackedNatTable.Block :=

(.branch 23 (
(.branch 11 (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x9840978097408a408900888088408820830082808240820080a078606d006ac059e059a053c0530052c04f404dc04d804ca04c804c404b2039603860382033e⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xf340f320e8a0e840da60da40d780d700d320d2a0cb20c9a0c860c7e0c7a0c5a0c560c520bc80bc00b9e0afe0a400a280a240a140a1009fe09f209ee09c609c2⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1370136c133c1336130812dc12d812ca12ba12b612b212861280125011a410e210de10a0109e1078107610721062102a101c10180fd20fc80fb00f9c0f520f4e⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x19b8190c18f21868181c177e170c170216fe16bc16861682163e162015f215e415e015c415c015ae15901550154814a4149c144a13d213c0139c138613841380⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1fe01fdc1f801f7e1f3c1f281f0a1ee81ec21ec01ea81e3c1e381e2c1d5a1d541d521d4e1c901b8e1a661a621a2a1a1a1a061a0019fe19fa19ea19e619c819c4⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x25ae25902550254c2548252624c824a824a6245c23f023ec23a623a22390238223302290228c225e224a222821c221ba21b621a8219c211220ee205620522044⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2c342b302ac02a9e2a962a922a8229a0296c29682952293e292e290428f828a2289e2880286c2866284c28482844281e281a280427e027bc2732272c26a225be⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x33b23382332a32c4329e32743262321c321831fc31f03166313230e430ca30c830a03022301c2ff82f882ee22ec82ec22e202e1a2d6c2d0c2d0a2ca42ca22c3a⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x383a37e837b436cc36b83686365a3656364836463642363a3626361a360a35ec35de35b03596355a3552353e353a352c352a351e351434ee34e63486342833f0⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3cf23ce43caa3c9a3c023bf63bcc3bc83ba43b8a3b743b4c3b143b0a3ae43a763a4039fc39f039e639dc39d639c239963930392c38dc38d43892388e38863880⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x17e05ba000204fc04980004045803ba034802de029e027641ae417040d240ba3f7e3ed43ec03e703e543dfe3dde3dd43dc83dc63dc23db63d663d3e3d3a3d24⟩]))))) (
(.branch 6 (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x135012be12aa12a01274123810420f680ee60ed40e6a0dbe0d360c880c280bde0b5e0aea0aac0aa20a6e09f6091e076c074c06d60648063a0634061e05fe05f0⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2442242a23d623862236221e220421d22130210420221f861f331ece1e501cc81cba1c1a1c0619ce19281902183a17da17ce176e16e6165216321576142013ac⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2ed82eaa2e9e2e402e362e102daa2d982d902d442d002c442c2a2b8a2a722a062998297e2910284e27ee271626aa2698266c2616260425e82578250424ba244e⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2510223021301fd01e701d701bf01a53f8c3e4a3d323c203b0c3a5e38ac36d83582356e352e350034c234b0348e347c341a31d431563144311c30d4306e2fae⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xbe10b090a890a710a4f0a2d09f909d5098b094b09350921087907ff07ed06fd06f106df05f305a5051304ff04830471045b042b03c3039b0355032d02e102b7⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x138b1353134312f7125d1215120311e711d511a9118b116f115f1149111d110710891045102f0fff0fdd0fb50f6b0f170ee90ebf0e6d0e3b0ded0dd30d390cd9⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1cff1c851c771c2d1bdd1b9f1b931b771b571b371b011aeb1adb1a9f1a831a7119ab192b18df180317ef16691579150914f914e314cd14bd14ab148313db13af⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x266f2641262b25f525eb25cb247d234922d5229722632153210720c720b120a12099208b20131fed1f5f1f3f1efd1eed1ed11e591db51da51d791d631d251d0f⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2d472d3b2d2d2d032cc92c812c712c5b2c4d2bf52bab2b492a5b2a1f2a0929eb29db29cd29b728db27f127cd27ab2775274b271926f526df26c726b526ad2679⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x382f381937d53675359b358534cb34913461341d339d3291323131af319f312530d7307b30552fe32fb12f692f592f052ee92ead2e832e6d2e572dcf2d712d4f⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x21c02141b5001fe1b4c01e801e001d809e801c04179412b411340754059402b3fd13faf3f953f353ee33e893e2d3d0f3c773c673c533b3f3aa5399b395f38f3⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x87a07c2078c07362a5406fe074406f206e00698052605140dcc0484047a0472151c042c040403e80de603c403ad03a4039c05320356191c030e02fa1b6c0224⟩]))))))) (
(.branch 12 (
(.branch 6 (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xfde1dd00fb60f840f260f180f02160c0e3c1d400dee15640dd40cf40cda0b260b420b0a0aba1cf80a2e0f7a09d60994098c0ab2094c0f2a093608ea08ce08a9⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x14ac182a13dc246c138c1b4612f812e61232120411f811e811de11d611fc11ce11aa11f411701168116011f0114a1126111e1bbc110812c410e41a5a10300ff4⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1b5823f61b381b201b301b0228581aec1ae41adc1ab41a841aae1a721a302b2a17f0178816cc15ca159a1608150a150214fa15f414e415fc14ce15f814be30b2⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x20c820be20b2206821141fee355c1f6023f21e5a1e141f7228861d7a28821d641d481d261d441d101d081d001c4437901c2e34e21bde1bb61ba01bb21b942194⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2a3e29b829ae28dc28c427b427ac27902764274c26fe26f6272026e0272426c82fba26b62954267a30142642285425f6241028d422d62f922264220a21e02128⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2eea2e8c2e842f1e2e6e2f1a2e582f222dec2d7232142d5031e22cca2c9a2c822c7a2c722c962c5c2c9e2c4e2bcc2b4a2a882a5c2a3629ec29e429dc2a3a29ce⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3a04397a391238403e7236a8367e36763f20359c34de34cc34983462333632ac31bc317c3b283bbe315c312630f030562ff02fe42fc22f762f362f282f062efe⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3aa024e824c425703bd83f1840b641761fbe127c0e9c3b60090808aa07ac0cb6086403ae192003504194407e40764064403c3fec3f503efe3ea43f2c3c823c2a⟩, ⟨0x52025811c08a04101d80c8056025012008c044021010007c034016008003801a00c0058028012008003801800a0040018008002000, 0x5ef0a690955091507490869015e2cc132013b1a32080242026639b339cd3940394e29ad342b372f340f3f97393400d835350f7f0457044304ad04ec1cd500eb02d5354135351cd50f7f029502d1124512371011105a1085008a139e136913641faa41ac0c9206c70b91070d0b8f0c3b0b8f0b910c3b01390c3b0c1d0b910b8f079f01370b910cac41b41d3c08b8085e03d208b703d10b460b20067e3de30b1f0d5005ce⟩]) (
.leaf #[⟨0x7703b01c80e207003401800b4054027813809804a02200f807603901b80d806a034019009004601c00d803c01c00d0060028006000, 0x5b806130b910b8f0c3b06710678013c0ca60caa0b8c0cad0bd20ca801240f670fa90f630ec10e65030902f50b540f672bc72bc53191319a14c90b8b0b8f0b930b910bd40b560b8f0b930b910b8b0b5d132e1ce3289a0e770e66091508690955074905ef0aa8091508690955074905ef015c091d09870954015c01630a470a6805860366161c17c6009c238f238d0b8b0fd7028d10390e4f0e5503650dab0b8f0b910e5100a7235e067019df19bb028d195b1a02012f198824692405241f0e5503650dab238d0b8f238f0b910b8b23fd1a971a9416dc027509180f7709be09f5360738c10ef713d50e740e660e77⟩, ⟨0x52027012408c04001d80e807203801b80d806a03301900c406002f01700b405802b01500a404801f00a80500260120058008002000, 0x5231ecd2d5f04531fad23dd1dc1147f1eab089c08590893286f1cef1d5d1cde3c9c1d8e20891555155f1525156e2ca623662cba2cb0258825a2129d1298338e32ee105b10560ff00a831a10193c1a0314782005212720df285e0184290735490fd725c615b429ad342b340f393415932082212720df20052a04195a19de19ba0a0909f509bb0ef70ec10f3b097e0a990b5d0dab0b8f0bd10b910b8b0e670db613a205c9⟩, ⟨0x7503781b80da06c03581a80c005f02f016c0b4057028012c08c04502100fc07603701880a805002701300480220100078014004000, 0x352724fb0e610e69352500cb137a2623247224f62540387323c123bf1211184d103b12451237106500a718a4187e2ab501842004101003a9153715250a0d091d0fa909cd38c1360713d505ef0749086908a1086d0d4c06c70c3b070d0cee0d6c09550aa80b3c074905ef0645074905ef06450137074905ef064501380749071305ef0645062b012f09550aa805ef074905ec08a10869243e0114230419f428fd0f7f1cd529060ef70a0d091d38c13cd50fa909bb267527610955222b226d222d0a69230519f5228422a623370a470dab0e550b8f0bd10b910b8b0365095809601cef1d911ce408360b3c⟩]))))) (
(.branch 6 (
(.branch 3 (
.leaf #[⟨0xb105782b01440a10500278132097047023411808803d81c00d806603281900c0057029812006e030017007c038015005002000e000, 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⟩, ⟨0xd406883341980c205d02d81680aa053028011e08e046823011608503f81ec0ee06a02e016008e035013809004402000d804000c000, 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⟩, ⟨0xe5071834c1a40c805c02cc14a097049021810808203a01c40da06802d013c094047021810808203e01a807802e0130060024006000, 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⟩]) (
.leaf #[⟨0x1550a5851c28a13809a84c024411608203c01be0cf06582cc13408604101c40da06b034817409c04001900a40480110030014006000, 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⟩, ⟨0x1870b2053028013f09f04e426812208804141de0eb073034c1980c205e82a814009904001a80b405402400a801e00e0048014006000, 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⟩, ⟨0x1d70de06bc35419f0c9863c30a17a0b6858c2b214e0a304ec25c11a07c03a41b60be05982ac10a06002c813409004401c80a8020000, 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⟩]))) (
(.branch 3 (
.leaf #[⟨0x6f03701b40d806b03501a40d006703301940c806303101840c005f02f01740b805b02d01640b005702b013c08e02f0120068016000, 0x2a270b8e0e2327150d35091c1fc10cef0a171fc20b6920ba1d381fc52a6e1bba31ce0b5c0bd00b54016401680b3c3b4e09543b4f05ef091507490e65030909553b4f05ef0749091503090e65095509ab156b0457152123ad23ab34be0915030928d30e653521074905ef2d4309630b5c0efb2a310a4d0e690e610fd710391fc31a57352735251a2110390fd718d50e690e61028d0e510915030928d30e653521074905ef2d4320f8012132ed05ef0a0d0ee4091d09552d430915030928d30e653521074937bf1fc2261e29092fff006d2dc13be62d9e2f542f9f2921260c⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1194368c0b901c730ee11592044a21921b660cbd044911841b8509d037390a0c0446118729ac0a2104ee29b32a8c1fc820f9351a2a28267434420456271232a4⟩, ⟨0x4301f80ec07203501900b805402000e006c02e0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x25c5156b03a9154a20df2127156b044e044e04f9044304ad04a1044e028d0100044f20df204b285e200500e0028d044f0100241f238f238d24052a3503650e552809245f23fd22130a6921f30121222c0a9e0e550365015d0e650e610aa90daa3a313a423a2b0c6a27600b8a27c1286e1cee1ced1c283798379700be00b1342a340e340d04ed⟩]) (
.leaf #[⟨0xa3051028413209404581f80f007503901b40d60570298134094047022010407603301800bc05c02a01400840300140058028010000, 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⟩, ⟨0xba05902c015a0a8052027812e09204602180fc07903a01c00d406402e016c09c04a023011407803a018009c04802200b005001a000, 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⟩, ⟨0x240120090048024012009004802401200900480240120090046022010808003e01e00e807003401600a8050026012007001c00a000, 0xd902a70442044104ac04f701200115242323fd238d238f044f028d13f80e540364015f1413145d0e55036503650e55044300d804ad00eb012102d5044e1413145d0e5503650fd7⟩]))))))))

def policySharedUnitFixed0Db (i : Nat) : List Int :=
  if i < 0x2331 then policyFixedCompact0Db i
  else policyFixedClauseDatabase 16 policySharedUnitFixed0Clauses (i - 0x2331)

def policySharedUnitFixed0HintLeaf0 : PackedNatTable.Table Nat := .leaf #[
0x47fc8ff11fd003,
0x9091211002,
0x909a332002,
0x485c90b1211003,
0x92e925c002,
0x9311261002,
0x931a336002,
0x9321261002,
0x9351269002,
0x935a339002,
0x49c89389269003,
0x940127f002,
0x940a33c002,
0x4a14942127f003,
0x4a6094b9296003,
0x4a6c94d1296003
]

def policySharedUnitFixed0HintLeaf1 : PackedNatTable.Table Nat := .leaf #[
0x96b12d5002,
0x4b8096f92de003,
0x4c40987930e003,
0x4cc0997932e003,
0x4ce499c1337003,
0x99d933a002,
0x99e2346002,
0x4cfc99f133a003,
0x9aba346002,
0x9ac2332002,
0x9ad1359002,
0x9ae935c002,
0x9b19337002,
0x9cc1397002,
0x9cca34e002,
0x9ce9397002
]

def policySharedUnitFixed0HintLeaf2 : PackedNatTable.Table Nat := .leaf #[
0x9d593aa002,
0x9d62351002,
0x9db13aa002,
0x9dba353002,
0x9dd139a002,
0x9e093c0002,
0x9e12356002,
0x9e393c0002,
0x9e42358002,
0x9e7a356002,
0x50009ff932e003,
0x5090a119420003,
0xa151429002,
0xa16142b002,
0xa241447002,
0xa24a35f002
]

def policySharedUnitFixed0HintLeaf3 : PackedNatTable.Table Nat := .leaf #[
0x512ca251447003,
0xa291451002,
0xa29a362002,
0x5158a2a9451003,
0xa2e1420002,
0x518ca311440003,
0x520ca411481003,
0x521ca431485003,
0xa4a1451002,
0xa4c9447002,
0xa5514a7002,
0xa55a36b002,
0x536ca6d14d9003,
0x5378a6e94dc003,
0xa841507002,
0xa84a36f002
]

def policySharedUnitFixed0HintLeaf4 : PackedNatTable.Table Nat := .leaf #[
0xa87150d002,
0xa8794d9002,
0x548ca911521003,
0x54a0a939521003,
0xa98236f002,
0x54d0a999507003,
0xaa19542002,
0xaa22377002,
0xaa39542002,
0x5550aa99552003,
0xaab9552002,
0xaac237b002,
0xaac9552002,
0xab21563002,
0xab2a37e002,
0x55d0ab99572003
]

def policySharedUnitFixed0HintLeaf5 : PackedNatTable.Table Nat := .leaf #[
0x55d8aba9572003,
0x5684ad0159f003,
0x572cae515c9003,
0xaee95dc002,
0xaef95c9002,
0xaf515e9002,
0xaf5a386002,
0x57b4af615e9003,
0x57c8af89563003,
0xafb11fd002,
0xafba38a002,
0xb011601002,
0xb051609002,
0xb061609002,
0xb0c1617002,
0xb0ca38f002
]

def policySharedUnitFixed0HintLeaf6 : PackedNatTable.Table Nat := .leaf #[
0xb0e1617002,
0xb0ea391002,
0xb0fa38f002,
0x5894a9a94dc003,
0xb15962a002,
0x58c0b17962a003,
0x593cb271649003,
0x597cb2f165d003,
0xb31165d002,
0xb451689002,
0xb46168b002,
0x5a74b4e169b003,
0xb532339002,
0xb56168b002,
0xb56a39e002,
0xb5b16b5002
]

def policySharedUnitFixed0HintLeaf7 : PackedNatTable.Table Nat := .leaf #[
0xb5ba3a0002,
0x5af0b5d96b5003,
0xb651601002,
0x5b48b6896d0003,
0xb7196e2002,
0xb7223a5002,
0x5bc4b7816ef003,
0xb8016ff002,
0xb80a3a8002,
0x5c14b8216ff003,
0x5ca0b939726003,
0x5d3cba7174d003,
0x5d88bb0975d003,
0x5e10bc19782003,
0x5e2cbc51789003,
0xbda97b4002
]

def policySharedUnitFixed0HintLeaf8 : PackedNatTable.Table Nat := .leaf #[
0xbdc97b4002,
0xbdd23b1002,
0xbe017bf002,
0xbe0a3b3002,
0xbe217bf002,
0xbe2a3b5002,
0xbe323b3002,
0xbe597ca002,
0x5f40be797ca003,
0x5f50be996d0003,
0xbf097e0002,
0xbf123bb002,
0x60a4c141827003,
0x6194c321863003,
0xc4b1895002,
0xc4ba3bf002
]

def policySharedUnitFixed0HintLeaf9 : PackedNatTable.Table Nat := .leaf #[
0xc4c2358002,
0x626cc4d1899003,
0x6328c6498c8003,
0xc6618c8002,
0xc66a3c4002,
0xc7118e1002,
0x63a0c7398e6003,
0xc7498e6002,
0x63d0c7998f2003,
0xc7e23c4002,
0x6408c809900003,
0x6420c839906003,
0x6474c8e191b003,
0xc8fa386002,
0xc9b9936002,
0xc9c23cf002
]

def policySharedUnitFixed0HintLeaf10 : PackedNatTable.Table Nat := .leaf #[
0x6538ca6994c003,
0xca8994c002,
0xca923d2002,
0x65e4cbc1977003,
0x6610cc19982003,
0xcd499a8002,
0xcd6a3d2002,
0xcd899b0002,
0xcd923d8002,
0xcdba377002,
0x6748ce899d0003,
0xcec19d7002,
0x6774cee19d7003,
0xcf399e6002,
0xcf423de002,
0xd071a0d002
]

def policySharedUnitFixed0HintLeaf11 : PackedNatTable.Table Nat := .leaf #[
0x688cd111a20003,
0xd1423a8002,
0x68acb52969b003,
0xd169a2c002,
0x6904d201a3f003,
0x690cd211a3f003,
0x697cd2f1a5d003,
0x69c4d381a6b003,
0xd391a6b002,
0x6a00d3f9a5d003,
0x6a60d4b9a93003,
0xd4f1a9d002,
0xd4fa3ec002,
0x6a84d501a9d003,
0xd589ab0002,
0x6aecd5d17b4003
]

def policySharedUnitFixed0HintLeaf12 : PackedNatTable.Table Nat := .leaf #[
0x6afcd5f1782003,
0x6bccd791af1003,
0x6c58d8a9b14003,
0x6c64d8c1b17003,
0x6cf8d9e9b3c003,
0x6d20da39b46003,
0xdaa9b54002,
0xdae1b5b002,
0xdaea3f8002,
0xdb39b5e002,
0xdb41982002,
0xdb4a3fb002,
0xdb99990002,
0x6dd8dba9b74003,
0xdbe1b7b002,
0xdc19b74002
]

def policySharedUnitFixed0HintLeaf13 : PackedNatTable.Table Nat := .leaf #[
0xdc22400002,
0x6e68dcc9b98003,
0x6e74dce1b98003,
0x6e94dd21af1003,
0x6ea8dd49ba8003,
0x6ebcdd71b14003,
0xdda9b46002,
0xddb2407002,
0xddf9bbe002,
0x6fdcdfb1bf5003,
0xdff9bfe002,
0xe00240b002,
0xe022351002,
0xe0a2336002,
0xe19a362002,
0x71e0e3b9c76003
]

def policySharedUnitFixed0HintLeaf14 : PackedNatTable.Table Nat := .leaf #[
0x71ece3d1c79003,
0xe4aa40b002,
0xe4b23b1002,
0xe591cb1002,
0xe59a414002,
0x7320e639cc6003,
0x73d0e799cf2003,
0x73dce7b1cf5003,
0x7474e8e1d1b003,
0x7480e8f9d1e003,
0x749ce931d25003,
0xea8a3ec002,
0x75b0eb59d6a003,
0xebb1d75002,
0x75e4d4a1a93003,
0x7658eca9d94003
]

def policySharedUnitFixed0HintLeaf15 : PackedNatTable.Table Nat := .leaf #[
0xed21da3002,
0xed2a421002,
0x76b0ed59daa003,
0x7704ee01dbf003,
0x7738ee69dcc003,
0xef82414002,
0x77ccef91cb1003,
0xefd23cf002,
0x77f0efd9cc6003,
0xf061e0b002,
0x7844f081e0f003,
0xf0d1e19002,
0x7890f119e22003,
0x78fcf1f1e37003,
0x7948f289e4f003,
0x7974f2e1e5b003
]

def policySharedUnitFixed0HintLeaf16 : PackedNatTable.Table Nat := .leaf #[
0x79b0f359e6a003,
0x79f4f3e1e7b003,
0x7a60f4b9e96003,
0xf5823b8002,
0xf5aa38d002,
0x7af4f5e1bfe003,
0xf601ebf002,
0xf61a3dc002,
0xf62a3b5002,
0xf651b85002,
0x7b38f669609003,
0x7b4cf691789003,
0xf6da395002,
0x7ba0f739ee6003,
0x7bc4f781ee6003,
0x7bf0f7d9d5c003
]

def policySharedUnitFixed0HintLeaf17 : PackedNatTable.Table Nat := .leaf #[
0x7c00f7f9b17003,
0xf85a391002,
0xf881f0f002,
0xf899f12002,
0xf8ea33c002,
0x7c84bf917e0003,
0xf9123bb002,
0xf91965d002,
0xf949ea2002,
0xf952449002,
0x7cd0f999f32003,
0xfa1a3a5002,
0x7d20fa39f44003,
0x7e40fc79f8e003,
0x7e80fcf9f9e003,
0x7eccfd91fb1003
]

def policySharedUnitFixed0HintLeaf18 : PackedNatTable.Table Nat := .leaf #[
0x7f0cfe11977003,
0xfe2997b002,
0xfe41b72002,
0xfe4a399002,
0xfed1fd9002,
0xfee1fdb002,
0xffd237b002,
0x7ff0ffd9cd8003,
0x805d00b2015003,
0x808d0112021003,
0x80b1015a02a003,
0x101823d8002,
0x80dd01b13f0003,
0x101e23fb002,
0x80fd01f1e6f003,
0x10279e0a002
]

def policySharedUnitFixed0HintLeaf19 : PackedNatTable.Table Nat := .leaf #[
0x816d02d2059003,
0x82150421e0f003,
0x823d0471e0b003,
0x824d026a04c003,
0x10569b85002,
0x830d0611d4a003,
0x1065a34e002,
0x8349068a071003,
0x836d06d1dd3003,
0x8378f281e4f003,
0x83a50741d3a003,
0x83c10779de1003,
0x1093a353002,
0x109820f2002,
0x8534f381e6f003,
0x10ab2400002
]

def policySharedUnitFixed0HintLeaf20 : PackedNatTable.Table Nat := .leaf #[
0x85a50b41fbc003,
0x85cd0b91542003,
0x10bd235f002,
0x86150c2217f003,
0x10d3217f002,
0x10d5a17f002,
0x10d7236b002,
0x10d8238c002,
0x86d50da1fd1003,
0x86e90dca1b8003,
0x871d0e321c5003,
0x87850f021df003,
0x87c50f81f9e003,
0x88251042207003,
0x884110799d0003,
0x112da02a002
]

def policySharedUnitFixed0HintLeaf21 : PackedNatTable.Table Nat := .leaf #[
0x1165199a002,
0x116b2421002,
0x8c2d1852309003,
0x8c98b999732003,
0x3648ea91d6003,
0x39c8ee91dc003,
0x4108f411e9003,
0x1203023e48049001202005,
0x4ec9109222003,
0x5809241249003,
0xb2124c002,
0x5bc92b9258003,
0x6309399274003,
0xc81277002,
0x70095112a3003,
0xe392a4002
]

def policySharedUnitFixed0HintLeaf22 : PackedNatTable.Table Nat := .leaf #[
0x74495612ad003,
0x74c95712af003,
0x79895992b2003,
0x7a895b92b6003,
0x4ae524a12b8003,
0x7b095e92be003,
0x83497112e3003,
0x8a09811303003,
0x8d09849308003,
0xa789c31387003,
0xb549dc13b9003,
0xbf09ed93dc003,
0xc489f213e3003,
0xc5c9f393e6003,
0x13f806464fd89fa93f7005,
0xd18a0c941a003
]

def policySharedUnitFixed0HintLeaf23 : PackedNatTable.Table Nat := .leaf #[
0xda0a181431003,
0xde8a1f143f003,
0xe50a2c1459003,
0xf40a44948a003,
0xfd4a5814b1003,
0x1078a6b14d7003,
0x43b087253b0a7814ee29da53bca7914f1009,
0x1110a7a14f5003,
0x1190a8b1517003,
0x1268aa7154f003,
0x1454ae295c6003,
0x15d70a445754aea15d6005,
0x14d4af295e4003,
0x14e8af415e7003,
0x1500af715ef003,
0x1598b099614003
]

def policySharedUnitFixed0HintLeaf24 : PackedNatTable.Table Nat := .leaf #[
0x160cb131627003,
0x1694b221645003,
0x17e4b4b1697003,
0x18b8b6716cf003,
0x16d80c665b58b6a96d7005,
0x1968b7d96fc003,
0x17210cf85c7cb8f1720005,
0x1a68b9e173b003,
0x1a80b9f973e003,
0x1ad8bab1757003,
0x1bb0bc39788003,
0x1bdcbc99794003,
0x1c84bdd97bc003,
0x1eb4c241847003,
0x1edcc25984a003,
0x1f70c391873003
]

def policySharedUnitFixed0HintLeaf25 : PackedNatTable.Table Nat := .leaf #[
0x1f84c3a9876003,
0x213cc6798d0003,
0x21c4c7718ef003,
0x4449905002,
0x227cc901921003,
0x2340ca41947003,
0x2454cc01981003,
0x2488cc6198d003,
0x2530cdd99bc003,
0x19c712aa6714ce219c6005,
0x2574ce719cf003,
0x258cce999d4003,
0x26e4d121a25003,
0x274cd1d1a3b003,
0x27a0d2a1a55003,
0x27e0d2c1a57003
]

def policySharedUnitFixed0HintLeaf26 : PackedNatTable.Table Nat := .leaf #[
0x27f8d2d9a5a003,
0x1a7a142c69e0d3b9a79005,
0x28a8d479a90003,
0x2920d561aad003,
0x29a8d659acc003,
0x29ccd6a1ad3003,
0x29f8d6b9ad6003,
0x2a64d731ae7003,
0x2a90d779af0003,
0x2aa8d7a1af5003,
0x2b1cd879b10003,
0x2becda59b4c003,
0x2c44db51b6b003,
0x2d20dcf1b9f003,
0x2da0ddc9bba003,
0x2db8dde1bbd003
]

def policySharedUnitFixed0HintLeaf27 : PackedNatTable.Table Nat := .leaf #[
0x2e2cded1bdb003,
0x2eacdf99bf4003,
0x2fd4e251c49003,
0x3074e3a1c75003,
0x3090e3e1c7d003,
0x315ce571caf003,
0x31b0e5e9cbe003,
0x3204e689cd2003,
0x3214e6a1cd3003,
0x3244e6b9cd6003,
0x32a4e781cf1003,
0x32d0e7d1cfb003,
0x32dce7e9cfe003,
0x3334e8a9d16003,
0x3348e8c1d19003,
0x3370e919d24003
]

def policySharedUnitFixed0HintLeaf28 : PackedNatTable.Table Nat := .leaf #[
0x3450ead1d5b003,
0x3504ec59d8a003,
0x3580ed39da8003,
0x35c8edd1dbb003,
0x35ecee31dc7003,
0x35fcee49dca003,
0x3674ef41de9003,
0x38c8f3c9e7a003,
0x392cf4a1e95003,
0x3948f4d9e9c003,
0x3968f501ea1003,
0x397cf529ea6003,
0x39c8f5c1eb9003,
0x39f8f631ec7003,
0x3a40f6f9ee0003,
0x3a5cf719ee4003
]

def policySharedUnitFixed0HintLeaf29 : PackedNatTable.Table Nat := .leaf #[
0x3bc0fa59f4c003,
0x3dbcfe79fd0003,
0x3f5502aa056003,
0x3ffd0482091003,
0x413d07ba0f8003,
0x42550b7a170003,
0x43610eea1de003,
0x4489130a262003,
0x5500ab015246948d491a7234c46a08d591aa00a,
0xac016002bc05711ad235c46bc8d891b0009,
0x16202cc8d991b4004,
0xb5017202e005b91b7237046e48dd91ba009,
0xba017c02f405e11bd237c46fc8e091c0009,
0x17e03048e191c4004,
0x18603148e391c8004,
0xce01a4034406811ce239e47408e911d1009
]

def policySharedUnitFixed0HintLeaf30 : PackedNatTable.Table Nat := .leaf #[
0x7c00f901ee47808f211e223c2478c8f311e500a,
0x81a487002,
0x47008e91f823f847e88fc91fb007,
0x484092012324124828906120b007,
0x26404d090d121b004,
0x27804f89121225004,
0x15202ac05540aa12412484490c9229244009,
0xafa48a002,
0x2ca059c927124f004,
0x16902da05b00b5925224a6495092b1255009,
0xc5a48d002,
0x6440ca019324f249e893e127b007,
0x36c06e094e929e004,
0xe7a491002,
0x838108821025ca4b9897412e7007,
0x424085097512eb004
]

def policySharedUnitFixed0HintLeaf31 : PackedNatTable.Table Nat := .leaf #[
0x85410c021725da4bb897812ef007,
0x95012a932726564ca4994132a007,
0x4ae0960996132d004,
0x4ee09e49aa1355004,
0x14ea49a002,
0x2a2054c0a94152138b27184e349c7938e009,
0x54e0aa49c89392004,
0x56a0adc9d013a1004,
0x2c9059a0b3016593af27604ec49d993b2009,
0x16a249b002,
0x2e405d00b9c17313ca27964f309e713cd009,
0x17a82f605e84f4c9eb93d527a84f589ec93d800a,
0x17da49c002,
0xc1c18413de27c44f809ef93e1007,
0x32b065e0cb8196940328085014a039406009,
0x1b3a4a1002
]

def policySharedUnitFixed0HintLeaf32 : PackedNatTable.Table Nat := .leaf #[
0x3b407700edc1db146e28de51c0a391471009,
0x1e724a4002,
0x3fa07fc0ff41fe14b6296e52e0a5d14b9009,
0x10002018402297a52f8a6014bf007,
0x104c20b0415299e5340a6914d1007,
0x20ea4a6002,
0x21d24a7002,
0x221a4a8002,
0x113822884502a005404a819502007,
0x231a4a9002,
0x11d423c04772a5454aca96952c007,
0x11fc24104812a6e54e0a9d1539007,
0x90c1220a9f153f004,
0x9261254aa5954c004,
0x24c24aa002,
0x95812b8aaf9560004
]

def policySharedUnitFixed0HintLeaf33 : PackedNatTable.Table Nat := .leaf #[
0x4cc09a0133c267157d2afc55fcac09580009,
0x9a2134cac19584004,
0x4dc09c0137c26f158b2b185634ac7958e009,
0x9c2138cac89592004,
0x4e509d213a027395952b2c565cacc9598009,
0x9d613b4acd959c004,
0x4f309ee13d827a95a32b485694ad395a6009,
0x9fa13fcad795b0004,
0xa02140cad995b4004,
0xa101428add15bb004,
0x28785100a1c56f4ae095bf2b7c5700ae195c200a,
0x148029095cf2ba65744ae815d2007,
0xa9a153caff15ff004,
0xabe1584b079610004,
0x2b224b0002,
0xaec15e0b111623004
]

def policySharedUnitFixed0HintLeaf34 : PackedNatTable.Table Nat := .leaf #[
0x2c124b1002,
0xb1e1644b1a9636004,
0xb7616f4b2c965a004,
0x171c2e505c92cca5998b341667007,
0xb961734b35166b004,
0x5cf0ba617482e8966d2cdc59bcb389670009,
0x5d40bb0175c2eb16732ce859d4b3b9676009,
0xbb2176cb3c967a004,
0x5dd0bc217802ef967d2cfc59fcb409680009,
0x2fc24b3002,
0xc6c18e0b6f16df004,
0xd441a90ba29746004,
0xd4c1aa0ba4974a004,
0x1b88371977d2f025dfcbbf1780007,
0x37aa4bc002,
0xe2c1c60bd897b2004
]

def policySharedUnitFixed0HintLeaf35 : PackedNatTable.Table Nat := .leaf #[
0x1d343a8074f2fca5f98bf417e7007,
0xea21d4cbf517eb004,
0xeb01d68bf717ef004,
0xecc1da0bfe17fd004,
0x76a0edc1db43b6180030026008c021803009,
0x76f0ee61dc83b89806300e6020c051809009,
0x1df03bf877e302a6058c0c1817007,
0x1e0c3c30785303a6078c10181f007,
0xf121e2cc119824004,
0xf221e4cc15982c004,
0x7940f301e5c3cb182e305e60c0c191831009,
0xf421e8cc1e983e004,
0x7ba0f7c1ef43de184e309e6140c291851009,
0x1f383e7985c30c06178c2e985f007,
0xfa21f48c309862004,
0xfe21fccc401881004
]

def policySharedUnitFixed0HintLeaf36 : PackedNatTable.Table Nat := .leaf #[
0x7f50ff21fe03fb9884310a6218c441887009,
0x7fa0ffc1ff43fe188a31166230c47188d009,
0x80a101c2034406189e313e6280c5118a1009,
0x80f1026204840898a4314a6298c5418a7009,
0x207840f98ab315e62b4c5618ae007,
0x10422088c5818b1004,
0x2140429885231a4634cc6a98d4007,
0x437a4c3002,
0x10ee21e0c7a98f6004,
0x21f443f18f731f663e4c7c18fa007,
0x111c223cc85190b004,
0x225444c089732266450c8b1915007,
0x8bd1182230045f993c327a64f8ca0193f009,
0x23344671942328c6510ca19945007,
0x23bc478195f32c66584cb01962007,
0x11e423cccb21965004
]

def policySharedUnitFixed0HintLeaf37 : PackedNatTable.Table Nat := .leaf #[
0x11ea23d8cb31967004,
0x11f223eccb5196b004,
0x8fe12042404480197032e265c8cba1973009,
0x489a4c7002,
0x495092b12526648ccb199433266654ccc199700a,
0x12da25bccf019e1004,
0x12f225eccf519eb004,
0x26244c6098b33f467eccfe99fc007,
0x26ac4d61a1634346860d0b9a19007,
0x140e2824d339a68004,
0x5318a6414c46b08d631ac435866b14d641ac700a,
0x534a4d5002,
0x14da29bcd679ad0004,
0x2a185439ad835b86b68d6c9adb007,
0xa8a151c2a345461adf35c06b84d719ae2009,
0x54c24d8002
]

def policySharedUnitFixed0HintLeaf38 : PackedNatTable.Table Nat := .leaf #[
0x2a6854e8a9c35d26ba8d761aeb007,
0x554a4da002,
0x2aac5570aad35ee6be0d7d1af9007,
0xaaf15662ac85589afc35fa6bf8d801aff009,
0xab415702adc55b1b0236066c10d831b05009,
0x15722aecd841b09004,
0x562a4db002,
0xad115aa2b505699b1d363c6c7cd909b20009,
0x56f0adf15ba6ca0d961b2a36526cacd971b2d00a,
0x15ca2b9cd9c9b3a004,
0x2bc45791b41368a6d0cda11b44007,
0x57d24dc002,
0x166e2ce4dca1b95004,
0xb7516f22de05bb9bc6378e6f20de51bc9009,
0x16f42df0de61bcd004,
0x16fa2dfcde79bd0004
]

def policySharedUnitFixed0HintLeaf39 : PackedNatTable.Table Nat := .leaf #[
0xb81170a2e105c19bd337a86f54deb9bd6009,
0x5c4a4e1002,
0x17222e48def9be0004,
0x2e805d18ba237dc6fbcdf89bf0007,
0x17c42f90e1e1c3d004,
0x6008c021800713ce299c5138a07148e2a9c5400a,
0x18183038e311c63004,
0x184a309ce3f9c80004,
0xc28185830ac6151c8239067210e431c85009,
0x185a30bce441c89004,
0xc31186a30d06199c8c391a7238e481c8f009,
0xc43188e31186229ca239467290e531ca5009,
0x62b24e6002,
0x31906329cb6397472e0e5b9cb9007,
0x18ce31a0e5d9cbc004,
0x635a4e7002
]

def policySharedUnitFixed0HintLeaf40 : PackedNatTable.Table Nat := .leaf #[
0x31b46380c6f39807304e619cc2007,
0xc7618f431e463c1cca39967330e671ccd009,
0x64f0c9f193a7374e709cdf39bc7380e719ce200a,
0xcbb197e32f865e9d043a0a7418e841d07009,
0xcc01988330c6611d0a3a167430e871d0d009,
0x198a331ce881d11004,
0x66824ef002,
0x33786708ce03a5274a8e961d2b007,
0x33946740ce73a6274c8e9a1d33007,
0x33f467f1d433a8e7514ea21d46007,
0x1a003404ea41d49004,
0x68924f1002,
0x1a3c3480eb39d68004,
0x34e069d8d3a3b087614ec39d86007,
0x35086a28d443b1a7638ec81d8f007,
0x6afa4f3002
]

def policySharedUnitFixed0HintLeaf41 : PackedNatTable.Table Nat := .leaf #[
0x1ae635d4ede9dbe004,
0x36446c91dda3bbc7770eed9ddd007,
0x1b283654eef9de0004,
0x6dc8dba1b707804f029e033c047810f039e0600a,
0x1b943730f0b9e18004,
0x1c1c3840f2c1e59004,
0x71824f8002,
0x390c7230e453d1c7a3cf489e90007,
0x72824fa002,
0x39807318e623d507aa4f559eaa007,
0x74b2500002,
0x3a6c74f0e9d3dd47bacf769eec007,
0x1da63b54f979f30004,
0x3cc87999f993f3a7e6cfcd1f9c007,
0x3d0c7a21fa83f587ea8fd49fab007,
0x1e923d28fd79fb0004
]

def policySharedUnitFixed0HintLeaf42 : PackedNatTable.Table Nat := .leaf #[
0x7bf8f801efc7f90ff41fe63fca7f9cff51fe900a,
0x7ce0f9d1f3680110042006400a801d005200900a,
0xfa41f503e9c7d320194034806d00ea01c009,
0x3fa87f5a06c40e081b9036a06f007,
0x201c403d05520ab004,
0x82c905a20b08421086210a4212842d087210d00a,
0x20b84175087a110004,
0x20c0418908c2119004,
0x211642350b22165004,
0x434086990d243ae87610ed21d9007,
0x87610ed21d687d90fd21f843ee87e50fe21fb00a,
0x88091022200888d113a22544488899114a22800a,
0x88a1115222689111242246448a891d125224900a,
0x8931127224a89a5136a26b44d489b1137a26e00a,
0x225044b0895912a44e289c913b227444e689d513c227700c,
0x8999134226489f1140227e44fa89fd141228100a
]

def policySharedUnitFixed0HintLeaf43 : PackedNatTable.Table Nat := .leaf #[
0x45148a3229445308a5914aa297007,
0x2298453915222a5004,
0x22a6455515622ad004,
0x117422f045dc8bb22f245e68bd117b22f5009,
0x117922fa45f08bda2f845f28be917e22fb009,
0x8c79190231c8c5518ca317462c8c6118da31a00a,
0x2b528511ac003,
0xb3928513b4003,
0x2c928591b2003,
0x2d128591b5003,
0x2d928611b6003,
0x1e05286181a003,
0x2ed28691bc003,
0x1e09286981b003,
0x30128711c2003,
0x30928711c5003
]

def policySharedUnitFixed0HintLeaf44 : PackedNatTable.Table Nat := .leaf #[
0x31128791c6003,
0x1e212879821003,
0x10f021c044408811ed23dc47c08f791ec009,
0x1130224045408a11f223e647d48fa11f1009,
0x2f205e39244178f004,
0x48928a1208003,
0x66928a1282003,
0x4cd28a9219003,
0x4d528a921c003,
0x136244004e090f121f005,
0x4f528b1223003,
0xffd28b14bb003,
0xa281442456051c0a40146245848c0917122d245e48c8918922a00e,
0xa50149029648d091a9233006,
0x54d28b9240003,
0x178928b9682003
]

def policySharedUnitFixed0HintLeaf45 : PackedNatTable.Table Nat := .leaf #[
0x59928c924d003,
0x5a128c9250003,
0x5a928d1251003,
0xfe528d14b4003,
0x64928e1278003,
0x65d28e127e003,
0x7f00f881f403e607c896012c125844b1096192d000b,
0x83d28f92e4003,
0x84d29012e9003,
0x8992901300003,
0x85929092ec003,
0x2e7d2909bec003,
0x2230444089411212fc25fa4bfc97f12fb009,
0x23b047408f411e131226264c5498a1311009,
0x91c123024a04920920990132126444c90991931f00b,
0x9e12921353003
]

def policySharedUnitFixed0HintLeaf46 : PackedNatTable.Table Nat := .leaf #[
0x28126ce0a0c9b29366005,
0x145028926da0a30146828b26dc4dc89b8136f26e24dd09b9936c00e,
0x147828e05204dd89bb9375006,
0xa8d293138a003,
0x114d2931505003,
0xaa12939390003,
0xc6129393e8003,
0xad9294139f003,
0xae129413a2003,
0xb2929493ae003,
0x119d294951a003,
0xb9529593c9003,
0x1fc1295987e003,
0x31a06320c7018d93ea27d64fb49f613e9009,
0xcb12979402003,
0xcdd2979414003
]

def policySharedUnitFixed0HintLeaf47 : PackedNatTable.Table Nat := .leaf #[
0x33206660cd0a05140e2818502ca069409009,
0xed5298946d003,
0xeed2989475003,
0xfed29994b5003,
0x17c12999693003,
0x100529a14bc003,
0x200529a1891003,
0x105129a94ce003,
0x188529a96c5003,
0x1128224844d0898112ca7d14fb29f853f8a7e94f900b,
0x113d29c94ff003,
0x114929c9504003,
0x11a4234046c08d611a8a8e151d2a3c5480a8f951b00b,
0x11d929d9529003,
0x20a529d98b6003,
0x120129e1536003
]

def policySharedUnitFixed0HintLeaf48 : PackedNatTable.Table Nat := .leaf #[
0x121529e153c003,
0x125129f154a003,
0x1d2129f17df003,
0x4c4096612d425a15662ace55a4ab41577009,
0x541096c12e025b956a2ad655b4ab615f0009,
0x13352a0957c003,
0x1e6d2a09835003,
0x13492a11582003,
0x13512a11585003,
0x13752a1958a003,
0x14112a195b5003,
0x13892a21590003,
0x13912a21593003,
0x13992a29594003,
0x14152a295b6003,
0x13d12a395a2003
]

def policySharedUnitFixed0HintLeaf49 : PackedNatTable.Table Nat := .leaf #[
0x13f12a395ad003,
0x141c27c04fb09f413e4ad415a92b5456b0ad595b800b,
0x13f92a415ae003,
0x14012a415b1003,
0x14092a495b2003,
0x14192a495b7003,
0x14252a515b9003,
0x144d2a515c4003,
0x54a0a9215302a595f92bf457f0afd95f8009,
0x15392a695fd003,
0x1e012a69819003,
0x15dd2a81621003,
0x28112a81a63003,
0x16412a91634003,
0x1ac12a91753003,
0x17212aa1664003
]

def policySharedUnitFixed0HintLeaf50 : PackedNatTable.Table Nat := .leaf #[
0x354d2aa1d9d003,
0x17312aa9669003,
0x186d2aa96be003,
0x17412ab166c003,
0x18712ab16bf003,
0x17552ab9672003,
0x18692ab96bd003,
0x17692ac1678003,
0x17712ac167b003,
0x17792ac967c003,
0x18812ac96c4003,
0x180430006040c061808b5016a12d445a90b51969f00b,
0x183c30706120c221840b5796b02d625accb5916ae00b,
0x32906510ca65bdcb7c16f6006,
0x2e585ca925b972b004,
0x1a8d2ae1744003
]

def policySharedUnitFixed0HintLeaf51 : PackedNatTable.Table Nat := .leaf #[
0x2f692ae1c31003,
0x73d0e781cfc39f17d62fae5f64bec17d5009,
0x1d392b097e4003,
0x1d752b097f3003,
0x1d492b117e9003,
0x1d792b117f4003,
0x1d9d2b217fb003,
0x1da52b217fe003,
0x1dad2b297ff003,
0x2c4d2b29b6d003,
0x1dc12b31805003,
0x1ded2b31813003,
0x7770eec1de43bc180f30206048c08980e009,
0x1df52b39814003,
0x27692b39a45003,
0x1e112b4181c003
]

def policySharedUnitFixed0HintLeaf52 : PackedNatTable.Table Nat := .leaf #[
0x24dd2b419a5003,
0x1e492b5182a003,
0x1e652b51833003,
0x1e552b5982d003,
0x1e692b59834003,
0x1e892b6183c003,
0x39992b61eae003,
0x1eed2b6984d003,
0x3c792b69f83003,
0x1f003df87c30f841f04c2a185530ac6160c2b985300b,
0x1fc92b8187f003,
0x1fd12b81882003,
0x1fd92b89883003,
0x20092b89892003,
0x1fed2b91889003,
0x200d2b91893003
]

def policySharedUnitFixed0HintLeaf53 : PackedNatTable.Table Nat := .leaf #[
0x202d2b9989d003,
0x2c812b99b7d003,
0x20412ba18a3003,
0x2c852ba1b7e003,
0x226841b0839107020dcc5e98be317e6304c60191800b,
0x20ec41d083e107a20f0c6198c4318a631cc6318c200b,
0x21452bb98d1003,
0x27652bb9a44003,
0x22592be1912003,
0x3a312be1edd003,
0x22f92be993b003,
0x245d2be9985003,
0x8e311c82394cab995b32b26560cad1956009,
0x23e92c11969003,
0x23f52c1196c003,
0x23fd2c1996f003
]

def policySharedUnitFixed0HintLeaf54 : PackedNatTable.Table Nat := .leaf #[
0x24792c1998a003,
0x94e129a25404a799be337e6704ce019bd009,
0x3394672126519c9004,
0x25b92c319df003,
0x342d2c31d55003,
0x26292c419f9003,
0x2cd92c41b92003,
0x9e113c0278c4f11a4f34a06948d289a4e009,
0x29b92c69ace003,
0x2c492c69b6c003,
0x2a2d2c79ade003,
0x34a52c79d73003,
0x2a6d2c89ae8003,
0x2d692c89bb0003,
0x2ab12c99af6003,
0x34552c99d5d003
]

def policySharedUnitFixed0HintLeaf55 : PackedNatTable.Table Nat := .leaf #[
0x2ac12ca1afb003,
0x2b252ca1b12003,
0x2ad52ca9b01003,
0x2b212ca9b11003,
0x2ae92cb1b07003,
0x2af12cb1b0a003,
0x2b492cc1b1c003,
0x2b5d2cc1b24003,
0x5708ae015c82b8c5711b3036626cd4d999b3236686cdcd9b1b2f00e,
0x2b992cd1b38003,
0x2ba12cd1b3b003,
0xb3316642cd459a1b8e371e6e44dc81b8d009,
0x2ce12ce9b93003,
0x2dcd2ce9bc4003,
0x2dd92cf1bc5003,
0x2e652cf1be7003
]

def policySharedUnitFixed0HintLeaf56 : PackedNatTable.Table Nat := .leaf #[
0x2ded2cf9bcb003,
0x2e612cf9be6003,
0x2df92d01bce003,
0x2e012d01bd1003,
0x2e092d09bd2003,
0x2e5d2d09be5003,
0x2e852d21bed003,
0x2ebd2d21bfc003,
0x2f8d2d29c3b003,
0x6020c03180e30186029c5738b07170e2d1c5938b67178e2e9c5600e,
0x30992d41c7e003,
0x30e52d41c93003,
0x30a52d49c81003,
0x30dd2d49c91003,
0x30b92d51c87003,
0x30c12d51c8a003
]

def policySharedUnitFixed0HintLeaf57 : PackedNatTable.Table Nat := .leaf #[
0x30c92d59c8b003,
0x30e12d59c92003,
0x31112d61ca1003,
0x36812d61ded003,
0x31b92d89cbf003,
0x36b92d89df8003,
0x31dd2d91cc9003,
0x6508ca01948328c6511ce539cc73a8e741ce739d273b0e759ce400e,
0xced197032e865c9cff3a007408e809d37009,
0x32f12da1d03003,
0x33ad2da1d35003,
0x33052da9d09003,
0x33b12da9d36003,
0x33192db1d0f003,
0x33212db1d12003,
0x337d2dc1d28003
]

def policySharedUnitFixed0HintLeaf58 : PackedNatTable.Table Nat := .leaf #[
0x33912dc1d2f003,
0x33992dc9d30003,
0x33bd2dc9d39003,
0x33c86788cf519e833cce9f1d3f3a807508ea09d3d00b,
0x340c6810d061a0a3410ea61d4d3a9c7540ea79d4b00b,
0x345c68b0d1a1a323460eaf9d603ac2758ceb11d5e00b,
0x347d2de9d66003,
0x34892de9d69003,
0x34e52df1d83003,
0x35992df9db1003,
0x35d12e09dbc003,
0x36012e09dcb003,
0x10341aee35e46bc1dc23b867714ee220d7009,
0x10071b0636146c21dcf3ba07748ee8a0a3009,
0x361c6c30d8a1b123620eea9dd63bae7764eec1dd400b,
0x365c6cb0d9a1b323660ef19de43bca779cef31de200b
]

def policySharedUnitFixed0HintLeaf59 : PackedNatTable.Table Nat := .leaf #[
0x37406e78dd31ba43744f0e9e1e3c3e7884f101e1c00b,
0x37cc6f90df61bea37d0f219e443c8a791cf231e4200b,
0x39112e41e8d003,
0x394d2e41e9d003,
0x39852e51ea7003,
0x39952e51ead003,
0x3a712e61ee9003,
0x44312e6223a003,
0x3b512e69f2e003,
0x3b592e69f31003,
0xee01dbe3b887709f3d3e7c7d00f9f9f3c009,
0x438c79a8f381e6e3cd8fd09fa23f467e94fd221f200b,
0x3d347a60f501e9e3d38fda9fb63f6e7ee4fdc1fb400b,
0x3e0c7c10f861f0a3e10ff79ff03fe27fccff91fee00b,
0x7cf8f9e1f443e847d0200c401a8045007a00e4020804d009200b00e,
0x3f087e08fc51f883f0d020a04240868115022204000b
]

def policySharedUnitFixed0HintLeaf60 : PackedNatTable.Table Nat := .leaf #[
0x4144828105420a6414907d20fb41f883f907ea0f900b,
0x4190831906720cc419508da11c423a847d08f211a00b,
0x443d2ed223f003,
0x87790ee21e443c487821fe43fe880d100a2004404881510221fd00e,
0x8821103220e4418882a22b445888c1117222d445e88c9118a22a00e,
0x88b91162234446488c224d449c8949128224f44a28951129a24c00e,
0x89b1135227244e089ba284450a8a25143a28645108a2d145228300e,
0x8a41147229645288a4a29a45368a7d14ea29c453c8a85150229900e,
0x1150229e45488a8a2a745508aa9154a2a6009,
0x45512f1a2ab003,
0x45592f1a2ae003,
0x8c91191232a46508c9a31d463c8c89190231f46428c91191a31c00e,
0x1207240c48112441205005,
0xbc8a5f5002,
0x4dd2fd121d003,
0x9c92fd134c003
]

def policySharedUnitFixed0HintLeaf61 : PackedNatTable.Table Nat := .leaf #[
0x146425784ae924a92bb005,
0x131b26344c6124a9319005,
0xa093089364003,
0xa59308937e003,
0x20b927f64fe524f93fa005,
0x14e429c6538524f94e2005,
0x15db2bb4576125615d9005,
0x1931326064b9256192f005,
0x23122db65b6525a96da005,
0x22c72e865d0525a9742005,
0x111a265f002,
0x10702693002,
0x1aab35546aa12651aa9005,
0x1a7e34fa69ed2691a7c005,
0x1a88350e6a152691a86005,
0x206b40d481a0ed80d653b5c76b4ed7a069009
]

def policySharedUnitFixed0HintLeaf62 : PackedNatTable.Table Nat := .leaf #[
0x38c07200e492a525524a9c95312a8038a024c04d249000c,
0x7b00f641ed148c29205238a46948f07ae026404da49000c,
0x33028229884a08140f005,
0x10c0437c9a350dea1bc005,
0x7e00fb92cf03f207e80fd92c825984b2896492cb258e4b3896692c600f,
0xcc53899408003,
0xce13899415003,
0x9f923f028205080a8923c4dfe97f52ff014d029805400a7814e246e48e091c923b247448d80a192282452489c91f123d01a,
0x1421382050c0a1c14b937f4c24984c1490291052a0a50149937926f44dec9be937c26f09c10144136a26d64da49c0938001a,
0x50138c1226003,
0x9c538c134b003,
0xa1538c9368003,
0x200138c9890003,
0x4400807b50f6c92fc3d707b0233e1ecc3d58f6d23401ec8c249fce00f,
0x146100020e781d282080414082410392dc46844b74113822b074c0e8498224984c1498381a803a407380e8c1cd03a2019,
0x11b023904700754986a343046e51940e901d404840968122824404864cc4126024b04b20934129826a065009a0134934300029c5413381d800ee4d09307934446b64d149932344264a4c78999131d03ae075803c12b049249835305130c032
]

def policySharedUnitFixed0HintLeaf63 : PackedNatTable.Table Nat := .leaf #[
0xed807a045e08cd24c81de03ba0765390037506e80dec1bc037706ec0260001943d28845104a20143c047e08f8120824003ca4c5d381131603c2078d24992b1022,
0x518400081e803ce519d24a12b828cc07a495a92b44c1498381cc83a8074e0e601bca7214944517d1b31460017,
0x1a98352069a0d30a0f039728bc00041c8834b06a80d241ca945a46b85075251839628b65088a109420016,
0x205f233299cc5f5119b1a14465ceaa26951a9c46687ed919800d,
0x45288a4114422a045399221146648cc93992532486498c94992800e,
0x15d02b9856f2c3415c4b1005630ace15a02ba85690ad458591c99615496015acb0da392013,
0x2b62726002,
0x2c305880b0e1610b14162c472a58cc000857d0b1c95442bf858b0b1816242c5162d472c58b8b191629016,
0x28e051b0a461474ae727072b9898c825d04b9098612f825e84bc008c0004ab7a3812adc98d132415cd016,
0x3da8000408080fc490e05e00bd017902ec040092fa33724c098592fe2630010,
0x5c00c1018303000604937926c24dc49b40b8817b02e405cc0ba125b02b67b50000810501e803d807a80fd4a22477c8f526164bf898c092d126624ca8cd40baa72a0210041c02991eb1d061b9437686e80dd492ecbc323af3d9e038006f812001c20390071006300be92188eda6fd23b4497919c125903f,
0x894a2794c12985130c26194ca699ed33e267d4cfe3e38ffea6e94dd4446d12f8001223889592efa270016,
0x3e4c7c920241f2a80047d2a0181f2280a07d7a0251f60974d013200000f,
0x19a03310df80cf239a03508e990c14376032d0e190c24a208700861a1c121889c510e111cc014,
0x82553618db23bfc9b1d3620dab3bea36c52d91dfd00b,
0x31e27f800041909018202e0c889fa270527e6985d30f031d06400c7c0d281a3034c069c944128c25144a2494593ef27e44fc49f813ee01d
]

def policySharedUnitFixed0HintLeaf64 : PackedNatTable.Table Nat := .leaf #[
0x2108420002,
0xb8c17102df05344f14170a1eb05360a7c17482a005428990000a48b4c28986130c938946b44e2124d262a4c563dc47b9045f08b0116422d0eb61cd839b4ff626174c5a9930f5b150c2a167f489e3235902b,
0x203331289c1133307ff311e0b7929293c44cca9c75313a67e4d009c0d38e26264d7630d8e4a260a4c3898545c39bd80002982533e8ccc1996335c6648cca41c40a7124d25f14c28985930c26194c3a99ed33e267f4da6744d20d1d1449dc9af936126bc4d7a9afd36026c1039,
0x32a86622e04195832c8658496c5be832a06640cc6196c32e09ba0cba1978b7f23e22dfa5c0d1d516f9016,
0x7540eb85fc43aa87594ac65fb476207450e881d083a18ec50e8c1d6cbf824472fb85f7522317ec015,
0x3ab2735002,
0x1ca473d872a13be2790d29a6464d30693521c87220e461cbc3920a0134c800052f9a64d34c08edcbde97c2017,
0x1c28bd780010e1e1c5038987152f5a5eb8bd607090e241c2c386070d0e201c4438717a62f525ea0bd297a42f565ea8bd397a301b,
0x10417c9044e08a412d822e00ea4ccd24c260a4c989ce01050209040e0818102820b03ec07d4116822c00e84c1496292e125b64b711a112dd01e,
0x4d789b6136426c4d0ea3e11360689800089ae136e26cc7c409b4136a687cffb9a21344068792669a1c016,
0xe72689d2f9a6304c8c98a436e06db0dc81b7c36e804d00025df11d7177b4cc49ce839c073b0e7418ac314805a00065f491dd17d101c,
0x1a4c34c869849701a503490034007,
0x31217470c44188cb6316c70d4a15482a88410081c103cb6585530c4a5b251d194cb2998580d1c616c8016,
0x9701310260049890aa334025e48600008125024e04a413d812a025648411a5120f025048349071214016,
0x6ac94c81b74a3a4a700d5026404c606e40dd027a037606f09502349253e4cf51a4128e013,
0xbcc17902ed05d60be524e02f105ee4f6929613d200b
]

def policySharedUnitFixed0HintLeaf65 : PackedNatTable.Table Nat := .leaf #[
0xc10046008e011a0c44185a49d007,
0xab09e1800105540b8417182e205be0a6814e249a278a8d649e302ab05680ab415702af204a0ac0158939648ce4e549ca139301b,
0x17fa7404e600c54189a741493c0bf4041030406220c2d24e93dd00e,
0x1040bf417fa7404e600c5524f13dd01160c34187830e06284f941862743010,
0x10e821c04374e6210d87da041c494c80b4a75a4a700b,
0x109d213e448c85910b321328b385939b824344899523aa17d213c86b084d10b7435a0005342108042aa86a923b217c019,
0x5562c2200042ae05604a9c58382aa8e820aae15602ac8e6b0ab4156cb0424352c0e581921d9605015,
0x6900d7d0c3035606aa0d741ac0357284c50bca12836549420d1c1f603eb067e0da45ee836a06d68288000a48e4e369c0130926134e080db81b6837106e00dbca1b1437287050e8a1c94354e3a989c75a9f071d660d641ae035a06b6691c1b183e707cc0fa41f4034229445294a5214a329420d281a4835406960d301a6945d069c0d3d01903604c20507d1b2941e283a8d70a0e1428285c50b51ae83ea075c0ec01e583b3076451dd38ba623077851d81d894744e2c98881dd03b907940efc1df0097012a0d001a224a028f08d9ca39946c290851aca53235e284e3ad0f829f06286670d0a5414a7286452a51b6141b080,
0x1ab835906b80d681ad9a460002922d381a71c07260e49251945706d89490a1a2626080a1010203840606869d2125014c22988530ca5194c108121020206040b08145318a6394c829945324a629428285c509c1ac035d06aa0d590c3034a06920d501a5834c069a51741a7034f40640d81308141f46ca5078a0ea35c28380d952509425285e50b51ae83ea075c0ec01e583b3076451dd38ba623077851d81d894744e2c98881dd03b907940efc1df009601280cf019f147846ce51cca36148428d652991af142606a,
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,
0xfba1f7880e80cf0c0d4b4e718413f829804da09b8137827d04fc3eed094a5e74be69cf937fa71a4bfa97f816402d105a00afc16002c1176a0b085d99be84bd297a930d25e84c2e98b85c31fbe4ca41738d2480014e369c004eda5303490995d329a6554cde995132b26584cb29abd358a6b34d689ad535b26b24d60700920693a8274e8d509d6a62f40724d849b0135f26924d209c2135e469609f00e6026504cc0ca819494134c3e9c5819b14120648505d310271706722014402033b0674023c19e941847805058a00934126804d6d1a62038071,
0xfb01f5045a08b003a130525a200041000202040207bc0f68072257e4b5d1a092d44e2a981c1058205040c0e80115025b045c01d403c807c26664b6c97092c5022,
0x3fe4b640fe81fe0406081096d12d225b04b540f701ef04d607c010012d4268c8d0495f92d3014,
0x12d100029d3538aa607005,
0x40a08181d0039f03d0079ca33a494257051980f492b525680e741cd839907500e9c1cc03794944517d1b3146006bc0d44115025b045c01d4999a71f041607d80fa822d045801d0117823303b807880f2272149264ac524c93054e9c4b1497092db034,
0x6b80da01b3252a8cfc0d79291000206fc0df12a1036206c00d91293252806a00d481b5035806b49a701bd491e9cf8947a340251a4a4939f929001f
]

def policySharedUnitFixed0HintLeaf66 : PackedNatTable.Table Nat := .leaf #[
0xe12750002,
0x5841d1616142c31629487a1600b1880014e5015f9258962800d,
0x15e82d605780aec15d1b5205560ab0da9857a05c24f193a0139327484e949de13bb055a4e511a82355057c6d452f983212030405c19113f44e0a4fcc16182c6058a0b041600bb43264991932d2600116472c12fc25f94bfe982930d25e84c8a996cfc925e74bd297a937fa71a4c1294a8e0193a846a44ea417982f205de0bb817f82fd01044f7458e906a216c42cc84ca2ce0fd61fa859507e7083e10b8216043208622cb05958b2d370e6e20dc4a7474e4c9d48dc30430165e6ddc404030101020c10188a49d31386e282198434086a5398a7514e829ce53a41870314062c0fd1252a49e27ca5394c3d1b8530f686890d4a1a848ea869d0c1a181430085f910e87ed30f89a05341881531522c683f608070fde1fb803f843f0882541930926134c38985c22402e305c40b7c14d02de311e985130b26184c32999530ea67d4cfe1ffcc4a00014e08999933da67c4e3a989d33f26804a4a4f109e2a35929f098b130aa4a830fa8f08dbc26824d082c8c40a0b19102e20580430084061262a91ff1b8042fe8608dbd13d14a584f4820b857c0af61060a6a239429a6986d33713a60de,
0x218a204084a139382aa27a0000415f13a64c2e98a9315a7474c989ca0813905520d00ae50922123420a8488da70afc15f0937106610a105b00b5c15e02bb05744e909d2a188025,
0x7192f6e000438ba5602f601c6806e8a5701b8036806d8c3b0e361c70bdc241323ae47611f817b3015,
0x1cb839687292f841cacbe407200e441c8c39787240e4a5ef91db97bd497a1c98be1a3b6013,
0x6fd0e0c5e7c37f87002f305e6438186fc0e101c1c37f07010e081c14381179b2f3c5e74bcd17a02f445e84bce1797019,
0x236846d8f6732f4027113d00a01284250405100a10092029405311244e583c1073b0e751ce67ae921b1f694bbc89a08d1a3d923449a45345a6903f94237846e88d411a623b92bf88ec11d623d12c085f644ce980530126064c0898912fe263a4c7c9a686cda0a74c7898f531da63f4be499f934008f737b000052f8a6094c28986130ca61d4cf699f133ea67f17149688deca699496665251e9994f053,
0xb0685551cfe7c2833d8a6714cc6b2926aa5f44bf89c9932627280c16183430606092d548e7cb559ec90aae15602ac8e6b0ab439a85a21eb4486a581cb03238e022,
0x90a17767038e0688d14d189a4404f009d36e0235846c08d711aa234c46a093d11b2236846d8f6732f49a2cfe5194f47ae6524ca523d132969a408d0997b021,
0x2dc85c42cc016e82de25532cb016e02e305c50b7c16fcf9205c00b825971224165b2cc2598d1cc9657016,
0x7340e6e1cd8be723b90e6a7abc00086f64abe1be037c8e670df41bec398979648685e54bc917cd015,
0x398275c002,
0x7360e6e1cd039a97cd47721bd03799f1e4eba3b0925e17ce00d,
0x6064214842108642b4856d09500014eaa9d593af215900c,
0x4af096412c4ab1237f09605d6000084a9095a950025504ab0a84120c242153b47125574aaf1561015
]

def policySharedUnitFixed0HintLeaf67 : PackedNatTable.Table Nat := .leaf #[
0x12a025384a42aaa1298aae049709361270aad049d093c55451be95504954127caab237c013,
0x2502761002,
0x1bd237b86f30de71bc83794f179e303c7278e0f1b8de821f637bc6f810fc444290b91101e31014,
0x38187058e071c143820f299e54007,
0x14a8015052d0a6414c029a24ad007,
0xa4b149a6adc5288a4749a86acc52a8a4f149c29245228a521c6a294c52a1ab53cfe6ad8d581ab4355c6ac91f79aaf019,
0x5248a561494292cd579ab847de29185281ab914989d9926a1aae00e,
0x2d886ee0b6416c66edcf151e29188072780008b65187838e061e8c3e39307a08e4d1c99392e937c61f9c9b017,
0xb64393a2d886201c9b393872645b18b6716cc937cf5980014ed039a4ddc1bb7011,
0x9b2136c26bc4d81a1c47c226c44dc1a8c4e74288d2669a1d00d,
0x393e9da93b32768004,
0xbda17a42f505eb0bd8179c2f416b80272922430b86190c30185807808f14b00239c47608eb11d201542f996b947445ae8b4316882d0e17b82f796a802b405640c3018502b80584302816202c649f4000a48b4bf617e92ad169824968e7492512704676491d300a6024c06981531285f1138026fc2fa169547c65a5132e1692044,
0x435242d88599099459c1fac3f51b7730f686890d42475434e860d0c0a18042fc8875340a683102a62a5341268416466e010bfa18201c,
0x4fa09bc137026d05304e109a4134904fc4d849b0135f00c,
0x433886910d0219843298e4478e68f0000a6324c68992139a2735113c22a526298e5012,
0x8b41b5e22d45801df94e0880cd381a71c4c4c9aec61b1c944c14987130a8b8737b097c5304a6144c30986530ea67d4cfe23dd053a63b4c7e97c933da67c4cfc9a0134c8d9b44ce98182ff8159030c06140ae127046765a7934d26bc4c82991538ea6274d8c6d612140b103db813c027904f109de13b82762546405e98e931e263d4c7c9ac535ea6c11e508270000815d4914980530126044c4897f135926bf4d809af9361159a2b3a8e08acf26404c86991132326424c8e9a2526e9934065
]

def policySharedUnitFixed0HintLeaf68 : PackedNatTable.Table Nat := .leaf #[
0x19503292826987d38b033628240c90a0ba6204e2e0ce4a0b140100e,
0xc044041b774d029a0cc4e008106080c441858089085e2cb8dc5249d00f,
0x2c0176864c930b26464cb498004591cb04bf097e52ffa60a4c3497a1322a65b3f2498252951c0305822ed416102c336a200052f3a5e94bd497cd37fa71a057c0b6016b82bc05760ae8da913a4274a4ef89de93bc27760ab49ca235046aa4e9817982f205da94b09e9261b4cdc4ea520693a803d,
0x9a113402670d05899e3b3200044a5894a4992251c4a409a31334266c4d11a0a34246844d0699b933746830d07a3e0019,
0x25f44c319f512fc26004bf898133de67c0cf7097c1310261c4c109831aa026104c299f23b3067d0cf899f633f067dccf999ed01b,
0x12e067b0000897612f4961ccf48e3b1c7425c44b90973207a25d04ba99e541c28f78cf219e33d0a7a10cf319e2018,
0x12b0684d3ba269212a425444ab09533386672d34999c24d289dd93ba895712bc25644ad8a7114f429e453b804414f829f453b004214fe2a20ecd8a8f15222a405658a9515282a4c01f803c14ea00f85530aa836169849309a69f4d422af855e8aca15802afc56325973626986130ca61c4c2a99cd35226a2361c6c351f99b0c4d469a9535324da35ca8fd0d72269b35ba935c54b9ed83daa979d2f4a5ea4c369929334a66b4c5e39b483b845b08b4116422c045f1ee43dc50f5a62a4c5616392a8857f0b1616302c48e783d9898593268b300adc15b42b405670aca953cf6400014c2e993139427554d2c9a60b09161547206e2cf60a3962c5c58c8fe9150b2a187ad931c26394cce99a1336264b4ce499d131ba69d4cd49360d6aa4d6499667351ed99cc09c,
0x7291cf61ca839597c348721c7cbe380014eac1cb125e97c200d,
0x26384cb9a061320263c4c89a00340267fc4cb098d133226604c909931aa826504ca9a033b3e6814d011a0734126820d0219fe01b,
0x27c84fa09f100e027dc4f624d0007,
0x13d812a04ea4e0d245a7034e384d440948126026004c4097027626ac000413a026204c206e80dc826304c806a814ca744270a8d2099e929f468e4d41308135246684854907a34a026,
0x8209808001044e08a412d822e00ea4ccd24c260d4c1408281048207040c081410581f603ea08b41160074260a9d3896292e125b64b711a112dd01f,
0xec807b00f807800f2249300f208cc117a77c04340864110821d0438087810f822025e64bdc97a92f425ec4bc897d12f925f04bc40f401e728ce925095c146603d24ad495a2499026,
0x11b023904700754986a343046e4c700e901d404840968122824404864cc4126024b04b20934129826a065009a013493434e2a099c0ec00772684983c9a2235b268a4c991a21325263c4cc898e81d703ac01e095824924c1408c411802350464086c0490001260e4c2c98512f8260c983811f823e048209000f2a77d262e9c0898b130c046,
0x3b601e81178233493209b00ef81dd03b29df80f081e34efa924c9589347010,
0x126025209ec0950275269e9238138276e04fe0a013bd81ce49224d889af234b04f84d6d1a6134a4e369c009a8a34a241e04c0098812e04ec4d58000827404c409840dd01b904c609900d502994e8809cc0d601b5035206a00d981b4035c09713bf9334467e4a54946a340269a097812e826004be073099b2345266a074128f01ca0396070c0e2275103820c94193832627fc4ff538892aa04ca09993b8934126804aac9c2a348267a4a7d1a393504c204d4919a1215061
]

def policySharedUnitFixed0HintLeaf69 : PackedNatTable.Table Nat := .leaf #[
0x7be527800083de07c40f841f1949c293a526c1be038506fc0dfc1c0109807020f80a4c2473288a51111b09497018,
0xeb41d603cc075e0eb8a3523684e440f3d29903d107a40f541eb03d307c8527d389148b07600f2c1d983b228ee9c5d31183bc28ec0ec4a3a27164c440ee8a39946c290851aca441469027,
0x4e0c0e6a48b04ea04b40960129024c04c0098812e04ec4d58000a61026a48cd090a920f46664d45381a71c017,
0x1ee287ac223844608aa111422095064c24984d30c26194c38985c22402e305c40b7c14d029c49344f151ac94f84c58985525414f646e053dd315262b1ee4117c22c045908b43ad87360e6d4284000524725e74bd297a9326262f3d6c5430a859fd2034,
0xc32186030b00f02d72185cb5c00010272179030f85e50bcc184cb5a248e4bf097e52fda5ff4cba5a14b61a3a02d089224b5d23a201c,
0x490212c1248aa324720922552400084874a7a1224245094509161230aa0a3da2a8054f42469545015,
0x216246c04e809e12142eec7ad8918123a6624fe01b7232f64684cc40052021a233c075005b11842310ca0a4c6018,
0x1b2036586ca2ed05dacbb506c92ed8000436286c40d8c5d94bb306c20d863e1c36606cd2eda7fd8bb717692ec65d90363976701b,
0x1b3c36c17770da01b4836886d32ee25dc8bb806ce0db41b6436a06d51f121b5836b97743ff05dd8bb997782ef45de4bba976f01b,
0x35ba15d4ec0992131aa6294c9e9e213c486dc0db61b9036f86dd009a0004bbe23ae2ef645808af86a10c5e5d01385175901a,
0x14686a940008a3a147e28f85201aa335486a885198a3d146a28d851b8d07147028e4d4e241c35366a691f71a99018,
0x145a34b05160a2b3522907c51720800002289c5188a3214482894d46a3eb352c934c5179a92014,
0xa1314242840d370a1134e800045030a084b1428285059a7314182834d3523e934d26998d37a3e8015,
0x15023fd103f80014f1a9e313c58ea81d527bdcf7c207e00c,
0xade3ae02b805712c3691082b1161e4e4e15c9258161a00c,
0x2909028a6174e8e9e3d34926944d2c9da93c68a1b1434288850e8a1c00d00004d411a8b35146a24d40a78b4ece29045220a4312a86a9d3869aa601f
]

def policySharedUnitFixed0HintLeaf70 : PackedNatTable.Table Nat := .leaf #[
0x3ba07750ee91dce7d15226a062000216582ca86810b2e58ecb96a65f2c7499287778eee1dda3bc464a00173e9a3b9881f1045208033d864a8c93002c7365072a0eb41c87d29280a6734ca23f807b50f8c1ed832006418c8d1918322000d8c8f1920321c00c8c922036830480e101a203c407480c8cfc19f696e867d0cf819ee006064320bd48cc82f936aa0bf49d47355274a4e83f9a91610309f46053,
0x1dd43ba07600ebe1d8465a87620ec65fdce7e17f92fec5fd43b2980b000297f52ff07644cce99a1334a66b2ff46034c0617f801b,
0x1d983b228ee9c5d31183bc28ec0ec4a3a27164c440ee8a39946c00e,
0x1be473386fa140685e084ba61605ee0be924e13da4c9a698921a06f80e6c1cdc39a0a02446c0004858252d05d40c0017f1083060c0c15297030401180238189a74404e606b00da81a9035006cc0da01ae04b89dfc99a233f252a4a351a0134d05624e593afa15827ba86785ca8b9421b82bf4da69be220420acc15902af055c4e551a7a0c634c28ee4be7179504b,
0x5560b653aa13be277a4ef09df93bb46a08d5481121284e4e985d315262b4e8e993139420c7014,
0x45a845908b191621cde39c127ea2cf08bc8b4d16922d008b4116422c045d08ac542ca8622d1014,
0x460d182a6084c2a99047449ed6202245e917b91844608461518323034bfe985130c26194c80990d322265b1bb6820504120831fea2c345848b6c16da9380f140e774a3e7af88baa5e445e245fc8c0918022fc07acffa260b4c1498692f426544cac996132ca66617262eb45d60b9b17342ea85d4a4e2465000052f3a5e94bd497e12fca6094c2e986d3a3a78f4cb4980134b276b1c6e2dac5b91bc336c86d78db18b07160c2c2110e0b691c6c7a011fd1b6036be9024f409bf237d29028df0a49645fa8c0518022ff45fc46092f2a30206f,
0x116a116422c645887378e7049fa8b3d169a2d245a0116822c845808be542ca8622d1012,
0x6f80e6c1cdc39a0a02446c000417c0b951728437057e9b4d37c469851dc97ce0df2399c37d0a0342f0425c81082b305640abc1571395469e831930b02f705f40ba924e13da4c9a698921a1795029,
0x105700014c28986130c8438086e1084216842b01149d04a72a53729d698ac22b845642a28dc423c87e61d023a0080820af4d06426c84d10a0213c427484f90b5163c9e6418002fe21060c18182a52e06080230047275f42b04f74dbd217d42f891d10bda0ac487461e8a97a3722a149901321a6444e8e9e3d34b276b042,
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,
0x2da053e0a6d3a1139e27384e689cda49a27100b6c15093a34916985130b02ac05560b6415d02bb05780b5815e82be27a0000415513a627784e949d213bf27768d411aa93934c3098649c4a357029,
0x105700014c28986130c8438086e108529b94eb4c56115c22b215146e211e4a97a3722a149901321a6444e8e9e3d34b276b01a,
0x12c025204980980131025c09d89ab261026a48cd090a920f025a09d49a78001491c09c13b7027f05009e0c9b1134a4e369c0013981ac036a06a40d401b3036806b812e277f26688cfc94a928d46804d349a8a33302d,
0x1b90390071e51511b20373292c0e1c1c30388289a51381c4838a17b80e2c1c6149300025141207944f28989c8d3c0943b01a,
0xf501ee03db4f3e0f74a489492007
]

def policySharedUnitFixed0HintLeaf71 : PackedNatTable.Table Nat := .leaf #[
0x1cd839907500e9c1cc03794944517d1b314604e9807800f22493073e07a01d503a903d29c8495aa70125680f35252271f06bc0e740ed274f06fa0df01c2837e06fe0e0084c038107047b2c000a6174c3c0f3d29903d107a40f541eb27a007a60f901f283bd2940527d389148b29100eb41d603cc075e0eb81d803cb4f265210a35946a46d051a4a232473288a51111b0944304e,
0x221d0fda61f1340a68316346de13412684009,
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,
0x8aa1118223a795055a4e5021c0437084294dca75845708ac85451b884792a5e8dc8a8514f7088a110023e847e087810f53cea7a308369d152530bb3058c0b1416082c005a6926c9d4235238042c78dbd14f346ec54c8a7b2370030,
0xc5918b6316863a8c5e18ba318d2d70c6218c0317c03589ee396a9058e5a22c24d8e31f063d806e13de27dc4f6007113e027d52681ccf01d,
0x145834b05168a2e3524907c5158a291450934cd4a8a304f182898d471a91010,
0x6630cc8195032a96f94754195cb8300014e68198525b170300d,
0x1bae37587fd0ff74426922d320a6434c889b1937820861bb03fe07fc8dcd1b9c8b14000a5f84bf297fd32c26594ca6995535726b74dce786d0439e25020,
0x25ac4b6096912d467691ee89601b8a784c0008dc412c49330f0919db00f,
0x35ac6b50d6d1ad835246a50d4b3b24764cedb1db83b6e765103ca6724d289de53d30be717cc2fa45f41c403882710ce211c3f1a8696fcec60fe31ace35a46b40d4d00720004ed91db43b66765d0329db502b,
0x68623381a1c344173149081a14346068b0d1a5cdcb9c173900021a24b9b1730011,
0x342068a0d041a0d3d5972e2e6a5cd0b9906850d0c467034386882e629210b98172f012,
0x1bfc79540008e041c129d906fe8e051bfe380070090381c04380cf27246a3c9a79312179e4b014,
0x2c6058a0b0416013a805869e7016902bf20d20b1c1642125088492a124725e74bd297a857c02ba36a40aac15613a349169858155139346a08d549d224dc275a91b49d3a49b055a0ab8157902505600ac49cb2467272a4e513a18273035806d40d481a8036606d00d7025c4efe4cd119f9295251a8d009a6808a085610b53a2841b4160000530a26184c3298ac806253841529901321a6444e8e9e3d34b276b494c53949d4a352059,
0x16302c505820b009d402c34f380b4815f9069058e0b21092a48e4bce97a52f5262b15f00ae816c82ab05584e8c000a48b4c28985815526184c324e4c9df93bb46a08d549d224dc275a91b49d3a49b055a0ab8157902505600ac49cb2467272a4e509d4a352036,
0x5907fad24725e74c2c11bcdf400014bd297a816793b54c3497a130ba62e4d669ad135b26b24d6098bc16882d0057e0b001608bb505840b0c9d4a40d27504e9d1aa13ad024
]

def policySharedUnitFixed0HintLeaf72 : PackedNatTable.Table Nat := .leaf #[
0x2f505e90bda17b82f796a70bf817f82fe85fb0bea17dc0caa4b32d328e70b4d16922d225a40b4796870bd617b02f385e84f0a178cf85067b14ca297c5308a6014ba962cd609ac94be897f1393264c4e5039fc2aa8e820aae15602ac8e6b0ab439a8f5a24352c0e581921d9ec92d0c5a38b46a39a0c0e18213ac8b4314bc5aa51cd9688046,
0x2144000297cc13981ac036a06a40d401b3036806b812e277f26688cfc94a928d46804d35323269816802d085a08b3c16766e592019b9b1ffc36ec7130c7d00de27bc4f989fa13f89344d2c9e714a0841d07fd8ffd1ff836cd046a463427841e050f0a21144026a4044000316746a11387a14503d,
0x6db8db61b78389863e806f13de27cc4fd09fc49a26964f38a2410aca953cb09264c4e509a605a00b4216822cf059d9b9648066e6c839907220ec36fd3d90e684b5a6fe8000a48e4bf097e52ffa6454d6e7ac859885740ae615bcb0d23923718782509d9078143c288451009a90110000c59d1a844e1e85152e21e00042,
0x1397a20e4d863124e538da844289b106d10da41b469098ef7a0964130825c62c2415012,
0xd90e1aa7034e38989858808b41b5e22d445b213a4c80990d32226c5326a90a0c9a24dd4c8c9908c4a00014e08999933da67c4e3a989d33f268001f,
0xcce4242992d33926a14d462b04d89a6734d4a9a9935226a24d949b3116e150600029849309a61c4c2e112017182e205be0a6814e02dc49344f151ac94f84c58985530a26164c309865315a64a4d9c9b3d365a6cd02d,
0x62e006d00d827b53d28c6118cc96bc6d60db01b549ed087ba20c1f9a3f307e5900121f03f38032912f226044c5197a48b4dd29ba937ba5e044f68835232204a189631280338c4c18d29ed43ff988f0002985130b26184c329ed9332a61d4cf699f133ea67f49ce72a12149df603a,
0xe78428697cc13981ac036a06a40d401b3036806b812e277f26688cfc94a928d46804d353268b300adc15b42b405674f662c305878b0e16142444c9925f84bf2986d323265a4c002ed12951c03498e6d951fe1b662c2a8e40dc585890b18162c2bf858e4f0811c823a047308e20c402381feb000292392f3a5e94bd49859317a53a2a4854951ba152605900b4416802bf274e8d509d6a5512c6458b91cb1ec1055,
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,
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,
0x2d0057e0b493ce02ad055c0abc81282b005624e5923393952728926c9d382d10590849524725e74bd297a930b262b15f00ae89cd939c273c9d091a8139a274893709d6a354025,
0x1075428c922d320a6434c8899153630dbe221a37586eb8dd81ff084f509f213f4f6690a8f0520873c4a88f111d9e084de08510000a5f304e606b00da81a9035006cc0da01ae04b89dfc99a233f252a4a351a0134d4c8c9a6059885740ae615bcb0d239237182d005a10b4116782cecdcb2403373641e050f0a21144026a4044000316746a11387a145049,
0x8b2116022e845608ae84a1393a6174c5498ad3a3a64c4e5040888121023055a4e51063950a2a28542c22d045b08b811813a58438086e108529b94eb2a2a544ca8915112a208dc423c87e61d023a0080820af4d06426c84d10a0213c427484f90b5163c6de90bea17c48e885ed056243a30f454bd1b9150c040,
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,
0x13a601e003c8924c1cd839907500e9c1cc03794944517d1b31460073e07a00f3946749284ae0a3301e94e424ad495a271f06bc0e740ed274f01e,
0x44f20005304a6144c309865329a67b4cf899f533fa28c22ca8b55374a6ea223a447c88f10cf1d1a3e3c7d98f8d4e58916cfff21d544ae44a52efa270020
]

def policySharedUnitFixed0HintLeaf73 : PackedNatTable.Table Nat := .leaf #[
0x3a153ac86f00de41bc437700e62f189bf8bc68a5e1d083a1c74306e90dd6039407780ed119695f846508c914d86b348ef248649767b4521e1ed001f,
0x215442b085590a9432286550ca2310214e429885710af214842950c72198432e864d0cb10a8431e8640856a192018,
0xb5816b82d685a12c868e5d18780010b54169125905a20b5216ac2d385a82c8c592cb2516492c8e5920851964d018,
0x35c86c02ec01acd25d06ba0d701b0435906b10d761af435f06bc2eb85d7cbaf175d2eb65d511d6975a016,
0xd641b0435c06b92eb48eb435886b50d6892e90af00014f881afcbaa9754010,
0xf01124624910f125f34c0298093018273035806d40d481a8036606d00d7025c4efe4cd119f9295251a8d009a6a6254d769afd36026c12124124084b04922a8c91c90b510d14bb48758cc7018202e005c40be109317707d8d24725f84bf297fc243a53d091212284a2848b128885d8000a6304e4c99313942633336a8f68aa0153d4c64702492c926d049,
0x680462200052fe27604f869941314a65e4f589f113c40f6b1ed43e307b60c7f0064000cfe6a4583f989f0888491080b2e58ed385972901d,
0x101c2034407880e901919f833ed2dd0cfa19f033dc00c0c86417a919905f20c12036324800c8c871920323c00d8c88191893a905fa6d501d,
0x5ea0bd227044de89be3e4c98152fe265c34545a1c2f589c2137626f105b80014bec97e12fca5ff4c64996132ca6554cc69994d14968801d,
0x1ea83d207a20ec01e5948428d6522c1eb27a007a60f901f283bd4f265280a4fa712012,
0x27544ea09d713ac27404e924ce347c8f953b788ac105a00a0c958824104622bc457051f0a7214dc297888d4af621e443d887c4af45799257192d4e1062c844524c41118222c4440884461c20d4420083f106820c8419887f10822108421888041402214c7e98cb479462e8c5da3c331789a1842308301058009c29618b932068f30c821a3d047,
0x145c28d05190a2c57211c185184f1427287b30f650b8a598522a1a36139a27304ec09cf13a29338d1ca3e63470147028d85230a3a14e029b27652bcc92b8ae727072b9a9f1428a0511138c271c4e2882f105c14a401198b8346668d4d1a05280a4e009029505344f9616f12a99658495a578d25595c703f,
0x6630cc819503a0055042b89d81314a64f0d6e45808af86a10c5e5d0138517594f8a9e213c486dc0db61b9036f86dd009a0004bbe23ae2ef61ce439c073b0e7418ac314805a00065f491dd17d14cc45f691d5065b0cb826e832e8741436497ec4e185c30b8416fc2df27cc2cb68e60d1926332fb68f88b7e9703041,
0x4a41f161294253155648ae1258aad80014ec2128d255155500d,
0x27113d275a1272240c484890712103d747af0f5c1ec47f1d2289fc132ec8f50cd50f5f1ec680c53489fc4017,
0xabc81282b005624e5923382ae055a9e709ca139500b
]

def policySharedUnitFixed0HintLeaf74 : PackedNatTable.Table Nat := .leaf #[
0x87a11f0a988441495010f023f047d088054c91bb14f300c,
0x20aa409d0c500012040428416c02d7277c4ef49de13bb43102bf057c24dc419841a015ca124424684150911b4e05780aec15d1b520556408909427274c2e111c23d847a088a53d91ba94f74c5498ad3a3a64c4e50831c1568b1d20d49db43f6987c430e2c683f608070fde1fb803f843f4fa261f51e11b784d049a105919b8010282c6440b881d164442045920b25164c9d183f587ea30f66e052381b7f31548ff8dbd139446a08d549d213a505c,
0x8e454b80008461495211d02398471062054951ba152600c,
0x161a2194c309865316261508cc11b823684652a308dcca8ca61b4c5a97c933da67c4d009b493cb1016087811f823e8440201a975440d081b103220812bb081c4aea2074591108116482c9459327460fd61fa8c3d9b8148e06dfca99237641660b1816282c105800afc83482c705907fac000a48e4bce97a52f5261608e094e93e9846008b8116c22d045908b0117422b04574fa410e021b84214a6e53ac59507e730f46e14a8515142a165430a8995122a2254411b88479084410902128419083453551b694d82a5e8dc8a8a84232a4898bc9d6a46d274e4ea11a913a9076,
0x13ba28004ff89aa13509624d2e23e713bc854d30ba7474f1e99313aea6964d303a2859f8b3e167a2ce80440003372e9008f6d1a4c01c,
0x274907040e101c1838006fe0df8a4d037c06fa9e093d0144346d45110a22a360288c0f3d29927ca29100fb41c7038d07140e241c7949506e40fb93d094ad46d25150a27a36329580eb41d603cc075e0eb81d803cb4f260ee41e503bf077c025804a033c28f08d9ca42146b28d48da0a34835f069042e485c03eb295291dca0d833f045,
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,
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,
0x2d105a00afc16002c1176a0b08161a7bb275290349d413a70590849524725e74bd297a930b262b15f00ae89cd939c273c9d091a8139a274893709d6a354021,
0x1b09a494e369c002e71fbe4ca4995132b26af4d622e193d826b34d689ad532c26594cae994d32aa66f3f2472c12ffa60a4c3497a1322a65b116464c8000a5f84bf29859323265a4c002ed129502c005822ed416102c3275290349d41c034bce97a52f526ff4e34982530da66e03a,
0x16227da002,
0x39e53c80e8a167e2cf859e8b3a0110000cdcba4023db49e9850c0a17142869d53871ec2013,
0x272d1f5480787d8a027005,
0xef51de83be477d0efb42dc922d300a6024c06989477e8efc1e003bfc77f1f5e3ebe7d80fb11f613eba7d70fa88ef61dee3be05dc1f63000292392fc25f94bfe98c8e049f52025,
0x2b3856f1d7015c0598a1444c8c9a60dc624422c3415a02ba85691660850c000a5f304e606b00da81a9035006cc0da01ae04b89dfc99a233f252a4a351a0134d4c9a6e2d1c99615026,
0x12907c584a51f1485dd2f98273035806d40d481a8036606d00d7025c4efe4cd119f9295251a8d009a6a6604cc47fe522b849b0938556824e894642ec000407000df024003848eda6fd23b498c1393264c4e5098cc74186e50dda1ba0373807600065e191d79ecf33708df4aa8155503b
]

def policySharedUnitFixed0HintLeaf75 : PackedNatTable.Table Nat := .leaf #[
0x1f0a0cf6299452f8a6114c029752c59ac1359297d12fe27264c989ca02f1a76c2d1c5a44b48168f2d1a8e6830386084f82230c461005b118e231802e16a9473617d80cb27b114d6232002e806101d003880722486359a1bc037906f10ddc0398bc626fe2f1a92cc5a18e7f0aaa3a082ab85580ab239ac2ad0e6a3d6890d4b03960648767b247428e841d0e3a1837486eb49767b4521e1ed0051,
0xb8817b02e405cd16b8001491c03d807a80fd4a22477d2fc25f94bfe9d813c326324ec249689331265466a05d492f233802e005b858a092e1e0696144930f023eaa2494cc7a3d647fa7d50fa99f663ece6db9246125902e,
0x17138207044e090bbd24b805c00c12175466a8f58936925900d,
0x27de3eb67d68fac9f583eae7d593f1010017729f8c5db8bb83ec692392fc25f94bfe98c8e04892312488b30000a6014c04980d30c26194c58985531827264ea49894cc71c0a025,
0x2c649f5245a5fb4c0698140caa2670002980530126064c0898912fe263a4c7898f531f061d2d809a680bf817e02c205700c2818602b20568923a33b24e0492919d124b024,
0x17c08688cf01d493180318061007,
0x847a7e01dd646308c586322da89c24fa490941ea83d587aa80303f7a941852c8a5814b6296837086de009c1a7834e173d49720004d5ea3f135784244848108e1d763cac7a9910a1eb23d687ac002f4e787efd11c1fbb3f2e8599238a167032,
0x35ba3114bf89d813e727c34ca098a532f27ac4f889e2036e06db0dc81b7c36e804d00025df11d7177b4f8445808af86a10c5e5d01385175901e,
0x2c28e8b0b0815fc2c5858c0b1239e10a1a64d3d828e58b171628487a1f8d16400014be609cc0d601b5035206a00d981b4035c09713bf9334467e4a54946a340269a9c1130a26184c3298ad38ea6e94dd43dc483e8eb71cdc1088f5b9fd222ae45608aca2b3456e8ad515a22b6227c44fc8a0114222864505147228f45268a451482292213a42790d6109a213682bc80810120fca1f98c3d246541589a0d0bda47642f8456c8ad115e22ba457115ca2ba457c8af115da2bd45808afd15c1878066,
0xf751ee83de47bd0f814430922d30a26184c3298ad3771fed3fc28ac91589ebf3fb27f6d157a2b03fae3dd87bb8f781cda8508239047408e611c4188152546e85499326058e4aa215fc2c5858c0b1239e10a1a5f304e606b00da81a9035006cc0da01ae04b89dfc99a233f252a4a351a0134d4c9a7b051cb162e2c647ad8ff01fdf3fbc7f7521b8f734fd23a2040a88141632205c40b008601080c242381feb000292392f3a5e94bd49859317a53a2a4862a91ff18a93fac915522b1fd8065,
0x44b4897112ea25e4f8038b0f3b248044b08964890112144c6000524726544cb0996533da67c4cfa99fd36526cc4d9c9b3d36c0e341c5638cc7170e2d1c5e2dd127c1e77486479f92842260028,
0x5670ade3ae02b80b314f646e31221161a0ad015d42b48b304fd46e2d1c99615011,
0x7f28fe71fcc3f91033271040ae99cc5f68bec17de2fb8e229c463890711ce2226da4db83f746a30d4c1a90351c02080033b22908102e206701e,
0x99c1aaa26744cf1a0c3b408f804a49a104ee8267d2649a0b00d,
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,
0x36134929c6d38005ce2d060625246a6524ca8995932c26594cae994d32aa66f3f2472c130526454cb622c8c9926164c8c22c10cd232c2d8200052fea5fe4bee97f132d26000c3c055c0ce019b03104a0d19f16c24bec97e12fca5fb4bfe99d9357a6b54c3497a130ba6b34d689ad935826774bce97a52f526ff4e34982530da66e045
]

def policySharedUnitFixed0HintLeaf76 : PackedNatTable.Table Nat := .leaf #[
0x714207740f081f07f90e271c528680f331e6540f681e8f399e7200e,
0xd3d1a7c34f000f8dfa1bf237ecf251e49009,
0x5ad0b42168cb2600010b4c9f0d25916430b5c16b0b26a39700d,
0x38006ff8e051bfa3f453f6a053485e793070090381c043fb103a0fee1fda81cd3398be54b4a70f936d0fdd1a8c35306a40d470082000cec8a42040b83f947f38fe61fc881993882067203e386c70d0e161c2a386070b8e193cc079850600e111c26796932527f34f589ae53d69e5f3cbc7990f319e62418a81c92351e4d043,
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,
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,
0xe794f5c3a2859f8b3e167a6e5d2011eda1430285c50a0e7d49fc69d53871ec2011,
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,
0x37046ea214c18d2939c6df106c20d684ad0ce9e0b4338375c6ec0ff8427a84f909fa7b83c14821cf129e0820ea9f7c5a00b4216822cf059d9b9648066e6c6e00dc31b8431387e40ff61f8c3f1d3de214b429236fcf04a42a48c03f247df0fc01f7e27d901ea45f409040006da8db71b6c36f13d90b310ae815cc2b7961a47246e307130c7d00de27bc4f99e714b8878010490b0c161e2c385850911326497e12fca61b4c8c99693000bb44a54700d2639b6547f86d982b385680aea15a459821434be609cc0d601b5035206a00d981b4035c09713bf9334467e4a54946a340269a993473c05890b18162c2bf858e4f080b8417182e205be0a689e2a359278c0a6c14f82e905409fe04fd09fc49a2696462a8ba449cc39f527f1078143c288451009a935089c3d0a2a35a27109268239047408e611c418804703fd6000524725e74bd297a930b262f4a745490a92a3742a4c0b2016882d0057e4e9d1aa13ad3faa7f50fe99f093e108dc473704223d6e90dd2a896322c5c8e58f609b8b472658550232462408e78392159e0d0d3,
0x41c69c0d38e26264c9432d867fa5bb19f29fbc5ab8abd15942b0055f8ac449b66c351f99bad49da38a866b0cd519a8334c668a5b742420005325a6724d429a8d352a6a615829b2936626ce4d9e745ce8d24193cea9b2d366a6c9030,
0x110a0fcd1f983f2c80090f81f9c0194897913022628cbd245a6e94dd49bdd2f0227b441a919102526c41b5237686ec89e616d42dbc5b48e3641600a849c4a62b08a88b6131626b24d7c9b087941f9316aa2d645ac0b5615862b0926d9bac480c6ead358a6bd4d7e9b01360a6a020260b6c16d029f053692689c4235741629d1d3c7a6964ed67a00de01b6236bc6d845840b6d443692392fc25f94bfe9901321a6444be49a013690ce941c46c4c000a61c4c2e9855339a6a54d4c9a9135125f14c28985930c26194c3a99ed33e267f4da69380db0240937767898f139df4076,
0xb6814f829b4fb292689c402db05429ebc9c4a35700b,
0x84908341055204e849880a1013416292392f3a5e94bd40b7929293c44c3a2bf057c24dc41980ae5091a10542446d3815e02bb05740b6415582ac2746922c15082db05b40a7c14d02df100c0b80224150600029849309a61c4c2e9ff1316261529f08f049e2938846ae4e2530a26160554986130c9393277e4eec15682ae055e409415802b1272c919c9ca939446a08d549d213a504f,
0x9ec453588c800ba9f9807100e4490c6b347428e841d0e3a1837486eb49767b4521e1ed00de01bc837886ee01cc5e3137f178d01b,
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,
0x9f78fad9f5a3eb27d60fab9f56007
]

def policySharedUnitFixed0HintLeaf77 : PackedNatTable.Table Nat := .leaf #[
0x847a177000297cc13981ac036a06a40d401b3036806b812e277f26688cfc94a928d46804d353180eeb2318462c31916d44e127d25330266214b2296052d8a5a0dc21b812af1abd47e26af07c504a8094e129024d849c2ab412744a327e421241240aa404922a8c8de50b519b846fa5540aaaa37c3ff242507aa0f561eaa00c0fdea506212242408470ebb1e563d4c8850f591eb43d60017a73c0d3a1a7d3f4017802f405e40bb010024be8cdc930010101f89f8940004874a7a54f5243a4b92e7a7efd11c1fbb3f2e8599238a16706e,
0x5e00bd017902ec040092fa3374fd0040407e08ba1214027804e809c44f424e44818909120e24207ae8f5e1eb83d887b1a0311236042c0291988014025084a080a20142012405280a622489f606041c660002923938da7004bbc89a08d1a3d923447f1d2289fc132ec8f50cd52691234265ecc9ca4870d3e1a753f38944091e123824504895002038006f812001c2476d37e91da1d061b9437686e80dce01d80019786475e7b3c084010700a647acaa02378336a5cf525c9260063,
0x1da03b807780e5490c4778076005e119e043540124c600c,
0x5ea0bd217b42f705ef2d500005245a5fb4c029809301a6054c4a17c44e009bf0be817d80cb27fe49665a551f196944cb85a48b4896902d1e5a1c2f585ec0bce17a13c285e33e1419ec5328a5f14c2298052ea58b35826b252fa25fc4e4c99313940e7f0aaa3a082ab85580ab239ac2ad0e6a3d6890d4b03960648767b24b43168e2d1a8e6830386084eb22d0c7428e841d0e3a1837486eb49767b4521e1ed00de01bc837886ee01cc5e3137f178d14bc29ac464005d4fcc03880722486359a5aa51cd9688069,
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,
0x4fc62edc5dc1f63491c97e12fca5ff3812248c49222c94916058c0bf817e02c20575160a6044c4897f1245124a4674492d300a6024c0698c8cc70bb902009f8940004874a7a12242450945091625113f38f52447a9bb08858f2c1e683cb8796802c3f30913d11c86950d2200d434c06990d1e00cc3470f5146543ce479d8f3a1e963cf479e0f424b9e3d047a00f484ba0397516ca6524cc099ed33e267e4d009a85352a6a616e887a0000a6534ccc99f5368a6e549f83cfc79f00310d207e9d2281fa64dda7ee925c19b547b45500a9e9c0a070,
0x2c68b25245a6014c04980c49209234fc62edc5dc1f63000292392fc25f94bfe121d29e84890914251424589444fce1a7434fa7e802f005e80bc817624be8cdc930010101f8921d25c973d336a8f68aa0153d4c6470245dc8100381466380bf817e02c29dc02fb08f44b0223ac47608ee4afe234c46a093d11b2236846d8f6732f4027045e090c121622e4c9c997c32f664e9345a6903f94653d1eb99494966492919d124b058,
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,
0xbc017a02f205d8080125f466e9fa008080fc1174242804f009d013889e849c89031212241c4840f5d1ebc3d707b10f63406202804a109410144028402480a5014c44913ec25de44d0468d1ec91a23f8e9144fe0997647a866a934891a132f664e5243869f0d3a5cf525c926003a,
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,
0x1c0109807020e093a483ed071c0e341c50389071e52541b903ee4f4252b51b49454289e8d8ca56035f069042e485c03eb295291dca0d833f288c91cc1bf837e29340df01bea7bf079e94c8a4403ad07580f301d783ae07600f2d3c9948428d651a91b41469079a9f281dc83ca077e0ef804b0094067851e11b3a4a428868da8a221445046,
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,
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,
0x3a8030006200bc233c086a4c6007,
0x5170a34146428b15c847061460ae627624f0c98c825d04b9098612f825e84bc008c0004ab7a3812adc98d028e051b0a46147429c05362bcc92b8ae727072b9a992028a0511138c271c4e2882f105c14a401198b8346668d4d1a05280a4e0090014852e0a62578d25595c7039,
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
]

def policySharedUnitFixed0HintLeaf78 : PackedNatTable.Table Nat := .leaf #[
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,
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,
0x1eec3ddc7bc1fe03fbe7f78feea43748aa91587ba8f741ef23de8ff0a2b245627afcfec9fdb455e8ac0feb9fd8018,
0x358000052fe27864c649d6c305860d0c181824b55239f2d5698a53d38a6714cc6b2926aa662014,
0x12c839e84b289664f52675921c096012d625b04b4896a33b48f74ced99d5010,
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,
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,
0x13c39c0e381a9a2d348268c4eb42410cba809c44f402804a109410144028402480a5014c44913f58e921d223a807498e9534929c6d38009db4a60a02c20d0419084a109021107e716541fad3a30b26164a2ca45940b22103a20712ba881b103440352ea84412a0c9849309844805c60b8816f829a053892689e2a35929f098b12541b7f48026e04c3d9b8530f453611b694d53490996132ca6574ca69955337a5003dc490fcf70a1154ca499ed33e267e4d009af5360a2174ce49a853518ac1362699cd352a6a64d489a8935fa6c04d7c9b0936da6dc4bbc89a08d1a3d9234424e44818909120e241402605f30bec899d30326044c4897f131d263c4c7a98f82ff8159030c06140ae08f83f2800052fda6014c04980c16e26184c32987130ba6154c4a9460cb4127046765a7934d24b332ec8f50cd526910a6,
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,
0x27971d142cfc59f0b3d372e9008f6d0e791430285c50a0e7d49fc69d53871ec223148c30487197d230e46188c4918804188c35304260a4c2a99cc560a1214c9699c9350a6a34d4a9a9936526cc199c8b7022124a84c28985930c26194c56992936726cf4d969b3535226a2492e8c21241a3071764243448b0910121e2c287de8b0b1618886c000a48e4bf097e52ffa6404c8699112f9267b4cf89a005b68b0844382da471b1e8047f49024db024e04da46d9922f1b6532fc8f54e00a7f7065,
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,
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,
0x14098f8144300005245a6144c309865315a6ee3fda39b4ff627db4c2e98b53261eb6012,
0x1f9c0194897913022628cbc000a48b4c28985930c26194dd29ba937ba5e044f643e08008fcb1f989e953d90db44f6e27e84fe008800062ce92689a593bfe8129232220d024,
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,
0x2787381c7035345a6901ebe7f11346009c44f424e44818909120e24207ae8f5e1eb83d887b1a0313f8e9144fe0997647a866a9348a7cf01d
]

def policySharedUnitFixed0HintLeaf79 : PackedNatTable.Table Nat := .leaf #[
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,
0x7e0a02c20da745085a10ac045274329ca92984eda53034929c6d38005ce3f7c994932a26564d5e9ac45c31be8000297a52f50bb3058c0b1416082c027508d48e01261a4bd0985d31726b64d649ac1359a6b44d6a996132ca6574ca699553379a4807de10981f903f107e80c593a20273035806d40d481a8036606d00d7025c4efe4cd119f9295251a8d009a6a7d04fb40b4924da49e494a52bd1b714ae054,
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,
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,
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,
0x9f5c05425090148028c02411a4049e2e412d1918a4618461c8c3118923100831186a6084c14986130ca6154ce62b0510ba1150002994933da67c4cfc9a013f591244bbc0298052804944d09af5360a6dc4ce49a85351a6a54d4c9afd36026be4d849b6d35226a2492e8c21241a30703b,
0x17b82f685e90bd417ac2f605e70bd09e14b43168e2d105a1c2f796a7032c17d925985e35042299452f8a6114c0297453588c800ba6b352c59ac1359217f02ff05fd0bf617d42f9804c120a241c484890312086dc134588c41184016d3f3280e00a4042c48da82033106505348197547a865d8b4ca39c2d345a48b4896902d1e5a351cd0607162c6dc4b54a39b04b,
0xa67503e182c306860c0c125aa91cf96ab01ca038d2430a6614bc29ac464005d4fcc6b34d6524d5015,
0x4a2848b12889f9c2b0254e2c1c66d4245048950022d0c07000df024003848eda6fd23b439fc2aa8e820aae15602ac8e6b0ab439a8f5a24352c0e581921d9ec91d061b9437686e80dce01d80019786475e7b3caa023da02e,
0xea51d483afc7600f053ed8922d352a6a64d447dacf7a0eba1d7a3af87791f4f0002923931b26384c72993cfa71f0e019,
0x1e943d207d50f4e1e983d407a90f546108c23184430866114c20986830ce6198c1f80014e7a993c3eb10cd21981f5cc3521d230e261bcc3707d830d861acc36987030d21e783ce87a00f3e60e0c1c983b307460dd33b184002f,
0xbc7178c2f0c5e11c1a17882f14e110bc0179040105e48bca3840826ce109c1f17827060e0c8bcb38367078e0e9c1c019,
0x2f345eb1c2b179e2f385e81c25384c70905ea8bcc17b02f5c5e88bd2200a2f4c5ea1c28413a70a8e139c2c385c70b4e149c2301b,
0x81c104085d0411082486c4000a6494c94533523c14cc081e5b2c2a985540b2486bd2fda6284c9c58111d194cb018,
0xbd627084dd89bc44cc97d83a60ec40e8a1d10beea4462fc69a646cf25be3bd468a42f505e9138226f44df1f264c0a97f1319265c0eb2958c3a107431d8a1d183a38749436497ec3a086600cbe197032d86630cc819503a0282e1dde3bb87768ef11928005cfa69f4a4a0216c02d7867f0b6216702cd059d0b3c58f0b20163e2c7a58fcb28a3ab2ca03ba07750ee91dce3b9881f1045208033d864a8c93002c00686448c8b39b28395075a0e43e8a9134fa305962c74270c2e185c20b7e16f82de25534586147028d85230a3a573938395cd4c6a98a431396cc0c625b4c31e16e14f4e27344e609d8139e274429c05364eca579925724ce34728f98d1c16582cb68e60d190e390c4c18c0315062c49685b351d21e831dd646308c586322da89c24fa4879c0c7e18f831d06390c6e956d04f89c90a30145c28d05190a2c57211c195c70a2814444e309c7138a20bc4170529004662e0d199a35346814a029380240a5414d02960027105820c105026861100210c4210845108820cc419087c4af421ec43c888d4af62134dfca5e74c12986d31c26394c9098dd3438ba6396000052f4a5ea4c1498692f424c231748f14c6598fd317292b4af1a4ab4e7a1aacba6264f5058a0b4b6e96e0474c60d875186ad0d581aa835486a74abaa0a8f8d1f193e307c5cf8b1f153e28910c75e0ebb1e563d4c8850f591ea488f48858f2c1e683cb879890e121c4437c87010dd21bc8b688b40f5a1eb000bd39e069d0d3e9fa07b58f6a1f183db064024e83f9a9160fe60680221244202cb8c83191a9f20659877a443497e12fca5ff4c8a992932da7924cce99a1335a66d49d87355274963b4e165ca525c973d3f7e9bb10f621ed48fa87b8fcc244f447288e0fdd9f973e229110ba4174b47587bccbed23aa2e065bf51d497db4c665f7922397dc2fda68a8b439688168,
0x1eb49e6c73c8a18142e2850d3aa70e3d842438cbe8e8a167e2cf859e8e7c13f827e93d28c54174a7da931b26384c7299d535c0bb2121a2458488090f12289610cbf997e47aa7005330a4e634b2934527f1b9748047b687ac002f4e781a7434fa7cd42e81d243a3874b0e941d0c3a107594ac69f25089a5f84bf2991932a26584cb2996930026644ccc22c941788852fda5f711de17de4f9c92e4b9e9fbf054
]

def policySharedUnitFixed0HintLeaf80 : PackedNatTable.Table Nat := .leaf #[
0x13cd0a010e501c9c39187220e409f5525e97bd476869813ed0e8a167e2cf859e8b3a0110000cdcba4023db439e450c0a17142869d53871ec201e,
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,
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,
0x6db8db61b78389863e806f13de27cc4fd09fc49a26964f388db520009ef10a5a1491b7e9ec859885740ae615bcb0d23923718782521524601cfa93f87e48fbe1f803efc4fb0e684b5a6fe8000a48e4bf097e52ffa6454d6e7ac901ea45f409082492e21e00036,
0x2bdc57b218d47ee413107a246e431883d4502a13120dc9758825904a20de41c45ca9be241e684bc8141b4a017,
0x9fc481c903a465c98e931e263d4c949b39367a6cb4d9a837c7f78ff0446a000524726674cd099b135ca075017,
0x27f44f5428212c51a664fdc34245098a12142069b91f41d5300d,
0x102f0d0a3aa837785120a32146228ac5160d2c145a34306ef91961fb82fad3921d56483e6a44d4b23eb3c583f787550ead1d582a587e81bb10002923931b26384c7299cd34f259040a47be9220205d02a,
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,
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,
0x42f29c0d38e26184c329871313261514061ccc39906f90df01cd839b87341404862c57ca4dc34c28ee4be717952f988ee0d31264d20440aacda902ba27488d411aaa0c7024,
0x1ac036a06a40d401b3036806b812e277f26688cfc94a928d468009cd0a180014be69934598056e0ada15a02b3a8342c2a8e40dc5934d01d,
0x20a13e305604a9c583873f85551d04155c2ac05591cd61568735283c16182c3c5870b0a1222931cdb2a3fc36cc7ad121a96072c0c90ecf6489460944128424e049b093294fcd6027864c52189c31306300c5418b125a16cd47485b313d3a66214b2296052d8a5a0dc21b812af27e81ed63da87c60f6c190093a0fe6a4583f981a0088491080b2e320c646a7c8192e32586558c991930004864d0c9b193873b531b2661194c32946550ca719507bd906226694d329981336269a4cd493ace77a41739dc9b212d99cdc39b69060e6d0cb30ef4886932527924cce99a1335a66d49d87355274963b4e165ca4d5ea3f135785534aa8237a3370120c2a104ab095412b52a0280f4eca14b0013882c106082804428883110e2218441088100404440888911244aa9bfd38d268f4d549aac6041c66491c305412e826004be073013282664ee22014402033b0674023c19e836506c49284a0c23c026824d0099b234538dc42f885e90bc21763db87aba24b4d1c94090d9a479436c9bd92eea24331fc8f2cc7fa6861100210c4210845108820cc419087c4af421ec43c888d4af62134dfca5e74c12986d3438ba6396097a52f5260a4c3497a132288b2422682dd2fb018f033206600c68189491a49d519e92764cc63934f4c89bc137627082f585ea0bd227044de89be3e4c9815319265c0eae7c9539b275b4e6842312ec88c7211423304648a6c14b829a033d24d5359a85890b19a2a345e5a1cb441a30345c8e684d6860834368f90d14a6464cc839207238e4c1c9239284969f1c030e999527c9e9348667a493330bae0a7814ec264853e33485a0d2fe26520b9c6924000a71b4e00a09132ba6534caa99bd32a26564cb0996532d26004bf097e52fda5ff4c7098e5324265b4ce898dd257957a470e6fe126118ba478a632cc7e98b92abc55751c498b5167,
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,
0x9c4d24a70050481738b4180014bf097e40c4818d1d8206380c7a7c60ac09538b070e7f0aaa58342ab9606471c7b2493b244524ea92352fe26524ca8995932d26004cb0996532ba6534caa99bd38c134b02b,
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
]

def policySharedUnitFixed0HintLeaf81 : PackedNatTable.Table Nat := .leaf #[
0x21744f9a1d243a3874b0e941d0c3a107594ac65fb4bee23bc2fbc42252c60a5c14d8232446508c721189764f92a7364eb69cd03aba7c9346068bcd17239a135a686d1f221134c8c995132c26594cb498013322666116488683bd0cb34f903234641a7c74f9c1b7036d86e40dbe1b7402680012ef88eb8bbd86b722c0457c350862f2e809c28baca4e939aa93b12fc25f94bfe9915325265b4f24999d334266b4cda858cd66a161210e183430606090c105aa91cfa15f061,
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,
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,
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,
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,
0x57e41a416382c84feca02c9d6a46d5044118441025761032a06525493a7010,
0x188031a3b040c7018f5042178d3b6168e2d225a40b47968d4734181cb54a39b14ca297c5308a6014ba962cd609ac9162e6dc493b244524ea066c0ce01570c3c5b04000a5f84bf204e4478a58011ce23b047588e900aa17cd244a5fd4bfc97dd2fe265a4c005b0919f1283039,
0x18d1d8206380c7a828189631280338c4c39503f1c7e30ff61f90811d231204618c231992d78c694f6a1ffcc47a6144c2c986130c82de4a4a4f11332a61d4cf699f133ea67f49ce0a8416d82da053e4e211ab938919d29ccc93b244503125a0d2fc25f94bf899482e71a4900029c6d38028244cae994d32aa66f4ca8995932c26594cb498012469275049,
0x20e89f7c7ff0dbb4a083fec7fe8ffc1b668235231a13c00c,
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,
0x107b1c4a31505d29f6a4c6c98e131ca6464cb4980133aa6b817647005330a4e63cdc41f07122147000292392fc25f94bfe991532d890e32fa9b84f36a46f021,
0x5881c3500029c0d38e03644c4c99013232642116836bc45a8b004222037806e8a5701b8036806d8c3b0e36277141d9a4b4826475c8ec23f023b2986130ca61c4bf8985531826414c869911322a6c620440aacda902ba27488d411aaa0c736b090a0c9a24dd036,
0xfd31fb0a0dc8151029205a40b07f48fe84ba8834123420ce1fa83f588158bf70016833d2818fd21fb43f647eb902e206e40c06c58bf817ec00285f90bf449c6712d06a20dd41a68161230a054029,
0x415882a9027204c415d2eb20cc420e8419082210336a883c9080104a209641308380af641e883cd080a105017,
0x43d4979d2f4a5ea4c3098653ed261c4c2a986d33025f24d009b48674a0ed1a2293c52f8a5f84bf297fd31c26394c8a996d31ba67b4cf899fd352a6a64d489a893698e4e42580005339269d4cc2344d2de1d594d409b59371a6e4030,
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
]

def policySharedUnitFixed0HintLeaf82 : PackedNatTable.Table Nat := .leaf #[
0x28dc6838a3818fca0e06af24f3141e28385058a0a141096293d50b5216a82d4c5a88b46374c9014dd38b47168a2d285a4803b14f829f526b9ba049bc9fb8d331a6934da69b0d359cd0483828d851a8a3d14663f7d3c88fe122ce45986ac0d243b4492090318fe24b8035686b10a831fe62a14542258e4f1c81f4ed4a06440c08fb8d4d1a9b047,
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,
0x6ec0dd740a036f46df214c1ba837046e00dc31b84313863524e73c1c90acf0690753c1078947fc107a20e441cd42590794fbe40006da8db71b6c36f12e21e004124852109da14a429236fd4248e2618fa01bc4f789f713d801c44f80bba13f227e84fe24d134b231505d29f6a4bf097e531b26464cb4980133aa6b8176470045ec9ef6418899482e71a4900029c6d38028244cae994d32aa66f4ca8995932c26594cd299ad34ca6384c729981333a6684cd899d131ba69a4cd499852731c0c49a079c483c0a1e144228804d49a844e1e85145a00b4216822cf059d8e7d49fc6e592019b9b3c1290a9230208707e,
0x198c33206540e8082ed30ba7474f1e98a533126964e745f691d5065b0cb826e832e874141740005318264c4eba9d553ab26332fb68f88b7e970301f,
0x14604e4a0b84c60147028d85230a3a573938395cd0a28144429405270048578d255a6354c989d753aaa756139a27304ec09cf13a214e029b27652bcc92b92671a3947cc68e04e50f661eca1714b30a454346c145c28d05190a2c27184e389c513888ca444c8847113821244240022109663391e699174d0a20bc4170529004614a829a27cb10f421d92bc886e3dbc98ed31fa6484d143ed427904f109de13b82762546405e98e931e263d4c7c991d3588f284138980530126044c489ac8acd159d470480b92618883110e2218441088100404440888911244aa9a3c85f10bd217842ec7b70f5744969a384962502436691e50db26f64bba890cc7f23cb31fe16f12a985be0b7e7c902e009c350a81d1c3a5874a0e861d083aca5634f9205680ac8186030a05700af248a24e08cec9238e4d3d32844d3320e481c8e39307248e4a37c811bd4110bb4326498592951c034cca98bd27c9e9348667a4933317ed2fb88ef0bef0e8a167e2cf859e8e7c49fc6e5d2011eda1cf2286050b8a1434ea9c38f6107390e701cec39d062b0c5a92d0be923ba2fa21b7036d86e40dbe1b74026869f0d3a9cf00178f581eb48b688b410e521c843cc87390e6005643a087490ea440c063c0cc8198031a0624b41a5fc491a49d519e92764dfe97ed38d25ff4d549aac6041c66491c305412e826004be073013282664ee22014402033b067402401a08343494050611e0134126804cd91a29c6e4de8976d0faa1f448fc87cc86f10dd21c0437c87110e11e623cc12e70f2f0d3639452e4a1144c6c99846530ca51954329c6541ef6418899482e71a494e369c0141226574ca69955337a6544cac996132ca6694cd69a6531c26394cc0999d334266c4ce898dd34d266a49d673bd20b9cee4dc67a690f7247d43da87b13761fbf2e7a92e4bbe23ae2ef6037806e8a5701b8036806d8c3b0e36277141d8a010e501c9c39187220e409f55429890d122c24404878912498e65f91eaa4bd2f7a8ed0d300af8422400052f3a5e94bd497e12fca6184c329f6930e26154c36991932d2600186c80cd381a71c4c4c9aed35ea6bf4d809b0535f26c24d789370d25a41323ae47611f811d934649120b2d9658495a62e0d199a35346857211c195c71b3,
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,
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,
0x5a00afc16927d04fb4926c9d382d105909ff49d6a35400c,
0x29b05ba9ed880aa0b2053e0ba4150101341628d689c4249a00d,
0xdc826304c806a814ca85750b210a0213842a08520690a70270629be06800cf8fb9034406840488001062c9e0124f128748ba4a1942c138546904cf40dd027a037609d13cf135e469609f09ada34c04bc0974130025f03984cd91a2933503a094780e501cb038607113a881c1064a0c9c19313fe27fa9c44955026504cc9dc49a0934025564d411a4929f04a,
0x6740cec5ed833550b470c91df9418008,
0x47a85b002,
0x19ea85c002,
0xd9542ea4a1003,
0x3430682024142da4a0005,
0xef626ff4e34a17933726b34d689ad935826d800a
]

def policySharedUnitFixed0HintLeaf83 : PackedNatTable.Table Nat := .leaf #[
0xf6ca6ff4e34a17931b26384c7299b9339a67500a,
0xfc925e74bd297a937fa71a4c12a17930da66e00a,
0x1cb0000297a52f525f84bf297fd305261a4bd0991532da86200d,
0xffe6250000a70450be999933da67c4e3a989d33f268000c,
0x11f865b4000a6014c04980d382285f4c4a9c75313a68f00c,
0xd1c1f603eb067ea174a54a36c007,
0x4592863002,
0x188f0002985130b26184c32999530ea67b4cf899f533fa86400d,
0x3b907940efc1df00960128a170a3c2367009,
0x19320002979d2f4a5ea4bf097e530b261b4c8c9969300286700d,
0x16e2868002,
0x13e52869002,
0x1b130002a1ad30c26194c38985d30aa6734d4a9a9935226a200d,
0x1f94000297ed300a6024c06a1ad30c26194c38985d30aa62500d,
0x79e94c94361488004,
0xbad17582e6c5cd0ba850c49388df4a40a009
]

def policySharedUnitFixed0HintLeaf84 : PackedNatTable.Table Nat := .leaf #[
0x219a4bd297a930d25e81160a1a930ba6b34d689ad9358267700d,
0x560a86d002,
0x206a86e002,
0x390871e0e411c7c38f471fa8601c807a1cf441e863d167a28f449e8c00f,
0x2a7c54f0aa515422a80551a86149b26bb91f91aed00b,
0x2e4d4381be1003,
0x3a254381ed6003,
0x48689161220243c48a258450c665fccbf23d500a,
0x243943c197d003,
0x2ec943c1c01003,
0x108a80014ca499ed33e267e4d009af5360a2174ce49a85351a6a54d4ca1c935fa6c04d7c9b0936da6dc016,
0x6140ae08f850dc9460cb41270007,
0x17182e205be0a6816f28684a4a4f109e2a35900a,
0x5ba287b002,
0x80bd31d263c4c7a98f9323a6b14d7a9b04794209c0002a1cd300a6024c0898912fe26b24d7e9b0135f26c2017,
0x61943e233b003
]

def policySharedUnitFixed0HintLeaf85 : PackedNatTable.Table Nat := .leaf #[
0xb8543e93c6003,
0x1e167ddc000a6124c2699d9365a6cd1e1c3c347880f0f3ee67dd0fbb1f753ee43c487888f171e283c4c78a9ff54e08a17d38ea6274d949b3136726cf4cee3c58fbd1f7b3ef27df8fbe9f7c3ef03c30fb81f7102c,
0x17660b1816282c105802ed1435252a38064ea11a91c0200c,
0x7900f1e1e343c6078a4ad2866d43525e94bd497bd2f8261a4bd0985d2f625ee4be46088c12a3bd015,
0x275287f002,
0xaca880002,
0x7580f301d783ae07600f2d3c9a869290851aca35236800c,
0x1e394421826003,
0x24e144219a7003,
0x5694431247003,
0x17fd443169e003,
0x1104a8300014c24984d30c26194c38985c224287d29f098b130aa4a800f,
0x1f2c7840f091e147db8fb7a882007,
0xeb54439469003,
0x3b6476c0ede1db63b6876e28711dba7cdcf9c1f363e767ce8f9c9f3500f,
0x13bc27704ec4a8ca1fcacd159d007
]

def policySharedUnitFixed0HintLeaf86 : PackedNatTable.Table Nat := .leaf #[
0xc2288a002,
0x7158e331c5c38b4718a5c750f679e0f3ba43200a,
0x38b14491e76003,
0x38d14491e7e003,
0xaa615506c2c000a6124c2699c934fa6a1157c2af45650ac0157e2b192cba86d361c6c351f99b0c4d469a9535324da019,
0x1f2895002,
0x3c7c7918f221e420034783a8823f0a7e20fc39f8600b,
0x3c8144b9f84003,
0x3c9544b9f8b003,
0x7ec100e1fbc3f7007f087ea230c3ea3c2009,
0x1fb544d187c003,
0x2c6944d1b78003,
0x15d42bcc5768aec0070a254da023f6008,
0x38207080e0c1c0037f06fc0e141be037d4f7ea1bd44703cd50d89290a21a361288851151b01446015,
0x2b585678ae915b22b6001b0ada15b62b710d280014bf097e537fa71a4bfe991532da66e50f29aa535526ab2162868485a2887434686901a428662836a23942f2599364e6c991fa9b23027,
0x7142f701c583ed4e90a1bd447289e50be52b1207944f00c
]

def policySharedUnitFixed0HintLeaf87 : PackedNatTable.Table Nat := .leaf #[
0xfcb200243e07e70064225a44b88b8117222e645c517522ee45d88bad176a2f045de9ef85759b3f15e8a274da4836250bc8ba5106a46401d,
0x43dd450a20c003,
0x1f9a3f31450a04a004,
0x3ee06e40e401c78389514051511b214ad009,
0xfc1405841b4e8a10b4215808a4e820c4ca72a4a650ba0fbc21303f207e20fd018b249e494a52bd1b714ae017,
0x5569dcd42f0b1d163e2c6c58e108242ae2cb821780893714a271341268421002c985928b2916502c8840e881c4aea206c40d100d4baaa23040c88204aec6dfd2009b8142aa6de51ff9b7a05586d4c2bd25f34e08985130c261951029d0017f82fd0104022c186830f061c0c309eea85f513ca1bd44728a44c3a9c753139393044,
0x9641cf425944b319d648702584cef000112bea05526619d500d,
0x287c50f0a21144026a4d42270f34269dd142c26174eaa9de134928a74d2826944d20a19134e26980400001342a8fa8d0a27764eea9a593bc9a8301f,
0xaff15ec2bdcd32a5f34e08985130c26195102a17d30ea71d4c4e280839a07370e6c5f391dc9a6136940ae815d82bc172c2e505caa1990002979d2f4a5ea4fb4986d32606f64abe1be037c8e670df4280d39ba8a450dea23944f1a6248685e54bc926af4d669ad135aa6d750c06f889d293a403d,
0x45d05e000101c0037c09000e123b69bf48ed010501e803d807a80f200a0014d407251123be47a92fa25fc4c989d753aaa756022c047808d01190236944c07200e2490c47dd19891f6027,
0x2887db009f01409f3cdb808dc11b6654134811a248b8029c4a00943127c24fccd6093a127824ec58c1b7233569a2ccd719b4336666c0cd791a301f,
0x8ba0bc0002038006f812001c2476d37e91da020203f007d28aa0210041c029a80e23d6921d2fa25fc4c989d753aaa756022c047808d01190236944c07200e2490c47dd19891f6026,
0x126524cc05ec0b9017302e8496c0ad925a466a05d40800176177e05dc0bc1260481c497c92f2338015,
0xaca88002b40610937815b50e606040c00183030405c00b8a8ad02b0055c0ce019b03104a0d19f12460312923492c926d24dc499519a8175020005d85df817702f04981207125f24bc8ce0936124702a,
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,
0x17a82f485ed0bdc17bc3031ad25114980530126034c0a9c1142fa6254cb8299452f9ac94e3a989cb4916912d205a3cb4385eb0bd8179c2f41f1f00029bfd38d285e4c649d6c30b86190c301858078013a465897d92fc25f94bf697fd33b26af4d669ad135aa87149125ae51d116ba4e689cd53370a6114c029752c59ac12d0c5a38b46a39a0c0e5aa51cd968804b
]

def policySharedUnitFixed0HintLeaf88 : PackedNatTable.Table Nat := .leaf #[
0x1392146028b851a0a321458ae423832b8e82e131826480a281445255a6354c989d753aaa756014,
0x9e2a24027904f04588136c26d052509b2135c26c052609aa1358e178001491c98d931c26394c8e5618af115872b105784af023840a48145828c851a0a2e1460ae3a3832b9057791c29589510a2720acf238202c,
0x9b81368c131814305c60c1c7150be989ce381c6c269009bc13e8c1118283058e37a85e4cdc3024e369c6a38d271a0e33a34b469a30400e6025f04c0097460a9c6e468a4cd8e329349027,
0x13bb8b5b0832109421214d846da6ec83f225364ea60fcc18a83134e8292792529879088e111822a8445511853d91b814f750d67f54fea1fd342828500f849f0846e239b821107e716549db544e289b10100c04040989c20d42c753b982ff05fa02081820311061692749eea85e05560ab0da9857a4be69c1130a26184c32a20542fa89e50dea239452261d4e3a989c9c99b7a10282c6440b8816010c021018498aa47fc6e14c3d1eb7486e11c823a047308e20c40a92a3742a4c9f6943aa89f50b0a29d3bca77806a,
0x84e10a821481a4062c9278a7027060850a295412842d08560228a72a8580628a2989f294df014,
0x17bcb5381960bec92cc2fe05fe0bfa17ec2faa76c11dc95fc46988d4127a236446d28ab162e6dc4ca7a3d73292178cf85067b4be897f1393264c4e5039fc2aa960d0aae15602ac8e6b0ab439a85a21eb4486a581cb03238e3d925a651ce169a0bdc17b42f485ea0bd617b02f385e814e06b452fc25f94bfe98c93ada65d4cb69cd05328a5f14c2298052ea58b35826b2539aa6674cd099a5335a6992d0c5a38b4416872d225a40b47968d4734181c304275914bc5aa51cd9692063,
0x5fa0bfd3a028b427ba020818203110616a2d53b9289b102a205058c8817102c0218042030931548ff8c54a49d018,
0xa2942140427085410a40d214e04e0c537d412842d085602293a0831329caa16018aa49e013,
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,
0xc0b182471ac606a5a738c23028609826d04dc09bc13e8c11181e7190e351c6938d04d249a41c6c38ce8d2d1a68c100398097c130025d04bc7198000a48e4e369c006041335468a4cd8e329c60029,
0x18d432016e50c6e956cb6e863d0c68190832086390c743b9031d863c2dc29130b7016e62dd05b9cb7116dc017,
0x30c05640ad1b6f123e980530126034e08a17d312a71d4c4e2490491a7e3176e2ee0e04000102b0055c0ce019b03101f8928d9f1c125a97e12fca5fb4bfe61dc941a33e248c9d813c326324ec2996132ca6574caa996d332892112409320cc59c09331c491d43e233b038,
0x85910d4216042b885610d62188431990900026380c6b18d710b42170c8f26471122224044a089311246434c87190f32226440c8618d801d,
0x4121c064bf6130026104c1097e12ec02280012ae08e00ab8a6484c6a208c45788ae0a3e64b538418b2016,
0x13c544804f209e08b1026d84da0a4a136426b84d80a4c135426b1c1700025618af115872b105784af023840a48145828c851a0a2e1460ae3a3832b9057791c29589510a2720acf2382027,
0x2888512002
]

def policySharedUnitFixed0HintLeaf89 : PackedNatTable.Table Nat := .leaf #[
0xa5e14c429b8539495c579829700290a6814a801205270a50a30028a24ab0a1814352a5850b200c9ca53c32762413c56f0af1a4ad01c,
0xc3015902b466d934728651248248d3f18bb717707054000815802ae06700cd81880fc4946cf8e092d4bf097e52fda5ff30ee4a0d19f12464c64996132ca6574caa996d3329c09331c491d43e233b02a,
0x28bd31d863acc7523c610c82194433086810d2219cc72a3c731c8638d1e4085b011,
0x140a0a5914b0296c52d06e10dbc01380009abd47e26af031386260c6018a8314005900065b351d216cc016,
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,
0x45508a1114c2280455992a4e4a22a444f24c500a,
0x132029e84c5098ca30cabc2388098e14fd257957900b,
0x226c42e885e31b20004c6d085f0a66213842a24c231b66468c8c98de00f,
0x518e21807b48f6810c2213442aa4c231ba7f2cc6f98de31b814f8264889d0994132d0dba6474ce499d1430a8c810b42164435085810ae2158435886210c6642400098e031d86358c6b98eb31d48f18432086510cc21a0434886731ca8f1cc7218e34790636042da6882af68f38abd24af03c,
0x145a0b4016842d0459e0b3b1cfa93f8dcb24033736287c50f0a21144026a4d42270f350626944d20a19134e26980400001342a8fa8d0a274005fe0bf4041030406220c2d24e93dd026,
0x5ea0bd227044de89be382c17f02ff05fd0bf617d42fb9eb14bf6a229300a6024c0698153200b10116836bc45a8b003bf29c1142fa6414c869911322a71d4c4e36b52d80c4e517277dd3631b58485064d126ea6464c849895259969947385a68d1516870bd627084dd89bc346297ad2f6a5ef4be097c52f9a5f84bf297fd44f286f511ca29132ea65b0e983b103a287440e841d0c76287460e8e82e931805460a90151c2a2011800e6000407280e351589218afa238b2bea99313aea7554eac98ccbef24472fb85f7522317e3511299c4d149688071,
0x389071e52541b903ee34a627904ef872e0e5a1ca439107230e5e1c90500a8a934c08edcbde97c2476c69352f9a89e50dea2393232698295a8da4a2a28a0021,
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,
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,
0x131429e84c8098e55e51c404c6517e14f8264889d0994132d459157b479c55e92579578013,
0x4e4a8cf002
]

def policySharedUnitFixed0HintLeaf90 : PackedNatTable.Table Nat := .leaf #[
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,
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,
0x14bc298852e005214d029524ad007,
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,
0x6288c4b18b031206d122141b523104efa1def482a72a06d08da61b4e3695025a8a34d8877c52139dee016,
0xb2e516a10bc0449b8a005,
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,
0x1d4a3a9075f8ec01d727c6d2fe275b4c529cf545da7a70d5c3a8875086af2ea27bc8ba9174d2ea097c933da67c4cfc9a01350a6a34d4a9a98f869ef41d743af475f0ef23e9e000524726364c7098e4353a55d2e90993cfa71f0e030,
0xc941930326864b2ddc8e9c32486470c8c1920b7596ec2de41914b7516ed010,
0xcd419a433397080cd05c702db05b40b6a19b033286660cd65c74b83970e2e1a59502db96552cac97f13ada6504c52a2ed32f27a72e125c30b85970a020,
0x192432786500c86191032728d92dd25bd4b7a16ef2de61928326064d0c965bb91d396ed013,
0x103f41d49b5082110412088410c657801341ce91ad073104019ec3254649801600340070e6ca0e5015,
0x410c8221041208483a881f904019ec8395073246b196032c46780cad195c32b116d8c95192600586478c901914321946e24ea39b29b50e7c1d3c3a7674e8e7ca0e7023,
0x3228643001c003432406478017002a3bb077796004be6a279437a88e514898a02cb11092210165cb1da70b2c743ba07750ee91dce3b98fa2a44d3e8c98c1324a64a0b6016bc33f85b10b3859451d596504a023b9481f104551ba32086470c84005a00042cc24e939aa83ad07224ea03b,
0x19d833c86782e305c68b8c86772e360004337066d0cde5c40b8886700ce219d033a86722e265c58b8a97142e245c3c339971701b,
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
]

def policySharedUnitFixed0HintLeaf91 : PackedNatTable.Table Nat := .leaf #[
0x116e22d058828d202b0055c0ce019b03101f8928d9f1c4bf097e52fda5ff4cb0996532ba6554cb69994c3b9283467c491926e993411702c00efc80014e08a17d320a6434c88991538ea6271b5a96c062728b93bee9b18dac23d0030,
0x230e11082220445888c11149310432886610d021a4433992c115a209041188af115c147cc96a7083164979d2f4a5ea4bf097e530b27da4c36130026104c1097e12ec02280012ae08e00ab8a6484c6a99693000825104e2098258956231688df8c59a62f518c22b04168028325663951e398e432088f304231903106a210041f8834106420cc43f88411084210c44020a0110a20c041600270a589d9429b05385182a33c256a5402abc92b8af318b931fa632d1e518ba31768f0cc5e2686065,
0x1a3c000298c931a26484e689cd44120823115e22b828f992d4e1062c84ea89d413ae27584e809d2499c68f91f29a3d019,
0xa1a143028928b10a50149c01228d30a6e14e525715e62bc6952c28590064170a341318051c0a36148c28e95ce4e0e573532426354c989d753aaa756139a27304ec09cf139c011c0019a3947cc68e104f15bc02c,
0x439a8c910dc930d471a8c6115820b4014052c325621d443a0872109821d92bc887a4f9616f12a996584eca14d829c28e413943d987b285c52cc29150d1b24ae2bcc63c11e498f1026,
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,
0x6180ac815a4f92a1cc30b86190c301858078013a465897d92fc25f94bf697fd33b26af4d669ad135aa87149125ae51d116ba346068bcd17239a135a18214581a1b47c8491d43e233b027,
0x1570338066c0c41283467c0561473018d1d8206380c7a8e714d6232002ea7e65158a2bc48219751272240c4848907120a01302f9997647a866a8d6685f1138026fc2fa05f644ce980530126064c0898912fe263a4c7ca22d34d0d9b414e98f131ea63b4c7e97c933f268011ee6f612f8a6094c28987533da67c4cfa99fc5c525a217182e3461d0b8e171e6f781060b904b46093c128024e04ac948c0f59ff44bd297a9305a61a4bd0a1d924b02514a44094c135032804d009a49a1a71504ce076003b81d9046608bd39ca74e4eae9d7124c93424c1e4d111ad9345492e982130526124c26986130ca61c4c2a6f752091bdc37b29a65259969547c65a507269e99422699193320e481c8e39307248e4a125a93e4f49a4333d24a19c3aca5630e841d0c76287460e8e82e84e185c30b8416fc2df28e51106221c443088211020080888111122248954000a6ff4e3497fd347a6aa4d56a2e945990be217a42f085d8f6e1eae892d2fc25f94ca8995932c26594cb49801333268e51c294090d9a479436c9bd92eea24331fc8f2cc7f965b473068c9318264c4eba9d553ab26332fbc911cbee17ed24ec911493a92460e5,
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,
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,
0x18124dea2440ada8730300060c0c1017002e205ec0b9017345ae923807b00f501fe03f8084010700a6a0388f591e74a22477d2fc25f9031e06640cc018d515c49d519e92764bfe9d813c326324ec24968933125924da49b8932a33502ea04000bb0bbf02ee05e145600e301ca01cc00081180a883d842a2854651d457d4fe3238a2be89218930240e24be497919c126c04d,
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,
0x28cc142a286050b8a1434ea9c38d3b09e713ca27a84f4806a4ef427ec4fea4d134b269592678b03160a2c1058089e636b28fe4dad1b5737c66d591aa8afd055c9dcd42f02ab05586d4c2bd25f34e08985130c261951029d0017f82fd01040c10188830b51ac92749eea85f513ca1bd44728a44c3a9c753139393369a8fdc4ef09dd140027fc4d509a84b1269711f39a4c04d,
0x28a812b0255c4af095912b6932cce6a3db3398254881e103b12a6670d38619c2011,
0x15202b2c54a8a94152600fc01e0a75512c6b951fa0a91151e766c5440a7f008429d853e8a7c008829dc53ca4d735ba9a6d44f9ae401c,
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
]

def policySharedUnitFixed0HintLeaf92 : PackedNatTable.Table Nat := .leaf #[
0x27ac62128d51bb437654769e263c4e7280034a77a13f627f547800e9030e056092305e60c2a18502f201392d8200052fc25f94bfa97f92fba5fc4cb4980030f01570338066c0c407e24a36a3b04ee071e0e3a036c06d00dc2f6c037406f28eb23b28ec08ec11d74764692cc3b9283467c5b09244968447425a152689a59043,
0x159510005680c2126f02b6a1cc0c08180030606080b8017102f605c80b9a2d70002923807b00f501fe03f88f3a51123be97e12fc818f033206600c6a8ae24ea8cf493b25ff4ec09e19319276124b4499892c926d24dc499519a8175020005d85df817702f04981207125f24bc8ce0936124703d,
0xfce1088212042508322d6d3958e7f0aaa58342ab85580ab239ac2ad0e6a1688a2d05a00b4216822cf059d8e7d49fc6e592019b9b143e28785108a2013526a113879a83134a269050c89a7134c0200d0aa3ea34287ad121a96072c0c8e38f64a87351221f9129b275307e60c54189a741493c9294c3c9bb246da5360595276d5138a26c4040301010262708350b1d4ee6a17815582ac36a615e92f9a7044c28986130ca88150bea279437a88e5148987538ea62727266de840a0b19102e20580430084061211c0df200014c2c9f6932ba6554cca98bcffa1ed74bce97a52f526094c3698e131ca6724ce898dc54ba8ef14f429c5477274005fe0bf4041030406220c2d46b249d27ba9358d6aa4d850ea9a7530628774c16982930d25e84ca8995932c26594ccca1d929d152431548ff8dc2987a0a4,
0x27ac62128d51bb437654769e263c4e7280034a77a13f627f54798158248c03a409c96c1000297e12fca5fd4bfc97dd2fe265a4c0018780ab819c033606203f1251b30ee4a0d19f16c24912061d47609dc0e3c1c7406d80da01b85ed806e80de5158a3c8084010700a647ac8eca3b023b0475d1d91a4b501c038c07280e60ddc272c37786f051e25e34d1ba5f52f1892192689a5904f,
0x2741011210bc59728b837140c4c18aa49e009,
0x642406080b832251ea4fd138293f3008,
0x20b857c0af610601f9a8f5494a53511ca14d300a,
0xa3d02d00ecc1d96167cb209f2b3b3c5c98b2105b30cfc19f42d9059b005c166400096522e4a5c90b9124b72e46594d47ba8f601b,
0x103820810ba0822104946f0c97192c32ac64c8c980024326864d8c9c39da99846530ca51954329c6541c304cc093ace77a41739dc9b212d99cdc39b69060e6d28f8299a91e0a66040f2d96154c2aa05922c6e97cd314079c0c7e18f831d06390c6e956d41586ab2e983c6478c0f271e341f68fc0244e3efe1f6c3ec8f1b1e4c3c7478e1f8c513299e07921f8a0fbe7e2533ca8983f047e34fc087de0fba00383da87b6497e61d126007ac0f621ed08cf07af001e1ee03dc87d43e8499e83e287c40f8e1f183e987c90f901f352b707cc511a1f283e8256f0fc03b8cfa087e24a3661dd447a6eb4982616d1df185a30b23b387668ed71da03b3c0060ed11da4463519284cb0a7814ec264853e33480629246a5fb4c90996d33a2637495e55e91c3957b4c6c98e131ca6474cec9abd359a6b44d6aa1c537e25e646287cb52259f2c30989c78c24a4be2dba5b811d318364c6038e4f418eeb3e92993875186ad0d581aa8354a8e01eb43d60017a73c0d3a1a7d25c973d3f7e18c48c6118b0c645b5138496d30c16183430606092d548e7cb558a6714cc297830428b014d6232002ea7e6359a17c44e009bf0be817d9133a6014c04981930226244bf898e931f288b4d34366d053a63c4c7a98ed31fa5f24cfc9a0134ca4b32d2a8f8cb4a018f033206600c69275467a49d8d6524d50c4e1898318062a0c5892d0b66a3a42d9823dcdec25f14c12985130ea67b4cf899f533f8b8a4b446f654748b8c171a30e85c70b8f37bc08305c825a3049e094012702564a4607acffa092d4bd297a9305a61a4bd0a1d924b02514a44094c135032804d009a49a1a71504ce076003b81d9046608bd39ca74e4eac9d553aba75c49324d09307934446b64d1524ba6084c149849309a6184c32987130a9bdd48246f7139da89e0e80195033206630cb619704dd065d0e82a3a0beda3e22dfa5c0d1d517da5148a1bd44709c30b8617082df85be51ca220c44388861104220401011102222444912aa6ff4e3497fd347a6aa4d56a2e945990be217a42f085d8f6e1eae892d2fc25f94ca8995932c26594cb49801333268e4a0486cd23ca1b64dec977512198fe479663fcb2da3983464a38547b28f70de01bc837886ee01cc5e3137f178d0a8c15202a38544023001cc00080e501c69218afa238b2beaa2b0ba5a3ac3de658111d194cb1c7,
0xde21bb807300e501c6a039479a4862f181bc837828f001d2061c0ac12460bcc185430a05e402725b04000a5f84bf297f52ff25f74bf89969300061e02ae06700cd81880fc4946d476187725068cf8b6124892d088e84b42a8ed51eca3dcbc6a6fe034,
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,
0x4fe89fb4ef4a3ecd2ca4d1006,
0xf8e092d3fe87b5d2f3a5e94bd4982530da6384c7299c933a2637152ea3bc53d0a7151dc9d0017f82fd01040c10188830b514c0c5018b28f5493c4f9547ba8f6493a4f7547e24d635aa936143aa69d4c18a1dd305a60a4c3497a132a26564ccca1d92fc25f94bf697fd32c26594cae995532da66503e,
0xc3a8fd002,
0xab819c033606203f1251b51fa61dc941a33e00a,
0x56147f9246003
]

def policySharedUnitFixed0HintLeaf93 : PackedNatTable.Table Nat := .leaf #[
0x4e4b6080014bf097e52fea5fe4bee97f132d26000c3ca3fcb61248900f,
0x74a901002,
0xde21bb807300e501c6a039479a4862f181bc837828f051eca3dd48128fe5200179830a86140bc8a404b4223a12d0aa3f0bc6a6fe01c
]

def policySharedUnitFixed0HintTable : PackedNatTable.Table Nat :=
(.branch 0x2f0
  ((.branch 0x170
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed0HintLeaf0)
  (policySharedUnitFixed0HintLeaf1)))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf2)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf3)
  (policySharedUnitFixed0HintLeaf4)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf5)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf6)
  (policySharedUnitFixed0HintLeaf7)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf8)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf9)
  (policySharedUnitFixed0HintLeaf10)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf11)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf12)
  (policySharedUnitFixed0HintLeaf13)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf14)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf15)
  (policySharedUnitFixed0HintLeaf16)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf17)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf18)
  (policySharedUnitFixed0HintLeaf19)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf20)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf21)
  (policySharedUnitFixed0HintLeaf22)))))))))))
  ((.branch 0xc0
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf23)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf24)
  (policySharedUnitFixed0HintLeaf25)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf26)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf27)
  (policySharedUnitFixed0HintLeaf28)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf29)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf30)
  (policySharedUnitFixed0HintLeaf31)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf32)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf33)
  (policySharedUnitFixed0HintLeaf34)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf35)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf36)
  (policySharedUnitFixed0HintLeaf37)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf38)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf39)
  (policySharedUnitFixed0HintLeaf40)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf41)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf42)
  (policySharedUnitFixed0HintLeaf43)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf44)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf45)
  (policySharedUnitFixed0HintLeaf46)))))))))))))
  ((.branch 0x170
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed0HintLeaf47)
  (policySharedUnitFixed0HintLeaf48)))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf49)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf50)
  (policySharedUnitFixed0HintLeaf51)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf52)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf53)
  (policySharedUnitFixed0HintLeaf54)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf55)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf56)
  (policySharedUnitFixed0HintLeaf57)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf58)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf59)
  (policySharedUnitFixed0HintLeaf60)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf61)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf62)
  (policySharedUnitFixed0HintLeaf63)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf64)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf65)
  (policySharedUnitFixed0HintLeaf66)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf67)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf68)
  (policySharedUnitFixed0HintLeaf69)))))))))))
  ((.branch 0xc0
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf70)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf71)
  (policySharedUnitFixed0HintLeaf72)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf73)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf74)
  (policySharedUnitFixed0HintLeaf75)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf76)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf77)
  (policySharedUnitFixed0HintLeaf78)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf79)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf80)
  (policySharedUnitFixed0HintLeaf81)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf82)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf83)
  (policySharedUnitFixed0HintLeaf84)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf85)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf86)
  (policySharedUnitFixed0HintLeaf87)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed0HintLeaf88)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf89)
  (policySharedUnitFixed0HintLeaf90)))))
  ((.branch 16
  (policySharedUnitFixed0HintLeaf91)
  ((.branch 16
  (policySharedUnitFixed0HintLeaf92)
  (policySharedUnitFixed0HintLeaf93))))))))))))))

def policySharedUnitFixed0Hints (i : Nat) : List Nat :=
  policyFixedHintDecode (policySharedUnitFixed0HintTable.get 0 (i - 0x2331))

def policySharedUnitFixed0_root_empty : policySharedUnitFixed0Db 0x2903 = [] := by
  decide +kernel

def policySharedUnitFixed1Clauses : PackedNatTable.Table PackedNatTable.Block :=

(.branch 23 (
(.branch 11 (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x860080407ec07c607ba06b406b006a4065c065a06560638060405e005620494042c0424042003b8039603740370032c02f0028a027a0276022601b001a0019c⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1052104e1038102810261022100c10080ffe0ffa0ff40ff00fe60fe20f7c0ed20e600e5a0e540d3c0d360cee0a4c0a2a0a1e0a1809f209d2091c08ec08d4086a⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x166e166a1612160a160615e4155815561552153c153814fa14f614e014de14d4142213ce132c12ec124c121611ec11e211de11a2112e110e10b8108a1086105c⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1bd01bc61bb41bb01bac1b5a1b581b541b3e1b121a701a661a2c1a2a1966193818a0188e183c180a18081806180217ca1788175a173a171616ce16cc16941670⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x20221ffa1ff61fcc1f981f7a1f201f0c1f081eb41e881e861e821e601e521e221dfe1df01dc81dbe1db01d6c1d681d201d101cde1ca01c1a1c161c121c0c1c08⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x26ea26b8269c2698262c262426202576256a253c250224d024ba24b82494244823ee23d42344234222fa228e221a21ca21c221b020c420bc20b82064205c204c⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2d2c2d222cf82cbe2be82be62b582aba2ab02a882a722a5c2a502a4429f429ec293e292e291c291828fa28da28d62846281a27fc27f82794276a273c26fe26f2⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x32b032ac324a3240320431e2319e319c31963174316431563132312e311e311c311630ae3076305830543012300e2f3a2ee62eb42eb22e8e2e462e222e1e2d4a⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3a3c39f63962395238c63860370c36d236c636ae367e36763672363435de35cc35a035903582356e34e834d434a2349e34683460343633d033a2333a333632ee⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3f7e3f563efc3efa3ef63ee43ede3ed83e883dea3dd23d9a3d7c3d5e3d5a3d1e3d063cfa3cd63c9e3c8a3c723c263c063b923b703b463b123b003ac23ab63aa6⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xef80e7a0e700d940d140c260b88096e090a08b8079806d606c6066f016005ea0536000200040356030e02f4025e02520246022a01fc01ee01823fe03fd83fb6⟩]))))) (
(.branch 6 (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1af01ad01ac61aae195c193e1890180c172e16d716bc15fa157614a81488147e144e13a2134e128c12601242122a11c61188115c111610c00fa60f640f220f02⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2bf02b522aa029ac298c2922290228ac28a02862285828042782275e274e26c82668265e260c259e23c4238c20a41f2f1e8e1e361de21d981d2a1bb81b6a1b08⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x31102bf01cb01bb01853e683e4a3c103a0439ec39c4397e397438ac383a37603724365e35d234ec3482342a340233ca325831fa306c2fea2d402d082cac2c4c⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x94b0935090d08f908bb08a308930845082f0817080b07d507510739071d06df068705ed051304e70481046d0461044b0431040503ed03dd03bd03a503790359⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xddb0dc30db10d9f0d6d0d210cdb0ca10c3b0c290c110bdf0bcf0ba70b910b6b0b550b3d0b250b0f0af30ae30ab10a9f0a890a770a6b0a3309db0987097b0971⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x157914ab14691451143313f513db13ad13a51385136f135b135112d512c312ad129b128f127b11f3115f10f1106d103d0fa90f670f250f0b0e8d0e310e070ded⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1fc11fb11f871f451ee51e9b1e111d7b1d531d371d2d1cb91ca71c691c411bbb1ed21a8f1a491a211a1119e5185b180f17ad170316dd169b1679163d15d315b5⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x260f25e725d125c325ad25a125932583251b24f1249923c7238f22ff22d522a321fd21e921d32183216d215b214f212f211f211320f720dd20d32081206f2027⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x31b33143307b2ffd2fed2fd72fc92f032e6f2e592e092d8b2d792d0b2ce72c8b2c772c432bcf2b852b712ac32a8d29f9299529252905286d27cf2785272b26cb⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x202038c01cc092801bc016c3f1d3e2d3da13d833cfd3c3b3c1b3b813b4b39fb39bb39ab391b373535d535c1351734db34a9340d3405333d329b326d31e531db⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x6ec08d606e006880522051404e804cc04a7052a04820476046e0496046204a0044c049c0432041a0406047a03ee03e603de0a5c03be03ae03a60d2e037a02aa⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0xaca0a6c0a6009dc09c3099009882148097c0ad2094c0a6409360cd408fa08da08a4089c089408f208300e200818080c12e6075212e2073a072e0726071e0702⟩]))))))) (
(.branch 11 (
(.branch 5 (
(.branch 2 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x1bee0c120be80be00bd80bd020600ba80bfe0b920b740b6c0ba00b560b9a0b3e0bc00b260bc40b101f240af40aec0ae40ace0ab223cc0aa00ad60a8a0a800a78⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x11f410d01982103e0fbe0f3831260f0c0ed813420e8e21440e320e280e080e240dee0de40ddc1eb60dc40e1c0db20e160da00d420d2a0d220ce40cdc0cbc0c76⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x19e61872185c188617ae1798237616de1816169c16001564140613fe13f62a8213ae138e138613c01370352e135c13c412d612cc12c425bc12ae3964129c1266⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x21302128212021bc20f821b820de2092208220962070205220281f901f881f741f461f7c1ee61ea226841d38201c1cba1c841f5e1c421bf61b7e1ed61a7623de⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x270a263a2e9025e825fa25d2263225c4260025ae2ee8262e251c244e2300232422d6221021fe21f221ea221421d42198218421a0216e2164215c219c215021b4⟩]))) (
(.branch 3 (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x373636e4353a36f2340e32ba328232b2326e30c8307c2ffe2f1e2e802e702d8c2c583fe22bd02b9a2bc82b862a9a2a8e2a302fde29fa29c02a182996282627ae⟩, ⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x3fc03fc83fdc31d61ed81cf431ac1dea191212681978123209d409c4050604a8029e02043f383ed03cc83c783c563b663b4c3ae03a423a2839d0393637663bde⟩, ⟨0x53026812408c04401e80e407003601a80d005c02600f8054028010007803801a00c0058028012008003801800a0040018008002000, 0x2a6929132a492a53208e27c1232922cc22d124da36a636a336ab333f23af1a8836a31d4f039d0d931fac00c50d931d4f36bf0c311d48296327a633c233ac03d0039d03430339034d030303d0039d02dd02fd029102a102b902a502dd02fd029102b902a102a502d902dd02fd029102b902a502a10340036b035302d817e22c7f1abf039d044527ea280e2e9e1e4a0ada09980997052604b604b5099d061416263908348a2986⟩]) (
.leaf #[⟨0x7a03b81cc0d406803201780b0056029013c09a04a022811008603b01d00c806002f015809c04802200d005001a00c0058014008000, 0x246601db23bf24bd24bf24c022d115eb1519157515c714973ccf36cf1495149d096d0145237b16f1234606a8155d0fdd0904155f0ce9151b149714953ccf36cf149d149b15a315720c301e271ef800b30f950f6f0fa10f6f0f710f6f0f710f4f0fdd0f6f143509030f9510e811bc02a1091f1dd71853233902fd142b100f1db702a1229f23a7091f0a23369902fd09271fef1fe31e7a229f226f3fad2ac531cb1f5c1f3e1f6e0d931cab044429ab0f63011f0116149515151497149d15190127039d029102dd24e103d0167502dd039d24e1029103d0167502d8164416c600ee250514971495017b24e816482c0f2c2e2bfd2bf6⟩, ⟨0x9b04d023010a07d03d81d00e206d035019c0c805a02a814c09c04a023810807e03a01b00d406803201580a403c01b008003000c000, 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⟩, ⟨0x6002e815c0ac05402901440a004f027013409804b022010c06e033017809c04001f00e006c03201600800340140080030014008000, 0x8b513a104470ef61347133d33d833f30ecb10ac3b9e36d821693d6e088a2e342f6212ee11ac12f411340777310f08cb211b30df080707d107ac30ff3ded3de11fdb3cdb34393dd91855159f1ffd33fb30f90e6d0d680c8b08b23cdb0f6d11b300e6157420cb159f1ffd0fdd1fdb09031fe124e90d0f161e14b3049a02dd00ee11d606a82ac506c3054a023301c60241023d024202fd02a502a1017b01c7010d03d01e2702dd1e2702dd02d902a122b702a123ab15b11fee061005e906a806b8⟩]))))) (
(.branch 6 (
(.branch 3 (
.leaf #[⟨0xd506683001760b3056829013a09704382080f6070033816c0a604c02180f8074034017009c04601f00d805401e0090018008002000, 0x13a10c30291e27a5186a1c5927e7281f0b512ef12a9f1ba72bc11bd313a1291e0c30186a1c5927a51f6f13a1281f291e27e727c9282127e5281f27e7291e2920209f288b13a127e7291e281f005c2091271926a9270526a7268f268d10e72689268b2a9f1ba72bc11bd31f111f1327810c301b4d1ad9188100bd00c70f190adf0f4f18353253182f1515186d1853149d149514970f9d0fdd1883186b3d5321f73d1721693d54149d15193ccf36cf14971495013808b30c660e691515186b14951497188c149d1853186d08c20c8b096b030d0f6d10cb11b311b7177f08b30c6614951853149d186d184f186b1515149718570e6927a527a927bd27bf1c590c3027a7186a27a527a927bd27bf27a710e700c62ab70f9d0fdd0f190adf0f4f182f183517bb2091291e28e528ed28352a692913208e27a42897291e27e72091281f005c288b282127e7281f27e5288922992a9f095f096b23612357018103d002a502a102fd02a102a502fd010d06c302a503d006a803d002a502a102fd00ee010c24da03d002a502a102fd023f02fd02a502a1017b00ef010d03d002a502a102fd02dd010c0611063401d4⟩, ⟨0x9a04a024412008f047023411808b04501fc0f807103781b00d606a03401980be05002300e4058021010006c03001600a8030004000, 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⟩, ⟨0xbf05d82e814409d04782000e806b03001680a404a024811808804001e80e406e03501980c804e02100e006c03000d004801c00a000, 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⟩]) (
.leaf #[⟨0x7e03d81d40e807303901c40e006f03701ac0c805f02c015409804701e80f007603a01a80c005e02b014008c040015008002c008000, 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⟩, ⟨0xbb05982c0138099048823411007f03f01f40e406202d015c0a4051024010808203c01d00d80680300158068030014007002c002000, 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⟩, ⟨0x15109f04cc24c12208a04042000ff07f03e81ec0f1076837c1b60cc05e02a414609503f81ec0c604601e808003c01500a002800e000, 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⟩]))) (
(.branch 3 (
.leaf #[⟨0x14309c849822611108684302040f607883b81ca0df06b034c1a00ce06082f41740b705a029812807a036017809403b0178080022000, 0x5f803d002dd01390fdd029102b9090323a705f501102e7f22992a9f095f096b268d2cb92ca5268f1ad922570a0005f803d00fdd0903013900ee05f82e7f010c03d022992a9f095f096b268d2cb92ca51853268f1ad91dd722570a0000ee05f40b510b86183f17bb04470fda17ea142b17db0b511ecb0f5d10e31cf91ef40ce9100e25cd26541f590b39186a28963c2d20910d1d1c591f730c251abc18811ad91b4d1abf1c59186a00b21f3e25cd1f83258126542bf62c0f265700b323dd0f9d02d802a523a7044505f80a002e8502a502d8024e2e7f2257041613a1291327a40fa50d93044434f8003e142b0fed14951853184f1515186d186b1497077708070d0f00e7133d37eb0043008f34f734f534f8350935ec35f135a43be4363725cd1f832bf625812c0f26540b391f2228963c2d20911c590d1d186a198815150ecb142b0807149714952b510fed25cd265428963c2d20910b390d1d1c591f2325ff39a23a59136b188c14970d1d142b149518530fed08071515186d25cd1f832bf62c0f26540b3928963c2d20911c5936ff0adf0d1d1c59186a1f3e25cd1f832bf625812c0f26540b391bd31f22268b1bd3186a1f3e25cd1f832bf625812c0f26541b4d0b391f22268b00b21f02186a1f3e25cd1f832bf625812c0f26541b4d0b392719270526a926a71bd31f22268b2e4f00b3268b1bd3186a1f3e25cd1f832bf625812c0f26541b4d0b391f221abc00c72719270526a926a72e4f1f220b01268b1bd310e7268f268d0d1d1c591f3e25cd1f832bf625812c0f26540b391f221bd310e7268b1b4c1bd3186a1f3e25cd1f832bf625812c0f26541aa90b391f22268b1ae11b4d1f3e25cd1f832bf625812c0f26541b4d1aa90b39268f1f22268b1bd310e7268d00b3⟩, ⟨0x127092048824211f08e84301fc0fc06d03401640a604c823c11608503b01d00e006402f814409404702280f006e0310148094032000, 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⟩, ⟨0xb705b02d41680b305902c41600af05702b41580ab05502a41500a705302941480a3051028410c07f032017008002b00d0054014000, 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⟩]) (
.leaf #[⟨0x2000f807803a01c00d806803201800b805802a0140098048022010007803801a00c0058028012008003801800a0040018008002000, 0x2606260523671514142d1506142a23f411b20134012e160e0136149c36ce14963cce36c814b71494234606a92c0e3b5e3a583c2c3a573a0e33900de80e2c0e4b⟩, ⟨0x5e02e81700b605a02c81600ae056029813c09204401f80e006c02c014009804601e0090028012008003801800a0040018008002000, 0xfa116aa0fdb00a61b4c0c301b68090203041fdb09030ce917ee09030f4f09030ce919a318241a681a00152d1fdb09031fe120101c592896136b1fdb0adf08072bf61c592896136b0adf39a21a32201313470adf136b133d3731371f377b37430ef6000808b3077b184f00e70807077a0adf090317ee0adf17bb090319a30ce913470adf136b37eb133d3731371f377b374336d936dd0ef60807136b0adf2bf61c59289639a20902308a0d0e0776077525fe309e261b30971f820d1c⟩, ⟨0x13009804c026013009804c026013009804c026013009804c024011008003c01c00d006002c014009004001800a0040018008002000, 0x2f4032381ef72c821e04268e00c71e261fd80d92080708070adf2056203e203d15b221a50117⟩]))))))))

def policySharedUnitFixed1Db (i : Nat) : List Int :=
  if i < 0x21e8 then policyFixedCompact1Db i
  else policyFixedClauseDatabase 16 policySharedUnitFixed1Clauses (i - 0x21e8)

def policySharedUnitFixed1HintLeaf0 : PackedNatTable.Table Nat := .leaf #[
0x87710ed002,
0x877a1e8002,
0x87910ed002,
0x44488889110003,
0x8909120002,
0x89121ec002,
0x44988929120003,
0x89f913e002,
0x8a6114b002,
0x8ae115b002,
0x8aea1f1002,
0x459c8b3115b003,
0x45c08b7913e003,
0x8c6918c002,
0x8c721f5002,
0x46448c8118c003
]

def policySharedUnitFixed1HintLeaf1 : PackedNatTable.Table Nat := .leaf #[
0x8d6a1f5002,
0x47948f211e0003,
0x4814902110b003,
0x4834906120b003,
0x90c9120002,
0x910121f002,
0x910a1fd002,
0x911121f002,
0x48d891a9234003,
0x91c9234002,
0x91d2201002,
0x49d49399272003,
0x93c1272002,
0x4a089409280003,
0x9449288002,
0x4a7c94f129d003
]

def policySharedUnitFixed1HintLeaf2 : PackedNatTable.Table Nat := .leaf #[
0x4a88950929d003,
0x4aec95d12b9003,
0x9601288002,
0x4b30965921f003,
0x97c12f7002,
0x4c0c9811301003,
0x9851309002,
0x986130b002,
0x988130f002,
0x98d931a002,
0x4ef09dd93ba003,
0x4f409e793ce003,
0x4f509e993d2003,
0x505ca0b1415003,
0x5068a0c9418003,
0x5074a0e141b003
]

def policySharedUnitFixed1HintLeaf3 : PackedNatTable.Table Nat := .leaf #[
0x50d0a199432003,
0x5160a2b9456003,
0xa36146b002,
0xa36a21a002,
0xa37946b002,
0xa38221c002,
0xa391471002,
0xa39a21e002,
0x51dca3b1471003,
0xa3c9478002,
0xa3f147d002,
0xa3fa222002,
0xa40147d002,
0x521ca431456003,
0xa47948e002,
0xa482226002
]

def policySharedUnitFixed1HintLeaf4 : PackedNatTable.Table Nat := .leaf #[
0x5250a49948e003,
0xa4e149b002,
0xa4ea229002,
0x52a0a5394a6003,
0x52fca5f14bb003,
0xa6294c4002,
0xa7094e0002,
0xa7614eb002,
0xa76a22f002,
0x53c4a7814eb003,
0x53f0a7d94fa003,
0x5434a86150b003,
0x54dca9b13ce003,
0x552caa51549003,
0x55ccab91571003,
0x5634ac6158b003
]

def policySharedUnitFixed1HintLeaf5 : PackedNatTable.Table Nat := .leaf #[
0xad895b0002,
0xada95b4002,
0xadb2239002,
0xadd95ba002,
0xade223b002,
0xae3a21c002,
0xae515c9002,
0xae795ce002,
0xae8223f002,
0xae895ce002,
0x57d8afa95f4003,
0xb019602002,
0xb022243002,
0xb031602002,
0xb0b9616002,
0xb0c2246002
]

def policySharedUnitFixed1HintLeaf6 : PackedNatTable.Table Nat := .leaf #[
0xb0c9616002,
0xb122243002,
0xb1ba245002,
0xb1c221a002,
0x592cb251649003,
0xb291651002,
0xb2d9655002,
0x59b0b359655003,
0xb3e967c002,
0xb45968a002,
0xb462251002,
0xb46968a002,
0xb472253002,
0xb51a253002,
0xb5ca22f002,
0x5b00b5f950b003
]

def policySharedUnitFixed1HintLeaf7 : PackedNatTable.Table Nat := .leaf #[
0x5b8cb7116e1003,
0x5bc4b7816ef003,
0xb921723002,
0xb92a25a002,
0xb9a9734002,
0x5ce4b9c1737003,
0x5d8cbb11761003,
0xbb5976a002,
0xbb8176f002,
0xbb8a260002,
0xbb9176f002,
0xbc39786002,
0xbc42263002,
0x5e28bc49786003,
0x5e3cbc7178d003,
0x5e4cbc9178d003
]

def policySharedUnitFixed1HintLeaf8 : PackedNatTable.Table Nat := .leaf #[
0xbd19799002,
0xbd22268002,
0xbd417a7002,
0xbd4a26a002,
0x5eacbd517a7003,
0x5f3cbe717cd003,
0x5f88bf095f4003,
0x5fb8bf697ec003,
0xbf917ec002,
0xc011801002,
0xc01a271002,
0xc099812002,
0x6060c0b9812003,
0x6070c0d9761003,
0x6094c121823003,
0x60a4c141827003
]

def policySharedUnitFixed1HintLeaf9 : PackedNatTable.Table Nat := .leaf #[
0x60ccc191831003,
0xc1d983a002,
0x6100c1f983a003,
0xc231845002,
0xc23a27b002,
0xc241845002,
0x6154c2a1831003,
0xc35986a002,
0xc36986c002,
0xc3a226a002,
0x6214c4217cd003,
0x6234c46188b003,
0x6264c4c1897003,
0xc51a279002,
0x6294c521827003,
0x62c4c581737003
]

def policySharedUnitFixed1HintLeaf10 : PackedNatTable.Table Nat := .leaf #[
0x62f0c5d98ba003,
0xc61223f002,
0x6318b1295ba003,
0xc6c98d8002,
0xc6d228b002,
0x6374c6e18d8003,
0x6464c8c1917003,
0xc8f2226002,
0xc909920002,
0x64d8a5e14bb003,
0x654cca91951003,
0xcb6196b002,
0x6604cc0197f003,
0xcc121ec002,
0x66b0cd599aa003,
0x66d0cd99723003
]

def policySharedUnitFixed1HintLeaf11 : PackedNatTable.Table Nat := .leaf #[
0x6730ce599ca003,
0x6774cee19db003,
0xcf49110002,
0xcf519e8002,
0x67c4cf8196b003,
0x6804d0019ff003,
0x6840d079a0e003,
0x6868d0c9a17003,
0x6874d0e188b003,
0xd221a43002,
0xd22a2a1002,
0x6920d239a43003,
0xd2f9a5e002,
0xd3022a4002,
0xd329a64002,
0x69bcd371a66003
]

def policySharedUnitFixed1HintLeaf12 : PackedNatTable.Table Nat := .leaf #[
0x69c8d389a70003,
0x69d4d3a1a70003,
0x6a20d439a86003,
0xd4b1a5e002,
0x6a88d509aa0003,
0xd5a9aa0002,
0xd5b22ad002,
0xd5fa2a4002,
0x6b2cd651ac9003,
0xd771aed002,
0xd781aef002,
0x6bf0d7d9aef003,
0xd811b01002,
0xd81a2b4002,
0x6c28d849ac9003,
0x6c3cd871b0d003
]

def policySharedUnitFixed1HintLeaf13 : PackedNatTable.Table Nat := .leaf #[
0x6ce8d9c9b38003,
0xd9e1b38002,
0xda89b3b002,
0x6d58daa9b54003,
0x6d6cdad1b54003,
0x6d84db01b5f003,
0x6da4db11b5f003,
0x6dd8dba9b0d003,
0xdc1a1fd002,
0xdd7a222002,
0x6f64dec1bd7003,
0xded2201002,
0x702ce051c09003,
0x706ce0d1c19003,
0x708ce111c21003,
0x709ce131c21003
]

def policySharedUnitFixed1HintLeaf14 : PackedNatTable.Table Nat := .leaf #[
0x70c0e179c2e003,
0xe301c5f002,
0xe30a2c9002,
0x71b0e359c67003,
0x71fce3f1c7d003,
0x7238e469823003,
0xe4822ab002,
0x7270e4d9c9a003,
0x72d0e599cb2003,
0xe7595ad002,
0xe762239002,
0xe809897002,
0xe8122d3002,
0x7424e841d07003,
0xe8b1d15002,
0x74d8e9a9d34003
]

def policySharedUnitFixed1HintLeaf15 : PackedNatTable.Table Nat := .leaf #[
0xe9c1285002,
0xe9ca20a002,
0xe9e1845002,
0xe9ea2da002,
0x7524ea41d47003,
0xea6a204002,
0xea8a251002,
0x7570d0299ff003,
0xeafa1f1002,
0xeb02246002,
0xebc2260002,
0x7604ec01d7f003,
0x764ce7c9cf8003,
0xeca9cf8002,
0xeda9db4002,
0xedb22e6002
]

def policySharedUnitFixed1HintLeaf16 : PackedNatTable.Table Nat := .leaf #[
0x772cee51649003,
0xef21418002,
0xef2a2e9002,
0x7818f029e04003,
0xf0a22e9002,
0x78a8f149e28003,
0x78c8f189e30003,
0x78d4f1a1e30003,
0xf229e44002,
0xf2322f0002,
0x7944f281e4e003,
0x795cf2b14a6003,
0x79e4f3c1e77003,
0xf3f1e7d002,
0x7a0cf411571003,
0x7a28f449e88003
]

def policySharedUnitFixed1HintLeaf17 : PackedNatTable.Table Nat := .leaf #[
0x7a4cf491e91003,
0xf4c9e98002,
0xf569eac002,
0xf5d9eba002,
0xf5e22fb002,
0x7afcf5f1eba003,
0xf6b9ed6002,
0xf71a2e6002,
0xf7522d3002,
0x7be0f7b94d5003,
0x7d50fa99a86003,
0x7da8fb49f68003,
0x7e4cfc91f91003,
0x7e68fcc9f98003,
0x7eecfdd1fb9003,
0x7f3cfe71fcd003
]

def policySharedUnitFixed1HintLeaf18 : PackedNatTable.Table Nat := .leaf #[
0x7fc0ff79fee003,
0x7fd4ffa1ff3003,
0xffc9ff8002,
0x803d007200d003,
0x8054a6b14d5003,
0x8085010201f003,
0x80c1017a02e003,
0x80e901ca038003,
0x817502e1549003,
0x81ad0352069003,
0x8209040a080003,
0x1044a2c9002,
0x8239046a08c003,
0x8288f279e4e003,
0x82b5056141b003,
0x82c50581d47003
]

def policySharedUnitFixed1HintLeaf19 : PackedNatTable.Table Nat := .leaf #[
0x82dd05b1e96003,
0x1061a0c2002,
0x1062a0c4002,
0x834506520c4003,
0x838106fa0de003,
0x83d4e341c67003,
0x83ed07d16ef003,
0x1097a270002,
0x10ada28b002,
0x10aea27b002,
0x8580f409e7f003,
0x85b90b6996b003,
0x10b82248002,
0x85c4cf99979003,
0x86490c89c9a003,
0x86910d19d34003
]

def policySharedUnitFixed1HintLeaf20 : PackedNatTable.Table Nat := .leaf #[
0x10e0a273002,
0x87550ea1882003,
0x8780ea793d2003,
0x25c87490ea003,
0x2d487f9100003,
0x1104016c44088809103005,
0x30c8899114003,
0x34c88b9116003,
0x36c88d1119003,
0x37c88e111d003,
0x4048a09142003,
0x42c8a31147003,
0x46c8ab9158003,
0x961169002,
0xa31183002,
0x6448ee11dd003
]

def policySharedUnitFixed1HintLeaf21 : PackedNatTable.Table Nat := .leaf #[
0x7009041209003,
0xe6920f002,
0xf09229002,
0x7f891e923e003,
0x80c9201241003,
0x8c4937126f003,
0x9ec95a92b6003,
0xa5096392c8003,
0xacc96f92e0003,
0xcac9b39368003,
0xd549c7138f003,
0xe449e293c6003,
0xed49f393e8003,
0xfbca10141f003,
0xfd4a119422003,
0x1064a1e943c003
]

def policySharedUnitFixed1HintLeaf22 : PackedNatTable.Table Nat := .leaf #[
0x1078a20143f003,
0x109ca229446003,
0x10e8a291453003,
0x113ca2f145f003,
0x1260a5614ad003,
0x12b0a6014c1003,
0x1300a6894d2003,
0x132ca6e14dd003,
0x136ca7394e8003,
0x150209e65400a7f9501005,
0x13eca84950a003,
0x15130a005444a881512005,
0x143ca8f9520003,
0x14fcaa99554003,
0x154cab39568003,
0x15fcacc959a003
]

def policySharedUnitFixed1HintLeaf23 : PackedNatTable.Table Nat := .leaf #[
0x164cad115a1003,
0x1668ad295a4003,
0x1684ad495aa003,
0x1758aed95dc003,
0x15fc0bf257e8afc95fb005,
0x18bcb191633003,
0x31a963a002,
0x1938b27164f003,
0x1a04b481691003,
0x1a84b5d16bb003,
0x1b34b7316e7003,
0x1b54b7696ee003,
0x1ca8ba4974a003,
0x1ce0ba7174d003,
0x1cfcba89750003,
0x17590e885d5cbab1758005
]

def policySharedUnitFixed1HintLeaf24 : PackedNatTable.Table Nat := .leaf #[
0x1d34baf9760003,
0x1d90bbc1779003,
0x1de0bc5978c003,
0x1f54bfa97f6003,
0x1fc4c07180f003,
0x2018c101821003,
0x2078c1b1837003,
0x20d8c25984c003,
0x4301877002,
0x2310c6a18d5003,
0x25e8ccb9998003,
0x2630cd399a8003,
0x2808d129a26003,
0x2870d1f9a40003,
0x28dcd299a52003,
0x28f4d2b1a55003
]

def policySharedUnitFixed1HintLeaf25 : PackedNatTable.Table Nat := .leaf #[
0x2948d339a68003,
0x1a8e14e66a30d459a8d005,
0x29dcd499a94003,
0x2a10d4d9a9c003,
0x2a98d5d1abb003,
0x1ad115746b3cd671ad0005,
0x2af0d6a9ad6003,
0x2b58d711ae1003,
0x2b74d729ae4003,
0x2bc4d7e9afe003,
0x2bf0d839b08003,
0x2c64d921b25003,
0x2c84d951b2b003,
0x2d68db79b70003,
0x2e18dd69bae003,
0x2eb8dee9bdc003
]

def policySharedUnitFixed1HintLeaf26 : PackedNatTable.Table Nat := .leaf #[
0x2f30df71bef003,
0x2f98e031c07003,
0x2ff0e0e9c1e003,
0x3030e161c2d003,
0x32ece701ce1003,
0x337ce829d06003,
0x3548ebe9d7e003,
0x35a0ecd9d9c003,
0x3700f089e12003,
0x374cf0e9e1e003,
0x3770f131e27003,
0x1e3d1bde78ecf1d1e3c005,
0x3828f2d1e59003,
0x3908f4a1e95003,
0x3990f5b1eb7003,
0x3a50f7e9efe003
]

def policySharedUnitFixed1HintLeaf27 : PackedNatTable.Table Nat := .leaf #[
0x3a88f869f0e003,
0x3b48fa39f48003,
0x3bb8fb21f65003,
0x3c84fcf1f9f003,
0x3c98fd09fa0003,
0x3cf0fd69fae003,
0x3d18fdb9fb8003,
0x3d30fdf1fbf003,
0x3f410312063003,
0x419508e211d003,
0x41c1092a126003,
0x4aa32b002,
0x148029887c10f9004,
0x14e02a487d90fc004,
0x7b00f701ea44d089c1136226a44dc89d113900a,
0x852333002
]

def policySharedUnitFixed1HintLeaf28 : PackedNatTable.Table Nat := .leaf #[
0x8ca334002,
0x122024c0494092115f22c045848b19162009,
0x25a04bc8b5916c004,
0x134027004dc09b117222e645d08bb1175009,
0x27a04fc8bd117b004,
0x141028a05100a1917e22fe46008c11181009,
0x51c0a50149230a46188c41187007,
0x15302ae05580aa9194232a46588cc1197009,
0x15902ba05700ad919a233646708cf119d009,
0x2bc05808d011a1004,
0x2c2058c8d191a4004,
0x16602d405a40b411a8235246a88d611ab009,
0x2f805f88e191c4004,
0x6180c4818823a247488ea11d3007,
0xdf2338002,
0x1e803d807ac0f5122e245e48c09191231009
]

def policySharedUnitFixed1HintLeaf29 : PackedNatTable.Table Nat := .leaf #[
0x40808189219244004,
0x422084c92a9256004,
0x2180438086c10d125c24ba4978930125f009,
0x874110021f24c4498c9329264007,
0x47c090093e127d004,
0x492092c945928c004,
0x24c04a0093c127128e251e4a409491291009,
0x4a2094c94a1295004,
0x4ac096094c1299004,
0x4d809b895612ad004,
0x9c0139827225604ac495992b2007,
0x13ca33e002,
0x5160a3496212c5004,
0x149a33f002,
0x29f05460a8815092d225a64b5096b12d5009,
0xa9015382a625b04b6496d92da007
]

def policySharedUnitFixed1HintLeaf30 : PackedNatTable.Table Nat := .leaf #[
0x158a340002,
0x5680ad897112e3004,
0x56e0ae497292e6004,
0x2ca059c0b3416612fc25fa4bf898012ff009,
0x16f02df05ba4c4c98b931526284c5898c931800a,
0x5ce0ba49919324004,
0x5d40bb09931327004,
0x2ee05e40bc4178132a26564cb0997132d009,
0xbcc17b02f526604cc49999332007,
0x2f705f60be817c9335266c4cdc99c9338009,
0x6040c109a09342004,
0x60c0c209a29346004,
0x30d06220c40187934a26964d309a7134d009,
0x312062c0c5418a135026a24d489aa1353009,
0x31706360c6818c935626ae4d609ad1359009,
0x31c06400c7c18f135c26ba4d789b0135f009
]

def policySharedUnitFixed1HintLeaf31 : PackedNatTable.Table Nat := .leaf #[
0x6420c8c9b11363004,
0x6580cb89b5136b004,
0x6620ccc9b79370004,
0x6760cf49bb9378004,
0x67e0d049bd937c004,
0xd2c1a7034d27104e249c5938a007,
0x1a9a342002,
0xd741af139027284e489c89393007,
0x1bd037b06f24e909d413a6274a4e9c9d513a900a,
0x7040e109db13b7004,
0x7260e549e413c9004,
0xea41d513dd27c24f7c9ef13e0007,
0xed81dc83b827d44fac9f693ec007,
0x7740ef09f793f0004,
0x3be07840f041e013f227e64fd09fb13f5009,
0x78a0f1c9fc93fa004
]

def policySharedUnitFixed1HintLeaf32 : PackedNatTable.Table Nat := .leaf #[
0x3c9079a0f301e593fd27fc4ffca009400009,
0xf3c1e903d128065010a031405007,
0x3d807b80f6c1ed140e281e5040a091411009,
0x3f807f80fec1fd1426284e50a0a151429009,
0x83e1084a211443004,
0x2132349002,
0x21ca34a002,
0x227234b002,
0x11d023b847629125228a46148b007,
0x8fe1204a4b9498004,
0x9401288a5b94b8004,
0x25f234e002,
0x139827484e829e653d0a7b14f5007,
0x142828595192a3a546ca8d151c007,
0x286a354002,
0x144028985122a44548ca929524007
]

def policySharedUnitFixed1HintLeaf33 : PackedNatTable.Table Nat := .leaf #[
0x5140a30145c28b15272a5054a4a95952a009,
0xa32146ca96952e004,
0xa3a147ca989532004,
0x29ea355002,
0x15002a185422aac555caac9558007,
0x5440a90151c2a3155b2ab85574aaf955e009,
0xa92152cab09562004,
0x2a92356002,
0x5540ab0155c2ab156a2ad655b0ab7156d009,
0x2b185640ac455d8abd15782aee55e4abe157b00a,
0xaca159cabf157f004,
0x2bd057b0af25644aca95932b245650acb959600a,
0x2bf2357002,
0x16302c6959c2b405678ace959f007,
0x2cfa35a002,
0x2eaa35b002
]

def policySharedUnitFixed1HintLeaf34 : PackedNatTable.Table Nat := .leaf #[
0x17ac2f615e82bd857a8af495eb007,
0x17cc2fa15ef2be657c4af815f2007,
0xc141830b079610004,
0xc341870b0e161d004,
0x189031386262c4e58a0b151629007,
0x6370c7618e831c963c2c7a58f8b20163f009,
0x191032296442c905918b229647007,
0xcce19a4b3b1677004,
0x33fa360002,
0x1a4834a86942d5a5ab8b5816af007,
0x6f40df01bdc37b17152e2c5c5cb8c9718009,
0x1c08381971c2e405c78b8e971f007,
0xe0a1c18b909722004,
0x38907130e225cb0b98172e2e5a5cbcb99173100a,
0x39287260e485d04ba297432e845d10ba3974600a,
0xc2e2367002
]

def policySharedUnitFixed1HintLeaf35 : PackedNatTable.Table Nat := .leaf #[
0x3bba36a002,
0x79c0f401e7c3cf17b42f6a5ed8bdc17b7009,
0x3d507ab0f525ef0be017be2f7a5efcbe117c100a,
0x1ed43db17d02fa85f48be897d3007,
0xf6e1eec3dd07b92fac5f5cbed97d92fb05f68bee97dc00c,
0x3e9a36b002,
0xfac1f60bfc97fa004,
0xfb81f78bfe97fe004,
0x1fa03f587ea30126028c06180b007,
0x204c40a182c306060b8c16982f007,
0x107020e8c279850004,
0x212c427084d30c66190c331865007,
0x86610d421a4434187b30f861f4c3f987e009,
0x10ec21e0c441889004,
0x2214443189031286248c489893007,
0x11102224c4a9896004
]

def policySharedUnitFixed1HintLeaf36 : PackedNatTable.Table Nat := .leaf #[
0x8a1114a229045198b3316862d4c5b98b6009,
0x22d845c88b831926328c6618cb007,
0x117422f0c6718cf004,
0x119c2340c7018e1004,
0x8d111aa235046998e331c86394c7398e6009,
0x235c46d08d931d263a8c7618eb007,
0x11ba237cc7798f0004,
0x11c02388c7918f3004,
0x8e411d0239c47318f631ee63e0c7d18f9009,
0x11d823b8c801901004,
0x11de23c4c819904004,
0x8f311ee23d847a990732106424c85990a009,
0x8f811f823ec47d190d321c643cc889910009,
0x90b121e24384869925324c649cc949928009,
0x12202448c95992c004,
0x9151232246048b992f326064c4c999932009
]

def policySharedUnitFixed1HintLeaf37 : PackedNatTable.Table Nat := .leaf #[
0x49f093f127a6564cae995b32b46570caf995e00a,
0x947129625284a4996432ca6598cb41967009,
0x95212ac25544aa196f32e065c4cb99972009,
0x4bca372002,
0x4c5a373002,
0x4e409c9138e677ccf199e133c06788cf299e400a,
0x27604ec99fa33fc67f0cfd99fd007,
0x27784f089e034106824d059a0a007,
0x27e84fd9a1e34446880d0f9a21007,
0x13fc27fcd119a24004,
0x500a374002,
0x28105038a06345068a4d159a2a007,
0x1412282cd171a2f004,
0x14182838d189a32004,
0xa11142a28505099a36346e68e0d1d1a39009,
0x50da375002
]

def policySharedUnitFixed1HintLeaf38 : PackedNatTable.Table Nat := .leaf #[
0x528a378002,
0x29b85379a81350a6a0cd411a84007,
0x541237b002,
0x2a5c54c1aad35626abcd571ab0007,
0x5608ac215806b60d6e1ada35b26b6cd6f1add00a,
0x5782381002,
0x57d2382002,
0x16342c70d939b28004,
0x2cc05998b32367c6cfcda09b40007,
0x16a82d58db59b6c004,
0x5b48b6a16d06e18dc51b88370e6e24dc61b8b00a,
0x2e4c5ca1bb837786ee8ddc9bbb007,
0x2e545cc0b97377c6efcde09bc0007,
0xba517522ea05d39bd237a66f50deb1bd5009,
0x17922f28df61bed004,
0x17aa2f5cdfc9bfa004
]

def policySharedUnitFixed1HintLeaf39 : PackedNatTable.Table Nat := .leaf #[
0x5f00be117be6ff4e009bff37fc7000e019c0200a,
0x2fd05fa9c1438307058e0a9c17007,
0x5fda38a002,
0x305c60d0c19387670f0e1f1c3d007,
0x18363074e201c41004,
0x187030e8e2d9c5c004,
0x189a313ce391c73004,
0x314c62b0c5538ee71e0e3d1c79007,
0x6408c8219007284e529ca339447290e539ca600a,
0x32c46591cd639b47360e6b9cd9007,
0x196832d4e6d9cdc004,
0x65d238c002,
0x32f86608cc039ca7398e741ce7007,
0x33846720ce33a167430e871d0d007,
0x34446891d423a8c7510ea19d45007,
0x1a6e34e4eb41d69004
]

def policySharedUnitFixed1HintLeaf40 : PackedNatTable.Table Nat := .leaf #[
0x1a903524ebb1d77004,
0x1a983534ebc9d7a004,
0x35b06b78d6e3b407684ed19da2007,
0x35d86bb9dae3b6476c0ed79db1007,
0x6d08da21b4077a0ef61dea3bd277acef71ded00a,
0x6e92391002,
0x37506eb8dd63c407884f119e22007,
0x1bee37e4f241e49004,
0x1c063814f299e54004,
0x70d0e1b1c327984f329e633cc47990f339e6600a,
0x1c7638f4f479e90004,
0x720a395002,
0x1d303a68f809f02004,
0x7878f101e1c7e00fc21f823f027e0cfc31f8500a,
0x3cd479b1fa63f547ea0fd39fa9007,
0x1e723ce8fd59fac004
]

def policySharedUnitFixed1HintLeaf41 : PackedNatTable.Table Nat := .leaf #[
0x1e923d28fde1fbd004,
0xf991f3a3e707cda02340488095013a026009,
0x3ea07d4a033406e80d501a2036007,
0x1fa83f55033a068004,
0x7ef8fe01fbc81bd039a07140e081c903aa07400a,
0x201a403905720af004,
0x206240c906ca0da004,
0x207440ed071a0e4004,
0x830106120be845508ca117422c846108da11a00a,
0x85310a7214a85f90c1218042fe86050c2218300a,
0x910120024c04910e421ca439c87310e3009,
0x2951d210f7003,
0xa711d212cf003,
0x2a11d290fa003,
0x49d1d29164003,
0x220e44151969106004
]

def policySharedUnitFixed1HintLeaf42 : PackedNatTable.Table Nat := .leaf #[
0xef01dc03c4078112f226044c8898912e009,
0x48d1d4915e003,
0xe5d1d493cc003,
0x4b91d5116a003,
0x4c11d5116d003,
0x4d51d59171003,
0xb911d5931f003,
0x4f91d61179003,
0x5011d6117c003,
0x5091d6917d003,
0x5951d691a6003,
0x5211d71184003,
0x5391d7118a003,
0x5511d79193003,
0x5b51d791af003,
0x5691d81199003
]

def policySharedUnitFixed1HintLeaf43 : PackedNatTable.Table Nat := .leaf #[
0x5b91d811b0003,
0x57d1d8919f003,
0x5b11d891ae003,
0x5891d911a2003,
0x5911d911a5003,
0x59d1d991a7003,
0x6311d991d7003,
0x16f236805c48d911b3005,
0xbc0177237405e80bd8179237646fc8de91bc237c47048e011b900e,
0x5f51da11c2003,
0x61d1da91d0003,
0x6291da91d5003,
0x7a51db922d003,
0x8151dc1242003,
0xa051dc12bc003,
0x820103820b04140824923124724904928924924500b
]

def policySharedUnitFixed1HintLeaf44 : PackedNatTable.Table Nat := .leaf #[
0x106820c2498083c108020e249a4944927924e24a0494c929124b00e,
0x8491dc9254003,
0x8511dc9257003,
0x10b0215042e496492d1258006,
0x8651dd125b003,
0x14851dd1534003,
0x8791dd9261003,
0x14891dd9535003,
0x9291de928a003,
0x9351df128d003,
0xf551df1409003,
0x9491df9293003,
0xa291df92c2003,
0x9b51e092ab003,
0x9bd1e092ae003,
0x9c51e112af003
]

def policySharedUnitFixed1HintLeaf45 : PackedNatTable.Table Nat := .leaf #[
0xa091e112bd003,
0xa311e212c3003,
0xe051e213b4003,
0xa811e312d1003,
0xb991e31321003,
0xa951e392d7003,
0xbfd1e3933c003,
0xad51e492e1003,
0x23ad1e498fd003,
0xae11e512e4003,
0xae91e512e7003,
0x2c525ea0b1c97992f4005,
0xb2d1e592fb003,
0xb951e59320003,
0xba11e69322003,
0xbf51e6933a003
]

def policySharedUnitFixed1HintLeaf46 : PackedNatTable.Table Nat := .leaf #[
0xbad1e71325003,
0xbb51e71328003,
0xbbd1e79329003,
0xc011e7933d003,
0xbd11e8132f003,
0x26351e819a9003,
0xbe11e89334003,
0xbf91e8933b003,
0xc0d1e91340003,
0xc151e91343003,
0xc1d1e99344003,
0x21751e99875003,
0xc391ea1349003,
0xce51ea1375003,
0xc4d1ea934f003,
0xce11ea9374003
]

def policySharedUnitFixed1HintLeaf47 : PackedNatTable.Table Nat := .leaf #[
0xc611eb1355003,
0xcbd1eb136c003,
0xc751eb935b003,
0xcc11eb936d003,
0xc891ec1361003,
0xc911ec1364003,
0xcb51ec9369003,
0xd1d1ec9383003,
0xcc91ed136e003,
0x22c91ed18c5003,
0xcf11ed9376003,
0xcf91ed9379003,
0xd011ee137a003,
0xd091ee137d003,
0xd311ee9387003,
0x1e151ee979c003
]

def policySharedUnitFixed1HintLeaf48 : PackedNatTable.Table Nat := .leaf #[
0xdb01b5836f06dc0db49cd939c273a4e7c9cf139a00b,
0x1be837c07000dfc1bf13ac275a4ec49d793ae27604ecc9d913ab00e,
0xe0d1f093b5003,
0xe151f093b8003,
0xe511f113c7003,
0xe591f113cb003,
0xe6c1cd039e073a0e709eb13d727b04f689ec93d500b,
0xedd1f213e9003,
0xf4d1f21407003,
0xeed1f293ee003,
0xf511f29408003,
0xefd1f313f1003,
0x21011f31856003,
0xf191f393f8003,
0xf211f393fb003,
0xf291f413fc003
]

def policySharedUnitFixed1HintLeaf49 : PackedNatTable.Table Nat := .leaf #[
0xf591f4140b003,
0xf411f49402003,
0xf5d1f4940c003,
0xf651f5140d003,
0x23a91f518fc003,
0xfe51f59425003,
0x14e51f5954e003,
0x103820684110820103ca1b1437287050e8a1c943500b,
0x10811f61441003,
0x34191f61d3b003,
0x10b0215842f085c10b4a25144b28985138a26944900b,
0x1150229845708ac1154a31946428ca519ca33146200b,
0x11d51f81488003,
0x1b751f816fb003,
0x49a0932127024d94b0296252cca5914af009,
0x139d1fa14f2003
]

def policySharedUnitFixed1HintLeaf50 : PackedNatTable.Table Nat := .leaf #[
0x2a2c54511a99515004,
0x14451fb9521003,
0x3c6d1fb9f9b003,
0x14551fc1526003,
0x28211fc1a2c003,
0x14691fc952c003,
0x14711fc952f003,
0x14791fd1530003,
0x15691fd1570003,
0x15051fe1555003,
0x38711fe1e68003,
0x15151fe955a003,
0x15651fe956f003,
0x15291ff1560003,
0x15311ff1563003,
0x15552001569003
]

def policySharedUnitFixed1HintLeaf51 : PackedNatTable.Table Nat := .leaf #[
0x2d452001b67003,
0x1599201157d003,
0x15a12011580003,
0x2b505690ada15b02b595822b06561cac295842b0c5624ac4158100e,
0x5cf0b9c17442e815d72bb05768aec95d6009,
0x2bfe57f51ae15fe004,
0x18952061626003,
0x1a092061693003,
0x18e1206963b003,
0x25c52069991003,
0x198c33106660cca1990b3816712ce459d0b39966f00b,
0x19a12079675003,
0x1a7120796b8003,
0x1a4d20896ac003,
0x6970d2c1a6434c16b22d665ad4b5a16b1009,
0x1bd52091714003
]

def policySharedUnitFixed1HintLeaf52 : PackedNatTable.Table Nat := .leaf #[
0x264920919b0003,
0x71a0e321c7038d973c2e7a5cfcb9f173b009,
0x617920b985d003,
0x1da03b3876b0ed41da4bbe977e2efe5e04bc0177c00b,
0x1e1c3c3078a0f121e20bcf179f2f405e88bd0979d00b,
0x1e7520c97b3003,
0x21b120c9880003,
0x3d687ac0f601ebc3d717c42f8a5f24be397c62f905f2cbe517c300e,
0x1ee120e17d5003,
0x227d20e18ae003,
0x1f5d20f17f8003,
0x290d20f1a5a003,
0x20ed2101851003,
0x21312119862003,
0x21d12119886003,
0x219d212187a003
]

def policySharedUnitFixed1HintLeaf53 : PackedNatTable.Table Nat := .leaf #[
0x21c92121883003,
0x21dd2129887003,
0x21e5212988a003,
0x228921418b2003,
0x22b121418be003,
0x22dd21498c8003,
0x230121498d1003,
0x22ed21518cd003,
0x22fd21518d0003,
0x234921618e2003,
0x2415216191b003,
0x236121698e8003,
0x2419216991c003,
0x238521798f1003,
0x238d21798f4003,
0x239521818f5003
]

def policySharedUnitFixed1HintLeaf54 : PackedNatTable.Table Nat := .leaf #[
0x2411218191a003,
0x23b521898ff003,
0x23fd2189913003,
0x23c12191902003,
0x23c92191905003,
0x23d12199906003,
0x24012199914003,
0x23e521a190c003,
0x23f921a1912003,
0x243121a9924003,
0x246d21a9935003,
0x244521b192a003,
0x244d21b192d003,
0x245921b992e003,
0x246921b9934003,
0x252121c9963003
]

def policySharedUnitFixed1HintLeaf55 : PackedNatTable.Table Nat := .leaf #[
0x257121c9977003,
0x254d21d196e003,
0x26c84d889b5136826ccce719cf33a06748ce899cd00b,
0x277d21f9a07003,
0x289121f9a49003,
0x31d84f389ea13d227a0d089a1234266854d0a1c9d00b,
0x28152219a27003,
0x285d2219a3d003,
0x28292221a2d003,
0x28952221a4a003,
0x28352229a30003,
0x28592229a3c003,
0x28492231a35003,
0x316d2231c80003,
0x289c5130a2a145228a0d261a4d349c6940d279a4b00b,
0xa6314c429945321a7934f469f0d3d9a78009
]

def policySharedUnitFixed1HintLeaf56 : PackedNatTable.Table Nat := .leaf #[
0xa8c15162a385469aa6354e6aa4d541aa5009,
0xaaf155c2ac45581ac235866b14d621ac1009,
0x2c6d2279b26003,
0x2ce52279b46003,
0x2c945920b28164e2c98d979b3036626cccd991b2e00b,
0x2cc52281b3d003,
0x32d92281cdd003,
0x2cf859e8b4116802cfcda61b4d369c6d40da79b4b00b,
0x2d552289b6a003,
0x2d612289b6e003,
0x2e5922a1bbd003,
0x2e9122a1bd0003,
0x5cd0b99173a2e705cd9bc337886f20de31bc5378e6f28de49bc200e,
0x2e9922a9bd1003,
0x438522aa1e6003,
0xbce179a2f405e79bf137e46fd0df99bf0009
]

def policySharedUnitFixed1HintLeaf57 : PackedNatTable.Table Nat := .leaf #[
0x307122e1c3f003,
0x315122f9c76003,
0x315d22f9c7b003,
0x6420c83190e32186429ca9395472b8e561cab395a72c0e579ca800e,
0x32fd2321ce4003,
0x33892329d0a003,
0x33c86788cf519e833cce919d243a4a749ce931d2200b,
0x35b52351d9f003,
0x35e92351db7003,
0x6b88d701ae835cc6b91da53b4c76a8ed41da73b5276b0ed59da400e,
0x35f06bd8d7f1afc35f4edc9dba3b7676f4ede1db800b,
0x37552371e1f003,
0x3a1d2371ef1003,
0x70f0e1d1c42388070f9e6a3cd679bcf369e6c3cdc79c4f381e6900e,
0xe841d063a187429eed3ddc7bc0f779eec009,
0x3a6523a1f00003
]

def policySharedUnitFixed1HintLeaf58 : PackedNatTable.Table Nat := .leaf #[
0x3f0123a2053003,
0xea31d3c3a8074f9f093e147c30f859f0f009,
0x7890f111e2a3c507899f883f127e34fc59f8a3f187e3cfc71f8700e,
0xf3e1e7a3d0079f9fb03f627eccfd91faf009,
0xf541ea63d587aa9fc93f947f30fe59fc8009,
0x3d687ac8f5d1eb83d6cfe89fd23fa67f54fea1fd000b,
0x3dec7bd0f7e1efa3df1001a004400a801d003200200b,
0x3e6923ca022003,
0x3e8123ca02b003,
0x7f10fe11fca3f907f1a07740f081f103d207940f681f903ea07600e,
0x3fa07f38feb1fd43fa50422085410c8221043a08300b,
0x3ff07fa0ff71fec3fd5048209141248251049a09800b,
0x42248429088210e42190a8a15242a685550aa215600b,
0x85490a8215842ac8552186430e862d0c4a188431486350c6218500e,
0x8842487002,
0x112d225844a9196912b005
]

def policySharedUnitFixed1HintLeaf59 : PackedNatTable.Table Nat := .leaf #[
0x5c124f91b1003,
0x61124f91cb003,
0xb1926192f2003,
0xb2526192fa003,
0x15062a0a540d1a89504005,
0x16f72dec5bd11a896f5005,
0xa8ba508002,
0x16dc2db65b651a996da005,
0xc11251d002,
0x1d652fce5f951ae17e6005,
0x17e92eb85d691b3975b005,
0xc2fa52a002,
0xeb9a52a002,
0x21d835226a3d1bc9a90005,
0x21cb3ea07d391bc9f4f005,
0x21c635a86b491be9ad3005
]

def policySharedUnitFixed1HintLeaf60 : PackedNatTable.Table Nat := .leaf #[
0x1b2236426c7d1be9b20005,
0x1e413c8078f91c99e3f005,
0x1f7c3e2e7c54f840e9d3e0c7c14f839f16009,
0xc0e182030496092c1a582cb05160c0c0c0214046233900c,
0x39807380e792102428484890892130396022c046a33900c,
0x57c0b2097b24a849560b0416002c405860b0897692ee25de4bc497812ec4b340afc97512eb014,
0xb911cf02e805d40c291cc494092840c0017f030606080c091c6238e47208e511c9238a96640bb11b7237046d88e711cd01a,
0x5cd2d711b5003,
0x62d2d711d6003,
0x15d92f9057a96b4974a20c006,
0xaf12d892e8003,
0xc052d8933e003,
0x40c0826307a207440e236e306a208c40b8828104e207c410089510422088c1ca285307060f913d1834016,
0xc6018c6722857da44e360c318857f0b0116002a245450b5f150e3184e44a2bf35486c3115b9c88015,
0x2aacd600008154a2a911be1ab9154e29f053d8a3e147e29005560a4115526af11579a5834ae6a5d1559abd017,
0xa9915426adc540a37b153429f45430a8014fe2a6c6260a9c153a6ad0e3822ad35666a651561ab2015
]

def policySharedUnitFixed1HintLeaf61 : PackedNatTable.Table Nat := .leaf #[
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,
0x6752d24002034024102d1e19cc33a067d0cec19dc33c0d1e0cf219e8b44a2de2d105a1d12a1686015,
0x829192029a045408a115322a445448a6a1ef43e004c48b7115422860021242a48812f803c807a00f301f28e98899999a01a,
0x450c004248501fa04cc09900ff01fc44f50fa113c4910040007c233200f,
0x478696811d02384565170011f4b7404600940129022c045c8bba335022a0450089810e021e04400888112021a4768082914300109215244097c01e403d007980f9474c44ccccd114822a0453c8a7114a2292454c8a91151229a87bd0f8013122dc4551243248b491892348aaa1f322ca8cd12dd915a03f,
0x1140226043808781100222044808691da229045288a4811522ee002119aa486491692312469154015,
0x1b70782c6da0db53c0e78206db8dae1b5a36ac6d48daa1b5e36a06db1e093c0077fcefc9dfa3bfc77f4efe1e0a018,
0xdb91b7c78406dd0dbb3c1a78386de8d5c1ab635686ac8d581aca35986de1e0f3b327660ec59d8c3b1e7638ec69e0c019,
0x5820b0316122c205858b0c36306c645810b0d36342c185838b0536226c54d899b1236286c5cd8b1b10016,
0xfb41f94c0207db0fba907cbfe07d90fce1f983ef87e021a01f843f11800438889c4bff9805300e6018c0097fb018,
0x79c502926383bd27ee9295277a4f11b5877ec5af1b7349ee93e52780d4f1a9c354c6a80d5142d48e38ebe22e33af693c9074076d0ed81dd43b7178344ca5e0927d03de07c00f7c1ee8b5936e2931927aa4f649f093ed289a5634a302d6d0a51e97492a0560cc8249a492c9261258a4de49e8212520c076f0ee021643b8884130ce002125024a1496a92d926fa4f349641d891b4a53530ae61cd131978430c0925d24ca49b493895352a7a56b4a2a945928ba5144a9695312a8254e4ac495a91c29413442a50503a907510efa1df01ac179144ce5d992992536074,
0x11ac66912702543120264584c119a349be1dd91b524e1438693b43b3077a0ef21d94bbd22662ef694ac3b907740ee61dc03b7876e0eea1db03b6a0dc0ec68da5258a4de4a6c5e0913297832f088990bc2a53249e82d74481890211b8236c46f242e31f692fd276254111d263f814192c64924927525a24b9051c5f792cca5b049741ed0c57a5984b5e0f38a0524c7077a4fdd252a4ef49e236b0efd8b5e36e693e52780d4f1a9c354c6a80d5142d492d525b24f3471c75f11719d7b49e492c927d03de07c00f7c1ee8b5936e2931927c24fb4a26958d28c0b5b42947a5d24a8158428c0021243248f4920924524d2496493092783d4241a0f4c1e9401b07a30f481ec43d087a242e833506698cd619aa33444420883484c22084400887484e9708e7fa2d43a0094dc668072d008a73f8bdca26d2f745eed297a4974932926d24e254d4a9e95ad28aa5164a2e94512a5a54c4aa095392b1256a470a504d10a94144a329469298a530496693d527b24f749f893012a2a5464a8e63b8c76a28e36e495212a125441cf839e869e07560eaa1d5c3af8e7b3dbc7b74f6e17692ed07b6cf6d1ed93db0897c73e87280e401cb039580462e967b8117f1edf0ec,
0xa40314a3c54136952447e9915435296612d7a4a24b32928d2d8254b4a9895412a5254e4a9a953cb1684590c66116822da163491e9241248a49e497493b528ca51a11ac66912a18901322c2d74481890211b8236c46f242e39d2002127024ec49ea93d927c24fb4a8295152a3254731dc63b51471b724a9095092a20da41b46369c6d30da53be077c4efa9df33be477d0efb9df63bde51a91259469053,
0x3af87570eaa1d5909c2139427441e4bb517682ed239ecf6f1edd3db87b6112fa2fe012,
0x1350269cdda255717146ecc4ad1bb24ab02d90dc219c400c,
0x2c785a31b5816408e1058e8b48168e2c7c5910b4316882c8cda10008466a95012a8a5534aa895552b60b2a16522d1459a0b35166c2d0859b8b3836c66d14da21b43366895b4d96a2bb36586d6515e1b2902b
]

def policySharedUnitFixed1HintLeaf62 : PackedNatTable.Table Nat := .leaf #[
0xbbd17782eec5e00bbf177c2f145e30bc737ce6facdf49be837d42f105e10bc1001a2ebcdf19be637ca6f90df121e317742ee40070bb0176e2ed80080bb117682ee0df01bdf37c22fac5f50bee17da2fb0e069c0e381e7044e081c0c031,
0xc3a1888b11860d0c3e187831016202c42587c2fe05fb0b7016d82db86320bfa1884b11224a2b7c56fd122161e018,
0x3144e289c6487a26d86c69dd033bc023803100c1018468180042485015c02b405b80b0015e43f92cb10fd491027706958d2a13ba681116f9a03465c0320063806401940348068806600d2035406c89d7487c8cc1197911502f,
0x315860f2c6a18b8316a35d2c6218c42d985b20b5e16b42d708b30b6818c0b1a228a2b6e56e111e1630016,
0x2d7862a0b6018acb18162f447618b0b1b00080c1c972d1ae95b800e,
0x1192029a045408a0113021c043c0880111022404348ed1148229445248aa01184668047c0908120023a04700940129022c045d2de915322a445448a8114f229c45350f7a1f0026245b808299f700109209241a48512f803c807a00f301f28e98899999a4b92972c8aaa1f322ca45650f9115a03d,
0x3f4099813201fe03f889ea1f433ee00212412483490a040007c25cd466497252e5913c013,
0xbdc580400424b94a38174c2e9006f00e28d6c2fb85f60bf417e0afc16004a3a57dc2f685f50be217c02f924090b2e165003e807a46b257b912115ed020,
0xaf21fa42bcc65ba19c05f87709246a4c64990932526524ce4974922869023ed3aa6931d267a4cb4a7e95592a9256e39bc819915a0aee1970853062f06db08f211e0214042408f611f021106dc3aa80021244a48b491892a1255a4b9491c5be91141492288e889cb7ca5054a8095452a9a5544aaa9134e6f9aff041,
0x1e7140a498e0ef49fba4a549de93c46d61dfb16bc6dcd27ba4f949e0353c6a70d531aa035450b524b5496c93cd1c71d7c45c675ed27924b2315e96612d7a4fa07bc0f801ef83dd16b26dc526324f549ec93e127da5134ac694605ada14a3d2e002124a8158492e926524da49c4a9a953d2b5a5154a2c945d28a254b4a9895412a725624ad48e14a09a2152828946528d253104e,
0x1cd801d87910f341ec8432888c1a7e626cc3c97b20e6e1cb8022872d19a0335c6a30871310475d0e7f2365017,
0xb7e43a49665251a5b017002dfc5c18b8217026ea0dd49baa37586eacdd38b8917102db05b58b6d206e2db85b79ba300108cd9250a5194a342dc45b80b7416e62dc8dc89b92372c6e50dc99b9537306e5cdc80b7616ea2ddcdcd1b9b37322de11da1b9c16f42de45be8b7c16f66e78dcf9ba037446e84dce9b8f41c26e94dc71b8d37626ec0dd21ba6049,
0x415184d001020c041a883446de61286848d08105620b0416908f105c20bcc2223213086610916d9841016,
0x20a040b8818314e0020c1a082710342064c5325b44ba88db8c1f227a00f,
0x5aa0b6016c82d105a486a8982130805c4260473a891d3702002014f00a30144027804c009921ea026814d9ecc05a0921096710f421da43ac87810f343d44b40c9c131e024,
0x1fd0c0d00080ff61fc11b618190fee1fd83f907ee0ff21fe83f607ed0ff0603513a1816302060511399811017
]

def policySharedUnitFixed1HintLeaf63 : PackedNatTable.Table Nat := .leaf #[
0x6de800424b908da11bc237046b08d451ed111947c0afa15c91aba51c00f,
0x1378b4284d946a0138827084e009b8135c27204e509aa1358a73223129de53a511814ea013,
0x49e296a0020250a3f2296c127c24e84a8094e128c252091c094a1298a5d2291297252f511614b4015,
0x8901194a3a044c4696111c233846608961140342045108a41188b4ba4b94a0697692eca5234b725184b4aa21e28c051d5110145d01c,
0x84611e8a4884254692108823e047b084810a0484042908545234004233549169231246a4ba4a049410a24228f288e5249114144401c,
0x86c10f4a2a0438469410d421f843e086e10d0239843008629770a27a22528a0515510c9451014,
0x8901194a3a044c4696111c2338466089651d5110145d00c,
0x2039083800849be948d294a5b44ba829984220847108c616d2d19a7d17c82f8c5ed0be70f2800f0e041c05471235806b10d61199873dd1721d92101a205440888101024908439e073a0e661cbc024174f46cc60ad13c182a02f,
0xbb617642ec05e10bc0175c2ee85d446b65794aee85dc0bb45778af115e02bbe5784af215e3014,
0xb50331073f85aa426a58b919b25984b5e56c82d385a91ffc16902d295a7466a96c92cd85b10b6616c82d785ad0b5c22cc2da05b53b9a002124215bd451456dcadc223c2b7256acad795ae028,
0x5bc0b9a16f82df85c00b9817042e115c62b8a5710ae185bd2b82002119aa48b4918923525d15c2015,
0x12cc82700040b8c376c9484b2081f203e248dd290198300c,
0x10c2218a43105d08ba017542e785cf9bcb466a93a92758b9248a62e445c80080376e95c92ba1bcc45846f350d621ae435a6f5c861a1b6001092f52d9259b49c893952b9a575218e431886490c8436086c50d9a1b2435e43285c7807f219686d10daa1ab035,
0xbf616e02db05b70c6417f42ff25e12c0a8928adf15bf0bf816e8b00800849729470ae02244014,
0x131c260c4c799eb4aae95652ac095d487465e0cd68986131226984d709af135626a44d5095f338a6718ce499c83354670ccd3229601c,
0xcc719923320663098839dc73c4e7819ca42de26291b99cef00d
]

def policySharedUnitFixed1HintLeaf64 : PackedNatTable.Table Nat := .leaf #[
0x19ed011e43884ada5c6131e66b4cbb19ec4bcc26104c1898e130c261402c09874bce26dc4dc89b81b1c26e84dd89bc1b3026f44df09c43bbe675cef019d633aa7748ee889cb017c02fc06000bc017a44390f5910f33ce8a6914d99d40154669914b19a5035,
0x138a272806300c401848cb806400c700c8032888a99e6138c90f44db0d8d340c921405700ad016e02c005790fe4b2c43f524409dc1a5634a84ee89d40108002006d00d8019c44611981a0445be680cee819de02c,
0x9738095812a02a40544083810902728ccc8c7a1f722d003ac07500ed01d844a52cb91280208040c02d006500d0035806d008400102751198114413a627484ed09d613aa67e514e99f8027,
0x82d2165494a949529310052008403c8030d101a1a01b800420a9462e82a027e850109fe543d2cf2113016,
0x45808ace951d2b3a5c33e4935822d250c4a1cf688e763a5a74b0942926c010,
0x41a12f5906420c4419c68c004e423e8e841f903f007d450851a306580cbc1964328065a0cba197032d8d171a2c01341f683ee468a7530b34966a2cd0599d127a120023,
0x3e507c90f8e1f20bfb80080f8c5fad13787cb0f9841dc3e687ce2fe28c7cbf817ef012,
0x1099a4df4a64959c5340a6714e029b05358a6a00740020d4022aa34fe336466c0ce019b8336802100013a088b54e81a57d01a,
0x598cb3206470caa192cb2d064a0c92193032786530cac192085c964c2cc45984b30165f449a33a885d165e2cba59411af964d01b,
0x36406c40d791f9036047f80d401aa035606cc0d601ad23ec47f48fc11f5035247cc8fa01ae23f447f08fd91f7018,
0x6700d291ef033c06740cf91e923d447a00d2019b034e06980d001a11b1806880d191ec3b9e47b88f591f023e447c48f691e701b,
0x337e67004d109a11340267c4ce899e337266e8cdd99be3378043008901110220043c0870113022845248a519bd018,
0x478696811d02384565170011f2324053408c01280252045808b9177466a0414ce98008490a97c92f881b5036806d8900120123fe93304ce19b84ab404548aa248649169231246915543e6459519a115a02b,
0x1b3237046cd8d9c43700f10ef1a2ec07620ecd1a21de100c,
0x25f322a645488a89150229e45388a6a1ef43e004c44d619ed011e4388cf625e6139a67b84e809cc139e27384a7005f00b867bd14e19f21308260c4c70986130a01604c399a6452c6694ce3916e33ec9330662a43c39da97d04e309c5018a0320063806400ce032c88aa43d33bc26904d189b0134a979c4db89b9137036384dd09bb137836604de89be1388777c0a589c0137e270c4e080d4138490ec8c48008466c9219247a4904922924cced19d945326760ceb9de033ac6754ee91dd11396679d14d229b33a8670914c19c106d,
0x1280668000401bc240c24eccac25d3126024dc49b092f03f607f519d99494524652886621ba014
]

def policySharedUnitFixed1HintLeaf65 : PackedNatTable.Table Nat := .leaf #[
0x5c59db312da2e30ddb0974476e665091c01f203e248dd2521bb500e,
0x474696811e023e73a926302fc267e002015724c84992931d267a4cb49949339245255a22b48b8008e01280252045808b9b7b490c922d246248d4b34933125f25b322aa87cc8b29159027,
0x11ac66912a18901322c86a52cc25af494493b45ae89031204237046d88de485c73a400424e049d893d527b24f849f695052a2a5464a8e63b8c76a28e36e495212a12544024,
0x25604ab89590192018c06500d201a20198034a32f32ea65e8004094d2130425c4a88950129e017802d996a464665a52ac997401b,
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,
0x137e270c4e080d433b28a644e01ddf138825dc6cb0d971b283654f008008466c9219247a490492292786c80d8f1b2636486c89dd63bae7760eed1dd93baa776ceef1ddd33b677711b919d8028,
0x4bd027004df89c313820350ceca29933b025dd1b909cd33dc27404e609cf139c253802f805c019667bd14e19f2018,
0x10b61096129a426084b895112a0253c02f005b32d48c8ccb4a55912b2032403180ca01a403440330069019897f9197997516c8426c4af09464bf801744c38960011e4388cbd897b33327750ee98cc5487873b44d209a3136026952f389b7137226e06c709ba137626f06cc09bd137c97f4095812a02a40544083810602d604ec09e25f622f087e08a2918f43ee45a0ceb9de033ac6754ee91dd1139602f805f80c0017802f488721eb221e679d14d229b33a802a8ce12298338265891929b84066,
0x2c400780b02160c2b985770af0976d20195902b3616482c8807a00fa11292ef044608e211c02220443088411c822004414bba5164a42945a28b65210a41948229028884234846a08d62e1c236046d087851f1160947b28f48890a2e2358032,
0x2b9846800ec160c2c0959b006,
0x3d05910b2416211ac007d00f601e130085700afa8d5c2bb85780aec15f0dbd0008497210ed300251c0f8034d869a87c10b325f912d097e3100220004048803100420151b6981f44ec6078acc24032b2016502cba35902e,
0x15d50010108c211047c08f61090a492228288810942140908085210a92f11448451e511d1a485bd0b7817342df05bf0b8017302e085c22b8c116c22e845c08b20a40149028e467e51a510d946a0b765714ae995c42b865750ae9223e0b8a17182e388af0b901724ae6a2892b98572d12095c203d,
0x2f725e50bee202040385f82bf09680afb85ed0bea17c42f805f2481257b912115ed012,
0x3d807d00f416502cba6040ba697802f205e200e216442c9058846b0579d1ada359012,
0xe001d0486807309624c0465f50fe112401c2259407109614bac0a680ee01db03b0075c0eb122303a80a5d2de12ca43fe487090ea1fe259a65f114a911e021,
0x4d09900132026087599ae43d0026c87b0008012802784bb009f014043c4ccb21ea21e08cac05090ec016
]

def policySharedUnitFixed1HintLeaf66 : PackedNatTable.Table Nat := .leaf #[
0x1c9038c070414b0970331e4b2490701ca038e078073a096c4bf007d891d8975332a7b34914a5ac015,
0x8943916002041ca422309c31903ff080c1014202c4468896111c224cc50a2863138609913b98a2015,
0x5e811222240449189f31409755304989e009,
0x2a8059e0ab415612dd441a0aa4dbf82af125025bc494896e3344002119aa4bd4b64966c4958924124e2498492993f32806504ca19942328e6634cc71945260265111a012dc025,
0x126e24d849781fb329224eccd001fc127024e4497093a3342002119b25984b5e247c48f092212422480c9d193b327864f8c9e993932ae6558caa995132a88ceccac2292024,
0x3f4099813201fe03f889ea1f4414a0021242810001f08cc9291a5b44ba896f92df913c013,
0x2324053408a81140226043808781100222044808691da229045288a4915402308cd008f81210240047408e01280252045808ba5bd025604a80a90151020e042409ca333231e87dc8b4115322a445448a8114f229c45350f7a1f0026245b8082a0a5001092144be00f201e803cc07d80fa4c1a44ed1d311333334948d2da25d44b7c96fc8aaa1f322ca45650f9115a04c,
0x1b820010920805c80b8017602e805900b446584428886910c2216442524280ae1a5234a005800af21fc756d24390fd019,
0x6800ce002,
0x9c6138a272806300c401848cb8cf3243d136c3634ee819de00d,
0x32e06680cc91e343f206608f300080320063d19b8192032642d80ca019523be866c8f091e023bc476c0cb11e2018,
0x25c014b01c3038807140dda5f703f88ced0fd920a259297e00fb123b12ea07d44b201f803ee022004301f924788a50cca998f01b,
0x4dc0d3e137426f14ea44ac1360a7704e34bb2137d1a814e900d,
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,
0x112a208445a98c349749490c638820103e209c414081720a68418004210544f460f8c1c2285014,
0x20a7497213d827a84fc09ee13e51a915084466541d2ed26144a0e948d292a5b44ba84014802100f200c3440686806e001082a518ba0a801d
]

def policySharedUnitFixed1HintLeaf67 : PackedNatTable.Table Nat := .leaf #[
0x10092010401c805900a07500e9d1f183a607480e8c027827541568c5905521d107c80f8c02903e607dc0fb402a83e707d88d14a0f24ee01d,
0x46408dc68c823a1a0a84d8004251020a0413c829105141fc83fd080a10041fa74e916e9274046608e011a0cf619f8841125d0cfe477a74c482423f441ec74a11019270024,
0x8f411e023724e808ec93d0008046008bd19e8232046608e011a023524e2880c938126d046c49dc93ca204017,
0x12f60cf819fe840d19aa4a9495492b5257a57e3a6433e867da102001092c1258a4b5496c92e125fa4f549ec93e127d9d2f01a,
0x4af2998002025984b909568d34a6584b2096212b425484b40a4e12d425b14c82a765324a6214c72984531911694c3019,
0x5290a605510293052b0a5854f8a9f85280a6414c4295052d21a814b829795414392550caa015452a8e5518aa1153d019,
0x9a2134026614de099c539400404ca09928d3c26304c72a74134826994e32a725380a6d14db09a8537ca71222e018,
0x292153c0010987130f261d006,
0x323864c1cc21920323c6489cbb397872e864a8c8d193432646490c93192c325c64a1cbe39827300e5e9cc3398a7310e5f9cb901b,
0x1888311ce348c2f185c30c0e2a1c5538a631146218c49189030c4619104718663118e33231d38ac71a91659c65018,
0x133026504c609a413412a304c84a9095412a6254a4a9c95512a900e,
0x40ad068101c2036407505da0bc4174408881290212032406906590172058833d05ca0bf418e8318810101e203e40b4813902a41a4002080a1016202a404c71f8e40472a82d118c20b52052833518da0bd417c8c6518d20ce02f,
0xfb01f5c3e387db0fb71f708129025a049407e3ec47d78fb540903ecc7da0fb240828115021a0424088811d0232040019,
0x24694ae0010124824b8496469852ac7040e07091c123c248049309281244a52a22b2948528d17994a2016,
0x1b9637346e30f851b90371c6e48dca3c2c7868f0c1e173c32105c6e18f8b40308048f0d8e311c6414d829a955149fa0ff8a1585342a9e15bc1fe840c08000ffc018002f081250b110c158e49fc5530f431e8502c,
0xec41d99e13490a85892432491493c875d2880adf35ce950129f253d118e232446408c51186634d269a53f11826349269237131ac8a30c6ba48f4920924924ea4b1494c93d11a20d991b82366c7ffa09e494a92d525b24b7498e93cd27ba4b249f82d70db8a4c649ea93d927c24fb4a26958d28c0b5b42947a5c0042495492e926524da49c4a9a953d2b5a5154a2c945d28a254b4a9895412a725624ad4827d1761de1057
]

def policySharedUnitFixed1HintLeaf68 : PackedNatTable.Table Nat := .leaf #[
0x7300e901d044910f700e7224e002005600de01ba8cc407000e112ca0388071911f452a447888d9123016,
0x3aa489c00401de03ba077c91292262448074c14c829803ac075c0ec0b6303b2076890f22c0243a4871105921b018,
0x39007440e801d2242c485c90c00084c0e98a1314921500c,
0xeb4b7804ac095015202a2041c08481394666463d0fb9168037006e80dc81b701620228000920243f4480c07500ed01d844a52cb912801d,
0x3200c701909845307911500ce035406ca33000a,
0x1a2016808181044c56451006900ce01b0036931625fe01968cc088c232f010,
0x32806801ac0369198005a02060411315914400a,
0xc8031c06426114c1e97fd309111501940348068806600d2035406ca62e019898b484d895e128c250c02b0b6516cc2d9d309a452370a658919281bc037607140e201c3052c25c12fc01f6247625d4cca998f259248290fd9206037e8ed9304262a03ea25900fc01f7011002180fc923c4528481d198232f040,
0x650064018e0321308a60f222a0348068806600d298b12ffa61201aa0365198232f012,
0x1a2016808181044c56451006900ce01b003691981118019898b9318232f010,
0x91d12466df12cc25af4944931927aa4f649f093ec4b402e3125a24b04b3896912d425acf740008490624c84988935126824ccca6194d329c6540ca7994b33186610ca41938025,
0x1ac6001094c929f8abb15888df85758aed15d82b845631ae945666be92db2569011,
0x2b905718ae815d22b80d820af415ec2bd45790aee15de2bdd1c09aff456a6c00d741af735ec6bd4d758ae515cc2b9c5751af9466c944d28aa5164a802ac8d6300084a6494fc5618abd157e2af8562a44c35ae6b7d2db256935f06bd0d799af235e22b893198ac8158e00605650ad515a02b6856e238035c68dfcd700ab515682adc55b0a961528912cd6422b0358e2ae086910d115726b352d39acc35d48ac51591aec057,
0x25c736a66d5cda90b2b16142cb05970b2f165a6cdd15c1b36366a8ae515d0a8f011,
0x15c62ba05748ae036082bd057b0af515e42bb85778af747026bfd15a9b0035d02b905728ae615ce2ba8d7c8008466c944d28aa5164a806be0d761aeb020,
0x22184420ce21a203449f4a49169231246a4bb4982930926224d24914940928216a228b4111023806870d1a852c004248f4920924524f24e34a46947d2a5a54c4a9a953cb53145b026
]

def policySharedUnitFixed1HintLeaf69 : PackedNatTable.Table Nat := .leaf #[
0xa66355400212eca5234b7294d129f8a450ffa1ff03e1074700c00004bf4227534ba95a06a28d44108c616d2d21a7d019,
0x1d783ae87590e505db43ad97ac0010937d2eca5234b721a6929487290e3e34f52e921373ade27c8d0da52e10f8623929c086b3aea222c43d888a10fc22106688e8119a4334c66a21744a6e3340396804539fc74011801cff311e8a10c4d08643d8894b469f09f113e62d841ad803706ae6ddd1501d6e3ada1cb039580460e5c1cdc39b00480e5e1ccc39d073c46cc5d3d1b2974b46c81d0024e84a8094e52f511617520e841f103e187430e7c5d552d117540e8c1d143a7074a0e921d3131c04a147e4128c252091c094a1d04ba9a291297252d91b4175e44bc5d74bb72261077,
0x28905100a1412403660cbe0da41b403e407c601481f3141e273259b49cc12be050e5ad800424a50d201a3c35286a409f013e91a916be44ae5aa835f06c00d7e1af41fa03f307e20fa4a10a3462dae967cb6c25254a4c4afc960a20a031,
0x217033ac32886500cb4197432e065b27400e201c3839907124ef910a13bd2cd259a8b3416533a2692e52ed26144a0e987d2f81e150010929d25424ab4958088811085230448088c1128398044c089cfca820204000e281c5838d071c4efc9e193c127804f081c60d1521c0346868d8d1c3d8c93a0ea7232a3a968cf1254a4aa4b3492f92d9a4ad495e49a5109926824ce88d09330d9c1b3c36746cc83b10766784d242a48f4920924924ea4b1496a92d925324f4468877851751de3064,
0x26e869f09b8135c27204e509aa1a6cb7c25264a485add11894ef29d28958348a63a0d4009a81b3065f06d20da01f203e300a450789cc966d27301a8c1f2805307cc5af51b096ab026,
0x1e403e05950894163c2cb059846b2568c2c4a60500e217882f225e00ba698111ad95e7013,
0x408481290222046830506020c7418c406480d20cb202e40610660008204882e0810101e203e40b4813902841928c6d05ea0be46328c6905ca0bf01f,
0x88811c0343868d3b34923d24824914936927124b2498493c947c37306740cfa19d8b43a2542e029584b530443088419c434406893e940021245a48c491a92ed260a4c24988934924525024a08948c34024100cee19e068f06790d1c1a78b7c25264a485aa516f16882d1e5a88a2d145b03c,
0x22071e0e525eb000424df4bb2948d2dca5290e841f103e187430e7c5d552d117540e8c1d143a7074a0e921d2003080012ebc8978baea364008c1cb839b873600901cbc399873a0e788d98ba7a36502a,
0x6180c2c42a83090614879526824d149b2936d2b9a575268e4d20429085410a62a150a28008496292d525b24c649ea93d927c24fb4a6493d0d4e9869020,
0xa3f147c31a05240a4934fc95892b39a61459c695c5200aac14822908d2d80084bb2948d2dca5344a6669651579a58019,
0x43ae2c6131a23834a2e94412a0253e008,
0xae415c62ba05748ae036082bd057b0af515e42bb85778af747026bfd15a9b0035d06bdcd7b1af535d62b945730ae715d46c145591ac6001094c929f8ac3157a2afc55f0ac548986b5cd6fa5b64ad26be0d7a1af335e46bc4571263335d48ac51591aec035,
0xad015a42b6856e238035c62b3c00e0ad5159400605638ac84c882ad455a0ab7156c2a58d6422b0358e2ae086910d115726b352d39acc15f02b7845e88cb11942308c6da28d35cc230c462908c118c2b7d321803500102a48d73a32031ac8dc4d70237f035,
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,
0x159c00745650ad546fe2c4456b8ad1159a006c5870b0f4b8098e45488a9015fa2a4cd5622b635562c4c5890b1516282a54d8f25a8363a2bfc57f0b0116002be4556a38236188adcd859b1b15b22b6c54a244b4c8a8e00d719b1c030
]

def policySharedUnitFixed1HintLeaf70 : PackedNatTable.Table Nat := .leaf #[
0x745650ad546fe2b385698ad1007,
0xaf497c82bb06028758004248501fa04cc09900ff01fc44f50fa113c4910040007c233249329305261259a498a92f125f257a267c88312d692e901f,
0x46480a681150228044c087010f02200444089010d23b445208a5114922a8046119a011f0242048008e811c025004a408b01174b7a04ac095015202a2041c08481394666463d0fb916822a645488a89150229e45388a6a1ef43e004c48b7010543ac0021242a48812f803c807a00f301f603e9324810402060168032806801ac0369198114401d603a807680ec2252965c89401b8037406e40db80b10114000490121fa240644ed1d3113333349265260a4c24b34931525e24be4b6695e88aaa1f322ca45650f9115a06b,
0x1990334065c0cc11e243f20638e7a80084c24332919b91e300d,
0x3300d101a40329197806900ce019006380c84c22857800425ff4c249215325a5f24bb2948d2dc9115016,
0x221043f088a10f6222ceba886b1a8c335ceba189a4508623c6688e8119a4334c66a21744a6e74011801cff017,
0xb1e168c6d605902384163a2d205a38b1f16442d0c5a20b2336848cd52a8a5534aa895552b60b2a16522d1459a0b35166c2d0859b8b3836d0002124da49c492c926126925134a2a94592a00a8f4ade9460da29b5336886d0cdab9b5216562c285960b2e165e2cb4d9ba2b8366c6cd515ca2ba366895b4d96a2bb36586d6515e1b29045,
0xfe443383f987f430228ca03f798154bae1fd51b6181000c,
0x4d6098813382610d445af1311026a0d4098e91b086a307ca014c1f316bd010,
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,
0x21a80846108823e047b08483480ee1248b4918923526302fc267e00212cd24c84992931d267a4be499696cd26524ce497492291f69d53292488a0a221053102e20a0413983e44f4841483d907a1a7416f82df85c012142330466a0a41036207c4100895104222d50b308b44a4c9490c63a28530708db9242a52331bc5710ae1a13f045,
0x83425eb20c841888338d18009c847d1d083f207e00fb01f380554bda50851a306580cbc1964328065a0cba197032d8d171a2c01341f683ee468a7530b34966a2cd0599d127a120026,
0x213d4ca4116c22e845c08b20a40314a3c54136923d2482491493c92e8b169469443651a8c91a13c4276648911f09090b8c2260457089a4164227044d88a0113a1bb003506de0dbe2279069a5984b5e946528d25314a92952d2a6254d4a9e98f88130e381c7c38e871c8e3c48e47a38f46a2f841902450dbca4bb498895292a8a5534aa895550ce885b3da6930526124c549789441269a50c4ac8803126302fc267e00212cd24c84992931d267a4be499696cd26524ce4a169435287250f4aca93492b025614c46906cc5698ac450e62ad29d98aa318262a4c8fa290075,
0x2d024060b44180430206050c0418d08498d8742c258e92d596084c087b9cf731ee50b3a16702d605ab2b6688e8ad3209d3dc816982d18d1f12e6978c4b919920c7c5908cc99d522b5888e116895a802a,
0x34548700d1a1a363470f6310da06d48740ea7232a07180e241cc838707104e8000424e8277a88509df1d4b017,
0x163c2c8058e00f216482c8a358007
]

def policySharedUnitFixed1HintLeaf71 : PackedNatTable.Table Nat := .leaf #[
0xc22773830da40b2c36184030c86120c26185069706150c2c585517096142c2658691241612014,
0x6030c169028b0880084b9899612e4960e009,
0xc0818042d10d1f12e6978c4b9199203e807cc0f201e34bc80ab8915220233267548b0406054cb2180831b235e2c82948031f063d0c8c190031f808205560abd1a0164344985908b1ca5ab028,
0x6050c0818042d10d1f12e6664cea916084cb2180831a10931b0e8584b1d25ab011,
0x41912f590680cb0197832c86502cce893d09003f207e050851a3106220ce3460027005407d00fad08fa3a1017,
0x40c08225ce025604a80a90151020e042409ca333231e87dc8b400eb01d403b407611294b2e44a04e989d213b427584ea99f9453a67e08a2005a01a2034806700d8223003312f509d7487c0365198232f02b,
0x2b885840b0434bc2c5858a480a163c2c38d3848ce75a92ed25d90d145a9033525b93ace1618699099a336c7588eb0959b1a6890110a224ba0d1c19f033d86780cee1a0120826370890111c2338466089651d5110145d2d3c5a74b4e16a12d405a7cb4da2210cd859e5128168f2d108948b54a524132211bc237046b08d41c2c38a107e2020835c4c999b14a50759800425270df41be438386fc0df601d003904492e36896cb8d08b00bcc01c132b98c44a76851cb9a172728f6888ccd79d64066,
0xbfe385200206010c0648b470a06008c0017fa2fe46020c0517ee2fe0e0e22c7384a707d1631c20015,
0x1942328064f0c9d3990327ce68800819363290e680ca219467334e679cce19387318e638ca539927330e659cca018,
0x1ab886c86b02d9287390e686af2d94002035386a60d505b08b6186a90d54397435586ac2d8a7ad0b6396c62d885b0435696c801b,
0x1b1cb7500080d821b3836623622dd21b2836486c60d881b14b7286c20d865b74b7216e12dbc5b7d12c16e0017,
0x1ae435e06bb2da65b54b6a06ba2dac002035906b10d665b30b6686b40d6a39bc35b06b72d9e7b08b6896d02d9c5b2c35c16d201b,
0x25d04b8096894d825b2534002012ba3c004a80954130025e04be4a811041296252e096494e2207015,
0x2371a3208e811d927745ba08b893b00084c3408e519e927400d,
0x36106c50d890c861909207064105580ac91e425e403c64b78ee4a2e81b10772000425201ce607b40f381ef03dc07980f2922b440048b0f659dc701f,
0xd143a7e999533224b94a009419283a6614cc699893048d0b1a14344c6870d0c00da0020ea0a2dc3a801b0035f86bd07e85b5d2cf9d4a01d
]

def policySharedUnitFixed1HintLeaf72 : PackedNatTable.Table Nat := .leaf #[
0x25d6128098304c0260b261c7b40f679ece009,
0x63c0c7c18f432306400c7e02040fd01fb4ccc590d12616421b16772000425201ce607b40f381ef03dc07980f2922b440048b0f659dcc01d,
0xfa41f583e800a80fb81f6a345007,
0x213c4274850109f080c10142038408285a50c4a17942e286010102010401005c85dd0bca178286442710f08f8a1b8400c420b0418082a00cc01a040a468e806127f2176024,
0x132f0b6243c493892a5a54c4aa09538341a18f4328002124aa4974a2a945928ba5144a20934d289248f4920924524da49c492c926124f24d24974947d1f79694022,
0x25e312e4664831f1642005,
0x82b309220a4415184144fa20cce9f00084ba8341d1b7984200d,
0x1083800849be948d294a5b44ba82f905f19c05471235806b10d61199873dd1721d92012,
0x186030b3b2c358c6b221340efc1e3c3c70328064e0ca91a0936644d65e54eca134810a441e06ae8d5e3b2e8cd9258a4b5496c9378645a1070010937d291a5294b6897505f10bdc17bc2f745ed9bfb48b06ff0e021d90426284c113f8d5f10a099bc5ed0be70f2800f039b07370e621cec39ea3662e9e8d94e04080e101a2054408881010249084c15a27830547645172986904e,
0x3a821c049cc1df83c7878e06500c9c195217349a0934526f24d949b68d049b3226b2f2a94b12a4a5534aa895592a907600ebe1d5c3aa87560ec21d4c3aa21c24bae9215247a49049249275258a4b5496c94c92e0a5362ece5da0bb49765032,
0xf961f483e8a5ee46d61f3083b87cd0f9c5fc518f97f000c,
0x3ae07c20ec01d925d10f685f7928ca51a4a608d109f32216075e4f9119b02764c4e0560cc8249b4938926924b24984962937927a0848334692d525b24df49e693d527b24f74964938527e09824bf464552cca4a34b6023f504d8008491e9241248a49e497495252a5a54c4a9a953d2a8254a4a9c929925c13e5041,
0x296462519b2486027805400a781060210784d2e887b42fbc927925d25194a3494c12532333228a87d88bc249149266df9242a48f49209251249249d49c42d88dbea4c749c62d70db8a4c649f093ed2b18b5b42947a5d24a81583320926924b24984962937927a0848334692d525b24df49e693d527b24f74964938527e09824bf486540042599494696c1287a5130ab699cd28c24974932926d24e254d4a9e95ad28aa5164a2e94512a5a54c4aa095392b1256a060,
0x1c8c39107200e3e1ca51b207210e4e5d2120b174000b,
0x3bf878d0f020d48f6a24c84992933d265a4d8064c4d9526d24df49d8939d1a117972f4a89a03c017a600108cd526824d149bc936526da4e60efc5e552961796022,
0xf061e081ac835447bc4e34bcc07840e9e5e501a7938c00108cd526824d149bc93641a503490f200d20193832810b40c9533b228126cc4e15136138649cc1d403b0075f0eae1d543ab07610ea61d50bc8077b0ea41d443be877c06b01d8d1b4979144ce5d98bb397772ed05da4bbb17752ee85dcd12f87580e501d646a5075a0eb65db9171176d2ed88988bb2875c2ec85e6cbcd1799050
]

def policySharedUnitFixed1HintLeaf73 : PackedNatTable.Table Nat := .leaf #[
0x84892eba5324b8294fd2e00b0f161c006c00f0ad815b68e00d8d8b1316242c5458a0a95363c96a0d8ea56920d641a883b106d20d841bd1d12124425c84b5094a123023,
0x2afc55f0ac515882aed1bf0abd15866b7d2261ad700b,
0x263635e86bccd791af735ec6bd4d788ae2158c2b845760aed15d66be91599ae935d48ac51590ab2015,
0x2660525099a1338a6f9538445c1320a720008099e98791a794de00e,
0x194085a064a1df90dfa4e64a5894c873c25c33daa5e551408327065485cd26824d149bc936526da54912286de400424bb49829309262254a4aa2954d2aa2555433a93492b025614aac95491a0936602a,
0x208086f533da66e4a68959d2be8ed71dac3b6476c0a6900720020fa923023ea24335208a1bc207e41088208cdd19b6010c000a0ec41dc83b4e83a0eb020,
0xc30185885506120c290f2a4d049a2936526da5734aea4d1c9a4085210a8214c5429a9e00108cd9258a4b5496c94c8d4e986901b,
0x5258a4a149c33b8691a1cf49be943528726724c9e95452a9a5544aaa94312b2256a38da2ff86008c0017fa707d1631c204c4295f4eab9a62149829346768cef3a3e002119b25134a2a9458603245a385095e0e8f1a6302e,
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,
0x17764ce21c8c391267c482c5d003a907510efa1df01ac179144ce5d98bbba6722eea5dd0bb9a25f0eb01ca073ea5c51cf239f12e11edf1cf086fd273077e0f1e1e381940327065485cd26824d149bc936526da54912286de400424bb49829309262254a4aa2954d2aa2555433a93492b025614aac95491a0936644d65e5529625323daa7b80bb62262049,
0x7fa0fd841150df00084a4c94d1299a0f10ff21fb83f910ce0fe640f933ea0ea46506040c0b2274015,
0x87145598ab821a4434455c9acd4b4e6b3129325344a7e95a083a87c70f921f28bf7a26f425841c8838907420e641b933c07d4483a5fd11d12128425684a9094a127023,
0x6178eb98d451a882118c2d8a664ce069f520b985d00b,
0x310061f8c3c187630e522e9cd2001094fd32fa5784c4298813301c5a38ba30f9340268220d21f403e787cc0f969a0cbf817f344e08484e2f22ca01f,
0x30d8e2c800818729174e2d0c37186a31086208c3b18783fb061e8c3e38bc8c4ce2e9c6238c8718ce2f9c58017,
0x3ce2814931c1de93f7494a784d242a162490c924524f253d118e232446408c51186634d269a53f11826349269237131ac8a30c6ba48f4920924924ea4b1494c93d1277a4f11b5877ec5af1b7349ee93e52780d4f1a9c354c6a80d5142d492d525b24f3471c75f11719d7b49e492c9050a4fa07bc0f801ef83dd16b26dc526324f549ec93e127da51816b68528f4b8008492a056124ba499493692712a6a54f4ad6945d28a254b4a9895412a725624ad48e14a09a2152828944d28aa5164ac6400123220a0069
]

def policySharedUnitFixed1HintLeaf74 : PackedNatTable.Table Nat := .leaf #[
0x8651118217c42825df30ee626c3d9079a0f2200ecbd9187900d,
0x10a700081484291c5230a40147e2a8d2f78a993564993d339237c34b08a94d2ca53314fc6a6132fa5784d0c988466c8cd819c0337066d00420002741116a9d034afa40cc86f10dd14e46a292d2a0dd02a,
0x3d8a4cfd2cd02fc43ce879526d877e2f2a95cd2baa4c64ae495d9263a4be4b6692f52d9259b4a1895892b20a183902932926703923da89321264a4cf49969360193078f0f1c0ca019383480f200d241a51a9f466a9341268830a10ae2158185830c10a421504298a85353c002119b24b1496a92d8d4e986926904d1d26ca532270c89b09c2936644d64d9526d24df49d8939d276a50b4a1a94392b1a565054,
0x59a8b34168a2ca45951b5836686d5cda18b3616842cdc59c1b7400108cd9289a5154a2c9500547a56f368a6d4cda90b2b16142cb05970b2f165a6cdd15c1b36366a8ae515d1b44026,
0x11c822004414bba10ecdbd24b90af815d8acc251c28b21108221844408e011c4223169600101120223846708cc112c22696a7466c923d248249149748d2ca3aa22028ba97692ec85780aee15cd20195904a4696e528f945c2908520ca41145b28b45214a40a22108d2976040088001012200c401080546da607d13b181e0f8034d869a87c10b3298f4bf225a12fc6160c2c080784c0a566ca3d2224053,
0x7c00f9002,
0x3552ffa6124bd203600671118007,
0x478696811d02384565170011f2324053408c01280252045808b9177466a045408a0113021c043c0880111022404348c58105414a0021242897c01e403d007980fb01f444ed1d311333334948d2da25d44b7c96fd24a114822a0453c8a7114a2292454c8a91151229a87bd0f801314c1a45b88aa248649169231246915543e6459519a115a047,
0x11e1a5a047408e115945c0047c8c9014d023004a00948116022e45dc0042335022a0450089810e021e04400888112021a462d24a1148229445248aa248649169231246915543e6459519a115a029,
0x84411f023d8424292488a021195d5084a10a048404290854570519aa48b49189234a24228f288e8d242de8d3b1a7416f82df85c00b9817042e115c800108cd9247a490492292e822f846108c01160148828f4c068cfca34221d28dc16ecae295d32b88570ceb61d6b2ba8574911f05c50b8c171c45785c80b92573514495cc2b968904ae11444048,
0xf401e69a3408023320208040c02d00d101a48cbc8a200f212f867dc00424824906921407580ea01da03b0894a5972250972430da40b2c36972c4e989d213b427584ea89d7487c036406b80cf4d1c276c84d10990c24584d1921a0222308cc0cfca29d33f066691d31133039,
0x59e119aa48b4918923528125044a4619acb5280084bb4976433a868c0d1619d8b43a2552d0c1a01208168f017,
0x4bb299e002025fa3f329a012f07460e8b098a13042610f8909861310a6a230c29a6535d18094ce015,
0x8fc1224a4f048047e25258243047d0916122824104831ee81210242949a3fec88a4a4c949f29425280a4d9495018,
0x25684b7095c12bca6194ca445a12a825c14cd096098711a694c200e,
0x53dd28026954c4a941934b26944c3c13c427804f409e413b8a7f259c29fa13ac27504ef09da13b0026041d0836105c20c041500581048209a1720a040fdc1fb05330a0a1410284a3f50a10141c28723f62a66926925da4c40a4055200042499495292a925624b949829309262a4bc09ec13d427e04f709f20fc81f81421468c8d48a8422332a0e976930a10b819d61944328065a0cba197032d8d171a2c01353351d4c2cd259a8b3416534c3e9425285a50d4a1c943ca8f040b2a3088d4a1224ff28768d1ca1f234829f288c8a7c250706f
]

def policySharedUnitFixed1HintLeaf75 : PackedNatTable.Table Nat := .leaf #[
0x127425404a70946129048e04a50e825d4d14894b9297a88b03a017ac0010937d2eca5234b721a692949752017,
0x15170a0213f427f26972a1c13fc1f903f028428d18a87a50800d,
0x3988732002,
0x2ad455a0ab7156c2a5854a244b35908ac0d6325324cf22b20563801815942b551bf9ae04cf42ae086910d115722b6c56ca648159a00685880ca642b4329c6548ca81fac32ac6550cb048c232bc6570cb348c42c810ce000849909325263a4cf499694fd2a9a5544aac95492b70cb715ec2bd45790aee15de2bdd1c09aff456a73791c21cd5462273512c91cd335c68e00d66a5a7359896d92b49ac7053,
0x4c662b20563801835c02ad455a0ab7156c2a5854a244b35908ac0d638ab821a4434455c8adb15b26b8d1c01acd4b4e6b30841108b2108420c8588ac9002e00705678ad2432c85410aca14f028,
0x7462f58002126fa5d94a4696e529487420f881f0c3a1873e2eaa9688baa26770ec48da43a2874e0e941d243a6073d0e769a6839b873646ca1cc0023803b0f221e6906d836306c40d8443d036006be0d711ef835a06b04e5514193964a5a5ec8ba7a36646d05d7912f175d039,
0x292c5250a4e19dc7474e8e1d1b34c429305268ced3a347464e8c1a6300f,
0x3b707729f5e1dbc3b7476f9f583eb27d5c7720edb1dce3b987700ee1216a3b887719f5b43347d74fad1f5f3ec27d80fae1f5601b,
0x1bcc78dc0040ddf1bd6378c6f21e2c3c5a78d86f40de71bca37886f48dea1bc03784f15a2ef3c6678b91771e2f018,
0x7798ef21de03bbcfb30ef1407800207758ef61dee3ba07749f623edc7db4fb41f6c47343bd0fb3a303016,
0x3be47811f771df63be877e1f713ee47dc07808ef81e083c0c77e8efe21643bfc7801f74432e7dd8fb99f783ef47de4fba9f6f01b,
0x1044208630586071c38182a70e40040c0f182242d06090c1338688664e1b1c33182070c4e190c14386e83c10779c35019,
0x30986148c2838947130e258c27389a002060f8c1e1840710ce220c21184442cc6118c24388c8660e241c47388a71086129c4901b,
0xa3e18d029205559abd459c2a88d5f0aa84b6c2aa91be1a5700d,
0x1db47dec00424df4d4a30206038c0d18143024012800138568b20e1526a31830916ce1d26a44b6a95f47538ea51d4c7c40f889f124d3e9a887830f051d527c512d51f55024,
0xe001d0486807309624c04116c22e845c08b20a40314a3c52c5a51a510d946a051c99cc2ada1954a1e944d28aa5164a3065f50fe112401c2259407109614cd006f00dd81c5038848290fd9206037e8ed9304262a240e0a680ee01db03b0075c0eb122303a80a5d31791d900109219247a49049229665251a5b0493c4b290ff921c243a87f8966930d441c0b840e1829612e097e00fb123b12ea07d44b201f803ee022004301f903fa8cec91e2294332a663c964931d441e65f114a911e065
]

def policySharedUnitFixed1HintLeaf76 : PackedNatTable.Table Nat := .leaf #[
0x2a005430a7d15326ac91560a7f15069128d5c00084b6e2a80d4d1a9900f,
0xb1e168c9a2c5a48b5316a42c58d91a2be36b82c811c21aaa4bb2948d2dca5344a7e97005878b0e00366c6c5488a9015fa2a4c549003535588ad8d55a56816262c4858a8b14152a2b7056d1ae347006c792d41b1d15fe2bf85808b0036188adcd858b1d16902d1c58f8cb348c432b86578cad195800646582461195432ac7eb0ca81952329d0ad0ca616200068566a6484d38855c004108a206840d881c1035002c2b31071231c42b096513540afb489c2a245450b5f150e2a213210a661a8a3510423185b4b4869f452287fd0ff81f083a3806000025fa113a9a5d35468afcd521b0639a69648e6a231139aa6d6515e1b29081,
0x221167a2cf659f8b3f96800cdc19b422184442d305a64ea80d1d44a051e0a2d945a012,
0x8861108239044008825a9433586750d181a2c33b168744aa5a18a2c948528b411102380471088c5a592ed25d90af015dc2b9a4032b2096e4a2e148429065208a40a22108d211a833626aa0d0c1a34b540448088e119c233044b089a5a9d19b248f4920924525d234b28ea8880a2ea51f2d4c1a24fa5000849169231246a4bb4982930926224d24914940928225230d009040b4796a22cf251e9112145b054,
0x6aa8284045a08b0115a1a0045208a90d2a335495292a9256a4af4afc49a8935926c048c760813f028004fe09f413e027a47864f900042336496292d525b12b4256e882495c24a649703550ec192833b0e7618ec29d84048e09201428d04050c0a1c95fa2d9257c4a1110322d803a,
0x135826204ce098435116bc4c4409a8350236100a,
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,
0x110c221047208801104b52866b0cea1a3034586762d0e8954b431459290a5168222047008e21118b4b25da4bb215e02bb8573480656412dc945c2908520ca411481444211a4235066c4d541a1834696a80890111c233846608961134b53a336491e9241248a4ba469651d5110145d4a3e5a98344967800108cd5245a48c491a940928225230d009040b4796a22cf251e9112145b04f,
0x8469aac42d9b7800109225245a48c49729305261248e498a92f0212a34949a6108823e047b084810a0484042908549abca24228f288e52491141444020,
0x22216982d325a683428445088c9778a2e14780886110823904400882977421d9459290a5205110846908d411ac5c3846c08da51f1160947b28f48890a2d145b022,
0x63d0c8c190031f808205560abd1a01643449899540fa01f303c8078d2f202ae2454880932ca691015,
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,
0x27884f009e813c827714fe4b3853dd25ca5004d2a989528325da4d2c9a5130f261409d613a827784ed09d8013000414f9446453e128394fd01e,
0x7599f241d6a7c88f918eb43e4a00207550eac1d563ab4f8d1f1b1d5c3abc7588eb21d607c74f901f1f3e3c7c70f8c9f2101a,
0xece21b0435c7678ddd3e868730fa31f4447267d14f9ea5104cc2960d35a8eb71d6c3ae0f939f283e4c3ae4f958eba3e527ca87658eca1d9a3b3072e002b00107cfcfa09f403d667cf875e0ebb1d7c3af4f969f2e3e607cbcf961f42031,
0x1f5837cc6fa1f184b063a6d22d9f033c8637c86f88df848de80f400424e34d40961d34fa6a13c8e790901f22f0018
]

def policySharedUnitFixed1HintLeaf77 : PackedNatTable.Table Nat := .leaf #[
0xdfc1bf638086fe9e4b45e479540040dfa1c0891c06ff0dff200238007009e4d462a7930f291e4a015,
0x4bfe98492e525ea0198035532e813a021004180b5813b027846240042336490c923d24824914926270921d99da22f087e08a2a33301c,
0x9a400a6097746e445408a7914e22a645488a8914d43e004c407f00ff228003f007e913c43de44f48b701054d249ae430da40b2c36276c84d10990c24584d1921a02023,
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,
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,
0x104b4c32413827804f409e413b8a7f259c41f838c084910911c5479ed1911e841ba237406e70dcc1b8a00c820b1e1b3c388e44825104d20981b4836a041d0836105ca1f234846c683e518f20f8029,
0x29b212e825da017299c131425ea01600109a55312a694469c535ca6c14d5010,
0x37107c38f864d7c3e21009a014007,
0x11f021106dc3aa8922525424ab491c10e0818247e0dfc1bfc37e870448281130b15a48f492092540ac19904934925924c24b149bc93d042419a3496a92d926fa4f349ea93d927ba4b249c293f04c125fa492e926524da49c4924927525ca51e46968d2928296fa08f610906901dc249169231246a4c605f84cfcf62a4bd4b64966d28625624ac82860e40839227940021252a4a7495292a92560390044a0e60113038f4d764f111099268468693b1276a50b4a1a94392b1a5654b349321264a4c7499e92f9265a5b34994933925d248a47da754ca492228073,
0x46108c52118231856fa1d716308e0d28ba5104a8094f8d73a32031ac232846588bd15bc99385a48b5316a42c58d91a2be36b86b9914698db01e,
0xb4b4c6a22f858ba383169a2d305a50ad44d826d7515e9b5e00d,
0x264214d0299c5380a6c14d629b52249a80455469fc52c0a5a14b2295cd3622a734da29d853a8a7414f229e00119a9514ac31a46448c6b18d4322853d0022396e7248e5b1c9135248de853890de21ba29c851d0a38146628bc0141a5446ee6a292d29a89035,
0xcce999e05c40b5498f02d405a60b5816c1b80441c6670905930805ae4c189839305012,
0x75c0eb122303a80a5d32512ca43fe48700ec0b6303b20a690ee829d05364b384b080e501c8038407000dc391e026c04e809c0132026004b23a34c64662ccc519893310661ccc31985441e884110882e0263843a0875a1e921d8920d28e2534466244790f6997c490824f121c01c24af4316062d0c5918a23140627245e3d94926526c24da42e69341268a4de49b2936d2a4891436f292ed262254a4aa2954d2aa2555433a216cf69a4c14984931525e251049a694312b2200c498c0bf099f80084b349321264a4c7499e92f9265a5b349949339285a50d4a1c943d2b2a4d24ac095852ab255249be71c4e3a22cc38f84b35160121d083,
0x1b3c36746cc83b107600f841d703af2b148cd89f2a21627cc77846ce21bb00109665251a5b0496292d525b24a64a32946928da4f4128098300de1206219886e8ef1a2ea024,
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
]

def policySharedUnitFixed1HintLeaf78 : PackedNatTable.Table Nat := .leaf #[
0x25d107640ec01f083ae075e562919b24a64a32946928d93e5442c4f991a219904936927124d2496493092c526f24f41090668c00424b5496c937d279a4f549ec93dd25924e149f826092fd26a703e807cc0f201e34d669b1c9152202031,
0x25f803ec48ec4ba9995005,
0xc050eb0008490a03ac07500ed01d844a52cb9128491006e00dd01b9036e02cc06ca330465848090fd120312f803c807a00f301f20410081805a01a2034806700d822308cbc8a223a62266666924ca4c149849669262a4bc497c95e92d8933e033,
0x1de03bc87798ef13ece8c0c7778eed1dd88e68fb58ef54d423ba8fb19f66010,
0x17a22fa45ea0bd317ac915c9c224d449ac936126d24dc49ba85cd26824d149bc936526da54912286de525da4c44a9495452a9a5544aaa280cd19a4c14984931525e250d4a1c28004fe244113ec27dc4fa89f4004828b91ba255e4a1895812b125614aac954927124df37f06fdd1620bd237ea938d29c8bcb179091585e1a5c8176a2eb53530ed71dac3b6476c0a6900720020fa923023ea29b2c76a10d621aa3b5451e0a3b147228c8d2a23773e9a9698fa6238737bc8e212bb9bf6064,
0x15e02bba6010ae015f51ab85760af85661201959000b,
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,
0x112e64dd26fa4ba0bbc901c2ef85e50bc617a530505e711626310af395e64a68172c2e505c70b8c2260457089a1132630045598bd4a7882c8004089c315694ecc5518c13152573112018a8028,
0x26aa0d0c1a350882491493c940cb5306892cf09408218843008e610d0219007300ea1bec37e07070df21be8b9b07160de61c6038b86f20de25c4912e97134a4e5c6912d971b28a08894a27a5044a461a0120806770cf0347833c868e0d3c98f01b39df849dc0e801cf83e207440e84028805004e84f7110b93db07d409e91e193e4494c92e095a26994cac0dc41b8038606e60dc8025837606ee0de09dca33549169231246a4e9497493a9275a3e027464e8910913a14be0599519b03af075c0f841d803b24ba2227920d86df0dbc01a8376089d1140226d367a67741b8923d2482492493a92e43b6876c0eea1db83bb236a2f068994bc125360ffe1ff8406080a1016223444b088e111e9b386e78e311c6414d829a955149fa0ff8a15853a2aa014d0aa7856f07fa103020003ff006000bc204942c4430563927f154c3d0c7a14c4ea2863138609913b981d450e62b0c5699904936927124d24964930937927a08483346937d279a4f549ec93dd25924e149f826092fd234427cc88589f2a4b1496a92d81c78226073008941c813ca494a929d254a4aa49580e48e40a4ca499c93b5285a56314307b1499f80084b349321264a4c7499e92f9265a5b3497a96c92cda50d4a1c94312b125644aca93b11a1926844264f1029c154d087698004cd86180c2e1850309a6ba2c28891ccdb96a945bc5a20b4796a210d,
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,
0x14cc841d26fa5234a522038406881510222040c15a278305496d12ea0d451a88211802c8008101e616d2d21a7d018,
0x39700460e561cb133aa69d06b20d4401c03923902932926724ed4a16958c50c1ec5267e966926424c9498e933d25f24cb4b6692f52d9259b4a1a943928625624ac895943a0049d0950129c25184a4123812943a09753452252e4a5ea22c2ea41a69368866c08d41c2c38a107e202034c50a397342e4e59e41ab803706b62d844f989f113e40d901b2939734368a80dbb974b0e6e1cd801d87910f34836d29687a20f421ec43d207a3006c1e943d307a82f98002119b2486027805400a78106228a87d88bc248f4920924528ca51a4a5e9068bdd97ba44da5ee4bd92365076,
0x25f02cca9a6532b038f044c0e60112839027949295253a4a9495492b01c91c8149949339276a50b4ac62860f62933f4b349321264a4c7499e92f9265a5b3497a96c92cda50d4a1c94312b125644aca93b11a1926844264f1029c05370adc15782ae80290abe15802b0958a4a32946928da4012aea55d111b954d07d498f01b39df849dc0e801cf83e207440e84028805004e84f7110b93db1336186030b86140c269ae8b0a2247336e09e91e193e400108cd9258a4b5496c929925c12b4065,
0x3cc07c81040206016806880d2019c036006d233022308cbc8a200f401e425f08a18008490a03ac07500ed01d844a52cb9128491006e00dd01b9036e02cd31801bc037607140e201c3052c25c1364998f259248290fd9206465848090fd1203037e8ed9304262a240e66691d3113303b,
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,
0x14fe2a0d225268a30de61c8c38987030dc2144428086146e035046a01d7030ec61a113fa28035342a005430a7d14fc9aa5320075b0ebc1d743ac87282eda8984bb7071d1a7a974909b9d6f13e4686d297253810d675d529b88643d8894b469f09f113e62d841ad803706ae6ddd1501d6e3ada6a611561a99040
]

def policySharedUnitFixed1HintLeaf79 : PackedNatTable.Table Nat := .leaf #[
0x79a41b60d8c1b1036110f40d801af835c47be0d681ac139545064e59296879100761cd839b872e008c1cac39626754d3a9b5c34d0740093a12a025394bd44585d48250a3f20946129048e04a50e825d4d14894b9296c5d2d1b297b2031,
0x105520a819803309cf42cdc842482b210d4218842d085225039e45ccce799729011,
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,
0x82a69022a0453c8a7115322a445448a6a1ef43e004c48b726d5138490ec8c48008466c921809e0150029e0418084013a4c6206f00dd81c50388070c14b09704d92663c964920a43f648180dfa3b64c1098a8903a333228a87d88bc248f4920924524999da036,
0xf301f20410081805a01a2034806700d801b48cc088c232f228803d0079097c2286002124280eb01d403b407611294b2e44a124401b8037406e40db80b34c6006f00dd81c50388070c90521fb240c8cb090121fa240606fd1db01c1038c07240e5262a038e078073a096c3d9a48a52d6120e052c25c0cc792c9240e66691d31133045,
0x8862e146c0070e0e201c3c386a6d920ae843d19aa5220dcc1a3034586762d0e8954b80a10e0e185ca0b9524152e5676fd1c3044408e011c422316964bb497642bc05770ae6900cac825b928b85210a41948229028884234846a0cd89aa8343068d2d501120223846708cc112c22696a7466c923d248249149748d2ca3aa22028ba947cb5306893e96923525da4c149849311269042a08f211e0214042408f611f021106dc3aa80021244a48b491892a1255a4b9491c10e11a525052df488a0a491447444e512021b0435087e10f821b843408e610c0218a6b0289e8894a2814554432514528225230d009040b4796a22cf251e9112145b084,
0x233844708905a580040446088a1a14234947a28b897692ec85780aee15cd20195904a4696e4a2e846608961134b53a336491e9241248a4ba4a3e8d2ca3aa220022,
0x1d7e7ce47610ec13e647ce07601f3c00103b147640ec31d8c3b1c7621f343e6e7cd8f9a9f331d927ce8f9d9f31018,
0x6c90d8c1b2cb7400084cc41b211b116df0d941b1cb70225800d,
0x24714aa09181234a5114a9294c1254f2c00084c4a38191a614a300e,
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,
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,
0x4fe09fa140427f950f4b3c9ad027b04f509f813dc27ca3522a1088cca83950e011,
0x341014302872d6c9295292a526257e0a1412426ae06d00f901f18052283c9ab435183e500a60f981f5027a47864f900042336496292d525b24a649704ad01f803f2468c5084b5e86be0d801afc35e83f42dae967cb6c099b0c30185c30a06134d74585112399b70d201a3c35286a409f013e91a916be44ae5aa895f22d9043,
0xe6e1cce39a1371a17520b23f247e40fcb1f94816d188205a1f003dfc7c10f8140148c2d0049eb91ccc39947358e6c1cbe3980a99a49a0a1c8fd82838508081614251fa85040a0a14cc1fb03f70a0485c927f8413082400b020a8418082e14f91fd9564466c9445289a5154a2c55491a3943b284888d4a8c151e0a407b2924ca4c54978936126d217349a0934526f24d949b6952448a1b79001092ed260a4c2498895292a8a5534aa895550cea4d24ac095852ab255249be9425285a50d4a1c943cf5aa2fd3d7a7ae0f60a2fb06d,
0x10c0239843408707551244a48b491892a1255a4b9491c1b70211047c08f610902140908085210a93711448451e511ca4922282df494151a51450444a10c5372869109c2138026e04d709c8139426a869b2df0266c30c06170c28184d35d1614448e66dd29325242d6e88c4a7794e944605aad37226cd0b001610acda6b1089a5a9d247a490492292e928fa34b083a106d373053a2aa014e029b856e0abc1574014855f0ac01584ac50008466c92c525aa4b6494c946528d251b480255d4aba22372a9a50f91a4144f06b
]

def policySharedUnitFixed1HintLeaf80 : PackedNatTable.Table Nat := .leaf #[
0x42a83090614721d25da4c14984931126824d149a4936526da5d94a4696e529a0a42148e29185200a3f154697bd354264f4ce428e851c0a3334a88ddd1be1a58454a69646258a9f153c2a6cd59a2ae38de4d1c185830c10a421504298a85353c94c8541a44a14fe2a005430a7d14fc9b0c5b01cb518da31b063a8c6f18dc00845171c94459e724d2ae8c7818ee322063d0c79003e31ec63e0c7f3962002119b24b1496a92d926f25194a3495ed2301ca0393e8b40e4f002714609b305f20be317b42f9c3ca003c381070151c48d601ac435846661cf745c87648d4c22ac35326a68d4e986f30d24d20c38186e10a2214042f888c10ca1ec83cd079100765ec8c3c989b30ee61a113fa28008e,
0x9a6839b873646ca1cc0023a6e814cc35146a2084630b69690d3e84a147e4128c252091c094a1d04ba9a291297252d852287fd0ff81f08bf4227534ba1cec39e874c0e921d283a707450e8c9a60baea25e2ebc8da11b3174f02f,
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,
0xa3f147c31a05240a4934fc00212b1256734c28b38d2b8a40155829045211c874976930526124c449a0934526924d949b69765291a5b94a6869651579a58021,
0x72c4cea9a603a107c40f861d0c39f17554b445d503a307450e9c1d283a4874800c20004baf225e2eba1cac023004906ac1ccc39d174f0e721cf11b3174b021,
0x6180c2c42a830906149bac250a3f20946129048e04a50e825d4d14894b9296c29986a28d44108c616d2d21a7d148a1ff43fe07c20e969bb0397804846d05fa113a9a5d268e61c09a4085210a861bcc37085110a0217c44608650f641e683c8803b2f6461e4c4d987730d089fd140186903c,
0x7c40f861d0c39f073d0e769a6839800472e9e8d98baa87424dd299d4396072b008c1cb839b873646ca5d2cbaa25a2019,
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,
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,
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,
0x4cea1cb0395804600920d5839c873c46cc5d2d34c07420f881f0c3a1873e2eaa9688baa26770ec498e51b487460e8a1d383a507490e9898e13458b4916a62d4858b1b23457c6d705a30b1e163a2d205a38b1f36b28af0d948b20196691886570caf195a32b000c8cb048c232a86558fd6195032a4653a15a194c2c4000d1cd34b2473511889cd547082a445480afd15262a4801a9aac456c6aac5898b12162a2c5054a8adc15b46b8d1c01b1e4b506c7457f8afe16022c00d8622b7361697005878b0e00362b35324269c42ae422881a1036207040d400b0acc41c48c710ac25944d502bed2270a8915142d7c5438a884dde2190f62252d1a7c27c44f98b6106b600e01a883523da89321264a4cf49969360193136549b4937d27624e746846ddd1501d6e0efc1e3c3c70328064e0ca90b9a4d049a2937926ca4db4a922450dbc80084976930526124c44a9495452a9a5544aaa867442da4d24ac095852ab255246824d99135979535468afcd521b06363612851f904a30948247025287412ea68a44a5c94b646d05d7912f175d0d4,
0xe371c6c395cf579e8c1cee3f1102b9ed2009,
0x1c9639287260e481c9281387290e471c8c7a70f4e9ea13d407a787298e541caa42ec85e219f1c9c39347288e501c9e7a8cf521ea53d4e7a98f51219e3d547aa4f4f9ea8024,
0x7068e0c002,
0xf181e343c6478b8e5e3f2c8c1535b26df1da23b407e28fcc1f8e3f190ba90591f923f207e58fca0a08141429983f607ee14090b924ff08261048016143b284888d4a8c205b4620816902ca05e40b03b4c20a002d3e928e653701f97031,
0x7fc6810d001a029ab0b5b099b0c30185c30a06134d74585112399b70d201a3c35286a409f013e91a916be44ae5aa835f06c00d7e1af41fa16d74b3e5b6135686a307ca014c1f303ea04f48f0c9f22336496292d525b24a649704ad01f803f2468c5084b5ea5254a4c74cd16b820127a29295254a4aa495892b817e1dc2491a931926424c94994933925d248a1a408fb4212047b08f8108836e1d5400109225245a48c495092ad25ca48e087010d0239843008629b94a27a22528a08d2928296fa44505248ea9a4c7499e932d19e123f06f
]

def policySharedUnitFixed1HintLeaf81 : PackedNatTable.Table Nat := .leaf #[
0x4dea382c00a0e101c1e3844f2e9e5c008,
0xc597de4922966524f0629478a0a4022c863308b418a0b158008491e924124a8158492e926524da49c4924927525ca51e2c58892ca34962d4974946528d07b44ba294c12d711d6026,
0x2d305a50ad416308e0cdae8b4d1696971cda99b5736a42cac5850b2c165c2cbc5969b3745706cd8d9aa2b9457422f90eba51015be232446408c51186634c0042495492e926d24e25154a2c945d28a24d34a7e2305361237131ac8a30d73a5404a7c2a3cdaf22bd037,
0x12fe9b2849e2438038425f9362097d052a3a0136e097802968dc8082a69022a0453c8a7115322a445448a6a1ef43e004c48b71ee9331e4b24ccd999f020,
0x1bd03829b1416d02db05b88f30989131105524b705f20be317b42f9c3ca003c381070151c487c01a6c34d43e085992fc89684bf18d601ac435846661cf745c876483a0049d0950129ca5ea22c2ea42004400080910062008402a63d4d228274f739ee63dca7b902d315ac44708b451b6981f44ec60784b1a64a019825dc0a626fb038c07240e5262a038e078919d123303da079c91624a403ec07d44b201f803ee022004301f924788a5091d92284b5848390b225984b5e928849d8937126c24bcca4a29232b08dc862c1c7c43c829812238a191444288c5078a10347628004fe244113ec27dc4fa8d4b48d227e522009eb13d827bc4f809ed13dc87792b30a2c145600985168a36146a9b0c5b01cb518da31b063a8c6f18dc00845170cb941ca945d28a0cbc14ba297c52f0a4f20786dc527c24fb4ac691210731a73455273892be238c39288b3ce49a55d14cc35146a2084630b69690d3e8a7e14fa2a185400a7f15069129320986f30e061b8428885010be223043288643d8894b469f09f113e62d841ad803706ae6ddd1501d6e0f641e683c8803b2f6461e4c4d987730d089fd1401a9a35328ab0d4c0a450ffa1ff03e1074b0e781ce8399872f00901cd839b872e008a1cb4668264d10e29918193136516b87f10edf2495492e359c6b48e7e1ad435acf7123364afe35d52358b8e171a01f8ed6a5813b3c8bfcecea38f4b0096083b9178543ce95c92bb188239fc8d94ba7a36646d05fa113a9a5d15102a1c5af8a8a15122bed22726470ec4619d25024a110821dd03b987700ede212520c18602f088990c2ba53546d29be82ada1954a26945528b251815e82bd857a8af215dc32e10a12540489a737cd7fa2b536001e883d087b10f481e8c01b07a50f4c1ea10a3012b025405480a88107031a8e9c8ec118f43ee45a128ca51a4a5e9068bdd97ba44da5ee53541b0635488afcd51a37634a231e063b8c8818f431e40100c7d18fc42910c724ea49d61df83c7878e06500c9c195234126cc89acbcaa595490285f4e4fa2d0393c686114f9a1646e895792b11a3445466918d3b0c5218b431646288c50189c9178f65249949b093690b9a4d049a2936526da54912286de525da4c44aa2954d2aa2555433a216cf69a4c14984931525e251049a694312b2200c4a169435287250f49a495812b0a5564aa471c4e3a22cc38ea95e52b2892a05500b3c15692dd441a651806c80d54c9812851f904a30948247025287414ca2996480a20b511fa404880b1015202638fc8172473322a952d2a625504a94953906a20b4463082cc218843008e610d021c1d54491292a1255a4b9491c1b70211047c08f610906901dc249169231246a4c605f84cfc157259a49909325263a4cf497c932d2d9a4ca499c92e924523ed3aa6524911416fa4a0a8d28a282225289e04e41b88370070c0dcc1b9004a06e80dd46cfa5c448d8779c9d122122742266c30c06170c28184d35d059d0b3816b02d585a31a3e25cccc99d522b6688e8ad305a0480c996c4b31dc31b0636086c28d841b1436243218642481c190415602b2479097900f192de03f677251741dc53b8894846c301ef03dc07980f2922b4400771933499832b50585112399b703c82eac0f8262f03fa8cec8eca486491e9241248a5fa1304668d26fa4f349ea93d927ba4b210906640004249b4938926924b2498496292d525b24de49e8938527e2599494696c124f22c324545d4d14894b9296c8cc0cbf233829d,
0xd601ac435846661cf745c89b305f20be317b42f9c3ca003c3810214042f888c10ca1ec83cd079100765ec8c3c989b30ee70151c49d9201d,
0xebc1d743ac87281a7a21c53268cd00e5a0114e7f18823ada5db43ada6980e841f103e187430e7c5d552d117544cea1cb039580460e5c5d2c3a307450e9c1d283a4874c0e7a1ced34d07370e6c8d9439800472e9e8d991b4175e44bc5d74bb72261034,
0xe8c5eb000424df4bb2948d2dca5294cea1cb0395804600920d5839a87342e981ce4ba587420f881f0c3a1873e2eaa9688baa07450e9c1d283a4874c0e7a1cecba7a36646d05d7912f175d028,
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,
0x2bc05770ae6839d245a48c491a9341268a4d849b41104338066f08d251e8a2ca5040fd29080c0425b74b6c96d5201959001a,
0x6760cfa19d033a968644a819f8b5200084b721a291b0168700d,
0x8c61140226162b492a925d24ca49b4938924924ea4b94a3c18a0b16234b28c01190229211000108cd9247a49049229279281845b28d4948ca30a21f020,
0x133f3d8a92f52d9259b4ac42860e4083923da8936126d24df069e4e3119a834a06921e401a4032946824e15136138649cc93b1273a4ed4ac6966817e200c3da6931525e251010b68674dbc80084976930526124c44a94954448a217349a0934526f24d949b695252a9a5544aac95492aaa56149a49581269a50c4ac8931926424c949949339285a50d4a1c943d2b2a4c7499e92f9265a5b3051,
0x2db05b49b144bf897e4d8825f4ccd999f26220b711e6131200d,
0x2606025604a80a90151020e042409ca333231e87dc8b401b8037406e40db80b3465848090fd120301d603a807680ec2252965c894010402060168032806822882501306130e3da07b3cf67130d441c0b8498ea20f1300982c0de01bb038a07100e1920a43f648180dfa3b603829c1406c80d546601f0069b0d350f821664bf225a12fc62004400080910062008402a36d303e89d8c0f1207051,
0x9818095812a02a40544083810902728ccc8c7a1f722d02501306130e3da07b3cf67130d441c0b8498ea20f037806ec0e281c4038648290fd9206020406f40e0a338023
]

def policySharedUnitFixed1HintLeaf82 : PackedNatTable.Table Nat := .leaf #[
0x4df8992414b8299053007580eb81d816c6076414d21dd053a0a6c967249912c2039407200e101c00370e47809b013a027004c8098012c8e8d319198b33146624cc41987330c6615107a21044220b8098e10e821d687a4876248349be94703e00d361a6a1f042cc97e44b425f8c40088001012200c401080546da607d13b181e4a688cc488f21ed32f89211260a4c24b34931525e24be4b6624f121c01c24e0e95e8966a2c0243a487110592ca05c,
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,
0x26544cb09940e021c0120986ff0dfa1c1120a058f0b1266c914b8997205e835929409980b0a01dccdb19b5017,
0x1322877d26fa4ba1a6890102b885840b0434bc2c38d3848ce75a800425da4bb29c08eb38586133266d8eb0959b3ac894d0237846e08d611a8385871420fc404106b89930df21c1c37e0701132826584ca8997205e8358cdaa29733645c6d12d99b14a5034c50a397342e4e51ed11199af03c,
0x32e065b1a2e3458026a66a3a98197432d265c07d2994c8018d091a1020ac416082d211e20b88012654113204e484a0c6518ce3198402236d39188b350b4088f111c2258446880b10729089344184e31388a18c4e85f71010201c2fc15f84b4057dc4b100e601d203a007000e112ca03884b0a5d6128098304c0260b0378481814d01dc03b607600eb81d62446075014ba62f259487fc90e121d43fc4b349871ed03d9e7b38986a20e05c24c7510781bf476c9821315120732f88a5488f112443dc65f5051a3213086610916da0a607e20fcd33386d00d9e1b5836886d346c65bb112c96eb0db01b5c36d06d90838106933585380a6e15b82af055d0052157c2b005614d8c24c049b8936125e6525149194a037607140e201c3052c25c1364998f259248290fda4012aea55d111b954d080640e523f850c401639b47350e691ccc3994731a3963d708bf0f60250a46a814f10ca2495492e945d28a218f0d068fbc224807200e81bec37e07070df21be8eb325271160179803818c44a76229c45308aa115222a0036043331728a20c5c0d304e16162c2c524050b109c2837f103048fc10e0eaa2489495092ad25ca48e0db8108823e047b08483480ee1248b4918923525d248a47da754ca4922282df494151a5089c1136228044e86ec00d41b7836f889e41a696612d7a5314a9295352a79012416698f88130e381c7c38e871c8e3c48e47a38f46a2f841902450dbca4bb498895452a9a5544aaa867442d9ed349829309262a4bc4a20934d28625644018931817e133f4d64266c30c06170c28184c30da40b4cba035532604a147e452d8b0d9614448e66dd2cd24c84992931d267a4be499696cd26524ce4a169435287256549a495812b09014202c40548098e3f205c91cd06a20b4463082d531188fd322a952d2a625504a94953920d98ad31588a1cc5590b70e80127425404a70946129048e04a50e825d4d14894b9297a88b0ba90d601ac435846661cf745c876485f20be317b42f9c3ca003c3810214042f888c10ca2190f62252d1a7c27c44f98b6106b600dc1ab9b77454075b83d9079a0f2200ecbd91879313661dce02a38914cc35146a2084630b69690d3e8a450ffa1ff03e1074b0e781ce8399872f00909bf83d107a10f621e903d180360f4a1e983d42146025604a80a90151020e06351d391d8231e87dc8b425194a3494bd20d17bb2f7489b4bdc876230ce928125088410ee81dcc3b8076f10929060c30178444c8615d29aa3692e9e8d991b417e844ea6974b8d225b2e365a5128fa51220fa38947178e260aa041f11ffa1403cea8bd90a0a35546905bcd2ce96f24d22174d2f005e40bc401c532b85960b309a9c0fa01f303c89c240fd81f603ea25900fc01f7011002180fc81fd467648f114a123b23b29219247a4904922927822d845d08b811641480629478a58b4a34a21b28d40a39339855b432a9665251a5b04a1e944d28aa5164a3048a910123592b46579d1ada66e468c5084b34166a4cac0dc41b8038606e60dc8025037406ea367d2e209823346937d279a4f549ec93dd25908483320002124da49c4934925924c24b1496a92d926f24f449c293f12361de7274488489d0966926a,
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,
0x45d08b81164148146908b6980814884580b86117822fa68c4d22266c30c06170c28184d35d1614448e66dca37223d28d08cfc4b100e601d203a007000e112ca03884b0a66832f88a5488f112443dc65f4a35221b02d,
0x130800cd00ca0348068a32f006,
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,
0x8a18008490a04153481150229e45388a9915222a245350f7a1f0026245b9244097c01e403d007980f94b768e98899999a01a,
0xd1f00084976930526124c410b69349285a50d4a1c428522109fd21be91044fc26f243b885e92b1a55f016,
0x7624cee9bfc399a369005,
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,
0x1da89a9876b8ed61db23b60534803900107d491811f514d96435886a8ed514787d352d31f4c014,
0x28c451b0a3546ec28c85180027007,
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
]

def policySharedUnitFixed1HintLeaf83 : PackedNatTable.Table Nat := .leaf #[
0xb1e168c9a2c5a48b5316a42c58d91a2be36b82c811c2263815222a4057e8a93152400d4d5622b635562c4c5890b1516282a5456e0ada35c68e00d8f25a8363a2bfc57f0b0116006c3115b9b0b4b802c3c587001b36362c745a40b47163e32cd2310cae195e32b46560019196091846550cab1fac32a06548ca742b43298588001a159a992134e21570010422881a1036207040d400b0acc41c48c710ac25944d502bed2271b0639a69648e6a231139aa6d6515e1b29061,
0x269e19d8748119aa50b4a1a9438e8a0cef3a3e002119b25134a2a94592bc1d1e011,
0x30c46240c4918863fb507a025747804a5d2718c2b185430b46161c4f38a07148e289c4e41148b2ce350c32208e30cc61a20f200109869258266418949170e370e5a48ca7ac4823025d04b8096894da20741e6715d18e9c5602f,
0x112e986482704f009e813c827714fe4b3883f0825904a209a413036906d4083a106c20b943e46908d8d07ca31e41f038c084910911c5479ed1911e840bbc901c2ef85e50bc617a530505e711626310af395e61ba237406e70dcc1b8a00c820b1e1b3c388e442e585ca0b8e171844c08ae11342264c6008ab1136228044e86f10de41c5c38c06f30e2c4304808a1a72e268974b8918ac450e62f529e20b2001094ecc5518c13152573112018a805c,
0x8e0111022184422cf459ecb4096822d069c04a3c145a28b611c422316974972940d2ed25d90af015dc2b9a4032b20948d2dc945c2908520ca411481444211a4a3d2224024,
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,
0x19b0b4d969f2d405a8434406714442894023527012d065a08b40a2242cf651e0b3d1679013,
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,
0x45d08b81164148146908b6980014884580b86117822f96a7089a9ac51a5a336491e9241248a4ba4a3e51b911e9468467e10eca35221b01d,
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,
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,
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,
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,
0x1386877e0f1e1e38194032706548d049b3226b2f2a3148e3a8c5818b431646288c50189c9178f65249949b093690b9a4d049a2937926ca4db4a922450dbca4bb498895292a8a5534aa895550ce885b3da6930526124c549789441269a50c4ac8803126302fc267e9ac82e9a5e00bc81788038a6570b2c16611ac95a32bce8d6c4cd86180c2e1850309861b481699748ec8008490c923d24824914b32928d2d8249e01aa9930250a3f20946129048e04a50e825d4d14894b9296c586cb0a2247336e966926424c9498e933d25f24cb4b669329267250b4a1a9439287a56549a495812b0a5564aa4937ce389c74459871f13922723082,
0x265103f607f519da659202882d447e9012202c40548098e3f205c91ccc8aa54b4a9895412a5254e41a882d118c20b313261be438386fc2e36896ccd88431086011cc21a1450444a513c224044708ce1198225870448281bf437f86fe206091f821c1d54491292a1255a4b9491c1b70211047c08f610906901dc249169231246a4c605f84cfc15725e44b349321264a4c7499e92f9265a5b34994933925d248a47da754ca4922282df494151a5070048261c044ca0996132a265c817a0d61138226c450089d0dd801a836f06df113c9acd20d98ad31588a1cc55a5281330161403ba605336c66d514b99b228ea8880a2ea72506e20dc01c3037306e401281ba03751b3e97104c119a349be93cd27aa4f649ee92c8424199002b0989cef324b81ace35a473f0d6a1ad67b8919b25194a3495fc6baa46b171c2e3403f01e33b5a9604ecf22ff3b3a8e3d2c025821b3836786ce8d9907620eccf09a485027247652432491493c923d2482492493a92991a21de145d4778c2ada19500109665251a5b04a1e944d28aa5164a30926d24e249a492c9261258a4b5496c937927a24e149f891b0ef393a244244e840f20bab03e09a9d31e899b0c30185c30a06134d74585112399b74d228274f739ee63dca7b902d315ac44708b442ce8cc3198416ac2d18d1f12e6664cea915b345a456982cd859e4cb68d69161922a10d,
0x6c20d8a1b12190c321240e0c820ab015923c84bc8078c96f1dc945d036146c10d833b8600204b32669330694846c301ef03dc07980f2922b44007718ee21dc5022
]

def policySharedUnitFixed1HintLeaf84 : PackedNatTable.Table Nat := .leaf #[
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,
0x36806cf0dac1b44369a3632dd88964e9fa6654cc8940128326614cc6998836c06d70db41b6420e041a4cd614f1336069d0d36135427284e409ae19c90a1a4b94a0e9a442e9a5e00bc81788038a6572bce8d6d291a5b90d201a3c35286a409f013e91a916be44ae5aa929284da46a05a10a77a2312d6e9c951aaa3482de69674b79266e4c12342c6850d131a1c343003680083a828b70ea00d140d801afc35e83f42dae967cea516eb05a,
0x442148c112022324ce88d0681a1b9072008941cc0226044e7e550e50008494a92b925aa4b649e692c9289a5154a2c4204326a35f4292958d28c0fff1b3c36746cc83b107668d10ef0a2ea413e92a525524a64b3492f92d9a4ad495e49a510992684686195c32a06530c9e192c32a965c20fe42012faa148449a8938b2d16502cb25960b2b96512caa5958b331d3704c,
0x21c1d54491292a1255a4b9491c1b70211047c08f610906901dc249169231246a4c605f84cfd2cd24c84992931d267a4be499696cd26524ce497492291f69d53292488a0b7d2505086601b045408a911542298453a654200420c8418882d105820acc2488292006859400424a54a4a9499053227d3084610d13e20a331708a20c5ca34a046,
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,
0x2b6856e26780fa890743e587cc20ee1f34834a6824d009a19090a31f2fe05fd11c00ad015aa2b2800c0ac7159099e53428acb207a1f903f187e00fbe1f7520fa6812ff85ffd13920e9107a20f041f883e101e0164c29a27e30a41d083e207c30e861cf8baaa5a22ea899d4396072b008c01241ab07390e789a110b9a4d049a2936526da54912286de400424bb49829309262254a4aa2954d2aa2555433a93492b025614aac95483b1a0dc491e9241249249d496292d525b24b949bc94d91b4a3662e966b811bf9ae306b,
0x78f0f1c0ca0193832a42e693792a4891436f295292a8a5534aa895550cea5604ac295592a9234126cc1df90dfa4bb4982930926224d049a2934926ca4db49cc94b073c25c51cf239f10e18008496292d525b24ed4a5694c927a25454a8c95212a125443dbe7b54bcaa26b039,
0x15b42b7133c07d4483a1f2c3e610770f9a41a534126804d0c848518f97f02fe88e005680ad5159400605638ac84cf29a14565903d0fc81f8c3f007df0fba907d39707660ef41de43b2977a44cc5dec73e87281a7a21c46a30cd7436e21b8431886210e621bc3d387a40f621e843d1217419a8334039680450e5c1cdc39b00480e5e1ccc39d073c46cc5d3d1b29cfe2f7289b4bdd1881450461e129b9d74310475b4f7017fc2ffe89c9074883d107820fc41f080f00b20020c29a27e30a41d083e207c30e861cf8baaa5a22ea86b811bf9ae3070,
0x1859d961ac6359109a077e0f1e1e38194032706548d049b3226b2f2a322d3691d940618214883c0d5d1abc859c00424b1496a92d9276a5234a5220384068815102220404092421305689e0c1525b44ba893d12a2a5464a9095092a20a661a8a3510423185b4b4869f45f10bdc17bc2f745ec8be70f2800f0e04245837f87010ec82131426089fc6af88504bbe011c39807320e761cf51b3174f3b228b94c349348056,
0xe5c0118395872c4cea9cbc6698cd619aa33444420883484c22084400887484e73fd16a1d002e961cdc39b00480e5e1ccc39d073c4e601d88c33a4a049422104c2ba53546d22d74db907720ee81dcc3b8076f2f088990bc2a17349a0934526f24d949b6952448a1b794976930526124c44a9495452a9a5544aaa867526925604ac295592a908d63348950c48089031204237046d88de485c73a527024ec49f093ed2a0a5454a8c951cc7718ed451c64584c119a3001092d525b24df49e693d527b24f749641dd83b707750ed81db5396978244ca5e0d1b524e149f88d98ba7a365078,
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,
0x13922732002,
0x668c00424b5496c937d279a4f549ec93dd25924e149f826092fd273200f,
0xb28165d399a359004,
0x13902735002,
0xcc800084936927124d2496493092c525aa4b649bc93d0424273400e
]

def policySharedUnitFixed1HintLeaf85 : PackedNatTable.Table Nat := .leaf #[
0xac2737002,
0x7c01a6c34d43e085994e665f912d097e3009,
0x18f432306400c7e02040fd01fc4e648cecb21a24c00b,
0x1e970010925539c24974932926d24e254b4a9895352a7a56b00d,
0x1ef43de07bf0f7c17bc04180084e665f8113717df00b,
0x3b6876c0eea1db83bb273446d45e0d132978200a,
0x42949ced28aa5164a2e94512a5a54c4aa095392b1256a00c,
0xdb88008498c93d527b24f849f6944d28aa5164ac694605ada73e00e,
0x5ae273f002,
0x5a70b3c16762ce85a7a73b16a06d94db31b4736946d24da41b6400e,
0x14b8296c5298a504e7c8de0d34a2a8008,
0x1fc40010926d24e24964930931d27aa4f649ee93f12b0a74000d,
0x1192232046288c331a6925524ba49b4938945528b25174a28934d29f88c131a4002139c249949a48dc4c6b228c018,
0x29513a11a6a003,
0x231d3a218d7003,
0x2b7d3a21ae7003
]

def policySharedUnitFixed1HintLeaf86 : PackedNatTable.Table Nat := .leaf #[
0x7c00f7c1ee8b594e7e8e14a09a215008,
0xf793a41414003,
0x2d793a41b73003,
0x6d88db31b6436c06df9b7d0010931d271a4f549ec93dd27e254b4a9895352a7a740472078091759e03016,
0x7a70f4d1ea43d3c7a827431ea27f08fe19fc13f8e7f18fe29fc000e,
0x3d787b68f611ec000087b10f631ec87fa400423364a3294692a5a54c4aa095a93a08f691ed03db07b58f6a3fc27f88ff31fe43fc67f94ff41fe73fc03d987b38f653fb27f74fed9fda3fb87f7cfef1fd83fae7fb0ff59fea02f,
0x3f607eb8fe61fb43f6400a8fdb1fb83f7503f8008466c92c52788dac1a9c354c6a80d5142d49cdd24aa4974932926d24e24b5496c93cd27924b2471c75f11719dfb4a3294692c8a47c40dc81b5189206c02b,
0x3d7d3a69fd6003,
0x3e793a6a028003,
0xf081e0e3c587850f0900123c2c7860f0d3f20002119b25134a2a945928ca51a4ac69d152c524753efe7df91821f7d019,
0x1f403e607900f1807e171a2e386baa46b3dc4002119b25194a3435ac6bc8d781ad2359cedf2743492a925d24da49c4ac096012c1238f3b3a8b9cecf257f4b0276b49152202025,
0x978c4b919920c7c9ce8b212752007,
0x5a0480c996d3a995a8005,
0x2d18d1f12e69d4ccc99d52006,
0xf7205a64eaa56b111c22d1006,
0x104ea756002
]

def policySharedUnitFixed1HintLeaf87 : PackedNatTable.Table Nat := .leaf #[
0xb3a16702d605ab4eaa56cd11d15a6008,
0x3dce7b98f72a756004,
0x266c30c06170c28184d35d27584ea8585112399b700b,
0x98153ad27574ea89d653ac2691007,
0xbfc97853ac27544eae9d653ad1605008,
0x3ba75b002,
0x3c275b002,
0x1366a75e002,
0x133016153ae99b6004,
0xb0616053af159b004,
0x2db86320bfa9d7112515be006,
0x2ba2761002,
0x5ba0bf817ec2dc05b64ec456fd12215c0009,
0x2312002119b2486027805400a78106021004e9318a333228a87d88bc248f49209245249a7110208040c02d270f01b003691981118228806e00dd01b9036e02cd196120243f4480c07580ea01da03b131811294b2e44a014b8299053007580eb81d816c6076414d270e261a8838170931d441e9d653ac27544eae06f00dd81c50388070c90521fb240c9ccc0dfa3b6038207180e481ca4c54071c0f00e7412d87b34914a5ac241c0a584b8198f2592481c966a2c0243a487110592ca064,
0x7b1415802aa010e02240fb81f812c807d5364a7524eca8a5091e2340497a96c92cda50d4a1c94312b12564017,
0x50c2766002
]

def policySharedUnitFixed1HintLeaf88 : PackedNatTable.Table Nat := .leaf #[
0x1c91c8100109321264a4ca499c93b5285a50d4a1c958d3b3a56500e,
0x43a9f940010937126ea4d749aa942d286a50e4a74958d3b3a56500e,
0x1d1200109321264a4cf49969da127625534aa895592a9256b00d,
0x1442288050e8a1a4ecc8dd4d20a2a2008,
0x674a76a002,
0x29553b59a6b003,
0x44c0e60112839027940021252a4a7495292a925624c84992933d265a76849d88d0c9342213014,
0x89d3b71269003,
0xe3d3b713c4003,
0x7390ce51ce23398673a76a19d07440e889d0f3d907b1cf459ec900e,
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,
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,
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,
0x110c221047208801104b52866b4e045164a42945a088811c023884462d2e1188229046408c61140226162b491e924124aa4974932926d24e2492493a9478314162c4696518110f94614a06116ca3525da4bb215e02bb85754ec6563d20195904b725170a42148329045205110846908d419b135506860d1a9c0d39c045d08b811641480292467e51a510d96a60d127d29246a4bb4982930926224d24914108ca222502086210c023984340870755000424894916923125424ab4972923836e042208f811ec2120428121010a421527740dcc1a3034586762d0e8954b809448451e511ca4922282df494151a51450444a513d28225230d009040b4796a22cf251e9112145b08b,
0x430085f90bd0400868485f21a6040207fc6810d001a029ab13b79d3345ae48fd19e02280454355c6ab022b045808b41420d55048c760813f028004fe09f413e027a47864f900042336496292d525b12b4256e882495c24a649703550ec192833b0e7618ec2926c24d67628ec49d883b08091c12402851a080a1814392bf45b24af8942220645b049a90d1232704b,
0x5b60b70188c2dc85ba2d6c0021252a7544eb09d68348068f0d4a1a9027c04fa46a45af912b96aa4e721af836006bf0d7a0fd0b6ba59f2db09ab435183e500a60f981f503f007e48d18a1096bd4a4a9c9539e25262b808924adfa762031
]

def policySharedUnitFixed1HintLeaf89 : PackedNatTable.Table Nat := .leaf #[
0x7d20fa31f543e987d28fa748f480c9187a7731e3a3c707b78f1f1e3c004c0009f9d46107e713120fad1f743ee40038f231e4a8e71026203101e,
0x16144cc20d6205e265c4ca899613281c0437e07070df2264d06b99b144b65c6ccd92297336a94a0cdb275d017,
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,
0x2e0213e1198233530b05d446b6177920385df0bca178c2f4a60a0bce22c4c6205ea4810164403d007d2bce579844b85cb0b94171cae622403150116ca351002106420c4416882c1056612441490034c2e9d7d3bb827a47864f9119b24b825689dd834884e109c0137026b84e409ca135434d96f80d3c1a3833e067b0cf019dd3ba968844a45aa53aa27584eb49d9139ca7254e78949929216b7446253bca74a2302d56829913e9842308689f105198de447c24242e30898115c226844c98c0115662f529e08ad317e82c929d88a7114c22a845488a800d61128c5ca288317062a8c6098a9323e8a402df88cf4856647519aa48d085411e423c0428084811ec23e04220db87551244a48b491892a1255a48e087040c123f06fe0dfe1bf43822414089858ad39c24994a3c8d2c38024130e0226504cb0995132e40bd06b089c1136228044e86ec00d41b7836f889e483662b4c562287315694a0cdaa29733648d2928296fa44505248a23a227289018a022e845c08b20a40314a3c52c5a51a510d962c11ac86a525124ed16ba6dc92a425424a88950c48089031204237046d88de485c63ed25fa4ec49f6950447498fe49300a0c9632495492e924924ea4b449720a38bef248f492092452cca5b0493c92e83da18af001096612d7a4c6079c87687ab8f4b1e9091e0798a77a075e0eb81f083b007640f111a213e6442c4f947508ea443b292c525aa4b6494c938d35da7604e6a9cc93b0a7704e6c93d12a5a54c4a9e9d2d2c4a398473e926d24e2496498e9d2927ca5614e98963127c24fa4e92946528d25314a6092cd27aa4f649ee93f126025454a8c951cc7718ed451c6458c6f95c4146,
0x4c2c17511ad88cd119884f911f0909323e8a40c6f05de480e177c2f285e30bd298282f388b1318817a9204059100f401f539a95e72bcc225c2e585ca0b8e171844c08ae11342264c6008ab317a94f045698bf41642270c55a53b114e229845508a9115001ac225044c2c560021247a490492a9ce124ba49949369271249249d49729478314162c469662e514418b831546304c5495cc448062a022d845d08b811641480292467e51a510d946a05c,
0x2e14221844408e011c4223169708c41148232046308a0518110f94614a06116ca3525da4bb215e02bb85734ec2900cac8145c2908520ca411481444211a4a3d222428b6360038707100e1e1c3536c9057421e8cd5245a48c491a10d821a843f087c10dc818247e0dfc1bfc37e870448281130b158008491e924124aa738492e926524da49c4924927525ca51e0c50117422e045905200a4919f9469443658b11a587004826515510c94514a089489291a5b9421c1c3038521110e101c24b9b25270df4423884686fc2e36857112d171a2e4c5c9cb94172a482a5cacedfa386077,
0x110c2210472088011053499459290a5168222047008e21118b4b846208a411902318450089858ad247a490492a925d24ca49b4938924924ea51e0c5058b11a59460443e518525ca50308b651a92ed25d90af015dc2b9a761480656412dc945c2908520ca411481444211a4235066c4d541a18346a7034e70117422e045905200a4919f946944365a98344967800108cd5245a48c491a940928225230d009040b4796a22cf251e9112145b05b,
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,
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,
0x20dc491e9241249249d496292d525b24b94f009cf526f253600d,
0x1d8d3c0a369003,
0x99dd3c0a768003,
0x1ab2782002,
0x45d08b8116414802924f008cfca34a21b009,
0x18a13c2962c003,
0x44c2c560021247a490492a9ce124ba49949369271249249d497294793c3234b011
]

def policySharedUnitFixed1HintLeaf90 : PackedNatTable.Table Nat := .leaf #[
0x2252787002,
0x481890211b8236c46f242e31f692fd27624f849f6950447498fe492c926014192c60010923d2482495492e926d24e2492493a92d125ca780496693d527b24f749f893012a2a5464a8e63b8c76a28e02a,
0x17a9204059100f401f53c42735007,
0x114c22a845488a800d69e20c5ca288008,
0x229d3c598b8003,
0x22b53c598bf003,
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,
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,
0x1d903b007c20eb81d7a78f27ca88589f3234400a,
0x223d35da7604e6a9cc93b0a7704e6c0f113c8189d00b,
0x41ca4221016223444b088e4f228a18c4e184e00a,
0x4470896111a202c405080c0ffc1ffd367a78c4f1a9e283a107c40f861d0c39f17554b445d513c1a6750e581cac02300494f081ce439e23662e9620f441e083f107c203c02c800830a689f8c29089b11402274376006a0dbc1b7c44f25d14f209cdd20d98ad31588a1cc0ea277304c6271143279103e,
0x14cc211042388464f26616d2d19a7d008,
0x203840688151022204040924214f2660ad13c182a00b,
0x5f3879400781cd839b87310e761cf53c9a3662e9e9e091b29c0800e,
0x21413378bda4f2c9e513c92795007
]

def policySharedUnitFixed1HintLeaf91 : PackedNatTable.Table Nat := .leaf #[
0x357d3cb9d91003,
0xc8b420e002126fa5234a529e553c925b44ba89e505f10bdc17bc2f745eca7974f2c9160dfe1c04015,
0x6180c2cecb0d631ac884c89c6233549a0934526c834a06921e401a403294d089e093c9279346824e15136138649cc939ceca134810a441e06ae8d5e3b2e002119b24b1496a92d939ea4de4f327641098a13044fe9e611729869030
]

def policySharedUnitFixed1HintTable : PackedNatTable.Table Nat :=
(.branch 0x2e0
  ((.branch 0x170
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed1HintLeaf0)
  (policySharedUnitFixed1HintLeaf1)))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf2)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf3)
  (policySharedUnitFixed1HintLeaf4)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf5)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf6)
  (policySharedUnitFixed1HintLeaf7)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf8)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf9)
  (policySharedUnitFixed1HintLeaf10)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf11)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf12)
  (policySharedUnitFixed1HintLeaf13)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf14)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf15)
  (policySharedUnitFixed1HintLeaf16)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf17)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf18)
  (policySharedUnitFixed1HintLeaf19)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf20)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf21)
  (policySharedUnitFixed1HintLeaf22)))))))))))
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed1HintLeaf23)
  (policySharedUnitFixed1HintLeaf24)))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf25)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf26)
  (policySharedUnitFixed1HintLeaf27)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf28)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf29)
  (policySharedUnitFixed1HintLeaf30)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf31)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf32)
  (policySharedUnitFixed1HintLeaf33)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf34)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf35)
  (policySharedUnitFixed1HintLeaf36)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf37)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf38)
  (policySharedUnitFixed1HintLeaf39)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf40)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf41)
  (policySharedUnitFixed1HintLeaf42)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf43)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf44)
  (policySharedUnitFixed1HintLeaf45)))))))))))))
  ((.branch 0x170
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed1HintLeaf46)
  (policySharedUnitFixed1HintLeaf47)))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf48)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf49)
  (policySharedUnitFixed1HintLeaf50)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf51)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf52)
  (policySharedUnitFixed1HintLeaf53)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf54)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf55)
  (policySharedUnitFixed1HintLeaf56)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf57)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf58)
  (policySharedUnitFixed1HintLeaf59)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf60)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf61)
  (policySharedUnitFixed1HintLeaf62)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf63)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf64)
  (policySharedUnitFixed1HintLeaf65)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf66)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf67)
  (policySharedUnitFixed1HintLeaf68)))))))))))
  ((.branch 0xb0
  ((.branch 80
  ((.branch 32
  ((.branch 16
  (policySharedUnitFixed1HintLeaf69)
  (policySharedUnitFixed1HintLeaf70)))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf71)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf72)
  (policySharedUnitFixed1HintLeaf73)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf74)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf75)
  (policySharedUnitFixed1HintLeaf76)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf77)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf78)
  (policySharedUnitFixed1HintLeaf79)))))))))
  ((.branch 96
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf80)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf81)
  (policySharedUnitFixed1HintLeaf82)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf83)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf84)
  (policySharedUnitFixed1HintLeaf85)))))))
  ((.branch 48
  ((.branch 16
  (policySharedUnitFixed1HintLeaf86)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf87)
  (policySharedUnitFixed1HintLeaf88)))))
  ((.branch 16
  (policySharedUnitFixed1HintLeaf89)
  ((.branch 16
  (policySharedUnitFixed1HintLeaf90)
  (policySharedUnitFixed1HintLeaf91))))))))))))))

def policySharedUnitFixed1Hints (i : Nat) : List Nat :=
  policyFixedHintDecode (policySharedUnitFixed1HintTable.get 0 (i - 0x21e8))

def policySharedUnitFixed1_root_empty : policySharedUnitFixed1Db 0x279a = [] := by
  decide +kernel

end Bounty

end PolicySubmissionPart56

/- Component PolicyBitsetBatch; SHA256 d823e5d2e4dd6ccfe7af5540e6aef9bbc36157ff744622d7cdcb2b838678d93f. -/
section PolicySubmissionPart57
/- Bounded finite batches of the proved Boolean propagation checker. -/
namespace Bounty

def policyBitActionIntervalGood (db : Nat → List Int) (hints : Nat → List Nat)
    (lo hi : Nat) : Bool :=
  (List.range' lo (hi - lo)).all (fun i => policyBitActionGood db i (hints i))

def policyBitActionIntervalGood_sound db hints lo hi
    (h : policyBitActionIntervalGood db hints lo hi = true) :
    ∀ i, lo ≤ i → i < hi → policyBitActionGood db i (hints i) = true := by
  simp only [policyBitActionIntervalGood, List.all_eq_true] at h
  intro i hli hih
  apply h i
  rw [List.mem_range']
  exact ⟨i - lo, by omega, by omega⟩

end Bounty

end PolicySubmissionPart57

/- Component PolicySharedUnitFixedTrace0; SHA256 d880cf80779e5d0325db75d6b15c4f9d264573f65319c52320ec465fb3a34c55. -/
section PolicySubmissionPart58
/- Complete ordinary kernel replay with shared units and fixed15 hints. -/
namespace Bounty

def policySharedUnitFixed0Check (lo hi : Nat) : Bool := policyBitActionIntervalGood policySharedUnitFixed0Db policySharedUnitFixed0Hints lo hi

def policySharedUnitFixed0_check9009 : policySharedUnitFixed0Check 0x2331 0x2351 = true := by
  decide +kernel

def policySharedUnitFixed0_range9009_9041 : ∀ i, 0x2331 ≤ i → i < 0x2351 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9009


def policySharedUnitFixed0_check9041 : policySharedUnitFixed0Check 0x2351 0x2371 = true := by
  decide +kernel

def policySharedUnitFixed0_range9041_9073 : ∀ i, 0x2351 ≤ i → i < 0x2371 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9041


def policySharedUnitFixed0_check9073 : policySharedUnitFixed0Check 0x2371 0x2391 = true := by
  decide +kernel

def policySharedUnitFixed0_range9073_9105 : ∀ i, 0x2371 ≤ i → i < 0x2391 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9073


def policySharedUnitFixed0_check9105 : policySharedUnitFixed0Check 0x2391 0x23b1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9105_9137 : ∀ i, 0x2391 ≤ i → i < 0x23b1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9105


def policySharedUnitFixed0_check9137 : policySharedUnitFixed0Check 0x23b1 0x23d1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9137_9169 : ∀ i, 0x23b1 ≤ i → i < 0x23d1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9137


def policySharedUnitFixed0_check9169 : policySharedUnitFixed0Check 0x23d1 0x23f1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9169_9201 : ∀ i, 0x23d1 ≤ i → i < 0x23f1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9169


def policySharedUnitFixed0_check9201 : policySharedUnitFixed0Check 0x23f1 0x2411 = true := by
  decide +kernel

def policySharedUnitFixed0_range9201_9233 : ∀ i, 0x23f1 ≤ i → i < 0x2411 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9201


def policySharedUnitFixed0_check9233 : policySharedUnitFixed0Check 0x2411 0x2431 = true := by
  decide +kernel

def policySharedUnitFixed0_range9233_9265 : ∀ i, 0x2411 ≤ i → i < 0x2431 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9233


def policySharedUnitFixed0_check9265 : policySharedUnitFixed0Check 0x2431 0x2451 = true := by
  decide +kernel

def policySharedUnitFixed0_range9265_9297 : ∀ i, 0x2431 ≤ i → i < 0x2451 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9265


def policySharedUnitFixed0_check9297 : policySharedUnitFixed0Check 0x2451 0x2471 = true := by
  decide +kernel

def policySharedUnitFixed0_range9297_9329 : ∀ i, 0x2451 ≤ i → i < 0x2471 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9297


def policySharedUnitFixed0_check9329 : policySharedUnitFixed0Check 0x2471 0x2491 = true := by
  decide +kernel

def policySharedUnitFixed0_range9329_9361 : ∀ i, 0x2471 ≤ i → i < 0x2491 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9329


def policySharedUnitFixed0_check9361 : policySharedUnitFixed0Check 0x2491 0x24b1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9361_9393 : ∀ i, 0x2491 ≤ i → i < 0x24b1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9361


def policySharedUnitFixed0_check9393 : policySharedUnitFixed0Check 0x24b1 0x24d1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9393_9425 : ∀ i, 0x24b1 ≤ i → i < 0x24d1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9393


def policySharedUnitFixed0_check9425 : policySharedUnitFixed0Check 0x24d1 0x24f1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9425_9457 : ∀ i, 0x24d1 ≤ i → i < 0x24f1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9425


def policySharedUnitFixed0_check9457 : policySharedUnitFixed0Check 0x24f1 0x2511 = true := by
  decide +kernel

def policySharedUnitFixed0_range9457_9489 : ∀ i, 0x24f1 ≤ i → i < 0x2511 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9457


def policySharedUnitFixed0_check9489 : policySharedUnitFixed0Check 0x2511 0x2531 = true := by
  decide +kernel

def policySharedUnitFixed0_range9489_9521 : ∀ i, 0x2511 ≤ i → i < 0x2531 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9489


def policySharedUnitFixed0_check9521 : policySharedUnitFixed0Check 0x2531 0x2551 = true := by
  decide +kernel

def policySharedUnitFixed0_range9521_9553 : ∀ i, 0x2531 ≤ i → i < 0x2551 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9521


def policySharedUnitFixed0_check9553 : policySharedUnitFixed0Check 0x2551 0x2571 = true := by
  decide +kernel

def policySharedUnitFixed0_range9553_9585 : ∀ i, 0x2551 ≤ i → i < 0x2571 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9553


def policySharedUnitFixed0_check9585 : policySharedUnitFixed0Check 0x2571 0x2591 = true := by
  decide +kernel

def policySharedUnitFixed0_range9585_9617 : ∀ i, 0x2571 ≤ i → i < 0x2591 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9585


def policySharedUnitFixed0_check9617 : policySharedUnitFixed0Check 0x2591 0x25b1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9617_9649 : ∀ i, 0x2591 ≤ i → i < 0x25b1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9617


def policySharedUnitFixed0_check9649 : policySharedUnitFixed0Check 0x25b1 0x25d1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9649_9681 : ∀ i, 0x25b1 ≤ i → i < 0x25d1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9649


def policySharedUnitFixed0_check9681 : policySharedUnitFixed0Check 0x25d1 0x25f1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9681_9713 : ∀ i, 0x25d1 ≤ i → i < 0x25f1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9681


def policySharedUnitFixed0_check9713 : policySharedUnitFixed0Check 0x25f1 0x2611 = true := by
  decide +kernel

def policySharedUnitFixed0_range9713_9745 : ∀ i, 0x25f1 ≤ i → i < 0x2611 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9713


def policySharedUnitFixed0_check9745 : policySharedUnitFixed0Check 0x2611 0x2631 = true := by
  decide +kernel

def policySharedUnitFixed0_range9745_9777 : ∀ i, 0x2611 ≤ i → i < 0x2631 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9745


def policySharedUnitFixed0_check9777 : policySharedUnitFixed0Check 0x2631 0x2651 = true := by
  decide +kernel

def policySharedUnitFixed0_range9777_9809 : ∀ i, 0x2631 ≤ i → i < 0x2651 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9777


def policySharedUnitFixed0_check9809 : policySharedUnitFixed0Check 0x2651 0x2671 = true := by
  decide +kernel

def policySharedUnitFixed0_range9809_9841 : ∀ i, 0x2651 ≤ i → i < 0x2671 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9809


def policySharedUnitFixed0_check9841 : policySharedUnitFixed0Check 0x2671 0x2691 = true := by
  decide +kernel

def policySharedUnitFixed0_range9841_9873 : ∀ i, 0x2671 ≤ i → i < 0x2691 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9841


def policySharedUnitFixed0_check9873 : policySharedUnitFixed0Check 0x2691 0x26b1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9873_9905 : ∀ i, 0x2691 ≤ i → i < 0x26b1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9873


def policySharedUnitFixed0_check9905 : policySharedUnitFixed0Check 0x26b1 0x26d1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9905_9937 : ∀ i, 0x26b1 ≤ i → i < 0x26d1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9905


def policySharedUnitFixed0_check9937 : policySharedUnitFixed0Check 0x26d1 0x26f1 = true := by
  decide +kernel

def policySharedUnitFixed0_range9937_9969 : ∀ i, 0x26d1 ≤ i → i < 0x26f1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9937


def policySharedUnitFixed0_check9969 : policySharedUnitFixed0Check 0x26f1 0x2711 = true := by
  decide +kernel

def policySharedUnitFixed0_range9969_10001 : ∀ i, 0x26f1 ≤ i → i < 0x2711 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check9969


def policySharedUnitFixed0_check10001 : policySharedUnitFixed0Check 0x2711 0x2731 = true := by
  decide +kernel

def policySharedUnitFixed0_range10001_10033 : ∀ i, 0x2711 ≤ i → i < 0x2731 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10001


def policySharedUnitFixed0_check10033 : policySharedUnitFixed0Check 0x2731 0x2751 = true := by
  decide +kernel

def policySharedUnitFixed0_range10033_10065 : ∀ i, 0x2731 ≤ i → i < 0x2751 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10033


def policySharedUnitFixed0_check10065 : policySharedUnitFixed0Check 0x2751 0x2771 = true := by
  decide +kernel

def policySharedUnitFixed0_range10065_10097 : ∀ i, 0x2751 ≤ i → i < 0x2771 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10065


def policySharedUnitFixed0_check10097 : policySharedUnitFixed0Check 0x2771 0x2791 = true := by
  decide +kernel

def policySharedUnitFixed0_range10097_10129 : ∀ i, 0x2771 ≤ i → i < 0x2791 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10097


def policySharedUnitFixed0_check10129 : policySharedUnitFixed0Check 0x2791 0x27b1 = true := by
  decide +kernel

def policySharedUnitFixed0_range10129_10161 : ∀ i, 0x2791 ≤ i → i < 0x27b1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10129


def policySharedUnitFixed0_check10161 : policySharedUnitFixed0Check 0x27b1 0x27d1 = true := by
  decide +kernel

def policySharedUnitFixed0_range10161_10193 : ∀ i, 0x27b1 ≤ i → i < 0x27d1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10161


def policySharedUnitFixed0_check10193 : policySharedUnitFixed0Check 0x27d1 0x27f1 = true := by
  decide +kernel

def policySharedUnitFixed0_range10193_10225 : ∀ i, 0x27d1 ≤ i → i < 0x27f1 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10193


def policySharedUnitFixed0_check10225 : policySharedUnitFixed0Check 0x27f1 0x280d = true := by
  decide +kernel

def policySharedUnitFixed0_range10225_10253 : ∀ i, 0x27f1 ≤ i → i < 0x280d → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10225


def policySharedUnitFixed0_check10253 : policySharedUnitFixed0Check 0x280d 0x2821 = true := by
  decide +kernel

def policySharedUnitFixed0_range10253_10273 : ∀ i, 0x280d ≤ i → i < 0x2821 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10253


def policySharedUnitFixed0_check10273 : policySharedUnitFixed0Check 0x2821 0x283a = true := by
  decide +kernel

def policySharedUnitFixed0_range10273_10298 : ∀ i, 0x2821 ≤ i → i < 0x283a → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10273


def policySharedUnitFixed0_check10298 : policySharedUnitFixed0Check 0x283a 0x2845 = true := by
  decide +kernel

def policySharedUnitFixed0_range10298_10309 : ∀ i, 0x283a ≤ i → i < 0x2845 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10298


def policySharedUnitFixed0_check10309 : policySharedUnitFixed0Check 0x2845 0x2865 = true := by
  decide +kernel

def policySharedUnitFixed0_range10309_10341 : ∀ i, 0x2845 ≤ i → i < 0x2865 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10309


def policySharedUnitFixed0_check10341 : policySharedUnitFixed0Check 0x2865 0x2885 = true := by
  decide +kernel

def policySharedUnitFixed0_range10341_10373 : ∀ i, 0x2865 ≤ i → i < 0x2885 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10341


def policySharedUnitFixed0_check10373 : policySharedUnitFixed0Check 0x2885 0x28a5 = true := by
  decide +kernel

def policySharedUnitFixed0_range10373_10405 : ∀ i, 0x2885 ≤ i → i < 0x28a5 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10373


def policySharedUnitFixed0_check10405 : policySharedUnitFixed0Check 0x28a5 0x28c5 = true := by
  decide +kernel

def policySharedUnitFixed0_range10405_10437 : ∀ i, 0x28a5 ≤ i → i < 0x28c5 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10405


def policySharedUnitFixed0_check10437 : policySharedUnitFixed0Check 0x28c5 0x28e5 = true := by
  decide +kernel

def policySharedUnitFixed0_range10437_10469 : ∀ i, 0x28c5 ≤ i → i < 0x28e5 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10437


def policySharedUnitFixed0_check10469 : policySharedUnitFixed0Check 0x28e5 0x2904 = true := by
  decide +kernel

def policySharedUnitFixed0_range10469_10500 : ∀ i, 0x28e5 ≤ i → i < 0x2904 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed0_check10469


def policySharedUnitFixed0_all_checked : ∀ i, 0x2331 ≤ i → i < 0x2904 → policyBitActionGood policySharedUnitFixed0Db i (policySharedUnitFixed0Hints i) = true :=
  (policyIntervalJoin _ 0x2331 0x2631 0x2904
  (policyIntervalJoin _ 0x2331 0x24b1 0x2631
  (policyIntervalJoin _ 0x2331 0x23f1 0x24b1
  (policyIntervalJoin _ 0x2331 0x2391 0x23f1
  (policyIntervalJoin _ 0x2331 0x2351 0x2391
  policySharedUnitFixed0_range9009_9041
  (policyIntervalJoin _ 0x2351 0x2371 0x2391
  policySharedUnitFixed0_range9041_9073
  policySharedUnitFixed0_range9073_9105))
  (policyIntervalJoin _ 0x2391 0x23b1 0x23f1
  policySharedUnitFixed0_range9105_9137
  (policyIntervalJoin _ 0x23b1 0x23d1 0x23f1
  policySharedUnitFixed0_range9137_9169
  policySharedUnitFixed0_range9169_9201)))
  (policyIntervalJoin _ 0x23f1 0x2451 0x24b1
  (policyIntervalJoin _ 0x23f1 0x2411 0x2451
  policySharedUnitFixed0_range9201_9233
  (policyIntervalJoin _ 0x2411 0x2431 0x2451
  policySharedUnitFixed0_range9233_9265
  policySharedUnitFixed0_range9265_9297))
  (policyIntervalJoin _ 0x2451 0x2471 0x24b1
  policySharedUnitFixed0_range9297_9329
  (policyIntervalJoin _ 0x2471 0x2491 0x24b1
  policySharedUnitFixed0_range9329_9361
  policySharedUnitFixed0_range9361_9393))))
  (policyIntervalJoin _ 0x24b1 0x2571 0x2631
  (policyIntervalJoin _ 0x24b1 0x2511 0x2571
  (policyIntervalJoin _ 0x24b1 0x24d1 0x2511
  policySharedUnitFixed0_range9393_9425
  (policyIntervalJoin _ 0x24d1 0x24f1 0x2511
  policySharedUnitFixed0_range9425_9457
  policySharedUnitFixed0_range9457_9489))
  (policyIntervalJoin _ 0x2511 0x2531 0x2571
  policySharedUnitFixed0_range9489_9521
  (policyIntervalJoin _ 0x2531 0x2551 0x2571
  policySharedUnitFixed0_range9521_9553
  policySharedUnitFixed0_range9553_9585)))
  (policyIntervalJoin _ 0x2571 0x25d1 0x2631
  (policyIntervalJoin _ 0x2571 0x2591 0x25d1
  policySharedUnitFixed0_range9585_9617
  (policyIntervalJoin _ 0x2591 0x25b1 0x25d1
  policySharedUnitFixed0_range9617_9649
  policySharedUnitFixed0_range9649_9681))
  (policyIntervalJoin _ 0x25d1 0x25f1 0x2631
  policySharedUnitFixed0_range9681_9713
  (policyIntervalJoin _ 0x25f1 0x2611 0x2631
  policySharedUnitFixed0_range9713_9745
  policySharedUnitFixed0_range9745_9777)))))
  (policyIntervalJoin _ 0x2631 0x27b1 0x2904
  (policyIntervalJoin _ 0x2631 0x26f1 0x27b1
  (policyIntervalJoin _ 0x2631 0x2691 0x26f1
  (policyIntervalJoin _ 0x2631 0x2651 0x2691
  policySharedUnitFixed0_range9777_9809
  (policyIntervalJoin _ 0x2651 0x2671 0x2691
  policySharedUnitFixed0_range9809_9841
  policySharedUnitFixed0_range9841_9873))
  (policyIntervalJoin _ 0x2691 0x26b1 0x26f1
  policySharedUnitFixed0_range9873_9905
  (policyIntervalJoin _ 0x26b1 0x26d1 0x26f1
  policySharedUnitFixed0_range9905_9937
  policySharedUnitFixed0_range9937_9969)))
  (policyIntervalJoin _ 0x26f1 0x2751 0x27b1
  (policyIntervalJoin _ 0x26f1 0x2711 0x2751
  policySharedUnitFixed0_range9969_10001
  (policyIntervalJoin _ 0x2711 0x2731 0x2751
  policySharedUnitFixed0_range10001_10033
  policySharedUnitFixed0_range10033_10065))
  (policyIntervalJoin _ 0x2751 0x2771 0x27b1
  policySharedUnitFixed0_range10065_10097
  (policyIntervalJoin _ 0x2771 0x2791 0x27b1
  policySharedUnitFixed0_range10097_10129
  policySharedUnitFixed0_range10129_10161))))
  (policyIntervalJoin _ 0x27b1 0x2845 0x2904
  (policyIntervalJoin _ 0x27b1 0x280d 0x2845
  (policyIntervalJoin _ 0x27b1 0x27d1 0x280d
  policySharedUnitFixed0_range10161_10193
  (policyIntervalJoin _ 0x27d1 0x27f1 0x280d
  policySharedUnitFixed0_range10193_10225
  policySharedUnitFixed0_range10225_10253))
  (policyIntervalJoin _ 0x280d 0x2821 0x2845
  policySharedUnitFixed0_range10253_10273
  (policyIntervalJoin _ 0x2821 0x283a 0x2845
  policySharedUnitFixed0_range10273_10298
  policySharedUnitFixed0_range10298_10309)))
  (policyIntervalJoin _ 0x2845 0x28a5 0x2904
  (policyIntervalJoin _ 0x2845 0x2865 0x28a5
  policySharedUnitFixed0_range10309_10341
  (policyIntervalJoin _ 0x2865 0x2885 0x28a5
  policySharedUnitFixed0_range10341_10373
  policySharedUnitFixed0_range10373_10405))
  (policyIntervalJoin _ 0x28a5 0x28c5 0x2904
  policySharedUnitFixed0_range10405_10437
  (policyIntervalJoin _ 0x28c5 0x28e5 0x2904
  policySharedUnitFixed0_range10437_10469
  policySharedUnitFixed0_range10469_10500))))))

def policySharedUnit0_false_compact (P : Nat → Prop)
    (hi : ∀ i, 0 < i → i < 0x2331 → policySignedClauseHolds P (policyFixedCompact0Db i)) : False := by
  apply policyBitGraph_false policySharedUnitFixed0Db 0x2331 0x2904 0x2903 policySharedUnitFixed0Hints P
    policySharedUnitFixed0_all_checked ?_ (by decide) (by decide) policySharedUnitFixed0_root_empty
  intro i hip hib
  simpa only [policySharedUnitFixed0Db, if_pos hib] using hi i hip hib

end Bounty

end PolicySubmissionPart58

/- Component PolicyMappedCircuitChecked1; SHA256 7f1d9f077e1dae6d0bc117e08be8f89e3783a1a2eab16dcaa2ee917b360fc035. -/
section PolicySubmissionPart59
namespace PolicyMappedCircuitChecked1
open ClosureCircuit ClosureSemantics Bounty

def test (start count : Nat) : Bool :=
  checkCircuitBlock (boundedProgram ClosureFixedWidthData1.program)
    policyMappedDatabase1 PolicyCircuitPacked1.records start count

def checked0 : test 0 32 = true := by
  decide +kernel

def checked1 : test 32 32 = true := by
  decide +kernel

def checked2 : test 64 32 = true := by
  decide +kernel

def checked3 : test 96 32 = true := by
  decide +kernel

def checked4 : test 0x80 32 = true := by
  decide +kernel

def checked5 : test 0xa0 32 = true := by
  decide +kernel

def checked6 : test 0xc0 32 = true := by
  decide +kernel

def checked7 : test 0xe0 32 = true := by
  decide +kernel

def checked8 : test 0x100 32 = true := by
  decide +kernel

def checked9 : test 0x120 32 = true := by
  decide +kernel

def checked10 : test 0x140 32 = true := by
  decide +kernel

def checked11 : test 0x160 32 = true := by
  decide +kernel

def checked12 : test 0x180 32 = true := by
  decide +kernel

def checked13 : test 0x1a0 32 = true := by
  decide +kernel

def checked14 : test 0x1c0 32 = true := by
  decide +kernel

def checked15 : test 0x1e0 32 = true := by
  decide +kernel

def checked16 : test 0x200 32 = true := by
  decide +kernel

def checked17 : test 0x220 32 = true := by
  decide +kernel

def checked18 : test 0x240 32 = true := by
  decide +kernel

def checked19 : test 0x260 32 = true := by
  decide +kernel

def checked20 : test 0x280 32 = true := by
  decide +kernel

def checked21 : test 0x2a0 32 = true := by
  decide +kernel

def checked22 : test 0x2c0 32 = true := by
  decide +kernel

def checked23 : test 0x2e0 32 = true := by
  decide +kernel

def checked24 : test 0x300 32 = true := by
  decide +kernel

def checked25 : test 0x320 32 = true := by
  decide +kernel

def checked26 : test 0x340 32 = true := by
  decide +kernel

def checked27 : test 0x360 32 = true := by
  decide +kernel

def checked28 : test 0x380 32 = true := by
  decide +kernel

def checked29 : test 0x3a0 32 = true := by
  decide +kernel

def checked30 : test 0x3c0 32 = true := by
  decide +kernel

def checked31 : test 0x3e0 32 = true := by
  decide +kernel

def checked32 : test 0x400 32 = true := by
  decide +kernel

def checked33 : test 0x420 32 = true := by
  decide +kernel

def checked34 : test 0x440 32 = true := by
  decide +kernel

def checked35 : test 0x460 32 = true := by
  decide +kernel

def checked36 : test 0x480 32 = true := by
  decide +kernel

def checked37 : test 0x4a0 32 = true := by
  decide +kernel

def checked38 : test 0x4c0 32 = true := by
  decide +kernel

def checked39 : test 0x4e0 32 = true := by
  decide +kernel

def checked40 : test 0x500 32 = true := by
  decide +kernel

def checked41 : test 0x520 32 = true := by
  decide +kernel

def checked42 : test 0x540 32 = true := by
  decide +kernel

def checked43 : test 0x560 32 = true := by
  decide +kernel

def checked44 : test 0x580 32 = true := by
  decide +kernel

def checked45 : test 0x5a0 32 = true := by
  decide +kernel

def checked46 : test 0x5c0 32 = true := by
  decide +kernel

def checked47 : test 0x5e0 32 = true := by
  decide +kernel

def checked48 : test 0x600 32 = true := by
  decide +kernel

def checked49 : test 0x620 32 = true := by
  decide +kernel

def checked50 : test 0x640 32 = true := by
  decide +kernel

def checked51 : test 0x660 32 = true := by
  decide +kernel

def checked52 : test 0x680 32 = true := by
  decide +kernel

def checked53 : test 0x6a0 32 = true := by
  decide +kernel

def checked54 : test 0x6c0 32 = true := by
  decide +kernel

def checked55 : test 0x6e0 32 = true := by
  decide +kernel

def checked56 : test 0x700 32 = true := by
  decide +kernel

def checked57 : test 0x720 32 = true := by
  decide +kernel

def checked58 : test 0x740 32 = true := by
  decide +kernel

def checked59 : test 0x760 32 = true := by
  decide +kernel

def checked60 : test 0x780 32 = true := by
  decide +kernel

def checked61 : test 0x7a0 32 = true := by
  decide +kernel

def checked62 : test 0x7c0 32 = true := by
  decide +kernel

def checked63 : test 0x7e0 32 = true := by
  decide +kernel

def checked64 : test 0x800 32 = true := by
  decide +kernel

def checked65 : test 0x820 32 = true := by
  decide +kernel

def checked66 : test 0x840 32 = true := by
  decide +kernel

def checked67 : test 0x860 32 = true := by
  decide +kernel

def checked68 : test 0x880 32 = true := by
  decide +kernel

def checked69 : test 0x8a0 32 = true := by
  decide +kernel

def checked70 : test 0x8c0 32 = true := by
  decide +kernel

def checked71 : test 0x8e0 32 = true := by
  decide +kernel

def checked72 : test 0x900 32 = true := by
  decide +kernel

def checked73 : test 0x920 32 = true := by
  decide +kernel

def checked74 : test 0x940 32 = true := by
  decide +kernel

def checked75 : test 0x960 32 = true := by
  decide +kernel

def checked76 : test 0x980 32 = true := by
  decide +kernel

def checked77 : test 0x9a0 32 = true := by
  decide +kernel

def checked78 : test 0x9c0 32 = true := by
  decide +kernel

def checked79 : test 0x9e0 32 = true := by
  decide +kernel

def checked80 : test 0xa00 32 = true := by
  decide +kernel

def checked81 : test 0xa20 32 = true := by
  decide +kernel

def checked82 : test 0xa40 32 = true := by
  decide +kernel

def checked83 : test 0xa60 32 = true := by
  decide +kernel

def checked84 : test 0xa80 32 = true := by
  decide +kernel

def checked85 : test 0xaa0 32 = true := by
  decide +kernel

def checked86 : test 0xac0 32 = true := by
  decide +kernel

def checked87 : test 0xae0 32 = true := by
  decide +kernel

def checked88 : test 0xb00 32 = true := by
  decide +kernel

def checked89 : test 0xb20 32 = true := by
  decide +kernel

def checked90 : test 0xb40 32 = true := by
  decide +kernel

def checked91 : test 0xb60 32 = true := by
  decide +kernel

def checked92 : test 0xb80 32 = true := by
  decide +kernel

def checked93 : test 0xba0 32 = true := by
  decide +kernel

def checked94 : test 0xbc0 32 = true := by
  decide +kernel

def checked95 : test 0xbe0 32 = true := by
  decide +kernel

def checked96 : test 0xc00 32 = true := by
  decide +kernel

def checked97 : test 0xc20 32 = true := by
  decide +kernel

def checked98 : test 0xc40 32 = true := by
  decide +kernel

def checked99 : test 0xc60 32 = true := by
  decide +kernel

def checked100 : test 0xc80 32 = true := by
  decide +kernel

def checked101 : test 0xca0 32 = true := by
  decide +kernel

def checked102 : test 0xcc0 32 = true := by
  decide +kernel

def checked103 : test 0xce0 32 = true := by
  decide +kernel

def checked104 : test 0xd00 32 = true := by
  decide +kernel

def checked105 : test 0xd20 32 = true := by
  decide +kernel

def checked106 : test 0xd40 32 = true := by
  decide +kernel

def checked107 : test 0xd60 32 = true := by
  decide +kernel

def checked108 : test 0xd80 32 = true := by
  decide +kernel

def checked109 : test 0xda0 32 = true := by
  decide +kernel

def checked110 : test 0xdc0 32 = true := by
  decide +kernel

def checked111 : test 0xde0 32 = true := by
  decide +kernel

def checked112 : test 0xe00 32 = true := by
  decide +kernel

def checked113 : test 0xe20 32 = true := by
  decide +kernel

def checked114 : test 0xe40 32 = true := by
  decide +kernel

def checked115 : test 0xe60 32 = true := by
  decide +kernel

def checked116 : test 0xe80 32 = true := by
  decide +kernel

def checked117 : test 0xea0 32 = true := by
  decide +kernel

def checked118 : test 0xec0 32 = true := by
  decide +kernel

def checked119 : test 0xee0 32 = true := by
  decide +kernel

def checked120 : test 0xf00 32 = true := by
  decide +kernel

def checked121 : test 0xf20 32 = true := by
  decide +kernel

def checked122 : test 0xf40 32 = true := by
  decide +kernel

def checked123 : test 0xf60 32 = true := by
  decide +kernel

def checked124 : test 0xf80 32 = true := by
  decide +kernel

def checked125 : test 0xfa0 32 = true := by
  decide +kernel

def checked126 : test 0xfc0 32 = true := by
  decide +kernel

def checked127 : test 0xfe0 32 = true := by
  decide +kernel

def checked128 : test 0x1000 32 = true := by
  decide +kernel

def checked129 : test 0x1020 32 = true := by
  decide +kernel

def checked130 : test 0x1040 32 = true := by
  decide +kernel

def checked131 : test 0x1060 32 = true := by
  decide +kernel

def checked132 : test 0x1080 32 = true := by
  decide +kernel

def checked133 : test 0x10a0 32 = true := by
  decide +kernel

def checked134 : test 0x10c0 32 = true := by
  decide +kernel

def checked135 : test 0x10e0 1 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 96 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67
  · exact checked68
  · exact checked69
  · exact checked70
  · exact checked71
  · exact checked72
  · exact checked73
  · exact checked74
  · exact checked75
  · exact checked76
  · exact checked77
  · exact checked78
  · exact checked79
  · exact checked80
  · exact checked81
  · exact checked82
  · exact checked83
  · exact checked84
  · exact checked85
  · exact checked86
  · exact checked87
  · exact checked88
  · exact checked89
  · exact checked90
  · exact checked91
  · exact checked92
  · exact checked93
  · exact checked94
  · exact checked95

def checkedRange96 : ∀ i : Nat, 96 ≤ i → i < 0x80 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked96
  · exact checked97
  · exact checked98
  · exact checked99
  · exact checked100
  · exact checked101
  · exact checked102
  · exact checked103
  · exact checked104
  · exact checked105
  · exact checked106
  · exact checked107
  · exact checked108
  · exact checked109
  · exact checked110
  · exact checked111
  · exact checked112
  · exact checked113
  · exact checked114
  · exact checked115
  · exact checked116
  · exact checked117
  · exact checked118
  · exact checked119
  · exact checked120
  · exact checked121
  · exact checked122
  · exact checked123
  · exact checked124
  · exact checked125
  · exact checked126
  · exact checked127

def checkedRange128 : ∀ i : Nat, 0x80 ≤ i → i < 0x88 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked128
  · exact checked129
  · exact checked130
  · exact checked131
  · exact checked132
  · exact checked133
  · exact checked134
  · exact checked135

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 0x88 → test (32 * i) (min 32 (0x10e1 - 32 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 64 0x88
  (Bounty.policyIntervalJoin _ 0 32 64
  checkedRange0
  checkedRange32)
  (Bounty.policyIntervalJoin _ 64 96 0x88
  checkedRange64
  (Bounty.policyIntervalJoin _ 96 0x80 0x88
  checkedRange96
  checkedRange128)))

def checked (i : Fin 0x88) : test (32 * i.val)
    (min 32 (0x10e1 - 32 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values)
    (i : Nat) (hi : i < 0x10e1) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase1 ((PolicyCircuitPacked1.records i).headD 0)) := by
  have hb : i / 32 < 0x88 := by omega
  have hw : i % 32 < min 32 (0x10e1 - 32 * (i / 32)) := by omega
  have h := checkCircuitBlock_sound (boundedProgram ClosureFixedWidthData1.program) input values he
    policyMappedDatabase1 PolicyCircuitPacked1.records (32 * (i / 32))
    (min 32 (0x10e1 - 32 * (i / 32))) (checked ⟨i / 32, hb⟩) (i % 32) hw
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyMappedCircuitChecked1

end PolicySubmissionPart59

/- Component PolicyMappedRewriteParametricChecked1; SHA256 424c4f5cc0a68c7bd2355f781f3fdf7a9cbf38f084dc5b9c388ae5e244cf7f5a. -/
section PolicySubmissionPart60
namespace PolicyMappedRewriteParametricChecked1
open ClosurePattern ClosureSemantics Bounty

def test (start count : Nat) : Bool :=
  checkSchemaBlock (boundedProgram ClosureFixedWidthData1.program)
    policyMappedDatabase1 PolicyRewriteParametricPacked1.records start count

def checked0 : test 0 32 = true := by
  decide +kernel

def checked1 : test 32 32 = true := by
  decide +kernel

def checked2 : test 64 32 = true := by
  decide +kernel

def checked3 : test 96 32 = true := by
  decide +kernel

def checked4 : test 0x80 32 = true := by
  decide +kernel

def checked5 : test 0xa0 32 = true := by
  decide +kernel

def checked6 : test 0xc0 32 = true := by
  decide +kernel

def checked7 : test 0xe0 32 = true := by
  decide +kernel

def checked8 : test 0x100 32 = true := by
  decide +kernel

def checked9 : test 0x120 32 = true := by
  decide +kernel

def checked10 : test 0x140 32 = true := by
  decide +kernel

def checked11 : test 0x160 32 = true := by
  decide +kernel

def checked12 : test 0x180 32 = true := by
  decide +kernel

def checked13 : test 0x1a0 32 = true := by
  decide +kernel

def checked14 : test 0x1c0 32 = true := by
  decide +kernel

def checked15 : test 0x1e0 32 = true := by
  decide +kernel

def checked16 : test 0x200 32 = true := by
  decide +kernel

def checked17 : test 0x220 32 = true := by
  decide +kernel

def checked18 : test 0x240 32 = true := by
  decide +kernel

def checked19 : test 0x260 32 = true := by
  decide +kernel

def checked20 : test 0x280 32 = true := by
  decide +kernel

def checked21 : test 0x2a0 32 = true := by
  decide +kernel

def checked22 : test 0x2c0 32 = true := by
  decide +kernel

def checked23 : test 0x2e0 32 = true := by
  decide +kernel

def checked24 : test 0x300 32 = true := by
  decide +kernel

def checked25 : test 0x320 32 = true := by
  decide +kernel

def checked26 : test 0x340 32 = true := by
  decide +kernel

def checked27 : test 0x360 32 = true := by
  decide +kernel

def checked28 : test 0x380 32 = true := by
  decide +kernel

def checked29 : test 0x3a0 32 = true := by
  decide +kernel

def checked30 : test 0x3c0 32 = true := by
  decide +kernel

def checked31 : test 0x3e0 32 = true := by
  decide +kernel

def checked32 : test 0x400 32 = true := by
  decide +kernel

def checked33 : test 0x420 32 = true := by
  decide +kernel

def checked34 : test 0x440 32 = true := by
  decide +kernel

def checked35 : test 0x460 32 = true := by
  decide +kernel

def checked36 : test 0x480 32 = true := by
  decide +kernel

def checked37 : test 0x4a0 32 = true := by
  decide +kernel

def checked38 : test 0x4c0 32 = true := by
  decide +kernel

def checked39 : test 0x4e0 32 = true := by
  decide +kernel

def checked40 : test 0x500 32 = true := by
  decide +kernel

def checked41 : test 0x520 32 = true := by
  decide +kernel

def checked42 : test 0x540 32 = true := by
  decide +kernel

def checked43 : test 0x560 32 = true := by
  decide +kernel

def checked44 : test 0x580 32 = true := by
  decide +kernel

def checked45 : test 0x5a0 32 = true := by
  decide +kernel

def checked46 : test 0x5c0 32 = true := by
  decide +kernel

def checked47 : test 0x5e0 32 = true := by
  decide +kernel

def checked48 : test 0x600 32 = true := by
  decide +kernel

def checked49 : test 0x620 32 = true := by
  decide +kernel

def checked50 : test 0x640 32 = true := by
  decide +kernel

def checked51 : test 0x660 32 = true := by
  decide +kernel

def checked52 : test 0x680 32 = true := by
  decide +kernel

def checked53 : test 0x6a0 32 = true := by
  decide +kernel

def checked54 : test 0x6c0 32 = true := by
  decide +kernel

def checked55 : test 0x6e0 32 = true := by
  decide +kernel

def checked56 : test 0x700 32 = true := by
  decide +kernel

def checked57 : test 0x720 32 = true := by
  decide +kernel

def checked58 : test 0x740 32 = true := by
  decide +kernel

def checked59 : test 0x760 32 = true := by
  decide +kernel

def checked60 : test 0x780 32 = true := by
  decide +kernel

def checked61 : test 0x7a0 32 = true := by
  decide +kernel

def checked62 : test 0x7c0 32 = true := by
  decide +kernel

def checked63 : test 0x7e0 32 = true := by
  decide +kernel

def checked64 : test 0x800 32 = true := by
  decide +kernel

def checked65 : test 0x820 32 = true := by
  decide +kernel

def checked66 : test 0x840 32 = true := by
  decide +kernel

def checked67 : test 0x860 32 = true := by
  decide +kernel

def checked68 : test 0x880 32 = true := by
  decide +kernel

def checked69 : test 0x8a0 32 = true := by
  decide +kernel

def checked70 : test 0x8c0 32 = true := by
  decide +kernel

def checked71 : test 0x8e0 32 = true := by
  decide +kernel

def checked72 : test 0x900 32 = true := by
  decide +kernel

def checked73 : test 0x920 32 = true := by
  decide +kernel

def checked74 : test 0x940 32 = true := by
  decide +kernel

def checked75 : test 0x960 32 = true := by
  decide +kernel

def checked76 : test 0x980 32 = true := by
  decide +kernel

def checked77 : test 0x9a0 32 = true := by
  decide +kernel

def checked78 : test 0x9c0 32 = true := by
  decide +kernel

def checked79 : test 0x9e0 32 = true := by
  decide +kernel

def checked80 : test 0xa00 32 = true := by
  decide +kernel

def checked81 : test 0xa20 32 = true := by
  decide +kernel

def checked82 : test 0xa40 32 = true := by
  decide +kernel

def checked83 : test 0xa60 32 = true := by
  decide +kernel

def checked84 : test 0xa80 32 = true := by
  decide +kernel

def checked85 : test 0xaa0 32 = true := by
  decide +kernel

def checked86 : test 0xac0 32 = true := by
  decide +kernel

def checked87 : test 0xae0 32 = true := by
  decide +kernel

def checked88 : test 0xb00 32 = true := by
  decide +kernel

def checked89 : test 0xb20 32 = true := by
  decide +kernel

def checked90 : test 0xb40 32 = true := by
  decide +kernel

def checked91 : test 0xb60 32 = true := by
  decide +kernel

def checked92 : test 0xb80 32 = true := by
  decide +kernel

def checked93 : test 0xba0 32 = true := by
  decide +kernel

def checked94 : test 0xbc0 32 = true := by
  decide +kernel

def checked95 : test 0xbe0 32 = true := by
  decide +kernel

def checked96 : test 0xc00 32 = true := by
  decide +kernel

def checked97 : test 0xc20 27 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (32 * i) (min 32 (0xc3b - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (32 * i) (min 32 (0xc3b - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 96 → test (32 * i) (min 32 (0xc3b - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67
  · exact checked68
  · exact checked69
  · exact checked70
  · exact checked71
  · exact checked72
  · exact checked73
  · exact checked74
  · exact checked75
  · exact checked76
  · exact checked77
  · exact checked78
  · exact checked79
  · exact checked80
  · exact checked81
  · exact checked82
  · exact checked83
  · exact checked84
  · exact checked85
  · exact checked86
  · exact checked87
  · exact checked88
  · exact checked89
  · exact checked90
  · exact checked91
  · exact checked92
  · exact checked93
  · exact checked94
  · exact checked95

def checkedRange96 : ∀ i : Nat, 96 ≤ i → i < 98 → test (32 * i) (min 32 (0xc3b - 32 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked96
  · exact checked97

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 98 → test (32 * i) (min 32 (0xc3b - 32 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 64 98
  (Bounty.policyIntervalJoin _ 0 32 64
  checkedRange0
  checkedRange32)
  (Bounty.policyIntervalJoin _ 64 96 98
  checkedRange64
  checkedRange96))

def checked (i : Fin 98) : test (32 * i.val)
    (min 32 (0xc3b - 32 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values)
    (i : Nat) (hi : i < 0xc3b) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase1 ((PolicyRewriteParametricPacked1.records i).headD 0)) := by
  have hb : i / 32 < 98 := by omega
  have hw : i % 32 < min 32 (0xc3b - 32 * (i / 32)) := by omega
  have h := checkSchemaBlock_sound (boundedProgram ClosureFixedWidthData1.program) input values he
    policyMappedDatabase1 PolicyRewriteParametricPacked1.records (32 * (i / 32))
    (min 32 (0xc3b - 32 * (i / 32))) (checked ⟨i / 32, hb⟩) (i % 32) hw
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyMappedRewriteParametricChecked1

end PolicySubmissionPart60

/- Component PolicyClosedConstantData1; SHA256 c3584300e27067840ad7f5bf7b3bfbeee7e3c40bdfe283b8d3fe04af8047c7ac. -/
section PolicySubmissionPart61
/- Every cache leaf contains its original node ID, closed-evaluation fuel,
and claimed full rational Value.  The table is untrusted until checked. -/
namespace PolicyClosedConstantData1
open ClosureSemantics PolicyClosedConstantCache

def certificate : Cache :=
  (.branch 0x1258 3 PolicyClosedConstantValues.q46
  (.branch 0xdfb 3 PolicyClosedConstantValues.q22
    (.branch 0xb02 3 PolicyClosedConstantValues.q1
      (.branch 0xa43 3 PolicyClosedConstantValues.q5
        (.branch 0x80a 3 PolicyClosedConstantValues.q36
          (.branch 0x804 3 PolicyClosedConstantValues.q3
            .empty
            .empty)
          (.branch 0xa1b 3 PolicyClosedConstantValues.q4
            .empty
            .empty))
        (.branch 0xa9b 3 PolicyClosedConstantValues.q25
          (.branch 0xa89 3 PolicyClosedConstantValues.q27
            .empty
            .empty)
          .empty))
      (.branch 0xd1a 3 PolicyClosedConstantValues.q7
        (.branch 0xcda 3 PolicyClosedConstantValues.q6
          (.branch 0xba5 3 PolicyClosedConstantValues.q38
            .empty
            .empty)
          (.branch 0xd00 3 PolicyClosedConstantValues.q0
            .empty
            .empty))
        (.branch 0xdea 3 PolicyClosedConstantValues.q10
          (.branch 0xda8 3 PolicyClosedConstantValues.q39
            .empty
            .empty)
          .empty)))
    (.branch 0x1080 3 PolicyClosedConstantValues.q11
      (.branch 0x1026 3 PolicyClosedConstantValues.q31
        (.branch 0xf01 3 PolicyClosedConstantValues.q29
          (.branch 0xeb1 3 PolicyClosedConstantValues.q2
            .empty
            .empty)
          (.branch 0xf22 3 PolicyClosedConstantValues.q28
            .empty
            .empty))
        (.branch 0x107d 3 PolicyClosedConstantValues.q50
          (.branch 0x102f 3 PolicyClosedConstantValues.q34
            .empty
            .empty)
          .empty))
      (.branch 0x1126 3 PolicyClosedConstantValues.q30
        (.branch 0x110f 3 PolicyClosedConstantValues.q8
          (.branch 0x10c1 3 PolicyClosedConstantValues.q24
            .empty
            .empty)
          .empty)
        (.branch 0x1194 3 PolicyClosedConstantValues.q51
          (.branch 0x117a 3 PolicyClosedConstantValues.q20
            .empty
            .empty)
          .empty))))
  (.branch 0x2513 3 PolicyClosedConstantValues.q35
    (.branch 0x181d 3 PolicyClosedConstantValues.q16
      (.branch 0x14a2 3 PolicyClosedConstantValues.q41
        (.branch 0x1320 3 PolicyClosedConstantValues.q9
          (.branch 0x12a5 3 PolicyClosedConstantValues.q33
            .empty
            .empty)
          (.branch 0x1342 3 PolicyClosedConstantValues.q32
            .empty
            .empty))
        (.branch 0x177d 3 PolicyClosedConstantValues.q14
          (.branch 0x175f 3 PolicyClosedConstantValues.q12
            .empty
            .empty)
          .empty))
      (.branch 0x215a 3 PolicyClosedConstantValues.q40
        (.branch 0x1c99 3 PolicyClosedConstantValues.q37
          (.branch 0x189e 3 PolicyClosedConstantValues.q47
            .empty
            .empty)
          .empty)
        (.branch 0x24b3 3 PolicyClosedConstantValues.q15
          (.branch 0x23c1 3 PolicyClosedConstantValues.q23
            .empty
            .empty)
          .empty)))
    (.branch 0x2f5f 3 PolicyClosedConstantValues.q49
      (.branch 0x2a1a 3 PolicyClosedConstantValues.q13
        (.branch 0x2573 3 PolicyClosedConstantValues.q21
          (.branch 0x256a 3 PolicyClosedConstantValues.q17
            .empty
            .empty)
          (.branch 0x25ed 3 PolicyClosedConstantValues.q19
            .empty
            .empty))
        (.branch 0x2e6a 3 PolicyClosedConstantValues.q18
          (.branch 0x2a27 3 PolicyClosedConstantValues.q26
            .empty
            .empty)
          .empty))
      (.branch 0x4196 3 PolicyClosedConstantValues.q43
        (.branch 0x321e 3 PolicyClosedConstantValues.q42
          (.branch 0x2fd6 3 PolicyClosedConstantValues.q48
            .empty
            .empty)
          .empty)
        (.branch 0x498a 3 PolicyClosedConstantValues.q45
          (.branch 0x4881 3 PolicyClosedConstantValues.q44
            .empty
            .empty)
          .empty)))))

def checked : certificate.check (boundedProgram ClosureFixedWidthData1.program) = true := by
  decide +kernel

def program : ℕ → Node := foldedProgram (boundedProgram ClosureFixedWidthData1.program) certificate

def equations (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values) :
    Equations program input values := by
  exact foldedProgram_equations (boundedProgram ClosureFixedWidthData1.program) certificate input values he checked

end PolicyClosedConstantData1

end PolicySubmissionPart61

/- Component PolicyCachedHotLiteralData1; SHA256 cffb197e7b6fdc6509d7d3c6231bb7a3765c2f2e2fc1c3923e9c10992c8b9b07. -/
section PolicySubmissionPart62
/- Full-Value certificates at the original bounded nodes, each with fuel 1. -/
namespace PolicyCachedHotLiteralData1
open ClosureSemantics PolicyClosedConstantCache

def zeroChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData1.program) 1 0x7f5 (0) = true := by
  decide +kernel

def negativeChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData1.program) 1 0x7f6 (-1) = true := by
  decide +kernel

def oneChecked : checkClosedRatValue (boundedProgram ClosureFixedWidthData1.program) 1 0 (1) = true := by
  decide +kernel

def program : ℕ → Node :=
  PolicyHotLiteralOverrides.program PolicyClosedConstantData1.program 0x7f5 0x7f6 0

def equations (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values) :
    Equations program input values := by
  exact PolicyHotLiteralOverrides.equations PolicyClosedConstantData1.program 0x7f5 0x7f6 0
    input values (PolicyClosedConstantData1.equations input values he)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData1.program) input values he 1 0x7f5 (0) zeroChecked)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData1.program) input values he 1 0x7f6 (-1) negativeChecked)
    (checkClosedRatValue_sound (boundedProgram ClosureFixedWidthData1.program) input values he 1 0 (1) oneChecked)

end PolicyCachedHotLiteralData1

end PolicySubmissionPart62

/- Component PolicyCachedHotArithmeticChecked1; SHA256 6a1fbeebcda7023c66774f46dfb2bc5246fe0e2c9b601fb0a2d225c26d911e52. -/
section PolicySubmissionPart63
/- Every required arithmetic initial clause, checked by ordinary kernel reduction. -/
namespace PolicyCachedHotArithmeticChecked1
open ClosureLinear ClosureSemantics Bounty

def checked0 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0 32 = true := by
  decide +kernel

def checked1 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 32 32 = true := by
  decide +kernel

def checked2 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 64 32 = true := by
  decide +kernel

def checked3 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 96 32 = true := by
  decide +kernel

def checked4 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x80 32 = true := by
  decide +kernel

def checked5 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0xa0 32 = true := by
  decide +kernel

def checked6 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0xc0 32 = true := by
  decide +kernel

def checked7 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0xe0 32 = true := by
  decide +kernel

def checked8 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x100 32 = true := by
  decide +kernel

def checked9 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x120 32 = true := by
  decide +kernel

def checked10 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x140 32 = true := by
  decide +kernel

def checked11 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x160 32 = true := by
  decide +kernel

def checked12 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x180 32 = true := by
  decide +kernel

def checked13 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x1a0 32 = true := by
  decide +kernel

def checked14 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x1c0 32 = true := by
  decide +kernel

def checked15 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x1e0 32 = true := by
  decide +kernel

def checked16 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x200 32 = true := by
  decide +kernel

def checked17 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x220 32 = true := by
  decide +kernel

def checked18 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x240 32 = true := by
  decide +kernel

def checked19 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x260 32 = true := by
  decide +kernel

def checked20 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x280 32 = true := by
  decide +kernel

def checked21 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x2a0 32 = true := by
  decide +kernel

def checked22 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x2c0 32 = true := by
  decide +kernel

def checked23 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x2e0 32 = true := by
  decide +kernel

def checked24 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x300 32 = true := by
  decide +kernel

def checked25 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x320 32 = true := by
  decide +kernel

def checked26 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x340 32 = true := by
  decide +kernel

def checked27 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x360 32 = true := by
  decide +kernel

def checked28 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x380 32 = true := by
  decide +kernel

def checked29 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x3a0 32 = true := by
  decide +kernel

def checked30 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x3c0 32 = true := by
  decide +kernel

def checked31 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x3e0 32 = true := by
  decide +kernel

def checked32 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x400 32 = true := by
  decide +kernel

def checked33 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x420 32 = true := by
  decide +kernel

def checked34 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x440 32 = true := by
  decide +kernel

def checked35 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x460 32 = true := by
  decide +kernel

def checked36 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x480 32 = true := by
  decide +kernel

def checked37 : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records 0x4a0 9 = true := by
  decide +kernel

def checked (i : Fin 38) : checkArithmeticBlock PolicyCachedHotLiteralData1.program
    policyMappedDatabase1 PolicyArithmeticPacked1.records (32 * i.val) (min 32 (0x4a9 - 32 * i.val)) = true := by
  rcases i with ⟨i, hi⟩
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37

def sound (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values) (i : ℕ) (hi : i < 0x4a9) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase1 ((PolicyArithmeticPacked1.records i).headD 0)) := by
  have hblock : i / 32 < 38 := by omega
  have hwithin : i % 32 < min 32 (0x4a9 - 32 * (i / 32)) := by omega
  have h := checkArithmeticBlock_sound PolicyCachedHotLiteralData1.program input values
    (PolicyCachedHotLiteralData1.equations input values he)
    policyMappedDatabase1 PolicyArithmeticPacked1.records (32 * (i / 32))
    (min 32 (0x4a9 - 32 * (i / 32))) (checked ⟨i / 32, hblock⟩) (i % 32) hwithin
  have hid : 32 * (i / 32) + i % 32 = i := by omega
  simpa only [hid] using h

end PolicyCachedHotArithmeticChecked1

end PolicySubmissionPart63

/- Component PolicyInitialFastCoverageChecked1; SHA256 20679ea648bf68c397881e2640a75ec9a2c0f48237209363fbbe6f45d03ed0ab. -/
section PolicySubmissionPart64
namespace PolicyInitialFastCoverage1
open ClosureCoverage

def test (start count : Nat) : Bool := checkBlock limits targets records start count

def checked0 : test 1 0x80 = true := by
  decide +kernel

def checked1 : test 0x81 0x80 = true := by
  decide +kernel

def checked2 : test 0x101 0x80 = true := by
  decide +kernel

def checked3 : test 0x181 0x80 = true := by
  decide +kernel

def checked4 : test 0x201 0x80 = true := by
  decide +kernel

def checked5 : test 0x281 0x80 = true := by
  decide +kernel

def checked6 : test 0x301 0x80 = true := by
  decide +kernel

def checked7 : test 0x381 0x80 = true := by
  decide +kernel

def checked8 : test 0x401 0x80 = true := by
  decide +kernel

def checked9 : test 0x481 0x80 = true := by
  decide +kernel

def checked10 : test 0x501 0x80 = true := by
  decide +kernel

def checked11 : test 0x581 0x80 = true := by
  decide +kernel

def checked12 : test 0x601 0x80 = true := by
  decide +kernel

def checked13 : test 0x681 0x80 = true := by
  decide +kernel

def checked14 : test 0x701 0x80 = true := by
  decide +kernel

def checked15 : test 0x781 0x80 = true := by
  decide +kernel

def checked16 : test 0x801 0x80 = true := by
  decide +kernel

def checked17 : test 0x881 0x80 = true := by
  decide +kernel

def checked18 : test 0x901 0x80 = true := by
  decide +kernel

def checked19 : test 0x981 0x80 = true := by
  decide +kernel

def checked20 : test 0xa01 0x80 = true := by
  decide +kernel

def checked21 : test 0xa81 0x80 = true := by
  decide +kernel

def checked22 : test 0xb01 0x80 = true := by
  decide +kernel

def checked23 : test 0xb81 0x80 = true := by
  decide +kernel

def checked24 : test 0xc01 0x80 = true := by
  decide +kernel

def checked25 : test 0xc81 0x80 = true := by
  decide +kernel

def checked26 : test 0xd01 0x80 = true := by
  decide +kernel

def checked27 : test 0xd81 0x80 = true := by
  decide +kernel

def checked28 : test 0xe01 0x80 = true := by
  decide +kernel

def checked29 : test 0xe81 0x80 = true := by
  decide +kernel

def checked30 : test 0xf01 0x80 = true := by
  decide +kernel

def checked31 : test 0xf81 0x80 = true := by
  decide +kernel

def checked32 : test 0x1001 0x80 = true := by
  decide +kernel

def checked33 : test 0x1081 0x80 = true := by
  decide +kernel

def checked34 : test 0x1101 0x80 = true := by
  decide +kernel

def checked35 : test 0x1181 0x80 = true := by
  decide +kernel

def checked36 : test 0x1201 0x80 = true := by
  decide +kernel

def checked37 : test 0x1281 0x80 = true := by
  decide +kernel

def checked38 : test 0x1301 0x80 = true := by
  decide +kernel

def checked39 : test 0x1381 0x80 = true := by
  decide +kernel

def checked40 : test 0x1401 0x80 = true := by
  decide +kernel

def checked41 : test 0x1481 0x80 = true := by
  decide +kernel

def checked42 : test 0x1501 0x80 = true := by
  decide +kernel

def checked43 : test 0x1581 0x80 = true := by
  decide +kernel

def checked44 : test 0x1601 0x80 = true := by
  decide +kernel

def checked45 : test 0x1681 0x80 = true := by
  decide +kernel

def checked46 : test 0x1701 0x80 = true := by
  decide +kernel

def checked47 : test 0x1781 0x80 = true := by
  decide +kernel

def checked48 : test 0x1801 0x80 = true := by
  decide +kernel

def checked49 : test 0x1881 0x80 = true := by
  decide +kernel

def checked50 : test 0x1901 0x80 = true := by
  decide +kernel

def checked51 : test 0x1981 0x80 = true := by
  decide +kernel

def checked52 : test 0x1a01 0x80 = true := by
  decide +kernel

def checked53 : test 0x1a81 0x80 = true := by
  decide +kernel

def checked54 : test 0x1b01 0x80 = true := by
  decide +kernel

def checked55 : test 0x1b81 0x80 = true := by
  decide +kernel

def checked56 : test 0x1c01 0x80 = true := by
  decide +kernel

def checked57 : test 0x1c81 0x80 = true := by
  decide +kernel

def checked58 : test 0x1d01 0x80 = true := by
  decide +kernel

def checked59 : test 0x1d81 0x80 = true := by
  decide +kernel

def checked60 : test 0x1e01 0x80 = true := by
  decide +kernel

def checked61 : test 0x1e81 0x80 = true := by
  decide +kernel

def checked62 : test 0x1f01 0x80 = true := by
  decide +kernel

def checked63 : test 0x1f81 0x80 = true := by
  decide +kernel

def checked64 : test 0x2001 0x80 = true := by
  decide +kernel

def checked65 : test 0x2081 0x80 = true := by
  decide +kernel

def checked66 : test 0x2101 0x80 = true := by
  decide +kernel

def checked67 : test 0x2181 0x67 = true := by
  decide +kernel

def checkedRange0 : ∀ i : Nat, 0 ≤ i → i < 32 → test (1 + 0x80 * i) (min 0x80 (0x21e7 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked0
  · exact checked1
  · exact checked2
  · exact checked3
  · exact checked4
  · exact checked5
  · exact checked6
  · exact checked7
  · exact checked8
  · exact checked9
  · exact checked10
  · exact checked11
  · exact checked12
  · exact checked13
  · exact checked14
  · exact checked15
  · exact checked16
  · exact checked17
  · exact checked18
  · exact checked19
  · exact checked20
  · exact checked21
  · exact checked22
  · exact checked23
  · exact checked24
  · exact checked25
  · exact checked26
  · exact checked27
  · exact checked28
  · exact checked29
  · exact checked30
  · exact checked31

def checkedRange32 : ∀ i : Nat, 32 ≤ i → i < 64 → test (1 + 0x80 * i) (min 0x80 (0x21e7 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked32
  · exact checked33
  · exact checked34
  · exact checked35
  · exact checked36
  · exact checked37
  · exact checked38
  · exact checked39
  · exact checked40
  · exact checked41
  · exact checked42
  · exact checked43
  · exact checked44
  · exact checked45
  · exact checked46
  · exact checked47
  · exact checked48
  · exact checked49
  · exact checked50
  · exact checked51
  · exact checked52
  · exact checked53
  · exact checked54
  · exact checked55
  · exact checked56
  · exact checked57
  · exact checked58
  · exact checked59
  · exact checked60
  · exact checked61
  · exact checked62
  · exact checked63

def checkedRange64 : ∀ i : Nat, 64 ≤ i → i < 68 → test (1 + 0x80 * i) (min 0x80 (0x21e7 - 0x80 * i)) = true := by
  intro i hlo hhi
  interval_cases i
  · exact checked64
  · exact checked65
  · exact checked66
  · exact checked67

def checkedAll : ∀ i : Nat, 0 ≤ i → i < 68 → test (1 + 0x80 * i) (min 0x80 (0x21e7 - 0x80 * i)) = true :=
  (Bounty.policyIntervalJoin _ 0 32 68
  checkedRange0
  (Bounty.policyIntervalJoin _ 32 64 68
  checkedRange32
  checkedRange64))

def checked (i : Fin 68) :
    test (1 + 0x80 * i.val)
      (min 0x80 (0x21e7 - 0x80 * i.val)) = true := by
  exact checkedAll i.val (Nat.zero_le _) i.isLt

def covers (P : Nat → Prop)
    (hs : ∀ k, k < 4 → ∀ i, i < limits k → P (targets k i))
    (cid : Nat) (hp : 0 < cid) (hi : cid < 0x21e8) : P cid := by
  have hb : (cid - 1) / 0x80 < 68 := by omega
  have hw : (cid - 1) % 0x80 < min 0x80 (0x21e7 - 0x80 * ((cid - 1) / 0x80)) := by omega
  have h := checkBlock_sound P limits targets hs records (1 + 0x80 * ((cid - 1) / 0x80))
    (min 0x80 (0x21e7 - 0x80 * ((cid - 1) / 0x80)))
    (checked ⟨(cid - 1) / 0x80, hb⟩) ((cid - 1) % 0x80) hw
  have hid : 1 + 0x80 * ((cid - 1) / 0x80) + (cid - 1) % 0x80 = cid := by omega
  simpa only [hid] using h
def covers_original (P : Nat → Prop)
    (hs : ∀ k, k < 4 → ∀ i, i < PolicyInitialCoverage1.limits k → P (PolicyInitialCoverage1.targets k i))
    (cid : Nat) (hp : 0 < cid) (hi : cid < 0x21e8) : P cid := by
  apply covers P ?_ cid hp hi
  intro k hk i hi
  rw [targets_eq]
  exact hs k hk i hi

end PolicyInitialFastCoverage1

end PolicySubmissionPart64

/- Component PolicySharedUnitFixedTrace1; SHA256 1f3f2c3a5ed28fff0fcd1e3743ac5257b0bc481dc00acee815cd388a8c461d13. -/
section PolicySubmissionPart65
/- Complete ordinary kernel replay with shared units and fixed15 hints. -/
namespace Bounty

def policySharedUnitFixed1Check (lo hi : Nat) : Bool := policyBitActionIntervalGood policySharedUnitFixed1Db policySharedUnitFixed1Hints lo hi

def policySharedUnitFixed1_check8680 : policySharedUnitFixed1Check 0x21e8 0x2208 = true := by
  decide +kernel

def policySharedUnitFixed1_range8680_8712 : ∀ i, 0x21e8 ≤ i → i < 0x2208 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8680


def policySharedUnitFixed1_check8712 : policySharedUnitFixed1Check 0x2208 0x2228 = true := by
  decide +kernel

def policySharedUnitFixed1_range8712_8744 : ∀ i, 0x2208 ≤ i → i < 0x2228 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8712


def policySharedUnitFixed1_check8744 : policySharedUnitFixed1Check 0x2228 0x2248 = true := by
  decide +kernel

def policySharedUnitFixed1_range8744_8776 : ∀ i, 0x2228 ≤ i → i < 0x2248 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8744


def policySharedUnitFixed1_check8776 : policySharedUnitFixed1Check 0x2248 0x2268 = true := by
  decide +kernel

def policySharedUnitFixed1_range8776_8808 : ∀ i, 0x2248 ≤ i → i < 0x2268 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8776


def policySharedUnitFixed1_check8808 : policySharedUnitFixed1Check 0x2268 0x2288 = true := by
  decide +kernel

def policySharedUnitFixed1_range8808_8840 : ∀ i, 0x2268 ≤ i → i < 0x2288 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8808


def policySharedUnitFixed1_check8840 : policySharedUnitFixed1Check 0x2288 0x22a8 = true := by
  decide +kernel

def policySharedUnitFixed1_range8840_8872 : ∀ i, 0x2288 ≤ i → i < 0x22a8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8840


def policySharedUnitFixed1_check8872 : policySharedUnitFixed1Check 0x22a8 0x22c8 = true := by
  decide +kernel

def policySharedUnitFixed1_range8872_8904 : ∀ i, 0x22a8 ≤ i → i < 0x22c8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8872


def policySharedUnitFixed1_check8904 : policySharedUnitFixed1Check 0x22c8 0x22e8 = true := by
  decide +kernel

def policySharedUnitFixed1_range8904_8936 : ∀ i, 0x22c8 ≤ i → i < 0x22e8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8904


def policySharedUnitFixed1_check8936 : policySharedUnitFixed1Check 0x22e8 0x2308 = true := by
  decide +kernel

def policySharedUnitFixed1_range8936_8968 : ∀ i, 0x22e8 ≤ i → i < 0x2308 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8936


def policySharedUnitFixed1_check8968 : policySharedUnitFixed1Check 0x2308 0x2328 = true := by
  decide +kernel

def policySharedUnitFixed1_range8968_9000 : ∀ i, 0x2308 ≤ i → i < 0x2328 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check8968


def policySharedUnitFixed1_check9000 : policySharedUnitFixed1Check 0x2328 0x2348 = true := by
  decide +kernel

def policySharedUnitFixed1_range9000_9032 : ∀ i, 0x2328 ≤ i → i < 0x2348 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9000


def policySharedUnitFixed1_check9032 : policySharedUnitFixed1Check 0x2348 0x2368 = true := by
  decide +kernel

def policySharedUnitFixed1_range9032_9064 : ∀ i, 0x2348 ≤ i → i < 0x2368 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9032


def policySharedUnitFixed1_check9064 : policySharedUnitFixed1Check 0x2368 0x2388 = true := by
  decide +kernel

def policySharedUnitFixed1_range9064_9096 : ∀ i, 0x2368 ≤ i → i < 0x2388 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9064


def policySharedUnitFixed1_check9096 : policySharedUnitFixed1Check 0x2388 0x23a8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9096_9128 : ∀ i, 0x2388 ≤ i → i < 0x23a8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9096


def policySharedUnitFixed1_check9128 : policySharedUnitFixed1Check 0x23a8 0x23c8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9128_9160 : ∀ i, 0x23a8 ≤ i → i < 0x23c8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9128


def policySharedUnitFixed1_check9160 : policySharedUnitFixed1Check 0x23c8 0x23e8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9160_9192 : ∀ i, 0x23c8 ≤ i → i < 0x23e8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9160


def policySharedUnitFixed1_check9192 : policySharedUnitFixed1Check 0x23e8 0x2408 = true := by
  decide +kernel

def policySharedUnitFixed1_range9192_9224 : ∀ i, 0x23e8 ≤ i → i < 0x2408 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9192


def policySharedUnitFixed1_check9224 : policySharedUnitFixed1Check 0x2408 0x2428 = true := by
  decide +kernel

def policySharedUnitFixed1_range9224_9256 : ∀ i, 0x2408 ≤ i → i < 0x2428 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9224


def policySharedUnitFixed1_check9256 : policySharedUnitFixed1Check 0x2428 0x2448 = true := by
  decide +kernel

def policySharedUnitFixed1_range9256_9288 : ∀ i, 0x2428 ≤ i → i < 0x2448 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9256


def policySharedUnitFixed1_check9288 : policySharedUnitFixed1Check 0x2448 0x2468 = true := by
  decide +kernel

def policySharedUnitFixed1_range9288_9320 : ∀ i, 0x2448 ≤ i → i < 0x2468 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9288


def policySharedUnitFixed1_check9320 : policySharedUnitFixed1Check 0x2468 0x2488 = true := by
  decide +kernel

def policySharedUnitFixed1_range9320_9352 : ∀ i, 0x2468 ≤ i → i < 0x2488 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9320


def policySharedUnitFixed1_check9352 : policySharedUnitFixed1Check 0x2488 0x24a8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9352_9384 : ∀ i, 0x2488 ≤ i → i < 0x24a8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9352


def policySharedUnitFixed1_check9384 : policySharedUnitFixed1Check 0x24a8 0x24c8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9384_9416 : ∀ i, 0x24a8 ≤ i → i < 0x24c8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9384


def policySharedUnitFixed1_check9416 : policySharedUnitFixed1Check 0x24c8 0x24e8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9416_9448 : ∀ i, 0x24c8 ≤ i → i < 0x24e8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9416


def policySharedUnitFixed1_check9448 : policySharedUnitFixed1Check 0x24e8 0x2508 = true := by
  decide +kernel

def policySharedUnitFixed1_range9448_9480 : ∀ i, 0x24e8 ≤ i → i < 0x2508 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9448


def policySharedUnitFixed1_check9480 : policySharedUnitFixed1Check 0x2508 0x2528 = true := by
  decide +kernel

def policySharedUnitFixed1_range9480_9512 : ∀ i, 0x2508 ≤ i → i < 0x2528 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9480


def policySharedUnitFixed1_check9512 : policySharedUnitFixed1Check 0x2528 0x2548 = true := by
  decide +kernel

def policySharedUnitFixed1_range9512_9544 : ∀ i, 0x2528 ≤ i → i < 0x2548 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9512


def policySharedUnitFixed1_check9544 : policySharedUnitFixed1Check 0x2548 0x2568 = true := by
  decide +kernel

def policySharedUnitFixed1_range9544_9576 : ∀ i, 0x2548 ≤ i → i < 0x2568 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9544


def policySharedUnitFixed1_check9576 : policySharedUnitFixed1Check 0x2568 0x2588 = true := by
  decide +kernel

def policySharedUnitFixed1_range9576_9608 : ∀ i, 0x2568 ≤ i → i < 0x2588 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9576


def policySharedUnitFixed1_check9608 : policySharedUnitFixed1Check 0x2588 0x25a8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9608_9640 : ∀ i, 0x2588 ≤ i → i < 0x25a8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9608


def policySharedUnitFixed1_check9640 : policySharedUnitFixed1Check 0x25a8 0x25c8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9640_9672 : ∀ i, 0x25a8 ≤ i → i < 0x25c8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9640


def policySharedUnitFixed1_check9672 : policySharedUnitFixed1Check 0x25c8 0x25e8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9672_9704 : ∀ i, 0x25c8 ≤ i → i < 0x25e8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9672


def policySharedUnitFixed1_check9704 : policySharedUnitFixed1Check 0x25e8 0x2608 = true := by
  decide +kernel

def policySharedUnitFixed1_range9704_9736 : ∀ i, 0x25e8 ≤ i → i < 0x2608 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9704


def policySharedUnitFixed1_check9736 : policySharedUnitFixed1Check 0x2608 0x2628 = true := by
  decide +kernel

def policySharedUnitFixed1_range9736_9768 : ∀ i, 0x2608 ≤ i → i < 0x2628 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9736


def policySharedUnitFixed1_check9768 : policySharedUnitFixed1Check 0x2628 0x2648 = true := by
  decide +kernel

def policySharedUnitFixed1_range9768_9800 : ∀ i, 0x2628 ≤ i → i < 0x2648 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9768


def policySharedUnitFixed1_check9800 : policySharedUnitFixed1Check 0x2648 0x2668 = true := by
  decide +kernel

def policySharedUnitFixed1_range9800_9832 : ∀ i, 0x2648 ≤ i → i < 0x2668 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9800


def policySharedUnitFixed1_check9832 : policySharedUnitFixed1Check 0x2668 0x2688 = true := by
  decide +kernel

def policySharedUnitFixed1_range9832_9864 : ∀ i, 0x2668 ≤ i → i < 0x2688 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9832


def policySharedUnitFixed1_check9864 : policySharedUnitFixed1Check 0x2688 0x26a8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9864_9896 : ∀ i, 0x2688 ≤ i → i < 0x26a8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9864


def policySharedUnitFixed1_check9896 : policySharedUnitFixed1Check 0x26a8 0x26c8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9896_9928 : ∀ i, 0x26a8 ≤ i → i < 0x26c8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9896


def policySharedUnitFixed1_check9928 : policySharedUnitFixed1Check 0x26c8 0x26e8 = true := by
  decide +kernel

def policySharedUnitFixed1_range9928_9960 : ∀ i, 0x26c8 ≤ i → i < 0x26e8 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9928


def policySharedUnitFixed1_check9960 : policySharedUnitFixed1Check 0x26e8 0x2708 = true := by
  decide +kernel

def policySharedUnitFixed1_range9960_9992 : ∀ i, 0x26e8 ≤ i → i < 0x2708 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9960


def policySharedUnitFixed1_check9992 : policySharedUnitFixed1Check 0x2708 0x2721 = true := by
  decide +kernel

def policySharedUnitFixed1_range9992_10017 : ∀ i, 0x2708 ≤ i → i < 0x2721 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check9992


def policySharedUnitFixed1_check10017 : policySharedUnitFixed1Check 0x2721 0x2732 = true := by
  decide +kernel

def policySharedUnitFixed1_range10017_10034 : ∀ i, 0x2721 ≤ i → i < 0x2732 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check10017


def policySharedUnitFixed1_check10034 : policySharedUnitFixed1Check 0x2732 0x2752 = true := by
  decide +kernel

def policySharedUnitFixed1_range10034_10066 : ∀ i, 0x2732 ≤ i → i < 0x2752 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check10034


def policySharedUnitFixed1_check10066 : policySharedUnitFixed1Check 0x2752 0x2772 = true := by
  decide +kernel

def policySharedUnitFixed1_range10066_10098 : ∀ i, 0x2752 ≤ i → i < 0x2772 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check10066


def policySharedUnitFixed1_check10098 : policySharedUnitFixed1Check 0x2772 0x2792 = true := by
  decide +kernel

def policySharedUnitFixed1_range10098_10130 : ∀ i, 0x2772 ≤ i → i < 0x2792 → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check10098


def policySharedUnitFixed1_check10130 : policySharedUnitFixed1Check 0x2792 0x279b = true := by
  decide +kernel

def policySharedUnitFixed1_range10130_10139 : ∀ i, 0x2792 ≤ i → i < 0x279b → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  policyBitActionIntervalGood_sound _ _ _ _ policySharedUnitFixed1_check10130


def policySharedUnitFixed1_all_checked : ∀ i, 0x21e8 ≤ i → i < 0x279b → policyBitActionGood policySharedUnitFixed1Db i (policySharedUnitFixed1Hints i) = true :=
  (policyIntervalJoin _ 0x21e8 0x24c8 0x279b
  (policyIntervalJoin _ 0x21e8 0x2348 0x24c8
  (policyIntervalJoin _ 0x21e8 0x2288 0x2348
  (policyIntervalJoin _ 0x21e8 0x2228 0x2288
  (policyIntervalJoin _ 0x21e8 0x2208 0x2228
  policySharedUnitFixed1_range8680_8712
  policySharedUnitFixed1_range8712_8744)
  (policyIntervalJoin _ 0x2228 0x2248 0x2288
  policySharedUnitFixed1_range8744_8776
  (policyIntervalJoin _ 0x2248 0x2268 0x2288
  policySharedUnitFixed1_range8776_8808
  policySharedUnitFixed1_range8808_8840)))
  (policyIntervalJoin _ 0x2288 0x22e8 0x2348
  (policyIntervalJoin _ 0x2288 0x22a8 0x22e8
  policySharedUnitFixed1_range8840_8872
  (policyIntervalJoin _ 0x22a8 0x22c8 0x22e8
  policySharedUnitFixed1_range8872_8904
  policySharedUnitFixed1_range8904_8936))
  (policyIntervalJoin _ 0x22e8 0x2308 0x2348
  policySharedUnitFixed1_range8936_8968
  (policyIntervalJoin _ 0x2308 0x2328 0x2348
  policySharedUnitFixed1_range8968_9000
  policySharedUnitFixed1_range9000_9032))))
  (policyIntervalJoin _ 0x2348 0x2408 0x24c8
  (policyIntervalJoin _ 0x2348 0x23a8 0x2408
  (policyIntervalJoin _ 0x2348 0x2368 0x23a8
  policySharedUnitFixed1_range9032_9064
  (policyIntervalJoin _ 0x2368 0x2388 0x23a8
  policySharedUnitFixed1_range9064_9096
  policySharedUnitFixed1_range9096_9128))
  (policyIntervalJoin _ 0x23a8 0x23c8 0x2408
  policySharedUnitFixed1_range9128_9160
  (policyIntervalJoin _ 0x23c8 0x23e8 0x2408
  policySharedUnitFixed1_range9160_9192
  policySharedUnitFixed1_range9192_9224)))
  (policyIntervalJoin _ 0x2408 0x2468 0x24c8
  (policyIntervalJoin _ 0x2408 0x2428 0x2468
  policySharedUnitFixed1_range9224_9256
  (policyIntervalJoin _ 0x2428 0x2448 0x2468
  policySharedUnitFixed1_range9256_9288
  policySharedUnitFixed1_range9288_9320))
  (policyIntervalJoin _ 0x2468 0x2488 0x24c8
  policySharedUnitFixed1_range9320_9352
  (policyIntervalJoin _ 0x2488 0x24a8 0x24c8
  policySharedUnitFixed1_range9352_9384
  policySharedUnitFixed1_range9384_9416)))))
  (policyIntervalJoin _ 0x24c8 0x2648 0x279b
  (policyIntervalJoin _ 0x24c8 0x2588 0x2648
  (policyIntervalJoin _ 0x24c8 0x2528 0x2588
  (policyIntervalJoin _ 0x24c8 0x24e8 0x2528
  policySharedUnitFixed1_range9416_9448
  (policyIntervalJoin _ 0x24e8 0x2508 0x2528
  policySharedUnitFixed1_range9448_9480
  policySharedUnitFixed1_range9480_9512))
  (policyIntervalJoin _ 0x2528 0x2548 0x2588
  policySharedUnitFixed1_range9512_9544
  (policyIntervalJoin _ 0x2548 0x2568 0x2588
  policySharedUnitFixed1_range9544_9576
  policySharedUnitFixed1_range9576_9608)))
  (policyIntervalJoin _ 0x2588 0x25e8 0x2648
  (policyIntervalJoin _ 0x2588 0x25a8 0x25e8
  policySharedUnitFixed1_range9608_9640
  (policyIntervalJoin _ 0x25a8 0x25c8 0x25e8
  policySharedUnitFixed1_range9640_9672
  policySharedUnitFixed1_range9672_9704))
  (policyIntervalJoin _ 0x25e8 0x2608 0x2648
  policySharedUnitFixed1_range9704_9736
  (policyIntervalJoin _ 0x2608 0x2628 0x2648
  policySharedUnitFixed1_range9736_9768
  policySharedUnitFixed1_range9768_9800))))
  (policyIntervalJoin _ 0x2648 0x2708 0x279b
  (policyIntervalJoin _ 0x2648 0x26a8 0x2708
  (policyIntervalJoin _ 0x2648 0x2668 0x26a8
  policySharedUnitFixed1_range9800_9832
  (policyIntervalJoin _ 0x2668 0x2688 0x26a8
  policySharedUnitFixed1_range9832_9864
  policySharedUnitFixed1_range9864_9896))
  (policyIntervalJoin _ 0x26a8 0x26c8 0x2708
  policySharedUnitFixed1_range9896_9928
  (policyIntervalJoin _ 0x26c8 0x26e8 0x2708
  policySharedUnitFixed1_range9928_9960
  policySharedUnitFixed1_range9960_9992)))
  (policyIntervalJoin _ 0x2708 0x2752 0x279b
  (policyIntervalJoin _ 0x2708 0x2721 0x2752
  policySharedUnitFixed1_range9992_10017
  (policyIntervalJoin _ 0x2721 0x2732 0x2752
  policySharedUnitFixed1_range10017_10034
  policySharedUnitFixed1_range10034_10066))
  (policyIntervalJoin _ 0x2752 0x2772 0x279b
  policySharedUnitFixed1_range10066_10098
  (policyIntervalJoin _ 0x2772 0x2792 0x279b
  policySharedUnitFixed1_range10098_10130
  policySharedUnitFixed1_range10130_10139))))))

def policySharedUnit1_false_compact (P : Nat → Prop)
    (hi : ∀ i, 0 < i → i < 0x21e8 → policySignedClauseHolds P (policyFixedCompact1Db i)) : False := by
  apply policyBitGraph_false policySharedUnitFixed1Db 0x21e8 0x279b 0x279a policySharedUnitFixed1Hints P
    policySharedUnitFixed1_all_checked ?_ (by decide) (by decide) policySharedUnitFixed1_root_empty
  intro i hip hib
  simpa only [policySharedUnitFixed1Db, if_pos hib] using hi i hip hib

end Bounty

end PolicySubmissionPart65

/- Component PolicyCachedHotClosureFalse; SHA256 1f992bbee3b767c02029cd1ccf49dfce363d77f6377ceb57469921ca388ff90b. -/
section PolicySubmissionPart66
/- Complete finite contradiction, conditional only on asserted input facts. -/
namespace PolicyCachedHotClosure
open ClosureSemantics Bounty

def contradiction0 (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData0.program) input values)
    (ha : ∀ i : Nat, i < 36 →
      policySignedClauseHolds (fun v => (values (v - 1)).b = true)
        (policyMappedDatabase0 ((PolicyAssertedPacked0.records i).headD 0))) : False := by
  apply policySharedUnit0_false_compact
    (fun v => (values (policyFixedCompact0Rename v - 1)).b = true)
  intro cid hp hi
  apply policyMappedDatabase0_model (fun v => (values (v - 1)).b = true) cid
  apply PolicyInitialFastCoverage0.covers_original
    (fun j => policySignedClauseHolds (fun v => (values (v - 1)).b = true) (policyMappedDatabase0 j))
    ?_ cid hp hi
  intro k hk i hi
  interval_cases k
  · exact PolicyMappedCircuitChecked0.sound input values he i hi
  · exact PolicyMappedRewriteParametricChecked0.sound input values he i hi
  · exact PolicyCachedHotArithmeticChecked0.sound input values he i hi
  · exact ha i hi

def contradiction1 (input values : Valuation)
    (he : Equations (boundedProgram ClosureFixedWidthData1.program) input values)
    (ha : ∀ i : Nat, i < 34 →
      policySignedClauseHolds (fun v => (values (v - 1)).b = true)
        (policyMappedDatabase1 ((PolicyAssertedPacked1.records i).headD 0))) : False := by
  apply policySharedUnit1_false_compact
    (fun v => (values (policyFixedCompact1Rename v - 1)).b = true)
  intro cid hp hi
  apply policyMappedDatabase1_model (fun v => (values (v - 1)).b = true) cid
  apply PolicyInitialFastCoverage1.covers_original
    (fun j => policySignedClauseHolds (fun v => (values (v - 1)).b = true) (policyMappedDatabase1 j))
    ?_ cid hp hi
  intro k hk i hi
  interval_cases k
  · exact PolicyMappedCircuitChecked1.sound input values he i hi
  · exact PolicyMappedRewriteParametricChecked1.sound input values he i hi
  · exact PolicyCachedHotArithmeticChecked1.sound input values he i hi
  · exact ha i hi

end PolicyCachedHotClosure

end PolicySubmissionPart66

/- Component ClosureAssertedCheck; SHA256 b1b31b6c0c15606432c29c9ab888a88faa693174539af829c27a55b07c55227d. -/
section PolicySubmissionPart67
/- A checked unit clause connects a semantic input fact to the SAT database. -/
namespace ClosureAssertedCheck
open ClosureSemantics Bounty

def checkEntry (clauses : Nat → List Int) (record : List Nat) : Bool :=
  decide (clauses (record.headD 0) = [((record.getD 1 0 + 1 : Nat) : Int)])

def checkEntry_sound (clauses : Nat → List Int) (record : List Nat)
    (values : Valuation) (hc : checkEntry clauses record = true)
    (ht : (values (record.getD 1 0)).b = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (clauses (record.headD 0)) := by
  have hshape : clauses (record.headD 0) = [((record.getD 1 0 + 1 : Nat) : Int)] :=
    of_decide_eq_true hc
  rw [hshape]
  refine ⟨((record.getD 1 0 + 1 : Nat) : Int), by simp, ?_⟩
  apply (ClosureCircuit.signed_pos (fun v => (values (v - 1)).b)
    (Nat.succ_pos (record.getD 1 0))).mpr
  simpa using ht

def checkBlock (clauses : Nat → List Int) (records : Nat → List Nat)
    (start count : Nat) : Bool :=
  (List.range count).all fun i => checkEntry clauses (records (start + i))

def checkBlock_sound (clauses : Nat → List Int) (records : Nat → List Nat)
    (start count : Nat) (hc : checkBlock clauses records start count = true)
    (i : Nat) (hi : i < count) (values : Valuation)
    (ht : (values ((records (start + i)).getD 1 0)).b = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (clauses ((records (start + i)).headD 0)) := by
  have h : ∀ j ∈ List.range count, checkEntry clauses (records (start + j)) = true := by
    simpa only [checkBlock, List.all_eq_true] using hc
  exact checkEntry_sound clauses (records (start + i)) values
    (h i (List.mem_range.mpr hi)) ht

end ClosureAssertedCheck

end PolicySubmissionPart67

/- Component PolicyMappedAssertedChecked0; SHA256 7618dd4aa58eb215c6dc6f4d5d0cb197963c993bd2295d241dd644c16f25ffa3. -/
section PolicySubmissionPart68
namespace PolicyMappedAssertedChecked0
open ClosureSemantics Bounty ClosureAssertedCheck

def test (start count : Nat) : Bool :=
  checkBlock policyMappedDatabase0 PolicyAssertedPacked0.records start count

def checked0 : test 0 16 = true := by
  decide +kernel

def checked1 : test 16 16 = true := by
  decide +kernel

def checked2 : test 32 4 = true := by
  decide +kernel

def checked (i : Fin 3) :
    test (16*i.val) (min 16 (36-16*i.val)) = true := by
  fin_cases i
  · exact checked0
  · exact checked1
  · exact checked2

def sound (values : Valuation) (i : Nat) (hi : i < 36)
    (ht : (values ((PolicyAssertedPacked0.records i).getD 1 0)).b = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase0 ((PolicyAssertedPacked0.records i).headD 0)) := by
  have hb : i / 16 < 3 := by omega
  have hw : i % 16 < min 16 (36 - 16 * (i / 16)) := by omega
  have hid : 16 * (i / 16) + i % 16 = i := by omega
  have h := checkBlock_sound policyMappedDatabase0 PolicyAssertedPacked0.records
    (16 * (i / 16)) (min 16 (36 - 16 * (i / 16)))
    (checked ⟨i / 16, hb⟩) (i % 16) hw values (by simpa only [hid] using ht)
  simpa only [hid] using h

end PolicyMappedAssertedChecked0

end PolicySubmissionPart68

/- Component PolicyMappedAssertedChecked1; SHA256 6882df2edffc9ff33352184dabb3dc0de7d2b0bbcb442d76b038eb0085bab67d. -/
section PolicySubmissionPart69
namespace PolicyMappedAssertedChecked1
open ClosureSemantics Bounty ClosureAssertedCheck

def test (start count : Nat) : Bool :=
  checkBlock policyMappedDatabase1 PolicyAssertedPacked1.records start count

def checked0 : test 0 16 = true := by
  decide +kernel

def checked1 : test 16 16 = true := by
  decide +kernel

def checked2 : test 32 2 = true := by
  decide +kernel

def checked (i : Fin 3) :
    test (16*i.val) (min 16 (34-16*i.val)) = true := by
  fin_cases i
  · exact checked0
  · exact checked1
  · exact checked2

def sound (values : Valuation) (i : Nat) (hi : i < 34)
    (ht : (values ((PolicyAssertedPacked1.records i).getD 1 0)).b = true) :
    policySignedClauseHolds (fun v => (values (v - 1)).b = true)
      (policyMappedDatabase1 ((PolicyAssertedPacked1.records i).headD 0)) := by
  have hb : i / 16 < 3 := by omega
  have hw : i % 16 < min 16 (34 - 16 * (i / 16)) := by omega
  have hid : 16 * (i / 16) + i % 16 = i := by omega
  have h := checkBlock_sound policyMappedDatabase1 PolicyAssertedPacked1.records
    (16 * (i / 16)) (min 16 (34 - 16 * (i / 16)))
    (checked ⟨i / 16, hb⟩) (i % 16) hw values (by simpa only [hid] using ht)
  simpa only [hid] using h

end PolicyMappedAssertedChecked1

end PolicySubmissionPart69

/- Component ClosureInputModel; SHA256 3aaafcaf11f9c588d0552d8a0dda8bec88297a92528ac1d84f674aafb612ba85. -/
section PolicySubmissionPart70
/- Input slots and local semantic bridges for the original assertion prefix. -/

namespace ClosureInputModel
open ClosureSemantics

noncomputable def inputValuation (X Y : Rat) (p : Nat → Prop) (r : Nat → Rat) : Valuation :=
  fun slot =>
    if slot = 0 then ratValue X
    else if slot = 1 then ratValue Y
    else if slot % 2 = 0 then
      boolValue (@decide (p ((slot - 2) / 2)) (Classical.propDecidable _))
    else ratValue (r ((slot - 3) / 2))

def programModel_eq_raw (raw : Nat → Node) (input : Valuation) (i : Nat)
    (h : ∀ j ∈ (raw i).children, j < i) :
    programModel raw input i = evalNode input (programModel raw input) (raw i) := by
  simpa only [boundedProgram_eq raw i h] using programModel_equations raw input i

def programModel_agrees_below (raw : Nat → Node) (input values : Valuation) (N : Nat)
    (h : ∀ i < N, values i = evalNode input values (boundedProgram raw i)) :
    ∀ i < N, programModel raw input i = values i := by
  intro i
  induction i using Nat.strong_induction_on with
  | h i ih =>
    intro hi
    calc
      programModel raw input i = evalNode input (programModel raw input) (boundedProgram raw i) :=
        programModel_equations raw input i
      _ = evalNode input values (boundedProgram raw i) := by
        apply evalNode_congr
        intro j hj
        have hji := boundedProgram_children raw i j hj
        exact ih j hji (hji.trans hi)
      _ = values i := (h i hi).symm

end ClosureInputModel

end PolicySubmissionPart70

/- Component ClosurePrefixAdapter; SHA256 7955e120dba069fa5b9136f79741f570bbedf0ed6857d55001eaa9978a189e4a. -/
section PolicySubmissionPart71
/- A short-record prefix adapter, whose records can be checked against packed data. -/
namespace ClosurePrefixAdapter
open ClosureSemantics ClosurePackedProgram PackedNatTable

abbrev Pattern := Op × List Nat

def interval_from_fin {P : Nat → Prop} (a n : Nat)
    (h : ∀ i : Fin n, P (a + i.val)) : ∀ i, a ≤ i → i < a+n → P i := by
  intro i ha hi
  simpa only [Nat.add_sub_of_le ha] using h ⟨i-a, by omega⟩

def interval_join {P : Nat → Prop} (a b c : Nat)
    (left : ∀ i, a ≤ i → i < b → P i)
    (right : ∀ i, b ≤ i → i < c → P i) : ∀ i, a ≤ i → i < c → P i := by
  intro i ha hc
  by_cases hb : i < b
  · exact left i ha hb
  · exact right i (by omega) hc

def zigzag : Int → Nat
  | .ofNat n => 2 * n
  | .negSucc n => 2 * n + 1

def Pattern.record (p : Pattern) : List Nat :=
  match p.1 with
  | .input k => [2,k]
  | .qConst q => [3,zigzag q.num,q.den]
  | .zConst z => [4,zigzag z]
  | .bConst false => [0]
  | .bConst true => [1]
  | .alias => 5 :: p.2
  | .bNot => 6 :: p.2
  | .bOr => 7 :: p.2
  | .bAnd => 8 :: p.2
  | .bEq => 9 :: p.2
  | .ite => 10 :: p.2
  | .qEq => 11 :: p.2
  | .zEq => 12 :: p.2
  | .qLe => 13 :: p.2
  | .zLe => 14 :: p.2
  | .qLt => 15 :: p.2
  | .zLt => 16 :: p.2
  | .qAdd => 17 :: p.2
  | .zAdd => 18 :: p.2
  | .qMul => 19 :: p.2
  | .zMul => 20 :: p.2
  | .qNeg => 21 :: p.2
  | .zNeg => 22 :: p.2
  | .qSub => 23 :: p.2
  | .zSub => 24 :: p.2
  | .qDiv => 25 :: p.2

def Pattern.node (p : Pattern) (i : Nat) : Node :=
  match p.1 with
  | .input k => ⟨.input k, []⟩
  | .qConst q => ⟨.qConst q, []⟩
  | .zConst z => ⟨.zConst z, []⟩
  | .bConst b => ⟨.bConst b, []⟩
  | op => ⟨op, p.2.map (fun d => i - d)⟩

def indexAt (indices : Table Nat) (i : Nat) : Nat :=
  (indices.get 0 (i / 4) >>> (12 * (i % 4))) &&& 0xfff

def patternAt (dictionary : Table Pattern) (indices : Table Nat) (i : Nat) : Pattern :=
  dictionary.get ⟨.bConst false, []⟩ (indexAt indices i)

def program (dictionary : Table Pattern) (indices : Table Nat) (i : Nat) : Node :=
  (patternAt dictionary indices i).node i

def check (source : Nat → Node) (dictionary : Table Pattern) (indices : Table Nat)
    (N i : Nat) : Bool :=
  if 0 < indexAt indices i then
    (ClosurePattern.sameOp (source i).op (program dictionary indices i).op &&
      ((source i).children == (program dictionary indices i).children)) &&
      (program dictionary indices i).children.all
        (fun j => decide (j < N ∧ 0 < indexAt indices j))
  else true

def check_sound (source : Nat → Node) (dictionary : Table Pattern) (indices : Table Nat)
    (N i : Nat) (h : check source dictionary indices N i = true) (hi : 0 < indexAt indices i) :
    source i = program dictionary indices i ∧
      ∀ j ∈ (program dictionary indices i).children, j < N ∧ 0 < indexAt indices j := by
  simp only [check, if_pos hi, Bool.and_eq_true, List.all_eq_true, decide_eq_true_eq] at h
  have ho := ClosurePattern.sameOp_sound _ _ h.1.1
  have hc : (source i).children = (program dictionary indices i).children := by
    simpa using h.1.2
  refine ⟨?_, h.2⟩
  have he : source i = ⟨(source i).op, (source i).children⟩ := rfl
  rw [he, ho, hc]

def model_eq_on_raw (source target : Nat → Node) (input : Valuation) (N : Nat)
    (S : Nat → Prop)
    (hshape : ∀ i < N, S i → source i = target i)
    (hclosed : ∀ i < N, S i → ∀ j ∈ (target i).children, j < N ∧ S j) :
    ∀ i < N, S i → programModel source input i = programModel target input i := by
  intro i
  induction i using Nat.strong_induction_on with
  | h i ih =>
    intro hi hs
    rw [programModel_equations source input i, programModel_equations target input i]
    have hb : boundedProgram source i = boundedProgram target i := by
      unfold boundedProgram
      rw [hshape i hi hs]
    rw [hb]
    apply evalNode_congr
    intro j hj
    have hji := boundedProgram_children target i j hj
    have hjraw : j ∈ (target i).children := List.mem_of_mem_filter hj
    have hjc := hclosed i hi hs j hjraw
    exact ih j hji hjc.1 hjc.2

def checked_model_eq (source : Nat → Node) (dictionary : Table Pattern)
    (indices : Table Nat) (input : Valuation) (N : Nat)
    (h : ∀ i < N, check source dictionary indices N i = true) :
    ∀ i < N, 0 < indexAt indices i →
      programModel source input i = programModel (program dictionary indices) input i := by
  apply model_eq_on_raw source (program dictionary indices) input N (fun i => 0 < indexAt indices i)
  · intro i hi hs
    exact (check_sound source dictionary indices N i (h i hi) hs).1
  · intro i hi hs
    exact (check_sound source dictionary indices N i (h i hi) hs).2

end ClosurePrefixAdapter

end PolicySubmissionPart71

/- Component ClosurePrefixAdapterData; SHA256 a517da09d06a3a19f526e3971aa63d97bf8792658f79b62361ec41fc0fa2cb16. -/
section PolicySubmissionPart72
/- Shared short-record dictionary for the exact original input prefixes. -/
namespace ClosurePrefixAdapterData
open ClosurePrefixAdapter PackedNatTable

def dictionaryLLLLL : Table Pattern := .leaf #[
  ⟨.bConst false, []⟩,
  ⟨.qConst (1), []⟩,
  ⟨.qConst (4), []⟩,
  ⟨.qDiv, [2, 1]⟩,
  ⟨.input 0, []⟩,
  ⟨.qLt, [2, 1]⟩,
  ⟨.qLe, [2, 5]⟩,
  ⟨.qConst (3), []⟩,
  ⟨.qDiv, [7, 1]⟩,
  ⟨.input 1, []⟩,
  ⟨.qLe, [2, 10]⟩,
  ⟨.bConst false, []⟩,
  ⟨.qConst (5), []⟩,
  ⟨.qDiv, [3, 19]⟩,
  ⟨.qConst (0x1000), []⟩,
  ⟨.qDiv, [22, 1]⟩,
  ⟨.qMul, [1, 20]⟩,
  ⟨.qMul, [1, 23]⟩,
  ⟨.qConst (10), []⟩,
  ⟨.qConst (9), []⟩,
  ⟨.qConst (0x19a1), []⟩,
  ⟨.qDiv, [33, 1]⟩,
  ⟨.qMul, [1, 26]⟩,
  ⟨.qMul, [1, 29]⟩,
  ⟨.qDiv, [39, 34]⟩]

def dictionaryLLLLR : Table Pattern := .leaf #[
  ⟨.zConst (1), []⟩,
  ⟨.zConst (0), []⟩,
  ⟨.qConst (2), []⟩,
  ⟨.bConst true, []⟩,
  ⟨.input 37, []⟩,
  ⟨.input 36, []⟩,
  ⟨.qConst (0x88b), []⟩,
  ⟨.qDiv, [0xd5, 1]⟩,
  ⟨.qMul, [1, 0xce]⟩,
  ⟨.qMul, [1, 0xd1]⟩,
  ⟨.input 39, []⟩,
  ⟨.input 38, []⟩,
  ⟨.qConst (0x4c9), []⟩,
  ⟨.qDiv, [0x123, 1]⟩,
  ⟨.qLe, [0x10c, 1]⟩,
  ⟨.ite, [1, 0x10d, 0x10e]⟩,
  ⟨.qLe, [81, 5]⟩,
  ⟨.ite, [1, 82, 83]⟩,
  ⟨.input 41, []⟩,
  ⟨.input 40, []⟩,
  ⟨.qConst (0x36b), []⟩,
  ⟨.qDiv, [0x173, 1]⟩,
  ⟨.qConst (0x400), []⟩,
  ⟨.qDiv, [0x175, 1]⟩,
  ⟨.qMul, [1, 0x173]⟩,
  ⟨.qMul, [1, 0x176]⟩]

def dictionaryLLLL : Table Pattern := .branch 25 dictionaryLLLLL dictionaryLLLLR

def dictionaryLLLRL : Table Pattern := .leaf #[
  ⟨.qLe, [1, 5]⟩,
  ⟨.ite, [1, 2, 3]⟩,
  ⟨.qLe, [0xa5, 9]⟩,
  ⟨.ite, [1, 0xa6, 0xa7]⟩,
  ⟨.input 43, []⟩,
  ⟨.input 42, []⟩,
  ⟨.qConst (0x271), []⟩,
  ⟨.qDiv, [0x1c7, 1]⟩,
  ⟨.qLe, [81, 1]⟩,
  ⟨.qMul, [0x1b6, 1]⟩,
  ⟨.qLt, [4, 1]⟩,
  ⟨.qConst (0x2d9), []⟩,
  ⟨.qDiv, [0x1cd, 1]⟩,
  ⟨.qMul, [1, 0x1c6]⟩,
  ⟨.qMul, [1, 0x1c9]⟩,
  ⟨.qLe, [1, 9]⟩,
  ⟨.qMul, [0x1b3, 1]⟩,
  ⟨.qLe, [1, 12]⟩,
  ⟨.qMul, [0x1ac, 3]⟩,
  ⟨.qLt, [14, 1]⟩,
  ⟨.bAnd, [0x15d, 11, 3, 1]⟩,
  ⟨.ite, [1, 0x1ab, 0x1aa]⟩,
  ⟨.qConst (0xc35), []⟩,
  ⟨.qDiv, [0x1d9, 1]⟩,
  ⟨.qLe, [0x1c2, 1]⟩,
  ⟨.ite, [1, 0x1c3, 0x1c4]⟩]

def dictionaryLLLRR : Table Pattern := .leaf #[
  ⟨.qMul, [0x1ac, 1]⟩,
  ⟨.qLe, [1, 4]⟩,
  ⟨.bNot, [1]⟩,
  ⟨.qLe, [0x1bc, 6]⟩,
  ⟨.ite, [1, 0x1bd, 0x1be]⟩,
  ⟨.qMul, [0x1b1, 1]⟩,
  ⟨.bAnd, [6, 1]⟩,
  ⟨.ite, [1, 0x1b9, 0x1b8]⟩,
  ⟨.zSub, [15, 1]⟩,
  ⟨.zLe, [0x1ba, 1]⟩,
  ⟨.zEq, [2, 0x1bb]⟩,
  ⟨.qDiv, [14, 0x1b9]⟩,
  ⟨.ite, [13, 14, 1]⟩,
  ⟨.qDiv, [10, 0x1e5]⟩,
  ⟨.ite, [10, 11, 1]⟩,
  ⟨.qLe, [1, 3]⟩,
  ⟨.ite, [1, 4, 2]⟩,
  ⟨.qLt, [3, 5]⟩,
  ⟨.qDiv, [6, 0x1ef]⟩,
  ⟨.qLe, [5, 1]⟩,
  ⟨.ite, [1, 2, 6]⟩,
  ⟨.qDiv, [7, 0x1ed]⟩,
  ⟨.qLe, [1, 10]⟩,
  ⟨.ite, [1, 11, 2]⟩,
  ⟨.ite, [7, 4, 1]⟩,
  ⟨.ite, [15, 9, 1]⟩]

def dictionaryLLLR : Table Pattern := .branch 26 dictionaryLLLRL dictionaryLLLRR

def dictionaryLLL : Table Pattern := .branch 51 dictionaryLLLL dictionaryLLLR

def dictionaryLLRLL : Table Pattern := .leaf #[
  ⟨.qLe, [1, 53]⟩,
  ⟨.ite, [17, 32, 11]⟩,
  ⟨.qLe, [55, 1]⟩,
  ⟨.qLt, [56, 2]⟩,
  ⟨.ite, [20, 2, 1]⟩,
  ⟨.bAnd, [22, 5, 1]⟩,
  ⟨.bAnd, [33, 28]⟩,
  ⟨.ite, [1, 0x1d3, 0x1d2]⟩,
  ⟨.zSub, [41, 1]⟩,
  ⟨.zLe, [0x1d4, 1]⟩,
  ⟨.zEq, [2, 0x1d5]⟩,
  ⟨.qLe, [35, 40]⟩,
  ⟨.ite, [1, 41, 36]⟩,
  ⟨.qLt, [37, 42]⟩,
  ⟨.qDiv, [43, 0x205]⟩,
  ⟨.qLe, [39, 1]⟩,
  ⟨.ite, [1, 2, 40]⟩,
  ⟨.qDiv, [41, 0x203]⟩,
  ⟨.qLe, [1, 47]⟩,
  ⟨.ite, [1, 48, 2]⟩,
  ⟨.ite, [11, 9, 1]⟩,
  ⟨.qLe, [1, 75]⟩,
  ⟨.ite, [13, 54, 11]⟩,
  ⟨.qLe, [77, 1]⟩,
  ⟨.qLt, [78, 2]⟩]

def dictionaryLLRLR : Table Pattern := .leaf #[
  ⟨.ite, [16, 2, 1]⟩,
  ⟨.bAnd, [18, 5, 1]⟩,
  ⟨.ite, [79, 23, 1]⟩,
  ⟨.qConst (6), []⟩,
  ⟨.bEq, [0x1d4, 0x291]⟩,
  ⟨.qMul, [0x2a1, 0x1d7]⟩,
  ⟨.qMul, [0x67, 0x1d8]⟩,
  ⟨.ite, [3, 2, 1]⟩,
  ⟨.bEq, [0x1fa, 0x24e]⟩,
  ⟨.ite, [1, 38, 37]⟩,
  ⟨.input 24, []⟩,
  ⟨.input 25, []⟩,
  ⟨.qConst (0xf5), []⟩,
  ⟨.qDiv, [0x2dc, 1]⟩,
  ⟨.qConst (0x100), []⟩,
  ⟨.qDiv, [0x2de, 1]⟩,
  ⟨.qMul, [1, 0x2dc]⟩,
  ⟨.qMul, [1, 0x2df]⟩,
  ⟨.qMul, [0x2cf, 1]⟩,
  ⟨.qLt, [8, 1]⟩,
  ⟨.qLe, [0x116, 9]⟩,
  ⟨.ite, [1, 0x117, 0x118]⟩,
  ⟨.qMul, [0x2c8, 1]⟩,
  ⟨.qMul, [0x2c1, 3]⟩,
  ⟨.bAnd, [0x272, 7, 3, 1]⟩,
  ⟨.ite, [1, 0x2c0, 0x2bf]⟩]

def dictionaryLLRL : Table Pattern := .branch 25 dictionaryLLRLL dictionaryLLRLR

def dictionaryLLRRL : Table Pattern := .leaf #[
  ⟨.qMul, [0x2bd, 0x1c8]⟩,
  ⟨.qLe, [1, 0x1cb]⟩,
  ⟨.qMul, [0x2bf, 0x1c6]⟩,
  ⟨.qLe, [1, 0x1cd]⟩,
  ⟨.bAnd, [3, 1]⟩,
  ⟨.ite, [1, 0x2c6, 0x2c5]⟩,
  ⟨.zSub, [7, 1]⟩,
  ⟨.zLe, [0x2c7, 1]⟩,
  ⟨.qConst (0x1324), []⟩,
  ⟨.qDiv, [0x2f0, 1]⟩,
  ⟨.zEq, [4, 0x2ca]⟩,
  ⟨.qLe, [0x1cf, 0x1d3]⟩,
  ⟨.ite, [1, 0x1d4, 0x1d0]⟩,
  ⟨.qLt, [0x1d1, 0x1d5]⟩,
  ⟨.qDiv, [0x1d6, 0x2fa]⟩,
  ⟨.qLe, [0x1d3, 1]⟩,
  ⟨.ite, [1, 2, 0x1d4]⟩,
  ⟨.qDiv, [0x1d5, 0x2f8]⟩,
  ⟨.qLe, [1, 0x1da]⟩,
  ⟨.ite, [1, 0x1db, 2]⟩,
  ⟨.qLe, [1, 13]⟩,
  ⟨.ite, [1, 14, 2]⟩,
  ⟨.bEq, [0x1e4, 0x2f5]⟩,
  ⟨.qMul, [0x305, 0x1e7]⟩,
  ⟨.qMul, [0xcb, 0x1e8]⟩,
  ⟨.ite, [1, 6, 2]⟩]

def dictionaryLLRRR : Table Pattern := .leaf #[
  ⟨.qLe, [0x67, 1]⟩,
  ⟨.ite, [1, 2, 0x68]⟩,
  ⟨.qLe, [11, 1]⟩,
  ⟨.ite, [23, 0x1eb, 21]⟩,
  ⟨.qLe, [3, 1]⟩,
  ⟨.qLt, [4, 2]⟩,
  ⟨.ite, [26, 2, 1]⟩,
  ⟨.bAnd, [30, 5, 1]⟩,
  ⟨.bNot, [37]⟩,
  ⟨.bNot, [36]⟩,
  ⟨.bAnd, [2, 1]⟩,
  ⟨.ite, [1, 0x2ea, 0x2e9]⟩,
  ⟨.zSub, [43, 1]⟩,
  ⟨.zLe, [0x2eb, 1]⟩,
  ⟨.zEq, [2, 0x2ec]⟩,
  ⟨.qDiv, [0x1f5, 0x2ea]⟩,
  ⟨.ite, [45, 46, 1]⟩,
  ⟨.qDiv, [45, 0x316]⟩,
  ⟨.qDiv, [6, 0x320]⟩,
  ⟨.qDiv, [7, 0x31e]⟩,
  ⟨.qLe, [1, 51]⟩,
  ⟨.ite, [1, 52, 2]⟩,
  ⟨.bEq, [0x20a, 0x2b2]⟩,
  ⟨.qLe, [9, 1]⟩,
  ⟨.ite, [25, 0x20f, 19]⟩,
  ⟨.ite, [28, 2, 1]⟩]

def dictionaryLLRR : Table Pattern := .branch 26 dictionaryLLRRL dictionaryLLRRR

def dictionaryLLR : Table Pattern := .branch 51 dictionaryLLRL dictionaryLLRR

def dictionaryLL : Table Pattern := .branch 0x67 dictionaryLLL dictionaryLLR

def dictionaryLRLLL : Table Pattern := .leaf #[
  ⟨.bOr, [37, 1]⟩,
  ⟨.input 26, []⟩,
  ⟨.bNot, [39]⟩,
  ⟨.ite, [76, 4, 1]⟩,
  ⟨.bEq, [3, 1]⟩,
  ⟨.input 27, []⟩,
  ⟨.ite, [5, 13, 49]⟩,
  ⟨.qEq, [2, 1]⟩,
  ⟨.qConst (0xaf), []⟩,
  ⟨.qDiv, [0x340, 1]⟩,
  ⟨.qLe, [97, 1]⟩,
  ⟨.ite, [1, 98, 99]⟩,
  ⟨.qMul, [0x32f, 1]⟩,
  ⟨.qConst (0xf3), []⟩,
  ⟨.qDiv, [0x346, 1]⟩,
  ⟨.qMul, [1, 0x33f]⟩,
  ⟨.qMul, [1, 0x342]⟩,
  ⟨.qMul, [0x32c, 1]⟩,
  ⟨.qMul, [0x325, 3]⟩,
  ⟨.bAnd, [0x2d6, 11, 3, 1]⟩,
  ⟨.ite, [1, 0x324, 0x323]⟩,
  ⟨.qMul, [0x321, 0x1d8]⟩,
  ⟨.qLe, [1, 0x1df]⟩,
  ⟨.qMul, [0x323, 0x1d6]⟩,
  ⟨.qLe, [1, 0x1e1]⟩]

def dictionaryLRLLR : Table Pattern := .leaf #[
  ⟨.ite, [1, 0x32a, 0x329]⟩,
  ⟨.zLe, [0x32b, 1]⟩,
  ⟨.qConst (0xdac), []⟩,
  ⟨.qDiv, [0x354, 1]⟩,
  ⟨.zEq, [4, 0x32e]⟩,
  ⟨.qLe, [0x1df, 0x1e3]⟩,
  ⟨.ite, [1, 0x1e4, 0x1e0]⟩,
  ⟨.qLt, [0x1e1, 0x1e5]⟩,
  ⟨.qDiv, [0x1e6, 0x35e]⟩,
  ⟨.qLe, [0x1e3, 1]⟩,
  ⟨.ite, [1, 2, 0x1e4]⟩,
  ⟨.qDiv, [0x1e5, 0x35c]⟩,
  ⟨.qLe, [1, 0x1ea]⟩,
  ⟨.ite, [1, 0x1eb, 2]⟩,
  ⟨.bEq, [0x1f8, 0x359]⟩,
  ⟨.qMul, [0x369, 0x1fb]⟩,
  ⟨.qMul, [0x12f, 0x1fc]⟩,
  ⟨.ite, [23, 0x1ff, 21]⟩,
  ⟨.ite, [1, 0x34e, 0x34d]⟩,
  ⟨.zLe, [0x34f, 1]⟩,
  ⟨.zEq, [2, 0x350]⟩,
  ⟨.qDiv, [0x205, 0x34e]⟩,
  ⟨.qDiv, [45, 0x37a]⟩,
  ⟨.qDiv, [6, 0x384]⟩,
  ⟨.qDiv, [7, 0x382]⟩,
  ⟨.bEq, [0x21e, 0x316]⟩]

def dictionaryLRLL : Table Pattern := .branch 25 dictionaryLRLLL dictionaryLRLLR

def dictionaryLRLRL : Table Pattern := .leaf #[
  ⟨.ite, [25, 0x223, 19]⟩,
  ⟨.input 28, []⟩,
  ⟨.input 29, []⟩,
  ⟨.qConst (0x7d), []⟩,
  ⟨.qDiv, [0x3a4, 1]⟩,
  ⟨.qLe, [0xc5, 1]⟩,
  ⟨.ite, [1, 0xc6, 0xc7]⟩,
  ⟨.qMul, [0x393, 1]⟩,
  ⟨.qLe, [97, 5]⟩,
  ⟨.qMul, [0x38c, 1]⟩,
  ⟨.qLe, [1, 8]⟩,
  ⟨.qMul, [0x385, 3]⟩,
  ⟨.qLt, [10, 1]⟩,
  ⟨.bAnd, [0x336, 7, 3, 1]⟩,
  ⟨.ite, [1, 0x384, 0x383]⟩,
  ⟨.qMul, [0x381, 0x1e8]⟩,
  ⟨.qLe, [1, 0x1eb]⟩,
  ⟨.qMul, [0x383, 0x1e2]⟩,
  ⟨.qLe, [1, 0x1ed]⟩,
  ⟨.ite, [1, 0x38a, 0x389]⟩,
  ⟨.zLe, [0x38b, 1]⟩,
  ⟨.qConst (0x9c4), []⟩,
  ⟨.qDiv, [0x3b4, 1]⟩,
  ⟨.zEq, [4, 0x38e]⟩,
  ⟨.qLe, [0x1eb, 0x1f3]⟩,
  ⟨.ite, [1, 0x1f4, 0x1ec]⟩]

def dictionaryLRLRR : Table Pattern := .leaf #[
  ⟨.qLt, [0x1ed, 0x1f5]⟩,
  ⟨.qDiv, [0x1f6, 0x3be]⟩,
  ⟨.qLe, [0x1ef, 1]⟩,
  ⟨.ite, [1, 2, 0x1f0]⟩,
  ⟨.qDiv, [0x1f1, 0x3bc]⟩,
  ⟨.qLe, [1, 0x1fa]⟩,
  ⟨.ite, [1, 0x1fb, 2]⟩,
  ⟨.bEq, [0x204, 0x3b9]⟩,
  ⟨.qMul, [0x3c9, 0x207]⟩,
  ⟨.qMul, [0x18f, 0x208]⟩,
  ⟨.qLe, [99, 1]⟩,
  ⟨.ite, [1, 2, 0x64]⟩,
  ⟨.ite, [23, 0x20b, 21]⟩,
  ⟨.ite, [1, 0x3ae, 0x3ad]⟩,
  ⟨.zLe, [0x3af, 1]⟩,
  ⟨.zEq, [2, 0x3b0]⟩,
  ⟨.qDiv, [0x215, 0x3ae]⟩,
  ⟨.qDiv, [45, 0x3da]⟩,
  ⟨.qDiv, [6, 0x3e4]⟩,
  ⟨.qDiv, [7, 0x3e2]⟩,
  ⟨.bEq, [0x22a, 0x376]⟩,
  ⟨.ite, [25, 0x22f, 19]⟩,
  ⟨.input 30, []⟩,
  ⟨.input 31, []⟩,
  ⟨.qConst (81), []⟩,
  ⟨.qDiv, [0x409, 1]⟩]

def dictionaryLRLR : Table Pattern := .branch 26 dictionaryLRLRL dictionaryLRLRR

def dictionaryLRL : Table Pattern := .branch 51 dictionaryLRLL dictionaryLRLR

def dictionaryLRRLL : Table Pattern := .leaf #[
  ⟨.qMul, [1, 0x402]⟩,
  ⟨.qMul, [1, 0x405]⟩,
  ⟨.bEq, [0x158, 0x41c]⟩,
  ⟨.qMul, [0x42c, 0x155]⟩,
  ⟨.qMul, [0x1f2, 0x156]⟩,
  ⟨.bEq, [0x182, 0x3dd]⟩,
  ⟨.ite, [1, 42, 41]⟩,
  ⟨.qConst (49), []⟩,
  ⟨.qDiv, [0x46d, 1]⟩,
  ⟨.qConst (64), []⟩,
  ⟨.qDiv, [0x46f, 1]⟩,
  ⟨.qMul, [1, 0x46d]⟩,
  ⟨.qMul, [1, 0x470]⟩,
  ⟨.qMul, [0x460, 1]⟩,
  ⟨.qLe, [0x6b, 9]⟩,
  ⟨.ite, [1, 0x6c, 0x6d]⟩,
  ⟨.qMul, [0x459, 1]⟩,
  ⟨.qMul, [0x452, 3]⟩,
  ⟨.bAnd, [0x403, 7, 3, 1]⟩,
  ⟨.ite, [1, 0x451, 0x450]⟩,
  ⟨.qMul, [0x44e, 0x19c]⟩,
  ⟨.qLe, [1, 0x1a3]⟩,
  ⟨.qMul, [0x450, 0x19a]⟩,
  ⟨.qLe, [1, 0x1a5]⟩,
  ⟨.ite, [1, 0x457, 0x456]⟩,
  ⟨.zLe, [0x458, 1]⟩]

def dictionaryLRRLR : Table Pattern := .leaf #[
  ⟨.qConst (0x3d4), []⟩,
  ⟨.qDiv, [0x481, 1]⟩,
  ⟨.zEq, [4, 0x45b]⟩,
  ⟨.qLe, [0x1a3, 0x1a7]⟩,
  ⟨.ite, [1, 0x1a8, 0x1a4]⟩,
  ⟨.qLt, [0x1a5, 0x1a9]⟩,
  ⟨.qDiv, [0x1aa, 0x48b]⟩,
  ⟨.qLe, [0x1a7, 1]⟩,
  ⟨.ite, [1, 2, 0x1a8]⟩,
  ⟨.qDiv, [0x1a9, 0x489]⟩,
  ⟨.qLe, [1, 0x1ae]⟩,
  ⟨.ite, [1, 0x1af, 2]⟩,
  ⟨.bEq, [0x15e, 0x486]⟩,
  ⟨.qMul, [0x496, 0x15b]⟩,
  ⟨.qMul, [0x25c, 0x15c]⟩,
  ⟨.qLe, [0x6d, 1]⟩,
  ⟨.ite, [1, 2, 0x6e]⟩,
  ⟨.ite, [23, 0x1c3, 21]⟩,
  ⟨.ite, [1, 0x47b, 0x47a]⟩,
  ⟨.zLe, [0x47c, 1]⟩,
  ⟨.zEq, [2, 0x47d]⟩,
  ⟨.qDiv, [0x1c9, 0x47b]⟩,
  ⟨.qDiv, [45, 0x4a7]⟩,
  ⟨.qDiv, [6, 0x4b1]⟩,
  ⟨.qDiv, [7, 0x4af]⟩,
  ⟨.bEq, [0x184, 0x443]⟩]

def dictionaryLRRL : Table Pattern := .branch 26 dictionaryLRRLL dictionaryLRRLR

def dictionaryLRRRL : Table Pattern := .leaf #[
  ⟨.qLe, [0x69, 1]⟩,
  ⟨.ite, [1, 2, 0x6a]⟩,
  ⟨.ite, [25, 0x1e7, 19]⟩,
  ⟨.input 16, []⟩,
  ⟨.input 17, []⟩,
  ⟨.qConst (35), []⟩,
  ⟨.qDiv, [0x4d1, 1]⟩,
  ⟨.qMul, [0x4c0, 1]⟩,
  ⟨.qLe, [0xcb, 5]⟩,
  ⟨.ite, [1, 0xcc, 0xcd]⟩,
  ⟨.qMul, [0x4b9, 1]⟩,
  ⟨.qMul, [0x4b2, 3]⟩,
  ⟨.bAnd, [0x463, 7, 3, 1]⟩,
  ⟨.ite, [1, 0x4b1, 0x4b0]⟩,
  ⟨.qMul, [0x4ae, 0x19c]⟩,
  ⟨.qLe, [1, 0x19f]⟩,
  ⟨.qMul, [0x4b0, 0x196]⟩,
  ⟨.qLe, [1, 0x1a1]⟩,
  ⟨.ite, [1, 0x4b7, 0x4b6]⟩,
  ⟨.zLe, [0x4b8, 1]⟩,
  ⟨.qConst (0x2bc), []⟩,
  ⟨.qDiv, [0x4e1, 1]⟩,
  ⟨.zEq, [4, 0x4bb]⟩,
  ⟨.qLe, [0x19f, 0x1a7]⟩,
  ⟨.ite, [1, 0x1a8, 0x1a0]⟩,
  ⟨.qLt, [0x1a1, 0x1a9]⟩]

def dictionaryLRRRR : Table Pattern := .leaf #[
  ⟨.qDiv, [0x1aa, 0x4eb]⟩,
  ⟨.qLe, [0x1a3, 1]⟩,
  ⟨.ite, [1, 2, 0x1a4]⟩,
  ⟨.qDiv, [0x1a5, 0x4e9]⟩,
  ⟨.bEq, [0x15a, 0x4e6]⟩,
  ⟨.qMul, [0x4f6, 0x157]⟩,
  ⟨.qMul, [0x2bc, 0x158]⟩,
  ⟨.ite, [23, 0x1bf, 21]⟩,
  ⟨.ite, [1, 0x4db, 0x4da]⟩,
  ⟨.zLe, [0x4dc, 1]⟩,
  ⟨.zEq, [2, 0x4dd]⟩,
  ⟨.qDiv, [0x1c9, 0x4db]⟩,
  ⟨.qDiv, [45, 0x507]⟩,
  ⟨.qDiv, [6, 0x511]⟩,
  ⟨.qDiv, [7, 0x50f]⟩,
  ⟨.bEq, [0x180, 0x4a3]⟩,
  ⟨.ite, [25, 0x1e3, 19]⟩,
  ⟨.input 18, []⟩,
  ⟨.input 19, []⟩,
  ⟨.qConst (25), []⟩,
  ⟨.qDiv, [0x531, 1]⟩,
  ⟨.qLe, [0xc1, 1]⟩,
  ⟨.ite, [1, 0xc2, 0xc3]⟩,
  ⟨.qMul, [0x520, 1]⟩,
  ⟨.qConst (27), []⟩,
  ⟨.qDiv, [0x537, 1]⟩]

def dictionaryLRRR : Table Pattern := .branch 26 dictionaryLRRRL dictionaryLRRRR

def dictionaryLRR : Table Pattern := .branch 52 dictionaryLRRL dictionaryLRRR

def dictionaryLR : Table Pattern := .branch 0x67 dictionaryLRL dictionaryLRR

def dictionaryL : Table Pattern := .branch 0xce dictionaryLL dictionaryLR

def dictionaryRLLLL : Table Pattern := .leaf #[
  ⟨.qMul, [1, 0x530]⟩,
  ⟨.qMul, [1, 0x533]⟩,
  ⟨.qMul, [0x51d, 1]⟩,
  ⟨.qMul, [0x516, 3]⟩,
  ⟨.bAnd, [0x4c7, 11, 3, 1]⟩,
  ⟨.ite, [1, 0x515, 0x514]⟩,
  ⟨.qMul, [0x512, 0x19c]⟩,
  ⟨.qMul, [0x514, 0x19a]⟩,
  ⟨.ite, [1, 0x51b, 0x51a]⟩,
  ⟨.zLe, [0x51c, 1]⟩,
  ⟨.qConst (0x1f4), []⟩,
  ⟨.qDiv, [0x545, 1]⟩,
  ⟨.zEq, [4, 0x51f]⟩,
  ⟨.qDiv, [0x1aa, 0x54f]⟩,
  ⟨.qDiv, [0x1a9, 0x54d]⟩,
  ⟨.bEq, [0x15e, 0x54a]⟩,
  ⟨.qMul, [0x55a, 0x15b]⟩,
  ⟨.qMul, [0x320, 0x15c]⟩,
  ⟨.ite, [1, 0x53f, 0x53e]⟩,
  ⟨.zLe, [0x540, 1]⟩,
  ⟨.zEq, [2, 0x541]⟩,
  ⟨.qDiv, [0x1c9, 0x53f]⟩,
  ⟨.qDiv, [45, 0x56b]⟩,
  ⟨.qDiv, [6, 0x575]⟩,
  ⟨.qDiv, [7, 0x573]⟩]

def dictionaryRLLLR : Table Pattern := .leaf #[
  ⟨.bEq, [0x184, 0x507]⟩,
  ⟨.input 20, []⟩,
  ⟨.input 21, []⟩,
  ⟨.qConst (16), []⟩,
  ⟨.qDiv, [0x596, 1]⟩,
  ⟨.qMul, [1, 0x594]⟩,
  ⟨.qMul, [1, 0x597]⟩,
  ⟨.bEq, [0xf4, 0x5ad]⟩,
  ⟨.qMul, [0x5bd, 0xf1]⟩,
  ⟨.qMul, [0x383, 0xf2]⟩,
  ⟨.bEq, [0x11e, 0x56e]⟩,
  ⟨.input 8, []⟩,
  ⟨.input 9, []⟩,
  ⟨.qConst (7), []⟩,
  ⟨.qDiv, [0x5fe, 1]⟩,
  ⟨.ite, [1, 0x68, 0x69]⟩,
  ⟨.qMul, [0x5ed, 1]⟩,
  ⟨.qDiv, [0x603, 0x5e5]⟩,
  ⟨.qMul, [1, 0x5fc]⟩,
  ⟨.qMul, [1, 0x5ff]⟩,
  ⟨.qMul, [0x5e9, 1]⟩,
  ⟨.qLe, [1, 11]⟩,
  ⟨.qMul, [0x5e2, 3]⟩,
  ⟨.qLt, [13, 1]⟩,
  ⟨.bAnd, [0x593, 10, 3, 1]⟩,
  ⟨.ite, [1, 0x5e1, 0x5e0]⟩]

def dictionaryRLLL : Table Pattern := .branch 25 dictionaryRLLLL dictionaryRLLLR

def dictionaryRLLRL : Table Pattern := .leaf #[
  ⟨.qMul, [0x5de, 0x13b]⟩,
  ⟨.qLe, [1, 0x13e]⟩,
  ⟨.qMul, [0x5e0, 0x139]⟩,
  ⟨.qLe, [1, 0x140]⟩,
  ⟨.ite, [1, 0x5e7, 0x5e6]⟩,
  ⟨.zLe, [0x5e8, 1]⟩,
  ⟨.qConst (0x8c), []⟩,
  ⟨.qDiv, [0x611, 1]⟩,
  ⟨.zEq, [4, 0x5eb]⟩,
  ⟨.qLe, [0x142, 0x146]⟩,
  ⟨.ite, [1, 0x147, 0x143]⟩,
  ⟨.qLt, [0x144, 0x148]⟩,
  ⟨.qDiv, [0x149, 0x61b]⟩,
  ⟨.qLe, [0x146, 1]⟩,
  ⟨.ite, [1, 2, 0x147]⟩,
  ⟨.qDiv, [0x148, 0x619]⟩,
  ⟨.qLe, [1, 0x14d]⟩,
  ⟨.ite, [1, 0x14e, 2]⟩,
  ⟨.bEq, [0xfd, 0x616]⟩,
  ⟨.qMul, [0x626, 0xfa]⟩,
  ⟨.qMul, [0x3ec, 0xfb]⟩,
  ⟨.qLe, [0x6c, 1]⟩,
  ⟨.ite, [1, 2, 0x6d]⟩,
  ⟨.ite, [23, 0x15e, 21]⟩,
  ⟨.ite, [1, 0x60b, 0x60a]⟩,
  ⟨.zLe, [0x60c, 1]⟩]

def dictionaryRLLRR : Table Pattern := .leaf #[
  ⟨.zEq, [2, 0x60d]⟩,
  ⟨.qDiv, [0x168, 0x60b]⟩,
  ⟨.qDiv, [45, 0x637]⟩,
  ⟨.qDiv, [6, 0x641]⟩,
  ⟨.qDiv, [7, 0x63f]⟩,
  ⟨.bEq, [0x123, 0x5d3]⟩,
  ⟨.qLe, [0x68, 1]⟩,
  ⟨.ite, [1, 2, 0x69]⟩,
  ⟨.ite, [25, 0x182, 19]⟩,
  ⟨.input 10, []⟩,
  ⟨.input 11, []⟩,
  ⟨.qDiv, [0x660, 0x64f]⟩,
  ⟨.qLe, [0xc9, 1]⟩,
  ⟨.ite, [1, 0xca, 0xcb]⟩,
  ⟨.qMul, [0x64f, 1]⟩,
  ⟨.qLe, [96, 5]⟩,
  ⟨.ite, [1, 97, 98]⟩,
  ⟨.qMul, [0x648, 1]⟩,
  ⟨.qMul, [0x641, 3]⟩,
  ⟨.bAnd, [0x5f2, 7, 3, 1]⟩,
  ⟨.ite, [1, 0x640, 0x63f]⟩,
  ⟨.qMul, [0x63d, 0x13a]⟩,
  ⟨.qLe, [1, 0x13d]⟩,
  ⟨.qMul, [0x63f, 0x134]⟩,
  ⟨.qLe, [1, 0x13f]⟩,
  ⟨.ite, [1, 0x646, 0x645]⟩]

def dictionaryRLLR : Table Pattern := .branch 26 dictionaryRLLRL dictionaryRLLRR

def dictionaryRLL : Table Pattern := .branch 51 dictionaryRLLL dictionaryRLLR

def dictionaryRLRLL : Table Pattern := .leaf #[
  ⟨.zLe, [0x647, 1]⟩,
  ⟨.qConst (0x64), []⟩,
  ⟨.qDiv, [0x670, 1]⟩,
  ⟨.zEq, [4, 0x64a]⟩,
  ⟨.qLe, [0x13d, 0x145]⟩,
  ⟨.ite, [1, 0x146, 0x13e]⟩,
  ⟨.qLt, [0x13f, 0x147]⟩,
  ⟨.qDiv, [0x148, 0x67a]⟩,
  ⟨.qLe, [0x141, 1]⟩,
  ⟨.ite, [1, 2, 0x142]⟩,
  ⟨.qDiv, [0x143, 0x678]⟩,
  ⟨.qLe, [1, 0x14c]⟩,
  ⟨.ite, [1, 0x14d, 2]⟩,
  ⟨.bEq, [0xf8, 0x675]⟩,
  ⟨.qMul, [0x685, 0xf5]⟩,
  ⟨.qMul, [0x44b, 0xf6]⟩,
  ⟨.qLe, [98, 1]⟩,
  ⟨.ite, [1, 2, 99]⟩,
  ⟨.ite, [23, 0x15d, 21]⟩,
  ⟨.ite, [1, 0x66a, 0x669]⟩,
  ⟨.zLe, [0x66b, 1]⟩,
  ⟨.zEq, [2, 0x66c]⟩,
  ⟨.qDiv, [0x167, 0x66a]⟩,
  ⟨.qDiv, [45, 0x696]⟩,
  ⟨.qDiv, [6, 0x6a0]⟩]

def dictionaryRLRLR : Table Pattern := .leaf #[
  ⟨.qDiv, [7, 0x69e]⟩,
  ⟨.bEq, [0x11e, 0x632]⟩,
  ⟨.ite, [25, 0x181, 19]⟩,
  ⟨.input 12, []⟩,
  ⟨.input 13, []⟩,
  ⟨.qDiv, [0x6ae, 0xc2]⟩,
  ⟨.qMul, [0x6be, 0x6bd]⟩,
  ⟨.qMul, [1, 0x6c0]⟩,
  ⟨.qMul, [0x6b0, 1]⟩,
  ⟨.qLt, [6, 1]⟩,
  ⟨.qMul, [0x6bf, 0x6be]⟩,
  ⟨.qMul, [1, 0x6c1]⟩,
  ⟨.qMul, [0x6ab, 1]⟩,
  ⟨.qMul, [0x6a4, 3]⟩,
  ⟨.bAnd, [0x6be, 9, 3, 1]⟩,
  ⟨.ite, [1, 0x6a3, 0x6a2]⟩,
  ⟨.qMul, [0x6a0, 0xd0]⟩,
  ⟨.qLe, [1, 0xd3]⟩,
  ⟨.qMul, [0x6a2, 0xcb]⟩,
  ⟨.qLe, [1, 0xd5]⟩,
  ⟨.ite, [1, 0x6a9, 0x6a8]⟩,
  ⟨.zLe, [0x6aa, 1]⟩,
  ⟨.qConst (28), []⟩,
  ⟨.qDiv, [0x6d3, 1]⟩,
  ⟨.zEq, [4, 0x6ad]⟩,
  ⟨.qLe, [0xd4, 0xdb]⟩]

def dictionaryRLRL : Table Pattern := .branch 25 dictionaryRLRLL dictionaryRLRLR

def dictionaryRLRRL : Table Pattern := .leaf #[
  ⟨.ite, [1, 0xdc, 0xd5]⟩,
  ⟨.qLt, [0xd6, 0xdd]⟩,
  ⟨.qDiv, [0xde, 0x6dd]⟩,
  ⟨.qLe, [0xd8, 1]⟩,
  ⟨.ite, [1, 2, 0xd9]⟩,
  ⟨.qDiv, [0xda, 0x6db]⟩,
  ⟨.qLe, [1, 0xe2]⟩,
  ⟨.ite, [1, 0xe3, 2]⟩,
  ⟨.bEq, [0x8f, 0x6d8]⟩,
  ⟨.qMul, [0x6e8, 0x8c]⟩,
  ⟨.qMul, [0x4ae, 0x8d]⟩,
  ⟨.bEq, [0xf8, 0x6de]⟩,
  ⟨.qMul, [0x6ee, 0xf5]⟩,
  ⟨.qMul, [0x4b4, 0xf6]⟩,
  ⟨.qLe, [15, 1]⟩,
  ⟨.ite, [27, 0xf7, 25]⟩,
  ⟨.ite, [30, 2, 1]⟩,
  ⟨.bAnd, [34, 5, 1]⟩,
  ⟨.bNot, [41]⟩,
  ⟨.bNot, [40]⟩,
  ⟨.ite, [1, 0x6d1, 0x6d0]⟩,
  ⟨.zSub, [47, 1]⟩,
  ⟨.zLe, [0x6d2, 1]⟩,
  ⟨.zEq, [2, 0x6d3]⟩,
  ⟨.qDiv, [0x101, 0x6d1]⟩,
  ⟨.ite, [49, 50, 1]⟩]

def dictionaryRLRRR : Table Pattern := .leaf #[
  ⟨.qDiv, [49, 0x6fd]⟩,
  ⟨.qDiv, [6, 0x707]⟩,
  ⟨.qDiv, [7, 0x705]⟩,
  ⟨.qLe, [1, 55]⟩,
  ⟨.ite, [1, 56, 2]⟩,
  ⟨.bEq, [0xb9, 0x699]⟩,
  ⟨.bEq, [0x120, 0x69d]⟩,
  ⟨.ite, [1, 40, 39]⟩,
  ⟨.ite, [27, 0x11d, 21]⟩,
  ⟨.bAnd, [32, 5, 1]⟩,
  ⟨.bOr, [39, 1]⟩,
  ⟨.input 4, []⟩,
  ⟨.ite, [82, 4, 1]⟩,
  ⟨.input 5, []⟩,
  ⟨.ite, [5, 13, 51]⟩,
  ⟨.qMul, [0x728, 0x725]⟩,
  ⟨.qMul, [1, 0x728]⟩,
  ⟨.qLe, [1, 0x72a]⟩,
  ⟨.qMul, [0x718, 1]⟩,
  ⟨.qLt, [0x72d, 1]⟩,
  ⟨.qMul, [0x72e, 0x726]⟩,
  ⟨.qMul, [1, 0x729]⟩,
  ⟨.qLe, [1, 0x730]⟩,
  ⟨.qMul, [0x713, 1]⟩,
  ⟨.qLe, [1, 0x733]⟩,
  ⟨.qMul, [0x70c, 3]⟩]

def dictionaryRLRR : Table Pattern := .branch 26 dictionaryRLRRL dictionaryRLRRR

def dictionaryRLR : Table Pattern := .branch 51 dictionaryRLRL dictionaryRLRR

def dictionaryRL : Table Pattern := .branch 0x67 dictionaryRLL dictionaryRLR

def dictionaryRRLLL : Table Pattern := .leaf #[
  ⟨.qLt, [0x735, 1]⟩,
  ⟨.bAnd, [0x6bd, 9, 3, 1]⟩,
  ⟨.ite, [1, 0x70b, 0x70a]⟩,
  ⟨.qMul, [0x708, 0xd6]⟩,
  ⟨.qLe, [1, 0xd9]⟩,
  ⟨.qMul, [0x70a, 0xd4]⟩,
  ⟨.qLe, [1, 0xdb]⟩,
  ⟨.ite, [1, 0x711, 0x710]⟩,
  ⟨.zLe, [0x712, 1]⟩,
  ⟨.qConst (20), []⟩,
  ⟨.qDiv, [0x73b, 1]⟩,
  ⟨.zEq, [4, 0x715]⟩,
  ⟨.qLe, [0xdd, 0xe1]⟩,
  ⟨.ite, [1, 0xe2, 0xde]⟩,
  ⟨.qLt, [0xdf, 0xe3]⟩,
  ⟨.qDiv, [0xe4, 0x745]⟩,
  ⟨.qLe, [0xe1, 1]⟩,
  ⟨.ite, [1, 2, 0xe2]⟩,
  ⟨.qDiv, [0xe3, 0x743]⟩,
  ⟨.qLe, [1, 0xe8]⟩,
  ⟨.ite, [1, 0xe9, 2]⟩,
  ⟨.bEq, [0x98, 0x740]⟩,
  ⟨.qMul, [0x750, 0x95]⟩,
  ⟨.qMul, [0x516, 0x96]⟩,
  ⟨.qLe, [0x6b, 1]⟩]

def dictionaryRRLLR : Table Pattern := .leaf #[
  ⟨.ite, [1, 2, 0x6c]⟩,
  ⟨.ite, [23, 0xf9, 21]⟩,
  ⟨.ite, [1, 0x735, 0x734]⟩,
  ⟨.zLe, [0x736, 1]⟩,
  ⟨.zEq, [2, 0x737]⟩,
  ⟨.qDiv, [0x103, 0x735]⟩,
  ⟨.qDiv, [45, 0x761]⟩,
  ⟨.qDiv, [6, 0x76b]⟩,
  ⟨.qDiv, [7, 0x769]⟩,
  ⟨.bEq, [0xbe, 0x6fd]⟩,
  ⟨.ite, [25, 0x11d, 19]⟩,
  ⟨.input 6, []⟩,
  ⟨.input 7, []⟩,
  ⟨.qMul, [0x789, 0x787]⟩,
  ⟨.qMul, [1, 0x78a]⟩,
  ⟨.qLe, [1, 0x77b]⟩,
  ⟨.qMul, [0x77a, 1]⟩,
  ⟨.qLt, [0x77e, 1]⟩,
  ⟨.qMul, [0x78a, 0x788]⟩,
  ⟨.qMul, [1, 0x78b]⟩,
  ⟨.qLe, [1, 0x781]⟩,
  ⟨.qMul, [0x775, 1]⟩,
  ⟨.qLe, [1, 0x784]⟩,
  ⟨.qMul, [0x76e, 3]⟩,
  ⟨.qLt, [0x786, 1]⟩,
  ⟨.bAnd, [0x788, 9, 3, 1]⟩]

def dictionaryRRLL : Table Pattern := .branch 25 dictionaryRRLLL dictionaryRRLLR

def dictionaryRRLRL : Table Pattern := .leaf #[
  ⟨.ite, [1, 0x76d, 0x76c]⟩,
  ⟨.qMul, [0x76a, 0x6f]⟩,
  ⟨.qLe, [1, 0x79b]⟩,
  ⟨.qMul, [0x76c, 0x6b]⟩,
  ⟨.qLe, [1, 0x79d]⟩,
  ⟨.ite, [1, 0x773, 0x772]⟩,
  ⟨.zLe, [0x774, 1]⟩,
  ⟨.qDiv, [0x79c, 0x7a1]⟩,
  ⟨.zEq, [3, 0x776]⟩,
  ⟨.qLe, [0x73, 0x79]⟩,
  ⟨.ite, [1, 0x7a, 0x74]⟩,
  ⟨.qLt, [0x75, 0x7b]⟩,
  ⟨.qDiv, [0x7c, 0x7a6]⟩,
  ⟨.qLe, [0x77, 1]⟩,
  ⟨.ite, [1, 2, 0x78]⟩,
  ⟨.qDiv, [0x79, 0x7a4]⟩,
  ⟨.qLe, [1, 0x80]⟩,
  ⟨.ite, [1, 0x81, 2]⟩,
  ⟨.bEq, [46, 0x7a1]⟩,
  ⟨.qMul, [0x7b1, 43]⟩,
  ⟨.qMul, [0x577, 44]⟩,
  ⟨.bEq, [0x96, 0x7a7]⟩,
  ⟨.qMul, [0x7b7, 0x93]⟩,
  ⟨.qMul, [0x57d, 0x94]⟩,
  ⟨.ite, [27, 0x7be, 25]⟩,
  ⟨.bAnd, [33, 5, 1]⟩]

def dictionaryRRLRR : Table Pattern := .leaf #[
  ⟨.ite, [1, 0x79b, 0x79a]⟩,
  ⟨.zLe, [0x79c, 1]⟩,
  ⟨.zEq, [2, 0x79d]⟩,
  ⟨.qDiv, [0xa0, 0x79b]⟩,
  ⟨.qDiv, [49, 0x7c7]⟩,
  ⟨.qDiv, [6, 0x7d1]⟩,
  ⟨.qDiv, [7, 0x7cf]⟩,
  ⟨.qLe, [1, 56]⟩,
  ⟨.ite, [1, 57, 2]⟩,
  ⟨.bEq, [89, 0x763]⟩,
  ⟨.ite, [1, 43, 42]⟩,
  ⟨.bEq, [0xbf, 0x767]⟩,
  ⟨.ite, [1, 41, 40]⟩,
  ⟨.ite, [27, 0x7e5, 21]⟩,
  ⟨.bAnd, [40, 1]⟩,
  ⟨.qDiv, [0xd4, 1]⟩,
  ⟨.qMul, [1, 0xcd]⟩,
  ⟨.qMul, [1, 0xd0]⟩,
  ⟨.qDiv, [0x172, 1]⟩,
  ⟨.qDiv, [0x174, 1]⟩,
  ⟨.qMul, [1, 0x172]⟩,
  ⟨.qMul, [1, 0x175]⟩,
  ⟨.qConst (0x30d4), []⟩,
  ⟨.qDiv, [0x1bb, 1]⟩,
  ⟨.qLe, [2, 1]⟩,
  ⟨.qDiv, [0x1c6, 1]⟩]

def dictionaryRRLR : Table Pattern := .branch 26 dictionaryRRLRL dictionaryRRLRR

def dictionaryRRL : Table Pattern := .branch 51 dictionaryRRLL dictionaryRRLR

def dictionaryRRRLL : Table Pattern := .leaf #[
  ⟨.qMul, [0x1b5, 1]⟩,
  ⟨.qDiv, [0x1cc, 1]⟩,
  ⟨.qMul, [1, 0x1c5]⟩,
  ⟨.qMul, [1, 0x1c8]⟩,
  ⟨.qMul, [0x1b2, 1]⟩,
  ⟨.qMul, [0x1ab, 3]⟩,
  ⟨.bAnd, [0x1c5, 11, 3, 1]⟩,
  ⟨.ite, [1, 0x1aa, 0x1a9]⟩,
  ⟨.qDiv, [0x1d8, 1]⟩,
  ⟨.qLe, [0x1c1, 1]⟩,
  ⟨.ite, [1, 0x1c2, 0x1c3]⟩,
  ⟨.qMul, [0x1ab, 1]⟩,
  ⟨.qLe, [0x1bb, 6]⟩,
  ⟨.ite, [1, 0x1bc, 0x1bd]⟩,
  ⟨.qMul, [0x1b0, 1]⟩,
  ⟨.ite, [1, 0x1b8, 0x1b7]⟩,
  ⟨.zLe, [0x1b9, 1]⟩,
  ⟨.zEq, [2, 0x1ba]⟩,
  ⟨.qDiv, [14, 0x1b8]⟩,
  ⟨.qDiv, [10, 0x1e4]⟩,
  ⟨.qDiv, [6, 0x1ee]⟩,
  ⟨.qDiv, [7, 0x1ec]⟩,
  ⟨.ite, [1, 0x1d2, 0x1d1]⟩,
  ⟨.zLe, [0x1d3, 1]⟩,
  ⟨.zEq, [2, 0x1d4]⟩,
  ⟨.qDiv, [43, 0x204]⟩]

def dictionaryRRRLR : Table Pattern := .leaf #[
  ⟨.qDiv, [41, 0x202]⟩,
  ⟨.qLe, [0x117, 9]⟩,
  ⟨.ite, [1, 0x118, 0x119]⟩,
  ⟨.bEq, [0x1e5, 0xcc]⟩,
  ⟨.qMul, [0x305, 0x1e8]⟩,
  ⟨.qMul, [0xcb, 0x1e9]⟩,
  ⟨.bEq, [0x20b, 0x31b]⟩,
  ⟨.bAnd, [0x33f, 11, 3, 1]⟩,
  ⟨.qMul, [0x321, 0x1d9]⟩,
  ⟨.qLe, [1, 0x1e0]⟩,
  ⟨.qMul, [0x323, 0x1d7]⟩,
  ⟨.qLe, [1, 0x1e2]⟩,
  ⟨.qLe, [0x1e0, 0x1e4]⟩,
  ⟨.ite, [1, 0x1e5, 0x1e1]⟩,
  ⟨.qLt, [0x1e2, 0x1e6]⟩,
  ⟨.qDiv, [0x1e7, 0x35e]⟩,
  ⟨.qLe, [0x1e4, 1]⟩,
  ⟨.ite, [1, 2, 0x1e5]⟩,
  ⟨.qDiv, [0x1e6, 0x35c]⟩,
  ⟨.ite, [1, 0x1ec, 2]⟩,
  ⟨.bEq, [0x1f9, 0x130]⟩,
  ⟨.qMul, [0x369, 0x1fc]⟩,
  ⟨.qMul, [0x12f, 0x1fd]⟩,
  ⟨.ite, [23, 0x200, 21]⟩,
  ⟨.qDiv, [0x206, 0x34e]⟩,
  ⟨.bEq, [0x21f, 0x37f]⟩]

def dictionaryRRRL : Table Pattern := .branch 26 dictionaryRRRLL dictionaryRRRLR

def dictionaryRRRRL : Table Pattern := .leaf #[
  ⟨.ite, [25, 0x224, 19]⟩,
  ⟨.bAnd, [0x39f, 7, 3, 1]⟩,
  ⟨.qMul, [0x381, 0x1e9]⟩,
  ⟨.qLe, [1, 0x1ec]⟩,
  ⟨.qMul, [0x383, 0x1e3]⟩,
  ⟨.qLe, [1, 0x1ee]⟩,
  ⟨.qLe, [0x1ec, 0x1f4]⟩,
  ⟨.ite, [1, 0x1f5, 0x1ed]⟩,
  ⟨.qLt, [0x1ee, 0x1f6]⟩,
  ⟨.qDiv, [0x1f7, 0x3be]⟩,
  ⟨.qLe, [0x1f0, 1]⟩,
  ⟨.ite, [1, 2, 0x1f1]⟩,
  ⟨.qDiv, [0x1f2, 0x3bc]⟩,
  ⟨.qLe, [1, 0x1fb]⟩,
  ⟨.ite, [1, 0x1fc, 2]⟩,
  ⟨.bEq, [0x205, 0x190]⟩,
  ⟨.qMul, [0x3c9, 0x208]⟩,
  ⟨.qMul, [0x18f, 0x209]⟩,
  ⟨.ite, [23, 0x20c, 21]⟩,
  ⟨.qDiv, [0x216, 0x3ae]⟩,
  ⟨.bEq, [0x22b, 0x3df]⟩,
  ⟨.ite, [25, 0x230, 19]⟩,
  ⟨.bEq, [0x158, 0x1f3]⟩,
  ⟨.bEq, [0x182, 0x446]⟩,
  ⟨.bAnd, [0x46c, 7, 3, 1]⟩,
  ⟨.bEq, [0x15e, 0x25d]⟩]

def dictionaryRRRRR : Table Pattern := .leaf #[
  ⟨.bEq, [0x184, 0x4ac]⟩,
  ⟨.bAnd, [0x4cc, 7, 3, 1]⟩,
  ⟨.bEq, [0x15a, 0x2bd]⟩,
  ⟨.bEq, [0x180, 0x50c]⟩,
  ⟨.bAnd, [0x530, 11, 3, 1]⟩,
  ⟨.bEq, [0x15e, 0x321]⟩,
  ⟨.bEq, [0x184, 0x570]⟩,
  ⟨.bEq, [0xf4, 0x384]⟩,
  ⟨.bEq, [0x11e, 0x5d7]⟩,
  ⟨.bAnd, [0x5fc, 10, 3, 1]⟩,
  ⟨.bEq, [0xfd, 0x3ed]⟩,
  ⟨.bEq, [0x123, 0x63c]⟩,
  ⟨.bAnd, [0x65b, 7, 3, 1]⟩,
  ⟨.bEq, [0xf8, 0x44c]⟩,
  ⟨.bEq, [0x11e, 0x69b]⟩,
  ⟨.bEq, [0x8f, 0x4af]⟩,
  ⟨.bEq, [0xf8, 0x4b5]⟩,
  ⟨.bEq, [0xb9, 0x702]⟩,
  ⟨.bEq, [0x120, 0x706]⟩,
  ⟨.bAnd, [0x726, 9, 3, 1]⟩,
  ⟨.bEq, [0x98, 0x517]⟩,
  ⟨.bEq, [0xbe, 0x766]⟩,
  ⟨.bEq, [46, 0x578]⟩,
  ⟨.bEq, [0x96, 0x57e]⟩,
  ⟨.bEq, [89, 0x7cc]⟩,
  ⟨.bEq, [0xbf, 0x7d0]⟩]

def dictionaryRRRR : Table Pattern := .branch 26 dictionaryRRRRL dictionaryRRRRR

def dictionaryRRR : Table Pattern := .branch 52 dictionaryRRRL dictionaryRRRR

def dictionaryRR : Table Pattern := .branch 0x67 dictionaryRRL dictionaryRRR

def dictionaryR : Table Pattern := .branch 0xce dictionaryRL dictionaryRR

def dictionary : Table Pattern := .branch 0x19d dictionaryL dictionaryR

def indices0LLLL : Table Nat := .leaf #[
  0x4003002001,
  0x8007006005,
  0xa005009,
  0x0,
  0xc00b,
  0x1000f00e00d,
  0x11,
  0x3013012000,
  0x17016015014,
  0x0,
  0x18,
  0x1a019,
  0x1b,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1c000]

def indices0LLLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1d000000000,
  0x1e000,
  0x0,
  0x2202102001f,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LLL : Table Nat := .branch 31 indices0LLLL indices0LLLR

def indices0LLRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x23000000000,
  0x26025024000,
  0x28027,
  0x2a029,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x2b000000000,
  0x2e02d02c000,
  0x3203103002f]

def indices0LLRR : Table Nat := .leaf #[
  0x34033,
  0x36035,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x37000000000,
  0x3a039038000,
  0x3d03c02a03b,
  0x4104003f03e,
  0x44043034042,
  0x48047046045,
  0x4c04b04a049,
  0x5004f04e04d,
  0x4f042052051,
  0x56055054053,
  0x5a059058057,
  0x5e05d05c05b,
  0x6206106005f,
  0x66065064063]

def indices0LLR : Table Nat := .branch 31 indices0LLRL indices0LLRR

def indices0LL : Table Nat := .branch 63 indices0LLL indices0LLR

def indices0LRLL : Table Nat := .leaf #[
  0x6a069068067,
  0x6e06d06c06b,
  0x7207107006f,
  0x76075074073,
  0x7a079078077,
  0x7d07c07b065,
  0x8108007f07e,
  0x82,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x83,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LRLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x86085084000,
  0x87,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x88000000000,
  0x89,
  0x0,
  0x0,
  0x8a,
  0x8c00000008b,
  0x9008f08e08d,
  0x92034033091,
  0x96095094093,
  0x98046097044,
  0x9c09b09a099,
  0xa009f09e09d]

def indices0LRL : Table Nat := .branch 31 indices0LRLL indices0LRLR

def indices0LRRL : Table Nat := .leaf #[
  0xa40a30a20a1,
  0xa80a70a60a5,
  0xac0ab0aa0a9,
  0xae07b0650ad,
  0xb20b10b00af,
  0xb40b3033087,
  0xb80b70b60b5,
  0xbc0bb0ba0b9,
  0xc00bf0be0bd,
  0xc40c30c20c1,
  0x5d05c0c40c5,
  0x610600c605e,
  0x650640630c7,
  0xca0c90c8066,
  0xb405d05c089,
  0xb80cc0cb0b5,
  0xce0bb0cd0b9,
  0xd20d10d00cf,
  0xd60d50d40d3,
  0xda0d90d80d7,
  0xdd0dc0db03d,
  0xdf0340420de,
  0xe10460e0044,
  0xe50e40e30e2,
  0xa00e709e0e6,
  0xeb0ea0e90e8,
  0xef0ee0ed0ec,
  0xf30f20f10f0,
  0xae07b0650f4,
  0xf70f60f50af,
  0xb40b3033087,
  0xb80f80b60b5]

def indices0LRRR : Table Nat := .leaf #[
  0xbc0bb0ba0b9,
  0xc00f90be0bd,
  0xc40fc0fb0fa,
  0x5d05c0c40fd,
  0x610600fe05e,
  0x650640630ff,
  0x1000c90c8066,
  0xb405d05c089,
  0xb81010cb0b5,
  0xce0bb0cd0b9,
  0xd20d10d0102,
  0x1040d50d4103,
  0x108107106105,
  0x10a0d910903d,
  0x10e10d10c10b,
  0x11211111010f,
  0xa011409e113,
  0x118117116115,
  0x11c11b11a119,
  0x12011f11e11d,
  0xae07b065121,
  0x1241231220af,
  0x1250b3033087,
  0xb81270b6126,
  0xbc0bb0ba0b9,
  0xc01280be0bd,
  0xc412b12a129,
  0x5d05c0c412c,
  0x6106012d05e,
  0x6506406312e,
  0x12f0c90c8066,
  0x12505d05c089]

def indices0LRR : Table Nat := .branch 32 indices0LRRL indices0LRRR

def indices0LR : Table Nat := .branch 63 indices0LRL indices0LRR

def indices0L : Table Nat := .branch 0x7e indices0LL indices0LR

def indices0RLLL : Table Nat := .leaf #[
  0xb81300cb126,
  0xce0bb0cd0b9,
  0xd20d10d0131,
  0xd50d4132,
  0x0,
  0x136135134133,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x87139138137,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x13b13a000000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x13f13e13d13c]

def indices0RLLR : Table Nat := .leaf #[
  0x34033141140,
  0x144143093142,
  0x46146044145,
  0x14a149148147,
  0x14d09e14c14b,
  0x15014f14e0a0,
  0x154153152151,
  0x158157156155,
  0x7b06515a159,
  0x15c15b0af0ae,
  0xb303308715d,
  0x1600b615f15e,
  0xbb0ba0b90b8,
  0x1610be0bd0bc,
  0x1641631620c0,
  0x5c0c41650c4,
  0x6016605e05d,
  0x64063167061,
  0xc90c8066065,
  0x5d05c089168,
  0x16b0cb16a169,
  0xbb0cd0b90b8,
  0xd10d016c0ce,
  0xd50d416d0d2,
  0xd90d816f16e,
  0x17217103d170,
  0x10d17410b173,
  0x178177176175,
  0x17b09e17a179,
  0x17e17d17c0a0,
  0x18218118017f,
  0x186185184183]

def indices0RLL : Table Nat := .branch 31 indices0RLLL indices0RLLR

def indices0RLRL : Table Nat := .leaf #[
  0x7b06515a159,
  0x1881870af0ae,
  0xb3033087189,
  0x18a0b6126125,
  0xbb0ba0b90b8,
  0x18b0be0bd0bc,
  0x18e18d18c0c0,
  0x5c0c418f0c4,
  0x6019005e05d,
  0x64063191061,
  0xc90c8066065,
  0x5d05c089192,
  0x1930cb126125,
  0xbb0cd0b90b8,
  0xd10d01940ce,
  0xd50d41950d2,
  0x199198197196,
  0x19c19b03d19a,
  0x3404219e19d,
  0x461a004419f,
  0x1781a31a21a1,
  0x1a509e17a1a4,
  0x1a81a71a60a0,
  0x1541531521a9,
  0x1ab1571561aa,
  0x7b06515a159,
  0x1ad1ac0af0ae,
  0xb30330871ae,
  0x18a0b60b50b4,
  0xbb0ba0b90b8,
  0x1af0be0bd0bc,
  0x1b21b11b00c0]

def indices0RLRR : Table Nat := .leaf #[
  0x5c0c41b30c4,
  0x601b405e05d,
  0x640631b5061,
  0xc90c8066065,
  0x5d05c0891b6,
  0x1930cb0b50b4,
  0xbb0cd0b90b8,
  0xd10d01b70ce,
  0xd50d41b80d2,
  0x1bb1ba1b9000,
  0x1bc,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1bf1be1bd000,
  0x87,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1c0000000000,
  0x13b,
  0x0]

def indices0RLR : Table Nat := .branch 32 indices0RLRL indices0RLRR

def indices0RL : Table Nat := .branch 63 indices0RLL indices0RLR

def indices0RRLL : Table Nat := .leaf #[
  0x0,
  0x1c1000000,
  0x1c2000000,
  0xb41c41c3000,
  0x1c703d1c61c5,
  0x3410b1c91c8,
  0x1cd1cc1cb1ca,
  0x1d11d01cf1ce,
  0x1d409e1d31d2,
  0x1d71d61d50a0,
  0x1db1da1d91d8,
  0x1df1de1dd1dc,
  0x7b0651e11e0,
  0x1e31e20af0ae,
  0xb30330871e4,
  0x1e70b61e61e5,
  0xbb0ba0b90b8,
  0x1e80be0bd0bc,
  0x1eb1ea1e90c0,
  0x5c0c41ec0c4,
  0x601ed05e05d,
  0x640631ee061,
  0xc90c8066065,
  0x5d05c0891ef,
  0x1f20cb1f11f0,
  0xbb0cd0b90b8,
  0xd10d01f30ce,
  0xd50d41f40d2,
  0x1f81f71f61f5,
  0x1fb1fa1f903d,
  0x1fd10d1fc10b]

def indices0RRLR : Table Nat := .leaf #[
  0x2012001ff1fe,
  0xa020309e202,
  0x207206205204,
  0x20b20a209208,
  0x20f20e20d20c,
  0xae07b065210,
  0x2132122110af,
  0x2140b3033087,
  0xb82160b6215,
  0xbc0bb0ba0b9,
  0xc02170be0bd,
  0xc421a219218,
  0x5d05c0c421b,
  0x6106021c05e,
  0x6506406321d,
  0x21e0c90c8066,
  0x21405d05c089,
  0xb821f0cb215,
  0xce0bb0cd0b9,
  0xd20d10d0220,
  0x2220d50d4221,
  0x3405c224223,
  0x228227226225,
  0x44229034042,
  0x22c22b04622a,
  0x23022f22e22d,
  0x2320a023109e,
  0x236235234233,
  0x23a239238237,
  0x23e23d23c23b,
  0xaf0ae07b065,
  0x8724124023f]

def indices0RRL : Table Nat := .branch 31 indices0RRLL indices0RRLR

def indices0RRRL : Table Nat := .leaf #[
  0x2432420b3033,
  0xb3033087244,
  0xb90b8246245,
  0x24a249248247,
  0x24d24c24b0be,
  0x25125024f24e,
  0x5e05d05c250,
  0x253061060252,
  0x66065064063,
  0x13b256255254,
  0x25825705d05c,
  0x2590b605d05c,
  0x25a2470b90b8,
  0x25d24925c25b,
  0xd525f25e0d2,
  0x34262261260,
  0x266265264263,
  0x269268034267,
  0x26d26c26b26a,
  0x27127026f26e,
  0x2730a027209e,
  0x277276275274,
  0x27b27a279278,
  0x27f27e27d27c,
  0xaf0ae07b065,
  0x87282281280,
  0x2842830b3033,
  0xb90b82850b6,
  0xbd0bc0bb0ba,
  0x2870c02860be,
  0x28a0c4289288,
  0x5e05d05c0c4]

def indices0RRRR : Table Nat := .leaf #[
  0x28c06106028b,
  0x66065064063,
  0x8928d0c90c8,
  0xb50b405d05c,
  0xb90b828e0cb,
  0x28f0ce0bb0cd,
  0x2900d20d10d0,
  0x2922910d50d4,
  0x295294034293,
  0x34298297296,
  0x29c29b29a299,
  0x2a029f29e29d,
  0x2a309e2a22a1,
  0x2a62a52a40a0,
  0x2aa2a92a82a7,
  0x2ae2ad2ac2ab,
  0xae07b0652af,
  0x2b22b12b00af,
  0x2b30b3033087,
  0x330872b52b4,
  0xb82b62450b3,
  0x4f2b72470b9,
  0x2b80be24a249,
  0x2bb2ba2b924c,
  0x5c2502bc250,
  0x602bd05e05d,
  0x640632be061,
  0x2c02bf066065,
  0x5d05c2c22c1,
  0x5d05c2c42c3,
  0xb90b82c50b6,
  0x2c604f25a247]

def indices0RRR : Table Nat := .branch 32 indices0RRRL indices0RRRR

def indices0RR : Table Nat := .branch 63 indices0RRL indices0RRR

def indices0R : Table Nat := .branch 0x7f indices0RL indices0RR

def indices0 : Table Nat := .branch 0xfd indices0L indices0R

def program0 : Nat → ClosureSemantics.Node := program dictionary indices0

def indices1LLLL : Table Nat := .leaf #[
  0x4003002001,
  0x8007006005,
  0xa005009,
  0x0,
  0xc01c,
  0x1000f00e00d,
  0x11,
  0x3013012000,
  0x17016015014,
  0x0,
  0x18,
  0x1a019,
  0x1b,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LLLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1f000000000,
  0x2c92c82c7,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LLL : Table Nat := .branch 31 indices1LLLL indices1LLLR

def indices1LLRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x23000000,
  0x24,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x2b000000,
  0x2f2ca02d02c,
  0x332cd2cc2cb]

def indices1LLRR : Table Nat := .leaf #[
  0x35000000034,
  0x36,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x2d00372cf2ce,
  0x3b2d1039038,
  0x3e03d2d202a,
  0x422d52d42d3,
  0x2d70442d6034,
  0x492d92d8046,
  0x2dd2dc2db2da,
  0x2df2de04f04e,
  0x5304f0422e0,
  0x2e32e20552e1,
  0x5b2e50592e4,
  0x2e605e05d05c,
  0x632e7061060,
  0x67066065064]

def indices1LLR : Table Nat := .branch 31 indices1LLRL indices1LLRR

def indices1LL : Table Nat := .branch 63 indices1LLL indices1LLR

def indices1LRLL : Table Nat := .leaf #[
  0x6b06a069068,
  0x6f2e806d06c,
  0x730722ea2e9,
  0x770762eb074,
  0x6507a0792ec,
  0x7e07d07c07b,
  0x8208108007f,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0xb000,
  0x83,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LRLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x8a,
  0x8c00000008b,
  0x9008f08e08d,
  0x34033091,
  0x2ee2ed000,
  0x0,
  0x0,
  0x0]

def indices1LRL : Table Nat := .branch 31 indices1LRLL indices1LRLR

def indices1LRRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x2f12f02ef000,
  0x87,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x2f2000000000,
  0x89,
  0x0,
  0x0,
  0xcf,
  0xd60000000d3,
  0xda0d90d80d7,
  0xdd0dc0db03d,
  0xdf0340420de,
  0x2f30460e0044,
  0x2f62f52f40e2,
  0xa00e709e2f7,
  0xeb0ea0e90e8,
  0x2fb2fa2f92f8,
  0x1112fe2fd2fc,
  0xae07b0652ff,
  0x3023013000af,
  0xb40b3033087,
  0xb83030b60b5]

def indices1LRRR : Table Nat := .leaf #[
  0xbc0bb0ba0b9,
  0xc00f90be0bd,
  0xc43040fb0fa,
  0x5d05c0c40fd,
  0x610600fe05e,
  0x650640630ff,
  0x3050c90c8066,
  0xb405d05c089,
  0xb83060cb0b5,
  0xce0bb0cd0b9,
  0xd20d10d0102,
  0x1040d50d4103,
  0x108107106105,
  0x10a0d910903d,
  0x30710d10c10b,
  0x30a30930810f,
  0xa011409e30b,
  0x118117116115,
  0x30f30e30d30c,
  0x313312311310,
  0xae07b065314,
  0x3173163150af,
  0x1250b3033087,
  0xb83180b6126,
  0xbc0bb0ba0b9,
  0xc01280be0bd,
  0xc431912a129,
  0x5d05c0c412c,
  0x6106012d05e,
  0x6506406312e,
  0x31a0c90c8066,
  0x12505d05c089]

def indices1LRR : Table Nat := .branch 32 indices1LRRL indices1LRRR

def indices1LR : Table Nat := .branch 63 indices1LRL indices1LRR

def indices1L : Table Nat := .branch 0x7e indices1LL indices1LR

def indices1RLLL : Table Nat := .leaf #[
  0xb831b0cb126,
  0xce0bb0cd0b9,
  0xd20d10d0131,
  0xd50d4132,
  0x0,
  0x136135134133,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x8713913831c,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x13b31d000000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x13f13e13d13c]

def indices1RLLR : Table Nat := .leaf #[
  0x34033141140,
  0x144143093142,
  0x46146044145,
  0x14a14914831e,
  0x14d09e14c14b,
  0x15014f14e0a0,
  0x154153152151,
  0x158157156155,
  0x7b06515a159,
  0x15c31f0af0ae,
  0xb303308715d,
  0x1600b615f15e,
  0xbb0ba0b90b8,
  0x1610be0bd0bc,
  0x1641631620c0,
  0x5c0c41650c4,
  0x6016605e05d,
  0x64063167061,
  0xc90c8066065,
  0x5d05c089320,
  0x16b0cb16a169,
  0xbb0cd0b90b8,
  0xd10d016c0ce,
  0xd50d416d0d2,
  0xd90d816f16e,
  0x17217103d170,
  0x10d17410b173,
  0x178177176321,
  0x17b09e17a179,
  0x17e17d17c0a0,
  0x18218118017f,
  0x186185184183]

def indices1RLL : Table Nat := .branch 31 indices1RLLL indices1RLLR

def indices1RLRL : Table Nat := .leaf #[
  0x7b06515a159,
  0x1883220af0ae,
  0xb3033087189,
  0x18a0b6126125,
  0xbb0ba0b90b8,
  0x18b0be0bd0bc,
  0x18e18d18c0c0,
  0x5c0c418f0c4,
  0x6019005e05d,
  0x64063191061,
  0xc90c8066065,
  0x5d05c089323,
  0x1930cb126125,
  0xbb0cd0b90b8,
  0xd10d01940ce,
  0xd50d41950d2,
  0x199198197196,
  0x19c19b03d19a,
  0x3404219e19d,
  0x461a004419f,
  0x1781a31a2324,
  0x1a509e17a1a4,
  0x1a81a71a60a0,
  0x1541531521a9,
  0x1ab1571561aa,
  0x7b06515a159,
  0x1ad3250af0ae,
  0xb30330871ae,
  0x18a0b60b50b4,
  0xbb0ba0b90b8,
  0x1af0be0bd0bc,
  0x1b21b11b00c0]

def indices1RLRR : Table Nat := .leaf #[
  0x5c0c41b30c4,
  0x601b405e05d,
  0x640631b5061,
  0xc90c8066065,
  0x5d05c089326,
  0x1930cb0b50b4,
  0xbb0cd0b90b8,
  0xd10d01b70ce,
  0xd50d41b80d2,
  0x1bb1ba1b9000,
  0x1bc,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1bf1be327000,
  0x87,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x328000000000,
  0x13b,
  0x0]

def indices1RLR : Table Nat := .branch 32 indices1RLRL indices1RLRR

def indices1RL : Table Nat := .branch 63 indices1RLL indices1RLR

def indices1RRLL : Table Nat := .leaf #[
  0x0,
  0x1c1000000,
  0x1c2000000,
  0xb41c41c3000,
  0x1c703d1c61c5,
  0x3410b1c91c8,
  0x1cd1cc1cb1ca,
  0x1d11d01cf329,
  0x1d409e1d31d2,
  0x1d71d61d50a0,
  0x1db1da1d91d8,
  0x1df1de1dd1dc,
  0x7b0651e11e0,
  0x1e332a0af0ae,
  0xb30330871e4,
  0x1e70b61e61e5,
  0xbb0ba0b90b8,
  0x1e80be0bd0bc,
  0x1eb1ea1e90c0,
  0x5c0c41ec0c4,
  0x601ed05e05d,
  0x640631ee061,
  0xc90c8066065,
  0x5d05c08932b,
  0x1f20cb1f11f0,
  0xbb0cd0b90b8,
  0xd10d01f30ce,
  0xd50d41f40d2,
  0x1f81f71f61f5,
  0x1fb1fa1f903d,
  0x32c10d1fc10b]

def indices1RRLR : Table Nat := .leaf #[
  0x2012001ff1fe,
  0xa020309e202,
  0x207206205204,
  0x20b20a209208,
  0x20f20e20d20c,
  0xae07b065210,
  0x21321232d0af,
  0x2140b3033087,
  0xb82160b6215,
  0xbc0bb0ba0b9,
  0xc02170be0bd,
  0xc421a219218,
  0x5d05c0c421b,
  0x6106021c05e,
  0x6506406321d,
  0x32e0c90c8066,
  0x21405d05c089,
  0xb821f0cb215,
  0xce0bb0cd0b9,
  0xd20d10d0220,
  0x2220d50d4221,
  0x3405c224223,
  0x228227226225,
  0x44229034042,
  0x22c22b04622a,
  0x23022f22e22d,
  0x2320a023109e,
  0x236235234233,
  0x23a239238237,
  0x23e23d23c23b,
  0xaf0ae07b065,
  0x8724124032f]

def indices1RRL : Table Nat := .branch 31 indices1RRLL indices1RRLR

def indices1RRRL : Table Nat := .leaf #[
  0x2433300b3033,
  0xb3033087244,
  0xb90b8246245,
  0x24a249248247,
  0x24d24c24b0be,
  0x25125024f24e,
  0x5e05d05c250,
  0x253061060252,
  0x66065064063,
  0x13b331255254,
  0x25833205d05c,
  0x2590b605d05c,
  0x25a2470b90b8,
  0x25d24925c25b,
  0xd525f25e0d2,
  0x34262261260,
  0x266265264263,
  0x269268034267,
  0x26d33326b26a,
  0x27127026f26e,
  0x2730a027209e,
  0x277276275274,
  0x27b27a279278,
  0x27f27e27d27c,
  0xaf0ae07b065,
  0x87282281334,
  0x2842830b3033,
  0xb90b82850b6,
  0xbd0bc0bb0ba,
  0x2870c02860be,
  0x28a0c4289288,
  0x5e05d05c0c4]

def indices1RRRR : Table Nat := .leaf #[
  0x28c06106028b,
  0x66065064063,
  0x893350c90c8,
  0xb50b405d05c,
  0xb90b828e0cb,
  0x28f0ce0bb0cd,
  0x2900d20d10d0,
  0x2922910d50d4,
  0x295294034293,
  0x34298297296,
  0x29c29b29a299,
  0x2a029f29e29d,
  0x2a309e2a22a1,
  0x2a62a52a40a0,
  0x2aa2a92a82a7,
  0x2ae2ad2ac2ab,
  0xae07b0652af,
  0x2b22b13360af,
  0x3370b3033087,
  0x330872b52b4,
  0xb82b62450b3,
  0x4f2b72470b9,
  0x2b80be24a249,
  0x2bb2ba2b924c,
  0x5c2502bc250,
  0x602bd05e05d,
  0x640632be061,
  0x2c02bf066065,
  0x5d05c2c2338,
  0x5d05c2c4339,
  0xb90b82c50b6,
  0x2c604f25a247]

def indices1RRR : Table Nat := .branch 32 indices1RRRL indices1RRRR

def indices1RR : Table Nat := .branch 63 indices1RRL indices1RRR

def indices1R : Table Nat := .branch 0x7f indices1RL indices1RR

def indices1 : Table Nat := .branch 0xfd indices1L indices1R

def program1 : Nat → ClosureSemantics.Node := program dictionary indices1

end ClosurePrefixAdapterData

end PolicySubmissionPart72

/- Component ClosureAdapterChecks0; SHA256 6bb201a26b5d4704314ad02e581db6ce4cf0e89178262b25f0080dfaef2c6527. -/
section PolicySubmissionPart73
/- Checked equality and child closure for a finite input adapter. -/
namespace ClosureAdapterChecks0
open ClosurePrefixAdapter ClosurePrefixAdapterData

abbrev Good (i : Nat) : Prop := check ClosureFixedWidthData0.program dictionary indices0 0x7ec i = true

def c0 : ∀ i : Fin 64, Good (0+i.val) := by decide +kernel

def c1 : ∀ i : Fin 64, Good (64+i.val) := by decide +kernel

def c2 : ∀ i : Fin 64, Good (0x80+i.val) := by decide +kernel

def c3 : ∀ i : Fin 64, Good (0xc0+i.val) := by decide +kernel

def c4 : ∀ i : Fin 64, Good (0x100+i.val) := by decide +kernel

def c5 : ∀ i : Fin 64, Good (0x140+i.val) := by decide +kernel

def c6 : ∀ i : Fin 64, Good (0x180+i.val) := by decide +kernel

def c7 : ∀ i : Fin 64, Good (0x1c0+i.val) := by decide +kernel

def c8 : ∀ i : Fin 64, Good (0x200+i.val) := by decide +kernel

def c9 : ∀ i : Fin 64, Good (0x240+i.val) := by decide +kernel

def c10 : ∀ i : Fin 64, Good (0x280+i.val) := by decide +kernel

def c11 : ∀ i : Fin 64, Good (0x2c0+i.val) := by decide +kernel

def c12 : ∀ i : Fin 64, Good (0x300+i.val) := by decide +kernel

def c13 : ∀ i : Fin 64, Good (0x340+i.val) := by decide +kernel

def c14 : ∀ i : Fin 64, Good (0x380+i.val) := by decide +kernel

def c15 : ∀ i : Fin 64, Good (0x3c0+i.val) := by decide +kernel

def c16 : ∀ i : Fin 64, Good (0x400+i.val) := by decide +kernel

def c17 : ∀ i : Fin 64, Good (0x440+i.val) := by decide +kernel

def c18 : ∀ i : Fin 64, Good (0x480+i.val) := by decide +kernel

def c19 : ∀ i : Fin 64, Good (0x4c0+i.val) := by decide +kernel

def c20 : ∀ i : Fin 64, Good (0x500+i.val) := by decide +kernel

def c21 : ∀ i : Fin 64, Good (0x540+i.val) := by decide +kernel

def c22 : ∀ i : Fin 64, Good (0x580+i.val) := by decide +kernel

def c23 : ∀ i : Fin 64, Good (0x5c0+i.val) := by decide +kernel

def c24 : ∀ i : Fin 64, Good (0x600+i.val) := by decide +kernel

def c25 : ∀ i : Fin 64, Good (0x640+i.val) := by decide +kernel

def c26 : ∀ i : Fin 64, Good (0x680+i.val) := by decide +kernel

def c27 : ∀ i : Fin 64, Good (0x6c0+i.val) := by decide +kernel

def c28 : ∀ i : Fin 64, Good (0x700+i.val) := by decide +kernel

def c29 : ∀ i : Fin 64, Good (0x740+i.val) := by decide +kernel

def c30 : ∀ i : Fin 64, Good (0x780+i.val) := by decide +kernel

def c31 : ∀ i : Fin 44, Good (0x7c0+i.val) := by decide +kernel

def checked : ∀ i < 0x7ec, Good i := by
  intro i hi
  exact (interval_join 0 0x400 0x7ec
  (interval_join 0 0x200 0x400
  (interval_join 0 0x100 0x200
  (interval_join 0 0x80 0x100
  (interval_join 0 64 0x80
  (interval_from_fin 0 64 c0)
  (interval_from_fin 64 64 c1))
  (interval_join 0x80 0xc0 0x100
  (interval_from_fin 0x80 64 c2)
  (interval_from_fin 0xc0 64 c3)))
  (interval_join 0x100 0x180 0x200
  (interval_join 0x100 0x140 0x180
  (interval_from_fin 0x100 64 c4)
  (interval_from_fin 0x140 64 c5))
  (interval_join 0x180 0x1c0 0x200
  (interval_from_fin 0x180 64 c6)
  (interval_from_fin 0x1c0 64 c7))))
  (interval_join 0x200 0x300 0x400
  (interval_join 0x200 0x280 0x300
  (interval_join 0x200 0x240 0x280
  (interval_from_fin 0x200 64 c8)
  (interval_from_fin 0x240 64 c9))
  (interval_join 0x280 0x2c0 0x300
  (interval_from_fin 0x280 64 c10)
  (interval_from_fin 0x2c0 64 c11)))
  (interval_join 0x300 0x380 0x400
  (interval_join 0x300 0x340 0x380
  (interval_from_fin 0x300 64 c12)
  (interval_from_fin 0x340 64 c13))
  (interval_join 0x380 0x3c0 0x400
  (interval_from_fin 0x380 64 c14)
  (interval_from_fin 0x3c0 64 c15)))))
  (interval_join 0x400 0x600 0x7ec
  (interval_join 0x400 0x500 0x600
  (interval_join 0x400 0x480 0x500
  (interval_join 0x400 0x440 0x480
  (interval_from_fin 0x400 64 c16)
  (interval_from_fin 0x440 64 c17))
  (interval_join 0x480 0x4c0 0x500
  (interval_from_fin 0x480 64 c18)
  (interval_from_fin 0x4c0 64 c19)))
  (interval_join 0x500 0x580 0x600
  (interval_join 0x500 0x540 0x580
  (interval_from_fin 0x500 64 c20)
  (interval_from_fin 0x540 64 c21))
  (interval_join 0x580 0x5c0 0x600
  (interval_from_fin 0x580 64 c22)
  (interval_from_fin 0x5c0 64 c23))))
  (interval_join 0x600 0x700 0x7ec
  (interval_join 0x600 0x680 0x700
  (interval_join 0x600 0x640 0x680
  (interval_from_fin 0x600 64 c24)
  (interval_from_fin 0x640 64 c25))
  (interval_join 0x680 0x6c0 0x700
  (interval_from_fin 0x680 64 c26)
  (interval_from_fin 0x6c0 64 c27)))
  (interval_join 0x700 0x780 0x7ec
  (interval_join 0x700 0x740 0x780
  (interval_from_fin 0x700 64 c28)
  (interval_from_fin 0x740 64 c29))
  (interval_join 0x780 0x7c0 0x7ec
  (interval_from_fin 0x780 64 c30)
  (interval_from_fin 0x7c0 44 c31)))))) i (Nat.zero_le i) hi

def model_agrees (input : ClosureSemantics.Valuation) :
    ∀ i < 0x7ec, 0 < indexAt indices0 i →
      ClosureSemantics.programModel ClosureFixedWidthData0.program input i =
        ClosureSemantics.programModel program0 input i :=
  checked_model_eq ClosureFixedWidthData0.program dictionary indices0 input 0x7ec checked

end ClosureAdapterChecks0

end PolicySubmissionPart73

/- Component ClosureAdapterChecks1; SHA256 5ebb7c3a6e4cd2d88ffcca206b2299c7e2c8c54606b54bcc976dc9302ffbdb47. -/
section PolicySubmissionPart74
/- Checked equality and child closure for a finite input adapter. -/
namespace ClosureAdapterChecks1
open ClosurePrefixAdapter ClosurePrefixAdapterData

abbrev Good (i : Nat) : Prop := check ClosureFixedWidthData1.program dictionary indices1 0x7ec i = true

def c0 : ∀ i : Fin 64, Good (0+i.val) := by decide +kernel

def c1 : ∀ i : Fin 64, Good (64+i.val) := by decide +kernel

def c2 : ∀ i : Fin 64, Good (0x80+i.val) := by decide +kernel

def c3 : ∀ i : Fin 64, Good (0xc0+i.val) := by decide +kernel

def c4 : ∀ i : Fin 64, Good (0x100+i.val) := by decide +kernel

def c5 : ∀ i : Fin 64, Good (0x140+i.val) := by decide +kernel

def c6 : ∀ i : Fin 64, Good (0x180+i.val) := by decide +kernel

def c7 : ∀ i : Fin 64, Good (0x1c0+i.val) := by decide +kernel

def c8 : ∀ i : Fin 64, Good (0x200+i.val) := by decide +kernel

def c9 : ∀ i : Fin 64, Good (0x240+i.val) := by decide +kernel

def c10 : ∀ i : Fin 64, Good (0x280+i.val) := by decide +kernel

def c11 : ∀ i : Fin 64, Good (0x2c0+i.val) := by decide +kernel

def c12 : ∀ i : Fin 64, Good (0x300+i.val) := by decide +kernel

def c13 : ∀ i : Fin 64, Good (0x340+i.val) := by decide +kernel

def c14 : ∀ i : Fin 64, Good (0x380+i.val) := by decide +kernel

def c15 : ∀ i : Fin 64, Good (0x3c0+i.val) := by decide +kernel

def c16 : ∀ i : Fin 64, Good (0x400+i.val) := by decide +kernel

def c17 : ∀ i : Fin 64, Good (0x440+i.val) := by decide +kernel

def c18 : ∀ i : Fin 64, Good (0x480+i.val) := by decide +kernel

def c19 : ∀ i : Fin 64, Good (0x4c0+i.val) := by decide +kernel

def c20 : ∀ i : Fin 64, Good (0x500+i.val) := by decide +kernel

def c21 : ∀ i : Fin 64, Good (0x540+i.val) := by decide +kernel

def c22 : ∀ i : Fin 64, Good (0x580+i.val) := by decide +kernel

def c23 : ∀ i : Fin 64, Good (0x5c0+i.val) := by decide +kernel

def c24 : ∀ i : Fin 64, Good (0x600+i.val) := by decide +kernel

def c25 : ∀ i : Fin 64, Good (0x640+i.val) := by decide +kernel

def c26 : ∀ i : Fin 64, Good (0x680+i.val) := by decide +kernel

def c27 : ∀ i : Fin 64, Good (0x6c0+i.val) := by decide +kernel

def c28 : ∀ i : Fin 64, Good (0x700+i.val) := by decide +kernel

def c29 : ∀ i : Fin 64, Good (0x740+i.val) := by decide +kernel

def c30 : ∀ i : Fin 64, Good (0x780+i.val) := by decide +kernel

def c31 : ∀ i : Fin 44, Good (0x7c0+i.val) := by decide +kernel

def checked : ∀ i < 0x7ec, Good i := by
  intro i hi
  exact (interval_join 0 0x400 0x7ec
  (interval_join 0 0x200 0x400
  (interval_join 0 0x100 0x200
  (interval_join 0 0x80 0x100
  (interval_join 0 64 0x80
  (interval_from_fin 0 64 c0)
  (interval_from_fin 64 64 c1))
  (interval_join 0x80 0xc0 0x100
  (interval_from_fin 0x80 64 c2)
  (interval_from_fin 0xc0 64 c3)))
  (interval_join 0x100 0x180 0x200
  (interval_join 0x100 0x140 0x180
  (interval_from_fin 0x100 64 c4)
  (interval_from_fin 0x140 64 c5))
  (interval_join 0x180 0x1c0 0x200
  (interval_from_fin 0x180 64 c6)
  (interval_from_fin 0x1c0 64 c7))))
  (interval_join 0x200 0x300 0x400
  (interval_join 0x200 0x280 0x300
  (interval_join 0x200 0x240 0x280
  (interval_from_fin 0x200 64 c8)
  (interval_from_fin 0x240 64 c9))
  (interval_join 0x280 0x2c0 0x300
  (interval_from_fin 0x280 64 c10)
  (interval_from_fin 0x2c0 64 c11)))
  (interval_join 0x300 0x380 0x400
  (interval_join 0x300 0x340 0x380
  (interval_from_fin 0x300 64 c12)
  (interval_from_fin 0x340 64 c13))
  (interval_join 0x380 0x3c0 0x400
  (interval_from_fin 0x380 64 c14)
  (interval_from_fin 0x3c0 64 c15)))))
  (interval_join 0x400 0x600 0x7ec
  (interval_join 0x400 0x500 0x600
  (interval_join 0x400 0x480 0x500
  (interval_join 0x400 0x440 0x480
  (interval_from_fin 0x400 64 c16)
  (interval_from_fin 0x440 64 c17))
  (interval_join 0x480 0x4c0 0x500
  (interval_from_fin 0x480 64 c18)
  (interval_from_fin 0x4c0 64 c19)))
  (interval_join 0x500 0x580 0x600
  (interval_join 0x500 0x540 0x580
  (interval_from_fin 0x500 64 c20)
  (interval_from_fin 0x540 64 c21))
  (interval_join 0x580 0x5c0 0x600
  (interval_from_fin 0x580 64 c22)
  (interval_from_fin 0x5c0 64 c23))))
  (interval_join 0x600 0x700 0x7ec
  (interval_join 0x600 0x680 0x700
  (interval_join 0x600 0x640 0x680
  (interval_from_fin 0x600 64 c24)
  (interval_from_fin 0x640 64 c25))
  (interval_join 0x680 0x6c0 0x700
  (interval_from_fin 0x680 64 c26)
  (interval_from_fin 0x6c0 64 c27)))
  (interval_join 0x700 0x780 0x7ec
  (interval_join 0x700 0x740 0x780
  (interval_from_fin 0x700 64 c28)
  (interval_from_fin 0x740 64 c29))
  (interval_join 0x780 0x7c0 0x7ec
  (interval_from_fin 0x780 64 c30)
  (interval_from_fin 0x7c0 44 c31)))))) i (Nat.zero_le i) hi

def model_agrees (input : ClosureSemantics.Valuation) :
    ∀ i < 0x7ec, 0 < indexAt indices1 i →
      ClosureSemantics.programModel ClosureFixedWidthData1.program input i =
        ClosureSemantics.programModel program1 input i :=
  checked_model_eq ClosureFixedWidthData1.program dictionary indices1 input 0x7ec checked

end ClosureAdapterChecks1

end PolicySubmissionPart74

/- Component ClosureSharedAnchorPatternDataExplicit; SHA256 41d2bc6f88ec02918d92865b567e98a7d477c7a36fb10d8583404ab44d500f5b. -/
section PolicySubmissionPart75
/- Explicit, hash-consed anchor patterns. Same interface as the packed
module: `patterns : Nat → Pattern`. Generated by
`prepare_explicit_anchor_patterns.py` from the packed decoder's own output. -/
namespace ClosureSharedAnchorPatternData
open ClosureSemantics ClosurePattern

def s0 := Pattern.node (Op.qConst (Int.cast 1)) []
def s1 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x271)) [])]
def s2 := Pattern.node (Op.qConst (Int.cast 5)) []
def s3 := Pattern.node (Op.qConst (Int.cast 4)) []
def s4 := Pattern.node Op.qDiv [s2, s3]
def s5 := Pattern.node (Op.input 0) []
def s6 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x400)) [])]), s5]
def s7 := Pattern.node Op.qMul [s6, s3]
def s8 := Pattern.node Op.ite [(Pattern.node Op.qLe [s7, s1]), s7, s6]
def s9 := Pattern.node Op.qLt [s1, (Pattern.node Op.qMul [s4, s8])]
def s10 := Pattern.node (Op.qConst (Int.cast 9)) []
def s11 := Pattern.node Op.qDiv [(Pattern.node (Op.qConst (Int.cast 10)) []), s10]
def s12 := Pattern.node (Op.input 1) []
def s13 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x2d9)) [])]), s12]
def s14 := Pattern.node (Op.qConst (Int.cast 3)) []
def s15 := Pattern.node Op.qMul [s13, s14]
def s16 := Pattern.node Op.ite [(Pattern.node Op.qLe [s15, s1]), s15, s13]
def s17 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s16]), s1]
def s18 := Pattern.node Op.qDiv [s3, s14]
def s19 := Pattern.node Op.qLt [s1, (Pattern.node Op.qMul [s18, s16])]
def s20 := Pattern.node (Op.qConst (Int.cast 2)) []
def s21 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x1000)) [])]), s5]
def s22 := Pattern.node Op.qMul [s21, s3]
def s23 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0xc35)) [])]
def s24 := Pattern.node Op.ite [(Pattern.node Op.qLe [s22, s23]), s22, s21]
def s25 := Pattern.node Op.qMul [s20, s24]
def s26 := Pattern.node Op.qLe [s25, s23]
def s27 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x19a1)) [])]), s12]
def s28 := Pattern.node Op.qMul [s27, s14]
def s29 := Pattern.node Op.ite [(Pattern.node Op.qLe [s28, s23]), s28, s27]
def s30 := Pattern.node Op.qMul [s20, s29]
def s31 := Pattern.node Op.qLe [s30, s23]
def s32 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s26]), (Pattern.node Op.bNot [s31])]
def s33 := Pattern.node Op.ite [s26, s25, (Pattern.node Op.qDiv [s24, s20])]
def s34 := Pattern.node Op.ite [s31, s30, (Pattern.node Op.qDiv [s30, s14])]
def s35 := Pattern.node (Op.bConst true) []
def s36 := Pattern.node (Op.zConst 1) []
def s37 := Pattern.node (Op.zConst 0) []
def s38 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0), (Pattern.hole 1), (Pattern.hole 2)]), s36, s37]
def s39 := Pattern.node Op.zSub [s38, (Pattern.node Op.ite [(Pattern.hole 3), s36, s37])]
def s40 := Pattern.node Op.zEq [s39, s37]
def s41 := Pattern.hole 5
def s42 := Pattern.hole 4
def s43 := Pattern.node Op.ite [(Pattern.node Op.qLe [s41, s42]), s42, s41]
def s44 := Pattern.node Op.qDiv [s42, s3]
def s45 := Pattern.node Op.qDiv [s41, s14]
def s46 := Pattern.node Op.ite [s40, s43, (Pattern.node Op.ite [(Pattern.node Op.qLt [s41, s42]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s41, s44]), s44, s41]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s45, s42]), s42, s45])])]
def s47 := Pattern.node (Op.input 43) []
def s48 := Pattern.node Op.ite [s40, s23, s43]
def s49 := Pattern.node Op.ite [s40, (Pattern.node Op.qLe [s47, s48]), (Pattern.node Op.qLt [s47, s48])]
def s50 := Pattern.node Op.bAnd [s26, s31]
def s51 := Pattern.node Op.qLe [s29, s24]
def s52 := Pattern.node Op.ite [(Pattern.hole 9), s24, s29]
def s53 := Pattern.node Op.qLt [s29, s24]
def s54 := Pattern.node Op.qDiv [s24, s3]
def s55 := Pattern.node Op.qLe [s29, s54]
def s56 := Pattern.node Op.ite [(Pattern.hole 12), s54, s29]
def s57 := Pattern.node Op.qDiv [s29, s14]
def s58 := Pattern.node Op.qLe [s57, s24]
def s59 := Pattern.node Op.ite [(Pattern.hole 14), s24, s57]
def s60 := Pattern.node Op.zSub [s38, (Pattern.node Op.ite [(Pattern.hole 8), s36, s37])]
def s61 := Pattern.node Op.zEq [s60, s37]
def s62 := Pattern.node Op.ite [s61, s23, (Pattern.hole 10)]
def s63 := Pattern.node Op.ite [s61, (Pattern.node Op.qLe [s47, s62]), (Pattern.node Op.qLt [s47, s62])]
def s64 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s60]), (Pattern.node Op.qLe [(Pattern.node Op.ite [s61, (Pattern.hole 10), (Pattern.node Op.ite [(Pattern.hole 11), (Pattern.hole 13), (Pattern.hole 15)])]), s47]), (Pattern.hole 16)]
def s65 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0xf5)) [])]
def s66 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x100)) [])]), s5]
def s67 := Pattern.node Op.qMul [s66, s3]
def s68 := Pattern.node Op.ite [(Pattern.node Op.qLe [s67, s65]), s67, s66]
def s69 := Pattern.node Op.qLt [s65, (Pattern.node Op.qMul [s4, s68])]
def s70 := Pattern.node Op.ite [(Pattern.node Op.qLe [s15, s65]), s15, s13]
def s71 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s70]), s65]
def s72 := Pattern.node Op.qLt [s65, (Pattern.node Op.qMul [s18, s70])]
def s73 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x4c9)) [])]
def s74 := Pattern.node Op.ite [(Pattern.node Op.qLe [s22, s73]), s22, s21]
def s75 := Pattern.node Op.qMul [s20, s74]
def s76 := Pattern.node Op.qLe [s75, s73]
def s77 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x88b)) [])]), s12]
def s78 := Pattern.node Op.qMul [s77, s14]
def s79 := Pattern.node Op.ite [(Pattern.node Op.qLe [s78, s73]), s78, s77]
def s80 := Pattern.node Op.qMul [s20, s79]
def s81 := Pattern.node Op.qLe [s80, s73]
def s82 := Pattern.node Op.bAnd [s76, s81]
def s83 := Pattern.node Op.qLe [s79, s74]
def s84 := Pattern.node Op.ite [(Pattern.hole 22), s74, s79]
def s85 := Pattern.node Op.qLt [s79, s74]
def s86 := Pattern.node Op.qDiv [s74, s3]
def s87 := Pattern.node Op.qLe [s79, s86]
def s88 := Pattern.node Op.ite [(Pattern.hole 25), s86, s79]
def s89 := Pattern.node Op.qDiv [s79, s14]
def s90 := Pattern.node Op.qLe [s89, s74]
def s91 := Pattern.node Op.ite [(Pattern.hole 27), s74, s89]
def s92 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 18), (Pattern.hole 19), (Pattern.hole 20)]), s36, s37]
def s93 := Pattern.node Op.zSub [s92, (Pattern.node Op.ite [(Pattern.hole 21), s36, s37])]
def s94 := Pattern.node Op.zEq [s93, s37]
def s95 := Pattern.node Op.ite [s94, (Pattern.hole 23), (Pattern.node Op.ite [(Pattern.hole 24), (Pattern.hole 26), (Pattern.hole 28)])]
def s96 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x1324)) [])]
def s97 := Pattern.node Op.ite [(Pattern.node Op.qLe [s95, s96]), s96, s95]
def s98 := Pattern.node (Op.input 36) []
def s99 := Pattern.node (Op.bConst false) []
def s100 := Pattern.node (Op.input 37) []
def s101 := Pattern.node Op.qMul [s3, s100]
def s102 := Pattern.node (Op.qConst (Int.cast 6)) []
def s103 := Pattern.node Op.qMul [s102, s100]
def s104 := Pattern.node Op.ite [(Pattern.node Op.bEq [s98, s99]), s101, s103]
def s105 := Pattern.node (Op.input 38) []
def s106 := Pattern.node (Op.input 39) []
def s107 := Pattern.node Op.qMul [s3, s106]
def s108 := Pattern.node Op.qMul [s102, s106]
def s109 := Pattern.node Op.ite [(Pattern.node Op.bEq [s105, s99]), s107, s108]
def s110 := Pattern.node Op.ite [(Pattern.node Op.qLe [s109, (Pattern.hole 29)]), (Pattern.hole 29), s109]
def s111 := Pattern.node Op.qLe [s104, s110]
def s112 := Pattern.node Op.ite [(Pattern.hole 30), s110, s104]
def s113 := Pattern.hole 31
def s114 := Pattern.node Op.ite [s94, s73, (Pattern.hole 23)]
def s115 := Pattern.node Op.ite [s94, (Pattern.node Op.qLe [s113, s114]), (Pattern.node Op.qLt [s113, s114])]
def s116 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s93]), (Pattern.node Op.qLe [s95, s113]), (Pattern.hole 32)]
def s117 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s76]), (Pattern.node Op.bNot [s81])]
def s118 := Pattern.node Op.ite [s76, s75, (Pattern.node Op.qDiv [s74, s20])]
def s119 := Pattern.node Op.ite [s81, s80, (Pattern.node Op.qDiv [s80, s14])]
def s120 := Pattern.node Op.zSub [s92, (Pattern.node Op.ite [(Pattern.hole 34), s36, s37])]
def s121 := Pattern.node Op.zEq [s120, s37]
def s122 := Pattern.hole 36
def s123 := Pattern.hole 35
def s124 := Pattern.node Op.ite [(Pattern.node Op.qLe [s122, s123]), s123, s122]
def s125 := Pattern.node Op.qDiv [s123, s3]
def s126 := Pattern.node Op.qDiv [s122, s14]
def s127 := Pattern.node Op.ite [s121, s124, (Pattern.node Op.ite [(Pattern.node Op.qLt [s122, s123]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s122, s125]), s125, s122]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s126, s123]), s123, s126])])]
def s128 := Pattern.node Op.ite [(Pattern.node Op.bEq [s105, s35]), s107, s108]
def s129 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 37), s96]), s96, (Pattern.hole 37)]
def s130 := Pattern.node Op.ite [(Pattern.node Op.qLe [s128, s129]), s129, s128]
def s131 := Pattern.node Op.ite [(Pattern.node Op.bEq [s98, s35]), s101, s103]
def s132 := Pattern.node Op.ite [(Pattern.node Op.qLe [s131, (Pattern.hole 38)]), (Pattern.hole 38), s131]
def s133 := Pattern.node Op.ite [s121, s73, s124]
def s134 := Pattern.node Op.qLe [s132, s133]
def s135 := Pattern.node Op.qLt [s132, s133]
def s136 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s120]), (Pattern.node Op.qLe [(Pattern.hole 37), s132]), (Pattern.node Op.ite [s121, (Pattern.hole 39), (Pattern.hole 40)])]
def s137 := Pattern.node Op.ite [s76, (Pattern.hole 41), (Pattern.node Op.bNot [(Pattern.hole 33)])]
def s138 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0xaf)) [])]
def s139 := Pattern.node Op.ite [(Pattern.node Op.qLe [s67, s138]), s67, s66]
def s140 := Pattern.node Op.qLt [s138, (Pattern.node Op.qMul [s4, s139])]
def s141 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0xf3)) [])]), s12]
def s142 := Pattern.node Op.qMul [s141, s14]
def s143 := Pattern.node Op.ite [(Pattern.node Op.qLe [s142, s138]), s142, s141]
def s144 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s143]), s138]
def s145 := Pattern.node Op.qLt [s138, (Pattern.node Op.qMul [s18, s143])]
def s146 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x36b)) [])]
def s147 := Pattern.node Op.ite [(Pattern.node Op.qLe [s7, s146]), s7, s6]
def s148 := Pattern.node Op.qMul [s20, s147]
def s149 := Pattern.node Op.qLe [s148, s146]
def s150 := Pattern.node Op.ite [(Pattern.node Op.qLe [s78, s146]), s78, s77]
def s151 := Pattern.node Op.qMul [s20, s150]
def s152 := Pattern.node Op.qLe [s151, s146]
def s153 := Pattern.node Op.bAnd [s149, s152]
def s154 := Pattern.node Op.qLe [s150, s147]
def s155 := Pattern.node Op.ite [(Pattern.hole 47), s147, s150]
def s156 := Pattern.node Op.qLt [s150, s147]
def s157 := Pattern.node Op.qDiv [s147, s3]
def s158 := Pattern.node Op.qLe [s150, s157]
def s159 := Pattern.node Op.ite [(Pattern.hole 50), s157, s150]
def s160 := Pattern.node Op.qDiv [s150, s14]
def s161 := Pattern.node Op.qLe [s160, s147]
def s162 := Pattern.node Op.ite [(Pattern.hole 52), s147, s160]
def s163 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 43), (Pattern.hole 44), (Pattern.hole 45)]), s36, s37]
def s164 := Pattern.node Op.zSub [s163, (Pattern.node Op.ite [(Pattern.hole 46), s36, s37])]
def s165 := Pattern.node Op.zEq [s164, s37]
def s166 := Pattern.node Op.ite [s165, (Pattern.hole 48), (Pattern.node Op.ite [(Pattern.hole 49), (Pattern.hole 51), (Pattern.hole 53)])]
def s167 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0xdac)) [])]
def s168 := Pattern.node Op.ite [(Pattern.node Op.qLe [s166, s167]), s167, s166]
def s169 := Pattern.node (Op.input 40) []
def s170 := Pattern.node (Op.input 41) []
def s171 := Pattern.node Op.qMul [s3, s170]
def s172 := Pattern.node Op.qMul [s102, s170]
def s173 := Pattern.node Op.ite [(Pattern.node Op.bEq [s169, s99]), s171, s172]
def s174 := Pattern.node Op.ite [(Pattern.node Op.qLe [s173, (Pattern.hole 54)]), (Pattern.hole 54), s173]
def s175 := Pattern.node Op.qLe [s109, s174]
def s176 := Pattern.node Op.ite [(Pattern.hole 55), s174, s109]
def s177 := Pattern.hole 56
def s178 := Pattern.node Op.ite [s165, s146, (Pattern.hole 48)]
def s179 := Pattern.node Op.ite [s165, (Pattern.node Op.qLe [s177, s178]), (Pattern.node Op.qLt [s177, s178])]
def s180 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s164]), (Pattern.node Op.qLe [s166, s177]), (Pattern.hole 57)]
def s181 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s149]), (Pattern.node Op.bNot [s152])]
def s182 := Pattern.node Op.ite [s149, s148, (Pattern.node Op.qDiv [s147, s20])]
def s183 := Pattern.node Op.ite [s152, s151, (Pattern.node Op.qDiv [s151, s14])]
def s184 := Pattern.node Op.zSub [s163, (Pattern.node Op.ite [(Pattern.hole 59), s36, s37])]
def s185 := Pattern.node Op.zEq [s184, s37]
def s186 := Pattern.hole 61
def s187 := Pattern.hole 60
def s188 := Pattern.node Op.ite [(Pattern.node Op.qLe [s186, s187]), s187, s186]
def s189 := Pattern.node Op.qDiv [s187, s3]
def s190 := Pattern.node Op.qDiv [s186, s14]
def s191 := Pattern.node Op.ite [s185, s188, (Pattern.node Op.ite [(Pattern.node Op.qLt [s186, s187]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s186, s189]), s189, s186]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s190, s187]), s187, s190])])]
def s192 := Pattern.node Op.ite [(Pattern.node Op.bEq [s169, s35]), s171, s172]
def s193 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 62), s167]), s167, (Pattern.hole 62)]
def s194 := Pattern.node Op.ite [(Pattern.node Op.qLe [s192, s193]), s193, s192]
def s195 := Pattern.node Op.ite [(Pattern.node Op.qLe [s128, (Pattern.hole 63)]), (Pattern.hole 63), s128]
def s196 := Pattern.node Op.ite [s185, s146, s188]
def s197 := Pattern.node Op.qLe [s195, s196]
def s198 := Pattern.node Op.qLt [s195, s196]
def s199 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s184]), (Pattern.node Op.qLe [(Pattern.hole 62), s195]), (Pattern.node Op.ite [s185, (Pattern.hole 64), (Pattern.hole 65)])]
def s200 := Pattern.node Op.ite [s149, (Pattern.hole 66), (Pattern.node Op.bNot [(Pattern.hole 58)])]
def s201 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 0x7d)) [])]
def s202 := Pattern.node Op.ite [(Pattern.node Op.qLe [s67, s201]), s67, s66]
def s203 := Pattern.node Op.qLt [s201, (Pattern.node Op.qMul [s4, s202])]
def s204 := Pattern.node Op.ite [(Pattern.node Op.qLe [s142, s201]), s142, s141]
def s205 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s204]), s201]
def s206 := Pattern.node Op.qLt [s201, (Pattern.node Op.qMul [s18, s204])]
def s207 := Pattern.node Op.qMul [s20, s8]
def s208 := Pattern.node Op.qLe [s207, s1]
def s209 := Pattern.node Op.qMul [s20, s16]
def s210 := Pattern.node Op.qLe [s209, s1]
def s211 := Pattern.node Op.bAnd [s208, s210]
def s212 := Pattern.node Op.qLe [s16, s8]
def s213 := Pattern.node Op.ite [(Pattern.hole 72), s8, s16]
def s214 := Pattern.node Op.qLt [s16, s8]
def s215 := Pattern.node Op.qDiv [s8, s3]
def s216 := Pattern.node Op.qLe [s16, s215]
def s217 := Pattern.node Op.ite [(Pattern.hole 75), s215, s16]
def s218 := Pattern.node Op.qDiv [s16, s14]
def s219 := Pattern.node Op.qLe [s218, s8]
def s220 := Pattern.node Op.ite [(Pattern.hole 77), s8, s218]
def s221 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 68), (Pattern.hole 69), (Pattern.hole 70)]), s36, s37]
def s222 := Pattern.node Op.zSub [s221, (Pattern.node Op.ite [(Pattern.hole 71), s36, s37])]
def s223 := Pattern.node Op.zEq [s222, s37]
def s224 := Pattern.node Op.ite [s223, (Pattern.hole 73), (Pattern.node Op.ite [(Pattern.hole 74), (Pattern.hole 76), (Pattern.hole 78)])]
def s225 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x9c4)) [])]
def s226 := Pattern.node Op.ite [(Pattern.node Op.qLe [s224, s225]), s225, s224]
def s227 := Pattern.node (Op.input 42) []
def s228 := Pattern.node Op.qMul [s3, s47]
def s229 := Pattern.node Op.qMul [s102, s47]
def s230 := Pattern.node Op.ite [(Pattern.node Op.bEq [s227, s99]), s228, s229]
def s231 := Pattern.node Op.ite [(Pattern.node Op.qLe [s230, (Pattern.hole 79)]), (Pattern.hole 79), s230]
def s232 := Pattern.node Op.qLe [s173, s231]
def s233 := Pattern.node Op.ite [(Pattern.hole 80), s231, s173]
def s234 := Pattern.hole 81
def s235 := Pattern.node Op.ite [s223, s1, (Pattern.hole 73)]
def s236 := Pattern.node Op.ite [s223, (Pattern.node Op.qLe [s234, s235]), (Pattern.node Op.qLt [s234, s235])]
def s237 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s222]), (Pattern.node Op.qLe [s224, s234]), (Pattern.hole 82)]
def s238 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s208]), (Pattern.node Op.bNot [s210])]
def s239 := Pattern.node Op.ite [s208, s207, (Pattern.node Op.qDiv [s8, s20])]
def s240 := Pattern.node Op.ite [s210, s209, (Pattern.node Op.qDiv [s209, s14])]
def s241 := Pattern.node Op.zSub [s221, (Pattern.node Op.ite [(Pattern.hole 84), s36, s37])]
def s242 := Pattern.node Op.zEq [s241, s37]
def s243 := Pattern.hole 86
def s244 := Pattern.hole 85
def s245 := Pattern.node Op.ite [(Pattern.node Op.qLe [s243, s244]), s244, s243]
def s246 := Pattern.node Op.qDiv [s244, s3]
def s247 := Pattern.node Op.qDiv [s243, s14]
def s248 := Pattern.node Op.ite [s242, s245, (Pattern.node Op.ite [(Pattern.node Op.qLt [s243, s244]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s243, s246]), s246, s243]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s247, s244]), s244, s247])])]
def s249 := Pattern.node Op.ite [(Pattern.node Op.bEq [s227, s35]), s228, s229]
def s250 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 87), s225]), s225, (Pattern.hole 87)]
def s251 := Pattern.node Op.ite [(Pattern.node Op.qLe [s249, s250]), s250, s249]
def s252 := Pattern.node Op.ite [(Pattern.node Op.qLe [s192, (Pattern.hole 88)]), (Pattern.hole 88), s192]
def s253 := Pattern.node Op.ite [s242, s1, s245]
def s254 := Pattern.node Op.qLe [s252, s253]
def s255 := Pattern.node Op.qLt [s252, s253]
def s256 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s241]), (Pattern.node Op.qLe [(Pattern.hole 87), s252]), (Pattern.node Op.ite [s242, (Pattern.hole 89), (Pattern.hole 90)])]
def s257 := Pattern.node Op.ite [s208, (Pattern.hole 91), (Pattern.node Op.bNot [(Pattern.hole 83)])]
def s258 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 49)) [])]
def s259 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 64)) [])]), s5]
def s260 := Pattern.node Op.qMul [s259, s3]
def s261 := Pattern.node Op.qLt [s258, (Pattern.node Op.qMul [s4, (Pattern.node Op.ite [(Pattern.node Op.qLe [s260, s258]), s260, s259])])]
def s262 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 81)) [])]), s12]
def s263 := Pattern.node Op.qMul [s262, s14]
def s264 := Pattern.node Op.ite [(Pattern.node Op.qLe [s263, s258]), s263, s262]
def s265 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s264]), s258]
def s266 := Pattern.node Op.qLt [s258, (Pattern.node Op.qMul [s18, s264])]
def s267 := Pattern.node Op.qMul [s20, s68]
def s268 := Pattern.node Op.qLe [s267, s65]
def s269 := Pattern.node Op.qMul [s20, s70]
def s270 := Pattern.node Op.qLe [s269, s65]
def s271 := Pattern.node Op.bAnd [s268, s270]
def s272 := Pattern.node Op.qLe [s70, s68]
def s273 := Pattern.node Op.ite [(Pattern.hole 97), s68, s70]
def s274 := Pattern.node Op.qLt [s70, s68]
def s275 := Pattern.node Op.qDiv [s68, s3]
def s276 := Pattern.node Op.qLe [s70, s275]
def s277 := Pattern.node Op.ite [(Pattern.hole 0x64), s275, s70]
def s278 := Pattern.node Op.qDiv [s70, s14]
def s279 := Pattern.node Op.qLe [s278, s68]
def s280 := Pattern.node Op.ite [(Pattern.hole 0x66), s68, s278]
def s281 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 93), (Pattern.hole 94), (Pattern.hole 95)]), s36, s37]
def s282 := Pattern.node Op.zSub [s281, (Pattern.node Op.ite [(Pattern.hole 96), s36, s37])]
def s283 := Pattern.node Op.zEq [s282, s37]
def s284 := Pattern.node Op.ite [s283, (Pattern.hole 98), (Pattern.node Op.ite [(Pattern.hole 99), (Pattern.hole 0x65), (Pattern.hole 0x67)])]
def s285 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x3d4)) [])]
def s286 := Pattern.node Op.ite [(Pattern.node Op.qLe [s284, s285]), s285, s284]
def s287 := Pattern.node (Op.input 24) []
def s288 := Pattern.node (Op.input 25) []
def s289 := Pattern.node Op.qMul [s3, s288]
def s290 := Pattern.node Op.qMul [s102, s288]
def s291 := Pattern.node Op.ite [(Pattern.node Op.bEq [s287, s99]), s289, s290]
def s292 := Pattern.node (Op.input 26) []
def s293 := Pattern.node (Op.input 27) []
def s294 := Pattern.node Op.qMul [s3, s293]
def s295 := Pattern.node Op.qMul [s102, s293]
def s296 := Pattern.node Op.ite [(Pattern.node Op.bEq [s292, s99]), s294, s295]
def s297 := Pattern.node Op.ite [(Pattern.node Op.qLe [s296, (Pattern.hole 0x68)]), (Pattern.hole 0x68), s296]
def s298 := Pattern.node Op.qLe [s291, s297]
def s299 := Pattern.node Op.ite [(Pattern.hole 0x69), s297, s291]
def s300 := Pattern.hole 0x6a
def s301 := Pattern.node Op.ite [s283, s65, (Pattern.hole 98)]
def s302 := Pattern.node Op.ite [s283, (Pattern.node Op.qLe [s300, s301]), (Pattern.node Op.qLt [s300, s301])]
def s303 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s282]), (Pattern.node Op.qLe [s284, s300]), (Pattern.hole 0x6b)]
def s304 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s268]), (Pattern.node Op.bNot [s270])]
def s305 := Pattern.node Op.ite [s268, s267, (Pattern.node Op.qDiv [s68, s20])]
def s306 := Pattern.node Op.ite [s270, s269, (Pattern.node Op.qDiv [s269, s14])]
def s307 := Pattern.node Op.zSub [s281, (Pattern.node Op.ite [(Pattern.hole 0x6d), s36, s37])]
def s308 := Pattern.node Op.zEq [s307, s37]
def s309 := Pattern.hole 0x6f
def s310 := Pattern.hole 0x6e
def s311 := Pattern.node Op.ite [(Pattern.node Op.qLe [s309, s310]), s310, s309]
def s312 := Pattern.node Op.qDiv [s310, s3]
def s313 := Pattern.node Op.qDiv [s309, s14]
def s314 := Pattern.node Op.ite [s308, s311, (Pattern.node Op.ite [(Pattern.node Op.qLt [s309, s310]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s309, s312]), s312, s309]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s313, s310]), s310, s313])])]
def s315 := Pattern.node Op.ite [(Pattern.node Op.bEq [s292, s35]), s294, s295]
def s316 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x70), s285]), s285, (Pattern.hole 0x70)]
def s317 := Pattern.node Op.ite [(Pattern.node Op.qLe [s315, s316]), s316, s315]
def s318 := Pattern.node Op.ite [(Pattern.node Op.bEq [s287, s35]), s289, s290]
def s319 := Pattern.node Op.ite [(Pattern.node Op.qLe [s318, (Pattern.hole 0x71)]), (Pattern.hole 0x71), s318]
def s320 := Pattern.node Op.ite [s308, s65, s311]
def s321 := Pattern.node Op.qLe [s319, s320]
def s322 := Pattern.node Op.qLt [s319, s320]
def s323 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s307]), (Pattern.node Op.qLe [(Pattern.hole 0x70), s319]), (Pattern.node Op.ite [s308, (Pattern.hole 0x72), (Pattern.hole 0x73)])]
def s324 := Pattern.node Op.ite [s268, (Pattern.hole 0x74), (Pattern.node Op.bNot [(Pattern.hole 0x6c)])]
def s325 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 35)) [])]
def s326 := Pattern.node Op.ite [(Pattern.node Op.qLe [s260, s325]), s260, s259]
def s327 := Pattern.node Op.qLt [s325, (Pattern.node Op.qMul [s4, s326])]
def s328 := Pattern.node Op.ite [(Pattern.node Op.qLe [s263, s325]), s263, s262]
def s329 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s328]), s325]
def s330 := Pattern.node Op.qLt [s325, (Pattern.node Op.qMul [s18, s328])]
def s331 := Pattern.node Op.qMul [s20, s139]
def s332 := Pattern.node Op.qLe [s331, s138]
def s333 := Pattern.node Op.qMul [s20, s143]
def s334 := Pattern.node Op.qLe [s333, s138]
def s335 := Pattern.node Op.bAnd [s332, s334]
def s336 := Pattern.node Op.qLe [s143, s139]
def s337 := Pattern.node Op.ite [(Pattern.hole 0x7a), s139, s143]
def s338 := Pattern.node Op.qLt [s143, s139]
def s339 := Pattern.node Op.qDiv [s139, s3]
def s340 := Pattern.node Op.qLe [s143, s339]
def s341 := Pattern.node Op.ite [(Pattern.hole 0x7d), s339, s143]
def s342 := Pattern.node Op.qDiv [s143, s14]
def s343 := Pattern.node Op.qLe [s342, s139]
def s344 := Pattern.node Op.ite [(Pattern.hole 0x7f), s139, s342]
def s345 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0x76), (Pattern.hole 0x77), (Pattern.hole 0x78)]), s36, s37]
def s346 := Pattern.node Op.zSub [s345, (Pattern.node Op.ite [(Pattern.hole 0x79), s36, s37])]
def s347 := Pattern.node Op.zEq [s346, s37]
def s348 := Pattern.node Op.ite [s347, (Pattern.hole 0x7b), (Pattern.node Op.ite [(Pattern.hole 0x7c), (Pattern.hole 0x7e), (Pattern.hole 0x80)])]
def s349 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x2bc)) [])]
def s350 := Pattern.node Op.ite [(Pattern.node Op.qLe [s348, s349]), s349, s348]
def s351 := Pattern.node (Op.input 28) []
def s352 := Pattern.node (Op.input 29) []
def s353 := Pattern.node Op.qMul [s3, s352]
def s354 := Pattern.node Op.qMul [s102, s352]
def s355 := Pattern.node Op.ite [(Pattern.node Op.bEq [s351, s99]), s353, s354]
def s356 := Pattern.node Op.ite [(Pattern.node Op.qLe [s355, (Pattern.hole 0x81)]), (Pattern.hole 0x81), s355]
def s357 := Pattern.node Op.qLe [s296, s356]
def s358 := Pattern.node Op.ite [(Pattern.hole 0x82), s356, s296]
def s359 := Pattern.hole 0x83
def s360 := Pattern.node Op.ite [s347, s138, (Pattern.hole 0x7b)]
def s361 := Pattern.node Op.ite [s347, (Pattern.node Op.qLe [s359, s360]), (Pattern.node Op.qLt [s359, s360])]
def s362 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s346]), (Pattern.node Op.qLe [s348, s359]), (Pattern.hole 0x84)]
def s363 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s332]), (Pattern.node Op.bNot [s334])]
def s364 := Pattern.node Op.ite [s332, s331, (Pattern.node Op.qDiv [s139, s20])]
def s365 := Pattern.node Op.ite [s334, s333, (Pattern.node Op.qDiv [s333, s14])]
def s366 := Pattern.node Op.zSub [s345, (Pattern.node Op.ite [(Pattern.hole 0x86), s36, s37])]
def s367 := Pattern.node Op.zEq [s366, s37]
def s368 := Pattern.hole 0x88
def s369 := Pattern.hole 0x87
def s370 := Pattern.node Op.ite [(Pattern.node Op.qLe [s368, s369]), s369, s368]
def s371 := Pattern.node Op.qDiv [s369, s3]
def s372 := Pattern.node Op.qDiv [s368, s14]
def s373 := Pattern.node Op.ite [s367, s370, (Pattern.node Op.ite [(Pattern.node Op.qLt [s368, s369]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s368, s371]), s371, s368]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s372, s369]), s369, s372])])]
def s374 := Pattern.node Op.ite [(Pattern.node Op.bEq [s351, s35]), s353, s354]
def s375 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x89), s349]), s349, (Pattern.hole 0x89)]
def s376 := Pattern.node Op.ite [(Pattern.node Op.qLe [s374, s375]), s375, s374]
def s377 := Pattern.node Op.ite [(Pattern.node Op.qLe [s315, (Pattern.hole 0x8a)]), (Pattern.hole 0x8a), s315]
def s378 := Pattern.node Op.ite [s367, s138, s370]
def s379 := Pattern.node Op.qLe [s377, s378]
def s380 := Pattern.node Op.qLt [s377, s378]
def s381 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s366]), (Pattern.node Op.qLe [(Pattern.hole 0x89), s377]), (Pattern.node Op.ite [s367, (Pattern.hole 0x8b), (Pattern.hole 0x8c)])]
def s382 := Pattern.node Op.ite [s332, (Pattern.hole 0x8d), (Pattern.node Op.bNot [(Pattern.hole 0x85)])]
def s383 := Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 25)) [])]
def s384 := Pattern.node Op.ite [(Pattern.node Op.qLe [s260, s383]), s260, s259]
def s385 := Pattern.node Op.qLt [s383, (Pattern.node Op.qMul [s4, s384])]
def s386 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 27)) [])]), s12]
def s387 := Pattern.node Op.qMul [s386, s14]
def s388 := Pattern.node Op.ite [(Pattern.node Op.qLe [s387, s383]), s387, s386]
def s389 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s388]), s383]
def s390 := Pattern.node Op.qLt [s383, (Pattern.node Op.qMul [s18, s388])]
def s391 := Pattern.node Op.qMul [s20, s202]
def s392 := Pattern.node Op.qLe [s391, s201]
def s393 := Pattern.node Op.qMul [s20, s204]
def s394 := Pattern.node Op.qLe [s393, s201]
def s395 := Pattern.node Op.bAnd [s392, s394]
def s396 := Pattern.node Op.qLe [s204, s202]
def s397 := Pattern.node Op.ite [(Pattern.hole 0x93), s202, s204]
def s398 := Pattern.node Op.qLt [s204, s202]
def s399 := Pattern.node Op.qDiv [s202, s3]
def s400 := Pattern.node Op.qLe [s204, s399]
def s401 := Pattern.node Op.ite [(Pattern.hole 0x96), s399, s204]
def s402 := Pattern.node Op.qDiv [s204, s14]
def s403 := Pattern.node Op.qLe [s402, s202]
def s404 := Pattern.node Op.ite [(Pattern.hole 0x98), s202, s402]
def s405 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0x8f), (Pattern.hole 0x90), (Pattern.hole 0x91)]), s36, s37]
def s406 := Pattern.node Op.zSub [s405, (Pattern.node Op.ite [(Pattern.hole 0x92), s36, s37])]
def s407 := Pattern.node Op.zEq [s406, s37]
def s408 := Pattern.node Op.ite [s407, (Pattern.hole 0x94), (Pattern.node Op.ite [(Pattern.hole 0x95), (Pattern.hole 0x97), (Pattern.hole 0x99)])]
def s409 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x1f4)) [])]
def s410 := Pattern.node Op.ite [(Pattern.node Op.qLe [s408, s409]), s409, s408]
def s411 := Pattern.node (Op.input 30) []
def s412 := Pattern.node (Op.input 31) []
def s413 := Pattern.node Op.qMul [s3, s412]
def s414 := Pattern.node Op.qMul [s102, s412]
def s415 := Pattern.node Op.ite [(Pattern.node Op.bEq [s411, s99]), s413, s414]
def s416 := Pattern.node Op.ite [(Pattern.node Op.qLe [s415, (Pattern.hole 0x9a)]), (Pattern.hole 0x9a), s415]
def s417 := Pattern.node Op.qLe [s355, s416]
def s418 := Pattern.node Op.ite [(Pattern.hole 0x9b), s416, s355]
def s419 := Pattern.hole 0x9c
def s420 := Pattern.node Op.ite [s407, s201, (Pattern.hole 0x94)]
def s421 := Pattern.node Op.ite [s407, (Pattern.node Op.qLe [s419, s420]), (Pattern.node Op.qLt [s419, s420])]
def s422 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s406]), (Pattern.node Op.qLe [s408, s419]), (Pattern.hole 0x9d)]
def s423 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s392]), (Pattern.node Op.bNot [s394])]
def s424 := Pattern.node Op.ite [s392, s391, (Pattern.node Op.qDiv [s202, s20])]
def s425 := Pattern.node Op.ite [s394, s393, (Pattern.node Op.qDiv [s393, s14])]
def s426 := Pattern.node Op.zSub [s405, (Pattern.node Op.ite [(Pattern.hole 0x9f), s36, s37])]
def s427 := Pattern.node Op.zEq [s426, s37]
def s428 := Pattern.hole 0xa1
def s429 := Pattern.hole 0xa0
def s430 := Pattern.node Op.ite [(Pattern.node Op.qLe [s428, s429]), s429, s428]
def s431 := Pattern.node Op.qDiv [s429, s3]
def s432 := Pattern.node Op.qDiv [s428, s14]
def s433 := Pattern.node Op.ite [s427, s430, (Pattern.node Op.ite [(Pattern.node Op.qLt [s428, s429]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s428, s431]), s431, s428]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s432, s429]), s429, s432])])]
def s434 := Pattern.node Op.ite [(Pattern.node Op.bEq [s411, s35]), s413, s414]
def s435 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0xa2), s409]), s409, (Pattern.hole 0xa2)]
def s436 := Pattern.node Op.ite [(Pattern.node Op.qLe [s434, s435]), s435, s434]
def s437 := Pattern.node Op.ite [(Pattern.node Op.qLe [s374, (Pattern.hole 0xa3)]), (Pattern.hole 0xa3), s374]
def s438 := Pattern.node Op.ite [s427, s201, s430]
def s439 := Pattern.node Op.qLe [s437, s438]
def s440 := Pattern.node Op.qLt [s437, s438]
def s441 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s426]), (Pattern.node Op.qLe [(Pattern.hole 0xa2), s437]), (Pattern.node Op.ite [s427, (Pattern.hole 0xa4), (Pattern.hole 0xa5)])]
def s442 := Pattern.node Op.ite [s392, (Pattern.hole 0xa6), (Pattern.node Op.bNot [(Pattern.hole 0x9e)])]
def s443 := Pattern.node (Op.qConst (Int.cast 7)) []
def s444 := Pattern.node Op.qDiv [s0, s443]
def s445 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, (Pattern.node (Op.qConst (Int.cast 16)) [])]), s5]
def s446 := Pattern.node Op.qMul [s445, s3]
def s447 := Pattern.node Op.ite [(Pattern.node Op.qLe [s446, s444]), s446, s445]
def s448 := Pattern.node Op.qLt [s444, (Pattern.node Op.qMul [s4, s447])]
def s449 := Pattern.node Op.qMul [(Pattern.node Op.qDiv [s0, s10]), s12]
def s450 := Pattern.node Op.qMul [s449, s14]
def s451 := Pattern.node Op.ite [(Pattern.node Op.qLe [s450, s444]), s450, s449]
def s452 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s451]), s444]
def s453 := Pattern.node Op.qLt [s444, (Pattern.node Op.qMul [s18, s451])]
def s454 := Pattern.node Op.qMul [s20, s326]
def s455 := Pattern.node Op.qLe [s454, s325]
def s456 := Pattern.node Op.qMul [s20, s328]
def s457 := Pattern.node Op.qLe [s456, s325]
def s458 := Pattern.node Op.bAnd [s455, s457]
def s459 := Pattern.node Op.qLe [s328, s326]
def s460 := Pattern.node Op.ite [(Pattern.hole 0xac), s326, s328]
def s461 := Pattern.node Op.qLt [s328, s326]
def s462 := Pattern.node Op.qDiv [s326, s3]
def s463 := Pattern.node Op.qLe [s328, s462]
def s464 := Pattern.node Op.ite [(Pattern.hole 0xaf), s462, s328]
def s465 := Pattern.node Op.qDiv [s328, s14]
def s466 := Pattern.node Op.qLe [s465, s326]
def s467 := Pattern.node Op.ite [(Pattern.hole 0xb1), s326, s465]
def s468 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0xa8), (Pattern.hole 0xa9), (Pattern.hole 0xaa)]), s36, s37]
def s469 := Pattern.node Op.zSub [s468, (Pattern.node Op.ite [(Pattern.hole 0xab), s36, s37])]
def s470 := Pattern.node Op.zEq [s469, s37]
def s471 := Pattern.node Op.ite [s470, (Pattern.hole 0xad), (Pattern.node Op.ite [(Pattern.hole 0xae), (Pattern.hole 0xb0), (Pattern.hole 0xb2)])]
def s472 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x8c)) [])]
def s473 := Pattern.node Op.ite [(Pattern.node Op.qLe [s471, s472]), s472, s471]
def s474 := Pattern.node (Op.input 16) []
def s475 := Pattern.node (Op.input 17) []
def s476 := Pattern.node Op.qMul [s3, s475]
def s477 := Pattern.node Op.qMul [s102, s475]
def s478 := Pattern.node Op.ite [(Pattern.node Op.bEq [s474, s99]), s476, s477]
def s479 := Pattern.node (Op.input 18) []
def s480 := Pattern.node (Op.input 19) []
def s481 := Pattern.node Op.qMul [s3, s480]
def s482 := Pattern.node Op.qMul [s102, s480]
def s483 := Pattern.node Op.ite [(Pattern.node Op.bEq [s479, s99]), s481, s482]
def s484 := Pattern.node Op.ite [(Pattern.node Op.qLe [s483, (Pattern.hole 0xb3)]), (Pattern.hole 0xb3), s483]
def s485 := Pattern.node Op.qLe [s478, s484]
def s486 := Pattern.node Op.ite [(Pattern.hole 0xb4), s484, s478]
def s487 := Pattern.hole 0xb5
def s488 := Pattern.node Op.ite [s470, s325, (Pattern.hole 0xad)]
def s489 := Pattern.node Op.ite [s470, (Pattern.node Op.qLe [s487, s488]), (Pattern.node Op.qLt [s487, s488])]
def s490 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s469]), (Pattern.node Op.qLe [s471, s487]), (Pattern.hole 0xb6)]
def s491 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s455]), (Pattern.node Op.bNot [s457])]
def s492 := Pattern.node Op.ite [s455, s454, (Pattern.node Op.qDiv [s326, s20])]
def s493 := Pattern.node Op.ite [s457, s456, (Pattern.node Op.qDiv [s456, s14])]
def s494 := Pattern.node Op.zSub [s468, (Pattern.node Op.ite [(Pattern.hole 0xb8), s36, s37])]
def s495 := Pattern.node Op.zEq [s494, s37]
def s496 := Pattern.hole 0xba
def s497 := Pattern.hole 0xb9
def s498 := Pattern.node Op.ite [(Pattern.node Op.qLe [s496, s497]), s497, s496]
def s499 := Pattern.node Op.qDiv [s497, s3]
def s500 := Pattern.node Op.qDiv [s496, s14]
def s501 := Pattern.node Op.ite [s495, s498, (Pattern.node Op.ite [(Pattern.node Op.qLt [s496, s497]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s496, s499]), s499, s496]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s500, s497]), s497, s500])])]
def s502 := Pattern.node Op.ite [(Pattern.node Op.bEq [s479, s35]), s481, s482]
def s503 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0xbb), s472]), s472, (Pattern.hole 0xbb)]
def s504 := Pattern.node Op.ite [(Pattern.node Op.qLe [s502, s503]), s503, s502]
def s505 := Pattern.node Op.ite [(Pattern.node Op.bEq [s474, s35]), s476, s477]
def s506 := Pattern.node Op.ite [(Pattern.node Op.qLe [s505, (Pattern.hole 0xbc)]), (Pattern.hole 0xbc), s505]
def s507 := Pattern.node Op.ite [s495, s325, s498]
def s508 := Pattern.node Op.qLe [s506, s507]
def s509 := Pattern.node Op.qLt [s506, s507]
def s510 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s494]), (Pattern.node Op.qLe [(Pattern.hole 0xbb), s506]), (Pattern.node Op.ite [s495, (Pattern.hole 0xbd), (Pattern.hole 0xbe)])]
def s511 := Pattern.node Op.ite [s455, (Pattern.hole 0xbf), (Pattern.node Op.bNot [(Pattern.hole 0xb7)])]
def s512 := Pattern.node Op.qDiv [s0, s2]
def s513 := Pattern.node Op.ite [(Pattern.node Op.qLe [s446, s512]), s446, s445]
def s514 := Pattern.node Op.qLt [s512, (Pattern.node Op.qMul [s4, s513])]
def s515 := Pattern.node Op.ite [(Pattern.node Op.qLe [s450, s512]), s450, s449]
def s516 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s515]), s512]
def s517 := Pattern.node Op.qLt [s512, (Pattern.node Op.qMul [s18, s515])]
def s518 := Pattern.node Op.qMul [s20, s384]
def s519 := Pattern.node Op.qLe [s518, s383]
def s520 := Pattern.node Op.qMul [s20, s388]
def s521 := Pattern.node Op.qLe [s520, s383]
def s522 := Pattern.node Op.bAnd [s519, s521]
def s523 := Pattern.node Op.qLe [s388, s384]
def s524 := Pattern.node Op.ite [(Pattern.hole 0xc5), s384, s388]
def s525 := Pattern.node Op.qLt [s388, s384]
def s526 := Pattern.node Op.qDiv [s384, s3]
def s527 := Pattern.node Op.qLe [s388, s526]
def s528 := Pattern.node Op.ite [(Pattern.hole 0xc8), s526, s388]
def s529 := Pattern.node Op.qDiv [s388, s14]
def s530 := Pattern.node Op.qLe [s529, s384]
def s531 := Pattern.node Op.ite [(Pattern.hole 0xca), s384, s529]
def s532 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0xc1), (Pattern.hole 0xc2), (Pattern.hole 0xc3)]), s36, s37]
def s533 := Pattern.node Op.zSub [s532, (Pattern.node Op.ite [(Pattern.hole 0xc4), s36, s37])]
def s534 := Pattern.node Op.zEq [s533, s37]
def s535 := Pattern.node Op.ite [s534, (Pattern.hole 0xc6), (Pattern.node Op.ite [(Pattern.hole 0xc7), (Pattern.hole 0xc9), (Pattern.hole 0xcb)])]
def s536 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x64)) [])]
def s537 := Pattern.node Op.ite [(Pattern.node Op.qLe [s535, s536]), s536, s535]
def s538 := Pattern.node (Op.input 20) []
def s539 := Pattern.node (Op.input 21) []
def s540 := Pattern.node Op.qMul [s3, s539]
def s541 := Pattern.node Op.qMul [s102, s539]
def s542 := Pattern.node Op.ite [(Pattern.node Op.bEq [s538, s99]), s540, s541]
def s543 := Pattern.node Op.ite [(Pattern.node Op.qLe [s542, (Pattern.hole 0xcc)]), (Pattern.hole 0xcc), s542]
def s544 := Pattern.node Op.qLe [s483, s543]
def s545 := Pattern.node Op.ite [(Pattern.hole 0xcd), s543, s483]
def s546 := Pattern.hole 0xce
def s547 := Pattern.node Op.ite [s534, s383, (Pattern.hole 0xc6)]
def s548 := Pattern.node Op.ite [s534, (Pattern.node Op.qLe [s546, s547]), (Pattern.node Op.qLt [s546, s547])]
def s549 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s533]), (Pattern.node Op.qLe [s535, s546]), (Pattern.hole 0xcf)]
def s550 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s519]), (Pattern.node Op.bNot [s521])]
def s551 := Pattern.node Op.ite [s519, s518, (Pattern.node Op.qDiv [s384, s20])]
def s552 := Pattern.node Op.ite [s521, s520, (Pattern.node Op.qDiv [s520, s14])]
def s553 := Pattern.node Op.zSub [s532, (Pattern.node Op.ite [(Pattern.hole 0xd1), s36, s37])]
def s554 := Pattern.node Op.zEq [s553, s37]
def s555 := Pattern.hole 0xd3
def s556 := Pattern.hole 0xd2
def s557 := Pattern.node Op.ite [(Pattern.node Op.qLe [s555, s556]), s556, s555]
def s558 := Pattern.node Op.qDiv [s556, s3]
def s559 := Pattern.node Op.qDiv [s555, s14]
def s560 := Pattern.node Op.ite [s554, s557, (Pattern.node Op.ite [(Pattern.node Op.qLt [s555, s556]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s555, s558]), s558, s555]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s559, s556]), s556, s559])])]
def s561 := Pattern.node Op.ite [(Pattern.node Op.bEq [s538, s35]), s540, s541]
def s562 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0xd4), s536]), s536, (Pattern.hole 0xd4)]
def s563 := Pattern.node Op.ite [(Pattern.node Op.qLe [s561, s562]), s562, s561]
def s564 := Pattern.node Op.ite [(Pattern.node Op.qLe [s502, (Pattern.hole 0xd5)]), (Pattern.hole 0xd5), s502]
def s565 := Pattern.node Op.ite [s554, s383, s557]
def s566 := Pattern.node Op.qLe [s564, s565]
def s567 := Pattern.node Op.qLt [s564, s565]
def s568 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s553]), (Pattern.node Op.qLe [(Pattern.hole 0xd4), s564]), (Pattern.node Op.ite [s554, (Pattern.hole 0xd6), (Pattern.hole 0xd7)])]
def s569 := Pattern.node Op.ite [s519, (Pattern.hole 0xd8), (Pattern.node Op.bNot [(Pattern.hole 0xd0)])]
def s570 := Pattern.node Op.qDiv [s2, s443]
def s571 := Pattern.node Op.qDiv [s0, s3]
def s572 := Pattern.node Op.qMul [s571, s5]
def s573 := Pattern.node Op.qMul [s572, s3]
def s574 := Pattern.node Op.qLt [s570, (Pattern.node Op.qMul [s4, (Pattern.node Op.ite [(Pattern.node Op.qLe [s573, s570]), s573, s572])])]
def s575 := Pattern.node Op.qDiv [s0, s14]
def s576 := Pattern.node Op.qMul [s575, s12]
def s577 := Pattern.node Op.qMul [s576, s14]
def s578 := Pattern.node Op.ite [(Pattern.node Op.qLe [s577, s570]), s577, s576]
def s579 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s578]), s570]
def s580 := Pattern.node Op.qLt [s570, (Pattern.node Op.qMul [s18, s578])]
def s581 := Pattern.node Op.qMul [s20, s447]
def s582 := Pattern.node Op.qLe [s581, s444]
def s583 := Pattern.node Op.qMul [s20, s451]
def s584 := Pattern.node Op.qLe [s583, s444]
def s585 := Pattern.node Op.bAnd [s582, s584]
def s586 := Pattern.node Op.qLe [s451, s447]
def s587 := Pattern.node Op.ite [(Pattern.hole 0xde), s447, s451]
def s588 := Pattern.node Op.qLt [s451, s447]
def s589 := Pattern.node Op.qDiv [s447, s3]
def s590 := Pattern.node Op.qLe [s451, s589]
def s591 := Pattern.node Op.ite [(Pattern.hole 0xe1), s589, s451]
def s592 := Pattern.node Op.qDiv [s451, s14]
def s593 := Pattern.node Op.qLe [s592, s447]
def s594 := Pattern.node Op.ite [(Pattern.hole 0xe3), s447, s592]
def s595 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s99, (Pattern.hole 0xda), (Pattern.hole 0xdb), (Pattern.hole 0xdc)]), s36, s37]
def s596 := Pattern.node Op.ite [(Pattern.hole 0xdd), s36, s37]
def s597 := Pattern.node Op.zSub [s595, s596]
def s598 := Pattern.node Op.zEq [s597, s37]
def s599 := Pattern.hole 0xdf
def s600 := Pattern.node Op.ite [(Pattern.hole 0xe0), (Pattern.hole 0xe2), (Pattern.hole 0xe4)]
def s601 := Pattern.node Op.ite [s598, s599, s600]
def s602 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 28)) [])]
def s603 := Pattern.node Op.ite [(Pattern.node Op.qLe [s601, s602]), s602, s601]
def s604 := Pattern.node (Op.input 8) []
def s605 := Pattern.node (Op.input 9) []
def s606 := Pattern.node Op.qMul [s3, s605]
def s607 := Pattern.node Op.qMul [s102, s605]
def s608 := Pattern.node Op.ite [(Pattern.node Op.bEq [s604, s99]), s606, s607]
def s609 := Pattern.node (Op.input 10) []
def s610 := Pattern.node (Op.input 11) []
def s611 := Pattern.node Op.qMul [s3, s610]
def s612 := Pattern.node Op.qMul [s102, s610]
def s613 := Pattern.node Op.ite [(Pattern.node Op.bEq [s609, s99]), s611, s612]
def s614 := Pattern.node Op.ite [(Pattern.node Op.qLe [s613, (Pattern.hole 0xe5)]), (Pattern.hole 0xe5), s613]
def s615 := Pattern.node Op.qLe [s608, s614]
def s616 := Pattern.node Op.ite [(Pattern.hole 0xe6), s614, s608]
def s617 := Pattern.hole 0xe7
def s618 := Pattern.node Op.ite [s598, s444, s599]
def s619 := Pattern.node Op.ite [s598, (Pattern.node Op.qLe [s617, s618]), (Pattern.node Op.qLt [s617, s618])]
def s620 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s597]), (Pattern.node Op.qLe [s601, s617]), (Pattern.hole 0xe8)]
def s621 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s582]), (Pattern.node Op.bNot [s584])]
def s622 := Pattern.node Op.ite [s582, s581, (Pattern.node Op.qDiv [s447, s20])]
def s623 := Pattern.node Op.ite [s584, s583, (Pattern.node Op.qDiv [s583, s14])]
def s624 := Pattern.node Op.ite [(Pattern.hole 0xea), s36, s37]
def s625 := Pattern.node Op.zSub [s595, s624]
def s626 := Pattern.node Op.zEq [s625, s37]
def s627 := Pattern.hole 0xec
def s628 := Pattern.hole 0xeb
def s629 := Pattern.node Op.ite [(Pattern.node Op.qLe [s627, s628]), s628, s627]
def s630 := Pattern.node Op.qDiv [s628, s3]
def s631 := Pattern.node Op.qDiv [s627, s14]
def s632 := Pattern.node Op.ite [(Pattern.node Op.qLt [s627, s628]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s627, s630]), s630, s627]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s631, s628]), s628, s631])]
def s633 := Pattern.node Op.ite [s626, s629, s632]
def s634 := Pattern.node Op.ite [(Pattern.node Op.bEq [s609, s35]), s611, s612]
def s635 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0xed), s602]), s602, (Pattern.hole 0xed)]
def s636 := Pattern.node Op.ite [(Pattern.node Op.qLe [s634, s635]), s635, s634]
def s637 := Pattern.node Op.ite [(Pattern.node Op.bEq [s604, s35]), s606, s607]
def s638 := Pattern.node Op.ite [(Pattern.node Op.qLe [s637, (Pattern.hole 0xee)]), (Pattern.hole 0xee), s637]
def s639 := Pattern.node Op.ite [s626, s444, s629]
def s640 := Pattern.node Op.qLe [s638, s639]
def s641 := Pattern.node Op.qLt [s638, s639]
def s642 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s625]), (Pattern.node Op.qLe [(Pattern.hole 0xed), s638]), (Pattern.node Op.ite [s626, (Pattern.hole 0xef), (Pattern.hole 0xf0)])]
def s643 := Pattern.node Op.ite [s582, (Pattern.hole 0xf1), (Pattern.node Op.bNot [(Pattern.hole 0xe9)])]
def s644 := Pattern.node Op.qMul [s0, s5]
def s645 := Pattern.node Op.qMul [s644, s3]
def s646 := Pattern.node Op.ite [(Pattern.node Op.qLe [s645, s0]), s645, s644]
def s647 := Pattern.node Op.qMul [s0, s12]
def s648 := Pattern.node Op.qMul [s647, s14]
def s649 := Pattern.node Op.ite [(Pattern.node Op.qLe [s648, s0]), s648, s647]
def s650 := Pattern.node Op.bAnd [s35, (Pattern.node Op.qLt [s0, (Pattern.node Op.qMul [s4, s646])]), (Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s649]), s0]), (Pattern.node Op.qLt [s0, (Pattern.node Op.qMul [s18, s649])])]
def s651 := Pattern.node Op.qMul [s20, s513]
def s652 := Pattern.node Op.qLe [s651, s512]
def s653 := Pattern.node Op.qMul [s20, s515]
def s654 := Pattern.node Op.qLe [s653, s512]
def s655 := Pattern.node Op.bAnd [s652, s654]
def s656 := Pattern.node Op.qLe [s515, s513]
def s657 := Pattern.node Op.ite [(Pattern.hole 0xf5), s513, s515]
def s658 := Pattern.node Op.qLt [s515, s513]
def s659 := Pattern.node Op.qDiv [s513, s3]
def s660 := Pattern.node Op.qLe [s515, s659]
def s661 := Pattern.node Op.ite [(Pattern.hole 0xf8), s659, s515]
def s662 := Pattern.node Op.qDiv [s515, s14]
def s663 := Pattern.node Op.qLe [s662, s513]
def s664 := Pattern.node Op.ite [(Pattern.hole 0xfa), s513, s662]
def s665 := Pattern.node Op.ite [(Pattern.hole 0xf3), s36, s37]
def s666 := Pattern.node Op.zSub [s665, (Pattern.node Op.ite [(Pattern.hole 0xf4), s36, s37])]
def s667 := Pattern.node Op.zEq [s666, s37]
def s668 := Pattern.node Op.ite [s667, (Pattern.hole 0xf6), (Pattern.node Op.ite [(Pattern.hole 0xf7), (Pattern.hole 0xf9), (Pattern.hole 0xfb)])]
def s669 := Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 20)) [])]
def s670 := Pattern.node Op.ite [(Pattern.node Op.qLe [s668, s669]), s669, s668]
def s671 := Pattern.node (Op.input 12) []
def s672 := Pattern.node (Op.input 13) []
def s673 := Pattern.node Op.qMul [s3, s672]
def s674 := Pattern.node Op.qMul [s102, s672]
def s675 := Pattern.node Op.ite [(Pattern.node Op.bEq [s671, s99]), s673, s674]
def s676 := Pattern.node Op.ite [(Pattern.node Op.qLe [s675, (Pattern.hole 0xfc)]), (Pattern.hole 0xfc), s675]
def s677 := Pattern.node Op.qLe [s613, s676]
def s678 := Pattern.node Op.ite [(Pattern.hole 0xfd), s676, s613]
def s679 := Pattern.hole 0xfe
def s680 := Pattern.node Op.ite [s667, s512, (Pattern.hole 0xf6)]
def s681 := Pattern.node Op.ite [s667, (Pattern.node Op.qLe [s679, s680]), (Pattern.node Op.qLt [s679, s680])]
def s682 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s666]), (Pattern.node Op.qLe [s668, s679]), (Pattern.hole 0xff)]
def s683 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s652]), (Pattern.node Op.bNot [s654])]
def s684 := Pattern.node Op.ite [s652, s651, (Pattern.node Op.qDiv [s513, s20])]
def s685 := Pattern.node Op.ite [s654, s653, (Pattern.node Op.qDiv [s653, s14])]
def s686 := Pattern.node Op.zSub [s665, (Pattern.node Op.ite [(Pattern.hole 0x101), s36, s37])]
def s687 := Pattern.node Op.zEq [s686, s37]
def s688 := Pattern.hole 0x103
def s689 := Pattern.hole 0x102
def s690 := Pattern.node Op.ite [(Pattern.node Op.qLe [s688, s689]), s689, s688]
def s691 := Pattern.node Op.qDiv [s689, s3]
def s692 := Pattern.node Op.qDiv [s688, s14]
def s693 := Pattern.node Op.ite [s687, s690, (Pattern.node Op.ite [(Pattern.node Op.qLt [s688, s689]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s688, s691]), s691, s688]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s692, s689]), s689, s692])])]
def s694 := Pattern.node Op.ite [(Pattern.node Op.bEq [s671, s35]), s673, s674]
def s695 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x104), s669]), s669, (Pattern.hole 0x104)]
def s696 := Pattern.node Op.ite [(Pattern.node Op.qLe [s694, s695]), s695, s694]
def s697 := Pattern.node Op.ite [(Pattern.node Op.qLe [s634, (Pattern.hole 0x105)]), (Pattern.hole 0x105), s634]
def s698 := Pattern.node Op.ite [s687, s512, s690]
def s699 := Pattern.node Op.qLe [s697, s698]
def s700 := Pattern.node Op.qLt [s697, s698]
def s701 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s686]), (Pattern.node Op.qLe [(Pattern.hole 0x104), s697]), (Pattern.node Op.ite [s687, (Pattern.hole 0x106), (Pattern.hole 0x107)])]
def s702 := Pattern.node Op.ite [s652, (Pattern.hole 0x108), (Pattern.node Op.bNot [(Pattern.hole 0x100)])]
def s703 := Pattern.node Op.qMul [s3, s5]
def s704 := Pattern.node Op.qMul [s703, s3]
def s705 := Pattern.node Op.qLt [s2, (Pattern.node Op.qMul [s4, (Pattern.node Op.ite [(Pattern.node Op.qLe [s704, s2]), s704, s703])])]
def s706 := Pattern.node Op.qMul [s14, s12]
def s707 := Pattern.node Op.qMul [s706, s14]
def s708 := Pattern.node Op.ite [(Pattern.node Op.qLe [s707, s2]), s707, s706]
def s709 := Pattern.node Op.qLe [(Pattern.node Op.qMul [s11, s708]), s2]
def s710 := Pattern.node Op.qLt [s2, (Pattern.node Op.qMul [s18, s708])]
def s711 := Pattern.node Op.bAnd [s99, s705, s709, s710]
def s712 := Pattern.node Op.qMul [s20, s646]
def s713 := Pattern.node Op.qLe [s712, s0]
def s714 := Pattern.node Op.qMul [s20, s649]
def s715 := Pattern.node Op.qLe [s714, s0]
def s716 := Pattern.node Op.bAnd [s713, s715]
def s717 := Pattern.node Op.qLe [s649, s646]
def s718 := Pattern.node Op.ite [(Pattern.hole 0x10c), s646, s649]
def s719 := Pattern.node Op.qLt [s649, s646]
def s720 := Pattern.node Op.qDiv [s646, s3]
def s721 := Pattern.node Op.qLe [s649, s720]
def s722 := Pattern.node Op.ite [(Pattern.hole 0x10f), s720, s649]
def s723 := Pattern.node Op.qDiv [s649, s14]
def s724 := Pattern.node Op.qLe [s723, s646]
def s725 := Pattern.node Op.ite [(Pattern.hole 0x111), s646, s723]
def s726 := Pattern.node Op.ite [(Pattern.hole 0x10a), s36, s37]
def s727 := Pattern.node Op.ite [(Pattern.hole 0x10b), s36, s37]
def s728 := Pattern.node Op.zSub [s726, s727]
def s729 := Pattern.node Op.zEq [s728, s37]
def s730 := Pattern.hole 0x10d
def s731 := Pattern.node Op.ite [(Pattern.hole 0x10e), (Pattern.hole 0x110), (Pattern.hole 0x112)]
def s732 := Pattern.node Op.ite [s729, s730, s731]
def s733 := Pattern.node Op.qDiv [s14, s3]
def s734 := Pattern.node Op.ite [(Pattern.node Op.qLe [s732, s733]), s733, s732]
def s735 := Pattern.node (Op.input 4) []
def s736 := Pattern.node (Op.input 5) []
def s737 := Pattern.node Op.qMul [s3, s736]
def s738 := Pattern.node Op.qMul [s102, s736]
def s739 := Pattern.node Op.ite [(Pattern.node Op.bEq [s735, s99]), s737, s738]
def s740 := Pattern.node (Op.input 6) []
def s741 := Pattern.node (Op.input 7) []
def s742 := Pattern.node Op.qMul [s3, s741]
def s743 := Pattern.node Op.qMul [s102, s741]
def s744 := Pattern.node Op.ite [(Pattern.node Op.bEq [s740, s99]), s742, s743]
def s745 := Pattern.node Op.ite [(Pattern.node Op.qLe [s744, (Pattern.hole 0x113)]), (Pattern.hole 0x113), s744]
def s746 := Pattern.node Op.qLe [s739, s745]
def s747 := Pattern.node Op.ite [(Pattern.hole 0x114), s745, s739]
def s748 := Pattern.node Op.ite [s729, s0, s730]
def s749 := Pattern.node Op.ite [s729, (Pattern.node Op.qLe [(Pattern.hole 0x115), s748]), (Pattern.node Op.qLt [(Pattern.hole 0x115), s748])]
def s750 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s728]), (Pattern.node Op.qLe [s732, (Pattern.hole 0x115)]), (Pattern.hole 0x116)]
def s751 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [s713]), (Pattern.node Op.bNot [s715])]
def s752 := Pattern.node Op.ite [s713, s712, (Pattern.node Op.qDiv [s646, s20])]
def s753 := Pattern.node Op.ite [s715, s714, (Pattern.node Op.qDiv [s714, s14])]
def s754 := Pattern.node Op.ite [(Pattern.hole 0x118), s36, s37]
def s755 := Pattern.node Op.zSub [s726, s754]
def s756 := Pattern.node Op.zEq [s755, s37]
def s757 := Pattern.hole 0x11a
def s758 := Pattern.hole 0x119
def s759 := Pattern.node Op.ite [(Pattern.node Op.qLe [s757, s758]), s758, s757]
def s760 := Pattern.node Op.qDiv [s758, s3]
def s761 := Pattern.node Op.qDiv [s757, s14]
def s762 := Pattern.node Op.ite [(Pattern.node Op.qLt [s757, s758]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s757, s760]), s760, s757]), (Pattern.node Op.ite [(Pattern.node Op.qLe [s761, s758]), s758, s761])]
def s763 := Pattern.node Op.ite [s756, s759, s762]
def s764 := Pattern.node Op.ite [(Pattern.node Op.bEq [s740, s35]), s742, s743]
def s765 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x11b), s733]), s733, (Pattern.hole 0x11b)]
def s766 := Pattern.node Op.ite [(Pattern.node Op.qLe [s764, s765]), s765, s764]
def s767 := Pattern.node Op.ite [(Pattern.node Op.bEq [s735, s35]), s737, s738]
def s768 := Pattern.node Op.ite [(Pattern.node Op.qLe [s767, (Pattern.hole 0x11c)]), (Pattern.hole 0x11c), s767]
def s769 := Pattern.node Op.ite [s756, s0, s759]
def s770 := Pattern.node Op.qLe [s768, s769]
def s771 := Pattern.node Op.qLt [s768, s769]
def s772 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s755]), (Pattern.node Op.qLe [(Pattern.hole 0x11b), s768]), (Pattern.node Op.ite [s756, (Pattern.hole 0x11d), (Pattern.hole 0x11e)])]
def s773 := Pattern.node Op.bEq [s609, (Pattern.hole 0xc0)]
def s774 := Pattern.node Op.qEq [s610, (Pattern.node Op.ite [s609, s506, s487])]
def s775 := Pattern.node Op.qLt [s571, s5]
def s776 := Pattern.node Op.qLe [s12, s0]
def s777 := Pattern.node Op.qLe [s5, s0]
def s778 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [(Pattern.hole 0x117)]), (Pattern.node Op.bNot [(Pattern.hole 0x11f)])]
def s779 := Pattern.node Op.bEq [s735, (Pattern.hole 0xf2)]
def s780 := Pattern.node Op.qEq [s736, (Pattern.node Op.ite [s735, s638, s617])]
def s781 := Pattern.node Op.bOr [(Pattern.hole 0xe9), (Pattern.hole 0xf1)]
def s782 := Pattern.node Op.qLt [s575, s12]
def s783 := Pattern.node Op.bOr [(Pattern.hole 0x100), (Pattern.hole 0x108)]
def s784 := Pattern.node Op.bEq [s740, (Pattern.hole 0x109)]
def s785 := Pattern.node Op.qEq [s741, (Pattern.node Op.ite [s740, s697, s679])]
def s786 := Pattern.node Op.qEq [s475, (Pattern.node Op.ite [s474, s319, s300])]
def s787 := Pattern.node Op.bOr [(Pattern.hole 0x6c), (Pattern.hole 0x74)]
def s788 := Pattern.node Op.bEq [s474, (Pattern.hole 0x75)]
def s789 := Pattern.node Op.qEq [s480, (Pattern.node Op.ite [s479, s377, s359])]
def s790 := Pattern.node Op.qEq [s352, (Pattern.node Op.ite [s351, s195, s177])]
def s791 := Pattern.node Op.bOr [(Pattern.hole 0x85), (Pattern.hole 0x8d)]
def s792 := Pattern.node Op.bEq [s479, (Pattern.hole 0x8e)]
def s793 := Pattern.node Op.bEq [s292, (Pattern.hole 42)]
def s794 := Pattern.node Op.bOr [(Pattern.hole 33), (Pattern.hole 41)]
def s795 := Pattern.node Op.qEq [s293, (Pattern.node Op.ite [s292, s132, s113])]
def s796 := Pattern.node Op.bOr [(Pattern.hole 0xb7), (Pattern.hole 0xbf)]
def s797 := Pattern.node Op.qEq [s539, (Pattern.node Op.ite [s538, s437, s419])]
def s798 := Pattern.node Op.bOr [(Pattern.hole 0xd0), (Pattern.hole 0xd8)]
def s799 := Pattern.node Op.bEq [s671, (Pattern.hole 0xd9)]
def s800 := Pattern.node Op.qEq [s672, (Pattern.node Op.ite [s671, s564, s546])]
def s801 := Pattern.node Op.bEq [s538, (Pattern.hole 0xa7)]
def s802 := Pattern.node Op.bOr [(Pattern.hole 0x9e), (Pattern.hole 0xa6)]
def s803 := Pattern.node Op.ite [s227, (Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s39]), (Pattern.node Op.qLe [(Pattern.hole 6), s47]), (Pattern.hole 7)]), (Pattern.hole 17)]
def s804 := Pattern.node Op.bEq [s351, (Pattern.hole 67)]
def s805 := Pattern.node Op.bOr [(Pattern.hole 58), (Pattern.hole 66)]
def s806 := Pattern.node Op.bEq [s411, (Pattern.hole 92)]
def s807 := Pattern.node Op.qEq [s412, (Pattern.node Op.ite [s411, s252, s234])]
def s808 := Pattern.node Op.bOr [(Pattern.hole 83), (Pattern.hole 91)]
def s809 := Pattern.node Op.ite [(Pattern.node Op.bAnd [s35, (Pattern.hole 0xda), (Pattern.hole 0xdb), (Pattern.hole 0xdc)]), s36, s37]
def s810 := Pattern.node Op.zSub [s809, s596]
def s811 := Pattern.node Op.zEq [s810, s37]
def s812 := Pattern.node Op.ite [s811, s599, s600]
def s813 := Pattern.node Op.ite [(Pattern.node Op.qLe [s812, s602]), s602, s812]
def s814 := Pattern.node Op.ite [(Pattern.node Op.qLe [s613, (Pattern.hole 0x144)]), (Pattern.hole 0x144), s613]
def s815 := Pattern.node Op.qLe [s608, s814]
def s816 := Pattern.node Op.ite [(Pattern.hole 0x145), s814, s608]
def s817 := Pattern.hole 0x146
def s818 := Pattern.node Op.ite [s811, s444, s599]
def s819 := Pattern.node Op.ite [s811, (Pattern.node Op.qLe [s817, s818]), (Pattern.node Op.qLt [s817, s818])]
def s820 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s810]), (Pattern.node Op.qLe [s812, s817]), (Pattern.hole 0x147)]
def s821 := Pattern.node Op.zSub [s809, s624]
def s822 := Pattern.node Op.zEq [s821, s37]
def s823 := Pattern.node Op.ite [s822, s629, s632]
def s824 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x149), s602]), s602, (Pattern.hole 0x149)]
def s825 := Pattern.node Op.ite [(Pattern.node Op.qLe [s634, s824]), s824, s634]
def s826 := Pattern.node Op.ite [(Pattern.node Op.qLe [s637, (Pattern.hole 0x14a)]), (Pattern.hole 0x14a), s637]
def s827 := Pattern.node Op.ite [s822, s444, s629]
def s828 := Pattern.node Op.qLe [s826, s827]
def s829 := Pattern.node Op.qLt [s826, s827]
def s830 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s821]), (Pattern.node Op.qLe [(Pattern.hole 0x149), s826]), (Pattern.node Op.ite [s822, (Pattern.hole 0x14b), (Pattern.hole 0x14c)])]
def s831 := Pattern.node Op.ite [s582, (Pattern.hole 0x14d), (Pattern.node Op.bNot [(Pattern.hole 0x148)])]
def s832 := Pattern.node Op.bAnd [s35, s705, s709, s710]
def s833 := Pattern.node Op.ite [(Pattern.hole 0x14f), s36, s37]
def s834 := Pattern.node Op.zSub [s833, s727]
def s835 := Pattern.node Op.zEq [s834, s37]
def s836 := Pattern.node Op.ite [s835, s730, s731]
def s837 := Pattern.node Op.ite [(Pattern.node Op.qLe [s836, s733]), s733, s836]
def s838 := Pattern.node Op.ite [(Pattern.node Op.qLe [s744, (Pattern.hole 0x150)]), (Pattern.hole 0x150), s744]
def s839 := Pattern.node Op.qLe [s739, s838]
def s840 := Pattern.node Op.ite [(Pattern.hole 0x151), s838, s739]
def s841 := Pattern.node Op.ite [s835, s0, s730]
def s842 := Pattern.node Op.ite [s835, (Pattern.node Op.qLe [(Pattern.hole 0x152), s841]), (Pattern.node Op.qLt [(Pattern.hole 0x152), s841])]
def s843 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s834]), (Pattern.node Op.qLe [s836, (Pattern.hole 0x152)]), (Pattern.hole 0x153)]
def s844 := Pattern.node Op.zSub [s833, s754]
def s845 := Pattern.node Op.zEq [s844, s37]
def s846 := Pattern.node Op.ite [s845, s759, s762]
def s847 := Pattern.node Op.ite [(Pattern.node Op.qLe [(Pattern.hole 0x155), s733]), s733, (Pattern.hole 0x155)]
def s848 := Pattern.node Op.ite [(Pattern.node Op.qLe [s764, s847]), s847, s764]
def s849 := Pattern.node Op.ite [(Pattern.node Op.qLe [s767, (Pattern.hole 0x156)]), (Pattern.hole 0x156), s767]
def s850 := Pattern.node Op.ite [s845, s0, s759]
def s851 := Pattern.node Op.qLe [s849, s850]
def s852 := Pattern.node Op.qLt [s849, s850]
def s853 := Pattern.node Op.bAnd [(Pattern.node Op.zLe [s37, s844]), (Pattern.node Op.qLe [(Pattern.hole 0x155), s849]), (Pattern.node Op.ite [s845, (Pattern.hole 0x157), (Pattern.hole 0x158)])]
def s854 := Pattern.node Op.qEq [s736, (Pattern.node Op.ite [s735, s826, s817])]
def s855 := Pattern.node Op.bOr [(Pattern.hole 0x148), (Pattern.hole 0x14d)]
def s856 := Pattern.node Op.bEq [s735, (Pattern.hole 0x14e)]
def s857 := Pattern.node Op.bAnd [(Pattern.node Op.bNot [(Pattern.hole 0x154)]), (Pattern.node Op.bNot [(Pattern.hole 0x159)])]
def s858 := Pattern.node Op.qLe [(Pattern.node Op.qDiv [s14, (Pattern.node (Op.qConst (Int.cast 0x30d4)) [])]), s47]

def patternTableLLLLL : PackedNatTable.Table Pattern := .leaf #[s9, s17, s19, s32, s33, s34, s46, s49, s50, s51, s52]
def patternTableLLLLR : PackedNatTable.Table Pattern := .leaf #[s53, s55, s56, s58, s59, s63, s64, s69, s71, s72, s82, s83]
def patternTableLLLL : PackedNatTable.Table Pattern := .branch 11 patternTableLLLLL patternTableLLLLR
def patternTableLLLRL : PackedNatTable.Table Pattern := .leaf #[s84, s85, s87, s88, s90, s91, s97, s111, s112, s115, s116, s117]
def patternTableLLLRR : PackedNatTable.Table Pattern := .leaf #[s118, s119, s127, s130, s134, s135, s136, s137, s140, s144, s145, s153]
def patternTableLLLR : PackedNatTable.Table Pattern := .branch 12 patternTableLLLRL patternTableLLLRR
def patternTableLLL : PackedNatTable.Table Pattern := .branch 23 patternTableLLLL patternTableLLLR
def patternTableLLRLL : PackedNatTable.Table Pattern := .leaf #[s154, s155, s156, s158, s159, s161, s162, s168, s175, s176, s179, s180]
def patternTableLLRLR : PackedNatTable.Table Pattern := .leaf #[s181, s182, s183, s191, s194, s197, s198, s199, s200, s203, s205, s206]
def patternTableLLRL : PackedNatTable.Table Pattern := .branch 12 patternTableLLRLL patternTableLLRLR
def patternTableLLRRL : PackedNatTable.Table Pattern := .leaf #[s211, s212, s213, s214, s216, s217, s219, s220, s226, s232, s233, s236]
def patternTableLLRRR : PackedNatTable.Table Pattern := .leaf #[s237, s238, s239, s240, s248, s251, s254, s255, s256, s257, s261, s265]
def patternTableLLRR : PackedNatTable.Table Pattern := .branch 12 patternTableLLRRL patternTableLLRRR
def patternTableLLR : PackedNatTable.Table Pattern := .branch 24 patternTableLLRL patternTableLLRR
def patternTableLL : PackedNatTable.Table Pattern := .branch 47 patternTableLLL patternTableLLR
def patternTableLRLLL : PackedNatTable.Table Pattern := .leaf #[s266, s271, s272, s273, s274, s276, s277, s279, s280, s286, s298]
def patternTableLRLLR : PackedNatTable.Table Pattern := .leaf #[s299, s302, s303, s304, s305, s306, s314, s317, s321, s322, s323, s324]
def patternTableLRLL : PackedNatTable.Table Pattern := .branch 11 patternTableLRLLL patternTableLRLLR
def patternTableLRLRL : PackedNatTable.Table Pattern := .leaf #[s327, s329, s330, s335, s336, s337, s338, s340, s341, s343, s344, s350]
def patternTableLRLRR : PackedNatTable.Table Pattern := .leaf #[s357, s358, s361, s362, s363, s364, s365, s373, s376, s379, s380, s381]
def patternTableLRLR : PackedNatTable.Table Pattern := .branch 12 patternTableLRLRL patternTableLRLRR
def patternTableLRL : PackedNatTable.Table Pattern := .branch 23 patternTableLRLL patternTableLRLR
def patternTableLRRLL : PackedNatTable.Table Pattern := .leaf #[s382, s385, s389, s390, s395, s396, s397, s398, s400, s401, s403, s404]
def patternTableLRRLR : PackedNatTable.Table Pattern := .leaf #[s410, s417, s418, s421, s422, s423, s424, s425, s433, s436, s439, s440]
def patternTableLRRL : PackedNatTable.Table Pattern := .branch 12 patternTableLRRLL patternTableLRRLR
def patternTableLRRRL : PackedNatTable.Table Pattern := .leaf #[s441, s442, s448, s452, s453, s458, s459, s460, s461, s463, s464, s466]
def patternTableLRRRR : PackedNatTable.Table Pattern := .leaf #[s467, s473, s485, s486, s489, s490, s491, s492, s493, s501, s504, s508]
def patternTableLRRR : PackedNatTable.Table Pattern := .branch 12 patternTableLRRRL patternTableLRRRR
def patternTableLRR : PackedNatTable.Table Pattern := .branch 24 patternTableLRRL patternTableLRRR
def patternTableLR : PackedNatTable.Table Pattern := .branch 47 patternTableLRL patternTableLRR
def patternTableL : PackedNatTable.Table Pattern := .branch 95 patternTableLL patternTableLR
def patternTableRLLLL : PackedNatTable.Table Pattern := .leaf #[s509, s510, s511, s514, s516, s517, s522, s523, s524, s525, s527]
def patternTableRLLLR : PackedNatTable.Table Pattern := .leaf #[s528, s530, s531, s537, s544, s545, s548, s549, s550, s551, s552, s560]
def patternTableRLLL : PackedNatTable.Table Pattern := .branch 11 patternTableRLLLL patternTableRLLLR
def patternTableRLLRL : PackedNatTable.Table Pattern := .leaf #[s563, s566, s567, s568, s569, s574, s579, s580, s585, s586, s587, s588]
def patternTableRLLRR : PackedNatTable.Table Pattern := .leaf #[s590, s591, s593, s594, s603, s615, s616, s619, s620, s621, s622, s623]
def patternTableRLLR : PackedNatTable.Table Pattern := .branch 12 patternTableRLLRL patternTableRLLRR
def patternTableRLL : PackedNatTable.Table Pattern := .branch 23 patternTableRLLL patternTableRLLR
def patternTableRLRLL : PackedNatTable.Table Pattern := .leaf #[s633, s636, s640, s641, s642, s643, s650, s655, s656, s657, s658, s660]
def patternTableRLRLR : PackedNatTable.Table Pattern := .leaf #[s661, s663, s664, s670, s677, s678, s681, s682, s683, s684, s685, s693]
def patternTableRLRL : PackedNatTable.Table Pattern := .branch 12 patternTableRLRLL patternTableRLRLR
def patternTableRLRRL : PackedNatTable.Table Pattern := .leaf #[s696, s699, s700, s701, s702, s711, s716, s717, s718, s719, s721, s722]
def patternTableRLRRR : PackedNatTable.Table Pattern := .leaf #[s724, s725, s734, s746, s747, s749, s750, s751, s752, s753, s763, s766]
def patternTableRLRR : PackedNatTable.Table Pattern := .branch 12 patternTableRLRRL patternTableRLRRR
def patternTableRLR : PackedNatTable.Table Pattern := .branch 24 patternTableRLRL patternTableRLRR
def patternTableRL : PackedNatTable.Table Pattern := .branch 47 patternTableRLL patternTableRLR
def patternTableRRLLL : PackedNatTable.Table Pattern := .leaf #[s770, s771, s772, s773, s774, s775, s776, s777, s778, s779, s780]
def patternTableRRLLR : PackedNatTable.Table Pattern := .leaf #[s781, s782, s783, s784, s785, s786, s787, s788, s789, s790, s791, s792]
def patternTableRRLL : PackedNatTable.Table Pattern := .branch 11 patternTableRRLLL patternTableRRLLR
def patternTableRRLRL : PackedNatTable.Table Pattern := .leaf #[s793, s794, s795, s796, s797, s798, s799, s800, s801, s802, s803, s804]
def patternTableRRLRR : PackedNatTable.Table Pattern := .leaf #[s805, s806, s807, s808, s813, s815, s816, s819, s820, s823, s825, s828]
def patternTableRRLR : PackedNatTable.Table Pattern := .branch 12 patternTableRRLRL patternTableRRLRR
def patternTableRRL : PackedNatTable.Table Pattern := .branch 23 patternTableRRLL patternTableRRLR
def patternTableRRRLL : PackedNatTable.Table Pattern := .leaf #[s829, s830, s831, s832, s837, s839, s840, s842, s843, s846, s848, s851]
def patternTableRRRLR : PackedNatTable.Table Pattern := .leaf #[s852, s853, s854, s855, s856, s776, s777, s775, s857, s782, s798, s799]
def patternTableRRRL : PackedNatTable.Table Pattern := .branch 12 patternTableRRRLL patternTableRRRLR
def patternTableRRRRL : PackedNatTable.Table Pattern := .leaf #[s802, s801, s797, s800, s783, s784, s785, s796, s773, s774, s791, s792]
def patternTableRRRRR : PackedNatTable.Table Pattern := .leaf #[s789, s786, s787, s788, s804, s805, s807, s806, s808, s790, s858, s803]
def patternTableRRRR : PackedNatTable.Table Pattern := .branch 12 patternTableRRRRL patternTableRRRRR
def patternTableRRR : PackedNatTable.Table Pattern := .branch 24 patternTableRRRL patternTableRRRR
def patternTableRR : PackedNatTable.Table Pattern := .branch 47 patternTableRRL patternTableRRR
def patternTableR : PackedNatTable.Table Pattern := .branch 95 patternTableRL patternTableRR
def patternTable : PackedNatTable.Table Pattern := .branch 0xbe patternTableL patternTableR

def fallback : Pattern := .node (.qConst 0) []

def patterns (j : Nat) : Pattern := patternTable.get fallback j

end ClosureSharedAnchorPatternData

end PolicySubmissionPart75

/- Component ClosureInputReflection; SHA256 a5517fb0181f57c4cd2d8371bffac0d6c1f389424d7cbe0501df7664e2ae866a. -/
section PolicySubmissionPart76
/- Decision-instance independent elementary input reflection. -/
namespace ClosureInputReflection
open ClosureSemantics

def boolValue_decide_irrel (p : Prop) (d e : Decidable p) :
    boolValue (@decide p d) = boolValue (@decide p e) :=
  congrArg (fun dec : Decidable p => boolValue (@decide p dec)) (Subsingleton.elim _ _)

end ClosureInputReflection

end PolicySubmissionPart76

/- Component ClosureAnchorSemantics; SHA256 552d19ff89828981d9491ed37b2fd0da82b202f012875ff5af8f90cd9cfb336e. -/
section PolicySubmissionPart77
/- A mathematical, typed interpretation with sparse formula anchors. -/
namespace ClosureAnchorSemantics
open ClosureSemantics ClosureInputModel

inductive SValue where
  | prop : Prop → SValue
  | int : Int → SValue
  | rat : Rat → SValue

def SValue.p : SValue → Prop | .prop p => p | _ => False
def SValue.z : SValue → Int | .int z => z | _ => 0
def SValue.q : SValue → Rat | .rat q => q | _ => 0
abbrev SValuation := Nat → SValue

def conjunction : List Prop → Prop
  | [] => True
  | [p] => p
  | p :: q :: ps => p ∧ conjunction (q :: ps)

def disjunction : List Prop → Prop
  | [] => False
  | [p] => p
  | p :: q :: ps => p ∨ disjunction (q :: ps)

noncomputable def sIte (p : Prop) (a b : SValue) : SValue := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  exact match a, b with
    | .prop a, .prop b => .prop (if p then a else b)
    | .int a, .int b => .int (if p then a else b)
    | .rat a, .rat b => .rat (if p then a else b)
    | a, b => if p then a else b

noncomputable def evalSOp (input : SValuation) : Op → List SValue → SValue
  | .input k, _ => input k
  | .qConst c, _ => .rat c
  | .zConst c, _ => .int c
  | .bConst true, _ => .prop True
  | .bConst false, _ => .prop False
  | .alias, [a] => a
  | .bNot, [a] => .prop (¬a.p)
  | .bOr, xs => .prop (disjunction (xs.map SValue.p))
  | .bAnd, xs => .prop (conjunction (xs.map SValue.p))
  | .bEq, [a,b] => .prop (a.p ↔ b.p)
  | .ite, [c,a,b] => sIte c.p a b
  | .qEq, [a,b] => .prop (a.q = b.q)
  | .zEq, [a,b] => .prop (a.z = b.z)
  | .qLe, [a,b] => .prop (a.q ≤ b.q)
  | .zLe, [a,b] => .prop (a.z ≤ b.z)
  | .qLt, [a,b] => .prop (a.q < b.q)
  | .zLt, [a,b] => .prop (a.z < b.z)
  | .qAdd, a :: rest => .rat ((rest.map SValue.q).foldl (· + ·) a.q)
  | .zAdd, a :: rest => .int ((rest.map SValue.z).foldl (· + ·) a.z)
  | .qMul, a :: rest => .rat ((rest.map SValue.q).foldl (· * ·) a.q)
  | .zMul, a :: rest => .int ((rest.map SValue.z).foldl (· * ·) a.z)
  | .qAdd, [] => .rat 0
  | .zAdd, [] => .int 0
  | .qMul, [] => .rat 1
  | .zMul, [] => .int 1
  | .qNeg, [a] => .rat (-a.q)
  | .zNeg, [a] => .int (-a.z)
  | .qSub, a :: rest => .rat ((rest.map SValue.q).foldl (· - ·) a.q)
  | .zSub, a :: rest => .int ((rest.map SValue.z).foldl (· - ·) a.z)
  | .qDiv, [a,b] => .rat (a.q / b.q)
  | _, _ => .rat 0

noncomputable def evalSNode (input values : SValuation) (n : Node) : SValue :=
  evalSOp input n.op (n.children.map values)

def evalSNode_congr (input values other : SValuation) (n : Node)
    (h : ∀ j ∈ n.children, values j = other j) :
    evalSNode input values n = evalSNode input other n := by
  unfold evalSNode
  congr 1
  exact List.map_congr_left h

noncomputable def sInput (X Y : Rat) (p : Nat → Prop) (r : Nat → Rat) : SValuation :=
  fun slot => if slot = 0 then .rat X else if slot = 1 then .rat Y
    else if slot % 2 = 0 then .prop (p ((slot - 2) / 2))
    else .rat (r ((slot - 3) / 2))

noncomputable def evalAnchored (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) : Nat → SValuation
  | 0, _ => .rat 0
  | fuel + 1, i => match anchor i with
    | some a => a
    | none => evalSNode input (evalAnchored raw input anchor fuel) (boundedProgram raw i)

noncomputable def anchoredValues (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) : SValuation :=
  fun i => evalAnchored raw input anchor (i + 1) i

noncomputable def anchorBody (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) (i : Nat) : SValue :=
  evalSNode input (evalAnchored raw input anchor i) (boundedProgram raw i)

def evalAnchored_stable (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) (i fuel : Nat) (hi : i < fuel) :
    evalAnchored raw input anchor fuel i = anchoredValues raw input anchor i := by
  induction i using Nat.strong_induction_on generalizing fuel with
  | h i ih =>
    cases fuel with
    | zero => omega
    | succ fuel =>
      unfold anchoredValues
      cases ha : anchor i with
      | some a => simp only [evalAnchored, ha]
      | none =>
        simp only [evalAnchored, ha]
        apply evalSNode_congr
        intro j hj
        have hji := boundedProgram_children raw i j hj
        rw [ih j hji fuel (by omega), ih j hji i hji]

def anchorBody_eq (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) (i : Nat) :
    anchorBody raw input anchor i =
      evalSNode input (anchoredValues raw input anchor) (boundedProgram raw i) := by
  apply evalSNode_congr
  intro j hj
  exact evalAnchored_stable raw input anchor j i (boundedProgram_children raw i j hj)

def anchoredValues_equation (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) (i : Nat)
    (h : ∀ a, anchor i = some a → a = anchorBody raw input anchor i) :
    anchoredValues raw input anchor i =
      evalSNode input (anchoredValues raw input anchor) (boundedProgram raw i) := by
  rw [← anchorBody_eq]
  unfold anchoredValues
  cases ha : anchor i with
  | none => simp only [evalAnchored, ha, anchorBody]
  | some a => simpa only [evalAnchored, ha] using h a ha

end ClosureAnchorSemantics

end PolicySubmissionPart77

/- Component ClosureAnchorEncoding; SHA256 c657aefdacd54976d9493b5fa69fe70a71e26dc611944ff67fa2f1d568f728a8. -/
section PolicySubmissionPart78
/- Boolean encoding of the mathematical anchored interpreter. -/
namespace ClosureAnchorSemantics
open ClosureSemantics ClosureInputModel ClosureInputReflection

noncomputable def encode : SValue → Value
  | .prop p => boolValue (@decide p (Classical.propDecidable p))
  | .int z => intValue z
  | .rat q => ratValue q

def encode_prop (p : Prop) : encode (.prop p) =
    boolValue (@decide p (Classical.propDecidable p)) := rfl
def encode_int (z : Int) : encode (.int z) = intValue z := rfl
def encode_rat (q : Rat) : encode (.rat q) = ratValue q := rfl

def encode_b (a : SValue) :
    (encode a).b = @decide a.p (Classical.propDecidable _) := by
  cases a with
  | prop p => rfl
  | int z => exact (decide_false (Classical.propDecidable False)).symm
  | rat q => exact (decide_false (Classical.propDecidable False)).symm

def encode_z (a : SValue) : (encode a).z = a.z := by cases a <;> rfl
def encode_q (a : SValue) : (encode a).q = a.q := by cases a <;> rfl

def decide_conjunction (ps : List Prop) :
    @decide (conjunction ps) (Classical.propDecidable _) =
      (ps.map (fun p => @decide p (Classical.propDecidable _))).all id := by
  induction ps with
  | nil => exact decide_true _
  | cons p ps ih =>
    cases ps with
    | nil => exact (Bool.and_true _).symm
    | cons q qs =>
      exact (@Bool.decide_and p (conjunction (q :: qs)) (Classical.propDecidable _)
        (Classical.propDecidable _) (Classical.propDecidable _)).trans
        (congrArg (fun b => @decide p (Classical.propDecidable _) && b) ih)

def decide_disjunction (ps : List Prop) :
    @decide (disjunction ps) (Classical.propDecidable _) =
      (ps.map (fun p => @decide p (Classical.propDecidable _))).any id := by
  induction ps with
  | nil => exact decide_false _
  | cons p ps ih =>
    cases ps with
    | nil => exact (Bool.or_false _).symm
    | cons q qs =>
      exact (@Bool.decide_or p (disjunction (q :: qs)) (Classical.propDecidable _)
        (Classical.propDecidable _) (Classical.propDecidable _)).trans
        (congrArg (fun b => @decide p (Classical.propDecidable _) || b) ih)

def encode_conjunction (xs : List SValue) :
    encode (.prop (conjunction (xs.map SValue.p))) =
      boolValue (((xs.map encode).map Value.b).all id) := by
  simp only [encode_prop, decide_conjunction, List.map_map, Function.comp_def, encode_b]

def encode_disjunction (xs : List SValue) :
    encode (.prop (disjunction (xs.map SValue.p))) =
      boolValue (((xs.map encode).map Value.b).any id) := by
  simp only [encode_prop, decide_disjunction, List.map_map, Function.comp_def, encode_b]

def encode_sIte (p : Prop) (a b : SValue) :
    encode (sIte p a b) =
      if @decide p (Classical.propDecidable _) then encode a else encode b := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  by_cases h : p <;> cases a <;> cases b <;> simp [sIte, encode, h]

def encode_evalSOp (input : SValuation) (op : Op) (xs : List SValue) :
    encode (evalSOp input op xs) = evalOp (fun i => encode (input i)) op (xs.map encode) := by
  letI : (a : Prop) → Decidable a := Classical.propDecidable
  cases op
  case bConst b => cases b <;> simp only [evalSOp, evalOp, encode_prop, decide_true, decide_false]
  case bOr => exact encode_disjunction xs
  case bAnd => exact encode_conjunction xs
  all_goals
    rcases xs with _ | ⟨a, _ | ⟨b, _ | ⟨c, _ | ⟨d, xs⟩⟩⟩⟩ <;>
    simp only [evalSOp, evalOp, List.map_cons, List.map_nil, encode_conjunction,
      encode_disjunction, encode_sIte, List.map_map, Function.comp_def, encode_q, encode_z,
      encode_b, encode_prop, encode_int, encode_rat, decide_true, decide_false,
      Bool.decide_iff_dist, decide_not]
  all_goals first | rfl | exact boolValue_decide_irrel _ _ _ | split_ifs <;> rfl

def encode_evalSNode (input values : SValuation) (n : Node) :
    encode (evalSNode input values n) =
      evalNode (fun i => encode (input i)) (fun i => encode (values i)) n := by
  simpa only [evalSNode, evalNode, List.map_map, Function.comp_def] using
    encode_evalSOp input n.op (n.children.map values)

def encode_sInput (X Y : Rat) (p : Nat → Prop) (r : Nat → Rat) :
    (fun i => encode (sInput X Y p r i)) = inputValuation X Y p r := by
  funext i
  unfold sInput inputValuation
  split_ifs <;> rfl

def anchored_model_agrees (raw : Nat → Node) (X Y : Rat) (p : Nat → Prop)
    (r : Nat → Rat) (anchor : Nat → Option SValue) (N : Nat)
    (h : ∀ i < N, ∀ a, anchor i = some a →
      a = anchorBody raw (sInput X Y p r) anchor i) :
    ∀ i < N, programModel raw (inputValuation X Y p r) i =
      encode (anchoredValues raw (sInput X Y p r) anchor i) := by
  apply programModel_agrees_below
  intro i hi
  rw [anchoredValues_equation raw (sInput X Y p r) anchor i (h i hi), encode_evalSNode,
    encode_sInput]

end ClosureAnchorSemantics

end PolicySubmissionPart78

/- Component ClosureAnchorAssertions; SHA256 a0b8f91e5defe8e9a444158460affe53955faa6e01ef8d278f9c3858055ce65c. -/
section PolicySubmissionPart79
/- From checked mathematical anchors to actual asserted SAT unit clauses. -/
namespace ClosureAnchorSemantics
open ClosureSemantics ClosureInputModel

def anchoredValues_of_some (raw : Nat → Node) (input : SValuation)
    (anchor : Nat → Option SValue) (i : Nat) (a : SValue) (ha : anchor i = some a) :
    anchoredValues raw input anchor i = a := by
  simp only [anchoredValues, evalAnchored, ha]

def anchor_model_true (raw : Nat → Node) (X Y : Rat) (p : Nat → Prop)
    (r : Nat → Rat) (anchor : Nat → Option SValue) (N i : Nat) (a : Prop)
    (hcheck : ∀ j < N, ∀ v, anchor j = some v →
      v = anchorBody raw (sInput X Y p r) anchor j)
    (hi : i < N) (ha : anchor i = some (.prop a)) (htruth : a) :
    (programModel raw (inputValuation X Y p r) i).b = true := by
  rw [anchored_model_agrees raw X Y p r anchor N hcheck i hi,
    anchoredValues_of_some raw (sInput X Y p r) anchor i (.prop a) ha]
  exact @decide_eq_true a (Classical.propDecidable a) htruth

def alias_model (raw : Nat → Node) (input : Valuation) (i j : Nat)
    (hnode : raw i = ⟨.alias, [j]⟩) (hback : j < i) :
    programModel raw input i = programModel raw input j := by
  rw [programModel_eq_raw raw input i (by simpa [hnode] using hback), hnode]
  rfl

end ClosureAnchorSemantics

end PolicySubmissionPart79

/- Component ClosureAnchorFuelPatternCheck; SHA256 46448ae0600e0a3d99dd721ad7dce7739b5bd5dc41612d760ec7b21231a7e9b1. -/
section PolicySubmissionPart80
/- Experimental anchor matching with an evaluator structurally recursive on fuel. -/
namespace ClosureAnchorFuelPatternCheck
open ClosureSemantics ClosureAnchorSemantics ClosurePattern

noncomputable def eval (input env : SValuation) (fuel : Nat) (pattern : Pattern) : SValue :=
  match fuel, pattern with
  | 0, _ => .rat 0
  | _ + 1, .hole k => env k
  | fuel + 1, .node op children =>
      evalSOp input op (children.map (eval input env fuel))
termination_by structural fuel

def check (program : Nat → Node) (indices : Nat → Nat) :
    Nat → Pattern → Nat → Bool
  | 0, _, _ => false
  | _ + 1, .hole k, i => indices i == k + 1
  | fuel + 1, .node op children, i =>
      (indices i == 0) && sameOp op (program i).op &&
        allPairs (check program indices fuel) children (program i).children

def check_sound (raw : Nat → Node) (input env : SValuation)
    (anchor : Nat → Option SValue) (indices : Nat → Nat)
    (hanchor : ∀ i, anchor i =
      if indices i = 0 then none else some (env (indices i - 1)))
    (fuel : Nat) (pattern : Pattern) (i : Nat)
    (hc : check (boundedProgram raw) indices fuel pattern i = true) :
    eval input env fuel pattern = anchoredValues raw input anchor i := by
  induction fuel generalizing pattern i with
  | zero => simp [check] at hc
  | succ fuel ih =>
    cases pattern with
    | hole k =>
      have hk : indices i = k + 1 := by
        simpa only [check, beq_iff_eq] using hc
      have ha : anchor i = some (env k) := by
        rw [hanchor, hk]
        simp
      simpa only [eval] using (anchoredValues_of_some raw input anchor i (env k) ha).symm
    | node op children =>
      have hh : (indices i = 0 ∧ sameOp op (boundedProgram raw i).op = true) ∧
          allPairs (check (boundedProgram raw) indices fuel)
            children (boundedProgram raw i).children = true := by
        simpa only [check, Bool.and_eq_true, beq_iff_eq] using hc
      have hn : anchor i = none := by
        rw [hanchor, hh.1.1] <;> rfl
      have hop := sameOp_sound op (boundedProgram raw i).op hh.1.2
      have hchildren := allPairs_map_eq
        (check (boundedProgram raw) indices fuel)
        (eval input env fuel) (anchoredValues raw input anchor)
        (fun p j hp => ih p j hp) children (boundedProgram raw i).children hh.2
      have hv : eval input env (fuel + 1) (.node op children) =
          evalSNode input (anchoredValues raw input anchor) (boundedProgram raw i) := by
        simp only [eval, evalSNode, hchildren, hop]
      have he := anchoredValues_equation raw input anchor i (by
        intro a ha
        rw [hn] at ha
        cases ha)
      exact hv.trans he.symm

def checkBody (program : Nat → Node) (indices : Nat → Nat)
    (fuel : Nat) (pattern : Pattern) (i : Nat) : Bool :=
  match pattern with
  | .hole _ => false
  | .node op children =>
      sameOp op (program i).op &&
        allPairs (check program indices fuel) children (program i).children

def checkBody_sound (raw : Nat → Node) (input env : SValuation)
    (anchor : Nat → Option SValue) (indices : Nat → Nat)
    (hanchor : ∀ i, anchor i =
      if indices i = 0 then none else some (env (indices i - 1)))
    (fuel : Nat) (pattern : Pattern) (i : Nat)
    (hc : checkBody (boundedProgram raw) indices fuel pattern i = true) :
    eval input env (fuel + 1) pattern = anchorBody raw input anchor i := by
  cases pattern with
  | hole k => simp [checkBody] at hc
  | node op children =>
    have hh : sameOp op (boundedProgram raw i).op = true ∧
        allPairs (check (boundedProgram raw) indices fuel)
          children (boundedProgram raw i).children = true := by
      simpa only [checkBody, Bool.and_eq_true] using hc
    have hop := sameOp_sound op (boundedProgram raw i).op hh.1
    have hchildren := allPairs_map_eq
      (check (boundedProgram raw) indices fuel)
      (eval input env fuel) (anchoredValues raw input anchor)
      (fun p j hp => check_sound raw input env anchor indices hanchor fuel p j hp)
      children (boundedProgram raw i).children hh.2
    rw [anchorBody_eq]
    simp only [eval, evalSNode, hchildren, hop]

def checkAnchor (program : Nat → Node) (indices : Nat → Nat)
    (patterns : Nat → Pattern) (N fuel i : Nat) : Bool :=
  if indices i = 0 then true else
    decide (indices i - 1 < N) &&
      checkBody program indices fuel (patterns (indices i - 1)) i

def anchor_good (raw : Nat → Node) (input env : SValuation)
    (anchor : Nat → Option SValue) (indices : Nat → Nat)
    (hanchor : ∀ i, anchor i =
      if indices i = 0 then none else some (env (indices i - 1)))
    (patterns : Nat → Pattern) (N fuel i : Nat)
    (hsemantic : ∀ j < N, env j = eval input env (fuel + 1) (patterns j))
    (hc : checkAnchor (boundedProgram raw) indices patterns N fuel i = true) :
    ∀ a, anchor i = some a → a = anchorBody raw input anchor i := by
  intro a ha
  by_cases hz : indices i = 0
  · have hn : anchor i = none := by
      rw [hanchor, hz] <;> rfl
    rw [hn] at ha
    cases ha
  · have hh : indices i - 1 < N ∧
        checkBody (boundedProgram raw) indices fuel (patterns (indices i - 1)) i = true := by
      simpa only [checkAnchor, if_neg hz, Bool.and_eq_true, decide_eq_true_eq] using hc
    have he : env (indices i - 1) = a := by
      apply Option.some.inj
      simpa only [hanchor i, if_neg hz] using ha
    exact he.symm.trans ((hsemantic (indices i - 1) hh.1).trans
      (checkBody_sound raw input env anchor indices hanchor fuel _ i hh.2))

end ClosureAnchorFuelPatternCheck

end PolicySubmissionPart80

/- Component ClosureAnchorData; SHA256 74f4f17411abe6e46ba3076712fa959369dbe7ddd987f9997fdf060d5a52604d. -/
section PolicySubmissionPart81
/- Sparse mathematical anchors for the actual asserted clauses. -/
namespace ClosureAnchorData
open ClosureAnchorSemantics PackedNatTable

def indexAt (indices : Table Nat) (i : Nat) : Nat :=
  (indices.get 0 (i / 4) >>> (12 * (i % 4))) &&& 0xfff

noncomputable def valuesLLLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q90 X),
  .prop (SelectiveSharedInputs.q91 Y),
  .prop (SelectiveSharedInputs.q92 Y),
  .prop (SelectiveSharedInputs.q93 X Y),
  .rat (SelectiveSharedInputs.q94 X),
  .rat (SelectiveSharedInputs.q95 Y),
  .rat (SelectiveSharedInputs.q96 X Y),
  .prop (SelectiveSharedInputs.q97 X Y r),
  .prop (SelectiveSharedInputs.q98 X Y),
  .prop (SelectiveSharedInputs.q99 X Y),
  .rat (SelectiveSharedInputs.q100 X Y),
  .prop (SelectiveSharedInputs.q101 X Y),
  .prop (SelectiveSharedInputs.q102 X Y),
  .rat (SelectiveSharedInputs.q103 X Y),
  .prop (SelectiveSharedInputs.q104 X Y),
  .rat (SelectiveSharedInputs.q105 X Y),
  .prop (SelectiveSharedInputs.q106 X Y r),
  .prop (SelectiveSharedInputs.q107 X Y r),
  .prop (SelectiveSharedInputs.q158 X),
  .prop (SelectiveSharedInputs.q159 Y),
  .prop (SelectiveSharedInputs.q160 Y),
  .prop (SelectiveSharedInputs.q161 X Y),
  .prop (SelectiveSharedInputs.q162 X Y)]

noncomputable def valuesLLLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .rat (SelectiveSharedInputs.q163 X Y),
  .prop (SelectiveSharedInputs.q164 X Y),
  .prop (SelectiveSharedInputs.q165 X Y),
  .rat (SelectiveSharedInputs.q166 X Y),
  .prop (SelectiveSharedInputs.q167 X Y),
  .rat (SelectiveSharedInputs.q168 X Y),
  .rat (SelectiveSharedInputs.q169 X Y),
  .prop (SelectiveSharedInputs.q170 X Y p r),
  .rat (SelectiveSharedInputs.q171 X Y p r),
  .prop (SelectiveSharedInputs.q172 X Y p r),
  .prop (SelectiveSharedInputs.q173 X Y p r),
  .prop (SelectiveSharedInputs.q174 X Y),
  .rat (SelectiveSharedInputs.q175 X),
  .rat (SelectiveSharedInputs.q176 Y),
  .rat (SelectiveSharedInputs.q177 X Y),
  .rat (SelectiveSharedInputs.q178 X Y p r),
  .prop (SelectiveSharedInputs.q179 X Y p r),
  .prop (SelectiveSharedInputs.q180 X Y p r),
  .prop (SelectiveSharedInputs.q181 X Y p r),
  .prop (SelectiveSharedInputs.q182 X Y p r),
  .prop (SelectiveSharedInputs.q183 X),
  .prop (SelectiveSharedInputs.q184 Y),
  .prop (SelectiveSharedInputs.q185 Y),
  .prop (SelectiveSharedInputs.q186 X Y)]

noncomputable def valuesLLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 23 (valuesLLLL X Y p r) (valuesLLLR X Y p r)

noncomputable def valuesLLRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q187 X Y),
  .rat (SelectiveSharedInputs.q188 X Y),
  .prop (SelectiveSharedInputs.q189 X Y),
  .prop (SelectiveSharedInputs.q190 X Y),
  .rat (SelectiveSharedInputs.q191 X Y),
  .prop (SelectiveSharedInputs.q192 X Y),
  .rat (SelectiveSharedInputs.q193 X Y),
  .rat (SelectiveSharedInputs.q194 X Y),
  .prop (SelectiveSharedInputs.q195 X Y p r),
  .rat (SelectiveSharedInputs.q196 X Y p r),
  .prop (SelectiveSharedInputs.q197 X Y p r),
  .prop (SelectiveSharedInputs.q198 X Y p r),
  .prop (SelectiveSharedInputs.q199 X Y),
  .rat (SelectiveSharedInputs.q200 X),
  .rat (SelectiveSharedInputs.q201 Y),
  .rat (SelectiveSharedInputs.q202 X Y),
  .rat (SelectiveSharedInputs.q203 X Y p r),
  .prop (SelectiveSharedInputs.q204 X Y p r),
  .prop (SelectiveSharedInputs.q205 X Y p r),
  .prop (SelectiveSharedInputs.q206 X Y p r),
  .prop (SelectiveSharedInputs.q207 X Y p r),
  .prop (SelectiveSharedInputs.q208 X),
  .prop (SelectiveSharedInputs.q209 Y),
  .prop (SelectiveSharedInputs.q210 Y)]

noncomputable def valuesLLRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q211 X Y),
  .prop (SelectiveSharedInputs.q212 X Y),
  .rat (SelectiveSharedInputs.q213 X Y),
  .prop (SelectiveSharedInputs.q214 X Y),
  .prop (SelectiveSharedInputs.q215 X Y),
  .rat (SelectiveSharedInputs.q216 X Y),
  .prop (SelectiveSharedInputs.q217 X Y),
  .rat (SelectiveSharedInputs.q218 X Y),
  .rat (SelectiveSharedInputs.q219 X Y),
  .prop (SelectiveSharedInputs.q220 X Y p r),
  .rat (SelectiveSharedInputs.q221 X Y p r),
  .prop (SelectiveSharedInputs.q222 X Y p r),
  .prop (SelectiveSharedInputs.q223 X Y p r),
  .prop (SelectiveSharedInputs.q224 X Y),
  .rat (SelectiveSharedInputs.q225 X),
  .rat (SelectiveSharedInputs.q226 Y),
  .rat (SelectiveSharedInputs.q227 X Y),
  .rat (SelectiveSharedInputs.q228 X Y p r),
  .prop (SelectiveSharedInputs.q229 X Y p r),
  .prop (SelectiveSharedInputs.q230 X Y p r),
  .prop (SelectiveSharedInputs.q231 X Y p r),
  .prop (SelectiveSharedInputs.q232 X Y p r),
  .prop (SelectiveSharedInputs.q258 X),
  .prop (SelectiveSharedInputs.q259 Y)]

noncomputable def valuesLLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 24 (valuesLLRL X Y p r) (valuesLLRR X Y p r)

noncomputable def valuesLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 47 (valuesLLL X Y p r) (valuesLLR X Y p r)

noncomputable def valuesLRLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q260 Y),
  .prop (SelectiveSharedInputs.q261 X Y),
  .prop (SelectiveSharedInputs.q262 X Y),
  .rat (SelectiveSharedInputs.q263 X Y),
  .prop (SelectiveSharedInputs.q264 X Y),
  .prop (SelectiveSharedInputs.q265 X Y),
  .rat (SelectiveSharedInputs.q266 X Y),
  .prop (SelectiveSharedInputs.q267 X Y),
  .rat (SelectiveSharedInputs.q268 X Y),
  .rat (SelectiveSharedInputs.q269 X Y),
  .prop (SelectiveSharedInputs.q270 X Y p r),
  .rat (SelectiveSharedInputs.q271 X Y p r),
  .prop (SelectiveSharedInputs.q272 X Y p r),
  .prop (SelectiveSharedInputs.q273 X Y p r),
  .prop (SelectiveSharedInputs.q274 X Y),
  .rat (SelectiveSharedInputs.q275 X),
  .rat (SelectiveSharedInputs.q276 Y),
  .rat (SelectiveSharedInputs.q277 X Y),
  .rat (SelectiveSharedInputs.q278 X Y p r),
  .prop (SelectiveSharedInputs.q279 X Y p r),
  .prop (SelectiveSharedInputs.q280 X Y p r),
  .prop (SelectiveSharedInputs.q281 X Y p r),
  .prop (SelectiveSharedInputs.q282 X Y p r)]

noncomputable def valuesLRLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q283 X),
  .prop (SelectiveSharedInputs.q284 Y),
  .prop (SelectiveSharedInputs.q285 Y),
  .prop (SelectiveSharedInputs.q286 X Y),
  .prop (SelectiveSharedInputs.q287 X Y),
  .rat (SelectiveSharedInputs.q288 X Y),
  .prop (SelectiveSharedInputs.q289 X Y),
  .prop (SelectiveSharedInputs.q290 X Y),
  .rat (SelectiveSharedInputs.q291 X Y),
  .prop (SelectiveSharedInputs.q292 X Y),
  .rat (SelectiveSharedInputs.q293 X Y),
  .rat (SelectiveSharedInputs.q294 X Y),
  .prop (SelectiveSharedInputs.q295 X Y p r),
  .rat (SelectiveSharedInputs.q296 X Y p r),
  .prop (SelectiveSharedInputs.q297 X Y p r),
  .prop (SelectiveSharedInputs.q298 X Y p r),
  .prop (SelectiveSharedInputs.q299 X Y),
  .rat (SelectiveSharedInputs.q300 X),
  .rat (SelectiveSharedInputs.q301 Y),
  .rat (SelectiveSharedInputs.q302 X Y),
  .rat (SelectiveSharedInputs.q303 X Y p r),
  .prop (SelectiveSharedInputs.q304 X Y p r),
  .prop (SelectiveSharedInputs.q305 X Y p r),
  .prop (SelectiveSharedInputs.q306 X Y p r)]

noncomputable def valuesLRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 23 (valuesLRLL X Y p r) (valuesLRLR X Y p r)

noncomputable def valuesLRRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q307 X Y p r),
  .prop (SelectiveSharedInputs.q308 X),
  .prop (SelectiveSharedInputs.q309 Y),
  .prop (SelectiveSharedInputs.q310 Y),
  .prop (SelectiveSharedInputs.q311 X Y),
  .prop (SelectiveSharedInputs.q312 X Y),
  .rat (SelectiveSharedInputs.q313 X Y),
  .prop (SelectiveSharedInputs.q314 X Y),
  .prop (SelectiveSharedInputs.q315 X Y),
  .rat (SelectiveSharedInputs.q316 X Y),
  .prop (SelectiveSharedInputs.q317 X Y),
  .rat (SelectiveSharedInputs.q318 X Y),
  .rat (SelectiveSharedInputs.q319 X Y),
  .prop (SelectiveSharedInputs.q320 X Y p r),
  .rat (SelectiveSharedInputs.q321 X Y p r),
  .prop (SelectiveSharedInputs.q322 X Y p r),
  .prop (SelectiveSharedInputs.q323 X Y p r),
  .prop (SelectiveSharedInputs.q324 X Y),
  .rat (SelectiveSharedInputs.q325 X),
  .rat (SelectiveSharedInputs.q326 Y),
  .rat (SelectiveSharedInputs.q327 X Y),
  .rat (SelectiveSharedInputs.q328 X Y p r),
  .prop (SelectiveSharedInputs.q329 X Y p r),
  .prop (SelectiveSharedInputs.q330 X Y p r)]

noncomputable def valuesLRRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q331 X Y p r),
  .prop (SelectiveSharedInputs.q332 X Y p r),
  .prop (SelectiveSharedInputs.q358 X),
  .prop (SelectiveSharedInputs.q359 Y),
  .prop (SelectiveSharedInputs.q360 Y),
  .prop (SelectiveSharedInputs.q361 X Y),
  .prop (SelectiveSharedInputs.q362 X Y),
  .rat (SelectiveSharedInputs.q363 X Y),
  .prop (SelectiveSharedInputs.q364 X Y),
  .prop (SelectiveSharedInputs.q365 X Y),
  .rat (SelectiveSharedInputs.q366 X Y),
  .prop (SelectiveSharedInputs.q367 X Y),
  .rat (SelectiveSharedInputs.q368 X Y),
  .rat (SelectiveSharedInputs.q369 X Y),
  .prop (SelectiveSharedInputs.q370 X Y p r),
  .rat (SelectiveSharedInputs.q371 X Y p r),
  .prop (SelectiveSharedInputs.q372 X Y p r),
  .prop (SelectiveSharedInputs.q373 X Y p r),
  .prop (SelectiveSharedInputs.q374 X Y),
  .rat (SelectiveSharedInputs.q375 X),
  .rat (SelectiveSharedInputs.q376 Y),
  .rat (SelectiveSharedInputs.q377 X Y),
  .rat (SelectiveSharedInputs.q378 X Y p r),
  .prop (SelectiveSharedInputs.q379 X Y p r)]

noncomputable def valuesLRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 24 (valuesLRRL X Y p r) (valuesLRRR X Y p r)

noncomputable def valuesLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 47 (valuesLRL X Y p r) (valuesLRR X Y p r)

noncomputable def valuesL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 95 (valuesLL X Y p r) (valuesLR X Y p r)

noncomputable def valuesRLLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q380 X Y p r),
  .prop (SelectiveSharedInputs.q381 X Y p r),
  .prop (SelectiveSharedInputs.q382 X Y p r),
  .prop (SelectiveSharedInputs.q383 X),
  .prop (SelectiveSharedInputs.q384 Y),
  .prop (SelectiveSharedInputs.q385 Y),
  .prop (SelectiveSharedInputs.q386 X Y),
  .prop (SelectiveSharedInputs.q387 X Y),
  .rat (SelectiveSharedInputs.q388 X Y),
  .prop (SelectiveSharedInputs.q389 X Y),
  .prop (SelectiveSharedInputs.q390 X Y),
  .rat (SelectiveSharedInputs.q391 X Y),
  .prop (SelectiveSharedInputs.q392 X Y),
  .rat (SelectiveSharedInputs.q393 X Y),
  .rat (SelectiveSharedInputs.q394 X Y),
  .prop (SelectiveSharedInputs.q395 X Y p r),
  .rat (SelectiveSharedInputs.q396 X Y p r),
  .prop (SelectiveSharedInputs.q397 X Y p r),
  .prop (SelectiveSharedInputs.q398 X Y p r),
  .prop (SelectiveSharedInputs.q399 X Y),
  .rat (SelectiveSharedInputs.q400 X),
  .rat (SelectiveSharedInputs.q401 Y),
  .rat (SelectiveSharedInputs.q402 X Y)]

noncomputable def valuesRLLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .rat (SelectiveSharedInputs.q403 X Y p r),
  .prop (SelectiveSharedInputs.q404 X Y p r),
  .prop (SelectiveSharedInputs.q405 X Y p r),
  .prop (SelectiveSharedInputs.q406 X Y p r),
  .prop (SelectiveSharedInputs.q407 X Y p r),
  .prop (SelectiveSharedInputs.q408 X),
  .prop (SelectiveSharedInputs.q409 Y),
  .prop (SelectiveSharedInputs.q410 Y),
  .prop (SelectiveSharedInputs.q411 X Y),
  .prop (SelectiveSharedInputs.q412 X Y),
  .rat (SelectiveSharedInputs.q413 X Y),
  .prop (SelectiveSharedInputs.q414 X Y),
  .prop (SelectiveSharedInputs.q415 X Y),
  .rat (SelectiveSharedInputs.q416 X Y),
  .prop (SelectiveSharedInputs.q417 X Y),
  .rat (SelectiveSharedInputs.q418 X Y),
  .rat (SelectiveSharedInputs.q419 X Y),
  .prop (SelectiveSharedInputs.q420 X Y p r),
  .rat (SelectiveSharedInputs.q421 X Y p r),
  .prop (SelectiveSharedInputs.q422 X Y p r),
  .prop (SelectiveSharedInputs.q423 X Y p r),
  .prop (SelectiveSharedInputs.q424 X Y),
  .rat (SelectiveSharedInputs.q425 X),
  .rat (SelectiveSharedInputs.q426 Y)]

noncomputable def valuesRLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 23 (valuesRLLL X Y p r) (valuesRLLR X Y p r)

noncomputable def valuesRLRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .rat (SelectiveSharedInputs.q427 X Y),
  .rat (SelectiveSharedInputs.q428 X Y p r),
  .prop (SelectiveSharedInputs.q429 X Y p r),
  .prop (SelectiveSharedInputs.q430 X Y p r),
  .prop (SelectiveSharedInputs.q431 X Y p r),
  .prop (SelectiveSharedInputs.q432 X Y p r),
  .prop (SelectiveSharedInputs.q433 X Y),
  .prop (SelectiveSharedInputs.q434 X Y),
  .prop (SelectiveSharedInputs.q435 X Y),
  .rat (SelectiveSharedInputs.q436 X Y),
  .prop (SelectiveSharedInputs.q437 X Y),
  .prop (SelectiveSharedInputs.q438 X Y),
  .rat (SelectiveSharedInputs.q439 X Y),
  .prop (SelectiveSharedInputs.q440 X Y),
  .rat (SelectiveSharedInputs.q441 X Y),
  .rat (SelectiveSharedInputs.q442 X Y),
  .prop (SelectiveSharedInputs.q443 X Y p r),
  .rat (SelectiveSharedInputs.q444 X Y p r),
  .prop (SelectiveSharedInputs.q445 X Y p r),
  .prop (SelectiveSharedInputs.q446 X Y p r),
  .prop (SelectiveSharedInputs.q447 X Y),
  .rat (SelectiveSharedInputs.q448 X),
  .rat (SelectiveSharedInputs.q449 Y),
  .rat (SelectiveSharedInputs.q450 X Y)]

noncomputable def valuesRLRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .rat (SelectiveSharedInputs.q451 X Y p r),
  .prop (SelectiveSharedInputs.q452 X Y p r),
  .prop (SelectiveSharedInputs.q453 X Y p r),
  .prop (SelectiveSharedInputs.q454 X Y p r),
  .prop (SelectiveSharedInputs.q455 X Y p r),
  .prop (SelectiveSharedInputs.q456 X Y),
  .prop (SelectiveSharedInputs.q457 X Y),
  .prop (SelectiveSharedInputs.q458 X Y),
  .rat (SelectiveSharedInputs.q459 X Y),
  .prop (SelectiveSharedInputs.q460 X Y),
  .prop (SelectiveSharedInputs.q461 X Y),
  .rat (SelectiveSharedInputs.q462 X Y),
  .prop (SelectiveSharedInputs.q463 X Y),
  .rat (SelectiveSharedInputs.q464 X Y),
  .rat (SelectiveSharedInputs.q465 X Y),
  .prop (SelectiveSharedInputs.q466 X Y p r),
  .rat (SelectiveSharedInputs.q467 X Y p r),
  .prop (SelectiveSharedInputs.q468 X Y p r),
  .prop (SelectiveSharedInputs.q469 X Y p r),
  .prop (SelectiveSharedInputs.q470 X Y),
  .rat (SelectiveSharedInputs.q471 X),
  .rat (SelectiveSharedInputs.q472 Y),
  .rat (SelectiveSharedInputs.q473 X Y),
  .rat (SelectiveSharedInputs.q474 X Y p r)]

noncomputable def valuesRLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 24 (valuesRLRL X Y p r) (valuesRLRR X Y p r)

noncomputable def valuesRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 47 (valuesRLL X Y p r) (valuesRLR X Y p r)

noncomputable def valuesRRLL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q475 X Y p r),
  .prop (SelectiveSharedInputs.q476 X Y p r),
  .prop (SelectiveSharedInputs.q477 X Y p r),
  .prop (ClosureOriginalInputs0.input_47 X Y p r),
  .prop (ClosureOriginalInputs0.input_48 X Y p r),
  .prop (ClosureOriginalInputs0.input_0 X Y p r),
  .prop (ClosureOriginalInputs0.input_3 X Y p r),
  .prop (ClosureOriginalInputs0.input_1 X Y p r),
  .prop (ClosureOriginalInputs0.input_58 X Y p r),
  .prop (ClosureOriginalInputs0.input_53 X Y p r),
  .prop (ClosureOriginalInputs0.input_54 X Y p r),
  .prop (ClosureOriginalInputs0.input_52 X Y p r),
  .prop (ClosureOriginalInputs0.input_2 X Y p r),
  .prop (ClosureOriginalInputs0.input_55 X Y p r),
  .prop (ClosureOriginalInputs0.input_56 X Y p r),
  .prop (ClosureOriginalInputs0.input_57 X Y p r),
  .prop (ClosureOriginalInputs0.input_36 X Y p r),
  .prop (ClosureOriginalInputs0.input_34 X Y p r),
  .prop (ClosureOriginalInputs0.input_35 X Y p r),
  .prop (ClosureOriginalInputs0.input_39 X Y p r),
  .prop (ClosureOriginalInputs0.input_27 X Y p r),
  .prop (ClosureOriginalInputs0.input_37 X Y p r),
  .prop (ClosureOriginalInputs0.input_38 X Y p r)]

noncomputable def valuesRRLR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (ClosureOriginalInputs0.input_23 X Y p r),
  .prop (ClosureOriginalInputs0.input_22 X Y p r),
  .prop (ClosureOriginalInputs0.input_24 X Y p r),
  .prop (ClosureOriginalInputs0.input_46 X Y p r),
  .prop (ClosureOriginalInputs0.input_42 X Y p r),
  .prop (ClosureOriginalInputs0.input_49 X Y p r),
  .prop (ClosureOriginalInputs0.input_50 X Y p r),
  .prop (ClosureOriginalInputs0.input_51 X Y p r),
  .prop (ClosureOriginalInputs0.input_41 X Y p r),
  .prop (ClosureOriginalInputs0.input_40 X Y p r),
  .prop (ClosureOriginalInputs0.input_15 X Y p r),
  .prop (ClosureOriginalInputs0.input_26 X Y p r),
  .prop (ClosureOriginalInputs0.input_25 X Y p r),
  .prop (ClosureOriginalInputs0.input_29 X Y p r),
  .prop (ClosureOriginalInputs0.input_30 X Y p r),
  .prop (ClosureOriginalInputs0.input_28 X Y p r),
  .rat (SelectiveSharedInputs.q515 X Y),
  .prop (SelectiveSharedInputs.q516 X Y p r),
  .rat (SelectiveSharedInputs.q517 X Y p r),
  .prop (SelectiveSharedInputs.q518 X Y p r),
  .prop (SelectiveSharedInputs.q519 X Y p r),
  .rat (SelectiveSharedInputs.q520 X Y),
  .rat (SelectiveSharedInputs.q521 X Y p r),
  .prop (SelectiveSharedInputs.q522 X Y p r)]

noncomputable def valuesRRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 23 (valuesRRLL X Y p r) (valuesRRLR X Y p r)

noncomputable def valuesRRRL (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (SelectiveSharedInputs.q523 X Y p r),
  .prop (SelectiveSharedInputs.q524 X Y p r),
  .prop (SelectiveSharedInputs.q525 X Y p r),
  .prop (SelectiveSharedInputs.q526 X Y),
  .rat (SelectiveSharedInputs.q527 X Y),
  .prop (SelectiveSharedInputs.q528 X Y p r),
  .rat (SelectiveSharedInputs.q529 X Y p r),
  .prop (SelectiveSharedInputs.q530 X Y p r),
  .prop (SelectiveSharedInputs.q531 X Y p r),
  .rat (SelectiveSharedInputs.q532 X Y),
  .rat (SelectiveSharedInputs.q533 X Y p r),
  .prop (SelectiveSharedInputs.q534 X Y p r),
  .prop (SelectiveSharedInputs.q535 X Y p r),
  .prop (SelectiveSharedInputs.q536 X Y p r),
  .prop (ClosureOriginalInputs1.input_54 X Y p r),
  .prop (ClosureOriginalInputs1.input_52 X Y p r),
  .prop (ClosureOriginalInputs1.input_53 X Y p r),
  .prop (ClosureOriginalInputs1.input_3 X Y p r),
  .prop (ClosureOriginalInputs1.input_1 X Y p r),
  .prop (ClosureOriginalInputs1.input_0 X Y p r),
  .prop (ClosureOriginalInputs1.input_58 X Y p r),
  .prop (ClosureOriginalInputs1.input_2 X Y p r),
  .prop (ClosureOriginalInputs1.input_49 X Y p r),
  .prop (ClosureOriginalInputs1.input_50 X Y p r)]

noncomputable def valuesRRRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue := .leaf #[
  .prop (ClosureOriginalInputs1.input_40 X Y p r),
  .prop (ClosureOriginalInputs1.input_41 X Y p r),
  .prop (ClosureOriginalInputs1.input_42 X Y p r),
  .prop (ClosureOriginalInputs1.input_51 X Y p r),
  .prop (ClosureOriginalInputs1.input_55 X Y p r),
  .prop (ClosureOriginalInputs1.input_56 X Y p r),
  .prop (ClosureOriginalInputs1.input_57 X Y p r),
  .prop (ClosureOriginalInputs1.input_46 X Y p r),
  .prop (ClosureOriginalInputs1.input_47 X Y p r),
  .prop (ClosureOriginalInputs1.input_48 X Y p r),
  .prop (ClosureOriginalInputs1.input_37 X Y p r),
  .prop (ClosureOriginalInputs1.input_38 X Y p r),
  .prop (ClosureOriginalInputs1.input_39 X Y p r),
  .prop (ClosureOriginalInputs1.input_36 X Y p r),
  .prop (ClosureOriginalInputs1.input_34 X Y p r),
  .prop (ClosureOriginalInputs1.input_35 X Y p r),
  .prop (ClosureOriginalInputs1.input_26 X Y p r),
  .prop (ClosureOriginalInputs1.input_25 X Y p r),
  .prop (ClosureOriginalInputs1.input_30 X Y p r),
  .prop (ClosureOriginalInputs1.input_29 X Y p r),
  .prop (ClosureOriginalInputs1.input_28 X Y p r),
  .prop (ClosureOriginalInputs1.input_27 X Y p r),
  .prop (ClosureOriginalInputs1.input_14 X Y p r),
  .prop (ClosureOriginalInputs1.input_15 X Y p r)]

noncomputable def valuesRRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 24 (valuesRRRL X Y p r) (valuesRRRR X Y p r)

noncomputable def valuesRR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 47 (valuesRRL X Y p r) (valuesRRR X Y p r)

noncomputable def valuesR (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 95 (valuesRL X Y p r) (valuesRR X Y p r)

noncomputable def values (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : Table SValue :=
  .branch 0xbe (valuesL X Y p r) (valuesR X Y p r)

def indices0LLLL : Table Nat := .leaf #[
  0x0,
  0x125123,
  0x12412a000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LLLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LLL : Table Nat :=
  .branch 31 (indices0LLLL) (indices0LLLR)

def indices0LLRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LLRR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x1000000000,
  0x0,
  0x2000000000,
  0x3000,
  0x0,
  0x0,
  0x0,
  0x4,
  0x5000000,
  0x6,
  0x0,
  0x7000000000]

def indices0LLR : Table Nat :=
  .branch 31 (indices0LLRL) (indices0LLRR)

def indices0LL : Table Nat :=
  .branch 63 (indices0LLL) (indices0LLR)

def indices0LRLL : Table Nat := .leaf #[
  0x0,
  0x9000008,
  0xa000000000,
  0xd00000c00b,
  0x1000f00000e,
  0x0,
  0x12011000000,
  0x13f,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0LRLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x13,
  0x15000014,
  0x0,
  0x16000]

def indices0LRL : Table Nat :=
  .branch 31 (indices0LRLL) (indices0LRLR)

def indices0LRRL : Table Nat := .leaf #[
  0x0,
  0x19018017,
  0x1c00001b01a,
  0x1d,
  0x1e,
  0x1f000000000,
  0x20,
  0x22021000,
  0x23000,
  0x24000000000,
  0x25000,
  0x0,
  0x0,
  0x26,
  0x27000000,
  0x28000000000,
  0x13602a000029,
  0x13502b000000,
  0x137000000,
  0x0,
  0x2c,
  0x0,
  0x2e00002d,
  0x0,
  0x2f000,
  0x0,
  0x32031030,
  0x35000034033,
  0x36,
  0x37,
  0x38000000000,
  0x39]

def indices0LRRR : Table Nat := .leaf #[
  0x3b03a000,
  0x3c000,
  0x3d000000000,
  0x3e000,
  0x0,
  0x0,
  0x3f,
  0x40000000,
  0x41000000000,
  0x141043000042,
  0x140044000000,
  0x132000000,
  0x0,
  0x45,
  0x47000046,
  0x0,
  0x48000,
  0x0,
  0x4b04a049,
  0x4e00004d04c,
  0x4f,
  0x50,
  0x51000000000,
  0x52,
  0x54053000,
  0x55000,
  0x56000000000,
  0x57000,
  0x0,
  0x0,
  0x58,
  0x59000000]

def indices0LRR : Table Nat :=
  .branch 32 (indices0LRRL) (indices0LRRR)

def indices0LR : Table Nat :=
  .branch 63 (indices0LRL) (indices0LRR)

def indices0L : Table Nat :=
  .branch 0x7e (indices0LL) (indices0LR)

def indices0RLLL : Table Nat := .leaf #[
  0x5a000000000,
  0x14405c00005b,
  0x14205d000000,
  0x143000000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0RLLR : Table Nat := .leaf #[
  0x0,
  0x5e000,
  0x6000005f000,
  0x0,
  0x61000000,
  0x0,
  0x64063062000,
  0x66065000,
  0x68067,
  0x69000,
  0x0,
  0x6b06a,
  0x6d06c000000,
  0x6e000000,
  0x0,
  0x7000006f,
  0x0,
  0x0,
  0x71000,
  0x72000000000,
  0x0,
  0x75000074073,
  0x7600000012f,
  0x12e000000130,
  0x0,
  0x77000,
  0x79000078000,
  0x0,
  0x7a000000,
  0x0,
  0x7d07c07b000,
  0x7f07e000]

def indices0RLL : Table Nat :=
  .branch 31 (indices0RLLL) (indices0RLLR)

def indices0RLRL : Table Nat := .leaf #[
  0x81080,
  0x82000,
  0x0,
  0x84083,
  0x86085000000,
  0x87000000,
  0x0,
  0x89000088,
  0x0,
  0x0,
  0x8a000,
  0x8b000000000,
  0x0,
  0x8e00008d08c,
  0x8f000000133,
  0x131000000134,
  0x0,
  0x90000,
  0x0,
  0x92000091000,
  0x0,
  0x93000000,
  0x0,
  0x96095094000,
  0x98097000,
  0x9a099,
  0x9b000,
  0x0,
  0x9d09c,
  0x9f09e000000,
  0xa0000000,
  0x0]

def indices0RLRR : Table Nat := .leaf #[
  0xa20000a1,
  0x0,
  0x0,
  0xa3000,
  0xa4000000000,
  0x0,
  0xa70000a60a5,
  0xa800000013e,
  0x13900000013d,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices0RLR : Table Nat :=
  .branch 32 (indices0RLRL) (indices0RLRR)

def indices0RL : Table Nat :=
  .branch 63 (indices0RLL) (indices0RLR)

def indices0RRLL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0xa9000000,
  0x0,
  0xab0000aa000,
  0x0,
  0xac000000,
  0x0,
  0xaf0ae0ad000,
  0xb10b0000,
  0xb30b2,
  0xb4000,
  0x0,
  0xb60b5,
  0xb80b7000000,
  0xb9000000,
  0x0,
  0xbb0000ba,
  0x0,
  0x0,
  0xbc000,
  0xbd000000000,
  0x0,
  0xc00000bf0be,
  0xc1000000138,
  0x122000000121,
  0x0,
  0xc2,
  0xc40000c3]

def indices0RRLR : Table Nat := .leaf #[
  0x0,
  0xc5000,
  0x0,
  0xc80c70c6,
  0xcb0000ca0c9,
  0xcc,
  0xcd,
  0xce000000000,
  0xcf,
  0xd10d0000,
  0xd2000,
  0xd3000000000,
  0xd4000,
  0x0,
  0x0,
  0xd5,
  0xd6000000,
  0xd7000000000,
  0x13a0d90000d8,
  0x13b0da000000,
  0x13c000000,
  0x0,
  0xdb000,
  0xdc000000000,
  0xdd000,
  0x0,
  0xde,
  0xdf000000000,
  0xe20000e10e0,
  0xe50e40000e3,
  0xe6000000000,
  0x0]

def indices0RRL : Table Nat :=
  .branch 31 (indices0RRLL) (indices0RRLR)

def indices0RRRL : Table Nat := .leaf #[
  0x0,
  0xe80e7000000,
  0x0,
  0xea0e9,
  0xeb,
  0xec000000,
  0xed,
  0x0,
  0xee000000000,
  0x0,
  0xef000,
  0x0,
  0xf20000f10f0,
  0xf3000000129,
  0x128000000127,
  0x0,
  0x0,
  0x0,
  0xf4000000,
  0x0,
  0xf5,
  0xf6000000000,
  0xf90000f80f7,
  0xfc0fb0000fa,
  0xfd000000000,
  0x0,
  0xff0fe000000,
  0x0,
  0x101100,
  0x102,
  0x103000000,
  0x104]

def indices0RRRR : Table Nat := .leaf #[
  0x0,
  0x105000000000,
  0x0,
  0x106000,
  0x108107000000,
  0x12b109000,
  0x12c10a000,
  0x12d000,
  0x0,
  0x0,
  0x0,
  0x10b,
  0x10c000000,
  0x0,
  0x10f10e10d,
  0x112000111110,
  0x113,
  0x114,
  0x0,
  0x115000000000,
  0x116,
  0x118117000,
  0x119000000,
  0x0,
  0x11b00011a,
  0x0,
  0x0,
  0x11c000,
  0x11d000000000,
  0x0,
  0x11f11e000000,
  0x126000120000]

def indices0RRR : Table Nat :=
  .branch 32 (indices0RRRL) (indices0RRRR)

def indices0RR : Table Nat :=
  .branch 63 (indices0RRL) (indices0RRR)

def indices0R : Table Nat :=
  .branch 0x7f (indices0RL) (indices0RR)

def indices0 : Table Nat :=
  .branch 0xfd (indices0L) (indices0R)

noncomputable def anchor0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Option SValue :=
  let j := indexAt indices0 i
  if j = 0 then none else some ((values X Y p r).get (.rat 0) (j-1))

def indices1LLLL : Table Nat := .leaf #[
  0x0,
  0x15f160,
  0x15e162000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LLLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LLL : Table Nat :=
  .branch 31 (indices1LLLL) (indices1LLLR)

def indices1LLRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LLRR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x17b000000000,
  0x0,
  0x1000000,
  0x0,
  0x2000000,
  0x3,
  0x0,
  0x0,
  0x4000000000,
  0x0,
  0x6000005000,
  0x0,
  0x0,
  0x7000000]

def indices1LLR : Table Nat :=
  .branch 31 (indices1LLRL) (indices1LLRR)

def indices1LL : Table Nat :=
  .branch 63 (indices1LLL) (indices1LLR)

def indices1LRLL : Table Nat := .leaf #[
  0x8000000000,
  0x9000,
  0xb00a000000,
  0xe00d00000c,
  0x1000f000,
  0x0,
  0x17c012011000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LRLR : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1LRL : Table Nat :=
  .branch 31 (indices1LRLL) (indices1LRLR)

def indices1LRRL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x2c,
  0x0,
  0x2e00002d,
  0x0,
  0x2f000,
  0x0,
  0x32031030,
  0x35000034033,
  0x36,
  0x37,
  0x38000000000,
  0x39]

def indices1LRRR : Table Nat := .leaf #[
  0x3b03a000,
  0x3c000,
  0x3d000000000,
  0x3e000,
  0x0,
  0x0,
  0x3f,
  0x40000000,
  0x41000000000,
  0x176043000042,
  0x175044000000,
  0x17a000000,
  0x0,
  0x45,
  0x47000046,
  0x0,
  0x48000,
  0x0,
  0x4b04a049,
  0x4e00004d04c,
  0x4f,
  0x50,
  0x51000000000,
  0x52,
  0x54053000,
  0x55000,
  0x56000000000,
  0x57000,
  0x0,
  0x0,
  0x58,
  0x59000000]

def indices1LRR : Table Nat :=
  .branch 32 (indices1LRRL) (indices1LRRR)

def indices1LR : Table Nat :=
  .branch 63 (indices1LRL) (indices1LRR)

def indices1L : Table Nat :=
  .branch 0x7e (indices1LL) (indices1LR)

def indices1RLLL : Table Nat := .leaf #[
  0x5a000000000,
  0x17905c00005b,
  0x17805d000000,
  0x177000000,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1RLLR : Table Nat := .leaf #[
  0x0,
  0x5e000,
  0x6000005f000,
  0x0,
  0x61000000,
  0x0,
  0x64063062000,
  0x66065000,
  0x68067,
  0x69000,
  0x0,
  0x6b06a,
  0x6d06c000000,
  0x6e000000,
  0x0,
  0x7000006f,
  0x0,
  0x0,
  0x71000,
  0x72000000000,
  0x0,
  0x75000074073,
  0x76000000173,
  0x172000000174,
  0x0,
  0x77000,
  0x79000078000,
  0x0,
  0x7a000000,
  0x0,
  0x7d07c07b000,
  0x7f07e000]

def indices1RLL : Table Nat :=
  .branch 31 (indices1RLLL) (indices1RLLR)

def indices1RLRL : Table Nat := .leaf #[
  0x81080,
  0x82000,
  0x0,
  0x84083,
  0x86085000000,
  0x87000000,
  0x0,
  0x89000088,
  0x0,
  0x0,
  0x8a000,
  0x8b000000000,
  0x0,
  0x8e00008d08c,
  0x8f00000016f,
  0x171000000170,
  0x0,
  0x90000,
  0x0,
  0x92000091000,
  0x0,
  0x93000000,
  0x0,
  0x96095094000,
  0x98097000,
  0x9a099,
  0x9b000,
  0x0,
  0x9d09c,
  0x9f09e000000,
  0xa0000000,
  0x0]

def indices1RLRR : Table Nat := .leaf #[
  0xa20000a1,
  0x0,
  0x0,
  0xa3000,
  0xa4000000000,
  0x0,
  0xa70000a60a5,
  0xa8000000165,
  0x167000000166,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0]

def indices1RLR : Table Nat :=
  .branch 32 (indices1RLRL) (indices1RLRR)

def indices1RL : Table Nat :=
  .branch 63 (indices1RLL) (indices1RLR)

def indices1RRLL : Table Nat := .leaf #[
  0x0,
  0x0,
  0x0,
  0x0,
  0xa9000000,
  0x0,
  0xab0000aa000,
  0x0,
  0xac000000,
  0x0,
  0xaf0ae0ad000,
  0xb10b0000,
  0xb30b2,
  0xb4000,
  0x0,
  0xb60b5,
  0xb80b7000000,
  0xb9000000,
  0x0,
  0xbb0000ba,
  0x0,
  0x0,
  0xbc000,
  0xbd000000000,
  0x0,
  0xc00000bf0be,
  0xc100000016c,
  0x16e00000016d,
  0x0,
  0xc2,
  0xc40000c3]

def indices1RRLR : Table Nat := .leaf #[
  0x0,
  0xc5000,
  0x0,
  0xc80c70c6,
  0xcb0000ca0c9,
  0xcc,
  0xcd,
  0xce000000000,
  0xcf,
  0xd10d0000,
  0xd2000,
  0xd3000000000,
  0xd4000,
  0x0,
  0x0,
  0xd5,
  0xd6000000,
  0xd7000000000,
  0x1630d90000d8,
  0x1640da000000,
  0x168000000,
  0x0,
  0xdb000,
  0xdc000000000,
  0xdd000,
  0x0,
  0xde,
  0xdf000000000,
  0xe20000e10e0,
  0xe50e40000e3,
  0x145000000000,
  0x0]

def indices1RRL : Table Nat :=
  .branch 31 (indices1RRLL) (indices1RRLR)

def indices1RRRL : Table Nat := .leaf #[
  0x0,
  0x147146000000,
  0x0,
  0x149148,
  0xeb,
  0xec000000,
  0xed,
  0x0,
  0x14a000000000,
  0x0,
  0x14b000,
  0x0,
  0x14e00014d14c,
  0x14f00000015c,
  0x15b00000015d,
  0x0,
  0x0,
  0x0,
  0xf4000000,
  0x0,
  0xf5,
  0xf6000000000,
  0xf90000f80f7,
  0xfc0fb0000fa,
  0xfd000000000,
  0x0,
  0xff0fe000000,
  0x0,
  0x101100,
  0x102,
  0x103000000,
  0x104]

def indices1RRRR : Table Nat := .leaf #[
  0x0,
  0x105000000000,
  0x0,
  0x106000,
  0x108107000000,
  0x169109000,
  0x16a10a000,
  0x16b000,
  0x0,
  0x0,
  0x0,
  0x150,
  0x10c000000,
  0x0,
  0x10f10e10d,
  0x112000111110,
  0x113,
  0x151,
  0x0,
  0x152000000000,
  0x153,
  0x155154000,
  0x119000000,
  0x0,
  0x11b00011a,
  0x0,
  0x0,
  0x156000,
  0x157000000000,
  0x0,
  0x159158000000,
  0x16100015a000]

def indices1RRR : Table Nat :=
  .branch 32 (indices1RRRL) (indices1RRRR)

def indices1RR : Table Nat :=
  .branch 63 (indices1RRL) (indices1RRR)

def indices1R : Table Nat :=
  .branch 0x7f (indices1RL) (indices1RR)

def indices1 : Table Nat :=
  .branch 0xfd (indices1L) (indices1R)

noncomputable def anchor1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Option SValue :=
  let j := indexAt indices1 i
  if j = 0 then none else some ((values X Y p r).get (.rat 0) (j-1))

end ClosureAnchorData

end PolicySubmissionPart81

/- Component ClosureSharedAnchorFuelSemanticsExplicit; SHA256 4e610f6358c6937b5792f6477085cf33d40cb26640eb3b86cbbfd42a5df4649e. -/
section PolicySubmissionPart82
/- Experimental fuel-recursive anchor route; shared root semantics use fuel 11.
All auxiliary proof declarations are synchronous proof-valued definitions. -/
namespace ClosureSharedAnchorFuelSemantics
open ClosureAnchorSemantics

noncomputable def env (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (j : Nat) : SValue :=
  (ClosureAnchorData.values X Y p r).get (.rat 0) j

def Good (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (j : Nat) : Prop :=
  env X Y p r j = ClosureAnchorFuelPatternCheck.eval (sInput X Y p r) (env X Y p r) 11 (ClosureSharedAnchorPatternData.patterns j)

def c0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c8 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c16 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (16+j.val) := by
  intro j
  fin_cases j <;> rfl

def c24 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (24+j.val) := by
  intro j
  fin_cases j <;> rfl

def c32 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (32+j.val) := by
  intro j
  fin_cases j <;> rfl

def c40 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (40+j.val) := by
  intro j
  fin_cases j <;> rfl

def c48 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (48+j.val) := by
  intro j
  fin_cases j <;> rfl

def c56 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (56+j.val) := by
  intro j
  fin_cases j <;> rfl

def c64 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (64+j.val) := by
  intro j
  fin_cases j <;> rfl

def c72 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (72+j.val) := by
  intro j
  fin_cases j <;> rfl

def c80 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (80+j.val) := by
  intro j
  fin_cases j <;> rfl

def c88 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (88+j.val) := by
  intro j
  fin_cases j <;> rfl

def c96 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (96+j.val) := by
  intro j
  fin_cases j <;> rfl

def c104 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x68+j.val) := by
  intro j
  fin_cases j <;> rfl

def c112 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x70+j.val) := by
  intro j
  fin_cases j <;> rfl

def c120 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x78+j.val) := by
  intro j
  fin_cases j <;> rfl

def c128 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x80+j.val) := by
  intro j
  fin_cases j <;> rfl

def c136 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x88+j.val) := by
  intro j
  fin_cases j <;> rfl

def c144 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x90+j.val) := by
  intro j
  fin_cases j <;> rfl

def c152 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x98+j.val) := by
  intro j
  fin_cases j <;> rfl

def c160 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xa0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c168 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xa8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c176 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xb0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c184 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xb8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c192 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xc0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c200 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xc8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c208 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xd0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c216 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xd8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c224 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xe0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c232 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xe8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c240 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xf0+j.val) := by
  intro j
  fin_cases j <;> rfl

def c248 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0xf8+j.val) := by
  intro j
  fin_cases j <;> rfl

def c256 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x100+j.val) := by
  intro j
  fin_cases j <;> rfl

def c264 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x108+j.val) := by
  intro j
  fin_cases j <;> rfl

def c272 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x110+j.val) := by
  intro j
  fin_cases j <;> rfl

def c280 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x118+j.val) := by
  intro j
  fin_cases j <;> rfl

def c288 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x120+j.val) := by
  intro j
  fin_cases j <;> rfl

def c296 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x128+j.val) := by
  intro j
  fin_cases j <;> rfl

def c304 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x130+j.val) := by
  intro j
  fin_cases j <;> rfl

def c312 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x138+j.val) := by
  intro j
  fin_cases j <;> rfl

def c320 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x140+j.val) := by
  intro j
  fin_cases j <;> rfl

def c328 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x148+j.val) := by
  intro j
  fin_cases j <;> rfl

def c336 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x150+j.val) := by
  intro j
  fin_cases j <;> rfl

def c344 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x158+j.val) := by
  intro j
  fin_cases j <;> rfl

def c352 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x160+j.val) := by
  intro j
  fin_cases j <;> rfl

def c360 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x168+j.val) := by
  intro j
  fin_cases j <;> rfl

def c368 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 8, Good X Y p r (0x170+j.val) := by
  intro j
  fin_cases j <;> rfl

def c376 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j : Fin 4, Good X Y p r (0x178+j.val) := by
  intro j
  fin_cases j <;> rfl

def checked (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ j < 0x17c, Good X Y p r j := by
  intro j hj
  exact (ClosurePrefixAdapter.interval_join 0 0xc0 0x17c
  (ClosurePrefixAdapter.interval_join 0 96 0xc0
  (ClosurePrefixAdapter.interval_join 0 48 96
  (ClosurePrefixAdapter.interval_join 0 24 48
  (ClosurePrefixAdapter.interval_join 0 8 24
  (ClosurePrefixAdapter.interval_from_fin 0 8 (c0 X Y p r))
  (ClosurePrefixAdapter.interval_join 8 16 24
  (ClosurePrefixAdapter.interval_from_fin 8 8 (c8 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 16 8 (c16 X Y p r))))
  (ClosurePrefixAdapter.interval_join 24 32 48
  (ClosurePrefixAdapter.interval_from_fin 24 8 (c24 X Y p r))
  (ClosurePrefixAdapter.interval_join 32 40 48
  (ClosurePrefixAdapter.interval_from_fin 32 8 (c32 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 40 8 (c40 X Y p r)))))
  (ClosurePrefixAdapter.interval_join 48 72 96
  (ClosurePrefixAdapter.interval_join 48 56 72
  (ClosurePrefixAdapter.interval_from_fin 48 8 (c48 X Y p r))
  (ClosurePrefixAdapter.interval_join 56 64 72
  (ClosurePrefixAdapter.interval_from_fin 56 8 (c56 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 64 8 (c64 X Y p r))))
  (ClosurePrefixAdapter.interval_join 72 80 96
  (ClosurePrefixAdapter.interval_from_fin 72 8 (c72 X Y p r))
  (ClosurePrefixAdapter.interval_join 80 88 96
  (ClosurePrefixAdapter.interval_from_fin 80 8 (c80 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 88 8 (c88 X Y p r))))))
  (ClosurePrefixAdapter.interval_join 96 0x90 0xc0
  (ClosurePrefixAdapter.interval_join 96 0x78 0x90
  (ClosurePrefixAdapter.interval_join 96 0x68 0x78
  (ClosurePrefixAdapter.interval_from_fin 96 8 (c96 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x68 0x70 0x78
  (ClosurePrefixAdapter.interval_from_fin 0x68 8 (c104 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x70 8 (c112 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0x78 0x80 0x90
  (ClosurePrefixAdapter.interval_from_fin 0x78 8 (c120 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x80 0x88 0x90
  (ClosurePrefixAdapter.interval_from_fin 0x80 8 (c128 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x88 8 (c136 X Y p r)))))
  (ClosurePrefixAdapter.interval_join 0x90 0xa8 0xc0
  (ClosurePrefixAdapter.interval_join 0x90 0x98 0xa8
  (ClosurePrefixAdapter.interval_from_fin 0x90 8 (c144 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x98 0xa0 0xa8
  (ClosurePrefixAdapter.interval_from_fin 0x98 8 (c152 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0xa0 8 (c160 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0xa8 0xb0 0xc0
  (ClosurePrefixAdapter.interval_from_fin 0xa8 8 (c168 X Y p r))
  (ClosurePrefixAdapter.interval_join 0xb0 0xb8 0xc0
  (ClosurePrefixAdapter.interval_from_fin 0xb0 8 (c176 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0xb8 8 (c184 X Y p r)))))))
  (ClosurePrefixAdapter.interval_join 0xc0 0x120 0x17c
  (ClosurePrefixAdapter.interval_join 0xc0 0xf0 0x120
  (ClosurePrefixAdapter.interval_join 0xc0 0xd8 0xf0
  (ClosurePrefixAdapter.interval_join 0xc0 0xc8 0xd8
  (ClosurePrefixAdapter.interval_from_fin 0xc0 8 (c192 X Y p r))
  (ClosurePrefixAdapter.interval_join 0xc8 0xd0 0xd8
  (ClosurePrefixAdapter.interval_from_fin 0xc8 8 (c200 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0xd0 8 (c208 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0xd8 0xe0 0xf0
  (ClosurePrefixAdapter.interval_from_fin 0xd8 8 (c216 X Y p r))
  (ClosurePrefixAdapter.interval_join 0xe0 0xe8 0xf0
  (ClosurePrefixAdapter.interval_from_fin 0xe0 8 (c224 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0xe8 8 (c232 X Y p r)))))
  (ClosurePrefixAdapter.interval_join 0xf0 0x108 0x120
  (ClosurePrefixAdapter.interval_join 0xf0 0xf8 0x108
  (ClosurePrefixAdapter.interval_from_fin 0xf0 8 (c240 X Y p r))
  (ClosurePrefixAdapter.interval_join 0xf8 0x100 0x108
  (ClosurePrefixAdapter.interval_from_fin 0xf8 8 (c248 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x100 8 (c256 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0x108 0x110 0x120
  (ClosurePrefixAdapter.interval_from_fin 0x108 8 (c264 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x110 0x118 0x120
  (ClosurePrefixAdapter.interval_from_fin 0x110 8 (c272 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x118 8 (c280 X Y p r))))))
  (ClosurePrefixAdapter.interval_join 0x120 0x150 0x17c
  (ClosurePrefixAdapter.interval_join 0x120 0x138 0x150
  (ClosurePrefixAdapter.interval_join 0x120 0x128 0x138
  (ClosurePrefixAdapter.interval_from_fin 0x120 8 (c288 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x128 0x130 0x138
  (ClosurePrefixAdapter.interval_from_fin 0x128 8 (c296 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x130 8 (c304 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0x138 0x140 0x150
  (ClosurePrefixAdapter.interval_from_fin 0x138 8 (c312 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x140 0x148 0x150
  (ClosurePrefixAdapter.interval_from_fin 0x140 8 (c320 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x148 8 (c328 X Y p r)))))
  (ClosurePrefixAdapter.interval_join 0x150 0x168 0x17c
  (ClosurePrefixAdapter.interval_join 0x150 0x158 0x168
  (ClosurePrefixAdapter.interval_from_fin 0x150 8 (c336 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x158 0x160 0x168
  (ClosurePrefixAdapter.interval_from_fin 0x158 8 (c344 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x160 8 (c352 X Y p r))))
  (ClosurePrefixAdapter.interval_join 0x168 0x170 0x17c
  (ClosurePrefixAdapter.interval_from_fin 0x168 8 (c360 X Y p r))
  (ClosurePrefixAdapter.interval_join 0x170 0x178 0x17c
  (ClosurePrefixAdapter.interval_from_fin 0x170 8 (c368 X Y p r))
  (ClosurePrefixAdapter.interval_from_fin 0x178 4 (c376 X Y p r)))))))) j (Nat.zero_le j) hj

end ClosureSharedAnchorFuelSemantics

end PolicySubmissionPart82

/- Component ClosureSharedAnchorFuelChecks0Explicit; SHA256 cc0cfa5e4a88959f52f02d79fc597d3fd1480986cd7bdc1bdb72c3502f5469c1. -/
section PolicySubmissionPart83
/- Experimental fuel-recursive anchor route; shared root semantics use fuel 11.
All auxiliary proof declarations are synchronous proof-valued definitions. -/
namespace ClosureSharedAnchorFuelChecks0
open ClosureAnchorSemantics

def Good (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Prop :=
  ∀ a, ClosureAnchorData.anchor0 X Y p r i = some a →
    a = anchorBody ClosurePrefixAdapterData.program0 (sInput X Y p r) (ClosureAnchorData.anchor0 X Y p r) i

abbrev NumericallyGood (i : Nat) : Prop :=
  ClosureAnchorFuelPatternCheck.checkAnchor (ClosureSemantics.boundedProgram ClosurePrefixAdapterData.program0)
    (ClosureAnchorData.indexAt ClosureAnchorData.indices0) ClosureSharedAnchorPatternData.patterns 0x17c 10 i = true

def c0 : ∀ i : Fin 32, NumericallyGood (0+i.val) := by
  decide +kernel

def c32 : ∀ i : Fin 32, NumericallyGood (32+i.val) := by
  decide +kernel

def c64 : ∀ i : Fin 32, NumericallyGood (64+i.val) := by
  decide +kernel

def c96 : ∀ i : Fin 32, NumericallyGood (96+i.val) := by
  decide +kernel

def c128 : ∀ i : Fin 32, NumericallyGood (0x80+i.val) := by
  decide +kernel

def c160 : ∀ i : Fin 32, NumericallyGood (0xa0+i.val) := by
  decide +kernel

def c192 : ∀ i : Fin 32, NumericallyGood (0xc0+i.val) := by
  decide +kernel

def c224 : ∀ i : Fin 32, NumericallyGood (0xe0+i.val) := by
  decide +kernel

def c256 : ∀ i : Fin 32, NumericallyGood (0x100+i.val) := by
  decide +kernel

def c288 : ∀ i : Fin 32, NumericallyGood (0x120+i.val) := by
  decide +kernel

def c320 : ∀ i : Fin 32, NumericallyGood (0x140+i.val) := by
  decide +kernel

def c352 : ∀ i : Fin 32, NumericallyGood (0x160+i.val) := by
  decide +kernel

def c384 : ∀ i : Fin 32, NumericallyGood (0x180+i.val) := by
  decide +kernel

def c416 : ∀ i : Fin 32, NumericallyGood (0x1a0+i.val) := by
  decide +kernel

def c448 : ∀ i : Fin 32, NumericallyGood (0x1c0+i.val) := by
  decide +kernel

def c480 : ∀ i : Fin 32, NumericallyGood (0x1e0+i.val) := by
  decide +kernel

def c512 : ∀ i : Fin 32, NumericallyGood (0x200+i.val) := by
  decide +kernel

def c544 : ∀ i : Fin 32, NumericallyGood (0x220+i.val) := by
  decide +kernel

def c576 : ∀ i : Fin 32, NumericallyGood (0x240+i.val) := by
  decide +kernel

def c608 : ∀ i : Fin 32, NumericallyGood (0x260+i.val) := by
  decide +kernel

def c640 : ∀ i : Fin 32, NumericallyGood (0x280+i.val) := by
  decide +kernel

def c672 : ∀ i : Fin 32, NumericallyGood (0x2a0+i.val) := by
  decide +kernel

def c704 : ∀ i : Fin 32, NumericallyGood (0x2c0+i.val) := by
  decide +kernel

def c736 : ∀ i : Fin 32, NumericallyGood (0x2e0+i.val) := by
  decide +kernel

def c768 : ∀ i : Fin 32, NumericallyGood (0x300+i.val) := by
  decide +kernel

def c800 : ∀ i : Fin 32, NumericallyGood (0x320+i.val) := by
  decide +kernel

def c832 : ∀ i : Fin 32, NumericallyGood (0x340+i.val) := by
  decide +kernel

def c864 : ∀ i : Fin 32, NumericallyGood (0x360+i.val) := by
  decide +kernel

def c896 : ∀ i : Fin 32, NumericallyGood (0x380+i.val) := by
  decide +kernel

def c928 : ∀ i : Fin 32, NumericallyGood (0x3a0+i.val) := by
  decide +kernel

def c960 : ∀ i : Fin 32, NumericallyGood (0x3c0+i.val) := by
  decide +kernel

def c992 : ∀ i : Fin 32, NumericallyGood (0x3e0+i.val) := by
  decide +kernel

def c1024 : ∀ i : Fin 32, NumericallyGood (0x400+i.val) := by
  decide +kernel

def c1056 : ∀ i : Fin 32, NumericallyGood (0x420+i.val) := by
  decide +kernel

def c1088 : ∀ i : Fin 32, NumericallyGood (0x440+i.val) := by
  decide +kernel

def c1120 : ∀ i : Fin 32, NumericallyGood (0x460+i.val) := by
  decide +kernel

def c1152 : ∀ i : Fin 32, NumericallyGood (0x480+i.val) := by
  decide +kernel

def c1184 : ∀ i : Fin 32, NumericallyGood (0x4a0+i.val) := by
  decide +kernel

def c1216 : ∀ i : Fin 32, NumericallyGood (0x4c0+i.val) := by
  decide +kernel

def c1248 : ∀ i : Fin 32, NumericallyGood (0x4e0+i.val) := by
  decide +kernel

def c1280 : ∀ i : Fin 32, NumericallyGood (0x500+i.val) := by
  decide +kernel

def c1312 : ∀ i : Fin 32, NumericallyGood (0x520+i.val) := by
  decide +kernel

def c1344 : ∀ i : Fin 32, NumericallyGood (0x540+i.val) := by
  decide +kernel

def c1376 : ∀ i : Fin 32, NumericallyGood (0x560+i.val) := by
  decide +kernel

def c1408 : ∀ i : Fin 32, NumericallyGood (0x580+i.val) := by
  decide +kernel

def c1440 : ∀ i : Fin 32, NumericallyGood (0x5a0+i.val) := by
  decide +kernel

def c1472 : ∀ i : Fin 32, NumericallyGood (0x5c0+i.val) := by
  decide +kernel

def c1504 : ∀ i : Fin 32, NumericallyGood (0x5e0+i.val) := by
  decide +kernel

def c1536 : ∀ i : Fin 32, NumericallyGood (0x600+i.val) := by
  decide +kernel

def c1568 : ∀ i : Fin 32, NumericallyGood (0x620+i.val) := by
  decide +kernel

def c1600 : ∀ i : Fin 32, NumericallyGood (0x640+i.val) := by
  decide +kernel

def c1632 : ∀ i : Fin 32, NumericallyGood (0x660+i.val) := by
  decide +kernel

def c1664 : ∀ i : Fin 32, NumericallyGood (0x680+i.val) := by
  decide +kernel

def c1696 : ∀ i : Fin 32, NumericallyGood (0x6a0+i.val) := by
  decide +kernel

def c1728 : ∀ i : Fin 32, NumericallyGood (0x6c0+i.val) := by
  decide +kernel

def c1760 : ∀ i : Fin 32, NumericallyGood (0x6e0+i.val) := by
  decide +kernel

def c1792 : ∀ i : Fin 32, NumericallyGood (0x700+i.val) := by
  decide +kernel

def c1824 : ∀ i : Fin 32, NumericallyGood (0x720+i.val) := by
  decide +kernel

def c1856 : ∀ i : Fin 32, NumericallyGood (0x740+i.val) := by
  decide +kernel

def c1888 : ∀ i : Fin 32, NumericallyGood (0x760+i.val) := by
  decide +kernel

def c1920 : ∀ i : Fin 32, NumericallyGood (0x780+i.val) := by
  decide +kernel

def c1952 : ∀ i : Fin 32, NumericallyGood (0x7a0+i.val) := by
  decide +kernel

def c1984 : ∀ i : Fin 32, NumericallyGood (0x7c0+i.val) := by
  decide +kernel

def c2016 : ∀ i : Fin 12, NumericallyGood (0x7e0+i.val) := by
  decide +kernel

def numeric_checked : ∀ i < 0x7ec, NumericallyGood i := by
  intro i hi
  exact (ClosurePrefixAdapter.interval_join 0 0x400 0x7ec
  (ClosurePrefixAdapter.interval_join 0 0x200 0x400
  (ClosurePrefixAdapter.interval_join 0 0x100 0x200
  (ClosurePrefixAdapter.interval_join 0 0x80 0x100
  (ClosurePrefixAdapter.interval_join 0 64 0x80
  (ClosurePrefixAdapter.interval_join 0 32 64
  (ClosurePrefixAdapter.interval_from_fin 0 32 (c0))
  (ClosurePrefixAdapter.interval_from_fin 32 32 (c32)))
  (ClosurePrefixAdapter.interval_join 64 96 0x80
  (ClosurePrefixAdapter.interval_from_fin 64 32 (c64))
  (ClosurePrefixAdapter.interval_from_fin 96 32 (c96))))
  (ClosurePrefixAdapter.interval_join 0x80 0xc0 0x100
  (ClosurePrefixAdapter.interval_join 0x80 0xa0 0xc0
  (ClosurePrefixAdapter.interval_from_fin 0x80 32 (c128))
  (ClosurePrefixAdapter.interval_from_fin 0xa0 32 (c160)))
  (ClosurePrefixAdapter.interval_join 0xc0 0xe0 0x100
  (ClosurePrefixAdapter.interval_from_fin 0xc0 32 (c192))
  (ClosurePrefixAdapter.interval_from_fin 0xe0 32 (c224)))))
  (ClosurePrefixAdapter.interval_join 0x100 0x180 0x200
  (ClosurePrefixAdapter.interval_join 0x100 0x140 0x180
  (ClosurePrefixAdapter.interval_join 0x100 0x120 0x140
  (ClosurePrefixAdapter.interval_from_fin 0x100 32 (c256))
  (ClosurePrefixAdapter.interval_from_fin 0x120 32 (c288)))
  (ClosurePrefixAdapter.interval_join 0x140 0x160 0x180
  (ClosurePrefixAdapter.interval_from_fin 0x140 32 (c320))
  (ClosurePrefixAdapter.interval_from_fin 0x160 32 (c352))))
  (ClosurePrefixAdapter.interval_join 0x180 0x1c0 0x200
  (ClosurePrefixAdapter.interval_join 0x180 0x1a0 0x1c0
  (ClosurePrefixAdapter.interval_from_fin 0x180 32 (c384))
  (ClosurePrefixAdapter.interval_from_fin 0x1a0 32 (c416)))
  (ClosurePrefixAdapter.interval_join 0x1c0 0x1e0 0x200
  (ClosurePrefixAdapter.interval_from_fin 0x1c0 32 (c448))
  (ClosurePrefixAdapter.interval_from_fin 0x1e0 32 (c480))))))
  (ClosurePrefixAdapter.interval_join 0x200 0x300 0x400
  (ClosurePrefixAdapter.interval_join 0x200 0x280 0x300
  (ClosurePrefixAdapter.interval_join 0x200 0x240 0x280
  (ClosurePrefixAdapter.interval_join 0x200 0x220 0x240
  (ClosurePrefixAdapter.interval_from_fin 0x200 32 (c512))
  (ClosurePrefixAdapter.interval_from_fin 0x220 32 (c544)))
  (ClosurePrefixAdapter.interval_join 0x240 0x260 0x280
  (ClosurePrefixAdapter.interval_from_fin 0x240 32 (c576))
  (ClosurePrefixAdapter.interval_from_fin 0x260 32 (c608))))
  (ClosurePrefixAdapter.interval_join 0x280 0x2c0 0x300
  (ClosurePrefixAdapter.interval_join 0x280 0x2a0 0x2c0
  (ClosurePrefixAdapter.interval_from_fin 0x280 32 (c640))
  (ClosurePrefixAdapter.interval_from_fin 0x2a0 32 (c672)))
  (ClosurePrefixAdapter.interval_join 0x2c0 0x2e0 0x300
  (ClosurePrefixAdapter.interval_from_fin 0x2c0 32 (c704))
  (ClosurePrefixAdapter.interval_from_fin 0x2e0 32 (c736)))))
  (ClosurePrefixAdapter.interval_join 0x300 0x380 0x400
  (ClosurePrefixAdapter.interval_join 0x300 0x340 0x380
  (ClosurePrefixAdapter.interval_join 0x300 0x320 0x340
  (ClosurePrefixAdapter.interval_from_fin 0x300 32 (c768))
  (ClosurePrefixAdapter.interval_from_fin 0x320 32 (c800)))
  (ClosurePrefixAdapter.interval_join 0x340 0x360 0x380
  (ClosurePrefixAdapter.interval_from_fin 0x340 32 (c832))
  (ClosurePrefixAdapter.interval_from_fin 0x360 32 (c864))))
  (ClosurePrefixAdapter.interval_join 0x380 0x3c0 0x400
  (ClosurePrefixAdapter.interval_join 0x380 0x3a0 0x3c0
  (ClosurePrefixAdapter.interval_from_fin 0x380 32 (c896))
  (ClosurePrefixAdapter.interval_from_fin 0x3a0 32 (c928)))
  (ClosurePrefixAdapter.interval_join 0x3c0 0x3e0 0x400
  (ClosurePrefixAdapter.interval_from_fin 0x3c0 32 (c960))
  (ClosurePrefixAdapter.interval_from_fin 0x3e0 32 (c992)))))))
  (ClosurePrefixAdapter.interval_join 0x400 0x600 0x7ec
  (ClosurePrefixAdapter.interval_join 0x400 0x500 0x600
  (ClosurePrefixAdapter.interval_join 0x400 0x480 0x500
  (ClosurePrefixAdapter.interval_join 0x400 0x440 0x480
  (ClosurePrefixAdapter.interval_join 0x400 0x420 0x440
  (ClosurePrefixAdapter.interval_from_fin 0x400 32 (c1024))
  (ClosurePrefixAdapter.interval_from_fin 0x420 32 (c1056)))
  (ClosurePrefixAdapter.interval_join 0x440 0x460 0x480
  (ClosurePrefixAdapter.interval_from_fin 0x440 32 (c1088))
  (ClosurePrefixAdapter.interval_from_fin 0x460 32 (c1120))))
  (ClosurePrefixAdapter.interval_join 0x480 0x4c0 0x500
  (ClosurePrefixAdapter.interval_join 0x480 0x4a0 0x4c0
  (ClosurePrefixAdapter.interval_from_fin 0x480 32 (c1152))
  (ClosurePrefixAdapter.interval_from_fin 0x4a0 32 (c1184)))
  (ClosurePrefixAdapter.interval_join 0x4c0 0x4e0 0x500
  (ClosurePrefixAdapter.interval_from_fin 0x4c0 32 (c1216))
  (ClosurePrefixAdapter.interval_from_fin 0x4e0 32 (c1248)))))
  (ClosurePrefixAdapter.interval_join 0x500 0x580 0x600
  (ClosurePrefixAdapter.interval_join 0x500 0x540 0x580
  (ClosurePrefixAdapter.interval_join 0x500 0x520 0x540
  (ClosurePrefixAdapter.interval_from_fin 0x500 32 (c1280))
  (ClosurePrefixAdapter.interval_from_fin 0x520 32 (c1312)))
  (ClosurePrefixAdapter.interval_join 0x540 0x560 0x580
  (ClosurePrefixAdapter.interval_from_fin 0x540 32 (c1344))
  (ClosurePrefixAdapter.interval_from_fin 0x560 32 (c1376))))
  (ClosurePrefixAdapter.interval_join 0x580 0x5c0 0x600
  (ClosurePrefixAdapter.interval_join 0x580 0x5a0 0x5c0
  (ClosurePrefixAdapter.interval_from_fin 0x580 32 (c1408))
  (ClosurePrefixAdapter.interval_from_fin 0x5a0 32 (c1440)))
  (ClosurePrefixAdapter.interval_join 0x5c0 0x5e0 0x600
  (ClosurePrefixAdapter.interval_from_fin 0x5c0 32 (c1472))
  (ClosurePrefixAdapter.interval_from_fin 0x5e0 32 (c1504))))))
  (ClosurePrefixAdapter.interval_join 0x600 0x700 0x7ec
  (ClosurePrefixAdapter.interval_join 0x600 0x680 0x700
  (ClosurePrefixAdapter.interval_join 0x600 0x640 0x680
  (ClosurePrefixAdapter.interval_join 0x600 0x620 0x640
  (ClosurePrefixAdapter.interval_from_fin 0x600 32 (c1536))
  (ClosurePrefixAdapter.interval_from_fin 0x620 32 (c1568)))
  (ClosurePrefixAdapter.interval_join 0x640 0x660 0x680
  (ClosurePrefixAdapter.interval_from_fin 0x640 32 (c1600))
  (ClosurePrefixAdapter.interval_from_fin 0x660 32 (c1632))))
  (ClosurePrefixAdapter.interval_join 0x680 0x6c0 0x700
  (ClosurePrefixAdapter.interval_join 0x680 0x6a0 0x6c0
  (ClosurePrefixAdapter.interval_from_fin 0x680 32 (c1664))
  (ClosurePrefixAdapter.interval_from_fin 0x6a0 32 (c1696)))
  (ClosurePrefixAdapter.interval_join 0x6c0 0x6e0 0x700
  (ClosurePrefixAdapter.interval_from_fin 0x6c0 32 (c1728))
  (ClosurePrefixAdapter.interval_from_fin 0x6e0 32 (c1760)))))
  (ClosurePrefixAdapter.interval_join 0x700 0x780 0x7ec
  (ClosurePrefixAdapter.interval_join 0x700 0x740 0x780
  (ClosurePrefixAdapter.interval_join 0x700 0x720 0x740
  (ClosurePrefixAdapter.interval_from_fin 0x700 32 (c1792))
  (ClosurePrefixAdapter.interval_from_fin 0x720 32 (c1824)))
  (ClosurePrefixAdapter.interval_join 0x740 0x760 0x780
  (ClosurePrefixAdapter.interval_from_fin 0x740 32 (c1856))
  (ClosurePrefixAdapter.interval_from_fin 0x760 32 (c1888))))
  (ClosurePrefixAdapter.interval_join 0x780 0x7c0 0x7ec
  (ClosurePrefixAdapter.interval_join 0x780 0x7a0 0x7c0
  (ClosurePrefixAdapter.interval_from_fin 0x780 32 (c1920))
  (ClosurePrefixAdapter.interval_from_fin 0x7a0 32 (c1952)))
  (ClosurePrefixAdapter.interval_join 0x7c0 0x7e0 0x7ec
  (ClosurePrefixAdapter.interval_from_fin 0x7c0 32 (c1984))
  (ClosurePrefixAdapter.interval_from_fin 0x7e0 12 (c2016)))))))) i (Nat.zero_le i) hi

def checked (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ i, 0 ≤ i → i < 0x7ec → Good X Y p r i := by
  intro i _ hi
  exact ClosureAnchorFuelPatternCheck.anchor_good ClosurePrefixAdapterData.program0 (sInput X Y p r)
    (ClosureSharedAnchorFuelSemantics.env X Y p r) (ClosureAnchorData.anchor0 X Y p r) (ClosureAnchorData.indexAt ClosureAnchorData.indices0) (by intro j; rfl)
    ClosureSharedAnchorPatternData.patterns 0x17c 10 i (ClosureSharedAnchorFuelSemantics.checked X Y p r) (numeric_checked i hi)

def model_agrees (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ∀ i < 0x7ec, ClosureSemantics.programModel ClosurePrefixAdapterData.program0
      (ClosureInputModel.inputValuation X Y p r) i =
      encode (anchoredValues ClosurePrefixAdapterData.program0 (sInput X Y p r) (ClosureAnchorData.anchor0 X Y p r) i) :=
  anchored_model_agrees ClosurePrefixAdapterData.program0 X Y p r (ClosureAnchorData.anchor0 X Y p r) 0x7ec
    (fun i hi => checked X Y p r i (Nat.zero_le i) hi)

end ClosureSharedAnchorFuelChecks0

end PolicySubmissionPart83

/- Component ClosureSharedAnchorFuelChecks1Explicit; SHA256 d22c37b075145e38a6f06b7576497f7ff22e99df0a5b2f5bc8c2bf75e85da902. -/
section PolicySubmissionPart84
/- Experimental fuel-recursive anchor route; shared root semantics use fuel 11.
All auxiliary proof declarations are synchronous proof-valued definitions. -/
namespace ClosureSharedAnchorFuelChecks1
open ClosureAnchorSemantics

def Good (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Prop :=
  ∀ a, ClosureAnchorData.anchor1 X Y p r i = some a →
    a = anchorBody ClosurePrefixAdapterData.program1 (sInput X Y p r) (ClosureAnchorData.anchor1 X Y p r) i

abbrev NumericallyGood (i : Nat) : Prop :=
  ClosureAnchorFuelPatternCheck.checkAnchor (ClosureSemantics.boundedProgram ClosurePrefixAdapterData.program1)
    (ClosureAnchorData.indexAt ClosureAnchorData.indices1) ClosureSharedAnchorPatternData.patterns 0x17c 10 i = true

def c0 : ∀ i : Fin 32, NumericallyGood (0+i.val) := by
  decide +kernel

def c32 : ∀ i : Fin 32, NumericallyGood (32+i.val) := by
  decide +kernel

def c64 : ∀ i : Fin 32, NumericallyGood (64+i.val) := by
  decide +kernel

def c96 : ∀ i : Fin 32, NumericallyGood (96+i.val) := by
  decide +kernel

def c128 : ∀ i : Fin 32, NumericallyGood (0x80+i.val) := by
  decide +kernel

def c160 : ∀ i : Fin 32, NumericallyGood (0xa0+i.val) := by
  decide +kernel

def c192 : ∀ i : Fin 32, NumericallyGood (0xc0+i.val) := by
  decide +kernel

def c224 : ∀ i : Fin 32, NumericallyGood (0xe0+i.val) := by
  decide +kernel

def c256 : ∀ i : Fin 32, NumericallyGood (0x100+i.val) := by
  decide +kernel

def c288 : ∀ i : Fin 32, NumericallyGood (0x120+i.val) := by
  decide +kernel

def c320 : ∀ i : Fin 32, NumericallyGood (0x140+i.val) := by
  decide +kernel

def c352 : ∀ i : Fin 32, NumericallyGood (0x160+i.val) := by
  decide +kernel

def c384 : ∀ i : Fin 32, NumericallyGood (0x180+i.val) := by
  decide +kernel

def c416 : ∀ i : Fin 32, NumericallyGood (0x1a0+i.val) := by
  decide +kernel

def c448 : ∀ i : Fin 32, NumericallyGood (0x1c0+i.val) := by
  decide +kernel

def c480 : ∀ i : Fin 32, NumericallyGood (0x1e0+i.val) := by
  decide +kernel

def c512 : ∀ i : Fin 32, NumericallyGood (0x200+i.val) := by
  decide +kernel

def c544 : ∀ i : Fin 32, NumericallyGood (0x220+i.val) := by
  decide +kernel

def c576 : ∀ i : Fin 32, NumericallyGood (0x240+i.val) := by
  decide +kernel

def c608 : ∀ i : Fin 32, NumericallyGood (0x260+i.val) := by
  decide +kernel

def c640 : ∀ i : Fin 32, NumericallyGood (0x280+i.val) := by
  decide +kernel

def c672 : ∀ i : Fin 32, NumericallyGood (0x2a0+i.val) := by
  decide +kernel

def c704 : ∀ i : Fin 32, NumericallyGood (0x2c0+i.val) := by
  decide +kernel

def c736 : ∀ i : Fin 32, NumericallyGood (0x2e0+i.val) := by
  decide +kernel

def c768 : ∀ i : Fin 32, NumericallyGood (0x300+i.val) := by
  decide +kernel

def c800 : ∀ i : Fin 32, NumericallyGood (0x320+i.val) := by
  decide +kernel

def c832 : ∀ i : Fin 32, NumericallyGood (0x340+i.val) := by
  decide +kernel

def c864 : ∀ i : Fin 32, NumericallyGood (0x360+i.val) := by
  decide +kernel

def c896 : ∀ i : Fin 32, NumericallyGood (0x380+i.val) := by
  decide +kernel

def c928 : ∀ i : Fin 32, NumericallyGood (0x3a0+i.val) := by
  decide +kernel

def c960 : ∀ i : Fin 32, NumericallyGood (0x3c0+i.val) := by
  decide +kernel

def c992 : ∀ i : Fin 32, NumericallyGood (0x3e0+i.val) := by
  decide +kernel

def c1024 : ∀ i : Fin 32, NumericallyGood (0x400+i.val) := by
  decide +kernel

def c1056 : ∀ i : Fin 32, NumericallyGood (0x420+i.val) := by
  decide +kernel

def c1088 : ∀ i : Fin 32, NumericallyGood (0x440+i.val) := by
  decide +kernel

def c1120 : ∀ i : Fin 32, NumericallyGood (0x460+i.val) := by
  decide +kernel

def c1152 : ∀ i : Fin 32, NumericallyGood (0x480+i.val) := by
  decide +kernel

def c1184 : ∀ i : Fin 32, NumericallyGood (0x4a0+i.val) := by
  decide +kernel

def c1216 : ∀ i : Fin 32, NumericallyGood (0x4c0+i.val) := by
  decide +kernel

def c1248 : ∀ i : Fin 32, NumericallyGood (0x4e0+i.val) := by
  decide +kernel

def c1280 : ∀ i : Fin 32, NumericallyGood (0x500+i.val) := by
  decide +kernel

def c1312 : ∀ i : Fin 32, NumericallyGood (0x520+i.val) := by
  decide +kernel

def c1344 : ∀ i : Fin 32, NumericallyGood (0x540+i.val) := by
  decide +kernel

def c1376 : ∀ i : Fin 32, NumericallyGood (0x560+i.val) := by
  decide +kernel

def c1408 : ∀ i : Fin 32, NumericallyGood (0x580+i.val) := by
  decide +kernel

def c1440 : ∀ i : Fin 32, NumericallyGood (0x5a0+i.val) := by
  decide +kernel

def c1472 : ∀ i : Fin 32, NumericallyGood (0x5c0+i.val) := by
  decide +kernel

def c1504 : ∀ i : Fin 32, NumericallyGood (0x5e0+i.val) := by
  decide +kernel

def c1536 : ∀ i : Fin 32, NumericallyGood (0x600+i.val) := by
  decide +kernel

def c1568 : ∀ i : Fin 32, NumericallyGood (0x620+i.val) := by
  decide +kernel

def c1600 : ∀ i : Fin 32, NumericallyGood (0x640+i.val) := by
  decide +kernel

def c1632 : ∀ i : Fin 32, NumericallyGood (0x660+i.val) := by
  decide +kernel

def c1664 : ∀ i : Fin 32, NumericallyGood (0x680+i.val) := by
  decide +kernel

def c1696 : ∀ i : Fin 32, NumericallyGood (0x6a0+i.val) := by
  decide +kernel

def c1728 : ∀ i : Fin 32, NumericallyGood (0x6c0+i.val) := by
  decide +kernel

def c1760 : ∀ i : Fin 32, NumericallyGood (0x6e0+i.val) := by
  decide +kernel

def c1792 : ∀ i : Fin 32, NumericallyGood (0x700+i.val) := by
  decide +kernel

def c1824 : ∀ i : Fin 32, NumericallyGood (0x720+i.val) := by
  decide +kernel

def c1856 : ∀ i : Fin 32, NumericallyGood (0x740+i.val) := by
  decide +kernel

def c1888 : ∀ i : Fin 32, NumericallyGood (0x760+i.val) := by
  decide +kernel

def c1920 : ∀ i : Fin 32, NumericallyGood (0x780+i.val) := by
  decide +kernel

def c1952 : ∀ i : Fin 32, NumericallyGood (0x7a0+i.val) := by
  decide +kernel

def c1984 : ∀ i : Fin 32, NumericallyGood (0x7c0+i.val) := by
  decide +kernel

def c2016 : ∀ i : Fin 12, NumericallyGood (0x7e0+i.val) := by
  decide +kernel

def numeric_checked : ∀ i < 0x7ec, NumericallyGood i := by
  intro i hi
  exact (ClosurePrefixAdapter.interval_join 0 0x400 0x7ec
  (ClosurePrefixAdapter.interval_join 0 0x200 0x400
  (ClosurePrefixAdapter.interval_join 0 0x100 0x200
  (ClosurePrefixAdapter.interval_join 0 0x80 0x100
  (ClosurePrefixAdapter.interval_join 0 64 0x80
  (ClosurePrefixAdapter.interval_join 0 32 64
  (ClosurePrefixAdapter.interval_from_fin 0 32 (c0))
  (ClosurePrefixAdapter.interval_from_fin 32 32 (c32)))
  (ClosurePrefixAdapter.interval_join 64 96 0x80
  (ClosurePrefixAdapter.interval_from_fin 64 32 (c64))
  (ClosurePrefixAdapter.interval_from_fin 96 32 (c96))))
  (ClosurePrefixAdapter.interval_join 0x80 0xc0 0x100
  (ClosurePrefixAdapter.interval_join 0x80 0xa0 0xc0
  (ClosurePrefixAdapter.interval_from_fin 0x80 32 (c128))
  (ClosurePrefixAdapter.interval_from_fin 0xa0 32 (c160)))
  (ClosurePrefixAdapter.interval_join 0xc0 0xe0 0x100
  (ClosurePrefixAdapter.interval_from_fin 0xc0 32 (c192))
  (ClosurePrefixAdapter.interval_from_fin 0xe0 32 (c224)))))
  (ClosurePrefixAdapter.interval_join 0x100 0x180 0x200
  (ClosurePrefixAdapter.interval_join 0x100 0x140 0x180
  (ClosurePrefixAdapter.interval_join 0x100 0x120 0x140
  (ClosurePrefixAdapter.interval_from_fin 0x100 32 (c256))
  (ClosurePrefixAdapter.interval_from_fin 0x120 32 (c288)))
  (ClosurePrefixAdapter.interval_join 0x140 0x160 0x180
  (ClosurePrefixAdapter.interval_from_fin 0x140 32 (c320))
  (ClosurePrefixAdapter.interval_from_fin 0x160 32 (c352))))
  (ClosurePrefixAdapter.interval_join 0x180 0x1c0 0x200
  (ClosurePrefixAdapter.interval_join 0x180 0x1a0 0x1c0
  (ClosurePrefixAdapter.interval_from_fin 0x180 32 (c384))
  (ClosurePrefixAdapter.interval_from_fin 0x1a0 32 (c416)))
  (ClosurePrefixAdapter.interval_join 0x1c0 0x1e0 0x200
  (ClosurePrefixAdapter.interval_from_fin 0x1c0 32 (c448))
  (ClosurePrefixAdapter.interval_from_fin 0x1e0 32 (c480))))))
  (ClosurePrefixAdapter.interval_join 0x200 0x300 0x400
  (ClosurePrefixAdapter.interval_join 0x200 0x280 0x300
  (ClosurePrefixAdapter.interval_join 0x200 0x240 0x280
  (ClosurePrefixAdapter.interval_join 0x200 0x220 0x240
  (ClosurePrefixAdapter.interval_from_fin 0x200 32 (c512))
  (ClosurePrefixAdapter.interval_from_fin 0x220 32 (c544)))
  (ClosurePrefixAdapter.interval_join 0x240 0x260 0x280
  (ClosurePrefixAdapter.interval_from_fin 0x240 32 (c576))
  (ClosurePrefixAdapter.interval_from_fin 0x260 32 (c608))))
  (ClosurePrefixAdapter.interval_join 0x280 0x2c0 0x300
  (ClosurePrefixAdapter.interval_join 0x280 0x2a0 0x2c0
  (ClosurePrefixAdapter.interval_from_fin 0x280 32 (c640))
  (ClosurePrefixAdapter.interval_from_fin 0x2a0 32 (c672)))
  (ClosurePrefixAdapter.interval_join 0x2c0 0x2e0 0x300
  (ClosurePrefixAdapter.interval_from_fin 0x2c0 32 (c704))
  (ClosurePrefixAdapter.interval_from_fin 0x2e0 32 (c736)))))
  (ClosurePrefixAdapter.interval_join 0x300 0x380 0x400
  (ClosurePrefixAdapter.interval_join 0x300 0x340 0x380
  (ClosurePrefixAdapter.interval_join 0x300 0x320 0x340
  (ClosurePrefixAdapter.interval_from_fin 0x300 32 (c768))
  (ClosurePrefixAdapter.interval_from_fin 0x320 32 (c800)))
  (ClosurePrefixAdapter.interval_join 0x340 0x360 0x380
  (ClosurePrefixAdapter.interval_from_fin 0x340 32 (c832))
  (ClosurePrefixAdapter.interval_from_fin 0x360 32 (c864))))
  (ClosurePrefixAdapter.interval_join 0x380 0x3c0 0x400
  (ClosurePrefixAdapter.interval_join 0x380 0x3a0 0x3c0
  (ClosurePrefixAdapter.interval_from_fin 0x380 32 (c896))
  (ClosurePrefixAdapter.interval_from_fin 0x3a0 32 (c928)))
  (ClosurePrefixAdapter.interval_join 0x3c0 0x3e0 0x400
  (ClosurePrefixAdapter.interval_from_fin 0x3c0 32 (c960))
  (ClosurePrefixAdapter.interval_from_fin 0x3e0 32 (c992)))))))
  (ClosurePrefixAdapter.interval_join 0x400 0x600 0x7ec
  (ClosurePrefixAdapter.interval_join 0x400 0x500 0x600
  (ClosurePrefixAdapter.interval_join 0x400 0x480 0x500
  (ClosurePrefixAdapter.interval_join 0x400 0x440 0x480
  (ClosurePrefixAdapter.interval_join 0x400 0x420 0x440
  (ClosurePrefixAdapter.interval_from_fin 0x400 32 (c1024))
  (ClosurePrefixAdapter.interval_from_fin 0x420 32 (c1056)))
  (ClosurePrefixAdapter.interval_join 0x440 0x460 0x480
  (ClosurePrefixAdapter.interval_from_fin 0x440 32 (c1088))
  (ClosurePrefixAdapter.interval_from_fin 0x460 32 (c1120))))
  (ClosurePrefixAdapter.interval_join 0x480 0x4c0 0x500
  (ClosurePrefixAdapter.interval_join 0x480 0x4a0 0x4c0
  (ClosurePrefixAdapter.interval_from_fin 0x480 32 (c1152))
  (ClosurePrefixAdapter.interval_from_fin 0x4a0 32 (c1184)))
  (ClosurePrefixAdapter.interval_join 0x4c0 0x4e0 0x500
  (ClosurePrefixAdapter.interval_from_fin 0x4c0 32 (c1216))
  (ClosurePrefixAdapter.interval_from_fin 0x4e0 32 (c1248)))))
  (ClosurePrefixAdapter.interval_join 0x500 0x580 0x600
  (ClosurePrefixAdapter.interval_join 0x500 0x540 0x580
  (ClosurePrefixAdapter.interval_join 0x500 0x520 0x540
  (ClosurePrefixAdapter.interval_from_fin 0x500 32 (c1280))
  (ClosurePrefixAdapter.interval_from_fin 0x520 32 (c1312)))
  (ClosurePrefixAdapter.interval_join 0x540 0x560 0x580
  (ClosurePrefixAdapter.interval_from_fin 0x540 32 (c1344))
  (ClosurePrefixAdapter.interval_from_fin 0x560 32 (c1376))))
  (ClosurePrefixAdapter.interval_join 0x580 0x5c0 0x600
  (ClosurePrefixAdapter.interval_join 0x580 0x5a0 0x5c0
  (ClosurePrefixAdapter.interval_from_fin 0x580 32 (c1408))
  (ClosurePrefixAdapter.interval_from_fin 0x5a0 32 (c1440)))
  (ClosurePrefixAdapter.interval_join 0x5c0 0x5e0 0x600
  (ClosurePrefixAdapter.interval_from_fin 0x5c0 32 (c1472))
  (ClosurePrefixAdapter.interval_from_fin 0x5e0 32 (c1504))))))
  (ClosurePrefixAdapter.interval_join 0x600 0x700 0x7ec
  (ClosurePrefixAdapter.interval_join 0x600 0x680 0x700
  (ClosurePrefixAdapter.interval_join 0x600 0x640 0x680
  (ClosurePrefixAdapter.interval_join 0x600 0x620 0x640
  (ClosurePrefixAdapter.interval_from_fin 0x600 32 (c1536))
  (ClosurePrefixAdapter.interval_from_fin 0x620 32 (c1568)))
  (ClosurePrefixAdapter.interval_join 0x640 0x660 0x680
  (ClosurePrefixAdapter.interval_from_fin 0x640 32 (c1600))
  (ClosurePrefixAdapter.interval_from_fin 0x660 32 (c1632))))
  (ClosurePrefixAdapter.interval_join 0x680 0x6c0 0x700
  (ClosurePrefixAdapter.interval_join 0x680 0x6a0 0x6c0
  (ClosurePrefixAdapter.interval_from_fin 0x680 32 (c1664))
  (ClosurePrefixAdapter.interval_from_fin 0x6a0 32 (c1696)))
  (ClosurePrefixAdapter.interval_join 0x6c0 0x6e0 0x700
  (ClosurePrefixAdapter.interval_from_fin 0x6c0 32 (c1728))
  (ClosurePrefixAdapter.interval_from_fin 0x6e0 32 (c1760)))))
  (ClosurePrefixAdapter.interval_join 0x700 0x780 0x7ec
  (ClosurePrefixAdapter.interval_join 0x700 0x740 0x780
  (ClosurePrefixAdapter.interval_join 0x700 0x720 0x740
  (ClosurePrefixAdapter.interval_from_fin 0x700 32 (c1792))
  (ClosurePrefixAdapter.interval_from_fin 0x720 32 (c1824)))
  (ClosurePrefixAdapter.interval_join 0x740 0x760 0x780
  (ClosurePrefixAdapter.interval_from_fin 0x740 32 (c1856))
  (ClosurePrefixAdapter.interval_from_fin 0x760 32 (c1888))))
  (ClosurePrefixAdapter.interval_join 0x780 0x7c0 0x7ec
  (ClosurePrefixAdapter.interval_join 0x780 0x7a0 0x7c0
  (ClosurePrefixAdapter.interval_from_fin 0x780 32 (c1920))
  (ClosurePrefixAdapter.interval_from_fin 0x7a0 32 (c1952)))
  (ClosurePrefixAdapter.interval_join 0x7c0 0x7e0 0x7ec
  (ClosurePrefixAdapter.interval_from_fin 0x7c0 32 (c1984))
  (ClosurePrefixAdapter.interval_from_fin 0x7e0 12 (c2016)))))))) i (Nat.zero_le i) hi

def checked (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) : ∀ i, 0 ≤ i → i < 0x7ec → Good X Y p r i := by
  intro i _ hi
  exact ClosureAnchorFuelPatternCheck.anchor_good ClosurePrefixAdapterData.program1 (sInput X Y p r)
    (ClosureSharedAnchorFuelSemantics.env X Y p r) (ClosureAnchorData.anchor1 X Y p r) (ClosureAnchorData.indexAt ClosureAnchorData.indices1) (by intro j; rfl)
    ClosureSharedAnchorPatternData.patterns 0x17c 10 i (ClosureSharedAnchorFuelSemantics.checked X Y p r) (numeric_checked i hi)

def model_agrees (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ∀ i < 0x7ec, ClosureSemantics.programModel ClosurePrefixAdapterData.program1
      (ClosureInputModel.inputValuation X Y p r) i =
      encode (anchoredValues ClosurePrefixAdapterData.program1 (sInput X Y p r) (ClosureAnchorData.anchor1 X Y p r) i) :=
  anchored_model_agrees ClosurePrefixAdapterData.program1 X Y p r (ClosureAnchorData.anchor1 X Y p r) 0x7ec
    (fun i hi => checked X Y p r i (Nat.zero_le i) hi)

end ClosureSharedAnchorFuelChecks1

end PolicySubmissionPart84

/- Component ClosureAliasCheck; SHA256 ca109b348bb954ac0598042ad2551ff362ad46be27a436f642f05bb85c06b72a. -/
section PolicySubmissionPart85
/- Reflect closed alias-node lookups without expanding them in the elaborator. -/
namespace ClosureAliasCheck
open ClosureSemantics

def check (node : Node) (target : Nat) : Bool :=
  match node.op with
  | .alias => decide (node.children = [target])
  | _ => false

def sound (node : Node) (target : Nat) (h : check node target = true) :
    node = ⟨.alias, [target]⟩ := by
  cases node with
  | mk op children => cases op <;> simp_all [check]

end ClosureAliasCheck

end PolicySubmissionPart85

/- Component PolicyAssertedSemanticsAnchorRoute; SHA256 91276a467a5705edcb62c3fea903b722aec207819888a9b6dfcdf4dd846d4bb7. -/
section PolicySubmissionPart86
/- Actual mathematical truth of every asserted unit in the two certificates. -/

namespace PolicyAssertedPacked0
open ClosureSemantics ClosureAnchorSemantics

def prefix_true (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) (a : Prop) (hi : i < 0x7ec)
    (hactive : 0 < ClosurePrefixAdapter.indexAt ClosurePrefixAdapterData.indices0 i)
    (ha : ClosureAnchorData.anchor0 X Y p r i = some (.prop a)) (htruth : a) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) i).b = true := by
  rw [ClosureAdapterChecks0.model_agrees (ClosureInputModel.inputValuation X Y p r) i hi hactive]
  exact anchor_model_true ClosurePrefixAdapterData.program0 X Y p r (ClosureAnchorData.anchor0 X Y p r) 0x7ec i a
    (fun j hj => ClosureSharedAnchorFuelChecks0.checked X Y p r j (Nat.zero_le j) hj) hi ha htruth

def value_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x903).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x903 0x65c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x65c (ClosureOriginalInputs0.input_47 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_47 X Y p r h)

def value_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x9a4).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x9a4 0x65f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x65f (ClosureOriginalInputs0.input_48 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_48 X Y p r h)

def value_2 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xa38).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xa38 4
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 4 (ClosureOriginalInputs0.input_0 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_0 X Y p r h)

def value_3 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xaa1).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xaa1 10
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 10 (ClosureOriginalInputs0.input_3 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_3 X Y p r h)

def value_4 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xb1a).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xb1a 5
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 5 (ClosureOriginalInputs0.input_1 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_1 X Y p r h)

def value_5 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xbce).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xbce 0x7eb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x7eb (ClosureOriginalInputs0.input_58 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_58 X Y p r h)

def value_6 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xc49).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xc49 0x724
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x724 (ClosureOriginalInputs0.input_53 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_53 X Y p r h)

def value_7 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xc5c).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xc5c 0x727
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x727 (ClosureOriginalInputs0.input_54 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_54 X Y p r h)

def value_8 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xdb7).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xdb7 0x720
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x720 (ClosureOriginalInputs0.input_52 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_52 X Y p r h)

def value_9 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xeea).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0xeea 9
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 9 (ClosureOriginalInputs0.input_2 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_2 X Y p r h)

def value_10 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x105e).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x105e 0x782
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x782 (ClosureOriginalInputs0.input_55 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_55 X Y p r h)

def value_11 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1071).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1071 0x786
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x786 (ClosureOriginalInputs0.input_56 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_56 X Y p r h)

def value_12 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x109c).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x109c 0x789
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x789 (ClosureOriginalInputs0.input_57 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_57 X Y p r h)

def value_13 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x170c).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x170c 0x4cf
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4cf (ClosureOriginalInputs0.input_36 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_36 X Y p r h)

def value_14 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1755).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1755 0x4c8
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4c8 (ClosureOriginalInputs0.input_34 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_34 X Y p r h)

def value_15 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1770).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1770 0x4cc
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4cc (ClosureOriginalInputs0.input_35 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_35 X Y p r h)

def value_16 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1a60).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1a60 0x52f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x52f (ClosureOriginalInputs0.input_39 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_39 X Y p r h)

def value_17 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1b37).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1b37 0x3a2
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3a2 (ClosureOriginalInputs0.input_27 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_27 X Y p r h)

def value_18 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1c0d).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1c0d 0x528
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x528 (ClosureOriginalInputs0.input_37 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_37 X Y p r h)

def value_19 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1c22).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1c22 0x52c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x52c (ClosureOriginalInputs0.input_38 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_38 X Y p r h)

def value_20 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1ffe).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x1ffe 0x33b
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x33b (ClosureOriginalInputs0.input_23 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_23 X Y p r h)

def value_21 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2020).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2020 0x337
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x337 (ClosureOriginalInputs0.input_22 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_22 X Y p r h)

def value_22 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x20a7).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x20a7 0x33e
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x33e (ClosureOriginalInputs0.input_24 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_24 X Y p r h)

def value_23 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2465).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2465 0x658
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x658 (ClosureOriginalInputs0.input_46 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_46 X Y p r h)

def value_24 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2611).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2611 0x593
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x593 (ClosureOriginalInputs0.input_42 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_42 X Y p r h)

def value_25 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2852).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x2852 0x6b7
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6b7 (ClosureOriginalInputs0.input_49 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_49 X Y p r h)

def value_26 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x286d).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x286d 0x6bb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6bb (ClosureOriginalInputs0.input_50 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_50 X Y p r h)

def value_27 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x28c4).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x28c4 0x6be
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6be (ClosureOriginalInputs0.input_51 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_51 X Y p r h)

def value_28 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x29d7).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x29d7 0x590
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x590 (ClosureOriginalInputs0.input_41 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_41 X Y p r h)

def value_29 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x29f9).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x29f9 0x58c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x58c (ClosureOriginalInputs0.input_40 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_40 X Y p r h)

def value_30 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x31cc).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x31cc 0x214
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x214 (ClosureOriginalInputs0.input_15 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_15 X Y p r h)

def value_31 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3417).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3417 0x39f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x39f (ClosureOriginalInputs0.input_26 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_26 X Y p r h)

def value_32 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x343c).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x343c 0x39b
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x39b (ClosureOriginalInputs0.input_25 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_25 X Y p r h)

def value_33 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3852).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3852 0x3ff
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3ff (ClosureOriginalInputs0.input_29 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_29 X Y p r h)

def value_34 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x399b).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x399b 0x402
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x402 (ClosureOriginalInputs0.input_30 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_30 X Y p r h)

def value_35 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3cc3).b = true := by
  rw [alias_model ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) 0x3cc3 0x3fb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3fb (ClosureOriginalInputs0.input_28 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs0.raw_input_28 X Y p r h)

def Good (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Prop :=
  (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) ((records i).getD 1 0)).b = true

def s0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) : ∀ i : Fin 32, Good X Y p r (0+i.val) := by
  intro i
  fin_cases i
  · exact value_0 X Y p r h
  · exact value_1 X Y p r h
  · exact value_2 X Y p r h
  · exact value_3 X Y p r h
  · exact value_4 X Y p r h
  · exact value_5 X Y p r h
  · exact value_6 X Y p r h
  · exact value_7 X Y p r h
  · exact value_8 X Y p r h
  · exact value_9 X Y p r h
  · exact value_10 X Y p r h
  · exact value_11 X Y p r h
  · exact value_12 X Y p r h
  · exact value_13 X Y p r h
  · exact value_14 X Y p r h
  · exact value_15 X Y p r h
  · exact value_16 X Y p r h
  · exact value_17 X Y p r h
  · exact value_18 X Y p r h
  · exact value_19 X Y p r h
  · exact value_20 X Y p r h
  · exact value_21 X Y p r h
  · exact value_22 X Y p r h
  · exact value_23 X Y p r h
  · exact value_24 X Y p r h
  · exact value_25 X Y p r h
  · exact value_26 X Y p r h
  · exact value_27 X Y p r h
  · exact value_28 X Y p r h
  · exact value_29 X Y p r h
  · exact value_30 X Y p r h
  · exact value_31 X Y p r h

def s32 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) : ∀ i : Fin 4, Good X Y p r (32+i.val) := by
  intro i
  fin_cases i
  · exact value_32 X Y p r h
  · exact value_33 X Y p r h
  · exact value_34 X Y p r h
  · exact value_35 X Y p r h

def sound (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 false X Y p r) (i : Nat) (hi : i < 36) :
    (programModel ClosureFixedWidthData0.program (ClosureInputModel.inputValuation X Y p r) ((records i).getD 1 0)).b = true :=
  (ClosurePrefixAdapter.interval_join 0 32 36
  (ClosurePrefixAdapter.interval_from_fin 0 32 (s0 X Y p r h))
  (ClosurePrefixAdapter.interval_from_fin 32 4 (s32 X Y p r h))) i (Nat.zero_le i) hi

end PolicyAssertedPacked0

namespace PolicyAssertedPacked1
open ClosureSemantics ClosureAnchorSemantics

def prefix_true (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) (a : Prop) (hi : i < 0x7ec)
    (hactive : 0 < ClosurePrefixAdapter.indexAt ClosurePrefixAdapterData.indices1 i)
    (ha : ClosureAnchorData.anchor1 X Y p r i = some (.prop a)) (htruth : a) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) i).b = true := by
  rw [ClosureAdapterChecks1.model_agrees (ClosureInputModel.inputValuation X Y p r) i hi hactive]
  exact anchor_model_true ClosurePrefixAdapterData.program1 X Y p r (ClosureAnchorData.anchor1 X Y p r) 0x7ec i a
    (fun j hj => ClosureSharedAnchorFuelChecks1.checked X Y p r j (Nat.zero_le j) hj) hi ha htruth

def value_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x86f).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x86f 0x727
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x727 (ClosureOriginalInputs1.input_54 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_54 X Y p r h)

def value_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x8d5).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x8d5 0x720
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x720 (ClosureOriginalInputs1.input_52 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_52 X Y p r h)

def value_2 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x8ea).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x8ea 0x724
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x724 (ClosureOriginalInputs1.input_53 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_53 X Y p r h)

def value_3 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xa13).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xa13 10
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 10 (ClosureOriginalInputs1.input_3 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_3 X Y p r h)

def value_4 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xa5e).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xa5e 5
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 5 (ClosureOriginalInputs1.input_1 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_1 X Y p r h)

def value_5 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xb06).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xb06 4
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 4 (ClosureOriginalInputs1.input_0 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_0 X Y p r h)

def value_6 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xc22).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xc22 0x7eb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x7eb (ClosureOriginalInputs1.input_58 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_58 X Y p r h)

def value_7 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xd04).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0xd04 9
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 9 (ClosureOriginalInputs1.input_2 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_2 X Y p r h)

def value_8 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x13e1).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x13e1 0x6b7
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6b7 (ClosureOriginalInputs1.input_49 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_49 X Y p r h)

def value_9 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x13f6).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x13f6 0x6bb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6bb (ClosureOriginalInputs1.input_50 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_50 X Y p r h)

def value_10 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1486).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1486 0x58c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x58c (ClosureOriginalInputs1.input_40 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_40 X Y p r h)

def value_11 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1499).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1499 0x590
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x590 (ClosureOriginalInputs1.input_41 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_41 X Y p r h)

def value_12 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1707).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1707 0x593
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x593 (ClosureOriginalInputs1.input_42 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_42 X Y p r h)

def value_13 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1734).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1734 0x6be
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x6be (ClosureOriginalInputs1.input_51 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_51 X Y p r h)

def value_14 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1916).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1916 0x782
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x782 (ClosureOriginalInputs1.input_55 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_55 X Y p r h)

def value_15 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x192b).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x192b 0x786
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x786 (ClosureOriginalInputs1.input_56 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_56 X Y p r h)

def value_16 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1ad9).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1ad9 0x789
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x789 (ClosureOriginalInputs1.input_57 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_57 X Y p r h)

def value_17 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f46).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f46 0x658
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x658 (ClosureOriginalInputs1.input_46 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_46 X Y p r h)

def value_18 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f5b).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f5b 0x65c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x65c (ClosureOriginalInputs1.input_47 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_47 X Y p r h)

def value_19 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f71).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x1f71 0x65f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x65f (ClosureOriginalInputs1.input_48 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_48 X Y p r h)

def value_20 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2ae1).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2ae1 0x528
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x528 (ClosureOriginalInputs1.input_37 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_37 X Y p r h)

def value_21 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2af5).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2af5 0x52c
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x52c (ClosureOriginalInputs1.input_38 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_38 X Y p r h)

def value_22 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2bcf).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2bcf 0x52f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x52f (ClosureOriginalInputs1.input_39 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_39 X Y p r h)

def value_23 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d02).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d02 0x4cf
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4cf (ClosureOriginalInputs1.input_36 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_36 X Y p r h)

def value_24 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d69).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d69 0x4c8
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4c8 (ClosureOriginalInputs1.input_34 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_34 X Y p r h)

def value_25 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d84).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x2d84 0x4cc
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x4cc (ClosureOriginalInputs1.input_35 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_35 X Y p r h)

def value_26 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x30f6).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x30f6 0x39f
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x39f (ClosureOriginalInputs1.input_26 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_26 X Y p r h)

def value_27 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x3118).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x3118 0x39b
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x39b (ClosureOriginalInputs1.input_25 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_25 X Y p r h)

def value_28 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4155).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4155 0x402
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x402 (ClosureOriginalInputs1.input_30 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_30 X Y p r h)

def value_29 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x41cb).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x41cb 0x3ff
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3ff (ClosureOriginalInputs1.input_29 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_29 X Y p r h)

def value_30 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x41ed).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x41ed 0x3fb
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3fb (ClosureOriginalInputs1.input_28 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_28 X Y p r h)

def value_31 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x47be).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x47be 0x3a2
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x3a2 (ClosureOriginalInputs1.input_27 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_27 X Y p r h)

def value_32 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4993).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4993 0x1c3
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x1c3 (ClosureOriginalInputs1.input_14 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_14 X Y p r h)

def value_33 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4bd6).b = true := by
  rw [alias_model ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) 0x4bd6 0x213
    (ClosureAliasCheck.sound _ _ (by decide +kernel)) (by omega)]
  exact prefix_true X Y p r 0x213 (ClosureOriginalInputs1.input_15 X Y p r) (by omega) (by decide +kernel)
    (by rfl) (ClosureOriginalInputs1.raw_input_15 X Y p r h)

def Good (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (i : Nat) : Prop :=
  (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) ((records i).getD 1 0)).b = true

def s0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) : ∀ i : Fin 32, Good X Y p r (0+i.val) := by
  intro i
  fin_cases i
  · exact value_0 X Y p r h
  · exact value_1 X Y p r h
  · exact value_2 X Y p r h
  · exact value_3 X Y p r h
  · exact value_4 X Y p r h
  · exact value_5 X Y p r h
  · exact value_6 X Y p r h
  · exact value_7 X Y p r h
  · exact value_8 X Y p r h
  · exact value_9 X Y p r h
  · exact value_10 X Y p r h
  · exact value_11 X Y p r h
  · exact value_12 X Y p r h
  · exact value_13 X Y p r h
  · exact value_14 X Y p r h
  · exact value_15 X Y p r h
  · exact value_16 X Y p r h
  · exact value_17 X Y p r h
  · exact value_18 X Y p r h
  · exact value_19 X Y p r h
  · exact value_20 X Y p r h
  · exact value_21 X Y p r h
  · exact value_22 X Y p r h
  · exact value_23 X Y p r h
  · exact value_24 X Y p r h
  · exact value_25 X Y p r h
  · exact value_26 X Y p r h
  · exact value_27 X Y p r h
  · exact value_28 X Y p r h
  · exact value_29 X Y p r h
  · exact value_30 X Y p r h
  · exact value_31 X Y p r h

def s32 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) : ∀ i : Fin 2, Good X Y p r (32+i.val) := by
  intro i
  fin_cases i
  · exact value_32 X Y p r h
  · exact value_33 X Y p r h

def sound (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) (h : Bounty.ClosureRawHypothesis5 true X Y p r) (i : Nat) (hi : i < 34) :
    (programModel ClosureFixedWidthData1.program (ClosureInputModel.inputValuation X Y p r) ((records i).getD 1 0)).b = true :=
  (ClosurePrefixAdapter.interval_join 0 32 34
  (ClosurePrefixAdapter.interval_from_fin 0 32 (s0 X Y p r h))
  (ClosurePrefixAdapter.interval_from_fin 32 2 (s32 X Y p r h))) i (Nat.zero_le i) hi

end PolicyAssertedPacked1

end PolicySubmissionPart86

/- Component PolicyDepth5ClosureBridge; SHA256 2fee1d7114b20485fdeb67b4b73f5c79de3dd3641420b8295fbbafa427b78eb2. -/
section PolicySubmissionPart87
/- Both finite depth-5 contradictions, lifted to the original depth-7 hypotheses. -/
namespace Bounty
open ClosureSemantics ClosureInputModel

def closureRaw5_false_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ¬ClosureRawHypothesis5 false X Y p r := by
  intro h
  apply PolicyCachedHotClosure.contradiction0 (inputValuation X Y p r)
    (programModel ClosureFixedWidthData0.program (inputValuation X Y p r))
    (programModel_equations ClosureFixedWidthData0.program (inputValuation X Y p r))
  intro i hi
  exact PolicyMappedAssertedChecked0.sound _ i hi (PolicyAssertedPacked0.sound X Y p r h i hi)

def closureRaw5_false_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ¬ClosureRawHypothesis5 true X Y p r := by
  intro h
  apply PolicyCachedHotClosure.contradiction1 (inputValuation X Y p r)
    (programModel ClosureFixedWidthData1.program (inputValuation X Y p r))
    (programModel_equations ClosureFixedWidthData1.program (inputValuation X Y p r))
  intro i hi
  exact PolicyMappedAssertedChecked1.sound _ i hi (PolicyAssertedPacked1.sound X Y p r h i hi)

def closureRaw_false_0 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ¬ClosureRawHypothesis false X Y p r := fun h =>
  closureRaw5_false_0 X Y p r (closureRawHypothesis5_of_raw false X Y p r h)

def closureRaw_false_1 (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ¬ClosureRawHypothesis true X Y p r := fun h =>
  closureRaw5_false_1 X Y p r (closureRawHypothesis5_of_raw true X Y p r h)

end Bounty

end PolicySubmissionPart87

/- Component PolicyClosureMath; SHA256 9d7b36812fbb4ac8dfe45961ec13f92d1c90a901f03adc5bb5df750c6de6fcad. -/
section PolicySubmissionPart88
/- Component StateProfile; SHA256 f32ea7c4e33d95846c55792a52f76f2166e7e9921870f1694468ecc883d8c9e7 -/
section SubmissionComponent_StateProfile
/- A local successful recursive choice gives the profile required at a leaf. -/

namespace Bounty

def cutoffState_profile_of_local {eps : Bool} {u : ℚ} (hu : 2 ≤ u)
    (h : cutoffAvailable u (quotaValue eps u) 0 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) ∨
      cutoffAvailable u (quotaValue eps u) 1 (cutoffState true (u / 5)) (cutoffState eps (u / 7))) :
    cutoffProfileValid eps (cutoffState eps u).1 u (cutoffState eps u).2 := by
  have hu1 : 1 ≤ u := by linarith
  have ha : cutoffAvailable u (quotaValue eps u) (cutoffState eps u).1
      (cutoffState true (u / 5)) (cutoffState eps (u / 7)) := by
    simpa only [cutoffState_of_large hu1] using cutoffCandidate_available h
  have hlo := (cutoffState_bounds (eps := eps) hu1).1
  apply (cutoffProfileValid_iff (cutoffState_parity eps u) hu (by linarith)).mpr
  constructor
  · have hh := ha.1
    rwa [← cutoffState_eq_trial hu1] at hh
  · have hh := cutoffTrial_size (by linarith : 0 ≤ u) ha
    rwa [← cutoffState_eq_trial hu1] at hh

def cutoffState_normalized_profile_of_local {eps : Bool} {u v : ℚ}
    (hu : 0 < u) (hv : 2 ≤ v * u)
    (h : cutoffAvailable (v * u) (quotaValue eps (v * u)) 0
        (cutoffState true (v * u / 5)) (cutoffState eps (v * u / 7)) ∨
      cutoffAvailable (v * u) (quotaValue eps (v * u)) 1
        (cutoffState true (v * u / 5)) (cutoffState eps (v * u / 7))) :
    normalizedStateValid eps (cutoffState eps (v * u)).1 v
      ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
      ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u)
      ((cutoffState eps (v * u)).2 / u) := by
  apply (cutoffProfileValid_iff_normalizedState eps (cutoffState eps (v * u)).1 hu hv).mp
  rw [div_mul_cancel₀ _ (ne_of_gt hu)]
  exact cutoffState_profile_of_local hv h

def cutoffState_normalized_lower {eps : Bool} {u v : ℚ}
    (hu : 0 < u) (hv : 1 ≤ v * u) :
    3 * v / 4 ≤ (cutoffState eps (v * u)).2 / u := by
  apply (le_div_iff₀ hu).mpr
  have hh := (cutoffState_bounds (eps := eps) hv).1
  calc
    (3 * v / 4) * u = 3 * (v * u) / 4 := by ring
    _ ≤ (cutoffState eps (v * u)).2 := hh


end Bounty

end SubmissionComponent_StateProfile

/- Component NormalizedPairs; SHA256 b722ed568e2d9fe1651568d96404fe21ff3ddaf31fef32611d3144d35a01fe72 -/
section SubmissionComponent_NormalizedPairs
/- Normalized rules with arbitrary actual child states. -/

namespace Bounty

def cutoffAvailable_iff_normalized_pair {eps : Bool} {p : ℕ} (hp : p < 2)
    (c5 c7 : ℕ × ℚ) {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffAvailable (v * u) (quotaValue eps (v * u)) p c5 c7 ↔
      normalizedTrialAvailable eps p c5.1 c7.1 v
        ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
        ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u)
        (c5.2 / u) (c7.2 / u) := by
  have hh := cutoffAvailable_iff_normalizedTrial (eps := eps) hp c5.1 c7.1
    (c5.2 / u) (c7.2 / u) hu hv
  simpa only [div_mul_cancel₀ _ (ne_of_gt hu), Prod.eta] using hh

def cutoffProfileTrial_normalized_pair (eps : Bool) (p : ℕ) (c5 c7 : ℕ × ℚ)
    {u v : ℚ} (hu : 0 < u) (hv : 2 ≤ v * u) :
    cutoffProfileTrial eps (v * u) p c5 c7 / u =
      normalizedTrialValue eps p c5.1 c7.1 v
        ((4 : ℚ) ^ Nat.log 4 ⌊v * u⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊v * u⌋₊ / u)
        ((4 : ℚ) ^ Nat.log 4 ⌊5 * (v * u)⌋₊ / u) ((3 : ℚ) ^ Nat.log 3 ⌊5 * (v * u)⌋₊ / u)
        (c5.2 / u) (c7.2 / u) := by
  have hh := cutoffProfileTrial_normalized eps p c5.1 c7.1 (c5.2 / u) (c7.2 / u) hu hv
  simp only [div_mul_cancel₀ _ (ne_of_gt hu), Prod.eta,
    cutoffDelta_normalized eps p hu hv] at hh
  exact hh

end Bounty

end SubmissionComponent_NormalizedPairs

/- Component ClosureGeometry; SHA256 0a383fca754322abcb396923852fc4043b6509f8f65c8e92ca177dd03976e8fe -/
section SubmissionComponent_ClosureGeometry
/- Uniform facts for the explicit thirty-six-node dependency table. -/

namespace Bounty

def closureNode_v_bounds {u : ℚ} (hu : 0x1921ee ≤ u) {k : ℕ} (hk : k < 36) :
    0 < (closureNode k).v ∧ (closureNode k).v ≤ 1 ∧ 2 ≤ (closureNode k).v * u := by
  interval_cases k <;> norm_num [closureNode] <;> linarith

def closureNode_v_shrink {k : ℕ} (hk0 : 0 < k) (hk : k < 36) :
    (closureNode k).v ≤ 1 / 5 := by
  interval_cases k <;> norm_num [closureNode]

def closureNode_floor_lt_root {u : ℚ} (hu : 0x1921ee ≤ u)
    {k : ℕ} (hk0 : 0 < k) (hk : k < 36) :
    ⌊(closureNode k).v * u⌋₊ < ⌊u⌋₊ := by
  have hv := closureNode_v_shrink hk0 hk
  have hle : (closureNode k).v * u ≤ u / 5 := by nlinarith
  exact (Nat.floor_mono hle).trans_lt (floor_div_lt_floor (d := 5) (by linarith) (by norm_num))

def closureNode_children {k : ℕ} (hk : k < 28) :
    (closureNode k).child5 < 36 ∧ (closureNode k).child7 < 36 ∧
    (closureNode (closureNode k).child5).v * 5 = (closureNode k).v ∧
    (closureNode (closureNode k).child7).v * 7 = (closureNode k).v := by
  interval_cases k <;> norm_num [closureNode]

def closureNode_child_types (eps : Bool) {k : ℕ} (hk : k < 28) :
    closureNodeType eps (closureNode k).child5 = true ∧
    closureNodeType eps (closureNode k).child7 = closureNodeType eps k := by
  interval_cases k <;> simp [closureNodeType, closureNode]

def closureNode_leaf_iff {k : ℕ} (hk : k < 36) :
    (closureNode k).leaf = true ↔ 28 ≤ k := by
  interval_cases k <;> norm_num [closureNode]


def closureNodeFour_coordinate {u : ℚ} (hu : 0x1921ee ≤ u) {k : ℕ} (hk : k < 36) :
    (4 : ℚ) ^ Nat.log 4 ⌊(closureNode k).v * u⌋₊ / u =
      closureNodeFour k ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  interval_cases k

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_3 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_3_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_4 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_3 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_3_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_4_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_5 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_4 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_3 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_3_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_4_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_5_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_6 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_5 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_4 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_3_3 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_4_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_5_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_6_0 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_0_7 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_1_6 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_2_5 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_3_4 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_4_3 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_5_2 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_6_1 hu

  · simpa only [closureNodeFour, closureNode] using closurePower4_node_7_0 hu



def closureLossFour_coordinate {u : ℚ} (hu : 0x1921ee ≤ u) {k : ℕ} (hk : k < 36) :
    (4 : ℚ) ^ Nat.log 4 ⌊5 * ((closureNode k).v * u)⌋₊ / u =
      closureLossFour k ((4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u) := by
  interval_cases k

  · have hh := closurePower4_loss_0_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_3 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_3_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_4 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_3 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_3_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_4_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_5 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_4 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_3 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_3_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_4_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_5_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_6 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_5 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_4 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_3_3 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_4_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_5_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_6_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_0_7 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_1_6 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_2_5 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_3_4 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_4_3 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_5_2 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_6_1 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower4_loss_7_0 hu
    norm_num only [closureLossFour, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh



def closureNodeThree_coordinate {u : ℚ} (hu : 0x1921ee ≤ u) {k : ℕ} (hk : k < 36) :
    (3 : ℚ) ^ Nat.log 3 ⌊(closureNode k).v * u⌋₊ / u =
      closureNodeThree k ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  interval_cases k

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_3 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_3_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_4 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_3 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_3_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_4_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_5 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_4 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_3 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_3_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_4_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_5_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_6 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_5 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_4 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_3_3 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_4_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_5_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_6_0 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_0_7 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_1_6 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_2_5 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_3_4 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_4_3 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_5_2 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_6_1 hu

  · simpa only [closureNodeThree, closureNode] using closurePower3_node_7_0 hu



def closureLossThree_coordinate {u : ℚ} (hu : 0x1921ee ≤ u) {k : ℕ} (hk : k < 36) :
    (3 : ℚ) ^ Nat.log 3 ⌊5 * ((closureNode k).v * u)⌋₊ / u =
      closureLossThree k ((3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u) := by
  interval_cases k

  · have hh := closurePower3_loss_0_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_3 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_3_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_4 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_3 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_3_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_4_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_5 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_4 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_3 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_3_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_4_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_5_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_6 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_5 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_4 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_3_3 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_4_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_5_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_6_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_0_7 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_1_6 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_2_5 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_3_4 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_4_3 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_5_2 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_6_1 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh

  · have hh := closurePower3_loss_7_0 hu
    norm_num only [closureLossThree, closureNode, ← mul_assoc, one_mul, mul_one] at hh ⊢
    exact hh



end Bounty

end SubmissionComponent_ClosureGeometry

/- Component ClosureActual; SHA256 330a72a33df1a785353687135798a08c3d9a644dcc0c03c31c2cc912f8664182 -/
section SubmissionComponent_ClosureActual
/- Interpret the finite dependency table by actual recursive cutoff states. -/

namespace Bounty

noncomputable def closureActualState (eps : Bool) (u : ℚ) (k : ℕ) : ℕ × ℚ :=
  cutoffState (closureNodeType eps k) ((closureNode k).v * u)

noncomputable def closureActualPhase (eps : Bool) (u : ℚ) (k : ℕ) : Prop :=
  (closureActualState eps u k).1 = 1

noncomputable def closureActualValue (eps : Bool) (u : ℚ) (k : ℕ) : ℚ :=
  (closureActualState eps u k).2 / u

def closureRootFour (u : ℚ) : ℚ := (4 : ℚ) ^ Nat.log 4 ⌊u⌋₊ / u
def closureRootThree (u : ℚ) : ℚ := (3 : ℚ) ^ Nat.log 3 ⌊u⌋₊ / u

def closureActual_parity (eps : Bool) (u : ℚ) (k : ℕ) :
    (closureActualState eps u k).1 < 2 := cutoffState_parity _ _

def closureActual_phase (eps : Bool) (u : ℚ) (k : ℕ) :
    closurePhase (closureActualPhase eps u k) = (closureActualState eps u k).1 :=
  closurePhase_of_nat (closureActual_parity eps u k)

def closureActual_child_five (eps : Bool) (u : ℚ) {k : ℕ} (hk : k < 28) :
    closureActualState eps u (closureNode k).child5 =
      cutoffState true ((closureNode k).v * u / 5) := by
  unfold closureActualState
  rw [(closureNode_child_types eps hk).1]
  congr 1
  apply (eq_div_iff (by norm_num : (5 : ℚ) ≠ 0)).mpr
  calc
    (closureNode (closureNode k).child5).v * u * 5 =
        ((closureNode (closureNode k).child5).v * 5) * u := by ring
    _ = (closureNode k).v * u := by rw [(closureNode_children hk).2.2.1]

def closureActual_child_seven (eps : Bool) (u : ℚ) {k : ℕ} (hk : k < 28) :
    closureActualState eps u (closureNode k).child7 =
      cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7) := by
  unfold closureActualState
  rw [(closureNode_child_types eps hk).2]
  congr 1
  apply (eq_div_iff (by norm_num : (7 : ℚ) ≠ 0)).mpr
  calc
    (closureNode (closureNode k).child7).v * u * 7 =
        ((closureNode (closureNode k).child7).v * 7) * u := by ring
    _ = (closureNode k).v * u := by rw [(closureNode_children hk).2.2.2]

def closureActual_available {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    {k phase : ℕ} (hk : k < 28) (hp : phase < 2) :
    cutoffAvailable ((closureNode k).v * u) (quotaValue (closureNodeType eps k) ((closureNode k).v * u))
      phase (cutoffState true ((closureNode k).v * u / 5))
      (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7)) ↔
    closureNodeAvailable eps k phase (closureRootFour u) (closureRootThree u)
      (closureActualPhase eps u) (closureActualValue eps u) := by
  have hk36 : k < 36 := by omega
  have hu0 : 0 < u := by linarith
  have hv := (closureNode_v_bounds hu hk36).2.2
  have hh := cutoffAvailable_iff_normalized_pair (eps := closureNodeType eps k) hp
    (closureActualState eps u (closureNode k).child5)
    (closureActualState eps u (closureNode k).child7) hu0 hv
  rw [closureNodeFour_coordinate hu hk36, closureNodeThree_coordinate hu hk36,
    closureLossFour_coordinate hu hk36, closureLossThree_coordinate hu hk36] at hh
  simpa only [closureNodeAvailable, closureNodeTrial, closureRootFour, closureRootThree,
    normalizedTrialAvailable, closureActual_phase, closureActualValue,
    closureActual_child_five eps u hk, closureActual_child_seven eps u hk] using hh

def closureActual_trial {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    {k : ℕ} (hk : k < 28) (phase : ℕ) :
    closureNodeTrial eps k phase (closureRootFour u) (closureRootThree u)
      (closureActualPhase eps u) (closureActualValue eps u) =
    cutoffProfileTrial (closureNodeType eps k) ((closureNode k).v * u) phase
      (cutoffState true ((closureNode k).v * u / 5))
      (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7)) / u := by
  have hk36 : k < 36 := by omega
  have hu0 : 0 < u := by linarith
  have hv := (closureNode_v_bounds hu hk36).2.2
  have hh := cutoffProfileTrial_normalized_pair (closureNodeType eps k) phase
    (closureActualState eps u (closureNode k).child5)
    (closureActualState eps u (closureNode k).child7) hu0 hv
  rw [closureNodeFour_coordinate hu hk36, closureNodeThree_coordinate hu hk36,
    closureLossFour_coordinate hu hk36, closureLossThree_coordinate hu hk36] at hh
  simpa only [closureNodeTrial, closureRootFour, closureRootThree, closureActual_phase,
    closureActualValue, closureActual_child_five eps u hk, closureActual_child_seven eps u hk] using hh.symm


end Bounty

end SubmissionComponent_ClosureActual

/- Component ClosureActualRules; SHA256 5f343a1defcd4fbfac1fdfde11ebdff5da92ee787c4d7374fdce3cab02466780 -/
section SubmissionComponent_ClosureActualRules
/- The recursive states obey the phase, value, and leaf rules of the finite model. -/

namespace Bounty

def closureActual_phase_rule {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    {k : ℕ} (hk : k < 28) :
    closureActualPhase eps u k ↔
      if 2 * closureNodeFour k (closureRootFour u) ≤ (closureNode k).v then
        closureNodeAvailable eps k 1 (closureRootFour u) (closureRootThree u)
          (closureActualPhase eps u) (closureActualValue eps u)
      else ¬closureNodeAvailable eps k 0 (closureRootFour u) (closureRootThree u)
          (closureActualPhase eps u) (closureActualValue eps u) := by
  have hk36 : k < 36 := by omega
  have hv := (closureNode_v_bounds hu hk36).2.2
  change (cutoffState (closureNodeType eps k) ((closureNode k).v * u)).1 = 1 ↔ _
  rw [cutoffState_of_large (by linarith : 1 ≤ (closureNode k).v * u), cutoffCandidate_phase_one_iff]
  simp only [preferred_phase_normalized (by linarith : 0 < u) (by linarith : 1 ≤ (closureNode k).v * u),
    closureNodeFour_coordinate hu hk36, closureActual_available hu hk (by norm_num : 0 < 2),
    closureActual_available hu hk (by norm_num : 1 < 2), closureRootFour]
  rfl

def closureActual_value_rule {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    {k : ℕ} (hk : k < 28)
    (ha : cutoffAvailable ((closureNode k).v * u) (quotaValue (closureNodeType eps k) ((closureNode k).v * u))
        0 (cutoffState true ((closureNode k).v * u / 5))
        (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7)) ∨
      cutoffAvailable ((closureNode k).v * u) (quotaValue (closureNodeType eps k) ((closureNode k).v * u))
        1 (cutoffState true ((closureNode k).v * u / 5))
        (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7))) :
    closureActualValue eps u k = if (closureActualState eps u k).1 = 1 then
        closureNodeTrial eps k 1 (closureRootFour u) (closureRootThree u)
          (closureActualPhase eps u) (closureActualValue eps u)
      else closureNodeTrial eps k 0 (closureRootFour u) (closureRootThree u)
          (closureActualPhase eps u) (closureActualValue eps u) := by
  have hv := (closureNode_v_bounds hu (show k < 36 by omega)).2.2
  simp only [closureActual_trial hu hk, closureActualValue, closureActualState,
    cutoffState_of_large (by linarith : 1 ≤ (closureNode k).v * u)]
  have hh := congrArg (fun r : ℚ => r / u) (cutoffCandidate_value_profile hv ha)
  split_ifs at hh ⊢ <;> exact hh

def closureActual_valid {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    {k : ℕ} (hk : k < 36)
    (ha : cutoffAvailable ((closureNode k).v * u) (quotaValue (closureNodeType eps k) ((closureNode k).v * u))
        0 (cutoffState true ((closureNode k).v * u / 5))
        (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7)) ∨
      cutoffAvailable ((closureNode k).v * u) (quotaValue (closureNodeType eps k) ((closureNode k).v * u))
        1 (cutoffState true ((closureNode k).v * u / 5))
        (cutoffState (closureNodeType eps k) ((closureNode k).v * u / 7))) :
    normalizedStateValid (closureNodeType eps k) (closureActualState eps u k).1 (closureNode k).v
      (closureNodeFour k (closureRootFour u)) (closureNodeThree k (closureRootThree u))
      (closureLossFour k (closureRootFour u)) (closureLossThree k (closureRootThree u))
      (closureActualValue eps u k) := by
  have hh := cutoffState_normalized_profile_of_local (by linarith : 0 < u)
    (closureNode_v_bounds hu hk).2.2 ha
  rw [closureNodeFour_coordinate hu hk, closureNodeThree_coordinate hu hk,
    closureLossFour_coordinate hu hk, closureLossThree_coordinate hu hk] at hh
  exact hh


end Bounty

end SubmissionComponent_ClosureActualRules

/- Component ClosureModel; SHA256 5c062851ec37e77d6a6dffa086e39111babd40f2acafea69306a9ab28482a639 -/
section SubmissionComponent_ClosureModel
/- A hypothetical recursive failure produces the finite model ruled out by the certificates. -/

namespace Bounty

def cutoffLocalAvailable (eps : Bool) (u : ℚ) : Prop :=
  cutoffAvailable u (quotaValue eps u) 0 (cutoffState true (u / 5)) (cutoffState eps (u / 7)) ∨
    cutoffAvailable u (quotaValue eps u) 1 (cutoffState true (u / 5)) (cutoffState eps (u / 7))

def cutoffInductionHypothesis (u : ℚ) : Prop :=
  ∀ eps v, 1 ≤ v → ⌊v⌋₊ < ⌊u⌋₊ → cutoffLocalAvailable eps v

def closureActual_raw_of_failure {eps : Bool} {u : ℚ} (hu : 0x1921ee ≤ u)
    (hi : cutoffInductionHypothesis u) (hf : ¬cutoffLocalAvailable eps u) :
    ClosureRawHypothesis eps (closureRootFour u) (closureRootThree u)
      (closureActualPhase eps u) (closureActualValue eps u) := by
  classical
  have hu0 : 0 < u := by linarith
  have hu1 : 1 ≤ u := by linarith
  have hx : 1 / 4 < closureRootFour u ∧ closureRootFour u ≤ 1 := by
    simpa only [Nat.cast_ofNat, closureRootFour] using normalized_power_bounds (b := 4) (by norm_num) hu1
  have hy : 1 / 3 < closureRootThree u ∧ closureRootThree u ≤ 1 := by
    simpa only [Nat.cast_ofNat, closureRootThree] using normalized_power_bounds (b := 3) (by norm_num) hu1
  refine ⟨hx.1, hx.2, hy.1, hy.2, ?_⟩
  intro k hk
  by_cases hk0 : k = 0
  · subst k
    change ¬closureNodeAvailable eps 0 0 (closureRootFour u) (closureRootThree u)
        (closureActualPhase eps u) (closureActualValue eps u) ∧
      ¬closureNodeAvailable eps 0 1 (closureRootFour u) (closureRootThree u)
        (closureActualPhase eps u) (closureActualValue eps u)
    have h0 := closureActual_available (eps := eps) hu (k := 0) (phase := 0) (by norm_num) (by norm_num)
    have h1 := closureActual_available (eps := eps) hu (k := 0) (phase := 1) (by norm_num) (by norm_num)
    simp only [closureNodeType, closureNode, ↓reduceIte, one_mul] at h0 h1
    exact ⟨fun h => hf (Or.inl (h0.mpr h)), fun h => hf (Or.inr (h1.mpr h))⟩
  · have hv := (closureNode_v_bounds hu hk).2.2
    have ha := hi (closureNodeType eps k) ((closureNode k).v * u) (by linarith)
      (closureNode_floor_lt_root hu (by omega) hk)
    by_cases hleaf : (closureNode k).leaf = true
    · simp only [closureNodeConstraint, if_neg hk0, if_pos hleaf]
      refine ⟨cutoffState_normalized_lower hu0 (by linarith : 1 ≤ (closureNode k).v * u), ?_⟩
      have hvld := closureActual_valid hu hk ha
      by_cases hp : closureActualPhase eps u k
      · rw [if_pos hp]
        have hp' : (closureActualState eps u k).1 = 1 := hp
        simpa only [hp'] using hvld
      · rw [if_neg hp]
        have hp' : (closureActualState eps u k).1 ≠ 1 := hp
        have hb := closureActual_parity eps u k
        have hz : (closureActualState eps u k).1 = 0 := by omega
        simpa only [hz] using hvld
    · have hk28 : k < 28 := by
        have hh : ¬28 ≤ k := fun h => hleaf ((closureNode_leaf_iff hk).mpr h)
        omega
      simp only [closureNodeConstraint, if_neg hk0, if_neg hleaf]
      refine ⟨?_, closureActual_phase_rule hu hk28, ?_⟩
      · exact ha.imp (closureActual_available hu hk28 (by norm_num : 0 < 2)).mp
          (closureActual_available hu hk28 (by norm_num : 1 < 2)).mp
      · have hh := closureActual_value_rule hu hk28 ha
        by_cases hp : closureActualPhase eps u k
        · rw [if_pos hp]
          have hp' : (closureActualState eps u k).1 = 1 := hp
          simpa only [if_pos hp'] using hh
        · rw [if_neg hp]
          have hp' : (closureActualState eps u k).1 ≠ 1 := hp
          simpa only [if_neg hp'] using hh


end Bounty

end SubmissionComponent_ClosureModel

/- Component ClosureInduction; SHA256 07be9ab9910c2a6d5134e25d9737358668863287c82893e314915b4c931c7444 -/
section SubmissionComponent_ClosureInduction
/- Strong induction reduces universal availability to the two finite closure contradictions. -/

namespace Bounty

def cutoffAvailability_of_closure
    (H : ∀ eps X Y p r, ¬ClosureRawHypothesis eps X Y p r) : CutoffAvailability := by
  have all : ∀ n : ℕ, ∀ eps u, ⌊u⌋₊ = n → 1 ≤ u → cutoffLocalAvailable eps u := by
    intro n
    induction n using Nat.strong_induction_on with
    | h n ih =>
      intro eps u hn hu1
      by_cases hb : u < 0x1921ee
      · exact cutoffAvailabilityBelow_base eps u hu1 hb
      · have hu : 0x1921ee ≤ u := le_of_not_gt hb
        by_contra hf
        have hi : cutoffInductionHypothesis u := by
          intro eps' v hv hsmall
          exact ih ⌊v⌋₊ (by omega) eps' v rfl hv
        exact H eps (closureRootFour u) (closureRootThree u)
          (closureActualPhase eps u) (closureActualValue eps u) (closureActual_raw_of_failure hu hi hf)
  intro eps u hu
  exact all ⌊u⌋₊ eps u rfl hu

end Bounty

end SubmissionComponent_ClosureInduction

/- Component GlobalExact; SHA256 0bd823ef2311337b330cc11bab8cddfe89bbd5255a95713396924e76bfb38535 -/
section SubmissionComponent_GlobalExact
/- Universal availability and the exact extremal formula, from both checked finite contradictions. -/

namespace Bounty

def closureRaw_false (eps : Bool) (X Y : ℚ) (p : ℕ → Prop) (r : ℕ → ℚ) :
    ¬ClosureRawHypothesis eps X Y p r := by
  cases eps with
  | false => exact closureRaw_false_0 X Y p r
  | true => exact closureRaw_false_1 X Y p r

def cutoffAvailability : CutoffAvailability := cutoffAvailability_of_closure closureRaw_false

def f_eq_globalUpper (n : ℕ) : Erdos1062.f n = globalUpper n :=
  f_eq_globalUpper_of_availability cutoffAvailability n


end Bounty

end SubmissionComponent_GlobalExact

end PolicySubmissionPart88

/- Component PolicyMathDensity; SHA256 eeaf1f08fd54d7d7665239bb4f60425bc6e1891adf1f02d57e55bdd2cce633df. -/
section PolicySubmissionPart89
/- Standalone proof of an integer polynomial index lemma.
This does not prove the Subspace Theorem or the Erdős1062(ii) target. -/

/- Component: PolynomialDegreeEchelon; SHA256 506fd270ae0af8512f5b657399384081a522482e4715dcb43bcef2af75b92760 -/
section RothComponent_PolynomialDegreeEchelon
/- A constant invertible row transformation makes polynomial degrees distinct. -/

open Polynomial

namespace Bounty

noncomputable section

def polynomialRowCombination {k : ℕ} (f : Fin k → ℚ[X])
    (A : Matrix (Fin k) (Fin k) ℚ) (i : Fin k) : ℚ[X] :=
  ∑ j, A i j • f j

def polynomialRowCombination_ne_zero {k : ℕ} (f : Fin k → ℚ[X])
    (hf : LinearIndependent ℚ f) (A : Matrix (Fin k) (Fin k) ℚ)
    (hA : A.det ≠ 0) (i : Fin k) : polynomialRowCombination f A i ≠ 0 := by
  intro hi
  have hrow : ∀ j, A i j = 0 := Fintype.linearIndependent_iff.mp hf (A i) hi
  exact hA (Matrix.det_eq_zero_of_row_eq_zero i hrow)

def polynomialRowCombination_updateRow {k : ℕ} (f : Fin k → ℚ[X])
    (A : Matrix (Fin k) (Fin k) ℚ) (i j : Fin k) (c : ℚ) :
    polynomialRowCombination f (A.updateRow i (A i + c • A j)) i =
      polynomialRowCombination f A i + c • polynomialRowCombination f A j := by
  simp only [polynomialRowCombination, Matrix.updateRow_self, Pi.add_apply, Pi.smul_apply,
    add_smul, Finset.sum_add_distrib, Finset.smul_sum, smul_smul, smul_eq_mul]

/-- Cancel the leading coefficient of two equal-degree polynomials. A nonzero
result has strictly smaller natural degree, including the degree-zero edge case. -/
def polynomial_natDegree_cancel_lead {p q : ℚ[X]} (hq : q ≠ 0)
    (hd : p.natDegree = q.natDegree)
    (hnew : p + (-(p.leadingCoeff / q.leadingCoeff)) • q ≠ 0) :
    (p + (-(p.leadingCoeff / q.leadingCoeff)) • q).natDegree < p.natDegree := by
  let c : ℚ := -(p.leadingCoeff / q.leadingCoeff)
  change (p + c • q).natDegree < p.natDegree
  have hle : (p + c • q).natDegree ≤ p.natDegree := by
    apply (Polynomial.natDegree_add_le _ _).trans
    apply max_le le_rfl
    exact (Polynomial.natDegree_smul_le c q).trans hd.symm.le
  have hc : (p + c • q).coeff p.natDegree = 0 := by
    rw [Polynomial.coeff_add, Polynomial.coeff_smul, Polynomial.coeff_natDegree, hd,
      Polynomial.coeff_natDegree]
    simp only [c, smul_eq_mul]
    field_simp [Polynomial.leadingCoeff_ne_zero.mpr hq]
    ring
  have hne : (p + c • q).natDegree ≠ p.natDegree := by
    intro he
    apply Polynomial.leadingCoeff_ne_zero.mpr hnew
    change (p + c • q).coeff (p + c • q).natDegree = 0
    rw [he]
    exact hc
  omega

/-- Every finite independent rational polynomial family has an invertible constant
change of basis whose resulting polynomials have pairwise distinct natural degrees.
The matrix acts on rows: `g i = ∑ j, A i j • f j`. -/
def polynomial_degree_echelon {k : ℕ} (f : Fin k → ℚ[X])
    (hf : LinearIndependent ℚ f) :
    ∃ A : Matrix (Fin k) (Fin k) ℚ, ∃ g : Fin k → ℚ[X],
      A.det ≠ 0 ∧ (∀ i, g i = ∑ j, A i j • f j) ∧
      (∀ i, g i ≠ 0) ∧ Function.Injective (fun i => (g i).natDegree) := by
  classical
  let measure : Matrix (Fin k) (Fin k) ℚ → ℕ :=
    fun A => ∑ i, (polynomialRowCombination f A i).natDegree
  have hex : ∃ n : ℕ, ∃ A : Matrix (Fin k) (Fin k) ℚ, A.det = 1 ∧ measure A = n :=
    ⟨measure 1, 1, by simp, rfl⟩
  obtain ⟨A, hA, hmeasure⟩ := Nat.find_spec hex
  have hmin (B : Matrix (Fin k) (Fin k) ℚ) (hB : B.det = 1) : measure A ≤ measure B := by
    rw [hmeasure]
    exact Nat.find_min' hex ⟨B, hB, rfl⟩
  have hA0 : A.det ≠ 0 := by rw [hA]; norm_num
  have hnonzero := polynomialRowCombination_ne_zero f hf A hA0
  refine ⟨A, polynomialRowCombination f A, hA0, fun _ => rfl, hnonzero, ?_⟩
  intro i j hd
  by_contra hij
  let c : ℚ := -((polynomialRowCombination f A i).leadingCoeff /
    (polynomialRowCombination f A j).leadingCoeff)
  let B : Matrix (Fin k) (Fin k) ℚ := A.updateRow i (A i + c • A j)
  have hB : B.det = 1 := (Matrix.det_updateRow_add_smul_self A hij c).trans hA
  have hBi : polynomialRowCombination f B i =
      polynomialRowCombination f A i + c • polynomialRowCombination f A j :=
    polynomialRowCombination_updateRow f A i j c
  have hBnz : polynomialRowCombination f B i ≠ 0 :=
    polynomialRowCombination_ne_zero f hf B (by rw [hB]; norm_num) i
  have hlt : (polynomialRowCombination f B i).natDegree <
      (polynomialRowCombination f A i).natDegree := by
    rw [hBi] at hBnz ⊢
    exact polynomial_natDegree_cancel_lead (hnonzero j) hd hBnz
  have hBt (t : Fin k) (hti : t ≠ i) :
      polynomialRowCombination f B t = polynomialRowCombination f A t := by
    simp only [polynomialRowCombination, B, Matrix.updateRow_ne hti]
  have hdrop : measure B < measure A := by
    apply Finset.sum_lt_sum
    · intro t ht
      by_cases hti : t = i
      · subst t
        exact hlt.le
      · rw [hBt t hti]
    · exact ⟨i, Finset.mem_univ i, hlt⟩
  exact (not_lt_of_ge (hmin B hB)) hdrop


end
end Bounty
end RothComponent_PolynomialDegreeEchelon

/- Component: UnivariateWronskian; SHA256 d13c46c193a9864197f28c3946420f6b1f105d08f4a4e66bde06ff2cb78f0c8f -/
section RothComponent_UnivariateWronskian
/- Arbitrary finite polynomial Wronskians over the rationals. -/

noncomputable section


open Polynomial Matrix Finset

namespace Bounty

def polynomialWronskian {n : ℕ} (f : Fin n → ℚ[X]) : ℚ[X] :=
  Matrix.det (fun i j : Fin n => Polynomial.hasseDeriv i.val (f j))

def choose_matrix_det_ne_zero {n : ℕ} (d : Fin n → ℕ)
    (hd : Function.Injective d) :
    Matrix.det (fun i j : Fin n => (Nat.choose (d j) i.val : ℚ)) ≠ 0 := by
  have hv : Function.Injective (fun i : Fin n => (d i : ℚ)) := by
    intro i j hij
    apply hd
    change (d i : ℚ) = (d j : ℚ) at hij
    exact_mod_cast hij
  have hvdet := Matrix.det_vandermonde_ne_zero_iff.mpr hv
  have heval := Matrix.det_eval_matrixOfPolynomials_eq_det_vandermonde
    (fun i : Fin n => (d i : ℚ)) (fun j : Fin n => descPochhammer ℚ j.val)
    (fun j => descPochhammer_natDegree ℚ j.val)
    (fun j => monic_descPochhammer ℚ j.val)
  have hentry (i j : Fin n) :
      (descPochhammer ℚ j.val).eval (d i : ℚ) =
        (Nat.factorial j.val : ℚ) * (Nat.choose (d i) j.val : ℚ) := by
    rw [descPochhammer_eval_eq_descFactorial]
    exact_mod_cast Nat.descFactorial_eq_factorial_mul_choose (d i) j.val
  have hdet := Matrix.det_mul_row (fun j : Fin n => (Nat.factorial j.val : ℚ))
    (fun i j : Fin n => (Nat.choose (d i) j.val : ℚ))
  have heq : (Matrix.of fun i j : Fin n =>
      (descPochhammer ℚ j.val).eval (d i : ℚ)) =
      (Matrix.of fun i j : Fin n =>
        (Nat.factorial j.val : ℚ) * (Nat.choose (d i) j.val : ℚ)) := by
    ext i j
    exact hentry i j
  have hnot : Matrix.det (fun i j : Fin n => (Nat.choose (d i) j.val : ℚ)) ≠ 0 := by
    intro hzero
    apply hvdet
    rw [heval, heq, hdet, hzero, mul_zero]
  change (Matrix.transpose (fun i j : Fin n =>
    (Nat.choose (d i) j.val : ℚ))).det ≠ 0
  erw [Matrix.det_transpose]
  exact hnot

def shifted_hasse_coeff (p : ℚ[X]) (i k : ℕ) :
    (X ^ i * Polynomial.hasseDeriv i p).coeff k =
      (Nat.choose k i : ℚ) * p.coeff k := by
  by_cases hik : i ≤ k
  · rw [Polynomial.coeff_X_pow_mul', if_pos hik, Polynomial.hasseDeriv_coeff,
      Nat.sub_add_cancel hik]
  · rw [Polynomial.coeff_X_pow_mul', if_neg hik,
      Nat.choose_eq_zero_of_lt (Nat.lt_of_not_ge hik)]
    simp

def shifted_hasse_natDegree_le (p : ℚ[X]) (i : ℕ) :
    (X ^ i * Polynomial.hasseDeriv i p).natDegree ≤ p.natDegree := by
  apply Polynomial.natDegree_le_iff_coeff_eq_zero.mpr
  intro k hk
  rw [shifted_hasse_coeff, Polynomial.coeff_eq_zero_of_natDegree_lt hk, mul_zero]

def coeff_prod_sum_of_natDegree_le {ι : Type*} [DecidableEq ι]
    (s : Finset ι) (f : ι → ℚ[X]) (d : ι → ℕ)
    (hd : ∀ i ∈ s, (f i).natDegree ≤ d i) :
    (∏ i ∈ s, f i).coeff (∑ i ∈ s, d i) = ∏ i ∈ s, (f i).coeff (d i) := by
  induction s using Finset.induction_on with
  | empty => simp
  | @insert a s ha ih =>
    have hds : ∀ i ∈ s, (f i).natDegree ≤ d i := fun i hi =>
      hd i (Finset.mem_insert_of_mem hi)
    have hprod : (∏ i ∈ s, f i).natDegree ≤ ∑ i ∈ s, d i := by
      exact (Polynomial.natDegree_prod_le _ _).trans
        (Finset.sum_le_sum hds)
    rw [Finset.prod_insert ha, Finset.sum_insert ha,
      Polynomial.coeff_mul_add_eq_of_natDegree_le (hd a (Finset.mem_insert_self _ _)) hprod,
      ih hds, Finset.prod_insert ha]

def coeff_det_sum_of_column_natDegree_le {n : ℕ}
    (A : Matrix (Fin n) (Fin n) ℚ[X]) (d : Fin n → ℕ)
    (hd : ∀ i j, (A i j).natDegree ≤ d j) :
    A.det.coeff (∑ j, d j) = Matrix.det (fun i j => (A i j).coeff (d j)) := by
  classical
  erw [Matrix.det_apply, Matrix.det_apply]
  simp only [Polynomial.finsetSum_coeff, Polynomial.coeff_smul]
  apply Finset.sum_congr rfl
  intro σ hσ
  congr 1
  exact coeff_prod_sum_of_natDegree_le Finset.univ
    (fun j => A (σ j) j) d (fun j _ => hd (σ j) j)

def polynomialWronskian_ne_zero_of_injective_natDegree {n : ℕ}
    (f : Fin n → ℚ[X]) (hf : ∀ j, f j ≠ 0)
    (hd : Function.Injective (fun j => (f j).natDegree)) :
    polynomialWronskian f ≠ 0 := by
  classical
  let A : Matrix (Fin n) (Fin n) ℚ[X] :=
    fun i j => X ^ i.val * Polynomial.hasseDeriv i.val (f j)
  have hAdeg : ∀ i j, (A i j).natDegree ≤ (f j).natDegree :=
    fun i j => shifted_hasse_natDegree_le (f j) i.val
  have hcoeff := coeff_det_sum_of_column_natDegree_le A
    (fun j => (f j).natDegree) hAdeg
  have hentry (i j : Fin n) : (A i j).coeff (f j).natDegree =
      (f j).leadingCoeff * (Nat.choose (f j).natDegree i.val : ℚ) := by
    change (X ^ i.val * Polynomial.hasseDeriv i.val (f j)).coeff (f j).natDegree = _
    rw [shifted_hasse_coeff, Polynomial.coeff_natDegree, mul_comm]
  have hmatrix : (fun i j : Fin n => (A i j).coeff (f j).natDegree) =
      (Matrix.of fun i j : Fin n =>
        (f j).leadingCoeff * (Nat.choose (f j).natDegree i.val : ℚ)) := by
    funext i j
    exact hentry i j
  rw [hmatrix] at hcoeff
  have hcoeff := hcoeff.trans (Matrix.det_mul_row
    (fun j : Fin n => (f j).leadingCoeff)
    (fun i j : Fin n => (Nat.choose (f j).natDegree i.val : ℚ)))
  have hcoeff_ne : A.det.coeff (∑ j, (f j).natDegree) ≠ 0 := by
    rw [hcoeff]
    apply mul_ne_zero
    · exact Finset.prod_ne_zero_iff.mpr fun j _ => Polynomial.leadingCoeff_ne_zero.mpr (hf j)
    · exact choose_matrix_det_ne_zero (fun j => (f j).natDegree) hd
  have hA : A.det ≠ 0 := by
    intro hzero
    exact hcoeff_ne (by rw [hzero, Polynomial.coeff_zero])
  have hscale : A.det = (∏ i : Fin n, (X : ℚ[X]) ^ i.val) * polynomialWronskian f := by
    exact Matrix.det_mul_column (fun i : Fin n => (X : ℚ[X]) ^ i.val)
      (fun i j : Fin n => Polynomial.hasseDeriv i.val (f j))
  intro hzero
  apply hA
  rw [hscale, hzero, mul_zero]

def polynomialWronskian_sum_smul {n : ℕ} (f g : Fin n → ℚ[X])
    (A : Matrix (Fin n) (Fin n) ℚ)
    (hg : ∀ i, g i = ∑ j, A i j • f j) :
    polynomialWronskian g = polynomialWronskian f * Polynomial.C A.det := by
  classical
  have hmatrix : (fun i j : Fin n => Polynomial.hasseDeriv i.val (g j)) =
      (Matrix.of fun i j : Fin n => Polynomial.hasseDeriv i.val (f j)) *
        Polynomial.C.mapMatrix A.transpose := by
    funext i j
    change Polynomial.hasseDeriv i.val (g j) =
      ∑ k, Polynomial.hasseDeriv i.val (f k) * Polynomial.C (A j k)
    rw [hg j, map_sum]
    apply Finset.sum_congr rfl
    intro k hk
    rw [map_smul, Polynomial.smul_eq_C_mul, mul_comm]
  unfold polynomialWronskian
  rw [hmatrix, Matrix.det_mul, ← Polynomial.C.map_det, Matrix.det_transpose]
  rfl

def polynomialWronskian_ne_zero {n : ℕ} (f : Fin n → ℚ[X])
    (hf : LinearIndependent ℚ f) : polynomialWronskian f ≠ 0 := by
  obtain ⟨A, g, _, hg, hgne, hdeg⟩ := polynomial_degree_echelon f hf
  have hgnz := polynomialWronskian_ne_zero_of_injective_natDegree g hgne hdeg
  intro hzero
  apply hgnz
  rw [polynomialWronskian_sum_smul f g A hg, hzero, zero_mul]

def iterated_derivative_matrix_det_ne_zero {n : ℕ} (f : Fin n → ℚ[X])
    (hf : LinearIndependent ℚ f) :
    Matrix.det (fun i j : Fin n => (Polynomial.derivative^[i.val]) (f j)) ≠ 0 := by
  classical
  have hentry (i j : Fin n) : (Polynomial.derivative^[i.val]) (f j) =
      Polynomial.C (Nat.factorial i.val : ℚ) * Polynomial.hasseDeriv i.val (f j) := by
    rw [← Polynomial.factorial_smul_hasseDeriv]
    change Nat.factorial i.val • Polynomial.hasseDeriv i.val (f j) = _
    simp only [nsmul_eq_mul, map_natCast]
  have hmatrix : (fun i j : Fin n => (Polynomial.derivative^[i.val]) (f j)) =
      (Matrix.of fun i j : Fin n => Polynomial.C (Nat.factorial i.val : ℚ) *
        Polynomial.hasseDeriv i.val (f j)) := by
    funext i j
    exact hentry i j
  erw [hmatrix, Matrix.det_mul_column]
  apply mul_ne_zero
  · apply Finset.prod_ne_zero_iff.mpr
    intro i hi
    exact Polynomial.C_ne_zero.mpr (by exact_mod_cast Nat.factorial_ne_zero i.val)
  · exact polynomialWronskian_ne_zero f hf


end Bounty
end
end RothComponent_UnivariateWronskian

/- Component: PolynomialKronecker; SHA256 3bcc5c80babd01f3df4f7edbb38072ba6017b49dcd8679b5734ed98cb90a582d -/
section RothComponent_PolynomialKronecker
/- Kronecker substitution is injective on a bounded box of monomial exponents. -/

open Polynomial

namespace Bounty

noncomputable section

def kroneckerExponent {m : ℕ} (M : ℕ) (e : Fin m →₀ ℕ) : ℕ :=
  ∑ j, e j * M ^ j.val

def polynomialKronecker (m M : ℕ) : MvPolynomial (Fin m) ℚ →ₐ[ℚ] ℚ[X] :=
  MvPolynomial.aeval fun j => Polynomial.X ^ (M ^ j.val)

def KroneckerBound {m : ℕ} (M : ℕ) (p : MvPolynomial (Fin m) ℚ) : Prop :=
  ∀ e ∈ p.support, ∀ j, e j < M

def kroneckerExponent_injective_on_digits {m M : ℕ} (hM : 1 < M)
    {e v : Fin m →₀ ℕ} (he : ∀ j, e j < M) (hv : ∀ j, v j < M)
    (h : kroneckerExponent M e = kroneckerExponent M v) : e = v := by
  refine Finsupp.ext <| congrFun <| List.ofFn_inj.mp ?_
  apply Nat.ofDigits_inj_of_len_eq hM (by simp)
  · intro a ha
    obtain ⟨j, rfl⟩ := List.mem_ofFn.mp ha
    exact he j
  · intro a ha
    obtain ⟨j, rfl⟩ := List.mem_ofFn.mp ha
    exact hv j
  · simpa only [Nat.ofDigits_eq_sum_mapIdx, List.mapIdx_eq_ofFn, List.get_ofFn,
      List.length_ofFn, Fin.val_cast, List.sum_ofFn, kroneckerExponent] using! h

def polynomialKronecker_monomial {m : ℕ} (M : ℕ) (e : Fin m →₀ ℕ) (a : ℚ) :
    polynomialKronecker m M (MvPolynomial.monomial e a) =
      Polynomial.monomial (kroneckerExponent M e) a := by
  rw [polynomialKronecker, MvPolynomial.aeval_monomial]
  rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _)]
  simp only [← pow_mul, Finset.prod_pow_eq_pow_sum, Polynomial.algebraMap_eq,
    Polynomial.C_mul_X_pow_eq_monomial]
  congr 1
  simp only [kroneckerExponent, mul_comm]

/-- On bounded support, the original coefficient is recovered at its encoded degree. -/
def polynomialKronecker_coeff {m M : ℕ} (hM : 1 < M)
    (p : MvPolynomial (Fin m) ℚ) (hp : KroneckerBound M p)
    (e : Fin m →₀ ℕ) (he : e ∈ p.support) :
    (polynomialKronecker m M p).coeff (kroneckerExponent M e) = MvPolynomial.coeff e p := by
  classical
  nth_rw 1 [MvPolynomial.as_sum p]
  rw [map_sum]
  simp only [polynomialKronecker_monomial, Polynomial.finsetSum_coeff]
  rw [Finset.sum_eq_single e]
  · exact Polynomial.coeff_monomial_same _ _
  · intro v hv hve
    apply Polynomial.coeff_monomial_of_ne
    intro hh
    exact hve (kroneckerExponent_injective_on_digits hM (hp v hv) (hp e he) hh.symm)
  · exact fun hnot => False.elim (hnot he)

def polynomialKronecker_eq_zero_iff {m M : ℕ} (hM : 1 < M)
    (p : MvPolynomial (Fin m) ℚ) (hp : KroneckerBound M p) :
    polynomialKronecker m M p = 0 ↔ p = 0 := by
  constructor
  · intro hzero
    by_contra hpzero
    obtain ⟨e, he⟩ := MvPolynomial.support_nonempty.mpr hpzero
    have hh := polynomialKronecker_coeff hM p hp e he
    rw [hzero, Polynomial.coeff_zero] at hh
    exact (MvPolynomial.mem_support_iff.mp he) hh.symm
  · rintro rfl
    exact map_zero _

def kroneckerBound_linearCombination {m k M : ℕ}
    (f : Fin k → MvPolynomial (Fin m) ℚ) (hf : ∀ i, KroneckerBound M (f i))
    (c : Fin k → ℚ) : KroneckerBound M (∑ i, c i • f i) := by
  classical
  intro e he j
  obtain ⟨i, hi, hei⟩ := Finset.mem_biUnion.mp (MvPolynomial.support_sum he)
  exact hf i e (MvPolynomial.support_smul hei) j

def polynomialKronecker_linearIndependent {m k M : ℕ} (hM : 1 < M)
    (f : Fin k → MvPolynomial (Fin m) ℚ) (hf : LinearIndependent ℚ f)
    (hbound : ∀ i, KroneckerBound M (f i)) :
    LinearIndependent ℚ (fun i => polynomialKronecker m M (f i)) := by
  apply Fintype.linearIndependent_iff.mpr
  intro c hc i
  have hmap : polynomialKronecker m M (∑ j, c j • f j) = 0 := by
    simpa only [map_sum, map_smul] using hc
  have hzero := (polynomialKronecker_eq_zero_iff hM _
    (kroneckerBound_linearCombination f hbound c)).mp hmap
  exact Fintype.linearIndependent_iff.mp hf c hzero i

/-- A common base can be chosen before taking any linear combinations. -/
def exists_polynomialKronecker_linearIndependent {m k : ℕ}
    (f : Fin k → MvPolynomial (Fin m) ℚ) (hf : LinearIndependent ℚ f) :
    ∃ M : ℕ, 2 ≤ M ∧ (∀ i, KroneckerBound M (f i)) ∧
      LinearIndependent ℚ (fun i => polynomialKronecker m M (f i)) := by
  let M : ℕ := 2 + ∑ i, (f i).totalDegree
  have hM : 2 ≤ M := by dsimp only [M]; omega
  have hb (i : Fin k) : KroneckerBound M (f i) := by
    intro e he j
    have hi : (f i).totalDegree ≤ ∑ l, (f l).totalDegree :=
      Finset.single_le_sum (f := fun l : Fin k => (f l).totalDegree)
        (fun _ _ => Nat.zero_le _) (Finset.mem_univ i)
    have hj := (MvPolynomial.monomial_le_degreeOf j he).trans
      (MvPolynomial.degreeOf_le_totalDegree (f i) j)
    dsimp only [M]
    omega
  exact ⟨M, hM, hb, polynomialKronecker_linearIndependent (by omega) f hf hb⟩


end
end Bounty
end RothComponent_PolynomialKronecker

/- Component: WeightedPolynomialIndex; SHA256 e4a7e147839dcc158d4ca744ea00bea9e0820af99684b92047421d25752a2c12 -/
section RothComponent_WeightedPolynomialIndex
/- Weighted Taylor orders of rational multivariate polynomials.  The polynomial
embedding into formal power series preserves every coefficient, allowing the
existing weighted-order domain theorem to supply product additivity. -/

namespace Bounty

noncomputable section
open scoped BigOperators

variable {I : Type*}

/-- Translation by the rational tuple `β`, so its coefficients are Taylor coefficients. -/
def weightedTaylor (β : I → ℚ) : MvPolynomial I ℚ →+* MvPolynomial I ℚ :=
  MvPolynomial.eval₂Hom MvPolynomial.C (fun i => MvPolynomial.X i + MvPolynomial.C (β i))

def weightedTaylor_C (β : I → ℚ) (a : ℚ) :
    weightedTaylor β (MvPolynomial.C a) = MvPolynomial.C a := by
  simp [weightedTaylor]

def weightedTaylor_X (β : I → ℚ) (i : I) :
    weightedTaylor β (MvPolynomial.X i) = MvPolynomial.X i + MvPolynomial.C (β i) := by
  simp [weightedTaylor]

def weightedTaylor_comp (β γ : I → ℚ) (p : MvPolynomial I ℚ) :
    weightedTaylor β (weightedTaylor γ p) = weightedTaylor (β + γ) p := by
  induction p using MvPolynomial.induction_on with
  | C a => simp [weightedTaylor_C]
  | add p q hp hq => simp [map_add, hp, hq]
  | mul_X p i hp => simp [map_mul, map_add, hp, Pi.add_apply, add_assoc,
      weightedTaylor_X, weightedTaylor_C]

def weightedTaylor_zero (p : MvPolynomial I ℚ) : weightedTaylor 0 p = p := by
  induction p using MvPolynomial.induction_on with
  | C a => simp [weightedTaylor_C]
  | add p q hp hq => simp [map_add, hp, hq]
  | mul_X p i hp => simp [map_mul, hp, weightedTaylor_X]

def weightedTaylor_injective (β : I → ℚ) : Function.Injective (weightedTaylor β) := by
  intro p q h
  have hh := congrArg (weightedTaylor (-β)) h
  simpa only [weightedTaylor_comp, neg_add_cancel, weightedTaylor_zero] using hh

def weightedTaylor_eq_zero (β : I → ℚ) (p : MvPolynomial I ℚ) :
    weightedTaylor β p = 0 ↔ p = 0 :=
  (weightedTaylor_injective β).eq_iff' (map_zero _)

/-- Minimum natural weight in the support, with value infinity for the zero polynomial.
The laws below hold even for weights zero; positive Roth weights are a special case. -/
def weightedPolynomialOrder (w : I → ℕ) (p : MvPolynomial I ℚ) : ℕ∞ :=
  MvPowerSeries.weightedOrder w (p : MvPowerSeries I ℚ)

/-- The weighted Taylor-support index at `β`. -/
def weightedPolynomialIndex (w : I → ℕ) (β : I → ℚ) (p : MvPolynomial I ℚ) : ℕ∞ :=
  weightedPolynomialOrder w (weightedTaylor β p)

def weightedPolynomialOrder_eq_top (w : I → ℕ) (p : MvPolynomial I ℚ) :
    weightedPolynomialOrder w p = ⊤ ↔ p = 0 := by
  simp [weightedPolynomialOrder, MvPolynomial.coe_eq_zero_iff]

def weightedPolynomialIndex_eq_top (w : I → ℕ) (β : I → ℚ)
    (p : MvPolynomial I ℚ) : weightedPolynomialIndex w β p = ⊤ ↔ p = 0 := by
  simp [weightedPolynomialIndex, weightedPolynomialOrder_eq_top, weightedTaylor_eq_zero]

def weightedPolynomialIndex_finite (w : I → ℕ) (β : I → ℚ)
    {p : MvPolynomial I ℚ} (hp : p ≠ 0) : weightedPolynomialIndex w β p < ⊤ := by
  exact lt_top_iff_ne_top.mpr (fun h => hp ((weightedPolynomialIndex_eq_top w β p).mp h))

def weightedPolynomialOrder_le_of_coeff (w : I → ℕ) {p : MvPolynomial I ℚ}
    {d : I →₀ ℕ} (hd : MvPolynomial.coeff d p ≠ 0) :
    weightedPolynomialOrder w p ≤ (Finsupp.weight w d : ℕ∞) := by
  exact MvPowerSeries.weightedOrder_le w (by simpa only [MvPolynomial.coeff_coe] using hd)

def weightedPolynomialOrder_le_iff (w : I → ℕ) (p : MvPolynomial I ℚ)
    (n : ℕ∞) : n ≤ weightedPolynomialOrder w p ↔
      ∀ d, MvPolynomial.coeff d p ≠ 0 → n ≤ (Finsupp.weight w d : ℕ∞) := by
  constructor
  · intro hn d hd
    exact hn.trans (weightedPolynomialOrder_le_of_coeff w hd)
  · intro h
    apply MvPowerSeries.le_weightedOrder w
    intro d hd
    change MvPolynomial.coeff d p = 0
    by_contra hc
    exact (not_le_of_gt hd) (h d hc)

def weightedPolynomialOrder_attained (w : I → ℕ) {p : MvPolynomial I ℚ}
    (hp : p ≠ 0) : ∃ d, MvPolynomial.coeff d p ≠ 0 ∧
      (Finsupp.weight w d : ℕ∞) = weightedPolynomialOrder w p := by
  have hp' : (p : MvPowerSeries I ℚ) ≠ 0 := by
    intro hz
    apply hp
    apply MvPolynomial.coe_injective I ℚ
    exact hz
  simpa only [MvPolynomial.coeff_coe, weightedPolynomialOrder] using
    MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder w
      ((MvPowerSeries.ne_zero_iff_weightedOrder_finite w).mp hp')

def weightedPolynomialIndex_attained (w : I → ℕ) (β : I → ℚ)
    {p : MvPolynomial I ℚ} (hp : p ≠ 0) : ∃ d ∈ (weightedTaylor β p).support,
      (Finsupp.weight w d : ℕ∞) = weightedPolynomialIndex w β p := by
  simpa only [MvPolynomial.mem_support_iff, weightedPolynomialIndex] using
    weightedPolynomialOrder_attained w (show weightedTaylor β p ≠ 0 by
      exact fun hz => hp ((weightedTaylor_eq_zero β p).mp hz))

def weightedPolynomialOrder_mul (w : I → ℕ) (p q : MvPolynomial I ℚ) :
    weightedPolynomialOrder w (p * q) = weightedPolynomialOrder w p + weightedPolynomialOrder w q := by
  simp only [weightedPolynomialOrder, MvPolynomial.coe_mul, MvPowerSeries.weightedOrder_mul]

def weightedPolynomialIndex_mul (w : I → ℕ) (β : I → ℚ) (p q : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (p * q) =
      weightedPolynomialIndex w β p + weightedPolynomialIndex w β q := by
  simp only [weightedPolynomialIndex, map_mul, weightedPolynomialOrder_mul]

def weightedPolynomialOrder_add (w : I → ℕ) (p q : MvPolynomial I ℚ) :
    min (weightedPolynomialOrder w p) (weightedPolynomialOrder w q) ≤
      weightedPolynomialOrder w (p + q) := by
  exact MvPowerSeries.min_weightedOrder_le_add w
    (f := (p : MvPowerSeries I ℚ)) (g := (q : MvPowerSeries I ℚ))

def weightedPolynomialIndex_add (w : I → ℕ) (β : I → ℚ) (p q : MvPolynomial I ℚ) :
    min (weightedPolynomialIndex w β p) (weightedPolynomialIndex w β q) ≤
      weightedPolynomialIndex w β (p + q) := by
  simpa only [weightedPolynomialIndex, map_add] using
    weightedPolynomialOrder_add w (weightedTaylor β p) (weightedTaylor β q)

def weightedTaylor_pderiv (β : I → ℚ) (i : I) (p : MvPolynomial I ℚ) :
    weightedTaylor β (MvPolynomial.pderiv i p) = MvPolynomial.pderiv i (weightedTaylor β p) := by
  classical
  induction p using MvPolynomial.induction_on with
  | C a => simp [weightedTaylor_C]
  | add p q hp hq => simp [map_add, hp, hq]
  | mul_X p j hp =>
    by_cases h : j = i
    · subst j
      simp [map_add, map_mul, hp, weightedTaylor_X]
    · simp [map_add, map_mul, hp, MvPolynomial.pderiv_X_of_ne h,
        weightedTaylor_X]

/-- A coordinate derivative can lower the order by at most its coordinate weight.
Writing the bound additively also covers zero polynomials and zero derivatives. -/
def weightedPolynomialOrder_pderiv (w : I → ℕ) (i : I) (p : MvPolynomial I ℚ) :
    weightedPolynomialOrder w p ≤
      weightedPolynomialOrder w (MvPolynomial.pderiv i p) + (w i : ℕ∞) := by
  by_cases hd : MvPolynomial.pderiv i p = 0
  · simp [hd, weightedPolynomialOrder]
  obtain ⟨d, hcoeff, hweight⟩ := weightedPolynomialOrder_attained w hd
  have hp : MvPolynomial.coeff (d + Finsupp.single i 1) p ≠ 0 := by
    rw [MvPolynomial.coeff_pderiv] at hcoeff
    exact left_ne_zero_of_mul hcoeff
  have hh := weightedPolynomialOrder_le_of_coeff w hp
  simpa only [map_add, Finsupp.weight_single, one_nsmul, Nat.cast_add, hweight] using hh

def weightedPolynomialIndex_pderiv (w : I → ℕ) (β : I → ℚ) (i : I)
    (p : MvPolynomial I ℚ) : weightedPolynomialIndex w β p ≤
      weightedPolynomialIndex w β (MvPolynomial.pderiv i p) + (w i : ℕ∞) := by
  simpa only [weightedPolynomialIndex, weightedTaylor_pderiv] using
    weightedPolynomialOrder_pderiv w i (weightedTaylor β p)


end
end Bounty
end RothComponent_WeightedPolynomialIndex

/- Component: WeightedIndexDeterminant; SHA256 c82bfb52fe2ad22ce0b1d32dde07300f80ce5aeeaa7dd4e31aa0a7e0907dc61a -/
section RothComponent_WeightedIndexDeterminant
/- Finite-sum, mixed-derivative, and determinant calculus for the actual weighted
Taylor index.  Derivative words are shared with the generalized Wronskian proof. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I J : Type*}

def weightedPolynomialIndex_zero (w : I → ℕ) (β : I → ℚ) :
    weightedPolynomialIndex w β (0 : MvPolynomial I ℚ) = ⊤ := by
  simp [weightedPolynomialIndex, weightedPolynomialOrder]

def weightedPolynomialIndex_C (w : I → ℕ) (β : I → ℚ) {a : ℚ} (ha : a ≠ 0) :
    weightedPolynomialIndex w β (MvPolynomial.C a) = 0 := by
  simp only [weightedPolynomialIndex, weightedTaylor_C]
  apply le_antisymm
  · have h := weightedPolynomialOrder_le_of_coeff w
      (p := MvPolynomial.C a) (d := 0) (by simpa using ha)
    simpa only [map_zero, Nat.cast_zero] using h
  · exact bot_le

def weightedPolynomialIndex_one (w : I → ℕ) (β : I → ℚ) :
    weightedPolynomialIndex w β (1 : MvPolynomial I ℚ) = 0 := by
  simpa using weightedPolynomialIndex_C w β (one_ne_zero : (1 : ℚ) ≠ 0)

def weightedPolynomialIndex_C_mul (w : I → ℕ) (β : I → ℚ)
    {a : ℚ} (ha : a ≠ 0) (p : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (MvPolynomial.C a * p) = weightedPolynomialIndex w β p := by
  rw [weightedPolynomialIndex_mul, weightedPolynomialIndex_C w β ha, zero_add]

def weightedPolynomialIndex_smul (w : I → ℕ) (β : I → ℚ)
    {a : ℚ} (ha : a ≠ 0) (p : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (a • p) = weightedPolynomialIndex w β p := by
  rw [MvPolynomial.smul_eq_C_mul]
  exact weightedPolynomialIndex_C_mul w β ha p

def weightedPolynomialIndex_neg (w : I → ℕ) (β : I → ℚ)
    (p : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (-p) = weightedPolynomialIndex w β p := by
  simpa only [neg_one_smul] using
    weightedPolynomialIndex_smul w β (neg_ne_zero.mpr (one_ne_zero : (1 : ℚ) ≠ 0)) p

def weightedPolynomialIndex_unit_smul (w : I → ℕ) (β : I → ℚ)
    (u : ℤˣ) (p : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (u • p) = weightedPolynomialIndex w β p := by
  rcases Int.units_eq_one_or u with rfl | rfl
  · simp
  · simp [weightedPolynomialIndex_neg]

def weightedPolynomialIndex_sum_lower (w : I → ℕ) (β : I → ℚ)
    (s : Finset J) (p : J → MvPolynomial I ℚ) (b : ℕ∞)
    (h : ∀ j ∈ s, b ≤ weightedPolynomialIndex w β (p j)) :
    b ≤ weightedPolynomialIndex w β (∑ j ∈ s, p j) := by
  classical
  induction s using Finset.induction_on with
  | empty => simp [weightedPolynomialIndex_zero]
  | @insert a s ha ih =>
    rw [Finset.sum_insert ha]
    exact (le_min (h a (by simp)) (ih (fun j hj => h j (by simp [hj])))).trans
      (weightedPolynomialIndex_add w β (p a) (∑ j ∈ s, p j))

def weightedPolynomialIndex_prod (w : I → ℕ) (β : I → ℚ)
    (s : Finset J) (p : J → MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (∏ j ∈ s, p j) =
      ∑ j ∈ s, weightedPolynomialIndex w β (p j) := by
  classical
  induction s using Finset.induction_on with
  | empty => simp [weightedPolynomialIndex_one]
  | @insert a s ha ih => simp only [Finset.prod_insert ha, Finset.sum_insert ha,
      weightedPolynomialIndex_mul, ih]

/-- A derivative word acts from the right: the head is the last derivative applied. -/
def wordPDeriv : List I → (MvPolynomial I ℚ →ₗ[ℚ] MvPolynomial I ℚ)
  | [] => LinearMap.id
  | i :: s => (MvPolynomial.pderiv i).toLinearMap.comp (wordPDeriv s)

def wordPDeriv_nil (p : MvPolynomial I ℚ) : wordPDeriv [] p = p := rfl

def wordPDeriv_cons (i : I) (s : List I) (p : MvPolynomial I ℚ) :
    wordPDeriv (i :: s) p = MvPolynomial.pderiv i (wordPDeriv s p) := rfl

def wordPDeriv_append (s t : List I) (p : MvPolynomial I ℚ) :
    wordPDeriv (s ++ t) p = wordPDeriv s (wordPDeriv t p) := by
  induction s with
  | nil => rfl
  | cons i s ih => simp only [List.cons_append, wordPDeriv_cons, ih]

def wordDerivativeWeight (w : I → ℕ) (s : List I) : ℕ := (s.map w).sum

def wordDerivativeWeight_nil (w : I → ℕ) : wordDerivativeWeight w [] = 0 := rfl

def wordDerivativeWeight_cons (w : I → ℕ) (i : I) (s : List I) :
    wordDerivativeWeight w (i :: s) = w i + wordDerivativeWeight w s := rfl

def weightedPolynomialIndex_wordPDeriv (w : I → ℕ) (β : I → ℚ)
    (s : List I) (p : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β p ≤ weightedPolynomialIndex w β (wordPDeriv s p) +
      (wordDerivativeWeight w s : ℕ∞) := by
  induction s with
  | nil => simp [wordPDeriv_nil, wordDerivativeWeight_nil]
  | cons i s ih =>
    calc
      weightedPolynomialIndex w β p ≤ weightedPolynomialIndex w β (wordPDeriv s p) +
          (wordDerivativeWeight w s : ℕ∞) := ih
      _ ≤ (weightedPolynomialIndex w β (MvPolynomial.pderiv i (wordPDeriv s p)) +
          (w i : ℕ∞)) + (wordDerivativeWeight w s : ℕ∞) :=
        add_le_add (weightedPolynomialIndex_pderiv w β i (wordPDeriv s p)) le_rfl
      _ = _ := by simp only [wordPDeriv_cons, wordDerivativeWeight_cons, Nat.cast_add, add_assoc]

def weightedPolynomialIndex_det_lower [Fintype J] [DecidableEq J]
    (w : I → ℕ) (β : I → ℚ) (A : Matrix J J (MvPolynomial I ℚ)) (b : ℕ∞)
    (h : ∀ σ : Equiv.Perm J, b ≤ ∑ j, weightedPolynomialIndex w β (A (σ j) j)) :
    b ≤ weightedPolynomialIndex w β A.det := by
  rw [Matrix.det_apply]
  apply weightedPolynomialIndex_sum_lower
  intro σ _
  rw [weightedPolynomialIndex_unit_smul, weightedPolynomialIndex_prod]
  exact h σ

def weightedPolynomialIndex_det_row_loss [Fintype J] [DecidableEq J]
    (w : I → ℕ) (β : I → ℚ) (A : Matrix J J (MvPolynomial I ℚ))
    (b : J → ℕ∞) (r : J → ℕ)
    (h : ∀ i j, b j ≤ weightedPolynomialIndex w β (A i j) + (r i : ℕ∞)) :
    (∑ j, b j) ≤ weightedPolynomialIndex w β A.det + (∑ i, r i : ℕ) := by
  have hb : (∑ j, b j) - (∑ i, r i : ℕ) ≤ weightedPolynomialIndex w β A.det := by
    apply weightedPolynomialIndex_det_lower
    intro σ
    apply tsub_le_iff_right.mpr
    have hh := Finset.sum_le_sum (fun j (_ : j ∈ Finset.univ) => h (σ j) j)
    simpa only [Finset.sum_add_distrib, ← Nat.cast_sum, Equiv.sum_comp σ r] using hh
  exact tsub_le_iff_right.mp hb

/-- Row and column derivative losses, in the truncated form used in the Roth determinant bound. -/
def weightedPolynomialIndex_det_row_column_loss [Fintype J] [DecidableEq J]
    (w : I → ℕ) (β : I → ℚ) (A : Matrix J J (MvPolynomial I ℚ))
    (b : ℕ∞) (r c : J → ℕ)
    (h : ∀ i j, b ≤ weightedPolynomialIndex w β (A i j) + (r i : ℕ∞) + (c j : ℕ∞)) :
    (∑ j : J, (b - (c j : ℕ∞))) ≤ weightedPolynomialIndex w β A.det + (∑ i : J, r i : ℕ) := by
  apply weightedPolynomialIndex_det_row_loss (J := J) w β A (fun j => b - (c j : ℕ∞)) r
  intro i j
  exact tsub_le_iff_right.mpr (h i j)

end
end Bounty
end RothComponent_WeightedIndexDeterminant

/- Component: GeneralizedWronskian; SHA256 fe9db46245ed4fe447e691295ad3976042dba63bf0b958848fcf1b9e81370dd9 -/
section RothComponent_GeneralizedWronskian
/- Generalized polynomial Wronskians via finite chain-rule expansions. -/

noncomputable section


open Polynomial MvPolynomial Matrix Finset

namespace Bounty

def derivative_aeval_eq_sum_pderiv {m : ℕ} (x : Fin m → ℚ[X])
    (p : MvPolynomial (Fin m) ℚ) :
    Polynomial.derivative (MvPolynomial.aeval x p) =
      ∑ j, Polynomial.derivative (x j) * MvPolynomial.aeval x (MvPolynomial.pderiv j p) := by
  classical
  induction p using MvPolynomial.induction_on with
  | C a => simp
  | add p q hp hq =>
    simp only [map_add, hp, hq, mul_add, Finset.sum_add_distrib]
  | mul_X p a hp =>
    simp only [map_mul, MvPolynomial.aeval_X, Polynomial.derivative_mul,
      MvPolynomial.pderiv_mul, map_add, MvPolynomial.pderiv_X,
      Pi.single_apply, hp]
    simp only [mul_add, Finset.sum_add_distrib]
    have hfirst :
        ∑ j : Fin m, Polynomial.derivative (x j) *
          (MvPolynomial.aeval x (MvPolynomial.pderiv j p) * x a) =
        (∑ j : Fin m, Polynomial.derivative (x j) *
          MvPolynomial.aeval x (MvPolynomial.pderiv j p)) * x a := by
      rw [Finset.sum_mul]
      apply Finset.sum_congr rfl
      intro j hj
      ring
    rw [hfirst]
    congr 1
    simp [mul_comm]

def ChainLabel (m : ℕ) : ℕ → Type
  | 0 => Unit
  | n + 1 => Option (Fin m) × ChainLabel m n

abbrev chainLabelFintype (m n : ℕ) : Fintype (ChainLabel m n) := by
  induction n with
  | zero => exact inferInstanceAs (Fintype Unit)
  | succ n ih =>
    letI := ih
    exact inferInstanceAs (Fintype (Option (Fin m) × ChainLabel m n))

def chainWord (m : ℕ) : (n : ℕ) → ChainLabel m n → List (Fin m)
  | 0, _ => []
  | n + 1, (none, a) => chainWord m n a
  | n + 1, (some j, a) => j :: chainWord m n a

def chainCoefficient {m : ℕ} (x : Fin m → ℚ[X]) :
    (n : ℕ) → ChainLabel m n → ℚ[X]
  | 0, _ => 1
  | n + 1, (none, a) => Polynomial.derivative (chainCoefficient x n a)
  | n + 1, (some j, a) => chainCoefficient x n a * Polynomial.derivative (x j)

def chainWord_length_le (m n : ℕ) (a : ChainLabel m n) :
    (chainWord m n a).length ≤ n := by
  induction n with
  | zero => simp [chainWord]
  | succ n ih =>
    rcases a with ⟨j, a⟩
    cases j with
    | none => simpa only [chainWord] using (ih a).trans (Nat.le_succ n)
    | some j => simpa only [chainWord, List.length_cons] using Nat.succ_le_succ (ih a)

def exists_det_summand_ne_zero {k : ℕ} {α : Fin k → Type*}
    [∀ i, Fintype (α i)] (v : ∀ i, α i → Fin k → ℚ[X])
    (h : Matrix.det (fun i j => ∑ a, v i a j) ≠ 0) :
    ∃ a : ∀ i, α i, Matrix.det (fun i j => v i (a i) j) ≠ 0 := by
  classical
  by_contra hnone
  push Not at hnone
  apply h
  have hsum := (Matrix.detRowAlternating (R := ℚ[X]) (n := Fin k)).toMultilinearMap.map_sum v
  change Matrix.det (fun i => ∑ a, v i a) =
    ∑ a : ∀ i, α i, Matrix.det (fun i => v i (a i)) at hsum
  have heq : (fun i j => ∑ a, v i a j) = (fun i => ∑ a, v i a) := by
    funext i j
    simp only [Finset.sum_apply]
  rw [heq, hsum]
  exact Finset.sum_eq_zero (fun a _ => hnone a)

def iterated_derivative_aeval_expansion {m : ℕ} (x : Fin m → ℚ[X])
    (n : ℕ) (p : MvPolynomial (Fin m) ℚ) :
    letI := chainLabelFintype m n
    (Polynomial.derivative^[n]) (MvPolynomial.aeval x p) =
      ∑ a : ChainLabel m n, chainCoefficient x n a *
        MvPolynomial.aeval x (wordPDeriv (chainWord m n a) p) := by
  classical
  letI (t : ℕ) : Fintype (ChainLabel m t) := chainLabelFintype m t
  induction n with
  | zero =>
    have hcard : Fintype.card (ChainLabel m 0) = 1 :=
      (Fintype.card_congr (Equiv.refl Unit)).trans Fintype.card_unit
    simp only [Function.iterate_zero_apply, chainCoefficient, chainWord, wordPDeriv_nil,
      one_mul, Finset.sum_const, Finset.card_univ, hcard, one_nsmul]
  | succ n ih =>
    rw [Function.iterate_succ_apply', ih, map_sum]
    change (∑ a : ChainLabel m n, Polynomial.derivative
      (chainCoefficient x n a * MvPolynomial.aeval x (wordPDeriv (chainWord m n a) p))) =
      ∑ a : Option (Fin m) × ChainLabel m n,
        chainCoefficient x (n + 1) a *
          MvPolynomial.aeval x (wordPDeriv (chainWord m (n + 1) a) p)
    rw [Fintype.sum_prod_type]
    simp only [Fintype.sum_option, chainCoefficient, chainWord, wordPDeriv_cons,
      Polynomial.derivative_mul, derivative_aeval_eq_sum_pderiv, Finset.sum_add_distrib]
    congr 1
    simp_rw [Finset.mul_sum, mul_assoc]
    exact Finset.sum_comm

def exists_generalizedWronskian_ne_zero {m k : ℕ}
    (f : Fin k → MvPolynomial (Fin m) ℚ) (hf : LinearIndependent ℚ f) :
    ∃ w : Fin k → List (Fin m), (∀ i, (w i).length ≤ i.val) ∧
      Matrix.det (fun i j : Fin k => wordPDeriv (w i) (f j)) ≠ 0 := by
  classical
  letI (t : ℕ) : Fintype (ChainLabel m t) := chainLabelFintype m t
  obtain ⟨M, _, _, hli⟩ := exists_polynomialKronecker_linearIndependent f hf
  let x : Fin m → ℚ[X] := fun j => Polynomial.X ^ (M ^ j.val)
  change LinearIndependent ℚ (fun j => MvPolynomial.aeval x (f j)) at hli
  have huniv := iterated_derivative_matrix_det_ne_zero
    (fun j => MvPolynomial.aeval x (f j)) hli
  have hrows : (fun i j : Fin k =>
      (Polynomial.derivative^[i.val]) (MvPolynomial.aeval x (f j))) =
      (fun i j : Fin k => ∑ a : ChainLabel m i.val, chainCoefficient x i.val a *
        MvPolynomial.aeval x (wordPDeriv (chainWord m i.val a) (f j))) := by
    funext i j
    exact iterated_derivative_aeval_expansion x i.val (f j)
  rw [hrows] at huniv
  obtain ⟨a, ha⟩ := exists_det_summand_ne_zero
    (fun (i : Fin k) (b : ChainLabel m i.val) (j : Fin k) =>
      chainCoefficient x i.val b *
        MvPolynomial.aeval x (wordPDeriv (chainWord m i.val b) (f j))) huniv
  refine ⟨fun i => chainWord m i.val (a i), fun i => chainWord_length_le m i.val (a i), ?_⟩
  intro hzero
  apply ha
  change (Matrix.of fun i j : Fin k => chainCoefficient x i.val (a i) *
    MvPolynomial.aeval x (wordPDeriv (chainWord m i.val (a i)) (f j))).det = 0
  erw [Matrix.det_mul_column]
  have hmap : Matrix.det (fun i j : Fin k => MvPolynomial.aeval x
      (wordPDeriv (chainWord m i.val (a i)) (f j))) =
      MvPolynomial.aeval x
        (Matrix.det (fun i j : Fin k => wordPDeriv (chainWord m i.val (a i)) (f j))) := by
    exact ((MvPolynomial.aeval x).map_det
      (fun i j : Fin k => wordPDeriv (chainWord m i.val (a i)) (f j))).symm
  rw [hmap, hzero, map_zero, mul_zero]


end Bounty
end
end RothComponent_GeneralizedWronskian

/- Component: PolynomialSeparatedRank; SHA256 36b5d05b012fc760cf6429bd8884270afd4493e553d7822b6bfe9da8f1799212 -/
section RothComponent_PolynomialSeparatedRank
/- Finite separated-variable rank decompositions obtained from selected coefficients. -/

open Polynomial Module

namespace Bounty

noncomputable section

/-- Select a basis from a finite family, retaining the original indices. -/
def finite_family_basis_indices {V : Type*} [AddCommGroup V] [Module ℚ V]
    {N : ℕ} (v : Fin N → V) :
    ∃ k : ℕ, k ≤ N ∧ ∃ a : Fin k → Fin N, Function.Injective a ∧
      LinearIndependent ℚ (fun j => v (a j)) ∧
      Submodule.span ℚ (Set.range (fun j => v (a j))) =
        Submodule.span ℚ (Set.range v) := by
  classical
  obtain ⟨K, a, ha, hspan, hli⟩ := exists_linearIndependent' ℚ v
  let : Fintype K := Fintype.ofInjective a ha
  let e : Fin (Fintype.card K) ≃ K := (Fintype.equivFin K).symm
  refine ⟨Fintype.card K, ?_, a ∘ e, ha.comp e.injective, hli.comp e e.injective, ?_⟩
  · simpa using Fintype.card_le_of_injective a ha
  · change Submodule.span ℚ (Set.range ((v ∘ a) ∘ e)) = _
    rw [e.surjective.range_comp]
    exact hspan

/-- Coordinates in that selected basis form an identity matrix on the selected rows. -/
def finite_family_coordinate_split {V : Type*} [AddCommGroup V] [Module ℚ V]
    {N : ℕ} (v : Fin N → V) :
    ∃ k : ℕ, k ≤ N ∧ ∃ a : Fin k → Fin N, Function.Injective a ∧
      LinearIndependent ℚ (fun j => v (a j)) ∧
      ∃ c : Fin N → Fin k → ℚ,
        (∀ i, v i = ∑ j, c i j • v (a j)) ∧
        (∀ i j, c (a i) j = if i = j then 1 else 0) := by
  classical
  obtain ⟨k, hk, a, ha, hli, hspan⟩ := finite_family_basis_indices v
  let S := Submodule.span ℚ (Set.range (fun j => v (a j)))
  have hv (i : Fin N) : v i ∈ S := by
    change v i ∈ Submodule.span ℚ (Set.range (fun j => v (a j)))
    rw [hspan]
    exact Submodule.subset_span (Set.mem_range_self i)
  let b := Basis.span hli
  let c (i : Fin N) (j : Fin k) : ℚ := b.repr ⟨v i, hv i⟩ j
  refine ⟨k, hk, a, ha, hli, c, ?_, ?_⟩
  · intro i
    have hh := congrArg (fun y : S => (y : V)) (b.sum_repr ⟨v i, hv i⟩)
    simpa only [Submodule.coe_sum, Submodule.coe_smul, b, Basis.coe_span_apply, c]
      using hh.symm
  · intro i j
    simp [c, b, Basis.span_repr_eq_single, Finsupp.single_apply]

/-- A polynomial over a rational algebra has a separated decomposition of its exact
coefficient rank. The left factors are distinct selected coefficients of the original
polynomial, and the right factors have no greater degree than the original polynomial. -/
def polynomial_separated_rank {A : Type*} [CommRing A] [Algebra ℚ A]
    (P : A[X]) (hP : P ≠ 0) :
    ∃ k : ℕ, 1 ≤ k ∧ k ≤ P.natDegree + 1 ∧
      ∃ a : Fin k → Fin (P.natDegree + 1), Function.Injective a ∧
      ∃ ψ : Fin k → ℚ[X],
        LinearIndependent ℚ (fun j => P.coeff (a j)) ∧
        LinearIndependent ℚ ψ ∧
        (∀ j, (ψ j).natDegree ≤ P.natDegree) ∧
        P = ∑ j, Polynomial.C (P.coeff (a j)) *
          (ψ j).map (algebraMap ℚ A) := by
  classical
  obtain ⟨k, hk, a, ha, hli, c, hc, hdelta⟩ :=
    finite_family_coordinate_split (fun i : Fin (P.natDegree + 1) => P.coeff i)
  let ψ (j : Fin k) : ℚ[X] := Polynomial.ofFn (P.natDegree + 1) (fun i => c i j)
  have hcoeff (j : Fin k) (i : Fin (P.natDegree + 1)) : (ψ j).coeff i = c i j := by
    simp [ψ, Polynomial.ofFn_coeff_eq_val_of_lt, i.isLt]
  have hψ : LinearIndependent ℚ ψ := by
    apply Fintype.linearIndependent_iff.mpr
    intro d hd j
    have hh := congrArg (fun q : ℚ[X] => q.coeff (a j)) hd
    simpa only [Polynomial.finsetSum_coeff, Polynomial.coeff_smul, hcoeff,
      hdelta, smul_eq_mul, mul_ite, mul_one, mul_zero, Finset.sum_ite_eq,
      Finset.mem_univ, if_true, Polynomial.coeff_zero] using hh
  have hdeg (j : Fin k) : (ψ j).natDegree ≤ P.natDegree := by
    have hh := Polynomial.ofFn_natDegree_lt (by omega : 1 ≤ P.natDegree + 1)
      (fun i => c i j)
    exact Nat.lt_succ_iff.mp hh
  have hsplit : P = ∑ j, Polynomial.C (P.coeff (a j)) *
      (ψ j).map (algebraMap ℚ A) := by
    ext n
    simp only [Polynomial.finsetSum_coeff, Polynomial.coeff_C_mul, Polynomial.coeff_map]
    by_cases hn : n < P.natDegree + 1
    · have hh := hc ⟨n, hn⟩
      simp only [Algebra.smul_def, mul_comm] at hh
      simpa only [ψ, Polynomial.ofFn_coeff_eq_val_of_lt _ hn] using hh
    · have hpzero : P.coeff n = 0 := Polynomial.coeff_eq_zero_of_natDegree_lt (by omega)
      rw [hpzero]
      symm
      apply Finset.sum_eq_zero
      intro j hj
      have hqzero : (ψ j).coeff n = 0 :=
        Polynomial.coeff_eq_zero_of_natDegree_lt (by have := hdeg j; omega)
      rw [hqzero, map_zero, mul_zero]
  have hkpos : 1 ≤ k := by
    by_contra hh
    have hkzero : k = 0 := by omega
    subst k
    simp only [Finset.univ_eq_empty, Finset.sum_empty] at hsplit
    exact hP hsplit
  exact ⟨k, hkpos, hk, a, ha, ψ, hli, hψ, hdeg, hsplit⟩

def mvPolynomial_separated_rank {m : ℕ}
    (P : (MvPolynomial (Fin m) ℚ)[X]) (hP : P ≠ 0) :
    ∃ k : ℕ, 1 ≤ k ∧ k ≤ P.natDegree + 1 ∧
      ∃ φ : Fin k → MvPolynomial (Fin m) ℚ, ∃ ψ : Fin k → ℚ[X],
        LinearIndependent ℚ φ ∧ LinearIndependent ℚ ψ ∧
        (∀ j, ∃ n ≤ P.natDegree, φ j = P.coeff n) ∧
        (∀ j, (ψ j).natDegree ≤ P.natDegree) ∧
        P = ∑ j, Polynomial.C (φ j) * (ψ j).map MvPolynomial.C := by
  obtain ⟨k, hkpos, hk, a, ha, ψ, hφ, hψ, hdeg, hsplit⟩ := polynomial_separated_rank P hP
  refine ⟨k, hkpos, hk, (fun j => P.coeff (a j)), ψ, hφ, hψ, ?_, hdeg, ?_⟩
  · intro j
    exact ⟨a j, Nat.lt_succ_iff.mp (a j).isLt, rfl⟩
  · exact hsplit


end
end Bounty
end RothComponent_PolynomialSeparatedRank

/- Component: RationalRootHeight; SHA256 5e47a2a77de45ae7abc1a312c125cb45978f4639e3fd60ab67ea32448faeab0f -/
section RothComponent_RationalRootHeight
/- The one-variable height estimate for the rational polynomial-index argument. -/

namespace Bounty

open Polynomial
noncomputable section

def integerPolynomialCoeffSum (P : ℤ[X]) : ℝ :=
  (P.map (Int.castRingHom ℂ)).sum fun _ a => ‖a‖

def polynomial_mahlerMeasure_pow (P : ℂ[X]) (n : ℕ) :
    (P ^ n).mahlerMeasure = P.mahlerMeasure ^ n := by
  induction n with
  | zero => simp
  | succ n ih => rw [pow_succ, Polynomial.mahlerMeasure_mul, ih, pow_succ]

def integer_linear_mahlerMeasure (p q : ℤ) (hq : q ≠ 0) :
    ((C q * X - C p).map (Int.castRingHom ℂ)).mahlerMeasure =
      max ‖(q : ℂ)‖ ‖(p : ℂ)‖ := by
  have hqc : (q : ℂ) ≠ 0 := by exact_mod_cast hq
  rw [Polynomial.map_sub, Polynomial.map_mul, Polynomial.map_C, Polynomial.map_X, Polynomial.map_C]
  change (C (q : ℂ) * X - C (p : ℂ)).mahlerMeasure = _
  rw [sub_eq_add_neg, ← Polynomial.C_neg]
  rw [Polynomial.mahlerMeasure_C_mul_X_add_C hqc]
  simp only [norm_neg]

def integer_linear_power_height_bound {P : ℤ[X]} (hP : P ≠ 0)
    (p q : ℤ) (hq : q ≠ 0) (n : ℕ) (hdiv : (C q * X - C p) ^ n ∣ P) :
    (max ‖(q : ℂ)‖ ‖(p : ℂ)‖) ^ n ≤ integerPolynomialCoeffSum P := by
  obtain ⟨Q, hPQ⟩ := hdiv
  have hQ : Q ≠ 0 := by
    intro hzero
    apply hP
    rw [hPQ, hzero, mul_zero]
  have hQ1 := Polynomial.one_le_mahlerMeasure_of_ne_zero hQ
  have hm : (P.map (Int.castRingHom ℂ)).mahlerMeasure =
      (max ‖(q : ℂ)‖ ‖(p : ℂ)‖) ^ n *
        (Q.map (Int.castRingHom ℂ)).mahlerMeasure := by
    rw [hPQ, Polynomial.map_mul, Polynomial.map_pow, Polynomial.mahlerMeasure_mul,
      polynomial_mahlerMeasure_pow, integer_linear_mahlerMeasure p q hq]
  calc
    _ ≤ (max ‖(q : ℂ)‖ ‖(p : ℂ)‖) ^ n *
        (Q.map (Int.castRingHom ℂ)).mahlerMeasure :=
      le_mul_of_one_le_right (by positivity) hQ1
    _ = (P.map (Int.castRingHom ℂ)).mahlerMeasure := hm.symm
    _ ≤ integerPolynomialCoeffSum P := Polynomial.mahlerMeasure_le_sum_norm_coeff _

def integer_linear_power_log_height_bound {P : ℤ[X]} (hP : P ≠ 0)
    (p q : ℤ) (hq : q ≠ 0) (n : ℕ) (hdiv : (C q * X - C p) ^ n ∣ P) :
    (n : ℝ) * Real.log (max ‖(q : ℂ)‖ ‖(p : ℂ)‖) ≤
      Real.log (integerPolynomialCoeffSum P) := by
  have hqc : (q : ℂ) ≠ 0 := by exact_mod_cast hq
  have hb : 0 < max ‖(q : ℂ)‖ ‖(p : ℂ)‖ :=
    (norm_pos_iff.mpr hqc).trans_le (le_max_left _ _)
  have hh := Real.log_le_log (pow_pos hb n) (integer_linear_power_height_bound hP p q hq n hdiv)
  simpa only [Real.log_pow] using hh


end
end Bounty
end RothComponent_RationalRootHeight

/- Component: RationalRootMultiplicityHeight; SHA256 f1a3f3c44217673bb3f2ce2b082df98020020d757fce49448b1557f555927f8d -/
section RothComponent_RationalRootMultiplicityHeight
/- Rational root multiplicity, primitive linear factors, and coefficient height. -/

namespace Bounty

open Polynomial
noncomputable section

def rationalRootFactor (β : ℚ) : ℤ[X] := C (β.den : ℤ) * X - C β.num

def rationalRootFactor_primitive (β : ℚ) : (rationalRootFactor β).IsPrimitive := by
  intro a ha
  have hc := (Polynomial.C_dvd_iff_dvd_coeff a _).mp ha
  have hq : a ∣ (β.den : ℤ) := by
    simpa only [rationalRootFactor, Polynomial.coeff_sub, Polynomial.coeff_C_mul_X,
      Polynomial.coeff_C, if_pos, if_neg, Nat.one_ne_zero, ite_false, sub_zero] using hc 1
  have hp : a ∣ β.num := by
    have hh : a ∣ -β.num := by simpa [rationalRootFactor] using hc 0
    simpa using hh
  have hcop : IsCoprime β.num (β.den : ℤ) := by
    apply Int.isCoprime_iff_gcd_eq_one.mpr
    simpa only [Int.gcd_def, Int.natAbs_natCast] using β.reduced
  exact hcop.isUnit_of_dvd' hp hq

def rationalRootFactor_pow_primitive (β : ℚ) (n : ℕ) :
    ((rationalRootFactor β) ^ n).IsPrimitive := by
  induction n with
  | zero => simp
  | succ n ih => simpa only [pow_succ] using ih.mul (rationalRootFactor_primitive β)

def rationalRootFactor_map (β : ℚ) :
    (rationalRootFactor β).map (Int.castRingHom ℚ) =
      C (β.den : ℚ) * (X - C β) := by
  have hden : (β.den : ℚ) ≠ 0 := by exact_mod_cast β.den_ne_zero
  have hnum : (β.den : ℚ) * β = (β.num : ℚ) := by
    calc
      (β.den : ℚ) * β = (β.den : ℚ) * ((β.num : ℚ) / (β.den : ℚ)) :=
        congrArg (fun x : ℚ => (β.den : ℚ) * x) β.num_div_den.symm
      _ = (β.num : ℚ) := by field_simp
  simp only [rationalRootFactor, Polynomial.map_sub, Polynomial.map_mul,
    Polynomial.map_C, Polynomial.map_X]
  change C (β.den : ℚ) * X - C (β.num : ℚ) = _
  rw [mul_sub, ← Polynomial.C_mul, hnum]

def rationalRootFactor_pow_dvd (P : ℤ[X]) (β : ℚ) (n : ℕ)
    (hdiv : (X - C β) ^ n ∣ P.map (Int.castRingHom ℚ)) :
    (rationalRootFactor β) ^ n ∣ P := by
  apply (Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast _ _
    (rationalRootFactor_pow_primitive β n)).mpr
  rw [Polynomial.map_pow, rationalRootFactor_map, mul_pow]
  have hc : IsUnit (C (β.den : ℚ) ^ n : ℚ[X]) :=
    (Polynomial.isUnit_C.mpr (isUnit_iff_ne_zero.mpr (by exact_mod_cast β.den_ne_zero))).pow n
  exact (hc.mul_left_dvd).mpr hdiv

def rational_rootMultiplicity_height_bound {P : ℤ[X]} (hP : P ≠ 0) (β : ℚ) :
    (Polynomial.rootMultiplicity β (P.map (Int.castRingHom ℚ)) : ℝ) *
      Real.log (max ‖(β.den : ℂ)‖ ‖(β.num : ℂ)‖) ≤
      Real.log (integerPolynomialCoeffSum P) := by
  apply integer_linear_power_log_height_bound hP β.num (β.den : ℤ)
    (by exact_mod_cast β.den_ne_zero)
  exact rationalRootFactor_pow_dvd P β _ (Polynomial.pow_rootMultiplicity_dvd _ β)


end
end Bounty
end RothComponent_RationalRootMultiplicityHeight

/- Component: RothIndexNormalization; SHA256 d5e8eae8f8d7c671604ec159d5dc9c64a65e8f32fbd166ec84330954f7532f43 -/
section RothComponent_RothIndexNormalization
/- Real Roth indices obtained by normalizing the actual weighted Taylor order.
The total real-valued definition sends the zero polynomial to zero; all minimum
characterizations and degree bounds below explicitly assume a nonzero polynomial. -/

namespace Bounty

noncomputable section
open scoped BigOperators

def rothDenominator {m : ℕ} (r : Fin m → ℕ) : ℕ := ∏ i, r i

def rothWeight {m : ℕ} (r : Fin m → ℕ) (i : Fin m) : ℕ :=
  ∏ j ∈ Finset.univ.erase i, r j

def rothMonomialWeight {m : ℕ} (r : Fin m → ℕ) (d : Fin m →₀ ℕ) : ℝ :=
  ∑ i, (d i : ℝ) / r i

def rothPolynomialIndex {m : ℕ} (r : Fin m → ℕ) (β : Fin m → ℚ)
    (P : MvPolynomial (Fin m) ℚ) : ℝ :=
  ((weightedPolynomialIndex (rothWeight r) β P).toNat : ℝ) / rothDenominator r

def rothDenominator_pos {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i) :
    0 < rothDenominator r := Finset.prod_pos (fun i _ => hr i)

def rothWeight_mul {m : ℕ} (r : Fin m → ℕ) (i : Fin m) :
    rothWeight r i * r i = rothDenominator r :=
  Finset.prod_erase_mul Finset.univ r (Finset.mem_univ i)

def rothWeight_div_denominator {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (i : Fin m) : (rothWeight r i : ℝ) / rothDenominator r = 1 / (r i : ℝ) := by
  have hD : (rothDenominator r : ℝ) ≠ 0 := by exact_mod_cast (rothDenominator_pos hr).ne'
  have hi : (r i : ℝ) ≠ 0 := by exact_mod_cast (hr i).ne'
  apply (div_eq_div_iff hD hi).mpr
  simpa only [one_mul, ← Nat.cast_mul] using congrArg (fun n : ℕ => (n : ℝ)) (rothWeight_mul r i)

def rothMonomialWeight_eq_normalized_weight {m : ℕ} {r : Fin m → ℕ}
    (hr : ∀ i, 0 < r i) (d : Fin m →₀ ℕ) :
    (Finsupp.weight (rothWeight r) d : ℝ) / rothDenominator r = rothMonomialWeight r d := by
  rw [Finsupp.weight_eq_sum]
  simp only [smul_eq_mul, Nat.cast_sum, Nat.cast_mul, Finset.sum_div, rothMonomialWeight]
  apply Finset.sum_congr rfl
  intro i hi
  rw [mul_div_assoc, rothWeight_div_denominator hr]
  ring

def rothPolynomialIndex_nonneg {m : ℕ} (r : Fin m → ℕ) (β : Fin m → ℚ)
    (P : MvPolynomial (Fin m) ℚ) : 0 ≤ rothPolynomialIndex r β P := by
  unfold rothPolynomialIndex
  positivity

/-- Every nonzero Taylor coefficient supplies an upper bound on the normalized index. -/
def rothPolynomialIndex_le_support {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin m → ℚ) (P : MvPolynomial (Fin m) ℚ)
    {d : Fin m →₀ ℕ} (hd : d ∈ (weightedTaylor β P).support) :
    rothPolynomialIndex r β P ≤ rothMonomialWeight r d := by
  have hh := weightedPolynomialOrder_le_of_coeff (rothWeight r)
    (MvPolynomial.mem_support_iff.mp hd)
  have hn : (weightedPolynomialIndex (rothWeight r) β P).toNat ≤
      Finsupp.weight (rothWeight r) d := ENat.toNat_le_of_le_natCast hh
  rw [← rothMonomialWeight_eq_normalized_weight hr]
  exact div_le_div_of_nonneg_right (by exact_mod_cast hn) (Nat.cast_nonneg _)

/-- The normalized index is attained by an actual nonzero Taylor coefficient. -/
def rothPolynomialIndex_attained {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin m → ℚ) {P : MvPolynomial (Fin m) ℚ} (hP : P ≠ 0) :
    ∃ d ∈ (weightedTaylor β P).support,
      rothPolynomialIndex r β P = rothMonomialWeight r d := by
  obtain ⟨d, hd, hweight⟩ := weightedPolynomialIndex_attained (rothWeight r) β hP
  refine ⟨d, hd, ?_⟩
  have hh := congrArg ENat.toNat hweight
  simp only [ENat.toNat_natCast] at hh
  rw [rothPolynomialIndex, ← hh]
  exact rothMonomialWeight_eq_normalized_weight hr d

def weightedTaylor_monomial_degreeOf_le {m : ℕ} (β : Fin m → ℚ)
    (d : Fin m →₀ ℕ) (a : ℚ) (i : Fin m) :
    (weightedTaylor β (MvPolynomial.monomial d a)).degreeOf i ≤ d i := by
  classical
  rw [weightedTaylor, MvPolynomial.eval₂Hom_monomial,
    Finsupp.prod_fintype _ _ (fun _ => pow_zero _)]
  apply (MvPolynomial.degreeOf_C_mul_le _ i a).trans
  apply (MvPolynomial.degreeOf_prod_le i _ _).trans
  calc
    (∑ j, ((MvPolynomial.X j + MvPolynomial.C (β j)) ^ d j).degreeOf i) ≤
        ∑ j, d j * (if i = j then 1 else 0) := by
      apply Finset.sum_le_sum
      intro j hj
      apply (MvPolynomial.degreeOf_pow_le i _ _).trans
      apply Nat.mul_le_mul_left
      simpa only [MvPolynomial.degreeOf_X, MvPolynomial.degreeOf_C, max_eq_left (Nat.zero_le _)]
        using MvPolynomial.degreeOf_add_le i (MvPolynomial.X j) (MvPolynomial.C (β j))
    _ = d i := by simp

def weightedTaylor_degreeOf_le {m : ℕ} (β : Fin m → ℚ)
    (P : MvPolynomial (Fin m) ℚ) (i : Fin m) :
    (weightedTaylor β P).degreeOf i ≤ P.degreeOf i := by
  classical
  nth_rw 1 [MvPolynomial.as_sum P]
  rw [map_sum]
  apply (MvPolynomial.degreeOf_sum_le i _ _).trans
  apply Finset.sup_le
  intro d hd
  exact (weightedTaylor_monomial_degreeOf_le β d (MvPolynomial.coeff d P) i).trans
    (MvPolynomial.monomial_le_degreeOf i hd)

def weightedTaylor_degreeOf {m : ℕ} (β : Fin m → ℚ)
    (P : MvPolynomial (Fin m) ℚ) (i : Fin m) :
    (weightedTaylor β P).degreeOf i = P.degreeOf i := by
  apply le_antisymm (weightedTaylor_degreeOf_le β P i)
  simpa only [weightedTaylor_comp, neg_add_cancel, weightedTaylor_zero] using
    weightedTaylor_degreeOf_le (-β) (weightedTaylor β P) i

def rothPolynomialIndex_le_dimension {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin m → ℚ) {P : MvPolynomial (Fin m) ℚ} (hP : P ≠ 0)
    (hdegree : ∀ i, P.degreeOf i ≤ r i) : rothPolynomialIndex r β P ≤ m := by
  obtain ⟨d, hd, heq⟩ := rothPolynomialIndex_attained hr β hP
  rw [heq, rothMonomialWeight]
  calc
    (∑ i : Fin m, (d i : ℝ) / r i) ≤ ∑ _i : Fin m, (1 : ℝ) := by
      apply Finset.sum_le_sum
      intro i hi
      apply (div_le_one (by exact_mod_cast hr i)).mpr
      exact_mod_cast (MvPolynomial.monomial_le_degreeOf i hd).trans
        ((weightedTaylor_degreeOf β P i).le.trans (hdegree i))
    _ = m := by simp

def rothMonomialWeight_scale {m : ℕ} (r : Fin m → ℕ) (k : ℕ)
    (d : Fin m →₀ ℕ) :
    rothMonomialWeight (fun i => k * r i) d = rothMonomialWeight r d / k := by
  simp only [rothMonomialWeight, Nat.cast_mul, Finset.sum_div]
  apply Finset.sum_congr rfl
  intro i hi
  rw [div_div, mul_comm]

def rothPolynomialIndex_scale {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin m → ℚ) {P : MvPolynomial (Fin m) ℚ} (hP : P ≠ 0)
    {k : ℕ} (hk : 0 < k) :
    rothPolynomialIndex (fun i => k * r i) β P = rothPolynomialIndex r β P / k := by
  have hkr (i : Fin m) : 0 < k * r i := Nat.mul_pos hk (hr i)
  have hkreal : (0 : ℝ) ≤ k := Nat.cast_nonneg k
  obtain ⟨d, hd, heq⟩ := rothPolynomialIndex_attained hr β hP
  obtain ⟨e, he, heq'⟩ := rothPolynomialIndex_attained hkr β hP
  apply le_antisymm
  · calc
      _ ≤ rothMonomialWeight (fun i => k * r i) d :=
        rothPolynomialIndex_le_support hkr β P hd
      _ = _ := by rw [rothMonomialWeight_scale, heq]
  · calc
      _ ≤ rothMonomialWeight r e / k :=
        div_le_div_of_nonneg_right (rothPolynomialIndex_le_support hr β P he) hkreal
      _ = _ := by rw [heq', rothMonomialWeight_scale]

def rothPolynomialIndex_mul {m : ℕ} (r : Fin m → ℕ) (β : Fin m → ℚ)
    {P Q : MvPolynomial (Fin m) ℚ} (hP : P ≠ 0) (hQ : Q ≠ 0) :
    rothPolynomialIndex r β (P * Q) = rothPolynomialIndex r β P + rothPolynomialIndex r β Q := by
  simp only [rothPolynomialIndex, weightedPolynomialIndex_mul,
    ENat.toNat_add (weightedPolynomialIndex_finite _ _ hP).ne
      (weightedPolynomialIndex_finite _ _ hQ).ne, Nat.cast_add, add_div]


end
end Bounty
end RothComponent_RothIndexNormalization

/- Component: RothUnivariateIndex; SHA256 8f7f621ecf9f8eb932902c07e9f454b1f4ffc64189fef0dc80602b18c0c6932c -/
section RothComponent_RothUnivariateIndex
/- The normalized one-variable Taylor index is rational-root multiplicity divided by degree. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Polynomial

def unique_weightedTaylor (β : Fin 1 → ℚ) (P : MvPolynomial (Fin 1) ℚ) :
    MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) (weightedTaylor β P) =
      (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) P).comp (Polynomial.X + Polynomial.C (β 0)) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [MvPolynomial.uniqueAlgEquiv_apply, weightedTaylor_C]
  | add P Q hP hQ => simp [map_add, hP, hQ]
  | mul_X P i hP =>
    have hi : i = 0 := Subsingleton.elim _ _
    subst i
    simp [map_mul, map_add, hP, MvPolynomial.uniqueAlgEquiv_apply,
      weightedTaylor_X]

def rothPolynomialIndex_eq_rootMultiplicity {r : Fin 1 → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin 1 → ℚ) {P : MvPolynomial (Fin 1) ℚ} (hP : P ≠ 0) :
    rothPolynomialIndex r β P =
      ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) P).rootMultiplicity (β 0) : ℝ) / r 0 := by
  rw [Polynomial.rootMultiplicity_eq_natTrailingDegree, ← unique_weightedTaylor]
  let T := weightedTaylor β P
  let Q := MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) T
  have hT : T ≠ 0 := fun hz => hP ((weightedTaylor_eq_zero β P).mp hz)
  have hQ : Q ≠ 0 := by
    intro hz
    apply hT
    exact (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).injective
      (hz.trans (map_zero _).symm)
  change rothPolynomialIndex r β P = (Q.natTrailingDegree : ℝ) / r 0
  apply le_antisymm
  · have hc := Polynomial.coeff_natTrailingDegree_ne_zero.mpr hQ
    change (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) T).coeff Q.natTrailingDegree ≠ 0 at hc
    rw [MvPolynomial.coeff_uniqueAlgEquiv] at hc
    have hu := rothPolynomialIndex_le_support hr β P (MvPolynomial.mem_support_iff.mpr hc)
    simpa [rothMonomialWeight] using hu
  · obtain ⟨d, hd, heq⟩ := rothPolynomialIndex_attained hr β hP
    have hd' : Q.coeff (d 0) ≠ 0 := by
      change (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) T).coeff (d 0) ≠ 0
      rw [MvPolynomial.coeff_uniqueAlgEquiv]
      have hdEq : Finsupp.single (0 : Fin 1) (d 0) = d := by
        simpa using (Finsupp.unique_single d).symm
      change MvPolynomial.coeff (Finsupp.single (0 : Fin 1) (d 0)) T ≠ 0
      rw [hdEq]
      exact MvPolynomial.mem_support_iff.mp hd
    have hn := Polynomial.natTrailingDegree_le_of_ne_zero hd'
    rw [heq]
    simp only [rothMonomialWeight, Fin.sum_univ_one]
    exact div_le_div_of_nonneg_right (by exact_mod_cast hn) (Nat.cast_nonneg _)

def rothUnivariate_integer_height_bound (r : Fin 1 → ℕ) (hr : ∀ i, 0 < r i)
    (β : Fin 1 → ℚ) {P : ℤ[X]} (hP : P ≠ 0) :
    rothPolynomialIndex r β ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm
      (P.map (Int.castRingHom ℚ))) *
        ((r 0 : ℝ) * Real.log (max ‖((β 0).den : ℂ)‖ ‖((β 0).num : ℂ)‖)) ≤
      Real.log (integerPolynomialCoeffSum P) := by
  have hPQ : P.map (Int.castRingHom ℚ) ≠ 0 := by
    intro hz
    apply hP
    exact (Polynomial.map_injective (Int.castRingHom ℚ) Int.cast_injective)
      (hz.trans (Polynomial.map_zero _).symm)
  have hM : (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm (P.map (Int.castRingHom ℚ)) ≠ 0 := by
    intro hz
    apply hPQ
    exact (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm.injective
      (hz.trans (map_zero _).symm)
  rw [rothPolynomialIndex_eq_rootMultiplicity hr β hM, AlgEquiv.apply_symm_apply]
  have hr0 : (r 0 : ℝ) ≠ 0 := by exact_mod_cast (hr 0).ne'
  rw [div_mul_eq_mul_div, mul_div_assoc, mul_div_cancel_left₀ _ hr0]
  exact rational_rootMultiplicity_height_bound hP (β 0)


end
end Bounty
end RothComponent_RothUnivariateIndex

/- Component: PolynomialCoefficientNorm; SHA256 3121619c6ec30ab1ef03b1743098af5be37e6d61132039e91563bcb5a8c2cc04 -/
section RothComponent_PolynomialCoefficientNorm
/- The coefficient sum norm needed in the rational Roth polynomial argument. -/

namespace Bounty

noncomputable section
open scoped BigOperators

variable {I R : Type*} [NormedCommRing R]

def polynomialCoeffL1 (P : MvPolynomial I R) : ℝ :=
  ∑ d ∈ P.support, ‖MvPolynomial.coeff d P‖

def polynomialCoeffL1_nonneg (P : MvPolynomial I R) : 0 ≤ polynomialCoeffL1 P := by
  exact Finset.sum_nonneg (fun _ _ => norm_nonneg _)

def polynomialCoeffL1_zero : polynomialCoeffL1 (0 : MvPolynomial I R) = 0 := by
  simp [polynomialCoeffL1]

def polynomialCoeffL1_sum_of_support_subset (P : MvPolynomial I R)
    (s : Finset (I →₀ ℕ)) (hs : P.support ⊆ s) :
    polynomialCoeffL1 P = ∑ d ∈ s, ‖MvPolynomial.coeff d P‖ := by
  classical
  apply Finset.sum_subset hs
  intro d _ hd
  rw [MvPolynomial.notMem_support_iff.mp hd, norm_zero]

def polynomialCoeffL1_add (P Q : MvPolynomial I R) :
    polynomialCoeffL1 (P + Q) ≤ polynomialCoeffL1 P + polynomialCoeffL1 Q := by
  classical
  let s := P.support ∪ Q.support
  rw [polynomialCoeffL1_sum_of_support_subset (P + Q) s MvPolynomial.support_add,
    polynomialCoeffL1_sum_of_support_subset P s Finset.subset_union_left,
    polynomialCoeffL1_sum_of_support_subset Q s Finset.subset_union_right,
    ← Finset.sum_add_distrib]
  exact Finset.sum_le_sum (fun d _ => by simpa using norm_add_le (MvPolynomial.coeff d P) (MvPolynomial.coeff d Q))

def polynomialCoeffL1_sum {J : Type*} (s : Finset J) (P : J → MvPolynomial I R) :
    polynomialCoeffL1 (∑ j ∈ s, P j) ≤ ∑ j ∈ s, polynomialCoeffL1 (P j) := by
  classical
  induction s using Finset.induction_on with
  | empty => simp [polynomialCoeffL1_zero]
  | @insert a s ha ih =>
    rw [Finset.sum_insert ha, Finset.sum_insert ha]
    exact (polynomialCoeffL1_add _ _).trans (add_le_add le_rfl ih)

def polynomialCoeffL1_monomial (d : I →₀ ℕ) (a : R) :
    polynomialCoeffL1 (MvPolynomial.monomial d a) = ‖a‖ := by
  classical
  exact MvPolynomial.sum_monomial_eq (norm_zero : ‖(0 : R)‖ = 0)

def polynomialCoeffL1_C (a : R) :
    polynomialCoeffL1 (MvPolynomial.C a : MvPolynomial I R) = ‖a‖ := by
  exact polynomialCoeffL1_monomial 0 a

def polynomialCoeffL1_one [NormOneClass R] :
    polynomialCoeffL1 (1 : MvPolynomial I R) = 1 := by
  rw [← MvPolynomial.C_1, polynomialCoeffL1_C, norm_one]

def polynomialCoeffL1_mul (P Q : MvPolynomial I R) :
    polynomialCoeffL1 (P * Q) ≤ polynomialCoeffL1 P * polynomialCoeffL1 Q := by
  classical
  have hprod : P * Q = ∑ d ∈ P.support, ∑ e ∈ Q.support,
      MvPolynomial.monomial (d + e) (MvPolynomial.coeff d P * MvPolynomial.coeff e Q) := by
    conv_lhs => rw [MvPolynomial.as_sum P, MvPolynomial.as_sum Q]
    simp only [Finset.sum_mul, Finset.mul_sum, MvPolynomial.monomial_mul]
    exact Finset.sum_comm
  rw [hprod]
  calc
    _ ≤ ∑ d ∈ P.support, polynomialCoeffL1 (∑ e ∈ Q.support,
        MvPolynomial.monomial (d + e) (MvPolynomial.coeff d P * MvPolynomial.coeff e Q)) :=
      polynomialCoeffL1_sum _ _
    _ ≤ ∑ d ∈ P.support, ∑ e ∈ Q.support,
        polynomialCoeffL1 (MvPolynomial.monomial (d + e)
          (MvPolynomial.coeff d P * MvPolynomial.coeff e Q)) :=
      Finset.sum_le_sum (fun _ _ => polynomialCoeffL1_sum _ _)
    _ ≤ ∑ d ∈ P.support, ∑ e ∈ Q.support,
        ‖MvPolynomial.coeff d P‖ * ‖MvPolynomial.coeff e Q‖ := by
      apply Finset.sum_le_sum
      intro d _
      apply Finset.sum_le_sum
      intro e _
      rw [polynomialCoeffL1_monomial]
      exact norm_mul_le _ _
    _ = polynomialCoeffL1 P * polynomialCoeffL1 Q := by
      simp only [polynomialCoeffL1, Finset.sum_mul, Finset.mul_sum]
      exact Finset.sum_comm

def polynomialCoeffL1_prod [NormOneClass R] {J : Type*} (s : Finset J)
    (P : J → MvPolynomial I R) :
    polynomialCoeffL1 (∏ j ∈ s, P j) ≤ ∏ j ∈ s, polynomialCoeffL1 (P j) := by
  classical
  induction s using Finset.induction_on with
  | empty => simp [polynomialCoeffL1_one]
  | @insert a s ha ih =>
    rw [Finset.prod_insert ha, Finset.prod_insert ha]
    exact (polynomialCoeffL1_mul _ _).trans
      (mul_le_mul_of_nonneg_left ih (polynomialCoeffL1_nonneg _))

def norm_coeff_le_polynomialCoeffL1 (P : MvPolynomial I R) (d : I →₀ ℕ) :
    ‖MvPolynomial.coeff d P‖ ≤ polynomialCoeffL1 P := by
  classical
  by_cases hd : d ∈ P.support
  · exact Finset.single_le_sum (fun _ _ => norm_nonneg _) hd
  · simp only [MvPolynomial.notMem_support_iff.mp hd, norm_zero]
    exact polynomialCoeffL1_nonneg _

def polynomialCoeffL1_pos {P : MvPolynomial I R} (hP : P ≠ 0) :
    0 < polynomialCoeffL1 P := by
  classical
  obtain ⟨d, hd⟩ := MvPolynomial.exists_coeff_ne_zero hP
  exact (norm_pos_iff.mpr hd).trans_le (norm_coeff_le_polynomialCoeffL1 P d)


end
end Bounty
end RothComponent_PolynomialCoefficientNorm

/- Component: PolynomialCoefficientDeterminant; SHA256 3776cae0ad95603c49cc4dcafcbfaa27ed1e8adda8cb741bae810b1d716bcca1 -/
section RothComponent_PolynomialCoefficientDeterminant
/- Coefficient norm bounds for determinant auxiliary polynomials. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I R J : Type*} [NormedCommRing R]

def polynomialCoeffL1_neg (P : MvPolynomial I R) :
    polynomialCoeffL1 (-P) = polynomialCoeffL1 P := by
  classical
  simp [polynomialCoeffL1]

def polynomialCoeffL1_unit_smul (u : ℤˣ) (P : MvPolynomial I R) :
    polynomialCoeffL1 (u • P) = polynomialCoeffL1 P := by
  rcases Int.units_eq_one_or u with rfl | rfl <;> simp [polynomialCoeffL1_neg]

def polynomialCoeffL1_det [NormOneClass R] [Fintype J] [DecidableEq J]
    (A : Matrix J J (MvPolynomial I R)) :
    polynomialCoeffL1 A.det ≤
      ∑ σ : Equiv.Perm J, ∏ j, polynomialCoeffL1 (A (σ j) j) := by
  rw [Matrix.det_apply]
  apply (polynomialCoeffL1_sum _ _).trans
  apply Finset.sum_le_sum
  intro σ _
  rw [polynomialCoeffL1_unit_smul]
  exact polynomialCoeffL1_prod _ _

def polynomialCoeffL1_det_le [NormOneClass R] [Fintype J] [DecidableEq J]
    (A : Matrix J J (MvPolynomial I R)) (B : ℝ) (_hB : 0 ≤ B)
    (hA : ∀ i j, polynomialCoeffL1 (A i j) ≤ B) :
    polynomialCoeffL1 A.det ≤ (Fintype.card J).factorial * B ^ Fintype.card J := by
  calc
    _ ≤ ∑ σ : Equiv.Perm J, ∏ j, polynomialCoeffL1 (A (σ j) j) := polynomialCoeffL1_det A
    _ ≤ ∑ _σ : Equiv.Perm J, ∏ _j : J, B := by
      apply Finset.sum_le_sum
      intro σ _
      exact Finset.prod_le_prod (fun j _ => polynomialCoeffL1_nonneg _) (fun j _ => hA (σ j) j)
    _ = (Fintype.card J).factorial * B ^ Fintype.card J := by
      simp [Fintype.card_perm]

def polynomialCoeffL1_det_log_le [NormOneClass R] [Fintype J] [DecidableEq J]
    (A : Matrix J J (MvPolynomial I R)) (hdet : A.det ≠ 0)
    (B : ℝ) (hB : 0 < B) (hA : ∀ i j, polynomialCoeffL1 (A i j) ≤ B) :
    Real.log (polynomialCoeffL1 A.det) ≤
      Real.log ((Fintype.card J).factorial : ℝ) + (Fintype.card J : ℝ) * Real.log B := by
  have hf : (0 : ℝ) < (Fintype.card J).factorial := by exact_mod_cast Nat.factorial_pos _
  have h := Real.log_le_log (polynomialCoeffL1_pos hdet)
    (polynomialCoeffL1_det_le A B hB.le hA)
  rwa [Real.log_mul hf.ne' (pow_pos hB _).ne', Real.log_pow] at h


end
end Bounty
end RothComponent_PolynomialCoefficientDeterminant

/- Component: DividedWordDerivatives; SHA256 1e32467e609f852e2772902b0b2f850f42fa8b5371df2ba893b288b35f59e72f -/
section RothComponent_DividedWordDerivatives
/- Exact coefficients of derivative words and their divided normalization. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I : Type*} [Fintype I] [DecidableEq I]

/-- The multiplicity of each coordinate in a derivative word. -/
def wordDerivativeCounts (s : List I) : I →₀ ℕ :=
  Finsupp.equivFunOnFinite.symm (fun i => s.count i)

def wordDerivativeCounts_apply (s : List I) (i : I) :
    wordDerivativeCounts s i = s.count i := rfl

def wordDerivativeCounts_nil : wordDerivativeCounts ([] : List I) = 0 := by
  ext i
  simp [wordDerivativeCounts_apply]

def wordDerivativeCounts_cons (i : I) (s : List I) :
    wordDerivativeCounts (i :: s) = Finsupp.single i 1 + wordDerivativeCounts s := by
  ext j
  by_cases h : j = i
  · subst j
    simp [add_comm, wordDerivativeCounts_apply]
  · simp [List.count_cons_of_ne (Ne.symm h), h, wordDerivativeCounts_apply]

def derivativeFallingProduct (a c : I →₀ ℕ) : ℚ :=
  ∏ i, ((a i + c i).descFactorial (c i) : ℚ)

private def descFactorial_step (a c : ℕ) :
    (a + (1 + c)).descFactorial (1 + c) =
      (a + 1 + c).descFactorial c * (a + 1) := by
  rw [Nat.add_comm 1 c, Nat.descFactorial_succ]
  have he : a + (c + 1) = a + 1 + c := by omega
  rw [he, Nat.add_sub_cancel]
  exact Nat.mul_comm _ _

private def derivativeFallingProduct_step (a c : I →₀ ℕ) (i : I) :
    derivativeFallingProduct a (Finsupp.single i 1 + c) =
      derivativeFallingProduct (a + Finsupp.single i 1) c * (a i + 1) := by
  have hfactor (j : I) :
      ((a j + (Finsupp.single i 1 + c : I →₀ ℕ) j).descFactorial
        ((Finsupp.single i 1 + c : I →₀ ℕ) j) : ℚ) =
        ((((a + Finsupp.single i 1 : I →₀ ℕ) j) + c j).descFactorial (c j) : ℚ) *
          (if j = i then (a i + 1 : ℚ) else 1) := by
    by_cases h : j = i
    · subst j
      simp only [Finsupp.add_apply, Finsupp.single_eq_same, if_pos rfl]
      exact_mod_cast descFactorial_step (a i) (c i)
    · simp [Finsupp.single_apply, h, Ne.symm h]
  simp only [derivativeFallingProduct, hfactor, Finset.prod_mul_distrib]
  simp

def coeff_wordPDeriv (s : List I) (P : MvPolynomial I ℚ) (a : I →₀ ℕ) :
    MvPolynomial.coeff a (wordPDeriv s P) =
      MvPolynomial.coeff (a + wordDerivativeCounts s) P *
        derivativeFallingProduct a (wordDerivativeCounts s) := by
  induction s generalizing a with
  | nil => simp [derivativeFallingProduct, wordPDeriv_nil, wordDerivativeCounts_nil]
  | cons i s ih =>
    rw [wordPDeriv_cons, MvPolynomial.coeff_pderiv, ih,
      wordDerivativeCounts_cons, derivativeFallingProduct_step]
    simp only [add_assoc, mul_assoc]

def coeff_wordPDeriv_descFactorial (s : List I) (P : MvPolynomial I ℚ) (a : I →₀ ℕ) :
    MvPolynomial.coeff a (wordPDeriv s P) =
      MvPolynomial.coeff (a + wordDerivativeCounts s) P *
        ∏ i, ((a i + s.count i).descFactorial (s.count i) : ℚ) := by
  simpa only [derivativeFallingProduct, wordDerivativeCounts_apply] using coeff_wordPDeriv s P a

/-- The nonzero rational product of the coordinate factorials. -/
def wordDerivativeFactorial (s : List I) : ℚ := ∏ i, ((s.count i).factorial : ℚ)

def wordDerivativeFactorial_ne_zero (s : List I) : wordDerivativeFactorial s ≠ 0 := by
  apply Finset.prod_ne_zero_iff.mpr
  intro i _
  exact Nat.cast_ne_zero.mpr (Nat.factorial_ne_zero _)

def dividedWordPDeriv (s : List I) : MvPolynomial I ℚ →ₗ[ℚ] MvPolynomial I ℚ :=
  (wordDerivativeFactorial s)⁻¹ • wordPDeriv s

def coeff_dividedWordPDeriv (s : List I) (P : MvPolynomial I ℚ) (a : I →₀ ℕ) :
    MvPolynomial.coeff a (dividedWordPDeriv s P) =
      MvPolynomial.coeff (a + wordDerivativeCounts s) P *
        ∏ i, ((a i + s.count i).choose (s.count i) : ℚ) := by
  change MvPolynomial.coeff a ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P) = _
  rw [MvPolynomial.coeff_smul, coeff_wordPDeriv_descFactorial, smul_eq_mul]
  simp_rw [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul]
  rw [Finset.prod_mul_distrib]
  change (wordDerivativeFactorial s)⁻¹ *
    (MvPolynomial.coeff (a + wordDerivativeCounts s) P *
      (wordDerivativeFactorial s * ∏ i, ((a i + s.count i).choose (s.count i) : ℚ))) = _
  calc
    _ = ((wordDerivativeFactorial s)⁻¹ * wordDerivativeFactorial s) *
        (MvPolynomial.coeff (a + wordDerivativeCounts s) P *
          ∏ i, ((a i + s.count i).choose (s.count i) : ℚ)) := by ring
    _ = _ := by rw [inv_mul_cancel₀ (wordDerivativeFactorial_ne_zero s), one_mul]

def dividedWordPDeriv_integral (s : List I) (P : MvPolynomial I ℚ)
    (hP : ∀ a, ∃ z : ℤ, MvPolynomial.coeff a P = (z : ℚ)) :
    ∀ a, ∃ z : ℤ, MvPolynomial.coeff a (dividedWordPDeriv s P) = (z : ℚ) := by
  intro a
  obtain ⟨z, hz⟩ := hP (a + wordDerivativeCounts s)
  refine ⟨z * ∏ i, ((a i + s.count i).choose (s.count i) : ℤ), ?_⟩
  rw [coeff_dividedWordPDeriv, hz]
  simp

def derivativeChooseProduct_le (s : List I) (a : I →₀ ℕ) (r : I → ℕ)
    (hr : ∀ i, a i + s.count i ≤ r i) :
    (∏ i, (a i + s.count i).choose (s.count i)) ≤ 2 ^ (∑ i, r i) := by
  calc
    _ ≤ ∏ i, 2 ^ r i := Finset.prod_le_prod' (fun i _ =>
      (Nat.choose_le_two_pow _ _).trans (Nat.pow_le_pow_right (by decide) (hr i)))
    _ = _ := Finset.prod_pow_eq_pow_sum Finset.univ r 2

def weightedPolynomialIndex_dividedWordPDeriv (w : I → ℕ) (β : I → ℚ)
    (s : List I) (P : MvPolynomial I ℚ) :
    weightedPolynomialIndex w β (dividedWordPDeriv s P) =
      weightedPolynomialIndex w β (wordPDeriv s P) := by
  exact weightedPolynomialIndex_smul w β
    (inv_ne_zero (wordDerivativeFactorial_ne_zero s)) (wordPDeriv s P)


end
end Bounty
end RothComponent_DividedWordDerivatives

/- Component: DividedDerivativeCoefficientNorm; SHA256 a39c7c7bfbfcd4a15a0bef6ac1f673e7eb83c5c91c953956674649d9958d50e8 -/
section RothComponent_DividedDerivativeCoefficientNorm
/- Divided derivatives have coefficient growth exponential in the total degree. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I : Type*} [Fintype I] [DecidableEq I]

def PolynomialBoxBound (r : I → ℕ) (P : MvPolynomial I ℚ) : Prop :=
  ∀ a ∈ P.support, ∀ i, a i ≤ r i

def dividedWordPDeriv_support_shift (s : List I) (P : MvPolynomial I ℚ)
    {a : I →₀ ℕ} (ha : a ∈ (dividedWordPDeriv s P).support) :
    a + wordDerivativeCounts s ∈ P.support := by
  apply MvPolynomial.mem_support_iff.mpr
  have h := MvPolynomial.mem_support_iff.mp ha
  rw [coeff_dividedWordPDeriv] at h
  exact left_ne_zero_of_mul h

def polynomialBoxBound_dividedWordPDeriv (s : List I) {r : I → ℕ}
    {P : MvPolynomial I ℚ} (hP : PolynomialBoxBound r P) :
    PolynomialBoxBound r (dividedWordPDeriv s P) := by
  intro a ha i
  exact (Nat.le_add_right (a i) (wordDerivativeCounts s i)).trans
    (hP _ (dividedWordPDeriv_support_shift s P ha) i)

def polynomialCoeffL1_dividedWordPDeriv (s : List I) (r : I → ℕ)
    (P : MvPolynomial I ℚ) (hP : PolynomialBoxBound r P) :
    polynomialCoeffL1 (dividedWordPDeriv s P) ≤
      (2 : ℝ) ^ (∑ i, r i) * polynomialCoeffL1 P := by
  classical
  let c := wordDerivativeCounts s
  have hentry (a : I →₀ ℕ) (ha : a ∈ (dividedWordPDeriv s P).support) :
      ‖MvPolynomial.coeff a (dividedWordPDeriv s P)‖ ≤
        (2 : ℝ) ^ (∑ i, r i) * ‖MvPolynomial.coeff (a + c) P‖ := by
    have hr : ∀ i, a i + s.count i ≤ r i :=
      fun i => hP _ (dividedWordPDeriv_support_shift s P ha) i
    have hchoose := derivativeChooseProduct_le s a r hr
    have hnorm : ‖(∏ i, ((a i + s.count i).choose (s.count i) : ℚ))‖ ≤
        (2 : ℝ) ^ (∑ i, r i) := by
      rw [← Nat.cast_prod]
      rw [← Rat.norm_cast_real]
      push_cast
      rw [Real.norm_of_nonneg (by positivity)]
      exact (show ((∏ i, (a i + s.count i).choose (s.count i)) : ℝ) ≤
          (2 : ℝ) ^ (∑ i, r i) from by exact_mod_cast hchoose)
    rw [coeff_dividedWordPDeriv, norm_mul, mul_comm]
    exact mul_le_mul_of_nonneg_right hnorm (norm_nonneg _)
  have hsum : (∑ a ∈ (dividedWordPDeriv s P).support,
      ‖MvPolynomial.coeff (a + c) P‖) ≤ polynomialCoeffL1 P := by
    rw [← Finset.sum_image (f := fun a : I →₀ ℕ => ‖MvPolynomial.coeff a P‖)
      (g := fun a : I →₀ ℕ => a + c)
      (s := (dividedWordPDeriv s P).support)
      (by intro a ha b hb hab; exact add_right_cancel hab)]
    apply Finset.sum_le_sum_of_subset_of_nonneg
    · intro b hb
      obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hb
      exact dividedWordPDeriv_support_shift s P ha
    · intro b _ _
      exact norm_nonneg _
  calc
    _ ≤ ∑ a ∈ (dividedWordPDeriv s P).support,
        (2 : ℝ) ^ (∑ i, r i) * ‖MvPolynomial.coeff (a + c) P‖ :=
      Finset.sum_le_sum hentry
    _ = (2 : ℝ) ^ (∑ i, r i) *
        (∑ a ∈ (dividedWordPDeriv s P).support, ‖MvPolynomial.coeff (a + c) P‖) :=
      (Finset.mul_sum ..).symm
    _ ≤ _ := mul_le_mul_of_nonneg_left hsum (by positivity)

def polynomialCoeffL1_double_dividedWordPDeriv (s t : List I) (r : I → ℕ)
    (P : MvPolynomial I ℚ) (hP : PolynomialBoxBound r P) :
    polynomialCoeffL1 (dividedWordPDeriv s (dividedWordPDeriv t P)) ≤
      (4 : ℝ) ^ (∑ i, r i) * polynomialCoeffL1 P := by
  calc
    _ ≤ (2 : ℝ) ^ (∑ i, r i) * polynomialCoeffL1 (dividedWordPDeriv t P) :=
      polynomialCoeffL1_dividedWordPDeriv s r _ (polynomialBoxBound_dividedWordPDeriv t hP)
    _ ≤ (2 : ℝ) ^ (∑ i, r i) * ((2 : ℝ) ^ (∑ i, r i) * polynomialCoeffL1 P) :=
      mul_le_mul_of_nonneg_left (polynomialCoeffL1_dividedWordPDeriv t r P hP) (by positivity)
    _ = _ := by rw [← mul_assoc, ← mul_pow]; norm_num

end
end Bounty
end RothComponent_DividedDerivativeCoefficientNorm

/- Component: IntegerRankOneFactors; SHA256 f8775fc8d0e76bdf1c7c6dc5e50b9844470bad72656928fd032690e50a3ac29d -/
section RothComponent_IntegerRankOneFactors
/- Integer factors of a nonzero rank-one integer matrix, obtained by making a
column primitive and using its integral Bezout coefficients. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I J : Type*} [Fintype I] [Fintype J]

/-- Rank-one integer matrices admit integral outer factors, with primitive left factor. -/
def integer_rankOne_factors (A : I → J → ℤ)
    (hA : ∃ i j, A i j ≠ 0)
    (hminor : ∀ i k j l, A i j * A k l = A i l * A k j) :
    ∃ (a : I → ℤ) (b : J → ℤ),
      (∀ i j, A i j = a i * b j) ∧ Finset.univ.gcd a = 1 := by
  classical
  obtain ⟨i₀, j₀, hnonzero⟩ := hA
  obtain ⟨a, ha, hprimitive⟩ := Finset.extract_gcd
    (s := Finset.univ) (fun i => A i j₀) ⟨i₀, Finset.mem_univ i₀⟩
  let g : ℤ := Finset.univ.gcd (fun i => A i j₀)
  have hscale (i : I) : A i j₀ = g * a i := ha i (Finset.mem_univ i)
  have hg : g ≠ 0 := Finset.gcd_ne_zero_iff.mpr ⟨i₀, Finset.mem_univ i₀, hnonzero⟩
  have hcross (i k : I) (j : J) : a i * A k j = a k * A i j := by
    apply mul_left_cancel₀ hg
    have hm := hminor i k j₀ j
    rw [hscale i, hscale k] at hm
    calc
      g * (a i * A k j) = (g * a i) * A k j := by ring
      _ = A i j * (g * a k) := hm
      _ = g * (a k * A i j) := by ring
  obtain ⟨f, hf⟩ := Finset.gcd_eq_sum_mul Finset.univ a
  rw [hprimitive] at hf
  let b : J → ℤ := fun j => ∑ k, f k * A k j
  refine ⟨a, b, ?_, hprimitive⟩
  intro i j
  symm
  change a i * (∑ k, f k * A k j) = A i j
  calc
    _ = ∑ k, a i * (f k * A k j) := Finset.mul_sum _ _ _
    _ = ∑ k, (a k * f k) * A i j := by
      apply Finset.sum_congr rfl
      intro k _
      calc
        a i * (f k * A k j) = f k * (a i * A k j) := by ring
        _ = f k * (a k * A i j) := by rw [hcross]
        _ = (a k * f k) * A i j := by ring
    _ = (∑ k, a k * f k) * A i j := (Finset.sum_mul _ _ _).symm
    _ = A i j := by rw [← hf, one_mul]

def integer_rankOne_factors_of_ne_zero (A : I → J → ℤ) (hA : A ≠ 0)
    (hminor : ∀ i k j l, A i j * A k l = A i l * A k j) :
    ∃ (a : I → ℤ) (b : J → ℤ),
      (∀ i j, A i j = a i * b j) ∧ Finset.univ.gcd a = 1 := by
  apply integer_rankOne_factors A _ hminor
  by_contra! hh
  exact hA (funext fun i => funext fun j => hh i j)

/-- A rational outer factorization of an integer matrix already forces integer factors. -/
def integer_rankOne_factors_of_rat (A : I → J → ℤ) (hA : A ≠ 0)
    (u : I → ℚ) (v : J → ℚ) (huv : ∀ i j, (A i j : ℚ) = u i * v j) :
    ∃ (a : I → ℤ) (b : J → ℤ),
      (∀ i j, A i j = a i * b j) ∧ Finset.univ.gcd a = 1 := by
  apply integer_rankOne_factors_of_ne_zero A hA
  intro i k j l
  have hh : (A i j : ℚ) * (A k l : ℚ) = (A i l : ℚ) * (A k j : ℚ) := by
    simp only [huv]
    ring
  exact_mod_cast hh

/-- Nonzero rational outer factors differ from the integral ones by reciprocal scalars. -/
def integer_rankOne_factors_with_rat_scalars (A : I → J → ℤ) (hA : A ≠ 0)
    (u : I → ℚ) (v : J → ℚ) (huv : ∀ i j, (A i j : ℚ) = u i * v j) :
    ∃ (a : I → ℤ) (b : J → ℤ) (c : ℚ), c ≠ 0 ∧
      (∀ i j, A i j = a i * b j) ∧ Finset.univ.gcd a = 1 ∧
      (∀ i, (a i : ℚ) = c * u i) ∧ (∀ j, (b j : ℚ) = c⁻¹ * v j) := by
  obtain ⟨a, b, hab, hprimitive⟩ := integer_rankOne_factors_of_rat A hA u v huv
  have hex : ∃ i j, A i j ≠ 0 := by
    by_contra! hh
    exact hA (funext fun i => funext fun j => hh i j)
  obtain ⟨i₀, j₀, hnonzero⟩ := hex
  have hnrat : (A i₀ j₀ : ℚ) ≠ 0 := Int.cast_ne_zero.mpr hnonzero
  have hu : u i₀ ≠ 0 := left_ne_zero_of_mul (huv i₀ j₀ ▸ hnrat)
  have hv : v j₀ ≠ 0 := right_ne_zero_of_mul (huv i₀ j₀ ▸ hnrat)
  have ha : (a i₀ : ℚ) ≠ 0 := by
    exact_mod_cast left_ne_zero_of_mul (hab i₀ j₀ ▸ hnonzero)
  have hb : (b j₀ : ℚ) ≠ 0 := by
    exact_mod_cast right_ne_zero_of_mul (hab i₀ j₀ ▸ hnonzero)
  let c : ℚ := v j₀ / (b j₀ : ℚ)
  have hc : c ≠ 0 := div_ne_zero hv hb
  have haq (i : I) : (a i : ℚ) = c * u i := by
    apply (mul_right_cancel₀ hb)
    calc
      (a i : ℚ) * (b j₀ : ℚ) = (A i j₀ : ℚ) := by rw [hab]; norm_cast
      _ = u i * v j₀ := huv i j₀
      _ = (c * u i) * (b j₀ : ℚ) := by
        dsimp [c]
        rw [mul_right_comm, div_mul_cancel₀ _ hb, mul_comm]
  have hbq (j : J) : (b j : ℚ) = c⁻¹ * v j := by
    apply (mul_left_cancel₀ ha)
    calc
      (a i₀ : ℚ) * (b j : ℚ) = (A i₀ j : ℚ) := by rw [hab]; norm_cast
      _ = u i₀ * v j := huv i₀ j
      _ = (a i₀ : ℚ) * (c⁻¹ * v j) := by
        rw [haq]
        calc
          u i₀ * v j = (c * c⁻¹) * (u i₀ * v j) := by rw [mul_inv_cancel₀ hc, one_mul]
          _ = _ := by ring
  exact ⟨a, b, c, hc, hab, hprimitive, haq, hbq⟩


end
end Bounty
end RothComponent_IntegerRankOneFactors

/- Component: IntegerSeparatedPolynomialFactors; SHA256 dc689aa94900a5b76e9ec64ef87efd347952f4ca61318992055d148b467b33c3 -/
section RothComponent_IntegerSeparatedPolynomialFactors
/- Integral separated factors of an integer polynomial known to split rationally.
The finite coefficient matrix is indexed by the supports of the rational factors. -/

namespace Bounty
noncomputable section
open scoped BigOperators Polynomial

variable {I : Type*}

def separatedPolynomial_coeff {R : Type*} [CommSemiring R]
    (U₂ : MvPolynomial I R) (U₁ : Polynomial R) (d : I →₀ ℕ) (n : ℕ) :
    MvPolynomial.coeff d ((Polynomial.C U₂ * U₁.map MvPolynomial.C).coeff n) =
      MvPolynomial.coeff d U₂ * U₁.coeff n := by
  rw [Polynomial.coeff_C_mul, Polynomial.coeff_map, mul_comm U₂,
    MvPolynomial.coeff_C_mul, mul_comm]

private def reconstruct_mv_rat (U : MvPolynomial I ℚ) (a : U.support → ℤ)
    (c : ℚ) (ha : ∀ d, (a d : ℚ) = c * MvPolynomial.coeff d.1 U) :
    MvPolynomial.map (Int.castRingHom ℚ)
        (∑ d : U.support, MvPolynomial.monomial d.1 (a d)) = c • U := by
  classical
  simp only [map_sum, MvPolynomial.map_monomial]
  calc
    (∑ d : U.support, MvPolynomial.monomial d.1 (a d : ℚ)) =
        ∑ d : U.support, c • MvPolynomial.monomial d.1 (MvPolynomial.coeff d.1 U) := by
      apply Finset.sum_congr rfl
      intro d _
      rw [ha]
      simp only [MvPolynomial.smul_monomial, smul_eq_mul]
    _ = c • (∑ d : U.support, MvPolynomial.monomial d.1 (MvPolynomial.coeff d.1 U)) :=
      Finset.smul_sum.symm
    _ = c • U := by
      congr 1
      calc
        _ = ∑ d ∈ U.support, MvPolynomial.monomial d (MvPolynomial.coeff d U) :=
          Finset.sum_coe_sort U.support (fun d => MvPolynomial.monomial d (MvPolynomial.coeff d U))
        _ = U := MvPolynomial.support_sum_monomial_coeff U

private def reconstruct_uni_rat (U : Polynomial ℚ) (a : U.support → ℤ)
    (c : ℚ) (ha : ∀ n, (a n : ℚ) = c * U.coeff n.1) :
    (∑ n : U.support, Polynomial.monomial n.1 (a n)).map (Int.castRingHom ℚ) = c • U := by
  classical
  simp only [Polynomial.map_sum, Polynomial.map_monomial]
  calc
    (∑ n : U.support, Polynomial.monomial n.1 (a n : ℚ)) =
        ∑ n : U.support, c • Polynomial.monomial n.1 (U.coeff n.1) := by
      apply Finset.sum_congr rfl
      intro n _
      rw [ha]
      simp only [Polynomial.smul_monomial, smul_eq_mul]
    _ = c • (∑ n : U.support, Polynomial.monomial n.1 (U.coeff n.1)) :=
      Finset.smul_sum.symm
    _ = c • U := by
      congr 1
      calc
        _ = ∑ n ∈ U.support, Polynomial.monomial n (U.coeff n) :=
          Finset.sum_coe_sort U.support (fun n => Polynomial.monomial n (U.coeff n))
        _ = U := Polynomial.sum_monomial_eq U

/-- An integer polynomial with a rational separated factorization has integer separated
factors.  Their rational images differ from the original factors by reciprocal scalars. -/
def integer_separated_polynomial_factors
    (V : Polynomial (MvPolynomial I ℤ)) (U₂ : MvPolynomial I ℚ) (U₁ : Polynomial ℚ)
    (hU₂ : U₂ ≠ 0) (hU₁ : U₁ ≠ 0)
    (hV : V.map (MvPolynomial.map (Int.castRingHom ℚ)) =
      Polynomial.C U₂ * U₁.map MvPolynomial.C) :
    ∃ (F₂ : MvPolynomial I ℤ) (F₁ : Polynomial ℤ) (c : ℚ),
      F₂ ≠ 0 ∧ F₁ ≠ 0 ∧ c ≠ 0 ∧
      V = Polynomial.C F₂ * F₁.map MvPolynomial.C ∧
      MvPolynomial.map (Int.castRingHom ℚ) F₂ = c • U₂ ∧
      F₁.map (Int.castRingHom ℚ) = c⁻¹ • U₁ := by
  classical
  let A : U₂.support → U₁.support → ℤ := fun d n => MvPolynomial.coeff d.1 (V.coeff n.1)
  have hcoeff (d : I →₀ ℕ) (n : ℕ) :
      ((MvPolynomial.coeff d (V.coeff n) : ℤ) : ℚ) = MvPolynomial.coeff d U₂ * U₁.coeff n := by
    have hh := congrArg (fun W : Polynomial (MvPolynomial I ℚ) =>
      MvPolynomial.coeff d (W.coeff n)) hV
    simpa only [Polynomial.coeff_map, MvPolynomial.coeff_map, Int.coe_castRingHom,
      separatedPolynomial_coeff] using hh
  have hA : A ≠ 0 := by
    obtain ⟨d, hd⟩ := MvPolynomial.support_nonempty.mpr hU₂
    obtain ⟨n, hn⟩ := Polynomial.support_nonempty.mpr hU₁
    intro hz
    have hh := hcoeff d n
    have haz : A ⟨d, hd⟩ ⟨n, hn⟩ = 0 := congrFun (congrFun hz ⟨d, hd⟩) ⟨n, hn⟩
    change MvPolynomial.coeff d (V.coeff n) = 0 at haz
    rw [haz, Int.cast_zero] at hh
    exact (mul_ne_zero (MvPolynomial.mem_support_iff.mp hd)
      (Polynomial.mem_support_iff.mp hn)) hh.symm
  obtain ⟨a, b, c, hc, hab, _, ha, hb⟩ := integer_rankOne_factors_with_rat_scalars A hA
    (fun d => MvPolynomial.coeff d.1 U₂) (fun n => U₁.coeff n.1)
    (fun d n => hcoeff d.1 n.1)
  let F₂ : MvPolynomial I ℤ := ∑ d : U₂.support, MvPolynomial.monomial d.1 (a d)
  let F₁ : Polynomial ℤ := ∑ n : U₁.support, Polynomial.monomial n.1 (b n)
  have hF₂ : MvPolynomial.map (Int.castRingHom ℚ) F₂ = c • U₂ := reconstruct_mv_rat U₂ a c ha
  have hF₁ : F₁.map (Int.castRingHom ℚ) = c⁻¹ • U₁ := reconstruct_uni_rat U₁ b c⁻¹ hb
  have hF₂ne : F₂ ≠ 0 := by
    intro hz
    rw [hz, map_zero] at hF₂
    exact (smul_ne_zero hc hU₂) hF₂.symm
  have hF₁ne : F₁ ≠ 0 := by
    intro hz
    rw [hz, Polynomial.map_zero] at hF₁
    exact (smul_ne_zero (inv_ne_zero hc) hU₁) hF₁.symm
  refine ⟨F₂, F₁, c, hF₂ne, hF₁ne, hc, ?_, hF₂, hF₁⟩
  apply Polynomial.ext
  intro n
  apply MvPolynomial.ext
  intro d
  apply (Int.cast_injective : Function.Injective (fun z : ℤ => (z : ℚ)))
  rw [separatedPolynomial_coeff, Int.cast_mul, hcoeff]
  have h₂ := congrArg (MvPolynomial.coeff d) hF₂
  have h₁ := congrArg (fun Q : Polynomial ℚ => Q.coeff n) hF₁
  simp only [MvPolynomial.coeff_map, Int.coe_castRingHom, MvPolynomial.coeff_smul,
    smul_eq_mul] at h₂
  simp only [Polynomial.coeff_map, Int.coe_castRingHom, Polynomial.coeff_smul,
    smul_eq_mul] at h₁
  rw [h₂, h₁]
  calc
    MvPolynomial.coeff d U₂ * U₁.coeff n =
        (c * c⁻¹) * (MvPolynomial.coeff d U₂ * U₁.coeff n) := by
      rw [mul_inv_cancel₀ hc, one_mul]
    _ = _ := by ring


end
end Bounty
end RothComponent_IntegerSeparatedPolynomialFactors

/- Component: SeparatedCoefficientNorm; SHA256 d7cff77cebfa685d57d33afcb03be5da94dc8ba82e823c0eeacbea75476bb77e -/
section RothComponent_SeparatedCoefficientNorm
/- Exact coefficient-sum norms for separated products, integral lower bounds,
and invariance under coefficient embeddings preserving the norm. -/

namespace Bounty
noncomputable section
open scoped BigOperators Polynomial

variable {I R S : Type*} [NormedCommRing R] [NormedCommRing S]

def univariateCoeffL1 (P : Polynomial R) : ℝ := ∑ n ∈ P.support, ‖P.coeff n‖

def iteratedCoeffL1 (V : Polynomial (MvPolynomial I R)) : ℝ :=
  ∑ n ∈ V.support, polynomialCoeffL1 (V.coeff n)

def univariateCoeffL1_nonneg (P : Polynomial R) : 0 ≤ univariateCoeffL1 P :=
  Finset.sum_nonneg (fun _ _ => norm_nonneg _)

def norm_coeff_le_univariateCoeffL1 (P : Polynomial R) (n : ℕ) :
    ‖P.coeff n‖ ≤ univariateCoeffL1 P := by
  classical
  by_cases hn : n ∈ P.support
  · exact Finset.single_le_sum (fun _ _ => norm_nonneg _) hn
  · simp only [Polynomial.notMem_support_iff.mp hn, norm_zero]
    exact univariateCoeffL1_nonneg P

def iteratedCoeffL1_sum_of_support_subset (V : Polynomial (MvPolynomial I R))
    (s : Finset ℕ) (hs : V.support ⊆ s) :
    iteratedCoeffL1 V = ∑ n ∈ s, polynomialCoeffL1 (V.coeff n) := by
  classical
  apply Finset.sum_subset hs
  intro n _ hn
  rw [Polynomial.notMem_support_iff.mp hn, polynomialCoeffL1_zero]

def polynomialCoeffL1_smul_eq [NormMulClass R] (a : R) (P : MvPolynomial I R) :
    polynomialCoeffL1 (a • P) = ‖a‖ * polynomialCoeffL1 P := by
  rw [polynomialCoeffL1_sum_of_support_subset (a • P) P.support MvPolynomial.support_smul]
  simp only [MvPolynomial.coeff_smul, smul_eq_mul, norm_mul, polynomialCoeffL1, Finset.mul_sum]

def iteratedCoeffL1_separated [NormMulClass R]
    (F₂ : MvPolynomial I R) (F₁ : Polynomial R) :
    iteratedCoeffL1 (Polynomial.C F₂ * F₁.map MvPolynomial.C) =
      polynomialCoeffL1 F₂ * univariateCoeffL1 F₁ := by
  classical
  have hs : (Polynomial.C F₂ * F₁.map MvPolynomial.C).support ⊆ F₁.support := by
    intro n hn
    by_contra hn'
    have hz : (Polynomial.C F₂ * F₁.map MvPolynomial.C).coeff n = 0 := by
      rw [Polynomial.coeff_C_mul, Polynomial.coeff_map, Polynomial.notMem_support_iff.mp hn',
        map_zero, mul_zero]
    exact Polynomial.mem_support_iff.mp hn hz
  rw [iteratedCoeffL1_sum_of_support_subset _ F₁.support hs]
  simp only [Polynomial.coeff_C_mul, Polynomial.coeff_map]
  have he (n : ℕ) : F₂ * MvPolynomial.C (F₁.coeff n) = (F₁.coeff n) • F₂ := by
    rw [MvPolynomial.smul_eq_C_mul, mul_comm]
  simp_rw [he, polynomialCoeffL1_smul_eq]
  rw [← Finset.sum_mul, mul_comm]
  rfl

def one_le_polynomialCoeffL1_int {P : MvPolynomial I ℤ} (hP : P ≠ 0) :
    1 ≤ polynomialCoeffL1 P := by
  obtain ⟨d, hd⟩ := MvPolynomial.exists_coeff_ne_zero hP
  have hnorm : (1 : ℝ) ≤ ‖MvPolynomial.coeff d P‖ := by
    rw [Int.norm_eq_abs]
    exact_mod_cast Int.one_le_abs hd
  exact hnorm.trans (norm_coeff_le_polynomialCoeffL1 P d)

def one_le_univariateCoeffL1_int {P : Polynomial ℤ} (hP : P ≠ 0) :
    1 ≤ univariateCoeffL1 P := by
  obtain ⟨n, hn⟩ := Polynomial.support_nonempty.mpr hP
  have hnorm : (1 : ℝ) ≤ ‖P.coeff n‖ := by
    rw [Int.norm_eq_abs]
    exact_mod_cast Int.one_le_abs (Polynomial.mem_support_iff.mp hn)
  exact hnorm.trans (norm_coeff_le_univariateCoeffL1 P n)

def separated_factor_log_bounds (F₂ : MvPolynomial I ℤ) (F₁ : Polynomial ℤ)
    (hF₂ : F₂ ≠ 0) (hF₁ : F₁ ≠ 0) :
    0 ≤ Real.log (polynomialCoeffL1 F₂) ∧ 0 ≤ Real.log (univariateCoeffL1 F₁) ∧
      Real.log (polynomialCoeffL1 F₂) ≤
        Real.log (iteratedCoeffL1 (Polynomial.C F₂ * F₁.map MvPolynomial.C)) ∧
      Real.log (univariateCoeffL1 F₁) ≤
        Real.log (iteratedCoeffL1 (Polynomial.C F₂ * F₁.map MvPolynomial.C)) := by
  have h₂ := one_le_polynomialCoeffL1_int hF₂
  have h₁ := one_le_univariateCoeffL1_int hF₁
  rw [iteratedCoeffL1_separated]
  refine ⟨Real.log_nonneg h₂, Real.log_nonneg h₁, ?_, ?_⟩
  · apply Real.log_le_log (lt_of_lt_of_le zero_lt_one h₂)
    exact le_mul_of_one_le_right (polynomialCoeffL1_nonneg F₂) h₁
  · apply Real.log_le_log (lt_of_lt_of_le zero_lt_one h₁)
    exact le_mul_of_one_le_left (univariateCoeffL1_nonneg F₁) h₂

def polynomialCoeffL1_map (f : R →+* S) (hf : Function.Injective f)
    (hnorm : ∀ a, ‖f a‖ = ‖a‖) (P : MvPolynomial I R) :
    polynomialCoeffL1 (MvPolynomial.map f P) = polynomialCoeffL1 P := by
  classical
  unfold polynomialCoeffL1
  rw [MvPolynomial.support_map_of_injective P hf]
  simp only [MvPolynomial.coeff_map, hnorm]

def univariateCoeffL1_map (f : R →+* S) (hf : Function.Injective f)
    (hnorm : ∀ a, ‖f a‖ = ‖a‖) (P : Polynomial R) :
    univariateCoeffL1 (P.map f) = univariateCoeffL1 P := by
  classical
  unfold univariateCoeffL1
  rw [Polynomial.support_map_of_injective P hf]
  simp only [Polynomial.coeff_map, hnorm]

def iteratedCoeffL1_map (f : R →+* S) (hf : Function.Injective f)
    (hnorm : ∀ a, ‖f a‖ = ‖a‖) (V : Polynomial (MvPolynomial I R)) :
    iteratedCoeffL1 (V.map (MvPolynomial.map f)) = iteratedCoeffL1 V := by
  classical
  unfold iteratedCoeffL1
  rw [Polynomial.support_map_of_injective V (MvPolynomial.map_injective f hf)]
  simp only [Polynomial.coeff_map, polynomialCoeffL1_map f hf hnorm]

def polynomialCoeffL1_map_int_rat (P : MvPolynomial I ℤ) :
    polynomialCoeffL1 (MvPolynomial.map (Int.castRingHom ℚ) P) = polynomialCoeffL1 P :=
  polynomialCoeffL1_map (Int.castRingHom ℚ) Int.cast_injective Int.norm_cast_rat P

def iteratedCoeffL1_map_int_rat (V : Polynomial (MvPolynomial I ℤ)) :
    iteratedCoeffL1 (V.map (MvPolynomial.map (Int.castRingHom ℚ))) = iteratedCoeffL1 V :=
  iteratedCoeffL1_map (Int.castRingHom ℚ) Int.cast_injective Int.norm_cast_rat V


end
end Bounty
end RothComponent_SeparatedCoefficientNorm

/- Component: RothDerivativeFactorization; SHA256 ee5830d1622c5270be282fd3d302ac68f47984767bb609af5be794a2e1973992 -/
section RothComponent_RothDerivativeFactorization
/- The actual mixed-derivative determinant in the rational Roth argument. -/

noncomputable section


open Polynomial MvPolynomial Matrix Finset

namespace Bounty

def wordCoefficientDerivative {m : ℕ} (w : List (Fin m)) :
    (MvPolynomial (Fin m) ℚ)[X] →ₗ[ℚ] (MvPolynomial (Fin m) ℚ)[X] :=
  Polynomial.lsum fun n =>
    ((Polynomial.monomial n).restrictScalars ℚ).comp (wordPDeriv w)

def wordCoefficientDerivative_coeff {m : ℕ} (w : List (Fin m))
    (P : (MvPolynomial (Fin m) ℚ)[X]) (n : ℕ) :
    (wordCoefficientDerivative w P).coeff n = wordPDeriv w (P.coeff n) := by
  classical
  by_cases hn : n ∈ P.support
  · simp [wordCoefficientDerivative, Polynomial.lsum_apply,
      Polynomial.sum_def, Polynomial.coeff_monomial, hn]
  · have hz : P.coeff n = 0 := Polynomial.notMem_support_iff.mp hn
    simp [wordCoefficientDerivative, Polynomial.lsum_apply,
      Polynomial.sum_def, Polynomial.coeff_monomial, hn, hz]

def wordCoefficientDerivative_C_mul_map {m : ℕ} (w : List (Fin m))
    (a : MvPolynomial (Fin m) ℚ) (q : ℚ[X]) :
    wordCoefficientDerivative w (Polynomial.C a * q.map MvPolynomial.C) =
      Polynomial.C (wordPDeriv w a) * q.map MvPolynomial.C := by
  ext n
  simp only [wordCoefficientDerivative_coeff, Polynomial.coeff_C_mul, Polynomial.coeff_map]
  rw [mul_comm a, MvPolynomial.C_mul', map_smul, ← MvPolynomial.C_mul', mul_comm]

def rothMixedDerivative {m : ℕ} (w : List (Fin m)) (n : ℕ)
    (P : (MvPolynomial (Fin m) ℚ)[X]) : (MvPolynomial (Fin m) ℚ)[X] :=
  Polynomial.derivative^[n] (wordCoefficientDerivative w P)

def rothMixedDerivative_separated_sum {m k : ℕ}
    (P : (MvPolynomial (Fin m) ℚ)[X])
    (φ : Fin k → MvPolynomial (Fin m) ℚ) (ψ : Fin k → ℚ[X])
    (hsplit : P = ∑ j, Polynomial.C (φ j) * (ψ j).map MvPolynomial.C)
    (w : List (Fin m)) (n : ℕ) :
    rothMixedDerivative w n P =
      ∑ j, Polynomial.C (wordPDeriv w (φ j)) *
        ((Polynomial.derivative^[n]) (ψ j)).map MvPolynomial.C := by
  unfold rothMixedDerivative
  rw [hsplit, map_sum, Polynomial.iterate_derivative_sum]
  apply Finset.sum_congr rfl
  intro j hj
  rw [wordCoefficientDerivative_C_mul_map, Polynomial.iterate_derivative_C_mul,
    Polynomial.iterate_derivative_map]

def rothMixedDerivative_matrix_factorization {m k : ℕ}
    (P : (MvPolynomial (Fin m) ℚ)[X])
    (φ : Fin k → MvPolynomial (Fin m) ℚ) (ψ : Fin k → ℚ[X])
    (hsplit : P = ∑ j, Polynomial.C (φ j) * (ψ j).map MvPolynomial.C)
    (w : Fin k → List (Fin m)) :
    (Matrix.of fun i j : Fin k => rothMixedDerivative (w i) j.val P) =
      Polynomial.C.mapMatrix (fun i j : Fin k => wordPDeriv (w i) (φ j)) *
      (Polynomial.mapRingHom MvPolynomial.C).mapMatrix
        (Matrix.transpose (fun i j : Fin k => (Polynomial.derivative^[i.val]) (ψ j))) := by
  funext i j
  change rothMixedDerivative (w i) j.val P =
    ∑ s, Polynomial.C (wordPDeriv (w i) (φ s)) *
      ((Polynomial.derivative^[j.val]) (ψ s)).map MvPolynomial.C
  exact rothMixedDerivative_separated_sum P φ ψ hsplit (w i) j.val

def rothMixedDerivative_det_factorization {m k : ℕ}
    (P : (MvPolynomial (Fin m) ℚ)[X])
    (φ : Fin k → MvPolynomial (Fin m) ℚ) (ψ : Fin k → ℚ[X])
    (hsplit : P = ∑ j, Polynomial.C (φ j) * (ψ j).map MvPolynomial.C)
    (w : Fin k → List (Fin m)) :
    Matrix.det (fun i j : Fin k => rothMixedDerivative (w i) j.val P) =
      Polynomial.C (Matrix.det (fun i j : Fin k => wordPDeriv (w i) (φ j))) *
      (Matrix.det (fun i j : Fin k => (Polynomial.derivative^[i.val]) (ψ j))).map
        MvPolynomial.C := by
  change (Matrix.of fun i j : Fin k => rothMixedDerivative (w i) j.val P).det = _
  erw [rothMixedDerivative_matrix_factorization P φ ψ hsplit w, Matrix.det_mul,
    ← Polynomial.C.map_det]
  congr 1
  exact ((Polynomial.mapRingHom MvPolynomial.C).map_det
    (Matrix.transpose (Matrix.of fun i j : Fin k =>
      (Polynomial.derivative^[i.val]) (ψ j)))).symm.trans (by rw [Matrix.det_transpose])

def polynomial_det_natDegree_le {k r : ℕ}
    (A : Matrix (Fin k) (Fin k) ℚ[X])
    (hA : ∀ i j, (A i j).natDegree ≤ r) : A.det.natDegree ≤ k * r := by
  classical
  rw [Matrix.det_apply]
  apply Polynomial.natDegree_sum_le_of_forall_le
  intro σ hσ
  calc
    (Equiv.Perm.sign σ • ∏ j, A (σ j) j).natDegree ≤
        (∏ j, A (σ j) j).natDegree := Polynomial.natDegree_smul_le _ _
    _ ≤ ∑ j, (A (σ j) j).natDegree := Polynomial.natDegree_prod_le _ _
    _ ≤ ∑ _j : Fin k, r := Finset.sum_le_sum (fun j _ => hA (σ j) j)
    _ = k * r := by simp

end Bounty
end
end RothComponent_RothDerivativeFactorization

/- Component: RothDividedFactorization; SHA256 395032c6da3ecff164cf75cbcf9df74464ca9dfec1858d98e6fd31a5bd719441 -/
section RothComponent_RothDividedFactorization
/- Divided derivative factorization with the last variable isolated. -/

noncomputable section
open Polynomial MvPolynomial Matrix Finset
namespace Bounty

def lastVariableEquiv (m : ℕ) : MvPolynomial (Fin (m + 1)) ℚ ≃ₐ[ℚ]
    (MvPolynomial (Fin m) ℚ)[X] :=
  (MvPolynomial.renameEquiv ℚ (finRotate (m + 1))).trans
    (MvPolynomial.finSuccEquiv ℚ m)

def finRotate_castSucc {m : ℕ} (i : Fin m) :
    finRotate (m + 1) i.castSucc = i.succ := by
  exact finRotate_of_lt i.isLt

def lastVariableEquiv_natDegree {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) :
    (lastVariableEquiv m P).natDegree = P.degreeOf (Fin.last m) := by
  change (MvPolynomial.finSuccEquiv ℚ m
    (MvPolynomial.rename (finRotate (m + 1)) P)).natDegree = _
  rw [MvPolynomial.natDegree_finSuccEquiv, ← finRotate_last]
  exact MvPolynomial.degreeOf_rename_of_injective (finRotate (m + 1)).injective _

def lastVariableEquiv_coeff_degreeOf {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (i : Fin m) (n : ℕ) :
    ((lastVariableEquiv m P).coeff n).degreeOf i ≤ P.degreeOf i.castSucc := by
  change ((MvPolynomial.finSuccEquiv ℚ m
    (MvPolynomial.rename (finRotate (m + 1)) P)).coeff n).degreeOf i ≤ _
  calc
    _ ≤ (MvPolynomial.rename (finRotate (m + 1)) P).degreeOf i.succ :=
      MvPolynomial.degreeOf_coeff_finSuccEquiv _ _ _
    _ = _ := by rw [← finRotate_castSucc i];
                exact MvPolynomial.degreeOf_rename_of_injective
                  (finRotate (m + 1)).injective i.castSucc

def finSuccEquiv_pderiv_zero {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) :
    MvPolynomial.finSuccEquiv ℚ m (MvPolynomial.pderiv 0 P) =
      Polynomial.derivative (MvPolynomial.finSuccEquiv ℚ m P) := by
  apply Polynomial.ext
  intro n
  apply MvPolynomial.ext
  intro a
  have he : a.cons n + Finsupp.single 0 1 = a.cons (n + 1) := by
    ext j
    cases j using Fin.cases <;> simp
  simp only [MvPolynomial.finSuccEquiv_coeff_coeff, MvPolynomial.coeff_pderiv,
    Polynomial.coeff_derivative, he, Finsupp.cons_zero]
  rw [show (n : MvPolynomial (Fin m) ℚ) + 1 = MvPolynomial.C (n + 1 : ℚ) by simp,
    mul_comm (((MvPolynomial.finSuccEquiv ℚ m) P).coeff (n + 1)),
    MvPolynomial.coeff_C_mul, MvPolynomial.finSuccEquiv_coeff_coeff, mul_comm]

def finSuccEquiv_pderiv_succ {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (i : Fin m) :
    MvPolynomial.finSuccEquiv ℚ m (MvPolynomial.pderiv i.succ P) =
      wordCoefficientDerivative [i] (MvPolynomial.finSuccEquiv ℚ m P) := by
  apply Polynomial.ext
  intro n
  apply MvPolynomial.ext
  intro a
  have he : a.cons n + Finsupp.single i.succ 1 =
      (a + Finsupp.single i 1).cons n := by
    ext j
    cases j using Fin.cases <;> simp [Finsupp.single_apply]
  simp only [wordCoefficientDerivative_coeff, wordPDeriv_cons, wordPDeriv_nil,
    MvPolynomial.finSuccEquiv_coeff_coeff, MvPolynomial.coeff_pderiv,
    he, Finsupp.cons_succ]

def lastVariableEquiv_pderiv_last {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) :
    lastVariableEquiv m (MvPolynomial.pderiv (Fin.last m) P) =
      Polynomial.derivative (lastVariableEquiv m P) := by
  change MvPolynomial.finSuccEquiv ℚ m
    (MvPolynomial.rename (finRotate (m + 1)) (MvPolynomial.pderiv _ P)) = _
  rw [← MvPolynomial.pderiv_rename (finRotate (m + 1)).injective, finRotate_last]
  exact finSuccEquiv_pderiv_zero _

def lastVariableEquiv_pderiv_castSucc {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (i : Fin m) :
    lastVariableEquiv m (MvPolynomial.pderiv i.castSucc P) =
      wordCoefficientDerivative [i] (lastVariableEquiv m P) := by
  change MvPolynomial.finSuccEquiv ℚ m
    (MvPolynomial.rename (finRotate (m + 1)) (MvPolynomial.pderiv _ P)) = _
  rw [← MvPolynomial.pderiv_rename (finRotate (m + 1)).injective,
    finRotate_castSucc]
  exact finSuccEquiv_pderiv_succ _ _

def lastVariableEquiv_word_castSucc {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (w : List (Fin m)) :
    lastVariableEquiv m (wordPDeriv (w.map Fin.castSucc) P) =
      wordCoefficientDerivative w (lastVariableEquiv m P) := by
  induction w with
  | nil =>
    apply Polynomial.ext
    intro n
    simp [wordCoefficientDerivative_coeff, wordPDeriv_nil]
  | cons i w hw =>
    simp only [List.map_cons, wordPDeriv_cons, lastVariableEquiv_pderiv_castSucc, hw]
    apply Polynomial.ext
    intro n
    simp [wordCoefficientDerivative_coeff, wordPDeriv_cons, wordPDeriv_nil]

def lastVariableEquiv_word_last {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (n : ℕ) :
    lastVariableEquiv m (wordPDeriv (List.replicate n (Fin.last m)) P) =
      (Polynomial.derivative^[n]) (lastVariableEquiv m P) := by
  induction n with
  | zero => simp [wordPDeriv_nil]
  | succ n hn =>
    rw [List.replicate_succ, wordPDeriv_cons, lastVariableEquiv_pderiv_last, hn,
      Function.iterate_succ_apply']

def degreeOf_pderiv_le {I : Type*} (P : MvPolynomial I ℚ) (i j : I) :
    (MvPolynomial.pderiv j P).degreeOf i ≤ P.degreeOf i := by
  classical
  apply MvPolynomial.degreeOf_le_iff.mpr
  intro a ha
  have hc := MvPolynomial.mem_support_iff.mp ha
  rw [MvPolynomial.coeff_pderiv] at hc
  have hmem : a + Finsupp.single j 1 ∈ P.support :=
    MvPolynomial.mem_support_iff.mpr (left_ne_zero_of_mul hc)
  exact (Nat.le_add_right _ _).trans
    (MvPolynomial.le_degreeOf_of_mem_support i hmem)

def degreeOf_wordPDeriv_le {I : Type*} (P : MvPolynomial I ℚ)
    (w : List I) (i : I) : (wordPDeriv w P).degreeOf i ≤ P.degreeOf i := by
  induction w with
  | nil => simp [wordPDeriv_nil]
  | cons j w hw => exact (degreeOf_pderiv_le _ i j).trans hw

def mvPolynomial_det_degreeOf_le {I : Type*} {k r : ℕ}
    (A : Matrix (Fin k) (Fin k) (MvPolynomial I ℚ)) (a : I)
    (hA : ∀ i j, (A i j).degreeOf a ≤ r) : A.det.degreeOf a ≤ k * r := by
  classical
  rw [Matrix.det_apply]
  apply (MvPolynomial.degreeOf_sum_le _ _ _).trans
  apply Finset.sup_le
  intro σ hσ
  have hs : (Equiv.Perm.sign σ • ∏ j, A (σ j) j).degreeOf a ≤
      (∏ j, A (σ j) j).degreeOf a := by
    simp only [MvPolynomial.degreeOf_eq_sup]
    exact Finset.sup_mono MvPolynomial.support_smul
  calc
    _ ≤ _ := hs
    _ ≤ ∑ j, (A (σ j) j).degreeOf a := MvPolynomial.degreeOf_prod_le _ _ _
    _ ≤ ∑ _j : Fin k, r := Finset.sum_le_sum (fun j _ => hA (σ j) j)
    _ = k * r := by simp

def lastVariableEquiv_rename_castSucc {m : ℕ} (P : MvPolynomial (Fin m) ℚ) :
    lastVariableEquiv m (MvPolynomial.rename Fin.castSucc P) = Polynomial.C P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [lastVariableEquiv, MvPolynomial.finSuccEquiv_apply]
  | add p q hp hq => simp [hp, hq]
  | mul_X p i hp =>
    rw [map_mul, map_mul, hp, map_mul]
    apply congrArg (fun q => Polynomial.C p * q)
    change MvPolynomial.finSuccEquiv ℚ m
      (MvPolynomial.rename (finRotate (m + 1))
        (MvPolynomial.rename Fin.castSucc (MvPolynomial.X i))) = _
    rw [MvPolynomial.rename_X, MvPolynomial.rename_X, finRotate_castSucc,
      MvPolynomial.finSuccEquiv_X_succ]

def lastVariableEquiv_aeval_last {m : ℕ} (P : ℚ[X]) :
    lastVariableEquiv m (Polynomial.aeval (MvPolynomial.X (Fin.last m)) P) =
      P.map MvPolynomial.C := by
  induction P using Polynomial.induction_on' with
  | add p q hp hq => simp [hp, hq]
  | monomial n a =>
    rw [← Polynomial.C_mul_X_pow_eq_monomial]
    simp [lastVariableEquiv, MvPolynomial.finSuccEquiv_apply]

def rothDividedDerivative {m : ℕ} (w : List (Fin m)) (n : ℕ)
    (P : MvPolynomial (Fin (m + 1)) ℚ) : MvPolynomial (Fin (m + 1)) ℚ :=
  dividedWordPDeriv (List.replicate n (Fin.last m))
    (dividedWordPDeriv (w.map Fin.castSucc) P)

def rothRowScalar {m : ℕ} (w : List (Fin m)) : ℚ :=
  (wordDerivativeFactorial (w.map Fin.castSucc))⁻¹

def rothColumnScalar (m n : ℕ) : ℚ :=
  (wordDerivativeFactorial (List.replicate n (Fin.last m)))⁻¹

def rothRowScalar_ne_zero {m : ℕ} (w : List (Fin m)) : rothRowScalar w ≠ 0 :=
  inv_ne_zero (wordDerivativeFactorial_ne_zero _)

def rothColumnScalar_ne_zero (m n : ℕ) : rothColumnScalar m n ≠ 0 :=
  inv_ne_zero (wordDerivativeFactorial_ne_zero _)

def lastVariableEquiv_rothDividedDerivative {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (w : List (Fin m)) (n : ℕ) :
    lastVariableEquiv m (rothDividedDerivative w n P) =
      rothColumnScalar m n • rothRowScalar w •
        rothMixedDerivative w n (lastVariableEquiv m P) := by
  unfold rothDividedDerivative dividedWordPDeriv
  simp only [LinearMap.smul_apply, map_smul]
  rw [lastVariableEquiv_word_last, lastVariableEquiv_word_castSucc]
  exact smul_comm _ _ _

def det_rational_row_smul {R : Type*} [CommRing R] [Algebra ℚ R]
    {k : ℕ} (c : Fin k → ℚ) (A : Matrix (Fin k) (Fin k) R) :
    Matrix.det (fun i j => c i • A i j) = (∏ i, c i) • A.det := by
  change (Matrix.of fun i j => c i • A i j).det = _
  simp only [Algebra.smul_def]
  rw [Matrix.det_mul_column, ← map_prod]

def det_rational_column_smul {R : Type*} [CommRing R] [Algebra ℚ R]
    {k : ℕ} (c : Fin k → ℚ) (A : Matrix (Fin k) (Fin k) R) :
    Matrix.det (fun i j => c j • A i j) = (∏ i, c i) • A.det := by
  change (Matrix.of fun i j => c j • A i j).det = _
  simp only [Algebra.smul_def]
  rw [Matrix.det_mul_row, ← map_prod]

def lastVariableEquiv_rothDivided_det {m k : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (w : Fin k → List (Fin m)) :
    lastVariableEquiv m (Matrix.det (fun i j : Fin k =>
      rothDividedDerivative (w i) j.val P)) =
      (∏ j : Fin k, rothColumnScalar m j.val) •
        (∏ i : Fin k, rothRowScalar (w i)) •
          Matrix.det (fun i j : Fin k =>
            rothMixedDerivative (w i) j.val (lastVariableEquiv m P)) := by
  change (lastVariableEquiv m).toRingHom ((Matrix.of fun i j : Fin k =>
    rothDividedDerivative (w i) j.val P).det) = _
  rw [(lastVariableEquiv m).toRingHom.map_det]
  change Matrix.det (fun i j : Fin k =>
    lastVariableEquiv m (rothDividedDerivative (w i) j.val P)) = _
  simp only [lastVariableEquiv_rothDividedDerivative]
  erw [det_rational_column_smul, det_rational_row_smul]

def rational_smul_separated (m : ℕ) (c d : ℚ)
    (A : MvPolynomial (Fin m) ℚ) (B : ℚ[X]) :
    d • c • (Polynomial.C A * B.map MvPolynomial.C) =
      Polynomial.C (c • A) * (d • B).map MvPolynomial.C := by
  apply Polynomial.ext
  intro n
  simp only [Polynomial.coeff_smul, Polynomial.coeff_C_mul, Polynomial.coeff_map]
  simp only [← MvPolynomial.C_mul', smul_eq_mul, map_mul]
  ring

def exists_rothDivided_factorization {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (hP : P ≠ 0)
    (r : Fin (m + 1) → ℕ) (hdegree : ∀ i, P.degreeOf i ≤ r i) :
    ∃ k : ℕ, 1 ≤ k ∧ k ≤ P.degreeOf (Fin.last m) + 1 ∧
      k ≤ r (Fin.last m) + 1 ∧
      ∃ w : Fin k → List (Fin m), (∀ i, (w i).length ≤ i.val) ∧
        ∃ U₂ : MvPolynomial (Fin m) ℚ, ∃ U₁ : ℚ[X],
          U₂ ≠ 0 ∧ U₁ ≠ 0 ∧
          (∀ a, U₂.degreeOf a ≤ k * r a.castSucc) ∧
          U₁.natDegree ≤ k * r (Fin.last m) ∧
          lastVariableEquiv m (Matrix.det (fun i j : Fin k =>
            rothDividedDerivative (w i) j.val P)) =
              Polynomial.C U₂ * U₁.map MvPolynomial.C ∧
          Matrix.det (fun i j : Fin k => rothDividedDerivative (w i) j.val P) =
            MvPolynomial.rename Fin.castSucc U₂ *
              Polynomial.aeval (MvPolynomial.X (Fin.last m)) U₁ ∧
          Matrix.det (fun i j : Fin k => rothDividedDerivative (w i) j.val P) ≠ 0 := by
  classical
  let Q := lastVariableEquiv m P
  have hQ : Q ≠ 0 :=
    (map_ne_zero_iff (lastVariableEquiv m) (lastVariableEquiv m).injective).mpr hP
  obtain ⟨k, hkpos, hk, φ, ψ, hφ, hψ, hφcoeff, hψdeg, hsplit⟩ :=
    mvPolynomial_separated_rank Q hQ
  obtain ⟨w, hw, hW₂⟩ := exists_generalizedWronskian_ne_zero φ hφ
  let W₂ := Matrix.det (fun i j : Fin k => wordPDeriv (w i) (φ j))
  let W₁ := Matrix.det (fun i j : Fin k => (Polynomial.derivative^[i.val]) (ψ j))
  let c : ℚ := ∏ i : Fin k, rothRowScalar (w i)
  let d : ℚ := ∏ j : Fin k, rothColumnScalar m j.val
  have hc : c ≠ 0 := Finset.prod_ne_zero_iff.mpr fun i _ => rothRowScalar_ne_zero (w i)
  have hd : d ≠ 0 := Finset.prod_ne_zero_iff.mpr fun j _ => rothColumnScalar_ne_zero m j.val
  have hW₁ : W₁ ≠ 0 := iterated_derivative_matrix_det_ne_zero ψ hψ
  have hW₂deg (a : Fin m) : W₂.degreeOf a ≤ k * r a.castSucc := by
    apply mvPolynomial_det_degreeOf_le
    intro i j
    obtain ⟨n, _, hn⟩ := hφcoeff j
    exact (degreeOf_wordPDeriv_le _ _ _).trans (by
      rw [hn]
      exact (lastVariableEquiv_coeff_degreeOf P a n).trans (hdegree a.castSucc))
  have hW₁deg : W₁.natDegree ≤ k * r (Fin.last m) := by
    apply polynomial_det_natDegree_le
    intro i j
    exact (Polynomial.natDegree_iterate_derivative (ψ j) i.val).trans
      ((Nat.sub_le _ _).trans ((hψdeg j).trans (by
        rw [lastVariableEquiv_natDegree]
        exact hdegree _)))
  let U₂ := c • W₂
  let U₁ := d • W₁
  have hU₂ : U₂ ≠ 0 := smul_ne_zero hc hW₂
  have hU₁ : U₁ ≠ 0 := smul_ne_zero hd hW₁
  have hU₂deg (a : Fin m) : U₂.degreeOf a ≤ k * r a.castSucc := by
    apply le_trans ?_ (hW₂deg a)
    change (c • W₂).degreeOf a ≤ W₂.degreeOf a
    simp only [MvPolynomial.degreeOf_eq_sup]
    exact Finset.sup_mono MvPolynomial.support_smul
  have hU₁deg : U₁.natDegree ≤ k * r (Fin.last m) :=
    (Polynomial.natDegree_smul_le _ _).trans hW₁deg
  have hfactor : lastVariableEquiv m (Matrix.det (fun i j : Fin k =>
      rothDividedDerivative (w i) j.val P)) =
        Polynomial.C U₂ * U₁.map MvPolynomial.C := by
    rw [lastVariableEquiv_rothDivided_det,
      rothMixedDerivative_det_factorization Q φ ψ hsplit w]
    exact rational_smul_separated m c d W₂ W₁
  have hactual : Matrix.det (fun i j : Fin k => rothDividedDerivative (w i) j.val P) =
      MvPolynomial.rename Fin.castSucc U₂ *
        Polynomial.aeval (MvPolynomial.X (Fin.last m)) U₁ := by
    apply (lastVariableEquiv m).injective
    rw [map_mul, lastVariableEquiv_rename_castSucc, lastVariableEquiv_aeval_last]
    exact hfactor
  have hnonzero : Matrix.det (fun i j : Fin k => rothDividedDerivative (w i) j.val P) ≠ 0 := by
    intro hz
    have hh : Polynomial.C U₂ * U₁.map MvPolynomial.C ≠ 0 :=
      mul_ne_zero (Polynomial.C_ne_zero.mpr hU₂) (Polynomial.map_ne_zero hU₁)
    apply hh
    rw [← hfactor, hz, map_zero]
  have hkactual : k ≤ P.degreeOf (Fin.last m) + 1 := by
    simpa only [Q, lastVariableEquiv_natDegree] using hk
  exact ⟨k, hkpos, hkactual, hkactual.trans (Nat.add_le_add_right (hdegree _) 1),
    w, hw, U₂, U₁, hU₂, hU₁, hU₂deg, hU₁deg, hfactor, hactual, hnonzero⟩

end Bounty
end
end RothComponent_RothDividedFactorization

/- Component: RothDeterminantIndexBound; SHA256 6c3d0930fe3041099d66f0af82d20cac4e4232af12c025172bffeceec79692dc -/
section RothComponent_RothDeterminantIndexBound
/- Real normalized determinant-index bounds and the finite triangular sum estimate. -/

namespace Bounty

noncomputable section
open scoped BigOperators

def rothWordWeight {m : ℕ} (r : Fin m → ℕ) (s : List (Fin m)) : ℝ :=
  (wordDerivativeWeight (rothWeight r) s : ℝ) / rothDenominator r

def rothWordWeight_eq_sum {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (s : List (Fin m)) : rothWordWeight r s = (s.map (fun i => (1 : ℝ) / r i)).sum := by
  induction s with
  | nil => simp [rothWordWeight, wordDerivativeWeight_nil]
  | cons i s ih =>
    simp only [rothWordWeight, wordDerivativeWeight_cons, Nat.cast_add, add_div,
      rothWeight_div_denominator hr, List.map_cons, List.sum_cons] at ih ⊢
    rw [ih]

def rothWordWeight_replicate {m : ℕ} {r : Fin m → ℕ} (hr : ∀ i, 0 < r i)
    (i : Fin m) (n : ℕ) : rothWordWeight r (List.replicate n i) = n / (r i : ℝ) := by
  rw [rothWordWeight_eq_sum hr]
  simp [List.map_replicate, List.sum_replicate, nsmul_eq_mul, div_eq_mul_inv]

def enat_normalized_sub {a : ℕ∞} (_ha : a ≠ ⊤) (b : ℕ) {D : ℝ} (hD : 0 < D) :
    ((a - (b : ℕ∞)).toNat : ℝ) / D = max ((a.toNat : ℝ) / D - b / D) 0 := by
  rw [ENat.toNat_sub (by simp), ENat.toNat_natCast]
  by_cases hb : b ≤ a.toNat
  · rw [Nat.cast_sub hb, sub_div, max_eq_left]
    exact sub_nonneg.mpr (div_le_div_of_nonneg_right (by exact_mod_cast hb) hD.le)
  · have hab : a.toNat ≤ b := by omega
    rw [Nat.sub_eq_zero_of_le hab, Nat.cast_zero, zero_div, max_eq_right]
    exact sub_nonpos.mpr (div_le_div_of_nonneg_right (by exact_mod_cast hab) hD.le)

def rothPolynomialIndex_det_row_column_loss {m : ℕ} {J : Type*} [Fintype J] [DecidableEq J]
    {r : Fin m → ℕ} (hr : ∀ i, 0 < r i) (β : Fin m → ℚ)
    (rows cols : J → List (Fin m)) (P : MvPolynomial (Fin m) ℚ) (hP : P ≠ 0)
    (A : Matrix J J (MvPolynomial (Fin m) ℚ)) (hdet : A.det ≠ 0)
    (hloss : ∀ i j, weightedPolynomialIndex (rothWeight r) β P ≤
      weightedPolynomialIndex (rothWeight r) β (A i j) +
        (wordDerivativeWeight (rothWeight r) (rows i) : ℕ∞) +
        (wordDerivativeWeight (rothWeight r) (cols j) : ℕ∞)) :
    (∑ j : J, max (rothPolynomialIndex r β P - rothWordWeight r (cols j)) 0) ≤
      rothPolynomialIndex r β A.det + ∑ i : J, rothWordWeight r (rows i) := by
  let a := weightedPolynomialIndex (rothWeight r) β P
  let V := A.det
  have ha : a ≠ ⊤ := (weightedPolynomialIndex_finite _ _ hP).ne
  have hV : weightedPolynomialIndex (rothWeight r) β V ≠ ⊤ :=
    (weightedPolynomialIndex_finite _ _ hdet).ne
  have hb (j : J) : a - (wordDerivativeWeight (rothWeight r) (cols j) : ℕ∞) ≠ ⊤ :=
    ne_top_of_le_ne_top ha tsub_le_self
  have hh := weightedPolynomialIndex_det_row_column_loss (rothWeight r) β A
    a (wordDerivativeWeight (rothWeight r) ∘ rows)
      (wordDerivativeWeight (rothWeight r) ∘ cols) hloss
  have hright : weightedPolynomialIndex (rothWeight r) β V +
      (∑ i, wordDerivativeWeight (rothWeight r) (rows i) : ℕ) ≠ ⊤ := by
    exact (ENat.add_lt_top.mpr ⟨lt_top_iff_ne_top.mpr hV, by simp⟩).ne
  have hn := ENat.toNat_le_toNat hh hright
  simp only [Function.comp_def] at hn
  rw [ENat.toNat_sum (fun j _ => hb j), ENat.toNat_add hV (by simp), ENat.toNat_natCast] at hn
  have hreal :
      ((∑ j : J, (a - (wordDerivativeWeight (rothWeight r) (cols j) : ℕ∞)).toNat : ℕ) : ℝ) ≤
        ((weightedPolynomialIndex (rothWeight r) β V).toNat : ℝ) +
          (∑ i : J, wordDerivativeWeight (rothWeight r) (rows i) : ℕ) := by
    exact_mod_cast hn
  have hD : (0 : ℝ) < rothDenominator r := by exact_mod_cast rothDenominator_pos hr
  have hnorm := div_le_div_of_nonneg_right hreal hD.le
  simp only [Nat.cast_sum, Finset.sum_div, add_div,
    enat_normalized_sub ha _ hD] at hnorm
  exact hnorm

def rothPolynomialIndex_divided_mixed_det {m : ℕ} {J : Type*} [Fintype J] [DecidableEq J]
    {r : Fin m → ℕ} (hr : ∀ i, 0 < r i) (β : Fin m → ℚ)
    (rows cols : J → List (Fin m)) (P : MvPolynomial (Fin m) ℚ) (hP : P ≠ 0)
    (hdet : Matrix.det (fun i j : J => dividedWordPDeriv (cols j) (dividedWordPDeriv (rows i) P)) ≠ 0) :
    (∑ j : J, max (rothPolynomialIndex r β P - rothWordWeight r (cols j)) 0) ≤
      rothPolynomialIndex r β
        (Matrix.det (fun i j : J => dividedWordPDeriv (cols j) (dividedWordPDeriv (rows i) P))) +
          ∑ i : J, rothWordWeight r (rows i) := by
  apply rothPolynomialIndex_det_row_column_loss hr β rows cols P hP _ hdet
  intro i j
  have hrow : weightedPolynomialIndex (rothWeight r) β P ≤
      weightedPolynomialIndex (rothWeight r) β (dividedWordPDeriv (rows i) P) +
        (wordDerivativeWeight (rothWeight r) (rows i) : ℕ∞) := by
    simpa only [weightedPolynomialIndex_dividedWordPDeriv] using
      weightedPolynomialIndex_wordPDeriv (rothWeight r) β (rows i) P
  have hcol : weightedPolynomialIndex (rothWeight r) β (dividedWordPDeriv (rows i) P) ≤
      weightedPolynomialIndex (rothWeight r) β (dividedWordPDeriv (cols j) (dividedWordPDeriv (rows i) P)) +
        (wordDerivativeWeight (rothWeight r) (cols j) : ℕ∞) := by
    simpa only [weightedPolynomialIndex_dividedWordPDeriv] using
      weightedPolynomialIndex_wordPDeriv (rothWeight r) β (cols j) (dividedWordPDeriv (rows i) P)
  have hh := hrow.trans (add_le_add hcol le_rfl)
  simpa only [add_assoc, add_comm, add_left_comm] using hh

def rothPolynomialIndex_divided_mixed_det_progression {m k : ℕ}
    {r : Fin m → ℕ} (hr : ∀ i, 0 < r i) (β : Fin m → ℚ)
    (rows : Fin k → List (Fin m)) (last : Fin m) (P : MvPolynomial (Fin m) ℚ)
    (hP : P ≠ 0)
    (hdet : Matrix.det (fun i j : Fin k =>
      dividedWordPDeriv (List.replicate j.val last) (dividedWordPDeriv (rows i) P)) ≠ 0)
    (γ : ℝ) (hrows : ∀ i, rothWordWeight r (rows i) ≤ γ) :
    (∑ j : Fin k, max (rothPolynomialIndex r β P - j.val / (r last : ℝ)) 0) ≤
      rothPolynomialIndex r β (Matrix.det (fun i j : Fin k =>
        dividedWordPDeriv (List.replicate j.val last) (dividedWordPDeriv (rows i) P))) + k * γ := by
  have hh := rothPolynomialIndex_divided_mixed_det hr β rows
    (fun j : Fin k => List.replicate j.val last) P hP hdet
  simp only [rothWordWeight_replicate hr] at hh
  apply hh.trans
  apply add_le_add le_rfl
  simpa using Finset.sum_le_sum (fun i (_ : i ∈ Finset.univ) => hrows i)

def fin_sum_real_val (k : ℕ) : (∑ j : Fin k, (j.val : ℝ)) = (k : ℝ) * (k - 1) / 2 := by
  induction k with
  | zero => simp
  | succ k ih =>
    rw [Fin.sum_univ_castSucc]
    simp only [Fin.val_castSucc, Fin.val_last, ih, Nat.cast_add, Nat.cast_one]
    ring

/-- The sum of a decreasing nonnegative arithmetic progression dominates its
triangular area. This discrete induction avoids rounding or integration. -/
def arithmetic_max_sum_triangle (k : ℕ) (x : ℝ) (hx : 0 ≤ x) (hxk : x ≤ k) :
    x ^ 2 ≤ 2 * ∑ j : Fin k, max (x - j.val) 0 := by
  induction k generalizing x with
  | zero => simp only [Nat.cast_zero] at hxk; simp; nlinarith
  | succ k ih =>
    rw [Fin.sum_univ_succ]
    simp only [Fin.val_zero, Nat.cast_zero, sub_zero, max_eq_left hx,
      Fin.val_succ, Nat.cast_add, Nat.cast_one]
    have htail : (∑ j : Fin k, max (x - ((j.val : ℝ) + 1)) 0) =
        ∑ j : Fin k, max ((x - 1) - j.val) 0 := by
      apply Finset.sum_congr rfl
      intro j hj
      congr 1
      ring
    rw [htail]
    by_cases hsmall : x ≤ 1
    · have hs : 0 ≤ ∑ j : Fin k, max ((x - 1) - j.val) 0 :=
        Finset.sum_nonneg (fun _ _ => le_max_right _ _)
      nlinarith [mul_nonneg hx (sub_nonneg.mpr hsmall)]
    · have hx1 : 0 ≤ x - 1 := by linarith
      have hxk' : x - 1 ≤ (k : ℝ) := by
        simp only [Nat.cast_add, Nat.cast_one] at hxk
        linarith
      have hh := ih (x - 1) hx1 hxk'
      nlinarith

/-- Estimate (E), with the exact constant `2*m`. -/
def roth_arithmetic_progression_lower {m r k : ℕ} (hm : 2 ≤ m) (hr : 1 ≤ r)
    (_hk : 1 ≤ k) (hkr : k ≤ r + 1) {I : ℝ} (hI : 0 ≤ I) (hIm : I ≤ m) :
    ((k : ℝ) / (2 * m)) * I ^ 2 ≤ ∑ j : Fin k, max (I - j.val / (r : ℝ)) 0 := by
  have hrpos : (0 : ℝ) < r := by exact_mod_cast (by omega : 0 < r)
  have hmpos : (0 : ℝ) < m := by exact_mod_cast (by omega : 0 < m)
  have hk0 : (0 : ℝ) ≤ k := Nat.cast_nonneg k
  let S : ℝ := ∑ j : Fin k, max (I - j.val / (r : ℝ)) 0
  change ((k : ℝ) / (2 * m)) * I ^ 2 ≤ S
  rw [div_mul_eq_mul_div]
  apply (div_le_iff₀ (by positivity : (0 : ℝ) < 2 * m)).mpr
  by_cases hhigh : ((k : ℝ) - 1) / r ≤ I
  · have hraw : (k : ℝ) * I - ((k : ℝ) * (k - 1) / 2) / r ≤ S := by
      have hh := Finset.sum_le_sum (fun j (_ : j ∈ (Finset.univ : Finset (Fin k))) =>
        le_max_left (I - j.val / (r : ℝ)) 0)
      simpa only [Finset.sum_sub_distrib, Finset.sum_const, Finset.card_univ,
        Fintype.card_fin, nsmul_eq_mul, ← Finset.sum_div, fin_sum_real_val] using hh
    have hcross : (k : ℝ) - 1 ≤ I * r := (div_le_iff₀ hrpos).mp hhigh
    have hhalf : ((k : ℝ) * (k - 1) / 2) / r ≤ (k : ℝ) * I / 2 := by
      apply (div_le_iff₀ hrpos).mpr
      nlinarith [mul_nonneg hk0 (sub_nonneg.mpr hcross)]
    have hlinear : (k : ℝ) * I ≤ 2 * S := by linarith
    have hquad : I ^ 2 ≤ (m : ℝ) * I := by
      nlinarith [mul_nonneg hI (sub_nonneg.mpr hIm)]
    have hh1 := mul_le_mul_of_nonneg_left hquad hk0
    have hh2 := mul_le_mul_of_nonneg_left hlinear hmpos.le
    nlinarith
  · have hx : (r : ℝ) * I ≤ (k : ℝ) := by
      have hh := (lt_div_iff₀ hrpos).mp (lt_of_not_ge hhigh)
      nlinarith
    have htriangle := arithmetic_max_sum_triangle k ((r : ℝ) * I) (mul_nonneg hrpos.le hI) hx
    have hscale : (∑ j : Fin k, max ((r : ℝ) * I - j.val) 0) = (r : ℝ) * S := by
      dsimp only [S]
      rw [Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro j hj
      rw [mul_max_of_nonneg _ _ hrpos.le, mul_zero, mul_sub,
        mul_div_cancel₀ _ hrpos.ne']
    rw [hscale] at htriangle
    have htri : (r : ℝ) * I ^ 2 ≤ 2 * S := by
      nlinarith [sq_nonneg I]
    have hkmr : (k : ℝ) ≤ (m : ℝ) * r := by
      exact_mod_cast (by nlinarith : k ≤ m * r)
    have hh1 := mul_le_mul_of_nonneg_right hkmr (sq_nonneg I)
    have hh2 := mul_le_mul_of_nonneg_left htri hmpos.le
    nlinarith

/-- The complete lower bound (E) for the actual divided mixed determinant. -/
def roth_divided_determinant_quadratic_lower {m k : ℕ} (hm : 2 ≤ m)
    {r : Fin m → ℕ} (hr : ∀ i, 0 < r i) (β : Fin m → ℚ)
    (rows : Fin k → List (Fin m)) (last : Fin m) (P : MvPolynomial (Fin m) ℚ)
    (hP : P ≠ 0) (hdegree : ∀ i, P.degreeOf i ≤ r i)
    (hk : 1 ≤ k) (hkr : k ≤ r last + 1)
    (hdet : Matrix.det (fun i j : Fin k =>
      dividedWordPDeriv (List.replicate j.val last) (dividedWordPDeriv (rows i) P)) ≠ 0)
    (γ : ℝ) (hrows : ∀ i, rothWordWeight r (rows i) ≤ γ) :
    ((k : ℝ) / (2 * m)) * (rothPolynomialIndex r β P) ^ 2 ≤
      rothPolynomialIndex r β (Matrix.det (fun i j : Fin k =>
        dividedWordPDeriv (List.replicate j.val last) (dividedWordPDeriv (rows i) P))) + k * γ := by
  exact (roth_arithmetic_progression_lower hm (hr last) hk hkr
    (rothPolynomialIndex_nonneg r β P) (rothPolynomialIndex_le_dimension hr β hP hdegree)).trans
      (rothPolynomialIndex_divided_mixed_det_progression hr β rows last P hP hdet γ hrows)


end
end Bounty
end RothComponent_RothDeterminantIndexBound

/- Component: RothDeterminantHeightBound; SHA256 6785610d8460d9d15b0e55412a25afde9deb8d22603f26686339cc075b4e74d5 -/
section RothComponent_RothDeterminantHeightBound
/- Conservative explicit constants for the Roth auxiliary determinant. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def roth_log_factorial_bound (k q : ℕ) (hk : k ≤ q + 1) :
    Real.log (k.factorial : ℝ) ≤ (k : ℝ) * q := by
  by_cases hk0 : k = 0
  · subst k; simp
  have hkp : (0 : ℝ) < k := by exact_mod_cast Nat.pos_of_ne_zero hk0
  have hfp : (0 : ℝ) < k.factorial := by exact_mod_cast Nat.factorial_pos k
  have hf : (k.factorial : ℝ) ≤ (k : ℝ) ^ k := by exact_mod_cast Nat.factorial_le_pow k
  have hlog := Real.log_le_log hfp hf
  rw [Real.log_pow] at hlog
  have hkq : (k : ℝ) - 1 ≤ q := by
    have hh : (k : ℝ) ≤ (q : ℝ) + 1 := by exact_mod_cast hk
    linarith
  exact hlog.trans (mul_le_mul_of_nonneg_left
    ((Real.log_le_sub_one_of_pos hkp).trans hkq) hkp.le)

def roth_log_four_le_two : Real.log 4 ≤ 2 := by
  have h := Real.log_le_sub_one_of_pos (show (0 : ℝ) < 2 by norm_num)
  have heq : Real.log 4 = 2 * Real.log 2 := by
    simpa only [show (2 : ℝ) ^ 2 = 4 by norm_num, Nat.cast_ofNat] using
      (Real.log_pow (2 : ℝ) 2)
  rw [heq]
  linarith

def roth_determinant_log_bound {I : Type*} [Fintype I] [DecidableEq I]
    {k : ℕ} (rows cols : Fin k → List I) (r : I → ℕ)
    (P : MvPolynomial I ℚ) (hP : P ≠ 0) (hbox : PolynomialBoxBound r P)
    (r₀ q : ℕ) (hk : k ≤ q + 1)
    (hR : ((∑ i, r i : ℕ) : ℝ) ≤ (4 / 3 : ℝ) * r₀)
    (hq : (q : ℝ) ≤ (r₀ : ℝ) / 4)
    (hdet : Matrix.det (fun i j : Fin k => dividedWordPDeriv (rows i)
      (dividedWordPDeriv (cols j) P)) ≠ 0) :
    Real.log (polynomialCoeffL1 (Matrix.det (fun i j : Fin k => dividedWordPDeriv (rows i)
      (dividedWordPDeriv (cols j) P)))) ≤
        (k : ℝ) * (Real.log (polynomialCoeffL1 P) + 3 * r₀) := by
  have hL := polynomialCoeffL1_pos hP
  have hA := polynomialCoeffL1_det_log_le
    (fun i j : Fin k => dividedWordPDeriv (rows i) (dividedWordPDeriv (cols j) P)) hdet
    ((4 : ℝ) ^ (∑ i, r i) * polynomialCoeffL1 P)
    (mul_pos (by positivity) hL)
    (fun i j => polynomialCoeffL1_double_dividedWordPDeriv _ _ r P hbox)
  simp only [Fintype.card_fin] at hA
  rw [Real.log_mul (by positivity) hL.ne', Real.log_pow] at hA
  have hfact := roth_log_factorial_bound k q hk
  have hlog4 := roth_log_four_le_two
  have hR0 : (0 : ℝ) ≤ (∑ i, r i : ℕ) := Nat.cast_nonneg _
  have hsmall : (q : ℝ) + (∑ i, r i : ℕ) * Real.log 4 ≤ 3 * r₀ := by
    have ht := mul_le_mul_of_nonneg_left hlog4 hR0
    have hr₀ : (0 : ℝ) ≤ r₀ := Nat.cast_nonneg _
    nlinarith
  have hmul := mul_le_mul_of_nonneg_left hsmall (Nat.cast_nonneg k : (0 : ℝ) ≤ k)
  nlinarith


end
end Bounty
end RothComponent_RothDeterminantHeightBound

/- Component: RothSeparatedIndex; SHA256 00b3c3db66b11d3832f066427d3e07bdcbf86da81a5f0fde6a0fe883df952929 -/
section RothComponent_RothSeparatedIndex
/- Exact normalized index formulas for polynomials on separated variable sets. -/

namespace Bounty

noncomputable section
open scoped BigOperators
open Polynomial

def weightedTaylor_rename {m n : ℕ} (f : Fin m → Fin n) (β : Fin n → ℚ)
    (P : MvPolynomial (Fin m) ℚ) :
    weightedTaylor β (MvPolynomial.rename f P) =
      MvPolynomial.rename f (weightedTaylor (β ∘ f) P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [weightedTaylor_C]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [map_mul, MvPolynomial.rename_X, weightedTaylor_X, map_add,
      MvPolynomial.rename_C, hP, Function.comp_apply]

def rothMonomialWeight_mapDomain {m n : ℕ} (f : Fin m → Fin n)
    (r : Fin n → ℕ) (d : Fin m →₀ ℕ) :
    rothMonomialWeight r (d.mapDomain f) = rothMonomialWeight (r ∘ f) d := by
  have hh := Finsupp.sum_mapDomain_index (f := f) (s := d)
    (h := fun i (v : ℕ) => (v : ℝ) / r i)
    (fun _ => by simp) (fun _ _ _ => by simp only [Nat.cast_add, add_div])
  rw [(d.mapDomain f).sum_fintype (fun i (v : ℕ) => (v : ℝ) / r i) (fun _ => by simp),
    d.sum_fintype (fun i (v : ℕ) => (v : ℝ) / r (f i)) (fun _ => by simp)] at hh
  exact hh

/-- Adding unused variables leaves the normalized index unchanged, with the
degree bounds and evaluation point restricted along the injection. -/
def rothPolynomialIndex_rename {m n : ℕ} {r : Fin n → ℕ} (hr : ∀ i, 0 < r i)
    (β : Fin n → ℚ) (f : Fin m → Fin n) (hf : Function.Injective f)
    (P : MvPolynomial (Fin m) ℚ) (hP : P ≠ 0) :
    rothPolynomialIndex r β (MvPolynomial.rename f P) =
      rothPolynomialIndex (r ∘ f) (β ∘ f) P := by
  classical
  have hr' (i : Fin m) : 0 < (r ∘ f) i := hr (f i)
  have hQ : MvPolynomial.rename f P ≠ 0 := by
    intro hh
    exact hP ((MvPolynomial.rename_eq_zero_iff_of_injective P hf).mp hh)
  have hsupport : (weightedTaylor β (MvPolynomial.rename f P)).support =
      Finset.image (Finsupp.mapDomain f) (weightedTaylor (β ∘ f) P).support := by
    rw [weightedTaylor_rename, MvPolynomial.support_rename_of_injective hf]
  apply le_antisymm
  · obtain ⟨d, hd, heq⟩ := rothPolynomialIndex_attained hr' (β ∘ f) hP
    have hmem : d.mapDomain f ∈ (weightedTaylor β (MvPolynomial.rename f P)).support := by
      rw [hsupport]
      exact Finset.mem_image.mpr ⟨d, hd, rfl⟩
    have hh := rothPolynomialIndex_le_support hr β (MvPolynomial.rename f P) hmem
    rw [rothMonomialWeight_mapDomain, ← heq] at hh
    exact hh
  · obtain ⟨e, he, heq⟩ := rothPolynomialIndex_attained hr β hQ
    rw [hsupport] at he
    obtain ⟨d, hd, rfl⟩ := Finset.mem_image.mp he
    rw [heq, rothMonomialWeight_mapDomain]
    exact rothPolynomialIndex_le_support hr' (β ∘ f) P hd

def rothPolynomialIndex_first_embedding {m : ℕ} {r : Fin (m + 1) → ℕ}
    (hr : ∀ i, 0 < r i) (β : Fin (m + 1) → ℚ)
    (P : MvPolynomial (Fin m) ℚ) (hP : P ≠ 0) :
    rothPolynomialIndex r β (MvPolynomial.rename Fin.castSucc P) =
      rothPolynomialIndex (r ∘ Fin.castSucc) (β ∘ Fin.castSucc) P :=
  rothPolynomialIndex_rename hr β Fin.castSucc (Fin.castSucc_injective m) P hP

def roth_last_embedding_eq_rename {m : ℕ} (F : ℚ[X]) :
    Polynomial.aeval (MvPolynomial.X (Fin.last m)) F =
      MvPolynomial.rename (fun _ : Fin 1 => Fin.last m)
        ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm F) := by
  rw [Polynomial.aeval_def, MvPolynomial.rename_eq_aeval, MvPolynomial.aeval_def]
  change F.eval₂ MvPolynomial.C (MvPolynomial.X (Fin.last m)) =
    ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm F).eval₂ MvPolynomial.C
      (fun _ => MvPolynomial.X (Fin.last m))
  exact MvPolynomial.eval₂_const_uniqueAlgEquiv_symm.symm

def roth_last_embedding_ne_zero {m : ℕ} {F : ℚ[X]} (hF : F ≠ 0) :
    Polynomial.aeval (MvPolynomial.X (R := ℚ) (Fin.last m)) F ≠ 0 := by
  change F.toMvPolynomial (Fin.last m) ≠ 0
  intro hh
  apply hF
  apply Polynomial.toMvPolynomial_injective (Fin.last m)
  exact hh.trans (map_zero _).symm

def rothPolynomialIndex_last_embedding {m : ℕ} {r : Fin (m + 1) → ℕ}
    (hr : ∀ i, 0 < r i) (β : Fin (m + 1) → ℚ) (F : ℚ[X]) (hF : F ≠ 0) :
    rothPolynomialIndex r β (Polynomial.aeval (MvPolynomial.X (Fin.last m)) F) =
      (F.rootMultiplicity (β (Fin.last m)) : ℝ) / r (Fin.last m) := by
  let f : Fin 1 → Fin (m + 1) := fun _ => Fin.last m
  have hf : Function.Injective f := fun _ _ _ => Subsingleton.elim _ _
  have hr' (i : Fin 1) : 0 < (r ∘ f) i := hr (f i)
  have hQ : (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm F ≠ 0 := by
    intro hh
    apply hF
    exact (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm.injective
      (hh.trans (map_zero _).symm)
  rw [roth_last_embedding_eq_rename]
  change rothPolynomialIndex r β (MvPolynomial.rename f
    ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm F)) = _
  rw [rothPolynomialIndex_rename hr β f hf _ hQ,
    rothPolynomialIndex_eq_rootMultiplicity hr' (β ∘ f) hQ, AlgEquiv.apply_symm_apply]
  rfl

/-- The exact separated-factor formula used in the induction on the number of variables. -/
def rothPolynomialIndex_separated_product {m : ℕ} {r : Fin (m + 1) → ℕ}
    (hr : ∀ i, 0 < r i) (β : Fin (m + 1) → ℚ)
    (F₂ : MvPolynomial (Fin m) ℚ) (hF₂ : F₂ ≠ 0) (F₁ : ℚ[X]) (hF₁ : F₁ ≠ 0) :
    rothPolynomialIndex r β (MvPolynomial.rename Fin.castSucc F₂ *
      Polynomial.aeval (MvPolynomial.X (Fin.last m)) F₁) =
        rothPolynomialIndex (r ∘ Fin.castSucc) (β ∘ Fin.castSucc) F₂ +
          (F₁.rootMultiplicity (β (Fin.last m)) : ℝ) / r (Fin.last m) := by
  have hleft : MvPolynomial.rename Fin.castSucc F₂ ≠ 0 := by
    intro hh
    exact hF₂ ((MvPolynomial.rename_eq_zero_iff_of_injective F₂ (Fin.castSucc_injective m)).mp hh)
  rw [rothPolynomialIndex_mul r β hleft (roth_last_embedding_ne_zero hF₁),
    rothPolynomialIndex_first_embedding hr β F₂ hF₂,
    rothPolynomialIndex_last_embedding hr β F₁ hF₁]

end
end Bounty
end RothComponent_RothSeparatedIndex

/- Component: IntegerPolynomialReification; SHA256 33472f3697cbca9b3a29d38c7a4772168ea8a575d55a97aadae0e1e2a8b17e20 -/
section RothComponent_IntegerPolynomialReification
/- Reification of integral rational coefficients via polynomial map-range criteria,
including divided derivative matrices and their ordinary determinants. -/

namespace Bounty
noncomputable section
open scoped BigOperators Polynomial

variable {I J : Type*}

def HasIntegerMvCoefficients (P : MvPolynomial I ℚ) : Prop :=
  ∀ d, ∃ z : ℤ, MvPolynomial.coeff d P = (z : ℚ)

def HasIntegerIteratedCoefficients (V : Polynomial (MvPolynomial I ℚ)) : Prop :=
  ∀ n, HasIntegerMvCoefficients (V.coeff n)

def hasIntegerMvCoefficients_map (P : MvPolynomial I ℤ) :
    HasIntegerMvCoefficients (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  intro d
  exact ⟨MvPolynomial.coeff d P, by simp [MvPolynomial.coeff_map]⟩

/-- The existing coefficient-range criterion constructs an actual integer polynomial. -/
def exists_integer_mvPolynomial (P : MvPolynomial I ℚ) (hP : HasIntegerMvCoefficients P) :
    ∃ Q : MvPolynomial I ℤ, MvPolynomial.map (Int.castRingHom ℚ) Q = P := by
  apply MvPolynomial.mem_range_map_iff_coeffs_subset.mpr
  intro a ha
  obtain ⟨d, _, rfl⟩ := MvPolynomial.mem_coeffs_iff.mp ha
  obtain ⟨z, hz⟩ := hP d
  exact ⟨z, hz.symm⟩

def hasIntegerMvCoefficients_iff_exists (P : MvPolynomial I ℚ) :
    HasIntegerMvCoefficients P ↔
      ∃ Q : MvPolynomial I ℤ, MvPolynomial.map (Int.castRingHom ℚ) Q = P := by
  constructor
  · exact exists_integer_mvPolynomial P
  · rintro ⟨Q, rfl⟩
    exact hasIntegerMvCoefficients_map Q

def exists_integer_iteratedPolynomial (V : Polynomial (MvPolynomial I ℚ))
    (hV : HasIntegerIteratedCoefficients V) :
    ∃ W : Polynomial (MvPolynomial I ℤ),
      W.map (MvPolynomial.map (Int.castRingHom ℚ)) = V := by
  apply (Polynomial.mem_lifts V).mp
  apply (Polynomial.lifts_iff_coeff_lifts V).mpr
  intro n
  exact exists_integer_mvPolynomial (V.coeff n) (hV n)

def hasIntegerMvCoefficients_dividedWordPDeriv [Fintype I] [DecidableEq I]
    (s : List I) (P : MvPolynomial I ℚ) (hP : HasIntegerMvCoefficients P) :
    HasIntegerMvCoefficients (dividedWordPDeriv s P) :=
  dividedWordPDeriv_integral s P hP

def exists_integer_dividedWordPDeriv [Fintype I] [DecidableEq I]
    (s : List I) (P : MvPolynomial I ℤ) :
    ∃ Q : MvPolynomial I ℤ, MvPolynomial.map (Int.castRingHom ℚ) Q =
      dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P) :=
  exists_integer_mvPolynomial _ (hasIntegerMvCoefficients_dividedWordPDeriv s _
    (hasIntegerMvCoefficients_map P))

/-- Reify the entries, then use the actual ring-homomorphism determinant identity. -/
def exists_integer_determinant [Fintype J] [DecidableEq J]
    (A : Matrix J J (MvPolynomial I ℚ))
    (hA : ∀ i j, HasIntegerMvCoefficients (A i j)) :
    ∃ Q : MvPolynomial I ℤ, MvPolynomial.map (Int.castRingHom ℚ) Q = A.det := by
  classical
  choose B hB using fun i j => exists_integer_mvPolynomial (A i j) (hA i j)
  refine ⟨Matrix.det (Matrix.of B), ?_⟩
  rw [RingHom.map_det]
  apply congrArg Matrix.det
  funext i j
  exact hB i j

def hasIntegerMvCoefficients_det [Fintype J] [DecidableEq J]
    (A : Matrix J J (MvPolynomial I ℚ))
    (hA : ∀ i j, HasIntegerMvCoefficients (A i j)) :
    HasIntegerMvCoefficients A.det :=
  (hasIntegerMvCoefficients_iff_exists A.det).mpr (exists_integer_determinant A hA)

def hasIntegerMvCoefficients_rename {K : Type*} (f : I → K)
    (P : MvPolynomial I ℚ) (hP : HasIntegerMvCoefficients P) :
    HasIntegerMvCoefficients (MvPolynomial.rename f P) := by
  obtain ⟨Q, rfl⟩ := exists_integer_mvPolynomial P hP
  rw [← MvPolynomial.map_rename]
  exact hasIntegerMvCoefficients_map (MvPolynomial.rename f Q)

def hasIntegerIteratedCoefficients_finSuccEquiv {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (hP : HasIntegerMvCoefficients P) :
    HasIntegerIteratedCoefficients (MvPolynomial.finSuccEquiv ℚ m P) := by
  intro n d
  rw [MvPolynomial.finSuccEquiv_coeff_coeff]
  exact hP _

/-- This expression is definitionally the `lastVariableEquiv` used in the Roth
factorization module; the bridge does not depend on that larger proof module. -/
def exists_integer_lastVariablePolynomial {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) ℚ) (hP : HasIntegerMvCoefficients P) :
    ∃ V : Polynomial (MvPolynomial (Fin m) ℤ),
      V.map (MvPolynomial.map (Int.castRingHom ℚ)) =
        MvPolynomial.finSuccEquiv ℚ m (MvPolynomial.rename (finRotate (m + 1)) P) := by
  apply exists_integer_iteratedPolynomial
  exact hasIntegerIteratedCoefficients_finSuccEquiv _
    (hasIntegerMvCoefficients_rename (finRotate (m + 1)) P hP)


end
end Bounty
end RothComponent_IntegerPolynomialReification

/- Component: RothDegreeBounds; SHA256 fe90c59dad2ce4930b12b6d5010fc538c0c25fafee4d8b5732393941fe7f6a8a -/
section RothComponent_RothDegreeBounds
/- Elementary consequences of the descending degree ratios in Roth's induction. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def roth_degree_decay_antitone {m : ℕ} (r : Fin (m + 1) → ℕ) (θ : ℝ)
    (hθ : θ ≤ 1) (hstep : ∀ i : Fin m, (r i.succ : ℝ) ≤ θ * r i.castSucc) :
    Antitone r := by
  apply Fin.antitone_iff_succ_le.mpr
  intro i
  have hh : (r i.succ : ℝ) ≤ r i.castSucc :=
    (hstep i).trans (by nlinarith [Nat.cast_nonneg (r i.castSucc) (α := ℝ)])
  exact_mod_cast hh

def roth_degree_decay_sum {m : ℕ} (r : Fin (m + 1) → ℕ) (θ : ℝ)
    (hθ : θ ≤ (1 / 4 : ℝ))
    (hstep : ∀ i : Fin m, (r i.succ : ℝ) ≤ θ * r i.castSucc) :
    ((∑ i, r i : ℕ) : ℝ) ≤ (4 / 3 : ℝ) * r 0 := by
  have ht : (∑ i : Fin m, (r i.succ : ℝ)) ≤
      (1 / 4 : ℝ) * (∑ i : Fin m, (r i.castSucc : ℝ)) := by
    rw [Finset.mul_sum]
    apply Finset.sum_le_sum
    intro i _
    exact (hstep i).trans (mul_le_mul_of_nonneg_right hθ (Nat.cast_nonneg _))
  have hhead : (∑ i : Fin m, (r i.castSucc : ℝ)) ≤ ∑ i : Fin (m + 1), (r i : ℝ) := by
    rw [Fin.sum_univ_castSucc]
    exact le_add_of_nonneg_right (Nat.cast_nonneg _)
  have hs := Fin.sum_univ_succ (fun i : Fin (m + 1) => (r i : ℝ))
  push_cast
  nlinarith

def roth_degree_decay_last {m : ℕ} (r : Fin (m + 2) → ℕ) (θ : ℝ)
    (hθ : θ ≤ (1 / 4 : ℝ))
    (hstep : ∀ i : Fin (m + 1), (r i.succ : ℝ) ≤ θ * r i.castSucc) :
    (r (Fin.last (m + 1)) : ℝ) ≤ (r 0 : ℝ) / 4 := by
  have hmono := roth_degree_decay_antitone r θ (by linarith) hstep
  have h0 : r (Fin.last (m + 1)) ≤ r (Fin.succ (0 : Fin (m + 1))) :=
    hmono (Fin.le_last _)
  have hh := hstep 0
  have hr0 : (0 : ℝ) ≤ r 0 := Nat.cast_nonneg _
  have h0r : (r (Fin.last (m + 1)) : ℝ) ≤ r (Fin.succ (0 : Fin (m + 1))) := by
    exact_mod_cast h0
  have hc : (0 : Fin (m + 1)).castSucc = (0 : Fin (m + 2)) := rfl
  rw [hc] at hh
  nlinarith

def roth_first_word_weight_bound {m : ℕ} {r : Fin (m + 2) → ℕ}
    (hr : ∀ i, 0 < r i) (hmono : Antitone r) (s : List (Fin (m + 1)))
    (hlen : s.length ≤ r (Fin.last (m + 1))) :
    rothWordWeight r (s.map Fin.castSucc) ≤
      (r (Fin.last (m + 1)) : ℝ) / r (Fin.castSucc (Fin.last m)) := by
  have hden : (0 : ℝ) < r (Fin.castSucc (Fin.last m)) := by exact_mod_cast hr _
  have hterm (i : Fin (m + 1)) : (1 : ℝ) / r i.castSucc ≤
      1 / (r (Fin.castSucc (Fin.last m)) : ℝ) := by
    apply one_div_le_one_div_of_le hden
    have hi : i.castSucc ≤ (Fin.last m).castSucc := by
      change i.val ≤ m
      omega
    exact_mod_cast hmono hi
  have hsum : (s.map (fun i => (1 : ℝ) / r i.castSucc)).sum ≤
      (s.length : ℝ) / r (Fin.castSucc (Fin.last m)) := by
    clear hlen
    induction s with
    | nil => simp
    | cons i s ih =>
      simp only [List.map_cons, List.sum_cons, List.length_cons, Nat.cast_add, Nat.cast_one, add_div]
      have hh := hterm i
      linarith
  rw [rothWordWeight_eq_sum hr, List.map_map]
  exact hsum.trans (div_le_div_of_nonneg_right (by exact_mod_cast hlen) hden.le)


end
end Bounty
end RothComponent_RothDegreeBounds

/- Component: RothUnivariateHeight; SHA256 ee5ae1c3484f1c20eed69765f491ec5cc08358a397a09fb352173fee0bb9930c -/
section RothComponent_RothUnivariateHeight
/- Standard rational height and raw integer coefficient norms for the Roth base case. -/

namespace Bounty
noncomputable section
open Polynomial
open scoped BigOperators

def rationalRoot_logHeight (β : ℚ) :
    Real.log (max ‖(β.den : ℂ)‖ ‖(β.num : ℂ)‖) = Height.logHeight₁ β := by
  rw [Rat.logHeight₁_eq_log_max]
  congr 1
  have ha : ((β.num.natAbs : ℕ) : ℝ) = |(β.num : ℝ)| := by
    calc
      (β.num.natAbs : ℝ) = ((β.num.natAbs : ℤ) : ℝ) := (Int.cast_natCast _).symm
      _ = ((|β.num| : ℤ) : ℝ) := congrArg (fun z : ℤ => (z : ℝ)) (Int.natCast_natAbs β.num)
      _ = |(β.num : ℝ)| := Int.cast_abs
  simp only [Complex.norm_natCast, Complex.norm_intCast, Nat.cast_max, ha]
  exact max_comm _ _

def integerPolynomialCoeffSum_eq_univariateCoeffL1 (P : ℤ[X]) :
    integerPolynomialCoeffSum P = univariateCoeffL1 P := by
  change univariateCoeffL1 (P.map (Int.castRingHom ℂ)) = _
  apply univariateCoeffL1_map (Int.castRingHom ℂ) Int.cast_injective
  intro a
  change ‖(a : ℂ)‖ = ‖a‖
  simp only [Complex.norm_intCast, Int.norm_eq_abs]

def univariateCoeffL1_uniqueAlgEquiv {R : Type*} [NormedCommRing R]
    (P : MvPolynomial (Fin 1) R) :
    univariateCoeffL1 (MvPolynomial.uniqueAlgEquiv R (Fin 1) P) = polynomialCoeffL1 P := by
  classical
  have hdEq (d : Fin 1 →₀ ℕ) : Finsupp.single (0 : Fin 1) (d 0) = d := by
    simpa using (Finsupp.unique_single d).symm
  have hs : (MvPolynomial.uniqueAlgEquiv R (Fin 1) P).support =
      P.support.image (fun d : Fin 1 →₀ ℕ => d 0) := by
    ext n
    simp only [Polynomial.mem_support_iff, Finset.mem_image, MvPolynomial.mem_support_iff,
      MvPolynomial.coeff_uniqueAlgEquiv]
    constructor
    · intro h
      exact ⟨Finsupp.single 0 n, h, by simp⟩
    · rintro ⟨d, hd, rfl⟩
      change MvPolynomial.coeff (Finsupp.single (0 : Fin 1) (d 0)) P ≠ 0
      rwa [hdEq d]
  have hinj : Function.Injective (fun d : Fin 1 →₀ ℕ => d 0) := by
    intro a b hab
    rw [← hdEq a, ← hdEq b]
    exact congrArg (Finsupp.single (0 : Fin 1)) hab
  rw [univariateCoeffL1, hs, Finset.sum_image hinj.injOn]
  apply Finset.sum_congr rfl
  intro d hd
  rw [MvPolynomial.coeff_uniqueAlgEquiv]
  change ‖MvPolynomial.coeff (Finsupp.single (0 : Fin 1) (d 0)) P‖ = _
  rw [hdEq d]

def rational_rootMultiplicity_standard_height_bound {P : ℤ[X]}
    (hP : P ≠ 0) (β : ℚ) :
    ((P.map (Int.castRingHom ℚ)).rootMultiplicity β : ℝ) * Height.logHeight₁ β ≤
      Real.log (univariateCoeffL1 P) := by
  simpa only [rationalRoot_logHeight, integerPolynomialCoeffSum_eq_univariateCoeffL1] using
    rational_rootMultiplicity_height_bound hP β

def rothUnivariate_standard_height_bound (r : Fin 1 → ℕ) (hr : ∀ i, 0 < r i)
    (β : Fin 1 → ℚ) {P : ℤ[X]} (hP : P ≠ 0) :
    rothPolynomialIndex r β ((MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm
      (P.map (Int.castRingHom ℚ))) * ((r 0 : ℝ) * Height.logHeight₁ (β 0)) ≤
      Real.log (univariateCoeffL1 P) := by
  simpa only [rationalRoot_logHeight, integerPolynomialCoeffSum_eq_univariateCoeffL1] using
    rothUnivariate_integer_height_bound r hr β hP

def uniqueAlgEquiv_map_int_rat (P : MvPolynomial (Fin 1) ℤ) :
    (MvPolynomial.uniqueAlgEquiv ℤ (Fin 1) P).map (Int.castRingHom ℚ) =
      MvPolynomial.uniqueAlgEquiv ℚ (Fin 1) (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  ext n
  simp only [Polynomial.coeff_map, MvPolynomial.coeff_uniqueAlgEquiv, MvPolynomial.coeff_map]

def rothUnivariate_mv_integer_height_bound (r : Fin 1 → ℕ) (hr : ∀ i, 0 < r i)
    (β : Fin 1 → ℚ) {P : MvPolynomial (Fin 1) ℤ} (hP : P ≠ 0) :
    rothPolynomialIndex r β (MvPolynomial.map (Int.castRingHom ℚ) P) *
      ((r 0 : ℝ) * Height.logHeight₁ (β 0)) ≤ Real.log (polynomialCoeffL1 P) := by
  let U := MvPolynomial.uniqueAlgEquiv ℤ (Fin 1) P
  have hU : U ≠ 0 := by
    intro hz
    apply hP
    exact (MvPolynomial.uniqueAlgEquiv ℤ (Fin 1)).injective
      (hz.trans (map_zero _).symm)
  have hh := rothUnivariate_standard_height_bound r hr β hU
  have he : (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).symm (U.map (Int.castRingHom ℚ)) =
      MvPolynomial.map (Int.castRingHom ℚ) P := by
    apply (MvPolynomial.uniqueAlgEquiv ℚ (Fin 1)).injective
    rw [AlgEquiv.apply_symm_apply]
    exact uniqueAlgEquiv_map_int_rat P
  rw [he] at hh
  simpa only [U, univariateCoeffL1_uniqueAlgEquiv] using hh


end
end Bounty
end RothComponent_RothUnivariateHeight

/- Component: LastVariableCoefficientNorm; SHA256 650c5c9fbf2a06be3a1dd0191ee8740cad52c2204cd5b33968a9ad23777325f0 -/
section RothComponent_LastVariableCoefficientNorm
/- Reindexing the coefficient sum by a variable injection or by separating
one variable preserves the exact coefficient-sum norm. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I J R : Type*} [NormedCommRing R]

def polynomialCoeffL1_rename_of_injective (f : I → J)
    (hf : Function.Injective f) (P : MvPolynomial I R) :
    polynomialCoeffL1 (MvPolynomial.rename f P) = polynomialCoeffL1 P := by
  classical
  unfold polynomialCoeffL1
  rw [MvPolynomial.support_rename_of_injective hf,
    Finset.sum_image (Finsupp.mapDomain_injective hf).injOn]
  simp only [MvPolynomial.coeff_rename_mapDomain f hf]

def polynomialCoeffL1_finSuccEquiv_coeff {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) R) (n : ℕ) :
    polynomialCoeffL1 ((MvPolynomial.finSuccEquiv R m P).coeff n) =
      ∑ d ∈ P.support with d 0 = n, ‖MvPolynomial.coeff d P‖ := by
  classical
  rw [← MvPolynomial.image_support_finSuccEquiv,
    Finset.sum_image (Finsupp.cons_right_injective n).injOn]
  simp only [polynomialCoeffL1, MvPolynomial.finSuccEquiv_coeff_coeff]

def iteratedCoeffL1_finSuccEquiv {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) R) :
    iteratedCoeffL1 (MvPolynomial.finSuccEquiv R m P) = polynomialCoeffL1 P := by
  classical
  unfold iteratedCoeffL1
  simp_rw [polynomialCoeffL1_finSuccEquiv_coeff]
  rw [MvPolynomial.support_finSuccEquiv]
  exact Finset.sum_fiberwise_of_maps_to
    (fun d hd => Finset.mem_image_of_mem (fun e : Fin (m + 1) →₀ ℕ => e 0) hd)
    (fun d => ‖MvPolynomial.coeff d P‖)

def iteratedCoeffL1_lastVariable {m : ℕ}
    (P : MvPolynomial (Fin (m + 1)) R) :
    iteratedCoeffL1 (MvPolynomial.finSuccEquiv R m
      (MvPolynomial.rename (finRotate (m + 1)) P)) = polynomialCoeffL1 P := by
  rw [iteratedCoeffL1_finSuccEquiv,
    polynomialCoeffL1_rename_of_injective _ (finRotate (m + 1)).injective]

end
end Bounty
end RothComponent_LastVariableCoefficientNorm

/- Component: IntegerRothTheorem; SHA256 59757cc1d82c5d7a0860cc5bef1c0893107ce3982b6bee164e7823038ff2068e -/
section RothComponent_IntegerRothTheorem
/- The integer coefficient-sum version of Roth's polynomial index lemma.
The theorem is proved by induction on the number of variables, using actual
nonzero divided derivative determinants and actual integer separated factors. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Polynomial

def integerMap_degreeOf {I : Type*} (P : MvPolynomial I ℤ) (i : I) :
    (MvPolynomial.map (Int.castRingHom ℚ) P).degreeOf i = P.degreeOf i := by
  classical
  simp only [MvPolynomial.degreeOf_def,
    MvPolynomial.degrees_map_of_injective P (f := Int.castRingHom ℚ) (Int.cast_injective :
      Function.Injective (Int.castRingHom ℚ))]

def integerMap_ne_zero {I : Type*} {P : MvPolynomial I ℤ} (hP : P ≠ 0) :
    MvPolynomial.map (Int.castRingHom ℚ) P ≠ 0 := by
  intro hh
  apply hP
  exact (MvPolynomial.map_injective (Int.castRingHom ℚ) Int.cast_injective)
    (hh.trans (map_zero _).symm)

def roth_theta_square (n : ℕ) (η : ℝ) : (η ^ 2) ^ (2 ^ n) = η ^ (2 ^ (n + 1)) := by
  rw [← pow_mul, pow_succ]
  congr 1
  ring

def roth_theta_step_bounds (n : ℕ) {η : ℝ} (hη : 0 < η) (hηhalf : η ≤ 1 / 2) :
    0 < η ^ (2 ^ (n + 1)) ∧ η ^ (2 ^ (n + 1)) ≤ η ^ 2 ∧
      η ^ (2 ^ (n + 1)) ≤ (1 / 4 : ℝ) := by
  have hηone : η ≤ 1 := by linarith
  have hpow : 2 ≤ 2 ^ (n + 1) := by
    rw [pow_succ]
    have := Nat.one_le_pow n 2 (by omega)
    omega
  have hh := pow_le_pow_of_le_one hη.le hηone hpow
  exact ⟨pow_pos hη _, hh, hh.trans (by
    nlinarith [mul_nonneg hη.le (sub_nonneg.mpr hηhalf)])⟩

/-- There are `n+1` variables, so this covers every positive dimension without
casts in the adjacent-degree condition. All height assumptions are pointwise. -/
def integer_roth_index_bound (n : ℕ) :
    ∀ (P : MvPolynomial (Fin (n + 1)) ℤ), P ≠ 0 →
    ∀ (r : Fin (n + 1) → ℕ), (∀ i, 0 < r i) → (∀ i, P.degreeOf i ≤ r i) →
    ∀ (β : Fin (n + 1) → ℚ) (η : ℝ), 0 < η → η ≤ 1 / 2 →
    (∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc) →
    (∀ i, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r i : ℝ) * Height.logHeight₁ (β i))) →
    rothPolynomialIndex r β (MvPolynomial.map (Int.castRingHom ℚ) P) ≤ 2 * (n + 1 : ℕ) * η := by
  induction n with
  | zero =>
    intro P hP r hr hdegree β η hη hηhalf hstep hheight
    have hroot := rothUnivariate_mv_integer_height_bound r hr β hP
    have hh := hheight 0
    simp only [Nat.zero_add, pow_zero, pow_one, Nat.cast_one] at hh ⊢
    have hL : 0 ≤ Real.log (polynomialCoeffL1 P) := Real.log_nonneg (one_le_polynomialCoeffL1_int hP)
    have hr0 : (0 : ℝ) < r 0 := by exact_mod_cast hr 0
    have hH : 0 < (r 0 : ℝ) * Height.logHeight₁ (β 0) := by
      by_contra hn
      have hneg := mul_nonpos_of_nonneg_of_nonpos hη.le (le_of_not_gt hn)
      nlinarith
    have hi : rothPolynomialIndex r β (MvPolynomial.map (Int.castRingHom ℚ) P) ≤ η := by
      apply (mul_le_mul_iff_left₀ hH).mp
      nlinarith
    linarith
  | succ n ih =>
    intro P hP r hr hdegree β η hη hηhalf hstep hheight
    let Q : MvPolynomial (Fin (n + 2)) ℚ := MvPolynomial.map (Int.castRingHom ℚ) P
    let θ : ℝ := η ^ (2 ^ (n + 1))
    have hQ : Q ≠ 0 := integerMap_ne_zero hP
    have hQdegree (i) : Q.degreeOf i ≤ r i := by
      simpa only [Q, integerMap_degreeOf] using hdegree i
    have hbox : PolynomialBoxBound r Q := fun d hd i =>
      (MvPolynomial.monomial_le_degreeOf i hd).trans (hQdegree i)
    obtain ⟨hθpos, hθη, hθquarter⟩ := roth_theta_step_bounds n hη hηhalf
    change 0 < θ at hθpos
    change θ ≤ η ^ 2 at hθη
    change θ ≤ (1 / 4 : ℝ) at hθquarter
    have hmono : Antitone r := roth_degree_decay_antitone r θ (by linarith) hstep
    have hR := roth_degree_decay_sum r θ hθquarter hstep
    have hlast := roth_degree_decay_last r θ hθquarter hstep
    obtain ⟨k, hkpos, hkactual, hk, w, hw, U₂, U₁, hU₂, hU₁, hU₂deg, hU₁deg,
      hfactor, hactual, hV⟩ := exists_rothDivided_factorization Q hQ r hQdegree
    let rows (i : Fin k) := (w i).map Fin.castSucc
    let cols (j : Fin k) := List.replicate j.val (Fin.last (n + 1))
    let A : Matrix (Fin k) (Fin k) (MvPolynomial (Fin (n + 2)) ℚ) :=
      fun i j => dividedWordPDeriv (cols j) (dividedWordPDeriv (rows i) Q)
    let V := A.det
    change V ≠ 0 at hV
    have hVk : Real.log (polynomialCoeffL1 V) ≤
        (k : ℝ) * (Real.log (polynomialCoeffL1 P) + 3 * (r 0 : ℝ)) := by
      have htranspose : Matrix.det (fun i j : Fin k =>
          dividedWordPDeriv (cols i) (dividedWordPDeriv (rows j) Q)) ≠ 0 := by
        change A.transpose.det ≠ 0
        rw [Matrix.det_transpose]
        exact hV
      have hh := roth_determinant_log_bound cols rows r Q hQ hbox (r 0)
        (r (Fin.last (n + 1))) hk hR hlast htranspose
      change Real.log (polynomialCoeffL1 A.transpose.det) ≤ _ at hh
      rw [Matrix.det_transpose] at hh
      simpa only [V, Q, polynomialCoeffL1_map_int_rat] using hh
    have hVint : HasIntegerMvCoefficients V := by
      apply hasIntegerMvCoefficients_det A
      intro i j
      exact hasIntegerMvCoefficients_dividedWordPDeriv (cols j) _
        (hasIntegerMvCoefficients_dividedWordPDeriv (rows i) _ (hasIntegerMvCoefficients_map P))
    obtain ⟨W, hW⟩ := exists_integer_lastVariablePolynomial V hVint
    have hWmap : W.map (MvPolynomial.map (Int.castRingHom ℚ)) = lastVariableEquiv (n + 1) V := hW
    obtain ⟨F₂, F₁, c, hF₂, hF₁, hc, hWfactor, hF₂map, hF₁map⟩ :=
      integer_separated_polynomial_factors W U₂ U₁ hU₂ hU₁ (hWmap.trans hfactor)
    have hWnorm : iteratedCoeffL1 W = polynomialCoeffL1 V := by
      calc
        _ = iteratedCoeffL1 (W.map (MvPolynomial.map (Int.castRingHom ℚ))) :=
          (iteratedCoeffL1_map_int_rat W).symm
        _ = iteratedCoeffL1 (lastVariableEquiv (n + 1) V) := congrArg iteratedCoeffL1 hWmap
        _ = _ := iteratedCoeffL1_lastVariable V
    obtain ⟨hF₂log0, hF₁log0, hF₂log, hF₁log⟩ := separated_factor_log_bounds F₂ F₁ hF₂ hF₁
    rw [← hWfactor, hWnorm] at hF₂log hF₁log
    have hF₂bound := hF₂log.trans hVk
    have hF₁bound := hF₁log.trans hVk
    have hF₂degree (i : Fin (n + 1)) : F₂.degreeOf i ≤ k * r i.castSucc := by
      rw [← integerMap_degreeOf F₂ i, hF₂map]
      apply le_trans ?_ (hU₂deg i)
      simp only [MvPolynomial.degreeOf_eq_sup]
      exact Finset.sup_mono MvPolynomial.support_smul
    have hF₂Q : MvPolynomial.map (Int.castRingHom ℚ) F₂ ≠ 0 := integerMap_ne_zero hF₂
    have hF₁Q : F₁.map (Int.castRingHom ℚ) ≠ 0 := by
      intro hz
      exact hF₁ ((Polynomial.map_injective (Int.castRingHom ℚ) Int.cast_injective)
        (hz.trans (Polynomial.map_zero _).symm))
    have hVfactor : V = MvPolynomial.rename Fin.castSucc (MvPolynomial.map (Int.castRingHom ℚ) F₂) *
        Polynomial.aeval (MvPolynomial.X (Fin.last (n + 1))) (F₁.map (Int.castRingHom ℚ)) := by
      rw [hF₂map, hF₁map, map_smul, map_smul, smul_mul_smul, mul_inv_cancel₀ hc, one_smul]
      exact hactual
    have hVindex := rothPolynomialIndex_separated_product hr β _ hF₂Q _ hF₁Q
    rw [← hVfactor] at hVindex
    let r' : Fin (n + 1) → ℕ := fun i => k * r i.castSucc
    have hr' (i) : 0 < r' i := Nat.mul_pos hkpos (hr _)
    have hηsq : 0 < η ^ 2 := pow_pos hη _
    have hηsqhalf : η ^ 2 ≤ (1 / 2 : ℝ) := by
      nlinarith [mul_nonneg hη.le (sub_nonneg.mpr hηhalf)]
    have hstep' (i : Fin n) : (r' i.succ : ℝ) ≤ (η ^ 2) ^ (2 ^ n) * r' i.castSucc := by
      have hh := mul_le_mul_of_nonneg_left (hstep i.castSucc) (Nat.cast_nonneg k : (0 : ℝ) ≤ k)
      rw [roth_theta_square]
      dsimp only [r']
      push_cast
      have hi : i.succ.castSucc = i.castSucc.succ := by ext; rfl
      simpa only [hi, mul_assoc, mul_left_comm, mul_comm] using hh
    have hheight' (i : Fin (n + 1)) :
        Real.log (polynomialCoeffL1 F₂) + 4 * (n + 1 : ℕ) * (r' 0 : ℝ) ≤
          (η ^ 2) ^ (2 ^ n) * ((r' i : ℝ) * Height.logHeight₁ (β i.castSucc)) := by
      have hh := mul_le_mul_of_nonneg_left (hheight i.castSucc) (Nat.cast_nonneg k : (0 : ℝ) ≤ k)
      rw [roth_theta_square]
      dsimp only [r']
      push_cast at hh ⊢
      have hr0 := Nat.cast_nonneg (r 0) (α := ℝ)
      have hk0 := Nat.cast_nonneg k (α := ℝ)
      rw [show (Fin.castSucc (0 : Fin (n + 1)) : Fin (n + 2)) = 0 from rfl]
      nlinarith only [hF₂bound, hh, mul_nonneg hk0 hr0]
    have hfirst := ih F₂ hF₂ r' hr' hF₂degree (β ∘ Fin.castSucc) (η ^ 2) hηsq hηsqhalf hstep' hheight'
    have hfirstscale := rothPolynomialIndex_scale (fun i : Fin (n + 1) => hr i.castSucc)
      (β ∘ Fin.castSucc) hF₂Q hkpos
    change rothPolynomialIndex r' (β ∘ Fin.castSucc) (MvPolynomial.map (Int.castRingHom ℚ) F₂) = _ at hfirstscale
    rw [hfirstscale] at hfirst
    have hkreal : (0 : ℝ) < k := by exact_mod_cast hkpos
    have hfirstbound : rothPolynomialIndex (r ∘ Fin.castSucc) (β ∘ Fin.castSucc)
        (MvPolynomial.map (Int.castRingHom ℚ) F₂) ≤ 2 * k * (n + 1 : ℕ) * η ^ 2 := by
      have hh := (div_le_iff₀ hkreal).mp hfirst
      simpa only [Function.comp_def, mul_assoc, mul_left_comm, mul_comm] using hh
    let H : ℝ := (r (Fin.last (n + 1)) : ℝ) * Height.logHeight₁ (β (Fin.last (n + 1)))
    have hL : 0 ≤ Real.log (polynomialCoeffL1 P) := Real.log_nonneg (one_le_polynomialCoeffL1_int hP)
    have hr0 : (0 : ℝ) < r 0 := by exact_mod_cast hr 0
    have hH : 0 < H := by
      have hh := hheight (Fin.last (n + 1))
      change Real.log (polynomialCoeffL1 P) + 4 * (n + 1 + 1 : ℕ) * (r 0 : ℝ) ≤ θ * H at hh
      by_contra hn
      have hneg := mul_nonpos_of_nonneg_of_nonpos hθpos.le (le_of_not_gt hn)
      have hn0 : (0 : ℝ) ≤ n := Nat.cast_nonneg n
      push_cast at hh
      nlinarith
    have hlastbound : ((F₁.map (Int.castRingHom ℚ)).rootMultiplicity (β (Fin.last (n + 1))) : ℝ) /
        r (Fin.last (n + 1)) ≤ (k : ℝ) * θ := by
      apply (mul_le_mul_iff_left₀ hH).mp
      have hroot := rational_rootMultiplicity_standard_height_bound hF₁ (β (Fin.last (n + 1)))
      have hh := mul_le_mul_of_nonneg_left (hheight (Fin.last (n + 1))) hkreal.le
      change (k : ℝ) * (Real.log (polynomialCoeffL1 P) + 4 * (n + 1 + 1 : ℕ) * (r 0 : ℝ)) ≤
        (k : ℝ) * (θ * H) at hh
      have hrden : (r (Fin.last (n + 1)) : ℝ) ≠ 0 := by exact_mod_cast (hr _).ne'
      change _ * ((r (Fin.last (n + 1)) : ℝ) * Height.logHeight₁ (β (Fin.last (n + 1)))) ≤ _
      rw [div_mul_eq_mul_div, mul_div_assoc, mul_div_cancel_left₀ _ hrden]
      change _ ≤ (k : ℝ) * θ * H
      push_cast at hh
      have hmargin : 3 * (r 0 : ℝ) ≤ 4 * ((n : ℝ) + 1 + 1) * (r 0 : ℝ) :=
        mul_le_mul_of_nonneg_right (by nlinarith [Nat.cast_nonneg n (α := ℝ)]) hr0.le
      have hscaled :
          (k : ℝ) * (Real.log (polynomialCoeffL1 P) + 3 * (r 0 : ℝ)) ≤
          (k : ℝ) * (Real.log (polynomialCoeffL1 P) +
            4 * ((n : ℝ) + 1 + 1) * (r 0 : ℝ)) :=
        mul_le_mul_of_nonneg_left (add_le_add le_rfl hmargin) hkreal.le
      have htotal := hroot.trans (hF₁bound.trans (hscaled.trans hh))
      nlinarith only [htotal]
    let γ : ℝ := (r (Fin.last (n + 1)) : ℝ) / r (Fin.castSucc (Fin.last n))
    have hγ : γ ≤ θ := by
      apply (div_le_iff₀ (by exact_mod_cast hr (Fin.castSucc (Fin.last n)))).mpr
      exact hstep (Fin.last n)
    have hrows (i : Fin k) : rothWordWeight r (rows i) ≤ γ := by
      apply roth_first_word_weight_bound hr hmono
      exact (hw i).trans (by have := i.isLt; omega)
    have hE := roth_divided_determinant_quadratic_lower (by omega : 2 ≤ n + 2)
      hr β rows (Fin.last (n + 1)) Q hQ hQdegree hkpos hk hV γ hrows
    change ((k : ℝ) / (2 * ((n + 2 : ℕ) : ℝ))) * (rothPolynomialIndex r β Q) ^ 2 ≤
      rothPolynomialIndex r β V + k * γ at hE
    push_cast at hE
    rw [hVindex] at hE
    have hfinal : ((k : ℝ) / (2 * (n + 2))) * (rothPolynomialIndex r β Q) ^ 2 ≤
        2 * k * (n + 2) * η ^ 2 := by
      have hhγ := mul_le_mul_of_nonneg_left (hγ.trans hθη) hkreal.le
      have hhθ := mul_le_mul_of_nonneg_left hθη hkreal.le
      push_cast at hfirstbound
      nlinarith
    have hcoef : (0 : ℝ) < (k : ℝ) / (2 * (n + 2)) := by positivity
    have heq : ((k : ℝ) / (2 * (n + 2))) * (2 * (n + 2) * η) ^ 2 =
        2 * k * (n + 2) * η ^ 2 := by field_simp
    rw [← heq] at hfinal
    have hsquare := (mul_le_mul_iff_right₀ hcoef).mp hfinal
    have hind : rothPolynomialIndex r β Q ≤ 2 * (n + 2) * η := by
      exact (sq_le_sq₀ (rothPolynomialIndex_nonneg r β Q) (by positivity)).mp hsquare
    change rothPolynomialIndex r β Q ≤ 2 * ((n + 1 + 1 : ℕ) : ℝ) * η
    push_cast
    nlinarith only [hind]


end
end Bounty
end RothComponent_IntegerRothTheorem


/- One-file proof candidate assembled from the actual local import graph.
A complete ordinary-kernel check and target axiom audit are still required. -/

/- Component LatticeProjection; SHA256 d1a0038da17b12bf8f0006e6161546b542b4e9e016d1186f40f694cefe606fe7 -/
section SubmissionComponent_LatticeProjection
/- Rounded lifts under projection away from one lattice vector. The proofs
give finite bounded intersections of the projected lattice, the primitive
kernel for a shortest vector, and the quantitative projected norm gap. -/

namespace Bounty
noncomputable section
open scoped InnerProductSpace

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

def latticeProjection (v : E) : E →L[ℝ] E := (ℝ ∙ v)ᗮ.starProjection

def latticeProjectionCoefficient (v x : E) : ℝ := inner ℝ v x / ‖v‖ ^ 2

def roundedLatticeLift (v x : E) : E :=
  x - (round (latticeProjectionCoefficient v x)) • v

def projectedLattice (L : Submodule ℤ E) (v : E) : Submodule ℤ E :=
  L.map ((latticeProjection v).toLinearMap.restrictScalars ℤ)

def latticeProjection_self (v : E) : latticeProjection v v = 0 :=
  Submodule.starProjection_orthogonalComplement_singleton_eq_zero v

def latticeProjection_eq (v x : E) :
    latticeProjection v x = x - latticeProjectionCoefficient v x • v := by
  rw [latticeProjection, Submodule.starProjection_orthogonal_val,
    Submodule.starProjection_singleton]
  rfl

def latticeProjection_inner (v x : E) : inner ℝ (latticeProjection v x) v = 0 := by
  apply Submodule.mem_orthogonal_singleton_iff_inner_left.mp
  exact Submodule.starProjection_apply_mem _ _

def roundedLatticeLift_mem (L : Submodule ℤ E) {v x : E}
    (hv : v ∈ L) (hx : x ∈ L) : roundedLatticeLift v x ∈ L :=
  L.sub_mem hx (L.smul_mem _ hv)

def latticeProjection_roundedLatticeLift (v x : E) :
    latticeProjection v (roundedLatticeLift v x) = latticeProjection v x := by
  simp only [roundedLatticeLift, map_sub, map_zsmul, latticeProjection_self,
    smul_zero, sub_zero]

def roundedLatticeLift_eq (v x : E) :
    roundedLatticeLift v x = latticeProjection v x +
      (latticeProjectionCoefficient v x - (round (latticeProjectionCoefficient v x) : ℝ)) • v := by
  rw [roundedLatticeLift, latticeProjection_eq, sub_smul, Int.cast_smul_eq_zsmul]
  abel

def roundedLatticeLift_norm_le (v x : E) :
    ‖roundedLatticeLift v x‖ ≤ ‖latticeProjection v x‖ + ‖v‖ / 2 := by
  rw [roundedLatticeLift_eq]
  apply (norm_add_le _ _).trans
  apply add_le_add_right
  rw [norm_smul, Real.norm_eq_abs]
  have hh := mul_le_mul_of_nonneg_right
    (abs_sub_round (latticeProjectionCoefficient v x)) (norm_nonneg v)
  nlinarith

def roundedLatticeLift_norm_sq (v x : E) :
    ‖roundedLatticeLift v x‖ ^ 2 = ‖latticeProjection v x‖ ^ 2 +
      (latticeProjectionCoefficient v x - (round (latticeProjectionCoefficient v x) : ℝ)) ^ 2 * ‖v‖ ^ 2 := by
  rw [roundedLatticeLift_eq]
  have horth : inner ℝ (latticeProjection v x)
      ((latticeProjectionCoefficient v x - (round (latticeProjectionCoefficient v x) : ℝ)) • v) = 0 := by
    rw [inner_smul_right, latticeProjection_inner, mul_zero]
  have hh := norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero _ _ horth
  simpa only [← sq, norm_smul, Real.norm_eq_abs, mul_pow, sq_abs] using hh

def roundedLatticeLift_norm_sq_le (v x : E) :
    ‖roundedLatticeLift v x‖ ^ 2 ≤ ‖latticeProjection v x‖ ^ 2 + ‖v‖ ^ 2 / 4 := by
  rw [roundedLatticeLift_norm_sq]
  have habs := abs_sub_round (latticeProjectionCoefficient v x)
  have hs : (latticeProjectionCoefficient v x -
      (round (latticeProjectionCoefficient v x) : ℝ)) ^ 2 ≤ (1 / 4 : ℝ) := by
    rcases abs_le.mp habs with ⟨hl, hu⟩
    nlinarith
  have hh := mul_le_mul_of_nonneg_right hs (sq_nonneg ‖v‖)
  linarith

/-- No primitivity or shortest-vector assumption is needed for finite bounded
intersections of the image under projection along a lattice vector. -/
def projectedLattice_finite_inter [FiniteDimensional ℝ E] (L : Submodule ℤ E) [DiscreteTopology L]
    {v : E} (hv : v ∈ L) {s : Set E} (hs : Bornology.IsBounded s) :
    Set.Finite (s ∩ (projectedLattice L v : Set E)) := by
  obtain ⟨R, hR⟩ := hs.exists_norm_le
  have hclosed : IsClosed (L : Set E) :=
    AddSubgroup.isClosed_of_discrete (H := L.toAddSubgroup)
  have hfinite : Set.Finite ((Metric.closedBall (0 : E) (R + ‖v‖ / 2)) ∩ (L : Set E)) :=
    Metric.finite_isBounded_inter_isClosed DiscreteTopology.isDiscrete
      Metric.isBounded_closedBall hclosed
  apply (hfinite.image (latticeProjection v)).subset
  rintro y ⟨hy, hyL⟩
  obtain ⟨x, hx, hxy⟩ := hyL
  change latticeProjection v x = y at hxy
  refine ⟨roundedLatticeLift v x, ⟨?_, roundedLatticeLift_mem L hv hx⟩, ?_⟩
  · rw [Metric.mem_closedBall, dist_zero_right]
    exact (roundedLatticeLift_norm_le v x).trans (by rw [hxy]; linarith [hR y hy])
  · rw [latticeProjection_roundedLatticeLift, hxy]

/-- Projecting along any lattice vector has a discrete image. -/
def projectedLattice_discreteTopology [FiniteDimensional ℝ E]
    (L : Submodule ℤ E) [DiscreteTopology L] {v : E} (hv : v ∈ L) :
    DiscreteTopology (projectedLattice L v) := by
  have hfin := projectedLattice_finite_inter L hv
    (s := Metric.closedBall (0 : E) 1) Metric.isBounded_closedBall
  have hpre := Set.Finite.preimage
    (f := (Subtype.val : projectedLattice L v → E)) Subtype.val_injective.injOn hfin
  have hball : Set.Finite (Metric.closedBall (0 : projectedLattice L v) 1) := by
    rw [show Metric.closedBall (0 : projectedLattice L v) 1 =
      {x : projectedLattice L v | ‖(x : E)‖ ≤ 1} by ext x; simp]
    simpa [Set.preimage, Metric.mem_closedBall, dist_zero_right] using hpre
  exact discreteTopology_iff_isOpen_singleton_zero.mpr
    (isOpen_singleton_of_finite_mem_nhds 0 (Metric.closedBall_mem_nhds _ (by norm_num)) hball)

/-- A shortest nonzero vector is obtained by minimizing on a finite ball. -/
def exists_shortest_lattice_vector [FiniteDimensional ℝ E]
    (L : Submodule ℤ E) [DiscreteTopology L] (hL : ∃ x ∈ L, x ≠ 0) :
    ∃ v ∈ L, v ≠ 0 ∧ ∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖ := by
  obtain ⟨x₀, hx₀, hx₀ne⟩ := hL
  have hclosed : IsClosed (L : Set E) :=
    AddSubgroup.isClosed_of_discrete (H := L.toAddSubgroup)
  have hfinite : Set.Finite (Metric.closedBall (0 : E) ‖x₀‖ ∩ (L : Set E)) :=
    Metric.finite_isBounded_inter_isClosed DiscreteTopology.isDiscrete
      Metric.isBounded_closedBall hclosed
  let s : Set E := (Metric.closedBall 0 ‖x₀‖ ∩ (L : Set E)) \ {0}
  have hs : s.Finite := hfinite.subset (by intro x hx; exact hx.1)
  have hx₀s : x₀ ∈ s := by
    exact ⟨⟨by simp, hx₀⟩, hx₀ne⟩
  obtain ⟨v, hv, hmin⟩ := Set.exists_min_image s (fun x => ‖x‖) hs ⟨x₀, hx₀s⟩
  refine ⟨v, hv.1.2, hv.2, ?_⟩
  intro x hx hxne
  by_cases hball : ‖x‖ ≤ ‖x₀‖
  · exact hmin x ⟨⟨by simpa using hball, hx⟩, hxne⟩
  · exact (hmin x₀ hx₀s).trans (le_of_lt (lt_of_not_ge hball))

/-- The exact primitive-kernel identity, deduced from shortestness by rounding. -/
def shortest_latticeProjection_eq_zero_iff (L : Submodule ℤ E) {v : E}
    (hvL : v ∈ L) (hv : v ≠ 0)
    (hshort : ∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖) {x : E} (hx : x ∈ L) :
    latticeProjection v x = 0 ↔ ∃ z : ℤ, z • v = x := by
  constructor
  · intro hz
    have hred : roundedLatticeLift v x = 0 := by
      by_contra hne
      have hmin := hshort _ (roundedLatticeLift_mem L hvL hx) hne
      have hnorm := roundedLatticeLift_norm_le v x
      rw [hz, norm_zero, zero_add] at hnorm
      have hvpos := norm_pos_iff.mpr hv
      linarith
    exact ⟨round (latticeProjectionCoefficient v x), (sub_eq_zero.mp hred).symm⟩
  · rintro ⟨z, rfl⟩
    simp [latticeProjection_self]

/-- The quantitative gap proves discreteness of the projected lattice before
choosing its own shortest vector. -/
def shortest_latticeProjection_norm_sq_gap (L : Submodule ℤ E) {v : E}
    (hvL : v ∈ L) (hshort : ∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖)
    {x : E} (hx : x ∈ L) (hproj : latticeProjection v x ≠ 0) :
    (3 / 4 : ℝ) * ‖v‖ ^ 2 ≤ ‖latticeProjection v x‖ ^ 2 := by
  have hred : roundedLatticeLift v x ≠ 0 := by
    intro hz
    apply hproj
    rw [← latticeProjection_roundedLatticeLift v x, hz, map_zero]
  have hmin := hshort _ (roundedLatticeLift_mem L hvL hx) hred
  have hsq := sq_le_sq₀ (norm_nonneg v) (norm_nonneg (roundedLatticeLift v x)) |>.mpr hmin
  have hbound := roundedLatticeLift_norm_sq_le v x
  linarith


end
end Bounty

end SubmissionComponent_LatticeProjection

/- Component ProjectedLatticeBasis; SHA256 054a2e44111522bfdd82c84aca2e9eb48fdf0c0dda3054fedb8cc4ba671a7560 -/
section SubmissionComponent_ProjectedLatticeBasis
/- Projection into the actual orthogonal-complement subtype, and integer
basis lifting using the shortest-vector kernel rather than a PID quotient. -/

namespace Bounty
noncomputable section
open scoped InnerProductSpace BigOperators
open Module

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

def latticeProjectionToOrthogonal (v : E) : E →ₗ[ℤ] (ℝ ∙ v)ᗮ :=
  (ℝ ∙ v)ᗮ.orthogonalProjectionOnto.toLinearMap.restrictScalars ℤ

def orthogonalProjectedLattice (L : Submodule ℤ E) (v : E) :
    Submodule ℤ (ℝ ∙ v)ᗮ := L.map (latticeProjectionToOrthogonal v)

def latticeProjectionMap (L : Submodule ℤ E) (v : E) :
    L →ₗ[ℤ] orthogonalProjectedLattice L v :=
  ((latticeProjectionToOrthogonal v).comp L.subtype).codRestrict _
    (fun x => ⟨x, x.property, rfl⟩)

def latticeProjectionMap_self (L : Submodule ℤ E) {v : E} (hv : v ∈ L) :
    latticeProjectionMap L v ⟨v, hv⟩ = 0 := by
  apply Subtype.ext
  apply Subtype.ext
  exact latticeProjection_self v

def latticeProjectionMap_surjective (L : Submodule ℤ E) (v : E) :
    Function.Surjective (latticeProjectionMap L v) := by
  rintro ⟨y, hy⟩
  obtain ⟨x, hx, hxy⟩ := hy
  exact ⟨⟨x, hx⟩, Subtype.ext hxy⟩

def orthogonalProjectedLattice_discreteTopology [FiniteDimensional ℝ E]
    (L : Submodule ℤ E) [DiscreteTopology L] {v : E} (hv : v ∈ L) :
    DiscreteTopology (orthogonalProjectedLattice L v) := by
  let _ := projectedLattice_discreteTopology L hv
  let f : orthogonalProjectedLattice L v → projectedLattice L v := fun y =>
    ⟨((y : (ℝ ∙ v)ᗮ) : E), by
      obtain ⟨x, hx, hxy⟩ := y.property
      exact ⟨x, hx, congrArg Subtype.val hxy⟩⟩
  have hf : Continuous f := by
    apply Continuous.subtype_mk
    exact continuous_subtype_val.comp continuous_subtype_val
  apply DiscreteTopology.of_continuous_injective hf
  intro x y h
  apply Subtype.ext
  apply Subtype.ext
  exact congrArg (fun z : projectedLattice L v => (z : E)) h

def orthogonalProjectedLattice_span (L : Submodule ℤ E) (v : E)
    (hspan : Submodule.span ℝ (L : Set E) = ⊤) :
    Submodule.span ℝ (orthogonalProjectedLattice L v : Set (ℝ ∙ v)ᗮ) = ⊤ := by
  have himage : (orthogonalProjectedLattice L v : Set (ℝ ∙ v)ᗮ) =
      (ℝ ∙ v)ᗮ.orthogonalProjectionOnto '' (L : Set E) := rfl
  rw [himage]
  change Submodule.span ℝ ((ℝ ∙ v)ᗮ.orthogonalProjectionOnto.toLinearMap '' (L : Set E)) = ⊤
  rw [← Submodule.map_span, hspan, Submodule.map_top]
  apply LinearMap.range_eq_top.mpr
  intro y
  exact ⟨y, Submodule.orthogonalProjectionOnto_mem_subspace_eq_self y⟩

def orthogonalProjectedLattice_isZLattice (L : Submodule ℤ E) (v : E)
    [DiscreteTopology (orthogonalProjectedLattice L v)]
    (hspan : Submodule.span ℝ (L : Set E) = ⊤) :
    IsZLattice ℝ (orthogonalProjectedLattice L v) :=
  ⟨orthogonalProjectedLattice_span L v hspan⟩

/-- A lift with both the projection and the half-unit reduction coefficient explicit. -/
def exists_rounded_orthogonal_lift (L : Submodule ℤ E) {v : E} (hv : v ∈ L)
    (y : orthogonalProjectedLattice L v) :
    ∃ x : L, latticeProjectionMap L v x = y ∧
      ∃ a : ℝ, |a| ≤ 1 / 2 ∧
        (x : E) = ((y : (ℝ ∙ v)ᗮ) : E) + a • v ∧
        ‖(x : E)‖ ^ 2 ≤ ‖((y : (ℝ ∙ v)ᗮ) : E)‖ ^ 2 + ‖v‖ ^ 2 / 4 := by
  obtain ⟨z, hz⟩ := latticeProjectionMap_surjective L v y
  have hze : latticeProjection v (z : E) = ((y : (ℝ ∙ v)ᗮ) : E) :=
    congrArg (fun q : orthogonalProjectedLattice L v => ((q : (ℝ ∙ v)ᗮ) : E)) hz
  refine ⟨⟨roundedLatticeLift v z, roundedLatticeLift_mem L hv z.property⟩, ?_,
    latticeProjectionCoefficient v z - (round (latticeProjectionCoefficient v z) : ℝ),
    abs_sub_round _, ?_, ?_⟩
  · apply Subtype.ext
    apply Subtype.ext
    change latticeProjection v (roundedLatticeLift v z) = _
    rw [latticeProjection_roundedLatticeLift, hze]
  · exact (roundedLatticeLift_eq v z).trans (by rw [hze])
  · simpa only [hze] using roundedLatticeLift_norm_sq_le v z

/-- Any chosen lifts of a projected basis, together with a shortest vector,
form an integer basis. No assertion about a PID quotient is assumed. -/
def exists_lattice_basis_of_projection_lifts (L : Submodule ℤ E) {v : E}
    (hvL : v ∈ L) (hv : v ≠ 0)
    (hshort : ∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖) {n : ℕ}
    (b : Basis (Fin n) ℤ (orthogonalProjectedLattice L v))
    (u : Fin n → L) (hu : ∀ i, latticeProjectionMap L v (u i) = b i) :
    ∃ B : Basis (Fin (n + 1)) ℤ L,
      B 0 = ⟨v, hvL⟩ ∧ ∀ i : Fin n, B i.succ = u i := by
  classical
  let w : Fin (n + 1) → L := Fin.cons ⟨v, hvL⟩ u
  have hli : LinearIndependent ℤ w := by
    apply Fintype.linearIndependent_iff.mpr
    intro c hc i
    have hp := congrArg (latticeProjectionMap L v) hc
    simp only [map_sum, map_smul, map_add, map_zero, Fin.sum_univ_succ, w,
      Fin.cons_zero, Fin.cons_succ, latticeProjectionMap_self, hu, smul_zero, zero_add] at hp
    have htail (j : Fin n) : c j.succ = 0 :=
      Fintype.linearIndependent_iff.mp b.linearIndependent _ hp j
    have hz : c 0 • (⟨v, hvL⟩ : L) = 0 := by
      simpa only [Fin.sum_univ_succ, w, Fin.cons_zero, Fin.cons_succ,
        htail, zero_smul, Finset.sum_const_zero, add_zero] using hc
    have hzero : c 0 = 0 := by
      have hzE : (c 0 : ℝ) • v = 0 := by
        rw [Int.cast_smul_eq_zsmul]
        exact congrArg Subtype.val hz
      have hzR : (c 0 : ℝ) = 0 := (smul_eq_zero.mp hzE).resolve_right hv
      exact_mod_cast hzR
    exact Fin.cases hzero htail i
  have hsp : ⊤ ≤ Submodule.span ℤ (Set.range w) := by
    intro x _
    let z : L := ∑ i : Fin n, b.repr (latticeProjectionMap L v x) i • u i
    have hz : latticeProjectionMap L v z = latticeProjectionMap L v x := by
      dsimp only [z]
      rw [map_sum]
      simp only [map_smul, hu]
      exact b.sum_repr _
    have hp : latticeProjectionMap L v (x - z) = 0 := by rw [map_sub, hz, sub_self]
    have hpe : latticeProjection v ((x - z : L) : E) = 0 :=
      congrArg (fun y : orthogonalProjectedLattice L v => ((y : (ℝ ∙ v)ᗮ) : E)) hp
    obtain ⟨a, ha⟩ := (shortest_latticeProjection_eq_zero_iff L hvL hv hshort
      (x - z).property).mp hpe
    have hxrep : x = a • (⟨v, hvL⟩ : L) + z := by
      apply Subtype.ext
      change (x : E) = a • v + (z : E)
      change a • v = (x : E) - (z : E) at ha
      exact (sub_eq_iff_eq_add).mp ha.symm
    rw [hxrep]
    apply Submodule.add_mem
    · exact Submodule.smul_mem _ a (Submodule.subset_span ⟨0, rfl⟩)
    · apply Submodule.sum_mem
      intro i _
      exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨i.succ, rfl⟩)
  let B := Basis.mk hli hsp
  refine ⟨B, ?_, ?_⟩
  · exact congrFun (Basis.coe_mk hli hsp) 0
  · intro i
    exact congrFun (Basis.coe_mk hli hsp) i.succ

/-- The induction interface: the lifted basis has the chosen shortest vector
first, exact projected tail, and explicit nearest-integer reduction bounds. -/
def exists_reduced_lattice_basis_lift (L : Submodule ℤ E) {v : E}
    (hvL : v ∈ L) (hv : v ≠ 0)
    (hshort : ∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖) {n : ℕ}
    (b : Basis (Fin n) ℤ (orthogonalProjectedLattice L v)) :
    ∃ B : Basis (Fin (n + 1)) ℤ L,
      B 0 = ⟨v, hvL⟩ ∧ ∀ i : Fin n,
        latticeProjectionMap L v (B i.succ) = b i ∧
        ∃ a : ℝ, |a| ≤ 1 / 2 ∧
          (B i.succ : E) = ((b i : (ℝ ∙ v)ᗮ) : E) + a • v ∧
          ‖(B i.succ : E)‖ ^ 2 ≤ ‖((b i : (ℝ ∙ v)ᗮ) : E)‖ ^ 2 + ‖v‖ ^ 2 / 4 := by
  classical
  choose u hu using fun i : Fin n => exists_rounded_orthogonal_lift L hvL (b i)
  obtain ⟨B, hB0, hB⟩ := exists_lattice_basis_of_projection_lifts L hvL hv hshort b u
    (fun i => (hu i).1)
  refine ⟨B, hB0, ?_⟩
  intro i
  rw [hB]
  exact hu i


end
end Bounty

end SubmissionComponent_ProjectedLatticeBasis

/- Component ReducedLatticeBasis; SHA256 cf044da05f2fa1ddd563749c15e84b308168c89fbb92013ab52eb9b1bd93eb51 -/
section SubmissionComponent_ReducedLatticeBasis
/- A recursively reduced integer lattice basis.  The recursion keeps the
actual orthogonal projected lattice, its basis, and the rounding coefficient
of every lift.  Thus the reduction conditions are data about the constructed
basis, rather than hypotheses about an unspecified Gram--Schmidt process. -/

namespace Bounty
noncomputable section
open scoped InnerProductSpace BigOperators
open Module

universe u

/-- Recursive shortest-projection reduction, with its successive orthogonal
lengths.  At each stage the first vector is shortest, and each remaining basis
vector is a half-unit-reduced lift of the recursively reduced projected basis. -/
def IsReducedLatticeBasis : (n : ℕ) → {E : Type u} →
    [NormedAddCommGroup E] → [InnerProductSpace ℝ E] →
    (L : Submodule ℤ E) → Basis (Fin n) ℤ L → (Fin n → ℝ) → Prop
  | 0, _, _, _, _, _, _ => True
  | n + 1, E, _, _, L, B, h =>
      ∃ (v : E) (hvL : v ∈ L), v ≠ 0 ∧
        (∀ x ∈ L, x ≠ 0 → ‖v‖ ≤ ‖x‖) ∧ B 0 = ⟨v, hvL⟩ ∧ h 0 = ‖v‖ ∧
        ∃ b : Basis (Fin n) ℤ (orthogonalProjectedLattice L v),
          IsReducedLatticeBasis n (orthogonalProjectedLattice L v) b
            (fun i => h i.succ) ∧
          ∀ i : Fin n, latticeProjectionMap L v (B i.succ) = b i ∧
            ∃ a : ℝ, |a| ≤ 1 / 2 ∧
              (B i.succ : E) = ((b i : (ℝ ∙ v)ᗮ) : E) + a • v ∧
              ‖(B i.succ : E)‖ ^ 2 ≤
                ‖((b i : (ℝ ∙ v)ᗮ) : E)‖ ^ 2 + ‖v‖ ^ 2 / 4

/-- Every full discrete lattice admits a recursively reduced integer basis. -/
def exists_reduced_lattice_basis (n : ℕ) :
    ∀ (E : Type u) [NormedAddCommGroup E] [InnerProductSpace ℝ E]
      [FiniteDimensional ℝ E] (L : Submodule ℤ E)
      [DiscreteTopology L] [IsZLattice ℝ L],
      finrank ℝ E = n →
      ∃ (B : Basis (Fin n) ℤ L) (h : Fin n → ℝ),
        IsReducedLatticeBasis n L B h := by
  induction n with
  | zero =>
      intro E _ _ _ L _ _ hdim
      let _ : Subsingleton E := Module.finrank_zero_iff.mp hdim
      exact ⟨Basis.empty L, fun i => Fin.elim0 i, trivial⟩
  | succ n ih =>
      intro E _ _ _ L _ _ hdim
      have hspan : Submodule.span ℝ (L : Set E) = ⊤ := IsZLattice.span_top
      have hnonzero : ∃ x ∈ L, x ≠ 0 := by
        by_contra! h
        have hbot : Submodule.span ℝ (L : Set E) = ⊥ := by
          apply le_antisymm _ bot_le
          exact Submodule.span_le.mpr (fun x hx => by simpa using h x hx)
        let _ : Subsingleton E := ⟨fun x y => by
          have hz (z : E) : z = 0 := by
            have : z ∈ (⊥ : Submodule ℝ E) := by
              rw [← hbot, hspan]
              trivial
            exact this
          rw [hz x, hz y]⟩
        have : finrank ℝ E = 0 := Module.finrank_eq_zero_of_subsingleton ℝ E
        omega
      obtain ⟨v, hvL, hv, hshort⟩ := exists_shortest_lattice_vector L hnonzero
      let _ := orthogonalProjectedLattice_discreteTopology L hvL
      let _ := orthogonalProjectedLattice_isZLattice L v hspan
      have hdim' : finrank ℝ (ℝ ∙ v)ᗮ = n := by
        apply Submodule.finrank_add_finrank_orthogonal'
        simpa [finrank_span_singleton hv, add_comm] using hdim.symm
      obtain ⟨b, h, hb⟩ := ih (ℝ ∙ v)ᗮ (orthogonalProjectedLattice L v) hdim'
      obtain ⟨B, hB0, hB⟩ := exists_reduced_lattice_basis_lift L hvL hv hshort b
      refine ⟨B, Fin.cons ‖v‖ h, v, hvL, hv, hshort, hB0, rfl, b, ?_, hB⟩
      exact hb

variable {E : Type u} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

def IsReducedLatticeBasis.length_pos {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) : ∀ i, 0 < h i := by
  induction n generalizing E with
  | zero => exact fun i => Fin.elim0 i
  | succ n ih =>
      obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
      exact Fin.cases (by rw [hh0]; exact norm_pos_iff.mpr hv) (ih hb)

def IsReducedLatticeBasis.first_length {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin (n + 1)) ℤ L} {h : Fin (n + 1) → ℝ}
    (hB : IsReducedLatticeBasis (n + 1) L B h) : h 0 = ‖(B 0 : E)‖ := by
  obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
  simpa [hB0] using hh0

def IsReducedLatticeBasis.first_gap {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin (n + 2)) ℤ L} {h : Fin (n + 2) → ℝ}
    (hB : IsReducedLatticeBasis (n + 2) L B h) :
    (3 / 4 : ℝ) * h 0 ^ 2 ≤ h (Fin.succ 0) ^ 2 := by
  obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
  have hp : latticeProjection v (B (Fin.succ 0) : E) =
      ((b 0 : (ℝ ∙ v)ᗮ) : E) :=
    congrArg (fun z : orthogonalProjectedLattice L v => ((z : (ℝ ∙ v)ᗮ) : E))
      (hlift 0).1
  have hn : ((b 0 : (ℝ ∙ v)ᗮ) : E) ≠ 0 := by
    intro hz
    exact b.ne_zero 0 (Subtype.ext (Subtype.ext hz))
  have hg := shortest_latticeProjection_norm_sq_gap L hvL hshort
    (B (Fin.succ 0)).property (hp ▸ hn)
  rw [hp] at hg
  simpa only [hh0, hb.first_length, Submodule.norm_coe] using hg

def IsReducedLatticeBasis.first_length_sq_le {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin (n + 1)) ℤ L} {h : Fin (n + 1) → ℝ}
    (hB : IsReducedLatticeBasis (n + 1) L B h) (i : Fin (n + 1)) :
    h 0 ^ 2 ≤ (4 / 3 : ℝ) ^ i.val * h i ^ 2 := by
  induction n generalizing E with
  | zero =>
      have hi : i = 0 := Fin.ext (by omega)
      simp [hi]
  | succ n ih =>
      refine Fin.cases (by simp) (fun j => ?_) i
      have hgap := hB.first_gap
      obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
      have ht := ih hb j
      calc
        h 0 ^ 2 ≤ (4 / 3 : ℝ) * h (Fin.succ 0) ^ 2 := by nlinarith
        _ ≤ (4 / 3 : ℝ) * ((4 / 3 : ℝ) ^ j.val * h j.succ ^ 2) :=
          mul_le_mul_of_nonneg_left ht (by norm_num)
        _ = (4 / 3 : ℝ) ^ j.succ.val * h j.succ ^ 2 := by
          rw [Fin.val_succ, pow_succ]
          ring

/-- The concrete lifted basis has the sharp geometric-series norm bound. -/
def IsReducedLatticeBasis.norm_sq_le {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) (i : Fin n) :
    ‖(B i : E)‖ ^ 2 ≤ (4 / 3 : ℝ) ^ i.val * h i ^ 2 := by
  induction n generalizing E with
  | zero => exact Fin.elim0 i
  | succ n ih =>
      refine Fin.cases (by simpa using le_of_eq (congrArg (fun t : ℝ => t ^ 2)
        hB.first_length.symm)) (fun j => ?_) i
      have hhead := hB.first_length_sq_le j.succ
      obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
      have ht := ih hb j
      rw [hh0] at hhead
      obtain ⟨a, ha, heq, hnorm⟩ := (hlift j).2
      calc
        ‖(B j.succ : E)‖ ^ 2 ≤
            ‖((b j : (ℝ ∙ v)ᗮ) : E)‖ ^ 2 + ‖v‖ ^ 2 / 4 := hnorm
        _ ≤ (4 / 3 : ℝ) ^ j.val * h j.succ ^ 2 +
            ((4 / 3 : ℝ) ^ j.succ.val * h j.succ ^ 2) / 4 :=
          add_le_add ht (div_le_div_of_nonneg_right hhead (by norm_num))
        _ = (4 / 3 : ℝ) ^ j.succ.val * h j.succ ^ 2 := by
          rw [Fin.val_succ, pow_succ]
          ring

def IsReducedLatticeBasis.norm_le {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) (i : Fin n) :
    ‖(B i : E)‖ ≤ (2 / Real.sqrt 3) ^ i.val * h i := by
  have hq : 0 ≤ 2 / Real.sqrt 3 := by positivity
  have hq2 : (2 / Real.sqrt 3) ^ 2 = (4 / 3 : ℝ) := by
    rw [div_pow, Real.sq_sqrt (by norm_num : (0 : ℝ) ≤ 3)]
    norm_num
  have hs : ((2 / Real.sqrt 3) ^ i.val * h i) ^ 2 =
      (4 / 3 : ℝ) ^ i.val * h i ^ 2 := by
    rw [mul_pow, ← pow_mul, Nat.mul_comm i.val 2, pow_mul, hq2]
  have hn : 0 ≤ (2 / Real.sqrt 3) ^ i.val * h i :=
    mul_nonneg (pow_nonneg hq _) (hB.length_pos i).le
  have hb := hB.norm_sq_le i
  nlinarith [norm_nonneg (B i : E)]

/-- The norm product is bounded by the product of successive orthogonal
lengths, with the explicit reduced-basis constant. -/
def IsReducedLatticeBasis.norm_product_le {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) :
    (∏ i : Fin n, ‖(B i : E)‖) ≤
      (2 / Real.sqrt 3) ^ (∑ i : Fin n, i.val) * ∏ i : Fin n, h i := by
  calc
    (∏ i : Fin n, ‖(B i : E)‖) ≤
        ∏ i : Fin n, (2 / Real.sqrt 3) ^ i.val * h i :=
      Finset.prod_le_prod (fun i _ => norm_nonneg _) (fun i _ => hB.norm_le i)
    _ = _ := by rw [Finset.prod_mul_distrib, Finset.prod_pow_eq_pow_sum]

def IsReducedLatticeBasis.norm_product_le_explicit {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) :
    (∏ i : Fin n, ‖(B i : E)‖) ≤
      (2 / Real.sqrt 3) ^ (n * (n - 1) / 2) * ∏ i : Fin n, h i := by
  have hs : (∑ i : Fin n, i.val) = n * (n - 1) / 2 := by
    rw [Fin.sum_univ_eq_sum_range (fun i : ℕ => i), Finset.sum_range_id]
  simpa only [hs] using hB.norm_product_le

/-- The recursive data give an actual orthogonal family in the original
ambient space and all the size-reduced triangular expansion coefficients. -/
def IsReducedLatticeBasis.exists_orthogonal_data {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) :
    ∃ (g : Fin n → E) (μ : Fin n → Fin n → ℝ),
      (∀ i, ‖g i‖ = h i) ∧
      Pairwise (fun i j => inner ℝ (g i) (g j) = 0) ∧
      (∀ i j, |μ i j| ≤ 1 / 2) ∧
      ∀ i, (B i : E) = g i + ∑ j : Fin n, if j < i then μ i j • g j else 0 := by
  classical
  induction n generalizing E with
  | zero =>
      refine ⟨fun i => Fin.elim0 i, fun i => Fin.elim0 i, ?_, ?_, ?_, ?_⟩ <;>
        intro i <;> exact Fin.elim0 i
  | succ n ih =>
      obtain ⟨v, hvL, hv, hshort, hB0, hh0, b, hb, hlift⟩ := hB
      obtain ⟨g, μ, hgnorm, hgorth, hμ, hexp⟩ := ih hb
      choose a ha heq hnorm using fun i => (hlift i).2
      let G : Fin (n + 1) → E := Fin.cons v (fun i => (g i : E))
      let M : Fin (n + 1) → Fin (n + 1) → ℝ :=
        Fin.cons (fun _ => 0) (fun i => Fin.cons (a i) (μ i))
      refine ⟨G, M, ?_, ?_, ?_, ?_⟩
      · exact Fin.cases hh0.symm hgnorm
      · intro i j
        refine Fin.cases ?_ (fun i => ?_) i
        · refine Fin.cases ?_ (fun j => ?_) j
          · exact fun hij => False.elim (hij rfl)
          · exact fun _ => Submodule.mem_orthogonal_singleton_iff_inner_right.mp (g j).property
        · refine Fin.cases ?_ (fun j => ?_) j
          · exact fun _ => Submodule.mem_orthogonal_singleton_iff_inner_left.mp (g i).property
          · exact fun hij => hgorth (fun h => hij (congrArg Fin.succ h))
      · intro i j
        refine Fin.cases (by norm_num [M]) (fun i => ?_) i
        exact Fin.cases (ha i) (hμ i) j
      · intro i
        refine Fin.cases ?_ (fun i => ?_) i
        · simp [G, hB0]
        · have hexp' := congrArg (fun z : (ℝ ∙ v)ᗮ => (z : E)) (hexp i)
          simp only [Submodule.coe_add, Submodule.coe_sum, Submodule.coe_smul,
            Submodule.coe_zero, apply_ite] at hexp'
          simp only [G, M, Fin.cons_succ, Fin.sum_univ_succ, Fin.cons_zero,
            Fin.succ_pos, ↓reduceIte, Fin.succ_lt_succ_iff]
          rw [heq i, hexp']
          abel


end
end Bounty

end SubmissionComponent_ReducedLatticeBasis

/- Component ReducedLatticeDeterminant; SHA256 962bf143e227ce3a6d8209aa3276ab80415f5e9db588b075057229a5da697a9c -/
section SubmissionComponent_ReducedLatticeDeterminant
/- Determinants and covolumes of the actual recursively reduced basis. -/

namespace Bounty
noncomputable section
open scoped InnerProductSpace BigOperators Matrix
open Module MeasureTheory

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

/-- A triangular expansion with diagonal one does not change the determinant. -/
def orthogonal_expansion_det {n : ℕ} (e : Basis (Fin n) ℝ E)
    (x g : Fin n → E) (μ : Fin n → Fin n → ℝ)
    (hexp : ∀ i, x i = g i + ∑ j : Fin n, if j < i then μ i j • g j else 0) :
    e.det x = e.det g := by
  classical
  let T : Matrix (Fin n) (Fin n) ℝ :=
    1 + Matrix.of (fun i j => if i < j then μ j i else 0)
  have hT : T.IsUpperTriangular := by
    intro i j hij
    change j < i at hij
    simp [T, ne_of_gt hij, not_lt_of_ge hij.le]
  have hdetT : T.det = 1 := by
    rw [Matrix.det_of_isUpperTriangular hT]
    simp [T]
  have hmat : e.toMatrix x = e.toMatrix g * T := by
    dsimp only [T]
    rw [Matrix.mul_add, Matrix.mul_one]
    ext i j
    change e.coord i (x j) = e.coord i (g j) +
      ∑ k : Fin n, e.coord i (g k) * (if k < j then μ j k else 0)
    rw [hexp j, map_add, map_sum]
    congr 1
    apply Finset.sum_congr rfl
    intro k _
    split_ifs <;> simp [map_smul, mul_comm]
  rw [Basis.det_apply, hmat, Matrix.det_mul, hdetT, mul_one, ← Basis.det_apply]

/-- In an orthonormal coordinate system, the absolute determinant of an
orthogonal family is exactly the product of its lengths. -/
def orthogonal_abs_det {n : ℕ} (e : OrthonormalBasis (Fin n) ℝ E)
    (g : Fin n → E) (hg : Pairwise (fun i j => inner ℝ (g i) (g j) = 0)) :
    |e.toBasis.det g| = ∏ i : Fin n, ‖g i‖ := by
  classical
  have hgram : Matrix.gram ℝ g = Matrix.diagonal (fun i => ‖g i‖ ^ 2) := by
    ext i j
    by_cases hij : i = j
    · subst j
      simp
    · simp [hij, hg hij]
  have hmat : Matrix.gram ℝ g = (e.toBasis.toMatrix g).transpose * e.toBasis.toMatrix g := by
    have he : e.toBasis.toMatrix g = Matrix.of (fun i j => e.repr (g j) i) := by
      ext i j
      exact e.coe_toBasis_repr_apply (g j) i
    rw [he]
    simpa only [Matrix.conjTranspose_eq_transpose_of_trivial]
      using Matrix.gram_eq_conjTranspose_mul e g
  have hs : (e.toBasis.det g) ^ 2 = (∏ i : Fin n, ‖g i‖) ^ 2 := by
    have hd := congrArg Matrix.det (hmat.symm.trans hgram)
    simpa only [Matrix.det_mul, Matrix.det_transpose, Matrix.det_diagonal,
      Basis.det_apply, ← sq, Finset.prod_pow] using hd
  have hp : 0 ≤ ∏ i : Fin n, ‖g i‖ := Finset.prod_nonneg (fun _ _ => norm_nonneg _)
  nlinarith [sq_abs (e.toBasis.det g), abs_nonneg (e.toBasis.det g)]

def IsReducedLatticeBasis.abs_det_eq_product {n : ℕ} {L : Submodule ℤ E}
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) (e : OrthonormalBasis (Fin n) ℝ E) :
    |e.toBasis.det (fun i => (B i : E))| = ∏ i : Fin n, h i := by
  obtain ⟨g, μ, hnorm, horth, hμ, hexp⟩ := hB.exists_orthogonal_data
  rw [orthogonal_expansion_det e.toBasis _ g μ hexp, orthogonal_abs_det e g horth]
  simp only [hnorm]

def IsReducedLatticeBasis.covolume_eq_product [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] {n : ℕ} {L : Submodule ℤ E}
    [DiscreteTopology L] [IsZLattice ℝ L]
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) (e : OrthonormalBasis (Fin n) ℝ E) :
    ZLattice.covolume L = ∏ i : Fin n, h i := by
  have hvol : volume.real (ZSpan.fundamentalDomain e.toBasis) = 1 := by
    rw [measureReal_congr (ZSpan.fundamentalDomain_ae_parallelepiped e.toBasis volume)]
    simp only [measureReal_def, e.coe_toBasis, e.volume_parallelepiped, ENNReal.toReal_one]
  rw [ZLattice.covolume_eq_det_mul_measureReal L volume B e.toBasis, hvol, mul_one]
  exact hB.abs_det_eq_product e

def IsReducedLatticeBasis.norm_product_le_covolume [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] {n : ℕ} {L : Submodule ℤ E}
    [DiscreteTopology L] [IsZLattice ℝ L]
    {B : Basis (Fin n) ℤ L} {h : Fin n → ℝ}
    (hB : IsReducedLatticeBasis n L B h) (e : OrthonormalBasis (Fin n) ℝ E) :
    (∏ i : Fin n, ‖(B i : E)‖) ≤
      (2 / Real.sqrt 3) ^ (n * (n - 1) / 2) * ZLattice.covolume L := by
  rw [hB.covolume_eq_product e]
  exact hB.norm_product_le_explicit

/-- Existence of an actual integer basis with the explicit covolume bound,
including dimension zero. -/
def exists_lattice_basis_norm_product_le_covolume [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] (L : Submodule ℤ E)
    [DiscreteTopology L] [IsZLattice ℝ L] :
    ∃ B : Basis (Fin (finrank ℝ E)) ℤ L,
      (∏ i : Fin (finrank ℝ E), ‖(B i : E)‖) ≤
        (2 / Real.sqrt 3) ^ (finrank ℝ E * (finrank ℝ E - 1) / 2) *
          ZLattice.covolume L := by
  obtain ⟨B, h, hB⟩ := exists_reduced_lattice_basis (finrank ℝ E) E L rfl
  exact ⟨B, hB.norm_product_le_covolume (stdOrthonormalBasis ℝ E)⟩


end
end Bounty

end SubmissionComponent_ReducedLatticeDeterminant

/- Component LatticeSuccessiveMinima; SHA256 308b65d5cf92bbad5e112996062e10028db8b71e49d6704b6c8e6cb19fefa6a1 -/
section SubmissionComponent_LatticeSuccessiveMinima
/- Successive Euclidean minima obtained by finite minimization in the actual
lattice.  The greedy construction is subsequently characterized intrinsically
by bounded independent tuples, so the minima do not depend on its choices. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Module

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

def latticePrefixSpan {n : ℕ} (v : Fin n → E) (k : ℕ) : Submodule ℝ E :=
  Submodule.span ℝ (v '' {i | i.val < k})

def latticePrefixSpan_eq_range {n k : ℕ} (v : Fin n → E) (hk : k ≤ n) :
    latticePrefixSpan v k =
      Submodule.span ℝ (Set.range (fun j : Fin k => v (Fin.castLE hk j))) := by
  change Submodule.span ℝ _ = Submodule.span ℝ _
  apply congrArg (Submodule.span ℝ)
  ext x
  constructor
  · rintro ⟨i, hi, rfl⟩
    exact ⟨⟨i.val, hi⟩, rfl⟩
  · rintro ⟨j, rfl⟩
    exact ⟨Fin.castLE hk j, j.isLt, rfl⟩

def latticePrefixSpan_zero {n : ℕ} (v : Fin n → E) :
    latticePrefixSpan v 0 = ⊥ := by simp [latticePrefixSpan]

def latticePrefixSpan_full {n : ℕ} (v : Fin n → E) :
    latticePrefixSpan v n = Submodule.span ℝ (Set.range v) := by
  rw [latticePrefixSpan_eq_range v le_rfl]
  rfl

def latticePrefixSpan_snoc {n k : ℕ} (v : Fin n → E) (x : E) (hk : k ≤ n) :
    latticePrefixSpan (Fin.snoc v x) k = latticePrefixSpan v k := by
  rw [latticePrefixSpan_eq_range _ (hk.trans (Nat.le_succ n)), latticePrefixSpan_eq_range _ hk]
  apply congrArg (Submodule.span ℝ)
  apply congrArg Set.range
  funext j
  rw [show Fin.castLE (hk.trans (Nat.le_succ n)) j = (Fin.castLE hk j).castSucc from rfl]
  simp only [Fin.snoc_castSucc]

def latticePrefixSpan_finrank_le [FiniteDimensional ℝ E] {n k : ℕ}
    (v : Fin n → E) (hk : k ≤ n) : finrank ℝ (latticePrefixSpan v k) ≤ k := by
  rw [latticePrefixSpan_eq_range v hk]
  simpa only [Fintype.card_fin, Set.finrank] using finrank_range_le_card (R := ℝ)
    (fun j : Fin k => v (Fin.castLE hk j))

def latticePrefixSpan_finrank [FiniteDimensional ℝ E] {n k : ℕ}
    {v : Fin n → E} (hv : LinearIndependent ℝ v) (hk : k ≤ n) :
    finrank ℝ (latticePrefixSpan v k) = k := by
  rw [latticePrefixSpan_eq_range v hk]
  simpa only [Fintype.card_fin, Function.comp_def] using finrank_span_eq_card
    (hv.comp (Fin.castLE hk) (Fin.castLE_injective hk))

/-- Shortest points outside any prescribed subspace exist whenever that
subspace does not contain all lattice points. -/
def exists_shortest_lattice_vector_outside [FiniteDimensional ℝ E]
    (L : Submodule ℤ E) [DiscreteTopology L] (S : Submodule ℝ E)
    (hL : ∃ x ∈ L, x ∉ S) :
    ∃ v ∈ L, v ∉ S ∧ ∀ x ∈ L, x ∉ S → ‖v‖ ≤ ‖x‖ := by
  obtain ⟨x₀, hx₀, hx₀ne⟩ := hL
  have hclosed : IsClosed (L : Set E) :=
    AddSubgroup.isClosed_of_discrete (H := L.toAddSubgroup)
  have hfinite : Set.Finite (Metric.closedBall (0 : E) ‖x₀‖ ∩ (L : Set E)) :=
    Metric.finite_isBounded_inter_isClosed DiscreteTopology.isDiscrete
      Metric.isBounded_closedBall hclosed
  let s : Set E := (Metric.closedBall 0 ‖x₀‖ ∩ (L : Set E)) \ (S : Set E)
  have hs : s.Finite := hfinite.subset (by intro x hx; exact hx.1)
  have hx₀s : x₀ ∈ s := ⟨⟨by simp, hx₀⟩, hx₀ne⟩
  obtain ⟨v, hv, hmin⟩ := Set.exists_min_image s (fun x => ‖x‖) hs ⟨x₀, hx₀s⟩
  refine ⟨v, hv.1.2, hv.2, ?_⟩
  intro x hx hxne
  by_cases hball : ‖x‖ ≤ ‖x₀‖
  · exact hmin x ⟨⟨by simpa using hball, hx⟩, hxne⟩
  · exact (hmin x₀ hx₀s).trans (le_of_lt (lt_of_not_ge hball))

def IsLatticeMinimumTuple (L : Submodule ℤ E) {n : ℕ} (v : Fin n → E) : Prop :=
  LinearIndependent ℝ v ∧ (∀ i, v i ∈ L) ∧
    ∀ i x, x ∈ L → x ∉ latticePrefixSpan v i.val → ‖v i‖ ≤ ‖x‖

def exists_lattice_minimum_tuple [FiniteDimensional ℝ E]
    (L : Submodule ℤ E) [DiscreteTopology L] [IsZLattice ℝ L]
    (n : ℕ) (hn : n ≤ finrank ℝ E) :
    ∃ v : Fin n → E, IsLatticeMinimumTuple L v := by
  induction n with
  | zero =>
      refine ⟨fun i => Fin.elim0 i, linearIndependent_empty_type, ?_, ?_⟩
      · exact fun i => Fin.elim0 i
      · exact fun i => Fin.elim0 i
  | succ n ih =>
      obtain ⟨v, hvli, hvL, hvmin⟩ := ih (Nat.le_of_succ_le hn)
      have hex : ∃ x ∈ L, x ∉ Submodule.span ℝ (Set.range v) := by
        by_contra! h
        have htop : Submodule.span ℝ (Set.range v) = ⊤ := by
          apply top_unique
          rw [← IsZLattice.span_top (K := ℝ) (L := L)]
          exact Submodule.span_le.mpr h
        have hr := finrank_span_eq_card hvli
        rw [htop] at hr
        simp only [finrank_top, Fintype.card_fin] at hr
        omega
      obtain ⟨x, hxL, hx, hxmin⟩ := exists_shortest_lattice_vector_outside L _ hex
      refine ⟨Fin.snoc v x, hvli.finSnoc hx, ?_, ?_⟩
      · exact Fin.lastCases (by simpa) (fun i => by simpa using hvL i)
      · intro i
        refine Fin.lastCases ?_ (fun j => ?_) i
        · simpa only [Fin.snoc_last, Fin.val_last, latticePrefixSpan_snoc v x le_rfl,
            latticePrefixSpan_full] using hxmin
        · simpa only [Fin.snoc_castSucc, Fin.val_castSucc,
            latticePrefixSpan_snoc v x (Nat.le_of_lt j.isLt)] using hvmin j

def IsLatticeMinimumTuple.monotone {n : ℕ} {L : Submodule ℤ E} {v : Fin n → E}
    (hv : IsLatticeMinimumTuple L v) : Monotone (fun i => ‖v i‖) := by
  intro i j hij
  apply hv.2.2 i (v j) (hv.2.1 j)
  exact hv.1.notMem_span_image (by simpa using not_lt_of_ge hij)

def IsLatticeMinimumTuple.norm_pos {n : ℕ} {L : Submodule ℤ E} {v : Fin n → E}
    (hv : IsLatticeMinimumTuple L v) (i : Fin n) : 0 < ‖v i‖ :=
  norm_pos_iff.mpr (hv.1.ne_zero i)

def IsLatticeMinimumTuple.short_mem_prefix {n : ℕ} {L : Submodule ℤ E}
    {v : Fin n → E} (hv : IsLatticeMinimumTuple L v) (i : Fin n) {x : E}
    (hx : x ∈ L) (hnorm : ‖x‖ < ‖v i‖) : x ∈ latticePrefixSpan v i.val := by
  by_contra h
  exact (not_le_of_gt hnorm) (hv.2.2 i x hx h)

def IsLatticeMinimumTuple.le_of_independent_tuple [FiniteDimensional ℝ E]
    {n : ℕ} {L : Submodule ℤ E} {v : Fin n → E}
    (hv : IsLatticeMinimumTuple L v) (i : Fin n) {R : ℝ}
    (w : Fin (i.val + 1) → E) (hw : LinearIndependent ℝ w)
    (hwL : ∀ j, w j ∈ L) (hwR : ∀ j, ‖w j‖ ≤ R) : ‖v i‖ ≤ R := by
  by_contra h
  have hlt : R < ‖v i‖ := lt_of_not_ge h
  have hspan : Submodule.span ℝ (Set.range w) ≤ latticePrefixSpan v i.val := by
    apply Submodule.span_le.mpr
    rintro x ⟨j, rfl⟩
    exact hv.short_mem_prefix i (hwL j) ((hwR j).trans_lt hlt)
  have hd := Submodule.finrank_mono hspan
  rw [finrank_span_eq_card hw, Fintype.card_fin] at hd
  have hp := latticePrefixSpan_finrank_le v (Nat.le_of_lt i.isLt)
  omega

def IsLatticeMinimumTuple.le_iff_independent_tuple [FiniteDimensional ℝ E]
    {n : ℕ} {L : Submodule ℤ E} {v : Fin n → E}
    (hv : IsLatticeMinimumTuple L v) (i : Fin n) (R : ℝ) :
    ‖v i‖ ≤ R ↔ ∃ w : Fin (i.val + 1) → E,
      LinearIndependent ℝ w ∧ (∀ j, w j ∈ L) ∧ (∀ j, ‖w j‖ ≤ R) := by
  constructor
  · intro hR
    let f := Fin.castLE (Nat.succ_le_of_lt i.isLt)
    refine ⟨fun j => v (f j), hv.1.comp f (Fin.castLE_injective _),
      fun j => hv.2.1 (f j), fun j => ?_⟩
    apply le_trans (hv.monotone (show f j ≤ i from ?_)) hR
    change j.val ≤ i.val
    omega
  · rintro ⟨w, hw, hwL, hwR⟩
    exact hv.le_of_independent_tuple i w hw hwL hwR

section Minima
variable [FiniteDimensional ℝ E] (L : Submodule ℤ E)
variable [DiscreteTopology L] [IsZLattice ℝ L]

def latticeMinimumVectors : Fin (finrank ℝ E) → E :=
  Classical.choose (exists_lattice_minimum_tuple L (finrank ℝ E) le_rfl)

def latticeMinimumVectors_spec : IsLatticeMinimumTuple L (latticeMinimumVectors L) :=
  Classical.choose_spec (exists_lattice_minimum_tuple L (finrank ℝ E) le_rfl)

def latticeSuccessiveMinimum (i : Fin (finrank ℝ E)) : ℝ := ‖latticeMinimumVectors L i‖

def latticeSuccessiveMinimum_pos (i : Fin (finrank ℝ E)) :
    0 < latticeSuccessiveMinimum L i := (latticeMinimumVectors_spec L).norm_pos i

def latticeSuccessiveMinimum_monotone : Monotone (latticeSuccessiveMinimum L) :=
  (latticeMinimumVectors_spec L).monotone

/-- Intrinsic characterization: the i-th (zero-indexed) minimum is at most R
exactly when the radius-R ball contains i+1 independent lattice vectors. -/
def latticeSuccessiveMinimum_le_iff (i : Fin (finrank ℝ E)) (R : ℝ) :
    latticeSuccessiveMinimum L i ≤ R ↔ ∃ w : Fin (i.val + 1) → E,
      LinearIndependent ℝ w ∧ (∀ j, w j ∈ L) ∧ (∀ j, ‖w j‖ ≤ R) :=
  (latticeMinimumVectors_spec L).le_iff_independent_tuple i R

def latticeMinimumVectors_attain :
    LinearIndependent ℝ (latticeMinimumVectors L) ∧
    (∀ i, latticeMinimumVectors L i ∈ L) ∧
    (∀ i, ‖latticeMinimumVectors L i‖ = latticeSuccessiveMinimum L i) :=
  ⟨(latticeMinimumVectors_spec L).1, (latticeMinimumVectors_spec L).2.1, fun _ => rfl⟩

def latticeSuccessiveMinimum_le_sorted_tuple (w : Fin (finrank ℝ E) → E)
    (hw : LinearIndependent ℝ w) (hwL : ∀ j, w j ∈ L)
    (hmono : Monotone (fun j => ‖w j‖)) (i : Fin (finrank ℝ E)) :
    latticeSuccessiveMinimum L i ≤ ‖w i‖ := by
  apply (latticeSuccessiveMinimum_le_iff L i _).mpr
  let f := Fin.castLE (Nat.succ_le_of_lt i.isLt)
  refine ⟨fun j => w (f j), hw.comp f (Fin.castLE_injective _),
    fun j => hwL (f j), fun j => hmono ?_⟩
  change j.val ≤ i.val
  omega

def latticeSuccessiveMinimum_product_le_tuple (w : Fin (finrank ℝ E) → E)
    (hw : LinearIndependent ℝ w) (hwL : ∀ j, w j ∈ L) :
    (∏ i, latticeSuccessiveMinimum L i) ≤ ∏ i, ‖w i‖ := by
  classical
  let σ := Tuple.sort (fun j => ‖w j‖)
  have hle (i : Fin (finrank ℝ E)) : latticeSuccessiveMinimum L i ≤ ‖w (σ i)‖ :=
    latticeSuccessiveMinimum_le_sorted_tuple L (w ∘ σ) (hw.comp σ σ.injective)
      (fun j => hwL (σ j)) (by
        simpa only [Function.comp_def] using Tuple.monotone_sort (fun j => ‖w j‖)) i
  calc
    (∏ i, latticeSuccessiveMinimum L i) ≤ ∏ i, ‖w (σ i)‖ :=
      Finset.prod_le_prod (fun i _ => (latticeSuccessiveMinimum_pos L i).le) (fun i _ => hle i)
    _ = _ := Equiv.prod_comp σ (fun j => ‖w j‖)

def latticeSuccessiveMinimum_product_le_covolume
    [MeasurableSpace E] [BorelSpace E] :
    (∏ i, latticeSuccessiveMinimum L i) ≤
      (2 / Real.sqrt 3) ^ (finrank ℝ E * (finrank ℝ E - 1) / 2) *
        ZLattice.covolume L := by
  obtain ⟨B, hB⟩ := exists_lattice_basis_norm_product_le_covolume L
  apply le_trans (latticeSuccessiveMinimum_product_le_tuple L
    (fun i => (B i : E)) ?_ (fun i => (B i).property)) hB
  have he : (fun i => (B i : E)) = (B.ofZLatticeBasis ℝ L : Fin (finrank ℝ E) → E) := by
    funext i
    exact (B.ofZLatticeBasis_apply ℝ L i).symm
  rw [he]
  exact (B.ofZLatticeBasis ℝ L).linearIndependent

end Minima

/-- The elementary Leibniz bound, with independent bounds on each column. -/
def lattice_matrix_abs_det_le {n : ℕ} (A : Matrix (Fin n) (Fin n) ℝ)
    (c : Fin n → ℝ) (hA : ∀ i j, |A i j| ≤ c j) :
    |A.det| ≤ (n.factorial : ℝ) * ∏ j, c j := by
  classical
  rw [Matrix.det_apply']
  calc
    |∑ σ : Equiv.Perm (Fin n), ((Equiv.Perm.sign σ : ℤ) : ℝ) * ∏ i, A (σ i) i| ≤
        ∑ σ : Equiv.Perm (Fin n),
          |((Equiv.Perm.sign σ : ℤ) : ℝ) * ∏ i, A (σ i) i| :=
      Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _σ : Equiv.Perm (Fin n), ∏ j, c j := by
      apply Finset.sum_le_sum
      intro σ _
      have hs : |((Equiv.Perm.sign σ : ℤ) : ℝ)| = 1 := by
        exact_mod_cast (Int.isUnit_iff_abs_eq.mp (Equiv.Perm.sign σ).isUnit)
      rw [abs_mul, hs, one_mul, Finset.abs_prod]
      exact Finset.prod_le_prod (fun _ _ => abs_nonneg _) (fun i _ => hA (σ i) i)
    _ = _ := by simp [Fintype.card_perm]

def lattice_abs_det_le_factorial_norm_product {n : ℕ}
    (e : OrthonormalBasis (Fin n) ℝ E) (w : Fin n → E) :
    |e.toBasis.det w| ≤ (n.factorial : ℝ) * ∏ i, ‖w i‖ := by
  rw [Basis.det_apply]
  apply lattice_matrix_abs_det_le
  intro i j
  rw [Basis.toMatrix_apply, e.coe_toBasis_repr_apply, e.repr_apply_apply]
  simpa only [Real.norm_eq_abs, e.norm_eq_one, one_mul] using
    norm_inner_le_norm (𝕜 := ℝ) (e i) (w j)

/-- Independent lattice vectors have absolute determinant at least the
lattice covolume, because their coordinates in an integer basis have a
nonzero integer determinant. -/
def lattice_covolume_le_abs_det [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] (L : Submodule ℤ E)
    [DiscreteTopology L] [IsZLattice ℝ L]
    (e : OrthonormalBasis (Fin (finrank ℝ E)) ℝ E)
    (w : Fin (finrank ℝ E) → E) (hw : LinearIndependent ℝ w)
    (hwL : ∀ i, w i ∈ L) : ZLattice.covolume L ≤ |e.toBasis.det w| := by
  classical
  obtain ⟨B, h, hB⟩ := exists_reduced_lattice_basis (finrank ℝ E) E L rfl
  let b := B.ofZLatticeBasis ℝ L
  let wL : Fin (finrank ℝ E) → L := fun i => ⟨w i, hwL i⟩
  let A : Matrix (Fin (finrank ℝ E)) (Fin (finrank ℝ E)) ℤ := B.toMatrix wL
  have hb : (b : Fin (finrank ℝ E) → E) = fun i => (B i : E) := by
    funext i
    exact B.ofZLatticeBasis_apply ℝ L i
  have hcov : ZLattice.covolume L = |e.toBasis.det b| := by
    rw [hb, hB.abs_det_eq_product e, hB.covolume_eq_product e]
  have hA : b.toMatrix w = A.map (Int.castRingHom ℝ) := by
    ext i j
    exact B.ofZLatticeBasis_repr_apply ℝ L (wL j) i
  have hcast : b.det w = (A.det : ℝ) := by
    rw [Basis.det_apply, hA]
    exact ((Int.castRingHom ℝ).map_det A).symm
  let bw := basisOfLinearIndependentOfCardEqFinrank' w hw (by simp)
  have hbw : (bw : Fin (finrank ℝ E) → E) = w :=
    coe_basisOfLinearIndependentOfCardEqFinrank' w hw _
  have hne : b.det w ≠ 0 := by
    rw [← hbw]
    exact (b.isUnit_det bw).ne_zero
  have hAz : A.det ≠ 0 := by
    intro hz
    apply hne
    rw [hcast, hz, Int.cast_zero]
  have habs : (1 : ℝ) ≤ |b.det w| := by
    rw [hcast]
    have hz : (1 : ℤ) ≤ |A.det| := by have := abs_pos.mpr hAz; omega
    exact_mod_cast hz
  have hfactor : e.toBasis.det w = e.toBasis.det b * b.det w := by
    have hf := congrArg (fun f : AlternatingMap ℝ E ℝ (Fin (finrank ℝ E)) => f w)
      (e.toBasis.det.eq_smul_basis_det b)
    simpa only [AlternatingMap.smul_apply, smul_eq_mul] using hf
  rw [hfactor, abs_mul, ← hcov]
  exact le_mul_of_one_le_right (ZLattice.covolume_pos L).le habs

def latticeSuccessiveMinimum_covolume_div_factorial_le [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] (L : Submodule ℤ E)
    [DiscreteTopology L] [IsZLattice ℝ L] :
    ZLattice.covolume L / (finrank ℝ E).factorial ≤
      ∏ i, latticeSuccessiveMinimum L i := by
  have ht := latticeMinimumVectors_attain L
  have hdet := lattice_covolume_le_abs_det L (stdOrthonormalBasis ℝ E)
    (latticeMinimumVectors L) ht.1 ht.2.1
  have hbound := lattice_abs_det_le_factorial_norm_product (stdOrthonormalBasis ℝ E)
    (latticeMinimumVectors L)
  apply (div_le_iff₀ (by exact_mod_cast Nat.factorial_pos (finrank ℝ E))).mpr
  simpa only [latticeSuccessiveMinimum, mul_comm] using hdet.trans hbound

/-- Both product bounds for the actual attained Euclidean successive minima. -/
def latticeSuccessiveMinimum_product_bounds [FiniteDimensional ℝ E]
    [MeasurableSpace E] [BorelSpace E] (L : Submodule ℤ E)
    [DiscreteTopology L] [IsZLattice ℝ L] :
    ZLattice.covolume L / (finrank ℝ E).factorial ≤ (∏ i, latticeSuccessiveMinimum L i) ∧
    (∏ i, latticeSuccessiveMinimum L i) ≤
      (2 / Real.sqrt 3) ^ (finrank ℝ E * (finrank ℝ E - 1) / 2) *
        ZLattice.covolume L :=
  ⟨latticeSuccessiveMinimum_covolume_div_factorial_le L,
    latticeSuccessiveMinimum_product_le_covolume L⟩


end
end Bounty

end SubmissionComponent_LatticeSuccessiveMinima

/- Component RationalBoxLattice; SHA256 535fbb6c0fd03f5c7a61ea5eeac877d53fa666fb73129a2be1abb3c66143bd66 -/
section SubmissionComponent_RationalBoxLattice
/- Actual Euclidean lattices associated to rational rectangular domains. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module MeasureTheory

abbrev BoxEuclidean (d : ℕ) := EuclideanSpace ℝ (Fin d)

def matrixEuclideanEquiv {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ) (hC : C.det ≠ 0) :
    BoxEuclidean d ≃ₗ[ℝ] BoxEuclidean d :=
  C.toLinearEquiv (EuclideanSpace.basisFun (Fin d) ℝ).toBasis (isUnit_iff_ne_zero.mpr hC)

def matrixEuclideanEquiv_apply {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ)
    (hC : C.det ≠ 0) (x : BoxEuclidean d) :
    matrixEuclideanEquiv C hC x = Matrix.toEuclideanLin C x := by
  rw [matrixEuclideanEquiv, Matrix.toLinearEquiv_apply,
    ← Matrix.toEuclideanLin_eq_toLin_orthonormal]

def matrixEuclideanBasis {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ) (hC : C.det ≠ 0) :
    Basis (Fin d) ℝ (BoxEuclidean d) :=
  (EuclideanSpace.basisFun (Fin d) ℝ).toBasis.map (matrixEuclideanEquiv C hC)

abbrev matrixEuclideanLattice {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ) (hC : C.det ≠ 0) :
    Submodule ℤ (BoxEuclidean d) := Submodule.span ℤ (Set.range (matrixEuclideanBasis C hC))

def matrixEuclideanBasis_toMatrix {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ)
    (hC : C.det ≠ 0) :
    (EuclideanSpace.basisFun (Fin d) ℝ).toBasis.toMatrix (matrixEuclideanBasis C hC) = C := by
  conv_rhs => rw [← LinearMap.toMatrix_toLin (EuclideanSpace.basisFun (Fin d) ℝ).toBasis
    (EuclideanSpace.basisFun (Fin d) ℝ).toBasis C]
  ext i j
  simp only [Basis.toMatrix_apply, LinearMap.toMatrix_apply, matrixEuclideanBasis,
    Basis.map_apply, matrixEuclideanEquiv, Matrix.toLinearEquiv_apply]

def matrixEuclideanLattice_covolume {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ)
    (hC : C.det ≠ 0) : ZLattice.covolume (matrixEuclideanLattice C hC) = |C.det| := by
  let e := EuclideanSpace.basisFun (Fin d) ℝ
  let b := matrixEuclideanBasis C hC
  have hvol : volume.real (ZSpan.fundamentalDomain e.toBasis) = 1 := by
    rw [measureReal_congr (ZSpan.fundamentalDomain_ae_parallelepiped e.toBasis volume)]
    simp only [measureReal_def, e.coe_toBasis, e.volume_parallelepiped, ENNReal.toReal_one]
  change ZLattice.covolume (Submodule.span ℤ (Set.range b)) = |C.det|
  rw [ZLattice.covolume_eq_det_mul_measureReal _ volume (b.restrictScalars ℤ) e.toBasis,
    hvol, mul_one]
  have hb : (fun i => ((b.restrictScalars ℤ i : matrixEuclideanLattice C hC) : BoxEuclidean d)) = b := by
    funext i
    exact b.restrictScalars_apply ℤ i
  change |e.toBasis.det (fun i => ((b.restrictScalars ℤ i : matrixEuclideanLattice C hC) : BoxEuclidean d))| = _
  rw [hb, Basis.det_apply, matrixEuclideanBasis_toMatrix]

def matrixEuclideanLattice_mem_iff {d : ℕ} (C : Matrix (Fin d) (Fin d) ℝ)
    (hC : C.det ≠ 0) (y : BoxEuclidean d) :
    y ∈ matrixEuclideanLattice C hC ↔ ∃ z : Fin d → ℤ,
      y = Matrix.toEuclideanLin C (WithLp.toLp 2 (fun i => (z i : ℝ))) := by
  let e := EuclideanSpace.basisFun (Fin d) ℝ
  let f := matrixEuclideanEquiv C hC
  rw [matrixEuclideanLattice, (matrixEuclideanBasis C hC).mem_span_iff_repr_mem ℤ]
  constructor
  · intro hy
    choose z hz using hy
    refine ⟨z, ?_⟩
    rw [← matrixEuclideanEquiv_apply C hC]
    apply f.symm.injective
    change f.symm y = f.symm (f _)
    rw [f.symm_apply_apply]
    ext i
    exact (hz i).symm
  · rintro ⟨z, rfl⟩ i
    refine ⟨z i, ?_⟩
    rw [← matrixEuclideanEquiv_apply C hC]
    change (z i : ℝ) = e.toBasis.repr (f.symm (f (WithLp.toLp 2 (fun i => (z i : ℝ))))) i
    rw [f.symm_apply_apply, e.coe_toBasis_repr_apply]
    rfl

def rationalBoxMatrix {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) (B : Fin d → ℝ) :
    Matrix (Fin d) (Fin d) ℝ :=
  Matrix.diagonal (fun i => (B i)⁻¹) * A.map (Rat.castHom ℝ)

def rationalBoxLatticeMatrix {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) : Matrix (Fin d) (Fin d) ℝ :=
  rationalBoxMatrix A B * Matrix.diagonal (fun i => (N i : ℝ))

def rationalBoxMatrix_det {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) (B : Fin d → ℝ) :
    (rationalBoxMatrix A B).det = (A.det : ℝ) / ∏ i, B i := by
  rw [rationalBoxMatrix, Matrix.det_mul, Matrix.det_diagonal]
  have hc : (A.map (Rat.castHom ℝ)).det = (A.det : ℝ) := ((Rat.castHom ℝ).map_det A).symm
  rw [hc, Finset.prod_inv_distrib, div_eq_mul_inv, mul_comm]

def rationalBoxLatticeMatrix_det {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) :
    (rationalBoxLatticeMatrix A B N).det = (A.det : ℝ) * (∏ i, (N i : ℝ)) / ∏ i, B i := by
  rw [rationalBoxLatticeMatrix, Matrix.det_mul, rationalBoxMatrix_det, Matrix.det_diagonal]
  ring

def rationalBoxMatrix_det_ne_zero {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i) :
    (rationalBoxMatrix A B).det ≠ 0 := by
  rw [rationalBoxMatrix_det]
  exact div_ne_zero (by exact_mod_cast hA) (Finset.prod_ne_zero_iff.mpr (fun i _ => (hB i).ne'))

def rationalBoxLatticeMatrix_det_ne_zero {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    (rationalBoxLatticeMatrix A B N).det ≠ 0 := by
  rw [rationalBoxLatticeMatrix, Matrix.det_mul, Matrix.det_diagonal]
  exact mul_ne_zero (rationalBoxMatrix_det_ne_zero A B hA hB)
    (Finset.prod_ne_zero_iff.mpr (fun i _ => by exact_mod_cast (hN i).ne'))

abbrev rationalBoxLattice {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) : Submodule ℤ (BoxEuclidean d) :=
  matrixEuclideanLattice (rationalBoxLatticeMatrix A B N)
    (rationalBoxLatticeMatrix_det_ne_zero A B N hA hB hN)

def rationalBoxLattice_covolume {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    ZLattice.covolume (rationalBoxLattice A B N hA hB hN) =
      |(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i := by
  have hn : (0 : ℝ) < ∏ i, (N i : ℝ) :=
    Finset.prod_pos (fun i _ => by exact_mod_cast hN i)
  have hb : (0 : ℝ) < ∏ i, B i := Finset.prod_pos (fun i _ => hB i)
  rw [rationalBoxLattice, matrixEuclideanLattice_covolume, rationalBoxLatticeMatrix_det,
    abs_div, abs_mul, abs_of_pos hn, abs_of_pos hb]

def rationalBoxTransform {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i) :
    BoxEuclidean d ≃ₗ[ℝ] BoxEuclidean d :=
  matrixEuclideanEquiv (rationalBoxMatrix A B) (rationalBoxMatrix_det_ne_zero A B hA hB)

def rationalBoxTransform_apply {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i)
    (x : BoxEuclidean d) (i : Fin d) :
    rationalBoxTransform A B hA hB x i =
      (A.map (Rat.castHom ℝ) *ᵥ WithLp.ofLp x) i / B i := by
  rw [rationalBoxTransform, matrixEuclideanEquiv_apply]
  change (rationalBoxMatrix A B *ᵥ WithLp.ofLp x) i = _
  simp [rationalBoxMatrix, ← Matrix.mulVec_mulVec, Matrix.mulVec_diagonal,
    div_eq_mul_inv, mul_comm]

def diagonalIntegerPoint {d : ℕ} (N : Fin d → ℕ) (z : Fin d → ℤ) : BoxEuclidean d :=
  WithLp.toLp 2 (fun i => (N i : ℝ) * (z i : ℝ))

def rationalBoxLattice_mem_iff {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (y : BoxEuclidean d) :
    y ∈ rationalBoxLattice A B N hA hB hN ↔ ∃ z : Fin d → ℤ,
      y = rationalBoxTransform A B hA hB (diagonalIntegerPoint N z) := by
  rw [rationalBoxLattice, matrixEuclideanLattice_mem_iff]
  apply exists_congr
  intro z
  apply Iff.of_eq
  apply congrArg (fun t : BoxEuclidean d => y = t)
  rw [rationalBoxTransform, matrixEuclideanEquiv_apply]
  ext i
  change ((rationalBoxMatrix A B * Matrix.diagonal (fun i => (N i : ℝ))) *ᵥ
    (fun i => (z i : ℝ))) i = (rationalBoxMatrix A B *ᵥ (fun i => (N i : ℝ) * (z i : ℝ))) i
  rw [← Matrix.mulVec_mulVec]
  apply congrArg (fun t : Fin d → ℝ => (rationalBoxMatrix A B *ᵥ t) i)
  ext j
  exact Matrix.mulVec_diagonal _ _ j

def rationalBoxContains {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (x : BoxEuclidean d) : Prop :=
  ∀ i, |(A.map (Rat.castHom ℝ) *ᵥ WithLp.ofLp x) i| ≤ B i

def rationalBoxContains_norm_le_sqrt {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i)
    (x : BoxEuclidean d) (hx : rationalBoxContains A B x) :
    ‖rationalBoxTransform A B hA hB x‖ ≤ Real.sqrt d := by
  let y := rationalBoxTransform A B hA hB x
  have hy (i : Fin d) : |y i| ≤ 1 := by
    rw [show y i = (A.map (Rat.castHom ℝ) *ᵥ WithLp.ofLp x) i / B i from
      rationalBoxTransform_apply A B hA hB x i, abs_div, abs_of_pos (hB i)]
    exact (div_le_one (hB i)).mpr (hx i)
  have hs : ‖y‖ ^ 2 ≤ (d : ℝ) := by
    rw [EuclideanSpace.real_norm_sq_eq]
    calc
      (∑ i, y i ^ 2) ≤ ∑ _i : Fin d, (1 : ℝ) := by
        apply Finset.sum_le_sum
        intro i _
        nlinarith [hy i, abs_nonneg (y i), sq_abs (y i)]
      _ = _ := by simp
  have hsq := Real.sq_sqrt (Nat.cast_nonneg d : (0 : ℝ) ≤ d)
  have hpos := Real.sqrt_nonneg (d : ℝ)
  change ‖y‖ ≤ _
  nlinarith [norm_nonneg y]

def boxDimensionEquiv (d : ℕ) : Fin d ≃ Fin (finrank ℝ (BoxEuclidean d)) :=
  finCongr (by simp [BoxEuclidean])

/-- The Euclidean successive minimum of the transformed lattice, measured
on the original domain by the norm `‖T x‖₂`. -/
def rationalBoxMinimumValue {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) : ℝ :=
  latticeSuccessiveMinimum (rationalBoxLattice A B N hA hB hN) (boxDimensionEquiv d i)

def rationalBoxMinimumPoints {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) : BoxEuclidean d :=
  (rationalBoxTransform A B hA hB).symm
    (latticeMinimumVectors (rationalBoxLattice A B N hA hB hN) (boxDimensionEquiv d i))

def rationalBoxMinimumPoints_integral {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) :
    ∃ z : Fin d → ℤ, rationalBoxMinimumPoints A B N hA hB hN i = diagonalIntegerPoint N z := by
  have hm := (latticeMinimumVectors_attain (rationalBoxLattice A B N hA hB hN)).2.1
    (boxDimensionEquiv d i)
  obtain ⟨z, hz⟩ := (rationalBoxLattice_mem_iff A B N hA hB hN _).mp hm
  refine ⟨z, ?_⟩
  unfold rationalBoxMinimumPoints
  rw [hz, LinearEquiv.symm_apply_apply]

def rationalBoxMinimumPoints_independent {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    LinearIndependent ℝ (rationalBoxMinimumPoints A B N hA hB hN) := by
  have hli := (latticeMinimumVectors_attain (rationalBoxLattice A B N hA hB hN)).1.comp
    (boxDimensionEquiv d) (boxDimensionEquiv d).injective
  exact hli.map' (rationalBoxTransform A B hA hB).symm.toLinearMap
    (LinearMap.ker_eq_bot.mpr (rationalBoxTransform A B hA hB).symm.injective)

def rationalBoxMinimumPoints_attain {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) :
    ‖rationalBoxTransform A B hA hB (rationalBoxMinimumPoints A B N hA hB hN i)‖ =
      rationalBoxMinimumValue A B N hA hB hN i := by
  simp [rationalBoxMinimumPoints, rationalBoxMinimumValue, latticeSuccessiveMinimum]

def rationalBoxMinimumValue_pos {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) :
    0 < rationalBoxMinimumValue A B N hA hB hN i :=
  latticeSuccessiveMinimum_pos _ _

def rationalBoxMinimumValue_monotone {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    Monotone (rationalBoxMinimumValue A B N hA hB hN) := by
  intro i j hij
  apply latticeSuccessiveMinimum_monotone
  exact hij

def rationalBoxMinimumValue_product_bounds {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    (|(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i) / d.factorial ≤
        (∏ i, rationalBoxMinimumValue A B N hA hB hN i) ∧
    (∏ i, rationalBoxMinimumValue A B N hA hB hN i) ≤
      (2 / Real.sqrt 3) ^ (d * (d - 1) / 2) *
        (|(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i) := by
  have hp : (∏ i, rationalBoxMinimumValue A B N hA hB hN i) =
      ∏ i, latticeSuccessiveMinimum (rationalBoxLattice A B N hA hB hN) i :=
    Equiv.prod_comp (boxDimensionEquiv d) _
  rw [hp]
  have h := latticeSuccessiveMinimum_product_bounds (rationalBoxLattice A B N hA hB hN)
  rw [rationalBoxLattice_covolume] at h
  simpa only [BoxEuclidean, finrank_euclideanSpace, Fintype.card_fin] using h

def box_prefix_finCongr {d n m : ℕ} (hn : n = m) (v : Fin m → BoxEuclidean d) (k : ℕ) :
    latticePrefixSpan (v ∘ finCongr hn) k = latticePrefixSpan v k := by
  subst m
  rfl

def box_prefix_map {d n : ℕ} (v : Fin n → BoxEuclidean d)
    (f : BoxEuclidean d ≃ₗ[ℝ] BoxEuclidean d) (k : ℕ) :
    (latticePrefixSpan v k).map f.toLinearMap = latticePrefixSpan (f ∘ v) k := by
  rw [latticePrefixSpan, Submodule.map_span, Set.image_image]
  rfl

end
end Bounty

end SubmissionComponent_RationalBoxLattice

/- Component DavenportBasisRounding; SHA256 2a4947a7306e1017ca39d6a46e094ec385d6a50b9123f5a9171f1ed261010674 -/
section SubmissionComponent_DavenportBasisRounding
/- Gaussian maximum-pivot elimination for the Davenport construction.
Columns are indexed from zero.  Elimination of n preceding pivots costs at
most 2^n in the coordinate bound. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Module

def davenportPivotStep {d : ℕ} (u x : Fin d → ℝ) (p : Fin d) : Fin d → ℝ :=
  x - (x p / u p) • u

def davenportPivotStep_zero {d : ℕ} (u x : Fin d → ℝ) (p : Fin d) (hp : u p ≠ 0) :
    davenportPivotStep u x p p = 0 := by
  simp [davenportPivotStep, div_mul_cancel₀ _ hp]

def davenportPivotStep_bound {d : ℕ} (u x : Fin d → ℝ) (p : Fin d)
    (hp : u p ≠ 0) (hdom : ∀ r, |u r| ≤ |u p|) {R : ℝ}
    (hx : ∀ r, |x r| ≤ R) : ∀ r, |davenportPivotStep u x p r| ≤ 2 * R := by
  intro r
  have hpos : 0 < |u p| := abs_pos.mpr hp
  have hmul : |(x p / u p) * u r| ≤ |x p| := by
    rw [abs_mul, abs_div]
    calc
      |x p| / |u p| * |u r| ≤ |x p| / |u p| * |u p| :=
        mul_le_mul_of_nonneg_left (hdom r) (div_nonneg (abs_nonneg _) hpos.le)
      _ = _ := div_mul_cancel₀ _ hpos.ne'
  change |x r - (x p / u p) * u r| ≤ _
  have ht := abs_sub_le (x r) 0 ((x p / u p) * u r)
  simp only [sub_zero, zero_sub, abs_neg] at ht
  linarith [hx r, hx p]

/-- Eliminate all preceding pivots, retaining an explicit residual, span
relation, zero pivot coordinates, and a uniform coordinate bound. -/
def exists_davenport_elimination {n d : ℕ}
    (u : Fin n → Fin d → ℝ) (p : Fin n → Fin d)
    (hp : ∀ i, u i (p i) ≠ 0)
    (hdom : ∀ i r, |u i r| ≤ |u i (p i)|)
    (hzero : ∀ i j, i < j → u j (p i) = 0)
    (x : Fin d → ℝ) {R : ℝ} (hR : 0 ≤ R) (hx : ∀ r, |x r| ≤ R) :
    ∃ y : Fin d → ℝ, y - x ∈ Submodule.span ℝ (Set.range u) ∧
      (∀ i, y (p i) = 0) ∧ (∀ r, |y r| ≤ (2 : ℝ) ^ n * R) := by
  induction n generalizing x R with
  | zero =>
      refine ⟨x, by simp, fun i => Fin.elim0 i, ?_⟩
      simpa using hx
  | succ n ih =>
      let u' : Fin n → Fin d → ℝ := fun i => u i.succ
      let p' : Fin n → Fin d := fun i => p i.succ
      let x' := davenportPivotStep (u 0) x (p 0)
      have hx' : ∀ r, |x' r| ≤ 2 * R := davenportPivotStep_bound _ _ _ (hp 0) (hdom 0) hx
      obtain ⟨y, hyspan, hyzero, hybound⟩ := ih u' p' (fun i => hp i.succ)
        (fun i => hdom i.succ) (fun i j hij => hzero i.succ j.succ (Fin.succ_lt_succ_iff.mpr hij))
        x' (mul_nonneg (by norm_num) hR) hx'
      have hsub : Submodule.span ℝ (Set.range u') ≤ Submodule.span ℝ (Set.range u) := by
        apply Submodule.span_mono
        rintro _ ⟨i, rfl⟩
        exact ⟨i.succ, rfl⟩
      have hxspan : x' - x ∈ Submodule.span ℝ (Set.range u) := by
        have hu : u 0 ∈ Submodule.span ℝ (Set.range u) := Submodule.subset_span ⟨0, rfl⟩
        convert (Submodule.span ℝ (Set.range u)).smul_mem (-(x (p 0) / u 0 (p 0))) hu using 1
        ·
          simp [x', davenportPivotStep, sub_eq_add_neg, add_assoc]
      have hspan : y - x ∈ Submodule.span ℝ (Set.range u) := by
        convert (Submodule.span ℝ (Set.range u)).add_mem (hsub hyspan) hxspan using 1
        · abel
      have hker : Submodule.span ℝ (Set.range u') ≤ LinearMap.ker (LinearMap.proj (p 0)) := by
        apply Submodule.span_le.mpr
        rintro _ ⟨i, rfl⟩
        exact hzero 0 i.succ (Fin.succ_pos i)
      have hz0 : y (p 0) = 0 := by
        have hz := hker hyspan
        change y (p 0) - x' (p 0) = 0 at hz
        rw [show x' (p 0) = 0 from davenportPivotStep_zero _ _ _ (hp 0)] at hz
        simpa using hz
      refine ⟨y, hspan, Fin.cases hz0 hyzero, ?_⟩
      intro r
      calc
        |y r| ≤ (2 : ℝ) ^ n * (2 * R) := hybound r
        _ = (2 : ℝ) ^ (n + 1) * R := by rw [pow_succ]; ring

/-- Extending two equal prefix spans by vectors differing within that span
preserves equality of the extended spans. -/
def davenport_span_snoc {n d : ℕ} (u g : Fin n → Fin d → ℝ) (y x : Fin d → ℝ)
    (hspan : Submodule.span ℝ (Set.range u) = Submodule.span ℝ (Set.range g))
    (hy : y - x ∈ Submodule.span ℝ (Set.range g)) :
    Submodule.span ℝ (Set.range (Fin.snoc u y)) =
      Submodule.span ℝ (Set.range (Fin.snoc g x)) := by
  have hu : Submodule.span ℝ (Set.range u) ≤ Submodule.span ℝ (Set.range (Fin.snoc u y)) := by
    apply Submodule.span_mono
    rintro _ ⟨i, rfl⟩
    exact ⟨i.castSucc, by simp⟩
  have hg : Submodule.span ℝ (Set.range g) ≤ Submodule.span ℝ (Set.range (Fin.snoc g x)) := by
    apply Submodule.span_mono
    rintro _ ⟨i, rfl⟩
    exact ⟨i.castSucc, by simp⟩
  apply le_antisymm
  · apply Submodule.span_le.mpr
    rintro _ ⟨i, rfl⟩
    refine Fin.lastCases ?_ (fun j => ?_) i
    · simp only [Fin.snoc_last]
      have hx := Submodule.subset_span (R := ℝ) (s := Set.range (Fin.snoc g x))
        (Set.mem_range_self (Fin.last n))
      simp only [Fin.snoc_last] at hx
      have hc := (Submodule.span ℝ (Set.range (Fin.snoc g x))).add_mem (hg hy) hx
      rw [sub_add_cancel] at hc
      exact hc
    · simp only [Fin.snoc_castSucc]
      exact hg (hspan ▸ Submodule.subset_span ⟨j, rfl⟩)
  · apply Submodule.span_le.mpr
    rintro _ ⟨i, rfl⟩
    refine Fin.lastCases ?_ (fun j => ?_) i
    · simp only [Fin.snoc_last]
      have hy' := Submodule.subset_span (R := ℝ) (s := Set.range (Fin.snoc u y))
        (Set.mem_range_self (Fin.last n))
      simp only [Fin.snoc_last] at hy'
      have hc := (Submodule.span ℝ (Set.range (Fin.snoc u y))).sub_mem hy' (hu (hspan.symm ▸ hy))
      rw [show y - (y - x) = x by abel] at hc
      exact hc
    · simp only [Fin.snoc_castSucc]
      exact hu (hspan.symm ▸ Submodule.subset_span ⟨j, rfl⟩)

variable {E : Type*} [AddCommGroup E] [Module ℝ E]

def davenportPrefixSpan {n : ℕ} (v : Fin n → E) (k : ℕ) : Submodule ℝ E :=
  Submodule.span ℝ (v '' {i | i.val < k})

def davenportPrefixSpan_eq_range {n k : ℕ} (v : Fin n → E) (hk : k ≤ n) :
    davenportPrefixSpan v k =
      Submodule.span ℝ (Set.range (fun j : Fin k => v (Fin.castLE hk j))) := by
  change Submodule.span ℝ _ = Submodule.span ℝ _
  apply congrArg (Submodule.span ℝ)
  ext x
  constructor
  · rintro ⟨i, hi, rfl⟩
    exact ⟨⟨i.val, hi⟩, rfl⟩
  · rintro ⟨j, rfl⟩
    exact ⟨Fin.castLE hk j, j.isLt, rfl⟩

def davenportPrefixSpan_full {n : ℕ} (v : Fin n → E) :
    davenportPrefixSpan v n = Submodule.span ℝ (Set.range v) := by
  rw [davenportPrefixSpan_eq_range v le_rfl]
  rfl

def davenportPrefixSpan_snoc {n k : ℕ} (v : Fin n → E) (x : E) (hk : k ≤ n) :
    davenportPrefixSpan (Fin.snoc v x) k = davenportPrefixSpan v k := by
  rw [davenportPrefixSpan_eq_range _ (hk.trans (Nat.le_succ n)), davenportPrefixSpan_eq_range _ hk]
  apply congrArg (Submodule.span ℝ)
  apply congrArg Set.range
  funext j
  rw [show Fin.castLE (hk.trans (Nat.le_succ n)) j = (Fin.castLE hk j).castSucc from rfl]
  simp only [Fin.snoc_castSucc]

structure DavenportGaussianData {n d : ℕ} (g : Fin n → Fin d → ℝ) (lam : Fin n → ℝ) where
  residual : Fin n → Fin d → ℝ
  pivot : Fin n → Fin d
  pivot_injective : Function.Injective pivot
  pivot_ne : ∀ i, residual i (pivot i) ≠ 0
  dominates : ∀ i r, |residual i r| ≤ |residual i (pivot i)|
  zeros : ∀ i j, i < j → residual j (pivot i) = 0
  bound : ∀ i r, |residual i r| ≤ (2 : ℝ) ^ i.val * lam i
  relation : ∀ i, residual i - g i ∈ davenportPrefixSpan g i.val
  span_eq : Submodule.span ℝ (Set.range residual) = Submodule.span ℝ (Set.range g)

/-- Actual Gaussian residuals, with maximum-coordinate pivots and explicit
exponential bounds.  No adapted-basis hypothesis is used. -/
def exists_davenport_gaussian {n d : ℕ} (g : Fin n → Fin d → ℝ) (lam : Fin n → ℝ)
    (hLI : LinearIndependent ℝ g) (hlam : ∀ i, 0 ≤ lam i)
    (hg : ∀ i r, |g i r| ≤ lam i) : Nonempty (DavenportGaussianData g lam) := by
  induction n with
  | zero =>
      exact ⟨⟨g, Fin.elim0, fun i => Fin.elim0 i, fun i => Fin.elim0 i,
        fun i => Fin.elim0 i, fun i => Fin.elim0 i, fun i => Fin.elim0 i,
        fun i => Fin.elim0 i, rfl⟩⟩
  | succ n ih =>
      let g' : Fin n → Fin d → ℝ := fun i => g i.castSucc
      let lam' : Fin n → ℝ := fun i => lam i.castSucc
      have hLI' : LinearIndependent ℝ g' := hLI.comp _ (Fin.castSucc_injective _)
      obtain ⟨G⟩ := ih g' lam' hLI' (fun i => hlam i.castSucc) (fun i => hg i.castSucc)
      obtain ⟨y, hyspan, hyzero, hybound⟩ := exists_davenport_elimination
        G.residual G.pivot G.pivot_ne G.dominates G.zeros (g (Fin.last n))
        (hlam (Fin.last n)) (hg (Fin.last n))
      have hyspan' : y - g (Fin.last n) ∈ Submodule.span ℝ (Set.range g') :=
        G.span_eq ▸ hyspan
      have hyne : y ≠ 0 := by
        intro hy
        have hlast : g (Fin.last n) ∉ Submodule.span ℝ (Set.range g') := by
          have hh := hLI.notMem_span_image (s := Set.range (Fin.castSucc : Fin n → Fin (n+1)))
            (x := Fin.last n) (by simp)
          simpa only [← Set.range_comp, Function.comp_def] using hh
        apply hlast
        have hn := (Submodule.span ℝ (Set.range g')).neg_mem hyspan'
        simpa [hy] using hn
      obtain ⟨r, hr⟩ : ∃ r, y r ≠ 0 := by
        by_contra! hh
        exact hyne (funext hh)
      obtain ⟨p, _, hpmax⟩ := Finset.exists_max_image Finset.univ (fun r => |y r|)
        ⟨r, Finset.mem_univ r⟩
      have hpne : y p ≠ 0 := by
        intro hp
        have hh := hpmax r (Finset.mem_univ r)
        rw [hp, abs_zero] at hh
        exact hr (abs_nonpos_iff.mp hh)
      have hpnew : p ∉ Set.range G.pivot := by
        rintro ⟨i, rfl⟩
        exact hpne (hyzero i)
      let u : Fin (n + 1) → Fin d → ℝ := Fin.snoc G.residual y
      let p' : Fin (n + 1) → Fin d := Fin.snoc G.pivot p
      have hgsnoc : Fin.snoc g' (g (Fin.last n)) = g := by
        ext i
        exact Fin.lastCases (by simp) (fun j => by simp [g']) i
      refine ⟨⟨u, p', Fin.snoc_injective_of_injective G.pivot_injective hpnew, ?_, ?_,
        ?_, ?_, ?_, ?_⟩⟩
      · intro i
        exact Fin.lastCases (by simpa [u, p'] using hpne)
          (fun j => by simpa [u, p'] using G.pivot_ne j) i
      · intro i
        refine Fin.lastCases ?_ (fun j => ?_) i
        · simpa [u, p'] using fun r => hpmax r (Finset.mem_univ r)
        · simpa [u, p'] using G.dominates j
      · intro i j
        refine Fin.lastCases ?_ (fun k => ?_) j
        · intro hij
          obtain ⟨l, rfl⟩ := Fin.exists_castSucc_eq.mpr (Fin.ne_last_of_lt hij)
          simpa [u, p'] using hyzero l
        · refine Fin.lastCases ?_ (fun l => ?_) i
          · intro hi
            exact (not_lt_of_ge (Fin.le_last _) hi).elim
          · intro hi
            simpa [u, p'] using G.zeros l k hi
      · intro i
        refine Fin.lastCases ?_ (fun j => ?_) i
        · simpa [u] using hybound
        · simpa [u, lam'] using G.bound j
      · intro i
        refine Fin.lastCases ?_ (fun j => ?_) i
        · change u (Fin.last n) - g (Fin.last n) ∈ davenportPrefixSpan g n
          rw [← hgsnoc, davenportPrefixSpan_snoc _ _ (le_refl n), davenportPrefixSpan_full]
          simpa [u] using hyspan'
        · have hh := G.relation j
          change u j.castSucc - g j.castSucc ∈ davenportPrefixSpan g j.val
          rw [← hgsnoc, davenportPrefixSpan_snoc _ _ (Nat.le_of_lt j.isLt)]
          simpa [u, g'] using hh
      · dsimp [u]
        rw [davenport_span_snoc _ _ _ _ G.span_eq hyspan', hgsnoc]

/-- In the square case the distinct pivot rows give an actual permutation.
The residual bound already has the row/column minimum required by rounding. -/
def exists_davenport_gaussian_permutation {d : ℕ} (g : Fin d → Fin d → ℝ)
    (lam : Fin d → ℝ) (hLI : LinearIndependent ℝ g) (hlam : ∀ i, 0 ≤ lam i)
    (hmono : Monotone lam) (hg : ∀ i r, |g i r| ≤ lam i) :
    ∃ (u : Fin d → Fin d → ℝ) (p : Equiv.Perm (Fin d)),
      (∀ j, u j - g j ∈ davenportPrefixSpan g j.val) ∧
      (∀ i j, i < j → u j (p i) = 0) ∧
      (∀ i, u i (p i) ≠ 0) ∧
      (∀ i r, |u i r| ≤ |u i (p i)|) ∧
      (∀ i j, |u j (p i)| ≤ (2 : ℝ) ^ j.val * min (lam i) (lam j)) := by
  obtain ⟨G⟩ := exists_davenport_gaussian g lam hLI hlam hg
  let p : Equiv.Perm (Fin d) := Equiv.ofBijective G.pivot
    (Finite.injective_iff_bijective.mp G.pivot_injective)
  refine ⟨G.residual, p, G.relation, G.zeros, G.pivot_ne, G.dominates, ?_⟩
  intro i j
  by_cases hij : i < j
  · change |G.residual j (G.pivot i)| ≤ _
    rw [G.zeros i j hij, abs_zero]
    exact mul_nonneg (by positivity) (le_min (hlam i) (hlam j))
  · rw [min_eq_right (hmono (le_of_not_gt hij))]
    exact G.bound j (p i)


end
end Bounty

end SubmissionComponent_DavenportBasisRounding

/- Component DavenportIntegerRounding; SHA256 e19b7f0a452e6cba126fcc004bb82835828690fb0e63912aa6a9f94b1ec0672e -/
section SubmissionComponent_DavenportIntegerRounding
namespace Bounty
noncomputable section
open scoped BigOperators
open Module

def davenport_integer_span_snoc {n d : ℕ} (u g : Fin n → Fin d → ℝ) (y x : Fin d → ℝ)
    (hspan : Submodule.span ℤ (Set.range u) = Submodule.span ℤ (Set.range g))
    (hy : y - x ∈ Submodule.span ℤ (Set.range g)) :
    Submodule.span ℤ (Set.range (Fin.snoc u y)) =
      Submodule.span ℤ (Set.range (Fin.snoc g x)) := by
  have hu : Submodule.span ℤ (Set.range u) ≤ Submodule.span ℤ (Set.range (Fin.snoc u y)) := by
    apply Submodule.span_mono
    rintro _ ⟨i, rfl⟩
    exact ⟨i.castSucc, by simp⟩
  have hg : Submodule.span ℤ (Set.range g) ≤ Submodule.span ℤ (Set.range (Fin.snoc g x)) := by
    apply Submodule.span_mono
    rintro _ ⟨i, rfl⟩
    exact ⟨i.castSucc, by simp⟩
  apply le_antisymm
  · apply Submodule.span_le.mpr
    rintro _ ⟨i, rfl⟩
    refine Fin.lastCases ?_ (fun j => ?_) i
    · simp only [Fin.snoc_last]
      have hx := Submodule.subset_span (R := ℤ) (s := Set.range (Fin.snoc g x))
        (Set.mem_range_self (Fin.last n))
      simp only [Fin.snoc_last] at hx
      have hc := (Submodule.span ℤ (Set.range (Fin.snoc g x))).add_mem (hg hy) hx
      rw [sub_add_cancel] at hc
      exact hc
    · simp only [Fin.snoc_castSucc]
      exact hg (hspan ▸ Submodule.subset_span ⟨j, rfl⟩)
  · apply Submodule.span_le.mpr
    rintro _ ⟨i, rfl⟩
    refine Fin.lastCases ?_ (fun j => ?_) i
    · simp only [Fin.snoc_last]
      have hy' := Submodule.subset_span (R := ℤ) (s := Set.range (Fin.snoc u y))
        (Set.mem_range_self (Fin.last n))
      simp only [Fin.snoc_last] at hy'
      have hc := (Submodule.span ℤ (Set.range (Fin.snoc u y))).sub_mem hy' (hu (hspan.symm ▸ hy))
      rw [show y - (y - x) = x by abel] at hc
      exact hc
    · simp only [Fin.snoc_castSucc]
      exact hu (hspan.symm ▸ Submodule.subset_span ⟨j, rfl⟩)

variable {E : Type*} [AddCommGroup E]
def davenportIntegerPrefixSpan {n : ℕ} (v : Fin n → E) (k : ℕ) : Submodule ℤ E :=
  Submodule.span ℤ (v '' {i | i.val < k})

def davenportIntegerPrefixSpan_eq_range {n k : ℕ} (v : Fin n → E) (hk : k ≤ n) :
    davenportIntegerPrefixSpan v k =
      Submodule.span ℤ (Set.range (fun j : Fin k => v (Fin.castLE hk j))) := by
  change Submodule.span ℤ _ = Submodule.span ℤ _
  apply congrArg (Submodule.span ℤ)
  ext x
  constructor
  · rintro ⟨i, hi, rfl⟩
    exact ⟨⟨i.val, hi⟩, rfl⟩
  · rintro ⟨j, rfl⟩
    exact ⟨Fin.castLE hk j, j.isLt, rfl⟩

def davenportIntegerPrefixSpan_full {n : ℕ} (v : Fin n → E) :
    davenportIntegerPrefixSpan v n = Submodule.span ℤ (Set.range v) := by
  rw [davenportIntegerPrefixSpan_eq_range v le_rfl]
  rfl

def davenportIntegerPrefixSpan_snoc {n k : ℕ} (v : Fin n → E) (x : E) (hk : k ≤ n) :
    davenportIntegerPrefixSpan (Fin.snoc v x) k = davenportIntegerPrefixSpan v k := by
  rw [davenportIntegerPrefixSpan_eq_range _ (hk.trans (Nat.le_succ n)), davenportIntegerPrefixSpan_eq_range _ hk]
  apply congrArg (Submodule.span ℤ)
  apply congrArg Set.range
  funext j
  rw [show Fin.castLE (hk.trans (Nat.le_succ n)) j = (Fin.castLE hk j).castSucc from rfl]
  simp only [Fin.snoc_castSucc]

def davenport_sum_two_pow (n : ℕ) :
    (∑ i : Fin n, (2 : ℝ) ^ i.val) = 2 ^ n - 1 := by
  induction n with
  | zero => simp
  | succ n ih =>
      rw [Fin.sum_univ_castSucc]
      change (∑ i : Fin n, (2 : ℝ) ^ i.val) + 2 ^ n = 2 ^ (n + 1) - 1
      rw [ih, pow_succ]
      ring

structure DavenportRoundingData {n d : ℕ} (g : Fin n → Fin d → ℝ)
    (lam : Fin n → ℝ) (rho : Fin d → ℝ) where
  vector : Fin n → Fin d → ℝ
  real_span : Submodule.span ℝ (Set.range vector) = Submodule.span ℝ (Set.range g)
  integer_span : Submodule.span ℤ (Set.range vector) = Submodule.span ℤ (Set.range g)
  integer_relation : ∀ j, vector j - g j ∈ davenportIntegerPrefixSpan g j.val
  bound : ∀ j r, |vector j r| ≤ (2 : ℝ) ^ (j.val + 1) * min (rho r) (lam j)

/-- Rounding actual residuals by nearest integers.  Every difference from
the original column lies in the integer span of preceding original columns. -/
def exists_davenport_rounding {n d : ℕ} (g u : Fin n → Fin d → ℝ)
    (lam : Fin n → ℝ) (rho : Fin d → ℝ)
    (hlam : ∀ j, 0 ≤ lam j) (hrho : ∀ r, 0 ≤ rho r) (hmono : Monotone lam)
    (hrel : ∀ j, u j - g j ∈ davenportPrefixSpan g j.val)
    (hu : ∀ j r, |u j r| ≤ (2 : ℝ) ^ j.val * min (rho r) (lam j)) :
    Nonempty (DavenportRoundingData g lam rho) := by
  classical
  induction n with
  | zero =>
      exact ⟨⟨g, rfl, rfl, fun j => Fin.elim0 j, fun j => Fin.elim0 j⟩⟩
  | succ n ih =>
      let g' : Fin n → Fin d → ℝ := fun j => g j.castSucc
      let u' : Fin n → Fin d → ℝ := fun j => u j.castSucc
      let lam' : Fin n → ℝ := fun j => lam j.castSucc
      have hgsnoc : Fin.snoc g' (g (Fin.last n)) = g := by
        ext i
        exact Fin.lastCases (by simp) (fun j => by simp [g']) i
      have hrel' : ∀ j, u' j - g' j ∈ davenportPrefixSpan g' j.val := by
        intro j
        have hh := hrel j.castSucc
        change u' j - g' j ∈ davenportPrefixSpan g j.val at hh
        rw [← hgsnoc, davenportPrefixSpan_snoc _ _ (Nat.le_of_lt j.isLt)] at hh
        exact hh
      obtain ⟨H⟩ := ih g' u' lam' (fun j => hlam j.castSucc)
        (fun i j hij => hmono hij) hrel' (fun j => hu j.castSucc)
      have hlast : u (Fin.last n) - g (Fin.last n) ∈
          Submodule.span ℝ (Set.range H.vector) := by
        rw [H.real_span]
        have hh := hrel (Fin.last n)
        change u (Fin.last n) - g (Fin.last n) ∈ davenportPrefixSpan g n at hh
        rw [← hgsnoc, davenportPrefixSpan_snoc _ _ le_rfl, davenportPrefixSpan_full] at hh
        simpa using hh
      obtain ⟨a, ha⟩ := (Submodule.mem_span_range_iff_exists_fun ℝ).mp hlast
      let w : Fin d → ℝ := g (Fin.last n) + ∑ i, (round (a i) : ℝ) • H.vector i
      have hwsub : w - g (Fin.last n) = ∑ i, (round (a i) : ℝ) • H.vector i := by
        dsimp [w]; abel
      have hwreal : w - g (Fin.last n) ∈ Submodule.span ℝ (Set.range g') := by
        rw [hwsub, ← H.real_span]
        exact Submodule.sum_mem _ fun i _ =>
          Submodule.smul_mem _ _ (Submodule.subset_span ⟨i, rfl⟩)
      have hwint : w - g (Fin.last n) ∈ Submodule.span ℤ (Set.range g') := by
        rw [hwsub, ← H.integer_span]
        apply Submodule.sum_mem
        intro i _
        rw [Int.cast_smul_eq_zsmul]
        exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨i, rfl⟩)
      have hwres : w = u (Fin.last n) + ∑ i, ((round (a i) : ℝ) - a i) • H.vector i := by
        simp_rw [sub_smul, Finset.sum_sub_distrib]
        rw [ha]
        dsimp [w]
        abel
      have hwbound : ∀ r, |w r| ≤ (2 : ℝ) ^ (n + 1) * min (rho r) (lam (Fin.last n)) := by
        intro r
        let M := min (rho r) (lam (Fin.last n))
        have hM : 0 ≤ M := le_min (hrho r) (hlam (Fin.last n))
        have heach : ∀ i : Fin n,
            |((round (a i) : ℝ) - a i) * H.vector i r| ≤ (2 : ℝ) ^ i.val * M := by
          intro i
          have hround : |(round (a i) : ℝ) - a i| ≤ 1 / 2 := by
            simpa only [abs_sub_comm] using abs_sub_round (a i)
          have hmin : min (rho r) (lam' i) ≤ M :=
            min_le_min le_rfl (hmono (Fin.le_last i.castSucc))
          have hh := (H.bound i r).trans (mul_le_mul_of_nonneg_left hmin (by positivity))
          calc
            _ = |(round (a i) : ℝ) - a i| * |H.vector i r| := abs_mul _ _
            _ ≤ (1 / 2) * ((2 : ℝ) ^ (i.val + 1) * M) :=
              mul_le_mul hround hh (abs_nonneg _) (by norm_num)
            _ = (2 : ℝ) ^ i.val * M := by rw [pow_succ]; ring
        have hsum : |∑ i : Fin n, ((round (a i) : ℝ) - a i) * H.vector i r| ≤
            ((2 : ℝ) ^ n - 1) * M := by
          calc
            _ ≤ ∑ i : Fin n, |((round (a i) : ℝ) - a i) * H.vector i r| :=
              Finset.abs_sum_le_sum_abs _ _
            _ ≤ ∑ i : Fin n, (2 : ℝ) ^ i.val * M := Finset.sum_le_sum fun i _ => heach i
            _ = _ := by rw [← Finset.sum_mul, davenport_sum_two_pow]
        have hh := congrFun hwres r
        simp only [Pi.add_apply, Finset.sum_apply, Pi.smul_apply, smul_eq_mul] at hh
        rw [hh]
        calc
          _ ≤ |u (Fin.last n) r| + |∑ i : Fin n, ((round (a i) : ℝ) - a i) * H.vector i r| :=
            abs_add_le _ _
          _ ≤ (2 : ℝ) ^ n * M + (2 ^ n - 1) * M := add_le_add (hu (Fin.last n) r) hsum
          _ ≤ (2 : ℝ) ^ (n + 1) * M := by rw [pow_succ]; nlinarith
      let h : Fin (n + 1) → Fin d → ℝ := Fin.snoc H.vector w
      refine ⟨⟨h, ?_, ?_, ?_, ?_⟩⟩
      · dsimp [h]
        rw [davenport_span_snoc _ _ _ _ H.real_span hwreal, hgsnoc]
      · dsimp [h]
        rw [davenport_integer_span_snoc _ _ _ _ H.integer_span hwint, hgsnoc]
      · intro j
        refine Fin.lastCases ?_ (fun i => ?_) j
        · change h (Fin.last n) - g (Fin.last n) ∈ davenportIntegerPrefixSpan g n
          rw [← hgsnoc, davenportIntegerPrefixSpan_snoc _ _ le_rfl, davenportIntegerPrefixSpan_full]
          simpa [h] using hwint
        · change h i.castSucc - g i.castSucc ∈ davenportIntegerPrefixSpan g i.val
          rw [← hgsnoc, davenportIntegerPrefixSpan_snoc _ _ (Nat.le_of_lt i.isLt)]
          simpa [h, g'] using H.integer_relation i
      · intro j
        refine Fin.lastCases ?_ (fun i => ?_) j
        · simpa [h] using hwbound
        · simpa [h, lam'] using H.bound i

def davenport_integer_prefix_coefficients {n d k : ℕ} (g : Fin n → Fin d → ℝ)
    (x : Fin d → ℝ) (hx : x ∈ davenportIntegerPrefixSpan g k) :
    ∃ c : Fin n → ℤ, x = ∑ i, if i.val < k then (c i : ℝ) • g i else 0 := by
  classical
  let s : Finset (Fin n) := Finset.univ.filter fun i => i.val < k
  have hs : (s : Set (Fin n)) = {i | i.val < k} := by ext i; simp [s]
  change x ∈ Submodule.span ℤ (g '' {i | i.val < k}) at hx
  rw [← hs] at hx
  obtain ⟨c, hc⟩ := (Submodule.mem_span_image_finset_iff_exists_fun' (R := ℤ)).mp hx
  refine ⟨c, ?_⟩
  simpa only [s, Finset.sum_filter, Int.cast_smul_eq_zsmul] using hc.symm

def davenport_integer_span_of_relation {n d : ℕ} (h g : Fin n → Fin d → ℝ)
    (hrel : ∀ j, h j - g j ∈ davenportIntegerPrefixSpan g j.val) :
    Submodule.span ℤ (Set.range h) = Submodule.span ℤ (Set.range g) := by
  induction n with
  | zero => simp
  | succ n ih =>
      let h' : Fin n → Fin d → ℝ := fun i => h i.castSucc
      let g' : Fin n → Fin d → ℝ := fun i => g i.castSucc
      have hh : Fin.snoc h' (h (Fin.last n)) = h := by ext i; exact Fin.lastCases (by simp) (fun j => by simp [h']) i
      have hg : Fin.snoc g' (g (Fin.last n)) = g := by ext i; exact Fin.lastCases (by simp) (fun j => by simp [g']) i
      have hrel' : ∀ j, h' j - g' j ∈ davenportIntegerPrefixSpan g' j.val := by
        intro j
        have ht := hrel j.castSucc
        change h' j - g' j ∈ davenportIntegerPrefixSpan g j.val at ht
        rw [← hg, davenportIntegerPrefixSpan_snoc _ _ (Nat.le_of_lt j.isLt)] at ht
        exact ht
      have hs := ih h' g' hrel'
      have hl : h (Fin.last n) - g (Fin.last n) ∈ Submodule.span ℤ (Set.range g') := by
        have ht := hrel (Fin.last n)
        change h (Fin.last n) - g (Fin.last n) ∈ davenportIntegerPrefixSpan g n at ht
        rw [← hg, davenportIntegerPrefixSpan_snoc _ _ le_rfl, davenportIntegerPrefixSpan_full] at ht
        simpa using ht
      simpa only [hh, hg] using davenport_integer_span_snoc h' g' _ _ hs hl

def davenportIntegerPrefixSpan_restrict {n k l : ℕ} (g : Fin n → E)
    (hk : k ≤ n) (hl : l ≤ k) :
    davenportIntegerPrefixSpan (fun i : Fin k => g (Fin.castLE hk i)) l =
      davenportIntegerPrefixSpan g l := by
  rw [davenportIntegerPrefixSpan_eq_range _ hl,
    davenportIntegerPrefixSpan_eq_range _ (hl.trans hk)]
  rfl

def davenport_integer_prefixes_of_relation {n d : ℕ} (h g : Fin n → Fin d → ℝ)
    (hrel : ∀ j, h j - g j ∈ davenportIntegerPrefixSpan g j.val) (k : ℕ) (hk : k ≤ n) :
    davenportIntegerPrefixSpan h k = davenportIntegerPrefixSpan g k := by
  rw [davenportIntegerPrefixSpan_eq_range _ hk, davenportIntegerPrefixSpan_eq_range _ hk]
  apply davenport_integer_span_of_relation
  intro j
  rw [davenportIntegerPrefixSpan_restrict _ hk (Nat.le_of_lt j.isLt)]
  exact hrel (Fin.castLE hk j)

def davenport_rational_prefixes_of_relation {n d : ℕ} (h g : Fin n → Fin d → ℝ)
    (hrel : ∀ j, h j - g j ∈ davenportIntegerPrefixSpan g j.val) (k : ℕ) (hk : k ≤ n) :
    Submodule.span ℚ (h '' {i | i.val < k}) = Submodule.span ℚ (g '' {i | i.val < k}) := by
  have hh := congrArg (fun S : Submodule ℤ (Fin d → ℝ) => Submodule.span ℚ (S : Set (Fin d → ℝ)))
    (davenport_integer_prefixes_of_relation h g hrel k hk)
  simpa only [davenportIntegerPrefixSpan, Submodule.span_span_of_tower] using hh

/-- The actual integer change-of-columns matrix. -/
def davenportIntegerMatrix {n : ℕ} (z : Fin n → Fin n → ℤ) : Matrix (Fin n) (Fin n) ℤ :=
  1 + Matrix.of (fun i j => if i < j then z j i else 0)

def davenportIntegerMatrix_upper {n : ℕ} (z : Fin n → Fin n → ℤ) :
    (davenportIntegerMatrix z).IsUpperTriangular := by
  intro i j hij
  change j < i at hij
  simp [davenportIntegerMatrix, ne_of_gt hij, not_lt_of_ge hij.le]

def davenportIntegerMatrix_diag {n : ℕ} (z : Fin n → Fin n → ℤ) (i : Fin n) :
    davenportIntegerMatrix z i i = 1 := by simp [davenportIntegerMatrix]

def davenportIntegerMatrix_det {n : ℕ} (z : Fin n → Fin n → ℤ) :
    (davenportIntegerMatrix z).det = 1 := by
  rw [Matrix.det_of_isUpperTriangular (davenportIntegerMatrix_upper z)]
  change (∏ i : Fin n, davenportIntegerMatrix z i i) = 1
  simp only [davenportIntegerMatrix_diag, Finset.prod_const_one]

def davenport_integer_matrix_identity {n d : ℕ} (h g : Fin n → Fin d → ℝ)
    (z : Fin n → Fin n → ℤ)
    (hexp : ∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0) :
    Matrix.of (fun i j => h j i) = Matrix.of (fun i j => g j i) *
      (davenportIntegerMatrix z).map (Int.castRingHom ℝ) := by
  classical
  have hmap : (davenportIntegerMatrix z).map (Int.castRingHom ℝ) =
      1 + Matrix.of (fun i j => if i < j then (z j i : ℝ) else 0) := by
    ext i j
    simp [davenportIntegerMatrix, Matrix.map_apply, Matrix.one_apply]
  rw [hmap, Matrix.mul_add, Matrix.mul_one]
  ext i j
  change h j i = g j i + ∑ k, g k i * (if k < j then (z j k : ℝ) else 0)
  rw [hexp j]
  simp only [Pi.add_apply, Finset.sum_apply]
  congr 1
  apply Finset.sum_congr rfl
  intro k _
  split_ifs <;> simp [mul_comm]

def davenport_integer_det_identity {d : ℕ} (h g : Fin d → Fin d → ℝ)
    (z : Fin d → Fin d → ℤ)
    (hexp : ∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0) :
    (Matrix.of (fun i j => h j i)).det = (Matrix.of (fun i j => g j i)).det := by
  rw [davenport_integer_matrix_identity h g z hexp, Matrix.det_mul]
  have hd := (Int.castRingHom ℝ).map_det (davenportIntegerMatrix z)
  change ((davenportIntegerMatrix z).det : ℝ) = ((davenportIntegerMatrix z).map (Int.castRingHom ℝ)).det at hd
  rw [← hd, davenportIntegerMatrix_det]
  simp

def exists_davenport_integer_rounding {d : ℕ} (g : Fin d → Fin d → ℝ)
    (lam : Fin d → ℝ) (hLI : LinearIndependent ℝ g) (hlam : ∀ j, 0 ≤ lam j)
    (hmono : Monotone lam) (hg : ∀ j r, |g j r| ≤ lam j) :
    ∃ (p : Equiv.Perm (Fin d)) (h : Fin d → Fin d → ℝ) (z : Fin d → Fin d → ℤ),
      (∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0) ∧
      (∀ k, k ≤ d → davenportIntegerPrefixSpan h k = davenportIntegerPrefixSpan g k) ∧
      (Matrix.of (fun i j => h j i)).det = (Matrix.of (fun i j => g j i)).det ∧
      LinearIndependent ℝ h ∧
      (∀ k, k ≤ d → Submodule.span ℚ (h '' {i | i.val < k}) =
        Submodule.span ℚ (g '' {i | i.val < k})) ∧
      (∀ i j, |h j (p i)| ≤ (2 : ℝ) ^ (j.val + 1) * min (lam i) (lam j)) := by
  classical
  obtain ⟨u, p, hrel, _, _, _, hu⟩ := exists_davenport_gaussian_permutation g lam hLI hlam hmono hg
  let rho : Fin d → ℝ := fun r => lam (p.symm r)
  have hur : ∀ j r, |u j r| ≤ (2 : ℝ) ^ j.val * min (rho r) (lam j) := by
    intro j r
    simpa [rho] using hu (p.symm r) j
  obtain ⟨H⟩ := exists_davenport_rounding g u lam rho hlam (fun r => hlam (p.symm r)) hmono hrel hur
  have hcoeff : ∀ j, ∃ c : Fin d → ℤ,
      H.vector j - g j = ∑ i, if i < j then (c i : ℝ) • g i else 0 := by
    intro j
    exact davenport_integer_prefix_coefficients g _ (H.integer_relation j)
  choose z hz using hcoeff
  have hexp : ∀ j, H.vector j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0 := by
    intro j
    rw [← hz j]
    abel
  have hLIH : LinearIndependent ℝ H.vector := by
    apply linearIndependent_iff_card_eq_finrank_span.mpr
    change Fintype.card (Fin d) = finrank ℝ (Submodule.span ℝ (Set.range H.vector))
    rw [H.real_span]
    exact (finrank_span_eq_card hLI).symm
  refine ⟨p, H.vector, z, hexp, davenport_integer_prefixes_of_relation _ _ H.integer_relation,
    davenport_integer_det_identity _ _ z hexp, hLIH,
    davenport_rational_prefixes_of_relation _ _ H.integer_relation, ?_⟩
  intro i j
  simpa [rho] using H.bound j (p i)

/-- Uniform dimension-only version, useful for compound-coordinate bounds. -/
def exists_davenport_integer_rounding_uniform {d : ℕ} (g : Fin d → Fin d → ℝ)
    (lam : Fin d → ℝ) (hLI : LinearIndependent ℝ g) (hlam : ∀ j, 0 ≤ lam j)
    (hmono : Monotone lam) (hg : ∀ j r, |g j r| ≤ lam j) :
    ∃ (p : Equiv.Perm (Fin d)) (h : Fin d → Fin d → ℝ) (z : Fin d → Fin d → ℤ),
      (∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0) ∧
      (∀ k, k ≤ d → davenportIntegerPrefixSpan h k = davenportIntegerPrefixSpan g k) ∧
      (Matrix.of (fun i j => h j i)).det = (Matrix.of (fun i j => g j i)).det ∧
      LinearIndependent ℝ h ∧
      (∀ k, k ≤ d → Submodule.span ℚ (h '' {i | i.val < k}) =
        Submodule.span ℚ (g '' {i | i.val < k})) ∧
      (∀ i j, |h j (p i)| ≤ (2 : ℝ) ^ d * min (lam i) (lam j)) := by
  obtain ⟨p, h, z, he, hp, hd, hli, hq, hb⟩ :=
    exists_davenport_integer_rounding g lam hLI hlam hmono hg
  refine ⟨p, h, z, he, hp, hd, hli, hq, ?_⟩
  intro i j
  apply (hb i j).trans
  apply mul_le_mul_of_nonneg_right _ (le_min (hlam i) (hlam j))
  exact pow_le_pow_right₀ (by norm_num) (Nat.succ_le_of_lt j.isLt)


end
end Bounty

end SubmissionComponent_DavenportIntegerRounding

/- Component RationalBoxDavenport; SHA256 01569f5c5577238df54d5078dd1ac7c97ef937c145158b3787cfbab9de15425c -/
section SubmissionComponent_RationalBoxDavenport
/- Integer Davenport columns for the actual rational rectangular lattice.
The minima used here are Euclidean minima of the transformed lattice. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module

def diagonalIntegerPoint_integer_expansion {d : ℕ} (N : Fin d → ℕ)
    (g h : Fin d → BoxEuclidean d) (z : Fin d → Fin d → ℤ)
    (hg : ∀ j, ∃ a : Fin d → ℤ, g j = diagonalIntegerPoint N a)
    (hexp : ∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0) :
    ∀ j, ∃ b : Fin d → ℤ, h j = diagonalIntegerPoint N b := by
  classical
  choose a ha using hg
  intro j
  refine ⟨fun r => a j r + ∑ i, if i < j then z j i * a i r else 0, ?_⟩
  rw [hexp j]
  simp_rw [ha]
  ext r
  simp only [PiLp.add_apply, WithLp.ofLp_sum, Finset.sum_apply, apply_ite,
    diagonalIntegerPoint, WithLp.ofLp_toLp, Int.cast_add, Int.cast_sum,
    Int.cast_mul, Int.cast_zero]
  rw [mul_add, Finset.mul_sum]
  congr 1
  apply Finset.sum_congr rfl
  intro i _
  split_ifs <;> simp [mul_left_comm]

/-- Actual diagonal-integer columns with the Davenport bound.  Their
integer change-of-columns matrix has diagonal one and determinant one. -/
def exists_rationalBox_davenport {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) :
    ∃ (p : Equiv.Perm (Fin d)) (h : Fin d → BoxEuclidean d)
      (z : Fin d → Fin d → ℤ),
      (∀ j, h j = rationalBoxMinimumPoints A B N hA hB hN j +
        ∑ i, if i < j then (z j i : ℝ) • rationalBoxMinimumPoints A B N hA hB hN i else 0) ∧
      (∀ j, ∃ b : Fin d → ℤ, h j = diagonalIntegerPoint N b) ∧
      LinearIndependent ℝ h ∧
      (∀ k, k ≤ d → Submodule.span ℚ (h '' {i | i.val < k}) =
        Submodule.span ℚ (rationalBoxMinimumPoints A B N hA hB hN '' {i | i.val < k})) ∧
      (∀ k, k ≤ d → latticePrefixSpan h k =
        latticePrefixSpan (rationalBoxMinimumPoints A B N hA hB hN) k) ∧
      (EuclideanSpace.basisFun (Fin d) ℝ).toBasis.det h =
        (EuclideanSpace.basisFun (Fin d) ℝ).toBasis.det (rationalBoxMinimumPoints A B N hA hB hN) ∧
      (∀ i j, |(A.map (Rat.castHom ℝ) *ᵥ WithLp.ofLp (h j)) (p i)| ≤
        (2 : ℝ) ^ d * B (p i) * min (rationalBoxMinimumValue A B N hA hB hN i)
          (rationalBoxMinimumValue A B N hA hB hN j)) := by
  classical
  let g := rationalBoxMinimumPoints A B N hA hB hN
  let lam := rationalBoxMinimumValue A B N hA hB hN
  let T := rationalBoxTransform A B hA hB
  let F : BoxEuclidean d ≃ₗ[ℝ] (Fin d → ℝ) := T.trans (WithLp.linearEquiv 2 ℝ (Fin d → ℝ))
  let y : Fin d → Fin d → ℝ := fun j => F (g j)
  have hyLI : LinearIndependent ℝ y := (rationalBoxMinimumPoints_independent A B N hA hB hN).map'
    F.toLinearMap (LinearMap.ker_eq_bot.mpr F.injective)
  have hyb : ∀ j r, |y j r| ≤ lam j := by
    intro j r
    have hh := PiLp.norm_apply_le (T (g j)) r
    rw [Real.norm_eq_abs, rationalBoxMinimumPoints_attain] at hh
    exact hh
  obtain ⟨p, v, z, hexp, hint, _, hvLI, hq, hb⟩ := exists_davenport_integer_rounding_uniform
    y lam hyLI (fun j => (rationalBoxMinimumValue_pos A B N hA hB hN j).le)
    (rationalBoxMinimumValue_monotone A B N hA hB hN) hyb
  let h : Fin d → BoxEuclidean d := fun j => F.symm (v j)
  have he : ∀ j, h j = g j + ∑ i, if i < j then (z j i : ℝ) • g i else 0 := by
    intro j
    have hh := congrArg F.symm (hexp j)
    simpa only [map_add, map_sum, apply_ite, map_smul, map_zero, y, LinearEquiv.symm_apply_apply] using hh
  have hpref (R : Type) [Field R] [Algebra R ℝ]
      (heq : ∀ k, k ≤ d → Submodule.span R (v '' {i | i.val < k}) =
        Submodule.span R (y '' {i | i.val < k})) (k : ℕ) (hk : k ≤ d) :
      Submodule.span R (h '' {i | i.val < k}) = Submodule.span R (g '' {i | i.val < k}) := by
    have hh := congrArg (Submodule.map (F.symm.restrictScalars R).toLinearMap) (heq k hk)
    simp only [Submodule.map_span, Set.image_image] at hh
    simpa only [LinearEquiv.coe_toLinearMap, LinearEquiv.restrictScalars_apply, Function.comp_def,
      y, LinearEquiv.symm_apply_apply] using hh
  have hr : ∀ k, k ≤ d → Submodule.span ℝ (v '' {i | i.val < k}) =
      Submodule.span ℝ (y '' {i | i.val < k}) := by
    intro k hk
    have hh := congrArg (fun S : Submodule ℤ (Fin d → ℝ) => Submodule.span ℝ (S : Set (Fin d → ℝ)))
      (hint k hk)
    simpa only [davenportIntegerPrefixSpan, Submodule.span_span_of_tower] using hh
  refine ⟨p, h, z, he, diagonalIntegerPoint_integer_expansion N g h z
    (rationalBoxMinimumPoints_integral A B N hA hB hN) he,
    hvLI.map' F.symm.toLinearMap (LinearMap.ker_eq_bot.mpr F.symm.injective),
    hpref ℚ hq, hpref ℝ hr,
    orthogonal_expansion_det (EuclideanSpace.basisFun (Fin d) ℝ).toBasis h g
      (fun j i => (z j i : ℝ)) he, ?_⟩
  intro i j
  have hF : T (h j) = WithLp.toLp 2 (v j) := by
    apply (WithLp.linearEquiv 2 ℝ (Fin d → ℝ)).injective
    exact F.apply_symm_apply (v j)
  have hh := hb i j
  rw [show v j (p i) = T (h j) (p i) by rw [hF],
    rationalBoxTransform_apply, abs_div, abs_of_pos (hB (p i))] at hh
  have hm := (div_le_iff₀ (hB (p i))).mp hh
  calc
    _ ≤ (2 : ℝ) ^ d * min (lam i) (lam j) * B (p i) := hm
    _ = _ := by ring


end
end Bounty

end SubmissionComponent_RationalBoxDavenport

/- Component EuclideanMinimumGap; SHA256 eb19d99235bd324f1eb9ee90ae74787413b9653f7f3642701df7fe11ca5b36f6 -/
section SubmissionComponent_EuclideanMinimumGap
/- Quantitative gaps selected above the Euclidean radius of the whole box.
The factor (sqrt d)^d is essential: these are Euclidean, not sup-norm minima. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Module

/-- A product exceeding the no-gap bound forces a large adjacent gap whose
upper endpoint also exceeds the specified domain radius. -/
def finite_positive_minima_gap {d : ℕ} (hd : 0 < d) (lam : Fin d → ℝ)
    {R G : ℝ} (hR : 0 ≤ R) (hG : 1 ≤ G) (hlam : ∀ i, 0 ≤ lam i)
    (hfirst : lam ⟨0, hd⟩ ≤ R)
    (hprod : R ^ d * G ^ (d * (d - 1)) < ∏ i, lam i) :
    ∃ i j : Fin d, j.val = i.val + 1 ∧ R < lam j ∧ G * lam i < lam j := by
  classical
  by_contra! hn
  have hb : ∀ i : Fin d, lam i ≤ R * G ^ i.val := by
    cases d with
    | zero => omega
    | succ n =>
        intro i
        refine Fin.induction ?_ (fun j ih => ?_) i
        · simpa using hfirst
        · by_cases hh : lam j.succ ≤ R
          · exact hh.trans (le_mul_of_one_le_right hR (one_le_pow₀ hG))
          · have hstep : lam j.succ ≤ G * lam j.castSucc :=
              hn j.castSucc j.succ rfl (lt_of_not_ge hh)
            calc
              _ ≤ G * lam j.castSucc := hstep
              _ ≤ G * (R * G ^ j.val) := mul_le_mul_of_nonneg_left ih (le_trans (by norm_num) hG)
              _ = R * G ^ j.succ.val := by simp only [Fin.val_succ, pow_succ]; ring
  have hb' : ∀ i, lam i ≤ R * G ^ (d - 1) := by
    intro i
    apply (hb i).trans
    apply mul_le_mul_of_nonneg_left _ hR
    exact pow_le_pow_right₀ hG (by omega)
  have hp : (∏ i, lam i) ≤ R ^ d * G ^ (d * (d - 1)) := by
    calc
      _ ≤ ∏ _i : Fin d, R * G ^ (d - 1) :=
        Finset.prod_le_prod (fun i _ => hlam i) (fun i _ => hb' i)
      _ = (R * G ^ (d - 1)) ^ d := by simp
      _ = _ := by rw [mul_pow, ← pow_mul, Nat.mul_comm (d - 1) d]
  exact (not_le_of_gt hprod) hp

/-- The actual original-coordinate diagonal-integer rectangular domain. -/
def rationalDiagonalBoxDomain {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) : Set (BoxEuclidean d) :=
  {x | ∃ z : Fin d → ℤ, x = diagonalIntegerPoint N z ∧ rationalBoxContains A B x}

def rationalBoxMinimumPoints_short_mem_prefix {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d) (z : Fin d → ℤ)
    (hz : ‖rationalBoxTransform A B hA hB (diagonalIntegerPoint N z)‖ <
      rationalBoxMinimumValue A B N hA hB hN i) :
    diagonalIntegerPoint N z ∈ latticePrefixSpan (rationalBoxMinimumPoints A B N hA hB hN) i.val := by
  let L := rationalBoxLattice A B N hA hB hN
  let T := rationalBoxTransform A B hA hB
  have hm := (latticeMinimumVectors_spec L).short_mem_prefix (boxDimensionEquiv d i)
    ((rationalBoxLattice_mem_iff A B N hA hB hN _).mpr ⟨z, rfl⟩) hz
  have hb : diagonalIntegerPoint N z ∈
      (latticePrefixSpan (latticeMinimumVectors L) i.val).map T.symm.toLinearMap :=
    ⟨T (diagonalIntegerPoint N z), hm, T.symm_apply_apply _⟩
  rw [box_prefix_map] at hb
  have heq : latticePrefixSpan (rationalBoxMinimumPoints A B N hA hB hN) i.val =
      latticePrefixSpan (T.symm ∘ latticeMinimumVectors L) i.val := by
    change latticePrefixSpan ((T.symm ∘ latticeMinimumVectors L) ∘ boxDimensionEquiv d) i.val = _
    unfold boxDimensionEquiv
    exact box_prefix_finCongr (by simp [BoxEuclidean])
      (T.symm ∘ latticeMinimumVectors L) i.val
  rw [heq]
  exact hb

def rationalDiagonalBoxDomain_mem_prefix {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (B : Fin d → ℝ) (N : Fin d → ℕ) (hA : A.det ≠ 0)
    (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i) (i : Fin d)
    (hi : Real.sqrt d < rationalBoxMinimumValue A B N hA hB hN i) :
    rationalDiagonalBoxDomain A B N ⊆
      latticePrefixSpan (rationalBoxMinimumPoints A B N hA hB hN) i.val := by
  rintro x ⟨z, rfl, hx⟩
  apply rationalBoxMinimumPoints_short_mem_prefix A B N hA hB hN i z
  exact (rationalBoxContains_norm_le_sqrt A B hA hB _ hx).trans_lt hi

def rationalBoxMinimumValue_first_le_domain_radius {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (B : Fin d → ℝ) (N : Fin d → ℕ)
    (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i)
    (hne : ∃ x ∈ rationalDiagonalBoxDomain A B N, x ≠ 0) :
    rationalBoxMinimumValue A B N hA hB hN ⟨0, hd⟩ ≤ Real.sqrt d := by
  obtain ⟨x, ⟨z, rfl, hx⟩, hne⟩ := hne
  let L := rationalBoxLattice A B N hA hB hN
  let T := rationalBoxTransform A B hA hB
  have hm := (latticeMinimumVectors_spec L).2.2 (boxDimensionEquiv d ⟨0, hd⟩)
    (T (diagonalIntegerPoint N z))
    ((rationalBoxLattice_mem_iff A B N hA hB hN _).mpr ⟨z, rfl⟩)
  have hout : T (diagonalIntegerPoint N z) ∉
      latticePrefixSpan (latticeMinimumVectors L) (boxDimensionEquiv d ⟨0, hd⟩).val := by
    change T (diagonalIntegerPoint N z) ∉ latticePrefixSpan (latticeMinimumVectors L) 0
    rw [latticePrefixSpan_zero, Submodule.mem_bot]
    exact fun h => hne (T.injective (h.trans T.map_zero.symm))
  exact (hm hout).trans (rationalBoxContains_norm_le_sqrt A B hA hB _ hx)

/-- A determinant-growth criterion giving an actual containing prefix.
The upper gap endpoint is above sqrt d, so containment is valid for every
point of the rectangular domain, not merely for the Euclidean unit ball. -/
def rationalDiagonalBoxDomain_large_gap {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (B : Fin d → ℝ) (N : Fin d → ℕ)
    (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i)
    (hne : ∃ x ∈ rationalDiagonalBoxDomain A B N, x ≠ 0)
    {G : ℝ} (hG : 1 ≤ G)
    (hdet : (d.factorial : ℝ) * (Real.sqrt d) ^ d * G ^ (d * (d - 1)) <
      |(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i) :
    ∃ i j : Fin d, j.val = i.val + 1 ∧
      Real.sqrt d < rationalBoxMinimumValue A B N hA hB hN j ∧
      G * rationalBoxMinimumValue A B N hA hB hN i < rationalBoxMinimumValue A B N hA hB hN j ∧
      rationalDiagonalBoxDomain A B N ⊆
        latticePrefixSpan (rationalBoxMinimumPoints A B N hA hB hN) j.val ∧
      finrank ℝ (Submodule.span ℝ (rationalDiagonalBoxDomain A B N)) ≤ j.val := by
  have hfac : (0 : ℝ) < d.factorial := by exact_mod_cast Nat.factorial_pos d
  have hp := (rationalBoxMinimumValue_product_bounds A B N hA hB hN).1
  have hprod : (Real.sqrt d) ^ d * G ^ (d * (d - 1)) <
      ∏ i, rationalBoxMinimumValue A B N hA hB hN i := by
    apply lt_of_lt_of_le _ hp
    apply (lt_div_iff₀ hfac).mpr
    nlinarith [hdet]
  obtain ⟨i, j, hij, hj, hgap⟩ := finite_positive_minima_gap hd
    (rationalBoxMinimumValue A B N hA hB hN) (Real.sqrt_nonneg d) hG
    (fun i => (rationalBoxMinimumValue_pos A B N hA hB hN i).le)
    (rationalBoxMinimumValue_first_le_domain_radius hd A B N hA hB hN hne) hprod
  have hsub := rationalDiagonalBoxDomain_mem_prefix A B N hA hB hN j hj
  refine ⟨i, j, hij, hj, hgap, hsub, ?_⟩
  have hh := Submodule.finrank_mono (Submodule.span_le.mpr hsub)
  rw [latticePrefixSpan_finrank (rationalBoxMinimumPoints_independent A B N hA hB hN)
    (Nat.le_of_lt j.isLt)] at hh
  exact hh


end
end Bounty

end SubmissionComponent_EuclideanMinimumGap

/- Component RationalBoxDavenportGap; SHA256 1b6f9c3b7e2c24fc42031cfb0cfeebcb02eff78c77231b0656769ea0355c0f57 -/
section SubmissionComponent_RationalBoxDavenportGap
/- Actual rounded diagonal-lattice columns and a quantitative containing
minimum gap, with the Euclidean sqrt(d) correction included. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module

def exists_rationalBox_davenport_gap {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (B : Fin d → ℝ) (N : Fin d → ℕ)
    (hA : A.det ≠ 0) (hB : ∀ i, 0 < B i) (hN : ∀ i, 0 < N i)
    (hne : ∃ x ∈ rationalDiagonalBoxDomain A B N, x ≠ 0)
    {G : ℝ} (hG : 1 ≤ G)
    (hdet : (d.factorial : ℝ) * (Real.sqrt d) ^ d * G ^ (d * (d - 1)) <
      |(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i) :
    ∃ (p : Equiv.Perm (Fin d)) (h : Fin d → BoxEuclidean d)
      (z : Fin d → Fin d → ℤ) (lo hi : Fin d),
      hi.val = lo.val + 1 ∧
      (∀ j, h j = rationalBoxMinimumPoints A B N hA hB hN j +
        ∑ i, if i < j then (z j i : ℝ) • rationalBoxMinimumPoints A B N hA hB hN i else 0) ∧
      (∀ j, ∃ b : Fin d → ℤ, h j = diagonalIntegerPoint N b) ∧
      LinearIndependent ℝ h ∧
      (∀ k, k ≤ d → Submodule.span ℚ (h '' {i | i.val < k}) =
        Submodule.span ℚ (rationalBoxMinimumPoints A B N hA hB hN '' {i | i.val < k})) ∧
      (∀ i j, |(A.map (Rat.castHom ℝ) *ᵥ WithLp.ofLp (h j)) (p i)| ≤
        (2 : ℝ) ^ d * B (p i) * min (rationalBoxMinimumValue A B N hA hB hN i)
          (rationalBoxMinimumValue A B N hA hB hN j)) ∧
      Real.sqrt d < rationalBoxMinimumValue A B N hA hB hN hi ∧
      G < rationalBoxMinimumValue A B N hA hB hN hi /
        rationalBoxMinimumValue A B N hA hB hN lo ∧
      rationalDiagonalBoxDomain A B N ⊆ latticePrefixSpan h hi.val ∧
      finrank ℝ (latticePrefixSpan h hi.val) = hi.val ∧
      finrank ℝ (Submodule.span ℝ (rationalDiagonalBoxDomain A B N)) ≤ hi.val := by
  obtain ⟨p, h, z, he, hz, hLI, hq, hr, _, hb⟩ := exists_rationalBox_davenport A B N hA hB hN
  obtain ⟨lo, hi, hidx, hhi, hgap, hsub, hrank⟩ :=
    rationalDiagonalBoxDomain_large_gap hd A B N hA hB hN hne hG hdet
  refine ⟨p, h, z, lo, hi, hidx, he, hz, hLI, hq, hb, hhi,
    (lt_div_iff₀ (rationalBoxMinimumValue_pos A B N hA hB hN lo)).mpr hgap, ?_,
    latticePrefixSpan_finrank hLI (Nat.le_of_lt hi.isLt), hrank⟩
  rw [hr hi.val (Nat.le_of_lt hi.isLt)]
  exact hsub


end
end Bounty

end SubmissionComponent_RationalBoxDavenportGap

/- Component PadicCeilingDivisibility; SHA256 b0d3e161676c9fd4d777cf7b7827d1396cfd86de83748d96616ae52eb239bb15 -/
section SubmissionComponent_PadicCeilingDivisibility
/- Exact real exponential cutoffs for integer p-adic norms, including zero. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def padicNorm_int_real_exp (p : ℕ) [Fact p.Prime] (z : ℤ) (hz : z ≠ 0) :
    (padicNorm p (z : ℚ) : ℝ) =
      Real.exp (-((padicValInt p z : ℝ) * Real.log p)) := by
  have hp : (0 : ℝ) < p := by exact_mod_cast (Fact.out : p.Prime).pos
  rw [padicNorm.eq_zpow_of_nonzero (by exact_mod_cast hz), padicValRat.of_int]
  simp only [zpow_neg, zpow_natCast, Rat.cast_inv, Rat.cast_pow, Rat.cast_natCast]
  rw [Real.exp_neg, Real.exp_nat_mul, Real.exp_log hp]

def prime_pow_dvd_int_iff_le_padicVal (p : ℕ) [Fact p.Prime] (z : ℤ)
    (hz : z ≠ 0) (n : ℕ) : ((p ^ n : ℕ) : ℤ) ∣ z ↔ n ≤ padicValInt p z := by
  rw [padicNorm.dvd_iff_norm_le,
    padicNorm.eq_zpow_of_nonzero (by exact_mod_cast hz), padicValRat.of_int,
    zpow_le_zpow_iff_right₀ (by exact_mod_cast (Fact.out : p.Prime).one_lt), neg_le_neg_iff]
  exact_mod_cast Iff.rfl

/-- Exact ceiling conversion.  The zero case is part of the equivalence. -/
def padicNorm_int_le_exp_iff_dvd (p : ℕ) [Fact p.Prime] (z : ℤ) (a : ℝ) :
    (padicNorm p (z : ℚ) : ℝ) ≤ Real.exp (-a) ↔
      ((p ^ Nat.ceil (a / Real.log p) : ℕ) : ℤ) ∣ z := by
  by_cases hz : z = 0
  · subst z
    simp [le_of_lt (Real.exp_pos (-a))]
  have hp : 0 < Real.log (p : ℝ) := Real.log_pos (by exact_mod_cast (Fact.out : p.Prime).one_lt)
  rw [padicNorm_int_real_exp p z hz, Real.exp_le_exp,
    prime_pow_dvd_int_iff_le_padicVal p z hz, Nat.ceil_le, div_le_iff₀ hp]
  constructor <;> intro h <;> linarith

/-- Rounding the prime exponent costs less than a factor p. -/
def prime_ceiling_power_bounds (p : ℕ) (hp : 1 < p) {a : ℝ} (ha : 0 ≤ a) :
    Real.exp a ≤ (p : ℝ) ^ Nat.ceil (a / Real.log p) ∧
      (p : ℝ) ^ Nat.ceil (a / Real.log p) < p * Real.exp a := by
  have hpl : 0 < Real.log (p : ℝ) := Real.log_pos (by exact_mod_cast hp)
  have hpp : (0 : ℝ) < p := by exact_mod_cast (by omega : 0 < p)
  have he : (p : ℝ) ^ Nat.ceil (a / Real.log p) =
      Real.exp ((Nat.ceil (a / Real.log p) : ℝ) * Real.log p) := by
    rw [Real.exp_nat_mul, Real.exp_log hpp]
  rw [he]
  constructor
  · apply Real.exp_le_exp.mpr
    exact (div_le_iff₀ hpl).mp (Nat.le_ceil _)
  · have hh := Nat.ceil_lt_add_one (div_nonneg ha hpl.le)
    have hm := mul_lt_mul_of_pos_right hh hpl
    have hab : (Nat.ceil (a / Real.log p) : ℝ) * Real.log p < a + Real.log p := by
      simpa only [add_mul, div_mul_cancel₀ _ hpl.ne', one_mul] using hm
    have hx := Real.exp_lt_exp.mpr hab
    simpa only [Real.exp_add, Real.exp_log hpp, mul_comm] using hx


end
end Bounty

end SubmissionComponent_PadicCeilingDivisibility

/- Component RationalThreePlaceDomain; SHA256 c8c7aec46a3a7180a2a476a04289d2c880fd7430c3dbd4f6c42d4310b26480fd -/
section SubmissionComponent_RationalThreePlaceDomain
/- Exact equality of the three-place integer domain and a diagonal lattice box. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def integerEuclideanPoint {d : ℕ} (x : Fin d → ℤ) : BoxEuclidean d :=
  WithLp.toLp 2 (fun i => (x i : ℝ))

def rationalThreePlaceDomain {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) : Set (Fin d → ℤ) :=
  {x | (∀ i, |(A.map (Rat.castHom ℝ) *ᵥ (fun j => (x j : ℝ))) i| ≤ Real.exp (c 0 i * q)) ∧
    (∀ i, (padicNorm 2 (x i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q)) ∧
    (∀ i, (padicNorm 3 (x i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q))}

def threePlaceWidth {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (i : Fin d) : ℝ :=
  Real.exp (c 0 i * q)

def threePlaceDiagonal {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (i : Fin d) : ℕ :=
  2 ^ Nat.ceil (-(c 1 i * q) / Real.log 2) * 3 ^ Nat.ceil (-(c 2 i * q) / Real.log 3)

def threePlaceWidth_pos {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (i : Fin d) :
    0 < threePlaceWidth c q i := Real.exp_pos _

def threePlaceDiagonal_pos {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (i : Fin d) :
    0 < threePlaceDiagonal c q i := by unfold threePlaceDiagonal; positivity

def two_three_pow_dvd_int_iff (u v : ℕ) (x : ℤ) :
    (((2 ^ u * 3 ^ v : ℕ) : ℤ) ∣ x) ↔
      (((2 ^ u : ℕ) : ℤ) ∣ x) ∧ (((3 ^ v : ℕ) : ℤ) ∣ x) := by
  rw [Nat.cast_mul]
  constructor
  · intro h
    exact ⟨(dvd_mul_right _ _).trans h, (dvd_mul_left _ _).trans h⟩
  · rintro ⟨h2, h3⟩
    have hc : Nat.Coprime (2 ^ u) (3 ^ v) := (by norm_num : Nat.Coprime 2 3).pow u v
    exact hc.isCoprime.mul_dvd h2 h3

def threePlaceDiagonal_dvd_iff {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    (q : ℝ) (i : Fin d) (x : ℤ) :
    ((threePlaceDiagonal c q i : ℤ) ∣ x) ↔
      (padicNorm 2 (x : ℚ) : ℝ) ≤ Real.exp (c 1 i * q) ∧
      (padicNorm 3 (x : ℚ) : ℝ) ≤ Real.exp (c 2 i * q) := by
  rw [threePlaceDiagonal, two_three_pow_dvd_int_iff]
  simpa only [neg_neg, Nat.cast_ofNat] using and_congr
    (padicNorm_int_le_exp_iff_dvd 2 x (-(c 1 i * q))).symm
    (padicNorm_int_le_exp_iff_dvd 3 x (-(c 2 i * q))).symm

def rationalThreePlaceDomain_iff_divisibility {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) (q : ℝ) (x : Fin d → ℤ) :
    x ∈ rationalThreePlaceDomain A c q ↔
      rationalBoxContains A (threePlaceWidth c q) (integerEuclideanPoint x) ∧
      ∀ i, (threePlaceDiagonal c q i : ℤ) ∣ x i := by
  simp only [rationalThreePlaceDomain, Set.mem_ofPred_eq, threePlaceDiagonal_dvd_iff,
    rationalBoxContains, threePlaceWidth, integerEuclideanPoint, WithLp.ofLp_toLp]
  aesop

/-- Equality at each actual integer point; it includes zero coordinates. -/
def rationalThreePlaceDomain_point_iff {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) (q : ℝ) (x : Fin d → ℤ) :
    x ∈ rationalThreePlaceDomain A c q ↔ integerEuclideanPoint x ∈
      rationalDiagonalBoxDomain A (threePlaceWidth c q) (threePlaceDiagonal c q) := by
  rw [rationalThreePlaceDomain_iff_divisibility]
  constructor
  · rintro ⟨hb, hd⟩
    choose z hz using hd
    refine ⟨z, ?_, hb⟩
    ext i
    change (x i : ℝ) = (threePlaceDiagonal c q i : ℝ) * (z i : ℝ)
    exact_mod_cast hz i
  · rintro ⟨z, hz, hb⟩
    refine ⟨hb, fun i => ⟨z i, ?_⟩⟩
    have hi := congrArg (fun v : BoxEuclidean d => v i) hz
    change (x i : ℝ) = (threePlaceDiagonal c q i : ℝ) * (z i : ℝ) at hi
    exact_mod_cast hi

/-- Exact set equality, not merely an inclusion or an abstract lattice model. -/
def rationalThreePlaceDomain_image {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) (q : ℝ) :
    integerEuclideanPoint '' rationalThreePlaceDomain A c q =
      rationalDiagonalBoxDomain A (threePlaceWidth c q) (threePlaceDiagonal c q) := by
  ext y
  constructor
  · rintro ⟨x, hx, rfl⟩
    exact (rationalThreePlaceDomain_point_iff A c q x).mp hx
  · rintro ⟨z, rfl, hb⟩
    let x : Fin d → ℤ := fun i => (threePlaceDiagonal c q i : ℤ) * z i
    have hx : integerEuclideanPoint x = diagonalIntegerPoint (threePlaceDiagonal c q) z := by
      ext i
      simp [integerEuclideanPoint, diagonalIntegerPoint, x]
    refine ⟨x, (rationalThreePlaceDomain_point_iff A c q x).mpr ?_, hx⟩
    rw [hx]
    exact ⟨z, rfl, hb⟩

/-- Each coordinate denominator differs from the exact real scaling by
less than a factor six. -/
def threePlaceDiagonal_bounds {d : ℕ} (c : Fin 3 → Fin d → ℝ) {q : ℝ}
    (hq : 0 ≤ q) (hc1 : ∀ i, c 1 i ≤ 0) (hc2 : ∀ i, c 2 i ≤ 0) (i : Fin d) :
    Real.exp (-(c 1 i + c 2 i) * q) ≤ (threePlaceDiagonal c q i : ℝ) ∧
      (threePlaceDiagonal c q i : ℝ) ≤ 6 * Real.exp (-(c 1 i + c 2 i) * q) := by
  have h2 := prime_ceiling_power_bounds 2 (by norm_num) (neg_nonneg.mpr (mul_nonpos_of_nonpos_of_nonneg (hc1 i) hq))
  have h3 := prime_ceiling_power_bounds 3 (by norm_num) (neg_nonneg.mpr (mul_nonpos_of_nonpos_of_nonneg (hc2 i) hq))
  have he : Real.exp (-(c 1 i + c 2 i) * q) =
      Real.exp (-(c 1 i * q)) * Real.exp (-(c 2 i * q)) := by
    rw [← Real.exp_add]
    congr 1
    ring
  rw [he, threePlaceDiagonal, Nat.cast_mul, Nat.cast_pow, Nat.cast_pow]
  constructor
  · exact mul_le_mul h2.1 h3.1 (Real.exp_nonneg _) (by positivity)
  · calc
      _ ≤ (2 * Real.exp (-(c 1 i * q))) * (3 * Real.exp (-(c 2 i * q))) :=
        mul_le_mul h2.2.le h3.2.le (by positivity) (by positivity)
      _ = _ := by ring


end
end Bounty

end SubmissionComponent_RationalThreePlaceDomain

/- Component ThreePlaceCovolume; SHA256 2bf668c0d1fd9828b1ac8b34e08b180e8e2f6e2ea457b626e04fd7ec26a5d88e -/
section SubmissionComponent_ThreePlaceCovolume
/- Covolume estimates for the exact three-place diagonal lattice. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Module MeasureTheory

def threePlaceProfileSum {d : ℕ} (c : Fin 3 → Fin d → ℝ) : ℝ :=
  ∑ v : Fin 3, ∑ i, c v i

def threePlaceProfileSum_eq {d : ℕ} (c : Fin 3 → Fin d → ℝ) :
    threePlaceProfileSum c = ∑ i : Fin d, (c 0 i + c 1 i + c 2 i) := by
  simp [threePlaceProfileSum, Fin.sum_univ_succ, Finset.sum_add_distrib, add_assoc]

abbrev rationalThreePlaceLattice {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0) : Submodule ℤ (BoxEuclidean d) :=
  rationalBoxLattice A (threePlaceWidth c q) (threePlaceDiagonal c q) hA
    (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)

def threePlaceCoordinateScale_bounds {d : ℕ} (c : Fin 3 → Fin d → ℝ) {q : ℝ}
    (hq : 0 ≤ q) (hc1 : ∀ i, c 1 i ≤ 0) (hc2 : ∀ i, c 2 i ≤ 0) (i : Fin d) :
    Real.exp (-(c 0 i + c 1 i + c 2 i) * q) ≤
        (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i ∧
      (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i ≤
        6 * Real.exp (-(c 0 i + c 1 i + c 2 i) * q) := by
  have hh := threePlaceDiagonal_bounds c hq hc1 hc2 i
  have hw := threePlaceWidth_pos c q i
  have he : Real.exp (-(c 1 i + c 2 i) * q) / threePlaceWidth c q i =
      Real.exp (-(c 0 i + c 1 i + c 2 i) * q) := by
    rw [threePlaceWidth, ← Real.exp_sub]
    congr 1
    ring
  constructor
  · rw [← he]
    exact div_le_div_of_nonneg_right hh.1 hw.le
  · rw [← he]
    calc
      _ ≤ (6 * Real.exp (-(c 1 i + c 2 i) * q)) / threePlaceWidth c q i :=
        div_le_div_of_nonneg_right hh.2 hw.le
      _ = _ := by ring

def threePlace_exp_product {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) :
    (∏ i, Real.exp (-(c 0 i + c 1 i + c 2 i) * q)) =
      Real.exp (-threePlaceProfileSum c * q) := by
  rw [← Real.exp_sum]
  congr 1
  rw [← Finset.sum_mul, Finset.sum_neg_distrib, threePlaceProfileSum_eq]

/-- Exact determinant formula for the actual full discrete lattice. -/
def rationalThreePlaceLattice_covolume {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0) :
    ZLattice.covolume (rationalThreePlaceLattice A c q hA) =
      |(A.det : ℝ)| * (∏ i, (threePlaceDiagonal c q i : ℝ)) / ∏ i, threePlaceWidth c q i :=
  rationalBoxLattice_covolume A _ _ hA _ _

/-- The upper estimate uses the exact profile sum; a lower bound on its
negative alone cannot supply an upper estimate with the same rho. -/
def rationalThreePlaceLattice_covolume_bounds {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) {q : ℝ} (hA : A.det ≠ 0)
    (hq : 0 ≤ q) (hc1 : ∀ i, c 1 i ≤ 0) (hc2 : ∀ i, c 2 i ≤ 0) :
    |(A.det : ℝ)| * Real.exp (-threePlaceProfileSum c * q) ≤
        ZLattice.covolume (rationalThreePlaceLattice A c q hA) ∧
      ZLattice.covolume (rationalThreePlaceLattice A c q hA) ≤
        (6 : ℝ) ^ d * |(A.det : ℝ)| * Real.exp (-threePlaceProfileSum c * q) := by
  have he : ZLattice.covolume (rationalThreePlaceLattice A c q hA) =
      |(A.det : ℝ)| * ∏ i, (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i := by
    rw [rationalThreePlaceLattice_covolume, Finset.prod_div_distrib]
    ring
  have hlo : (∏ i, Real.exp (-(c 0 i + c 1 i + c 2 i) * q)) ≤
      ∏ i, (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i :=
    Finset.prod_le_prod (fun _ _ => Real.exp_nonneg _)
      (fun i _ => (threePlaceCoordinateScale_bounds c hq hc1 hc2 i).1)
  have hhi : (∏ i, (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i) ≤
      ∏ i, 6 * Real.exp (-(c 0 i + c 1 i + c 2 i) * q) :=
    Finset.prod_le_prod (fun i _ => div_nonneg (Nat.cast_nonneg _) (threePlaceWidth_pos c q i).le)
      (fun i _ => (threePlaceCoordinateScale_bounds c hq hc1 hc2 i).2)
  rw [threePlace_exp_product] at hlo
  rw [Finset.prod_mul_distrib, threePlace_exp_product] at hhi
  simp only [Finset.prod_const, Finset.card_univ, Fintype.card_fin] at hhi
  rw [he]
  refine ⟨mul_le_mul_of_nonneg_left hlo (abs_nonneg _), ?_⟩
  calc
    _ ≤ |(A.det : ℝ)| * ((6 : ℝ) ^ d * Real.exp (-threePlaceProfileSum c * q)) :=
      mul_le_mul_of_nonneg_left hhi (abs_nonneg _)
    _ = _ := by ring

def rationalThreePlaceLattice_covolume_lower {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) {q ρ : ℝ} (hA : A.det ≠ 0)
    (hq : 0 ≤ q) (hc1 : ∀ i, c 1 i ≤ 0) (hc2 : ∀ i, c 2 i ≤ 0)
    (hsum : threePlaceProfileSum c ≤ -ρ) :
    |(A.det : ℝ)| * Real.exp (ρ * q) ≤ ZLattice.covolume (rationalThreePlaceLattice A c q hA) := by
  apply le_trans _ (rationalThreePlaceLattice_covolume_bounds A c hA hq hc1 hc2).1
  apply mul_le_mul_of_nonneg_left _ (abs_nonneg _)
  apply Real.exp_le_exp.mpr
  have hh := mul_le_mul_of_nonneg_right hsum hq
  nlinarith


end
end Bounty

end SubmissionComponent_ThreePlaceCovolume

/- Component ThreePlaceDavenportGap; SHA256 def74f57f06f1be4c9b18fb2544ea81569838e0803694de3dcee33744a912444 -/
section SubmissionComponent_ThreePlaceDavenportGap
/- The full geometric bridge for the actual three-place integer domain. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module

def threePlaceMinimumValue {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0) : Fin d → ℝ :=
  rationalBoxMinimumValue A (threePlaceWidth c q) (threePlaceDiagonal c q) hA
    (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)

def threePlaceMinimumPoints {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0) : Fin d → BoxEuclidean d :=
  rationalBoxMinimumPoints A (threePlaceWidth c q) (threePlaceDiagonal c q) hA
    (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)

def integerEuclideanPoint_injective {d : ℕ} :
    Function.Injective (@integerEuclideanPoint d) := by
  intro x y h
  funext i
  have hi := congrArg (fun v : BoxEuclidean d => v i) h
  change (x i : ℝ) = (y i : ℝ) at hi
  exact_mod_cast hi

/-- With the explicit Euclidean gap threshold, the three-place domain
admits actual integer Davenport columns and a containing proper prefix. -/
def exists_threePlace_davenport_gap {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) {q ρ G : ℝ}
    (hA : A.det ≠ 0) (hq : 0 ≤ q)
    (hc1 : ∀ i, c 1 i ≤ 0) (hc2 : ∀ i, c 2 i ≤ 0)
    (hsum : threePlaceProfileSum c ≤ -ρ)
    (hne : ∃ x ∈ rationalThreePlaceDomain A c q, x ≠ 0) (hG : 1 ≤ G)
    (hgrowth : (d.factorial : ℝ) * (Real.sqrt d) ^ d * G ^ (d * (d - 1)) <
      |(A.det : ℝ)| * Real.exp (ρ * q)) :
    ∃ (p : Equiv.Perm (Fin d)) (H : Fin d → Fin d → ℤ) (z : Fin d → Fin d → ℤ)
      (lo hi : Fin d),
      hi.val = lo.val + 1 ∧
      (∀ j i, (threePlaceDiagonal c q i : ℤ) ∣ H j i) ∧
      (∀ j, integerEuclideanPoint (H j) = threePlaceMinimumPoints A c q hA j +
        ∑ i, if i < j then (z j i : ℝ) • threePlaceMinimumPoints A c q hA i else 0) ∧
      LinearIndependent ℝ (fun j => integerEuclideanPoint (H j)) ∧
      (∀ k, k ≤ d → Submodule.span ℚ ((fun j => integerEuclideanPoint (H j)) '' {i | i.val < k}) =
        Submodule.span ℚ (threePlaceMinimumPoints A c q hA '' {i | i.val < k})) ∧
      (∀ i j, |(A.map (Rat.castHom ℝ) *ᵥ (fun r => (H j r : ℝ))) (p i)| ≤
        (2 : ℝ) ^ d * Real.exp (c 0 (p i) * q) *
          min (threePlaceMinimumValue A c q hA i) (threePlaceMinimumValue A c q hA j)) ∧
      Real.sqrt d < threePlaceMinimumValue A c q hA hi ∧
      G < threePlaceMinimumValue A c q hA hi / threePlaceMinimumValue A c q hA lo ∧
      (∀ x ∈ rationalThreePlaceDomain A c q, integerEuclideanPoint x ∈
        latticePrefixSpan (fun j => integerEuclideanPoint (H j)) hi.val) ∧
      finrank ℝ (latticePrefixSpan (fun j => integerEuclideanPoint (H j)) hi.val) = hi.val ∧
      finrank ℝ (Submodule.span ℝ (integerEuclideanPoint '' rationalThreePlaceDomain A c q)) ≤ hi.val := by
  let B := threePlaceWidth c q
  let N := threePlaceDiagonal c q
  have hboxne : ∃ x ∈ rationalDiagonalBoxDomain A B N, x ≠ 0 := by
    obtain ⟨x, hx, hxne⟩ := hne
    refine ⟨integerEuclideanPoint x, (rationalThreePlaceDomain_point_iff A c q x).mp hx, ?_⟩
    intro hz
    apply hxne
    apply integerEuclideanPoint_injective
    have hzero : integerEuclideanPoint (0 : Fin d → ℤ) = 0 := by ext i; simp [integerEuclideanPoint]
    exact hz.trans hzero.symm
  have hdet : (d.factorial : ℝ) * (Real.sqrt d) ^ d * G ^ (d * (d - 1)) <
      |(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, B i := by
    have hh := rationalThreePlaceLattice_covolume_lower A c hA hq hc1 hc2 hsum
    rw [rationalThreePlaceLattice_covolume] at hh
    exact hgrowth.trans_le hh
  obtain ⟨p, h, z, lo, hi, hidx, he, hint, hLI, hpref, hb, hhi, hgap, hsub, hdim, hrank⟩ :=
    exists_rationalBox_davenport_gap hd A B N hA (threePlaceWidth_pos c q)
      (threePlaceDiagonal_pos c q) hboxne hG hdet
  choose b hbdiag using hint
  let H : Fin d → Fin d → ℤ := fun j i => (N i : ℤ) * b j i
  have hH : (fun j => integerEuclideanPoint (H j)) = h := by
    funext j
    rw [hbdiag j]
    ext i
    simp [integerEuclideanPoint, diagonalIntegerPoint, H]
  refine ⟨p, H, z, lo, hi, hidx, (fun j i => ⟨b j i, rfl⟩), ?_, ?_, ?_, ?_, hhi, hgap, ?_, ?_, ?_⟩
  · intro j
    rw [congrFun hH j]
    exact he j
  · rw [hH]
    exact hLI
  · rw [hH]
    exact hpref
  · intro i j
    have hh := hb i j
    rw [← congrFun hH j] at hh
    exact hh
  · intro x hx
    rw [hH]
    exact hsub ((rationalThreePlaceDomain_point_iff A c q x).mp hx)
  · rw [hH]
    exact hdim
  · rw [rationalThreePlaceDomain_image]
    exact hrank


end
end Bounty

end SubmissionComponent_ThreePlaceDavenportGap

/- Component ThreePlaceMinimaBounds; SHA256 c0972339d911636ab9a0dd1b4b43834b23ef2d3f200c949d53592405ba76f848 -/
section SubmissionComponent_ThreePlaceMinimaBounds
/- Uniform exponential bounds for the actual transformed Euclidean minima. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module MeasureTheory

def rationalMatrixSize {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) : ℝ :=
  1 + ∑ i, ∑ j, |(A i j : ℝ)|

def rationalMatrixSize_one_le {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) :
    1 ≤ rationalMatrixSize A := by
  unfold rationalMatrixSize
  exact le_add_of_nonneg_right (Finset.sum_nonneg (fun i _ => Finset.sum_nonneg (fun j _ => abs_nonneg _)))

def rationalMatrixSize_entry {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) (i j : Fin d) :
    |(A i j : ℝ)| ≤ rationalMatrixSize A := by
  have h1 : |(A i j : ℝ)| ≤ ∑ k : Fin d, |(A i k : ℝ)| :=
    Finset.single_le_sum (f := fun k : Fin d => |(A i k : ℝ)|)
      (fun k _ => abs_nonneg _) (Finset.mem_univ j)
  have h2 : (∑ k : Fin d, |(A i k : ℝ)|) ≤ ∑ l : Fin d, ∑ k : Fin d, |(A l k : ℝ)| :=
    Finset.single_le_sum (f := fun l : Fin d => ∑ k : Fin d, |(A l k : ℝ)|)
      (fun l _ => Finset.sum_nonneg (fun k _ => abs_nonneg _)) (Finset.mem_univ i)
  unfold rationalMatrixSize
  linarith

def boxEuclidean_norm_le_sum_abs {d : ℕ} (x : BoxEuclidean d) :
    ‖x‖ ≤ ∑ i, |x i| := by
  let e := EuclideanSpace.basisFun (Fin d) ℝ
  have hx : (∑ i, x i • e i) = x := e.toBasis.sum_repr x
  calc
    ‖x‖ = ‖∑ i, x i • e i‖ := congrArg norm hx.symm
    _ ≤ ∑ i, ‖x i • e i‖ := norm_sum_le _ _
    _ = _ := by simp [norm_smul, e.norm_eq_one, Real.norm_eq_abs]

def threePlaceDiagonal_uniform_upper {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    {M q : ℝ} (hM : 0 ≤ M) (hq : 0 ≤ q) (hc : ∀ v i, |c v i| ≤ M) (i : Fin d) :
    (threePlaceDiagonal c q i : ℝ) ≤ 6 * Real.exp (2 * M * q) := by
  have hp (p : ℕ) (hp : 1 < p) (v : Fin 3) :
      (p : ℝ) ^ Nat.ceil (-(c v i * q) / Real.log p) ≤ p * Real.exp (M * q) := by
    have hlog : 0 < Real.log (p : ℝ) := Real.log_pos (by exact_mod_cast hp)
    have hcv : -(c v i * q) ≤ M * q := by
      have hh := mul_le_mul_of_nonneg_right ((neg_le_abs (c v i)).trans (hc v i)) hq
      linarith
    have hceil := Nat.ceil_mono (div_le_div_of_nonneg_right hcv hlog.le)
    exact (pow_le_pow_right₀ (by exact_mod_cast (Nat.le_of_lt hp)) hceil).trans
      (prime_ceiling_power_bounds p hp (mul_nonneg hM hq)).2.le
  have h2 := hp 2 (by norm_num) 1
  have h3 := hp 3 (by norm_num) 2
  simp only [Nat.cast_ofNat] at h2 h3
  rw [threePlaceDiagonal, Nat.cast_mul, Nat.cast_pow, Nat.cast_pow]
  calc
    _ ≤ (2 * Real.exp (M * q)) * (3 * Real.exp (M * q)) :=
      mul_le_mul h2 h3 (by positivity) (by positivity)
    _ = 6 * Real.exp (M * q + M * q) := by rw [Real.exp_add]; ring
    _ = _ := by congr 2; ring

def threePlaceWidth_uniform_bounds {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    {M q : ℝ} (hq : 0 ≤ q) (hc : ∀ v i, |c v i| ≤ M) (i : Fin d) :
    threePlaceWidth c q i ≤ Real.exp (M * q) ∧
      (threePlaceWidth c q i)⁻¹ ≤ Real.exp (M * q) := by
  constructor
  · exact Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right ((le_abs_self _).trans (hc 0 i)) hq)
  · rw [threePlaceWidth, ← Real.exp_neg]
    apply Real.exp_le_exp.mpr
    have hh := mul_le_mul_of_nonneg_right ((neg_le_abs _).trans (hc 0 i)) hq
    linarith

def threePlaceBasis_norm_bound {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) {M q : ℝ} (hA : A.det ≠ 0) (hM : 0 ≤ M) (hq : 0 ≤ q)
    (hc : ∀ v i, |c v i| ≤ M) (j : Fin d) :
    ‖matrixEuclideanBasis (rationalBoxLatticeMatrix A (threePlaceWidth c q) (threePlaceDiagonal c q))
      (rationalBoxLatticeMatrix_det_ne_zero A _ _ hA (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)) j‖ ≤
      (6 * (d + 1 : ℝ) * rationalMatrixSize A) * Real.exp (3 * M * q) := by
  let B := threePlaceWidth c q
  let N := threePlaceDiagonal c q
  let C := rationalBoxLatticeMatrix A B N
  let hC := rationalBoxLatticeMatrix_det_ne_zero A B N hA (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)
  let b := matrixEuclideanBasis C hC
  have hKA : 0 ≤ rationalMatrixSize A := le_trans (by norm_num) (rationalMatrixSize_one_le A)
  have hentry (i : Fin d) : |b j i| ≤ 6 * rationalMatrixSize A * Real.exp (3 * M * q) := by
    have he : b j i = C i j := congrArg (fun D : Matrix (Fin d) (Fin d) ℝ => D i j)
      (matrixEuclideanBasis_toMatrix C hC)
    rw [he]
    have hCij : C i j = (B i)⁻¹ * (A i j : ℝ) * (N j : ℝ) := by
      simp [C, rationalBoxLatticeMatrix, rationalBoxMatrix, Matrix.diagonal_mul, Matrix.mul_diagonal]
    rw [hCij, abs_mul, abs_mul, abs_of_nonneg (inv_nonneg.mpr (threePlaceWidth_pos c q i).le),
      abs_of_nonneg (show (0 : ℝ) ≤ N j from Nat.cast_nonneg _)]
    calc
      _ ≤ (Real.exp (M * q) * rationalMatrixSize A) * (6 * Real.exp (2 * M * q)) :=
        mul_le_mul (mul_le_mul (threePlaceWidth_uniform_bounds c hq hc i).2
          (rationalMatrixSize_entry A i j) (abs_nonneg _) (Real.exp_nonneg _))
          (threePlaceDiagonal_uniform_upper c hM hq hc j) (Nat.cast_nonneg _)
          (mul_nonneg (Real.exp_nonneg _) hKA)
      _ = 6 * rationalMatrixSize A * Real.exp (M * q + 2 * M * q) := by rw [Real.exp_add]; ring
      _ = _ := by congr 2; ring
  have hK : 0 ≤ 6 * rationalMatrixSize A * Real.exp (3 * M * q) :=
    mul_nonneg (mul_nonneg (by norm_num) (le_trans (by norm_num) (rationalMatrixSize_one_le A))) (Real.exp_nonneg _)
  calc
    ‖b j‖ ≤ ∑ i, |b j i| := boxEuclidean_norm_le_sum_abs _
    _ ≤ ∑ _i : Fin d, 6 * rationalMatrixSize A * Real.exp (3 * M * q) :=
      Finset.sum_le_sum (fun i _ => hentry i)
    _ = (d : ℝ) * (6 * rationalMatrixSize A * Real.exp (3 * M * q)) := by simp
    _ ≤ (d + 1 : ℝ) * (6 * rationalMatrixSize A * Real.exp (3 * M * q)) :=
      mul_le_mul_of_nonneg_right (by linarith) hK
    _ = _ := by ring

def threePlaceMinimumValue_uniform_upper {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) {M q : ℝ} (hA : A.det ≠ 0) (hM : 0 ≤ M) (hq : 0 ≤ q)
    (hc : ∀ v i, |c v i| ≤ M) (i : Fin d) :
    threePlaceMinimumValue A c q hA i ≤
      (6 * (d + 1 : ℝ) * rationalMatrixSize A) * Real.exp (3 * M * q) := by
  let B := threePlaceWidth c q
  let N := threePlaceDiagonal c q
  let L := rationalBoxLattice A B N hA (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)
  let C := rationalBoxLatticeMatrix A B N
  let hC := rationalBoxLatticeMatrix_det_ne_zero A B N hA (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)
  let b := matrixEuclideanBasis C hC
  apply (latticeSuccessiveMinimum_le_iff L (boxDimensionEquiv d i) _).mpr
  let f := Fin.castLE (Nat.succ_le_of_lt i.isLt)
  refine ⟨fun j => b (f j), b.linearIndependent.comp f (Fin.castLE_injective _), ?_, ?_⟩
  · intro j
    exact Submodule.subset_span ⟨f j, rfl⟩
  · intro j
    exact threePlaceBasis_norm_bound A c hA hM hq hc (f j)

def positive_constant_exp_bounds {C q : ℝ} (hC : 0 < C) (hq : 1 ≤ q) :
    Real.exp (-|Real.log C| * q) ≤ C ∧ C ≤ Real.exp (|Real.log C| * q) := by
  have hh : |Real.log C| ≤ |Real.log C| * q := le_mul_of_one_le_right (abs_nonneg _) hq
  constructor
  · calc
      _ ≤ Real.exp (Real.log C) := Real.exp_le_exp.mpr (by nlinarith [neg_abs_le (Real.log C)])
      _ = C := Real.exp_log hC
  · calc
      C = Real.exp (Real.log C) := (Real.exp_log hC).symm
      _ ≤ _ := Real.exp_le_exp.mpr ((le_abs_self _).trans hh)

def threePlaceMinimumValue_exp_upper {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) {M q : ℝ} (hA : A.det ≠ 0) (hM : 0 ≤ M) (hq : 1 ≤ q)
    (hc : ∀ v i, |c v i| ≤ M) (i : Fin d) :
    threePlaceMinimumValue A c q hA i ≤
      Real.exp ((3 * M + |Real.log (6 * (d + 1 : ℝ) * rationalMatrixSize A)|) * q) := by
  have hK : 0 < 6 * (d + 1 : ℝ) * rationalMatrixSize A :=
    mul_pos (mul_pos (by norm_num) (by positivity)) ((by norm_num : (0 : ℝ) < 1).trans_le (rationalMatrixSize_one_le A))
  apply (threePlaceMinimumValue_uniform_upper A c hA hM (le_trans (by norm_num) hq) hc i).trans
  calc
    _ ≤ Real.exp (|Real.log (6 * (d + 1 : ℝ) * rationalMatrixSize A)| * q) * Real.exp (3 * M * q) :=
      mul_le_mul_of_nonneg_right (positive_constant_exp_bounds hK hq).2 (Real.exp_nonneg _)
    _ = _ := by rw [← Real.exp_add]; congr 1; ring

def threePlaceMinimumValue_product_exp_lower {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (c : Fin 3 → Fin d → ℝ) {M q : ℝ}
    (hA : A.det ≠ 0) (hq : 0 ≤ q) (hc : ∀ v i, |c v i| ≤ M) :
    (|(A.det : ℝ)| / d.factorial) * Real.exp (-((d : ℝ) * M) * q) ≤
      ∏ i, threePlaceMinimumValue A c q hA i := by
  have hscale (i : Fin d) : Real.exp (-(M * q)) ≤
      (threePlaceDiagonal c q i : ℝ) / threePlaceWidth c q i := by
    rw [Real.exp_neg, inv_eq_one_div]
    calc
      _ ≤ 1 / threePlaceWidth c q i :=
        one_div_le_one_div_of_le (threePlaceWidth_pos c q i) (threePlaceWidth_uniform_bounds c hq hc i).1
      _ ≤ _ := div_le_div_of_nonneg_right
        (by exact_mod_cast (threePlaceDiagonal_pos c q i)) (threePlaceWidth_pos c q i).le
  have hs := Finset.prod_le_prod (fun _ _ => Real.exp_nonneg _) (fun i (_ : i ∈ Finset.univ) => hscale i)
  have he : (∏ _i : Fin d, Real.exp (-(M * q))) = Real.exp (-((d : ℝ) * M) * q) := by
    simp only [Finset.prod_const, Finset.card_univ, Fintype.card_fin, ← Real.exp_nat_mul]
    congr 1
    ring
  rw [he, Finset.prod_div_distrib] at hs
  have hp := (rationalBoxMinimumValue_product_bounds A (threePlaceWidth c q) (threePlaceDiagonal c q)
    hA (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)).1
  apply le_trans _ hp
  have hfac : (0 : ℝ) < d.factorial := by exact_mod_cast Nat.factorial_pos d
  have ht := div_le_div_of_nonneg_right (mul_le_mul_of_nonneg_left hs (abs_nonneg (A.det : ℝ))) hfac.le
  convert ht using 1 <;> ring

def finite_minima_exp_lower {d : ℕ} (lam : Fin d → ℝ) {C U V q : ℝ}
    (hC : 0 < C) (hU : 0 ≤ U) (hq : 1 ≤ q) (hlam : ∀ i, 0 ≤ lam i)
    (hupper : ∀ i, lam i ≤ Real.exp (U * q))
    (hprod : C * Real.exp (-V * q) ≤ ∏ i, lam i) (i : Fin d) :
    Real.exp (-(V + U * d + |Real.log C|) * q) ≤ lam i := by
  classical
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq
  have he1 : 1 ≤ Real.exp (U * q) := Real.one_le_exp_iff.mpr (mul_nonneg hU hq0)
  have hother : (∏ j ∈ Finset.univ.erase i, lam j) ≤ Real.exp (U * q) ^ d := by
    calc
      _ ≤ ∏ _j ∈ Finset.univ.erase i, Real.exp (U * q) :=
        Finset.prod_le_prod (fun j _ => hlam j) (fun j _ => hupper j)
      _ = Real.exp (U * q) ^ (d - 1) := by simp
      _ ≤ _ := pow_le_pow_right₀ he1 (Nat.sub_le _ _)
  have hp : (∏ j, lam j) ≤ lam i * Real.exp (U * q) ^ d := by
    rw [← Finset.mul_prod_erase Finset.univ lam (Finset.mem_univ i)]
    exact mul_le_mul_of_nonneg_left hother (hlam i)
  have hlow : Real.exp (-(V + U * d + |Real.log C|) * q) * Real.exp (U * q) ^ d ≤
      C * Real.exp (-V * q) := by
    have hh := mul_le_mul_of_nonneg_right (positive_constant_exp_bounds hC hq).1 (Real.exp_nonneg (-V * q))
    calc
      _ = Real.exp (-|Real.log C| * q) * Real.exp (-V * q) := by
        rw [← Real.exp_nat_mul, ← Real.exp_add, ← Real.exp_add]
        congr 1
        ring
      _ ≤ _ := hh
  exact (mul_le_mul_iff_left₀ (pow_pos (Real.exp_pos _) d)).mp (by
    simpa only [mul_comm] using hlow.trans (hprod.trans hp))

def exists_threePlaceMinimumValue_uniform_exp_bounds {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0) (M : ℝ) :
    ∃ L : ℝ, 0 ≤ L ∧ ∀ (c : Fin 3 → Fin d → ℝ) (q : ℝ), 1 ≤ q →
      (∀ v i, |c v i| ≤ M) → ∀ i,
      Real.exp (-L * q) ≤ threePlaceMinimumValue A c q hA i ∧
        threePlaceMinimumValue A c q hA i ≤ Real.exp (L * q) := by
  let M' := max M 0
  let U := 3 * M' + |Real.log (6 * (d + 1 : ℝ) * rationalMatrixSize A)|
  let C := |(A.det : ℝ)| / d.factorial
  let V := (d : ℝ) * M'
  let L := U + V + U * d + |Real.log C|
  have hM : 0 ≤ M' := le_max_right _ _
  have hU : 0 ≤ U := add_nonneg (mul_nonneg (by norm_num) hM) (abs_nonneg _)
  have hV : 0 ≤ V := mul_nonneg (Nat.cast_nonneg _) hM
  have hC : 0 < C := div_pos (abs_pos.mpr (by exact_mod_cast hA)) (by exact_mod_cast Nat.factorial_pos d)
  have hUd : 0 ≤ U * d := mul_nonneg hU (Nat.cast_nonneg _)
  refine ⟨L, by dsimp [L]; positivity, ?_⟩
  intro c q hq hc i
  have hc' : ∀ v i, |c v i| ≤ M' := fun v i => (hc v i).trans (le_max_left _ _)
  have hu := threePlaceMinimumValue_exp_upper A c hA hM hq hc'
  have hp := threePlaceMinimumValue_product_exp_lower A c hA (le_trans (by norm_num) hq) hc'
  have hl := finite_minima_exp_lower (threePlaceMinimumValue A c q hA) hC hU hq
    (fun i => (rationalBoxMinimumValue_pos A _ _ hA _ _ i).le) hu hp i
  constructor
  · apply le_trans _ hl
    apply Real.exp_le_exp.mpr
    have hq0 : 0 ≤ q := le_trans (by norm_num) hq
    have hh := mul_nonneg hU hq0
    dsimp [L]
    nlinarith
  · apply (hu i).trans
    apply Real.exp_le_exp.mpr
    apply mul_le_mul_of_nonneg_right _ (le_trans (by norm_num) hq)
    dsimp [L]
    linarith [abs_nonneg (Real.log C)]


end
end Bounty

end SubmissionComponent_ThreePlaceMinimaBounds

/- Component CompoundMatrixAlgebra; SHA256 c1ff7533b9aa2449de13aa80682fbb7ff19db56e8ce111b2b67d1795324c687c -/
section SubmissionComponent_CompoundMatrixAlgebra
/- The actual compound matrix in the increasing-subset exterior-power basis.
Its entries are the usual minors, and its composition and column action are
deduced from the exterior-power functor. -/

namespace Bounty
noncomputable section
open scoped BigOperators

abbrev CompoundIndex (d ell : ℕ) := Set.powersetCard (Fin d) ell

def compoundIndexEmbedding {d ell : ℕ} (s : CompoundIndex d ell) : Fin ell ↪o Fin d :=
  Set.powersetCard.ofFinEmbEquiv.symm s

def compoundIndex_card (d ell : ℕ) : Fintype.card (CompoundIndex d ell) = d.choose ell := by
  rw [Fintype.card_eq_nat_card, Set.powersetCard.card, Nat.card_fin]

def compoundExteriorBasis (R : Type*) [CommRing R] (d ell : ℕ) :
    Module.Basis (CompoundIndex d ell) R (⋀[R]^ell (Fin d → R)) :=
  (Pi.basisFun R (Fin d)).exteriorPower ell

def compoundMatrix {R : Type*} [CommRing R] {d : ℕ} (ell : ℕ)
    (M : Matrix (Fin d) (Fin d) R) : Matrix (CompoundIndex d ell) (CompoundIndex d ell) R := by
  classical
  exact LinearMap.toMatrix (compoundExteriorBasis R d ell) (compoundExteriorBasis R d ell)
    (exteriorPower.map ell (Matrix.toLin' M))

def compoundWedgeCoordinates {R : Type*} [CommRing R] {d ell : ℕ}
    (v : Fin ell → Fin d → R) : CompoundIndex d ell → R :=
  (compoundExteriorBasis R d ell).repr (exteriorPower.ιMulti R ell v)

def compoundWedgeCoordinates_apply {R : Type*} [CommRing R] {d ell : ℕ}
    (v : Fin ell → Fin d → R) (s : CompoundIndex d ell) :
    compoundWedgeCoordinates v s =
      (Matrix.of (fun i j : Fin ell => v j (compoundIndexEmbedding s i))).det := by
  rw [compoundWedgeCoordinates, compoundExteriorBasis, exteriorPower.basis_repr_apply,
    exteriorPower.ιMultiDual_apply_ιMulti]
  simp only [Module.Basis.coord_apply, Pi.basisFun_repr]
  have heq : (Matrix.of (fun i j : Fin ell => v i (Set.powersetCard.ofFinEmbEquiv.symm s j))) =
      (Matrix.of (fun i j : Fin ell => v j (compoundIndexEmbedding s i))).transpose := by
    ext i j
    rfl
  exact (congrArg Matrix.det heq).trans (Matrix.det_transpose _)

/-- The entry indexed by row subset `s` and column subset `t` is their minor,
with both subsets enumerated increasingly. -/
def compoundMatrix_apply {R : Type*} [CommRing R] {d : ℕ} (ell : ℕ)
    (M : Matrix (Fin d) (Fin d) R) (s t : CompoundIndex d ell) :
    compoundMatrix ell M s t =
      (M.submatrix (compoundIndexEmbedding s) (compoundIndexEmbedding t)).det := by
  classical
  rw [compoundMatrix, LinearMap.toMatrix_apply]
  simp only [compoundExteriorBasis, exteriorPower.basis_apply, exteriorPower.ιMulti_family,
    exteriorPower.map_apply_ιMulti]
  change compoundWedgeCoordinates
    (fun j => Matrix.toLin' M (Pi.basisFun R (Fin d) (compoundIndexEmbedding t j))) s = _
  rw [compoundWedgeCoordinates_apply]
  congr 1
  ext i j
  simp only [Matrix.of_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
    Matrix.mulVec_single_one, Matrix.col_apply, Matrix.submatrix_apply]

def compoundMatrix_mul {R : Type*} [CommRing R] {d : ℕ} (ell : ℕ)
    (M N : Matrix (Fin d) (Fin d) R) :
    compoundMatrix ell (M * N) = compoundMatrix ell M * compoundMatrix ell N := by
  classical
  simp only [compoundMatrix, Matrix.toLin'_mul, exteriorPower.map_comp]
  exact LinearMap.toMatrix_comp (compoundExteriorBasis R d ell)
    (compoundExteriorBasis R d ell) (compoundExteriorBasis R d ell) _ _

def compoundMatrix_column {R : Type*} [CommRing R] {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) R) (t : CompoundIndex d ell) :
    compoundWedgeCoordinates (fun j i => M i (compoundIndexEmbedding t j)) =
      fun s => compoundMatrix ell M s t := by
  funext s
  rw [compoundWedgeCoordinates_apply, compoundMatrix_apply]
  rfl

def compoundMatrix_map {R S : Type*} [CommRing R] [CommRing S] {d : ℕ}
    (f : R →+* S) (ell : ℕ) (M : Matrix (Fin d) (Fin d) R) :
    compoundMatrix ell (f.mapMatrix M) = f.mapMatrix (compoundMatrix ell M) := by
  ext s t
  change compoundMatrix ell (f.mapMatrix M) s t = f (compoundMatrix ell M s t)
  rw [compoundMatrix_apply, compoundMatrix_apply, RingHom.map_det]
  rfl

def compoundMatrix_one {R : Type*} [CommRing R] (d ell : ℕ) :
    compoundMatrix ell (1 : Matrix (Fin d) (Fin d) R) = 1 := by
  classical
  simp only [compoundMatrix, Matrix.toLin'_one, exteriorPower.map_id, LinearMap.toMatrix_id]

/-- The compound acts on actual minors of any tuple of columns. -/
def compoundMatrix_wedge_action {R : Type*} [CommRing R] {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) R) (v : Fin ell → Fin d → R) :
    (compoundMatrix ell M).mulVec (compoundWedgeCoordinates v) =
      compoundWedgeCoordinates (fun j => M.mulVec (v j)) := by
  classical
  have hh := LinearMap.toMatrix_mulVec_repr (compoundExteriorBasis R d ell)
    (compoundExteriorBasis R d ell) (exteriorPower.map ell (Matrix.toLin' M))
    (exteriorPower.ιMulti R ell v)
  simpa only [compoundMatrix, compoundWedgeCoordinates, exteriorPower.map_apply_ιMulti,
    Function.comp_def, Matrix.toLin'_apply] using hh

def compoundMatrix_mul_inverse {K : Type*} [Field K] {d : ℕ} (ell : ℕ)
    (M : Matrix (Fin d) (Fin d) K) (hM : M.det ≠ 0) :
    compoundMatrix ell M * compoundMatrix ell M⁻¹ = 1 := by
  rw [← compoundMatrix_mul, Matrix.mul_nonsing_inv _ (isUnit_iff_ne_zero.mpr hM), compoundMatrix_one]

def compoundMatrix_det_ne_zero {K : Type*} [Field K] {d : ℕ} (ell : ℕ)
    (M : Matrix (Fin d) (Fin d) K) (hM : M.det ≠ 0) :
    (compoundMatrix ell M).det ≠ 0 := by
  classical
  intro hz
  have hh := congrArg Matrix.det (compoundMatrix_mul_inverse ell M hM)
  rw [Matrix.det_mul, hz, zero_mul, Matrix.det_one] at hh
  exact zero_ne_one hh

end
end Bounty

end SubmissionComponent_CompoundMatrixAlgebra

/- Component CofactorNormal; SHA256 ce1cff96605c23a71d159136c0ea6c08db3c24c59ca15439f37689026f9ff05c -/
section SubmissionComponent_CofactorNormal
/- Signed maximal minors of a rectangular matrix with one more row than
column. The transformation formula is proved by applying the adjugate
product identity to a zero-column completion. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def cofactorCompletion {R : Type*} [Zero R] {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) R) : Matrix (Fin (n + 1)) (Fin (n + 1)) R :=
  fun i j => Fin.cases 0 (X i) j

def cofactorNormal {R : Type*} [CommRing R] {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) R) : Fin (n + 1) → R :=
  fun i => (-1) ^ i.val * (X.submatrix i.succAbove id).det

def cofactorNormal_eq_adjugate {R : Type*} [CommRing R] {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) R) (i : Fin (n + 1)) :
    cofactorNormal X i = (cofactorCompletion X).adjugate 0 i := by
  rw [Matrix.adjugate_fin_succ_eq_det_submatrix]
  simp [cofactorNormal, cofactorCompletion, Matrix.submatrix]

def cofactorCompletion_mul {R : Type*} [CommRing R] {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) R)
    (X : Matrix (Fin (n + 1)) (Fin n) R) :
    cofactorCompletion (A * X) = A * cofactorCompletion X := by
  ext i j
  refine Fin.cases ?_ (fun k => ?_) j
  · simp [cofactorCompletion, Matrix.mul_apply]
  · simp [cofactorCompletion, Matrix.mul_apply]

def cofactorNormal_mul {R : Type*} [CommRing R] {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) R)
    (X : Matrix (Fin (n + 1)) (Fin n) R) :
    cofactorNormal (A * X) = A.adjugate.transpose.mulVec (cofactorNormal X) := by
  ext i
  simp_rw [cofactorNormal_eq_adjugate]
  rw [cofactorCompletion_mul, Matrix.adjugate_mul_distrib]
  simp only [Matrix.mul_apply, Matrix.mulVec, dotProduct, Matrix.transpose_apply]
  exact Finset.sum_congr rfl fun j _ => by rw [cofactorNormal_eq_adjugate]; ring

def cofactorNormal_dot_column {R : Type*} [CommRing R] {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) R) (j : Fin n) :
    dotProduct (cofactorNormal X) (X.col j) = 0 := by
  have h := congrArg (fun M : Matrix (Fin (n + 1)) (Fin (n + 1)) R => M 0 j.succ)
    (Matrix.adjugate_mul (cofactorCompletion X))
  simpa [Matrix.mul_apply, cofactorNormal_eq_adjugate, dotProduct,
    cofactorCompletion, Matrix.col, Matrix.one_apply, Ne.symm (Fin.succ_ne_zero j)] using h

def cofactorNormal_map {R S : Type*} [CommRing R] [CommRing S] {n : ℕ}
    (f : R →+* S) (X : Matrix (Fin (n + 1)) (Fin n) R) :
    cofactorNormal (X.map f) = fun i => f (cofactorNormal X i) := by
  ext i
  simp only [cofactorNormal, map_mul, map_pow, map_neg, map_one]
  congr 1
  exact (f.map_det (X.submatrix i.succAbove id)).symm

def cofactorNormal_ne_zero {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℚ)
    (hX : LinearIndependent ℚ X.col) : cofactorNormal X ≠ 0 := by
  obtain ⟨v, hv⟩ := exists_linearIndependent_cons_of_lt_finrank hX
    (by simp : n < Module.finrank ℚ (Fin (n + 1) → ℚ))
  let B : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ :=
    fun i j => Fin.cases (v i) (X i) j
  have hcol : B.col = Fin.cons v X.col := by
    ext j i
    refine Fin.cases ?_ (fun k => ?_) j <;> rfl
  have hB : B.det ≠ 0 := Matrix.nonsingular_iff_det_ne_zero.mp
    (Matrix.Nonsingular.of_linearIndependent_col (by rw [hcol]; exact hv))
  intro hz
  apply hB
  rw [Matrix.det_succ_column_zero]
  apply Finset.sum_eq_zero
  intro i _
  have hi : cofactorNormal X i = 0 := congrFun hz i
  change (-1 : ℚ) ^ i.val * v i * (X.submatrix i.succAbove id).det = 0
  rw [mul_right_comm, ← cofactorNormal, hi, zero_mul]

end
end Bounty

end SubmissionComponent_CofactorNormal

/- Component LocalPolynomialEvaluation; SHA256 9ae647c462f81b6f00997fa074be0e49ee1312a9c0ece63d5671dbadc679bfbd -/
section SubmissionComponent_LocalPolynomialEvaluation
/- Local evaluation bounds with actual maximizing supported monomials.
Different places may choose different exponents. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rationalPadicNormMulHom (p : ℕ) [Fact p.Prime] : ℚ →* ℚ where
  toFun := padicNorm p
  map_one' := padicNorm.one
  map_mul' := padicNorm.mul

def padicNorm_finset_prod {I : Type*} (p : ℕ) [Fact p.Prime]
    (s : Finset I) (f : I → ℚ) :
    padicNorm p (∏ i ∈ s, f i) = ∏ i ∈ s, padicNorm p (f i) :=
  map_prod (rationalPadicNormMulHom p) f s

def padicNorm_nat_pow (p : ℕ) [Fact p.Prime] (x : ℚ) (n : ℕ) :
    padicNorm p (x ^ n) = (padicNorm p x) ^ n :=
  map_pow (rationalPadicNormMulHom p) x n

def rational_polynomial_eval_norm_le {I : Type*} [Fintype I]
    (P : MvPolynomial I ℚ) (x : I → ℚ) (M : ℝ)
    (hM : ∀ e ∈ P.support, ∏ i, ‖x i‖ ^ e i ≤ M) :
    ‖MvPolynomial.eval x P‖ ≤ polynomialCoeffL1 P * M := by
  classical
  rw [MvPolynomial.eval_eq']
  calc
    _ ≤ ∑ e ∈ P.support, ‖MvPolynomial.coeff e P * ∏ i, x i ^ e i‖ := norm_sum_le _ _
    _ = ∑ e ∈ P.support, ‖MvPolynomial.coeff e P‖ * ∏ i, ‖x i‖ ^ e i := by
      simp only [norm_mul, norm_prod, norm_pow]
    _ ≤ ∑ e ∈ P.support, ‖MvPolynomial.coeff e P‖ * M :=
      Finset.sum_le_sum fun e he => mul_le_mul_of_nonneg_left (hM e he) (norm_nonneg _)
    _ = _ := by rw [← Finset.sum_mul]; rfl

def rational_polynomial_eval_norm_le_some_monomial {I : Type*} [Fintype I]
    (P : MvPolynomial I ℚ) (hP : P ≠ 0) (x : I → ℚ) :
    ∃ e ∈ P.support,
      ‖MvPolynomial.eval x P‖ ≤ polynomialCoeffL1 P * ∏ i, ‖x i‖ ^ e i := by
  classical
  obtain ⟨e, he, hmax⟩ := Finset.exists_max_image P.support
    (fun e => ∏ i, ‖x i‖ ^ e i) (MvPolynomial.support_nonempty.mpr hP)
  exact ⟨e, he, rational_polynomial_eval_norm_le P x _ hmax⟩

def integer_polynomial_eval₂_padicNorm_le {I : Type*} [Fintype I]
    (p : ℕ) [Fact p.Prime] (P : MvPolynomial I ℤ) (x : I → ℚ) (M : ℚ) (hM : 0 ≤ M)
    (hterms : ∀ e ∈ P.support, ∏ i, (padicNorm p (x i)) ^ e i ≤ M) :
    padicNorm p (MvPolynomial.eval₂ (Int.castRingHom ℚ) x P) ≤ M := by
  rw [MvPolynomial.eval₂_eq']
  apply padicNorm.sum_le' _ hM
  intro e he
  rw [padicNorm.mul, padicNorm_finset_prod]
  simp_rw [padicNorm_nat_pow]
  calc
    _ ≤ 1 * (∏ i, (padicNorm p (x i)) ^ e i) :=
      mul_le_mul_of_nonneg_right (padicNorm.of_int (MvPolynomial.coeff e P))
        (Finset.prod_nonneg fun i _ => pow_nonneg (padicNorm.nonneg _) _)
    _ ≤ M := by simpa only [one_mul] using hterms e he

def integer_polynomial_eval₂_padicNorm_le_some_monomial {I : Type*} [Fintype I]
    (p : ℕ) [Fact p.Prime] (P : MvPolynomial I ℤ) (hP : P ≠ 0) (x : I → ℚ) :
    ∃ e ∈ P.support, padicNorm p (MvPolynomial.eval₂ (Int.castRingHom ℚ) x P) ≤
      ∏ i, (padicNorm p (x i)) ^ e i := by
  classical
  obtain ⟨e, he, hmax⟩ := Finset.exists_max_image P.support
    (fun e => ∏ i, (padicNorm p (x i)) ^ e i) (MvPolynomial.support_nonempty.mpr hP)
  exact ⟨e, he, integer_polynomial_eval₂_padicNorm_le p P x _
    (Finset.prod_nonneg fun i _ => pow_nonneg (padicNorm.nonneg _) _) hmax⟩


end
end Bounty

end SubmissionComponent_LocalPolynomialEvaluation

/- Component LocalDeterminantBounds; SHA256 2440a31b92033387b9f771d99f97f99fb1c2550374aac214f8bdae770bd3f5cf -/
section SubmissionComponent_LocalDeterminantBounds
/- Rowwise determinant bounds at the real and finite places, including the
omitted-row exponent for the actual signed cofactor normal. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def rational_det_norm_le_row_bounds {n : ℕ}
    (A : Matrix (Fin n) (Fin n) ℚ) (b : Fin n → ℝ)
    (hb : ∀ i, 0 ≤ b i) (hA : ∀ i j, ‖A i j‖ ≤ b i) :
    ‖A.det‖ ≤ (n.factorial : ℝ) * ∏ i, b i := by
  classical
  rw [Matrix.det_apply']
  calc
    _ ≤ ∑ σ : Equiv.Perm (Fin n), ‖((Equiv.Perm.sign σ : ℤ) : ℚ) * ∏ i, A (σ i) i‖ :=
      norm_sum_le _ _
    _ ≤ ∑ _σ : Equiv.Perm (Fin n), ∏ i, b i := by
      apply Finset.sum_le_sum
      intro σ _
      have hs : ‖((Equiv.Perm.sign σ : ℤ) : ℚ)‖ = 1 := by
        rcases Int.units_eq_one_or (Equiv.Perm.sign σ) with h | h <;> simp [h]
      rw [norm_mul, hs, one_mul, norm_prod, ← Equiv.prod_comp σ b]
      exact Finset.prod_le_prod (fun _ _ => norm_nonneg _) (fun i _ => hA (σ i) i)
    _ = _ := by simp [Fintype.card_perm]

def padicNorm_sum_cast_le {I : Type*} (p : ℕ) [Fact p.Prime]
    (s : Finset I) (f : I → ℚ) (B : ℝ) (hB : 0 ≤ B)
    (hf : ∀ i ∈ s, (padicNorm p (f i) : ℝ) ≤ B) :
    (padicNorm p (∑ i ∈ s, f i) : ℝ) ≤ B := by
  classical
  induction s using Finset.induction_on with
  | empty => simpa using hB
  | @insert a s ha ih =>
      rw [Finset.sum_insert ha]
      have hu : (padicNorm p (f a + ∑ i ∈ s, f i) : ℝ) ≤
          max (padicNorm p (f a) : ℝ) (padicNorm p (∑ i ∈ s, f i) : ℝ) := by
        exact_mod_cast (padicNorm.nonarchimedean (p := p) (q := f a) (r := ∑ i ∈ s, f i))
      exact hu.trans (max_le (hf a (Finset.mem_insert_self _ _))
        (ih (fun i hi => hf i (Finset.mem_insert_of_mem hi))))

def rational_det_padicNorm_le_row_bounds {n : ℕ}
    (p : ℕ) [Fact p.Prime] (A : Matrix (Fin n) (Fin n) ℚ) (b : Fin n → ℝ)
    (hb : ∀ i, 0 ≤ b i) (hA : ∀ i j, (padicNorm p (A i j) : ℝ) ≤ b i) :
    (padicNorm p A.det : ℝ) ≤ ∏ i, b i := by
  classical
  rw [Matrix.det_apply']
  apply padicNorm_sum_cast_le _ _ _ _ (Finset.prod_nonneg (fun i _ => hb i))
  intro σ _
  have hs : padicNorm p (((Equiv.Perm.sign σ : ℤ) : ℚ)) = 1 := by
    rcases Int.units_eq_one_or (Equiv.Perm.sign σ) with h | h <;> simp [h]
  rw [padicNorm.mul, hs, one_mul, padicNorm_finset_prod, Rat.cast_prod,
    ← Equiv.prod_comp σ b]
  exact Finset.prod_le_prod (fun i _ => by exact_mod_cast padicNorm.nonneg (A (σ i) i))
    (fun i _ => hA (σ i) i)

def cofactorNormal_norm_le {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℚ) (b : Fin (n + 1) → ℝ)
    (hb : ∀ i, 0 ≤ b i) (hX : ∀ i j, ‖X i j‖ ≤ b i) (i : Fin (n + 1)) :
    ‖cofactorNormal X i‖ ≤ (n.factorial : ℝ) * ∏ j : Fin n, b (i.succAbove j) := by
  simpa [cofactorNormal, norm_mul, norm_pow] using
    rational_det_norm_le_row_bounds (X.submatrix i.succAbove id)
      (fun j => b (i.succAbove j)) (fun j => hb _) (fun j k => hX _ _)

def cofactorNormal_padicNorm_le {n : ℕ}
    (p : ℕ) [Fact p.Prime] (X : Matrix (Fin (n + 1)) (Fin n) ℚ)
    (b : Fin (n + 1) → ℝ) (hb : ∀ i, 0 ≤ b i)
    (hX : ∀ i j, (padicNorm p (X i j) : ℝ) ≤ b i) (i : Fin (n + 1)) :
    (padicNorm p (cofactorNormal X i) : ℝ) ≤ ∏ j : Fin n, b (i.succAbove j) := by
  simpa [cofactorNormal, padicNorm_nat_pow] using
    rational_det_padicNorm_le_row_bounds p (X.submatrix i.succAbove id)
      (fun j => b (i.succAbove j)) (fun j => hb _) (fun j k => hX _ _)

def prod_exp_omit_coordinate {n : ℕ} (c : Fin (n + 1) → ℝ)
    (t : ℝ) (i : Fin (n + 1)) :
    (∏ j : Fin n, Real.exp (c (i.succAbove j) * t)) =
      Real.exp (((∑ j, c j) - c i) * t) := by
  rw [← Real.exp_sum, ← Finset.sum_mul]
  congr 2
  have h := Fin.sum_univ_succAbove c i
  linarith

def cofactorNormal_norm_le_exp {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℚ) (c : Fin (n + 1) → ℝ) (t : ℝ)
    (hX : ∀ i j, ‖X i j‖ ≤ Real.exp (c i * t)) (i : Fin (n + 1)) :
    ‖cofactorNormal X i‖ ≤ (n.factorial : ℝ) *
      Real.exp (((∑ j, c j) - c i) * t) := by
  simpa only [prod_exp_omit_coordinate] using
    cofactorNormal_norm_le X (fun i => Real.exp (c i * t))
      (fun i => (Real.exp_pos _).le) hX i

def cofactorNormal_padicNorm_le_exp {n : ℕ}
    (p : ℕ) [Fact p.Prime] (X : Matrix (Fin (n + 1)) (Fin n) ℚ)
    (c : Fin (n + 1) → ℝ) (t : ℝ)
    (hX : ∀ i j, (padicNorm p (X i j) : ℝ) ≤ Real.exp (c i * t)) (i : Fin (n + 1)) :
    (padicNorm p (cofactorNormal X i) : ℝ) ≤ Real.exp (((∑ j, c j) - c i) * t) := by
  simpa only [prod_exp_omit_coordinate] using
    cofactorNormal_padicNorm_le p X (fun i => Real.exp (c i * t))
      (fun i => (Real.exp_pos _).le) hX i


end
end Bounty

end SubmissionComponent_LocalDeterminantBounds

/- Component CompoundMatrixBounds; SHA256 6ba8c99fef16eddca4dbfa1712aa33ff10cfbaf2034e963d39443261a4c3e879 -/
section SubmissionComponent_CompoundMatrixBounds
/- Actual archimedean and finite-place bounds for compound entries. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def product_min_le_min_product {I : Type*} [Fintype I]
    (a b : I → ℝ) (ha : ∀ i, 0 ≤ a i) (hb : ∀ i, 0 ≤ b i) :
    (∏ i, min (a i) (b i)) ≤ min (∏ i, a i) (∏ i, b i) := by
  apply le_min
  · exact Finset.prod_le_prod (fun i _ => le_min (ha i) (hb i))
      (fun i _ => min_le_left _ _)
  · exact Finset.prod_le_prod (fun i _ => le_min (ha i) (hb i))
      (fun i _ => min_le_right _ _)

def rational_det_norm_le_permutation_bound {n : ℕ}
    (A : Matrix (Fin n) (Fin n) ℚ) (B : ℝ)
    (hA : ∀ σ : Equiv.Perm (Fin n), (∏ i, ‖A (σ i) i‖) ≤ B) :
    ‖A.det‖ ≤ (n.factorial : ℝ) * B := by
  classical
  rw [Matrix.det_apply']
  calc
    _ ≤ ∑ σ : Equiv.Perm (Fin n), ‖((Equiv.Perm.sign σ : ℤ) : ℚ) * ∏ i, A (σ i) i‖ :=
      norm_sum_le _ _
    _ ≤ ∑ _σ : Equiv.Perm (Fin n), B := by
      apply Finset.sum_le_sum
      intro σ _
      have hs : ‖((Equiv.Perm.sign σ : ℤ) : ℚ)‖ = 1 := by
        rcases Int.units_eq_one_or (Equiv.Perm.sign σ) with h | h <;> simp [h]
      simpa only [norm_mul, hs, one_mul, norm_prod] using hA σ
    _ = _ := by simp [Fintype.card_perm]

def rational_det_norm_le_row_column_min {n : ℕ}
    (A : Matrix (Fin n) (Fin n) ℚ) (K : ℝ) (b r c : Fin n → ℝ)
    (hK : 0 ≤ K) (hb : ∀ i, 0 ≤ b i) (hr : ∀ i, 0 ≤ r i) (hc : ∀ i, 0 ≤ c i)
    (hA : ∀ i j, ‖A i j‖ ≤ K * b i * min (r i) (c j)) :
    ‖A.det‖ ≤ (n.factorial : ℝ) * K ^ n * (∏ i, b i) *
      min (∏ i, r i) (∏ i, c i) := by
  have hh := rational_det_norm_le_permutation_bound A
    (K ^ n * (∏ i, b i) * min (∏ i, r i) (∏ i, c i)) (by
      intro σ
      calc
        _ ≤ ∏ i, K * b (σ i) * min (r (σ i)) (c i) :=
          Finset.prod_le_prod (fun i _ => norm_nonneg _) (fun i _ => hA (σ i) i)
        _ = K ^ n * (∏ i, b i) * (∏ i, min (r (σ i)) (c i)) := by
          rw [Finset.prod_mul_distrib, Finset.prod_mul_distrib, Finset.prod_const]
          simp only [Finset.card_univ, Fintype.card_fin, Equiv.prod_comp]
        _ ≤ _ := by
          apply mul_le_mul_of_nonneg_left _
            (mul_nonneg (pow_nonneg hK _) (Finset.prod_nonneg (fun i _ => hb i)))
          simpa only [Equiv.prod_comp] using
            product_min_le_min_product (fun i => r (σ i)) c (fun i => hr _) hc)
  simpa only [mul_assoc] using hh

def compoundCoordinateProduct {d ell : ℕ} (b : Fin d → ℝ)
    (s : CompoundIndex d ell) : ℝ := ∏ i : Fin ell, b (compoundIndexEmbedding s i)

def compoundCoordinateProduct_nonneg {d ell : ℕ} (b : Fin d → ℝ)
    (hb : ∀ i, 0 ≤ b i) (s : CompoundIndex d ell) :
    0 ≤ compoundCoordinateProduct b s := Finset.prod_nonneg (fun _ _ => hb _)

def compoundCoordinateProduct_pos {d ell : ℕ} (b : Fin d → ℝ)
    (hb : ∀ i, 0 < b i) (s : CompoundIndex d ell) :
    0 < compoundCoordinateProduct b s := Finset.prod_pos (fun _ _ => hb _)

def compoundMatrix_norm_le_min {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) ℚ) (K : ℝ) (b r c : Fin d → ℝ)
    (hK : 0 ≤ K) (hb : ∀ i, 0 ≤ b i) (hr : ∀ i, 0 ≤ r i) (hc : ∀ i, 0 ≤ c i)
    (hM : ∀ i j, ‖M i j‖ ≤ K * b i * min (r i) (c j))
    (s t : CompoundIndex d ell) :
    ‖compoundMatrix ell M s t‖ ≤
      (ell.factorial : ℝ) * K ^ ell * compoundCoordinateProduct b s *
        min (compoundCoordinateProduct r s) (compoundCoordinateProduct c t) := by
  rw [compoundMatrix_apply]
  exact rational_det_norm_le_row_column_min _ K
    (fun i => b (compoundIndexEmbedding s i)) (fun i => r (compoundIndexEmbedding s i))
    (fun j => c (compoundIndexEmbedding t j)) hK (fun _ => hb _) (fun _ => hr _)
    (fun _ => hc _) (fun _ _ => hM _ _)

def compoundMatrix_padicNorm_le {d ell : ℕ}
    (p : ℕ) [Fact p.Prime] (M : Matrix (Fin d) (Fin d) ℚ)
    (b : Fin d → ℝ) (hb : ∀ i, 0 ≤ b i)
    (hM : ∀ i j, (padicNorm p (M i j) : ℝ) ≤ b i)
    (s t : CompoundIndex d ell) :
    (padicNorm p (compoundMatrix ell M s t) : ℝ) ≤ compoundCoordinateProduct b s := by
  rw [compoundMatrix_apply]
  exact rational_det_padicNorm_le_row_bounds p _
    (fun i => b (compoundIndexEmbedding s i)) (fun _ => hb _) (fun _ _ => hM _ _)

def compoundMatrix_davenport_bound {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) ℚ) (p : Equiv.Perm (Fin d))
    (K : ℝ) (b lam : Fin d → ℝ) (hK : 0 ≤ K)
    (hb : ∀ i, 0 ≤ b i) (hlam : ∀ i, 0 ≤ lam i)
    (hM : ∀ i j, ‖M (p i) j‖ ≤ K * b (p i) * min (lam i) (lam j))
    (s t : CompoundIndex d ell) :
    ‖compoundMatrix ell M s t‖ ≤
      (ell.factorial : ℝ) * K ^ ell * compoundCoordinateProduct b s *
        min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundCoordinateProduct lam t) := by
  apply compoundMatrix_norm_le_min M K b (lam ∘ p.symm) lam hK hb (fun _ => hlam _) hlam
  intro i j
  simpa only [p.apply_symm_apply, Function.comp_apply] using hM (p.symm i) j

end
end Bounty

end SubmissionComponent_CompoundMatrixBounds

/- Component FiniteExponentProfiles; SHA256 4809703dd70bbb7a13f0da999b455eeecf4e348962d738cdc9c0824e623a11fd -/
section SubmissionComponent_FiniteExponentProfiles
/- A finite partition by coordinatewise upper mesh rounding, preserving
nonpositive coordinates and half of a negative total exponent margin. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def exponentProfileMesh (I : Type*) [Fintype I] (ρ : ℝ) : ℝ :=
  ρ / (2 * Fintype.card I)

def upperMeshProfile {I : Type*} (δ : ℝ) (a : I → ℝ) (i : I) : ℝ :=
  δ * (Int.ceil (a i / δ) : ℝ)

def exponentProfileMesh_pos (I : Type*) [Fintype I] [Nonempty I]
    (ρ : ℝ) (hρ : 0 < ρ) : 0 < exponentProfileMesh I ρ := by
  unfold exponentProfileMesh
  exact div_pos hρ (mul_pos (by norm_num) (by exact_mod_cast Fintype.card_pos))

def upperMeshProfile_bounds {I : Type*} (δ : ℝ) (hδ : 0 < δ)
    (a : I → ℝ) (i : I) : a i ≤ upperMeshProfile δ a i ∧
      upperMeshProfile δ a i < a i + δ := by
  have heq : δ * (a i / δ) = a i := by field_simp
  constructor
  · have hh := mul_le_mul_of_nonneg_left (Int.le_ceil (a i / δ)) hδ.le
    simpa only [heq, upperMeshProfile] using hh
  · have hh := mul_lt_mul_of_pos_left (Int.ceil_lt_add_one (a i / δ)) hδ
    simpa only [mul_add, heq, mul_one, upperMeshProfile] using hh

def upperMeshProfile_nonpos {I : Type*} (δ : ℝ) (hδ : 0 < δ)
    (a : I → ℝ) (i : I) (ha : a i ≤ 0) : upperMeshProfile δ a i ≤ 0 := by
  have hh : Int.ceil (a i / δ) ≤ 0 :=
    Int.ceil_nonpos.mpr (div_nonpos_of_nonpos_of_nonneg ha hδ.le)
  exact mul_nonpos_of_nonneg_of_nonpos hδ.le (by exact_mod_cast hh)

def upperMeshProfile_abs_le {I : Type*} (δ : ℝ) (hδ : 0 < δ)
    (M : ℝ) (a : I → ℝ) (ha : ∀ i, |a i| ≤ M) (i : I) :
    |upperMeshProfile δ a i| ≤ M + δ := by
  obtain ⟨hlo, hhi⟩ := upperMeshProfile_bounds δ hδ a i
  obtain ⟨hal, har⟩ := abs_le.mp (ha i)
  exact abs_le.mpr ⟨by linarith, by linarith⟩

def upperMeshProfile_sum_le_half {I : Type*} [Fintype I] [Nonempty I]
    (ρ : ℝ) (hρ : 0 < ρ) (a : I → ℝ) (ha : ∑ i, a i ≤ -ρ) :
    ∑ i, upperMeshProfile (exponentProfileMesh I ρ) a i ≤ -ρ / 2 := by
  have hδ := exponentProfileMesh_pos I ρ hρ
  have hs : (∑ i, upperMeshProfile (exponentProfileMesh I ρ) a i) ≤
      ∑ i, (a i + exponentProfileMesh I ρ) :=
    Finset.sum_le_sum (fun i _ => (upperMeshProfile_bounds _ hδ a i).2.le)
  have hn : (Fintype.card I : ℝ) ≠ 0 := by exact_mod_cast Fintype.card_pos.ne'
  have hmass : (Fintype.card I : ℝ) * exponentProfileMesh I ρ = ρ / 2 := by
    unfold exponentProfileMesh
    field_simp
  simp only [Finset.sum_add_distrib, Finset.sum_const, Finset.card_univ,
    nsmul_eq_mul, hmass] at hs
  linarith

/-- The integer tuples in this explicit box enumerate all possible rounded
profiles for coordinates in `[-M,M]`. -/
def exponentProfileIntegerBox (I : Type*) [Fintype I] (M δ : ℝ) : Finset (I → ℤ) := by
  classical
  exact Fintype.piFinset (fun _ => Finset.Icc (Int.ceil (-M / δ)) (Int.ceil (M / δ)))

def exponentProfiles (I : Type*) [Fintype I] (M ρ : ℝ) : Finset (I → ℝ) := by
  classical
  let δ := exponentProfileMesh I ρ
  exact ((exponentProfileIntegerBox I M δ).image (fun v i => δ * (v i : ℝ))).filter
    (fun c => (∀ i, |c i| ≤ M + δ) ∧ ∑ i, c i ≤ -ρ / 2)

def exponentProfiles_properties {I : Type*} [Fintype I] (M ρ : ℝ)
    (c : I → ℝ) (hc : c ∈ exponentProfiles I M ρ) :
    (∀ i, |c i| ≤ M + ρ / (2 * Fintype.card I)) ∧ ∑ i, c i ≤ -ρ / 2 := by
  classical
  exact (Finset.mem_filter.mp hc).2

def upperMeshProfile_mem_exponentProfiles {I : Type*} [Fintype I] [Nonempty I]
    (M ρ : ℝ) (hρ : 0 < ρ) (a : I → ℝ)
    (hab : ∀ i, |a i| ≤ M) (has : ∑ i, a i ≤ -ρ) :
    upperMeshProfile (exponentProfileMesh I ρ) a ∈ exponentProfiles I M ρ := by
  classical
  have hδ := exponentProfileMesh_pos I ρ hρ
  apply Finset.mem_filter.mpr
  constructor
  · apply Finset.mem_image.mpr
    refine ⟨fun i => Int.ceil (a i / exponentProfileMesh I ρ), ?_, rfl⟩
    apply Fintype.mem_piFinset.mpr
    intro i
    obtain ⟨hlo, hhi⟩ := abs_le.mp (hab i)
    exact Finset.mem_Icc.mpr ⟨Int.ceil_mono (div_le_div_of_nonneg_right hlo hδ.le),
      Int.ceil_mono (div_le_div_of_nonneg_right hhi hδ.le)⟩
  · exact ⟨upperMeshProfile_abs_le _ hδ M a hab, upperMeshProfile_sum_le_half ρ hρ a has⟩

/-- Every bounded exponent tuple of total at most `-ρ` is dominated by one
member of an actual finite family.  All members have the stated size and
negative-sum bounds, and the selected member preserves every nonpositive
coordinate of the input. -/
def exists_finite_exponent_profiles (I : Type*) [Fintype I] [Nonempty I]
    (M ρ : ℝ) (hρ : 0 < ρ) :
    ∃ C : Finset (I → ℝ),
      (∀ c ∈ C, (∀ i, |c i| ≤ M + ρ / (2 * Fintype.card I)) ∧ ∑ i, c i ≤ -ρ / 2) ∧
      ∀ a : I → ℝ, (∀ i, |a i| ≤ M) → (∑ i, a i ≤ -ρ) →
        ∃ c ∈ C, (∀ i, a i ≤ c i) ∧ (∀ i, a i ≤ 0 → c i ≤ 0) := by
  refine ⟨exponentProfiles I M ρ, fun c hc => exponentProfiles_properties M ρ c hc, ?_⟩
  intro a hab has
  have hδ := exponentProfileMesh_pos I ρ hρ
  exact ⟨upperMeshProfile (exponentProfileMesh I ρ) a,
    upperMeshProfile_mem_exponentProfiles M ρ hρ a hab has,
    fun i => (upperMeshProfile_bounds _ hδ a i).1,
    fun i hi => upperMeshProfile_nonpos _ hδ a i hi⟩

/-- All members can be required to be nonpositive on a designated set of
coordinates, while still covering every input with those signs. -/
def exists_finite_exponent_profiles_nonpos_on (I : Type*) [Fintype I] [Nonempty I]
    (S : Set I) (M ρ : ℝ) (hρ : 0 < ρ) :
    ∃ C : Finset (I → ℝ),
      (∀ c ∈ C, (∀ i, |c i| ≤ M + ρ / (2 * Fintype.card I)) ∧
        (∑ i, c i ≤ -ρ / 2) ∧ (∀ i ∈ S, c i ≤ 0)) ∧
      ∀ a : I → ℝ, (∀ i, |a i| ≤ M) → (∑ i, a i ≤ -ρ) →
        (∀ i ∈ S, a i ≤ 0) → ∃ c ∈ C, (∀ i, a i ≤ c i) ∧
          (∀ i, a i ≤ 0 → c i ≤ 0) := by
  classical
  obtain ⟨C, hC, hcover⟩ := exists_finite_exponent_profiles I M ρ hρ
  refine ⟨C.filter (fun c => ∀ i ∈ S, c i ≤ 0), ?_, ?_⟩
  · intro c hc
    obtain ⟨hc, hs⟩ := Finset.mem_filter.mp hc
    exact ⟨(hC c hc).1, (hC c hc).2, hs⟩
  · intro a hab has haS
    obtain ⟨c, hc, hle, hsign⟩ := hcover a hab has
    exact ⟨c, Finset.mem_filter.mpr ⟨hc, fun i hi => hsign i (haS i hi)⟩, hle, hsign⟩

end
end Bounty

end SubmissionComponent_FiniteExponentProfiles

/- Component ProductExponentProfiles; SHA256 4d87cc5f3e8e374f359cd4d824443a00f3f23ba330b117abe283fec03860c85d -/
section SubmissionComponent_ProductExponentProfiles
/- A small product of positive local values is covered by finitely many fixed profiles. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def normalized_log_profile_bounds {I : Type*} [Fintype I]
    (f : I → ℝ) (q M ρ : ℝ) (hq : 0 < q)
    (hlo : ∀ i, Real.exp (-M * q) ≤ f i)
    (hhi : ∀ i, f i ≤ Real.exp (M * q))
    (hprod : ∏ i, f i ≤ Real.exp (-ρ * q)) :
    (∀ i, |Real.log (f i) / q| ≤ M) ∧
      (∑ i, Real.log (f i) / q) ≤ -ρ := by
  have hpos : ∀ i, 0 < f i := fun i => (Real.exp_pos _).trans_le (hlo i)
  constructor
  · intro i
    apply abs_le.mpr
    constructor
    · apply (le_div_iff₀ hq).mpr
      exact (Real.le_log_iff_exp_le (hpos i)).mpr (hlo i)
    · apply (div_le_iff₀ hq).mpr
      exact (Real.log_le_iff_le_exp (hpos i)).mpr (hhi i)
  · rw [← Finset.sum_div]
    apply (div_le_iff₀ hq).mpr
    rw [← Real.log_prod (fun i _ => (hpos i).ne')]
    exact (Real.log_le_iff_le_exp (Finset.prod_pos (fun i _ => hpos i))).mpr hprod

def exists_finite_product_profiles (I : Type*) [Fintype I] [Nonempty I]
    (S : Set I) (M ρ : ℝ) (hρ : 0 < ρ) :
    ∃ C : Finset (I → ℝ),
      (∀ c ∈ C, (∀ i, |c i| ≤ M + ρ / (2 * Fintype.card I)) ∧
        (∑ i, c i ≤ -ρ / 2) ∧ (∀ i ∈ S, c i ≤ 0)) ∧
      ∀ (q : ℝ) (f : I → ℝ), 0 < q →
        (∀ i, Real.exp (-M * q) ≤ f i) →
        (∀ i, f i ≤ Real.exp (M * q)) →
        (∏ i, f i ≤ Real.exp (-ρ * q)) →
        (∀ i ∈ S, f i ≤ 1) →
        ∃ c ∈ C, ∀ i, f i ≤ Real.exp (c i * q) := by
  obtain ⟨C, hC, hcover⟩ := exists_finite_exponent_profiles_nonpos_on I S M ρ hρ
  refine ⟨C, hC, ?_⟩
  intro q f hq hlo hhi hprod hsign
  have hpos : ∀ i, 0 < f i := fun i => (Real.exp_pos _).trans_le (hlo i)
  obtain ⟨hab, has⟩ := normalized_log_profile_bounds f q M ρ hq hlo hhi hprod
  obtain ⟨c, hc, hle, _⟩ := hcover (fun i => Real.log (f i) / q) hab has (by
    intro i hi
    apply div_nonpos_of_nonpos_of_nonneg _ hq.le
    exact Real.log_nonpos (hpos i).le (hsign i hi))
  refine ⟨c, hc, fun i => ?_⟩
  apply (Real.log_le_iff_le_exp (hpos i)).mp
  exact (div_le_iff₀ hq).mp (hle i)

def exists_finite_three_place_product_profiles (d : ℕ) (hd : 0 < d)
    (M ρ : ℝ) (hρ : 0 < ρ) :
    ∃ C : Finset (Fin 3 → Fin d → ℝ),
      (∀ c ∈ C, (∀ v i, |c v i| ≤ M + ρ / (6 * d)) ∧
        (∑ v, ∑ i, c v i) ≤ -ρ / 2 ∧ (∀ v i, v ≠ 0 → c v i ≤ 0)) ∧
      ∀ (q : ℝ) (f : Fin 3 → Fin d → ℝ), 0 < q →
        (∀ v i, Real.exp (-M * q) ≤ f v i) →
        (∀ v i, f v i ≤ Real.exp (M * q)) →
        (∏ v, ∏ i, f v i) ≤ Real.exp (-ρ * q) →
        (∀ v i, v ≠ 0 → f v i ≤ 1) →
        ∃ c ∈ C, ∀ v i, f v i ≤ Real.exp (c v i * q) := by
  classical
  let : NeZero d := ⟨hd.ne'⟩
  obtain ⟨C, hC, hcover⟩ := exists_finite_product_profiles (Fin 3 × Fin d)
    {i | i.1 ≠ 0} M ρ hρ
  refine ⟨C.image Function.curry, ?_, ?_⟩
  · intro c hc
    obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hc
    obtain ⟨hab, has, hsign⟩ := hC a ha
    refine ⟨?_, ?_, ?_⟩
    · intro v i
      convert hab (v, i) using 1 <;> simp [Function.curry, Fintype.card_prod, Nat.cast_mul]
      ring
    · simpa only [Fintype.sum_prod_type, Function.curry] using has
    · intro v i hv
      exact hsign (v, i) hv
  · intro q f hq hlo hhi hprod hsign
    obtain ⟨c, hc, hbound⟩ := hcover q (Function.uncurry f) hq
      (fun i => hlo i.1 i.2) (fun i => hhi i.1 i.2)
      (by simpa only [Fintype.prod_prod_type, Function.uncurry] using hprod)
      (fun i hi => hsign i.1 i.2 hi)
    exact ⟨Function.curry c, Finset.mem_image.mpr ⟨c, hc, rfl⟩, fun v i => hbound (v, i)⟩

end
end Bounty

end SubmissionComponent_ProductExponentProfiles

/- Component CompoundBoxProfiles; SHA256 b3037859c962e75c896700972a36e8b9d055f44f351dd59197ed8eeb61855545 -/
section SubmissionComponent_CompoundBoxProfiles
/- Actual clipped compound boxes and their logarithmic three-place profiles. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def compoundLocalWidths {d ell : ℕ} (K : ℝ) (b : Fin 3 → Fin d → ℝ)
    (lam : Fin d → ℝ) (p : Equiv.Perm (Fin d)) (tau : ℝ) :
    Fin 3 → CompoundIndex d ell → ℝ :=
  ![fun s => (ell.factorial : ℝ) * K ^ ell * compoundCoordinateProduct (b 0) s *
      min (compoundCoordinateProduct (lam ∘ p.symm) s) tau,
    compoundCoordinateProduct (b 1), compoundCoordinateProduct (b 2)]

def compoundLogProfile {d ell : ℕ} (K : ℝ) (b : Fin 3 → Fin d → ℝ)
    (lam : Fin d → ℝ) (p : Equiv.Perm (Fin d)) (tau q : ℝ) :
    Fin 3 → CompoundIndex d ell → ℝ :=
  fun v s => Real.log (compoundLocalWidths K b lam p tau v s) / q

def compoundLocalWidths_pos {d ell : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (tau : ℝ) (hK : 0 < K)
    (hb : ∀ v i, 0 < b v i) (hlam : ∀ i, 0 < lam i) (htau : 0 < tau)
    (v : Fin 3) (s : CompoundIndex d ell) :
    0 < compoundLocalWidths K b lam p tau v s := by
  fin_cases v
  · change 0 < (ell.factorial : ℝ) * K ^ ell * compoundCoordinateProduct (b 0) s *
      min (compoundCoordinateProduct (lam ∘ p.symm) s) tau
    exact mul_pos (mul_pos (mul_pos (by exact_mod_cast Nat.factorial_pos ell)
      (pow_pos hK _)) (compoundCoordinateProduct_pos _ (hb 0) s))
      (lt_min (compoundCoordinateProduct_pos _ (fun i => hlam _) s) htau)
  · exact compoundCoordinateProduct_pos _ (hb 1) s
  · exact compoundCoordinateProduct_pos _ (hb 2) s

def exp_compoundLogProfile {d ell : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (tau q : ℝ) (hK : 0 < K)
    (hb : ∀ v i, 0 < b v i) (hlam : ∀ i, 0 < lam i)
    (htau : 0 < tau) (hq : q ≠ 0) (v : Fin 3) (s : CompoundIndex d ell) :
    Real.exp (compoundLogProfile K b lam p tau q v s * q) =
      compoundLocalWidths K b lam p tau v s := by
  rw [compoundLogProfile, div_mul_cancel₀ _ hq, Real.exp_log
    (compoundLocalWidths_pos K b lam p tau hK hb hlam htau v s)]

def compoundMatrix_clipped_local_bounds {d ell : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (H : Matrix (Fin d) (Fin d) ℤ)
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (tau : ℝ) (hK : 0 ≤ K)
    (hb : ∀ v i, 0 ≤ b v i) (hlam : ∀ i, 0 ≤ lam i)
    (hInf : ∀ i j, ‖(A * H.map (Int.castRingHom ℚ)) (p i) j‖ ≤
      K * b 0 (p i) * min (lam i) (lam j))
    (hTwo : ∀ i j, (padicNorm 2 (H i j : ℚ) : ℝ) ≤ b 1 i)
    (hThree : ∀ i j, (padicNorm 3 (H i j : ℚ) : ℝ) ≤ b 2 i)
    (t : CompoundIndex d ell) (ht : compoundCoordinateProduct lam t ≤ tau) :
    (∀ s, ‖(compoundMatrix ell A * (compoundMatrix ell H).map (Int.castRingHom ℚ)) s t‖ ≤
      compoundLocalWidths K b lam p tau 0 s) ∧
    (∀ s, (padicNorm 2 ((compoundMatrix ell H s t : ℤ) : ℚ) : ℝ) ≤
      compoundLocalWidths K b lam p tau 1 s) ∧
    (∀ s, (padicNorm 3 ((compoundMatrix ell H s t : ℤ) : ℚ) : ℝ) ≤
      compoundLocalWidths K b lam p tau 2 s) := by
  have hmap : compoundMatrix ell (H.map (Int.castRingHom ℚ)) =
      (compoundMatrix ell H).map (Int.castRingHom ℚ) :=
    compoundMatrix_map (Int.castRingHom ℚ) ell H
  constructor
  · intro s
    rw [← hmap, ← compoundMatrix_mul]
    apply (compoundMatrix_davenport_bound _ p K (b 0) lam hK (hb 0) hlam hInf s t).trans
    apply mul_le_mul_of_nonneg_left (min_le_min_left _ ht)
    exact mul_nonneg (mul_nonneg (by exact_mod_cast Nat.factorial_pos ell |>.le)
      (pow_nonneg hK _)) (compoundCoordinateProduct_nonneg _ (hb 0) s)
  · constructor
    · intro s
      have hh := compoundMatrix_padicNorm_le 2 (H.map (Int.castRingHom ℚ)) (b 1) (hb 1) hTwo s t
      rw [hmap] at hh
      change (padicNorm 2 ((compoundMatrix ell H s t : ℤ) : ℚ) : ℝ) ≤ compoundCoordinateProduct (b 1) s
      exact hh
    · intro s
      have hh := compoundMatrix_padicNorm_le 3 (H.map (Int.castRingHom ℚ)) (b 2) (hb 2) hThree s t
      rw [hmap] at hh
      change (padicNorm 3 ((compoundMatrix ell H s t : ℤ) : ℚ) : ℝ) ≤ compoundCoordinateProduct (b 2) s
      exact hh

def compoundLogProfile_sum {d ell : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (tau q : ℝ) (hK : 0 < K)
    (hb : ∀ v i, 0 < b v i) (hlam : ∀ i, 0 < lam i) (htau : 0 < tau) :
    (∑ v, ∑ s : CompoundIndex d ell, compoundLogProfile K b lam p tau q v s) =
      Real.log (∏ v, ∏ s : CompoundIndex d ell, compoundLocalWidths K b lam p tau v s) / q := by
  simp only [compoundLogProfile, ← Finset.sum_div]
  congr 1
  rw [Real.log_prod (fun v _ => (Finset.prod_pos (fun s _ =>
    compoundLocalWidths_pos K b lam p tau hK hb hlam htau v s)).ne')]
  apply Finset.sum_congr rfl
  intro v _
  exact (Real.log_prod (fun s _ =>
    (compoundLocalWidths_pos K b lam p tau hK hb hlam htau v s).ne')).symm

end
end Bounty

end SubmissionComponent_CompoundBoxProfiles

/- Component ThreePlaceExactWidths; SHA256 d11b013ea9a03a431010fa87bfdd38cb850086277657b7615b7b588df0d70634 -/
section SubmissionComponent_ThreePlaceExactWidths
/- Exact prime-power local widths, with no rounding loss in their product. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix
open Module MeasureTheory

def threePlaceExactWidths {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) : Fin 3 → Fin d → ℝ :=
  ![threePlaceWidth c q,
    fun i => Real.exp (-(Nat.ceil (-(c 1 i * q) / Real.log 2) : ℝ) * Real.log 2),
    fun i => Real.exp (-(Nat.ceil (-(c 2 i * q) / Real.log 3) : ℝ) * Real.log 3)]

def threePlaceExactWidths_zero {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (i : Fin d) :
    threePlaceExactWidths c q 0 i = threePlaceWidth c q i := rfl

def threePlaceExactWidths_pos {d : ℕ} (c : Fin 3 → Fin d → ℝ) (q : ℝ) (v : Fin 3) (i : Fin d) :
    0 < threePlaceExactWidths c q v i := by fin_cases v <;> exact Real.exp_pos _

def prime_power_width (p : ℕ) (hp : 0 < p) (n : ℕ) :
    Real.exp (-(n : ℝ) * Real.log p) = ((p : ℝ) ^ n)⁻¹ := by
  rw [neg_mul, Real.exp_neg, Real.exp_nat_mul, Real.exp_log (by exact_mod_cast hp)]

def threePlaceExactWidths_finite_product {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    (q : ℝ) (i : Fin d) :
    threePlaceExactWidths c q 1 i * threePlaceExactWidths c q 2 i =
      (threePlaceDiagonal c q i : ℝ)⁻¹ := by
  change Real.exp _ * Real.exp _ = _
  have h2 := prime_power_width 2 (by norm_num) (Nat.ceil (-(c 1 i * q) / Real.log 2))
  have h3 := prime_power_width 3 (by norm_num) (Nat.ceil (-(c 2 i * q) / Real.log 3))
  norm_num only [Nat.cast_ofNat] at h2 h3
  rw [h2, h3]
  simp only [threePlaceDiagonal, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat, mul_inv_rev]
  ring

def padicNorm_int_le_prime_power_width (p : ℕ) [Fact p.Prime] (n : ℕ) (x : ℤ)
    (hx : ((p ^ n : ℕ) : ℤ) ∣ x) :
    (padicNorm p (x : ℚ) : ℝ) ≤ Real.exp (-(n : ℝ) * Real.log p) := by
  rw [prime_power_width p (Fact.out : p.Prime).pos n]
  have hh := (padicNorm.dvd_iff_norm_le (p := p)).mp hx
  simp only [zpow_neg, zpow_natCast] at hh
  have hhR : (padicNorm p (x : ℚ) : ℝ) ≤ ((((p : ℚ) ^ n)⁻¹ : ℚ) : ℝ) := by exact_mod_cast hh
  simpa only [Rat.cast_inv, Rat.cast_pow, Rat.cast_natCast] using hhR

def threePlaceExactWidths_padic_bounds {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    (q : ℝ) (i : Fin d) (x : ℤ) (hx : (threePlaceDiagonal c q i : ℤ) ∣ x) :
    (padicNorm 2 (x : ℚ) : ℝ) ≤ threePlaceExactWidths c q 1 i ∧
      (padicNorm 3 (x : ℚ) : ℝ) ≤ threePlaceExactWidths c q 2 i := by
  obtain ⟨h2, h3⟩ := (two_three_pow_dvd_int_iff _ _ x).mp hx
  exact ⟨padicNorm_int_le_prime_power_width 2 _ x h2, padicNorm_int_le_prime_power_width 3 _ x h3⟩

def prime_exact_width_exp_bounds (p : ℕ) (hp : 1 < p) (hp3 : p ≤ 3)
    {t M q : ℝ} (hM : 0 ≤ M) (hq : 1 ≤ q) (ht : |t| ≤ M) :
    Real.exp (-(M + Real.log 3) * q) ≤
        Real.exp (-(Nat.ceil (-(t * q) / Real.log p) : ℝ) * Real.log p) ∧
      Real.exp (-(Nat.ceil (-(t * q) / Real.log p) : ℝ) * Real.log p) ≤
        Real.exp ((M + Real.log 3) * q) := by
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq
  have hpl : 0 < Real.log (p : ℝ) := Real.log_pos (by exact_mod_cast hp)
  have h3 : 0 < Real.log (3 : ℝ) := Real.log_pos (by norm_num)
  have hcv : -(t * q) ≤ M * q := by
    have hh := mul_le_mul_of_nonneg_right ((neg_le_abs t).trans ht) hq0
    linarith
  have hceil := Nat.ceil_mono (div_le_div_of_nonneg_right hcv hpl.le)
  have hceilR : (Nat.ceil (-(t * q) / Real.log p) : ℝ) ≤ Nat.ceil (M * q / Real.log p) := by exact_mod_cast hceil
  have hb := Nat.ceil_lt_add_one (div_nonneg (mul_nonneg hM hq0) hpl.le)
  have hm := mul_le_mul_of_nonneg_right (hceilR.trans hb.le) hpl.le
  rw [add_mul, div_mul_cancel₀ _ hpl.ne', one_mul] at hm
  have hpL : Real.log (p : ℝ) ≤ Real.log 3 := Real.log_le_log (by exact_mod_cast (by omega : 0 < p)) (by exact_mod_cast hp3)
  have h3q : Real.log (3 : ℝ) ≤ Real.log 3 * q := le_mul_of_one_le_right h3.le hq
  constructor
  · apply Real.exp_le_exp.mpr
    nlinarith
  · apply Real.exp_le_exp.mpr
    have hn : (0 : ℝ) ≤ Nat.ceil (-(t * q) / Real.log p) := Nat.cast_nonneg _
    nlinarith

def threePlaceExactWidths_exp_bounds {d : ℕ} (c : Fin 3 → Fin d → ℝ)
    {M q : ℝ} (hM : 0 ≤ M) (hq : 1 ≤ q) (hc : ∀ v i, |c v i| ≤ M)
    (v : Fin 3) (i : Fin d) :
    Real.exp (-(M + Real.log 3) * q) ≤ threePlaceExactWidths c q v i ∧
      threePlaceExactWidths c q v i ≤ Real.exp ((M + Real.log 3) * q) := by
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq
  have h3 : 0 ≤ Real.log (3 : ℝ) := (Real.log_pos (by norm_num)).le
  fin_cases v
  · constructor <;> apply Real.exp_le_exp.mpr
    · have hh := mul_le_mul_of_nonneg_right (abs_le.mp (hc 0 i)).1 hq0
      have hh3 := mul_nonneg h3 hq0
      nlinarith
    · have hh := mul_le_mul_of_nonneg_right (abs_le.mp (hc 0 i)).2 hq0
      have hh3 := mul_nonneg h3 hq0
      nlinarith
  · exact prime_exact_width_exp_bounds 2 (by norm_num) (by norm_num) hM hq (hc 1 i)
  · exact prime_exact_width_exp_bounds 3 (by norm_num) (by norm_num) hM hq (hc 2 i)


end
end Bounty

end SubmissionComponent_ThreePlaceExactWidths

/- Component CompoundMatrixDeterminant; SHA256 f8bc5f8dd604617b7f586aded752ccf2a26bcbe07ff372e8d01162051172411b -/
section SubmissionComponent_CompoundMatrixDeterminant
/- Determinants of actual compound matrices. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def compoundIndexEmbedding_prod {R : Type*} [CommMonoid R] {d ell : ℕ}
    (s : CompoundIndex d ell) (D : Fin d → R) :
    (∏ j, D (compoundIndexEmbedding s j)) = ∏ i ∈ s.val, D i := by
  classical
  apply Finset.prod_bij (fun j _ => compoundIndexEmbedding s j)
  · intro j _
    exact (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem s _).mp ⟨j, rfl⟩
  · intro a _ b _ hab
    exact (compoundIndexEmbedding s).injective hab
  · intro b hb
    obtain ⟨j, hj⟩ := (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem s b).mpr hb
    exact ⟨j, Finset.mem_univ _, hj⟩
  · intro _ _; rfl

def compoundIndex_card_containing {d ell : ℕ} (hell : 1 ≤ ell) (i : Fin d) :
    ((Finset.univ : Finset (CompoundIndex d ell)).filter (fun s => i ∈ s.val)).card =
      (d - 1).choose (ell - 1) := by
  classical
  have himage :
      (((Finset.univ : Finset (CompoundIndex d ell)).filter (fun s => i ∈ s.val)).image
        Subtype.val) = (Finset.univ.powersetCard ell).filter (fun s : Finset (Fin d) => i ∈ s) := by
    ext s
    simp only [Finset.mem_image, Finset.mem_filter, Finset.mem_univ, true_and,
      Finset.mem_powersetCard, Finset.subset_univ]
    constructor
    · rintro ⟨t, hit, rfl⟩
      exact ⟨t.prop, hit⟩
    · rintro ⟨hs, his⟩
      exact ⟨⟨s, hs⟩, his, rfl⟩
  have hc := Finset.card_filter_powersetCard_subset ({i} : Finset (Fin d))
    Finset.univ ell (Finset.subset_univ _) (by simpa using hell)
  rw [← Finset.card_image_of_injective _ Subtype.val_injective, himage]
  simpa only [Finset.singleton_subset_iff, Finset.card_univ, Fintype.card_fin,
    Finset.card_singleton] using hc

def compoundIndex_prod {R : Type*} [CommMonoid R] {d ell : ℕ}
    (hell : 1 ≤ ell) (D : Fin d → R) :
    (∏ s : CompoundIndex d ell, ∏ j, D (compoundIndexEmbedding s j)) =
      (∏ i, D i) ^ ((d - 1).choose (ell - 1)) := by
  classical
  have hprod : (∏ s : CompoundIndex d ell, ∏ j, D (compoundIndexEmbedding s j)) =
      ∏ s : CompoundIndex d ell, ∏ i : Fin d, if i ∈ s.val then D i else 1 := by
    apply Finset.prod_congr rfl
    intro s _
    rw [compoundIndexEmbedding_prod, Finset.prod_ite_mem_eq]
  rw [hprod]
  rw [Finset.prod_comm]
  simp_rw [← Finset.prod_filter, Finset.prod_const, compoundIndex_card_containing hell]
  rw [Finset.prod_pow]

end
end Bounty

end SubmissionComponent_CompoundMatrixDeterminant

/- Component CompoundIndexProducts; SHA256 77e18031c0a6a11547aa024ddd509054191fe6b61e36c61fe1861b59c90cae6c -/
section SubmissionComponent_CompoundIndexProducts
/- Ordered compound-coordinate products and the exact loss from clipping one maximum. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def compoundIndexPerm {d : ℕ} (ell : ℕ) (p : Equiv.Perm (Fin d)) :
    Equiv.Perm (CompoundIndex d ell) where
  toFun := Set.powersetCard.map ell p.toEmbedding
  invFun := Set.powersetCard.map ell p.symm.toEmbedding
  left_inv s := by
    apply Subtype.ext
    ext i
    simp [Set.powersetCard.map]
  right_inv s := by
    apply Subtype.ext
    ext i
    simp [Set.powersetCard.map]

def compoundCoordinateProduct_permute {d ell : ℕ} (p : Equiv.Perm (Fin d))
    (b : Fin d → ℝ) (s : CompoundIndex d ell) :
    compoundCoordinateProduct b (compoundIndexPerm ell p s) =
      compoundCoordinateProduct (b ∘ p) s := by
  classical
  unfold compoundCoordinateProduct
  rw [compoundIndexEmbedding_prod, compoundIndexEmbedding_prod]
  change (∏ i ∈ s.val.map p.toEmbedding, b i) = ∏ i ∈ s.val, (b ∘ p) i
  rw [Finset.prod_map]
  rfl

def compoundCoordinateProduct_prod {d ell : ℕ} (hell : 1 ≤ ell) (b : Fin d → ℝ) :
    (∏ s : CompoundIndex d ell, compoundCoordinateProduct b s) =
      (∏ i, b i) ^ ((d - 1).choose (ell - 1)) :=
  compoundIndex_prod hell b

def compoundCoordinateProduct_prod_permute {d ell : ℕ}
    (p : Equiv.Perm (Fin d)) (b : Fin d → ℝ) (f : ℝ → ℝ) :
    (∏ s : CompoundIndex d ell, f (compoundCoordinateProduct (b ∘ p) s)) =
      ∏ s : CompoundIndex d ell, f (compoundCoordinateProduct b s) := by
  simp_rw [← compoundCoordinateProduct_permute]
  exact Equiv.prod_comp (compoundIndexPerm ell p)
    (fun s : CompoundIndex d ell => f (compoundCoordinateProduct b s))

def compoundTailEmbedding (d k : ℕ) : Fin (d - k) ↪o Fin d :=
  OrderEmbedding.ofStrictMono (fun j => ⟨k + j.val, by omega⟩)
    (by intro i j hij; exact Nat.add_lt_add_left hij k)

def compoundTailIndex (d k : ℕ) : CompoundIndex d (d - k) :=
  Set.powersetCard.ofFinEmbEquiv (compoundTailEmbedding d k)

def compoundIndexEmbedding_tail (d k : ℕ) :
    compoundIndexEmbedding (compoundTailIndex d k) = compoundTailEmbedding d k :=
  Set.powersetCard.ofFinEmbEquiv.symm_apply_apply _

def compoundIndex_mem_tail {d k : ℕ} (i : Fin d) :
    i ∈ (compoundTailIndex d k).val ↔ k ≤ i.val := by
  change i ∈ Set.powersetCard.ofFinEmbEquiv (compoundTailEmbedding d k) ↔ _
  rw [Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range]
  constructor
  · rintro ⟨j, rfl⟩
    exact Nat.le_add_right k _
  · intro hi
    refine ⟨⟨i.val - k, by omega⟩, ?_⟩
    apply Fin.ext
    change k + (i.val - k) = i.val
    omega

def orderEmbedding_fin_upper {d ell : ℕ} (hell : ell ≤ d)
    (e : Fin ell ↪o Fin d) (i : Fin ell) : (e i).val ≤ d - ell + i.val := by
  cases ell with
  | zero => exact Fin.elim0 i
  | succ n =>
    refine Fin.reverseInduction ?_ ?_ i
    · have h := (e (Fin.last n)).isLt
      simp only [Fin.val_last]
      omega
    · intro j ih
      have hs := e.strictMono j.castSucc_lt_succ
      change (e j.castSucc).val < (e j.succ).val at hs
      simp only [Fin.val_castSucc, Fin.val_succ] at ih ⊢
      omega

def orderEmbedding_fin_lower {d ell : ℕ} (hell : 0 < ell)
    (e : Fin ell ↪o Fin d) (i : Fin ell) : (e ⟨0, hell⟩).val + i.val ≤ (e i).val := by
  cases ell with
  | zero => omega
  | succ n =>
  refine Fin.induction ?_ ?_ i
  · simp
  · intro j ih
    have hs := e.strictMono j.castSucc_lt_succ
    change (e j.castSucc).val < (e j.succ).val at hs
    simp only [Fin.val_castSucc, Fin.val_succ] at ih ⊢
    omega

def compoundIndex_first_lt_of_ne_tail {d k : ℕ} (hk : k < d)
    (s : CompoundIndex d (d - k)) (hs : s ≠ compoundTailIndex d k) :
    (compoundIndexEmbedding s ⟨0, by omega⟩).val < k := by
  by_contra hn
  apply hs
  apply Set.powersetCard.ofFinEmbEquiv.symm.injective
  change compoundIndexEmbedding s = compoundIndexEmbedding (compoundTailIndex d k)
  rw [compoundIndexEmbedding_tail]
  ext j
  have hu := orderEmbedding_fin_upper (Nat.sub_le d k) (compoundIndexEmbedding s) j
  have hl := orderEmbedding_fin_lower (Nat.sub_pos_of_lt hk) (compoundIndexEmbedding s) j
  change (compoundIndexEmbedding s j).val = k + j.val
  omega

def compoundGapRatio {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d) : ℝ :=
  lam ⟨k, hk⟩ / lam ⟨k - 1, by omega⟩

def compoundClipLevel {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d) : ℝ :=
  compoundCoordinateProduct lam (compoundTailIndex d k) / compoundGapRatio lam hk

def compoundGapRatio_pos {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) : 0 < compoundGapRatio lam hk :=
  div_pos (hpos _) (hpos _)

def compoundGapRatio_one_le {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam) : 1 ≤ compoundGapRatio lam hk := by
  apply (le_div_iff₀ (hpos _)).mpr
  simpa only [one_mul] using hmono (show (⟨k - 1, by omega⟩ : Fin d) ≤ ⟨k, hk⟩ from by
    change k - 1 ≤ k; omega)

def compoundClipLevel_pos {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) : 0 < compoundClipLevel lam hk :=
  div_pos (compoundCoordinateProduct_pos lam hpos _) (compoundGapRatio_pos lam hk hpos)

def compoundClipLevel_le_tail {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam) :
    compoundClipLevel lam hk ≤ compoundCoordinateProduct lam (compoundTailIndex d k) := by
  exact div_le_self (compoundCoordinateProduct_pos lam hpos _).le
    (compoundGapRatio_one_le lam hk hpos hmono)

def compoundCoordinateProduct_le_clip_of_ne_tail {d k : ℕ}
    (lam : Fin d → ℝ) (hkpos : 1 ≤ k) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam)
    (s : CompoundIndex d (d - k)) (hs : s ≠ compoundTailIndex d k) :
    compoundCoordinateProduct lam s ≤ compoundClipLevel lam hk := by
  classical
  let z : Fin (d - k) := ⟨0, by omega⟩
  let tailRest : ℝ := ∏ j ∈ Finset.univ.erase z, lam (compoundTailEmbedding d k j)
  have htail : compoundCoordinateProduct lam (compoundTailIndex d k) =
      lam ⟨k, hk⟩ * tailRest := by
    unfold compoundCoordinateProduct
    rw [compoundIndexEmbedding_tail]
    exact (Finset.mul_prod_erase Finset.univ
      (fun j => lam (compoundTailEmbedding d k j)) (Finset.mem_univ z)).symm
  have hclip : compoundClipLevel lam hk = lam ⟨k - 1, by omega⟩ * tailRest := by
    rw [compoundClipLevel, htail, compoundGapRatio]
    field_simp [ne_of_gt (hpos ⟨k, hk⟩), ne_of_gt (hpos ⟨k - 1, by omega⟩)]
  rw [hclip]
  unfold compoundCoordinateProduct
  rw [← Finset.mul_prod_erase Finset.univ
    (fun j => lam (compoundIndexEmbedding s j)) (Finset.mem_univ z)]
  apply mul_le_mul
  · apply hmono
    have hfirst := compoundIndex_first_lt_of_ne_tail hk s hs
    change (compoundIndexEmbedding s z).val ≤ k - 1
    change (compoundIndexEmbedding s z).val < k at hfirst
    omega
  · apply Finset.prod_le_prod (fun _ _ => (hpos _).le)
    intro j _
    apply hmono
    have hu := orderEmbedding_fin_upper (Nat.sub_le d k) (compoundIndexEmbedding s) j
    change (compoundIndexEmbedding s j).val ≤ k + j.val
    omega
  · exact Finset.prod_nonneg (fun _ _ => (hpos _).le)
  · exact (hpos _).le

/-- Clipping the unique large coordinate removes exactly the adjacent-minimum gap. -/
def compoundCoordinateProduct_clipped_prod {d k : ℕ}
    (lam : Fin d → ℝ) (hkpos : 1 ≤ k) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam) :
    (∏ s : CompoundIndex d (d - k), min (compoundCoordinateProduct lam s)
      (compoundClipLevel lam hk)) =
        (∏ i, lam i) ^ ((d - 1).choose (d - k - 1)) / compoundGapRatio lam hk := by
  classical
  let s₀ := compoundTailIndex d k
  have hrest : (∏ s ∈ Finset.univ.erase s₀,
      min (compoundCoordinateProduct lam s) (compoundClipLevel lam hk)) =
        ∏ s ∈ Finset.univ.erase s₀, compoundCoordinateProduct lam s := by
    apply Finset.prod_congr rfl
    intro s hs
    exact min_eq_left (compoundCoordinateProduct_le_clip_of_ne_tail lam hkpos hk hpos hmono s
      (Finset.mem_erase.mp hs).1)
  calc
    _ = compoundClipLevel lam hk *
        ∏ s ∈ Finset.univ.erase s₀, compoundCoordinateProduct lam s := by
      rw [← Finset.mul_prod_erase Finset.univ
        (fun s => min (compoundCoordinateProduct lam s) (compoundClipLevel lam hk))
        (Finset.mem_univ s₀), hrest,
        min_eq_right (compoundClipLevel_le_tail lam hk hpos hmono)]
    _ = (∏ s : CompoundIndex d (d - k), compoundCoordinateProduct lam s) /
        compoundGapRatio lam hk := by
      rw [← Finset.mul_prod_erase Finset.univ (compoundCoordinateProduct lam)
        (Finset.mem_univ s₀)]
      unfold compoundClipLevel
      ring
    _ = _ := by rw [compoundCoordinateProduct_prod (by omega)]

def compoundCoordinateProduct_clipped_prod_permute {d k : ℕ}
    (p : Equiv.Perm (Fin d)) (lam : Fin d → ℝ) (hkpos : 1 ≤ k) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam) :
    (∏ s : CompoundIndex d (d - k), min (compoundCoordinateProduct (lam ∘ p.symm) s)
      (compoundClipLevel lam hk)) =
        (∏ i, lam i) ^ ((d - 1).choose (d - k - 1)) / compoundGapRatio lam hk := by
  rw [compoundCoordinateProduct_prod_permute p.symm lam
    (fun a => min a (compoundClipLevel lam hk))]
  exact compoundCoordinateProduct_clipped_prod lam hkpos hk hpos hmono


end
end Bounty

end SubmissionComponent_CompoundIndexProducts

/- Component CompoundProfileBounds; SHA256 7f16e28bac4cac780d37a448ff5fe3efd79c023447ae3d2b82696172b06f2f26 -/
section SubmissionComponent_CompoundProfileBounds
/- Uniform bounds for actual clipped compound logarithmic profiles. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def abs_log_le_of_exp_bounds {x M q : ℝ}
    (hlo : Real.exp (-M * q) ≤ x) (hhi : x ≤ Real.exp (M * q)) :
    |Real.log x| ≤ M * q := by
  have hx := (Real.exp_pos _).trans_le hlo
  exact abs_le.mpr ⟨(Real.le_log_iff_exp_le hx).mpr (by simpa only [neg_mul] using hlo),
    (Real.log_le_iff_le_exp hx).mpr hhi⟩

def abs_sub_le_abs_add_abs_local (a b : ℝ) : |a - b| ≤ |a| + |b| := by
  simpa only [sub_zero, zero_sub, abs_neg] using abs_sub_le a 0 b

def compoundCoordinateProduct_log_bound {d ell : ℕ} (b : Fin d → ℝ)
    (hpos : ∀ i, 0 < b i) {C : ℝ} (hb : ∀ i, |Real.log (b i)| ≤ C)
    (s : CompoundIndex d ell) : |Real.log (compoundCoordinateProduct b s)| ≤ ell * C := by
  rw [compoundCoordinateProduct, Real.log_prod (fun i _ => (hpos _).ne')]
  calc
    _ ≤ ∑ i : Fin ell, |Real.log (b (compoundIndexEmbedding s i))| := Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _i : Fin ell, C := Finset.sum_le_sum (fun i _ => hb _)
    _ = _ := by simp

def compoundClipLevel_log_bound {d k : ℕ} (lam : Fin d → ℝ) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) {L q : ℝ} (hlam : ∀ i, |Real.log (lam i)| ≤ L * q) :
    |Real.log (compoundClipLevel lam hk)| ≤ ((d - k : ℕ) + 2 : ℝ) * L * q := by
  rw [compoundClipLevel, Real.log_div (compoundCoordinateProduct_pos lam hpos _).ne'
    (compoundGapRatio_pos lam hk hpos).ne', compoundGapRatio,
    Real.log_div (hpos _).ne' (hpos _).ne']
  calc
    _ ≤ |Real.log (compoundCoordinateProduct lam (compoundTailIndex d k))| +
      |Real.log (lam ⟨k, hk⟩) - Real.log (lam ⟨k - 1, by omega⟩)| := abs_sub_le_abs_add_abs_local _ _
    _ ≤ |Real.log (compoundCoordinateProduct lam (compoundTailIndex d k))| +
      (|Real.log (lam ⟨k, hk⟩)| + |Real.log (lam ⟨k - 1, by omega⟩)|) :=
        add_le_add le_rfl (abs_sub_le_abs_add_abs_local _ _)
    _ ≤ ((d - k : ℕ) : ℝ) * (L * q) + (L * q + L * q) :=
      add_le_add (compoundCoordinateProduct_log_bound lam hpos hlam _)
        (add_le_add (hlam _) (hlam _))
    _ = _ := by ring

def compoundLogProfile_clip_abs_bound {d k : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (hk : k < d) {B L q : ℝ}
    (hK : 0 < K) (hbpos : ∀ v i, 0 < b v i) (hlpos : ∀ i, 0 < lam i)
    (_hB : 0 ≤ B) (hL : 0 ≤ L) (hq : 1 ≤ q)
    (hb : ∀ v i, |Real.log (b v i)| ≤ B * q)
    (hl : ∀ i, |Real.log (lam i)| ≤ L * q)
    (v : Fin 3) (s : CompoundIndex d (d - k)) :
    |compoundLogProfile K b lam p (compoundClipLevel lam hk) q v s| ≤
      |Real.log (((d - k).factorial : ℝ) * K ^ (d - k))| +
        (d - k : ℕ) * B + ((d - k : ℕ) + 2 : ℝ) * L := by
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq
  have hqp : 0 < q := lt_of_lt_of_le (by norm_num) hq
  let C : ℝ := (d - k).factorial * K ^ (d - k)
  have hC : 0 < C := mul_pos (by exact_mod_cast Nat.factorial_pos (d - k)) (pow_pos hK _)
  have hLc : |Real.log C| ≤ |Real.log C| * q := le_mul_of_one_le_right (abs_nonneg _) hq
  have hLq : 0 ≤ L * q := mul_nonneg hL hq0
  have hm : |Real.log (min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundClipLevel lam hk))| ≤
      ((d - k : ℕ) + 2 : ℝ) * L * q := by
    by_cases h : compoundCoordinateProduct (lam ∘ p.symm) s ≤ compoundClipLevel lam hk
    · rw [min_eq_left h]
      apply (compoundCoordinateProduct_log_bound (lam ∘ p.symm) (fun i => hlpos _) (fun i => hl _) s).trans
      nlinarith
    · rw [min_eq_right (le_of_not_ge h)]
      exact compoundClipLevel_log_bound lam hk hlpos hl
  unfold compoundLogProfile
  rw [abs_div, abs_of_pos hqp]
  apply (div_le_iff₀ hqp).mpr
  fin_cases v
  · change |Real.log (C * compoundCoordinateProduct (b 0) s *
        min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundClipLevel lam hk))| ≤ _
    have hminpos : 0 < min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundClipLevel lam hk) :=
      lt_min (compoundCoordinateProduct_pos (lam ∘ p.symm) (fun i => hlpos (p.symm i)) s)
        (compoundClipLevel_pos lam hk hlpos)
    rw [Real.log_mul (mul_pos hC (compoundCoordinateProduct_pos _ (hbpos 0) s)).ne' hminpos.ne',
      Real.log_mul hC.ne' (compoundCoordinateProduct_pos _ (hbpos 0) s).ne']
    have hb0 := compoundCoordinateProduct_log_bound (b 0) (hbpos 0) (hb 0) s
    have ht := (abs_add_le (Real.log C + Real.log (compoundCoordinateProduct (b 0) s))
      (Real.log (min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundClipLevel lam hk)))).trans
      (add_le_add (abs_add_le (Real.log C) (Real.log (compoundCoordinateProduct (b 0) s))) le_rfl)
    change _ ≤ (|Real.log C| + _ + _) * q
    nlinarith
  · change |Real.log (compoundCoordinateProduct (b 1) s)| ≤ _
    have hh := compoundCoordinateProduct_log_bound (b 1) (hbpos 1) (hb 1) s
    have hc0 : 0 ≤ |Real.log C| * q := mul_nonneg (abs_nonneg _) hq0
    have hl0 : 0 ≤ ((d - k : ℕ) + 2 : ℝ) * (L * q) := mul_nonneg (by positivity) hLq
    change _ ≤ (|Real.log C| + _ + _) * q
    nlinarith
  · change |Real.log (compoundCoordinateProduct (b 2) s)| ≤ _
    have hh := compoundCoordinateProduct_log_bound (b 2) (hbpos 2) (hb 2) s
    have hc0 : 0 ≤ |Real.log C| * q := mul_nonneg (abs_nonneg _) hq0
    have hl0 : 0 ≤ ((d - k : ℕ) + 2 : ℝ) * (L * q) := mul_nonneg (by positivity) hLq
    change _ ≤ (|Real.log C| + _ + _) * q
    nlinarith

def exists_threePlace_compoundLogProfile_bound {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0) (M : ℝ) :
    ∃ C : ℝ, 0 ≤ C ∧ ∀ (c : Fin 3 → Fin d → ℝ) (q : ℝ), 1 ≤ q →
      (∀ v i, |c v i| ≤ M) → ∀ (k : ℕ) (hk : k < d) (p : Equiv.Perm (Fin d))
      (v : Fin 3) (s : CompoundIndex d (d - k)),
      |compoundLogProfile ((2 : ℝ) ^ d) (threePlaceExactWidths c q)
        (threePlaceMinimumValue A c q hA) p
        (compoundClipLevel (threePlaceMinimumValue A c q hA) hk) q v s| ≤ C := by
  classical
  obtain ⟨L, hL, hmins⟩ := exists_threePlaceMinimumValue_uniform_exp_bounds A hA M
  let B := max M 0 + Real.log 3
  have hB : 0 ≤ B := add_nonneg (le_max_right _ _) (Real.log_nonneg (by norm_num))
  let D := ∑ ell : Fin (d + 1), |Real.log ((ell.val.factorial : ℝ) * ((2 : ℝ) ^ d) ^ ell.val)|
  have hD : 0 ≤ D := Finset.sum_nonneg (fun _ _ => abs_nonneg _)
  let C := D + d * B + ((d : ℝ) + 2) * L
  refine ⟨C, by dsimp [C]; positivity, ?_⟩
  intro c q hq hc k hk p v s
  have hb : ∀ v i, |Real.log (threePlaceExactWidths c q v i)| ≤ B * q := by
    intro v i
    have hh := threePlaceExactWidths_exp_bounds c (le_max_right M 0) hq
      (fun v i => (hc v i).trans (le_max_left M 0)) v i
    exact abs_log_le_of_exp_bounds hh.1 hh.2
  have hl : ∀ i, |Real.log (threePlaceMinimumValue A c q hA i)| ≤ L * q := by
    intro i
    exact abs_log_le_of_exp_bounds (hmins c q hq hc i).1 (hmins c q hq hc i).2
  have hh := compoundLogProfile_clip_abs_bound ((2 : ℝ) ^ d) (threePlaceExactWidths c q)
    (threePlaceMinimumValue A c q hA) p hk (by positivity) (threePlaceExactWidths_pos c q)
    (fun i => rationalBoxMinimumValue_pos A _ _ hA _ _ i) hB hL hq hb hl v s
  have hconst : |Real.log (((d - k).factorial : ℝ) * ((2 : ℝ) ^ d) ^ (d - k))| ≤ D := by
    exact Finset.single_le_sum
      (f := fun ell : Fin (d + 1) => |Real.log ((ell.val.factorial : ℝ) * ((2 : ℝ) ^ d) ^ ell.val)|)
      (fun ell _ => abs_nonneg _) (Finset.mem_univ (⟨d - k, by omega⟩ : Fin (d + 1)))
  apply hh.trans
  have hkd : ((d - k : ℕ) : ℝ) ≤ d := by exact_mod_cast Nat.sub_le d k
  have hbmul := mul_le_mul_of_nonneg_right hkd hB
  have hlmul := mul_le_mul_of_nonneg_right (add_le_add_right hkd 2) hL
  dsimp [C]
  linarith


end
end Bounty

end SubmissionComponent_CompoundProfileBounds

/- Component CompoundWidthProduct; SHA256 a434f222dc9fa11621c6d40a1cc3ecafd3da9b5ac41115b172de2dda3a086fad -/
section SubmissionComponent_CompoundWidthProduct
/- The minimum gap supplies the exact compound volume loss and a negative profile sum. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def compoundLocalWidths_product {d k : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (hkpos : 1 ≤ k) (hk : k < d)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam) :
    (∏ v, ∏ s : CompoundIndex d (d - k),
      compoundLocalWidths K b lam p (compoundClipLevel lam hk) v s) =
        ((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
          ((∏ v, ∏ i, b v i) * (∏ i, lam i)) ^ ((d - 1).choose (d - k - 1)) /
          compoundGapRatio lam hk := by
  have hell : 1 ≤ d - k := by omega
  have harch : (∏ s : CompoundIndex d (d - k),
      compoundLocalWidths K b lam p (compoundClipLevel lam hk) 0 s) =
        ((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
          (∏ i, b 0 i) ^ ((d - 1).choose (d - k - 1)) *
          ((∏ i, lam i) ^ ((d - 1).choose (d - k - 1)) / compoundGapRatio lam hk) := by
    change (∏ s : CompoundIndex d (d - k),
      ((d - k).factorial * K ^ (d - k)) * compoundCoordinateProduct (b 0) s *
        min (compoundCoordinateProduct (lam ∘ p.symm) s) (compoundClipLevel lam hk)) = _
    rw [Finset.prod_mul_distrib, Finset.prod_mul_distrib, Finset.prod_const,
      Finset.card_univ, compoundIndex_card, compoundCoordinateProduct_prod hell,
      compoundCoordinateProduct_clipped_prod_permute p lam hkpos hk hpos hmono]
  have hfinite (v : Fin 3) (hv : v ≠ 0) :
      (∏ s : CompoundIndex d (d - k),
        compoundLocalWidths K b lam p (compoundClipLevel lam hk) v s) =
          (∏ i, b v i) ^ ((d - 1).choose (d - k - 1)) := by
    fin_cases v
    · exact False.elim (hv rfl)
    · exact compoundCoordinateProduct_prod hell (b 1)
    · exact compoundCoordinateProduct_prod hell (b 2)
  rw [Fin.prod_univ_three, harch, hfinite 1 (by decide), hfinite 2 (by decide),
    Fin.prod_univ_three]
  simp only [mul_pow]
  ring

def compoundLocalWidths_product_le {d k : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (hkpos : 1 ≤ k) (hk : k < d)
    (hK : 0 ≤ K) (hb : ∀ v i, 0 ≤ b v i)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam)
    (L : ℝ) (hL : ((∏ v, ∏ i, b v i) * (∏ i, lam i)) ≤ L) :
    (∏ v, ∏ s : CompoundIndex d (d - k),
      compoundLocalWidths K b lam p (compoundClipLevel lam hk) v s) ≤
        ((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
          L ^ ((d - 1).choose (d - k - 1)) / compoundGapRatio lam hk := by
  rw [compoundLocalWidths_product K b lam p hkpos hk hpos hmono]
  apply div_le_div_of_nonneg_right _ (compoundGapRatio_pos lam hk hpos).le
  apply mul_le_mul_of_nonneg_left _ (by positivity)
  apply pow_le_pow_left₀ _ hL
  exact mul_nonneg (Finset.prod_nonneg (fun v _ => Finset.prod_nonneg (fun i _ => hb v i)))
    (Finset.prod_nonneg (fun i _ => (hpos i).le))

def compoundLogProfile_sum_le_of_growth {d k : ℕ}
    (K : ℝ) (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ)
    (p : Equiv.Perm (Fin d)) (hkpos : 1 ≤ k) (hk : k < d)
    (hK : 0 < K) (hb : ∀ v i, 0 < b v i)
    (hpos : ∀ i, 0 < lam i) (hmono : Monotone lam)
    (L q ρ : ℝ) (hLpos : 0 < L) (hq : 0 < q)
    (hL : ((∏ v, ∏ i, b v i) * (∏ i, lam i)) ≤ L)
    (hconst : Real.log (((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
      L ^ ((d - 1).choose (d - k - 1))) ≤ ρ * q)
    (hgap : Real.exp (2 * ρ * q) ≤ compoundGapRatio lam hk) :
    (∑ v, ∑ s : CompoundIndex d (d - k),
      compoundLogProfile K b lam p (compoundClipLevel lam hk) q v s) ≤ -ρ := by
  have hBpos : 0 < ((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
      L ^ ((d - 1).choose (d - k - 1)) := by positivity
  have hB := (Real.log_le_iff_le_exp hBpos).mp hconst
  have hquot :
      ((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
        L ^ ((d - 1).choose (d - k - 1)) / compoundGapRatio lam hk ≤ Real.exp (-ρ * q) := by
    apply (div_le_iff₀ (compoundGapRatio_pos lam hk hpos)).mpr
    apply hB.trans
    calc
      Real.exp (ρ * q) = Real.exp (2 * ρ * q) * Real.exp (-ρ * q) := by
        rw [← Real.exp_add]
        congr 1
        ring
      _ ≤ _ := mul_le_mul_of_nonneg_right hgap (Real.exp_nonneg _)
      _ = _ := by ring
  have hprod := (compoundLocalWidths_product_le K b lam p hkpos hk hK.le
    (fun v i => (hb v i).le) hpos hmono L hL).trans hquot
  rw [compoundLogProfile_sum K b lam p (compoundClipLevel lam hk) q hK hb hpos
    (compoundClipLevel_pos lam hk hpos)]
  apply (div_le_iff₀ hq).mpr
  apply (Real.log_le_iff_le_exp (Finset.prod_pos (fun v _ => Finset.prod_pos (fun s _ =>
    compoundLocalWidths_pos K b lam p (compoundClipLevel lam hk) hK hb hpos
      (compoundClipLevel_pos lam hk hpos) v s)))).mpr
  exact hprod

end
end Bounty

end SubmissionComponent_CompoundWidthProduct

/- Component CompoundUniformDeficit; SHA256 266ce16bcdec52c68f8d611063d94c865dcc77ab5a701bf64b17b38097aab8d3 -/
section SubmissionComponent_CompoundUniformDeficit
/- A single scale threshold works for every proper minimum-prefix dimension. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def compoundCoefficientBudget (d k : ℕ) (K L : ℝ) : ℝ :=
  Real.log (((d - k).factorial * K ^ (d - k)) ^ (d.choose (d - k)) *
    L ^ ((d - 1).choose (d - k - 1)))

def exists_uniform_compound_deficit_threshold (d : ℕ) (K L γ : ℝ)
    (hγ : 0 < γ) :
    ∃ T : ℝ, 1 ≤ T ∧ ∀ q : ℝ, T ≤ q → ∀ k : ℕ, k < d →
      compoundCoefficientBudget d k K L ≤ (γ / 2) * q := by
  let B : ℝ := ∑ j : Fin d, |compoundCoefficientBudget d j.val K L|
  have hB : 0 ≤ B := Finset.sum_nonneg (fun _ _ => abs_nonneg _)
  have hT : 1 ≤ 1 + 2 * B / γ := by
    have hnonneg : 0 ≤ 2 * B / γ := by positivity
    linarith
  refine ⟨1 + 2 * B / γ, hT, ?_⟩
  intro q hq k hk
  have hle : compoundCoefficientBudget d k K L ≤ B := by
    apply (le_abs_self _).trans
    exact Finset.single_le_sum (fun j _ => abs_nonneg (compoundCoefficientBudget d j.val K L))
      (Finset.mem_univ (⟨k, hk⟩ : Fin d))
  have hmul := (div_le_iff₀ hγ).mp (show 2 * B / γ ≤ q by linarith)
  linarith

def exists_uniform_compound_negative_profiles (d : ℕ) (K L γ : ℝ)
    (hK : 0 < K) (hL : 0 < L) (hγ : 0 < γ) :
    ∃ T : ℝ, 1 ≤ T ∧ ∀ (q : ℝ), T ≤ q →
      ∀ (k : ℕ) (_hkpos : 1 ≤ k) (hk : k < d)
        (b : Fin 3 → Fin d → ℝ) (lam : Fin d → ℝ) (p : Equiv.Perm (Fin d)),
      (∀ v i, 0 < b v i) → (∀ i, 0 < lam i) → Monotone lam →
      ((∏ v, ∏ i, b v i) * (∏ i, lam i)) ≤ L →
      Real.exp (γ * q) ≤ compoundGapRatio lam hk →
      (∑ v, ∑ s : CompoundIndex d (d - k),
        compoundLogProfile K b lam p (compoundClipLevel lam hk) q v s) ≤ -(γ / 2) := by
  obtain ⟨T, hT, hbound⟩ := exists_uniform_compound_deficit_threshold d K L γ hγ
  refine ⟨T, hT, ?_⟩
  intro q hq k hkpos hk b lam p hb hlam hmono hprod hgap
  apply compoundLogProfile_sum_le_of_growth K b lam p hkpos hk hK hb hlam hmono
    L q (γ / 2) hL (by linarith) hprod (hbound q hq k hk)
  convert hgap using 1
  congr 2
  ring

end
end Bounty

end SubmissionComponent_CompoundUniformDeficit

/- Component LatticeProfileMass; SHA256 6f153cfbb040c1b3442ff5ccecf8bc4f913243112d2c3ef3d8d339c87720529c -/
section SubmissionComponent_LatticeProfileMass
/- Exact finite-place widths cancel the diagonal lattice determinant in the product bound. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def latticeProfileMassConstant {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) : ℝ :=
  (2 / Real.sqrt 3) ^ (d * (d - 1) / 2) * |(A.det : ℝ)|

def latticeProfileMassConstant_pos {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0) :
    0 < latticeProfileMassConstant A := by
  apply mul_pos
  · apply pow_pos
    exact div_pos (by norm_num) (Real.sqrt_pos.mpr (by norm_num))
  · exact abs_pos.mpr (by exact_mod_cast hA)

def rationalBoxMinimum_threePlace_mass_bound {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (b : Fin 3 → Fin d → ℝ) (N : Fin d → ℕ)
    (hA : A.det ≠ 0) (hb : ∀ i, 0 < b 0 i) (hN : ∀ i, 0 < N i)
    (hfinite : ∀ i, b 1 i * b 2 i = (N i : ℝ)⁻¹) :
    ((∏ v, ∏ i, b v i) * ∏ i, rationalBoxMinimumValue A (b 0) N hA hb hN i) ≤
      latticeProfileMassConstant A := by
  have hB : (0 : ℝ) < ∏ i, b 0 i := Finset.prod_pos (fun i _ => hb i)
  have hNprod : (0 : ℝ) < ∏ i, (N i : ℝ) :=
    Finset.prod_pos (fun i _ => by exact_mod_cast hN i)
  have hfiniteprod : (∏ i, b 1 i) * (∏ i, b 2 i) = (∏ i, (N i : ℝ))⁻¹ := by
    rw [← Finset.prod_mul_distrib]
    simp_rw [hfinite]
    rw [Finset.prod_inv_distrib]
  have hscale : (∏ v, ∏ i, b v i) = (∏ i, b 0 i) / ∏ i, (N i : ℝ) := by
    rw [Fin.prod_univ_three, mul_assoc, hfiniteprod, div_eq_mul_inv]
  rw [hscale]
  have hmin := (rationalBoxMinimumValue_product_bounds A (b 0) N hA hb hN).2
  calc
    _ ≤ ((∏ i, b 0 i) / ∏ i, (N i : ℝ)) *
        ((2 / Real.sqrt 3) ^ (d * (d - 1) / 2) *
          (|(A.det : ℝ)| * (∏ i, (N i : ℝ)) / ∏ i, b 0 i)) :=
      mul_le_mul_of_nonneg_left hmin (div_nonneg hB.le hNprod.le)
    _ = latticeProfileMassConstant A := by
      unfold latticeProfileMassConstant
      field_simp
      <;> ring

end
end Bounty

end SubmissionComponent_LatticeProfileMass

/- Component ThreePlaceGapRate; SHA256 a31630e5c4986bda309882a0983b775fca014d2139cd7adbb9e79fbb544077ab -/
section SubmissionComponent_ThreePlaceGapRate
/- A fixed positive exponential gap rate and a threshold absorbing the
actual determinant and Euclidean dimension constants. -/

namespace Bounty
noncomputable section

def threePlaceGapRate (d : ℕ) (ρ : ℝ) : ℝ := ρ / (2 * (d * (d - 1) : ℕ))

def threePlaceGapRate_pos {d : ℕ} (hd : 2 ≤ d) {ρ : ℝ} (hρ : 0 < ρ) :
    0 < threePlaceGapRate d ρ := by
  have hn : 0 < d * (d - 1) := Nat.mul_pos (by omega) (by omega)
  exact div_pos hρ (mul_pos (by norm_num) (by exact_mod_cast hn))

def exists_threePlace_gap_threshold {d : ℕ} (hd : 2 ≤ d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0) {ρ : ℝ} (hρ : 0 < ρ) :
    ∃ q₀ : ℝ, 1 ≤ q₀ ∧ ∀ q : ℝ, q₀ ≤ q →
      1 ≤ Real.exp (threePlaceGapRate d ρ * q) ∧
      (d.factorial : ℝ) * (Real.sqrt d) ^ d *
          (Real.exp (threePlaceGapRate d ρ * q)) ^ (d * (d - 1)) <
        |(A.det : ℝ)| * Real.exp (ρ * q) := by
  let C : ℝ := d.factorial * (Real.sqrt d) ^ d
  let a : ℝ := |(A.det : ℝ)|
  have ha : 0 < a := abs_pos.mpr (by exact_mod_cast hA)
  have hC : 0 < C := mul_pos (by exact_mod_cast Nat.factorial_pos d)
    (pow_pos (Real.sqrt_pos.mpr (by exact_mod_cast (by omega : 0 < d))) d)
  let S := |Real.log C| + |Real.log a|
  have hS : 0 ≤ S := add_nonneg (abs_nonneg _) (abs_nonneg _)
  let q₀ := 1 + 2 * S / ρ
  have hq₀ : 1 ≤ q₀ := le_add_of_nonneg_right (div_nonneg (mul_nonneg (by norm_num) hS) hρ.le)
  refine ⟨q₀, hq₀, ?_⟩
  intro q hq
  have hq1 : 1 ≤ q := hq₀.trans hq
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq1
  refine ⟨Real.one_le_exp_iff.mpr (mul_nonneg (threePlaceGapRate_pos hd hρ).le hq0), ?_⟩
  have hlarge : S < ρ * q / 2 := by
    have hh := mul_le_mul_of_nonneg_right hq hρ.le
    dsimp [q₀] at hh
    rw [add_mul, div_mul_cancel₀ _ hρ.ne', one_mul] at hh
    nlinarith
  have hn : (d * (d - 1) : ℕ) ≠ 0 := ne_of_gt (Nat.mul_pos (by omega) (by omega))
  have hnr : ((d * (d - 1) : ℕ) : ℝ) ≠ 0 := by exact_mod_cast hn
  have hexp : (Real.exp (threePlaceGapRate d ρ * q)) ^ (d * (d - 1)) = Real.exp (ρ * q / 2) := by
    rw [← Real.exp_nat_mul]
    congr 1
    unfold threePlaceGapRate
    field_simp [hnr]
  rw [hexp]
  change C * Real.exp (ρ * q / 2) < a * Real.exp (ρ * q)
  calc
    _ = Real.exp (Real.log C + ρ * q / 2) := by rw [Real.exp_add, Real.exp_log hC]
    _ < Real.exp (Real.log a + ρ * q) := by
      apply Real.exp_lt_exp.mpr
      dsimp [S] at hlarge
      nlinarith [le_abs_self (Real.log C), neg_abs_le (Real.log a)]
    _ = _ := by rw [Real.exp_add, Real.exp_log ha]


end
end Bounty

end SubmissionComponent_ThreePlaceGapRate

/- Component RationalSpanDescent; SHA256 f2c1eb58e67308300db324d5c30694789c06981ed85e74e9a4d929f9e44a05eb -/
section SubmissionComponent_RationalSpanDescent
/- Rational points in a real span of rational vectors already belong to the rational span. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rationalDualRealExtension {I : Type*} [Fintype I] [DecidableEq I]
    (f : (I → ℚ) →ₗ[ℚ] ℚ) : (I → ℝ) →ₗ[ℝ] ℝ :=
  ∑ i, (f (Pi.single i 1) : ℝ) • (LinearMap.proj i : (I → ℝ) →ₗ[ℝ] ℝ)

def rationalDualRealExtension_cast {I : Type*} [Fintype I] [DecidableEq I]
    (f : (I → ℚ) →ₗ[ℚ] ℚ) (x : I → ℚ) :
    rationalDualRealExtension f (fun i => (x i : ℝ)) = (f x : ℝ) := by
  have hexp : f x = ∑ i, x i * f (Pi.single i 1) := by
    conv_lhs => rw [← (Pi.basisFun ℚ I).sum_repr x]
    simp only [map_sum, map_smul, Pi.basisFun_repr, Pi.basisFun_apply, smul_eq_mul]
  rw [hexp]
  simp only [rationalDualRealExtension, LinearMap.sum_apply, LinearMap.smul_apply,
    LinearMap.proj_apply, smul_eq_mul, Rat.cast_sum, Rat.cast_mul]
  apply Finset.sum_congr rfl
  intro i _
  ring

def rational_mem_span_of_real_mem_span {I : Type*} [Fintype I] [DecidableEq I]
    (s : Set (I → ℚ)) (x : I → ℚ)
    (hx : (fun i => (x i : ℝ)) ∈
      Submodule.span ℝ ((fun z : I → ℚ => fun i => (z i : ℝ)) '' s)) :
    x ∈ Submodule.span ℚ s := by
  by_contra hn
  obtain ⟨f, hfx, hf⟩ := Submodule.exists_dual_map_eq_bot_of_notMem hn inferInstance
  have hker : Submodule.span ℝ ((fun z : I → ℚ => fun i => (z i : ℝ)) '' s) ≤
      LinearMap.ker (rationalDualRealExtension f) := by
    apply Submodule.span_le.mpr
    rintro y ⟨z, hz, rfl⟩
    change rationalDualRealExtension f (fun i => (z i : ℝ)) = 0
    rw [rationalDualRealExtension_cast]
    have hzmem : f z ∈ (Submodule.span ℚ s).map f :=
      Submodule.mem_map_of_mem (Submodule.subset_span hz)
    rw [hf] at hzmem
    have hz0 : f z = 0 := hzmem
    rw [hz0, Rat.cast_zero]
  have hxzero := hker hx
  rw [LinearMap.mem_ker, rationalDualRealExtension_cast] at hxzero
  exact hfx (by exact_mod_cast hxzero)

def rational_mem_span_of_euclidean_mem_span {d : ℕ}
    (s : Set (Fin d → ℚ)) (x : Fin d → ℚ)
    (hx : (WithLp.toLp 2 (fun i => (x i : ℝ)) : BoxEuclidean d) ∈
      Submodule.span ℝ ((fun z : Fin d → ℚ => WithLp.toLp 2 (fun i => (z i : ℝ))) '' s)) :
    x ∈ Submodule.span ℚ s := by
  apply rational_mem_span_of_real_mem_span s x
  have hm := Submodule.mem_map_of_mem
    (f := (WithLp.linearEquiv 2 ℝ (Fin d → ℝ)).toLinearMap) hx
  rw [Submodule.map_span, Set.image_image] at hm
  exact hm

def integer_mem_rational_prefix_of_real_prefix {d : ℕ}
    (H : Fin d → Fin d → ℤ) (x : Fin d → ℤ) (k : ℕ)
    (hx : integerEuclideanPoint x ∈ latticePrefixSpan (fun j => integerEuclideanPoint (H j)) k) :
    (fun i => (x i : ℚ)) ∈ Submodule.span ℚ
      ((fun j i => (H j i : ℚ)) '' {j : Fin d | j.val < k}) := by
  apply rational_mem_span_of_euclidean_mem_span
    ((fun j i => (H j i : ℚ)) '' {j : Fin d | j.val < k}) (fun i => (x i : ℚ))
  rw [Set.image_image]
  simpa only [latticePrefixSpan, integerEuclideanPoint, Function.comp_def, Rat.cast_intCast] using hx

def integer_matrix_det_ne_zero_of_euclidean_independent {d : ℕ}
    (X : Matrix (Fin d) (Fin d) ℤ)
    (hX : LinearIndependent ℝ (fun j => integerEuclideanPoint (X.col j))) :
    (X.map (Int.castRingHom ℚ)).det ≠ 0 := by
  have hreal := hX.map' (WithLp.linearEquiv 2 ℝ (Fin d → ℝ)).toLinearMap
    (LinearMap.ker_eq_bot.mpr (WithLp.linearEquiv 2 ℝ (Fin d → ℝ)).injective)
  change LinearIndependent ℝ (X.map (Int.castRingHom ℝ)).col at hreal
  have hdet : (X.map (Int.castRingHom ℝ)).det ≠ 0 :=
    Matrix.nonsingular_iff_det_ne_zero.mp (Matrix.Nonsingular.of_linearIndependent_col hreal)
  intro hz
  have hmap : (X.map (Int.castRingHom ℚ)).det = (X.det : ℚ) :=
    ((Int.castRingHom ℚ).map_det X).symm
  rw [hmap] at hz
  have hzZ : X.det = 0 := by exact_mod_cast hz
  apply hdet
  calc
    _ = (X.det : ℝ) := ((Int.castRingHom ℝ).map_det X).symm
    _ = 0 := by rw [hzZ, Int.cast_zero]

end
end Bounty

end SubmissionComponent_RationalSpanDescent

/- Component ThreePlaceCompoundWitness; SHA256 2111c1a0da3abbd52f08a697fb15c45006ed24ca9cabeb849aec8c4a3a71d0af -/
section SubmissionComponent_ThreePlaceCompoundWitness
/- Actual compound witnesses for every sufficiently large three-place domain. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def threePlaceCompoundProfile {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0)
    (p : Equiv.Perm (Fin d)) (k : Fin d) : Fin 3 → CompoundIndex d (d - k.val) → ℝ :=
  compoundLogProfile ((2 : ℝ) ^ d) (threePlaceExactWidths c q)
    (threePlaceMinimumValue A c q hA) p
    (compoundClipLevel (threePlaceMinimumValue A c q hA) k.isLt) q

def ThreePlaceCompoundWitnessData {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ)
    (c : Fin 3 → Fin d → ℝ) (q : ℝ) (hA : A.det ≠ 0) (C ρ : ℝ)
    (k : Fin d) (p : Equiv.Perm (Fin d)) (H : Matrix (Fin d) (Fin d) ℤ) : Prop :=
        1 ≤ k.val ∧ (H.map (Int.castRingHom ℚ)).det ≠ 0 ∧
        (∀ v s, |threePlaceCompoundProfile A c q hA p k v s| ≤ C) ∧
        (∑ v, ∑ s, threePlaceCompoundProfile A c q hA p k v s) ≤ -(threePlaceGapRate d ρ / 2) ∧
        (∀ (t : CompoundIndex d (d - k.val)), t ≠ compoundTailIndex d k.val →
          (∀ s, ‖(compoundMatrix (d - k.val) A *
            (compoundMatrix (d - k.val) H).map (Int.castRingHom ℚ)) s t‖ ≤
              Real.exp (threePlaceCompoundProfile A c q hA p k 0 s * q)) ∧
          (∀ s, (padicNorm 2 ((compoundMatrix (d - k.val) H s t : ℤ) : ℚ) : ℝ) ≤
              Real.exp (threePlaceCompoundProfile A c q hA p k 1 s * q)) ∧
          (∀ s, (padicNorm 3 ((compoundMatrix (d - k.val) H s t : ℤ) : ℚ) : ℝ) ≤
              Real.exp (threePlaceCompoundProfile A c q hA p k 2 s * q))) ∧
        (∀ x ∈ rationalThreePlaceDomain A c q,
          (fun i => (x i : ℚ)) ∈ Submodule.span ℚ
            (((H.map (Int.castRingHom ℚ)).col) '' {j : Fin d | j.val < k.val}))

def exists_threePlace_compound_witnesses {d : ℕ} (hd : 2 ≤ d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0) (M ρ : ℝ) (hρ : 0 < ρ) :
    ∃ C T : ℝ, 0 ≤ C ∧ 1 ≤ T ∧ ∀ (c : Fin 3 → Fin d → ℝ) (q : ℝ),
      (∀ v i, |c v i| ≤ M) → (∀ i, c 1 i ≤ 0) → (∀ i, c 2 i ≤ 0) →
      (∑ v, ∑ i, c v i) ≤ -ρ → T ≤ q →
      (∃ x ∈ rationalThreePlaceDomain A c q, x ≠ 0) →
      ∃ (k : Fin d) (p : Equiv.Perm (Fin d)) (H : Matrix (Fin d) (Fin d) ℤ),
        ThreePlaceCompoundWitnessData A c q hA C ρ k p H := by
  obtain ⟨C, hC, hbound⟩ := exists_threePlace_compoundLogProfile_bound A hA M
  have hγ := threePlaceGapRate_pos hd hρ
  obtain ⟨T₁, hT₁, hgaprate⟩ := exists_threePlace_gap_threshold hd A hA hρ
  obtain ⟨T₂, hT₂, hdeficit⟩ := exists_uniform_compound_negative_profiles d ((2 : ℝ) ^ d)
    (latticeProfileMassConstant A) (threePlaceGapRate d ρ) (by positivity)
    (latticeProfileMassConstant_pos A hA) hγ
  refine ⟨C, max T₁ T₂, hC, hT₁.trans (le_max_left _ _), ?_⟩
  intro c q hc hc1 hc2 hsum hq hne
  have hq₁ : T₁ ≤ q := (le_max_left _ _).trans hq
  have hq₂ : T₂ ≤ q := (le_max_right _ _).trans hq
  have hq1 : 1 ≤ q := hT₁.trans hq₁
  have hq0 : 0 ≤ q := le_trans (by norm_num) hq1
  have hqp : 0 < q := lt_of_lt_of_le (by norm_num) hq1
  obtain ⟨hG, hgrowth⟩ := hgaprate q hq₁
  obtain ⟨p, W, z, lo, hi, hidx, hdiv, _, hLI, _, harch, _, hgap, hcontain, _, _⟩ :=
    exists_threePlace_davenport_gap (by omega : 0 < d) A c hA hq0 hc1 hc2 hsum hne hG hgrowth
  let H : Matrix (Fin d) (Fin d) ℤ := fun i j => W j i
  let lam := threePlaceMinimumValue A c q hA
  let b := threePlaceExactWidths c q
  have hpos : ∀ i, 0 < lam i := fun i => rationalBoxMinimumValue_pos A _ _ hA _ _ i
  have hmono : Monotone lam := rationalBoxMinimumValue_monotone A _ _ hA _ _
  have hhipos : 1 ≤ hi.val := by omega
  have hdet : (H.map (Int.castRingHom ℚ)).det ≠ 0 :=
    integer_matrix_det_ne_zero_of_euclidean_independent H hLI
  have hratio : compoundGapRatio lam hi.isLt = lam hi / lam lo := by
    have hprev : (⟨hi.val - 1, by omega⟩ : Fin d) = lo := by
      apply Fin.ext
      change hi.val - 1 = lo.val
      omega
    change lam hi / lam ⟨hi.val - 1, _⟩ = lam hi / lam lo
    rw [hprev]
  have hmass : ((∏ v, ∏ i, b v i) * ∏ i, lam i) ≤ latticeProfileMassConstant A :=
    rationalBoxMinimum_threePlace_mass_bound A b (threePlaceDiagonal c q) hA
      (threePlaceWidth_pos c q) (threePlaceDiagonal_pos c q)
      (threePlaceExactWidths_finite_product c q)
  have hlocal : ∀ i j, ‖(A * H.map (Int.castRingHom ℚ)) (p i) j‖ ≤
      (2 : ℝ) ^ d * b 0 (p i) * min (lam i) (lam j) := by
    intro i j
    change ‖(∑ r, A (p i) r * (W j r : ℚ) : ℚ)‖ ≤ _
    rw [← Rat.norm_cast_real, Real.norm_eq_abs]
    simpa [Matrix.mulVec, dotProduct, Matrix.map_apply, Rat.cast_sum, Rat.cast_mul,
      b, threePlaceExactWidths_zero, threePlaceWidth, lam] using harch i j
  refine ⟨hi, p, H, ?_⟩
  unfold ThreePlaceCompoundWitnessData
  refine ⟨hhipos, hdet, ?_, ?_, ?_, ?_⟩
  · exact hbound c q hq1 hc hi.val hi.isLt p
  · apply hdeficit q hq₂ hi.val hhipos hi.isLt b lam p
      (threePlaceExactWidths_pos c q) hpos hmono hmass
    rw [hratio]
    exact hgap.le
  · intro t ht
    have htclip := compoundCoordinateProduct_le_clip_of_ne_tail lam hhipos hi.isLt hpos hmono t ht
    have hloc := compoundMatrix_clipped_local_bounds A H ((2 : ℝ) ^ d) b lam p
      (compoundClipLevel lam hi.isLt) (by positivity)
      (fun v i => (threePlaceExactWidths_pos c q v i).le) (fun i => (hpos i).le) hlocal
      (fun i j => (threePlaceExactWidths_padic_bounds c q i (W j i) (hdiv j i)).1)
      (fun i j => (threePlaceExactWidths_padic_bounds c q i (W j i) (hdiv j i)).2) t htclip
    have he (v : Fin 3) (s : CompoundIndex d (d - hi.val)) :
        Real.exp (threePlaceCompoundProfile A c q hA p hi v s * q) =
          compoundLocalWidths ((2 : ℝ) ^ d) b lam p (compoundClipLevel lam hi.isLt) v s :=
      exp_compoundLogProfile _ b lam p _ q (by positivity) (threePlaceExactWidths_pos c q)
        hpos (compoundClipLevel_pos lam hi.isLt hpos) hqp.ne' v s
    simpa only [he] using hloc
  · intro x hx
    exact integer_mem_rational_prefix_of_real_prefix W x hi.val (hcontain x hx)

end
end Bounty

end SubmissionComponent_ThreePlaceCompoundWitness

/- Component IntegerThreePlaceProduct; SHA256 e8dcdc1fe5df96148d3907fb8e00955aebb91749daeb892517b278b0a5331752 -/
section SubmissionComponent_IntegerThreePlaceProduct
/- The three-place product lower bound for actual nonzero integers, proved
from coprime prime-power divisibility rather than a product-formula premise. -/

namespace Bounty
noncomputable section

def padicNorm_int_inverse_power (p : ℕ) (z : ℤ) (hz : z ≠ 0) :
    padicNorm p (z : ℚ) = ((p : ℚ) ^ padicValNat p z.natAbs)⁻¹ := by
  rw [padicNorm.eq_zpow_of_nonzero (by exact_mod_cast hz), padicValRat.of_int]
  simp only [padicValInt, zpow_neg, zpow_natCast]

def two_prime_valuation_power_dvd (p q n : ℕ)
    (hp : p.Prime) (hq : q.Prime) (hpq : p ≠ q) :
    p ^ padicValNat p n * q ^ padicValNat q n ∣ n := by
  have hc : Nat.Coprime p q := (Nat.coprime_primes hp hq).mpr hpq
  exact (hc.pow _ _).mul_dvd_of_dvd_of_dvd pow_padicValNat_dvd pow_padicValNat_dvd

def integer_two_prime_product_lower_rat (p q : ℕ)
    (hp : p.Prime) (hq : q.Prime) (hpq : p ≠ q)
    (z : ℤ) (hz : z ≠ 0) :
    (1 : ℚ) ≤ |(z : ℚ)| * padicNorm p (z : ℚ) * padicNorm q (z : ℚ) := by
  have hn : 0 < z.natAbs := Int.natAbs_pos.mpr hz
  have hb := Nat.le_of_dvd hn (two_prime_valuation_power_dvd p q z.natAbs hp hq hpq)
  have hbq : (p : ℚ) ^ padicValNat p z.natAbs *
      (q : ℚ) ^ padicValNat q z.natAbs ≤ (z.natAbs : ℚ) := by exact_mod_cast hb
  have hp0 : (0 : ℚ) < p := by exact_mod_cast hp.pos
  have hq0 : (0 : ℚ) < q := by exact_mod_cast hq.pos
  have habs : |(z : ℚ)| = (z.natAbs : ℚ) := by rw [Nat.cast_natAbs, Int.cast_abs]
  rw [padicNorm_int_inverse_power p z hz, padicNorm_int_inverse_power q z hz,
    habs]
  calc
    _ ≤ (z.natAbs : ℚ) /
        ((p : ℚ) ^ padicValNat p z.natAbs * (q : ℚ) ^ padicValNat q z.natAbs) :=
      (one_le_div₀ (by positivity)).mpr hbq
    _ = _ := by rw [div_eq_mul_inv, mul_inv_rev]; ring

def integer_two_prime_product_lower (p q : ℕ)
    (hp : p.Prime) (hq : q.Prime) (hpq : p ≠ q)
    (z : ℤ) (hz : z ≠ 0) :
    (1 : ℝ) ≤ |(z : ℝ)| * (padicNorm p (z : ℚ) : ℝ) * (padicNorm q (z : ℚ) : ℝ) := by
  exact_mod_cast integer_two_prime_product_lower_rat p q hp hq hpq z hz

def integer_three_place_product_lower_rat (z : ℤ) (hz : z ≠ 0) :
    (1 : ℚ) ≤ |(z : ℚ)| * padicNorm 2 (z : ℚ) * padicNorm 3 (z : ℚ) :=
  integer_two_prime_product_lower_rat 2 3 (by norm_num) (by norm_num) (by norm_num) z hz

def integer_three_place_product_lower (z : ℤ) (hz : z ≠ 0) :
    (1 : ℝ) ≤ |(z : ℝ)| * (padicNorm 2 (z : ℚ) : ℝ) * (padicNorm 3 (z : ℚ) : ℝ) :=
  integer_two_prime_product_lower 2 3 (by norm_num) (by norm_num) (by norm_num) z hz


end
end Bounty

end SubmissionComponent_IntegerThreePlaceProduct

/- Component PrimitiveCofactorHeight; SHA256 8a1741a0bf788e8d6666ef17216d4c3fbc04c2e4cc3c9e02a72ead29879d6091 -/
section SubmissionComponent_PrimitiveCofactorHeight
/- Primitive normalization and the arithmetic lower bounds for a selected
nonzero real coordinate and two selected nonzero finite-place coordinates. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def integer_vector_primitive_factor {I : Type*} [Fintype I]
    (w : I → ℤ) (hw : w ≠ 0) :
    ∃ (g : ℤ) (a : I → ℤ), 0 < g ∧ a ≠ 0 ∧
      Finset.univ.gcd a = 1 ∧ ∀ i, w i = g * a i := by
  classical
  obtain ⟨i, hi⟩ : ∃ i, w i ≠ 0 := by simpa [funext_iff] using hw
  obtain ⟨a, ha, hprim⟩ := Finset.extract_gcd w ⟨i, Finset.mem_univ i⟩
  have hg : Finset.univ.gcd w ≠ 0 := Finset.gcd_ne_zero_iff.mpr ⟨i, Finset.mem_univ i, hi⟩
  refine ⟨Finset.univ.gcd w, a, lt_of_le_of_ne Finset.Int.finsetGcd_nonneg (Ne.symm hg),
    ?_, hprim, fun j => ha j (Finset.mem_univ j)⟩
  intro hz
  apply hi
  simpa [hz] using ha i (Finset.mem_univ i)

def integer_cofactor_primitive_factor {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℤ)
    (hX : LinearIndependent ℚ (X.map (Int.castRingHom ℚ)).col) :
    ∃ (g : ℤ) (a : Fin (n + 1) → ℤ), 0 < g ∧ a ≠ 0 ∧
      Finset.univ.gcd a = 1 ∧ ∀ i, cofactorNormal X i = g * a i := by
  apply integer_vector_primitive_factor
  intro hz
  apply cofactorNormal_ne_zero _ hX
  rw [cofactorNormal_map]
  ext i
  simp [hz]

def integerVectorMax {I : Type*} [Fintype I] (a : I → ℤ) : ℝ :=
  ((⨆ i, |a i|) : ℤ)

def integerVectorMax_ge_one {I : Type*} [Fintype I]
    (a : I → ℤ) (ha : a ≠ 0) : 1 ≤ integerVectorMax a := by
  classical
  obtain ⟨i, hi⟩ : ∃ i, a i ≠ 0 := by simpa [funext_iff] using ha
  have hi' : (1 : ℤ) ≤ |a i| := by have := abs_pos.mpr hi; omega
  have hh := hi'.trans (Finite.le_ciSup (fun i => |a i|) i)
  unfold integerVectorMax
  exact_mod_cast hh

def integer_coord_abs_le_max {I : Type*} [Fintype I]
    (a : I → ℤ) (i : I) : |(a i : ℝ)| ≤ integerVectorMax a := by
  unfold integerVectorMax
  exact_mod_cast Finite.le_ciSup (fun i => |a i|) i

def primitive_integer_logHeight {I : Type*} [Fintype I] [Nonempty I]
    (a : I → ℤ) (ha : Finset.univ.gcd a = 1) :
    Height.logHeight (fun i => (a i : ℚ)) = Real.log (integerVectorMax a) :=
  Rat.logHeight_eq_max_abs_of_gcd_eq_one ha

def padicNorm_integer_reciprocal_lower (p : ℕ) (hp : p.Prime)
    (z : ℤ) (hz : z ≠ 0) :
    1 / |(z : ℝ)| ≤ (padicNorm p (z : ℚ) : ℝ) := by
  have hn : 0 < z.natAbs := Int.natAbs_pos.mpr hz
  have hp0 : (0 : ℝ) < p := by exact_mod_cast hp.pos
  have hb : (p : ℝ) ^ padicValNat p z.natAbs ≤ (z.natAbs : ℝ) := by
    exact_mod_cast Nat.le_of_dvd hn (pow_padicValNat_dvd (p := p) (n := z.natAbs))
  rw [padicNorm_int_inverse_power p z hz]
  simp only [Rat.cast_inv, Rat.cast_pow, Rat.cast_natCast]
  have habs : |(z : ℝ)| = (z.natAbs : ℝ) := by rw [Nat.cast_natAbs, Int.cast_abs]
  rw [habs, ← one_div]
  exact one_div_le_one_div_of_le (pow_pos hp0 _) hb

def padicNorm_integer_le_height_reciprocal {I : Type*} [Fintype I]
    (p : ℕ) (hp : p.Prime) (a : I → ℤ) (i : I) (hi : a i ≠ 0) :
    1 / integerVectorMax a ≤ (padicNorm p (a i : ℚ) : ℝ) := by
  have hi0 : (0 : ℝ) < |(a i : ℝ)| := abs_pos.mpr (by exact_mod_cast hi)
  exact (one_div_le_one_div_of_le hi0 (integer_coord_abs_le_max a i)).trans
    (padicNorm_integer_reciprocal_lower p hp _ hi)

def nonzero_rational_scaled_integer_norm_lower (x : ℚ) (D z : ℤ)
    (hD : 0 < D) (hx : x ≠ 0) (hz : (D : ℚ) * x = z) :
    1 / (D : ℝ) ≤ ‖x‖ := by
  have hz0 : z ≠ 0 := by
    intro h
    have : (D : ℚ) * x = 0 := by simpa [h] using hz
    exact (mul_ne_zero (by exact_mod_cast hD.ne') hx) this
  have hz1 : (1 : ℤ) ≤ |z| := by have := abs_pos.mpr hz0; omega
  have hzreal : (1 : ℝ) ≤ |(z : ℝ)| := by exact_mod_cast hz1
  have hh := congrArg norm hz
  have hDreal : (0 : ℝ) < D := by exact_mod_cast hD
  simp only [norm_mul, Int.norm_cast_rat, Int.norm_eq_abs,
    abs_of_pos hDreal] at hh
  exact (div_le_iff₀ hDreal).mpr (by nlinarith [hh])

def primitive_normal_selected_product_lower {I : Type*} [Fintype I]
    (a : I → ℤ) (i₂ i₃ : I) (hi₂ : a i₂ ≠ 0) (hi₃ : a i₃ ≠ 0)
    (x : ℚ) (D z : ℤ) (hD : 0 < D) (hx : x ≠ 0) (hz : (D : ℚ) * x = z) :
    1 / ((D : ℝ) * integerVectorMax a ^ 2) ≤
      ‖x‖ * (padicNorm 2 (a i₂ : ℚ) : ℝ) * (padicNorm 3 (a i₃ : ℚ) : ℝ) := by
  have ha : a ≠ 0 := by intro hh; exact hi₂ (congrFun hh i₂)
  have hH : 0 < integerVectorMax a := lt_of_lt_of_le (by norm_num) (integerVectorMax_ge_one a ha)
  have hDr : (0 : ℝ) < D := by exact_mod_cast hD
  have h₀ := nonzero_rational_scaled_integer_norm_lower x D z hD hx hz
  have h₂ := padicNorm_integer_le_height_reciprocal 2 (by norm_num) a i₂ hi₂
  have h₃ := padicNorm_integer_le_height_reciprocal 3 (by norm_num) a i₃ hi₃
  have hp₂ : (0 : ℝ) ≤ padicNorm 2 (a i₂ : ℚ) := by exact_mod_cast padicNorm.nonneg (a i₂ : ℚ)
  calc
    _ = (1 / (D : ℝ)) * (1 / integerVectorMax a) * (1 / integerVectorMax a) := by ring
    _ ≤ _ := mul_le_mul (mul_le_mul h₀ h₂ (by positivity) (norm_nonneg _))
      h₃ (by positivity) (mul_nonneg (norm_nonneg _) hp₂)

def remove_integer_three_place_scalar (g : ℤ) (hg : g ≠ 0)
    (x y z : ℚ) :
    ‖x‖ * (padicNorm 2 y : ℝ) * (padicNorm 3 z : ℝ) ≤
      ‖(g : ℚ) * x‖ * (padicNorm 2 ((g : ℚ) * y) : ℝ) *
        (padicNorm 3 ((g : ℚ) * z) : ℝ) := by
  have hgprod := integer_three_place_product_lower g hg
  have hp₂ : (0 : ℝ) ≤ padicNorm 2 y := by exact_mod_cast padicNorm.nonneg y
  have hp₃ : (0 : ℝ) ≤ padicNorm 3 z := by exact_mod_cast padicNorm.nonneg z
  have hbase : 0 ≤ ‖x‖ * (padicNorm 2 y : ℝ) * (padicNorm 3 z : ℝ) := by positivity
  have h := mul_le_mul_of_nonneg_right hgprod hbase
  simp only [norm_mul, padicNorm.mul, Rat.cast_mul, Int.norm_cast_rat, Int.norm_eq_abs]
  nlinarith [h]


end
end Bounty

end SubmissionComponent_PrimitiveCofactorHeight

/- Component CofactorHeightLower; SHA256 907b8311f072161f135a23d02c0e8e633cc805670a718cec177cdbbd158418d6 -/
section SubmissionComponent_CofactorHeightLower
/- The large-height branch for an actual primitive cofactor normal.
The integer common factor is removed with its three-place product lower
bound; no affine height of an unnormalized normal is substituted. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def cofactorTransform {n : ℕ} (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) :=
  A.adjugate.transpose

def exists_integer_scaled_rational_matrix {I J : Type*} [Fintype I] [Fintype J]
    (F : Matrix I J ℚ) :
    ∃ D : ℤ, 0 < D ∧ ∃ B : Matrix I J ℤ, ∀ i j, (B i j : ℚ) = (D : ℚ) * F i j := by
  obtain ⟨D, hD⟩ := IsLocalization.exist_integer_multiples_of_finite (Submonoid.pos ℤ)
    (fun z : I × J => F z.1 z.2)
  choose B hB using hD
  refine ⟨D.val, D.property, fun i j => B (i, j), ?_⟩
  intro i j
  simpa [Algebra.smul_def] using hB (i, j)

def exists_cofactor_denominator {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) :
    ∃ D : ℤ, 0 < D ∧ ∀ (a : Fin (n + 1) → ℤ) (i : Fin (n + 1)),
      ∃ z : ℤ, (D : ℚ) * (cofactorTransform A).mulVec (fun j => (a j : ℚ)) i = z := by
  obtain ⟨D, hD, B, hB⟩ := exists_integer_scaled_rational_matrix (cofactorTransform A)
  refine ⟨D, hD, fun a i => ⟨∑ j, B i j * a j, ?_⟩⟩
  simp only [Matrix.mulVec, dotProduct, Finset.mul_sum, Int.cast_sum, Int.cast_mul, hB]
  apply Finset.sum_congr rfl
  intro j _
  ring

def cofactor_three_place_upper {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ)
    (X : Matrix (Fin (n + 1)) (Fin n) ℚ)
    (c : Fin 3 → Fin (n + 1) → ℝ) (t : ℝ)
    (hInf : ∀ i j, ‖(A * X) i j‖ ≤ Real.exp (c 0 i * t))
    (h₂ : ∀ i j, (padicNorm 2 (X i j) : ℝ) ≤ Real.exp (c 1 i * t))
    (h₃ : ∀ i j, (padicNorm 3 (X i j) : ℝ) ≤ Real.exp (c 2 i * t))
    (i : Fin 3 → Fin (n + 1)) :
    ‖cofactorNormal (A * X) (i 0)‖ *
        (padicNorm 2 (cofactorNormal X (i 1)) : ℝ) *
        (padicNorm 3 (cofactorNormal X (i 2)) : ℝ) ≤
      (n.factorial : ℝ) * Real.exp (((∑ v, ∑ j, c v j) - ∑ v, c v (i v)) * t) := by
  have h₀ := cofactorNormal_norm_le_exp (A * X) (c 0) t hInf (i 0)
  have h₂' := cofactorNormal_padicNorm_le_exp 2 X (c 1) t h₂ (i 1)
  have h₃' := cofactorNormal_padicNorm_le_exp 3 X (c 2) t h₃ (i 2)
  have hp₂ : (0 : ℝ) ≤ padicNorm 2 (cofactorNormal X (i 1)) := by
    exact_mod_cast padicNorm.nonneg (cofactorNormal X (i 1))
  have hp₃ : (0 : ℝ) ≤ padicNorm 3 (cofactorNormal X (i 2)) := by
    exact_mod_cast padicNorm.nonneg (cofactorNormal X (i 2))
  calc
    _ ≤ ((n.factorial : ℝ) * Real.exp (((∑ j, c 0 j) - c 0 (i 0)) * t)) *
        Real.exp (((∑ j, c 1 j) - c 1 (i 1)) * t) *
        Real.exp (((∑ j, c 2 j) - c 2 (i 2)) * t) :=
      mul_le_mul (mul_le_mul h₀ h₂' hp₂ (by positivity)) h₃' hp₃ (by positivity)
    _ = _ := by
      rw [mul_assoc, mul_assoc, ← Real.exp_add, ← Real.exp_add]
      congr 2
      simp only [Fin.sum_univ_succ, Fin.sum_univ_zero]
      norm_num
      ring

def primitive_cofactor_three_place_upper {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ)
    (X : Matrix (Fin (n + 1)) (Fin n) ℤ)
    (g : ℤ) (hg : g ≠ 0) (a : Fin (n + 1) → ℤ)
    (hfactor : ∀ j, cofactorNormal X j = g * a j)
    (c : Fin 3 → Fin (n + 1) → ℝ) (t : ℝ)
    (hInf : ∀ i j, ‖(A * X.map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c 0 i * t))
    (h₂ : ∀ i j, (padicNorm 2 (X i j : ℚ) : ℝ) ≤ Real.exp (c 1 i * t))
    (h₃ : ∀ i j, (padicNorm 3 (X i j : ℚ) : ℝ) ≤ Real.exp (c 2 i * t))
    (i : Fin 3 → Fin (n + 1)) :
    ‖(cofactorTransform A).mulVec (fun j => (a j : ℚ)) (i 0)‖ *
        (padicNorm 2 (a (i 1) : ℚ) : ℝ) * (padicNorm 3 (a (i 2) : ℚ) : ℝ) ≤
      (n.factorial : ℝ) * Real.exp (((∑ v, ∑ j, c v j) - ∑ v, c v (i v)) * t) := by
  have hnormal : cofactorNormal (X.map (Int.castRingHom ℚ)) =
      (g : ℚ) • (fun j => (a j : ℚ)) := by
    ext j
    rw [cofactorNormal_map]
    change ((cofactorNormal X j : ℤ) : ℚ) = (g : ℚ) * (a j : ℚ)
    rw [hfactor, Int.cast_mul]
  have htrans : cofactorNormal (A * X.map (Int.castRingHom ℚ)) =
      (g : ℚ) • (cofactorTransform A).mulVec (fun j => (a j : ℚ)) := by
    rw [cofactorNormal_mul, hnormal, Matrix.mulVec_smul]
    rfl
  have hupper := cofactor_three_place_upper A (X.map (Int.castRingHom ℚ)) c t hInf h₂ h₃ i
  rw [hnormal, htrans] at hupper
  exact (remove_integer_three_place_scalar g hg _ _ _).trans hupper

def primitive_cofactor_height_lower {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ)
    (X : Matrix (Fin (n + 1)) (Fin n) ℤ)
    (g : ℤ) (hg : g ≠ 0) (a : Fin (n + 1) → ℤ)
    (hprimitive : Finset.univ.gcd a = 1)
    (hfactor : ∀ j, cofactorNormal X j = g * a j)
    (c : Fin 3 → Fin (n + 1) → ℝ) (t ρ : ℝ) (ht : 0 ≤ t)
    (hInf : ∀ i j, ‖(A * X.map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c 0 i * t))
    (h₂ : ∀ i j, (padicNorm 2 (X i j : ℚ) : ℝ) ≤ Real.exp (c 1 i * t))
    (h₃ : ∀ i j, (padicNorm 3 (X i j : ℚ) : ℝ) ≤ Real.exp (c 2 i * t))
    (hc : (∑ v, ∑ j, c v j) ≤ -ρ)
    (i : Fin 3 → Fin (n + 1)) (hi : -ρ / 2 ≤ ∑ v, c v (i v))
    (hi₂ : a (i 1) ≠ 0) (hi₃ : a (i 2) ≠ 0)
    (D z : ℤ) (hD : 0 < D)
    (hx : (cofactorTransform A).mulVec (fun j => (a j : ℚ)) (i 0) ≠ 0)
    (hz : (D : ℚ) * (cofactorTransform A).mulVec (fun j => (a j : ℚ)) (i 0) = z) :
    ρ * t / 4 - Real.log ((D : ℝ) * (n.factorial : ℝ)) / 2 ≤
      Height.logHeight (fun j => (a j : ℚ)) := by
  have hu := primitive_cofactor_three_place_upper A X g hg a hfactor c t hInf h₂ h₃ i
  have he : ((∑ v, ∑ j, c v j) - ∑ v, c v (i v)) * t ≤ -ρ * t / 2 := by
    have h : (∑ v, ∑ j, c v j) - ∑ v, c v (i v) ≤ -ρ / 2 := by linarith
    nlinarith [mul_le_mul_of_nonneg_right h ht]
  have hu' := hu.trans (mul_le_mul_of_nonneg_left (Real.exp_le_exp.mpr he)
    (show (0 : ℝ) ≤ n.factorial by positivity))
  have hl := primitive_normal_selected_product_lower a (i 1) (i 2) hi₂ hi₃ _ D z hD hx hz
  have hboth := hl.trans hu'
  have ha : a ≠ 0 := by intro h; exact hi₂ (congrFun h (i 1))
  have hH : 0 < integerVectorMax a := lt_of_lt_of_le (by norm_num) (integerVectorMax_ge_one a ha)
  have hDr : (0 : ℝ) < D := by exact_mod_cast hD
  have hf : (0 : ℝ) < n.factorial := by exact_mod_cast Nat.factorial_pos n
  have hlog := Real.log_le_log (by positivity : 0 < 1 / ((D : ℝ) * integerVectorMax a ^ 2)) hboth
  rw [primitive_integer_logHeight a hprimitive]
  rw [Real.log_div one_ne_zero (by positivity), Real.log_one,
    Real.log_mul hDr.ne' (by positivity), Real.log_pow,
    Real.log_mul hf.ne' (Real.exp_ne_zero _), Real.log_exp] at hlog
  rw [Real.log_mul hDr.ne' hf.ne']
  nlinarith


end
end Bounty

end SubmissionComponent_CofactorHeightLower

/- Component HyperplaneIndexSpecialization; SHA256 31e52aedcfb013b82de805ce732f687030e82431ae0d53f8e1ce4e79a642c88a -/
section SubmissionComponent_HyperplaneIndexSpecialization
/- Saturation and specialization of weighted monomial orders.  Removing
zero-weight variables preserves the order during exact monomial division and
can only increase it during specialization.  The coefficient maps are actual
injections of subvectors, so the coefficient sum norm does not increase. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I J R : Type*}

def polynomialCoeffL1_le_coeff_embedding [NormedCommRing R]
    (P : MvPolynomial I R) (Q : MvPolynomial J R)
    (f : (J →₀ ℕ) → (I →₀ ℕ)) (hf : Function.Injective f)
    (hcoeff : ∀ d, MvPolynomial.coeff d Q = MvPolynomial.coeff (f d) P) :
    polynomialCoeffL1 Q ≤ polynomialCoeffL1 P := by
  classical
  have hs : Q.support.image f ⊆ P.support := by
    intro e he
    obtain ⟨d, hd, rfl⟩ := Finset.mem_image.mp he
    simpa only [MvPolynomial.mem_support_iff, ← hcoeff] using hd
  calc
    _ = ∑ e ∈ Q.support.image f, ‖MvPolynomial.coeff e P‖ := by
      rw [Finset.sum_image hf.injOn]
      simp only [polynomialCoeffL1, hcoeff]
    _ ≤ _ := Finset.sum_le_sum_of_subset_of_nonneg hs (fun _ _ _ => norm_nonneg _)

def polynomialCoeffL1_divMonomial_le [NormedCommRing R]
    (P : MvPolynomial I R) (s : I →₀ ℕ) :
    polynomialCoeffL1 (P.divMonomial s) ≤ polynomialCoeffL1 P :=
  polynomialCoeffL1_le_coeff_embedding P _ (s + ·) (add_right_injective s)
    (fun _ => MvPolynomial.coeff_divMonomial _ _ _)

def polynomialCoeffL1_killCompl_le [NormedCommRing R]
    (f : I → J) (hf : Function.Injective f) (P : MvPolynomial J R) :
    polynomialCoeffL1 (P.killCompl hf) ≤ polynomialCoeffL1 P :=
  polynomialCoeffL1_le_coeff_embedding P _ (Finsupp.mapDomain f)
    (Finsupp.mapDomain_injective hf) (fun _ => MvPolynomial.coeff_killCompl hf)

def specialization_weight_mapDomain (w : J → ℕ) (f : I → J) (d : I →₀ ℕ) :
    Finsupp.weight w (d.mapDomain f) = Finsupp.weight (w ∘ f) d := by
  exact Finsupp.sum_mapDomain_index (f := f) (s := d)
    (h := fun i (v : ℕ) => v • w i) (fun _ => zero_smul _ _)
    (fun _ _ _ => add_smul ..)

def weightedPolynomialOrder_killCompl_le (w : J → ℕ) (f : I → J)
    (hf : Function.Injective f) (P : MvPolynomial J ℚ) :
    weightedPolynomialOrder w P ≤ weightedPolynomialOrder (w ∘ f) (P.killCompl hf) := by
  apply (weightedPolynomialOrder_le_iff _ _ _).mpr
  intro d hd
  rw [MvPolynomial.coeff_killCompl] at hd
  simpa only [specialization_weight_mapDomain] using weightedPolynomialOrder_le_of_coeff w hd

def weightedPolynomialOrder_monomial_one (w : I → ℕ) (s : I →₀ ℕ) :
    weightedPolynomialOrder w (MvPolynomial.monomial s (1 : ℚ)) = Finsupp.weight w s := by
  classical
  apply le_antisymm
  · apply weightedPolynomialOrder_le_of_coeff
    simp
  · apply (weightedPolynomialOrder_le_iff _ _ _).mpr
    intro d hd
    have hds : d = s := by
      by_contra hh
      simp [MvPolynomial.coeff_monomial, Ne.symm hh] at hd
    subst d
    exact le_rfl

def monomial_mul_divMonomial_of_support [CommSemiring R]
    (P : MvPolynomial I R) (s : I →₀ ℕ)
    (hs : ∀ d ∈ P.support, s ≤ d) :
    MvPolynomial.monomial s 1 * P.divMonomial s = P := by
  have hz : P.modMonomial s = 0 := by
    ext d
    by_cases hsd : s ≤ d
    · simp [MvPolynomial.coeff_modMonomial_of_le P hsd]
    · rw [MvPolynomial.coeff_modMonomial_of_not_le P hsd, MvPolynomial.coeff_zero]
      exact MvPolynomial.notMem_support_iff.mp (fun hd => hsd (hs d hd))
  simpa only [hz, add_zero] using P.divMonomial_add_modMonomial s

def degreeOf_divMonomial_le [CommSemiring R] (P : MvPolynomial I R)
    (s : I →₀ ℕ) (i : I) :
    (P.divMonomial s).degreeOf i ≤ P.degreeOf i := by
  apply MvPolynomial.degreeOf_le_iff.mpr
  intro d hd
  have hp : s + d ∈ P.support := by
    simpa only [MvPolynomial.mem_support_iff, MvPolynomial.coeff_divMonomial] using hd
  exact (Nat.le_add_left _ _).trans (MvPolynomial.monomial_le_degreeOf i hp)

def zeroCoordinateSpecialization [CommSemiring R] (z : I) :
    MvPolynomial I R →ₐ[R] MvPolynomial {i : I // i ≠ z} R :=
  MvPolynomial.killCompl (f := Subtype.val) Subtype.val_injective

/-- The coefficient slice at exponent `k` in the variable `z`. -/
def coordinateSlice [CommSemiring R] (z : I) (k : ℕ) (P : MvPolynomial I R) :
    MvPolynomial {i : I // i ≠ z} R :=
  zeroCoordinateSpecialization z (P.divMonomial (Finsupp.single z k))

def coordinateSlice_coeff [CommSemiring R] (z : I) (k : ℕ)
    (P : MvPolynomial I R) (d : {i : I // i ≠ z} →₀ ℕ) :
    MvPolynomial.coeff d (coordinateSlice z k P) =
      MvPolynomial.coeff (Finsupp.single z k + d.mapDomain Subtype.val) P := by
  exact (MvPolynomial.coeff_killCompl Subtype.val_injective).trans
    (MvPolynomial.coeff_divMonomial _ _ _)

def coordinate_exponent_split (z : I) (d : I →₀ ℕ) :
    Finsupp.single z (d z) +
      (d.comapDomain (Subtype.val : {i : I // i ≠ z} → I)
        Subtype.val_injective.injOn).mapDomain Subtype.val = d := by
  classical
  let e := d.comapDomain (Subtype.val : {i : I // i ≠ z} → I) Subtype.val_injective.injOn
  have hz : e.mapDomain Subtype.val z = 0 := by
    apply Finsupp.mapDomain_of_not_mem_image_support
    rintro ⟨j, _, hj⟩
    exact j.property hj
  ext i
  by_cases hi : i = z
  · subst i
    change (Finsupp.single z (d z)) z + e.mapDomain Subtype.val z = d z
    simp only [Finsupp.single_eq_same, hz, add_zero]
  · have hh := Finsupp.mapDomain_apply Subtype.val_injective e (⟨i, hi⟩ : {i : I // i ≠ z})
    change (Finsupp.single z (d z)) i + e.mapDomain Subtype.val i = d i
    rw [hh]
    simp only [e, Finsupp.comapDomain_apply, Finsupp.single_eq_of_ne hi, zero_add]

def coordinateSlice_ne_zero_of_coeff [CommSemiring R]
    (z : I) (P : MvPolynomial I R) {d : I →₀ ℕ}
    (hd : MvPolynomial.coeff d P ≠ 0) : coordinateSlice z (d z) P ≠ 0 := by
  intro hz
  let e := d.comapDomain (Subtype.val : {i : I // i ≠ z} → I) Subtype.val_injective.injOn
  have hh := congrArg (MvPolynomial.coeff e) hz
  rw [coordinateSlice_coeff, MvPolynomial.coeff_zero] at hh
  have he : Finsupp.single z (d z) + e.mapDomain Subtype.val = d := coordinate_exponent_split z d
  exact hd (he ▸ hh)

end
end Bounty

end SubmissionComponent_HyperplaneIndexSpecialization

/- Component BlockHomogeneousDehomogenization; SHA256 80530dd4143d107cdac1261107f14a03bfeab0def789c269e60b29a457317d85 -/
section SubmissionComponent_BlockHomogeneousDehomogenization
/- Exact dehomogenization of two-coordinate homogeneous blocks.  The variable
`Sum.inl i` is retained and `Sum.inr i` is set to one.  Fixed block degrees
make the map on supported exponents injective, preventing coefficient collisions. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {I R S : Type*}

open scoped Classical in
def blockLeftExponent (e : I ⊕ I →₀ ℕ) : I →₀ ℕ :=
  e.comapDomain Sum.inl Sum.inl_injective.injOn

open scoped Classical in
def blockLeftExponent_apply (e : I ⊕ I →₀ ℕ) (i : I) :
    blockLeftExponent e i = e (Sum.inl i) := rfl

open scoped Classical in
def BlockHomogeneous [CommSemiring R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) : Prop :=
  ∀ e ∈ P.support, ∀ i, e (Sum.inl i) + e (Sum.inr i) = r i

open scoped Classical in
def blockDehomogenize [CommSemiring R] :
    MvPolynomial (I ⊕ I) R →ₐ[R] MvPolynomial I R :=
  MvPolynomial.aeval (Sum.elim MvPolynomial.X (fun _ => 1))

open scoped Classical in
def blockDehomogenize_C [CommSemiring R] (a : R) :
    blockDehomogenize (I := I) (MvPolynomial.C a) = MvPolynomial.C a := by
  simp [blockDehomogenize]

open scoped Classical in
def blockDehomogenize_X_inl [CommSemiring R] (i : I) :
    blockDehomogenize (MvPolynomial.X (R := R) (Sum.inl i)) = MvPolynomial.X i := by
  simp [blockDehomogenize]

open scoped Classical in
def blockDehomogenize_X_inr [CommSemiring R] (i : I) :
    blockDehomogenize (MvPolynomial.X (R := R) (Sum.inr i)) = 1 := by
  simp [blockDehomogenize]

open scoped Classical in
def blockLeftExponent_injective_fixed (r : I → ℕ) {e d : I ⊕ I →₀ ℕ}
    (he : ∀ i, e (Sum.inl i) + e (Sum.inr i) = r i)
    (hd : ∀ i, d (Sum.inl i) + d (Sum.inr i) = r i)
    (h : blockLeftExponent e = blockLeftExponent d) : e = d := by
  ext j
  cases j with
  | inl i => exact DFunLike.congr_fun h i
  | inr i =>
    have hi : e (Sum.inl i) = d (Sum.inl i) := DFunLike.congr_fun h i
    have := he i
    have := hd i
    omega

open scoped Classical in
def blockDehomogenize_monomial [CommSemiring R]
    (e : I ⊕ I →₀ ℕ) (a : R) :
    blockDehomogenize (MvPolynomial.monomial e a) =
      MvPolynomial.monomial (blockLeftExponent e) a := by
  rw [blockDehomogenize, MvPolynomial.aeval_monomial, MvPolynomial.monomial_eq]
  congr 1
  nth_rw 1 [← Finsupp.comapDomain_sumElim_comapDomain e]
  rw [Finsupp.prod_sumElim]
  simp [blockLeftExponent, Function.comp_def]

open scoped Classical in
def blockDehomogenize_as_sum [CommSemiring R] (P : MvPolynomial (I ⊕ I) R) :
    blockDehomogenize P = ∑ e ∈ P.support,
      MvPolynomial.monomial (blockLeftExponent e) (MvPolynomial.coeff e P) := by
  nth_rw 1 [MvPolynomial.as_sum P]
  simp only [map_sum, blockDehomogenize_monomial]

/- Every supported original coefficient is recovered exactly after dehomogenization. -/
open scoped Classical in
def blockDehomogenize_coeff [CommSemiring R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) (hP : BlockHomogeneous r P)
    (e : I ⊕ I →₀ ℕ) (he : e ∈ P.support) :
    MvPolynomial.coeff (blockLeftExponent e) (blockDehomogenize P) = MvPolynomial.coeff e P := by
  classical
  rw [blockDehomogenize_as_sum, MvPolynomial.coeff_sum, Finset.sum_eq_single e]
  · simp
  · intro d hd hde
    have hh : blockLeftExponent d ≠ blockLeftExponent e :=
      fun hh => hde (blockLeftExponent_injective_fixed r (hP d hd) (hP e he) hh)
    simp [MvPolynomial.coeff_monomial, hh]
  · exact fun hn => False.elim (hn he)

open scoped Classical in
def blockDehomogenize_support_subset [CommSemiring R]
    (P : MvPolynomial (I ⊕ I) R) :
    (blockDehomogenize P).support ⊆ P.support.image blockLeftExponent := by
  classical
  rw [blockDehomogenize_as_sum]
  intro d hd
  obtain ⟨e, he, hde⟩ := Finset.mem_biUnion.mp (MvPolynomial.support_sum hd)
  have hh := MvPolynomial.support_monomial_subset hde
  exact Finset.mem_image.mpr ⟨e, he, (Finset.mem_singleton.mp hh).symm⟩

open scoped Classical in
def blockDehomogenize_support [CommSemiring R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) (hP : BlockHomogeneous r P) :
    (blockDehomogenize P).support = P.support.image blockLeftExponent := by
  classical
  apply Finset.Subset.antisymm (blockDehomogenize_support_subset P)
  intro d hd
  obtain ⟨e, he, rfl⟩ := Finset.mem_image.mp hd
  rw [MvPolynomial.mem_support_iff, blockDehomogenize_coeff r P hP e he]
  exact MvPolynomial.mem_support_iff.mp he

open scoped Classical in
def blockDehomogenize_ne_zero [CommSemiring R] (r : I → ℕ)
    {P : MvPolynomial (I ⊕ I) R} (hP : BlockHomogeneous r P) (hne : P ≠ 0) :
    blockDehomogenize P ≠ 0 := by
  classical
  obtain ⟨e, he⟩ := MvPolynomial.support_nonempty.mpr hne
  intro hz
  have hh := blockDehomogenize_coeff r P hP e he
  rw [hz, MvPolynomial.coeff_zero] at hh
  exact (MvPolynomial.mem_support_iff.mp he) hh.symm

open scoped Classical in
def blockDehomogenize_coeffL1 [NormedCommRing R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) (hP : BlockHomogeneous r P) :
    polynomialCoeffL1 (blockDehomogenize P) = polynomialCoeffL1 P := by
  classical
  unfold polynomialCoeffL1
  rw [blockDehomogenize_support r P hP, Finset.sum_image]
  · exact Finset.sum_congr rfl (fun e he => congrArg norm (blockDehomogenize_coeff r P hP e he))
  · intro e he d hd hh
    exact blockLeftExponent_injective_fixed r (hP e he) (hP d hd) hh

open scoped Classical in
def blockDehomogenize_degreeOf_le [CommSemiring R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) (hP : BlockHomogeneous r P) (i : I) :
    (blockDehomogenize P).degreeOf i ≤ r i := by
  classical
  apply MvPolynomial.degreeOf_le_iff.mpr
  intro d hd
  obtain ⟨e, he, rfl⟩ := Finset.mem_image.mp (blockDehomogenize_support_subset P hd)
  have := hP e he i
  simp only [blockLeftExponent_apply]
  omega

open scoped Classical in
def blockDehomogenize_map [CommSemiring R] [CommSemiring S]
    (f : R →+* S) (P : MvPolynomial (I ⊕ I) R) :
    MvPolynomial.map f (blockDehomogenize P) = blockDehomogenize (MvPolynomial.map f P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i <;> simp only [map_mul, MvPolynomial.map_X, blockDehomogenize_X_inl,
      blockDehomogenize_X_inr, map_one, hP]

open scoped Classical in
def block_weight_left (w : I → ℕ) (e : I ⊕ I →₀ ℕ) :
    Finsupp.weight (Sum.elim w (fun _ => 0)) e = Finsupp.weight w (blockLeftExponent e) := by
  rw [Finsupp.weight_apply, Finsupp.weight_apply]
  nth_rw 1 [← Finsupp.comapDomain_sumElim_comapDomain e]
  rw [Finsupp.sum_sumElim]
  simp [blockLeftExponent, Function.comp_def]

open scoped Classical in
def blockDehomogenize_order (r w : I → ℕ)
    (P : MvPolynomial (I ⊕ I) ℚ) (hP : BlockHomogeneous r P) :
    weightedPolynomialOrder (Sum.elim w (fun _ => 0)) P =
      weightedPolynomialOrder w (blockDehomogenize P) := by
  apply le_antisymm
  · apply (weightedPolynomialOrder_le_iff _ _ _).mpr
    intro d hd
    obtain ⟨e, he, rfl⟩ := Finset.mem_image.mp (blockDehomogenize_support_subset P
      (MvPolynomial.mem_support_iff.mpr hd))
    simpa only [block_weight_left] using weightedPolynomialOrder_le_of_coeff
      (Sum.elim w (fun _ => 0)) (MvPolynomial.mem_support_iff.mp he)
  · apply (weightedPolynomialOrder_le_iff _ _ _).mpr
    intro e he
    have hc : MvPolynomial.coeff (blockLeftExponent e) (blockDehomogenize P) ≠ 0 := by
      rw [blockDehomogenize_coeff r P hP e (MvPolynomial.mem_support_iff.mpr he)]
      exact he
    simpa only [block_weight_left] using weightedPolynomialOrder_le_of_coeff w hc

/- A substitution homogeneous of the weight of each input variable preserves
weighted homogeneity.  This is used for changes of coordinates inside blocks. -/
open scoped Classical in
def weightedHomogeneous_aeval [CommSemiring R] {J : Type*}
    (w : J → ℕ) (g : J → MvPolynomial J R)
    (hg : ∀ j, MvPolynomial.IsWeightedHomogeneous w (g j) (w j))
    (P : MvPolynomial J R) (n : ℕ) (hP : MvPolynomial.IsWeightedHomogeneous w P n) :
    MvPolynomial.IsWeightedHomogeneous w (MvPolynomial.aeval g P) n := by
  classical
  nth_rw 1 [MvPolynomial.as_sum P]
  rw [map_sum]
  apply MvPolynomial.IsWeightedHomogeneous.sum
  intro e he
  rw [MvPolynomial.aeval_monomial]
  change MvPolynomial.IsWeightedHomogeneous w
    (MvPolynomial.C (MvPolynomial.coeff e P) * e.prod (fun j a => g j ^ a)) n
  have hprod := MvPolynomial.IsWeightedHomogeneous.prod e.support
    (fun j => g j ^ e j) (fun j => e j • w j) (fun j _ => (hg j).pow (e j))
  have hsum : ∑ j ∈ e.support, e j • w j = n := hP (MvPolynomial.mem_support_iff.mp he)
  rw [hsum] at hprod
  exact hprod.C_mul _

open scoped Classical in
def blockDegreeWeight (i : I) : I ⊕ I → ℕ :=
  Sum.elim (Pi.single i 1) (Pi.single i 1)

open scoped Classical in
def blockDegreeWeight_apply (i : I) (e : I ⊕ I →₀ ℕ) :
    Finsupp.weight (blockDegreeWeight i) e = e (Sum.inl i) + e (Sum.inr i) := by
  rw [Finsupp.weight_apply]
  nth_rw 1 [← Finsupp.comapDomain_sumElim_comapDomain e]
  rw [Finsupp.sum_sumElim]
  change Finsupp.weight (Pi.single i 1) (e.comapDomain Sum.inl Sum.inl_injective.injOn) +
    Finsupp.weight (Pi.single i 1) (e.comapDomain Sum.inr Sum.inr_injective.injOn) = _
  simp only [Finsupp.weight_single_one_apply, Finsupp.comapDomain_apply]

open scoped Classical in
def blockHomogeneous_iff_weighted [CommSemiring R] (r : I → ℕ)
    (P : MvPolynomial (I ⊕ I) R) :
    BlockHomogeneous r P ↔
      ∀ i, MvPolynomial.IsWeightedHomogeneous (blockDegreeWeight i) P (r i) := by
  constructor
  · intro h i e he
    rw [blockDegreeWeight_apply]
    exact h e (MvPolynomial.mem_support_iff.mpr he) i
  · intro h e he i
    simpa only [blockDegreeWeight_apply] using h i (MvPolynomial.mem_support_iff.mp he)

/- Homogeneous Taylor translation in each pair `(X_i,Y_i)`. -/
open scoped Classical in
def blockTaylor [CommSemiring R] (β : I → R) :
    MvPolynomial (I ⊕ I) R →ₐ[R] MvPolynomial (I ⊕ I) R :=
  MvPolynomial.aeval (Sum.elim
    (fun i => MvPolynomial.X (Sum.inl i) + MvPolynomial.C (β i) * MvPolynomial.X (Sum.inr i))
    (fun i => MvPolynomial.X (Sum.inr i)))

open scoped Classical in
open scoped Classical in
def blockTaylor_X_inl [CommSemiring R] (β : I → R) (i : I) :
    blockTaylor β (MvPolynomial.X (Sum.inl i)) =
      MvPolynomial.X (Sum.inl i) + MvPolynomial.C (β i) * MvPolynomial.X (Sum.inr i) := by
  simp [blockTaylor]

open scoped Classical in
def blockTaylor_X_inr [CommSemiring R] (β : I → R) (i : I) :
    blockTaylor β (MvPolynomial.X (Sum.inr i)) = MvPolynomial.X (Sum.inr i) := by
  simp [blockTaylor]

open scoped Classical in
def blockTaylor_homogeneous [CommSemiring R] (r : I → ℕ) (β : I → R)
    (P : MvPolynomial (I ⊕ I) R) (hP : BlockHomogeneous r P) :
    BlockHomogeneous r (blockTaylor β P) := by
  apply (blockHomogeneous_iff_weighted r _).mpr
  intro i
  apply weightedHomogeneous_aeval
  · intro j
    cases j with
    | inl j =>
      exact (MvPolynomial.isWeightedHomogeneous_X R (blockDegreeWeight i) (Sum.inl j)).add
        ((MvPolynomial.isWeightedHomogeneous_X R (blockDegreeWeight i) (Sum.inr j)).C_mul (β j))
    | inr j => exact MvPolynomial.isWeightedHomogeneous_X R _ _
  · exact (blockHomogeneous_iff_weighted r P).mp hP i

open scoped Classical in
def blockDehomogenize_blockTaylor (β : I → ℚ) (P : MvPolynomial (I ⊕ I) ℚ) :
    blockDehomogenize (blockTaylor β P) = weightedTaylor β (blockDehomogenize P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [weightedTaylor_C]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P j hP =>
    cases j <;> simp only [map_mul, blockTaylor_X_inl, blockTaylor_X_inr,
      blockDehomogenize_X_inl, blockDehomogenize_X_inr, map_add, blockDehomogenize_C,
      mul_one, weightedTaylor_X, map_one, hP]

/- The order in the homogeneous forms `X_i - β_i Y_i` becomes the ordinary
Taylor index at `β` after dehomogenization. -/
open scoped Classical in
def blockDehomogenize_hyperplane_index (r w : I → ℕ) (β : I → ℚ)
    (P : MvPolynomial (I ⊕ I) ℚ) (hP : BlockHomogeneous r P) :
    weightedPolynomialOrder (Sum.elim w (fun _ => 0)) (blockTaylor β P) =
      weightedPolynomialIndex w β (blockDehomogenize P) := by
  rw [blockDehomogenize_order r w _ (blockTaylor_homogeneous r β P hP),
    blockDehomogenize_blockTaylor]
  rfl


end
end Bounty

end SubmissionComponent_BlockHomogeneousDehomogenization

/- Component RationalHyperplanePairHeight; SHA256 a9ece804862ac1f70bc8c3432e983633d3d69a1de9ae845d73baf482114ccd4e -/
section SubmissionComponent_RationalHyperplanePairHeight
/- A rational hyperplane has a coefficient pair whose height is at least
the projective coefficient height divided by the projective dimension. -/

namespace Bounty
noncomputable section
open scoped BigOperators

/-- Each coordinate is a coordinate of the Segre product of the pairs
`[x_i,1]`.  Projection cannot increase projective height. -/
def projective_logHeight_le_sum_coordinate_heights
    {K I : Type*} [Field K] [Height.AdmissibleAbsValues K] [Fintype I]
    (x : I → K) : Height.logHeight x ≤ ∑ i, Height.logHeight₁ (x i) := by
  classical
  let y (i : I) : Fin 2 → K := ![x i, 1]
  have hy (i : I) : y i ≠ 0 := by
    intro hz
    have hh := congrFun hz 1
    simp [y] at hh
  let pick (i : I) (a : I) : Fin 2 := if a = i then 0 else 1
  have hpick : (fun v : I → Fin 2 => ∏ a, y a (v a)) ∘ pick = x := by
    funext i
    change (∏ a, y a (if a = i then 0 else 1)) = x i
    rw [Finset.prod_eq_single i]
    · simp [y]
    · intro a _ hai
      simp [hai, y]
    · simp
  have hh := Height.logHeight_comp_le pick (fun v : I → Fin 2 => ∏ a, y a (v a))
  rw [hpick, Height.logHeight_fun_prod_eq hy] at hh
  simpa only [y, ← Height.logHeight₁_eq_logHeight] using hh

def rational_hyperplane_height_le_sum_ratios {I : Type*} [Fintype I] [DecidableEq I]
    (b : I → ℚ) (j : I) (hj : b j ≠ 0) :
    Height.logHeight b ≤ ∑ i ∈ Finset.univ.erase j, Height.logHeight₁ (b i / b j) := by
  have hscale : Height.logHeight (fun i => b i / b j) = Height.logHeight b := by
    have he : (fun i => b i / b j) = (b j)⁻¹ • b := by
      ext i
      simp only [Pi.smul_apply, smul_eq_mul, div_eq_mul_inv, mul_comm]
    rw [he, Height.logHeight_smul_eq_logHeight b (inv_ne_zero hj)]
  have hh := projective_logHeight_le_sum_coordinate_heights (fun i => b i / b j)
  rw [hscale, ← Finset.sum_erase_add Finset.univ
    (fun i => Height.logHeight₁ (b i / b j)) (Finset.mem_univ j)] at hh
  simpa only [div_self hj, Height.logHeight₁_one, add_zero] using hh

/-- Any nonzero coefficient may be used as the denominator of the selected ratio. -/
def exists_rational_hyperplane_height_pair {d : ℕ} (hd : 1 ≤ d)
    (b : Fin (d + 1) → ℚ) (j : Fin (d + 1)) (hj : b j ≠ 0) :
    ∃ i : Fin (d + 1), i ≠ j ∧
      Height.logHeight b / (d : ℝ) ≤ Height.logHeight₁ (-b i / b j) := by
  classical
  let s : Finset (Fin (d + 1)) := Finset.univ.erase j
  have hcard : s.card = d := by simp [s]
  have hs : s.Nonempty := Finset.card_pos.mp (by omega)
  obtain ⟨i, hi, hmax⟩ := s.exists_max_image (fun a => Height.logHeight₁ (b a / b j)) hs
  have hsum : (∑ a ∈ s, Height.logHeight₁ (b a / b j)) ≤
      (d : ℝ) * Height.logHeight₁ (b i / b j) := by
    calc
      _ ≤ ∑ _a ∈ s, Height.logHeight₁ (b i / b j) := Finset.sum_le_sum hmax
      _ = _ := by simp only [Finset.sum_const, nsmul_eq_mul, hcard]
  refine ⟨i, (Finset.mem_erase.mp hi).1, ?_⟩
  rw [neg_div, Height.logHeight₁_neg]
  apply (div_le_iff₀ (by exact_mod_cast (show 0 < d by omega))).mpr
  simpa only [mul_comm] using (rational_hyperplane_height_le_sum_ratios b j hj).trans hsum

end
end Bounty

end SubmissionComponent_RationalHyperplanePairHeight

/- Component RationalHyperplaneIndex; SHA256 ee5fc430ea06146f893b39c9c8b8d922fe741359ec652c92207155859472be5f -/
section SubmissionComponent_RationalHyperplaneIndex
/- Concrete coordinate changes and saturation for the rational hyperplane
index.  Pivots and complementary variables are separated by a sum type. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {B C I J R : Type*}

/- Set one variable to zero while keeping the ambient variable type fixed. -/
open scoped Classical in
def zeroVariable [CommSemiring R] (z : I) : MvPolynomial I R →ₐ[R] MvPolynomial I R :=
  MvPolynomial.aeval (fun i => if i = z then 0 else MvPolynomial.X i)

open scoped Classical in
open scoped Classical in
def zeroVariable_X [CommSemiring R] (z i : I) :
    zeroVariable z (MvPolynomial.X (R := R) i) = if i = z then 0 else MvPolynomial.X i := by
  simp [zeroVariable]

open scoped Classical in
def zeroCoordinateSpecialization_X_self [CommSemiring R] (z : I) :
    zeroCoordinateSpecialization z (MvPolynomial.X (R := R) z) = 0 := by
  change (MvPolynomial.monomial (Finsupp.single z 1) (1 : R)).killCompl Subtype.val_injective = 0
  apply MvPolynomial.killCompl_monomial_eq_zero_of_notMem_range _ _ (a := z)
  · simp
  · rintro ⟨i, hi⟩
    exact i.property hi

open scoped Classical in
def zeroCoordinateSpecialization_X_ne [CommSemiring R] (z i : I) (hi : i ≠ z) :
    zeroCoordinateSpecialization z (MvPolynomial.X (R := R) i) = MvPolynomial.X ⟨i, hi⟩ := by
  simpa only [zeroCoordinateSpecialization, MvPolynomial.rename_X] using MvPolynomial.killCompl_rename_app Subtype.val_injective
    (MvPolynomial.X (R := R) (⟨i, hi⟩ : {i : I // i ≠ z}))

open scoped Classical in
def zeroVariable_eq_rename_specialization [CommSemiring R] (z : I) (P : MvPolynomial I R) :
    zeroVariable z P = MvPolynomial.rename Subtype.val (zeroCoordinateSpecialization z P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [zeroCoordinateSpecialization]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    rw [map_mul, map_mul, map_mul, hP, zeroVariable_X]
    by_cases hi : i = z
    · subst i
      simp only [zeroCoordinateSpecialization_X_self, map_zero, ite_true]
    · rw [if_neg hi, zeroCoordinateSpecialization_X_ne z i hi, MvPolynomial.rename_X]

open scoped Classical in
def zeroVariable_coeffL1_le [NormedCommRing R] (z : I) (P : MvPolynomial I R) :
    polynomialCoeffL1 (zeroVariable z P) ≤ polynomialCoeffL1 P := by
  rw [zeroVariable_eq_rename_specialization,
    polynomialCoeffL1_rename_of_injective _ Subtype.val_injective]
  exact polynomialCoeffL1_killCompl_le _ Subtype.val_injective P

open scoped Classical in
def zeroVariable_support_subset [CommSemiring R] (z : I) (P : MvPolynomial I R) :
    (zeroVariable z P).support ⊆ P.support := by
  rw [zeroVariable_eq_rename_specialization]
  exact MvPolynomial.support_rename_killCompl_subset Subtype.val_injective

open scoped Classical in
def zeroVariable_degreeOf_le [CommSemiring R] (z : I) (P : MvPolynomial I R) (i : I) :
    (zeroVariable z P).degreeOf i ≤ P.degreeOf i := by
  simp only [MvPolynomial.degreeOf_eq_sup]
  exact Finset.sup_mono (zeroVariable_support_subset z P)

open scoped Classical in
def weightedPolynomialOrder_rename_injective (w : J → ℕ) (f : I → J)
    (hf : Function.Injective f) (P : MvPolynomial I ℚ) :
    weightedPolynomialOrder w (MvPolynomial.rename f P) = weightedPolynomialOrder (w ∘ f) P := by
  classical
  apply le_antisymm
  · apply (weightedPolynomialOrder_le_iff _ _ _).mpr
    intro d hd
    have hh : MvPolynomial.coeff (d.mapDomain f) (MvPolynomial.rename f P) ≠ 0 := by
      rwa [MvPolynomial.coeff_rename_mapDomain f hf]
    simpa only [specialization_weight_mapDomain] using weightedPolynomialOrder_le_of_coeff w hh
  · apply (weightedPolynomialOrder_le_iff _ _ _).mpr
    intro e he
    have hs : e ∈ (MvPolynomial.rename f P).support := MvPolynomial.mem_support_iff.mpr he
    rw [MvPolynomial.support_rename_of_injective hf] at hs
    obtain ⟨d, hd, rfl⟩ := Finset.mem_image.mp hs
    simpa only [specialization_weight_mapDomain] using weightedPolynomialOrder_le_of_coeff
      (w ∘ f) (MvPolynomial.mem_support_iff.mp hd)

open scoped Classical in
def zeroVariable_order_le (w : I → ℕ) (z : I) (P : MvPolynomial I ℚ) :
    weightedPolynomialOrder w P ≤ weightedPolynomialOrder w (zeroVariable z P) := by
  rw [zeroVariable_eq_rename_specialization, weightedPolynomialOrder_rename_injective _ _
    Subtype.val_injective]
  exact weightedPolynomialOrder_killCompl_le _ _ Subtype.val_injective P

/- An invertible triangular change: every pivot is translated by a polynomial
in the complementary variables, which themselves are fixed. -/
open scoped Classical in
def complementShear [CommSemiring R] (g : B → MvPolynomial C R) :
    MvPolynomial (B ⊕ C) R →ₐ[R] MvPolynomial (B ⊕ C) R :=
  MvPolynomial.aeval (Sum.elim
    (fun b => MvPolynomial.X (Sum.inl b) + MvPolynomial.rename Sum.inr (g b))
    (fun c => MvPolynomial.X (Sum.inr c)))

open scoped Classical in
open scoped Classical in
def complementShear_X_inl [CommSemiring R] (g : B → MvPolynomial C R) (b : B) :
    complementShear g (MvPolynomial.X (Sum.inl b)) =
      MvPolynomial.X (Sum.inl b) + MvPolynomial.rename Sum.inr (g b) := by simp [complementShear]

open scoped Classical in
def complementShear_X_inr [CommSemiring R] (g : B → MvPolynomial C R) (c : C) :
    complementShear g (MvPolynomial.X (Sum.inr c)) = MvPolynomial.X (Sum.inr c) := by
  simp [complementShear]

open scoped Classical in
def complementShear_rename_inr [CommSemiring R] (g : B → MvPolynomial C R)
    (P : MvPolynomial C R) :
    complementShear g (MvPolynomial.rename Sum.inr P) = MvPolynomial.rename Sum.inr P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P c hP => simp only [map_mul, MvPolynomial.rename_X, complementShear_X_inr, hP]

open scoped Classical in
def complementShear_comp [CommSemiring R] (g h : B → MvPolynomial C R)
    (P : MvPolynomial (B ⊕ C) R) :
    complementShear g (complementShear h P) = complementShear (g + h) P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i <;> simp only [map_mul, complementShear_X_inl, complementShear_X_inr,
      map_add, complementShear_rename_inr, Pi.add_apply, hP, add_assoc]

open scoped Classical in
def complementShear_zero [CommSemiring R] (P : MvPolynomial (B ⊕ C) R) :
    complementShear (0 : B → MvPolynomial C R) P = P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i <;> simp only [map_mul, complementShear_X_inl, complementShear_X_inr,
      Pi.zero_apply, map_zero, add_zero, hP]

open scoped Classical in
def complementShear_inverse [CommRing R] (g : B → MvPolynomial C R)
    (P : MvPolynomial (B ⊕ C) R) : complementShear (-g) (complementShear g P) = P := by
  rw [complementShear_comp, neg_add_cancel, complementShear_zero]

open scoped Classical in
def complementShear_injective [CommRing R] (g : B → MvPolynomial C R) :
    Function.Injective (complementShear g) := by
  intro P Q h
  have hh := congrArg (complementShear (-g)) h
  simpa only [complementShear_inverse] using hh

open scoped Classical in
def zeroVariable_rename_inr [CommSemiring R] (c : C) (P : MvPolynomial C R) :
    zeroVariable (Sum.inr c : B ⊕ C) (MvPolynomial.rename Sum.inr P) =
      MvPolynomial.rename Sum.inr (zeroVariable c P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [map_mul, MvPolynomial.rename_X, zeroVariable_X, Sum.inr.injEq, hP]
    split_ifs <;> simp only [map_zero, MvPolynomial.rename_X]

open scoped Classical in
def zeroVariable_complementShear [CommSemiring R] (g : B → MvPolynomial C R)
    (c : C) (P : MvPolynomial (B ⊕ C) R) :
    zeroVariable (Sum.inr c) (complementShear g P) =
      complementShear (fun b => zeroVariable c (g b)) (zeroVariable (Sum.inr c) P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i with
    | inl b =>
      simp only [map_mul, complementShear_X_inl, map_add, zeroVariable_X,
        Sum.inl_ne_inr, if_false, zeroVariable_rename_inr, hP]
    | inr i =>
      simp only [map_mul, complementShear_X_inr, zeroVariable_X, Sum.inr.injEq, hP]
      split_ifs <;> simp only [map_zero, complementShear_X_inr]

/- The support order after the concrete inverse-form coordinate change. -/
open scoped Classical in
def complementHyperplaneIndex (w : B → ℕ) (g : B → MvPolynomial C ℚ)
    (P : MvPolynomial (B ⊕ C) ℚ) : ℕ∞ :=
  weightedPolynomialOrder (Sum.elim w (fun _ => 0)) (complementShear g P)

open scoped Classical in
def zeroVariable_map {S : Type*} [CommSemiring R] [CommSemiring S]
    (f : R →+* S) (z : I) (P : MvPolynomial I R) :
    MvPolynomial.map f (zeroVariable z P) = zeroVariable z (MvPolynomial.map f P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [map_mul, MvPolynomial.map_X, zeroVariable_X, hP]
    split_ifs <;> simp only [map_zero, MvPolynomial.map_X]

open scoped Classical in
def zeroVariable_degreeOf_self [CommSemiring R] (z : I) (P : MvPolynomial I R) :
    (zeroVariable z P).degreeOf z = 0 := by
  apply Nat.eq_zero_of_le_zero
  apply MvPolynomial.degreeOf_le_iff.mpr
  intro e he
  rw [zeroVariable_eq_rename_specialization,
    MvPolynomial.support_rename_of_injective Subtype.val_injective] at he
  obtain ⟨d, _, rfl⟩ := Finset.mem_image.mp he
  apply Nat.le_zero.mpr
  apply Finsupp.mapDomain_of_not_mem_image_support
  rintro ⟨i, _, hi⟩
  exact i.property hi

open scoped Classical in
def complementHyperplaneIndex_saturation (w : B → ℕ)
    (g : B → MvPolynomial C ℚ) (c : C) (k : ℕ) (P : MvPolynomial (B ⊕ C) ℚ) :
    complementHyperplaneIndex w g (MvPolynomial.X (Sum.inr c) ^ k * P) =
      complementHyperplaneIndex w g P := by
  unfold complementHyperplaneIndex
  rw [map_mul, map_pow, complementShear_X_inr, weightedPolynomialOrder_mul,
    MvPolynomial.X_pow_eq_monomial, weightedPolynomialOrder_monomial_one]
  simp only [Finsupp.weight_single, Sum.elim_inr, smul_zero, Nat.cast_zero, zero_add]

open scoped Classical in
def complementHyperplaneIndex_specialization (w : B → ℕ)
    (g : B → MvPolynomial C ℚ) (c : C) (P : MvPolynomial (B ⊕ C) ℚ) :
    complementHyperplaneIndex w g P ≤
      complementHyperplaneIndex w (fun b => zeroVariable c (g b)) (zeroVariable (Sum.inr c) P) := by
  have hh := zeroVariable_order_le (Sum.elim w (fun _ => 0)) (Sum.inr c) (complementShear g P)
  rw [zeroVariable_complementShear] at hh
  exact hh

/- Fixed block degrees, expressed using the concrete weights of a block map. -/
open scoped Classical in
def MultiBlockHomogeneous {H : Type*} [CommSemiring R]
    (block : I → H) (r : H → ℕ) (P : MvPolynomial I R) : Prop :=
  ∀ h, MvPolynomial.IsWeightedHomogeneous (fun i => if block i = h then 1 else 0) P (r h)

open scoped Classical in
def weightedHomogeneous_divMonomial [CommSemiring R] (w : I → ℕ)
    (P : MvPolynomial I R) (n : ℕ) (hP : MvPolynomial.IsWeightedHomogeneous w P n)
    (s : I →₀ ℕ) :
    MvPolynomial.IsWeightedHomogeneous w (P.divMonomial s) (n - Finsupp.weight w s) := by
  intro e he
  rw [MvPolynomial.coeff_divMonomial] at he
  have hh := hP he
  rw [map_add] at hh
  omega

open scoped Classical in
def weightedHomogeneous_zeroVariable [CommSemiring R] (w : I → ℕ)
    (P : MvPolynomial I R) (n : ℕ) (hP : MvPolynomial.IsWeightedHomogeneous w P n)
    (z : I) : MvPolynomial.IsWeightedHomogeneous w (zeroVariable z P) n := by
  intro e he
  exact hP (MvPolynomial.mem_support_iff.mp
    (zeroVariable_support_subset z P (MvPolynomial.mem_support_iff.mpr he)))

/- An actual integer coefficient slice in a complementary variable preserves
nonzero, lowers block degrees, and cannot lower the concrete hyperplane index. -/
open scoped Classical in
def exists_integer_complement_specialization {H : Type*} [DecidableEq H]
    (block : B ⊕ C → H) (r : H → ℕ) (w : B → ℕ) (g : B → MvPolynomial C ℚ)
    (c : C) (P : MvPolynomial (B ⊕ C) ℤ) (hP : P ≠ 0) (hhom : MultiBlockHomogeneous block r P) :
    ∃ k : ℕ, ∃ Q : MvPolynomial (B ⊕ C) ℤ,
      Q = zeroVariable (Sum.inr c) (P.divMonomial (Finsupp.single (Sum.inr c) k)) ∧
      Q ≠ 0 ∧ Q.degreeOf (Sum.inr c) = 0 ∧
      (∀ i, Q.degreeOf i ≤ P.degreeOf i) ∧ polynomialCoeffL1 Q ≤ polynomialCoeffL1 P ∧
      MultiBlockHomogeneous block (fun h => r h - if block (Sum.inr c) = h then k else 0) Q ∧
      complementHyperplaneIndex w g (MvPolynomial.map (Int.castRingHom ℚ) P) ≤
        complementHyperplaneIndex w (fun b => zeroVariable c (g b))
          (MvPolynomial.map (Int.castRingHom ℚ) Q) := by
  classical
  obtain ⟨d, hd, hmin⟩ := P.support.exists_min_image (fun e => e (Sum.inr c))
    (MvPolynomial.support_nonempty.mpr hP)
  let k := d (Sum.inr c)
  let V := P.divMonomial (Finsupp.single (Sum.inr c) k)
  let Q := zeroVariable (Sum.inr c) V
  have hdiv : ∀ e ∈ P.support, Finsupp.single (Sum.inr c) k ≤ e := by
    intro e he
    exact Finsupp.single_le_iff.mpr (hmin e he)
  have hfactor : P = MvPolynomial.X (Sum.inr c) ^ k * V := by
    rw [MvPolynomial.X_pow_eq_monomial]
    exact (monomial_mul_divMonomial_of_support P _ hdiv).symm
  have hQ : Q ≠ 0 := by
    rw [show Q = MvPolynomial.rename Subtype.val (coordinateSlice (Sum.inr c) k P) from
      zeroVariable_eq_rename_specialization _ _]
    exact fun hz => (coordinateSlice_ne_zero_of_coeff (Sum.inr c) P
      (MvPolynomial.mem_support_iff.mp hd))
      ((MvPolynomial.rename_eq_zero_iff_of_injective _ Subtype.val_injective).mp hz)
  refine ⟨k, Q, rfl, hQ, zeroVariable_degreeOf_self _ _, ?_, ?_, ?_, ?_⟩
  · intro i
    exact (zeroVariable_degreeOf_le _ _ i).trans (degreeOf_divMonomial_le P _ i)
  · exact (zeroVariable_coeffL1_le _ V).trans (polynomialCoeffL1_divMonomial_le P _)
  · intro h
    have hh := weightedHomogeneous_zeroVariable _ V _
      (weightedHomogeneous_divMonomial _ P _ (hhom h) _) (Sum.inr c)
    simpa only [Finsupp.weight_single, smul_eq_mul, mul_ite, mul_one, mul_zero] using hh
  · have hh := complementHyperplaneIndex_specialization w g c
      (MvPolynomial.map (Int.castRingHom ℚ) V)
    have hf := congrArg (MvPolynomial.map (Int.castRingHom ℚ)) hfactor
    simp only [map_mul, map_pow, MvPolynomial.map_X] at hf
    rw [← zeroVariable_map] at hh
    rw [hf, complementHyperplaneIndex_saturation]
    exact hh


end
end Bounty

end SubmissionComponent_RationalHyperplaneIndex

/- Component BalancedMonomialCounting; SHA256 1707de2028969a92cf3881739d0bf662b6e44eb9bd72d62a885e0373addd8d6d -/
section SubmissionComponent_BalancedMonomialCounting
/- Exact finite second-moment counting for arrays of weak compositions. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def finite_product_mixed_sum_zero
    {I : Type*} [Fintype I] [DecidableEq I]
    {β : I → Type*} [∀ i, Fintype (β i)]
    (f : ∀ i, β i → ℝ) (hf : ∀ i, ∑ t, f i t = 0)
    {i j : I} (hij : i ≠ j) :
    ∑ x : ∀ i, β i, f i (x i) * f j (x j) = 0 := by
  classical
  have hji : j ≠ i := Ne.symm hij
  calc
    _ = ∑ y : β i × (∀ a : {a // a ≠ i}, β a),
        f i y.1 * f j (y.2 ⟨j, hji⟩) := by
      apply Fintype.sum_equiv (Equiv.piSplitAt i β)
      intro x
      rfl
    _ = 0 := by
      rw [Fintype.sum_prod_type]
      simp_rw [← Finset.mul_sum]
      rw [← Finset.sum_mul, hf i, zero_mul]

def finite_product_second_moment
    {I : Type*} [Fintype I] [DecidableEq I]
    {β : I → Type*} [∀ i, Fintype (β i)]
    (f : ∀ i, β i → ℝ) (hf : ∀ i, ∑ t, f i t = 0) :
    (∑ x : ∀ i, β i, (∑ i, f i (x i)) ^ 2) =
      ∑ i, ∑ x : ∀ i, β i, (f i (x i)) ^ 2 := by
  classical
  simp_rw [pow_two, Fintype.sum_mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  rw [Finset.sum_comm]
  rw [Finset.sum_eq_single i]
  · intro j _ hji
    exact finite_product_mixed_sum_zero f hf (Ne.symm hji)
  · simp

def finite_product_second_moment_le
    {I : Type*} [Fintype I] [DecidableEq I]
    {β : I → Type*} [∀ i, Fintype (β i)]
    (f : ∀ i, β i → ℝ) (hf : ∀ i, ∑ t, f i t = 0)
    (hbound : ∀ i t, (f i t) ^ 2 ≤ 1) :
    (∑ x : ∀ i, β i, (∑ i, f i (x i)) ^ 2) ≤
      (Fintype.card (∀ i, β i) : ℝ) * Fintype.card I := by
  rw [finite_product_second_moment f hf]
  calc
    _ ≤ ∑ _i : I, ∑ _x : ∀ i, β i, (1 : ℝ) := by
      exact Finset.sum_le_sum fun i _ => Finset.sum_le_sum fun x _ => hbound i (x i)
    _ = _ := by simp [mul_comm]

abbrev WeakComposition (d r : ℕ) := ↥(Finset.Nat.antidiagonalTuple d r)

def weakComposition_sum {d r : ℕ} (v : WeakComposition d r) :
    ∑ i, v.val i = r := Finset.Nat.mem_antidiagonalTuple.mp v.property

def weakComposition_coord_le {d r : ℕ} (v : WeakComposition d r) (i : Fin d) :
    v.val i ≤ r := by
  exact (Finset.single_le_sum (fun _ _ => Nat.zero_le _) (Finset.mem_univ i)).trans_eq
    (weakComposition_sum v)

def weakCompositionPerm {d r : ℕ} (e : Equiv.Perm (Fin d)) :
    WeakComposition d r ≃ WeakComposition d r where
  toFun v := ⟨fun i => v.val (e i), Finset.Nat.mem_antidiagonalTuple.mpr
    ((Equiv.sum_comp e v.val).trans (weakComposition_sum v))⟩
  invFun v := ⟨fun i => v.val (e.symm i), Finset.Nat.mem_antidiagonalTuple.mpr
    ((Equiv.sum_comp e.symm v.val).trans (weakComposition_sum v))⟩
  left_inv v := by ext i; simp
  right_inv v := by ext i; simp

def weakComposition_coordinate_sum_eq {d r : ℕ} (i j : Fin d) :
    (∑ v : WeakComposition d r, (v.val i : ℝ)) =
      ∑ v : WeakComposition d r, (v.val j : ℝ) := by
  classical
  apply Fintype.sum_equiv (weakCompositionPerm (r := r) (Equiv.swap i j))
  intro v
  simp [weakCompositionPerm]

def weakComposition_coordinate_sum {d r : ℕ} (i : Fin d) :
    (d : ℝ) * (∑ v : WeakComposition d r, (v.val i : ℝ)) =
      (Fintype.card (WeakComposition d r) : ℝ) * r := by
  calc
    _ = ∑ j : Fin d, ∑ v : WeakComposition d r, (v.val j : ℝ) := by
      simp_rw [← weakComposition_coordinate_sum_eq i]
      simp
    _ = ∑ v : WeakComposition d r, ∑ j : Fin d, (v.val j : ℝ) :=
      Finset.sum_comm
    _ = _ := by
      simp_rw [← Nat.cast_sum, weakComposition_sum]
      simp

def compositionCentered {d r : ℕ} (i : Fin d) (v : WeakComposition d r) : ℝ :=
  (v.val i : ℝ) / r - 1 / d

def compositionCentered_sum {d r : ℕ} (hd : 0 < d) (hr : 0 < r) (i : Fin d) :
    ∑ v : WeakComposition d r, compositionCentered i v = 0 := by
  have hd0 : (d : ℝ) ≠ 0 := by positivity
  have hr0 : (r : ℝ) ≠ 0 := by positivity
  have hs := weakComposition_coordinate_sum (r := r) i
  simp only [compositionCentered, Finset.sum_sub_distrib, ← Finset.sum_div,
    Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
  field_simp
  nlinarith

def compositionCentered_sq_le_one {d r : ℕ} (hd : 0 < d) (hr : 0 < r)
    (i : Fin d) (v : WeakComposition d r) : (compositionCentered i v) ^ 2 ≤ 1 := by
  have hd1 : (1 : ℝ) ≤ d := by exact_mod_cast hd
  have hr0 : (0 : ℝ) < r := by positivity
  have hc0 : (0 : ℝ) ≤ v.val i := by positivity
  have hc1 : (v.val i : ℝ) ≤ r := by exact_mod_cast weakComposition_coord_le v i
  have hq0 : (0 : ℝ) ≤ (v.val i : ℝ) / r := div_nonneg hc0 (le_of_lt hr0)
  have hq1 : (v.val i : ℝ) / r ≤ 1 := (div_le_one hr0).mpr hc1
  have hz0 : (0 : ℝ) ≤ 1 / d := by positivity
  have hz1 : (1 : ℝ) / d ≤ 1 := (div_le_one (by positivity)).mpr hd1
  dsimp [compositionCentered]
  nlinarith [mul_nonneg (sub_nonneg.mpr hq1) hq0,
    mul_nonneg (sub_nonneg.mpr hz1) hz0]

abbrev CompositionArray (m d : ℕ) (r : Fin m → ℕ) :=
  ∀ h : Fin m, WeakComposition d (r h)

def compositionArray_nonempty {m d : ℕ} (r : Fin m → ℕ) (hd : 0 < d) :
    Nonempty (CompositionArray m d r) := by
  classical
  refine ⟨fun h => ⟨fun i => if i = (⟨0, hd⟩ : Fin d) then r h else 0, ?_⟩⟩
  apply Finset.Nat.mem_antidiagonalTuple.mpr
  simp

def compositionArray_card_pos {m d : ℕ} (r : Fin m → ℕ) (hd : 0 < d) :
    0 < Fintype.card (CompositionArray m d r) :=
  Fintype.card_pos_iff.mpr (compositionArray_nonempty r hd)

def compositionDeviation {m d : ℕ} {r : Fin m → ℕ}
    (i : Fin d) (J : CompositionArray m d r) : ℝ :=
  (∑ h, ((J h).val i : ℝ) / r h) - (m : ℝ) / d

def compositionDeviation_eq_sum {m d : ℕ} {r : Fin m → ℕ}
    (i : Fin d) (J : CompositionArray m d r) :
    compositionDeviation i J = ∑ h, compositionCentered i (J h) := by
  simp [compositionDeviation, compositionCentered, Finset.sum_sub_distrib, div_eq_mul_inv]

def compositionArray_second_moment {m d : ℕ} (r : Fin m → ℕ)
    (hd : 0 < d) (hr : ∀ h, 0 < r h) (i : Fin d) :
    (∑ J : CompositionArray m d r, (compositionDeviation i J) ^ 2) ≤
      (Fintype.card (CompositionArray m d r) : ℝ) * m := by
  simp_rw [compositionDeviation_eq_sum]
  simpa using finite_product_second_moment_le
    (fun h (v : WeakComposition d (r h)) => compositionCentered i v)
    (fun h => compositionCentered_sum hd (hr h) i)
    (fun h => compositionCentered_sq_le_one hd (hr h) i)

def finite_bad_card_sq_le {Ω : Type*} [Fintype Ω]
    (f : Ω → ℝ) (a : ℝ) (ha : 0 ≤ a) :
    ((Finset.univ.filter (fun x => a ≤ |f x|)).card : ℝ) * a ^ 2 ≤
      ∑ x, (f x) ^ 2 := by
  classical
  calc
    _ = ∑ _x ∈ Finset.univ.filter (fun x => a ≤ |f x|), a ^ 2 := by simp
    _ ≤ ∑ x ∈ Finset.univ.filter (fun x => a ≤ |f x|), (f x) ^ 2 := by
      apply Finset.sum_le_sum
      intro x hx
      have hx' := (Finset.mem_filter.mp hx).2
      nlinarith [sq_abs (f x), mul_nonneg (sub_nonneg.mpr hx') (add_nonneg (abs_nonneg (f x)) ha)]
    _ ≤ ∑ x, (f x) ^ 2 :=
      Finset.sum_le_sum_of_subset_of_nonneg (Finset.filter_subset _ _)
        (fun x _ _ => sq_nonneg (f x))

def badCompositionCoordinate {m d : ℕ} (r : Fin m → ℕ) (η : ℝ) (i : Fin d) :
    Finset (CompositionArray m d r) := by
  classical
  exact Finset.univ.filter (fun J => (m : ℝ) * η ≤ |compositionDeviation i J|)

def badCompositionCoordinate_card_bound {m d : ℕ} (r : Fin m → ℕ)
    (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (η : ℝ) (hη : 0 ≤ η) (i : Fin d) :
    ((badCompositionCoordinate r η i).card : ℝ) * m * η ^ 2 ≤
      Fintype.card (CompositionArray m d r) := by
  have hm' : (0 : ℝ) < m := by positivity
  have hfirst := finite_bad_card_sq_le (compositionDeviation (r := r) i)
    ((m : ℝ) * η) (mul_nonneg (le_of_lt hm') hη)
  have hsecond := compositionArray_second_moment r hd hr i
  change ((badCompositionCoordinate r η i).card : ℝ) * ((m : ℝ) * η) ^ 2 ≤ _ at hfirst
  have hle : (m : ℝ) * (((badCompositionCoordinate r η i).card : ℝ) * m * η ^ 2) ≤
      (m : ℝ) * Fintype.card (CompositionArray m d r) := by nlinarith
  exact (mul_le_mul_iff_right₀ hm').mp hle

def badCompositionArrays {m d : ℕ} (r : Fin m → ℕ) (η : ℝ) :
    Finset (CompositionArray m d r) := by
  classical
  exact Finset.univ.biUnion (badCompositionCoordinate r η)

def mem_badCompositionArrays {m d : ℕ} (r : Fin m → ℕ) (η : ℝ)
    (J : CompositionArray m d r) :
    J ∈ badCompositionArrays r η ↔
      ∃ i : Fin d, (m : ℝ) * η ≤ |compositionDeviation i J| := by
  classical
  simp [badCompositionArrays, badCompositionCoordinate]

def not_mem_badCompositionArrays {m d : ℕ} (r : Fin m → ℕ) (η : ℝ)
    (J : CompositionArray m d r) :
    J ∉ badCompositionArrays r η ↔
      ∀ i : Fin d, |compositionDeviation i J| < (m : ℝ) * η := by
  rw [mem_badCompositionArrays]
  simp

def badCompositionArrays_card_bound {m d : ℕ} (r : Fin m → ℕ)
    (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (η : ℝ) (hη : 0 ≤ η) :
    ((badCompositionArrays (d := d) r η).card : ℝ) * m * η ^ 2 ≤
      (d : ℝ) * Fintype.card (CompositionArray m d r) := by
  classical
  have hu : (badCompositionArrays (d := d) r η).card ≤
      ∑ i : Fin d, (badCompositionCoordinate r η i).card := Finset.card_biUnion_le
  have hu' : ((badCompositionArrays (d := d) r η).card : ℝ) ≤
      ∑ i : Fin d, ((badCompositionCoordinate r η i).card : ℝ) := by exact_mod_cast hu
  calc
    _ = ((badCompositionArrays (d := d) r η).card : ℝ) * ((m : ℝ) * η ^ 2) := by ring
    _ ≤ (∑ i : Fin d, ((badCompositionCoordinate r η i).card : ℝ)) *
        ((m : ℝ) * η ^ 2) := mul_le_mul_of_nonneg_right hu' (by positivity)
    _ = ∑ i : Fin d, ((badCompositionCoordinate r η i).card : ℝ) * m * η ^ 2 := by
      rw [Finset.sum_mul]
      apply Finset.sum_congr rfl
      intro i _
      ring
    _ ≤ ∑ _i : Fin d, (Fintype.card (CompositionArray m d r) : ℝ) :=
      Finset.sum_le_sum fun i _ => badCompositionCoordinate_card_bound r hm hd hr η hη i
    _ = _ := by simp

def badCompositionArrays_quarter {m d : ℕ} (r : Fin m → ℕ)
    (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (s : ℕ) (η : ℝ) (hη : 0 ≤ η)
    (hlarge : 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2) :
    4 * (s * (badCompositionArrays (d := d) r η).card) ≤ Fintype.card (CompositionArray m d r) := by
  have hd' : (0 : ℝ) < d := by positivity
  have hbound := badCompositionArrays_card_bound r hm hd hr η hη
  have hle : (d : ℝ) * (4 * (s : ℝ) * (badCompositionArrays (d := d) r η).card) ≤
      (d : ℝ) * Fintype.card (CompositionArray m d r) := by
    calc
      _ = ((badCompositionArrays (d := d) r η).card : ℝ) * (4 * (s : ℝ) * d) := by ring
      _ ≤ ((badCompositionArrays (d := d) r η).card : ℝ) * ((m : ℝ) * η ^ 2) :=
        mul_le_mul_of_nonneg_left hlarge (by positivity)
      _ ≤ _ := by simpa [mul_assoc] using hbound
  have hle' := (mul_le_mul_iff_right₀ hd').mp hle
  rw [← mul_assoc]
  exact_mod_cast hle'


end
end Bounty

end SubmissionComponent_BalancedMonomialCounting

/- Component IntegerSmallKernel; SHA256 dee44ae4bf41e5bc51f97b9207be460928d6ffd0421111822775745ee89dc436 -/
section SubmissionComponent_IntegerSmallKernel
/- A coefficient-sum form of the integer small-kernel lemma for at most half as many equations. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Matrix

def exists_integer_small_kernel {I J : Type*} [Fintype I] [Fintype J]
    (A : Matrix I J ℤ) (hN : 0 < Fintype.card J)
    (hhalf : 2 * Fintype.card I ≤ Fintype.card J)
    (H : ℝ) (hH : 1 ≤ H) (hentry : ∀ i j, ‖A i j‖ ≤ H) :
    ∃ c : J → ℤ, c ≠ 0 ∧ A *ᵥ c = 0 ∧
      (∀ j, ‖c j‖ ≤ Fintype.card J * H) ∧
      (∑ j, ‖c j‖) ≤ (Fintype.card J : ℝ) ^ 2 * H := by
  classical
  letI : SeminormedAddCommGroup (Matrix I J ℤ) := Matrix.seminormedAddCommGroup
  have hNreal : (1 : ℝ) ≤ Fintype.card J := by exact_mod_cast hN
  have hprod : 1 ≤ (Fintype.card J : ℝ) * H := one_le_mul_of_one_le_of_one_le hNreal hH
  suffices hh : ∃ c : J → ℤ, c ≠ 0 ∧ A *ᵥ c = 0 ∧
      (∀ j, ‖c j‖ ≤ Fintype.card J * H) by
    obtain ⟨c, hc, hAc, hbound⟩ := hh
    refine ⟨c, hc, hAc, hbound, ?_⟩
    calc
      ∑ j, ‖c j‖ ≤ ∑ _j : J, (Fintype.card J : ℝ) * H := Finset.sum_le_sum (fun j _ => hbound j)
      _ = (Fintype.card J : ℝ) ^ 2 * H := by simp; ring
  by_cases hm : 0 < Fintype.card I
  · have hlt : Fintype.card I < Fintype.card J := by omega
    obtain ⟨c, hc, hAc, hnorm⟩ := Int.Matrix.exists_ne_zero_int_vec_norm_le A hlt hm
    have hAnorm : ‖A‖ ≤ H := (Matrix.norm_le_iff (by linarith : 0 ≤ H)).mpr hentry
    have hb : 1 ≤ (Fintype.card J : ℝ) * max 1 ‖A‖ :=
      one_le_mul_of_one_le_of_one_le hNreal (le_max_left _ _)
    have hden : (0 : ℝ) < Fintype.card J - Fintype.card I :=
      sub_pos.mpr (by exact_mod_cast hlt)
    have he : (Fintype.card I : ℝ) / (Fintype.card J - Fintype.card I) ≤ 1 := by
      apply (div_le_one hden).mpr
      have hh : 2 * (Fintype.card I : ℝ) ≤ Fintype.card J := by exact_mod_cast hhalf
      linarith
    have hp := Real.rpow_le_rpow_of_exponent_le hb he
    rw [Real.rpow_one] at hp
    have hsmall : ‖c‖ ≤ (Fintype.card J : ℝ) * H := hnorm.trans (hp.trans
      (mul_le_mul_of_nonneg_left (max_le hH hAnorm) (Nat.cast_nonneg _)))
    exact ⟨c, hc, hAc, fun j => (norm_le_pi_norm c j).trans hsmall⟩
  · have hz : Fintype.card I = 0 := by omega
    letI : IsEmpty I := Fintype.card_eq_zero_iff.mp hz
    obtain ⟨j⟩ := Fintype.card_pos_iff.mp hN
    refine ⟨fun _ => 1, ?_, ?_, ?_⟩
    · intro h
      have hh := congrFun h j
      norm_num at hh
    · ext i
      exact isEmptyElim i
    · intro j
      simpa using hprod


end
end Bounty

end SubmissionComponent_IntegerSmallKernel

/- Component AuxiliaryPolynomialKernel; SHA256 e77ff86c8268168d08db3f0094d85f28f661f36ccecc2760f58166b6114ff002 -/
section SubmissionComponent_AuxiliaryPolynomialKernel
/- Actual nonzero integer polynomials satisfying finitely many small linear conditions. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Matrix

def indexedIntegerPolynomial {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (c : J → ℤ) : MvPolynomial V ℤ :=
  ∑ j, MvPolynomial.monomial (e j) (c j)

def indexedIntegerPolynomial_coeff {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (he : Function.Injective e) (c : J → ℤ) (j : J) :
    MvPolynomial.coeff (e j) (indexedIntegerPolynomial e c) = c j := by
  classical
  simp only [indexedIntegerPolynomial, MvPolynomial.coeff_sum, MvPolynomial.coeff_monomial]
  rw [Finset.sum_eq_single j]
  · simp
  · intro k _ hk
    rw [if_neg (fun h => hk (he h))]
  · simp

def indexedIntegerPolynomial_ne_zero {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (he : Function.Injective e) {c : J → ℤ} (hc : c ≠ 0) :
    indexedIntegerPolynomial e c ≠ 0 := by
  intro hz
  apply hc
  funext j
  have hh := indexedIntegerPolynomial_coeff e he c j
  simpa only [hz, MvPolynomial.coeff_zero, Pi.zero_apply] using hh.symm

def indexedIntegerPolynomial_support {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (c : J → ℤ) {a : V →₀ ℕ}
    (ha : a ∈ (indexedIntegerPolynomial e c).support) : ∃ j, e j = a := by
  classical
  by_contra hh
  push Not at hh
  apply MvPolynomial.mem_support_iff.mp ha
  simp only [indexedIntegerPolynomial, MvPolynomial.coeff_sum, MvPolynomial.coeff_monomial]
  exact Finset.sum_eq_zero (fun j _ => if_neg (hh j))

def indexedIntegerPolynomial_norm_le {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (c : J → ℤ) :
    polynomialCoeffL1 (indexedIntegerPolynomial e c) ≤ ∑ j, ‖c j‖ := by
  simpa only [indexedIntegerPolynomial, polynomialCoeffL1_monomial] using
    polynomialCoeffL1_sum Finset.univ (fun j => MvPolynomial.monomial (e j) (c j))

def indexedIntegerPolynomial_linearMap {V J : Type*} [Fintype J]
    (e : J → V →₀ ℕ) (c : J → ℤ) (F : MvPolynomial V ℤ →ₗ[ℤ] ℤ) :
    F (indexedIntegerPolynomial e c) = ∑ j, F (MvPolynomial.monomial (e j) 1) * c j := by
  simp only [indexedIntegerPolynomial, map_sum]
  apply Finset.sum_congr rfl
  intro j _
  have hh : MvPolynomial.monomial (e j) (c j) = c j • MvPolynomial.monomial (e j) (1 : ℤ) := by
    rw [MvPolynomial.smul_monomial, smul_eq_mul, mul_one]
  rw [hh, map_smul, smul_eq_mul, mul_comm]

def exists_small_integer_auxiliary_polynomial {V I J : Type*} [Fintype I] [Fintype J]
    (e : J → V →₀ ℕ) (he : Function.Injective e)
    (F : I → MvPolynomial V ℤ →ₗ[ℤ] ℤ)
    (hN : 0 < Fintype.card J) (hhalf : 2 * Fintype.card I ≤ Fintype.card J)
    (H : ℝ) (hH : 1 ≤ H)
    (hentry : ∀ i j, ‖F i (MvPolynomial.monomial (e j) 1)‖ ≤ H) :
    ∃ P : MvPolynomial V ℤ, P ≠ 0 ∧
      (∀ a ∈ P.support, ∃ j, e j = a) ∧ (∀ i, F i P = 0) ∧
      polynomialCoeffL1 P ≤ (Fintype.card J : ℝ) ^ 2 * H := by
  let A : Matrix I J ℤ := fun i j => F i (MvPolynomial.monomial (e j) 1)
  obtain ⟨c, hc, hAc, _, hsum⟩ := exists_integer_small_kernel A hN hhalf H hH hentry
  refine ⟨indexedIntegerPolynomial e c, indexedIntegerPolynomial_ne_zero e he hc,
    fun a ha => indexedIntegerPolynomial_support e c ha, ?_,
    (indexedIntegerPolynomial_norm_le e c).trans hsum⟩
  intro i
  rw [indexedIntegerPolynomial_linearMap]
  exact congrFun hAc i


end
end Bounty

end SubmissionComponent_AuxiliaryPolynomialKernel

/- Component PolynomialSubstitutionNorm; SHA256 4c5a98171eb2c58a8019c0dc230dcb91d61ed6b85677e9d608c4db125718ef9d -/
section SubmissionComponent_PolynomialSubstitutionNorm
/- Explicit coefficient-sum bounds for substituted monomials. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def polynomialCoeffL1_pow {V R : Type*} [NormedCommRing R] [NormOneClass R]
    (P : MvPolynomial V R) (n : ℕ) : polynomialCoeffL1 (P ^ n) ≤ polynomialCoeffL1 P ^ n := by
  induction n with
  | zero => simp [polynomialCoeffL1_one]
  | succ n ih =>
    rw [pow_succ, pow_succ]
    exact (polynomialCoeffL1_mul _ _).trans
      (mul_le_mul_of_nonneg_right ih (polynomialCoeffL1_nonneg P))

def polynomialCoeffL1_aeval_monomial_one {I V : Type*} [Fintype I]
    (f : I → MvPolynomial V ℤ) (e : I →₀ ℕ) {C : ℝ}
    (hC : 0 ≤ C) (hf : ∀ i, polynomialCoeffL1 (f i) ≤ C) :
    polynomialCoeffL1 (MvPolynomial.aeval f (MvPolynomial.monomial e (1 : ℤ))) ≤
      C ^ (∑ i, e i) := by
  classical
  rw [MvPolynomial.aeval_monomial]
  simp only [map_one, one_mul]
  rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _)]
  calc
    _ ≤ ∏ i, polynomialCoeffL1 (f i ^ e i) := polynomialCoeffL1_prod _ _
    _ ≤ ∏ i, polynomialCoeffL1 (f i) ^ e i :=
      Finset.prod_le_prod (fun i _ => polynomialCoeffL1_nonneg _) (fun i _ => polynomialCoeffL1_pow _ _)
    _ ≤ ∏ i, C ^ e i := Finset.prod_le_prod
      (fun i _ => pow_nonneg (polynomialCoeffL1_nonneg _) _)
      (fun i _ => pow_le_pow_left₀ (polynomialCoeffL1_nonneg _) (hf i) _)
    _ = C ^ (∑ i, e i) := Finset.prod_pow_eq_pow_sum _ _ _

def norm_coeff_aeval_monomial_one_le {I V : Type*} [Fintype I]
    (f : I → MvPolynomial V ℤ) (e : I →₀ ℕ) (a : V →₀ ℕ) {C : ℝ}
    (hC : 0 ≤ C) (hf : ∀ i, polynomialCoeffL1 (f i) ≤ C) :
    ‖MvPolynomial.coeff a (MvPolynomial.aeval f (MvPolynomial.monomial e (1 : ℤ)))‖ ≤
      C ^ (∑ i, e i) :=
  (norm_coeff_le_polynomialCoeffL1 _ _).trans (polynomialCoeffL1_aeval_monomial_one f e hC hf)

end
end Bounty

end SubmissionComponent_PolynomialSubstitutionNorm

/- Component BalancedAuxiliaryPolynomial; SHA256 dc164d0e99dfddc7eb1bef11f7577aca766e3616652c14a4928dddc2d32310e0 -/
section SubmissionComponent_BalancedAuxiliaryPolynomial
/- An actual nonzero integer auxiliary polynomial with balanced monomial
support after finitely many integer changes of coordinates within blocks. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def compositionExponent {m d : ℕ} {r : Fin m → ℕ}
    (J : CompositionArray m d r) : (Fin m × Fin d) →₀ ℕ :=
  Finsupp.equivFunOnFinite.symm (fun x => (J x.1).val x.2)

def compositionExponent_apply {m d : ℕ} {r : Fin m → ℕ}
    (J : CompositionArray m d r) (h : Fin m) (i : Fin d) :
    compositionExponent J (h, i) = (J h).val i := rfl

def compositionExponent_injective {m d : ℕ} (r : Fin m → ℕ) :
    Function.Injective (compositionExponent (m := m) (d := d) (r := r)) := by
  intro J K hJK
  funext h
  apply Subtype.ext
  funext i
  exact congrArg (fun e : (Fin m × Fin d) →₀ ℕ => e (h, i)) hJK

def compositionExponent_block_sum {m d : ℕ} {r : Fin m → ℕ}
    (J : CompositionArray m d r) (h : Fin m) :
    ∑ i, compositionExponent J (h, i) = r h := weakComposition_sum (J h)

def compositionExponent_total {m d : ℕ} {r : Fin m → ℕ}
    (J : CompositionArray m d r) :
    ∑ x : Fin m × Fin d, compositionExponent J x = ∑ h, r h := by
  rw [Fintype.sum_prod_type]
  simp_rw [compositionExponent_block_sum]

def exists_compositionExponent_iff {m d : ℕ} (r : Fin m → ℕ)
    (e : (Fin m × Fin d) →₀ ℕ) :
    (∃ J : CompositionArray m d r, compositionExponent J = e) ↔
      ∀ h, ∑ i, e (h, i) = r h := by
  constructor
  · rintro ⟨J, rfl⟩
    exact compositionExponent_block_sum J
  · intro he
    refine ⟨fun h => ⟨fun i => e (h, i), Finset.Nat.mem_antidiagonalTuple.mpr (he h)⟩, ?_⟩
    ext x
    rfl

def ProductBlockHomogeneous {m d : ℕ} {R : Type*} [CommSemiring R]
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) R) : Prop :=
  ∀ e ∈ P.support, ∀ h, ∑ i, e (h, i) = r h

def productBlockWeight {m d : ℕ} (h : Fin m) (x : Fin m × Fin d) : ℕ :=
  if x.1 = h then 1 else 0

def productBlockWeight_apply {m d : ℕ} (h : Fin m)
    (e : (Fin m × Fin d) →₀ ℕ) :
    Finsupp.weight (productBlockWeight h) e = ∑ i, e (h, i) := by
  rw [Finsupp.weight_eq_sum, Fintype.sum_prod_type]
  simp [productBlockWeight]

def productBlockHomogeneous_iff_weighted {m d : ℕ} {R : Type*} [CommSemiring R]
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) R) :
    ProductBlockHomogeneous r P ↔
      ∀ h, MvPolynomial.IsWeightedHomogeneous (productBlockWeight h) P (r h) := by
  constructor
  · intro hP h e he
    rw [productBlockWeight_apply]
    exact hP e (MvPolynomial.mem_support_iff.mpr he) h
  · intro hP e he h
    simpa only [productBlockWeight_apply] using hP h (MvPolynomial.mem_support_iff.mp he)

def blockLinearForm {m d : ℕ} (A : Fin m → Fin d → Fin d → ℤ)
    (x : Fin m × Fin d) : MvPolynomial (Fin m × Fin d) ℤ :=
  ∑ j, MvPolynomial.C (A x.1 x.2 j) * MvPolynomial.X (x.1, j)

def blockLinearSubstitution {m d : ℕ} (A : Fin m → Fin d → Fin d → ℤ) :
    MvPolynomial (Fin m × Fin d) ℤ →ₐ[ℤ] MvPolynomial (Fin m × Fin d) ℤ :=
  MvPolynomial.aeval (blockLinearForm A)

def blockLinearForm_homogeneous {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℤ) (h : Fin m) (x : Fin m × Fin d) :
    MvPolynomial.IsWeightedHomogeneous (productBlockWeight h)
      (blockLinearForm A x) (productBlockWeight h x) := by
  apply MvPolynomial.IsWeightedHomogeneous.sum
  intro j _
  exact (MvPolynomial.isWeightedHomogeneous_X ℤ (productBlockWeight h) (x.1, j)).C_mul _

def blockLinearSubstitution_homogeneous {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℤ) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℤ) (hP : ProductBlockHomogeneous r P) :
    ProductBlockHomogeneous r (blockLinearSubstitution A P) := by
  apply (productBlockHomogeneous_iff_weighted r _).mpr
  intro h
  exact weightedHomogeneous_aeval (productBlockWeight h) (blockLinearForm A)
    (blockLinearForm_homogeneous A h) P (r h)
    ((productBlockHomogeneous_iff_weighted r P).mp hP h)

def blockLinearForm_norm_le {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℤ) (x : Fin m × Fin d) :
    polynomialCoeffL1 (blockLinearForm A x) ≤ ∑ j, ‖A x.1 x.2 j‖ := by
  calc
    _ ≤ ∑ j, polynomialCoeffL1
        (MvPolynomial.C (A x.1 x.2 j) * MvPolynomial.X (x.1, j)) :=
      polynomialCoeffL1_sum _ _
    _ = _ := by
      apply Finset.sum_congr rfl
      intro j _
      rw [MvPolynomial.C_mul_X_eq_monomial, polynomialCoeffL1_monomial]

def balancedCoefficientCondition {m d s : ℕ} (r : Fin m → ℕ) (η : ℝ)
    (A : Fin s → Fin m → Fin d → Fin d → ℤ)
    (z : Fin s × ↥(badCompositionArrays (d := d) r η)) :
    MvPolynomial (Fin m × Fin d) ℤ →ₗ[ℤ] ℤ :=
  (MvPolynomial.lcoeff ℤ (compositionExponent z.2.val)).comp
    (blockLinearSubstitution (A z.1)).toLinearMap

def exists_balanced_integer_auxiliary_of_bound {m d s : ℕ}
    (r : Fin m → ℕ) (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (η : ℝ) (hη : 0 ≤ η) (hlarge : 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2)
    (A : Fin s → Fin m → Fin d → Fin d → ℤ)
    (H : ℝ) (hH : 1 ≤ H)
    (hentry : ∀ v (J K : CompositionArray m d r),
      ‖MvPolynomial.coeff (compositionExponent K)
        (blockLinearSubstitution (A v) (MvPolynomial.monomial (compositionExponent J) 1))‖ ≤ H) :
    ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧
      ProductBlockHomogeneous r P ∧
      polynomialCoeffL1 P ≤ (Fintype.card (CompositionArray m d r) : ℝ) ^ 2 * H ∧
      ∀ v e, MvPolynomial.coeff e (blockLinearSubstitution (A v) P) ≠ 0 →
        (∀ h, ∑ i, e (h, i) = r h) ∧
        ∀ i : Fin d, |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < (m : ℝ) * η := by
  classical
  let I := Fin s × ↥(badCompositionArrays (d := d) r η)
  have hquarter := badCompositionArrays_quarter r hm hd hr s η hη hlarge
  have hhalf : 2 * Fintype.card I ≤ Fintype.card (CompositionArray m d r) := by
    have hcard : Fintype.card I = s * (badCompositionArrays (d := d) r η).card := by
      simp [I]
    rw [hcard]
    omega
  obtain ⟨P, hP, hsupp, hzero, hnorm⟩ := exists_small_integer_auxiliary_polynomial
    (compositionExponent (d := d) (r := r)) (compositionExponent_injective r)
    (balancedCoefficientCondition r η A) (compositionArray_card_pos r hd) hhalf H hH
    (fun z J => hentry z.1 J z.2.val)
  have hhom : ProductBlockHomogeneous r P := by
    intro e he
    obtain ⟨J, rfl⟩ := hsupp e he
    exact compositionExponent_block_sum J
  refine ⟨P, hP, hhom, hnorm, ?_⟩
  intro v e he
  have hehom := blockLinearSubstitution_homogeneous (A v) r P hhom e
    (MvPolynomial.mem_support_iff.mpr he)
  obtain ⟨J, hJ⟩ := (exists_compositionExponent_iff r e).mpr hehom
  have hgood : J ∉ badCompositionArrays r η := by
    intro hbad
    have hh := hzero (v, ⟨J, hbad⟩)
    change MvPolynomial.coeff (compositionExponent J) (blockLinearSubstitution (A v) P) = 0 at hh
    rw [hJ] at hh
    exact he hh
  refine ⟨hehom, ?_⟩
  intro i
  have hh := (not_mem_badCompositionArrays r η J).mp hgood i
  simpa only [compositionDeviation, ← hJ, compositionExponent_apply] using hh

def exists_balanced_integer_auxiliary {m d s : ℕ}
    (r : Fin m → ℕ) (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (η : ℝ) (hη : 0 ≤ η) (hlarge : 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2)
    (A : Fin s → Fin m → Fin d → Fin d → ℤ)
    (C : ℝ) (hC : 1 ≤ C) (hA : ∀ v h i, ∑ j, ‖A v h i j‖ ≤ C) :
    ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧
      ProductBlockHomogeneous r P ∧
      polynomialCoeffL1 P ≤ (Fintype.card (CompositionArray m d r) : ℝ) ^ 2 * C ^ (∑ h, r h) ∧
      ∀ v e, MvPolynomial.coeff e (blockLinearSubstitution (A v) P) ≠ 0 →
        (∀ h, ∑ i, e (h, i) = r h) ∧
        ∀ i : Fin d, |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < (m : ℝ) * η := by
  apply exists_balanced_integer_auxiliary_of_bound r hm hd hr η hη hlarge A
    (C ^ (∑ h, r h)) (one_le_pow₀ hC)
  intro v J K
  have hf : ∀ x, polynomialCoeffL1 (blockLinearForm (A v) x) ≤ C :=
    fun x => (blockLinearForm_norm_le (A v) x).trans (hA v x.1 x.2)
  simpa only [blockLinearSubstitution, compositionExponent_total] using
    norm_coeff_aeval_monomial_one_le (blockLinearForm (A v))
      (compositionExponent J) (compositionExponent K) (le_trans zero_le_one hC) hf


end
end Bounty

end SubmissionComponent_BalancedAuxiliaryPolynomial

/- Component HyperplaneCoordinateReindex; SHA256 0a0ae811d41f0b1e2e300e28f74678fee5ed456f40fe1deaf029723cb9df13a8 -/
section SubmissionComponent_HyperplaneCoordinateReindex
/- Explicit pivot/complement coordinates for block rational hyperplanes. -/

namespace Bounty
noncomputable section
open scoped BigOperators

abbrev HyperplaneComplement {m d : ℕ} (p : Fin m → Fin (d + 1)) :=
  {x : Fin m × Fin (d + 1) // x.2 ≠ p x.1}

def hyperplanePivotEquiv {m d : ℕ} (p : Fin m → Fin (d + 1)) :
    (Fin m × Fin (d + 1)) ≃ Fin m ⊕ HyperplaneComplement p where
  toFun x := if h : x.2 = p x.1 then Sum.inl x.1 else Sum.inr ⟨x, h⟩
  invFun := Sum.elim (fun h => (h, p h)) Subtype.val
  left_inv := by
    intro x
    dsimp
    split_ifs with hx
    · exact Prod.ext rfl hx.symm
    · rfl
  right_inv := by
    intro x
    cases x with
    | inl h =>
      change (if h' : p h = p h then Sum.inl h else Sum.inr (⟨(h, p h), h'⟩ : HyperplaneComplement p)) = Sum.inl h
      rw [dif_pos rfl]
    | inr x =>
      change (if h : x.val.2 = p x.val.1 then Sum.inl x.val.1 else Sum.inr (⟨x.val, h⟩ : HyperplaneComplement p)) = Sum.inr x
      rw [dif_neg x.property]

def hyperplanePivotEquiv_pivot {m d : ℕ} (p : Fin m → Fin (d + 1)) (h : Fin m) :
    hyperplanePivotEquiv p (h, p h) = Sum.inl h := by simp [hyperplanePivotEquiv]

def hyperplanePivotEquiv_complement {m d : ℕ} (p : Fin m → Fin (d + 1))
    (x : HyperplaneComplement p) : hyperplanePivotEquiv p x.val = Sum.inr x := by
  change (if h : x.val.2 = p x.val.1 then Sum.inl x.val.1 else Sum.inr (⟨x.val, h⟩ : HyperplaneComplement p)) = Sum.inr x
  rw [dif_neg x.property]

def hyperplaneCoordinateBlock {m d : ℕ} (p : Fin m → Fin (d + 1)) :
    Fin m ⊕ HyperplaneComplement p → Fin m := Sum.elim id (fun x => x.val.1)

def hyperplaneCoordinateBlock_pivotEquiv {m d : ℕ}
    (p : Fin m → Fin (d + 1)) (x : Fin m × Fin (d + 1)) :
    hyperplaneCoordinateBlock p (hyperplanePivotEquiv p x) = x.1 := by
  simp only [hyperplanePivotEquiv, Equiv.coe_fn_mk]
  split_ifs <;> rfl

def multiBlockHomogeneous_rename {I J H R : Type*} [CommSemiring R]
    [DecidableEq H] (f : I → J) (hf : Function.Injective f) (block : J → H)
    (r : H → ℕ) (P : MvPolynomial I R)
    (hP : MultiBlockHomogeneous (block ∘ f) r P) :
    MultiBlockHomogeneous block r (MvPolynomial.rename f P) := by
  classical
  intro h e he
  have he' := MvPolynomial.mem_support_iff.mpr he
  rw [MvPolynomial.support_rename_of_injective hf] at he'
  obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp he'
  rw [specialization_weight_mapDomain]
  exact hP h (MvPolynomial.mem_support_iff.mp ha)

def productBlockHomogeneous_pivotRename {m d : ℕ} {R : Type*} [CommSemiring R]
    (p : Fin m → Fin (d + 1)) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin (d + 1)) R) (hP : ProductBlockHomogeneous r P) :
    MultiBlockHomogeneous (hyperplaneCoordinateBlock p) r
      (MvPolynomial.rename (hyperplanePivotEquiv p) P) := by
  apply multiBlockHomogeneous_rename _ (hyperplanePivotEquiv p).injective
  intro h e he
  rw [Finsupp.weight_eq_sum, Fintype.sum_prod_type]
  simpa [Function.comp, hyperplaneCoordinateBlock_pivotEquiv] using hP e (MvPolynomial.mem_support_iff.mpr he) h

def pivotRename_coeffL1 {m d : ℕ} {R : Type*} [NormedCommRing R]
    (p : Fin m → Fin (d + 1)) (P : MvPolynomial (Fin m × Fin (d + 1)) R) :
    polynomialCoeffL1 (MvPolynomial.rename (hyperplanePivotEquiv p) P) = polynomialCoeffL1 P :=
  polynomialCoeffL1_rename_of_injective _ (hyperplanePivotEquiv p).injective P

end
end Bounty

end SubmissionComponent_HyperplaneCoordinateReindex

/- Component RationalHyperplaneReduction; SHA256 e76a8e1e9a1b6ba0028fed4997bafaec1c0ab653ee4001d5788949166cf03668 -/
section SubmissionComponent_RationalHyperplaneReduction
/- Finite iteration of the actual integer saturation/specialization step. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {B C I R : Type*}

open scoped Classical in
def zeroVariables [CommSemiring R] (s : Finset I) : MvPolynomial I R →ₐ[R] MvPolynomial I R :=
  MvPolynomial.aeval (fun i => if i ∈ s then 0 else MvPolynomial.X i)

open scoped Classical in
def zeroVariables_C [CommSemiring R] (s : Finset I) (a : R) :
    zeroVariables s (MvPolynomial.C a) = MvPolynomial.C a := by simp [zeroVariables]

open scoped Classical in
def zeroVariables_X [CommSemiring R] (s : Finset I) (i : I) :
    zeroVariables s (MvPolynomial.X (R := R) i) = if i ∈ s then 0 else MvPolynomial.X i := by
  simp [zeroVariables]

open scoped Classical in
def zeroVariables_empty [CommSemiring R] (P : MvPolynomial I R) :
    zeroVariables ∅ P = P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP => simp only [map_mul, zeroVariables_X, Finset.notMem_empty, if_false, hP]

open scoped Classical in
def zeroVariables_insert [CommSemiring R] (s : Finset I) (z : I) (P : MvPolynomial I R) :
    zeroVariables (insert z s) P = zeroVariable z (zeroVariables s P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [map_mul, zeroVariables_X, Finset.mem_insert, hP]
    by_cases hi : i = z
    · subst i
      by_cases hs : z ∈ s <;> simp [hs, zeroVariable_X]
    · by_cases hs : i ∈ s <;> simp [hi, hs, zeroVariable_X]

open scoped Classical in
def exists_integer_complement_elimination {H : Type*} [DecidableEq H]
    (block : B ⊕ C → H) (r : H → ℕ) (w : B → ℕ) (g : B → MvPolynomial C ℚ)
    (s : Finset C) (P : MvPolynomial (B ⊕ C) ℤ) (hP : P ≠ 0)
    (hhom : MultiBlockHomogeneous block r P) :
    ∃ r' : H → ℕ, ∃ Q : MvPolynomial (B ⊕ C) ℤ,
      (∀ h, r' h ≤ r h) ∧ Q ≠ 0 ∧ MultiBlockHomogeneous block r' Q ∧
      (∀ i, Q.degreeOf i ≤ P.degreeOf i) ∧ polynomialCoeffL1 Q ≤ polynomialCoeffL1 P ∧
      (∀ c ∈ s, Q.degreeOf (Sum.inr c) = 0) ∧
      complementHyperplaneIndex w g (MvPolynomial.map (Int.castRingHom ℚ) P) ≤
        complementHyperplaneIndex w (fun b => zeroVariables s (g b))
          (MvPolynomial.map (Int.castRingHom ℚ) Q) := by
  classical
  induction s using Finset.induction_on generalizing r P with
  | empty =>
    refine ⟨r, P, fun _ => le_rfl, hP, hhom, fun _ => le_rfl, le_rfl, ?_, ?_⟩
    · simp
    · simp only [zeroVariables_empty]
      exact le_rfl
  | @insert c s hc ih =>
    obtain ⟨r₁, P₁, hr₁, hP₁, hhom₁, hdeg₁, hnorm₁, hzero₁, hindex₁⟩ := ih r P hP hhom
    obtain ⟨k, Q, hQeq, hQ, hzero, hdeg, hnorm, hhomQ, hindex⟩ :=
      exists_integer_complement_specialization block r₁ w (fun b => zeroVariables s (g b))
        c P₁ hP₁ hhom₁
    refine ⟨fun h => r₁ h - if block (Sum.inr c) = h then k else 0,
      Q, ?_, hQ, hhomQ, ?_, hnorm.trans hnorm₁, ?_, ?_⟩
    · intro h
      exact (Nat.sub_le _ _).trans (hr₁ h)
    · intro i
      exact (hdeg i).trans (hdeg₁ i)
    · intro a ha
      rcases Finset.mem_insert.mp ha with rfl | ha
      · exact hzero
      · exact Nat.eq_zero_of_le_zero ((hdeg _).trans_eq (hzero₁ a ha))
    · simpa only [zeroVariables_insert] using hindex₁.trans hindex

open scoped Classical in
def MultiBlockHomogeneous_rename_pullback {H J : Type*} [DecidableEq H] [CommSemiring R]
    (f : I → J) (hf : Function.Injective f) (block : J → H) (r : H → ℕ)
    (P : MvPolynomial I R) (hP : MultiBlockHomogeneous block r (MvPolynomial.rename f P)) :
    MultiBlockHomogeneous (block ∘ f) r P := by
  intro h e he
  have hh : MvPolynomial.coeff (e.mapDomain f) (MvPolynomial.rename f P) ≠ 0 := by
    rwa [MvPolynomial.coeff_rename_mapDomain f hf]
  simpa only [specialization_weight_mapDomain, Function.comp_def] using hP h hh

open scoped Classical in
def multiBlockHomogeneous_pair_iff [CommSemiring R] (r : B → ℕ)
    (P : MvPolynomial (B ⊕ B) R) :
    MultiBlockHomogeneous (Sum.elim id id) r P ↔ BlockHomogeneous r P := by
  rw [blockHomogeneous_iff_weighted]
  have hw (h : B) : (fun i : B ⊕ B => if Sum.elim id id i = h then 1 else 0) =
      blockDegreeWeight h := by
    funext i
    cases i <;> simp [blockDegreeWeight, Pi.single_apply, eq_comm]
  simp only [MultiBlockHomogeneous, hw]

open scoped Classical in
def retainedPairEmbedding (t : B → C) : B ⊕ B → B ⊕ C := Sum.map id t

open scoped Classical in
def retainedPairEmbedding_injective (t : B → C) (ht : Function.Injective t) :
    Function.Injective (retainedPairEmbedding t) := Sum.map_injective.mpr ⟨Function.injective_id, ht⟩

open scoped Classical in
def exists_retainedPair_polynomial [CommSemiring R] (t : B → C) (ht : Function.Injective t)
    (Q : MvPolynomial (B ⊕ C) R)
    (hzero : ∀ c, c ∉ Set.range t → Q.degreeOf (Sum.inr c) = 0) :
    ∃ U : MvPolynomial (B ⊕ B) R, MvPolynomial.rename (retainedPairEmbedding t) U = Q := by
  apply MvPolynomial.exists_rename_eq_of_vars_subset_range Q _ (retainedPairEmbedding_injective t ht)
  intro i hi
  cases i with
  | inl b => exact ⟨Sum.inl b, rfl⟩
  | inr c =>
    have hc : c ∈ Set.range t := by
      by_contra hn
      exact (MvPolynomial.mem_vars_iff_degreeOf_ne_zero.mp hi) (hzero c hn)
    obtain ⟨b, rfl⟩ := hc
    exact ⟨Sum.inr b, rfl⟩

open scoped Classical in
def retainedPair_homogeneous [CommSemiring R] (q : C → B) (t : B → C)
    (hqt : ∀ b, q (t b) = b) (r : B → ℕ) (U : MvPolynomial (B ⊕ B) R)
    (hU : MultiBlockHomogeneous (Sum.elim id q) r (MvPolynomial.rename (retainedPairEmbedding t) U)) :
    BlockHomogeneous r U := by
  have ht : Function.Injective t := fun a b hab => by
    have := congrArg q hab
    simpa only [hqt] using this
  have hh := MultiBlockHomogeneous_rename_pullback (retainedPairEmbedding t)
    (retainedPairEmbedding_injective t ht) (Sum.elim id q) r U hU
  have hb : Sum.elim id q ∘ retainedPairEmbedding t = Sum.elim id id := by
    funext i
    cases i <;> simp [retainedPairEmbedding, hqt]
  rw [hb] at hh
  exact (multiBlockHomogeneous_pair_iff r U).mp hh

open scoped Classical in
def blockHomogeneous_map {S : Type*} [CommSemiring R] [CommSemiring S]
    (f : R →+* S) (r : B → ℕ) (P : MvPolynomial (B ⊕ B) R) (hP : BlockHomogeneous r P) :
    BlockHomogeneous r (MvPolynomial.map f P) := by
  intro e he
  exact hP e (MvPolynomial.support_map_subset f P he)

open scoped Classical in
def complementShear_retainedPair (t : B → C) (β : B → ℚ)
    (P : MvPolynomial (B ⊕ B) ℚ) :
    complementShear (fun b => MvPolynomial.C (β b) * MvPolynomial.X (t b))
      (MvPolynomial.rename (retainedPairEmbedding t) P) =
      MvPolynomial.rename (retainedPairEmbedding t) (blockTaylor β P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    dsimp only [retainedPairEmbedding] at hP
    cases i <;> simp only [map_mul, MvPolynomial.rename_X, retainedPairEmbedding,
      Sum.map_inl, Sum.map_inr, id_eq, complementShear_X_inl, complementShear_X_inr,
      map_add, MvPolynomial.rename_C, blockTaylor_X_inl, blockTaylor_X_inr, hP]

open scoped Classical in
def retainedPair_hyperplane_index (t : B → C) (ht : Function.Injective t)
    (r w : B → ℕ) (β : B → ℚ) (P : MvPolynomial (B ⊕ B) ℚ) (hP : BlockHomogeneous r P) :
    complementHyperplaneIndex w (fun b => MvPolynomial.C (β b) * MvPolynomial.X (t b))
      (MvPolynomial.rename (retainedPairEmbedding t) P) =
      weightedPolynomialIndex w β (blockDehomogenize P) := by
  unfold complementHyperplaneIndex
  rw [complementShear_retainedPair, weightedPolynomialOrder_rename_injective _ _
    (retainedPairEmbedding_injective t ht)]
  have hw : Sum.elim w (fun _ : C => 0) ∘ retainedPairEmbedding t = Sum.elim w (fun _ : B => 0) := by
    funext i
    cases i <;> rfl
  rw [hw]
  exact blockDehomogenize_hyperplane_index r w β P hP

open scoped Classical in
def blockComplementLinear [Fintype C] (q : C → B) (a : C → ℚ) (b : B) : MvPolynomial C ℚ :=
  ∑ c ∈ Finset.univ.filter (fun c => q c = b), MvPolynomial.C (a c) * MvPolynomial.X c

open scoped Classical in
def zeroVariables_blockComplementLinear [Fintype C] (q : C → B) (t : B → C)
    (hqt : ∀ b, q (t b) = b) (a : C → ℚ) (b : B) :
    zeroVariables (Finset.univ.filter (fun c => c ∉ Set.range t)) (blockComplementLinear q a b) =
      MvPolynomial.C (a (t b)) * MvPolynomial.X (t b) := by
  classical
  unfold blockComplementLinear
  rw [map_sum, Finset.sum_eq_single (t b)]
  · simp only [map_mul, zeroVariables_C, zeroVariables_X]
    simp
  · intro c hc hct
    have hqc : q c = b := (Finset.mem_filter.mp hc).2
    have hn : c ∉ Set.range t := by
      rintro ⟨u, rfl⟩
      have hu : u = b := (hqt u).symm.trans hqc
      exact hct (congrArg t hu)
    rw [map_mul, zeroVariables_C, zeroVariables_X,
      if_pos (Finset.mem_filter.mpr ⟨Finset.mem_univ c, hn⟩), mul_zero]
  · intro hn
    exact False.elim (hn (by simp [hqt]))

/- Eliminate every unselected complement, then dehomogenize the actual
remaining integer polynomial.  No index-monotonicity assumption is supplied. -/
open scoped Classical in
def exists_integer_scalar_hyperplane_reduction [Fintype C]
    (q : C → B) (t : B → C) (hqt : ∀ b, q (t b) = b) (a : C → ℚ)
    (r w : B → ℕ) (P : MvPolynomial (B ⊕ C) ℤ) (hP : P ≠ 0)
    (hhom : MultiBlockHomogeneous (Sum.elim id q) r P) :
    ∃ R : MvPolynomial B ℤ, R ≠ 0 ∧ (∀ b, R.degreeOf b ≤ r b) ∧
      polynomialCoeffL1 R ≤ polynomialCoeffL1 P ∧
      complementHyperplaneIndex w (blockComplementLinear q a)
          (MvPolynomial.map (Int.castRingHom ℚ) P) ≤
        weightedPolynomialIndex w (fun b => a (t b)) (MvPolynomial.map (Int.castRingHom ℚ) R) := by
  classical
  let s : Finset C := Finset.univ.filter (fun c => c ∉ Set.range t)
  have ht : Function.Injective t := fun u v huv => by
    have := congrArg q huv
    simpa only [hqt] using this
  obtain ⟨r', Q, hr', hQ, hhomQ, hdegQ, hnormQ, hzero, hindex⟩ :=
    exists_integer_complement_elimination (Sum.elim id q) r w
      (blockComplementLinear q a) s P hP hhom
  obtain ⟨U, hUeq⟩ := exists_retainedPair_polynomial t ht Q
    (fun c hc => hzero c (Finset.mem_filter.mpr ⟨Finset.mem_univ c, hc⟩))
  have hU : U ≠ 0 := by intro hz; simp only [hz, map_zero] at hUeq; exact hQ hUeq.symm
  have hhomU : BlockHomogeneous r' U := retainedPair_homogeneous q t hqt r' U (hUeq.symm ▸ hhomQ)
  refine ⟨blockDehomogenize U, blockDehomogenize_ne_zero r' hhomU hU, ?_, ?_, ?_⟩
  · intro b
    exact (blockDehomogenize_degreeOf_le r' U hhomU b).trans (hr' b)
  · rw [blockDehomogenize_coeffL1 r' U hhomU,
      ← polynomialCoeffL1_rename_of_injective _ (retainedPairEmbedding_injective t ht), hUeq]
    exact hnormQ
  · have hg : (fun b => zeroVariables s (blockComplementLinear q a b)) =
        (fun b => MvPolynomial.C (a (t b)) * MvPolynomial.X (t b)) := by
      funext b
      exact zeroVariables_blockComplementLinear q t hqt a b
    rw [hg, ← hUeq, MvPolynomial.map_rename,
      retainedPair_hyperplane_index t ht r' w _ _
        (blockHomogeneous_map (Int.castRingHom ℚ) r' U hhomU), ← blockDehomogenize_map] at hindex
    exact hindex

open scoped Classical in
def normalizedComplementHyperplaneIndex {m : ℕ} (r : Fin m → ℕ)
    (g : Fin m → MvPolynomial C ℚ) (P : MvPolynomial (Fin m ⊕ C) ℚ) : ℝ :=
  ((complementHyperplaneIndex (rothWeight r) g P).toNat : ℝ) / rothDenominator r

/- The proved integer Roth theorem applied to the polynomial constructed by
finite saturation and dehomogenization.  Heights refer to the selected ratios. -/
open scoped Classical in
def integer_complement_hyperplane_roth_bound {n : ℕ} [Fintype C]
    (q : C → Fin (n + 1)) (t : Fin (n + 1) → C) (hqt : ∀ b, q (t b) = b)
    (a : C → ℚ) (r : Fin (n + 1) → ℕ) (hr : ∀ i, 0 < r i)
    (P : MvPolynomial (Fin (n + 1) ⊕ C) ℤ) (hP : P ≠ 0)
    (hhom : MultiBlockHomogeneous (Sum.elim id q) r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ i, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r i : ℝ) * Height.logHeight₁ (a (t i)))) :
    normalizedComplementHyperplaneIndex r (blockComplementLinear q a)
      (MvPolynomial.map (Int.castRingHom ℚ) P) ≤ 2 * (n + 1 : ℕ) * η := by
  obtain ⟨R, hR, hdegree, hnorm, hindex⟩ :=
    exists_integer_scalar_hyperplane_reduction q t hqt a r (rothWeight r) P hP hhom
  have hlog : Real.log (polynomialCoeffL1 R) ≤ Real.log (polynomialCoeffL1 P) :=
    Real.log_le_log (polynomialCoeffL1_pos hR) hnorm
  have hheightR (i) : Real.log (polynomialCoeffL1 R) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r i : ℝ) * Height.logHeight₁ (a (t i))) := by
    linarith [hheight i]
  have hroth := integer_roth_index_bound n R hR r hr hdegree (fun i => a (t i))
    η hη hηhalf hstep hheightR
  have hn := ENat.toNat_le_toNat hindex
    (weightedPolynomialIndex_finite (rothWeight r) (fun i => a (t i)) (integerMap_ne_zero hR)).ne
  have hnormalized : normalizedComplementHyperplaneIndex r (blockComplementLinear q a)
      (MvPolynomial.map (Int.castRingHom ℚ) P) ≤
      rothPolynomialIndex r (fun i => a (t i)) (MvPolynomial.map (Int.castRingHom ℚ) R) :=
    div_le_div_of_nonneg_right (by exact_mod_cast hn) (Nat.cast_nonneg _)
  exact hnormalized.trans hroth


end
end Bounty

end SubmissionComponent_RationalHyperplaneReduction

/- Component ProductHyperplaneRoth; SHA256 436a70c448518844c612e1d612a35c03f4b9b9bfb0dc017537490c974df85a33 -/
section SubmissionComponent_ProductHyperplaneRoth
/- Integer Roth's lemma for actual rational hyperplanes in product coordinates. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def pivotComplementCoefficient {m d : ℕ} (b : Fin m → Fin (d + 1) → ℚ)
    (p : Fin m → Fin (d + 1)) (x : HyperplaneComplement p) : ℚ :=
  -(b x.val.1 x.val.2 / b x.val.1 (p x.val.1))

def productHyperplaneIndex {m d : ℕ} (b : Fin m → Fin (d + 1) → ℚ)
    (p : Fin m → Fin (d + 1)) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin (d + 1)) ℚ) : ℝ :=
  normalizedComplementHyperplaneIndex r
    (blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
      (pivotComplementCoefficient b p))
    (MvPolynomial.rename (hyperplanePivotEquiv p) P)

def integer_product_hyperplane_roth_bound {n d : ℕ} (hd : 1 ≤ d)
    (b : Fin (n + 1) → Fin (d + 1) → ℚ) (p : Fin (n + 1) → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0)
    (r : Fin (n + 1) → ℕ) (hr : ∀ h, 0 < r h)
    (P : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ h, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d))) :
    productHyperplaneIndex b p r (MvPolynomial.map (Int.castRingHom ℚ) P) ≤
      2 * (n + 1 : ℕ) * η := by
  classical
  choose j hj hpair using fun h => exists_rational_hyperplane_height_pair hd (b h) (p h) (hp h)
  let t (h : Fin (n + 1)) : HyperplaneComplement p := ⟨(h, j h), hj h⟩
  let Q := MvPolynomial.rename (hyperplanePivotEquiv p) P
  have hQ : Q ≠ 0 := by
    exact fun hz => hP ((MvPolynomial.rename_eq_zero_iff_of_injective P
      (hyperplanePivotEquiv p).injective).mp hz)
  have hhomQ : MultiBlockHomogeneous
      (Sum.elim id (fun x : HyperplaneComplement p => x.val.1)) r Q :=
    productBlockHomogeneous_pivotRename p r P hhom
  have hheightQ (h : Fin (n + 1)) :
      Real.log (polynomialCoeffL1 Q) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * Height.logHeight₁ (pivotComplementCoefficient b p (t h))) := by
    rw [show polynomialCoeffL1 Q = polynomialCoeffL1 P from pivotRename_coeffL1 p P]
    apply (hheight h).trans
    apply mul_le_mul_of_nonneg_left _ (pow_nonneg hη.le _)
    apply mul_le_mul_of_nonneg_left _ (Nat.cast_nonneg _)
    simpa only [pivotComplementCoefficient, t, neg_div] using hpair h
  have hbound := integer_complement_hyperplane_roth_bound
    (fun x : HyperplaneComplement p => x.val.1) t (fun _ => rfl)
    (pivotComplementCoefficient b p) r hr Q hQ hhomQ η hη hηhalf hstep hheightQ
  simpa only [productHyperplaneIndex, Q, MvPolynomial.map_rename] using hbound


end
end Bounty

end SubmissionComponent_ProductHyperplaneRoth

/- Component BoundedGridNonvanishing; SHA256 40d6010e6df02fc5b50d10669a98e0f67bf0c4c84c4bb1d9dff779c65c85b3b7 -/
section SubmissionComponent_BoundedGridNonvanishing
/- A bounded integer grid detects a low-order divided derivative. -/

namespace Bounty
noncomputable section
open scoped BigOperators
open Polynomial

def sum_rootMultiplicity_le_natDegree {K : Type*} [CommRing K] [IsDomain K]
    (P : K[X]) (S : Finset K) :
    ∑ z ∈ S, P.rootMultiplicity z ≤ P.natDegree := by
  classical
  simp_rw [← Polynomial.count_roots]
  calc
    ∑ z ∈ S, P.roots.count z ≤ ∑ z ∈ S ∪ P.roots.toFinset, P.roots.count z :=
      Finset.sum_le_sum_of_subset Finset.subset_union_left
    _ = P.roots.card := Multiset.sum_count_eq_card (fun z hz =>
      Finset.mem_union_right S (Multiset.mem_toFinset.mpr hz))
    _ ≤ P.natDegree := Polynomial.card_roots' P

def hasseDeriv_rootMultiplicity_eval_ne_zero {K : Type*} [CommRing K]
    {P : K[X]} (hP : P ≠ 0) (z : K) :
    (Polynomial.hasseDeriv (P.rootMultiplicity z) P).eval z ≠ 0 := by
  rw [← Polynomial.taylor_coeff, Polynomial.rootMultiplicity_eq_natTrailingDegree]
  change (P.taylor z).coeff (P.taylor z).natTrailingDegree ≠ 0
  exact Polynomial.coeff_natTrailingDegree_ne_zero.mpr ((Polynomial.taylor_eq_zero z P).not.mpr hP)

def exists_finite_grid_hasseDeriv_ne_zero {K : Type*} [CommRing K] [IsDomain K]
    {P : K[X]} (hP : P ≠ 0) (S : Finset K) (k : ℕ)
    (hcard : P.natDegree < S.card * (k + 1)) :
    ∃ z ∈ S, ∃ i ≤ k, (Polynomial.hasseDeriv i P).eval z ≠ 0 := by
  classical
  by_contra hh
  push_neg at hh
  have hm (z) (hz : z ∈ S) : k + 1 ≤ P.rootMultiplicity z := by
    by_contra hn
    have hk : P.rootMultiplicity z ≤ k := by omega
    exact hasseDeriv_rootMultiplicity_eval_ne_zero hP z (hh z hz _ hk)
  have hsum := Finset.sum_le_sum hm
  have hdegree := sum_rootMultiplicity_le_natDegree P S
  simp only [Finset.sum_const, smul_eq_mul] at hsum
  omega

def exists_nat_grid_hasseDeriv_ne_zero {K : Type*} [CommRing K] [IsDomain K]
    [CharZero K] {P : K[X]} (hP : P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ z ≤ B, ∃ i ≤ P.natDegree / B,
      (Polynomial.hasseDeriv i P).eval (z : K) ≠ 0 := by
  classical
  let S : Finset K := (Finset.range (B + 1)).image (fun z : ℕ => (z : K))
  have hScard : S.card = B + 1 := by
    rw [Finset.card_image_of_injective _ Nat.cast_injective, Finset.card_range]
  have hsize : P.natDegree < S.card * (P.natDegree / B + 1) := by
    rw [hScard]
    have hdiv := Nat.mod_lt P.natDegree hB
    have hrepr := Nat.mod_add_div P.natDegree B
    nlinarith
  obtain ⟨z, hz, i, hi, hne⟩ := exists_finite_grid_hasseDeriv_ne_zero hP S _ hsize
  obtain ⟨a, ha, rfl⟩ := Finset.mem_image.mp hz
  exact ⟨a, by simpa only [Finset.mem_range, Nat.lt_succ_iff] using ha, i, hi, hne⟩


end
end Bounty

end SubmissionComponent_BoundedGridNonvanishing

/- Component MultivariateGridNonvanishing; SHA256 e51477a995bbb4af6eb8a743834eaf047f8e03959d3a6bddd97daf11ee271ee9 -/
section SubmissionComponent_MultivariateGridNonvanishing
/- Iterated coefficient-exact divided derivatives on a bounded integer grid. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def firstVariableHasseJet {n : ℕ} (P : MvPolynomial (Fin (n + 1)) ℚ)
    (z i : ℕ) : MvPolynomial (Fin n) ℚ :=
  (Polynomial.hasseDeriv i (MvPolynomial.finSuccEquiv ℚ n P)).eval (z : MvPolynomial (Fin n) ℚ)

def firstVariableHasseJet_degreeOf {n : ℕ} (P : MvPolynomial (Fin (n + 1)) ℚ)
    (z i : ℕ) (j : Fin n) :
    (firstVariableHasseJet P z i).degreeOf j ≤ P.degreeOf j.succ := by
  classical
  rw [firstVariableHasseJet, Polynomial.eval_eq_sum, Polynomial.sum_def]
  apply (MvPolynomial.degreeOf_sum_le _ _ _).trans
  apply Finset.sup_le
  intro a ha
  rw [Polynomial.hasseDeriv_coeff]
  have hc : ((a + i).choose i : MvPolynomial (Fin n) ℚ) =
      MvPolynomial.C ((a + i).choose i : ℚ) := by simp
  have hz : (z : MvPolynomial (Fin n) ℚ) ^ a = MvPolynomial.C ((z : ℚ) ^ a) := by simp
  rw [hc, hz, mul_assoc, mul_comm _ (MvPolynomial.C _), ← mul_assoc,
    ← MvPolynomial.C_mul]
  exact (MvPolynomial.degreeOf_C_mul_le _ _ _).trans
    (MvPolynomial.degreeOf_coeff_finSuccEquiv P j (a + i))

def exists_firstVariableHasseJet_ne_zero {n : ℕ}
    {P : MvPolynomial (Fin (n + 1)) ℚ} (hP : P ≠ 0)
    (B : ℕ) (hB : 0 < B) :
    ∃ z ≤ B, ∃ i ≤ P.degreeOf 0 / B, firstVariableHasseJet P z i ≠ 0 := by
  have hp : MvPolynomial.finSuccEquiv ℚ n P ≠ 0 := by
    intro hz
    apply hP
    exact (MvPolynomial.finSuccEquiv ℚ n).injective (hz.trans (map_zero _).symm)
  simpa only [MvPolynomial.natDegree_finSuccEquiv, firstVariableHasseJet] using
    exists_nat_grid_hasseDeriv_ne_zero hp B hB

def gridHasseJet : {n : ℕ} → MvPolynomial (Fin n) ℚ → (Fin n → ℕ) → (Fin n → ℕ) → ℚ
  | 0, P, _, _ => MvPolynomial.eval (fun i => Fin.elim0 i) P
  | _n + 1, P, z, a => gridHasseJet (firstVariableHasseJet P (z 0) (a 0))
      (fun i => z i.succ) (fun i => a i.succ)

def exists_bounded_gridHasseJet_ne_zero (n : ℕ)
    (P : MvPolynomial (Fin n) ℚ) (hP : P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ z a : Fin n → ℕ, (∀ i, z i ≤ B) ∧
      (∀ i, a i ≤ P.degreeOf i / B) ∧ gridHasseJet P z a ≠ 0 := by
  induction n with
  | zero =>
    refine ⟨Fin.elim0, Fin.elim0, (fun i => Fin.elim0 i), (fun i => Fin.elim0 i), ?_⟩
    change MvPolynomial.eval (fun i : Fin 0 => Fin.elim0 i) P ≠ 0
    intro hz
    have hC : MvPolynomial.C (MvPolynomial.eval (fun i : Fin 0 => Fin.elim0 i) P) = P := by
      clear hP hz
      induction P using MvPolynomial.induction_on with
      | C c => simp
      | add P Q hP hQ => simp [map_add, hP, hQ]
      | mul_X P i h => exact Fin.elim0 i
    rw [hz, map_zero] at hC
    exact hP hC.symm
  | succ n ih =>
    obtain ⟨z0, hz0, a0, ha0, hjet⟩ := exists_firstVariableHasseJet_ne_zero hP B hB
    obtain ⟨z, a, hz, ha, hne⟩ := ih (firstVariableHasseJet P z0 a0) hjet
    refine ⟨Fin.cons z0 z, Fin.cons a0 a, ?_, ?_, ?_⟩
    · intro i
      refine Fin.cases hz0 (fun j => ?_) i
      exact hz j
    · intro i
      refine Fin.cases ha0 (fun j => ?_) i
      exact (ha j).trans (Nat.div_le_div_right (firstVariableHasseJet_degreeOf P z0 a0 j))
    · simpa only [gridHasseJet, Fin.cons_zero, Fin.cons_succ] using hne


end
end Bounty

end SubmissionComponent_MultivariateGridNonvanishing

/- Component GridTaylorNonvanishing; SHA256 65425dbe043c4776e958538248ccfdc33885d2afc6e656abbccb4ee5a08fe6f8 -/
section SubmissionComponent_GridTaylorNonvanishing
/- The recursive bounded-grid jets are the actual multivariate Taylor coefficients. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def polynomial_map_hasseDeriv {R S : Type*} [CommSemiring R] [CommSemiring S]
    (f : R →+* S) (P : Polynomial R) (i : ℕ) :
    (Polynomial.hasseDeriv i P).map f = Polynomial.hasseDeriv i (P.map f) := by
  ext n
  simp [Polynomial.hasseDeriv_coeff]

def finSuccEquiv_weightedTaylor {n : ℕ} (β : Fin (n + 1) → ℚ)
    (P : MvPolynomial (Fin (n + 1)) ℚ) :
    MvPolynomial.finSuccEquiv ℚ n (weightedTaylor β P) =
      Polynomial.taylor (MvPolynomial.C (β 0))
        ((MvPolynomial.finSuccEquiv ℚ n P).map (weightedTaylor (fun i => β i.succ))) := by
  have hC (a : ℚ) : MvPolynomial.finSuccEquiv ℚ n (MvPolynomial.C a) =
      Polynomial.C (MvPolynomial.C a) := by simp [MvPolynomial.finSuccEquiv_apply]
  induction P using MvPolynomial.induction_on with
  | C a => simp [MvPolynomial.finSuccEquiv_apply, weightedTaylor_C]
  | add P Q hP hQ => simp only [map_add, Polynomial.map_add, hP, hQ]
  | mul_X P i hP =>
    refine Fin.cases ?_ (fun j => ?_) i
    · simp [map_mul, map_add, hP, MvPolynomial.finSuccEquiv_X_zero,
        Polynomial.taylor_apply, Polynomial.mul_comp, hC, weightedTaylor_X]
    · simp [map_mul, map_add, hP, MvPolynomial.finSuccEquiv_X_succ,
        Polynomial.taylor_apply, Polynomial.mul_comp, hC, weightedTaylor_X]

def weightedTaylor_firstVariableHasseJet {n : ℕ}
    (P : MvPolynomial (Fin (n + 1)) ℚ) (z i : ℕ) (β : Fin n → ℚ) :
    weightedTaylor β (firstVariableHasseJet P z i) =
      (MvPolynomial.finSuccEquiv ℚ n
        (weightedTaylor (Fin.cons (z : ℚ) β) P)).coeff i := by
  rw [finSuccEquiv_weightedTaylor, Polynomial.taylor_coeff]
  simp only [Fin.cons_zero, Fin.cons_succ]
  rw [← polynomial_map_hasseDeriv]
  have hz : MvPolynomial.C (z : ℚ) = weightedTaylor β (z : MvPolynomial (Fin n) ℚ) := by simp
  rw [hz, Polynomial.eval_map_apply]
  rfl

def gridHasseJet_eq_taylorCoeff (n : ℕ) (P : MvPolynomial (Fin n) ℚ)
    (z a : Fin n → ℕ) :
    gridHasseJet P z a = MvPolynomial.coeff (Finsupp.equivFunOnFinite.symm a)
      (weightedTaylor (fun i => (z i : ℚ)) P) := by
  induction n with
  | zero =>
    have hz : (fun i : Fin 0 => (z i : ℚ)) = 0 := funext (fun i => Fin.elim0 i)
    have ha : Finsupp.equivFunOnFinite.symm a = 0 := by ext i; exact Fin.elim0 i
    have he : (fun i : Fin 0 => (Fin.elim0 i : ℚ)) = 0 := funext (fun i => Fin.elim0 i)
    simp only [gridHasseJet, hz, ha, he, weightedTaylor_zero,
      MvPolynomial.eval_zero, MvPolynomial.constantCoeff_eq]
  | succ n ih =>
    rw [gridHasseJet, ih]
    rw [weightedTaylor_firstVariableHasseJet]
    rw [MvPolynomial.finSuccEquiv_coeff_coeff]
    congr 1
    · ext i
      refine Fin.cases ?_ (fun j => ?_) i <;> simp
    · congr 1
      apply congrArg weightedTaylor
      funext i
      refine Fin.cases ?_ (fun j => ?_) i <;> simp

def exists_bounded_grid_taylorCoeff_ne_zero (n : ℕ)
    (P : MvPolynomial (Fin n) ℚ) (hP : P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ (z : Fin n → ℕ) (a : Fin n →₀ ℕ), (∀ i, z i ≤ B) ∧
      (∀ i, a i ≤ P.degreeOf i / B) ∧
      MvPolynomial.coeff a (weightedTaylor (fun i => (z i : ℚ)) P) ≠ 0 := by
  obtain ⟨z, a, hz, ha, hne⟩ := exists_bounded_gridHasseJet_ne_zero n P hP B hB
  exact ⟨z, Finsupp.equivFunOnFinite.symm a, hz, ha,
    (gridHasseJet_eq_taylorCoeff n P z a) ▸ hne⟩


end
end Bounty

end SubmissionComponent_GridTaylorNonvanishing

/- Component GridDividedDerivative; SHA256 96225ae74321bcb2aa39fe73e035991612fea04ea64f7d7e086c5302ff0d1540 -/
section SubmissionComponent_GridDividedDerivative
/- Bounded-grid nonvanishing for the same divided derivative operators used by Roth. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def constantCoeff_weightedTaylor {I : Type*} (β : I → ℚ)
    (P : MvPolynomial I ℚ) :
    MvPolynomial.constantCoeff (weightedTaylor β P) = MvPolynomial.eval β P := by
  induction P using MvPolynomial.induction_on with
  | C c => simp [weightedTaylor_C]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP => simp [map_mul, map_add, hP, weightedTaylor_X]

def weightedTaylor_wordPDeriv {I : Type*} (β : I → ℚ)
    (s : List I) (P : MvPolynomial I ℚ) :
    weightedTaylor β (wordPDeriv s P) = wordPDeriv s (weightedTaylor β P) := by
  induction s with
  | nil => rfl
  | cons i s ih => rw [wordPDeriv_cons, weightedTaylor_pderiv, ih, wordPDeriv_cons]

def weightedTaylor_dividedWordPDeriv {I : Type*} [Fintype I] [DecidableEq I]
    (β : I → ℚ) (s : List I) (P : MvPolynomial I ℚ) :
    weightedTaylor β (dividedWordPDeriv s P) = dividedWordPDeriv s (weightedTaylor β P) := by
  change weightedTaylor β ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P) =
    (wordDerivativeFactorial s)⁻¹ • wordPDeriv s (weightedTaylor β P)
  simp only [MvPolynomial.smul_eq_C_mul, map_mul, weightedTaylor_C, weightedTaylor_wordPDeriv]

def eval_dividedWordPDeriv_eq_taylorCoeff {I : Type*} [Fintype I] [DecidableEq I]
    (β : I → ℚ) (s : List I) (P : MvPolynomial I ℚ) :
    MvPolynomial.eval β (dividedWordPDeriv s P) =
      MvPolynomial.coeff (wordDerivativeCounts s) (weightedTaylor β P) := by
  rw [← constantCoeff_weightedTaylor, MvPolynomial.constantCoeff_eq,
    weightedTaylor_dividedWordPDeriv, coeff_dividedWordPDeriv]
  simp

def exists_wordDerivativeCounts {I : Type*} [Fintype I] [DecidableEq I]
    (a : I →₀ ℕ) : ∃ s : List I, wordDerivativeCounts s = a := by
  refine ⟨a.toMultiset.toList, ?_⟩
  ext i
  rw [wordDerivativeCounts_apply, ← Multiset.coe_count, Multiset.coe_toList,
    Finsupp.count_toMultiset]

def exists_bounded_grid_dividedWordPDeriv_ne_zero (n : ℕ)
    (P : MvPolynomial (Fin n) ℚ) (hP : P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ (z : Fin n → ℕ) (s : List (Fin n)), (∀ i, z i ≤ B) ∧
      (∀ i, s.count i ≤ P.degreeOf i / B) ∧
      MvPolynomial.eval (fun i => (z i : ℚ)) (dividedWordPDeriv s P) ≠ 0 := by
  obtain ⟨z, a, hz, ha, hne⟩ := exists_bounded_grid_taylorCoeff_ne_zero n P hP B hB
  obtain ⟨s, hs⟩ := exists_wordDerivativeCounts a
  refine ⟨z, s, hz, ?_, ?_⟩
  · intro i
    simpa only [← hs, wordDerivativeCounts_apply] using ha i
  · rwa [eval_dividedWordPDeriv_eq_taylorCoeff, hs]


end
end Bounty

end SubmissionComponent_GridDividedDerivative

/- Component HyperplaneDerivativeWitness; SHA256 442ba4f39c72d251b0a37ee5e78d8be942cb30e28605dceb041aa3e53ea1f5a4 -/
section SubmissionComponent_HyperplaneDerivativeWitness
/- Actual coordinate derivatives witnessing the weighted hyperplane index. -/

namespace Bounty
noncomputable section
open scoped BigOperators

variable {B C : Type*}

def pderiv_inl_rename_inr (b : B) (P : MvPolynomial C ℚ) :
    MvPolynomial.pderiv (Sum.inl b) (MvPolynomial.rename (Sum.inr : C → B ⊕ C) P) = 0 := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ, add_zero]
  | mul_X P c hP => simp [map_mul, hP]

def pderiv_inl_complementShear (g : B → MvPolynomial C ℚ)
    (b : B) (P : MvPolynomial (B ⊕ C) ℚ) :
    MvPolynomial.pderiv (Sum.inl b) (complementShear g P) =
      complementShear g (MvPolynomial.pderiv (Sum.inl b) P) := by
  classical
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i <;> simp [map_mul, MvPolynomial.pderiv_X, Pi.single_apply,
      complementShear_X_inl, complementShear_X_inr, pderiv_inl_rename_inr, hP, apply_ite]

def wordPDeriv_inl_complementShear (g : B → MvPolynomial C ℚ)
    (s : List B) (P : MvPolynomial (B ⊕ C) ℚ) :
    wordPDeriv (s.map Sum.inl) (complementShear g P) =
      complementShear g (wordPDeriv (s.map Sum.inl) P) := by
  induction s with
  | nil => rfl
  | cons b s ih =>
    simp only [List.map_cons, wordPDeriv_cons, ih, pderiv_inl_complementShear]

def dividedWordPDeriv_inl_complementShear [Fintype B] [Fintype C]
    [DecidableEq B] [DecidableEq C] (g : B → MvPolynomial C ℚ)
    (s : List B) (P : MvPolynomial (B ⊕ C) ℚ) :
    dividedWordPDeriv (s.map Sum.inl) (complementShear g P) =
      complementShear g (dividedWordPDeriv (s.map Sum.inl) P) := by
  change (wordDerivativeFactorial (s.map Sum.inl))⁻¹ •
      wordPDeriv (s.map Sum.inl) (complementShear g P) =
    complementShear g ((wordDerivativeFactorial (s.map Sum.inl))⁻¹ •
      wordPDeriv (s.map Sum.inl) P)
  rw [map_smul, wordPDeriv_inl_complementShear]

def complementRestriction (g : B → MvPolynomial C ℚ)
    (P : MvPolynomial (B ⊕ C) ℚ) : MvPolynomial C ℚ :=
  (complementShear g P).killCompl Sum.inr_injective

def wordDerivativeCounts_map_inl [Fintype B] [Fintype C]
    [DecidableEq B] [DecidableEq C] (s : List B) :
    wordDerivativeCounts (s.map (Sum.inl : B → B ⊕ C)) =
      (wordDerivativeCounts s).mapDomain Sum.inl := by
  induction s with
  | nil => simp only [List.map_nil, wordDerivativeCounts_nil, Finsupp.mapDomain_zero]
  | cons b s ih =>
    rw [List.map_cons, wordDerivativeCounts_cons, wordDerivativeCounts_cons,
      Finsupp.mapDomain_add, Finsupp.mapDomain_single, ih]

def exponent_map_inr_inl (a : C →₀ ℕ) (b : B) :
    a.mapDomain (Sum.inr : C → B ⊕ C) (Sum.inl b) = 0 :=
  Finsupp.mapDomain_of_notMem_range _ _ (by simp)

def exponent_map_inl_inr (a : B →₀ ℕ) (c : C) :
    a.mapDomain (Sum.inl : B → B ⊕ C) (Sum.inr c) = 0 :=
  Finsupp.mapDomain_of_notMem_range _ _ (by simp)

def sum_exponent_parts (e : (B ⊕ C) →₀ ℕ) :
    (e.comapDomain Sum.inr Sum.inr_injective.injOn).mapDomain Sum.inr +
      (e.comapDomain Sum.inl Sum.inl_injective.injOn).mapDomain Sum.inl = e := by
  ext i
  cases i <;> simp only [Finsupp.add_apply,
    Finsupp.mapDomain_apply Sum.inl_injective, Finsupp.mapDomain_apply Sum.inr_injective,
    Finsupp.comapDomain_apply, exponent_map_inr_inl, exponent_map_inl_inr,
    zero_add, add_zero]

def coeff_restricted_pivot_derivative [Fintype B] [Fintype C]
    [DecidableEq B] [DecidableEq C] (P : MvPolynomial (B ⊕ C) ℚ)
    (e : (B ⊕ C) →₀ ℕ) (s : List B)
    (hs : wordDerivativeCounts s = e.comapDomain Sum.inl Sum.inl_injective.injOn) :
    MvPolynomial.coeff (e.comapDomain Sum.inr Sum.inr_injective.injOn)
        ((dividedWordPDeriv (s.map Sum.inl) P).killCompl Sum.inr_injective) =
      MvPolynomial.coeff e P := by
  rw [MvPolynomial.coeff_killCompl, coeff_dividedWordPDeriv]
  change MvPolynomial.coeff (_ + wordDerivativeCounts (s.map Sum.inl)) P *
    (∏ i, (((e.comapDomain Sum.inr Sum.inr_injective.injOn).mapDomain Sum.inr i +
      wordDerivativeCounts (s.map Sum.inl) i).choose
      (wordDerivativeCounts (s.map Sum.inl) i) : ℚ)) = _
  rw [wordDerivativeCounts_map_inl, hs, sum_exponent_parts]
  have hf (i : B ⊕ C) :
      (((e.comapDomain Sum.inr Sum.inr_injective.injOn).mapDomain Sum.inr i +
          (e.comapDomain Sum.inl Sum.inl_injective.injOn).mapDomain Sum.inl i).choose
        ((e.comapDomain Sum.inl Sum.inl_injective.injOn).mapDomain Sum.inl i) : ℚ) = 1 := by
    cases i <;> simp [exponent_map_inr_inl, exponent_map_inl_inr]
  simp only [hf, Finset.prod_const_one, mul_one]

def exists_pivot_derivative_restriction [Fintype B] [Fintype C]
    [DecidableEq B] [DecidableEq C] (w : B → ℕ) (g : B → MvPolynomial C ℚ)
    (P : MvPolynomial (B ⊕ C) ℚ) (hP : P ≠ 0) :
    ∃ s : List B,
      complementRestriction g (dividedWordPDeriv (s.map Sum.inl) P) ≠ 0 ∧
      Finsupp.weight w (wordDerivativeCounts s) = (complementHyperplaneIndex w g P).toNat := by
  have hS : complementShear g P ≠ 0 := by
    intro hz
    exact hP ((complementShear_injective g) (hz.trans (map_zero _).symm))
  obtain ⟨e, he, hweight⟩ := weightedPolynomialOrder_attained (Sum.elim w (fun _ : C => 0)) hS
  obtain ⟨s, hs⟩ := exists_wordDerivativeCounts
    (e.comapDomain Sum.inl Sum.inl_injective.injOn)
  refine ⟨s, ?_, ?_⟩
  · intro hz
    have hc := coeff_restricted_pivot_derivative (complementShear g P) e s hs
    rw [dividedWordPDeriv_inl_complementShear] at hc
    change MvPolynomial.coeff _ (complementRestriction g _) = _ at hc
    rw [hz, MvPolynomial.coeff_zero] at hc
    exact he hc.symm
  · have hn := congrArg ENat.toNat hweight
    simp only [ENat.toNat_natCast] at hn
    rw [hs]
    change _ = (weightedPolynomialOrder (Sum.elim w (fun _ : C => 0))
      (complementShear g P)).toNat
    rw [← hn, Finsupp.weight_eq_sum, Finsupp.weight_eq_sum, Fintype.sum_sum_type]
    simp [Finsupp.comapDomain_apply]

def exists_normalized_pivot_derivative_restriction {m : ℕ} [Fintype C] [DecidableEq C]
    (r : Fin m → ℕ) (hr : ∀ i, 0 < r i) (g : Fin m → MvPolynomial C ℚ)
    (P : MvPolynomial (Fin m ⊕ C) ℚ) (hP : P ≠ 0) :
    ∃ s : List (Fin m),
      complementRestriction g (dividedWordPDeriv (s.map Sum.inl) P) ≠ 0 ∧
      (∑ i, ((s.count i : ℕ) : ℝ) / r i) = normalizedComplementHyperplaneIndex r g P := by
  obtain ⟨s, hs, heq⟩ := exists_pivot_derivative_restriction (rothWeight r) g P hP
  refine ⟨s, hs, ?_⟩
  rw [normalizedComplementHyperplaneIndex, ← heq,
    rothMonomialWeight_eq_normalized_weight hr]
  rfl


end
end Bounty

end SubmissionComponent_HyperplaneDerivativeWitness

/- Component HyperplaneGraph; SHA256 8fbd8810802a6ac638830614b53e07561fbf7ef25dc4e1d34211e399372e0343 -/
section SubmissionComponent_HyperplaneGraph
/- The concrete shear restricts to the kernel of the given rational forms. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def sum_complement_fiber {m d : ℕ} {R : Type*} [AddCommMonoid R]
    (p : Fin m → Fin (d + 1)) (f : Fin m × Fin (d + 1) → R) (h : Fin m) :
    (∑ k ∈ Finset.univ.erase (p h), f (h, k)) =
      ∑ x ∈ Finset.univ.filter (fun x : HyperplaneComplement p => x.val.1 = h), f x.val := by
  classical
  refine Finset.sum_bij (fun k hk =>
    (⟨(h, k), (Finset.mem_erase.mp hk).1⟩ : HyperplaneComplement p)) ?_ ?_ ?_ ?_
  · intro k hk
    exact Finset.mem_filter.mpr ⟨Finset.mem_univ _, rfl⟩
  · intro k hk l hl he
    exact congrArg (fun x : HyperplaneComplement p => x.val.2) he
  · intro x hx
    have hh : x.val.1 = h := (Finset.mem_filter.mp hx).2
    have hk : x.val.2 ≠ p h := by simpa only [← hh] using x.property
    refine ⟨x.val.2, Finset.mem_erase.mpr ⟨hk, Finset.mem_univ _⟩, ?_⟩
    apply Subtype.ext
    exact Prod.ext hh.symm rfl
  · intro k hk
    rfl

def productHyperplaneLinearForm {m d : ℕ} (b : Fin m → Fin (d + 1) → ℚ)
    (h : Fin m) : MvPolynomial (Fin m × Fin (d + 1)) ℚ :=
  ∑ k, MvPolynomial.C (b h k) * MvPolynomial.X (h, k)

def pivot_scaled_complement_form {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (h : Fin m) (hp : b h (p h) ≠ 0) :
    MvPolynomial.C (b h (p h)) *
      MvPolynomial.rename (Sum.inr : HyperplaneComplement p → Fin m ⊕ HyperplaneComplement p)
        (blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
          (pivotComplementCoefficient b p) h) =
      -(∑ x ∈ Finset.univ.filter (fun x : HyperplaneComplement p => x.val.1 = h),
        MvPolynomial.C (b x.val.1 x.val.2) * MvPolynomial.X (Sum.inr x)) := by
  classical
  unfold blockComplementLinear
  rw [map_sum, Finset.mul_sum, ← Finset.sum_neg_distrib]
  refine Finset.sum_congr ?_ ?_
  · ext x
    simp
  intro x hx
  have hh : x.val.1 = h := (Finset.mem_filter.mp hx).2
  simp only [map_mul, MvPolynomial.rename_C, MvPolynomial.rename_X,
    pivotComplementCoefficient, hh]
  rw [← mul_assoc, ← MvPolynomial.C_mul]
  have hc : b h (p h) * -(b h x.val.2 / b h (p h)) = -(b h x.val.2) := by
    field_simp
  rw [hc, MvPolynomial.C_neg, neg_mul]

def rename_productHyperplaneLinearForm {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (h : Fin m) (hp : b h (p h) ≠ 0) :
    MvPolynomial.rename (hyperplanePivotEquiv p) (productHyperplaneLinearForm b h) =
      MvPolynomial.C (b h (p h)) *
        (MvPolynomial.X (Sum.inl h) -
          MvPolynomial.rename Sum.inr
            (blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
              (pivotComplementCoefficient b p) h)) := by
  classical
  unfold productHyperplaneLinearForm
  rw [map_sum]
  simp only [map_mul, MvPolynomial.rename_C, MvPolynomial.rename_X]
  rw [← Finset.sum_erase_add Finset.univ _ (Finset.mem_univ (p h))]
  rw [sum_complement_fiber p (fun x => MvPolynomial.C (b x.1 x.2) *
    MvPolynomial.X (hyperplanePivotEquiv p x)) h]
  simp only [hyperplanePivotEquiv_complement, hyperplanePivotEquiv_pivot]
  rw [mul_sub, pivot_scaled_complement_form b p h hp]
  ring

variable {B C : Type*}

def killCompl_inr_X_inl (b : B) :
    (MvPolynomial.X (R := ℚ) (Sum.inl b : B ⊕ C)).killCompl Sum.inr_injective = 0 := by
  change (MvPolynomial.monomial (Finsupp.single (Sum.inl b) 1) (1 : ℚ)).killCompl _ = 0
  apply MvPolynomial.killCompl_monomial_eq_zero_of_notMem_range _ _ (a := Sum.inl b)
  · simp
  · simp

def killCompl_inr_X_inr (c : C) :
    (MvPolynomial.X (R := ℚ) (Sum.inr c : B ⊕ C)).killCompl Sum.inr_injective = MvPolynomial.X c := by
  simpa only [MvPolynomial.rename_X] using MvPolynomial.killCompl_rename_app
    (f := (Sum.inr : C → B ⊕ C)) Sum.inr_injective (MvPolynomial.X (R := ℚ) c)

def complementRestriction_eq_aeval (g : B → MvPolynomial C ℚ)
    (P : MvPolynomial (B ⊕ C) ℚ) :
    complementRestriction g P = MvPolynomial.aeval (Sum.elim g MvPolynomial.X) P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [complementRestriction]
  | add P Q hP hQ => simpa only [complementRestriction, map_add] using congrArg₂ (· + ·) hP hQ
  | mul_X P i hP =>
    unfold complementRestriction at *
    cases i <;> simp only [map_mul, MvPolynomial.aeval_X, Sum.elim_inl, Sum.elim_inr,
      complementShear_X_inl, complementShear_X_inr, map_add,
      killCompl_inr_X_inl, killCompl_inr_X_inr, MvPolynomial.killCompl_rename_app,
      zero_add, hP]

def complementRestriction_productHyperplaneLinearForm {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (h : Fin m) (hp : b h (p h) ≠ 0) :
    complementRestriction
      (blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
        (pivotComplementCoefficient b p))
      (MvPolynomial.rename (hyperplanePivotEquiv p) (productHyperplaneLinearForm b h)) = 0 := by
  rw [rename_productHyperplaneLinearForm b p h hp]
  simp [complementRestriction, map_mul, map_sub, complementShear_rename_inr,
    complementShear_X_inl, killCompl_inr_X_inl]


end
end Bounty

end SubmissionComponent_HyperplaneGraph

/- Component DividedDerivativeRename; SHA256 0ac17492adcbfef7e918b335642f839749e74db7c48cee00cd6e567b23b78db1 -/
section SubmissionComponent_DividedDerivativeRename
/- Exact coordinate transport for divided derivative words. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def wordPDeriv_rename {I J : Type*} (f : I → J) (hf : Function.Injective f)
    (s : List I) (P : MvPolynomial I ℚ) :
    wordPDeriv (s.map f) (MvPolynomial.rename f P) =
      MvPolynomial.rename f (wordPDeriv s P) := by
  induction s with
  | nil => rfl
  | cons i s ih =>
    simp only [List.map_cons, wordPDeriv_cons, ih, MvPolynomial.pderiv_rename hf]

def wordDerivativeCounts_map_injective {I J : Type*}
    [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J]
    (f : I → J) (s : List I) :
    wordDerivativeCounts (s.map f) = (wordDerivativeCounts s).mapDomain f := by
  induction s with
  | nil => simp only [List.map_nil, wordDerivativeCounts_nil, Finsupp.mapDomain_zero]
  | cons i s ih =>
    rw [List.map_cons, wordDerivativeCounts_cons, wordDerivativeCounts_cons,
      Finsupp.mapDomain_add, Finsupp.mapDomain_single, ih]

def wordDerivativeFactorial_map_equiv {I J : Type*}
    [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J]
    (e : I ≃ J) (s : List I) : wordDerivativeFactorial (s.map e) = wordDerivativeFactorial s := by
  change (∏ j, ((wordDerivativeCounts (s.map e) j).factorial : ℚ)) =
    ∏ i, ((wordDerivativeCounts s i).factorial : ℚ)
  rw [wordDerivativeCounts_map_injective]
  calc
    _ = ∏ i, (((wordDerivativeCounts s).mapDomain e (e i)).factorial : ℚ) :=
      (Equiv.prod_comp e _).symm
    _ = _ := by simp only [Finsupp.mapDomain_apply e.injective]

def dividedWordPDeriv_rename_equiv {I J : Type*}
    [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J]
    (e : I ≃ J) (s : List I) (P : MvPolynomial I ℚ) :
    dividedWordPDeriv (s.map e) (MvPolynomial.rename e P) =
      MvPolynomial.rename e (dividedWordPDeriv s P) := by
  change (wordDerivativeFactorial (s.map e))⁻¹ • wordPDeriv (s.map e) (MvPolynomial.rename e P) =
    MvPolynomial.rename e ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P)
  rw [map_smul, wordPDeriv_rename _ e.injective, wordDerivativeFactorial_map_equiv]


end
end Bounty

end SubmissionComponent_DividedDerivativeRename

/- Component BalancedAuxiliaryHeight; SHA256 c0f42411c2cd8b645813e768c4d07ae693e05a3f2eb3cfee7212e78e2f635e05 -/
section SubmissionComponent_BalancedAuxiliaryHeight
/- Degree-uniform coefficient heights for the constructed balanced auxiliary
polynomial.  All counting estimates are for the actual composition-array type. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def weakComposition_card_le (d r : ℕ) :
    Fintype.card (WeakComposition d r) ≤ (r + 1) ^ d := by
  let f : WeakComposition d r → Fin d → Fin (r + 1) :=
    fun v i => ⟨v.val i, Nat.lt_succ_of_le (weakComposition_coord_le v i)⟩
  have hf : Function.Injective f := by
    intro v w hvw
    apply Subtype.ext
    funext i
    exact congrArg (fun z : Fin d → Fin (r + 1) => (z i).val) hvw
  simpa using Fintype.card_le_of_injective f hf

def compositionArray_card_le_product {m d : ℕ} (r : Fin m → ℕ) :
    Fintype.card (CompositionArray m d r) ≤ ∏ h, (r h + 1) ^ d := by
  rw [Fintype.card_pi]
  exact Finset.prod_le_prod (fun h _ => Nat.zero_le _)
    (fun h _ => weakComposition_card_le d (r h))

def compositionArray_card_le_two_pow {m d : ℕ} (r : Fin m → ℕ) :
    Fintype.card (CompositionArray m d r) ≤ 2 ^ (d * ∑ h, r h) := by
  calc
    _ ≤ ∏ h, (r h + 1) ^ d := compositionArray_card_le_product r
    _ ≤ ∏ h, (2 ^ r h) ^ d := Finset.prod_le_prod (fun h _ => Nat.zero_le _)
      (fun h _ => Nat.pow_le_pow_left (r h).lt_two_pow_self d)
    _ = _ := by
      simp_rw [← pow_mul]
      rw [Finset.prod_pow_eq_pow_sum]
      congr 1
      rw [← Finset.sum_mul, mul_comm]

def compositionArray_log_card_le {m d : ℕ} (r : Fin m → ℕ) (hd : 0 < d) :
    Real.log (Fintype.card (CompositionArray m d r)) ≤
      (d : ℝ) * (∑ h, (r h : ℝ)) * Real.log 2 := by
  have hN : (0 : ℝ) < Fintype.card (CompositionArray m d r) := by
    exact_mod_cast compositionArray_card_pos r hd
  have hbound : (Fintype.card (CompositionArray m d r) : ℝ) ≤
      (2 : ℝ) ^ (d * ∑ h, r h) := by
    exact_mod_cast compositionArray_card_le_two_pow (d := d) r
  have hh := Real.log_le_log hN hbound
  simpa only [Real.log_pow, Nat.cast_mul, Nat.cast_sum] using hh

def balanced_auxiliary_log_bound {m d : ℕ} (r : Fin m → ℕ) (hd : 0 < d)
    (P : MvPolynomial (Fin m × Fin d) ℤ) (hP : P ≠ 0)
    (C : ℝ) (hC : 1 ≤ C)
    (hbound : polynomialCoeffL1 P ≤
      (Fintype.card (CompositionArray m d r) : ℝ) ^ 2 * C ^ (∑ h, r h)) :
    Real.log (polynomialCoeffL1 P) ≤
      (2 * (d : ℝ) * Real.log 2 + Real.log C) * (∑ h, (r h : ℝ)) := by
  have hN : (0 : ℝ) < Fintype.card (CompositionArray m d r) := by
    exact_mod_cast compositionArray_card_pos r hd
  have hC0 : 0 < C := lt_of_lt_of_le zero_lt_one hC
  have hlogN := compositionArray_log_card_le r hd
  calc
    _ ≤ Real.log ((Fintype.card (CompositionArray m d r) : ℝ) ^ 2 * C ^ (∑ h, r h)) :=
      Real.log_le_log (polynomialCoeffL1_pos hP) hbound
    _ = 2 * Real.log (Fintype.card (CompositionArray m d r)) +
        (∑ h, (r h : ℝ)) * Real.log C := by
      rw [Real.log_mul (pow_ne_zero _ (ne_of_gt hN)) (pow_ne_zero _ (ne_of_gt hC0)),
        Real.log_pow, Real.log_pow]
      norm_num [Nat.cast_sum]
    _ ≤ _ := by nlinarith

def exists_balanced_integer_auxiliary_log_bound {m d s : ℕ}
    (r : Fin m → ℕ) (hm : 0 < m) (hd : 0 < d) (hr : ∀ h, 0 < r h)
    (η : ℝ) (hη : 0 ≤ η) (hlarge : 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2)
    (A : Fin s → Fin m → Fin d → Fin d → ℤ)
    (C : ℝ) (hC : 1 ≤ C) (hA : ∀ v h i, ∑ j, ‖A v h i j‖ ≤ C) :
    ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧
      ProductBlockHomogeneous r P ∧
      Real.log (polynomialCoeffL1 P) ≤
        (2 * (d : ℝ) * Real.log 2 + Real.log C) * (∑ h, (r h : ℝ)) ∧
      ∀ v e, MvPolynomial.coeff e (blockLinearSubstitution (A v) P) ≠ 0 →
        (∀ h, ∑ i, e (h, i) = r h) ∧
        ∀ i : Fin d, |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < (m : ℝ) * η := by
  obtain ⟨P, hP, hhom, hnorm, hbalance⟩ :=
    exists_balanced_integer_auxiliary r hm hd hr η hη hlarge A C hC hA
  exact ⟨P, hP, hhom, balanced_auxiliary_log_bound r hd P hP C hC hnorm, hbalance⟩


end
end Bounty

end SubmissionComponent_BalancedAuxiliaryHeight

/- Component RationalBalancedAuxiliary; SHA256 a2a9d196f4a912803c47e3a8ca6b684b434403b22380573724f497d074424dbe -/
section SubmissionComponent_RationalBalancedAuxiliary
/- Common-denominator transfer of the actual balanced integer auxiliary
polynomial to fixed rational changes of coordinates inside blocks. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rationalBlockLinearForm {m d : ℕ} (B : Fin m → Fin d → Fin d → ℚ)
    (x : Fin m × Fin d) : MvPolynomial (Fin m × Fin d) ℚ :=
  ∑ j, MvPolynomial.C (B x.1 x.2 j) * MvPolynomial.X (x.1, j)

def rationalBlockLinearSubstitution {m d : ℕ} (B : Fin m → Fin d → Fin d → ℚ) :
    MvPolynomial (Fin m × Fin d) ℚ →ₐ[ℚ] MvPolynomial (Fin m × Fin d) ℚ :=
  MvPolynomial.aeval (rationalBlockLinearForm B)

def integer_map_aeval {I : Type*} (g : I → MvPolynomial I ℤ)
    (P : MvPolynomial I ℤ) :
    MvPolynomial.map (Int.castRingHom ℚ) (MvPolynomial.aeval g P) =
      MvPolynomial.aeval (fun i => MvPolynomial.map (Int.castRingHom ℚ) (g i))
        (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  induction P using MvPolynomial.induction_on with
  | C a => simp only [MvPolynomial.aeval_C, MvPolynomial.algebraMap_eq,
      MvPolynomial.map_C, Int.coe_castRingHom]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP => simp only [map_mul, MvPolynomial.aeval_X, MvPolynomial.map_X, hP]

def aeval_scaled_of_fixed_total {I : Type*} [Fintype I]
    (P : MvPolynomial I ℚ) (R : ℕ)
    (hP : ∀ e ∈ P.support, ∑ i, e i = R)
    (g : I → MvPolynomial I ℚ) (c : ℚ) :
    MvPolynomial.aeval (fun i => MvPolynomial.C c * g i) P =
      MvPolynomial.C (c ^ R) * MvPolynomial.aeval g P := by
  classical
  conv_lhs => rw [MvPolynomial.as_sum P]
  conv_rhs => rw [MvPolynomial.as_sum P]
  simp only [map_sum, Finset.mul_sum]
  apply Finset.sum_congr rfl
  intro e he
  rw [MvPolynomial.aeval_monomial, MvPolynomial.aeval_monomial]
  simp only [MvPolynomial.algebraMap_eq]
  rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _),
    Finsupp.prod_fintype _ _ (fun _ => pow_zero _)]
  simp_rw [mul_pow]
  rw [Finset.prod_mul_distrib, Finset.prod_pow_eq_pow_sum, hP e he, ← map_pow]
  ring

def productBlockHomogeneous_integer_map_total {m d : ℕ} (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℤ) (hP : ProductBlockHomogeneous r P)
    (e : (Fin m × Fin d) →₀ ℕ)
    (he : e ∈ (MvPolynomial.map (Int.castRingHom ℚ) P).support) :
    ∑ x : Fin m × Fin d, e x = ∑ h, r h := by
  have hc : MvPolynomial.coeff e P ≠ 0 := by
    intro hz
    have hh := MvPolynomial.mem_support_iff.mp he
    simp [MvPolynomial.coeff_map, hz] at hh
  rw [Fintype.sum_prod_type]
  exact Finset.sum_congr rfl (fun h _ => hP e (MvPolynomial.mem_support_iff.mpr hc) h)

def map_blockLinearForm_scaled {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℤ) (B : Fin m → Fin d → Fin d → ℚ)
    (D : ℤ) (hAB : ∀ h i j, (A h i j : ℚ) = (D : ℚ) * B h i j)
    (x : Fin m × Fin d) :
    MvPolynomial.map (Int.castRingHom ℚ) (blockLinearForm A x) =
      MvPolynomial.C (D : ℚ) * rationalBlockLinearForm B x := by
  simp only [blockLinearForm, rationalBlockLinearForm, map_sum, map_mul,
    MvPolynomial.map_C, MvPolynomial.map_X, Int.coe_castRingHom, Finset.mul_sum]
  apply Finset.sum_congr rfl
  intro j _
  rw [hAB, map_mul, mul_assoc]

def rationalBlockLinearSubstitution_scale_identity {m d : ℕ}
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) ℤ)
    (hP : ProductBlockHomogeneous r P)
    (A : Fin m → Fin d → Fin d → ℤ) (B : Fin m → Fin d → Fin d → ℚ)
    (D : ℤ) (hAB : ∀ h i j, (A h i j : ℚ) = (D : ℚ) * B h i j) :
    MvPolynomial.map (Int.castRingHom ℚ) (blockLinearSubstitution A P) =
      MvPolynomial.C ((D : ℚ) ^ (∑ h, r h)) *
        rationalBlockLinearSubstitution B (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  rw [blockLinearSubstitution, integer_map_aeval]
  simp_rw [map_blockLinearForm_scaled A B D hAB]
  exact aeval_scaled_of_fixed_total _ _ (productBlockHomogeneous_integer_map_total r P hP)
    (rationalBlockLinearForm B) (D : ℚ)

def rationalBlockLinearSubstitution_coeff_ne_zero {m d : ℕ}
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) ℤ)
    (hP : ProductBlockHomogeneous r P)
    (A : Fin m → Fin d → Fin d → ℤ) (B : Fin m → Fin d → Fin d → ℚ)
    (D : ℤ) (hD : D ≠ 0) (hAB : ∀ h i j, (A h i j : ℚ) = (D : ℚ) * B h i j)
    (e : (Fin m × Fin d) →₀ ℕ)
    (he : MvPolynomial.coeff e
      (rationalBlockLinearSubstitution B (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0) :
    MvPolynomial.coeff e (blockLinearSubstitution A P) ≠ 0 := by
  have hh := congrArg (MvPolynomial.coeff e)
    (rationalBlockLinearSubstitution_scale_identity r P hP A B D hAB)
  rw [MvPolynomial.coeff_map, MvPolynomial.coeff_C_mul] at hh
  have hDq : (D : ℚ) ≠ 0 := by exact_mod_cast hD
  intro hz
  simp only [hz, map_zero] at hh
  exact (mul_ne_zero (pow_ne_zero _ hDq) he) hh.symm

def exists_integer_scaled_block_matrices {m d s : ℕ}
    (B : Fin s → Fin m → Fin d → Fin d → ℚ) :
    ∃ D : ℤ, 0 < D ∧ ∃ A : Fin s → Fin m → Fin d → Fin d → ℤ,
      ∀ v h i j, (A v h i j : ℚ) = (D : ℚ) * B v h i j := by
  obtain ⟨D, hD⟩ := IsLocalization.exist_integer_multiples_of_finite (Submonoid.pos ℤ)
    (fun z : Fin s × Fin m × Fin d × Fin d => B z.1 z.2.1 z.2.2.1 z.2.2.2)
  choose A hA using hD
  refine ⟨D.val, D.property, fun v h i j => A (v, h, i, j), ?_⟩
  intro v h i j
  simpa [Algebra.smul_def] using hA (v, h, i, j)

def exists_integer_block_matrix_norm_bound {m d s : ℕ}
    (A : Fin s → Fin m → Fin d → Fin d → ℤ) :
    ∃ C : ℝ, 1 ≤ C ∧ ∀ v h i, ∑ j, ‖A v h i j‖ ≤ C := by
  let T : ℝ := ∑ v, ∑ h, ∑ i, ∑ j, ‖A v h i j‖
  have hT : 0 ≤ T := by dsimp [T]; positivity
  refine ⟨1 + T, by linarith, ?_⟩
  intro v h i
  have hi : (∑ j, ‖A v h i j‖) ≤ ∑ k, ∑ j, ‖A v h k j‖ :=
    Finset.single_le_sum (f := fun k : Fin d => ∑ j, ‖A v h k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ i)
  have hh : (∑ k, ∑ j, ‖A v h k j‖) ≤ ∑ t, ∑ k, ∑ j, ‖A v t k j‖ :=
    Finset.single_le_sum (f := fun t : Fin m => ∑ k, ∑ j, ‖A v t k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ h)
  have hv : (∑ t, ∑ k, ∑ j, ‖A v t k j‖) ≤ T :=
    Finset.single_le_sum (f := fun w : Fin s => ∑ t, ∑ k, ∑ j, ‖A w t k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ v)
  linarith [hi.trans (hh.trans hv)]

/-- The height constant is chosen from the fixed rational matrices before the
positive degree tuple and the balance tolerance.  Invertibility is not needed
for construction, so in particular the theorem applies to invertible matrices. -/
def exists_rational_balanced_auxiliary_constant {m d s : ℕ}
    (hm : 0 < m) (hd : 0 < d)
    (B : Fin s → Fin m → Fin d → Fin d → ℚ) :
    ∃ K : ℝ, 0 ≤ K ∧ ∀ (r : Fin m → ℕ), (∀ h, 0 < r h) →
      ∀ η : ℝ, 0 ≤ η → 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2 →
      ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧
        ProductBlockHomogeneous r P ∧
        Real.log (polynomialCoeffL1 P) ≤ K * (∑ h, (r h : ℝ)) ∧
        ∀ v e, MvPolynomial.coeff e
          (rationalBlockLinearSubstitution (B v) (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0 →
          (∀ h, ∑ i, e (h, i) = r h) ∧
          ∀ i : Fin d,
            |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < (m : ℝ) * η := by
  obtain ⟨D, hD, A, hAB⟩ := exists_integer_scaled_block_matrices B
  obtain ⟨C, hC, hA⟩ := exists_integer_block_matrix_norm_bound A
  refine ⟨2 * (d : ℝ) * Real.log 2 + Real.log C, ?_, ?_⟩
  · exact add_nonneg (mul_nonneg (by positivity) (Real.log_nonneg (by norm_num)))
      (Real.log_nonneg hC)
  · intro r hr η hη hlarge
    obtain ⟨P, hP, hhom, hnorm, hbalance⟩ :=
      exists_balanced_integer_auxiliary_log_bound r hm hd hr η hη hlarge A C hC hA
    refine ⟨P, hP, hhom, hnorm, ?_⟩
    intro v e he
    exact hbalance v e (rationalBlockLinearSubstitution_coeff_ne_zero r P hhom
      (A v) (B v) D (ne_of_gt hD) (hAB v) e he)


end
end Bounty

end SubmissionComponent_RationalBalancedAuxiliary

/- Component BalancedDerivativeSupport; SHA256 9b55965576a0bdab1f309355e0c9cd93c35b356c1083fa5013d7d41306f36468 -/
section SubmissionComponent_BalancedDerivativeSupport
/- Actual chain-rule support origins and preservation of balanced columns
under a small divided derivative in the original coordinates. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def pderiv_aeval_eq_sum_pderiv {I J : Type*} [Fintype I]
    (g : I → MvPolynomial J ℚ) (P : MvPolynomial I ℚ) (j : J) :
    MvPolynomial.pderiv j (MvPolynomial.aeval g P) =
      ∑ i, MvPolynomial.pderiv j (g i) * MvPolynomial.aeval g (MvPolynomial.pderiv i P) := by
  classical
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ, mul_add, Finset.sum_add_distrib]
  | mul_X P a hP =>
    simp only [map_mul, MvPolynomial.aeval_X, MvPolynomial.pderiv_mul, map_add,
      MvPolynomial.pderiv_X, Pi.single_apply, hP, mul_add, Finset.sum_add_distrib]
    have hfirst :
        ∑ i, MvPolynomial.pderiv j (g i) * (MvPolynomial.aeval g (MvPolynomial.pderiv i P) * g a) =
        (∑ i, MvPolynomial.pderiv j (g i) * MvPolynomial.aeval g (MvPolynomial.pderiv i P)) * g a := by
      rw [Finset.sum_mul]
      exact Finset.sum_congr rfl (fun _ _ => by ring)
    rw [hfirst]
    congr 1
    simp [mul_comm]

def rationalBlockLinearSubstitution_C {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (a : ℚ) :
    rationalBlockLinearSubstitution A (MvPolynomial.C a) = MvPolynomial.C a := by
  simp [rationalBlockLinearSubstitution]

def rationalBlockLinearSubstitution_X {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (x : Fin m × Fin d) :
    rationalBlockLinearSubstitution A (MvPolynomial.X x) = rationalBlockLinearForm A x := by
  simp [rationalBlockLinearSubstitution]

def pderiv_rationalBlockLinearForm {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (h a : Fin m) (j i : Fin d) :
    MvPolynomial.pderiv (h, j) (rationalBlockLinearForm A (a, i)) =
      if a = h then MvPolynomial.C (A a i j) else 0 := by
  classical
  unfold rationalBlockLinearForm
  simp only [map_sum, MvPolynomial.pderiv_C_mul, MvPolynomial.pderiv_X, Pi.single_apply]
  by_cases hah : a = h
  · subst a
    simp only [Prod.mk.injEq, true_and]
    simp
  · simp [Prod.mk.injEq, hah]

def pderiv_rationalBlockLinearSubstitution {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (P : MvPolynomial (Fin m × Fin d) ℚ)
    (h : Fin m) (j : Fin d) :
    MvPolynomial.pderiv (h, j) (rationalBlockLinearSubstitution A P) =
      ∑ i, MvPolynomial.C (A h i j) * rationalBlockLinearSubstitution A (MvPolynomial.pderiv (h, i) P) := by
  change MvPolynomial.pderiv (h, j) (MvPolynomial.aeval (rationalBlockLinearForm A) P) =
    ∑ i, MvPolynomial.C (A h i j) * MvPolynomial.aeval (rationalBlockLinearForm A) (MvPolynomial.pderiv (h, i) P)
  rw [pderiv_aeval_eq_sum_pderiv, Fintype.sum_prod_type]
  simp only [pderiv_rationalBlockLinearForm, ite_mul, zero_mul]
  simp
  
def rationalBlockLinearSubstitution_linearForm {m d : ℕ}
    (A B : Fin m → Matrix (Fin d) (Fin d) ℚ) (x : Fin m × Fin d) :
    rationalBlockLinearSubstitution A (rationalBlockLinearForm B x) =
      rationalBlockLinearForm (fun h => B h * A h) x := by
  simp only [rationalBlockLinearForm, map_sum, map_mul, rationalBlockLinearSubstitution_C,
    rationalBlockLinearSubstitution_X, Matrix.mul_apply, Finset.mul_sum, map_sum, Finset.sum_mul]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro j _
  exact (mul_assoc _ _ _).symm

def rationalBlockLinearSubstitution_comp {m d : ℕ}
    (A B : Fin m → Matrix (Fin d) (Fin d) ℚ) (P : MvPolynomial (Fin m × Fin d) ℚ) :
    rationalBlockLinearSubstitution A (rationalBlockLinearSubstitution B P) =
      rationalBlockLinearSubstitution (fun h => B h * A h) P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [map_mul, rationalBlockLinearSubstitution_X, rationalBlockLinearSubstitution_linearForm, hP]

def rationalBlockLinearSubstitution_one {m d : ℕ}
    (P : MvPolynomial (Fin m × Fin d) ℚ) :
    rationalBlockLinearSubstitution (fun _ => (1 : Matrix (Fin d) (Fin d) ℚ)) P = P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P x hP =>
    simp [map_mul, rationalBlockLinearSubstitution_X, rationalBlockLinearForm, Matrix.one_apply, hP]

/-- The inverse chain rule is derived from the actual invertible block matrices. -/
def rationalBlockLinearSubstitution_pderiv {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (h : Fin m) (i : Fin d) :
    rationalBlockLinearSubstitution A (MvPolynomial.pderiv (h, i) P) =
      ∑ j, MvPolynomial.C ((A h)⁻¹ j i) *
        MvPolynomial.pderiv (h, j) (rationalBlockLinearSubstitution A P) := by
  let Ainv : Fin m → Matrix (Fin d) (Fin d) ℚ := fun h => (A h)⁻¹
  change rationalBlockLinearSubstitution A (MvPolynomial.pderiv (h, i) P) =
    ∑ j, MvPolynomial.C (Ainv h j i) * MvPolynomial.pderiv (h, j) (rationalBlockLinearSubstitution A P)
  have hleft (Q : MvPolynomial (Fin m × Fin d) ℚ) :
      rationalBlockLinearSubstitution Ainv (rationalBlockLinearSubstitution A Q) = Q := by
    rw [rationalBlockLinearSubstitution_comp]
    have hh : (fun h => A h * Ainv h) = fun _ => (1 : Matrix (Fin d) (Fin d) ℚ) := by
      funext h
      exact Matrix.mul_nonsing_inv _ (isUnit_iff_ne_zero.mpr (hA h))
    exact (congrArg (fun T : Fin m → Matrix (Fin d) (Fin d) ℚ =>
      rationalBlockLinearSubstitution T Q) hh).trans (rationalBlockLinearSubstitution_one Q)
  have hright (Q : MvPolynomial (Fin m × Fin d) ℚ) :
      rationalBlockLinearSubstitution A (rationalBlockLinearSubstitution Ainv Q) = Q := by
    rw [rationalBlockLinearSubstitution_comp]
    have hh : (fun h => Ainv h * A h) = fun _ => (1 : Matrix (Fin d) (Fin d) ℚ) := by
      funext h
      exact Matrix.nonsing_inv_mul _ (isUnit_iff_ne_zero.mpr (hA h))
    exact (congrArg (fun T : Fin m → Matrix (Fin d) (Fin d) ℚ =>
      rationalBlockLinearSubstitution T Q) hh).trans (rationalBlockLinearSubstitution_one Q)
  have hh := pderiv_rationalBlockLinearSubstitution Ainv
    (rationalBlockLinearSubstitution A P) h i
  rw [hleft] at hh
  have hh' := congrArg (rationalBlockLinearSubstitution A) hh
  simpa only [map_sum, map_mul, rationalBlockLinearSubstitution_C, hright] using hh'

/-- The number of differentiations made in a particular block. -/
def derivativeBlockCount {m d : ℕ} (s : List (Fin m × Fin d)) (h : Fin m) : ℕ :=
  ∑ i, wordDerivativeCounts s (h, i)

def derivativeBlockCount_nil {m d : ℕ} (h : Fin m) :
    derivativeBlockCount ([] : List (Fin m × Fin d)) h = 0 := by
  simp [derivativeBlockCount, wordDerivativeCounts_nil]

def sum_block_single {m d : ℕ} (x : Fin m × Fin d) (h : Fin m) :
    ∑ i : Fin d, (Finsupp.single x 1 : (Fin m × Fin d) →₀ ℕ) (h, i) =
      if x.1 = h then 1 else 0 := by
  classical
  rcases x with ⟨a, j⟩
  by_cases hah : a = h
  · subst a
    simp [Finsupp.single_apply, Prod.mk.injEq]
  · simp [Prod.mk.injEq, hah]

def derivativeBlockCount_cons {m d : ℕ} (x : Fin m × Fin d)
    (s : List (Fin m × Fin d)) (h : Fin m) :
    derivativeBlockCount (x :: s) h =
      (if x.1 = h then 1 else 0) + derivativeBlockCount s h := by
  simp only [derivativeBlockCount, wordDerivativeCounts_cons, Finsupp.add_apply,
    Finset.sum_add_distrib, sum_block_single]

/-- Invertible block substitutions can redistribute the derivative counts within
a block, but every surviving monomial comes from an original monomial with
exactly the prescribed total loss in each block. -/
def rationalBlockLinearSubstitution_wordPDeriv_support_origin {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0)
    (s : List (Fin m × Fin d)) (P : MvPolynomial (Fin m × Fin d) ℚ)
    (e : (Fin m × Fin d) →₀ ℕ)
    (he : MvPolynomial.coeff e (rationalBlockLinearSubstitution A (wordPDeriv s P)) ≠ 0) :
    ∃ K : (Fin m × Fin d) →₀ ℕ,
      MvPolynomial.coeff (e + K) (rationalBlockLinearSubstitution A P) ≠ 0 ∧
      ∀ h, ∑ i, K (h, i) = derivativeBlockCount s h := by
  classical
  induction s generalizing e with
  | nil => exact ⟨0, by simpa [wordPDeriv_nil] using he, by simp [derivativeBlockCount_nil]⟩
  | cons x s ih =>
    rw [wordPDeriv_cons, rationalBlockLinearSubstitution_pderiv A hA,
      MvPolynomial.coeff_sum] at he
    obtain ⟨j, _, hj⟩ := Finset.exists_ne_zero_of_sum_ne_zero he
    rw [MvPolynomial.coeff_C_mul, MvPolynomial.coeff_pderiv] at hj
    have hcoeff : MvPolynomial.coeff (e + Finsupp.single (x.1, j) 1)
        (rationalBlockLinearSubstitution A (wordPDeriv s P)) ≠ 0 :=
      left_ne_zero_of_mul (right_ne_zero_of_mul hj)
    obtain ⟨K, hK, hcount⟩ := ih _ hcoeff
    refine ⟨Finsupp.single (x.1, j) 1 + K, ?_, ?_⟩
    · simpa only [add_assoc] using hK
    · intro h
      simp only [Finsupp.add_apply, Finset.sum_add_distrib, sum_block_single,
        hcount, derivativeBlockCount_cons]

def rationalBlockLinearSubstitution_dividedWordPDeriv_support_origin {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0)
    (s : List (Fin m × Fin d)) (P : MvPolynomial (Fin m × Fin d) ℚ)
    (e : (Fin m × Fin d) →₀ ℕ)
    (he : MvPolynomial.coeff e
      (rationalBlockLinearSubstitution A (dividedWordPDeriv s P)) ≠ 0) :
    ∃ K : (Fin m × Fin d) →₀ ℕ,
      MvPolynomial.coeff (e + K) (rationalBlockLinearSubstitution A P) ≠ 0 ∧
      ∀ h, ∑ i, K (h, i) = derivativeBlockCount s h := by
  change MvPolynomial.coeff e (rationalBlockLinearSubstitution A
    ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P)) ≠ 0 at he
  rw [map_smul, MvPolynomial.coeff_smul, smul_eq_mul] at he
  exact rationalBlockLinearSubstitution_wordPDeriv_support_origin A hA s P e
    (right_ne_zero_of_mul he)

/-- The total normalized number of derivatives, summed over the blocks. -/
def blockDerivativeWeight {m d : ℕ} (r : Fin m → ℕ)
    (s : List (Fin m × Fin d)) : ℝ :=
  ∑ h, (derivativeBlockCount s h : ℝ) / r h

def derivativeBlockCount_map_pivot {m d : ℕ}
    (p : Fin m → Fin d) (s : List (Fin m)) (h : Fin m) :
    derivativeBlockCount (s.map (fun a => (a, p a))) h = s.count h := by
  induction s with
  | nil => simp [derivativeBlockCount_nil]
  | cons a s ih =>
    by_cases ha : a = h
    · subst a
      simp [derivativeBlockCount_cons, ih, add_comm]
    · simp [derivativeBlockCount_cons, ih, ha]

def blockDerivativeWeight_map_pivot {m d : ℕ}
    (r : Fin m → ℕ) (p : Fin m → Fin d) (s : List (Fin m)) :
    blockDerivativeWeight r (s.map (fun h => (h, p h))) =
      ∑ h, (s.count h : ℝ) / r h := by
  simp [blockDerivativeWeight, derivativeBlockCount_map_pivot]

def blockDerivativeWeight_column_bound {m d : ℕ} (r : Fin m → ℕ)
    (s : List (Fin m × Fin d)) (K : (Fin m × Fin d) →₀ ℕ)
    (hK : ∀ h, ∑ i, K (h, i) = derivativeBlockCount s h) (i : Fin d) :
    (∑ h, (K (h, i) : ℝ) / r h) ≤ blockDerivativeWeight r s := by
  apply Finset.sum_le_sum
  intro h _
  apply div_le_div_of_nonneg_right _ (Nat.cast_nonneg _)
  exact_mod_cast (show K (h, i) ≤ derivativeBlockCount s h from
    (Finset.single_le_sum (fun j _ => Nat.zero_le (K (h, j))) (Finset.mem_univ i)).trans_eq (hK h))

/-- A divided derivative with total normalized block count at most `m * η`
preserves strict column balance with tolerance enlarged from `m * η` to
`2 * m * η`.  This is proved from the actual inverse chain rule. -/
def rationalBlockLinearSubstitution_dividedWordPDeriv_balanced {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0)
    (r : Fin m → ℕ) (η : ℝ) (s : List (Fin m × Fin d))
    (P : MvPolynomial (Fin m × Fin d) ℚ)
    (hbalanced : ∀ e, MvPolynomial.coeff e (rationalBlockLinearSubstitution A P) ≠ 0 →
      ∀ i, |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < (m : ℝ) * η)
    (hsmall : blockDerivativeWeight r s ≤ (m : ℝ) * η) :
    ∀ e, MvPolynomial.coeff e
      (rationalBlockLinearSubstitution A (dividedWordPDeriv s P)) ≠ 0 →
      ∀ i, |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| < 2 * (m : ℝ) * η := by
  intro e he i
  obtain ⟨K, hK, hcount⟩ :=
    rationalBlockLinearSubstitution_dividedWordPDeriv_support_origin A hA s P e he
  have hbound := hbalanced (e + K) hK i
  have hcolumn := (blockDerivativeWeight_column_bound r s K hcount i).trans hsmall
  have hnonneg : 0 ≤ ∑ h, (K (h, i) : ℝ) / r h :=
    Finset.sum_nonneg (fun h _ => div_nonneg (Nat.cast_nonneg _) (Nat.cast_nonneg _))
  have heq : (∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d =
      ((∑ h, ((e + K) (h, i) : ℝ) / r h) - (m : ℝ) / d) -
        (∑ h, (K (h, i) : ℝ) / r h) := by
    simp only [Finsupp.add_apply, Nat.cast_add, add_div, Finset.sum_add_distrib]
    ring
  rw [heq]
  calc
    _ ≤ |(∑ h, ((e + K) (h, i) : ℝ) / r h) - (m : ℝ) / d| +
        |∑ h, (K (h, i) : ℝ) / r h| := abs_sub _ _
    _ < 2 * (m : ℝ) * η := by rw [abs_of_nonneg hnonneg]; linarith

/-- Block degrees drop by exactly the number of derivatives in that block,
even after an invertible change of coordinates within every block. -/
def rationalBlockLinearSubstitution_dividedWordPDeriv_block_degrees {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0)
    (r : Fin m → ℕ) (s : List (Fin m × Fin d))
    (P : MvPolynomial (Fin m × Fin d) ℚ)
    (hhom : ∀ e, MvPolynomial.coeff e (rationalBlockLinearSubstitution A P) ≠ 0 →
      ∀ h, ∑ i, e (h, i) = r h)
    (e : (Fin m × Fin d) →₀ ℕ)
    (he : MvPolynomial.coeff e
      (rationalBlockLinearSubstitution A (dividedWordPDeriv s P)) ≠ 0) :
    ∀ h, (∑ i, e (h, i)) + derivativeBlockCount s h = r h := by
  obtain ⟨K, hK, hcount⟩ :=
    rationalBlockLinearSubstitution_dividedWordPDeriv_support_origin A hA s P e he
  intro h
  simpa only [Finsupp.add_apply, Finset.sum_add_distrib, hcount] using hhom (e + K) hK h


end
end Bounty

end SubmissionComponent_BalancedDerivativeSupport

/- Component ProductHyperplaneNonvanishing; SHA256 54ef0fc14e019411677fd9f88ac9eaa976933a20be9c0d78739264695ca4748e -/
section SubmissionComponent_ProductHyperplaneNonvanishing
/- Small coordinate derivatives nonzero at actual points on rational hyperplanes. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def eval_complementRestriction {B C : Type*} (g : B → MvPolynomial C ℚ)
    (P : MvPolynomial (B ⊕ C) ℚ) (z : C → ℚ) :
    MvPolynomial.eval z (complementRestriction g P) =
      MvPolynomial.eval (Sum.elim (fun b => MvPolynomial.eval z (g b)) z) P := by
  rw [complementRestriction_eq_aeval]
  induction P using MvPolynomial.induction_on with
  | C a => simp
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    cases i <;> simp only [map_mul, MvPolynomial.aeval_X, Sum.elim_inl,
      Sum.elim_inr, MvPolynomial.eval_X, hP]

def productHyperplanePoint {m d : ℕ} (b : Fin m → Fin (d + 1) → ℚ)
    (p : Fin m → Fin (d + 1)) (z : HyperplaneComplement p → ℚ) :
    Fin m × Fin (d + 1) → ℚ :=
  (Sum.elim (fun h => MvPolynomial.eval z
    (blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
      (pivotComplementCoefficient b p) h)) z) ∘ hyperplanePivotEquiv p

def eval_complementRestriction_pivotRename {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (z : HyperplaneComplement p → ℚ) (P : MvPolynomial (Fin m × Fin (d + 1)) ℚ) :
    MvPolynomial.eval z
      (complementRestriction (blockComplementLinear
        (fun x : HyperplaneComplement p => x.val.1) (pivotComplementCoefficient b p))
        (MvPolynomial.rename (hyperplanePivotEquiv p) P)) =
      MvPolynomial.eval (productHyperplanePoint b p z) P := by
  rw [eval_complementRestriction, MvPolynomial.eval_rename]
  rfl

def productHyperplanePoint_mem {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (z : HyperplaneComplement p → ℚ) (h : Fin m) :
    ∑ k, b h k * productHyperplanePoint b p z (h, k) = 0 := by
  have hc := congrArg (MvPolynomial.eval z)
    (complementRestriction_productHyperplaneLinearForm b p h (hp h))
  rw [eval_complementRestriction_pivotRename] at hc
  simpa only [productHyperplaneLinearForm, map_sum, map_mul, MvPolynomial.eval_C,
    MvPolynomial.eval_X, map_zero] using hc

def exists_nonzero_eval_on_product_hyperplanes {m d : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (P : MvPolynomial (Fin m × Fin (d + 1)) ℚ)
    (hP : complementRestriction (blockComplementLinear
      (fun x : HyperplaneComplement p => x.val.1) (pivotComplementCoefficient b p))
      (MvPolynomial.rename (hyperplanePivotEquiv p) P) ≠ 0) :
    ∃ x : Fin m × Fin (d + 1) → ℚ,
      (∀ h, ∑ k, b h k * x (h, k) = 0) ∧ MvPolynomial.eval x P ≠ 0 := by
  classical
  have hex : ∃ z : HyperplaneComplement p → ℚ,
      MvPolynomial.eval z (complementRestriction (blockComplementLinear
        (fun x : HyperplaneComplement p => x.val.1) (pivotComplementCoefficient b p))
        (MvPolynomial.rename (hyperplanePivotEquiv p) P)) ≠ 0 := by
    by_contra! hn
    apply hP
    apply MvPolynomial.funext
    intro z
    simpa only [map_zero] using hn z
  obtain ⟨z, hz⟩ := hex
  refine ⟨productHyperplanePoint b p z, productHyperplanePoint_mem b p hp z, ?_⟩
  rwa [eval_complementRestriction_pivotRename] at hz

def exists_product_hyperplane_derivative {n d : ℕ} (hd : 1 ≤ d)
    (b : Fin (n + 1) → Fin (d + 1) → ℚ) (p : Fin (n + 1) → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (r : Fin (n + 1) → ℕ) (hr : ∀ h, 0 < r h)
    (P : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ h, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d))) :
    ∃ s : List (Fin (n + 1) × Fin (d + 1)),
      blockDerivativeWeight r s ≤ 2 * (n + 1 : ℕ) * η ∧
      complementRestriction (blockComplementLinear
        (fun x : HyperplaneComplement p => x.val.1) (pivotComplementCoefficient b p))
        (MvPolynomial.rename (hyperplanePivotEquiv p)
          (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P))) ≠ 0 ∧
      ∃ x : Fin (n + 1) × Fin (d + 1) → ℚ,
        (∀ h, ∑ k, b h k * x (h, k) = 0) ∧
        MvPolynomial.eval x (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0 := by
  classical
  let Q := MvPolynomial.map (Int.castRingHom ℚ) P
  let g := blockComplementLinear (fun x : HyperplaneComplement p => x.val.1)
    (pivotComplementCoefficient b p)
  have hQ : MvPolynomial.rename (hyperplanePivotEquiv p) Q ≠ 0 := by
    exact fun hz => integerMap_ne_zero hP
      ((MvPolynomial.rename_eq_zero_iff_of_injective Q (hyperplanePivotEquiv p).injective).mp hz)
  obtain ⟨t, ht, hw⟩ := exists_normalized_pivot_derivative_restriction r hr g
    (MvPolynomial.rename (hyperplanePivotEquiv p) Q) hQ
  let s := t.map (fun h => (h, p h))
  have hmap : s.map (hyperplanePivotEquiv p) = t.map Sum.inl := by
    simp only [s, List.map_map]
    congr 1
    funext h
    exact hyperplanePivotEquiv_pivot p h
  have hderiv := dividedWordPDeriv_rename_equiv (hyperplanePivotEquiv p) s Q
  rw [hmap] at hderiv
  rw [hderiv] at ht
  refine ⟨s, ?_, ht, ?_⟩
  · rw [show blockDerivativeWeight r s = ∑ h, (t.count h : ℝ) / r h from
      blockDerivativeWeight_map_pivot r p t, hw]
    exact integer_product_hyperplane_roth_bound hd b p hp r hr P hP hhom
      η hη hηhalf hstep hheight
  · exact exists_nonzero_eval_on_product_hyperplanes b p hp _ ht


end
end Bounty

end SubmissionComponent_ProductHyperplaneNonvanishing

/- Component SpanningPolynomialNonvanishing; SHA256 48a2ff4315f7697eb2482ff61cc017765c1fc4c6fea9ce5960703d73a091894f -/
section SubmissionComponent_SpanningPolynomialNonvanishing
/- Polynomial nonvanishing is preserved by parametrizing an actual spanning family. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def eval_rational_aeval {I J : Type*} (f : I → MvPolynomial J ℚ)
    (P : MvPolynomial I ℚ) (z : J → ℚ) :
    MvPolynomial.eval z (MvPolynomial.aeval f P) =
      MvPolynomial.eval (fun i => MvPolynomial.eval z (f i)) P := by
  simpa only [MvPolynomial.aeval_eq_eval] using
    MvPolynomial.comp_aeval_apply (f := f) (MvPolynomial.aeval z) P

def blockSpanningSubstitution {m d k : ℕ} (y : Fin m → Fin k → Fin d → ℚ) :
    MvPolynomial (Fin m × Fin d) ℚ →ₐ[ℚ] MvPolynomial (Fin m × Fin k) ℚ :=
  MvPolynomial.aeval (fun x => ∑ j, MvPolynomial.C (y x.1 j x.2) * MvPolynomial.X (x.1, j))

def block_spanning_polynomial_ne_zero {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (x : Fin m × Fin d → ℚ)
    (hx : ∀ h, (fun i => x (h, i)) ∈ Submodule.span ℚ (Set.range (y h)))
    (P : MvPolynomial (Fin m × Fin d) ℚ) (hP : MvPolynomial.eval x P ≠ 0) :
    blockSpanningSubstitution y P ≠ 0 := by
  classical
  choose c hc using fun h => (Submodule.mem_span_range_iff_exists_fun ℚ).mp (hx h)
  let z (a : Fin m × Fin k) : ℚ := c a.1 a.2
  have he (a : Fin m × Fin d) :
      MvPolynomial.eval z (∑ j, MvPolynomial.C (y a.1 j a.2) * MvPolynomial.X (a.1, j)) = x a := by
    have hh := congrFun (hc a.1) a.2
    simpa only [map_sum, map_mul, MvPolynomial.eval_C, MvPolynomial.eval_X,
      Finset.sum_apply, Pi.smul_apply, smul_eq_mul, z, mul_comm] using hh
  intro hz
  have hh := congrArg (MvPolynomial.eval z) hz
  change MvPolynomial.eval z (MvPolynomial.aeval _ P) = _ at hh
  rw [eval_rational_aeval] at hh
  simp only [he, map_zero] at hh
  exact hP hh

def rationalHyperplaneKernel {d : ℕ} (b : Fin d → ℚ) : Submodule ℚ (Fin d → ℚ) :=
  LinearMap.ker (∑ i, b i • (LinearMap.proj i : (Fin d → ℚ) →ₗ[ℚ] ℚ))

def mem_rationalHyperplaneKernel {d : ℕ} (b x : Fin d → ℚ) :
    x ∈ rationalHyperplaneKernel b ↔ ∑ i, b i * x i = 0 := by
  simp [rationalHyperplaneKernel, LinearMap.mem_ker]

def hyperplane_spanning_substitution_ne_zero {m d k : ℕ}
    (b : Fin m → Fin (d + 1) → ℚ) (p : Fin m → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (y : Fin m → Fin k → Fin (d + 1) → ℚ)
    (hy : ∀ h, Submodule.span ℚ (Set.range (y h)) = rationalHyperplaneKernel (b h))
    (P : MvPolynomial (Fin m × Fin (d + 1)) ℚ)
    (hP : complementRestriction (blockComplementLinear
      (fun x : HyperplaneComplement p => x.val.1) (pivotComplementCoefficient b p))
      (MvPolynomial.rename (hyperplanePivotEquiv p) P) ≠ 0) :
    blockSpanningSubstitution y P ≠ 0 := by
  obtain ⟨x, hx, hne⟩ := exists_nonzero_eval_on_product_hyperplanes b p hp P hP
  apply block_spanning_polynomial_ne_zero y x _ P hne
  intro h
  rw [hy h, mem_rationalHyperplaneKernel]
  exact hx h

def product_hyperplane_derivative_spanning {n d k : ℕ} (hd : 1 ≤ d)
    (b : Fin (n + 1) → Fin (d + 1) → ℚ) (p : Fin (n + 1) → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (r : Fin (n + 1) → ℕ) (hr : ∀ h, 0 < r h)
    (y : Fin (n + 1) → Fin k → Fin (d + 1) → ℚ)
    (hy : ∀ h, Submodule.span ℚ (Set.range (y h)) = rationalHyperplaneKernel (b h))
    (P : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ h, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d))) :
    ∃ s : List (Fin (n + 1) × Fin (d + 1)),
      blockDerivativeWeight r s ≤ 2 * (n + 1 : ℕ) * η ∧
      blockSpanningSubstitution y (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0 := by
  obtain ⟨s, hs, hrestrict, _⟩ := exists_product_hyperplane_derivative hd b p hp r hr
    P hP hhom η hη hηhalf hstep hheight
  exact ⟨s, hs, hyperplane_spanning_substitution_ne_zero b p hp y hy _ hrestrict⟩


end
end Bounty

end SubmissionComponent_SpanningPolynomialNonvanishing

/- Component HyperplaneLocalArithmetic; SHA256 d73eaae49ae46441b317dadfec0c748cc1320d25ced8723ddd0cf03a280554f5 -/
section SubmissionComponent_HyperplaneLocalArithmetic
/- Integer pairings at three actual places and the rational kernels they
annihilate. These bounds support the finite support-pattern exception step. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def rationalHyperplaneKernel_ne_top {n : ℕ} (b : Fin n → ℚ) (hb : b ≠ 0) :
    rationalHyperplaneKernel b ≠ ⊤ := by
  obtain ⟨i, hi⟩ : ∃ i, b i ≠ 0 := by simpa [funext_iff] using hb
  intro h
  have hx : Pi.single i 1 ∈ rationalHyperplaneKernel b := by rw [h]; trivial
  apply hi
  simpa [mem_rationalHyperplaneKernel, Pi.single_apply] using hx

def independent_span_eq_hyperplane {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℚ) (hX : LinearIndependent ℚ X.col)
    (b : Fin (n + 1) → ℚ) (hb : b ≠ 0)
    (horth : ∀ j, dotProduct b (X.col j) = 0) :
    Submodule.span ℚ (Set.range X.col) = rationalHyperplaneKernel b := by
  apply Submodule.eq_of_le_of_finrank_le
  · apply Submodule.span_le.mpr
    rintro _ ⟨j, rfl⟩
    exact (mem_rationalHyperplaneKernel _ _).mpr (horth j)
  · have hk := Submodule.finrank_lt (rationalHyperplaneKernel_ne_top b hb)
    rw [finrank_span_eq_card hX]
    simpa using Nat.le_of_lt_succ (by simpa using hk)

def cofactorTransform_left_identity {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) :
    A.transpose * cofactorTransform A = A.det • 1 := by
  rw [cofactorTransform, ← Matrix.transpose_mul, Matrix.adjugate_mul,
    Matrix.transpose_smul, Matrix.transpose_one]

def cofactorTransform_mulVec_ne_zero {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (hA : IsUnit A.det)
    (b : Fin (n + 1) → ℚ) (hb : b ≠ 0) :
    (cofactorTransform A).mulVec b ≠ 0 := by
  intro h
  have hh := congrArg A.transpose.mulVec h
  rw [Matrix.mulVec_mulVec, cofactorTransform_left_identity, Matrix.smul_mulVec,
    Matrix.one_mulVec, Matrix.mulVec_zero] at hh
  exact hb ((smul_eq_zero.mp hh).resolve_left hA.ne_zero)

def cofactorTransform_pairing {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (b x : Fin (n + 1) → ℚ) :
    dotProduct ((cofactorTransform A).mulVec b) (A.mulVec x) =
      A.det * dotProduct b x := by
  rw [← Matrix.dotProduct_transpose_mulVec, Matrix.mulVec_mulVec,
    cofactorTransform_left_identity, Matrix.smul_mulVec, Matrix.one_mulVec,
    dotProduct_smul, dotProduct_comm]
  rfl

def cofactorEvaluationConstant {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (z : Fin (n + 1) → ℤ) : ℝ :=
  (∑ i, ‖(cofactorTransform A).mulVec (fun j => (z j : ℚ)) i‖) / ‖A.det‖

def integer_dot_archimedean_bound {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (hA : IsUnit A.det)
    (z x : Fin (n + 1) → ℤ) (c : Fin (n + 1) → ℝ) (t u : ℝ) (ht : 0 ≤ t)
    (hx : ∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c i * t))
    (hc : ∀ i, (cofactorTransform A).mulVec (fun j => (z j : ℚ)) i ≠ 0 → c i ≤ u) :
    |((∑ i, z i * x i : ℤ) : ℝ)| ≤ cofactorEvaluationConstant A z * Real.exp (u * t) := by
  let b : Fin (n + 1) → ℚ := fun i => z i
  let y : Fin (n + 1) → ℚ := fun i => x i
  have hp := congrArg norm (cofactorTransform_pairing A b y)
  have hsum : ‖dotProduct ((cofactorTransform A).mulVec b) (A.mulVec y)‖ ≤
      (∑ i, ‖(cofactorTransform A).mulVec b i‖) * Real.exp (u * t) := by
    calc
      _ ≤ ∑ i, ‖(cofactorTransform A).mulVec b i * A.mulVec y i‖ := norm_sum_le _ _
      _ ≤ ∑ i, ‖(cofactorTransform A).mulVec b i‖ * Real.exp (u * t) := by
        apply Finset.sum_le_sum
        intro i _
        rw [norm_mul]
        by_cases hi : (cofactorTransform A).mulVec b i = 0
        · simp [hi]
        · exact mul_le_mul_of_nonneg_left ((hx i).trans
            (Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right (hc i hi) ht))) (norm_nonneg _)
      _ = _ := by rw [Finset.sum_mul]
  have hdet : 0 < ‖A.det‖ := norm_pos_iff.mpr hA.ne_zero
  have hcast : ‖dotProduct b y‖ = |((∑ i, z i * x i : ℤ) : ℝ)| := by
    have hh : dotProduct b y = ((∑ i, z i * x i : ℤ) : ℚ) := by simp [b, y, dotProduct]
    rw [hh, Int.norm_cast_rat, Int.norm_eq_abs]
  rw [norm_mul, hcast] at hp
  change _ ≤ ((∑ i, ‖(cofactorTransform A).mulVec b i‖) / ‖A.det‖) * Real.exp (u * t)
  rw [div_mul_eq_mul_div]
  apply (le_div_iff₀ hdet).mpr
  nlinarith [hsum]

def integer_dot_padic_bound {n : ℕ}
    (p : ℕ) [Fact p.Prime] (z x : Fin n → ℤ) (c : Fin n → ℝ)
    (t u : ℝ) (ht : 0 ≤ t)
    (hx : ∀ i, (padicNorm p (x i : ℚ) : ℝ) ≤ Real.exp (c i * t))
    (hc : ∀ i, z i ≠ 0 → c i ≤ u) :
    (padicNorm p ((∑ i, z i * x i : ℤ) : ℚ) : ℝ) ≤ Real.exp (u * t) := by
  simp only [Int.cast_sum, Int.cast_mul]
  apply padicNorm_sum_cast_le _ _ _ _ (Real.exp_nonneg _)
  intro i _
  by_cases hi : z i = 0
  · simp [hi, (Real.exp_pos _).le]
  · rw [padicNorm.mul, Rat.cast_mul]
    have hz : (padicNorm p (z i : ℚ) : ℝ) ≤ 1 := by exact_mod_cast padicNorm.of_int (p := p) (z i)
    have hn : (0 : ℝ) ≤ padicNorm p (x i : ℚ) := by exact_mod_cast padicNorm.nonneg (x i : ℚ)
    exact (mul_le_mul_of_nonneg_right hz hn).trans (by
      simpa using (hx i).trans (Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right (hc i hi) ht)))

def integer_dot_zero_of_local_product {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (hA : IsUnit A.det)
    (z x : Fin (n + 1) → ℤ) (c : Fin 3 → Fin (n + 1) → ℝ)
    (t : ℝ) (u : Fin 3 → ℝ) (ht : 0 ≤ t)
    (hInf : ∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c 0 i * t))
    (h₂ : ∀ i, (padicNorm 2 (x i : ℚ) : ℝ) ≤ Real.exp (c 1 i * t))
    (h₃ : ∀ i, (padicNorm 3 (x i : ℚ) : ℝ) ≤ Real.exp (c 2 i * t))
    (hcInf : ∀ i, (cofactorTransform A).mulVec (fun j => (z j : ℚ)) i ≠ 0 → c 0 i ≤ u 0)
    (hc₂ : ∀ i, z i ≠ 0 → c 1 i ≤ u 1)
    (hc₃ : ∀ i, z i ≠ 0 → c 2 i ≤ u 2)
    (hsmall : cofactorEvaluationConstant A z * Real.exp ((∑ v, u v) * t) < 1) :
    ∑ i, z i * x i = 0 := by
  by_contra hn
  have hlow := integer_three_place_product_lower _ hn
  have h₀ := integer_dot_archimedean_bound A hA z x (c 0) t (u 0) ht hInf hcInf
  have h₂' := integer_dot_padic_bound 2 z x (c 1) t (u 1) ht h₂ hc₂
  have h₃' := integer_dot_padic_bound 3 z x (c 2) t (u 2) ht h₃ hc₃
  have hp₂ : (0 : ℝ) ≤ padicNorm 2 ((∑ i, z i * x i : ℤ) : ℚ) := by
    exact_mod_cast padicNorm.nonneg ((∑ i, z i * x i : ℤ) : ℚ)
  have hp₃ : (0 : ℝ) ≤ padicNorm 3 ((∑ i, z i * x i : ℤ) : ℚ) := by
    exact_mod_cast padicNorm.nonneg ((∑ i, z i * x i : ℤ) : ℚ)
  have hC : 0 ≤ cofactorEvaluationConstant A z := by unfold cofactorEvaluationConstant; positivity
  have hupper := mul_le_mul (mul_le_mul h₀ h₂' hp₂ (by positivity)) h₃' hp₃ (by positivity)
  have he : cofactorEvaluationConstant A z * Real.exp (u 0 * t) *
      Real.exp (u 1 * t) * Real.exp (u 2 * t) =
        cofactorEvaluationConstant A z * Real.exp ((∑ v, u v) * t) := by
    rw [mul_assoc, mul_assoc, ← Real.exp_add, ← Real.exp_add]
    congr 2
    simp [Fin.sum_univ_succ]
    ring
  rw [he] at hupper
  exact (not_lt_of_ge (hlow.trans hupper)) hsmall


end
end Bounty

end SubmissionComponent_HyperplaneLocalArithmetic

/- Component HyperplaneHeightDichotomy; SHA256 179dad553cbd5fbbb54819a9bdc21f98920523532c4b5543f6e4875387fddac0 -/
section SubmissionComponent_HyperplaneHeightDichotomy
/- A finite support-pattern choice of exceptional rational hyperplanes.
Outside this fixed finite collection the primitive normal has a logarithmic
height bounded below linearly in the profile parameter. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

abbrev HyperplaneSupportPattern (n : ℕ) :=
  Finset (Fin (n + 1)) × Finset (Fin (n + 1))

def RealizesHyperplanePattern {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ)
    (s : HyperplaneSupportPattern n) (a : Fin (n + 1) → ℤ) : Prop :=
  a ≠ 0 ∧
    (∀ i, (cofactorTransform A).mulVec (fun j => (a j : ℚ)) i ≠ 0 → i ∈ s.1) ∧
    (∀ i, a i ≠ 0 → i ∈ s.2)

def selectedPatternNormal {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ)
    (s : HyperplaneSupportPattern n) : Fin (n + 1) → ℤ := by
  classical
  exact if h : ∃ a, RealizesHyperplanePattern A s a then h.choose else Pi.single 0 1

def selectedPatternNormal_realizes {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (s : HyperplaneSupportPattern n)
    (h : ∃ a, RealizesHyperplanePattern A s a) :
    RealizesHyperplanePattern A s (selectedPatternNormal A s) := by
  classical
  rw [selectedPatternNormal, dif_pos h]
  exact h.choose_spec

def exceptionalPatternHyperplanes {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) :
    Finset (Submodule ℚ (Fin (n + 1) → ℚ)) := by
  classical
  exact Finset.univ.image (fun s : HyperplaneSupportPattern n =>
    rationalHyperplaneKernel (fun i => (selectedPatternNormal A s i : ℚ)))

def patternEvaluationBound {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) : ℝ :=
  1 + ∑ s : HyperplaneSupportPattern n, cofactorEvaluationConstant A (selectedPatternNormal A s)

def patternEvaluationBound_ge_one {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) : 1 ≤ patternEvaluationBound A := by
  have hn : 0 ≤ ∑ s : HyperplaneSupportPattern n,
      cofactorEvaluationConstant A (selectedPatternNormal A s) := by
    apply Finset.sum_nonneg
    intro s _
    unfold cofactorEvaluationConstant
    positivity
  unfold patternEvaluationBound
  linarith

def cofactorEvaluationConstant_le_patternBound {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (s : HyperplaneSupportPattern n) :
    cofactorEvaluationConstant A (selectedPatternNormal A s) ≤ patternEvaluationBound A := by
  have hn : ∀ t : HyperplaneSupportPattern n,
      0 ≤ cofactorEvaluationConstant A (selectedPatternNormal A t) := by
    intro t
    unfold cofactorEvaluationConstant
    positivity
  have hh := Finset.single_le_sum (fun t _ => hn t) (Finset.mem_univ s)
  change _ ≤ 1 + ∑ t : HyperplaneSupportPattern n, cofactorEvaluationConstant A (selectedPatternNormal A t)
  linarith

def exists_pattern_smallness_threshold {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (ρ : ℝ) (hρ : 0 < ρ) :
    ∃ T : ℝ, 0 ≤ T ∧ ∀ t, T ≤ t →
      patternEvaluationBound A * Real.exp (-ρ * t / 2) < 1 := by
  let C := patternEvaluationBound A
  have hC1 : 1 ≤ C := patternEvaluationBound_ge_one A
  have hC : 0 < C := lt_of_lt_of_le (by norm_num) hC1
  have hlog : 0 ≤ Real.log C := Real.log_nonneg hC1
  refine ⟨2 * (Real.log C + 1) / ρ, by positivity, ?_⟩
  intro t ht
  have hh := (div_le_iff₀ hρ).mp ht
  have hn : Real.log C + (-ρ * t / 2) < 0 := by nlinarith
  calc
    _ = Real.exp (Real.log C + (-ρ * t / 2)) := by rw [Real.exp_add, Real.exp_log hC]
    _ < 1 := by simpa using Real.exp_lt_exp.mpr hn

def primitive_cofactor_span_eq {n : ℕ}
    (X : Matrix (Fin (n + 1)) (Fin n) ℤ)
    (hX : LinearIndependent ℚ (X.map (Int.castRingHom ℚ)).col)
    (g : ℤ) (hg : g ≠ 0) (a : Fin (n + 1) → ℤ) (ha : a ≠ 0)
    (hfactor : ∀ i, cofactorNormal X i = g * a i) :
    Submodule.span ℚ (Set.range (X.map (Int.castRingHom ℚ)).col) =
      rationalHyperplaneKernel (fun i => (a i : ℚ)) := by
  have haq : (fun i => (a i : ℚ)) ≠ 0 := by
    intro h
    apply ha
    ext i
    have hi : (a i : ℚ) = 0 := congrFun h i
    exact_mod_cast hi
  apply independent_span_eq_hyperplane _ hX _ haq
  intro j
  have hh := cofactorNormal_dot_column (X.map (Int.castRingHom ℚ)) j
  have hw : cofactorNormal (X.map (Int.castRingHom ℚ)) = (g : ℚ) • (fun i => (a i : ℚ)) := by
    ext i
    rw [cofactorNormal_map]
    change ((cofactorNormal X i : ℤ) : ℚ) = (g : ℚ) * (a i : ℚ)
    rw [hfactor, Int.cast_mul]
  rw [hw, smul_dotProduct] at hh
  exact (mul_eq_zero.mp hh).resolve_left (by exact_mod_cast hg)

def moving_hyperplane_height_dichotomy {n : ℕ}
    (A : Matrix (Fin (n + 1)) (Fin (n + 1)) ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → Fin (n + 1) → ℝ) (ρ : ℝ) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ) :
    ∃ T C : ℝ, 0 ≤ T ∧ 0 ≤ C ∧ ∀ t, T ≤ t →
      ∀ X : Matrix (Fin (n + 1)) (Fin n) ℤ,
      LinearIndependent ℚ (X.map (Int.castRingHom ℚ)).col →
      (∀ i j, ‖(A * X.map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c 0 i * t)) →
      (∀ i j, (padicNorm 2 (X i j : ℚ) : ℝ) ≤ Real.exp (c 1 i * t)) →
      (∀ i j, (padicNorm 3 (X i j : ℚ) : ℝ) ≤ Real.exp (c 2 i * t)) →
      ∃ a : Fin (n + 1) → ℤ, a ≠ 0 ∧ Finset.univ.gcd a = 1 ∧
        Submodule.span ℚ (Set.range (X.map (Int.castRingHom ℚ)).col) =
          rationalHyperplaneKernel (fun i => (a i : ℚ)) ∧
        (rationalHyperplaneKernel (fun i => (a i : ℚ)) ∈ exceptionalPatternHyperplanes A ∨
          ρ * t / 4 - C ≤ Height.logHeight (fun i => (a i : ℚ))) := by
  classical
  obtain ⟨T, hT, hsmall⟩ := exists_pattern_smallness_threshold A ρ hρ
  obtain ⟨D, hD, hden⟩ := exists_cofactor_denominator A
  refine ⟨T, |Real.log ((D : ℝ) * (n.factorial : ℝ))| / 2, hT, by positivity, ?_⟩
  intro t ht X hX hInf h₂ h₃
  have ht0 : 0 ≤ t := hT.trans ht
  obtain ⟨g, a, hg, ha, hprim, hfactor⟩ := integer_cofactor_primitive_factor X hX
  have hspan := primitive_cofactor_span_eq X hX g hg.ne' a ha hfactor
  have haq : (fun i => (a i : ℚ)) ≠ 0 := by
    intro h
    apply ha
    ext i
    have hi : (a i : ℚ) = 0 := congrFun h i
    exact_mod_cast hi
  let S₀ : Finset (Fin (n + 1)) := Finset.univ.filter
    (fun i => (cofactorTransform A).mulVec (fun j => (a j : ℚ)) i ≠ 0)
  let S₁ : Finset (Fin (n + 1)) := Finset.univ.filter (fun i => a i ≠ 0)
  have hS₀ : S₀.Nonempty := by
    have hn := cofactorTransform_mulVec_ne_zero A hA _ haq
    obtain ⟨i, hi⟩ : ∃ i, (cofactorTransform A).mulVec (fun j => (a j : ℚ)) i ≠ 0 :=
      by simpa [funext_iff] using hn
    exact ⟨i, Finset.mem_filter.mpr ⟨Finset.mem_univ i, hi⟩⟩
  have hS₁ : S₁.Nonempty := by
    obtain ⟨i, hi⟩ : ∃ i, a i ≠ 0 := by simpa [funext_iff] using ha
    exact ⟨i, Finset.mem_filter.mpr ⟨Finset.mem_univ i, hi⟩⟩
  obtain ⟨i₀, hi₀, hmax₀⟩ := Finset.exists_max_image S₀ (c 0) hS₀
  obtain ⟨i₂, hi₂, hmax₂⟩ := Finset.exists_max_image S₁ (c 1) hS₁
  obtain ⟨i₃, hi₃, hmax₃⟩ := Finset.exists_max_image S₁ (c 2) hS₁
  let idx : Fin 3 → Fin (n + 1) := ![i₀, i₂, i₃]
  refine ⟨a, ha, hprim, hspan, ?_⟩
  by_cases hhigh : -ρ / 2 ≤ ∑ v, c v (idx v)
  · right
    obtain ⟨z, hz⟩ := hden a i₀
    have hl := primitive_cofactor_height_lower A X g hg.ne' a hprim hfactor c t ρ ht0
      hInf h₂ h₃ hc idx hhigh (Finset.mem_filter.mp hi₂).2 (Finset.mem_filter.mp hi₃).2
      D z hD (Finset.mem_filter.mp hi₀).2 hz
    have hab := le_abs_self (Real.log ((D : ℝ) * (n.factorial : ℝ)))
    exact le_trans (by linarith) hl
  · left
    let s : HyperplaneSupportPattern n := (S₀, S₁)
    have hreal : RealizesHyperplanePattern A s a := by
      refine ⟨ha, ?_, ?_⟩
      · intro i hi
        exact Finset.mem_filter.mpr ⟨Finset.mem_univ i, hi⟩
      · intro i hi
        exact Finset.mem_filter.mpr ⟨Finset.mem_univ i, hi⟩
    let z := selectedPatternNormal A s
    have hzreal := selectedPatternNormal_realizes A s ⟨a, hreal⟩
    let u : Fin 3 → ℝ := fun v => c v (idx v)
    have hu : (∑ v, u v) < -ρ / 2 := lt_of_not_ge hhigh
    have hC : 0 ≤ patternEvaluationBound A := (by norm_num : (0 : ℝ) ≤ 1).trans
      (patternEvaluationBound_ge_one A)
    have hzsmall : cofactorEvaluationConstant A z * Real.exp ((∑ v, u v) * t) < 1 := by
      calc
        _ ≤ patternEvaluationBound A * Real.exp ((∑ v, u v) * t) :=
          mul_le_mul_of_nonneg_right (cofactorEvaluationConstant_le_patternBound A s) (Real.exp_nonneg _)
        _ ≤ patternEvaluationBound A * Real.exp (-ρ * t / 2) :=
          mul_le_mul_of_nonneg_left (Real.exp_le_exp.mpr (by nlinarith [mul_le_mul_of_nonneg_right hu.le ht0])) hC
        _ < 1 := hsmall t ht
    have horth : ∀ j, dotProduct (fun i => (z i : ℚ)) ((X.map (Int.castRingHom ℚ)).col j) = 0 := by
      intro j
      have hh := integer_dot_zero_of_local_product A hA z (fun i => X i j) c t u ht0
        (fun i => hInf i j) (fun i => h₂ i j) (fun i => h₃ i j)
        (fun i hi => hmax₀ i (hzreal.2.1 i hi))
        (fun i hi => hmax₂ i (hzreal.2.2 i hi))
        (fun i hi => hmax₃ i (hzreal.2.2 i hi)) hzsmall
      change ∑ i, (z i : ℚ) * (X i j : ℚ) = 0
      exact_mod_cast hh
    have hzq : (fun i => (z i : ℚ)) ≠ 0 := by
      intro h
      apply hzreal.1
      ext i
      have hi : (z i : ℚ) = 0 := congrFun h i
      exact_mod_cast hi
    have hspz := independent_span_eq_hyperplane _ hX _ hzq horth
    rw [← hspan, hspz]
    exact Finset.mem_image.mpr ⟨s, Finset.mem_univ s, rfl⟩


end
end Bounty

end SubmissionComponent_HyperplaneHeightDichotomy

/- Component DerivativeSubstitutionHeight; SHA256 11bad84064d35312f7a2cf9810b404f7de1be5676e5e70943b3776c5c632b557 -/
section SubmissionComponent_DerivativeSubstitutionHeight
/- A uniform coefficient-height bound for transformed integer divided derivatives. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rational_polynomialCoeffL1_aeval_monomial {I J : Type*} [Fintype I]
    (f : I → MvPolynomial J ℚ) (e : I →₀ ℕ) (a : ℚ) (C : ℝ)
    (hC : 0 ≤ C) (hf : ∀ i, polynomialCoeffL1 (f i) ≤ C) :
    polynomialCoeffL1 (MvPolynomial.aeval f (MvPolynomial.monomial e a)) ≤
      ‖a‖ * C ^ (∑ i, e i) := by
  classical
  rw [MvPolynomial.aeval_monomial]
  change polynomialCoeffL1 (MvPolynomial.C a * _) ≤ _
  rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _)]
  apply (polynomialCoeffL1_mul _ _).trans
  rw [polynomialCoeffL1_C]
  apply mul_le_mul_of_nonneg_left _ (norm_nonneg _)
  calc
    _ ≤ ∏ i, polynomialCoeffL1 (f i ^ e i) := polynomialCoeffL1_prod _ _
    _ ≤ ∏ i, polynomialCoeffL1 (f i) ^ e i := Finset.prod_le_prod
      (fun i _ => polynomialCoeffL1_nonneg _) (fun i _ => polynomialCoeffL1_pow _ _)
    _ ≤ ∏ i, C ^ e i := Finset.prod_le_prod
      (fun i _ => pow_nonneg (polynomialCoeffL1_nonneg _) _)
      (fun i _ => pow_le_pow_left₀ (polynomialCoeffL1_nonneg _) (hf i) _)
    _ = _ := Finset.prod_pow_eq_pow_sum _ _ _

def rational_polynomialCoeffL1_aeval_degree_bound {I J : Type*} [Fintype I]
    (f : I → MvPolynomial J ℚ) (P : MvPolynomial I ℚ) (D : ℕ) (C : ℝ)
    (hC : 1 ≤ C) (hf : ∀ i, polynomialCoeffL1 (f i) ≤ C)
    (hD : ∀ e ∈ P.support, ∑ i, e i ≤ D) :
    polynomialCoeffL1 (MvPolynomial.aeval f P) ≤ C ^ D * polynomialCoeffL1 P := by
  classical
  nth_rw 1 [MvPolynomial.as_sum P]
  rw [map_sum]
  calc
    _ ≤ ∑ e ∈ P.support, polynomialCoeffL1 (MvPolynomial.aeval f
        (MvPolynomial.monomial e (MvPolynomial.coeff e P))) := polynomialCoeffL1_sum _ _
    _ ≤ ∑ e ∈ P.support, ‖MvPolynomial.coeff e P‖ * C ^ D := by
      apply Finset.sum_le_sum
      intro e he
      exact (rational_polynomialCoeffL1_aeval_monomial f e _ C (zero_le_one.trans hC) hf).trans
        (mul_le_mul_of_nonneg_left (pow_le_pow_right₀ hC (hD e he)) (norm_nonneg _))
    _ = _ := by rw [← Finset.sum_mul]; exact mul_comm _ _

def productBlockHomogeneous_integerMap {m d : ℕ} (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℤ) (hP : ProductBlockHomogeneous r P) :
    ProductBlockHomogeneous r (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  intro e he
  exact hP e (MvPolynomial.support_map_subset _ _ he)

def productBlockHomogeneous_boxBound {m d : ℕ} (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (hP : ProductBlockHomogeneous r P) :
    PolynomialBoxBound (fun x => r x.1) P := by
  intro e he x
  exact (Finset.single_le_sum (fun _ _ => Nat.zero_le _) (Finset.mem_univ x.2)).trans_eq
    (hP e he x.1)

def productBlockHomogeneous_divided_total_le {m d : ℕ} (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (hP : ProductBlockHomogeneous r P)
    (s : List (Fin m × Fin d)) :
    ∀ e ∈ (dividedWordPDeriv s P).support, ∑ x, e x ≤ ∑ h, r h := by
  intro e he
  have hsource := hP _ (dividedWordPDeriv_support_shift s P he)
  calc
    _ ≤ ∑ x, (e + wordDerivativeCounts s) x :=
      Finset.sum_le_sum fun x _ => Nat.le_add_right _ _
    _ = _ := by rw [Fintype.sum_prod_type]; simp_rw [hsource]

def rationalBlockLinearForm_coeffL1_le {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℚ) (x : Fin m × Fin d) :
    polynomialCoeffL1 (rationalBlockLinearForm A x) ≤ ∑ j, ‖A x.1 x.2 j‖ := by
  calc
    _ ≤ ∑ j, polynomialCoeffL1
        (MvPolynomial.C (A x.1 x.2 j) * MvPolynomial.X (x.1, j)) := polynomialCoeffL1_sum _ _
    _ = _ := by
      apply Finset.sum_congr rfl
      intro j _
      rw [MvPolynomial.C_mul_X_eq_monomial, polynomialCoeffL1_monomial]

def transformed_integer_derivative_height {m d : ℕ}
    (A : Fin m → Fin d → Fin d → ℚ) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P) (s : List (Fin m × Fin d))
    (C K : ℝ) (hC : 1 ≤ C) (hA : ∀ h i, ∑ j, ‖A h i j‖ ≤ C)
    (hheight : Real.log (polynomialCoeffL1 P) ≤ K * (∑ h, (r h : ℝ)))
    (hF : rationalBlockLinearSubstitution A
      (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0) :
    Real.log (polynomialCoeffL1 (rationalBlockLinearSubstitution A
      (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P)))) ≤
        (K + (d : ℝ) * Real.log 2 + Real.log C) * (∑ h, (r h : ℝ)) := by
  let Q := MvPolynomial.map (Int.castRingHom ℚ) P
  have hhomQ : ProductBlockHomogeneous r Q := productBlockHomogeneous_integerMap r P hhom
  have hsub := rational_polynomialCoeffL1_aeval_degree_bound (rationalBlockLinearForm A)
    (dividedWordPDeriv s Q) (∑ h, r h) C hC
    (fun x => (rationalBlockLinearForm_coeffL1_le A x).trans (hA x.1 x.2))
    (productBlockHomogeneous_divided_total_le r Q hhomQ s)
  have hderiv := polynomialCoeffL1_dividedWordPDeriv s (fun x => r x.1) Q
    (productBlockHomogeneous_boxBound r Q hhomQ)
  have hsum : (∑ x : Fin m × Fin d, r x.1) = d * ∑ h, r h := by
    simp [Fintype.sum_prod_type, Finset.mul_sum, Nat.mul_comm]
  rw [hsum, polynomialCoeffL1_map_int_rat] at hderiv
  have hnorm : polynomialCoeffL1 (rationalBlockLinearSubstitution A (dividedWordPDeriv s Q)) ≤
      C ^ (∑ h, r h) * ((2 : ℝ) ^ (d * ∑ h, r h) * polynomialCoeffL1 P) :=
    hsub.trans (mul_le_mul_of_nonneg_left hderiv (pow_nonneg (zero_le_one.trans hC) _))
  have hlog := Real.log_le_log (polynomialCoeffL1_pos hF) hnorm
  have hCpos : 0 < C := zero_lt_one.trans_le hC
  have hPpos := polynomialCoeffL1_pos hP
  rw [Real.log_mul (pow_ne_zero _ hCpos.ne') (mul_ne_zero (pow_ne_zero _ (by norm_num)) hPpos.ne'),
    Real.log_mul (pow_ne_zero _ (by norm_num)) hPpos.ne', Real.log_pow, Real.log_pow] at hlog
  simp only [Nat.cast_mul, Nat.cast_sum] at hlog
  change Real.log (polynomialCoeffL1 (rationalBlockLinearSubstitution A (dividedWordPDeriv s Q))) ≤ _
  nlinarith [hheight]


end
end Bounty

end SubmissionComponent_DerivativeSubstitutionHeight

/- Component ThreePlacePolynomialBounds; SHA256 a51d88efc4e3bed754da254948a3a5de093d49ec4dd21088907ca360dc78d405 -/
section SubmissionComponent_ThreePlacePolynomialBounds
/- Actual polynomial evaluations at the real place and two finite places,
with independently selected supported monomials. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def blockExponentSum {m d : ℕ} (c : Fin d → ℝ) (q : Fin m → ℝ)
    (e : (Fin m × Fin d) →₀ ℕ) : ℝ :=
  ∑ i, ∑ h, c i * (e (h, i) : ℝ) * q h

def product_powers_le_exp_sum {I : Type*} [Fintype I]
    (a b : I → ℝ) (e : I → ℕ) (ha : ∀ i, 0 ≤ a i)
    (hab : ∀ i, a i ≤ Real.exp (b i)) :
    (∏ i, (a i) ^ e i) ≤ Real.exp (∑ i, (e i : ℝ) * b i) := by
  calc
    _ ≤ ∏ i, (Real.exp (b i)) ^ e i := Finset.prod_le_prod
      (fun i _ => pow_nonneg (ha i) _) (fun i _ => pow_le_pow_left₀ (ha i) (hab i) _)
    _ = _ := by simp only [← Real.exp_nat_mul, ← Real.exp_sum]

def block_exponent_sum_identity {m d : ℕ} (c : Fin d → ℝ) (q : Fin m → ℝ)
    (e : (Fin m × Fin d) →₀ ℕ) :
    (∑ x : Fin m × Fin d, (e x : ℝ) * (c x.2 * q x.1)) = blockExponentSum c q e := by
  rw [Fintype.sum_prod_type, Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro h _
  ring

def block_monomial_exp_bound {m d : ℕ}
    (a : Fin m × Fin d → ℝ) (c : Fin d → ℝ) (q : Fin m → ℝ)
    (e : (Fin m × Fin d) →₀ ℕ) (ha : ∀ x, 0 ≤ a x)
    (hab : ∀ h i, a (h, i) ≤ Real.exp (c i * q h)) :
    (∏ x, (a x) ^ e x) ≤ Real.exp (blockExponentSum c q e) := by
  simpa only [block_exponent_sum_identity] using product_powers_le_exp_sum
    a (fun x => c x.2 * q x.1) e ha (fun x => hab x.1 x.2)

def block_monomial_exp_bound_with_constant {m d : ℕ}
    (r : Fin m → ℕ) (a : Fin m × Fin d → ℝ) (c : Fin d → ℝ) (q : Fin m → ℝ)
    (e : (Fin m × Fin d) →₀ ℕ) (K : ℝ) (hK : 1 ≤ K)
    (ha : ∀ x, 0 ≤ a x) (hab : ∀ h i, a (h, i) ≤ K * Real.exp (c i * q h))
    (hdegree : ∀ h, ∑ i, e (h, i) ≤ r h) :
    (∏ x, (a x) ^ e x) ≤ Real.exp
      (Real.log K * (∑ h, (r h : ℝ)) + blockExponentSum c q e) := by
  have hK0 : 0 < K := lt_of_lt_of_le zero_lt_one hK
  have hh := product_powers_le_exp_sum a (fun x => Real.log K + c x.2 * q x.1) e ha
    (fun x => by simpa only [Real.exp_add, Real.exp_log hK0] using hab x.1 x.2)
  have he : (∑ x : Fin m × Fin d, (e x : ℝ)) ≤ ∑ h, (r h : ℝ) := by
    rw [Fintype.sum_prod_type]
    exact Finset.sum_le_sum fun h _ => by exact_mod_cast hdegree h
  refine hh.trans (Real.exp_le_exp.mpr ?_)
  calc
    _ = Real.log K * (∑ x : Fin m × Fin d, (e x : ℝ)) + blockExponentSum c q e := by
      simp only [mul_add, Finset.sum_add_distrib, ← Finset.sum_mul,
        block_exponent_sum_identity]
      ring
    _ ≤ _ := add_le_add (mul_le_mul_of_nonneg_left he (Real.log_nonneg hK)) le_rfl

def blockMatrixValues {m d : ℕ} (A : Fin m → Matrix (Fin d) (Fin d) ℚ)
    (x : Fin m × Fin d → ℚ) : Fin m × Fin d → ℚ :=
  fun hi => (A hi.1).mulVec (fun j => x (hi.1, j)) hi.2

def rationalBlockLinearSubstitution_eval {m d : ℕ}
    (B : Fin m → Matrix (Fin d) (Fin d) ℚ)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (y : Fin m × Fin d → ℚ) :
    MvPolynomial.eval y (rationalBlockLinearSubstitution B P) =
      MvPolynomial.eval (blockMatrixValues B y) P := by
  change MvPolynomial.aeval y (MvPolynomial.aeval (rationalBlockLinearForm B) P) = _
  rw [MvPolynomial.comp_aeval_apply]
  change MvPolynomial.eval (fun i => MvPolynomial.eval y (rationalBlockLinearForm B i)) P = _
  apply congrArg (fun f => MvPolynomial.eval f P)
  funext x
  simp [rationalBlockLinearForm, blockMatrixValues, Matrix.mulVec, dotProduct]

def inverseBlockMatrices {m d : ℕ} (A : Fin m → Matrix (Fin d) (Fin d) ℚ) :
    Fin m → Matrix (Fin d) (Fin d) ℚ := fun h => (A h)⁻¹

def inverse_block_substitution_eval {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, IsUnit (A h).det)
    (T : MvPolynomial (Fin m × Fin d) ℤ) (x : Fin m × Fin d → ℤ) :
    MvPolynomial.eval (blockMatrixValues A (fun hi => (x hi : ℚ)))
      (rationalBlockLinearSubstitution (inverseBlockMatrices A)
        (MvPolynomial.map (Int.castRingHom ℚ) T)) = (MvPolynomial.eval x T : ℚ) := by
  rw [rationalBlockLinearSubstitution_eval]
  have hid : blockMatrixValues (inverseBlockMatrices A)
      (blockMatrixValues A (fun hi => (x hi : ℚ))) = (fun hi => (x hi : ℚ)) := by
    funext hi
    change ((A hi.1)⁻¹.mulVec ((A hi.1).mulVec (fun j => (x (hi.1, j) : ℚ)))) hi.2 = _
    rw [Matrix.mulVec_mulVec, Matrix.nonsing_inv_mul _ (hA hi.1), Matrix.one_mulVec]
  simp only [hid]
  simpa only [Int.coe_castRingHom, Function.comp_def] using
    (MvPolynomial.map_eval (Int.castRingHom ℚ) x T).symm

def integer_eval₂_cast {I : Type*} (T : MvPolynomial I ℤ) (x : I → ℤ) :
    MvPolynomial.eval₂ (Int.castRingHom ℚ) (fun i => (x i : ℚ)) T = (MvPolynomial.eval x T : ℚ) := by
  rw [MvPolynomial.eval₂_eq_eval_map]
  simpa only [Int.coe_castRingHom, Function.comp_def] using
    (MvPolynomial.map_eval (Int.castRingHom ℚ) x T).symm

def integer_padic_eval_le_exp_some_monomial {m d : ℕ}
    (p : ℕ) [Fact p.Prime] (T : MvPolynomial (Fin m × Fin d) ℤ) (hT : T ≠ 0)
    (x : Fin m × Fin d → ℤ) (q : Fin m → ℝ) (c : Fin d → ℝ)
    (hx : ∀ h i, (padicNorm p (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c i * q h)) :
    ∃ e ∈ T.support, (padicNorm p (MvPolynomial.eval x T : ℚ) : ℝ) ≤
      Real.exp (blockExponentSum c q e) := by
  obtain ⟨e, he, hbound⟩ := integer_polynomial_eval₂_padicNorm_le_some_monomial
    p T hT (fun i => (x i : ℚ))
  rw [integer_eval₂_cast] at hbound
  have hbound' : (padicNorm p (MvPolynomial.eval x T : ℚ) : ℝ) ≤
      ∏ i, (padicNorm p (x i : ℚ) : ℝ) ^ e i := by exact_mod_cast hbound
  exact ⟨e, he, hbound'.trans (block_monomial_exp_bound _ c q e
    (fun i => by exact_mod_cast (padicNorm.nonneg (p := p) (x i : ℚ))) hx)⟩

def rational_eval_le_exp_some_monomial {m d : ℕ}
    (F : MvPolynomial (Fin m × Fin d) ℚ) (hF : F ≠ 0) (y : Fin m × Fin d → ℚ)
    (r : Fin m → ℕ) (q : Fin m → ℝ) (c : Fin d → ℝ) (C K : ℝ) (hK : 1 ≤ K)
    (hdegree : ∀ e ∈ F.support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hheight : Real.log (polynomialCoeffL1 F) ≤ C * ∑ h, (r h : ℝ))
    (hy : ∀ h i, ‖y (h, i)‖ ≤ K * Real.exp (c i * q h)) :
    ∃ e ∈ F.support, ‖MvPolynomial.eval y F‖ ≤
      Real.exp ((C + Real.log K) * (∑ h, (r h : ℝ)) + blockExponentSum c q e) := by
  obtain ⟨e, he, hbound⟩ := rational_polynomial_eval_norm_le_some_monomial F hF y
  have hcoeff : polynomialCoeffL1 F ≤ Real.exp (C * ∑ h, (r h : ℝ)) := by
    simpa only [Real.exp_log (polynomialCoeffL1_pos hF)] using Real.exp_le_exp.mpr hheight
  have hmono := block_monomial_exp_bound_with_constant r (fun i => ‖y i‖) c q e K hK
    (fun i => norm_nonneg _) hy (hdegree e he)
  refine ⟨e, he, hbound.trans ?_⟩
  calc
    _ ≤ Real.exp (C * ∑ h, (r h : ℝ)) *
        Real.exp (Real.log K * (∑ h, (r h : ℝ)) + blockExponentSum c q e) :=
      mul_le_mul hcoeff hmono (Finset.prod_nonneg fun i _ => pow_nonneg (norm_nonneg _) _)
        (Real.exp_nonneg _)
    _ = _ := by rw [← Real.exp_add]; congr 1; ring


end
end Bounty

end SubmissionComponent_ThreePlacePolynomialBounds

/- Component UniformBalancedDerivativeAuxiliary; SHA256 f7c7e83edbb956f7ff073c5c91674fae6c9b30ece711f25e842226a4b34dac96 -/
section SubmissionComponent_UniformBalancedDerivativeAuxiliary
/- One auxiliary polynomial supplies integral, balanced, uniformly bounded derivatives. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rationalBlockLinearSubstitution_injective {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, (A h).det ≠ 0) :
    Function.Injective (rationalBlockLinearSubstitution A) := by
  intro P Q hPQ
  have hh := congrArg (rationalBlockLinearSubstitution (inverseBlockMatrices A)) hPQ
  have hmul : (fun h => A h * inverseBlockMatrices A h) =
      (fun _ => (1 : Matrix (Fin d) (Fin d) ℚ)) := by
    funext h
    exact Matrix.mul_nonsing_inv _ (isUnit_iff_ne_zero.mpr (hA h))
  simpa only [rationalBlockLinearSubstitution_comp, hmul,
    rationalBlockLinearSubstitution_one] using hh

def exists_rational_block_matrix_norm_bound {m d s : ℕ}
    (A : Fin s → Fin m → Fin d → Fin d → ℚ) :
    ∃ C : ℝ, 1 ≤ C ∧ ∀ v h i, ∑ j, ‖A v h i j‖ ≤ C := by
  let T : ℝ := ∑ v, ∑ h, ∑ i, ∑ j, ‖A v h i j‖
  have hT : 0 ≤ T := by dsimp [T]; positivity
  refine ⟨1 + T, by linarith, ?_⟩
  intro v h i
  have hi : (∑ j, ‖A v h i j‖) ≤ ∑ k, ∑ j, ‖A v h k j‖ :=
    Finset.single_le_sum (f := fun k : Fin d => ∑ j, ‖A v h k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ i)
  have hh : (∑ k, ∑ j, ‖A v h k j‖) ≤ ∑ t, ∑ k, ∑ j, ‖A v t k j‖ :=
    Finset.single_le_sum (f := fun t : Fin m => ∑ k, ∑ j, ‖A v t k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ h)
  have hv : (∑ t, ∑ k, ∑ j, ‖A v t k j‖) ≤ T :=
    Finset.single_le_sum (f := fun w : Fin s => ∑ t, ∑ k, ∑ j, ‖A w t k j‖)
      (fun _ _ => by positivity) (Finset.mem_univ v)
  linarith [hi.trans (hh.trans hv)]

def exists_balanced_integer_derivative_auxiliary {m d s : ℕ}
    (hm : 0 < m) (hd : 0 < d)
    (B : Fin s → Fin m → Matrix (Fin d) (Fin d) ℚ)
    (hB : ∀ v h, (B v h).det ≠ 0) :
    ∃ K L : ℝ, 0 ≤ K ∧ 0 ≤ L ∧
      ∀ (r : Fin m → ℕ), (∀ h, 0 < r h) →
      ∀ η : ℝ, 0 ≤ η → 4 * (s : ℝ) * d ≤ (m : ℝ) * η ^ 2 →
      ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧ ProductBlockHomogeneous r P ∧
        Real.log (polynomialCoeffL1 P) ≤ K * (∑ h, (r h : ℝ)) ∧
        ∀ t : List (Fin m × Fin d), blockDerivativeWeight r t ≤ (m : ℝ) * η →
          dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P) ≠ 0 →
          ∃ T : MvPolynomial (Fin m × Fin d) ℤ, T ≠ 0 ∧
            MvPolynomial.map (Int.castRingHom ℚ) T =
              dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P) ∧
            ∀ v : Fin s,
              (∀ e ∈ (rationalBlockLinearSubstitution (B v)
                (MvPolynomial.map (Int.castRingHom ℚ) T)).support,
                (∀ h, ∑ i, e (h, i) ≤ r h) ∧
                ∀ i : Fin d,
                  |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * (m : ℝ) * η) ∧
              Real.log (polynomialCoeffL1 (rationalBlockLinearSubstitution (B v)
                (MvPolynomial.map (Int.castRingHom ℚ) T))) ≤ L * (∑ h, (r h : ℝ)) := by
  obtain ⟨K, hK, haux⟩ := exists_rational_balanced_auxiliary_constant hm hd B
  obtain ⟨C, hC, hnormB⟩ := exists_rational_block_matrix_norm_bound B
  let L := K + (d : ℝ) * Real.log 2 + Real.log C
  have hL : 0 ≤ L := add_nonneg (add_nonneg hK
    (mul_nonneg (Nat.cast_nonneg _) (Real.log_nonneg (by norm_num)))) (Real.log_nonneg hC)
  refine ⟨K, L, hK, hL, ?_⟩
  intro r hr η hη hlarge
  obtain ⟨P, hP, hhom, hheight, hbalance⟩ := haux r hr η hη hlarge
  refine ⟨P, hP, hhom, hheight, ?_⟩
  intro t ht hderiv
  obtain ⟨T, hTmap⟩ := exists_integer_dividedWordPDeriv t P
  have hT : T ≠ 0 := by
    intro hz
    apply hderiv
    simpa only [hz, map_zero] using hTmap.symm
  refine ⟨T, hT, hTmap, ?_⟩
  intro v
  have htransformed : rationalBlockLinearSubstitution (B v)
      (dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0 := by
    intro hz
    exact hderiv ((rationalBlockLinearSubstitution_injective (B v) (hB v))
      (hz.trans (map_zero _).symm))
  constructor
  · intro e he
    have he' : MvPolynomial.coeff e (rationalBlockLinearSubstitution (B v)
        (dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P))) ≠ 0 := by
      simpa only [hTmap] using MvPolynomial.mem_support_iff.mp he
    constructor
    · intro h
      have hh := rationalBlockLinearSubstitution_dividedWordPDeriv_block_degrees
        (B v) (hB v) r t (MvPolynomial.map (Int.castRingHom ℚ) P)
        (fun e he => (hbalance v e he).1) e he' h
      omega
    · intro i
      exact (rationalBlockLinearSubstitution_dividedWordPDeriv_balanced
        (B v) (hB v) r η t (MvPolynomial.map (Int.castRingHom ℚ) P)
        (fun e he => (hbalance v e he).2) ht e he' i).le
  · rw [hTmap]
    exact transformed_integer_derivative_height (B v) r P hP hhom t C K hC
      (hnormB v) hheight htransformed


end
end Bounty

end SubmissionComponent_UniformBalancedDerivativeAuxiliary

/- Component BalancedExponentEstimate; SHA256 69dcab77191dbe80821fadc1a990d78a1b032b02e93b6d9e61689f660e3ce643 -/
section SubmissionComponent_BalancedExponentEstimate
/- Exact finite-sum exponent budgets.  The hypotheses are concrete scale,
coordinate, and balance inequalities; no geometry or limiting premise occurs. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def balanced_block_scale_error {m : ℕ} (r q e : Fin m → ℝ) (D : ℝ)
    (hr : ∀ h, 0 < r h) (he0 : ∀ h, 0 ≤ e h) (her : ∀ h, e h ≤ r h)
    (hscale : ∀ h, |r h * q h - D| ≤ q h) :
    |(∑ h, e h * q h) - D * (∑ h, e h / r h)| ≤ ∑ h, q h := by
  have hterm (h : Fin m) : |e h * q h - D * (e h / r h)| ≤ q h := by
    have hepos : 0 ≤ e h / r h := div_nonneg (he0 h) (le_of_lt (hr h))
    have hele : e h / r h ≤ 1 := (div_le_one (hr h)).mpr (her h)
    have hid : e h * q h - D * (e h / r h) =
        (e h / r h) * (r h * q h - D) := by
      field_simp [ne_of_gt (hr h)]
    rw [hid, abs_mul, abs_of_nonneg hepos]
    exact (mul_le_mul hele (hscale h) (abs_nonneg _) zero_le_one).trans_eq (one_mul _)
  rw [Finset.mul_sum, ← Finset.sum_sub_distrib]
  exact (Finset.abs_sum_le_sum_abs _ _).trans (Finset.sum_le_sum fun h _ => hterm h)

def balanced_coordinate_scale_estimate {m d : ℕ}
    (r q e : Fin m → ℝ) (D η : ℝ) (hD : 0 ≤ D)
    (hr : ∀ h, 0 < r h) (he0 : ∀ h, 0 ≤ e h) (her : ∀ h, e h ≤ r h)
    (hscale : ∀ h, |r h * q h - D| ≤ q h)
    (hbalance : |(∑ h, e h / r h) - (m : ℝ) / d| ≤ 2 * m * η) :
    |(∑ h, e h * q h) - D * (m : ℝ) / d| ≤ D * (2 * m * η) + ∑ h, q h := by
  have hid : (∑ h, e h * q h) - D * (m : ℝ) / d =
      ((∑ h, e h * q h) - D * (∑ h, e h / r h)) +
        D * ((∑ h, e h / r h) - (m : ℝ) / d) := by ring
  rw [hid]
  calc
    _ ≤ |(∑ h, e h * q h) - D * (∑ h, e h / r h)| +
        |D * ((∑ h, e h / r h) - (m : ℝ) / d)| := abs_add_le _ _
    _ ≤ (∑ h, q h) + D * (2 * m * η) := by
      rw [abs_mul, abs_of_nonneg hD]
      exact add_le_add (balanced_block_scale_error r q e D hr he0 her hscale)
        (mul_le_mul_of_nonneg_left hbalance hD)
    _ = _ := by ring

def signed_weight_of_abs_error (c S T E : ℝ) (herror : |S - T| ≤ E) :
    c * S ≤ c * T + |c| * E := by
  have hh : c * (S - T) ≤ |c| * E := calc
    _ ≤ |c * (S - T)| := le_abs_self _
    _ = |c| * |S - T| := abs_mul _ _
    _ ≤ _ := mul_le_mul_of_nonneg_left herror (abs_nonneg c)
  nlinarith

def exponentCoefficientMass {s d : ℕ} (c : Fin s → Fin d → ℝ) : ℝ :=
  ∑ v, ∑ i, |c v i|

def balanced_exponent_estimate_real {m d s : ℕ}
    (r q : Fin m → ℝ) (e : Fin s → Fin m → Fin d → ℝ)
    (c : Fin s → Fin d → ℝ) (D η ρ : ℝ) (hd : 0 < d) (hD : 0 ≤ D)
    (hr : ∀ h, 0 < r h)
    (he0 : ∀ v h i, 0 ≤ e v h i) (her : ∀ v h i, e v h i ≤ r h)
    (hscale : ∀ h, |r h * q h - D| ≤ q h)
    (hbalance : ∀ v i, |(∑ h, e v h i / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ) :
    (∑ v, ∑ i, ∑ h, c v i * e v h i * q h) ≤
      D * (-(m : ℝ) * ρ / d + 2 * m * η * exponentCoefficientMass c) +
        exponentCoefficientMass c * ∑ h, q h := by
  let T : ℝ := D * (m : ℝ) / d
  let E : ℝ := D * (2 * m * η) + ∑ h, q h
  have hT : 0 ≤ T := by dsimp [T]; positivity
  have hterm (v : Fin s) (i : Fin d) :
      c v i * (∑ h, e v h i * q h) ≤ c v i * T + |c v i| * E :=
    signed_weight_of_abs_error _ _ _ _ (balanced_coordinate_scale_estimate
      r q (fun h => e v h i) D η hD hr (fun h => he0 v h i) (fun h => her v h i)
        hscale (hbalance v i))
  calc
    _ = ∑ v, ∑ i, c v i * (∑ h, e v h i * q h) := by
      simp only [Finset.mul_sum, mul_assoc]
    _ ≤ ∑ v, ∑ i, (c v i * T + |c v i| * E) :=
      Finset.sum_le_sum fun v _ => Finset.sum_le_sum fun i _ => hterm v i
    _ = (∑ v, ∑ i, c v i) * T + exponentCoefficientMass c * E := by
      simp only [Finset.sum_add_distrib, ← Finset.sum_mul, exponentCoefficientMass]
    _ ≤ (-ρ) * T + exponentCoefficientMass c * E :=
      add_le_add (mul_le_mul_of_nonneg_right hc hT) le_rfl
    _ = _ := by dsimp [T, E]; ring

def balanced_exponent_estimate {m d s : ℕ}
    (r : Fin m → ℕ) (q : Fin m → ℝ) (e : Fin s → Fin m → Fin d → ℕ)
    (c : Fin s → Fin d → ℝ) (D η ρ : ℝ) (hd : 0 < d) (hD : 0 ≤ D)
    (hr : ∀ h, 0 < r h) (her : ∀ v h i, e v h i ≤ r h)
    (hscale : ∀ h, |(r h : ℝ) * q h - D| ≤ q h)
    (hbalance : ∀ v i, |(∑ h, (e v h i : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ) :
    (∑ v, ∑ i, ∑ h, c v i * (e v h i : ℝ) * q h) ≤
      D * (-(m : ℝ) * ρ / d + 2 * m * η * exponentCoefficientMass c) +
        exponentCoefficientMass c * ∑ h, q h := by
  exact balanced_exponent_estimate_real (fun h => (r h : ℝ)) q
    (fun v h i => (e v h i : ℝ)) c D η ρ hd hD (fun h => by exact_mod_cast hr h)
    (fun _ _ _ => by positivity) (fun v h i => by exact_mod_cast her v h i)
    hscale hbalance hc

def deficit_le_exponentCoefficientMass {s d : ℕ} (c : Fin s → Fin d → ℝ)
    (ρ : ℝ) (hc : (∑ v, ∑ i, c v i) ≤ -ρ) :
    ρ ≤ exponentCoefficientMass c := by
  have hh : -(∑ v, ∑ i, c v i) ≤ exponentCoefficientMass c := by
    calc
      _ = ∑ v, ∑ i, -(c v i) := by simp only [Finset.sum_neg_distrib]
      _ ≤ _ := Finset.sum_le_sum fun v _ => Finset.sum_le_sum fun i _ => neg_le_abs (c v i)
  linarith

def balanced_exponent_negative_coefficient {m d s : ℕ}
    (c : Fin s → Fin d → ℝ) (η ρ : ℝ) (hd : 0 < d) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hη : η ≤ ρ / (8 * (d : ℝ) * exponentCoefficientMass c)) :
    -(m : ℝ) * ρ / d + 2 * m * η * exponentCoefficientMass c ≤
      -3 * (m : ℝ) * ρ / (4 * d) := by
  have hd' : (0 : ℝ) < d := by exact_mod_cast hd
  have hmass : 0 < exponentCoefficientMass c :=
    hρ.trans_le (deficit_le_exponentCoefficientMass c ρ hc)
  have hη' := (le_div_iff₀ (show 0 < 8 * (d : ℝ) * exponentCoefficientMass c by positivity)).mp hη
  have hsmall : 2 * (m : ℝ) * η * exponentCoefficientMass c ≤
      (m : ℝ) * ρ / (4 * d) := by
    apply (le_div_iff₀ (by positivity : (0 : ℝ) < 4 * d)).mpr
    calc
      _ = (m : ℝ) * (η * (8 * d * exponentCoefficientMass c)) := by ring
      _ ≤ (m : ℝ) * ρ := mul_le_mul_of_nonneg_left hη' (by positivity)
  calc
    _ ≤ -(m : ℝ) * ρ / d + (m : ℝ) * ρ / (4 * d) := add_le_add le_rfl hsmall
    _ = _ := by field_simp; ring

def balanced_exponent_estimate_negative {m d s : ℕ}
    (r : Fin m → ℕ) (q : Fin m → ℝ) (e : Fin s → Fin m → Fin d → ℕ)
    (c : Fin s → Fin d → ℝ) (D η ρ : ℝ) (hd : 0 < d) (hD : 0 ≤ D) (hρ : 0 < ρ)
    (hr : ∀ h, 0 < r h) (her : ∀ v h i, e v h i ≤ r h)
    (hscale : ∀ h, |(r h : ℝ) * q h - D| ≤ q h)
    (hbalance : ∀ v i, |(∑ h, (e v h i : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hη : η ≤ ρ / (8 * (d : ℝ) * exponentCoefficientMass c)) :
    (∑ v, ∑ i, ∑ h, c v i * (e v h i : ℝ) * q h) ≤
      -3 * (m : ℝ) * ρ * D / (4 * d) + exponentCoefficientMass c * ∑ h, q h := by
  calc
    _ ≤ D * (-(m : ℝ) * ρ / d + 2 * m * η * exponentCoefficientMass c) +
        exponentCoefficientMass c * ∑ h, q h :=
      balanced_exponent_estimate r q e c D η ρ hd hD hr her hscale hbalance hc
    _ ≤ D * (-3 * (m : ℝ) * ρ / (4 * d)) + exponentCoefficientMass c * ∑ h, q h :=
      add_le_add (mul_le_mul_of_nonneg_left
        (balanced_exponent_negative_coefficient c η ρ hd hρ hc hη) hD) le_rfl
    _ = _ := by ring

def exponent_quarter_budgets_of_large_scales {m d : ℕ}
    (C R q₀ M Q ρ D : ℝ) (hd : 0 < d) (hC : 0 ≤ C) (hD : 0 < D) (hq₀ : 0 < q₀)
    (hR : R ≤ 2 * D / q₀)
    (hqLarge : 8 * (d : ℝ) * C ≤ (m : ℝ) * ρ * q₀)
    (hDLarge : 4 * (d : ℝ) * M * Q ≤ (m : ℝ) * ρ * D) :
    C * R ≤ (m : ℝ) * ρ * D / (4 * d) ∧
      M * Q ≤ (m : ℝ) * ρ * D / (4 * d) := by
  have hd' : (0 : ℝ) < d := by exact_mod_cast hd
  constructor
  · refine (mul_le_mul_of_nonneg_left hR hC).trans ?_
    apply (le_div_iff₀ (by positivity : (0 : ℝ) < 4 * d)).mpr
    have hh := mul_le_mul_of_nonneg_right hqLarge (le_of_lt hD)
    have hid : (C * (2 * D / q₀)) * (4 * (d : ℝ)) = (8 * d * C * D) / q₀ := by ring
    rw [hid]
    apply (div_le_iff₀ hq₀).mpr
    nlinarith
  · apply (le_div_iff₀ (by positivity : (0 : ℝ) < 4 * d)).mpr
    nlinarith

def exponent_three_quarter_budget_negative {m d : ℕ}
    (C R M Q ρ D E : ℝ) (hm : 0 < m) (hd : 0 < d) (hρ : 0 < ρ) (hD : 0 < D)
    (hR : C * R ≤ (m : ℝ) * ρ * D / (4 * d))
    (hQ : M * Q ≤ (m : ℝ) * ρ * D / (4 * d))
    (hE : E ≤ -3 * (m : ℝ) * ρ * D / (4 * d) + M * Q) :
    C * R + E < 0 := by
  have hpos : 0 < (m : ℝ) * ρ * D / (4 * d) := by positivity
  have hid : -3 * (m : ℝ) * ρ * D / (4 * d) =
      -3 * ((m : ℝ) * ρ * D / (4 * d)) := by ring
  rw [hid] at hE
  linarith

def balanced_exponent_contradiction {m d s : ℕ}
    (r : Fin m → ℕ) (q : Fin m → ℝ) (e : Fin s → Fin m → Fin d → ℕ)
    (c : Fin s → Fin d → ℝ) (D η ρ C q₀ : ℝ)
    (hm : 0 < m) (hd : 0 < d) (hD : 0 < D) (hρ : 0 < ρ) (hC : 0 ≤ C) (hq₀ : 0 < q₀)
    (hr : ∀ h, 0 < r h) (her : ∀ v h i, e v h i ≤ r h)
    (hscale : ∀ h, |(r h : ℝ) * q h - D| ≤ q h)
    (hbalance : ∀ v i, |(∑ h, (e v h i : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hη : η ≤ ρ / (8 * (d : ℝ) * exponentCoefficientMass c))
    (hR : (∑ h, (r h : ℝ)) ≤ 2 * D / q₀)
    (hqLarge : 8 * (d : ℝ) * C ≤ (m : ℝ) * ρ * q₀)
    (hDLarge : 4 * (d : ℝ) * exponentCoefficientMass c * (∑ h, q h) ≤ (m : ℝ) * ρ * D) :
    C * (∑ h, (r h : ℝ)) + (∑ v, ∑ i, ∑ h, c v i * (e v h i : ℝ) * q h) < 0 := by
  obtain ⟨hR', hQ'⟩ := exponent_quarter_budgets_of_large_scales
    C (∑ h, (r h : ℝ)) q₀ (exponentCoefficientMass c) (∑ h, q h) ρ D
    hd hC hD hq₀ hR hqLarge hDLarge
  exact exponent_three_quarter_budget_negative C (∑ h, (r h : ℝ))
    (exponentCoefficientMass c) (∑ h, q h) ρ D _ hm hd hρ hD hR' hQ'
    (balanced_exponent_estimate_negative r q e c D η ρ hd (le_of_lt hD) hρ hr her hscale hbalance hc hη)


end
end Bounty

end SubmissionComponent_BalancedExponentEstimate

/- Component ActualThreePlacePolynomialContradiction; SHA256 b9ee0dc12e43ce1f135678ffe33725fde4cc32ea061c3d14e3777fa199a69a65 -/
section SubmissionComponent_ActualThreePlacePolynomialContradiction
/- The actual three-place contradiction for a nonzero integer polynomial
evaluation.  Archimedean coefficients may be rational; finite-place estimates
are applied directly to the integer polynomial. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def actual_three_place_polynomial_upper {m d : ℕ}
    (T : MvPolynomial (Fin m × Fin d) ℤ) (F : MvPolynomial (Fin m × Fin d) ℚ)
    (x : Fin m × Fin d → ℤ) (y : Fin m × Fin d → ℚ)
    (heval : MvPolynomial.eval y F = (MvPolynomial.eval x T : ℚ))
    (hne : MvPolynomial.eval x T ≠ 0)
    (r : Fin m → ℕ) (q : Fin m → ℝ) (c : Fin 3 → Fin d → ℝ) (C K : ℝ) (hK : 1 ≤ K)
    (hdegree : ∀ e ∈ F.support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hheight : Real.log (polynomialCoeffL1 F) ≤ C * ∑ h, (r h : ℝ))
    (hy : ∀ h i, ‖y (h, i)‖ ≤ K * Real.exp (c 0 i * q h))
    (hx₂ : ∀ h i, (padicNorm 2 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 1 i * q h))
    (hx₃ : ∀ h i, (padicNorm 3 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 2 i * q h)) :
    ∃ eInf ∈ F.support, ∃ e₂ ∈ T.support, ∃ e₃ ∈ T.support,
      |(MvPolynomial.eval x T : ℝ)| * (padicNorm 2 (MvPolynomial.eval x T : ℚ) : ℝ) *
        (padicNorm 3 (MvPolynomial.eval x T : ℚ) : ℝ) ≤
      Real.exp ((C + Real.log K) * (∑ h, (r h : ℝ)) + blockExponentSum (c 0) q eInf +
        blockExponentSum (c 1) q e₂ + blockExponentSum (c 2) q e₃) := by
  have hT : T ≠ 0 := by intro hz; apply hne; simp [hz]
  have hF : F ≠ 0 := by
    intro hz
    have hh : (MvPolynomial.eval x T : ℚ) = 0 := by simpa [hz] using heval.symm
    apply hne
    exact_mod_cast hh
  obtain ⟨eInf, heInf, hbInf⟩ := rational_eval_le_exp_some_monomial F hF y r q (c 0) C K hK hdegree hheight hy
  obtain ⟨e₂, he₂, hb₂⟩ := integer_padic_eval_le_exp_some_monomial 2 T hT x q (c 1) hx₂
  obtain ⟨e₃, he₃, hb₃⟩ := integer_padic_eval_le_exp_some_monomial 3 T hT x q (c 2) hx₃
  have hbInf' : |(MvPolynomial.eval x T : ℝ)| ≤
      Real.exp ((C + Real.log K) * (∑ h, (r h : ℝ)) + blockExponentSum (c 0) q eInf) := by
    simpa only [heval, Int.norm_cast_rat, ← Real.norm_eq_abs, Int.norm_cast_real] using hbInf
  have hp₂ : 0 ≤ (padicNorm 2 (MvPolynomial.eval x T : ℚ) : ℝ) := by
    exact_mod_cast (padicNorm.nonneg (p := 2) (MvPolynomial.eval x T : ℚ))
  have hp₃ : 0 ≤ (padicNorm 3 (MvPolynomial.eval x T : ℚ) : ℝ) := by
    exact_mod_cast (padicNorm.nonneg (p := 3) (MvPolynomial.eval x T : ℚ))
  refine ⟨eInf, heInf, e₂, he₂, e₃, he₃, ?_⟩
  calc
    _ ≤ (Real.exp ((C + Real.log K) * (∑ h, (r h : ℝ)) + blockExponentSum (c 0) q eInf) *
        Real.exp (blockExponentSum (c 1) q e₂)) * Real.exp (blockExponentSum (c 2) q e₃) :=
      mul_le_mul (mul_le_mul hbInf' hb₂ hp₂ (Real.exp_nonneg _)) hb₃ hp₃
        (mul_nonneg (Real.exp_nonneg _) (Real.exp_nonneg _))
    _ = _ := by rw [← Real.exp_add, ← Real.exp_add]

def threePlaceExponents {m d : ℕ} (eInf e₂ e₃ : (Fin m × Fin d) →₀ ℕ) :
    Fin 3 → Fin m → Fin d → ℕ :=
  fun v h i => ![eInf, e₂, e₃] v (h, i)

def threePlaceExponents_sum {m d : ℕ}
    (c : Fin 3 → Fin d → ℝ) (q : Fin m → ℝ) (eInf e₂ e₃ : (Fin m × Fin d) →₀ ℕ) :
    (∑ v, ∑ i, ∑ h, c v i * (threePlaceExponents eInf e₂ e₃ v h i : ℝ) * q h) =
      blockExponentSum (c 0) q eInf + blockExponentSum (c 1) q e₂ + blockExponentSum (c 2) q e₃ := by
  simp [threePlaceExponents, blockExponentSum, Fin.sum_univ_succ, add_assoc]

def actual_three_place_polynomial_contradiction {m d : ℕ}
    (T : MvPolynomial (Fin m × Fin d) ℤ) (F : MvPolynomial (Fin m × Fin d) ℚ)
    (x : Fin m × Fin d → ℤ) (y : Fin m × Fin d → ℚ)
    (heval : MvPolynomial.eval y F = (MvPolynomial.eval x T : ℚ))
    (hne : MvPolynomial.eval x T ≠ 0)
    (r : Fin m → ℕ) (q : Fin m → ℝ) (c : Fin 3 → Fin d → ℝ) (D η ρ C K q₀ : ℝ)
    (hm : 0 < m) (hd : 0 < d) (hD : 0 < D) (hρ : 0 < ρ) (hC : 0 ≤ C)
    (hK : 1 ≤ K) (hq₀ : 0 < q₀) (hr : ∀ h, 0 < r h)
    (hdegreeF : ∀ e ∈ F.support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hdegreeT : ∀ e ∈ T.support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hbalanceF : ∀ e ∈ F.support, ∀ i : Fin d,
      |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hbalanceT : ∀ e ∈ T.support, ∀ i : Fin d,
      |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hscale : ∀ h, |(r h : ℝ) * q h - D| ≤ q h)
    (hheight : Real.log (polynomialCoeffL1 F) ≤ C * ∑ h, (r h : ℝ))
    (hy : ∀ h i, ‖y (h, i)‖ ≤ K * Real.exp (c 0 i * q h))
    (hx₂ : ∀ h i, (padicNorm 2 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 1 i * q h))
    (hx₃ : ∀ h i, (padicNorm 3 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 2 i * q h))
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hη : η ≤ ρ / (8 * (d : ℝ) * exponentCoefficientMass c))
    (hR : (∑ h, (r h : ℝ)) ≤ 2 * D / q₀)
    (hqLarge : 8 * (d : ℝ) * (C + Real.log K) ≤ (m : ℝ) * ρ * q₀)
    (hDLarge : 4 * (d : ℝ) * exponentCoefficientMass c * (∑ h, q h) ≤ (m : ℝ) * ρ * D) :
    False := by
  classical
  obtain ⟨eInf, heInf, e₂, he₂, e₃, he₃, hupper⟩ :=
    actual_three_place_polynomial_upper T F x y heval hne r q c C K hK hdegreeF hheight hy hx₂ hx₃
  have hpoint {e : (Fin m × Fin d) →₀ ℕ} (hdeg : ∀ h, ∑ i, e (h, i) ≤ r h)
      (h : Fin m) (i : Fin d) : e (h, i) ≤ r h :=
    (Finset.single_le_sum (fun _ _ => Nat.zero_le _) (Finset.mem_univ i)).trans (hdeg h)
  have her : ∀ v h i, threePlaceExponents eInf e₂ e₃ v h i ≤ r h := by
    intro v h i
    fin_cases v
    · exact hpoint (hdegreeF eInf heInf) h i
    · exact hpoint (hdegreeT e₂ he₂) h i
    · exact hpoint (hdegreeT e₃ he₃) h i
  have hbalance : ∀ v i, |(∑ h, (threePlaceExponents eInf e₂ e₃ v h i : ℝ) / r h) -
      (m : ℝ) / d| ≤ 2 * m * η := by
    intro v i
    fin_cases v
    · exact hbalanceF eInf heInf i
    · exact hbalanceT e₂ he₂ i
    · exact hbalanceT e₃ he₃ i
  have hnegative := balanced_exponent_contradiction r q (threePlaceExponents eInf e₂ e₃) c
    D η ρ (C + Real.log K) q₀ hm hd hD hρ (add_nonneg hC (Real.log_nonneg hK)) hq₀
    hr her hscale hbalance hc hη hR hqLarge hDLarge
  rw [threePlaceExponents_sum] at hnegative
  have hexp : Real.exp ((C + Real.log K) * (∑ h, (r h : ℝ)) + blockExponentSum (c 0) q eInf +
      blockExponentSum (c 1) q e₂ + blockExponentSum (c 2) q e₃) < 1 := by
    apply Real.exp_lt_one_iff.mpr
    simpa only [add_assoc] using hnegative
  have hlower := integer_three_place_product_lower (MvPolynomial.eval x T) hne
  exact (not_lt_of_ge hlower) (hupper.trans_lt hexp)

def inverseBlockPolynomial {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (T : MvPolynomial (Fin m × Fin d) ℤ) :
    MvPolynomial (Fin m × Fin d) ℚ :=
  rationalBlockLinearSubstitution (inverseBlockMatrices A) (MvPolynomial.map (Int.castRingHom ℚ) T)

/-- Specialization to actual invertible rational block matrices at infinity.
The two finite places still evaluate the original integer polynomial. -/
def inverse_block_three_place_polynomial_contradiction {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, IsUnit (A h).det)
    (T : MvPolynomial (Fin m × Fin d) ℤ) (x : Fin m × Fin d → ℤ)
    (hne : MvPolynomial.eval x T ≠ 0)
    (r : Fin m → ℕ) (q : Fin m → ℝ) (c : Fin 3 → Fin d → ℝ) (D η ρ C K q₀ : ℝ)
    (hm : 0 < m) (hd : 0 < d) (hD : 0 < D) (hρ : 0 < ρ) (hC : 0 ≤ C)
    (hK : 1 ≤ K) (hq₀ : 0 < q₀) (hr : ∀ h, 0 < r h)
    (hdegreeF : ∀ e ∈ (inverseBlockPolynomial A T).support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hdegreeT : ∀ e ∈ T.support, ∀ h, ∑ i, e (h, i) ≤ r h)
    (hbalanceF : ∀ e ∈ (inverseBlockPolynomial A T).support, ∀ i : Fin d,
      |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hbalanceT : ∀ e ∈ T.support, ∀ i : Fin d,
      |(∑ h : Fin m, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * m * η)
    (hscale : ∀ h, |(r h : ℝ) * q h - D| ≤ q h)
    (hheight : Real.log (polynomialCoeffL1 (inverseBlockPolynomial A T)) ≤ C * ∑ h, (r h : ℝ))
    (hy : ∀ h i, ‖blockMatrixValues A (fun hi => (x hi : ℚ)) (h, i)‖ ≤
      K * Real.exp (c 0 i * q h))
    (hx₂ : ∀ h i, (padicNorm 2 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 1 i * q h))
    (hx₃ : ∀ h i, (padicNorm 3 (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c 2 i * q h))
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hη : η ≤ ρ / (8 * (d : ℝ) * exponentCoefficientMass c))
    (hR : (∑ h, (r h : ℝ)) ≤ 2 * D / q₀)
    (hqLarge : 8 * (d : ℝ) * (C + Real.log K) ≤ (m : ℝ) * ρ * q₀)
    (hDLarge : 4 * (d : ℝ) * exponentCoefficientMass c * (∑ h, q h) ≤ (m : ℝ) * ρ * D) :
    False := by
  exact actual_three_place_polynomial_contradiction T (inverseBlockPolynomial A T)
    x (blockMatrixValues A (fun hi => (x hi : ℚ)))
    (inverse_block_substitution_eval A hA T x) hne r q c D η ρ C K q₀
    hm hd hD hρ hC hK hq₀ hr hdegreeF hdegreeT hbalanceF hbalanceT hscale hheight
    hy hx₂ hx₃ hc hη hR hqLarge hDLarge


end
end Bounty

end SubmissionComponent_ActualThreePlacePolynomialContradiction

/- Component TwoBasisBalancedAuxiliary; SHA256 a9090b89e1ca3dd9ded374ffb3c77455ac89b5510bdd69ba81bdd001e3336526 -/
section SubmissionComponent_TwoBasisBalancedAuxiliary
/- Balanced integer auxiliaries in the inverse archimedean basis and the identity basis. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def threePlaceAuxiliaryBases {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) :
    Fin 2 → Fin m → Matrix (Fin d) (Fin d) ℚ :=
  ![inverseBlockMatrices A, fun _ => 1]

structure ThreePlaceDerivativeBounds {m d : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (r : Fin m → ℕ) (η L : ℝ)
    (T : MvPolynomial (Fin m × Fin d) ℤ) : Prop where
  degreeInf : ∀ e ∈ (inverseBlockPolynomial A T).support, ∀ h, ∑ i, e (h, i) ≤ r h
  degreeInt : ∀ e ∈ T.support, ∀ h, ∑ i, e (h, i) ≤ r h
  balanceInf : ∀ e ∈ (inverseBlockPolynomial A T).support, ∀ i : Fin d,
    |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * (m : ℝ) * η
  balanceInt : ∀ e ∈ T.support, ∀ i : Fin d,
    |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * (m : ℝ) * η
  heightInf : Real.log (polynomialCoeffL1 (inverseBlockPolynomial A T)) ≤
    L * (∑ h, (r h : ℝ))

def exists_two_basis_balanced_auxiliary {m d : ℕ} (hm : 0 < m) (hd : 0 < d)
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ) (hA : ∀ h, IsUnit (A h).det) :
    ∃ K L : ℝ, 0 ≤ K ∧ 0 ≤ L ∧
      ∀ (r : Fin m → ℕ), (∀ h, 0 < r h) →
      ∀ η : ℝ, 0 ≤ η → 8 * (d : ℝ) ≤ (m : ℝ) * η ^ 2 →
      ∃ P : MvPolynomial (Fin m × Fin d) ℤ, P ≠ 0 ∧ ProductBlockHomogeneous r P ∧
        Real.log (polynomialCoeffL1 P) ≤ K * (∑ h, (r h : ℝ)) ∧
        ∀ t : List (Fin m × Fin d), blockDerivativeWeight r t ≤ (m : ℝ) * η →
          dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P) ≠ 0 →
          ∃ T : MvPolynomial (Fin m × Fin d) ℤ, T ≠ 0 ∧
            MvPolynomial.map (Int.castRingHom ℚ) T =
              dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P) ∧
            ThreePlaceDerivativeBounds A r η L T := by
  classical
  have hB : ∀ v h, (threePlaceAuxiliaryBases A v h).det ≠ 0 := by
    intro v h
    fin_cases v
    · exact (Matrix.isUnit_nonsing_inv_det (A h) (hA h)).ne_zero
    · simp [threePlaceAuxiliaryBases]
  obtain ⟨K, L, hK, hL, haux⟩ := exists_balanced_integer_derivative_auxiliary
    hm hd (threePlaceAuxiliaryBases A) hB
  refine ⟨K, L, hK, hL, ?_⟩
  intro r hr η hη hlarge
  have hlarge' : 4 * (2 : ℝ) * d ≤ (m : ℝ) * η ^ 2 := by norm_num; exact hlarge
  obtain ⟨P, hP, hhom, hheight, hderiv⟩ := haux r hr η hη hlarge'
  refine ⟨P, hP, hhom, hheight, ?_⟩
  intro t ht htne
  obtain ⟨T, hT, hTmap, hbounds⟩ := hderiv t ht htne
  have hInf := hbounds 0
  have hInt := hbounds 1
  change (∀ e ∈ (inverseBlockPolynomial A T).support,
      (∀ h, ∑ i, e (h, i) ≤ r h) ∧
      ∀ i, |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * (m : ℝ) * η) ∧
    Real.log (polynomialCoeffL1 (inverseBlockPolynomial A T)) ≤ L * (∑ h, (r h : ℝ)) at hInf
  have hInt' : ∀ e ∈ T.support,
      (∀ h, ∑ i, e (h, i) ≤ r h) ∧
      ∀ i, |(∑ h, (e (h, i) : ℝ) / r h) - (m : ℝ) / d| ≤ 2 * (m : ℝ) * η := by
    intro e he
    have hmap : e ∈ (MvPolynomial.map (Int.castRingHom ℚ) T).support := by
      rw [MvPolynomial.support_map_of_injective _ Int.cast_injective]
      exact he
    have hh := hInt.1 e
    simpa only [threePlaceAuxiliaryBases, Matrix.cons_val_one, Matrix.cons_val_zero,
      rationalBlockLinearSubstitution_one] using hh (by simpa [threePlaceAuxiliaryBases, rationalBlockLinearSubstitution_one] using hmap)
  refine ⟨T, hT, hTmap, ?_⟩
  exact ⟨fun e he => (hInf.1 e he).1, fun e he => (hInt' e he).1,
    fun e he => (hInf.1 e he).2, fun e he => (hInt' e he).2, hInf.2⟩


end
end Bounty

end SubmissionComponent_TwoBasisBalancedAuxiliary

/- Component LinearParametrizationGridDerivative; SHA256 4d07eb4b75a2218bb6326c7d27926a0aadb57961461642cf53c1ae7ea422548c -/
section SubmissionComponent_LinearParametrizationGridDerivative
/- Actual coordinate derivatives detected on a bounded grid after a rectangular
linear parametrization.  No inverse or injectivity of the parametrization is
assumed. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def rationalLinearParametrization {I J : Type*} [Fintype J]
    (A : I → J → ℚ) (i : I) : MvPolynomial J ℚ :=
  ∑ j, MvPolynomial.C (A i j) * MvPolynomial.X j

def rationalLinearSubstitution {I J : Type*} [Fintype J]
    (A : I → J → ℚ) : MvPolynomial I ℚ →ₐ[ℚ] MvPolynomial J ℚ :=
  MvPolynomial.aeval (rationalLinearParametrization A)

def rationalLinearPoint {I J : Type*} [Fintype J]
    (A : I → J → ℚ) (z : J → ℚ) (i : I) : ℚ := ∑ j, A i j * z j

def eval_rationalLinearParametrization {I J : Type*} [Fintype J]
    (A : I → J → ℚ) (z : J → ℚ) (i : I) :
    MvPolynomial.eval z (rationalLinearParametrization A i) = rationalLinearPoint A z i := by
  simp [rationalLinearParametrization, rationalLinearPoint]

def eval_rationalLinearSubstitution {I J : Type*} [Fintype J]
    (A : I → J → ℚ) (z : J → ℚ) (P : MvPolynomial I ℚ) :
    MvPolynomial.eval z (rationalLinearSubstitution A P) =
      MvPolynomial.eval (rationalLinearPoint A z) P := by
  induction P using MvPolynomial.induction_on with
  | C a => simp [rationalLinearSubstitution]
  | add P Q hP hQ => simp only [map_add, hP, hQ]
  | mul_X P i hP =>
    simp only [rationalLinearSubstitution] at hP
    simp only [map_mul, rationalLinearSubstitution, MvPolynomial.aeval_X, hP,
      eval_rationalLinearParametrization, MvPolynomial.eval_X]

def pderiv_rationalLinearParametrization {I J : Type*} [Fintype J]
    (A : I → J → ℚ) (i : I) (j : J) :
    MvPolynomial.pderiv j (rationalLinearParametrization A i) = MvPolynomial.C (A i j) := by
  classical
  simp [rationalLinearParametrization, MvPolynomial.pderiv_X,
    Pi.single_apply]

def pderiv_rationalLinearSubstitution {I J : Type*} [Fintype I] [Fintype J]
    (A : I → J → ℚ) (j : J) (P : MvPolynomial I ℚ) :
    MvPolynomial.pderiv j (rationalLinearSubstitution A P) =
      ∑ i, MvPolynomial.C (A i j) * rationalLinearSubstitution A (MvPolynomial.pderiv i P) := by
  rw [rationalLinearSubstitution, pderiv_aeval_eq_sum_pderiv]
  simp only [pderiv_rationalLinearParametrization]

def wordPDeriv_C_mul {I : Type*} (s : List I) (c : ℚ) (P : MvPolynomial I ℚ) :
    wordPDeriv s (MvPolynomial.C c * P) = MvPolynomial.C c * wordPDeriv s P := by
  simpa only [MvPolynomial.smul_eq_C_mul] using (wordPDeriv s).map_smul c P

def eval_dividedWordPDeriv_ne_zero_iff {I : Type*} [Fintype I] [DecidableEq I]
    (z : I → ℚ) (s : List I) (P : MvPolynomial I ℚ) :
    MvPolynomial.eval z (dividedWordPDeriv s P) ≠ 0 ↔
      MvPolynomial.eval z (wordPDeriv s P) ≠ 0 := by
  change MvPolynomial.eval z ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P) ≠ 0 ↔ _
  simp only [MvPolynomial.smul_eq_C_mul, map_mul, MvPolynomial.eval_C]
  exact mul_ne_zero_iff.trans (and_iff_right (inv_ne_zero (wordDerivativeFactorial_ne_zero s)))

/-- A nonzero parameter derivative contains an actual source coordinate
derivative with the identical sequence of block labels. -/
def rationalLinearSubstitution_wordPDeriv_detection
    {I J H : Type*} [Fintype I] [Fintype J]
    (A : I → J → ℚ) (qI : I → H) (qJ : J → H)
    (hA : ∀ i j, A i j ≠ 0 → qI i = qJ j)
    (z : J → ℚ) (s : List J) (P : MvPolynomial I ℚ)
    (hne : MvPolynomial.eval z (wordPDeriv s (rationalLinearSubstitution A P)) ≠ 0) :
    ∃ t : List I, t.map qI = s.map qJ ∧
      MvPolynomial.eval (rationalLinearPoint A z) (wordPDeriv t P) ≠ 0 := by
  classical
  induction s using List.reverseRecOn generalizing P with
  | nil => exact ⟨[], rfl, by simpa [wordPDeriv_nil, eval_rationalLinearSubstitution] using hne⟩
  | append_singleton s j ih =>
    simp only [wordPDeriv_append, wordPDeriv_cons, wordPDeriv_nil,
      pderiv_rationalLinearSubstitution, map_sum, wordPDeriv_C_mul, map_mul,
      MvPolynomial.eval_C] at hne
    obtain ⟨i, _, hi⟩ := Finset.exists_ne_zero_of_sum_ne_zero hne
    obtain ⟨t, ht, hnonzero⟩ := ih (MvPolynomial.pderiv i P) (right_ne_zero_of_mul hi)
    refine ⟨t ++ [i], ?_, ?_⟩
    · simp only [List.map_append, List.map_cons, List.map_nil, ht,
        hA i j (left_ne_zero_of_mul hi)]
    · simpa only [wordPDeriv_append, wordPDeriv_cons, wordPDeriv_nil] using hnonzero

def rationalLinearSubstitution_dividedWordPDeriv_detection
    {I J H : Type*} [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J]
    (A : I → J → ℚ) (qI : I → H) (qJ : J → H)
    (hA : ∀ i j, A i j ≠ 0 → qI i = qJ j)
    (z : J → ℚ) (s : List J) (P : MvPolynomial I ℚ)
    (hne : MvPolynomial.eval z (dividedWordPDeriv s (rationalLinearSubstitution A P)) ≠ 0) :
    ∃ t : List I, t.map qI = s.map qJ ∧
      MvPolynomial.eval (rationalLinearPoint A z) (dividedWordPDeriv t P) ≠ 0 := by
  obtain ⟨t, ht, hne'⟩ := rationalLinearSubstitution_wordPDeriv_detection A qI qJ hA z s P
    ((eval_dividedWordPDeriv_ne_zero_iff z s _).mp hne)
  exact ⟨t, ht, (eval_dividedWordPDeriv_ne_zero_iff _ t P).mpr hne'⟩

def linearParametrization_wordPDeriv_rename {I J : Type*} (f : I → J) (hf : Function.Injective f)
    (s : List I) (P : MvPolynomial I ℚ) :
    wordPDeriv (s.map f) (MvPolynomial.rename f P) = MvPolynomial.rename f (wordPDeriv s P) := by
  induction s with
  | nil => rfl
  | cons i s ih => simp only [List.map_cons, wordPDeriv_cons, ih, MvPolynomial.pderiv_rename hf]

/-- The checked finite grid theorem, transported to any finite variable type. -/
def exists_fintype_bounded_grid_dividedWordPDeriv_ne_zero
    {J : Type*} [Fintype J] [DecidableEq J]
    (P : MvPolynomial J ℚ) (hP : P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ (z : J → ℕ) (s : List J), (∀ j, z j ≤ B) ∧
      (∀ j, s.count j ≤ P.degreeOf j / B) ∧
      MvPolynomial.eval (fun j => (z j : ℚ)) (dividedWordPDeriv s P) ≠ 0 := by
  classical
  let e := Fintype.equivFin J
  let Q := MvPolynomial.rename e P
  have hQ : Q ≠ 0 := by
    intro hh
    apply hP
    apply MvPolynomial.rename_injective e e.injective
    simpa only [map_zero] using hh
  obtain ⟨z, s, hz, hs, hne⟩ := exists_bounded_grid_dividedWordPDeriv_ne_zero _ Q hQ B hB
  refine ⟨fun j => z (e j), s.map e.symm, fun j => hz (e j), ?_, ?_⟩
  · intro j
    have hc : (s.map e.symm).count j = s.count (e j) := by
      simpa only [Equiv.symm_apply_apply] using List.count_map_of_injective s e.symm e.symm.injective (e j)
    rw [hc]
    simpa only [Q, MvPolynomial.degreeOf_rename_of_injective e.injective] using hs (e j)
  · apply (eval_dividedWordPDeriv_ne_zero_iff _ _ _).mpr
    have hne' := (eval_dividedWordPDeriv_ne_zero_iff _ _ _).mp hne
    have hback : MvPolynomial.rename e.symm Q = P := by simp [Q, MvPolynomial.rename_rename]
    rw [← hback, linearParametrization_wordPDeriv_rename e.symm e.symm.injective]
    simpa only [MvPolynomial.eval_rename, Function.comp_def, Equiv.apply_symm_apply] using hne'

def sum_count_mul_eq_sum_map {J : Type*} [Fintype J] [DecidableEq J]
    (s : List J) (w : J → ℝ) :
    (∑ j, (s.count j : ℝ) * w j) = (s.map w).sum := by
  classical
  induction s with
  | nil => simp
  | cons a s ih =>
    have hc (j : J) : ((a :: s).count j : ℝ) =
        (if j = a then 1 else 0) + (s.count j : ℝ) := by
      by_cases hj : j = a
      · subst j; simp; ring
      · simp [hj, Ne.symm hj]
    simp only [hc, add_mul, Finset.sum_add_distrib, ih, List.map_cons, List.sum_cons]
    simp

def sum_count_div_eq_of_map_eq {I J H : Type*} [Fintype I] [Fintype J]
    [DecidableEq I] [DecidableEq J] (qI : I → H) (qJ : J → H) (r : H → ℕ)
    (t : List I) (s : List J) (ht : t.map qI = s.map qJ) :
    (∑ i, (t.count i : ℝ) / r (qI i)) = ∑ j, (s.count j : ℝ) / r (qJ j) := by
  simp only [div_eq_mul_inv]
  rw [sum_count_mul_eq_sum_map, sum_count_mul_eq_sum_map]
  have hh := congrArg (fun l : List H => (l.map (fun h => ((r h : ℝ)⁻¹))).sum) ht
  simpa only [List.map_map, Function.comp_def] using hh

/-- A nonzero polynomial on a linear parametrization has a nonzero actual
coordinate divided derivative at a bounded parameter grid point.  The extra
weight is bounded by the sum of the parameter degrees divided by the grid
size and the corresponding block degree. -/
def exists_linearParametrization_bounded_grid_derivative
    {I J H : Type*} [Fintype I] [Fintype J] [DecidableEq I] [DecidableEq J]
    (A : I → J → ℚ) (qI : I → H) (qJ : J → H)
    (hA : ∀ i j, A i j ≠ 0 → qI i = qJ j)
    (r : H → ℕ) (P : MvPolynomial I ℚ)
    (hP : rationalLinearSubstitution A P ≠ 0) (B : ℕ) (hB : 0 < B) :
    ∃ (z : J → ℕ) (t : List I), (∀ j, z j ≤ B) ∧
      MvPolynomial.eval (rationalLinearPoint A (fun j => (z j : ℚ)))
        (dividedWordPDeriv t P) ≠ 0 ∧
      (∑ i, (t.count i : ℝ) / r (qI i)) ≤
        ∑ j, ((rationalLinearSubstitution A P).degreeOf j : ℝ) / ((B : ℝ) * r (qJ j)) := by
  obtain ⟨z, s, hz, hs, hne⟩ :=
    exists_fintype_bounded_grid_dividedWordPDeriv_ne_zero _ hP B hB
  obtain ⟨t, ht, hnonzero⟩ :=
    rationalLinearSubstitution_dividedWordPDeriv_detection A qI qJ hA _ s P hne
  refine ⟨z, t, hz, hnonzero, ?_⟩
  rw [sum_count_div_eq_of_map_eq qI qJ r t s ht]
  apply Finset.sum_le_sum
  intro j _
  have hc : (s.count j : ℝ) ≤ (rationalLinearSubstitution A P).degreeOf j / (B : ℝ) :=
    (show (s.count j : ℝ) ≤ ((rationalLinearSubstitution A P).degreeOf j / B : ℕ) by
      exact_mod_cast hs j).trans Nat.cast_div_le
  calc
    _ ≤ (((rationalLinearSubstitution A P).degreeOf j : ℝ) / B) / r (qJ j) :=
      div_le_div_of_nonneg_right hc (Nat.cast_nonneg _)
    _ = _ := div_div _ _ _

def blockDerivativeWeight_eq_sum_count_div {m d : ℕ} (r : Fin m → ℕ)
    (s : List (Fin m × Fin d)) :
    blockDerivativeWeight r s = ∑ i : Fin m × Fin d, (s.count i : ℝ) / r i.1 := by
  simp only [blockDerivativeWeight, derivativeBlockCount, wordDerivativeCounts_apply,
    Nat.cast_sum, Finset.sum_div, Fintype.sum_prod_type, List.count_eq_countP,
    Bool.beq_eq_decide_eq]

def exists_blockLinearParametrization_bounded_grid_derivative {m d e : ℕ}
    (A : (Fin m × Fin d) → (Fin m × Fin e) → ℚ)
    (hA : ∀ i j, A i j ≠ 0 → i.1 = j.1)
    (r : Fin m → ℕ) (hr : ∀ h, 0 < r h)
    (P : MvPolynomial (Fin m × Fin d) ℚ)
    (hP : rationalLinearSubstitution A P ≠ 0)
    (hdeg : ∀ j, (rationalLinearSubstitution A P).degreeOf j ≤ r j.1)
    (B : ℕ) (hB : 0 < B) :
    ∃ (z : (Fin m × Fin e) → ℕ) (t : List (Fin m × Fin d)),
      (∀ j, z j ≤ B) ∧
      MvPolynomial.eval (rationalLinearPoint A (fun j => (z j : ℚ)))
        (dividedWordPDeriv t P) ≠ 0 ∧
      blockDerivativeWeight r t ≤ (m : ℝ) * e / B := by
  obtain ⟨z, t, hz, hne, hweight⟩ :=
    exists_linearParametrization_bounded_grid_derivative A Prod.fst Prod.fst hA r P hP B hB
  refine ⟨z, t, hz, hne, ?_⟩
  rw [blockDerivativeWeight_eq_sum_count_div]
  simp only [List.count_eq_countP, Bool.beq_eq_decide_eq] at hweight ⊢
  apply hweight.trans
  calc
    _ ≤ ∑ _j : Fin m × Fin e, (1 : ℝ) / B := by
      apply Finset.sum_le_sum
      intro j _
      have hrj : (0 : ℝ) < r j.1 := by exact_mod_cast hr j.1
      have hBr : (0 : ℝ) < B := by exact_mod_cast hB
      calc
        _ ≤ (r j.1 : ℝ) / ((B : ℝ) * r j.1) :=
          div_le_div_of_nonneg_right (by exact_mod_cast hdeg j) (le_of_lt (mul_pos hBr hrj))
        _ = _ := by field_simp
    _ = _ := by simp [Fintype.card_prod, Nat.cast_mul, div_eq_mul_inv, mul_assoc]

/-- Composing divided coordinate derivatives changes the concatenated divided
derivative only by a nonzero rational factor, hence preserves evaluated
nonvanishing. -/
def eval_dividedWordPDeriv_comp_ne_zero_iff {I : Type*} [Fintype I] [DecidableEq I]
    (z : I → ℚ) (t s : List I) (P : MvPolynomial I ℚ) :
    MvPolynomial.eval z (dividedWordPDeriv t (dividedWordPDeriv s P)) ≠ 0 ↔
      MvPolynomial.eval z (dividedWordPDeriv (t ++ s) P) ≠ 0 := by
  rw [eval_dividedWordPDeriv_ne_zero_iff, eval_dividedWordPDeriv_ne_zero_iff,
    wordPDeriv_append]
  change MvPolynomial.eval z (wordPDeriv t ((wordDerivativeFactorial s)⁻¹ • wordPDeriv s P)) ≠ 0 ↔ _
  rw [map_smul, MvPolynomial.smul_eq_C_mul, map_mul, MvPolynomial.eval_C]
  exact mul_ne_zero_iff.trans (and_iff_right (inv_ne_zero (wordDerivativeFactorial_ne_zero s)))

def blockDerivativeWeight_append {m d : ℕ} (r : Fin m → ℕ)
    (t s : List (Fin m × Fin d)) :
    blockDerivativeWeight r (t ++ s) = blockDerivativeWeight r t + blockDerivativeWeight r s := by
  simp only [blockDerivativeWeight_eq_sum_count_div, List.count_append,
    Nat.cast_add, add_div, Finset.sum_add_distrib]


end
end Bounty

end SubmissionComponent_LinearParametrizationGridDerivative

/- Component SpanningGridDerivative; SHA256 73ab8f53bac50f59990a474549f20588fd8431f313816c3ee4affd26f2a91b01 -/
section SubmissionComponent_SpanningGridDerivative
/- A bounded integer combination of spanning hyperplane vectors detects an
actual divided coordinate derivative, with its full normalized weight bounded
by the Roth index estimate plus the explicit grid loss. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def weightedHomogeneous_aeval_between {I J : Type*}
    (w : I → ℕ) (v : J → ℕ) (g : I → MvPolynomial J ℚ)
    (hg : ∀ i, MvPolynomial.IsWeightedHomogeneous v (g i) (w i))
    (P : MvPolynomial I ℚ) (n : ℕ) (hP : MvPolynomial.IsWeightedHomogeneous w P n) :
    MvPolynomial.IsWeightedHomogeneous v (MvPolynomial.aeval g P) n := by
  classical
  nth_rw 1 [MvPolynomial.as_sum P]
  rw [map_sum]
  apply MvPolynomial.IsWeightedHomogeneous.sum
  intro a ha
  rw [MvPolynomial.aeval_monomial]
  change MvPolynomial.IsWeightedHomogeneous v
    (MvPolynomial.C (MvPolynomial.coeff a P) * a.prod (fun i b => g i ^ b)) n
  have hprod := MvPolynomial.IsWeightedHomogeneous.prod a.support
    (fun i => g i ^ a i) (fun i => a i • w i) (fun i _ => (hg i).pow (a i))
  have hsum : ∑ i ∈ a.support, a i • w i = n := hP (MvPolynomial.mem_support_iff.mp ha)
  rw [hsum] at hprod
  exact hprod.C_mul _

def productBlockHomogeneous_integer_map {m d : ℕ}
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) ℤ)
    (hP : ProductBlockHomogeneous r P) :
    ProductBlockHomogeneous r (MvPolynomial.map (Int.castRingHom ℚ) P) := by
  intro a ha
  apply hP a
  rw [MvPolynomial.mem_support_iff] at ha ⊢
  intro hz
  exact ha (by simp [MvPolynomial.coeff_map, hz])

def productBlockHomogeneous_dividedWordPDeriv {m d : ℕ}
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) ℚ)
    (hP : ProductBlockHomogeneous r P) (s : List (Fin m × Fin d)) :
    ProductBlockHomogeneous (fun h => r h - derivativeBlockCount s h) (dividedWordPDeriv s P) := by
  intro a ha h
  have hc := MvPolynomial.mem_support_iff.mp ha
  rw [coeff_dividedWordPDeriv] at hc
  have hh := hP (a + wordDerivativeCounts s)
    (MvPolynomial.mem_support_iff.mpr (left_ne_zero_of_mul hc)) h
  simp only [Finsupp.add_apply, Finset.sum_add_distrib] at hh
  change (∑ i, a (h, i)) + derivativeBlockCount s h = r h at hh
  change (∑ i, a (h, i)) = r h - derivativeBlockCount s h
  omega

def blockSpanningSubstitution_homogeneous {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (hP : ProductBlockHomogeneous r P) :
    ProductBlockHomogeneous r (blockSpanningSubstitution y P) := by
  apply (productBlockHomogeneous_iff_weighted r _).mpr
  intro h
  apply weightedHomogeneous_aeval_between (productBlockWeight h) (productBlockWeight h)
  · intro x
    apply MvPolynomial.IsWeightedHomogeneous.sum
    intro j _
    exact (MvPolynomial.isWeightedHomogeneous_X ℚ (productBlockWeight h) (x.1, j)).C_mul _
  · exact (productBlockHomogeneous_iff_weighted r P).mp hP h

def productBlockHomogeneous_degreeOf_le {m d : ℕ}
    (r : Fin m → ℕ) (P : MvPolynomial (Fin m × Fin d) ℚ)
    (hP : ProductBlockHomogeneous r P) (x : Fin m × Fin d) :
    P.degreeOf x ≤ r x.1 := by
  apply MvPolynomial.degreeOf_le_iff.mpr
  intro a ha
  exact (Finset.single_le_sum (fun i _ => Nat.zero_le (a (x.1, i)))
    (Finset.mem_univ x.2)).trans_eq (hP a ha x.1)

def blockSpanningSubstitution_dividedWordPDeriv_degreeOf_le {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (r : Fin m → ℕ)
    (P : MvPolynomial (Fin m × Fin d) ℚ) (hP : ProductBlockHomogeneous r P)
    (s : List (Fin m × Fin d)) (x : Fin m × Fin k) :
    (blockSpanningSubstitution y (dividedWordPDeriv s P)).degreeOf x ≤ r x.1 := by
  exact (productBlockHomogeneous_degreeOf_le _ _
    (blockSpanningSubstitution_homogeneous y _ _ (productBlockHomogeneous_dividedWordPDeriv r P hP s)) x).trans
      (Nat.sub_le _ _)

def blockSpanningMatrix {m d k : ℕ} (y : Fin m → Fin k → Fin d → ℚ)
    (x : Fin m × Fin d) (z : Fin m × Fin k) : ℚ :=
  if x.1 = z.1 then y x.1 z.2 x.2 else 0

def blockSpanningMatrix_block {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (x : Fin m × Fin d) (z : Fin m × Fin k)
    (h : blockSpanningMatrix y x z ≠ 0) : x.1 = z.1 := by
  by_contra hh
  exact h (if_neg hh)

def rationalLinearSubstitution_blockSpanningMatrix {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (P : MvPolynomial (Fin m × Fin d) ℚ) :
    rationalLinearSubstitution (blockSpanningMatrix y) P = blockSpanningSubstitution y P := by
  have hg (x : Fin m × Fin d) : rationalLinearParametrization (blockSpanningMatrix y) x =
      ∑ j, MvPolynomial.C (y x.1 j x.2) * MvPolynomial.X (x.1, j) := by
    classical
    simp only [rationalLinearParametrization, blockSpanningMatrix, Fintype.sum_prod_type]
    simp_rw [apply_ite MvPolynomial.C, map_zero, ite_mul, zero_mul]
    simp
  exact congrArg (fun g : (Fin m × Fin d) → MvPolynomial (Fin m × Fin k) ℚ =>
    MvPolynomial.aeval g P) (funext hg)

def blockSpanningPoint {m d k : ℕ} (y : Fin m → Fin k → Fin d → ℚ)
    (z : Fin m → Fin k → ℕ) (x : Fin m × Fin d) : ℚ :=
  ∑ j, (z x.1 j : ℚ) * y x.1 j x.2

def rationalLinearPoint_blockSpanningMatrix {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℚ) (z : (Fin m × Fin k) → ℕ) :
    rationalLinearPoint (blockSpanningMatrix y) (fun x => (z x : ℚ)) =
      blockSpanningPoint y (fun h j => z (h, j)) := by
  classical
  funext x
  simp [rationalLinearPoint, blockSpanningMatrix, Fintype.sum_prod_type,
    blockSpanningPoint, mul_comm]

def product_hyperplane_bounded_grid_derivative {n d k : ℕ} (hd : 1 ≤ d)
    (b : Fin (n + 1) → Fin (d + 1) → ℚ) (p : Fin (n + 1) → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (r : Fin (n + 1) → ℕ) (hr : ∀ h, 0 < r h)
    (y : Fin (n + 1) → Fin k → Fin (d + 1) → ℚ)
    (hy : ∀ h, Submodule.span ℚ (Set.range (y h)) = rationalHyperplaneKernel (b h))
    (P : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ h, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d)))
    (B : ℕ) (hB : 0 < B) :
    ∃ (z : Fin (n + 1) → Fin k → ℕ) (t : List (Fin (n + 1) × Fin (d + 1))),
      (∀ h j, z h j ≤ B) ∧
      MvPolynomial.eval (blockSpanningPoint y z)
        (dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0 ∧
      blockDerivativeWeight r t ≤ 2 * (n + 1 : ℕ) * η + (n + 1 : ℕ) * k / (B : ℝ) := by
  obtain ⟨s, hs, hne⟩ := product_hyperplane_derivative_spanning hd b p hp r hr y hy
    P hP hhom η hη hηhalf hstep hheight
  let Q := MvPolynomial.map (Int.castRingHom ℚ) P
  have hQ : ProductBlockHomogeneous r Q := productBlockHomogeneous_integer_map r P hhom
  have hparam : rationalLinearSubstitution (blockSpanningMatrix y) (dividedWordPDeriv s Q) ≠ 0 := by
    simpa only [rationalLinearSubstitution_blockSpanningMatrix] using hne
  have hdeg (x : Fin (n + 1) × Fin k) :
      (rationalLinearSubstitution (blockSpanningMatrix y) (dividedWordPDeriv s Q)).degreeOf x ≤ r x.1 := by
    rw [rationalLinearSubstitution_blockSpanningMatrix]
    exact blockSpanningSubstitution_dividedWordPDeriv_degreeOf_le y r Q hQ s x
  obtain ⟨z, t, hz, htne, htweight⟩ := exists_blockLinearParametrization_bounded_grid_derivative
    (blockSpanningMatrix y) (blockSpanningMatrix_block y) r hr (dividedWordPDeriv s Q)
      hparam hdeg B hB
  refine ⟨fun h j => z (h, j), t ++ s, fun h j => hz (h, j), ?_, ?_⟩
  · rw [rationalLinearPoint_blockSpanningMatrix] at htne
    exact (eval_dividedWordPDeriv_comp_ne_zero_iff _ t s Q).mp htne
  · rw [blockDerivativeWeight_append]
    linarith


end
end Bounty

end SubmissionComponent_SpanningGridDerivative

/- Component IntegerHyperplaneGrid; SHA256 430330693af6be165db67f46f58fc3782a6bdd1d398c69535b478fd895db86de -/
section SubmissionComponent_IntegerHyperplaneGrid
/- Integer grid points, actual nonzero integer evaluations, and archimedean
and finite-place bounds for their rational linear forms. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def integerLinearCombination {d k : ℕ} (y : Fin k → Fin d → ℤ)
    (z : Fin k → ℕ) (i : Fin d) : ℤ := ∑ j, (z j : ℤ) * y j i

def integerBlockSpanningPoint {m d k : ℕ} (y : Fin m → Fin k → Fin d → ℤ)
    (z : Fin m → Fin k → ℕ) (x : Fin m × Fin d) : ℤ :=
  integerLinearCombination (y x.1) (z x.1) x.2

def integerBlockSpanningPoint_cast {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℤ) (z : Fin m → Fin k → ℕ) :
    (fun x => (integerBlockSpanningPoint y z x : ℚ)) =
      blockSpanningPoint (fun h j i => (y h j i : ℚ)) z := by
  funext x
  simp [integerBlockSpanningPoint, integerLinearCombination, blockSpanningPoint]

def integer_eval_map_cast {I : Type*} (T : MvPolynomial I ℤ) (x : I → ℤ) :
    MvPolynomial.eval (fun i => (x i : ℚ)) (MvPolynomial.map (Int.castRingHom ℚ) T) =
      (MvPolynomial.eval x T : ℚ) := by
  simpa only [Int.coe_castRingHom, Function.comp_def] using
    (MvPolynomial.map_eval (Int.castRingHom ℚ) x T).symm

def integer_grid_derivative_eval_ne_zero {m d k : ℕ}
    (y : Fin m → Fin k → Fin d → ℤ) (z : Fin m → Fin k → ℕ)
    (P T : MvPolynomial (Fin m × Fin d) ℤ) (s : List (Fin m × Fin d))
    (hT : MvPolynomial.map (Int.castRingHom ℚ) T =
      dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P))
    (hne : MvPolynomial.eval (blockSpanningPoint (fun h j i => (y h j i : ℚ)) z)
      (dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P)) ≠ 0) :
    MvPolynomial.eval (integerBlockSpanningPoint y z) T ≠ 0 := by
  rw [← hT, ← integerBlockSpanningPoint_cast, integer_eval_map_cast] at hne
  exact_mod_cast hne

def integerLinearCombination_linear_form {d k : ℕ} (a : Fin d → ℚ)
    (y : Fin k → Fin d → ℤ) (z : Fin k → ℕ) :
    (∑ i, a i * (integerLinearCombination y z i : ℚ)) =
      ∑ j, (z j : ℚ) * (∑ i, a i * (y j i : ℚ)) := by
  simp only [integerLinearCombination, Int.cast_sum, Int.cast_mul, Int.cast_natCast,
    Finset.mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro j _
  apply Finset.sum_congr rfl
  intro i _
  ring

def rational_nat_combination_arch_bound {k : ℕ} (f : Fin k → ℚ)
    (z : Fin k → ℕ) (B : ℕ) (hz : ∀ j, z j ≤ B)
    (M : ℝ) (hf : ∀ j, |(f j : ℝ)| ≤ M) :
    |((∑ j, (z j : ℚ) * f j : ℚ) : ℝ)| ≤ (k : ℝ) * B * M := by
  simp only [Rat.cast_sum, Rat.cast_mul, Rat.cast_natCast]
  calc
    _ ≤ ∑ j, |(z j : ℝ) * (f j : ℝ)| := Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _j : Fin k, (B : ℝ) * M := by
      apply Finset.sum_le_sum
      intro j _
      rw [abs_mul, abs_of_nonneg (Nat.cast_nonneg _)]
      exact mul_le_mul (by exact_mod_cast hz j) (hf j) (abs_nonneg _) (Nat.cast_nonneg _)
    _ = _ := by simp [mul_assoc]

def padicNorm_real_sum_le {J : Type*} (p : ℕ) [Fact p.Prime]
    (S : Finset J) (f : J → ℚ) (M : ℝ) (hM : 0 ≤ M)
    (hf : ∀ j ∈ S, (padicNorm p (f j) : ℝ) ≤ M) :
    (padicNorm p (∑ j ∈ S, f j) : ℝ) ≤ M := by
  classical
  induction S using Finset.induction_on with
  | empty => simpa using hM
  | @insert a S ha ih =>
    rw [Finset.sum_insert ha]
    have hh : (padicNorm p (f a + ∑ j ∈ S, f j) : ℝ) ≤
        max (padicNorm p (f a) : ℝ) (padicNorm p (∑ j ∈ S, f j) : ℝ) := by
      exact_mod_cast (padicNorm.nonarchimedean (p := p) (q := f a) (r := ∑ j ∈ S, f j))
    exact hh.trans (max_le (hf a (Finset.mem_insert_self _ _))
      (ih (fun j hj => hf j (Finset.mem_insert_of_mem hj))))

/-- Integer coefficients cause no enlargement at any prime, including 2 and 3. -/
def rational_integer_combination_padic_bound {J : Type*} [Fintype J]
    (p : ℕ) [Fact p.Prime] (f : J → ℚ) (z : J → ℤ)
    (M : ℝ) (hM : 0 ≤ M) (hf : ∀ j, (padicNorm p (f j) : ℝ) ≤ M) :
    (padicNorm p (∑ j, (z j : ℚ) * f j) : ℝ) ≤ M := by
  apply padicNorm_real_sum_le p Finset.univ _ M hM
  intro j _
  rw [padicNorm.mul, Rat.cast_mul]
  have hz : (padicNorm p (z j : ℚ) : ℝ) ≤ 1 := by exact_mod_cast padicNorm.of_int (p := p) (z j)
  have hn : (0 : ℝ) ≤ padicNorm p (f j) := by exact_mod_cast padicNorm.nonneg (p := p) (f j)
  exact (mul_le_mul_of_nonneg_right hz hn).trans (by simpa using hf j)

def integerLinearCombination_arch_bound {d k : ℕ} (a : Fin d → ℚ)
    (y : Fin k → Fin d → ℤ) (z : Fin k → ℕ) (B : ℕ) (hz : ∀ j, z j ≤ B)
    (E : ℝ) (hy : ∀ j, |((∑ i, a i * (y j i : ℚ) : ℚ) : ℝ)| ≤ Real.exp E) :
    |((∑ i, a i * (integerLinearCombination y z i : ℚ) : ℚ) : ℝ)| ≤
      (k : ℝ) * B * Real.exp E := by
  rw [integerLinearCombination_linear_form]
  exact rational_nat_combination_arch_bound _ z B hz _ hy

def integerLinearCombination_padic_bound {d k : ℕ} (p : ℕ) [Fact p.Prime]
    (a : Fin d → ℚ) (y : Fin k → Fin d → ℤ) (z : Fin k → ℕ)
    (E : ℝ) (hy : ∀ j, (padicNorm p (∑ i, a i * (y j i : ℚ)) : ℝ) ≤ Real.exp E) :
    (padicNorm p (∑ i, a i * (integerLinearCombination y z i : ℚ)) : ℝ) ≤ Real.exp E := by
  rw [integerLinearCombination_linear_form]
  simpa only [Int.cast_natCast] using rational_integer_combination_padic_bound p
    (fun j => ∑ i, a i * (y j i : ℚ)) (fun j => (z j : ℤ)) _ (Real.exp_pos _).le hy

def integerBlockSpanningPoint_arch_bound {m d k : ℕ}
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ)
    (y : Fin m → Fin k → Fin d → ℤ) (z : Fin m → Fin k → ℕ)
    (B : ℕ) (hz : ∀ h j, z h j ≤ B) (c : Fin d → ℝ) (q : Fin m → ℝ)
    (hy : ∀ h j i, |((∑ a, A h i a * (y h j a : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c i * q h)) :
    ∀ h i, |((∑ a, A h i a * (integerBlockSpanningPoint y z (h, a) : ℚ) : ℚ) : ℝ)| ≤
      (k : ℝ) * B * Real.exp (c i * q h) := by
  intro h i
  exact integerLinearCombination_arch_bound (A h i) (y h) (z h) B (hz h) _ (fun j => hy h j i)

def integerBlockSpanningPoint_padic_bound {m d k : ℕ} (p : ℕ) [Fact p.Prime]
    (A : Fin m → Matrix (Fin d) (Fin d) ℚ)
    (y : Fin m → Fin k → Fin d → ℤ) (z : Fin m → Fin k → ℕ)
    (c : Fin d → ℝ) (q : Fin m → ℝ)
    (hy : ∀ h j i, (padicNorm p (∑ a, A h i a * (y h j a : ℚ)) : ℝ) ≤ Real.exp (c i * q h)) :
    ∀ h i, (padicNorm p (∑ a, A h i a * (integerBlockSpanningPoint y z (h, a) : ℚ)) : ℝ) ≤
      Real.exp (c i * q h) := by
  intro h i
  exact integerLinearCombination_padic_bound p (A h i) (y h) (z h) _ (fun j => hy h j i)

def product_hyperplane_integer_grid_derivative {n d k : ℕ} (hd : 1 ≤ d)
    (b : Fin (n + 1) → Fin (d + 1) → ℚ) (p : Fin (n + 1) → Fin (d + 1))
    (hp : ∀ h, b h (p h) ≠ 0) (r : Fin (n + 1) → ℕ) (hr : ∀ h, 0 < r h)
    (y : Fin (n + 1) → Fin k → Fin (d + 1) → ℤ)
    (hy : ∀ h, Submodule.span ℚ (Set.range (fun j i => (y h j i : ℚ))) = rationalHyperplaneKernel (b h))
    (P : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ) (hP : P ≠ 0)
    (hhom : ProductBlockHomogeneous r P)
    (η : ℝ) (hη : 0 < η) (hηhalf : η ≤ 1 / 2)
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ η ^ (2 ^ n) * r i.castSucc)
    (hheight : ∀ h, Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      η ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d)))
    (B : ℕ) (hB : 0 < B) :
    ∃ (z : Fin (n + 1) → Fin k → ℕ) (s : List (Fin (n + 1) × Fin (d + 1)))
      (T : MvPolynomial (Fin (n + 1) × Fin (d + 1)) ℤ),
      (∀ h j, z h j ≤ B) ∧
      MvPolynomial.map (Int.castRingHom ℚ) T =
        dividedWordPDeriv s (MvPolynomial.map (Int.castRingHom ℚ) P) ∧
      MvPolynomial.eval (integerBlockSpanningPoint y z) T ≠ 0 ∧
      blockDerivativeWeight r s ≤ 2 * (n + 1 : ℕ) * η + (n + 1 : ℕ) * k / (B : ℝ) := by
  obtain ⟨z, s, hz, hne, hweight⟩ := product_hyperplane_bounded_grid_derivative hd b p hp r hr
    (fun h j i => (y h j i : ℚ)) hy P hP hhom η hη hηhalf hstep hheight B hB
  obtain ⟨T, hT⟩ := exists_integer_dividedWordPDeriv s P
  exact ⟨z, s, T, hz, hT, integer_grid_derivative_eval_ne_zero y z P T s hT hne, hweight⟩


end
end Bounty

end SubmissionComponent_IntegerHyperplaneGrid

/- Component FiniteHyperplaneConfiguration; SHA256 5e56536ce4fa0c1765c5563b36db58022982373f82554ceed54e89e68b55238a -/
section SubmissionComponent_FiniteHyperplaneConfiguration
/- A concrete finite hyperplane configuration is excluded by the polynomial argument. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def exists_finite_hyperplane_configuration_constants {n d : ℕ} (hd : 1 ≤ d)
    (A : Fin (n + 1) → Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ)
    (hA : ∀ h, IsUnit (A h).det) :
    ∃ K L : ℝ, 0 ≤ K ∧ 0 ≤ L ∧
      ∀ (r : Fin (n + 1) → ℕ) (q : Fin (n + 1) → ℝ)
        (c : Fin 3 → Fin (d + 1) → ℝ) (D η ρ : ℝ) (B : ℕ),
      (∀ h, 0 < r h) → 0 < q 0 → 0 < D → 0 < ρ → 0 < η → η ≤ 1 / 2 →
      0 < B → (d : ℝ) / B ≤ η / 2 →
      8 * (d + 1 : ℕ) ≤ (n + 1 : ℕ) * η ^ 2 →
      (∀ i : Fin n, (r i.succ : ℝ) ≤ (η / 4) ^ (2 ^ n) * r i.castSucc) →
      (∀ h, |(r h : ℝ) * q h - D| ≤ q h) →
      (∑ v, ∑ i, c v i) ≤ -ρ →
      η ≤ ρ / (8 * (d + 1 : ℕ) * exponentCoefficientMass c) →
      (∑ h, (r h : ℝ)) ≤ 2 * D / q 0 →
      8 * (d + 1 : ℕ) * (L + Real.log ((d : ℝ) * B)) ≤ (n + 1 : ℕ) * ρ * q 0 →
      4 * (d + 1 : ℕ) * exponentCoefficientMass c * (∑ h, q h) ≤ (n + 1 : ℕ) * ρ * D →
      ∀ (b : Fin (n + 1) → Fin (d + 1) → ℚ)
        (p : Fin (n + 1) → Fin (d + 1)),
      (∀ h, b h (p h) ≠ 0) →
      (∀ h, K * (∑ j, (r j : ℝ)) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
        (η / 4) ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d))) →
      ∀ y : Fin (n + 1) → Fin d → Fin (d + 1) → ℤ,
      (∀ h, Submodule.span ℚ (Set.range (fun j i => (y h j i : ℚ))) = rationalHyperplaneKernel (b h)) →
      (∀ h j i, |((∑ a, A h i a * (y h j a : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c 0 i * q h)) →
      (∀ h j i, (padicNorm 2 (y h j i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q h)) →
      (∀ h j i, (padicNorm 3 (y h j i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q h)) → False := by
  obtain ⟨K, L, hK, hL, haux⟩ := exists_two_basis_balanced_auxiliary
    (by omega : 0 < n + 1) (by omega : 0 < d + 1) A hA
  refine ⟨K, L, hK, hL, ?_⟩
  intro r q c D η ρ B hr hq0 hD hρ hη hηhalf hB hgrid hlarge hstep hscale
    hc hηmass hR hqLarge hDLarge b p hp hheight y hy hyInf hy2 hy3
  obtain ⟨P, hP, hhom, hheightP, hderiv⟩ := haux r hr η hη.le hlarge
  have hRothHeight (h : Fin (n + 1)) :
      Real.log (polynomialCoeffL1 P) + 4 * (n + 1 : ℕ) * (r 0 : ℝ) ≤
      (η / 4) ^ (2 ^ n) * ((r h : ℝ) * (Height.logHeight (b h) / d)) := by
    linarith [hheight h]
  obtain ⟨z, t, T₀, hz, hT₀map, hT₀eval, ht⟩ := product_hyperplane_integer_grid_derivative
    hd b p hp r hr y hy P hP hhom (η / 4) (by positivity) (by linarith)
      hstep hRothHeight B hB
  have hsmall : blockDerivativeWeight r t ≤ (n + 1 : ℕ) * η := by
    have hh := mul_le_mul_of_nonneg_left hgrid (Nat.cast_nonneg (α := ℝ) (n + 1))
    rw [← mul_div_assoc] at hh
    linarith
  have hT₀ : T₀ ≠ 0 := by intro hz; apply hT₀eval; simp [hz]
  have hdiv : dividedWordPDeriv t (MvPolynomial.map (Int.castRingHom ℚ) P) ≠ 0 := by
    rw [← hT₀map]
    exact integerMap_ne_zero hT₀
  obtain ⟨T, hT, hTmap, hbounds⟩ := hderiv t hsmall hdiv
  have heq : T = T₀ := MvPolynomial.map_injective (Int.castRingHom ℚ) Int.cast_injective
    (hTmap.trans hT₀map.symm)
  subst T₀
  let x := integerBlockSpanningPoint y z
  have hgridConst : 1 ≤ (d : ℝ) * B := by
    have hdR : (1 : ℝ) ≤ d := by exact_mod_cast hd
    have hBR : (1 : ℝ) ≤ B := by exact_mod_cast (show 1 ≤ B by omega)
    nlinarith
  have harch : ∀ h i, ‖blockMatrixValues A (fun hi => (x hi : ℚ)) (h, i)‖ ≤
      ((d : ℝ) * B) * Real.exp (c 0 i * q h) := by
    intro h i
    have hh := integerBlockSpanningPoint_arch_bound A y z B hz (c 0) q hyInf h i
    simpa only [x, blockMatrixValues, Matrix.mulVec, dotProduct,
      ← Rat.norm_cast_real, Real.norm_eq_abs] using hh
  have hfinite (p' : ℕ) [Fact p'.Prime] (v : Fin 3)
      (hyv : ∀ h j i, (padicNorm p' (y h j i : ℚ) : ℝ) ≤ Real.exp (c v i * q h)) :
      ∀ h i, (padicNorm p' (x (h, i) : ℚ) : ℝ) ≤ Real.exp (c v i * q h) := by
    have hh := integerBlockSpanningPoint_padic_bound p'
      (fun _ => (1 : Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ)) y z (c v) q
      (by simpa [Matrix.one_apply] using hyv)
    simpa [x, Matrix.one_apply] using hh
  exact inverse_block_three_place_polynomial_contradiction A hA T x hT₀eval r q c D η ρ L
    ((d : ℝ) * B) (q 0) (by omega) (by omega) hD hρ hL hgridConst hq0 hr
    hbounds.degreeInf hbounds.degreeInt hbounds.balanceInf hbounds.balanceInt hscale
    hbounds.heightInf harch (hfinite 2 1 hy2) (hfinite 3 2 hy3)
    hc hηmass hR hqLarge hDLarge


end
end Bounty

end SubmissionComponent_FiniteHyperplaneConfiguration

/- Component BalancedDegreeSelection; SHA256 c1ec687a7c050225cea4ca0f680c7546536ce2b49212da54986db0f5ea832647 -/
section SubmissionComponent_BalancedDegreeSelection
/- Explicit floor choices for the block degrees in the polynomial contradiction. -/

namespace Bounty
noncomputable section

def balancedBlockDegree (D q : ℝ) : ℕ := ⌊D / q⌋₊

def balancedBlockDegree_bounds {D q : ℝ} (hq : 0 < q) (hD : 2 * q ≤ D) :
    0 < balancedBlockDegree D q ∧
      (balancedBlockDegree D q : ℝ) * q ≤ D ∧
      D ≤ 2 * (balancedBlockDegree D q : ℝ) * q ∧
      |(balancedBlockDegree D q : ℝ) * q - D| ≤ q := by
  have hDpos : 0 < D := by linarith
  have ht : 2 ≤ D / q := (le_div_iff₀ hq).mpr (by simpa using hD)
  have hlo := Nat.floor_le (div_nonneg hDpos.le hq.le)
  have hhi := Nat.lt_floor_add_one (D / q)
  have hpos : 0 < balancedBlockDegree D q := by
    change 0 < ⌊D / q⌋₊
    by_contra hh
    have hz : ⌊D / q⌋₊ = 0 := by omega
    rw [hz] at hhi
    norm_num at hhi
    linarith
  change (balancedBlockDegree D q : ℝ) ≤ D / q at hlo
  change D / q < (balancedBlockDegree D q : ℝ) + 1 at hhi
  have hlomul := (le_div_iff₀ hq).mp hlo
  have hhimul := (div_lt_iff₀ hq).mp hhi
  refine ⟨hpos, hlomul, ?_, ?_⟩
  · nlinarith
  · rw [abs_le]
    constructor <;> nlinarith

def balancedBlockDegree_ratio {D q q' θ : ℝ}
    (hq : 0 < q) (hq' : 0 < q') (hD : 2 * q ≤ D) (hD' : 2 * q' ≤ D)
    (hθ : 0 ≤ θ) (hsep : 2 * q ≤ θ * q') :
    (balancedBlockDegree D q' : ℝ) ≤ θ * balancedBlockDegree D q := by
  have hb := balancedBlockDegree_bounds hq hD
  have hb' := balancedBlockDegree_bounds hq' hD'
  have hs := mul_le_mul_of_nonneg_left hsep (Nat.cast_nonneg (α := ℝ) (balancedBlockDegree D q))
  apply (mul_le_mul_iff_left₀ hq').mp
  nlinarith

def balancedBlockDegree_height_budget {D q q0 a θ H C : ℝ}
    (hq : 0 < q) (hq0 : 0 < q0) (hD : 2 * q ≤ D) (hD0 : 2 * q0 ≤ D)
    (ha : 0 ≤ a) (hθ : 0 ≤ θ) (hH : a * q ≤ H)
    (hbudget : 2 * C ≤ θ * a * q0) :
    C * (balancedBlockDegree D q0 : ℝ) ≤ θ * ((balancedBlockDegree D q : ℝ) * H) := by
  have hb := balancedBlockDegree_bounds hq hD
  have hb0 := balancedBlockDegree_bounds hq0 hD0
  have hr : (0 : ℝ) ≤ balancedBlockDegree D q := Nat.cast_nonneg _
  have hr0 : (0 : ℝ) ≤ balancedBlockDegree D q0 := Nat.cast_nonneg _
  have h1 := mul_le_mul_of_nonneg_right hbudget hr0
  have h2 := mul_le_mul_of_nonneg_left hb0.2.1 (mul_nonneg hθ ha)
  have h3 := mul_le_mul_of_nonneg_left hb.2.2.1 (mul_nonneg hθ ha)
  have h4 := mul_le_mul_of_nonneg_left hH (mul_nonneg hθ hr)
  nlinarith

end
end Bounty

end SubmissionComponent_BalancedDegreeSelection

/- Component AuxiliaryParameterSelection; SHA256 ebd95c4b38ec2be80494c73c506acd03a8f229eecf6fd958bcdbdf7d20a86859 -/
section SubmissionComponent_AuxiliaryParameterSelection
/- Explicit finite parameter selection for the auxiliary polynomial argument.
The common scale is chosen by a finite sum, not an asymptotic premise. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def exists_separated_logs_in_unbounded_set (S : Set ℝ) (hS : ¬ BddAbove S)
    (θ M : ℝ) (hθ : 0 < θ) (n : ℕ) :
    ∃ q : Fin (n + 1) → ℝ, (∀ i, q i ∈ S) ∧ (∀ i, 0 < q i) ∧ M ≤ q 0 ∧
      ∀ i : Fin n, 2 * q i.castSucc ≤ θ * q i.succ := by
  classical
  choose pick hpick hgt using (not_bddAbove_iff.mp hS)
  let u : ℕ → ℝ := Nat.rec (pick (max M 1)) (fun _ v => pick (max 1 (2 * v / θ)))
  have hu0 : u 0 = pick (max M 1) := rfl
  have hus (j : ℕ) : u (j + 1) = pick (max 1 (2 * u j / θ)) := rfl
  have hmem (j : ℕ) : u j ∈ S := by
    cases j with
    | zero => rw [hu0]; exact hpick _
    | succ j => rw [hus]; exact hpick _
  have hpos (j : ℕ) : 0 < u j := by
    cases j with
    | zero => rw [hu0]; linarith [le_max_right M (1 : ℝ), hgt (max M 1)]
    | succ j => rw [hus]; linarith [le_max_left (1 : ℝ) (2 * u j / θ), hgt (max 1 (2 * u j / θ))]
  have hstep (j : ℕ) : 2 * u j ≤ θ * u (j + 1) := by
    have hh : 2 * u j / θ ≤ u (j + 1) := by
      rw [hus]
      exact (le_max_right _ _).trans (le_of_lt (hgt _))
    have hh' := (div_le_iff₀ hθ).mp hh
    nlinarith
  refine ⟨fun i => u i.val, fun i => hmem i.val, fun i => hpos i.val, ?_, ?_⟩
  · change M ≤ u 0
    rw [hu0]
    exact (le_max_left _ _).trans (le_of_lt (hgt _))
  · intro i
    exact hstep i.val

def half_decay_degree_sum {n : ℕ} (r : Fin (n + 1) → ℕ) (θ : ℝ)
    (hθ : θ ≤ (1 / 2 : ℝ))
    (hstep : ∀ i : Fin n, (r i.succ : ℝ) ≤ θ * r i.castSucc) :
    (∑ i, (r i : ℝ)) ≤ 2 * r 0 := by
  have ht : (∑ i : Fin n, (r i.succ : ℝ)) ≤
      (1 / 2 : ℝ) * (∑ i : Fin n, (r i.castSucc : ℝ)) := by
    rw [Finset.mul_sum]
    apply Finset.sum_le_sum
    intro i _
    exact (hstep i).trans (mul_le_mul_of_nonneg_right hθ (Nat.cast_nonneg _))
  have hhead : (∑ i : Fin n, (r i.castSucc : ℝ)) ≤ ∑ i : Fin (n + 1), (r i : ℝ) := by
    rw [Fin.sum_univ_castSucc]
    exact le_add_of_nonneg_right (Nat.cast_nonneg _)
  have hs := Fin.sum_univ_succ (fun i : Fin (n + 1) => (r i : ℝ))
  nlinarith

def auxiliaryFirstLogThreshold (m d : ℕ) (a θ K C₂ ρ : ℝ) : ℝ :=
  max 1 (max (2 * (2 * K + 4 * m) / (θ * a)) (8 * d * C₂ / ((m : ℝ) * ρ)))

def auxiliaryFirstLogThreshold_budgets {m d : ℕ}
    (a θ K C₂ ρ q₀ : ℝ) (hm : 0 < m) (ha : 0 < a) (hθ : 0 < θ) (hρ : 0 < ρ)
    (hfirst : auxiliaryFirstLogThreshold m d a θ K C₂ ρ ≤ q₀) :
    0 < q₀ ∧ 2 * (2 * K + 4 * m) ≤ θ * a * q₀ ∧
      8 * (d : ℝ) * C₂ ≤ (m : ℝ) * ρ * q₀ := by
  have h1 : (1 : ℝ) ≤ q₀ := (le_max_left _ _).trans hfirst
  have htwo : 2 * (2 * K + 4 * m) / (θ * a) ≤ q₀ :=
    (le_max_left _ _).trans ((le_max_right _ _).trans hfirst)
  have hthree : 8 * (d : ℝ) * C₂ / ((m : ℝ) * ρ) ≤ q₀ :=
    (le_max_right _ _).trans ((le_max_right _ _).trans hfirst)
  refine ⟨by linarith, ?_, ?_⟩
  · have hh := (div_le_iff₀ (mul_pos hθ ha)).mp htwo
    nlinarith
  · have hh := (div_le_iff₀ (show (0 : ℝ) < m * ρ by positivity)).mp hthree
    nlinarith

def auxiliaryCommonScale {m : ℕ} (q : Fin m → ℝ) (d : ℕ) (Cc ρ : ℝ) : ℝ :=
  1 + (∑ i, |2 * q i|) + |4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ)|

def auxiliaryCommonScale_budgets {m : ℕ} (q : Fin m → ℝ)
    (d : ℕ) (Cc ρ D : ℝ) (hm : 0 < m) (hρ : 0 < ρ)
    (hD : auxiliaryCommonScale q d Cc ρ ≤ D) :
    0 < D ∧ (∀ i, 2 * q i ≤ D) ∧
      4 * (d : ℝ) * Cc * (∑ i, q i) ≤ (m : ℝ) * ρ * D := by
  have hsum : 0 ≤ ∑ i, |2 * q i| := Finset.sum_nonneg fun i _ => abs_nonneg _
  have hraw : 1 + (∑ i, |2 * q i|) +
      |4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ)| ≤ D := hD
  refine ⟨by linarith [abs_nonneg (4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ))], ?_, ?_⟩
  · intro i
    have hh := Finset.single_le_sum (s := Finset.univ) (f := fun i => |2 * q i|)
      (fun j _ => abs_nonneg _) (Finset.mem_univ i)
    linarith [le_abs_self (2 * q i), abs_nonneg (4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ))]
  · have hh : 4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ) ≤ D := by
      linarith [le_abs_self (4 * (d : ℝ) * Cc * (∑ i, q i) / ((m : ℝ) * ρ))]
    have hh' := (div_le_iff₀ (show (0 : ℝ) < m * ρ by positivity)).mp hh
    nlinarith

def selectedAuxiliaryDegrees {n : ℕ} (D : ℝ) (q : Fin (n + 1) → ℝ) : Fin (n + 1) → ℕ :=
  fun i => balancedBlockDegree D (q i)

/-- Every field concerns the actual floor degrees at this common scale. -/
structure AuxiliaryDegreeBudgets {n : ℕ} (q H : Fin (n + 1) → ℝ)
    (d : ℕ) (θ K C₂ Cc ρ D : ℝ) : Prop where
  scale_pos : 0 < D
  degree_pos : ∀ i, 0 < selectedAuxiliaryDegrees D q i
  scale_error : ∀ i, |(selectedAuxiliaryDegrees D q i : ℝ) * q i - D| ≤ q i
  degree_separation : ∀ i : Fin n,
    (selectedAuxiliaryDegrees D q i.succ : ℝ) ≤ θ * selectedAuxiliaryDegrees D q i.castSucc
  total_degree : (∑ i, (selectedAuxiliaryDegrees D q i : ℝ)) ≤ 2 * D / q 0
  roth_budget : ∀ i,
    K * (∑ j, (selectedAuxiliaryDegrees D q j : ℝ)) +
      4 * (↑(n + 1) : ℝ) * selectedAuxiliaryDegrees D q 0 ≤
        θ * ((selectedAuxiliaryDegrees D q i : ℝ) * H i)
  first_scale_budget : 8 * (d : ℝ) * C₂ ≤ (↑(n + 1) : ℝ) * ρ * q 0
  error_budget : 4 * (d : ℝ) * Cc * (∑ i, q i) ≤ (↑(n + 1) : ℝ) * ρ * D

def auxiliary_selected_degree_budgets {n : ℕ} (q H : Fin (n + 1) → ℝ)
    (d : ℕ) (a θ K C₂ Cc ρ D : ℝ)
    (hq : ∀ i, 0 < q i) (ha : 0 < a) (hθ : 0 < θ) (hθhalf : θ ≤ 1 / 2)
    (hK : 0 ≤ K) (hρ : 0 < ρ)
    (hsep : ∀ i : Fin n, 2 * q i.castSucc ≤ θ * q i.succ)
    (hH : ∀ i, a * q i ≤ H i)
    (hfirst : auxiliaryFirstLogThreshold (n + 1) d a θ K C₂ ρ ≤ q 0)
    (hD : auxiliaryCommonScale q d Cc ρ ≤ D) :
    AuxiliaryDegreeBudgets q H d θ K C₂ Cc ρ D := by
  obtain ⟨hDpos, hDscale, herror⟩ := auxiliaryCommonScale_budgets q d Cc ρ D (by omega) hρ hD
  obtain ⟨_, hfirstRoth, hfirstError⟩ :=
    auxiliaryFirstLogThreshold_budgets a θ K C₂ ρ (q 0) (by omega) ha hθ hρ hfirst
  have hb (i : Fin (n + 1)) := balancedBlockDegree_bounds (hq i) (hDscale i)
  have hstep : ∀ i : Fin n,
      (selectedAuxiliaryDegrees D q i.succ : ℝ) ≤ θ * selectedAuxiliaryDegrees D q i.castSucc := by
    intro i
    exact balancedBlockDegree_ratio (hq i.castSucc) (hq i.succ)
      (hDscale i.castSucc) (hDscale i.succ) hθ.le (hsep i)
  have hsum := half_decay_degree_sum (selectedAuxiliaryDegrees D q) θ hθhalf hstep
  have hhead : (selectedAuxiliaryDegrees D q 0 : ℝ) ≤ D / q 0 :=
    (le_div_iff₀ (hq 0)).mpr (hb 0).2.1
  refine ⟨hDpos, fun i => (hb i).1, fun i => (hb i).2.2.2, hstep, ?_, ?_, hfirstError, herror⟩
  · exact hsum.trans (by simpa only [mul_div_assoc] using
      mul_le_mul_of_nonneg_left hhead (show (0 : ℝ) ≤ 2 by norm_num))
  · intro i
    calc
      _ ≤ K * (2 * (selectedAuxiliaryDegrees D q 0 : ℝ)) +
          4 * (↑(n + 1) : ℝ) * selectedAuxiliaryDegrees D q 0 :=
        add_le_add (mul_le_mul_of_nonneg_left hsum hK) le_rfl
      _ = (2 * K + 4 * (↑(n + 1) : ℝ)) * selectedAuxiliaryDegrees D q 0 := by ring
      _ ≤ _ := balancedBlockDegree_height_budget (hq i) (hq 0) (hDscale i) (hDscale 0)
        ha.le hθ.le (hH i) hfirstRoth

def exists_complete_auxiliary_parameters (S : Set ℝ) (hS : ¬ BddAbove S)
    (H : ℝ → ℝ) (n d : ℕ) (a θ K C₂ Cc ρ M : ℝ)
    (ha : 0 < a) (hθ : 0 < θ) (hθhalf : θ ≤ 1 / 2) (hK : 0 ≤ K) (hρ : 0 < ρ)
    (hH : ∀ t ∈ S, a * t ≤ H t) :
    ∃ q : Fin (n + 1) → ℝ, (∀ i, q i ∈ S) ∧ (∀ i, 0 < q i) ∧ M ≤ q 0 ∧
      (∀ i : Fin n, 2 * q i.castSucc ≤ θ * q i.succ) ∧
      0 < auxiliaryCommonScale q d Cc ρ ∧
      ∀ D ≥ auxiliaryCommonScale q d Cc ρ,
        AuxiliaryDegreeBudgets q (fun i => H (q i)) d θ K C₂ Cc ρ D := by
  obtain ⟨q, hmem, hq, hfirst, hsep⟩ := exists_separated_logs_in_unbounded_set S hS θ
    (max M (auxiliaryFirstLogThreshold (n + 1) d a θ K C₂ ρ)) hθ n
  have hbase : auxiliaryFirstLogThreshold (n + 1) d a θ K C₂ ρ ≤ q 0 :=
    (le_max_right _ _).trans hfirst
  refine ⟨q, hmem, hq, (le_max_left _ _).trans hfirst, hsep, ?_, ?_⟩
  · exact (auxiliaryCommonScale_budgets q d Cc ρ _ (by omega) hρ le_rfl).1
  · intro D hD
    exact auxiliary_selected_degree_budgets q (fun i => H (q i)) d a θ K C₂ Cc ρ D
      hq ha hθ hθhalf hK hρ hsep (fun i => hH (q i) (hmem i)) hbase hD


end
end Bounty

end SubmissionComponent_AuxiliaryParameterSelection

/- Component HighHyperplaneBoundedness; SHA256 8b87455601f31b371afde983c083a2bd4660c2d304724004328a8adf9e8a19b4 -/
section SubmissionComponent_HighHyperplaneBoundedness
/- Families of large-height hyperplanes satisfying a fixed negative profile are bounded. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def exists_hyperplane_polynomial_parameters {d : ℕ} (hd : 1 ≤ d)
    (c : Fin 3 → Fin (d + 1) → ℝ) (ρ : ℝ) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ) :
    ∃ (η : ℝ) (n B : ℕ), 0 < η ∧ η ≤ 1 / 2 ∧
      η ≤ ρ / (8 * (d + 1 : ℕ) * exponentCoefficientMass c) ∧
      0 < B ∧ (d : ℝ) / B ≤ η / 2 ∧
      8 * (d + 1 : ℕ) ≤ (n + 1 : ℕ) * η ^ 2 := by
  have hmass : 0 < exponentCoefficientMass c :=
    hρ.trans_le (deficit_le_exponentCoefficientMass c ρ hc)
  let η : ℝ := min (1 / 2) (ρ / (8 * (d + 1 : ℕ) * exponentCoefficientMass c))
  have hη : 0 < η := lt_min (by norm_num) (by positivity)
  obtain ⟨n, hn⟩ := exists_nat_ge (8 * (d + 1 : ℕ) / η ^ 2)
  obtain ⟨B, hB⟩ := exists_nat_ge (1 + 2 * (d : ℝ) / η)
  have hBreal : (0 : ℝ) < B := by
    have hh : 0 ≤ 2 * (d : ℝ) / η := by positivity
    linarith
  refine ⟨η, n, B, hη, min_le_left _ _, min_le_right _ _,
    by exact_mod_cast hBreal, ?_, ?_⟩
  · apply (div_le_iff₀ hBreal).mpr
    have hh : 2 * (d : ℝ) / η ≤ B := by linarith
    have hmul := (div_le_iff₀ hη).mp hh
    nlinarith
  · have hmul := (div_le_iff₀ (sq_pos_of_pos hη)).mp hn
    simp only [Nat.cast_add, Nat.cast_one] at hmul ⊢
    nlinarith [sq_nonneg η]

def bounded_high_hyperplane_family {d : ℕ} (hd : 1 ≤ d)
    (A : Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → Fin (d + 1) → ℝ) (ρ a : ℝ) (hρ : 0 < ρ) (ha : 0 < a)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (S : Set ℝ) (b : ℝ → Fin (d + 1) → ℚ) (p : ℝ → Fin (d + 1))
    (y : ℝ → Fin d → Fin (d + 1) → ℤ)
    (hp : ∀ q ∈ S, b q (p q) ≠ 0)
    (hheight : ∀ q ∈ S, a * q ≤ Height.logHeight (b q) / d)
    (hspan : ∀ q ∈ S, Submodule.span ℚ (Set.range (fun j i => (y q j i : ℚ))) =
      rationalHyperplaneKernel (b q))
    (hInf : ∀ q ∈ S, ∀ j i,
      |((∑ k, A i k * (y q j k : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ j i, (padicNorm 2 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q))
    (hThree : ∀ q ∈ S, ∀ j i, (padicNorm 3 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) :
    BddAbove S := by
  classical
  by_contra hS
  obtain ⟨η, n, B, hη, hηhalf, hηmass, hB, hgrid, hlarge⟩ :=
    exists_hyperplane_polynomial_parameters hd c ρ hρ hc
  obtain ⟨K, L, hK, hL, hconfig⟩ := exists_finite_hyperplane_configuration_constants
    (n := n) hd (fun _ => A) (fun _ => hA)
  let θ : ℝ := (η / 4) ^ (2 ^ n)
  have hθ : 0 < θ := by positivity
  have hθhalf : θ ≤ 1 / 2 := by
    have hh : (η / 4) ^ (2 ^ n) ≤ η / 4 := by
      simpa only [pow_one] using pow_le_pow_of_le_one (by positivity : 0 ≤ η / 4)
        (by linarith : η / 4 ≤ 1)
        (show 1 ≤ 2 ^ n by have hh : 0 < (2 : ℕ) ^ n := pow_pos (by decide) n; omega)
    dsimp [θ]
    linarith
  obtain ⟨q, hqmem, hqpos, _, hqsep, hDpos, hbudgets⟩ :=
    exists_complete_auxiliary_parameters S hS (fun q => Height.logHeight (b q) / d)
      n (d + 1) a θ K (L + Real.log ((d : ℝ) * B)) (exponentCoefficientMass c) ρ 0
      ha hθ hθhalf hK hρ hheight
  let D := auxiliaryCommonScale q (d + 1) (exponentCoefficientMass c) ρ
  have hb := hbudgets D le_rfl
  let r := selectedAuxiliaryDegrees D q
  exact hconfig r q c D η ρ B hb.degree_pos (hqpos 0) hb.scale_pos hρ hη hηhalf hB hgrid hlarge
    hb.degree_separation hb.scale_error hc hηmass hb.total_degree hb.first_scale_budget hb.error_budget
    (fun h => b (q h)) (fun h => p (q h)) (fun h => hp (q h) (hqmem h))
    hb.roth_budget (fun h => y (q h)) (fun h => hspan (q h) (hqmem h))
    (fun h => hInf (q h) (hqmem h)) (fun h => hTwo (q h) (hqmem h))
    (fun h => hThree (q h) (hqmem h))


end
end Bounty

end SubmissionComponent_HighHyperplaneBoundedness

/- Component BoundedRationalBoxes; SHA256 0106503e3eb71b650e68873dc0bb21dc7ec2e0d0436464f23e4cbc0cc7f20b40 -/
section SubmissionComponent_BoundedRationalBoxes
/- Finiteness of actual integer points and rational spans in bounded rational boxes. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def finite_rational_box_integer_points {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (B : Fin d → ℝ) (hB : ∀ i, 0 < B i) :
    Set.Finite {z : Fin d → ℤ | ∀ i,
      |((∑ j, A i j * (z j : ℚ) : ℚ) : ℝ)| ≤ B i} := by
  let N : Fin d → ℕ := fun _ => 1
  have hN : ∀ i, 0 < N i := by intro i; exact Nat.zero_lt_one
  let L := rationalBoxLattice A B N hA hB hN
  letI : DiscreteTopology L := by dsimp [L]; infer_instance
  let f : (Fin d → ℤ) → BoxEuclidean d := fun z =>
    rationalBoxTransform A B hA hB (diagonalIntegerPoint N z)
  have hf : Function.Injective f := by
    intro z w h
    have hh := (rationalBoxTransform A B hA hB).injective h
    funext i
    have hi := congrArg (fun x : BoxEuclidean d => x i) hh
    simpa [diagonalIntegerPoint, N] using hi
  have hclosed : IsClosed (L : Set (BoxEuclidean d)) :=
    AddSubgroup.isClosed_of_discrete (H := L.toAddSubgroup)
  have hfin : Set.Finite (Metric.closedBall (0 : BoxEuclidean d) (Real.sqrt d) ∩
      (L : Set (BoxEuclidean d))) :=
    Metric.finite_isBounded_inter_isClosed DiscreteTopology.isDiscrete
      Metric.isBounded_closedBall hclosed
  apply (Set.Finite.preimage hf.injOn hfin).subset
  intro z hz
  refine ⟨?_, ?_⟩
  · rw [Metric.mem_closedBall, dist_zero_right]
    apply rationalBoxContains_norm_le_sqrt A B hA hB
    intro i
    simpa [Matrix.mulVec, dotProduct, diagonalIntegerPoint, N,
      Matrix.map_apply, Rat.cast_sum, Rat.cast_mul] using hz i
  · exact (rationalBoxLattice_mem_iff A B N hA hB hN (f z)).mpr ⟨z, rfl⟩

def finite_bounded_exponential_integer_points {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : Fin d → ℝ) (M : ℝ) :
    Set.Finite {z : Fin d → ℤ | ∃ q : ℝ, 0 ≤ q ∧ q ≤ M ∧
      ∀ i, |((∑ j, A i j * (z j : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c i * q)} := by
  let B : Fin d → ℝ := fun i => Real.exp (|c i| * max M 0)
  apply (finite_rational_box_integer_points A hA B (fun i => Real.exp_pos _)).subset
  rintro z ⟨q, hq, hqM, hz⟩ i
  apply (hz i).trans
  apply Real.exp_le_exp.mpr
  exact (mul_le_mul_of_nonneg_right (le_abs_self _) hq).trans
    (mul_le_mul_of_nonneg_left (hqM.trans (le_max_left _ _)) (abs_nonneg _))

def finite_spans_of_finite_integer_points {d : ℕ} (s : Set (Fin d → ℤ))
    (hs : s.Finite) :
    Set.Finite {V : Submodule ℚ (Fin d → ℚ) | ∃ t : Set (Fin d → ℤ),
      t ⊆ s ∧ V = Submodule.span ℚ ((fun z i => (z i : ℚ)) '' t)} := by
  apply (hs.powerset.image (fun t => Submodule.span ℚ ((fun z i => (z i : ℚ)) '' t))).subset
  rintro V ⟨t, ht, rfl⟩
  exact ⟨t, ht, rfl⟩

def finite_bounded_exponential_spans {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : Fin d → ℝ) (M : ℝ) :
    Set.Finite {V : Submodule ℚ (Fin d → ℚ) | ∃ (q : ℝ) (t : Set (Fin d → ℤ)),
      0 ≤ q ∧ q ≤ M ∧
      (∀ z ∈ t, ∀ i, |((∑ j, A i j * (z j : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c i * q)) ∧
      V = Submodule.span ℚ ((fun z i => (z i : ℚ)) '' t)} := by
  apply (finite_spans_of_finite_integer_points _
    (finite_bounded_exponential_integer_points A hA c M)).subset
  rintro V ⟨q, t, hq, hqM, ht, rfl⟩
  refine ⟨t, ?_, rfl⟩
  intro z hz
  exact ⟨q, hq, hqM, ht z hz⟩

end
end Bounty

end SubmissionComponent_BoundedRationalBoxes

/- Component FiniteHyperplaneFamilies; SHA256 b09df8a57dd0eb66dacb0cf8c379ee875717aed7d4bc9f0538a0271731e1dee3 -/
section SubmissionComponent_FiniteHyperplaneFamilies
/- Affine height growth, together with actual box bounds, gives finite kernel families. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def bounded_hyperplane_family_of_affine_height {d : ℕ} (hd : 1 ≤ d)
    (A : Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → Fin (d + 1) → ℝ) (ρ a C : ℝ) (hρ : 0 < ρ) (ha : 0 < a)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (S : Set ℝ) (b : ℝ → Fin (d + 1) → ℚ) (p : ℝ → Fin (d + 1))
    (y : ℝ → Fin d → Fin (d + 1) → ℤ)
    (hp : ∀ q ∈ S, b q (p q) ≠ 0)
    (hheight : ∀ q ∈ S, a * q - C ≤ Height.logHeight (b q) / d)
    (hspan : ∀ q ∈ S, Submodule.span ℚ (Set.range (fun j i => (y q j i : ℚ))) =
      rationalHyperplaneKernel (b q))
    (hInf : ∀ q ∈ S, ∀ j i,
      |((∑ k, A i k * (y q j k : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ j i, (padicNorm 2 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q))
    (hThree : ∀ q ∈ S, ∀ j i, (padicNorm 3 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) :
    BddAbove S := by
  let T : Set ℝ := {q | q ∈ S ∧ 2 * C / a ≤ q}
  have hT : BddAbove T := bounded_high_hyperplane_family hd A hA c ρ (a / 2) hρ
    (by positivity) hc T b p y
    (fun q hq => hp q hq.1)
    (fun q hq => by
      have hmul := (div_le_iff₀ ha).mp hq.2
      have hh := hheight q hq.1
      linarith)
    (fun q hq => hspan q hq.1)
    (fun q hq => hInf q hq.1)
    (fun q hq => hTwo q hq.1)
    (fun q hq => hThree q hq.1)
  obtain ⟨M, hM⟩ := hT
  refine ⟨max M (2 * C / a), ?_⟩
  intro q hq
  by_cases hlarge : 2 * C / a ≤ q
  · exact (hM ⟨hq, hlarge⟩).trans (le_max_left _ _)
  · exact (le_of_not_ge hlarge).trans (le_max_right _ _)

def finite_hyperplane_family_of_height_dichotomy {d : ℕ} (hd : 1 ≤ d)
    (A : Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → Fin (d + 1) → ℝ) (ρ a C : ℝ) (hρ : 0 < ρ) (ha : 0 < a)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (b : ℝ → Fin (d + 1) → ℚ) (p : ℝ → Fin (d + 1))
    (y : ℝ → Fin d → Fin (d + 1) → ℤ)
    (F : Set (Submodule ℚ (Fin (d + 1) → ℚ))) (hF : F.Finite)
    (hp : ∀ q ∈ S, b q (p q) ≠ 0)
    (hheight : ∀ q ∈ S, rationalHyperplaneKernel (b q) ∈ F ∨
      a * q - C ≤ Height.logHeight (b q) / d)
    (hspan : ∀ q ∈ S, Submodule.span ℚ (Set.range (fun j i => (y q j i : ℚ))) =
      rationalHyperplaneKernel (b q))
    (hInf : ∀ q ∈ S, ∀ j i,
      |((∑ k, A i k * (y q j k : ℚ) : ℚ) : ℝ)| ≤ Real.exp (c 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ j i, (padicNorm 2 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q))
    (hThree : ∀ q ∈ S, ∀ j i, (padicNorm 3 (y q j i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) :
    Set.Finite ((fun q => rationalHyperplaneKernel (b q)) '' S) := by
  classical
  let T : Set ℝ := {q | q ∈ S ∧ rationalHyperplaneKernel (b q) ∉ F}
  have hT : BddAbove T := bounded_hyperplane_family_of_affine_height hd A hA c ρ a C
    hρ ha hc T b p y
    (fun q hq => hp q hq.1)
    (fun q hq => (hheight q hq.1).resolve_left hq.2)
    (fun q hq => hspan q hq.1)
    (fun q hq => hInf q hq.1)
    (fun q hq => hTwo q hq.1)
    (fun q hq => hThree q hq.1)
  obtain ⟨M, hM⟩ := hT
  have hsmall := finite_bounded_exponential_spans A (isUnit_iff_ne_zero.mp hA) (c 0) M
  apply (hF.union hsmall).subset
  rintro V ⟨q, hq, rfl⟩
  by_cases hex : rationalHyperplaneKernel (b q) ∈ F
  · exact Or.inl hex
  · right
    refine ⟨q, Set.range (y q), hS q hq, hM ⟨hq, hex⟩, ?_, ?_⟩
    · rintro z ⟨j, rfl⟩ i
      exact hInf q hq j i
    · change rationalHyperplaneKernel (b q) = _
      rw [← hspan q hq]
      congr 1
      exact Set.range_comp (fun z i => (z i : ℚ)) (y q)

end
end Bounty

end SubmissionComponent_FiniteHyperplaneFamilies

/- Component FixedProfileHyperplanes; SHA256 c39d60a9a0df37c84145d5fc0618ab79d308788400edc67f25ece9bd73ac9451 -/
section SubmissionComponent_FixedProfileHyperplanes
/- Finiteness of actual codimension-one integer spans in a fixed negative profile. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def finite_fixed_profile_hyperplane_spans {d : ℕ} (hd : 1 ≤ d)
    (A : Matrix (Fin (d + 1)) (Fin (d + 1)) ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → Fin (d + 1) → ℝ) (ρ : ℝ) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (X : ℝ → Matrix (Fin (d + 1)) (Fin d) ℤ)
    (hX : ∀ q ∈ S, LinearIndependent ℚ ((X q).map (Int.castRingHom ℚ)).col)
    (hInf : ∀ q ∈ S, ∀ i j,
      ‖(A * (X q).map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i j,
      (padicNorm 2 (X q i j : ℚ) : ℝ) ≤ Real.exp (c 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i j,
      (padicNorm 3 (X q i j : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) :
    Set.Finite ((fun q => Submodule.span ℚ
      (Set.range ((X q).map (Int.castRingHom ℚ)).col)) '' S) := by
  classical
  obtain ⟨T, C, hT, _, hdichotomy⟩ := moving_hyperplane_height_dichotomy A hA c ρ hρ hc
  let U : Set ℝ := {q | q ∈ S ∧ T ≤ q}
  have hex : ∀ q : ℝ, ∃ a : Fin (d + 1) → ℤ, q ∈ U →
      a ≠ 0 ∧ Finset.univ.gcd a = 1 ∧
      Submodule.span ℚ (Set.range ((X q).map (Int.castRingHom ℚ)).col) =
        rationalHyperplaneKernel (fun i => (a i : ℚ)) ∧
      (rationalHyperplaneKernel (fun i => (a i : ℚ)) ∈ exceptionalPatternHyperplanes A ∨
        ρ * q / 4 - C ≤ Height.logHeight (fun i => (a i : ℚ))) := by
    intro q
    by_cases hq : q ∈ U
    · obtain ⟨a, ha⟩ := hdichotomy q hq.2 (X q) (hX q hq.1)
        (hInf q hq.1) (hTwo q hq.1) (hThree q hq.1)
      exact ⟨a, fun _ => ha⟩
    · exact ⟨0, fun h => False.elim (hq h)⟩
  choose a ha using hex
  let b : ℝ → Fin (d + 1) → ℚ := fun q i => (a q i : ℚ)
  have hp_exists : ∀ q : ℝ, ∃ p : Fin (d + 1), q ∈ U → b q p ≠ 0 := by
    intro q
    by_cases hq : q ∈ U
    · obtain ⟨i, hi⟩ : ∃ i, a q i ≠ 0 := by simpa [funext_iff] using (ha q hq).1
      exact ⟨i, fun _ => by dsimp [b]; exact_mod_cast hi⟩
    · exact ⟨0, fun h => False.elim (hq h)⟩
  choose p hp using hp_exists
  have hdreal : (0 : ℝ) < d := by exact_mod_cast hd
  have hfinite : Set.Finite ((fun q => rationalHyperplaneKernel (b q)) '' U) :=
    finite_hyperplane_family_of_height_dichotomy hd A hA c ρ (ρ / (4 * d)) (C / d)
      hρ (by positivity) hc U (fun q hq => hS q hq.1) b p (fun q j i => X q i j)
      (exceptionalPatternHyperplanes A : Set _) (exceptionalPatternHyperplanes A).finite_toSet hp
      (by
        intro q hq
        rcases (ha q hq).2.2.2 with h | h
        · exact Or.inl h
        · right
          have hh := div_le_div_of_nonneg_right h hdreal.le
          dsimp [b]
          calc
            ρ / (4 * (d : ℝ)) * q - C / d = (ρ * q / 4 - C) / d := by ring
            _ ≤ _ := hh)
      (fun q hq => (ha q hq).2.2.1)
      (by
        intro q hq j i
        rw [← Real.norm_eq_abs, Rat.norm_cast_real]
        exact hInf q hq.1 i j)
      (fun q hq j i => hTwo q hq.1 i j)
      (fun q hq j i => hThree q hq.1 i j)
  have hsmall := finite_bounded_exponential_spans A (isUnit_iff_ne_zero.mp hA) (c 0) T
  apply (hfinite.union hsmall).subset
  rintro V ⟨q, hq, rfl⟩
  by_cases hlarge : T ≤ q
  · left
    refine ⟨q, ⟨hq, hlarge⟩, ?_⟩
    exact ((ha q ⟨hq, hlarge⟩).2.2.1).symm
  · right
    refine ⟨q, Set.range (fun j i => X q i j), hS q hq,
      le_of_not_ge hlarge, ?_, ?_⟩
    · rintro z ⟨j, rfl⟩ i
      rw [← Real.norm_eq_abs, Rat.norm_cast_real]
      exact hInf q hq i j
    · change Submodule.span ℚ (Set.range (fun j i => (X q i j : ℚ))) = _
      congr 1
      exact Set.range_comp (fun z i => (z i : ℚ)) (fun j i => X q i j)

end
end Bounty

end SubmissionComponent_FixedProfileHyperplanes

/- Component FiniteIndexProfileHyperplanes; SHA256 16e6aacc0800fd6936926bf23485f6746739cb92b9d754a6ea6939051c97d89c -/
section SubmissionComponent_FiniteIndexProfileHyperplanes
/- Transport of fixed-profile hyperplane finiteness to arbitrary finite coordinate types. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

/-- The coordinate change induced by an actual bijection of row labels. -/
def profileCoordinateEquiv {I I' : Type*} (e : I ≃ I') :
    (I → ℚ) ≃ₗ[ℚ] (I' → ℚ) where
  toFun x i := x (e.symm i)
  invFun y i := y (e i)
  left_inv x := by funext i; simp
  right_inv y := by funext i; simp
  map_add' _ _ := rfl
  map_smul' _ _ := rfl

def profile_column_span_reindex {I I' J J' : Type*}
    (e : I ≃ I') (f : J ≃ J') (X : Matrix I J ℚ) :
    (Submodule.span ℚ (Set.range X.col)).map (profileCoordinateEquiv e).toLinearMap =
      Submodule.span ℚ (Set.range (Matrix.reindex e f X).col) := by
  rw [Submodule.map_span, ← Set.range_comp]
  congr 1
  ext v
  constructor
  · rintro ⟨j, rfl⟩
    refine ⟨f j, ?_⟩
    ext i
    simp [profileCoordinateEquiv, Matrix.reindex_apply, Matrix.col, Matrix.submatrix]
    rfl
  · rintro ⟨j, rfl⟩
    exact ⟨f.symm j, rfl⟩

def profile_column_independent_reindex {I I' J J' : Type*}
    (e : I ≃ I') (f : J ≃ J') (X : Matrix I J ℚ)
    (hX : LinearIndependent ℚ X.col) :
    LinearIndependent ℚ (Matrix.reindex e f X).col := by
  exact (hX.map' (profileCoordinateEquiv e).toLinearMap
    (LinearMap.ker_eq_bot.mpr (profileCoordinateEquiv e).injective)).comp f.symm f.symm.injective

def profile_reindex_mul {I I' J J' : Type*} [Fintype I] [Fintype I']
    (e : I ≃ I') (f : J ≃ J') (A : Matrix I I ℚ) (X : Matrix I J ℚ) :
    Matrix.reindex e e A * Matrix.reindex e f X = Matrix.reindex e f (A * X) :=
  Matrix.submatrix_mul_equiv A X e.symm e.symm f.symm

/-- The finite-index form of the checked fixed-profile theorem, with genuine transported spans. -/
def finite_fixed_profile_hyperplane_spans_fintype
    {I J : Type*} [Fintype I] [Fintype J] [DecidableEq I]
    (hcard : Fintype.card I = Fintype.card J + 1) (hJ : 1 ≤ Fintype.card J)
    (A : Matrix I I ℚ) (hA : IsUnit A.det)
    (c : Fin 3 → I → ℝ) (ρ : ℝ) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (X : ℝ → Matrix I J ℤ)
    (hX : ∀ q ∈ S, LinearIndependent ℚ ((X q).map (Int.castRingHom ℚ)).col)
    (hInf : ∀ q ∈ S, ∀ i j,
      ‖(A * (X q).map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i j,
      (padicNorm 2 (X q i j : ℚ) : ℝ) ≤ Real.exp (c 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i j,
      (padicNorm 3 (X q i j : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) :
    Set.Finite ((fun q => Submodule.span ℚ
      (Set.range ((X q).map (Int.castRingHom ℚ)).col)) '' S) := by
  classical
  let e : I ≃ Fin (Fintype.card J + 1) := Fintype.equivFinOfCardEq hcard
  let f : J ≃ Fin (Fintype.card J) := Fintype.equivFin J
  let A' := Matrix.reindex e e A
  let c' : Fin 3 → Fin (Fintype.card J + 1) → ℝ := fun v i => c v (e.symm i)
  let X' : ℝ → Matrix (Fin (Fintype.card J + 1)) (Fin (Fintype.card J)) ℤ :=
    fun q => Matrix.reindex e f (X q)
  have hcast (q : ℝ) : (X' q).map (Int.castRingHom ℚ) =
      Matrix.reindex e f ((X q).map (Int.castRingHom ℚ)) := rfl
  have hA' : IsUnit A'.det := by
    simpa only [A', Matrix.det_reindex_self] using hA
  have hc' : (∑ v, ∑ i, c' v i) ≤ -ρ := by
    simpa only [c', Equiv.sum_comp] using hc
  have hX' : ∀ q ∈ S, LinearIndependent ℚ ((X' q).map (Int.castRingHom ℚ)).col := by
    intro q hq
    rw [hcast]
    exact profile_column_independent_reindex e f _ (hX q hq)
  have hInf' : ∀ q ∈ S, ∀ i j,
      ‖(A' * (X' q).map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c' 0 i * q) := by
    intro q hq i j
    rw [hcast, profile_reindex_mul]
    exact hInf q hq (e.symm i) (f.symm j)
  have hTwo' : ∀ q ∈ S, ∀ i j,
      (padicNorm 2 (X' q i j : ℚ) : ℝ) ≤ Real.exp (c' 1 i * q) := by
    intro q hq i j
    exact hTwo q hq (e.symm i) (f.symm j)
  have hThree' : ∀ q ∈ S, ∀ i j,
      (padicNorm 3 (X' q i j : ℚ) : ℝ) ≤ Real.exp (c' 2 i * q) := by
    intro q hq i j
    exact hThree q hq (e.symm i) (f.symm j)
  have hfinite := finite_fixed_profile_hyperplane_spans hJ A' hA' c' ρ hρ hc' S hS
    X' hX' hInf' hTwo' hThree'
  have himage : Submodule.map (profileCoordinateEquiv e).toLinearMap ''
      ((fun q => Submodule.span ℚ (Set.range ((X q).map (Int.castRingHom ℚ)).col)) '' S) =
      ((fun q => Submodule.span ℚ (Set.range ((X' q).map (Int.castRingHom ℚ)).col)) '' S) := by
    rw [Set.image_image]
    congr 1
    funext q
    rw [hcast]
    exact profile_column_span_reindex e f _
  rw [← himage] at hfinite
  exact hfinite.of_finite_image
    (Submodule.map_injective_of_injective (profileCoordinateEquiv e).injective).injOn


end
end Bounty

end SubmissionComponent_FiniteIndexProfileHyperplanes

/- Component VaryingProfileHyperplanes; SHA256 aa918076e45a3ae1625d5dbade003a3eb62eff09e77e5f95e4747906b84e5141 -/
section SubmissionComponent_VaryingProfileHyperplanes
/- Bounded varying profiles reduce to an actual finite collection of fixed upper profiles. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def finite_varying_profile_hyperplane_spans
    {I J : Type*} [Fintype I] [Fintype J] [DecidableEq I]
    (hcard : Fintype.card I = Fintype.card J + 1) (hJ : 1 ≤ Fintype.card J)
    (A : Matrix I I ℚ) (hA : IsUnit A.det)
    (c : ℝ → Fin 3 → I → ℝ) (M ρ : ℝ) (hρ : 0 < ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (hcBound : ∀ q ∈ S, ∀ v i, |c q v i| ≤ M)
    (hcSum : ∀ q ∈ S, (∑ v, ∑ i, c q v i) ≤ -ρ)
    (X : ℝ → Matrix I J ℤ)
    (hX : ∀ q ∈ S, LinearIndependent ℚ ((X q).map (Int.castRingHom ℚ)).col)
    (hInf : ∀ q ∈ S, ∀ i j,
      ‖(A * (X q).map (Int.castRingHom ℚ)) i j‖ ≤ Real.exp (c q 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i j,
      (padicNorm 2 (X q i j : ℚ) : ℝ) ≤ Real.exp (c q 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i j,
      (padicNorm 3 (X q i j : ℚ) : ℝ) ≤ Real.exp (c q 2 i * q)) :
    Set.Finite ((fun q => Submodule.span ℚ
      (Set.range ((X q).map (Int.castRingHom ℚ)).col)) '' S) := by
  classical
  let : Nonempty I := Fintype.card_pos_iff.mp (by omega)
  obtain ⟨C, hC, hcover⟩ := exists_finite_exponent_profiles_nonpos_on
    (Fin 3 × I) ∅ M ρ hρ
  let U (a : Fin 3 × I → ℝ) : Set ℝ :=
    {q | q ∈ S ∧ ∀ v i, c q v i ≤ a (v, i)}
  let V (q : ℝ) := Submodule.span ℚ (Set.range ((X q).map (Int.castRingHom ℚ)).col)
  have hfinite (a : Fin 3 × I → ℝ) (ha : a ∈ C) : Set.Finite (V '' U a) := by
    have hsum : (∑ v, ∑ i, a (v, i)) ≤ -(ρ / 2) := by
      have hh := (hC a ha).2.1
      simpa only [Fintype.sum_prod_type, neg_div] using hh
    apply finite_fixed_profile_hyperplane_spans_fintype hcard hJ A hA
      (fun v i => a (v, i)) (ρ / 2) (by positivity) hsum (U a)
      (fun q hq => hS q hq.1) X (fun q hq => hX q hq.1)
    · intro q hq i j
      exact (hInf q hq.1 i j).trans (Real.exp_le_exp.mpr
        (mul_le_mul_of_nonneg_right (hq.2 0 i) (hS q hq.1)))
    · intro q hq i j
      exact (hTwo q hq.1 i j).trans (Real.exp_le_exp.mpr
        (mul_le_mul_of_nonneg_right (hq.2 1 i) (hS q hq.1)))
    · intro q hq i j
      exact (hThree q hq.1 i j).trans (Real.exp_le_exp.mpr
        (mul_le_mul_of_nonneg_right (hq.2 2 i) (hS q hq.1)))
  have hU : Set.Finite (⋃ a ∈ (C : Set (Fin 3 × I → ℝ)), V '' U a) :=
    C.finite_toSet.biUnion hfinite
  apply hU.subset
  rintro W ⟨q, hq, rfl⟩
  obtain ⟨a, ha, hle, _⟩ := hcover (fun x => c q x.1 x.2)
    (fun x => hcBound q hq x.1 x.2)
    (by simpa only [Fintype.sum_prod_type] using hcSum q hq)
    (by simp)
  exact Set.mem_iUnion.mpr ⟨a, Set.mem_iUnion.mpr
    ⟨ha, q, ⟨hq, fun v i => hle (v, i)⟩, rfl⟩⟩


end
end Bounty

end SubmissionComponent_VaryingProfileHyperplanes

/- Component CompoundProfileHyperplanes; SHA256 9e4bc642b774e9ffa674c1de21a5a8c3919549f227ac1815272769454fb1c0c0 -/
section SubmissionComponent_CompoundProfileHyperplanes
/- Finiteness for the actual integer compound columns with one column removed. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def compoundDeletedColumns {d ell : ℕ} (s₀ : CompoundIndex d ell)
    (H : Matrix (Fin d) (Fin d) ℤ) :
    Matrix (CompoundIndex d ell) {t : CompoundIndex d ell // t ≠ s₀} ℤ :=
  (compoundMatrix ell H).submatrix id Subtype.val

def compoundDeletedColumns_map {d ell : ℕ} (s₀ : CompoundIndex d ell)
    (H : Matrix (Fin d) (Fin d) ℤ) :
    (compoundDeletedColumns s₀ H).map (Int.castRingHom ℚ) =
      (compoundMatrix ell (H.map (Int.castRingHom ℚ))).submatrix id Subtype.val := by
  exact (congrArg (fun X : Matrix (CompoundIndex d ell) (CompoundIndex d ell) ℚ =>
    X.submatrix id (Subtype.val : {t : CompoundIndex d ell // t ≠ s₀} → CompoundIndex d ell))
    (compoundMatrix_map (Int.castRingHom ℚ) ell H)).symm

def compoundIndex_two_le_card {d ell : ℕ} (hell : 0 < ell) (held : ell < d) :
    2 ≤ Fintype.card (CompoundIndex d ell) := by
  rw [compoundIndex_card]
  have hp := Nat.choose_pos held.le
  have hn : d.choose ell ≠ 1 := by
    intro heq
    have hh := Nat.choose_eq_one_iff.mp heq
    omega
  omega

def compoundIndex_deleted_card {d ell : ℕ} (s₀ : CompoundIndex d ell) :
    Fintype.card {t : CompoundIndex d ell // t ≠ s₀} =
      Fintype.card (CompoundIndex d ell) - 1 := by
  classical
  simpa only [Fintype.card_subtype_eq] using
    Fintype.card_subtype_compl (fun t : CompoundIndex d ell => t = s₀)

def compoundDeletedColumns_independent {d ell : ℕ} (s₀ : CompoundIndex d ell)
    (H : Matrix (Fin d) (Fin d) ℤ) (hH : (H.map (Int.castRingHom ℚ)).det ≠ 0) :
    LinearIndependent ℚ ((compoundDeletedColumns s₀ H).map (Int.castRingHom ℚ)).col := by
  classical
  rw [compoundDeletedColumns_map]
  exact (Matrix.linearIndependent_cols_of_det_ne_zero
    (compoundMatrix_det_ne_zero ell _ hH)).comp Subtype.val Subtype.val_injective

def compoundDeletedColumns_span {d ell : ℕ} (s₀ : CompoundIndex d ell)
    (H : Matrix (Fin d) (Fin d) ℤ) :
    Submodule.span ℚ (Set.range ((compoundDeletedColumns s₀ H).map (Int.castRingHom ℚ)).col) =
      Submodule.span ℚ ((compoundMatrix ell (H.map (Int.castRingHom ℚ))).col '' {t | t ≠ s₀}) := by
  rw [compoundDeletedColumns_map, Set.image_eq_range]
  rfl

def compoundDeletedColumns_span_ne_top {d ell : ℕ} (s₀ : CompoundIndex d ell)
    (H : Matrix (Fin d) (Fin d) ℚ) (hH : H.det ≠ 0) :
    Submodule.span ℚ ((compoundMatrix ell H).col '' {t | t ≠ s₀}) ≠ ⊤ := by
  classical
  have hli := Matrix.linearIndependent_cols_of_det_ne_zero
    (compoundMatrix_det_ne_zero ell H hH)
  have hn := hli.notMem_span_image (s := {t | t ≠ s₀}) (x := s₀) (by simp)
  intro heq
  rw [heq] at hn
  exact hn (Submodule.mem_top : (compoundMatrix ell H).col s₀ ∈ ⊤)

def finite_varying_profile_compound_deleted_spans {d ell : ℕ}
    (hell : 0 < ell) (held : ell < d) (s₀ : CompoundIndex d ell)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : ℝ → Fin 3 → CompoundIndex d ell → ℝ) (M ρ : ℝ) (hρ : 0 < ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (hcBound : ∀ q ∈ S, ∀ v i, |c q v i| ≤ M)
    (hcSum : ∀ q ∈ S, (∑ v, ∑ i, c q v i) ≤ -ρ)
    (H : ℝ → Matrix (Fin d) (Fin d) ℤ)
    (hH : ∀ q ∈ S, ((H q).map (Int.castRingHom ℚ)).det ≠ 0)
    (hInf : ∀ q ∈ S, ∀ i t, t ≠ s₀ →
      ‖(compoundMatrix ell A * compoundMatrix ell ((H q).map (Int.castRingHom ℚ))) i t‖ ≤
        Real.exp (c q 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i t, t ≠ s₀ →
      (padicNorm 2 (compoundMatrix ell ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i t, t ≠ s₀ →
      (padicNorm 3 (compoundMatrix ell ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 2 i * q)) :
    Set.Finite ((fun q => Submodule.span ℚ
      ((compoundMatrix ell ((H q).map (Int.castRingHom ℚ))).col '' {t | t ≠ s₀})) '' S) := by
  classical
  have hN := compoundIndex_two_le_card hell held
  have hcard := compoundIndex_deleted_card s₀
  have hfinite := finite_varying_profile_hyperplane_spans (I := CompoundIndex d ell)
    (J := {t : CompoundIndex d ell // t ≠ s₀}) (by omega) (by omega)
    (compoundMatrix ell A) (isUnit_iff_ne_zero.mpr (compoundMatrix_det_ne_zero ell A hA))
    c M ρ hρ S hS hcBound hcSum (fun q => compoundDeletedColumns s₀ (H q))
    (fun q hq => compoundDeletedColumns_independent s₀ (H q) (hH q hq))
    (by
      intro q hq i t
      rw [compoundDeletedColumns_map]
      have heq := Matrix.submatrix_mul_equiv (compoundMatrix ell A)
        (compoundMatrix ell ((H q).map (Int.castRingHom ℚ))) id
        (Equiv.refl (CompoundIndex d ell))
        (Subtype.val : {t : CompoundIndex d ell // t ≠ s₀} → CompoundIndex d ell)
      simp only [Equiv.coe_refl, Matrix.submatrix_id_id] at heq
      rw [heq]
      exact hInf q hq i t.val t.property)
    (by
      intro q hq i t
      have heq := congrArg (fun X : Matrix (CompoundIndex d ell)
          {t : CompoundIndex d ell // t ≠ s₀} ℚ => X i t)
        (compoundDeletedColumns_map s₀ (H q))
      change (padicNorm 2 (((compoundDeletedColumns s₀ (H q)).map (Int.castRingHom ℚ)) i t) : ℝ) ≤ _
      rw [heq]
      exact hTwo q hq i t.val t.property)
    (by
      intro q hq i t
      have heq := congrArg (fun X : Matrix (CompoundIndex d ell)
          {t : CompoundIndex d ell // t ≠ s₀} ℚ => X i t)
        (compoundDeletedColumns_map s₀ (H q))
      change (padicNorm 3 (((compoundDeletedColumns s₀ (H q)).map (Int.castRingHom ℚ)) i t) : ℝ) ≤ _
      rw [heq]
      exact hThree q hq i t.val t.property)
  simpa only [compoundDeletedColumns_span] using hfinite

def finite_varying_profile_compound_tail_spans {d k : ℕ}
    (hkpos : 1 ≤ k) (hk : k < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : ℝ → Fin 3 → CompoundIndex d (d - k) → ℝ) (M ρ : ℝ) (hρ : 0 < ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (hcBound : ∀ q ∈ S, ∀ v i, |c q v i| ≤ M)
    (hcSum : ∀ q ∈ S, (∑ v, ∑ i, c q v i) ≤ -ρ)
    (H : ℝ → Matrix (Fin d) (Fin d) ℤ)
    (hH : ∀ q ∈ S, ((H q).map (Int.castRingHom ℚ)).det ≠ 0)
    (hInf : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      ‖(compoundMatrix (d - k) A * compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ))) i t‖ ≤
        Real.exp (c q 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 2 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 3 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 2 i * q)) :
    Set.Finite ((fun q => Submodule.span ℚ
      ((compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ))).col ''
        {t | t ≠ compoundTailIndex d k})) '' S) :=
  finite_varying_profile_compound_deleted_spans (by omega) (by omega)
    (compoundTailIndex d k) A hA c M ρ hρ S hS hcBound hcSum H hH hInf hTwo hThree


end
end Bounty

end SubmissionComponent_CompoundProfileHyperplanes

/- Component CompoundProfileFamilies; SHA256 32c64d9b5347c90026d25a15f33a7908bc0087968d6b4b809db5702ec270a959 -/
section SubmissionComponent_CompoundProfileFamilies
/- A finite family of proper compound hyperplanes for the varying-profile construction. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def exists_finite_varying_profile_compound_tail_family {d k : ℕ}
    (hkpos : 1 ≤ k) (hk : k < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : ℝ → Fin 3 → CompoundIndex d (d - k) → ℝ) (M ρ : ℝ) (hρ : 0 < ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (hcBound : ∀ q ∈ S, ∀ v i, |c q v i| ≤ M)
    (hcSum : ∀ q ∈ S, (∑ v, ∑ i, c q v i) ≤ -ρ)
    (H : ℝ → Matrix (Fin d) (Fin d) ℤ)
    (hH : ∀ q ∈ S, ((H q).map (Int.castRingHom ℚ)).det ≠ 0)
    (hInf : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      ‖(compoundMatrix (d - k) A * compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ))) i t‖ ≤
        Real.exp (c q 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 2 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 3 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 2 i * q)) :
    ∃ F : Finset (Submodule ℚ (CompoundIndex d (d - k) → ℚ)),
      (∀ V ∈ F, V ≠ ⊤) ∧ ∀ q ∈ S,
        Submodule.span ℚ ((compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ))).col ''
          {t | t ≠ compoundTailIndex d k}) ∈ F := by
  classical
  have hfinite := finite_varying_profile_compound_tail_spans hkpos hk A hA c M ρ hρ
    S hS hcBound hcSum H hH hInf hTwo hThree
  refine ⟨hfinite.toFinset, ?_, ?_⟩
  · intro V hV
    obtain ⟨q, hq, rfl⟩ := hfinite.mem_toFinset.mp hV
    exact compoundDeletedColumns_span_ne_top (compoundTailIndex d k)
      ((H q).map (Int.castRingHom ℚ)) (hH q hq)
  · intro q hq
    exact hfinite.mem_toFinset.mpr ⟨q, hq, rfl⟩


end
end Bounty

end SubmissionComponent_CompoundProfileFamilies

/- Component CompoundRecoveryCore; SHA256 7f925663a82a946efc9d5f5c6fdf4c64b932f80c884e0acba76929aecbed15ba -/
section SubmissionComponent_CompoundRecoveryCore
/- Canonical recovery of an original subspace from a compound subspace,
using all wedge tuples with one prescribed vector. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def compoundSlotMap {d ell : ℕ} (v : Fin ell → Fin d → ℚ) (j : Fin ell) :
    (Fin d → ℚ) →ₗ[ℚ] (CompoundIndex d ell → ℚ) where
  toFun x := compoundWedgeCoordinates (Function.update v j x)
  map_add' x y := by
    ext s
    simp [compoundWedgeCoordinates, AlternatingMap.map_update_add]
  map_smul' c x := by
    ext s
    simp [compoundWedgeCoordinates, AlternatingMap.map_update_smul]

def compoundRecovery {d ell : ℕ} (H : Submodule ℚ (CompoundIndex d ell → ℚ)) :
    Submodule ℚ (Fin d → ℚ) :=
  ⨅ v : Fin ell → Fin d → ℚ, ⨅ j : Fin ell, H.comap (compoundSlotMap v j)

def mem_compoundRecovery {d ell : ℕ}
    (H : Submodule ℚ (CompoundIndex d ell → ℚ)) (x : Fin d → ℚ) :
    x ∈ compoundRecovery H ↔ ∀ (v : Fin ell → Fin d → ℚ) (j : Fin ell),
      compoundWedgeCoordinates (Function.update v j x) ∈ H := by
  simp only [compoundRecovery, Submodule.mem_iInf, Submodule.mem_comap]
  rfl

def mem_compoundRecovery_iff_tuple {d ell : ℕ}
    (H : Submodule ℚ (CompoundIndex d ell → ℚ)) (x : Fin d → ℚ) :
    x ∈ compoundRecovery H ↔ ∀ (v : Fin ell → Fin d → ℚ) (j : Fin ell),
      v j = x → compoundWedgeCoordinates v ∈ H := by
  rw [mem_compoundRecovery]
  constructor
  · intro h v j hj
    simpa [← hj, Function.update_eq_self] using h v j
  · intro h v j
    exact h (Function.update v j x) j (Function.update_self _ _ _)

def compoundCoordinateHyperplane {d ell : ℕ} (s : CompoundIndex d ell) :
    Submodule ℚ (CompoundIndex d ell → ℚ) := LinearMap.ker (LinearMap.proj s)

def mem_compoundCoordinateHyperplane {d ell : ℕ}
    (s : CompoundIndex d ell) (x : CompoundIndex d ell → ℚ) :
    x ∈ compoundCoordinateHyperplane s ↔ x s = 0 := Iff.rfl

def det_identity_updateCol {I : Type*} [Fintype I] [DecidableEq I]
    (j : I) (x : I → ℚ) : ((1 : Matrix I I ℚ).updateCol j x).det = x j := by
  have h := Matrix.det_updateCol_sum (1 : Matrix I I ℚ) j x
  simpa [Matrix.one_apply] using h

def compoundWedgeCoordinates_basis_update {d ell : ℕ}
    (s : CompoundIndex d ell) (j : Fin ell) (x : Fin d → ℚ) :
    compoundWedgeCoordinates
      (Function.update (fun k => Pi.single (compoundIndexEmbedding s k) (1 : ℚ)) j x) s =
        x (compoundIndexEmbedding s j) := by
  classical
  let v : Fin ell → Fin d → ℚ := fun k => Pi.single (compoundIndexEmbedding s k) 1
  change compoundWedgeCoordinates (Function.update v j x) s = _
  rw [compoundWedgeCoordinates_apply]
  have hmat : (Matrix.of (fun i k : Fin ell =>
      Function.update v j x k
        (compoundIndexEmbedding s i))) =
      (1 : Matrix (Fin ell) (Fin ell) ℚ).updateCol j (fun i => x (compoundIndexEmbedding s i)) := by
    ext i k
    by_cases hk : k = j
    · simp [hk]
    · simp [v, hk, Pi.single_apply, Matrix.one_apply, (compoundIndexEmbedding s).injective.eq_iff]
  rw [hmat, det_identity_updateCol]

def mem_compoundRecovery_coordinate {d ell : ℕ}
    (s : CompoundIndex d ell) (x : Fin d → ℚ) :
    x ∈ compoundRecovery (compoundCoordinateHyperplane s) ↔
      ∀ j, x (compoundIndexEmbedding s j) = 0 := by
  classical
  rw [mem_compoundRecovery]
  constructor
  · intro h j
    have hh := h (fun k => Pi.single (compoundIndexEmbedding s k) (1 : ℚ)) j
    simpa only [mem_compoundCoordinateHyperplane, compoundWedgeCoordinates_basis_update] using hh
  · intro hx v j
    rw [mem_compoundCoordinateHyperplane, compoundWedgeCoordinates_apply]
    apply Matrix.det_eq_zero_of_column_eq_zero j
    intro i
    simpa using hx i

def compoundWedgeCoordinates_basis {d ell : ℕ} (s : CompoundIndex d ell) :
    compoundWedgeCoordinates (fun j => Pi.single (compoundIndexEmbedding s j) (1 : ℚ)) =
      Pi.single s 1 := by
  classical
  have hv : (fun j => Pi.single (compoundIndexEmbedding s j) (1 : ℚ)) =
      (fun j i => (1 : Matrix (Fin d) (Fin d) ℚ) i (compoundIndexEmbedding s j)) := by
    funext j i
    simp [Matrix.one_apply, Pi.single_apply]
  rw [hv, compoundMatrix_column, compoundMatrix_one]
  funext t
  simp [Matrix.one_apply, Pi.single_apply, eq_comm]

def compoundRecovery_ne_top {d ell : ℕ} (hell : 0 < ell)
    (H : Submodule ℚ (CompoundIndex d ell → ℚ)) (hH : H ≠ ⊤) :
    compoundRecovery H ≠ ⊤ := by
  classical
  intro htop
  apply hH
  apply eq_top_iff.mpr
  intro x _
  have hb : ∀ s : CompoundIndex d ell, Pi.single s (1 : ℚ) ∈ H := by
    intro s
    let v : Fin ell → Fin d → ℚ := fun j => Pi.single (compoundIndexEmbedding s j) 1
    have hv : v ⟨0, hell⟩ ∈ compoundRecovery H := by rw [htop]; trivial
    have hh := (mem_compoundRecovery_iff_tuple H _).mp hv v ⟨0, hell⟩ rfl
    simpa only [v, compoundWedgeCoordinates_basis] using hh
  have he : x = ∑ s, x s • Pi.single s (1 : ℚ) := by
    ext s
    simp [Pi.single_apply]
  rw [he]
  exact H.sum_mem (fun s _ => H.smul_mem (x s) (hb s))


end
end Bounty

end SubmissionComponent_CompoundRecoveryCore

/- Component CompoundHyperplaneRecovery; SHA256 5c956447589b5be0e4cd523737e55d1b309d07e0e08728df2d882067e37b7bf1 -/
section SubmissionComponent_CompoundHyperplaneRecovery
/- Recovery commutes with invertible column changes. In particular, the
compound hyperplane omitting a subset recovers the original columns outside
that subset. Finite families therefore pull back without a height argument. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def compoundRecovery_map {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) ℚ) (hM : M.det ≠ 0)
    (H : Submodule ℚ (CompoundIndex d ell → ℚ)) :
    compoundRecovery (H.map (Matrix.toLin' (compoundMatrix ell M))) =
      (compoundRecovery H).map (Matrix.toLin' M) := by
  classical
  have hu : IsUnit M.det := isUnit_iff_ne_zero.mpr hM
  have hCinj : Function.Injective (compoundMatrix ell M).mulVec :=
    Matrix.mulVec_injective_iff_isUnit.mpr
      ((compoundMatrix ell M).isUnit_iff_isUnit_det.mpr
        (isUnit_iff_ne_zero.mpr (compoundMatrix_det_ne_zero ell M hM)))
  ext x
  constructor
  · intro hx
    let y := M⁻¹.mulVec x
    have hMy : M.mulVec y = x := by
      dsimp [y]
      rw [Matrix.mulVec_mulVec, Matrix.mul_nonsing_inv M hu, Matrix.one_mulVec]
    refine Submodule.mem_map.mpr ⟨y, ?_, hMy⟩
    rw [mem_compoundRecovery_iff_tuple]
    intro v j hj
    have hh := (mem_compoundRecovery_iff_tuple _ _).mp hx
      (fun k => M.mulVec (v k)) j (by rw [hj]; exact hMy)
    rw [← compoundMatrix_wedge_action] at hh
    obtain ⟨w, hw, he⟩ := Submodule.mem_map.mp hh
    have he' : w = compoundWedgeCoordinates v := hCinj he
    simpa [he'] using hw
  · rintro ⟨y, hy, rfl⟩
    rw [mem_compoundRecovery_iff_tuple]
    intro v j hj
    let w : Fin ell → Fin d → ℚ := fun k => M⁻¹.mulVec (v k)
    have hwj : w j = y := by
      dsimp [w]
      rw [hj]
      change M⁻¹.mulVec (M.mulVec y) = y
      rw [Matrix.mulVec_mulVec, Matrix.nonsing_inv_mul M hu, Matrix.one_mulVec]
    have hh := (mem_compoundRecovery_iff_tuple _ _).mp hy w j hwj
    refine Submodule.mem_map.mpr ⟨compoundWedgeCoordinates w, hh, ?_⟩
    change (compoundMatrix ell M).mulVec (compoundWedgeCoordinates w) = _
    rw [compoundMatrix_wedge_action]
    congr 1
    funext k
    dsimp [w]
    rw [Matrix.mulVec_mulVec, Matrix.mul_nonsing_inv M hu, Matrix.one_mulVec]

def coordinateVanishingSpace {I : Type*} (s : Finset I) : Submodule ℚ (I → ℚ) where
  carrier := {x | ∀ i ∈ s, x i = 0}
  zero_mem' := by simp
  add_mem' hx hy := by intro i hi; simp [hx i hi, hy i hi]
  smul_mem' c x hx := by intro i hi; simp [hx i hi]

def mem_coordinateVanishingSpace {I : Type*} (s : Finset I) (x : I → ℚ) :
    x ∈ coordinateVanishingSpace s ↔ ∀ i ∈ s, x i = 0 := Iff.rfl

def coordinateVanishingSpace_eq_span {I : Type*} [Fintype I] [DecidableEq I]
    (s : Finset I) :
    coordinateVanishingSpace s =
      Submodule.span ℚ ((fun i => Pi.single i (1 : ℚ)) '' {i | i ∉ s}) := by
  apply le_antisymm
  · intro x hx
    have he : x = ∑ i, x i • Pi.single i (1 : ℚ) := by
      ext i
      simp [Pi.single_apply]
    rw [he]
    apply Submodule.sum_mem
    intro i _
    by_cases hi : i ∈ s
    · simp [(mem_coordinateVanishingSpace s x).mp hx i hi]
    · exact Submodule.smul_mem _ (x i) (Submodule.subset_span ⟨i, hi, rfl⟩)
  · apply Submodule.span_le.mpr
    rintro _ ⟨i, hi, rfl⟩
    intro j hj
    have hij : j ≠ i := by intro h; subst j; exact hi hj
    simp [Pi.single_apply, hij, Ne.symm hij]

def coordinateVanishingSpace_map_matrix {I : Type*} [Fintype I] [DecidableEq I]
    (M : Matrix I I ℚ) (s : Finset I) :
    (coordinateVanishingSpace s).map (Matrix.toLin' M) =
      Submodule.span ℚ (M.col '' {i | i ∉ s}) := by
  rw [coordinateVanishingSpace_eq_span, Submodule.map_span, Set.image_image]
  congr 1
  congr 1
  funext i
  exact Matrix.mulVec_single_one M i

def compoundRecovery_coordinate_eq {d ell : ℕ} (s : CompoundIndex d ell) :
    compoundRecovery (compoundCoordinateHyperplane s) = coordinateVanishingSpace s.val := by
  ext x
  rw [mem_compoundRecovery_coordinate, mem_coordinateVanishingSpace]
  constructor
  · intro hx i hi
    obtain ⟨j, rfl⟩ := (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem s i).mpr hi
    exact hx j
  · intro hx j
    apply hx
    exact (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem s _).mp ⟨j, rfl⟩

def compoundCoordinateHyperplane_eq_vanishing {d ell : ℕ} (s : CompoundIndex d ell) :
    compoundCoordinateHyperplane s = coordinateVanishingSpace {s} := by
  classical
  ext x
  simp [mem_compoundCoordinateHyperplane, mem_coordinateVanishingSpace]

def compound_hyperplane_span_eq_map {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) ℚ) (s : CompoundIndex d ell) :
    Submodule.span ℚ ((compoundMatrix ell M).col '' {t | t ≠ s}) =
      (compoundCoordinateHyperplane s).map (Matrix.toLin' (compoundMatrix ell M)) := by
  classical
  rw [compoundCoordinateHyperplane_eq_vanishing, coordinateVanishingSpace_map_matrix]
  simp

def compoundRecovery_span_except {d ell : ℕ}
    (M : Matrix (Fin d) (Fin d) ℚ) (hM : M.det ≠ 0) (s : CompoundIndex d ell) :
    compoundRecovery (Submodule.span ℚ ((compoundMatrix ell M).col '' {t | t ≠ s})) =
      Submodule.span ℚ (M.col '' {i | i ∉ s.val}) := by
  rw [compound_hyperplane_span_eq_map, compoundRecovery_map M hM,
    compoundRecovery_coordinate_eq, coordinateVanishingSpace_map_matrix]

def finite_compound_hyperplane_recovery {d ell : ℕ} (hell : 0 < ell)
    (F : Finset (Submodule ℚ (CompoundIndex d ell → ℚ)))
    (hF : ∀ H ∈ F, H ≠ ⊤) :
    ∃ G : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ G, V ≠ ⊤) ∧
      ∀ (M : Matrix (Fin d) (Fin d) ℚ), M.det ≠ 0 → ∀ s : CompoundIndex d ell,
        Submodule.span ℚ ((compoundMatrix ell M).col '' {t | t ≠ s}) ∈ F →
        Submodule.span ℚ (M.col '' {i | i ∉ s.val}) ∈ G := by
  classical
  refine ⟨F.image compoundRecovery, ?_, ?_⟩
  · intro V hV
    obtain ⟨H, hH, rfl⟩ := Finset.mem_image.mp hV
    exact compoundRecovery_ne_top hell H (hF H hH)
  · intro M hM s hs
    exact Finset.mem_image.mpr ⟨_, hs, compoundRecovery_span_except M hM s⟩


end
end Bounty

end SubmissionComponent_CompoundHyperplaneRecovery

/- Component CompoundPrefixRecovery; SHA256 66e943858f76ab65cf702a8e9cc60f9d96a156756ef627dded008ba12ff1481f -/
section SubmissionComponent_CompoundPrefixRecovery
/- The canonical tail compound hyperplane recovers exactly the original prefix. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def matrix_prefix_image_eq_range {d k : ℕ} (hk : k ≤ d)
    (M : Matrix (Fin d) (Fin d) ℚ) :
    M.col '' {i | i.val < k} = Set.range (fun i : Fin k => M.col (i.castLE hk)) := by
  ext x
  constructor
  · rintro ⟨i, hi, rfl⟩
    exact ⟨⟨i.val, hi⟩, rfl⟩
  · rintro ⟨i, rfl⟩
    exact ⟨i.castLE hk, i.isLt, rfl⟩

def finite_compound_prefix_recovery {d k : ℕ} (hk : k < d)
    (F : Finset (Submodule ℚ (CompoundIndex d (d - k) → ℚ)))
    (hF : ∀ H ∈ F, H ≠ ⊤) :
    ∃ G : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ G, V ≠ ⊤) ∧
      ∀ (M : Matrix (Fin d) (Fin d) ℚ), M.det ≠ 0 →
        Submodule.span ℚ
          ((compoundMatrix (d - k) M).col '' {t | t ≠ compoundTailIndex d k}) ∈ F →
        Submodule.span ℚ (Set.range (fun i : Fin k => M.col (i.castLE hk.le))) ∈ G := by
  obtain ⟨G, hG, hcover⟩ := finite_compound_hyperplane_recovery (Nat.sub_pos_of_lt hk) F hF
  refine ⟨G, hG, ?_⟩
  intro M hM hmem
  have hh := hcover M hM (compoundTailIndex d k) hmem
  simpa only [compoundIndex_mem_tail, not_le, matrix_prefix_image_eq_range hk.le] using hh


end
end Bounty

end SubmissionComponent_CompoundPrefixRecovery

/- Component VaryingProfilePrefixFamilies; SHA256 547289eb7f89beb1ade727de55e1c63c382aaff003ca252b27b0d5713c022625 -/
section SubmissionComponent_VaryingProfilePrefixFamilies
/- Actual bounded compound profiles give a finite family of proper original prefix spans. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def exists_finite_varying_profile_prefix_family {d k : ℕ}
    (hkpos : 1 ≤ k) (hk : k < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : ℝ → Fin 3 → CompoundIndex d (d - k) → ℝ) (M ρ : ℝ) (hρ : 0 < ρ)
    (S : Set ℝ) (hS : ∀ q ∈ S, 0 ≤ q)
    (hcBound : ∀ q ∈ S, ∀ v i, |c q v i| ≤ M)
    (hcSum : ∀ q ∈ S, (∑ v, ∑ i, c q v i) ≤ -ρ)
    (H : ℝ → Matrix (Fin d) (Fin d) ℤ)
    (hH : ∀ q ∈ S, ((H q).map (Int.castRingHom ℚ)).det ≠ 0)
    (hInf : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      ‖(compoundMatrix (d - k) A * compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ))) i t‖ ≤
        Real.exp (c q 0 i * q))
    (hTwo : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 2 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 1 i * q))
    (hThree : ∀ q ∈ S, ∀ i t, t ≠ compoundTailIndex d k →
      (padicNorm 3 (compoundMatrix (d - k) ((H q).map (Int.castRingHom ℚ)) i t) : ℝ) ≤
        Real.exp (c q 2 i * q)) :
    ∃ G : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ G, V ≠ ⊤) ∧
      ∀ q ∈ S, Submodule.span ℚ (((H q).map (Int.castRingHom ℚ)).col '' {i | i.val < k}) ∈ G := by
  obtain ⟨F, hF, hcover⟩ := exists_finite_varying_profile_compound_tail_family
    hkpos hk A hA c M ρ hρ S hS hcBound hcSum H hH hInf hTwo hThree
  obtain ⟨G, hG, hprefix⟩ := finite_compound_prefix_recovery hk F hF
  refine ⟨G, hG, ?_⟩
  intro q hq
  have hh := hprefix ((H q).map (Int.castRingHom ℚ)) (hH q hq) (hcover q hq)
  simpa only [matrix_prefix_image_eq_range hk.le] using hh


end
end Bounty

end SubmissionComponent_VaryingProfilePrefixFamilies

/- Component ActualLocalValueBounds; SHA256 9e0824591f0829076dbf6db3287517e909c0db7c64e17a0b9aae1ee6a2796414 -/
section SubmissionComponent_ActualLocalValueBounds
/- Actual rational matrix values and finite-place coordinates lie in a
uniform logarithmic box. The constants depend only on the fixed matrix. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def matrixEntryBound {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) : ℝ :=
  1 + ∑ i, ∑ j, ‖A i j‖

def matrixEntryBound_ge_one {d : ℕ} (A : Matrix (Fin d) (Fin d) ℚ) :
    1 ≤ matrixEntryBound A := by
  have hh : 0 ≤ ∑ i, ∑ j, ‖A i j‖ := Finset.sum_nonneg (fun i _ => Finset.sum_nonneg (fun j _ => norm_nonneg _))
  unfold matrixEntryBound
  linarith

def rational_matrix_integer_norm_upper {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (x : Fin d → ℤ) (hx : x ≠ 0) (i : Fin d) :
    ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ matrixEntryBound A * integerVectorMax x := by
  have hH : 0 ≤ integerVectorMax x := (by norm_num : (0 : ℝ) ≤ 1).trans (integerVectorMax_ge_one x hx)
  have hrow : (∑ j, ‖A i j‖) ≤ matrixEntryBound A := by
    have hh : (∑ j, ‖A i j‖) ≤ ∑ k, ∑ j, ‖A k j‖ :=
      Finset.single_le_sum (fun k _ => Finset.sum_nonneg (fun j _ => norm_nonneg (A k j))) (Finset.mem_univ i)
    unfold matrixEntryBound
    linarith
  calc
    _ ≤ ∑ j, ‖A i j * (x j : ℚ)‖ := norm_sum_le _ _
    _ ≤ ∑ j, ‖A i j‖ * integerVectorMax x := by
      apply Finset.sum_le_sum
      intro j _
      rw [norm_mul, Int.norm_cast_rat, Int.norm_eq_abs]
      exact mul_le_mul_of_nonneg_left (integer_coord_abs_le_max x j) (norm_nonneg _)
    _ = (∑ j, ‖A i j‖) * integerVectorMax x := (Finset.sum_mul _ _ _).symm
    _ ≤ _ := mul_le_mul_of_nonneg_right hrow hH

def rational_matrix_integer_norm_lower {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (D : ℤ) (hD : 0 < D)
    (B : Matrix (Fin d) (Fin d) ℤ) (hB : ∀ i j, (B i j : ℚ) = (D : ℚ) * A i j)
    (x : Fin d → ℤ) (i : Fin d) (hi : A.mulVec (fun j => (x j : ℚ)) i ≠ 0) :
    1 / (D : ℝ) ≤ ‖A.mulVec (fun j => (x j : ℚ)) i‖ := by
  apply nonzero_rational_scaled_integer_norm_lower _ D (∑ j, B i j * x j) hD hi
  simp only [Matrix.mulVec, dotProduct, Finset.mul_sum, Int.cast_sum, Int.cast_mul, hB]
  apply Finset.sum_congr rfl
  intro j _
  ring

def actualThreePlaceValues {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (x : Fin d → ℤ) : Fin 3 → Fin d → ℝ :=
  ![(fun i => ‖A.mulVec (fun j => (x j : ℚ)) i‖),
    (fun i => (padicNorm 2 (x i : ℚ) : ℝ)),
    (fun i => (padicNorm 3 (x i : ℚ) : ℝ))]

def actualThreePlaceValues_finite_le_one {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) (x : Fin d → ℤ) :
    ∀ v i, v ≠ 0 → actualThreePlaceValues A x v i ≤ 1 := by
  intro v i hv
  fin_cases v
  · exact (hv rfl).elim
  · change (padicNorm 2 (x i : ℚ) : ℝ) ≤ 1
    exact_mod_cast padicNorm.of_int (p := 2) (x i)
  · change (padicNorm 3 (x i : ℚ) : ℝ) ≤ 1
    exact_mod_cast padicNorm.of_int (p := 3) (x i)

def exists_actual_three_place_log_bounds {d : ℕ}
    (A : Matrix (Fin d) (Fin d) ℚ) :
    ∃ M : ℝ, 1 ≤ M ∧ ∀ (q : ℝ) (x : Fin d → ℤ),
      1 ≤ q → x ≠ 0 → integerVectorMax x ≤ Real.exp q →
      (∀ i, x i ≠ 0) → (∀ i, A.mulVec (fun j => (x j : ℚ)) i ≠ 0) →
      ∀ v i, Real.exp (-M * q) ≤ actualThreePlaceValues A x v i ∧
        actualThreePlaceValues A x v i ≤ Real.exp (M * q) := by
  obtain ⟨D, hD, B, hB⟩ := exists_integer_scaled_rational_matrix A
  have hDr : (0 : ℝ) < D := by exact_mod_cast hD
  have hD1 : (1 : ℝ) ≤ D := by exact_mod_cast (show (1 : ℤ) ≤ D by omega)
  let C := matrixEntryBound A
  have hC1 : 1 ≤ C := matrixEntryBound_ge_one A
  have hC : 0 < C := lt_of_lt_of_le (by norm_num) hC1
  have hlogD : 0 ≤ Real.log (D : ℝ) := Real.log_nonneg hD1
  have hlogC : 0 ≤ Real.log C := Real.log_nonneg hC1
  let M : ℝ := 1 + Real.log (D : ℝ) + Real.log C
  have hM : 1 ≤ M := by dsimp [M]; linarith
  refine ⟨M, hM, ?_⟩
  intro q x hq hx hH hxn hAx v i
  have hq0 : 0 ≤ q := (by norm_num : (0 : ℝ) ≤ 1).trans hq
  have hM0 : 0 ≤ M := (by norm_num : (0 : ℝ) ≤ 1).trans hM
  have hMq : q ≤ M * q := by nlinarith
  have hH0 : 0 < integerVectorMax x := lt_of_lt_of_le (by norm_num) (integerVectorMax_ge_one x hx)
  have hloInf : Real.exp (-M * q) ≤ 1 / (D : ℝ) := by
    calc
      _ ≤ Real.exp (-Real.log (D : ℝ)) := Real.exp_le_exp.mpr (by
        have hMm : M ≤ M * q := by nlinarith
        dsimp [M] at hMm ⊢
        linarith)
      _ = _ := by rw [Real.exp_neg, Real.exp_log hDr, one_div]
  have hhiInf : C * Real.exp q ≤ Real.exp (M * q) := by
    calc
      _ = Real.exp (Real.log C + q) := by rw [Real.exp_add, Real.exp_log hC]
      _ ≤ _ := Real.exp_le_exp.mpr (by dsimp [M]; nlinarith)
  have hloFin (p : ℕ) (hp : p.Prime) :
      Real.exp (-M * q) ≤ (padicNorm p (x i : ℚ) : ℝ) := by
    calc
      _ ≤ Real.exp (-q) := Real.exp_le_exp.mpr (by linarith)
      _ = 1 / Real.exp q := by rw [Real.exp_neg, one_div]
      _ ≤ 1 / integerVectorMax x := one_div_le_one_div_of_le hH0 hH
      _ ≤ _ := padicNorm_integer_le_height_reciprocal p hp x i (hxn i)
  have hhiFin (p : ℕ) [Fact p.Prime] :
      (padicNorm p (x i : ℚ) : ℝ) ≤ Real.exp (M * q) := by
    have hh : (padicNorm p (x i : ℚ) : ℝ) ≤ 1 := by exact_mod_cast padicNorm.of_int (p := p) (x i)
    exact hh.trans (Real.one_le_exp (mul_nonneg hM0 hq0))
  fin_cases v
  · exact ⟨hloInf.trans (rational_matrix_integer_norm_lower A D hD B hB x i (hAx i)),
      (rational_matrix_integer_norm_upper A x hx i).trans
        ((mul_le_mul_of_nonneg_left hH hC.le).trans hhiInf)⟩
  · exact ⟨hloFin 2 (by norm_num), hhiFin 2⟩
  · exact ⟨hloFin 3 (by norm_num), hhiFin 3⟩

def primitive_integer_mulHeight {d : ℕ} (hd : 0 < d)
    (x : Fin d → ℤ) (hx : Finset.univ.gcd x = 1) :
    Height.mulHeight (fun i => (x i : ℚ)) = integerVectorMax x := by
  let : NeZero d := ⟨hd.ne'⟩
  exact Rat.mulHeight_eq_max_abs_of_gcd_eq_one hx

def primitive_integer_exp_logHeight {d : ℕ} (hd : 0 < d)
    (x : Fin d → ℤ) (hx : Finset.univ.gcd x = 1) :
    Real.exp (Height.logHeight (fun i => (x i : ℚ))) = integerVectorMax x := by
  rw [Height.logHeight_eq_log_mulHeight, Real.exp_log (Height.mulHeight_pos _)]
  exact primitive_integer_mulHeight hd x hx


end
end Bounty

end SubmissionComponent_ActualLocalValueBounds

/- Component ActualProductProfiles; SHA256 f89629e531498930902081c66e4ce99bd6d6ef3e3e5876a1ba69f28924b36691 -/
section SubmissionComponent_ActualProductProfiles
/- Fixed finite exponent profiles for actual local values of primitive
integer points, with the parameter equal to their projective log height. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def exists_finite_actual_three_place_profiles {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (ρ : ℝ) (hρ : 0 < ρ) :
    ∃ M : ℝ, 1 ≤ M ∧ ∃ C : Finset (Fin 3 → Fin d → ℝ),
      (∀ c ∈ C, (∀ v i, |c v i| ≤ M + ρ / (6 * d)) ∧
        (∑ v, ∑ i, c v i) ≤ -ρ / 2 ∧ (∀ v i, v ≠ 0 → c v i ≤ 0)) ∧
      ∀ (q : ℝ) (x : Fin d → ℤ), 1 ≤ q → x ≠ 0 →
        integerVectorMax x ≤ Real.exp q →
        (∀ i, x i ≠ 0) → (∀ i, A.mulVec (fun j => (x j : ℚ)) i ≠ 0) →
        (∏ v, ∏ i, actualThreePlaceValues A x v i) ≤ Real.exp (-ρ * q) →
        ∃ c ∈ C, ∀ v i, actualThreePlaceValues A x v i ≤ Real.exp (c v i * q) := by
  obtain ⟨M, hM, hb⟩ := exists_actual_three_place_log_bounds A
  obtain ⟨C, hC, hcover⟩ := exists_finite_three_place_product_profiles d hd M ρ hρ
  refine ⟨M, hM, C, hC, ?_⟩
  intro q x hq hx hH hxn hAx hprod
  have hbounds := hb q x hq hx hH hxn hAx
  exact hcover q (actualThreePlaceValues A x) (lt_of_lt_of_le (by norm_num) hq)
    (fun v i => (hbounds v i).1) (fun v i => (hbounds v i).2) hprod
    (actualThreePlaceValues_finite_le_one A x)

def exists_finite_primitive_three_place_profiles {d : ℕ} (hd : 0 < d)
    (A : Matrix (Fin d) (Fin d) ℚ) (ρ : ℝ) (hρ : 0 < ρ) :
    ∃ M : ℝ, 1 ≤ M ∧ ∃ C : Finset (Fin 3 → Fin d → ℝ),
      (∀ c ∈ C, (∀ v i, |c v i| ≤ M + ρ / (6 * d)) ∧
        (∑ v, ∑ i, c v i) ≤ -ρ / 2 ∧ (∀ v i, v ≠ 0 → c v i ≤ 0)) ∧
      ∀ x : Fin d → ℤ, Finset.univ.gcd x = 1 →
        1 ≤ Height.logHeight (fun i => (x i : ℚ)) →
        (∀ i, x i ≠ 0) → (∀ i, A.mulVec (fun j => (x j : ℚ)) i ≠ 0) →
        (∏ v, ∏ i, actualThreePlaceValues A x v i) ≤
          Height.mulHeight (fun i => (x i : ℚ)) ^ (-ρ) →
        ∃ c ∈ C, ∀ v i, actualThreePlaceValues A x v i ≤
          Real.exp (c v i * Height.logHeight (fun i => (x i : ℚ))) := by
  obtain ⟨M, hM, C, hC, hcover⟩ := exists_finite_actual_three_place_profiles hd A ρ hρ
  refine ⟨M, hM, C, hC, ?_⟩
  intro x hprim hq hxn hAx hprod
  have hx : x ≠ 0 := by
    intro h
    exact hxn ⟨0, hd⟩ (congrFun h ⟨0, hd⟩)
  have hprod' : (∏ v, ∏ i, actualThreePlaceValues A x v i) ≤
      Real.exp (-ρ * Height.logHeight (fun i => (x i : ℚ))) := by
    convert hprod using 1
    rw [Real.rpow_def_of_pos (Height.mulHeight_pos _), Height.logHeight_eq_log_mulHeight]
    congr 1
    ring
  exact hcover _ x hq hx (primitive_integer_exp_logHeight hd x hprim).ge hxn hAx hprod'


end
end Bounty

end SubmissionComponent_ActualProductProfiles

/- Component FiniteEventGap; SHA256 2a751e67763f8e1e3084fdcbc7f65f0fc1c289decdc2ba54c7a6c124cfaa4b8c -/
section SubmissionComponent_FiniteEventGap
/- A fixed-size empty interval among at most 48 event times. -/

namespace Bounty

def finite_events_gap (E : Finset ℝ) (hcard : E.card ≤ 48) {L : ℝ}
    (hL : 0 < L) (a : ℝ) :
    ∃ t : ℝ, a < t ∧ t + L / 0x64 < a + L ∧
      ∀ x ∈ E, x < t ∨ t + L / 0x64 < x := by
  classical
  let t : Fin 50 → ℝ := fun j => a + (4 * (j.val : ℝ) + 1) * L / 0xc8
  have hsep {i j : Fin 50} (hij : i.val < j.val) : t i + L / 0x64 < t j := by
    have hR : (i.val : ℝ) + 1 ≤ j.val := by exact_mod_cast (Nat.succ_le_of_lt hij)
    have hp := mul_le_mul_of_nonneg_right hR hL.le
    dsimp only [t]
    nlinarith
  have hgap : ∃ j : Fin 50, ∀ x ∈ E, x < t j ∨ t j + L / 0x64 < x := by
    by_contra hh
    push_neg at hh
    let f : Fin 50 → E := fun j => ⟨(hh j).choose, (hh j).choose_spec.1⟩
    have hf (j : Fin 50) : t j ≤ (f j : ℝ) ∧ (f j : ℝ) ≤ t j + L / 0x64 :=
      (hh j).choose_spec.2
    have hinj : Function.Injective f := by
      intro i j hij
      apply Fin.ext
      have he : (f i : ℝ) = (f j : ℝ) := congrArg Subtype.val hij
      have hi := hf i
      have hj := hf j
      by_contra hne
      rcases lt_or_gt_of_ne hne with hlt | hgt
      · have hs := hsep hlt
        linarith
      · have hs := hsep hgt
        linarith
    have hc : 50 ≤ E.card := by
      simpa using Fintype.card_le_of_injective f hinj
    omega
  obtain ⟨j, hj⟩ := hgap
  refine ⟨t j, ?_, ?_, hj⟩
  · have hj0 : (0 : ℝ) ≤ j.val := Nat.cast_nonneg _
    have hp := mul_nonneg hj0 hL.le
    dsimp only [t]
    nlinarith
  · have hj49 : (j.val : ℝ) ≤ 49 := by exact_mod_cast (by have hh := j.isLt; omega : j.val ≤ 49)
    have hp := mul_le_mul_of_nonneg_right hj49 hL.le
    dsimp only [t]
    nlinarith

end Bounty

end SubmissionComponent_FiniteEventGap

/- Component SeparatedEventCount; SHA256 3e9cc6c7b4f5e8642d0f5bee936d390507a410aaa0aabd233309789a25d43e77 -/
section SubmissionComponent_SeparatedEventCount
/- Count event times separated by half the window length. -/

namespace Bounty

def separated_events_card_le_three (E : Finset ℝ) {a L : ℝ} (hL : 0 < L)
    (hbounds : ∀ x ∈ E, a ≤ x ∧ x ≤ a + L)
    (hsep : ∀ x ∈ E, ∀ y ∈ E, x ≠ y → L / 2 ≤ |x - y|) : E.card ≤ 3 := by
  classical
  have hz (x : E) : 0 ≤ 2 * ((x : ℝ) - a) / L ∧ 2 * ((x : ℝ) - a) / L ≤ 2 := by
    have hx := hbounds x x.property
    constructor
    · exact div_nonneg (by linarith) hL.le
    · apply (div_le_iff₀ hL).mpr
      linarith
  let f : E → ↥(Finset.Icc (0 : ℤ) 2) := fun x =>
    ⟨⌊2 * ((x : ℝ) - a) / L⌋, Finset.mem_Icc.mpr
      ⟨Int.floor_nonneg.mpr (hz x).1, Int.floor_le_iff.mpr (by
        norm_num only [Int.cast_ofNat]
        linarith [(hz x).2])⟩⟩
  have hinj : Function.Injective f := by
    intro x y hf
    apply Subtype.ext
    by_contra hxy
    have heq : ⌊2 * ((x : ℝ) - a) / L⌋ = ⌊2 * ((y : ℝ) - a) / L⌋ :=
      congrArg Subtype.val hf
    have hh := Int.abs_sub_lt_one_of_floor_eq_floor heq
    have he : 2 * ((x : ℝ) - a) / L - 2 * ((y : ℝ) - a) / L =
        2 * ((x : ℝ) - y) / L := by ring
    rw [he, abs_div, abs_mul, abs_of_pos hL] at hh
    norm_num at hh
    have hsmall := (div_lt_iff₀ hL).mp hh
    have hlarge := hsep x x.property y y.property hxy
    linarith
  have hc := Fintype.card_le_of_injective f hinj
  simpa using hc

end Bounty

end SubmissionComponent_SeparatedEventCount

/- Component LinearEventWindows; SHA256 bbe21ef6c1c85bfeec8e6c48b48fda451fb6cc20db19df9c45f5f973f8b067e0 -/
section SubmissionComponent_LinearEventWindows
/- Finite windows of linearly indexed events and simultaneous gaps for finitely many families. -/

namespace Bounty

noncomputable def linearEventWindow (step offset a b : ℝ) (visit : ℕ → Prop) : Finset ℝ := by
  classical
  exact ((Finset.range (⌈(b + offset) / step⌉₊ + 1)).filter
    (fun n => visit n ∧ a ≤ (n : ℝ) * step - offset ∧ (n : ℝ) * step - offset ≤ b)).image
      (fun n : ℕ => (n : ℝ) * step - offset)

def mem_linearEventWindow {step offset a b x : ℝ} {visit : ℕ → Prop}
    (hstep : 0 < step) :
    x ∈ linearEventWindow step offset a b visit ↔
      ∃ n : ℕ, visit n ∧ x = (n : ℝ) * step - offset ∧ a ≤ x ∧ x ≤ b := by
  classical
  constructor
  · intro hx
    obtain ⟨n, hn, he⟩ := Finset.mem_image.mp hx
    obtain ⟨_, hv, hlo, hhi⟩ := Finset.mem_filter.mp hn
    exact ⟨n, hv, he.symm, he ▸ hlo, he ▸ hhi⟩
  · rintro ⟨n, hv, rfl, hlo, hhi⟩
    have hnr : (n : ℝ) ≤ (b + offset) / step := (le_div_iff₀ hstep).mpr (by linarith)
    have hn : n ≤ ⌈(b + offset) / step⌉₊ := by
      exact_mod_cast hnr.trans (Nat.le_ceil _)
    exact Finset.mem_image.mpr ⟨n, Finset.mem_filter.mpr
      ⟨Finset.mem_range.mpr (by omega), hv, hlo, hhi⟩, rfl⟩

def linearEventWindow_card {step offset a L : ℝ} {visit : ℕ → Prop}
    (hstep : 0 < step) (hL : 0 < L)
    (hsep : ∀ m n : ℕ, visit m → visit n → m < n →
      L / 2 ≤ (n : ℝ) * step - (m : ℝ) * step) :
    (linearEventWindow step offset a (a + L) visit).card ≤ 3 := by
  apply separated_events_card_le_three _ hL
  · intro x hx
    obtain ⟨n, hv, he, hlo, hhi⟩ := (mem_linearEventWindow hstep).mp hx
    exact ⟨hlo, hhi⟩
  · intro x hx y hy hxy
    obtain ⟨m, hm, rfl, _, _⟩ := (mem_linearEventWindow hstep).mp hx
    obtain ⟨n, hn, rfl, _, _⟩ := (mem_linearEventWindow hstep).mp hy
    have hmn : m ≠ n := by rintro rfl; exact hxy rfl
    rcases lt_or_gt_of_ne hmn with hlt | hgt
    · have hh := hsep m n hm hn hlt
      have ha := neg_le_abs (((m : ℝ) * step - offset) - ((n : ℝ) * step - offset))
      linarith
    · have hh := hsep n m hn hm hgt
      have ha := le_abs_self (((m : ℝ) * step - offset) - ((n : ℝ) * step - offset))
      linarith

def linear_event_families_gap {ι : Type*} [Fintype ι]
    (hcard : Fintype.card ι ≤ 16) (step offset : ι → ℝ) (visit : ι → ℕ → Prop)
    (hstep : ∀ i, 0 < step i) {L : ℝ} (hL : 0 < L)
    (hsep : ∀ i m n, visit i m → visit i n → m < n →
      L / 2 ≤ (n : ℝ) * step i - (m : ℝ) * step i) (a : ℝ) :
    ∃ t : ℝ, a < t ∧ t + L / 0x64 < a + L ∧
      ∀ i n, visit i n → (n : ℝ) * step i - offset i < t ∨
        t + L / 0x64 < (n : ℝ) * step i - offset i := by
  classical
  let E (i : ι) := linearEventWindow (step i) (offset i) a (a + L) (visit i)
  have hc (i : ι) : (E i).card ≤ 3 := linearEventWindow_card (hstep i) hL (hsep i)
  have htotal : (Finset.univ.biUnion E).card ≤ 48 := by
    calc
      (Finset.univ.biUnion E).card ≤ ∑ i ∈ Finset.univ, (E i).card := Finset.card_biUnion_le
      _ ≤ ∑ i ∈ (Finset.univ : Finset ι), 3 := Finset.sum_le_sum (fun i _ => hc i)
      _ = 3 * Fintype.card ι := by simp [mul_comm]
      _ ≤ 48 := by omega
  obtain ⟨t, hlo, hhi, hgap⟩ := finite_events_gap (Finset.univ.biUnion E) htotal hL a
  refine ⟨t, hlo, hhi, ?_⟩
  intro i n hv
  by_cases hna : a ≤ (n : ℝ) * step i - offset i
  · by_cases hnb : (n : ℝ) * step i - offset i ≤ a + L
    · have hm : (n : ℝ) * step i - offset i ∈ E i :=
        (mem_linearEventWindow (hstep i)).mpr ⟨n, hv, rfl, hna, hnb⟩
      exact hgap _ (Finset.mem_biUnion.mpr ⟨i, Finset.mem_univ i, hm⟩)
    · exact Or.inr (hhi.trans (lt_of_not_ge hnb))
  · exact Or.inl ((lt_of_not_ge hna).trans hlo)


end Bounty

end SubmissionComponent_LinearEventWindows

/- Component CoprimeCount; SHA256 d3495edc8911ccfeed9ad95a1ddfd61d334116e615f37cd5a7c52791c29af056 -/
section SubmissionComponent_CoprimeCount
/- Exact counts of the cores, and a uniform error from density one third. -/

namespace Bounty

def coprime_six_iff_mod (n : ℕ) : n.Coprime 6 ↔ n % 6 = 1 ∨ n % 6 = 5 := by
  rw [Nat.coprime_iff_gcd_eq_one, Nat.gcd_comm n 6, Nat.gcd_rec]
  have hmod : n % 6 < 6 := Nat.mod_lt _ (by omega)
  interval_cases hm : n % 6 <;> norm_num

def coprimeCores_succ (n : ℕ) :
    coprimeCores (n + 1) = if (n + 1).Coprime 6 then insert (n + 1) (coprimeCores n)
      else coprimeCores n := by
  ext q
  by_cases hc : (n + 1).Coprime 6
  · simp only [if_pos hc, coprimeCores, Finset.mem_filter, Finset.mem_Icc, Finset.mem_insert]
    constructor
    · rintro ⟨⟨hq1, hqn⟩, hq6⟩
      by_cases he : q = n + 1
      · exact Or.inl he
      · exact Or.inr ⟨⟨hq1, by omega⟩, hq6⟩
    · rintro (rfl | ⟨⟨hq1, hqn⟩, hq6⟩)
      · exact ⟨⟨by omega, le_rfl⟩, hc⟩
      · exact ⟨⟨hq1, by omega⟩, hq6⟩
  · simp only [if_neg hc, coprimeCores, Finset.mem_filter, Finset.mem_Icc]
    constructor
    · rintro ⟨⟨hq1, hqn⟩, hq6⟩
      have he : q ≠ n + 1 := by intro hh; apply hc; simpa only [← hh] using hq6
      exact ⟨⟨hq1, by omega⟩, hq6⟩
    · rintro ⟨⟨hq1, hqn⟩, hq6⟩
      exact ⟨⟨hq1, by omega⟩, hq6⟩

def coprimeCores_card_succ (n : ℕ) :
    (coprimeCores (n + 1)).card = (coprimeCores n).card + if (n + 1).Coprime 6 then 1 else 0 := by
  rw [coprimeCores_succ]
  have hn : n + 1 ∉ coprimeCores n := by simp [coprimeCores]
  by_cases hc : (n + 1).Coprime 6
  · rw [if_pos hc, if_pos hc, Finset.card_insert_of_notMem hn]
  · simp only [if_neg hc, Nat.add_zero]

def coprimeCores_card (n : ℕ) :
    (coprimeCores n).card = (n + 5) / 6 + (n + 1) / 6 := by
  induction n with
  | zero => norm_num [coprimeCores]
  | succ n ih =>
    rw [coprimeCores_card_succ, ih]
    simp only [coprime_six_iff_mod]
    split_ifs <;> omega

def coprimeCores_card_error (n : ℕ) :
    |(coprimeCores n).card - (n : ℝ) / 3| ≤ 1 := by
  have hcount := coprimeCores_card n
  have hlo : n ≤ 3 * (coprimeCores n).card + 3 := by omega
  have hhi : 3 * (coprimeCores n).card ≤ n + 3 := by omega
  have hlo' : (n : ℝ) ≤ 3 * (coprimeCores n).card + 3 := by exact_mod_cast hlo
  have hhi' : (3 : ℝ) * (coprimeCores n).card ≤ n + 3 := by exact_mod_cast hhi
  rw [abs_le]
  constructor <;> linarith


end Bounty

end SubmissionComponent_CoprimeCount

/- Component CoreConvolution; SHA256 8fda3cecf413fae36aeb718236e89c2e458b686f124119f34b2049d30b18ee99 -/
section SubmissionComponent_CoreConvolution
/- Write the extremal bound as a signed convolution with the core-count function. -/

namespace Bounty

noncomputable def signedRank (n : ℕ) : ℝ := by
  classical
  exact (smoothRankBound n : ℝ) - if badWindow n then 1 else 0

def signedRank_zero : signedRank 0 = 0 := by
  have hb : ¬badWindow 0 := by intro h; have hh := badWindow_ge_ten h; omega
  simp [signedRank, hb, smoothRankBound]

def globalUpper_cast_sum (n : ℕ) :
    (globalUpper n : ℝ) = ∑ q ∈ coprimeCores n, signedRank (n / q) := by
  classical
  have hle : (lossCores n).card ≤ ∑ q ∈ coprimeCores n, smoothRankBound (n / q) := by
    have hh := forkFree_card_with_losses (n := n) (A := ∅) (by simp)
      (by simpa only [Finset.coe_empty] using forkFree_empty)
    simpa only [Finset.card_empty, zero_add] using hh
  unfold globalUpper
  rw [Nat.cast_sub hle]
  simp only [lossCores, Finset.card_filter, Nat.cast_sum]
  rw [← Finset.sum_sub_distrib]
  apply Finset.sum_congr rfl
  intro q hq
  by_cases hb : badWindow (n / q) <;> simp [signedRank, hb]

def sum_rank_jumps (g : ℕ → ℝ) (hg : g 0 = 0) (n m : ℕ) (hm : m ≤ n) :
    g m = ∑ j ∈ Finset.range n, if j < m then g (j + 1) - g j else 0 := by
  have he : (Finset.range n).filter (fun j => j < m) = Finset.range m := by
    ext j
    simp only [Finset.mem_filter, Finset.mem_range]
    omega
  rw [← Finset.sum_filter, he, Finset.sum_range_sub, hg, sub_zero]

def coprimeCores_filter_quotient (n j : ℕ) :
    (coprimeCores n).filter (fun q => j < n / q) = coprimeCores (n / (j + 1)) := by
  ext q
  simp only [coprimeCores, Finset.mem_filter, Finset.mem_Icc]
  constructor
  · rintro ⟨⟨⟨hq1, _⟩, hq6⟩, hj⟩
    have hm : (j + 1) * q ≤ n := (Nat.le_div_iff_mul_le hq1).mp (by omega)
    have hqhi : q ≤ n / (j + 1) :=
      (Nat.le_div_iff_mul_le (Nat.succ_pos j)).mpr (by simpa only [Nat.mul_comm] using hm)
    exact ⟨⟨hq1, hqhi⟩, hq6⟩
  · rintro ⟨⟨hq1, hqhi⟩, hq6⟩
    have hm : q * (j + 1) ≤ n := (Nat.le_div_iff_mul_le (Nat.succ_pos j)).mp hqhi
    have hj : j + 1 ≤ n / q :=
      (Nat.le_div_iff_mul_le hq1).mpr (by simpa only [Nat.mul_comm] using hm)
    exact ⟨⟨⟨hq1, hqhi.trans (Nat.div_le_self _ _)⟩, hq6⟩, by omega⟩

def sum_over_cores_eq_jumps (g : ℕ → ℝ) (hg : g 0 = 0) (n : ℕ) :
    (∑ q ∈ coprimeCores n, g (n / q)) =
      ∑ j ∈ Finset.range n, (g (j + 1) - g j) * ((coprimeCores (n / (j + 1))).card : ℝ) := by
  classical
  calc
    (∑ q ∈ coprimeCores n, g (n / q)) =
        ∑ q ∈ coprimeCores n, ∑ j ∈ Finset.range n,
          if j < n / q then g (j + 1) - g j else 0 := by
      apply Finset.sum_congr rfl
      intro q hq
      exact sum_rank_jumps g hg n (n / q) (Nat.div_le_self n q)
    _ = ∑ j ∈ Finset.range n, ∑ q ∈ coprimeCores n,
          if j < n / q then g (j + 1) - g j else 0 := Finset.sum_comm
    _ = _ := by
      apply Finset.sum_congr rfl
      intro j hj
      rw [← Finset.sum_filter, coprimeCores_filter_quotient]
      simp only [Finset.sum_const, nsmul_eq_mul, mul_comm]

noncomputable def signedRankJump (j : ℕ) : ℝ := signedRank (j + 1) - signedRank j

def globalUpper_cast_jumps (n : ℕ) :
    (globalUpper n : ℝ) = ∑ j ∈ Finset.range n,
      signedRankJump j * ((coprimeCores (n / (j + 1))).card : ℝ) := by
  rw [globalUpper_cast_sum, sum_over_cores_eq_jumps signedRank signedRank_zero]
  rfl


end Bounty

end SubmissionComponent_CoreConvolution

/- Component ObstructionJumps; SHA256 98ee629ddd001c1b697421382d013d544107233c299e4a1b0766a16b39d4ecb7 -/
section SubmissionComponent_ObstructionJumps
/- Changes in the obstruction indicator occur on four geometric sequences. -/

namespace Bounty

noncomputable def obstructionIndicator (n : ℕ) : ℝ := by
  classical
  exact if badWindow n then 1 else 0

def obstructionEndpoint (m : ℕ) : Prop :=
  (∃ j, m = 4 ^ j) ∨ (∃ j, m = 5 * 4 ^ j) ∨
    (∃ b, m = 10 * 3 ^ b) ∨ (∃ b, m = 12 * 3 ^ b)

def badWindow_enter {n : ℕ} (hn : ¬badWindow n) (hs : badWindow (n + 1)) :
    (∃ j, n + 1 = 4 ^ j) ∨ (∃ b, n + 1 = 10 * 3 ^ b) := by
  obtain ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩ := hs
  by_cases he4 : n + 1 = 4 ^ j
  · exact Or.inl ⟨j, he4⟩
  by_cases he3 : n + 1 = 10 * 3 ^ b
  · exact Or.inr ⟨b, he3⟩
  exact (hn ⟨j, b, by omega, by omega, by omega, by omega⟩).elim

def badWindow_exit {n : ℕ} (hn : badWindow n) (hs : ¬badWindow (n + 1)) :
    (∃ j, n + 1 = 5 * 4 ^ j) ∨ (∃ b, n + 1 = 12 * 3 ^ b) := by
  obtain ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩ := hn
  have h3pos : 0 < (3 : ℕ) ^ b := by positivity
  have hj : j ≠ 0 := by
    intro he
    simp only [he, pow_zero] at h4hi
    omega
  obtain ⟨j, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hj
  have h4pow : (4 : ℕ) ^ (j + 1) = 4 ^ j * 4 := pow_succ 4 j
  by_cases he4 : n + 1 = 5 * 4 ^ j
  · exact Or.inl ⟨j, he4⟩
  by_cases he3 : n + 1 = 12 * 3 ^ b
  · exact Or.inr ⟨b, he3⟩
  exact (hs ⟨j + 1, b, by omega, by omega, by omega, by omega⟩).elim

def obstruction_change_endpoint {n : ℕ}
    (h : obstructionIndicator (n + 1) ≠ obstructionIndicator n) : obstructionEndpoint (n + 1) := by
  classical
  by_cases hs : badWindow (n + 1)
  · by_cases hn : badWindow n
    · exact (h (by simp [obstructionIndicator, hn, hs])).elim
    · rcases badWindow_enter hn hs with h4 | h3
      · exact Or.inl h4
      · exact Or.inr (Or.inr (Or.inl h3))
  · by_cases hn : badWindow n
    · rcases badWindow_exit hn hs with h4 | h3
      · exact Or.inr (Or.inl h4)
      · exact Or.inr (Or.inr (Or.inr h3))
    · exact (h (by simp [obstructionIndicator, hn, hs])).elim

def obstruction_jump_abs_le_one (n : ℕ) :
    |obstructionIndicator (n + 1) - obstructionIndicator n| ≤ 1 := by
  classical
  by_cases hs : badWindow (n + 1) <;> by_cases hn : badWindow n <;>
    norm_num [obstructionIndicator, hn, hs]


end Bounty

end SubmissionComponent_ObstructionJumps

/- Component GeometricSupport; SHA256 fe012c70b951305de3c432c8e1992cd49aa85e02a370e7be8a3e5ef6c65ff895 -/
section SubmissionComponent_GeometricSupport
/- Weighted indicators of geometric sets, and summability of obstruction jumps. -/

namespace Bounty

noncomputable def geometricEndpointTerm (a b m : ℕ) : ℝ := by
  classical
  exact if ∃ j, m = a * b ^ j then 1 / (m : ℝ) else 0

def geometricEndpointTerm_nonneg (a b m : ℕ) : 0 ≤ geometricEndpointTerm a b m := by
  classical
  unfold geometricEndpointTerm
  split_ifs <;> positivity

def geometricEndpointTerm_at {a b m : ℕ} (h : ∃ j, m = a * b ^ j) :
    geometricEndpointTerm a b m = 1 / (m : ℝ) := by
  classical
  simp only [geometricEndpointTerm, if_pos h]

def geometricEndpointTerm_summable {a b : ℕ} (ha : 0 < a) (hb : 1 < b) :
    Summable (geometricEndpointTerm a b) := by
  classical
  have hi : Function.Injective (fun j : ℕ => a * b ^ j) := by
    intro i j hij
    apply Nat.pow_right_injective (by omega : 2 ≤ b)
    nlinarith
  apply (hi.summable_iff (f := geometricEndpointTerm a b) ?_).mp
  · have hs : Summable (fun j : ℕ => (1 / (a : ℝ)) / (b : ℝ) ^ j) :=
      weighted_summable (by exact_mod_cast hb) (fun _ => le_refl |1 / (a : ℝ)|)
    apply hs.congr
    intro j
    simp only [Function.comp_apply, geometricEndpointTerm_at ⟨j, rfl⟩,
      Nat.cast_mul, Nat.cast_pow, div_div]
  · intro m hm
    have hn : ¬∃ j, m = a * b ^ j := by simpa only [Set.mem_range, eq_comm] using hm
    simp only [geometricEndpointTerm, if_neg hn]

def geometricEndpointTerm_summable_shift {a b : ℕ} (ha : 0 < a) (hb : 1 < b) :
    Summable (fun n : ℕ => geometricEndpointTerm a b (n + 1)) :=
  (summable_nat_add_iff 1).mpr (geometricEndpointTerm_summable ha hb)

def obstruction_jump_geometric_bound (n : ℕ) :
    |obstructionIndicator (n + 1) - obstructionIndicator n| / (n + 1 : ℕ) ≤
      geometricEndpointTerm 1 4 (n + 1) + geometricEndpointTerm 5 4 (n + 1) +
        geometricEndpointTerm 10 3 (n + 1) + geometricEndpointTerm 12 3 (n + 1) := by
  have h1 := geometricEndpointTerm_nonneg 1 4 (n + 1)
  have h5 := geometricEndpointTerm_nonneg 5 4 (n + 1)
  have h10 := geometricEndpointTerm_nonneg 10 3 (n + 1)
  have h12 := geometricEndpointTerm_nonneg 12 3 (n + 1)
  by_cases he : obstructionIndicator (n + 1) = obstructionIndicator n
  · simp only [he, sub_self, abs_zero, zero_div]
    linarith
  · have hb := div_le_div_of_nonneg_right (obstruction_jump_abs_le_one n)
      (Nat.cast_nonneg (α := ℝ) (n + 1))
    rcases obstruction_change_endpoint he with h | h | h | h
    · have ht := geometricEndpointTerm_at (a := 1) (b := 4) (by simpa only [one_mul] using h)
      linarith
    · have ht := geometricEndpointTerm_at h
      linarith
    · have ht := geometricEndpointTerm_at h
      linarith
    · have ht := geometricEndpointTerm_at h
      linarith

def obstruction_jumps_summable :
    Summable (fun n : ℕ => |obstructionIndicator (n + 1) - obstructionIndicator n| / (n + 1 : ℕ)) := by
  have h1 := geometricEndpointTerm_summable_shift (a := 1) (b := 4) (by norm_num) (by norm_num)
  have h5 := geometricEndpointTerm_summable_shift (a := 5) (b := 4) (by norm_num) (by norm_num)
  have h10 := geometricEndpointTerm_summable_shift (a := 10) (b := 3) (by norm_num) (by norm_num)
  have h12 := geometricEndpointTerm_summable_shift (a := 12) (b := 3) (by norm_num) (by norm_num)
  apply (((h1.add h5).add h10).add h12).of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_of_nonneg (by positivity :
    0 ≤ |obstructionIndicator (n + 1) - obstructionIndicator n| / (n + 1 : ℕ))]
  exact obstruction_jump_geometric_bound n


end Bounty

end SubmissionComponent_GeometricSupport

/- Component RankJumps; SHA256 bc15f246c20c419c82f9b29f9d97eca9e81b4ceecb888445aea0284ee5e7def8 -/
section SubmissionComponent_RankJumps
/- Rank jumps have bounded size and lie on three geometric sequences. -/

namespace Bounty

def rankEndpoint (m : ℕ) : Prop :=
  (∃ j, m = 2 ^ j) ∨ (∃ j, m = 3 ^ j) ∨ (∃ j, m = 2 * 3 ^ j)

def nat_log_succ_eq_of_not_power {b n : ℕ} (hb : 1 < b)
    (he : n + 1 ≠ b ^ Nat.log b (n + 1)) : Nat.log b (n + 1) = Nat.log b n := by
  have hlo := Nat.pow_log_le_self b (Nat.succ_ne_zero n)
  have hhi := Nat.lt_pow_succ_log_self hb (n + 1)
  simp only [Nat.succ_eq_add_one] at hlo hhi
  symm
  exact Nat.log_eq_of_pow_le_of_lt_pow (by omega) (by omega)

def nat_log_succ_bounds {b n : ℕ} (hb : 1 < b) (hn : 0 < n) :
    Nat.log b n ≤ Nat.log b (n + 1) ∧ Nat.log b (n + 1) ≤ Nat.log b n + 1 := by
  constructor
  · exact Nat.log_mono_right (by omega)
  · have hnle : n + 1 ≤ n * b := by nlinarith
    have hh := Nat.log_mono_right (b := b) hnle
    rwa [Nat.log_mul_base hb (ne_of_gt hn)] at hh

def smoothRank_change_endpoint {n : ℕ}
    (h : smoothRankBound (n + 1) ≠ smoothRankBound n) : rankEndpoint (n + 1) := by
  by_cases hn : n = 0
  · subst n
    exact Or.inl ⟨0, by norm_num⟩
  by_cases h2 : n + 1 = 2 ^ Nat.log 2 (n + 1)
  · exact Or.inl ⟨_, h2⟩
  by_cases h3 : n + 1 = 3 ^ Nat.log 3 (n + 1)
  · exact Or.inr (Or.inl ⟨_, h3⟩)
  by_cases he : n + 1 = 2 * 3 ^ Nat.log 3 n
  · exact Or.inr (Or.inr ⟨_, he⟩)
  have hl2 := nat_log_succ_eq_of_not_power (by norm_num : 1 < 2) h2
  have hl3 := nat_log_succ_eq_of_not_power (by norm_num : 1 < 3) h3
  have hc : (2 * 3 ^ Nat.log 3 n ≤ n + 1) ↔ (2 * 3 ^ Nat.log 3 n ≤ n) := by omega
  apply False.elim
  apply h
  simp only [smoothRankBound, hn, Nat.succ_ne_zero, ↓reduceIte, hl2, hl3, hc]

def smoothRank_succ_bounds (n : ℕ) :
    smoothRankBound (n + 1) ≤ smoothRankBound n + 3 ∧
      smoothRankBound n ≤ smoothRankBound (n + 1) + 3 := by
  by_cases hn : n = 0
  · subst n
    norm_num [smoothRankBound]
  have h2 := nat_log_succ_bounds (b := 2) (by norm_num) (by omega : 0 < n)
  have h3 := nat_log_succ_bounds (b := 3) (by norm_num) (by omega : 0 < n)
  simp only [smoothRankBound, hn, Nat.succ_ne_zero, ↓reduceIte]
  split_ifs <;> omega

def smoothRank_jump_abs (n : ℕ) :
    |(smoothRankBound (n + 1) : ℝ) - smoothRankBound n| ≤ 3 := by
  have hh := smoothRank_succ_bounds n
  have hlo : (smoothRankBound (n + 1) : ℝ) ≤ smoothRankBound n + 3 := by exact_mod_cast hh.1
  have hhi : (smoothRankBound n : ℝ) ≤ smoothRankBound (n + 1) + 3 := by exact_mod_cast hh.2
  rw [abs_le]
  constructor <;> linarith


end Bounty

end SubmissionComponent_RankJumps

/- Component JumpSummability; SHA256 fd83812df6869dbb62b2b08ed3d540559b8755bdab642a09f419f6ff42ea744c -/
section SubmissionComponent_JumpSummability
/- Absolute weighted summability of every jump in the exact extremal formula. -/

namespace Bounty

def rank_jump_geometric_bound (n : ℕ) :
    |(smoothRankBound (n + 1) : ℝ) - smoothRankBound n| / (n + 1 : ℕ) ≤
      3 * (geometricEndpointTerm 1 2 (n + 1) + geometricEndpointTerm 1 3 (n + 1) +
        geometricEndpointTerm 2 3 (n + 1)) := by
  have h2 := geometricEndpointTerm_nonneg 1 2 (n + 1)
  have h3 := geometricEndpointTerm_nonneg 1 3 (n + 1)
  have h23 := geometricEndpointTerm_nonneg 2 3 (n + 1)
  by_cases he : smoothRankBound (n + 1) = smoothRankBound n
  · simp only [he, sub_self, abs_zero, zero_div]
    linarith
  · have hb := div_le_div_of_nonneg_right (smoothRank_jump_abs n)
      (Nat.cast_nonneg (α := ℝ) (n + 1))
    rcases smoothRank_change_endpoint he with h | h | h
    · have ht := geometricEndpointTerm_at (a := 1) (b := 2) (by simpa only [one_mul] using h)
      rw [show (3 : ℝ) / (n + 1 : ℕ) = 3 * (1 / (n + 1 : ℕ)) by ring] at hb
      linarith
    · have ht := geometricEndpointTerm_at (a := 1) (b := 3) (by simpa only [one_mul] using h)
      rw [show (3 : ℝ) / (n + 1 : ℕ) = 3 * (1 / (n + 1 : ℕ)) by ring] at hb
      linarith
    · have ht := geometricEndpointTerm_at h
      rw [show (3 : ℝ) / (n + 1 : ℕ) = 3 * (1 / (n + 1 : ℕ)) by ring] at hb
      linarith

def rank_jumps_summable :
    Summable (fun n : ℕ => |(smoothRankBound (n + 1) : ℝ) - smoothRankBound n| / (n + 1 : ℕ)) := by
  have h2 := geometricEndpointTerm_summable_shift (a := 1) (b := 2) (by norm_num) (by norm_num)
  have h3 := geometricEndpointTerm_summable_shift (a := 1) (b := 3) (by norm_num) (by norm_num)
  have h23 := geometricEndpointTerm_summable_shift (a := 2) (b := 3) (by norm_num) (by norm_num)
  apply (((h2.add h3).add h23).mul_left 3).of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_of_nonneg (by positivity :
    0 ≤ |(smoothRankBound (n + 1) : ℝ) - smoothRankBound n| / (n + 1 : ℕ))]
  exact rank_jump_geometric_bound n

def signedRankJump_decomposition (n : ℕ) :
    signedRankJump n = ((smoothRankBound (n + 1) : ℝ) - smoothRankBound n) -
      (obstructionIndicator (n + 1) - obstructionIndicator n) := by
  unfold signedRankJump signedRank obstructionIndicator
  ring

def signedRank_jumps_summable :
    Summable (fun n : ℕ => |signedRankJump n| / (n + 1 : ℕ)) := by
  apply (rank_jumps_summable.add obstruction_jumps_summable).of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_of_nonneg (by positivity : 0 ≤ |signedRankJump n| / (n + 1 : ℕ)),
    signedRankJump_decomposition]
  have hh : |((smoothRankBound (n + 1) : ℝ) - smoothRankBound n) -
        (obstructionIndicator (n + 1) - obstructionIndicator n)| ≤
      |(smoothRankBound (n + 1) : ℝ) - smoothRankBound n| +
        |obstructionIndicator (n + 1) - obstructionIndicator n| := by
    simpa only [sub_zero, zero_sub, abs_neg] using
      abs_sub_le ((smoothRankBound (n + 1) : ℝ) - smoothRankBound n) 0
        (obstructionIndicator (n + 1) - obstructionIndicator n)
  simpa only [add_div] using div_le_div_of_nonneg_right hh (Nat.cast_nonneg (α := ℝ) (n + 1))


end Bounty

end SubmissionComponent_JumpSummability

/- Component CoprimeLimit; SHA256 69cbf0abef3ea6690a02d6a04f8adab64f01cc41e052e2ab277e95973d957e72 -/
section SubmissionComponent_CoprimeLimit
/- Uniform approximation and limiting density for dilated core counts. -/

open Filter
open scoped Topology

namespace Bounty

def coprimeCores_div_error {n d : ℕ} (hn : 0 < n) (hd : 0 < d) :
    |((coprimeCores (n / d)).card : ℝ) / n - 1 / (3 * d)| ≤ (4 / 3 : ℝ) / n := by
  have hn0 : (0 : ℝ) < n := by exact_mod_cast hn
  have hd0 : (0 : ℝ) < d := by exact_mod_cast hd
  have hdown : n / d * d ≤ n := Nat.div_mul_le_self n d
  have hup : n < (n / d + 1) * d := by
    have hr := Nat.mod_lt n hd
    have he := Nat.div_add_mod n d
    nlinarith
  have hdown' : (n / d : ℕ) ≤ (n : ℝ) / d := by
    apply (le_div_iff₀ hd0).mpr
    exact_mod_cast hdown
  have hup' : (n : ℝ) / d - 1 ≤ (n / d : ℕ) := by
    have hh : (n : ℝ) / d < (n / d : ℕ) + 1 := by
      apply (div_lt_iff₀ hd0).mpr
      exact_mod_cast hup
    linarith
  have hc := abs_le.mp (coprimeCores_card_error (n / d))
  have hc' : |((coprimeCores (n / d)).card : ℝ) - (n : ℝ) / (3 * d)| ≤ 4 / 3 := by
    have he : (n : ℝ) / (3 * d) = ((n : ℝ) / d) / 3 := by ring
    rw [he, abs_le]
    constructor <;> linarith
  have he : ((coprimeCores (n / d)).card : ℝ) / n - 1 / (3 * d) =
      (((coprimeCores (n / d)).card : ℝ) - (n : ℝ) / (3 * d)) / n := by
    field_simp
  rw [he, abs_div, abs_of_pos hn0]
  exact div_le_div_of_nonneg_right hc' hn0.le

def tendsto_coprimeCores_div {d : ℕ} (hd : 0 < d) :
    Tendsto (fun n : ℕ => ((coprimeCores (n / d)).card : ℝ) / n)
      atTop (nhds (1 / (3 * (d : ℝ)))) := by
  rw [Metric.tendsto_nhds]
  intro ε hε
  have he : ∀ᶠ n : ℕ in atTop, (4 / 3 : ℝ) / n < ε :=
    (tendsto_const_div_atTop_nhds_zero_nat (4 / 3 : ℝ)).eventually (gt_mem_nhds hε)
  filter_upwards [he, eventually_ge_atTop 1] with n hn hn1
  rw [Real.dist_eq]
  exact (coprimeCores_div_error (by omega) hd).trans_lt hn

def coprimeCores_card_le (n : ℕ) : (coprimeCores n).card ≤ n := by
  have hh : (coprimeCores n).card ≤ (Finset.Icc 1 n).card :=
    Finset.card_le_card (Finset.filter_subset _ _)
  simpa only [Nat.card_Icc, Nat.add_sub_cancel] using hh

def coprimeCores_div_bound {n d : ℕ} (hn : 0 < n) (hd : 0 < d) :
    0 ≤ ((coprimeCores (n / d)).card : ℝ) / n ∧
      ((coprimeCores (n / d)).card : ℝ) / n ≤ 1 / (d : ℝ) := by
  have hn0 : (0 : ℝ) < n := by exact_mod_cast hn
  have hd0 : (0 : ℝ) < d := by exact_mod_cast hd
  constructor
  · positivity
  · apply (div_le_div_iff₀ hn0 hd0).mpr
    have hh := Nat.mul_le_mul_right d (coprimeCores_card_le (n / d))
    have he := Nat.div_mul_le_self n d
    norm_num only [one_mul]
    exact_mod_cast hh.trans he


end Bounty

end SubmissionComponent_CoprimeLimit

/- Component CoreConvolutionLimit; SHA256 91f1c53b10af5e40623001278220dac12a8fc796fa5ed144d7726ab4c6a7e408 -/
section SubmissionComponent_CoreConvolutionLimit
/- A dominated-convergence theorem for signed core convolutions. -/

open Filter
open scoped Topology

namespace Bounty

def tendsto_core_weighted_series {a : ℕ → ℝ}
    (ha : Summable (fun d : ℕ => |a d| / (d + 1 : ℕ))) :
    Tendsto (fun n : ℕ => ∑' d : ℕ,
        a d * (((coprimeCores (n / (d + 1))).card : ℝ) / n))
      atTop (nhds (∑' d : ℕ, a d / (3 * (d + 1 : ℕ)))) := by
  apply tendsto_tsum_of_dominated_convergence ha
  · intro d
    have hh := (tendsto_coprimeCores_div (Nat.succ_pos d)).const_mul (a d)
    simpa only [mul_one_div] using hh
  · filter_upwards [eventually_ge_atTop 1] with n hn d
    have hb := coprimeCores_div_bound (n := n) (d := d + 1) (by omega) (by omega)
    rw [Real.norm_eq_abs, abs_mul, abs_of_nonneg hb.1]
    have hh := mul_le_mul_of_nonneg_left hb.2 (abs_nonneg (a d))
    simpa only [mul_one_div] using hh

def core_weighted_series_eq_sum (a : ℕ → ℝ) (n : ℕ) :
    (∑' d : ℕ, a d * (((coprimeCores (n / (d + 1))).card : ℝ) / n)) =
      (∑ d ∈ Finset.range n, a d * ((coprimeCores (n / (d + 1))).card : ℝ)) / n := by
  have hz : ∀ d ∉ Finset.range n,
      a d * (((coprimeCores (n / (d + 1))).card : ℝ) / n) = 0 := by
    intro d hd
    have hnd : n < d + 1 := by simp only [Finset.mem_range] at hd; omega
    simp [Nat.div_eq_of_lt hnd, coprimeCores]
  rw [tsum_eq_sum hz]
  simp only [Finset.sum_div, mul_div_assoc]

def tendsto_core_weighted_sum {a : ℕ → ℝ}
    (ha : Summable (fun d : ℕ => |a d| / (d + 1 : ℕ))) :
    Tendsto (fun n : ℕ =>
        (∑ d ∈ Finset.range n, a d * ((coprimeCores (n / (d + 1))).card : ℝ)) / n)
      atTop (nhds (∑' d : ℕ, a d / (3 * (d + 1 : ℕ)))) := by
  simpa only [core_weighted_series_eq_sum] using tendsto_core_weighted_series ha


end Bounty

end SubmissionComponent_CoreConvolutionLimit

/- Component JumpDensity; SHA256 a84b8cfc4532cf67cd97fd894fdd3ea011a8cc194d70fec31ef8b8c90f5f20cc -/
section SubmissionComponent_JumpDensity
/- The remaining analytic hypothesis for the exact bound is weighted summability of its jumps. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def jumpDensity : ℝ := ∑' j : ℕ, signedRankJump j / (3 * (j + 1 : ℕ))

def tendsto_globalUpper_of_summable_jumps
    (h : Summable (fun j : ℕ => |signedRankJump j| / (j + 1 : ℕ))) :
    Tendsto (fun n : ℕ => (globalUpper n : ℝ) / n) atTop (nhds jumpDensity) := by
  simpa only [← globalUpper_cast_jumps, jumpDensity, Nat.cast_mul, Nat.cast_ofNat] using tendsto_core_weighted_sum h

def tendsto_f_of_exact_and_summable_jumps
    (he : ∀ n, Erdos1062.f n = globalUpper n)
    (h : Summable (fun j : ℕ => |signedRankJump j| / (j + 1 : ℕ))) :
    Tendsto (fun n : ℕ => (Erdos1062.f n : ℝ) / n) atTop (nhds jumpDensity) := by
  simpa only [he] using tendsto_globalUpper_of_summable_jumps h


end Bounty

end SubmissionComponent_JumpDensity

/- Component DiscreteAbel; SHA256 83ad651cb91b1992dca3cdb7b8d3d82fa6a008b7ccf13e1f406c16b0a2d610ad -/
section SubmissionComponent_DiscreteAbel
/- Summation by parts for reciprocal weights, with an explicit boundary term. -/

open Filter
open scoped Topology

namespace Bounty

def sum_reciprocal_kernel (N : ℕ) :
    (∑ n ∈ Finset.range N, (1 : ℝ) / ((n + 1 : ℕ) * (n + 2 : ℕ))) =
      1 - 1 / (N + 1 : ℕ) := by
  induction N with
  | zero => norm_num
  | succ N ih =>
    rw [Finset.sum_range_succ, ih]
    push_cast
    have h1 : (N : ℝ) + 1 ≠ 0 := by positivity
    have h2 : (N : ℝ) + 2 ≠ 0 := by positivity
    field_simp
    ring

def hasSum_reciprocal_kernel :
    HasSum (fun n : ℕ => (1 : ℝ) / ((n + 1 : ℕ) * (n + 2 : ℕ))) 1 := by
  apply (hasSum_iff_tendsto_nat_of_nonneg (fun n => by positivity) 1).mpr
  simp only [sum_reciprocal_kernel]
  have h : Tendsto (fun n : ℕ => (1 : ℝ) / (n + 1 : ℕ)) atTop (nhds 0) :=
    (tendsto_const_div_atTop_nhds_zero_nat (1 : ℝ)).comp (tendsto_add_atTop_nat 1)
  simpa only [sub_zero] using tendsto_const_nhds.sub h

def bounded_reciprocal_kernel_summable {w : ℕ → ℝ} {M : ℝ}
    (hw : ∀ n, |w n| ≤ M) :
    Summable (fun n : ℕ => w (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ))) := by
  apply (hasSum_reciprocal_kernel.summable.mul_left M).of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_div, abs_of_nonneg (by positivity :
    (0 : ℝ) ≤ (n + 1 : ℕ) * (n + 2 : ℕ))]
  simpa only [mul_one_div] using
    div_le_div_of_nonneg_right (hw (n + 1))
      (by positivity : (0 : ℝ) ≤ (n + 1 : ℕ) * (n + 2 : ℕ))

def sum_reciprocal_jumps (w : ℕ → ℝ) (hw : w 0 = 0) (N : ℕ) :
    (∑ n ∈ Finset.range N, (w (n + 1) - w n) / (n + 1 : ℕ)) =
      w N / (N + 1 : ℕ) +
        ∑ n ∈ Finset.range N, w (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ)) := by
  induction N with
  | zero => simp [hw]
  | succ N ih =>
    rw [Finset.sum_range_succ, Finset.sum_range_succ, ih]
    push_cast
    have h1 : (N : ℝ) + 1 ≠ 0 := by positivity
    have h2 : (N : ℝ) + 2 ≠ 0 := by positivity
    field_simp
    ring

def tsum_reciprocal_jumps {w : ℕ → ℝ} (hw : w 0 = 0)
    (hj : Summable (fun n : ℕ => (w (n + 1) - w n) / (n + 1 : ℕ)))
    (hk : Summable (fun n : ℕ => w (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ))))
    (ht : Tendsto (fun N : ℕ => w N / (N + 1 : ℕ)) atTop (nhds 0)) :
    (∑' n : ℕ, (w (n + 1) - w n) / (n + 1 : ℕ)) =
      ∑' n : ℕ, w (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ)) := by
  have hlim := ht.add hk.hasSum.tendsto_sum_nat
  simp only [zero_add, ← sum_reciprocal_jumps w hw] at hlim
  exact tendsto_nhds_unique hj.hasSum.tendsto_sum_nat hlim

def bounded_div_nat_tendsto_zero {w : ℕ → ℝ} {M : ℝ}
    (hw : ∀ n, |w n| ≤ M) :
    Tendsto (fun N : ℕ => w N / (N + 1 : ℕ)) atTop (nhds 0) := by
  rw [Metric.tendsto_nhds]
  intro ε hε
  have ht : Tendsto (fun N : ℕ => M / (N + 1 : ℕ)) atTop (nhds 0) :=
    (tendsto_const_div_atTop_nhds_zero_nat M).comp (tendsto_add_atTop_nat 1)
  filter_upwards [ht.eventually (gt_mem_nhds hε)] with n hn
  rw [Real.dist_eq, sub_zero, abs_div,
    abs_of_nonneg (Nat.cast_nonneg (α := ℝ) (n + 1))]
  exact (div_le_div_of_nonneg_right (hw n) (Nat.cast_nonneg (α := ℝ) (n + 1))).trans_lt hn


end Bounty

end SubmissionComponent_DiscreteAbel

/- Component LogJumpSeries; SHA256 4c47fb1149ab0a63731fa53ef000a1700531467cf90e09cdb9962dbd60656a5d -/
section SubmissionComponent_LogJumpSeries
/- The reciprocal jumps of the integer logarithm have an exact rational sum. -/

namespace Bounty

def geometricEndpointTerm_hasSum {a b : ℕ} (ha : 0 < a) (hb : 1 < b) :
    HasSum (geometricEndpointTerm a b) ((1 / (a : ℝ)) * (1 - 1 / (b : ℝ))⁻¹) := by
  classical
  have hi : Function.Injective (fun j : ℕ => a * b ^ j) := by
    intro i j hij
    apply Nat.pow_right_injective (by omega : 2 ≤ b)
    nlinarith
  apply (hi.hasSum_iff (f := geometricEndpointTerm a b) ?_).mp
  · have hbr : (1 : ℝ) < b := by exact_mod_cast hb
    have hgeo := (hasSum_geometric_of_lt_one
      (by positivity : (0 : ℝ) ≤ 1 / (b : ℝ))
      (by simpa only [one_div] using inv_lt_one_of_one_lt₀ hbr)).mul_left (1 / (a : ℝ))
    apply hgeo.congr_fun
    intro j
    simp only [Function.comp_apply, geometricEndpointTerm_at ⟨j, rfl⟩,
      Nat.cast_mul, Nat.cast_pow, div_pow, one_pow]
    ring
  · intro m hm
    have hn : ¬∃ j, m = a * b ^ j := by simpa only [Set.mem_range, eq_comm] using hm
    simp only [geometricEndpointTerm, if_neg hn]

def geometricEndpointTerm_zero {a b : ℕ} (ha : 0 < a) (hb : 0 < b) :
    geometricEndpointTerm a b 0 = 0 := by
  classical
  have hn : ¬∃ j, 0 = a * b ^ j := by
    rintro ⟨j, hj⟩
    have hp : 0 < a * b ^ j := by positivity
    omega
  simp only [geometricEndpointTerm, if_neg hn]

def geometricEndpointTerm_tsum_shift {a b : ℕ} (ha : 0 < a) (hb : 1 < b) :
    (∑' n : ℕ, geometricEndpointTerm a b (n + 1)) =
      (1 / (a : ℝ)) * (1 - 1 / (b : ℝ))⁻¹ := by
  have hs := geometricEndpointTerm_hasSum ha hb
  have he := hs.summable.sum_add_tsum_nat_add 1
  simpa only [Finset.sum_range_one, geometricEndpointTerm_zero ha (by omega : 0 < b),
    zero_add, hs.tsum_eq] using he

open scoped Classical in
def nat_log_jump {b : ℕ} (hb : 1 < b) (n : ℕ) :
    ((Nat.log b (n + 1) : ℝ) - Nat.log b n) =
      if ∃ j, n + 1 = b * b ^ j then 1 else 0 := by
  classical
  by_cases he : ∃ j, n + 1 = b * b ^ j
  · obtain ⟨j, hj⟩ := he
    have hp : n + 1 = b ^ (j + 1) := by simpa only [pow_succ', Nat.succ_eq_add_one] using hj
    have hpow : 0 < b ^ j := by positivity
    have hlo : b ^ j ≤ n := by nlinarith
    have hl := Nat.log_eq_of_pow_le_of_lt_pow hlo (by omega : n < b ^ (j + 1))
    rw [if_pos ⟨j, hj⟩, hl, hp, Nat.log_pow hb]
    push_cast
    ring
  · rw [if_neg he]
    by_cases hn : n = 0
    · subst n
      simp
    have hh : n + 1 ≠ b ^ Nat.log b (n + 1) := by
      intro hh
      have hk : Nat.log b (n + 1) ≠ 0 := by
        intro hk
        rw [hk, pow_zero] at hh
        omega
      obtain ⟨j, hj⟩ := Nat.exists_eq_succ_of_ne_zero hk
      apply he
      exact ⟨j, by simpa only [hj, pow_succ', Nat.succ_eq_add_one] using hh⟩
    rw [nat_log_succ_eq_of_not_power hb hh, sub_self]

def nat_log_jump_div {b : ℕ} (hb : 1 < b) (n : ℕ) :
    ((Nat.log b (n + 1) : ℝ) - Nat.log b n) / (n + 1 : ℕ) =
      geometricEndpointTerm b b (n + 1) := by
  classical
  rw [nat_log_jump hb]
  unfold geometricEndpointTerm
  split_ifs <;> simp

def nat_log_jumps_summable {b : ℕ} (hb : 1 < b) :
    Summable (fun n : ℕ => ((Nat.log b (n + 1) : ℝ) - Nat.log b n) / (n + 1 : ℕ)) := by
  simpa only [nat_log_jump_div hb] using
    geometricEndpointTerm_summable_shift (a := b) (b := b) (by omega) hb

def nat_log_jumps_tsum {b : ℕ} (hb : 1 < b) :
    (∑' n : ℕ, ((Nat.log b (n + 1) : ℝ) - Nat.log b n) / (n + 1 : ℕ)) =
      1 / ((b : ℝ) - 1) := by
  simp only [nat_log_jump_div hb]
  rw [geometricEndpointTerm_tsum_shift (by omega : 0 < b) hb]
  have hbr : (1 : ℝ) < b := by exact_mod_cast hb
  field_simp


end Bounty

end SubmissionComponent_LogJumpSeries

/- Component DensityCorrection; SHA256 48f32369bac030c9134216d1427de234afac9a29afe301a6f01c0f5de3303c91 -/
section SubmissionComponent_DensityCorrection
/- The density is a rational contribution plus the overlap minus obstruction correction. -/

namespace Bounty

def overlapWindow (n : ℕ) : Prop :=
  0 < n ∧ 2 * 4 ^ Nat.log 4 n ≤ n ∧ 2 * 3 ^ Nat.log 3 n ≤ n

noncomputable def overlapIndicator (n : ℕ) : ℝ := by
  classical
  exact if overlapWindow n then 1 else 0

noncomputable def correctionIndicator (n : ℕ) : ℝ :=
  overlapIndicator n - obstructionIndicator n

def overlapWindow_iff_intervals (n : ℕ) :
    overlapWindow n ↔ ∃ j b : ℕ, 2 * 4 ^ j ≤ n ∧ n < 4 ^ (j + 1) ∧
      2 * 3 ^ b ≤ n ∧ n < 3 ^ (b + 1) := by
  constructor
  · rintro ⟨hn, h4, h3⟩
    exact ⟨Nat.log 4 n, Nat.log 3 n, h4,
      Nat.lt_pow_succ_log_self (by norm_num) n, h3,
      Nat.lt_pow_succ_log_self (by norm_num) n⟩
  · rintro ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩
    have h4pos : 0 < (4 : ℕ) ^ j := by positivity
    have h4 := Nat.log_eq_of_pow_le_of_lt_pow (by omega : 4 ^ j ≤ n) h4hi
    have h3 := Nat.log_eq_of_pow_le_of_lt_pow (by omega : 3 ^ b ≤ n) h3hi
    exact ⟨by omega, by rwa [h4], by rwa [h3]⟩

def correctionIndicator_zero : correctionIndicator 0 = 0 := by
  classical
  have hn : ¬badWindow 0 := by
    rintro ⟨j, b, hj, _, _, _⟩
    have hp : 0 < (4 : ℕ) ^ j := by positivity
    omega
  simp [correctionIndicator, overlapIndicator, overlapWindow, obstructionIndicator, hn]

def correctionIndicator_bound (n : ℕ) : |correctionIndicator n| ≤ 1 := by
  classical
  unfold correctionIndicator overlapIndicator obstructionIndicator
  split_ifs <;> norm_num

def signedRank_log_decomposition (n : ℕ) :
    signedRank n = (if n = 0 then 0 else 1) + (Nat.log 3 n : ℝ) + Nat.log 4 n +
      correctionIndicator n := by
  classical
  by_cases hn : n = 0
  · subst n
    simp [signedRank_zero, correctionIndicator_zero]
  have hp := log_two_odd_iff_four_threshold (by omega : 0 < n)
  simp only [signedRank, smoothRankBound, hn, ↓reduceIte, correctionIndicator,
    overlapIndicator, obstructionIndicator, overlapWindow, show 0 < n by omega,
    true_and, ← log_four_eq, hp]
  split_ifs <;> push_cast <;> ring

def signedRankJump_log_decomposition (n : ℕ) :
    signedRankJump n / (n + 1 : ℕ) =
      (if n = 0 then 1 else 0) +
      ((Nat.log 3 (n + 1) : ℝ) - Nat.log 3 n) / (n + 1 : ℕ) +
      ((Nat.log 4 (n + 1) : ℝ) - Nat.log 4 n) / (n + 1 : ℕ) +
      (correctionIndicator (n + 1) - correctionIndicator n) / (n + 1 : ℕ) := by
  unfold signedRankJump
  rw [signedRank_log_decomposition, signedRank_log_decomposition]
  by_cases hn : n = 0
  · subst n
    norm_num
    ring
  · simp only [hn, Nat.succ_ne_zero, ↓reduceIte]
    ring

def signedRank_jumps_summable_signed :
    Summable (fun n : ℕ => signedRankJump n / (n + 1 : ℕ)) := by
  apply signedRank_jumps_summable.of_norm_bounded
  intro n
  simp only [Real.norm_eq_abs, abs_div, abs_of_nonneg (Nat.cast_nonneg (α := ℝ) (n + 1))]
  exact le_refl _

def correction_jumps_summable :
    Summable (fun n : ℕ => (correctionIndicator (n + 1) - correctionIndicator n) / (n + 1 : ℕ)) := by
  have hs := (((signedRank_jumps_summable_signed.sub (hasSum_ite_eq 0 (1 : ℝ)).summable).sub
    (nat_log_jumps_summable (by norm_num : 1 < 3))).sub
    (nat_log_jumps_summable (by norm_num : 1 < 4)))
  apply hs.congr
  intro n
  rw [signedRankJump_log_decomposition]
  ring

def correction_kernel_summable :
    Summable (fun n : ℕ => correctionIndicator (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ))) :=
  bounded_reciprocal_kernel_summable correctionIndicator_bound

def correction_jumps_eq_kernel :
    (∑' n : ℕ, (correctionIndicator (n + 1) - correctionIndicator n) / (n + 1 : ℕ)) =
      ∑' n : ℕ, correctionIndicator (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ)) :=
  tsum_reciprocal_jumps correctionIndicator_zero correction_jumps_summable
    correction_kernel_summable (bounded_div_nat_tendsto_zero correctionIndicator_bound)

def jumpDensity_eq_correction_series :
    jumpDensity = 11 / 18 +
      (∑' n : ℕ, correctionIndicator (n + 1) / ((n + 1 : ℕ) * (n + 2 : ℕ))) / 3 := by
  have h3 := (nat_log_jumps_summable (by norm_num : 1 < 3)).hasSum
  have h4 := (nat_log_jumps_summable (by norm_num : 1 < 4)).hasSum
  rw [nat_log_jumps_tsum (by norm_num : 1 < 3)] at h3
  rw [nat_log_jumps_tsum (by norm_num : 1 < 4)] at h4
  have hsum := (((hasSum_ite_eq 0 (1 : ℝ)).add h3).add h4).add correction_jumps_summable.hasSum
  have hs : HasSum (fun n : ℕ => signedRankJump n / (n + 1 : ℕ))
      (1 + 1 / ((3 : ℝ) - 1) + 1 / ((4 : ℝ) - 1) +
        ∑' n : ℕ, (correctionIndicator (n + 1) - correctionIndicator n) / (n + 1 : ℕ)) := by
    apply hsum.congr_fun
    exact signedRankJump_log_decomposition
  have he : jumpDensity = (∑' n : ℕ, signedRankJump n / (n + 1 : ℕ)) / 3 := by
    rw [← tsum_div_const]
    apply tsum_congr
    intro n
    ring
  rw [he, hs.tsum_eq, correction_jumps_eq_kernel]
  ring


end Bounty

end SubmissionComponent_DensityCorrection

/- Component GeometricBands; SHA256 d5b9fae9327a431c11cce647ce104ea0599c4155229e60ebf7f08698b0da2817 -/
section SubmissionComponent_GeometricBands
/- Exact boundary jumps of disjoint families of geometric intervals. -/

namespace Bounty

def geometricBand (lo hi b n : ℕ) : Prop :=
  ∃ j : ℕ, lo * b ^ j ≤ n ∧ n < hi * b ^ j

noncomputable def geometricBandIndicator (lo hi b n : ℕ) : ℝ := by
  classical
  exact if geometricBand lo hi b n then 1 else 0

def geometricBand_enter {lo hi b n : ℕ}
    (hn : ¬geometricBand lo hi b n) (hs : geometricBand lo hi b (n + 1)) :
    ∃ j : ℕ, n + 1 = lo * b ^ j := by
  obtain ⟨j, hjlo, hjhi⟩ := hs
  by_contra hh
  have he : n + 1 ≠ lo * b ^ j := by aesop
  exact hn ⟨j, by omega, by omega⟩

def geometricBand_exit {lo hi b n : ℕ}
    (hn : geometricBand lo hi b n) (hs : ¬geometricBand lo hi b (n + 1)) :
    ∃ j : ℕ, n + 1 = hi * b ^ j := by
  obtain ⟨j, hjlo, hjhi⟩ := hn
  by_contra hh
  have he : n + 1 ≠ hi * b ^ j := by aesop
  exact hs ⟨j, by omega, by omega⟩

def geometricBand_at_lower {lo hi b : ℕ} (hl : lo < hi) (hb : 0 < b) (j : ℕ) :
    geometricBand lo hi b (lo * b ^ j) := by
  have hp : 0 < b ^ j := by positivity
  exact ⟨j, le_refl _, by nlinarith⟩

def geometricBand_before_lower {lo hi b n j : ℕ} (hgap : hi < lo * b)
    (hb : 1 < b) (he : n + 1 = lo * b ^ j) : ¬geometricBand lo hi b n := by
  rintro ⟨k, hklo, hkhi⟩
  rcases le_or_gt j k with hjk | hkj
  · have hp := Nat.pow_le_pow_right (by omega : 0 < b) hjk
    have hm := Nat.mul_le_mul_left lo hp
    omega
  · have hp := Nat.pow_le_pow_right (by omega : 0 < b) (by omega : k + 1 ≤ j)
    have hkpos : 0 < b ^ k := by positivity
    have hm := Nat.mul_le_mul_left lo hp
    rw [pow_succ] at hm
    nlinarith

def geometricBand_at_upper_false {lo hi b j : ℕ} (hgap : hi < lo * b)
    (hb : 1 < b) : ¬geometricBand lo hi b (hi * b ^ j) := by
  rintro ⟨k, hklo, hkhi⟩
  rcases le_or_gt k j with hkj | hjk
  · have hp := Nat.pow_le_pow_right (by omega : 0 < b) hkj
    have hm := Nat.mul_le_mul_left hi hp
    omega
  · have hp := Nat.pow_le_pow_right (by omega : 0 < b) (by omega : j + 1 ≤ k)
    have hjpos : 0 < b ^ j := by positivity
    have hm := Nat.mul_le_mul_left lo hp
    rw [pow_succ] at hm
    nlinarith

def geometricBand_before_upper {lo hi b n j : ℕ} (hl : lo < hi)
    (hb : 0 < b) (he : n + 1 = hi * b ^ j) : geometricBand lo hi b n := by
  have hp : 0 < b ^ j := by positivity
  exact ⟨j, by nlinarith, by omega⟩

def geometricBand_endpoints_disjoint {lo hi b n : ℕ} (hl : lo < hi)
    (hgap : hi < lo * b) (hb : 1 < b)
    (hs : ∃ j, n = lo * b ^ j) : ¬∃ j, n = hi * b ^ j := by
  obtain ⟨j, rfl⟩ := hs
  rintro ⟨k, hk⟩
  have h := geometricBand_at_lower hl (by omega : 0 < b) j
  rw [hk] at h
  exact geometricBand_at_upper_false hgap hb h

open scoped Classical in
def geometricBandIndicator_jump {lo hi b : ℕ} (hl : lo < hi)
    (hgap : hi < lo * b) (hb : 1 < b) (n : ℕ) :
    geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n =
      (if ∃ j, n + 1 = lo * b ^ j then 1 else 0) -
        (if ∃ j, n + 1 = hi * b ^ j then 1 else 0) := by
  classical
  by_cases hs : ∃ j, n + 1 = lo * b ^ j
  · have hnend := geometricBand_endpoints_disjoint hl hgap hb hs
    obtain ⟨j, hj⟩ := hs
    have hcurr : geometricBand lo hi b (n + 1) := by
      rw [hj]
      exact geometricBand_at_lower hl (by omega) j
    have hprev := geometricBand_before_lower hgap hb hj
    simp only [geometricBandIndicator, if_pos hcurr, if_neg hprev,
      if_pos (show ∃ j, n + 1 = lo * b ^ j from ⟨j, hj⟩), if_neg hnend]
  · by_cases he : ∃ j, n + 1 = hi * b ^ j
    · obtain ⟨j, hj⟩ := he
      have hcurr : ¬geometricBand lo hi b (n + 1) := by
        rw [hj]
        exact geometricBand_at_upper_false hgap hb
      have hprev := geometricBand_before_upper hl (by omega : 0 < b) hj
      simp only [geometricBandIndicator, if_neg hcurr, if_pos hprev,
        if_neg hs, if_pos (show ∃ j, n + 1 = hi * b ^ j from ⟨j, hj⟩)]
    · by_cases hn : geometricBand lo hi b n
      · have hcurr : geometricBand lo hi b (n + 1) := by
          by_contra hh
          exact he (geometricBand_exit hn hh)
        simp only [geometricBandIndicator, if_pos hn, if_pos hcurr,
          if_neg hs, if_neg he, sub_self]
      · have hcurr : ¬geometricBand lo hi b (n + 1) := by
          intro hh
          exact hs (geometricBand_enter hn hh)
        simp only [geometricBandIndicator, if_neg hn, if_neg hcurr,
          if_neg hs, if_neg he, sub_self]

def geometricBandIndicator_bound (lo hi b n : ℕ) :
    |geometricBandIndicator lo hi b n| ≤ 1 := by
  classical
  unfold geometricBandIndicator
  split_ifs <;> norm_num

def product_jump (f g : ℕ → ℝ) (n : ℕ) :
    f (n + 1) * g (n + 1) - f n * g n =
      (f (n + 1) - f n) * g (n + 1) +
      (g (n + 1) - g n) * f (n + 1) -
      (f (n + 1) - f n) * (g (n + 1) - g n) := by ring


end Bounty

end SubmissionComponent_GeometricBands

/- Component WeightedGeometric; SHA256 e238b9a2e8227418e3daa0bdecaa241f30e5df6efef6369f24e1bf68c19a7731 -/
section SubmissionComponent_WeightedGeometric
/- Regrouping weighted boundary events by their geometric exponents. -/

namespace Bounty

noncomputable def endpointSeries (a b : ℕ) (w : ℕ → ℝ) : ℝ :=
  ∑' j : ℕ, w (a * b ^ j) / (a * b ^ j : ℕ)

def weighted_geometric_summable {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (ha : 0 < a) (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    Summable (fun n : ℕ => w n * geometricEndpointTerm a b n) := by
  apply ((geometricEndpointTerm_summable ha hb).mul_left M).of_norm_bounded
  intro n
  rw [Real.norm_eq_abs, abs_mul, abs_of_nonneg (geometricEndpointTerm_nonneg a b n)]
  exact mul_le_mul_of_nonneg_right (hw n) (geometricEndpointTerm_nonneg a b n)

def weighted_geometric_summable_shift {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (ha : 0 < a) (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    Summable (fun n : ℕ => w (n + 1) * geometricEndpointTerm a b (n + 1)) :=
  (summable_nat_add_iff 1).mpr (weighted_geometric_summable ha hb hw)

def weighted_geometric_tsum {a b : ℕ} (ha : 0 < a) (hb : 1 < b) (w : ℕ → ℝ) :
    (∑' n : ℕ, w n * geometricEndpointTerm a b n) = endpointSeries a b w := by
  classical
  have hi : Function.Injective (fun j : ℕ => a * b ^ j) := by
    intro i j hij
    apply Nat.pow_right_injective (by omega : 2 ≤ b)
    nlinarith
  have hs : Function.support (fun n => w n * geometricEndpointTerm a b n) ⊆
      Set.range (fun j : ℕ => a * b ^ j) := by
    intro n hn
    by_contra he
    have hh : ¬∃ j, n = a * b ^ j := by simpa only [Set.mem_range, eq_comm] using he
    simp only [Function.mem_support, geometricEndpointTerm, if_neg hh, mul_zero, ne_eq,
      not_true_eq_false] at hn
  rw [← hi.tsum_eq hs]
  unfold endpointSeries
  apply tsum_congr
  intro j
  rw [geometricEndpointTerm_at ⟨j, rfl⟩]
  ring

def weighted_geometric_tsum_shift {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (ha : 0 < a) (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    (∑' n : ℕ, w (n + 1) * geometricEndpointTerm a b (n + 1)) = endpointSeries a b w := by
  have he := (weighted_geometric_summable ha hb hw).sum_add_tsum_nat_add 1
  simpa only [Finset.sum_range_one, geometricEndpointTerm_zero ha (by omega : 0 < b),
    mul_zero, zero_add, weighted_geometric_tsum ha hb w] using he

def band_weighted_jump_decomposition {lo hi b : ℕ} (hl : lo < hi)
    (hgap : hi < lo * b) (hb : 1 < b) (w : ℕ → ℝ) (n : ℕ) :
    (geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n) *
        w (n + 1) / (n + 1 : ℕ) =
      w (n + 1) * geometricEndpointTerm lo b (n + 1) -
        w (n + 1) * geometricEndpointTerm hi b (n + 1) := by
  classical
  rw [geometricBandIndicator_jump hl hgap hb]
  unfold geometricEndpointTerm
  split_ifs <;> ring

def band_weighted_jumps_summable {lo hi b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hlo : 0 < lo) (hl : lo < hi) (hgap : hi < lo * b) (hb : 1 < b)
    (hw : ∀ n, |w n| ≤ M) :
    Summable (fun n : ℕ =>
      (geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n) *
        w (n + 1) / (n + 1 : ℕ)) := by
  simp only [band_weighted_jump_decomposition hl hgap hb]
  exact (weighted_geometric_summable_shift hlo hb hw).sub
    (weighted_geometric_summable_shift (by omega : 0 < hi) hb hw)

def band_weighted_jumps_tsum {lo hi b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hlo : 0 < lo) (hl : lo < hi) (hgap : hi < lo * b) (hb : 1 < b)
    (hw : ∀ n, |w n| ≤ M) :
    (∑' n : ℕ, (geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n) *
        w (n + 1) / (n + 1 : ℕ)) = endpointSeries lo b w - endpointSeries hi b w := by
  simp only [band_weighted_jump_decomposition hl hgap hb]
  rw [(weighted_geometric_summable_shift hlo hb hw).tsum_sub
    (weighted_geometric_summable_shift (by omega : 0 < hi) hb hw),
    weighted_geometric_tsum_shift hlo hb hw,
    weighted_geometric_tsum_shift (by omega : 0 < hi) hb hw]


end Bounty

end SubmissionComponent_WeightedGeometric

/- Component SpecialBands; SHA256 ed3571155a75f6251241def6d8f27c212f7cef9e386e828c9e18a68e6cbc2358 -/
section SubmissionComponent_SpecialBands
/- The overlap and obstruction as products of geometric interval indicators. -/

namespace Bounty

def overlapWindow_iff_bands (n : ℕ) :
    overlapWindow n ↔ geometricBand 2 4 4 n ∧ geometricBand 2 3 3 n := by
  rw [overlapWindow_iff_intervals]
  constructor
  · rintro ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩
    exact ⟨⟨j, h4lo, by simpa only [pow_succ'] using h4hi⟩,
      ⟨b, h3lo, by simpa only [pow_succ'] using h3hi⟩⟩
  · rintro ⟨⟨j, h4lo, h4hi⟩, ⟨b, h3lo, h3hi⟩⟩
    exact ⟨j, b, h4lo, by simpa only [pow_succ'] using h4hi,
      h3lo, by simpa only [pow_succ'] using h3hi⟩

def badWindow_iff_bands (n : ℕ) :
    badWindow n ↔ geometricBand 4 5 4 n ∧ geometricBand 10 12 3 n := by
  constructor
  · rintro ⟨j, b, h4lo, h4hi, h3lo, h3hi⟩
    have h3pos : 0 < (3 : ℕ) ^ b := by positivity
    have hj : j ≠ 0 := by
      intro hj
      simp only [hj, pow_zero] at h4hi
      omega
    obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hj
    rw [pow_succ'] at h4lo h4hi
    exact ⟨⟨k, h4lo, by omega⟩, ⟨b, h3lo, h3hi⟩⟩
  · rintro ⟨⟨j, h4lo, h4hi⟩, ⟨b, h3lo, h3hi⟩⟩
    refine ⟨j + 1, b, ?_, ?_, h3lo, h3hi⟩
    · simpa only [pow_succ'] using h4lo
    · rw [pow_succ']
      omega

def overlapIndicator_eq_product (n : ℕ) :
    overlapIndicator n = geometricBandIndicator 2 4 4 n * geometricBandIndicator 2 3 3 n := by
  classical
  simp only [overlapIndicator, overlapWindow_iff_bands, geometricBandIndicator]
  split_ifs <;> norm_num <;> tauto

def obstructionIndicator_eq_product (n : ℕ) :
    obstructionIndicator n = geometricBandIndicator 4 5 4 n * geometricBandIndicator 10 12 3 n := by
  classical
  simp only [obstructionIndicator, badWindow_iff_bands, geometricBandIndicator]
  split_ifs <;> norm_num <;> tauto

def geometricBand_change_endpoint {lo hi b n : ℕ} (hl : lo < hi)
    (hgap : hi < lo * b) (hb : 1 < b)
    (h : geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n ≠ 0) :
    (∃ j, n + 1 = lo * b ^ j) ∨ (∃ j, n + 1 = hi * b ^ j) := by
  classical
  by_cases hs : ∃ j, n + 1 = lo * b ^ j
  · exact Or.inl hs
  by_cases he : ∃ j, n + 1 = hi * b ^ j
  · exact Or.inr he
  rw [geometricBandIndicator_jump hl hgap hb, if_neg hs, if_neg he, sub_self] at h
  exact (h rfl).elim

def three_not_dvd_scaled_four {a : ℕ} (ha : ¬3 ∣ a) (j : ℕ) : ¬3 ∣ a * 4 ^ j := by
  intro hh
  rcases Nat.prime_three.dvd_mul.mp hh with h | h
  · exact ha h
  · have ht := Nat.prime_three.dvd_of_dvd_pow h
    norm_num at ht

def endpoint_two_three_or_dvd {a b m : ℕ} (he : m = a * 3 ^ b) :
    m = a ∨ 3 ∣ m := by
  by_cases hb : b = 0
  · exact Or.inl (by simpa only [hb, pow_zero, mul_one] using he)
  · obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hb
    apply Or.inr
    refine ⟨a * 3 ^ k, ?_⟩
    rw [he, pow_succ']
    ring

def overlap_common_endpoint {m : ℕ}
    (h4 : (∃ j, m = 2 * 4 ^ j) ∨ (∃ j, m = 4 * 4 ^ j))
    (h3 : (∃ j, m = 2 * 3 ^ j) ∨ (∃ j, m = 3 * 3 ^ j)) : m = 2 := by
  have hn : ¬3 ∣ m := by
    rcases h4 with ⟨j, rfl⟩ | ⟨j, rfl⟩
    · exact three_not_dvd_scaled_four (by decide) j
    · exact three_not_dvd_scaled_four (by decide) j
  rcases h3 with ⟨j, hj⟩ | ⟨j, hj⟩
  · exact (endpoint_two_three_or_dvd hj).resolve_right hn
  · exact (hn (hj ▸ dvd_mul_right 3 (3 ^ j))).elim

def obstruction_endpoints_disjoint {m : ℕ}
    (h4 : (∃ j, m = 4 * 4 ^ j) ∨ (∃ j, m = 5 * 4 ^ j)) :
    ¬((∃ j, m = 10 * 3 ^ j) ∨ (∃ j, m = 12 * 3 ^ j)) := by
  have hn3 : ¬3 ∣ m := by
    rcases h4 with ⟨j, rfl⟩ | ⟨j, rfl⟩
    · exact three_not_dvd_scaled_four (by decide) j
    · exact three_not_dvd_scaled_four (by decide) j
  intro h3
  have hm : m = 10 := by
    rcases h3 with ⟨j, hj⟩ | ⟨j, hj⟩
    · exact (endpoint_two_three_or_dvd hj).resolve_right hn3
    · have hd : 3 ∣ m := by
        rw [hj]
        exact dvd_mul_of_dvd_left (by decide : 3 ∣ 12) _
      exact (hn3 hd).elim
  rcases h4 with ⟨j, hj⟩ | ⟨j, hj⟩
  · have hd : 4 ∣ m := hj ▸ dvd_mul_right 4 (4 ^ j)
    norm_num [hm] at hd
  · by_cases hz : j = 0
    · simp only [hz, pow_zero, mul_one, hm] at hj
      omega
    · obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hz
      have hd : 4 ∣ m := by
        refine ⟨5 * 4 ^ k, ?_⟩
        rw [hj, pow_succ']
        ring
      norm_num [hm] at hd

def band_two_jump {hi b : ℕ} (hl : 2 < hi) (hgap : hi < 2 * b) (hb : 1 < b) :
    geometricBandIndicator 2 hi b 2 - geometricBandIndicator 2 hi b 1 = 1 := by
  classical
  have hs : geometricBand 2 hi b 2 := by
    simpa only [pow_zero, mul_one] using geometricBand_at_lower hl (by omega : 0 < b) 0
  have hn : ¬geometricBand 2 hi b 1 :=
    geometricBand_before_lower (j := 0) hgap hb (by norm_num)
  simp only [geometricBandIndicator, if_pos hs, if_neg hn, sub_zero]

def overlap_jump_product (n : ℕ) :
    (geometricBandIndicator 2 4 4 (n + 1) - geometricBandIndicator 2 4 4 n) *
      (geometricBandIndicator 2 3 3 (n + 1) - geometricBandIndicator 2 3 3 n) =
        if n = 1 then 1 else 0 := by
  by_cases hn : n = 1
  · subst n
    norm_num only [Nat.reduceAdd, if_pos rfl, if_true]
    rw [band_two_jump (by norm_num : 2 < 4) (by norm_num) (by norm_num),
      band_two_jump (by norm_num : 2 < 3) (by norm_num) (by norm_num), one_mul]
  · rw [if_neg hn]
    by_contra hh
    have h4 : geometricBandIndicator 2 4 4 (n + 1) - geometricBandIndicator 2 4 4 n ≠ 0 := by
      intro he
      exact hh (by rw [he, zero_mul])
    have h3 : geometricBandIndicator 2 3 3 (n + 1) - geometricBandIndicator 2 3 3 n ≠ 0 := by
      intro he
      exact hh (by rw [he, mul_zero])
    have he := overlap_common_endpoint
      (geometricBand_change_endpoint (by norm_num) (by norm_num) (by norm_num) h4)
      (geometricBand_change_endpoint (by norm_num) (by norm_num) (by norm_num) h3)
    omega

def obstruction_jump_product (n : ℕ) :
    (geometricBandIndicator 4 5 4 (n + 1) - geometricBandIndicator 4 5 4 n) *
      (geometricBandIndicator 10 12 3 (n + 1) - geometricBandIndicator 10 12 3 n) = 0 := by
  by_contra hh
  have h4 : geometricBandIndicator 4 5 4 (n + 1) - geometricBandIndicator 4 5 4 n ≠ 0 := by
    intro he
    exact hh (by rw [he, zero_mul])
  have h3 : geometricBandIndicator 10 12 3 (n + 1) - geometricBandIndicator 10 12 3 n ≠ 0 := by
    intro he
    exact hh (by rw [he, mul_zero])
  exact obstruction_endpoints_disjoint
    (geometricBand_change_endpoint (by norm_num) (by norm_num) (by norm_num) h4)
    (geometricBand_change_endpoint (by norm_num) (by norm_num) (by norm_num) h3)


end Bounty

end SubmissionComponent_SpecialBands

/- Component EndpointDensity; SHA256 aa1b5970cac720866a807cc0a3c594f92e9b3205c8a157cd12aa8b6ca27e9db1 -/
section SubmissionComponent_EndpointDensity
/- Group the correction jumps into their eight geometric boundary series. -/

namespace Bounty

def band_weighted_jumps_hasSum {lo hi b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hlo : 0 < lo) (hl : lo < hi) (hgap : hi < lo * b) (hb : 1 < b)
    (hw : ∀ n, |w n| ≤ M) :
    HasSum (fun n : ℕ =>
      (geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n) *
        w (n + 1) / (n + 1 : ℕ)) (endpointSeries lo b w - endpointSeries hi b w) := by
  have hs := (band_weighted_jumps_summable hlo hl hgap hb hw).hasSum
  rwa [band_weighted_jumps_tsum hlo hl hgap hb hw] at hs

def product_bands_jumps_hasSum {lo hi b lo' hi' b' : ℕ} {cross : ℕ → ℝ} {C : ℝ}
    (hlo : 0 < lo) (hl : lo < hi) (hgap : hi < lo * b) (hb : 1 < b)
    (hlo' : 0 < lo') (hl' : lo' < hi') (hgap' : hi' < lo' * b') (hb' : 1 < b')
    (hcross : ∀ n,
      (geometricBandIndicator lo hi b (n + 1) - geometricBandIndicator lo hi b n) *
        (geometricBandIndicator lo' hi' b' (n + 1) - geometricBandIndicator lo' hi' b' n) /
          (n + 1 : ℕ) = cross n)
    (hc : HasSum cross C) :
    HasSum (fun n : ℕ =>
      (geometricBandIndicator lo hi b (n + 1) * geometricBandIndicator lo' hi' b' (n + 1) -
        geometricBandIndicator lo hi b n * geometricBandIndicator lo' hi' b' n) / (n + 1 : ℕ))
      ((endpointSeries lo b (geometricBandIndicator lo' hi' b') -
        endpointSeries hi b (geometricBandIndicator lo' hi' b')) +
       (endpointSeries lo' b' (geometricBandIndicator lo hi b) -
        endpointSeries hi' b' (geometricBandIndicator lo hi b)) - C) := by
  have h1 := band_weighted_jumps_hasSum hlo hl hgap hb (geometricBandIndicator_bound lo' hi' b')
  have h2 := band_weighted_jumps_hasSum hlo' hl' hgap' hb' (geometricBandIndicator_bound lo hi b)
  apply ((h1.add h2).sub hc).congr_fun
  intro n
  rw [product_jump, ← hcross n]
  ring

def overlap_jumps_hasSum :
    HasSum (fun n : ℕ => (overlapIndicator (n + 1) - overlapIndicator n) / (n + 1 : ℕ))
      ((endpointSeries 2 4 (geometricBandIndicator 2 3 3) -
        endpointSeries 4 4 (geometricBandIndicator 2 3 3)) +
       (endpointSeries 2 3 (geometricBandIndicator 2 4 4) -
        endpointSeries 3 3 (geometricBandIndicator 2 4 4)) - 1 / 2) := by
  have hc : ∀ n : ℕ,
      (geometricBandIndicator 2 4 4 (n + 1) - geometricBandIndicator 2 4 4 n) *
        (geometricBandIndicator 2 3 3 (n + 1) - geometricBandIndicator 2 3 3 n) /
          (n + 1 : ℕ) = if n = 1 then (1 / 2 : ℝ) else 0 := by
    intro n
    rw [overlap_jump_product]
    by_cases hn : n = 1 <;> simp [hn]
  simpa only [← overlapIndicator_eq_product] using
    product_bands_jumps_hasSum (by norm_num : 0 < 2) (by norm_num : 2 < 4)
      (by norm_num : 4 < 2 * 4) (by norm_num : 1 < 4)
      (by norm_num : 0 < 2) (by norm_num : 2 < 3)
      (by norm_num : 3 < 2 * 3) (by norm_num : 1 < 3) hc (hasSum_ite_eq 1 (1 / 2 : ℝ))

def obstruction_jumps_hasSum :
    HasSum (fun n : ℕ => (obstructionIndicator (n + 1) - obstructionIndicator n) / (n + 1 : ℕ))
      ((endpointSeries 4 4 (geometricBandIndicator 10 12 3) -
        endpointSeries 5 4 (geometricBandIndicator 10 12 3)) +
       (endpointSeries 10 3 (geometricBandIndicator 4 5 4) -
        endpointSeries 12 3 (geometricBandIndicator 4 5 4))) := by
  have hc : ∀ n : ℕ,
      (geometricBandIndicator 4 5 4 (n + 1) - geometricBandIndicator 4 5 4 n) *
        (geometricBandIndicator 10 12 3 (n + 1) - geometricBandIndicator 10 12 3 n) /
          (n + 1 : ℕ) = 0 := by
    intro n
    rw [obstruction_jump_product, zero_div]
  simpa only [← obstructionIndicator_eq_product, sub_zero] using
    product_bands_jumps_hasSum (by norm_num : 0 < 4) (by norm_num : 4 < 5)
      (by norm_num : 5 < 4 * 4) (by norm_num : 1 < 4)
      (by norm_num : 0 < 10) (by norm_num : 10 < 12)
      (by norm_num : 12 < 10 * 3) (by norm_num : 1 < 3) hc (hasSum_zero (α := ℝ))

def correction_jumps_tsum_endpoints :
    (∑' n : ℕ, (correctionIndicator (n + 1) - correctionIndicator n) / (n + 1 : ℕ)) =
      ((endpointSeries 2 4 (geometricBandIndicator 2 3 3) -
        endpointSeries 4 4 (geometricBandIndicator 2 3 3)) +
       (endpointSeries 2 3 (geometricBandIndicator 2 4 4) -
        endpointSeries 3 3 (geometricBandIndicator 2 4 4)) - 1 / 2) -
      ((endpointSeries 4 4 (geometricBandIndicator 10 12 3) -
        endpointSeries 5 4 (geometricBandIndicator 10 12 3)) +
       (endpointSeries 10 3 (geometricBandIndicator 4 5 4) -
        endpointSeries 12 3 (geometricBandIndicator 4 5 4))) := by
  apply HasSum.tsum_eq
  apply (overlap_jumps_hasSum.sub obstruction_jumps_hasSum).congr_fun
  intro n
  simp only [correctionIndicator]
  ring


end Bounty

end SubmissionComponent_EndpointDensity

/- Component BandLocalization; SHA256 9f737571e217be11e84d598de91d992c50a071d4e0772ab28595d344486328f9 -/
section SubmissionComponent_BandLocalization
/- Localizing a geometric interval index from bounds on a scaled argument. -/

namespace Bounty

def band_index_lower {hi b x z k d a c j : ℕ}
    (hb : 1 < b) (ha : 0 < a) (hx : b ^ k ≤ x) (he : a * z = c * x)
    (hscale : a * hi * b ^ d ≤ c * b) (hj : z < hi * b ^ j) : k + d ≤ j := by
  by_contra hh
  have hp := Nat.pow_le_pow_right (by omega : 0 < b) (by omega : j + 1 ≤ k + d)
  rw [pow_succ', pow_add] at hp
  have hu : a * (hi * b ^ j) ≤ c * b ^ k := by
    apply (mul_le_mul_iff_left₀ (by omega : 0 < b)).mp
    calc
      a * (hi * b ^ j) * b = (a * hi) * (b * b ^ j) := by ring
      _ ≤ (a * hi) * (b ^ k * b ^ d) := Nat.mul_le_mul_left _ hp
      _ = b ^ k * (a * hi * b ^ d) := by ring
      _ ≤ b ^ k * (c * b) := Nat.mul_le_mul_left _ hscale
      _ = c * b ^ k * b := by ring
  have hzl := Nat.mul_lt_mul_of_pos_left hj ha
  have hxl := Nat.mul_le_mul_left c hx
  omega

def band_index_upper {lo b x z k d a c j : ℕ}
    (hb : 1 < b) (hc : 0 < c) (hx : x < b * b ^ k) (he : a * z = c * x)
    (hscale : c ≤ a * lo * b ^ d) (hj : lo * b ^ j ≤ z) : j ≤ k + d := by
  by_contra hh
  have hp := Nat.pow_le_pow_right (by omega : 0 < b) (by omega : k + d + 1 ≤ j)
  rw [pow_succ', pow_add] at hp
  have hl : c * (b * b ^ k) ≤ a * (lo * b ^ j) := by
    calc
      c * (b * b ^ k) ≤ (a * lo * b ^ d) * (b * b ^ k) := Nat.mul_le_mul_right _ hscale
      _ = (a * lo) * (b * (b ^ k * b ^ d)) := by ring
      _ ≤ (a * lo) * b ^ j := Nat.mul_le_mul_left _ hp
      _ = a * (lo * b ^ j) := by ring
  have hzl := Nat.mul_le_mul_left a hj
  have hxu := Nat.mul_lt_mul_of_pos_left hx hc
  omega

def band_scaled_iff_single {lo hi b x z k d a c : ℕ}
    (hb : 1 < b) (ha : 0 < a) (hc : 0 < c)
    (hxlo : b ^ k ≤ x) (hxhi : x < b * b ^ k) (he : a * z = c * x)
    (hbelow : a * hi * b ^ d ≤ c * b) (habove : c ≤ a * lo * b ^ d) :
    geometricBand lo hi b z ↔ lo * b ^ (k + d) ≤ z ∧ z < hi * b ^ (k + d) := by
  constructor
  · rintro ⟨j, hjlo, hjhi⟩
    have hjl := band_index_lower hb ha hxlo he hbelow hjhi
    have hju := band_index_upper hb hc hxhi he habove hjlo
    have hj : j = k + d := by omega
    simpa only [hj] using And.intro hjlo hjhi
  · intro hz
    exact ⟨k + d, hz⟩

def band_scaled_iff_two {lo hi b x z k a c : ℕ}
    (hb : 1 < b) (ha : 0 < a) (hc : 0 < c)
    (hxlo : b ^ k ≤ x) (hxhi : x < b * b ^ k) (he : a * z = c * x)
    (hbelow : a * hi ≤ c * b) (habove : c ≤ a * lo * b) :
    geometricBand lo hi b z ↔
      (lo * b ^ k ≤ z ∧ z < hi * b ^ k) ∨
      (lo * b ^ (k + 1) ≤ z ∧ z < hi * b ^ (k + 1)) := by
  constructor
  · rintro ⟨j, hjlo, hjhi⟩
    have hjl := band_index_lower (d := 0) hb ha hxlo he
      (by simpa only [pow_zero, mul_one] using hbelow) hjhi
    have hju := band_index_upper (d := 1) hb hc hxhi he
      (by simpa only [pow_one] using habove) hjlo
    have hh : j = k ∨ j = k + 1 := by omega
    rcases hh with rfl | rfl
    · exact Or.inl ⟨hjlo, hjhi⟩
    · exact Or.inr ⟨hjlo, hjhi⟩
  · rintro (hz | hz)
    · exact ⟨k, hz⟩
    · exact ⟨k + 1, hz⟩


end Bounty

end SubmissionComponent_BandLocalization

/- Component ThirdSeriesTable; SHA256 ed92cbf86f0cc0a2074b0e2579cc2833b74d2d855a687fc5a8ea26918ba78fc7 -/
section SubmissionComponent_ThirdSeriesTable
/- The five coefficient values in the powers-of-three boundary series. -/

namespace Bounty

def fourBand_at_self {x : ℕ} (hx : 0 < x) :
    geometricBand 2 4 4 x ↔ 2 * 4 ^ Nat.log 4 x ≤ x := by
  have hlo := Nat.pow_log_le_self 4 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 4) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 4) (lo := 2) (hi := 4)
    (k := Nat.log 4 x) (d := 0) (a := 1) (c := 1) (x := x) (z := x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi rfl (by norm_num) (by norm_num)
  simpa only [Nat.add_zero, and_iff_left hhi] using he

def fourBand_at_double {x : ℕ} (hx : 0 < x) :
    geometricBand 2 4 4 (2 * x) ↔ x < 2 * 4 ^ Nat.log 4 x := by
  have hlo := Nat.pow_log_le_self 4 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 4) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 4) (lo := 2) (hi := 4)
    (k := Nat.log 4 x) (d := 0) (a := 1) (c := 2) (x := x) (z := 2 * x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  simp only [Nat.add_zero] at he
  exact he.trans (by omega)

def fourGap_at_ten {x : ℕ} (hx : 0 < x) :
    geometricBand 4 5 4 (10 * x) ↔
      8 * 4 ^ Nat.log 4 x ≤ 5 * x ∧ x < 2 * 4 ^ Nat.log 4 x := by
  have hlo := Nat.pow_log_le_self 4 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 4) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 4) (lo := 4) (hi := 5)
    (k := Nat.log 4 x) (d := 1) (a := 1) (c := 10) (x := x) (z := 10 * x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  rw [pow_succ'] at he
  exact he.trans (by omega)

def fourGap_at_twelve {x : ℕ} (hx : 0 < x) :
    geometricBand 4 5 4 (12 * x) ↔
      4 * 4 ^ Nat.log 4 x ≤ 3 * x ∧ 3 * x < 5 * 4 ^ Nat.log 4 x := by
  have hlo := Nat.pow_log_le_self 4 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 4) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 4) (lo := 4) (hi := 5)
    (k := Nat.log 4 x) (d := 1) (a := 1) (c := 12) (x := x) (z := 12 * x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  rw [pow_succ'] at he
  exact he.trans (by omega)

def coefficient3_eq_boundaries (n : ℕ) :
    (coefficient3 n : ℝ) / 60 =
      geometricBandIndicator 2 4 4 (2 * 3 ^ n) / 2 -
      geometricBandIndicator 2 4 4 (3 ^ n) -
      geometricBandIndicator 4 5 4 (10 * 3 ^ n) / 10 +
      geometricBandIndicator 4 5 4 (12 * 3 ^ n) / 12 := by
  classical
  have hp : 0 < (3 : ℕ) ^ n := by positivity
  simp only [geometricBandIndicator, fourBand_at_double hp, fourBand_at_self hp,
    fourGap_at_ten hp, fourGap_at_twelve hp]
  unfold coefficient3
  dsimp only
  split_ifs <;> norm_num <;> omega


end Bounty

end SubmissionComponent_ThirdSeriesTable

/- Component FourthSeriesTable; SHA256 6d2b329f015a6e365ffef6e8dde629b8996ab0674be4f9336bdbb46be4304619 -/
section SubmissionComponent_FourthSeriesTable
/- The seven coefficient values in the powers-of-four boundary series. -/

namespace Bounty

def threeBand_at_self {x : ℕ} (hx : 0 < x) :
    geometricBand 2 3 3 x ↔ 2 * 3 ^ Nat.log 3 x ≤ x := by
  have hlo := Nat.pow_log_le_self 3 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 3) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 3) (lo := 2) (hi := 3)
    (k := Nat.log 3 x) (d := 0) (a := 1) (c := 1) (x := x) (z := x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi rfl (by norm_num) (by norm_num)
  simpa only [Nat.add_zero, and_iff_left hhi] using he

def threeBand_at_double {x : ℕ} (hx : 0 < x) :
    geometricBand 2 3 3 (2 * x) ↔ 2 * x < 3 * 3 ^ Nat.log 3 x := by
  have hlo := Nat.pow_log_le_self 3 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 3) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 3) (lo := 2) (hi := 3)
    (k := Nat.log 3 x) (d := 0) (a := 1) (c := 2) (x := x) (z := 2 * x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  simp only [Nat.add_zero] at he
  exact he.trans (by omega)

def threeGap_mul_nine (x : ℕ) :
    geometricBand 10 12 3 (9 * x) ↔ geometricBand 10 12 3 x := by
  constructor
  · rintro ⟨j, hjlo, hjhi⟩
    have hj : 2 ≤ j := by
      by_contra hh
      have hj : j = 0 ∨ j = 1 := by omega
      rcases hj with rfl | rfl <;> norm_num at hjlo hjhi <;> omega
    have he : j = j - 2 + 2 := by omega
    have hp : (3 : ℕ) ^ j = 9 * 3 ^ (j - 2) := by
      rw [he, pow_add]
      norm_num
      ring
    rw [hp] at hjlo hjhi
    exact ⟨j - 2, by omega, by omega⟩
  · rintro ⟨j, hjlo, hjhi⟩
    refine ⟨j + 2, ?_, ?_⟩ <;> rw [pow_add] <;> norm_num <;> omega

def threeGap_at_self {x : ℕ} (hx : 0 < x) :
    geometricBand 10 12 3 x ↔
      10 * 3 ^ Nat.log 3 x ≤ 9 * x ∧ 3 * x < 4 * 3 ^ Nat.log 3 x := by
  have hlo := Nat.pow_log_le_self 3 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 3) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_single (b := 3) (lo := 10) (hi := 12)
    (k := Nat.log 3 x) (d := 0) (a := 1) (c := 9) (x := x) (z := 9 * x)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  rw [threeGap_mul_nine] at he
  simp only [Nat.add_zero] at he
  exact he.trans (by omega)

def threeGap_at_five_quarters {x z : ℕ} (hx : 0 < x) (hz : 4 * z = 5 * x) :
    geometricBand 10 12 3 z ↔
      15 * x < 16 * 3 ^ Nat.log 3 x ∨ 8 * 3 ^ Nat.log 3 x ≤ 3 * x := by
  have hlo := Nat.pow_log_le_self 3 (ne_of_gt hx)
  have hhi := Nat.lt_pow_succ_log_self (by norm_num : 1 < 3) x
  rw [pow_succ'] at hhi
  have he := band_scaled_iff_two (b := 3) (lo := 10) (hi := 12)
    (k := Nat.log 3 x) (a := 4) (c := 45) (x := x) (z := 9 * z)
    (by norm_num) (by norm_num) (by norm_num) hlo hhi (by omega) (by norm_num) (by norm_num)
  rw [threeGap_mul_nine, pow_succ'] at he
  exact he.trans (by omega)

def coefficient4_succ_eq_boundaries (n : ℕ) :
    (coefficient4 (n + 1) : ℝ) / 60 =
      geometricBandIndicator 2 3 3 (2 * 4 ^ (n + 1)) / 2 -
      geometricBandIndicator 2 3 3 (4 ^ (n + 1)) -
      geometricBandIndicator 10 12 3 (4 ^ (n + 1)) +
      4 / 5 * geometricBandIndicator 10 12 3 (5 * 4 ^ n) := by
  classical
  have hp : 0 < (4 : ℕ) ^ (n + 1) := by positivity
  have he : 4 * (5 * 4 ^ n) = 5 * 4 ^ (n + 1) := by rw [pow_succ']; ring
  simp only [geometricBandIndicator, threeBand_at_double hp, threeBand_at_self hp,
    threeGap_at_self hp, threeGap_at_five_quarters hp he]
  unfold coefficient4
  dsimp only
  split_ifs <;> norm_num <;> omega


end Bounty

end SubmissionComponent_FourthSeriesTable

/- Component EndpointSeriesAlgebra; SHA256 06bdc8cadbc5417e7be7d7f2b3e877ef90a53fafa56ba020359594a7f34d8f43 -/
section SubmissionComponent_EndpointSeriesAlgebra
/- Absolute convergence, scaling, and removal of the first geometric term. -/

namespace Bounty

def endpointSeries_summable {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    Summable (fun j : ℕ => w (a * b ^ j) / (a * b ^ j : ℕ)) := by
  have hh : ∀ j, |w (a * b ^ j) / (a : ℝ)| ≤ M / |(a : ℝ)| := by
    intro j
    rw [abs_div]
    exact div_le_div_of_nonneg_right (hw _) (abs_nonneg _)
  simpa only [div_div, Nat.cast_mul, Nat.cast_pow] using
    weighted_summable (by exact_mod_cast hb) hh

def endpointSeries_hasSum {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    HasSum (fun j : ℕ => w (a * b ^ j) / (a * b ^ j : ℕ)) (endpointSeries a b w) :=
  (endpointSeries_summable hb hw).hasSum

def endpointSeries_hasSum_weighted {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    HasSum (fun j : ℕ => (w (a * b ^ j) / (a : ℝ)) / (b : ℝ) ^ j) (endpointSeries a b w) := by
  simpa only [div_div, Nat.cast_mul, Nat.cast_pow] using endpointSeries_hasSum (a := a) hb hw

def hasSum_nat_tail_sub {f : ℕ → ℝ} (hs : Summable f) :
    HasSum (fun n : ℕ => f (n + 1)) ((∑' n : ℕ, f n) - f 0) := by
  have ht := ((summable_nat_add_iff 1).mpr hs).hasSum
  have he := hs.sum_add_tsum_nat_add 1
  simp only [Finset.sum_range_one] at he
  have hh : (∑' n : ℕ, f (n + 1)) = (∑' n : ℕ, f n) - f 0 := by linarith
  rwa [hh] at ht

def endpointSeries_hasSum_tail {a b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    HasSum (fun j : ℕ => w (a * b ^ (j + 1)) / (a * b ^ (j + 1) : ℕ))
      (endpointSeries a b w - w a / (a : ℝ)) := by
  simpa only [pow_zero, mul_one, endpointSeries] using
    hasSum_nat_tail_sub (endpointSeries_summable (a := a) hb hw)

def endpointSeries_base {b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) :
    endpointSeries b b w = (∑' j : ℕ, w (b ^ j) / (b : ℝ) ^ j) - w 1 := by
  have hs : Summable (fun j : ℕ => w (b ^ j) / (b : ℝ) ^ j) :=
    weighted_summable (by exact_mod_cast hb) (fun j => hw _)
  have ht := hasSum_nat_tail_sub hs
  simp only [pow_zero, div_one] at ht
  have he : (fun j : ℕ => w (b ^ (j + 1)) / (b : ℝ) ^ (j + 1)) =
      (fun j : ℕ => w (b * b ^ j) / (b * b ^ j : ℕ)) := by
    funext j
    simp only [pow_succ', Nat.cast_mul, Nat.cast_pow]
  rw [he] at ht
  exact ht.tsum_eq

def powers_hasSum_endpoint {b : ℕ} {w : ℕ → ℝ} {M : ℝ}
    (hb : 1 < b) (hw : ∀ n, |w n| ≤ M) (h1 : w 1 = 0) :
    HasSum (fun j : ℕ => w (b ^ j) / (b : ℝ) ^ j) (endpointSeries b b w) := by
  have hs : Summable (fun j : ℕ => w (b ^ j) / (b : ℝ) ^ j) :=
    weighted_summable (by exact_mod_cast hb) (fun j => hw _)
  simpa only [endpointSeries_base hb hw, h1, sub_zero] using hs.hasSum

def geometricBandIndicator_one {lo hi b : ℕ} (hlo : 1 < lo) (hb : 0 < b) :
    geometricBandIndicator lo hi b 1 = 0 := by
  classical
  have hh : ¬geometricBand lo hi b 1 := by
    rintro ⟨j, hj, _⟩
    have hp : 0 < b ^ j := by positivity
    nlinarith
  simp only [geometricBandIndicator, if_neg hh]


end Bounty

end SubmissionComponent_EndpointSeriesAlgebra

/- Component CoefficientSeries; SHA256 9fe75861c055132b578a720545607a030921e23b520e8787428075f3d285bd89 -/
section SubmissionComponent_CoefficientSeries
/- Identification of the two grouped boundary sums with their coefficient series. -/

namespace Bounty

def third_endpoints_eq_series :
    (endpointSeries 2 3 (geometricBandIndicator 2 4 4) -
      endpointSeries 3 3 (geometricBandIndicator 2 4 4)) -
    (endpointSeries 10 3 (geometricBandIndicator 4 5 4) -
      endpointSeries 12 3 (geometricBandIndicator 4 5 4)) =
        (∑' n : ℕ, (coefficient3 n : ℝ) / (3 : ℝ) ^ n) / 60 := by
  have h2 := endpointSeries_hasSum_weighted (a := 2) (by norm_num : 1 < 3)
    (geometricBandIndicator_bound 2 4 4)
  have h3 := powers_hasSum_endpoint (by norm_num : 1 < 3)
    (geometricBandIndicator_bound 2 4 4) (geometricBandIndicator_one (by norm_num) (by norm_num))
  have h10 := endpointSeries_hasSum_weighted (a := 10) (by norm_num : 1 < 3)
    (geometricBandIndicator_bound 4 5 4)
  have h12 := endpointSeries_hasSum_weighted (a := 12) (by norm_num : 1 < 3)
    (geometricBandIndicator_bound 4 5 4)
  have h : HasSum (fun n : ℕ => ((coefficient3 n : ℝ) / (3 : ℝ) ^ n) / 60)
      (((endpointSeries 2 3 (geometricBandIndicator 2 4 4) -
        endpointSeries 3 3 (geometricBandIndicator 2 4 4)) -
        endpointSeries 10 3 (geometricBandIndicator 4 5 4)) +
        endpointSeries 12 3 (geometricBandIndicator 4 5 4)) := by
    apply (((h2.sub h3).sub h10).add h12).congr_fun
    intro n
    rw [show ((coefficient3 n : ℝ) / (3 : ℝ) ^ n) / 60 =
      ((coefficient3 n : ℝ) / 60) / (3 : ℝ) ^ n by ring, coefficient3_eq_boundaries]
    norm_num only [Nat.cast_ofNat]
    ring
  have he := h.tsum_eq
  rw [tsum_div_const] at he
  linarith

def fourth_endpoints_eq_series :
    (endpointSeries 2 4 (geometricBandIndicator 2 3 3) -
      endpointSeries 4 4 (geometricBandIndicator 2 3 3)) -
    (endpointSeries 4 4 (geometricBandIndicator 10 12 3) -
      endpointSeries 5 4 (geometricBandIndicator 10 12 3)) =
        (∑' n : ℕ, (coefficient4 n : ℝ) / (4 : ℝ) ^ n) / 60 - 4 / 5 := by
  have htwo : geometricBandIndicator 2 3 3 2 = 1 := by
    classical
    have hh : geometricBand 2 3 3 2 := ⟨0, by norm_num, by norm_num⟩
    simp only [geometricBandIndicator, if_pos hh]
  have h2 := endpointSeries_hasSum_tail (a := 2) (by norm_num : 1 < 4)
    (geometricBandIndicator_bound 2 3 3)
  rw [htwo] at h2
  have h4 := endpointSeries_hasSum (a := 4) (by norm_num : 1 < 4)
    (geometricBandIndicator_bound 2 3 3)
  have hg4 := endpointSeries_hasSum (a := 4) (by norm_num : 1 < 4)
    (geometricBandIndicator_bound 10 12 3)
  have hg5 := endpointSeries_hasSum (a := 5) (by norm_num : 1 < 4)
    (geometricBandIndicator_bound 10 12 3)
  have h : HasSum (fun n : ℕ => ((coefficient4 (n + 1) : ℝ) / (4 : ℝ) ^ (n + 1)) / 60)
      ((((endpointSeries 2 4 (geometricBandIndicator 2 3 3) - 1 / 2) -
        endpointSeries 4 4 (geometricBandIndicator 2 3 3)) -
        endpointSeries 4 4 (geometricBandIndicator 10 12 3)) +
        endpointSeries 5 4 (geometricBandIndicator 10 12 3)) := by
    apply (((h2.sub h4).sub hg4).add hg5).congr_fun
    intro n
    rw [show ((coefficient4 (n + 1) : ℝ) / (4 : ℝ) ^ (n + 1)) / 60 =
      ((coefficient4 (n + 1) : ℝ) / 60) / (4 : ℝ) ^ (n + 1) by ring,
      coefficient4_succ_eq_boundaries]
    simp only [pow_succ', Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat]
    ring
  have ht := (hasSum_nat_tail_sub coefficient4_summable).div_const 60
  have hz : (coefficient4 0 : ℝ) = 78 := by norm_num [coefficient4]
  simp only [pow_zero, div_one, hz] at ht
  have he := ht.unique h
  norm_num only [Nat.cast_ofNat] at he
  linarith


end Bounty

end SubmissionComponent_CoefficientSeries

/- Component DensityIdentification; SHA256 585e75d7cbb68e7546dd75fed239dd3ea4ce2252dfa86f7955a1bf90dce6e723 -/
section SubmissionComponent_DensityIdentification
/- The checked jump density equals the explicit mixed-base coefficient series. -/

namespace Bounty

def jumpDensity_eq_explicitDensity : jumpDensity = explicitDensity := by
  rw [jumpDensity_eq_correction_series, ← correction_jumps_eq_kernel,
    correction_jumps_tsum_endpoints]
  unfold explicitDensity
  linarith [third_endpoints_eq_series, fourth_endpoints_eq_series]


end Bounty

end SubmissionComponent_DensityIdentification

/- Component RotationCoordinates; SHA256 bb14d9b4e9c7f15bc4de45a15f4bf825227d09e227fe6d712753d8e9e24dd136 -/
section SubmissionComponent_RotationCoordinates
/- Relate the arithmetic coefficient indices to rotations by logarithmic ratios. -/

namespace Bounty

noncomputable def rotationSlope : ℝ := Real.log 4 / Real.log 3

def rotationSlope_irrational : Irrational rotationSlope :=
  irrational_log_four_div_log_three

def rotationSlope_bounds : 1 < rotationSlope ∧ rotationSlope < 2 := by
  have h3 : 0 < Real.log 3 := Real.log_pos (by norm_num)
  have hlo : Real.log 3 < Real.log 4 := Real.log_lt_log (by norm_num) (by norm_num)
  have hhi : Real.log 4 < 2 * Real.log 3 := by
    have hh := Real.log_lt_log (by norm_num : (0 : ℝ) < 4) (by norm_num : (4 : ℝ) < 3 ^ 2)
    simpa only [Real.log_pow, Nat.cast_ofNat] using hh
  constructor
  · exact (lt_div_iff₀ h3).mpr (by simpa only [one_mul] using hlo)
  · exact (div_lt_iff₀ h3).mpr hhi

def inverse_rotationSlope : Real.logb 4 3 = 1 / rotationSlope := by
  unfold Real.logb rotationSlope
  simp only [one_div_div]

def logb_nat_floor_int (a b : ℕ) :
    ⌊Real.logb (b : ℝ) (a : ℝ)⌋ = (Nat.log b a : ℤ) := by
  rw [Real.floor_logb_natCast (Nat.cast_nonneg a), Int.log_natCast]

def normalized_power_eq_rotation {a b : ℕ} (ha : 0 < a) (hb : 1 < b) (n : ℕ) :
    ((a : ℝ) ^ n / (b : ℝ) ^ Nat.log b (a ^ n)) =
      (b : ℝ) ^ Int.fract ((n : ℝ) * Real.logb (b : ℝ) (a : ℝ)) := by
  have hbpos : (0 : ℝ) < b := by exact_mod_cast (by omega : 0 < b)
  have hbne : (b : ℝ) ≠ 1 := by exact_mod_cast (by omega : b ≠ 1)
  have hapos : (0 : ℝ) < (a ^ n : ℕ) := by exact_mod_cast (pow_pos ha n)
  have hl : Real.logb (b : ℝ) ((a ^ n : ℕ) : ℝ) =
      (n : ℝ) * Real.logb (b : ℝ) (a : ℝ) := by
    rw [Nat.cast_pow, Real.logb_pow]
  rw [← hl, Int.fract, logb_nat_floor_int, Int.cast_natCast,
    Real.rpow_sub hbpos, Real.rpow_logb hbpos hbne hapos, Real.rpow_natCast, Nat.cast_pow]

def normalized_four_eq_rotation (n : ℕ) :
    ((4 : ℝ) ^ n / (3 : ℝ) ^ Nat.log 3 (4 ^ n)) =
      (3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope) := by
  simpa only [Real.logb, rotationSlope, Nat.cast_ofNat] using
    normalized_power_eq_rotation (by norm_num : 0 < 4) (by norm_num : 1 < 3) n

def normalized_three_eq_rotation (n : ℕ) :
    ((3 : ℝ) ^ n / (4 : ℝ) ^ Nat.log 4 (3 ^ n)) =
      (4 : ℝ) ^ Int.fract ((n : ℝ) / rotationSlope) := by
  have hh := normalized_power_eq_rotation (by norm_num : 0 < 3) (by norm_num : 1 < 4) n
  norm_num only [Nat.cast_ofNat] at hh
  simpa only [inverse_rotationSlope, mul_one_div] using hh


end Bounty

end SubmissionComponent_RotationCoordinates

/- Component RotationCoding; SHA256 4d8017c476b97ac216f94bbc4e6e3a01643c1db5f5115a56b3baddea23d6f217 -/
section SubmissionComponent_RotationCoding
/- The two integer coefficient sequences are exact codings of irrational rotations. -/

namespace Bounty

noncomputable def realCoefficient4 (x : ℝ) : ℤ := by
  classical
  exact if 15 * x < 16 then 78
    else if 9 * x < 10 then 30
    else if 3 * x < 4 then -30
    else if 2 * x < 3 then 30
    else if x < 2 then 0
    else if 3 * x < 8 then -60
    else -12

noncomputable def realCoefficient3 (x : ℝ) : ℤ := by
  classical
  exact if 3 * x < 4 then 30
    else if 5 * x < 8 then 35
    else if 3 * x < 5 then 29
    else if x < 2 then 24
    else -60

def scaled_nat_ratio_lt {x y : ℕ} (hy : 0 < y) (a c : ℕ) :
    (a : ℝ) * ((x : ℝ) / (y : ℝ)) < (c : ℝ) ↔ a * x < c * y := by
  rw [← mul_div_assoc, div_lt_iff₀ (by exact_mod_cast hy : (0 : ℝ) < y)]
  norm_cast

def realCoefficient4_normalized (n : ℕ) :
    realCoefficient4 ((4 : ℝ) ^ n / (3 : ℝ) ^ Nat.log 3 (4 ^ n)) = coefficient4 n := by
  have hh (p q : ℕ) :
      (p : ℝ) * ((4 : ℝ) ^ n / (3 : ℝ) ^ Nat.log 3 (4 ^ n)) < (q : ℝ) ↔
        p * 4 ^ n < q * 3 ^ Nat.log 3 (4 ^ n) := by
    simpa only [Nat.cast_pow, Nat.cast_ofNat] using
      scaled_nat_ratio_lt (x := 4 ^ n) (by positivity : 0 < (3 : ℕ) ^ Nat.log 3 (4 ^ n)) p q
  have h15 := hh 15 16
  have h9 := hh 9 10
  have h3 := hh 3 4
  have h2 := hh 2 3
  have h1 := hh 1 2
  have h8 := hh 3 8
  norm_num only [Nat.cast_ofNat, Nat.cast_one, one_mul] at h15 h9 h3 h2 h1 h8
  simp only [realCoefficient4, coefficient4, h15, h9, h3, h2, h1, h8]

def realCoefficient3_normalized (n : ℕ) :
    realCoefficient3 ((3 : ℝ) ^ n / (4 : ℝ) ^ Nat.log 4 (3 ^ n)) = coefficient3 n := by
  have hh (p q : ℕ) :
      (p : ℝ) * ((3 : ℝ) ^ n / (4 : ℝ) ^ Nat.log 4 (3 ^ n)) < (q : ℝ) ↔
        p * 3 ^ n < q * 4 ^ Nat.log 4 (3 ^ n) := by
    simpa only [Nat.cast_pow, Nat.cast_ofNat] using
      scaled_nat_ratio_lt (x := 3 ^ n) (by positivity : 0 < (4 : ℕ) ^ Nat.log 4 (3 ^ n)) p q
  have h3 := hh 3 4
  have h5 := hh 5 8
  have h35 := hh 3 5
  have h1 := hh 1 2
  norm_num only [Nat.cast_ofNat, Nat.cast_one, one_mul] at h3 h5 h35 h1
  simp only [realCoefficient3, coefficient3, h3, h5, h35, h1]

def coefficient4_rotation (n : ℕ) :
    coefficient4 n = realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope)) := by
  rw [← realCoefficient4_normalized, normalized_four_eq_rotation]

def coefficient3_rotation (n : ℕ) :
    coefficient3 n = realCoefficient3 ((4 : ℝ) ^ Int.fract ((n : ℝ) / rotationSlope)) := by
  rw [← realCoefficient3_normalized, normalized_three_eq_rotation]


end Bounty

end SubmissionComponent_RotationCoding

/- Component RotationSeparation; SHA256 2fd960aca7b09d88db238c99cd09b06192600196e4b83ac2be0b8ce7f9bf7f51 -/
section SubmissionComponent_RotationSeparation
/- A direct determinant proof of the separation bound between consecutive rational returns. -/

namespace Bounty

def return_pair_best_approximation {α : ℝ} {p P : ℤ} {q Q n : ℕ} (k : ℤ)
    (hq : 0 < q) (hn : 0 < n) (hnQ : n < Q)
    (hdet : (q : ℤ) * P - p * Q = 1)
    (hd : 0 < (q : ℝ) * α - p) (hd' : 0 < (P : ℝ) - Q * α) :
    (q : ℝ) * α - p ≤ |(n : ℝ) * α - k| := by
  let a : ℤ := P * n - Q * k
  let b : ℤ := q * k - p * n
  have hlin : a * q + b * Q = n := by
    dsimp [a, b]
    calc
      (P * n - Q * k) * q + (q * k - p * n) * Q =
        ((q : ℤ) * P - p * Q) * n := by ring
      _ = n := by rw [hdet, one_mul]
  have hdetR : (q : ℝ) * P - p * Q = 1 := by exact_mod_cast hdet
  have herr : (a : ℝ) * ((q : ℝ) * α - p) -
      (b : ℝ) * ((P : ℝ) - Q * α) = (n : ℝ) * α - k := by
    dsimp [a, b]
    push_cast
    calc
      ((P : ℝ) * n - Q * k) * ((q : ℝ) * α - p) -
          ((q : ℝ) * k - p * n) * ((P : ℝ) - Q * α) =
        ((q : ℝ) * P - p * Q) * ((n : ℝ) * α - k) := by ring
      _ = (n : ℝ) * α - k := by rw [hdetR, one_mul]
  have hqZ : (0 : ℤ) < q := by exact_mod_cast hq
  have hnZ : (0 : ℤ) < n := by exact_mod_cast hn
  have hQZ : (0 : ℤ) < Q := by exact_mod_cast (by omega : 0 < Q)
  have hnQZ : (n : ℤ) < Q := by exact_mod_cast hnQ
  by_cases hb : b ≤ 0
  · have ha : 1 ≤ a := by
      by_contra hh
      have han : a ≤ 0 := by omega
      have h1 := mul_nonpos_of_nonpos_of_nonneg han hqZ.le
      have h2 := mul_nonpos_of_nonpos_of_nonneg hb hQZ.le
      omega
    have haR : (1 : ℝ) ≤ a := by exact_mod_cast ha
    have hbR : (b : ℝ) ≤ 0 := by exact_mod_cast hb
    have h1 := mul_le_mul_of_nonneg_right haR hd.le
    have h2 := mul_nonpos_of_nonpos_of_nonneg hbR hd'.le
    have habs := le_abs_self ((n : ℝ) * α - k)
    nlinarith
  · have hbpos : 1 ≤ b := by omega
    have ha : a ≤ -1 := by
      by_contra hh
      have han : 0 ≤ a := by omega
      have h1 := mul_nonneg han hqZ.le
      have h2 := mul_le_mul_of_nonneg_right hbpos hQZ.le
      nlinarith
    have haR : (a : ℝ) ≤ -1 := by exact_mod_cast ha
    have hbR : (0 : ℝ) ≤ b := by exact_mod_cast (by omega : 0 ≤ b)
    have h1 := mul_le_mul_of_nonneg_right haR hd.le
    have h2 := mul_nonneg hbR hd'.le
    have habs := neg_le_abs ((n : ℝ) * α - k)
    nlinarith

def return_pair_error_identity {α : ℝ} {p P : ℤ} {q Q : ℕ}
    (hdet : (q : ℤ) * P - p * Q = 1) :
    (Q : ℝ) * ((q : ℝ) * α - p) + (q : ℝ) * ((P : ℝ) - Q * α) = 1 := by
  have hh : (q : ℝ) * P - p * Q = 1 := by exact_mod_cast hdet
  nlinarith

def return_pair_positive_error_bound {α : ℝ} {p P : ℤ} {q Q : ℕ}
    (hq : 0 < q) (hQ : 0 < Q) (hdet : (q : ℤ) * P - p * Q = 1)
    (hd' : 0 < (P : ℝ) - Q * α) :
    (q : ℝ) * α - p < 1 / (Q : ℝ) := by
  have hqr : (0 : ℝ) < q := by exact_mod_cast hq
  have hQr : (0 : ℝ) < Q := by exact_mod_cast hQ
  have hpos := mul_pos hqr hd'
  have hh := return_pair_error_identity (α := α) hdet
  apply (lt_div_iff₀ hQr).mpr
  nlinarith

end Bounty

end SubmissionComponent_RotationSeparation

/- Component RotationCoverage; SHA256 595f3ad4399bb6edbaaedadaf630f093208ec2c88ba9c472f0a1136a19bd916a -/
section SubmissionComponent_RotationCoverage
/- A finite-minimum proof that every short rotation arc is visited in a bounded block. -/

namespace Bounty

def fract_sub_small {x d : ℝ} (hd : 0 < d) (hxd : d ≤ Int.fract x) :
    Int.fract (x - d) = Int.fract x - d := by
  have he : x - d = (Int.fract x - d) + (⌊x⌋ : ℝ) := by
    rw [Int.fract]
    ring
  rw [he, Int.fract_add_intCast]
  exact Int.fract_eq_self.mpr ⟨by linarith, by linarith [Int.fract_lt_one x]⟩

def return_pair_arc_covered {α : ℝ} {p P : ℤ} {q Q : ℕ}
    (hq : 0 < q) (hQ : 0 < Q)
    (hd : 0 < (q : ℝ) * α - p) (hd' : 0 < (P : ℝ) - Q * α)
    (hle : (P : ℝ) - Q * α ≤ (q : ℝ) * α - p) (t : ℝ) :
    ∃ j : ℕ, j < q + Q ∧ Int.fract ((j : ℝ) * α - t) < (q : ℝ) * α - p := by
  let f : ℕ → ℝ := fun j => Int.fract ((j : ℝ) * α - t)
  have hne : (Finset.range (q + Q)).Nonempty := ⟨0, Finset.mem_range.mpr (by omega)⟩
  obtain ⟨j, hj, hmin⟩ := Finset.exists_min_image (Finset.range (q + Q)) f hne
  have hjlt := Finset.mem_range.mp hj
  refine ⟨j, hjlt, ?_⟩
  by_contra hh
  have hdf : (q : ℝ) * α - p ≤ f j := le_of_not_gt hh
  by_cases hqj : q ≤ j
  · have hk : j - q < q + Q := by omega
    have hmin' := hmin (j - q) (Finset.mem_range.mpr hk)
    have he : ((j - q : ℕ) : ℝ) * α - t =
        (((j : ℝ) * α - t) - ((q : ℝ) * α - p)) - p := by
      rw [Nat.cast_sub hqj]
      ring
    have hf : f (j - q) = f j - ((q : ℝ) * α - p) := by
      dsimp only [f]
      rw [he, Int.fract_sub_intCast, fract_sub_small hd hdf]
    rw [hf] at hmin'
    linarith
  · have hk : j + Q < q + Q := by omega
    have hmin' := hmin (j + Q) (Finset.mem_range.mpr hk)
    have he : ((j + Q : ℕ) : ℝ) * α - t =
        (((j : ℝ) * α - t) - ((P : ℝ) - Q * α)) + P := by
      push_cast
      ring
    have hf : f (j + Q) = f j - ((P : ℝ) - Q * α) := by
      dsimp only [f]
      rw [he, Int.fract_add_intCast, fract_sub_small hd' (hle.trans hdf)]
    rw [hf] at hmin'
    linarith

def return_pair_arc_covered_block {α : ℝ} {p P : ℤ} {q Q : ℕ}
    (hq : 0 < q) (hQ : 0 < Q)
    (hd : 0 < (q : ℝ) * α - p) (hd' : 0 < (P : ℝ) - Q * α)
    (hle : (P : ℝ) - Q * α ≤ (q : ℝ) * α - p) (t : ℝ) (N : ℕ) :
    ∃ j : ℕ, N ≤ j ∧ j < N + q + Q ∧
      Int.fract ((j : ℝ) * α - t) < (q : ℝ) * α - p := by
  obtain ⟨k, hk, hh⟩ := return_pair_arc_covered hq hQ hd hd' hle (t - (N : ℝ) * α)
  refine ⟨N + k, by omega, by omega, ?_⟩
  have he : ((N + k : ℕ) : ℝ) * α - t = (k : ℝ) * α - (t - (N : ℝ) * α) := by
    push_cast
    ring
  rwa [he]


end Bounty

end SubmissionComponent_RotationCoverage

/- Component ReturnBrackets; SHA256 e10f3ceb601dc46ec297fbea9fe9ca635b94cbd86e990c27a4f4f070c076895d -/
section SubmissionComponent_ReturnBrackets
/- Unbounded unimodular return pairs, constructed directly by mediants. -/

namespace Bounty

def irrational_nat_mul_ne_int {α : ℝ} (hα : Irrational α)
    {q : ℕ} (hq : 0 < q) (p : ℤ) : (q : ℝ) * α ≠ p := by
  intro he
  apply hα.ne_rational p (q : ℤ)
  have hqr : (q : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hq)
  rw [Int.cast_natCast, eq_div_iff hqr]
  nlinarith

def positive_remainder_exists {x y : ℝ} (hy : 0 < y) (hxy : y < x)
    (hne : ∀ k : ℕ, x ≠ (k : ℝ) * y) :
    ∃ k : ℕ, 0 < k ∧ 0 < x - (k : ℝ) * y ∧ x - (k : ℝ) * y < y := by
  let k : ℕ := ⌊x / y⌋₊
  have hratio : 1 < x / y := (lt_div_iff₀ hy).mpr (by simpa using hxy)
  have hk : 0 < k := Nat.floor_pos.mpr hratio.le
  have hlo : (k : ℝ) * y ≤ x := (le_div_iff₀ hy).mp (Nat.floor_le (by linarith))
  have hhi : x < ((k : ℝ) + 1) * y :=
    (div_lt_iff₀ hy).mp (Nat.lt_floor_add_one (x / y))
  refine ⟨k, hk, ?_, by nlinarith⟩
  have hne' := hne k
  have hlt : (k : ℝ) * y < x := lt_of_le_of_ne hlo (Ne.symm hne')
  linarith

structure ReturnBracket (α : ℝ) where
  p : ℤ
  P : ℤ
  q : ℕ
  Q : ℕ
  q_pos : 0 < q
  Q_pos : 0 < Q
  q_le_Q : q ≤ Q
  determinant : (q : ℤ) * P - p * Q = 1
  lower_pos : 0 < (q : ℝ) * α - p
  upper_pos : 0 < (P : ℝ) - Q * α
  upper_lt_lower : (P : ℝ) - Q * α < (q : ℝ) * α - p

def ReturnBracket.next_exists {α : ℝ} (hα : Irrational α) (s : ReturnBracket α) :
    ∃ t : ReturnBracket α, s.q < t.q ∧ s.Q < t.Q := by
  have hsq := s.q_pos
  have hsQ := s.Q_pos
  let d : ℝ := (s.q : ℝ) * α - s.p
  let e : ℝ := (s.P : ℝ) - s.Q * α
  have hd : 0 < d := s.lower_pos
  have he : 0 < e := s.upper_pos
  have hed : e < d := s.upper_lt_lower
  have hne : ∀ k : ℕ, d ≠ (k : ℝ) * e := by
    intro k hh
    have hq : 0 < s.q + k * s.Q := by omega
    apply irrational_nat_mul_ne_int hα hq (s.p + (k : ℤ) * s.P)
    dsimp [d, e] at hh
    push_cast
    nlinarith
  obtain ⟨a, ha, hda, hdae⟩ := positive_remainder_exists he hed hne
  let p' : ℤ := s.p + (a : ℤ) * s.P
  let q' : ℕ := s.q + a * s.Q
  let d' : ℝ := (q' : ℝ) * α - p'
  have hd'eq : d' = d - (a : ℝ) * e := by
    dsimp [d', q', p', d, e]
    push_cast
    ring
  have hd' : 0 < d' := hd'eq ▸ hda
  have hd'e : d' < e := hd'eq ▸ hdae
  have hq' : 0 < q' := by dsimp [q']; omega
  have hne' : ∀ k : ℕ, e ≠ (k : ℝ) * d' := by
    intro k hh
    have hQ : 0 < s.Q + k * q' := by omega
    apply irrational_nat_mul_ne_int hα hQ (s.P + (k : ℤ) * p')
    dsimp [e, d'] at hh
    push_cast
    nlinarith
  obtain ⟨b, hb, heb, hebd⟩ := positive_remainder_exists hd' hd'e hne'
  let P' : ℤ := s.P + (b : ℤ) * p'
  let Q' : ℕ := s.Q + b * q'
  have hQ' : 0 < Q' := by dsimp [Q']; omega
  have hqQ' : q' ≤ Q' := by
    have hh : q' ≤ b * q' := by nlinarith
    dsimp [Q']
    omega
  have hdet' : (q' : ℤ) * s.P - p' * s.Q = 1 := by
    dsimp [q', p']
    push_cast
    nlinarith [s.determinant]
  have hdet'' : (q' : ℤ) * P' - p' * Q' = 1 := by
    dsimp [P', Q']
    push_cast
    nlinarith [hdet']
  have he'eq : (P' : ℝ) - Q' * α = e - (b : ℝ) * d' := by
    dsimp [P', Q', e, d']
    push_cast
    ring
  let t : ReturnBracket α :=
    { p := p', P := P', q := q', Q := Q',
      q_pos := hq', Q_pos := hQ', q_le_Q := hqQ', determinant := hdet'',
      lower_pos := hd', upper_pos := he'eq ▸ heb,
      upper_lt_lower := he'eq ▸ hebd }
  refine ⟨t, ?_, ?_⟩
  · change s.q < q'
    have hh : 0 < a * s.Q := Nat.mul_pos ha s.Q_pos
    dsimp [q']
    omega
  · change s.Q < Q'
    have hh : 0 < b * q' := Nat.mul_pos hb hq'
    dsimp [Q']
    omega

def returnBracket_nonempty {α : ℝ} (hα : Irrational α) (hlo : 1 < α)
    (hhi : α < 2) : Nonempty (ReturnBracket α) := by
  let d : ℝ := α - 1
  let e : ℝ := 2 - α
  have hd : 0 < d := by dsimp [d]; linarith
  have he : 0 < e := by dsimp [e]; linarith
  have hne : e ≠ d := by
    intro hh
    apply hα.ne_rational 3 2
    dsimp [e, d] at hh
    norm_num
    linarith
  by_cases hed : e < d
  · exact ⟨{ p := 1, P := 2, q := 1, Q := 1,
             q_pos := by norm_num, Q_pos := by norm_num, q_le_Q := le_rfl,
             determinant := by norm_num,
             lower_pos := by simpa [d] using hd,
             upper_pos := by simpa [e] using he,
             upper_lt_lower := by simpa [d, e] using hed }⟩
  · have hde : d < e := lt_of_le_of_ne (le_of_not_gt hed) (Ne.symm hne)
    have hmultiple : ∀ k : ℕ, e ≠ (k : ℝ) * d := by
      intro k hh
      apply irrational_nat_mul_ne_int hα (Nat.succ_pos k) (2 + k)
      dsimp [e, d] at hh
      push_cast
      nlinarith
    obtain ⟨k, hk, hrem, hremd⟩ := positive_remainder_exists hd hde hmultiple
    have herr : ((2 + (k : ℤ) : ℤ) : ℝ) - (1 + k : ℕ) * α = e - (k : ℝ) * d := by
      dsimp [e, d]
      push_cast
      ring
    exact ⟨{ p := 1, P := 2 + k, q := 1, Q := 1 + k,
             q_pos := by norm_num, Q_pos := by omega, q_le_Q := by omega,
             determinant := by push_cast; ring,
             lower_pos := by simpa [d] using hd,
             upper_pos := herr ▸ hrem,
             upper_lt_lower := by simpa only [Nat.cast_one, Int.cast_one, one_mul] using
               (show ((2 + (k : ℤ) : ℤ) : ℝ) - (1 + k : ℕ) * α < d from herr ▸ hremd) }⟩


end Bounty

end SubmissionComponent_ReturnBrackets

/- Component ReturnSequence; SHA256 2f8dc55053bcb6273e6119c6de833d275fc60d98d6478c0535d74adfed32421c -/
section SubmissionComponent_ReturnSequence
/- A sequence of return pairs with diverging denominators and vanishing errors. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def returnBracketNext {α : ℝ} (hα : Irrational α)
    (s : ReturnBracket α) : ReturnBracket α := Classical.choose (s.next_exists hα)

def returnBracketNext_growth {α : ℝ} (hα : Irrational α) (s : ReturnBracket α) :
    s.q < (returnBracketNext hα s).q ∧ s.Q < (returnBracketNext hα s).Q :=
  Classical.choose_spec (s.next_exists hα)

noncomputable def returnBracketSequence {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) : ℕ → ReturnBracket α
  | 0 => Classical.choice (returnBracket_nonempty hα hlo hhi)
  | n + 1 => returnBracketNext hα (returnBracketSequence hα hlo hhi n)

def returnBracketSequence_growth {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) (n : ℕ) :
    (returnBracketSequence hα hlo hhi n).q < (returnBracketSequence hα hlo hhi (n + 1)).q ∧
    (returnBracketSequence hα hlo hhi n).Q < (returnBracketSequence hα hlo hhi (n + 1)).Q :=
  returnBracketNext_growth hα (returnBracketSequence hα hlo hhi n)

def returnBracketSequence_lower_bound {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) (n : ℕ) :
    n + 1 ≤ (returnBracketSequence hα hlo hhi n).q ∧
    n + 1 ≤ (returnBracketSequence hα hlo hhi n).Q := by
  induction n with
  | zero =>
    have hh := (returnBracketSequence hα hlo hhi 0).q_pos
    have hh' := (returnBracketSequence hα hlo hhi 0).Q_pos
    omega
  | succ n ih =>
    have hh := returnBracketSequence_growth hα hlo hhi n
    omega

def returnBracketSequence_q_tendsto {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) :
    Tendsto (fun n => (returnBracketSequence hα hlo hhi n).q) atTop atTop := by
  refine tendsto_atTop.2 (fun N => ?_)
  filter_upwards [eventually_ge_atTop N] with n hn
  have hh := (returnBracketSequence_lower_bound hα hlo hhi n).1
  omega

def returnBracketSequence_Q_tendsto {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) :
    Tendsto (fun n => (returnBracketSequence hα hlo hhi n).Q) atTop atTop := by
  refine tendsto_atTop.2 (fun N => ?_)
  filter_upwards [eventually_ge_atTop N] with n hn
  have hh := (returnBracketSequence_lower_bound hα hlo hhi n).2
  omega

def ReturnBracket.lower_error_lt {α : ℝ} (s : ReturnBracket α) :
    (s.q : ℝ) * α - s.p < 1 / (s.Q : ℝ) :=
  return_pair_positive_error_bound s.q_pos s.Q_pos s.determinant s.upper_pos

def ReturnBracket.lower_error_lt_one {α : ℝ} (s : ReturnBracket α) :
    (s.q : ℝ) * α - s.p < 1 := by
  have hQ : (1 : ℝ) ≤ s.Q := by exact_mod_cast s.Q_pos
  have hh : 1 / (s.Q : ℝ) ≤ 1 := by
    apply (div_le_iff₀ (by linarith : (0 : ℝ) < s.Q)).mpr
    nlinarith
  exact s.lower_error_lt.trans_le hh

def ReturnBracket.numerator_bounds {α : ℝ} (s : ReturnBracket α)
    (hlo : 1 < α) (hhi : α < 2) :
    (s.q : ℤ) ≤ s.p ∧ s.p < 2 * s.q ∧
    (s.Q : ℤ) < s.P ∧ s.P ≤ 2 * s.Q ∧ s.p < s.P := by
  have hq : (0 : ℝ) < s.q := by exact_mod_cast s.q_pos
  have hQ : (0 : ℝ) < s.Q := by exact_mod_cast s.Q_pos
  have hd := s.lower_pos
  have he := s.upper_pos
  have he_lt := s.upper_lt_lower
  have hd_one := s.lower_error_lt_one
  have hqlo : (s.q : ℝ) < s.q * α := by nlinarith
  have hqhi : (s.q : ℝ) * α < 2 * s.q := by nlinarith
  have hQlo : (s.Q : ℝ) < s.Q * α := by nlinarith
  have hQhi : (s.Q : ℝ) * α < 2 * s.Q := by nlinarith
  have hp : (s.q : ℤ) ≤ s.p := by
    by_contra hh
    have hhZ : s.p + 1 ≤ (s.q : ℤ) := by omega
    have hhR : (s.p : ℝ) + 1 ≤ s.q := by exact_mod_cast hhZ
    linarith
  have hp' : s.p < 2 * s.q := by
    have hh : (s.p : ℝ) < 2 * s.q := by linarith
    exact_mod_cast hh
  have hP : (s.Q : ℤ) < s.P := by
    have hh : (s.Q : ℝ) < s.P := by linarith
    exact_mod_cast hh
  have hP' : s.P ≤ 2 * s.Q := by
    by_contra hh
    have hhZ : 2 * (s.Q : ℤ) + 1 ≤ s.P := by omega
    have hhR : 2 * (s.Q : ℝ) + 1 ≤ s.P := by exact_mod_cast hhZ
    linarith
  have hqQ : (s.q : ℝ) ≤ s.Q := by exact_mod_cast s.q_le_Q
  have hpP : s.p < s.P := by
    have hh : (s.p : ℝ) < s.P := by nlinarith
    exact_mod_cast hh
  exact ⟨hp, hp', hP, hP', hpP⟩

def returnBracketSequence_error_tendsto {α : ℝ} (hα : Irrational α)
    (hlo : 1 < α) (hhi : α < 2) :
    Tendsto (fun n => ((returnBracketSequence hα hlo hhi n).q : ℝ) * α -
      (returnBracketSequence hα hlo hhi n).p) atTop (nhds 0) := by
  have hlim : Tendsto (fun n => 1 / ((returnBracketSequence hα hlo hhi n).Q : ℝ))
      atTop (nhds 0) :=
    tendsto_one_div_atTop_nhds_zero_nat.comp (returnBracketSequence_Q_tendsto hα hlo hhi)
  exact squeeze_zero
    (fun n => (returnBracketSequence hα hlo hhi n).lower_pos.le)
    (fun n => (returnBracketSequence hα hlo hhi n).lower_error_lt.le) hlim

noncomputable def rotationReturns : ℕ → ReturnBracket rotationSlope :=
  returnBracketSequence rotationSlope_irrational rotationSlope_bounds.1 rotationSlope_bounds.2

def rotationReturns_denominators_tendsto :
    Tendsto (fun n => (rotationReturns n).q) atTop atTop ∧
    Tendsto (fun n => (rotationReturns n).Q) atTop atTop :=
  ⟨returnBracketSequence_q_tendsto _ _ _, returnBracketSequence_Q_tendsto _ _ _⟩

def rotationReturns_error_tendsto :
    Tendsto (fun n => ((rotationReturns n).q : ℝ) * rotationSlope -
      (rotationReturns n).p) atTop (nhds 0) :=
  returnBracketSequence_error_tendsto _ _ _


end Bounty

end SubmissionComponent_ReturnSequence

/- Component ReturnScale; SHA256 13ff160f1964d8740c2042d0a088a38914b4159a1d650f0efba27eed6bcb568a -/
section SubmissionComponent_ReturnScale
/- The common logarithmic scale of the two rotation codings. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def returnScale (n : ℕ) : ℝ := (rotationReturns n).P * Real.log 3

def ReturnBracket.log_bounds (s : ReturnBracket rotationSlope) :
    (s.p : ℝ) * Real.log 3 < (s.q : ℝ) * Real.log 4 ∧
    (s.q : ℝ) * Real.log 4 ≤ (s.Q : ℝ) * Real.log 4 ∧
    (s.Q : ℝ) * Real.log 4 < (s.P : ℝ) * Real.log 3 ∧
    (s.P : ℝ) * Real.log 3 ≤ 2 * ((s.Q : ℝ) * Real.log 4) := by
  have h3 : 0 < Real.log 3 := Real.log_pos (by norm_num)
  have h4 : 0 < Real.log 4 := Real.log_pos (by norm_num)
  have h34 : Real.log 3 < Real.log 4 :=
    Real.log_lt_log (by norm_num) (by norm_num)
  have hrel : rotationSlope * Real.log 3 = Real.log 4 := by
    dsimp [rotationSlope]
    exact div_mul_cancel₀ _ (ne_of_gt h3)
  have hd := mul_pos s.lower_pos h3
  have he := mul_pos s.upper_pos h3
  have hlo : (s.p : ℝ) * Real.log 3 < (s.q : ℝ) * Real.log 4 := by
    nlinarith [hrel]
  have hhi : (s.Q : ℝ) * Real.log 4 < (s.P : ℝ) * Real.log 3 := by
    nlinarith [hrel]
  have hqQ : (s.q : ℝ) ≤ s.Q := by exact_mod_cast s.q_le_Q
  have hmid := mul_le_mul_of_nonneg_right hqQ h4.le
  have hP : (s.P : ℝ) ≤ 2 * s.Q := by
    exact_mod_cast (s.numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2).2.2.2.1
  have hQ : (0 : ℝ) < s.Q := by exact_mod_cast s.Q_pos
  have hPln := mul_le_mul_of_nonneg_right hP h3.le
  refine ⟨hlo, hmid, hhi, ?_⟩
  nlinarith

def returnScale_pos (n : ℕ) : 0 < returnScale n := by
  have h3 : 0 < Real.log 3 := Real.log_pos (by norm_num)
  have hh := (rotationReturns n).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
  have hQ := (rotationReturns n).Q_pos
  have hP : (0 : ℝ) < (rotationReturns n).P := by
    exact_mod_cast (by omega : 0 < (rotationReturns n).P)
  exact mul_pos hP h3

def returnScale_bounds (n : ℕ) :
    ((rotationReturns n).q : ℝ) * Real.log 4 ≤ returnScale n ∧
    ((rotationReturns n).p : ℝ) * Real.log 3 ≤ returnScale n ∧
    returnScale n / 2 ≤ ((rotationReturns n).Q : ℝ) * Real.log 4 ∧
    ((rotationReturns n).Q : ℝ) * Real.log 4 ≤ returnScale n := by
  have hh := (rotationReturns n).log_bounds
  dsimp only [returnScale]
  constructor
  · exact hh.2.1.trans hh.2.2.1.le
  constructor
  · exact (hh.1.trans_le hh.2.1).le.trans hh.2.2.1.le
  constructor
  · linarith [hh.2.2.2]
  · exact hh.2.2.1.le

def returnScale_tendsto : Tendsto returnScale atTop atTop := by
  have hQ : Tendsto (fun n => ((rotationReturns n).Q : ℝ)) atTop atTop :=
    tendsto_natCast_atTop_atTop.comp rotationReturns_denominators_tendsto.2
  have hh : Tendsto (fun n => ((rotationReturns n).Q : ℝ) * Real.log 4) atTop atTop :=
    (tendsto_mul_const_atTop_of_pos (Real.log_pos (by norm_num : (1 : ℝ) < 4))).2 hQ
  exact tendsto_atTop_mono (fun n => (returnScale_bounds n).2.2.2) hh


end Bounty

end SubmissionComponent_ReturnScale

/- Component RotationOrbitSeparation; SHA256 975abbb0963357e1a5555aa26c5c4b89e887d1fa20146f782a7bdb977be8048f -/
section SubmissionComponent_RotationOrbitSeparation
/- Uniform separation of shrinking visits to different rotation orbits. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def integerDistance (x : ℝ) : ℝ :=
  min (Int.fract x) (1 - Int.fract x)

def integerDistance_pos {x : ℝ} (hx : ∀ k : ℤ, x ≠ k) :
    0 < integerDistance x := by
  exact lt_min (Int.fract_pos.mpr (hx ⌊x⌋)) (sub_pos.mpr (Int.fract_lt_one x))

def integerDistance_le_abs (x : ℝ) (k : ℤ) : integerDistance x ≤ |x - k| := by
  by_cases hk : k ≤ ⌊x⌋
  · have hkr : (k : ℝ) ≤ (⌊x⌋ : ℝ) := by exact_mod_cast hk
    have hf : Int.fract x ≤ x - k := by
      change x - (⌊x⌋ : ℝ) ≤ x - k
      linarith
    exact (min_le_left _ _).trans (hf.trans (le_abs_self _))
  · have hk' : ⌊x⌋ + 1 ≤ k := by omega
    have hkr : (⌊x⌋ : ℝ) + 1 ≤ k := by exact_mod_cast hk'
    have hf : 1 - Int.fract x ≤ -(x - k) := by
      change 1 - (x - (⌊x⌋ : ℝ)) ≤ -(x - k)
      linarith
    exact (min_le_right _ _).trans (hf.trans (neg_le_abs _))

def two_visits_distance_lt {α t u δ : ℝ} {i j : ℤ}
    (hi : Int.fract ((i : ℝ) * α - t) < δ)
    (hj : Int.fract ((j : ℝ) * α - u) < δ) :
    integerDistance (((j - i : ℤ) : ℝ) * α - (u - t)) < δ := by
  let x : ℝ := (i : ℝ) * α - t
  let y : ℝ := (j : ℝ) * α - u
  have he : (((j - i : ℤ) : ℝ) * α - (u - t)) -
      ((⌊y⌋ - ⌊x⌋ : ℤ) : ℝ) = Int.fract y - Int.fract x := by
    change _ = (y - (⌊y⌋ : ℝ)) - (x - (⌊x⌋ : ℝ))
    dsimp only [x, y]
    push_cast
    ring
  have hh := integerDistance_le_abs (((j - i : ℤ) : ℝ) * α - (u - t)) (⌊y⌋ - ⌊x⌋)
  rw [he] at hh
  have hh' : |Int.fract y - Int.fract x| < δ := by
    have hxn := Int.fract_nonneg x
    have hyn := Int.fract_nonneg y
    rw [abs_lt]
    constructor <;> linarith
  exact hh.trans_lt hh'

def distinct_orbit_visits_separate {α t u : ℝ} {δ : ℕ → ℝ}
    (hδ : Tendsto δ atTop (nhds 0))
    (horbit : ∀ h k : ℤ, (h : ℝ) * α - (u - t) ≠ k) (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : ℤ,
      Int.fract ((i : ℝ) * α - t) < δ r →
      Int.fract ((j : ℝ) * α - u) < δ r → (M : ℤ) < |j - i| := by
  have hsmall : ∀ᶠ r in atTop, ∀ h ∈ Finset.Icc (-(M : ℤ)) M,
      δ r < integerDistance ((h : ℝ) * α - (u - t)) := by
    apply (eventually_all_finset _).mpr
    intro h hh
    exact hδ.eventually (gt_mem_nhds (integerDistance_pos (horbit h)))
  filter_upwards [hsmall] with r hr i j hi hj
  by_contra hh
  have habs : |j - i| ≤ (M : ℤ) := le_of_not_gt hh
  have hmem : j - i ∈ Finset.Icc (-(M : ℤ)) M := by
    simpa only [Finset.mem_Icc, abs_le] using habs
  have hlarge := hr (j - i) hmem
  have hclose := two_visits_distance_lt hi hj
  linarith

end Bounty

end SubmissionComponent_RotationOrbitSeparation

/- Component JumpOrbitArithmetic; SHA256 3e5bd5dd7bf3f67ac9e88879f3255eb517f9238077437c3b7f28b9d116a54af1 -/
section SubmissionComponent_JumpOrbitArithmetic
/- Prime valuations distinguish all four jump orbits in either coding. -/

namespace Bounty

def rationalPrimeMonomial (a b c : ℤ) : ℚ := (2 : ℚ) ^ a * (3 : ℚ) ^ b * (5 : ℚ) ^ c

def rationalPrimeMonomial_pos (a b c : ℤ) : 0 < rationalPrimeMonomial a b c := by
  unfold rationalPrimeMonomial
  positivity

def padicValRat_nat_zero {p n : ℕ} (h : ¬ p ∣ n) : padicValRat p (n : ℚ) = 0 := by
  rw [padicValRat.of_nat, padicValNat.eq_zero_of_not_dvd h, Nat.cast_zero]

def rationalPrimeMonomial_val_two (a b c : ℤ) :
    padicValRat 2 (rationalPrimeMonomial a b c) = a := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have h2 : padicValRat 2 2 = 1 := padicValRat.self (by norm_num)
  have h3 : padicValRat 2 3 = 0 := padicValRat_nat_zero (by norm_num : ¬ 2 ∣ 3)
  have h5 : padicValRat 2 5 = 0 := padicValRat_nat_zero (by norm_num : ¬ 2 ∣ 5)
  unfold rationalPrimeMonomial
  rw [padicValRat.mul (by positivity) (by positivity),
    padicValRat.mul (by positivity) (by positivity)]
  simp only [padicValRat.zpow, h2, h3, h5]
  ring

def rationalPrimeMonomial_val_five (a b c : ℤ) :
    padicValRat 5 (rationalPrimeMonomial a b c) = c := by
  let : Fact (Nat.Prime 5) := ⟨by norm_num⟩
  have h2 : padicValRat 5 2 = 0 := padicValRat_nat_zero (by norm_num : ¬ 5 ∣ 2)
  have h3 : padicValRat 5 3 = 0 := padicValRat_nat_zero (by norm_num : ¬ 5 ∣ 3)
  have h5 : padicValRat 5 5 = 1 := padicValRat.self (by norm_num)
  unfold rationalPrimeMonomial
  rw [padicValRat.mul (by positivity) (by positivity),
    padicValRat.mul (by positivity) (by positivity)]
  simp only [padicValRat.zpow, h2, h3, h5]
  ring

def rationalPrimeMonomial_mul (a b c x y z : ℤ) :
    rationalPrimeMonomial a b c * rationalPrimeMonomial x y z =
      rationalPrimeMonomial (a + x) (b + y) (c + z) := by
  unfold rationalPrimeMonomial
  rw [zpow_add₀ (by norm_num : (2 : ℚ) ≠ 0),
    zpow_add₀ (by norm_num : (3 : ℚ) ≠ 0),
    zpow_add₀ (by norm_num : (5 : ℚ) ≠ 0)]
  ring

def rational_four_three_monomial (h k : ℤ) :
    (4 : ℚ) ^ h * (3 : ℚ) ^ k = rationalPrimeMonomial (2 * h) k 0 := by
  unfold rationalPrimeMonomial
  have hh : (4 : ℚ) ^ h = (2 : ℚ) ^ (2 * h) := by
    rw [zpow_mul]
    norm_num
  simp only [hh, zpow_zero, mul_one]

def jumpExponent4 (i : Fin 4) : ℤ := ![0, 1, 0, 1] i
def jumpExponent3 (i : Fin 4) : ℤ := ![0, 1, 3, -2] i
def jumpFiveExponent (i : Fin 4) : ℤ := ![0, 0, -1, 1] i
def jumpThreeExponent4 (i : Fin 4) : ℤ := ![0, 0, 2, -2] i

def jumpRepresentative4 (i : Fin 4) : ℚ :=
  rationalPrimeMonomial (jumpExponent4 i) (jumpThreeExponent4 i) (jumpFiveExponent i)

def jumpRepresentative3 (i : Fin 4) : ℚ :=
  rationalPrimeMonomial (jumpExponent3 i) 0 (jumpFiveExponent i)

def jumpRepresentative4_table : jumpRepresentative4 = ![1, 2, 9 / 5, 10 / 9] := by
  funext i
  fin_cases i <;> norm_num [jumpRepresentative4, jumpExponent4, jumpThreeExponent4,
    jumpFiveExponent, rationalPrimeMonomial]

def jumpRepresentative3_table : jumpRepresentative3 = ![1, 2, 8 / 5, 5 / 4] := by
  funext i
  fin_cases i <;> norm_num [jumpRepresentative3, jumpExponent3,
    jumpFiveExponent, rationalPrimeMonomial]

def jumpRepresentative4_distinct_orbits {i j : Fin 4} (hij : i ≠ j) (h k : ℤ) :
    jumpRepresentative4 i ≠ jumpRepresentative4 j * ((4 : ℚ) ^ h * (3 : ℚ) ^ k) := by
  intro he
  rw [rational_four_three_monomial, jumpRepresentative4, jumpRepresentative4,
    rationalPrimeMonomial_mul] at he
  have h2 := congrArg (padicValRat 2) he
  have h5 := congrArg (padicValRat 5) he
  simp only [rationalPrimeMonomial_val_two] at h2
  simp only [rationalPrimeMonomial_val_five] at h5
  fin_cases i <;> fin_cases j <;>
    norm_num [jumpExponent4] at h2 <;>
    norm_num [jumpFiveExponent] at h5 <;> omega

def jumpRepresentative3_distinct_orbits {i j : Fin 4} (hij : i ≠ j) (h k : ℤ) :
    jumpRepresentative3 i ≠ jumpRepresentative3 j * ((4 : ℚ) ^ h * (3 : ℚ) ^ k) := by
  intro he
  rw [rational_four_three_monomial, jumpRepresentative3, jumpRepresentative3,
    rationalPrimeMonomial_mul] at he
  have h2 := congrArg (padicValRat 2) he
  have h5 := congrArg (padicValRat 5) he
  simp only [rationalPrimeMonomial_val_two] at h2
  simp only [rationalPrimeMonomial_val_five] at h5
  fin_cases i <;> fin_cases j <;>
    norm_num [jumpExponent3] at h2 <;>
    norm_num [jumpFiveExponent] at h5 <;> omega


end Bounty

end SubmissionComponent_JumpOrbitArithmetic

/- Component ReciprocalReturns; SHA256 e0c1440bcbbd126242ff54590d6645485c482c46249143837b13fd34f2ae8264 -/
section SubmissionComponent_ReciprocalReturns
/- Transfer the return pair to the reciprocal rotation by reversing its sign. -/

namespace Bounty

def ReturnBracket.negativeInverse {α : ℝ} (s : ReturnBracket α)
    (hlo : 1 < α) (hhi : α < 2) : ReturnBracket (-1 / α) := by
  have hb := s.numerator_bounds hlo hhi
  have hq := s.q_pos
  have hQ := s.Q_pos
  have hp : 0 < s.p := by omega
  have hP : 0 < s.P := by omega
  have hα : 0 < α := by linarith
  have hpZ : (s.p.toNat : ℤ) = s.p := Int.toNat_of_nonneg hp.le
  have hPZ : (s.P.toNat : ℤ) = s.P := Int.toNat_of_nonneg hP.le
  have hpR : (s.p.toNat : ℝ) = s.p := by exact_mod_cast hpZ
  have hPR : (s.P.toNat : ℝ) = s.P := by exact_mod_cast hPZ
  have hlower : (s.p.toNat : ℝ) * (-1 / α) - ((-(s.q : ℤ) : ℤ) : ℝ) =
      ((s.q : ℝ) * α - s.p) / α := by
    rw [hpR]
    push_cast
    field_simp
    ring
  have hupper : ((-(s.Q : ℤ) : ℤ) : ℝ) - (s.P.toNat : ℝ) * (-1 / α) =
      ((s.P : ℝ) - s.Q * α) / α := by
    rw [hPR]
    push_cast
    field_simp
    ring
  refine { p := -(s.q : ℤ), P := -(s.Q : ℤ), q := s.p.toNat, Q := s.P.toNat,
           q_pos := Int.pos_iff_toNat_pos.mp hp,
           Q_pos := Int.pos_iff_toNat_pos.mp hP,
           q_le_Q := Int.toNat_le_toNat hb.2.2.2.2.le,
           determinant := ?_, lower_pos := ?_, upper_pos := ?_, upper_lt_lower := ?_ }
  · rw [hpZ, hPZ]
    nlinarith [s.determinant]
  · rw [hlower]
    exact div_pos s.lower_pos hα
  · rw [hupper]
    exact div_pos s.upper_pos hα
  · rw [hupper, hlower]
    exact div_lt_div_of_pos_right s.upper_lt_lower hα

def ReturnBracket.reciprocal_best_approximation {α : ℝ} (s : ReturnBracket α)
    (hlo : 1 < α) (hhi : α < 2) {n : ℕ} (hn : 0 < n) (hnP : n < s.P.toNat)
    (k : ℤ) : ((s.q : ℝ) * α - s.p) / α ≤ |(n : ℝ) / α - k| := by
  let t := s.negativeInverse hlo hhi
  have hp : 0 < s.p := by
    have hb := s.numerator_bounds hlo hhi
    have hq := s.q_pos
    omega
  have hpR : (s.p.toNat : ℝ) = s.p := by exact_mod_cast Int.toNat_of_nonneg hp.le
  have hh := return_pair_best_approximation (α := -1 / α) (-k)
    t.q_pos hn hnP t.determinant t.lower_pos t.upper_pos
  change (s.p.toNat : ℝ) * (-1 / α) - ((-(s.q : ℤ) : ℤ) : ℝ) ≤
    |(n : ℝ) * (-1 / α) - ((-k : ℤ) : ℝ)| at hh
  have he : (s.p.toNat : ℝ) * (-1 / α) - ((-(s.q : ℤ) : ℤ) : ℝ) =
      ((s.q : ℝ) * α - s.p) / α := by
    rw [hpR]
    push_cast
    field_simp
    ring
  have he' : (n : ℝ) * (-1 / α) - ((-k : ℤ) : ℝ) = -((n : ℝ) / α - k) := by
    push_cast
    ring
  simpa only [he, he', abs_neg] using hh

end Bounty

end SubmissionComponent_ReciprocalReturns

/- Component JumpOrbits; SHA256 f44b7eee2553f15d1225b2c68f2dcf5c55dcfebbce65e9e1f33fe7c62f7b656a -/
section SubmissionComponent_JumpOrbits
/- The logarithmic jump locations lie in pairwise distinct rotation orbits. -/

namespace Bounty

def logarithmic_relation_implies_monomial {a b r s : ℚ}
    (ha : 0 < a) (hb : 1 < b) (hr : 0 < r) (hs : 0 < s) (h k : ℤ)
    (he : (h : ℝ) * (Real.log (a : ℝ) / Real.log (b : ℝ)) -
      (Real.logb (b : ℝ) (s : ℝ) - Real.logb (b : ℝ) (r : ℝ)) = k) :
    s = r * (a ^ h * b ^ (-k)) := by
  have haR : (0 : ℝ) < a := by exact_mod_cast ha
  have hbR : (1 : ℝ) < b := by exact_mod_cast hb
  have hrR : (0 : ℝ) < r := by exact_mod_cast hr
  have hsR : (0 : ℝ) < s := by exact_mod_cast hs
  have hlog : Real.log (b : ℝ) ≠ 0 := ne_of_gt (Real.log_pos hbR)
  have hratio : ((h : ℝ) * Real.log (a : ℝ) -
      (Real.log (s : ℝ) - Real.log (r : ℝ))) / Real.log (b : ℝ) = k := by
    calc
      _ = (h : ℝ) * (Real.log (a : ℝ) / Real.log (b : ℝ)) -
          (Real.log (s : ℝ) / Real.log (b : ℝ) -
            Real.log (r : ℝ) / Real.log (b : ℝ)) := by ring
      _ = k := by simpa only [Real.logb] using he
  have hcross := (div_eq_iff hlog).mp hratio
  have hapos : (0 : ℝ) < (a : ℝ) ^ h := zpow_pos haR h
  have hbpos : (0 : ℝ) < (b : ℝ) ^ (-k) := zpow_pos (by linarith) (-k)
  have hprod : (0 : ℝ) < (r : ℝ) * ((a : ℝ) ^ h * (b : ℝ) ^ (-k)) :=
    mul_pos hrR (mul_pos hapos hbpos)
  have hlogs : Real.log ((r : ℝ) * ((a : ℝ) ^ h * (b : ℝ) ^ (-k))) =
      Real.log (s : ℝ) := by
    rw [Real.log_mul (ne_of_gt hrR) (ne_of_gt (mul_pos hapos hbpos)),
      Real.log_mul (ne_of_gt hapos) (ne_of_gt hbpos), Real.log_zpow, Real.log_zpow,
      Int.cast_neg]
    linarith
  have hreal : (s : ℝ) = (r : ℝ) * ((a : ℝ) ^ h * (b : ℝ) ^ (-k)) :=
    (Real.log_injOn_pos hprod hsR hlogs).symm
  exact_mod_cast hreal

noncomputable def jumpCoordinate4 (i : Fin 4) : ℝ := Real.logb 3 (jumpRepresentative4 i)
noncomputable def jumpCoordinate3 (i : Fin 4) : ℝ := Real.logb 4 (jumpRepresentative3 i)

def jumpOrbits4_distinct {i j : Fin 4} (hij : i ≠ j) (h k : ℤ) :
    (h : ℝ) * rotationSlope - (jumpCoordinate4 j - jumpCoordinate4 i) ≠ k := by
  intro he
  have hi : 0 < jumpRepresentative4 i := rationalPrimeMonomial_pos _ _ _
  have hj : 0 < jumpRepresentative4 j := rationalPrimeMonomial_pos _ _ _
  have hh := logarithmic_relation_implies_monomial (a := 4) (b := 3)
    (by norm_num) (by norm_num) hi hj h k
    (by simpa only [Rat.cast_ofNat, rotationSlope, jumpCoordinate4] using he)
  exact jumpRepresentative4_distinct_orbits (Ne.symm hij) h (-k) hh

def jumpOrbits3_distinct {i j : Fin 4} (hij : i ≠ j) (h k : ℤ) :
    (h : ℝ) * (1 / rotationSlope) - (jumpCoordinate3 j - jumpCoordinate3 i) ≠ k := by
  intro he
  have hi : 0 < jumpRepresentative3 i := rationalPrimeMonomial_pos _ _ _
  have hj : 0 < jumpRepresentative3 j := rationalPrimeMonomial_pos _ _ _
  have hh := logarithmic_relation_implies_monomial (a := 3) (b := 4)
    (by norm_num) (by norm_num) hi hj h k
    (by simpa only [Rat.cast_ofNat, ← inverse_rotationSlope, Real.logb, jumpCoordinate3] using he)
  rw [mul_comm ((3 : ℚ) ^ h) ((4 : ℚ) ^ (-k))] at hh
  exact jumpRepresentative3_distinct_orbits (Ne.symm hij) (-k) h hh

def jumpCoordinate4_zero : jumpCoordinate4 0 = 0 := by
  rw [jumpCoordinate4, jumpRepresentative4_table]
  norm_num [Real.logb]

def jumpCoordinate3_zero : jumpCoordinate3 0 = 0 := by
  rw [jumpCoordinate3, jumpRepresentative3_table]
  norm_num [Real.logb]

end Bounty

end SubmissionComponent_JumpOrbits

/- Component SmallRotationJumps; SHA256 e0aa8d4c0ea48ca11f96f75adeec3334882a6c78fa295c2a074a65b931079535 -/
section SubmissionComponent_SmallRotationJumps
/- Half-open circular jump indicators, with exact floor-difference identities. -/

namespace Bounty

noncomputable def forwardJump (δ t x : ℝ) : ℤ := by
  classical
  exact if 1 - δ ≤ Int.fract (x - t) then 1 else 0

noncomputable def backwardJump (δ t x : ℝ) : ℤ := by
  classical
  exact if Int.fract (x - t) < δ then 1 else 0

def floor_forward_jump {δ : ℝ} (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    ⌊x + δ⌋ - ⌊x⌋ = forwardJump δ 0 x := by
  classical
  have hf0 := Int.fract_nonneg x
  have hf1 := Int.fract_lt_one x
  have hfx : Int.fract x = x - (⌊x⌋ : ℝ) := rfl
  by_cases h : 1 - δ ≤ Int.fract x
  · have he : ⌊x + δ⌋ = ⌊x⌋ + 1 := by
      apply Int.floor_eq_iff.mpr
      push_cast
      constructor <;> linarith
    simp only [forwardJump, sub_zero, if_pos h, he]
    omega
  · have he : ⌊x + δ⌋ = ⌊x⌋ := by
      apply Int.floor_eq_iff.mpr
      constructor <;> linarith
    simp only [forwardJump, sub_zero, if_neg h, he, sub_self]

def floor_backward_jump {δ : ℝ} (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    ⌊x - δ⌋ - ⌊x⌋ = -backwardJump δ 0 x := by
  classical
  have hf0 := Int.fract_nonneg x
  have hf1 := Int.fract_lt_one x
  have hfx : Int.fract x = x - (⌊x⌋ : ℝ) := rfl
  by_cases h : Int.fract x < δ
  · have he : ⌊x - δ⌋ = ⌊x⌋ - 1 := by
      apply Int.floor_eq_iff.mpr
      push_cast
      constructor <;> linarith
    simp only [backwardJump, sub_zero, if_pos h, he]
    omega
  · have he : ⌊x - δ⌋ = ⌊x⌋ := by
      apply Int.floor_eq_iff.mpr
      constructor <;> linarith
    simp only [backwardJump, sub_zero, if_neg h, he, sub_self, neg_zero]

noncomputable def circleStep (t x : ℝ) : ℤ := by
  classical
  exact if t ≤ Int.fract x then 1 else 0

def circleStep_eq_floors {t : ℝ} (ht0 : 0 ≤ t) (ht1 : t < 1) (x : ℝ) :
    circleStep t x = 1 + ⌊x - t⌋ - ⌊x⌋ := by
  classical
  have hh := floor_backward_jump ht0 ht1 x
  by_cases h : t ≤ Int.fract x
  · have hn : ¬ Int.fract x < t := not_lt_of_ge h
    simp only [circleStep, if_pos h, backwardJump, sub_zero, if_neg hn, neg_zero] at *
    omega
  · have hn : Int.fract x < t := lt_of_not_ge h
    simp only [circleStep, if_neg h, backwardJump, sub_zero, if_pos hn] at *
    omega

def circleStep_forward_difference {t δ : ℝ}
    (ht0 : 0 ≤ t) (ht1 : t < 1) (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    circleStep t (x + δ) - circleStep t x =
      forwardJump δ t x - forwardJump δ 0 x := by
  rw [circleStep_eq_floors ht0 ht1, circleStep_eq_floors ht0 ht1]
  have hh := floor_forward_jump hd0 hd1 (x - t)
  have hh' := floor_forward_jump hd0 hd1 x
  have he : x - t + δ = x + δ - t := by ring
  rw [he] at hh
  have hj : forwardJump δ 0 (x - t) = forwardJump δ t x := by
    simp only [forwardJump, sub_zero]
  rw [hj] at hh
  omega

def circleStep_backward_difference {t δ : ℝ}
    (ht0 : 0 ≤ t) (ht1 : t < 1) (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    circleStep t (x - δ) - circleStep t x =
      -backwardJump δ t x + backwardJump δ 0 x := by
  rw [circleStep_eq_floors ht0 ht1, circleStep_eq_floors ht0 ht1]
  have hh := floor_backward_jump hd0 hd1 (x - t)
  have hh' := floor_backward_jump hd0 hd1 x
  have he : x - t - δ = x - δ - t := by ring
  rw [he] at hh
  have hj : backwardJump δ 0 (x - t) = backwardJump δ t x := by
    simp only [backwardJump, sub_zero]
  rw [hj] at hh
  omega

def forwardJump_integer_shift (δ t x : ℝ) (k : ℤ) :
    forwardJump δ (t + k) x = forwardJump δ t x := by
  have he : x - (t + (k : ℝ)) = (x - t) - k := by ring
  simp only [forwardJump, he, Int.fract_sub_intCast]

def backwardJump_integer_shift (δ t x : ℝ) (k : ℤ) :
    backwardJump δ (t + k) x = backwardJump δ t x := by
  have he : x - (t + (k : ℝ)) = (x - t) - k := by ring
  simp only [backwardJump, he, Int.fract_sub_intCast]

def forwardJump_orbit_shift (δ t α : ℝ) (n k : ℤ) :
    forwardJump δ (t + (k : ℝ) * α) ((n : ℝ) * α) =
      forwardJump δ t (((n - k : ℤ) : ℝ) * α) := by
  have he : (n : ℝ) * α - (t + (k : ℝ) * α) = ((n - k : ℤ) : ℝ) * α - t := by
    push_cast
    ring
  simp only [forwardJump, he]

def backwardJump_orbit_shift (δ t α : ℝ) (n k : ℤ) :
    backwardJump δ (t + (k : ℝ) * α) ((n : ℝ) * α) =
      backwardJump δ t (((n - k : ℤ) : ℝ) * α) := by
  have he : (n : ℝ) * α - (t + (k : ℝ) * α) = ((n - k : ℤ) : ℝ) * α - t := by
    push_cast
    ring
  simp only [backwardJump, he]


end Bounty

end SubmissionComponent_SmallRotationJumps

/- Component VanishingJumps; SHA256 90be37583a6485a86d9d2ea122bf13167efb9dc1caac4524ebf22520ef4dc2ea -/
section SubmissionComponent_VanishingJumps
/- Exact initial visits and disappearance of all other fixed-index jump terms. -/

open Filter
open scoped Topology

namespace Bounty

def irrational_int_mul_ne_int {α : ℝ} (hα : Irrational α) {n : ℤ}
    (hn : n ≠ 0) (k : ℤ) : (n : ℝ) * α ≠ k := by
  intro he
  apply hα.ne_rational k n
  have hnR : (n : ℝ) ≠ 0 := by exact_mod_cast hn
  apply (eq_div_iff hnR).mpr
  nlinarith

def jumpOrbit4_int_index_ne {i : Fin 4} {n : ℤ} (hn : i ≠ 0 ∨ n ≠ 0) (k : ℤ) :
    (n : ℝ) * rotationSlope - jumpCoordinate4 i ≠ k := by
  by_cases hi : i = 0
  · subst i
    rw [jumpCoordinate4_zero, sub_zero]
    exact irrational_int_mul_ne_int rotationSlope_irrational (hn.resolve_left (by simp)) k
  · simpa only [jumpCoordinate4_zero, sub_zero] using
      jumpOrbits4_distinct (i := 0) (j := i) (Ne.symm hi) n k

def jumpOrbit3_int_index_ne {i : Fin 4} {n : ℤ} (hn : i ≠ 0 ∨ n ≠ 0) (k : ℤ) :
    (n : ℝ) * (1 / rotationSlope) - jumpCoordinate3 i ≠ k := by
  by_cases hi : i = 0
  · subst i
    rw [jumpCoordinate3_zero, sub_zero]
    have hIrr : Irrational (1 / rotationSlope) := by
      simpa only [one_div] using rotationSlope_irrational.inv
    exact irrational_int_mul_ne_int hIrr (hn.resolve_left (by simp)) k
  · simpa only [jumpCoordinate3_zero, sub_zero] using
      jumpOrbits3_distinct (i := 0) (j := i) (Ne.symm hi) n k

def jumps_eventually_zero {δ : ℕ → ℝ} (hδ : Tendsto δ atTop (nhds 0))
    {x t : ℝ} (hx : ∀ k : ℤ, x - t ≠ k) :
    ∀ᶠ r in atTop, forwardJump (δ r) t x = 0 ∧ backwardJump (δ r) t x = 0 := by
  classical
  have hh := hδ.eventually (gt_mem_nhds (integerDistance_pos hx))
  filter_upwards [hh] with r hr
  have hleft := lt_of_lt_of_le hr (min_le_left (Int.fract (x - t)) (1 - Int.fract (x - t)))
  have hright := lt_of_lt_of_le hr (min_le_right (Int.fract (x - t)) (1 - Int.fract (x - t)))
  have hf : ¬ 1 - δ r ≤ Int.fract (x - t) := by linarith
  have hb : ¬ Int.fract (x - t) < δ r := by linarith
  simp only [forwardJump, backwardJump, if_neg hf, if_neg hb, and_self]

noncomputable def returnError (r : ℕ) : ℝ :=
  ((rotationReturns r).q : ℝ) * rotationSlope - (rotationReturns r).p

def returnError_pos (r : ℕ) : 0 < returnError r := (rotationReturns r).lower_pos

def returnError_lt_one (r : ℕ) : returnError r < 1 := (rotationReturns r).lower_error_lt_one

def returnError_tendsto : Tendsto returnError atTop (nhds 0) := rotationReturns_error_tendsto

def reciprocal_returnError_tendsto :
    Tendsto (fun r => returnError r / rotationSlope) atTop (nhds 0) := by
  simpa only [zero_div] using returnError_tendsto.div_const rotationSlope

noncomputable def jumpVisit4 (r : ℕ) (i : Fin 4) (n : ℤ) : ℤ :=
  forwardJump (returnError r) (jumpCoordinate4 i) ((n : ℝ) * rotationSlope)

noncomputable def jumpVisit3 (r : ℕ) (i : Fin 4) (n : ℤ) : ℤ :=
  backwardJump (returnError r / rotationSlope) (jumpCoordinate3 i) ((n : ℝ) / rotationSlope)

def jumpVisit4_initial (r : ℕ) : jumpVisit4 r 0 0 = 0 := by
  classical
  have hh : ¬ 1 - returnError r ≤ 0 := by linarith [returnError_lt_one r]
  simp only [jumpVisit4, jumpCoordinate4_zero, Int.cast_zero, zero_mul,
    forwardJump, sub_zero, Int.fract_zero, if_neg hh]

def jumpVisit3_initial (r : ℕ) : jumpVisit3 r 0 0 = 1 := by
  classical
  have hh : 0 < returnError r / rotationSlope :=
    div_pos (returnError_pos r) (by linarith [rotationSlope_bounds.1])
  simp only [jumpVisit3, jumpCoordinate3_zero, Int.cast_zero, zero_div,
    backwardJump, sub_zero, Int.fract_zero, if_pos hh]

def jumpVisit4_fixed_eventually_zero {i : Fin 4} {n : ℤ} (hn : i ≠ 0 ∨ n ≠ 0) :
    ∀ᶠ r in atTop, jumpVisit4 r i n = 0 := by
  have hh := jumps_eventually_zero returnError_tendsto (jumpOrbit4_int_index_ne hn)
  exact hh.mono (fun r hr => hr.1)

def jumpVisit3_fixed_eventually_zero {i : Fin 4} {n : ℤ} (hn : i ≠ 0 ∨ n ≠ 0) :
    ∀ᶠ r in atTop, jumpVisit3 r i n = 0 := by
  have horbit : ∀ k : ℤ, (n : ℝ) / rotationSlope - jumpCoordinate3 i ≠ k := by
    simpa only [mul_one_div] using jumpOrbit3_int_index_ne hn
  have hh := jumps_eventually_zero reciprocal_returnError_tendsto horbit
  exact hh.mono (fun r hr => hr.2)


end Bounty

end SubmissionComponent_VanishingJumps

/- Component JumpVisitSpacing; SHA256 11cce2fe1611c20ac1629b15f934e9978300b75cfaf718ae592c68d964ef190c -/
section SubmissionComponent_JumpVisitSpacing
/- Quantitative separation of the actual forward and backward visit sequences. -/

namespace Bounty

def forwardJump_lift {δ t x : ℝ} (h : forwardJump δ t x ≠ 0) :
    t - δ ≤ x - ((⌊x - t⌋ + 1 : ℤ) : ℝ) ∧
      x - ((⌊x - t⌋ + 1 : ℤ) : ℝ) < t := by
  classical
  have hh : 1 - δ ≤ Int.fract (x - t) := by
    by_contra hn
    simp only [forwardJump, if_neg hn, ne_eq, not_true_eq_false] at h
  have hu := Int.fract_lt_one (x - t)
  change 1 - δ ≤ x - t - (⌊x - t⌋ : ℝ) at hh
  change x - t - (⌊x - t⌋ : ℝ) < 1 at hu
  push_cast
  constructor <;> linarith

def backwardJump_lift {δ t x : ℝ} (h : backwardJump δ t x ≠ 0) :
    t ≤ x - (⌊x - t⌋ : ℝ) ∧ x - (⌊x - t⌋ : ℝ) < t + δ := by
  classical
  have hh : Int.fract (x - t) < δ := by
    by_contra hn
    simp only [backwardJump, if_neg hn, ne_eq, not_true_eq_false] at h
  have hl := Int.fract_nonneg (x - t)
  change x - t - (⌊x - t⌋ : ℝ) < δ at hh
  change 0 ≤ x - t - (⌊x - t⌋ : ℝ) at hl
  constructor <;> linarith

def short_lifted_visits_separated {α δ t : ℝ} {Q i j : ℕ} {a b : ℤ}
    (happrox : ∀ n : ℕ, 0 < n → n < Q → ∀ k : ℤ, δ ≤ |(n : ℝ) * α - k|)
    (hij : i < j)
    (hi : t ≤ (i : ℝ) * α - a ∧ (i : ℝ) * α - a < t + δ)
    (hj : t ≤ (j : ℝ) * α - b ∧ (j : ℝ) * α - b < t + δ) :
    Q ≤ j - i := by
  by_contra hh
  have hl := happrox (j - i) (by omega) (by omega) (b - a)
  have he : ((j - i : ℕ) : ℝ) * α - ((b - a : ℤ) : ℝ) =
      ((j : ℝ) * α - b) - ((i : ℝ) * α - a) := by
    rw [Nat.cast_sub (by omega : i ≤ j), Int.cast_sub]
    ring
  rw [he] at hl
  have hs : |((j : ℝ) * α - b) - ((i : ℝ) * α - a)| < δ := by
    rw [abs_lt]
    constructor <;> linarith [hi.1, hi.2, hj.1, hj.2]
  linarith

def jumpVisit4_separated (r : ℕ) (i : Fin 4) {m n : ℕ} (hmn : m < n)
    (hm : jumpVisit4 r i m ≠ 0) (hn : jumpVisit4 r i n ≠ 0) :
    (rotationReturns r).Q ≤ n - m := by
  have hm' := forwardJump_lift hm
  have hn' := forwardJump_lift hn
  simp only [Int.cast_natCast] at hm' hn'
  have hap (k : ℕ) (hk : 0 < k) (hkQ : k < (rotationReturns r).Q) (l : ℤ) :
      returnError r ≤ |(k : ℝ) * rotationSlope - l| :=
    return_pair_best_approximation l (rotationReturns r).q_pos hk hkQ
      (rotationReturns r).determinant (rotationReturns r).lower_pos (rotationReturns r).upper_pos
  exact short_lifted_visits_separated hap hmn
    ⟨hm'.1, by linarith [hm'.2]⟩ ⟨hn'.1, by linarith [hn'.2]⟩

def jumpVisit3_separated (r : ℕ) (i : Fin 4) {m n : ℕ} (hmn : m < n)
    (hm : jumpVisit3 r i m ≠ 0) (hn : jumpVisit3 r i n ≠ 0) :
    (rotationReturns r).P.toNat ≤ n - m := by
  have hm' := backwardJump_lift hm
  have hn' := backwardJump_lift hn
  simp only [Int.cast_natCast] at hm' hn'
  have hap (k : ℕ) (hk : 0 < k) (hkP : k < (rotationReturns r).P.toNat) (l : ℤ) :
      returnError r / rotationSlope ≤ |(k : ℝ) * (1 / rotationSlope) - l| := by
    simpa only [returnError, mul_one_div] using (rotationReturns r).reciprocal_best_approximation
      rotationSlope_bounds.1 rotationSlope_bounds.2 hk hkP l
  apply short_lifted_visits_separated hap hmn
  · simpa only [mul_one_div] using hm'
  · simpa only [mul_one_div] using hn'

def jumpVisit4_time_separation (r : ℕ) (i : Fin 4) {m n : ℕ} (hmn : m < n)
    (hm : jumpVisit4 r i m ≠ 0) (hn : jumpVisit4 r i n ≠ 0) :
    returnScale r / 2 ≤ (n : ℝ) * Real.log 4 - (m : ℝ) * Real.log 4 := by
  have hh : ((rotationReturns r).Q : ℝ) ≤ ((n - m : ℕ) : ℝ) := by
    exact_mod_cast jumpVisit4_separated r i hmn hm hn
  rw [Nat.cast_sub hmn.le] at hh
  have hl := mul_le_mul_of_nonneg_right hh (Real.log_pos (by norm_num : (1 : ℝ) < 4)).le
  have hs := (returnScale_bounds r).2.2.1
  nlinarith

def jumpVisit3_time_separation (r : ℕ) (i : Fin 4) {m n : ℕ} (hmn : m < n)
    (hm : jumpVisit3 r i m ≠ 0) (hn : jumpVisit3 r i n ≠ 0) :
    returnScale r ≤ (n : ℝ) * Real.log 3 - (m : ℝ) * Real.log 3 := by
  have hh : ((rotationReturns r).P.toNat : ℝ) ≤ ((n - m : ℕ) : ℝ) := by
    exact_mod_cast jumpVisit3_separated r i hmn hm hn
  have hP : 0 ≤ (rotationReturns r).P := by
    have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
    have hQ := (rotationReturns r).Q_pos
    omega
  have he : ((rotationReturns r).P.toNat : ℝ) = (rotationReturns r).P := by
    exact_mod_cast Int.toNat_of_nonneg hP
  rw [he, Nat.cast_sub hmn.le] at hh
  have hl := mul_le_mul_of_nonneg_right hh (Real.log_pos (by norm_num : (1 : ℝ) < 3)).le
  unfold returnScale
  nlinarith


end Bounty

end SubmissionComponent_JumpVisitSpacing

/- Component ReturnEventFamilies; SHA256 a1cf329568775017fa1aa72bfa6a0c7d16f966cd9063e9e14ef9893f00158656 -/
section SubmissionComponent_ReturnEventFamilies
/- The sixteen logarithmic event sequences of the exact remainder, and their two cutoffs. -/

namespace Bounty

abbrev ReturnEventFamily := Fin 4 × Fin 4

noncomputable def returnEventStep (i : ReturnEventFamily) : ℝ :=
  if i.1 < 2 then Real.log 4 else Real.log 3

noncomputable def returnEventOffset (r : ℕ) (i : ReturnEventFamily) : ℝ :=
  if i.1 = 0 then ((rotationReturns r).p.toNat : ℝ) * Real.log 3
  else if i.1 = 2 then ((rotationReturns r).q : ℝ) * Real.log 4 else 0

noncomputable def returnEventVisit (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : Prop :=
  0 < n ∧ if i.1 < 2 then jumpVisit4 r i.2 n ≠ 0 else jumpVisit3 r i.2 n ≠ 0

noncomputable def returnEventTime (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : ℝ :=
  (n : ℝ) * returnEventStep i - returnEventOffset r i

def returnEventStep_pos (i : ReturnEventFamily) : 0 < returnEventStep i := by
  unfold returnEventStep
  split <;> exact Real.log_pos (by norm_num)

def returnEventVisit_separation (r : ℕ) (i : ReturnEventFamily) {m n : ℕ}
    (hm : returnEventVisit r i m) (hn : returnEventVisit r i n) (hmn : m < n) :
    returnScale r / 2 ≤ (n : ℝ) * returnEventStep i - (m : ℝ) * returnEventStep i := by
  by_cases hi : i.1 < 2
  · have hm' : jumpVisit4 r i.2 m ≠ 0 := by
      simpa only [returnEventVisit, if_pos hi] using hm.2
    have hn' : jumpVisit4 r i.2 n ≠ 0 := by
      simpa only [returnEventVisit, if_pos hi] using hn.2
    simpa only [returnEventStep, if_pos hi] using jumpVisit4_time_separation r i.2 hmn hm' hn'
  · have hm' : jumpVisit3 r i.2 m ≠ 0 := by
      simpa only [returnEventVisit, if_neg hi] using hm.2
    have hn' : jumpVisit3 r i.2 n ≠ 0 := by
      simpa only [returnEventVisit, if_neg hi] using hn.2
    have hh := jumpVisit3_time_separation r i.2 hmn hm' hn'
    simp only [returnEventStep, if_neg hi]
    linarith [returnScale_pos r]

def returnEventTime_gap (r : ℕ) (a : ℝ) :
    ∃ t : ℝ, a < t ∧ t + returnScale r / 0x64 < a + returnScale r ∧
      ∀ i n, returnEventVisit r i n →
        returnEventTime r i n < t ∨ t + returnScale r / 0x64 < returnEventTime r i n := by
  exact linear_event_families_gap (by norm_num : Fintype.card ReturnEventFamily ≤ 16)
    returnEventStep (returnEventOffset r) (returnEventVisit r) returnEventStep_pos
    (returnScale_pos r) (fun i m n hm hn hmn => returnEventVisit_separation r i hm hn hmn) a

end Bounty

end SubmissionComponent_ReturnEventFamilies

/- Component IntegerIndexSeries; SHA256 d133e28f528910f2edf079b063475b8b14584c1ee4f35c9fcb3f6eedcbb2716f -/
section SubmissionComponent_IntegerIndexSeries
/- Weighted series under the integer shifts occurring in the jump-orbit tables. -/

namespace Bounty

noncomputable def integerIndexSeries (b : ℝ) (f : ℤ → ℝ) : ℝ :=
  ∑' n : ℕ, f (n : ℤ) / b ^ n

def integerIndexSeries_summable {b M : ℝ} {f : ℤ → ℝ}
    (hb : 1 < b) (hf : ∀ k, |f k| ≤ M) :
    Summable (fun n : ℕ => f (n : ℤ) / b ^ n) :=
  weighted_summable hb (fun n => hf (n : ℤ))

def integerIndexSeries_up_one {b M : ℝ} {f : ℤ → ℝ}
    (hb : 1 < b) (hf : ∀ k, |f k| ≤ M) :
    integerIndexSeries b (fun k => f (k + 1)) =
      b * (integerIndexSeries b f - f 0) := by
  have hb0 : b ≠ 0 := ne_of_gt (by linarith : 0 < b)
  have ht := hasSum_nat_tail_sub (integerIndexSeries_summable hb hf)
  simp only [Nat.cast_add, Nat.cast_one, Nat.cast_zero, pow_zero, div_one] at ht
  have hs : HasSum (fun n : ℕ => f ((n : ℤ) + 1) / b ^ n)
      (b * (integerIndexSeries b f - f 0)) := by
    apply (ht.mul_left b).congr_fun
    intro n
    rw [pow_succ]
    field_simp
  exact hs.tsum_eq

def integerIndexSeries_down_one {b M : ℝ} {f : ℤ → ℝ}
    (hb : 1 < b) (hf : ∀ k, |f k| ≤ M) :
    integerIndexSeries b (fun k => f (k - 1)) =
      f (-1) + integerIndexSeries b f / b := by
  have hb0 : b ≠ 0 := ne_of_gt (by linarith : 0 < b)
  have hh := integerIndexSeries_up_one hb (fun k => hf (k - 1))
  simp only [add_sub_cancel_right, zero_sub] at hh
  field_simp
  nlinarith

def integerIndexSeries_down_two {b M : ℝ} {f : ℤ → ℝ}
    (hb : 1 < b) (hf : ∀ k, |f k| ≤ M) :
    integerIndexSeries b (fun k => f (k - 2)) =
      f (-2) + f (-1) / b + integerIndexSeries b f / b ^ 2 := by
  have hh := integerIndexSeries_down_one hb (fun k => hf (k - 1))
  change integerIndexSeries b (fun k => f ((k - 1) - 1)) =
    f ((-1 : ℤ) - 1) + integerIndexSeries b (fun k => f (k - 1)) / b at hh
  have he : (fun k : ℤ => f ((k - 1) - 1)) = (fun k : ℤ => f (k - 2)) := by
    funext k
    congr 1
    ring
  rw [he, show (-1 : ℤ) - 1 = -2 by norm_num, integerIndexSeries_down_one hb hf] at hh
  rw [hh]
  simp only [add_div, div_div, pow_two]
  ring


end Bounty

end SubmissionComponent_IntegerIndexSeries

/- Component CoefficientSteps; SHA256 cda139637f48df8ce7e69bceeb02a0b5dd738c31128953a15331ddb9b494e5d3 -/
section SubmissionComponent_CoefficientSteps
/- Write both coefficient tables as finite sums of circular steps. -/

namespace Bounty

noncomputable def coefficientCut (a c x : ℝ) : ℤ := by
  classical
  exact if a * x < c then 0 else 1

def realCoefficient4_eq_cuts (x : ℝ) :
    realCoefficient4 x = 78 - 48 * coefficientCut 15 16 x - 60 * coefficientCut 9 10 x +
      60 * coefficientCut 3 4 x - 30 * coefficientCut 2 3 x -
      60 * coefficientCut 1 2 x + 48 * coefficientCut 3 8 x := by
  classical
  simp only [realCoefficient4, coefficientCut, one_mul]
  split_ifs <;> norm_num at * <;> linarith

def realCoefficient3_eq_cuts (x : ℝ) :
    realCoefficient3 x = 30 + 5 * coefficientCut 3 4 x - 6 * coefficientCut 5 8 x -
      5 * coefficientCut 3 5 x - 84 * coefficientCut 1 2 x := by
  classical
  simp only [realCoefficient3, coefficientCut, one_mul]
  split_ifs <;> norm_num at * <;> linarith

def circleStep_logb_cut {a b c : ℝ} (ha : 0 < a) (hb : 1 < b) (hc : 0 < c)
    (x : ℝ) : circleStep (Real.logb b (c / a)) x = coefficientCut a c (b ^ Int.fract x) := by
  classical
  have hh : Real.logb b (c / a) ≤ Int.fract x ↔ c ≤ a * b ^ Int.fract x := by
    rw [Real.logb_le_iff_le_rpow hb (div_pos hc ha), div_le_iff₀ ha, mul_comm]
  simp only [circleStep, coefficientCut, hh]
  by_cases h : a * b ^ Int.fract x < c
  · simp only [h, if_true, not_le_of_gt h, if_false]
  · simp only [h, if_false, le_of_not_gt h, if_true]

def coefficient4_circle_steps (x : ℝ) :
    realCoefficient4 ((3 : ℝ) ^ Int.fract x) =
      78 - 48 * circleStep (Real.logb 3 (16 / 15)) x -
      60 * circleStep (Real.logb 3 (10 / 9)) x +
      60 * circleStep (Real.logb 3 (4 / 3)) x -
      30 * circleStep (Real.logb 3 (3 / 2)) x -
      60 * circleStep (Real.logb 3 2) x +
      48 * circleStep (Real.logb 3 (8 / 3)) x := by
  rw [realCoefficient4_eq_cuts]
  have hh (a c : ℝ) (ha : 0 < a) (hc : 0 < c) := circleStep_logb_cut ha
    (by norm_num : (1 : ℝ) < 3) hc x
  rw [hh 15 16 (by norm_num) (by norm_num), hh 9 10 (by norm_num) (by norm_num),
    hh 3 4 (by norm_num) (by norm_num), hh 2 3 (by norm_num) (by norm_num),
    hh 3 8 (by norm_num) (by norm_num)]
  have h2 := hh 1 2 (by norm_num) (by norm_num)
  norm_num only [div_one] at h2
  rw [h2]

def coefficient3_circle_steps (x : ℝ) :
    realCoefficient3 ((4 : ℝ) ^ Int.fract x) =
      30 + 5 * circleStep (Real.logb 4 (4 / 3)) x -
      6 * circleStep (Real.logb 4 (8 / 5)) x -
      5 * circleStep (Real.logb 4 (5 / 3)) x -
      84 * circleStep (Real.logb 4 2) x := by
  rw [realCoefficient3_eq_cuts]
  have hh (a c : ℝ) (ha : 0 < a) (hc : 0 < c) := circleStep_logb_cut ha
    (by norm_num : (1 : ℝ) < 4) hc x
  rw [hh 3 4 (by norm_num) (by norm_num), hh 5 8 (by norm_num) (by norm_num),
    hh 3 5 (by norm_num) (by norm_num)]
  have h2 := hh 1 2 (by norm_num) (by norm_num)
  norm_num only [div_one] at h2
  rw [h2]


end Bounty

end SubmissionComponent_CoefficientSteps

/- Component CoefficientJumps; SHA256 a74467303ff4aae8b31420d73b1a499539d0143b77423f2d12f22dd5e77d67b7 -/
section SubmissionComponent_CoefficientJumps
/- Exact signed jump identities for the two coefficient tables. -/

namespace Bounty

def logb_unit_interval {b y : ℝ} (hb : 1 < b) (hy : 1 ≤ y) (hyb : y < b) :
    0 ≤ Real.logb b y ∧ Real.logb b y < 1 := by
  refine ⟨Real.logb_nonneg hb hy, ?_⟩
  apply (Real.logb_lt_iff_lt_rpow hb (by linarith : 0 < y)).mpr
  simpa only [Real.rpow_one] using hyb

def coefficient4_forward_jumps {δ : ℝ} (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    realCoefficient4 ((3 : ℝ) ^ Int.fract (x + δ)) -
      realCoefficient4 ((3 : ℝ) ^ Int.fract x) =
      90 * forwardJump δ 0 x - 48 * forwardJump δ (Real.logb 3 (16 / 15)) x -
      60 * forwardJump δ (Real.logb 3 (10 / 9)) x +
      60 * forwardJump δ (Real.logb 3 (4 / 3)) x -
      30 * forwardJump δ (Real.logb 3 (3 / 2)) x -
      60 * forwardJump δ (Real.logb 3 2) x +
      48 * forwardJump δ (Real.logb 3 (8 / 3)) x := by
  rw [coefficient4_circle_steps, coefficient4_circle_steps]
  have hh (y : ℝ) (hy : 1 ≤ y) (hyb : y < 3) :=
    logb_unit_interval (by norm_num : (1 : ℝ) < 3) hy hyb
  have h1 := hh (16 / 15) (by norm_num) (by norm_num)
  have h2 := hh (10 / 9) (by norm_num) (by norm_num)
  have h3 := hh (4 / 3) (by norm_num) (by norm_num)
  have h4 := hh (3 / 2) (by norm_num) (by norm_num)
  have h5 := hh 2 (by norm_num) (by norm_num)
  have h6 := hh (8 / 3) (by norm_num) (by norm_num)
  have he1 := circleStep_forward_difference h1.1 h1.2 hd0 hd1 x
  have he2 := circleStep_forward_difference h2.1 h2.2 hd0 hd1 x
  have he3 := circleStep_forward_difference h3.1 h3.2 hd0 hd1 x
  have he4 := circleStep_forward_difference h4.1 h4.2 hd0 hd1 x
  have he5 := circleStep_forward_difference h5.1 h5.2 hd0 hd1 x
  have he6 := circleStep_forward_difference h6.1 h6.2 hd0 hd1 x
  omega

def coefficient3_backward_jumps {δ : ℝ} (hd0 : 0 ≤ δ) (hd1 : δ < 1) (x : ℝ) :
    realCoefficient3 ((4 : ℝ) ^ Int.fract (x - δ)) -
      realCoefficient3 ((4 : ℝ) ^ Int.fract x) =
      -90 * backwardJump δ 0 x - 5 * backwardJump δ (Real.logb 4 (4 / 3)) x +
      6 * backwardJump δ (Real.logb 4 (8 / 5)) x +
      5 * backwardJump δ (Real.logb 4 (5 / 3)) x +
      84 * backwardJump δ (Real.logb 4 2) x := by
  rw [coefficient3_circle_steps, coefficient3_circle_steps]
  have hh (y : ℝ) (hy : 1 ≤ y) (hyb : y < 4) :=
    logb_unit_interval (by norm_num : (1 : ℝ) < 4) hy hyb
  have h1 := hh (4 / 3) (by norm_num) (by norm_num)
  have h2 := hh (8 / 5) (by norm_num) (by norm_num)
  have h3 := hh (5 / 3) (by norm_num) (by norm_num)
  have h4 := hh 2 (by norm_num) (by norm_num)
  have he1 := circleStep_backward_difference h1.1 h1.2 hd0 hd1 x
  have he2 := circleStep_backward_difference h2.1 h2.2 hd0 hd1 x
  have he3 := circleStep_backward_difference h3.1 h3.2 hd0 hd1 x
  have he4 := circleStep_backward_difference h4.1 h4.2 hd0 hd1 x
  omega


end Bounty

end SubmissionComponent_CoefficientJumps

/- Component CoefficientReturnShifts; SHA256 4512f73aaabb9cb35501f37f574b23b006cf0934f440d74d2b75747eb5d141cd -/
section SubmissionComponent_CoefficientReturnShifts
/- Relate integer index shifts to the small positive and negative rotations. -/

namespace Bounty

def coefficient4_return_shift (r n : ℕ) :
    coefficient4 (n + (rotationReturns r).q) =
      realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope + returnError r)) := by
  rw [coefficient4_rotation]
  have he : ((n + (rotationReturns r).q : ℕ) : ℝ) * rotationSlope =
      ((n : ℝ) * rotationSlope + returnError r) + (rotationReturns r).p := by
    dsimp only [returnError]
    push_cast
    ring
  rw [he, Int.fract_add_intCast]

def coefficient3_return_shift (r n : ℕ) :
    coefficient3 (n + (rotationReturns r).p.toNat) =
      realCoefficient3 ((4 : ℝ) ^ Int.fract
        ((n : ℝ) / rotationSlope - returnError r / rotationSlope)) := by
  rw [coefficient3_rotation]
  have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
  have hq := (rotationReturns r).q_pos
  have hp : 0 ≤ (rotationReturns r).p := by omega
  have hpR : ((rotationReturns r).p.toNat : ℝ) = (rotationReturns r).p := by
    exact_mod_cast Int.toNat_of_nonneg hp
  have hα : rotationSlope ≠ 0 := ne_of_gt (by linarith [rotationSlope_bounds.1])
  have he : ((n + (rotationReturns r).p.toNat : ℕ) : ℝ) / rotationSlope =
      ((n : ℝ) / rotationSlope - returnError r / rotationSlope) +
        (((rotationReturns r).q : ℤ) : ℝ) := by
    dsimp only [returnError]
    rw [Nat.cast_add, hpR, Int.cast_natCast]
    field_simp
    <;> ring
  rw [he, Int.fract_add_intCast]

def reciprocal_returnError_lt_one (r : ℕ) : returnError r / rotationSlope < 1 := by
  have hα : 0 < rotationSlope := by linarith [rotationSlope_bounds.1]
  apply (div_lt_iff₀ hα).mpr
  linarith [returnError_lt_one r, rotationSlope_bounds.1]

def coefficient4_difference_is_forward (r n : ℕ) :
    coefficient4 (n + (rotationReturns r).q) - coefficient4 n =
      realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope + returnError r)) -
      realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope)) := by
  rw [coefficient4_return_shift, coefficient4_rotation n]

def coefficient3_difference_is_backward (r n : ℕ) :
    coefficient3 (n + (rotationReturns r).p.toNat) - coefficient3 n =
      realCoefficient3 ((4 : ℝ) ^ Int.fract
        ((n : ℝ) / rotationSlope - returnError r / rotationSlope)) -
      realCoefficient3 ((4 : ℝ) ^ Int.fract ((n : ℝ) / rotationSlope)) := by
  rw [coefficient3_return_shift, coefficient3_rotation n]


end Bounty

end SubmissionComponent_CoefficientReturnShifts

/- Component JumpCoordinateShifts; SHA256 ec4bc4c901ccebe73af2f6e63d4c551317e7a5dd72690af963574f2af9bf5e62 -/
section SubmissionComponent_JumpCoordinateShifts
/- Exact orbit shifts of every discontinuity in the coefficient tables. -/

namespace Bounty

def logb_monomial {a b r : ℝ} (ha : 0 < a) (hb : 1 < b) (hr : 0 < r)
    (k l : ℤ) :
    Real.logb b (r * (a ^ k * b ^ l)) =
      Real.logb b r + (k : ℝ) * (Real.log a / Real.log b) + l := by
  have hlog : Real.log b ≠ 0 := ne_of_gt (Real.log_pos hb)
  have hak : 0 < a ^ k := zpow_pos ha k
  have hbl : 0 < b ^ l := zpow_pos (by linarith) l
  simp only [Real.logb]
  rw [Real.log_mul (ne_of_gt hr) (ne_of_gt (mul_pos hak hbl)),
    Real.log_mul (ne_of_gt hak) (ne_of_gt hbl), Real.log_zpow, Real.log_zpow]
  field_simp
  ring

def jumpCoordinate4_table :
    jumpCoordinate4 = ![0, Real.logb 3 2, Real.logb 3 (9 / 5), Real.logb 3 (10 / 9)] := by
  funext i
  fin_cases i <;> norm_num [jumpCoordinate4, jumpRepresentative4_table, Real.logb]

def jumpCoordinate3_table :
    jumpCoordinate3 = ![0, Real.logb 4 2, Real.logb 4 (8 / 5), Real.logb 4 (5 / 4)] := by
  funext i
  fin_cases i <;> norm_num [jumpCoordinate3, jumpRepresentative3_table, Real.logb]

def jump4_four_thirds : Real.logb 3 (4 / 3) = jumpCoordinate4 0 + rotationSlope - 1 := by
  have hh := logb_monomial (a := 4) (b := 3) (r := 1)
    (by norm_num) (by norm_num) (by norm_num) 1 (-1)
  norm_num at hh
  simpa [jumpCoordinate4_zero, rotationSlope, sub_eq_add_neg] using hh

def jump4_three_halves : Real.logb 3 (3 / 2) = jumpCoordinate4 1 - rotationSlope + 1 := by
  have hh := logb_monomial (a := 4) (b := 3) (r := 2)
    (by norm_num) (by norm_num) (by norm_num) (-1) 1
  norm_num at hh
  simpa [jumpCoordinate4_table, rotationSlope, sub_eq_add_neg] using hh

def jump4_eight_thirds : Real.logb 3 (8 / 3) = jumpCoordinate4 1 + rotationSlope - 1 := by
  have hh := logb_monomial (a := 4) (b := 3) (r := 2)
    (by norm_num) (by norm_num) (by norm_num) 1 (-1)
  norm_num at hh
  simpa [jumpCoordinate4_table, rotationSlope, sub_eq_add_neg] using hh

def jump4_sixteen_fifteenths :
    Real.logb 3 (16 / 15) = jumpCoordinate4 2 + 2 * rotationSlope - 3 := by
  have hh := logb_monomial (a := 4) (b := 3) (r := 9 / 5)
    (by norm_num) (by norm_num) (by norm_num) 2 (-3)
  norm_num at hh
  simpa [jumpCoordinate4_table, rotationSlope, sub_eq_add_neg] using hh

def jump3_four_thirds :
    Real.logb 4 (4 / 3) = jumpCoordinate3 0 - (1 / rotationSlope) + 1 := by
  have hh := logb_monomial (a := 3) (b := 4) (r := 1)
    (by norm_num) (by norm_num) (by norm_num) (-1) 1
  norm_num at hh
  rw [← inverse_rotationSlope]
  simpa [jumpCoordinate3_zero, Real.logb, sub_eq_add_neg] using hh

def jump3_five_thirds :
    Real.logb 4 (5 / 3) = jumpCoordinate3 3 - (1 / rotationSlope) + 1 := by
  have hh := logb_monomial (a := 3) (b := 4) (r := 5 / 4)
    (by norm_num) (by norm_num) (by norm_num) (-1) 1
  norm_num at hh
  rw [← inverse_rotationSlope]
  simpa [jumpCoordinate3_table, Real.logb, sub_eq_add_neg] using hh


end Bounty

end SubmissionComponent_JumpCoordinateShifts

/- Component OrbitJumpTables; SHA256 521809bd0966883052522674b4be7dc5558fd79ceac6d4f08a37ba5fdd44479f -/
section SubmissionComponent_OrbitJumpTables
/- Rewrite the signed coefficient jumps in the four representative orbits. -/

namespace Bounty

def forwardJump_two_shifts (δ t α : ℝ) (n k l : ℤ) :
    forwardJump δ (t + (k : ℝ) * α + l) ((n : ℝ) * α) =
      forwardJump δ t (((n - k : ℤ) : ℝ) * α) := by
  rw [forwardJump_integer_shift, forwardJump_orbit_shift]

def backwardJump_two_shifts (δ t α : ℝ) (n k l : ℤ) :
    backwardJump δ (t + (k : ℝ) * α + l) ((n : ℝ) * α) =
      backwardJump δ t (((n - k : ℤ) : ℝ) * α) := by
  rw [backwardJump_integer_shift, backwardJump_orbit_shift]

def coefficient4_forward_visits (r : ℕ) (n : ℤ) :
    realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope + returnError r)) -
      realCoefficient4 ((3 : ℝ) ^ Int.fract ((n : ℝ) * rotationSlope)) =
      90 * jumpVisit4 r 0 n - 48 * jumpVisit4 r 2 (n - 2) - 60 * jumpVisit4 r 3 n +
      60 * jumpVisit4 r 0 (n - 1) - 30 * jumpVisit4 r 1 (n + 1) -
      60 * jumpVisit4 r 1 n + 48 * jumpVisit4 r 1 (n - 1) := by
  rw [coefficient4_forward_jumps (returnError_pos r).le (returnError_lt_one r)]
  have hs (t : ℝ) (k l : ℤ) :=
    forwardJump_two_shifts (returnError r) t rotationSlope n k l
  have h0 : forwardJump (returnError r) 0 ((n : ℝ) * rotationSlope) = jumpVisit4 r 0 n := by
    simp only [jumpVisit4, jumpCoordinate4_zero]
  have h16 : forwardJump (returnError r) (Real.logb 3 (16 / 15)) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 2 (n - 2) := by
    rw [jump4_sixteen_fifteenths]
    simpa only [jumpVisit4, Int.cast_ofNat, Int.cast_neg, sub_eq_add_neg] using
      hs (jumpCoordinate4 2) 2 (-3)
  have h10 : forwardJump (returnError r) (Real.logb 3 (10 / 9)) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 3 n := by
    have ht : jumpCoordinate4 3 = Real.logb 3 (10 / 9) := by rw [jumpCoordinate4_table]; rfl
    simp only [jumpVisit4, ht]
  have h4 : forwardJump (returnError r) (Real.logb 3 (4 / 3)) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 0 (n - 1) := by
    rw [jump4_four_thirds]
    simpa only [jumpVisit4, Int.cast_one, Int.cast_neg, one_mul, sub_eq_add_neg] using
      hs (jumpCoordinate4 0) 1 (-1)
  have h3 : forwardJump (returnError r) (Real.logb 3 (3 / 2)) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 1 (n + 1) := by
    rw [jump4_three_halves]
    simpa only [jumpVisit4, Int.cast_one, Int.cast_neg, neg_one_mul, sub_neg_eq_add,
      sub_eq_add_neg, neg_neg] using hs (jumpCoordinate4 1) (-1) 1
  have h2 : forwardJump (returnError r) (Real.logb 3 2) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 1 n := by
    have ht : jumpCoordinate4 1 = Real.logb 3 2 := by rw [jumpCoordinate4_table]; rfl
    simp only [jumpVisit4, ht]
  have h8 : forwardJump (returnError r) (Real.logb 3 (8 / 3)) ((n : ℝ) * rotationSlope) =
      jumpVisit4 r 1 (n - 1) := by
    rw [jump4_eight_thirds]
    simpa only [jumpVisit4, Int.cast_one, Int.cast_neg, one_mul, sub_eq_add_neg] using
      hs (jumpCoordinate4 1) 1 (-1)
  rw [h0, h16, h10, h4, h3, h2, h8]

def coefficient3_backward_visits (r : ℕ) (n : ℤ) :
    realCoefficient3 ((4 : ℝ) ^ Int.fract
        ((n : ℝ) / rotationSlope - returnError r / rotationSlope)) -
      realCoefficient3 ((4 : ℝ) ^ Int.fract ((n : ℝ) / rotationSlope)) =
      -90 * jumpVisit3 r 0 n - 5 * jumpVisit3 r 0 (n + 1) + 6 * jumpVisit3 r 2 n +
      5 * jumpVisit3 r 3 (n + 1) + 84 * jumpVisit3 r 1 n := by
  have hd : 0 ≤ returnError r / rotationSlope :=
    div_nonneg (returnError_pos r).le (by linarith [rotationSlope_bounds.1])
  rw [coefficient3_backward_jumps hd (reciprocal_returnError_lt_one r)]
  have hs (t : ℝ) (k l : ℤ) :=
    backwardJump_two_shifts (returnError r / rotationSlope) t (1 / rotationSlope) n k l
  have h0 : backwardJump (returnError r / rotationSlope) 0 ((n : ℝ) / rotationSlope) =
      jumpVisit3 r 0 n := by
    simp only [jumpVisit3, jumpCoordinate3_zero]
  have h4 : backwardJump (returnError r / rotationSlope) (Real.logb 4 (4 / 3))
      ((n : ℝ) / rotationSlope) = jumpVisit3 r 0 (n + 1) := by
    rw [jump3_four_thirds]
    simpa only [jumpVisit3, Int.cast_one, Int.cast_neg, neg_one_mul, sub_neg_eq_add,
      sub_eq_add_neg, mul_one_div, neg_neg, neg_div] using hs (jumpCoordinate3 0) (-1) 1
  have h8 : backwardJump (returnError r / rotationSlope) (Real.logb 4 (8 / 5))
      ((n : ℝ) / rotationSlope) = jumpVisit3 r 2 n := by
    have ht : jumpCoordinate3 2 = Real.logb 4 (8 / 5) := by rw [jumpCoordinate3_table]; rfl
    simp only [jumpVisit3, ht]
  have h5 : backwardJump (returnError r / rotationSlope) (Real.logb 4 (5 / 3))
      ((n : ℝ) / rotationSlope) = jumpVisit3 r 3 (n + 1) := by
    rw [jump3_five_thirds]
    simpa only [jumpVisit3, Int.cast_one, Int.cast_neg, neg_one_mul, sub_neg_eq_add,
      sub_eq_add_neg, mul_one_div, neg_neg, neg_div] using hs (jumpCoordinate3 3) (-1) 1
  have h2 : backwardJump (returnError r / rotationSlope) (Real.logb 4 2)
      ((n : ℝ) / rotationSlope) = jumpVisit3 r 1 n := by
    have ht : jumpCoordinate3 1 = Real.logb 4 2 := by rw [jumpCoordinate3_table]; rfl
    simp only [jumpVisit3, ht]
  rw [h0, h4, h8, h5, h2]

def coefficient4_return_visits (r n : ℕ) :
    coefficient4 (n + (rotationReturns r).q) - coefficient4 n =
      90 * jumpVisit4 r 0 n - 48 * jumpVisit4 r 2 ((n : ℤ) - 2) - 60 * jumpVisit4 r 3 n +
      60 * jumpVisit4 r 0 ((n : ℤ) - 1) - 30 * jumpVisit4 r 1 ((n : ℤ) + 1) -
      60 * jumpVisit4 r 1 n + 48 * jumpVisit4 r 1 ((n : ℤ) - 1) := by
  rw [coefficient4_difference_is_forward]
  simpa only [Int.cast_natCast] using coefficient4_forward_visits r (n : ℤ)

def coefficient3_return_visits (r n : ℕ) :
    coefficient3 (n + (rotationReturns r).p.toNat) - coefficient3 n =
      -90 * jumpVisit3 r 0 n - 5 * jumpVisit3 r 0 ((n : ℤ) + 1) + 6 * jumpVisit3 r 2 n +
      5 * jumpVisit3 r 3 ((n : ℤ) + 1) + 84 * jumpVisit3 r 1 n := by
  rw [coefficient3_difference_is_backward]
  simpa only [Int.cast_natCast] using coefficient3_backward_visits r (n : ℤ)


end Bounty

end SubmissionComponent_OrbitJumpTables

/- Component GroupedJumpSeries; SHA256 3a7f84ffb11af317c8912946eaa4f361e37dfad83e9a68b4d66e08024175e7d8 -/
section SubmissionComponent_GroupedJumpSeries
/- Group the weighted jumps by representative orbit, including all initial terms. -/

open Filter
open scoped Topology

namespace Bounty

def jumpVisit4_abs_le_one (r : ℕ) (i : Fin 4) (n : ℤ) :
    |(jumpVisit4 r i n : ℝ)| ≤ 1 := by
  classical
  unfold jumpVisit4 forwardJump
  split <;> norm_num

def jumpVisit3_abs_le_one (r : ℕ) (i : Fin 4) (n : ℤ) :
    |(jumpVisit3 r i n : ℝ)| ≤ 1 := by
  classical
  unfold jumpVisit3 backwardJump
  split <;> norm_num

noncomputable def positiveJumpSeries4 (r : ℕ) (i : Fin 4) : ℝ :=
  ∑' n : ℕ, (jumpVisit4 r i (n + 1) : ℝ) / (4 : ℝ) ^ (n + 1)

noncomputable def positiveJumpSeries3 (r : ℕ) (i : Fin 4) : ℝ :=
  ∑' n : ℕ, (jumpVisit3 r i (n + 1) : ℝ) / (3 : ℝ) ^ (n + 1)

def positiveJumpSeries4_eq (r : ℕ) (i : Fin 4) :
    positiveJumpSeries4 r i =
      integerIndexSeries 4 (fun k => (jumpVisit4 r i k : ℝ)) - jumpVisit4 r i 0 := by
  have hh := hasSum_nat_tail_sub
    (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 4) (jumpVisit4_abs_le_one r i))
  simp only [Nat.cast_add, Nat.cast_one, Nat.cast_zero, pow_zero, div_one] at hh
  exact hh.tsum_eq

def positiveJumpSeries3_eq (r : ℕ) (i : Fin 4) :
    positiveJumpSeries3 r i =
      integerIndexSeries 3 (fun k => (jumpVisit3 r i k : ℝ)) - jumpVisit3 r i 0 := by
  have hh := hasSum_nat_tail_sub
    (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 3) (jumpVisit3_abs_le_one r i))
  simp only [Nat.cast_add, Nat.cast_one, Nat.cast_zero, pow_zero, div_one] at hh
  exact hh.tsum_eq

def coefficient4_return_series_raw (r : ℕ) :
    (∑' n : ℕ, ((coefficient4 (n + (rotationReturns r).q) - coefficient4 n : ℤ) : ℝ) /
        (4 : ℝ) ^ n) =
      90 * integerIndexSeries 4 (fun k => (jumpVisit4 r 0 k : ℝ)) -
      48 * integerIndexSeries 4 (fun k => (jumpVisit4 r 2 (k - 2) : ℝ)) -
      60 * integerIndexSeries 4 (fun k => (jumpVisit4 r 3 k : ℝ)) +
      60 * integerIndexSeries 4 (fun k => (jumpVisit4 r 0 (k - 1) : ℝ)) -
      30 * integerIndexSeries 4 (fun k => (jumpVisit4 r 1 (k + 1) : ℝ)) -
      60 * integerIndexSeries 4 (fun k => (jumpVisit4 r 1 k : ℝ)) +
      48 * integerIndexSeries 4 (fun k => (jumpVisit4 r 1 (k - 1) : ℝ)) := by
  have hs (i : Fin 4) (k : ℤ) :=
    (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 4)
      (fun n => jumpVisit4_abs_le_one r i (n + k))).hasSum
  have hh := ((((((hs 0 0).mul_left 90).sub ((hs 2 (-2)).mul_left 48)).sub
    ((hs 3 0).mul_left 60)).add ((hs 0 (-1)).mul_left 60)).sub
    ((hs 1 1).mul_left 30)).sub ((hs 1 0).mul_left 60) |>.add ((hs 1 (-1)).mul_left 48)
  simp only [add_zero, ← sub_eq_add_neg] at hh
  apply HasSum.tsum_eq
  apply hh.congr_fun
  intro n
  rw [coefficient4_return_visits]
  push_cast
  ring

def coefficient3_return_series_raw (r : ℕ) :
    (∑' n : ℕ, ((coefficient3 (n + (rotationReturns r).p.toNat) - coefficient3 n : ℤ) : ℝ) /
        (3 : ℝ) ^ n) =
      -90 * integerIndexSeries 3 (fun k => (jumpVisit3 r 0 k : ℝ)) -
      5 * integerIndexSeries 3 (fun k => (jumpVisit3 r 0 (k + 1) : ℝ)) +
      6 * integerIndexSeries 3 (fun k => (jumpVisit3 r 2 k : ℝ)) +
      5 * integerIndexSeries 3 (fun k => (jumpVisit3 r 3 (k + 1) : ℝ)) +
      84 * integerIndexSeries 3 (fun k => (jumpVisit3 r 1 k : ℝ)) := by
  have hs (i : Fin 4) (k : ℤ) :=
    (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 3)
      (fun n => jumpVisit3_abs_le_one r i (n + k))).hasSum
  have hh := (((((hs 0 0).mul_left (-90)).sub ((hs 0 1).mul_left 5)).add
    ((hs 2 0).mul_left 6)).add ((hs 3 1).mul_left 5)).add ((hs 1 0).mul_left 84)
  simp only [add_zero] at hh
  apply HasSum.tsum_eq
  apply hh.congr_fun
  intro n
  rw [coefficient3_return_visits]
  push_cast
  ring

def coefficient4_return_series_grouped :
    ∀ᶠ r in atTop,
      (∑' n : ℕ, ((coefficient4 (n + (rotationReturns r).q) - coefficient4 n : ℤ) : ℝ) /
          (4 : ℝ) ^ n) =
        0x69 * positiveJumpSeries4 r 0 - 0xa8 * positiveJumpSeries4 r 1 -
        3 * positiveJumpSeries4 r 2 - 60 * positiveJumpSeries4 r 3 := by
  have h01 := jumpVisit4_fixed_eventually_zero (i := 0) (n := -1) (by decide)
  have h11 := jumpVisit4_fixed_eventually_zero (i := 1) (n := -1) (by decide)
  have h10 := jumpVisit4_fixed_eventually_zero (i := 1) (n := 0) (by decide)
  have h21 := jumpVisit4_fixed_eventually_zero (i := 2) (n := -1) (by decide)
  have h22 := jumpVisit4_fixed_eventually_zero (i := 2) (n := -2) (by decide)
  have h20 := jumpVisit4_fixed_eventually_zero (i := 2) (n := 0) (by decide)
  have h30 := jumpVisit4_fixed_eventually_zero (i := 3) (n := 0) (by decide)
  filter_upwards [h01, h11, h10, h21, h22, h20, h30] with r h01 h11 h10 h21 h22 h20 h30
  rw [coefficient4_return_series_raw]
  rw [integerIndexSeries_down_two (by norm_num : (1 : ℝ) < 4) (jumpVisit4_abs_le_one r 2),
    integerIndexSeries_down_one (by norm_num : (1 : ℝ) < 4) (jumpVisit4_abs_le_one r 0),
    integerIndexSeries_up_one (by norm_num : (1 : ℝ) < 4) (jumpVisit4_abs_le_one r 1),
    integerIndexSeries_down_one (by norm_num : (1 : ℝ) < 4) (jumpVisit4_abs_le_one r 1)]
  simp only [positiveJumpSeries4_eq, jumpVisit4_initial, h01, h11, h10, h21, h22, h20, h30,
    Int.cast_zero]
  ring

def coefficient3_return_series_grouped :
    ∀ᶠ r in atTop,
      (∑' n : ℕ, ((coefficient3 (n + (rotationReturns r).p.toNat) - coefficient3 n : ℤ) : ℝ) /
          (3 : ℝ) ^ n) =
        -90 - 0x69 * positiveJumpSeries3 r 0 + 84 * positiveJumpSeries3 r 1 +
        6 * positiveJumpSeries3 r 2 + 15 * positiveJumpSeries3 r 3 := by
  have h10 := jumpVisit3_fixed_eventually_zero (i := 1) (n := 0) (by decide)
  have h20 := jumpVisit3_fixed_eventually_zero (i := 2) (n := 0) (by decide)
  have h30 := jumpVisit3_fixed_eventually_zero (i := 3) (n := 0) (by decide)
  filter_upwards [h10, h20, h30] with r h10 h20 h30
  rw [coefficient3_return_series_raw]
  rw [integerIndexSeries_up_one (by norm_num : (1 : ℝ) < 3) (jumpVisit3_abs_le_one r 0),
    integerIndexSeries_up_one (by norm_num : (1 : ℝ) < 3) (jumpVisit3_abs_le_one r 3)]
  simp only [positiveJumpSeries3_eq, jumpVisit3_initial, h10, h20, h30, Int.cast_zero,
    Int.cast_one]
  ring


end Bounty

end SubmissionComponent_GroupedJumpSeries

/- Component ReturnDifferenceIdentity; SHA256 332603a11b26e82cad59ee40d4884e5a7f7167bd3264ae8dee8cf7a0e4826e03 -/
section SubmissionComponent_ReturnDifferenceIdentity
/- An integer prefix and the exact four-family remainder for each small return. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def groupedJump4 (r : ℕ) : ℝ :=
  0x69 * positiveJumpSeries4 r 0 - 0xa8 * positiveJumpSeries4 r 1 -
    3 * positiveJumpSeries4 r 2 - 60 * positiveJumpSeries4 r 3

noncomputable def groupedJump3 (r : ℕ) : ℝ :=
  -0x69 * positiveJumpSeries3 r 0 + 84 * positiveJumpSeries3 r 1 +
    6 * positiveJumpSeries3 r 2 + 15 * positiveJumpSeries3 r 3

noncomputable def returnIntegerPrefix (r : ℕ) : ℤ :=
  ((3 : ℤ) ^ (rotationReturns r).p.toNat - 1) *
      integerPrefix coefficient4 4 (rotationReturns r).q +
    ((4 : ℤ) ^ (rotationReturns r).q - 1) *
      (integerPrefix coefficient3 3 (rotationReturns r).p.toNat - 90)

noncomputable def returnRemainder (r : ℕ) : ℝ :=
  ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) * groupedJump4 r +
    ((4 : ℝ) ^ (rotationReturns r).q - 1) * groupedJump3 r

def returnDifferenceIdentity :
    ∀ᶠ r in atTop,
      ((4 : ℝ) ^ (rotationReturns r).q - 1) *
        ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) * (0xb4 * explicitDensity - 32) -
          returnIntegerPrefix r = returnRemainder r := by
  filter_upwards [coefficient4_return_series_grouped, coefficient3_return_series_grouped]
    with r h4 h3
  have ha := integer_weighted_shift (by norm_num : 1 < (4 : ℕ))
    coefficient4_bound (rotationReturns r).q
  have hb := integer_weighted_shift (by norm_num : 1 < (3 : ℕ))
    coefficient3_bound (rotationReturns r).p.toNat
  norm_num only [Nat.cast_ofNat] at ha hb
  rw [h4] at ha
  rw [h3] at hb
  have hz : 0xb4 * explicitDensity - 32 =
      (∑' n : ℕ, (coefficient4 n : ℝ) / (4 : ℝ) ^ n) +
      (∑' n : ℕ, (coefficient3 n : ℝ) / (3 : ℝ) ^ n) := by
    unfold explicitDensity
    ring
  rw [hz]
  calc
    _ = ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) *
        (((4 : ℝ) ^ (rotationReturns r).q - 1) *
          (∑' n : ℕ, (coefficient4 n : ℝ) / (4 : ℝ) ^ n)) +
      ((4 : ℝ) ^ (rotationReturns r).q - 1) *
        (((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) *
          (∑' n : ℕ, (coefficient3 n : ℝ) / (3 : ℝ) ^ n)) -
      returnIntegerPrefix r := by ring
    _ = returnRemainder r := by
      rw [ha, hb]
      unfold returnIntegerPrefix returnRemainder groupedJump4 groupedJump3
      push_cast
      ring


end Bounty

end SubmissionComponent_ReturnDifferenceIdentity

/- Component ReturnEventSeries; SHA256 f58e196b7ba93d2326f2c6a08e99d6b8716dd77f314bd6e3378eb22a549fc664 -/
section SubmissionComponent_ReturnEventSeries
/- The exact remainder as sixteen absolutely convergent exponential event series. -/

namespace Bounty

def returnEventCoefficient4 (i : Fin 4) : ℤ := ![0x69, -0xa8, -3, -60] i

def returnEventCoefficient3 (i : Fin 4) : ℤ := ![0x69, -84, -6, -15] i

def returnEventCoefficient (i : ReturnEventFamily) : ℤ :=
  if i.1 = 0 then returnEventCoefficient4 i.2
  else if i.1 = 1 then -returnEventCoefficient4 i.2
  else if i.1 = 2 then -returnEventCoefficient3 i.2
  else returnEventCoefficient3 i.2

noncomputable def returnEventTerm (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : ℝ := by
  classical
  exact if returnEventVisit r i n then
    (returnEventCoefficient i : ℝ) * Real.exp (-returnEventTime r i n) else 0

def jumpVisit4_eq_one_of_ne_zero {r : ℕ} {i : Fin 4} {n : ℤ}
    (h : jumpVisit4 r i n ≠ 0) : jumpVisit4 r i n = 1 := by
  unfold jumpVisit4 forwardJump at *
  split at * <;> simp_all

def jumpVisit3_eq_one_of_ne_zero {r : ℕ} {i : Fin 4} {n : ℤ}
    (h : jumpVisit3 r i n ≠ 0) : jumpVisit3 r i n = 1 := by
  unfold jumpVisit3 backwardJump at *
  split at * <;> simp_all

def exp_neg_event_time {b : ℝ} (hb : 0 < b) (offset : ℝ) (n : ℕ) :
    Real.exp (-((n : ℝ) * Real.log b - offset)) = Real.exp offset / b ^ n := by
  rw [neg_sub, Real.exp_sub, Real.exp_nat_mul, Real.exp_log hb]

def returnEventTerm_eq_weighted (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    returnEventTerm r i n =
      if 0 < n then
        (returnEventCoefficient i : ℝ) * Real.exp (returnEventOffset r i) *
          (if i.1 < 2 then (jumpVisit4 r i.2 n : ℝ) / (4 : ℝ) ^ n
          else (jumpVisit3 r i.2 n : ℝ) / (3 : ℝ) ^ n)
      else 0 := by
  classical
  by_cases hn : 0 < n
  · by_cases hi : i.1 < 2
    · by_cases hj : jumpVisit4 r i.2 n ≠ 0
      · have he := jumpVisit4_eq_one_of_ne_zero hj
        have hv : returnEventVisit r i n := by
          simpa only [returnEventVisit, if_pos hi] using And.intro hn hj
        rw [returnEventTerm, if_pos hv, if_pos hn, if_pos hi, he, Int.cast_one]
        simp only [returnEventTime, returnEventStep, if_pos hi]
        rw [exp_neg_event_time (by norm_num : (0 : ℝ) < 4)]
        ring
      · have he : jumpVisit4 r i.2 n = 0 := not_ne_iff.mp hj
        simp [returnEventTerm, returnEventVisit, hn, hi, he]
    · by_cases hj : jumpVisit3 r i.2 n ≠ 0
      · have he := jumpVisit3_eq_one_of_ne_zero hj
        have hv : returnEventVisit r i n := by
          simpa only [returnEventVisit, if_neg hi] using And.intro hn hj
        rw [returnEventTerm, if_pos hv, if_pos hn, if_neg hi, he, Int.cast_one]
        simp only [returnEventTime, returnEventStep, if_neg hi]
        rw [exp_neg_event_time (by norm_num : (0 : ℝ) < 3)]
        ring
      · have he : jumpVisit3 r i.2 n = 0 := not_ne_iff.mp hj
        simp [returnEventTerm, returnEventVisit, hn, hi, he]
  · simp [returnEventTerm, returnEventVisit, hn]

def returnEventTerm_hasSum (r : ℕ) (i : ReturnEventFamily) :
    HasSum (returnEventTerm r i)
      ((returnEventCoefficient i : ℝ) * Real.exp (returnEventOffset r i) *
        (if i.1 < 2 then positiveJumpSeries4 r i.2 else positiveJumpSeries3 r i.2)) := by
  classical
  rw [← hasSum_nat_add_iff' 1]
  simp only [Finset.sum_range_one, returnEventTerm_eq_weighted, Nat.lt_irrefl,
    if_false, sub_zero]
  by_cases hi : i.1 < 2
  · have hs := ((summable_nat_add_iff 1).mpr
      (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 4)
        (jumpVisit4_abs_le_one r i.2))).hasSum
    have hh := hs.mul_left
      ((returnEventCoefficient i : ℝ) * Real.exp (returnEventOffset r i))
    simpa only [Nat.cast_add, Nat.cast_one, Nat.zero_lt_succ, if_pos, hi,
      positiveJumpSeries4] using hh
  · have hs := ((summable_nat_add_iff 1).mpr
      (integerIndexSeries_summable (by norm_num : (1 : ℝ) < 3)
        (jumpVisit3_abs_le_one r i.2))).hasSum
    have hh := hs.mul_left
      ((returnEventCoefficient i : ℝ) * Real.exp (returnEventOffset r i))
    simpa only [Nat.cast_add, Nat.cast_one, Nat.zero_lt_succ, if_pos, if_neg hi,
      positiveJumpSeries3] using hh

def returnEventTerm_summable (r : ℕ) (i : ReturnEventFamily) :
    Summable (returnEventTerm r i) := (returnEventTerm_hasSum r i).summable

def returnEventTerm_tsum (r : ℕ) (i : ReturnEventFamily) :
    (∑' n : ℕ, returnEventTerm r i n) =
      (returnEventCoefficient i : ℝ) * Real.exp (returnEventOffset r i) *
        (if i.1 < 2 then positiveJumpSeries4 r i.2 else positiveJumpSeries3 r i.2) :=
  (returnEventTerm_hasSum r i).tsum_eq

def returnRemainder_event_series (r : ℕ) :
    returnRemainder r = ∑ i : ReturnEventFamily, ∑' n : ℕ, returnEventTerm r i n := by
  simp only [returnEventTerm_tsum, Fintype.sum_prod_type, Fin.sum_univ_four]
  norm_num [Fin.lt_def, Fin.ext_iff, Matrix.cons_val_two, Matrix.cons_val_three,
    returnEventCoefficient, returnEventCoefficient4,
    returnEventCoefficient3, returnEventOffset, Real.exp_nat_mul,
    Real.exp_log (by norm_num : (0 : ℝ) < 3),
    Real.exp_log (by norm_num : (0 : ℝ) < 4)]
  unfold returnRemainder groupedJump4 groupedJump3
  ring


end Bounty

end SubmissionComponent_ReturnEventSeries

/- Component SparseGeometricTail; SHA256 0c64c5aa3060bb0b59e167193718d8021131fc7d14f8bde100cc6a728f407e89 -/
section SubmissionComponent_SparseGeometricTail
/- Geometric tails supported on separated natural-number indices. -/

namespace Bounty

/-- A finite set of indices with spacing at least `Q` has geometric mass
at most that of the progression starting at any lower bound `N`. -/
def sparse_geometric_finset_bound {r : ℝ} (hr0 : 0 ≤ r) (hr1 : r < 1)
    {Q : ℕ} (hQ : 0 < Q) (s : Finset ℕ) (N : ℕ)
    (hN : ∀ n ∈ s, N ≤ n)
    (hsep : ∀ m ∈ s, ∀ n ∈ s, m < n → Q ≤ n - m) :
    ∑ n ∈ s, r ^ n ≤ r ^ N / (1 - r ^ Q) := by
  classical
  have hd : 0 < 1 - r ^ Q := sub_pos.mpr (pow_lt_one₀ hr0 hr1 (Nat.ne_of_gt hQ))
  induction s using Finset.strongInductionOn generalizing N with
  | _ s ih =>
    by_cases hs : s.Nonempty
    · let m := s.min' hs
      have hm : m ∈ s := Finset.min'_mem s hs
      have hmin (n : ℕ) (hn : n ∈ s) : m ≤ n := Finset.min'_le s n hn
      have hrest : ∑ n ∈ s.erase m, r ^ n ≤ r ^ (m + Q) / (1 - r ^ Q) := by
        apply ih (s.erase m) (Finset.erase_ssubset hm) (m + Q)
        · intro n hn
          have hn' := Finset.mem_erase.mp hn
          have hmn : m < n := lt_of_le_of_ne (hmin n hn'.2) (Ne.symm hn'.1)
          have hg := hsep m hm n hn'.2 hmn
          omega
        · intro a ha b hb hab
          exact hsep a (Finset.mem_of_mem_erase ha) b (Finset.mem_of_mem_erase hb) hab
      calc
        ∑ n ∈ s, r ^ n = r ^ m + ∑ n ∈ s.erase m, r ^ n := by
          rw [← Finset.sum_erase_add _ _ hm]
          ring
        _ ≤ r ^ m + r ^ (m + Q) / (1 - r ^ Q) := add_le_add le_rfl hrest
        _ = r ^ m / (1 - r ^ Q) := by
          rw [pow_add]
          field_simp
          <;> ring
        _ ≤ r ^ N / (1 - r ^ Q) :=
          div_le_div_of_nonneg_right (pow_le_pow_of_le_one hr0 hr1.le (hN m hm)) hd.le
    · have he : s = ∅ := Finset.not_nonempty_iff_eq_empty.mp hs
      subst s
      simpa using div_nonneg (pow_nonneg hr0 N) hd.le

/-- Summability and the sharp geometric upper bound for separated visits. -/
def sparse_geometric_tail_pow {r : ℝ} (hr0 : 0 ≤ r) (hr1 : r < 1)
    {Q : ℕ} (hQ : 0 < Q) (V : ℕ → Prop) [DecidablePred V] (N : ℕ)
    (hsep : ∀ m n, V m → V n → m < n → Q ≤ n - m) :
    Summable (fun n => if V n ∧ N ≤ n then r ^ n else 0) ∧
      (∑' n, if V n ∧ N ≤ n then r ^ n else 0) ≤ r ^ N / (1 - r ^ Q) := by
  classical
  have hnonneg : 0 ≤ (fun n => if V n ∧ N ≤ n then r ^ n else 0) := by
    intro n
    dsimp only [Pi.zero_apply]
    split_ifs <;> positivity
  have hbound (s : Finset ℕ) :
      ∑ n ∈ s, (if V n ∧ N ≤ n then r ^ n else 0) ≤ r ^ N / (1 - r ^ Q) := by
    rw [← Finset.sum_filter]
    apply sparse_geometric_finset_bound hr0 hr1 hQ
    · intro n hn
      exact (Finset.mem_filter.mp hn).2.2
    · intro m hm n hn hmn
      exact hsep m n (Finset.mem_filter.mp hm).2.1 (Finset.mem_filter.mp hn).2.1 hmn
  exact ⟨summable_of_sum_le hnonneg hbound, Real.tsum_le_of_sum_le hnonneg hbound⟩

end Bounty

end SubmissionComponent_SparseGeometricTail

/- Component SparseExponentialTail; SHA256 09025d47469001596818f18079809f9940e664b5e7e6f1d240e49d7f1ac286b3 -/
section SubmissionComponent_SparseExponentialTail
/- Sparse exponential tails with a real event-time cutoff. -/

namespace Bounty

/-- Event times `n * step - offset` separated by at least `Q * step`
have a geometric tail bound measured directly from the real cutoff `T`. -/
def sparse_exponential_tail {step : ℝ} (hstep : 0 < step)
    {Q : ℕ} (hQ : 0 < Q) (offset T : ℝ)
    (V : ℕ → Prop) [DecidablePred V]
    (hsep : ∀ m n, V m → V n → m < n → Q ≤ n - m)
    (htime : ∀ n, V n → T ≤ (n : ℝ) * step - offset) :
    Summable (fun n => if V n then Real.exp (-((n : ℝ) * step - offset)) else 0) ∧
      (∑' n, if V n then Real.exp (-((n : ℝ) * step - offset)) else 0) ≤
        Real.exp (-T) / (1 - Real.exp (-(Q : ℝ) * step)) := by
  classical
  have hr0 : 0 ≤ Real.exp (-step) := (Real.exp_pos _).le
  have hr1 : Real.exp (-step) < 1 := Real.exp_lt_one_iff.mpr (by linarith)
  have hpow (n : ℕ) : Real.exp (-step) ^ n = Real.exp (-(n : ℝ) * step) := by
    rw [← Real.exp_nat_mul]
    congr 1
    ring
  have hweight (n : ℕ) : Real.exp (-((n : ℝ) * step - offset)) =
      Real.exp offset * Real.exp (-step) ^ n := by
    rw [hpow, ← Real.exp_add]
    congr 1
    ring
  have hd : 0 < 1 - Real.exp (-(Q : ℝ) * step) := by
    apply sub_pos.mpr
    apply Real.exp_lt_one_iff.mpr
    have hQr : 0 < (Q : ℝ) := by exact_mod_cast hQ
    nlinarith [mul_pos hQr hstep]
  by_cases hex : ∃ n, V n
  · let N := Nat.find hex
    have hVN : V N := Nat.find_spec hex
    have hN (n : ℕ) (hn : V n) : N ≤ n := Nat.find_min' hex hn
    obtain ⟨hsum, hbound⟩ := sparse_geometric_tail_pow hr0 hr1 hQ V N hsep
    have hfun :
        (fun n => if V n then Real.exp (-((n : ℝ) * step - offset)) else 0) =
        (fun n => Real.exp offset *
          (if V n ∧ N ≤ n then Real.exp (-step) ^ n else 0)) := by
      funext n
      by_cases hn : V n
      · simp only [hn, hN n hn, and_self, ite_true, hweight]
      · simp only [hn, false_and, ite_false, mul_zero]
    rw [hfun]
    refine ⟨hsum.mul_left _, ?_⟩
    rw [tsum_mul_left]
    calc
      Real.exp offset * (∑' n, if V n ∧ N ≤ n then Real.exp (-step) ^ n else 0) ≤
          Real.exp offset * (Real.exp (-step) ^ N / (1 - Real.exp (-step) ^ Q)) :=
        mul_le_mul_of_nonneg_left hbound (Real.exp_pos _).le
      _ = Real.exp (-((N : ℝ) * step - offset)) /
          (1 - Real.exp (-(Q : ℝ) * step)) := by
        rw [← mul_div_assoc, ← hweight, hpow Q]
      _ ≤ Real.exp (-T) / (1 - Real.exp (-(Q : ℝ) * step)) := by
        apply div_le_div_of_nonneg_right _ hd.le
        apply Real.exp_le_exp.mpr
        linarith [htime N hVN]
  · have hempty (n : ℕ) : ¬V n := fun hn => hex ⟨n, hn⟩
    simp only [hempty, ite_false, summable_zero, tsum_zero, true_and]
    exact div_nonneg (Real.exp_pos _).le hd.le


end Bounty

end SubmissionComponent_SparseExponentialTail

/- Component ReturnEventTail; SHA256 836a7bd83088527d5905085bec240c1f7d414050a3fd5e3e783018b1711c83f7 -/
section SubmissionComponent_ReturnEventTail
/- Quantitative tails of the sixteen return-event series. -/

namespace Bounty

noncomputable def returnEventOmittedTerm (r : ℕ) (T : ℝ)
    (i : ReturnEventFamily) (n : ℕ) : ℝ := by
  classical
  exact if T ≤ returnEventTime r i n then returnEventTerm r i n else 0

noncomputable def returnEventTailWeight (r : ℕ) (T : ℝ)
    (i : ReturnEventFamily) (n : ℕ) : ℝ := by
  classical
  exact if returnEventVisit r i n ∧ T ≤ returnEventTime r i n then
    Real.exp (-returnEventTime r i n) else 0

def returnEventCoefficient_abs_le (i : ReturnEventFamily) :
    |(returnEventCoefficient i : ℝ)| ≤ 0xa8 := by
  rcases i with ⟨j, k⟩
  fin_cases j <;> fin_cases k <;>
    norm_num [returnEventCoefficient, returnEventCoefficient4, returnEventCoefficient3, Fin.ext_iff]

def returnEventOmittedTerm_summable (r : ℕ) (T : ℝ) (i : ReturnEventFamily) :
    Summable (returnEventOmittedTerm r T i) := by
  classical
  have hs := (returnEventTerm_summable r i).indicator {n | T ≤ returnEventTime r i n}
  exact hs.congr (fun n => by
    by_cases ht : T ≤ returnEventTime r i n <;> simp [ht, returnEventOmittedTerm])

def returnEventTailWeight_nonneg (r : ℕ) (T : ℝ) (i : ReturnEventFamily) (n : ℕ) :
    0 ≤ returnEventTailWeight r T i n := by
  unfold returnEventTailWeight
  split_ifs <;> positivity

def returnEventOmittedTerm_eq (r : ℕ) (T : ℝ) (i : ReturnEventFamily) (n : ℕ) :
    returnEventOmittedTerm r T i n =
      (returnEventCoefficient i : ℝ) * returnEventTailWeight r T i n := by
  classical
  by_cases hv : returnEventVisit r i n <;>
    by_cases ht : T ≤ returnEventTime r i n <;>
      simp [returnEventOmittedTerm, returnEventTerm, returnEventTailWeight, hv, ht]

/-- Each event family has an integral index spacing whose time spacing is at least half the scale. -/
def returnEventVisit_discrete_spacing (r : ℕ) (i : ReturnEventFamily) :
    ∃ q : ℕ, 0 < q ∧ returnScale r / 2 ≤ (q : ℝ) * returnEventStep i ∧
      ∀ m n, returnEventVisit r i m → returnEventVisit r i n → m < n → q ≤ n - m := by
  by_cases hi : i.1 < 2
  · refine ⟨(rotationReturns r).Q, (rotationReturns r).Q_pos, ?_, ?_⟩
    · simpa only [returnEventStep, if_pos hi] using (returnScale_bounds r).2.2.1
    · intro m n hm hn hmn
      apply jumpVisit4_separated r i.2 hmn
      · simpa only [returnEventVisit, if_pos hi] using hm.2
      · simpa only [returnEventVisit, if_pos hi] using hn.2
  · have hP : 0 < (rotationReturns r).P := by
      have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
      have hQ := (rotationReturns r).Q_pos
      omega
    have hPn : 0 < (rotationReturns r).P.toNat := by omega
    have hcast : ((rotationReturns r).P.toNat : ℝ) = (rotationReturns r).P := by
      exact_mod_cast Int.toNat_of_nonneg hP.le
    refine ⟨(rotationReturns r).P.toNat, hPn, ?_, ?_⟩
    · rw [returnEventStep, if_neg hi, hcast]
      change returnScale r / 2 ≤ returnScale r
      linarith [returnScale_pos r]
    · intro m n hm hn hmn
      apply jumpVisit3_separated r i.2 hmn
      · simpa only [returnEventVisit, if_neg hi] using hm.2
      · simpa only [returnEventVisit, if_neg hi] using hn.2

def returnEventTail_denominator_pos (r : ℕ) :
    0 < 1 - Real.exp (-returnScale r / 2) := by
  apply sub_pos.mpr
  apply Real.exp_lt_one_iff.mpr
  linarith [returnScale_pos r]

/-- Removing all terms before an empty interval gains the full length of that interval. -/
def returnEventTailWeight_bound (r : ℕ) (T : ℝ) (i : ReturnEventFamily)
    (hgap : ∀ n, returnEventVisit r i n →
      returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) :
    Summable (returnEventTailWeight r T i) ∧
      (∑' n, returnEventTailWeight r T i n) ≤
        Real.exp (-T - returnScale r / 0x64) / (1 - Real.exp (-returnScale r / 2)) := by
  classical
  obtain ⟨q, hq, hscale, hsep⟩ := returnEventVisit_discrete_spacing r i
  let V : ℕ → Prop := fun n => returnEventVisit r i n ∧ T ≤ returnEventTime r i n
  have htime (n : ℕ) (hn : V n) :
      T + returnScale r / 0x64 ≤ (n : ℝ) * returnEventStep i - returnEventOffset r i := by
    change T + returnScale r / 0x64 ≤ returnEventTime r i n
    rcases hgap n hn.1 with h | h
    · linarith [hn.2]
    · exact h.le
  obtain ⟨hsum, hbound⟩ := sparse_exponential_tail (returnEventStep_pos i) hq
    (returnEventOffset r i) (T + returnScale r / 0x64) V
    (fun m n hm hn hmn => hsep m n hm.1 hn.1 hmn) htime
  have hsum' : Summable (returnEventTailWeight r T i) := by
    change Summable (fun n => if returnEventVisit r i n ∧ T ≤ returnEventTime r i n then
      Real.exp (-returnEventTime r i n) else 0)
    simpa only [returnEventTime, V] using hsum
  have hb : (∑' n, returnEventTailWeight r T i n) ≤
      Real.exp (-T - returnScale r / 0x64) /
        (1 - Real.exp (-(q : ℝ) * returnEventStep i)) := by
    simpa only [returnEventTailWeight, returnEventTime, V, neg_add_rev, sub_eq_add_neg,
      add_comm] using hbound
  refine ⟨hsum', hb.trans ?_⟩
  apply div_le_div_of_nonneg_left (Real.exp_pos _).le (returnEventTail_denominator_pos r)
  have hexp : Real.exp (-(q : ℝ) * returnEventStep i) ≤ Real.exp (-returnScale r / 2) := by
    apply Real.exp_le_exp.mpr
    linarith
  linarith

def returnEventOmittedTerm_family_bound (r : ℕ) (T : ℝ) (i : ReturnEventFamily)
    (hgap : ∀ n, returnEventVisit r i n →
      returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) :
    |∑' n, returnEventOmittedTerm r T i n| ≤
      0xa8 * Real.exp (-T - returnScale r / 0x64) / (1 - Real.exp (-returnScale r / 2)) := by
  have hb := (returnEventTailWeight_bound r T i hgap).2
  have hnonneg : 0 ≤ ∑' n, returnEventTailWeight r T i n :=
    tsum_nonneg (returnEventTailWeight_nonneg r T i)
  have hfun : returnEventOmittedTerm r T i =
      fun n => (returnEventCoefficient i : ℝ) * returnEventTailWeight r T i n := by
    funext n
    exact returnEventOmittedTerm_eq r T i n
  rw [hfun, tsum_mul_left, abs_mul, abs_of_nonneg hnonneg]
  calc
    |(returnEventCoefficient i : ℝ)| * (∑' n, returnEventTailWeight r T i n) ≤
        0xa8 * (Real.exp (-T - returnScale r / 0x64) / (1 - Real.exp (-returnScale r / 2))) :=
      mul_le_mul (returnEventCoefficient_abs_le i) hb hnonneg (by norm_num)
    _ = _ := by ring

def returnEventOmittedTerm_total_bound (r : ℕ) (T : ℝ)
    (hgap : ∀ i n, returnEventVisit r i n →
      returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) :
    |∑ i : ReturnEventFamily, ∑' n, returnEventOmittedTerm r T i n| ≤
      (16 * 0xa8 : ℝ) * Real.exp (-T - returnScale r / 0x64) /
        (1 - Real.exp (-returnScale r / 2)) := by
  calc
    |∑ i : ReturnEventFamily, ∑' n, returnEventOmittedTerm r T i n| ≤
        ∑ i : ReturnEventFamily, |∑' n, returnEventOmittedTerm r T i n| :=
      Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _i : ReturnEventFamily,
        0xa8 * Real.exp (-T - returnScale r / 0x64) / (1 - Real.exp (-returnScale r / 2)) :=
      Finset.sum_le_sum (fun i _ => returnEventOmittedTerm_family_bound r T i (hgap i))
    _ = _ := by norm_num [ReturnEventFamily]; ring


end Bounty

end SubmissionComponent_ReturnEventTail

/- Component ReturnEventBounds; SHA256 e05d18a97b07da3007f7881de0e40be70c622180361706dde82fe51f8bc8ba7c -/
section SubmissionComponent_ReturnEventBounds
/- Bounds for the offsets, exponents, and number of coordinates below a return cutoff. -/

namespace Bounty

def returnEventOffset_bounds (r : ℕ) (i : ReturnEventFamily) :
    0 ≤ returnEventOffset r i ∧ returnEventOffset r i ≤ returnScale r := by
  have h3 : 0 < Real.log 3 := Real.log_pos (by norm_num)
  have h4 : 0 < Real.log 4 := Real.log_pos (by norm_num)
  have hp : 0 ≤ (rotationReturns r).p := by
    have hb := (rotationReturns r).numerator_bounds
      rotationSlope_bounds.1 rotationSlope_bounds.2
    have hq := (rotationReturns r).q_pos
    omega
  have he : ((rotationReturns r).p.toNat : ℝ) = (rotationReturns r).p := by
    exact_mod_cast Int.toNat_of_nonneg hp
  unfold returnEventOffset
  split
  · constructor
    · positivity
    · rw [he]
      exact (returnScale_bounds r).2.1
  · split
    · exact ⟨by positivity, (returnScale_bounds r).1⟩
    · exact ⟨le_refl 0, (returnScale_pos r).le⟩

def returnEventTime_gt_neg_scale (r : ℕ) (i : ReturnEventFamily) {n : ℕ}
    (hn : returnEventVisit r i n) : -returnScale r < returnEventTime r i n := by
  have hnR : (0 : ℝ) < n := by exact_mod_cast hn.1
  have hh := mul_pos hnR (returnEventStep_pos i)
  have ho := (returnEventOffset_bounds r i).2
  unfold returnEventTime
  linarith

def returnEventExponent_le (r : ℕ) (i : ReturnEventFamily) {n : ℕ} {k : ℝ}
    (hn : returnEventTime r i n ≤ k * returnScale r) :
    (n : ℝ) * returnEventStep i ≤ (k + 1) * returnScale r := by
  have ho := (returnEventOffset_bounds r i).2
  unfold returnEventTime at hn
  nlinarith

def separated_events_card_le_bins (E : Finset ℝ) {a gap : ℝ} (N : ℕ)
    (hgap : 0 < gap)
    (hbounds : ∀ x ∈ E, a ≤ x ∧ x ≤ a + (N : ℝ) * gap)
    (hsep : ∀ x ∈ E, ∀ y ∈ E, x ≠ y → gap ≤ |x - y|) :
    E.card ≤ N + 1 := by
  classical
  have hz (x : E) : 0 ≤ ((x : ℝ) - a) / gap ∧ ((x : ℝ) - a) / gap ≤ N := by
    have hx := hbounds x x.property
    constructor
    · exact div_nonneg (by linarith) hgap.le
    · apply (div_le_iff₀ hgap).mpr
      linarith
  let f : E → ↥(Finset.Icc (0 : ℤ) (N : ℤ)) := fun x =>
    ⟨⌊((x : ℝ) - a) / gap⌋, Finset.mem_Icc.mpr
      ⟨Int.floor_nonneg.mpr (hz x).1, Int.floor_le_iff.mpr (by
        push_cast
        linarith [(hz x).2])⟩⟩
  have hinj : Function.Injective f := by
    intro x y hf
    apply Subtype.ext
    by_contra hxy
    have heq : ⌊((x : ℝ) - a) / gap⌋ = ⌊((y : ℝ) - a) / gap⌋ :=
      congrArg Subtype.val hf
    have hh := Int.abs_sub_lt_one_of_floor_eq_floor heq
    have he : ((x : ℝ) - a) / gap - ((y : ℝ) - a) / gap =
        ((x : ℝ) - y) / gap := by ring
    rw [he, abs_div, abs_of_pos hgap] at hh
    have hsmall := (div_lt_iff₀ hgap).mp hh
    have hlarge := hsep x x.property y y.property hxy
    linarith
  have hc := Fintype.card_le_of_injective f hinj
  simpa using hc

def returnEventWindow_card (r k : ℕ) (i : ReturnEventFamily) :
    (linearEventWindow (returnEventStep i) (returnEventOffset r i)
      (-returnScale r) ((k : ℝ) * returnScale r) (returnEventVisit r i)).card ≤ 2 * k + 3 := by
  have hc : (linearEventWindow (returnEventStep i) (returnEventOffset r i)
      (-returnScale r) ((k : ℝ) * returnScale r) (returnEventVisit r i)).card ≤
      (2 * k + 2) + 1 := by
    apply separated_events_card_le_bins _ (2 * k + 2)
      (show 0 < returnScale r / 2 by linarith [returnScale_pos r])
    · intro x hx
      obtain ⟨n, hv, he, hlo, hhi⟩ := (mem_linearEventWindow (returnEventStep_pos i)).mp hx
      refine ⟨hlo, ?_⟩
      push_cast
      nlinarith
    · intro x hx y hy hxy
      obtain ⟨m, hm, rfl, _, _⟩ := (mem_linearEventWindow (returnEventStep_pos i)).mp hx
      obtain ⟨n, hn, rfl, _, _⟩ := (mem_linearEventWindow (returnEventStep_pos i)).mp hy
      have hmn : m ≠ n := by rintro rfl; exact hxy rfl
      rcases lt_or_gt_of_ne hmn with hlt | hgt
      · have hh := returnEventVisit_separation r i hm hn hlt
        have ha := neg_le_abs (((m : ℝ) * returnEventStep i - returnEventOffset r i) -
          ((n : ℝ) * returnEventStep i - returnEventOffset r i))
        linarith
      · have hh := returnEventVisit_separation r i hn hm hgt
        have ha := le_abs_self (((m : ℝ) * returnEventStep i - returnEventOffset r i) -
          ((n : ℝ) * returnEventStep i - returnEventOffset r i))
        linarith
  omega

end Bounty

end SubmissionComponent_ReturnEventBounds

/- Component ReturnEventTruncation; SHA256 206f46103455ab5d78632f7ce33e9c08abcb129ea1d0742935dcac10b042f709 -/
section SubmissionComponent_ReturnEventTruncation
/- Finite truncations of the actual return series and their quantified errors. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable def returnTruncationIndices (r : ℕ) (T : ℝ) (i : ReturnEventFamily) : Finset ℕ := by
  classical
  exact (Finset.range (⌈(T + returnEventOffset r i) / returnEventStep i⌉₊ + 1)).filter
    (fun n => returnEventVisit r i n ∧ returnEventTime r i n < T)

def mem_returnTruncationIndices (r : ℕ) (T : ℝ) (i : ReturnEventFamily) (n : ℕ) :
    n ∈ returnTruncationIndices r T i ↔
      returnEventVisit r i n ∧ returnEventTime r i n < T := by
  classical
  constructor
  · intro hn
    exact (Finset.mem_filter.mp hn).2
  · intro hn
    have hnr : (n : ℝ) ≤ (T + returnEventOffset r i) / returnEventStep i := by
      apply (le_div_iff₀ (returnEventStep_pos i)).mpr
      have hh := hn.2
      unfold returnEventTime at hh
      linarith
    have hnat : n ≤ ⌈(T + returnEventOffset r i) / returnEventStep i⌉₊ := by
      exact_mod_cast hnr.trans (Nat.le_ceil _)
    exact Finset.mem_filter.mpr ⟨Finset.mem_range.mpr (by omega), hn⟩

noncomputable def returnTruncation (r : ℕ) (T : ℝ) : ℝ :=
  ∑ i : ReturnEventFamily, ∑ n ∈ returnTruncationIndices r T i, returnEventTerm r i n

def returnEventTerm_retained_tsum (r : ℕ) (T : ℝ) (i : ReturnEventFamily) :
    (∑' n : ℕ, if returnEventTime r i n < T then returnEventTerm r i n else 0) =
      ∑ n ∈ returnTruncationIndices r T i, returnEventTerm r i n := by
  classical
  calc
    _ = ∑ n ∈ returnTruncationIndices r T i,
        (if returnEventTime r i n < T then returnEventTerm r i n else 0) := by
      apply tsum_eq_sum
      intro n hn
      by_cases ht : returnEventTime r i n < T
      · have hv : ¬ returnEventVisit r i n := by
          intro hv
          exact hn ((mem_returnTruncationIndices r T i n).mpr ⟨hv, ht⟩)
        simp only [if_pos ht, returnEventTerm, if_neg hv]
      · simp only [if_neg ht]
    _ = _ := by
      apply Finset.sum_congr rfl
      intro n hn
      exact if_pos ((mem_returnTruncationIndices r T i n).mp hn).2

def returnEventTerm_split_at_cutoff (r : ℕ) (T : ℝ) (i : ReturnEventFamily) :
    (∑' n : ℕ, returnEventTerm r i n) =
      (∑ n ∈ returnTruncationIndices r T i, returnEventTerm r i n) +
        ∑' n : ℕ, returnEventOmittedTerm r T i n := by
  classical
  have hret : Summable (fun n : ℕ =>
      if returnEventTime r i n < T then returnEventTerm r i n else 0) := by
    have hs := (returnEventTerm_summable r i).indicator {n | returnEventTime r i n < T}
    exact hs.congr (fun n => by simp only [Set.indicator_apply, Set.mem_ofPred_eq])
  have hsplit (n : ℕ) : returnEventTerm r i n =
      (if returnEventTime r i n < T then returnEventTerm r i n else 0) +
        returnEventOmittedTerm r T i n := by
    unfold returnEventOmittedTerm
    by_cases ht : returnEventTime r i n < T
    · simp only [if_pos ht, if_neg (not_le_of_gt ht), add_zero]
    · simp only [if_neg ht, if_pos (le_of_not_gt ht), zero_add]
  calc
    _ = ∑' n : ℕ,
        ((if returnEventTime r i n < T then returnEventTerm r i n else 0) +
          returnEventOmittedTerm r T i n) := tsum_congr hsplit
    _ = (∑' n : ℕ, if returnEventTime r i n < T then returnEventTerm r i n else 0) +
        ∑' n : ℕ, returnEventOmittedTerm r T i n :=
      (hret.hasSum.add (returnEventOmittedTerm_summable r T i).hasSum).tsum_eq
    _ = _ := by rw [returnEventTerm_retained_tsum]

def returnRemainder_split_at_cutoff (r : ℕ) (T : ℝ) :
    returnRemainder r = returnTruncation r T +
      ∑ i : ReturnEventFamily, ∑' n : ℕ, returnEventOmittedTerm r T i n := by
  rw [returnRemainder_event_series]
  simp only [returnEventTerm_split_at_cutoff r T, Finset.sum_add_distrib, returnTruncation]

def returnTruncation_error_bound (r : ℕ) (T : ℝ)
    (hgap : ∀ i n, returnEventVisit r i n →
      returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) :
    |returnRemainder r - returnTruncation r T| ≤
      (16 * 0xa8 : ℝ) * Real.exp (-T - returnScale r / 0x64) /
        (1 - Real.exp (-returnScale r / 2)) := by
  rw [returnRemainder_split_at_cutoff r T]
  simpa only [add_sub_cancel_left] using returnEventOmittedTerm_total_bound r T hgap

end Bounty

end SubmissionComponent_ReturnEventTruncation

/- Component ReturnRationalUnits; SHA256 0fe91e0b79a760a14c9ba8159b256520a1476d5deb8de1e8bfd1b47cd57ec98e -/
section SubmissionComponent_ReturnRationalUnits
/- Rational units, with prime support in {2, 3}, for the finite return truncations. -/

namespace Bounty

noncomputable section

def returnRationalUnit (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : ℚ :=
  if i.1 = 0 then (3 : ℚ) ^ (rotationReturns r).p.toNat / (4 : ℚ) ^ n
  else if i.1 = 1 then 1 / (4 : ℚ) ^ n
  else if i.1 = 2 then (4 : ℚ) ^ (rotationReturns r).q / (3 : ℚ) ^ n
  else 1 / (3 : ℚ) ^ n

def returnRationalUnit_pos (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    0 < returnRationalUnit r i n := by
  unfold returnRationalUnit
  split
  · positivity
  · split
    · positivity
    · split <;> positivity

def returnRationalUnit_ne_zero (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    returnRationalUnit r i n ≠ 0 := ne_of_gt (returnRationalUnit_pos r i n)

def returnRationalUnit_cast (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    (returnRationalUnit r i n : ℝ) = Real.exp (-returnEventTime r i n) := by
  rcases i with ⟨j, k⟩
  fin_cases j <;>
    norm_num [returnRationalUnit, returnEventTime, returnEventStep, returnEventOffset,
      Fin.lt_def, Fin.ext_iff,
      exp_neg_event_time (by norm_num : (0 : ℝ) < 4),
      exp_neg_event_time (by norm_num : (0 : ℝ) < 3), Real.exp_sub, Real.exp_neg,
      Real.exp_nat_mul,
      Real.exp_log (by norm_num : (0 : ℝ) < 3),
      Real.exp_log (by norm_num : (0 : ℝ) < 4)]

def returnUnitFourExponent (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : ℤ :=
  if i.1 < 2 then -(n : ℤ)
  else if i.1 = 2 then ((rotationReturns r).q : ℤ) else 0

def returnUnitThreeExponent (r : ℕ) (i : ReturnEventFamily) (n : ℕ) : ℤ :=
  if i.1 = 0 then ((rotationReturns r).p.toNat : ℤ)
  else if i.1 < 2 then 0 else -(n : ℤ)

def returnRationalUnit_eq_four_three_zpow (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    returnRationalUnit r i n =
      (4 : ℚ) ^ returnUnitFourExponent r i n *
        (3 : ℚ) ^ returnUnitThreeExponent r i n := by
  rcases i with ⟨j, k⟩
  dsimp only [returnRationalUnit, returnUnitFourExponent, returnUnitThreeExponent]
  generalize hp : (rotationReturns r).p.toNat = p
  fin_cases j <;>
    norm_num [returnRationalUnit, returnUnitFourExponent, returnUnitThreeExponent,
      Fin.lt_def, Fin.ext_iff, zpow_neg, div_eq_mul_inv, mul_comm]

def returnRationalUnit_primeMonomial (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    returnRationalUnit r i n =
      rationalPrimeMonomial (2 * returnUnitFourExponent r i n)
        (returnUnitThreeExponent r i n) 0 := by
  rw [returnRationalUnit_eq_four_three_zpow, rational_four_three_monomial]

def returnRationalTruncation (r : ℕ) (T : ℝ) : ℚ :=
  ∑ i : ReturnEventFamily, ∑ n ∈ returnTruncationIndices r T i,
    (returnEventCoefficient i : ℚ) * returnRationalUnit r i n

def returnRationalTruncation_cast (r : ℕ) (T : ℝ) :
    (returnRationalTruncation r T : ℝ) = returnTruncation r T := by
  classical
  unfold returnRationalTruncation returnTruncation
  push_cast
  apply Finset.sum_congr rfl
  intro i hi
  apply Finset.sum_congr rfl
  intro n hn
  have hv := ((mem_returnTruncationIndices r T i n).mp hn).1
  rw [returnEventTerm, if_pos hv, returnRationalUnit_cast]


end

end Bounty

end SubmissionComponent_ReturnRationalUnits

/- Component ReturnTruncationSize; SHA256 c8217a9efd11b4cc681d76ca8d6a555eff050da23023247060fc9395938d82d4 -/
section SubmissionComponent_ReturnTruncationSize
/- Coordinate counts and exponent bounds for the actual finite return truncations. -/

namespace Bounty

def returnEventTime_injective (r : ℕ) (i : ReturnEventFamily) :
    Function.Injective (returnEventTime r i) := by
  intro m n h
  have hm : (m : ℝ) * returnEventStep i = (n : ℝ) * returnEventStep i := by
    unfold returnEventTime at h
    linarith
  exact_mod_cast mul_right_cancel₀ (ne_of_gt (returnEventStep_pos i)) hm

def returnTruncationIndices_card (r k : ℕ) (T : ℝ) (i : ReturnEventFamily)
    (hT : T ≤ (k : ℝ) * returnScale r) :
    (returnTruncationIndices r T i).card ≤ 2 * k + 3 := by
  classical
  have hsub : (returnTruncationIndices r T i).image (returnEventTime r i) ⊆
      linearEventWindow (returnEventStep i) (returnEventOffset r i)
        (-returnScale r) ((k : ℝ) * returnScale r) (returnEventVisit r i) := by
    intro t ht
    obtain ⟨n, hn, rfl⟩ := Finset.mem_image.mp ht
    obtain ⟨hv, hlt⟩ := (mem_returnTruncationIndices r T i n).mp hn
    exact (mem_linearEventWindow (returnEventStep_pos i)).mpr
      ⟨n, hv, rfl, (returnEventTime_gt_neg_scale r i hv).le, hlt.le.trans hT⟩
  calc
    (returnTruncationIndices r T i).card =
        ((returnTruncationIndices r T i).image (returnEventTime r i)).card :=
      (Finset.card_image_of_injective _ (returnEventTime_injective r i)).symm
    _ ≤ (linearEventWindow (returnEventStep i) (returnEventOffset r i)
        (-returnScale r) ((k : ℝ) * returnScale r) (returnEventVisit r i)).card :=
      Finset.card_le_card hsub
    _ ≤ 2 * k + 3 := returnEventWindow_card r k i

def returnTruncationIndices_total_card (r k : ℕ) (T : ℝ)
    (hT : T ≤ (k : ℝ) * returnScale r) :
    (∑ i : ReturnEventFamily, (returnTruncationIndices r T i).card) ≤ 16 * (2 * k + 3) := by
  calc
    _ ≤ ∑ _i : ReturnEventFamily, (2 * k + 3) :=
      Finset.sum_le_sum (fun i _ => returnTruncationIndices_card r k T i hT)
    _ = 16 * (2 * k + 3) := by simp [ReturnEventFamily, mul_comm]

def returnTruncationIndices_exponent_le (r k : ℕ) (T : ℝ) (i : ReturnEventFamily)
    {n : ℕ} (hT : T ≤ (k : ℝ) * returnScale r)
    (hn : n ∈ returnTruncationIndices r T i) :
    (n : ℝ) * returnEventStep i ≤ ((k : ℝ) + 1) * returnScale r := by
  exact returnEventExponent_le r i (((mem_returnTruncationIndices r T i n).mp hn).2.le.trans hT)

end Bounty

end SubmissionComponent_ReturnTruncationSize

/- Component ReturnTruncationError; SHA256 efb54cd73ade5b50f0ffe4ab8955d4d85deffde024a983af4eb1c446d3143e42 -/
section SubmissionComponent_ReturnTruncationError
/- Absorb the uniform geometric-tail constant into an exponential gain. -/

open Filter
open scoped Topology

namespace Bounty

def returnEventTail_denominator_eventually :
    ∀ᶠ r in atTop, (1 : ℝ) / 2 ≤ 1 - Real.exp (-returnScale r / 2) := by
  have hh := returnScale_tendsto.eventually (eventually_ge_atTop (2 * Real.log 2))
  filter_upwards [hh] with r hr
  have he : Real.exp (-Real.log 2) = (1 : ℝ) / 2 := by
    rw [Real.exp_neg, Real.exp_log (by norm_num : (0 : ℝ) < 2)]
    norm_num
  have hx : Real.exp (-returnScale r / 2) ≤ Real.exp (-Real.log 2) :=
    Real.exp_le_exp.mpr (by linarith)
  rw [he] at hx
  linarith

def returnTruncation_error_uniform :
    ∀ᶠ r in atTop, ∀ T : ℝ,
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) →
      |returnRemainder r - returnTruncation r T| ≤
        0x1500 * Real.exp (-T - returnScale r / 0x64) := by
  filter_upwards [returnEventTail_denominator_eventually] with r hr T hgap
  have hh := returnTruncation_error_bound r T hgap
  apply hh.trans
  apply (div_le_iff₀ (returnEventTail_denominator_pos r)).mpr
  have hm := mul_le_mul_of_nonneg_left hr (Real.exp_pos (-T - returnScale r / 0x64)).le
  nlinarith

def returnTruncation_error_exponential :
    ∀ᶠ r in atTop, ∀ T : ℝ,
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) →
      |returnRemainder r - returnTruncation r T| ≤ Real.exp (-T - returnScale r / 0xc8) := by
  have hlarge := returnScale_tendsto.eventually (eventually_ge_atTop (0xc8 * Real.log 0x1500))
  filter_upwards [returnTruncation_error_uniform, hlarge] with r hr hL T hgap
  calc
    _ ≤ 0x1500 * Real.exp (-T - returnScale r / 0x64) := hr T hgap
    _ = Real.exp (Real.log 0x1500 - T - returnScale r / 0x64) := by
      rw [show Real.log 0x1500 - T - returnScale r / 0x64 =
        Real.log 0x1500 + (-T - returnScale r / 0x64) by ring, Real.exp_add,
        Real.exp_log (by norm_num : (0 : ℝ) < 0x1500)]
    _ ≤ Real.exp (-T - returnScale r / 0xc8) := Real.exp_le_exp.mpr (by linarith)

def returnDensity_truncation_exponential :
    ∀ᶠ r in atTop, ∀ T : ℝ,
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) →
      |((4 : ℝ) ^ (rotationReturns r).q - 1) *
        ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) * (0xb4 * explicitDensity - 32) -
          returnIntegerPrefix r - returnTruncation r T| ≤ Real.exp (-T - returnScale r / 0xc8) := by
  filter_upwards [returnDifferenceIdentity, returnTruncation_error_exponential] with r hid herr T hgap
  rw [hid]
  exact herr T hgap


end Bounty

end SubmissionComponent_ReturnTruncationError

/- Component ReturnPrefixBounds; SHA256 3009413143d21752f9f6509ca5d40d5024ec8181c9f882356070ae158fa32441 -/
section SubmissionComponent_ReturnPrefixBounds
/- Archimedean size bounds for the integer coordinates in the return approximation. -/

open Filter
open scoped Topology

namespace Bounty

def integerPrefix_abs_le {a : ℕ → ℤ} {b : ℕ} {M : ℝ}
    (hb : 1 < b) (ha : ∀ n, |(a n : ℝ)| ≤ M) (q : ℕ) :
    |(integerPrefix a b q : ℝ)| ≤ 2 * M * (b : ℝ) ^ q := by
  have hb0 : 0 < (b : ℝ) := by exact_mod_cast (by omega : 0 < b)
  have hb1 : 1 < (b : ℝ) := by exact_mod_cast hb
  have hb2 : 2 ≤ (b : ℝ) := by exact_mod_cast (by omega : 2 ≤ b)
  have hM : 0 ≤ M := (abs_nonneg _).trans (ha 0)
  have hinv : 1 / (b : ℝ) ≤ (1 : ℝ) / 2 := by
    apply (div_le_iff₀ hb0).mpr
    linarith
  have hden : 0 < 1 - 1 / (b : ℝ) := by linarith
  have hgeo : (∑ n ∈ Finset.range q, (1 / (b : ℝ)) ^ n) ≤ 2 := by
    have hh := sparse_geometric_finset_bound (by positivity : 0 ≤ 1 / (b : ℝ))
      (by simpa only [one_div] using inv_lt_one_of_one_lt₀ hb1)
      (by omega : 0 < (1 : ℕ)) (Finset.range q) 0
      (fun n _ => Nat.zero_le n) (fun m _ n _ hmn => by omega)
    simp only [pow_zero, pow_one] at hh
    apply hh.trans
    apply (div_le_iff₀ hden).mpr
    linarith
  have hsum : |∑ n ∈ Finset.range q, (a n : ℝ) / (b : ℝ) ^ n| ≤ 2 * M := by
    calc
      _ ≤ ∑ n ∈ Finset.range q, |(a n : ℝ) / (b : ℝ) ^ n| :=
        Finset.abs_sum_le_sum_abs _ _
      _ ≤ ∑ n ∈ Finset.range q, M * (1 / (b : ℝ)) ^ n := by
        apply Finset.sum_le_sum
        intro n _
        calc
          |(a n : ℝ) / (b : ℝ) ^ n| = |(a n : ℝ)| / (b : ℝ) ^ n := by
            rw [abs_div, abs_of_pos (pow_pos hb0 n)]
          _ ≤ M / (b : ℝ) ^ n := div_le_div_of_nonneg_right (ha n) (pow_pos hb0 n).le
          _ = M * (1 / (b : ℝ)) ^ n := by rw [one_div, inv_pow, div_eq_mul_inv]
      _ = M * ∑ n ∈ Finset.range q, (1 / (b : ℝ)) ^ n := (Finset.mul_sum _ _ _).symm
      _ ≤ M * 2 := mul_le_mul_of_nonneg_left hgeo hM
      _ = 2 * M := mul_comm _ _
  rw [integerPrefix_cast a (by omega) q, abs_mul, abs_of_pos (pow_pos hb0 q)]
  calc
    _ ≤ (b : ℝ) ^ q * (2 * M) := mul_le_mul_of_nonneg_left hsum (pow_pos hb0 q).le
    _ = _ := by ring

def returnPrefix_base_power_bounds (r : ℕ) :
    (4 : ℝ) ^ (rotationReturns r).q ≤ Real.exp (returnScale r) ∧
      (3 : ℝ) ^ (rotationReturns r).p.toNat ≤ Real.exp (returnScale r) := by
  have hp : 0 ≤ (rotationReturns r).p := by
    have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
    have hq := (rotationReturns r).q_pos
    omega
  have hcast : ((rotationReturns r).p.toNat : ℝ) = (rotationReturns r).p := by
    exact_mod_cast Int.toNat_of_nonneg hp
  constructor
  · have he : Real.exp (((rotationReturns r).q : ℝ) * Real.log 4) =
        (4 : ℝ) ^ (rotationReturns r).q := by
      rw [Real.exp_nat_mul, Real.exp_log (by norm_num : (0 : ℝ) < 4)]
    rw [← he]
    exact Real.exp_le_exp.mpr (returnScale_bounds r).1
  · have he : Real.exp (((rotationReturns r).p.toNat : ℝ) * Real.log 3) =
        (3 : ℝ) ^ (rotationReturns r).p.toNat := by
      rw [Real.exp_nat_mul, Real.exp_log (by norm_num : (0 : ℝ) < 3)]
    rw [← he]
    apply Real.exp_le_exp.mpr
    rw [hcast]
    exact (returnScale_bounds r).2.1

def returnPrefix_power_product_bound (r : ℕ) :
    (4 : ℝ) ^ (rotationReturns r).q * (3 : ℝ) ^ (rotationReturns r).p.toNat ≤
      Real.exp (2 * returnScale r) := by
  have hh := returnPrefix_base_power_bounds r
  calc
    _ ≤ Real.exp (returnScale r) * Real.exp (returnScale r) :=
      mul_le_mul hh.1 hh.2 (by positivity) (Real.exp_pos _).le
    _ = Real.exp (2 * returnScale r) := by rw [← Real.exp_add]; congr 1; ring

def returnIntegerPrefix_abs_le_power_product (r : ℕ) :
    |(returnIntegerPrefix r : ℝ)| ≤
      0x16e * (4 : ℝ) ^ (rotationReturns r).q * (3 : ℝ) ^ (rotationReturns r).p.toNat := by
  let A : ℝ := (4 : ℝ) ^ (rotationReturns r).q
  let B : ℝ := (3 : ℝ) ^ (rotationReturns r).p.toNat
  let IA : ℝ := (integerPrefix coefficient4 4 (rotationReturns r).q : ℝ)
  let IB : ℝ := (integerPrefix coefficient3 3 (rotationReturns r).p.toNat : ℝ)
  have hA1 : 1 ≤ A := one_le_pow₀ (by norm_num : (1 : ℝ) ≤ 4)
  have hB1 : 1 ≤ B := one_le_pow₀ (by norm_num : (1 : ℝ) ≤ 3)
  have hIA : |IA| ≤ 0x9c * A := by
    have hh := integerPrefix_abs_le (by norm_num : 1 < (4 : ℕ)) coefficient4_bound
      (rotationReturns r).q
    norm_num at hh
    exact hh
  have hIB : |IB| ≤ 0x78 * B := by
    have hh := integerPrefix_abs_le (by norm_num : 1 < (3 : ℕ)) coefficient3_bound
      (rotationReturns r).p.toNat
    norm_num at hh
    exact hh
  have hIB90 : |IB - 90| ≤ 0xd2 * B := by
    have hh : |IB - 90| ≤ |IB| + 90 := by
      simpa only [sub_eq_add_neg, abs_neg, abs_of_nonneg (by norm_num : (0 : ℝ) ≤ 90)]
        using abs_add_le IB (-90)
    linarith
  have hAm1 : |A - 1| ≤ A := by rw [abs_of_nonneg (by linarith : 0 ≤ A - 1)]; linarith
  have hBm1 : |B - 1| ≤ B := by rw [abs_of_nonneg (by linarith : 0 ≤ B - 1)]; linarith
  have he : (returnIntegerPrefix r : ℝ) = (B - 1) * IA + (A - 1) * (IB - 90) := by
    simp [returnIntegerPrefix, A, B, IA, IB]
  rw [he]
  change |(B - 1) * IA + (A - 1) * (IB - 90)| ≤ 0x16e * A * B
  calc
    _ ≤ |(B - 1) * IA| + |(A - 1) * (IB - 90)| := abs_add_le _ _
    _ ≤ B * (0x9c * A) + A * (0xd2 * B) := by
      rw [abs_mul, abs_mul]
      exact add_le_add (mul_le_mul hBm1 hIA (abs_nonneg _) (by linarith))
        (mul_le_mul hAm1 hIB90 (abs_nonneg _) (by linarith))
    _ = 0x16e * A * B := by ring

def returnIntegerPrefix_abs_le_exp (r : ℕ) :
    |(returnIntegerPrefix r : ℝ)| ≤ 0x16e * Real.exp (2 * returnScale r) := by
  calc
    _ ≤ 0x16e * (4 : ℝ) ^ (rotationReturns r).q * (3 : ℝ) ^ (rotationReturns r).p.toNat :=
      returnIntegerPrefix_abs_le_power_product r
    _ = 0x16e * ((4 : ℝ) ^ (rotationReturns r).q * (3 : ℝ) ^ (rotationReturns r).p.toNat) := by ring
    _ ≤ 0x16e * Real.exp (2 * returnScale r) :=
      mul_le_mul_of_nonneg_left (returnPrefix_power_product_bound r) (by norm_num)

noncomputable def returnClearedIntegerHead (z : ℚ) (r : ℕ) : ℤ :=
  z.num * (((4 : ℤ) ^ (rotationReturns r).q - 1) *
      ((3 : ℤ) ^ (rotationReturns r).p.toNat - 1)) -
    (z.den : ℤ) * returnIntegerPrefix r

def returnClearedIntegerHead_cast (z : ℚ) (r : ℕ) :
    (returnClearedIntegerHead z r : ℝ) = (z.den : ℝ) *
      (((4 : ℝ) ^ (rotationReturns r).q - 1) *
        ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) * (z : ℝ) - returnIntegerPrefix r) := by
  have hden : (z.den : ℝ) ≠ 0 := by exact_mod_cast z.den_nz
  have hnum : (z.num : ℝ) = (z.den : ℝ) * (z : ℝ) := by
    rw [Rat.cast_def]
    field_simp
  unfold returnClearedIntegerHead
  push_cast
  rw [hnum]
  ring

def returnClearedIntegerHead_abs_le_exp (z : ℚ) (r : ℕ) :
    |(returnClearedIntegerHead z r : ℝ)| ≤
      (|(z.num : ℝ)| + 0x16e * (z.den : ℝ)) * Real.exp (2 * returnScale r) := by
  let A : ℝ := (4 : ℝ) ^ (rotationReturns r).q
  let B : ℝ := (3 : ℝ) ^ (rotationReturns r).p.toNat
  have hA1 : 1 ≤ A := one_le_pow₀ (by norm_num : (1 : ℝ) ≤ 4)
  have hB1 : 1 ≤ B := one_le_pow₀ (by norm_num : (1 : ℝ) ≤ 3)
  have hAm1 : |A - 1| ≤ A := by rw [abs_of_nonneg (by linarith : 0 ≤ A - 1)]; linarith
  have hBm1 : |B - 1| ≤ B := by rw [abs_of_nonneg (by linarith : 0 ≤ B - 1)]; linarith
  have hprod : |(A - 1) * (B - 1)| ≤ Real.exp (2 * returnScale r) := by
    rw [abs_mul]
    exact (mul_le_mul hAm1 hBm1 (abs_nonneg _) (by linarith)).trans
      (returnPrefix_power_product_bound r)
  have hden : 0 ≤ (z.den : ℝ) := Nat.cast_nonneg _
  have he : (returnClearedIntegerHead z r : ℝ) =
      (z.num : ℝ) * ((A - 1) * (B - 1)) - (z.den : ℝ) * (returnIntegerPrefix r : ℝ) := by
    simp [returnClearedIntegerHead, A, B]
  rw [he, sub_eq_add_neg]
  calc
    _ ≤ |(z.num : ℝ) * ((A - 1) * (B - 1))| +
        |-((z.den : ℝ) * (returnIntegerPrefix r : ℝ))| := abs_add_le _ _
    _ = |(z.num : ℝ)| * |(A - 1) * (B - 1)| +
        (z.den : ℝ) * |(returnIntegerPrefix r : ℝ)| := by
      simp only [abs_neg, abs_mul, abs_of_nonneg hden]
    _ ≤ |(z.num : ℝ)| * Real.exp (2 * returnScale r) +
        (z.den : ℝ) * (0x16e * Real.exp (2 * returnScale r)) :=
      add_le_add (mul_le_mul_of_nonneg_left hprod (abs_nonneg _))
        (mul_le_mul_of_nonneg_left (returnIntegerPrefix_abs_le_exp r) hden)
    _ = _ := by ring

def returnClearedIntegerHead_eventually_exp (z : ℚ) :
    ∀ᶠ r in atTop, |(returnClearedIntegerHead z r : ℝ)| ≤ Real.exp (3 * returnScale r) := by
  let C : ℝ := |(z.num : ℝ)| + 0x16e * (z.den : ℝ)
  have hden : 0 < (z.den : ℝ) := by exact_mod_cast z.den_pos
  have hC : 0 < C := by dsimp [C]; positivity
  have hlarge := returnScale_tendsto.eventually (eventually_ge_atTop (Real.log C))
  filter_upwards [hlarge] with r hr
  calc
    _ ≤ C * Real.exp (2 * returnScale r) := returnClearedIntegerHead_abs_le_exp z r
    _ = Real.exp (Real.log C + 2 * returnScale r) := by rw [Real.exp_add, Real.exp_log hC]
    _ ≤ Real.exp (3 * returnScale r) := Real.exp_le_exp.mpr (by linarith)

def returnClearedIntegerHead_of_rational_density (h : ¬Irrational explicitDensity) :
    ∃ z : ℚ, (z : ℝ) = 0xb4 * explicitDensity - 32 ∧
      (∀ r : ℕ, (returnClearedIntegerHead z r : ℝ) = (z.den : ℝ) *
        (((4 : ℝ) ^ (rotationReturns r).q - 1) *
          ((3 : ℝ) ^ (rotationReturns r).p.toNat - 1) *
            (0xb4 * explicitDensity - 32) - returnIntegerPrefix r)) ∧
      ∀ᶠ r in atTop, |(returnClearedIntegerHead z r : ℝ)| ≤ Real.exp (3 * returnScale r) := by
  obtain ⟨a, ha⟩ := exists_rat_of_not_irrational h
  let z : ℚ := 0xb4 * a - 32
  have hz : (z : ℝ) = 0xb4 * explicitDensity - 32 := by
    dsimp [z]
    push_cast
    rw [ha]
  refine ⟨z, hz, ?_, returnClearedIntegerHead_eventually_exp z⟩
  intro r
  rw [returnClearedIntegerHead_cast, hz]


end Bounty

end SubmissionComponent_ReturnPrefixBounds

/- Component ReturnCoordinateHeight; SHA256 d1c928de757918ab5bc37515261b495ee6767b291ae8936cd9f44b6e380566e1 -/
section SubmissionComponent_ReturnCoordinateHeight
/- Common denominators and projective height bounds for return coordinates. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable section

def returnHeadUnit (r : ℕ) (j : Fin 4) : ℚ :=
  if j = 0 then (4 : ℚ) ^ (rotationReturns r).q * (3 : ℚ) ^ (rotationReturns r).p.toNat
  else if j = 1 then (4 : ℚ) ^ (rotationReturns r).q
  else if j = 2 then (3 : ℚ) ^ (rotationReturns r).p.toNat else 1

def returnHeadFourExponent (r : ℕ) (j : Fin 4) : ℤ :=
  if j < 2 then ((rotationReturns r).q : ℤ) else 0

def returnHeadThreeExponent (r : ℕ) (j : Fin 4) : ℤ :=
  if j = 0 ∨ j = 2 then ((rotationReturns r).p.toNat : ℤ) else 0

def returnHeadUnit_pos (r : ℕ) (j : Fin 4) : 0 < returnHeadUnit r j := by
  unfold returnHeadUnit
  split_ifs <;> positivity

def returnHeadUnit_ne_zero (r : ℕ) (j : Fin 4) : returnHeadUnit r j ≠ 0 :=
  ne_of_gt (returnHeadUnit_pos r j)

def returnHeadUnit_eq_four_three_zpow (r : ℕ) (j : Fin 4) :
    returnHeadUnit r j = (4 : ℚ) ^ returnHeadFourExponent r j *
      (3 : ℚ) ^ returnHeadThreeExponent r j := by
  dsimp only [returnHeadUnit, returnHeadFourExponent, returnHeadThreeExponent]
  generalize hp : (rotationReturns r).p.toNat = p
  fin_cases j <;>
    norm_num [returnHeadUnit, returnHeadFourExponent, returnHeadThreeExponent,
      Fin.ext_iff, Fin.lt_def]

def returnHeadUnit_primeMonomial (r : ℕ) (j : Fin 4) :
    returnHeadUnit r j = rationalPrimeMonomial (2 * returnHeadFourExponent r j)
      (returnHeadThreeExponent r j) 0 := by
  rw [returnHeadUnit_eq_four_three_zpow, rational_four_three_monomial]

def returnHeadUnit_den (r : ℕ) (j : Fin 4) : (returnHeadUnit r j).den = 1 := by
  fin_cases j <;> simp [returnHeadUnit, Fin.ext_iff]
  have he : (4 : ℚ) ^ (rotationReturns r).q * (3 : ℚ) ^ (rotationReturns r).p.toNat =
      ((4 ^ (rotationReturns r).q * 3 ^ (rotationReturns r).p.toNat : ℕ) : ℚ) := by
    push_cast
    rfl
  rw [he]
  exact Rat.den_natCast _

/-- A finite integer tuple has projective height at most any common absolute-value bound at least one. -/
def rational_integer_tuple_height_le {ι : Type*} [Fintype ι]
    (x : ι → ℤ) {B : ℝ} (hB : 1 ≤ B) (hx : ∀ i, |(x i : ℝ)| ≤ B) :
    Height.mulHeight (fun i => (x i : ℚ)) ≤ B := by
  classical
  let y : Option ι → ℤ := fun j => match j with | none => 1 | some i => x i
  have hg : Finset.univ.gcd y = 1 := by
    rw [← Finset.insert_erase (Finset.mem_univ (none : Option ι)), Finset.gcd_insert]
    simp [y]
  have hh := Rat.mulHeight_eq_max_abs_of_gcd_eq_one hg
  rw [Finite.map_iSup_of_monotone _ Int.cast_mono] at hh
  simp only [Int.cast_abs] at hh
  have hcomp : Height.mulHeight (fun i => (x i : ℚ)) ≤
      Height.mulHeight (fun j : Option ι => (y j : ℚ)) := by
    simpa only [Function.comp_def, y] using
      Height.mulHeight_comp_le (some : ι → Option ι) (fun j : Option ι => (y j : ℚ))
  apply hcomp.trans
  rw [show Height.mulHeight (fun j : Option ι => (y j : ℚ)) =
      ⨆ j : Option ι, |(y j : ℝ)| by exact hh]
  apply ciSup_le
  intro j
  cases j with
  | none => simpa [y] using hB
  | some i => simpa [y] using hx i

def returnDenominatorExponent (r k : ℕ) (b : ℝ) : ℕ :=
  ⌊((k : ℝ) + 1) * returnScale r / Real.log b⌋₊

def returnCommonDenominator (r k : ℕ) : ℕ :=
  4 ^ returnDenominatorExponent r k 4 * 3 ^ returnDenominatorExponent r k 3

def returnCommonDenominator_pos (r k : ℕ) : 0 < returnCommonDenominator r k := by
  unfold returnCommonDenominator
  positivity

def returnDenominatorExponent_bound (r k : ℕ) {b : ℝ} (hb : 1 < b) :
    (returnDenominatorExponent r k b : ℝ) * Real.log b ≤ ((k : ℝ) + 1) * returnScale r := by
  have hl : 0 < Real.log b := Real.log_pos hb
  have hL := returnScale_pos r
  apply (le_div_iff₀ hl).mp
  exact Nat.floor_le (by positivity)

def returnCommonDenominator_bound (r k : ℕ) :
    (returnCommonDenominator r k : ℝ) ≤ Real.exp ((2 * (k : ℝ) + 2) * returnScale r) := by
  have h4 := returnDenominatorExponent_bound r k (by norm_num : (1 : ℝ) < 4)
  have h3 := returnDenominatorExponent_bound r k (by norm_num : (1 : ℝ) < 3)
  have he4 : Real.exp ((returnDenominatorExponent r k 4 : ℝ) * Real.log 4) =
      (4 : ℝ) ^ returnDenominatorExponent r k 4 := by
    rw [Real.exp_nat_mul, Real.exp_log (by norm_num : (0 : ℝ) < 4)]
  have he3 : Real.exp ((returnDenominatorExponent r k 3 : ℝ) * Real.log 3) =
      (3 : ℝ) ^ returnDenominatorExponent r k 3 := by
    rw [Real.exp_nat_mul, Real.exp_log (by norm_num : (0 : ℝ) < 3)]
  simp only [returnCommonDenominator, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat]
  rw [← he4, ← he3, ← Real.exp_add]
  apply Real.exp_le_exp.mpr
  nlinarith

def rational_nat_div_den_dvd (a b : ℕ) : ((a : ℚ) / b).den ∣ b := by
  have hh : ((((a : ℚ) / b).den : ℤ)) ∣ (b : ℤ) := by
    simpa only [Rat.divInt_eq_div, Int.cast_natCast] using Rat.den_dvd (a : ℤ) (b : ℤ)
  exact Int.natCast_dvd_natCast.mp hh

def returnRationalUnit_den_dvd_base_power (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    (returnRationalUnit r i n).den ∣ (if i.1 < 2 then 4 ^ n else 3 ^ n) := by
  rcases i with ⟨j, l⟩
  fin_cases j
  · simpa [returnRationalUnit, Fin.ext_iff, Fin.lt_def] using
      rational_nat_div_den_dvd (3 ^ (rotationReturns r).p.toNat) (4 ^ n)
  · simpa [returnRationalUnit, Fin.ext_iff, Fin.lt_def] using
      rational_nat_div_den_dvd 1 (4 ^ n)
  · simpa [returnRationalUnit, Fin.ext_iff, Fin.lt_def] using
      rational_nat_div_den_dvd (4 ^ (rotationReturns r).q) (3 ^ n)
  · simpa [returnRationalUnit, Fin.ext_iff, Fin.lt_def] using
      rational_nat_div_den_dvd 1 (3 ^ n)

def returnRationalUnit_den_dvd_common (r k : ℕ) (T : ℝ) (i : ReturnEventFamily)
    {n : ℕ} (hT : T ≤ (k : ℝ) * returnScale r)
    (hn : n ∈ returnTruncationIndices r T i) :
    (returnRationalUnit r i n).den ∣ returnCommonDenominator r k := by
  have he := returnTruncationIndices_exponent_le r k T i hT hn
  have hd := returnRationalUnit_den_dvd_base_power r i n
  by_cases hi : i.1 < 2
  · simp only [returnEventStep, if_pos hi] at he
    simp only [if_pos hi] at hd
    have hnM : n ≤ returnDenominatorExponent r k 4 :=
      Nat.le_floor ((le_div_iff₀ (Real.log_pos (by norm_num : (1 : ℝ) < 4))).mpr he)
    exact hd.trans ((pow_dvd_pow 4 hnM).trans (dvd_mul_right _ _))
  · simp only [returnEventStep, if_neg hi] at he
    simp only [if_neg hi] at hd
    have hnM : n ≤ returnDenominatorExponent r k 3 :=
      Nat.le_floor ((le_div_iff₀ (Real.log_pos (by norm_num : (1 : ℝ) < 3))).mpr he)
    exact hd.trans ((pow_dvd_pow 3 hnM).trans (dvd_mul_left _ _))

/-- Any enumeration of the integer prefix, four heads, and actual retained units is permitted. -/
def IsReturnCoordinate (r : ℕ) (T : ℝ) (x : ℚ) : Prop :=
  x = (returnIntegerPrefix r : ℚ) ∨ (∃ j : Fin 4, x = returnHeadUnit r j) ∨
    ∃ i n, n ∈ returnTruncationIndices r T i ∧ x = returnRationalUnit r i n

def returnCoordinate_den_dvd_common (r k : ℕ) (T : ℝ) {x : ℚ}
    (hT : T ≤ (k : ℝ) * returnScale r) (hx : IsReturnCoordinate r T x) :
    x.den ∣ returnCommonDenominator r k := by
  rcases hx with rfl | ⟨j, rfl⟩ | ⟨i, n, hn, rfl⟩
  · simpa only [Rat.den_intCast] using one_dvd (returnCommonDenominator r k)
  · rw [returnHeadUnit_den]
    exact one_dvd _
  · exact returnRationalUnit_den_dvd_common r k T i hT hn

def returnHeadUnit_abs_le_exp (r : ℕ) (j : Fin 4) :
    |(returnHeadUnit r j : ℝ)| ≤ Real.exp (2 * returnScale r) := by
  have hpos : 0 < (returnHeadUnit r j : ℝ) := by exact_mod_cast returnHeadUnit_pos r j
  rw [abs_of_pos hpos]
  have hh := returnPrefix_base_power_bounds r
  have hscale : Real.exp (returnScale r) ≤ Real.exp (2 * returnScale r) :=
    Real.exp_le_exp.mpr (by linarith [returnScale_pos r])
  have hone : 1 ≤ Real.exp (2 * returnScale r) :=
    Real.one_le_exp_iff.mpr (by linarith [returnScale_pos r])
  fin_cases j
  · simpa [returnHeadUnit, Fin.ext_iff] using returnPrefix_power_product_bound r
  · simpa [returnHeadUnit, Fin.ext_iff] using hh.1.trans hscale
  · simpa [returnHeadUnit, Fin.ext_iff] using hh.2.trans hscale
  · simpa [returnHeadUnit, Fin.ext_iff] using hone

def returnCoordinate_abs_le_exp (r : ℕ) (T : ℝ) {x : ℚ}
    (hx : IsReturnCoordinate r T x) :
    |(x : ℝ)| ≤ 0x16e * Real.exp (2 * returnScale r) := by
  rcases hx with rfl | ⟨j, rfl⟩ | ⟨i, n, hn, rfl⟩
  · simpa using returnIntegerPrefix_abs_le_exp r
  · have hh := returnHeadUnit_abs_le_exp r j
    nlinarith [Real.exp_pos (2 * returnScale r)]
  · rw [returnRationalUnit_cast, abs_of_pos (Real.exp_pos _)]
    have hv := ((mem_returnTruncationIndices r T i n).mp hn).1
    have hh : Real.exp (-returnEventTime r i n) ≤ Real.exp (2 * returnScale r) := by
      apply Real.exp_le_exp.mpr
      linarith [returnEventTime_gt_neg_scale r i hv, returnScale_pos r]
    nlinarith [Real.exp_pos (2 * returnScale r)]

def rational_clear_of_den_dvd {x : ℚ} {D : ℕ} (hd : x.den ∣ D) :
    ∃ a : ℤ, (D : ℚ) * x = a := by
  obtain ⟨m, hm⟩ := hd
  refine ⟨(m : ℤ) * x.num, ?_⟩
  rw [hm, Nat.cast_mul, mul_right_comm, Rat.den_mul_eq_num]
  push_cast
  ring

def rational_tuple_height_le_of_den_dvd {ι : Type*} [Fintype ι]
    (x : ι → ℚ) {D : ℕ} (hD : 0 < D) (hd : ∀ i, (x i).den ∣ D)
    {B : ℝ} (hB : 1 ≤ B) (hx : ∀ i, |(D : ℝ) * (x i : ℝ)| ≤ B) :
    Height.mulHeight x ≤ B := by
  classical
  choose y hy using fun i => rational_clear_of_den_dvd (hd i)
  have hh : Height.mulHeight (fun i => (y i : ℚ)) ≤ B := by
    apply rational_integer_tuple_height_le y hB
    intro i
    have he : (y i : ℝ) = (D : ℝ) * (x i : ℝ) := by exact_mod_cast (hy i).symm
    rw [he]
    exact hx i
  have hfun : (fun i => (y i : ℚ)) = (D : ℚ) • x := by
    funext i
    exact (hy i).symm
  rw [hfun, Height.mulHeight_smul_eq_mulHeight x (by exact_mod_cast hD.ne')] at hh
  exact hh

def returnCoordinate_cleared_abs_le (r k : ℕ) (T : ℝ) {x : ℚ}
    (hx : IsReturnCoordinate r T x) :
    |(returnCommonDenominator r k : ℝ) * (x : ℝ)| ≤
      0x16e * Real.exp ((2 * (k : ℝ) + 4) * returnScale r) := by
  rw [abs_mul, abs_of_nonneg (Nat.cast_nonneg _)]
  calc
    _ ≤ Real.exp ((2 * (k : ℝ) + 2) * returnScale r) *
        (0x16e * Real.exp (2 * returnScale r)) :=
      mul_le_mul (returnCommonDenominator_bound r k) (returnCoordinate_abs_le_exp r T hx)
        (abs_nonneg _) (Real.exp_pos _).le
    _ = 0x16e * Real.exp ((2 * (k : ℝ) + 4) * returnScale r) := by
      rw [mul_left_comm, ← Real.exp_add]
      congr 1
      ring

/-- The full tuple may use any finite actual-label index type; no padding or repeated units is needed. -/
def returnCoordinateHeight_bound {ι : Type*} [Fintype ι]
    (r k : ℕ) (T : ℝ) (x : ι → ℚ)
    (hT : T ≤ (k : ℝ) * returnScale r) (hx : ∀ i, IsReturnCoordinate r T (x i)) :
    Height.mulHeight x ≤ 0x16e * Real.exp ((2 * (k : ℝ) + 4) * returnScale r) := by
  have hL := returnScale_pos r
  have hone : 1 ≤ Real.exp ((2 * (k : ℝ) + 4) * returnScale r) :=
    Real.one_le_exp_iff.mpr (by positivity)
  apply rational_tuple_height_le_of_den_dvd x (returnCommonDenominator_pos r k)
    (fun i => returnCoordinate_den_dvd_common r k T hT (hx i)) (by linarith)
  exact fun i => returnCoordinate_cleared_abs_le r k T (hx i)

def returnCoordinateHeight_eventually :
    ∀ᶠ r in atTop, ∀ (k : ℕ) (T : ℝ) (ι : Type) [Fintype ι] (x : ι → ℚ),
      T ≤ (k : ℝ) * returnScale r → (∀ i, IsReturnCoordinate r T (x i)) →
      Height.mulHeight x ≤ Real.exp ((2 * (k : ℝ) + 5) * returnScale r) := by
  have hlarge := returnScale_tendsto.eventually (eventually_ge_atTop (Real.log 0x16e))
  filter_upwards [hlarge] with r hr k T ι inst x hT hx
  calc
    _ ≤ 0x16e * Real.exp ((2 * (k : ℝ) + 4) * returnScale r) :=
      returnCoordinateHeight_bound r k T x hT hx
    _ = Real.exp (Real.log 0x16e + (2 * (k : ℝ) + 4) * returnScale r) := by
      rw [Real.exp_add, Real.exp_log (by norm_num : (0 : ℝ) < 0x16e)]
    _ ≤ Real.exp ((2 * (k : ℝ) + 5) * returnScale r) := Real.exp_le_exp.mpr (by nlinarith)

def returnCoordinateHeight_eventually_eleven :
    ∀ᶠ r in atTop, ∀ (T : ℝ) (ι : Type) [Fintype ι] (x : ι → ℚ),
      T ≤ 11 * returnScale r → (∀ i, IsReturnCoordinate r T (x i)) →
      Height.mulHeight x ≤ Real.exp (27 * returnScale r) := by
  filter_upwards [returnCoordinateHeight_eventually] with r hr T ι inst x hT hx
  have hh := hr 11 T ι x hT hx
  norm_num at hh
  exact hh


end
end Bounty

end SubmissionComponent_ReturnCoordinateHeight

/- Component ReturnFiniteApproximation; SHA256 7ba0967cb028c8f6e0c6f6a53189afe3d3b8d339157291c83a5b8b0bdf8049ea -/
section SubmissionComponent_ReturnFiniteApproximation
/- Exact finite rational linear forms underlying the two return approximations. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable section

abbrev ReturnTailLabel (r : ℕ) (T : ℝ) :=
  Σ i : ReturnEventFamily, {n : ℕ // n ∈ returnTruncationIndices r T i}

abbrev ReturnApproximationLabel (r : ℕ) (T : ℝ) := Fin 4 ⊕ ReturnTailLabel r T

def returnApproximationUnit (r : ℕ) (T : ℝ) : ReturnApproximationLabel r T → ℚ :=
  Sum.elim (returnHeadUnit r) (fun a => returnRationalUnit r a.1 a.2.1)

def returnApproximationCoefficient (z : ℚ) (r : ℕ) (T : ℝ) :
    ReturnApproximationLabel r T → ℚ :=
  Sum.elim (fun j => if j = 0 ∨ j = 3 then z else -z)
    (fun a => -(returnEventCoefficient a.1 : ℚ))

def returnCoefficientPalette (z : ℚ) : Finset ℚ :=
  {z, -z} ∪ Finset.univ.image (fun i : ReturnEventFamily => -(returnEventCoefficient i : ℚ))

def returnApproximationUnit_pos (r : ℕ) (T : ℝ) (i : ReturnApproximationLabel r T) :
    0 < returnApproximationUnit r T i := by
  cases i with
  | inl j => exact returnHeadUnit_pos r j
  | inr a => exact returnRationalUnit_pos r a.1 a.2.1

def returnApproximationCoefficient_mem (z : ℚ) (r : ℕ) (T : ℝ)
    (i : ReturnApproximationLabel r T) :
    returnApproximationCoefficient z r T i ∈ returnCoefficientPalette z := by
  classical
  cases i with
  | inl j =>
    change (if j = 0 ∨ j = 3 then z else -z) ∈ _
    split_ifs <;> simp [returnCoefficientPalette]
  | inr a =>
    apply Finset.mem_union_right
    exact Finset.mem_image.mpr ⟨a.1, Finset.mem_univ _, rfl⟩

def returnApproximationLabel_card (r k : ℕ) (T : ℝ)
    (hT : T ≤ (k : ℝ) * returnScale r) :
    Fintype.card (ReturnApproximationLabel r T) ≤ 4 + 16 * (2 * k + 3) := by
  classical
  have hh := returnTruncationIndices_total_card r k T hT
  simpa [ReturnApproximationLabel, ReturnTailLabel, Fintype.card_sigma] using
    Nat.add_le_add_left hh 4

def returnHeadUnit_one_le (r : ℕ) (j : Fin 4) : (1 : ℚ) ≤ returnHeadUnit r j := by
  have h4 : (1 : ℚ) ≤ 4 ^ (rotationReturns r).q := one_le_pow₀ (by norm_num)
  have h3 : (1 : ℚ) ≤ 3 ^ (rotationReturns r).p.toNat := one_le_pow₀ (by norm_num)
  unfold returnHeadUnit
  split_ifs
  · exact one_le_mul_of_one_le_of_one_le h4 h3
  · exact h4
  · exact h3
  · rfl

def returnApproximationUnit_lower (r : ℕ) (T : ℝ) (hT : 0 ≤ T)
    (i : ReturnApproximationLabel r T) :
    Real.exp (-T) ≤ (returnApproximationUnit r T i : ℝ) := by
  cases i with
  | inl j =>
    have hh : (1 : ℝ) ≤ (returnHeadUnit r j : ℝ) := by exact_mod_cast returnHeadUnit_one_le r j
    have he : Real.exp (-T) ≤ 1 := by
      rw [← Real.exp_zero]
      exact Real.exp_le_exp.mpr (by linarith)
    exact he.trans hh
  | inr a =>
    have ht := ((mem_returnTruncationIndices r T a.1 a.2.1).mp a.2.2).2
    change Real.exp (-T) ≤ (returnRationalUnit r a.1 a.2.1 : ℝ)
    rw [returnRationalUnit_cast]
    exact Real.exp_le_exp.mpr (by linarith)

def returnApproximation_linear_form (z : ℚ) (r : ℕ) (T : ℝ) :
    (∑ i : ReturnApproximationLabel r T,
      returnApproximationCoefficient z r T i * returnApproximationUnit r T i) -
        (returnIntegerPrefix r : ℚ) =
      ((4 : ℚ) ^ (rotationReturns r).q - 1) *
        ((3 : ℚ) ^ (rotationReturns r).p.toNat - 1) * z -
          returnIntegerPrefix r - returnRationalTruncation r T := by
  classical
  have htail : (∑ a : ReturnTailLabel r T,
      (returnEventCoefficient a.1 : ℚ) * returnRationalUnit r a.1 a.2.1) =
      returnRationalTruncation r T := by
    simp only [ReturnTailLabel, returnRationalTruncation, Fintype.sum_sigma,
      Finset.univ_eq_attach]
    apply Finset.sum_congr rfl
    intro i _
    exact Finset.sum_attach (returnTruncationIndices r T i)
      (fun n : ℕ => (returnEventCoefficient i : ℚ) * returnRationalUnit r i n)
  rw [Fintype.sum_sum_type]
  change (∑ j : Fin 4, (if j = 0 ∨ j = 3 then z else -z) * returnHeadUnit r j) +
    (∑ a : ReturnTailLabel r T, -(returnEventCoefficient a.1 : ℚ) *
      returnRationalUnit r a.1 a.2.1) - _ = _
  simp_rw [neg_mul]
  rw [Finset.sum_neg_distrib, htail]
  simp only [Fin.sum_univ_four]
  norm_num [returnHeadUnit, Fin.ext_iff]
  ring

def returnApproximation_error (z : ℚ)
    (hz : (z : ℝ) = 0xb4 * explicitDensity - 32) :
    ∀ᶠ r in atTop, ∀ T : ℝ,
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) →
      |(((∑ i : ReturnApproximationLabel r T,
        returnApproximationCoefficient z r T i * returnApproximationUnit r T i) -
          (returnIntegerPrefix r : ℚ) : ℚ) : ℝ)| ≤ Real.exp (-T - returnScale r / 0xc8) := by
  filter_upwards [returnDensity_truncation_exponential] with r hr T hgap
  rw [returnApproximation_linear_form]
  push_cast
  rw [hz, returnRationalTruncation_cast]
  exact hr T hgap


end

end Bounty

end SubmissionComponent_ReturnFiniteApproximation

/- Component EventIndexDivergence; SHA256 9afd2b78a6efa14f404f05b116d19adef02dabe3a21c493ab059e1f73b4e3bed -/
section SubmissionComponent_EventIndexDivergence
/- Uniform disappearance of bounded indices and separation between distinct jump orbits. -/

open Filter
open scoped Topology

namespace Bounty

def two_forward_visits_distance_lt {α t u δ : ℝ} {i j : ℤ}
    (hi : 1 - δ ≤ Int.fract ((i : ℝ) * α - t))
    (hj : 1 - δ ≤ Int.fract ((j : ℝ) * α - u)) :
    integerDistance (((j - i : ℤ) : ℝ) * α - (u - t)) < δ := by
  let x : ℝ := (i : ℝ) * α - t
  let y : ℝ := (j : ℝ) * α - u
  have he : (((j - i : ℤ) : ℝ) * α - (u - t)) -
      ((⌊y⌋ - ⌊x⌋ : ℤ) : ℝ) = Int.fract y - Int.fract x := by
    change _ = (y - (⌊y⌋ : ℝ)) - (x - (⌊x⌋ : ℝ))
    dsimp only [x, y]
    push_cast
    ring
  have hh := integerDistance_le_abs (((j - i : ℤ) : ℝ) * α - (u - t)) (⌊y⌋ - ⌊x⌋)
  rw [he] at hh
  have hs : |Int.fract y - Int.fract x| < δ := by
    have hxu := Int.fract_lt_one x
    have hyu := Int.fract_lt_one y
    rw [abs_lt]
    constructor <;> linarith
  exact hh.trans_lt hs

def distinct_orbit_forward_visits_separate {α t u : ℝ} {δ : ℕ → ℝ}
    (hδ : Tendsto δ atTop (nhds 0))
    (horbit : ∀ h k : ℤ, (h : ℝ) * α - (u - t) ≠ k) (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : ℤ,
      1 - δ r ≤ Int.fract ((i : ℝ) * α - t) →
      1 - δ r ≤ Int.fract ((j : ℝ) * α - u) → (M : ℤ) < |j - i| := by
  have hsmall : ∀ᶠ r in atTop, ∀ h ∈ Finset.Icc (-(M : ℤ)) M,
      δ r < integerDistance ((h : ℝ) * α - (u - t)) := by
    apply (eventually_all_finset _).mpr
    intro h _
    exact hδ.eventually (gt_mem_nhds (integerDistance_pos (horbit h)))
  filter_upwards [hsmall] with r hr i j hi hj
  by_contra hh
  have habs : |j - i| ≤ (M : ℤ) := le_of_not_gt hh
  have hmem : j - i ∈ Finset.Icc (-(M : ℤ)) M := by
    simpa only [Finset.mem_Icc, abs_le] using habs
  have hlarge := hr (j - i) hmem
  have hclose := two_forward_visits_distance_lt hi hj
  linarith

def jumpVisit4_distinct_orbits_separate {i j : Fin 4} (hij : i ≠ j) (M : ℕ) :
    ∀ᶠ r in atTop, ∀ m n : ℤ,
      jumpVisit4 r i m ≠ 0 → jumpVisit4 r j n ≠ 0 → (M : ℤ) < |n - m| := by
  have hh := distinct_orbit_forward_visits_separate returnError_tendsto
    (jumpOrbits4_distinct hij) M
  filter_upwards [hh] with r hr m n hm hn
  apply hr m n
  · by_contra hx
    simp only [jumpVisit4, forwardJump, if_neg hx, ne_eq, not_true_eq_false] at hm
  · by_contra hx
    simp only [jumpVisit4, forwardJump, if_neg hx, ne_eq, not_true_eq_false] at hn

def jumpVisit3_distinct_orbits_separate {i j : Fin 4} (hij : i ≠ j) (M : ℕ) :
    ∀ᶠ r in atTop, ∀ m n : ℤ,
      jumpVisit3 r i m ≠ 0 → jumpVisit3 r j n ≠ 0 → (M : ℤ) < |n - m| := by
  have hh := distinct_orbit_visits_separate reciprocal_returnError_tendsto
    (jumpOrbits3_distinct hij) M
  filter_upwards [hh] with r hr m n hm hn
  apply hr m n
  · by_contra hx
    simp only [mul_one_div] at hx
    simp only [jumpVisit3, backwardJump, if_neg hx, ne_eq, not_true_eq_false] at hm
  · by_contra hx
    simp only [mul_one_div] at hx
    simp only [jumpVisit3, backwardJump, if_neg hx, ne_eq, not_true_eq_false] at hn

def returnEventVisit_fixed_disappears (i : ReturnEventFamily) (n : ℕ) :
    ∀ᶠ r in atTop, ¬ returnEventVisit r i n := by
  by_cases hn : n = 0
  · subst n
    exact Eventually.of_forall (fun _ h => (Nat.lt_irrefl 0) h.1)
  have hnZ : (n : ℤ) ≠ 0 := by exact_mod_cast hn
  by_cases hi : i.1 < 2
  · have hh := jumpVisit4_fixed_eventually_zero (i := i.2) (n := n) (Or.inr hnZ)
    filter_upwards [hh] with r hr hv
    have hv' : jumpVisit4 r i.2 n ≠ 0 := by simpa only [if_pos hi] using hv.2
    exact hv' hr
  · have hh := jumpVisit3_fixed_eventually_zero (i := i.2) (n := n) (Or.inr hnZ)
    filter_upwards [hh] with r hr hv
    have hv' : jumpVisit3 r i.2 n ≠ 0 := by simpa only [if_neg hi] using hv.2
    exact hv' hr

def returnEventVisit_indices_diverge (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i n, returnEventVisit r i n → M < n := by
  have hh : ∀ᶠ r in atTop, ∀ i ∈ (Finset.univ : Finset ReturnEventFamily),
      ∀ n ∈ Finset.range (M + 1), ¬ returnEventVisit r i n := by
    apply (eventually_all_finset _).mpr
    intro i _
    apply (eventually_all_finset _).mpr
    intro n _
    exact returnEventVisit_fixed_disappears i n
  filter_upwards [hh] with r hr i n hv
  by_contra hn
  exact hr i (Finset.mem_univ i) n (Finset.mem_range.mpr (by omega)) hv


end Bounty

end SubmissionComponent_EventIndexDivergence

/- Component ReturnVisitCoverage; SHA256 193c806ef7b5f7bfc91486c7022b3cc923da025b28eecc7c7731cf9ee63d7e1a -/
section SubmissionComponent_ReturnVisitCoverage
/- Positive jump visits cover bounded index blocks and logarithmic intervals. -/

open Filter
open scoped Topology

namespace Bounty

def forwardJump_eq_one_of_shifted_fract {δ t x : ℝ} (hδ : 0 ≤ δ)
    (h : Int.fract (x - (t - δ)) < δ) : forwardJump δ t x = 1 := by
  classical
  have hf : 1 - δ ≤ Int.fract (x - t) := by
    by_contra hh
    have hu : Int.fract (x - t) + δ < 1 := by linarith
    have he : x - (t - δ) = (Int.fract (x - t) + δ) + (⌊x - t⌋ : ℝ) := by
      rw [Int.fract]
      ring
    have hfract : Int.fract (x - (t - δ)) = Int.fract (x - t) + δ := by
      rw [he, Int.fract_add_intCast]
      exact Int.fract_eq_self.mpr ⟨by linarith [Int.fract_nonneg (x - t)], hu⟩
    rw [hfract] at h
    linarith [Int.fract_nonneg (x - t)]
  exact if_pos hf

def jumpVisit4_covered_block (r : ℕ) (i : Fin 4) (N : ℕ) :
    ∃ n : ℕ, N ≤ n ∧ n < N + (rotationReturns r).q + (rotationReturns r).Q ∧
      jumpVisit4 r i n = 1 := by
  obtain ⟨n, hlo, hhi, hv⟩ := return_pair_arc_covered_block
    (rotationReturns r).q_pos (rotationReturns r).Q_pos
    (rotationReturns r).lower_pos (rotationReturns r).upper_pos
    (rotationReturns r).upper_lt_lower.le (jumpCoordinate4 i - returnError r) N
  refine ⟨n, hlo, hhi, ?_⟩
  simpa only [jumpVisit4, Int.cast_natCast] using
    forwardJump_eq_one_of_shifted_fract (returnError_pos r).le hv

def returnVisitBlock_log_lt (r : ℕ) :
    (((rotationReturns r).q + (rotationReturns r).Q : ℕ) : ℝ) * Real.log 4 <
      2 * returnScale r := by
  have hh := (rotationReturns r).log_bounds
  rw [Nat.cast_add, add_mul]
  unfold returnScale
  linarith [hh.2.1, hh.2.2.1]

def jumpVisit4_log_covered (r : ℕ) (i : Fin 4) (T : ℝ)
    (hT : 2 * returnScale r < T) :
    ∃ n : ℕ, 0 < n ∧ T - 2 * returnScale r < (n : ℝ) * Real.log 4 ∧
      (n : ℝ) * Real.log 4 < T ∧ jumpVisit4 r i n = 1 := by
  let K : ℕ := (rotationReturns r).q + (rotationReturns r).Q
  let G : ℝ := (K : ℝ) * Real.log 4
  have hlog : 0 < Real.log 4 := Real.log_pos (by norm_num)
  have hG : G < 2 * returnScale r := returnVisitBlock_log_lt r
  let a : ℝ := (T - G) / Real.log 4
  have ha : 0 < a := div_pos (by linarith) hlog
  let N : ℕ := ⌈a⌉₊
  obtain ⟨n, hnlo, hnhi, hv⟩ := jumpVisit4_covered_block r i N
  have hNpos : 0 < N := Nat.ceil_pos.mpr ha
  have hNa : a ≤ (N : ℝ) := Nat.le_ceil a
  have hNa' : (N : ℝ) < a + 1 := Nat.ceil_lt_add_one ha.le
  have hnr : (N : ℝ) ≤ n := by exact_mod_cast hnlo
  have hnK : (n : ℝ) + 1 ≤ (N : ℝ) + K := by
    have hh : n + 1 ≤ N + K := by dsimp only [K]; omega
    exact_mod_cast hh
  have hcross : a * Real.log 4 = T - G := by
    dsimp only [a]
    exact div_mul_cancel₀ _ (ne_of_gt hlog)
  have hlo := mul_le_mul_of_nonneg_right (hNa.trans hnr) hlog.le
  have hhi := mul_lt_mul_of_pos_right (by linarith : (n : ℝ) < a + K) hlog
  refine ⟨n, by omega, ?_, ?_, hv⟩
  · rw [hcross] at hlo
    linarith
  · rw [add_mul, hcross] at hhi
    change (n : ℝ) * Real.log 4 < T - G + G at hhi
    linarith

def jumpVisit4_all_indices_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ (i j : Fin 4) (m n : ℕ),
      jumpVisit4 r i m ≠ 0 → jumpVisit4 r j n ≠ 0 →
      (i ≠ j ∨ m ≠ n) → (M : ℤ) < |(n : ℤ) - m| := by
  have horbits : ∀ᶠ r in atTop, ∀ i ∈ (Finset.univ : Finset (Fin 4)),
      ∀ j ∈ (Finset.univ : Finset (Fin 4)), i ≠ j → ∀ m n : ℤ,
        jumpVisit4 r i m ≠ 0 → jumpVisit4 r j n ≠ 0 → (M : ℤ) < |n - m| := by
    apply (eventually_all_finset _).mpr
    intro i _
    apply (eventually_all_finset _).mpr
    intro j _
    by_cases hij : i = j
    · exact Eventually.of_forall (fun _ h => False.elim (h hij))
    · exact (jumpVisit4_distinct_orbits_separate hij M).mono (fun _ h _ => h)
  have hQ := rotationReturns_denominators_tendsto.2.eventually (eventually_ge_atTop (M + 1))
  filter_upwards [horbits, hQ] with r hr hQr i j m n hm hn hne
  by_cases hij : i = j
  · subst j
    have hmn : m ≠ n := hne.resolve_left (by simp)
    rcases lt_or_gt_of_ne hmn with hlt | hgt
    · have hh := jumpVisit4_separated r i hlt hm hn
      rw [abs_of_nonneg (by omega : (0 : ℤ) ≤ (n : ℤ) - m)]
      omega
    · have hh := jumpVisit4_separated r i hgt hn hm
      rw [abs_of_nonpos (by omega : (n : ℤ) - m ≤ 0)]
      omega
  · exact hr i (Finset.mem_univ i) j (Finset.mem_univ j) hij m n hm hn

def returnEventTime_nonvanishing_cutoffs (r : ℕ) :
    ∃ T₁ T₂ : ℝ,
      4 * returnScale r < T₁ ∧ T₁ < 5 * returnScale r ∧
      10 * returnScale r < T₂ ∧ T₂ < 11 * returnScale r ∧
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T₁ ∨ T₁ + returnScale r / 0x64 < returnEventTime r i n) ∧
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T₂ ∨ T₂ + returnScale r / 0x64 < returnEventTime r i n) := by
  obtain ⟨T₁, hlo₁, hhi₁, hgap₁⟩ := returnEventTime_gap r (4 * returnScale r)
  obtain ⟨T₂, hlo₂, hhi₂, hgap₂⟩ := returnEventTime_gap r (10 * returnScale r)
  have hL := returnScale_pos r
  exact ⟨T₁, T₂, hlo₁, by linarith, hlo₂, by linarith, hgap₁, hgap₂⟩


end Bounty

end SubmissionComponent_ReturnVisitCoverage

/- Component ReturnApproximationConditions; SHA256 27ea1e303b3ca0214e6a4677d74e4f6e76603b0f2e87547155caf5fc98d70db2 -/
section SubmissionComponent_ReturnApproximationConditions
/- Packaged analytic, size, and coefficient conditions for both return approximations. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable section

/-- `none` is the integral prefix, while `some i` is the corresponding positive unit. -/
def returnApproximationVector (r : ℕ) (T : ℝ) : Option (ReturnApproximationLabel r T) → ℚ :=
  fun i => match i with
  | none => (returnIntegerPrefix r : ℚ)
  | some j => returnApproximationUnit r T j

def returnApproximationError (z : ℚ) (r : ℕ) (T : ℝ) : ℝ :=
  (((∑ i : ReturnApproximationLabel r T,
    returnApproximationCoefficient z r T i * returnApproximationUnit r T i) -
      (returnIntegerPrefix r : ℚ) : ℚ) : ℝ)

def returnApproximationVector_coordinate (r : ℕ) (T : ℝ)
    (i : Option (ReturnApproximationLabel r T)) :
    IsReturnCoordinate r T (returnApproximationVector r T i) := by
  cases i with
  | none => exact Or.inl rfl
  | some j =>
    cases j with
    | inl a => exact Or.inr (Or.inl ⟨a, rfl⟩)
    | inr a => exact Or.inr (Or.inr ⟨a.1, a.2.1, a.2.2, rfl⟩)

def returnApproximationLabel_card_lower (r : ℕ) (T : ℝ) :
    4 ≤ Fintype.card (ReturnApproximationLabel r T) := by
  classical
  simp [ReturnApproximationLabel]

def returnApproximationLabel_card_eleven (r : ℕ) (T : ℝ)
    (hT : T ≤ 11 * returnScale r) :
    Fintype.card (ReturnApproximationLabel r T) ≤ 0x194 := by
  simpa using returnApproximationLabel_card r 11 T hT

def returnApproximationVector_height :
    ∀ᶠ r in atTop, ∀ T : ℝ, T ≤ 11 * returnScale r →
      Height.mulHeight (returnApproximationVector r T) ≤ Real.exp (27 * returnScale r) := by
  filter_upwards [returnCoordinateHeight_eventually_eleven] with r hr T hT
  exact hr T (Option (ReturnApproximationLabel r T)) (returnApproximationVector r T) hT
    (returnApproximationVector_coordinate r T)

/-- Conditions for a bounded finite unit sum to approximate the shared integral prefix. -/
def ReturnApproximationConditions (z : ℚ) (r : ℕ) (T : ℝ) : Prop :=
  Fintype.card (ReturnApproximationLabel r T) ≤ 0x194 ∧
  (∀ i : ReturnApproximationLabel r T,
    returnApproximationCoefficient z r T i ∈ returnCoefficientPalette z) ∧
  (∀ i : ReturnApproximationLabel r T, 0 < returnApproximationUnit r T i) ∧
  (∀ i : ReturnApproximationLabel r T, Real.exp (-T) ≤ (returnApproximationUnit r T i : ℝ)) ∧
  Height.mulHeight (returnApproximationVector r T) ≤ Real.exp (27 * returnScale r) ∧
  |returnApproximationError z r T| ≤ Real.exp (-T - returnScale r / 0xc8)

def returnApproximation_conditions (z : ℚ)
    (hz : (z : ℝ) = 0xb4 * explicitDensity - 32) :
    ∀ᶠ r in atTop, ∀ T : ℝ, 0 ≤ T → T ≤ 11 * returnScale r →
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T ∨ T + returnScale r / 0x64 < returnEventTime r i n) →
      ReturnApproximationConditions z r T := by
  filter_upwards [returnApproximationVector_height, returnApproximation_error z hz]
    with r hheight herror T hT0 hT hgap
  refine ⟨returnApproximationLabel_card_eleven r T hT,
    returnApproximationCoefficient_mem z r T, returnApproximationUnit_pos r T,
    returnApproximationUnit_lower r T hT0, hheight T hT, ?_⟩
  exact herror T hgap

/-- The two cutoffs have a gap of more than five scales and both satisfy all approximation bounds. -/
def returnApproximation_two_cutoffs (z : ℚ)
    (hz : (z : ℝ) = 0xb4 * explicitDensity - 32) :
    ∀ᶠ r in atTop, ∃ T₁ T₂ : ℝ,
      4 * returnScale r < T₁ ∧ T₁ < 5 * returnScale r ∧
      10 * returnScale r < T₂ ∧ T₂ < 11 * returnScale r ∧
      5 * returnScale r < T₂ - T₁ ∧
      ReturnApproximationConditions z r T₁ ∧ ReturnApproximationConditions z r T₂ ∧
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T₁ ∨ T₁ + returnScale r / 0x64 < returnEventTime r i n) ∧
      (∀ i n, returnEventVisit r i n →
        returnEventTime r i n < T₂ ∨ T₂ + returnScale r / 0x64 < returnEventTime r i n) := by
  filter_upwards [returnApproximation_conditions z hz] with r hr
  obtain ⟨T₁, T₂, hlo₁, hhi₁, hlo₂, hhi₂, hgap₁, hgap₂⟩ :=
    returnEventTime_nonvanishing_cutoffs r
  have hL := returnScale_pos r
  refine ⟨T₁, T₂, hlo₁, hhi₁, hlo₂, hhi₂, ?_, ?_, ?_, hgap₁, hgap₂⟩
  · linarith
  · exact hr T₁ (by linarith) (by linarith) hgap₁
  · exact hr T₂ (by linarith) hhi₂.le hgap₂


end
end Bounty

end SubmissionComponent_ReturnApproximationConditions

/- Component ReturnApproximationSUnits; SHA256 defb2db749cacfdf1489b593c19e337bdd511598dedbf273b9bf09b181f96cff -/
section SubmissionComponent_ReturnApproximationSUnits
/- The finite approximation units have prime support exactly within {2,3}. -/

namespace Bounty

def TwoThreeUnit (x : ℚ) : Prop := ∃ a b : ℤ, x = (2 : ℚ) ^ a * (3 : ℚ) ^ b

def TwoThreeInteger (x : ℚ) : Prop :=
  ∃ a b : ℕ, ∃ z : ℤ, x = (z : ℚ) / ((2 : ℚ) ^ a * (3 : ℚ) ^ b)

def returnApproximationUnit_twoThreeUnit (r : ℕ) (T : ℝ)
    (i : ReturnApproximationLabel r T) : TwoThreeUnit (returnApproximationUnit r T i) := by
  cases i with
  | inl j =>
    refine ⟨2 * returnHeadFourExponent r j, returnHeadThreeExponent r j, ?_⟩
    change returnHeadUnit r j = _
    rw [returnHeadUnit_primeMonomial]
    simp only [rationalPrimeMonomial, zpow_zero, mul_one]
  | inr a =>
    refine ⟨2 * returnUnitFourExponent r a.1 a.2.1,
      returnUnitThreeExponent r a.1 a.2.1, ?_⟩
    change returnRationalUnit r a.1 a.2.1 = _
    rw [returnRationalUnit_primeMonomial]
    simp only [rationalPrimeMonomial, zpow_zero, mul_one]

end Bounty

end SubmissionComponent_ReturnApproximationSUnits

/- Component TwoThreeProductFormula; SHA256 cc84f294510e33414a2f32794604551572bc1467300225a98a6f497075674dee -/
section SubmissionComponent_TwoThreeProductFormula
/- Exact finite-place products for the remaining arithmetic argument.
No Subspace Theorem or irrationality assertion is assumed in this module. -/

namespace Bounty

noncomputable section

def twoThreeUnit_pos {x : ℚ} (hx : TwoThreeUnit x) : 0 < x := by
  obtain ⟨a, b, rfl⟩ := hx
  positivity

def twoThreeUnit_product_formula {x : ℚ} (hx : TwoThreeUnit x) :
    |x| * (padicNorm 2 x * padicNorm 3 x) = 1 := by
  obtain ⟨a, b, rfl⟩ := hx
  have h2 : (2 : ℚ) ^ a ≠ 0 := zpow_ne_zero a (by norm_num)
  have h3 : (3 : ℚ) ^ b ≠ 0 := zpow_ne_zero b (by norm_num)
  have hpos : 0 < (2 : ℚ) ^ a * (3 : ℚ) ^ b := by positivity
  have hv2 : padicValRat 2 ((2 : ℚ) ^ a * (3 : ℚ) ^ b) = a := by
    have hs : padicValRat 2 2 = 1 := padicValRat.self (by norm_num)
    have ht : padicValRat 2 3 = 0 := padicValRat_nat_zero (by norm_num : ¬ 2 ∣ 3)
    rw [padicValRat.mul h2 h3]
    simp only [padicValRat.zpow, hs, ht, mul_one, mul_zero, add_zero]
  have hv3 : padicValRat 3 ((2 : ℚ) ^ a * (3 : ℚ) ^ b) = b := by
    have hs : padicValRat 3 3 = 1 := padicValRat.self (by norm_num)
    have ht : padicValRat 3 2 = 0 := padicValRat_nat_zero (by norm_num : ¬ 3 ∣ 2)
    rw [padicValRat.mul h2 h3]
    simp only [padicValRat.zpow, hs, ht, mul_one, mul_zero, zero_add]
  rw [abs_of_pos hpos, padicNorm.eq_zpow_of_nonzero (mul_ne_zero h2 h3),
    padicNorm.eq_zpow_of_nonzero (mul_ne_zero h2 h3), hv2, hv3]
  simp only [Nat.cast_ofNat, zpow_neg]
  field_simp

def twoThree_integer_finite_norm_bound (P : ℤ) :
    padicNorm 2 (P : ℚ) * padicNorm 3 (P : ℚ) ≤ 1 := by
  exact (mul_le_mul (padicNorm.of_int P) (padicNorm.of_int P)
    (padicNorm.nonneg _) (by norm_num)).trans_eq (one_mul 1)

def twoThreeOneFormProduct {ι : Type*} [Fintype ι] [DecidableEq ι]
    (d x : ι → ℚ) (k : ι) : ℚ :=
  |∑ i, d i * x i| * (∏ i ∈ Finset.univ.erase k, |x i|) *
    ∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i))

def twoThreeOneFormProduct_units {ι : Type*} [Fintype ι] [DecidableEq ι]
    (d x : ι → ℚ) (k : ι) (hx : ∀ i, TwoThreeUnit (x i)) :
    twoThreeOneFormProduct d x k = |∑ i, d i * x i| / |x k| := by
  have hpos : 0 < |x k| := abs_pos.mpr (twoThreeUnit_pos (hx k)).ne'
  apply (eq_div_iff hpos.ne').mpr
  have he : (∏ i ∈ Finset.univ.erase k, |x i|) * |x k| = ∏ i, |x i| :=
    Finset.prod_erase_mul _ _ (Finset.mem_univ k)
  calc
    twoThreeOneFormProduct d x k * |x k| =
        |∑ i, d i * x i| *
          ((∏ i ∈ Finset.univ.erase k, |x i|) * |x k|) *
          (∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i))) := by
            unfold twoThreeOneFormProduct
            ring
    _ = |∑ i, d i * x i| *
          (∏ i, |x i| * (padicNorm 2 (x i) * padicNorm 3 (x i))) := by
            rw [he]
            simp only [Finset.prod_mul_distrib, mul_assoc]
    _ = |∑ i, d i * x i| := by
      simp only [twoThreeUnit_product_formula (hx _), Finset.prod_const_one, mul_one]

def finite_prod_option_erase_none {ι : Type*} [Fintype ι] [DecidableEq ι]
    (f : Option ι → ℚ) :
    (∏ i ∈ Finset.univ.erase none, f i) = ∏ i, f (some i) := by
  have he : (Finset.univ : Finset (Option ι)).erase none =
      (Finset.univ : Finset ι).map Function.Embedding.some := by
    ext i
    cases i <;> simp
  rw [he, Finset.prod_map]
  rfl

def twoThreeOneFormProduct_integer {ι : Type*} [Fintype ι] [DecidableEq ι]
    (d : Option ι → ℚ) (P : ℤ) (u : ι → ℚ) (hu : ∀ i, TwoThreeUnit (u i)) :
    twoThreeOneFormProduct d (fun i => i.elim (P : ℚ) u) none =
      |∑ i, d i * i.elim (P : ℚ) u| *
        (padicNorm 2 (P : ℚ) * padicNorm 3 (P : ℚ)) := by
  unfold twoThreeOneFormProduct
  rw [finite_prod_option_erase_none, Fintype.prod_option]
  simp only [Option.elim_some, Option.elim_none]
  have hprod : (∏ i, |u i|) *
      (∏ i, (padicNorm 2 (u i) * padicNorm 3 (u i))) = 1 := by
    rw [← Finset.prod_mul_distrib]
    simp only [twoThreeUnit_product_formula (hu _), Finset.prod_const_one]
  calc
    _ = |∑ i, d i * i.elim (P : ℚ) u| *
      (padicNorm 2 (P : ℚ) * padicNorm 3 (P : ℚ)) *
        ((∏ i, |u i|) * ∏ i, (padicNorm 2 (u i) * padicNorm 3 (u i))) := by ring
    _ = _ := by rw [hprod, mul_one]

def twoThreeOneFormProduct_integer_le {ι : Type*} [Fintype ι] [DecidableEq ι]
    (d : Option ι → ℚ) (P : ℤ) (u : ι → ℚ) (hu : ∀ i, TwoThreeUnit (u i)) :
    twoThreeOneFormProduct d (fun i => i.elim (P : ℚ) u) none ≤
      |∑ i, d i * i.elim (P : ℚ) u| := by
  rw [twoThreeOneFormProduct_integer d P u hu]
  exact mul_le_of_le_one_right (abs_nonneg _) (twoThree_integer_finite_norm_bound P)


end
end Bounty

end SubmissionComponent_TwoThreeProductFormula

/- Component OneFormDenominatorClearing; SHA256 61e96d39cc05adf9e393425b739d9eec9fd8867631a63fbe8e94c682bddb9494 -/
section SubmissionComponent_OneFormDenominatorClearing
/- Clear a common {2,3}-unit denominator without changing the one-form product. -/

namespace Bounty

noncomputable section

/-- Every finite tuple of {2,3}-integers can be cleared by one positive natural
denominator which is itself a {2,3}-unit. This includes the empty tuple. -/
def twoThreeInteger_common_denominator {ι : Type*} [Fintype ι]
    (x : ι → ℚ) (hx : ∀ i, TwoThreeInteger (x i)) :
    ∃ D : ℕ, 0 < D ∧ TwoThreeUnit (D : ℚ) ∧
      ∀ i, ∃ z : ℤ, (D : ℚ) * x i = (z : ℚ) := by
  classical
  choose a b z hz using hx
  let den : ι → ℕ := fun i => 2 ^ a i * 3 ^ b i
  let D : ℕ := ∏ i, den i
  have hd (i : ι) : 0 < den i := by
    dsimp only [den]
    positivity
  have hD : 0 < D := Finset.prod_pos fun i hi => hd i
  have hunit : TwoThreeUnit (D : ℚ) := by
    refine ⟨((∑ i, a i : ℕ) : ℤ), ((∑ i, b i : ℕ) : ℤ), ?_⟩
    simp only [D, den, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat,
      zpow_natCast, Finset.prod_mul_distrib, Finset.prod_pow_eq_pow_sum]
  refine ⟨D, hD, hunit, ?_⟩
  intro i
  let rest : ℕ := ∏ j ∈ Finset.univ.erase i, den j
  have hprod : rest * den i = D :=
    Finset.prod_erase_mul Finset.univ den (Finset.mem_univ i)
  have hprodQ : (D : ℚ) = (rest : ℚ) * (den i : ℚ) := by
    exact_mod_cast hprod.symm
  have hxi : x i = (z i : ℚ) / (den i : ℚ) := by
    simpa only [den, Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] using hz i
  have hden : (den i : ℚ) ≠ 0 := by exact_mod_cast (hd i).ne'
  refine ⟨(rest : ℤ) * z i, ?_⟩
  rw [hprodQ, hxi]
  simp only [Int.cast_mul, Int.cast_natCast]
  field_simp [hden]

/-- The product is invariant under scaling by a {2,3}-unit, even when the
distinguished coordinate, another coordinate, or the linear form is zero. -/
def twoThreeOneFormProduct_unit_scale {ι : Type*} [Fintype ι] [DecidableEq ι]
    (d x : ι → ℚ) (k : ι) {c : ℚ} (hc : TwoThreeUnit c) :
    twoThreeOneFormProduct d (fun i => c * x i) k = twoThreeOneFormProduct d x k := by
  have hsum : (∑ i, d i * (c * x i)) = c * ∑ i, d i * x i := by
    rw [Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro i hi
    ring
  have harch : (∏ i ∈ Finset.univ.erase k, |c * x i|) =
      (∏ i ∈ Finset.univ.erase k, |c|) * (∏ i ∈ Finset.univ.erase k, |x i|) := by
    simp only [abs_mul, Finset.prod_mul_distrib]
  have hnorm (i : ι) : padicNorm 2 (c * x i) * padicNorm 3 (c * x i) =
      (padicNorm 2 c * padicNorm 3 c) * (padicNorm 2 (x i) * padicNorm 3 (x i)) := by
    rw [padicNorm.mul, padicNorm.mul]
    ring
  have hfinite : (∏ i, (padicNorm 2 (c * x i) * padicNorm 3 (c * x i))) =
      (∏ _i : ι, (padicNorm 2 c * padicNorm 3 c)) *
        ∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i)) := by
    simp only [hnorm, Finset.prod_mul_distrib]
  have hfactor : |c| * (∏ i ∈ Finset.univ.erase k, |c|) *
      (∏ _i : ι, (padicNorm 2 c * padicNorm 3 c)) = 1 := by
    rw [Finset.mul_prod_erase Finset.univ (fun _ : ι => |c|) (Finset.mem_univ k)]
    rw [← Finset.prod_mul_distrib]
    simp only [twoThreeUnit_product_formula hc, Finset.prod_const_one]
  unfold twoThreeOneFormProduct
  rw [hsum, abs_mul, harch, hfinite]
  calc
    _ = (|c| * (∏ i ∈ Finset.univ.erase k, |c|) *
          (∏ _i : ι, (padicNorm 2 c * padicNorm 3 c))) *
        (|∑ i, d i * x i| * (∏ i ∈ Finset.univ.erase k, |x i|) *
          ∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i))) := by ring
    _ = _ := by rw [hfactor, one_mul]


end
end Bounty

end SubmissionComponent_OneFormDenominatorClearing

/- Component OneFormIntegerBridge; SHA256 05422bc5b7a8d984cd8a7e41f2f3c350f987201f76069f1ca7e3fbb36bdf0e8e -/
section SubmissionComponent_OneFormIntegerBridge
/- A finite cover for integer points gives the identical cover for {2,3}-integers.
The covering theorem is an explicit hypothesis; no arithmetic axiom is added. -/

namespace Bounty

noncomputable section

def oneForm_integer_cover_to_sInteger {I : Type*} [Fintype I] [DecidableEq I]
    (d : I → ℚ) (k : I) (ε : ℝ) (F : Finset (I → ℚ))
    (hcover : ∀ z : I → ℤ, z ≠ 0 →
      (twoThreeOneFormProduct d (fun i => (z i : ℚ)) k : ℝ) <
        Height.mulHeight (fun i => (z i : ℚ)) ^ (-ε) →
      ∃ a ∈ F, (∑ i, a i * (z i : ℚ)) = 0)
    (x : I → ℚ) (hSI : ∀ i, TwoThreeInteger (x i)) (hx : x ≠ 0)
    (hsmall : (twoThreeOneFormProduct d x k : ℝ) < Height.mulHeight x ^ (-ε)) :
    ∃ a ∈ F, (∑ i, a i * x i) = 0 := by
  classical
  obtain ⟨D, hD, hDU, hclear⟩ := twoThreeInteger_common_denominator x hSI
  choose z hz using hclear
  have hD0 : (D : ℚ) ≠ 0 := by exact_mod_cast hD.ne'
  have he : (fun i => (z i : ℚ)) = (fun i => (D : ℚ) * x i) := by
    funext i
    exact (hz i).symm
  have hz0 : z ≠ 0 := by
    intro hzero
    apply hx
    funext i
    have hh : (D : ℚ) * x i = 0 := by rw [hz i, hzero]; rfl
    exact (mul_eq_zero.mp hh).resolve_left hD0
  have hheight : Height.mulHeight (fun i => (z i : ℚ)) = Height.mulHeight x := by
    rw [he]
    exact Height.mulHeight_smul_eq_mulHeight x hD0
  have hproduct : twoThreeOneFormProduct d (fun i => (z i : ℚ)) k =
      twoThreeOneFormProduct d x k := by
    rw [he]
    exact twoThreeOneFormProduct_unit_scale d x k hDU
  obtain ⟨a, ha, haz⟩ := hcover z hz0 (by simpa only [hheight, hproduct] using hsmall)
  refine ⟨a, ha, ?_⟩
  have hs : (D : ℚ) * (∑ i, a i * x i) = ∑ i, a i * (z i : ℚ) := by
    rw [Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro i hi
    rw [← hz i]
    ring
  exact (mul_eq_zero.mp (hs.trans haz)).resolve_left hD0


end
end Bounty

end SubmissionComponent_OneFormIntegerBridge

/- Component PrimitiveOneFormReduction; SHA256 69e5ab39381a1bee816e6fee1d0f14997a2c17f890fdda82fe47b50e3e0e14ac -/
section SubmissionComponent_PrimitiveOneFormReduction
/- Primitive normalization preserves the strict one-form approximation inequality. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def twoThreeOneFormProduct_nonneg {I : Type*} [Fintype I] [DecidableEq I]
    (d x : I → ℚ) (k : I) : 0 ≤ twoThreeOneFormProduct d x k := by
  exact mul_nonneg (mul_nonneg (abs_nonneg _)
    (Finset.prod_nonneg (fun i _ => abs_nonneg _)))
    (Finset.prod_nonneg (fun i _ => mul_nonneg (padicNorm.nonneg _) (padicNorm.nonneg _)))

def twoThreeOneFormProduct_scale {I : Type*} [Fintype I] [DecidableEq I]
    (d x : I → ℚ) (k : I) (c : ℚ) :
    twoThreeOneFormProduct d (fun i => c * x i) k =
      (|c| * padicNorm 2 c * padicNorm 3 c) ^ Fintype.card I *
        twoThreeOneFormProduct d x k := by
  have hsum : (∑ i, d i * (c * x i)) = c * ∑ i, d i * x i := by
    rw [Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro i _
    ring
  have harch : (∏ i ∈ Finset.univ.erase k, |c * x i|) =
      (∏ i ∈ Finset.univ.erase k, |c|) * (∏ i ∈ Finset.univ.erase k, |x i|) := by
    simp only [abs_mul, Finset.prod_mul_distrib]
  have hnorm (i : I) : padicNorm 2 (c * x i) * padicNorm 3 (c * x i) =
      (padicNorm 2 c * padicNorm 3 c) * (padicNorm 2 (x i) * padicNorm 3 (x i)) := by
    rw [padicNorm.mul, padicNorm.mul]
    ring
  have hfinite : (∏ i, (padicNorm 2 (c * x i) * padicNorm 3 (c * x i))) =
      (∏ _i : I, (padicNorm 2 c * padicNorm 3 c)) *
        ∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i)) := by
    simp only [hnorm, Finset.prod_mul_distrib]
  have hfactor : |c| * (∏ i ∈ Finset.univ.erase k, |c|) *
      (∏ _i : I, (padicNorm 2 c * padicNorm 3 c)) =
        (|c| * padicNorm 2 c * padicNorm 3 c) ^ Fintype.card I := by
    rw [Finset.mul_prod_erase Finset.univ (fun _ : I => |c|) (Finset.mem_univ k)]
    rw [← Finset.prod_mul_distrib]
    simp only [Finset.prod_const, Finset.card_univ]
    congr 1
    ring
  unfold twoThreeOneFormProduct
  rw [hsum, abs_mul, harch, hfinite]
  calc
    _ = (|c| * (∏ i ∈ Finset.univ.erase k, |c|) *
          (∏ _i : I, (padicNorm 2 c * padicNorm 3 c))) *
        (|∑ i, d i * x i| * (∏ i ∈ Finset.univ.erase k, |x i|) *
          ∏ i, (padicNorm 2 (x i) * padicNorm 3 (x i))) := by ring
    _ = _ := by rw [hfactor]

def twoThreeOneFormProduct_le_integer_scale {I : Type*} [Fintype I] [DecidableEq I]
    (d x : I → ℚ) (k : I) (g : ℤ) (hg : g ≠ 0) :
    twoThreeOneFormProduct d x k ≤
      twoThreeOneFormProduct d (fun i => (g : ℚ) * x i) k := by
  rw [twoThreeOneFormProduct_scale]
  have hpow : (1 : ℚ) ≤ (|(g : ℚ)| * padicNorm 2 (g : ℚ) * padicNorm 3 (g : ℚ)) ^
      Fintype.card I := one_le_pow₀ (integer_three_place_product_lower_rat g hg)
  exact le_mul_of_one_le_left (twoThreeOneFormProduct_nonneg d x k) hpow

def exists_primitive_oneForm_approximation {I : Type*} [Fintype I] [DecidableEq I]
    (d : I → ℚ) (k : I) (ε : ℝ) (x : I → ℤ) (hx : x ≠ 0)
    (hsmall : (twoThreeOneFormProduct d (fun i => (x i : ℚ)) k : ℝ) <
      Height.mulHeight (fun i => (x i : ℚ)) ^ (-ε)) :
    ∃ (g : ℤ) (a : I → ℤ), 0 < g ∧ a ≠ 0 ∧ Finset.univ.gcd a = 1 ∧
      (∀ i, x i = g * a i) ∧
      (twoThreeOneFormProduct d (fun i => (a i : ℚ)) k : ℝ) <
        Height.mulHeight (fun i => (a i : ℚ)) ^ (-ε) := by
  obtain ⟨g, a, hg, ha, hprim, hfactor⟩ := integer_vector_primitive_factor x hx
  refine ⟨g, a, hg, ha, hprim, hfactor, ?_⟩
  have hcast : (fun i => (x i : ℚ)) = fun i => (g : ℚ) * (a i : ℚ) := by
    funext i
    rw [hfactor i, Int.cast_mul]
  have hheight : Height.mulHeight (fun i => (x i : ℚ)) =
      Height.mulHeight (fun i => (a i : ℚ)) := by
    rw [hcast]
    exact Height.mulHeight_smul_eq_mulHeight _ (by exact_mod_cast hg.ne')
  have hle : (twoThreeOneFormProduct d (fun i => (a i : ℚ)) k : ℝ) ≤
      (twoThreeOneFormProduct d (fun i => (x i : ℚ)) k : ℝ) := by
    rw [hcast]
    exact_mod_cast twoThreeOneFormProduct_le_integer_scale d (fun i => (a i : ℚ)) k g hg.ne'
  exact hle.trans_lt (by simpa only [hheight] using hsmall)

def oneForm_primitive_cover_to_integer {I : Type*} [Fintype I] [DecidableEq I]
    (d : I → ℚ) (k : I) (ε : ℝ) (F : Finset (I → ℚ))
    (hcover : ∀ a : I → ℤ, a ≠ 0 → Finset.univ.gcd a = 1 →
      (twoThreeOneFormProduct d (fun i => (a i : ℚ)) k : ℝ) <
        Height.mulHeight (fun i => (a i : ℚ)) ^ (-ε) →
      ∃ b ∈ F, (∑ i, b i * (a i : ℚ)) = 0)
    (x : I → ℤ) (hx : x ≠ 0)
    (hsmall : (twoThreeOneFormProduct d (fun i => (x i : ℚ)) k : ℝ) <
      Height.mulHeight (fun i => (x i : ℚ)) ^ (-ε)) :
    ∃ b ∈ F, (∑ i, b i * (x i : ℚ)) = 0 := by
  obtain ⟨g, a, _, ha, hprim, hfactor, hsmall⟩ :=
    exists_primitive_oneForm_approximation d k ε x hx hsmall
  obtain ⟨b, hb, hba⟩ := hcover a ha hprim hsmall
  refine ⟨b, hb, ?_⟩
  calc
    _ = (g : ℚ) * ∑ i, b i * (a i : ℚ) := by
      rw [Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro i _
      rw [hfactor i, Int.cast_mul]
      ring
    _ = 0 := by rw [hba, mul_zero]

end
end Bounty

end SubmissionComponent_PrimitiveOneFormReduction

/- Component OneFormMatrixProfiles; SHA256 8e9471e0f398bc0fad20a0e76502c8f244824ab0446d8ad3217b00b3a40594b6 -/
section SubmissionComponent_OneFormMatrixProfiles
/- Replacing one identity row by the given rational form realizes exactly
the one-form three-place product, and hence the finite-profile reduction. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def oneFormRowMatrix {I : Type*} [Fintype I] [DecidableEq I]
    (a : I → ℚ) (k : I) : Matrix I I ℚ := (1 : Matrix I I ℚ).updateRow k a

def oneFormRowMatrix_mulVec {I : Type*} [Fintype I] [DecidableEq I]
    (a x : I → ℚ) (k : I) :
    (oneFormRowMatrix a k).mulVec x = Function.update x k (∑ i, a i * x i) := by
  rw [oneFormRowMatrix, Matrix.updateRow_mulVec, Matrix.one_mulVec]
  rfl

def oneFormRowMatrix_det {I : Type*} [Fintype I] [DecidableEq I]
    (a : I → ℚ) (k : I) : (oneFormRowMatrix a k).det = a k := by
  have h := Matrix.det_updateRow_sum (1 : Matrix I I ℚ) k a
  have he : (∑ i, a i • (1 : Matrix I I ℚ) i) = a := by
    ext j
    simp [Matrix.one_apply, Finset.sum_apply]
  simpa [he, oneFormRowMatrix] using h

def oneFormRowMatrix_values_ne_zero {I : Type*} [Fintype I] [DecidableEq I]
    (a x : I → ℚ) (k : I) (hx : ∀ i, x i ≠ 0) (hax : (∑ i, a i * x i) ≠ 0) :
    ∀ i, (oneFormRowMatrix a k).mulVec x i ≠ 0 := by
  intro i
  rw [oneFormRowMatrix_mulVec]
  by_cases hi : i = k
  · simpa [hi] using hax
  · simpa [Function.update_of_ne hi] using hx i

def oneFormRowMatrix_abs_product {I : Type*} [Fintype I] [DecidableEq I]
    (a x : I → ℚ) (k : I) :
    (∏ i, |(oneFormRowMatrix a k).mulVec x i|) =
      |∑ i, a i * x i| * ∏ i ∈ Finset.univ.erase k, |x i| := by
  have he : (fun i => |(oneFormRowMatrix a k).mulVec x i|) =
      Function.update (fun i => |x i|) k |∑ i, a i * x i| := by
    ext i
    rw [oneFormRowMatrix_mulVec]
    by_cases hi : i = k <;> simp [hi]
  rw [he, Finset.prod_update_of_mem (Finset.mem_univ k)]
  simp only [Finset.sdiff_singleton_eq_erase]

def rational_norm_eq_cast_abs (x : ℚ) : ‖x‖ = ((|x| : ℚ) : ℝ) := by
  rw [← Rat.norm_cast_real, Real.norm_eq_abs, Rat.cast_abs]

def oneForm_actual_three_place_product {d : ℕ}
    (a : Fin d → ℚ) (k : Fin d) (x : Fin d → ℤ) :
    (∏ v, ∏ i, actualThreePlaceValues (oneFormRowMatrix a k) x v i) =
      (twoThreeOneFormProduct a (fun i => (x i : ℚ)) k : ℝ) := by
  calc
    _ = (((∏ i, |(oneFormRowMatrix a k).mulVec (fun j => (x j : ℚ)) i|) *
        (∏ i, padicNorm 2 (x i : ℚ)) * (∏ i, padicNorm 3 (x i : ℚ)) : ℚ) : ℝ) := by
      simp [actualThreePlaceValues, Fin.prod_univ_succ, rational_norm_eq_cast_abs,
        Rat.cast_prod, Rat.cast_mul, mul_assoc]
    _ = _ := by
      congr 1
      rw [oneFormRowMatrix_abs_product]
      simp only [twoThreeOneFormProduct, Finset.prod_mul_distrib]
      ring

def exists_finite_primitive_oneForm_profiles {d : ℕ} (hd : 0 < d)
    (a : Fin d → ℚ) (k : Fin d) (ρ : ℝ) (hρ : 0 < ρ) :
    ∃ M : ℝ, 1 ≤ M ∧ ∃ C : Finset (Fin 3 → Fin d → ℝ),
      (∀ c ∈ C, (∀ v i, |c v i| ≤ M + ρ / (6 * d)) ∧
        (∑ v, ∑ i, c v i) ≤ -ρ / 2 ∧ (∀ v i, v ≠ 0 → c v i ≤ 0)) ∧
      ∀ x : Fin d → ℤ, Finset.univ.gcd x = 1 →
        1 ≤ Height.logHeight (fun i => (x i : ℚ)) → (∀ i, x i ≠ 0) →
        (∑ i, a i * (x i : ℚ)) ≠ 0 →
        (twoThreeOneFormProduct a (fun i => (x i : ℚ)) k : ℝ) <
          Height.mulHeight (fun i => (x i : ℚ)) ^ (-ρ) →
        ∃ c ∈ C, ∀ v i, actualThreePlaceValues (oneFormRowMatrix a k) x v i ≤
          Real.exp (c v i * Height.logHeight (fun i => (x i : ℚ))) := by
  obtain ⟨M, hM, C, hC, hcover⟩ := exists_finite_primitive_three_place_profiles hd
    (oneFormRowMatrix a k) ρ hρ
  refine ⟨M, hM, C, hC, ?_⟩
  intro x hprim hq hxn hax hprod
  apply hcover x hprim hq hxn
  · exact oneFormRowMatrix_values_ne_zero a (fun i => (x i : ℚ)) k
      (fun i => by exact_mod_cast hxn i) hax
  · rw [oneForm_actual_three_place_product]
    exact hprod.le


end
end Bounty

end SubmissionComponent_OneFormMatrixProfiles

/- Component RationalSubspaceCoverExceptions; SHA256 9b4470b3a211e26300f6696672059eef6ec311b62cfb0d8fe455af03f8b5912e -/
section SubmissionComponent_RationalSubspaceCoverExceptions
/- Concrete finite exceptional families and conversion of proper rational
subspaces to nonzero rational equations. No covering theorem is assumed here. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def proper_rational_subspace_normal {I : Type*} [Fintype I] [DecidableEq I]
    (V : Submodule ℚ (I → ℚ)) (hV : V ≠ ⊤) :
    ∃ a : I → ℚ, a ≠ 0 ∧ ∀ x ∈ V, (∑ i, a i * x i) = 0 := by
  obtain ⟨f, hf, hker⟩ := V.exists_le_ker_of_lt_top hV.lt_top
  let a : I → ℚ := fun i => f (Pi.single i 1)
  have he (x : I → ℚ) : (∑ i, a i * x i) = f x := by
    have hx : x = ∑ i, x i • Pi.single i (1 : ℚ) := by ext i; simp [Pi.single_apply]
    conv_rhs => rw [hx, map_sum]
    apply Finset.sum_congr rfl
    intro i _
    simp [a, mul_comm]
  refine ⟨a, ?_, ?_⟩
  · intro ha
    apply hf
    apply LinearMap.ext
    intro x
    simpa [ha] using (he x).symm
  · intro x hx
    rw [he]
    exact hker hx

def finite_proper_subspaces_normals {I : Type*} [Fintype I] [DecidableEq I]
    (F : Finset (Submodule ℚ (I → ℚ))) (hF : ∀ V ∈ F, V ≠ ⊤) :
    ∃ G : Finset (I → ℚ), (∀ a ∈ G, a ≠ 0) ∧
      ∀ x : I → ℚ, (∃ V ∈ F, x ∈ V) → ∃ a ∈ G, (∑ i, a i * x i) = 0 := by
  classical
  choose a ha hvan using fun V : ↥F => proper_rational_subspace_normal V.val (hF V.val V.property)
  refine ⟨Finset.univ.image a, ?_, ?_⟩
  · intro b hb
    obtain ⟨V, _, rfl⟩ := Finset.mem_image.mp hb
    exact ha V
  · rintro x ⟨V, hV, hx⟩
    exact ⟨a ⟨V, hV⟩, Finset.mem_image.mpr ⟨⟨V, hV⟩, Finset.mem_univ _, rfl⟩,
      hvan ⟨V, hV⟩ x hx⟩

def finite_primitive_integer_small_height {I : Type*} [Fintype I] [Nonempty I] :
    Set.Finite {x : I → ℤ | x ≠ 0 ∧ Finset.univ.gcd x = 1 ∧
      Height.logHeight (fun i => (x i : ℚ)) < 1} := by
  classical
  let N : ℤ := ⌈Real.exp 1⌉
  apply (Set.finite_Icc (a := fun _ : I => -N) (b := fun _ : I => N)).subset
  rintro x ⟨hx, hprim, hsmall⟩
  have hH : 0 < integerVectorMax x := lt_of_lt_of_le (by norm_num) (integerVectorMax_ge_one x hx)
  have hHsmall : integerVectorMax x < Real.exp 1 := by
    rw [← Real.exp_log hH]
    exact Real.exp_lt_exp.mpr (by simpa [primitive_integer_logHeight x hprim] using hsmall)
  have hcoord (i : I) : |(x i : ℝ)| ≤ (N : ℝ) :=
    (integer_coord_abs_le_max x i).trans (hHsmall.le.trans (Int.le_ceil _))
  constructor <;> intro i
  · exact_mod_cast (abs_le.mp (hcoord i)).1
  · exact_mod_cast (abs_le.mp (hcoord i)).2

def rational_singleton_span_ne_top {I : Type*} [Fintype I]
    (hI : 2 ≤ Fintype.card I) (x : I → ℚ) : Submodule.span ℚ {x} ≠ ⊤ := by
  classical
  have hdim : Module.finrank ℚ (Submodule.span ℚ {x}) ≤ 1 := by
    simpa using (finrank_span_le_card ({x} : Set (I → ℚ)))
  intro htop
  rw [htop, finrank_top, Module.finrank_pi] at hdim
  omega

def finite_small_height_normal_cover {I : Type*} [Fintype I] [DecidableEq I]
    (hI : 2 ≤ Fintype.card I) :
    ∃ G : Finset (I → ℚ), (∀ a ∈ G, a ≠ 0) ∧
      ∀ x : I → ℤ, x ≠ 0 → Finset.univ.gcd x = 1 →
        Height.logHeight (fun i => (x i : ℚ)) < 1 →
        ∃ a ∈ G, (∑ i, a i * (x i : ℚ)) = 0 := by
  classical
  let : Nonempty I := Fintype.card_pos_iff.mp (by omega)
  let S := (finite_primitive_integer_small_height (I := I)).toFinset
  let F := S.image (fun x : I → ℤ => Submodule.span ℚ {fun i => (x i : ℚ)})
  obtain ⟨G, hG, hcover⟩ := finite_proper_subspaces_normals F (by
    intro V hV
    obtain ⟨x, _, rfl⟩ := Finset.mem_image.mp hV
    exact rational_singleton_span_ne_top hI _)
  refine ⟨G, hG, ?_⟩
  intro x hx hprim hsmall
  apply hcover
  refine ⟨_, Finset.mem_image.mpr ⟨x, ?_, rfl⟩, Submodule.subset_span (Set.mem_singleton _)⟩
  exact (Set.Finite.mem_toFinset _).mpr ⟨hx, hprim, hsmall⟩


end
end Bounty

end SubmissionComponent_RationalSubspaceCoverExceptions

/- Component BoundedBoxSubspaceCover; SHA256 7f91d940265c2f52223db9bf0d1cd452e98f801cb3bee120107744b650adfadf -/
section SubmissionComponent_BoundedBoxSubspaceCover
/- Bounded logarithmic parameters contribute an actual finite proper-subspace cover. -/

namespace Bounty
noncomputable section
open scoped BigOperators

def exists_bounded_exponential_subspace_cover {d : ℕ} (hd : 2 ≤ d)
    (A : Matrix (Fin d) (Fin d) ℚ) (hA : A.det ≠ 0)
    (c : Fin d → ℝ) (T : ℝ) :
    ∃ F : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ F, V ≠ ⊤) ∧
      ∀ q : ℝ, 0 ≤ q → q ≤ T → ∀ x : Fin d → ℤ,
        (∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c i * q)) →
        ∃ V ∈ F, (fun i => (x i : ℚ)) ∈ V := by
  classical
  let S := (finite_bounded_exponential_integer_points A hA c T).toFinset
  refine ⟨S.image (fun x : Fin d → ℤ => Submodule.span ℚ {fun i => (x i : ℚ)}), ?_, ?_⟩
  · intro V hV
    obtain ⟨x, _, rfl⟩ := Finset.mem_image.mp hV
    exact rational_singleton_span_ne_top (by simpa using hd) _
  · intro q hq hqT x hx
    refine ⟨Submodule.span ℚ {fun i => (x i : ℚ)},
      Finset.mem_image.mpr ⟨x, ?_, rfl⟩, Submodule.subset_span (Set.mem_singleton _)⟩
    change x ∈ (finite_bounded_exponential_integer_points A hA c T).toFinset
    rw [Set.Finite.mem_toFinset]
    refine ⟨q, hq, hqT, fun i => ?_⟩
    rw [← Real.norm_eq_abs, Rat.norm_cast_real]
    exact hx i

end
end Bounty

end SubmissionComponent_BoundedBoxSubspaceCover

/- Component RationalThreePlaceSubspaceCover; SHA256 fcaca9dca9f10a8c58d0dc845ce09c19a331820d665725bfe1d986bd45c0edf3 -/
section SubmissionComponent_RationalThreePlaceSubspaceCover
/- The precise geometric covering contract used by the final arithmetic
application. This file defines a proposition; it does not assert the contract. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def RationalThreePlaceSubspaceCover : Prop :=
  ∀ (I : Type) [Fintype I] [DecidableEq I], 2 ≤ Fintype.card I →
    ∀ (A : Matrix I I ℚ), A.det ≠ 0 →
    ∀ (c : Fin 3 → I → ℝ) (ρ : ℝ), 0 < ρ →
      (∑ v, ∑ i, c v i) ≤ -ρ →
      (∀ v i, v ≠ 0 → c v i ≤ 0) →
      ∃ F : Finset (Submodule ℚ (I → ℚ)), (∀ V ∈ F, V ≠ ⊤) ∧
        ∀ (q : ℝ), 0 ≤ q → ∀ x : I → ℤ,
          (∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c 0 i * q)) →
          (∀ i, (padicNorm 2 (x i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q)) →
          (∀ i, (padicNorm 3 (x i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) →
          ∃ V ∈ F, (fun i => (x i : ℚ)) ∈ V

def three_place_subspace_cover_normals (h : RationalThreePlaceSubspaceCover)
    (I : Type) [Fintype I] [DecidableEq I] (hI : 2 ≤ Fintype.card I)
    (A : Matrix I I ℚ) (hA : A.det ≠ 0)
    (c : Fin 3 → I → ℝ) (ρ : ℝ) (hρ : 0 < ρ)
    (hc : (∑ v, ∑ i, c v i) ≤ -ρ)
    (hcfin : ∀ v i, v ≠ 0 → c v i ≤ 0) :
    ∃ G : Finset (I → ℚ), (∀ a ∈ G, a ≠ 0) ∧
      ∀ (q : ℝ), 0 ≤ q → ∀ x : I → ℤ,
        (∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c 0 i * q)) →
        (∀ i, (padicNorm 2 (x i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q)) →
        (∀ i, (padicNorm 3 (x i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) →
        ∃ a ∈ G, (∑ i, a i * (x i : ℚ)) = 0 := by
  obtain ⟨F, hF, hcover⟩ := h I hI A hA c ρ hρ hc hcfin
  obtain ⟨G, hG, hnormal⟩ := finite_proper_subspaces_normals F hF
  exact ⟨G, hG, fun q hq x h₀ h₂ h₃ => hnormal _ (hcover q hq x h₀ h₂ h₃)⟩


end
end Bounty

end SubmissionComponent_RationalThreePlaceSubspaceCover

/- Component ThreePlaceSubspaceCoverReindex; SHA256 7f94130876bd3a0d33f01049ff63ce775d9763335bfc3e07c4180c5d2de86d71 -/
section SubmissionComponent_ThreePlaceSubspaceCoverReindex
/- Exact finite-coordinate transport of the three-place rational subspace-cover contract. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

/-- The same geometric contract on the standard finite coordinate types. -/
def RationalThreePlaceSubspaceCoverFin : Prop :=
  ∀ d : ℕ, 2 ≤ d → ∀ A : Matrix (Fin d) (Fin d) ℚ, A.det ≠ 0 →
    ∀ (c : Fin 3 → Fin d → ℝ) (ρ : ℝ), 0 < ρ →
      (∑ v, ∑ i, c v i) ≤ -ρ →
      (∀ v i, v ≠ 0 → c v i ≤ 0) →
      ∃ F : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ F, V ≠ ⊤) ∧
        ∀ (q : ℝ), 0 ≤ q → ∀ x : Fin d → ℤ,
          (∀ i, ‖A.mulVec (fun j => (x j : ℚ)) i‖ ≤ Real.exp (c 0 i * q)) →
          (∀ i, (padicNorm 2 (x i : ℚ) : ℝ) ≤ Real.exp (c 1 i * q)) →
          (∀ i, (padicNorm 3 (x i : ℚ) : ℝ) ≤ Real.exp (c 2 i * q)) →
          ∃ V ∈ F, (fun i => (x i : ℚ)) ∈ V

def profile_mulVec_reindex {I I' : Type*} [Fintype I] [Fintype I']
    (e : I ≃ I') (A : Matrix I I ℚ) (x : I → ℚ) :
    (Matrix.reindex e e A).mulVec (profileCoordinateEquiv e x) =
      profileCoordinateEquiv e (A.mulVec x) := by
  change (A.submatrix e.symm e.symm).mulVec (x ∘ e.symm) = (A.mulVec x) ∘ e.symm
  rw [Matrix.submatrix_mulVec_equiv]
  simp only [Equiv.symm_symm, Function.comp_assoc, Equiv.symm_comp_self, Function.comp_id]

def rationalThreePlaceSubspaceCover_of_fin
    (hfin : RationalThreePlaceSubspaceCoverFin) : RationalThreePlaceSubspaceCover := by
  classical
  intro I _ _ hI A hA c ρ hρ hc hcfin
  let e : I ≃ Fin (Fintype.card I) := Fintype.equivFin I
  let E := profileCoordinateEquiv e
  let A' := Matrix.reindex e e A
  let c' : Fin 3 → Fin (Fintype.card I) → ℝ := fun v i => c v (e.symm i)
  have hA' : A'.det ≠ 0 := by simpa only [A', Matrix.det_reindex_self] using hA
  have hc' : (∑ v, ∑ i, c' v i) ≤ -ρ := by
    simpa only [c', Equiv.sum_comp] using hc
  have hcfin' : ∀ v i, v ≠ 0 → c' v i ≤ 0 := fun v i hv => hcfin v (e.symm i) hv
  obtain ⟨F, hF, hcover⟩ := hfin (Fintype.card I) hI A' hA' c' ρ hρ hc' hcfin'
  refine ⟨F.image (fun V => V.map E.symm.toLinearMap), ?_, ?_⟩
  · intro V hV
    obtain ⟨W, hW, rfl⟩ := Finset.mem_image.mp hV
    exact Submodule.map_ne_top_iff.mpr (hF W hW)
  · intro q hq x hInf hTwo hThree
    let x' : Fin (Fintype.card I) → ℤ := fun i => x (e.symm i)
    have hInf' : ∀ i, ‖A'.mulVec (fun j => (x' j : ℚ)) i‖ ≤ Real.exp (c' 0 i * q) := by
      have heq := profile_mulVec_reindex e A (fun j => (x j : ℚ))
      change A'.mulVec (fun j => (x' j : ℚ)) =
        profileCoordinateEquiv e (A.mulVec (fun j => (x j : ℚ))) at heq
      intro i
      rw [heq]
      exact hInf (e.symm i)
    have hTwo' : ∀ i, (padicNorm 2 (x' i : ℚ) : ℝ) ≤ Real.exp (c' 1 i * q) :=
      fun i => hTwo (e.symm i)
    have hThree' : ∀ i, (padicNorm 3 (x' i : ℚ) : ℝ) ≤ Real.exp (c' 2 i * q) :=
      fun i => hThree (e.symm i)
    obtain ⟨V, hV, hxV⟩ := hcover q hq x' hInf' hTwo' hThree'
    refine ⟨V.map E.symm.toLinearMap, Finset.mem_image.mpr ⟨V, hV, rfl⟩, ?_⟩
    refine Submodule.mem_map.mpr ⟨(fun i => (x' i : ℚ)), hxV, ?_⟩
    change E.symm (E (fun i => (x i : ℚ))) = _
    exact E.symm_apply_apply _

end
end Bounty

end SubmissionComponent_ThreePlaceSubspaceCoverReindex

/- Component RationalThreePlaceSubspaceTheorem; SHA256 8268d47b982520135b40928dde99c90448e87c0e19e55c98c35e93bd081babce -/
section SubmissionComponent_RationalThreePlaceSubspaceTheorem
/- The rational three-place Subspace Theorem for integer coordinate forms at 2 and 3. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def rational_three_place_subspace_cover_fin : RationalThreePlaceSubspaceCoverFin := by
  classical
  intro d hd A hA c ρ hρ hsum hcfin
  let : NeZero d := ⟨by omega⟩
  let M : ℝ := ∑ v, ∑ i, |c v i|
  have hcBound : ∀ v i, |c v i| ≤ M := by
    intro v i
    exact (Finset.single_le_sum (fun j _ => abs_nonneg (c v j)) (Finset.mem_univ i)).trans
      (Finset.single_le_sum (fun w _ => Finset.sum_nonneg (fun j _ => abs_nonneg (c w j)))
        (Finset.mem_univ v))
  obtain ⟨C, T, _, hT, hwitness⟩ := exists_threePlace_compound_witnesses hd A hA M ρ hρ
  let S : Set ℝ := {q | T ≤ q ∧ ∃ x ∈ rationalThreePlaceDomain A c q, x ≠ 0}
  have hS (q : ℝ) (hq : q ∈ S) : 0 ≤ q := le_trans (by linarith) hq.1
  have hex : ∀ q : ℝ, ∃ (k : Fin d) (p : Equiv.Perm (Fin d))
      (H : Matrix (Fin d) (Fin d) ℤ),
      q ∈ S → ThreePlaceCompoundWitnessData A c q hA C ρ k p H := by
    intro q
    by_cases hq : q ∈ S
    · obtain ⟨k, p, H, hdata⟩ := hwitness c q hcBound
        (fun i => hcfin 1 i (by decide)) (fun i => hcfin 2 i (by decide)) hsum hq.1 hq.2
      exact ⟨k, p, H, fun _ => hdata⟩
    · exact ⟨⟨1, by omega⟩, Equiv.refl _, 1, fun h => False.elim (hq h)⟩
  choose cut p H hdata using hex
  let K := {k : Fin d // 1 ≤ k.val}
  let U (k : K) : Set ℝ := {q | q ∈ S ∧ cut q = k.val}
  have hfam (k : K) : ∃ G : Finset (Submodule ℚ (Fin d → ℚ)), (∀ V ∈ G, V ≠ ⊤) ∧
      ∀ q ∈ U k, Submodule.span ℚ
        (((H q).map (Int.castRingHom ℚ)).col '' {i : Fin d | i.val < k.val.val}) ∈ G := by
    refine exists_finite_varying_profile_prefix_family k.property k.val.isLt A hA
      (fun q => threePlaceCompoundProfile A c q hA (p q) k.val) C (threePlaceGapRate d ρ / 2)
      (by exact div_pos (threePlaceGapRate_pos hd hρ) (by norm_num)) (U k)
      (fun q hq => hS q hq.1) ?_ ?_ H ?_ ?_ ?_ ?_
    · intro q hq v s
      have hh := (hdata q hq.1).2.2.1
      rw [hq.2] at hh
      exact hh v s
    · intro q hq
      have hh := (hdata q hq.1).2.2.2.1
      rw [hq.2] at hh
      exact hh
    · intro q hq
      exact (hdata q hq.1).2.1
    · intro q hq i t ht
      have hh := (hdata q hq.1).2.2.2.2.1
      rw [hq.2] at hh
      have hmap : compoundMatrix (d - k.val.val) ((H q).map (Int.castRingHom ℚ)) =
          (compoundMatrix (d - k.val.val) (H q)).map (Int.castRingHom ℚ) :=
        compoundMatrix_map (Int.castRingHom ℚ) _ (H q)
      rw [hmap]
      exact (hh t ht).1 i
    · intro q hq i t ht
      have hh := (hdata q hq.1).2.2.2.2.1
      rw [hq.2] at hh
      have hmap : compoundMatrix (d - k.val.val) ((H q).map (Int.castRingHom ℚ)) =
          (compoundMatrix (d - k.val.val) (H q)).map (Int.castRingHom ℚ) :=
        compoundMatrix_map (Int.castRingHom ℚ) _ (H q)
      rw [hmap]
      exact (hh t ht).2.1 i
    · intro q hq i t ht
      have hh := (hdata q hq.1).2.2.2.2.1
      rw [hq.2] at hh
      have hmap : compoundMatrix (d - k.val.val) ((H q).map (Int.castRingHom ℚ)) =
          (compoundMatrix (d - k.val.val) (H q)).map (Int.castRingHom ℚ) :=
        compoundMatrix_map (Int.castRingHom ℚ) _ (H q)
      rw [hmap]
      exact (hh t ht).2.2 i
  choose G hG hcover using hfam
  obtain ⟨B, hB, hsmall⟩ := exists_bounded_exponential_subspace_cover hd A hA (c 0) T
  let F : Finset (Submodule ℚ (Fin d → ℚ)) := B ∪ ({⊥} ∪ Finset.univ.biUnion G)
  refine ⟨F, ?_, ?_⟩
  · intro V hV
    rcases Finset.mem_union.mp hV with hV | hV
    · exact hB V hV
    · rcases Finset.mem_union.mp hV with hV | hV
      · have hv : V = ⊥ := Finset.mem_singleton.mp hV
        rw [hv]
        exact bot_ne_top
      · obtain ⟨k, _, hk⟩ := Finset.mem_biUnion.mp hV
        exact hG k V hk
  · intro q hq x hInf hTwo hThree
    by_cases hx : x = 0
    · refine ⟨⊥, Finset.mem_union_right _ (Finset.mem_union_left _ (Finset.mem_singleton_self _)), ?_⟩
      simp only [hx, Pi.zero_apply, Int.cast_zero, Submodule.mem_bot]
      rfl
    by_cases hqT : q ≤ T
    · obtain ⟨V, hV, hxV⟩ := hsmall q hq hqT x hInf
      exact ⟨V, Finset.mem_union_left _ hV, hxV⟩
    have hxD : x ∈ rationalThreePlaceDomain A c q := by
      refine ⟨?_, hTwo, hThree⟩
      intro i
      have hh := hInf i
      rw [← Rat.norm_cast_real, Real.norm_eq_abs] at hh
      simpa [Matrix.mulVec, dotProduct, Matrix.map_apply, Rat.cast_sum, Rat.cast_mul] using hh
    have hqS : q ∈ S := ⟨le_of_not_ge hqT, x, hxD, hx⟩
    let k : K := ⟨cut q, (hdata q hqS).1⟩
    let V := Submodule.span ℚ
      (((H q).map (Int.castRingHom ℚ)).col '' {i : Fin d | i.val < (cut q).val})
    refine ⟨V, Finset.mem_union_right _ (Finset.mem_union_right _ ?_), ?_⟩
    · apply Finset.mem_biUnion.mpr
      exact ⟨k, Finset.mem_univ k, hcover k q ⟨hqS, rfl⟩⟩
    · exact (hdata q hqS).2.2.2.2.2 x hxD

def rational_three_place_subspace_cover : RationalThreePlaceSubspaceCover :=
  rationalThreePlaceSubspaceCover_of_fin rational_three_place_subspace_cover_fin

end
end Bounty

end SubmissionComponent_RationalThreePlaceSubspaceTheorem

/- Component ThreePlaceOneFormFiniteCover; SHA256 92a2aa7d7d20125da3544ce3517209561ab7868d469a2b9242b3de1ee471be42 -/
section SubmissionComponent_ThreePlaceOneFormFiniteCover
/- The geometric cover implies the actual integer one-form cover in each
finite dimension. Zero values and small primitive heights are included. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def integer_oneForm_finite_cover_of_three_place
    (hST : RationalThreePlaceSubspaceCover) {d : ℕ} (hd : 2 ≤ d)
    (a : Fin d → ℚ) (k : Fin d) (hak : a k ≠ 0)
    (ε : ℝ) (hε : 0 < ε) :
    ∃ G : Finset (Fin d → ℚ), (∀ b ∈ G, b ≠ 0) ∧
      ∀ x : Fin d → ℤ, x ≠ 0 →
        (twoThreeOneFormProduct a (fun i => (x i : ℚ)) k : ℝ) <
          Height.mulHeight (fun i => (x i : ℚ)) ^ (-ε) →
        ∃ b ∈ G, (∑ i, b i * (x i : ℚ)) = 0 := by
  classical
  have hd' : 2 ≤ Fintype.card (Fin d) := by simpa using hd
  obtain ⟨M, hM, C, hC, hprofile⟩ := exists_finite_primitive_oneForm_profiles
    (by omega : 0 < d) a k ε hε
  have hAc : (oneFormRowMatrix a k).det ≠ 0 := by rwa [oneFormRowMatrix_det]
  have hcovers (c : ↥C) := three_place_subspace_cover_normals hST (Fin d) hd'
    (oneFormRowMatrix a k) hAc c.val (ε / 2) (by positivity)
    (by simpa only [neg_div] using (hC c.val c.property).2.1)
    (hC c.val c.property).2.2
  choose F hF hcover using hcovers
  obtain ⟨S, hS, hsmallcover⟩ := finite_small_height_normal_cover hd'
  let E : Finset (Fin d → ℚ) := Finset.univ.image (fun i => Pi.single i 1)
  let P : Finset (Fin d → ℚ) := Finset.univ.biUnion F
  let G : Finset (Fin d → ℚ) := P ∪ (S ∪ ({a} ∪ E))
  have ha : a ≠ 0 := by intro h; exact hak (congrFun h k)
  have hE : ∀ b ∈ E, b ≠ 0 := by
    intro b hb
    obtain ⟨i, _, rfl⟩ := Finset.mem_image.mp hb
    intro h
    have hh := congrFun h i
    simpa using hh
  have hG : ∀ b ∈ G, b ≠ 0 := by
    intro b hb
    rcases Finset.mem_union.mp hb with hb | hb
    · obtain ⟨c, _, hc⟩ := Finset.mem_biUnion.mp hb
      exact hF c b hc
    · rcases Finset.mem_union.mp hb with hb | hb
      · exact hS b hb
      · rcases Finset.mem_union.mp hb with hb | hb
        · simpa only [Finset.mem_singleton.mp hb] using ha
        · exact hE b hb
  refine ⟨G, hG, ?_⟩
  apply oneForm_primitive_cover_to_integer a k ε G
  intro x hx hprim hprod
  by_cases hcoords : ∀ i, x i ≠ 0
  · by_cases hax : (∑ i, a i * (x i : ℚ)) = 0
    · exact ⟨a, by simp [G], hax⟩
    · by_cases hheight : 1 ≤ Height.logHeight (fun i => (x i : ℚ))
      · obtain ⟨c, hc, hp⟩ := hprofile x hprim hheight hcoords hax hprod
        obtain ⟨b, hb, hbx⟩ := hcover ⟨c, hc⟩
          (Height.logHeight (fun i => (x i : ℚ))) (by linarith) x
          (fun i => hp 0 i) (fun i => hp 1 i) (fun i => hp 2 i)
        refine ⟨b, Finset.mem_union_left _ ?_, hbx⟩
        exact Finset.mem_biUnion.mpr ⟨⟨c, hc⟩, Finset.mem_univ _, hb⟩
      · obtain ⟨b, hb, hbx⟩ := hsmallcover x hx hprim (lt_of_not_ge hheight)
        exact ⟨b, Finset.mem_union_right _ (Finset.mem_union_left _ hb), hbx⟩
  · push_neg at hcoords
    obtain ⟨i, hi⟩ := hcoords
    refine ⟨Pi.single i 1, ?_, ?_⟩
    · apply Finset.mem_union_right
      apply Finset.mem_union_right
      apply Finset.mem_union_right
      exact Finset.mem_image.mpr ⟨i, Finset.mem_univ _, rfl⟩
    · simp [Pi.single_apply, hi]


end
end Bounty

end SubmissionComponent_ThreePlaceOneFormFiniteCover

/- Component FiniteHyperplaneElimination; SHA256 914801643fb8c3288c4f6723f2932ed213ba1febb5f159342fc387ce3d531e16 -/
section SubmissionComponent_FiniteHyperplaneElimination
/- Exact deletion of a coordinate subject to a fixed rational hyperplane relation. -/

namespace Bounty

universe u

def hyperplaneDeleteCoefficient {I : Type u} (a d : I → ℚ) (k : I) :
    {i : I // i ≠ k} → ℚ :=
  fun i => d i - d k * a i / a k

/-- Substitute for a coordinate with nonzero hyperplane coefficient. The remaining
coordinates are the original coordinates restricted to the complement of the pivot. -/
def finite_hyperplane_eliminate {I : Type u} [Fintype I] [DecidableEq I]
    (a d x : I → ℚ) (k : I) (hak : a k ≠ 0) (hax : ∑ i, a i * x i = 0) :
    (∑ i, d i * x i) =
      ∑ i : {i : I // i ≠ k}, hyperplaneDeleteCoefficient a d k i * x i := by
  have hfull : (∑ i, (d i - d k * a i / a k) * x i) = ∑ i, d i * x i := by
    calc
      _ = (∑ i, d i * x i) - (d k / a k) * ∑ i, a i * x i := by
        rw [Finset.mul_sum, ← Finset.sum_sub_distrib]
        apply Finset.sum_congr rfl
        intro i hi
        ring
      _ = _ := by rw [hax, mul_zero, sub_zero]
  have hpivot : (d k - d k * a k / a k) * x k = 0 := by
    field_simp [hak]
    ring
  have hdelete := Fintype.sum_eq_add_sum_subtype_ne
    (fun i => (d i - d k * a i / a k) * x i) k
  rw [hpivot, zero_add] at hdelete
  exact hfull.symm.trans hdelete

/-- A nonzero coefficient vector supplies a single pivot that works for every
target linear form and every vector on the hyperplane. -/
def finite_hyperplane_exists_elimination {I : Type u} [Fintype I] [DecidableEq I]
    (a : I → ℚ) (ha : a ≠ 0) :
    ∃ k : I, a k ≠ 0 ∧ ∀ d x : I → ℚ, (∑ i, a i * x i) = 0 →
      (∑ i, d i * x i) =
        ∑ i : {i : I // i ≠ k}, hyperplaneDeleteCoefficient a d k i * x i := by
  have hex : ∃ k, a k ≠ 0 := by
    by_contra! hh
    apply ha
    funext i
    exact hh i
  obtain ⟨k, hk⟩ := hex
  exact ⟨k, hk, fun d x hx => finite_hyperplane_eliminate a d x k hk hx⟩

def finite_hyperplane_delete_card_lt {I : Type u} [Fintype I] [DecidableEq I] (k : I) :
    Fintype.card {i : I // i ≠ k} < Fintype.card I :=
  Fintype.card_subtype_lt (x := k) (by simp)

def hyperplaneOptionVector {I : Type u} (P : ℚ) (x : I → ℚ) : Option I → ℚ
  | none => P
  | some i => x i

/-- If the integer coordinate has nonzero hyperplane coefficient, removing it
converts the integer approximation error into a linear form in the unit coordinates. -/
def finite_option_hyperplane_eliminate_integer {I : Type u} [Fintype I]
    (a : Option I → ℚ) (d x : I → ℚ) (P : ℤ) (ha : a none ≠ 0)
    (hax : ∑ j, a j * hyperplaneOptionVector (P : ℚ) x j = 0) :
    (∑ i, d i * x i) - (P : ℚ) =
      ∑ i, (d i + a (some i) / a none) * x i := by
  have hh : a none * (P : ℚ) + ∑ i, a (some i) * x i = 0 := by
    simpa only [Fintype.sum_option, hyperplaneOptionVector] using hax
  have hP : (P : ℚ) = -(∑ i, a (some i) * x i) / a none := by
    apply (eq_div_iff ha).mpr
    linear_combination hh
  rw [hP]
  calc
    _ = (∑ i, d i * x i) + (∑ i, a (some i) * x i) / a none := by ring
    _ = (∑ i, d i * x i) + ∑ i, (a (some i) / a none) * x i := by
      rw [Finset.sum_div]
      congr 1
      apply Finset.sum_congr rfl
      intro i hi
      ring
    _ = _ := by
      rw [← Finset.sum_add_distrib]
      apply Finset.sum_congr rfl
      intro i hi
      ring

/-- If the hyperplane omits the integer coordinate, the integer stays unchanged
while one of the other coordinates is deleted. -/
def finite_option_hyperplane_eliminate_unit {I : Type u} [Fintype I] [DecidableEq I]
    (a : Option I → ℚ) (d x : I → ℚ) (P : ℤ) (ha : a none = 0)
    (k : I) (hak : a (some k) ≠ 0)
    (hax : ∑ j, a j * hyperplaneOptionVector (P : ℚ) x j = 0) :
    (∑ i, d i * x i) - (P : ℚ) =
      (∑ i : {i : I // i ≠ k},
        hyperplaneDeleteCoefficient (fun j => a (some j)) d k i * x i) - (P : ℚ) := by
  have hh : ∑ i, a (some i) * x i = 0 := by
    simpa only [Fintype.sum_option, hyperplaneOptionVector, ha, zero_mul, zero_add] using hax
  rw [finite_hyperplane_eliminate (fun j => a (some j)) d x k hak hh]


end Bounty

end SubmissionComponent_FiniteHyperplaneElimination

/- Component OneFormRigidity; SHA256 f0c0e2c69242908ef6d6778e2ad990a015476f5af5f5f8158396e4ecce1dd438 -/
section SubmissionComponent_OneFormRigidity
/- Finite-hyperplane induction conditional on the actual one-form S-arithmetic
Subspace Theorem. No arithmetic axiom or unconditional target is introduced. -/

namespace Bounty

noncomputable section
open scoped BigOperators

def oneFormExponent : ℝ := 1 / 0x2a30

def oneFormHeightFactor {I : Type*} [Fintype I] (x : I → ℚ) : ℝ :=
  Height.mulHeight x ^ (-oneFormExponent)

def oneFormHeightFactor_pos {I : Type*} [Fintype I] (x : I → ℚ) :
    0 < oneFormHeightFactor x :=
  Real.rpow_pos_of_pos (Height.mulHeight_pos x) _

def oneFormHeightFactor_le_one {I : Type*} [Fintype I] (x : I → ℚ) :
    oneFormHeightFactor x ≤ 1 := by
  apply Real.rpow_le_one_of_one_le_of_nonpos (Height.one_le_mulHeight x)
  norm_num [oneFormExponent]

def oneFormHeightFactor_project {I J : Type*} [Fintype I] [Fintype J]
    (f : J → I) (x : I → ℚ) :
    oneFormHeightFactor x ≤ oneFormHeightFactor (x ∘ f) := by
  apply Real.rpow_le_rpow_of_nonpos (Height.mulHeight_pos (x ∘ f))
    (Height.mulHeight_comp_le f x)
  norm_num [oneFormExponent]

def twoThreeInteger_of_int (P : ℤ) : TwoThreeInteger (P : ℚ) := by
  exact ⟨0, 0, P, by simp⟩

def twoThreeInteger_of_unit {x : ℚ} (hx : TwoThreeUnit x) : TwoThreeInteger x := by
  obtain ⟨a, b, rfl⟩ := hx
  cases a with
  | ofNat a =>
    cases b with
    | ofNat b =>
      refine ⟨0, 0, (2 : ℤ) ^ a * (3 : ℤ) ^ b, ?_⟩
      simp
    | negSucc b =>
      refine ⟨0, b + 1, (2 : ℤ) ^ a, ?_⟩
      simp [zpow_negSucc, div_eq_mul_inv]
  | negSucc a =>
    cases b with
    | ofNat b =>
      refine ⟨a + 1, 0, (3 : ℤ) ^ b, ?_⟩
      simp [zpow_negSucc, div_eq_mul_inv, mul_comm]
    | negSucc b =>
      refine ⟨a + 1, b + 1, 1, ?_⟩
      simp [zpow_negSucc, div_eq_mul_inv, mul_comm]

/-- The actual finite rational hyperplane-cover assertion, specialized only in
dimension, places, and exponent. This is a proposition, not an axiom. -/
def OneFormCover405 : Prop :=
  ∀ (I : Type) [Fintype I] [DecidableEq I],
    2 ≤ Fintype.card I → Fintype.card I ≤ 0x195 →
    ∀ (d : I → ℚ) (k : I), d k ≠ 0 →
    ∃ F : Finset (I → ℚ), (∀ a ∈ F, a ≠ 0) ∧
      ∀ x : I → ℚ, (∀ i, TwoThreeInteger (x i)) → x ≠ 0 →
        (twoThreeOneFormProduct d x k : ℝ) < oneFormHeightFactor x →
        ∃ a ∈ F, (∑ i, a i * x i) = 0

private def positive_common_bound {A : Type*} [Fintype A]
    (c : A → ℝ) (hc : ∀ a, 0 < c a) :
    ∃ C : ℝ, 0 < C ∧ C ≤ 1 ∧ ∀ a, C ≤ c a := by
  classical
  have hh : ∀ s : Finset A, (∀ a ∈ s, 0 < c a) →
      ∃ C : ℝ, 0 < C ∧ C ≤ 1 ∧ ∀ a ∈ s, C ≤ c a := by
    intro s
    induction s using Finset.induction_on with
    | empty =>
      intro hs
      exact ⟨1, by norm_num, le_rfl, by simp⟩
    | @insert a s ha ih =>
      intro hs
      obtain ⟨C, hC, hC1, hCs⟩ := ih (fun b hb => hs b (by simp [hb]))
      refine ⟨min (c a) C, lt_min (hs a (by simp)) hC,
        (min_le_right _ _).trans hC1, ?_⟩
      intro b hb
      rcases Finset.mem_insert.mp hb with rfl | hb
      · exact min_le_left _ _
      · exact (min_le_right _ _).trans (hCs b hb)
  obtain ⟨C, hC, hC1, hCs⟩ := hh Finset.univ (fun a _ => hc a)
  exact ⟨C, hC, hC1, fun a => hCs a (Finset.mem_univ a)⟩

def UnitOneFormLowerBound {I : Type} [Fintype I] (d : I → ℚ) : Prop :=
  ∃ C : ℝ, 0 < C ∧ ∀ (u : I → ℚ), (∀ i, TwoThreeUnit (u i)) →
    ∀ t : ℝ, 0 < t → (∀ i, t ≤ |(u i : ℝ)|) →
      (∑ i, d i * u i) ≠ 0 →
      C * t * oneFormHeightFactor u ≤ |((∑ i, d i * u i : ℚ) : ℝ)|

def oneForm_unit_rigidity (hST : OneFormCover405)
    {I : Type} [Fintype I] [DecidableEq I]
    (hI : Fintype.card I ≤ 0x195) (d : I → ℚ) : UnitOneFormLowerBound d := by
  classical
  suffices h : ∀ n : ℕ, ∀ (J : Type) [Fintype J] [DecidableEq J],
      Fintype.card J = n → n ≤ 0x195 → ∀ c : J → ℚ, UnitOneFormLowerBound c by
    exact h (Fintype.card I) I rfl hI d
  intro n
  induction n using Nat.strong_induction_on with
  | h n ih =>
    intro J instF instD hcard hmax c
    by_cases hc : c = 0
    · refine ⟨1, by norm_num, ?_⟩
      intro u hu t ht htu hn
      simp [hc] at hn
    have hex : ∃ k, c k ≠ 0 := by
      by_contra! hh
      exact hc (funext hh)
    obtain ⟨k, hk⟩ := hex
    by_cases hlarge : 2 ≤ Fintype.card J
    · obtain ⟨F, hF, hcover⟩ := hST J hlarge (by omega) c k hk
      have hlocal : ∀ a : F, ∃ C : ℝ, 0 < C ∧
          ∀ (u : J → ℚ), (∀ i, TwoThreeUnit (u i)) →
          ∀ t : ℝ, 0 < t → (∀ i, t ≤ |(u i : ℝ)|) →
          (∑ i, c i * u i) ≠ 0 → (∑ i, a.1 i * u i) = 0 →
          C * t * oneFormHeightFactor u ≤ |((∑ i, c i * u i : ℚ) : ℝ)| := by
        intro a
        obtain ⟨l, hl, _⟩ := finite_hyperplane_exists_elimination a.1 (hF a.1 a.2)
        let K := {i : J // i ≠ l}
        have hlt : Fintype.card K < n := by
          simpa only [K, ← hcard] using finite_hyperplane_delete_card_lt l
        obtain ⟨C, hC, hbound⟩ := ih (Fintype.card K) hlt K rfl (by omega)
          (hyperplaneDeleteCoefficient a.1 c l)
        refine ⟨C, hC, ?_⟩
        intro u hu t ht htu hn hax
        have heq := finite_hyperplane_eliminate a.1 c u l hl hax
        have hn' : (∑ i : K, hyperplaneDeleteCoefficient a.1 c l i * u i) ≠ 0 := by
          rw [← heq]
          exact hn
        have hb := hbound (fun i : K => u i) (fun i => hu i) t ht
          (fun i => htu i) hn'
        rw [← heq] at hb
        calc
          C * t * oneFormHeightFactor u ≤
              C * t * oneFormHeightFactor (fun i : K => u i) :=
            mul_le_mul_of_nonneg_left (oneFormHeightFactor_project Subtype.val u)
              (mul_nonneg hC.le ht.le)
          _ ≤ _ := hb
      choose C hC hbound using hlocal
      obtain ⟨B, hB, hB1, hBC⟩ := positive_common_bound C hC
      refine ⟨B, hB, ?_⟩
      intro u hu t ht htu hn
      by_cases hp : (twoThreeOneFormProduct c u k : ℝ) < oneFormHeightFactor u
      · have hune : u ≠ 0 := by
          intro hzero
          simp [hzero] at hn
        obtain ⟨a, ha, hax⟩ := hcover u (fun i => twoThreeInteger_of_unit (hu i)) hune hp
        let af : F := ⟨a, ha⟩
        calc
          B * t * oneFormHeightFactor u ≤ C af * t * oneFormHeightFactor u :=
            mul_le_mul_of_nonneg_right
              (mul_le_mul_of_nonneg_right (hBC af) ht.le)
              (oneFormHeightFactor_pos u).le
          _ ≤ _ := hbound af u hu t ht htu hn hax
      · have hdiv : oneFormHeightFactor u ≤
            |((∑ i, c i * u i : ℚ) : ℝ)| / |(u k : ℝ)| := by
          have hh := le_of_not_gt hp
          rw [twoThreeOneFormProduct_units c u k hu] at hh
          simpa only [Rat.cast_div, Rat.cast_abs] using hh
        have huk : 0 < |(u k : ℝ)| := by
          exact_mod_cast abs_pos.mpr (twoThreeUnit_pos (hu k)).ne'
        have hm := (le_div_iff₀ huk).mp hdiv
        have hBt : B * t ≤ |(u k : ℝ)| :=
          (mul_le_mul_of_nonneg_right hB1 ht.le).trans (by simpa using htu k)
        exact (mul_le_mul_of_nonneg_right hBt (oneFormHeightFactor_pos u).le).trans
          (by simpa only [mul_comm] using hm)
    · haveI : Subsingleton J := Fintype.card_le_one_iff_subsingleton.mp (by omega)
      have hck : 0 < |(c k : ℝ)| := by exact_mod_cast abs_pos.mpr hk
      refine ⟨|(c k : ℝ)|, hck, ?_⟩
      intro u hu t ht htu hn
      have hs : (∑ i, c i * u i) = c k * u k := by
        apply Fintype.sum_eq_single k
        intro i hi
        exact False.elim (hi (Subsingleton.elim i k))
      rw [hs, Rat.cast_mul, abs_mul]
      calc
        |(c k : ℝ)| * t * oneFormHeightFactor u ≤
            |(c k : ℝ)| * |(u k : ℝ)| * oneFormHeightFactor u :=
          mul_le_mul_of_nonneg_right
            (mul_le_mul_of_nonneg_left (htu k) hck.le) (oneFormHeightFactor_pos u).le
        _ ≤ _ := mul_le_of_le_one_right (by positivity) (oneFormHeightFactor_le_one u)


def optionOneFormCoefficient {I : Type*} (d : I → ℚ) : Option I → ℚ
  | none => -1
  | some i => d i

def optionOneFormCoefficient_sum {I : Type*} [Fintype I]
    (d u : I → ℚ) (P : ℤ) :
    (∑ j, optionOneFormCoefficient d j * hyperplaneOptionVector (P : ℚ) u j) =
      (∑ i, d i * u i) - (P : ℚ) := by
  simp only [Fintype.sum_option, optionOneFormCoefficient, hyperplaneOptionVector]
  ring

def oneFormHeightFactor_option_project {I J : Type*} [Fintype I] [Fintype J]
    (f : J → I) (P : ℚ) (u : I → ℚ) :
    oneFormHeightFactor (hyperplaneOptionVector P u) ≤
      oneFormHeightFactor (hyperplaneOptionVector P (u ∘ f)) := by
  have he : hyperplaneOptionVector P u ∘ Option.map f =
      hyperplaneOptionVector P (u ∘ f) := by
    funext j
    cases j <;> rfl
  simpa only [he] using
    oneFormHeightFactor_project (Option.map f) (hyperplaneOptionVector P u)

def oneForm_integer_product_le {I : Type*} [Fintype I] [DecidableEq I]
    (d u : I → ℚ) (P : ℤ) (hu : ∀ i, TwoThreeUnit (u i)) :
    (twoThreeOneFormProduct (optionOneFormCoefficient d)
      (hyperplaneOptionVector (P : ℚ) u) none : ℝ) ≤
        |(((∑ i, d i * u i) - (P : ℚ) : ℚ) : ℝ)| := by
  have hh := twoThreeOneFormProduct_integer_le (optionOneFormCoefficient d) P u hu
  have he : (fun i : Option I => i.elim (P : ℚ) u) =
      hyperplaneOptionVector (P : ℚ) u := by
    funext i
    cases i <;> rfl
  rw [he] at hh
  have he' (i : Option I) : i.elim (P : ℚ) u = hyperplaneOptionVector (P : ℚ) u i :=
    congrFun he i
  simp_rw [he'] at hh
  rw [optionOneFormCoefficient_sum] at hh
  exact_mod_cast hh

def IntegerOneFormLowerBound {I : Type} [Fintype I] (d : I → ℚ) : Prop :=
  ∃ C : ℝ, 0 < C ∧ ∀ (P : ℤ) (u : I → ℚ), (∀ i, TwoThreeUnit (u i)) →
    ∀ t : ℝ, 0 < t → t ≤ 1 → (∀ i, t ≤ |(u i : ℝ)|) →
      ((∑ i, d i * u i) - (P : ℚ)) ≠ 0 →
      C * t * oneFormHeightFactor (hyperplaneOptionVector (P : ℚ) u) ≤
        |(((∑ i, d i * u i) - (P : ℚ) : ℚ) : ℝ)|

def oneForm_integer_rigidity (hST : OneFormCover405)
    {I : Type} [Fintype I] [DecidableEq I]
    (hI : Fintype.card I + 1 ≤ 0x195) (d : I → ℚ) : IntegerOneFormLowerBound d := by
  classical
  suffices h : ∀ n : ℕ, ∀ (J : Type) [Fintype J] [DecidableEq J],
      Fintype.card J = n → n + 1 ≤ 0x195 → ∀ c : J → ℚ, IntegerOneFormLowerBound c by
    exact h (Fintype.card I) I rfl hI d
  intro n
  induction n using Nat.strong_induction_on with
  | h n ih =>
    intro J instF instD hcard hmax c
    by_cases hz : Fintype.card J = 0
    · haveI : IsEmpty J := Fintype.card_eq_zero_iff.mp hz
      refine ⟨1, by norm_num, ?_⟩
      intro P u hu t ht ht1 htu hn
      have hP : P ≠ 0 := by
        intro hzero
        simp [hzero] at hn
      have hPabs : 1 ≤ |(P : ℝ)| := by
        have hp : (0 : ℤ) < |P| := abs_pos.mpr hP
        have hp1 : (1 : ℤ) ≤ |P| := by omega
        exact_mod_cast hp1
      have he : |(((∑ i, c i * u i) - (P : ℚ) : ℚ) : ℝ)| = |(P : ℝ)| := by simp
      rw [he, one_mul]
      exact ((mul_le_mul_of_nonneg_right ht1
        (oneFormHeightFactor_pos (hyperplaneOptionVector (P : ℚ) u)).le).trans
          (by simpa using oneFormHeightFactor_le_one (hyperplaneOptionVector (P : ℚ) u))).trans hPabs
    · obtain ⟨F, hF, hcover⟩ := hST (Option J) (by simp; omega)
        (by simpa only [Fintype.card_option, hcard] using hmax)
        (optionOneFormCoefficient c) none (by simp [optionOneFormCoefficient])
      have hlocal : ∀ a : F, ∃ C : ℝ, 0 < C ∧
          ∀ (P : ℤ) (u : J → ℚ), (∀ i, TwoThreeUnit (u i)) →
          ∀ t : ℝ, 0 < t → t ≤ 1 → (∀ i, t ≤ |(u i : ℝ)|) →
          ((∑ i, c i * u i) - (P : ℚ)) ≠ 0 →
          (∑ j, a.1 j * hyperplaneOptionVector (P : ℚ) u j) = 0 →
          C * t * oneFormHeightFactor (hyperplaneOptionVector (P : ℚ) u) ≤
            |(((∑ i, c i * u i) - (P : ℚ) : ℚ) : ℝ)| := by
        intro a
        by_cases ha0 : a.1 none = 0
        · have hex : ∃ l : J, a.1 (some l) ≠ 0 := by
            by_contra! hh
            apply hF a.1 a.2
            funext j
            cases j with
            | none => exact ha0
            | some i => exact hh i
          obtain ⟨l, hl⟩ := hex
          let K := {i : J // i ≠ l}
          have hlt : Fintype.card K < n := by
            simpa only [K, ← hcard] using finite_hyperplane_delete_card_lt l
          obtain ⟨C, hC, hbound⟩ := ih (Fintype.card K) hlt K rfl (by omega)
            (hyperplaneDeleteCoefficient (fun i => a.1 (some i)) c l)
          refine ⟨C, hC, ?_⟩
          intro P u hu t ht ht1 htu hn hax
          have heq := finite_option_hyperplane_eliminate_unit a.1 c u P ha0 l hl hax
          have hn' : ((∑ i : K,
              hyperplaneDeleteCoefficient (fun j => a.1 (some j)) c l i * u i) - (P : ℚ)) ≠ 0 := by
            rw [← heq]
            exact hn
          have hb := hbound P (fun i : K => u i) (fun i => hu i) t ht ht1
            (fun i => htu i) hn'
          rw [← heq] at hb
          calc
            C * t * oneFormHeightFactor (hyperplaneOptionVector (P : ℚ) u) ≤
                C * t * oneFormHeightFactor
                  (hyperplaneOptionVector (P : ℚ) (fun i : K => u i)) :=
              mul_le_mul_of_nonneg_left (oneFormHeightFactor_option_project Subtype.val (P : ℚ) u)
                (mul_nonneg hC.le ht.le)
            _ ≤ _ := hb
        · obtain ⟨C, hC, hbound⟩ := oneForm_unit_rigidity hST (by omega : Fintype.card J ≤ 0x195)
            (fun i => c i + a.1 (some i) / a.1 none)
          refine ⟨C, hC, ?_⟩
          intro P u hu t ht ht1 htu hn hax
          have heq := finite_option_hyperplane_eliminate_integer a.1 c u P ha0 hax
          have hn' : (∑ i, (c i + a.1 (some i) / a.1 none) * u i) ≠ 0 := by
            rw [← heq]
            exact hn
          have hb := hbound u hu t ht htu hn'
          rw [← heq] at hb
          calc
            C * t * oneFormHeightFactor (hyperplaneOptionVector (P : ℚ) u) ≤
                C * t * oneFormHeightFactor u :=
              mul_le_mul_of_nonneg_left
                (oneFormHeightFactor_project some (hyperplaneOptionVector (P : ℚ) u))
                (mul_nonneg hC.le ht.le)
            _ ≤ _ := hb
      choose C hC hbound using hlocal
      obtain ⟨B, hB, hB1, hBC⟩ := positive_common_bound C hC
      refine ⟨B, hB, ?_⟩
      intro P u hu t ht ht1 htu hn
      let x := hyperplaneOptionVector (P : ℚ) u
      by_cases hp : (twoThreeOneFormProduct (optionOneFormCoefficient c) x none : ℝ) <
          oneFormHeightFactor x
      · have hxs : ∀ j, TwoThreeInteger (x j) := by
          intro j
          cases j with
          | none => exact twoThreeInteger_of_int P
          | some i => exact twoThreeInteger_of_unit (hu i)
        have hxne : x ≠ 0 := by
          intro hzero
          have he := optionOneFormCoefficient_sum c u P
          change (∑ j, optionOneFormCoefficient c j * x j) = _ at he
          simp only [hzero, Pi.zero_apply, mul_zero, Finset.sum_const_zero] at he
          exact hn he.symm
        obtain ⟨a, ha, hax⟩ := hcover x hxs hxne hp
        let af : F := ⟨a, ha⟩
        calc
          B * t * oneFormHeightFactor x ≤ C af * t * oneFormHeightFactor x :=
            mul_le_mul_of_nonneg_right
              (mul_le_mul_of_nonneg_right (hBC af) ht.le) (oneFormHeightFactor_pos x).le
          _ ≤ _ := hbound af P u hu t ht ht1 htu hn hax
      · have hfac : oneFormHeightFactor x ≤
            |(((∑ i, c i * u i) - (P : ℚ) : ℚ) : ℝ)| :=
          (le_of_not_gt hp).trans (oneForm_integer_product_le c u P hu)
        have hBt : B * t ≤ 1 :=
          (mul_le_mul_of_nonneg_right hB1 ht.le).trans (by simpa using ht1)
        exact (mul_le_mul_of_nonneg_right hBt (oneFormHeightFactor_pos x).le).trans
          (by simpa using hfac)


end
end Bounty

end SubmissionComponent_OneFormRigidity

/- Component ReturnTruncationNonzero; SHA256 bf4cf6c23eff274b784d81d78fbca28bb84906c97bc8418bc32151c6452ef6ff -/
section SubmissionComponent_ReturnTruncationNonzero
/- Elementary valuation lemmas for nonvanishing of separated return truncations. -/

namespace Bounty

open Filter
open scoped Topology

def returnCoefficient4_ne_zero (i : Fin 4) : returnEventCoefficient4 i ≠ 0 := by
  fin_cases i <;> norm_num [returnEventCoefficient4]

def returnCoefficient4_twoAdic (i : Fin 4) :
    padicValRat 2 (returnEventCoefficient4 i : ℚ) = (![0, 3, 0, 2] : Fin 4 → ℤ) i := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have h2 : padicValRat 2 (2 : ℚ) = 1 := padicValRat.self (by norm_num)
  have h105 : padicValRat 2 (0x69 : ℚ) = 0 := padicValRat_nat_zero (by norm_num)
  have h3 : padicValRat 2 (3 : ℚ) = 0 := padicValRat_nat_zero (by norm_num)
  have h21 : padicValRat 2 (21 : ℚ) = 0 := padicValRat_nat_zero (by norm_num)
  have h15 : padicValRat 2 (15 : ℚ) = 0 := padicValRat_nat_zero (by norm_num)
  have h168 : padicValRat 2 (0xa8 : ℚ) = 3 := by
    rw [show (0xa8 : ℚ) = (2 : ℚ) ^ 3 * 21 by norm_num,
      padicValRat.mul (by norm_num) (by norm_num), padicValRat.pow, h2, h21]
    norm_num
  have h60 : padicValRat 2 (60 : ℚ) = 2 := by
    rw [show (60 : ℚ) = (2 : ℚ) ^ 2 * 15 by norm_num,
      padicValRat.mul (by norm_num) (by norm_num), padicValRat.pow, h2, h15]
    norm_num
  fin_cases i <;> norm_num [returnEventCoefficient4, h105, h168, h3, h60]

def returnCoefficient4_twoAdic_bounds (i : Fin 4) :
    0 ≤ padicValRat 2 (returnEventCoefficient4 i : ℚ) ∧
      padicValRat 2 (returnEventCoefficient4 i : ℚ) ≤ 3 := by
  rw [returnCoefficient4_twoAdic]
  fin_cases i <;> norm_num

def twoAdic_int_nonneg (z : ℤ) : 0 ≤ padicValRat 2 (z : ℚ) := by
  rw [padicValRat.of_int]
  positivity

def twoAdic_four : padicValRat 2 (4 : ℚ) = 2 := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have h2 : padicValRat 2 (2 : ℚ) = 1 := padicValRat.self (by norm_num)
  rw [show (4 : ℚ) = (2 : ℚ) ^ 2 by norm_num, padicValRat.pow, h2]
  norm_num

def twoAdic_three : padicValRat 2 (3 : ℚ) = 0 :=
  padicValRat_nat_zero (by norm_num : ¬ 2 ∣ 3)

def twoAdic_dyadic_int (z : ℤ) (hz : z ≠ 0) (n : ℕ) :
    padicValRat 2 ((z : ℚ) / (4 : ℚ) ^ n) = padicValRat 2 (z : ℚ) - 2 * n := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have hzQ : (z : ℚ) ≠ 0 := by exact_mod_cast hz
  rw [padicValRat.div hzQ (by positivity), padicValRat.pow, twoAdic_four]
  ring

def twoAdic_add_ne_zero_of_lt {x y : ℚ}
    (hval : padicValRat 2 x < padicValRat 2 y) : x + y ≠ 0 := by
  intro hzero
  have he : x = -y := eq_neg_of_add_eq_zero_left hzero
  rw [he, padicValRat.neg] at hval
  exact (lt_irrefl _ hval)

def twoAdic_sum_lower_bound {ι : Type*} (s : Finset ι) (f : ι → ℚ) (k : ℤ)
    (hf : ∀ i ∈ s, f i ≠ 0 → k ≤ padicValRat 2 (f i))
    (hs : (∑ i ∈ s, f i) ≠ 0) : k ≤ padicValRat 2 (∑ i ∈ s, f i) := by
  classical
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  revert hf hs
  induction s using Finset.induction_on with
  | empty => simp
  | @insert a s ha ih =>
    intro hf hs
    rw [Finset.sum_insert ha] at hs ⊢
    have hrest : ∀ i ∈ s, f i ≠ 0 → k ≤ padicValRat 2 (f i) :=
      fun i hi => hf i (Finset.mem_insert_of_mem hi)
    by_cases hfa : f a = 0
    · simp only [hfa, zero_add] at hs ⊢
      exact ih hrest hs
    by_cases hfs : (∑ i ∈ s, f i) = 0
    · simp only [hfs, add_zero]
      exact hf a (Finset.mem_insert_self a s) hfa
    exact (le_min (hf a (Finset.mem_insert_self a s) hfa) (ih hrest hfs)).trans
      (padicValRat.min_le_padicValRat_add hs)

def twoAdic_sum_unique_min {ι : Type*} (s : Finset ι) (f : ι → ℚ)
    {a : ι} (ha : a ∈ s) (hfa : f a ≠ 0)
    (hmin : ∀ i ∈ s, i ≠ a → f i ≠ 0 → padicValRat 2 (f a) < padicValRat 2 (f i)) :
    (∑ i ∈ s, f i) ≠ 0 ∧ padicValRat 2 (∑ i ∈ s, f i) = padicValRat 2 (f a) := by
  classical
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  rw [← Finset.add_sum_erase s f ha]
  by_cases hz : (∑ i ∈ s.erase a, f i) = 0
  · simp only [hz, add_zero]
    exact ⟨hfa, trivial⟩
  have hbound : padicValRat 2 (f a) + 1 ≤ padicValRat 2 (∑ i ∈ s.erase a, f i) := by
    apply twoAdic_sum_lower_bound (s.erase a) f _ _ hz
    intro i hi hfi
    have hh := hmin i (Finset.mem_of_mem_erase hi) (Finset.ne_of_mem_erase hi) hfi
    omega
  have hlt : padicValRat 2 (f a) < padicValRat 2 (∑ i ∈ s.erase a, f i) := by omega
  have hne := twoAdic_add_ne_zero_of_lt hlt
  exact ⟨hne, padicValRat.add_eq_of_lt hne hfa hz hlt⟩

def dyadic_integer_sum_unique_largest {ι : Type*} (s : Finset ι)
    (c : ι → ℤ) (n : ι → ℕ) {a : ι} (ha : a ∈ s) (hca : c a ≠ 0)
    (hgap : ∀ i ∈ s, i ≠ a →
      padicValRat 2 (c a : ℚ) < 2 * ((n a : ℤ) - n i)) :
    (∑ i ∈ s, (c i : ℚ) / (4 : ℚ) ^ n i) ≠ 0 ∧
      padicValRat 2 (∑ i ∈ s, (c i : ℚ) / (4 : ℚ) ^ n i) =
        padicValRat 2 (c a : ℚ) - 2 * n a := by
  have hcaQ : (c a : ℚ) ≠ 0 := by exact_mod_cast hca
  have haTerm : (c a : ℚ) / (4 : ℚ) ^ n a ≠ 0 := div_ne_zero hcaQ (by positivity)
  have hh := twoAdic_sum_unique_min s (fun i => (c i : ℚ) / (4 : ℚ) ^ n i)
    ha haTerm (by
      intro i hi hia hfi
      have hci : c i ≠ 0 := by
        intro hz
        simp [hz] at hfi
      rw [twoAdic_dyadic_int _ hca, twoAdic_dyadic_int _ hci]
      have hb := twoAdic_int_nonneg (c i)
      have hg := hgap i hi hia
      omega)
  simpa only [twoAdic_dyadic_int _ hca] using hh

def twoAdic_nat_log_bound (N : ℕ) (hN : 0 < N) :
    (padicValRat 2 (N : ℚ) : ℝ) * Real.log 2 ≤ Real.log (N : ℝ) := by
  have hdvd : (2 : ℕ) ^ padicValNat 2 N ∣ N := pow_padicValNat_dvd
  have hle : (2 : ℕ) ^ padicValNat 2 N ≤ N := Nat.le_of_dvd hN hdvd
  have hleR : (2 : ℝ) ^ padicValNat 2 N ≤ (N : ℝ) := by exact_mod_cast hle
  have hh := Real.log_le_log (by positivity : (0 : ℝ) < (2 : ℝ) ^ padicValNat 2 N) hleR
  rw [Real.log_pow] at hh
  simpa only [padicValRat.of_nat, Int.cast_natCast] using hh

def twoAdic_three_pow_sub_one_log_bound (p : ℕ) (hp : 0 < p) :
    (padicValRat 2 ((3 : ℚ) ^ p - 1) : ℝ) * Real.log 2 ≤ (p : ℝ) * Real.log 3 := by
  have hpw : 1 < (3 : ℕ) ^ p := one_lt_pow₀ (by norm_num) (by omega)
  have hN : 0 < (3 : ℕ) ^ p - 1 := Nat.sub_pos_of_lt hpw
  have hcast : (((3 : ℕ) ^ p - 1 : ℕ) : ℚ) = (3 : ℚ) ^ p - 1 := by
    rw [Nat.cast_sub hpw.le]
    norm_num
  have hh := twoAdic_nat_log_bound ((3 : ℕ) ^ p - 1) hN
  rw [hcast] at hh
  have hNreal : (0 : ℝ) < (((3 : ℕ) ^ p - 1 : ℕ) : ℝ) := by exact_mod_cast hN
  have hleR : (((3 : ℕ) ^ p - 1 : ℕ) : ℝ) ≤ ((3 : ℕ) ^ p : ℝ) := by
    exact_mod_cast (Nat.sub_le ((3 : ℕ) ^ p) 1)
  have hlog := Real.log_le_log hNreal hleR
  norm_num only [Nat.cast_pow, Nat.cast_ofNat, Real.log_pow] at hlog
  exact hh.trans hlog

def returnCoefficient4_shifted_twoAdic (p : ℕ) (i : Fin 4) :
    padicValRat 2 ((3 : ℚ) ^ p * (returnEventCoefficient4 i : ℚ)) =
      padicValRat 2 (returnEventCoefficient4 i : ℚ) := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have hc : (returnEventCoefficient4 i : ℚ) ≠ 0 := by
    exact_mod_cast returnCoefficient4_ne_zero i
  rw [padicValRat.mul (by positivity) hc, padicValRat.pow, twoAdic_three]
  ring

def returnMiddleCoefficient_twoAdic_bound (r : ℕ) (i : Fin 4) :
    (padicValRat 2 (((3 : ℚ) ^ (rotationReturns r).p.toNat - 1) *
      (returnEventCoefficient4 i : ℚ)) : ℝ) * Real.log 2 ≤
        returnScale r + 3 * Real.log 2 := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have hp : 0 < (rotationReturns r).p.toNat := by
    have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
    have hq := (rotationReturns r).q_pos
    omega
  have hfactor : (3 : ℚ) ^ (rotationReturns r).p.toNat - 1 ≠ 0 :=
    ne_of_gt (sub_pos.mpr (one_lt_pow₀ (by norm_num) (by omega)))
  have hc : (returnEventCoefficient4 i : ℚ) ≠ 0 := by
    exact_mod_cast returnCoefficient4_ne_zero i
  have hv := twoAdic_three_pow_sub_one_log_bound (rotationReturns r).p.toNat hp
  have hC : (padicValRat 2 (returnEventCoefficient4 i : ℚ) : ℝ) ≤ 3 := by
    exact_mod_cast (returnCoefficient4_twoAdic_bounds i).2
  have hlog : 0 < Real.log 2 := Real.log_pos (by norm_num)
  have hCb := mul_le_mul_of_nonneg_right hC hlog.le
  have hoffset : ((rotationReturns r).p.toNat : ℝ) * Real.log 3 ≤ returnScale r := by
    simpa [returnEventOffset, Fin.ext_iff] using
      (returnEventOffset_bounds r (0, 0)).2
  rw [padicValRat.mul hfactor hc, Int.cast_add, add_mul]
  linarith

def twoAdic_sum_nonneg {ι : Type*} (s : Finset ι) (f : ι → ℚ)
    (hf : ∀ i ∈ s, 0 ≤ padicValRat 2 (f i)) :
    0 ≤ padicValRat 2 (∑ i ∈ s, f i) := by
  by_cases hz : (∑ i ∈ s, f i) = 0
  · simp [hz]
  exact twoAdic_sum_lower_bound s f 0 (fun i hi _ => hf i hi) hz

def twoAdic_add_nonneg {x y : ℚ}
    (hx : 0 ≤ padicValRat 2 x) (hy : 0 ≤ padicValRat 2 y) :
    0 ≤ padicValRat 2 (x + y) := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  by_cases hz : x + y = 0
  · simp [hz]
  exact (le_min hx hy).trans (padicValRat.min_le_padicValRat_add hz)

def twoAdic_sub_nonneg {x y : ℚ}
    (hx : 0 ≤ padicValRat 2 x) (hy : 0 ≤ padicValRat 2 y) :
    0 ≤ padicValRat 2 (x - y) := by
  rw [sub_eq_add_neg]
  exact twoAdic_add_nonneg hx (by simpa only [padicValRat.neg] using hy)

def returnTernaryWeightedUnit_twoAdic (r : ℕ) (i : ReturnEventFamily) (n : ℕ)
    (hi : 2 ≤ i.1) :
    0 ≤ padicValRat 2 ((returnEventCoefficient i : ℚ) * returnRationalUnit r i n) := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  by_cases hc : returnEventCoefficient i = 0
  · simp [hc]
  have hcQ : (returnEventCoefficient i : ℚ) ≠ 0 := by exact_mod_cast hc
  rw [padicValRat.mul hcQ (returnRationalUnit_ne_zero r i n),
    returnRationalUnit_primeMonomial, rationalPrimeMonomial_val_two]
  apply add_nonneg (twoAdic_int_nonneg _)
  unfold returnUnitFourExponent
  rw [if_neg (not_lt.mpr hi)]
  split <;> positivity

noncomputable def returnDyadicTruncation (r : ℕ) (T : ℝ) : ℚ :=
  ∑ i : Fin 4,
    ((∑ n ∈ returnTruncationIndices r T (0, i),
      (returnEventCoefficient (0, i) : ℚ) * returnRationalUnit r (0, i) n) +
     (∑ n ∈ returnTruncationIndices r T (1, i),
      (returnEventCoefficient (1, i) : ℚ) * returnRationalUnit r (1, i) n))

noncomputable def returnTernaryTruncation (r : ℕ) (T : ℝ) : ℚ :=
  ∑ i : Fin 4,
    ((∑ n ∈ returnTruncationIndices r T (2, i),
      (returnEventCoefficient (2, i) : ℚ) * returnRationalUnit r (2, i) n) +
     (∑ n ∈ returnTruncationIndices r T (3, i),
      (returnEventCoefficient (3, i) : ℚ) * returnRationalUnit r (3, i) n))

def returnRationalTruncation_split_primes (r : ℕ) (T : ℝ) :
    returnRationalTruncation r T = returnDyadicTruncation r T + returnTernaryTruncation r T := by
  simp only [returnRationalTruncation, returnDyadicTruncation, returnTernaryTruncation,
    Fintype.sum_prod_type, Fin.sum_univ_four]
  ring

def returnTernaryTruncation_twoAdic (r : ℕ) (T : ℝ) :
    0 ≤ padicValRat 2 (returnTernaryTruncation r T) := by
  unfold returnTernaryTruncation
  apply twoAdic_sum_nonneg
  intro i _
  apply twoAdic_add_nonneg
  · apply twoAdic_sum_nonneg
    intro n _
    exact returnTernaryWeightedUnit_twoAdic r (2, i) n (by norm_num [Fin.le_def])
  · apply twoAdic_sum_nonneg
    intro n _
    exact returnTernaryWeightedUnit_twoAdic r (3, i) n (by norm_num [Fin.le_def])

def returnTernaryTruncation_difference_twoAdic (r : ℕ) (T₁ T₂ : ℝ) :
    0 ≤ padicValRat 2 (returnTernaryTruncation r T₂ - returnTernaryTruncation r T₁) :=
  twoAdic_sub_nonneg (returnTernaryTruncation_twoAdic r T₂)
    (returnTernaryTruncation_twoAdic r T₁)

def returnRationalTruncation_ne_of_dyadic_valuation (r : ℕ) (T₁ T₂ : ℝ)
    (hdyadic : padicValRat 2 (returnDyadicTruncation r T₂ - returnDyadicTruncation r T₁) < 0) :
    returnRationalTruncation r T₂ ≠ returnRationalTruncation r T₁ := by
  have hternary := returnTernaryTruncation_difference_twoAdic r T₁ T₂
  have hne := twoAdic_add_ne_zero_of_lt (hdyadic.trans_le hternary)
  intro he
  apply hne
  rw [returnRationalTruncation_split_primes, returnRationalTruncation_split_primes] at he
  linear_combination he

abbrev ReturnDyadicIndex := Σ _ : Fin 4, ℕ

noncomputable def returnDyadicIndices (r : ℕ) (T : ℝ) : Finset ReturnDyadicIndex :=
  Finset.univ.sigma (fun i => returnTruncationIndices r T (0, i))

noncomputable def returnDyadicNumerator (r : ℕ) (T : ℝ) (a : ReturnDyadicIndex) : ℤ := by
  classical
  exact returnEventCoefficient4 a.1 * ((3 : ℤ) ^ (rotationReturns r).p.toNat -
    if (a.2 : ℝ) * Real.log 4 < T then 1 else 0)

def mem_returnDyadicIndices (r : ℕ) (T : ℝ) (a : ReturnDyadicIndex) :
    a ∈ returnDyadicIndices r T ↔
      0 < a.2 ∧ jumpVisit4 r a.1 a.2 ≠ 0 ∧
        (a.2 : ℝ) * Real.log 4 - ((rotationReturns r).p.toNat : ℝ) * Real.log 3 < T := by
  classical
  simp [returnDyadicIndices, mem_returnTruncationIndices, returnEventVisit, returnEventTime,
    returnEventStep, returnEventOffset, Fin.lt_def, and_assoc]

def mem_returnUnshiftedDyadicIndices (r : ℕ) (T : ℝ) (i : Fin 4) (n : ℕ) :
    n ∈ returnTruncationIndices r T (1, i) ↔
      0 < n ∧ jumpVisit4 r i n ≠ 0 ∧ (n : ℝ) * Real.log 4 < T := by
  classical
  simp [mem_returnTruncationIndices, returnEventVisit, returnEventTime,
    returnEventStep, returnEventOffset, Fin.lt_def, Fin.ext_iff, and_assoc]

def returnUnshiftedDyadicIndices_subset (r : ℕ) (T : ℝ) (i : Fin 4) :
    returnTruncationIndices r T (1, i) ⊆ returnTruncationIndices r T (0, i) := by
  intro n hn
  have hh := (mem_returnUnshiftedDyadicIndices r T i n).mp hn
  have ho : 0 ≤ ((rotationReturns r).p.toNat : ℝ) * Real.log 3 := by positivity
  have hmem : (⟨i, n⟩ : ReturnDyadicIndex) ∈ returnDyadicIndices r T := by
    apply (mem_returnDyadicIndices r T ⟨i, n⟩).mpr
    exact ⟨hh.1, hh.2.1, by linarith [hh.2.2]⟩
  simpa only [returnDyadicIndices, Finset.mem_sigma, Finset.mem_univ, true_and] using hmem

def returnDyadicTruncation_expanded (r : ℕ) (T : ℝ) :
    returnDyadicTruncation r T = ∑ i : Fin 4,
      ((3 : ℚ) ^ (rotationReturns r).p.toNat *
        (∑ n ∈ returnTruncationIndices r T (0, i), (returnEventCoefficient4 i : ℚ) / (4 : ℚ) ^ n) -
        ∑ n ∈ returnTruncationIndices r T (1, i), (returnEventCoefficient4 i : ℚ) / (4 : ℚ) ^ n) := by
  unfold returnDyadicTruncation
  apply Finset.sum_congr rfl
  intro i _
  rw [Finset.mul_sum, sub_eq_add_neg, ← Finset.sum_neg_distrib]
  congr 1
  · apply Finset.sum_congr rfl
    intro n _
    norm_num [returnEventCoefficient, returnRationalUnit, Fin.ext_iff]
    ring
  · apply Finset.sum_congr rfl
    intro n _
    norm_num [returnEventCoefficient, returnRationalUnit, Fin.ext_iff]
    ring

def returnDyadicTruncation_as_integer_sum (r : ℕ) (T : ℝ) :
    returnDyadicTruncation r T =
      ∑ a ∈ returnDyadicIndices r T, (returnDyadicNumerator r T a : ℚ) / (4 : ℚ) ^ a.2 := by
  classical
  rw [returnDyadicTruncation_expanded]
  simp only [returnDyadicIndices, Finset.sum_sigma]
  apply Finset.sum_congr rfl
  intro i _
  have hsub := returnUnshiftedDyadicIndices_subset r T i
  have hsum :
      (∑ n ∈ returnTruncationIndices r T (1, i), (returnEventCoefficient4 i : ℚ) / (4 : ℚ) ^ n) =
      ∑ n ∈ returnTruncationIndices r T (0, i),
        if (n : ℝ) * Real.log 4 < T then (returnEventCoefficient4 i : ℚ) / (4 : ℚ) ^ n else 0 := by
    apply Finset.sum_subset_zero_on_sdiff hsub
    · intro n hn
      have hns := (Finset.mem_sdiff.mp hn).1
      have hnu := (Finset.mem_sdiff.mp hn).2
      have hmem : (⟨i, n⟩ : ReturnDyadicIndex) ∈ returnDyadicIndices r T := by
        simpa only [returnDyadicIndices, Finset.mem_sigma, Finset.mem_univ, true_and] using hns
      have hh := (mem_returnDyadicIndices r T ⟨i, n⟩).mp hmem
      have ht : ¬ (n : ℝ) * Real.log 4 < T := by
        intro ht
        exact hnu ((mem_returnUnshiftedDyadicIndices r T i n).mpr ⟨hh.1, hh.2.1, ht⟩)
      simp only [if_neg ht]
    · intro n hn
      have ht := ((mem_returnUnshiftedDyadicIndices r T i n).mp hn).2.2
      simp only [if_pos ht]
  rw [hsum, Finset.mul_sum, ← Finset.sum_sub_distrib]
  apply Finset.sum_congr rfl
  intro n _
  by_cases ht : (n : ℝ) * Real.log 4 < T <;>
    simp [returnDyadicNumerator, ht] <;> ring

def twoAdic_sum_scaled_lower_bound {ι : Type*} (s : Finset ι) (f : ι → ℚ)
    (k c : ℝ) (hc : 0 < c)
    (hf : ∀ i ∈ s, f i ≠ 0 → k < (padicValRat 2 (f i) : ℝ) * c)
    (hs : (∑ i ∈ s, f i) ≠ 0) : k < (padicValRat 2 (∑ i ∈ s, f i) : ℝ) * c := by
  classical
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  revert hf hs
  induction s using Finset.induction_on with
  | empty => simp
  | @insert a s ha ih =>
    intro hf hs
    rw [Finset.sum_insert ha] at hs ⊢
    have hrest : ∀ i ∈ s, f i ≠ 0 → k < (padicValRat 2 (f i) : ℝ) * c :=
      fun i hi => hf i (Finset.mem_insert_of_mem hi)
    by_cases hfa : f a = 0
    · simp only [hfa, zero_add] at hs ⊢
      exact ih hrest hs
    by_cases hfs : (∑ i ∈ s, f i) = 0
    · simp only [hfs, add_zero]
      exact hf a (Finset.mem_insert_self a s) hfa
    have hmin := padicValRat.min_le_padicValRat_add (p := 2) hs
    rcases le_total (padicValRat 2 (f a)) (padicValRat 2 (∑ i ∈ s, f i)) with hle | hle
    · rw [min_eq_left hle] at hmin
      have hminR : (padicValRat 2 (f a) : ℝ) ≤
          (padicValRat 2 (f a + ∑ i ∈ s, f i) : ℝ) := by exact_mod_cast hmin
      exact (hf a (Finset.mem_insert_self a s) hfa).trans_le
        (mul_le_mul_of_nonneg_right hminR hc.le)
    · rw [min_eq_right hle] at hmin
      have hminR : (padicValRat 2 (∑ i ∈ s, f i) : ℝ) ≤
          (padicValRat 2 (f a + ∑ i ∈ s, f i) : ℝ) := by exact_mod_cast hmin
      exact (ih hrest hfs).trans_le (mul_le_mul_of_nonneg_right hminR hc.le)

def return_log_four_eq_two_log_two : Real.log 4 = 2 * Real.log 2 := by
  rw [show (4 : ℝ) = (2 : ℝ) ^ 2 by norm_num, Real.log_pow]
  norm_num

def returnDyadicTruncation_small_cutoff (r : ℕ) (T : ℝ)
    (hT : T < 5 * returnScale r) :
    -6 * returnScale r < (padicValRat 2 (returnDyadicTruncation r T) : ℝ) * Real.log 2 := by
  have hlog : 0 < Real.log 2 := Real.log_pos (by norm_num)
  have hL := returnScale_pos r
  by_cases hz : returnDyadicTruncation r T = 0
  · simp only [hz, padicValRat.zero, Int.cast_zero, zero_mul]
    linarith
  rw [returnDyadicTruncation_as_integer_sum] at hz ⊢
  apply twoAdic_sum_scaled_lower_bound _ _ _ _ hlog _ hz
  intro a ha hterm
  have hnum : returnDyadicNumerator r T a ≠ 0 := by
    intro he
    simp [he] at hterm
  rw [twoAdic_dyadic_int _ hnum]
  have hidx := ((mem_returnDyadicIndices r T a).mp ha).2.2
  have hoffset : ((rotationReturns r).p.toNat : ℝ) * Real.log 3 ≤ returnScale r := by
    simpa [returnEventOffset, Fin.ext_iff] using (returnEventOffset_bounds r (0, 0)).2
  have hval : (0 : ℝ) ≤ (padicValRat 2 (returnDyadicNumerator r T a : ℚ) : ℝ) := by
    exact_mod_cast twoAdic_int_nonneg (returnDyadicNumerator r T a)
  have hpos := mul_nonneg hval hlog.le
  rw [return_log_four_eq_two_log_two] at hidx
  push_cast
  nlinarith

def returnDyadicIndices_largest (r : ℕ) (T : ℝ)
    (hT : 2 * returnScale r < T)
    (hsep : ∀ (i j : Fin 4) (m n : ℕ), jumpVisit4 r i m ≠ 0 →
      jumpVisit4 r j n ≠ 0 → (i ≠ j ∨ m ≠ n) → (1 : ℤ) < |(n : ℤ) - m|) :
    ∃ a ∈ returnDyadicIndices r T,
      T - 2 * returnScale r < (a.2 : ℝ) * Real.log 4 ∧
      (∀ b ∈ returnDyadicIndices r T, b.2 ≤ a.2) ∧
      (∀ b ∈ returnDyadicIndices r T, b ≠ a → b.2 + 2 ≤ a.2) := by
  classical
  obtain ⟨n, hn, hlow, hupp, hvisit⟩ := jumpVisit4_log_covered r 0 T hT
  have hnmem : (⟨0, n⟩ : ReturnDyadicIndex) ∈ returnDyadicIndices r T := by
    apply (mem_returnDyadicIndices r T ⟨0, n⟩).mpr
    have ho : 0 ≤ ((rotationReturns r).p.toNat : ℝ) * Real.log 3 := by positivity
    exact ⟨hn, by rw [hvisit]; norm_num, by linarith⟩
  obtain ⟨a, ha, hmax⟩ := Finset.exists_max_image (returnDyadicIndices r T)
    (fun a => a.2) ⟨⟨0, n⟩, hnmem⟩
  have hlog : 0 < Real.log 4 := Real.log_pos (by norm_num)
  refine ⟨a, ha, ?_, hmax, ?_⟩
  · have hna : (n : ℝ) ≤ (a.2 : ℝ) := by exact_mod_cast hmax ⟨0, n⟩ hnmem
    exact hlow.trans_le (mul_le_mul_of_nonneg_right hna hlog.le)
  · intro b hb hba
    have hne : b.1 ≠ a.1 ∨ b.2 ≠ a.2 := by
      by_contra hh
      push Not at hh
      exact hba (Sigma.ext hh.1 (heq_of_eq hh.2))
    have hs := hsep b.1 a.1 b.2 a.2
      ((mem_returnDyadicIndices r T b).mp hb).2.1
      ((mem_returnDyadicIndices r T a).mp ha).2.1 hne
    have hm := hmax b hb
    rw [abs_of_nonneg (by omega : (0 : ℤ) ≤ (a.2 : ℤ) - b.2)] at hs
    omega

def returnDyadicTruncation_large_cutoff (r : ℕ) (T : ℝ)
    (hL : 3 * Real.log 2 < returnScale r) (hT : 10 * returnScale r < T)
    (hsep : ∀ (i j : Fin 4) (m n : ℕ), jumpVisit4 r i m ≠ 0 →
      jumpVisit4 r j n ≠ 0 → (i ≠ j ∨ m ≠ n) → (1 : ℤ) < |(n : ℤ) - m|) :
    returnDyadicTruncation r T ≠ 0 ∧
      (padicValRat 2 (returnDyadicTruncation r T) : ℝ) * Real.log 2 < -6 * returnScale r := by
  classical
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have hlog : 0 < Real.log 2 := Real.log_pos (by norm_num)
  have hscale := returnScale_pos r
  obtain ⟨a, ha, hlow, hmax, hgap⟩ := returnDyadicIndices_largest r T (by linarith) hsep
  have hidx : 8 * returnScale r < (a.2 : ℝ) * (2 * Real.log 2) := by
    rw [return_log_four_eq_two_log_two] at hlow
    linarith
  by_cases ht : (a.2 : ℝ) * Real.log 4 < T
  · have hnum : ∀ b ∈ returnDyadicIndices r T,
        returnDyadicNumerator r T b = returnEventCoefficient4 b.1 *
          ((3 : ℤ) ^ (rotationReturns r).p.toNat - 1) := by
      intro b hb
      have hba : (b.2 : ℝ) ≤ (a.2 : ℝ) := by exact_mod_cast hmax b hb
      have hbt : (b.2 : ℝ) * Real.log 4 < T :=
        (mul_le_mul_of_nonneg_right hba (Real.log_pos (by norm_num)).le).trans_lt ht
      simp [returnDyadicNumerator, hbt]
    have hsum := dyadic_integer_sum_unique_largest (returnDyadicIndices r T)
      (fun b => returnEventCoefficient4 b.1) (fun b => b.2) ha
      (returnCoefficient4_ne_zero a.1) (by
        intro b hb hba
        have hv := (returnCoefficient4_twoAdic_bounds a.1).2
        have hg := hgap b hb hba
        omega)
    have hp : 0 < (rotationReturns r).p.toNat := by
      have hb := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
      have hq := (rotationReturns r).q_pos
      omega
    have hfactor : (3 : ℚ) ^ (rotationReturns r).p.toNat - 1 ≠ 0 :=
      ne_of_gt (sub_pos.mpr (one_lt_pow₀ (by norm_num) (by omega)))
    have hc : (returnEventCoefficient4 a.1 : ℚ) ≠ 0 := by
      exact_mod_cast returnCoefficient4_ne_zero a.1
    have hD : returnDyadicTruncation r T = ((3 : ℚ) ^ (rotationReturns r).p.toNat - 1) *
        (∑ b ∈ returnDyadicIndices r T, (returnEventCoefficient4 b.1 : ℚ) / (4 : ℚ) ^ b.2) := by
      rw [returnDyadicTruncation_as_integer_sum, Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro b hb
      rw [hnum b hb]
      push_cast
      ring
    have hv : padicValRat 2 (returnDyadicTruncation r T) =
        padicValRat 2 (((3 : ℚ) ^ (rotationReturns r).p.toNat - 1) *
          (returnEventCoefficient4 a.1 : ℚ)) - 2 * a.2 := by
      rw [hD, padicValRat.mul hfactor hsum.1, hsum.2, padicValRat.mul hfactor hc]
      ring
    refine ⟨by rw [hD]; exact mul_ne_zero hfactor hsum.1, ?_⟩
    have hb := returnMiddleCoefficient_twoAdic_bound r a.1
    rw [hv]
    push_cast
    nlinarith
  · have hnum : returnDyadicNumerator r T a = returnEventCoefficient4 a.1 *
        (3 : ℤ) ^ (rotationReturns r).p.toNat := by
      simp [returnDyadicNumerator, ht]
    have hnum_ne : returnDyadicNumerator r T a ≠ 0 := by
      rw [hnum]
      exact mul_ne_zero (returnCoefficient4_ne_zero a.1) (by positivity)
    have hval : padicValRat 2 (returnDyadicNumerator r T a : ℚ) =
        padicValRat 2 (returnEventCoefficient4 a.1 : ℚ) := by
      rw [hnum]
      push_cast
      rw [mul_comm, returnCoefficient4_shifted_twoAdic]
    have hsum := dyadic_integer_sum_unique_largest (returnDyadicIndices r T)
      (returnDyadicNumerator r T) (fun b => b.2) ha hnum_ne (by
        intro b hb hba
        rw [hval]
        have hv := (returnCoefficient4_twoAdic_bounds a.1).2
        have hg := hgap b hb hba
        omega)
    rw [returnDyadicTruncation_as_integer_sum]
    refine ⟨hsum.1, ?_⟩
    rw [hsum.2, hval]
    have hv : (padicValRat 2 (returnEventCoefficient4 a.1 : ℚ) : ℝ) ≤ 3 := by
      exact_mod_cast (returnCoefficient4_twoAdic_bounds a.1).2
    have hvbound := mul_le_mul_of_nonneg_right hv hlog.le
    push_cast
    nlinarith

def returnDyadicTruncation_difference_negative (r : ℕ) (T₁ T₂ : ℝ)
    (hL : 3 * Real.log 2 < returnScale r)
    (hT₁ : T₁ < 5 * returnScale r) (hT₂ : 10 * returnScale r < T₂)
    (hsep : ∀ (i j : Fin 4) (m n : ℕ), jumpVisit4 r i m ≠ 0 →
      jumpVisit4 r j n ≠ 0 → (i ≠ j ∨ m ≠ n) → (1 : ℤ) < |(n : ℤ) - m|) :
    padicValRat 2 (returnDyadicTruncation r T₂ - returnDyadicTruncation r T₁) < 0 := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  have hlog : 0 < Real.log 2 := Real.log_pos (by norm_num)
  have hfirst := returnDyadicTruncation_small_cutoff r T₁ hT₁
  have hsecond := returnDyadicTruncation_large_cutoff r T₂ hL hT₂ hsep
  have hltR : (padicValRat 2 (returnDyadicTruncation r T₂) : ℝ) <
      (padicValRat 2 (returnDyadicTruncation r T₁) : ℝ) := by nlinarith [hsecond.2]
  have hlt : padicValRat 2 (returnDyadicTruncation r T₂) <
      padicValRat 2 (returnDyadicTruncation r T₁) := by exact_mod_cast hltR
  have hneg : padicValRat 2 (returnDyadicTruncation r T₂) < 0 := by
    have hscale := returnScale_pos r
    have hnegR : (padicValRat 2 (returnDyadicTruncation r T₂) : ℝ) < 0 := by
      nlinarith [hsecond.2]
    exact_mod_cast hnegR
  by_cases hzero : returnDyadicTruncation r T₁ = 0
  · simpa only [hzero, sub_zero] using hneg
  have hneg_ne : -returnDyadicTruncation r T₁ ≠ 0 := neg_ne_zero.mpr hzero
  have hltneg : padicValRat 2 (returnDyadicTruncation r T₂) <
      padicValRat 2 (-returnDyadicTruncation r T₁) := by simpa only [padicValRat.neg] using hlt
  have hsum_ne := twoAdic_add_ne_zero_of_lt hltneg
  rw [sub_eq_add_neg, padicValRat.add_eq_of_lt hsum_ne hsecond.1 hneg_ne hltneg]
  exact hneg

/-- The actual rational truncations at the two cutoff scales are eventually distinct.
This conclusion uses only visit coverage, visit separation, and integer valuations. -/
def returnRationalTruncation_separated_cutoffs :
    ∀ᶠ r in atTop, ∀ T₁ T₂ : ℝ,
      T₁ < 5 * returnScale r → 10 * returnScale r < T₂ →
      returnRationalTruncation r T₂ ≠ returnRationalTruncation r T₁ := by
  have hscale := returnScale_tendsto.eventually (eventually_gt_atTop (3 * Real.log 2))
  filter_upwards [hscale, jumpVisit4_all_indices_separate 1] with r hr hsep T₁ T₂ hT₁ hT₂
  exact returnRationalTruncation_ne_of_dyadic_valuation r T₁ T₂
    (returnDyadicTruncation_difference_negative r T₁ T₂ hr hT₁ hT₂ hsep)

end Bounty

end SubmissionComponent_ReturnTruncationNonzero

/- Component ReturnErrorDifference; SHA256 a922b78606dc12375ed413c10bb570c9cfea0021b1a5a18d882ed1534cf4ca7e -/
section SubmissionComponent_ReturnErrorDifference
/- The two errors have a common rational head and integral prefix. -/

namespace Bounty

def returnApproximationError_difference (z : ℚ) (r : ℕ) (T U : ℝ) :
    returnApproximationError z r U - returnApproximationError z r T =
      (returnRationalTruncation r T : ℝ) - (returnRationalTruncation r U : ℝ) := by
  unfold returnApproximationError
  rw [returnApproximation_linear_form, returnApproximation_linear_form]
  push_cast
  ring

def returnApproximationError_ne_zero_of_truncations_ne
    (z : ℚ) (r : ℕ) (T U : ℝ)
    (h : returnRationalTruncation r T ≠ returnRationalTruncation r U) :
    returnApproximationError z r T ≠ 0 ∨ returnApproximationError z r U ≠ 0 := by
  by_contra hh
  push Not at hh
  have he := returnApproximationError_difference z r T U
  rw [hh.1, hh.2, sub_self] at he
  have hr : (returnRationalTruncation r T : ℝ) = (returnRationalTruncation r U : ℝ) := by linarith
  exact h (Rat.cast_injective hr)


end Bounty

end SubmissionComponent_ReturnErrorDifference

/- Component ReturnUnitSeparation; SHA256 f648432f13523998682a8090dec82db6677fc4c02e63d1538c1d7f43e3cfdbf3 -/
section SubmissionComponent_ReturnUnitSeparation
/- Uniform arithmetic separation of the moving rational event units. -/

open Filter
open scoped Topology

namespace Bounty

def rationalPrimeMonomial_val_three (a b c : ℤ) :
    padicValRat 3 (rationalPrimeMonomial a b c) = b := by
  let : Fact (Nat.Prime 3) := ⟨by norm_num⟩
  have h2 : padicValRat 3 2 = 0 := padicValRat_nat_zero (by norm_num : ¬ 3 ∣ 2)
  have h3 : padicValRat 3 3 = 1 := padicValRat.self (by norm_num)
  have h5 : padicValRat 3 5 = 0 := padicValRat_nat_zero (by norm_num : ¬ 3 ∣ 5)
  unfold rationalPrimeMonomial
  rw [padicValRat.mul (by positivity) (by positivity),
    padicValRat.mul (by positivity) (by positivity)]
  simp only [padicValRat.zpow, h2, h3, h5]
  ring

def returnRationalUnit_val_two (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    padicValRat 2 (returnRationalUnit r i n) = 2 * returnUnitFourExponent r i n := by
  rw [returnRationalUnit_primeMonomial, rationalPrimeMonomial_val_two]

def returnRationalUnit_val_three (r : ℕ) (i : ReturnEventFamily) (n : ℕ) :
    padicValRat 3 (returnRationalUnit r i n) = returnUnitThreeExponent r i n := by
  rw [returnRationalUnit_primeMonomial, rationalPrimeMonomial_val_three]

def jumpVisit3_all_indices_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : Fin 4, ∀ m n : ℕ,
      jumpVisit3 r i m ≠ 0 → jumpVisit3 r j n ≠ 0 →
      (i ≠ j ∨ m ≠ n) → (M : ℤ) < |(n : ℤ) - m| := by
  have hQ := rotationReturns_denominators_tendsto.2.eventually (eventually_gt_atTop M)
  have hh : ∀ᶠ r in atTop, ∀ i ∈ (Finset.univ : Finset (Fin 4)),
      ∀ j ∈ (Finset.univ : Finset (Fin 4)), ∀ m n : ℕ,
      jumpVisit3 r i m ≠ 0 → jumpVisit3 r j n ≠ 0 →
      (i ≠ j ∨ m ≠ n) → (M : ℤ) < |(n : ℤ) - m| := by
    apply (eventually_all_finset _).mpr
    intro i _
    apply (eventually_all_finset _).mpr
    intro j _
    by_cases hij : i = j
    · subst j
      filter_upwards [hQ] with r hr m n hm hn hne
      have hP := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
      have hmn : m ≠ n := hne.resolve_left (not_not.mpr rfl)
      rcases lt_or_gt_of_ne hmn with hlt | hlt
      · have hs := jumpVisit3_separated r i hlt hm hn
        rw [abs_of_nonneg (by omega : (0 : ℤ) ≤ (n : ℤ) - m)]
        omega
      · have hs := jumpVisit3_separated r i hlt hn hm
        rw [abs_of_nonpos (by omega : (n : ℤ) - m ≤ 0)]
        omega
    · filter_upwards [jumpVisit3_distinct_orbits_separate hij M] with r hr m n hm hn _
      exact hr m n hm hn
  filter_upwards [hh] with r hr i j
  exact hr i (Finset.mem_univ i) j (Finset.mem_univ j)

def returnUnitExponent_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : ReturnEventFamily, ∀ m n : ℕ,
      returnEventVisit r i m → returnEventVisit r j n →
      (i ≠ j ∨ m ≠ n) →
      (M : ℤ) < |returnUnitFourExponent r i m - returnUnitFourExponent r j n| ∨
      (M : ℤ) < |returnUnitThreeExponent r i m - returnUnitThreeExponent r j n| := by
  have hq := rotationReturns_denominators_tendsto.1.eventually (eventually_gt_atTop M)
  filter_upwards [hq, returnEventVisit_indices_diverge M,
    jumpVisit4_all_indices_separate M, jumpVisit3_all_indices_separate M]
    with r hqr hidx h4 h3 i j m n hm hn hne
  have hmr : M < m := hidx i m hm
  have hnr : M < n := hidx j n hn
  have hnum := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
  have hpr : (M : ℤ) < (rotationReturns r).p.toNat := by omega
  rcases i with ⟨a, b⟩
  rcases j with ⟨c, d⟩
  by_cases hac : a = c
  · subst c
    have hbd : b ≠ d ∨ m ≠ n := by
      by_contra hh
      push Not at hh
      have he : (a, b) = (a, d) := by rw [hh.1]
      exact hne.elim (fun h => h he) (fun h => h hh.2)
    by_cases ha : a < 2
    · have hm' : jumpVisit4 r b m ≠ 0 := by simpa only [returnEventVisit, if_pos ha] using hm.2
      have hn' : jumpVisit4 r d n ≠ 0 := by simpa only [returnEventVisit, if_pos ha] using hn.2
      have hs := h4 b d m n hm' hn' hbd
      left
      simpa only [returnUnitFourExponent, if_pos ha, neg_sub_neg] using hs
    · have hm' : jumpVisit3 r b m ≠ 0 := by simpa only [returnEventVisit, if_neg ha] using hm.2
      have hn' : jumpVisit3 r d n ≠ 0 := by simpa only [returnEventVisit, if_neg ha] using hn.2
      have hs := h3 b d m n hm' hn' hbd
      have ha0 : a ≠ 0 := by intro he; subst a; norm_num [Fin.lt_def] at ha
      right
      simpa only [returnUnitThreeExponent, if_neg ha0, if_neg ha, neg_sub_neg] using hs
  · fin_cases a <;> fin_cases c <;> norm_num [Fin.ext_iff] at hac <;>
      norm_num [returnUnitFourExponent, returnUnitThreeExponent, Fin.lt_def, Fin.ext_iff] <;>
      (try simp only [lt_abs]) <;> omega

def returnRationalUnit_quotient_valuations_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : ReturnEventFamily, ∀ m n : ℕ,
      returnEventVisit r i m → returnEventVisit r j n →
      (i ≠ j ∨ m ≠ n) →
      (M : ℤ) < |padicValRat 2 (returnRationalUnit r i m / returnRationalUnit r j n)| ∨
      (M : ℤ) < |padicValRat 3 (returnRationalUnit r i m / returnRationalUnit r j n)| := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  let : Fact (Nat.Prime 3) := ⟨by norm_num⟩
  filter_upwards [returnUnitExponent_separate M] with r hr i j m n hm hn hne
  rw [padicValRat.div (returnRationalUnit_ne_zero r i m) (returnRationalUnit_ne_zero r j n),
    padicValRat.div (returnRationalUnit_ne_zero r i m) (returnRationalUnit_ne_zero r j n),
    returnRationalUnit_val_two, returnRationalUnit_val_two,
    returnRationalUnit_val_three, returnRationalUnit_val_three]
  rcases hr i j m n hm hn hne with h | h
  · left
    rw [← mul_sub, abs_mul]
    norm_num
    omega
  · exact Or.inr h

def returnRationalUnit_quotient_escapes_finset (s : Finset ℚ) :
    ∀ᶠ r in atTop, ∀ i j : ReturnEventFamily, ∀ m n : ℕ,
      returnEventVisit r i m → returnEventVisit r j n →
      (i ≠ j ∨ m ≠ n) →
      returnRationalUnit r i m / returnRationalUnit r j n ∉ s := by
  let f : ℚ → ℕ := fun x => max (padicValRat 2 x).natAbs (padicValRat 3 x).natAbs
  let M := s.sup f
  have hb (x : ℚ) (hx : x ∈ s) :
      |padicValRat 2 x| ≤ (M : ℤ) ∧ |padicValRat 3 x| ≤ (M : ℤ) := by
    have hh : f x ≤ M := Finset.le_sup hx
    have h2 : (padicValRat 2 x).natAbs ≤ M := (le_max_left _ _).trans hh
    have h3 : (padicValRat 3 x).natAbs ≤ M := (le_max_right _ _).trans hh
    constructor
    · simpa only [Int.natCast_natAbs] using (Nat.cast_le.mpr h2 :
        ((padicValRat 2 x).natAbs : ℤ) ≤ (M : ℤ))
    · simpa only [Int.natCast_natAbs] using (Nat.cast_le.mpr h3 :
        ((padicValRat 3 x).natAbs : ℤ) ≤ (M : ℤ))
  filter_upwards [returnRationalUnit_quotient_valuations_separate M]
    with r hr i j m n hm hn hne hmem
  have hb' := hb _ hmem
  exact (hr i j m n hm hn hne).elim (fun h => (not_lt_of_ge hb'.1) h)
    (fun h => (not_lt_of_ge hb'.2) h)

def returnRationalUnit_quotient_height_diverge (B : ℝ) :
    ∀ᶠ r in atTop, ∀ i j : ReturnEventFamily, ∀ m n : ℕ,
      returnEventVisit r i m → returnEventVisit r j n →
      (i ≠ j ∨ m ≠ n) →
      B < Height.mulHeight₁ (returnRationalUnit r i m / returnRationalUnit r j n) := by
  classical
  let s := (NumberField.finite_setOfPred_mulHeight₁_le ℚ B).toFinset
  filter_upwards [returnRationalUnit_quotient_escapes_finset s]
    with r hr i j m n hm hn hne
  apply lt_of_not_ge
  intro h
  apply hr i j m n hm hn hne
  simpa only [s, Set.Finite.mem_toFinset, Set.mem_ofPred_eq] using h

end Bounty

end SubmissionComponent_ReturnUnitSeparation

/- Component ReturnHeadSeparation; SHA256 5a2111dedc756cb181cfddb6e39d7bf02bfb393f59aaead62405a2775ca522e1 -/
section SubmissionComponent_ReturnHeadSeparation
/- Head-to-head and head-to-tail arithmetic separation. -/

open Filter
open scoped Topology

namespace Bounty

def rational_height_escape_of_valuations (V : ℕ → ℚ → Prop)
    (hV : ∀ M : ℕ, ∀ᶠ r in atTop, ∀ x : ℚ, V r x →
      (M : ℤ) < |padicValRat 2 x| ∨ (M : ℤ) < |padicValRat 3 x|) (B : ℝ) :
    ∀ᶠ r in atTop, ∀ x : ℚ, V r x → B < Height.mulHeight₁ x := by
  classical
  let s := (NumberField.finite_setOfPred_mulHeight₁_le ℚ B).toFinset
  let f : ℚ → ℕ := fun x => max (padicValRat 2 x).natAbs (padicValRat 3 x).natAbs
  let M := s.sup f
  have hb (x : ℚ) (hx : x ∈ s) :
      |padicValRat 2 x| ≤ (M : ℤ) ∧ |padicValRat 3 x| ≤ (M : ℤ) := by
    have hh : f x ≤ M := Finset.le_sup hx
    have h2 : (padicValRat 2 x).natAbs ≤ M := (le_max_left _ _).trans hh
    have h3 : (padicValRat 3 x).natAbs ≤ M := (le_max_right _ _).trans hh
    constructor
    · simpa only [Int.natCast_natAbs] using (Nat.cast_le.mpr h2 :
        ((padicValRat 2 x).natAbs : ℤ) ≤ (M : ℤ))
    · simpa only [Int.natCast_natAbs] using (Nat.cast_le.mpr h3 :
        ((padicValRat 3 x).natAbs : ℤ) ≤ (M : ℤ))
  filter_upwards [hV M] with r hr x hx
  apply lt_of_not_ge
  intro h
  have hmem : x ∈ s := by
    simpa only [s, Set.Finite.mem_toFinset, Set.mem_ofPred_eq] using h
  have hb' := hb x hmem
  exact (hr x hx).elim (fun hh => (not_lt_of_ge hb'.1) hh)
    (fun hh => (not_lt_of_ge hb'.2) hh)

def returnHeadUnit_val_two (r : ℕ) (j : Fin 4) :
    padicValRat 2 (returnHeadUnit r j) = 2 * returnHeadFourExponent r j := by
  rw [returnHeadUnit_primeMonomial, rationalPrimeMonomial_val_two]

def returnHeadUnit_val_three (r : ℕ) (j : Fin 4) :
    padicValRat 3 (returnHeadUnit r j) = returnHeadThreeExponent r j := by
  rw [returnHeadUnit_primeMonomial, rationalPrimeMonomial_val_three]

def returnHeadUnit_quotient_valuations_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ i j : Fin 4, i ≠ j →
      (M : ℤ) < |padicValRat 2 (returnHeadUnit r i / returnHeadUnit r j)| ∨
      (M : ℤ) < |padicValRat 3 (returnHeadUnit r i / returnHeadUnit r j)| := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  let : Fact (Nat.Prime 3) := ⟨by norm_num⟩
  have hq := rotationReturns_denominators_tendsto.1.eventually (eventually_gt_atTop M)
  filter_upwards [hq] with r hqr i j hij
  have hnum := (rotationReturns r).numerator_bounds rotationSlope_bounds.1 rotationSlope_bounds.2
  have hpr : (M : ℤ) < (rotationReturns r).p.toNat := by omega
  rw [padicValRat.div (returnHeadUnit_ne_zero r i) (returnHeadUnit_ne_zero r j),
    padicValRat.div (returnHeadUnit_ne_zero r i) (returnHeadUnit_ne_zero r j),
    returnHeadUnit_val_two, returnHeadUnit_val_two,
    returnHeadUnit_val_three, returnHeadUnit_val_three]
  fin_cases i <;> fin_cases j <;> norm_num [Fin.ext_iff] at hij <;>
    norm_num [returnHeadFourExponent, returnHeadThreeExponent, Fin.lt_def, Fin.ext_iff] <;>
    (try simp only [lt_abs]) <;> omega

def returnHeadTail_quotient_valuations_separate (M : ℕ) :
    ∀ᶠ r in atTop, ∀ j : Fin 4, ∀ i : ReturnEventFamily, ∀ n : ℕ,
      returnEventVisit r i n →
      (M : ℤ) < |padicValRat 2 (returnHeadUnit r j / returnRationalUnit r i n)| ∨
      (M : ℤ) < |padicValRat 3 (returnHeadUnit r j / returnRationalUnit r i n)| := by
  let : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩
  let : Fact (Nat.Prime 3) := ⟨by norm_num⟩
  filter_upwards [returnEventVisit_indices_diverge M] with r hr j i n hn
  have hnr := hr i n hn
  have h4 : 0 ≤ returnHeadFourExponent r j := by
    unfold returnHeadFourExponent
    split_ifs <;> omega
  have h3 : 0 ≤ returnHeadThreeExponent r j := by
    unfold returnHeadThreeExponent
    split_ifs <;> omega
  rw [padicValRat.div (returnHeadUnit_ne_zero r j) (returnRationalUnit_ne_zero r i n),
    padicValRat.div (returnHeadUnit_ne_zero r j) (returnRationalUnit_ne_zero r i n),
    returnHeadUnit_val_two, returnRationalUnit_val_two,
    returnHeadUnit_val_three, returnRationalUnit_val_three]
  by_cases hi : i.1 < 2
  · left
    rw [returnUnitFourExponent, if_pos hi]
    apply lt_abs.mpr
    left
    omega
  · right
    have hi0 : i.1 ≠ 0 := by intro he; rw [he] at hi; norm_num [Fin.lt_def] at hi
    rw [returnUnitThreeExponent, if_neg hi0, if_neg hi]
    apply lt_abs.mpr
    left
    omega

def returnHeadUnit_quotient_height_diverge (B : ℝ) :
    ∀ᶠ r in atTop, ∀ i j : Fin 4, i ≠ j →
      B < Height.mulHeight₁ (returnHeadUnit r i / returnHeadUnit r j) := by
  let V : ℕ → ℚ → Prop := fun r x =>
    ∃ i j : Fin 4, i ≠ j ∧ x = returnHeadUnit r i / returnHeadUnit r j
  have hV (M : ℕ) : ∀ᶠ r in atTop, ∀ x : ℚ, V r x →
      (M : ℤ) < |padicValRat 2 x| ∨ (M : ℤ) < |padicValRat 3 x| := by
    filter_upwards [returnHeadUnit_quotient_valuations_separate M] with r hr x hx
    obtain ⟨i, j, hij, rfl⟩ := hx
    exact hr i j hij
  filter_upwards [rational_height_escape_of_valuations V hV B] with r hr i j hij
  exact hr _ ⟨i, j, hij, rfl⟩

def returnHeadTail_quotient_height_diverge (B : ℝ) :
    ∀ᶠ r in atTop, ∀ j : Fin 4, ∀ i : ReturnEventFamily, ∀ n : ℕ,
      returnEventVisit r i n →
      B < Height.mulHeight₁ (returnHeadUnit r j / returnRationalUnit r i n) := by
  let V : ℕ → ℚ → Prop := fun r x =>
    ∃ j : Fin 4, ∃ i : ReturnEventFamily, ∃ n : ℕ,
      returnEventVisit r i n ∧ x = returnHeadUnit r j / returnRationalUnit r i n
  have hV (M : ℕ) : ∀ᶠ r in atTop, ∀ x : ℚ, V r x →
      (M : ℤ) < |padicValRat 2 x| ∨ (M : ℤ) < |padicValRat 3 x| := by
    filter_upwards [returnHeadTail_quotient_valuations_separate M] with r hr x hx
    obtain ⟨j, i, n, hn, rfl⟩ := hx
    exact hr j i n hn
  filter_upwards [rational_height_escape_of_valuations V hV B] with r hr j i n hn
  exact hr _ ⟨j, i, n, hn, rfl⟩


end Bounty

end SubmissionComponent_ReturnHeadSeparation

/- Component ReturnApproximationSeparation; SHA256 979896e4db78ee31dbadea053e7e761bafe90ea4559da05108f970ae17fe8ad8 -/
section SubmissionComponent_ReturnApproximationSeparation
/- Separation is uniform across both changing cutoff sets, including their four heads. -/

open Filter
open scoped Topology

namespace Bounty

abbrev ReturnUnitKey := Fin 4 ⊕ (ReturnEventFamily × ℕ)

def returnApproximationKey {r : ℕ} {T : ℝ} : ReturnApproximationLabel r T → ReturnUnitKey :=
  Sum.elim Sum.inl (fun a => Sum.inr (a.1, a.2.1))

def returnApproximationKey_injective (r : ℕ) (T : ℝ) :
    Function.Injective (returnApproximationKey (r := r) (T := T)) := by
  intro i j h
  cases i with
  | inl a =>
    cases j with
    | inl b => exact congrArg Sum.inl (Sum.inl.inj h)
    | inr b => cases h
  | inr a =>
    cases j with
    | inl b => cases h
    | inr b =>
      have he : a.1 = b.1 ∧ a.2.1 = b.2.1 := by
        have hh := Sum.inr.inj h
        exact ⟨congrArg Prod.fst hh, congrArg Prod.snd hh⟩
      obtain ⟨a, m, hm⟩ := a
      obtain ⟨b, n, hn⟩ := b
      dsimp only at he
      rcases he with ⟨rfl, rfl⟩
      rfl

def returnApproximationUnit_quotient_height_diverge (B : ℝ) :
    ∀ᶠ r in atTop, ∀ T U : ℝ,
      ∀ i : ReturnApproximationLabel r T, ∀ j : ReturnApproximationLabel r U,
      returnApproximationKey i ≠ returnApproximationKey j →
      B < Height.mulHeight₁ (returnApproximationUnit r T i / returnApproximationUnit r U j) := by
  filter_upwards [returnHeadUnit_quotient_height_diverge B,
    returnHeadTail_quotient_height_diverge B, returnRationalUnit_quotient_height_diverge B]
    with r hhead hcross htail T U i j hij
  cases i with
  | inl a =>
    cases j with
    | inl b =>
      exact hhead a b (fun he => hij (by cases he; rfl))
    | inr b =>
      exact hcross a b.1 b.2.1
        ((mem_returnTruncationIndices r U b.1 b.2.1).mp b.2.2).1
  | inr a =>
    cases j with
    | inl b =>
      change B < Height.mulHeight₁ (returnRationalUnit r a.1 a.2.1 / returnHeadUnit r b)
      rw [show returnRationalUnit r a.1 a.2.1 / returnHeadUnit r b =
        (returnHeadUnit r b / returnRationalUnit r a.1 a.2.1)⁻¹ by rw [inv_div],
        Height.mulHeight₁_inv]
      exact hcross b a.1 a.2.1
        ((mem_returnTruncationIndices r T a.1 a.2.1).mp a.2.2).1
    | inr b =>
      have hdiff : a.1 ≠ b.1 ∨ a.2.1 ≠ b.2.1 := by
        by_contra hh
        push Not at hh
        apply hij
        exact congrArg Sum.inr (Prod.ext hh.1 hh.2)
      exact htail a.1 b.1 a.2.1 b.2.1
        ((mem_returnTruncationIndices r T a.1 a.2.1).mp a.2.2).1
        ((mem_returnTruncationIndices r U b.1 b.2.1).mp b.2.2).1 hdiff

end Bounty

end SubmissionComponent_ReturnApproximationSeparation

/- Component ReturnApproximationObstruction; SHA256 16bc16627d0259379b6ee8a764306c4d88535330d7c00b06ebe0d43ecc6d5ec7 -/
section SubmissionComponent_ReturnApproximationObstruction
/- Rationality would give nonzero exceptionally small finite return approximations. -/

open Filter
open scoped Topology

namespace Bounty

def returnApproximation_two_errors_not_zero (z : ℚ) :
    ∀ᶠ r in atTop, ∀ T U : ℝ,
      T < 5 * returnScale r → 10 * returnScale r < U →
      returnApproximationError z r T ≠ 0 ∨ returnApproximationError z r U ≠ 0 := by
  filter_upwards [returnRationalTruncation_separated_cutoffs] with r hr T U hT hU
  exact returnApproximationError_ne_zero_of_truncations_ne z r T U (hr T U hT hU).symm

def returnApproximation_nonzero_witness (z : ℚ)
    (hz : (z : ℝ) = 0xb4 * explicitDensity - 32) :
    ∀ᶠ r in atTop, ∃ T : ℝ,
      4 * returnScale r < T ∧ T < 11 * returnScale r ∧
      ReturnApproximationConditions z r T ∧ returnApproximationError z r T ≠ 0 := by
  filter_upwards [returnApproximation_two_cutoffs z hz,
    returnApproximation_two_errors_not_zero z] with r hcut hnz
  obtain ⟨T, U, hTlo, hThi, hUlo, hUhi, hdiff, hT, hU, hgapT, hgapU⟩ := hcut
  have hL := returnScale_pos r
  rcases hnz T U hThi hUlo with h | h
  · exact ⟨T, hTlo, by linarith, hT, h⟩
  · exact ⟨U, by linarith, hUhi, hU, h⟩

def rational_density_nonzero_return_approximations (h : ¬Irrational explicitDensity) :
    ∃ z : ℚ, (z : ℝ) = 0xb4 * explicitDensity - 32 ∧
      ∀ᶠ r in atTop, ∃ T : ℝ,
        4 * returnScale r < T ∧ T < 11 * returnScale r ∧
        ReturnApproximationConditions z r T ∧ returnApproximationError z r T ≠ 0 := by
  obtain ⟨z, hz, _, _⟩ := returnClearedIntegerHead_of_rational_density h
  exact ⟨z, hz, returnApproximation_nonzero_witness z hz⟩

def rational_density_nonzero_return_approximation_sequence
    (h : ¬Irrational explicitDensity) :
    ∃ z : ℚ, ∃ T : ℕ → ℝ,
      (z : ℝ) = 0xb4 * explicitDensity - 32 ∧
      ∀ᶠ r in atTop,
        4 * returnScale r < T r ∧ T r < 11 * returnScale r ∧
        ReturnApproximationConditions z r (T r) ∧ returnApproximationError z r (T r) ≠ 0 := by
  classical
  obtain ⟨z, hz, hh⟩ := rational_density_nonzero_return_approximations h
  obtain ⟨N, hN⟩ := eventually_atTop.mp hh
  have hex (r : ℕ) : ∃ T : ℝ, N ≤ r →
      4 * returnScale r < T ∧ T < 11 * returnScale r ∧
      ReturnApproximationConditions z r T ∧ returnApproximationError z r T ≠ 0 := by
    by_cases hr : N ≤ r
    · obtain ⟨T, hT⟩ := hN r hr
      exact ⟨T, fun _ => hT⟩
    · exact ⟨0, fun h => False.elim (hr h)⟩
  choose T hT using hex
  refine ⟨z, T, hz, ?_⟩
  exact eventually_atTop.mpr ⟨N, hT⟩


end Bounty

end SubmissionComponent_ReturnApproximationObstruction

/- Component BoundedCoefficientPatterns; SHA256 d204d8d4a98d27eed4975b59696d022f833bd098844c6472ea6dcce29a635ffe -/
section SubmissionComponent_BoundedCoefficientPatterns
/- Extract one coefficient pattern from rows of bounded finite size. -/

open Filter

namespace Bounty

universe u v

/-- A sequence in a finite type is constant along a strictly increasing subsequence. -/
def finite_constant_subsequence {α : Type u} [Finite α] (f : ℕ → α) :
    ∃ a : α, ∃ σ : ℕ → ℕ, StrictMono σ ∧ ∀ n, f (σ n) = a := by
  have h : ∃ᶠ n in atTop, ∃ a : α, f n = a :=
    Frequently.of_forall fun n => ⟨f n, rfl⟩
  obtain ⟨a, ha⟩ := frequently_exists.mp h
  obtain ⟨σ, hσ, hconst⟩ := extraction_of_frequently_atTop ha
  exact ⟨a, σ, hσ, hconst⟩

/-- Bounded row sizes and a finite palette give one fixed ordered coefficient row
on an increasing subsequence. The row equivalences retain every actual label. -/
def bounded_coefficient_patterns {α : Type u} [DecidableEq α]
    (I : ℕ → Type v) [∀ n, Fintype (I n)] (N : ℕ) (C : Finset α)
    (c : (n : ℕ) → I n → α)
    (hcard : ∀ n, Fintype.card (I n) ≤ N)
    (hC : ∀ n i, c n i ∈ C) :
    ∃ m ≤ N, ∃ d : Fin m → α, ∃ σ : ℕ → ℕ, StrictMono σ ∧
      ∃ e : (n : ℕ) → Fin m ≃ I (σ n),
        (∀ i, d i ∈ C) ∧ ∀ n i, c (σ n) (e n i) = d i := by
  classical
  let Pattern := Σ m : Fin (N + 1), Fin m.val → ↥C
  let row : ℕ → Pattern := fun n =>
    ⟨⟨Fintype.card (I n), Nat.lt_succ_of_le (hcard n)⟩,
      fun i => ⟨c n ((Fintype.equivFin (I n)).symm i), hC n _⟩⟩
  have row_equiv (n : ℕ) (p : Pattern) (hp : row n = p) :
      ∃ e : Fin p.1.val ≃ I n, ∀ i, c n (e i) = (p.2 i).val := by
    subst p
    exact ⟨(Fintype.equivFin (I n)).symm, fun _ => rfl⟩
  obtain ⟨p, σ, hσ, hrow⟩ := finite_constant_subsequence row
  choose e he using fun n => row_equiv (σ n) p (hrow n)
  exact ⟨p.1.val, Nat.le_of_lt_succ p.1.isLt, fun i => (p.2 i).val,
    σ, hσ, e, fun i => (p.2 i).property, he⟩

/-- The same extraction works when the bounds and palette are only eventually valid. -/
def bounded_coefficient_patterns_eventually {α : Type u} [DecidableEq α]
    (I : ℕ → Type v) [∀ n, Fintype (I n)] (N : ℕ) (C : Finset α)
    (c : (n : ℕ) → I n → α)
    (hcard : ∀ᶠ n in atTop, Fintype.card (I n) ≤ N)
    (hC : ∀ᶠ n in atTop, ∀ i, c n i ∈ C) :
    ∃ m ≤ N, ∃ d : Fin m → α, ∃ σ : ℕ → ℕ, StrictMono σ ∧
      ∃ e : (n : ℕ) → Fin m ≃ I (σ n),
        (∀ i, d i ∈ C) ∧ ∀ n i, c (σ n) (e n i) = d i := by
  have h : ∀ᶠ n in atTop, Fintype.card (I n) ≤ N ∧ ∀ i, c n i ∈ C :=
    hcard.and hC
  obtain ⟨K, hK⟩ := eventually_atTop.mp h
  obtain ⟨m, hm, d, σ, hσ, e, hd, he⟩ :=
    bounded_coefficient_patterns (fun n => I (K + n)) N C (fun n => c (K + n))
      (fun n => (hK (K + n) (Nat.le_add_right K n)).1)
      (fun n => (hK (K + n) (Nat.le_add_right K n)).2)
  refine ⟨m, hm, d, (fun n => K + σ n), ?_, e, hd, he⟩
  exact fun _ _ hij => Nat.add_lt_add_left (hσ hij) K


end Bounty

end SubmissionComponent_BoundedCoefficientPatterns

/- Component ReturnFixedApproximation; SHA256 db39dae26c9cac3193889998aa53e3f024c7dce75e2253a2254d0346bbff5d1d -/
section SubmissionComponent_ReturnFixedApproximation
/- The elementary reduction to a fixed finite sum of {2,3}-units. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable section

def fixedApproximationVector {m : ℕ} (P : ℤ) (u : Fin m → ℚ) : Option (Fin m) → ℚ
  | none => (P : ℚ)
  | some i => u i

def fixedApproximationError {m : ℕ} (d u : Fin m → ℚ) (P : ℤ) : ℚ :=
  (∑ i, d i * u i) - (P : ℚ)

def fixedApproximationVector_return_height {m : ℕ} (r : ℕ) (T : ℝ)
    (e : Fin m ≃ ReturnApproximationLabel r T) :
    Height.mulHeight (fixedApproximationVector (returnIntegerPrefix r)
      (fun i => returnApproximationUnit r T (e i))) =
        Height.mulHeight (returnApproximationVector r T) := by
  have h : fixedApproximationVector (returnIntegerPrefix r)
      (fun i => returnApproximationUnit r T (e i)) =
        returnApproximationVector r T ∘ e.optionCongr := by
    funext i
    cases i <;> rfl
  rw [h]
  exact Height.mulHeight_comp_equiv e.optionCongr (returnApproximationVector r T)

def fixedApproximationError_return {m : ℕ} (z : ℚ) (r : ℕ) (T : ℝ)
    (d : Fin m → ℚ) (e : Fin m ≃ ReturnApproximationLabel r T)
    (hd : ∀ i, returnApproximationCoefficient z r T (e i) = d i) :
    ((fixedApproximationError d (fun i => returnApproximationUnit r T (e i))
      (returnIntegerPrefix r) : ℚ) : ℝ) = returnApproximationError z r T := by
  have hs : (∑ i, d i * returnApproximationUnit r T (e i)) =
      ∑ j, returnApproximationCoefficient z r T j * returnApproximationUnit r T j := by
    calc
      _ = ∑ i, returnApproximationCoefficient z r T (e i) *
          returnApproximationUnit r T (e i) := by simp only [hd]
      _ = _ := e.sum_comp (fun j =>
        returnApproximationCoefficient z r T j * returnApproximationUnit r T j)
  simpa only [fixedApproximationError, returnApproximationError, hs]

/-- A fixed-dimensional family with the exact numerical bounds needed in the
arithmetic argument. All coefficients are independent of the sequence index. -/
structure FixedReturnApproximation where
  dimension : ℕ
  dimension_lower : 4 ≤ dimension
  dimension_upper : dimension ≤ 0x194
  coefficient : Fin dimension → ℚ
  unit : ℕ → Fin dimension → ℚ
  integerPart : ℕ → ℤ
  scale : ℕ → ℝ
  cutoff : ℕ → ℝ
  scale_tendsto : Tendsto scale atTop atTop
  unit_twoThreeUnit : ∀ n i, TwoThreeUnit (unit n i)
  unit_pos : ∀ n i, 0 < unit n i
  eventual_estimates : ∀ᶠ n in atTop,
    scale n ≤ cutoff n ∧
    (∀ i, Real.exp (-cutoff n) ≤ (unit n i : ℝ)) ∧
    Height.mulHeight (fixedApproximationVector (integerPart n) (unit n)) ≤
      Real.exp (27 * scale n) ∧
    fixedApproximationError coefficient (unit n) (integerPart n) ≠ 0 ∧
    |((fixedApproximationError coefficient (unit n) (integerPart n) : ℚ) : ℝ)| ≤
      Real.exp (-cutoff n - scale n / 0xc8)
  quotient_height_diverge : ∀ B : ℝ, ∀ᶠ n in atTop, ∀ i j : Fin dimension,
    i ≠ j → B < Height.mulHeight₁ (unit n i / unit n j)

def rational_density_fixed_return_approximation (h : ¬Irrational explicitDensity) :
    Nonempty FixedReturnApproximation := by
  classical
  obtain ⟨z, T, hz, hgood⟩ := rational_density_nonzero_return_approximation_sequence h
  let I : ℕ → Type := fun r => ReturnApproximationLabel r (T r)
  let c : (r : ℕ) → I r → ℚ := fun r => returnApproximationCoefficient z r (T r)
  have hcard : ∀ᶠ r in atTop, Fintype.card (I r) ≤ 0x194 := by
    filter_upwards [hgood] with r hr
    exact hr.2.2.1.1
  have hC : ∀ᶠ r in atTop, ∀ i, c r i ∈ returnCoefficientPalette z :=
    Eventually.of_forall fun r => returnApproximationCoefficient_mem z r (T r)
  obtain ⟨m, hm, d, σ, hσ, e, hd, he⟩ :=
    bounded_coefficient_patterns_eventually I 0x194 (returnCoefficientPalette z) c hcard hC
  have hmlo : 4 ≤ m := by
    have hc : Fintype.card (I (σ 0)) = m := by
      simpa only [Fintype.card_fin] using (Fintype.card_congr (e 0)).symm
    rw [← hc]
    exact returnApproximationLabel_card_lower (σ 0) (T (σ 0))
  let u : ℕ → Fin m → ℚ := fun n i => returnApproximationUnit (σ n) (T (σ n)) (e n i)
  let P : ℕ → ℤ := fun n => returnIntegerPrefix (σ n)
  let L : ℕ → ℝ := fun n => returnScale (σ n)
  let U : ℕ → ℝ := fun n => T (σ n)
  have herr (n : ℕ) : ((fixedApproximationError d (u n) (P n) : ℚ) : ℝ) =
      returnApproximationError z (σ n) (T (σ n)) :=
    fixedApproximationError_return z (σ n) (T (σ n)) d (e n) (he n)
  have hheight (n : ℕ) : Height.mulHeight (fixedApproximationVector (P n) (u n)) =
      Height.mulHeight (returnApproximationVector (σ n) (T (σ n))) :=
    fixedApproximationVector_return_height (σ n) (T (σ n)) (e n)
  refine ⟨{
    dimension := m
    dimension_lower := hmlo
    dimension_upper := hm
    coefficient := d
    unit := u
    integerPart := P
    scale := L
    cutoff := U
    scale_tendsto := returnScale_tendsto.comp hσ.tendsto_atTop
    unit_twoThreeUnit := fun n i =>
      returnApproximationUnit_twoThreeUnit (σ n) (T (σ n)) (e n i)
    unit_pos := fun n i => returnApproximationUnit_pos (σ n) (T (σ n)) (e n i)
    eventual_estimates := ?_
    quotient_height_diverge := ?_ }⟩
  · filter_upwards [hσ.tendsto_atTop.eventually hgood] with n hn
    rcases hn with ⟨hTlo, hThi, hcond, hnz⟩
    rcases hcond with ⟨_, _, _, hlower, hH, herror⟩
    have hL := returnScale_pos (σ n)
    refine ⟨?_, fun i => hlower (e n i), ?_, ?_, ?_⟩
    · change returnScale (σ n) ≤ T (σ n)
      linarith
    · rw [hheight n]
      exact hH
    · intro hzero
      apply hnz
      rw [← herr n, hzero, Rat.cast_zero]
    · rw [herr n]
      exact herror
  · intro B
    filter_upwards [hσ.tendsto_atTop.eventually
      (returnApproximationUnit_quotient_height_diverge B)] with n hn i j hij
    apply hn (T (σ n)) (T (σ n)) (e n i) (e n j)
    intro hk
    exact hij ((e n).injective (returnApproximationKey_injective (σ n) (T (σ n)) hk))


end
end Bounty

end SubmissionComponent_ReturnFixedApproximation

/- Component ExistenceLimit; SHA256 be4fd53db1fc9b9f11cf041def94f41cc8c1693802099414005a1031a4a3d64c -/
section SubmissionComponent_ExistenceLimit
/- The extremal density exists and equals the absolutely convergent signed-jump series. -/

open Filter
open scoped Topology

namespace Bounty

def tendsto_f_jumpDensity :
    Tendsto (fun n : ℕ => (Erdos1062.f n : ℝ) / n) atTop (nhds jumpDensity) :=
  tendsto_f_of_exact_and_summable_jumps f_eq_globalUpper signedRank_jumps_summable

def target_iff_irrational_jumpDensity :
    (fcTypeOfName% "Erdos1062.erdos_1062.parts.ii") ↔ Irrational jumpDensity := by
  simp only [iff_true]
  constructor
  · rintro ⟨l, hl, hi⟩
    have he : l = jumpDensity := tendsto_nhds_unique hl tendsto_f_jumpDensity
    rwa [he] at hi
  · intro hi
    exact ⟨jumpDensity, tendsto_f_jumpDensity, hi⟩


end Bounty

end SubmissionComponent_ExistenceLimit

/- Component ExplicitLimit; SHA256 f7d3ef3aa538186f49d1be8257a1515d87d77a97e98bdc62cda44fc3ee6bb61a -/
section SubmissionComponent_ExplicitLimit
/- The extremal ratio converges to the manuscript's explicit coefficient series. -/

open Filter
open scoped Topology

namespace Bounty

def target_iff_irrational_explicitDensity :
    (fcTypeOfName% "Erdos1062.erdos_1062.parts.ii") ↔ Irrational explicitDensity := by
  rw [target_iff_irrational_jumpDensity, jumpDensity_eq_explicitDensity]


end Bounty

end SubmissionComponent_ExplicitLimit

/- Component OneFormReturnContradiction; SHA256 1e3c3fc81a0ee1d7e30ae7473371ddb2a5e8c698e2442b561064c48a5ca44f1a -/
section SubmissionComponent_OneFormReturnContradiction
/- The exact remaining arithmetic implication. The covering theorem is an
explicit hypothesis, not a proved theorem or an added axiom. -/

open Filter
open scoped Topology

namespace Bounty

noncomputable section

def oneFormHeightFactor_of_exponential_bound {I : Type*} [Fintype I]
    (x : I → ℚ) (L : ℝ) (hH : Height.mulHeight x ≤ Real.exp (27 * L)) :
    Real.exp (-L / 0x190) ≤ oneFormHeightFactor x := by
  have hh := Real.rpow_le_rpow_of_nonpos (Height.mulHeight_pos x) hH
    (show -oneFormExponent ≤ 0 by norm_num [oneFormExponent])
  have he : Real.exp (27 * L) ^ (-oneFormExponent) = Real.exp (-L / 0x190) := by
    rw [Real.rpow_def_of_pos (Real.exp_pos _), Real.log_exp]
    congr 1
    norm_num [oneFormExponent]
    ring
  simpa only [he, oneFormHeightFactor] using hh

def no_fixedReturnApproximation_of_oneForm_cover (hST : OneFormCover405) :
    ¬Nonempty FixedReturnApproximation := by
  rintro ⟨a⟩
  have hdim : Fintype.card (Fin a.dimension) + 1 ≤ 0x195 := by
    simpa only [Fintype.card_fin] using Nat.add_le_add_right a.dimension_upper 1
  obtain ⟨C, hC, hbound⟩ := oneForm_integer_rigidity hST hdim a.coefficient
  have hlarge : ∀ᶠ n in atTop, -0x190 * Real.log C < a.scale n :=
    a.scale_tendsto.eventually (eventually_gt_atTop _)
  have hpositive : ∀ᶠ n in atTop, 0 ≤ a.scale n :=
    a.scale_tendsto.eventually (eventually_ge_atTop _)
  obtain ⟨n, hn, hLn, hL0⟩ := (a.eventual_estimates.and (hlarge.and hpositive)).exists
  rcases hn with ⟨hLT, hu, hH, hne, herror⟩
  have hT0 : 0 ≤ a.cutoff n := hL0.trans hLT
  have htu : ∀ i, Real.exp (-a.cutoff n) ≤ |(a.unit n i : ℝ)| := by
    intro i
    rw [abs_of_pos (by exact_mod_cast a.unit_pos n i)]
    exact hu i
  have ht1 : Real.exp (-a.cutoff n) ≤ 1 := by
    rw [Real.exp_le_one_iff]
    linarith
  have hlower := hbound (a.integerPart n) (a.unit n) (a.unit_twoThreeUnit n)
    (Real.exp (-a.cutoff n)) (Real.exp_pos _) ht1 htu hne
  have hvec : hyperplaneOptionVector ((a.integerPart n : ℤ) : ℚ) (a.unit n) =
      fixedApproximationVector (a.integerPart n) (a.unit n) := by
    funext i
    cases i <;> rfl
  rw [hvec] at hlower
  have hfac := oneFormHeightFactor_of_exponential_bound
    (fixedApproximationVector (a.integerPart n) (a.unit n)) (a.scale n) hH
  have he : C * Real.exp (-a.cutoff n) * Real.exp (-a.scale n / 0x190) ≤
      Real.exp (-a.cutoff n - a.scale n / 0xc8) := by
    exact (mul_le_mul_of_nonneg_left hfac (mul_nonneg hC.le (Real.exp_pos _).le)).trans
      (hlower.trans herror)
  have hexp : Real.exp (-a.cutoff n - a.scale n / 0xc8) =
      Real.exp (-a.scale n / 0x190) *
        (Real.exp (-a.cutoff n) * Real.exp (-a.scale n / 0x190)) := by
    rw [← Real.exp_add, ← Real.exp_add]
    congr 1
    ring
  rw [hexp, mul_assoc] at he
  have hsmall : C ≤ Real.exp (-a.scale n / 0x190) :=
    le_of_mul_le_mul_right he (mul_pos (Real.exp_pos _) (Real.exp_pos _))
  have hstrict : Real.exp (-a.scale n / 0x190) < C := by
    rw [← Real.exp_log hC]
    apply Real.exp_lt_exp.mpr
    linarith
  exact (not_lt_of_ge hsmall) hstrict

def irrational_explicitDensity_of_oneForm_cover (hST : OneFormCover405) :
    Irrational explicitDensity := by
  by_contra h
  exact no_fixedReturnApproximation_of_oneForm_cover hST
    (rational_density_fixed_return_approximation h)

def target_of_oneForm_cover (hST : OneFormCover405) :
    fcTypeOfName% "Erdos1062.erdos_1062.parts.ii" := by
  exact target_iff_irrational_explicitDensity.mpr
    (irrational_explicitDensity_of_oneForm_cover hST)

/-- The remaining theorem can be stated using integer vectors alone. -/
def IntegerOneFormCover405 : Prop :=
  ∀ (I : Type) [Fintype I] [DecidableEq I],
    2 ≤ Fintype.card I → Fintype.card I ≤ 0x195 →
    ∀ (d : I → ℚ) (k : I), d k ≠ 0 →
    ∃ F : Finset (I → ℚ), (∀ a ∈ F, a ≠ 0) ∧
      ∀ x : I → ℤ, x ≠ 0 →
        (twoThreeOneFormProduct d (fun i => (x i : ℚ)) k : ℝ) <
          oneFormHeightFactor (fun i => (x i : ℚ)) →
        ∃ a ∈ F, (∑ i, a i * (x i : ℚ)) = 0

def oneForm_cover_of_integer_cover (h : IntegerOneFormCover405) : OneFormCover405 := by
  intro I instF instD hmin hmax d k hdk
  obtain ⟨F, hF, hcover⟩ := h I hmin hmax d k hdk
  refine ⟨F, hF, ?_⟩
  intro x hx hne hsmall
  exact oneForm_integer_cover_to_sInteger d k oneFormExponent F hcover x hx hne hsmall

def target_of_integer_oneForm_cover (h : IntegerOneFormCover405) :
    fcTypeOfName% "Erdos1062.erdos_1062.parts.ii" :=
  target_of_oneForm_cover (oneForm_cover_of_integer_cover h)


end
end Bounty

end SubmissionComponent_OneFormReturnContradiction

/- Component OneFormCoverReindex; SHA256 77cfa3568f678b3c482ff8abcca6135f5707f6f0f41e58e8dc3dd2eaa3752d9c -/
section SubmissionComponent_OneFormCoverReindex
/- Reindexing the actual one-form product completes the conditional bridge
to the existing arithmetic application. The geometric contract remains an
explicit hypothesis throughout; no unconditional target is declared. -/

namespace Bounty
noncomputable section
open scoped BigOperators Matrix

def twoThreeOneFormProduct_comp_equiv {I J : Type*}
    [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J]
    (e : I ≃ J) (a x : J → ℚ) (k : I) :
    twoThreeOneFormProduct (a ∘ e) (x ∘ e) k = twoThreeOneFormProduct a x (e k) := by
  have hs : (∑ i, a (e i) * x (e i)) = ∑ j, a j * x j :=
    Equiv.sum_comp e (fun j => a j * x j)
  have hp : (∏ i ∈ Finset.univ.erase k, |x (e i)|) =
      ∏ j ∈ Finset.univ.erase (e k), |x j| := by
    apply Finset.prod_equiv e
    · intro i
      simp
    · intro i _
      rfl
  have hf : (∏ i, padicNorm 2 (x (e i)) * padicNorm 3 (x (e i))) =
      ∏ j, padicNorm 2 (x j) * padicNorm 3 (x j) :=
    Equiv.prod_comp e (fun j => padicNorm 2 (x j) * padicNorm 3 (x j))
  simpa only [twoThreeOneFormProduct, Function.comp_apply, hs, hp, hf]

def integer_oneForm_cover_of_three_place (hST : RationalThreePlaceSubspaceCover) :
    IntegerOneFormCover405 := by
  classical
  intro I instF instD hmin _hmax a k hak
  let e : Fin (Fintype.card I) ≃ I := (Fintype.equivFin I).symm
  obtain ⟨F, hF, hcover⟩ := integer_oneForm_finite_cover_of_three_place hST hmin
    (a ∘ e) (e.symm k) (by simpa using hak) oneFormExponent (by norm_num [oneFormExponent])
  refine ⟨F.image (fun b => b ∘ e.symm), ?_, ?_⟩
  · intro b hb
    obtain ⟨b', hb', rfl⟩ := Finset.mem_image.mp hb
    intro hz
    apply hF b' hb'
    funext i
    have hh := congrFun hz (e i)
    simpa using hh
  · intro x hx hsmall
    have hx' : (x ∘ e) ≠ 0 := by
      intro hz
      apply hx
      funext i
      have hh := congrFun hz (e.symm i)
      simpa using hh
    have hp : twoThreeOneFormProduct (a ∘ e) (fun i => ((x ∘ e) i : ℚ)) (e.symm k) =
        twoThreeOneFormProduct a (fun i => (x i : ℚ)) k := by
      simpa only [Function.comp_def, Equiv.apply_symm_apply] using
        twoThreeOneFormProduct_comp_equiv e a (fun i => (x i : ℚ)) (e.symm k)
    have hH : Height.mulHeight (fun i => ((x ∘ e) i : ℚ)) =
        Height.mulHeight (fun i => (x i : ℚ)) :=
      Height.mulHeight_comp_equiv e (fun i => (x i : ℚ))
    obtain ⟨b, hb, hbx⟩ := hcover (x ∘ e) hx' (by
      simpa only [hp, hH, oneFormHeightFactor] using hsmall)
    refine ⟨b ∘ e.symm, Finset.mem_image.mpr ⟨b, hb, rfl⟩, ?_⟩
    have heq := Equiv.sum_comp e (fun i => (b ∘ e.symm) i * (x i : ℚ))
    exact heq.symm.trans (by simpa using hbx)


end
end Bounty

end SubmissionComponent_OneFormCoverReindex

/- Component FinalErdos1062; SHA256 fd6c1baa34ce01ee343bef278c958f26beed86202c799d0fea253b3bfb7501b7 -/
section SubmissionComponent_FinalErdos1062
/- The exact Erdős 1062(ii) challenge, with the three-place covering theorem proved. -/

namespace Bounty

theorem target : fcTypeOfName% "Erdos1062.erdos_1062.parts.ii" :=
  target_of_integer_oneForm_cover
    (integer_oneForm_cover_of_three_place rational_three_place_subspace_cover)

end Bounty


end SubmissionComponent_FinalErdos1062

end PolicySubmissionPart89

namespace Bounty