end Bounty
noncomputable section
/- 
# Green 24: packed single-file candidate — full verification pending
Riley Sturgill — rileysturgill1@gmail.com
AI assistance: OpenAI ChatGPT/Codex assisted with the mathematics,
certificate generation,Lean formalization,verification,and presentation.
Original source attributions and licenses are retained below.
This candidate inlines the exact Bounty.target and all its project dependencies.
Its numerical data are decoded by ordinary total Lean functions and must pass
the proved checker. No external certificate file is required.
The packed checker has passed representative tests. See the accompanying reports
for current size,policy,and verification results. Submission readiness requires
a successful whole-file Lean check and the pinned validator checks.
The original 300 MB file and its running check are preserved separately.
-/
section 
namespace Green24Proof
noncomputable def rho (x y:ℝ):ℝ :=
  if max x y ≤ 3 * min x y then (x - y) ^ 2 / 4
  else x * y - 2 * (min x y) ^ 2
theorem rho_comm (x y:ℝ):rho x y = rho y x:=by
  unfold rho
  rw [max_comm y x,min_comm y x]
  split_ifs <;> ring
theorem rho_eq_balanced {x y:ℝ} (hyx:y ≤ x) (hxy:x ≤ 3 * y) :
    rho x y = (x - y) ^ 2 / 4:=by
  simp only [rho,max_eq_left hyx,min_eq_right hyx,if_pos hxy]
theorem rho_eq_unbalanced {x y:ℝ} (hyx:y ≤ x) (hxy:3 * y ≤ x) :
    rho x y = x * y - 2 * y ^ 2:=by
  simp only [rho,max_eq_left hyx,min_eq_right hyx]
  split_ifs with h
  · have:x = 3 * y:=le_antisymm h hxy
    rw [this]
    ring
  · rfl
private def zz1:"s0001"="s0001":=by decide+kernel
theorem rho_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y):0 ≤ rho x y:=by
  unfold rho
  split_ifs with h
  · positivity
  · rcases le_total x y with hxy | hyx
    · rw [max_eq_right hxy,min_eq_left hxy] at h
      rw [min_eq_left hxy]
      have hprod:=mul_nonneg hx (by linarith:0 ≤ y - 2 * x)
      nlinarith
    · rw [max_eq_left hyx,min_eq_right hyx] at h
      rw [min_eq_right hyx]
      have hprod:=mul_nonneg hy (by linarith:0 ≤ x - 2 * y)
      nlinarith
theorem rho_self {x:ℝ} (hx:0 ≤ x):rho x x = 0:=by
  rw [rho_eq_balanced (le_refl x) (by linarith)]
  ring
theorem rho_zero {x:ℝ} (hx:0 ≤ x):rho x 0 = 0:=by
  rw [rho_eq_unbalanced hx (by simpa using hx)]
  ring
theorem rho_zero_left {x:ℝ} (hx:0 ≤ x):rho 0 x = 0:=by
  rw [rho_comm,rho_zero hx]
private def zz2:"s0002"="s0002":=by decide+kernel
theorem rho_positive_part_identity {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    4 * rho x y = (x - y) ^ 2 - max (x - 3 * y) 0 ^ 2 - max (y - 3 * x) 0 ^ 2:=by
  rcases le_total y x with hyx | hxy
  · have hy3x:y - 3 * x ≤ 0:=by linarith
    rw [max_eq_right hy3x]
    by_cases h:x ≤ 3 * y
    · rw [rho_eq_balanced hyx h,max_eq_right (by linarith:x - 3 * y ≤ 0)]
      ring
    · rw [rho_eq_unbalanced hyx (le_of_not_ge h),
        max_eq_left (by linarith:0 ≤ x - 3 * y)]
      ring
  · have hx3y:x - 3 * y ≤ 0:=by linarith
    rw [rho_comm,max_eq_right hx3y]
    by_cases h:y ≤ 3 * x
    · rw [rho_eq_balanced hxy h,max_eq_right (by linarith:y - 3 * x ≤ 0)]
      ring
    · rw [rho_eq_unbalanced hxy (le_of_not_ge h),
        max_eq_left (by linarith:0 ≤ y - 3 * x)]
      ring
noncomputable def energy {ι:Type*} [Fintype ι] (u:ι → ℝ):ℝ :=
  (∑ i, ∑ j,rho (u i) (u j)) / 2
theorem energy_nonneg {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i):0 ≤ energy u:=by
  unfold energy
  exact div_nonneg (Finset.sum_nonneg fun i _ =>
    Finset.sum_nonneg fun j _ => rho_nonneg (hu i) (hu j)) (by norm_num)
theorem energy_sum_identity {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) :
    4 * energy u = (Fintype.card ι:ℝ) * (∑ i,u i ^ 2) - (∑ i,u i) ^ 2 -
      ∑ i, ∑ j,max (u i - 3 * u j) 0 ^ 2:=by
  have hid:=Finset.sum_congr rfl (fun i (_:i ∈ (Finset.univ:Finset ι)) =>
    Finset.sum_congr rfl (fun j (_:j ∈ (Finset.univ:Finset ι)) =>
      rho_positive_part_identity (hu i) (hu j)))
  have hswap:(∑ i, ∑ j,max (u j - 3 * u i) 0 ^ 2) =
      ∑ i, ∑ j,max (u i - 3 * u j) 0 ^ 2:=Finset.sum_comm
  simp_rw [sub_sq] at hid
  simp only [Finset.sum_sub_distrib,Finset.sum_add_distrib,Finset.sum_const,
    Finset.card_univ,nsmul_eq_mul, ← Finset.mul_sum, ← Finset.sum_mul] at hid
  rw [hswap] at hid
  unfold energy
  nlinarith [hid]
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def mass {ι:Type*} [Fintype ι] (u:ι → ℝ):ℝ:=∑ i,u i
noncomputable def truncatedMass {ι:Type*} [Fintype ι] (u:ι → ℝ) (t:ℝ):ℝ :=
  ∑ i,min (u i) t
noncomputable def overlap {ι:Type*} [Fintype ι] (T:ι → ι) (u:ι → ℝ):ℝ :=
  ∑ i,min (u (T i)) (3 * u i)
theorem min_threshold (x y t:ℝ):min x y ≤ max (x - t) 0 + min t y:=by
  simp only [min_def,max_def]
  split_ifs <;> linarith
private def zz3:"s0003"="s0003":=by decide+kernel
theorem sum_comp_le_card {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (N:ℕ) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ N)
    (f:ι → ℝ) (hf:∀ i,0 ≤ f i) :
    ∑ i,f (T i) ≤ N * ∑ i,f i:=by
  calc
    ∑ i,f (T i) = ∑ i, ∑ j,if T i = j then f j else 0:=by simp
    _ = ∑ j, ∑ i,if T i = j then f j else 0:=Finset.sum_comm
    _ ≤ ∑ j,(N:ℝ) * f j:=by
      apply Finset.sum_le_sum
      intro j _
      rw [← Finset.sum_filter]
      simp only [Finset.sum_const,nsmul_eq_mul]
      apply mul_le_mul_of_nonneg_right _ (hf j)
      exact_mod_cast hT j
    _ = N * ∑ j,f j:=(Finset.mul_sum _ _ _).symm
theorem sum_comp_le_three {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ 3)
    (f:ι → ℝ) (hf:∀ i,0 ≤ f i) :
    ∑ i,f (T i) ≤ 3 * ∑ i,f i:=by
  simpa only [Nat.cast_ofNat] using sum_comp_le_card T 3 hT f hf
theorem overlap_le_truncation {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ 3)
    (u:ι → ℝ) (t:ℝ) :
    overlap T u ≤ 3 * mass u - 3 * (truncatedMass u t - truncatedMass u (t / 3)):=by
  have hthreshold:=Finset.sum_le_sum (s:=Finset.univ) (fun i _ =>
    min_threshold (u (T i)) (3 * u i) t)
  have hpreimages:=sum_comp_le_three T hT (fun i => max (u i - t) 0)
    (fun i => le_max_right _ _)
  have hmax (x:ℝ):max (x - t) 0 = x - min x t:=by
    simp only [max_def,min_def]
    split_ifs <;> linarith
  have hmin (x:ℝ):min t (3 * x) = 3 * min x (t / 3):=by
    simp only [min_def]
    split_ifs <;> linarith
  simp_rw [hmax] at hpreimages hthreshold
  simp_rw [hmin] at hthreshold
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib, ← Finset.mul_sum] at hpreimages hthreshold
  unfold overlap mass truncatedMass
  linarith
theorem truncation_difference_bounds {ι:Type*} [Fintype ι]
    (u:ι → ℝ) (hu:∀ i,0 ≤ u i) {t:ℝ} (ht:0 ≤ t) :
    0 ≤ truncatedMass u t - truncatedMass u (t / 3) ∧
      truncatedMass u t - truncatedMass u (t / 3) ≤ (2 / 3) * truncatedMass u t:=by
  have h₁:truncatedMass u (t / 3) ≤ truncatedMass u t:=by
    apply Finset.sum_le_sum
    intro i _
    exact min_le_min_left _ (by linarith)
  have h₂:truncatedMass u t ≤ 3 * truncatedMass u (t / 3):=by
    unfold truncatedMass
    rw [Finset.mul_sum]
    apply Finset.sum_le_sum
    intro i _
    have hi:=hu i
    simp only [min_def]
    split_ifs <;> linarith
  constructor <;> linarith
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def Q12 (A B:ℝ):ℝ :=
  -(97 / 0x64) * A ^ 2 + (61 / 25) * A * B - (79 / 50) * B ^ 2
noncomputable def Q18 (A B:ℝ):ℝ :=
  -(17 / 25) * A ^ 2 + (0x6d / 50) * A * B - (93 / 50) * B ^ 2
private def zz4:"s0004"="s0004":=by decide+kernel
theorem Q12_interval_identity (A B:ℝ) :
    Q12 A B + (9 / 0x100) * (A + B) ^ 2 =
      (0x175f / 0x1900) * (A - B) * ((8 / 5) * B - A) +
      (49 / 0x640) * B ^ 2 + (0x1de5 / 0x27100) * (5 / 3) * B * (A - B):=by
  unfold Q12
  ring
theorem Q12_lower {A B:ℝ} (hB:0 ≤ B) (hAB:B ≤ A)
    (hupper:A ≤ (8 / 5) * B) :
    -(9 / 0x100) * (A + B) ^ 2 ≤ Q12 A B:=by
  have h₁:=mul_nonneg (sub_nonneg.mpr hAB) (sub_nonneg.mpr hupper)
  have h₂:=mul_nonneg hB (sub_nonneg.mpr hAB)
  have hid:=Q12_interval_identity A B
  nlinarith [sq_nonneg B]
theorem Q18_interval_identity (A B:ℝ) :
    Q18 A B + (9 / 0x100) * (A + B) ^ 2 =
      (0x101f / 0x1900) * (A - (8 / 5) * B) * ((0x83 / 61) * B - A) +
      (0x4e09 / 0x27100) * B * (((0x83 / 61) * B - A) / (0x83 / 61 - 8 / 5)) +
      (0xc4a / 0x16b61) * B * ((A - (8 / 5) * B) / (0x83 / 61 - 8 / 5)):=by
  unfold Q18
  ring
theorem Q18_lower {A B:ℝ} (hB:0 ≤ B)
    (hlower:(8 / 5) * B ≤ A) (hupper:A ≤ (0x83 / 61) * B) :
    -(9 / 0x100) * (A + B) ^ 2 ≤ Q18 A B:=by
  have h₁:=mul_nonneg (sub_nonneg.mpr hlower) (sub_nonneg.mpr hupper)
  have h₂:=mul_nonneg hB (sub_nonneg.mpr hupper)
  have h₃:=mul_nonneg hB (sub_nonneg.mpr hlower)
  have hid:=Q18_interval_identity A B
  norm_num at hid
  nlinarith
private def zz5:"s0005"="s0005":=by decide+kernel
theorem height_cover {A B H d:ℝ} (hB:0 ≤ B) (hAB:B ≤ A)
    (hupper:A ≤ (0x83 / 61) * B)
    (h12:(2 / 5) * H + Q12 A B ≤ d)
    (h18:(2 / 5) * H + Q18 A B ≤ d) :
    (2 / 5) * H - (9 / 0x100) * (A + B) ^ 2 ≤ d:=by
  by_cases hcut:A ≤ (8 / 5) * B
  · linarith [Q12_lower hB hAB hcut]
  · linarith [Q18_lower hB (le_of_not_ge hcut) hupper]
theorem overlap_of_energy_estimate {U A H R:ℝ}
    (hH:(2 * U - 3 * A) ^ 2 ≤ 8 * H)
    (hR:R ≤ 3 * U - 3 * A) :
    R ≤ U + Real.sqrt (8 * H):=by
  have hnonneg:0 ≤ 8 * H:=(sq_nonneg _).trans hH
  have hsqrt:=Real.sq_sqrt hnonneg
  have hsqrt_nonneg:=Real.sqrt_nonneg (8 * H)
  have hle:2 * U - 3 * A ≤ Real.sqrt (8 * H):=by
    nlinarith
  linarith
theorem weighted_overlap {U H R C:ℝ} (hU:0 ≤ U) (hH:0 ≤ H)
    (hC:0 < C) (hR:R ≤ U + Real.sqrt (8 * H)) :
    U * R ≤ (1 + 2 / C) * U ^ 2 + C * H:=by
  have hsqrt:=Real.sq_sqrt (mul_nonneg (by norm_num:(0:ℝ) ≤ 8) hH)
  have hmul:=mul_le_mul_of_nonneg_left hR hU
  have hsq:=sq_nonneg (C * Real.sqrt (8 * H) - 4 * U)
  have hyoung:C * U * Real.sqrt (8 * H) ≤ 2 * U ^ 2 + C ^ 2 * H:=by
    nlinarith [hsqrt]
  apply (mul_le_mul_iff_right₀ hC).mp
  have hmulC:=mul_le_mul_of_nonneg_right hmul hC.le
  have hdiv:(2 / C:ℝ) * C = 2:=div_mul_cancel₀ 2 (ne_of_gt hC)
  nlinarith [hdiv]
theorem overlap_bound_of_height {U H R d:ℝ} (hU:0 ≤ U) (hH:0 ≤ H)
    (hoverlap:R ≤ U + Real.sqrt (8 * H))
    (hheight:(2 / 5) * H - (9 / 0x100) * U ^ 2 ≤ d) :
    U * R ≤ (61 / 32) * U ^ 2 + 8 * d:=by
  have h:=weighted_overlap hU hH (by norm_num:(0:ℝ) < 16 / 5) hoverlap
  norm_num at h
  linarith
private def zz6:"s0006"="s0006":=by decide+kernel
theorem overlap_bound_of_mass_imbalance {A B R d:ℝ}
    (hA:0 ≤ A) (hB:0 ≤ B) (hratio:(0x83 / 61) * B ≤ A)
    (hR:R ≤ 6 * B) (hd:0 ≤ d) :
    (A + B) * R ≤ (61 / 32) * (A + B) ^ 2 + 8 * d:=by
  have hlinear:R ≤ (61 / 32) * (A + B):=by linarith
  have hmul:=mul_le_mul_of_nonneg_left hlinear (add_nonneg hA hB)
  nlinarith
theorem overlap_bound {A B H R d:ℝ} (hB:0 ≤ B) (hAB:B ≤ A)
    (hH:0 ≤ H) (hd:0 ≤ d)
    (hoverlap:R ≤ A + B + Real.sqrt (8 * H)) (hparity:R ≤ 6 * B)
    (h12:(2 / 5) * H + Q12 A B ≤ d)
    (h18:(2 / 5) * H + Q18 A B ≤ d) :
    (A + B) * R ≤ (61 / 32) * (A + B) ^ 2 + 8 * d:=by
  by_cases hratio:A ≤ (0x83 / 61) * B
  · exact overlap_bound_of_height (by linarith) hH hoverlap
      (height_cover hB hAB hratio h12 h18)
  · exact overlap_bound_of_mass_imbalance (hB.trans hAB) hB
      (le_of_not_ge hratio) hparity hd
theorem boundary_descent {U V R du dv dg:ℝ} (hU:0 < U) (hV:0 ≤ V)
    (hoverlap:U * R ≤ (61 / 32) * U ^ 2 + 8 * du)
    (hexpansion:du + dv + 4 * U * V - 3 * V ^ 2 - 2 * V * R ≤ dg) :
    (1 - 16 * V / U) * du + dv + V * ((3 / 16) * U - 3 * V) ≤ dg:=by
  have hscaled:=mul_le_mul_of_nonneg_left hoverlap (by positivity:0 ≤ 2 * V)
  apply (mul_le_mul_iff_right₀ hU).mp
  have hexpansionU:=mul_le_mul_of_nonneg_right hexpansion hU.le
  have hcancel:(16 * V / U) * U = 16 * V:=div_mul_cancel₀ _ (ne_of_gt hU)
  nlinarith [congrArg (fun x:ℝ => x * du) hcancel]
theorem boundary_nonneg {U V R du dv dg:ℝ} (hU:0 < U) (hV:0 ≤ V)
    (hratio:16 * V ≤ U) (hdu:0 ≤ du) (hdv:0 ≤ dv)
    (hoverlap:U * R ≤ (61 / 32) * U ^ 2 + 8 * du)
    (hexpansion:du + dv + 4 * U * V - 3 * V ^ 2 - 2 * V * R ≤ dg) :
    0 ≤ dg:=by
  have hdesc:=boundary_descent hU hV hoverlap hexpansion
  have hcoef:0 ≤ 1 - 16 * V / U:=by
    have hdiv:16 * V / U ≤ 1:=(div_le_one hU).mpr hratio
    linarith
  have h₁:=mul_nonneg hcoef hdu
  have h₂:0 ≤ V * ((3 / 16) * U - 3 * V) :=
    mul_nonneg hV (by linarith)
  linarith
end Green24Proof
end 
section 
open Set Filter MeasureTheory
open scoped Topology
namespace Green24Proof
noncomputable def tailCount {ι:Type*} [Fintype ι] (u:ι → ℝ) (t:ℝ):ℝ :=
  ∑ i,if t < u i then 1 else 0
private def zz7:"s0007"="s0007":=by decide+kernel
theorem tailCount_nonneg {ι:Type*} [Fintype ι] (u:ι → ℝ) (t:ℝ) :
    0 ≤ tailCount u t:=by
  unfold tailCount
  exact Finset.sum_nonneg (fun _ _ => by split_ifs <;> norm_num)
theorem tailCount_antitone {ι:Type*} [Fintype ι] (u:ι → ℝ) :
    Antitone (tailCount u):=by
  intro s t hst
  unfold tailCount
  apply Finset.sum_le_sum
  intro i _
  split_ifs <;> norm_num at *; linarith
theorem truncatedMass_continuous {ι:Type*} [Fintype ι] (u:ι → ℝ) :
    Continuous (truncatedMass u):=by
  unfold truncatedMass
  fun_prop
theorem hasDerivWithinAt_min_right (a t:ℝ) :
    HasDerivWithinAt (fun s:ℝ => min a s) (if t < a then 1 else 0) (Ioi t) t:=by
  by_cases h:t < a
  · simp only [if_pos h]
    apply (hasDerivAt_id t).hasDerivWithinAt.congr_of_eventuallyEq
    · filter_upwards [nhdsWithin_le_nhds (Iio_mem_nhds h)] with s hs
      exact min_eq_right (le_of_lt hs)
    · exact min_eq_right h.le
  · simp only [if_neg h]
    apply (hasDerivWithinAt_const t (Ioi t) a).congr
    · intro s hs
      exact min_eq_left ((le_of_not_gt h).trans hs.le)
    · exact min_eq_left (le_of_not_gt h)
private def zz8:"s0008"="s0008":=by decide+kernel
theorem truncatedMass_hasDeriv_right {ι:Type*} [Fintype ι] (u:ι → ℝ) (t:ℝ) :
    HasDerivWithinAt (truncatedMass u) (tailCount u t) (Ioi t) t:=by
  unfold truncatedMass tailCount
  exact HasDerivWithinAt.fun_sum fun i _ => hasDerivWithinAt_min_right (u i) t
theorem integral_tailCount {ι:Type*} [Fintype ι] (u:ι → ℝ) {a b:ℝ}
    (hab:a ≤ b) :
    (∫ t in a..b,tailCount u t) = truncatedMass u b - truncatedMass u a:=by
  exact intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le hab
    (truncatedMass_continuous u).continuousOn
    (fun t _ => truncatedMass_hasDeriv_right u t) (tailCount_antitone u).intervalIntegrable
theorem integral_tailCount_mul_mass {ι:Type*} [Fintype ι] (u:ι → ℝ) {a b:ℝ}
    (hab:a ≤ b) :
    (∫ t in a..b,tailCount u t * truncatedMass u t) =
      (truncatedMass u b ^ 2 - truncatedMass u a ^ 2) / 2:=by
  have hderiv (t:ℝ):HasDerivWithinAt (fun s => truncatedMass u s ^ 2 / 2)
      (tailCount u t * truncatedMass u t) (Ioi t) t:=by
    convert ((truncatedMass_hasDeriv_right u t).pow 2).div_const 2 using 1
    all_goals first | rfl | ring
  have h:=intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le hab
    (f:=fun s => truncatedMass u s ^ 2 / 2)
    (((truncatedMass_continuous u).pow 2).div_const 2).continuousOn (fun t _ => hderiv t)
    ((tailCount_antitone u).intervalIntegrable.mul_continuousOn
      (truncatedMass_continuous u).continuousOn)
  convert h using 1
  ring
theorem posSquare_hasDeriv_right (c t:ℝ) :
    HasDerivWithinAt (fun s:ℝ => max (s - c) 0 ^ 2)
      (2 * max (t - c) 0) (Ioi t) t:=by
  by_cases h:t < c
  · rw [max_eq_right (by linarith:t - c ≤ 0),mul_zero]
    apply (hasDerivWithinAt_const t (Ioi t) (0:ℝ)).congr_of_eventuallyEq
    · filter_upwards [nhdsWithin_le_nhds (Iio_mem_nhds h)] with s hs
      rw [max_eq_right (by linarith [show s < c from hs]:s - c ≤ 0)]
      norm_num
    · rw [max_eq_right (by linarith:t - c ≤ 0)]
      norm_num
  · rw [max_eq_left (by linarith:0 ≤ t - c)]
    have hpoly:=(((hasDerivAt_id t).sub_const c).pow 2).hasDerivWithinAt (s:=Ioi t)
    simp only [Nat.reduceSub,pow_one,mul_one,id_eq] at hpoly
    apply hpoly.congr
    · intro s hs
      rw [max_eq_left (by linarith [show t < s from hs]:0 ≤ s - c)]
      rfl
    · rw [max_eq_left (by linarith:0 ≤ t - c)]
      rfl
private def zz9:"s0009"="s0009":=by decide+kernel
theorem integral_min_linear {x c:ℝ} (hx:0 ≤ x) (hc:0 ≤ c) :
    (∫ t in (0:ℝ)..x,min t c) = (x ^ 2 - max (x - c) 0 ^ 2) / 2:=by
  have hderiv (t:ℝ):HasDerivWithinAt
      (fun s:ℝ => (s ^ 2 - max (s - c) 0 ^ 2) / 2) (min t c) (Ioi t) t:=by
    have h:=(((hasDerivAt_id t).pow 2).hasDerivWithinAt.sub
      (posSquare_hasDeriv_right c t)).div_const 2
    convert h using 1
    all_goals first | rfl | (simp only [id_eq,Nat.reduceSub,pow_one,mul_one,min_def,max_def]; split_ifs <;> linarith)
  have h:=intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le hx
    (f:=fun s:ℝ => (s ^ 2 - max (s - c) 0 ^ 2) / 2)
    (by fun_prop) (fun t _ => hderiv t)
    ((continuous_id.min continuous_const).intervalIntegrable 0 x)
  simpa [max_eq_right (neg_nonpos.mpr hc)] using h
theorem indicator_lt_antitone (x:ℝ) :
    Antitone (fun t:ℝ => if t < x then (1:ℝ) else 0):=by
  intro s t hst
  dsimp only
  split_ifs <;> norm_num at *; linarith
theorem integral_indicator_lt_mul {x M:ℝ} (hx:0 ≤ x) (hxM:x ≤ M)
    (f:ℝ → ℝ) :
    (∫ t in (0:ℝ)..M,(if t < x then 1 else 0) * f t) = ∫ t in (0:ℝ)..x,f t:=by
  rw [← intervalIntegral.integral_indicator (f:=f) ⟨hx,hxM⟩]
  apply intervalIntegral.integral_congr_ae
  filter_upwards [volume.ae_ne x] with t ht _
  simp only [Set.indicator_apply,mem_ofPred_eq]
  by_cases h:t < x
  · simp [h,h.le]
  · have hnot:¬t ≤ x:=fun hle => h (lt_of_le_of_ne hle ht)
    simp [h,hnot]
theorem mass_nonneg {ι:Type*} [Fintype ι] {u:ι → ℝ} (hu:∀ i,0 ≤ u i) :
    0 ≤ mass u:=Finset.sum_nonneg (fun i _ => hu i)
private def zz10:"s000a"="s000a":=by decide+kernel
theorem height_le_mass {ι:Type*} [Fintype ι] {u:ι → ℝ} (hu:∀ i,0 ≤ u i) (i:ι) :
    u i ≤ mass u:=Finset.single_le_sum (fun j _ => hu j) (Finset.mem_univ i)
theorem truncatedMass_zero {ι:Type*} [Fintype ι] {u:ι → ℝ} (hu:∀ i,0 ≤ u i) :
    truncatedMass u 0 = 0:=by
  simp [truncatedMass,min_eq_right (hu _)]
theorem truncatedMass_mass {ι:Type*} [Fintype ι] {u:ι → ℝ} (hu:∀ i,0 ≤ u i) :
    truncatedMass u (mass u) = mass u:=by
  unfold truncatedMass mass
  apply Finset.sum_congr rfl
  intro i _
  exact min_eq_left (height_le_mass hu i)
theorem truncatedMass_le_mass {ι:Type*} [Fintype ι] (u:ι → ℝ) (t:ℝ) :
    truncatedMass u t ≤ mass u:=Finset.sum_le_sum (fun i _ => min_le_left (u i) t)
private def zz11:"s000b"="s000b":=by decide+kernel
theorem integral_tail_mul {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) (f:ℝ → ℝ) (hf:Continuous f) :
    (∫ t in (0:ℝ)..mass u,tailCount u t * f t) =
      ∑ i, ∫ t in (0:ℝ)..u i,f t:=by
  simp only [tailCount,Finset.sum_mul]
  rw [intervalIntegral.integral_finsetSum]
  · apply Finset.sum_congr rfl
    intro i _
    exact integral_indicator_lt_mul (hu i) (height_le_mass hu i) f
  · intro i _
    exact (indicator_lt_antitone (u i)).intervalIntegrable.mul_continuousOn hf.continuousOn
theorem integral_min_third {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    (∫ t in (0:ℝ)..x,min y (t / 3)) = (x ^ 2 - max (x - 3 * y) 0 ^ 2) / 6:=by
  have hmin (t:ℝ):min y (t / 3) = min t (3 * y) / 3:=by
    simp only [min_def]
    split_ifs <;> linarith
  simp_rw [hmin]
  rw [intervalIntegral.integral_div,integral_min_linear hx (by linarith:0 ≤ 3 * y)]
  ring
theorem integral_tail_mul_third {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) :
    (∫ t in (0:ℝ)..mass u,tailCount u t * truncatedMass u (t / 3)) =
      (4 * energy u + mass u ^ 2) / 6:=by
  rw [integral_tail_mul hu (fun t => truncatedMass u (t / 3))
    ((truncatedMass_continuous u).comp (continuous_id.div_const 3))]
  have hscalar (i:ι):(∫ t in (0:ℝ)..u i,truncatedMass u (t / 3)) =
      ∑ j,(u i ^ 2 - max (u i - 3 * u j) 0 ^ 2) / 6:=by
    unfold truncatedMass
    rw [intervalIntegral.integral_finsetSum]
    · exact Finset.sum_congr rfl (fun j _ => integral_min_third (hu i) (hu j))
    · intro j _
      exact (continuous_const.min (continuous_id.div_const 3)).intervalIntegrable 0 (u i)
  simp_rw [hscalar]
  simp only [← Finset.sum_div,Finset.sum_sub_distrib,Finset.sum_const,Finset.card_univ,
    nsmul_eq_mul, ← Finset.mul_sum]
  have he:=energy_sum_identity hu
  unfold mass
  linarith
theorem energy_integral_identity {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) :
    energy u = mass u ^ 2 / 2 - (3 / 2) *
      (∫ t in (0:ℝ)..mass u,
        tailCount u t * (truncatedMass u t - truncatedMass u (t / 3))):=by
  simp_rw [mul_sub]
  rw [intervalIntegral.integral_sub]
  · rw [integral_tailCount_mul_mass u (mass_nonneg hu),truncatedMass_mass hu,
      truncatedMass_zero hu,integral_tail_mul_third hu]
    ring
  · exact (tailCount_antitone u).intervalIntegrable.mul_continuousOn
      (truncatedMass_continuous u).continuousOn
  · exact (tailCount_antitone u).intervalIntegrable.mul_continuousOn
      ((truncatedMass_continuous u).comp (continuous_id.div_const 3)).continuousOn
private def zz12:"s000c"="s000c":=by decide+kernel
theorem energyIntegrand_intervalIntegrable {ι:Type*} [Fintype ι]
    (u:ι → ℝ) (a b:ℝ) :
    IntervalIntegrable
      (fun t => tailCount u t * (truncatedMass u t - truncatedMass u (t / 3)))
      volume a b :=
  (tailCount_antitone u).intervalIntegrable.mul_continuousOn
    ((truncatedMass_continuous u).sub
      ((truncatedMass_continuous u).comp (continuous_id.div_const 3))).continuousOn
theorem energy_integral_upper {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) {A:ℝ} (hA:0 ≤ A) (hAU:A ≤ (2 / 3) * mass u)
    (hbound:∀ t ∈ Icc (0:ℝ) (mass u),
      truncatedMass u t - truncatedMass u (t / 3) ≤ A) :
    (∫ t in (0:ℝ)..mass u,
      tailCount u t * (truncatedMass u t - truncatedMass u (t / 3))) ≤
      A * mass u - (3 / 4) * A ^ 2:=by
  have hU:=mass_nonneg hu
  have hvalue:(3 / 2) * A ∈ Icc (truncatedMass u 0) (truncatedMass u (mass u)):=by
    rw [truncatedMass_zero hu,truncatedMass_mass hu]
    constructor <;> linarith
  obtain ⟨s,hs,hLs⟩ :=
    (intermediate_value_Icc hU (truncatedMass_continuous u).continuousOn) hvalue
  have hleft:(∫ t in (0:ℝ)..s,
      tailCount u t * (truncatedMass u t - truncatedMass u (t / 3))) ≤
      (2 / 3) * ((truncatedMass u s ^ 2 - truncatedMass u 0 ^ 2) / 2):=by
    have hmono:=intervalIntegral.integral_mono_on hs.1
      (energyIntegrand_intervalIntegrable u 0 s)
      (((tailCount_antitone u).intervalIntegrable.mul_continuousOn
        (truncatedMass_continuous u).continuousOn).const_mul (2 / 3))
      (fun t (ht:t ∈ Icc (0:ℝ) s) => ?_)
    · simpa only [intervalIntegral.integral_const_mul,integral_tailCount_mul_mass u hs.1]
        using hmono
    · have h:=mul_le_mul_of_nonneg_left (truncation_difference_bounds u hu ht.1).2
        (tailCount_nonneg u t)
      nlinarith
  have hright:(∫ t in s..mass u,
      tailCount u t * (truncatedMass u t - truncatedMass u (t / 3))) ≤
      A * (mass u - truncatedMass u s):=by
    have hmono:=intervalIntegral.integral_mono_on hs.2
      (energyIntegrand_intervalIntegrable u s (mass u))
      ((tailCount_antitone u).intervalIntegrable.const_mul A)
      (fun t (ht:t ∈ Icc s (mass u)) => ?_)
    · simpa only [intervalIntegral.integral_const_mul,integral_tailCount u hs.2,
        truncatedMass_mass hu] using hmono
    · have h:=mul_le_mul_of_nonneg_left (hbound t ⟨hs.1.trans ht.1,ht.2⟩)
        (tailCount_nonneg u t)
      nlinarith
  have hsplit:=intervalIntegral.integral_add_adjacent_intervals
    (energyIntegrand_intervalIntegrable u 0 s)
    (energyIntegrand_intervalIntegrable u s (mass u))
  simp only [truncatedMass_zero hu,hLs] at hleft hright
  nlinarith
theorem energy_ge_truncation_max {ι:Type*} [Fintype ι] {u:ι → ℝ}
    (hu:∀ i,0 ≤ u i) {A:ℝ} (hA:0 ≤ A) (hAU:A ≤ (2 / 3) * mass u)
    (hbound:∀ t ∈ Icc (0:ℝ) (mass u),
      truncatedMass u t - truncatedMass u (t / 3) ≤ A) :
    (2 * mass u - 3 * A) ^ 2 ≤ 8 * energy u:=by
  have henergy:=energy_integral_identity hu
  have hint:=energy_integral_upper hu hA hAU hbound
  nlinarith
theorem sharp_overlap {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ 3)
    (u:ι → ℝ) (hu:∀ i,0 ≤ u i) :
    overlap T u ≤ mass u + Real.sqrt (8 * energy u):=by
  have hU:=mass_nonneg hu
  have hcont:Continuous (fun t => truncatedMass u t - truncatedMass u (t / 3)) :=
    (truncatedMass_continuous u).sub
      ((truncatedMass_continuous u).comp (continuous_id.div_const 3))
  obtain ⟨t,ht,hmax⟩:=isCompact_Icc.exists_isMaxOn (nonempty_Icc.mpr hU) hcont.continuousOn
  have hA:=(truncation_difference_bounds u hu ht.1).1
  have hAU:truncatedMass u t - truncatedMass u (t / 3) ≤ (2 / 3) * mass u:=by
    have h₁:=(truncation_difference_bounds u hu ht.1).2
    have h₂:=truncatedMass_le_mass u t
    linarith
  exact overlap_of_energy_estimate (energy_ge_truncation_max hu hA hAU hmax)
    (overlap_le_truncation T hT u t)
private def zz13:"s000d"="s000d":=by decide+kernel
theorem sharp_weighted_overlap {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ 3)
    (u:ι → ℝ) (hu:∀ i,0 ≤ u i) {C:ℝ} (hC:0 < C) :
    mass u * overlap T u ≤ (1 + 2 / C) * mass u ^ 2 + C * energy u :=
  weighted_overlap (mass_nonneg hu) (energy_nonneg hu) hC (sharp_overlap T hT u hu)
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def kernel (a b c:ℝ):ℝ :=
  (2 * a * b + 2 * b * c + 2 * c * a - a ^ 2 - b ^ 2 - c ^ 2 +
    max (a - b - c) 0 ^ 2 + max (b - a - c) 0 ^ 2 + max (c - a - b) 0 ^ 2) / 4
theorem kernel_swap12 (a b c:ℝ):kernel a b c = kernel b a c:=by
  unfold kernel
  rw [show c - b - a = c - a - b by ring]
  ring
theorem kernel_swap23 (a b c:ℝ):kernel a b c = kernel a c b:=by
  unfold kernel
  rw [show a - c - b = a - b - c by ring,
    show c - a - b = c - b - a by ring,
    show b - a - c = b - c - a by ring]
  ring
theorem kernel_cycle (a b c:ℝ):kernel a b c = kernel b c a:=by
  rw [kernel_swap12 a b c,kernel_swap23 b a c]
private def zz14:"s000e"="s000e":=by decide+kernel
theorem kernel_eq_product {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:a + b ≤ c) :
    kernel a b c = a * b:=by
  unfold kernel
  rw [max_eq_right (by linarith:a - b - c ≤ 0),
    max_eq_right (by linarith:b - a - c ≤ 0),
    max_eq_left (by linarith:0 ≤ c - a - b)]
  ring
theorem kernel_eq_triangle {a b c:ℝ}
    (ha:a ≤ b + c) (hb:b ≤ a + c) (hc:c ≤ a + b) :
    kernel a b c = a * b - (a + b - c) ^ 2 / 4:=by
  unfold kernel
  rw [max_eq_right (by linarith:a - b - c ≤ 0),
    max_eq_right (by linarith:b - a - c ≤ 0),
    max_eq_right (by linarith:c - a - b ≤ 0)]
  ring
theorem kernel_eq_sorted {a b c:ℝ} (ha:0 ≤ a) (hab:a ≤ b) (hbc:b ≤ c) :
    kernel a b c = a * b - max (a + b - c) 0 ^ 2 / 4:=by
  by_cases h:a + b ≤ c
  · rw [kernel_eq_product ha (ha.trans hab) h,
      max_eq_right (by linarith:a + b - c ≤ 0)]
    ring
  · rw [kernel_eq_triangle (by linarith) (by linarith) (le_of_not_ge h),
      max_eq_left (by linarith:0 ≤ a + b - c)]
theorem kernel_le_product {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    kernel a b c ≤ a * b:=by
  by_cases hcmax:a + b ≤ c
  · exact (kernel_eq_product ha hb hcmax).le
  by_cases hamax:b + c ≤ a
  · rw [kernel_cycle,kernel_eq_product hb hc hamax]
    nlinarith [mul_nonneg hb (by linarith:0 ≤ a - c)]
  by_cases hbmax:a + c ≤ b
  · rw [kernel_swap23,kernel_eq_product ha hc hbmax]
    nlinarith [mul_nonneg ha (by linarith:0 ≤ b - c)]
  rw [kernel_eq_triangle (le_of_not_ge hamax) (le_of_not_ge hbmax) (le_of_not_ge hcmax)]
  linarith [sq_nonneg (a + b - c)]
private def zz15:"s000f"="s000f":=by decide+kernel
theorem kernel_nonneg {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    0 ≤ kernel a b c:=by
  by_cases hcmax:a + b ≤ c
  · rw [kernel_eq_product ha hb hcmax]
    exact mul_nonneg ha hb
  by_cases hamax:b + c ≤ a
  · rw [kernel_cycle,kernel_eq_product hb hc hamax]
    exact mul_nonneg hb hc
  by_cases hbmax:a + c ≤ b
  · rw [kernel_swap23,kernel_eq_product ha hc hbmax]
    exact mul_nonneg ha hc
  rw [kernel_eq_triangle (le_of_not_ge hamax) (le_of_not_ge hbmax) (le_of_not_ge hcmax)]
  rcases le_total a b with hab | hba
  · have h₁:=mul_nonneg (by linarith:0 ≤ 2 * a + (a + b - c))
      (by linarith:0 ≤ 2 * a - (a + b - c))
    have h₂:=mul_nonneg ha (by linarith:0 ≤ b - a)
    nlinarith
  · have h₁:=mul_nonneg (by linarith:0 ≤ 2 * b + (a + b - c))
      (by linarith:0 ≤ 2 * b - (a + b - c))
    have h₂:=mul_nonneg hb (by linarith:0 ≤ a - b)
    nlinarith
noncomputable def profileFunctional {q:ℕ} [NeZero q] (g:ZMod q → ℝ):ℝ :=
  ∑ j, ∑ k,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k)
noncomputable def deficit {q:ℕ} [NeZero q] (g:ZMod q → ℝ):ℝ :=
  2 * mass g ^ 2 - profileFunctional g
theorem profileFunctional_nonneg {q:ℕ} [NeZero q] (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i):0 ≤ profileFunctional g:=by
  apply Finset.sum_nonneg
  intro j _
  apply Finset.sum_nonneg
  intro k _
  exact kernel_nonneg (hg _) (mul_nonneg (by norm_num) (hg _))
    (mul_nonneg (by norm_num) (hg _))
theorem profileFunctional_le_of_bijective {q:ℕ} [NeZero q] (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i)
    (hbij:∀ j:ZMod q,Function.Bijective (fun k:ZMod q => 3 * k - 2 * j)) :
    profileFunctional g ≤ 2 * mass g ^ 2:=by
  have hrow (j:ZMod q):(∑ k,g (3 * k - 2 * j) * (2 * g j)) = mass g * (2 * g j):=by
    rw [← Finset.sum_mul,(hbij j).sum_comp]
    rfl
  calc
    profileFunctional g ≤ ∑ j, ∑ k,g (3 * k - 2 * j) * (2 * g j):=by
      apply Finset.sum_le_sum
      intro j _
      apply Finset.sum_le_sum
      intro k _
      exact kernel_le_product (hg _) (mul_nonneg (by norm_num) (hg _))
        (mul_nonneg (by norm_num) (hg _))
    _ = ∑ j,mass g * (2 * g j):=Finset.sum_congr rfl (fun j _ => hrow j)
    _ = 2 * mass g ^ 2:=by
      simp only [← Finset.mul_sum]
      unfold mass
      ring
theorem deficit_nonneg_of_three_not_dvd {q:ℕ} [NeZero q]
    (hq:¬3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):0 ≤ deficit g:=by
  have hu:IsUnit (3:ZMod q):=ZMod.isUnit_prime_of_not_dvd Nat.prime_three hq
  have hmul:=IsUnit.isUnit_iff_mulLeft_bijective.mp hu
  have hbij (j:ZMod q):Function.Bijective (fun k:ZMod q => 3 * k - 2 * j):=by
    exact (Equiv.subRight (2 * j)).bijective.comp hmul
  exact sub_nonneg.mpr (profileFunctional_le_of_bijective g hg hbij)
private def zz16:"s0010"="s0010":=by decide+kernel
theorem affine_preimages {q:ℕ} [NeZero q] (N:ℕ) (hN:0 < N) (c y:ZMod q) :
    (Finset.univ.filter fun x:ZMod q => N * x + c = y).card ≤ N:=by
  let s:=Finset.univ.filter (fun x:ZMod q => N * x + c = y)
  change s.card ≤ N
  rcases s.eq_empty_or_nonempty with h | ⟨x₀,hx₀⟩
  · rw [h]
    simp
  · have hx₀eq:N * x₀ + c = y:=(Finset.mem_filter.mp hx₀).2
    have hcard:s.card ≤ (Finset.univ.filter fun x:ZMod q => N • x = 0).card:=by
      apply Finset.card_le_card_of_injOn (fun x:ZMod q => x - x₀)
      · intro x hx
        have hxeq:N * x + c = y:=(Finset.mem_filter.mp hx).2
        have heq:N * x = N * x₀:=add_right_cancel (hxeq.trans hx₀eq.symm)
        apply Finset.mem_filter.mpr
        refine ⟨Finset.mem_univ _, ?_⟩
        simp only [nsmul_eq_mul,mul_sub,heq,sub_self]
      · intro x _ z _ hxz
        have h:=congrArg (fun a:ZMod q => a + x₀) hxz
        simpa using h
    exact hcard.trans (IsAddCyclic.card_nsmul_eq_zero_le hN)
theorem affine_three_preimages {q:ℕ} [NeZero q] (c y:ZMod q) :
    (Finset.univ.filter fun x:ZMod q => 3 * x + c = y).card ≤ 3:=by
  simpa only [Nat.cast_ofNat] using affine_preimages 3 (by norm_num) c y
def overlapMap {q:ℕ} (j k:ZMod q):ZMod q:=3 * k - 2 * j - 1
theorem overlapMap_preimages {q:ℕ} [NeZero q] (j y:ZMod q) :
    (Finset.univ.filter fun k => overlapMap j k = y).card ≤ 3:=by
  have heq:overlapMap j = fun k:ZMod q => 3 * k + (-2 * j - 1):=by
    funext k
    unfold overlapMap
    ring
  rw [heq]
  exact affine_three_preimages _ _
theorem cyclic_sharp_overlap {q:ℕ} [NeZero q] (u:ZMod q → ℝ)
    (hu:∀ k,0 ≤ u k) (j:ZMod q) :
    overlap (overlapMap j) u ≤ mass u + Real.sqrt (8 * energy u) :=
  sharp_overlap (overlapMap j) (overlapMap_preimages j) u hu
private def zz17:"s0011"="s0011":=by decide+kernel
theorem cyclic_weighted_overlap {q:ℕ} [NeZero q] (u:ZMod q → ℝ)
    (hu:∀ k,0 ≤ u k) (j:ZMod q) {C:ℝ} (hC:0 < C) :
    mass u * overlap (overlapMap j) u ≤ (1 + 2 / C) * mass u ^ 2 + C * energy u :=
  sharp_weighted_overlap (overlapMap j) (overlapMap_preimages j) u hu hC
end Green24Proof
end 
section 
namespace Green24Proof.KernelPairMajorant
theorem gap_nonneg {A B C:ℝ} (hA:A ≤ B + C) (hB:B ≤ A + C) :
    0 ≤ C ^ 2 - (A - B) ^ 2:=by
  have h:=mul_nonneg (by linarith:0 ≤ C - A + B) (by linarith:0 ≤ C + A - B)
  nlinarith only [h]
theorem triangle_quadratic_bound {A B C:ℝ} (hA:0 < A) (hB:0 < B) (hC:0 < C)
    (hAB:A ≤ B + C) (hBC:B ≤ A + C) (hCA:C ≤ A + B) (a b c:ℝ) :
    4 * A * B * C * (a * b - (a + b - c) ^ 2 / 4) ≤
      (C * (C ^ 2 - (A - B) ^ 2)) * a * b +
      (B * (B ^ 2 - (A - C) ^ 2)) * a * c +
      (A * (A ^ 2 - (B - C) ^ 2)) * b * c:=by
  let P:=(C * (C ^ 2 - (A - B) ^ 2)) * a * b +
    (B * (B ^ 2 - (A - C) ^ 2)) * a * c +
    (A * (A ^ 2 - (B - C) ^ 2)) * b * c -
    4 * A * B * C * (a * b - (a + b - c) ^ 2 / 4)
  have hD:0 ≤ (A + B + C) * (A + B - C) * (A + C - B) * (B + C - A):=by
    exact mul_nonneg (mul_nonneg (mul_nonneg (by positivity) (by linarith))
      (by linarith)) (by linarith)
  have hid:(4 * A * B * C) * P =
      (2 * A * B * C * a - C * (A ^ 2 + B ^ 2 - C ^ 2) * b -
        B * (A ^ 2 + C ^ 2 - B ^ 2) * c) ^ 2 +
      ((A + B + C) * (A + B - C) * (A + C - B) * (B + C - A)) *
        (C * b - B * c) ^ 2:=by
    dsimp [P]
    ring
  have hp:0 ≤ (4 * A * B * C) * P:=by
    rw [hid]
    exact add_nonneg (sq_nonneg _) (mul_nonneg hD (sq_nonneg _))
  have hP:0 ≤ P:=nonneg_of_mul_nonneg_right hp (by positivity:0 < 4 * A * B * C)
  dsimp [P] at hP
  linarith only [hP]
theorem kernel_majorant {A B C:ℝ} (hA:0 < A) (hB:0 < B) (hC:0 < C)
    (hAB:A ≤ B + C) (hBC:B ≤ A + C) (hCA:C ≤ A + B)
    {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    4 * A * B * C * kernel a b c ≤
      (C * (C ^ 2 - (A - B) ^ 2)) * a * b +
      (B * (B ^ 2 - (A - C) ^ 2)) * a * c +
      (A * (A ^ 2 - (B - C) ^ 2)) * b * c:=by
  let L:=C * (C ^ 2 - (A - B) ^ 2)
  let M:=B * (B ^ 2 - (A - C) ^ 2)
  let N:=A * (A ^ 2 - (B - C) ^ 2)
  have hL:0 ≤ L:=mul_nonneg hC.le (gap_nonneg hAB hBC)
  have hM:0 ≤ M:=mul_nonneg hB.le (gap_nonneg (by linarith) hCA)
  have hN:0 ≤ N:=mul_nonneg hA.le (gap_nonneg (by linarith) (by linarith))
  have hq (x y z:ℝ):=triangle_quadratic_bound hA hB hC hAB hBC hCA x y z
  change 4 * A * B * C * kernel a b c ≤ L * a * b + M * a * c + N * b * c
  by_cases hcab:a + b ≤ c
  · rw [kernel_eq_product ha hb hcab]
    have h:=hq a b (a + b)
    change 4 * A * B * C * (a * b - (a + b - (a + b)) ^ 2 / 4) ≤
      L * a * b + M * a * (a + b) + N * b * (a + b) at h
    nlinarith only [h,mul_nonneg (mul_nonneg hM ha) (sub_nonneg.mpr hcab),
      mul_nonneg (mul_nonneg hN hb) (sub_nonneg.mpr hcab)]
  by_cases habc:b + c ≤ a
  · rw [kernel_cycle,kernel_eq_product hb hc habc]
    have h:=hq (b + c) b c
    change 4 * A * B * C * ((b + c) * b - (b + c + b - c) ^ 2 / 4) ≤
      L * (b + c) * b + M * (b + c) * c + N * b * c at h
    nlinarith only [h,mul_nonneg (mul_nonneg hL hb) (sub_nonneg.mpr habc),
      mul_nonneg (mul_nonneg hM hc) (sub_nonneg.mpr habc)]
  by_cases hbac:a + c ≤ b
  · rw [kernel_swap23,kernel_eq_product ha hc hbac]
    have h:=hq a (a + c) c
    change 4 * A * B * C * (a * (a + c) - (a + (a + c) - c) ^ 2 / 4) ≤
      L * a * (a + c) + M * a * c + N * (a + c) * c at h
    nlinarith only [h,mul_nonneg (mul_nonneg hL ha) (sub_nonneg.mpr hbac),
      mul_nonneg (mul_nonneg hN hc) (sub_nonneg.mpr hbac)]
  rw [kernel_eq_triangle (le_of_not_ge habc) (le_of_not_ge hbac) (le_of_not_ge hcab)]
  exact hq a b c
private def zz18:"s0012"="s0012":=by decide+kernel
theorem exists_pair_majorant {A B C:ℝ} (hA:0 ≤ A) (hB:0 ≤ B) (hC:0 ≤ C) :
    ∃ L M N:ℝ,
      (∀ a b c:ℝ,0 ≤ a → 0 ≤ b → 0 ≤ c →
        kernel a b c ≤ L * a * b + M * a * c + N * b * c) ∧
      kernel A B C = L * A * B + M * A * C + N * B * C:=by
  by_cases hcab:A + B ≤ C
  · refine ⟨1,0,0, ?_, ?_⟩
    · intro a b c ha hb hc
      simpa using kernel_le_product ha hb hc
    · simp [kernel_eq_product hA hB hcab]
  by_cases habc:B + C ≤ A
  · refine ⟨0,0,1, ?_, ?_⟩
    · intro a b c ha hb hc
      simpa only [zero_mul,zero_add,one_mul,kernel_cycle a b c] using
        kernel_le_product hb hc ha
    · rw [kernel_cycle,kernel_eq_product hB hC habc]
      simp
  by_cases hbac:A + C ≤ B
  · refine ⟨0,1,0, ?_, ?_⟩
    · intro a b c ha hb hc
      simpa only [zero_mul,zero_add,add_zero,one_mul,kernel_swap23 a b c] using
        kernel_le_product ha hc hb
    · rw [kernel_swap23,kernel_eq_product hA hC hbac]
      simp
  have hA':0 < A:=by linarith
  have hB':0 < B:=by linarith
  have hC':0 < C:=by linarith
  let D:=4 * A * B * C
  have hD:0 < D:=by dsimp [D]; positivity
  refine ⟨C * (C ^ 2 - (A - B) ^ 2) / D,
    B * (B ^ 2 - (A - C) ^ 2) / D,
    A * (A ^ 2 - (B - C) ^ 2) / D, ?_, ?_⟩
  · intro a b c ha hb hc
    have h:=kernel_majorant hA' hB' hC' (le_of_not_ge habc)
      (le_of_not_ge hbac) (le_of_not_ge hcab) ha hb hc
    calc
      kernel a b c ≤ ((C * (C ^ 2 - (A - B) ^ 2)) * a * b +
        (B * (B ^ 2 - (A - C) ^ 2)) * a * c +
        (A * (A ^ 2 - (B - C) ^ 2)) * b * c) / D:=by
        apply (le_div_iff₀ hD).mpr
        dsimp [D]
        nlinarith only [h]
      _ = _:=by ring
  · rw [kernel_eq_triangle (le_of_not_ge habc) (le_of_not_ge hbac) (le_of_not_ge hcab)]
    dsimp [D]
    field_simp
    ring
end Green24Proof.KernelPairMajorant
private def zz1994:"s07ca"="s07ca":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteKernelSum
open scoped BigOperators
theorem kernel_sum_of_bijective {κ:Type*} [Fintype κ]
    (r:κ → κ → κ) (hr:∀ j,Function.Bijective (r j))
    (hc:∀ k,Function.Bijective (fun j => r j k)) (f g h:κ → ℝ)
    (hf:∀ i,0 ≤ f i) (hg:∀ i,0 ≤ g i) (hh:∀ i,0 ≤ h i) :
    (∑ j, ∑ k,kernel (f (r j k)) (g j) (h k)) ≤
      kernel (∑ i,f i) (∑ i,g i) (∑ i,h i):=by
  have hrow (j:κ):(∑ k,f (r j k)) = ∑ i,f i:=(hr j).sum_comp f
  have hcol (k:κ):(∑ j,f (r j k)) = ∑ i,f i:=(hc k).sum_comp f
  have hfg:(∑ j, ∑ k,f (r j k) * g j) = (∑ i,f i) * ∑ i,g i:=by
    simp_rw [← Finset.sum_mul,hrow]
    rw [← Finset.mul_sum]
  have hfh:(∑ j, ∑ k,f (r j k) * h k) = (∑ i,f i) * ∑ i,h i:=by
    rw [Finset.sum_comm]
    simp_rw [← Finset.sum_mul,hcol]
    rw [← Finset.mul_sum]
  obtain ⟨L,M,N,hb,heq⟩:=KernelPairMajorant.exists_pair_majorant
    (A:=∑ i,f i) (B:=∑ i,g i) (C:=∑ i,h i)
    (Finset.sum_nonneg (fun i _ => hf i)) (Finset.sum_nonneg (fun i _ => hg i))
    (Finset.sum_nonneg (fun i _ => hh i))
  calc
    _ ≤ ∑ j, ∑ k,(L * (f (r j k) * g j) + M * (f (r j k) * h k) + N * (g j * h k)):=by
      apply Finset.sum_le_sum
      intro j _
      apply Finset.sum_le_sum
      intro k _
      simpa only [mul_assoc] using hb (f (r j k)) (g j) (h k) (hf _) (hg _) (hh _)
    _ = L * ((∑ i,f i) * ∑ i,g i) + M * ((∑ i,f i) * ∑ i,h i) +
        N * ((∑ i,g i) * ∑ i,h i):=by
      simp only [Finset.sum_add_distrib, ← Finset.mul_sum,hfg,hfh]
      rw [← Finset.sum_mul]
    _ = _:=by rw [heq]; ring
theorem cyclic_kernel_sum {q:ℕ} [NeZero q] (f g h:ZMod q → ℝ)
    (hf:∀ i,0 ≤ f i) (hg:∀ i,0 ≤ g i) (hh:∀ i,0 ≤ h i) :
    (∑ j, ∑ k,kernel (f (k - j)) (g j) (h k)) ≤
      kernel (∑ i,f i) (∑ i,g i) (∑ i,h i):=by
  apply kernel_sum_of_bijective (fun j k => k - j)
    (fun j => (Equiv.subRight j).bijective) _ f g h hf hg hh
  intro k
  exact (Equiv.subLeft k).bijective
theorem coefficient_kernel_sum {q:ℕ} [NeZero q]
    (h2:Nat.Coprime 2 q) (h3:Nat.Coprime 3 q) (f g h:ZMod q → ℝ)
    (hf:∀ i,0 ≤ f i) (hg:∀ i,0 ≤ g i) (hh:∀ i,0 ≤ h i) :
    (∑ j, ∑ k,kernel (f (3 * k - 2 * j)) (g j) (h k)) ≤
      kernel (∑ i,f i) (∑ i,g i) (∑ i,h i):=by
  have hmul2:Function.Bijective (fun x:ZMod q => 2 * x) :=
    IsUnit.isUnit_iff_mulLeft_bijective.mp ((ZMod.isUnit_iff_coprime 2 q).mpr h2)
  have hmul3:Function.Bijective (fun x:ZMod q => 3 * x) :=
    IsUnit.isUnit_iff_mulLeft_bijective.mp ((ZMod.isUnit_iff_coprime 3 q).mpr h3)
  exact kernel_sum_of_bijective (fun j k => 3 * k - 2 * j)
    (fun j => (Equiv.subRight (2 * j)).bijective.comp hmul3)
    (fun k => (Equiv.subLeft (3 * k)).bijective.comp hmul2) f g h hf hg hh
end Green24Proof.FiniteKernelSum
private def zz1995:"s07cb"="s07cb":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileCoprimeCollapse
open scoped BigOperators
variable {m n q:ℕ} [NeZero m] [NeZero n] [NeZero q]
noncomputable def fiberMass (g:ZMod m × ZMod n → ℝ) (j:ZMod m):ℝ :=
  ∑ u:ZMod n,g (j,u)
private def zz19:"s0013"="s0013":=by decide+kernel
omit [NeZero m] in
theorem fiberMass_nonneg (g:ZMod m × ZMod n → ℝ) (hg:∀ i,0 ≤ g i)
    (j:ZMod m):0 ≤ fiberMass g j:=Finset.sum_nonneg (fun u _ => hg (j,u))
theorem mass_fiberMass (g:ZMod m × ZMod n → ℝ):mass (fiberMass g) = mass g:=by
  simp only [mass,fiberMass,Fintype.sum_prod_type]
theorem product_profile_le (h2:Nat.Coprime 2 n) (h3:Nat.Coprime 3 n)
    (g:ZMod m × ZMod n → ℝ) (hg:∀ i,0 ≤ g i) :
    (∑ j:ZMod m × ZMod n, ∑ k:ZMod m × ZMod n,
      kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k)) ≤ profileFunctional (fiberMass g):=by
  simp only [Fintype.sum_prod_type]
  change (∑ j:ZMod m, ∑ u:ZMod n, ∑ k:ZMod m, ∑ v:ZMod n,
    kernel (g (3 * k - 2 * j,3 * v - 2 * u)) (2 * g (j,u)) (3 * g (k,v))) ≤
    ∑ j:ZMod m, ∑ k:ZMod m,
      kernel (fiberMass g (3 * k - 2 * j)) (2 * fiberMass g j) (3 * fiberMass g k)
  apply Finset.sum_le_sum
  intro j _
  rw [Finset.sum_comm]
  apply Finset.sum_le_sum
  intro k _
  have h:=FiniteKernelSum.coefficient_kernel_sum h2 h3
    (fun r => g (3 * k - 2 * j,r)) (fun u => 2 * g (j,u)) (fun v => 3 * g (k,v))
    (fun _ => hg _) (fun _ => mul_nonneg (by norm_num) (hg _))
    (fun _ => mul_nonneg (by norm_num) (hg _))
  simpa only [fiberMass, ← Finset.mul_sum] using h
theorem mass_equiv (e:ZMod q ≃+* ZMod m × ZMod n) (g:ZMod q → ℝ) :
    mass (fun x => g (e.symm x)) = mass g:=e.symm.toEquiv.sum_comp g
private def zz20:"s0014"="s0014":=by decide+kernel
theorem profile_equiv (e:ZMod q ≃+* ZMod m × ZMod n) (g:ZMod q → ℝ) :
    profileFunctional g = ∑ j:ZMod m × ZMod n, ∑ k:ZMod m × ZMod n,
      kernel (g (e.symm (3 * k - 2 * j))) (2 * g (e.symm j)) (3 * g (e.symm k)):=by
  have he (j k:ZMod m × ZMod n):e.symm (3 * k - 2 * j) =
      3 * e.symm k - 2 * e.symm j:=by
    simp only [map_sub,map_mul,map_ofNat]
  unfold profileFunctional
  rw [← e.symm.toEquiv.sum_comp (fun j:ZMod q =>
    ∑ k:ZMod q,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k))]
  apply Finset.sum_congr rfl
  intro j _
  change (∑ k:ZMod q,kernel (g (3 * k - 2 * e.symm j))
    (2 * g (e.symm j)) (3 * g k)) = _
  rw [← e.symm.toEquiv.sum_comp (fun k:ZMod q =>
    kernel (g (3 * k - 2 * e.symm j)) (2 * g (e.symm j)) (3 * g k))]
  simp only [he]
  rfl
theorem profileFunctional_le_fiber (e:ZMod q ≃+* ZMod m × ZMod n)
    (h2:Nat.Coprime 2 n) (h3:Nat.Coprime 3 n) (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i) :
    profileFunctional g ≤ profileFunctional (fiberMass (fun x => g (e.symm x))):=by
  rw [profile_equiv e g]
  exact product_profile_le h2 h3 (fun x => g (e.symm x)) (fun _ => hg _)
theorem bound_of_equiv (e:ZMod q ≃+* ZMod m × ZMod n)
    (h2:Nat.Coprime 2 n) (h3:Nat.Coprime 3 n)
    (hb:∀ f:ZMod m → ℝ,(∀ i,0 ≤ f i) → profileFunctional f ≤ 2 * mass f ^ 2)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):profileFunctional g ≤ 2 * mass g ^ 2:=by
  have h:=(profileFunctional_le_fiber e h2 h3 g hg).trans
    (hb _ (fiberMass_nonneg _ (fun _ => hg _)))
  rwa [mass_fiberMass,mass_equiv e g] at h
end Green24Proof.ProfileCoprimeCollapse
private def zz1996:"s07cc"="s07cc":=by decide+kernel
end 
section 
namespace Green24Proof.QuadraticCertificates
abbrev Linear:=Fin 4 → ℚ
abbrev Quadratic:=Fin 4 → Fin 4 → ℚ
abbrev Point:=Fin 4 → ℝ
def linearEq (a b:Linear):Bool:=(List.finRange 4).all fun i => a i == b i
theorem linearEq_eq_true (a b:Linear):linearEq a b = true ↔ a = b:=by
  simp only [linearEq,List.all_eq_true,List.mem_finRange,forall_true_left,beq_iff_eq]
  exact ⟨funext,fun h i => congrFun h i⟩
def quadraticEq (Q R:Quadratic):Bool:=(List.finRange 4).all fun i => linearEq (Q i) (R i)
private def zz21:"s0015"="s0015":=by decide+kernel
theorem quadraticEq_eq_true (Q R:Quadratic):quadraticEq Q R = true ↔ Q = R:=by
  simp only [quadraticEq,List.all_eq_true,List.mem_finRange,forall_true_left,linearEq_eq_true]
  exact ⟨funext,fun h i => congrFun h i⟩
def linearEval (a:Linear) (x:Point):ℝ:=∑ i,(a i:ℝ) * x i
def quadraticEval (Q:Quadratic) (x:Point):ℝ :=
  ∑ i, ∑ j,(Q i j:ℝ) * x i * x j
def product (a b:Linear):Quadratic:=fun i j => a i * b j
theorem linearEval_zero (x:Point):linearEval 0 x = 0:=by simp [linearEval]
theorem linearEval_neg (a:Linear) (x:Point):linearEval (-a) x = -linearEval a x:=by
  simp [linearEval,Finset.sum_neg_distrib]
theorem linearEval_add (a b:Linear) (x:Point) :
    linearEval (a + b) x = linearEval a x + linearEval b x:=by
  simp [linearEval,add_mul,Finset.sum_add_distrib]
private def zz22:"s0016"="s0016":=by decide+kernel
theorem linearEval_smul (c:ℚ) (a:Linear) (x:Point) :
    linearEval (c • a) x = (c:ℝ) * linearEval a x:=by
  simp [linearEval,mul_assoc,Finset.mul_sum]
theorem quadraticEval_zero (x:Point):quadraticEval 0 x = 0:=by simp [quadraticEval]
theorem quadraticEval_add (Q R:Quadratic) (x:Point) :
    quadraticEval (Q + R) x = quadraticEval Q x + quadraticEval R x:=by
  simp [quadraticEval,add_mul,Finset.sum_add_distrib]
theorem quadraticEval_smul (c:ℚ) (Q:Quadratic) (x:Point) :
    quadraticEval (c • Q) x = (c:ℝ) * quadraticEval Q x:=by
  simp [quadraticEval,mul_assoc,Finset.mul_sum]
private def zz23:"s0017"="s0017":=by decide+kernel
theorem quadraticEval_product (a b:Linear) (x:Point) :
    quadraticEval (product a b) x = linearEval a x * linearEval b x:=by
  simp only [quadraticEval,product,Rat.cast_mul,linearEval,Finset.sum_mul,Finset.mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro j _
  ring
abbrev Combination (n:ℕ):=List (ℚ × Fin n)
def combine {n:ℕ} (C:Fin n → Linear) (w:Combination n):Linear :=
  (w.map fun t => t.1 • C t.2).sum
def nonnegativeWeights {n:ℕ} (w:Combination n):Bool :=
  w.all fun t => decide (0 ≤ t.1)
theorem combine_nonneg {n:ℕ} (C:Fin n → Linear) (w:Combination n) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:nonnegativeWeights w = true) :
    0 ≤ linearEval (combine C w) x:=by
  induction w with
  | nil => simp [combine,linearEval_zero]
  | cons t ts ih =>
    simp only [nonnegativeWeights,List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [combine,List.map_cons,List.sum_cons,linearEval_add,linearEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (hC t.2)) (ih hw.2)
inductive NonnegativeTerm (n:ℕ) where
  | square (a:Linear)
  | pair (i j:Fin n)
def termMatrix {n:ℕ} (C:Fin n → Linear):NonnegativeTerm n → Quadratic
  | .square a => product a a
  | .pair i j => product (C i) (C j)
theorem termMatrix_nonneg {n:ℕ} (C:Fin n → Linear) (t:NonnegativeTerm n)
    (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termMatrix C t) x:=by
  cases t with
  | square a => simpa only [termMatrix,quadraticEval_product, ← sq] using sq_nonneg (linearEval a x)
  | pair i j => simpa only [termMatrix,quadraticEval_product] using mul_nonneg (hC i) (hC j)
abbrev Decomposition (n:ℕ):=List (ℚ × NonnegativeTerm n)
def decompositionMatrix {n:ℕ} (C:Fin n → Linear) (d:Decomposition n):Quadratic :=
  (d.map fun t => t.1 • termMatrix C t.2).sum
def decompositionCheck {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (d:Decomposition n):Bool :=
  (d.all fun t => decide (0 ≤ t.1)) && quadraticEq (decompositionMatrix C d) Q
theorem decomposition_nonneg {n:ℕ} (C:Fin n → Linear) (d:Decomposition n) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun t => decide (0 ≤ t.1)) = true) :
    0 ≤ quadraticEval (decompositionMatrix C d) x:=by
  induction d with
  | nil => simp [decompositionMatrix,quadraticEval_zero]
  | cons t ts ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionMatrix,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (termMatrix_nonneg C t.2 x hC)) (ih hw.2)
private def zz24:"s0018"="s0018":=by decide+kernel
theorem decompositionCheck_sound {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (d:Decomposition n) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:decompositionCheck C Q d = true):0 ≤ quadraticEval Q x:=by
  simp only [decompositionCheck,Bool.and_eq_true,quadraticEq_eq_true] at h
  rw [← h.2]
  exact decomposition_nonneg C d x hC h.1
abbrev Hinges:=List (ℚ × Linear)
def hingeEval (hs:Hinges) (x:Point):ℝ :=
  (hs.map fun t => (t.1:ℝ) * max (linearEval t.2 x) 0 ^ 2).sum
inductive Certificate:ℕ → Type where
  | leaf {n:ℕ} (d:Decomposition n):Certificate n
  | split {n:ℕ} (positive negative:Certificate (n + 1)):Certificate n
  | positive {n:ℕ} (w:Combination n) (next:Certificate (n + 1)):Certificate n
  | negative {n:ℕ} (w:Combination n) (next:Certificate (n + 1)):Certificate n
def check {n:ℕ} (cert:Certificate n) (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .leaf d,[] => decompositionCheck C Q d
  | .split p m,(c,a) :: hs =>
      check p (Fin.cons a C) (Q + c • product a a) hs &&
      check m (Fin.cons (-a) C) Q hs
  | .positive w p,(c,a) :: hs =>
      nonnegativeWeights w && linearEq (combine C w) a &&
      check p (Fin.cons a C) (Q + c • product a a) hs
  | .negative w m,(_,a) :: hs =>
      nonnegativeWeights w && linearEq (combine C w) (-a) &&
      check m (Fin.cons (-a) C) Q hs
  | _,_ => false
theorem check_split_valid {n:ℕ} (p m:Certificate (n + 1)) (C:Fin n → Linear)
    (Q:Quadratic) (c:ℚ) (a:Linear) (hs:Hinges)
    (hp:check p (Fin.cons a C) (Q + c • product a a) hs = true)
    (hm:check m (Fin.cons (-a) C) Q hs = true) :
    check (.split p m) C Q ((c,a) :: hs) = true:=by
  simp only [check,hp,hm,Bool.and_true]
theorem check_positive_valid {n:ℕ} (w:Combination n) (p:Certificate (n + 1))
    (C:Fin n → Linear) (Q:Quadratic) (c:ℚ) (a:Linear) (hs:Hinges)
    (hw:nonnegativeWeights w = true) (ha:combine C w = a)
    (hp:check p (Fin.cons a C) (Q + c • product a a) hs = true) :
    check (.positive w p) C Q ((c,a) :: hs) = true:=by
  simp only [check,Bool.and_eq_true,linearEq_eq_true]
  exact ⟨⟨hw,ha⟩,hp⟩
theorem check_negative_valid {n:ℕ} (w:Combination n) (m:Certificate (n + 1))
    (C:Fin n → Linear) (Q:Quadratic) (c:ℚ) (a:Linear) (hs:Hinges)
    (hw:nonnegativeWeights w = true) (ha:combine C w = -a)
    (hm:check m (Fin.cons (-a) C) Q hs = true) :
    check (.negative w m) C Q ((c,a) :: hs) = true:=by
  simp only [check,Bool.and_eq_true,linearEq_eq_true]
  exact ⟨⟨hw,ha⟩,hm⟩
private def zz25:"s0019"="s0019":=by decide+kernel
theorem cons_constraints {n:ℕ} (C:Fin n → Linear) (a:Linear) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (ha:0 ≤ linearEval a x) :
    ∀ i:Fin (n + 1),0 ≤ linearEval ((Fin.cons a C:Fin (n + 1) → Linear) i) x:=by
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · simpa using ha
  · simpa using hC j
theorem positive_step (Q:Quadratic) (c:ℚ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:0 ≤ linearEval a x)
    (h:0 ≤ quadraticEval (Q + c • product a a) x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_left ha,quadraticEval_add,
    quadraticEval_smul,quadraticEval_product,pow_two,add_assoc] using h
theorem negative_step (Q:Quadratic) (c:ℚ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:linearEval a x ≤ 0) (h:0 ≤ quadraticEval Q x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_right ha,zero_pow (by decide:2 ≠ 0),
    mul_zero,zero_add] using h
theorem check_sound {n:ℕ} (cert:Certificate n) (C:Fin n → Linear)
    (Q:Quadratic) (hs:Hinges) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check cert C Q hs = true):0 ≤ quadraticEval Q x + hingeEval hs x:=by
  induction cert generalizing Q hs with
  | leaf d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q d x hC h
    | cons t ts => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
          (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a ts x (le_of_not_ge ha)
          (hm (Fin.cons (-a) C) Q ts (cons_constraints C (-a) x hC ha') h.2)
  | positive w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true,linearEq_eq_true] at h
      have ha:=combine_nonneg C w x hC h.1.1
      rw [h.1.2] at ha
      exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
        (cons_constraints C a x hC ha) h.2)
  | negative w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true,linearEq_eq_true] at h
      have ha:=combine_nonneg C w x hC h.1.1
      rw [h.1.2] at ha
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a ts x ha' (hm (Fin.cons (-a) C) Q ts
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.QuadraticCertificates
private def zz1997:"s07cd"="s07cd":=by decide+kernel
end 
section 
namespace Green24Proof.IntegerQuadraticCertificates
abbrev Linear:=Fin 4 → ℤ
abbrev Quadratic:=Fin 4 → Fin 4 → ℤ
abbrev Point:=Fin 4 → ℝ
def linearEq (a b:Linear):Bool:=(List.finRange 4).all fun i => a i == b i
private def zz26:"s001a"="s001a":=by decide+kernel
theorem linearEq_eq_true (a b:Linear):linearEq a b = true ↔ a = b:=by
  simp only [linearEq,List.all_eq_true,List.mem_finRange,forall_true_left,beq_iff_eq]
  exact ⟨funext,fun h i => congrFun h i⟩
def quadraticEq (Q R:Quadratic):Bool:=(List.finRange 4).all fun i => linearEq (Q i) (R i)
theorem quadraticEq_eq_true (Q R:Quadratic):quadraticEq Q R = true ↔ Q = R:=by
  simp only [quadraticEq,List.all_eq_true,List.mem_finRange,forall_true_left,linearEq_eq_true]
  exact ⟨funext,fun h i => congrFun h i⟩
def linearEval (a:Linear) (x:Point):ℝ:=∑ i,(a i:ℝ) * x i
def quadraticEval (Q:Quadratic) (x:Point):ℝ :=
  ∑ i, ∑ j,(Q i j:ℝ) * x i * x j
def product (a b:Linear):Quadratic:=fun i j => a i * b j
theorem linearEval_zero (x:Point):linearEval 0 x = 0:=by simp [linearEval]
theorem linearEval_neg (a:Linear) (x:Point):linearEval (-a) x = -linearEval a x:=by
  simp [linearEval,Finset.sum_neg_distrib]
private def zz27:"s001b"="s001b":=by decide+kernel
theorem linearEval_add (a b:Linear) (x:Point) :
    linearEval (a + b) x = linearEval a x + linearEval b x:=by
  simp [linearEval,add_mul,Finset.sum_add_distrib]
theorem linearEval_smul (c:ℤ) (a:Linear) (x:Point) :
    linearEval (c • a) x = (c:ℝ) * linearEval a x:=by
  simp [linearEval,mul_assoc,Finset.mul_sum]
theorem quadraticEval_zero (x:Point):quadraticEval 0 x = 0:=by simp [quadraticEval]
theorem quadraticEval_add (Q R:Quadratic) (x:Point) :
    quadraticEval (Q + R) x = quadraticEval Q x + quadraticEval R x:=by
  simp [quadraticEval,add_mul,Finset.sum_add_distrib]
private def zz28:"s001c"="s001c":=by decide+kernel
theorem quadraticEval_smul (c:ℤ) (Q:Quadratic) (x:Point) :
    quadraticEval (c • Q) x = (c:ℝ) * quadraticEval Q x:=by
  simp [quadraticEval,mul_assoc,Finset.mul_sum]
theorem quadraticEval_product (a b:Linear) (x:Point) :
    quadraticEval (product a b) x = linearEval a x * linearEval b x:=by
  simp only [quadraticEval,product,Int.cast_mul,linearEval,Finset.sum_mul,Finset.mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro j _
  ring
abbrev Combination (n:ℕ):=List (ℤ × Fin n)
def combine {n:ℕ} (C:Fin n → Linear) (w:Combination n):Linear :=
  (w.map fun t => t.1 • C t.2).sum
def nonnegativeWeights {n:ℕ} (w:Combination n):Bool :=
  w.all fun t => decide (0 ≤ t.1)
theorem combine_nonneg {n:ℕ} (C:Fin n → Linear) (w:Combination n) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:nonnegativeWeights w = true) :
    0 ≤ linearEval (combine C w) x:=by
  induction w with
  | nil => simp [combine,linearEval_zero]
  | cons t ts ih =>
    simp only [nonnegativeWeights,List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [combine,List.map_cons,List.sum_cons,linearEval_add,linearEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (hC t.2)) (ih hw.2)
inductive NonnegativeTerm (n:ℕ) where
  | square (a:Linear)
  | pair (i j:Fin n)
def termMatrix {n:ℕ} (C:Fin n → Linear):NonnegativeTerm n → Quadratic
  | .square a => product a a
  | .pair i j => product (C i) (C j)
theorem termMatrix_nonneg {n:ℕ} (C:Fin n → Linear) (t:NonnegativeTerm n)
    (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termMatrix C t) x:=by
  cases t with
  | square a => simpa only [termMatrix,quadraticEval_product, ← sq] using sq_nonneg (linearEval a x)
  | pair i j => simpa only [termMatrix,quadraticEval_product] using mul_nonneg (hC i) (hC j)
abbrev Decomposition (n:ℕ):=List (ℤ × NonnegativeTerm n)
def decompositionMatrix {n:ℕ} (C:Fin n → Linear) (d:Decomposition n):Quadratic :=
  (d.map fun t => t.1 • termMatrix C t.2).sum
def decompositionCheck {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n):Bool :=
  decide (0 < s) && (d.all fun t => decide (0 ≤ t.1)) &&
    quadraticEq (decompositionMatrix C d) (s • Q)
private def zz29:"s001d"="s001d":=by decide+kernel
theorem decomposition_nonneg {n:ℕ} (C:Fin n → Linear) (d:Decomposition n) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun t => decide (0 ≤ t.1)) = true) :
    0 ≤ quadraticEval (decompositionMatrix C d) x:=by
  induction d with
  | nil => simp [decompositionMatrix,quadraticEval_zero]
  | cons t ts ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionMatrix,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (termMatrix_nonneg C t.2 x hC)) (ih hw.2)
theorem decompositionCheck_sound {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:decompositionCheck C Q s d = true):0 ≤ quadraticEval Q x:=by
  simp only [decompositionCheck,Bool.and_eq_true,quadraticEq_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d x hC h.1.2
  rw [h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
def combinationCheck {n:ℕ} (C:Fin n → Linear) (s:ℤ) (w:Combination n)
    (a:Linear):Bool :=
  decide (0 < s) && nonnegativeWeights w && linearEq (combine C w) (s • a)
theorem combinationCheck_sound {n:ℕ} (C:Fin n → Linear) (s:ℤ) (w:Combination n)
    (a:Linear) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:combinationCheck C s w a = true):0 ≤ linearEval a x:=by
  simp only [combinationCheck,Bool.and_eq_true,linearEq_eq_true,decide_eq_true_eq] at h
  have ha:=combine_nonneg C w x hC h.1.2
  rw [h.2,linearEval_smul] at ha
  exact nonneg_of_mul_nonneg_right ha (by exact_mod_cast h.1.1:(0:ℝ) < s)
abbrev Hinges:=List (ℤ × Linear)
def hingeEval (hs:Hinges) (x:Point):ℝ :=
  (hs.map fun t => (t.1:ℝ) * max (linearEval t.2 x) 0 ^ 2).sum
inductive Certificate:ℕ → Type where
  | leaf {n:ℕ} (scale:ℤ) (d:Decomposition n):Certificate n
  | split {n:ℕ} (positive negative:Certificate (n + 1)):Certificate n
  | cut {n:ℕ} (a:Linear) (positive negative:Certificate (n + 1)):Certificate n
  | positive {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
  | negative {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
def check {n:ℕ} (cert:Certificate n) (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs => check p (Fin.cons a C) Q hs && check m (Fin.cons (-a) C) Q hs
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (Fin.cons a C) (Q + c • product a a) hs &&
      check m (Fin.cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (Fin.cons a C) (Q + c • product a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) &&
      check m (Fin.cons (-a) C) Q hs
  | _,_ => false
theorem cons_constraints {n:ℕ} (C:Fin n → Linear) (a:Linear) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (ha:0 ≤ linearEval a x) :
    ∀ i:Fin (n + 1),0 ≤ linearEval ((Fin.cons a C:Fin (n + 1) → Linear) i) x:=by
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · simpa using ha
  · simpa using hC j
private def zz30:"s001e"="s001e":=by decide+kernel
theorem positive_step (Q:Quadratic) (c:ℤ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:0 ≤ linearEval a x)
    (h:0 ≤ quadraticEval (Q + c • product a a) x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_left ha,quadraticEval_add,
    quadraticEval_smul,quadraticEval_product,pow_two,add_assoc] using h
theorem negative_step (Q:Quadratic) (c:ℤ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:linearEval a x ≤ 0) (h:0 ≤ quadraticEval Q x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_right ha,zero_pow (by decide:2 ≠ 0),
    mul_zero,zero_add] using h
theorem check_sound {n:ℕ} (cert:Certificate n) (C:Fin n → Linear)
    (Q:Quadratic) (hs:Hinges) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check cert C Q hs = true):0 ≤ quadraticEval Q x + hingeEval hs x:=by
  induction cert generalizing Q hs with
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q s d x hC h
    | cons t ts => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
          (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a ts x (le_of_not_ge ha)
          (hm (Fin.cons (-a) C) Q ts (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (Fin.cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (Fin.cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
        (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a ts x ha' (hm (Fin.cons (-a) C) Q ts
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.IntegerQuadraticCertificates
private def zz1998:"s07ce"="s07ce":=by decide+kernel
end 
section 
open Set Filter MeasureTheory
open scoped Topology
namespace Green24Proof
theorem kernel_eq_positive_parts (a b c:ℝ) :
    kernel a b c = a * b - max (a + b - c) 0 ^ 2 / 4 +
      max (a - b - c) 0 ^ 2 / 4 + max (b - a - c) 0 ^ 2 / 4:=by
  unfold kernel
  by_cases h:a + b ≤ c
  · rw [max_eq_right (by linarith:a + b - c ≤ 0),
      max_eq_left (by linarith:0 ≤ c - a - b)]
    ring
  · rw [max_eq_left (by linarith:0 ≤ a + b - c),
      max_eq_right (by linarith:c - a - b ≤ 0)]
    ring
private def zz31:"s001f"="s001f":=by decide+kernel
theorem negPosSquare_hasDeriv_right (c t:ℝ) :
    HasDerivWithinAt (fun s:ℝ => max (c - s) 0 ^ 2)
      (-2 * max (c - t) 0) (Ioi t) t:=by
  by_cases h:t < c
  · rw [max_eq_left (by linarith:0 ≤ c - t)]
    have hd:=(((hasDerivAt_id t).const_sub c).pow 2).hasDerivWithinAt (s:=Ioi t)
    simp only [Nat.reduceSub,pow_one,id_eq] at hd
    have hd':HasDerivWithinAt (fun s:ℝ => (c - s) ^ 2)
        (-2 * (c - t)) (Ioi t) t:=by
      convert hd using 1 <;> first | rfl | ring
    apply hd'.congr_of_eventuallyEq
    · filter_upwards [nhdsWithin_le_nhds (Iio_mem_nhds h)] with s hs
      rw [max_eq_left (by linarith [show s < c from hs]:0 ≤ c - s)]
    · rw [max_eq_left (by linarith:0 ≤ c - t)]
  · rw [max_eq_right (by linarith:c - t ≤ 0),mul_zero]
    apply (hasDerivWithinAt_const t (Ioi t) (0:ℝ)).congr
    · intro s hs
      rw [max_eq_right (by linarith [show t < s from hs]:c - s ≤ 0)]
      norm_num
    · rw [max_eq_right (by linarith:c - t ≤ 0)]
      norm_num
noncomputable def kernelSlope (a b c:ℝ):ℝ :=
  min b (min c (max ((b + c - a) / 2) 0))
theorem kernelSlope_eq {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    kernelSlope a b c = b - max (a + b - c) 0 / 2 +
      max (a - b - c) 0 / 2 - max (b - a - c) 0 / 2:=by
  unfold kernelSlope
  simp only [min_def,max_def]
  split_ifs <;> linarith
theorem kernel_hasDeriv_right {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    HasDerivWithinAt (fun s:ℝ => kernel s b c) (kernelSlope a b c) (Ioi a) a:=by
  have hd:=(((((hasDerivAt_id a).mul_const b).hasDerivWithinAt.sub
    ((posSquare_hasDeriv_right (c - b) a).div_const 4)).add
    ((posSquare_hasDeriv_right (b + c) a).div_const 4)).add
    ((negPosSquare_hasDeriv_right (b - c) a).div_const 4))
  convert hd using 1 <;> try rfl
  · funext s
    change kernel s b c = s * b - max (s - (c - b)) 0 ^ 2 / 4 +
      max (s - (b + c)) 0 ^ 2 / 4 + max (b - c - s) 0 ^ 2 / 4
    rw [kernel_eq_positive_parts]
    rw [show s - (c - b) = s + b - c by ring,
      show s - (b + c) = s - b - c by ring,
      show b - c - s = b - s - c by ring]
  · rw [kernelSlope_eq ha hb hc]
    rw [show a - (c - b) = a + b - c by ring,
      show a - (b + c) = a - b - c by ring,
      show b - c - a = b - a - c by ring]
    ring
theorem kernel_continuous:Continuous (fun p:ℝ × ℝ × ℝ => kernel p.1 p.2.1 p.2.2):=by
  unfold kernel
  fun_prop
private def zz32:"s0020"="s0020":=by decide+kernel
theorem kernelSlope_continuous (b c:ℝ):Continuous (fun a => kernelSlope a b c):=by
  unfold kernelSlope
  fun_prop
theorem kernelSlope_mono_middle (a c:ℝ):Monotone (fun b => kernelSlope a b c):=by
  intro b d hbd
  unfold kernelSlope
  exact min_le_min hbd (min_le_min_left c (max_le_max_right 0 (by linarith)))
theorem kernel_integral_slope {a d b c:ℝ} (ha:0 ≤ a) (had:a ≤ d)
    (hb:0 ≤ b) (hc:0 ≤ c) :
    (∫ t in a..d,kernelSlope t b c) = kernel d b c - kernel a b c:=by
  apply intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le had
  · unfold kernel
    fun_prop
  · intro t ht
    exact kernel_hasDeriv_right (ha.trans ht.1.le) hb hc
  · exact (kernelSlope_continuous b c).intervalIntegrable _ _
theorem kernel_supermodular {a b c d z:ℝ} (ha:0 ≤ a) (hb:0 ≤ b)
    (hz:0 ≤ z) (hac:a ≤ c) (hbd:b ≤ d) :
    kernel a d z + kernel c b z ≤ kernel a b z + kernel c d z:=by
  have h:=intervalIntegral.integral_mono_on (μ:=volume) hac
    ((kernelSlope_continuous b z).intervalIntegrable a c)
    ((kernelSlope_continuous d z).intervalIntegrable a c)
    (fun t _ => kernelSlope_mono_middle t z hbd)
  rw [kernel_integral_slope ha hac hb hz,
    kernel_integral_slope ha hac (hb.trans hbd) hz] at h
  linarith
end Green24Proof
end 
section 
/-
Copyright (c) 2022 Mantas Bakšys. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mantas Bakšys
The finite swap argument below adapts Mathlib's
`MonovaryOn.sum_smul_comp_perm_le_sum_smul` to a supermodular kernel.
-/
namespace Green24Proof
open Finset Equiv Equiv.Perm Function
open scoped NNReal
private def zz33:"s0021"="s0021":=by decide+kernel
theorem supermodular_rearrangement_on {ι α β:Type*} [LinearOrder α] [LinearOrder β]
    (F:α → β → ℝ)
    (hF:∀ a a' b b',a ≤ a' → b ≤ b' → F a b' + F a' b ≤ F a b + F a' b')
    {s:Finset ι} {σ:Equiv.Perm ι} {f:ι → α} {g:ι → β}
    (hfg:MonovaryOn f g s) (hσ:{x | σ x ≠ x} ⊆ s) :
    ∑ i ∈ s,F (f i) (g (σ i)) ≤ ∑ i ∈ s,F (f i) (g i):=by
  classical
  induction s using induction_on_max_value fun i => toLex (g i,f i) generalizing σ with
  | empty => simp only [le_rfl,Finset.sum_empty]
  | insert a s has hamax hind => ?_
  set τ:Perm ι:=σ.trans (swap a (σ a)) with hτ
  have hτs:{x | τ x ≠ x} ⊆ s:=by
    intro x hx
    simp only [τ,Ne,Set.mem_ofPred_eq,Equiv.swap_comp_apply] at hx
    split_ifs at hx with h₁ h₂
    · obtain rfl | hax:=eq_or_ne x a
      · contradiction
      · exact mem_of_mem_insert_of_ne (hσ fun h => hax <| h.symm.trans h₁) hax
    · exact (hx <| σ.injective h₂.symm).elim
    · exact mem_of_mem_insert_of_ne (hσ hx) (ne_of_apply_ne _ h₂)
  specialize hind (hfg.subset <| Finset.subset_insert _ _) hτs
  simp_rw [sum_insert has]
  grw [← hind]
  obtain hσa | hσa:=eq_or_ne a (σ a)
  · rw [hτ, ← hσa,swap_self,trans_refl]
  have h1s:σ.symm a ∈ s:=by
    rw [Ne, ← inv_eq_iff_eq] at hσa
    refine mem_of_mem_insert_of_ne (hσ fun h => hσa ?_) hσa
    rwa [apply_symm_apply,eq_comm] at h
  simp only [← s.sum_erase_add _ h1s,add_comm]
  rw [← add_assoc, ← add_assoc]
  simp only [hτ,swap_apply_left,Function.comp_apply,Equiv.coe_trans,apply_symm_apply]
  refine add_le_add ?_ (sum_congr rfl fun x hx => ?_).le
  · rw [add_comm (F (f a) _),add_comm (F (f a) _)]
    apply hF
    · specialize hamax (σ.symm a) h1s
      rw [Prod.Lex.toLex_le_toLex] at hamax
      rcases hamax with hamax | hamax
      · exact hfg (mem_insert_of_mem h1s) (mem_insert_self _ _) hamax
      · exact hamax.2
    · specialize hamax (σ a) (mem_of_mem_insert_of_ne (hσ <| σ.injective.ne hσa.symm) hσa.symm)
      rw [Prod.Lex.toLex_le_toLex] at hamax
      rcases hamax with hamax | hamax
      · exact hamax.le
      · exact hamax.1.le
  · rw [mem_erase,Ne,eq_symm_apply] at hx
    rw [swap_apply_of_ne_of_ne hx.1 (σ.injective.ne _)]
    rintro rfl
    exact has hx.2
theorem supermodular_rearrangement {ι α β:Type*} [Fintype ι]
    [LinearOrder α] [LinearOrder β] (F:α → β → ℝ)
    (hF:∀ a a' b b',a ≤ a' → b ≤ b' → F a b' + F a' b ≤ F a b + F a' b')
    {f:ι → α} {g:ι → β} (hfg:Monovary f g) (σ:Equiv.Perm ι) :
    ∑ i,F (f i) (g (σ i)) ≤ ∑ i,F (f i) (g i) :=
  supermodular_rearrangement_on F hF (hfg.monovaryOn _) (fun _ _ => mem_univ _)
theorem kernel_rearrangement {ι:Type*} [Fintype ι] (u:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (σ:Equiv.Perm ι) {z:ℝ} (hz:0 ≤ z) :
    (∑ i,kernel (u i) (2 * u (σ i)) z) ≤ ∑ i,kernel (u i) (2 * u i) z:=by
  let f:ι → ℝ≥0:=fun i => ⟨u i,hu i⟩
  have hfg:Monovary f f:=fun _ _ h => le_of_lt h
  exact supermodular_rearrangement (fun a b:ℝ≥0 => kernel a (2 * b) z)
    (fun a a' b b' ha hb => kernel_supermodular a.coe_nonneg
      (mul_nonneg (by norm_num) b.coe_nonneg) hz ha (by exact_mod_cast mul_le_mul_of_nonneg_left hb (by norm_num:(0:ℝ≥0) ≤ 2)))
    hfg σ
theorem exists_sorted_equiv {ι:Type*} [Fintype ι] (u:ι → ℝ) :
    ∃ e:Fin (Fintype.card ι) ≃ ι,Monotone (fun i => u (e i)):=by
  classical
  let idx:=Fintype.equivFin ι
  let:LinearOrder ι:=LinearOrder.lift'
    (fun i => toLex (u i,idx i)) (by
      intro i j h
      exact idx.injective (congrArg (fun p:ℝ ×ₗ Fin (Fintype.card ι) => (ofLex p).2) h))
  let e:=monoEquivOfFin ι rfl
  refine ⟨e.toEquiv, ?_⟩
  intro i j hij
  have h:=e.monotone hij
  change toLex (u (e i),idx (e i)) ≤ toLex (u (e j),idx (e j)) at h
  rw [Prod.Lex.toLex_le_toLex] at h
  exact h.elim (fun h => h.le) (fun h => h.1.le)
private def zz34:"s0022"="s0022":=by decide+kernel
theorem kernel_two_profiles_rearrangement {ι:Type*} [Fintype ι]
    (u v:ι → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (eu ev:Fin (Fintype.card ι) ≃ ι)
    (heu:Monotone (fun i => u (eu i))) (hev:Monotone (fun i => v (ev i)))
    (σ:Equiv.Perm ι) {z:ℝ} (hz:0 ≤ z) :
    (∑ i,kernel (u (σ i)) (2 * v i) z) ≤
      ∑ i,kernel (u (eu i)) (2 * v (ev i)) z:=by
  let f:Fin (Fintype.card ι) → ℝ≥0:=fun i => ⟨u (eu i),hu _⟩
  let g:Fin (Fintype.card ι) → ℝ≥0:=fun i => ⟨v (ev i),hv _⟩
  have hf:Monotone f:=heu
  have hg:Monotone g:=hev
  have h:=supermodular_rearrangement (fun a b:ℝ≥0 => kernel a (2 * b) z)
    (fun a a' b b' ha hb => kernel_supermodular a.coe_nonneg
      (mul_nonneg (by norm_num) b.coe_nonneg) hz ha
      (by exact_mod_cast mul_le_mul_of_nonneg_left hb (by norm_num:(0:ℝ≥0) ≤ 2)))
    (hf.monovary hg) ((eu.trans σ.symm).trans ev.symm)
  have heq:=(eu.trans σ.symm).sum_comp (fun i => kernel (u (σ i)) (2 * v i) z)
  simp only [Equiv.trans_apply,Equiv.apply_symm_apply] at heq
  rw [← heq]
  change (∑ i,kernel (u (eu i)) (2 * v (ev (((eu.trans σ.symm).trans ev.symm) i))) z) ≤
    ∑ i,kernel (u (eu i)) (2 * v (ev i)) z at h
  simpa only [Equiv.trans_apply,Equiv.apply_symm_apply] using h
end Green24Proof
end 
section 
namespace Green24Proof
theorem kernel_zero_first {b c:ℝ} (hb:0 ≤ b) (hc:0 ≤ c):kernel 0 b c = 0:=by
  have h₁:=kernel_nonneg (le_refl 0) hb hc
  have h₂:=kernel_le_product (le_refl 0) hb hc
  linarith
theorem kernel_zero_middle {a c:ℝ} (ha:0 ≤ a) (hc:0 ≤ c):kernel a 0 c = 0:=by
  rw [kernel_swap12,kernel_zero_first ha hc]
theorem kernel_zero_last {a b:ℝ} (ha:0 ≤ a) (hb:0 ≤ b):kernel a b 0 = 0:=by
  rw [kernel_cycle,kernel_swap12,kernel_zero_first hb ha]
private def zz35:"s0023"="s0023":=by decide+kernel
theorem kernel_diagonal_pair_ordered {x y:ℝ} (hy:0 ≤ y) (hyx:y ≤ x) :
    kernel x (2 * x) (3 * y) + kernel y (2 * y) (3 * x) = 4 * x * y - rho x y:=by
  rw [kernel_eq_product hy (by positivity) (by linarith:y + 2 * y ≤ 3 * x)]
  by_cases h:x ≤ 3 * y
  · rw [rho_eq_balanced hyx h,kernel_eq_triangle (by linarith) (by linarith)
      (by linarith)]
    ring
  · rw [rho_eq_unbalanced hyx (le_of_not_ge h),kernel_swap23,
      kernel_eq_product (hy.trans hyx) (by positivity) (by linarith)]
    ring
theorem kernel_diagonal_pair {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    kernel x (2 * x) (3 * y) + kernel y (2 * y) (3 * x) = 4 * x * y - rho x y:=by
  rcases le_total y x with h | h
  · exact kernel_diagonal_pair_ordered hy h
  · have heq:=kernel_diagonal_pair_ordered hx h
    rw [rho_comm y x] at heq
    nlinarith [heq]
theorem kernel_mixed_linear {b s d:ℝ} (hb:0 ≤ b) (hs:0 ≤ s) (hd:0 ≤ d) :
    kernel b s (3 * d) ≤ 2 * d * s + d * max (b - 2 * d) 0:=by
  by_cases h:b ≤ 2 * d
  · rw [max_eq_right (by linarith:b - 2 * d ≤ 0)]
    have hk:=kernel_le_product hb hs (by positivity:0 ≤ 3 * d)
    nlinarith [mul_nonneg hs (by linarith:0 ≤ 2 * d - b)]
  rw [max_eq_left (by linarith:0 ≤ b - 2 * d)]
  by_cases h₁:b + s ≤ 3 * d
  · rw [kernel_eq_product hb hs h₁]
    nlinarith [mul_nonneg (by linarith:0 ≤ b - 2 * d) (by linarith:0 ≤ d - s)]
  by_cases h₂:b + 3 * d ≤ s
  · rw [kernel_swap23,kernel_eq_product hb (by positivity) h₂]
    nlinarith [mul_nonneg hd (by linarith:0 ≤ s - b - d)]
  by_cases h₃:s + 3 * d ≤ b
  · rw [kernel_cycle,kernel_eq_product hs (by positivity) h₃]
    nlinarith [mul_nonneg hd (by linarith:0 ≤ b - s - 2 * d)]
  rw [kernel_eq_triangle (le_of_not_ge h₃) (le_of_not_ge h₂) (le_of_not_ge h₁)]
  nlinarith [sq_nonneg (s - b + d)]
theorem rho_ge_mixed_linear {b d:ℝ} (hb:0 ≤ b) (hd:0 ≤ d) :
    d * max (b - 2 * d) 0 ≤ rho b d:=by
  by_cases h:b ≤ 2 * d
  · rw [max_eq_right (by linarith:b - 2 * d ≤ 0),mul_zero]
    exact rho_nonneg hb hd
  rw [max_eq_left (by linarith:0 ≤ b - 2 * d)]
  have hdb:d ≤ b:=by linarith
  by_cases h':b ≤ 3 * d
  · rw [rho_eq_balanced hdb h']
    nlinarith [sq_nonneg (b - 3 * d)]
  · rw [rho_eq_unbalanced hdb (le_of_not_ge h')]
    ring_nf
    exact le_refl _
private def zz36:"s0024"="s0024":=by decide+kernel
theorem kernel_mixed_bound {a b d:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hd:0 ≤ d) :
    kernel b (2 * a) (3 * d) ≤ 4 * a * d + rho b d:=by
  have h₁:=kernel_mixed_linear hb (by positivity:0 ≤ 2 * a) hd
  have h₂:=rho_ge_mixed_linear hb hd
  nlinarith
noncomputable def kernelError (a b c:ℝ):ℝ:=2 * a * b - kernel a (2 * b) (3 * c)
theorem kernelError_identity (a b c:ℝ) :
    4 * kernelError a b c = max (a + 2 * b - 3 * c) 0 ^ 2 -
      max (a - 2 * b - 3 * c) 0 ^ 2 - max (2 * b - a - 3 * c) 0 ^ 2:=by
  unfold kernelError
  rw [kernel_eq_positive_parts]
  ring
theorem kernelError_common_add (a b c:ℝ) {t:ℝ} (ht:0 ≤ t) :
    kernelError a b c ≤ kernelError (a + t) (b + t) (c + t):=by
  have h₁:=kernelError_identity a b c
  have h₂:=kernelError_identity (a + t) (b + t) (c + t)
  rw [show a + t + 2 * (b + t) - 3 * (c + t) = a + 2 * b - 3 * c by ring] at h₂
  have hleft:max (a + t - 2 * (b + t) - 3 * (c + t)) 0 ^ 2 ≤
      max (a - 2 * b - 3 * c) 0 ^ 2:=by
    exact pow_le_pow_left₀ (le_max_right _ _) (max_le_max_right 0 (by linarith)) 2
  have hright:max (2 * (b + t) - (a + t) - 3 * (c + t)) 0 ^ 2 ≤
      max (2 * b - a - 3 * c) 0 ^ 2:=by
    exact pow_le_pow_left₀ (le_max_right _ _) (max_le_max_right 0 (by linarith)) 2
  linarith
noncomputable def mixedPair (a b c d:ℝ):ℝ :=
  kernel a (2 * a) (3 * c) + kernel a (2 * b) (3 * c) +
    kernel b (2 * a) (3 * d) + kernel b (2 * b) (3 * d)
noncomputable def eightSlack (a b c d:ℝ):ℝ :=
  4 * (a + b) * (c + d) - mixedPair a b c d - mixedPair c d a b
theorem eightSlack_errors (a b c d:ℝ) :
    eightSlack a b c d = -2 * (a + b - c - d) ^ 2 +
      kernelError a a c + kernelError a b c + kernelError b a d + kernelError b b d +
      kernelError c c a + kernelError c d a + kernelError d c b + kernelError d d b:=by
  unfold eightSlack mixedPair kernelError
  ring
private def zz37:"s0025"="s0025":=by decide+kernel
theorem eightSlack_common_add (a b c d:ℝ) {t:ℝ} (ht:0 ≤ t) :
    eightSlack a b c d ≤ eightSlack (a + t) (b + t) (c + t) (d + t):=by
  rw [eightSlack_errors,eightSlack_errors]
  rw [show a + t + (b + t) - (c + t) - (d + t) = a + b - c - d by ring]
  linarith [kernelError_common_add a a c ht,kernelError_common_add a b c ht,
    kernelError_common_add b a d ht,kernelError_common_add b b d ht,
    kernelError_common_add c c a ht,kernelError_common_add c d a ht,
    kernelError_common_add d c b ht,kernelError_common_add d d b ht]
theorem eightSlack_swap_pairs (a b c d:ℝ):eightSlack a b c d = eightSlack c d a b:=by
  unfold eightSlack
  ring
theorem eightSlack_swap_both (a b c d:ℝ):eightSlack a b c d = eightSlack b a d c:=by
  unfold eightSlack mixedPair
  ring
theorem eightSlack_boundary {a b d:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hd:0 ≤ d) :
    0 ≤ eightSlack a b 0 d:=by
  unfold eightSlack mixedPair
  simp only [mul_zero,zero_add,kernel_zero_last ha (by positivity:0 ≤ 2 * a),
    kernel_zero_last ha (by positivity:0 ≤ 2 * b),
    kernel_zero_first (by positivity:0 ≤ 2 * d) (by positivity:0 ≤ 3 * a),
    kernel_zero_first (le_refl 0) (by positivity:0 ≤ 3 * a),
    kernel_zero_middle hd (by positivity:0 ≤ 3 * b)]
  have h₁:=kernel_diagonal_pair hb hd
  have h₂:=kernel_mixed_bound ha hb hd
  linarith
private def zz38:"s0026"="s0026":=by decide+kernel
theorem mixedPair_eight_term {a b c d:ℝ}
    (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) (hd:0 ≤ d) :
    mixedPair a b c d + mixedPair c d a b ≤ 4 * (a + b) * (c + d):=by
  suffices 0 ≤ eightSlack a b c d by unfold eightSlack at this; linarith
  have hmin (w x y z:ℝ) (hy:0 ≤ y) (hyx:y ≤ x) (hyw:y ≤ w) (hyz:y ≤ z) :
      0 ≤ eightSlack w x y z:=by
    have h₁:=eightSlack_boundary (sub_nonneg.mpr hyw) (sub_nonneg.mpr hyx)
      (sub_nonneg.mpr hyz)
    have h₂:=eightSlack_common_add (w - y) (x - y) 0 (z - y) hy
    simp only [sub_add_cancel,zero_add] at h₂
    exact h₁.trans h₂
  rcases le_total a b with hab | hba <;> rcases le_total c d with hcd | hdc
  · rcases le_total a c with hac | hca
    · rw [eightSlack_swap_pairs]
      exact hmin c d a b ha (hac.trans hcd) hac hab
    · exact hmin a b c d hc (hca.trans hab) hca hcd
  · rcases le_total a d with had | hda
    · rw [eightSlack_swap_pairs]
      exact hmin c d a b ha had (had.trans hdc) hab
    · rw [eightSlack_swap_both]
      exact hmin b a d c hd hda (hda.trans hab) hdc
  · rcases le_total b c with hbc | hcb
    · rw [eightSlack_swap_both,eightSlack_swap_pairs]
      exact hmin d c b a hb hbc (hbc.trans hcd) hba
    · exact hmin a b c d hc hcb (hcb.trans hba) hcd
  · rcases le_total b d with hbd | hdb
    · rw [eightSlack_swap_both,eightSlack_swap_pairs]
      exact hmin d c b a hb (hbd.trans hdc) hbd hba
    · rw [eightSlack_swap_both]
      exact hmin b a d c hd (hdb.trans hba) hdb hdc
end Green24Proof
end 
section 
namespace Green24Proof
theorem kernel_rearrangement_left {ι:Type*} [Fintype ι] (u:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (σ:Equiv.Perm ι) {z:ℝ} (hz:0 ≤ z) :
    (∑ i,kernel (u (σ i)) (2 * u i) z) ≤ ∑ i,kernel (u i) (2 * u i) z:=by
  have hsum:=σ.symm.sum_comp (fun i => kernel (u (σ i)) (2 * u i) z)
  simp only [Equiv.apply_symm_apply] at hsum
  rw [← hsum]
  exact kernel_rearrangement u hu σ.symm hz
theorem aligned_kernel_sum {ι:Type*} [Fintype ι] (u:ι → ℝ) (hu:∀ i,0 ≤ u i) :
    (∑ i, ∑ j,kernel (u i) (2 * u i) (3 * u j)) = 2 * mass u ^ 2 - energy u:=by
  have hswap:(∑ i, ∑ j,kernel (u j) (2 * u j) (3 * u i)) =
      ∑ i, ∑ j,kernel (u i) (2 * u i) (3 * u j):=Finset.sum_comm
  have hpair:(∑ i, ∑ j,(kernel (u i) (2 * u i) (3 * u j) +
      kernel (u j) (2 * u j) (3 * u i))) = ∑ i, ∑ j,(4 * u i * u j - rho (u i) (u j)):=by
    apply Finset.sum_congr rfl
    intro i _
    exact Finset.sum_congr rfl (fun j _ => kernel_diagonal_pair (hu i) (hu j))
  have hprod:(∑ i, ∑ j,4 * u i * u j) = 4 * mass u ^ 2:=by
    simp only [← Finset.mul_sum, ← Finset.sum_mul]
    unfold mass
    ring
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib] at hpair
  rw [hswap,hprod] at hpair
  unfold energy
  linarith
theorem profileFunctional_le_of_middle_bijective {q:ℕ} [NeZero q]
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (hbij:∀ k:ZMod q,Function.Bijective (fun j:ZMod q => 3 * k - 2 * j)) :
    profileFunctional g ≤ 2 * mass g ^ 2 - energy g:=by
  unfold profileFunctional
  rw [Finset.sum_comm]
  calc
    (∑ k, ∑ j,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k)) ≤
        ∑ k, ∑ j,kernel (g j) (2 * g j) (3 * g k):=by
      apply Finset.sum_le_sum
      intro k _
      exact kernel_rearrangement_left g hg (Equiv.ofBijective _ (hbij k))
        (mul_nonneg (by norm_num) (hg k))
    _ = 2 * mass g ^ 2 - energy g:=by
      rw [Finset.sum_comm]
      exact aligned_kernel_sum g hg
private def zz39:"s0027"="s0027":=by decide+kernel
theorem energy_le_deficit_of_odd {q:ℕ} [NeZero q]
    (hq:Odd q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):energy g ≤ deficit g:=by
  have hu:IsUnit (2:ZMod q):=ZMod.isUnit_prime_of_not_dvd Nat.prime_two
    (by simpa only [← even_iff_two_dvd,Nat.not_even_iff_odd] using hq)
  have hmul:=IsUnit.isUnit_iff_mulLeft_bijective.mp hu
  have hbij (k:ZMod q):Function.Bijective (fun j:ZMod q => 3 * k - 2 * j) :=
    (Equiv.subLeft (3 * k)).bijective.comp hmul
  have h:=profileFunctional_le_of_middle_bijective g hg hbij
  unfold deficit
  linarith
theorem deficit_nonneg_of_odd {q:ℕ} [NeZero q]
    (hq:Odd q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):0 ≤ deficit g :=
  (energy_nonneg hg).trans (energy_le_deficit_of_odd hq g hg)
end Green24Proof
end 
section 
namespace Green24Proof
theorem sorted_pair_sum_bound {ι:Type*} [Fintype ι]
    (u v:ι → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (eu ev:Fin (Fintype.card ι) ≃ ι)
    (heu:Monotone (fun i => u (eu i))) (hev:Monotone (fun i => v (ev i)))
    (σ:ι → Equiv.Perm ι) :
    (∑ k, ∑ j,kernel (u (σ k j)) (2 * v j) (3 * u k)) ≤
      ∑ k, ∑ i,kernel (u (eu i)) (2 * v (ev i)) (3 * u (eu k)):=by
  calc
    _ ≤ ∑ k, ∑ i,kernel (u (eu i)) (2 * v (ev i)) (3 * u k):=by
      exact Finset.sum_le_sum fun k _ => kernel_two_profiles_rearrangement u v hu hv
        eu ev heu hev (σ k) (mul_nonneg (by norm_num) (hu k))
    _ = _:=(eu.sum_comp _).symm
noncomputable def pairedFunctional {ι:Type*} [Fintype ι]
    (u v:ι → ℝ) (σ:ι → Equiv.Perm ι):ℝ :=
  ∑ k, ∑ j,(kernel (u (σ k j)) (2 * u j) (3 * u k) +
    kernel (u (σ k j)) (2 * v j) (3 * u k) +
    kernel (v (σ k j)) (2 * u j) (3 * v k) +
    kernel (v (σ k j)) (2 * v j) (3 * v k))
theorem mixedPair_sum_bound {ι:Type*} [Fintype ι] (u v:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (∑ i, ∑ k,mixedPair (u i) (v i) (u k) (v k)) ≤ 2 * (mass u + mass v) ^ 2:=by
  have h:=Finset.sum_le_sum (s:=Finset.univ) (fun i _ =>
    Finset.sum_le_sum (s:=Finset.univ) (fun k _ =>
      mixedPair_eight_term (hu i) (hv i) (hu k) (hv k)))
  have hswap:(∑ i, ∑ k,mixedPair (u k) (v k) (u i) (v i)) =
      ∑ i, ∑ k,mixedPair (u i) (v i) (u k) (v k):=Finset.sum_comm
  have hprod:(∑ i, ∑ k,4 * (u i + v i) * (u k + v k)) =
      4 * (mass u + mass v) ^ 2:=by
    simp only [← Finset.mul_sum, ← Finset.sum_mul,Finset.sum_add_distrib]
    unfold mass
    ring
  simp only [Finset.sum_add_distrib] at h
  rw [hswap,hprod] at h
  linarith
private def zz40:"s0028"="s0028":=by decide+kernel
theorem pairedFunctional_le {ι:Type*} [Fintype ι] (u v:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (σ:ι → Equiv.Perm ι) :
    pairedFunctional u v σ ≤ 2 * (mass u + mass v) ^ 2:=by
  obtain ⟨eu,heu⟩:=exists_sorted_equiv u
  obtain ⟨ev,hev⟩:=exists_sorted_equiv v
  have h₁:=sorted_pair_sum_bound u u hu hu eu eu heu heu σ
  have h₂:=sorted_pair_sum_bound u v hu hv eu ev heu hev σ
  have h₃:=sorted_pair_sum_bound v u hv hu ev eu hev heu σ
  have h₄:=sorted_pair_sum_bound v v hv hv ev ev hev hev σ
  have hsum:=mixedPair_sum_bound (fun i => u (eu i)) (fun i => v (ev i))
    (fun i => hu _) (fun i => hv _)
  have hmu:mass (fun i => u (eu i)) = mass u:=eu.sum_comp u
  have hmv:mass (fun i => v (ev i)) = mass v:=ev.sum_comp v
  rw [hmu,hmv,Finset.sum_comm] at hsum
  unfold mixedPair at hsum
  unfold pairedFunctional
  simp only [Finset.sum_add_distrib] at hsum ⊢
  linarith
noncomputable def ringFunctional {R:Type*} [Fintype R] [CommRing R] (g:R → ℝ):ℝ :=
  ∑ j, ∑ k,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k)
theorem ringFunctional_equiv {R S:Type*} [Fintype R] [Fintype S]
    [CommRing R] [CommRing S] (e:R ≃+* S) (g:R → ℝ) :
    ringFunctional g = ringFunctional (fun x => g (e.symm x)):=by
  unfold ringFunctional
  rw [← e.symm.toEquiv.sum_comp]
  apply Finset.sum_congr rfl
  intro j _
  rw [← e.symm.toEquiv.sum_comp]
  simp only [map_sub,map_mul,map_ofNat,RingEquiv.toEquiv_eq_coe,RingEquiv.coe_toEquiv]
theorem mass_ringEquiv {R S:Type*} [Fintype R] [Fintype S]
    [CommRing R] [CommRing S] (e:R ≃+* S) (g:R → ℝ) :
    mass g = mass (fun x => g (e.symm x)):=(e.symm.toEquiv.sum_comp g).symm
theorem sum_zmod_two (f:ZMod 2 → ℝ):(∑ i,f i) = f 0 + f 1 :=
  Fin.sum_univ_two f
private def zz41:"s0029"="s0029":=by decide+kernel
theorem productFunctional_eq {R:Type*} [Fintype R] [CommRing R]
    (g:ZMod 2 × R → ℝ) (σ:R → Equiv.Perm R)
    (hσ:∀ k j,σ k j = 3 * k - 2 * j) :
    ringFunctional g = pairedFunctional (fun i => g (0,i)) (fun i => g (1,i)) σ:=by
  have hp (j k:ZMod 2):3 * k - 2 * j = k:=by
    rw [show (3:ZMod 2) = 1 from rfl,show (2:ZMod 2) = 0 from rfl]
    simp only [one_mul,zero_mul,sub_zero]
  unfold ringFunctional pairedFunctional
  simp only [Fintype.sum_prod_type]
  change (∑ r:ZMod 2, ∑ j:R, ∑ s:ZMod 2, ∑ k:R,
    kernel (g (3 * s - 2 * r,3 * k - 2 * j)) (2 * g (r,j)) (3 * g (s,k))) = _
  simp only [hp,sum_zmod_two,Finset.sum_add_distrib,hσ]
  rw [Finset.sum_comm (f:=fun j k:R =>
      kernel (g (0,3 * k - 2 * j)) (2 * g (0,j)) (3 * g (0,k))),
    Finset.sum_comm (f:=fun j k:R =>
      kernel (g (1,3 * k - 2 * j)) (2 * g (0,j)) (3 * g (1,k))),
    Finset.sum_comm (f:=fun j k:R =>
      kernel (g (0,3 * k - 2 * j)) (2 * g (1,j)) (3 * g (0,k))),
    Finset.sum_comm (f:=fun j k:R =>
      kernel (g (1,3 * k - 2 * j)) (2 * g (1,j)) (3 * g (1,k)))]
  ring
theorem productFunctional_le {R:Type*} [Fintype R] [CommRing R]
    (g:ZMod 2 × R → ℝ) (hg:∀ i,0 ≤ g i) (hunit:IsUnit (2:R)) :
    ringFunctional g ≤ 2 * mass g ^ 2:=by
  have hmul:=IsUnit.isUnit_iff_mulLeft_bijective.mp hunit
  let σ (k:R):Equiv.Perm R:=Equiv.ofBijective (fun j => 3 * k - 2 * j)
    ((Equiv.subLeft (3 * k)).bijective.comp hmul)
  rw [productFunctional_eq g σ (fun _ _ => rfl)]
  have hm:mass g = mass (fun i => g (0,i)) + mass (fun i => g (1,i)):=by
    unfold mass
    rw [Fintype.sum_prod_type,sum_zmod_two]
  rw [hm]
  exact pairedFunctional_le _ _ (fun i => hg _) (fun i => hg _) σ
theorem deficit_nonneg_of_twice_odd {m:ℕ} [NeZero m] (hm:Odd m)
    (g:ZMod (2 * m) → ℝ) (hg:∀ i,0 ≤ g i):0 ≤ deficit g:=by
  have hndvd:¬2 ∣ m:=by simpa only [← even_iff_two_dvd,Nat.not_even_iff_odd] using hm
  have hcop:Nat.Coprime 2 m:=(Nat.prime_two.coprime_iff_not_dvd).mpr hndvd
  let e:=ZMod.chineseRemainder hcop
  have h:=productFunctional_le (fun x => g (e.symm x)) (fun x => hg _)
    (ZMod.isUnit_prime_of_not_dvd Nat.prime_two hndvd)
  rw [← ringFunctional_equiv e g, ← mass_ringEquiv e g] at h
  exact sub_nonneg.mpr h
theorem deficit_nonneg_of_twelve_not_dvd {q:ℕ} [NeZero q]
    (hq:¬12 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):0 ≤ deficit g:=by
  by_cases h3:3 ∣ q
  · have h4:¬4 ∣ q:=by
      intro h4
      exact hq ((by decide:Nat.Coprime 3 4).mul_dvd_of_dvd_of_dvd h3 h4)
    by_cases h2:2 ∣ q
    · obtain ⟨m,rfl⟩:=h2
      have hm0:m ≠ 0:=by
        intro hm
        exact NeZero.ne (2 * m) (by rw [hm,mul_zero])
      have:NeZero m:=⟨hm0⟩
      have hm:Odd m:=by
        rw [← Nat.not_even_iff_odd,even_iff_two_dvd]
        rintro ⟨k,hk⟩
        apply h4
        refine ⟨k, ?_⟩
        omega
      exact deficit_nonneg_of_twice_odd hm g hg
    · exact deficit_nonneg_of_odd
        (by simpa only [← even_iff_two_dvd,Nat.not_even_iff_odd] using h2) g hg
  · exact deficit_nonneg_of_three_not_dvd h3 g hg
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def doubleResidue (m:ℕ):ZMod m →+ ZMod (2 * m) :=
  ZMod.lift m ⟨
    { toFun:=fun z:ℤ => 2 * (z:ZMod (2 * m))
      map_zero':=by simp
      map_add':=by intros; simp [mul_add] },by
      change 2 * ((m:ℤ):ZMod (2 * m)) = 0
      simpa only [Int.cast_natCast,Nat.cast_mul,Nat.cast_ofNat] using
        (ZMod.natCast_self (2 * m))⟩
private def zz42:"s002a"="s002a":=by decide+kernel
theorem doubleResidue_natCast (m n:ℕ):doubleResidue m (n:ZMod m) = 2 * (n:ZMod (2 * m)):=by
  unfold doubleResidue
  rw [← Int.cast_natCast n,ZMod.lift_coe]
  simp only [Int.cast_natCast,AddMonoidHom.coe_mk,ZeroHom.coe_mk]
theorem doubleResidue_val {m:ℕ} [NeZero m] (x:ZMod m) :
    doubleResidue m x = 2 * (x.val:ZMod (2 * m)):=by
  conv_lhs => rw [← ZMod.natCast_zmod_val x]
  exact doubleResidue_natCast m x.val
theorem doubleResidue_mul_nat (m n:ℕ) (x:ZMod m) :
    doubleResidue m (n * x) = n * doubleResidue m x:=by
  simpa only [nsmul_eq_mul] using (doubleResidue m).map_nsmul n x
noncomputable def parityEquiv (m:ℕ) [NeZero m]:(ZMod 2 × ZMod m) ≃ ZMod (2 * m) where
  toFun p:=((2 * p.2.val + p.1.val:ℕ):ZMod (2 * m))
  invFun x:=(((x.val % 2:ℕ):ZMod 2),((x.val / 2:ℕ):ZMod m))
  left_inv:=by
    rintro ⟨r,i⟩
    have hr:=r.val_lt
    have hi:=i.val_lt
    have hlt:2 * i.val + r.val < 2 * m:=by omega
    simp only [ZMod.val_natCast_of_lt hlt]
    apply Prod.ext
    · have hmod:(2 * i.val + r.val) % 2 = r.val:=by omega
      simp only [hmod,ZMod.natCast_zmod_val]
    · have hdiv:(2 * i.val + r.val) / 2 = i.val:=by omega
      simp only [hdiv,ZMod.natCast_zmod_val]
  right_inv:=by
    intro x
    have hx:=x.val_lt
    have hmod:x.val % 2 < 2:=Nat.mod_lt _ (by norm_num)
    have hdiv:x.val / 2 < m:=by omega
    simp only [ZMod.val_natCast_of_lt hmod,ZMod.val_natCast_of_lt hdiv]
    rw [show 2 * (x.val / 2) + x.val % 2 = x.val by omega]
    exact ZMod.natCast_zmod_val x
theorem parityEquiv_apply {m:ℕ} [NeZero m] (r:ZMod 2) (i:ZMod m) :
    parityEquiv m (r,i) = doubleResidue m i + (r.val:ZMod (2 * m)):=by
  change ((2 * i.val + r.val:ℕ):ZMod (2 * m)) = _
  rw [Nat.cast_add,Nat.cast_mul,Nat.cast_ofNat,doubleResidue_val]
private def zz43:"s002b"="s002b":=by decide+kernel
theorem parityEquiv_affine {m:ℕ} [NeZero m] (r s:ZMod 2) (j k:ZMod m) :
    3 * parityEquiv m (s,k) - 2 * parityEquiv m (r,j) =
      parityEquiv m (s,3 * k - 2 * j + (s.val:ZMod m) - (r.val:ZMod m)):=by
  rw [parityEquiv_apply,parityEquiv_apply,parityEquiv_apply]
  have h3:doubleResidue m (3 * k) = 3 * doubleResidue m k:=by
    simpa only [Nat.cast_ofNat] using doubleResidue_mul_nat m 3 k
  have h2:doubleResidue m (2 * j) = 2 * doubleResidue m j:=by
    simpa only [Nat.cast_ofNat] using doubleResidue_mul_nat m 2 j
  rw [map_sub,map_add,map_sub,h3,h2,doubleResidue_natCast,doubleResidue_natCast]
  ring
noncomputable def interleave {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (x:ZMod (2 * m)):ℝ :=
  if ((parityEquiv m).symm x).1 = 0 then u ((parityEquiv m).symm x).2
  else v ((parityEquiv m).symm x).2
theorem interleave_even {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (i:ZMod m) :
    interleave u v (parityEquiv m (0,i)) = u i:=by
  simp [interleave]
theorem interleave_odd {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (i:ZMod m) :
    interleave u v (parityEquiv m (1,i)) = v i:=by
  simp [interleave]
theorem interleave_nonneg {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i):∀ i,0 ≤ interleave u v i:=by
  intro i
  unfold interleave
  split_ifs <;> first | exact hu _ | exact hv _
private def zz44:"s002c"="s002c":=by decide+kernel
theorem mass_interleave {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    mass (interleave u v) = mass u + mass v:=by
  unfold mass
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [interleave_even,interleave_odd]
noncomputable def mixedFunctional {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (t:ZMod m):ℝ :=
  ∑ j, ∑ k,kernel (u (3 * k - 2 * j + t)) (2 * v j) (3 * u k)
theorem profileFunctional_interleave {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    profileFunctional (interleave u v) = profileFunctional u + profileFunctional v +
      mixedFunctional u v (-1) + mixedFunctional v u 1:=by
  unfold profileFunctional
  rw [← (parityEquiv m).sum_comp]
  simp only [Fintype.sum_prod_type,sum_zmod_two]
  have hrow (r:ZMod 2) (j:ZMod m) :
      (∑ k,kernel (interleave u v (3 * k - 2 * parityEquiv m (r,j)))
        (2 * interleave u v (parityEquiv m (r,j))) (3 * interleave u v k)) =
      ∑ s:ZMod 2, ∑ k:ZMod m,
        kernel (interleave u v (parityEquiv m
          (s,3 * k - 2 * j + (s.val:ZMod m) - (r.val:ZMod m))))
          (2 * interleave u v (parityEquiv m (r,j)))
          (3 * interleave u v (parityEquiv m (s,k))):=by
    rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type]
    simp only [parityEquiv_affine]
  simp_rw [hrow]
  simp only [sum_zmod_two,ZMod.val_zero,ZMod.val_one,Nat.cast_zero,Nat.cast_one,
    sub_zero,add_zero,add_sub_cancel_right,interleave_even,interleave_odd,
    Finset.sum_add_distrib]
  unfold mixedFunctional
  simp only [sub_eq_add_neg]
  ring
end Green24Proof
end 
section 
namespace Green24Proof
theorem kernel_le_middle_min {a b c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c) :
    kernel a b c ≤ b * min a c:=by
  have h₁:=kernel_le_product ha hb hc
  have h₂:=kernel_le_product hb hc ha
  rw [← kernel_cycle a b c] at h₂
  rcases le_total a c with h | h
  · rw [min_eq_left h]
    nlinarith
  · rw [min_eq_right h]
    exact h₂
theorem mixedFunctional_le_overlap {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) {R:ℝ}
    (hR:∀ j,overlap (overlapMap j) u ≤ R) :
    mixedFunctional u v (-1) ≤ 2 * mass v * R:=by
  unfold mixedFunctional
  calc
    _ ≤ ∑ j, ∑ k,2 * v j * min (u (3 * k - 2 * j + -1)) (3 * u k):=by
      apply Finset.sum_le_sum
      intro j _
      exact Finset.sum_le_sum fun k _ =>
        kernel_le_middle_min (hu _) (mul_nonneg (by norm_num) (hv _))
          (mul_nonneg (by norm_num) (hu _))
    _ = ∑ j,2 * v j * overlap (overlapMap j) u:=by
      simp only [overlap,overlapMap,sub_eq_add_neg,Finset.mul_sum]
    _ ≤ ∑ j,2 * v j * R:=by
      exact Finset.sum_le_sum fun j _ => mul_le_mul_of_nonneg_left (hR j)
        (mul_nonneg (by norm_num) (hv j))
    _ = 2 * mass v * R:=by
      unfold mass
      rw [← Finset.sum_mul, ← Finset.mul_sum]
noncomputable def classMass {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (u:ι → ℝ)
    (r:ZMod 2):ℝ:=∑ i,if χ i = r then u i else 0
private def zz45:"s002d"="s002d":=by decide+kernel
theorem classMass_nonneg {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (u:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (r:ZMod 2):0 ≤ classMass χ u r:=by
  exact Finset.sum_nonneg fun i _ => by split_ifs <;> first | exact hu _ | rfl
theorem classMass_sum {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (u:ι → ℝ) :
    classMass χ u 0 + classMass χ u 1 = mass u:=by
  rw [← sum_zmod_two]
  unfold classMass
  rw [Finset.sum_comm]
  simp only [Finset.sum_ite_eq,Finset.mem_univ,if_true,mass]
theorem zmod_two_eq_zero_or_one (r:ZMod 2):r = 0 ∨ r = 1:=by
  have hr:=r.val_lt
  have h:r.val = 0 ∨ r.val = 1:=by omega
  rcases h with h | h
  · left
    apply ZMod.val_injective 2
    simpa using h
  · right
    apply ZMod.val_injective 2
    change r.val = 1
    exact h
theorem two_class_cross_sum {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (u:ι → ℝ) :
    (∑ i,u i * classMass χ u (χ i + 1)) = 2 * classMass χ u 0 * classMass χ u 1:=by
  have hpoint (i:ι):u i * classMass χ u (χ i + 1) =
      (if χ i = 0 then u i else 0) * classMass χ u 1 +
      (if χ i = 1 then u i else 0) * classMass χ u 0:=by
    rcases zmod_two_eq_zero_or_one (χ i) with h | h
    · simp [h]
    · simp [h,show (1:ZMod 2) + 1 = 0 from rfl]
  simp_rw [hpoint]
  rw [Finset.sum_add_distrib, ← Finset.sum_mul, ← Finset.sum_mul]
  change classMass χ u 0 * classMass χ u 1 + classMass χ u 1 * classMass χ u 0 = _
  ring
private def zz46:"s002e"="s002e":=by decide+kernel
theorem odd_shift_correlation_le_parity {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) :
    (∑ k, ∑ j,u (3 * k - 2 * j + 1) * u k) ≤
      4 * classMass (ZMod.castHom h2 (ZMod 2)) u 0 *
        classMass (ZMod.castHom h2 (ZMod 2)) u 1:=by
  let χ:=ZMod.castHom h2 (ZMod 2)
  have hrow (k:ZMod m):(∑ j,u (3 * k - 2 * j + 1)) ≤
      2 * classMass χ u (χ k + 1):=by
    let f (i:ZMod m):ℝ:=if χ i = χ k + 1 then u i else 0
    have hχ (j:ZMod m):χ (2 * j + (3 * k + 1)) = χ k + 1:=by
      simp only [map_add,map_mul,map_ofNat,map_one,
        show (2:ZMod 2) = 0 from rfl,show (3:ZMod 2) = 1 from rfl,
        zero_mul,zero_add,one_mul]
    have hpre (y:ZMod m):(Finset.univ.filter fun j => 2 * j + (3 * k + 1) = y).card ≤ 2:=by
      simpa only [Nat.cast_ofNat] using affine_preimages 2 (by norm_num) (3 * k + 1) y
    have h:=sum_comp_le_card (fun j:ZMod m => 2 * j + (3 * k + 1)) 2 hpre f
      (fun i => by dsimp [f]; split_ifs <;> first | exact hu _ | rfl)
    simp only [f,hχ,if_true,Nat.cast_ofNat] at h
    change (∑ j,u (2 * j + (3 * k + 1))) ≤ 2 * classMass χ u (χ k + 1) at h
    have heq:=Equiv.sum_comp (Equiv.neg (ZMod m)) (fun j => u (3 * k - 2 * j + 1))
    have hid (j:ZMod m):3 * k - 2 * (-j) + 1 = 2 * j + (3 * k + 1):=by ring
    simp only [Equiv.neg_apply,hid] at heq
    rw [← heq]
    exact h
  have hsum:=Finset.sum_le_sum (s:=Finset.univ)
    (fun k _ => mul_le_mul_of_nonneg_right (hrow k) (hu k))
  have hcross:=two_class_cross_sum χ u
  simp only [Finset.sum_mul] at hsum
  have hid:(∑ k,2 * classMass χ u (χ k + 1) * u k) =
      2 * (∑ k,u k * classMass χ u (χ k + 1)):=by
    rw [Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro k _
    ring
  rw [hid,hcross] at hsum
  nlinarith
theorem odd_shift_correlation_le_even {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) :
    (∑ k, ∑ j,u (3 * k - 2 * j + 1) * u k) ≤ mass u ^ 2:=by
  let χ:=ZMod.castHom h2 (ZMod 2)
  have hsum:=odd_shift_correlation_le_parity h2 u hu
  have hm:=classMass_sum χ u
  rw [← hm]
  nlinarith [sq_nonneg (classMass χ u 0 - classMass χ u 1)]
theorem odd_shift_correlation_le {m:ℕ} [NeZero m]
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) :
    (∑ k, ∑ j,u (3 * k - 2 * j + 1) * u k) ≤ mass u ^ 2:=by
  by_cases h2:2 ∣ m
  · exact odd_shift_correlation_le_even h2 u hu
  · have hunit:=ZMod.isUnit_prime_of_not_dvd Nat.prime_two h2
    have hmul:=IsUnit.isUnit_iff_mulLeft_bijective.mp hunit
    have hrow (k:ZMod m):(∑ j,u (3 * k - 2 * j + 1)) = mass u:=by
      have hbij:Function.Bijective (fun j:ZMod m => 3 * k - 2 * j + 1) :=
        (Equiv.addRight (1:ZMod m)).bijective.comp ((Equiv.subLeft (3 * k)).bijective.comp hmul)
      exact hbij.sum_comp u
    simp only [← Finset.sum_mul,hrow, ← Finset.mul_sum]
    unfold mass
    nlinarith
theorem mixedFunctional_le_three_mass_sq {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    mixedFunctional v u 1 ≤ 3 * mass v ^ 2:=by
  have hcorr:=odd_shift_correlation_le v hv
  unfold mixedFunctional
  calc
    _ ≤ ∑ j, ∑ k,3 * (v (3 * k - 2 * j + 1) * v k):=by
      apply Finset.sum_le_sum
      intro j _
      apply Finset.sum_le_sum
      intro k _
      have h:=kernel_le_product (hv (3 * k - 2 * j + 1))
        (mul_nonneg (by norm_num:(0:ℝ) ≤ 3) (hv k))
        (mul_nonneg (by norm_num:(0:ℝ) ≤ 2) (hu j))
      rw [kernel_swap23] at h
      nlinarith
    _ = 3 * (∑ k, ∑ j,v (3 * k - 2 * j + 1) * v k):=by
      simp only [← Finset.mul_sum]
      rw [Finset.sum_comm]
    _ ≤ 3 * mass v ^ 2:=mul_le_mul_of_nonneg_left hcorr (by norm_num)
private def zz47:"s002f"="s002f":=by decide+kernel
theorem profileFunctional_interleave_le {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) {R:ℝ}
    (hR:∀ j,overlap (overlapMap j) u ≤ R) :
    profileFunctional (interleave u v) ≤ profileFunctional u + profileFunctional v +
      3 * mass v ^ 2 + 2 * mass v * R:=by
  rw [profileFunctional_interleave]
  linarith [mixedFunctional_le_overlap u v hu hv hR,mixedFunctional_le_three_mass_sq u v hu hv]
theorem deficit_interleave_expansion {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) {R:ℝ}
    (hR:∀ j,overlap (overlapMap j) u ≤ R) :
    deficit u + deficit v + 4 * mass u * mass v - 3 * mass v ^ 2 - 2 * mass v * R ≤
      deficit (interleave u v):=by
  have h:=profileFunctional_interleave_le u v hu hv hR
  unfold deficit
  rw [mass_interleave]
  nlinarith
end Green24Proof
end 
section 
namespace Green24Proof
structure HeightCoefficients where
  S:ℝ
  e:ℝ
  o:ℝ
  f:ℝ
  h:ℝ
  tau:ℝ
  omega:ℝ
  eta:ℝ
noncomputable def HeightCoefficients.massBound (c:HeightCoefficients) (A B:ℝ):ℝ :=
  c.eta * (A + B) ^ 2 - (1 / 4) * (A - c.S * B) * (c.e * A + c.o * B) -
    ((-c.f) * (c.S - 1) / 4) * A * B -
    (c.h * A - (c.h * c.S + c.tau) * B) ^ 2 / (16 * c.omega)
def HeightCoefficients.Aggregate (c:HeightCoefficients) (A B dw dz H d:ℝ):Prop :=
  -4 * d + (8 / 5) * H + 4 * c.eta * (A + B) ^ 2 ≤
    (A - c.S * B) * (c.e * A + c.o * B + c.f * dw + c.h * dz) -
      c.tau * B * dz - c.omega * dz ^ 2
theorem even_error_bound {A B S f dw:ℝ} (hB:0 ≤ B) (hAB:B ≤ A)
    (hS:1 ≤ S) (hf:f ≤ 0) (hdw:0 ≤ dw) (hdwA:dw ≤ A) :
    f * (A - S * B) * dw ≤ (-f) * (S - 1) * A * B:=by
  have hA:0 ≤ A:=hB.trans hAB
  by_cases hs:0 ≤ A - S * B
  · have hleft:=mul_nonpos_of_nonpos_of_nonneg
      (mul_nonpos_of_nonpos_of_nonneg hf hs) hdw
    have hright:0 ≤ (-f) * (S - 1) * A * B :=
      mul_nonneg (mul_nonneg (mul_nonneg (neg_nonneg.mpr hf)
        (sub_nonneg.mpr hS)) hA) hB
    exact hleft.trans hright
  · have h₁:=mul_le_mul_of_nonneg_left hdwA
      (mul_nonneg_of_nonpos_of_nonpos hf (le_of_not_ge hs))
    have h₂:=mul_nonpos_of_nonpos_of_nonneg hf
      (mul_nonneg hA (sub_nonneg.mpr hAB))
    nlinarith
theorem completed_square_bound {p omega z:ℝ} (hw:0 < omega) :
    p * z - omega * z ^ 2 ≤ p ^ 2 / (4 * omega):=by
  apply (le_div_iff₀ (by positivity:0 < 4 * omega)).mpr
  nlinarith [sq_nonneg (p - 2 * omega * z)]
private def zz48:"s0030"="s0030":=by decide+kernel
theorem height_mass_bound {c:HeightCoefficients} {A B dw dz H d:ℝ}
    (hS:1 ≤ c.S) (hf:c.f ≤ 0) (hw:0 < c.omega)
    (hB:0 ≤ B) (hAB:B ≤ A) (hdw:0 ≤ dw) (hdwA:dw ≤ A)
    (hc:c.Aggregate A B dw dz H d) :
    (2 / 5) * H + c.massBound A B ≤ d:=by
  have heven:=even_error_bound hB hAB hS hf hdw hdwA
  have hodd:=completed_square_bound
    (p:=c.h * A - (c.h * c.S + c.tau) * B) (z:=dz) hw
  unfold HeightCoefficients.Aggregate at hc
  unfold HeightCoefficients.massBound
  have hdiv:(c.h * A - (c.h * c.S + c.tau) * B) ^ 2 / (16 * c.omega) =
      ((c.h * A - (c.h * c.S + c.tau) * B) ^ 2 / (4 * c.omega)) / 4:=by
    ring
  rw [hdiv]
  nlinarith
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def height12:HeightCoefficients where
  S:=(6 / 5)
  e:=(0xbbb54f / 0x30d400)
  o:=(-0x7d055ec5 / 0x17d78400)
  f:=(-0x13295c7 / 0x77359400)
  h:=(-0x87af2f / 0x77359400)
  tau:=(0 / 1)
  omega:=(0x149a115b / 0xbebc200)
  eta:=(-0x1b0311 / 0x3b9aca00)
theorem height12_massBound_ge {A B:ℝ} (hA:0 ≤ A) (hB:0 ≤ B) :
    Q12 A B ≤ height12.massBound A B:=by
  unfold HeightCoefficients.massBound height12 Q12
  norm_num
  nlinarith only [sq_nonneg A,sq_nonneg B,mul_nonneg hA hB]
theorem height12_of_aggregate {A B dw dz H d:ℝ}
    (hB:0 ≤ B) (hAB:B ≤ A) (hdw:0 ≤ dw) (hdwA:dw ≤ A)
    (hc:height12.Aggregate A B dw dz H d) :
    (2 / 5) * H + Q12 A B ≤ d:=by
  have h:=height_mass_bound (c:=height12)
    (by norm_num [height12]) (by norm_num [height12])
    (by norm_num [height12]) hB hAB hdw hdwA hc
  linarith [height12_massBound_ge (hB.trans hAB) hB]
noncomputable def height18:HeightCoefficients where
  S:=(9 / 5)
  e:=(0x13b983a43 / 0x77359400)
  o:=(-0x4df97f5 / 0x1312d00)
  f:=(-0x19b86e7 / 0x77359400)
  h:=(-0x585c71 / 0x3b9aca00)
  tau:=(0 / 1)
  omega:=(0x3919bbd / 0x17d7840)
  eta:=(-13 / 0x3e8)
theorem height18_massBound_ge {A B:ℝ} :
    Q18 A B ≤ height18.massBound A B:=by
  unfold HeightCoefficients.massBound height18 Q18
  norm_num
  nlinarith only [sq_nonneg A,sq_nonneg B,sq_nonneg (A + B)]
private def zz49:"s0031"="s0031":=by decide+kernel
theorem height18_of_aggregate {A B dw dz H d:ℝ}
    (hB:0 ≤ B) (hAB:B ≤ A) (hdw:0 ≤ dw) (hdwA:dw ≤ A)
    (hc:height18.Aggregate A B dw dz H d) :
    (2 / 5) * H + Q18 A B ≤ d:=by
  have h:=height_mass_bound (c:=height18)
    (by norm_num [height18]) (by norm_num [height18])
    (by norm_num [height18]) hB hAB hdw hdwA hc
  linarith [height18_massBound_ge (A:=A) (B:=B)]
end Green24Proof
end 
section 
namespace Green24Proof
theorem zmod_two_flip_of_ne {r s:ZMod 2} (h:s ≠ r):s + 1 = r:=by
  rcases zmod_two_eq_zero_or_one r with rfl | rfl <;>
    rcases zmod_two_eq_zero_or_one s with rfl | rfl
  · exact (h rfl).elim
  · rfl
  · rfl
  · exact (h rfl).elim
theorem overlap_le_six_classMass {ι:Type*} [Fintype ι] [DecidableEq ι]
    (T:ι → ι) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card ≤ 3)
    (χ:ι → ZMod 2) (hχ:∀ i,χ (T i) = χ i + 1) (u:ι → ℝ)
    (hu:∀ i,0 ≤ u i) (r:ZMod 2):overlap T u ≤ 6 * classMass χ u r:=by
  let f (i:ι):ℝ:=if χ i = r then u i else 0
  have hf (i:ι):0 ≤ f i:=by dsimp [f]; split_ifs <;> first | exact hu _ | rfl
  have hpoint (i:ι):min (u (T i)) (3 * u i) ≤ f (T i) + 3 * f i:=by
    by_cases hi:χ i = r
    · have heq:f i = u i:=if_pos hi
      rw [heq]
      linarith [min_le_right (u (T i)) (3 * u i),hf (T i)]
    · have hi':χ (T i) = r:=(hχ i).trans (zmod_two_flip_of_ne hi)
      simp only [f,if_pos hi',if_neg hi,mul_zero,add_zero]
      exact min_le_left _ _
  have hsum:=Finset.sum_le_sum (s:=Finset.univ) (fun i _ => hpoint i)
  have hpre:=sum_comp_le_three T hT f hf
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum] at hsum
  change (∑ i,min (u (T i)) (3 * u i)) ≤ _ at hsum
  change (∑ i,min (u (T i)) (3 * u i)) ≤ 6 * ∑ i,f i
  linarith
theorem parityCast_apply {m:ℕ} [NeZero m] (r:ZMod 2) (i:ZMod m) :
    ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) (parityEquiv m (r,i)) = r:=by
  rw [parityEquiv_apply,doubleResidue_val]
  simp only [map_add,map_mul,map_ofNat,map_natCast,
    show (2:ZMod 2) = 0 from rfl,zero_mul,zero_add,ZMod.natCast_zmod_val]
private def zz50:"s0032"="s0032":=by decide+kernel
theorem classMass_interleave_even {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) (interleave u v) 0 = mass u:=by
  unfold classMass mass
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [parityCast_apply,interleave_even,interleave_odd,if_true,
    one_ne_zero,if_false,Finset.sum_const_zero,add_zero]
theorem classMass_interleave_odd {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) (interleave u v) 1 = mass v:=by
  unfold classMass mass
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [parityCast_apply,interleave_even,interleave_odd,if_true,
    zero_ne_one,if_false,Finset.sum_const_zero,zero_add]
theorem cyclic_overlap_le_six_classMass {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (j:ZMod m) (r:ZMod 2) :
    overlap (overlapMap j) u ≤ 6 * classMass (ZMod.castHom h2 (ZMod 2)) u r:=by
  apply overlap_le_six_classMass _ (overlapMap_preimages j) _ _ u hu r
  intro i
  change ZMod.castHom h2 (ZMod 2) (3 * i - 2 * j - 1) =
    ZMod.castHom h2 (ZMod 2) i + 1
  rw [map_sub,map_sub,map_mul,map_mul,map_ofNat,map_ofNat,map_one]
  simp only [
    show (2:ZMod 2) = 0 from rfl,show (3:ZMod 2) = 1 from rfl,
    zero_mul,one_mul,sub_eq_add_neg,neg_zero,add_zero,
    show -(1:ZMod 2) = 1 from rfl]
noncomputable def overlapMaximum {m:ℕ} [NeZero m] (u:ZMod m → ℝ):ℝ :=
  Finset.univ.sup' Finset.univ_nonempty (fun j => overlap (overlapMap j) u)
theorem overlap_le_maximum {m:ℕ} [NeZero m] (u:ZMod m → ℝ) (j:ZMod m) :
    overlap (overlapMap j) u ≤ overlapMaximum u:=by
  unfold overlapMaximum
  exact Finset.le_sup' (fun j:ZMod m => overlap (overlapMap j) u) (Finset.mem_univ j)
private def zz51:"s0033"="s0033":=by decide+kernel
theorem overlapMaximum_sharp {m:ℕ} [NeZero m] (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) :
    overlapMaximum u ≤ mass u + Real.sqrt (8 * energy u):=by
  exact Finset.sup'_le Finset.univ_nonempty _ (fun j _ => cyclic_sharp_overlap u hu j)
theorem overlapMaximum_parity {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (r:ZMod 2) :
    overlapMaximum u ≤ 6 * classMass (ZMod.castHom h2 (ZMod 2)) u r:=by
  exact Finset.sup'_le Finset.univ_nonempty _ (fun j _ => cyclic_overlap_le_six_classMass h2 u hu j r)
theorem profile_overlap_bound_of_height {m:ℕ} [NeZero m]
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i)
    (hheight:(2 / 5) * energy u - (9 / 0x100) * mass u ^ 2 ≤ deficit u) :
    mass u * overlapMaximum u ≤ (61 / 32) * mass u ^ 2 + 8 * deficit u :=
  overlap_bound_of_height (mass_nonneg hu) (energy_nonneg hu) (overlapMaximum_sharp u hu) hheight
theorem profile_overlap_bound {m:ℕ} [NeZero m] (w z:ZMod m → ℝ)
    (hw:∀ i,0 ≤ w i) (hz:∀ i,0 ≤ z i) (horder:mass z ≤ mass w)
    (hd:0 ≤ deficit (interleave w z))
    (h12:(2 / 5) * energy (interleave w z) + Q12 (mass w) (mass z) ≤ deficit (interleave w z))
    (h18:(2 / 5) * energy (interleave w z) + Q18 (mass w) (mass z) ≤ deficit (interleave w z)) :
    mass (interleave w z) * overlapMaximum (interleave w z) ≤
      (61 / 32) * mass (interleave w z) ^ 2 + 8 * deficit (interleave w z):=by
  have hg:=interleave_nonneg w z hw hz
  have hoverlap:=overlapMaximum_sharp (interleave w z) hg
  have hparity:=overlapMaximum_parity (dvd_mul_right 2 m) (interleave w z) hg 1
  rw [classMass_interleave_odd] at hparity
  rw [mass_interleave] at hoverlap ⊢
  exact overlap_bound (mass_nonneg hz) horder (energy_nonneg hg) hd hoverlap hparity h12 h18
private def zz52:"s0034"="s0034":=by decide+kernel
theorem profile_boundary_descent {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hU:0 < mass u)
    (hheight:(2 / 5) * energy u - (9 / 0x100) * mass u ^ 2 ≤ deficit u) :
    (1 - 16 * mass v / mass u) * deficit u + deficit v +
      mass v * ((3 / 16) * mass u - 3 * mass v) ≤ deficit (interleave u v) :=
  boundary_descent hU (mass_nonneg hv) (profile_overlap_bound_of_height u hu hheight)
    (deficit_interleave_expansion u v hu hv (overlap_le_maximum u))
theorem profile_boundary_nonneg {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hU:0 < mass u)
    (hratio:16 * mass v ≤ mass u) (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hheight:(2 / 5) * energy u - (9 / 0x100) * mass u ^ 2 ≤ deficit u) :
    0 ≤ deficit (interleave u v) :=
  boundary_nonneg hU (mass_nonneg hv) hratio hdu hdv
    (profile_overlap_bound_of_height u hu hheight)
    (deficit_interleave_expansion u v hu hv (overlap_le_maximum u))
end Green24Proof
end 
section 
namespace Green24Proof
theorem mass_eq_zero_iff {ι:Type*} [Fintype ι] (u:ι → ℝ) (hu:∀ i,0 ≤ u i) :
    mass u = 0 ↔ ∀ i,u i = 0:=by
  unfold mass
  simpa only [Finset.mem_univ,forall_true_left] using
    Finset.sum_eq_zero_iff_of_nonneg (s:=Finset.univ) (fun i _ => hu i)
theorem mass_translate {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (t:ZMod m) :
    mass (fun i => g (i + t)) = mass g:=Equiv.sum_comp (Equiv.addRight t) g
private def zz53:"s0035"="s0035":=by decide+kernel
theorem profileFunctional_translate {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (t:ZMod m) :
    profileFunctional (fun i => g (i + t)) = profileFunctional g:=by
  unfold profileFunctional
  have hrow (j:ZMod m) :
      (∑ k,kernel (g (3 * k - 2 * j + t)) (2 * g (j + t)) (3 * g (k + t))) =
      ∑ k,kernel (g (3 * k - 2 * (j + t))) (2 * g (j + t)) (3 * g k):=by
    have h:=Equiv.sum_comp (Equiv.addRight t)
      (fun k => kernel (g (3 * k - 2 * (j + t))) (2 * g (j + t)) (3 * g k))
    simpa only [Equiv.coe_addRight,show ∀ k,3 * (k + t) - 2 * (j + t) =
      3 * k - 2 * j + t by intro k; ring] using h
  simp_rw [hrow]
  exact Equiv.sum_comp (Equiv.addRight t)
    (fun j => ∑ k,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k))
theorem deficit_translate {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (t:ZMod m) :
    deficit (fun i => g (i + t)) = deficit g:=by
  unfold deficit
  rw [mass_translate,profileFunctional_translate]
theorem mass_reflect {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    mass (fun i => g (-i)) = mass g:=Equiv.sum_comp (Equiv.neg (ZMod m)) g
theorem profileFunctional_reflect {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    profileFunctional (fun i => g (-i)) = profileFunctional g:=by
  unfold profileFunctional
  have hrow (j:ZMod m) :
      (∑ k,kernel (g (-(3 * k - 2 * j))) (2 * g (-j)) (3 * g (-k))) =
      ∑ k,kernel (g (3 * k - 2 * (-j))) (2 * g (-j)) (3 * g k):=by
    have h:=Equiv.sum_comp (Equiv.neg (ZMod m))
      (fun k => kernel (g (3 * k - 2 * (-j))) (2 * g (-j)) (3 * g k))
    simpa only [Equiv.neg_apply,show ∀ k,3 * (-k) - 2 * (-j) =
      -(3 * k - 2 * j) by intro k; ring] using h
  simp_rw [hrow]
  exact Equiv.sum_comp (Equiv.neg (ZMod m))
    (fun j => ∑ k,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k))
private def zz54:"s0036"="s0036":=by decide+kernel
theorem deficit_reflect {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    deficit (fun i => g (-i)) = deficit g:=by
  unfold deficit
  rw [mass_reflect,profileFunctional_reflect]
theorem kernel_scale (a b c:ℝ) {s:ℝ} (hs:0 ≤ s) :
    kernel (s * a) (s * b) (s * c) = s ^ 2 * kernel a b c:=by
  have hmax (x:ℝ):max (s * x) 0 = s * max x 0:=by
    rw [mul_max_of_nonneg _ _ hs,mul_zero]
  unfold kernel
  rw [show s * a - s * b - s * c = s * (a - b - c) by ring,
    show s * b - s * a - s * c = s * (b - a - c) by ring,
    show s * c - s * a - s * b = s * (c - a - b) by ring]
  simp only [hmax]
  ring
theorem mass_scale {ι:Type*} [Fintype ι] (g:ι → ℝ) (s:ℝ) :
    mass (fun i => s * g i) = s * mass g:=(Finset.mul_sum _ _ _).symm
theorem profileFunctional_scale {m:ℕ} [NeZero m] (g:ZMod m → ℝ) {s:ℝ} (hs:0 ≤ s) :
    profileFunctional (fun i => s * g i) = s ^ 2 * profileFunctional g:=by
  unfold profileFunctional
  have h (j k:ZMod m) :
      kernel (s * g (3 * k - 2 * j)) (2 * (s * g j)) (3 * (s * g k)) =
      s ^ 2 * kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k):=by
    rw [show 2 * (s * g j) = s * (2 * g j) by ring,
      show 3 * (s * g k) = s * (3 * g k) by ring]
    exact kernel_scale _ _ _ hs
  simp_rw [h]
  simp only [← Finset.mul_sum]
private def zz55:"s0037"="s0037":=by decide+kernel
theorem deficit_scale {m:ℕ} [NeZero m] (g:ZMod m → ℝ) {s:ℝ} (hs:0 ≤ s) :
    deficit (fun i => s * g i) = s ^ 2 * deficit g:=by
  unfold deficit
  rw [mass_scale,profileFunctional_scale g hs]
  ring
theorem rho_scale {x y s:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) (hs:0 ≤ s) :
    rho (s * x) (s * y) = s ^ 2 * rho x y:=by
  have h₁:=rho_positive_part_identity hx hy
  have h₂:=rho_positive_part_identity (mul_nonneg hs hx) (mul_nonneg hs hy)
  have hmax (a:ℝ):max (s * a) 0 = s * max a 0:=by
    rw [mul_max_of_nonneg _ _ hs,mul_zero]
  rw [show s * x - 3 * (s * y) = s * (x - 3 * y) by ring,
    show s * y - 3 * (s * x) = s * (y - 3 * x) by ring,hmax,hmax] at h₂
  linear_combination (h₂ - s ^ 2 * h₁) / 4
theorem energy_scale {ι:Type*} [Fintype ι] (g:ι → ℝ) (hg:∀ i,0 ≤ g i)
    {s:ℝ} (hs:0 ≤ s):energy (fun i => s * g i) = s ^ 2 * energy g:=by
  unfold energy
  simp_rw [rho_scale (hg _) (hg _) hs]
  simp only [← Finset.mul_sum]
  ring
theorem sum_comp_eq_card {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (T:ι → κ) (N:ℕ) (hT:∀ j,(Finset.univ.filter fun i => T i = j).card = N)
    (f:κ → ℝ):(∑ i,f (T i)) = N * ∑ j,f j:=by
  calc
    (∑ i,f (T i)) = ∑ i, ∑ j,if T i = j then f j else 0:=by simp
    _ = ∑ j, ∑ i,if T i = j then f j else 0:=Finset.sum_comm
    _ = ∑ j,(N:ℝ) * f j:=by
      apply Finset.sum_congr rfl
      intro j _
      rw [← Finset.sum_filter]
      simp only [Finset.sum_const,nsmul_eq_mul,hT]
    _ = _:=(Finset.mul_sum _ _ _).symm
private def zz56:"s0038"="s0038":=by decide+kernel
theorem double_quotient_fibers {m:ℕ} [NeZero m] (y:ZMod m) :
    (Finset.univ.filter fun x:ZMod (2 * m) =>
      ZMod.castHom (dvd_mul_left m 2) (ZMod m) x = y).card = 2:=by
  let π:=ZMod.castHom (dvd_mul_left m 2) (ZMod m)
  have hsurj:=ZMod.castHom_surjective (dvd_mul_left m 2)
  have hsame (z:ZMod m):(Finset.univ.filter fun x => π x = z).card =
      (Finset.univ.filter fun x => π x = y).card :=
    AddMonoidHom.card_fiber_eq_of_mem_range π (hsurj z) (hsurj y)
  have htotal:Fintype.card (ZMod (2 * m)) =
      ∑ z:ZMod m,(Finset.univ.filter fun x => π x = z).card :=
    Finset.card_eq_sum_card_fiberwise (fun _ _ => Finset.mem_univ _)
  simp_rw [hsame] at htotal
  simp only [Finset.sum_const,Finset.card_univ,ZMod.card,nsmul_eq_mul] at htotal
  have h:=Nat.eq_of_mul_eq_mul_left (NeZero.pos m) (by
    simpa only [mul_comm 2 m,Nat.cast_id] using htotal)
  exact h.symm
noncomputable def periodicLift {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (x:ZMod (2 * m)):ℝ :=
  (1 / 2) * g (ZMod.castHom (dvd_mul_left m 2) (ZMod m) x)
theorem mass_periodicLift {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    mass (periodicLift g) = mass g:=by
  unfold periodicLift mass
  rw [← Finset.mul_sum,sum_comp_eq_card _ 2 double_quotient_fibers]
  norm_num
  ring
theorem profileFunctional_periodicLift {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    profileFunctional (periodicLift g) = profileFunctional g:=by
  let π:=ZMod.castHom (dvd_mul_left m 2) (ZMod m)
  unfold periodicLift
  rw [profileFunctional_scale _ (by norm_num:(0:ℝ) ≤ 1 / 2)]
  unfold profileFunctional
  change (1 / 2:ℝ) ^ 2 * (∑ j, ∑ k,kernel (g (π (3 * k - 2 * j)))
    (2 * g (π j)) (3 * g (π k))) = _
  simp only [map_sub,map_mul,map_ofNat]
  have hrow (j:ZMod (2 * m)) :
      (∑ k,kernel (g (3 * π k - 2 * π j)) (2 * g (π j)) (3 * g (π k))) =
      2 * ∑ k:ZMod m,kernel (g (3 * k - 2 * π j)) (2 * g (π j)) (3 * g k):=by
    simpa only [Nat.cast_ofNat] using sum_comp_eq_card π 2 double_quotient_fibers
      (fun k => kernel (g (3 * k - 2 * π j)) (2 * g (π j)) (3 * g k))
  simp_rw [hrow]
  rw [← Finset.mul_sum,sum_comp_eq_card π 2 double_quotient_fibers
    (fun j => ∑ k,kernel (g (3 * k - 2 * j)) (2 * g j) (3 * g k))]
  norm_num
  ring
theorem deficit_periodicLift {m:ℕ} [NeZero m] (g:ZMod m → ℝ) :
    deficit (periodicLift g) = deficit g:=by
  unfold deficit
  rw [mass_periodicLift,profileFunctional_periodicLift]
private def zz57:"s0039"="s0039":=by decide+kernel
theorem energy_periodicLift {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (hg:∀ i,0 ≤ g i) :
    energy (periodicLift g) = energy g:=by
  let π:=ZMod.castHom (dvd_mul_left m 2) (ZMod m)
  unfold periodicLift
  rw [energy_scale _ (fun i => hg _) (by norm_num:(0:ℝ) ≤ 1 / 2)]
  unfold energy
  change (1 / 2:ℝ) ^ 2 * ((∑ i, ∑ j,rho (g (π i)) (g (π j))) / 2) = _
  have hrow (i:ZMod (2 * m)):(∑ j,rho (g (π i)) (g (π j))) =
      2 * ∑ j:ZMod m,rho (g (π i)) (g j):=by
    simpa only [Nat.cast_ofNat] using sum_comp_eq_card π 2 double_quotient_fibers
      (fun j => rho (g (π i)) (g j))
  simp_rw [hrow]
  rw [← Finset.mul_sum,sum_comp_eq_card π 2 double_quotient_fibers
    (fun i => ∑ j,rho (g i) (g j))]
  norm_num
  ring
end Green24Proof
end 
section 
namespace Green24Proof
def companionMap {q:ℕ} (p:ZMod q × ZMod q):ZMod q × ZMod q :=
  (3 * p.2 - 2 * p.1,3 * p.1 - 2 * p.2)
theorem companionMap_bijective {q:ℕ} (h5:¬5 ∣ q):Function.Bijective (@companionMap q):=by
  have hu:IsUnit (5:ZMod q):=ZMod.isUnit_prime_of_not_dvd (by norm_num) h5
  obtain ⟨s,hs⟩:=hu.exists_right_inv
  have hinj:=(IsUnit.isUnit_iff_mulLeft_bijective.mp hu).injective
  constructor
  · rintro ⟨j,k⟩ ⟨l,m⟩ h
    have h₁:3 * k - 2 * j = 3 * m - 2 * l:=congrArg Prod.fst h
    have h₂:3 * j - 2 * k = 3 * l - 2 * m:=congrArg Prod.snd h
    apply Prod.ext
    · apply hinj
      linear_combination 2 * h₁ + 3 * h₂
    · apply hinj
      linear_combination 3 * h₁ + 2 * h₂
  · rintro ⟨a,b⟩
    refine ⟨(s * (2 * a + 3 * b),s * (3 * a + 2 * b)), ?_⟩
    apply Prod.ext
    · change 3 * (s * (3 * a + 2 * b)) - 2 * (s * (2 * a + 3 * b)) = a
      linear_combination a * hs
    · change 3 * (s * (2 * a + 3 * b)) - 2 * (s * (3 * a + 2 * b)) = b
      linear_combination b * hs
theorem companion_sum {q:ℕ} [NeZero q] (h5:¬5 ∣ q) (f:ZMod q → ZMod q → ℝ) :
    (∑ j, ∑ k,f (3 * k - 2 * j) (3 * j - 2 * k)) = ∑ i, ∑ l,f i l:=by
  have h:=(companionMap_bijective h5).sum_comp (fun p => f p.1 p.2)
  simpa only [Fintype.sum_prod_type,companionMap] using h
theorem companion_symmetry {q:ℕ} (j k:ZMod q) :
    companionMap (k,j) = ((companionMap (j,k)).2,(companionMap (j,k)).1):=rfl
private def zz58:"s003a"="s003a":=by decide+kernel
theorem affine_preimages_exact {q N:ℕ} [NeZero q] (hN:0 < N) (hdiv:N ∣ q)
    (c y:ZMod q) (hex:∃ x,(N:ZMod q) * x + c = y) :
    (Finset.univ.filter fun x:ZMod q => N * x + c = y).card = N:=by
  apply le_antisymm (affine_preimages N hN c y)
  obtain ⟨m,rfl⟩:=hdiv
  obtain ⟨x₀,hx₀⟩:=hex
  have hm:0 < m:=by
    apply Nat.pos_of_ne_zero
    intro hm
    exact NeZero.ne (N * m) (by rw [hm,mul_zero])
  have hnm:(N:ZMod (N * m)) * m = 0:=by
    simpa only [Nat.cast_mul] using ZMod.natCast_self (N * m)
  have hcard:(Finset.univ:Finset (Fin N)).card ≤
      (Finset.univ.filter fun x:ZMod (N * m) => N * x + c = y).card:=by
    apply Finset.card_le_card_of_injOn (fun r:Fin N => x₀ + ((m * r.val:ℕ):ZMod (N * m)))
    · intro r _
      apply Finset.mem_filter.mpr
      refine ⟨Finset.mem_univ _, ?_⟩
      dsimp only
      rw [Nat.cast_mul]
      calc
        (N:ZMod (N * m)) * (x₀ + m * r.val) + c = N * x₀ + c + (N * m) * r.val:=by ring
        _ = y:=by rw [hnm,zero_mul,add_zero,hx₀]
    · intro r _ s _ h
      have heq:=add_left_cancel h
      have hr:m * r.val < N * m:=by simpa only [mul_comm N m] using Nat.mul_lt_mul_of_pos_left r.isLt hm
      have hs:m * s.val < N * m:=by simpa only [mul_comm N m] using Nat.mul_lt_mul_of_pos_left s.isLt hm
      have hv:=congrArg ZMod.val heq
      rw [ZMod.val_natCast_of_lt hr,ZMod.val_natCast_of_lt hs] at hv
      exact Fin.ext (Nat.eq_of_mul_eq_mul_left hm hv)
  simpa only [Finset.card_univ,Fintype.card_fin] using hcard
theorem mul_fiber_card {q N:ℕ} [NeZero q] (hN:0 < N) (hdiv:N ∣ q) (y:ZMod q) :
    (Finset.univ.filter fun x:ZMod q => N * x = y).card =
      if ZMod.castHom hdiv (ZMod N) y = 0 then N else 0:=by
  classical
  let π:=ZMod.castHom hdiv (ZMod N)
  by_cases hy:π y = 0
  · rw [if_pos hy]
    have hv:N ∣ y.val:=by
      apply (ZMod.natCast_eq_zero_iff y.val N).mp
      simpa only [π,ZMod.castHom_apply,ZMod.cast_eq_val] using hy
    obtain ⟨r,hr⟩:=hv
    have hex:∃ x:ZMod q,N * x + 0 = y:=by
      refine ⟨(r:ZMod q), ?_⟩
      rw [add_zero, ← Nat.cast_mul, ← hr,ZMod.natCast_zmod_val]
    simpa only [add_zero] using affine_preimages_exact hN hdiv 0 y hex
  · rw [if_neg hy]
    apply Finset.card_eq_zero.mpr
    apply Finset.eq_empty_iff_forall_notMem.mpr
    intro x hx
    have heq:=congrArg π (Finset.mem_filter.mp hx).2
    rw [map_mul,map_natCast,ZMod.natCast_self,zero_mul] at heq
    exact hy heq.symm
theorem first_middle_fiber {q:ℕ} [NeZero q] (h3:3 ∣ q) (i j:ZMod q) :
    (Finset.univ.filter fun k:ZMod q => 3 * k - 2 * j = i).card =
      if ZMod.castHom h3 (ZMod 3) i = ZMod.castHom h3 (ZMod 3) j then 3 else 0:=by
  simp only [sub_eq_iff_eq_add]
  have h:=mul_fiber_card (by norm_num:0 < 3) h3 (i + 2 * j)
  simp only [Nat.cast_ofNat] at h
  have hcond:ZMod.castHom h3 (ZMod 3) (i + 2 * j) = 0 ↔
      ZMod.castHom h3 (ZMod 3) i = ZMod.castHom h3 (ZMod 3) j:=by
    rw [map_add,map_mul,map_ofNat,show (2:ZMod 3) = -1 from rfl,neg_one_mul,
      ← sub_eq_add_neg,sub_eq_zero]
  simpa only [hcond] using h
theorem first_last_fiber {q:ℕ} [NeZero q] (h2:2 ∣ q) (i k:ZMod q) :
    (Finset.univ.filter fun j:ZMod q => 3 * k - 2 * j = i).card =
      if ZMod.castHom h2 (ZMod 2) i = ZMod.castHom h2 (ZMod 2) k then 2 else 0:=by
  have hpred (j:ZMod q):3 * k - 2 * j = i ↔ 2 * j = 3 * k - i:=by
    constructor <;> intro h <;> linear_combination -h
  simp_rw [hpred]
  have h:=mul_fiber_card (by norm_num:0 < 2) h2 (3 * k - i)
  simp only [Nat.cast_ofNat] at h
  have hcond:ZMod.castHom h2 (ZMod 2) (3 * k - i) = 0 ↔
      ZMod.castHom h2 (ZMod 2) i = ZMod.castHom h2 (ZMod 2) k:=by
    rw [map_sub,map_mul,map_ofNat,show (3:ZMod 2) = 1 from rfl,
      one_mul,sub_eq_zero,eq_comm]
  simpa only [hcond] using h
private def zz59:"s003b"="s003b":=by decide+kernel
theorem sum_comp_eq_fibers {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (T:ι → κ) (f:κ → ℝ) :
    (∑ i,f (T i)) = ∑ j,((Finset.univ.filter fun i => T i = j).card:ℝ) * f j:=by
  calc
    (∑ i,f (T i)) = ∑ i, ∑ j,if T i = j then f j else 0:=by simp
    _ = ∑ j, ∑ i,if T i = j then f j else 0:=Finset.sum_comm
    _ = _:=by
      apply Finset.sum_congr rfl
      intro j _
      rw [← Finset.sum_filter]
      simp only [Finset.sum_const,nsmul_eq_mul]
theorem first_middle_marginal {q:ℕ} [NeZero q] (h3:3 ∣ q) (f:ZMod q → ZMod q → ℝ) :
    (∑ j, ∑ k,f (3 * k - 2 * j) j) =
      3 * ∑ i, ∑ j,if ZMod.castHom h3 (ZMod 3) i = ZMod.castHom h3 (ZMod 3) j
        then f i j else 0:=by
  have hrow (j:ZMod q):(∑ k,f (3 * k - 2 * j) j) =
      3 * ∑ i,if ZMod.castHom h3 (ZMod 3) i = ZMod.castHom h3 (ZMod 3) j then f i j else 0:=by
    rw [sum_comp_eq_fibers (fun k:ZMod q => 3 * k - 2 * j) (fun i => f i j),Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro i _
    rw [first_middle_fiber h3]
    split_ifs <;> norm_num
  simp_rw [hrow]
  rw [← Finset.mul_sum,Finset.sum_comm]
theorem first_last_marginal {q:ℕ} [NeZero q] (h2:2 ∣ q) (f:ZMod q → ZMod q → ℝ) :
    (∑ j, ∑ k,f (3 * k - 2 * j) k) =
      2 * ∑ i, ∑ k,if ZMod.castHom h2 (ZMod 2) i = ZMod.castHom h2 (ZMod 2) k
        then f i k else 0:=by
  rw [Finset.sum_comm]
  have hrow (k:ZMod q):(∑ j,f (3 * k - 2 * j) k) =
      2 * ∑ i,if ZMod.castHom h2 (ZMod 2) i = ZMod.castHom h2 (ZMod 2) k then f i k else 0:=by
    rw [sum_comp_eq_fibers (fun j:ZMod q => 3 * k - 2 * j) (fun i => f i k),Finset.mul_sum]
    apply Finset.sum_congr rfl
    intro i _
    rw [first_last_fiber h2]
    split_ifs <;> norm_num
  simp_rw [hrow]
  rw [← Finset.mul_sum,Finset.sum_comm]
end Green24Proof
end 
section 
namespace Green24Proof
noncomputable def squarePotential (r x y:ℝ):ℝ :=
  (x ^ 2 - max (x - r * y) 0 ^ 2) / (2 * r)
theorem sum_swap_average {ι:Type*} [Fintype ι] (f:ι → ι → ℝ) :
    (∑ i, ∑ j,(f i j + f j i) / 2) = ∑ i, ∑ j,f i j:=by
  have hswap:(∑ i, ∑ j,f j i) = ∑ i, ∑ j,f i j:=Finset.sum_comm
  simp only [add_div,Finset.sum_add_distrib, ← Finset.sum_div]
  rw [hswap]
  ring
private def zz60:"s003c"="s003c":=by decide+kernel
theorem first_middle_marginal_of_support {q:ℕ} [NeZero q] (h3:3 ∣ q)
    (f:ZMod q → ZMod q → ℝ)
    (hf:∀ i j,ZMod.castHom h3 (ZMod 3) i ≠ ZMod.castHom h3 (ZMod 3) j → f i j = 0) :
    (∑ j, ∑ k,f (3 * k - 2 * j) j) = 3 * ∑ i, ∑ j,f i j:=by
  rw [first_middle_marginal h3]
  congr 1
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro j _
  split_ifs with h
  · rfl
  · exact (hf i j h).symm
theorem first_last_marginal_of_support {q:ℕ} [NeZero q] (h2:2 ∣ q)
    (f:ZMod q → ZMod q → ℝ)
    (hf:∀ i k,ZMod.castHom h2 (ZMod 2) i ≠ ZMod.castHom h2 (ZMod 2) k → f i k = 0) :
    (∑ j, ∑ k,f (3 * k - 2 * j) k) = 2 * ∑ i, ∑ k,f i k:=by
  rw [first_last_marginal h2]
  congr 1
  apply Finset.sum_congr rfl
  intro i _
  apply Finset.sum_congr rfl
  intro k _
  split_ifs with h
  · rfl
  · exact (hf i k h).symm
noncomputable def firstMiddlePotentialRow {q:ℕ} (f:ZMod q → ZMod q → ℝ)
    (j k:ZMod q):ℝ :=
  (f (3 * k - 2 * j) j + f (3 * j - 2 * k) k) / 2 - 3 * ((f j k + f k j) / 2)
noncomputable def firstLastPotentialRow {q:ℕ} (f:ZMod q → ZMod q → ℝ)
    (j k:ZMod q):ℝ :=
  (f (3 * k - 2 * j) k + f (3 * j - 2 * k) j) / 2 - 2 * ((f j k + f k j) / 2)
noncomputable def companionPotentialRow {q:ℕ} (f:ZMod q → ZMod q → ℝ)
    (j k:ZMod q):ℝ:=f (3 * k - 2 * j) (3 * j - 2 * k) - f j k
theorem firstMiddlePotentialRow_sum {q:ℕ} [NeZero q] (h3:3 ∣ q)
    (f:ZMod q → ZMod q → ℝ)
    (hf:∀ i j,ZMod.castHom h3 (ZMod 3) i ≠ ZMod.castHom h3 (ZMod 3) j → f i j = 0) :
    (∑ j, ∑ k,firstMiddlePotentialRow f j k) = 0:=by
  unfold firstMiddlePotentialRow
  simp only [Finset.sum_sub_distrib, ← Finset.mul_sum]
  rw [sum_swap_average (fun j k => f (3 * k - 2 * j) j),sum_swap_average,
    first_middle_marginal_of_support h3 f hf,sub_self]
theorem firstLastPotentialRow_sum {q:ℕ} [NeZero q] (h2:2 ∣ q)
    (f:ZMod q → ZMod q → ℝ)
    (hf:∀ i k,ZMod.castHom h2 (ZMod 2) i ≠ ZMod.castHom h2 (ZMod 2) k → f i k = 0) :
    (∑ j, ∑ k,firstLastPotentialRow f j k) = 0:=by
  unfold firstLastPotentialRow
  simp only [Finset.sum_sub_distrib, ← Finset.mul_sum]
  rw [sum_swap_average (fun j k => f (3 * k - 2 * j) k),sum_swap_average,
    first_last_marginal_of_support h2 f hf,sub_self]
private def zz61:"s003d"="s003d":=by decide+kernel
theorem companionPotentialRow_sum {q:ℕ} [NeZero q] (h5:¬5 ∣ q)
    (f:ZMod q → ZMod q → ℝ):(∑ j, ∑ k,companionPotentialRow f j k) = 0:=by
  simp only [companionPotentialRow,Finset.sum_sub_distrib,companion_sum h5,sub_self]
end Green24Proof
end 
section 
namespace Green24Proof.ExpressionCertificates
open QuadraticCertificates
abbrev NormalForm:=Quadratic × Hinges
noncomputable def normalEval (f:NormalForm) (x:Point):ℝ :=
  quadraticEval f.1 x + hingeEval f.2 x
def normalAdd (f g:NormalForm):NormalForm:=(f.1 + g.1,f.2 ++ g.2)
def normalScale (c:ℚ) (f:NormalForm):NormalForm :=
  (c • f.1,f.2.map fun t => (c * t.1,t.2))
theorem hingeEval_append (hs ts:Hinges) (x:Point) :
    hingeEval (hs ++ ts) x = hingeEval hs x + hingeEval ts x:=by
  simp [hingeEval]
theorem hingeEval_scale (c:ℚ) (hs:Hinges) (x:Point) :
    hingeEval (hs.map fun t => (c * t.1,t.2)) x = (c:ℝ) * hingeEval hs x:=by
  induction hs with
  | nil => simp [hingeEval]
  | cons t ts ih =>
    simp only [List.map_cons,hingeEval,List.map_cons,List.sum_cons,Rat.cast_mul] at *
    rw [ih]
    ring
theorem normalEval_add (f g:NormalForm) (x:Point) :
    normalEval (normalAdd f g) x = normalEval f x + normalEval g x:=by
  simp only [normalEval,normalAdd,quadraticEval_add,hingeEval_append]
  ring
private def zz62:"s003e"="s003e":=by decide+kernel
theorem normalEval_scale (c:ℚ) (f:NormalForm) (x:Point) :
    normalEval (normalScale c f) x = (c:ℝ) * normalEval f x:=by
  simp only [normalEval,normalScale,quadraticEval_smul,hingeEval_scale]
  ring
def normalSum (fs:List NormalForm):NormalForm:=fs.foldr normalAdd (0,[])
theorem normalEval_sum (fs:List NormalForm) (x:Point) :
    normalEval (normalSum fs) x = (fs.map fun f => normalEval f x).sum:=by
  induction fs with
  | nil => simp [normalSum,normalEval,quadraticEval_zero,hingeEval]
  | cons f fs ih =>
    simpa only [normalSum,List.foldr_cons,List.map_cons,List.sum_cons,normalEval_add]
      using congrArg (fun y => normalEval f x + y) ih
def symmetricProduct (a b:Linear):Quadratic:=(1 / 2:ℚ) • (product a b + product b a)
theorem symmetricProduct_eval (a b:Linear) (x:Point) :
    quadraticEval (symmetricProduct a b) x = linearEval a x * linearEval b x:=by
  simp only [symmetricProduct,quadraticEval_smul,quadraticEval_add,quadraticEval_product]
  norm_num
  ring
theorem linearEval_sub (a b:Linear) (x:Point) :
    linearEval (a - b) x = linearEval a x - linearEval b x:=by
  rw [sub_eq_add_neg,linearEval_add,linearEval_neg]
  rfl
inductive Atom where
  | prod (a b:Linear)
  | area (a b c:Linear)
  | potential (r:ℚ) (a b:Linear)
noncomputable def atomEval (t:Atom) (x:Point):ℝ :=
  match t with
  | .prod a b => linearEval a x * linearEval b x
  | .area a b c => 4 * kernel (linearEval a x) (linearEval b x) (linearEval c x)
  | .potential r a b => squarePotential (r:ℝ) (linearEval a x) (linearEval b x)
def compileAtom:Atom → NormalForm
  | .prod a b => (symmetricProduct a b,[])
  | .area a b c =>
      ((2:ℚ) • symmetricProduct a b + (2:ℚ) • symmetricProduct b c + (2:ℚ) • symmetricProduct c a -
        product a a - product b b - product c c,
        [(1,a - b - c),(1,b - a - c),(1,c - a - b)])
  | .potential r a b =>
      ((1 / (2 * r):ℚ) • product a a,[(-1 / (2 * r),a - r • b)])
private def zz63:"s003f"="s003f":=by decide+kernel
theorem quadraticEval_neg (Q:Quadratic) (x:Point) :
    quadraticEval (-Q) x = -quadraticEval Q x:=by
  simp [quadraticEval,Finset.sum_neg_distrib]
theorem quadraticEval_sub (Q R:Quadratic) (x:Point) :
    quadraticEval (Q - R) x = quadraticEval Q x - quadraticEval R x:=by
  rw [sub_eq_add_neg,quadraticEval_add,quadraticEval_neg]
  rfl
theorem compileAtom_sound (t:Atom) (x:Point) :
    normalEval (compileAtom t) x = atomEval t x:=by
  cases t with
  | prod a b => simp [compileAtom,normalEval,atomEval,hingeEval,symmetricProduct_eval]
  | area a b c =>
    simp only [compileAtom,normalEval,quadraticEval_sub,quadraticEval_add,
      quadraticEval_smul,symmetricProduct_eval,quadraticEval_product,
      hingeEval,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
      Rat.cast_one,Rat.cast_ofNat,one_mul,linearEval_sub,atomEval,kernel]
    ring
  | potential r a b =>
    simp only [compileAtom,normalEval,quadraticEval_smul,quadraticEval_product,
      hingeEval,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
      Rat.cast_div,Rat.cast_mul,Rat.cast_ofNat,Rat.cast_one,Rat.cast_neg,
      linearEval_sub,linearEval_smul,atomEval,squarePotential]
    ring
abbrev Expression:=List (ℚ × Atom)
noncomputable def expressionEval (e:Expression) (x:Point):ℝ :=
  (e.map fun t => (t.1:ℝ) * atomEval t.2 x).sum
def compile (e:Expression):NormalForm:=normalSum (e.map fun t => normalScale t.1 (compileAtom t.2))
theorem compile_sound (e:Expression) (x:Point) :
    normalEval (compile e) x = expressionEval e x:=by
  simp only [compile,normalEval_sum,List.map_map,normalEval_scale,compileAtom_sound,
    expressionEval,Function.comp_def]
private def zz64:"s0040"="s0040":=by decide+kernel
theorem max_mul_sq_of_nonneg (s a:ℝ) (hs:0 ≤ s) :
    max (s * a) 0 ^ 2 = s ^ 2 * max a 0 ^ 2:=by
  rw [show max (s * a) 0 = s * max a 0 by
    simpa using (mul_max_of_nonneg a 0 hs).symm]
  ring
theorem max_neg_sq (a:ℝ):max (-a) 0 ^ 2 = a ^ 2 - max a 0 ^ 2:=by
  by_cases h:0 ≤ a
  · rw [max_eq_left h,max_eq_right (neg_nonpos.mpr h)]
    ring
  · have h':=le_of_not_ge h
    rw [max_eq_right h',max_eq_left (neg_nonneg.mpr h')]
    ring
def rewriteHinge (c s:ℚ) (a:Linear):NormalForm :=
  if 0 ≤ s then (0,[(c * s ^ 2,a)])
  else ((c * s ^ 2) • product a a,[(-c * s ^ 2,a)])
theorem rewriteHinge_sound (c s:ℚ) (a:Linear) (x:Point) :
    normalEval (rewriteHinge c s a) x = (c:ℝ) * max (linearEval (s • a) x) 0 ^ 2:=by
  rw [linearEval_smul]
  by_cases hs:0 ≤ s
  · rw [rewriteHinge,if_pos hs,normalEval,quadraticEval_zero]
    simp only [hingeEval,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
      Rat.cast_mul,Rat.cast_pow,add_zero,zero_add]
    rw [max_mul_sq_of_nonneg _ _ (by exact_mod_cast hs)]
    ring
  · have hs':0 ≤ -(s:ℝ):=by exact_mod_cast (neg_nonneg.mpr (le_of_not_ge hs))
    rw [rewriteHinge,if_neg hs,normalEval,quadraticEval_smul,quadraticEval_product]
    simp only [hingeEval,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
      Rat.cast_mul,Rat.cast_pow,Rat.cast_neg,add_zero]
    rw [show (s:ℝ) * linearEval a x = (-(s:ℝ)) * (-linearEval a x) by ring,
      max_mul_sq_of_nonneg _ _ hs',max_neg_sq]
    ring
abbrev Rewrites:=List (ℚ × Linear)
def rewriteCheck:Hinges → Rewrites → Bool
  | [],[] => true
  | (_,v) :: hs,(s,a) :: ws => linearEq v (s • a) && rewriteCheck hs ws
  | _,_ => false
def rewriteAll:Hinges → Rewrites → NormalForm
  | (c,_) :: hs,(s,a) :: ws => normalAdd (rewriteHinge c s a) (rewriteAll hs ws)
  | _,_ => (0,[])
theorem rewriteAll_sound (hs:Hinges) (ws:Rewrites) (x:Point)
    (h:rewriteCheck hs ws = true):normalEval (rewriteAll hs ws) x = hingeEval hs x:=by
  induction hs generalizing ws with
  | nil =>
    cases ws with
    | nil => simp [rewriteAll,normalEval,quadraticEval_zero,hingeEval]
    | cons w ws => simp [rewriteCheck] at h
  | cons t hs ih =>
    cases ws with
    | nil => simp [rewriteCheck] at h
    | cons w ws =>
      rcases t with ⟨c,v⟩
      rcases w with ⟨s,a⟩
      simp only [rewriteCheck,Bool.and_eq_true,linearEq_eq_true] at h
      simp only [rewriteAll,normalEval_add,rewriteHinge_sound,ih ws h.2,hingeEval,
        List.map_cons,List.sum_cons,h.1]
def insertHinge (c:ℚ) (a:Linear):Hinges → Hinges
  | [] => [(c,a)]
  | (d,b) :: hs => if linearEq a b then (c + d,b) :: hs else (d,b) :: insertHinge c a hs
private def zz65:"s0041"="s0041":=by decide+kernel
theorem insertHinge_sound (c:ℚ) (a:Linear) (hs:Hinges) (x:Point) :
    hingeEval (insertHinge c a hs) x = (c:ℝ) * max (linearEval a x) 0 ^ 2 + hingeEval hs x:=by
  induction hs with
  | nil => simp [insertHinge,hingeEval]
  | cons t hs ih =>
    rcases t with ⟨d,b⟩
    by_cases h:linearEq a b = true
    · have hab:=(linearEq_eq_true a b).mp h
      rw [insertHinge,if_pos h]
      simp only [hingeEval,List.map_cons,List.sum_cons,Rat.cast_add,hab]
      ring
    · have h':linearEq a b = false:=Bool.eq_false_iff.mpr h
      simp only [insertHinge,h',Bool.false_eq_true,if_false,hingeEval,
        List.map_cons,List.sum_cons] at *
      rw [ih]
      ring
def collect:Hinges → Hinges
  | [] => []
  | (c,a) :: hs => insertHinge c a (collect hs)
theorem collect_sound (hs:Hinges) (x:Point):hingeEval (collect hs) x = hingeEval hs x:=by
  induction hs with
  | nil => rfl
  | cons t hs ih =>
    change hingeEval (insertHinge t.1 t.2 (collect hs)) x = hingeEval (t :: hs) x
    rw [insertHinge_sound,ih]
    rfl
def zeroHinges (hs:Hinges):Bool:=hs.all fun t => t.1 == 0
theorem zeroHinges_sound (hs:Hinges) (x:Point) (h:zeroHinges hs = true) :
    hingeEval hs x = 0:=by
  induction hs with
  | nil => simp [hingeEval]
  | cons t hs ih =>
    simp only [zeroHinges,List.all_cons,Bool.and_eq_true,beq_iff_eq] at h
    simpa [hingeEval,h.1] using ih h.2
def normalEqual (f g:NormalForm):Bool :=
  quadraticEq f.1 g.1 && zeroHinges (collect (f.2 ++ (g.2.map fun t => (-t.1,t.2))))
theorem normalEqual_sound (f g:NormalForm) (x:Point) (h:normalEqual f g = true) :
    normalEval f x = normalEval g x:=by
  simp only [normalEqual,Bool.and_eq_true,quadraticEq_eq_true] at h
  have hz:=zeroHinges_sound _ x h.2
  rw [collect_sound,hingeEval_append] at hz
  have hn:hingeEval (g.2.map fun t => (-t.1,t.2)) x = -hingeEval g.2 x:=by
    simpa only [neg_one_mul,Rat.cast_neg,Rat.cast_one] using hingeEval_scale (-1) g.2 x
  rw [hn] at hz
  simp only [normalEval,h.1]
  linarith
def identityCheck (e:Expression) (ws:Rewrites) (target:NormalForm):Bool :=
  rewriteCheck (compile e).2 ws &&
    normalEqual (normalAdd ((compile e).1,[]) (rewriteAll (compile e).2 ws)) target
private def zz66:"s0042"="s0042":=by decide+kernel
theorem identityCheck_sound (e:Expression) (ws:Rewrites) (target:NormalForm)
    (x:Point) (h:identityCheck e ws target = true) :
    expressionEval e x = normalEval target x:=by
  simp only [identityCheck,Bool.and_eq_true] at h
  have he:=normalEqual_sound _ target x h.2
  rw [normalEval_add,rewriteAll_sound _ _ x h.1] at he
  simpa only [normalEval,hingeEval,List.map_nil,List.sum_nil,add_zero,
    ← compile_sound e x] using he
def rationalLinear (a:IntegerQuadraticCertificates.Linear):Linear:=fun i => a i
def rationalQuadratic (Q:IntegerQuadraticCertificates.Quadratic):Quadratic:=fun i j => Q i j
def rationalHinges (hs:IntegerQuadraticCertificates.Hinges):Hinges :=
  hs.map fun t => (t.1,rationalLinear t.2)
theorem rationalLinear_eval (a:IntegerQuadraticCertificates.Linear) (x:Point) :
    linearEval (rationalLinear a) x = IntegerQuadraticCertificates.linearEval a x:=by
  simp [linearEval,rationalLinear,IntegerQuadraticCertificates.linearEval]
theorem rationalQuadratic_eval (Q:IntegerQuadraticCertificates.Quadratic) (x:Point) :
    quadraticEval (rationalQuadratic Q) x = IntegerQuadraticCertificates.quadraticEval Q x:=by
  simp [quadraticEval,rationalQuadratic,IntegerQuadraticCertificates.quadraticEval]
theorem rationalHinges_eval (hs:IntegerQuadraticCertificates.Hinges) (x:Point) :
    hingeEval (rationalHinges hs) x = IntegerQuadraticCertificates.hingeEval hs x:=by
  simp [hingeEval,rationalHinges,IntegerQuadraticCertificates.hingeEval,
    Function.comp_def,rationalLinear_eval]
def rationalNormal (Q:IntegerQuadraticCertificates.Quadratic)
    (hs:IntegerQuadraticCertificates.Hinges) (den:ℤ):NormalForm :=
  normalScale (1 / (den:ℚ)) (rationalQuadratic Q,rationalHinges hs)
private def zz67:"s0043"="s0043":=by decide+kernel
theorem rationalNormal_eval (Q:IntegerQuadraticCertificates.Quadratic)
    (hs:IntegerQuadraticCertificates.Hinges) (den:ℤ) (x:Point) :
    normalEval (rationalNormal Q hs den) x =
      (IntegerQuadraticCertificates.quadraticEval Q x + IntegerQuadraticCertificates.hingeEval hs x) / den:=by
  rw [rationalNormal,normalEval_scale]
  simp only [normalEval,rationalQuadratic_eval,
    rationalHinges_eval,Rat.cast_div,Rat.cast_one,Rat.cast_intCast]
  ring
end Green24Proof.ExpressionCertificates
private def zz1999:"s07cf"="s07cf":=by decide+kernel
end 
section 
namespace Green24Proof.FullPhaseRows
open QuadraticCertificates ExpressionCertificates
abbrev Phase:=ZMod 4
def coordinate (i:Fin 4) (s:ℚ:=1):Linear:=fun j => if j = i then s else 0
def scale (c:ℚ) (e:Expression):Expression:=e.map fun t => (c * t.1,t.2)
theorem expressionEval_scale (c:ℚ) (e:Expression) (x:Point) :
    expressionEval (scale c e) x = (c:ℝ) * expressionEval e x:=by
  induction e with
  | nil => simp [scale,expressionEval]
  | cons t ts ih =>
    simp only [scale,List.map_cons,expressionEval,List.map_cons,List.sum_cons,Rat.cast_mul] at *
    rw [ih]
    ring
theorem expressionEval_append (e f:Expression) (x:Point) :
    expressionEval (e ++ f) x = expressionEval e x + expressionEval f x:=by
  simp [expressionEval]
theorem coordinate_eval (i:Fin 4) (s:ℚ) (x:Point) :
    linearEval (coordinate i s) x = (s:ℝ) * x i:=by
  simp [linearEval,coordinate,apply_ite,ite_mul]
def area:Expression :=
  [(1 / 2, .area (coordinate 0) (coordinate 1 2) (coordinate 2 3)),
   (1 / 2, .area (coordinate 3) (coordinate 2 2) (coordinate 1 3))]
private def zz68:"s0044"="s0044":=by decide+kernel
theorem area_eval (x:Point):expressionEval area x =
    2 * kernel (x 0) (2 * x 1) (3 * x 2) + 2 * kernel (x 3) (2 * x 2) (3 * x 1):=by
  simp only [area,expressionEval,List.map_cons,List.map_nil,List.sum_cons,
    List.sum_nil,atomEval,coordinate_eval,Rat.cast_div,Rat.cast_one,Rat.cast_ofNat,one_mul]
  ring
def rhoExpression:Expression :=
  [(4, .prod (coordinate 0) (coordinate 1)),
   (-1 / 4, .area (coordinate 0) (coordinate 0 2) (coordinate 1 3)),
   (-1 / 4, .area (coordinate 1) (coordinate 1 2) (coordinate 0 3))]
inductive Position where
  | firstMiddle | firstLast | middleLast | companion
def positionDecidableEq:DecidableEq Position:=by
  intro a b
  cases a <;> cases b <;>
    first | exact .isTrue rfl | exact .isFalse (by intro h; cases h)
def Position.indices:Position → Fin 4 × Fin 4
  | .firstMiddle => (0,1)
  | .firstLast => (0,2)
  | .middleLast => (1,2)
  | .companion => (0,3)
def Position.unordered:Position → Bool
  | .middleLast | .companion => true
  | _ => false
inductive Shape where
  | bilinear
  | potential (r:ℚ)
structure Potential where
  position:Position
  left:Phase
  right:Phase
  same:Bool
  shape:Shape
  sign:ℚ
def phi (l:Potential) (a b:Linear) (p q:Phase) (same:Bool) (w:ℚ):Expression :=
  let (a,b,p,q):=if l.position.unordered ∧ q.val < p.val then (b,a,q,p) else (a,b,p,q)
  if p = l.left ∧ q = l.right ∧ same = l.same then
    match l.shape with
    | .bilinear => [(w, .prod a b)]
    | .potential r =>
        if l.position.unordered ∧ p = q then
          [(w / 2, .potential r a b),(w / 2, .potential r b a)]
        else [(w, .potential r a b)]
  else []
def quadPhases (p q:Phase):Fin 4 → Phase:=![3 * q - 2 * p,p,q,3 * p - 2 * q]
def quadSame (a b:Fin 4) (same:Bool):Bool:=if a.val / 2 = b.val / 2 then true else same
def potentialQuad (l:Potential) (p q:Phase) (same:Bool):Expression :=
  let (a,b):=l.position.indices
  let phases:=quadPhases p q
  if l.position.unordered then
    phi l (coordinate a) (coordinate b) (phases a) (phases b) (quadSame a b same) l.sign
  else
    phi l (coordinate a) (coordinate b) (phases a) (phases b) (quadSame a b same) (l.sign / 2) ++
    phi l (coordinate (3 - a)) (coordinate (3 - b)) (phases (3 - a)) (phases (3 - b))
      (quadSame (3 - a) (3 - b) same) (l.sign / 2)
def potentialPair (l:Potential) (p q:Phase) (same:Bool):Expression :=
  letI:=FullPhaseRows.positionDecidableEq
  if l.position.unordered then
    phi l (coordinate 0) (coordinate 1) p q same (-l.sign)
  else
    let fac:ℚ:=if l.position = .firstMiddle then 3 / 2 else 1
    phi l (coordinate 0) (coordinate 1) p q same (-fac * l.sign) ++
    phi l (coordinate 1) (coordinate 0) q p same (-fac * l.sign)
inductive Label where
  | potential (l:Potential)
  | balance (phase:Phase) (sign:ℚ)
  | child (parity:Fin 2)
  | grandchild (phase:Phase)
  | heightChild (parity:Fin 2)
  | ordered (parity:Fin 2)
  | massSquare (coloured:Bool) (coefficients:Phase → ℚ)
  | normalization
def pairProduct (w:ℚ):Expression:=[(w, .prod (coordinate 0) (coordinate 1))]
def parity (p:Phase):Fin 2:=⟨p.val % 2,Nat.mod_lt _ (by decide)⟩
def rowQuad (l:Label) (p q:Phase) (same:Bool):Expression :=
  match l with
  | .potential l => potentialQuad l p q same
  | .child r | .heightChild r => if parity p = r ∧ parity q = r then area else []
  | .grandchild r => if p = r ∧ q = r then area else []
  | _ => []
def rowPair (S:ℚ) (l:Label) (p q:Phase) (same:Bool):Expression :=
  match l with
  | .potential l => potentialPair l p q same
  | .balance r s =>
      let w (p:Phase):ℚ:=if parity p = 0 then 1 else -S
      pairProduct (s * ((if p = r then w q else 0) + (if q = r then w p else 0)) / 2)
  | .child r => if parity p = r ∧ parity q = r then pairProduct (-8) else []
  | .grandchild r => if p = r ∧ q = r then pairProduct (-8) else []
  | .heightChild r =>
      if parity p = r ∧ parity q = r then
        pairProduct (-8 - (24 / 5:ℚ) * (-1) ^ (p.val / 2 + q.val / 2)) ++ scale (49 / 0x7d) rhoExpression
      else []
  | .ordered r =>
      if parity p = r ∧ parity q = r then
        let w (p:Phase):ℚ:=if p.val < 2 then -1 else 1
        pairProduct ((w p + w q) / 2)
      else []
  | .massSquare coloured v =>
      let fac:ℚ:=if coloured then (if same then 2 / 3 else -1 / 3) else 1
      pairProduct (-fac * v p * v q)
  | .normalization => pairProduct 1
def weightedQuad (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun t => scale t.1 (rowQuad t.2 p q same)
def weightedPair (S:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun t => scale t.1 (rowPair S t.2 p q same)
def quadSlack (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  weightedQuad rows p q same ++ scale (-1) area
def pairSlack (S margin:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  weightedPair S rows p q same ++ pairProduct (8 - 4 * margin)
end Green24Proof.FullPhaseRows
private def zz2000:"s07d0"="s07d0":=by decide+kernel
end 
section 
namespace Green24Proof.ParityPhaseRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows
abbrev Phase:=ZMod 2
structure Potential where
  position:Position
  left:Phase
  right:Phase
  same:Bool
  shape:Shape
  sign:ℚ
def phi (l:Potential) (a b:Linear) (p q:Phase) (same:Bool) (w:ℚ):Expression :=
  let (a,b,p,q):=if l.position.unordered ∧ q.val < p.val then (b,a,q,p) else (a,b,p,q)
  if p = l.left ∧ q = l.right ∧ same = l.same then
    match l.shape with
    | .bilinear => [(w, .prod a b)]
    | .potential r =>
        if l.position.unordered ∧ p = q then
          [(w / 2, .potential r a b),(w / 2, .potential r b a)]
        else [(w, .potential r a b)]
  else []
def quadPhases (p q:Phase):Fin 4 → Phase:=![q,p,q,p]
def quadSame (a b:Fin 4) (same:Bool):Bool:=if a.val / 2 = b.val / 2 then true else same
def potentialQuad (l:Potential) (p q:Phase) (same:Bool):Expression :=
  let (a,b):=l.position.indices
  let phases:=quadPhases p q
  if l.position.unordered then
    phi l (coordinate a) (coordinate b) (phases a) (phases b) (quadSame a b same) l.sign
  else
    phi l (coordinate a) (coordinate b) (phases a) (phases b) (quadSame a b same) (l.sign / 2) ++
    phi l (coordinate (3 - a)) (coordinate (3 - b)) (phases (3 - a)) (phases (3 - b))
      (quadSame (3 - a) (3 - b) same) (l.sign / 2)
def potentialPair (l:Potential) (p q:Phase) (same:Bool):Expression :=
  letI:=FullPhaseRows.positionDecidableEq
  if l.position.unordered then
    phi l (coordinate 0) (coordinate 1) p q same (-l.sign)
  else
    let fac:ℚ:=if l.position = .firstMiddle then 3 / 2 else 1
    phi l (coordinate 0) (coordinate 1) p q same (-fac * l.sign) ++
    phi l (coordinate 1) (coordinate 0) q p same (-fac * l.sign)
def weightedQuad (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun t => scale t.1 (potentialQuad t.2 p q same)
def weightedPair (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun t => scale t.1 (potentialPair t.2 p q same)
def quadSlack (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool):Expression :=
  weightedQuad rows p q same ++ scale (-1) area
def balanceCoefficient (μ:Phase → ℚ) (p q:Phase):ℚ :=
  (μ p * (if q = 0 then 1 else -1) + μ q * (if p = 0 then 1 else -1)) / 2
def pairSlack (rows:List (ℚ × Potential)) (μ:Phase → ℚ) (lam:ℚ)
    (p q:Phase) (same:Bool):Expression :=
  weightedPair rows p q same ++
  pairProduct (balanceCoefficient μ p q + if p = 0 ∧ q = 0 then 32 else 0) ++
  scale (-2 * lam) rhoExpression
end Green24Proof.ParityPhaseRows
private def zz2001:"s07d1"="s07d1":=by decide+kernel
end 
section 
namespace Green24Proof.FullPhaseSemantics
open QuadraticCertificates ExpressionCertificates FullPhaseRows
noncomputable def potentialValue (l:Potential) (a b:ℝ) (p q:Phase) (same:Bool):ℝ :=
  let (a,b,p,q):=if l.position.unordered ∧ q.val < p.val then (b,a,q,p) else (a,b,p,q)
  if p = l.left ∧ q = l.right ∧ same = l.same then
    match l.shape with
    | .bilinear => a * b
    | .potential r =>
        if l.position.unordered ∧ p = q then
          (squarePotential (r:ℝ) a b + squarePotential (r:ℝ) b a) / 2
        else squarePotential (r:ℝ) a b
  else 0
theorem phi_eval (l:Potential) (a b:Linear) (p q:Phase) (same:Bool) (w:ℚ) (x:Point) :
    expressionEval (phi l a b p q same w) x =
      (w:ℝ) * potentialValue l (linearEval a x) (linearEval b x) p q same:=by
  cases hs:l.shape <;> simp only [phi,potentialValue,hs]
  all_goals split_ifs <;> simp [expressionEval,atomEval] <;> ring
theorem rhoExpression_eval (x:Point) (hx:0 ≤ x 0) (hy:0 ≤ x 1) :
    expressionEval rhoExpression x = rho (x 0) (x 1):=by
  simp only [rhoExpression,expressionEval,List.map_cons,List.map_nil,
    List.sum_cons,List.sum_nil,atomEval,coordinate_eval,Rat.cast_ofNat,
    Rat.cast_div,Rat.cast_neg,Rat.cast_one,one_mul]
  have h:=kernel_diagonal_pair hx hy
  linarith
theorem pairProduct_eval (w:ℚ) (x:Point) :
    expressionEval (pairProduct w) x = (w:ℝ) * x 0 * x 1:=by
  simp [pairProduct,expressionEval,atomEval,coordinate_eval,mul_assoc]
private def zz69:"s0045"="s0045":=by decide+kernel
theorem weightedQuad_eval (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedQuad rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (rowQuad t.2 p q same) x).sum:=by
  induction rows with
  | nil => simp [weightedQuad,expressionEval]
  | cons t ts ih =>
    simp only [weightedQuad,List.flatMap_cons,expressionEval_append,
      expressionEval_scale,List.map_cons,List.sum_cons] at *
    rw [ih]
theorem weightedPair_eval (S:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedPair S rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (rowPair S t.2 p q same) x).sum:=by
  induction rows with
  | nil => simp [weightedPair,expressionEval]
  | cons t ts ih =>
    simp only [weightedPair,List.flatMap_cons,expressionEval_append,
      expressionEval_scale,List.map_cons,List.sum_cons] at *
    rw [ih]
theorem quadSlack_eval (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (rowQuad t.2 p q same) x).sum -
      (2 * kernel (x 0) (2 * x 1) (3 * x 2) + 2 * kernel (x 3) (2 * x 2) (3 * x 1)):=by
  rw [quadSlack,expressionEval_append,weightedQuad_eval,expressionEval_scale,area_eval]
  norm_num
  ring
theorem pairSlack_eval (S margin:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack S margin rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (rowPair S t.2 p q same) x).sum +
      (8 - 4 * (margin:ℝ)) * x 0 * x 1:=by
  rw [pairSlack,expressionEval_append,weightedPair_eval,pairProduct_eval]
  norm_cast
noncomputable def potentialQuadValue (l:Potential) (p q:Phase) (same:Bool) (x:Point):ℝ :=
  match l.position with
  | .firstMiddle => (l.sign:ℝ) / 2 *
      (potentialValue l (x 0) (x 1) (3 * q - 2 * p) p true +
       potentialValue l (x 3) (x 2) (3 * p - 2 * q) q true)
  | .firstLast => (l.sign:ℝ) / 2 *
      (potentialValue l (x 0) (x 2) (3 * q - 2 * p) q same +
       potentialValue l (x 3) (x 1) (3 * p - 2 * q) p same)
  | .middleLast => (l.sign:ℝ) * potentialValue l (x 1) (x 2) p q same
  | .companion => (l.sign:ℝ) * potentialValue l (x 0) (x 3) (3 * q - 2 * p) (3 * p - 2 * q) same
private def zz70:"s0046"="s0046":=by decide+kernel
theorem potentialQuad_eval (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialQuad l p q same) x = potentialQuadValue l p q same x:=by
  cases h:l.position <;>
    simp [potentialQuad,potentialQuadValue,h,Position.indices,Position.unordered,
      quadSame,quadPhases,phi_eval,expressionEval_append,coordinate_eval,
      Matrix.cons_val_two,Matrix.cons_val_three] <;> ring
noncomputable def potentialPairValue (l:Potential) (p q:Phase) (same:Bool) (x:Point):ℝ :=
  match l.position with
  | .firstMiddle => -(3 / 2:ℝ) * (l.sign:ℝ) *
      (potentialValue l (x 0) (x 1) p q same + potentialValue l (x 1) (x 0) q p same)
  | .firstLast => -(l.sign:ℝ) *
      (potentialValue l (x 0) (x 1) p q same + potentialValue l (x 1) (x 0) q p same)
  | .middleLast | .companion => -(l.sign:ℝ) * potentialValue l (x 0) (x 1) p q same
theorem potentialPair_eval (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialPair l p q same) x = potentialPairValue l p q same x:=by
  cases h:l.position <;>
    simp [potentialPair,potentialPairValue,h,Position.unordered,
      phi_eval,expressionEval_append,coordinate_eval] <;> ring
def quadPoint {q:ℕ} (g:ZMod q → ℝ) (j k:ZMod q):Point :=
  ![g (3 * k - 2 * j),g j,g k,g (3 * j - 2 * k)]
def pairPoint {q:ℕ} (g:ZMod q → ℝ) (j k:ZMod q):Point:=![g j,g k,0,0]
def sameColour {q:ℕ} (h3:3 ∣ q) (j k:ZMod q):Bool :=
  decide (ZMod.castHom h3 (ZMod 3) j = ZMod.castHom h3 (ZMod 3) k)
theorem cast_three_affine {q:ℕ} (h3:3 ∣ q) (j k:ZMod q) :
    ZMod.castHom h3 (ZMod 3) (3 * k - 2 * j) = ZMod.castHom h3 (ZMod 3) j:=by
  simp only [map_sub,map_mul,map_ofNat]
  have h30:(3:ZMod 3) = 0:=by decide
  have h21:(2:ZMod 3) = -1:=by decide
  rw [h30,h21]
  ring
theorem cast_four_affine {q:ℕ} (h4:4 ∣ q) (j k:ZMod q) :
    ZMod.castHom h4 (ZMod 4) (3 * k - 2 * j) =
      3 * ZMod.castHom h4 (ZMod 4) k - 2 * ZMod.castHom h4 (ZMod 4) j:=by
  simp only [map_sub,map_mul,map_ofNat]
private def zz71:"s0047"="s0047":=by decide+kernel
theorem sameColour_refl {q:ℕ} (h3:3 ∣ q) (j:ZMod q):sameColour h3 j j = true:=by
  simp [sameColour]
theorem sameColour_affine_left {q:ℕ} (h3:3 ∣ q) (j k t:ZMod q) :
    sameColour h3 (3 * k - 2 * j) t = sameColour h3 j t:=by
  simp only [sameColour,cast_three_affine]
theorem sameColour_affine_right {q:ℕ} (h3:3 ∣ q) (j k t:ZMod q) :
    sameColour h3 t (3 * k - 2 * j) = sameColour h3 t j:=by
  simp only [sameColour,cast_three_affine]
noncomputable def globalPotential {q:ℕ} (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (i j:ZMod q):ℝ :=
  potentialValue l (g i) (g j) (ZMod.castHom h4 (ZMod 4) i) (ZMod.castHom h4 (ZMod 4) j)
    (sameColour h3 i j)
noncomputable def potentialRow {q:ℕ} (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (j k:ZMod q):ℝ :=
  expressionEval (potentialQuad l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (quadPoint g j k) +
  expressionEval (potentialPair l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (pairPoint g j k)
theorem potentialRow_eq {q:ℕ} (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (j k:ZMod q) :
    potentialRow h4 h3 g l j k = (l.sign:ℝ) *
      match l.position with
      | .firstMiddle => firstMiddlePotentialRow (globalPotential h4 h3 g l) j k
      | .firstLast => firstLastPotentialRow (globalPotential h4 h3 g l) j k
      | .middleLast => 0
      | .companion => companionPotentialRow (globalPotential h4 h3 g l) j k:=by
  rw [potentialRow,potentialQuad_eval,potentialPair_eval]
  have hc:sameColour h3 k j = sameColour h3 j k:=by
    apply Bool.eq_iff_iff.mpr
    simp only [sameColour,decide_eq_true_eq]
    exact eq_comm
  cases h:l.position <;>
    simp only [potentialQuadValue,potentialPairValue,h,firstMiddlePotentialRow,
      firstLastPotentialRow,companionPotentialRow,globalPotential,cast_four_affine,
      sameColour_affine_left,sameColour_affine_right,sameColour_refl,hc]
  all_goals
    simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three]
    <;> ring
def admissible (l:Potential):Bool :=
  match l.position with
  | .firstMiddle => l.same
  | .firstLast => decide (parity l.left = parity l.right)
  | _ => true
private def zz72:"s0048"="s0048":=by decide+kernel
theorem potentialValue_firstMiddle_offColour (l:Potential) (hpos:l.position = .firstMiddle)
    (hs:l.same = true) (a b:ℝ) (p q:Phase):potentialValue l a b p q false = 0:=by
  simp [potentialValue,hpos,Position.unordered,hs]
theorem globalPotential_firstMiddle_support {q:ℕ} (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hpos:l.position = .firstMiddle)
    (hs:l.same = true) (i j:ZMod q)
    (hij:ZMod.castHom h3 (ZMod 3) i ≠ ZMod.castHom h3 (ZMod 3) j) :
    globalPotential h4 h3 g l i j = 0:=by
  unfold globalPotential
  have hc:sameColour h3 i j = false:=by
    exact decide_eq_false hij
  rw [hc]
  exact potentialValue_firstMiddle_offColour l hpos hs _ _ _ _
theorem potentialValue_firstLast_offParity (l:Potential) (hpos:l.position = .firstLast)
    (hl:parity l.left = parity l.right) (a b:ℝ) (p q:Phase) (same:Bool)
    (hpq:parity p ≠ parity q):potentialValue l a b p q same = 0:=by
  simp only [potentialValue,hpos,Position.unordered,Bool.false_eq_true,false_and,if_false]
  split_ifs with h
  · exact False.elim (hpq (by rw [h.1,h.2.1]; exact hl))
  · rfl
theorem parity_cast_four (p:Phase) :
    (parity p:ZMod 2) = ZMod.castHom (by decide:2 ∣ 4) (ZMod 2) p:=by
  fin_cases p <;> rfl
private def zz73:"s0049"="s0049":=by decide+kernel
theorem parity_cast {q:ℕ} (h4:4 ∣ q) (h2:2 ∣ q) (i:ZMod q) :
    (parity (ZMod.castHom h4 (ZMod 4) i):ZMod 2) = ZMod.castHom h2 (ZMod 2) i:=by
  rw [parity_cast_four]
  exact congrArg (fun f:ZMod q →+* ZMod 2 => f i)
    (ZMod.castHom_comp (by decide:2 ∣ 4) h4)
theorem globalPotential_firstLast_support {q:ℕ} (h4:4 ∣ q) (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hpos:l.position = .firstLast)
    (hl:parity l.left = parity l.right) (i j:ZMod q)
    (hij:ZMod.castHom h2 (ZMod 2) i ≠ ZMod.castHom h2 (ZMod 2) j) :
    globalPotential h4 h3 g l i j = 0:=by
  apply potentialValue_firstLast_offParity l hpos hl
  intro he
  apply hij
  have he':(parity (ZMod.castHom h4 (ZMod 4) i):ZMod 2) =
      parity (ZMod.castHom h4 (ZMod 4) j):=he
  rw [parity_cast h4 h2,parity_cast h4 h2] at he'
  exact he'
theorem potentialRow_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hl:admissible l = true) :
    (∑ j, ∑ k,potentialRow h4 h3 g l j k) = 0:=by
  simp_rw [potentialRow_eq]
  simp_rw [← Finset.mul_sum]
  cases hpos:l.position with
  | firstMiddle =>
    have hs:l.same = true:=by simpa only [admissible,hpos] using hl
    rw [firstMiddlePotentialRow_sum h3 (globalPotential h4 h3 g l)
      (globalPotential_firstMiddle_support h4 h3 g l hpos hs)]
    ring
  | firstLast =>
    have hp:parity l.left = parity l.right:=by
      simpa only [admissible,hpos,decide_eq_true_eq] using hl
    have h2:2 ∣ q:=dvd_trans (by decide:2 ∣ 4) h4
    rw [firstLastPotentialRow_sum h2 (globalPotential h4 h3 g l)
      (globalPotential_firstLast_support h4 h2 h3 g l hpos hp)]
    ring
  | middleLast => simp
  | companion => rw [companionPotentialRow_sum h5]; ring
end Green24Proof.FullPhaseSemantics
private def zz2002:"s07d2"="s07d2":=by decide+kernel
end 
section 
namespace Green24Proof.FullPhaseSymmetry
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
theorem potentialValue_swap (l:Potential) (hu:l.position.unordered = true)
    (a b:ℝ) (p q:Phase) (same:Bool) :
    potentialValue l b a q p same = potentialValue l a b p q same:=by
  rcases lt_trichotomy p.val q.val with h | h | h
  · simp [potentialValue,hu,h,not_lt_of_gt h]
  · have hpq:p = q:=ZMod.val_injective 4 h
    subst q
    cases hs:l.shape <;> simp only [potentialValue,hu,lt_self_iff_false,
      true_and,and_false,if_false,hs]
    all_goals split_ifs <;> ring
  · simp [potentialValue,hu,h,not_lt_of_gt h]
def reversePoint (x:Point):Point:=![x 3,x 2,x 1,x 0]
def swapPair (x:Point):Point:=![x 1,x 0,x 2,x 3]
private def zz74:"s004a"="s004a":=by decide+kernel
theorem reversePoint_nonneg (x:Point) (hx:∀ i,0 ≤ x i):∀ i,0 ≤ reversePoint x i:=by
  intro i
  fin_cases i <;> simpa [reversePoint] using hx _
theorem swapPair_nonneg (x:Point) (hx:∀ i,0 ≤ x i):∀ i,0 ≤ swapPair x i:=by
  intro i
  fin_cases i <;> simpa [swapPair] using hx _
theorem area_reverse (x:Point):expressionEval area (reversePoint x) = expressionEval area x:=by
  simp [area_eval,reversePoint,Matrix.cons_val_two,Matrix.cons_val_three]
  ring
theorem potentialQuad_reverse (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialQuad l q p same) (reversePoint x) =
      expressionEval (potentialQuad l p q same) x:=by
  rw [potentialQuad_eval,potentialQuad_eval]
  cases h:l.position with
  | firstMiddle =>
    simp only [potentialQuadValue,h,reversePoint,Matrix.cons_val_zero,Matrix.cons_val_one,
      Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
    ring
  | firstLast =>
    simp only [potentialQuadValue,h,reversePoint,Matrix.cons_val_zero,Matrix.cons_val_one,
      Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
    ring
  | middleLast =>
    simp only [potentialQuadValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [reversePoint,Matrix.cons_val_two] using
      congrArg (fun y => (l.sign:ℝ) * y) (potentialValue_swap l hu (x 1) (x 2) p q same)
  | companion =>
    simp only [potentialQuadValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [reversePoint,Matrix.cons_val_three] using
      congrArg (fun y => (l.sign:ℝ) * y)
        (potentialValue_swap l hu (x 0) (x 3) (3 * q - 2 * p) (3 * p - 2 * q) same)
private def zz75:"s004b"="s004b":=by decide+kernel
theorem potentialPair_swap (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialPair l q p same) (swapPair x) =
      expressionEval (potentialPair l p q same) x:=by
  rw [potentialPair_eval,potentialPair_eval]
  cases h:l.position with
  | firstMiddle =>
    simp only [potentialPairValue,h,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    ring
  | firstLast =>
    simp only [potentialPairValue,h,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    ring
  | middleLast =>
    simp only [potentialPairValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [swapPair] using
      congrArg (fun y => -(l.sign:ℝ) * y) (potentialValue_swap l hu (x 0) (x 1) p q same)
  | companion =>
    simp only [potentialPairValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [swapPair] using
      congrArg (fun y => -(l.sign:ℝ) * y) (potentialValue_swap l hu (x 0) (x 1) p q same)
theorem rhoExpression_swap (x:Point) :
    expressionEval rhoExpression (swapPair x) = expressionEval rhoExpression x:=by
  simp only [rhoExpression,expressionEval,List.map_cons,List.map_nil,List.sum_cons,
    List.sum_nil,atomEval,coordinate_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  ring
theorem rowQuad_reverse (l:Label) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowQuad l q p same) (reversePoint x) =
      expressionEval (rowQuad l p q same) x:=by
  cases l with
  | potential l => exact potentialQuad_reverse l p q same x
  | child r | heightChild r =>
    simp only [rowQuad,and_comm]
    split_ifs
    · exact area_reverse x
    · rfl
  | grandchild r =>
    simp only [rowQuad,and_comm]
    split_ifs
    · exact area_reverse x
    · rfl
  | balance r s => rfl
  | ordered r => rfl
  | massSquare c v => rfl
  | normalization => rfl
theorem rowPair_swap (S:ℚ) (l:Label) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowPair S l q p same) (swapPair x) =
      expressionEval (rowPair S l p q same) x:=by
  cases l with
  | potential l => exact potentialPair_swap l p q same x
  | balance r s =>
    simp only [rowPair,pairProduct_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one,
      Rat.cast_div,Rat.cast_mul,Rat.cast_add]
    ring
  | child r | grandchild r | ordered r | heightChild r =>
    simp only [rowPair,and_comm,Nat.add_comm]
    split_ifs
    all_goals try rfl
    all_goals
      simp only [expressionEval_append,expressionEval_scale,pairProduct_eval,rhoExpression_swap]
      simp only [swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
      push_cast
      ring
  | massSquare c v =>
    simp only [rowPair,pairProduct_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one,
      Rat.cast_mul,Rat.cast_neg]
    ring
  | normalization =>
    simp only [rowPair,pairProduct_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    ring
private def zz76:"s004c"="s004c":=by decide+kernel
theorem weightedQuad_reverse (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedQuad rows q p same) (reversePoint x) =
      expressionEval (weightedQuad rows p q same) x:=by
  simp only [weightedQuad_eval,rowQuad_reverse]
theorem weightedPair_swap (S:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedPair S rows q p same) (swapPair x) =
      expressionEval (weightedPair S rows p q same) x:=by
  simp only [weightedPair_eval,rowPair_swap]
theorem quadSlack_reverse (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows q p same) (reversePoint x) =
      expressionEval (quadSlack rows p q same) x:=by
  simp only [quadSlack,expressionEval_append,expressionEval_scale,weightedQuad_reverse,area_reverse]
theorem pairSlack_swap (S margin:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack S margin rows q p same) (swapPair x) =
      expressionEval (pairSlack S margin rows p q same) x:=by
  simp only [pairSlack,expressionEval_append]
  rw [weightedPair_swap]
  simp only [pairProduct_eval,
    swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  ring
end Green24Proof.FullPhaseSymmetry
private def zz2003:"s07d3"="s07d3":=by decide+kernel
end 
section 
namespace Green24Proof.ExtendedFullPhaseRows
open QuadraticCertificates ExpressionCertificates
open FullPhaseRows (Phase parity area pairProduct scale expressionEval_append expressionEval_scale)
open FullPhaseSemantics (pairProduct_eval)
open FullPhaseSymmetry (reversePoint swapPair area_reverse)
inductive Scope where
  | whole
  | parity (r:Fin 2)
  | phase (r:Phase)
def scopeActive:Scope → Phase → Phase → Bool
  | .whole,_,_ => true
  | .parity r,p,q => decide (parity p = r ∧ parity q = r)
  | .phase r,p,q => decide (p = r ∧ q = r)
private def zz77:"s004d"="s004d":=by decide+kernel
theorem scopeActive_swap (s:Scope) (p q:Phase):scopeActive s q p = scopeActive s p q:=by
  cases s <;> simp only [scopeActive,and_comm]
structure Correction where
  retained:ℚ
  even:ℚ
  mixed:ℚ
  odd:ℚ
def correctionCoefficient (c:Correction) (a p q:Phase):ℚ :=
  if p = q then (if p = a then c.even else c.odd) else c.mixed / 2
theorem correctionCoefficient_swap (c:Correction) (a p q:Phase) :
    correctionCoefficient c a q p = correctionCoefficient c a p q:=by
  by_cases h:p = q
  · subst q; rfl
  · simp only [correctionCoefficient,h,Ne.symm h,if_false]
inductive Label where
  | base (l:FullPhaseRows.Label)
  | colourChild (scope:Scope)
  | massProduct (left right:Phase → ℚ)
  | massCorrection (r:Fin 2) (leading:Phase) (coefficients:Correction)
  | massCoercivity (coefficient:ℚ)
def rowQuad (l:Label) (p q:Phase) (same:Bool):Expression :=
  match l with
  | .base l => FullPhaseRows.rowQuad l p q same
  | .colourChild s => if scopeActive s p q && same then area else []
  | .massProduct _ _ => []
  | .massCorrection r a c =>
      if parity p = r ∧ parity q = r then
        scale (1 - if p = q ∧ p = a then c.retained else 0) area
      else []
  | .massCoercivity _ => if parity p = 0 ∧ parity q = 0 then area else []
def rowPair (S:ℚ) (l:Label) (p q:Phase) (same:Bool):Expression :=
  match l with
  | .base l => FullPhaseRows.rowPair S l p q same
  | .colourChild s => if scopeActive s p q && same then pairProduct (-8) else []
  | .massProduct a b => pairProduct (-(a p * b q + b p * a q) / 2)
  | .massCorrection r a c =>
      if parity p = r ∧ parity q = r then
        pairProduct (-8 + (if p = q ∧ p = a then 8 * c.retained else 0) +
          4 * correctionCoefficient c a p q)
      else []
  | .massCoercivity c => if parity p = 0 ∧ parity q = 0 then
      pairProduct (-8 + 4 * c * (-1) ^ (p.val / 2 + q.val / 2)) else []
def weightedQuad (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun v => scale v.1 (rowQuad v.2 p q same)
def weightedPair (S:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  rows.flatMap fun v => scale v.1 (rowPair S v.2 p q same)
def quadSlack (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  weightedQuad rows p q same ++ scale (-1) area
def pairSlack (S margin:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool):Expression :=
  weightedPair S rows p q same ++ pairProduct (8 - 4 * margin)
theorem expressionEval_nil (x:Point):expressionEval [] x = 0:=rfl
theorem paritySelected_swap (r:Fin 2) (p q:Phase) :
    (parity q = r ∧ parity p = r) ↔ (parity p = r ∧ parity q = r):=and_comm
private def zz78:"s004e"="s004e":=by decide+kernel
theorem selected_swap (a p q:Phase):(q = p ∧ q = a) ↔ (p = q ∧ p = a):=by
  constructor <;> rintro ⟨h,h'⟩ <;> constructor <;> aesop
theorem rowQuad_reverse (l:Label) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowQuad l q p same) (reversePoint x) = expressionEval (rowQuad l p q same) x:=by
  cases l with
  | base l => exact FullPhaseSymmetry.rowQuad_reverse l p q same x
  | colourChild s =>
    simp only [rowQuad,scopeActive_swap]
    split_ifs <;> simp only [area_reverse,expressionEval_nil]
  | massProduct a b => simp only [rowQuad,expressionEval_nil]
  | massCorrection r a c =>
    simp only [rowQuad,paritySelected_swap r p q,selected_swap]
    split_ifs <;> simp only [expressionEval_scale,area_reverse,
      expressionEval_nil]
  | massCoercivity c =>
    simp only [rowQuad,paritySelected_swap 0 p q]
    split_ifs <;> simp only [area_reverse,expressionEval_nil]
theorem pairProduct_swap (w:ℚ) (x:Point) :
    expressionEval (pairProduct w) (swapPair x) = expressionEval (pairProduct w) x:=by
  simp only [pairProduct_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  ring
theorem rowPair_swap (S:ℚ) (l:Label) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowPair S l q p same) (swapPair x) = expressionEval (rowPair S l p q same) x:=by
  cases l with
  | base l => exact FullPhaseSymmetry.rowPair_swap S l p q same x
  | colourChild s =>
    simp only [rowPair,scopeActive_swap]
    split_ifs <;> simp only [pairProduct_swap,expressionEval_nil]
  | massProduct a b =>
    simp only [rowPair,pairProduct_eval,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    push_cast
    ring
  | massCorrection r a c =>
    simp only [rowPair,paritySelected_swap r p q,selected_swap,correctionCoefficient_swap]
    split_ifs <;> simp only [pairProduct_swap,expressionEval_nil]
  | massCoercivity c =>
    simp only [rowPair,paritySelected_swap 0 p q,add_comm (q.val / 2) (p.val / 2)]
    split_ifs <;> simp only [pairProduct_swap,expressionEval_nil]
private def zz79:"s004f"="s004f":=by decide+kernel
theorem weightedQuad_reverse (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedQuad rows q p same) (reversePoint x) =
      expressionEval (weightedQuad rows p q same) x:=by
  induction rows with
  | nil => rfl
  | cons v vs ih =>
    simp only [weightedQuad,List.flatMap_cons,expressionEval_append,expressionEval_scale,
      rowQuad_reverse] at *
    rw [ih]
theorem weightedPair_swap (S:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedPair S rows q p same) (swapPair x) =
      expressionEval (weightedPair S rows p q same) x:=by
  induction rows with
  | nil => rfl
  | cons v vs ih =>
    simp only [weightedPair,List.flatMap_cons,expressionEval_append,expressionEval_scale,
      rowPair_swap] at *
    rw [ih]
theorem quadSlack_reverse (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows q p same) (reversePoint x) = expressionEval (quadSlack rows p q same) x:=by
  simp only [quadSlack,expressionEval_append,weightedQuad_reverse,expressionEval_scale,area_reverse]
theorem pairSlack_swap (S margin:ℚ) (rows:List (ℚ × Label)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack S margin rows q p same) (swapPair x) = expressionEval (pairSlack S margin rows p q same) x:=by
  simp only [pairSlack,expressionEval_append,weightedPair_swap,pairProduct_swap]
end Green24Proof.ExtendedFullPhaseRows
private def zz2004:"s07d4"="s07d4":=by decide+kernel
end 
section 
/-  Total decoding of rational coefficients and phase labels from bounded
natural-number chunks. The identity checks remain the proof authority. -/
namespace Green24Proof.PackedPhaseRowsData
open FullPhaseRows
abbrev Reader (α:Type):=StateT (List Nat) Option α
def fail {α:Type}:Reader α:=fun _ => none
def readByte:Reader Nat
  | [] => none
  | n :: rest =>
    if n < 0x100 then readByte rest
    else some (n % 0x100,n / 0x100 :: rest)
def readPacked:Nat → Reader Nat
  | 0 => fail
  | fuel + 1 => do
    let b ← readByte
    if b < 0x80 then return b
    else return b % 0x80 + 0x80 * (← readPacked fuel)
def readNat:Reader Nat:=readPacked 0x80
def unzig (n:Nat):Int:=if n % 2 = 0 then n / 2 else -((n / 2:Nat):Int) - 1
def readRat:Reader ℚ:=do
  let n ← readNat
  let d ← readNat
  return (unzig n:ℚ) / (d:ℚ)
def position (n:Nat):Position :=
  match n % 4 with
  | 0 => .firstMiddle
  | 1 => .firstLast
  | 2 => .middleLast
  | _ => .companion
def smallShape (n:Nat):Shape :=
  match n % 4 with
  | 0 => .bilinear
  | 1 => .potential (1 / 3)
  | 2 => .potential 1
  | _ => .potential 3
def smallPotential (n:Nat):Potential :=
  ⟨position n,((n / 4) % 4:Nat),((n / 16) % 4:Nat),
    n / 64 % 2 == 1,smallShape (n / 0x80),if n / 0x200 % 2 = 0 then 1 else -1⟩
def extendedShape (n:Nat):Shape :=
  match n % 8 with
  | 0 => .bilinear
  | 1 => .potential (1 / 3)
  | 2 => .potential 1
  | 3 => .potential 3
  | 4 => .potential (1 / 2)
  | 5 => .potential (2 / 3)
  | 6 => .potential (3 / 2)
  | _ => .potential 2
def extendedPotential (n:Nat):Potential :=
  ⟨position n,((n / 4) % 4:Nat),((n / 16) % 4:Nat),
    n / 64 % 2 == 1,extendedShape (n / 0x80),if n / 0x400 % 2 = 0 then 1 else -1⟩
def readLabel:Reader Label:=do
  let n ← readNat
  if n < 0x400 then return .potential (smallPotential n)
  else if n < 0x408 then
    return .balance ((n - 0x400) / 2:Nat) (if (n - 0x400) % 2 = 0 then 1 else -1)
  else if n < 0x40a then
    return .child ⟨(n - 0x408) % 2,Nat.mod_lt _ (by decide)⟩
  else if n < 0x40e then return .grandchild (n - 0x40a:Nat)
  else if n < 0x410 then
    return .heightChild ⟨(n - 0x40e) % 2,Nat.mod_lt _ (by decide)⟩
  else if n < 0x412 then
    return .ordered ⟨(n - 0x410) % 2,Nat.mod_lt _ (by decide)⟩
  else if 0x800 ≤ n ∧ n < 0x1000 then return .potential (extendedPotential (n - 0x800))
  else match n with
  | 0x412 | 0x413 =>
    let a ← readRat
    let b ← readRat
    let c ← readRat
    let d ← readRat
    return .massSquare (n == 0x413) (fun p => (![a,b,c,d]:Fin 4 → ℚ) p)
  | 0x414 => return .normalization
  | _ => fail
def readRows:Nat → Reader (List (ℚ × Label))
  | 0 => pure []
  | count + 1 => do
    let weight ← readRat
    let label ← readLabel
    return (weight,label) :: (← readRows count)
def decode (chunks:List Nat):List (ℚ × Label) :=
  match (do readRows (← readNat)) chunks with
  | some (rows,_) => rows
  | none => []
def parityPotential (n:Nat):ParityPhaseRows.Potential :=
  ⟨position n,((n / 4) % 4:Nat),((n / 16) % 4:Nat),
    n / 64 % 2 == 1,smallShape (n / 0x80),if n / 0x200 % 2 = 0 then 1 else -1⟩
def extendedParityPotential (n:Nat):ParityPhaseRows.Potential :=
  ⟨position n,((n / 4) % 4:Nat),((n / 16) % 4:Nat),
    n / 64 % 2 == 1,extendedShape (n / 0x80),if n / 0x400 % 2 = 0 then 1 else -1⟩
def readParityRows:Nat → Reader (List (ℚ × ParityPhaseRows.Potential))
  | 0 => pure []
  | count + 1 => do
    let weight ← readRat
    let tag ← readNat
    if tag < 0x400 then
      return (weight,parityPotential tag) :: (← readParityRows count)
    else if 0x800 ≤ tag ∧ tag < 0x1000 then
      return (weight,extendedParityPotential (tag - 0x800)) :: (← readParityRows count)
    else fail
def decodeParity (chunks:List Nat):List (ℚ × ParityPhaseRows.Potential) :=
  match (do readParityRows (← readNat)) chunks with
  | some (rows,_) => rows
  | none => []
def readPhaseVector:Reader (FullPhaseRows.Phase → ℚ):=do
  let a ← readRat
  let b ← readRat
  let c ← readRat
  let d ← readRat
  return fun p => (![a,b,c,d]:Fin 4 → ℚ) p
def readExtendedLabel:Reader ExtendedFullPhaseRows.Label:=do
  match ← readNat with
  | 0 => return .base (← readLabel)
  | 1 => return .colourChild .whole
  | 2 =>
    let r ← readNat
    return .colourChild (.parity ⟨r % 2,Nat.mod_lt _ (by decide)⟩)
  | 3 => return .colourChild (.phase (← readNat))
  | 4 => return .massProduct (← readPhaseVector) (← readPhaseVector)
  | 5 =>
    let r ← readNat
    let p ← readNat
    let a ← readRat
    let b ← readRat
    let c ← readRat
    let d ← readRat
    return .massCorrection ⟨r % 2,Nat.mod_lt _ (by decide)⟩ p ⟨a,b,c,d⟩
  | 6 => return .massCoercivity (← readRat)
  | _ => fail
def readExtendedRows:Nat → Reader (List (ℚ × ExtendedFullPhaseRows.Label))
  | 0 => pure []
  | count + 1 => do
    let weight ← readRat
    let label ← readExtendedLabel
    return (weight,label) :: (← readExtendedRows count)
def decodeExtended (chunks:List Nat):List (ℚ × ExtendedFullPhaseRows.Label) :=
  match (do readExtendedRows (← readNat)) chunks with
  | some (rows,_) => rows
  | none => []
end Green24Proof.PackedPhaseRowsData
private def zz2005:"s07d5"="s07d5":=by decide+kernel
end 
section 
namespace Green24Proof.RewriteAtoms
open QuadraticCertificates
def r0:ℚ × Linear:=(1, ![1, -1,0,0])
def r1:ℚ × Linear:=(-1, ![0,0,1, -1])
def r2:ℚ × Linear:=(1, ![1, -3,0,0])
def r3:ℚ × Linear:=(-1, ![0,0,3, -1])
def r4:ℚ × Linear:=((1 / 3), ![3,0, -1,0])
def r5:ℚ × Linear:=((-1 / 3), ![0,1,0, -3])
def r6:ℚ × Linear:=(1, ![1,0, -1,0])
def r7:ℚ × Linear:=(-1, ![0,1,0, -1])
def r8:ℚ × Linear:=(1, ![1,0, -3,0])
def r9:ℚ × Linear:=(-1, ![0,3,0, -1])
def r10:ℚ × Linear:=(1, ![1, -2, -3,0])
def r11:ℚ × Linear:=(-1, ![1, -2,3,0])
def r12:ℚ × Linear:=(-1, ![1,2, -3,0])
def r13:ℚ × Linear:=(-1, ![0,3,2, -1])
def r14:ℚ × Linear:=(-1, ![0,3, -2,1])
def r15:ℚ × Linear:=(1, ![0,3, -2, -1])
def r16:ℚ × Linear:=(1, ![1,0,0, -3])
def r17:ℚ × Linear:=(-1, ![3,0,0, -1])
def r18:ℚ × Linear:=((1 / 3), ![3, -1,0,0])
def r19:ℚ × Linear:=((-1 / 3), ![0,0,1, -3])
def r20:ℚ × Linear:=(1, ![0,1, -3,0])
def r21:ℚ × Linear:=(-1, ![0,3, -1,0])
def r22:ℚ × Linear:=((1 / 3), ![0,3, -1,0])
def r23:ℚ × Linear:=(-1, ![1,0,0, -1])
def r24:ℚ × Linear:=(1, ![0,1, -1,0])
def r25:ℚ × Linear:=((-1 / 3), ![1,0,0, -3])
def r26:ℚ × Linear:=((-1 / 3), ![1, -3,0,0])
def r27:ℚ × Linear:=(-1, ![1, -1,0,0])
def r28:ℚ × Linear:=(-1, ![3, -1,0,0])
def r29:ℚ × Linear:=((-1 / 3), ![0,1, -3,0])
def r30:ℚ × Linear:=((1 / 3), ![3,0,0, -1])
def r31:ℚ × Linear:=(-1, ![0,1, -1,0])
def r32:ℚ × Linear:=(1, ![1,0,0, -1])
def r33:ℚ × Linear:=(2, ![1, -2, -3,0])
def r34:ℚ × Linear:=(-2, ![1, -2,3,0])
def r35:ℚ × Linear:=(-2, ![1,2, -3,0])
def r36:ℚ × Linear:=(-2, ![0,3,2, -1])
def r37:ℚ × Linear:=(-2, ![0,3, -2,1])
def r38:ℚ × Linear:=(2, ![0,3, -2, -1])
def r39:ℚ × Linear:=(1, ![1, -4, -3,0])
def r40:ℚ × Linear:=(-1, ![1, -4,3,0])
def r41:ℚ × Linear:=(-1, ![1,4, -3,0])
def r42:ℚ × Linear:=(-2, ![0,3,1, -1])
def r43:ℚ × Linear:=(-2, ![0,3, -1,1])
def r44:ℚ × Linear:=(2, ![0,3, -1, -1])
def r45:ℚ × Linear:=(1, ![0,1, -2,0])
def r46:ℚ × Linear:=(-1, ![0,2, -1,0])
def r47:ℚ × Linear:=((1 / 2), ![2, -1,0,0])
def r48:ℚ × Linear:=((-1 / 2), ![0,0,1, -2])
def r49:ℚ × Linear:=((1 / 3), ![3, -2,0,0])
def r50:ℚ × Linear:=((-1 / 3), ![0,0,2, -3])
def r51:ℚ × Linear:=((1 / 2), ![2, -3,0,0])
def r52:ℚ × Linear:=((-1 / 2), ![0,0,3, -2])
def r53:ℚ × Linear:=(1, ![1, -2,0,0])
def r54:ℚ × Linear:=(-1, ![0,0,2, -1])
def r55:ℚ × Linear:=((1 / 2), ![2,0, -1,0])
def r56:ℚ × Linear:=((-1 / 2), ![0,1,0, -2])
def r57:ℚ × Linear:=(1, ![1,0, -2,0])
def r58:ℚ × Linear:=(-1, ![0,2,0, -1])
def r59:ℚ × Linear:=((1 / 2), ![0,2, -3,0])
def r60:ℚ × Linear:=((-1 / 2), ![0,3, -2,0])
def r61:ℚ × Linear:=((1 / 2), ![2,0,0, -3])
def r62:ℚ × Linear:=((-1 / 2), ![3,0,0, -2])
def r63:ℚ × Linear:=((1 / 2), ![2,0, -3,0])
def r64:ℚ × Linear:=((-1 / 2), ![0,3,0, -2])
def r65:ℚ × Linear:=((1 / 2), ![0,2, -1,0])
def r66:ℚ × Linear:=((1 / 3), ![0,3, -2,0])
def r67:ℚ × Linear:=((-1 / 3), ![2,0,0, -3])
def r68:ℚ × Linear:=(-1, ![2,0,0, -1])
def r69:ℚ × Linear:=(-1, ![2, -1,0,0])
def r70:ℚ × Linear:=((-1 / 2), ![1, -2,0,0])
def r71:ℚ × Linear:=((-1 / 2), ![3, -2,0,0])
def r72:ℚ × Linear:=((-1 / 3), ![2, -3,0,0])
def r73:ℚ × Linear:=(-1, ![1,3,0,0])
def r74:ℚ × Linear:=(-3, ![1, -1,0,0])
def r75:ℚ × Linear:=(-1, ![3,1,0,0])
def r76:ℚ × Linear:=(3, ![1, -1,0,0])
def r77:ℚ × Linear:=(1, ![1,0,0, -2])
def r78:ℚ × Linear:=((1 / 3), ![3,0, -2,0])
def r79:ℚ × Linear:=((-1 / 3), ![0,2,0, -3])
def r80:ℚ × Linear:=((-1 / 2), ![1,0,0, -2])
def r81:ℚ × Linear:=((1 / 2), ![2,0,0, -1])
def r82:ℚ × Linear:=((1 / 3), ![3,0,0, -2])
end Green24Proof.RewriteAtoms
private def zz2006:"s07d6"="s07d6":=by decide+kernel
end 
section 
namespace Green24Proof.ParityPhaseSemantics
open QuadraticCertificates ExpressionCertificates ParityPhaseRows
open FullPhaseRows (Position Shape coordinate coordinate_eval expressionEval_append expressionEval_scale)
open FullPhaseSemantics (quadPoint pairPoint sameColour sameColour_refl
  sameColour_affine_left sameColour_affine_right)
noncomputable def potentialValue (l:Potential) (a b:ℝ) (p q:Phase) (same:Bool):ℝ :=
  let (a,b,p,q):=if l.position.unordered ∧ q.val < p.val then (b,a,q,p) else (a,b,p,q)
  if p = l.left ∧ q = l.right ∧ same = l.same then
    match l.shape with
    | .bilinear => a * b
    | .potential r =>
        if l.position.unordered ∧ p = q then
          (squarePotential (r:ℝ) a b + squarePotential (r:ℝ) b a) / 2
        else squarePotential (r:ℝ) a b
  else 0
private def zz80:"s0050"="s0050":=by decide+kernel
theorem phi_eval (l:Potential) (a b:Linear) (p q:Phase) (same:Bool) (w:ℚ) (x:Point) :
    expressionEval (phi l a b p q same w) x =
      (w:ℝ) * potentialValue l (linearEval a x) (linearEval b x) p q same:=by
  cases hs:l.shape <;> simp only [phi,potentialValue,hs]
  all_goals split_ifs <;> simp [expressionEval,atomEval] <;> ring
noncomputable def potentialQuadValue (l:Potential) (p q:Phase) (same:Bool) (x:Point):ℝ :=
  match l.position with
  | .firstMiddle => (l.sign:ℝ) / 2 *
      (potentialValue l (x 0) (x 1) q p true +
       potentialValue l (x 3) (x 2) p q true)
  | .firstLast => (l.sign:ℝ) / 2 *
      (potentialValue l (x 0) (x 2) q q same +
       potentialValue l (x 3) (x 1) p p same)
  | .middleLast => (l.sign:ℝ) * potentialValue l (x 1) (x 2) p q same
  | .companion => (l.sign:ℝ) * potentialValue l (x 0) (x 3) q p same
theorem potentialQuad_eval (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialQuad l p q same) x = potentialQuadValue l p q same x:=by
  cases h:l.position <;>
    simp [potentialQuad,potentialQuadValue,h,Position.indices,Position.unordered,
      quadSame,quadPhases,phi_eval,expressionEval_append,coordinate_eval,
      Matrix.cons_val_two,Matrix.cons_val_three] <;> ring
noncomputable def potentialPairValue (l:Potential) (p q:Phase) (same:Bool) (x:Point):ℝ :=
  match l.position with
  | .firstMiddle => -(3 / 2:ℝ) * (l.sign:ℝ) *
      (potentialValue l (x 0) (x 1) p q same + potentialValue l (x 1) (x 0) q p same)
  | .firstLast => -(l.sign:ℝ) *
      (potentialValue l (x 0) (x 1) p q same + potentialValue l (x 1) (x 0) q p same)
  | .middleLast | .companion => -(l.sign:ℝ) * potentialValue l (x 0) (x 1) p q same
theorem potentialPair_eval (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialPair l p q same) x = potentialPairValue l p q same x:=by
  cases h:l.position <;>
    simp [potentialPair,potentialPairValue,h,Position.unordered,
      phi_eval,expressionEval_append,coordinate_eval] <;> ring
theorem cast_two_affine {q:ℕ} (h2:2 ∣ q) (j k:ZMod q) :
    ZMod.castHom h2 (ZMod 2) (3 * k - 2 * j) = ZMod.castHom h2 (ZMod 2) k:=by
  simp only [map_sub,map_mul,map_ofNat]
  have h3:(3:ZMod 2) = 1:=by decide
  have h0:(2:ZMod 2) = 0:=by decide
  rw [h3,h0]
  ring
noncomputable def globalPotential {q:ℕ} (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (i j:ZMod q):ℝ :=
  potentialValue l (g i) (g j) (ZMod.castHom h2 (ZMod 2) i) (ZMod.castHom h2 (ZMod 2) j)
    (sameColour h3 i j)
noncomputable def potentialRow {q:ℕ} (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (j k:ZMod q):ℝ :=
  expressionEval (potentialQuad l (ZMod.castHom h2 (ZMod 2) j) (ZMod.castHom h2 (ZMod 2) k)
      (sameColour h3 j k)) (quadPoint g j k) +
  expressionEval (potentialPair l (ZMod.castHom h2 (ZMod 2) j) (ZMod.castHom h2 (ZMod 2) k)
      (sameColour h3 j k)) (pairPoint g j k)
private def zz81:"s0051"="s0051":=by decide+kernel
theorem potentialRow_eq {q:ℕ} (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (j k:ZMod q) :
    potentialRow h2 h3 g l j k = (l.sign:ℝ) *
      match l.position with
      | .firstMiddle => firstMiddlePotentialRow (globalPotential h2 h3 g l) j k
      | .firstLast => firstLastPotentialRow (globalPotential h2 h3 g l) j k
      | .middleLast => 0
      | .companion => companionPotentialRow (globalPotential h2 h3 g l) j k:=by
  rw [potentialRow,potentialQuad_eval,potentialPair_eval]
  have hc:sameColour h3 k j = sameColour h3 j k:=by
    apply Bool.eq_iff_iff.mpr
    simp only [sameColour,decide_eq_true_eq]
    exact eq_comm
  cases h:l.position <;>
    simp only [potentialQuadValue,potentialPairValue,h,firstMiddlePotentialRow,
      firstLastPotentialRow,companionPotentialRow,globalPotential,cast_two_affine,
      sameColour_affine_left,sameColour_affine_right,sameColour_refl,hc]
  all_goals
    simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three]
    <;> ring
def admissible (l:Potential):Bool :=
  match l.position with
  | .firstMiddle => l.same
  | .firstLast => decide (l.left = l.right)
  | _ => true
theorem potentialValue_firstMiddle_offColour (l:Potential) (hpos:l.position = .firstMiddle)
    (hs:l.same = true) (a b:ℝ) (p q:Phase):potentialValue l a b p q false = 0:=by
  simp [potentialValue,hpos,Position.unordered,hs]
theorem globalPotential_firstMiddle_support {q:ℕ} (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hpos:l.position = .firstMiddle)
    (hs:l.same = true) (i j:ZMod q)
    (hij:ZMod.castHom h3 (ZMod 3) i ≠ ZMod.castHom h3 (ZMod 3) j) :
    globalPotential h2 h3 g l i j = 0:=by
  unfold globalPotential
  have hc:sameColour h3 i j = false:=by
    exact decide_eq_false hij
  rw [hc]
  exact potentialValue_firstMiddle_offColour l hpos hs _ _ _ _
theorem potentialValue_firstLast_offParity (l:Potential) (hpos:l.position = .firstLast)
    (hl:l.left = l.right) (a b:ℝ) (p q:Phase) (same:Bool)
    (hpq:p ≠ q):potentialValue l a b p q same = 0:=by
  simp only [potentialValue,hpos,Position.unordered,Bool.false_eq_true,false_and,if_false]
  split_ifs with h
  · exact False.elim (hpq (by rw [h.1,h.2.1]; exact hl))
  · rfl
private def zz82:"s0052"="s0052":=by decide+kernel
theorem globalPotential_firstLast_support {q:ℕ} (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hpos:l.position = .firstLast)
    (hl:l.left = l.right) (i j:ZMod q)
    (hij:ZMod.castHom h2 (ZMod 2) i ≠ ZMod.castHom h2 (ZMod 2) j) :
    globalPotential h2 h3 g l i j = 0:=by
  exact potentialValue_firstLast_offParity l hpos hl _ _ _ _ _ hij
theorem potentialRow_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (l:Potential) (hl:admissible l = true) :
    (∑ j, ∑ k,potentialRow h2 h3 g l j k) = 0:=by
  simp_rw [potentialRow_eq]
  simp_rw [← Finset.mul_sum]
  cases hpos:l.position with
  | firstMiddle =>
    have hs:l.same = true:=by simpa only [admissible,hpos] using hl
    rw [firstMiddlePotentialRow_sum h3 (globalPotential h2 h3 g l)
      (globalPotential_firstMiddle_support h2 h3 g l hpos hs)]
    ring
  | firstLast =>
    have hp:l.left = l.right:=by
      simpa only [admissible,hpos,decide_eq_true_eq] using hl
    rw [firstLastPotentialRow_sum h2 (globalPotential h2 h3 g l)
      (globalPotential_firstLast_support h2 h3 g l hpos hp)]
    ring
  | middleLast => simp
  | companion => rw [companionPotentialRow_sum h5]; ring
theorem weightedQuad_eval (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedQuad rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (potentialQuad t.2 p q same) x).sum:=by
  induction rows with
  | nil => simp [weightedQuad,expressionEval]
  | cons t ts ih =>
    simp only [weightedQuad,List.flatMap_cons,expressionEval_append,
      expressionEval_scale,List.map_cons,List.sum_cons] at *
    rw [ih]
theorem weightedPair_eval (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedPair rows p q same) x =
      (rows.map fun t => (t.1:ℝ) * expressionEval (potentialPair t.2 p q same) x).sum:=by
  induction rows with
  | nil => simp [weightedPair,expressionEval]
  | cons t ts ih =>
    simp only [weightedPair,List.flatMap_cons,expressionEval_append,
      expressionEval_scale,List.map_cons,List.sum_cons] at *
    rw [ih]
end Green24Proof.ParityPhaseSemantics
private def zz2007:"s07d7"="s07d7":=by decide+kernel
end 
section 
namespace Green24Proof.ParityPhaseSymmetry
open QuadraticCertificates ExpressionCertificates ParityPhaseRows ParityPhaseSemantics
open FullPhaseRows (Position expressionEval_append expressionEval_scale)
open FullPhaseSemantics (pairProduct_eval)
open FullPhaseSymmetry (reversePoint swapPair area_reverse rhoExpression_swap)
private def zz83:"s0053"="s0053":=by decide+kernel
theorem potentialValue_swap (l:Potential) (hu:l.position.unordered = true)
    (a b:ℝ) (p q:Phase) (same:Bool) :
    potentialValue l b a q p same = potentialValue l a b p q same:=by
  rcases lt_trichotomy p.val q.val with h | h | h
  · simp [potentialValue,hu,h,not_lt_of_gt h]
  · have hpq:p = q:=ZMod.val_injective 2 h
    subst q
    cases hs:l.shape <;> simp only [potentialValue,hu,lt_self_iff_false,
      true_and,and_false,if_false,hs]
    all_goals split_ifs <;> ring
  · simp [potentialValue,hu,h,not_lt_of_gt h]
theorem potentialQuad_reverse (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialQuad l q p same) (reversePoint x) =
      expressionEval (potentialQuad l p q same) x:=by
  rw [potentialQuad_eval,potentialQuad_eval]
  cases h:l.position with
  | firstMiddle =>
    simp only [potentialQuadValue,h,reversePoint,Matrix.cons_val_zero,Matrix.cons_val_one,
      Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
    ring
  | firstLast =>
    simp only [potentialQuadValue,h,reversePoint,Matrix.cons_val_zero,Matrix.cons_val_one,
      Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
    ring
  | middleLast =>
    simp only [potentialQuadValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [reversePoint,Matrix.cons_val_two] using
      congrArg (fun y => (l.sign:ℝ) * y) (potentialValue_swap l hu (x 1) (x 2) p q same)
  | companion =>
    simp only [potentialQuadValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [reversePoint,Matrix.cons_val_three] using
      congrArg (fun y => (l.sign:ℝ) * y)
        (potentialValue_swap l hu (x 0) (x 3) q p same)
theorem potentialPair_swap (l:Potential) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (potentialPair l q p same) (swapPair x) =
      expressionEval (potentialPair l p q same) x:=by
  rw [potentialPair_eval,potentialPair_eval]
  cases h:l.position with
  | firstMiddle =>
    simp only [potentialPairValue,h,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    ring
  | firstLast =>
    simp only [potentialPairValue,h,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
    ring
  | middleLast =>
    simp only [potentialPairValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [swapPair] using
      congrArg (fun y => -(l.sign:ℝ) * y) (potentialValue_swap l hu (x 0) (x 1) p q same)
  | companion =>
    simp only [potentialPairValue,h]
    have hu:l.position.unordered = true:=by simp [h,Position.unordered]
    simpa [swapPair] using
      congrArg (fun y => -(l.sign:ℝ) * y) (potentialValue_swap l hu (x 0) (x 1) p q same)
theorem weightedQuad_reverse (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedQuad rows q p same) (reversePoint x) =
      expressionEval (weightedQuad rows p q same) x:=by
  simp only [weightedQuad_eval,potentialQuad_reverse]
private def zz84:"s0054"="s0054":=by decide+kernel
theorem weightedPair_swap (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (weightedPair rows q p same) (swapPair x) =
      expressionEval (weightedPair rows p q same) x:=by
  simp only [weightedPair_eval,potentialPair_swap]
theorem quadSlack_reverse (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows q p same) (reversePoint x) =
      expressionEval (quadSlack rows p q same) x:=by
  simp only [quadSlack,expressionEval_append,expressionEval_scale,weightedQuad_reverse,area_reverse]
theorem pairSlack_swap (rows:List (ℚ × Potential)) (μ:Phase → ℚ) (lam:ℚ)
    (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack rows μ lam q p same) (swapPair x) =
      expressionEval (pairSlack rows μ lam p q same) x:=by
  simp only [pairSlack,expressionEval_append,expressionEval_scale]
  rw [weightedPair_swap,rhoExpression_swap]
  simp only [pairProduct_eval,balanceCoefficient,and_comm,
    swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  push_cast
  ring
end Green24Proof.ParityPhaseSymmetry
private def zz2008:"s07d8"="s07d8":=by decide+kernel
end 
section 
namespace Green24Proof.ParityCorrectionRows
open QuadraticCertificates ExpressionCertificates
open ParityPhaseRows (Phase Potential weightedQuad weightedPair)
open FullPhaseRows (area pairProduct scale expressionEval_append expressionEval_scale)
open FullPhaseSemantics (pairProduct_eval)
open FullPhaseSymmetry (reversePoint swapPair area_reverse)
open ParityPhaseSymmetry (weightedQuad_reverse weightedPair_swap)
def areaWeight (r:ℚ) (p q:Phase):ℚ:=if p = 0 ∧ q = 0 then 2 * r - r ^ 2 else 1
def balanceCoefficient (r:ℚ) (μ:Phase → ℚ) (p q:Phase):ℚ :=
  (μ p * (if q = 0 then r else -1) + μ q * (if p = 0 then r else -1)) / 2
def quadSlack (rows:List (ℚ × Potential)) (r:ℚ) (p q:Phase) (same:Bool):Expression :=
  weightedQuad rows p q same ++ scale (-areaWeight r p q) area
def pairSlack (rows:List (ℚ × Potential)) (r:ℚ) (μ:Phase → ℚ) (normalization:ℚ)
    (p q:Phase) (same:Bool):Expression :=
  weightedPair rows p q same ++
  pairProduct (balanceCoefficient r μ p q + normalization + if p ≠ q then 16 else 0)
theorem quadSlack_reverse (rows:List (ℚ × Potential)) (r:ℚ)
    (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows r q p same) (reversePoint x) =
      expressionEval (quadSlack rows r p q same) x:=by
  simp only [quadSlack,expressionEval_append,expressionEval_scale,
    weightedQuad_reverse,area_reverse,areaWeight,and_comm]
private def zz85:"s0055"="s0055":=by decide+kernel
theorem pairSlack_swap (rows:List (ℚ × Potential)) (r:ℚ) (μ:Phase → ℚ) (normalization:ℚ)
    (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack rows r μ normalization q p same) (swapPair x) =
      expressionEval (pairSlack rows r μ normalization p q same) x:=by
  simp only [pairSlack,expressionEval_append]
  rw [weightedPair_swap]
  simp only [pairProduct_eval,
    balanceCoefficient,ne_comm,swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  push_cast
  ring
end Green24Proof.ParityCorrectionRows
private def zz2009:"s07d9"="s07d9":=by decide+kernel
end 
section 
namespace Green24Proof
theorem outer_product_sum {ι:Type*} [Fintype ι] (f g:ι → ℝ) :
    (∑ i, ∑ j,f i * g j) = (∑ i,f i) * ∑ j,g j:=by
  simp only [Finset.sum_mul,Finset.mul_sum]
  exact Finset.sum_comm
theorem negative_symmetric_product_sum {ι:Type*} [Fintype ι] (f g:ι → ℝ) :
    (∑ i, ∑ j, -(f i * g j + g i * f j) / 2) = -(∑ i,f i) * ∑ j,g j:=by
  simp only [neg_div,add_div,Finset.sum_neg_distrib,Finset.sum_add_distrib, ← Finset.sum_div]
  rw [outer_product_sum,outer_product_sum]
  ring
theorem negative_symmetric_product_sum_nonpos {ι:Type*} [Fintype ι] (f g:ι → ℝ)
    (hf:0 ≤ ∑ i,f i) (hg:0 ≤ ∑ j,g j) :
    (∑ i, ∑ j, -(f i * g j + g i * f j) / 2) ≤ 0:=by
  rw [negative_symmetric_product_sum]
  exact mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr hf) hg
private def zz86:"s0056"="s0056":=by decide+kernel
theorem negative_square_row_sum_nonpos {ι:Type*} [Fintype ι] (f:ι → ℝ) :
    (∑ i, ∑ j, -(f i * f j)) ≤ 0:=by
  simp only [Finset.sum_neg_distrib,outer_product_sum]
  nlinarith [sq_nonneg (∑ i,f i)]
noncomputable def colourTotal {ι κ:Type*} [Fintype ι] [DecidableEq κ]
    (χ:ι → κ) (f:ι → ℝ) (c:κ):ℝ:=∑ i,if χ i = c then f i else 0
theorem sum_colourTotal {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (χ:ι → κ) (f:ι → ℝ):(∑ c,colourTotal χ f c) = ∑ i,f i:=by
  unfold colourTotal
  rw [Finset.sum_comm]
  simp
theorem same_colour_product_sum {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (χ:ι → κ) (f:ι → ℝ) :
    (∑ i, ∑ j,if χ i = χ j then f i * f j else 0) = ∑ c,colourTotal χ f c ^ 2:=by
  let g (c:κ) (i:ι):ℝ:=if χ i = c then f i else 0
  have hp (i j:ι):(if χ i = χ j then f i * f j else 0) = ∑ c,g c i * g c j:=by
    simp [g,ite_mul,mul_ite,eq_comm]
  simp_rw [hp]
  calc
    _ = ∑ i, ∑ c, ∑ j,g c i * g c j:=by
      apply Finset.sum_congr rfl
      intro i _
      exact Finset.sum_comm
    _ = ∑ c, ∑ i, ∑ j,g c i * g c j:=Finset.sum_comm
    _ = _:=by
      apply Finset.sum_congr rfl
      intro c _
      rw [outer_product_sum]
      change colourTotal χ f c * colourTotal χ f c = colourTotal χ f c ^ 2
      ring
noncomputable def colourVarianceRow {ι κ:Type*} [Fintype κ] [DecidableEq κ]
    (χ:ι → κ) (f:ι → ℝ) (i j:ι):ℝ :=
  -((if χ i = χ j then 1 else 0) - 1 / (Fintype.card κ:ℝ)) * f i * f j
theorem colourVarianceRow_sum {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (χ:ι → κ) (f:ι → ℝ) :
    (∑ i, ∑ j,colourVarianceRow χ f i j) =
      -(∑ c,colourTotal χ f c ^ 2) + (∑ i,f i) ^ 2 / (Fintype.card κ:ℝ):=by
  have hp (i j:ι):colourVarianceRow χ f i j =
      -(if χ i = χ j then f i * f j else 0) + (1 / (Fintype.card κ:ℝ)) * (f i * f j):=by
    unfold colourVarianceRow
    split_ifs <;> ring
  simp_rw [hp]
  simp only [Finset.sum_add_distrib,Finset.sum_neg_distrib, ← Finset.mul_sum]
  rw [same_colour_product_sum, ← Finset.sum_mul]
  ring
private def zz87:"s0057"="s0057":=by decide+kernel
theorem colourVarianceRow_sum_nonpos {ι κ:Type*} [Fintype ι] [Fintype κ]
    [Nonempty κ] [DecidableEq κ] (χ:ι → κ) (f:ι → ℝ) :
    (∑ i, ∑ j,colourVarianceRow χ f i j) ≤ 0:=by
  rw [colourVarianceRow_sum]
  have hcs:=sq_sum_le_card_mul_sum_sq (s:=Finset.univ) (f:=colourTotal χ f)
  rw [Finset.card_univ,sum_colourTotal] at hcs
  have hc:(0:ℝ) < Fintype.card κ:=by exact_mod_cast Fintype.card_pos
  have hdiv:(∑ i,f i) ^ 2 / (Fintype.card κ:ℝ) ≤ ∑ c,colourTotal χ f c ^ 2:=by
    apply (div_le_iff₀ hc).mpr
    nlinarith
  linarith
end Green24Proof
end 
section 
namespace Green24Proof.FullPhaseAggregation
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics FullPhaseSymmetry
noncomputable def rowValue {q:ℕ} (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Label) (j k:ZMod q):ℝ :=
  expressionEval (rowQuad l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (quadPoint g j k) +
  expressionEval (rowPair S l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (pairPoint g j k)
noncomputable def rowAggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Label):ℝ:=∑ j, ∑ k,rowValue S h4 h3 g l j k
noncomputable def weightedAggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)):ℝ :=
  (rows.map fun t => (t.1:ℝ) * rowAggregate S h4 h3 g t.2).sum
theorem potential_aggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (h5:¬5 ∣ q) (g:ZMod q → ℝ) (l:Potential) (hl:admissible l = true) :
    rowAggregate S h4 h3 g (.potential l) = 0 :=
  potentialRow_sum h4 h3 h5 g l hl
theorem quadPoint_nonneg {q:ℕ} (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (j k:ZMod q) :
    ∀ i,0 ≤ quadPoint g j k i:=by
  intro i
  fin_cases i <;> simpa [quadPoint] using hg _
theorem pairPoint_nonneg {q:ℕ} (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (j k:ZMod q) :
    ∀ i,0 ≤ pairPoint g j k i:=by
  intro i
  fin_cases i
  · exact hg j
  · exact hg k
  · exact le_refl 0
  · exact le_refl 0
private def zz88:"s0058"="s0058":=by decide+kernel
theorem area_sum {q:ℕ} [NeZero q] (g:ZMod q → ℝ) :
    (∑ j, ∑ k,expressionEval area (quadPoint g j k)) = 4 * profileFunctional g:=by
  simp only [area_eval,quadPoint,Matrix.cons_val_zero,Matrix.cons_val_one,
    Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum]
  have hswap:(∑ j, ∑ k,kernel (g (3 * j - 2 * k)) (2 * g k) (3 * g j)) =
      profileFunctional g:=Finset.sum_comm
  rw [hswap]
  change 2 * profileFunctional g + 2 * profileFunctional g = 4 * profileFunctional g
  ring
theorem pairProduct_sum {q:ℕ} [NeZero q] (w:ℚ) (g:ZMod q → ℝ) :
    (∑ j, ∑ k,expressionEval (pairProduct w) (pairPoint g j k)) = (w:ℝ) * mass g ^ 2:=by
  simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
  simp only [← Finset.mul_sum, ← Finset.sum_mul]
  unfold mass
  ring
theorem weightedRows_sum {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (weightedQuad rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (weightedPair S rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate S h4 h3 g rows:=by
  induction rows with
  | nil => simp [weightedQuad,weightedPair,expressionEval,weightedAggregate]
  | cons t ts ih =>
    simp only [weightedQuad,weightedPair,List.flatMap_cons,expressionEval_append,
      expressionEval_scale] at *
    have hdistrib (j k:ZMod q) :
        (t.1:ℝ) * expressionEval (rowQuad t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (rowQuad t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)))) (quadPoint g j k) +
        ((t.1:ℝ) * expressionEval (rowPair S t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (rowPair S t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)))) (pairPoint g j k)) =
        (t.1:ℝ) * rowValue S h4 h3 g t.2 j k +
        (expressionEval (weightedQuad ts (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval (weightedPair S ts (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k)):=by
      unfold rowValue weightedQuad weightedPair
      ring
    simp_rw [hdistrib]
    simp only [Finset.sum_add_distrib] at ih
    simp only [Finset.sum_add_distrib, ← Finset.mul_sum,weightedQuad,weightedPair]
    rw [ih]
    rfl
theorem local_slacks_sum {q:ℕ} [NeZero q] (S margin:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (quadSlack rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack S margin rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate S h4 h3 g rows + 4 * deficit g - 4 * (margin:ℝ) * mass g ^ 2:=by
  have hw:=weightedRows_sum S h4 h3 g rows
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadSlack,pairSlack,expressionEval_append,expressionEval_scale,Rat.cast_neg,Rat.cast_one]
  simp_rw [show ∀ a b c d:ℝ,a + -1 * b + (c + d) = (a + c) - b + d by intros; ring]
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib,
    area_sum,pairProduct_sum]
  rw [← hw]
  push_cast
  unfold deficit
  ring
def labelAdmissible:Label → Bool
  | .potential l => admissible l
  | _ => true
def rowsAdmissible (rows:List (ℚ × Label)):Bool:=rows.all fun t => labelAdmissible t.2
def stripPotentials:List (ℚ × Label) → List (ℚ × Label)
  | [] => []
  | (_, .potential _) :: ts => stripPotentials ts
  | t :: ts => t :: stripPotentials ts
private def zz89:"s0059"="s0059":=by decide+kernel
theorem weightedAggregate_cons {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (t:ℚ × Label) (ts:List (ℚ × Label)) :
    weightedAggregate S h4 h3 g (t :: ts) =
      (t.1:ℝ) * rowAggregate S h4 h3 g t.2 + weightedAggregate S h4 h3 g ts:=rfl
theorem stripPotentials_sound {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (h5:¬5 ∣ q) (g:ZMod q → ℝ) (rows:List (ℚ × Label))
    (hrows:rowsAdmissible rows = true) :
    weightedAggregate S h4 h3 g rows = weightedAggregate S h4 h3 g (stripPotentials rows):=by
  induction rows with
  | nil => rfl
  | cons t ts ih =>
    simp only [rowsAdmissible,List.all_cons,Bool.and_eq_true] at hrows
    rcases t with ⟨w,l⟩
    cases l with
    | potential l =>
      have hl:admissible l = true:=hrows.1
      simp only [stripPotentials,weightedAggregate_cons,potential_aggregate S h4 h3 h5 g l hl,
        mul_zero,zero_add]
      exact ih hrows.2
    | balance r s | child r | grandchild r | heightChild r | ordered r | massSquare c v | normalization =>
      simp only [stripPotentials,weightedAggregate_cons]
      rw [ih hrows.2]
end Green24Proof.FullPhaseAggregation
private def zz2010:"s07da"="s07da":=by decide+kernel
end 
section 
namespace Green24Proof.PhaseMassRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics FullPhaseAggregation
theorem sum_phase (f:Phase → ℝ):(∑ r,f r) = f 0 + f 1 + f 2 + f 3 :=
  Fin.sum_univ_four f
noncomputable def phaseTotal {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) (r:Phase):ℝ :=
  colourTotal (ZMod.castHom h4 (ZMod 4)) g r
noncomputable def massWeighted {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (w:Phase → ℝ):ℝ:=∑ i,w (ZMod.castHom h4 (ZMod 4) i) * g i
theorem weighted_colourTotal {ι κ:Type*} [Fintype ι] [Fintype κ] [DecidableEq κ]
    (χ:ι → κ) (g:ι → ℝ) (w:κ → ℝ) :
    (∑ i,w (χ i) * g i) = ∑ r,w r * colourTotal χ g r:=by
  symm
  simp only [colourTotal,Finset.mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro i _
  simp [mul_ite,eq_comm]
private def zz90:"s005a"="s005a":=by decide+kernel
theorem massWeighted_phaseTotal {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (w:Phase → ℝ):massWeighted h4 g w = ∑ r,w r * phaseTotal h4 g r :=
  weighted_colourTotal _ g w
theorem phaseTotal_nonneg {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i) (r:Phase):0 ≤ phaseTotal h4 g r:=by
  exact Finset.sum_nonneg fun i _ => by split_ifs <;> first | exact hg i | rfl
theorem phaseTotal_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) :
    phaseTotal h4 g 0 + phaseTotal h4 g 1 + phaseTotal h4 g 2 + phaseTotal h4 g 3 = mass g:=by
  have h:=sum_colourTotal (ZMod.castHom h4 (ZMod 4)) g
  rw [sum_phase] at h
  exact h
noncomputable def balanceWeight (S:ℚ) (p:Phase):ℝ:=if parity p = 0 then 1 else -(S:ℝ)
theorem balanceWeight_sum {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (g:ZMod q → ℝ) :
    massWeighted h4 g (balanceWeight S) =
      phaseTotal h4 g 0 + phaseTotal h4 g 2 - (S:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
  rw [massWeighted_phaseTotal,sum_phase]
  norm_num [balanceWeight,parity,ZMod.val_ofNat,ZMod.val_one_eq_one_mod]
  ring
private def zz91:"s005b"="s005b":=by decide+kernel
theorem symmetric_product_sum {ι:Type*} [Fintype ι] (a b:ι → ℝ) :
    (∑ i, ∑ j,(a i * b j + a j * b i) / 2) = (∑ i,a i) * ∑ j,b j:=by
  rw [sum_swap_average,outer_product_sum]
theorem rowAggregate_balance {q:ℕ} [NeZero q] (S s:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (r:Phase) :
    rowAggregate S h4 h3 g (.balance r s) = (s:ℝ) * phaseTotal h4 g r *
      (phaseTotal h4 g 0 + phaseTotal h4 g 2 - (S:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)):=by
  let a (i:ZMod q):ℝ:=if ZMod.castHom h4 (ZMod 4) i = r then g i else 0
  let b (i:ZMod q):ℝ:=balanceWeight S (ZMod.castHom h4 (ZMod 4) i) * g i
  have hp (j k:ZMod q):rowValue S h4 h3 g (.balance r s) j k =
      (s:ℝ) * ((a j * b k + a k * b j) / 2):=by
    simp only [rowValue,rowQuad,rowPair]
    rw [pairProduct_eval]
    simp only [expressionEval,List.map_nil,List.sum_nil,zero_add,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
    dsimp only [a,b,balanceWeight]
    simp only [apply_ite]
    split_ifs <;> push_cast <;> ring
  unfold rowAggregate
  simp_rw [hp]
  simp only [← Finset.mul_sum,symmetric_product_sum]
  have ha:(∑ i,a i) = phaseTotal h4 g r:=rfl
  have hb:(∑ i,b i) = massWeighted h4 g (balanceWeight S):=rfl
  rw [ha,hb,balanceWeight_sum]
  ring
theorem rowAggregate_normalization {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ):rowAggregate S h4 h3 g .normalization = mass g ^ 2:=by
  unfold rowAggregate
  simp only [rowValue,rowQuad,rowPair]
  simp only [expressionEval,List.map_nil,List.sum_nil,zero_add]
  change (∑ j, ∑ k,expressionEval (pairProduct 1) (pairPoint g j k)) = mass g ^ 2
  rw [pairProduct_sum]
  norm_num
theorem rowAggregate_massSquare {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (v:Phase → ℚ) :
    rowAggregate S h4 h3 g (.massSquare false v) = -massWeighted h4 g (fun p => (v p:ℝ)) ^ 2:=by
  have hp (j k:ZMod q):rowValue S h4 h3 g (.massSquare false v) j k =
      -(((v (ZMod.castHom h4 (ZMod 4) j):ℚ):ℝ) * g j *
        (((v (ZMod.castHom h4 (ZMod 4) k):ℚ):ℝ) * g k)):=by
    simp only [rowValue,rowQuad,rowPair,Bool.false_eq_true,if_false]
    rw [pairProduct_eval]
    simp only [expressionEval,List.map_nil,List.sum_nil,zero_add,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
    push_cast
    ring
  unfold rowAggregate
  simp_rw [hp]
  simp only [Finset.sum_neg_distrib,outer_product_sum]
  unfold massWeighted
  ring
noncomputable def parityWeight (r:Fin 2) (p:Phase):ℝ:=if parity p = r then 1 else 0
noncomputable def orderedWeight (r:Fin 2) (p:Phase):ℝ :=
  if parity p = r then (if p.val < 2 then -1 else 1) else 0
private def zz92:"s005c"="s005c":=by decide+kernel
theorem parityWeight_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) (r:Fin 2) :
    massWeighted h4 g (parityWeight r) =
      phaseTotal h4 g (r.val:Phase) + phaseTotal h4 g ((r.val:Phase) + 2):=by
  rw [massWeighted_phaseTotal,sum_phase]
  fin_cases r <;> norm_num [parityWeight,parity,ZMod.val_ofNat,ZMod.val_one_eq_one_mod]
theorem orderedWeight_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) (r:Fin 2) :
    massWeighted h4 g (orderedWeight r) =
      phaseTotal h4 g ((r.val:Phase) + 2) - phaseTotal h4 g (r.val:Phase):=by
  rw [massWeighted_phaseTotal,sum_phase]
  fin_cases r <;> norm_num [orderedWeight,parity,ZMod.val_ofNat,ZMod.val_one_eq_one_mod] <;> ring
theorem rowPair_ordered_eval (S:ℚ) (r:Fin 2) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowPair S (.ordered r) p q same) x =
      ((orderedWeight r p * x 0) * (parityWeight r q * x 1) +
        (orderedWeight r q * x 1) * (parityWeight r p * x 0)) / 2:=by
  fin_cases r <;> fin_cases p <;> fin_cases q
  all_goals
    norm_num [rowPair,parity,orderedWeight,parityWeight,pairProduct,ZMod.val,expressionEval,atomEval,coordinate_eval]
    <;> ring
theorem rowAggregate_ordered {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (r:Fin 2) :
    rowAggregate S h4 h3 g (.ordered r) =
      (phaseTotal h4 g ((r.val:Phase) + 2) - phaseTotal h4 g (r.val:Phase)) *
      (phaseTotal h4 g (r.val:Phase) + phaseTotal h4 g ((r.val:Phase) + 2)):=by
  let a (i:ZMod q):ℝ:=orderedWeight r (ZMod.castHom h4 (ZMod 4) i) * g i
  let b (i:ZMod q):ℝ:=parityWeight r (ZMod.castHom h4 (ZMod 4) i) * g i
  have hp (j k:ZMod q):rowValue S h4 h3 g (.ordered r) j k =
      (a j * b k + a k * b j) / 2:=by
    simp only [rowValue,rowQuad]
    rw [rowPair_ordered_eval]
    simp only [expressionEval,List.map_nil,List.sum_nil,zero_add,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
    rfl
  unfold rowAggregate
  simp_rw [hp]
  rw [symmetric_product_sum]
  have ha:(∑ i,a i) = massWeighted h4 g (orderedWeight r):=rfl
  have hb:(∑ i,b i) = massWeighted h4 g (parityWeight r):=rfl
  rw [ha,hb,orderedWeight_sum,parityWeight_sum]
private def zz93:"s005d"="s005d":=by decide+kernel
theorem rowAggregate_ordered_nonpos {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (r:Fin 2)
    (hr:phaseTotal h4 g ((r.val:Phase) + 2) ≤ phaseTotal h4 g (r.val:Phase)) :
    rowAggregate S h4 h3 g (.ordered r) ≤ 0:=by
  rw [rowAggregate_ordered]
  exact mul_nonpos_of_nonpos_of_nonneg (sub_nonpos.mpr hr)
    (add_nonneg (phaseTotal_nonneg h4 g hg _) (phaseTotal_nonneg h4 g hg _))
theorem rowAggregate_massSquare_nonpos {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (v:Phase → ℚ):rowAggregate S h4 h3 g (.massSquare false v) ≤ 0:=by
  rw [rowAggregate_massSquare]
  exact neg_nonpos.mpr (sq_nonneg _)
end Green24Proof.PhaseMassRows
private def zz2011:"s07db"="s07db":=by decide+kernel
end 
section 
namespace Green24Proof.ParityPhaseAggregation
open QuadraticCertificates ExpressionCertificates ParityPhaseRows ParityPhaseSemantics
open FullPhaseRows (scale area pairProduct rhoExpression expressionEval_append expressionEval_scale)
open FullPhaseSemantics (quadPoint pairPoint sameColour pairProduct_eval rhoExpression_eval)
open FullPhaseAggregation (area_sum)
open PhaseMassRows (weighted_colourTotal symmetric_product_sum)
noncomputable def weightedAggregate {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Potential)):ℝ :=
  (rows.map fun t => (t.1:ℝ) * (∑ j, ∑ k,potentialRow h2 h3 g t.2 j k)).sum
theorem weightedRows_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Potential)) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (weightedQuad rows (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (weightedPair rows (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate h2 h3 g rows:=by
  induction rows with
  | nil => simp [weightedQuad,weightedPair,expressionEval,weightedAggregate]
  | cons t ts ih =>
    simp only [weightedQuad,weightedPair,List.flatMap_cons,expressionEval_append,
      expressionEval_scale] at *
    have hdistrib (j k:ZMod q) :
        (t.1:ℝ) * expressionEval (potentialQuad t.2 (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (potentialQuad t.2 (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)))) (quadPoint g j k) +
        ((t.1:ℝ) * expressionEval (potentialPair t.2 (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (pairPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (potentialPair t.2 (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)))) (pairPoint g j k)) =
        (t.1:ℝ) * potentialRow h2 h3 g t.2 j k +
        (expressionEval (weightedQuad ts (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval (weightedPair ts (ZMod.castHom h2 (ZMod 2) j)
          (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (pairPoint g j k)):=by
      unfold potentialRow weightedQuad weightedPair
      ring
    simp_rw [hdistrib]
    simp only [Finset.sum_add_distrib] at ih
    simp only [Finset.sum_add_distrib, ← Finset.mul_sum,weightedQuad,weightedPair]
    rw [ih]
    rfl
def rowsAdmissible (rows:List (ℚ × Potential)):Bool:=rows.all fun t => admissible t.2
theorem weightedAggregate_zero {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q)
    (h5:¬5 ∣ q) (g:ZMod q → ℝ) (rows:List (ℚ × Potential))
    (hr:rowsAdmissible rows = true):weightedAggregate h2 h3 g rows = 0:=by
  induction rows with
  | nil => rfl
  | cons t ts ih =>
    simp only [rowsAdmissible,List.all_cons,Bool.and_eq_true] at hr
    simp only [weightedAggregate,List.map_cons,List.sum_cons]
    rw [potentialRow_sum h2 h3 h5 g t.2 hr.1,mul_zero,zero_add]
    exact ih hr.2
private def zz94:"s005e"="s005e":=by decide+kernel
theorem weighted_classMass {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (g:ι → ℝ)
    (w:ZMod 2 → ℝ) :
    (∑ i,w (χ i) * g i) = w 0 * classMass χ g 0 + w 1 * classMass χ g 1:=by
  rw [weighted_colourTotal,sum_zmod_two]
  rfl
theorem balance_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ) (μ:Phase → ℚ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (pairProduct (balanceCoefficient μ (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k))) (pairPoint g j k)) =
      ((μ 0:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 0 +
       (μ 1:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 1) *
      (classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1):=by
  let a (i:ZMod q):ℝ:=(μ (ZMod.castHom h2 (ZMod 2) i):ℝ) * g i
  let b (i:ZMod q):ℝ:=(if ZMod.castHom h2 (ZMod 2) i = 0 then 1 else -1) * g i
  have hp (j k:ZMod q):expressionEval
      (pairProduct (balanceCoefficient μ (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k))) (pairPoint g j k) = (a j * b k + a k * b j) / 2:=by
    rw [pairProduct_eval]
    simp only [balanceCoefficient,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one,
      Rat.cast_div,Rat.cast_add,Rat.cast_mul,Rat.cast_ofNat,apply_ite]
    dsimp only [a,b]
    split_ifs <;> push_cast <;> ring
  simp_rw [hp]
  rw [symmetric_product_sum]
  have ha:(∑ i,a i) = (μ 0:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 0 +
      (μ 1:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 1:=weighted_classMass (ZMod.castHom h2 (ZMod 2)) g (fun r => (μ r:ℝ))
  have hb:(∑ i,b i) = classMass (ZMod.castHom h2 (ZMod 2)) g 0 -
      classMass (ZMod.castHom h2 (ZMod 2)) g 1:=by
    dsimp only [b]
    simpa [sub_eq_add_neg] using (weighted_classMass (ZMod.castHom h2 (ZMod 2)) g (fun r => if r = 0 then (1:ℝ) else -1))
  rw [ha,hb]
theorem selected_product_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (pairProduct (if ZMod.castHom h2 (ZMod 2) j = 0 ∧ ZMod.castHom h2 (ZMod 2) k = 0 then 32 else 0))
      (pairPoint g j k)) = 32 * classMass (ZMod.castHom h2 (ZMod 2)) g 0 ^ 2:=by
  let a (i:ZMod q):=if ZMod.castHom h2 (ZMod 2) i = 0 then g i else 0
  have hp (j k:ZMod q):expressionEval
      (pairProduct (if ZMod.castHom h2 (ZMod 2) j = 0 ∧ ZMod.castHom h2 (ZMod 2) k = 0 then 32 else 0))
      (pairPoint g j k) = 32 * (a j * a k):=by
    by_cases hj:ZMod.castHom h2 (ZMod 2) j = 0 <;>
      by_cases hk:ZMod.castHom h2 (ZMod 2) k = 0
    all_goals
      simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one,
        a,hj,hk,and_self,false_and,and_false,if_true,if_false]
      norm_num
      <;> ring
  simp_rw [hp]
  simp only [← Finset.mul_sum, ← Finset.sum_mul]
  have ha:(∑ i,a i) = classMass (ZMod.castHom h2 (ZMod 2)) g 0:=by
    simp only [a,classMass,eq_comm]
  rw [ha]
  ring
theorem rho_sum {q:ℕ} [NeZero q] (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (∑ j, ∑ k,expressionEval rhoExpression (pairPoint g j k)) = 2 * energy g:=by
  have hp (j k:ZMod q):expressionEval rhoExpression (pairPoint g j k) = rho (g j) (g k) :=
    rhoExpression_eval (pairPoint g j k) (hg j) (hg k)
  simp_rw [hp]
  simp only [energy]
  ring
private def zz95:"s005f"="s005f":=by decide+kernel
theorem product_add (a b:ℚ) (x:Point) :
    expressionEval (pairProduct (a + b)) x =
      expressionEval (pairProduct a) x + expressionEval (pairProduct b) x:=by
  simp only [pairProduct_eval,Rat.cast_add]
  ring
theorem local_slacks_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (rows:List (ℚ × Potential))
    (μ:Phase → ℚ) (lam:ℚ) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (quadSlack rows (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack rows μ lam (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate h2 h3 g rows - 4 * profileFunctional g - 4 * (lam:ℝ) * energy g +
      32 * classMass (ZMod.castHom h2 (ZMod 2)) g 0 ^ 2 +
      ((μ 0:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 0 +
       (μ 1:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 1) *
      (classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1):=by
  have hw:=weightedRows_sum h2 h3 g rows
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadSlack,pairSlack,expressionEval_append,expressionEval_scale,product_add]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum,area_sum,selected_product_sum,
    balance_sum,rho_sum g hg]
  rw [← hw]
  push_cast
  ring
end Green24Proof.ParityPhaseAggregation
private def zz2012:"s07dc"="s07dc":=by decide+kernel
end 
section 
namespace Green24Proof.ChildRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows
theorem phase_parity_even {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (i:ZMod m) :
    parity (ZMod.castHom h4 (ZMod 4) (parityEquiv m (0,i))) = (0:Fin 2):=by
  have h:=parity_cast h4 (dvd_mul_right 2 m) (parityEquiv m (0,i))
  rw [parityCast_apply] at h
  exact h
theorem phase_parity_odd {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (i:ZMod m) :
    parity (ZMod.castHom h4 (ZMod 4) (parityEquiv m (1,i))) = (1:Fin 2):=by
  have h:=parity_cast h4 (dvd_mul_right 2 m) (parityEquiv m (1,i))
  rw [parityCast_apply] at h
  exact h
private def zz96:"s0060"="s0060":=by decide+kernel
theorem sum_parity_pairs {m:ℕ} [NeZero m] (f:ZMod (2 * m) → ZMod (2 * m) → ℝ) :
    (∑ j, ∑ k,f j k) =
      (∑ j:ZMod m, ∑ k:ZMod m,f (parityEquiv m (0,j)) (parityEquiv m (0,k))) +
      (∑ j:ZMod m, ∑ k:ZMod m,f (parityEquiv m (0,j)) (parityEquiv m (1,k))) +
      (∑ j:ZMod m, ∑ k:ZMod m,f (parityEquiv m (1,j)) (parityEquiv m (0,k))) +
      (∑ j:ZMod m, ∑ k:ZMod m,f (parityEquiv m (1,j)) (parityEquiv m (1,k))):=by
  have hk (j:ZMod (2 * m)):(∑ k,f j k) =
      ∑ r:ZMod 2, ∑ k:ZMod m,f j (parityEquiv m (r,k)):=by
    rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type]
  simp_rw [hk]
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type]
  simp only [sum_zmod_two,Finset.sum_add_distrib]
  ring
theorem child_value_even {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (u v:ZMod m → ℝ) (j k:ZMod m) :
    rowValue S h4 h3 (interleave u v) (.child 0) (parityEquiv m (0,j)) (parityEquiv m (0,k)) =
      expressionEval area (quadPoint u j k) + expressionEval (pairProduct (-8)) (pairPoint u j k):=by
  simp only [rowValue,rowQuad,rowPair,phase_parity_even,and_self,if_true]
  rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
  simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,parityEquiv_affine,
    interleave_even,ZMod.val_zero]
theorem child_value_odd {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (u v:ZMod m → ℝ) (j k:ZMod m) :
    rowValue S h4 h3 (interleave u v) (.child 1) (parityEquiv m (1,j)) (parityEquiv m (1,k)) =
      expressionEval area (quadPoint v j k) + expressionEval (pairProduct (-8)) (pairPoint v j k):=by
  simp only [rowValue,rowQuad,rowPair,phase_parity_odd,and_self,if_true]
  rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
  simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,parityEquiv_affine,
    interleave_odd]
theorem child_value_off {q:ℕ} (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (r:Fin 2) (j k:ZMod q)
    (h:¬(parity (ZMod.castHom h4 (ZMod 4) j) = r ∧ parity (ZMod.castHom h4 (ZMod 4) k) = r)) :
    rowValue S h4 h3 g (.child r) j k = 0:=by
  simp only [rowValue,rowQuad,rowPair,if_neg h,expressionEval,List.map_nil,List.sum_nil,add_zero]
private def zz97:"s0061"="s0061":=by decide+kernel
theorem rowAggregate_child_even {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (u v:ZMod m → ℝ):rowAggregate S h4 h3 (interleave u v) (.child 0) = -4 * deficit u:=by
  unfold rowAggregate
  rw [sum_parity_pairs]
  simp only [child_value_even]
  have hoff (j k:ZMod (2 * m))
      (h:parity (ZMod.castHom h4 (ZMod 4) j) ≠ 0 ∨ parity (ZMod.castHom h4 (ZMod 4) k) ≠ 0) :
      rowValue S h4 h3 (interleave u v) (.child 0) j k = 0:=by
    have hn:¬(parity (ZMod.castHom h4 (ZMod 4) j) = 0 ∧ parity (ZMod.castHom h4 (ZMod 4) k) = 0):=by tauto
    simp only [rowValue,rowQuad,rowPair,if_neg hn,expressionEval,List.map_nil,List.sum_nil,add_zero]
  have h01 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 0)
      (parityEquiv m (0,j)) (parityEquiv m (1,k)) = 0 :=
    hoff _ _ (Or.inr (by rw [phase_parity_odd]; decide))
  have h10 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 0)
      (parityEquiv m (1,j)) (parityEquiv m (0,k)) = 0 :=
    hoff _ _ (Or.inl (by rw [phase_parity_odd]; decide))
  have h11 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 0)
      (parityEquiv m (1,j)) (parityEquiv m (1,k)) = 0 :=
    hoff _ _ (Or.inl (by rw [phase_parity_odd]; decide))
  simp only [h01,h10,h11,Finset.sum_const_zero,add_zero,Finset.sum_add_distrib,
    area_sum,pairProduct_sum]
  unfold deficit
  norm_num
  ring
theorem rowAggregate_child_odd {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (u v:ZMod m → ℝ):rowAggregate S h4 h3 (interleave u v) (.child 1) = -4 * deficit v:=by
  unfold rowAggregate
  rw [sum_parity_pairs]
  simp only [child_value_odd]
  have h00 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 1)
      (parityEquiv m (0,j)) (parityEquiv m (0,k)) = 0 :=
    child_value_off S h4 h3 (interleave u v) 1 _ _ (by rw [phase_parity_even,phase_parity_even]; decide)
  have h01 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 1)
      (parityEquiv m (0,j)) (parityEquiv m (1,k)) = 0 :=
    child_value_off S h4 h3 (interleave u v) 1 _ _ (by rw [phase_parity_even,phase_parity_odd]; decide)
  have h10 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.child 1)
      (parityEquiv m (1,j)) (parityEquiv m (0,k)) = 0 :=
    child_value_off S h4 h3 (interleave u v) 1 _ _ (by rw [phase_parity_odd,phase_parity_even]; decide)
  simp only [h00,h01,h10,Finset.sum_const_zero,zero_add,Finset.sum_add_distrib,
    area_sum,pairProduct_sum]
  unfold deficit
  norm_num
  ring
end Green24Proof.ChildRows
private def zz2013:"s07dd"="s07dd":=by decide+kernel
end 
section 
namespace Green24Proof.ParityCorrectionAggregation
open QuadraticCertificates ExpressionCertificates
open ParityPhaseRows (Phase Potential weightedQuad weightedPair)
open FullPhaseRows (area pairProduct scale expressionEval_append expressionEval_scale area_eval)
open FullPhaseSemantics (quadPoint pairPoint sameColour pairProduct_eval)
open FullPhaseAggregation (area_sum pairProduct_sum)
open ParityPhaseAggregation (weighted_classMass weightedRows_sum weightedAggregate)
open ParityCorrectionRows
theorem weighted_pair_classMass {ι:Type*} [Fintype ι] (χ:ι → ZMod 2) (g:ι → ℝ)
    (w:ZMod 2 → ZMod 2 → ℝ) :
    (∑ j, ∑ k,w (χ j) (χ k) * g j * g k) =
      (w 0 0 * classMass χ g 0 + w 1 0 * classMass χ g 1) * classMass χ g 0 +
      (w 0 1 * classMass χ g 0 + w 1 1 * classMass χ g 1) * classMass χ g 1:=by
  have hinner (j:ι):(∑ k,w (χ j) (χ k) * g j * g k) =
      (w (χ j) 0 * g j) * classMass χ g 0 + (w (χ j) 1 * g j) * classMass χ g 1:=by
    have h:=weighted_classMass χ g (w (χ j))
    have he:(∑ k,w (χ j) (χ k) * g j * g k) = g j * ∑ k,w (χ j) (χ k) * g k:=by
      rw [Finset.mul_sum]
      congr 1
      funext k
      ring
    rw [he,h]
    ring
  simp_rw [hinner]
  simp only [Finset.sum_add_distrib, ← Finset.sum_mul]
  rw [weighted_classMass χ g (fun p => w p 0),weighted_classMass χ g (fun p => w p 1)]
theorem balance_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ)
    (r:ℚ) (μ:Phase → ℚ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (pairProduct (balanceCoefficient r μ (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k))) (pairPoint g j k)) =
      ((μ 0:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 0 +
       (μ 1:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 1) *
      ((r:ℝ) * classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1):=by
  simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
  rw [weighted_pair_classMass (ZMod.castHom h2 (ZMod 2)) g (fun p q => (balanceCoefficient r μ p q:ℝ))]
  norm_num [balanceCoefficient]
  ring
private def zz98:"s0062"="s0062":=by decide+kernel
theorem cross_product_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (pairProduct (if ZMod.castHom h2 (ZMod 2) j ≠ ZMod.castHom h2 (ZMod 2) k then 16 else 0))
      (pairPoint g j k)) =
      32 * classMass (ZMod.castHom h2 (ZMod 2)) g 0 * classMass (ZMod.castHom h2 (ZMod 2)) g 1:=by
  simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
  rw [weighted_pair_classMass (ZMod.castHom h2 (ZMod 2)) g
    (fun p q => ((if p ≠ q then 16 else 0:ℚ):ℝ))]
  norm_num
  ring
theorem classMass_interleave_zero {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) (interleave u v) 0 = mass u:=by
  unfold classMass
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [parityCast_apply,interleave_even,interleave_odd]
  norm_num
  rfl
theorem classMass_interleave_one {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) (interleave u v) 1 = mass v:=by
  have h:=classMass_sum (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) (interleave u v)
  rw [classMass_interleave_zero,mass_interleave] at h
  linarith
theorem selected_area_sum {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),
      if ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j = 0 ∧
        ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k = 0
      then expressionEval area (quadPoint (interleave u v) j k) else 0) = 4 * profileFunctional u:=by
  rw [ChildRows.sum_parity_pairs]
  simp only [parityCast_apply]
  norm_num
  have hp (j k:ZMod m) :
      expressionEval area (quadPoint (interleave u v) (parityEquiv m (0,j)) (parityEquiv m (0,k))) =
      expressionEval area (quadPoint u j k):=by
    rw [area_eval,area_eval]
    simp [quadPoint,Matrix.cons_val_two,Matrix.cons_val_three,parityEquiv_affine,interleave_even]
  simp_rw [hp]
  exact area_sum u
private def zz99:"s0063"="s0063":=by decide+kernel
theorem weighted_area_sum {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (r:ℚ) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),expressionEval
      (scale (areaWeight r (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k)) area) (quadPoint (interleave u v) j k)) =
      4 * profileFunctional (interleave u v) - 4 * (1 - (r:ℝ)) ^ 2 * profileFunctional u:=by
  have hp (p q:Phase) (x:Point):expressionEval (scale (areaWeight r p q) area) x =
      expressionEval area x - (1 - (r:ℝ)) ^ 2 *
        (if p = 0 ∧ q = 0 then expressionEval area x else 0):=by
    rw [expressionEval_scale]
    unfold areaWeight
    split_ifs <;> push_cast <;> ring
  simp_rw [hp]
  simp only [Finset.sum_sub_distrib, ← Finset.mul_sum,area_sum,selected_area_sum]
  ring
theorem quadSlack_eval (rows:List (ℚ × Potential)) (r:ℚ) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows r p q same) x =
      expressionEval (weightedQuad rows p q same) x -
      expressionEval (scale (areaWeight r p q) area) x:=by
  simp only [quadSlack,expressionEval_append,expressionEval_scale,Rat.cast_neg]
  ring
theorem local_slacks_sum {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (u v:ZMod m → ℝ)
    (rows:List (ℚ × Potential)) (r:ℚ) (μ:Phase → ℚ) (normalization:ℚ) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),(
      expressionEval (quadSlack rows r (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (quadPoint (interleave u v) j k) +
      expressionEval (pairSlack rows r μ normalization (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (pairPoint (interleave u v) j k))) =
      weightedAggregate (dvd_mul_right 2 m) h3 (interleave u v) rows -
      4 * profileFunctional (interleave u v) + 4 * (1 - (r:ℝ)) ^ 2 * profileFunctional u +
      (normalization:ℝ) * (mass u + mass v) ^ 2 + 32 * mass u * mass v +
      ((μ 0:ℝ) * mass u + (μ 1:ℝ) * mass v) * ((r:ℝ) * mass u - mass v):=by
  have hw:=weightedRows_sum (dvd_mul_right 2 m) h3 (interleave u v) rows
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadSlack_eval,pairSlack,expressionEval_append,ParityPhaseAggregation.product_add]
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib,weighted_area_sum,
    balance_sum,cross_product_sum,pairProduct_sum,classMass_interleave_zero,
    classMass_interleave_one,mass_interleave]
  rw [← hw]
  ring
theorem correction_of_local_rows {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (rows:List (ℚ × Potential)) (r:ℚ) (μ:Phase → ℚ) (normalization:ℚ)
    (hadmissible:ParityPhaseAggregation.rowsAdmissible rows = true)
    (hquad:∀ p q same x,(∀ i,0 ≤ x i) → 0 ≤ expressionEval (quadSlack rows r p q same) x)
    (hpair:∀ p q same x,(∀ i,0 ≤ x i) → 0 ≤ expressionEval (pairSlack rows r μ normalization p q same) x)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 - (r:ℝ)) ^ 2 * deficit u + ((r:ℝ) * mass u - mass v) *
      ((4 - 2 * (r:ℝ) - (μ 0:ℝ) / 4) * mass u + (-2 - (μ 1:ℝ) / 4) * mass v) -
      (normalization:ℝ) / 4 * (mass u + mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hl (j k:ZMod (2 * m)):0 ≤
      expressionEval (quadSlack rows r (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (quadPoint (interleave u v) j k) +
      expressionEval (pairSlack rows r μ normalization (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (pairPoint (interleave u v) j k) :=
    add_nonneg (hquad _ _ _ _ (FullPhaseAggregation.quadPoint_nonneg _ hg j k))
      (hpair _ _ _ _ (FullPhaseAggregation.pairPoint_nonneg _ hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,
    ParityPhaseAggregation.weightedAggregate_zero (dvd_mul_right 2 m) h3 h5 _ rows hadmissible] at hs
  unfold deficit
  rw [mass_interleave]
  nlinarith only [hs]
end Green24Proof.ParityCorrectionAggregation
private def zz2014:"s07de"="s07de":=by decide+kernel
end 
section 
namespace Green24Proof
def NearBalanceHypothesis (U V du dg:ℝ):Prop :=
  ∀ h:ℝ,0 ≤ h → h ≤ 1 / 10 →
    h ^ 2 * du + ((1 - h) * U - V) * (-(1 + h) * U + (1 + 3 * h / 2) * V) -
      (3 / 0xfa) * h ^ 2 * (U + V) ^ 2 ≤ dg
private def zz100:"s0064"="s0064":=by decide+kernel
theorem near_balance_product_identity {U V h:ℝ} (hV:V = (1 - 3 * h / 4) * U) :
    ((1 - h) * U - V) * (-(1 + h) * U + (1 + 3 * h / 2) * V) =
      (h ^ 2 / 16 + 9 * h ^ 3 / 32) * U ^ 2:=by
  rw [hV]
  ring
theorem near_balance_gain {U V h:ℝ} (hU:0 ≤ U) (hV0:0 ≤ V) (hVU:V ≤ U)
    (hh:0 ≤ h) (hV:V = (1 - 3 * h / 4) * U) :
    (29 / 0x7d0) * h ^ 2 * U ^ 2 ≤
      ((1 - h) * U - V) * (-(1 + h) * U + (1 + 3 * h / 2) * V) -
        (3 / 0xfa) * h ^ 2 * (U + V) ^ 2:=by
  rw [near_balance_product_identity hV]
  have hsq:(U + V) ^ 2 ≤ 4 * U ^ 2:=by
    nlinarith [mul_nonneg (sub_nonneg.mpr hVU) (by linarith:0 ≤ 3 * U + V)]
  have hscaled:=mul_le_mul_of_nonneg_left hsq (sq_nonneg h)
  have hcubic:0 ≤ h ^ 3 * U ^ 2:=mul_nonneg (pow_nonneg hh 3) (sq_nonneg U)
  nlinarith
theorem near_balance_descent {U V du dg:ℝ} (hV:0 < V) (hVU:V ≤ U)
    (hratio:U ≤ (40 / 37) * V) (hc:NearBalanceHypothesis U V du dg) :
    (16 * (U - V) ^ 2 / (9 * U ^ 2)) * du + (29 / 0x465) * (U - V) ^ 2 ≤ dg:=by
  have hU:0 < U:=hV.trans_le hVU
  let h:ℝ:=4 * (U - V) / (3 * U)
  have hh0:0 ≤ h:=div_nonneg (mul_nonneg (by norm_num) (sub_nonneg.mpr hVU))
    (by positivity)
  have hh1:h ≤ 1 / 10:=by
    dsimp [h]
    apply (div_le_iff₀ (by positivity:0 < 3 * U)).mpr
    linarith
  have hhU:h * U = (4 / 3) * (U - V):=by
    dsimp [h]
    field_simp
  have hrel:V = (1 - 3 * h / 4) * U:=by nlinarith [hhU]
  have hgain:=near_balance_gain hU.le hV.le hVU hh0 hrel
  have hcert:=hc h hh0 hh1
  have hcoef:h ^ 2 = 16 * (U - V) ^ 2 / (9 * U ^ 2):=by
    dsimp [h]
    ring
  have hmargin:(29 / 0x7d0) * h ^ 2 * U ^ 2 = (29 / 0x465) * (U - V) ^ 2:=by
    dsimp [h]
    field_simp
    ring
  have hlower:h ^ 2 * du + (29 / 0x7d0) * h ^ 2 * U ^ 2 ≤ dg:=by linarith
  rw [hmargin,hcoef] at hlower
  exact hlower
theorem near_balance_nonneg {U V du dg:ℝ} (hV:0 ≤ V) (hVU:V ≤ U)
    (hratio:U ≤ (40 / 37) * V) (hdu:0 ≤ du) (hc:NearBalanceHypothesis U V du dg) :
    0 ≤ dg:=by
  rcases hV.eq_or_lt with hzero | hpos
  · have hU:U = 0:=by linarith
    have h:=hc 0 (by norm_num) (by norm_num)
    simpa [hU, ← hzero] using h
  · have h:=near_balance_descent hpos hVU hratio hc
    have hcoef:0 ≤ (16 * (U - V) ^ 2 / (9 * U ^ 2)) * du:=by positivity
    nlinarith [sq_nonneg (U - V)]
private def zz101:"s0065"="s0065":=by decide+kernel
theorem profile_near_balance_nonneg {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hv:∀ i,0 ≤ v i) (horder:mass v ≤ mass u)
    (hratio:mass u ≤ (40 / 37) * mass v) (hdu:0 ≤ deficit u)
    (hc:NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v))) :
    0 ≤ deficit (interleave u v) :=
  near_balance_nonneg (mass_nonneg hv) horder hratio hdu hc
end Green24Proof
end 
section 
namespace Green24Proof.NearBalanceParameterRows
open QuadraticCertificates ExpressionCertificates
open ParityPhaseRows (Phase Potential weightedQuad weightedPair)
open FullPhaseRows (area pairProduct scale expressionEval_append expressionEval_scale)
open FullPhaseSemantics (quadPoint pairPoint sameColour pairProduct_eval)
open FullPhaseSymmetry (reversePoint swapPair area_reverse)
open ParityPhaseSymmetry (weightedQuad_reverse weightedPair_swap)
abbrev Degree:=Fin 3
abbrev Rows:=Degree → List (ℚ × Potential)
def areaConstant (d:Degree):ℚ:=if d = 0 then -1 else 0
def areaSelected (d:Degree):ℚ:=if d = 2 then 1 / 0x64 else 0
def pairEven (d:Degree):ℚ:=if d = 0 then 12 else if d = 1 then 0 else -0x2eb / 0x186a
def pairOdd (d:Degree):ℚ:=if d = 0 then 12 else if d = 1 then 3 / 5 else 3 / 0x186a
def pairMixed (d:Degree):ℚ:=if d = 0 then 4 else if d = 1 then -3 / 10 else 0x17d / 0x30d4
def pairCoefficient (d:Degree) (p q:Phase):ℚ :=
  if p = 0 ∧ q = 0 then pairEven d else if p = 1 ∧ q = 1 then pairOdd d else pairMixed d
def quadComponent (rows:Rows) (d:Degree) (p q:Phase) (same:Bool):Expression :=
  weightedQuad (rows d) p q same ++
    scale (areaConstant d + if p = 0 ∧ q = 0 then areaSelected d else 0) area
def pairComponent (rows:Rows) (d:Degree) (p q:Phase) (same:Bool):Expression :=
  weightedPair (rows d) p q same ++ pairProduct (pairCoefficient d p q)
noncomputable def parameterEval (e:Degree → Expression) (t:ℝ) (x:Point):ℝ :=
  expressionEval (e 0) x + t * expressionEval (e 1) x + t ^ 2 * expressionEval (e 2) x
theorem quadComponent_reverse (rows:Rows) (d:Degree) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadComponent rows d q p same) (reversePoint x) =
      expressionEval (quadComponent rows d p q same) x:=by
  simp only [quadComponent,expressionEval_append,expressionEval_scale,
    weightedQuad_reverse,area_reverse,and_comm]
theorem pairComponent_swap (rows:Rows) (d:Degree) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairComponent rows d q p same) (swapPair x) =
      expressionEval (pairComponent rows d p q same) x:=by
  simp only [pairComponent,expressionEval_append]
  rw [weightedPair_swap]
  simp only [pairProduct_eval,pairCoefficient,and_comm,
    swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  ring
theorem parameterQuad_reverse (rows:Rows) (p q:Phase) (same:Bool) (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d q p same) t (reversePoint x) =
      parameterEval (fun d => quadComponent rows d p q same) t x:=by
  simp only [parameterEval,quadComponent_reverse]
private def zz102:"s0066"="s0066":=by decide+kernel
theorem parameterPair_swap (rows:Rows) (p q:Phase) (same:Bool) (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d q p same) t (swapPair x) =
      parameterEval (fun d => pairComponent rows d p q same) t x:=by
  simp only [parameterEval,pairComponent_swap]
theorem area_part_sum {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (d:Degree) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),expressionEval
      (scale (areaConstant d + if ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j = 0 ∧
        ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k = 0 then areaSelected d else 0) area)
      (quadPoint (interleave u v) j k)) =
      4 * (areaConstant d:ℝ) * profileFunctional (interleave u v) +
      4 * (areaSelected d:ℝ) * profileFunctional u:=by
  have hp (p q:Phase) (x:Point) :
      expressionEval (scale (areaConstant d + if p = 0 ∧ q = 0 then areaSelected d else 0) area) x =
      (areaConstant d:ℝ) * expressionEval area x +
      (areaSelected d:ℝ) * (if p = 0 ∧ q = 0 then expressionEval area x else 0):=by
    rw [expressionEval_scale]
    split_ifs <;> push_cast <;> ring
  simp_rw [hp]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum,FullPhaseAggregation.area_sum,
    ParityCorrectionAggregation.selected_area_sum]
  ring
theorem pair_part_sum {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (d:Degree) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),expressionEval
      (pairProduct (pairCoefficient d (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k))) (pairPoint (interleave u v) j k)) =
      (pairEven d:ℝ) * mass u ^ 2 + 2 * (pairMixed d:ℝ) * mass u * mass v +
      (pairOdd d:ℝ) * mass v ^ 2:=by
  simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
  rw [ParityCorrectionAggregation.weighted_pair_classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2))
    (interleave u v) (fun p q => (pairCoefficient d p q:ℝ))]
  simp only [ParityCorrectionAggregation.classMass_interleave_zero,
    ParityCorrectionAggregation.classMass_interleave_one]
  norm_num [pairCoefficient]
  ring
theorem component_sum {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (u v:ZMod m → ℝ)
    (rows:Rows) (d:Degree) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),(
      expressionEval (quadComponent rows d (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (quadPoint (interleave u v) j k) +
      expressionEval (pairComponent rows d (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (pairPoint (interleave u v) j k))) =
      ParityPhaseAggregation.weightedAggregate (dvd_mul_right 2 m) h3 (interleave u v) (rows d) +
      4 * (areaConstant d:ℝ) * profileFunctional (interleave u v) +
      4 * (areaSelected d:ℝ) * profileFunctional u +
      (pairEven d:ℝ) * mass u ^ 2 + 2 * (pairMixed d:ℝ) * mass u * mass v +
      (pairOdd d:ℝ) * mass v ^ 2:=by
  have hw:=ParityPhaseAggregation.weightedRows_sum (dvd_mul_right 2 m) h3 (interleave u v) (rows d)
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadComponent,pairComponent,expressionEval_append,Finset.sum_add_distrib,
    area_part_sum,pair_part_sum]
  rw [← hw]
  ring
private def zz103:"s0067"="s0067":=by decide+kernel
theorem parameter_bound_of_local_rows {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (rows:Rows)
    (hadmissible:∀ d,ParityPhaseAggregation.rowsAdmissible (rows d) = true)
    (hquad:∀ p q same t,0 ≤ t → t ≤ 1 → ∀ x,(∀ i,0 ≤ x i) →
      0 ≤ parameterEval (fun d => quadComponent rows d p q same) t x)
    (hpair:∀ p q same t,0 ≤ t → t ≤ 1 → ∀ x,(∀ i,0 ≤ x i) →
      0 ≤ parameterEval (fun d => pairComponent rows d p q same) t x)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v)):=by
  intro h hh0 hh1
  have ht0:0 ≤ 10 * h:=mul_nonneg (by norm_num) hh0
  have ht1:10 * h ≤ 1:=by linarith
  have hg:=interleave_nonneg u v hu hv
  let X (j k:ZMod (2 * m)) (d:Degree) :=
    expressionEval (quadComponent rows d (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
      (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (quadPoint (interleave u v) j k)
  let Y (j k:ZMod (2 * m)) (d:Degree) :=
    expressionEval (pairComponent rows d (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
      (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (pairPoint (interleave u v) j k)
  have hp (j k:ZMod (2 * m)):0 ≤
      (X j k 0 + Y j k 0) + (10 * h) * (X j k 1 + Y j k 1) +
        (10 * h) ^ 2 * (X j k 2 + Y j k 2):=by
    have ha:=hquad (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
      (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k) _ ht0 ht1 _
      (FullPhaseAggregation.quadPoint_nonneg _ hg j k)
    have hb:=hpair (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
      (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k) _ ht0 ht1 _
      (FullPhaseAggregation.pairPoint_nonneg _ hg j k)
    change 0 ≤ X j k 0 + (10 * h) * X j k 1 + (10 * h) ^ 2 * X j k 2 at ha
    change 0 ≤ Y j k 0 + (10 * h) * Y j k 1 + (10 * h) ^ 2 * Y j k 2 at hb
    linarith
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hp j k
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum] at hs
  have hsum (d:Degree):(∑ j, ∑ k,(X j k d + Y j k d)) =
      4 * (areaConstant d:ℝ) * profileFunctional (interleave u v) +
      4 * (areaSelected d:ℝ) * profileFunctional u +
      (pairEven d:ℝ) * mass u ^ 2 + 2 * (pairMixed d:ℝ) * mass u * mass v +
      (pairOdd d:ℝ) * mass v ^ 2:=by
    dsimp only [X,Y]
    rw [component_sum,ParityPhaseAggregation.weightedAggregate_zero
      (dvd_mul_right 2 m) h3 h5 _ _ (hadmissible d),zero_add]
  simp only [Finset.sum_add_distrib] at hsum
  rw [hsum 0,hsum 1,hsum 2] at hs
  have h02:(0:Degree) ≠ 2:=by decide
  have h12:(1:Degree) ≠ 2:=by decide
  have h20:(2:Degree) ≠ 0:=by decide
  have h21:(2:Degree) ≠ 1:=by decide
  norm_num [areaConstant,areaSelected,pairEven,pairMixed,pairOdd,h02,h12,h20,h21] at hs
  unfold deficit
  rw [mass_interleave]
  nlinarith only [hs]
end Green24Proof.NearBalanceParameterRows
private def zz2015:"s07df"="s07df":=by decide+kernel
end 
section 
namespace Green24Proof.NearBalancePairs
theorem quadratic_nonnegative {A B C:ℝ} (hA:0 ≤ A) (hC:0 ≤ C)
    (hdet:0 ≤ A * C - B ^ 2) (x y:ℝ) :
    0 ≤ A * x ^ 2 + 2 * B * x * y + C * y ^ 2:=by
  by_cases hz:A = 0
  · have hB:B = 0:=by nlinarith [sq_nonneg B]
    simp only [hz,hB,zero_mul,mul_zero,zero_add]
    exact mul_nonneg hC (sq_nonneg y)
  · have hpos:0 < A:=lt_of_le_of_ne hA (Ne.symm hz)
    have h:0 ≤ A * (A * x ^ 2 + 2 * B * x * y + C * y ^ 2):=by
      calc
        _ = (A * x + B * y) ^ 2 + (A * C - B ^ 2) * y ^ 2:=by ring
        _ ≥ 0:=add_nonneg (sq_nonneg _) (mul_nonneg hdet (sq_nonneg y))
    exact nonneg_of_mul_nonneg_right h hpos
noncomputable def pair_6 (t x y:ℝ):ℝ :=
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) +
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) * t +
  ((0:ℝ) * x ^ 2 + (3 / 0x2710:ℝ) * x * y + (0:ℝ) * y ^ 2) * t ^ 2
theorem pair_6_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_6 t x y:=by
  have hA:0 ≤ (0:ℝ):=by
    norm_num
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((3 / 0x4e20:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
  have hgram:0 ≤ (0:ℝ) * y ^ 2 + 2 * ((3 / 0x4e20:ℝ) * t ^ 2) * y * (x - (0:ℝ) * y) + (0:ℝ) * (x - (0:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_6
  nlinarith only [hgram]
noncomputable def pair_7 (t x y:ℝ):ℝ :=
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) +
  ((-0x5d42cb / 0x1dcd6500:ℝ) * x ^ 2 + (0x5d42cb / 0x3b9aca00:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-0x5d42cb / 0xee6b2800:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (0x5d42cb / 0xee6b2800:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t +
  ((0x5d42cb / 0x1dcd6500:ℝ) * x ^ 2 + (-0x5b6e0b / 0x3b9aca00:ℝ) * x * y + (0:ℝ) * y ^ 2 + (0x5d42cb / 0xee6b2800:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (-0x5d42cb / 0xee6b2800:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t ^ 2
theorem pair_7_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_7 t x y:=by
  by_cases h0:x ≤ (1 / 3:ℝ) * y
  ·
    have hA:0 ≤ (0:ℝ):=by
      norm_num
    have hC:0 ≤ ((0x5d42cb / 0x218711a00:ℝ) * t + (-0x57c48b / 0x218711a00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xaf8916:ℝ))]
    have hB:0 ≤ ((0x5d42cb / 0x165a0bc00:ℝ) * t + (-0x5b6e0b / 0x165a0bc00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xb6dc16:ℝ))]
    have hgram:0 ≤ (0:ℝ) * ((1 / 3:ℝ) * y - x) ^ 2 + 2 * ((0x5d42cb / 0x165a0bc00:ℝ) * t + (-0x5b6e0b / 0x165a0bc00:ℝ) * t ^ 2) * ((1 / 3:ℝ) * y - x) * (x - (0:ℝ) * y) + ((0x5d42cb / 0x218711a00:ℝ) * t + (-0x57c48b / 0x218711a00:ℝ) * t ^ 2) * (x - (0:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_7
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((3:ℝ) * x + (-1:ℝ) * y) ≤ 0)]
    nlinarith only [hgram]
  by_cases h1:x ≤ (3:ℝ) * y
  ·
    have hlow:(1 / 3:ℝ) * y ≤ x:=le_of_not_ge h0
    have hA:0 ≤ ((0x5d42cb / 0x218711a00:ℝ) * t + (-0x57c48b / 0x218711a00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xaf8916:ℝ))]
    have hC:0 ≤ ((0x5d42cb / 0x3b9aca00:ℝ) * t + (-0x57c48b / 0x3b9aca00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xaf8916:ℝ))]
    by_cases ht:t ≤ (19 / 20:ℝ)
    ·
      have hfac:0 ≤ ((0x5d42cb / 0x44364c5bb00:ℝ) - (0x5f178b / 0x44364c5bb00:ℝ) * t):=by nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1)]
      have hdet:0 ≤ (((0x5d42cb / 0x218711a00:ℝ) * t + (-0x57c48b / 0x218711a00:ℝ) * t ^ 2) * ((0x5d42cb / 0x3b9aca00:ℝ) * t + (-0x57c48b / 0x3b9aca00:ℝ) * t ^ 2) - ((-0x5d42cb / 0xb2d05e00:ℝ) * t + (0x666a8b / 0xb2d05e00:ℝ) * t ^ 2) ^ 2):=by
        have hh:=mul_nonneg (pow_nonneg _ht0 3) hfac
        nlinarith only [hh]
      have hgram:=quadratic_nonnegative hA hC hdet ((3:ℝ) * y - x) (x - (1 / 3:ℝ) * y)
      unfold pair_7
      rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
        max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
      nlinarith only [hgram]
    ·
      have hB:0 ≤ ((-0x5d42cb / 0xb2d05e00:ℝ) * t + (0x666a8b / 0xb2d05e00:ℝ) * t ^ 2):=by
        nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xccd516:ℝ))]
      have hgram:0 ≤ ((0x5d42cb / 0x218711a00:ℝ) * t + (-0x57c48b / 0x218711a00:ℝ) * t ^ 2) * ((3:ℝ) * y - x) ^ 2 + 2 * ((-0x5d42cb / 0xb2d05e00:ℝ) * t + (0x666a8b / 0xb2d05e00:ℝ) * t ^ 2) * ((3:ℝ) * y - x) * (x - (1 / 3:ℝ) * y) + ((0x5d42cb / 0x3b9aca00:ℝ) * t + (-0x57c48b / 0x3b9aca00:ℝ) * t ^ 2) * (x - (1 / 3:ℝ) * y) ^ 2 :=
        add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
          (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
          (mul_nonneg hC (sq_nonneg _))
      unfold pair_7
      rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
        max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
      nlinarith only [hgram]
  have hlow:(3:ℝ) * y ≤ x:=le_of_not_ge h1
  have hA:0 ≤ ((0x5d42cb / 0x3b9aca00:ℝ) * t + (-0x57c48b / 0x3b9aca00:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xaf8916:ℝ))]
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((0x5d42cb / 0x77359400:ℝ) * t + (-0x5b6e0b / 0x77359400:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x5d42cb / 0xb6dc16:ℝ))]
  have hgram:0 ≤ ((0x5d42cb / 0x3b9aca00:ℝ) * t + (-0x57c48b / 0x3b9aca00:ℝ) * t ^ 2) * y ^ 2 + 2 * ((0x5d42cb / 0x77359400:ℝ) * t + (-0x5b6e0b / 0x77359400:ℝ) * t ^ 2) * y * (x - (3:ℝ) * y) + (0:ℝ) * (x - (3:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_7
  rw [max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-3:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
  nlinarith only [hgram]
noncomputable def pair_8 (t x y:ℝ):ℝ :=
  ((-0x920eef174c9 / 0x38d7ea4c6800:ℝ) * x ^ 2 + (0x920eef174c9 / 0x71afd498d000:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-0x920eef174c9 / 0x1c6bf52634000:ℝ) * max ((1:ℝ) * x + (-1:ℝ) * y) 0 ^ 2 + (0x920eef174c9 / 0x1c6bf52634000:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) +
  ((0x106f8927 / 0x4a817c80:ℝ) * x ^ 2 + (-0x106f8927 / 0x9502f900:ℝ) * x * y + (0:ℝ) * y ^ 2 + (0x106f8927 / 0x2540be400:ℝ) * max ((1:ℝ) * x + (-1:ℝ) * y) 0 ^ 2 + (-0x106f8927 / 0x2540be400:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t +
  ((-3 / 50:ℝ) * x ^ 2 + (0x5f1 / 0xc350:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-3 / 0x190:ℝ) * max ((1:ℝ) * x + (-1:ℝ) * y) 0 ^ 2 + (3 / 0x190:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t ^ 2
private def zz104:"s0068"="s0068":=by decide+kernel
theorem pair_8_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_8 t x y:=by
  by_cases h0:x ≤ (1 / 3:ℝ) * y
  ·
    have hA:0 ≤ (0:ℝ):=by
      norm_num
    have hC:0 ≤ ((0x103a8c57ec1 / 0x71afd498d000:ℝ) + (-0x57a830d / 0x1bf08eb00:ℝ) * t + (0x209 / 0x249f0:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x57a830d / 0x31afba0:ℝ))]
    have hB:0 ≤ ((0x30afa507c43 / 0xe35fa931a000:ℝ) + (-0x57a830d / 0x12a05f200:ℝ) * t + (0x1fb / 0x186a0:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x57a830d / 0x3059ee0:ℝ))]
    have hgram:0 ≤ (0:ℝ) * ((1 / 3:ℝ) * y - x) ^ 2 + 2 * ((0x30afa507c43 / 0xe35fa931a000:ℝ) + (-0x57a830d / 0x12a05f200:ℝ) * t + (0x1fb / 0x186a0:ℝ) * t ^ 2) * ((1 / 3:ℝ) * y - x) * (x - (0:ℝ) * y) + ((0x103a8c57ec1 / 0x71afd498d000:ℝ) + (-0x57a830d / 0x1bf08eb00:ℝ) * t + (0x209 / 0x249f0:ℝ) * t ^ 2) * (x - (0:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_8
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-1:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((3:ℝ) * x + (-1:ℝ) * y) ≤ 0)]
    nlinarith only [hgram]
  by_cases h1:x ≤ (1:ℝ) * y
  ·
    have hlow:(1 / 3:ℝ) * y ≤ x:=le_of_not_ge h0
    have hA:0 ≤ ((0x103a8c57ec1 / 0x71afd498d000:ℝ) + (-0x57a830d / 0x1bf08eb00:ℝ) * t + (0x209 / 0x249f0:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x57a830d / 0x31afba0:ℝ))]
    have hC:0 ≤ ((21 / 0xc350:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hB:0 ≤ ((7 / 0x61a8:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hgram:0 ≤ ((0x103a8c57ec1 / 0x71afd498d000:ℝ) + (-0x57a830d / 0x1bf08eb00:ℝ) * t + (0x209 / 0x249f0:ℝ) * t ^ 2) * ((1:ℝ) * y - x) ^ 2 + 2 * ((7 / 0x61a8:ℝ) * t ^ 2) * ((1:ℝ) * y - x) * (x - (1 / 3:ℝ) * y) + ((21 / 0xc350:ℝ) * t ^ 2) * (x - (1 / 3:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_8
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-1:ℝ) * y) ≤ 0),
      max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
    nlinarith only [hgram]
  have hlow:(1:ℝ) * y ≤ x:=le_of_not_ge h1
  have hA:0 ≤ ((21 / 0xc350:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((21 / 0x186a0:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
  have hgram:0 ≤ ((21 / 0xc350:ℝ) * t ^ 2) * y ^ 2 + 2 * ((21 / 0x186a0:ℝ) * t ^ 2) * y * (x - (1:ℝ) * y) + (0:ℝ) * (x - (1:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_8
  rw [max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-1:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
  nlinarith only [hgram]
noncomputable def pair_9 (t x y:ℝ):ℝ :=
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) +
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-0x28901bd / 0xee6b2800:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (0x28901bd / 0xee6b2800:ℝ) * max ((1:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t +
  ((-1 / 0x3b9aca00:ℝ) * x ^ 2 + (0xafc81 / 0xb2d05e00:ℝ) * x * y + (0:ℝ) * y ^ 2 + (0x79b0539 / 0x2cb417800:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (-0x1856773 / 0x8f0d1800:ℝ) * max ((1:ℝ) * x + (-1:ℝ) * y) 0 ^ 2 + (1 / 0x165a0bc00:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t ^ 2
theorem pair_9_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_9 t x y:=by
  by_cases h0:x ≤ (1 / 3:ℝ) * y
  ·
    have hA:0 ≤ (0:ℝ):=by
      norm_num
    have hC:0 ≤ ((1 / 0x30d4:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hB:0 ≤ ((0xafc81 / 0x430e23400:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hgram:0 ≤ (0:ℝ) * ((1 / 3:ℝ) * y - x) ^ 2 + 2 * ((0xafc81 / 0x430e23400:ℝ) * t ^ 2) * ((1 / 3:ℝ) * y - x) * (x - (0:ℝ) * y) + ((1 / 0x30d4:ℝ) * t ^ 2) * (x - (0:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_9
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((1:ℝ) * x + (-1:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((3:ℝ) * x + (-1:ℝ) * y) ≤ 0)]
    nlinarith only [hgram]
  by_cases h1:x ≤ (1:ℝ) * y
  ·
    have hlow:(1 / 3:ℝ) * y ≤ x:=le_of_not_ge h0
    have hA:0 ≤ ((1 / 0x30d4:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hC:0 ≤ ((3 / 0x30d4:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hB:0 ≤ ((0x15f8ff / 0x218711a00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hgram:0 ≤ ((1 / 0x30d4:ℝ) * t ^ 2) * ((1:ℝ) * y - x) ^ 2 + 2 * ((0x15f8ff / 0x218711a00:ℝ) * t ^ 2) * ((1:ℝ) * y - x) * (x - (1 / 3:ℝ) * y) + ((3 / 0x30d4:ℝ) * t ^ 2) * (x - (1 / 3:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_9
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((1:ℝ) * x + (-1:ℝ) * y) ≤ 0),
      max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
    nlinarith only [hgram]
  by_cases h2:x ≤ (3:ℝ) * y
  ·
    have hlow:(1:ℝ) * y ≤ x:=le_of_not_ge h1
    have hA:0 ≤ ((3 / 0x30d4:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hC:0 ≤ ((0x28901bd / 0x3b9aca00:ℝ) * t + (-0x27e053d / 0x3b9aca00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x28901bd / 0x4fc0a7a:ℝ))]
    have hB:0 ≤ ((0x15f901 / 0xb2d05e00:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hgram:0 ≤ ((3 / 0x30d4:ℝ) * t ^ 2) * ((3:ℝ) * y - x) ^ 2 + 2 * ((0x15f901 / 0xb2d05e00:ℝ) * t ^ 2) * ((3:ℝ) * y - x) * (x - (1:ℝ) * y) + ((0x28901bd / 0x3b9aca00:ℝ) * t + (-0x27e053d / 0x3b9aca00:ℝ) * t ^ 2) * (x - (1:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_9
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-1:ℝ) * y)),
      max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
    nlinarith only [hgram]
  have hlow:(3:ℝ) * y ≤ x:=le_of_not_ge h2
  have hA:0 ≤ ((0x28901bd / 0x3b9aca00:ℝ) * t + (-0x27e053d / 0x3b9aca00:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x28901bd / 0x4fc0a7a:ℝ))]
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((0x28901bd / 0x77359400:ℝ) * t + (-0xf20117 / 0x2cb41780:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0x1162551 / 0x2292710:ℝ))]
  have hgram:0 ≤ ((0x28901bd / 0x3b9aca00:ℝ) * t + (-0x27e053d / 0x3b9aca00:ℝ) * t ^ 2) * y ^ 2 + 2 * ((0x28901bd / 0x77359400:ℝ) * t + (-0xf20117 / 0x2cb41780:ℝ) * t ^ 2) * y * (x - (3:ℝ) * y) + (0:ℝ) * (x - (3:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_9
  rw [max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-3:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-1:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
  nlinarith only [hgram]
noncomputable def pair_10 (t x y:ℝ):ℝ :=
  ((-0x794822419fb / 0x38d7ea4c6800:ℝ) * x ^ 2 + (0x794822419fb / 0x71afd498d000:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-0x794822419fb / 0x1c6bf52634000:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (0x794822419fb / 0x1c6bf52634000:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) +
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) * t +
  ((0:ℝ) * x ^ 2 + (3 / 0x2710:ℝ) * x * y + (0:ℝ) * y ^ 2) * t ^ 2
theorem pair_10_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_10 t x y:=by
  by_cases h0:x ≤ (1 / 3:ℝ) * y
  ·
    have hA:0 ≤ (0:ℝ):=by
      norm_num
    have hC:0 ≤ ((0x286d60c08a9 / 0x1550f7dca7000:ℝ) + (1 / 0x2710:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hB:0 ≤ ((0x286d60c08a9 / 0xe35fa931a000:ℝ) + (1 / 0x4e20:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hgram:0 ≤ (0:ℝ) * ((1 / 3:ℝ) * y - x) ^ 2 + 2 * ((0x286d60c08a9 / 0xe35fa931a000:ℝ) + (1 / 0x4e20:ℝ) * t ^ 2) * ((1 / 3:ℝ) * y - x) * (x - (0:ℝ) * y) + ((0x286d60c08a9 / 0x1550f7dca7000:ℝ) + (1 / 0x2710:ℝ) * t ^ 2) * (x - (0:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_10
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((3:ℝ) * x + (-1:ℝ) * y) ≤ 0)]
    nlinarith only [hgram]
  by_cases h1:x ≤ (3:ℝ) * y
  ·
    have hlow:(1 / 3:ℝ) * y ≤ x:=le_of_not_ge h0
    have hA:0 ≤ ((0x286d60c08a9 / 0x1550f7dca7000:ℝ) + (1 / 0x2710:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hC:0 ≤ ((0x794822419fb / 0x71afd498d000:ℝ) + (9 / 0x2710:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
    have hfac:0 ≤ ((0x286d60c08a9 / 0x1158e460913d000:ℝ) - (1 / 0x5f5e10:ℝ) * t ^ 2):=by nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1)]
    have hdet:0 ≤ (((0x286d60c08a9 / 0x1550f7dca7000:ℝ) + (1 / 0x2710:ℝ) * t ^ 2) * ((0x794822419fb / 0x71afd498d000:ℝ) + (9 / 0x2710:ℝ) * t ^ 2) - ((-0x286d60c08a9 / 0x71afd498d000:ℝ) + (1 / 0x7d0:ℝ) * t ^ 2) ^ 2):=by
      have hh:=mul_nonneg (pow_nonneg _ht0 2) hfac
      nlinarith only [hh]
    have hgram:=quadratic_nonnegative hA hC hdet ((3:ℝ) * y - x) (x - (1 / 3:ℝ) * y)
    unfold pair_10
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
    nlinarith only [hgram]
  have hlow:(3:ℝ) * y ≤ x:=le_of_not_ge h1
  have hA:0 ≤ ((0x794822419fb / 0x71afd498d000:ℝ) + (9 / 0x2710:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((0x794822419fb / 0xe35fa931a000:ℝ) + (3 / 0x4e20:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (0:ℝ))]
  have hgram:0 ≤ ((0x794822419fb / 0x71afd498d000:ℝ) + (9 / 0x2710:ℝ) * t ^ 2) * y ^ 2 + 2 * ((0x794822419fb / 0xe35fa931a000:ℝ) + (3 / 0x4e20:ℝ) * t ^ 2) * y * (x - (3:ℝ) * y) + (0:ℝ) * (x - (3:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_10
  rw [max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-3:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
  nlinarith only [hgram]
noncomputable def pair_11 (t x y:ℝ):ℝ :=
  ((0:ℝ) * x ^ 2 + (0:ℝ) * x * y + (0:ℝ) * y ^ 2) +
  ((-0x50d21 / 0x12a05f20:ℝ) * x ^ 2 + (0x50d21 / 0x2540be40:ℝ) * x * y + (0:ℝ) * y ^ 2 + (-0x50d21 / 0x9502f900:ℝ) * max ((1:ℝ) * x + (-3:ℝ) * y) 0 ^ 2 + (0x50d21 / 0x9502f900:ℝ) * max ((3:ℝ) * x + (-1:ℝ) * y) 0 ^ 2) * t +
  ((0:ℝ) * x ^ 2 + (3 / 0x61a8:ℝ) * x * y + (0:ℝ) * y ^ 2) * t ^ 2
theorem pair_11_nonneg {t x y:ℝ} (_ht0:0 ≤ t) (_ht1:t ≤ 1) (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ pair_11 t x y:=by
  by_cases h0:x ≤ (1 / 3:ℝ) * y
  ·
    have hA:0 ≤ (0:ℝ):=by
      norm_num
    have hC:0 ≤ ((0x1af0b / 0x6fc23ac0:ℝ) * t + (1 / 0x61a8:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0x249f0:ℝ))]
    have hB:0 ≤ ((0x1af0b / 0x4a817c80:ℝ) * t + (1 / 0xc350:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0xc350:ℝ))]
    have hgram:0 ≤ (0:ℝ) * ((1 / 3:ℝ) * y - x) ^ 2 + 2 * ((0x1af0b / 0x4a817c80:ℝ) * t + (1 / 0xc350:ℝ) * t ^ 2) * ((1 / 3:ℝ) * y - x) * (x - (0:ℝ) * y) + ((0x1af0b / 0x6fc23ac0:ℝ) * t + (1 / 0x61a8:ℝ) * t ^ 2) * (x - (0:ℝ) * y) ^ 2 :=
      add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
        (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
        (mul_nonneg hC (sq_nonneg _))
    unfold pair_11
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_right (by linarith:((3:ℝ) * x + (-1:ℝ) * y) ≤ 0)]
    nlinarith only [hgram]
  by_cases h1:x ≤ (3:ℝ) * y
  ·
    have hlow:(1 / 3:ℝ) * y ≤ x:=le_of_not_ge h0
    have hA:0 ≤ ((0x1af0b / 0x6fc23ac0:ℝ) * t + (1 / 0x61a8:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0x249f0:ℝ))]
    have hC:0 ≤ ((0x50d21 / 0x2540be40:ℝ) * t + (9 / 0x61a8:ℝ) * t ^ 2):=by
      nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0x249f0:ℝ))]
    have hfac:0 ≤ ((0x1af0b / 0xe35fa931a0:ℝ) - (1 / 0x2540be4:ℝ) * t):=by nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1)]
    have hdet:0 ≤ (((0x1af0b / 0x6fc23ac0:ℝ) * t + (1 / 0x61a8:ℝ) * t ^ 2) * ((0x50d21 / 0x2540be40:ℝ) * t + (9 / 0x61a8:ℝ) * t ^ 2) - ((-0x1af0b / 0x2540be40:ℝ) * t + (1 / 0x1388:ℝ) * t ^ 2) ^ 2):=by
      have hh:=mul_nonneg (pow_nonneg _ht0 3) hfac
      nlinarith only [hh]
    have hgram:=quadratic_nonnegative hA hC hdet ((3:ℝ) * y - x) (x - (1 / 3:ℝ) * y)
    unfold pair_11
    rw [max_eq_right (by linarith:((1:ℝ) * x + (-3:ℝ) * y) ≤ 0),
      max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
    nlinarith only [hgram]
  have hlow:(3:ℝ) * y ≤ x:=le_of_not_ge h1
  have hA:0 ≤ ((0x50d21 / 0x2540be40:ℝ) * t + (9 / 0x61a8:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0x249f0:ℝ))]
  have hC:0 ≤ (0:ℝ):=by
    norm_num
  have hB:0 ≤ ((0x50d21 / 0x4a817c80:ℝ) * t + (3 / 0xc350:ℝ) * t ^ 2):=by
    nlinarith [mul_nonneg _ht0 (sub_nonneg.mpr _ht1),sq_nonneg t,sq_nonneg (t - (-0x1af0b / 0xc350:ℝ))]
  have hgram:0 ≤ ((0x50d21 / 0x2540be40:ℝ) * t + (9 / 0x61a8:ℝ) * t ^ 2) * y ^ 2 + 2 * ((0x50d21 / 0x4a817c80:ℝ) * t + (3 / 0xc350:ℝ) * t ^ 2) * y * (x - (3:ℝ) * y) + (0:ℝ) * (x - (3:ℝ) * y) ^ 2 :=
    add_nonneg (add_nonneg (mul_nonneg hA (sq_nonneg _))
      (mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) hB) (by linarith)) (by linarith)))
      (mul_nonneg hC (sq_nonneg _))
  unfold pair_11
  rw [max_eq_left (by linarith:0 ≤ ((1:ℝ) * x + (-3:ℝ) * y)),
    max_eq_left (by linarith:0 ≤ ((3:ℝ) * x + (-1:ℝ) * y))]
  nlinarith only [hgram]
end Green24Proof.NearBalancePairs
private def zz2016:"s07e0"="s07e0":=by decide+kernel
end 
section 
namespace Green24Proof.NearBalanceCertificate
open QuadraticCertificates ExpressionCertificates NearBalanceParameterRows
open ParityPhaseRows (Phase Potential)
def rows0Chunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [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]
def rows0Chunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x101d505d7cca0faa08004f2bc938be39e03950baf98c1f4c08007849a9c9eb4ce02950baf98c1f4c08001a09c8ad5caf38e01950e9afed2b1d0800ec097cfd69cc203c10baf98c1f4c08009cdeeb78e85b202c102a384f3cac08020d8de9eede2da01c10e9afed2b1d0800bb68995b6ecc203810baf98c1f4c08008eeb496d7cbaa028105d7cca0faa080528b8ff8ccb4d601810baf98c1f4c08008eeb496d7cbaa03d405d7cca0faa0800194dee289a4c602d41186e4e2eee0800194dee289a4c503c40191c2b9e5a0802398c7d0e9c602c403b4c7adafe0802398c7d0e9c503d00baf98c1f4c08002c1a7c0a9abe202d0228dc9c5ddc08002c1a7c0a9abe103c002ebe690bd908015b39a95cbf202c008c3b2b1b7b08015b39a95cbf1571186e4e2eee08004f2bc938be39e170e9afed2b1d08004eadd9ac7b49614]
def rows0Chunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103d50baf98c1f4c08008d0ff85f9d0c202d50baf98c1f4c08001a2dac087cdc58602]
def rows0:List (ℚ × Potential) :=
  rows0Chunk0 ++ rows0Chunk1 ++ rows0Chunk2
def rows1Chunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x102d00b96c1bc801584f0c903c003dceb948002ebc58102c00b96c1bc8002ebc5825702e5d0af806fd2aba11704d485f98001cccee4c902d33bcdb2c00b86cede01d32fd7c2800394b6c95325a0afc8800ad8c9979d029303dceb948044b9a3c6019303dceb948010b7b09a1303dceb948001a299bed55602e5d0af8002bdc1a6dd1604d485f98003fed1f9b503d203dceb94805cb3b3a502d22fd7c2802d01d203dceb9480018d9f81e15225a0afc88002d4999eb9029202aa82fcc009f4a1d1019209a88bf28003b3c4efb51212d097e4805dc9b9b514]
def rows1Chunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x155050615050603c103dceb948004bde99d4107b9d6a88001bfa38a02d43bcdb2c00dbc9501d402aa82fcc028b4c203c401eeb5ca8039ceb6c102c401eeb5ca80139a929603d003dceb94801584f0ca09]
def rows1:List (ℚ × Potential) :=
  rows1Chunk0 ++ rows1Chunk1
def rows2Chunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x1171de6d9a00c96b602d31389b4804f9afa53068da00601931de6d9a001a6ccde13068da0064301bede8802eeb90383779ae58016f1d6b903068da0065601eeb5ca8001eaae1601eeb5ca80048d938603d203dceb94802eb4f58902d202e5d0af800101d201eeb5ca8002ce5205cba0de802afad1c2029201c80501921de6d9a001b0dcca12068da00603c217ebe1800142018f86c68009a3e79d02779ae58005dbc2ad14]
def rows2Chunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x102d52fd7c280058fa18d5503dceb948013d3a1d2029501eeb5ca8004eaf1d5150386d00602c15faf848008838cf101c103dceb948014e7a6a541029e8d8c8034ff81018101eeb5ca8016f1d6b9010386d0065401bede880382440386d00603d003e8a480499caa02d003dceb948017eaee9901d001eeb5ca8001dd5001eeb5ca8003d5aa03c001eeb5ca800482dc9502c003dceb948002d7929a01c003dceb94804a400b96c1bc8015fbf65701eeb5ca800681eec614]
def rows2:List (ℚ × Potential) :=
  rows2Chunk0 ++ rows2Chunk1
def rows:Rows:=![rows0,rows1,rows2]
def quad0Degree0:Expression:=quadComponent rows 0 0 0 false
def quad0Degree0Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Degree0Target:NormalForm:=(![![(0x4a1ed77f5647 / 0x2d79883d2000), -1,(-3 / 2),(0x5e88b23a647 / 0x5af3107a4000)], ![-1,(-0x18871912b3647 / 0x2d79883d2000),(0xaffd95d0d9b9 / 0x5af3107a4000),(1 / 2)], ![(-3 / 2),(0xaffd95d0d9b9 / 0x5af3107a4000),(-0x6f2dd5b7b0f9 / 0x110d9316ec00),(0x448be5fe62f9 / 0x44364c5bb000)], ![(0x5e88b23a647 / 0x5af3107a4000),(1 / 2),(0x448be5fe62f9 / 0x44364c5bb000),(-1 / 2)]],[((-0x5599a2b2f9 / 0x886c98b76000), ![0,0,1, -1]),((0x5599a2b2f9 / 0x886c98b76000), ![0,0,3, -1]),((0x5e88b23a647 / 0xb5e620f48000), ![0,1,0, -3]),((0xa42c7f898d2b / 0x5af3107a4000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((0x5e88b23a647 / 0xb5e620f48000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x5599a2b2f9 / 0x886c98b76000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x5599a2b2f9 / 0x886c98b76000), ![1, -1,0,0]),((-0x5e88b23a647 / 0xb5e620f48000), ![1,0, -3,0]),((-0xa42c7f898d2b / 0x5af3107a4000), ![1,0, -1,0]),((1 / 2), ![1,2, -3,0]),((-0x5e88b23a647 / 0xb5e620f48000), ![3,0, -1,0])])
private def zz105:"s0069"="s0069":=by decide+kernel
theorem quad0Degree0_identity:identityCheck quad0Degree0 quad0Degree0Rewrites quad0Degree0Target = true:=by decide +kernel
def quad0Degree1:Expression:=quadComponent rows 1 0 0 false
def quad0Degree1Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Degree1Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,(0x2d7141 / 0x59682f00),(-0x2d7141 / 0x165a0bc00)], ![0,0,(-0x2d7141 / 0x165a0bc00),0]],[((0x2d7141 / 0x2cb417800), ![0,0,1, -1]),((-0x2d7141 / 0x2cb417800), ![0,0,3, -1]),((0x2d7141 / 0x2cb417800), ![1, -3,0,0]),((-0x2d7141 / 0x2cb417800), ![1, -1,0,0])])
theorem quad0Degree1_identity:identityCheck quad0Degree1 quad0Degree1Rewrites quad0Degree1Target = true:=by decide +kernel
def quad0Degree2:Expression:=quadComponent rows 2 0 0 false
def quad0Degree2Rewrites:Rewrites:=[RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Degree2Target:NormalForm:=(![![(0x1f789df / 0x3b9aca00),(0x729ccfb / 0x2cb417800),(0xbbb / 0x30d40),(-0x16dfb05 / 0x3b9aca00)], ![(0x729ccfb / 0x2cb417800),(0x839b65f / 0x77359400),(-0x5b7097 / 0x1dcd6500),(0x5c0313 / 0x77359400)], ![(0xbbb / 0x30d40),(-0x5b7097 / 0x1dcd6500),(0x1941a5fd / 0x165a0bc00),(-0x1a1223d / 0x8f0d1800)], ![(-0x16dfb05 / 0x3b9aca00),(0x5c0313 / 0x77359400),(-0x1a1223d / 0x8f0d1800),(1 / 0xc8)]],[((37 / 0x2cb417800), ![0,0,1, -3]),((0x2ae48d / 0xee6b2800), ![0,0,1, -1]),((-0x157259 / 0x77359400), ![0,0,3, -1]),((-0x7a11df / 0x77359400), ![0,1,0, -3]),((1 / 0xc8), ![0,3, -2, -1]),((-1 / 0xc8), ![0,3, -2,1]),((-1 / 0xc8), ![0,3,2, -1]),((0x157259 / 0x77359400), ![1, -3,0,0]),((1 / 0xc8), ![1, -2, -3,0]),((-1 / 0xc8), ![1, -2,3,0]),((-0x2ae48d / 0xee6b2800), ![1, -1,0,0]),((0x7a11df / 0x3b9aca00), ![1,0,0, -3]),((-1 / 0xc8), ![1,2, -3,0]),((-37 / 0x2cb417800), ![3, -1,0,0]),((0x7a11df / 0x77359400), ![3,0, -1,0]),((-0x7a11df / 0x3b9aca00), ![3,0,0, -1])])
theorem quad0Degree2_identity:identityCheck quad0Degree2 quad0Degree2Rewrites quad0Degree2Target = true:=by decide +kernel
noncomputable def quad0Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad0Degree0Target x + t * normalEval quad0Degree1Target x + t ^ 2 * normalEval quad0Degree2Target x
theorem quad0_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 0 0 false) t x = quad0Polynomial t x:=by
  change expressionEval quad0Degree0 x + t * expressionEval quad0Degree1 x + t ^ 2 * expressionEval quad0Degree2 x = _
  rw [identityCheck_sound quad0Degree0 quad0Degree0Rewrites quad0Degree0Target x quad0Degree0_identity,identityCheck_sound quad0Degree1 quad0Degree1Rewrites quad0Degree1Target x quad0Degree1_identity,identityCheck_sound quad0Degree2 quad0Degree2Rewrites quad0Degree2Target x quad0Degree2_identity]
  rfl
def quad1Degree0:Expression:=quadComponent rows 0 0 0 true
def quad1Degree0Rewrites:Rewrites:=[RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Degree0Target:NormalForm:=(![![(0x24ac0093a051 / 0x1550f7dca700), -1,(-3 / 2),(0x1ef475bf62db / 0x2aa1efb94e000)], ![-1,(-0xb85685bc3c87b / 0x1550f7dca7000),(0x29346b23e04df / 0x1550f7dca7000),(0xe4f107d0be13 / 0x1c6bf52634000)], ![(-3 / 2),(0x29346b23e04df / 0x1550f7dca7000),(-0x6f2dd5b7b0f9 / 0x110d9316ec00),(0x448be5fe62f9 / 0x44364c5bb000)], ![(0x1ef475bf62db / 0x2aa1efb94e000),(0xe4f107d0be13 / 0x1c6bf52634000),(0x448be5fe62f9 / 0x44364c5bb000),(-1 / 2)]],[((-0x5599a2b2f9 / 0x886c98b76000), ![0,0,1, -1]),((0x5599a2b2f9 / 0x886c98b76000), ![0,0,3, -1]),((0x16d84956db21 / 0x2aa1efb94e000), ![0,1,0, -3]),((0x4162f1edb8ad / 0x246139ca8000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((0x13377371c159 / 0x221b262dd8000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x5599a2b2f9 / 0x886c98b76000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x5599a2b2f9 / 0x886c98b76000), ![1, -1,0,0]),((-0x13377371c159 / 0x221b262dd8000), ![1,0, -3,0]),((-0x4162f1edb8ad / 0x246139ca8000), ![1,0, -1,0]),((0x4e95efa1bcd / 0x1c6bf52634000), ![1,0,0, -3]),((1 / 2), ![1,2, -3,0]),((-0x16d84956db21 / 0x2aa1efb94e000), ![3,0, -1,0]),((-0x4e95efa1bcd / 0x1c6bf52634000), ![3,0,0, -1])])
private def zz106:"s006a"="s006a":=by decide+kernel
theorem quad1Degree0_identity:identityCheck quad1Degree0 quad1Degree0Rewrites quad1Degree0Target = true:=by decide +kernel
def quad1Degree1:Expression:=quadComponent rows 1 0 0 true
def quad1Degree1Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Degree1Target:NormalForm:=(![![(-0x17e8c5 / 0xee6b2800),0,(0x17e8c5 / 0x1dcd65000),0], ![0,(0xd72eed / 0xee6b2800),0,(-0x17e8c5 / 0x5f5e1000)], ![(0x17e8c5 / 0x1dcd65000),0,(0x2d7141 / 0x59682f00),(-0x2d7141 / 0x165a0bc00)], ![0,(-0x17e8c5 / 0x5f5e1000),(-0x2d7141 / 0x165a0bc00),0]],[((0x2d7141 / 0x2cb417800), ![0,0,1, -1]),((-0x2d7141 / 0x2cb417800), ![0,0,3, -1]),((-0x17e8c5 / 0xee6b2800), ![0,3,0, -1]),((0x2d7141 / 0x2cb417800), ![1, -3,0,0]),((-0x2d7141 / 0x2cb417800), ![1, -1,0,0]),((0x17e8c5 / 0xee6b2800), ![1,0, -3,0])])
theorem quad1Degree1_identity:identityCheck quad1Degree1 quad1Degree1Rewrites quad1Degree1Target = true:=by decide +kernel
def quad1Degree2:Expression:=quadComponent rows 2 0 0 true
def quad1Degree2Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Degree2Target:NormalForm:=(![![(-0x14ddfe3 / 0x3b9aca00),(0x729ccfb / 0x2cb417800),(0x21eb13f / 0x8f0d1800),(-0x5b9d / 0x5f5e10)], ![(0x729ccfb / 0x2cb417800),(0x1ba84ac5 / 0x165a0bc00),(-0x4a3ce9 / 0x11e1a300),(-0xd316d5 / 0x2cb417800)], ![(0x21eb13f / 0x8f0d1800),(-0x4a3ce9 / 0x11e1a300),(0x1941a5fd / 0x165a0bc00),(-0x1a1223d / 0x8f0d1800)], ![(-0x5b9d / 0x5f5e10),(-0xd316d5 / 0x2cb417800),(-0x1a1223d / 0x8f0d1800),(1 / 0xc8)]],[((37 / 0x2cb417800), ![0,0,1, -3]),((0x2ae48d / 0xee6b2800), ![0,0,1, -1]),((-0x157259 / 0x77359400), ![0,0,3, -1]),((1 / 0x23c34600), ![0,1, -3,0]),((-0x14ce993 / 0x2cb417800), ![0,1,0, -3]),((-0x806339 / 0x2faf0800), ![0,1,0, -1]),((1 / 0xc8), ![0,3, -2, -1]),((-1 / 0xc8), ![0,3, -2,1]),((-1 / 0x23c34600), ![0,3, -1,0]),((-1 / 0xc8), ![0,3,2, -1]),((0x157259 / 0x77359400), ![1, -3,0,0]),((1 / 0xc8), ![1, -2, -3,0]),((-1 / 0xc8), ![1, -2,3,0]),((-0x2ae48d / 0xee6b2800), ![1, -1,0,0]),((0x806339 / 0x2faf0800), ![1,0, -1,0]),((-1 / 0xc8), ![1,2, -3,0]),((-37 / 0x2cb417800), ![3, -1,0,0]),((0x14ce993 / 0x2cb417800), ![3,0, -1,0])])
theorem quad1Degree2_identity:identityCheck quad1Degree2 quad1Degree2Rewrites quad1Degree2Target = true:=by decide +kernel
noncomputable def quad1Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad1Degree0Target x + t * normalEval quad1Degree1Target x + t ^ 2 * normalEval quad1Degree2Target x
theorem quad1_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 0 0 true) t x = quad1Polynomial t x:=by
  change expressionEval quad1Degree0 x + t * expressionEval quad1Degree1 x + t ^ 2 * expressionEval quad1Degree2 x = _
  rw [identityCheck_sound quad1Degree0 quad1Degree0Rewrites quad1Degree0Target x quad1Degree0_identity,identityCheck_sound quad1Degree1 quad1Degree1Rewrites quad1Degree1Target x quad1Degree1_identity,identityCheck_sound quad1Degree2 quad1Degree2Rewrites quad1Degree2Target x quad1Degree2_identity]
  rfl
def quad2Degree0:Expression:=quadComponent rows 0 0 1 false
def quad2Degree0Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r23,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Degree0Target:NormalForm:=(![![(0x3009737cdbd21 / 0x1c6bf52634000), -1,(-3 / 2),(0x5e88b23a647 / 0x5af3107a4000)], ![-1,(-0xf0247453303b5 / 0x1c6bf52634000),(0x1aa48901ff121 / 0xe35fa931a000),(1 / 2)], ![(-3 / 2),(0x1aa48901ff121 / 0xe35fa931a000),(-0x1c0662c5922f1 / 0x44364c5bb000),(0x115de6d73eaf1 / 0x110d9316ec000)], ![(0x5e88b23a647 / 0x5af3107a4000),(1 / 2),(0x115de6d73eaf1 / 0x110d9316ec000),(-1 / 2)]],[((-0x5053c052af1 / 0x221b262dd8000), ![0,0,1, -1]),((0x5053c052af1 / 0x221b262dd8000), ![0,0,3, -1]),((0x5e88b23a647 / 0xb5e620f48000), ![0,1,0, -3]),((0xa42c7f898d2b / 0x5af3107a4000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((-0x920eef174c9 / 0x1c6bf52634000), ![0,3, -1,0]),((0x5e88b23a647 / 0xb5e620f48000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x8cc47a1a63 / 0x3691d6afc000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x8cc47a1a63 / 0x3691d6afc000), ![1, -1,0,0]),((-0x4b045ebef0d / 0xb5e620f48000), ![1,0, -3,0]),((-0x1407055595cc7 / 0xb5e620f48000), ![1,0, -1,0]),((-0x920eef174c9 / 0x1c6bf52634000), ![1,0,0, -1]),((1 / 2), ![1,2, -3,0]),((-0x9aae9a8ed0b / 0xe35fa931a000), ![3,0, -1,0])])
private def zz107:"s006b"="s006b":=by decide+kernel
theorem quad2Degree0_identity:identityCheck quad2Degree0 quad2Degree0Rewrites quad2Degree0Target = true:=by decide +kernel
def quad2Degree1:Expression:=quadComponent rows 1 0 1 false
def quad2Degree1Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Degree1Target:NormalForm:=(![![(-0x6ee335b / 0xb2d05e00),0,(3 / 20),(-0x9e597 / 0xf42400)], ![0,(-0x5423f535 / 0x12a05f200),(-0x5d92e5b / 0x2540be400),0], ![(3 / 20),(-0x5d92e5b / 0x2540be400),(-0x1509c25 / 0x59682f00),(0x1509c25 / 0x165a0bc00)], ![(-0x9e597 / 0xf42400),0,(0x1509c25 / 0x165a0bc00),0]],[((-0x1509c25 / 0x2cb417800), ![0,0,1, -1]),((0x1509c25 / 0x2cb417800), ![0,0,3, -1]),((0x9e8869 / 0x4a817c80), ![0,1, -1,0]),((0x1b389bdb / 0x37e11d600), ![0,3, -1,0]),((0x133448b / 0x77359400), ![1, -3,0,0]),((-0x133448b / 0x77359400), ![1, -1,0,0]),((0x106ec0d / 0x165a0bc00), ![1,0,0, -3]),((0x44728e3 / 0x77359400), ![1,0,0, -1])])
theorem quad2Degree1_identity:identityCheck quad2Degree1 quad2Degree1Rewrites quad2Degree1Target = true:=by decide +kernel
def quad2Degree2:Expression:=quadComponent rows 2 0 1 false
def quad2Degree2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r25,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Degree2Target:NormalForm:=(![![(-0x2354831 / 0x165a0bc00),(3 / 0x30d40),(3 / 0x30d40),(0xa6d41 / 0x3b9aca0)], ![(3 / 0x30d40),(0x3b9870f / 0x77359400),(3 / 0x30d40),(-0x16dc06d / 0x77359400)], ![(3 / 0x30d40),(3 / 0x30d40),(-0x2fab8fb / 0x3b9aca00),(0x5f747 / 0x1dcd650)], ![(0xa6d41 / 0x3b9aca0),(-0x16dc06d / 0x77359400),(0x5f747 / 0x1dcd650),0]],[((-37 / 0x77359400), ![0,0,1, -3]),((-0x17d5b8d / 0xee6b2800), ![0,0,1, -1]),((0x30d07 / 0x1e84800), ![0,0,3, -1]),((3 / 0x190), ![0,1, -1,0]),((-0x7a11df / 0x77359400), ![0,1,0, -3]),((-0x161725 / 0x165a0bc0), ![0,3, -1,0]),((0x4d5c6b / 0x77359400), ![1,0, -1,0]),((0x14d32f / 0x165a0bc0), ![1,0,0, -3])])
theorem quad2Degree2_identity:identityCheck quad2Degree2 quad2Degree2Rewrites quad2Degree2Target = true:=by decide +kernel
noncomputable def quad2Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad2Degree0Target x + t * normalEval quad2Degree1Target x + t ^ 2 * normalEval quad2Degree2Target x
theorem quad2_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 0 1 false) t x = quad2Polynomial t x:=by
  change expressionEval quad2Degree0 x + t * expressionEval quad2Degree1 x + t ^ 2 * expressionEval quad2Degree2 x = _
  rw [identityCheck_sound quad2Degree0 quad2Degree0Rewrites quad2Degree0Target x quad2Degree0_identity,identityCheck_sound quad2Degree1 quad2Degree1Rewrites quad2Degree1Target x quad2Degree1_identity,identityCheck_sound quad2Degree2 quad2Degree2Rewrites quad2Degree2Target x quad2Degree2_identity]
  rfl
def quad3Degree0:Expression:=quadComponent rows 0 0 1 true
def quad3Degree0Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Degree0Target:NormalForm:=(![![(0x46fff7d70f127 / 0x2aa1efb94e000), -1,(-3 / 2),(0x2ac53977657 / 0x2aa1efb94e00)], ![-1,(-0x166299a526ff29 / 0x2aa1efb94e000),(0x3fb3f3456ed9 / 0x221b262dd800),(0xe4f107d0be13 / 0x1c6bf52634000)], ![(-3 / 2),(0x3fb3f3456ed9 / 0x221b262dd800),(-0x1c0662c5922f1 / 0x44364c5bb000),(0x115de6d73eaf1 / 0x110d9316ec000)], ![(0x2ac53977657 / 0x2aa1efb94e00),(0xe4f107d0be13 / 0x1c6bf52634000),(0x115de6d73eaf1 / 0x110d9316ec000),(-1 / 2)]],[((-0x5053c052af1 / 0x221b262dd8000), ![0,0,1, -1]),((0x5053c052af1 / 0x221b262dd8000), ![0,0,3, -1]),((0xde4c393607f / 0x221b262dd8000), ![0,1, -3,0]),((0x83fc63 / 0xaa87bee538000), ![0,1, -1,0]),((0x16d84956db21 / 0x2aa1efb94e000), ![0,1,0, -3]),((0x4162f1edb8ad / 0x246139ca8000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((-0x8cc47a1a63 / 0x12309ce54000), ![0,3, -1,0]),((0x13377371c159 / 0x221b262dd8000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x8cc47a1a63 / 0x3691d6afc000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x8cc47a1a63 / 0x3691d6afc000), ![1, -1,0,0]),((-0x1143f85f3421 / 0x221b262dd8000), ![1,0, -3,0]),((-0x1456a0079b143 / 0xb5e620f48000), ![1,0, -1,0]),((-0xe593573eb / 0x1550f7dca700), ![1,0,0, -1]),((1 / 2), ![1,2, -3,0]),((-0x9c9e13178cf / 0x110d9316ec000), ![3,0, -1,0]),((-0x4abc1f0815 / 0x886c98b76000), ![3,0,0, -1])])
private def zz108:"s006c"="s006c":=by decide+kernel
theorem quad3Degree0_identity:identityCheck quad3Degree0 quad3Degree0Rewrites quad3Degree0Target = true:=by decide +kernel
def quad3Degree1:Expression:=quadComponent rows 1 0 1 true
def quad3Degree1Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Degree1Target:NormalForm:=(![![(-0x74d27fb / 0xb2d05e00),0,(3 / 20),(-0x32065393 / 0x4a817c800)], ![0,(-0x37f9b367 / 0xee6b2800),(-0x1543279d / 0x4a817c800),(-0x17e8c5 / 0x5f5e1000)], ![(3 / 20),(-0x1543279d / 0x4a817c800),(-0x1509c25 / 0x59682f00),(0x1509c25 / 0x165a0bc00)], ![(-0x32065393 / 0x4a817c800),(-0x17e8c5 / 0x5f5e1000),(0x1509c25 / 0x165a0bc00),0]],[((-0x1509c25 / 0x2cb417800), ![0,0,1, -1]),((0x1509c25 / 0x2cb417800), ![0,0,3, -1]),((0x1eccef1 / 0x77359400), ![0,1, -3,0]),((23 / 0xbebc200), ![0,1, -1,0]),((0x8d3e071 / 0x165a0bc00), ![0,3, -1,0]),((-0x17e8c5 / 0xee6b2800), ![0,3,0, -1]),((0x133448b / 0x77359400), ![1, -3,0,0]),((-0x133448b / 0x77359400), ![1, -1,0,0]),((-0x328da5 / 0x23c34600), ![1,0,0, -3]),((0xb0d3af / 0xee6b280), ![1,0,0, -1])])
theorem quad3Degree1_identity:identityCheck quad3Degree1 quad3Degree1Rewrites quad3Degree1Target = true:=by decide +kernel
def quad3Degree2:Expression:=quadComponent rows 2 0 1 true
def quad3Degree2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r23,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Degree2Target:NormalForm:=(![![(-0x106d3f / 0x2faf080),(3 / 0x30d40),(0x13a6869 / 0xee6b2800),(0x9eb6d / 0x4c4b400)], ![(3 / 0x30d40),(0x26adf1 / 0x23c34600),(0x2af5461 / 0xb2d05e00),(-0xb8dabd5 / 0x2cb417800)], ![(0x13a6869 / 0xee6b2800),(0x2af5461 / 0xb2d05e00),(-0x2fab8fb / 0x3b9aca00),(0x5f747 / 0x1dcd650)], ![(0x9eb6d / 0x4c4b400),(-0xb8dabd5 / 0x2cb417800),(0x5f747 / 0x1dcd650),0]],[((-37 / 0x77359400), ![0,0,1, -3]),((-0x17d5b8d / 0xee6b2800), ![0,0,1, -1]),((0x30d07 / 0x1e84800), ![0,0,3, -1]),((0x2e69d45 / 0x165a0bc00), ![0,1, -3,0]),((1 / 0x59682f00), ![0,1, -1,0]),((-0x14ce993 / 0x2cb417800), ![0,1,0, -3]),((-0x806339 / 0x2faf0800), ![0,1,0, -1]),((-0xa7 / 0xb2d05e00), ![0,3, -1,0]),((0x51e847 / 0x17d78400), ![1,0, -1,0]),((0x9e6bd / 0x4c4b400), ![1,0,0, -1])])
theorem quad3Degree2_identity:identityCheck quad3Degree2 quad3Degree2Rewrites quad3Degree2Target = true:=by decide +kernel
noncomputable def quad3Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad3Degree0Target x + t * normalEval quad3Degree1Target x + t ^ 2 * normalEval quad3Degree2Target x
theorem quad3_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 0 1 true) t x = quad3Polynomial t x:=by
  change expressionEval quad3Degree0 x + t * expressionEval quad3Degree1 x + t ^ 2 * expressionEval quad3Degree2 x = _
  rw [identityCheck_sound quad3Degree0 quad3Degree0Rewrites quad3Degree0Target x quad3Degree0_identity,identityCheck_sound quad3Degree1 quad3Degree1Rewrites quad3Degree1Target x quad3Degree1_identity,identityCheck_sound quad3Degree2 quad3Degree2Rewrites quad3Degree2Target x quad3Degree2_identity]
  rfl
def quad4Degree0:Expression:=quadComponent rows 0 1 1 false
def quad4Degree0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Degree0Target:NormalForm:=(![![(0x5eeec91b890b / 0x38d7ea4c6800), -1,(-3 / 2),(0x9aae9a8ed0b / 0x71afd498d000)], ![-1,(-0x3d9bda724970b / 0x71afd498d000),(0xdd87a2faaa6d / 0x71afd498d000),(0xd42560299715 / 0x1c6bf52634000)], ![(-3 / 2),(0xdd87a2faaa6d / 0x71afd498d000),(-0xe0036e4b2523 / 0x221b262dd800),(0x8abf8ed88923 / 0x886c98b76000)], ![(0x9aae9a8ed0b / 0x71afd498d000),(0xd42560299715 / 0x1c6bf52634000),(0x8abf8ed88923 / 0x886c98b76000),(-1 / 2)]],[((-0x252f6212923 / 0x110d9316ec000), ![0,0,1, -1]),((0x252f6212923 / 0x110d9316ec000), ![0,0,3, -1]),((-0x1878e2d963 / 0x5af3107a400), ![0,1, -3,0]),((0x9aae9a8ed0b / 0xe35fa931a000), ![0,1,0, -3]),((0x1407055595cc7 / 0xb5e620f48000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((0x1878e2d963 / 0x5af3107a400), ![0,3, -1,0]),((0x4b045ebef0d / 0xb5e620f48000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x252f6212923 / 0x110d9316ec000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x252f6212923 / 0x110d9316ec000), ![1, -1,0,0]),((-0x4b045ebef0d / 0xb5e620f48000), ![1,0, -3,0]),((-0x1407055595cc7 / 0xb5e620f48000), ![1,0, -1,0]),((1 / 2), ![1,2, -3,0]),((-0x9aae9a8ed0b / 0xe35fa931a000), ![3,0, -1,0])])
private def zz109:"s006d"="s006d":=by decide+kernel
theorem quad4Degree0_identity:identityCheck quad4Degree0 quad4Degree0Rewrites quad4Degree0Target = true:=by decide +kernel
def quad4Degree1:Expression:=quadComponent rows 1 1 1 false
def quad4Degree1Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Degree1Target:NormalForm:=(![![(0x1af0b / 0x2540be40),0,(3 / 20),(-0xcc9d925 / 0x9502f900)], ![0,0,(-0x1fea3e5b / 0x9502f900),(3 / 20)], ![(3 / 20),(-0x1fea3e5b / 0x9502f900),(0x1af0b / 0x2540be40),(-0x1af0b / 0x4a817c80)], ![(-0xcc9d925 / 0x9502f900),(3 / 20),(-0x1af0b / 0x4a817c80),0]],[((0x1af0b / 0x9502f900), ![0,0,1, -3]),((-0x1af0b / 0x1dcd6500), ![0,0,1, -1]),((0x1af0b / 0x1dcd6500), ![1, -1,0,0]),((-0x1af0b / 0x9502f900), ![3, -1,0,0])])
theorem quad4Degree1_identity:identityCheck quad4Degree1 quad4Degree1Rewrites quad4Degree1Target = true:=by decide +kernel
def quad4Degree2:Expression:=quadComponent rows 2 1 1 false
def quad4Degree2Rewrites:Rewrites:=[RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Degree2Target:NormalForm:=(![![(-0x4d5c6b / 0x77359400),(0xc1 / 0xbebc20),(3 / 0x30d40),(0x1859b / 0x7735940)], ![(0xc1 / 0xbebc20),(0x4d5c6b / 0x77359400),(0x41a4c3 / 0x3b9aca00),(-0x4ce73b / 0x77359400)], ![(3 / 0x30d40),(0x41a4c3 / 0x3b9aca00),0,(0xc1 / 0xbebc20)], ![(0x1859b / 0x7735940),(-0x4ce73b / 0x77359400),(0xc1 / 0xbebc20),0]],[((-0x4d5c6b / 0x77359400), ![0,1,0, -1]),((0x4d5c6b / 0x77359400), ![1,0, -1,0])])
theorem quad4Degree2_identity:identityCheck quad4Degree2 quad4Degree2Rewrites quad4Degree2Target = true:=by decide +kernel
noncomputable def quad4Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad4Degree0Target x + t * normalEval quad4Degree1Target x + t ^ 2 * normalEval quad4Degree2Target x
theorem quad4_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 1 1 false) t x = quad4Polynomial t x:=by
  change expressionEval quad4Degree0 x + t * expressionEval quad4Degree1 x + t ^ 2 * expressionEval quad4Degree2 x = _
  rw [identityCheck_sound quad4Degree0 quad4Degree0Rewrites quad4Degree0Target x quad4Degree0_identity,identityCheck_sound quad4Degree1 quad4Degree1Rewrites quad4Degree1Target x quad4Degree1_identity,identityCheck_sound quad4Degree2 quad4Degree2Rewrites quad4Degree2Target x quad4Degree2_identity]
  rfl
def quad5Degree0:Expression:=quadComponent rows 0 1 1 true
def quad5Degree0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Degree0Target:NormalForm:=(![![(0x701b53bb00cf / 0x44364c5bb000), -1,(-3 / 2),(0x9c9e13178cf / 0x886c98b76000)], ![-1,(-0x120fab7bccbbd / 0x221b262dd800),(0x1026637dd8945 / 0x886c98b76000),(0x8f0da94824d / 0x12309ce54000)], ![(-3 / 2),(0x1026637dd8945 / 0x886c98b76000),(-0xe0036e4b2523 / 0x221b262dd800),(0x8abf8ed88923 / 0x886c98b76000)], ![(0x9c9e13178cf / 0x886c98b76000),(0x8f0da94824d / 0x12309ce54000),(0x8abf8ed88923 / 0x886c98b76000),(-1 / 2)]],[((-0x252f6212923 / 0x110d9316ec000), ![0,0,1, -1]),((0x252f6212923 / 0x110d9316ec000), ![0,0,3, -1]),((0x636cb2a529 / 0x16bcc41e9000), ![0,1, -3,0]),((0x9c9e13178cf / 0x110d9316ec000), ![0,1,0, -3]),((0x1456a0079b143 / 0xb5e620f48000), ![0,1,0, -1]),((-1 / 2), ![0,3, -2, -1]),((1 / 2), ![0,3, -2,1]),((-0x636cb2a529 / 0x16bcc41e9000), ![0,3, -1,0]),((0x1143f85f3421 / 0x221b262dd8000), ![0,3,0, -1]),((1 / 2), ![0,3,2, -1]),((-0x252f6212923 / 0x110d9316ec000), ![1, -3,0,0]),((-1 / 2), ![1, -2, -3,0]),((1 / 2), ![1, -2,3,0]),((0x252f6212923 / 0x110d9316ec000), ![1, -1,0,0]),((-0x1143f85f3421 / 0x221b262dd8000), ![1,0, -3,0]),((-0x1456a0079b143 / 0xb5e620f48000), ![1,0, -1,0]),((1 / 2), ![1,2, -3,0]),((-0x9c9e13178cf / 0x110d9316ec000), ![3,0, -1,0])])
private def zz110:"s006e"="s006e":=by decide+kernel
theorem quad5Degree0_identity:identityCheck quad5Degree0 quad5Degree0Rewrites quad5Degree0Target = true:=by decide +kernel
def quad5Degree1:Expression:=quadComponent rows 1 1 1 true
def quad5Degree1Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Degree1Target:NormalForm:=(![![(0x1af0b / 0x2540be40),0,(3 / 20),(-0x6fa4ad1 / 0x59682f00)], ![0,0,(-0x13d829af / 0x59682f00),(3 / 20)], ![(3 / 20),(-0x13d829af / 0x59682f00),(0x1af0b / 0x2540be40),(-0x1af0b / 0x4a817c80)], ![(-0x6fa4ad1 / 0x59682f00),(3 / 20),(-0x1af0b / 0x4a817c80),0]],[((0x1af0b / 0x9502f900), ![0,0,1, -3]),((-0x1af0b / 0x1dcd6500), ![0,0,1, -1]),((0x1af0b / 0x1dcd6500), ![1, -1,0,0]),((-0x1af0b / 0x9502f900), ![3, -1,0,0])])
theorem quad5Degree1_identity:identityCheck quad5Degree1 quad5Degree1Rewrites quad5Degree1Target = true:=by decide +kernel
def quad5Degree2:Expression:=quadComponent rows 2 1 1 true
def quad5Degree2Rewrites:Rewrites:=[RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Degree2Target:NormalForm:=(![![(-0x51e847 / 0x17d78400),(0xc1 / 0xbebc20),(0x13a6869 / 0xee6b2800),(0x603ba3 / 0x3b9aca00)], ![(0xc1 / 0xbebc20),(0x51e847 / 0x17d78400),(0x3a97 / 0x3b9aca00),(-0x1f8aa5d / 0xee6b2800)], ![(0x13a6869 / 0xee6b2800),(0x3a97 / 0x3b9aca00),0,(0xc1 / 0xbebc20)], ![(0x603ba3 / 0x3b9aca00),(-0x1f8aa5d / 0xee6b2800),(0xc1 / 0xbebc20),0]],[((-0x51e847 / 0x17d78400), ![0,1,0, -1]),((0x51e847 / 0x17d78400), ![1,0, -1,0])])
theorem quad5Degree2_identity:identityCheck quad5Degree2 quad5Degree2Rewrites quad5Degree2Target = true:=by decide +kernel
noncomputable def quad5Polynomial (t:ℝ) (x:Point):ℝ :=
  normalEval quad5Degree0Target x + t * normalEval quad5Degree1Target x + t ^ 2 * normalEval quad5Degree2Target x
theorem quad5_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => quadComponent rows d 1 1 true) t x = quad5Polynomial t x:=by
  change expressionEval quad5Degree0 x + t * expressionEval quad5Degree1 x + t ^ 2 * expressionEval quad5Degree2 x = _
  rw [identityCheck_sound quad5Degree0 quad5Degree0Rewrites quad5Degree0Target x quad5Degree0_identity,identityCheck_sound quad5Degree1 quad5Degree1Rewrites quad5Degree1Target x quad5Degree1_identity,identityCheck_sound quad5Degree2 quad5Degree2Rewrites quad5Degree2Target x quad5Degree2_identity]
  rfl
def pair6Degree0:Expression:=pairComponent rows 0 0 0 false
def pair6Degree0Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Degree0Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
private def zz111:"s006f"="s006f":=by decide+kernel
theorem pair6Degree0_identity:identityCheck pair6Degree0 pair6Degree0Rewrites pair6Degree0Target = true:=by decide +kernel
def pair6Degree1:Expression:=pairComponent rows 1 0 0 false
def pair6Degree1Rewrites:Rewrites:=[]
def pair6Degree1Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair6Degree1_identity:identityCheck pair6Degree1 pair6Degree1Rewrites pair6Degree1Target = true:=by decide +kernel
def pair6Degree2:Expression:=pairComponent rows 2 0 0 false
def pair6Degree2Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26]
def pair6Degree2Target:NormalForm:=(![![0,(3 / 0x4e20),0,0], ![(3 / 0x4e20),0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair6Degree2_identity:identityCheck pair6Degree2 pair6Degree2Rewrites pair6Degree2Target = true:=by decide +kernel
theorem pair6_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 0 0 false) t x = NearBalancePairs.pair_6 t (x 0) (x 1):=by
  change expressionEval pair6Degree0 x + t * expressionEval pair6Degree1 x + t ^ 2 * expressionEval pair6Degree2 x = _
  rw [identityCheck_sound pair6Degree0 pair6Degree0Rewrites pair6Degree0Target x pair6Degree0_identity,identityCheck_sound pair6Degree1 pair6Degree1Rewrites pair6Degree1Target x pair6Degree1_identity,identityCheck_sound pair6Degree2 pair6Degree2Rewrites pair6Degree2Target x pair6Degree2_identity]
  norm_num [pair6Degree0Target,pair6Degree1Target,pair6Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_6]
  all_goals ring_nf
private def zz112:"s0070"="s0070":=by decide+kernel
theorem pair6_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 0 0 false) t x:=by
  rw [pair6_eval]
  exact NearBalancePairs.pair_6_nonneg ht0 ht1 (hx 0) (hx 1)
def pair7Degree0:Expression:=pairComponent rows 0 0 0 true
def pair7Degree0Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Degree0Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair7Degree0_identity:identityCheck pair7Degree0 pair7Degree0Rewrites pair7Degree0Target = true:=by decide +kernel
def pair7Degree1:Expression:=pairComponent rows 1 0 0 true
def pair7Degree1Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Degree1Target:NormalForm:=(![![(-0x5d42cb / 0x1dcd6500),(0x5d42cb / 0x77359400),0,0], ![(0x5d42cb / 0x77359400),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-0x5d42cb / 0xee6b2800), ![1, -3,0,0]),((0x5d42cb / 0xee6b2800), ![3, -1,0,0])])
theorem pair7Degree1_identity:identityCheck pair7Degree1 pair7Degree1Rewrites pair7Degree1Target = true:=by decide +kernel
def pair7Degree2:Expression:=pairComponent rows 2 0 0 true
def pair7Degree2Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27]
def pair7Degree2Target:NormalForm:=(![![(0x5d42cb / 0x1dcd6500),(-0x5b6e0b / 0x77359400),0,0], ![(-0x5b6e0b / 0x77359400),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((0x5d42cb / 0xee6b2800), ![1, -3,0,0]),((-0x5d42cb / 0xee6b2800), ![3, -1,0,0])])
theorem pair7Degree2_identity:identityCheck pair7Degree2 pair7Degree2Rewrites pair7Degree2Target = true:=by decide +kernel
private def zz113:"s0071"="s0071":=by decide+kernel
theorem pair7_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 0 0 true) t x = NearBalancePairs.pair_7 t (x 0) (x 1):=by
  change expressionEval pair7Degree0 x + t * expressionEval pair7Degree1 x + t ^ 2 * expressionEval pair7Degree2 x = _
  rw [identityCheck_sound pair7Degree0 pair7Degree0Rewrites pair7Degree0Target x pair7Degree0_identity,identityCheck_sound pair7Degree1 pair7Degree1Rewrites pair7Degree1Target x pair7Degree1_identity,identityCheck_sound pair7Degree2 pair7Degree2Rewrites pair7Degree2Target x pair7Degree2_identity]
  norm_num [pair7Degree0Target,pair7Degree1Target,pair7Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_7]
  all_goals ring_nf
theorem pair7_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 0 0 true) t x:=by
  rw [pair7_eval]
  exact NearBalancePairs.pair_7_nonneg ht0 ht1 (hx 0) (hx 1)
def pair8Degree0:Expression:=pairComponent rows 0 0 1 false
def pair8Degree0Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0]
def pair8Degree0Target:NormalForm:=(![![(-0x920eef174c9 / 0x38d7ea4c6800),(0x920eef174c9 / 0xe35fa931a000),0,0], ![(0x920eef174c9 / 0xe35fa931a000),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-0x920eef174c9 / 0x1c6bf52634000), ![1, -1,0,0]),((0x920eef174c9 / 0x1c6bf52634000), ![3, -1,0,0])])
theorem pair8Degree0_identity:identityCheck pair8Degree0 pair8Degree0Rewrites pair8Degree0Target = true:=by decide +kernel
def pair8Degree1:Expression:=pairComponent rows 1 0 1 false
def pair8Degree1Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r18,RewriteAtoms.r0]
def pair8Degree1Target:NormalForm:=(![![(0x106f8927 / 0x4a817c80),(-0x106f8927 / 0x12a05f200),0,0], ![(-0x106f8927 / 0x12a05f200),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((0x106f8927 / 0x2540be400), ![1, -1,0,0]),((-0x106f8927 / 0x2540be400), ![3, -1,0,0])])
theorem pair8Degree1_identity:identityCheck pair8Degree1 pair8Degree1Rewrites pair8Degree1Target = true:=by decide +kernel
def pair8Degree2:Expression:=pairComponent rows 2 0 1 false
def pair8Degree2Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r18]
def pair8Degree2Target:NormalForm:=(![![(-3 / 50),(0x5f1 / 0x186a0),0,0], ![(0x5f1 / 0x186a0),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-3 / 0x190), ![1, -1,0,0]),((3 / 0x190), ![3, -1,0,0])])
private def zz114:"s0072"="s0072":=by decide+kernel
theorem pair8Degree2_identity:identityCheck pair8Degree2 pair8Degree2Rewrites pair8Degree2Target = true:=by decide +kernel
theorem pair8_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 0 1 false) t x = NearBalancePairs.pair_8 t (x 0) (x 1):=by
  change expressionEval pair8Degree0 x + t * expressionEval pair8Degree1 x + t ^ 2 * expressionEval pair8Degree2 x = _
  rw [identityCheck_sound pair8Degree0 pair8Degree0Rewrites pair8Degree0Target x pair8Degree0_identity,identityCheck_sound pair8Degree1 pair8Degree1Rewrites pair8Degree1Target x pair8Degree1_identity,identityCheck_sound pair8Degree2 pair8Degree2Rewrites pair8Degree2Target x pair8Degree2_identity]
  norm_num [pair8Degree0Target,pair8Degree1Target,pair8Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_8]
  all_goals ring_nf
theorem pair8_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 0 1 false) t x:=by
  rw [pair8_eval]
  exact NearBalancePairs.pair_8_nonneg ht0 ht1 (hx 0) (hx 1)
def pair9Degree0:Expression:=pairComponent rows 0 0 1 true
def pair9Degree0Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r28]
def pair9Degree0Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair9Degree0_identity:identityCheck pair9Degree0 pair9Degree0Rewrites pair9Degree0Target = true:=by decide +kernel
def pair9Degree1:Expression:=pairComponent rows 1 0 1 true
def pair9Degree1Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r28]
def pair9Degree1Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-0x28901bd / 0xee6b2800), ![1, -3,0,0]),((0x28901bd / 0xee6b2800), ![1, -1,0,0])])
private def zz115:"s0073"="s0073":=by decide+kernel
theorem pair9Degree1_identity:identityCheck pair9Degree1 pair9Degree1Rewrites pair9Degree1Target = true:=by decide +kernel
def pair9Degree2:Expression:=pairComponent rows 2 0 1 true
def pair9Degree2Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair9Degree2Target:NormalForm:=(![![(-1 / 0x3b9aca00),(0xafc81 / 0x165a0bc00),0,0], ![(0xafc81 / 0x165a0bc00),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((0x79b0539 / 0x2cb417800), ![1, -3,0,0]),((-0x1856773 / 0x8f0d1800), ![1, -1,0,0]),((1 / 0x165a0bc00), ![3, -1,0,0])])
theorem pair9Degree2_identity:identityCheck pair9Degree2 pair9Degree2Rewrites pair9Degree2Target = true:=by decide +kernel
theorem pair9_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 0 1 true) t x = NearBalancePairs.pair_9 t (x 0) (x 1):=by
  change expressionEval pair9Degree0 x + t * expressionEval pair9Degree1 x + t ^ 2 * expressionEval pair9Degree2 x = _
  rw [identityCheck_sound pair9Degree0 pair9Degree0Rewrites pair9Degree0Target x pair9Degree0_identity,identityCheck_sound pair9Degree1 pair9Degree1Rewrites pair9Degree1Target x pair9Degree1_identity,identityCheck_sound pair9Degree2 pair9Degree2Rewrites pair9Degree2Target x pair9Degree2_identity]
  norm_num [pair9Degree0Target,pair9Degree1Target,pair9Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_9]
  all_goals ring_nf
theorem pair9_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 0 1 true) t x:=by
  rw [pair9_eval]
  exact NearBalancePairs.pair_9_nonneg ht0 ht1 (hx 0) (hx 1)
def pair10Degree0:Expression:=pairComponent rows 0 1 1 false
def pair10Degree0Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Degree0Target:NormalForm:=(![![(-0x794822419fb / 0x38d7ea4c6800),(0x794822419fb / 0xe35fa931a000),0,0], ![(0x794822419fb / 0xe35fa931a000),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-0x794822419fb / 0x1c6bf52634000), ![1, -3,0,0]),((0x794822419fb / 0x1c6bf52634000), ![3, -1,0,0])])
private def zz116:"s0074"="s0074":=by decide+kernel
theorem pair10Degree0_identity:identityCheck pair10Degree0 pair10Degree0Rewrites pair10Degree0Target = true:=by decide +kernel
def pair10Degree1:Expression:=pairComponent rows 1 1 1 false
def pair10Degree1Rewrites:Rewrites:=[]
def pair10Degree1Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair10Degree1_identity:identityCheck pair10Degree1 pair10Degree1Rewrites pair10Degree1Target = true:=by decide +kernel
def pair10Degree2:Expression:=pairComponent rows 2 1 1 false
def pair10Degree2Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27]
def pair10Degree2Target:NormalForm:=(![![0,(3 / 0x4e20),0,0], ![(3 / 0x4e20),0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair10Degree2_identity:identityCheck pair10Degree2 pair10Degree2Rewrites pair10Degree2Target = true:=by decide +kernel
theorem pair10_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 1 1 false) t x = NearBalancePairs.pair_10 t (x 0) (x 1):=by
  change expressionEval pair10Degree0 x + t * expressionEval pair10Degree1 x + t ^ 2 * expressionEval pair10Degree2 x = _
  rw [identityCheck_sound pair10Degree0 pair10Degree0Rewrites pair10Degree0Target x pair10Degree0_identity,identityCheck_sound pair10Degree1 pair10Degree1Rewrites pair10Degree1Target x pair10Degree1_identity,identityCheck_sound pair10Degree2 pair10Degree2Rewrites pair10Degree2Target x pair10Degree2_identity]
  norm_num [pair10Degree0Target,pair10Degree1Target,pair10Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_10]
  all_goals ring_nf
private def zz117:"s0075"="s0075":=by decide+kernel
theorem pair10_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 1 1 false) t x:=by
  rw [pair10_eval]
  exact NearBalancePairs.pair_10_nonneg ht0 ht1 (hx 0) (hx 1)
def pair11Degree0:Expression:=pairComponent rows 0 1 1 true
def pair11Degree0Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair11Degree0Target:NormalForm:=(![![0,0,0,0], ![0,0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair11Degree0_identity:identityCheck pair11Degree0 pair11Degree0Rewrites pair11Degree0Target = true:=by decide +kernel
def pair11Degree1:Expression:=pairComponent rows 1 1 1 true
def pair11Degree1Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27]
def pair11Degree1Target:NormalForm:=(![![(-0x50d21 / 0x12a05f20),(0x50d21 / 0x4a817c80),0,0], ![(0x50d21 / 0x4a817c80),0,0,0], ![0,0,0,0], ![0,0,0,0]],[((-0x50d21 / 0x9502f900), ![1, -3,0,0]),((0x50d21 / 0x9502f900), ![3, -1,0,0])])
theorem pair11Degree1_identity:identityCheck pair11Degree1 pair11Degree1Rewrites pair11Degree1Target = true:=by decide +kernel
def pair11Degree2:Expression:=pairComponent rows 2 1 1 true
def pair11Degree2Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27]
def pair11Degree2Target:NormalForm:=(![![0,(3 / 0xc350),0,0], ![(3 / 0xc350),0,0,0], ![0,0,0,0], ![0,0,0,0]],[])
theorem pair11Degree2_identity:identityCheck pair11Degree2 pair11Degree2Rewrites pair11Degree2Target = true:=by decide +kernel
private def zz118:"s0076"="s0076":=by decide+kernel
theorem pair11_eval (t:ℝ) (x:Point) :
    parameterEval (fun d => pairComponent rows d 1 1 true) t x = NearBalancePairs.pair_11 t (x 0) (x 1):=by
  change expressionEval pair11Degree0 x + t * expressionEval pair11Degree1 x + t ^ 2 * expressionEval pair11Degree2 x = _
  rw [identityCheck_sound pair11Degree0 pair11Degree0Rewrites pair11Degree0Target x pair11Degree0_identity,identityCheck_sound pair11Degree1 pair11Degree1Rewrites pair11Degree1Target x pair11Degree1_identity,identityCheck_sound pair11Degree2 pair11Degree2Rewrites pair11Degree2Target x pair11Degree2_identity]
  norm_num [pair11Degree0Target,pair11Degree1Target,pair11Degree2Target,normalEval,quadraticEval,hingeEval,linearEval,Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three,NearBalancePairs.pair_11]
  all_goals ring_nf
theorem pair11_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d 1 1 true) t x:=by
  rw [pair11_eval]
  exact NearBalancePairs.pair_11_nonneg ht0 ht1 (hx 0) (hx 1)
theorem pair_nonneg_sorted (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (t:ℝ) (ht0:0 ≤ t) (ht1:t ≤ 1) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d p q same) t x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg t x ht0 ht1 hx
  · exact pair7_nonneg t x ht0 ht1 hx
  · exact pair8_nonneg t x ht0 ht1 hx
  · exact pair9_nonneg t x ht0 ht1 hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg t x ht0 ht1 hx
  · exact pair11_nonneg t x ht0 ht1 hx
theorem pair_nonneg (p q:Phase) (same:Bool) (t:ℝ) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => pairComponent rows d p q same) t x:=by
  rcases le_total p.val q.val with h | h
  · exact pair_nonneg_sorted p q h same t ht0 ht1 x hx
  · rw [← parameterPair_swap rows p q same t x]
    exact pair_nonneg_sorted q p h same t ht0 ht1 (FullPhaseSymmetry.swapPair x)
      (FullPhaseSymmetry.swapPair_nonneg x hx)
private def zz119:"s0077"="s0077":=by decide+kernel
theorem rows_admissible:∀ d,ParityPhaseAggregation.rowsAdmissible (rows d) = true:=by decide +kernel
theorem parameter_bound_of_quad_rows {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (hquad:∀ p q same t,0 ≤ t → t ≤ 1 → ∀ x,(∀ i,0 ≤ x i) →
      0 ≤ parameterEval (fun d => quadComponent rows d p q same) t x)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v)) :=
  parameter_bound_of_local_rows h3 h5 rows rows_admissible hquad pair_nonneg u v hu hv
end Green24Proof.NearBalanceCertificate
private def zz2017:"s07e1"="s07e1":=by decide+kernel
end 
section 
namespace Green24Proof.ParametricQuadraticCertificates
open IntegerQuadraticCertificates (Linear Point linearEval linearEval_neg product
  Combination combinationCheck combinationCheck_sound cons_constraints
  quadraticEq quadraticEq_eq_true)
abbrev Coefficient:=Fin 3 → ℤ
abbrev Quadratic:=Fin 3 → IntegerQuadraticCertificates.Quadratic
def coefficientEval (c:Coefficient) (t:ℝ):ℝ:=c 0 + t * c 1 + t ^ 2 * c 2
def quadraticEval (Q:Quadratic) (t:ℝ) (x:Point):ℝ :=
  IntegerQuadraticCertificates.quadraticEval (Q 0) x +
    t * IntegerQuadraticCertificates.quadraticEval (Q 1) x +
    t ^ 2 * IntegerQuadraticCertificates.quadraticEval (Q 2) x
def polynomialEq (Q R:Quadratic):Bool :=
  (List.finRange 3).all fun d => quadraticEq (Q d) (R d)
theorem polynomialEq_eq_true (Q R:Quadratic):polynomialEq Q R = true ↔ Q = R:=by
  simp only [polynomialEq,List.all_eq_true,List.mem_finRange,forall_true_left,
    quadraticEq_eq_true]
  exact ⟨funext,fun h i => congrFun h i⟩
theorem quadraticEval_zero (t:ℝ) (x:Point):quadraticEval 0 t x = 0:=by
  simp [quadraticEval,IntegerQuadraticCertificates.quadraticEval_zero]
private def zz120:"s0078"="s0078":=by decide+kernel
theorem quadraticEval_add (Q R:Quadratic) (t:ℝ) (x:Point) :
    quadraticEval (Q + R) t x = quadraticEval Q t x + quadraticEval R t x:=by
  simp only [quadraticEval,Pi.add_apply,IntegerQuadraticCertificates.quadraticEval_add]
  ring
theorem quadraticEval_smul (c:ℤ) (Q:Quadratic) (t:ℝ) (x:Point) :
    quadraticEval (c • Q) t x = (c:ℝ) * quadraticEval Q t x:=by
  simp only [quadraticEval,Pi.smul_apply,IntegerQuadraticCertificates.quadraticEval_smul]
  ring
def coefficientProduct (c:Coefficient) (a b:Linear):Quadratic :=
  fun d => c d • product a b
theorem coefficientProduct_eval (c:Coefficient) (a b:Linear) (t:ℝ) (x:Point) :
    quadraticEval (coefficientProduct c a b) t x =
      coefficientEval c t * linearEval a x * linearEval b x:=by
  simp only [quadraticEval,coefficientProduct,coefficientEval,
    IntegerQuadraticCertificates.quadraticEval_smul,
    IntegerQuadraticCertificates.quadraticEval_product]
  ring
inductive NonnegativeTerm (n:ℕ) where
  | square (a b:Linear)
  | middleSquare (a:Linear)
  | pair (degree:Fin 3) (i j:Fin n)
def termPolynomial {n:ℕ} (C:Fin n → Linear):NonnegativeTerm n → Quadratic
  | .square a b => ![product a a,product a b + product b a,product b b]
  | .middleSquare a => ![0,product a a,(-1:ℤ) • product a a]
  | .pair d i j =>
      let A:=product (C i) (C j)
      if d = 0 then ![A,(-2:ℤ) • A,A]
      else if d = 1 then ![0,(2:ℤ) • A,(-2:ℤ) • A]
      else ![0,0,A]
theorem termPolynomial_nonneg {n:ℕ} (C:Fin n → Linear) (v:NonnegativeTerm n)
    (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termPolynomial C v) t x:=by
  have h1:0 ≤ 1 - t:=sub_nonneg.mpr ht1
  cases v with
  | square a b =>
    change 0 ≤ IntegerQuadraticCertificates.quadraticEval (product a a) x +
      t * IntegerQuadraticCertificates.quadraticEval (product a b + product b a) x +
      t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product b b) x
    simp only [IntegerQuadraticCertificates.quadraticEval_add,
      IntegerQuadraticCertificates.quadraticEval_product]
    nlinarith only [sq_nonneg (linearEval a x + t * linearEval b x)]
  | middleSquare a =>
    change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
      t * IntegerQuadraticCertificates.quadraticEval (product a a) x +
      t ^ 2 * IntegerQuadraticCertificates.quadraticEval ((-1:ℤ) • product a a) x
    simp only [IntegerQuadraticCertificates.quadraticEval_zero,
      IntegerQuadraticCertificates.quadraticEval_smul,
      IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_one]
    nlinarith only [mul_nonneg (mul_nonneg ht0 h1) (sq_nonneg (linearEval a x))]
  | pair d i j =>
    have h:=mul_nonneg (hC i) (hC j)
    by_cases hd0:d = 0
    · simp only [termPolynomial,hd0, ↓reduceIte]
      change 0 ≤ IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x +
        t * IntegerQuadraticCertificates.quadraticEval ((-2:ℤ) • product (C i) (C j)) x +
        t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x
      simp only [IntegerQuadraticCertificates.quadraticEval_smul,
        IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_ofNat]
      nlinarith only [mul_nonneg (sq_nonneg (1 - t)) h]
    · by_cases hd1:d = 1
      · simp only [termPolynomial,hd1, ↓reduceIte]
        change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
          t * IntegerQuadraticCertificates.quadraticEval ((2:ℤ) • product (C i) (C j)) x +
          t ^ 2 * IntegerQuadraticCertificates.quadraticEval ((-2:ℤ) • product (C i) (C j)) x
        simp only [IntegerQuadraticCertificates.quadraticEval_zero,
          IntegerQuadraticCertificates.quadraticEval_smul,
          IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_ofNat]
        nlinarith only [mul_nonneg (mul_nonneg ht0 h1) h]
      · simp only [termPolynomial,hd0,hd1, ↓reduceIte]
        change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
          t * IntegerQuadraticCertificates.quadraticEval 0 x +
          t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x
        simpa only [IntegerQuadraticCertificates.quadraticEval_zero,
          IntegerQuadraticCertificates.quadraticEval_product,mul_zero,zero_add]
          using mul_nonneg (sq_nonneg t) h
abbrev Decomposition (n:ℕ):=List (ℤ × NonnegativeTerm n)
def decompositionPolynomial {n:ℕ} (C:Fin n → Linear) (d:Decomposition n):Quadratic :=
  (d.map fun v => v.1 • termPolynomial C v.2).sum
def decompositionCheck {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n):Bool :=
  decide (0 < s) && (d.all fun v => decide (0 ≤ v.1)) &&
    polynomialEq (decompositionPolynomial C d) (s • Q)
private def zz121:"s0079"="s0079":=by decide+kernel
theorem decomposition_nonneg {n:ℕ} (C:Fin n → Linear) (d:Decomposition n)
    (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun v => decide (0 ≤ v.1)) = true) :
    0 ≤ quadraticEval (decompositionPolynomial C d) t x:=by
  induction d with
  | nil => simp [decompositionPolynomial,quadraticEval_zero]
  | cons v vs ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionPolynomial,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using add_nonneg
      (mul_nonneg (by exact_mod_cast hw.1) (termPolynomial_nonneg C v.2 t x ht0 ht1 hC))
      (ih hw.2)
theorem decompositionCheck_sound {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n) (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:decompositionCheck C Q s d = true) :
    0 ≤ quadraticEval Q t x:=by
  simp only [decompositionCheck,Bool.and_eq_true,polynomialEq_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d t x ht0 ht1 hC h.1.2
  rw [h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
abbrev Hinges:=List (Coefficient × Linear)
def hingeEval (hs:Hinges) (t:ℝ) (x:Point):ℝ :=
  (hs.map fun v => coefficientEval v.1 t * max (linearEval v.2 x) 0 ^ 2).sum
inductive Certificate:ℕ → Type where
  | leaf {n:ℕ} (scale:ℤ) (d:Decomposition n):Certificate n
  | split {n:ℕ} (positive negative:Certificate (n + 1)):Certificate n
  | cut {n:ℕ} (a:Linear) (positive negative:Certificate (n + 1)):Certificate n
  | positive {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
  | negative {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
def check {n:ℕ} (cert:Certificate n) (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs => check p (Fin.cons a C) Q hs && check m (Fin.cons (-a) C) Q hs
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (Fin.cons a C) (Q + coefficientProduct c a a) hs &&
      check m (Fin.cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (Fin.cons a C) (Q + coefficientProduct c a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) && check m (Fin.cons (-a) C) Q hs
  | _,_ => false
theorem positive_step (Q:Quadratic) (c:Coefficient) (a:Linear) (hs:Hinges)
    (t:ℝ) (x:Point) (ha:0 ≤ linearEval a x)
    (h:0 ≤ quadraticEval (Q + coefficientProduct c a a) t x + hingeEval hs t x) :
    0 ≤ quadraticEval Q t x + hingeEval ((c,a) :: hs) t x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_left ha,quadraticEval_add,
    coefficientProduct_eval,pow_two,mul_assoc,add_assoc] using h
theorem negative_step (Q:Quadratic) (c:Coefficient) (a:Linear) (hs:Hinges)
    (t:ℝ) (x:Point) (ha:linearEval a x ≤ 0)
    (h:0 ≤ quadraticEval Q t x + hingeEval hs t x) :
    0 ≤ quadraticEval Q t x + hingeEval ((c,a) :: hs) t x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_right ha,
    zero_pow (by decide:2 ≠ 0),mul_zero,zero_add] using h
private def zz122:"s007a"="s007a":=by decide+kernel
theorem check_sound {n:ℕ} (cert:Certificate n) (C:Fin n → Linear)
    (Q:Quadratic) (hs:Hinges) (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:check cert C Q hs = true) :
    0 ≤ quadraticEval Q t x + hingeEval hs t x:=by
  induction cert generalizing Q hs with
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q s d t x ht0 ht1 hC h
    | cons v vs => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a vs t x ha (hp (Fin.cons a C)
          (Q + coefficientProduct c a a) vs (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a vs t x (le_of_not_ge ha)
          (hm (Fin.cons (-a) C) Q vs (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (Fin.cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (Fin.cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a vs t x ha (hp (Fin.cons a C)
        (Q + coefficientProduct c a a) vs (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a vs t x ha' (hm (Fin.cons (-a) C) Q vs
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.ParametricQuadraticCertificates
private def zz2018:"s07e2"="s07e2":=by decide+kernel
end 
section 
namespace Green24Proof.ParametricQuadraticInterop
open ParametricQuadraticCertificates
open IntegerQuadraticCertificates (Point)
open ExpressionCertificates (NormalForm rationalNormal normalEval rationalNormal_eval)
def componentHinges (hs:Hinges) (d:Fin 3):IntegerQuadraticCertificates.Hinges :=
  hs.map fun v => (v.1 d,v.2)
theorem hingeEval_components (hs:Hinges) (t:ℝ) (x:Point) :
    hingeEval hs t x = IntegerQuadraticCertificates.hingeEval (componentHinges hs 0) x +
      t * IntegerQuadraticCertificates.hingeEval (componentHinges hs 1) x +
      t ^ 2 * IntegerQuadraticCertificates.hingeEval (componentHinges hs 2) x:=by
  induction hs with
  | nil => simp [hingeEval,componentHinges,IntegerQuadraticCertificates.hingeEval]
  | cons v vs ih =>
    simp only [hingeEval,componentHinges,IntegerQuadraticCertificates.hingeEval,
      List.map_cons,List.sum_cons] at *
    rw [ih]
    simp only [coefficientEval]
    ring
def componentNormal (Q:Quadratic) (hs:Hinges) (den:ℤ) (d:Fin 3):NormalForm :=
  rationalNormal (Q d) (componentHinges hs d) den
theorem componentNormal_eval (Q:Quadratic) (hs:Hinges) (den:ℤ) (t:ℝ) (x:Point) :
    normalEval (componentNormal Q hs den 0) x +
      t * normalEval (componentNormal Q hs den 1) x +
      t ^ 2 * normalEval (componentNormal Q hs den 2) x =
      (quadraticEval Q t x + hingeEval hs t x) / den:=by
  simp only [componentNormal,rationalNormal_eval,quadraticEval,hingeEval_components]
  ring
end Green24Proof.ParametricQuadraticInterop
private def zz2019:"s07e3"="s07e3":=by decide+kernel
end 
section 
namespace Green24Proof.CompactPair
structure Quadratic where
  xx:ℚ
  xy:ℚ
  yy:ℚ
noncomputable def quadraticEval (q:Quadratic) (x y:ℝ):ℝ :=
  (q.xx:ℝ) * x ^ 2 + (q.xy:ℝ) * x * y + (q.yy:ℝ) * y ^ 2
def boundedCheck (q:Quadratic) (lo hi:ℚ):Bool :=
  decide (lo < hi ∧
    0 ≤ q.xx * lo ^ 2 + q.xy * lo + q.yy ∧
    0 ≤ 2 * q.xx * lo * hi + q.xy * (lo + hi) + 2 * q.yy ∧
    0 ≤ q.xx * hi ^ 2 + q.xy * hi + q.yy)
def tailCheck (q:Quadratic) (lo:ℚ):Bool :=
  decide (0 ≤ q.xx ∧ 0 ≤ 2 * q.xx * lo + q.xy ∧
    0 ≤ q.xx * lo ^ 2 + q.xy * lo + q.yy)
theorem boundedCheck_sound {q:Quadratic} {lo hi:ℚ}
    (h:boundedCheck q lo hi = true) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    0 ≤ quadraticEval q x y:=by
  have hh:lo < hi ∧
      0 ≤ q.xx * lo ^ 2 + q.xy * lo + q.yy ∧
      0 ≤ 2 * q.xx * lo * hi + q.xy * (lo + hi) + 2 * q.yy ∧
      0 ≤ q.xx * hi ^ 2 + q.xy * hi + q.yy:=of_decide_eq_true h
  rcases hh with ⟨hlt,hA,hB,hC⟩
  have hltR:(lo:ℝ) < (hi:ℝ):=by exact_mod_cast hlt
  have hAR:0 ≤ (q.xx:ℝ) * (lo:ℝ) ^ 2 + (q.xy:ℝ) * (lo:ℝ) + q.yy:=by
    exact_mod_cast hA
  have hBR:0 ≤ 2 * (q.xx:ℝ) * (lo:ℝ) * (hi:ℝ) +
      (q.xy:ℝ) * ((lo:ℝ) + (hi:ℝ)) + 2 * (q.yy:ℝ):=by
    exact_mod_cast hB
  have hCR:0 ≤ (q.xx:ℝ) * (hi:ℝ) ^ 2 + (q.xy:ℝ) * (hi:ℝ) + q.yy:=by
    exact_mod_cast hC
  have hu:0 ≤ (hi:ℝ) * y - x:=sub_nonneg.mpr hhi
  have hv:0 ≤ x - (lo:ℝ) * y:=sub_nonneg.mpr hlo
  have hid:((hi:ℝ) - (lo:ℝ)) ^ 2 * quadraticEval q x y =
      ((q.xx:ℝ) * (lo:ℝ) ^ 2 + (q.xy:ℝ) * (lo:ℝ) + q.yy) *
        ((hi:ℝ) * y - x) ^ 2 +
      (2 * (q.xx:ℝ) * (lo:ℝ) * (hi:ℝ) +
        (q.xy:ℝ) * ((lo:ℝ) + (hi:ℝ)) + 2 * (q.yy:ℝ)) *
        ((hi:ℝ) * y - x) * (x - (lo:ℝ) * y) +
      ((q.xx:ℝ) * (hi:ℝ) ^ 2 + (q.xy:ℝ) * (hi:ℝ) + q.yy) *
        (x - (lo:ℝ) * y) ^ 2:=by
    unfold quadraticEval
    ring
  have hp:0 ≤ ((hi:ℝ) - (lo:ℝ)) ^ 2 * quadraticEval q x y:=by
    rw [hid]
    exact add_nonneg (add_nonneg (mul_nonneg hAR (sq_nonneg _))
      (mul_nonneg (mul_nonneg hBR hu) hv)) (mul_nonneg hCR (sq_nonneg _))
  exact nonneg_of_mul_nonneg_right hp (sq_pos_of_pos (sub_pos.mpr hltR))
private def zz123:"s007b"="s007b":=by decide+kernel
theorem tailCheck_sound {q:Quadratic} {lo:ℚ}
    (h:tailCheck q lo = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x) :
    0 ≤ quadraticEval q x y:=by
  have hh:0 ≤ q.xx ∧ 0 ≤ 2 * q.xx * lo + q.xy ∧
      0 ≤ q.xx * lo ^ 2 + q.xy * lo + q.yy:=of_decide_eq_true h
  rcases hh with ⟨hA,hB,hC⟩
  have hAR:0 ≤ (q.xx:ℝ):=by exact_mod_cast hA
  have hBR:0 ≤ 2 * (q.xx:ℝ) * (lo:ℝ) + q.xy:=by exact_mod_cast hB
  have hCR:0 ≤ (q.xx:ℝ) * (lo:ℝ) ^ 2 + (q.xy:ℝ) * (lo:ℝ) + q.yy:=by
    exact_mod_cast hC
  have hu:0 ≤ x - (lo:ℝ) * y:=sub_nonneg.mpr hlo
  have hid:quadraticEval q x y =
      (q.xx:ℝ) * (x - (lo:ℝ) * y) ^ 2 +
      (2 * (q.xx:ℝ) * (lo:ℝ) + q.xy) * (x - (lo:ℝ) * y) * y +
      ((q.xx:ℝ) * (lo:ℝ) ^ 2 + (q.xy:ℝ) * (lo:ℝ) + q.yy) * y ^ 2:=by
    unfold quadraticEval
    ring
  rw [hid]
  exact add_nonneg (add_nonneg (mul_nonneg hAR (sq_nonneg _))
    (mul_nonneg (mul_nonneg hBR hu) hy)) (mul_nonneg hCR (sq_nonneg _))
def check (lo:ℚ) (pieces:List (ℚ × Quadratic)) (tail:Quadratic):Bool :=
  match pieces with
  | [] => tailCheck tail lo
  | (hi,q) :: rest => boundedCheck q lo hi && check hi rest tail
noncomputable def piecewiseEval (pieces:List (ℚ × Quadratic)) (tail:Quadratic)
    (x y:ℝ):ℝ :=
  match pieces with
  | [] => quadraticEval tail x y
  | (hi,q) :: rest =>
    if x ≤ (hi:ℝ) * y then quadraticEval q x y else piecewiseEval rest tail x y
theorem check_sound {lo:ℚ} {pieces:List (ℚ × Quadratic)} {tail:Quadratic}
    (h:check lo pieces tail = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x) :
    0 ≤ piecewiseEval pieces tail x y:=by
  induction pieces generalizing lo with
  | nil => exact tailCheck_sound h hy hlo
  | cons piece rest ih =>
    rcases piece with ⟨hi,q⟩
    have hh:boundedCheck q lo hi = true ∧ check hi rest tail = true :=
      Bool.and_eq_true_iff.mp h
    by_cases hhi:x ≤ (hi:ℝ) * y
    · simp only [piecewiseEval,if_pos hhi]
      exact boundedCheck_sound hh.1 hlo hhi
    · simp only [piecewiseEval,if_neg hhi]
      exact ih hh.2 (le_of_lt (lt_of_not_ge hhi))
end Green24Proof.CompactPair
private def zz2020:"s07e4"="s07e4":=by decide+kernel
end 
section 
namespace Green24Proof.CompactPair
structure Hinge where
  weight:ℚ
  a:ℚ
  b:ℚ
def addQuadratic (q r:Quadratic):Quadratic :=
  ⟨q.xx + r.xx,q.xy + r.xy,q.yy + r.yy⟩
def squareQuadratic (h:Hinge):Quadratic :=
  ⟨h.weight * h.a ^ 2,2 * h.weight * h.a * h.b,h.weight * h.b ^ 2⟩
noncomputable def hingesEval:List Hinge → ℝ → ℝ → ℝ
  | [],_,_ => 0
  | h :: rest,x,y =>
      (h.weight:ℝ) * max ((h.a:ℝ) * x + (h.b:ℝ) * y) 0 ^ 2 + hingesEval rest x y
noncomputable def expressionEval (q:Quadratic) (hs:List Hinge) (x y:ℝ):ℝ :=
  quadraticEval q x y + hingesEval hs x y
theorem quadraticEval_add (q r:Quadratic) (x y:ℝ) :
    quadraticEval (addQuadratic q r) x y = quadraticEval q x y + quadraticEval r x y:=by
  simp only [addQuadratic,quadraticEval,Rat.cast_add]
  ring
theorem quadraticEval_square (h:Hinge) (x y:ℝ) :
    quadraticEval (squareQuadratic h) x y =
      (h.weight:ℝ) * ((h.a:ℝ) * x + (h.b:ℝ) * y) ^ 2:=by
  simp only [squareQuadratic,quadraticEval,Rat.cast_mul,Rat.cast_pow,Rat.cast_ofNat]
  ring
private def zz124:"s007c"="s007c":=by decide+kernel
theorem bounded_linear_nonneg {a b lo hi:ℚ} (hlt:lo < hi)
    (hl:0 ≤ a * lo + b) (hh:0 ≤ a * hi + b) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    0 ≤ (a:ℝ) * x + (b:ℝ) * y:=by
  have hlR:0 ≤ (a:ℝ) * (lo:ℝ) + b:=by exact_mod_cast hl
  have hhR:0 ≤ (a:ℝ) * (hi:ℝ) + b:=by exact_mod_cast hh
  have hltR:(lo:ℝ) < (hi:ℝ):=by exact_mod_cast hlt
  have hid:((hi:ℝ) - (lo:ℝ)) * ((a:ℝ) * x + (b:ℝ) * y) =
      ((a:ℝ) * (lo:ℝ) + b) * ((hi:ℝ) * y - x) +
      ((a:ℝ) * (hi:ℝ) + b) * (x - (lo:ℝ) * y):=by ring
  have hp:0 ≤ ((hi:ℝ) - (lo:ℝ)) * ((a:ℝ) * x + (b:ℝ) * y):=by
    rw [hid]
    exact add_nonneg (mul_nonneg hlR (sub_nonneg.mpr hhi))
      (mul_nonneg hhR (sub_nonneg.mpr hlo))
  exact nonneg_of_mul_nonneg_right hp (sub_pos.mpr hltR)
theorem bounded_linear_nonpos {a b lo hi:ℚ} (hlt:lo < hi)
    (hl:a * lo + b ≤ 0) (hh:a * hi + b ≤ 0) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    (a:ℝ) * x + (b:ℝ) * y ≤ 0:=by
  have hn:=bounded_linear_nonneg (a:=-a) (b:=-b) hlt
    (by linarith) (by linarith) hlo hhi
  simpa only [Rat.cast_neg,neg_mul, ← neg_add,neg_nonneg] using hn
theorem tail_linear_nonneg {a b lo:ℚ} (ha:0 ≤ a) (hl:0 ≤ a * lo + b)
    {x y:ℝ} (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x) :
    0 ≤ (a:ℝ) * x + (b:ℝ) * y:=by
  have haR:0 ≤ (a:ℝ):=by exact_mod_cast ha
  have hlR:0 ≤ (a:ℝ) * (lo:ℝ) + b:=by exact_mod_cast hl
  have hid:(a:ℝ) * x + (b:ℝ) * y =
      (a:ℝ) * (x - (lo:ℝ) * y) + ((a:ℝ) * (lo:ℝ) + b) * y:=by ring
  rw [hid]
  exact add_nonneg (mul_nonneg haR (sub_nonneg.mpr hlo)) (mul_nonneg hlR hy)
theorem tail_linear_nonpos {a b lo:ℚ} (ha:a ≤ 0) (hl:a * lo + b ≤ 0)
    {x y:ℝ} (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x) :
    (a:ℝ) * x + (b:ℝ) * y ≤ 0:=by
  have hn:=tail_linear_nonneg (a:=-a) (b:=-b)
    (by linarith) (by linarith) hy hlo
  simpa only [Rat.cast_neg,neg_mul, ← neg_add,neg_nonneg] using hn
def boundedSigns (lo hi:ℚ):List Hinge → Bool
  | [] => true
  | h :: rest => decide ((0 ≤ h.a * lo + h.b ∧ 0 ≤ h.a * hi + h.b) ∨
      (h.a * lo + h.b ≤ 0 ∧ h.a * hi + h.b ≤ 0)) && boundedSigns lo hi rest
def boundedNormalize (lo hi:ℚ):List Hinge → Quadratic
  | [] => ⟨0,0,0⟩
  | h :: rest => if 0 ≤ h.a * lo + h.b ∧ 0 ≤ h.a * hi + h.b
      then addQuadratic (squareQuadratic h) (boundedNormalize lo hi rest)
      else boundedNormalize lo hi rest
def tailSigns (lo:ℚ):List Hinge → Bool
  | [] => true
  | h :: rest => decide ((0 ≤ h.a ∧ 0 ≤ h.a * lo + h.b) ∨
      (h.a ≤ 0 ∧ h.a * lo + h.b ≤ 0)) && tailSigns lo rest
def tailNormalize (lo:ℚ):List Hinge → Quadratic
  | [] => ⟨0,0,0⟩
  | h :: rest => if 0 ≤ h.a ∧ 0 ≤ h.a * lo + h.b
      then addQuadratic (squareQuadratic h) (tailNormalize lo rest)
      else tailNormalize lo rest
private def zz125:"s007d"="s007d":=by decide+kernel
theorem boundedNormalize_sound {lo hi:ℚ} {hs:List Hinge} (hlt:lo < hi)
    (h:boundedSigns lo hi hs = true) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    hingesEval hs x y = quadraticEval (boundedNormalize lo hi hs) x y:=by
  induction hs with
  | nil => simp [hingesEval,boundedNormalize,quadraticEval]
  | cons head rest ih =>
    have hh:=Bool.and_eq_true_iff.mp h
    have hs:(0 ≤ head.a * lo + head.b ∧ 0 ≤ head.a * hi + head.b) ∨
        (head.a * lo + head.b ≤ 0 ∧ head.a * hi + head.b ≤ 0):=of_decide_eq_true hh.1
    by_cases hp:0 ≤ head.a * lo + head.b ∧ 0 ≤ head.a * hi + head.b
    · have hn:=bounded_linear_nonneg hlt hp.1 hp.2 hlo hhi
      simp only [hingesEval,boundedNormalize,if_pos hp,quadraticEval_add,
        quadraticEval_square,max_eq_left hn,ih hh.2]
    · have hneg:=hs.resolve_left hp
      have hn:=bounded_linear_nonpos hlt hneg.1 hneg.2 hlo hhi
      simp only [hingesEval,boundedNormalize,if_neg hp,max_eq_right hn,
        zero_pow (by decide:2 ≠ 0),mul_zero,zero_add,ih hh.2]
theorem tailNormalize_sound {lo:ℚ} {hs:List Hinge}
    (h:tailSigns lo hs = true) {x y:ℝ} (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x) :
    hingesEval hs x y = quadraticEval (tailNormalize lo hs) x y:=by
  induction hs with
  | nil => simp [hingesEval,tailNormalize,quadraticEval]
  | cons head rest ih =>
    have hh:=Bool.and_eq_true_iff.mp h
    have hs:(0 ≤ head.a ∧ 0 ≤ head.a * lo + head.b) ∨
        (head.a ≤ 0 ∧ head.a * lo + head.b ≤ 0):=of_decide_eq_true hh.1
    by_cases hp:0 ≤ head.a ∧ 0 ≤ head.a * lo + head.b
    · have hn:=tail_linear_nonneg hp.1 hp.2 hy hlo
      simp only [hingesEval,tailNormalize,if_pos hp,quadraticEval_add,
        quadraticEval_square,max_eq_left hn,ih hh.2]
    · have hneg:=hs.resolve_left hp
      have hn:=tail_linear_nonpos hneg.1 hneg.2 hy hlo
      simp only [hingesEval,tailNormalize,if_neg hp,max_eq_right hn,
        zero_pow (by decide:2 ≠ 0),mul_zero,zero_add,ih hh.2]
def boundedExpressionCheck (q:Quadratic) (hs:List Hinge) (lo hi:ℚ):Bool :=
  boundedSigns lo hi hs && boundedCheck (addQuadratic q (boundedNormalize lo hi hs)) lo hi
def tailExpressionCheck (q:Quadratic) (hs:List Hinge) (lo:ℚ):Bool :=
  tailSigns lo hs && tailCheck (addQuadratic q (tailNormalize lo hs)) lo
theorem boundedExpressionCheck_sound {q:Quadratic} {hs:List Hinge} {lo hi:ℚ}
    (h:boundedExpressionCheck q hs lo hi = true) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    0 ≤ expressionEval q hs x y:=by
  have hh:=Bool.and_eq_true_iff.mp h
  have hlt:lo < hi:=(of_decide_eq_true hh.2).1
  have hn:=boundedCheck_sound hh.2 hlo hhi
  rw [quadraticEval_add, ← boundedNormalize_sound hlt hh.1 hlo hhi] at hn
  exact hn
theorem tailExpressionCheck_sound {q:Quadratic} {hs:List Hinge} {lo:ℚ}
    (h:tailExpressionCheck q hs lo = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x):0 ≤ expressionEval q hs x y:=by
  have hh:=Bool.and_eq_true_iff.mp h
  have hn:=tailCheck_sound hh.2 hy hlo
  rw [quadraticEval_add, ← tailNormalize_sound hh.1 hy hlo] at hn
  exact hn
def expressionCheck (q:Quadratic) (hs:List Hinge) (lo:ℚ):List ℚ → Bool
  | [] => tailExpressionCheck q hs lo
  | hi :: rest => boundedExpressionCheck q hs lo hi && expressionCheck q hs hi rest
private def zz126:"s007e"="s007e":=by decide+kernel
theorem expressionCheck_sound {q:Quadratic} {hs:List Hinge} {lo:ℚ} {cuts:List ℚ}
    (h:expressionCheck q hs lo cuts = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x):0 ≤ expressionEval q hs x y:=by
  induction cuts generalizing lo with
  | nil => exact tailExpressionCheck_sound h hy hlo
  | cons hi rest ih =>
    have hh:=Bool.and_eq_true_iff.mp h
    by_cases hhi:x ≤ (hi:ℝ) * y
    · exact boundedExpressionCheck_sound hh.1 hlo hhi
    · exact ih hh.2 (le_of_lt (lt_of_not_ge hhi))
end Green24Proof.CompactPair
private def zz2021:"s07e5"="s07e5":=by decide+kernel
end 
section 
namespace Green24Proof.CompactPair
def toNormal (q:Quadratic) (hs:List Hinge):ExpressionCertificates.NormalForm :=
  (![![q.xx,q.xy / 2,0,0], ![q.xy / 2,q.yy,0,0],
      ![0,0,0,0], ![0,0,0,0]],
    hs.map fun h => (h.weight, ![h.a,h.b,0,0]))
theorem toNormal_eval (q:Quadratic) (hs:List Hinge)
    (x:QuadraticCertificates.Point) :
    ExpressionCertificates.normalEval (toNormal q hs) x =
      expressionEval q hs (x 0) (x 1):=by
  have hlinear (h:Hinge) :
      QuadraticCertificates.linearEval ![h.a,h.b,0,0] x =
        (h.a:ℝ) * x 0 + (h.b:ℝ) * x 1:=by
    norm_num [QuadraticCertificates.linearEval,Fin.sum_univ_four,
      Matrix.cons_val_two,Matrix.cons_val_three]
  have hhinges :
      QuadraticCertificates.hingeEval
        (hs.map fun h => (h.weight, ![h.a,h.b,0,0])) x =
      hingesEval hs (x 0) (x 1):=by
    induction hs with
    | nil => simp [QuadraticCertificates.hingeEval,hingesEval]
    | cons h hs ih =>
      simp only [List.map_cons,QuadraticCertificates.hingeEval,
        List.map_cons,List.sum_cons,hingesEval] at *
      rw [hlinear,ih]
  unfold ExpressionCertificates.normalEval toNormal expressionEval
  rw [hhinges]
  congr 1
  norm_num [QuadraticCertificates.quadraticEval,quadraticEval,
    Fin.sum_univ_four,Matrix.cons_val_two,Matrix.cons_val_three]
  ring
end Green24Proof.CompactPair
private def zz2022:"s07e6"="s07e6":=by decide+kernel
end 
section 
namespace Green24Proof.CompactPair
def psdCheck (q:Quadratic):Bool :=
  decide (0 ≤ q.xx ∧ 0 ≤ q.yy ∧ q.xy ^ 2 ≤ 4 * q.xx * q.yy)
theorem psdCheck_sound {q:Quadratic} (h:psdCheck q = true) (x y:ℝ) :
    0 ≤ quadraticEval q x y:=by
  have hh:0 ≤ q.xx ∧ 0 ≤ q.yy ∧ q.xy ^ 2 ≤ 4 * q.xx * q.yy:=of_decide_eq_true h
  have hA:0 ≤ (q.xx:ℝ):=by exact_mod_cast hh.1
  have hC:0 ≤ (q.yy:ℝ):=by exact_mod_cast hh.2.1
  have hdet:(q.xy:ℝ) ^ 2 ≤ 4 * (q.xx:ℝ) * (q.yy:ℝ):=by exact_mod_cast hh.2.2
  by_cases hz:(q.xx:ℝ) = 0
  · have hB:(q.xy:ℝ) = 0:=by nlinarith [sq_nonneg (q.xy:ℝ)]
    simp only [quadraticEval,hz,hB,zero_mul,mul_zero,zero_add]
    exact mul_nonneg hC (sq_nonneg y)
  · have hpos:0 < (q.xx:ℝ):=lt_of_le_of_ne hA (Ne.symm hz)
    have hid:(4 * (q.xx:ℝ)) * quadraticEval q x y =
        (2 * (q.xx:ℝ) * x + (q.xy:ℝ) * y) ^ 2 +
        (4 * (q.xx:ℝ) * (q.yy:ℝ) - (q.xy:ℝ) ^ 2) * y ^ 2:=by
      unfold quadraticEval
      ring
    have hp:0 ≤ (4 * (q.xx:ℝ)) * quadraticEval q x y:=by
      rw [hid]
      exact add_nonneg (sq_nonneg _) (mul_nonneg (sub_nonneg.mpr hdet) (sq_nonneg y))
    exact nonneg_of_mul_nonneg_right hp (mul_pos (by norm_num) hpos)
def boundedExpressionCheckPSD (q:Quadratic) (hs:List Hinge) (lo hi:ℚ):Bool :=
  decide (lo < hi) && (boundedSigns lo hi hs &&
    (boundedCheck (addQuadratic q (boundedNormalize lo hi hs)) lo hi ||
      psdCheck (addQuadratic q (boundedNormalize lo hi hs))))
def tailExpressionCheckPSD (q:Quadratic) (hs:List Hinge) (lo:ℚ):Bool :=
  tailSigns lo hs &&
    (tailCheck (addQuadratic q (tailNormalize lo hs)) lo ||
      psdCheck (addQuadratic q (tailNormalize lo hs)))
theorem boundedExpressionCheckPSD_sound {q:Quadratic} {hs:List Hinge} {lo hi:ℚ}
    (h:boundedExpressionCheckPSD q hs lo hi = true) {x y:ℝ}
    (hlo:(lo:ℝ) * y ≤ x) (hhi:x ≤ (hi:ℝ) * y) :
    0 ≤ expressionEval q hs x y:=by
  have hh:=Bool.and_eq_true_iff.mp h
  have hlt:lo < hi:=of_decide_eq_true hh.1
  have hr:=Bool.and_eq_true_iff.mp hh.2
  have hn:0 ≤ quadraticEval (addQuadratic q (boundedNormalize lo hi hs)) x y:=by
    rcases Bool.or_eq_true_iff.mp hr.2 with hc | hc
    · exact boundedCheck_sound hc hlo hhi
    · exact psdCheck_sound hc x y
  rw [quadraticEval_add, ← boundedNormalize_sound hlt hr.1 hlo hhi] at hn
  exact hn
private def zz127:"s007f"="s007f":=by decide+kernel
theorem tailExpressionCheckPSD_sound {q:Quadratic} {hs:List Hinge} {lo:ℚ}
    (h:tailExpressionCheckPSD q hs lo = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x):0 ≤ expressionEval q hs x y:=by
  have hh:=Bool.and_eq_true_iff.mp h
  have hn:0 ≤ quadraticEval (addQuadratic q (tailNormalize lo hs)) x y:=by
    rcases Bool.or_eq_true_iff.mp hh.2 with hc | hc
    · exact tailCheck_sound hc hy hlo
    · exact psdCheck_sound hc x y
  rw [quadraticEval_add, ← tailNormalize_sound hh.1 hy hlo] at hn
  exact hn
def expressionCheckPSD (q:Quadratic) (hs:List Hinge) (lo:ℚ):List ℚ → Bool
  | [] => tailExpressionCheckPSD q hs lo
  | hi :: rest => boundedExpressionCheckPSD q hs lo hi && expressionCheckPSD q hs hi rest
theorem expressionCheckPSD_sound {q:Quadratic} {hs:List Hinge} {lo:ℚ} {cuts:List ℚ}
    (h:expressionCheckPSD q hs lo cuts = true) {x y:ℝ}
    (hy:0 ≤ y) (hlo:(lo:ℝ) * y ≤ x):0 ≤ expressionEval q hs x y:=by
  induction cuts generalizing lo with
  | nil => exact tailExpressionCheckPSD_sound h hy hlo
  | cons hi rest ih =>
    have hh:=Bool.and_eq_true_iff.mp h
    by_cases hhi:x ≤ (hi:ℝ) * y
    · exact boundedExpressionCheckPSD_sound hh.1 hlo hhi
    · exact ih hh.2 (le_of_lt (lt_of_not_ge hhi))
end Green24Proof.CompactPair
private def zz2023:"s07e7"="s07e7":=by decide+kernel
end 
section 
namespace Green24Proof.LocalParityFourFifthsPairs
def compact_parityFourFifths_pair_6_base:CompactPair.Quadratic:=⟨0,(0x1387 / 0x2faf080),0⟩
def compact_parityFourFifths_pair_6_hinges:List CompactPair.Hinge:=[]
noncomputable def parityFourFifths_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_6_base compact_parityFourFifths_pair_6_hinges x y
def compact_parityFourFifths_pair_6_cuts:List ℚ:=[]
theorem compact_parityFourFifths_pair_6_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_6_base compact_parityFourFifths_pair_6_hinges 0 compact_parityFourFifths_pair_6_cuts = true :=
  by decide +kernel
theorem compact_parityFourFifths_pair_6_representation (x y:ℝ) :
    parityFourFifths_pair_6 x y = CompactPair.expressionEval compact_parityFourFifths_pair_6_base compact_parityFourFifths_pair_6_hinges x y:=by rfl
private def zz128:"s0080"="s0080":=by decide+kernel
theorem parityFourFifths_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_6 x y:=by
  rw [compact_parityFourFifths_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_6_check hy (by simpa using hx)
def compact_parityFourFifths_pair_7_base:CompactPair.Quadratic:=⟨(1 / 0xe4e1c0),(0xfa3 / 0x5f5e100),0⟩
def compact_parityFourFifths_pair_7_hinges:List CompactPair.Hinge:=[⟨(1 / 0x7270e00),1, -3⟩,⟨(-1 / 0x7270e00),3, -1⟩]
noncomputable def parityFourFifths_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_7_base compact_parityFourFifths_pair_7_hinges x y
def compact_parityFourFifths_pair_7_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityFourFifths_pair_7_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_7_base compact_parityFourFifths_pair_7_hinges 0 compact_parityFourFifths_pair_7_cuts = true :=
  by decide +kernel
theorem compact_parityFourFifths_pair_7_representation (x y:ℝ) :
    parityFourFifths_pair_7 x y = CompactPair.expressionEval compact_parityFourFifths_pair_7_base compact_parityFourFifths_pair_7_hinges x y:=by rfl
theorem parityFourFifths_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_7 x y:=by
  rw [compact_parityFourFifths_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_7_check hy (by simpa using hx)
def compact_parityFourFifths_pair_8_base:CompactPair.Quadratic:=⟨0,(0xdab / 0x17d7840),0⟩
def compact_parityFourFifths_pair_8_hinges:List CompactPair.Hinge:=[]
noncomputable def parityFourFifths_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_8_base compact_parityFourFifths_pair_8_hinges x y
def compact_parityFourFifths_pair_8_cuts:List ℚ:=[]
private def zz129:"s0081"="s0081":=by decide+kernel
theorem compact_parityFourFifths_pair_8_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_8_base compact_parityFourFifths_pair_8_hinges 0 compact_parityFourFifths_pair_8_cuts = true :=
  by decide +kernel
theorem compact_parityFourFifths_pair_8_representation (x y:ℝ) :
    parityFourFifths_pair_8 x y = CompactPair.expressionEval compact_parityFourFifths_pair_8_base compact_parityFourFifths_pair_8_hinges x y:=by rfl
theorem parityFourFifths_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_8 x y:=by
  rw [compact_parityFourFifths_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_8_check hy (by simpa using hx)
def compact_parityFourFifths_pair_9_base:CompactPair.Quadratic:=⟨0,(0xf99 / 0x2faf080),0⟩
def compact_parityFourFifths_pair_9_hinges:List CompactPair.Hinge:=[]
noncomputable def parityFourFifths_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_9_base compact_parityFourFifths_pair_9_hinges x y
def compact_parityFourFifths_pair_9_cuts:List ℚ:=[]
theorem compact_parityFourFifths_pair_9_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_9_base compact_parityFourFifths_pair_9_hinges 0 compact_parityFourFifths_pair_9_cuts = true :=
  by decide +kernel
private def zz130:"s0082"="s0082":=by decide+kernel
theorem compact_parityFourFifths_pair_9_representation (x y:ℝ) :
    parityFourFifths_pair_9 x y = CompactPair.expressionEval compact_parityFourFifths_pair_9_base compact_parityFourFifths_pair_9_hinges x y:=by rfl
theorem parityFourFifths_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_9 x y:=by
  rw [compact_parityFourFifths_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_9_check hy (by simpa using hx)
def compact_parityFourFifths_pair_10_base:CompactPair.Quadratic:=⟨0,(0x3e9 / 0x989680),0⟩
def compact_parityFourFifths_pair_10_hinges:List CompactPair.Hinge:=[]
noncomputable def parityFourFifths_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_10_base compact_parityFourFifths_pair_10_hinges x y
def compact_parityFourFifths_pair_10_cuts:List ℚ:=[]
theorem compact_parityFourFifths_pair_10_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_10_base compact_parityFourFifths_pair_10_hinges 0 compact_parityFourFifths_pair_10_cuts = true :=
  by decide +kernel
theorem compact_parityFourFifths_pair_10_representation (x y:ℝ) :
    parityFourFifths_pair_10 x y = CompactPair.expressionEval compact_parityFourFifths_pair_10_base compact_parityFourFifths_pair_10_hinges x y:=by rfl
private def zz131:"s0083"="s0083":=by decide+kernel
theorem parityFourFifths_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_10 x y:=by
  rw [compact_parityFourFifths_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_10_check hy (by simpa using hx)
def compact_parityFourFifths_pair_11_base:CompactPair.Quadratic:=⟨(-1 / 0xe4e1c0),(0x31f / 0x1312d00),0⟩
def compact_parityFourFifths_pair_11_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x7270e00),1, -3⟩,⟨(1 / 0x7270e00),3, -1⟩]
noncomputable def parityFourFifths_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityFourFifths_pair_11_base compact_parityFourFifths_pair_11_hinges x y
def compact_parityFourFifths_pair_11_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityFourFifths_pair_11_check :
    CompactPair.expressionCheckPSD compact_parityFourFifths_pair_11_base compact_parityFourFifths_pair_11_hinges 0 compact_parityFourFifths_pair_11_cuts = true :=
  by decide +kernel
theorem compact_parityFourFifths_pair_11_representation (x y:ℝ) :
    parityFourFifths_pair_11 x y = CompactPair.expressionEval compact_parityFourFifths_pair_11_base compact_parityFourFifths_pair_11_hinges x y:=by rfl
theorem parityFourFifths_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityFourFifths_pair_11 x y:=by
  rw [compact_parityFourFifths_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityFourFifths_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalParityFourFifthsPairs
private def zz2024:"s07e8"="s07e8":=by decide+kernel
end 
section 
namespace Green24Proof.LowerHingeQuadratic
open IntegerQuadraticCertificates
def lowerMatrix (hs:Hinges):Quadratic :=
  (hs.map fun v => min v.1 0 • product v.2 v.2).sum
private def zz132:"s0084"="s0084":=by decide+kernel
theorem scalar_lower (c:Int) (z:ℝ) :
    (min c 0:Int) * z ^ 2 ≤ (c:ℝ) * (max z 0) ^ 2:=by
  by_cases hz:0 ≤ z
  · rw [max_eq_left hz]
    exact mul_le_mul_of_nonneg_right (by exact_mod_cast min_le_left c 0) (sq_nonneg z)
  · rw [max_eq_right (le_of_not_ge hz),zero_pow (by decide:2 ≠ 0),mul_zero]
    exact mul_nonpos_of_nonpos_of_nonneg (by exact_mod_cast min_le_right c 0) (sq_nonneg z)
theorem lowerMatrix_le (hs:Hinges) (x:Point) :
    quadraticEval (lowerMatrix hs) x ≤ hingeEval hs x:=by
  induction hs with
  | nil => simp [lowerMatrix,hingeEval,quadraticEval_zero]
  | cons v vs ih =>
    simpa only [lowerMatrix,hingeEval,List.map_cons,List.sum_cons,
      quadraticEval_add,quadraticEval_smul,quadraticEval_product, ← sq] using
      add_le_add (scalar_lower v.1 (linearEval v.2 x)) ih
theorem nonnegative_of_lower (Q:Quadratic) (hs:Hinges) (x:Point)
    (h:0 ≤ quadraticEval (Q + lowerMatrix hs) x) :
    0 ≤ quadraticEval Q x + hingeEval hs x:=by
  rw [quadraticEval_add] at h
  exact le_trans h (add_le_add (le_refl _) (lowerMatrix_le hs x))
end Green24Proof.LowerHingeQuadratic
private def zz2025:"s07e9"="s07e9":=by decide+kernel
end 
section 
namespace Green24Proof.OrthantHingeBounds
open IntegerQuadraticCertificates
def positivePart (a:Linear):Linear:=fun i => max (a i) 0
def negativePart (a:Linear):Linear:=fun i => max (-a i) 0
theorem eval_positive_nonneg (a:Linear) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ linearEval (positivePart a) x:=by
  apply Finset.sum_nonneg
  intro i _
  exact mul_nonneg (by exact_mod_cast (le_max_right (a i) 0)) (hx i)
private def zz133:"s0085"="s0085":=by decide+kernel
theorem eval_negative_nonneg (a:Linear) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ linearEval (negativePart a) x:=by
  apply Finset.sum_nonneg
  intro i _
  exact mul_nonneg (by exact_mod_cast (le_max_right (-a i) 0)) (hx i)
theorem eval_difference (a:Linear) (x:Point) :
    linearEval a x = linearEval (positivePart a) x - linearEval (negativePart a) x:=by
  have ha:a = positivePart a + -(negativePart a):=by
    funext i
    change a i = max (a i) 0 + -max (-a i) 0
    omega
  calc
    linearEval a x = linearEval (positivePart a + -(negativePart a)) x:=congrArg (fun b => linearEval b x) ha
    _ = _:=by rw [linearEval_add,linearEval_neg]; ring
theorem hinge_lower (p n:ℝ) (hp:0 ≤ p) (_hn:0 ≤ n) :
    (p - n) ^ 2 - n ^ 2 ≤ max (p - n) 0 ^ 2:=by
  by_cases h:0 ≤ p - n
  · rw [max_eq_left h]
    nlinarith [sq_nonneg n]
  · rw [max_eq_right (le_of_not_ge h)]
    have hprod:=mul_nonneg hp (show 0 ≤ n - p by linarith)
    nlinarith [sq_nonneg p]
theorem hinge_upper (p n:ℝ) (hp:0 ≤ p) (hn:0 ≤ n) :
    max (p - n) 0 ^ 2 ≤ p ^ 2:=by
  by_cases h:0 ≤ p - n
  · rw [max_eq_left h]
    have hprod:=mul_nonneg hn (show 0 ≤ 2 * p - n by linarith)
    nlinarith
  · rw [max_eq_right (le_of_not_ge h)]
    simpa using sq_nonneg p
private def zz134:"s0086"="s0086":=by decide+kernel
theorem hinge_upper_square (z:ℝ):max z 0 ^ 2 ≤ z ^ 2:=by
  by_cases h:0 ≤ z
  · rw [max_eq_left h]
  · rw [max_eq_right (le_of_not_ge h)]
    simpa using sq_nonneg z
def squareDifference (a b:Linear):Quadratic :=
  product a a + (-1:ℤ) • product b b
theorem eval_squareDifference (a b:Linear) (x:Point) :
    quadraticEval (squareDifference a b) x = linearEval a x ^ 2 - linearEval b x ^ 2:=by
  simp only [squareDifference,quadraticEval_add,quadraticEval_smul,quadraticEval_product,
    Int.cast_neg,Int.cast_one]
  ring
def singleLower (scale c t:ℤ) (a:Linear):Quadratic :=
  if 0 ≤ c then t • squareDifference a (negativePart a)
  else (scale * c) • product a a + t • squareDifference a (positivePart a)
theorem singleLower_le (scale c t:ℤ) (a:Linear) (x:Point)
    (hx:∀ i,0 ≤ x i) (ht:0 ≤ t) (htc:t ≤ scale * |c|) :
    quadraticEval (singleLower scale c t a) x ≤
      (scale:ℝ) * (c:ℝ) * max (linearEval a x) 0 ^ 2:=by
  have hp:=eval_positive_nonneg a x hx
  have hn:=eval_negative_nonneg a x hx
  have htR:(0:ℝ) ≤ t:=by exact_mod_cast ht
  have hdiff:=eval_difference a x
  by_cases hc:0 ≤ c
  · rw [abs_of_nonneg hc] at htc
    have htcR:(t:ℝ) ≤ (scale:ℝ) * c:=by exact_mod_cast htc
    have hl:=hinge_lower (linearEval (positivePart a) x) (linearEval (negativePart a) x) hp hn
    rw [← hdiff] at hl
    have h1:=mul_le_mul_of_nonneg_left hl htR
    have h2:=mul_le_mul_of_nonneg_right htcR (sq_nonneg (max (linearEval a x) 0))
    simp only [singleLower,if_pos hc,quadraticEval_smul,eval_squareDifference]
    exact le_trans h1 h2
  · rw [abs_of_neg (lt_of_not_ge hc)] at htc
    have htcR:(t:ℝ) ≤ (scale:ℝ) * -(c:ℝ):=by exact_mod_cast htc
    rw [mul_neg] at htcR
    have hu:=hinge_upper (linearEval (positivePart a) x) (linearEval (negativePart a) x) hp hn
    rw [← hdiff] at hu
    have h1:=mul_le_mul_of_nonneg_left (hinge_upper_square (linearEval a x))
      (sub_nonneg.mpr htcR)
    have h2:=mul_le_mul_of_nonneg_left hu htR
    simp only [singleLower,if_neg hc,quadraticEval_add,quadraticEval_smul,
      quadraticEval_product,eval_squareDifference,Int.cast_mul]
    nlinarith
def weightsCheck (scale:ℤ):Hinges → List ℤ → Bool
  | [],[] => true
  | (c,_) :: hs,t :: ts => decide (0 ≤ t) && decide (t ≤ scale * |c|) && weightsCheck scale hs ts
  | _,_ => false
def lowerMatrix (scale:ℤ):Hinges → List ℤ → Quadratic
  | (c,a) :: hs,t :: ts => singleLower scale c t a + lowerMatrix scale hs ts
  | _,_ => 0
theorem lowerMatrix_le (scale:ℤ) (hs:Hinges) (ts:List ℤ) (x:Point)
    (hx:∀ i,0 ≤ x i) (h:weightsCheck scale hs ts = true) :
    quadraticEval (lowerMatrix scale hs ts) x ≤ (scale:ℝ) * hingeEval hs x:=by
  induction hs generalizing ts with
  | nil =>
    cases ts with
    | nil => simp [lowerMatrix,hingeEval,quadraticEval_zero]
    | cons t ts => simp [weightsCheck] at h
  | cons v vs ih =>
    cases ts with
    | nil => simp [weightsCheck] at h
    | cons t ts =>
      rcases v with ⟨c,a⟩
      simp only [weightsCheck,Bool.and_eq_true,decide_eq_true_eq] at h
      have hl:=add_le_add (singleLower_le scale c t a x hx h.1.1 h.1.2) (ih ts h.2)
      simpa only [lowerMatrix,quadraticEval_add,hingeEval,List.map_cons,List.sum_cons,
        mul_add,mul_assoc] using hl
private def zz135:"s0087"="s0087":=by decide+kernel
theorem nonnegative_of_lower (scale:ℤ) (Q:Quadratic) (hs:Hinges) (ts:List ℤ)
    (x:Point) (hx:∀ i,0 ≤ x i) (hs0:0 < scale)
    (hw:weightsCheck scale hs ts = true)
    (h:0 ≤ quadraticEval (scale • Q + lowerMatrix scale hs ts) x) :
    0 ≤ quadraticEval Q x + hingeEval hs x:=by
  have hl:=lowerMatrix_le scale hs ts x hx hw
  rw [quadraticEval_add,quadraticEval_smul] at h
  apply nonneg_of_mul_nonneg_right (a:=(scale:ℝ))
  · nlinarith
  · exact_mod_cast hs0
end Green24Proof.OrthantHingeBounds
private def zz2026:"s07ea"="s07ea":=by decide+kernel
end 
section 
namespace Green24Proof.PureCertificateData
open IntegerQuadraticCertificates
abbrev Reader (α:Type):=StateT (List Nat) Option α
def fail {α:Type}:Reader α:=fun _ => none
def readNat:Reader Nat
  | [] => none
  | a :: rest => some (a,rest)
def unzig (a:Nat):Int :=
  if a % 2 = 0 then Int.ofNat (a / 2) else -(Int.ofNat (a / 2)) - 1
def readInt:Reader Int:=do
  return unzig (← readNat)
def readIndex (n:Nat):Reader (Fin n):=do
  let i ← readNat
  if h:i < n then return ⟨i,h⟩ else fail
def readLinear:Reader Linear:=do
  let a ← readInt
  let b ← readInt
  let c ← readInt
  let d ← readInt
  return ![a,b,c,d]
def readCombination (n:Nat):Nat → Reader (Combination n)
  | 0 => pure []
  | count + 1 => do
    let weight ← readInt
    let i ← readIndex n
    let rest ← readCombination n count
    return (weight,i) :: rest
def readTerm (n:Nat):Reader (NonnegativeTerm n):=do
  match ← readNat with
  | 0 => return .square (← readLinear)
  | 1 => return .pair (← readIndex n) (← readIndex n)
  | _ => fail
def readDecomposition (n:Nat):Nat → Reader (Decomposition n)
  | 0 => pure []
  | count + 1 => do
    let weight ← readInt
    let term ← readTerm n
    let rest ← readDecomposition n count
    return (weight,term) :: rest
def readTree:Nat → (n:Nat) → Reader (Certificate n)
  | 0,_ => fail
  | fuel + 1,n => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition n count)
    | 1 => return .split (← readTree fuel (n + 1)) (← readTree fuel (n + 1))
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree fuel (n + 1)) (← readTree fuel (n + 1))
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let weights ← readCombination n count
      return .positive scale weights (← readTree fuel (n + 1))
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let weights ← readCombination n count
      return .negative scale weights (← readTree fuel (n + 1))
    | _ => fail
def decode (fuel n:Nat) (text:String):Certificate n :=
  match (do
    let data ← (text.splitOn ",").mapM String.toNat?
    readTree fuel n data:Option (Certificate n × List Nat)) with
  | some (certificate,[]) => certificate
  | _ => .leaf 0 []
def readPacked:Nat → Nat → Nat × Nat
  | 0,data => (0,data)
  | fuel + 1,data =>
    let byte:=data % 256
    if byte < 128 then (byte,data / 256)
    else
      let (next,rest):=readPacked fuel (data / 256)
      (byte % 128 + 128 * next,rest)
def unpack:Nat → Nat → List Nat
  | 0,_ => []
  | count + 1,data =>
    let (value,rest):=readPacked 128 data
    value :: unpack count rest
def decodeNumbers (fuel n:Nat) (data:List Nat):Certificate n :=
  match readTree fuel n data with
  | some (certificate,[]) => certificate
  | _ => .leaf 0 []
theorem decoded_sound (fuel n:Nat) (text:String)
    (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check (decode fuel n text) C Q hs = true) :
    0 ≤ quadraticEval Q x + hingeEval hs x :=
  check_sound (decode fuel n text) C Q hs x hC h
end Green24Proof.PureCertificateData
private def zz2027:"s07eb"="s07eb":=by decide+kernel
end 
section 
namespace Green24Proof.IntegerPSDCheck
abbrev IntMatrix (n:ℕ):=Fin n → Fin n → ℤ
noncomputable def eval {n:ℕ} (Q:IntMatrix n) (x:Fin n → ℝ):ℝ :=
  ∑ i, ∑ j,(Q i j:ℝ) * x i * x j
def tail {n:ℕ} (Q:IntMatrix (n + 1)):IntMatrix n :=
  fun i j => Q i.succ j.succ
def schur {n:ℕ} (Q:IntMatrix (n + 1)):IntMatrix n :=
  fun i j => Q 0 0 * Q i.succ j.succ - Q 0 i.succ * Q 0 j.succ
theorem eval_succ {n:ℕ} (Q:IntMatrix (n + 1)) (x:Fin (n + 1) → ℝ)
    (hsym:∀ i:Fin n,Q i.succ 0 = Q 0 i.succ) :
    eval Q x = (Q 0 0:ℝ) * x 0 ^ 2 +
      2 * x 0 * (∑ i:Fin n,(Q 0 i.succ:ℝ) * x i.succ) +
      eval (tail Q) (fun i => x i.succ):=by
  unfold eval tail
  rw [Fin.sum_univ_succ]
  simp_rw [Fin.sum_univ_succ,hsym,Finset.sum_add_distrib]
  simp_rw [show ∀ i:Fin n,(Q 0 i.succ:ℝ) * x 0 * x i.succ =
    x 0 * ((Q 0 i.succ:ℝ) * x i.succ) by intro i; ring,
    show ∀ i:Fin n,(Q 0 i.succ:ℝ) * x i.succ * x 0 =
    x 0 * ((Q 0 i.succ:ℝ) * x i.succ) by intro i; ring,
    ← Finset.mul_sum]
  ring
theorem eval_schur {n:ℕ} (Q:IntMatrix (n + 1)) (x:Fin n → ℝ) :
    eval (schur Q) x = (Q 0 0:ℝ) * eval (tail Q) x -
      (∑ i,(Q 0 i.succ:ℝ) * x i) ^ 2:=by
  unfold eval schur tail
  simp only [Int.cast_sub,Int.cast_mul,sub_mul,Finset.sum_sub_distrib,
    pow_two,Finset.sum_mul,Finset.mul_sum]
  congr 1
  · apply Finset.sum_congr rfl
    intro i _
    apply Finset.sum_congr rfl
    intro j _
    ring
  · apply Finset.sum_congr rfl
    intro i _
    apply Finset.sum_congr rfl
    intro j _
    ring
def check:(n:ℕ) → IntMatrix n → Bool
  | 0,_ => true
  | n + 1,Q =>
    ((List.finRange n).all fun i => Q i.succ 0 == Q 0 i.succ) &&
    if Q 0 0 = 0 then
      ((List.finRange n).all fun i => Q 0 i.succ == 0) && check n (tail Q)
    else decide (0 < Q 0 0) && check n (schur Q)
private def zz136:"s0088"="s0088":=by decide+kernel
theorem check_sound (n:ℕ) (Q:IntMatrix n) (h:check n Q = true)
    (x:Fin n → ℝ):0 ≤ eval Q x:=by
  induction n with
  | zero => simp [eval]
  | succ n ih =>
    simp only [check,Bool.and_eq_true] at h
    have hsym:∀ i:Fin n,Q i.succ 0 = Q 0 i.succ:=by
      simpa only [List.all_eq_true,List.mem_finRange,forall_true_left,beq_iff_eq] using h.1
    by_cases hzero:Q 0 0 = 0
    · simp only [hzero, ↓reduceIte,Bool.and_eq_true] at h
      have hrow:∀ i:Fin n,Q 0 i.succ = 0:=by
        simpa only [List.all_eq_true,List.mem_finRange,forall_true_left,beq_iff_eq] using h.2.1
      rw [eval_succ Q x hsym]
      simpa [hzero,hrow] using ih (tail Q) h.2.2 (fun i => x i.succ)
    · simp only [hzero, ↓reduceIte,Bool.and_eq_true,decide_eq_true_eq] at h
      have hp:(0:ℝ) < Q 0 0:=by exact_mod_cast h.2.1
      have hs:=ih (schur Q) h.2.2 (fun i => x i.succ)
      rw [eval_schur] at hs
      rw [eval_succ Q x hsym]
      have hsq:=sq_nonneg ((Q 0 0:ℝ) * x 0 +
        ∑ i:Fin n,(Q 0 i.succ:ℝ) * x i.succ)
      apply nonneg_of_mul_nonneg_left (b:=(Q 0 0:ℝ)) ?_ hp
      nlinarith
end Green24Proof.IntegerPSDCheck
private def zz2028:"s07ec"="s07ec":=by decide+kernel
end 
section 
namespace Green24Proof.QuadraticCoefficientCheck
open IntegerQuadraticCertificates
def coefficientEq (Q R:Quadratic):Bool :=
  [(Q 0 0,R 0 0),(Q 1 1,R 1 1),(Q 2 2,R 2 2),(Q 3 3,R 3 3),
   (Q 0 1 + Q 1 0,R 0 1 + R 1 0),(Q 0 2 + Q 2 0,R 0 2 + R 2 0),
   (Q 0 3 + Q 3 0,R 0 3 + R 3 0),(Q 1 2 + Q 2 1,R 1 2 + R 2 1),
   (Q 1 3 + Q 3 1,R 1 3 + R 3 1),(Q 2 3 + Q 3 2,R 2 3 + R 3 2)].all
    fun entry => entry.1 == entry.2
theorem quadraticEval_coefficients (Q:Quadratic) (x:Point) :
    quadraticEval Q x =
      (Q 0 0:ℝ) * x 0 ^ 2 + (Q 1 1:ℝ) * x 1 ^ 2 +
      (Q 2 2:ℝ) * x 2 ^ 2 + (Q 3 3:ℝ) * x 3 ^ 2 +
      ((Q 0 1 + Q 1 0:ℤ):ℝ) * x 0 * x 1 +
      ((Q 0 2 + Q 2 0:ℤ):ℝ) * x 0 * x 2 +
      ((Q 0 3 + Q 3 0:ℤ):ℝ) * x 0 * x 3 +
      ((Q 1 2 + Q 2 1:ℤ):ℝ) * x 1 * x 2 +
      ((Q 1 3 + Q 3 1:ℤ):ℝ) * x 1 * x 3 +
      ((Q 2 3 + Q 3 2:ℤ):ℝ) * x 2 * x 3:=by
  simp only [quadraticEval,Fin.sum_univ_four,Int.cast_add]
  ring
theorem coefficientEq_eval_eq (Q R:Quadratic) (h:coefficientEq Q R = true)
    (x:Point):quadraticEval Q x = quadraticEval R x:=by
  simp only [coefficientEq,List.all_cons,List.all_nil,Bool.and_eq_true,
    Bool.and_true,beq_iff_eq] at h
  rcases h with ⟨h00,h11,h22,h33,h01,h02,h03,h12,h13,h23⟩
  simp only [quadraticEval_coefficients,h00,h11,h22,h33,
    h01,h02,h03,h12,h13,h23]
def decompositionCheck {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n):Bool :=
  decide (0 < s) && (d.all fun term => decide (0 ≤ term.1)) &&
    coefficientEq (decompositionMatrix C d) (s • Q)
theorem decompositionCheck_sound {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:decompositionCheck C Q s d = true) :
    0 ≤ quadraticEval Q x:=by
  simp only [decompositionCheck,Bool.and_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d x hC h.1.2
  rw [coefficientEq_eval_eq _ _ h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
private def zz137:"s0089"="s0089":=by decide+kernel
theorem of_matrix_check {n:ℕ} (C:Fin n → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition n)
    (h:IntegerQuadraticCertificates.decompositionCheck C Q s d = true) :
    decompositionCheck C Q s d = true:=by
  simp only [IntegerQuadraticCertificates.decompositionCheck,Bool.and_eq_true,
    quadraticEq_eq_true,decide_eq_true_eq] at h
  simp only [decompositionCheck,Bool.and_eq_true,decide_eq_true_eq]
  refine ⟨h.1, ?_⟩
  rw [h.2]
  simp [coefficientEq]
end Green24Proof.QuadraticCoefficientCheck
private def zz2029:"s07ed"="s07ed":=by decide+kernel
end 
section 
namespace Green24Proof.CoefficientPSDQuadraticCertificates
open IntegerQuadraticCertificates
inductive Certificate:ℕ → Type where
  | psd {n:ℕ}:Certificate n
  | leaf {n:ℕ} (scale:ℤ) (d:Decomposition n):Certificate n
  | split {n:ℕ} (positive negative:Certificate (n + 1)):Certificate n
  | cut {n:ℕ} (a:Linear) (positive negative:Certificate (n + 1)):Certificate n
  | positive {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
  | negative {n:ℕ} (scale:ℤ) (w:Combination n) (next:Certificate (n + 1)):Certificate n
def check {n:ℕ} (cert:Certificate n) (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs => check p (Fin.cons a C) Q hs && check m (Fin.cons (-a) C) Q hs
  | .psd,[] => IntegerPSDCheck.check 4 Q
  | .leaf s d,[] => QuadraticCoefficientCheck.decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (Fin.cons a C) (Q + c • product a a) hs &&
      check m (Fin.cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (Fin.cons a C) (Q + c • product a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) &&
      check m (Fin.cons (-a) C) Q hs
  | _,_ => false
theorem cons_constraints {n:ℕ} (C:Fin n → Linear) (a:Linear) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (ha:0 ≤ linearEval a x) :
    ∀ i:Fin (n + 1),0 ≤ linearEval ((Fin.cons a C:Fin (n + 1) → Linear) i) x:=by
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · simpa using ha
  · simpa using hC j
theorem positive_step (Q:Quadratic) (c:ℤ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:0 ≤ linearEval a x)
    (h:0 ≤ quadraticEval (Q + c • product a a) x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_left ha,quadraticEval_add,
    quadraticEval_smul,quadraticEval_product,pow_two,add_assoc] using h
theorem negative_step (Q:Quadratic) (c:ℤ) (a:Linear) (hs:Hinges) (x:Point)
    (ha:linearEval a x ≤ 0) (h:0 ≤ quadraticEval Q x + hingeEval hs x) :
    0 ≤ quadraticEval Q x + hingeEval ((c,a) :: hs) x:=by
  simpa only [hingeEval,List.map_cons,List.sum_cons,max_eq_right ha,zero_pow (by decide:2 ≠ 0),
    mul_zero,zero_add] using h
private def zz138:"s008a"="s008a":=by decide+kernel
theorem check_sound {n:ℕ} (cert:Certificate n) (C:Fin n → Linear)
    (Q:Quadratic) (hs:Hinges) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check cert C Q hs = true):0 ≤ quadraticEval Q x + hingeEval hs x:=by
  induction cert generalizing Q hs with
  | psd =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero,
        quadraticEval,IntegerPSDCheck.eval] using
        IntegerPSDCheck.check_sound 4 Q h x
    | cons t ts => simp [check] at h
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        QuadraticCoefficientCheck.decompositionCheck_sound C Q s d x hC h
    | cons t ts => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
          (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a ts x (le_of_not_ge ha)
          (hm (Fin.cons (-a) C) Q ts (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (Fin.cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (Fin.cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a ts x ha (hp (Fin.cons a C) (Q + c • product a a) ts
        (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a ts x ha' (hm (Fin.cons (-a) C) Q ts
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.CoefficientPSDQuadraticCertificates
private def zz2030:"s07ee"="s07ee":=by decide+kernel
end 
section 
namespace Green24Proof.PureIntegerSupportCertificateData
open IntegerQuadraticCertificates hiding Certificate check check_sound
open CoefficientPSDQuadraticCertificates
open PureCertificateData (Reader fail readNat readInt readIndex readLinear
  readCombination readDecomposition)
def liftOption {α:Type} (value:Option α):Reader α :=
  fun rest => value.map fun result => (result,rest)
def solveScaled (columns:Array (Array Int)) (target:Array Int) :
    Option (Int × Array Int):=do
  let width:=columns.size
  let height:=target.size
  let mut rows:=(List.range height).toArray.map fun i =>
    (columns.map fun column => column[i]!).push target[i]!
  let mut rank:=0
  let mut pivots:Array Nat:=#[]
  let mut previous:Int:=1
  for column in [:width] do
    let mut pivot:Option Nat:=none
    for i in [rank:height] do
      if (rows[i]!)[column]! != 0 then
        pivot:=some i
        break
    if let some i:=pivot then
      let old:=rows[rank]!
      rows:=(rows.set! rank rows[i]!).set! i old
      let pivotRow:=rows[rank]!
      let coefficient:=pivotRow[column]!
      for j in [:height] do
        if j != rank then
          let row:=rows[j]!
          let entry:=row[column]!
          rows:=rows.set! j ((List.range (width + 1)).toArray.map fun k =>
            if k == column then 0
            else (coefficient * row[k]! - entry * pivotRow[k]!) / previous)
      previous:=coefficient
      pivots:=pivots.push column
      rank:=rank + 1
  let mut scale:Nat:=1
  for i in [:pivots.size] do
    scale:=Nat.lcm scale (rows[i]!)[pivots[i]!]!.natAbs
  let mut solution:Array Int:=Array.replicate width 0
  for i in [:pivots.size] do
    let denominator:=(rows[i]!)[pivots[i]!]!
    let numerator:=(rows[i]!)[width]!
    let weight:=numerator * Int.ofNat (scale / denominator.natAbs)
    solution:=solution.set! pivots[i]! (if denominator < 0 then -weight else weight)
  return (Int.ofNat scale,solution)
def linearColumn (a:Linear):Array Int :=
  (List.finRange 4).toArray.map fun i => a i
def pairColumn (a b:Linear):Array Int :=
  #[a 0 * b 0,a 1 * b 1,a 2 * b 2,a 3 * b 3,
    a 0 * b 1 + a 1 * b 0,a 0 * b 2 + a 2 * b 0,
    a 0 * b 3 + a 3 * b 0,a 1 * b 2 + a 2 * b 1,
    a 1 * b 3 + a 3 * b 1,a 2 * b 3 + a 3 * b 2].map
    fun value => value
def matrixColumn (Q:Quadratic):Array Int :=
  #[Q 0 0,Q 1 1,Q 2 2,Q 3 3,
    Q 0 1 + Q 1 0,Q 0 2 + Q 2 0,Q 0 3 + Q 3 0,
    Q 1 2 + Q 2 1,Q 1 3 + Q 3 1,Q 2 3 + Q 3 2].map
    fun value => value
def readSupport (n:Nat):Nat → Reader (List (Fin n))
  | 0 => pure []
  | count + 1 => do
    let index ← readIndex n
    return index :: (← readSupport n count)
def readPairs (n:Nat):Nat → Reader (List (Fin n × Fin n))
  | 0 => pure []
  | count + 1 => do
    let i ← readIndex n
    let j ← readIndex n
    return (i,j) :: (← readPairs n count)
def recoverLinear {n:Nat} (C:Fin n → Linear) (a:Linear)
    (support:List (Fin n)):Option (Int × Combination n):=do
  let (scale,weights) ← solveScaled (support.toArray.map fun i => linearColumn (C i))
    (linearColumn a)
  return (scale,weights.toList.zip support)
def recoverLeaf {n:Nat} (C:Fin n → Linear) (Q:Quadratic)
    (support:List (Fin n × Fin n)):Option (Certificate n):=do
  let (scale,weights) ← solveScaled
    (support.toArray.map fun (i,j) => pairColumn (C i) (C j)) (matrixColumn Q)
  let terms:Decomposition n:=(weights.toList.zip support).map fun (weight,i,j) =>
    (weight, .pair i j)
  return .leaf scale terms
def readTree:Nat → (n:Nat) → (Fin n → Linear) → Quadratic → Hinges →
    Reader (Certificate n)
  | 0,_,_,_,_ => fail
  | fuel + 1,n,C,Q,hs => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition n count)
    | 1 =>
      match hs with
      | [] => fail
      | (c,a) :: rest =>
        let p ← readTree fuel (n + 1) (Fin.cons a C) (Q + c • product a a) rest
        let m ← readTree fuel (n + 1) (Fin.cons (-a) C) Q rest
        return .split p m
    | 2 =>
      let a ← readLinear
      let p ← readTree fuel (n + 1) (Fin.cons a C) Q hs
      let m ← readTree fuel (n + 1) (Fin.cons (-a) C) Q hs
      return .cut a p m
    | 3 =>
      match hs with
      | [] => fail
      | (c,a) :: rest =>
        let scale ← readInt
        let count ← readNat
        let weights ← readCombination n count
        return .positive scale weights
          (← readTree fuel (n + 1) (Fin.cons a C) (Q + c • product a a) rest)
    | 4 =>
      match hs with
      | [] => fail
      | (_,a) :: rest =>
        let scale ← readInt
        let count ← readNat
        let weights ← readCombination n count
        return .negative scale weights
          (← readTree fuel (n + 1) (Fin.cons (-a) C) Q rest)
    | 5 => return .psd
    | 6 =>
      let count ← readNat
      let support ← readPairs n count
      liftOption (recoverLeaf C Q support)
    | 7 =>
      match hs with
      | [] => fail
      | (c,a) :: rest =>
        let count ← readNat
        let support ← readSupport n count
        let (scale,weights) ← liftOption (recoverLinear C a support)
        return .positive scale weights
          (← readTree fuel (n + 1) (Fin.cons a C) (Q + c • product a a) rest)
    | 8 =>
      match hs with
      | [] => fail
      | (_,a) :: rest =>
        let count ← readNat
        let support ← readSupport n count
        let (scale,weights) ← liftOption (recoverLinear C (-a) support)
        return .negative scale weights
          (← readTree fuel (n + 1) (Fin.cons (-a) C) Q rest)
    | _ => fail
def decode (fuel n:Nat) (C:Fin n → Linear) (Q:Quadratic) (hs:Hinges)
    (data:List Nat):Certificate n :=
  match readTree fuel n C Q hs data with
  | some (certificate,[]) => certificate
  | _ => .leaf 0 []
theorem decoded_sound (fuel n:Nat) (C:Fin n → Linear) (Q:Quadratic)
    (hs:Hinges) (data:List Nat) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check (decode fuel n C Q hs data) C Q hs = true) :
    0 ≤ quadraticEval Q x + hingeEval hs x :=
  CoefficientPSDQuadraticCertificates.check_sound (decode fuel n C Q hs data) C Q hs x hC h
end Green24Proof.PureIntegerSupportCertificateData
private def zz2031:"s07ef"="s07ef":=by decide+kernel
end 
section 
namespace Green24Proof.ListIntegerElimination
def selectPivot:List (List Int) → Option (List Int × List (List Int))
  | [] => none
  | row :: rows =>
    if row.headD 0 != 0 then some (row,rows)
    else do
      let (pivot,rest) ← selectPivot rows
      return (pivot,row :: rest)
def normalize (scale:Int) (weights:List Int):Int × List Int :=
  let g:=weights.foldl (fun d w => Nat.gcd d w.natAbs) scale.natAbs
  let divisor:Int:=if scale < 0 then -(g:Int) else (g:Int)
  (scale / divisor,weights.map fun w => w / divisor)
def solveAux:Nat → Int → List (List Int) → Option (Int × List Int)
  | 0,_,_ => some (1,[])
  | count + 1,previous,rows => do
    let (pivotRow,rest) ← selectPivot rows
    let pivot:=pivotRow.headD 0
    let reduced:=rest.map fun row =>
      List.zipWith (fun v p => (pivot * v - row.headD 0 * p) / previous)
        row.tail pivotRow.tail
    let (scale,weights) ← solveAux count pivot reduced
    let numerator:=pivotRow.getLastD 0 * scale -
      (List.zipWith (fun a w => a * w) pivotRow.tail weights).sum
    return normalize (pivot * scale) (numerator :: weights.map fun w => pivot * w)
def solveScaled (columns:Array (Array Int)) (target:Array Int) :
    Option (Int × Array Int):=do
  let rows:=(List.range target.size).map fun i =>
    (columns.toList.map fun column => column[i]!) ++ [target[i]!]
  let (scale,weights) ← solveAux columns.size 1 rows
  return (scale,weights.toArray)
end Green24Proof.ListIntegerElimination
private def zz2032:"s07f0"="s07f0":=by decide+kernel
end 
section 
namespace FixedRowBacksubProbe
structure Row where
  c0:Int
  c1:Int
  c2:Int
  c3:Int
  c4:Int
  c5:Int
  c6:Int
  c7:Int
  c8:Int
  c9:Int
  rhs:Int
def selectPivot:List Row → Option (Row × List Row)
  | [] => none
  | row :: rows =>
    if row.c0 != 0 then some (row,rows)
    else do
      let (pivot,rest) ← selectPivot rows
      return (pivot,row :: rest)
def reduceRow (previous pivot:Int) (p row:Row):Row :=
  ⟨(pivot * row.c1 - row.c0 * p.c1) / previous,
    (pivot * row.c2 - row.c0 * p.c2) / previous,
    (pivot * row.c3 - row.c0 * p.c3) / previous,
    (pivot * row.c4 - row.c0 * p.c4) / previous,
    (pivot * row.c5 - row.c0 * p.c5) / previous,
    (pivot * row.c6 - row.c0 * p.c6) / previous,
    (pivot * row.c7 - row.c0 * p.c7) / previous,
    (pivot * row.c8 - row.c0 * p.c8) / previous,
    (pivot * row.c9 - row.c0 * p.c9) / previous,
    0,(pivot * row.rhs - row.c0 * p.rhs) / previous⟩
def dotTail (row:Row) (weights:List Int):Int :=
  (match weights with
    | [] => 0
    | w0 :: ws0 => row.c1 * w0 + (match ws0 with
    | [] => 0
    | w1 :: ws1 => row.c2 * w1 + (match ws1 with
    | [] => 0
    | w2 :: ws2 => row.c3 * w2 + (match ws2 with
    | [] => 0
    | w3 :: ws3 => row.c4 * w3 + (match ws3 with
    | [] => 0
    | w4 :: ws4 => row.c5 * w4 + (match ws4 with
    | [] => 0
    | w5 :: ws5 => row.c6 * w5 + (match ws5 with
    | [] => 0
    | w6 :: ws6 => row.c7 * w6 + (match ws6 with
    | [] => 0
    | w7 :: ws7 => row.c8 * w7 + (match ws7 with
    | [] => 0
    | w8 :: ws8 => row.c9 * w8 + 0)))))))))
def solveAux:Nat → Int → List Row → Option (Int × List Int)
  | 0,_,_ => some (1,[])
  | count + 1,previous,rows => do
    let (pivotRow,rest) ← selectPivot rows
    let pivot:=pivotRow.c0
    if count == 0 then
      return (pivot.natAbs,[if pivot < 0 then -pivotRow.rhs else pivotRow.rhs])
    else
      let reduced:=rest.map (reduceRow previous pivot pivotRow)
      let (scale,weights) ← solveAux count pivot reduced
      let numerator:=pivotRow.rhs * scale - dotTail pivotRow weights
      return (scale,numerator / pivot :: weights)
def solveScaled (columns:Array (Array Int)) (target:Array Int) :
    Option (Int × Array Int):=do
  let rows:=(List.range target.size).map fun i =>
    Row.mk ((columns[0]!)[i]!) ((columns[1]!)[i]!) ((columns[2]!)[i]!) ((columns[3]!)[i]!) ((columns[4]!)[i]!) ((columns[5]!)[i]!) ((columns[6]!)[i]!) ((columns[7]!)[i]!) ((columns[8]!)[i]!) ((columns[9]!)[i]!) (target[i]!)
  let (scale,weights) ← solveAux columns.size 1 rows
  let result:=Green24Proof.ListIntegerElimination.normalize scale weights
  return (result.1,result.2.toArray)
end FixedRowBacksubProbe
namespace Green24Proof.BacksubIntegerElimination
open ListIntegerElimination (selectPivot normalize)
def solveAux:Nat → Int → List (List Int) → Option (Int × List Int)
  | 0,_,_ => some (1,[])
  | count + 1,previous,rows => do
    let (pivotRow,rest) ← selectPivot rows
    let pivot:=pivotRow.headD 0
    if count == 0 then
      return (pivot.natAbs,[if pivot < 0 then -pivotRow.getLastD 0 else pivotRow.getLastD 0])
    else
      let reduced:=rest.map fun row =>
        List.zipWith (fun v p => (pivot * v - row.headD 0 * p) / previous)
          row.tail pivotRow.tail
      let (scale,weights) ← solveAux count pivot reduced
      let numerator:=pivotRow.getLastD 0 * scale -
        (List.zipWith (fun a w => a * w) pivotRow.tail weights).sum
      return (scale,numerator / pivot :: weights)
def solveScaled:=FixedRowBacksubProbe.solveScaled
end Green24Proof.BacksubIntegerElimination
private def zz2033:"s07f1"="s07f1":=by decide+kernel
end 
section 
namespace Green24Proof.OrthantQuadraticCertificates
open IntegerQuadraticCertificates (Linear Quadratic Point linearEq linearEq_eq_true
  linearEval linearEval_zero linearEval_add linearEval_smul linearEval_neg product
  quadraticEval quadraticEval_zero quadraticEval_add quadraticEval_smul quadraticEval_product
  Hinges hingeEval positive_step negative_step)
abbrev Combination:=List (ℤ × ℕ)
def combine (C:ℕ → Linear) (w:Combination):Linear :=
  (w.map fun t => t.1 • C t.2).sum
def nonnegativeWeights (w:Combination):Bool :=
  w.all fun t => decide (0 ≤ t.1)
theorem combine_nonneg (C:ℕ → Linear) (w:Combination) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:nonnegativeWeights w = true) :
    0 ≤ linearEval (combine C w) x:=by
  induction w with
  | nil => simp [combine,linearEval_zero]
  | cons t ts ih =>
    simp only [nonnegativeWeights,List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [combine,List.map_cons,List.sum_cons,linearEval_add,linearEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (hC t.2)) (ih hw.2)
inductive NonnegativeTerm where
  | square (a:Linear)
  | pair (i j:ℕ)
def termMatrix (C:ℕ → Linear):NonnegativeTerm → Quadratic
  | .square a => product a a
  | .pair i j => product (C i) (C j)
theorem termMatrix_nonneg (C:ℕ → Linear) (t:NonnegativeTerm)
    (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termMatrix C t) x:=by
  cases t with
  | square a => simpa only [termMatrix,quadraticEval_product, ← sq] using sq_nonneg (linearEval a x)
  | pair i j => simpa only [termMatrix,quadraticEval_product] using mul_nonneg (hC i) (hC j)
abbrev Decomposition:=List (ℤ × NonnegativeTerm)
def decompositionMatrix (C:ℕ → Linear) (d:Decomposition):Quadratic :=
  (d.map fun t => t.1 • termMatrix C t.2).sum
def decompositionCheck (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition):Bool :=
  decide (0 < s) && (d.all fun t => decide (0 ≤ t.1)) &&
    QuadraticCoefficientCheck.coefficientEq (decompositionMatrix C d) (s • Q)
private def zz139:"s008b"="s008b":=by decide+kernel
theorem decomposition_nonneg (C:ℕ → Linear) (d:Decomposition) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun t => decide (0 ≤ t.1)) = true) :
    0 ≤ quadraticEval (decompositionMatrix C d) x:=by
  induction d with
  | nil => simp [decompositionMatrix,quadraticEval_zero]
  | cons t ts ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionMatrix,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (termMatrix_nonneg C t.2 x hC)) (ih hw.2)
theorem decompositionCheck_sound (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:decompositionCheck C Q s d = true):0 ≤ quadraticEval Q x:=by
  simp only [decompositionCheck,Bool.and_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d x hC h.1.2
  rw [QuadraticCoefficientCheck.coefficientEq_eval_eq _ _ h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
def combinationCheck (C:ℕ → Linear) (s:ℤ) (w:Combination)
    (a:Linear):Bool :=
  decide (0 < s) && nonnegativeWeights w && linearEq (combine C w) (s • a)
theorem combinationCheck_sound (C:ℕ → Linear) (s:ℤ) (w:Combination)
    (a:Linear) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:combinationCheck C s w a = true):0 ≤ linearEval a x:=by
  simp only [combinationCheck,Bool.and_eq_true,linearEq_eq_true,decide_eq_true_eq] at h
  have ha:=combine_nonneg C w x hC h.1.2
  rw [h.2,linearEval_smul] at ha
  exact nonneg_of_mul_nonneg_right ha (by exact_mod_cast h.1.1:(0:ℝ) < s)
abbrev WeightFormula:=List (Nat × Int)
abbrev Plan:=List (Nat × Nat × WeightFormula)
def coefficient (Q:Quadratic):Nat → Int
  | 0 => Q 0 0
  | 1 => Q 1 1
  | 2 => Q 2 2
  | 3 => Q 3 3
  | 4 => Q 0 1 + Q 1 0
  | 5 => Q 0 2 + Q 2 0
  | 6 => Q 0 3 + Q 3 0
  | 7 => Q 1 2 + Q 2 1
  | 8 => Q 1 3 + Q 3 1
  | 9 => Q 2 3 + Q 3 2
  | _ => 0
def planDecomposition (Q:Quadratic) (rows:Plan):Decomposition :=
  rows.map fun (i,j,terms) =>
    ((terms.map fun (k,multiplier) => multiplier * coefficient Q k).sum, .pair i j)
namespace FourBasisRecovery
open IntegerQuadraticCertificates (Linear Quadratic)
structure Vec where
  a:Int
  b:Int
  c:Int
  d:Int
structure Mat where
  a:Vec
  b:Vec
  c:Vec
  d:Vec
def ofVec (a:Linear):Vec:=⟨a 0,a 1,a 2,a 3⟩
def ofMat (Q:Quadratic):Mat:=⟨ofVec (Q 0),ofVec (Q 1),ofVec (Q 2),ofVec (Q 3)⟩
def dot (a b:Vec):Int:=a.a*b.a+a.b*b.b+a.c*b.c+a.d*b.d
def transpose (A:Mat):Mat:=⟨⟨A.a.a,A.b.a,A.c.a,A.d.a⟩,⟨A.a.b,A.b.b,A.c.b,A.d.b⟩,⟨A.a.c,A.b.c,A.c.c,A.d.c⟩,⟨A.a.d,A.b.d,A.c.d,A.d.d⟩⟩
def add (A B:Mat):Mat:=⟨⟨A.a.a+B.a.a,A.a.b+B.a.b,A.a.c+B.a.c,A.a.d+B.a.d⟩,⟨A.b.a+B.b.a,A.b.b+B.b.b,A.b.c+B.b.c,A.b.d+B.b.d⟩,⟨A.c.a+B.c.a,A.c.b+B.c.b,A.c.c+B.c.c,A.c.d+B.c.d⟩,⟨A.d.a+B.d.a,A.d.b+B.d.b,A.d.c+B.d.c,A.d.d+B.d.d⟩⟩
def mul (A B:Mat):Mat :=
  let T:=transpose B
  ⟨⟨dot A.a T.a,dot A.a T.b,dot A.a T.c,dot A.a T.d⟩,⟨dot A.b T.a,dot A.b T.b,dot A.b T.c,dot A.b T.d⟩,⟨dot A.c T.a,dot A.c T.b,dot A.c T.c,dot A.c T.d⟩,⟨dot A.d T.a,dot A.d T.b,dot A.d T.c,dot A.d T.d⟩⟩
def det3 (a b c d e f g h i:Int):Int:=a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g)
def adjugate (A:Mat):Mat:=⟨⟨(det3 A.b.b A.b.c A.b.d A.c.b A.c.c A.c.d A.d.b A.d.c A.d.d),(-(det3 A.a.b A.a.c A.a.d A.c.b A.c.c A.c.d A.d.b A.d.c A.d.d)),(det3 A.a.b A.a.c A.a.d A.b.b A.b.c A.b.d A.d.b A.d.c A.d.d),(-(det3 A.a.b A.a.c A.a.d A.b.b A.b.c A.b.d A.c.b A.c.c A.c.d))⟩,⟨(-(det3 A.b.a A.b.c A.b.d A.c.a A.c.c A.c.d A.d.a A.d.c A.d.d)),(det3 A.a.a A.a.c A.a.d A.c.a A.c.c A.c.d A.d.a A.d.c A.d.d),(-(det3 A.a.a A.a.c A.a.d A.b.a A.b.c A.b.d A.d.a A.d.c A.d.d)),(det3 A.a.a A.a.c A.a.d A.b.a A.b.c A.b.d A.c.a A.c.c A.c.d)⟩,⟨(det3 A.b.a A.b.b A.b.d A.c.a A.c.b A.c.d A.d.a A.d.b A.d.d),(-(det3 A.a.a A.a.b A.a.d A.c.a A.c.b A.c.d A.d.a A.d.b A.d.d)),(det3 A.a.a A.a.b A.a.d A.b.a A.b.b A.b.d A.d.a A.d.b A.d.d),(-(det3 A.a.a A.a.b A.a.d A.b.a A.b.b A.b.d A.c.a A.c.b A.c.d))⟩,⟨(-(det3 A.b.a A.b.b A.b.c A.c.a A.c.b A.c.c A.d.a A.d.b A.d.c)),(det3 A.a.a A.a.b A.a.c A.c.a A.c.b A.c.c A.d.a A.d.b A.d.c),(-(det3 A.a.a A.a.b A.a.c A.b.a A.b.b A.b.c A.d.a A.d.b A.d.c)),(det3 A.a.a A.a.b A.a.c A.b.a A.b.b A.b.c A.c.a A.c.b A.c.c)⟩⟩
def recover (C:Nat → Linear) (Q:Quadratic) (pairs:List (Nat × Nat)):Int × Decomposition :=
  match pairs with
  | _ :: (i,j) :: (k,l) :: [] =>
    let A:Mat:=⟨ofVec (C i),ofVec (C j),ofVec (C k),ofVec (C l)⟩
    let B:=adjugate A
    let determinant:=dot A.a (transpose B).a
    let Q:=ofMat Q
    let R:=mul (transpose B) (mul (add Q (transpose Q)) B)
    (2*determinant*determinant,
      [(R.a.a, .pair i i),(R.b.b, .pair j j),(R.c.c, .pair k k),(R.d.d, .pair l l),
       (R.a.b+R.b.a, .pair i j),(R.a.c+R.c.a, .pair i k),(R.a.d+R.d.a, .pair i l),
       (R.b.c+R.c.b, .pair j k),(R.b.d+R.d.b, .pair j l),(R.c.d+R.d.c, .pair k l)])
  | _ => (0,[])
end FourBasisRecovery
def supportDecomposition (C:Nat → Linear) (Q:Quadratic)
    (pairs:List (Nat × Nat)):Int × Decomposition :=
  if pairs.headD (0,0) == (64,3) then FourBasisRecovery.recover C Q pairs
  else match BacksubIntegerElimination.solveScaled
      (pairs.toArray.map fun (i,j) =>
        PureIntegerSupportCertificateData.pairColumn (C i) (C j))
      (PureIntegerSupportCertificateData.matrixColumn Q) with
  | none => (0,[])
  | some (scale,weights) =>
      (scale,(weights.toList.zip pairs).map fun (weight,i,j) => (weight, .pair i j))
def mixedSupportDecomposition (C:Nat → Linear) (Q:Quadratic)
    (pairs:List (Nat × Nat)) (squares:List Linear):Int × Decomposition :=
  let terms:=(pairs.map fun (i,j) => NonnegativeTerm.pair i j) ++
    (squares.map NonnegativeTerm.square)
  match BacksubIntegerElimination.solveScaled
      (terms.toArray.map fun term =>
        PureIntegerSupportCertificateData.matrixColumn (termMatrix C term))
      (PureIntegerSupportCertificateData.matrixColumn Q) with
  | none => (0,[])
  | some (scale,weights) => (scale,weights.toList.zip terms)
def expandWeights (scale:ℤ) (hs:Hinges) (weights:List ℤ):List ℤ :=
  (hs.zip weights).map fun (v,t) => if t < 0 then scale * |v.1| else t
def cons (a:Linear) (C:ℕ → Linear):ℕ → Linear
  | 0 => a
  | i + 1 => C i
theorem cons_constraints (C:ℕ → Linear) (a:Linear) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (ha:0 ≤ linearEval a x) :
    ∀ i,0 ≤ linearEval (cons a C i) x:=by
  intro i
  cases i with
  | zero => exact ha
  | succ j => exact hC j
inductive Certificate:Type where
  | orthantSupport (scale:ℤ) (weights:List ℤ) (pairs:List (Nat × Nat)):Certificate
  | mixedSupport (pairs:List (Nat × Nat)) (squares:List Linear):Certificate
  | lowerSupport (pairs:List (Nat × Nat)):Certificate
  | lowerPsd:Certificate
  | support (pairs:List (Nat × Nat)):Certificate
  | plan (scale:ℤ) (rows:Plan):Certificate
  | psd:Certificate
  | leaf (scale:ℤ) (d:Decomposition):Certificate
  | split (positive negative:Certificate):Certificate
  | cut (a:Linear) (positive negative:Certificate):Certificate
  | positive (scale:ℤ) (w:Combination) (next:Certificate):Certificate
  | negative (scale:ℤ) (w:Combination) (next:Certificate):Certificate
def check (cert:Certificate) (C:ℕ → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .orthantSupport scale weights pairs,hs =>
      let weights:=expandWeights scale hs weights
      let lower:=scale • Q + OrthantHingeBounds.lowerMatrix scale hs weights
      let (s,d):=supportDecomposition C lower pairs
      decide (0 < scale) && OrthantHingeBounds.weightsCheck scale hs weights &&
        decompositionCheck C lower s d
  | .lowerSupport pairs,hs =>
      let lower:=Q + LowerHingeQuadratic.lowerMatrix hs
      let (scale,d):=supportDecomposition C lower pairs
      decompositionCheck C lower scale d
  | .lowerPsd,hs => IntegerPSDCheck.check 4 (Q + LowerHingeQuadratic.lowerMatrix hs)
  | .cut a p m,hs => check p (cons a C) Q hs && check m (cons (-a) C) Q hs
  | .mixedSupport pairs squares,[] =>
      let (scale,d):=mixedSupportDecomposition C Q pairs squares
      decompositionCheck C Q scale d
  | .support pairs,[] =>
      let (scale,d):=supportDecomposition C Q pairs
      decompositionCheck C Q scale d
  | .plan scale rows,[] => decompositionCheck C Q scale (planDecomposition Q rows)
  | .psd,[] => IntegerPSDCheck.check 4 Q
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (cons a C) (Q + c • product a a) hs &&
      check m (cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (cons a C) (Q + c • product a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) &&
      check m (cons (-a) C) Q hs
  | _,_ => false
private def zz140:"s008c"="s008c":=by decide+kernel
theorem check_sound (cert:Certificate) (C:ℕ → Linear)
    (Q:Quadratic) (hs:Hinges) (x:Point) (hx:∀ i,0 ≤ x i)
    (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check cert C Q hs = true):0 ≤ quadraticEval Q x + hingeEval hs x:=by
  induction cert generalizing C Q hs with
  | orthantSupport scale weights pairs =>
    simp only [check,Bool.and_eq_true,decide_eq_true_eq] at h
    apply OrthantHingeBounds.nonnegative_of_lower scale Q hs (expandWeights scale hs weights) x hx h.1.1 h.1.2
    exact decompositionCheck_sound C (scale • Q + OrthantHingeBounds.lowerMatrix scale hs (expandWeights scale hs weights))
      (supportDecomposition C (scale • Q + OrthantHingeBounds.lowerMatrix scale hs (expandWeights scale hs weights)) pairs).1
      (supportDecomposition C (scale • Q + OrthantHingeBounds.lowerMatrix scale hs (expandWeights scale hs weights)) pairs).2 x hC h.2
  | lowerSupport pairs =>
    apply LowerHingeQuadratic.nonnegative_of_lower Q hs x
    exact decompositionCheck_sound C (Q + LowerHingeQuadratic.lowerMatrix hs)
      (supportDecomposition C (Q + LowerHingeQuadratic.lowerMatrix hs) pairs).1
      (supportDecomposition C (Q + LowerHingeQuadratic.lowerMatrix hs) pairs).2 x hC h
  | lowerPsd =>
    apply LowerHingeQuadratic.nonnegative_of_lower Q hs x
    exact IntegerPSDCheck.check_sound 4 (Q + LowerHingeQuadratic.lowerMatrix hs) h x
  | mixedSupport pairs squares =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q (mixedSupportDecomposition C Q pairs squares).1
          (mixedSupportDecomposition C Q pairs squares).2 x hC h
    | cons t ts => simp [check] at h
  | support pairs =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q (supportDecomposition C Q pairs).1
          (supportDecomposition C Q pairs).2 x hC h
    | cons t ts => simp [check] at h
  | plan scale rows =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q scale (planDecomposition Q rows) x hC h
    | cons t ts => simp [check] at h
  | psd =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero,
        quadraticEval,IntegerPSDCheck.eval] using
        IntegerPSDCheck.check_sound 4 Q h x
    | cons t ts => simp [check] at h
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q s d x hC h
    | cons t ts => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a ts x ha (hp (cons a C) (Q + c • product a a) ts
          (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a ts x (le_of_not_ge ha)
          (hm (cons (-a) C) Q ts (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a ts x ha (hp (cons a C) (Q + c • product a a) ts
        (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a ts x ha' (hm (cons (-a) C) Q ts
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.OrthantQuadraticCertificates
private def zz2034:"s07f2"="s07f2":=by decide+kernel
end 
section 
namespace Green24Proof.ScalarRowDefaults
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
def constraints:Fin 4 → Linear :=
  ![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
theorem nonnegative (certificate:Certificate) (Q:Quadratic) (hs:Hinges)
    (D:Int) (valid:check certificate constraintsNat Q hs = true)
    (hD:0 ≤ D) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ (quadraticEval Q x + hingeEval hs x) / (D:ℝ):=by
  apply div_nonneg
  · apply check_sound certificate constraintsNat Q hs x hx _ valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · exact_mod_cast hD
end Green24Proof.ScalarRowDefaults
private def zz2035:"s07f3"="s07f3":=by decide+kernel
end 
section 
namespace Green24Proof.CheckpointPathData
open IntegerQuadraticCertificates (Linear Quadratic Hinges product)
open OrthantQuadraticCertificates
structure State where
  constraints:Nat → Linear
  quadratic:Quadratic
  hinges:Hinges
def step (positive:Bool) (s:State):State :=
  match s.hinges with
  | [] => s
  | (c,a) :: hs =>
    if positive then ⟨cons a s.constraints,s.quadratic + c • product a a,hs⟩
    else ⟨cons (-a) s.constraints,s.quadratic,hs⟩
def follow:Nat → Nat → State → State
  | 0,_,s => s
  | fuel + 1,bits,s =>
    if bits < 2 then s
    else follow fuel (bits / 2) (step (bits % 2 == 1) s)
def path (bits:Nat) (s:State):State:=follow 7 bits s
def V (certificate:Certificate) (s:State):Prop :=
  check certificate s.constraints s.quadratic s.hinges = true
end Green24Proof.CheckpointPathData
private def zz2036:"s07f4"="s07f4":=by decide+kernel
end 
section 
namespace Green24Proof.BranchWitnessAtoms
open OrthantQuadraticCertificates
def bp (w:Int × Combination) (p:Certificate):Certificate:=.positive w.1 w.2 p
def bm (w:Int × Combination) (p:Certificate):Certificate:=.negative w.1 w.2 p
def w0:Int × Combination:=(1,[(1,0),(1,1)])
def w1:Int × Combination:=(1,[(1,0),(1,2)])
def w2:Int × Combination:=(1,[(1,0),(1,2),(1,7)])
def w3:Int × Combination:=(1,[(1,0),(1,3)])
def w4:Int × Combination:=(1,[(1,0),(1,3),(1,4)])
def w5:Int × Combination:=(1,[(1,0),(1,4)])
def w6:Int × Combination:=(1,[(1,0),(1,5)])
def w7:Int × Combination:=(1,[(1,0),(1,6)])
def w8:Int × Combination:=(1,[(1,0),(1,7)])
def w9:Int × Combination:=(1,[(1,0),(1,8)])
def w10:Int × Combination:=(1,[(1,0),(1,9)])
def w11:Int × Combination:=(1,[(1,0),(1,10)])
def w12:Int × Combination:=(1,[(1,0),(1,11)])
def w13:Int × Combination:=(1,[(1,0),(1,12)])
def w14:Int × Combination:=(1,[(1,0),(1,13)])
def w15:Int × Combination:=(1,[(1,0),(1,14)])
def w16:Int × Combination:=(1,[(1,0),(1,15)])
def w17:Int × Combination:=(1,[(1,0),(1,16)])
def w18:Int × Combination:=(1,[(1,0),(1,17)])
def w19:Int × Combination:=(1,[(1,0),(1,19)])
def w20:Int × Combination:=(1,[(1,0),(1,20)])
def w21:Int × Combination:=(1,[(1,0),(1,21)])
def w22:Int × Combination:=(1,[(1,0),(2,2)])
def w23:Int × Combination:=(1,[(1,0),(2,3)])
def w24:Int × Combination:=(1,[(1,0),(2,4)])
def w25:Int × Combination:=(1,[(1,0),(2,5)])
def w26:Int × Combination:=(1,[(1,0),(2,15)])
def w27:Int × Combination:=(1,[(1,0),(2,22)])
def w28:Int × Combination:=(1,[(1,0),(3,2)])
def w29:Int × Combination:=(1,[(1,0),(3,4)])
def w30:Int × Combination:=(1,[(1,0),(3,5)])
def w31:Int × Combination:=(1,[(1,0),(3,8)])
def w32:Int × Combination:=(1,[(1,1),(1,2)])
def w33:Int × Combination:=(1,[(1,1),(1,2),(1,8)])
def w34:Int × Combination:=(1,[(1,1),(1,2),(1,9)])
def w35:Int × Combination:=(1,[(1,1),(1,2),(1,10)])
def w36:Int × Combination:=(1,[(1,1),(1,2),(1,12)])
def w37:Int × Combination:=(1,[(1,1),(1,3)])
def w38:Int × Combination:=(1,[(1,1),(1,3),(1,8)])
def w39:Int × Combination:=(1,[(1,1),(1,3),(1,9)])
def w40:Int × Combination:=(1,[(1,1),(1,4)])
def w41:Int × Combination:=(1,[(1,1),(1,5)])
def w42:Int × Combination:=(1,[(1,1),(1,6)])
def w43:Int × Combination:=(1,[(1,1),(1,9)])
def w44:Int × Combination:=(1,[(1,1),(1,10)])
def w45:Int × Combination:=(1,[(1,1),(1,11)])
def w46:Int × Combination:=(1,[(1,1),(1,12)])
def w47:Int × Combination:=(1,[(1,1),(1,13)])
def w48:Int × Combination:=(1,[(1,1),(1,14)])
def w49:Int × Combination:=(1,[(1,1),(1,17)])
def w50:Int × Combination:=(1,[(1,1),(1,19)])
def w51:Int × Combination:=(1,[(1,1),(2,4)])
def w52:Int × Combination:=(1,[(1,1),(2,5)])
def w53:Int × Combination:=(1,[(1,1),(2,6)])
def w54:Int × Combination:=(1,[(1,1),(2,7)])
def w55:Int × Combination:=(1,[(1,1),(3,3)])
def w56:Int × Combination:=(1,[(1,1),(3,4)])
def w57:Int × Combination:=(1,[(1,1),(3,5)])
def w58:Int × Combination:=(1,[(1,1),(3,6)])
def w59:Int × Combination:=(1,[(1,1),(3,9)])
def w60:Int × Combination:=(1,[(1,1),(3,11)])
def w61:Int × Combination:=(1,[(1,1),(3,12)])
def w62:Int × Combination:=(1,[(1,2),(1,3)])
def w63:Int × Combination:=(1,[(1,2),(1,3),(1,11)])
def w64:Int × Combination:=(1,[(1,2),(1,4)])
def w65:Int × Combination:=(1,[(1,2),(1,4),(1,10)])
def w66:Int × Combination:=(1,[(1,2),(1,6)])
def w67:Int × Combination:=(1,[(1,2),(1,7)])
def w68:Int × Combination:=(1,[(1,2),(1,8)])
def w69:Int × Combination:=(1,[(1,2),(1,9)])
def w70:Int × Combination:=(1,[(1,2),(1,10)])
def w71:Int × Combination:=(1,[(1,2),(1,11)])
def w72:Int × Combination:=(1,[(1,2),(1,12)])
def w73:Int × Combination:=(1,[(1,2),(1,13)])
def w74:Int × Combination:=(1,[(1,2),(1,15)])
def w75:Int × Combination:=(1,[(1,2),(1,16)])
def w76:Int × Combination:=(1,[(1,2),(2,4)])
def w77:Int × Combination:=(1,[(1,2),(2,7)])
def w78:Int × Combination:=(1,[(1,2),(2,8)])
def w79:Int × Combination:=(1,[(1,2),(2,16)])
def w80:Int × Combination:=(1,[(1,2),(2,18)])
def w81:Int × Combination:=(1,[(1,2),(3,6)])
def w82:Int × Combination:=(1,[(1,2),(3,7)])
def w83:Int × Combination:=(1,[(1,3),(1,4)])
def w84:Int × Combination:=(1,[(1,3),(1,5)])
def w85:Int × Combination:=(1,[(1,3),(1,7)])
def w86:Int × Combination:=(1,[(1,3),(1,8)])
def w87:Int × Combination:=(1,[(1,3),(1,9)])
def w88:Int × Combination:=(1,[(1,3),(1,10)])
def w89:Int × Combination:=(1,[(1,3),(1,11)])
def w90:Int × Combination:=(1,[(1,3),(1,12)])
def w91:Int × Combination:=(1,[(1,3),(1,13)])
def w92:Int × Combination:=(1,[(1,3),(1,14)])
def w93:Int × Combination:=(1,[(1,3),(1,15)])
def w94:Int × Combination:=(1,[(1,3),(1,16)])
def w95:Int × Combination:=(1,[(1,3),(1,17)])
def w96:Int × Combination:=(1,[(1,3),(2,5)])
def w97:Int × Combination:=(1,[(1,3),(2,6)])
def w98:Int × Combination:=(1,[(1,4),(1,5)])
def w99:Int × Combination:=(1,[(1,4),(1,8)])
def w100:Int × Combination:=(1,[(1,4),(1,12)])
def w101:Int × Combination:=(1,[(1,4),(1,13)])
def w102:Int × Combination:=(1,[(1,4),(1,14)])
def w103:Int × Combination:=(1,[(1,4),(2,6)])
def w104:Int × Combination:=(1,[(1,4),(2,7)])
def w105:Int × Combination:=(1,[(1,5),(1,13)])
def w106:Int × Combination:=(1,[(1,7),(3,12)])
def w107:Int × Combination:=(1,[(1,7),(3,13)])
def w108:Int × Combination:=(1,[(1,8),(3,13)])
def w109:Int × Combination:=(1,[(1,9),(3,14)])
def w110:Int × Combination:=(1,[(1,9),(3,15)])
def w111:Int × Combination:=(1,[(1,10),(3,16)])
def w112:Int × Combination:=(1,[(1,11),(1,17)])
def w113:Int × Combination:=(1,[(1,11),(3,17)])
def w114:Int × Combination:=(1,[(1,12),(1,23)])
def w115:Int × Combination:=(1,[(1,12),(1,25)])
def w116:Int × Combination:=(1,[(1,12),(3,17)])
def w117:Int × Combination:=(1,[(1,12),(3,18)])
def w118:Int × Combination:=(1,[(1,13),(1,26)])
def w119:Int × Combination:=(1,[(1,13),(3,19)])
def w120:Int × Combination:=(1,[(1,14),(3,19)])
def w121:Int × Combination:=(1,[(2,0),(1,3)])
def w122:Int × Combination:=(1,[(2,0),(1,4)])
def w123:Int × Combination:=(1,[(2,0),(1,5)])
def w124:Int × Combination:=(1,[(2,0),(1,6)])
def w125:Int × Combination:=(1,[(2,0),(1,7)])
def w126:Int × Combination:=(1,[(2,0),(1,8)])
def w127:Int × Combination:=(1,[(2,0),(1,9)])
def w128:Int × Combination:=(1,[(2,0),(1,10)])
def w129:Int × Combination:=(1,[(2,0),(1,11)])
def w130:Int × Combination:=(1,[(2,1),(1,5)])
def w131:Int × Combination:=(1,[(2,1),(1,7)])
def w132:Int × Combination:=(1,[(2,1),(1,8)])
def w133:Int × Combination:=(1,[(2,1),(1,9)])
def w134:Int × Combination:=(1,[(2,1),(1,10)])
def w135:Int × Combination:=(1,[(2,1),(1,11)])
def w136:Int × Combination:=(1,[(2,1),(1,12)])
def w137:Int × Combination:=(1,[(2,1),(3,4)])
def w138:Int × Combination:=(1,[(2,1),(3,8)])
def w139:Int × Combination:=(1,[(2,2),(1,3)])
def w140:Int × Combination:=(1,[(2,2),(3,10)])
def w141:Int × Combination:=(1,[(2,2),(3,11)])
def w142:Int × Combination:=(1,[(2,4),(1,7),(1,9)])
def w143:Int × Combination:=(1,[(2,4),(1,10)])
def w144:Int × Combination:=(1,[(2,5),(1,10)])
def w145:Int × Combination:=(1,[(2,5),(1,11)])
def w146:Int × Combination:=(1,[(2,5),(3,8)])
def w147:Int × Combination:=(1,[(2,6),(1,11)])
def w148:Int × Combination:=(1,[(3,0),(2,4)])
def w149:Int × Combination:=(1,[(3,2),(2,8)])
def w150:Int × Combination:=(1,[(3,2),(2,9)])
def w151:Int × Combination:=(1,[(3,2),(2,11)])
def w152:Int × Combination:=(1,[(3,3),(1,11)])
def w153:Int × Combination:=(1,[(3,3),(2,10)])
def w154:Int × Combination:=(1,[(3,3),(2,12)])
def w155:Int × Combination:=(1,[(3,4),(1,10)])
def w156:Int × Combination:=(1,[(3,4),(1,12)])
def w157:Int × Combination:=(1,[(3,4),(2,11)])
def w158:Int × Combination:=(1,[(3,4),(2,13)])
def w159:Int × Combination:=(1,[(3,5),(1,14)])
def w160:Int × Combination:=(1,[(3,7),(1,16)])
def w161:Int × Combination:=(1,[(3,11),(1,15)])
def w162:Int × Combination:=(1,[(3,12),(1,15)])
def w163:Int × Combination:=(2,[(1,0),(1,1),(1,3)])
def w164:Int × Combination:=(2,[(1,0),(1,1),(1,7)])
def w165:Int × Combination:=(2,[(1,0),(1,1),(1,21)])
def w166:Int × Combination:=(2,[(1,0),(1,1),(2,4)])
def w167:Int × Combination:=(2,[(1,0),(1,1),(2,8)])
def w168:Int × Combination:=(2,[(1,0),(1,2),(1,3)])
def w169:Int × Combination:=(2,[(1,0),(1,2),(2,6)])
def w170:Int × Combination:=(2,[(1,0),(1,2),(2,9)])
def w171:Int × Combination:=(2,[(1,0),(1,2),(2,11)])
def w172:Int × Combination:=(2,[(1,0),(1,2),(2,12)])
def w173:Int × Combination:=(2,[(1,0),(1,2),(2,13)])
def w174:Int × Combination:=(2,[(1,0),(1,2),(2,14)])
def w175:Int × Combination:=(2,[(1,0),(1,3)])
def w176:Int × Combination:=(2,[(1,0),(1,3),(1,4)])
def w177:Int × Combination:=(2,[(1,0),(1,3),(2,11)])
def w178:Int × Combination:=(2,[(1,0),(1,3),(2,13)])
def w179:Int × Combination:=(2,[(1,0),(1,3),(2,14)])
def w180:Int × Combination:=(2,[(1,0),(1,4)])
def w181:Int × Combination:=(2,[(1,0),(1,5)])
def w182:Int × Combination:=(2,[(1,0),(1,6)])
def w183:Int × Combination:=(2,[(1,0),(1,7)])
def w184:Int × Combination:=(2,[(1,0),(1,9)])
def w185:Int × Combination:=(2,[(1,0),(1,10)])
def w186:Int × Combination:=(2,[(1,0),(1,12)])
def w187:Int × Combination:=(2,[(1,0),(2,2),(1,5)])
def w188:Int × Combination:=(2,[(1,0),(2,3),(1,13)])
def w189:Int × Combination:=(2,[(1,0),(2,8),(1,10)])
def w190:Int × Combination:=(2,[(1,0),(3,1),(3,2)])
def w191:Int × Combination:=(2,[(1,0),(3,3)])
def w192:Int × Combination:=(2,[(1,0),(3,4)])
def w193:Int × Combination:=(2,[(1,0),(3,8)])
def w194:Int × Combination:=(2,[(1,1),(2,3),(1,13)])
def w195:Int × Combination:=(2,[(1,1),(2,4),(3,6)])
def w196:Int × Combination:=(2,[(1,1),(2,5),(1,9)])
def w197:Int × Combination:=(2,[(1,1),(2,5),(3,7)])
def w198:Int × Combination:=(2,[(1,1),(2,6),(1,10)])
def w199:Int × Combination:=(2,[(1,1),(3,4)])
def w200:Int × Combination:=(2,[(1,1),(3,6),(1,9)])
def w201:Int × Combination:=(2,[(1,2),(1,3),(1,6)])
def w202:Int × Combination:=(2,[(1,2),(1,4),(1,10)])
def w203:Int × Combination:=(2,[(1,2),(2,4),(1,14)])
def w204:Int × Combination:=(2,[(1,2),(2,4),(1,15)])
def w205:Int × Combination:=(2,[(1,2),(3,8)])
def w206:Int × Combination:=(2,[(1,2),(3,10)])
def w207:Int × Combination:=(2,[(1,2),(3,12)])
def w208:Int × Combination:=(2,[(1,3),(3,6),(2,9)])
def w209:Int × Combination:=(2,[(1,3),(3,10)])
def w210:Int × Combination:=(2,[(1,4),(3,13)])
def w211:Int × Combination:=(2,[(2,0),(1,6),(1,8)])
def w212:Int × Combination:=(2,[(2,0),(3,5),(1,7)])
def w213:Int × Combination:=(2,[(2,1),(1,3),(1,11)])
def w214:Int × Combination:=(2,[(2,1),(1,3),(1,12)])
def w215:Int × Combination:=(2,[(3,0),(1,1)])
def w216:Int × Combination:=(2,[(3,0),(1,2)])
def w217:Int × Combination:=(2,[(3,0),(1,4)])
def w218:Int × Combination:=(2,[(3,0),(1,4),(1,8)])
def w219:Int × Combination:=(2,[(3,0),(1,5)])
def w220:Int × Combination:=(2,[(3,0),(1,6)])
def w221:Int × Combination:=(2,[(3,0),(1,6),(1,10)])
def w222:Int × Combination:=(2,[(3,0),(1,7)])
def w223:Int × Combination:=(2,[(3,0),(1,7),(1,12)])
def w224:Int × Combination:=(2,[(3,0),(1,8),(1,13)])
def w225:Int × Combination:=(2,[(3,0),(1,9),(1,13)])
def w226:Int × Combination:=(2,[(3,1),(1,2)])
def w227:Int × Combination:=(2,[(3,1),(1,3)])
def w228:Int × Combination:=(2,[(3,1),(1,3),(2,8)])
def w229:Int × Combination:=(2,[(3,1),(1,4)])
def w230:Int × Combination:=(2,[(3,1),(1,4),(2,9)])
def w231:Int × Combination:=(2,[(3,1),(1,6)])
def w232:Int × Combination:=(2,[(3,1),(1,7)])
def w233:Int × Combination:=(2,[(3,1),(1,7),(1,12)])
def w234:Int × Combination:=(2,[(3,1),(1,7),(2,9)])
def w235:Int × Combination:=(2,[(3,1),(1,7),(3,8)])
def w236:Int × Combination:=(2,[(3,1),(1,8)])
def w237:Int × Combination:=(2,[(3,1),(1,8),(1,12)])
def w238:Int × Combination:=(2,[(3,1),(1,8),(2,9)])
def w239:Int × Combination:=(2,[(3,1),(1,9),(1,12)])
def w240:Int × Combination:=(2,[(3,1),(1,9),(1,14)])
def w241:Int × Combination:=(2,[(3,1),(1,10),(1,14)])
def w242:Int × Combination:=(2,[(3,1),(1,11)])
def w243:Int × Combination:=(2,[(3,1),(3,8),(1,9)])
def w244:Int × Combination:=(2,[(3,2),(1,3)])
def w245:Int × Combination:=(2,[(3,2),(1,4)])
def w246:Int × Combination:=(2,[(3,2),(1,7)])
def w247:Int × Combination:=(2,[(3,2),(1,8)])
def w248:Int × Combination:=(2,[(3,2),(1,9)])
def w249:Int × Combination:=(2,[(3,2),(1,10)])
def w250:Int × Combination:=(2,[(3,2),(1,11)])
def w251:Int × Combination:=(2,[(3,2),(1,12)])
def w252:Int × Combination:=(2,[(3,2),(1,14)])
def w253:Int × Combination:=(2,[(3,2),(2,12),(1,14)])
def w254:Int × Combination:=(2,[(3,3),(1,5)])
def w255:Int × Combination:=(2,[(3,3),(1,11)])
def w256:Int × Combination:=(2,[(3,3),(1,12)])
def w257:Int × Combination:=(2,[(3,3),(1,13)])
def w258:Int × Combination:=(2,[(3,3),(1,15)])
def w259:Int × Combination:=(2,[(3,4),(1,11)])
def w260:Int × Combination:=(2,[(3,4),(1,13)])
def w261:Int × Combination:=(2,[(3,4),(1,14)])
def w262:Int × Combination:=(2,[(3,4),(1,17)])
def w263:Int × Combination:=(3,[(1,0),(1,1),(5,4)])
def w264:Int × Combination:=(3,[(1,0),(2,1),(1,7)])
def w265:Int × Combination:=(3,[(1,0),(2,1),(1,11)])
def w266:Int × Combination:=(3,[(1,0),(2,1),(1,12)])
def w267:Int × Combination:=(3,[(1,0),(2,1),(1,13)])
def w268:Int × Combination:=(3,[(1,0),(2,2),(3,5)])
def w269:Int × Combination:=(3,[(1,0),(2,3)])
def w270:Int × Combination:=(3,[(1,0),(2,4)])
def w271:Int × Combination:=(3,[(1,0),(2,5)])
def w272:Int × Combination:=(3,[(1,0),(2,6)])
def w273:Int × Combination:=(3,[(1,0),(2,7)])
def w274:Int × Combination:=(3,[(1,0),(2,8)])
def w275:Int × Combination:=(3,[(1,0),(2,9)])
def w276:Int × Combination:=(3,[(1,0),(2,10)])
def w277:Int × Combination:=(3,[(1,0),(2,11)])
def w278:Int × Combination:=(3,[(1,0),(3,1),(1,5)])
def w279:Int × Combination:=(3,[(1,0),(3,1),(1,6)])
def w280:Int × Combination:=(3,[(1,0),(3,2),(1,10)])
def w281:Int × Combination:=(3,[(1,0),(3,2),(1,11)])
def w282:Int × Combination:=(3,[(1,0),(3,2),(1,15)])
def w283:Int × Combination:=(3,[(1,0),(3,2),(2,10)])
def w284:Int × Combination:=(3,[(1,0),(3,2),(2,11)])
def w285:Int × Combination:=(3,[(1,0),(3,3),(1,15)])
def w286:Int × Combination:=(3,[(1,0),(3,3),(1,17)])
def w287:Int × Combination:=(3,[(1,0),(3,3),(1,18)])
def w288:Int × Combination:=(3,[(1,0),(3,4),(1,15)])
def w289:Int × Combination:=(3,[(1,0),(3,7),(2,9)])
def w290:Int × Combination:=(3,[(1,0),(4,3)])
def w291:Int × Combination:=(3,[(1,0),(4,4)])
def w292:Int × Combination:=(3,[(1,0),(4,5)])
def w293:Int × Combination:=(3,[(1,0),(4,6)])
def w294:Int × Combination:=(3,[(1,0),(4,7)])
def w295:Int × Combination:=(3,[(1,0),(4,8)])
def w296:Int × Combination:=(3,[(1,0),(4,9)])
def w297:Int × Combination:=(3,[(1,0),(4,10)])
def w298:Int × Combination:=(3,[(1,0),(4,11)])
def w299:Int × Combination:=(3,[(1,0),(4,12)])
def w300:Int × Combination:=(3,[(1,0),(4,13)])
def w301:Int × Combination:=(3,[(1,0),(4,14)])
def w302:Int × Combination:=(3,[(1,0),(8,3)])
def w303:Int × Combination:=(3,[(1,1),(1,2),(5,6)])
def w304:Int × Combination:=(3,[(1,1),(1,2),(5,7)])
def w305:Int × Combination:=(3,[(1,1),(2,3)])
def w306:Int × Combination:=(3,[(1,1),(2,4)])
def w307:Int × Combination:=(3,[(1,1),(2,7)])
def w308:Int × Combination:=(3,[(1,1),(2,9)])
def w309:Int × Combination:=(3,[(1,1),(2,10)])
def w310:Int × Combination:=(3,[(1,1),(2,12)])
def w311:Int × Combination:=(3,[(1,1),(3,2),(1,5)])
def w312:Int × Combination:=(3,[(1,1),(3,2),(1,6)])
def w313:Int × Combination:=(3,[(1,1),(3,2),(1,7)])
def w314:Int × Combination:=(3,[(1,1),(3,2),(1,8)])
def w315:Int × Combination:=(3,[(1,1),(3,7),(2,9)])
def w316:Int × Combination:=(3,[(1,1),(5,4)])
def w317:Int × Combination:=(3,[(1,1),(8,4)])
def w318:Int × Combination:=(3,[(1,4),(5,13)])
def w319:Int × Combination:=(3,[(1,5),(5,13)])
def w320:Int × Combination:=(3,[(1,9),(1,10),(9,17)])
def w321:Int × Combination:=(3,[(1,10),(1,11),(9,17)])
def w322:Int × Combination:=(3,[(1,11),(1,12),(9,19)])
def w323:Int × Combination:=(3,[(1,12),(1,13),(9,17)])
def w324:Int × Combination:=(3,[(1,12),(1,13),(9,19)])
def w325:Int × Combination:=(3,[(1,13),(1,14),(9,20)])
def w326:Int × Combination:=(3,[(1,14),(1,15),(9,22)])
def w327:Int × Combination:=(3,[(1,15),(1,16),(9,23)])
def w328:Int × Combination:=(3,[(1,16),(1,17),(9,23)])
def w329:Int × Combination:=(3,[(2,0),(1,1),(1,9)])
def w330:Int × Combination:=(3,[(2,0),(1,1),(1,11)])
def w331:Int × Combination:=(3,[(2,0),(1,2)])
def w332:Int × Combination:=(3,[(2,0),(1,2),(1,11)])
def w333:Int × Combination:=(3,[(2,0),(1,3)])
def w334:Int × Combination:=(3,[(2,0),(1,3),(4,11)])
def w335:Int × Combination:=(3,[(2,0),(1,5)])
def w336:Int × Combination:=(3,[(2,0),(1,6)])
def w337:Int × Combination:=(3,[(2,0),(1,7)])
def w338:Int × Combination:=(3,[(2,0),(1,8)])
def w339:Int × Combination:=(3,[(2,0),(1,9)])
def w340:Int × Combination:=(3,[(2,0),(1,11)])
def w341:Int × Combination:=(3,[(2,0),(2,1),(1,7)])
def w342:Int × Combination:=(3,[(2,0),(2,2),(1,7)])
def w343:Int × Combination:=(3,[(2,0),(2,2),(1,8)])
def w344:Int × Combination:=(3,[(2,0),(2,3),(1,4)])
def w345:Int × Combination:=(3,[(2,0),(2,3),(1,7)])
def w346:Int × Combination:=(3,[(2,0),(2,3),(1,9)])
def w347:Int × Combination:=(3,[(2,0),(2,3),(1,10)])
def w348:Int × Combination:=(3,[(2,0),(2,4),(1,10)])
def w349:Int × Combination:=(3,[(2,0),(2,4),(1,11)])
def w350:Int × Combination:=(3,[(2,0),(3,3),(1,8)])
def w351:Int × Combination:=(3,[(2,0),(3,4),(1,9)])
def w352:Int × Combination:=(3,[(2,0),(4,2),(1,8)])
def w353:Int × Combination:=(3,[(2,0),(5,3)])
def w354:Int × Combination:=(3,[(2,0),(5,4)])
def w355:Int × Combination:=(3,[(2,0),(5,5)])
def w356:Int × Combination:=(3,[(2,1),(3,5),(1,9)])
def w357:Int × Combination:=(3,[(2,1),(7,4)])
def w358:Int × Combination:=(3,[(2,2),(1,8),(1,12)])
def w359:Int × Combination:=(3,[(3,0),(1,1),(1,4)])
def w360:Int × Combination:=(3,[(3,0),(1,2),(4,4)])
def w361:Int × Combination:=(3,[(3,0),(2,3),(1,12)])
def w362:Int × Combination:=(3,[(4,0),(1,1)])
def w363:Int × Combination:=(3,[(4,0),(1,2)])
def w364:Int × Combination:=(3,[(4,0),(1,3),(1,4)])
def w365:Int × Combination:=(3,[(4,0),(1,4),(1,5)])
def w366:Int × Combination:=(3,[(4,0),(1,8),(1,9)])
def w367:Int × Combination:=(3,[(4,1),(1,3),(3,9)])
def w368:Int × Combination:=(3,[(4,1),(1,3),(3,10)])
def w369:Int × Combination:=(3,[(4,4),(1,8)])
def w370:Int × Combination:=(3,[(5,0),(1,3)])
def w371:Int × Combination:=(3,[(5,1),(1,4)])
def w372:Int × Combination:=(4,[(1,0),(3,1),(1,6)])
def w373:Int × Combination:=(4,[(1,0),(3,1),(1,7)])
def w374:Int × Combination:=(4,[(1,0),(3,1),(1,8)])
def w375:Int × Combination:=(4,[(1,0),(3,1),(1,9)])
def w376:Int × Combination:=(4,[(1,0),(3,1),(1,13)])
def w377:Int × Combination:=(4,[(1,0),(3,1),(1,14)])
def w378:Int × Combination:=(4,[(1,0),(3,1),(1,15)])
def w379:Int × Combination:=(4,[(1,0),(3,1),(1,16)])
def w380:Int × Combination:=(4,[(1,0),(3,1),(2,3)])
def w381:Int × Combination:=(4,[(1,0),(3,2),(1,6)])
def w382:Int × Combination:=(4,[(1,0),(3,2),(2,4)])
def w383:Int × Combination:=(4,[(1,0),(3,3),(2,5)])
def w384:Int × Combination:=(4,[(1,0),(5,1),(4,6)])
def w385:Int × Combination:=(4,[(1,0),(5,1),(4,7)])
def w386:Int × Combination:=(4,[(1,0),(5,1),(4,8)])
def w387:Int × Combination:=(4,[(1,2),(1,3),(8,4)])
def w388:Int × Combination:=(4,[(2,0),(3,3),(1,10)])
def w389:Int × Combination:=(4,[(2,0),(3,3),(1,16)])
def w390:Int × Combination:=(4,[(2,0),(3,4),(1,12)])
def w391:Int × Combination:=(4,[(3,0),(1,2),(6,8)])
def w392:Int × Combination:=(4,[(3,0),(2,2),(3,5)])
def w393:Int × Combination:=(4,[(3,0),(2,3),(1,6)])
def w394:Int × Combination:=(4,[(3,0),(2,3),(1,7)])
def w395:Int × Combination:=(4,[(3,0),(2,3),(1,10)])
def w396:Int × Combination:=(4,[(3,0),(2,3),(3,9)])
def w397:Int × Combination:=(4,[(3,0),(2,4),(3,12)])
def w398:Int × Combination:=(4,[(3,0),(5,1),(1,5)])
def w399:Int × Combination:=(4,[(3,0),(5,1),(1,6)])
def w400:Int × Combination:=(4,[(3,0),(5,2),(1,6)])
def w401:Int × Combination:=(4,[(3,0),(5,2),(1,7)])
def w402:Int × Combination:=(4,[(3,0),(5,3),(1,8)])
def w403:Int × Combination:=(4,[(3,1),(1,2),(2,10)])
def w404:Int × Combination:=(4,[(3,1),(2,2),(1,7)])
def w405:Int × Combination:=(4,[(3,1),(2,2),(1,9)])
def w406:Int × Combination:=(4,[(3,1),(2,3),(1,8)])
def w407:Int × Combination:=(4,[(3,1),(2,3),(1,9)])
def w408:Int × Combination:=(4,[(3,1),(2,3),(1,10)])
def w409:Int × Combination:=(4,[(3,1),(2,3),(3,7)])
def w410:Int × Combination:=(4,[(3,1),(2,4),(1,10)])
def w411:Int × Combination:=(4,[(3,1),(2,4),(1,11)])
def w412:Int × Combination:=(4,[(3,1),(2,4),(3,8)])
def w413:Int × Combination:=(4,[(3,1),(5,2),(2,9)])
def w414:Int × Combination:=(4,[(3,1),(5,3),(2,11)])
def w415:Int × Combination:=(4,[(3,2),(2,5),(1,12)])
def w416:Int × Combination:=(4,[(3,2),(2,9),(5,14)])
def w417:Int × Combination:=(4,[(3,3),(2,6),(1,12)])
def w418:Int × Combination:=(4,[(3,3),(3,8),(2,14)])
def w419:Int × Combination:=(4,[(4,0),(1,1),(3,12)])
def w420:Int × Combination:=(4,[(4,0),(3,1),(3,4)])
def w421:Int × Combination:=(4,[(4,0),(3,2),(3,3)])
def w422:Int × Combination:=(4,[(4,0),(3,9),(1,15)])
def w423:Int × Combination:=(4,[(4,0),(3,10),(1,15)])
def w424:Int × Combination:=(4,[(4,1),(3,2),(3,4)])
def w425:Int × Combination:=(4,[(4,1),(3,3),(3,5)])
def w426:Int × Combination:=(4,[(4,1),(3,3),(3,6)])
def w427:Int × Combination:=(4,[(5,0),(1,1)])
def w428:Int × Combination:=(4,[(5,0),(2,3),(1,5)])
def w429:Int × Combination:=(4,[(5,0),(2,3),(1,6)])
def w430:Int × Combination:=(4,[(5,0),(2,4),(1,6)])
def w431:Int × Combination:=(4,[(5,0),(3,3)])
def w432:Int × Combination:=(4,[(5,1),(1,2)])
def w433:Int × Combination:=(4,[(5,2),(1,3)])
def w434:Int × Combination:=(4,[(5,3),(1,4)])
def w435:Int × Combination:=(4,[(5,4),(1,5)])
def w436:Int × Combination:=(4,[(7,0),(1,1)])
def w437:Int × Combination:=(5,[(1,0),(4,1),(2,7)])
def w438:Int × Combination:=(5,[(1,0),(4,2),(3,8)])
def w439:Int × Combination:=(5,[(1,0),(4,3),(3,12)])
def w440:Int × Combination:=(5,[(1,0),(4,3),(3,13)])
def w441:Int × Combination:=(5,[(1,0),(4,3),(3,14)])
def w442:Int × Combination:=(5,[(1,0),(4,3),(3,15)])
def w443:Int × Combination:=(5,[(1,0),(6,1),(4,7)])
def w444:Int × Combination:=(5,[(1,0),(6,1),(4,8)])
def w445:Int × Combination:=(5,[(1,0),(6,2),(2,11)])
def w446:Int × Combination:=(5,[(1,0),(6,2),(2,14)])
def w447:Int × Combination:=(5,[(1,0),(6,2),(8,10)])
def w448:Int × Combination:=(5,[(1,0),(6,2),(8,11)])
def w449:Int × Combination:=(5,[(1,0),(6,3),(1,8)])
def w450:Int × Combination:=(5,[(1,0),(6,4),(1,11)])
def w451:Int × Combination:=(5,[(1,0),(6,5),(1,13)])
def w452:Int × Combination:=(5,[(1,0),(9,1),(6,4)])
def w453:Int × Combination:=(5,[(2,0),(3,1),(1,8)])
def w454:Int × Combination:=(5,[(2,0),(3,1),(1,9)])
def w455:Int × Combination:=(5,[(2,0),(3,1),(1,10)])
def w456:Int × Combination:=(5,[(2,0),(3,1),(1,12)])
def w457:Int × Combination:=(5,[(2,0),(3,1),(1,13)])
def w458:Int × Combination:=(5,[(2,0),(3,1),(1,14)])
def w459:Int × Combination:=(5,[(2,0),(3,1),(1,15)])
def w460:Int × Combination:=(5,[(2,0),(3,1),(2,3)])
def w461:Int × Combination:=(5,[(2,0),(3,1),(2,4)])
def w462:Int × Combination:=(5,[(2,0),(3,2),(1,5)])
def w463:Int × Combination:=(5,[(2,0),(3,2),(2,4)])
def w464:Int × Combination:=(5,[(2,0),(3,2),(2,5)])
def w465:Int × Combination:=(5,[(2,0),(6,1),(3,5)])
def w466:Int × Combination:=(5,[(2,0),(6,2),(1,9)])
def w467:Int × Combination:=(5,[(2,0),(6,3),(1,8)])
def w468:Int × Combination:=(5,[(2,0),(6,3),(1,10)])
def w469:Int × Combination:=(5,[(2,0),(6,3),(1,11)])
def w470:Int × Combination:=(5,[(2,2),(11,3),(2,9)])
def w471:Int × Combination:=(5,[(3,0),(3,1),(1,14)])
def w472:Int × Combination:=(5,[(3,0),(3,1),(2,9)])
def w473:Int × Combination:=(5,[(3,0),(3,1),(2,10)])
def w474:Int × Combination:=(5,[(3,0),(3,2),(1,13)])
def w475:Int × Combination:=(5,[(3,0),(3,2),(1,15)])
def w476:Int × Combination:=(5,[(3,0),(3,2),(4,16)])
def w477:Int × Combination:=(5,[(3,0),(3,3),(1,13)])
def w478:Int × Combination:=(5,[(3,0),(3,3),(1,14)])
def w479:Int × Combination:=(5,[(3,0),(3,3),(1,15)])
def w480:Int × Combination:=(5,[(3,0),(3,3),(1,16)])
def w481:Int × Combination:=(5,[(3,0),(3,3),(1,18)])
def w482:Int × Combination:=(5,[(3,0),(3,3),(1,19)])
def w483:Int × Combination:=(5,[(3,0),(3,4),(1,7)])
def w484:Int × Combination:=(5,[(3,0),(3,4),(1,11)])
def w485:Int × Combination:=(5,[(3,0),(3,4),(1,12)])
def w486:Int × Combination:=(5,[(3,0),(3,4),(1,13)])
def w487:Int × Combination:=(5,[(3,0),(3,4),(1,14)])
def w488:Int × Combination:=(5,[(3,0),(3,5),(1,12)])
def w489:Int × Combination:=(5,[(3,0),(3,5),(1,13)])
def w490:Int × Combination:=(5,[(3,0),(3,5),(1,14)])
def w491:Int × Combination:=(5,[(3,0),(4,2),(3,4)])
def w492:Int × Combination:=(5,[(3,0),(5,3),(1,6)])
def w493:Int × Combination:=(5,[(3,0),(7,2),(1,9)])
def w494:Int × Combination:=(5,[(3,0),(7,3),(1,11)])
def w495:Int × Combination:=(5,[(3,1),(3,5),(1,16)])
def w496:Int × Combination:=(5,[(3,1),(4,2),(1,6)])
def w497:Int × Combination:=(5,[(3,1),(4,3),(1,7)])
def w498:Int × Combination:=(5,[(3,1),(4,3),(1,9)])
def w499:Int × Combination:=(5,[(3,1),(4,4),(3,7)])
def w500:Int × Combination:=(5,[(3,1),(4,4),(3,8)])
def w501:Int × Combination:=(5,[(3,1),(5,3),(1,7)])
def w502:Int × Combination:=(5,[(4,0),(1,2),(2,11)])
def w503:Int × Combination:=(5,[(4,0),(1,2),(2,13)])
def w504:Int × Combination:=(5,[(4,0),(1,3),(2,14)])
def w505:Int × Combination:=(5,[(5,0),(1,1),(3,6)])
def w506:Int × Combination:=(5,[(5,0),(1,1),(7,4)])
def w507:Int × Combination:=(5,[(5,0),(1,7),(1,9)])
def w508:Int × Combination:=(5,[(5,0),(1,12),(3,17)])
def w509:Int × Combination:=(5,[(5,0),(2,3),(2,5)])
def w510:Int × Combination:=(5,[(5,0),(3,1),(3,3)])
def w511:Int × Combination:=(5,[(5,0),(3,2),(3,4)])
def w512:Int × Combination:=(5,[(5,1),(1,8),(1,10)])
def w513:Int × Combination:=(5,[(5,1),(1,9),(1,11)])
def w514:Int × Combination:=(5,[(5,1),(1,10),(1,12)])
def w515:Int × Combination:=(5,[(5,1),(3,3),(3,4)])
def w516:Int × Combination:=(5,[(5,1),(3,3),(3,5)])
def w517:Int × Combination:=(5,[(5,1),(3,6),(3,8)])
def w518:Int × Combination:=(5,[(5,2),(3,4),(3,6)])
def w519:Int × Combination:=(5,[(7,0),(1,2)])
def w520:Int × Combination:=(5,[(7,0),(1,3)])
def w521:Int × Combination:=(5,[(7,0),(3,1)])
def w522:Int × Combination:=(5,[(7,0),(3,2)])
def w523:Int × Combination:=(5,[(7,1),(1,4)])
def w524:Int × Combination:=(5,[(7,3),(1,9),(5,19)])
def w525:Int × Combination:=(5,[(8,0),(1,2)])
def w526:Int × Combination:=(5,[(8,0),(1,3)])
def w527:Int × Combination:=(5,[(8,0),(1,4)])
def w528:Int × Combination:=(5,[(8,1),(1,3)])
def w529:Int × Combination:=(5,[(8,1),(1,4)])
def w530:Int × Combination:=(5,[(8,1),(1,5)])
def w531:Int × Combination:=(5,[(8,4),(1,10)])
def w532:Int × Combination:=(5,[(8,5),(1,11)])
def w533:Int × Combination:=(5,[(9,0),(1,2),(3,5)])
def w534:Int × Combination:=(5,[(9,1),(1,2),(2,8)])
def w535:Int × Combination:=(6,[(5,0),(1,2),(2,9)])
def w536:Int × Combination:=(6,[(5,0),(1,2),(2,11)])
def w537:Int × Combination:=(6,[(7,0),(2,1),(5,11)])
def w538:Int × Combination:=(6,[(7,1),(2,2),(5,12)])
def w539:Int × Combination:=(6,[(9,2),(1,9),(1,11)])
def w540:Int × Combination:=(6,[(9,2),(1,11),(1,14)])
def w541:Int × Combination:=(6,[(9,3),(1,13),(1,16)])
def w542:Int × Combination:=(6,[(9,4),(1,12),(1,15)])
def w543:Int × Combination:=(6,[(9,4),(1,14),(1,17)])
def w544:Int × Combination:=(7,[(1,0),(6,1),(2,6)])
def w545:Int × Combination:=(7,[(1,0),(6,1),(2,7)])
def w546:Int × Combination:=(7,[(1,0),(6,1),(2,8)])
def w547:Int × Combination:=(7,[(1,0),(6,1),(2,9)])
def w548:Int × Combination:=(7,[(1,0),(6,1),(2,10)])
def w549:Int × Combination:=(7,[(1,0),(6,1),(4,3)])
def w550:Int × Combination:=(7,[(1,0),(12,1),(4,10)])
def w551:Int × Combination:=(7,[(1,0),(12,1),(4,12)])
def w552:Int × Combination:=(7,[(3,0),(6,1),(1,11)])
def w553:Int × Combination:=(7,[(3,0),(6,1),(8,9)])
def w554:Int × Combination:=(7,[(3,0),(6,2),(1,11)])
def w555:Int × Combination:=(7,[(3,0),(6,2),(1,12)])
def w556:Int × Combination:=(7,[(3,0),(6,3),(1,8)])
def w557:Int × Combination:=(7,[(3,0),(6,3),(1,11)])
def w558:Int × Combination:=(7,[(3,0),(6,3),(1,12)])
def w559:Int × Combination:=(7,[(3,0),(6,3),(1,13)])
def w560:Int × Combination:=(7,[(3,0),(6,3),(1,14)])
def w561:Int × Combination:=(7,[(3,0),(6,3),(1,16)])
def w562:Int × Combination:=(7,[(3,0),(6,3),(1,18)])
def w563:Int × Combination:=(7,[(3,0),(6,4),(1,12)])
def w564:Int × Combination:=(7,[(3,1),(6,5),(1,15)])
def w565:Int × Combination:=(7,[(4,0),(3,1),(1,5)])
def w566:Int × Combination:=(7,[(4,0),(3,1),(2,2)])
def w567:Int × Combination:=(7,[(4,0),(3,1),(2,3)])
def w568:Int × Combination:=(7,[(4,0),(3,1),(2,10)])
def w569:Int × Combination:=(7,[(4,0),(3,2),(2,4)])
def w570:Int × Combination:=(7,[(5,0),(3,3),(1,7)])
def w571:Int × Combination:=(7,[(5,0),(9,1),(6,3)])
def w572:Int × Combination:=(7,[(7,0),(2,11),(3,14)])
def w573:Int × Combination:=(7,[(7,0),(2,12),(3,15)])
def w574:Int × Combination:=(7,[(7,0),(3,1),(6,3)])
def w575:Int × Combination:=(7,[(7,0),(3,2),(5,5)])
def w576:Int × Combination:=(7,[(7,0),(3,3),(5,5)])
def w577:Int × Combination:=(7,[(7,0),(3,3),(5,7)])
def w578:Int × Combination:=(7,[(7,0),(4,3),(2,5)])
def w579:Int × Combination:=(7,[(7,0),(6,2),(3,6)])
def w580:Int × Combination:=(7,[(7,1),(1,7),(2,9)])
def w581:Int × Combination:=(7,[(7,1),(3,3),(5,6)])
def w582:Int × Combination:=(7,[(7,1),(6,3),(3,5)])
def w583:Int × Combination:=(7,[(7,1),(6,3),(3,7)])
def w584:Int × Combination:=(7,[(8,0),(3,2)])
def w585:Int × Combination:=(7,[(8,0),(3,3)])
def w586:Int × Combination:=(7,[(8,0),(3,4)])
def w587:Int × Combination:=(7,[(8,0),(3,5)])
def w588:Int × Combination:=(7,[(8,1),(3,10)])
def w589:Int × Combination:=(7,[(8,1),(3,11)])
def w590:Int × Combination:=(7,[(8,1),(3,12)])
def w591:Int × Combination:=(7,[(9,0),(5,2),(3,6)])
def w592:Int × Combination:=(7,[(12,0),(2,1),(3,3)])
def w593:Int × Combination:=(7,[(12,0),(2,1),(3,4)])
def w594:Int × Combination:=(8,[(2,0),(9,1),(1,9)])
def w595:Int × Combination:=(8,[(2,0),(9,2),(1,9)])
def w596:Int × Combination:=(8,[(2,0),(9,2),(1,10)])
def w597:Int × Combination:=(8,[(2,0),(9,3),(1,9)])
def w598:Int × Combination:=(8,[(2,0),(9,3),(1,10)])
def w599:Int × Combination:=(8,[(2,0),(9,3),(1,11)])
def w600:Int × Combination:=(8,[(2,0),(9,3),(1,12)])
def w601:Int × Combination:=(8,[(5,0),(3,1),(1,4)])
def w602:Int × Combination:=(8,[(7,1),(3,2),(4,4)])
def w603:Int × Combination:=(8,[(8,0),(1,7),(3,12)])
def w604:Int × Combination:=(8,[(8,0),(1,8),(3,14)])
def w605:Int × Combination:=(8,[(8,0),(1,9),(3,14)])
def w606:Int × Combination:=(8,[(8,0),(1,9),(3,15)])
def w607:Int × Combination:=(8,[(8,0),(1,10),(3,15)])
def w608:Int × Combination:=(8,[(8,0),(1,10),(3,16)])
def w609:Int × Combination:=(8,[(8,0),(1,11),(3,17)])
def w610:Int × Combination:=(8,[(9,0),(1,3),(6,12)])
def w611:Int × Combination:=(8,[(9,0),(1,3),(6,15)])
def w612:Int × Combination:=(8,[(15,0),(1,1),(3,7)])
def w613:Int × Combination:=(8,[(15,0),(1,1),(3,8)])
def w614:Int × Combination:=(9,[(2,1),(6,7),(7,9)])
def w615:Int × Combination:=(9,[(3,1),(8,2),(5,5)])
def w616:Int × Combination:=(9,[(3,1),(8,2),(5,6)])
def w617:Int × Combination:=(9,[(3,1),(8,2),(5,7)])
def w618:Int × Combination:=(9,[(4,1),(6,4),(5,9)])
def w619:Int × Combination:=(9,[(4,1),(6,5),(5,9)])
def w620:Int × Combination:=(9,[(7,0),(3,2),(4,14)])
def w621:Int × Combination:=(9,[(7,0),(3,2),(4,15)])
def w622:Int × Combination:=(9,[(7,0),(3,2),(4,17)])
def w623:Int × Combination:=(9,[(7,0),(6,2),(1,4)])
def w624:Int × Combination:=(9,[(11,0),(5,3),(1,5)])
def w625:Int × Combination:=(9,[(11,0),(5,4),(1,6)])
def w626:Int × Combination:=(9,[(13,1),(1,3),(15,8)])
def w627:Int × Combination:=(9,[(14,3),(1,6),(2,10)])
def w628:Int × Combination:=(9,[(14,3),(1,6),(2,13)])
def w629:Int × Combination:=(9,[(14,4),(1,8),(2,15)])
def w630:Int × Combination:=(10,[(3,0),(14,2),(1,8)])
def w631:Int × Combination:=(10,[(3,0),(14,3),(1,8)])
def w632:Int × Combination:=(10,[(3,0),(14,3),(1,9)])
def w633:Int × Combination:=(10,[(9,0),(2,3),(3,7)])
def w634:Int × Combination:=(10,[(11,0),(5,2),(3,3)])
def w635:Int × Combination:=(11,[(3,0),(16,3),(1,6)])
def w636:Int × Combination:=(11,[(3,0),(16,3),(1,7)])
def w637:Int × Combination:=(11,[(3,0),(16,3),(1,8)])
def w638:Int × Combination:=(11,[(7,0),(6,1),(8,10)])
def w639:Int × Combination:=(11,[(7,0),(6,1),(8,11)])
def w640:Int × Combination:=(11,[(7,0),(6,2),(1,6)])
def w641:Int × Combination:=(11,[(7,0),(6,2),(1,7)])
def w642:Int × Combination:=(11,[(7,0),(6,2),(1,9)])
def w643:Int × Combination:=(11,[(7,0),(6,2),(1,11)])
def w644:Int × Combination:=(11,[(7,0),(6,3),(1,8)])
def w645:Int × Combination:=(11,[(7,0),(6,3),(1,9)])
def w646:Int × Combination:=(11,[(7,0),(6,3),(1,10)])
def w647:Int × Combination:=(11,[(7,0),(6,3),(1,11)])
def w648:Int × Combination:=(11,[(7,0),(6,3),(1,12)])
def w649:Int × Combination:=(11,[(7,0),(6,3),(1,13)])
def w650:Int × Combination:=(11,[(9,0),(3,1),(4,11)])
def w651:Int × Combination:=(11,[(9,0),(3,1),(4,13)])
def w652:Int × Combination:=(11,[(9,0),(4,3),(3,6)])
def w653:Int × Combination:=(12,[(4,0),(9,1),(5,2)])
def w654:Int × Combination:=(12,[(4,1),(9,2),(5,3)])
def w655:Int × Combination:=(12,[(9,0),(1,1),(8,2)])
def w656:Int × Combination:=(12,[(9,0),(1,1),(8,3)])
def w657:Int × Combination:=(12,[(10,0),(3,4),(5,10)])
def w658:Int × Combination:=(12,[(10,0),(3,4),(5,15)])
def w659:Int × Combination:=(12,[(10,0),(3,5),(5,16)])
def w660:Int × Combination:=(12,[(10,0),(3,5),(5,17)])
def w661:Int × Combination:=(12,[(13,0),(3,7),(8,9)])
def w662:Int × Combination:=(13,[(8,0),(8,2),(1,9)])
def w663:Int × Combination:=(13,[(8,0),(8,3),(1,10)])
def w664:Int × Combination:=(13,[(8,0),(8,3),(1,11)])
def w665:Int × Combination:=(14,[(15,0),(3,11),(7,17)])
def w666:Int × Combination:=(14,[(17,0),(7,4),(2,5)])
def w667:Int × Combination:=(14,[(21,3),(1,8),(5,10)])
def w668:Int × Combination:=(14,[(21,3),(1,10),(5,13)])
def w669:Int × Combination:=(15,[(5,0),(12,1),(4,6)])
def w670:Int × Combination:=(15,[(5,0),(12,1),(4,7)])
def w671:Int × Combination:=(15,[(12,0),(10,1),(1,3)])
def w672:Int × Combination:=(15,[(12,0),(10,2),(1,4)])
def w673:Int × Combination:=(15,[(18,0),(5,3),(4,5)])
def w674:Int × Combination:=(15,[(18,1),(5,3),(4,5)])
def w675:Int × Combination:=(16,[(8,0),(13,1),(15,8)])
def w676:Int × Combination:=(16,[(8,0),(13,1),(15,13)])
def w677:Int × Combination:=(16,[(9,0),(14,1),(3,5)])
def w678:Int × Combination:=(16,[(9,0),(14,3),(3,7)])
def w679:Int × Combination:=(16,[(9,0),(14,3),(3,8)])
def w680:Int × Combination:=(16,[(9,0),(14,4),(3,8)])
def w681:Int × Combination:=(16,[(9,0),(14,4),(3,9)])
def w682:Int × Combination:=(16,[(15,0),(2,2),(5,6)])
def w683:Int × Combination:=(16,[(15,0),(2,3),(5,7)])
def w684:Int × Combination:=(16,[(19,0),(10,3),(1,6)])
def w685:Int × Combination:=(16,[(19,0),(10,3),(1,7)])
def w686:Int × Combination:=(16,[(19,0),(10,4),(1,7)])
def w687:Int × Combination:=(16,[(19,0),(10,4),(1,8)])
def w688:Int × Combination:=(17,[(9,0),(16,3),(3,5)])
def w689:Int × Combination:=(17,[(9,0),(16,3),(3,6)])
def w690:Int × Combination:=(17,[(9,0),(16,3),(3,7)])
def w691:Int × Combination:=(17,[(9,0),(16,4),(3,7)])
def w692:Int × Combination:=(17,[(9,0),(16,4),(3,8)])
def w693:Int × Combination:=(17,[(15,3),(3,4),(10,12)])
def w694:Int × Combination:=(17,[(20,0),(11,3),(1,9)])
def w695:Int × Combination:=(17,[(20,0),(11,3),(1,10)])
def w696:Int × Combination:=(17,[(20,0),(11,4),(1,10)])
def w697:Int × Combination:=(21,[(22,0),(3,9),(7,16)])
def w698:Int × Combination:=(21,[(22,0),(3,10),(7,17)])
def w699:Int × Combination:=(21,[(23,0),(6,11),(7,15)])
def w700:Int × Combination:=(21,[(24,0),(7,7),(2,10)])
def w701:Int × Combination:=(21,[(24,0),(7,8),(2,11)])
def w702:Int × Combination:=(23,[(15,0),(12,3),(5,8)])
def w703:Int × Combination:=(23,[(15,0),(12,4),(5,8)])
def w704:Int × Combination:=(23,[(15,0),(12,4),(5,9)])
def w705:Int × Combination:=(23,[(15,0),(12,4),(5,13)])
def w706:Int × Combination:=(23,[(15,0),(12,5),(5,10)])
def w707:Int × Combination:=(23,[(15,0),(12,5),(5,14)])
def w708:Int × Combination:=(23,[(15,0),(12,5),(5,15)])
def w709:Int × Combination:=(23,[(21,0),(3,3),(7,11)])
def w710:Int × Combination:=(23,[(21,0),(3,4),(7,10)])
def w711:Int × Combination:=(23,[(21,0),(3,4),(7,13)])
def w712:Int × Combination:=(23,[(21,0),(3,5),(7,11)])
def w713:Int × Combination:=(23,[(21,0),(3,5),(7,12)])
def w714:Int × Combination:=(23,[(21,0),(3,5),(7,13)])
def w715:Int × Combination:=(23,[(21,0),(3,5),(7,14)])
def w716:Int × Combination:=(24,[(15,0),(16,5),(5,12)])
def w717:Int × Combination:=(25,[(21,0),(6,4),(7,8)])
def w718:Int × Combination:=(25,[(21,0),(6,4),(7,12)])
def w719:Int × Combination:=(25,[(21,0),(6,5),(7,10)])
def w720:Int × Combination:=(25,[(21,0),(6,5),(7,12)])
def w721:Int × Combination:=(25,[(21,0),(6,5),(7,13)])
def w722:Int × Combination:=(25,[(21,0),(12,7),(7,10)])
def w723:Int × Combination:=(25,[(21,0),(12,8),(7,12)])
def w724:Int × Combination:=(25,[(28,0),(9,5),(2,7)])
def w725:Int × Combination:=(25,[(28,0),(9,7),(2,10)])
def w726:Int × Combination:=(25,[(28,0),(9,8),(2,11)])
def w727:Int × Combination:=(25,[(28,0),(9,8),(2,12)])
def w728:Int × Combination:=(29,[(25,0),(6,2),(7,9)])
def w729:Int × Combination:=(29,[(25,0),(6,3),(7,11)])
end Green24Proof.BranchWitnessAtoms
private def zz2037:"s07f5"="s07f5":=by decide+kernel
end 
section 
namespace Green24Proof.OrthantPackedCertificateData
open IntegerQuadraticCertificates (Linear)
open OrthantQuadraticCertificates
abbrev Reader (α:Type):=StateT (List Nat) Option α
def fail {α:Type}:Reader α:=fun _ => none
def readByte:Reader Nat
  | [] => none
  | n :: rest =>
    if n < 256 then readByte rest
    else some (n % 256,n / 256 :: rest)
def readPacked:Nat → Reader Nat
  | 0 => fail
  | fuel + 1 => do
    let b ← readByte
    if b < 128 then return b
    else return b % 128 + 128 * (← readPacked fuel)
def readNat:Reader Nat:=readPacked 128
def readInt:Reader Int:=do
  return PureCertificateData.unzig (← readNat)
def readLinear:Reader Linear:=do
  let a ← readInt
  let b ← readInt
  let c ← readInt
  let d ← readInt
  return ![a,b,c,d]
def readCombination:Nat → Reader Combination
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let i ← readNat
    return (w,i) :: (← readCombination count)
def readTerm:Reader NonnegativeTerm:=do
  match ← readNat with
  | 0 => return .square (← readLinear)
  | 1 => return .pair (← readNat) (← readNat)
  | _ => fail
def readDecomposition:Nat → Reader Decomposition
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let t ← readTerm
    return (w,t) :: (← readDecomposition count)
def readPairs:Nat → Reader (List (Nat × Nat))
  | 0 => pure []
  | count + 1 => do
    let i ← readNat
    let j ← readNat
    return (i,j) :: (← readPairs count)
def readSquares:Nat → Reader (List Linear)
  | 0 => pure []
  | count + 1 => do
    let a ← readLinear
    return a :: (← readSquares count)
def readIntegers:Nat → Reader (List ℤ)
  | 0 => pure []
  | count + 1 => do
    let value ← readInt
    return value :: (← readIntegers count)
def readTree:Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree fuel) (← readTree fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree fuel) (← readTree fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree fuel)
    | 5 => return .psd
    | 6 => return .support (← readPairs (← readNat))
    | 9 => return .lowerSupport (← readPairs (← readNat))
    | 10 => return .lowerPsd
    | 12 =>
      let scale ← readInt
      let weights ← readIntegers (← readNat)
      let pairs ← readPairs (← readNat)
      return .orthantSupport scale weights pairs
    | 11 =>
      let pairs ← readPairs (← readNat)
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | _ => fail
def decode (fuel:Nat) (chunks:List Nat):Certificate :=
  match readTree fuel chunks with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.OrthantPackedCertificateData
private def zz2038:"s07f6"="s07f6":=by decide+kernel
end 
section 
namespace Green24Proof.OrthantCheckSteps
open IntegerQuadraticCertificates (Linear Quadratic Hinges product)
open OrthantQuadraticCertificates
theorem split_valid (p m:Certificate) (C:Nat → Linear) (Q:Quadratic)
    (c:Int) (a:Linear) (hs:Hinges)
    (hp:check p (cons a C) (Q + c • product a a) hs = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.split p m) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hp hm
theorem cut_valid (a:Linear) (p m:Certificate) (C:Nat → Linear)
    (Q:Quadratic) (hs:Hinges)
    (hp:check p (cons a C) Q hs = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.cut a p m) C Q hs = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hp hm
private def zz141:"s008d"="s008d":=by decide+kernel
theorem positive_valid (s:Int) (w:Combination) (p:Certificate)
    (C:Nat → Linear) (Q:Quadratic) (c:Int) (a:Linear) (hs:Hinges)
    (hw:combinationCheck C s w a = true)
    (hp:check p (cons a C) (Q + c • product a a) hs = true) :
    check (.positive s w p) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hw hp
theorem negative_valid (s:Int) (w:Combination) (m:Certificate)
    (C:Nat → Linear) (Q:Quadratic) (c:Int) (a:Linear) (hs:Hinges)
    (hw:combinationCheck C s w (-a) = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.negative s w m) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hw hm
end Green24Proof.OrthantCheckSteps
private def zz2039:"s07f7"="s07f7":=by decide+kernel
end 
section 
namespace Green24Proof.CheckpointStateProofTerms
open IntegerQuadraticCertificates (Linear Quadratic Hinges product)
open OrthantQuadraticCertificates
open CheckpointPathData (State V step)
def headVector (s:State):Linear:=(s.hinges.headD (0,0)).2
theorem K {p:Certificate} {s:State}
    (h:V p s:=by unfold V; decide +kernel):V p s:=h
theorem S {p m:Certificate} {s:State}
    (hp:V p (step true s)) (hm:V m (step false s))
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.split p m) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      exact OrthantCheckSteps.split_valid p m Cs Q c a hs hp hm
private def zz142:"s008e"="s008e":=by decide+kernel
theorem P {scale:Int} {weights:Combination} {p:Certificate} {s:State}
    (hp:V p (step true s))
    (hw:combinationCheck s.constraints scale weights (headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.positive scale weights p) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      exact OrthantCheckSteps.positive_valid scale weights p Cs Q c a hs hw hp
theorem M {scale:Int} {weights:Combination} {p:Certificate} {s:State}
    (hp:V p (step false s))
    (hw:combinationCheck s.constraints scale weights (-headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.negative scale weights p) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      exact OrthantCheckSteps.negative_valid scale weights p Cs Q c a hs hw hp
end Green24Proof.CheckpointStateProofTerms
private def zz2040:"s07f8"="s07f8":=by decide+kernel
end 
section 
namespace Green24Proof.StateCompactData
open IntegerQuadraticCertificates (Linear Quadratic product)
open OrthantQuadraticCertificates (cons)
def qs (Q:Quadratic) (c:Int) (a:Linear):Quadratic :=
  Q + c • product a a
def cn (a:Linear) (C:Nat → Linear):Nat → Linear :=
  cons (-a) C
end Green24Proof.StateCompactData
private def zz2041:"s07f9"="s07f9":=by decide+kernel
end 
section 
namespace Green24Proof.NumericLinearAtoms
open IntegerQuadraticCertificates (Linear)
def l0:Linear:=![-11999994000,-92854043966,29135465868,-7005711846]
def l1:Linear:=![-12000000000,-23999998800,15169293600,1200]
def l2:Linear:=![-12000000000,-23999998800,22473249000,1200]
def l3:Linear:=![0,0,0,1]
def l4:Linear:=![0,0,1,-1]
def l5:Linear:=![0,0,1,-2]
def l6:Linear:=![0,0,1,-3]
def l7:Linear:=![0,0,1,0]
def l8:Linear:=![0,0,2,-1]
def l9:Linear:=![0,0,2,-3]
def l10:Linear:=![0,0,3,-1]
def l11:Linear:=![0,0,3,-2]
def l12:Linear:=![0,1,-1,0]
def l13:Linear:=![0,1,-2,0]
def l14:Linear:=![0,1,-3,0]
def l15:Linear:=![0,1,0,-1]
def l16:Linear:=![0,1,0,-2]
def l17:Linear:=![0,1,0,-3]
def l18:Linear:=![0,1,0,0]
def l19:Linear:=![0,1,1,1]
def l20:Linear:=![0,2,-1,0]
def l21:Linear:=![0,2,-3,0]
def l22:Linear:=![0,2,0,-1]
def l23:Linear:=![0,2,0,-3]
def l24:Linear:=![0,3,-1,-1]
def l25:Linear:=![0,3,-1,0]
def l26:Linear:=![0,3,-1,1]
def l27:Linear:=![0,3,-2,-1]
def l28:Linear:=![0,3,-2,0]
def l29:Linear:=![0,3,-2,1]
def l30:Linear:=![0,3,0,-1]
def l31:Linear:=![0,3,0,-2]
def l32:Linear:=![0,3,1,-1]
def l33:Linear:=![0,3,2,-1]
def l34:Linear:=![1,-1,0,0]
def l35:Linear:=![1,-2,-3,0]
def l36:Linear:=![1,-2,0,0]
def l37:Linear:=![1,-2,3,0]
def l38:Linear:=![1,-3,0,0]
def l39:Linear:=![1,-4,-3,0]
def l40:Linear:=![1,-4,3,0]
def l41:Linear:=![1,0,-1,0]
def l42:Linear:=![1,0,-2,0]
def l43:Linear:=![1,0,-3,0]
def l44:Linear:=![1,0,0,-1]
def l45:Linear:=![1,0,0,-2]
def l46:Linear:=![1,0,0,-3]
def l47:Linear:=![1,0,0,0]
def l48:Linear:=![1,0,1,1]
def l49:Linear:=![1,1,0,1]
def l50:Linear:=![1,1,1,0]
def l51:Linear:=![1,2,-3,0]
def l52:Linear:=![1,4,-3,0]
def l53:Linear:=![187966769,-119999400,-160267515,600]
def l54:Linear:=![2,-1,0,0]
def l55:Linear:=![2,-3,0,0]
def l56:Linear:=![2,0,-1,0]
def l57:Linear:=![2,0,-3,0]
def l58:Linear:=![2,0,0,-1]
def l59:Linear:=![2,0,0,-3]
def l60:Linear:=![3,-1,0,0]
def l61:Linear:=![3,-2,0,0]
def l62:Linear:=![3,0,-1,0]
def l63:Linear:=![3,0,-2,0]
def l64:Linear:=![3,0,0,-1]
def l65:Linear:=![3,0,0,-2]
def l66:Linear:=![300,64131828,51517866,-25758783]
def l67:Linear:=![30440989229,-23976000000,-11432037552,24000000]
def l68:Linear:=![600,55422675,44521764,-22260582]
end Green24Proof.NumericLinearAtoms
private def zz2042:"s07fa"="s07fa":=by decide+kernel
end 
section 
namespace Green24Proof.DictionaryOrthantPackedData
open OrthantQuadraticCertificates
open OrthantPackedCertificateData
abbrev LinearWitness:=Int × Combination
def readTable:Nat → Reader (List LinearWitness)
  | 0 => pure []
  | n + 1 => do
    let scale ← readInt
    let weights ← readCombination (← readNat)
    return (scale,weights) :: (← readTable n)
def decodeTable (chunks:List Nat):Array LinearWitness :=
  match (do readTable (← readNat)) chunks with
  | some (entries,_) => entries.toArray
  | none => #[]
def readTree (table:Array LinearWitness):Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree table fuel) (← readTree table fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree table fuel) (← readTree table fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree table fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree table fuel)
    | 5 => return .psd
    | 6 => return .support (← readPairs (← readNat))
    | 9 => return .lowerSupport (← readPairs (← readNat))
    | 10 => return .lowerPsd
    | 11 =>
      let pairs ← readPairs (← readNat)
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | 12 =>
      let scale ← readInt
      let weights ← readIntegers (← readNat)
      let pairs ← readPairs (← readNat)
      return .orthantSupport scale weights pairs
    | 13 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .positive scale weights (← readTree table fuel)
    | 14 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .negative scale weights (← readTree table fuel)
    | _ => fail
def decode (fuel:Nat) (table:Array LinearWitness) (chunks:List Nat):Certificate :=
  match readTree table fuel chunks with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.DictionaryOrthantPackedData
private def zz2043:"s07fb"="s07fb":=by decide+kernel
end 
section 
namespace Green24Proof.DenseOrthantPackedData
open OrthantQuadraticCertificates
open OrthantPackedCertificateData
open DictionaryOrthantPackedData (LinearWitness)
def endpointWeights:Nat → Nat → List Int
  | 0,_ => []
  | count + 1,mask =>
    (if mask % 2 = 0 then 0 else -1) :: endpointWeights count (mask / 2)
def readRadixWeights:Nat → Nat → Reader (List Int)
  | 0,_ => pure []
  | count + 1,mask => do
    let value ← match mask % 4 with
      | 0 => pure 0
      | 1 => pure (-1)
      | 2 => readInt
      | _ => fail
    return value :: (← readRadixWeights count (mask / 4))
def readPairDeltas:Nat → Nat → Reader (List (Nat × Nat))
  | 0,_ => pure []
  | count + 1,previous => do
    let rank:=previous + (← readNat)
    return (rank / 64,rank % 64) :: (← readPairDeltas count rank)
def readTree (table:Array LinearWitness):Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree table fuel) (← readTree table fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree table fuel) (← readTree table fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree table fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree table fuel)
    | 5 => return .psd
    | 6 => return .support (← readPairs (← readNat))
    | 9 => return .lowerSupport (← readPairs (← readNat))
    | 10 => return .lowerPsd
    | 11 =>
      let pairs ← readPairs (← readNat)
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | 12 =>
      let scale ← readInt
      let weights ← readIntegers (← readNat)
      let pairs ← readPairs (← readNat)
      return .orthantSupport scale weights pairs
    | 13 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .positive scale weights (← readTree table fuel)
    | 14 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .negative scale weights (← readTree table fuel)
    | 15 => return .support (← readPairDeltas (← readNat) 0)
    | 16 => return .lowerSupport (← readPairDeltas (← readNat) 0)
    | 17 =>
      let pairs ← readPairDeltas (← readNat) 0
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | 18 =>
      let scale ← readInt
      let count ← readNat
      let weights:=endpointWeights count (← readNat)
      let pairs ← readPairDeltas (← readNat) 0
      return .orthantSupport scale weights pairs
    | 19 =>
      let scale ← readInt
      let count ← readNat
      let weights ← readRadixWeights count (← readNat)
      let pairs ← readPairDeltas (← readNat) 0
      return .orthantSupport scale weights pairs
    | _ => fail
def decode (fuel:Nat) (table:Array LinearWitness) (chunks:List Nat):Certificate :=
  match readTree table fuel chunks with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.DenseOrthantPackedData
private def zz2044:"s07fc"="s07fc":=by decide+kernel
end 
section 
namespace Green24Proof.FiveBitDenseData
open IntegerQuadraticCertificates (Linear)
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
abbrev Reader (α:Type):=StateT (List Nat) Option α
def fail {α:Type}:Reader α:=fun _ => none
def readGroup:Reader Nat
  | [] => none
  | n :: rest =>
    if n < 32 then readGroup rest
    else some (n % 32,n / 32 :: rest)
def readPacked:Nat → Reader Nat
  | 0 => fail
  | fuel + 1 => do
    let b ← readGroup
    if b < 16 then return b
    else return b % 16 + 16 * (← readPacked fuel)
def readNat:Reader Nat:=readPacked 224
def readInt:Reader Int:=do
  return PureCertificateData.unzig (← readNat)
def readLinear:Reader Linear:=do
  let a ← readInt
  let b ← readInt
  let c ← readInt
  let d ← readInt
  return ![a,b,c,d]
def readCombination:Nat → Reader Combination
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let i ← readNat
    return (w,i) :: (← readCombination count)
def readTerm:Reader NonnegativeTerm:=do
  match ← readNat with
  | 0 => return .square (← readLinear)
  | 1 => return .pair (← readNat) (← readNat)
  | _ => fail
def readDecomposition:Nat → Reader Decomposition
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let t ← readTerm
    return (w,t) :: (← readDecomposition count)
def readPairs:Nat → Reader (List (Nat × Nat))
  | 0 => pure []
  | count + 1 => do
    let i ← readNat
    let j ← readNat
    return (i,j) :: (← readPairs count)
def readSquares:Nat → Reader (List Linear)
  | 0 => pure []
  | count + 1 => do
    let a ← readLinear
    return a :: (← readSquares count)
def readIntegers:Nat → Reader (List ℤ)
  | 0 => pure []
  | count + 1 => do
    let value ← readInt
    return value :: (← readIntegers count)
def readTable:Nat → Reader (List LinearWitness)
  | 0 => pure []
  | n + 1 => do
    let scale ← readInt
    let weights ← readCombination (← readNat)
    return (scale,weights) :: (← readTable n)
def decodeTable (data:List Nat):Array LinearWitness :=
  match (do readTable (← readNat)) data with
  | some (entries,_) => entries.toArray
  | none => #[]
def endpointWeights:Nat → Nat → List Int
  | 0,_ => []
  | count + 1,mask =>
    (if mask % 2 = 0 then 0 else -1) :: endpointWeights count (mask / 2)
def readRadixWeights:Nat → Nat → Reader (List Int)
  | 0,_ => pure []
  | count + 1,mask => do
    let value ← match mask % 4 with
      | 0 => pure 0
      | 1 => pure (-1)
      | 2 => readInt
      | _ => fail
    return value :: (← readRadixWeights count (mask / 4))
def readPairDeltas:Nat → Nat → Reader (List (Nat × Nat))
  | 0,_ => pure []
  | count + 1,previous => do
    let rank:=previous + (← readNat)
    return (rank / 64,rank % 64) :: (← readPairDeltas count rank)
def readTree (table:Array LinearWitness):Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree table fuel) (← readTree table fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree table fuel) (← readTree table fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree table fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree table fuel)
    | 5 => return .psd
    | 6 => return .support (← readPairs (← readNat))
    | 9 => return .lowerSupport (← readPairs (← readNat))
    | 10 => return .lowerPsd
    | 11 =>
      let pairs ← readPairs (← readNat)
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | 12 =>
      let scale ← readInt
      let weights ← readIntegers (← readNat)
      let pairs ← readPairs (← readNat)
      return .orthantSupport scale weights pairs
    | 13 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .positive scale weights (← readTree table fuel)
    | 14 =>
      let (scale,weights):=table.getD (← readNat) (0,[])
      return .negative scale weights (← readTree table fuel)
    | 15 => return .support (← readPairDeltas (← readNat) 0)
    | 16 => return .lowerSupport (← readPairDeltas (← readNat) 0)
    | 17 =>
      let pairs ← readPairDeltas (← readNat) 0
      let squares ← readSquares (← readNat)
      return .mixedSupport pairs squares
    | 18 =>
      let scale ← readInt
      let count ← readNat
      let weights:=endpointWeights count (← readNat)
      let pairs ← readPairDeltas (← readNat) 0
      return .orthantSupport scale weights pairs
    | 19 =>
      let scale ← readInt
      let count ← readNat
      let weights ← readRadixWeights count (← readNat)
      let pairs ← readPairDeltas (← readNat) 0
      return .orthantSupport scale weights pairs
    | _ => fail
def decode (fuel:Nat) (table:Array LinearWitness) (data:List Nat):Certificate :=
  match readTree table fuel data with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.FiveBitDenseData
private def zz2045:"s07fd"="s07fd":=by decide+kernel
end 
section 
/-  Fixed-field integer arithmetic for the existing certificate language.
The fast check is proved equal to the already justified checker. -/
namespace Green24Proof.EndToEndTupleCheck
open IntegerQuadraticCertificates (Linear Quadratic Point Hinges product linearEval quadraticEval hingeEval)
open OrthantQuadraticCertificates (Certificate Combination NonnegativeTerm Decomposition)
structure Vec where
  a:Int
  b:Int
  c:Int
  d:Int
structure Mat where
  a:Vec
  b:Vec
  c:Vec
  d:Vec
def vec (v:Vec):Linear:=![v.a,v.b,v.c,v.d]
def mat (m:Mat):Quadratic:=![vec m.a,vec m.b,vec m.c,vec m.d]
def ofVec (v:Linear):Vec:=⟨v 0,v 1,v 2,v 3⟩
def ofMat (m:Quadratic):Mat:=⟨ofVec (m 0),ofVec (m 1),ofVec (m 2),ofVec (m 3)⟩
def zeroV:Vec:=⟨0,0,0,0⟩
def zeroM:Mat:=⟨zeroV,zeroV,zeroV,zeroV⟩
def addV (v w:Vec):Vec:=⟨v.a + w.a,v.b + w.b,v.c + w.c,v.d + w.d⟩
def scaleV (k:Int) (v:Vec):Vec:=⟨k * v.a,k * v.b,k * v.c,k * v.d⟩
def addM (m n:Mat):Mat:=⟨addV m.a n.a,addV m.b n.b,addV m.c n.c,addV m.d n.d⟩
def scaleM (k:Int) (m:Mat):Mat:=⟨scaleV k m.a,scaleV k m.b,scaleV k m.c,scaleV k m.d⟩
def productM (v w:Vec):Mat:=⟨scaleV v.a w,scaleV v.b w,scaleV v.c w,scaleV v.d w⟩
theorem vec_ofVec (v:Linear):vec (ofVec v) = v:=by
  funext i
  fin_cases i <;> rfl
theorem mat_ofMat (m:Quadratic):mat (ofMat m) = m:=by
  funext i j
  fin_cases i <;> fin_cases j <;> rfl
private def zz143:"s008f"="s008f":=by decide+kernel
theorem vec_zero:vec zeroV = 0:=by
  funext i
  fin_cases i <;> rfl
theorem mat_zero:mat zeroM = 0:=by
  funext i j
  fin_cases i <;> fin_cases j <;> rfl
theorem vec_add (v w:Vec):vec (addV v w) = vec v + vec w:=by
  funext i
  fin_cases i <;> rfl
theorem vec_scale (k:Int) (v:Vec):vec (scaleV k v) = k • vec v:=by
  funext i
  fin_cases i <;> simp [vec,scaleV,Pi.smul_apply]
private def zz144:"s0090"="s0090":=by decide+kernel
theorem mat_add (m n:Mat):mat (addM m n) = mat m + mat n:=by
  funext i j
  fin_cases i <;> fin_cases j <;> rfl
theorem mat_scale (k:Int) (m:Mat):mat (scaleM k m) = k • mat m:=by
  funext i j
  fin_cases i <;> fin_cases j <;> simp [mat,scaleM,vec,scaleV,Pi.smul_apply]
theorem mat_product (v w:Vec):mat (productM v w) = product (vec v) (vec w):=by
  funext i j
  fin_cases i <;> fin_cases j <;> rfl
def context (C:Nat → Vec):Nat → Linear:=fun i => vec (C i)
def cons (v:Vec) (C:Nat → Vec):Nat → Vec
  | 0 => v
  | i + 1 => C i
theorem context_cons (v:Linear) (C:Nat → Vec) :
    context (cons (ofVec v) C) = OrthantQuadraticCertificates.cons v (context C):=by
  funext i
  cases i with
  | zero => exact vec_ofVec v
  | succ i => rfl
private def zz145:"s0091"="s0091":=by decide+kernel
theorem context_of (C:Nat → Linear):context (fun i => ofVec (C i)) = C:=by
  funext i
  exact vec_ofVec (C i)
def combine (C:Nat → Vec):Combination → Vec
  | [] => zeroV
  | (k,i) :: rest => addV (scaleV k (C i)) (combine C rest)
theorem vec_combine (C:Nat → Vec) (w:Combination) :
    vec (combine C w) = OrthantQuadraticCertificates.combine (context C) w:=by
  induction w with
  | nil => exact vec_zero
  | cons t ts ih =>
    simp only [combine,OrthantQuadraticCertificates.combine,List.map_cons,List.sum_cons,
      vec_add,vec_scale,ih,context]
def term (C:Nat → Vec):NonnegativeTerm → Mat
  | .square v => productM (ofVec v) (ofVec v)
  | .pair i j => productM (C i) (C j)
theorem mat_term (C:Nat → Vec) (t:NonnegativeTerm) :
    mat (term C t) = OrthantQuadraticCertificates.termMatrix (context C) t:=by
  cases t <;> simp only [term,OrthantQuadraticCertificates.termMatrix,mat_product,vec_ofVec,context]
def decompose (C:Nat → Vec):Decomposition → Mat
  | [] => zeroM
  | (k,t) :: rest => addM (scaleM k (term C t)) (decompose C rest)
theorem mat_decompose (C:Nat → Vec) (d:Decomposition) :
    mat (decompose C d) = OrthantQuadraticCertificates.decompositionMatrix (context C) d:=by
  induction d with
  | nil => exact mat_zero
  | cons t ts ih =>
    simp only [decompose,OrthantQuadraticCertificates.decompositionMatrix,List.map_cons,
      List.sum_cons,mat_add,mat_scale,mat_term,ih]
def vecEq (v w:Vec):Bool :=
  [(v.a,w.a),(v.b,w.b),(v.c,w.c),(v.d,w.d)].all fun p => p.1 == p.2
private def zz146:"s0092"="s0092":=by decide+kernel
theorem vecEq_eq (v w:Vec) :
    vecEq v w = IntegerQuadraticCertificates.linearEq (vec v) (vec w):=by
  rfl
def coefficientEq (Q R:Mat):Bool :=
  [(Q.a.a,R.a.a),(Q.b.b,R.b.b),(Q.c.c,R.c.c),(Q.d.d,R.d.d),
   (Q.a.b + Q.b.a,R.a.b + R.b.a),(Q.a.c + Q.c.a,R.a.c + R.c.a),
   (Q.a.d + Q.d.a,R.a.d + R.d.a),(Q.b.c + Q.c.b,R.b.c + R.c.b),
   (Q.b.d + Q.d.b,R.b.d + R.d.b),(Q.c.d + Q.d.c,R.c.d + R.d.c)].all
    fun p => p.1 == p.2
theorem coefficientEq_eq (Q R:Mat) :
    coefficientEq Q R = QuadraticCoefficientCheck.coefficientEq (mat Q) (mat R):=by
  rfl
def combinationCheck (C:Nat → Vec) (s:Int) (w:Combination) (v:Linear):Bool :=
  decide (0 < s) && OrthantQuadraticCertificates.nonnegativeWeights w &&
    vecEq (combine C w) (scaleV s (ofVec v))
theorem combinationCheck_eq (C:Nat → Vec) (s:Int) (w:Combination) (v:Linear) :
    combinationCheck C s w v = OrthantQuadraticCertificates.combinationCheck (context C) s w v:=by
  simp only [combinationCheck,OrthantQuadraticCertificates.combinationCheck,
    vecEq_eq,vec_combine,vec_scale,vec_ofVec]
def decompositionCheck (C:Nat → Vec) (Q:Mat) (s:Int) (d:Decomposition):Bool :=
  decide (0 < s) && (d.all fun t => decide (0 ≤ t.1)) &&
    coefficientEq (decompose C d) (scaleM s Q)
theorem decompositionCheck_eq (C:Nat → Vec) (Q:Mat) (s:Int) (d:Decomposition) :
    decompositionCheck C Q s d =
      OrthantQuadraticCertificates.decompositionCheck (context C) (mat Q) s d:=by
  simp only [decompositionCheck,OrthantQuadraticCertificates.decompositionCheck,
    coefficientEq_eq,mat_decompose,mat_scale]
def coefficients (Q:Mat):Array Int :=
  #[Q.a.a,Q.b.b,Q.c.c,Q.d.d,Q.a.b + Q.b.a,Q.a.c + Q.c.a,
    Q.a.d + Q.d.a,Q.b.c + Q.c.b,Q.b.d + Q.d.b,Q.c.d + Q.d.c]
private def zz147:"s0093"="s0093":=by decide+kernel
theorem coefficients_eq (Q:Mat) :
    coefficients Q = PureIntegerSupportCertificateData.matrixColumn (mat Q):=by
  simp [coefficients,PureIntegerSupportCertificateData.matrixColumn,mat,vec]
theorem pairColumn_eq (a b:Vec) :
    coefficients (productM a b) = PureIntegerSupportCertificateData.pairColumn (vec a) (vec b):=by
  simp [coefficients,productM,scaleV,PureIntegerSupportCertificateData.pairColumn,vec]
def supportDecomposition (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)) :
    Int × Decomposition :=
  if pairs.headD (0,0) == (64,3) then OrthantQuadraticCertificates.FourBasisRecovery.recover (context C) (mat Q) pairs
  else match BacksubIntegerElimination.solveScaled
      (pairs.toArray.map fun (i,j) => coefficients (productM (C i) (C j)))
      (coefficients Q) with
  | none => (0,[])
  | some (scale,weights) =>
      (scale,(weights.toList.zip pairs).map fun (weight,i,j) => (weight, .pair i j))
theorem supportDecomposition_eq (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)) :
    supportDecomposition C Q pairs =
      OrthantQuadraticCertificates.supportDecomposition (context C) (mat Q) pairs:=by
  unfold supportDecomposition OrthantQuadraticCertificates.supportDecomposition
  split
  · rfl
  · simp only [pairColumn_eq]
    simp only [coefficients_eq,context] <;> split <;> simp_all
def mixedSupportDecomposition (C:Nat → Vec) (Q:Mat)
    (pairs:List (Nat × Nat)) (squares:List Linear):Int × Decomposition :=
  let terms:=(pairs.map fun (i,j) => NonnegativeTerm.pair i j) ++
    (squares.map NonnegativeTerm.square)
  match BacksubIntegerElimination.solveScaled
      (terms.toArray.map fun t => coefficients (term C t)) (coefficients Q) with
  | none => (0,[])
  | some (scale,weights) => (scale,weights.toList.zip terms)
theorem mixedSupportDecomposition_eq (C:Nat → Vec) (Q:Mat)
    (pairs:List (Nat × Nat)) (squares:List Linear) :
    mixedSupportDecomposition C Q pairs squares =
      OrthantQuadraticCertificates.mixedSupportDecomposition (context C) (mat Q) pairs squares:=by
  simp only [mixedSupportDecomposition,OrthantQuadraticCertificates.mixedSupportDecomposition,
    coefficients_eq,mat_term] <;> split <;> simp_all
def lowerMatrix:Hinges → Mat
  | [] => zeroM
  | (c,a) :: hs => addM (scaleM (min c 0) (productM (ofVec a) (ofVec a))) (lowerMatrix hs)
private def zz148:"s0094"="s0094":=by decide+kernel
theorem mat_lowerMatrix (hs:Hinges) :
    mat (lowerMatrix hs) = LowerHingeQuadratic.lowerMatrix hs:=by
  induction hs with
  | nil => simp only [lowerMatrix,LowerHingeQuadratic.lowerMatrix,List.map_nil,List.sum_nil,mat_zero]
  | cons h hs ih =>
    obtain ⟨c,a⟩:=h
    simp only [lowerMatrix,LowerHingeQuadratic.lowerMatrix,List.map_cons,List.sum_cons,
      mat_add,mat_scale,mat_product,vec_ofVec,ih]
def positiveV (v:Vec):Vec:=⟨max v.a 0,max v.b 0,max v.c 0,max v.d 0⟩
def negativeV (v:Vec):Vec:=⟨max (-v.a) 0,max (-v.b) 0,max (-v.c) 0,max (-v.d) 0⟩
theorem vec_positiveV (v:Vec):vec (positiveV v) = OrthantHingeBounds.positivePart (vec v):=by
  funext i
  fin_cases i <;> rfl
theorem vec_negativeV (v:Vec):vec (negativeV v) = OrthantHingeBounds.negativePart (vec v):=by
  funext i
  fin_cases i <;> rfl
def squareDifference (a b:Vec):Mat:=addM (productM a a) (scaleM (-1) (productM b b))
theorem mat_squareDifference (a b:Vec) :
    mat (squareDifference a b) = OrthantHingeBounds.squareDifference (vec a) (vec b):=by
  simp only [squareDifference,OrthantHingeBounds.squareDifference,mat_add,mat_scale,mat_product]
def singleLower (scale c t:Int) (a:Linear):Mat :=
  let v:=ofVec a
  if 0 ≤ c then scaleM t (squareDifference v (negativeV v))
  else addM (scaleM (scale * c) (productM v v)) (scaleM t (squareDifference v (positiveV v)))
private def zz149:"s0095"="s0095":=by decide+kernel
theorem mat_singleLower (scale c t:Int) (a:Linear) :
    mat (singleLower scale c t a) = OrthantHingeBounds.singleLower scale c t a:=by
  by_cases hc:0 ≤ c <;>
    simp only [singleLower,OrthantHingeBounds.singleLower,hc,if_true,if_false,
      mat_add,mat_scale,mat_product,mat_squareDifference,vec_positiveV,vec_negativeV,vec_ofVec]
def orthantLowerMatrix (scale:Int):Hinges → List Int → Mat
  | (c,a) :: hs,t :: ts => addM (singleLower scale c t a) (orthantLowerMatrix scale hs ts)
  | _,_ => zeroM
theorem mat_orthantLowerMatrix (scale:Int) (hs:Hinges) (ts:List Int) :
    mat (orthantLowerMatrix scale hs ts) = OrthantHingeBounds.lowerMatrix scale hs ts:=by
  induction hs generalizing ts with
  | nil => cases ts <;> simp only [orthantLowerMatrix,OrthantHingeBounds.lowerMatrix,mat_zero]
  | cons h hs ih =>
    obtain ⟨c,a⟩:=h
    cases ts <;> simp only [orthantLowerMatrix,OrthantHingeBounds.lowerMatrix,
      mat_zero,mat_add,mat_singleLower,ih]
def check (cert:Certificate) (C:Nat → Vec) (Q:Mat) (hs:Hinges):Bool :=
  match cert,hs with
  | .orthantSupport scale weights pairs,hs =>
      let weights:=OrthantQuadraticCertificates.expandWeights scale hs weights
      let lower:=addM (scaleM scale Q) (orthantLowerMatrix scale hs weights)
      let (s,d):=supportDecomposition C lower pairs
      decide (0 < scale) && OrthantHingeBounds.weightsCheck scale hs weights &&
        decompositionCheck C lower s d
  | .lowerSupport pairs,hs =>
      let lower:=addM Q (lowerMatrix hs)
      let (scale,d):=supportDecomposition C lower pairs
      decompositionCheck C lower scale d
  | .lowerPsd,hs => IntegerPSDCheck.check 4 (mat (addM Q (lowerMatrix hs)))
  | .cut a p m,hs => check p (cons (ofVec a) C) Q hs && check m (cons (ofVec (-a)) C) Q hs
  | .mixedSupport pairs squares,[] =>
      let (scale,d):=mixedSupportDecomposition C Q pairs squares
      decompositionCheck C Q scale d
  | .support pairs,[] =>
      let (scale,d):=supportDecomposition C Q pairs
      decompositionCheck C Q scale d
  | .plan scale rows,[] =>
      decompositionCheck C Q scale (OrthantQuadraticCertificates.planDecomposition (mat Q) rows)
  | .psd,[] => IntegerPSDCheck.check 4 (mat Q)
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (cons (ofVec a) C) (addM Q (scaleM c (productM (ofVec a) (ofVec a)))) hs &&
      check m (cons (ofVec (-a)) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (cons (ofVec a) C) (addM Q (scaleM c (productM (ofVec a) (ofVec a)))) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) && check m (cons (ofVec (-a)) C) Q hs
  | _,_ => false
theorem check_eq (cert:Certificate) (C:Nat → Vec) (Q:Mat) (hs:Hinges) :
    check cert C Q hs = OrthantQuadraticCertificates.check cert (context C) (mat Q) hs:=by
  induction cert generalizing C Q hs <;> cases hs <;>
    simp only [check,OrthantQuadraticCertificates.check,combinationCheck_eq,
      decompositionCheck_eq,supportDecomposition_eq,mixedSupportDecomposition_eq,
      mat_add,mat_scale,mat_product,vec_ofVec,context_cons,
      mat_lowerMatrix,mat_orthantLowerMatrix, *]
theorem K {p:Certificate} {s:CheckpointPathData.State}
    (h:check p (fun i => ofVec (s.constraints i)) (ofMat s.quadratic) s.hinges = true :=
      by decide +kernel):CheckpointPathData.V p s:=by
  rw [check_eq,context_of,mat_ofMat] at h
  exact h
end Green24Proof.EndToEndTupleCheck
private def zz2046:"s07fe"="s07fe":=by decide+kernel
namespace Green24Proof.EndToEndTupleState
open IntegerQuadraticCertificates (Linear Quadratic Hinges)
open OrthantQuadraticCertificates (Certificate Combination)
open EndToEndTupleCheck hiding K
structure State where
  constraints:Nat → Vec
  quadratic:Mat
  hinges:Hinges
def initial (C:Nat → Linear) (Q:Quadratic) (hs:Hinges):State :=
  ⟨fun i => ofVec (C i),ofMat Q,hs⟩
def step (positive:Bool) (s:State):State :=
  match s.hinges with
  | [] => s
  | (c,a) :: hs =>
    if positive then
      ⟨cons (ofVec a) s.constraints,
        addM s.quadratic (scaleM c (productM (ofVec a) (ofVec a))),hs⟩
    else ⟨cons (ofVec (-a)) s.constraints,s.quadratic,hs⟩
def follow:Nat → Nat → State → State
  | 0,_,s => s
  | fuel + 1,bits,s =>
    if bits < 2 then s
    else follow fuel (bits / 2) (step (bits % 2 == 1) s)
def path (bits:Nat) (s:State):State:=follow 7 bits s
def V (p:Certificate) (s:State):Prop :=
  check p s.constraints s.quadratic s.hinges = true
def headVector (s:State):Linear:=(s.hinges.headD (0,0)).2
private def zz150:"s0096"="s0096":=by decide+kernel
theorem K {p:Certificate} {s:State}
    (h:V p s:=by unfold V; decide +kernel):V p s:=h
theorem S {p m:Certificate} {s:State}
    (hp:V p (step true s)) (hm:V m (step false s))
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.split p m) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      simpa [V,step,check] using And.intro hp hm
theorem P {scale:Int} {weights:Combination} {p:Certificate} {s:State}
    (hp:V p (step true s))
    (hw:combinationCheck s.constraints scale weights (headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.positive scale weights p) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      simpa [V,step,check,headVector] using And.intro hw hp
theorem M {scale:Int} {weights:Combination} {p:Certificate} {s:State}
    (hp:V p (step false s))
    (hw:combinationCheck s.constraints scale weights (-headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel) :
    V (.negative scale weights p) s:=by
  cases s with
  | mk Cs Q hs =>
    cases hs with
    | nil => cases hne
    | cons h hs =>
      rcases h with ⟨c,a⟩
      simpa [V,step,check,headVector] using And.intro hw hp
private def zz151:"s0097"="s0097":=by decide+kernel
theorem root {p:Certificate} {C:Nat → Linear} {Q:Quadratic} {hs:Hinges}
    (h:V p (initial C Q hs)):OrthantQuadraticCertificates.check p C Q hs = true:=by
  change check p (fun i => ofVec (C i)) (ofMat Q) hs = true at h
  rw [check_eq,context_of,mat_ofMat] at h
  exact h
end Green24Proof.EndToEndTupleState
namespace Green24Proof.EndToEndTupleState
def unpackStateInt (w data i:Nat):Int :=
  let n:=(data >>> (i*w)) % (2^w)
  if n % 2 = 0 then Int.ofNat (n/2) else -(Int.ofNat (n/2))-1
def unpackStateMat (n:Nat):EndToEndTupleCheck.Mat :=
  let w:=n % 256
  let d:=n / 256
  let a:=unpackStateInt w d 0
  let b:=unpackStateInt w d 1
  let c:=unpackStateInt w d 2
  let e:=unpackStateInt w d 3
  let f:=unpackStateInt w d 4
  let g:=unpackStateInt w d 5
  let h:=unpackStateInt w d 6
  let i:=unpackStateInt w d 7
  let j:=unpackStateInt w d 8
  let k:=unpackStateInt w d 9
  ⟨⟨a,f,g,h⟩,⟨f,b,i,j⟩,⟨g,i,c,k⟩,⟨h,j,k,e⟩⟩
def qPath (packet:Nat) (s:State):State :=
  let next:=path (packet % 256) s
  ⟨next.constraints,unpackStateMat (packet / 256),next.hinges⟩
end Green24Proof.EndToEndTupleState
private def zz2047:"s07ff"="s07ff":=by decide+kernel
namespace Green24Proof.ExistentialState
open IntegerQuadraticCertificates (Linear Quadratic Hinges)
open OrthantQuadraticCertificates (Certificate Combination)
open EndToEndTupleState (State initial step headVector)
structure V (s:State):Prop where
  checked:∃ p,EndToEndTupleState.V p s
theorem K (p:Certificate) {s:State}
    (h:EndToEndTupleState.V p s:=by unfold EndToEndTupleState.V; decide +kernel):V s :=
  ⟨p,h⟩
theorem S {s:State} (hp:V (step true s)) (hm:V (step false s))
    (hne:s.hinges.isEmpty = false:=by decide +kernel):V s:=by
  obtain ⟨p,hp⟩:=hp.checked
  obtain ⟨m,hm⟩:=hm.checked
  exact ⟨.split p m,EndToEndTupleState.S hp hm hne⟩
theorem P (w:Int × Combination) {s:State} (hp:V (step true s))
    (hw:EndToEndTupleCheck.combinationCheck s.constraints w.1 w.2 (headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel):V s:=by
  obtain ⟨p,hp⟩:=hp.checked
  exact ⟨.positive w.1 w.2 p,EndToEndTupleState.P hp hw hne⟩
theorem M (w:Int × Combination) {s:State} (hp:V (step false s))
    (hw:EndToEndTupleCheck.combinationCheck s.constraints w.1 w.2 (-headVector s) = true:=by decide +kernel)
    (hne:s.hinges.isEmpty = false:=by decide +kernel):V s:=by
  obtain ⟨p,hp⟩:=hp.checked
  exact ⟨.negative w.1 w.2 p,EndToEndTupleState.M hp hw hne⟩
theorem root {C:Nat → Linear} {Q:Quadratic} {hs:Hinges} (h:V (initial C Q hs)) :
    ∃ p,OrthantQuadraticCertificates.check p C Q hs = true:=by
  obtain ⟨p,hp⟩:=h.checked
  exact ⟨p,EndToEndTupleState.root hp⟩
end Green24Proof.ExistentialState
namespace Green24Proof.IndexedNatTreeCheck
open DictionaryOrthantPackedData (LinearWitness)
open EndToEndTupleState (State step headVector)
open EndToEndTupleCheck (combinationCheck)
open ExistentialState (V)
structure Table where
  indexBits:Nat
  data:Array Nat
def readPairs:Nat → Nat → OrthantQuadraticCertificates.Combination
  | 0,_ => []
  | count + 1,code =>
    (Int.ofNat (code % 256),(code >>> 8) % 64) :: readPairs count (code >>> 14)
def witness (table:Table) (index:Nat):LinearWitness :=
  let word:=table.data.getD (index / 64) 0
  let code:=(word >>> (66 * (index % 64))) % (1 <<< 66)
  (Int.ofNat ((code >>> 2) % 256),readPairs (code % 4 + 1) (code >>> 10))
def check (table:Table):Nat → Nat → State → Bool
  | 0,_,_ => false
  | fuel + 1,code,s =>
    if code % 8 = 1 then
      let width:=(code >>> 3) % 65536
      let content:=code >>> 19
      (!s.hinges.isEmpty) &&
        check table fuel (content % (1 <<< width)) (step true s) &&
        check table fuel (content >>> width) (step false s)
    else if code % 8 = 2 then
      let w:=witness table ((code >>> 3) % (1 <<< table.indexBits))
      (!s.hinges.isEmpty) && combinationCheck s.constraints w.1 w.2 (headVector s) &&
        check table fuel (code >>> (3 + table.indexBits)) (step true s)
    else if code % 8 = 3 then
      let w:=witness table ((code >>> 3) % (1 <<< table.indexBits))
      (!s.hinges.isEmpty) && combinationCheck s.constraints w.1 w.2 (-headVector s) &&
        check table fuel (code >>> (3 + table.indexBits)) (step false s)
    else if code % 8 = 0 then
      EndToEndTupleCheck.check (FiveBitDenseData.decode (fuel + 1) #[] [code >>> 3])
        s.constraints s.quadratic s.hinges
    else false
theorem check_sound (table:Table) (fuel code:Nat) (s:State)
    (h:check table fuel code s = true):V s:=by
  induction fuel generalizing code s with
  | zero => simp [check] at h
  | succ fuel ih =>
    simp only [check] at h
    split at h
    · simp only [Bool.and_eq_true] at h
      exact ExistentialState.S (ih _ _ h.1.2) (ih _ _ h.2) (by simpa using h.1.1)
    · split at h
      · simp only [Bool.and_eq_true] at h
        exact ExistentialState.P _ (ih _ _ h.2) h.1.2 (by simpa using h.1.1)
      · split at h
        · simp only [Bool.and_eq_true] at h
          exact ExistentialState.M _ (ih _ _ h.2) h.1.2 (by simpa using h.1.1)
        · split at h
          · exact ⟨_,h⟩
          · cases h
theorem K (fuel:Nat) (table:Table) (code:Nat) {s:State}
    (h:check table fuel code s = true:=by decide +kernel):V s :=
  check_sound table fuel code s h
end Green24Proof.IndexedNatTreeCheck
namespace Green24Proof.DynamicHingeCheck
open IntegerQuadraticCertificates
open EndToEndTupleCheck hiding check
open OrthantQuadraticCertificates (Combination Decomposition)

def pick : Nat → Hinges → (Int × Linear) × Hinges
  | _, [] => ((0, 0), [])
  | 0, h :: hs => (h, hs)
  | n+1, h :: hs =>
    let selected := pick n hs
    (selected.1, h :: selected.2)

theorem pick_eval (n : Nat) (hs : Hinges) (x : Point) :
    hingeEval ((pick n hs).1 :: (pick n hs).2) x = hingeEval hs x := by
  induction n generalizing hs with
  | zero => cases hs <;> simp [pick, hingeEval]
  | succ n ih =>
    cases hs with
    | nil => simp [pick, hingeEval]
    | cons h hs =>
      simp only [pick]
      have hi := ih hs
      simp only [hingeEval, List.map_cons, List.sum_cons] at hi ⊢
      rw [← hi]
      ring

inductive Tree where
  | raw (p : OrthantQuadraticCertificates.Certificate)
  | mixed (scale : Int) (weights : List Int) (d : Decomposition)
  | split (p m : Tree)
  | cut (a : Linear) (p m : Tree)
  | positive (scale : Int) (w : Combination) (p : Tree)
  | negative (scale : Int) (w : Combination) (m : Tree)
  | positiveAt (index : Nat) (scale : Int) (w : Combination) (p : Tree)
  | negativeAt (index : Nat) (scale : Int) (w : Combination) (m : Tree)

def check (t : Tree) (C : Nat → Vec) (Q : Mat) (hs : Hinges) : Bool :=
  match t, hs with
  | .raw p, hs => EndToEndTupleCheck.check p C Q hs
  | .mixed scale weights d, hs =>
    let lower := addM (scaleM scale Q) (orthantLowerMatrix scale hs weights)
    let remainder := addM lower (scaleM (-1) (decompose C d))
    decide (0 < scale) && OrthantHingeBounds.weightsCheck scale hs weights &&
      ((d.all fun term => decide (0 ≤ term.1)) && IntegerPSDCheck.check 4 (mat remainder))
  | .split p m, (c,a)::hs =>
    check p (cons (ofVec a) C) (addM Q (scaleM c (productM (ofVec a) (ofVec a)))) hs &&
    check m (cons (ofVec (-a)) C) Q hs
  | .cut a p m, hs =>
    check p (cons (ofVec a) C) Q hs && check m (cons (ofVec (-a)) C) Q hs
  | .positive scale w p, (c,a)::hs =>
    combinationCheck C scale w a &&
    check p (cons (ofVec a) C) (addM Q (scaleM c (productM (ofVec a) (ofVec a)))) hs
  | .negative scale w m, (_,a)::hs =>
    combinationCheck C scale w (-a) && check m (cons (ofVec (-a)) C) Q hs
  | .positiveAt index scale w p, hs =>
    let selected := pick index hs
    combinationCheck C scale w selected.1.2 &&
    check p C (addM Q (scaleM selected.1.1 (productM (ofVec selected.1.2) (ofVec selected.1.2)))) selected.2
  | .negativeAt index scale w m, hs =>
    let selected := pick index hs
    combinationCheck C scale w (-selected.1.2) && check m C Q selected.2
  | _, _ => false

theorem check_sound (t : Tree) (C : Nat → Vec) (Q : Mat) (hs : Hinges)
    (x : Point) (hx : ∀ i, 0 ≤ x i)
    (hC : ∀ i, 0 ≤ linearEval (context C i) x)
    (h : check t C Q hs = true) :
    0 ≤ quadraticEval (mat Q) x + hingeEval hs x := by
  induction t generalizing C Q hs with
  | raw p =>
    rw [check, EndToEndTupleCheck.check_eq] at h
    exact OrthantQuadraticCertificates.check_sound p (context C) (mat Q) hs x hx hC h
  | mixed scale weights d =>
    simp only [check, Bool.and_eq_true, decide_eq_true_eq] at h
    apply OrthantHingeBounds.nonnegative_of_lower scale (mat Q) hs weights x hx h.1.1 h.1.2
    have hp := OrthantQuadraticCertificates.decomposition_nonneg (context C) d x hC h.2.1
    have hr := IntegerPSDCheck.check_sound 4 _ h.2.2 x
    change 0 ≤ quadraticEval (mat (addM
      (addM (scaleM scale Q) (orthantLowerMatrix scale hs weights))
      (scaleM (-1) (decompose C d)))) x at hr
    simp only [mat_add, mat_scale, mat_decompose, mat_orthantLowerMatrix,
      quadraticEval_add, quadraticEval_smul, Int.cast_neg, Int.cast_one, neg_one_mul] at hr ⊢
    linarith
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v hs =>
      rcases v with ⟨c,a⟩
      simp only [check, Bool.and_eq_true] at h
      by_cases ha : 0 ≤ linearEval a x
      · apply positive_step (mat Q) c a hs x ha
        have hc := OrthantQuadraticCertificates.cons_constraints (context C) a x hC ha
        rw [← context_cons] at hc
        simpa only [mat_add, mat_scale, mat_product, vec_ofVec] using hp _ _ _ hc h.1
      · have ha' : 0 ≤ linearEval (-a) x := by rw [linearEval_neg]; linarith
        apply negative_step (mat Q) c a hs x (le_of_not_ge ha)
        have hc := OrthantQuadraticCertificates.cons_constraints (context C) (-a) x hC ha'
        rw [← context_cons] at hc
        exact hm _ _ _ hc h.2
  | cut a p m hp hm =>
    simp only [check, Bool.and_eq_true] at h
    by_cases ha : 0 ≤ linearEval a x
    · have hc := OrthantQuadraticCertificates.cons_constraints (context C) a x hC ha
      rw [← context_cons] at hc
      exact hp _ _ _ hc h.1
    · have ha' : 0 ≤ linearEval (-a) x := by rw [linearEval_neg]; linarith
      have hc := OrthantQuadraticCertificates.cons_constraints (context C) (-a) x hC ha'
      rw [← context_cons] at hc
      exact hm _ _ _ hc h.2
  | positive scale w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons v hs =>
      rcases v with ⟨c,a⟩
      simp only [check, Bool.and_eq_true, combinationCheck_eq] at h
      have ha := OrthantQuadraticCertificates.combinationCheck_sound _ _ _ _ x hC h.1
      apply positive_step (mat Q) c a hs x ha
      have hc := OrthantQuadraticCertificates.cons_constraints (context C) a x hC ha
      rw [← context_cons] at hc
      simpa only [mat_add, mat_scale, mat_product, vec_ofVec] using hp _ _ _ hc h.2
  | negative scale w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v hs =>
      rcases v with ⟨c,a⟩
      simp only [check, Bool.and_eq_true, combinationCheck_eq] at h
      have ha := OrthantQuadraticCertificates.combinationCheck_sound _ _ _ _ x hC h.1
      have ha' : linearEval a x ≤ 0 := by rw [linearEval_neg] at ha; linarith
      apply negative_step (mat Q) c a hs x ha'
      have hc := OrthantQuadraticCertificates.cons_constraints (context C) (-a) x hC ha
      rw [← context_cons] at hc
      exact hm _ _ _ hc h.2
  | positiveAt index scale w p hp =>
    simp only [check, Bool.and_eq_true, combinationCheck_eq] at h
    have ha := OrthantQuadraticCertificates.combinationCheck_sound _ _ _ _ x hC h.1
    have hd := hp _ _ _ hC h.2
    have he := positive_step (mat Q) (pick index hs).1.1 (pick index hs).1.2
      (pick index hs).2 x ha
      (by simpa only [mat_add, mat_scale, mat_product, vec_ofVec] using hd)
    simpa only [Prod.mk.eta, pick_eval] using he
  | negativeAt index scale w m hm =>
    simp only [check, Bool.and_eq_true, combinationCheck_eq] at h
    have ha := OrthantQuadraticCertificates.combinationCheck_sound _ _ _ _ x hC h.1
    have ha' : linearEval (pick index hs).1.2 x ≤ 0 := by
      rw [linearEval_neg] at ha
      linarith
    have he := negative_step (mat Q) (pick index hs).1.1 (pick index hs).1.2
      (pick index hs).2 x ha' (hm _ _ _ hC h.2)
    simpa only [Prod.mk.eta, pick_eval] using he
end Green24Proof.DynamicHingeCheck

namespace Green24Proof.DynamicPackedCheck
open IntegerQuadraticCertificates (Linear Hinges)
open EndToEndTupleCheck
open OrthantQuadraticCertificates (Combination Decomposition)
open DynamicHingeCheck (Tree pick)

structure Tables where
  stride : Nat
  witnesses : Array Nat
  cuts : Array Linear

def witnessCode (tables : Tables) (index : Nat) : Nat :=
  let word := tables.witnesses.getD (index / 64) 0
  (word >>> (tables.stride * (index % 64))) % (1 <<< tables.stride)

def readPairs (width : Nat) : Nat → Nat → Combination
  | 0, _ => []
  | n+1, code =>
    (Int.ofNat (code % (1 <<< width)), (code >>> width) % 64) ::
      readPairs width n (code >>> (width + 6))

def witness (code : Nat) : Int × Combination :=
  let width := code % 1024
  let count := (code >>> 10) % 16
  let body := code >>> 14
  (Int.ofNat (body % (1 <<< width)), readPairs width count (body >>> width))

def readWeights : Nat → Nat → Nat → Int → Hinges → List Int × Nat
  | 0, _, code, _, _ => ([], code)
  | _+1, _, code, _, [] => ([], code)
  | n+1, width, code, scale, (c,_)::hs =>
    let tag := code % 4
    let value := if tag = 1 then scale * Int.ofNat c.natAbs
      else if tag = 2 then Int.ofNat ((code >>> 2) % (1 <<< width)) else 0
    let next := if tag = 2 then code >>> (2 + width) else code >>> 2
    let rest := readWeights n width next scale hs
    (value :: rest.1, rest.2)

def readTerms (width : Nat) : Nat → Nat → Decomposition
  | 0, _ => []
  | n+1, code =>
    let weight := Int.ofNat (code % (1 <<< width))
    let i := (code >>> width) % 64
    let j := (code >>> (width+6)) % 64
    let rest := readTerms width n (code >>> (width+12))
    if i = j then (weight, .pair i j) :: rest
    else (weight, .pair i j) :: (weight, .pair j i) :: rest

def leaf (code : Nat) (hs : Hinges) : Tree :=
  let scaleWidth := code % 1024
  let width := (code >>> 10) % 1024
  let count := (code >>> 20) % 64
  let terms := (code >>> 26) % 16
  let body := code >>> 30
  let scale := Int.ofNat (body % (1 <<< scaleWidth))
  let weights := readWeights count width (body >>> scaleWidth) scale hs
  .mixed scale weights.1 (readTerms width terms weights.2)

def readSupportPairs : Nat → Nat → List (Nat × Nat) × Nat
  | 0, code => ([], code)
  | n+1, code =>
    let rest := readSupportPairs n (code >>> 12)
    (((code % 64, (code >>> 6) % 64) :: rest.1), rest.2)

def signed (n : Nat) : Int := if n % 2 = 0 then Int.ofNat (n / 2) else -(Int.ofNat (n / 2) + 1)

def readSquares : Nat → Nat → List Linear
  | 0, _ => []
  | n+1, code =>
    let width := code % 1024
    let data := code >>> 10
    let mask := 1 <<< width
    ![signed (data % mask), signed ((data >>> width) % mask),
      signed ((data >>> (2 * width)) % mask), signed ((data >>> (3 * width)) % mask)] ::
      readSquares n (data >>> (4 * width))

def symmetricTerms (d : Decomposition) : Decomposition :=
  d.flatMap fun (w, t) => match t with
    | .pair i j => [(w, .pair i j), (w, .pair j i)]
    | .square a => [(2 * w, .square a)]

def supportLeaf (code : Nat) (C : Nat → Vec) (Q : Mat) (hs : Hinges) : Tree :=
  let scaleWidth := code % 1024
  let width := (code >>> 10) % 1024
  let count := (code >>> 20) % 64
  let terms := (code >>> 26) % 16
  let body := code >>> 30
  let scale := Int.ofNat (body % (1 <<< scaleWidth))
  let weights := readWeights count width (body >>> scaleWidth) scale hs
  let pairs := readSupportPairs terms weights.2
  let squares := readSquares (pairs.2 % 16) (pairs.2 >>> 4)
  let lower := addM (scaleM scale Q) (orthantLowerMatrix scale hs weights.1)
  let recovered := mixedSupportDecomposition C lower pairs.1 squares
  .mixed (2 * scale * recovered.1) (weights.1.map fun t => 2 * t * recovered.1)
    (symmetricTerms recovered.2)

def check (tables : Tables) : Nat → Nat → (Nat → Vec) → Mat → Hinges → Bool
  | 0, _, _, _, _ => false
  | fuel+1, code, C, Q, hs =>
    if code % 8 = 0 ∨ code % 8 = 5 then
      DynamicHingeCheck.check
        (if code % 8 = 5 then supportLeaf (code >>> 3) C Q hs else leaf (code >>> 3) hs) C Q hs
    else if code % 8 = 1 then
      match hs with
      | [] => false
      | (c,a)::tail =>
        let width := (code >>> 3) % (1 <<< 24)
        let data := code >>> 27
        check tables fuel (data % (1 <<< width)) (cons (ofVec a) C)
          (addM Q (scaleM c (productM (ofVec a) (ofVec a)))) tail &&
        check tables fuel (data >>> width) (cons (ofVec (-a)) C) Q tail
    else if code % 8 = 2 then
      let index := (code >>> 3) % 64
      let w := witness (witnessCode tables ((code >>> 9) % 4096))
      let selected := pick index hs
      combinationCheck C w.1 w.2 selected.1.2 &&
        check tables fuel (code >>> 21) C
          (addM Q (scaleM selected.1.1 (productM (ofVec selected.1.2) (ofVec selected.1.2)))) selected.2
    else if code % 8 = 3 then
      let index := (code >>> 3) % 64
      let w := witness (witnessCode tables ((code >>> 9) % 4096))
      let selected := pick index hs
      combinationCheck C w.1 w.2 (-selected.1.2) &&
        check tables fuel (code >>> 21) C Q selected.2
    else if code % 8 = 4 then
      let a := tables.cuts.getD ((code >>> 3) % 4096) 0
      let width := (code >>> 15) % (1 <<< 24)
      let data := code >>> 39
      check tables fuel (data % (1 <<< width)) (cons (ofVec a) C) Q hs &&
        check tables fuel (data >>> width) (cons (ofVec (-a)) C) Q hs
    else false

theorem check_exists (tables : Tables) (fuel code : Nat) (C : Nat → Vec) (Q : Mat) (hs : Hinges)
    (h : check tables fuel code C Q hs = true) :
    ∃ t, DynamicHingeCheck.check t C Q hs = true := by
  induction fuel generalizing code C Q hs with
  | zero => cases h
  | succ fuel ih =>
    simp only [check] at h
    split at h
    · exact ⟨_, h⟩
    · split at h
      · cases hs with
        | nil => cases h
        | cons head tail =>
          rcases head with ⟨c,a⟩
          simp only [Bool.and_eq_true] at h
          obtain ⟨p,hp⟩ := ih _ _ _ _ h.1
          obtain ⟨m,hm⟩ := ih _ _ _ _ h.2
          exact ⟨.split p m, by simpa only [DynamicHingeCheck.check, Bool.and_eq_true] using And.intro hp hm⟩
      · split at h
        · simp only [Bool.and_eq_true] at h
          obtain ⟨p,hp⟩ := ih _ _ _ _ h.2
          exact ⟨.positiveAt _ _ _ p, by simpa only [DynamicHingeCheck.check, Bool.and_eq_true] using And.intro h.1 hp⟩
        · split at h
          · simp only [Bool.and_eq_true] at h
            obtain ⟨m,hm⟩ := ih _ _ _ _ h.2
            exact ⟨.negativeAt _ _ _ m, by simpa only [DynamicHingeCheck.check, Bool.and_eq_true] using And.intro h.1 hm⟩
          · split at h
            · simp only [Bool.and_eq_true] at h
              obtain ⟨p,hp⟩ := ih _ _ _ _ h.1
              obtain ⟨m,hm⟩ := ih _ _ _ _ h.2
              exact ⟨.cut _ p m, by simpa only [DynamicHingeCheck.check, Bool.and_eq_true] using And.intro hp hm⟩
            · cases h

theorem check_sound (tables : Tables) (fuel code : Nat) (C : Nat → Vec) (Q : Mat) (hs : Hinges)
    (x : IntegerQuadraticCertificates.Point) (hx : ∀ i, 0 ≤ x i)
    (hC : ∀ i, 0 ≤ IntegerQuadraticCertificates.linearEval (context C i) x)
    (h : check tables fuel code C Q hs = true) :
    0 ≤ IntegerQuadraticCertificates.quadraticEval (mat Q) x + IntegerQuadraticCertificates.hingeEval hs x := by
  obtain ⟨t,ht⟩ := check_exists tables fuel code C Q hs h
  exact DynamicHingeCheck.check_sound t C Q hs x hx hC ht
end Green24Proof.DynamicPackedCheck

namespace Green24Proof.DynamicPackedCheck
open IntegerQuadraticCertificates (Quadratic Hinges Point linearEval quadraticEval hingeEval)

theorem scalar_nonnegative (tables : Tables) (fuel code : Nat) (Q : Quadratic)
    (hs : Hinges) (D : Int)
    (valid : check tables fuel code
      (fun i => EndToEndTupleCheck.ofVec (ScalarRowDefaults.constraintsNat i))
      (EndToEndTupleCheck.ofMat Q) hs = true)
    (hD : 0 ≤ D) (x : Point) (hx : ∀ i, 0 ≤ x i) :
    0 ≤ (quadraticEval Q x + hingeEval hs x) / (D : ℝ) := by
  apply div_nonneg
  · have hC : ∀ i, 0 ≤ linearEval (ScalarRowDefaults.constraintsNat i) x := by
      intro i
      have hc (j : Fin 4) : 0 ≤ linearEval (ScalarRowDefaults.constraints j) x := by
        fin_cases j <;> simpa [ScalarRowDefaults.constraints, linearEval, Fin.sum_univ_succ] using hx _
      exact hc ⟨i % 4, Nat.mod_lt _ (by decide)⟩
    have h := check_sound tables fuel code _ _ hs x hx
      (by simpa only [EndToEndTupleCheck.context_of] using hC) valid
    simpa only [EndToEndTupleCheck.mat_ofMat] using h
  · exact_mod_cast hD
end Green24Proof.DynamicPackedCheck

namespace Green24Proof.QuadParityFourFifthsCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l25 l27 l29 l30 l33 l34 l35 l37 l4 l41 l43 l51 l6 l60)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x9c5fc0d, -0x6dd746b, -0xa4cb5a8,0x703a88], ![-0x6dd746b, -0x34cf3bd5,0xb48304c,0x42c87d5], ![-0xa4cb5a8,0xb48304c, -0x2ca98588,0x6e37a41], ![0x703a88,0x42c87d5,0x6e37a41, -0x36ee800]]
noncomputable def hinges:Hinges:=[(-0x1376e,l6),(0x8f4f6,l4),(0x1425b88,l14),(0xc95b431,l15),(-0x36ee800,l27),(0x36ee800,l29),(-0x1425b88,l25),(0xa12dc4,l30),(0x36ee800,l33),(-0x36ee800,l35),(0x36ee800,l37),(-0x8f4f6,l34),(-0xa12dc4,l43),(-0xc95b431,l41),(0x36ee800,l51),(0x1376e,l60)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x36ee800,l27),(0x36ee800,l29),(0x36ee800,l33),(-0x36ee800,l35),(0x36ee800,l37),(0x36ee800,l51),(0xc95b431,l15),(-0xc95b431,l41),(0x1425b88,l14),(-0x1425b88,l25),(0xa12dc4,l30),(-0xa12dc4,l43),(0x8f4f6,l4),(-0x8f4f6,l34),(-0x1376e,l6),(0x1376e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase0" = "QuadParityFourFifthsCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase0
private def zz2048:"s0800"="s0800":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityFourFifthsCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l25 l27 l29 l30 l33 l34 l35 l37 l4 l41 l43 l46 l51 l6 l60 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa5a8144, -0x6dd746b, -0xa4cb5a8,0x59c241], ![-0x6dd746b, -0x346708f4,0xaf1de58,0x459eb38], ![-0xa4cb5a8,0xaf1de58, -0x2ca98588,0x6e37a41], ![0x59c241,0x459eb38,0x6e37a41, -0x36ee800]]
noncomputable def hinges:Hinges:=[(-0x1376e,l6),(0x8f4f6,l4),(0x16a02dc,l14),(0xc6f4566,l15),(-0x36ee800,l27),(0x36ee800,l29),(-0x16a02dc,l25),(0xbd1e7e,l30),(0x36ee800,l33),(-0x36ee800,l35),(0x36ee800,l37),(-0x8f4f6,l34),(-0xbd1e7e,l43),(-0xc6f4566,l41),(0x13e069,l46),(0x36ee800,l51),(0x1376e,l60),(-0x13e069,l64)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x36ee800,l27),(0x36ee800,l29),(0x36ee800,l33),(-0x36ee800,l35),(0x36ee800,l37),(0x36ee800,l51),(0xc6f4566,l15),(-0xc6f4566,l41),(0x16a02dc,l14),(-0x16a02dc,l25),(0xbd1e7e,l30),(-0xbd1e7e,l43),(0x13e069,l46),(-0x13e069,l64),(0x8f4f6,l4),(-0x8f4f6,l34),(-0x1376e,l6),(0x1376e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0x2e0a03cc02000090130370c040027408c00a4c05000260130064c040000188a4058c0300000000901c802000000002c0c80100026043004cc0400000261301cc0200000098004c804000000019018802000002a1101cc0200000000b014802a20ca10805c100500000001a014802000000005018802000138110058c0400250982402d003000000078024803000001e09038c02f208a0b40631005000019894028c03000001b11018c02], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase1" = "QuadParityFourFifthsCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase1
private def zz2049:"s0801"="s0801":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityFourFifthsCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l27 l29 l30 l33 l35 l37 l41 l43 l51 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xafcd975, -0x7270ba8, -0x84c9222,0x258], ![-0x7270ba8, -0x40be2b15,0xd25c75a,0x3beaad5], ![-0x84c9222,0xd25c75a, -0x2ec9040e,0x73c9c1a], ![0x258,0x3beaad5,0x73c9c1a, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x20bca,l6),(0x89418,l10),(0xc95b431,l15),(-0x3938700,l27),(0x3938700,l29),(0xa12dc4,l30),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(-0x5b0094,l43),(-0xb025aad,l41),(0x3938700,l51),(-0x5b0094,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xc95b431,l15),(-0xb025aad,l41),(0xa12dc4,l30),(-0x5b0094,l43),(-0x5b0094,l62),(0x89418,l10),(-0x20bca,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1a014802000000000280c4010000000443c0530080004a1304805a0060000000078024803000150901603c801800000034240f3008000000003c02900400001a8110050c04000000d02201c601800000064580e300800861202803d20080000000022014802000000150a81c6010018c32088096401000003c320a02a004000000151103cc0200000000d060660080000003c1c0a30080000000241819802003c0841a0271004000000000480c401000000882101a300c000000221a07980400000000e140cc01a10520210019a803001582405809d401000a41502401ea008005c0a01c0175004000000004c0124018000000003805200800000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 14 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase2" = "QuadParityFourFifthsCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 14 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase2
private def zz2050:"s0802"="s0802":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityFourFifthsCase3
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l27 l29 l30 l33 l35 l37 l41 l43 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xce18fae, -0x7270ba8, -0x8a215be,0x3e1690], ![-0x7270ba8, -0x41a446ec,0xcda4c2a,0x3ec0e38], ![-0x8a215be,0xcda4c2a, -0x2ec9040e,0x73c9c1a], ![0x3e1690,0x3ec0e38,0x73c9c1a, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x20bca,l6),(0x89418,l10),(0x111418,l14),(0xc6f4566,l15),(-0x3938700,l27),(0x3938700,l29),(0xbd1e7e,l30),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(-0x71e955,l43),(-0xa5da709,l41),(0x6235e,l46),(0x3938700,l51),(-0x98a38e,l62),(-0x8a830,l64)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xc6f4566,l15),(-0xa5da709,l41),(0xbd1e7e,l30),(-0x98a38e,l62),(-0x71e955,l43),(0x111418,l14),(-0x8a830,l64),(0x89418,l10),(0x6235e,l46),(-0x20bca,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase3" = "QuadParityFourFifthsCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase3
private def zz2051:"s0803"="s0803":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityFourFifthsCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l35 l37 l38 l41 l43 l51 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xad3bbdc, -0x71e4793, -0x84c9222,0x258], ![-0x71e4793, -0x3d0e3b75,0xaa2efb4,0x4d7cc03], ![-0x84c9222,0xaa2efb4, -0x2f23493f,0x7551fd2], ![0x258,0x4d7cc03,0x7551fd2, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x6b182,l6),(0x131ff9,l10),(0x5b0094,l17),(0xb025aad,l15),(-0x3938700,l27),(0x3938700,l29),(0x5b0094,l30),(0x3938700,l33),(-0x131ff9,l38),(-0x3938700,l35),(0x3938700,l37),(-0x5b0094,l43),(-0xb025aad,l41),(0x3938700,l51),(0x6b182,l60),(-0x5b0094,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xb025aad,l15),(-0xb025aad,l41),(0x5b0094,l17),(0x5b0094,l30),(-0x5b0094,l43),(-0x5b0094,l62),(0x131ff9,l10),(-0x131ff9,l38),(-0x6b182,l6),(0x6b182,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x2600132010000000000a031004000000110f014c020001284c12016801800000001e009200c000000150009900800010211c0940c05000000068301c6010000a8480b01e400c0000001a120798040000001e09038c02000000000f00a401000006a0440143010000340208013180a000001a044038c030000000e8300c601000000064580e30080000000345819802000000250d028c020001a0841805c8018010c2405007a401000c42904604b2008000000220d038c02000000150a81c601000000000a805200800078330500d200600630c822025900400000f0c8280a801000000054440f300800000003418198020000000f07028c0200000005c00264020000000005805200818c118158079200a0000000120c0cc010000000d0681c6010000000006805200800f81e04203c2008003c0841a0271004000000000480c40100000006c2c0a300800000441080d180600000000220148020000000682814601002605810c07a4010000421c0700f2006000000110d03cc020000000a8700c601000000038240e300800000001c28198020000011854028c03a10520210019a803001582405809d401000a41502401ea008005c0a01c0175004000000004c0124018000000003805200800000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase4" = "QuadParityFourFifthsCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase4
private def zz2052:"s0804"="s0804":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityFourFifthsCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l35 l37 l38 l41 l43 l51 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc70abc3, -0x71e4793, -0x8a215be,0x258], ![-0x71e4793, -0x3d755994,0xaa2a466,0x4db37f4], ![-0x8a215be,0xaa2a466, -0x2f23493f,0x7551fd2], ![0x258,0x4db37f4,0x7551fd2, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x6b182,l6),(0x131ff9,l10),(0x98a38e,l17),(0xa5da709,l15),(-0x3938700,l27),(0x3938700,l29),(0x71e955,l30),(0x3938700,l33),(-0x131ff9,l38),(-0x3938700,l35),(0x3938700,l37),(-0x71e955,l43),(-0xa5da709,l41),(0x3938700,l51),(0x6b182,l60),(-0x98a38e,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xa5da709,l15),(-0xa5da709,l41),(0x98a38e,l17),(-0x98a38e,l62),(0x71e955,l30),(-0x71e955,l43),(0x131ff9,l10),(-0x131ff9,l38),(-0x6b182,l6),(0x6b182,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityFourFifthsCase5" = "QuadParityFourFifthsCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityFourFifthsCase5
private def zz2053:"s0805"="s0805":=by decide+kernel
end 
section 
namespace Green24Proof.ParityFourFifthsRows
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x105c002b196c004eeee407a898018b657068da00217068da00207d34ca5d004aa8601d37a898004f4c6537a898012c99a13068da00201c304e2ad80019f81d24304e2ad80289682030198cba025b4b65604e2ad801cae98a21602b196c00e97a59e07d20198cba0118a865204e2ad8022a3888e1204e2ad802387da9e01c20198cba005d482ee4202b196c008f7f1f601824ca5d002c2ade2023d84c00280938614]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x101d502b196c004e2c78e5502b196c005cbaa9603950198cba001b680ca029504e2ad803adbce9e01950198cba001b680ca1502b196c006bdacca03c13d84c00197a5e602c102b196c02194aea2410386d00203810198cba002c2ade202817a89800db69efe010386d00203d404e2ad800198fff205d402b196c01ae382547a898004d786440386d00203d00386d02bf605d03d84c001d1c2502692e829e202c002b196c00bf8d214]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103d504e2ad80078fa5aa02d504e2ad8037a4b48602]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2
def mu:Phase → ℚ:=![(0x43c7773 / 0x4c4b40),(-0x3e2f8fb / 0x4c4b40)]
def parameter:ℚ:=(4 / 5)
def normalization:ℚ:=(1 / 0x186a)
def quad0:Expression:=quadSlack rows parameter 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadParityFourFifthsCase0.base QuadParityFourFifthsCase0.hinges QuadParityFourFifthsCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
private def zz158:"s009e"="s009e":=by decide+kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase0.base QuadParityFourFifthsCase0.hinges QuadParityFourFifthsCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows parameter 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r30,RewriteAtoms.r25,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadParityFourFifthsCase1.base QuadParityFourFifthsCase1.hinges QuadParityFourFifthsCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase1.base QuadParityFourFifthsCase1.hinges QuadParityFourFifthsCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows parameter 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r19,RewriteAtoms.r3,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadParityFourFifthsCase2.base QuadParityFourFifthsCase2.hinges QuadParityFourFifthsCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
private def zz159:"s009f"="s009f":=by decide+kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase2.base QuadParityFourFifthsCase2.hinges QuadParityFourFifthsCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows parameter 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r3,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadParityFourFifthsCase3.base QuadParityFourFifthsCase3.hinges QuadParityFourFifthsCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase3.base QuadParityFourFifthsCase3.hinges QuadParityFourFifthsCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows parameter 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadParityFourFifthsCase4.base QuadParityFourFifthsCase4.hinges QuadParityFourFifthsCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
private def zz160:"s00a0"="s00a0":=by decide+kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase4.base QuadParityFourFifthsCase4.hinges QuadParityFourFifthsCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows parameter 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadParityFourFifthsCase5.base QuadParityFourFifthsCase5.hinges QuadParityFourFifthsCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityFourFifthsCase5.base QuadParityFourFifthsCase5.hinges QuadParityFourFifthsCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityFourFifthsCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows parameter mu normalization 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_6_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_6_hinges
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
private def zz161:"s00a1"="s00a1":=by decide+kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_6_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows parameter mu normalization 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_7_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_7_hinges
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_7_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_7_hinges x
private def zz162:"s00a2"="s00a2":=by decide+kernel
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows parameter mu normalization 0 1 false
def pair8Rewrites:Rewrites:=[]
def pair8Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_8_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_8_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_8_hinges x
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows parameter mu normalization 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair9Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_9_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_9_hinges
private def zz163:"s00a3"="s00a3":=by decide+kernel
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_9_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_9_hinges x
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows parameter mu normalization 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_10_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_10_hinges
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
private def zz164:"s00a4"="s00a4":=by decide+kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_10_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows parameter mu normalization 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair11Target:NormalForm:=CompactPair.toNormal LocalParityFourFifthsPairs.compact_parityFourFifths_pair_11_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_11_hinges
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalParityFourFifthsPairs.parityFourFifths_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityFourFifthsPairs.compact_parityFourFifths_pair_11_base LocalParityFourFifthsPairs.compact_parityFourFifths_pair_11_hinges x
private def zz165:"s00a5"="s00a5":=by decide+kernel
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalParityFourFifthsPairs.parityFourFifths_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows parameter p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows parameter mu normalization p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ParityFourFifthsRows
private def zz2054:"s0806"="s0806":=by decide+kernel
end 
section 
namespace Green24Proof.ParityFourFifths
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ParityFourFifthsRows.rows ParityFourFifthsRows.parameter p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityFourFifthsRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ParityFourFifthsRows.rows ParityFourFifthsRows.parameter p q same x]
    exact ParityFourFifthsRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz166:"s00a6"="s00a6":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ParityFourFifthsRows.rows ParityFourFifthsRows.parameter ParityFourFifthsRows.mu ParityFourFifthsRows.normalization p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityFourFifthsRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ParityFourFifthsRows.rows ParityFourFifthsRows.parameter ParityFourFifthsRows.mu ParityFourFifthsRows.normalization p q same x]
    exact ParityFourFifthsRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible ParityFourFifthsRows.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  ((4 / 5:ℝ) * U - V) * ((-0x1600b73 / 0x1312d00:ℝ) * U + (0x1809efb / 0x1312d00:ℝ) * V) -
    (1 / 0x61a8:ℝ) * (U + V) ^ 2
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 25:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ParityCorrectionAggregation.correction_of_local_rows h3 h5
    ParityFourFifthsRows.rows ParityFourFifthsRows.parameter ParityFourFifthsRows.mu
    ParityFourFifthsRows.normalization rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ParityFourFifthsRows.mu 0 = (0x43c7773 / 0x4c4b40:ℚ):=by decide +kernel
  have hmu1:ParityFourFifthsRows.mu 1 = (-0x3e2f8fb / 0x4c4b40:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num [ParityFourFifthsRows.parameter,ParityFourFifthsRows.normalization] at hc
  unfold massCorrection
  nlinarith only [hc]
theorem massCorrection_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(11 / 10:ℝ) * V ≤ U) (hhigh:U ≤ (31 / 25:ℝ) * V) :
    (0x416319 / 0x12a05f200:ℝ) * V ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith
private def zz167:"s00a7"="s00a7":=by decide+kernel
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (31 / 25:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_lower_bound hV hlow hhigh
  nlinarith [sq_nonneg (mass v)]
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(11 / 10:ℝ) * V ≤ U) (hhigh:U ≤ (31 / 25:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [sq_nonneg V]
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (31 / 25:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ParityFourFifths
private def zz2055:"s0807"="s0807":=by decide+kernel
end 
section 
namespace Green24Proof.LocalParityTwoThirdsPairs
def compact_parityTwoThirds_pair_6_base:CompactPair.Quadratic:=⟨(-1 / 0xe4e1c0),(0x7d1 / 0x1312d00),0⟩
def compact_parityTwoThirds_pair_6_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x7270e00),1, -3⟩,⟨(1 / 0x7270e00),3, -1⟩]
noncomputable def parityTwoThirds_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_6_base compact_parityTwoThirds_pair_6_hinges x y
def compact_parityTwoThirds_pair_6_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityTwoThirds_pair_6_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_6_base compact_parityTwoThirds_pair_6_hinges 0 compact_parityTwoThirds_pair_6_cuts = true :=
  by decide +kernel
private def zz168:"s00a8"="s00a8":=by decide+kernel
theorem compact_parityTwoThirds_pair_6_representation (x y:ℝ) :
    parityTwoThirds_pair_6 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_6_base compact_parityTwoThirds_pair_6_hinges x y:=by rfl
theorem parityTwoThirds_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_6 x y:=by
  rw [compact_parityTwoThirds_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_6_check hy (by simpa using hx)
def compact_parityTwoThirds_pair_7_base:CompactPair.Quadratic:=⟨(-1 / 0xe4e1c0),(0x191 / 0x989680),0⟩
def compact_parityTwoThirds_pair_7_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x7270e00),1, -3⟩,⟨(1 / 0x7270e00),3, -1⟩]
noncomputable def parityTwoThirds_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_7_base compact_parityTwoThirds_pair_7_hinges x y
def compact_parityTwoThirds_pair_7_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityTwoThirds_pair_7_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_7_base compact_parityTwoThirds_pair_7_hinges 0 compact_parityTwoThirds_pair_7_cuts = true :=
  by decide +kernel
theorem compact_parityTwoThirds_pair_7_representation (x y:ℝ) :
    parityTwoThirds_pair_7 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_7_base compact_parityTwoThirds_pair_7_hinges x y:=by rfl
private def zz169:"s00a9"="s00a9":=by decide+kernel
theorem parityTwoThirds_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_7 x y:=by
  rw [compact_parityTwoThirds_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_7_check hy (by simpa using hx)
def compact_parityTwoThirds_pair_8_base:CompactPair.Quadratic:=⟨0,(0x1069 / 0x1c9c380),0⟩
def compact_parityTwoThirds_pair_8_hinges:List CompactPair.Hinge:=[]
noncomputable def parityTwoThirds_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_8_base compact_parityTwoThirds_pair_8_hinges x y
def compact_parityTwoThirds_pair_8_cuts:List ℚ:=[]
theorem compact_parityTwoThirds_pair_8_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_8_base compact_parityTwoThirds_pair_8_hinges 0 compact_parityTwoThirds_pair_8_cuts = true :=
  by decide +kernel
theorem compact_parityTwoThirds_pair_8_representation (x y:ℝ) :
    parityTwoThirds_pair_8 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_8_base compact_parityTwoThirds_pair_8_hinges x y:=by rfl
theorem parityTwoThirds_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_8 x y:=by
  rw [compact_parityTwoThirds_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_8_check hy (by simpa using hx)
def compact_parityTwoThirds_pair_9_base:CompactPair.Quadratic:=⟨(-1 / 0x3938700),(0x961 / 0x1c9c380),0⟩
def compact_parityTwoThirds_pair_9_hinges:List CompactPair.Hinge:=[⟨(1 / 0x3938700),1, -3⟩]
noncomputable def parityTwoThirds_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_9_base compact_parityTwoThirds_pair_9_hinges x y
def compact_parityTwoThirds_pair_9_cuts:List ℚ:=[3]
private def zz170:"s00aa"="s00aa":=by decide+kernel
theorem compact_parityTwoThirds_pair_9_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_9_base compact_parityTwoThirds_pair_9_hinges 0 compact_parityTwoThirds_pair_9_cuts = true :=
  by decide +kernel
theorem compact_parityTwoThirds_pair_9_representation (x y:ℝ) :
    parityTwoThirds_pair_9 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_9_base compact_parityTwoThirds_pair_9_hinges x y:=by rfl
theorem parityTwoThirds_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_9 x y:=by
  rw [compact_parityTwoThirds_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_9_check hy (by simpa using hx)
def compact_parityTwoThirds_pair_10_base:CompactPair.Quadratic:=⟨0,(1 / 0x2710),0⟩
def compact_parityTwoThirds_pair_10_hinges:List CompactPair.Hinge:=[]
noncomputable def parityTwoThirds_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_10_base compact_parityTwoThirds_pair_10_hinges x y
def compact_parityTwoThirds_pair_10_cuts:List ℚ:=[]
theorem compact_parityTwoThirds_pair_10_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_10_base compact_parityTwoThirds_pair_10_hinges 0 compact_parityTwoThirds_pair_10_cuts = true :=
  by decide +kernel
private def zz171:"s00ab"="s00ab":=by decide+kernel
theorem compact_parityTwoThirds_pair_10_representation (x y:ℝ) :
    parityTwoThirds_pair_10 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_10_base compact_parityTwoThirds_pair_10_hinges x y:=by rfl
theorem parityTwoThirds_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_10 x y:=by
  rw [compact_parityTwoThirds_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_10_check hy (by simpa using hx)
def compact_parityTwoThirds_pair_11_base:CompactPair.Quadratic:=⟨(1 / 0xe4e1c0),(0x191 / 0x989680),0⟩
def compact_parityTwoThirds_pair_11_hinges:List CompactPair.Hinge:=[⟨(1 / 0x7270e00),1, -3⟩,⟨(-1 / 0x7270e00),3, -1⟩]
noncomputable def parityTwoThirds_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoThirds_pair_11_base compact_parityTwoThirds_pair_11_hinges x y
def compact_parityTwoThirds_pair_11_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityTwoThirds_pair_11_check :
    CompactPair.expressionCheckPSD compact_parityTwoThirds_pair_11_base compact_parityTwoThirds_pair_11_hinges 0 compact_parityTwoThirds_pair_11_cuts = true :=
  by decide +kernel
theorem compact_parityTwoThirds_pair_11_representation (x y:ℝ) :
    parityTwoThirds_pair_11 x y = CompactPair.expressionEval compact_parityTwoThirds_pair_11_base compact_parityTwoThirds_pair_11_hinges x y:=by rfl
private def zz172:"s00ac"="s00ac":=by decide+kernel
theorem parityTwoThirds_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoThirds_pair_11 x y:=by
  rw [compact_parityTwoThirds_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoThirds_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalParityTwoThirdsPairs
private def zz2056:"s0808"="s0808":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1ea34645, -0x12fb4de2, -0x1c9c30f8,0x1e12dc5], ![-0x12fb4de2, -0x81289b88,0x15ea185a,0xefa81e4], ![-0x1c9c30f8,0x15ea185a, -0x7c0fae45,0x133fbd1f], ![0x1e12dc5,0xefa81e4,0x133fbd1f, -0x9896800]]
noncomputable def hinges:Hinges:=[(-0x1a899e,l6),(0x7f93d7,l4),(-0x8d954,l10),(0x85b01b0,l14),(0x75b54a,l17),(0x1b88069e,l15),(-0x9896800,l27),(0x9896800,l29),(-0x85b01b0,l25),(0x4e48420,l30),(0x9896800,l33),(0x8d954,l38),(-0x9896800,l35),(0x9896800,l37),(-0x7f93d7,l34),(-0x4e48420,l43),(-0x1b88069e,l41),(0x829bff,l46),(0x9896800,l51),(0x1a899e,l60),(-0x75b54a,l62),(-0x829bff,l64)]
def normalizationDenominator:ℤ:=0x15752a00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x9896800,l27),(0x9896800,l29),(0x9896800,l33),(-0x9896800,l35),(0x9896800,l37),(0x9896800,l51),(0x85b01b0,l14),(-0x85b01b0,l25),(0x1b88069e,l15),(-0x1b88069e,l41),(0x4e48420,l30),(-0x4e48420,l43),(0x829bff,l46),(-0x829bff,l64),(0x75b54a,l17),(-0x75b54a,l62),(0x7f93d7,l4),(-0x7f93d7,l34),(-0x1a899e,l6),(0x1a899e,l60),(-0x8d954,l10),(0x8d954,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((0x1c604c93f39a57ee29469851f9a5d794004f390382482038010e34701132a79821ca8fb38c3525d9f1e187546974f0a195fa32182d642b69081372f1f600000005e48a01074021c699d2bec4513000a78548798228a2ce038c0f9051d89e3cedd0c698f08a2e52b061830bd489cc3c0476211ad8a00040669e0a24108406000037841f027e606fdf8667180001e949e3956d5ff878637118ff9e125193cc270344de2799008783ded80000000bc914020f0042260007da3f6798175660cf9c600000d2f078ee5264fe91e18082288dc70330918f62100870c78d1c8800121cdc71e00cb6e) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase0" = "QuadParityTwoThirdsCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase0
private def zz2057:"s0809"="s0809":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x14927d0e, -0x12fb4de2, -0x1c9c30f8,0x18de80a], ![-0x12fb4de2, -0x74b0f3c9,0x15ac7ff7,0xedc5f2b], ![-0x1c9c30f8,0x15ac7ff7, -0x7c0fae45,0x133fbd1f], ![0x18de80a,0xedc5f2b,0x133fbd1f, -0x9896800]]
noncomputable def hinges:Hinges:=[(-0x1a899e,l6),(0x7f93d7,l4),(-0x8d954,l10),(0x9424473,l14),(-0xf5d6de,l17),(0x23a7cbfc,l15),(-0x9896800,l27),(0x9896800,l29),(-0x9424473,l25),(0x390c2eb,l30),(0x9896800,l33),(0x8d954,l38),(-0x9896800,l35),(0x9896800,l37),(-0x7f93d7,l34),(-0x390c2eb,l43),(-0x23a7cbfc,l41),(0x9896800,l51),(0x1a899e,l60),(0xf5d6de,l62)]
def normalizationDenominator:ℤ:=0x15752a00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x9896800,l27),(0x9896800,l29),(0x9896800,l33),(-0x9896800,l35),(0x9896800,l37),(0x9896800,l51),(0x9424473,l14),(-0x9424473,l25),(0x23a7cbfc,l15),(-0x23a7cbfc,l41),(0x390c2eb,l30),(-0x390c2eb,l43),(-0xf5d6de,l17),(0xf5d6de,l62),(0x7f93d7,l4),(-0x7f93d7,l34),(-0x1a899e,l6),(0x1a899e,l60),(-0x8d954,l10),(0x8d954,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x640620081842143100b8200a000000001e014802000000000281a40100000000034092008000000000a031004000000110f014c02000009c08802c602000094260900b400c00000000f004900600001a8110050c04000000c812018601800068041002630140000034088071806000000211d03cc020000000001206400800000064580530080000000005819002000001a0b404cc03000000000a812401000000064580b300800000410980a18060000002d0701cc02000000170c81c6010000000a4340a30080000004c2207180400530d02401e9004], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase1" = "QuadParityTwoThirdsCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase1
private def zz2058:"s080a"="s080a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l44 l46 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x57e65eb, -0x39385d4, -0x3d40e8c,0xadb977], ![-0x39385d4, -0x23530d2f,0x6a3a6f7,0x1e67f26], ![-0x3d40e8c,0x6a3a6f7, -0x17beff90,0x3b38cb0], ![0xadb977,0x1e67f26,0x3b38cb0, -0x1c9c380]]
noncomputable def hinges:Hinges:=[(-0x100242,l4),(0x100242,l10),(0xfb0caf,l12),(0x139e37,l17),(0x496abc5,l15),(-0x1c9c380,l27),(0x1c9c380,l29),(-0x19c6cc,l25),(0xd0c0b0,l30),(0x1c9c380,l33),(-0x1c9c380,l35),(0x1c9c380,l37),(-0x54a009,l43),(-0x4db2ef4,l41),(-0x19c6cc,l46),(0xfb0caf,l44),(0x1c9c380,l51),(-0x54a009,l62)]
def normalizationDenominator:ℤ:=0x3938700
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1c9c380,l27),(0x1c9c380,l29),(0x1c9c380,l33),(-0x1c9c380,l35),(0x1c9c380,l37),(0x1c9c380,l51),(-0x4db2ef4,l41),(0x496abc5,l15),(0xd0c0b0,l30),(-0x54a009,l43),(-0x54a009,l62),(0xfb0caf,l12),(0xfb0caf,l44),(-0x19c6cc,l25),(-0x19c6cc,l46),(0x139e37,l17),(0x100242,l10),(-0x100242,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x110f014c02000000881201c601800094260900b400c00000000f00490060000000003c0c8010000000e8d01e601000000000a805200800054240580f20060000000d06018c02], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase2" = "QuadParityTwoThirdsCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase2
private def zz2059:"s080b"="s080b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l44 l46 l51 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc2bb3dc, -0x7270ba8, -0x7ce990f,0xe8a5b0], ![-0x7270ba8, -0x45c74a71,0xd474dee,0x3c2f2b9], ![-0x7ce990f,0xd474dee, -0x2f7dff20,0x7671960], ![0xe8a5b0,0x3c2f2b9,0x7671960, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x200484,l4),(0x200484,l10),(0x679368,l14),(0x5b902c,l12),(-0x51f24a,l17),(0xbe29954,l15),(-0x3938700,l27),(0x3938700,l29),(0x77c02,l25),(0x13040f9,l30),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(-0x9fba23,l43),(-0x9d50cd5,l41),(0x77c02,l46),(0xbb9db8,l44),(0x3938700,l51),(-0xb3b20c,l62),(0x785de,l64)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xbe29954,l15),(-0x9d50cd5,l41),(0x13040f9,l30),(-0xb3b20c,l62),(-0x9fba23,l43),(0x679368,l14),(-0x51f24a,l17),(0xbb9db8,l44),(0x200484,l10),(0x5b902c,l12),(-0x200484,l4),(0x785de,l64),(0x77c02,l25),(0x77c02,l46)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    0xd82eeaaa2ce85fc51250d7df0971611ae0671284554e4ba1d59d422beb07c91a486a12861eb6cbaa3cd1030c4771521014da0d24a006d2a0a490206802165c061fe8f11b2f318288d134bc10156c3f8a4810320100000b9205c1b02d09d153a28a7122826167638028447608318a0d004000027481600e49f19c7834061fb742004309981800ce6a21012838300080000be20563a000376202a0a00094320542ba1d120eaa1c31fd4c9850819ce04241f6fc60464081a00871ec6de6624102a6b80b0105d0d418000775c92810340080000bb205212028090138480982604a120240901182c0880404202020010001329000f202006c6e61e25741de3156dfea126af53ebe5bd67cfe1f70900000000000000070c1deb1dc1deb1e34358a7000000000ebd34279e34a6878e8b183eee0bebae33b6b323857840000000000000000000000000000000000000000000aa6206182300280080aa0a1452c82a6556e86b4686dcaff40be34f0212916941908e22bcc672fde63bb6605081bed048cb1c88af9b59182016161e10d72f7984253be8b190a642f89fa9907ee26d36f2a8614cad13714a3060d3f642b743dd1491f35415f52a8002f59003f9a200fe4675dc62b23ba302f584d4802b38dca70820bb77156d1b80a90e38e18e08c088086002028a353e4798148c4b112392629cc29706abfd45dd2a6aa6ee8c31dca1b055bc40000953e0c02bc603439c0218fa413bb198a97f3580948300303f85e807b2cda27a7a8c657bc6303491714bbb59d2cd88c9644040000dfdd12041a904e56a03257761d98a64fe3ed040dec480c01945a01a2b83489609e2e80e1252b57096b9b71d7d49c34fe4059ce91cf74996ab33fbdfed68e20939ec5c311b4786f94440800012a7c180578c0687380431f48277633152fe6b0129060908d3f341c072d13cc0a4832595460772a87319bfcd9110e5f05f83deba1229172f3348add9a63a4dc9570223dcfb10a30ca90000cc0407c84004028181acff914132a2f422023d4315840369ab7e8804830360100150580f00f882ff9739019a006fc2040274038617744cdc303453fd80c000201b000330c0d0042442cd14dc810e3ad06103df0cb7470acc30171024141a0084886e739c902084c5ec207531dde9212a5212038528f0e606171435403001f9b6988938a0d00400004d48001099c1762bee6103857ac58606bd850810174ed87880920e0d004000031880020f901d1500e06c04c374417b472450c73ac879011533c1630507c21d80001060a812840d0042c7372ea9480cce05b31c38cd9434304380412240150d3184004513b326041a008610375fcb90250bd34c2042d31c80608467ec2500136f4dca0034010c200c9f82204b922ab44001140d58c00680200001264000634800157901b0d80d02c044160200ba105f860820408ee3f05103b7bcc3030f98b9c90e0fa14f201ea77dbca002c2944140218c4e8a010680212204d090b2044ba19de60618f0ebc40e323ccf90085c15d894006c020032020000f9321996eb577c3ec1a48e320500f33b8b102870c0a24b432d30c1c0ec37cc1610b487c0e20654e5bd08f7ebe4636316bc8f5a7e81b0140043a0b85bf11e8db51ea653eec41d9b60605a0227b6f85dcfa9c84991b991e1d1074033c1933422f3d727c631126c8108d71483b64855aad1191af4a0ce70f282408d00060040007c0405c3601a03a18b94e2be67bed883bac3406253ae23ed7ff20209f930bbc08a71f8cff00dfe2537556b8f470a256bcac34e73d4ec8f565fd9f65408a230182260464208c50ca1a4e4bdebdb47c73887a8a00b8f1daef6acfbcba0b659c4e10fc923c3d1042d9c971bf6c9fdda3971224a229c327e88d0925a6671af671461b24691439e5148a1c0000208900a010005669016198068c805447c951b052df8f2253e2b3eb5124996ec1c9bc71389ed05d2290129799e70e4079b8251f8f6da7be64a9d854a85b391a24cae3c39c6558fca1756c2ccddef0d9c8121b62d7a2e0942196f87ebd9af6b982f8ce8adc05565441a2c20bb40900187cbf20019004400004010000044704a0ab2c400c1006588105c0200000d26c38cdae0120314404522081900800003790140dd0534724e120059b6c230018afa50046203401000009b2000500404c340241a0110580802f02c6c2121041600800780c03805419404a330085233e2802118e108c20600210040100448036499e18091e79891020c80400001b4800055100015532011f99f61c3281e0ed31f1f99b17346a12c8e8efe50c7a7e1784128af1d52bd3b94b071c01be67e79e4d0c00e04aa392257999780ea65da44e2f1df92abd65713223ffcf1503b8cfa9c41a969b182d51b940330aef0128128b0720aebc349f1b9b86b0c514df7ccc85adffa1f39cbc478a3309379d84f1d62dae2abf0b0469371a5bb8c919a5d8c6d0d1ca8116546383609194766a19a8fc4c647c726f8524638aa4a4ae01c6108a6268000155c8060480340760fa31750c09e7c4504016ee4482019ccd402120a0c004284b405085800c36623017261048846283001000009620181200018120163a00a0100049f9000f092003c984008f48d1722fad090a1842c08991413a95241a2020000258040014ebcbb060000004b008009dacbcca0a4e383e010c30201d60c28bba69a2a8c18000070828608abe548a09f4ba154202000009602000000258888033c504571c1e0040000b890091d00402801c1400c0a00501002008000d948019c80085400202000010018379))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase3" = "QuadParityTwoThirdsCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase3
private def zz2060:"s080c"="s080c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xcbf579c, -0x7270ba8, -0x7a81d18,0x258], ![-0x7270ba8, -0x3ed0b99c,0x8f3664c,0x605c13c], ![-0x7a81d18,0x8f3664c, -0x2ee85a88,0x741b03a], ![0x258,0x605c13c,0x741b03a, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0xd4ff1,l4),(0xd4ff1,l10),(0xa94012,l17),(0x9b65de8,l15),(-0x3938700,l27),(0x3938700,l29),(0xa94012,l30),(0x3938700,l33),(-0xd4ff1,l38),(-0x3938700,l35),(0x3938700,l37),(0xd4ff1,l34),(-0xa94012,l43),(-0x9b65de8,l41),(0x3938700,l51),(-0xa94012,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0x9b65de8,l15),(-0x9b65de8,l41),(0xa94012,l17),(0xa94012,l30),(-0xa94012,l43),(-0xa94012,l62),(0xd4ff1,l10),(-0xd4ff1,l38),(-0xd4ff1,l4),(0xd4ff1,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase4" = "QuadParityTwoThirdsCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase4
private def zz2061:"s080d"="s080d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoThirdsCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xd328264, -0x7270ba8, -0x7ce990f,0x258], ![-0x7270ba8, -0x3ea4251c,0x8fa9060,0x600b853], ![-0x7ce990f,0x8fa9060, -0x2ee85a88,0x741b03a], ![0x258,0x600b853,0x741b03a, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0xd4ff1,l4),(0xd4ff1,l10),(0xb3b20c,l17),(0x9d50cd5,l15),(-0x3938700,l27),(0x3938700,l29),(0x9fba23,l30),(0x3938700,l33),(-0xd4ff1,l38),(-0x3938700,l35),(0x3938700,l37),(0xd4ff1,l34),(-0x9fba23,l43),(-0x9d50cd5,l41),(0x3938700,l51),(-0xb3b20c,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0x9d50cd5,l15),(-0x9d50cd5,l41),(0xb3b20c,l17),(-0xb3b20c,l62),(0x9fba23,l30),(-0x9fba23,l43),(0xd4ff1,l10),(-0xd4ff1,l38),(-0xd4ff1,l4),(0xd4ff1,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoThirdsCase5" = "QuadParityTwoThirdsCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoThirdsCase5
private def zz2062:"s080e"="s080e":=by decide+kernel
end 
section 
namespace Green24Proof.ParityTwoThirdsRows
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x153068da002029304e2ad80059dbbca05930198cba033c6e613068da0024304e2ad8001b0ecba07837a898045d4a20304e2ad80038480b2562692e801bfc6821602b196c00bf7cce207d20198cba067c9da06d202b196c03d85b205d204e2ad801df8825204e2ad8023b4b3fa069204e2ad80059dbbca01920198cba033c6e61204e2ad8023b4b3fa07c204e2ad8031b0dba2424ca5d005bfa5da07822692e802e4c0920204e2ad8029e1b19a14]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103811389b468b096028102b196c018bcbaae018102b196c0019cf8ee010386d00203d404e2ad806abfe206d404e2ad8023bff6540386d002440386d00203d00198cba04084c206d00198cba015ac96500386d00207c00198cba005f38e02c004e2ad8071b3be05c002b196c023b18a4002b196c00ab9ae57068da00217068da00203d304e2ad801e8bde02d30198cba03ec4fa01d304e2ad801df88214]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103d504f1800a9cbe02d504e2ad8034b8918e01d50198cba002e7b2865504e2ad800fcacff6039502b196c005a5809202954ca5d006bce4fe019502b196c005a58092154ca5d0028693fe03c104e2ad80138283f202c10198cba00fecb38e05c102b196c002c7e4ca410386d0020c]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2
def mu:Phase → ℚ:=![(0x24fd89f / 0x2625a0),(-0x40cbf3d / 0x4c4b40)]
def parameter:ℚ:=(2 / 3)
def normalization:ℚ:=(1 / 0x186a)
def quad0:Expression:=quadSlack rows parameter 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase0.base QuadParityTwoThirdsCase0.hinges QuadParityTwoThirdsCase0.normalizationDenominator
private def zz181:"s00b5"="s00b5":=by decide+kernel
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase0.base QuadParityTwoThirdsCase0.hinges QuadParityTwoThirdsCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows parameter 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase1.base QuadParityTwoThirdsCase1.hinges QuadParityTwoThirdsCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase1.base QuadParityTwoThirdsCase1.hinges QuadParityTwoThirdsCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows parameter 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase2.base QuadParityTwoThirdsCase2.hinges QuadParityTwoThirdsCase2.normalizationDenominator
private def zz182:"s00b6"="s00b6":=by decide+kernel
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase2.base QuadParityTwoThirdsCase2.hinges QuadParityTwoThirdsCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows parameter 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase3.base QuadParityTwoThirdsCase3.hinges QuadParityTwoThirdsCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase3.base QuadParityTwoThirdsCase3.hinges QuadParityTwoThirdsCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows parameter 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase4.base QuadParityTwoThirdsCase4.hinges QuadParityTwoThirdsCase4.normalizationDenominator
private def zz183:"s00b7"="s00b7":=by decide+kernel
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase4.base QuadParityTwoThirdsCase4.hinges QuadParityTwoThirdsCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows parameter 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadParityTwoThirdsCase5.base QuadParityTwoThirdsCase5.hinges QuadParityTwoThirdsCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoThirdsCase5.base QuadParityTwoThirdsCase5.hinges QuadParityTwoThirdsCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoThirdsCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows parameter mu normalization 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_6_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_6_hinges
private def zz184:"s00b8"="s00b8":=by decide+kernel
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_6_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows parameter mu normalization 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_7_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_7_hinges
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
private def zz185:"s00b9"="s00b9":=by decide+kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_7_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows parameter mu normalization 0 1 false
def pair8Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r18,RewriteAtoms.r0]
def pair8Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_8_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_8_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_8_hinges x
private def zz186:"s00ba"="s00ba":=by decide+kernel
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows parameter mu normalization 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2]
def pair9Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_9_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_9_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_9_hinges x
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows parameter mu normalization 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_10_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_10_hinges
private def zz187:"s00bb"="s00bb":=by decide+kernel
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_10_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows parameter mu normalization 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair11Target:NormalForm:=CompactPair.toNormal LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_11_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_11_hinges
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
private def zz188:"s00bc"="s00bc":=by decide+kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalParityTwoThirdsPairs.parityTwoThirds_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_11_base LocalParityTwoThirdsPairs.compact_parityTwoThirds_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalParityTwoThirdsPairs.parityTwoThirds_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows parameter p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows parameter mu normalization p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ParityTwoThirdsRows
private def zz2063:"s080f"="s080f":=by decide+kernel
end 
section 
namespace Green24Proof.ParityTwoThirds
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
private def zz189:"s00bd"="s00bd":=by decide+kernel
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ParityTwoThirdsRows.rows ParityTwoThirdsRows.parameter p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityTwoThirdsRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ParityTwoThirdsRows.rows ParityTwoThirdsRows.parameter p q same x]
    exact ParityTwoThirdsRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ParityTwoThirdsRows.rows ParityTwoThirdsRows.parameter ParityTwoThirdsRows.mu ParityTwoThirdsRows.normalization p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityTwoThirdsRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ParityTwoThirdsRows.rows ParityTwoThirdsRows.parameter ParityTwoThirdsRows.mu ParityTwoThirdsRows.normalization p q same x]
    exact ParityTwoThirdsRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible ParityTwoThirdsRows.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  ((2 / 3:ℝ) * U - V) * ((-0x22ad5dd / 0x1c9c380:ℝ) * U + (0x1aa653d / 0x1312d00:ℝ) * V) -
    (1 / 0x61a8:ℝ) * (U + V) ^ 2
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 9:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ParityCorrectionAggregation.correction_of_local_rows h3 h5
    ParityTwoThirdsRows.rows ParityTwoThirdsRows.parameter ParityTwoThirdsRows.mu
    ParityTwoThirdsRows.normalization rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ParityTwoThirdsRows.mu 0 = (0x24fd89f / 0x2625a0:ℚ):=by decide +kernel
  have hmu1:ParityTwoThirdsRows.mu 1 = (-0x40cbf3d / 0x4c4b40:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num [ParityTwoThirdsRows.parameter,ParityTwoThirdsRows.normalization] at hc
  unfold massCorrection
  nlinarith only [hc]
private def zz190:"s00be"="s00be":=by decide+kernel
theorem massCorrection_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(6 / 5:ℝ) * V ≤ U) (hhigh:U ≤ (0x95 / 0x64:ℝ) * V) :
    (0x42703f5b / 0x68c6171400:ℝ) * V ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(6 / 5:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x95 / 0x64:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_lower_bound hV hlow hhigh
  nlinarith [sq_nonneg (mass v)]
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(6 / 5:ℝ) * V ≤ U) (hhigh:U ≤ (0x95 / 0x64:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [sq_nonneg V,mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(6 / 5:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x95 / 0x64:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ParityTwoThirds
private def zz2064:"s0810"="s0810":=by decide+kernel
end 
section 
namespace Green24Proof.ScaleTwoRows
open QuadraticCertificates ExpressionCertificates
open ParityPhaseRows (Phase Potential weightedQuad weightedPair balanceCoefficient)
open FullPhaseRows (area pairProduct scale coordinate expressionEval_append expressionEval_scale coordinate_eval area_eval)
open FullPhaseSemantics (pairProduct_eval)
open FullPhaseSymmetry (reversePoint swapPair area_reverse)
open ParityPhaseSymmetry (weightedQuad_reverse weightedPair_swap)
def stretchFactor (p:Phase):ℚ:=if p = 0 then 2 else 1
def stretchedArea (p q:Phase):Expression :=
  [(1 / 2, .area (coordinate 0 (stretchFactor q))
    (coordinate 1 (2 * stretchFactor p)) (coordinate 2 (3 * stretchFactor q))),
   (1 / 2, .area (coordinate 3 (stretchFactor p))
    (coordinate 2 (2 * stretchFactor q)) (coordinate 1 (3 * stretchFactor p)))]
def cost (p q:Phase):Expression :=
  stretchedArea p q ++ scale (if p = 0 ∧ q = 0 then -1 else 0) area
def quadSlack (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool):Expression :=
  weightedQuad rows p q same ++ scale (-1) (cost p q)
def pairSlack (rows:List (ℚ × Potential)) (μ:Phase → ℚ)
    (p q:Phase) (same:Bool):Expression :=
  weightedPair rows p q same ++
    pairProduct (balanceCoefficient μ p q + if p = 0 ∧ q = 0 then 64 else 0)
private def zz191:"s00bf"="s00bf":=by decide+kernel
theorem stretchedArea_eval (p q:Phase) (x:Point) :
    expressionEval (stretchedArea p q) x =
      2 * kernel ((stretchFactor q:ℝ) * x 0)
        (2 * ((stretchFactor p:ℝ) * x 1)) (3 * ((stretchFactor q:ℝ) * x 2)) +
      2 * kernel ((stretchFactor p:ℝ) * x 3)
        (2 * ((stretchFactor q:ℝ) * x 2)) (3 * ((stretchFactor p:ℝ) * x 1)):=by
  simp only [stretchedArea,expressionEval,List.map_cons,List.map_nil,List.sum_cons,
    List.sum_nil,atomEval,coordinate_eval,Rat.cast_div,Rat.cast_one,
    Rat.cast_ofNat,Rat.cast_mul,mul_assoc]
  ring
theorem cost_eval (p q:Phase) (x:Point) :
    expressionEval (cost p q) x = expressionEval (stretchedArea p q) x -
      (if p = 0 ∧ q = 0 then expressionEval area x else 0):=by
  simp only [cost,expressionEval_append,expressionEval_scale]
  split_ifs <;> simp [sub_eq_add_neg]
theorem stretchedArea_reverse (p q:Phase) (x:Point) :
    expressionEval (stretchedArea q p) (reversePoint x) =
      expressionEval (stretchedArea p q) x:=by
  rw [stretchedArea_eval,stretchedArea_eval]
  simp only [reversePoint,Matrix.cons_val_zero,Matrix.cons_val_one,
    Matrix.cons_val_two,Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons]
  ring
theorem quadSlack_reverse (rows:List (ℚ × Potential)) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (quadSlack rows q p same) (reversePoint x) =
      expressionEval (quadSlack rows p q same) x:=by
  simp only [quadSlack,expressionEval_append,expressionEval_scale,
    weightedQuad_reverse,cost_eval,stretchedArea_reverse,area_reverse,and_comm]
private def zz192:"s00c0"="s00c0":=by decide+kernel
theorem pairSlack_swap (rows:List (ℚ × Potential)) (μ:Phase → ℚ)
    (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack rows μ q p same) (swapPair x) =
      expressionEval (pairSlack rows μ p q same) x:=by
  simp only [pairSlack,expressionEval_append]
  rw [weightedPair_swap]
  simp only [pairProduct_eval,balanceCoefficient,and_comm,
    swapPair,Matrix.cons_val_zero,Matrix.cons_val_one]
  push_cast
  ring
end Green24Proof.ScaleTwoRows
private def zz2065:"s0811"="s0811":=by decide+kernel
end 
section 
namespace Green24Proof.LocalScaleTwoPairs
def compact_scaleTwo_pair_6_base:CompactPair.Quadratic:=⟨0,0,0⟩
def compact_scaleTwo_pair_6_hinges:List CompactPair.Hinge:=[]
noncomputable def scaleTwo_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_6_base compact_scaleTwo_pair_6_hinges x y
def compact_scaleTwo_pair_6_cuts:List ℚ:=[]
theorem compact_scaleTwo_pair_6_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_6_base compact_scaleTwo_pair_6_hinges 0 compact_scaleTwo_pair_6_cuts = true :=
  by decide +kernel
theorem compact_scaleTwo_pair_6_representation (x y:ℝ) :
    scaleTwo_pair_6 x y = CompactPair.expressionEval compact_scaleTwo_pair_6_base compact_scaleTwo_pair_6_hinges x y:=by rfl
theorem scaleTwo_pair_6_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_6 x y:=by
  rw [compact_scaleTwo_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_6_check _hy (by simpa using _hx)
def compact_scaleTwo_pair_7_base:CompactPair.Quadratic:=⟨0,0,0⟩
def compact_scaleTwo_pair_7_hinges:List CompactPair.Hinge:=[]
noncomputable def scaleTwo_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_7_base compact_scaleTwo_pair_7_hinges x y
def compact_scaleTwo_pair_7_cuts:List ℚ:=[]
private def zz193:"s00c1"="s00c1":=by decide+kernel
theorem compact_scaleTwo_pair_7_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_7_base compact_scaleTwo_pair_7_hinges 0 compact_scaleTwo_pair_7_cuts = true :=
  by decide +kernel
theorem compact_scaleTwo_pair_7_representation (x y:ℝ) :
    scaleTwo_pair_7 x y = CompactPair.expressionEval compact_scaleTwo_pair_7_base compact_scaleTwo_pair_7_hinges x y:=by rfl
theorem scaleTwo_pair_7_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_7 x y:=by
  rw [compact_scaleTwo_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_7_check _hy (by simpa using _hx)
def compact_scaleTwo_pair_8_base:CompactPair.Quadratic:=⟨0,0,0⟩
def compact_scaleTwo_pair_8_hinges:List CompactPair.Hinge:=[]
noncomputable def scaleTwo_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_8_base compact_scaleTwo_pair_8_hinges x y
def compact_scaleTwo_pair_8_cuts:List ℚ:=[]
theorem compact_scaleTwo_pair_8_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_8_base compact_scaleTwo_pair_8_hinges 0 compact_scaleTwo_pair_8_cuts = true :=
  by decide +kernel
private def zz194:"s00c2"="s00c2":=by decide+kernel
theorem compact_scaleTwo_pair_8_representation (x y:ℝ) :
    scaleTwo_pair_8 x y = CompactPair.expressionEval compact_scaleTwo_pair_8_base compact_scaleTwo_pair_8_hinges x y:=by rfl
theorem scaleTwo_pair_8_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_8 x y:=by
  rw [compact_scaleTwo_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_8_check _hy (by simpa using _hx)
def compact_scaleTwo_pair_9_base:CompactPair.Quadratic:=⟨0,0,0⟩
def compact_scaleTwo_pair_9_hinges:List CompactPair.Hinge:=[]
noncomputable def scaleTwo_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_9_base compact_scaleTwo_pair_9_hinges x y
def compact_scaleTwo_pair_9_cuts:List ℚ:=[]
theorem compact_scaleTwo_pair_9_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_9_base compact_scaleTwo_pair_9_hinges 0 compact_scaleTwo_pair_9_cuts = true :=
  by decide +kernel
theorem compact_scaleTwo_pair_9_representation (x y:ℝ) :
    scaleTwo_pair_9 x y = CompactPair.expressionEval compact_scaleTwo_pair_9_base compact_scaleTwo_pair_9_hinges x y:=by rfl
private def zz195:"s00c3"="s00c3":=by decide+kernel
theorem scaleTwo_pair_9_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_9 x y:=by
  rw [compact_scaleTwo_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_9_check _hy (by simpa using _hx)
def compact_scaleTwo_pair_10_base:CompactPair.Quadratic:=⟨(-11 / 50),(11 / 0x64),0⟩
def compact_scaleTwo_pair_10_hinges:List CompactPair.Hinge:=[⟨(-11 / 0x190),1, -3⟩,⟨(11 / 0x190),3, -1⟩]
noncomputable def scaleTwo_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_10_base compact_scaleTwo_pair_10_hinges x y
def compact_scaleTwo_pair_10_cuts:List ℚ:=[(1 / 3),3]
theorem compact_scaleTwo_pair_10_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_10_base compact_scaleTwo_pair_10_hinges 0 compact_scaleTwo_pair_10_cuts = true :=
  by decide +kernel
theorem compact_scaleTwo_pair_10_representation (x y:ℝ) :
    scaleTwo_pair_10 x y = CompactPair.expressionEval compact_scaleTwo_pair_10_base compact_scaleTwo_pair_10_hinges x y:=by rfl
theorem scaleTwo_pair_10_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_10 x y:=by
  rw [compact_scaleTwo_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_10_check _hy (by simpa using _hx)
def compact_scaleTwo_pair_11_base:CompactPair.Quadratic:=⟨0,0,0⟩
def compact_scaleTwo_pair_11_hinges:List CompactPair.Hinge:=[]
noncomputable def scaleTwo_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_scaleTwo_pair_11_base compact_scaleTwo_pair_11_hinges x y
def compact_scaleTwo_pair_11_cuts:List ℚ:=[]
private def zz196:"s00c4"="s00c4":=by decide+kernel
theorem compact_scaleTwo_pair_11_check :
    CompactPair.expressionCheckPSD compact_scaleTwo_pair_11_base compact_scaleTwo_pair_11_hinges 0 compact_scaleTwo_pair_11_cuts = true :=
  by decide +kernel
theorem compact_scaleTwo_pair_11_representation (x y:ℝ) :
    scaleTwo_pair_11 x y = CompactPair.expressionEval compact_scaleTwo_pair_11_base compact_scaleTwo_pair_11_hinges x y:=by rfl
theorem scaleTwo_pair_11_nonneg {x y:ℝ} (_hx:0 ≤ x) (_hy:0 ≤ y) :
    0 ≤ scaleTwo_pair_11 x y:=by
  rw [compact_scaleTwo_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_scaleTwo_pair_11_check _hy (by simpa using _hx)
end Green24Proof.LocalScaleTwoPairs
private def zz2066:"s0812"="s0812":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4d95, -0x8c8e, -0xd2f0,0x19b6], ![-0x8c8e, -0x22c59,0x5910,0x6a23], ![-0xd2f0,0x5910, -0x3774c,0x8ca0], ![0x19b6,0x6a23,0x8ca0, -0x4650]]
noncomputable def hinges:Hinges:=[(-0x198,l6),(0x13a7,l4),(-0x4fb,l10),(0x7988,l14),(-0x1460,l17),(0xf9d8,l15),(-0x4650,l27),(0x4650,l29),(-0x7988,l25),(0x2ac9,l30),(0x4650,l33),(0x4fb,l38),(-0x4650,l35),(0x4650,l37),(-0x13a7,l34),(-0x2ac9,l43),(-0xf9d8,l41),(0x4ca,l46),(0x4650,l51),(0x198,l60),(0x1460,l62),(-0x4ca,l64)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x4650,l27),(0x4650,l29),(0x4650,l33),(-0x4650,l35),(0x4650,l37),(0x4650,l51),(0x7988,l14),(-0x7988,l25),(0xf9d8,l15),(-0xf9d8,l41),(0x2ac9,l30),(-0x2ac9,l43),(-0x1460,l17),(0x1460,l62),(-0x4fb,l10),(0x4fb,l38),(0x13a7,l4),(-0x13a7,l34),(0x4ca,l46),(-0x4ca,l64),(-0x198,l6),(0x198,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase0" = "QuadScaleTwoCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase0
private def zz2067:"s0813"="s0813":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x233e, -0x8c8e, -0xd2f0,0x1c68], ![-0x8c8e, -0x1e80a,0x4626,0x7224], ![-0xd2f0,0x4626, -0x3774c,0x8ca0], ![0x1c68,0x7224,0x8ca0, -0x4650]]
noncomputable def hinges:Hinges:=[(-0x198,l6),(0x13a7,l4),(-0x4fb,l10),(0x8613,l14),(-0x227a,l17),(0x12e3d,l15),(-0x4650,l27),(0x4650,l29),(-0x8613,l25),(0x2a17,l30),(0x4650,l33),(0x4fb,l38),(-0x4650,l35),(0x4650,l37),(-0x13a7,l34),(-0x2a17,l43),(-0x12e3d,l41),(0x8e6,l46),(0x4650,l51),(0x198,l60),(0x227a,l62),(-0x8e6,l64)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x4650,l27),(0x4650,l29),(0x4650,l33),(-0x4650,l35),(0x4650,l37),(0x4650,l51),(0x8613,l14),(-0x8613,l25),(0x12e3d,l15),(-0x12e3d,l41),(0x2a17,l30),(-0x2a17,l43),(-0x227a,l17),(0x227a,l62),(0x8e6,l46),(-0x8e6,l64),(-0x4fb,l10),(0x4fb,l38),(0x13a7,l4),(-0x13a7,l34),(-0x198,l6),(0x198,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x360e03cc0200000003200132010000000003201c802000003404c0dc3010000000000d01c802000000280b01c300e071c7183025910060000007209016300c00000000190188020000000a8240530080000000a8004c804], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase1" = "QuadScaleTwoCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase1
private def zz2068:"s0814"="s0814":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l24 l25 l26 l30 l32 l39 l4 l40 l41 l43 l44 l46 l52 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x38a2, -0x5dc0, -0x3c4e,0x2f52], ![-0x5dc0, -0x73fdf,0xd689,0x23d3], ![-0x3c4e,0xd689, -0x15668,0x6f7e], ![0x2f52,0x23d3,0x6f7e, -0x5dc0]]
noncomputable def hinges:Hinges:=[(-0x214,l6),(0x1011,l4),(0x2a3,l10),(0x436,l14),(0x2ad8,l12),(-0x1460,l17),(0xf9d8,l15),(-0x5dc0,l24),(-0x2b8,l25),(0x5dc0,l26),(0x2ac9,l30),(0x5dc0,l32),(-0x1770,l39),(0x1770,l40),(-0xc6e,l43),(-0x24ed,l41),(-0x2b8,l46),(0x2ad8,l44),(0x1770,l52),(-0xc15,l62),(0x436,l64)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x5dc0,l24),(0x5dc0,l26),(0x5dc0,l32),(-0x1770,l39),(0x1770,l40),(0x1770,l52),(0xf9d8,l15),(0x2ac9,l30),(-0x1460,l17),(-0xc6e,l43),(-0xc15,l62),(0x2ad8,l12),(0x2ad8,l44),(-0x24ed,l41),(0x436,l14),(0x436,l64),(0x1011,l4),(-0x2b8,l25),(-0x2b8,l46),(0x2a3,l10),(-0x214,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x5c02900400001043100a0c04a0866840811a08030000000483c053008000000001e0290040001200840098c05000000901201c601800094260a013400c00000000f0049006000000001e01c80200000003c00264020000025074066301000001884a0631808000000001a014802000000b0440166018000054120013301000000001600490060000000580044804000000d01201460180000000014062008000340208013180a000001a044038c030000000e8c81e6010000e82609016400c00000340d80618060000001d1b028c02000228fc2c02c80180000510c40283010000000000a069004000000026440cc010000000b8280a6010000000006c0520081c828c1680f9a00a00560cc2300a1004], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase2" = "QuadScaleTwoCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase2
private def zz2069:"s0815"="s0815":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l24 l25 l26 l30 l32 l39 l4 l40 l41 l43 l44 l46 l52 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x369e, -0x5dc0, -0x3324,0x279c], ![-0x5dc0, -0x78c12,0xd689,0x2bd4], ![-0x3324,0xd689, -0x15668,0x6f7e], ![0x279c,0x2bd4,0x6f7e, -0x5dc0]]
noncomputable def hinges:Hinges:=[(-0x214,l6),(0x1011,l4),(0x2a3,l10),(0x7e9,l14),(0x4a3d,l12),(-0x227a,l17),(0x12e3d,l15),(-0x5dc0,l24),(-0x1b6,l25),(0x5dc0,l26),(0x2a17,l30),(0x5dc0,l32),(-0x1770,l39),(0x1770,l40),(-0xaaf,l43),(-0x405c,l41),(0x486,l46),(0x1a0a,l44),(0x1770,l52),(-0x3bb,l62)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x5dc0,l24),(0x5dc0,l26),(0x5dc0,l32),(-0x1770,l39),(0x1770,l40),(0x1770,l52),(0x12e3d,l15),(0x2a17,l30),(-0x227a,l17),(0x4a3d,l12),(-0x405c,l41),(-0xaaf,l43),(0x7e9,l14),(0x1a0a,l44),(0x486,l46),(0x1011,l4),(-0x3bb,l62),(0x2a3,l10),(-0x214,l6),(-0x1b6,l25)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x1700a40150433420408d040180000000034029004000000120f014c02000000000780a401000048021002630140000024048071806000250982804d003000000003c0124018000025074066301000002a090009980800000000b0024803000000b0440166018000000160011201000000001b0049006000001a024028c03000000000280c4010000680410026301400000340880718060000001d1903cc02], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase3" = "QuadScaleTwoCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase3
private def zz2070:"s0816"="s0816":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x86a8, -0x2ee0, -0x3c4e,0], ![-0x2ee0, -0x1c1b0,0x3a7a,0x3228], ![-0x3c4e,0x3a7a, -0x13148,0x2f06], ![0,0x3228,0x2f06, -0x1770]]
noncomputable def hinges:Hinges:=[(-19,l4),(19,l10),(0x1fc,l14),(0xc15,l17),(0x24ed,l15),(-0x1770,l27),(0x1770,l29),(-0x1fc,l25),(0xc6e,l30),(0x1770,l33),(-19,l38),(-0x1770,l35),(0x1770,l37),(19,l34),(-0xc6e,l43),(-0x24ed,l41),(0x1770,l51),(-0xc15,l62)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1770,l27),(0x1770,l29),(0x1770,l33),(-0x1770,l35),(0x1770,l37),(0x1770,l51),(0xc6e,l30),(-0xc6e,l43),(0xc15,l17),(-0xc15,l62),(0x24ed,l15),(-0x24ed,l41),(0x1fc,l14),(-0x1fc,l25),(19,l10),(-19,l38),(-19,l4),(19,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase4" = "QuadScaleTwoCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase4
private def zz2071:"s0817"="s0817":=by decide+kernel
end 
section 
namespace Green24Proof.QuadScaleTwoCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x5386, -0x2ee0, -0x3324,0x6a], ![-0x2ee0, -0x1623e,0x1d42,0x3876], ![-0x3324,0x1d42, -0x13148,0x2f06], ![0x6a,0x3876,0x2f06, -0x1770]]
noncomputable def hinges:Hinges:=[(-19,l4),(19,l10),(0xe56,l14),(0x3bb,l17),(0x405c,l15),(-0x1770,l27),(0x1770,l29),(-0xe56,l25),(0xaaf,l30),(0x1770,l33),(-19,l38),(-0x1770,l35),(0x1770,l37),(19,l34),(-0xaaf,l43),(-0x405c,l41),(-53,l46),(0x1770,l51),(-0x3bb,l62),(53,l64)]
def normalizationDenominator:ℤ:=0x2ee0
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1770,l27),(0x1770,l29),(0x1770,l33),(-0x1770,l35),(0x1770,l37),(0x1770,l51),(0x405c,l15),(-0x405c,l41),(0xe56,l14),(-0xe56,l25),(0xaaf,l30),(-0xaaf,l43),(0x3bb,l17),(-0x3bb,l62),(-53,l46),(53,l64),(19,l10),(-19,l38),(-19,l4),(19,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x540920081441942100b8200a000000001a014802000000000280c4010000000443c05300800002702200b1808000250982402d003000000003c0124018001047431024400c1e41141680c6200a0000000001c0c801000006812807260200000001a001320100000003622031804000014848004cc04], #[]⟩
def dynamicCode : Nat := (((((((0x71d0050f306ed1c6038838907e470e36a81040098a0018e000431d8000f00471a098a0f3073c69c60811b38a053bc7903bc5810400e41c052e4a2400c9c788001301400008e1e3a00a0f304214e307fa4e241f90e1836a8500392c1002cbe7001000871a126a9e60b67e) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadScaleTwoCase5" = "QuadScaleTwoCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadScaleTwoCase5
private def zz2072:"s0818"="s0818":=by decide+kernel
end 
section 
namespace Green24Proof.ScaleTwoCertificate
open QuadraticCertificates ExpressionCertificates ScaleTwoRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x104d62ef03d92039607e81bc6019607e823be1603f403de07d25001a206d2039013e601d207e803b6520fd0029e86079207e808b6069201fa0792019201fa01ae120fd0029e8607c207e801f8a606c203f423ba01c27d2480420fd07cde078203f4019ac2028207e801fad6018203f458c6020fd00214]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x14003f40603d701fa1605d707e812572ef00202d307e811ae01d307e80986039307e808b6029301fa0792059301fa01ae07c3192e02c37d028001c303f40ace4307e807c207837d019202837d03d2018303f40582037d2207d607e809c202d607e8158a01d607e82fea14]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x101d501c802fe5501fa06b2039503f418ee029507e8319e019507e830aa1503f406d603c12806de02c107e80392fe05c103f444fa038107e801ab9202811908aa05817d0a9803d407e82606d417b82603d0283602d007e815b605d001fa028a07c0286602c007e81a9a05c07d6614]
def rowsChunk3:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103d501c808c602d501fa15ba02]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3
def mu:Phase → ℚ:=![(-0x3e97 / 0x1f4),(-0x35ab / 0x3e8)]
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r24,RewriteAtoms.r31,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r30,RewriteAtoms.r25,RewriteAtoms.r32,RewriteAtoms.r23,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r33,RewriteAtoms.r34,RewriteAtoms.r35,RewriteAtoms.r36,RewriteAtoms.r37,RewriteAtoms.r38,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadScaleTwoCase0.base QuadScaleTwoCase0.hinges QuadScaleTwoCase0.normalizationDenominator
private def zz207:"s00cf"="s00cf":=by decide+kernel
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase0.base QuadScaleTwoCase0.hinges QuadScaleTwoCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r24,RewriteAtoms.r31,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r30,RewriteAtoms.r25,RewriteAtoms.r32,RewriteAtoms.r23,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r33,RewriteAtoms.r34,RewriteAtoms.r35,RewriteAtoms.r36,RewriteAtoms.r37,RewriteAtoms.r38,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadScaleTwoCase1.base QuadScaleTwoCase1.hinges QuadScaleTwoCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase1.base QuadScaleTwoCase1.hinges QuadScaleTwoCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r39,RewriteAtoms.r40,RewriteAtoms.r41,RewriteAtoms.r42,RewriteAtoms.r43,RewriteAtoms.r44,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadScaleTwoCase2.base QuadScaleTwoCase2.hinges QuadScaleTwoCase2.normalizationDenominator
private def zz208:"s00d0"="s00d0":=by decide+kernel
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase2.base QuadScaleTwoCase2.hinges QuadScaleTwoCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r39,RewriteAtoms.r40,RewriteAtoms.r41,RewriteAtoms.r42,RewriteAtoms.r43,RewriteAtoms.r44,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadScaleTwoCase3.base QuadScaleTwoCase3.hinges QuadScaleTwoCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase3.base QuadScaleTwoCase3.hinges QuadScaleTwoCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadScaleTwoCase4.base QuadScaleTwoCase4.hinges QuadScaleTwoCase4.normalizationDenominator
private def zz209:"s00d1"="s00d1":=by decide+kernel
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase4.base QuadScaleTwoCase4.hinges QuadScaleTwoCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r29,RewriteAtoms.r24,RewriteAtoms.r31,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r30,RewriteAtoms.r25,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadScaleTwoCase5.base QuadScaleTwoCase5.hinges QuadScaleTwoCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadScaleTwoCase5.base QuadScaleTwoCase5.hinges QuadScaleTwoCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadScaleTwoCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows mu 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_6_base LocalScaleTwoPairs.compact_scaleTwo_pair_6_hinges
private def zz210:"s00d2"="s00d2":=by decide+kernel
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalScaleTwoPairs.scaleTwo_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_6_base LocalScaleTwoPairs.compact_scaleTwo_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows mu 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_7_base LocalScaleTwoPairs.compact_scaleTwo_pair_7_hinges
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
private def zz211:"s00d3"="s00d3":=by decide+kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalScaleTwoPairs.scaleTwo_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_7_base LocalScaleTwoPairs.compact_scaleTwo_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows mu 0 1 false
def pair8Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair8Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_8_base LocalScaleTwoPairs.compact_scaleTwo_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalScaleTwoPairs.scaleTwo_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_8_base LocalScaleTwoPairs.compact_scaleTwo_pair_8_hinges x
private def zz212:"s00d4"="s00d4":=by decide+kernel
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows mu 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair9Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_9_base LocalScaleTwoPairs.compact_scaleTwo_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalScaleTwoPairs.scaleTwo_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_9_base LocalScaleTwoPairs.compact_scaleTwo_pair_9_hinges x
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows mu 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_10_base LocalScaleTwoPairs.compact_scaleTwo_pair_10_hinges
private def zz213:"s00d5"="s00d5":=by decide+kernel
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalScaleTwoPairs.scaleTwo_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_10_base LocalScaleTwoPairs.compact_scaleTwo_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows mu 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair11Target:NormalForm:=CompactPair.toNormal LocalScaleTwoPairs.compact_scaleTwo_pair_11_base LocalScaleTwoPairs.compact_scaleTwo_pair_11_hinges
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
private def zz214:"s00d6"="s00d6":=by decide+kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalScaleTwoPairs.scaleTwo_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalScaleTwoPairs.compact_scaleTwo_pair_11_base LocalScaleTwoPairs.compact_scaleTwo_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalScaleTwoPairs.scaleTwo_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows mu p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ScaleTwoCertificate
private def zz2073:"s0819"="s0819":=by decide+kernel
end 
section 
namespace Green24Proof.ScaleTwoAggregation
open QuadraticCertificates ExpressionCertificates ScaleTwoRows
open ParityPhaseRows (Phase Potential weightedQuad weightedPair)
open FullPhaseRows (area pairProduct scale expressionEval_append expressionEval_scale area_eval)
open FullPhaseSemantics (quadPoint pairPoint sameColour pairProduct_eval)
open FullPhaseAggregation (area_sum)
open ParityPhaseAggregation (weightedRows_sum weightedAggregate product_add)
open ParityCorrectionAggregation (classMass_interleave_zero classMass_interleave_one selected_area_sum)
noncomputable def stretch {q:ℕ} (h2:2 ∣ q) (g:ZMod q → ℝ) (i:ZMod q):ℝ :=
  (stretchFactor (ZMod.castHom h2 (ZMod 2) i):ℝ) * g i
private def zz215:"s00d7"="s00d7":=by decide+kernel
theorem stretch_interleave {m:ℕ} [NeZero m] (a b:ZMod m → ℝ) :
    stretch (dvd_mul_right 2 m) (interleave a b) = interleave (fun i => 2 * a i) b:=by
  funext i
  obtain ⟨⟨r,j⟩,rfl⟩:=(parityEquiv m).surjective i
  have hr:r = 0 ∨ r = 1:=by
    fin_cases r
    · exact Or.inl rfl
    · exact Or.inr rfl
  rcases hr with rfl | rfl
  · simp only [stretch,parityCast_apply,interleave_even]
    norm_num [stretchFactor]
  · simp only [stretch,parityCast_apply,interleave_odd]
    norm_num [stretchFactor]
theorem stretchedArea_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (stretchedArea (ZMod.castHom h2 (ZMod 2) j) (ZMod.castHom h2 (ZMod 2) k)) (quadPoint g j k)) =
      4 * profileFunctional (stretch h2 g):=by
  have hp (j k:ZMod q):expressionEval
      (stretchedArea (ZMod.castHom h2 (ZMod 2) j) (ZMod.castHom h2 (ZMod 2) k)) (quadPoint g j k) =
      expressionEval area (quadPoint (stretch h2 g) j k):=by
    rw [stretchedArea_eval,area_eval]
    simp only [quadPoint,Matrix.cons_val_zero,Matrix.cons_val_one,Matrix.cons_val_two,
      Matrix.cons_val_three,Matrix.head_cons,Matrix.tail_cons,stretch,ParityPhaseSemantics.cast_two_affine]
  simp_rw [hp]
  exact area_sum _
theorem cost_sum {m:ℕ} [NeZero m] (a b:ZMod m → ℝ) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),expressionEval
      (cost (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k)) (quadPoint (interleave a b) j k)) =
      4 * profileFunctional (interleave (fun i => 2 * a i) b) - 4 * profileFunctional a:=by
  simp_rw [cost_eval]
  simp only [Finset.sum_sub_distrib,stretchedArea_sum,selected_area_sum,stretch_interleave]
theorem selected_product_sum {q:ℕ} [NeZero q] (h2:2 ∣ q) (g:ZMod q → ℝ) :
    (∑ j:ZMod q, ∑ k:ZMod q,expressionEval
      (pairProduct (if ZMod.castHom h2 (ZMod 2) j = 0 ∧ ZMod.castHom h2 (ZMod 2) k = 0 then 64 else 0))
      (pairPoint g j k)) = 64 * classMass (ZMod.castHom h2 (ZMod 2)) g 0 ^ 2:=by
  simp only [pairProduct_eval,pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
  rw [ParityCorrectionAggregation.weighted_pair_classMass (ZMod.castHom h2 (ZMod 2)) g
    (fun p q => ((if p = 0 ∧ q = 0 then 64 else 0:ℚ):ℝ))]
  norm_num
  ring
private def zz216:"s00d8"="s00d8":=by decide+kernel
theorem local_slacks_sum {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (a b:ZMod m → ℝ)
    (rows:List (ℚ × Potential)) (μ:Phase → ℚ) :
    (∑ j:ZMod (2 * m), ∑ k:ZMod (2 * m),(
      expressionEval (quadSlack rows (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (quadPoint (interleave a b) j k) +
      expressionEval (pairSlack rows μ (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
        (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k)) (pairPoint (interleave a b) j k))) =
      weightedAggregate (dvd_mul_right 2 m) h3 (interleave a b) rows -
      4 * profileFunctional (interleave (fun i => 2 * a i) b) + 4 * profileFunctional a +
      64 * mass a ^ 2 + ((μ 0:ℝ) * mass a + (μ 1:ℝ) * mass b) * (mass a - mass b):=by
  have hw:=weightedRows_sum (dvd_mul_right 2 m) h3 (interleave a b) rows
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadSlack,pairSlack,expressionEval_append,expressionEval_scale,product_add]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum,cost_sum,
    ParityPhaseAggregation.balance_sum,selected_product_sum,classMass_interleave_zero,
    classMass_interleave_one]
  rw [← hw]
  push_cast
  ring
theorem correction_of_local_rows {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (rows:List (ℚ × Potential)) (μ:Phase → ℚ)
    (hadmissible:ParityPhaseAggregation.rowsAdmissible rows = true)
    (hquad:∀ p q same x,(∀ i,0 ≤ x i) → 0 ≤ expressionEval (quadSlack rows p q same) x)
    (hpair:∀ p q same x,(∀ i,0 ≤ x i) → 0 ≤ expressionEval (pairSlack rows μ p q same) x)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 4:ℝ) * deficit u - (5 / 2 + (μ 0:ℝ) / 16) * (mass u) ^ 2 +
      (4 + (μ 0:ℝ) / 8 - (μ 1:ℝ) / 8) * mass u * mass v +
      (2 + (μ 1:ℝ) / 4) * mass v ^ 2 ≤ deficit (interleave u v):=by
  let a:ZMod m → ℝ:=fun i => (1 / 2:ℝ) * u i
  have ha:∀ i,0 ≤ a i:=fun i => mul_nonneg (by norm_num) (hu i)
  have hg:=interleave_nonneg a v ha hv
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ =>
      add_nonneg
        (hquad (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
          (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k) _
          (FullPhaseAggregation.quadPoint_nonneg _ hg j k))
        (hpair (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) j)
          (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2) k) (sameColour h3 j k) _
          (FullPhaseAggregation.pairPoint_nonneg _ hg j k))
  rw [local_slacks_sum,
    ParityPhaseAggregation.weightedAggregate_zero (dvd_mul_right 2 m) h3 h5 _ rows hadmissible] at hs
  have hdouble:(fun i => 2 * a i) = u:=by funext i; dsimp [a]; ring
  have hmass:mass a = (1 / 2:ℝ) * mass u:=mass_scale u _
  have hfunctional:profileFunctional a = (1 / 2:ℝ) ^ 2 * profileFunctional u :=
    profileFunctional_scale u (by norm_num)
  rw [hdouble,hmass,hfunctional] at hs
  unfold deficit
  rw [mass_interleave]
  nlinarith only [hs]
end Green24Proof.ScaleTwoAggregation
private def zz2074:"s081a"="s081a":=by decide+kernel
end 
section 
namespace Green24Proof.ScaleTwo
open QuadraticCertificates ExpressionCertificates ScaleTwoRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ScaleTwoCertificate.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ScaleTwoCertificate.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ScaleTwoCertificate.rows p q same x]
    exact ScaleTwoCertificate.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ScaleTwoCertificate.rows ScaleTwoCertificate.mu p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ScaleTwoCertificate.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ScaleTwoCertificate.rows ScaleTwoCertificate.mu p q same x]
    exact ScaleTwoCertificate.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
private def zz217:"s00d9"="s00d9":=by decide+kernel
theorem rows_admissible:rowsAdmissible ScaleTwoCertificate.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  -(0xf89 / 0x1f40:ℝ) * (U - 2 * V) * (U - (0x166b / 0xf89:ℝ) * V)
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 4:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ScaleTwoAggregation.correction_of_local_rows h3 h5
    ScaleTwoCertificate.rows ScaleTwoCertificate.mu rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ScaleTwoCertificate.mu 0 = (-0x3e97 / 0x1f4:ℚ):=by decide +kernel
  have hmu1:ScaleTwoCertificate.mu 1 = (-0x35ab / 0x3e8:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num at hc
  unfold massCorrection
  nlinarith only [hc]
theorem massCorrection_nonneg {U V:ℝ} (hV:0 ≤ V)
    (hlow:(37 / 25:ℝ) * V ≤ U) (hhigh:U ≤ 2 * V):0 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hhigh)
    (show 0 ≤ U - (0x166b / 0xf89:ℝ) * V by linarith)
  unfold massCorrection
  nlinarith only [hp]
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(37 / 25:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ 2 * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_nonneg hV hlow hhigh
  linarith
private def zz218:"s00da"="s00da":=by decide+kernel
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(37 / 25:ℝ) * V ≤ U) (hhigh:U ≤ (0x18d / 0xc8:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  have hh:=mul_nonneg hV (sub_nonneg.mpr hhigh)
  unfold massCorrection
  nlinarith [sq_nonneg V]
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(37 / 25:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x18d / 0xc8:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ScaleTwo
private def zz2075:"s081b"="s081b":=by decide+kernel
end 
section 
namespace Green24Proof.ParityIntervals
theorem coercivity_eleven_tenths_to_149_100 {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x95 / 0x64:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (31 / 25:ℝ) * mass v
  · exact ParityFourFifths.coercivity h3 h5 u v hu hv hd hlow h
  · have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
    exact ParityTwoThirds.coercivity h3 h5 u v hu hv hd (by linarith) hhigh
theorem interval_eleven_tenths_to_149_100 {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x95 / 0x64:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  exact (mul_nonneg (by norm_num) (sq_nonneg (mass u - mass v))).trans
    (coercivity_eleven_tenths_to_149_100 h3 h5 u v hu hv hd hlow hhigh)
private def zz219:"s00db"="s00db":=by decide+kernel
theorem coercivity_eleven_tenths_to_397_200 {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0x18d / 0xc8:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (0x95 / 0x64:ℝ) * mass v
  · exact coercivity_eleven_tenths_to_149_100 h3 h5 u v hu hv hd hlow h
  · have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
    exact ScaleTwo.coercivity h3 h5 u v hu hv hd (by linarith) hhigh
theorem interval_eleven_tenths_to_two {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(11 / 10:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ 2 * mass v):0 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (0x95 / 0x64:ℝ) * mass v
  · exact interval_eleven_tenths_to_149_100 h3 h5 u v hu hv hd hlow h
  · have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
    exact ScaleTwo.interval_nonneg h3 h5 u v hu hv hd (by linarith) hhigh
end Green24Proof.ParityIntervals
private def zz2076:"s081c"="s081c":=by decide+kernel
end 
section 
namespace Green24Proof.LocalParityTwoFifthsPairs
def compact_parityTwoFifths_pair_6_base:CompactPair.Quadratic:=⟨(7 / 0xe4e1c00),(0x9c5 / 0x17d7840),0⟩
def compact_parityTwoFifths_pair_6_hinges:List CompactPair.Hinge:=[⟨(1 / 0x7270e00),1, -3⟩,⟨(-1 / 0x4c4b400),1, -2⟩,⟨(1 / 0x4c4b400),2, -1⟩,⟨(-1 / 0x7270e00),3, -1⟩]
noncomputable def parityTwoFifths_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_6_base compact_parityTwoFifths_pair_6_hinges x y
def compact_parityTwoFifths_pair_6_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
theorem compact_parityTwoFifths_pair_6_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_6_base compact_parityTwoFifths_pair_6_hinges 0 compact_parityTwoFifths_pair_6_cuts = true :=
  by decide +kernel
theorem compact_parityTwoFifths_pair_6_representation (x y:ℝ) :
    parityTwoFifths_pair_6 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_6_base compact_parityTwoFifths_pair_6_hinges x y:=by rfl
private def zz220:"s00dc"="s00dc":=by decide+kernel
theorem parityTwoFifths_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_6 x y:=by
  rw [compact_parityTwoFifths_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_6_check hy (by simpa using hx)
def compact_parityTwoFifths_pair_7_base:CompactPair.Quadratic:=⟨(-11 / 0x3938700),(0x7d7 / 0x2faf080),0⟩
def compact_parityTwoFifths_pair_7_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2625a00),1, -3⟩,⟨(1 / 0x4c4b400),1, -2⟩,⟨(-1 / 0xe4e1c00),2, -3⟩,⟨(-1 / 0x4c4b400),2, -1⟩,⟨(1 / 0xe4e1c00),3, -2⟩,⟨(1 / 0x2625a00),3, -1⟩]
noncomputable def parityTwoFifths_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_7_base compact_parityTwoFifths_pair_7_hinges x y
def compact_parityTwoFifths_pair_7_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_parityTwoFifths_pair_7_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_7_base compact_parityTwoFifths_pair_7_hinges 0 compact_parityTwoFifths_pair_7_cuts = true :=
  by decide +kernel
theorem compact_parityTwoFifths_pair_7_representation (x y:ℝ) :
    parityTwoFifths_pair_7 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_7_base compact_parityTwoFifths_pair_7_hinges x y:=by rfl
theorem parityTwoFifths_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_7 x y:=by
  rw [compact_parityTwoFifths_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_7_check hy (by simpa using hx)
def compact_parityTwoFifths_pair_8_base:CompactPair.Quadratic:=⟨(0x261239 / 0xb71b00),(0x36ad / 0x5f5e100),0⟩
def compact_parityTwoFifths_pair_8_hinges:List CompactPair.Hinge:=[⟨(0xb43541 / 0x1312d00),1, -1⟩,⟨(-0x29f197 / 0x16e3600),2, -3⟩,⟨(0x262e21 / 0x2625a00),2, -1⟩,⟨(-0xf047 / 0xe4e1c),3, -1⟩]
noncomputable def parityTwoFifths_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_8_base compact_parityTwoFifths_pair_8_hinges x y
def compact_parityTwoFifths_pair_8_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2)]
private def zz221:"s00dd"="s00dd":=by decide+kernel
theorem compact_parityTwoFifths_pair_8_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_8_base compact_parityTwoFifths_pair_8_hinges 0 compact_parityTwoFifths_pair_8_cuts = true :=
  by decide +kernel
theorem compact_parityTwoFifths_pair_8_representation (x y:ℝ) :
    parityTwoFifths_pair_8 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_8_base compact_parityTwoFifths_pair_8_hinges x y:=by rfl
theorem parityTwoFifths_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_8 x y:=by
  rw [compact_parityTwoFifths_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_8_check hy (by simpa using hx)
def compact_parityTwoFifths_pair_9_base:CompactPair.Quadratic:=⟨(7 / 0xe4e1c00),(0x1f3d / 0x5f5e100),0⟩
def compact_parityTwoFifths_pair_9_hinges:List CompactPair.Hinge:=[⟨(-0x859dd / 0x2625a0),1, -3⟩,⟨(0x859ddd / 0x2625a00),1, -2⟩,⟨(-11 / 0x7270e00),2, -3⟩,⟨(-1 / 0x2625a00),2, -1⟩,⟨(1 / 0x4c4b400),3, -2⟩]
noncomputable def parityTwoFifths_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_9_base compact_parityTwoFifths_pair_9_hinges x y
def compact_parityTwoFifths_pair_9_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_parityTwoFifths_pair_9_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_9_base compact_parityTwoFifths_pair_9_hinges 0 compact_parityTwoFifths_pair_9_cuts = true :=
  by decide +kernel
private def zz222:"s00de"="s00de":=by decide+kernel
theorem compact_parityTwoFifths_pair_9_representation (x y:ℝ) :
    parityTwoFifths_pair_9 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_9_base compact_parityTwoFifths_pair_9_hinges x y:=by rfl
theorem parityTwoFifths_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_9 x y:=by
  rw [compact_parityTwoFifths_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_9_check hy (by simpa using hx)
def compact_parityTwoFifths_pair_10_base:CompactPair.Quadratic:=⟨(0x16da5d / 0x4c4b40),(0x3e9 / 0x989680),0⟩
def compact_parityTwoFifths_pair_10_hinges:List CompactPair.Hinge:=[⟨(0x79e1f / 0x4c4b40),1, -2⟩,⟨(-0x79e1f / 0x4c4b40),2, -1⟩]
noncomputable def parityTwoFifths_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_10_base compact_parityTwoFifths_pair_10_hinges x y
def compact_parityTwoFifths_pair_10_cuts:List ℚ:=[(1 / 2),2]
theorem compact_parityTwoFifths_pair_10_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_10_base compact_parityTwoFifths_pair_10_hinges 0 compact_parityTwoFifths_pair_10_cuts = true :=
  by decide +kernel
theorem compact_parityTwoFifths_pair_10_representation (x y:ℝ) :
    parityTwoFifths_pair_10 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_10_base compact_parityTwoFifths_pair_10_hinges x y:=by rfl
private def zz223:"s00df"="s00df":=by decide+kernel
theorem parityTwoFifths_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_10 x y:=by
  rw [compact_parityTwoFifths_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_10_check hy (by simpa using hx)
def compact_parityTwoFifths_pair_11_base:CompactPair.Quadratic:=⟨0,(0x18f / 0x989680),0⟩
def compact_parityTwoFifths_pair_11_hinges:List CompactPair.Hinge:=[]
noncomputable def parityTwoFifths_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityTwoFifths_pair_11_base compact_parityTwoFifths_pair_11_hinges x y
def compact_parityTwoFifths_pair_11_cuts:List ℚ:=[]
theorem compact_parityTwoFifths_pair_11_check :
    CompactPair.expressionCheckPSD compact_parityTwoFifths_pair_11_base compact_parityTwoFifths_pair_11_hinges 0 compact_parityTwoFifths_pair_11_cuts = true :=
  by decide +kernel
theorem compact_parityTwoFifths_pair_11_representation (x y:ℝ) :
    parityTwoFifths_pair_11 x y = CompactPair.expressionEval compact_parityTwoFifths_pair_11_base compact_parityTwoFifths_pair_11_hinges x y:=by rfl
theorem parityTwoFifths_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityTwoFifths_pair_11 x y:=by
  rw [compact_parityTwoFifths_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityTwoFifths_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalParityTwoFifthsPairs
private def zz2077:"s081d"="s081d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l16 l17 l20 l22 l25 l27 l29 l33 l34 l35 l36 l37 l38 l4 l42 l46 l5 l51 l54 l55 l56 l6 l60 l61 l62 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3baabfb, -0x927bb50, -0xdbb9b50,0x1b8dc2a], ![-0x927bb50, -0x1c528b76,0x47c110e,0x61c55c4], ![-0xdbb9b50,0x47c110e, -0x3a975601,0x927c4aa], ![0x1b8dc2a,0x61c55c4,0x927c4aa, -0x493e000]]
noncomputable def hinges:Hinges:=[(0x1a5dc,l6),(-0x1856739,l5),(0x1479e9a,l4),(0xa42cc5,l9),(-0x3473c94,l8),(0x634b98,l11),(0xb54c68,l10),(0x3f96b84,l14),(0xda83bc9,l13),(-0x2600bea,l17),(0x353f643,l16),(-0xda83bc9,l20),(0xa281426,l22),(-0x493e000,l27),(0x493e000,l29),(-0x3f96b84,l25),(0x493e000,l33),(-0xb54c68,l38),(-0x493e000,l35),(0x3473c94,l36),(0x493e000,l37),(-0x1479e9a,l34),(-0xa281426,l42),(0xc6ac4e,l46),(0x493e000,l51),(-0x634b98,l55),(0x1856739,l54),(-0x353f643,l56),(-0xa42cc5,l61),(-0x1a5dc,l60),(0x2600bea,l62),(-0xc6ac4e,l64)]
def normalizationDenominator:ℤ:=0xe4e1c00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x493e000,l27),(0x493e000,l29),(0x493e000,l33),(-0x493e000,l35),(0x493e000,l37),(0x493e000,l51),(0xda83bc9,l13),(-0xda83bc9,l20),(0xa281426,l22),(-0xa281426,l42),(0x3f96b84,l14),(-0x3f96b84,l25),(-0x2600bea,l17),(0x2600bea,l62),(0x353f643,l16),(-0x353f643,l56),(-0x3473c94,l8),(0x3473c94,l36),(0xa42cc5,l9),(-0xa42cc5,l61),(-0x1856739,l5),(0x1856739,l54),(0xc6ac4e,l46),(-0xc6ac4e,l64),(0xb54c68,l10),(-0xb54c68,l38),(0x634b98,l11),(-0x634b98,l55),(0x1479e9a,l4),(-0x1479e9a,l34),(0x1a5dc,l6),(-0x1a5dc,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase0" = "QuadParityTwoFifthsCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase0
private def zz2078:"s081e"="s081e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l43 l46 l5 l51 l54 l55 l56 l57 l59 l6 l60 l61 l62 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4096609, -0x927bb50, -0xdbb9b50,0x1a9bab8], ![-0x927bb50, -0x1d648947,0x4f71e52,0x5e65fde], ![-0xdbb9b50,0x4f71e52, -0x3a975601,0x927c4aa], ![0x1a9bab8,0x5e65fde,0x927c4aa, -0x493e000]]
noncomputable def hinges:Hinges:=[(0x1a5dc,l6),(-0x1856739,l5),(0x1479e9a,l4),(0xa42cc5,l9),(-0x3473c94,l8),(0x634b98,l11),(0xb54c68,l10),(0x83187c6,l14),(0x8b152,l13),(-0x127d20c,l17),(-0x2a718b3,l16),(0xd812fc0,l15),(0x13f1b4c,l21),(-0x8b152,l20),(-0x493e000,l27),(-0x13f1b4c,l28),(0x493e000,l29),(-0x83187c6,l25),(0x1674a00,l31),(0x228e7a8,l30),(0x493e000,l33),(-0xb54c68,l38),(-0x493e000,l35),(0x3473c94,l36),(0x493e000,l37),(-0x1479e9a,l34),(-0x228e7a8,l43),(-0xd812fc0,l41),(0x8adf4c,l46),(0x493e000,l51),(-0x634b98,l55),(0x1856739,l54),(-0x1674a00,l57),(0x2a718b3,l56),(0xccd52e,l59),(-0xa42cc5,l61),(-0x1a5dc,l60),(0x127d20c,l62),(-0xccd52e,l65),(-0x8adf4c,l64)]
def normalizationDenominator:ℤ:=0xe4e1c00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x493e000,l27),(0x493e000,l29),(0x493e000,l33),(-0x493e000,l35),(0x493e000,l37),(0x493e000,l51),(0x83187c6,l14),(-0x83187c6,l25),(0xd812fc0,l15),(-0xd812fc0,l41),(0x1674a00,l31),(-0x1674a00,l57),(0x228e7a8,l30),(-0x228e7a8,l43),(0x13f1b4c,l21),(-0x13f1b4c,l28),(-0x3473c94,l8),(0x3473c94,l36),(-0x2a718b3,l16),(0x2a718b3,l56),(0xccd52e,l59),(-0xccd52e,l65),(-0x127d20c,l17),(0x127d20c,l62),(0xa42cc5,l9),(-0xa42cc5,l61),(-0x1856739,l5),(0x1856739,l54),(0xb54c68,l10),(-0xb54c68,l38),(0x634b98,l11),(-0x634b98,l55),(0x8adf4c,l46),(-0x8adf4c,l64),(0x1479e9a,l4),(-0x1479e9a,l34),(0x8b152,l13),(-0x8b152,l20),(0x1a5dc,l6),(-0x1a5dc,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase1" = "QuadParityTwoFifthsCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase1
private def zz2079:"s081f"="s081f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l16 l17 l20 l21 l22 l27 l29 l33 l35 l37 l42 l44 l46 l51 l56 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x128d84da, -0xe4e1750, -0xdad6d26,0x5a1aebc], ![-0xe4e1750, -0x89895d71,0x24894ed0, -0x19d343c], ![-0xdad6d26,0x24894ed0, -0x63dcc8d8,0x115d4c1e], ![0x5a1aebc, -0x19d343c,0x115d4c1e, -0x7270e00]]
noncomputable def hinges:Hinges:=[(-0x620085,l9),(0x604f1a,l8),(0xc46d64,l11),(-0x2600bea,l17),(0x353f643,l16),(0x1a36fe6,l21),(-0xe514c6,l20),(0xa281426,l22),(-0x7270e00,l27),(0x7270e00,l29),(0x7270e00,l33),(-0x7270e00,l35),(0x7270e00,l37),(-0x736d14e,l42),(-0xf04700,l46),(0x8727f0c,l44),(0x7270e00,l51),(-0x67ffe66,l56)]
def normalizationDenominator:ℤ:=0xe4e1c00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x7270e00,l27),(0x7270e00,l29),(0x7270e00,l33),(-0x7270e00,l35),(0x7270e00,l37),(0x7270e00,l51),(0xa281426,l22),(-0x736d14e,l42),(-0x67ffe66,l56),(0x1a36fe6,l21),(-0x2600bea,l17),(0x8727f0c,l44),(0x353f643,l16),(0xc46d64,l11),(-0xf04700,l46),(-0x620085,l9),(-0xe514c6,l20),(0x604f1a,l8)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,0x2e0148020000002086601418080029c39047029340140000000000780a40100000001282402cc03000004a1304805a0060000000001e009200c007904505a03188028000000000d002c80300000002a12805980600000005821013300c000000000580124018000000000d80248030000000340480518060000000640b01c300c000000d410802c602000001a01040098c050000000032120398040040c73846011040140000000c45a0686018000611741802a10040000000331580a180600000006a2d014300e0a8c08148043948038000028a13c0768c0500000a21204812200600000000a4580e30080000000001580c40100000000015402880300011a3c068013a008000000b468140a400800a190205a04a88028000b31881500a9004], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase2" = "QuadParityTwoFifthsCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase2
private def zz2080:"s0820"="s0820":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l14 l15 l16 l17 l20 l21 l25 l27 l28 l29 l30 l31 l33 l35 l37 l41 l42 l46 l51 l56 l58 l59 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x12c3b839, -0xe4e1750, -0x10203906,0x6f1b18c], ![-0xe4e1750, -0x86bfb9db,0x24894ed0, -0x1d32a22], ![-0x10203906,0x24894ed0, -0x63dcc8d8,0x115d4c1e], ![0x6f1b18c, -0x1d32a22,0x115d4c1e, -0x7270e00]]
noncomputable def hinges:Hinges:=[(-0x620085,l9),(0x604f1a,l8),(0xc46d64,l11),(0x321b2e0,l14),(-0x127d20c,l17),(-0x2a718b3,l16),(0xd812fc0,l15),(0x24d4842,l21),(6,l20),(-0x7270e00,l27),(0xdadae,l28),(0x7270e00,l29),(-0x16ca8cc,l25),(0x1674a00,l31),(0x228e7a8,l30),(0x7270e00,l33),(-0x7270e00,l35),(0x7270e00,l37),(-0x68a39b7,l42),(-0xc29f2c2,l41),(-0x16ca8cc,l46),(0x7270e00,l51),(-0x4a6f15d,l56),(0x133af40,l59),(0x200c5e0,l58)]
def normalizationDenominator:ℤ:=0xe4e1c00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x7270e00,l27),(0x7270e00,l29),(0x7270e00,l33),(-0x7270e00,l35),(0x7270e00,l37),(0x7270e00,l51),(-0x68a39b7,l42),(0x24d4842,l21),(0xd812fc0,l15),(0x321b2e0,l14),(-0xc29f2c2,l41),(-0x4a6f15d,l56),(0x1674a00,l31),(0x228e7a8,l30),(0x133af40,l59),(-0x2a718b3,l16),(-0x16ca8cc,l25),(-0x16ca8cc,l46),(0xc46d64,l11),(-0x127d20c,l17),(0x200c5e0,l58),(-0x620085,l9),(0x604f1a,l8),(0xdadae,l28),(6,l20)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,0x3b0188020000000008406200800a32307302ad004000000000980520098210d0c2023410060000c8461a02c400c000000001d0248020000000003c0520080000138110058c040000004a0900b300c000250982402d003000000001e009200c0f208a0b4063100500000250740c630100000000027018802000000003400b200c00000000d404c803000000003700b200c000001509402cc0300000005848073008000001608404cc03000000002c009200c00000000d8024803000000680900a300c0001a01040098c05000000640b01c300c00001a8210058c04], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((0xe30b1ed4818c33dac37428c2cca403820d2ad64ac888c28d03630b0d1411c06994a00588a472420004887db12901040028e382b6699071a503f0a83cc9ab96fb9c42723d0f4f1c183097a78494d589b980074021c7749797c68e344274725a7987d4d86f038c07611fce9e3b4cce2670e146a8094cc88000002a303c030f63cc94a0008405000031860580001c20038bc8ea632446967ff69770101c0a43b9219c32c3b7fda840309f52bbea70301b7be57000001d4f012181008460400001a220008f6436807a58b068307fa1c496a) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 26 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase3" = "QuadParityTwoFifthsCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 26 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase3
private def zz2081:"s0821"="s0821":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase4
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l16 l22 l27 l29 l33 l35 l37 l42 l51 l56)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x457f4d1, -0x2625938, -0x2479231,0x12ad94], ![-0x2625938, -0x1563d445,0x2b652b4,0x24ab30b], ![-0x2479231,0x2b652b4, -0xf7f4900,0x2625ac8], ![0x12ad94,0x24ab30b,0x2625ac8, -0x1312d00]]
noncomputable def hinges:Hinges:=[(0x1155511,l16),(0x133cd8d,l22),(-0x1312d00,l27),(0x1312d00,l29),(0x1312d00,l33),(-0x1312d00,l35),(0x1312d00,l37),(-0x133cd8d,l42),(0x1312d00,l51),(-0x1155511,l56)]
def normalizationDenominator:ℤ:=0x2625a00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1312d00,l27),(0x1312d00,l29),(0x1312d00,l33),(-0x1312d00,l35),(0x1312d00,l37),(0x1312d00,l51),(0x133cd8d,l22),(-0x133cd8d,l42),(0x1155511,l16),(-0x1155511,l56)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[0x2301880200250982402d0030000000780248030000000d80248030001a8210058c0400000190901cc020000198ac050c0300000000e0148020740d02101e100403c0841400f100400000d84c050c03a20ae08801b500505409c1401b500405c0a01c0175004000000098024803000000070024803000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 11 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase4" = "QuadParityTwoFifthsCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 11 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase4
private def zz2082:"s0822"="s0822":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityTwoFifthsCase5
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l13 l15 l16 l20 l22 l27 l29 l33 l35 l37 l41 l42 l51 l56)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa0da14f, -0x4c4b270, -0x5601302,0x190], ![-0x4c4b270, -0x298b44f5,0x4169ddc,0x624054c], ![-0x5601302,0x4169ddc, -0x1efe9200,0x4c4b590], ![0x190,0x624054c,0x4c4b590, -0x2625a00]]
noncomputable def hinges:Hinges:=[(0x142303c,l13),(0x18cfb1f,l16),(0x40dfb96,l15),(-0x142303c,l20),(0x22e133d,l22),(-0x2625a00,l27),(0x2625a00,l29),(0x2625a00,l33),(-0x2625a00,l35),(0x2625a00,l37),(-0x22e133d,l42),(-0x40dfb96,l41),(0x2625a00,l51),(-0x18cfb1f,l56)]
def normalizationDenominator:ℤ:=0x4c4b400
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2625a00,l27),(0x2625a00,l29),(0x2625a00,l33),(-0x2625a00,l35),(0x2625a00,l37),(0x2625a00,l51),(0x22e133d,l22),(-0x22e133d,l42),(0x40dfb96,l15),(-0x40dfb96,l41),(0x18cfb1f,l16),(-0x18cfb1f,l56),(0x142303c,l13),(-0x142303c,l20)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityTwoFifthsCase5" = "QuadParityTwoFifthsCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityTwoFifthsCase5
private def zz2083:"s0823"="s0823":=by decide+kernel
end 
section 
namespace Green24Proof.ParityTwoFifthsRows
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x10304e2ad8005b3a0ae1fd61ec2a00180f0865604e2ad801ab5feaa1602b196c00aecd2da07d24ca5d001c8b6ae1ed204e2ad8012b590c21dd27a89800af8d61cd204e2ad800201d204e2ad8005d9a8e6520198cba00c96f19e1e927a898002cfc6ae149204e2ad8002b1b8c2120198cba00c96f19e07c27d800db6a61fc202b196c00bcbc61ec20198cba004fe9ba6420198cba00caecfd6078202b196c00ff2ebc21f8204e2ad8048eba5860204e2ad803aa5eeb214]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x11fc00198cba004afbeee16c04ca5d063a5e602c004e2ad8003b4e9de15c07a89800286d7821cc004e2ad80088eb4a601c002b196c003a5ee400386d00257068da0021702b196c025adca17d32692e82addca15d31389b426bafa05d304e2ad8005d9a8e653068da002029304e2ad800ba1d582059309c4da07c18e13068da00207c302b196c00295dfa61ec302b196c006b3aaae430198cba002d99cd2078304e2ad80069ad8ce14]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x1179502b196c0139eb69a149502b196c011aad4a21504e2ad8014dfd39e03c10198cba004a8f3ea16c104e2ad16baa802c11389b4019086aa1cc104e2ad800e92f6a205c102b196c004cfd286410386d002178102b196c01b8ae2e2148104e2ad8011dff382058104e2ad80138097ea010386d002540386d002440386d00217d002b196c00180b4de16d01ec2a04ec98a1dd004e2ad800690828a500386d00203c00198cba001b5a69a14]
def rowsChunk3:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x117d504e2ad8022f0ccfa02d504e2ad8020b7f79614d504e2ad8018e7ecbe5504e2ad800e9bf5fe04]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3
def mu:Phase → ℚ:=![(0x98fa941 / 0x989680),(-0x88eaca7 / 0x989680)]
def parameter:ℚ:=(2 / 5)
def normalization:ℚ:=(1 / 0x186a)
def quad0:Expression:=quadSlack rows parameter 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase0.base QuadParityTwoFifthsCase0.hinges QuadParityTwoFifthsCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase0.base QuadParityTwoFifthsCase0.hinges QuadParityTwoFifthsCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows parameter 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase1.base QuadParityTwoFifthsCase1.hinges QuadParityTwoFifthsCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz257:"s0101"="s0101":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase1.base QuadParityTwoFifthsCase1.hinges QuadParityTwoFifthsCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows parameter 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r58,RewriteAtoms.r55,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase2.base QuadParityTwoFifthsCase2.hinges QuadParityTwoFifthsCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase2.base QuadParityTwoFifthsCase2.hinges QuadParityTwoFifthsCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows parameter 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r59,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r67,RewriteAtoms.r68,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase3.base QuadParityTwoFifthsCase3.hinges QuadParityTwoFifthsCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz258:"s0102"="s0102":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase3.base QuadParityTwoFifthsCase3.hinges QuadParityTwoFifthsCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows parameter 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase4.base QuadParityTwoFifthsCase4.hinges QuadParityTwoFifthsCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase4.base QuadParityTwoFifthsCase4.hinges QuadParityTwoFifthsCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows parameter 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadParityTwoFifthsCase5.base QuadParityTwoFifthsCase5.hinges QuadParityTwoFifthsCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz259:"s0103"="s0103":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityTwoFifthsCase5.base QuadParityTwoFifthsCase5.hinges QuadParityTwoFifthsCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityTwoFifthsCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows parameter mu normalization 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r53,RewriteAtoms.r69]
def pair6Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_6_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_6_hinges
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_6_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows parameter mu normalization 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_7_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_7_hinges
private def zz260:"s0104"="s0104":=by decide+kernel
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_7_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows parameter mu normalization 0 1 false
def pair8Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r18,RewriteAtoms.r0]
def pair8Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_8_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
private def zz261:"s0105"="s0105":=by decide+kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_8_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_8_hinges x
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows parameter mu normalization 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53]
def pair9Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_9_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_9_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_9_hinges x
private def zz262:"s0106"="s0106":=by decide+kernel
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows parameter mu normalization 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r53,RewriteAtoms.r69]
def pair10Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_10_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_10_hinges
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_10_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows parameter mu normalization 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69]
def pair11Target:NormalForm:=CompactPair.toNormal LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_11_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_11_hinges
private def zz263:"s0107"="s0107":=by decide+kernel
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalParityTwoFifthsPairs.parityTwoFifths_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_11_base LocalParityTwoFifthsPairs.compact_parityTwoFifths_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalParityTwoFifthsPairs.parityTwoFifths_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows parameter p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
private def zz264:"s0108"="s0108":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows parameter mu normalization p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ParityTwoFifthsRows
private def zz2084:"s0824"="s0824":=by decide+kernel
end 
section 
namespace Green24Proof.ParityTwoFifths
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ParityTwoFifthsRows.rows ParityTwoFifthsRows.parameter p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityTwoFifthsRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ParityTwoFifthsRows.rows ParityTwoFifthsRows.parameter p q same x]
    exact ParityTwoFifthsRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ParityTwoFifthsRows.rows ParityTwoFifthsRows.parameter ParityTwoFifthsRows.mu ParityTwoFifthsRows.normalization p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityTwoFifthsRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ParityTwoFifthsRows.rows ParityTwoFifthsRows.parameter ParityTwoFifthsRows.mu ParityTwoFifthsRows.normalization p q same x]
    exact ParityTwoFifthsRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible ParityTwoFifthsRows.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  ((2 / 5:ℝ) * U - V) * ((-0x1ee8941 / 0x2625a00:ℝ) * U + (0x3c9f8a7 / 0x2625a00:ℝ) * V) -
    (1 / 0x61a8:ℝ) * (U + V) ^ 2
private def zz265:"s0109"="s0109":=by decide+kernel
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (9 / 25:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ParityCorrectionAggregation.correction_of_local_rows h3 h5
    ParityTwoFifthsRows.rows ParityTwoFifthsRows.parameter ParityTwoFifthsRows.mu
    ParityTwoFifthsRows.normalization rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ParityTwoFifthsRows.mu 0 = (0x98fa941 / 0x989680:ℚ):=by decide +kernel
  have hmu1:ParityTwoFifthsRows.mu 1 = (-0x88eaca7 / 0x989680:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num [ParityTwoFifthsRows.parameter,ParityTwoFifthsRows.normalization] at hc
  unfold massCorrection
  nlinarith only [hc]
theorem massCorrection_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(2:ℝ) * V ≤ U) (hhigh:U ≤ (0xf9 / 0x64:ℝ) * V) :
    (0x49143a5d / 0xe8d4a51000:ℝ) * V ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(2:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (0xf9 / 0x64:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_lower_bound hV hlow hhigh
  nlinarith [sq_nonneg (mass v)]
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(0x18d / 0xc8:ℝ) * V ≤ U) (hhigh:U ≤ (11 / 5:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [sq_nonneg V,mul_nonneg hV (sub_nonneg.mpr hhigh)]
private def zz266:"s010a"="s010a":=by decide+kernel
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(0x18d / 0xc8:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (11 / 5:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ParityTwoFifths
private def zz2085:"s0825"="s0825":=by decide+kernel
end 
section 
namespace Green24Proof.LocalParityNineTenthsPairs
def compact_parityNineTenths_pair_6_base:CompactPair.Quadratic:=⟨(-1 / 0xe4e1c0),(0x270f / 0x5f5e100),0⟩
def compact_parityNineTenths_pair_6_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x7270e00),1, -3⟩,⟨(1 / 0x7270e00),3, -1⟩]
noncomputable def parityNineTenths_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_6_base compact_parityNineTenths_pair_6_hinges x y
def compact_parityNineTenths_pair_6_cuts:List ℚ:=[(1 / 3),3]
theorem compact_parityNineTenths_pair_6_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_6_base compact_parityNineTenths_pair_6_hinges 0 compact_parityNineTenths_pair_6_cuts = true :=
  by decide +kernel
theorem compact_parityNineTenths_pair_6_representation (x y:ℝ) :
    parityNineTenths_pair_6 x y = CompactPair.expressionEval compact_parityNineTenths_pair_6_base compact_parityNineTenths_pair_6_hinges x y:=by rfl
theorem parityNineTenths_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_6 x y:=by
  rw [compact_parityNineTenths_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_6_check hy (by simpa using hx)
def compact_parityNineTenths_pair_7_base:CompactPair.Quadratic:=⟨0,(0x3e9 / 0x17d7840),0⟩
def compact_parityNineTenths_pair_7_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineTenths_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_7_base compact_parityNineTenths_pair_7_hinges x y
def compact_parityNineTenths_pair_7_cuts:List ℚ:=[]
private def zz267:"s010b"="s010b":=by decide+kernel
theorem compact_parityNineTenths_pair_7_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_7_base compact_parityNineTenths_pair_7_hinges 0 compact_parityNineTenths_pair_7_cuts = true :=
  by decide +kernel
theorem compact_parityNineTenths_pair_7_representation (x y:ℝ) :
    parityNineTenths_pair_7 x y = CompactPair.expressionEval compact_parityNineTenths_pair_7_base compact_parityNineTenths_pair_7_hinges x y:=by rfl
theorem parityNineTenths_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_7 x y:=by
  rw [compact_parityNineTenths_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_7_check hy (by simpa using hx)
def compact_parityNineTenths_pair_8_base:CompactPair.Quadratic:=⟨0,(0x36b3 / 0x5f5e100),0⟩
def compact_parityNineTenths_pair_8_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineTenths_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_8_base compact_parityNineTenths_pair_8_hinges x y
def compact_parityNineTenths_pair_8_cuts:List ℚ:=[]
theorem compact_parityNineTenths_pair_8_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_8_base compact_parityNineTenths_pair_8_hinges 0 compact_parityNineTenths_pair_8_cuts = true :=
  by decide +kernel
private def zz268:"s010c"="s010c":=by decide+kernel
theorem compact_parityNineTenths_pair_8_representation (x y:ℝ) :
    parityNineTenths_pair_8 x y = CompactPair.expressionEval compact_parityNineTenths_pair_8_base compact_parityNineTenths_pair_8_hinges x y:=by rfl
theorem parityNineTenths_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_8 x y:=by
  rw [compact_parityNineTenths_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_8_check hy (by simpa using hx)
def compact_parityNineTenths_pair_9_base:CompactPair.Quadratic:=⟨(-1 / 0x1c9c380),(0x7cd / 0x17d7840),0⟩
def compact_parityNineTenths_pair_9_hinges:List CompactPair.Hinge:=[⟨(1 / 0x7270e00),1, -3⟩,⟨(-1 / 0x1312d00),1, -1⟩,⟨(1 / 0x7270e00),3, -1⟩]
noncomputable def parityNineTenths_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_9_base compact_parityNineTenths_pair_9_hinges x y
def compact_parityNineTenths_pair_9_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_parityNineTenths_pair_9_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_9_base compact_parityNineTenths_pair_9_hinges 0 compact_parityNineTenths_pair_9_cuts = true :=
  by decide +kernel
theorem compact_parityNineTenths_pair_9_representation (x y:ℝ) :
    parityNineTenths_pair_9 x y = CompactPair.expressionEval compact_parityNineTenths_pair_9_base compact_parityNineTenths_pair_9_hinges x y:=by rfl
private def zz269:"s010d"="s010d":=by decide+kernel
theorem parityNineTenths_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_9 x y:=by
  rw [compact_parityNineTenths_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_9_check hy (by simpa using hx)
def compact_parityNineTenths_pair_10_base:CompactPair.Quadratic:=⟨0,(1 / 0x2710),0⟩
def compact_parityNineTenths_pair_10_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineTenths_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_10_base compact_parityNineTenths_pair_10_hinges x y
def compact_parityNineTenths_pair_10_cuts:List ℚ:=[]
theorem compact_parityNineTenths_pair_10_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_10_base compact_parityNineTenths_pair_10_hinges 0 compact_parityNineTenths_pair_10_cuts = true :=
  by decide +kernel
theorem compact_parityNineTenths_pair_10_representation (x y:ℝ) :
    parityNineTenths_pair_10 x y = CompactPair.expressionEval compact_parityNineTenths_pair_10_base compact_parityNineTenths_pair_10_hinges x y:=by rfl
theorem parityNineTenths_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_10 x y:=by
  rw [compact_parityNineTenths_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_10_check hy (by simpa using hx)
def compact_parityNineTenths_pair_11_base:CompactPair.Quadratic:=⟨(1 / 0xe4e1c0),(0x31f / 0x1312d00),0⟩
def compact_parityNineTenths_pair_11_hinges:List CompactPair.Hinge:=[⟨(1 / 0x7270e00),1, -3⟩,⟨(-1 / 0x7270e00),3, -1⟩]
noncomputable def parityNineTenths_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineTenths_pair_11_base compact_parityNineTenths_pair_11_hinges x y
def compact_parityNineTenths_pair_11_cuts:List ℚ:=[(1 / 3),3]
private def zz270:"s010e"="s010e":=by decide+kernel
theorem compact_parityNineTenths_pair_11_check :
    CompactPair.expressionCheckPSD compact_parityNineTenths_pair_11_base compact_parityNineTenths_pair_11_hinges 0 compact_parityNineTenths_pair_11_cuts = true :=
  by decide +kernel
theorem compact_parityNineTenths_pair_11_representation (x y:ℝ) :
    parityNineTenths_pair_11 x y = CompactPair.expressionEval compact_parityNineTenths_pair_11_base compact_parityNineTenths_pair_11_hinges x y:=by rfl
theorem parityNineTenths_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineTenths_pair_11 x y:=by
  rw [compact_parityNineTenths_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineTenths_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalParityNineTenthsPairs
private def zz2086:"s0826"="s0826":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa7a5f38, -0x714bc28, -0xa9f1b68,0x5bb42c], ![-0x714bc28, -0x3b6b8c31,0xda9535f,0x3877e15], ![-0xa9f1b68,0xda9535f, -0x2e2f5e47,0x71ee2d9], ![0x5bb42c,0x3877e15,0x71ee2d9, -0x38a5f40]]
noncomputable def hinges:Hinges:=[(-0x51102,l4),(0x51101,l10),(0x280221,l14),(0x189c7,l17),(0xde15ba3,l15),(-0x38a5f40,l27),(0x38a5f40,l29),(-0x280221,l25),(0x158ad7,l30),(0x38a5f40,l33),(-0x51101,l38),(-0x38a5f40,l35),(0x38a5f40,l37),(0x51102,l34),(-0x158ad7,l43),(-0xde15ba3,l41),(0x38a5f40,l51),(-0x189c7,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x38a5f40,l27),(0x38a5f40,l29),(0x38a5f40,l33),(-0x38a5f40,l35),(0x38a5f40,l37),(0x38a5f40,l51),(0xde15ba3,l15),(-0xde15ba3,l41),(0x280221,l14),(-0x280221,l25),(0x158ad7,l30),(-0x158ad7,l43),(0x51101,l10),(-0x51101,l38),(0x189c7,l17),(-0x189c7,l62),(-0x51102,l4),(0x51102,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    0x91b120004d208a48083601081009c88e104bbf0c74a0c35b02c26083400800009420002dc40ac360541b0290980802c0a00401e039265e0f708210f4f905143d2138808e46808500e49c0c0025181800851577fa68c318e89a486f27780c043e6fe00505058011865deed70e3822b0d1618633639600e00828a0094fe2812860c00434dc0567e308046dd420817b28e24725951930613186d0942060021a6d8da6320801ee906080c232cd0009b309200a360500002246416081700400007b10001ea365dfb3201451450930e2823e039a00742ae980101eb19400d746a80cc203001000010120007f84001324c10fb5bd438fadcbec4084bd362208b9b2903815198d81809573f60004c38300100001072026320006fc204e3b8135cb08303fa32c9020a00238f038b4201274064810500100000c2607076878c36eede850283a1a2000e39b090205402000015240983404a1a0240d01182808804042020200180f80800092880063f9001e8e3e098431c683311e8e8ed245d966ffbc296157266c000000000000001c0115204d40cd0aa51be1a2b8474cda0706daaa80000000000000669a92edde83548d5b8a15351ea0090992f9ba80000000000001898c30818c00a002020000466c22897bfd1d6e62ccfb4a01e3d64e4e640ca6b442460d328719514270eb322e32f5e51800739d61c3ed90e6b42726de5f84ee654f9c0d84babd0a82d44e919b8c204ce6eb1cdb4f126df0d128a6a8293d01e010002c110029442006aae6c5a985a1a41a641cf5d40781711c71c51c30c21c11811010c00400154c90008036b56f8bcae24d1a33e93a45dba8fa796dcde5af80000000000000000000000000000000000000004e12082021c21421c10c004000001070380200d925641e300a20503b1d24342cf91a4070e67c2060d1564ff120830d49f0c008e3200100e675bb405a0506c0215ab7c5e571268d19f49d22edd47d3cb6e6f2d7c0000000000000000000000000000000000000002709451421220e21218e08a00600260400401b6592650b452c50c2e288e8431628000124f8050b49a3160261028000124f80508663f91a4606005a24fc94e0fd070c2602c71c0fe3be82c6d42e49c09194f7229214172c83008a0069893e618025ad1724400ac5ddc60a3840f00a347190c2bf060f8c2d1878a1c0000bb81010b8e1b9108103df8bdc6818e4d70a830041705d300042ec3a26290083e028e20ebeb302690d64b5f12c800000019a3b003afd8e19197581e58a0000e0a0817025f3c1a06beca9f0300173ccf5a40074031c704eea721c6031a3429c48018b019a490697769c40286f6c1a458b038b100000082ace003801000013920005ce40012008002f4100079120012f840744400161e400340080e0ac00c0503012677028400069ec5040547200808fb74b11400adc5d2201a59a080026101b00800d80f0c0005030a1118678a1030631990a04189596012080d004304050e1b840401cc15840a9ed55d0c003f3106101c9d7ef4025101b00800007590001c62034130190900c04c05c2743490ef2a40449d3b30e10084c6e30504d0b410001386d8300851e7286000fbfba4e0834010a181b99538619b619101828e6c54410015fb85890106c02000017e4058260240b0100180780f083ade660910adaa22204d3fa730c0c2bba6f103c2fba88a0009c7c320016534ec9c1068021840392b93244148d13240908a3ad4c0c0eefcd081a5b2d2625041b008000073101505d8e614a12901c2fbd84387d923488612a008722820af10c9600d582da04c183401000010b34320e5e9620835e8220e1476cfdc305bfa549840ad533e25002d625a06003e7966013880d00400004cc80508800133080a0cc04c570100100400900c044040200300f01c043641418342c090220c150084825898f080de4c5a1826077798006e30c4809d539812860b0040000344c0cf1374307555772bd179860782193cdd848f8e39f8769d697cafd2580aa862d4cc54148efe014b810a85e5c12b296aba15a329b6d7bff28c01263cfee274aaf5fde4e6a6c17d4819acda472e5dcd1f122b3c7b600b1c84c95b3787e36343fde19579d2d4743514f256f6613f28ff9949c9fa398471e72732ac3e46f047c38916edcb5a0c32fa1d6621ac610000463201c0a82071fdd3d55ddcc754c75105bb2767eaf14146cdeaa8a2260c505356e53abad1de81674c4d143479dd7b59f4a4a62423a82529408772a16fd7599c9c75c7c69e9f58481d4afe5f3a1b864b1ca21cfa845feacf27bd826c94b86d60a4cdef8f981c82e91c485ee9180253fbcf16e3f6cec19343cb182f512a013b446198456000d0d00602c02c040008764028540014a44002b8c80093510015e1345eefd60aa050c16e82e8018101ca84dc0505041bfe241010032b5bd040021135a2d0800b873fff800a38a1100a38e56eb9e09cc103085984a3b1934e38415dd27d18c003057b1c5866bdfc284861b84dd2f9220083b080610e9201e848061030054410a51a3340e3d23b659c38a0df8ab4901816ed0b0386d4711208c1802891640800b786c70000e80c910000601a914060f0042491f7a2810411219b079891803d135c1220157b46a20434aebdf608215ed6ef0400012e3348ce103e0109181e57df2a920662243aaa649101362d9c67204887fc0898c9080f1c5511f200cf928a8c5030004f3bf7500fa0e104c05800018c20005f240012a48003339009190040a801c2400c0a005010020080021bc8018c80086400202000010016939))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase0" = "QuadParityNineTenthsCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase0
private def zz2087:"s0827"="s0827":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa8dd015, -0x714bc28, -0xa9f1b68,0x368c1c], ![-0x714bc28, -0x3a548e3e,0xd566117,0x3b4583e], ![-0xa9f1b68,0xd566117, -0x2e2f5e47,0x71ee2d9], ![0x368c1c,0x3b4583e,0x71ee2d9, -0x38a5f40]]
noncomputable def hinges:Hinges:=[(-0x51102,l4),(0x51101,l10),(0x636ad3,l14),(0x63ce0,l17),(0xdafb2ae,l15),(-0x38a5f40,l27),(0x38a5f40,l29),(-0x636ad3,l25),(0x3058c8,l30),(0x38a5f40,l33),(-0x51101,l38),(-0x38a5f40,l35),(0x38a5f40,l37),(0x51102,l34),(-0x3058c8,l43),(-0xdafb2ae,l41),(0x38a5f40,l51),(-0x63ce0,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x38a5f40,l27),(0x38a5f40,l29),(0x38a5f40,l33),(-0x38a5f40,l35),(0x38a5f40,l37),(0x38a5f40,l51),(0xdafb2ae,l15),(-0xdafb2ae,l41),(0x636ad3,l14),(-0x636ad3,l25),(0x3058c8,l30),(-0x3058c8,l43),(0x63ce0,l17),(-0x63ce0,l62),(0x51101,l10),(-0x51101,l38),(-0x51102,l4),(0x51102,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x1441942100b8200a000000001a014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase1" = "QuadParityNineTenthsCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase1
private def zz2088:"s0828"="s0828":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l53 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l53, ![-0x7270ba8, -0x3d22a1f9,0xd838736,0x36c06d5], ![-0x98d7cfb,0xd838736, -0x2f2683a1,0x7527351], ![0x258,0x36c06d5,0x7527351, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x258dc,l6),(-0xeeaa0,l4),(0x14a875,l10),(0x189c7,l17),(0xde15ba3,l15),(-0x3938700,l27),(0x3938700,l29),(0x158ad7,l30),(0x3938700,l33),(-0x4cc69,l38),(-0x3938700,l35),(0x3938700,l37),(0x4cc68,l34),(-0x3801d0,l43),(-0xc979a10,l41),(0x3938700,l51),(-0x3801d0,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xde15ba3,l15),(-0xc979a10,l41),(-0x3801d0,l43),(-0x3801d0,l62),(0x158ad7,l30),(0x14a875,l10),(-0x4cc69,l38),(-0xeeaa0,l4),(-0x258dc,l6),(0x189c7,l17),(0x4cc68,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x1b00a401000000000980720081441942100b8200a000000001a014802000000000280c4010000000443c0530080004a1304805a0060000000078024803], #[]⟩
def dynamicCode : Nat := (((((((0x59767a4fee2ca02d72619451bfeb6b0b218d25a085102231b9728700987a11000018aee89c107402008e03b2e661c00d8b2830a98e38c24c39b983cb2430a9835450808c27a2c4085bcb76c8c0582fba2c8a3821000a2cb8a2e76962ca0af378d93890008cf613092bee54eb2c90af34ea914201fbe4c810214a5f9e2301577d3bf8380002b35ea25208400280001b2200064e68ac7e581ee2c848014ff528818070c032c433c494ff28125b231900410ece953a0c0005ad5730401896be7fa4001000a011c0765c78874a0b2812d1a7e6124f0af912c904b467d1829df76608b08bad3ac660299fe51b9c007402165d0728cdf0b28152c04ba61258c2fd8c2c9054ad6fe982a1ac02000b08d24a0344702002c0ce53015) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase2" = "QuadParityNineTenthsCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase2
private def zz2089:"s0829"="s0829":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l46 l51 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xaf0ddfe, -0x7270ba8, -0x98214f0,0x258], ![-0x7270ba8, -0x3cac5cc4,0xd298bf2,0x398e0fe], ![-0x98214f0,0xd298bf2, -0x2f2683a1,0x7527351], ![0x258,0x398e0fe,0x7527351, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x258dc,l6),(-0xeeaa0,l4),(0x14a875,l10),(0x3df95e,l14),(-0x1e5aa2,l12),(0x63ce0,l17),(0xdafb2ae,l15),(-0x3938700,l27),(0x3938700,l29),(-0x26769e,l25),(0x3058c8,l30),(0x3938700,l33),(-0x4cc69,l38),(-0x3938700,l35),(0x3938700,l37),(0x4cc68,l34),(-0xd0328ee,l41),(-0x1106ce,l46),(0x3938700,l51),(-0x28e979,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xdafb2ae,l15),(-0xd0328ee,l41),(0x3df95e,l14),(0x3058c8,l30),(-0x28e979,l62),(-0x26769e,l25),(0x14a875,l10),(-0x1106ce,l46),(-0x1e5aa2,l12),(0x63ce0,l17),(-0x4cc69,l38),(-0xeeaa0,l4),(-0x258dc,l6),(0x4cc68,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((0x110e10221c1ed8de4db1bca05ca172c7d8e7a6ea0d0e45415230c34b2cb3092c930804124030080200d06801e19db4206861627156ae694977eec8614272942430404054202044a4bed66832fa1c324e0838010c3216a1116430b0b00acaf4f2800233d8434a2a8b854c0c282c0209fd1820124567ac40853941b0934155b8b4b50f0000acd7a8244821100e000071880018e1d27330d2732f2cd0dbe553a0067c6544a35554933431ff4769b69d97042f28000000000000000000000000000000000004622cb3092c93052c10410c0040c000080341a0078645437670c2c13811f06944c8c32730a04e53d99a31d2b42c0c08bb7c33a68297042569c0074021864de3330a0c2c15f9558069455fd5e4e30a057e2b301a320c73fdc8c08d311676c782002c0ce5341555ff8fd1e00013671ce4900210180000dd100031520ce1200056c324db6e3aa2d124001b1d49018384d722fd71438ecc7f00a92382121f6de141a3e1d86b718102cd76a2f9408ff63b7ca0c001110a51c006348812010000077cc117d4553458c275c2e248cc6cda8840c219d1364843e8419438004b92003002ef3ffa20ce283801000014320cc0b926b4bb5550a1c6313363891c1d4c01804100448d7a870800f2b94430872a21a04c041c71e2aca04540d2b4cc0058b7e1000724408004124fea84661838f2e8d5943a47441f9239fc86a49418e23c9d0e002e658b0601343dc608ce203801000014130478db5561630e929bb1232d3844990306f49a3121104864704087108330c00c1797708b38a0e004000050c833088001218c0d0baa70d4cb2442eece6a9310e232e5075315c6114df858f0ec48240e20fd18c20030a423e27a8a0307431b5880400167a90d2d410000bb709e8001149c412405207800021b20302be3e505fc711430424880d14284685b4110293a811a30e28445c03808105ab5f860415d0b9c9f1008d18334290016b85e83800f48c1000838f0824cc850c3eac1e850a23f737440ac288f3e2803620f4e00328c0e00400003d0c0c42b95767a922ac08ecbd8848839ece3d6f0e2163281c2e4308a756d2369100465df813442806992496f5040027b77a3de080fd081c2602c0000e4106519010028001358e62d847f7a0d2e57b01f730a6d207088707665462da211b688481676dac0de39ee5d2ecb1a6054c61870c40c7084082045004d23e5e431010504e31df449817080a41932cb1312f36a232d76070056084586c5467145abb16) <<< 16000) +
    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)) <<< 16000) +
    0xfd7000000000000003411c62442432031c21000408f73b5a9466672ce148273aa847ac4555a11ad2083c92359c558edc5e977047f1ae80011f105009c1006963c5a0101ab50945174386b79524916081dd59e65bdc304c0ff86e5f8a1486fc40516204c8876b51b08080001356001021111fac4f63048013018208029956d7e0101a220fbb8cfc70d21bec8954820726e12f80791824b7a989dc80a138d093711c44093e50e8054220200003d090008107310a33ccce209002903c00010599136a4c52b83a409c18ddac0122434f21f9e46c901dc6c5e5683470a7ffa11fbda2827bb3785d3918007cba8fa2013881c10a40f0000346410406000bcc413c45033182be19a40a00004d580e2e9eb3ee803852288808f8c12cef1b3e03823dd616e90c0804f4022c1805efad05f8210a0508807000034041386409a0a04c0102580812804001c824124b60905b047298098ac118371adc47ee39bbccd57f9ac0af580f6d697849ca5b25e5778c3be5230000000000000000000000000000000007e4288400380280100020a0977b7435eae19606f8dfe9010f06646ff2a18619cea58fbe24643f5ff67478895a22f30539bd16bf73b4ee62323e9720094882e0740f0aba4182d43ce9f8409c9376435b2cb64c796b1dfb83d6dc119ec2bda0b89cec919d12fc6930b30a0d4f308a7bc5aaa4d965a82d4164d7f6f8cc205001008a03042016189037f8305ae25981e080bfaa0f00fada7e480832010c0f7426e10521a1a1413f5ca860c8069d90105402000014e411026086130001a3301b7114a2357b35197e533f7fca4b1876a14e86dc92a1b97f3c462552c9c7449118196d0d96a8815cefe1c01a8f9c63a9b05f168835cda9893c9bd378ff217aa599c2245ca8a6b176c5a0c6ca0c159e20327de91f18008d54ccd5a98c779f714cd2f73f8ce0fb7a6fcd7d2fdc92753c7049667af1c8e3a9e7dd8d22a1bdb6905e859182a666a0ac1a7e18952bb215e79f596840a1de05a40c8f6db6192dc2b10089d58ddee7c302b6ac1397140e1f4e3c393a82f393215cc74ceb850c4743236f07fcffff36d41f25b48f4b80ec1fd186a426601080581d9f8e8142fa430878113c5bc23081700860711f04486d81922853b1ea18573db03408140040000521041098000b1100082d20782b924d97a1020a79bce380a2857e11840b80420100200800002220801b808e893e7013915716004958a400512f4012060b004200802008800227508081dbfeab2204190080000369d0243d6610840a804000011880008590001d4207e1b03c0500017c903e11cb07f7a0d2e57b01f752b46e07165034b62bf3cc44c7fbcaa740197a5725a018902cc90c5043042049004001b3b483cbda26324654e6d860341307cce5b135f4eb5ce8ab9b104f2ef3a87fbf518522c77b4203ffae11034a3a7fa48484019144096498cf8615732d5c0800954d8233040d8042841fdee0c40baf1f840c29ccf6e470403316818005d0b8040024185b098206802000021240f4040780200025d202a320131180c0280014f481d92c0e87701001004608032f1e470c07e287861f947bb2080034d5562481836010e00b65af0c0bfdda0048305c0100000d6400052481c86e0806ef185f12180de358706080120ec2e10503b6f17a2010efd024b060870bf69941000727d290a51c308405121c336e303045f5a7e8a0963ca08183483c810c0089c9c21013195a3013060d004000042c80a8880600400056a40bc5405c1b038090160480a8140009a840742787d2ed5416091266f22002c7ca184610340108020080228bf2f0a71a1841072c7001fc45d960026981b2000d00420000200800002220001ea40004c880a86c0843606e1b0130d01b06c0d4240220392621d2dc20800651c34008fcfe8c002f339c5006fc9860084a3832010a2afcacbc48a00abf104119cdc01200f8d6b801905064021014232dda4614bbde788800031fe9c602188f9ec1903070021a6e3d56fa232332f08200a730f13041800469b87b91a2400548f68e0100d6588c106402000012440d0160002a06cbd412fe143006ee1870c0b64667804a0d3f0090406402000017a4000c2c819808000fe8c1190dc501a56844dd1ea2884de3f8a9cd9ca3be513342e76b0408056f110966675b39be5b7857e6ce4f82aaf4f65ab23614dc20865b373a9eebdf75e5a107657fbb641d6e4b8a739f9a48890380691d20cf01cf92907a3dd8f0c90099acb76e183afd3162cc1804a7dce7160e5ff11ecf8d58dc01002de36f66240a085e7b800010234a1ce9772b64f006ebf9dacc3e3760ec8a091c4b82b01b7b84e40d28edbbdc18d8759395da98d51506cf08c520c02a40002ca10180900056090322981890e0707a143c1c74b0d41c1c3026981e14202188e814103a05510419158f8c5260c1c00840ecdc1d050085c9e8204b62b80230c170080000481030110178680b81605a0202c010158080a804052030280100013f9001015200515067b1c04748a37e9cc969aef69fa68dc761e2cd7158000000000000006e982ef2ec714e297f977293419cf02b22c2078c68000000000000001b09cd7d1354f95c41f19aa1ea20c6242cf080000000000005c6206186300280080a00001c7ec4d3937cdc223a86b46d86a1f5f800f6c094d75dcc71301038fde627d99ab7bead7d3e61a91085c49e99ed1e6ebd7733be3e31c8a7b83ff5b8b75b2123b779972415126d4c4192a021712b4d504f526a000ada400cc6c803bc89e3dfe017b01ef887147bbe8feb7290386560)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase3" = "QuadParityNineTenthsCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase3
private def zz2090:"s082a"="s082a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l53 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l53, ![-0x7270ba8, -0x3d458730,0xc5d13b0,0x45a27f5], ![-0x98d7cfb,0xc5d13b0, -0x2f580d89,0x75d9cfb], ![0x258,0x45a27f5,0x75d9cfb, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x1b4650,l4),(0x1b4651,l10),(0x3801d0,l17),(0xc979a10,l15),(-0x3938700,l27),(0x3938700,l29),(0x3801d0,l30),(0x3938700,l33),(-0x1b4651,l38),(-0x3938700,l35),(0x3938700,l37),(0x1b4650,l34),(-0x3801d0,l43),(-0xc979a10,l41),(0x3938700,l51),(-0x3801d0,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xc979a10,l15),(-0xc979a10,l41),(0x3801d0,l17),(0x3801d0,l30),(-0x3801d0,l43),(-0x3801d0,l62),(0x1b4651,l10),(-0x1b4651,l38),(-0x1b4650,l4),(0x1b4650,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase4" = "QuadParityNineTenthsCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase4
private def zz2091:"s082b"="s082b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineTenthsCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l33 l34 l35 l37 l38 l4 l41 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xadfd730, -0x7270ba8, -0x98214f0,0x258], ![-0x7270ba8, -0x3ba9ed67,0xc5f4ccc,0x3fbd069], ![-0x98214f0,0xc5f4ccc, -0x2f580d89,0x75d9cfb], ![0x258,0x3fbd069,0x75d9cfb, -0x3938700]]
noncomputable def hinges:Hinges:=[(-0x1b4650,l4),(0x1b4651,l10),(0x28e979,l17),(0xd0328ee,l15),(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x1b4651,l38),(-0x3938700,l35),(0x3938700,l37),(0x1b4650,l34),(-0xd0328ee,l41),(0x3938700,l51),(-0x28e979,l62)]
def normalizationDenominator:ℤ:=0x7270e00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3938700,l27),(0x3938700,l29),(0x3938700,l33),(-0x3938700,l35),(0x3938700,l37),(0x3938700,l51),(0xd0328ee,l15),(-0xd0328ee,l41),(0x28e979,l17),(-0x28e979,l62),(0x1b4651,l10),(-0x1b4651,l38),(-0x1b4650,l4),(0x1b4650,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineTenthsCase5" = "QuadParityNineTenthsCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineTenthsCase5
private def zz2092:"s082c"="s082c":=by decide+kernel
end 
section 
namespace Green24Proof.ParityNineTenthsRows
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x106c002b196c006e0d6400386d00257068da00217068da00205d304e2ad80448dce5304e2ad80448f9613068da0024302b196c024aeda030c9ac002b9825602b196c010bfc4a2160fa19069c0aa07d204e2ad8001f7f2de02d204e2ad8028bcb601d204e2ad800199ed9e527a89800782c5ee1204e2ad802484da9207c204e2ad80069baba6424ca5d004eae2e607827a89804081da027a898007c4d09e14]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x1157a898001a0cad603c14ca5d030acb202c10c9ac001baeeca01c161d407fe410386d002038104e2ad8001acabae028104e2ad804a83cfc2018104e2ad800ca78e010386d00203d404e2ad8001da99a206d42692e804c5ee540386d00203c404e2ad8026b1d206c44ca5d001ccde440386d00203d07a89802186e206d01389b4019f8e05d01ec2a078965002b196c004c0e203c004e2ad8028c48214]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x102d502b196c022d9c5fa01d504e2ad8002c7a5f2552692e8348ad6039507d0c805ccf202952692e80499a296019507d0c805ccf206]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2
def mu:Phase → ℚ:=![(0x3eb2ae9 / 0x4c4b40),(-0x3bd6429 / 0x4c4b40)]
def parameter:ℚ:=(9 / 10)
def normalization:ℚ:=(1 / 0x186a)
def quad0:Expression:=quadSlack rows parameter 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadParityNineTenthsCase0.base QuadParityNineTenthsCase0.hinges QuadParityNineTenthsCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase0.base QuadParityNineTenthsCase0.hinges QuadParityNineTenthsCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows parameter 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadParityNineTenthsCase1.base QuadParityNineTenthsCase1.hinges QuadParityNineTenthsCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz280:"s0118"="s0118":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase1.base QuadParityNineTenthsCase1.hinges QuadParityNineTenthsCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows parameter 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadParityNineTenthsCase2.base QuadParityNineTenthsCase2.hinges QuadParityNineTenthsCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase2.base QuadParityNineTenthsCase2.hinges QuadParityNineTenthsCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows parameter 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadParityNineTenthsCase3.base QuadParityNineTenthsCase3.hinges QuadParityNineTenthsCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz281:"s0119"="s0119":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase3.base QuadParityNineTenthsCase3.hinges QuadParityNineTenthsCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows parameter 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadParityNineTenthsCase4.base QuadParityNineTenthsCase4.hinges QuadParityNineTenthsCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase4.base QuadParityNineTenthsCase4.hinges QuadParityNineTenthsCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows parameter 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadParityNineTenthsCase5.base QuadParityNineTenthsCase5.hinges QuadParityNineTenthsCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz282:"s011a"="s011a":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineTenthsCase5.base QuadParityNineTenthsCase5.hinges QuadParityNineTenthsCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineTenthsCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows parameter mu normalization 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_6_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_6_hinges
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_6_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows parameter mu normalization 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_7_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_7_hinges
private def zz283:"s011b"="s011b":=by decide+kernel
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_7_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows parameter mu normalization 0 1 false
def pair8Rewrites:Rewrites:=[]
def pair8Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_8_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
private def zz284:"s011c"="s011c":=by decide+kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_8_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_8_hinges x
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows parameter mu normalization 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r28]
def pair9Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_9_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_9_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_9_hinges x
private def zz285:"s011d"="s011d":=by decide+kernel
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows parameter mu normalization 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_10_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_10_hinges
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_10_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows parameter mu normalization 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27]
def pair11Target:NormalForm:=CompactPair.toNormal LocalParityNineTenthsPairs.compact_parityNineTenths_pair_11_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_11_hinges
private def zz286:"s011e"="s011e":=by decide+kernel
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalParityNineTenthsPairs.parityNineTenths_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineTenthsPairs.compact_parityNineTenths_pair_11_base LocalParityNineTenthsPairs.compact_parityNineTenths_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalParityNineTenthsPairs.parityNineTenths_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows parameter p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
private def zz287:"s011f"="s011f":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows parameter mu normalization p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ParityNineTenthsRows
private def zz2093:"s082d"="s082d":=by decide+kernel
end 
section 
namespace Green24Proof.ParityNineTenths
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ParityNineTenthsRows.rows ParityNineTenthsRows.parameter p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityNineTenthsRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ParityNineTenthsRows.rows ParityNineTenthsRows.parameter p q same x]
    exact ParityNineTenthsRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ParityNineTenthsRows.rows ParityNineTenthsRows.parameter ParityNineTenthsRows.mu ParityNineTenthsRows.normalization p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityNineTenthsRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ParityNineTenthsRows.rows ParityNineTenthsRows.parameter ParityNineTenthsRows.mu ParityNineTenthsRows.normalization p q same x]
    exact ParityNineTenthsRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible ParityNineTenthsRows.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  ((9 / 10:ℝ) * U - V) * ((-0x14bc7e9 / 0x1312d00:ℝ) * U + (0x15b0a29 / 0x1312d00:ℝ) * V) -
    (1 / 0x61a8:ℝ) * (U + V) ^ 2
private def zz288:"s0120"="s0120":=by decide+kernel
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 0x64:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ParityCorrectionAggregation.correction_of_local_rows h3 h5
    ParityNineTenthsRows.rows ParityNineTenthsRows.parameter ParityNineTenthsRows.mu
    ParityNineTenthsRows.normalization rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ParityNineTenthsRows.mu 0 = (0x3eb2ae9 / 0x4c4b40:ℚ):=by decide +kernel
  have hmu1:ParityNineTenthsRows.mu 1 = (-0x3bd6429 / 0x4c4b40:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num [ParityNineTenthsRows.parameter,ParityNineTenthsRows.normalization] at hc
  unfold massCorrection
  nlinarith only [hc]
theorem massCorrection_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(21 / 20:ℝ) * V ≤ U) (hhigh:U ≤ (11 / 10:ℝ) * V) :
    (0x5774c3 / 0x12a05f2000:ℝ) * V ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(21 / 20:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (11 / 10:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_lower_bound hV hlow hhigh
  nlinarith [sq_nonneg (mass v)]
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(21 / 20:ℝ) * V ≤ U) (hhigh:U ≤ (11 / 10:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [sq_nonneg V,mul_nonneg hV (sub_nonneg.mpr hhigh)]
private def zz289:"s0121"="s0121":=by decide+kernel
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(21 / 20:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (11 / 10:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ParityNineTenths
private def zz2094:"s082e"="s082e":=by decide+kernel
end 
section 
namespace Green24Proof.LocalParityNineteenTwentiethsPairs
def compact_parityNineteenTwentieths_pair_6_base:CompactPair.Quadratic:=⟨0,(0x18699 / 0x2540be400),0⟩
def compact_parityNineteenTwentieths_pair_6_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineteenTwentieths_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_6_base compact_parityNineteenTwentieths_pair_6_hinges x y
def compact_parityNineteenTwentieths_pair_6_cuts:List ℚ:=[]
theorem compact_parityNineteenTwentieths_pair_6_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_6_base compact_parityNineteenTwentieths_pair_6_hinges 0 compact_parityNineteenTwentieths_pair_6_cuts = true :=
  by decide +kernel
theorem compact_parityNineteenTwentieths_pair_6_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_6 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_6_base compact_parityNineteenTwentieths_pair_6_hinges x y:=by rfl
theorem parityNineteenTwentieths_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_6 x y:=by
  rw [compact_parityNineteenTwentieths_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_6_check hy (by simpa using hx)
def compact_parityNineteenTwentieths_pair_7_base:CompactPair.Quadratic:=⟨0,(0x4e1f / 0x12a05f200),0⟩
def compact_parityNineteenTwentieths_pair_7_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineteenTwentieths_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_7_base compact_parityNineteenTwentieths_pair_7_hinges x y
def compact_parityNineteenTwentieths_pair_7_cuts:List ℚ:=[]
private def zz290:"s0122"="s0122":=by decide+kernel
theorem compact_parityNineteenTwentieths_pair_7_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_7_base compact_parityNineteenTwentieths_pair_7_hinges 0 compact_parityNineteenTwentieths_pair_7_cuts = true :=
  by decide +kernel
theorem compact_parityNineteenTwentieths_pair_7_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_7 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_7_base compact_parityNineteenTwentieths_pair_7_hinges x y:=by rfl
theorem parityNineteenTwentieths_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_7 x y:=by
  rw [compact_parityNineteenTwentieths_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_7_check hy (by simpa using hx)
def compact_parityNineteenTwentieths_pair_8_base:CompactPair.Quadratic:=⟨0,(0x445c7 / 0x4a817c800),0⟩
def compact_parityNineteenTwentieths_pair_8_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineteenTwentieths_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_8_base compact_parityNineteenTwentieths_pair_8_hinges x y
def compact_parityNineteenTwentieths_pair_8_cuts:List ℚ:=[]
theorem compact_parityNineteenTwentieths_pair_8_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_8_base compact_parityNineteenTwentieths_pair_8_hinges 0 compact_parityNineteenTwentieths_pair_8_cuts = true :=
  by decide +kernel
private def zz291:"s0123"="s0123":=by decide+kernel
theorem compact_parityNineteenTwentieths_pair_8_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_8 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_8_base compact_parityNineteenTwentieths_pair_8_hinges x y:=by rfl
theorem parityNineteenTwentieths_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_8 x y:=by
  rw [compact_parityNineteenTwentieths_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_8_check hy (by simpa using hx)
def compact_parityNineteenTwentieths_pair_9_base:CompactPair.Quadratic:=⟨(-3 / 0xee6b2800),(0x2711b / 0x4a817c800),0⟩
def compact_parityNineteenTwentieths_pair_9_hinges:List CompactPair.Hinge:=[⟨(-1 / 0xee6b2800),1, -3⟩,⟨(-1 / 0x77359400),1, -1⟩,⟨(1 / 0x165a0bc00),3, -1⟩]
noncomputable def parityNineteenTwentieths_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_9_base compact_parityNineteenTwentieths_pair_9_hinges x y
def compact_parityNineteenTwentieths_pair_9_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_parityNineteenTwentieths_pair_9_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_9_base compact_parityNineteenTwentieths_pair_9_hinges 0 compact_parityNineteenTwentieths_pair_9_cuts = true :=
  by decide +kernel
theorem compact_parityNineteenTwentieths_pair_9_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_9 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_9_base compact_parityNineteenTwentieths_pair_9_hinges x y:=by rfl
private def zz292:"s0124"="s0124":=by decide+kernel
theorem parityNineteenTwentieths_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_9 x y:=by
  rw [compact_parityNineteenTwentieths_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_9_check hy (by simpa using hx)
def compact_parityNineteenTwentieths_pair_10_base:CompactPair.Quadratic:=⟨0,(0x270f / 0x3b9aca00),0⟩
def compact_parityNineteenTwentieths_pair_10_hinges:List CompactPair.Hinge:=[]
noncomputable def parityNineteenTwentieths_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_10_base compact_parityNineteenTwentieths_pair_10_hinges x y
def compact_parityNineteenTwentieths_pair_10_cuts:List ℚ:=[]
theorem compact_parityNineteenTwentieths_pair_10_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_10_base compact_parityNineteenTwentieths_pair_10_hinges 0 compact_parityNineteenTwentieths_pair_10_cuts = true :=
  by decide +kernel
theorem compact_parityNineteenTwentieths_pair_10_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_10 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_10_base compact_parityNineteenTwentieths_pair_10_hinges x y:=by rfl
theorem parityNineteenTwentieths_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_10 x y:=by
  rw [compact_parityNineteenTwentieths_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_10_check hy (by simpa using hx)
def compact_parityNineteenTwentieths_pair_11_base:CompactPair.Quadratic:=⟨(-1 / 0x59682f00),(0x1f3d / 0x77359400),0⟩
def compact_parityNineteenTwentieths_pair_11_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def parityNineteenTwentieths_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_parityNineteenTwentieths_pair_11_base compact_parityNineteenTwentieths_pair_11_hinges x y
def compact_parityNineteenTwentieths_pair_11_cuts:List ℚ:=[(1 / 3),3]
private def zz293:"s0125"="s0125":=by decide+kernel
theorem compact_parityNineteenTwentieths_pair_11_check :
    CompactPair.expressionCheckPSD compact_parityNineteenTwentieths_pair_11_base compact_parityNineteenTwentieths_pair_11_hinges 0 compact_parityNineteenTwentieths_pair_11_cuts = true :=
  by decide +kernel
theorem compact_parityNineteenTwentieths_pair_11_representation (x y:ℝ) :
    parityNineteenTwentieths_pair_11 x y = CompactPair.expressionEval compact_parityNineteenTwentieths_pair_11_base compact_parityNineteenTwentieths_pair_11_hinges x y:=by rfl
theorem parityNineteenTwentieths_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ parityNineteenTwentieths_pair_11 x y:=by
  rw [compact_parityNineteenTwentieths_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_parityNineteenTwentieths_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalParityNineteenTwentiethsPairs
private def zz2095:"s082f"="s082f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x42835246d, -0x2c9779d10, -0x42e337750,0x2055a16a], ![-0x2c9779d10, -0x17aa7b13ee,0x57e8bd0ce,0x1590944ca], ![-0x42e337750,0x57e8bd0ce, -0x1228c4a8df,0x2cc4670d7], ![0x2055a16a,0x1590944ca,0x2cc4670d7, -0x164bbda40]]
noncomputable def hinges:Hinges:=[(-0x1675275,l4),(0x1675274,l10),(0x16d10a5,l17),(0x57eae583c,l15),(-0x164bbda40,l27),(0x164bbda40,l29),(0x16d10a5,l30),(0x164bbda40,l33),(-0x1675274,l38),(-0x164bbda40,l35),(0x164bbda40,l37),(0x1675275,l34),(-0x16d10a5,l43),(-0x57eae583c,l41),(0x164bbda40,l51),(-0x16d10a5,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x164bbda40,l27),(0x164bbda40,l29),(0x164bbda40,l33),(-0x164bbda40,l35),(0x164bbda40,l37),(0x164bbda40,l51),(0x57eae583c,l15),(-0x57eae583c,l41),(0x16d10a5,l17),(0x16d10a5,l30),(-0x16d10a5,l43),(-0x16d10a5,l62),(0x1675274,l10),(-0x1675274,l38),(-0x1675275,l4),(0x1675275,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((0x2cb98389ea0a30a029c7dd5128a05e8297462c8552c115aa288016e1a88f041012f7568620000000a01f270424008515cf60dd06834900000232694489fa438ebcd20000008ca6590b19e1fd5c28807d46a95b880840825d594204be063bc4e5816e417d44c32410940400003bc7fba1080000001109d3e5c72408640f0924983943923941920080000060200401a00020a649878ab195858c26f0c32c491973f115b9122849094f851c003465f0e83002e8b94e5010021aa252f80010e884f7e0280c230080000cf9fee842000000044274f971c9021903c238e50a40a38a10440220008003810010068000849e58b0821de3607543c3094ca016ed3dc7d708c461491071061090480050040020014c8a0080340004c880782ffba1080000001109d3e5c72408640f08c31229220e20c20608208e00260400401b22fdc71c7a49139b1c7106388cc93bcff184395904e48a07d8def22c2023ba8cd46093081080400004dc8188880c02400050a40bc4702ad0b5154c212db595bddf0959e40f5641194b302ec74b016b28dd01c2100a26a595a6a311f8ad35188fa1272c58410ef1b03aa1e184a6500b769ee3eb846830c384204182102020578bc9074cf3d9ee550f8e179ecd877af948d6ae4604208360819b1160a17bf58dbf30edfdf5935772216e87329880d84050f3ce37a65600870cdc891524ff3828002251ecc86ef34094d2f75398e8b53389ab26e505b3c537899f27000000000000000002088c10610c08608c00a0080200138a39decbbf3964bd771accccc327330d034bfdd6c3845b876961610dd31e448e74585ef360a728a6216800162902e210168280b005034e6051f22260e13795c3f57390c12953fdeaddc0a1162a04ced591001294870ab5d0e02037ce250b08a00b36334ea228238088d87f0051145bf774b95c638e1601430a248eac92de87924e891421281ec0a1895475af8e20648c0a273ef5d2e024402d35654aa0c140a030c16057d20a0237245e8b37dc28000491d1359a009c4101062078c2800b032fb98481deb3a20249587ef287c50ed88bcc41ca1b76db24d49230afce1ccd18000d0a099613841180400005b8cdf5152725c326f57f0601597cc7b84dc637ae166282d4d07e261450c504302202082500280180801006e14ab1623af0e380e65647050deef3801a12325c5e884260228feafd902094a3a4a9c40009282a9d8c015e439758140411004000065480018019bea2a4e4b864deafe0c02b2f98f709b8c6f5c2cc505a9a0fc4a20814910810710704a00100030200200d00015420260be234ca2b32bc5d2678b2e8d447203009f67cab0719c9c8dc3e256387a099bf1ce01b882ad48838ec60c1caf725258a49ca1dd897710208116715f7c792a7a5dd4534c08000a6c1c89c6cb43f8aeec496000d76e102587108b233ddb84bb8c6f5c2cc505a9ac30be1e8000348200174a7880e25769e61423f83477dd8c0804e9c9984507d8481b216301d640d0dbb140009d39330a0094e9cbb0b97b101280600005f081590c04c46054230290dc72408648551e6631894807e1d3edbb03f5e3f81a2bc7f03382cf6061059ec0c40f90a21000e00a0040020a68ed3825ed2d92a0342a2fc5bee5a2453ae825dc9e2a53dde021188f1680526d70107fbc67af93924ec5a7a9575ebbac0c0fe7067f42143ceb8efa5539cd8973b44d68675d8de2de2c18cd4b2707bb65b5813be071242edf429626b937ccc700a7b6c9b048103c010e2c11ca62a592631648f24904cdb15161d3e08a58b0605970d2b2840e80400003c8e02d3790e040954eb42044183601000007320501bd05f861f36102a891d971c01ecaad98c0139c67e000264ecf8804a183a010e092338a1310188729f6c10453a8564380698f070c24081e00850f04cc7c8404c1f97422041b00860a17bf3e9a580cf9431822813a12ca3a4608400100000a72000264400086881384c000cf8f1c0d66c06c48620bb1bc324201da65980a0848f937f0306e2e6a1a210368e28ea810003422aa983386108042080015f3441418773acc1460810102fb8205a5999a0a0c2857e339712821080420807afc2c022841773a76fc283017694d0418209a103386102e6ebb7aec0c2da392315514004b95091a28e08480280001762032020002aa20462200f05000228102605c0300401004a13a100f0d4e1a30408b6174d102e8f30dca460042010a1271c3c0803045a557aed1023d071e968208afc71038900ee36649428017a7605598008402000025e78e685b520a243885b61208a093aeef364305baa3d3c230021b7640b0000ef3f1fe13021080400004c081184803c140006ce4078440481a01b090001fc101311f1c05b99f3a0c3898662878908179a4738180001707e744000507e0ff094208802104010ef80ac20912bb61fc14182ed568143000112464904001884cc6a4a08440109240ab75d9a145899097d88b100a93cd452400209d357a4002200848a013443678a2c4c020e44308073e49b6c600440100000ab200033e4000b0c81186c088360421b00c05c11e31da301c70196f410e1b0352a5830c6f7a910205030692f1002ecaf45) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase0" = "QuadParityNineteenTwentiethsCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase0
private def zz2096:"s0830"="s0830":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x42af09cea, -0x2c9779d10, -0x42e337750,0xf7d369a], ![-0x2c9779d10, -0x176fffa6eb,0x578b65cb4,0x1602a3ce3], ![-0x42e337750,0x578b65cb4, -0x1228c4a8df,0x2cc4670d7], ![0xf7d369a,0x1602a3ce3,0x2cc4670d7, -0x164bbda40]]
noncomputable def hinges:Hinges:=[(-0x1675275,l4),(0x1675274,l10),(0xb17c204,l14),(0x20c2368,l17),(0x577c22fc7,l15),(-0x164bbda40,l27),(0x164bbda40,l29),(-0xb17c204,l25),(0x57d08bc,l30),(0x164bbda40,l33),(-0x1675274,l38),(-0x164bbda40,l35),(0x164bbda40,l37),(0x1675275,l34),(-0x57d08bc,l43),(-0x577c22fc7,l41),(0x164bbda40,l51),(-0x20c2368,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x164bbda40,l27),(0x164bbda40,l29),(0x164bbda40,l33),(-0x164bbda40,l35),(0x164bbda40,l37),(0x164bbda40,l51),(0x577c22fc7,l15),(-0x577c22fc7,l41),(0xb17c204,l14),(-0xb17c204,l25),(0x57d08bc,l30),(-0x57d08bc,l43),(0x20c2368,l17),(-0x20c2368,l62),(0x1675274,l10),(-0x1675274,l38),(-0x1675275,l4),(0x1675275,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0xa80720081441942100b8200a000000001a014802000000000280c4010000000443c05300800002702200b1808000250982402d003], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    0xde04dabd487c27fd9ad29b6f2fe2540000000000000001e308311ccc7529f134e2083596d1851e13cee490cd7384c4fc0000000000000000000000000000000000000000000000000c2430c306206182300280080a00000b7380100680018b900327f2008ce072ebaf76b6ba1ad975d41311c71c51c31c11811011000c00400044c90008037ac890943a36d991438055c861d7628ac50528bb662800000000000000000000000000000000000000000005612082021c21421c10c004000000470380200da200946abf44860ffba895901d22121020306343b31198810a818a240180205c46d584013c7db22e004e2844010a291b988708284000005dc0913847713cc1c40b61b395890e5977f97e1c10a7d313e85003303d7110c007bea1290068102200861811437977ec50b738dcfe611205084115c04714220a8ed316c4b005740559b842800fda31c92c0c0039c315f3f00000b96f91ce00c880c2902075912128746db3228700ab90c3aec5158a0a5176cc500000000000000000000000000000000000000000000ac269a51268e60e50e60c68a60180001006e102f16a9ff8d1c0f7dabaa983c25ccd9ae3060e667cb5c0800e6751e4650023008000086101f01f1282e83fc3a3880ebb7b0f81640000034bc0410000034b9c40429bb7af440c287667bb5694082b2f135c09051265cb85610111437e1e594801280a24900000ea5b0e205b6042f813489f532e61749084803a16b93819039dce7ec800000057e1804002655f4cee8e004c0280001823c416e0339c29a42a93ac8d59640000023281a3a8ef6a8b91c31884aebf0963000002326860ac7d63b951a058450cb430400142ff1a069002400c71c11c4c4120d246efa4e08924800005dbe38803df538286911dd91818c8000000464e4c004601000013b20006504001af48004fe1000beb2001b3e407834001e76400453080e8ec00c0586c599e321144564884ae748953c1de5e25d9f88fb611d8c000000000000000010447de6564742c51aab0d61b888e5737fe68f9a00512d55a7800000000000000004060da05d0aa5e34d03f347054c40c5044044003001000290fd6c67281331f14fbd49111aa8aebfc1b112df7018aa33fdce5931a1e01d8f6e130cb1a66cb0d9f1f2100db28caa99fbcfd4da3d241a699818bd8c9b652584a4fe24ec2c6326152244af080000127b8a103ef3c603101000006ce41023ec3b4a28106743b05830204e90143480098408c021440009b3d6a304003c294242051428e4b0820c7c38a390080501d3eb140128811804000044c800138101c1180d8880682603213a1a6c7d90d0405b17819071c20cc0fbe50c11f7a161745002dce99cc0804aaeef0426042100858f5c90dbca486275af534387fb7d33223040815860248005b188b63809d17164e2000823d60d380100042c70087c93108222e082e0870fab35a78e1800072d2f30800048eace4a004201000010220004e4406026028130120180880f0810a8aeb3922069871c00812f599f2ee2073c26c4d5280016a4361100019a2d74c500088edad64e084201091000072f92409628fca1c1445b5acca80818a97d0fb09010840200001ae405c17e2bffbdbfe8ae176de0e8a512cb0758def77c470603e9a7f855000000000000000000452fcd2ed93ef02d83681742a978d340fcd1c152ee2a442acec076cb0a9f0550b1c80c70c308b00b9dacfed116670b6cf66e3d932200287718dcca526980a620369021ce55118caef6279a924989dfb8b52d52ddfbfa2805d14f4798a67a4ceccc802867a1bb400111cd0c16e6b5b11c21cac2cfc8c161dd335582062adc455250003c87c831094408402000021440282400100240586602a1b80800802005026026120120180880e01002008a1cd61bde902db306133409843f7c50169fc6482810360080000c0320bec936ac700a62ee2e201d53e17a0230c1d00800005118144d098e081ae629fe3428e0d628102d7cfccc90106c02143a15b99488163215a5c68122d5caa2804d7b67b92020e804000031cd07d7a4a48805f53a890a09391b258c006c02141f4aa97e100b6671f08a0dc61c891401a9cbde4800380100000c120200a000187201e1a000358201c12b04e04093080b37bb5022081a00848c80c42f8c353bfa20280d9315691820d00420080200800002220001a44034340181300b010000ce900a0d00038790007a0200282640070acd1714f719e902861ce93e79b1414a713d7d588080925f978840058ab783c618001efa6d340800e27c474680138a128043086054655fcb1c206e3780e3a0c178b597bf7ac50963bd22861420201ad1d7424041a5b7061a690802c568ae4cd80321c40a4081c7aad1647d8e9838a10c97f09033470d39aee825451861005d67cc65180410595db5c20cc4000c99733db70460006f41bc98ad8a0004778acfd6803e8406178162492dbfba7f0208fb18c623b2060210163c824400f7d369a20456d5c67db1c4002cebc57041000005dbd08001efb9ddb0c041200228a129d0f188892649122a210287002d8a6f34a140605ffcfd2452a7e439d44500008a6a6d526042600852f98a7d2b0babccc978a18b31ac0e4ccfa2227ef36d800000000000000077d64484a1d1b6cc8a1c02ae430ebb1456282945db31400000000000000000000000000000000000000000002b11239429228e092010002017040100680016a100043e2000bfa400207c8004ed90091900406801c2400c0a00501002008002fd48018c8008640020200001001d999))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase1" = "QuadParityNineteenTwentiethsCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase1
private def zz2097:"s0831"="s0831":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x42cc500c5, -0x2cb416090, -0x3e8984dfd,0x1758], ![-0x2cb416090, -0x17d2977366,0x56f4d6830,0x1565a9f8a], ![-0x3e8984dfd,0x56f4d6830, -0x12445e2c7e,0x2d22605a5], ![0x1758,0x1565a9f8a,0x2d22605a5, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x2aa2f1,l6),(-0x2f3af36,l4),(0x35e8cbd,l10),(-0x38f9d20,l14),(0x16d10a5,l17),(0x57eae583c,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x38f9d18,l25),(0x16d10a5,l30),(0x165a0bc00,l33),(-0x77e97b,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x77e97a,l34),(-0x43a59ef,l43),(-0x54ba15066,l41),(0x38f9d18,l46),(0x165a0bc00,l51),(-0x43a59ef,l62),(-0x38f9d20,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x57eae583c,l15),(-0x54ba15066,l41),(-0x43a59ef,l43),(-0x43a59ef,l62),(-0x38f9d20,l14),(-0x38f9d20,l64),(0x38f9d18,l25),(0x38f9d18,l46),(0x35e8cbd,l10),(0x16d10a5,l17),(0x16d10a5,l30),(-0x2f3af36,l4),(-0x77e97b,l38),(-0x2aa2f1,l6),(0x77e97a,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase2" = "QuadParityNineteenTwentiethsCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase2
private def zz2098:"s0832"="s0832":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x42caa2ff3, -0x2cb416090, -0x3eca47712,0x35d4ce], ![-0x2cb416090, -0x17c11c200f,0x5630ed64c,0x15d7b97a3], ![-0x3eca47712,0x5630ed64c, -0x12445e2c7e,0x2d22605a5], ![0x35d4ce,0x15d7b97a3,0x2d22605a5, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x2aa2f1,l6),(-0x2f3af36,l4),(0x35e8cbd,l10),(0x782ab52,l14),(-0x773512e,l12),(0x20c2368,l17),(0x577c22fc7,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x22560e0,l25),(0x57d08bc,l30),(0x165a0bc00,l33),(-0x77e97b,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x77e97a,l34),(-0x55bc5dd35,l41),(-0x3dbb9a,l46),(0x165a0bc00,l51),(-0x36ef1e3,l62),(-0x298fae8,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x577c22fc7,l15),(-0x55bc5dd35,l41),(0x782ab52,l14),(0x57d08bc,l30),(-0x36ef1e3,l62),(0x35e8cbd,l10),(-0x298fae8,l64),(-0x22560e0,l25),(0x20c2368,l17),(-0x773512e,l12),(-0x2f3af36,l4),(-0x77e97b,l38),(-0x3dbb9a,l46),(-0x2aa2f1,l6),(0x77e97a,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x1b00a401000000000b80720080000001900099008000000001501880205106508402e0802800000000680520080000022048071806000000110f014c02000009c08802c602000094260900b400c00000000f00490060005a188a4091003000000000f00a40103c82282d018c40140000003622031804000014848004cc040000000b0900e601000000002c009200c00000001b004900600001a8110050c04000000c8120186018000680410026301400000340880718060000002105028c02000000000480e401000000000340720080000003a0c031804000000001d018802], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase3" = "QuadParityNineteenTwentiethsCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase3
private def zz2099:"s0833"="s0833":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4104817bd, -0x2cb416090, -0x3e8984dfd,0x1770], ![-0x2cb416090, -0x179f125fbc,0x5379edd9e,0x17c671e03], ![-0x3e8984dfd,0x5379edd9e, -0x123b7940b9,0x2cfd57c9f], ![0x1770,0x17c671e03,0x2cfd57c9f, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x249f696,l4),(0x249f697,l10),(0x43a59ef,l17),(0x54ba15066,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x43a59ef,l30),(0x165a0bc00,l33),(-0x249f697,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x249f696,l34),(-0x43a59ef,l43),(-0x54ba15066,l41),(0x165a0bc00,l51),(-0x43a59ef,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x54ba15066,l15),(-0x54ba15066,l41),(0x43a59ef,l17),(0x43a59ef,l30),(-0x43a59ef,l43),(-0x43a59ef,l62),(0x249f697,l10),(-0x249f697,l38),(-0x249f696,l4),(0x249f696,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase4" = "QuadParityNineteenTwentiethsCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase4
private def zz2100:"s0834"="s0834":=by decide+kernel
end 
section 
namespace Green24Proof.QuadParityNineteenTwentiethsCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l17 l27 l29 l33 l34 l35 l37 l38 l4 l41 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4150ba231, -0x2cb416090, -0x3eca47712,0x1770], ![-0x2cb416090, -0x17885e5b18,0x537ed2cac,0x1796e3bcc], ![-0x3eca47712,0x537ed2cac, -0x123b7940b9,0x2cfd57c9f], ![0x1770,0x1796e3bcc,0x2cfd57c9f, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x249f696,l4),(0x249f697,l10),(0x36ef1e3,l17),(0x55bc5dd35,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x249f697,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x249f696,l34),(-0x55bc5dd35,l41),(0x165a0bc00,l51),(-0x36ef1e3,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x55bc5dd35,l15),(-0x55bc5dd35,l41),(0x36ef1e3,l17),(-0x36ef1e3,l62),(0x249f697,l10),(-0x249f697,l38),(-0x249f696,l4),(0x249f696,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadParityNineteenTwentiethsCase5" = "QuadParityNineteenTwentiethsCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadParityNineteenTwentiethsCase5
private def zz2101:"s0835"="s0835":=by decide+kernel
end 
section 
namespace Green24Proof.ParityNineteenTwentiethsRows
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x107d3779ae5800598fdba05d303dceb948001f6f79a532fd7c28002a9eeb6079305faf8a02dcaaa0193779ae580078fcec6133d84c0024303dceb948029a6f9de0303dceb9480569cebce5601eeb5ca800df59e8ef21603dceb94801be9d3e98a07d21389b48002b3d0a202d203dceb948013ef8bba01d21de6d9a00189ac8e5201eeb5ca800eaedf9ce2039205faf8a02dcaaa0592779ae580078fcec61202b196c012c6bed207c2779ae5802cafc282424ca5d004e3eb820203dceb94801da6e58b9a14]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x1411ec2a002038103dceb948016e8c2ca0281779ae5800ed3c9c88a018103dceb948016e8c2ca011ec2a00203d403dceb948024cfdaae06d401eeb5ca80068da4b2541ec2a00203c45faf848001bfedfe06c401eeb5ca80019ff0fe441ec2a00203d003dceb948035f4b2fa06d001eeb5ca8007efca9205d01389b4800dd2b25003dceb948001a1a9fa03c0779ae58005ced2ba06c003dceb948007be98ce401ec2a002573d84c002173d84c00214]
def rowsChunk2:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x102d503dceb948039948fd1ce01d503dceb948036f7c7c65501f4928001baac8203951389b48002daad8e029501eeb5ca801c9f81e0a201951389b48002daad8e1503dceb94800381c5888203c1779ae58015fa88de02c103dceb94803aa9b0bfda01c13bcdb2c0048c91da0a]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2
def mu:Phase → ℚ:=![(0x1768138df / 0x1dcd6500),(-0x16d90675f / 0x1dcd6500)]
def parameter:ℚ:=(19 / 20)
def normalization:ℚ:=(1 / 0xf424)
def quad0:Expression:=quadSlack rows parameter 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase0.base QuadParityNineteenTwentiethsCase0.hinges QuadParityNineteenTwentiethsCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase0.base QuadParityNineteenTwentiethsCase0.hinges QuadParityNineteenTwentiethsCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows parameter 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase1.base QuadParityNineteenTwentiethsCase1.hinges QuadParityNineteenTwentiethsCase1.normalizationDenominator
private def zz303:"s012f"="s012f":=by decide+kernel
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase1.base QuadParityNineteenTwentiethsCase1.hinges QuadParityNineteenTwentiethsCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows parameter 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase2.base QuadParityNineteenTwentiethsCase2.hinges QuadParityNineteenTwentiethsCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase2.base QuadParityNineteenTwentiethsCase2.hinges QuadParityNineteenTwentiethsCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows parameter 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase3.base QuadParityNineteenTwentiethsCase3.hinges QuadParityNineteenTwentiethsCase3.normalizationDenominator
private def zz304:"s0130"="s0130":=by decide+kernel
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase3.base QuadParityNineteenTwentiethsCase3.hinges QuadParityNineteenTwentiethsCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows parameter 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase4.base QuadParityNineteenTwentiethsCase4.hinges QuadParityNineteenTwentiethsCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase4.base QuadParityNineteenTwentiethsCase4.hinges QuadParityNineteenTwentiethsCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows parameter 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadParityNineteenTwentiethsCase5.base QuadParityNineteenTwentiethsCase5.hinges QuadParityNineteenTwentiethsCase5.normalizationDenominator
private def zz305:"s0131"="s0131":=by decide+kernel
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadParityNineteenTwentiethsCase5.base QuadParityNineteenTwentiethsCase5.hinges QuadParityNineteenTwentiethsCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadParityNineteenTwentiethsCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows parameter mu normalization 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair6Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_6_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_6_hinges
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_6_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_6_hinges x
private def zz306:"s0132"="s0132":=by decide+kernel
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows parameter mu normalization 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair7Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_7_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_7_hinges
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_7_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows parameter mu normalization 0 1 false
def pair8Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair8Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_8_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_8_hinges
private def zz307:"s0133"="s0133":=by decide+kernel
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_8_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_8_hinges x
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows parameter mu normalization 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r28]
def pair9Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_9_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
private def zz308:"s0134"="s0134":=by decide+kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_9_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_9_hinges x
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows parameter mu normalization 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair10Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_10_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_10_hinges
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_10_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_10_hinges x
private def zz309:"s0135"="s0135":=by decide+kernel
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows parameter mu normalization 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27]
def pair11Target:NormalForm:=CompactPair.toNormal LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_11_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_11_hinges
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_11_base LocalParityNineteenTwentiethsPairs.compact_parityNineteenTwentieths_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalParityNineteenTwentiethsPairs.parityNineteenTwentieths_pair_11_nonneg (hx 0) (hx 1)
private def zz310:"s0136"="s0136":=by decide+kernel
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows parameter p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows parameter mu normalization p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.ParityNineteenTwentiethsRows
private def zz2102:"s0836"="s0836":=by decide+kernel
end 
section 
namespace Green24Proof.ParityNineteenTwentieths
open QuadraticCertificates ExpressionCertificates ParityCorrectionRows
open ParityPhaseRows (Phase Potential)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ParityPhaseAggregation (rowsAdmissible)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack ParityNineteenTwentiethsRows.rows ParityNineteenTwentiethsRows.parameter p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityNineteenTwentiethsRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse ParityNineteenTwentiethsRows.rows ParityNineteenTwentiethsRows.parameter p q same x]
    exact ParityNineteenTwentiethsRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack ParityNineteenTwentiethsRows.rows ParityNineteenTwentiethsRows.parameter ParityNineteenTwentiethsRows.mu ParityNineteenTwentiethsRows.normalization p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact ParityNineteenTwentiethsRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap ParityNineteenTwentiethsRows.rows ParityNineteenTwentiethsRows.parameter ParityNineteenTwentiethsRows.mu ParityNineteenTwentiethsRows.normalization p q same x]
    exact ParityNineteenTwentiethsRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
private def zz311:"s0137"="s0137":=by decide+kernel
theorem rows_admissible:rowsAdmissible ParityNineteenTwentiethsRows.rows = true:=by decide +kernel
noncomputable def massCorrection (U V:ℝ):ℝ :=
  ((19 / 20:ℝ) * U - V) * ((-0x7c2a4edf / 0x77359400:ℝ) * U + (0x7f253f5f / 0x77359400:ℝ) * V) -
    (1 / 0x3d090:ℝ) * (U + V) ^ 2
theorem correction {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    (1 / 0x190:ℝ) * deficit u + massCorrection (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hc:=ParityCorrectionAggregation.correction_of_local_rows h3 h5
    ParityNineteenTwentiethsRows.rows ParityNineteenTwentiethsRows.parameter ParityNineteenTwentiethsRows.mu
    ParityNineteenTwentiethsRows.normalization rows_admissible quad_nonneg pair_nonneg u v hu hv
  have hmu0:ParityNineteenTwentiethsRows.mu 0 = (0x1768138df / 0x1dcd6500:ℚ):=by decide +kernel
  have hmu1:ParityNineteenTwentiethsRows.mu 1 = (-0x16d90675f / 0x1dcd6500:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hc
  norm_num [ParityNineteenTwentiethsRows.parameter,ParityNineteenTwentiethsRows.normalization] at hc
  unfold massCorrection
  nlinarith only [hc]
theorem massCorrection_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(0x67 / 0x64:ℝ) * V ≤ U) (hhigh:U ≤ (21 / 20:ℝ) * V) :
    (0x308783df / 0xe8d4a510000:ℝ) * V ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem interval_nonneg {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (21 / 20:ℝ) * mass v):0 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_lower_bound hV hlow hhigh
  nlinarith [sq_nonneg (mass v)]
private def zz312:"s0138"="s0138":=by decide+kernel
theorem massCorrection_coercivity {U V:ℝ} (hV:0 ≤ V)
    (hlow:(0x67 / 0x64:ℝ) * V ≤ U) (hhigh:U ≤ (21 / 20:ℝ) * V) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ massCorrection U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massCorrection
  nlinarith [sq_nonneg V,mul_nonneg hV (sub_nonneg.mpr hhigh)]
theorem coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hd:0 ≤ deficit u) (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (21 / 20:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hc:=correction h3 h5 u v hu hv
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  have hm:=massCorrection_coercivity hV hlow hhigh
  linarith
end Green24Proof.ParityNineteenTwentieths
private def zz2103:"s0837"="s0837":=by decide+kernel
end 
section 
namespace Green24Proof.PackedPhaseRowsEquality
open FullPhaseRows
def positionEq:Position → Position → Bool
  | .firstMiddle, .firstMiddle => true
  | .firstLast, .firstLast => true
  | .middleLast, .middleLast => true
  | .companion, .companion => true
  | _,_ => false
theorem positionEq_iff (a b:Position):positionEq a b = true ↔ a = b:=by
  cases a <;> cases b <;> simp [positionEq]
def shapeEq:Shape → Shape → Bool
  | .bilinear, .bilinear => true
  | .potential a, .potential b => a == b
  | _,_ => false
theorem shapeEq_iff (a b:Shape):shapeEq a b = true ↔ a = b:=by
  cases a <;> cases b <;> simp [shapeEq]
def potentialEq (a b:Potential):Bool :=
  positionEq a.position b.position && (a.left == b.left && (a.right == b.right &&
    (a.same == b.same && (shapeEq a.shape b.shape && a.sign == b.sign))))
private def zz313:"s0139"="s0139":=by decide+kernel
theorem potentialEq_iff (a b:Potential):potentialEq a b = true ↔ a = b:=by
  cases a; cases b
  simp [potentialEq,positionEq_iff,shapeEq_iff]
def labelEq:Label → Label → Bool
  | .potential a, .potential b => potentialEq a b
  | .balance a s, .balance b t => a == b && s == t
  | .child a, .child b => a == b
  | .grandchild a, .grandchild b => a == b
  | .heightChild a, .heightChild b => a == b
  | .ordered a, .ordered b => a == b
  | .massSquare a v, .massSquare b w => a == b &&
      (List.finRange 4).all (fun i => v i == w i)
  | .normalization, .normalization => true
  | _,_ => false
theorem labelEq_iff (a b:Label):labelEq a b = true ↔ a = b:=by
  cases a <;> cases b <;>
    simp [labelEq,potentialEq_iff,funext_iff]
  intro _
  constructor
  · intro h x
    have hx:(⟨x.val,x.val_lt⟩:Fin 4) = x:=by
      apply Fin.ext
      rfl
    simpa only [hx] using h ⟨x.val,x.val_lt⟩
  · intro h x
    exact h _
def rowsEq:List (ℚ × Label) → List (ℚ × Label) → Bool
  | [],[] => true
  | (q,a) :: xs,(r,b) :: ys => q == r && (labelEq a b && rowsEq xs ys)
  | _,_ => false
theorem rowsEq_iff (xs ys:List (ℚ × Label)):rowsEq xs ys = true ↔ xs = ys:=by
  induction xs generalizing ys with
  | nil => cases ys <;> simp [rowsEq]
  | cons x xs ih =>
    rcases x with ⟨q,a⟩
    cases ys with
    | nil => simp [rowsEq]
    | cons y ys =>
      rcases y with ⟨r,b⟩
      simp [rowsEq,labelEq_iff,ih,and_assoc]
end Green24Proof.PackedPhaseRowsEquality
private def zz2104:"s0838"="s0838":=by decide+kernel
end 
section 
namespace Green24Proof.CombinedPolicyPackedRowsEquality
open PackedPhaseRowsEquality
def parityEq (a b:ParityPhaseRows.Potential):Bool :=
  positionEq a.position b.position && (a.left == b.left && (a.right == b.right &&
    (a.same == b.same && (shapeEq a.shape b.shape && a.sign == b.sign))))
theorem parityEq_iff (a b:ParityPhaseRows.Potential):parityEq a b = true ↔ a = b:=by
  cases a; cases b
  simp [parityEq,positionEq_iff,shapeEq_iff]
def scopeEq:ExtendedFullPhaseRows.Scope → ExtendedFullPhaseRows.Scope → Bool
  | .whole, .whole => true
  | .parity a, .parity b => a == b
  | .phase a, .phase b => a == b
  | _,_ => false
private def zz314:"s013a"="s013a":=by decide+kernel
theorem scopeEq_iff (a b:ExtendedFullPhaseRows.Scope):scopeEq a b = true ↔ a = b:=by
  cases a <;> cases b <;> simp [scopeEq]
def vectorEq (a b:FullPhaseRows.Phase → ℚ):Bool :=
  (List.finRange 4).all (fun i => a i == b i)
theorem vectorEq_iff (a b:FullPhaseRows.Phase → ℚ):vectorEq a b = true ↔ a = b:=by
  simp [vectorEq,funext_iff]
  constructor
  · intro h x
    have hx:(⟨x.val,x.val_lt⟩:Fin 4) = x:=by
      apply Fin.ext
      rfl
    simpa only [hx] using h ⟨x.val,x.val_lt⟩
  · intro h x
    exact h _
def correctionEq (a b:ExtendedFullPhaseRows.Correction):Bool :=
  a.retained == b.retained && (a.even == b.even && (a.mixed == b.mixed && a.odd == b.odd))
theorem correctionEq_iff (a b:ExtendedFullPhaseRows.Correction):correctionEq a b = true ↔ a = b:=by
  cases a; cases b
  simp [correctionEq]
def extendedEq:ExtendedFullPhaseRows.Label → ExtendedFullPhaseRows.Label → Bool
  | .base a, .base b => labelEq a b
  | .colourChild a, .colourChild b => scopeEq a b
  | .massProduct a b, .massProduct c d => vectorEq a c && vectorEq b d
  | .massCorrection a b c, .massCorrection d e f => a == d && (b == e && correctionEq c f)
  | .massCoercivity a, .massCoercivity b => a == b
  | _,_ => false
theorem extendedEq_iff (a b:ExtendedFullPhaseRows.Label):extendedEq a b = true ↔ a = b:=by
  cases a <;> cases b <;>
    simp [extendedEq,labelEq_iff,scopeEq_iff,vectorEq_iff,correctionEq_iff]
def rowsEqWith {α:Type} (eq:α → α → Bool):List (ℚ × α) → List (ℚ × α) → Bool
  | [],[] => true
  | (q,a) :: xs,(r,b) :: ys => q == r && (eq a b && rowsEqWith eq xs ys)
  | _,_ => false
private def zz315:"s013b"="s013b":=by decide+kernel
theorem rowsEqWith_iff {α:Type} (eq:α → α → Bool)
    (h:∀ a b,eq a b = true ↔ a = b) (xs ys:List (ℚ × α)) :
    rowsEqWith eq xs ys = true ↔ xs = ys:=by
  induction xs generalizing ys with
  | nil => cases ys <;> simp [rowsEqWith]
  | cons x xs ih =>
    rcases x with ⟨q,a⟩
    cases ys with
    | nil => simp [rowsEqWith]
    | cons y ys =>
      rcases y with ⟨r,b⟩
      simp [rowsEqWith,h,ih,and_assoc]
end Green24Proof.CombinedPolicyPackedRowsEquality
private def zz2105:"s0839"="s0839":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFull27Pairs
def compact_full27_pair_20_base:CompactPair.Quadratic:=⟨(-1 / 0x59682f00),(0xfa1 / 0x17d78400),0⟩
def compact_full27_pair_20_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_20_base compact_full27_pair_20_hinges x y
def compact_full27_pair_20_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_20_check :
    CompactPair.expressionCheckPSD compact_full27_pair_20_base compact_full27_pair_20_hinges 0 compact_full27_pair_20_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_20_representation (x y:ℝ) :
    full27_pair_20 x y = CompactPair.expressionEval compact_full27_pair_20_base compact_full27_pair_20_hinges x y:=by rfl
theorem full27_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_20 x y:=by
  rw [compact_full27_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_20_check hy (by simpa using hx)
def compact_full27_pair_21_base:CompactPair.Quadratic:=⟨0,(0x1f3f / 0x77359400),0⟩
def compact_full27_pair_21_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_21_base compact_full27_pair_21_hinges x y
def compact_full27_pair_21_cuts:List ℚ:=[]
private def zz316:"s013c"="s013c":=by decide+kernel
theorem compact_full27_pair_21_check :
    CompactPair.expressionCheckPSD compact_full27_pair_21_base compact_full27_pair_21_hinges 0 compact_full27_pair_21_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_21_representation (x y:ℝ) :
    full27_pair_21 x y = CompactPair.expressionEval compact_full27_pair_21_base compact_full27_pair_21_hinges x y:=by rfl
theorem full27_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_21 x y:=by
  rw [compact_full27_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_21_check hy (by simpa using hx)
def compact_full27_pair_22_base:CompactPair.Quadratic:=⟨0,(0xdac3 / 0xee6b2800),0⟩
def compact_full27_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_22_base compact_full27_pair_22_hinges x y
def compact_full27_pair_22_cuts:List ℚ:=[]
theorem compact_full27_pair_22_check :
    CompactPair.expressionCheckPSD compact_full27_pair_22_base compact_full27_pair_22_hinges 0 compact_full27_pair_22_cuts = true :=
  by decide +kernel
private def zz317:"s013d"="s013d":=by decide+kernel
theorem compact_full27_pair_22_representation (x y:ℝ) :
    full27_pair_22 x y = CompactPair.expressionEval compact_full27_pair_22_base compact_full27_pair_22_hinges x y:=by rfl
theorem full27_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_22 x y:=by
  rw [compact_full27_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_22_check hy (by simpa using hx)
def compact_full27_pair_23_base:CompactPair.Quadratic:=⟨(13 / 0x2cb417800),(0x7d01 / 0xee6b2800),0⟩
def compact_full27_pair_23_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_23_base compact_full27_pair_23_hinges x y
def compact_full27_pair_23_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_full27_pair_23_check :
    CompactPair.expressionCheckPSD compact_full27_pair_23_base compact_full27_pair_23_hinges 0 compact_full27_pair_23_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_23_representation (x y:ℝ) :
    full27_pair_23 x y = CompactPair.expressionEval compact_full27_pair_23_base compact_full27_pair_23_hinges x y:=by rfl
private def zz318:"s013e"="s013e":=by decide+kernel
theorem full27_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_23 x y:=by
  rw [compact_full27_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_23_check hy (by simpa using hx)
def compact_full27_pair_24_base:CompactPair.Quadratic:=⟨0,(0x4e23 / 0x77359400),0⟩
def compact_full27_pair_24_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_24_base compact_full27_pair_24_hinges x y
def compact_full27_pair_24_cuts:List ℚ:=[]
theorem compact_full27_pair_24_check :
    CompactPair.expressionCheckPSD compact_full27_pair_24_base compact_full27_pair_24_hinges 0 compact_full27_pair_24_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_24_representation (x y:ℝ) :
    full27_pair_24 x y = CompactPair.expressionEval compact_full27_pair_24_base compact_full27_pair_24_hinges x y:=by rfl
theorem full27_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_24 x y:=by
  rw [compact_full27_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_24_check hy (by simpa using hx)
def compact_full27_pair_25_base:CompactPair.Quadratic:=⟨(-1 / 0x77359400),(0x1f41 / 0x77359400),0⟩
def compact_full27_pair_25_hinges:List CompactPair.Hinge:=[⟨(-1 / 0xee6b2800),1, -3⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_25_base compact_full27_pair_25_hinges x y
def compact_full27_pair_25_cuts:List ℚ:=[(1 / 3),3]
private def zz319:"s013f"="s013f":=by decide+kernel
theorem compact_full27_pair_25_check :
    CompactPair.expressionCheckPSD compact_full27_pair_25_base compact_full27_pair_25_hinges 0 compact_full27_pair_25_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_25_representation (x y:ℝ) :
    full27_pair_25 x y = CompactPair.expressionEval compact_full27_pair_25_base compact_full27_pair_25_hinges x y:=by rfl
theorem full27_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_25 x y:=by
  rw [compact_full27_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_25_check hy (by simpa using hx)
def compact_full27_pair_26_base:CompactPair.Quadratic:=⟨0,(0xdac3 / 0xee6b2800),0⟩
def compact_full27_pair_26_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_26_base compact_full27_pair_26_hinges x y
def compact_full27_pair_26_cuts:List ℚ:=[]
theorem compact_full27_pair_26_check :
    CompactPair.expressionCheckPSD compact_full27_pair_26_base compact_full27_pair_26_hinges 0 compact_full27_pair_26_cuts = true :=
  by decide +kernel
private def zz320:"s0140"="s0140":=by decide+kernel
theorem compact_full27_pair_26_representation (x y:ℝ) :
    full27_pair_26 x y = CompactPair.expressionEval compact_full27_pair_26_base compact_full27_pair_26_hinges x y:=by rfl
theorem full27_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_26 x y:=by
  rw [compact_full27_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_26_check hy (by simpa using hx)
def compact_full27_pair_27_base:CompactPair.Quadratic:=⟨(13 / 0x2cb417800),(0x7cff / 0xee6b2800),0⟩
def compact_full27_pair_27_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_27_base compact_full27_pair_27_hinges x y
def compact_full27_pair_27_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_full27_pair_27_check :
    CompactPair.expressionCheckPSD compact_full27_pair_27_base compact_full27_pair_27_hinges 0 compact_full27_pair_27_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_27_representation (x y:ℝ) :
    full27_pair_27 x y = CompactPair.expressionEval compact_full27_pair_27_base compact_full27_pair_27_hinges x y:=by rfl
private def zz321:"s0141"="s0141":=by decide+kernel
theorem full27_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_27 x y:=by
  rw [compact_full27_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_27_check hy (by simpa using hx)
def compact_full27_pair_28_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1d34b615f / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_28_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_28_base compact_full27_pair_28_hinges x y
def compact_full27_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_28_check :
    CompactPair.expressionCheckPSD compact_full27_pair_28_base compact_full27_pair_28_hinges 0 compact_full27_pair_28_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_28_representation (x y:ℝ) :
    full27_pair_28 x y = CompactPair.expressionEval compact_full27_pair_28_base compact_full27_pair_28_hinges x y:=by rfl
theorem full27_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_28 x y:=by
  rw [compact_full27_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_28_check hy (by simpa using hx)
def compact_full27_pair_29_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1d34c4bbf / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_29_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_29_base compact_full27_pair_29_hinges x y
def compact_full27_pair_29_cuts:List ℚ:=[(1 / 3),3]
private def zz322:"s0142"="s0142":=by decide+kernel
theorem compact_full27_pair_29_check :
    CompactPair.expressionCheckPSD compact_full27_pair_29_base compact_full27_pair_29_hinges 0 compact_full27_pair_29_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_29_representation (x y:ℝ) :
    full27_pair_29 x y = CompactPair.expressionEval compact_full27_pair_29_base compact_full27_pair_29_hinges x y:=by rfl
theorem full27_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_29 x y:=by
  rw [compact_full27_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_29_check hy (by simpa using hx)
def compact_full27_pair_30_base:CompactPair.Quadratic:=⟨0,(0x222e7 / 0x2540be400),0⟩
def compact_full27_pair_30_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_30_base compact_full27_pair_30_hinges x y
def compact_full27_pair_30_cuts:List ℚ:=[]
theorem compact_full27_pair_30_check :
    CompactPair.expressionCheckPSD compact_full27_pair_30_base compact_full27_pair_30_hinges 0 compact_full27_pair_30_cuts = true :=
  by decide +kernel
private def zz323:"s0143"="s0143":=by decide+kernel
theorem compact_full27_pair_30_representation (x y:ℝ) :
    full27_pair_30 x y = CompactPair.expressionEval compact_full27_pair_30_base compact_full27_pair_30_hinges x y:=by rfl
theorem full27_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_30 x y:=by
  rw [compact_full27_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_30_check hy (by simpa using hx)
def compact_full27_pair_31_base:CompactPair.Quadratic:=⟨(-1 / 0x59682f00),(0x13891 / 0x2540be400),0⟩
def compact_full27_pair_31_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_31_base compact_full27_pair_31_hinges x y
def compact_full27_pair_31_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_full27_pair_31_check :
    CompactPair.expressionCheckPSD compact_full27_pair_31_base compact_full27_pair_31_hinges 0 compact_full27_pair_31_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_31_representation (x y:ℝ) :
    full27_pair_31 x y = CompactPair.expressionEval compact_full27_pair_31_base compact_full27_pair_31_hinges x y:=by rfl
private def zz324:"s0144"="s0144":=by decide+kernel
theorem full27_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_31 x y:=by
  rw [compact_full27_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_31_check hy (by simpa using hx)
def compact_full27_pair_32_base:CompactPair.Quadratic:=⟨(-0x3aa08530f / 0x77359400),(0x7edcb54eb / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0xa386abd / 0xbebc200),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x6699eb29 / 0x77359400),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_32_base compact_full27_pair_32_hinges x y
def compact_full27_pair_32_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_32_check :
    CompactPair.expressionCheckPSD compact_full27_pair_32_base compact_full27_pair_32_hinges 0 compact_full27_pair_32_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_32_representation (x y:ℝ) :
    full27_pair_32 x y = CompactPair.expressionEval compact_full27_pair_32_base compact_full27_pair_32_hinges x y:=by rfl
theorem full27_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_32 x y:=by
  rw [compact_full27_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_32_check hy (by simpa using hx)
def compact_full27_pair_33_base:CompactPair.Quadratic:=⟨(-0x9b97a1de5 / 0x165a0bc00),(0x439ea510f / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0x10b73c811 / 0x165a0bc00),1, -3⟩,⟨(0x30429d / 0x77359400),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x3576d4fb / 0x47868c00),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_33_base compact_full27_pair_33_hinges x y
def compact_full27_pair_33_cuts:List ℚ:=[(1 / 3),1,3]
private def zz325:"s0145"="s0145":=by decide+kernel
theorem compact_full27_pair_33_check :
    CompactPair.expressionCheckPSD compact_full27_pair_33_base compact_full27_pair_33_hinges 0 compact_full27_pair_33_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_33_representation (x y:ℝ) :
    full27_pair_33 x y = CompactPair.expressionEval compact_full27_pair_33_base compact_full27_pair_33_hinges x y:=by rfl
theorem full27_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_33 x y:=by
  rw [compact_full27_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_33_check hy (by simpa using hx)
def compact_full27_pair_34_base:CompactPair.Quadratic:=⟨(-1 / 0x59682f00),(0x4e1d / 0x77359400),0⟩
def compact_full27_pair_34_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_34_base compact_full27_pair_34_hinges x y
def compact_full27_pair_34_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_34_check :
    CompactPair.expressionCheckPSD compact_full27_pair_34_base compact_full27_pair_34_hinges 0 compact_full27_pair_34_cuts = true :=
  by decide +kernel
private def zz326:"s0146"="s0146":=by decide+kernel
theorem compact_full27_pair_34_representation (x y:ℝ) :
    full27_pair_34 x y = CompactPair.expressionEval compact_full27_pair_34_base compact_full27_pair_34_hinges x y:=by rfl
theorem full27_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_34 x y:=by
  rw [compact_full27_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_34_check hy (by simpa using hx)
def compact_full27_pair_35_base:CompactPair.Quadratic:=⟨(-1 / 0x59682f00),(0x7cf / 0x1dcd6500),0⟩
def compact_full27_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full27_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_35_base compact_full27_pair_35_hinges x y
def compact_full27_pair_35_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_35_check :
    CompactPair.expressionCheckPSD compact_full27_pair_35_base compact_full27_pair_35_hinges 0 compact_full27_pair_35_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_35_representation (x y:ℝ) :
    full27_pair_35 x y = CompactPair.expressionEval compact_full27_pair_35_base compact_full27_pair_35_hinges x y:=by rfl
private def zz327:"s0147"="s0147":=by decide+kernel
theorem full27_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_35 x y:=by
  rw [compact_full27_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_35_check hy (by simpa using hx)
def compact_full27_pair_36_base:CompactPair.Quadratic:=⟨0,(0x222dd / 0x2540be400),0⟩
def compact_full27_pair_36_hinges:List CompactPair.Hinge:=[]
noncomputable def full27_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_36_base compact_full27_pair_36_hinges x y
def compact_full27_pair_36_cuts:List ℚ:=[]
theorem compact_full27_pair_36_check :
    CompactPair.expressionCheckPSD compact_full27_pair_36_base compact_full27_pair_36_hinges 0 compact_full27_pair_36_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_36_representation (x y:ℝ) :
    full27_pair_36 x y = CompactPair.expressionEval compact_full27_pair_36_base compact_full27_pair_36_hinges x y:=by rfl
theorem full27_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_36 x y:=by
  rw [compact_full27_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_36_check hy (by simpa using hx)
def compact_full27_pair_37_base:CompactPair.Quadratic:=⟨(1 / 0x1c9c3800),(0x1387d / 0x2540be400),0⟩
def compact_full27_pair_37_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x77359400),1, -1⟩,⟨(-1 / 0x165a0bc00),3, -1⟩]
noncomputable def full27_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_37_base compact_full27_pair_37_hinges x y
def compact_full27_pair_37_cuts:List ℚ:=[(1 / 3),1,3]
private def zz328:"s0148"="s0148":=by decide+kernel
theorem compact_full27_pair_37_check :
    CompactPair.expressionCheckPSD compact_full27_pair_37_base compact_full27_pair_37_hinges 0 compact_full27_pair_37_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_37_representation (x y:ℝ) :
    full27_pair_37 x y = CompactPair.expressionEval compact_full27_pair_37_base compact_full27_pair_37_hinges x y:=by rfl
theorem full27_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_37 x y:=by
  rw [compact_full27_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_37_check hy (by simpa using hx)
def compact_full27_pair_38_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1d34b615f / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_38_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_38_base compact_full27_pair_38_hinges x y
def compact_full27_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_38_check :
    CompactPair.expressionCheckPSD compact_full27_pair_38_base compact_full27_pair_38_hinges 0 compact_full27_pair_38_cuts = true :=
  by decide +kernel
private def zz329:"s0149"="s0149":=by decide+kernel
theorem compact_full27_pair_38_representation (x y:ℝ) :
    full27_pair_38 x y = CompactPair.expressionEval compact_full27_pair_38_base compact_full27_pair_38_hinges x y:=by rfl
theorem full27_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_38 x y:=by
  rw [compact_full27_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_38_check hy (by simpa using hx)
def compact_full27_pair_39_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1d34c4bbf / 0x2540be400),(-49 / 50)⟩
def compact_full27_pair_39_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full27_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full27_pair_39_base compact_full27_pair_39_hinges x y
def compact_full27_pair_39_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full27_pair_39_check :
    CompactPair.expressionCheckPSD compact_full27_pair_39_base compact_full27_pair_39_hinges 0 compact_full27_pair_39_cuts = true :=
  by decide +kernel
theorem compact_full27_pair_39_representation (x y:ℝ) :
    full27_pair_39 x y = CompactPair.expressionEval compact_full27_pair_39_base compact_full27_pair_39_hinges x y:=by rfl
private def zz330:"s014a"="s014a":=by decide+kernel
theorem full27_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full27_pair_39 x y:=by
  rw [compact_full27_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full27_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFull27Pairs
private def zz2106:"s083a"="s083a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x144ba752c, -0xde2c256c, -0x14d424545,0x888579c], ![-0xde2c256c, -0x3dffaf5cd,0x10e63ed,0x143aa3218], ![-0x14d424545,0x10e63ed, -0x5a34b0cf9,0xde2c544f], ![0x888579c,0x143aa3218,0xde2c544f, -0x6f161e6e]]
noncomputable def hinges:Hinges:=[(-0x51d29,l6),(0x7eb3f7,l4),(-0x251ed3,l10),(0xdd6ad0c9,l14),(-0xe46eb7,l17),(0x1495b75a8,l15),(-0x6f161e6e,l27),(0x6f161e6e,l29),(-0xdd6ad0c9,l25),(0x6e14c49e,l30),(0x6f161e6e,l33),(0x251ed3,l38),(-0x6f161e6e,l35),(0x6f161e6e,l37),(-0x7eb3f7,l34),(-0x6e14c49e,l43),(-0x1495b75a8,l41),(0x8795e2,l46),(0x6f161e6e,l51),(0x51d29,l60),(0xe46eb7,l62),(-0x8795e2,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6f161e6e,l27),(0x6f161e6e,l29),(0x6f161e6e,l33),(-0x6f161e6e,l35),(0x6f161e6e,l37),(0x6f161e6e,l51),(0xdd6ad0c9,l14),(-0xdd6ad0c9,l25),(0x6e14c49e,l30),(-0x6e14c49e,l43),(0x1495b75a8,l15),(-0x1495b75a8,l41),(-0xe46eb7,l17),(0xe46eb7,l62),(0x8795e2,l46),(-0x8795e2,l64),(-0x251ed3,l10),(0x251ed3,l38),(0x7eb3f7,l4),(-0x7eb3f7,l34),(-0x51d29,l6),(0x51d29,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0x6804100263014000001a044038c03000000007850330040000001916014c020000000000b032004006116013014d004000000682d013300c000000191602cc0200000000054092008000002e0c4028c030000000006406200800001b110903900200000002e00132010000000002e01c8020000000b4180730080000001b1201cc0200210610780564010000000211e038c020000000088f0330040000002d0d028c020000000b43c0a30080000002a15038c0200000a854180e400800000000210388020018c440d007a40100000001906018c020000000a4340a300800002d2a070290020000000078d0330040000003a25038c02000000000e80520080005c298a80690030000000ac580e30080000000029038802000000000090320040005c298a80a900300000b8a45405400800000002a2c0cc010000000001409200800003202800e4c0400000c20880393010000000360e03cc020000006613024300c0000014824090c030000000a85c0730080000000a8004c804000000280b01c300c000000c84c070c030000000004c052008000000001501c802000005d04c04c3010000000150701cc02000000000340d200a4920608e033d5006000000380900c300c000000000f01480200000000044072008000000261301cc02000000000780520080000000000c0c801000000000340720080000000c8004c804000000000c80720080000000036014802,0xc8380f30080000110130370c0400009d06300293014006114412022100400000980cc019301000000188a4058c030000000983c0730080000016024030c03000000000240d20080000000011018802000000000140d200800000000260148020000000003409200800000000050188020000000443c0530080000138110058c04000094260900b400c00000000780248030001047431024400c0f208a0b40631005000006a04401430100000019024030c03], #[![7, 0, -15, 8],![39, -25, 0, 4]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case0" = "QuadFull27Case0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case0
private def zz2107:"s083b"="s083b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l6 l60)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x14352498a, -0xde2c256c, -0x14d424545,0x898d36a], ![-0xde2c256c, -0x3dce09eeb,0x1f2d68,0x144198f78], ![-0x14d424545,0x1f2d68, -0x5a34b0cf9,0xde2c544f], ![0x898d36a,0x144198f78,0xde2c544f, -0x6f161e6e]]
noncomputable def hinges:Hinges:=[(-0x51d29,l6),(0x7eb3f7,l4),(-0x251ed3,l10),(0xdebef67a,l14),(0x142ad5b89,l15),(-0x6f161e6e,l27),(0x6f161e6e,l29),(-0xdebef67a,l25),(0x6f8f7dbc,l30),(0x6f161e6e,l33),(0x251ed3,l38),(-0x6f161e6e,l35),(0x6f161e6e,l37),(-0x7eb3f7,l34),(-0x6f8f7dbc,l43),(-0x142ad5b89,l41),(0x6f161e6e,l51),(0x51d29,l60)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6f161e6e,l27),(0x6f161e6e,l29),(0x6f161e6e,l33),(-0x6f161e6e,l35),(0x6f161e6e,l37),(0x6f161e6e,l51),(0xdebef67a,l14),(-0xdebef67a,l25),(0x6f8f7dbc,l30),(-0x6f8f7dbc,l43),(0x142ad5b89,l15),(-0x142ad5b89,l41),(-0x251ed3,l10),(0x251ed3,l38),(0x7eb3f7,l4),(-0x7eb3f7,l34),(-0x51d29,l6),(0x51d29,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0x2601c80200000001101880200000000503480200000000d02480200000000501880200000110f014c02000138110058c0400250982402d0030000000780248030001a8110050c04000019024030c0300001a044038c03000001916014c02000000002c0c80100000191602cc0200000001502480200002e0c4028c0300000001901880200000130a038c0200000211e038c02000002a15038c02000000021038802], #[]⟩
def dynamicCode : Nat := ((((((((((0x3864c6ddc52fd92f04a8a242a3fc1688a15d0be7132862fb729973eabcb18089e80d7b37af8ecec13c70217327f906801c64ce9480af06b204b5f68cd5f2527f8496af809ab74ee57e0dec54dbe9bb75d74841161a1a06e220b7248f28e3831a1db974d45be8cd76ff0a7ef0f3ea7ec24266a5e05384636035882dd7bd5fac0f65a366c79073cf861bdf4fe4cd7061c052e129ba479a1635dfa999a223088824ed2600) <<< 16000) +
    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)) <<< 16000) +
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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case1" = "QuadFull27Case1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case1
private def zz2108:"s083c"="s083c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l0 l10 l15 l17 l27 l29 l30 l33 l35 l37 l4 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x821397f8e, -0x2cb416090, -0x1bc0c90d8,0x14668c8],l0, ![-0x1bc0c90d8,0x6c89bed8c, -0x14fc37665e,0x4200a24ce], ![0x14668c8, -0x1a192ade6,0x4200a24ce, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x65575028,l6),(0x1aaa197bd,l4),(0x2c322cc1,l10),(-0x6c7df020,l17),(0x3ce3f89e0,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x22de70e,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0xce377c,l46),(0x165a0bc00,l51),(-0x10f905726,l62),(0xab7324,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x10f905726,l62),(0x3ce3f89e0,l15),(-0x6c7df020,l17),(0x1aaa197bd,l4),(-0x65575028,l6),(0x2c322cc1,l10),(0x22de70e,l30),(-0xce377c,l46),(0xab7324,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x1c629d5f38608161d82d34a1c548b5bc2b4501d859b1f2040168b04df8465102200840e2d0cacf0891a29e739789030615dac082431887e513e4056680f6cd8904b36a0dcc00000000694e1270c230086728f120000000622861f6c8d386c1d12882462062442c12412012c0170180200d00010720005244024079ca3c48000000188a187db234e1b07448186189149107106109083000530300200d00010d337650c0351bf7e4abb310159a90ee1e95802ddc95) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case2" = "QuadFull27Case2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case2
private def zz2109:"s083d"="s083d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x8049fd1e7, -0x2cb416090, -0x3847bf66c,0x17a43d802], ![-0x2cb416090, -0xf91acc3f4,0x598a0782e, -0x1a1cdf8b4], ![-0x3847bf66c,0x598a0782e, -0x14fc37665e,0x4200a24ce], ![0x17a43d802, -0x1a1cdf8b4,0x4200a24ce, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x65575028,l6),(0x1aaa197bd,l4),(0x2c322cc1,l10),(0x1275c701a,l14),(0x4bed4d064,l12),(-0x6c20b97a,l17),(0x3caf389ae,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x15439e882,l25),(0x2d64234,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x4babc17a,l43),(-0x350a2ecd7,l41),(-0x211c8d88,l46),(0x165a0bc00,l51),(-0x136f85870,l62),(0x958b4f52,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x15439e882,l25),(-0x136f85870,l62),(0x4bed4d064,l12),(0x1275c701a,l14),(0x3caf389ae,l15),(-0x350a2ecd7,l41),(0x958b4f52,l64),(-0x6c20b97a,l17),(0x1aaa197bd,l4),(-0x65575028,l6),(-0x4babc17a,l43),(0x2c322cc1,l10),(-0x211c8d88,l46),(0x2d64234,l30)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0x6402900400000c42100a0c04000000000280c4010000000443c05300800002702200b18080000011024038c030001284c12016801800000001e009200c1e41141680c6200a000000078004c804], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case3" = "QuadFull27Case3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case3
private def zz2110:"s083e"="s083e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1580e4316, -0xde2c256c, -0x14d424542,0x9012e40], ![-0xde2c256c, -0x3f42c0b31,0x101aa4a,0x143aa3218], ![-0x14d424542,0x101aa4a, -0x5a340ef48,0xde2c544c], ![0x9012e40,0x143aa3218,0xde2c544c, -0x6f161e6e]]
noncomputable def hinges:Hinges:=[(-0x8c115,l6),(0x92527b,l4),(-0x280514,l10),(0xda75b09a,l14),(-0xe46eb7,l17),(0x1495b75a8,l15),(-0x6f161e6e,l27),(0x6f161e6e,l29),(-0xdad8590e,l25),(0x6e14c49e,l30),(0x6f161e6e,l33),(0x443360,l38),(-0x6f161e6e,l35),(0x6f161e6e,l37),(-0xe8c239,l34),(-0x6d5fb7ee,l43),(-0x148c8f6bd,l41),(0x28704f8,l46),(0x6f161e6e,l51),(0x962b3,l60),(0x1051919,l62),(-0x3272b04,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6f161e6e,l27),(0x6f161e6e,l29),(0x6f161e6e,l33),(-0x6f161e6e,l35),(0x6f161e6e,l37),(0x6f161e6e,l51),(-0xdad8590e,l25),(0xda75b09a,l14),(0x6e14c49e,l30),(-0x6d5fb7ee,l43),(0x1495b75a8,l15),(-0x148c8f6bd,l41),(-0x3272b04,l64),(0x28704f8,l46),(0x1051919,l62),(-0xe46eb7,l17),(0x443360,l38),(-0xe8c239,l34),(-0x280514,l10),(0x92527b,l4),(0x962b3,l60),(-0x8c115,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0x1700a40100000002a0013201000000000540390040000002e0903cc02000000000480e40100000002600132010000000004c039004000000320f01cc020000000e868146010000000320013201000000000120690040000000011018802], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case4" = "QuadFull27Case4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case4
private def zz2111:"s083f"="s083f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x146954882, -0xde2c256c, -0x14d424545,0x82d8ac4], ![-0xde2c256c, -0x3e11fc1bd,0xc751ec,0x144198f78], ![-0x14d424545,0xc751ec, -0x5a340ef48,0xde2c544c], ![0x82d8ac4,0x144198f78,0xde2c544c, -0x6f161e6e]]
noncomputable def hinges:Hinges:=[(-0x8c115,l6),(0x92527b,l4),(-0x280514,l10),(0xde6c7a30,l14),(0x142ad5b89,l15),(-0x6f161e6e,l27),(0x6f161e6e,l29),(-0xde3d013e,l25),(0x6f8f7dbc,l30),(0x6f161e6e,l33),(0x443360,l38),(-0x6f161e6e,l35),(0x6f161e6e,l37),(-0xe8c239,l34),(-0x6e89c95c,l43),(-0x142a375e5,l41),(-0x98db74,l46),(0x6f161e6e,l51),(0x962b3,l60),(0x22e6e7,l62),(-0x88d06c,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6f161e6e,l27),(0x6f161e6e,l29),(0x6f161e6e,l33),(-0x6f161e6e,l35),(0x6f161e6e,l37),(0x6f161e6e,l51),(0xde6c7a30,l14),(-0xde3d013e,l25),(0x6f8f7dbc,l30),(-0x6e89c95c,l43),(0x142ad5b89,l15),(-0x142a375e5,l41),(-0x98db74,l46),(-0x88d06c,l64),(0x443360,l38),(-0xe8c239,l34),(-0x280514,l10),(0x92527b,l4),(0x22e6e7,l62),(0x962b3,l60),(-0x8c115,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0x321203cc02000000128481c601000003404c0dc3010000000004c0390040000002111028c02000000000880e401000000480900c300c00000000220310040000000907014c02000000000281a40100000000034092008000000000a031004000000110f014c02], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case5" = "QuadFull27Case5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case5
private def zz2112:"s0840"="s0840":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l0 l10 l15 l17 l27 l29 l30 l33 l35 l37 l4 l44 l46 l51 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x8308d3ca7, -0x2cb416090, -0x1bedffee5,0x5a7cb0],l0, ![-0x1bedffee5,0x6c89bed8c, -0x150180157b,0x4214e9497], ![0x5a7cb0, -0x1a192ade6,0x4214e9497, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x638d2970,l6),(0x1a6da661a,l4),(0x2d010889,l10),(-0x6c7df020,l17),(0x3ce3f89e0,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x22de70e,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0xeeaa58,l46),(0x18efc04,l44),(0x165a0bc00,l51),(-0x110c1967b,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x110c1967b,l62),(0x3ce3f89e0,l15),(-0x6c7df020,l17),(0x1a6da661a,l4),(-0x638d2970,l6),(0x2d010889,l10),(0x22de70e,l30),(-0xeeaa58,l46),(0x18efc04,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x91c9ef2557a38c7eb5399d2059723e8770e2856d7aa2c501e6a8691c23510210044112) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case6" = "QuadFull27Case6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case6
private def zz2113:"s0841"="s0841":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l44 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7e57f524c, -0x2cb416090, -0x383f1fa02,0x17cd3dfec], ![-0x2cb416090, -0xfc490722a,0x5a3570f4e, -0x1a1cdf8b4], ![-0x383f1fa02,0x5a3570f4e, -0x150180157b,0x4214e9497], ![0x17cd3dfec, -0x1a1cdf8b4,0x4214e9497, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x638d2970,l6),(0x1a6da661a,l4),(0x2d010889,l10),(0x12a6a1838,l14),(0x4a9eec99c,l12),(-0x6c20b97a,l17),(0x3caf389ae,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x14c96caa2,l25),(0x2d64234,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x4e90bb5f,l43),(-0x35133b4ae,l41),(-0x1ecf2048,l46),(-0x332a198,l44),(0x165a0bc00,l51),(-0x133f1bf61,l62),(0x9675fc3a,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x14c96caa2,l25),(-0x133f1bf61,l62),(0x4a9eec99c,l12),(0x12a6a1838,l14),(0x3caf389ae,l15),(-0x35133b4ae,l41),(0x9675fc3a,l64),(-0x6c20b97a,l17),(0x1a6da661a,l4),(-0x638d2970,l6),(-0x4e90bb5f,l43),(0x2d010889,l10),(-0x1ecf2048,l46),(0x2d64234,l30),(-0x332a198,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0xc805200800001884201418080000000005018802000000088780a601000004e04401630100000022048071806000250982402d003000000003c01240183c82282d018c40140000000f00099008000000001e01c802000000001100a40100000005848073008000029090009980800000000b0024803000000006c012401800006a044014301000000320480618060001a01040098c05000000d02201c60182983084100d2401414c19c238069200a0000000016014802], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case7" = "QuadFull27Case7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case7
private def zz2114:"s0842"="s0842":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case8
private def zz2115:"s0843"="s0843":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz344:"s0158"="s0158":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case9
private def zz2116:"s0844"="s0844":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case10
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l14 l17 l27 l29 l33 l34 l35 l37 l38 l41 l43 l51 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x3412c6a33, -0x26deb9ac7, -0x430e21c90,0x1770], ![-0x26deb9ac7, -0x133819917a,0x6e9c24dea,0x172a4749a], ![-0x430e21c90,0x6e9c24dea, -0x1229298c00,0x2cb418f70], ![0x1770,0x172a4749a,0x2cb418f70, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0xeeaa58,l14),(-0x18efc04,l12),(0x10f905726,l17),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x2fbe0d5f,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x194f19acb,l34),(-0x2507daf,l43),(-0x3ce3f89e0,l41),(0x165a0bc00,l51),(0x67230997,l60),(0x6c81c7f5,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x10f905726,l17),(-0x3ce3f89e0,l41),(0x6c81c7f5,l62),(0x67230997,l60),(-0x194f19acb,l34),(-0x2fbe0d5f,l38),(-0x2507daf,l43),(0xeeaa58,l14),(-0x18efc04,l12)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[0x5018802000000090024803000011024038c03000138110058c0400250982402d00300000007802480300000001101c802000001b11018c02000019894028c0300014848004cc0400000161201cc020000000b00248030000000d8024803001a01040098c05000000022014802000008828030c03000000009018802000000a0603cc02000000f07028c02000010864034c0300000001601480200310c844035003c608c0ac03c900500000000e014802000000e09038c020000000e140cc0105c0a01c0175004000000098024803000000070024803000000012014802], #[![-111, -675, 112, 0],![3, -45, 4, 0],![3, -17, -1, 0]]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case10" = "QuadFull27Case10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case10
private def zz2117:"s0845"="s0845":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l41 l43 l46 l51 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x3e7ff2af1, -0x26deb9ac7, -0x430e21c90,0x20d944a0], ![-0x26deb9ac7, -0xbb880f345,0x16eef2a8e,0x454134429], ![-0x430e21c90,0x16eef2a8e, -0x1229298c00,0x2cb418f70], ![0x20d944a0,0x454134429,0x2cb418f70, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0x14ed510be,l14),(-0x4fcb2259c,l12),(0x136f85870,l17),(0x350a2ecd7,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x11b0c827e,l25),(0x4babc17a,l30),(0x165a0bc00,l33),(-0x2fbe0d5f,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x194f19acb,l34),(-0x387df64,l43),(-0x3cb75314b,l41),(-0x9a089cea,l46),(0x165a0bc00,l51),(0x67230997,l60),(0x6c54fc21,l62),(0x23a69e5c,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x14ed510be,l14),(-0x4fcb2259c,l12),(0x136f85870,l17),(-0x11b0c827e,l25),(-0x3cb75314b,l41),(0x350a2ecd7,l15),(-0x9a089cea,l46),(0x6c54fc21,l62),(0x67230997,l60),(-0x194f19acb,l34),(0x4babc17a,l30),(-0x2fbe0d5f,l38),(0x23a69e5c,l64),(-0x387df64,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case11" = "QuadFull27Case11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case11
private def zz2118:"s0846"="s0846":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz348:"s015c"="s015c":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case12
private def zz2119:"s0847"="s0847":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz349:"s015d"="s015d":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case13
private def zz2120:"s0848"="s0848":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1434f7a54, -0xdca1fe88, -0x14af30aec,0x7a26df7], ![-0xdca1fe88, -0x3d875189e,0x18011a,0x142e5c850], ![-0x14af30aec,0x18011a, -0x599768102,0xdca22d68], ![0x7a26df7,0x142e5c850,0xdca22d68, -0x6e510afc]]
noncomputable def hinges:Hinges:=[(-0x3fb41,l6),(0x6373e9,l4),(-0x1d2b62,l10),(0xdc393966,l14),(-0x1051919,l17),(0x148c8f6bd,l15),(-0x6e510afc,l27),(0x6e510afc,l29),(-0xdc393966,l25),(0x6d5fb7ee,l30),(0x6e510afc,l33),(0x1d2b62,l38),(-0x6e510afc,l35),(0x6e510afc,l37),(-0x6373e9,l34),(-0x6d5fb7ee,l43),(-0x148c8f6bd,l41),(0x9068a9,l46),(0x6e510afc,l51),(0x3fb41,l60),(0x1051919,l62),(-0x9068a9,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x1b8955684285cb90a000030023400f44dbee295e615d71b943fd0f0dc22d8b7b322e10b37b0ea313b2869ef4a82407 s0
def s2:=qPath 0x1b9445ad0285cb90a000030023400f44dbee295e615d71b943fd0f0dca215f7b32ed02037b0ea313b2869ef4a82402 s0
def s3:=qPath 0x1b92c774a285cb90a000030023400f44dbee295e615d71b943fd0f0dc1584e9b343327157b0ea313b2869ef4a8240b s2
def s4:=qPath 0x1b9445ad0285cb90a000030023400f44dbee295e615d71b943fd0f0dca215f7b32ed02037b0ea313b2869ef4a82402 s2
def s5:=qPath 0x1b9f35f1c285cb90a000030023400f44dbee295e615d71b943fd0f0dcdc6cbbb34fa0ee77b0ea313b2869ef4a82411 s4
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨8, #[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,0x3c58c01080c10909c0000000c020004050000b08100c0080980002418101000412000080618100050780000000b060804053410a040c0c01011cd0c281c6071004330000b01040c0090a8000180c204000416000090208081010380003420907100c220000f0220081030380003404601040c0e0000c011404301018d0628106030c041b000120118082010180003c08a01140406000120134040030380000000402000c0500010033804303018d02283080400141f3410a09200c10509c000000020104040500000004804403014000200460110080a0000b06200470102800024047030010120000d012c04002028000000070100040500000001804001014901200410600041f0000e012404103038c03200c20200141f3804c01140c00102c0004008b02040c0e3004a010c1800608c00034048010c04063418b01280c60406c0001804303000c120000501080c004059301340c50300181f00000003c04101014d01300430300181f000130214042030280000000f01080c054008a01041400207c000140820300040a000050110040010180004408d020404060000f012c04101018000140810200040600000004c0400101400000014020c040500000003c0c101014000300830104040a4408c04100430104c000300ca090010123420c09286c11018c000180c4010010120000000080c0010140002c103030430363004a01041801214c0003004a0114180a,0x1820501003c3200008181804405088000180c10100101200005030810001048000100c10400101e00006070c0c00b0a80000c0c10300101200000000c04002014000000090810040d0000816180c3050980000000b020804050000a020404001028f1220042030420230000b020c0c0020380000000f06000405]⟩
theorem v0:V s1:=(P w317 (S (K 19 nt 0x866f0c82324069036a1786c219203481a400826488473d922458c7447d218019430801d0c35b479c0d795bcc0685645be4b9900391220214f42840c5892470c40ba16550104002843906a0c4027c61ad799a06bcd6aa8e78bbf691f97ee8cdbb70e2dad55b7b7ac5be8b98803a1a242bf8902749077d3938620450821541c851062134034a6a02083d0720d41884d092005637d29f8fece872579fc39f7217c235484ae117f8648e2658a1838620450820f41c8350620b414825009f1894d0c46480c21084200dbfc9dab89f0082e9802103a00b020c81502203404805002) (S (K 15 nt 0x8f0cc0433c85412203087edc442a7106624886143f0a15f0e6f06890c014327600f248d03b9581a006480d22060688192034800363524601920348003123a8714080c08324060084211425de465eaeac100521bee4c0015c4066893225521f64884c7ebf662914299c4190af873f490648271e8e90f2bceca5d9f830918760cc12300b424681dcfb240985d4291f8830a9354883210203028c901802108404dfe76972d29dec00a5779698002cc809c10640a80aacc3090fe11f830a9264812c80ef11bd758c0691fdf7de4bc194a8814741982240ee12a0c32406008401023579f2b7bf80148a8c1015061920300421081d7843b2e6af0b00291ef3a6000a9202a241902a21405146f7144324069040a17944324069040800f0c320d9e519203481f4308014489b127648900cfec832c8240772a1418080a19046480d2000d8c30907fe332281cd83c150a0c04012886480d2000c48056188a19106480d20790c2004c226e481241e4423d12e3f84a5506022706c01920348903238c6480d2000d88c2008a31864f38c9018021189803906a0c400e04062081bd10772243300c901a440478c6480c0101754b7bf5ac2f79007b87e3aa7a75b19bda418003448ea1c53fc92107971c8249b501b7714b467595fc1ad3082dfb20cc0e200cd2042041902a0440681bb080a) (S (K 12 nt 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) (K 17 nt 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)))))
theorem v1:V s3:=(S (K 18 nt 0xb9e510c901a41021870fb77e43560fb5cffe571ee71a7d56ecaf20a4f8504fe2061438621450825243ea1952f390715e43e4f5fc1f7f7067eb2d225dd69dea7f81af339897961fe22ddc52f1374142c2fc0b1e903098a9046c289061430620450825243e807508177113624e19b83200c901a44ae0c843240690006c461d98e6248d4ed54565d57bb3246ff677550d6d3a6435e43547fefaa071296607b763734f1fc96fa2e6291488a240921d121860c1885142094127296fe2e3a70f8cb17282e444185054c922baa891232680c408a104a09390074902cb226e8dc2c58c721ae354906b9dfb65bf8b8e9c3e1079067423f0cfe0861740620450824f49c85126a8613ceac1cced999699c4051cde2fefafa2661ed06b2bf22ec5f10173c4c173f26a45e4af48fe45b5656f62e2eef1855bb2bc482840993d947b063230620450820f41c9210620230206f241c1083b892d08c90180211e27ac72f8b58200010a9300e2852d50c901802108402d53fbfca5d873c042b75d300e200b4202ce41902a0448893100a) (S (S (K 16 nt 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) (K 16 nt 0x56182443240690c0cbdc7f1f06125c37c05c7e95418080304946480d2000d892300b724681dc3089227f18925f06490c2a4d5220c84076146480c01084200d75d8421fcdb000a474f3000521013320c9611a2b8336806480d22d7b8032406915000092009a5718c35f6bcea0ba8552e31872eec3c6438b0f5d2d3d9ceec1ec7dbd9634af27d00830812a284107fa263b23e80c42aa5b4a6aa02093d000f980315986480d2000d880d715a6040256503b8fc4915fb10c7f1102a645220c84076186480c01084206777dac79d90029249800254808a9064b095d021a9)) (M w148 (K 16 nt 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))))
theorem v2:V s5:=(S (K 16 nt 0x24806921f043ea8fa1944a0c0441834a32406903e9218026113624ee6980324069113c60192033096bd966342e6f6b6365a7b39dd4baafebed0434a07fc6a203b922cf9c31001de5b5009f1b4317006480d2227866019203308f5d0e2c3c64bbb00b1a5793e87b1f6f65a7b39dd841a50900f32891e010c59340620044888201662035e461c8193cc3240690209412e214600c444dcce7946480d204127a5c492d7d461834e32406008062600e46ac310038100eb2099a41dc474046480c01012f19ce1cfc64001b96e7772958087c1807140651c6480c01084201633fbcafed00290f980025480b8106454811222) (S (S (K 14 nt 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) (K 14 nt 0x146a9095c39f7217c3a1c95e7f7d29f8fec142f0325462865123862045bbb8634c429f1cfb887e01d77f89f321d77f89f3415ec95187f638d28920310f2ce98082975630ce5bb3818418c90185b0c5e540000109c4c000ee5e103b94327186480c2000005130401938c3240690006c606946324069000624750e281ca10c90180210843f9c25b852720802934980026880d49942137772863674c007cbab18672dd9ca18dc0d6246480d2000c48aa75630ca193b008f2e881dca64806480d379ebda95000000a19698204a02324069000626041c6324069000624750e2804520c901802108401005226000682033440b88b13)) (K 15 nt 0x977ed239e0d79ad5435af3346deded0716d6be8cdb9747e5eb87402e625be861e49164503fe0d2891c31084d05cbf87c5ac86bcb43c1ada3399e5efe9dc9cee1946b1a0654e52ccfc7700da918ed75fe62be6fff0e805cc4b7d103cb1061a54f471831096d0180e410e630cfd97b9c347286480cc12dc019b523240690006c455073186ccc9d806092340ee50c9e919203766dcac7c0017f887ec028a4c103d21192034800313039031920348003123a87140e5946480c0108420080291300034101ae2f4989b0b)))
private def zz350:"s015e"="s015e":=by decide+kernel
theorem v3:V s4:=(S (S (K 19 nt 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) (M w28 (S (K 17 nt 0x92210ff840b22911be19a830040861c5ea07f70d7618d822a482844823aafaf4552188554209490fa48601ac44d893864d3006480d225a6839d873a2d2e5d57f5f68b9bdad8d9737b5b1b2eabfafb421d3a7c1fe167ca188554da804a0cce0c803240691501040028401748c3a8082504b8851801a9137501049e97124b5f52bc3118c901a40820f41ca30cc3148c901a40820f41c8017086200d12024840dd883b890c08c90180217e3deadff2bd80067336e77d20205d8300e2850c50c901802108404d53b3c475602032601c40136405d88322a408911362) v2))) (K 14 nt 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))
theorem v4:V s2:=(S (P w24 (S (K 19 nt 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) v1)) v3)
theorem v5:V s0:=(S (P w269 v0) v4)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v5
private def zz351:"s015f"="s015f":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case14
private def zz2121:"s0849"="s0849":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1432efa14, -0xdca1fe88, -0x14af30aef,0x7a3e66e], ![-0xdca1fe88, -0x3d8722196,0x17f4a2,0x142e51255], ![-0x14af30aef,0x17f4a2, -0x599768102,0xdca22d68], ![0x7a3e66e,0x142e51255,0xdca22d68, -0x6e510afc]]
noncomputable def hinges:Hinges:=[(-0x3fb41,l6),(0x6373e9,l4),(-0x1d2b62,l10),(0xdce0820e,l14),(-0x22e6e7,l17),(0x142a375e5,l15),(-0x6e510afc,l27),(0x6e510afc,l29),(-0xdce0820e,l25),(0x6e89c95c,l30),(0x6e510afc,l33),(0x1d2b62,l38),(-0x6e510afc,l35),(0x6e510afc,l37),(-0x6373e9,l34),(-0x6e89c95c,l43),(-0x142a375e5,l41),(0x2d4e16,l46),(0x6e510afc,l51),(0x3fb41,l60),(0x22e6e7,l62),(-0x2d4e16,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x1b8955684285ca24aa0002fe94400f47ccdc295e615dd1b943fd0f0dc22d8b7b322e10b37b0e4432b2865df4282407 s0
def s2:=qPath 0x1b9445ad0285ca24aa0002fe94400f47ccdc295e615dd1b943fd0f0dca215f7b32ed02037b0e4432b2865df4282402 s0
def s3:=qPath 0x1b92c774a285ca24aa0002fe94400f47ccdc295e615dd1b943fd0f0dc1584e9b343327157b0e4432b2865df4282413 s2
def s4:=qPath 0x1b9445ad0285ca24aa0002fe94400f47ccdc295e615dd1b943fd0f0dca215f7b32ed02037b0e4432b2865df4282402 s2
def s5:=qPath 0x1b9f35f1c285ca24aa0002fe94400f47ccdc295e615dd1b943fd0f0dcdc6cbbb34fa0ee77b0e4432b2865df4282411 s4
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨8, #[0x3004a01041801214c0003004a0114180a2004601041800208cf01180c4030004130000b1824047050880000000b01140c050000701040c0010480000000b01180c055008a01040c00407ca06081010300082700000002c0c5010140000000701080c050000602040c001028000140420100140a0000708140c00d0c80000000a020c0405200c703081c0040bc000200460100101200007011404004048000380ca030c04063408c03240480302c000180420100040a0000402082400e0b8000000070110040500006030c042030480003408606002c26000000028204010348031c0c304080c1f343890a180c5030ecd183004a0d18406300005040c0c00d0e800000012021004052c04a01100410504c0000000302040c0500000003808201034000340890304040e4838e0a2c0ca030ed2063814a0300041f3808b02280810707c000000100100040500012040c0c00c0d8000000140810040d00000004c084010140000000c0108040500000002c040010140000000a01000405280830304180040bcc01240410900606f00005030c04002028a01200420204040f0001102400c101038000000100200040d3c108031c0c2090dc0003808101000412000100228080010190033404a0304080f0000000200400101400000007010404050000604100c00c0d8000140410100080e000000028080010140001c10202000c0e00000001808001034000140830300040e,0x3c48801080c10808c0002c0830300080e00000003c18001014f163004203042427000000030080010140002c2040300202600009060404001048000201860400141e00000002c18201014d0428103030040473430a07181c4010cc0002c0410300242a00006030810001058000240820204040e0000d08241c4030880003c08802040c0e0000d01180410303800030045010c04063418a04180c30106c0003c08a011404064808e03181810305c0004804d01000c0e00000001008003014d02283080400141f3410a09200c10509c000000020104040500000004804403014000200460110080a0000b06200470102800024047030010120000d012c04002028000000070100040500000001804001014901200410600041f0000e012404103038c03200c20200141f3804c01140c00102c0004008b02040c0e3004a010c1800608c00034048010c04063418b01280c60406c0001804303000c120000501080c004059301340c50300181f3404c010c0c00607c0004c08501080c0a00000003c041010140000000f01080c054008a01041400207c000140820300040a000050110040010180004408d020404060000f012c04101018000140810200040600000004c0400101400000014020c040500000003c0c101014000300830104040a4408c04100430104c000300ca090010123420c09286c11018c000180c4010010120000000080c0010140002c10303043036,0x608140400f0c8000206060110142200006030404004048000140c20400041200004030410004078000181c303002c2a0000303040c00404800000003010008050000000242040103400020586030c142600000002c08201014000280810100040a]⟩
theorem v0:V s1:=(P w317 (S (K 19 nt 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) (S (K 15 nt 0x8f0cc9033a85412203085e3a454e60cc4910c287e142be1cde0d121802864ec01e491a0772b03400c901a440c0d103240690006c6a48c0324069000624750e281018106480c01084238f3319d718e040148b526000a42032049912a90fb244263f5fb3148a14ce20c84935f4c7e861209c7a3a517c661a856023064198246015448d03b8cfb240985d923f1061522a910642040605192030042108116edf9bac7bda00290d2ba6000ae2026641902a029c30c243f847e0c2a499204b21d7ec711ce9b3ff391a4f8194a8814741982240ee224c7b25d7e1e49a20525acebacd3b9d16128a436c066202a0c3240600842103af3dd6d78775c00523de74c00152405d08320544280a8cdee2886480d208142f2886480d2081001e18641b3ca32406903e8610028913624ec91201ffc2caa0901dca8506020286411920348003630c241ff8cc8a07360f054283010043610c901a4001b100b131143220c901a40f2184009844dc902483c8847a25c7f094aa0c044e0d8032406912064718c901a4001b11840114630c9e719203480e41a831002b9016f206c241dc890cc03240691011e31920300001f4b96ef778bd3c0546d8d5e32f68c4cf20c001984750e29fe49083cb8e4124da83e79496b9cfea81ad3080f6960cc0e200c82040c41902a0440681b2480a) (S (K 12 nt 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) (K 17 nt 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)))))
theorem v1:V s3:=(S (S (K 16 nt 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) (K 16 nt 0x56182443240690bccbdc7f1fc24b86f80b8f7315418080304946480d2000d892300b724681dc3089227f18925f06490c2a455220c84076146480c01084203cef5856d0850014863a60009f2025c4192b23457066d00c901a45e1a3803240691500009200a45698c35d6b8ea0b68552d31874dbbddbb73ce5d48c43984afa0cedca22f29d3c3d529c46730ed44185091142080c24890e61820310a2965292a80824d4003e600c56619203480036203c0561811995740ee18487e248afe92422120250600714076186480c010842067a96dcbdda0029249800254808d9064ac95502391)) (M w148 (S (K 15 nt 0x2c0c9c019203489443594f4bdde818fab4d071ae5be2c8605cd0b7b87990f3a5960b4d0c38b0e901047c704e188012b34771da4001fc2bdbe2a1f5f14d52c114201a41053cc30a3c9140621250073102402b4c61aeb5c71ee50a8edf9f035b6e7c0d65587c21a54910ef4d648716ae61a24310928f90aa5a630e1bdff326e90e8712d56018ff37ca339876a8bca74f23d6dfac8ce61da883480a102a03092e2188d0188494b29495404126a001f26ac06b0ac302e12ae81dc887006480d2207286324069000624750e280ab38c90180210840fefabfb465200525d30004a9013320c9812fa) (K 15 nt 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))))
theorem v2:V s5:=(S (K 16 nt 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) (S (S (K 14 nt 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) (K 14 nt 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)) (K 15 nt 0x25dfb28eec35e6afc0d6bcdf592b6641b6f778aebabed7bfeaa1d00b9896fa18792459140ff834a2470c42033f72fe91156e1af2bee06b68d6a9dcf100cbfe9fdf5fee8fbfbd20e805cc4b7d0d160d2830ce6191e8e38621259f3016921cc619eb2f713d25192030fbd2b4b000067c8d60028bcc0c8c9d805312340ee50c9e9192030dbb3ee70001a1ee7b0028a4c103d21192034800313039031920348003123a87140e5946480c0108420080291300034101ae2ee981afb)))
private def zz352:"s0160"="s0160":=by decide+kernel
theorem v3:V s4:=(S (S (K 19 nt 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) (M w28 (S (K 17 nt 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) v2))) (K 14 nt 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))
theorem v4:V s2:=(S (P w24 (S (K 19 nt 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) (S (K 18 nt 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) v1))) v3)
theorem v5:V s0:=(S (P w269 v0) v4)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v5
private def zz353:"s0161"="s0161":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case15
private def zz2122:"s084a"="s084a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l51 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x8312d8e53, -0x2cb416090, -0x1bedffee5,0x1770], ![-0x2cb416090, -0x15992738da,0x6e86e14d0, -0x1a1367182], ![-0x1bedffee5,0x6e86e14d0, -0x15054d87ad,0x4177bb205], ![0x1770, -0x1a1367182,0x4177bb205, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x62fab96d,l6),(0x18dfa4333,l4),(0x30207e6f,l10),(0xab7324,l14),(-0x6c81c7f5,l17),(0x3ce3f89e0,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0xce377c,l25),(0x2507daf,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x110c1967b,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x110c1967b,l62),(0x3ce3f89e0,l15),(-0x6c81c7f5,l17),(0x18dfa4333,l4),(-0x62fab96d,l6),(0x30207e6f,l10),(0x2507daf,l30),(-0xce377c,l25),(0xab7324,l14)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1300a401000004e0440163010000000221e029804000250982402d003000000003c01240180003204d007230140001a4178028180a005311413006100400000a82200726020000000002406200800003502200a18080000019024030c030000d0082004c602800000681100e300c000000002c0290040000001d1a038c0200000000f1a066008000000b8640e30080000011050061806000000002e014802000000078381460150829010800cd401800b81403802ea0080000000098024803000000088580c6010000000003805200800000000e00490060000000012014802], #[![207, 1500, -2069, 0],![8, -169, 279, 0],![-27, -15, 68, 0],![33, 150, -211, 0]]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case16" = "QuadFull27Case16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case16
private def zz2123:"s084b"="s084b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7d33fb258, -0x2cb416090, -0x383f1fa02,0x183eeb030], ![-0x2cb416090, -0x100f49de6a,0x5d4a032b6, -0x19fd4417c], ![-0x383f1fa02,0x5d4a032b6, -0x15054d87ad,0x4177bb205], ![0x183eeb030, -0x19fd4417c,0x4177bb205, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x62fab96d,l6),(0x18dfa4333,l4),(0x30207e6f,l10),(0x11c8e68ee,l14),(0x4f48f3254,l12),(-0x6c54fc21,l17),(0x3cb75314b,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x14bc409d6,l25),(0x387df64,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x4e90bb5f,l43),(-0x35133b4ae,l41),(-0x1ed0cbbe,l46),(0x165a0bc00,l51),(-0x133f1bf61,l62),(0x982247fc,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x14bc409d6,l25),(0x4f48f3254,l12),(-0x133f1bf61,l62),(0x11c8e68ee,l14),(0x3cb75314b,l15),(-0x35133b4ae,l41),(0x982247fc,l64),(-0x6c54fc21,l17),(0x18dfa4333,l4),(-0x62fab96d,l6),(-0x4e90bb5f,l43),(0x30207e6f,l10),(-0x1ed0cbbe,l46),(0x387df64,l30)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0x6210805060200000000034092008000000000a031004000000110f014c02], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull27Case17" = "QuadFull27Case17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull27Case17
private def zz2124:"s084c"="s084c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz356:"s0164"="s0164":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case18
private def zz2125:"s084d"="s084d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull27Case19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull27Case19
private def zz2126:"s084e"="s084e":=by decide+kernel
end 
section 
namespace Green24Proof.Full27Rows
open QuadraticCertificates ExpressionCertificates FullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107f2779ae58004d4ea8c8e06f201eeb5ca800cb7f4c39a01f203dceb948014e4db95a27203dceb94801e88f48a9a3201eeb5ca80128bbda4c207e20bf5f0c02cbe868e01e203dceb94800df1f482be6201eeb5ca800184f0d207a25faf848002ddc4c6d201a203dceb94800dd6e1b28e2203dceb948002d7c6ee07d25faf848003d8c9f9d206d201eeb5ca800cd3e39ae601d203dceb948015a1e7d1825203dceb94801decaba5ba1201eeb5ca80128bbda4c207c22fd7c28002e4b2afb2425faf848002e4bad7ca078203dceb94801bd6d6c39202779ae58003bbc4f98614]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decode [0x101fa5faf84800492e9d0de7a03dceb94801f8caaf79207ba01eeb5ca8002d6f39201ba2fd7c28052bea63a3bcdb2c004cdbd81de07ea01eeb5ca800de782848e6a01eeb5ca8006f3d0fea207aa01eeb5ca800de1e4f2e62a01eeb5ca8006f182b9e2763d84c002363d84c00207e603dceb948014f6d4a1be02e601eeb5ca800da6a1b79a01e603dceb948011d8b284fe6603dceb948007d2bef1da07a6779ae58001eed59602a601eeb5ca800289fed62603dceb948024efaddece563d84c002163d84c00214]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decode [0x105f301eeb5ca80018ecd9eae731de6d9a005bce2ee333d84c00207e301eeb5ca800291d0b605e301eeb5ca8002b1dbba6301eeb5ca800fb784e607a301eeb5ca800cceab8201a3779ae580058782be232fd7c28002f3b5ae03d301eeb5ca8004e0c4c7fe05d303dceb948001f6c397be535faf84800ce4eeaa133d84c0024303dceb948016f6b7ce07832fd7c2806cbbfa0303dceb94801afee6967e3d84c0023e3d84c00207fa03dceb948011e4b9d1ee06fa2fd7c28002d2a494b614]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decode [0x17b2fd7c28007dcdf8e03bb01eeb5ca8002d6f39205bb2fd7c28052bea63b3bcdb2c047e4be07eb2fd7c280249f9e6b02b196c00df98207ab03dceb94800983a2d22b03dceb948018efc5a6773d84c002373d84c00203e7779ae5803dcf909202e7779ae5800290f0a205e703dceb948009b3d7f8ba6730ea8067fef203a7779ae58001eed59606a701eeb5ca800289fed6270bf5f0c003828a573d84c002173d84c00203f303dceb948009d0a2b9ea14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decode [0x103f003dceb9480068283f9de02f05faf848003a8c19aba05f003dceb94800cafd5e5da70779ae58073df8da207e017ebe18010818202e003dceb9480038698d205e003dceb94804684aa601ec2a00203d05faf84800198e3a4a602d003dceb948010efd9ceb205d003dceb94800cf298a6ae5003dceb948003f1e4fca607c003dceb948002a8fba602c003dceb948002d1effa05c05faf84800897aa401ec2a0027f3d84c0023f3d84c00203fb03dceb948009acad9ed205fb779ae580429cc6e214]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decode [0x103f803dceb948005d088a29202f801eeb5ca8008e7cdeede05f81de6d9a063c6caae7801eeb5ca8001dcf490e607e809c4da8004d5b202e803dceb948002899ac605e803dceb94801fed82681ec2a00203d803dceb948005c391b38202d803dceb948011e3aef4fe05d83bcdb2c001cad7a88a5801eeb5ca8001e49dffc207c84ca5d057a602c803dceb948004ecd8a605c803dceb94804b8ae6481ec2a002741ec2a002641ec2a002541ec2a002441ec2a00214]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1151ec2a00203e1779ae5800e8fdfb202e103dceb948028bd8decb205e103dceb94800dc5a7f0c2611ec2a00203a103dceb94802583f6de02a10ef3acd001a2affb8a05a103dceb94800dc88e9fea211ec2a00203c1779ae58003be9efdde02c103dceb94800db8f8fa864103dceb94801dae038101eeb5ca8006f0d3899e02810bf5f0c02bf583f6058103dceb94800ea3baee0103dceb94801dae7c1ec2a0026c1ec2a0025c1ec2a0024c1ec2a00214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decode [0x16903dceb94801dae03a909c4da8022fffa9e02a903dceb94800dd9c2c8fe05a903dceb948010a8e4b2290bf5f0c05e03c9779ae5800bacc29a02c901eeb5ca80149d9a86ba05c901eeb5ca8006e182f2fa491ec2a002038901eeb5ca8011b7ce8e02890ef3acd001a2affb8a05894ca5d00295ded2091ec2a00203f503dceb948009e985edbe02f501eeb5ca8011d8c4f8ba01f503dceb948026bf8dfdc27501eeb5ca8003cd95d1aa01b503dceb9480228c8cd9f63503dceb94801a8adb9c92551ec2a00214]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decode [0x10101010001020100089204e2ad801db1d3ca08900bf5f0c061fc92088c5faf848034c6ee088f0102088803dceb94800591b8e986088703dceb948015dff096d608843bcdb2c0018cbcd7c2088303dceb948015dff096d608805faf848001edffa2da7d1ec2a0023d1ec2a00203dd01eeb5ca8004ddaf82fa02dd03dceb948023ae87e6ba01dd1de6d9a002b6fc968e5d779ae58001e5eee9ee019d2fd7c28003b2c0a2ee1d3bcdb2c003a39cc5ee03e917ebe18058b78ed602e903dceb94800db8dec7ee05e95faf848037ebf614]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1089403e8a40201]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFull27Case0.base QuadFull27Case0.hinges QuadFull27Case0.normalizationDenominator
private def zz357:"s0165"="s0165":=by decide+kernel
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case0.base QuadFull27Case0.hinges QuadFull27Case0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFull27Case1.base QuadFull27Case1.hinges QuadFull27Case1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case1.base QuadFull27Case1.hinges QuadFull27Case1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFull27Case2.base QuadFull27Case2.hinges QuadFull27Case2.normalizationDenominator
private def zz358:"s0166"="s0166":=by decide+kernel
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case2.base QuadFull27Case2.hinges QuadFull27Case2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFull27Case3.base QuadFull27Case3.hinges QuadFull27Case3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case3.base QuadFull27Case3.hinges QuadFull27Case3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFull27Case4.base QuadFull27Case4.hinges QuadFull27Case4.normalizationDenominator
private def zz359:"s0167"="s0167":=by decide+kernel
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case4.base QuadFull27Case4.hinges QuadFull27Case4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFull27Case5.base QuadFull27Case5.hinges QuadFull27Case5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case5.base QuadFull27Case5.hinges QuadFull27Case5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFull27Case6.base QuadFull27Case6.hinges QuadFull27Case6.normalizationDenominator
private def zz360:"s0168"="s0168":=by decide+kernel
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case6.base QuadFull27Case6.hinges QuadFull27Case6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFull27Case7.base QuadFull27Case7.hinges QuadFull27Case7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case7.base QuadFull27Case7.hinges QuadFull27Case7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFull27Case8.base QuadFull27Case8.hinges QuadFull27Case8.normalizationDenominator
private def zz361:"s0169"="s0169":=by decide+kernel
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case8.base QuadFull27Case8.hinges QuadFull27Case8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFull27Case9.base QuadFull27Case9.hinges QuadFull27Case9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case9.base QuadFull27Case9.hinges QuadFull27Case9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFull27Case10.base QuadFull27Case10.hinges QuadFull27Case10.normalizationDenominator
private def zz362:"s016a"="s016a":=by decide+kernel
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case10.base QuadFull27Case10.hinges QuadFull27Case10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r16,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFull27Case11.base QuadFull27Case11.hinges QuadFull27Case11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case11.base QuadFull27Case11.hinges QuadFull27Case11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFull27Case12.base QuadFull27Case12.hinges QuadFull27Case12.normalizationDenominator
private def zz363:"s016b"="s016b":=by decide+kernel
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case12.base QuadFull27Case12.hinges QuadFull27Case12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFull27Case13.base QuadFull27Case13.hinges QuadFull27Case13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case13.base QuadFull27Case13.hinges QuadFull27Case13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFull27Case14.base QuadFull27Case14.hinges QuadFull27Case14.normalizationDenominator
private def zz364:"s016c"="s016c":=by decide+kernel
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case14.base QuadFull27Case14.hinges QuadFull27Case14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFull27Case15.base QuadFull27Case15.hinges QuadFull27Case15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case15.base QuadFull27Case15.hinges QuadFull27Case15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFull27Case16.base QuadFull27Case16.hinges QuadFull27Case16.normalizationDenominator
private def zz365:"s016d"="s016d":=by decide+kernel
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case16.base QuadFull27Case16.hinges QuadFull27Case16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFull27Case17.base QuadFull27Case17.hinges QuadFull27Case17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case17.base QuadFull27Case17.hinges QuadFull27Case17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFull27Case18.base QuadFull27Case18.hinges QuadFull27Case18.normalizationDenominator
private def zz366:"s016e"="s016e":=by decide+kernel
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case18.base QuadFull27Case18.hinges QuadFull27Case18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFull27Case19.base QuadFull27Case19.hinges QuadFull27Case19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull27Case19.base QuadFull27Case19.hinges QuadFull27Case19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull27Case19.nonnegative x hx
def pair20:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_20_base LocalFull27Pairs.compact_full27_pair_20_hinges
private def zz367:"s016f"="s016f":=by decide+kernel
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFull27Pairs.full27_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_20_base LocalFull27Pairs.compact_full27_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFull27Pairs.full27_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_21_base LocalFull27Pairs.compact_full27_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
private def zz368:"s0170"="s0170":=by decide+kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFull27Pairs.full27_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_21_base LocalFull27Pairs.compact_full27_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFull27Pairs.full27_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_22_base LocalFull27Pairs.compact_full27_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFull27Pairs.full27_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_22_base LocalFull27Pairs.compact_full27_pair_22_hinges x
private def zz369:"s0171"="s0171":=by decide+kernel
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFull27Pairs.full27_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_23_base LocalFull27Pairs.compact_full27_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFull27Pairs.full27_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_23_base LocalFull27Pairs.compact_full27_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFull27Pairs.full27_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_24_base LocalFull27Pairs.compact_full27_pair_24_hinges
private def zz370:"s0172"="s0172":=by decide+kernel
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFull27Pairs.full27_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_24_base LocalFull27Pairs.compact_full27_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFull27Pairs.full27_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_25_base LocalFull27Pairs.compact_full27_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
private def zz371:"s0173"="s0173":=by decide+kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFull27Pairs.full27_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_25_base LocalFull27Pairs.compact_full27_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFull27Pairs.full27_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 3 false
def pair26Rewrites:Rewrites:=[]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_26_base LocalFull27Pairs.compact_full27_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFull27Pairs.full27_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_26_base LocalFull27Pairs.compact_full27_pair_26_hinges x
private def zz372:"s0174"="s0174":=by decide+kernel
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFull27Pairs.full27_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_27_base LocalFull27Pairs.compact_full27_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFull27Pairs.full27_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_27_base LocalFull27Pairs.compact_full27_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFull27Pairs.full27_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_28_base LocalFull27Pairs.compact_full27_pair_28_hinges
private def zz373:"s0175"="s0175":=by decide+kernel
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFull27Pairs.full27_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_28_base LocalFull27Pairs.compact_full27_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFull27Pairs.full27_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_29_base LocalFull27Pairs.compact_full27_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
private def zz374:"s0176"="s0176":=by decide+kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFull27Pairs.full27_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_29_base LocalFull27Pairs.compact_full27_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFull27Pairs.full27_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_30_base LocalFull27Pairs.compact_full27_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFull27Pairs.full27_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_30_base LocalFull27Pairs.compact_full27_pair_30_hinges x
private def zz375:"s0177"="s0177":=by decide+kernel
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFull27Pairs.full27_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_31_base LocalFull27Pairs.compact_full27_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFull27Pairs.full27_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_31_base LocalFull27Pairs.compact_full27_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFull27Pairs.full27_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_32_base LocalFull27Pairs.compact_full27_pair_32_hinges
private def zz376:"s0178"="s0178":=by decide+kernel
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFull27Pairs.full27_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_32_base LocalFull27Pairs.compact_full27_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFull27Pairs.full27_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_33_base LocalFull27Pairs.compact_full27_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
private def zz377:"s0179"="s0179":=by decide+kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFull27Pairs.full27_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_33_base LocalFull27Pairs.compact_full27_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFull27Pairs.full27_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_34_base LocalFull27Pairs.compact_full27_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFull27Pairs.full27_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_34_base LocalFull27Pairs.compact_full27_pair_34_hinges x
private def zz378:"s017a"="s017a":=by decide+kernel
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFull27Pairs.full27_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_35_base LocalFull27Pairs.compact_full27_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFull27Pairs.full27_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_35_base LocalFull27Pairs.compact_full27_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFull27Pairs.full27_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_36_base LocalFull27Pairs.compact_full27_pair_36_hinges
private def zz379:"s017b"="s017b":=by decide+kernel
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFull27Pairs.full27_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_36_base LocalFull27Pairs.compact_full27_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFull27Pairs.full27_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_37_base LocalFull27Pairs.compact_full27_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
private def zz380:"s017c"="s017c":=by decide+kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFull27Pairs.full27_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_37_base LocalFull27Pairs.compact_full27_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFull27Pairs.full27_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_38_base LocalFull27Pairs.compact_full27_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFull27Pairs.full27_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_38_base LocalFull27Pairs.compact_full27_pair_38_hinges x
private def zz381:"s017d"="s017d":=by decide+kernel
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFull27Pairs.full27_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack ((27 / 10)) (1 / 0x186a0) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFull27Pairs.compact_full27_pair_39_base LocalFull27Pairs.compact_full27_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFull27Pairs.full27_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull27Pairs.compact_full27_pair_39_base LocalFull27Pairs.compact_full27_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFull27Pairs.full27_pair_39_nonneg (hx 0) (hx 1)
private def zz382:"s017e"="s017e":=by decide+kernel
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack ((27 / 10)) (1 / 0x186a0) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.Full27Rows
private def zz2127:"s084f"="s084f":=by decide+kernel
end 
section 
namespace Green24Proof.Full27Cyclic
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseSymmetry FullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack Full27Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact Full27Rows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse Full27Rows.rows p q same x]
    exact Full27Rows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack (27 / 10) (1 / 0x186a0) Full27Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact Full27Rows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap (27 / 10) (1 / 0x186a0) Full27Rows.rows p q same x]
    exact Full27Rows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
private def zz383:"s017f"="s017f":=by decide+kernel
theorem rows_admissible:rowsAdmissible Full27Rows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials Full27Rows.rows
theorem remaining_rows_count:remainingRows.length = 10:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
      weightedAggregate (27 / 10) h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack Full27Rows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack (27 / 10) (1 / 0x186a0) Full27Rows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound (27 / 10) h4 h3 h5 g Full27Rows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
    weightedAggregate (27 / 10) h4 h3 g (stripPotentials Full27Rows.rows) + 4 * deficit g
  linarith
end Green24Proof.Full27Cyclic
private def zz2128:"s0850"="s0850":=by decide+kernel
end 
section 
namespace Green24Proof.Full27Mass
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows
theorem remainingRows_eq:Full27Cyclic.remainingRows = [
  ((0xedfe8ad / 0xbebc200), .balance 0 (1)),
  ((0xadfe05ab / 0x3b9aca00), .balance 1 (-1)),
  ((0x8c795e1 / 0x7735940), .balance 2 (1)),
  ((0xadfe05ab / 0x3b9aca00), .balance 3 (-1)),
  ((0x29171a43 / 0x3b9aca00), .child 0),
  (1, .heightChild 1),
  ((0x691b7 / 0xbebc200), .grandchild 2),
  ((0xc3f09 / 0x17d7840), .ordered 0),
  ((0x1d634e5 / 0x989680), .massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((1 / 0xf424), .normalization)]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff PackedPhaseRowsEquality.labelEq PackedPhaseRowsEquality.labelEq_iff _ _).mp
  decide +kernel
def oddDifference:Phase → ℚ:=fun p => (![0,1,0, -1]:Fin 4 → ℚ) p
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  ((0xedfe8ad / 0xbebc200:ℝ) * phaseTotal h4 g 0 +
    (0x8c795e1 / 0x7735940:ℝ) * phaseTotal h4 g 2 -
    (0xadfe05ab / 0x3b9aca00:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) *
  (phaseTotal h4 g 0 + phaseTotal h4 g 2 -
    (27 / 10:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
private def zz384:"s0180"="s0180":=by decide+kernel
theorem weighted_remaining_eq {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    weightedAggregate (27 / 10) h4 h3 g Full27Cyclic.remainingRows =
      balanceMass h4 g +
      (0x29171a43 / 0x3b9aca00:ℝ) * rowAggregate (27 / 10) h4 h3 g (.child 0) +
      rowAggregate (27 / 10) h4 h3 g (.heightChild 1) +
      (0x691b7 / 0xbebc200:ℝ) * rowAggregate (27 / 10) h4 h3 g (.grandchild 2) +
      (0xc3f09 / 0x17d7840:ℝ) * rowAggregate (27 / 10) h4 h3 g (.ordered 0) +
      (0x1d634e5 / 0x989680:ℝ) * rowAggregate (27 / 10) h4 h3 g (.massSquare false oddDifference) +
      (1 / 0xf424:ℝ) * mass g ^ 2:=by
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_balance,rowAggregate_normalization]
  norm_num
  unfold balanceMass oddDifference
  ring
theorem balanceMass_nonpos {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hlow:(49 / 20:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤
      phaseTotal h4 g 0 + phaseTotal h4 g 2)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (27 / 10:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)):balanceMass h4 g ≤ 0:=by
  have hv:=add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)
  have hp:0 ≤ (0xedfe8ad / 0xbebc200:ℝ) * phaseTotal h4 g 0 +
      (0x8c795e1 / 0x7735940:ℝ) * phaseTotal h4 g 2 -
      (0xadfe05ab / 0x3b9aca00:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    linarith
  exact mul_nonpos_of_nonneg_of_nonpos hp (sub_nonpos.mpr hhigh)
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hlow:(49 / 20:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤
      phaseTotal h4 g 0 + phaseTotal h4 g 2)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (27 / 10:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate (27 / 10) h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate (27 / 10) h4 h3 g (.heightChild 1) ≤ 0)
    (hgrandchild:rowAggregate (27 / 10) h4 h3 g (.grandchild 2) ≤ 0) :
    weightedAggregate (27 / 10) h4 h3 g Full27Cyclic.remainingRows ≤ (1 / 0xf424:ℝ) * mass g ^ 2:=by
  rw [weighted_remaining_eq]
  have hb:=balanceMass_nonpos h4 g hg horder hlow hhigh
  have ho:rowAggregate (27 / 10) h4 h3 g (.ordered 0) ≤ 0 :=
    rowAggregate_ordered_nonpos (27 / 10) h4 h3 g hg 0 (by simpa using horder)
  have hm:=rowAggregate_massSquare_nonpos (27 / 10) h4 h3 g oddDifference
  linarith
theorem deficit_lower_bound_of_child_rows {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hlow:(49 / 20:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤
      phaseTotal h4 g 0 + phaseTotal h4 g 2)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (27 / 10:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate (27 / 10) h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate (27 / 10) h4 h3 g (.heightChild 1) ≤ 0)
    (hgrandchild:rowAggregate (27 / 10) h4 h3 g (.grandchild 2) ≤ 0) :
    (3 / 0x7a120:ℝ) * mass g ^ 2 ≤ deficit g:=by
  have hc:=Full27Cyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg horder hlow hhigh hchild hheight hgrandchild
  linarith
end Green24Proof.Full27Mass
private def zz2129:"s0851"="s0851":=by decide+kernel
end 
section 
namespace Green24Proof.GrandchildRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics FullPhaseAggregation
noncomputable def quadResidue (m:ℕ):ZMod m →+ ZMod (4 * m) :=
  ZMod.lift m ⟨
    { toFun:=fun z:ℤ => 4 * (z:ZMod (4 * m))
      map_zero':=by simp
      map_add':=by intros; simp [mul_add] },by
      change 4 * ((m:ℤ):ZMod (4 * m)) = 0
      simpa only [Int.cast_natCast,Nat.cast_mul,Nat.cast_ofNat] using
        (ZMod.natCast_self (4 * m))⟩
private def zz385:"s0181"="s0181":=by decide+kernel
theorem quadResidue_natCast (m n:ℕ):quadResidue m (n:ZMod m) = 4 * (n:ZMod (4 * m)):=by
  unfold quadResidue
  rw [← Int.cast_natCast n,ZMod.lift_coe]
  simp only [Int.cast_natCast,AddMonoidHom.coe_mk,ZeroHom.coe_mk]
theorem quadResidue_val {m:ℕ} [NeZero m] (x:ZMod m) :
    quadResidue m x = 4 * (x.val:ZMod (4 * m)):=by
  conv_lhs => rw [← ZMod.natCast_zmod_val x]
  exact quadResidue_natCast m x.val
theorem quadResidue_mul_nat (m n:ℕ) (x:ZMod m) :
    quadResidue m (n * x) = n * quadResidue m x:=by
  simpa only [nsmul_eq_mul] using (quadResidue m).map_nsmul n x
noncomputable def phaseEquiv (m:ℕ) [NeZero m]:(ZMod 4 × ZMod m) ≃ ZMod (4 * m) where
  toFun p:=((4 * p.2.val + p.1.val:ℕ):ZMod (4 * m))
  invFun x:=(((x.val % 4:ℕ):ZMod 4),((x.val / 4:ℕ):ZMod m))
  left_inv:=by
    rintro ⟨r,i⟩
    have hr:=r.val_lt
    have hi:=i.val_lt
    have hlt:4 * i.val + r.val < 4 * m:=by omega
    simp only [ZMod.val_natCast_of_lt hlt]
    apply Prod.ext
    · have hmod:(4 * i.val + r.val) % 4 = r.val:=by omega
      simp only [hmod,ZMod.natCast_zmod_val]
    · have hdiv:(4 * i.val + r.val) / 4 = i.val:=by omega
      simp only [hdiv,ZMod.natCast_zmod_val]
  right_inv:=by
    intro x
    have hx:=x.val_lt
    have hmod:x.val % 4 < 4:=Nat.mod_lt _ (by norm_num)
    have hdiv:x.val / 4 < m:=by omega
    simp only [ZMod.val_natCast_of_lt hmod,ZMod.val_natCast_of_lt hdiv]
    rw [show 4 * (x.val / 4) + x.val % 4 = x.val by omega]
    exact ZMod.natCast_zmod_val x
theorem phaseEquiv_apply {m:ℕ} [NeZero m] (r:ZMod 4) (i:ZMod m) :
    phaseEquiv m (r,i) = quadResidue m i + (r.val:ZMod (4 * m)):=by
  change ((4 * i.val + r.val:ℕ):ZMod (4 * m)) = _
  rw [Nat.cast_add,Nat.cast_mul,Nat.cast_ofNat,quadResidue_val]
private def zz386:"s0182"="s0182":=by decide+kernel
theorem phaseCast_apply {m:ℕ} [NeZero m] (r:Phase) (i:ZMod m) :
    ZMod.castHom (dvd_mul_right 4 m) (ZMod 4) (phaseEquiv m (r,i)) = r:=by
  rw [phaseEquiv_apply,quadResidue_val]
  simp only [map_add,map_mul,map_ofNat,map_natCast,
    show (4:ZMod 4) = 0 from rfl,zero_mul,zero_add,ZMod.natCast_zmod_val]
theorem phaseEquiv_affine_same {m:ℕ} [NeZero m] (r:Phase) (j k:ZMod m) :
    3 * phaseEquiv m (r,k) - 2 * phaseEquiv m (r,j) = phaseEquiv m (r,3 * k - 2 * j):=by
  rw [phaseEquiv_apply,phaseEquiv_apply,phaseEquiv_apply]
  have h3:quadResidue m (3 * k) = 3 * quadResidue m k:=by
    simpa only [Nat.cast_ofNat] using quadResidue_mul_nat m 3 k
  have h2:quadResidue m (2 * j) = 2 * quadResidue m j:=by
    simpa only [Nat.cast_ofNat] using quadResidue_mul_nat m 2 j
  rw [map_sub,h3,h2]
  ring
noncomputable def grandchild {m:ℕ} [NeZero m] (g:ZMod (4 * m) → ℝ) (r:Phase):ZMod m → ℝ :=
  fun i => g (phaseEquiv m (r,i))
theorem grandchild_nonneg {m:ℕ} [NeZero m] (g:ZMod (4 * m) → ℝ) (hg:∀ i,0 ≤ g i) (r:Phase) :
    ∀ i,0 ≤ grandchild g r i:=fun i => hg (phaseEquiv m (r,i))
theorem grandchild_value {m:ℕ} [NeZero m] (S:ℚ) (h3:3 ∣ 4 * m)
    (g:ZMod (4 * m) → ℝ) (r a b:Phase) (j k:ZMod m) :
    rowValue S (dvd_mul_right 4 m) h3 g (.grandchild r) (phaseEquiv m (a,j)) (phaseEquiv m (b,k)) =
      if a = r ∧ b = r then
        expressionEval area (quadPoint (grandchild g r) j k) +
        expressionEval (pairProduct (-8)) (pairPoint (grandchild g r) j k)
      else 0:=by
  by_cases h:a = r ∧ b = r
  · rcases h with ⟨rfl,rfl⟩
    simp only [rowValue,rowQuad,rowPair,phaseCast_apply,and_self,if_true]
    rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
    simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,phaseEquiv_affine_same,grandchild]
  · simp only [rowValue,rowQuad,rowPair,phaseCast_apply,if_neg h,
      expressionEval,List.map_nil,List.sum_nil,add_zero]
private def zz387:"s0183"="s0183":=by decide+kernel
theorem rowAggregate_grandchild {m:ℕ} [NeZero m] (S:ℚ) (h3:3 ∣ 4 * m)
    (g:ZMod (4 * m) → ℝ) (r:Phase) :
    rowAggregate S (dvd_mul_right 4 m) h3 g (.grandchild r) = -4 * deficit (grandchild g r):=by
  unfold rowAggregate
  have hk (a:Phase) (j:ZMod m) :
      (∑ k,rowValue S (dvd_mul_right 4 m) h3 g (.grandchild r) (phaseEquiv m (a,j)) k) =
      ∑ b:Phase, ∑ k:ZMod m,
        rowValue S (dvd_mul_right 4 m) h3 g (.grandchild r) (phaseEquiv m (a,j)) (phaseEquiv m (b,k)):=by
    rw [← (phaseEquiv m).sum_comp,Fintype.sum_prod_type]
  rw [← (phaseEquiv m).sum_comp,Fintype.sum_prod_type]
  simp_rw [hk,grandchild_value]
  simp only [ite_and,Finset.sum_ite_irrel,Finset.sum_const_zero,
    Finset.sum_ite_eq',Finset.mem_univ,if_true]
  simp only [Finset.sum_add_distrib,area_sum,pairProduct_sum]
  unfold deficit
  norm_num
  ring
theorem grandchild_mass {m:ℕ} [NeZero m] (g:ZMod (4 * m) → ℝ) (r:Phase) :
    mass (grandchild g r) = PhaseMassRows.phaseTotal (dvd_mul_right 4 m) g r:=by
  unfold PhaseMassRows.phaseTotal colourTotal
  rw [← (phaseEquiv m).sum_comp,Fintype.sum_prod_type]
  simp only [phaseCast_apply,Finset.sum_ite_irrel,Finset.sum_const_zero,
    Finset.sum_ite_eq',Finset.mem_univ,if_true]
  rfl
end Green24Proof.GrandchildRows
private def zz2130:"s0852"="s0852":=by decide+kernel
end 
section 
namespace Green24Proof.HeightChildRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows ChildRows
def heightDifference (r:Fin 2) (p:Phase):ℚ :=
  if parity p = r then (if p.val < 2 then 1 else -1) else 0
private theorem expressionEval_nil (x:Point):expressionEval [] x = 0:=rfl
theorem height_pair_decomposition (S:ℚ) (r:Fin 2) (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (rowPair S (.heightChild r) p q same) x =
      expressionEval (rowPair S (.child r) p q same) x +
      (24 / 5:ℝ) * expressionEval (rowPair S (.massSquare false (heightDifference r)) p q same) x +
      if parity p = r ∧ parity q = r then (49 / 0x7d:ℝ) * expressionEval rhoExpression x else 0:=by
  fin_cases r <;> fin_cases p <;> fin_cases q
  all_goals
    norm_num [rowPair,parity,ZMod.val,heightDifference,expressionEval_append,
      expressionEval_scale,pairProduct_eval,expressionEval_nil]
    <;> ring
noncomputable def selectedRho {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) (r:Fin 2):ℝ :=
  ∑ j, ∑ k,if parity (ZMod.castHom h4 (ZMod 4) j) = r ∧
    parity (ZMod.castHom h4 (ZMod 4) k) = r then rho (g j) (g k) else 0
private def zz388:"s0184"="s0184":=by decide+kernel
theorem height_value_decomposition {q:ℕ} (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (r:Fin 2) (j k:ZMod q) :
    rowValue S h4 h3 g (.heightChild r) j k = rowValue S h4 h3 g (.child r) j k +
      (24 / 5:ℝ) * rowValue S h4 h3 g (.massSquare false (heightDifference r)) j k +
      (49 / 0x7d:ℝ) * (if parity (ZMod.castHom h4 (ZMod 4) j) = r ∧
        parity (ZMod.castHom h4 (ZMod 4) k) = r then rho (g j) (g k) else 0):=by
  unfold rowValue
  rw [height_pair_decomposition]
  have hrho:expressionEval rhoExpression (pairPoint g j k) = rho (g j) (g k) :=
    rhoExpression_eval _ (hg j) (hg k)
  rw [hrho]
  simp only [rowQuad,expressionEval_nil]
  split_ifs <;> ring
theorem rowAggregate_height_decomposition {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (r:Fin 2) :
    rowAggregate S h4 h3 g (.heightChild r) = rowAggregate S h4 h3 g (.child r) +
      (24 / 5:ℝ) * rowAggregate S h4 h3 g (.massSquare false (heightDifference r)) +
      (49 / 0x7d:ℝ) * selectedRho h4 g r:=by
  unfold rowAggregate
  simp_rw [height_value_decomposition S h4 h3 g hg r]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum]
  rfl
theorem selectedRho_even {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (u v:ZMod m → ℝ) :
    selectedRho h4 (interleave u v) 0 = 2 * energy u:=by
  unfold selectedRho
  rw [sum_parity_pairs]
  simp only [phase_parity_even,phase_parity_odd,interleave_even,interleave_odd]
  norm_num
  unfold energy
  ring
theorem selectedRho_odd {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (u v:ZMod m → ℝ) :
    selectedRho h4 (interleave u v) 1 = 2 * energy v:=by
  unfold selectedRho
  rw [sum_parity_pairs]
  simp only [phase_parity_even,phase_parity_odd,interleave_even,interleave_odd]
  norm_num
  unfold energy
  ring
private def zz389:"s0185"="s0185":=by decide+kernel
theorem heightDifference_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ) (r:Fin 2) :
    massWeighted h4 g (fun p => (heightDifference r p:ℝ)) =
      phaseTotal h4 g (r.val:Phase) - phaseTotal h4 g ((r.val:Phase) + 2):=by
  rw [massWeighted_phaseTotal,sum_phase]
  fin_cases r <;> norm_num [heightDifference,parity,ZMod.val_ofNat,ZMod.val_one_eq_one_mod] <;> ring
theorem rowAggregate_height_odd {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    rowAggregate S h4 h3 (interleave u v) (.heightChild 1) = -4 * deficit v +
      (98 / 0x7d:ℝ) * energy v -
      (24 / 5:ℝ) * (phaseTotal h4 (interleave u v) 1 - phaseTotal h4 (interleave u v) 3) ^ 2:=by
  rw [rowAggregate_height_decomposition S h4 h3 (interleave u v) (interleave_nonneg u v hu hv),
    rowAggregate_child_odd,rowAggregate_massSquare,selectedRho_odd,heightDifference_sum]
  norm_num
  ring
theorem cast_four_double {m:ℕ} (h4:4 ∣ 2 * m) (h2:2 ∣ m) (x:ZMod m) :
    ZMod.castHom h4 (ZMod 4) (doubleResidue m x) =
      doubleResidue 2 (ZMod.castHom h2 (ZMod 2) x):=by
  obtain ⟨z,rfl⟩:=ZMod.intCast_surjective x
  simp only [map_intCast,doubleResidue,ZMod.lift_coe,AddMonoidHom.coe_mk,ZeroHom.coe_mk,
    map_mul,map_ofNat]
theorem cast_four_even {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m) (x:ZMod m) :
    ZMod.castHom h4 (ZMod 4) (parityEquiv m (0,x)) =
      doubleResidue 2 (ZMod.castHom h2 (ZMod 2) x):=by
  rw [parityEquiv_apply]
  simp only [ZMod.val_zero,Nat.cast_zero,add_zero,cast_four_double h4 h2]
private def zz390:"s0186"="s0186":=by decide+kernel
theorem cast_four_odd {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m) (x:ZMod m) :
    ZMod.castHom h4 (ZMod 4) (parityEquiv m (1,x)) =
      doubleResidue 2 (ZMod.castHom h2 (ZMod 2) x) + 1:=by
  rw [parityEquiv_apply,map_add,cast_four_double h4 h2,map_natCast]
  norm_num [ZMod.val_one_eq_one_mod]
theorem doubleResidue_two_one:doubleResidue 2 (1:ZMod 2) = (2:ZMod 4):=by
  simpa using doubleResidue_natCast 2 1
theorem phaseTotal_interleave_one {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) :
    phaseTotal h4 (interleave u v) 1 = classMass (ZMod.castHom h2 (ZMod 2)) v 0:=by
  unfold phaseTotal colourTotal
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [cast_four_even h4 h2,cast_four_odd h4 h2,interleave_even,interleave_odd]
  have he (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) = (1:ZMod 4) then u i else 0) = 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero,if_neg (by decide:(0:ZMod 4) ≠ 1)]
    · rw [h,doubleResidue_two_one,if_neg (by decide:(2:ZMod 4) ≠ 1)]
  have ho (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) + 1 = (1:ZMod 4) then v i else 0) =
        if ZMod.castHom h2 (ZMod 2) i = 0 then v i else 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; norm_num
    · rw [h,doubleResidue_two_one]; norm_num [show (3:ZMod 4) ≠ 1 by decide]
  simp only [he,ho,Finset.sum_const_zero,zero_add]
  rfl
theorem phaseTotal_interleave_three {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) :
    phaseTotal h4 (interleave u v) 3 = classMass (ZMod.castHom h2 (ZMod 2)) v 1:=by
  unfold phaseTotal colourTotal
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [cast_four_even h4 h2,cast_four_odd h4 h2,interleave_even,interleave_odd]
  have he (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) = (3:ZMod 4) then u i else 0) = 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero,if_neg (by decide:(0:ZMod 4) ≠ 3)]
    · rw [h,doubleResidue_two_one,if_neg (by decide:(2:ZMod 4) ≠ 3)]
  have ho (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) + 1 = (3:ZMod 4) then v i else 0) =
        if ZMod.castHom h2 (ZMod 2) i = 1 then v i else 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; norm_num [show (1:ZMod 4) ≠ 3 by decide]
    · rw [h,doubleResidue_two_one]; norm_num
  simp only [he,ho,Finset.sum_const_zero,zero_add]
  rfl
private def zz391:"s0187"="s0187":=by decide+kernel
theorem rowAggregate_height_odd_nonpos {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 2 * m)
    (h3:3 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hh:(49 / 0xfa:ℝ) * energy v - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) v 0 - classMass (ZMod.castHom h2 (ZMod 2)) v 1) ^ 2 ≤ deficit v) :
    rowAggregate S h4 h3 (interleave u v) (.heightChild 1) ≤ 0:=by
  rw [rowAggregate_height_odd S h4 h3 u v hu hv,
    phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2]
  linarith
end Green24Proof.HeightChildRows
private def zz2131:"s0853"="s0853":=by decide+kernel
end 
section 
namespace Green24Proof.LocalHeightStrongPairs
def compact_heightStrong_pair_6_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_6_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_6 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_6_base compact_heightStrong_pair_6_hinges x y
def compact_heightStrong_pair_6_cuts:List ℚ:=[]
theorem compact_heightStrong_pair_6_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_6_base compact_heightStrong_pair_6_hinges 0 compact_heightStrong_pair_6_cuts = true :=
  by decide +kernel
theorem compact_heightStrong_pair_6_representation (x y:ℝ) :
    heightStrong_pair_6 x y = CompactPair.expressionEval compact_heightStrong_pair_6_base compact_heightStrong_pair_6_hinges x y:=by rfl
theorem heightStrong_pair_6_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_6 x y:=by
  rw [compact_heightStrong_pair_6_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_6_check hy (by simpa using hx)
def compact_heightStrong_pair_7_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_7_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_7 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_7_base compact_heightStrong_pair_7_hinges x y
def compact_heightStrong_pair_7_cuts:List ℚ:=[]
private def zz392:"s0188"="s0188":=by decide+kernel
theorem compact_heightStrong_pair_7_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_7_base compact_heightStrong_pair_7_hinges 0 compact_heightStrong_pair_7_cuts = true :=
  by decide +kernel
theorem compact_heightStrong_pair_7_representation (x y:ℝ) :
    heightStrong_pair_7 x y = CompactPair.expressionEval compact_heightStrong_pair_7_base compact_heightStrong_pair_7_hinges x y:=by rfl
theorem heightStrong_pair_7_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_7 x y:=by
  rw [compact_heightStrong_pair_7_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_7_check hy (by simpa using hx)
def compact_heightStrong_pair_8_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_8_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_8 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_8_base compact_heightStrong_pair_8_hinges x y
def compact_heightStrong_pair_8_cuts:List ℚ:=[]
theorem compact_heightStrong_pair_8_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_8_base compact_heightStrong_pair_8_hinges 0 compact_heightStrong_pair_8_cuts = true :=
  by decide +kernel
private def zz393:"s0189"="s0189":=by decide+kernel
theorem compact_heightStrong_pair_8_representation (x y:ℝ) :
    heightStrong_pair_8 x y = CompactPair.expressionEval compact_heightStrong_pair_8_base compact_heightStrong_pair_8_hinges x y:=by rfl
theorem heightStrong_pair_8_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_8 x y:=by
  rw [compact_heightStrong_pair_8_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_8_check hy (by simpa using hx)
def compact_heightStrong_pair_9_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_9_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_9 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_9_base compact_heightStrong_pair_9_hinges x y
def compact_heightStrong_pair_9_cuts:List ℚ:=[]
theorem compact_heightStrong_pair_9_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_9_base compact_heightStrong_pair_9_hinges 0 compact_heightStrong_pair_9_cuts = true :=
  by decide +kernel
theorem compact_heightStrong_pair_9_representation (x y:ℝ) :
    heightStrong_pair_9 x y = CompactPair.expressionEval compact_heightStrong_pair_9_base compact_heightStrong_pair_9_hinges x y:=by rfl
private def zz394:"s018a"="s018a":=by decide+kernel
theorem heightStrong_pair_9_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_9 x y:=by
  rw [compact_heightStrong_pair_9_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_9_check hy (by simpa using hx)
def compact_heightStrong_pair_10_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_10_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_10 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_10_base compact_heightStrong_pair_10_hinges x y
def compact_heightStrong_pair_10_cuts:List ℚ:=[]
theorem compact_heightStrong_pair_10_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_10_base compact_heightStrong_pair_10_hinges 0 compact_heightStrong_pair_10_cuts = true :=
  by decide +kernel
theorem compact_heightStrong_pair_10_representation (x y:ℝ) :
    heightStrong_pair_10 x y = CompactPair.expressionEval compact_heightStrong_pair_10_base compact_heightStrong_pair_10_hinges x y:=by rfl
theorem heightStrong_pair_10_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_10 x y:=by
  rw [compact_heightStrong_pair_10_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_10_check hy (by simpa using hx)
def compact_heightStrong_pair_11_base:CompactPair.Quadratic:=⟨(49 / 50),(0x93 / 0x7d),(49 / 50)⟩
def compact_heightStrong_pair_11_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1,3⟩,⟨(-49 / 0x1f4),3,1⟩]
noncomputable def heightStrong_pair_11 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_heightStrong_pair_11_base compact_heightStrong_pair_11_hinges x y
def compact_heightStrong_pair_11_cuts:List ℚ:=[]
private def zz395:"s018b"="s018b":=by decide+kernel
theorem compact_heightStrong_pair_11_check :
    CompactPair.expressionCheckPSD compact_heightStrong_pair_11_base compact_heightStrong_pair_11_hinges 0 compact_heightStrong_pair_11_cuts = true :=
  by decide +kernel
theorem compact_heightStrong_pair_11_representation (x y:ℝ) :
    heightStrong_pair_11 x y = CompactPair.expressionEval compact_heightStrong_pair_11_base compact_heightStrong_pair_11_hinges x y:=by rfl
theorem heightStrong_pair_11_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ heightStrong_pair_11 x y:=by
  rw [compact_heightStrong_pair_11_representation]
  exact CompactPair.expressionCheckPSD_sound compact_heightStrong_pair_11_check hy (by simpa using hx)
end Green24Proof.LocalHeightStrongPairs
private def zz2132:"s0854"="s0854":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase0
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x176d004aa36, -0x8bb2c97000, -0xd18c2e2800,0], ![-0x8bb2c97000, -0x4d713f6eb4e,0xc2e0afba7a,0x7df663e9cc], ![-0xd18c2e2800,0xc2e0afba7a, -0x38c0a1d5800,0x8bb2c97000], ![0,0x7df663e9cc,0x8bb2c97000, -0x45d964b800]]
noncomputable def hinges:Hinges:=[(0xeb72327ba,l14),(0x1b8b4e6b09,l17),(0xa8b52805ff,l15),(-0x45d964b800,l27),(0x45d964b800,l29),(-0xeb72327ba,l25),(0x1c0e7f98e6,l30),(0x45d964b800,l33),(-0x45d964b800,l35),(0x45d964b800,l37),(-0x1c0e7f98e6,l43),(-0xa8b52805ff,l41),(0x45d964b800,l51),(-0x1b8b4e6b09,l62)]
def normalizationDenominator:ℤ:=0x8bb2c97000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x45d964b800,l27),(0x45d964b800,l29),(0x45d964b800,l33),(-0x45d964b800,l35),(0x45d964b800,l37),(0x45d964b800,l51),(0xa8b52805ff,l15),(-0xa8b52805ff,l41),(0x1c0e7f98e6,l30),(-0x1c0e7f98e6,l43),(0x1b8b4e6b09,l17),(-0x1b8b4e6b09,l62),(0xeb72327ba,l14),(-0xeb72327ba,l25)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase0" = "QuadHeightStrongCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase0
private def zz2133:"s0855"="s0855":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase1
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x18fccd1c6a, -0x9502f9000, -0xdf8475800,0], ![-0x9502f9000, -0x566818345a,0xee47e852a,0x77277ecd2], ![-0xdf8475800,0xee47e852a, -0x3c89352800,0x9502f9000], ![0,0x77277ecd2,0x9502f9000, -0x4a817c800]]
noncomputable def hinges:Hinges:=[(0x7da0204,l14),(0x1d6164b67,l17),(0xbb8ec2b62,l15),(-0x4a817c800,l27),(0x4a817c800,l29),(-0x7da0204,l25),(0x165301269,l30),(0x4a817c800,l33),(-0x4a817c800,l35),(0x4a817c800,l37),(-0x165301269,l43),(-0xbb8ec2b62,l41),(0x4a817c800,l51),(-0x1d6164b67,l62)]
def normalizationDenominator:ℤ:=0x9502f9000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x4a817c800,l27),(0x4a817c800,l29),(0x4a817c800,l33),(-0x4a817c800,l35),(0x4a817c800,l37),(0x4a817c800,l51),(0xbb8ec2b62,l15),(-0xbb8ec2b62,l41),(0x1d6164b67,l17),(-0x1d6164b67,l62),(0x165301269,l30),(-0x165301269,l43),(0x7da0204,l14),(-0x7da0204,l25)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1a014802000000000280c401000004e04401630100004a1304805a00600000000780248030000d0082004c602800000681100e300c0000000345819802000321504c079003000000843803c6018000000007406200800000000540290040000016084078c03000198682403c801800000054440f300800003c320a02a00400000001a0c0cc01000000000f00a4010000000005805200800000110500618060000000009018802000000001100a401000000044340f300800000001c28198020056090160275004a10520210019a803001482a04803d401000b81403802ea0080000000098024803000000088580c6010000000003805200800000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase1" = "QuadHeightStrongCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase1
private def zz2134:"s0856"="s0856":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l44 l46 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x16f7f9c20de, -0x8bb2c97000, -0xcfb81405aa,0], ![-0x8bb2c97000, -0x4baa22e5eee,0xbbc43d9762,0x7df663e9cc], ![-0xcfb81405aa,0xbbc43d9762, -0x38efe933dd0,0x8c6fe6e974], ![0,0x7df663e9cc,0x8c6fe6e974, -0x45d964b800]]
noncomputable def hinges:Hinges:=[(-0x5e8ebcba,l4),(0x5e8ebcba,l10),(0xdb0c0cc00,l14),(0x4949b6d46,l12),(0x1b8b4e6b09,l17),(0xa8b52805ff,l15),(-0x45d964b800,l27),(0x45d964b800,l29),(-0x12455c3946,l25),(0x1c0e7f98e6,l30),(0x45d964b800,l33),(-0x10f4ee77,l38),(-0x45d964b800,l35),(0x45d964b800,l37),(0x10f4ee77,l34),(-0x13c8e0f3de,l43),(-0xb1e4d3bc32,l41),(-0x4949b6d46,l46),(0x4949b6d46,l44),(0x45d964b800,l51),(-0x1aa14159de,l62)]
def normalizationDenominator:ℤ:=0x8bb2c97000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x45d964b800,l27),(0x45d964b800,l29),(0x45d964b800,l33),(-0x45d964b800,l35),(0x45d964b800,l37),(0x45d964b800,l51),(-0xb1e4d3bc32,l41),(0xa8b52805ff,l15),(0x1c0e7f98e6,l30),(0x1b8b4e6b09,l17),(-0x1aa14159de,l62),(-0x13c8e0f3de,l43),(-0x12455c3946,l25),(0xdb0c0cc00,l14),(-0x4949b6d46,l46),(0x4949b6d46,l12),(0x4949b6d46,l44),(0x5e8ebcba,l10),(-0x5e8ebcba,l4),(-0x10f4ee77,l38),(0x10f4ee77,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase2" = "QuadHeightStrongCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase2
private def zz2135:"s0857"="s0857":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l44 l46 l51 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x14cbd04fb16, -0x8bb2c97000, -0xd18c2e2800,0xa84bfebc8], ![-0x8bb2c97000, -0x480ffd4e51e,0xbb9d04426c,0x6fb506e04e], ![-0xd18c2e2800,0xbb9d04426c, -0x38efe933dd0,0x8c6fe6e974], ![0xa84bfebc8,0x6fb506e04e,0x8c6fe6e974, -0x45d964b800]]
noncomputable def hinges:Hinges:=[(-0x5e8ebcba,l4),(0x5e8ebcba,l10),(0x140eccf812,l14),(-0x1b5d41451,l12),(0x1b8b4e6b09,l17),(0xafd5d68abe,l15),(-0x45d964b800,l27),(0x45d964b800,l29),(-0x1258f8e3c1,l25),(0x14edd11427,l30),(0x45d964b800,l33),(-0x10f4ee77,l38),(-0x45d964b800,l35),(0x45d964b800,l37),(0x10f4ee77,l34),(-0x16f49e5297,l43),(-0xadcf094c4e,l41),(-0x475594c5c,l46),(-0xcd06a988,l44),(0x45d964b800,l51),(-0x1b8b4e6b09,l62),(0x5425ff5e4,l64)]
def normalizationDenominator:ℤ:=0x8bb2c97000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x45d964b800,l27),(0x45d964b800,l29),(0x45d964b800,l33),(-0x45d964b800,l35),(0x45d964b800,l37),(0x45d964b800,l51),(0xafd5d68abe,l15),(-0xadcf094c4e,l41),(0x1b8b4e6b09,l17),(-0x1b8b4e6b09,l62),(-0x16f49e5297,l43),(0x14edd11427,l30),(0x140eccf812,l14),(-0x1258f8e3c1,l25),(0x5425ff5e4,l64),(-0x475594c5c,l46),(-0x1b5d41451,l12),(0x5e8ebcba,l10),(-0xcd06a988,l44),(-0x5e8ebcba,l4),(-0x10f4ee77,l38),(0x10f4ee77,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase3" = "QuadHeightStrongCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase3
private def zz2136:"s0858"="s0858":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase4
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l15 l17 l27 l29 l30 l33 l35 l37 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xb7bfce106f, -0x45d964b800, -0x67dc0a02d5,0], ![-0x45d964b800, -0x285500d806f,0x70277b04f7,0x36b5934fde], ![-0x67dc0a02d5,0x70277b04f7, -0x1c6050eac00,0x45d964b800], ![0,0x36b5934fde,0x45d964b800, -0x22ecb25c00]]
noncomputable def hinges:Hinges:=[(0xd50a0acef,l17),(0x58f269de19,l15),(-0x22ecb25c00,l27),(0x22ecb25c00,l29),(0x9e47079ef,l30),(0x22ecb25c00,l33),(-0x22ecb25c00,l35),(0x22ecb25c00,l37),(-0x9e47079ef,l43),(-0x58f269de19,l41),(0x22ecb25c00,l51),(-0xd50a0acef,l62)]
def normalizationDenominator:ℤ:=0x45d964b800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x22ecb25c00,l27),(0x22ecb25c00,l29),(0x22ecb25c00,l33),(-0x22ecb25c00,l35),(0x22ecb25c00,l37),(0x22ecb25c00,l51),(0x58f269de19,l15),(-0x58f269de19,l41),(0xd50a0acef,l17),(-0xd50a0acef,l62),(0x9e47079ef,l30),(-0x9e47079ef,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x3402900400000000050188020001284c12016801800000001e009200c00000001b00490060001a01040098c05000000d02201c6018000000068b0330040000000054029004000000151103cc0200000f0c8280a80100000000683033004000000003c0290040000000016014802000000000480c40100000000088052008000000221a07980400000000e140cc01002b0480b013a80250829010800cd401800a41502401ea008005c0a01c0175004000000004c0124018000000003805200800000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 13 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase4" = "QuadHeightStrongCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 13 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase4
private def zz2137:"s0859"="s0859":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightStrongCase5
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l41 l43 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7cf0018e12, -0x2e90edd000, -0x45d964b800,0], ![-0x2e90edd000, -0x1aaa1005f42,0x47c2bc4692,0x269635c9ba], ![-0x45d964b800,0x47c2bc4692, -0x12eae09c800,0x2e90edd000], ![0,0x269635c9ba,0x2e90edd000, -0x174876e800]]
noncomputable def hinges:Hinges:=[(0x1812033b4,l14),(0x92e6f7903,l17),(0x39efadc41a,l15),(-0x174876e800,l27),(0x174876e800,l29),(-0x1812033b4,l25),(0x7a6df70dd,l30),(0x174876e800,l33),(-0x174876e800,l35),(0x174876e800,l37),(-0x7a6df70dd,l43),(-0x39efadc41a,l41),(0x174876e800,l51),(-0x92e6f7903,l62)]
def normalizationDenominator:ℤ:=0x2e90edd000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x174876e800,l27),(0x174876e800,l29),(0x174876e800,l33),(-0x174876e800,l35),(0x174876e800,l37),(0x174876e800,l51),(0x39efadc41a,l15),(-0x39efadc41a,l41),(0x92e6f7903,l17),(-0x92e6f7903,l62),(0x7a6df70dd,l30),(-0x7a6df70dd,l43),(0x1812033b4,l14),(-0x1812033b4,l25)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightStrongCase5" = "QuadHeightStrongCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightStrongCase5
private def zz2138:"s085a"="s085a":=by decide+kernel
end 
section 
namespace Green24Proof.HeightStrongRows
open QuadraticCertificates ExpressionCertificates ParityPhaseRows
def rowsChunk0:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x105d35d90f6f48023d5b2ccae532ec8bbba800bf1e699ba029301baa1ede88018b6f9f3c2059301baa1ede88049a4eddac6135d90f6f48018b6f9f3c207d62ec8bbba80248dc19b8e5601baa1ede88009c4b0f3c3ae1607b9d6a8802fed8eea8a07d201baa1ede88002c0f6b3f09202d20ef3acd0805db3d1a601d202f4c3dbd08004cb8fc78f82525d90f6f48003f4a6d89692079201fa02a6069201baa1ede88018b6f9f3c2019201baa1ede88002a4aaf0f2c61201baa1ede88007e9b5fce4f607c209a88bf2805e9c86864225a0afc88001efe0b296b607825d90f6f48001ebb98ccfba02018bd9b2ae8007bc8c9998ea14]
def rowsChunk1:List (ℚ × Potential):=PackedPhaseRowsData.decodeParity [0x103d501baa1ede88005dec9f2caae02d55d90f6f480079efdb7889a01d507b9d6a88023a0eb81e203955d90f6f48002bcc783e7de02950297b2e4dc80169ea6cef8b201955d90f6f48003aa8a85b3de150297b2e4dc801da0e8c4d603c125a0afc8800185f981dcf602c112d097e48001bbc7b0d6e201c107b9d6a88023a0eb81e203815d90f6f48003c0f3feb1e6028104aee5c9b8802a96d2c097fe018107b9d6a88023a0eb81e203c401baa1ede880028fa7b9ee06c404aee5c9b880028fa7b9ee03d012d097e4800197a5b1f206d037f0c7ac800197a5b1f203d35d90f6f4802a89bff5f206d32ec8bbba800188d7c6f613]
def rows:List (ℚ × Potential) :=
  rowsChunk0 ++ rowsChunk1
def mu:Phase → ℚ:=![(-0x8f22b1a85 / 0x77359400),(-0x5f487657b / 0x77359400)]
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadHeightStrongCase0.base QuadHeightStrongCase0.hinges QuadHeightStrongCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase0.base QuadHeightStrongCase0.hinges QuadHeightStrongCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadHeightStrongCase1.base QuadHeightStrongCase1.hinges QuadHeightStrongCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz404:"s0194"="s0194":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase1.base QuadHeightStrongCase1.hinges QuadHeightStrongCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadHeightStrongCase2.base QuadHeightStrongCase2.hinges QuadHeightStrongCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase2.base QuadHeightStrongCase2.hinges QuadHeightStrongCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadHeightStrongCase3.base QuadHeightStrongCase3.hinges QuadHeightStrongCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz405:"s0195"="s0195":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase3.base QuadHeightStrongCase3.hinges QuadHeightStrongCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 1 1 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadHeightStrongCase4.base QuadHeightStrongCase4.hinges QuadHeightStrongCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase4.base QuadHeightStrongCase4.hinges QuadHeightStrongCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 1 1 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadHeightStrongCase5.base QuadHeightStrongCase5.hinges QuadHeightStrongCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz406:"s0196"="s0196":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightStrongCase5.base QuadHeightStrongCase5.hinges QuadHeightStrongCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightStrongCase5.nonnegative x hx
def pair6:Expression:=pairSlack rows mu (49 / 0xfa) 0 0 false
def pair6Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair6Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_6_base LocalHeightStrongPairs.compact_heightStrong_pair_6_hinges
theorem pair6_identity:identityCheck pair6 pair6Rewrites pair6Target = true:=by decide +kernel
theorem pair6_target_eval (x:Point):normalEval pair6Target x = LocalHeightStrongPairs.heightStrong_pair_6 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_6_base LocalHeightStrongPairs.compact_heightStrong_pair_6_hinges x
theorem pair6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair6 x:=by
  rw [identityCheck_sound _ _ _ x pair6_identity,pair6_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_6_nonneg (hx 0) (hx 1)
def pair7:Expression:=pairSlack rows mu (49 / 0xfa) 0 0 true
def pair7Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair7Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_7_base LocalHeightStrongPairs.compact_heightStrong_pair_7_hinges
private def zz407:"s0197"="s0197":=by decide+kernel
theorem pair7_identity:identityCheck pair7 pair7Rewrites pair7Target = true:=by decide +kernel
theorem pair7_target_eval (x:Point):normalEval pair7Target x = LocalHeightStrongPairs.heightStrong_pair_7 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_7_base LocalHeightStrongPairs.compact_heightStrong_pair_7_hinges x
theorem pair7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair7 x:=by
  rw [identityCheck_sound _ _ _ x pair7_identity,pair7_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_7_nonneg (hx 0) (hx 1)
def pair8:Expression:=pairSlack rows mu (49 / 0xfa) 0 1 false
def pair8Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair8Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_8_base LocalHeightStrongPairs.compact_heightStrong_pair_8_hinges
theorem pair8_identity:identityCheck pair8 pair8Rewrites pair8Target = true:=by decide +kernel
private def zz408:"s0198"="s0198":=by decide+kernel
theorem pair8_target_eval (x:Point):normalEval pair8Target x = LocalHeightStrongPairs.heightStrong_pair_8 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_8_base LocalHeightStrongPairs.compact_heightStrong_pair_8_hinges x
theorem pair8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair8 x:=by
  rw [identityCheck_sound _ _ _ x pair8_identity,pair8_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_8_nonneg (hx 0) (hx 1)
def pair9:Expression:=pairSlack rows mu (49 / 0xfa) 0 1 true
def pair9Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair9Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_9_base LocalHeightStrongPairs.compact_heightStrong_pair_9_hinges
theorem pair9_identity:identityCheck pair9 pair9Rewrites pair9Target = true:=by decide +kernel
theorem pair9_target_eval (x:Point):normalEval pair9Target x = LocalHeightStrongPairs.heightStrong_pair_9 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_9_base LocalHeightStrongPairs.compact_heightStrong_pair_9_hinges x
private def zz409:"s0199"="s0199":=by decide+kernel
theorem pair9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair9 x:=by
  rw [identityCheck_sound _ _ _ x pair9_identity,pair9_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_9_nonneg (hx 0) (hx 1)
def pair10:Expression:=pairSlack rows mu (49 / 0xfa) 1 1 false
def pair10Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair10Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_10_base LocalHeightStrongPairs.compact_heightStrong_pair_10_hinges
theorem pair10_identity:identityCheck pair10 pair10Rewrites pair10Target = true:=by decide +kernel
theorem pair10_target_eval (x:Point):normalEval pair10Target x = LocalHeightStrongPairs.heightStrong_pair_10 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_10_base LocalHeightStrongPairs.compact_heightStrong_pair_10_hinges x
theorem pair10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair10 x:=by
  rw [identityCheck_sound _ _ _ x pair10_identity,pair10_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_10_nonneg (hx 0) (hx 1)
def pair11:Expression:=pairSlack rows mu (49 / 0xfa) 1 1 true
def pair11Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair11Target:NormalForm:=CompactPair.toNormal LocalHeightStrongPairs.compact_heightStrong_pair_11_base LocalHeightStrongPairs.compact_heightStrong_pair_11_hinges
private def zz410:"s019a"="s019a":=by decide+kernel
theorem pair11_identity:identityCheck pair11 pair11Rewrites pair11Target = true:=by decide +kernel
theorem pair11_target_eval (x:Point):normalEval pair11Target x = LocalHeightStrongPairs.heightStrong_pair_11 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalHeightStrongPairs.compact_heightStrong_pair_11_base LocalHeightStrongPairs.compact_heightStrong_pair_11_hinges x
theorem pair11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair11 x:=by
  rw [identityCheck_sound _ _ _ x pair11_identity,pair11_target_eval]
  exact LocalHeightStrongPairs.heightStrong_pair_11_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
private def zz411:"s019b"="s019b":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack rows mu (49 / 0xfa) p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair6_nonneg x hx
  · exact pair7_nonneg x hx
  · exact pair8_nonneg x hx
  · exact pair9_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair10_nonneg x hx
  · exact pair11_nonneg x hx
end Green24Proof.HeightStrongRows
private def zz2139:"s085b"="s085b":=by decide+kernel
end 
section 
namespace Green24Proof.HeightStrong
open QuadraticCertificates ExpressionCertificates ParityPhaseRows ParityPhaseSemantics
open ParityPhaseSymmetry ParityPhaseAggregation
open FullPhaseSemantics (quadPoint pairPoint sameColour)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack HeightStrongRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightStrongRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse HeightStrongRows.rows p q same x]
    exact HeightStrongRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack HeightStrongRows.rows HeightStrongRows.mu (49 / 0xfa) p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightStrongRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap HeightStrongRows.rows HeightStrongRows.mu (49 / 0xfa) p q same x]
    exact HeightStrongRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible HeightStrongRows.rows = true:=by decide +kernel
private def zz412:"s019c"="s019c":=by decide+kernel
theorem certificate_bound {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (49 / 0xfa:ℝ) * energy g - (0x23adac57b / 0x1dcd65000:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1) ^ 2 ≤ deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack HeightStrongRows.rows (ZMod.castHom h2 (ZMod 2) j)
        (ZMod.castHom h2 (ZMod 2) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack HeightStrongRows.rows HeightStrongRows.mu (49 / 0xfa)
        (ZMod.castHom h2 (ZMod 2) j) (ZMod.castHom h2 (ZMod 2) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum h2 h3 g hg,weightedAggregate_zero h2 h3 h5 g HeightStrongRows.rows rows_admissible] at hs
  have hmu0:HeightStrongRows.mu 0 = (-0x8f22b1a85 / 0x77359400:ℚ):=by decide +kernel
  have hmu1:HeightStrongRows.mu 1 = (-0x5f487657b / 0x77359400:ℚ):=by decide +kernel
  rw [hmu0,hmu1] at hs
  norm_num at hs
  have hm:=classMass_sum (ZMod.castHom h2 (ZMod 2)) g
  unfold deficit
  rw [← hm]
  nlinarith
theorem strong_height_bound {q:ℕ} [NeZero q] (h2:2 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (49 / 0xfa:ℝ) * energy g - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1) ^ 2 ≤ deficit g:=by
  have hc:=certificate_bound h2 h3 h5 g hg
  nlinarith [sq_nonneg (classMass (ZMod.castHom h2 (ZMod 2)) g 0 - classMass (ZMod.castHom h2 (ZMod 2)) g 1)]
end Green24Proof.HeightStrong
private def zz2140:"s085c"="s085c":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileOrientation
open FullPhaseRows (Phase)
open PhaseMassRows
theorem phaseTotal_translate {q:ℕ} [NeZero q] (h4:4 ∣ q)
    (g:ZMod q → ℝ) (t:ZMod q) (r:Phase) :
    phaseTotal h4 (fun i => g (i + t)) r =
      phaseTotal h4 g (r + ZMod.castHom h4 (ZMod 4) t):=by
  unfold phaseTotal colourTotal
  have h:=Equiv.sum_comp (Equiv.addRight t)
    (fun i => if ZMod.castHom h4 (ZMod 4) i = r + ZMod.castHom h4 (ZMod 4) t then g i else 0)
  simpa only [Equiv.coe_addRight,map_add,add_left_inj] using h
theorem parityEquiv_add {m:ℕ} [NeZero m] (r:ZMod 2) (i t:ZMod m) :
    parityEquiv m (r,i) + doubleResidue m t = parityEquiv m (r,i + t):=by
  simp only [parityEquiv_apply,map_add]
  ring
private def zz413:"s019d"="s019d":=by decide+kernel
theorem interleave_translate {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) (t:ZMod m) :
    interleave (fun i => u (i + t)) (fun i => v (i + t)) =
      fun i => interleave u v (i + doubleResidue m t):=by
  funext x
  obtain ⟨⟨r,i⟩,rfl⟩:=(parityEquiv m).surjective x
  rw [parityEquiv_add]
  rcases zmod_two_eq_zero_or_one r with rfl | rfl
  · rw [interleave_even,interleave_even]
  · rw [interleave_odd,interleave_odd]
theorem phaseTotal_shift_children {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m)
    (u v:ZMod m → ℝ) (r:Phase) :
    phaseTotal h4 (interleave (fun i => u (i + 1)) (fun i => v (i + 1))) r =
      phaseTotal h4 (interleave u v) (r + 2):=by
  rw [interleave_translate,phaseTotal_translate]
  have ht:doubleResidue m 1 = 2:=by simpa using doubleResidue_natCast m 1
  rw [ht,map_ofNat]
theorem orient_even_child {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    ∃ u' v':ZMod m → ℝ,(∀ i,0 ≤ u' i) ∧ (∀ i,0 ≤ v' i) ∧
      mass u' = mass u ∧ mass v' = mass v ∧ deficit (interleave u' v') = deficit (interleave u v) ∧
      phaseTotal h4 (interleave u' v') 2 ≤ phaseTotal h4 (interleave u' v') 0:=by
  rcases le_total (phaseTotal h4 (interleave u v) 2) (phaseTotal h4 (interleave u v) 0) with h | h
  · exact ⟨u,v,hu,hv,rfl,rfl,rfl,h⟩
  · refine ⟨(fun i => u (i + 1)),(fun i => v (i + 1)),(fun i => hu _),(fun i => hv _),
      mass_translate u 1,mass_translate v 1, ?_, ?_⟩
    · rw [interleave_translate,deficit_translate]
    · rw [phaseTotal_shift_children,phaseTotal_shift_children]
      simpa only [zero_add,show (2 + 2:Phase) = 0 from rfl] using h
end Green24Proof.ProfileOrientation
private def zz2141:"s085d"="s085d":=by decide+kernel
end 
section 
namespace Green24Proof.Full27ProfileInterval
open FullPhaseRows FullPhaseAggregation PhaseMassRows ChildRows GrandchildRows HeightChildRows
theorem grandchild_nonpos_of_induction {q:ℕ} [NeZero q] (S:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (r:Phase)
    (ih:∀ (n:ℕ) [NeZero n],n < q → n ∣ q →
      ∀ u:ZMod n → ℝ,(∀ i,0 ≤ u i) → 0 ≤ deficit u) :
    rowAggregate S h4 h3 g (.grandchild r) ≤ 0:=by
  rcases h4 with ⟨n,rfl⟩
  have hn:0 < n:=by have hp:=NeZero.pos (4 * n); omega
  let:NeZero n:=⟨by omega⟩
  rw [rowAggregate_grandchild]
  have hd:=ih n (by omega) (dvd_mul_left n 4) (grandchild g r) (grandchild_nonneg g hg r)
  linarith
private def zz414:"s019e"="s019e":=by decide+kernel
theorem interval_bound_of_height {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hh:(49 / 0xfa:ℝ) * energy v - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) v 0 - classMass (ZMod.castHom h2 (ZMod 2)) v 1) ^ 2 ≤ deficit v)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hlow:(49 / 20:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (27 / 10:ℝ) * mass v) :
    (3 / 0x7a120:ℝ) * (mass u + mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    have ht:=phaseTotal_sum h4 (interleave u v)
    rw [mass_interleave] at ht
    linarith
  have hchild:rowAggregate (27 / 10) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have hheight:=rowAggregate_height_odd_nonpos (27 / 10) h4 h3 h2 u v hu hv hh
  have hgrandchild:=grandchild_nonpos_of_induction (27 / 10) h4 h3 (interleave u v) hg 2 ih
  have hc:=Full27Mass.deficit_lower_bound_of_child_rows h4 h3 h5 (interleave u v) hg horder
    (by rw [hU,hV]; exact hlow) (by rw [hU,hV]; exact hhigh) hchild hheight hgrandchild
  simpa only [mass_interleave] using hc
theorem interval_bound_ordered {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hlow:(49 / 20:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (27 / 10:ℝ) * mass v) :
    (3 / 0x7a120:ℝ) * (mass u + mass v) ^ 2 ≤ deficit (interleave u v):=by
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  exact interval_bound_of_height h4 h3 h5 h2 u v hu hv ih
    (HeightStrong.strong_height_bound h2 h3m h5m v hv) horder hlow hhigh
theorem interval_bound {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(49 / 20:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (27 / 10:ℝ) * mass v) :
    (3 / 0x7a120:ℝ) * (mass u + mass v) ^ 2 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,horder⟩:=ProfileOrientation.orient_even_child h4 u v hu hv
  have hb:=interval_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih horder
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hU,hV,hd] using hb
end Green24Proof.Full27ProfileInterval
private def zz2142:"s085e"="s085e":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFull30Pairs
def compact_full30_pair_20_base:CompactPair.Quadratic:=⟨0,(0x2713 / 0x3b9aca00),0⟩
def compact_full30_pair_20_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_20_base compact_full30_pair_20_hinges x y
def compact_full30_pair_20_cuts:List ℚ:=[]
theorem compact_full30_pair_20_check :
    CompactPair.expressionCheckPSD compact_full30_pair_20_base compact_full30_pair_20_hinges 0 compact_full30_pair_20_cuts = true :=
  by decide +kernel
private def zz415:"s019f"="s019f":=by decide+kernel
theorem compact_full30_pair_20_representation (x y:ℝ) :
    full30_pair_20 x y = CompactPair.expressionEval compact_full30_pair_20_base compact_full30_pair_20_hinges x y:=by rfl
theorem full30_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_20 x y:=by
  rw [compact_full30_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_20_check hy (by simpa using hx)
def compact_full30_pair_21_base:CompactPair.Quadratic:=⟨(-1 / 0x2cb41780),(0xfa3 / 0x3b9aca00),0⟩
def compact_full30_pair_21_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(1 / 0x165a0bc00),3, -1⟩]
noncomputable def full30_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_21_base compact_full30_pair_21_hinges x y
def compact_full30_pair_21_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full30_pair_21_check :
    CompactPair.expressionCheckPSD compact_full30_pair_21_base compact_full30_pair_21_hinges 0 compact_full30_pair_21_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_21_representation (x y:ℝ) :
    full30_pair_21 x y = CompactPair.expressionEval compact_full30_pair_21_base compact_full30_pair_21_hinges x y:=by rfl
private def zz416:"s01a0"="s01a0":=by decide+kernel
theorem full30_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_21 x y:=by
  rw [compact_full30_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_21_check hy (by simpa using hx)
def compact_full30_pair_22_base:CompactPair.Quadratic:=⟨0,(0x6d5f / 0x77359400),0⟩
def compact_full30_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_22_base compact_full30_pair_22_hinges x y
def compact_full30_pair_22_cuts:List ℚ:=[]
theorem compact_full30_pair_22_check :
    CompactPair.expressionCheckPSD compact_full30_pair_22_base compact_full30_pair_22_hinges 0 compact_full30_pair_22_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_22_representation (x y:ℝ) :
    full30_pair_22 x y = CompactPair.expressionEval compact_full30_pair_22_base compact_full30_pair_22_hinges x y:=by rfl
theorem full30_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_22 x y:=by
  rw [compact_full30_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_22_check hy (by simpa using hx)
def compact_full30_pair_23_base:CompactPair.Quadratic:=⟨(-3 / 0xee6b2800),(1 / 0x1e848),0⟩
def compact_full30_pair_23_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def full30_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_23_base compact_full30_pair_23_hinges x y
def compact_full30_pair_23_cuts:List ℚ:=[(1 / 3)]
private def zz417:"s01a1"="s01a1":=by decide+kernel
theorem compact_full30_pair_23_check :
    CompactPair.expressionCheckPSD compact_full30_pair_23_base compact_full30_pair_23_hinges 0 compact_full30_pair_23_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_23_representation (x y:ℝ) :
    full30_pair_23 x y = CompactPair.expressionEval compact_full30_pair_23_base compact_full30_pair_23_hinges x y:=by rfl
theorem full30_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_23 x y:=by
  rw [compact_full30_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_23_check hy (by simpa using hx)
def compact_full30_pair_24_base:CompactPair.Quadratic:=⟨0,(0x4e27 / 0x77359400),0⟩
def compact_full30_pair_24_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_24_base compact_full30_pair_24_hinges x y
def compact_full30_pair_24_cuts:List ℚ:=[]
theorem compact_full30_pair_24_check :
    CompactPair.expressionCheckPSD compact_full30_pair_24_base compact_full30_pair_24_hinges 0 compact_full30_pair_24_cuts = true :=
  by decide +kernel
private def zz418:"s01a2"="s01a2":=by decide+kernel
theorem compact_full30_pair_24_representation (x y:ℝ) :
    full30_pair_24 x y = CompactPair.expressionEval compact_full30_pair_24_base compact_full30_pair_24_hinges x y:=by rfl
theorem full30_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_24 x y:=by
  rw [compact_full30_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_24_check hy (by simpa using hx)
def compact_full30_pair_25_base:CompactPair.Quadratic:=⟨(-1 / 0xee6b2800),(0xfa3 / 0x3b9aca00),0⟩
def compact_full30_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -1⟩]
noncomputable def full30_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_25_base compact_full30_pair_25_hinges x y
def compact_full30_pair_25_cuts:List ℚ:=[1]
theorem compact_full30_pair_25_check :
    CompactPair.expressionCheckPSD compact_full30_pair_25_base compact_full30_pair_25_hinges 0 compact_full30_pair_25_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_25_representation (x y:ℝ) :
    full30_pair_25 x y = CompactPair.expressionEval compact_full30_pair_25_base compact_full30_pair_25_hinges x y:=by rfl
private def zz419:"s01a3"="s01a3":=by decide+kernel
theorem full30_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_25 x y:=by
  rw [compact_full30_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_25_check hy (by simpa using hx)
def compact_full30_pair_26_base:CompactPair.Quadratic:=⟨0,(0x6d61 / 0x77359400),0⟩
def compact_full30_pair_26_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_26_base compact_full30_pair_26_hinges x y
def compact_full30_pair_26_cuts:List ℚ:=[]
theorem compact_full30_pair_26_check :
    CompactPair.expressionCheckPSD compact_full30_pair_26_base compact_full30_pair_26_hinges 0 compact_full30_pair_26_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_26_representation (x y:ℝ) :
    full30_pair_26 x y = CompactPair.expressionEval compact_full30_pair_26_base compact_full30_pair_26_hinges x y:=by rfl
theorem full30_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_26 x y:=by
  rw [compact_full30_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_26_check hy (by simpa using hx)
def compact_full30_pair_27_base:CompactPair.Quadratic:=⟨(1 / 0x47868c00),(0x3e7f / 0x77359400),0⟩
def compact_full30_pair_27_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def full30_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_27_base compact_full30_pair_27_hinges x y
def compact_full30_pair_27_cuts:List ℚ:=[(1 / 3),1,3]
private def zz420:"s01a4"="s01a4":=by decide+kernel
theorem compact_full30_pair_27_check :
    CompactPair.expressionCheckPSD compact_full30_pair_27_base compact_full30_pair_27_hinges 0 compact_full30_pair_27_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_27_representation (x y:ℝ) :
    full30_pair_27 x y = CompactPair.expressionEval compact_full30_pair_27_base compact_full30_pair_27_hinges x y:=by rfl
theorem full30_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_27 x y:=by
  rw [compact_full30_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_27_check hy (by simpa using hx)
def compact_full30_pair_28_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1323f / 0x186a0),(-49 / 50)⟩
def compact_full30_pair_28_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_28_base compact_full30_pair_28_hinges x y
def compact_full30_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full30_pair_28_check :
    CompactPair.expressionCheckPSD compact_full30_pair_28_base compact_full30_pair_28_hinges 0 compact_full30_pair_28_cuts = true :=
  by decide +kernel
private def zz421:"s01a5"="s01a5":=by decide+kernel
theorem compact_full30_pair_28_representation (x y:ℝ) :
    full30_pair_28 x y = CompactPair.expressionEval compact_full30_pair_28_base compact_full30_pair_28_hinges x y:=by rfl
theorem full30_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_28 x y:=by
  rw [compact_full30_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_28_check hy (by simpa using hx)
def compact_full30_pair_29_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2fd9f / 0x3d090),(-49 / 50)⟩
def compact_full30_pair_29_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_29_base compact_full30_pair_29_hinges x y
def compact_full30_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full30_pair_29_check :
    CompactPair.expressionCheckPSD compact_full30_pair_29_base compact_full30_pair_29_hinges 0 compact_full30_pair_29_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_29_representation (x y:ℝ) :
    full30_pair_29 x y = CompactPair.expressionEval compact_full30_pair_29_base compact_full30_pair_29_hinges x y:=by rfl
private def zz422:"s01a6"="s01a6":=by decide+kernel
theorem full30_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_29 x y:=by
  rw [compact_full30_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_29_check hy (by simpa using hx)
def compact_full30_pair_30_base:CompactPair.Quadratic:=⟨0,(7 / 0x7a120),0⟩
def compact_full30_pair_30_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_30_base compact_full30_pair_30_hinges x y
def compact_full30_pair_30_cuts:List ℚ:=[]
theorem compact_full30_pair_30_check :
    CompactPair.expressionCheckPSD compact_full30_pair_30_base compact_full30_pair_30_hinges 0 compact_full30_pair_30_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_30_representation (x y:ℝ) :
    full30_pair_30 x y = CompactPair.expressionEval compact_full30_pair_30_base compact_full30_pair_30_hinges x y:=by rfl
theorem full30_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_30 x y:=by
  rw [compact_full30_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_30_check hy (by simpa using hx)
def compact_full30_pair_31_base:CompactPair.Quadratic:=⟨(-1 / 0x2cb417800),(0x3e81 / 0x77359400),0⟩
def compact_full30_pair_31_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(3 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def full30_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_31_base compact_full30_pair_31_hinges x y
def compact_full30_pair_31_cuts:List ℚ:=[(1 / 3),1,3]
private def zz423:"s01a7"="s01a7":=by decide+kernel
theorem compact_full30_pair_31_check :
    CompactPair.expressionCheckPSD compact_full30_pair_31_base compact_full30_pair_31_hinges 0 compact_full30_pair_31_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_31_representation (x y:ℝ) :
    full30_pair_31 x y = CompactPair.expressionEval compact_full30_pair_31_base compact_full30_pair_31_hinges x y:=by rfl
theorem full30_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_31 x y:=by
  rw [compact_full30_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_31_check hy (by simpa using hx)
def compact_full30_pair_32_base:CompactPair.Quadratic:=⟨(-0x38b44ccc1 / 0x77359400),(0x21fae293 / 0x7735940),(-49 / 50)⟩
def compact_full30_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x13c59ed / 0x17d7840),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x1286f399b / 0x165a0bc00),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_32_base compact_full30_pair_32_hinges x y
def compact_full30_pair_32_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full30_pair_32_check :
    CompactPair.expressionCheckPSD compact_full30_pair_32_base compact_full30_pair_32_hinges 0 compact_full30_pair_32_cuts = true :=
  by decide +kernel
private def zz424:"s01a8"="s01a8":=by decide+kernel
theorem compact_full30_pair_32_representation (x y:ℝ) :
    full30_pair_32 x y = CompactPair.expressionEval compact_full30_pair_32_base compact_full30_pair_32_hinges x y:=by rfl
theorem full30_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_32 x y:=by
  rw [compact_full30_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_32_check hy (by simpa using hx)
def compact_full30_pair_33_base:CompactPair.Quadratic:=⟨(-0x305a086e7 / 0xb2d05e00),(0x17a7f97 / 0x2faf080),(-49 / 50)⟩
def compact_full30_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0x52f845c7 / 0xb2d05e00),1, -3⟩,⟨(0x83c43d / 0xbebc200),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x4ad94603 / 0xb2d05e00),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_33_base compact_full30_pair_33_hinges x y
def compact_full30_pair_33_cuts:List ℚ:=[(1 / 3),1,3]
theorem compact_full30_pair_33_check :
    CompactPair.expressionCheckPSD compact_full30_pair_33_base compact_full30_pair_33_hinges 0 compact_full30_pair_33_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_33_representation (x y:ℝ) :
    full30_pair_33 x y = CompactPair.expressionEval compact_full30_pair_33_base compact_full30_pair_33_hinges x y:=by rfl
private def zz425:"s01a9"="s01a9":=by decide+kernel
theorem full30_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_33 x y:=by
  rw [compact_full30_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_33_check hy (by simpa using hx)
def compact_full30_pair_34_base:CompactPair.Quadratic:=⟨0,(0x9c5 / 0xee6b280),0⟩
def compact_full30_pair_34_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_34_base compact_full30_pair_34_hinges x y
def compact_full30_pair_34_cuts:List ℚ:=[]
theorem compact_full30_pair_34_check :
    CompactPair.expressionCheckPSD compact_full30_pair_34_base compact_full30_pair_34_hinges 0 compact_full30_pair_34_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_34_representation (x y:ℝ) :
    full30_pair_34 x y = CompactPair.expressionEval compact_full30_pair_34_base compact_full30_pair_34_hinges x y:=by rfl
theorem full30_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_34 x y:=by
  rw [compact_full30_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_34_check hy (by simpa using hx)
def compact_full30_pair_35_base:CompactPair.Quadratic:=⟨(1 / 0x59682f00),(1 / 0x3d090),0⟩
def compact_full30_pair_35_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def full30_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_35_base compact_full30_pair_35_hinges x y
def compact_full30_pair_35_cuts:List ℚ:=[(1 / 3),3]
private def zz426:"s01aa"="s01aa":=by decide+kernel
theorem compact_full30_pair_35_check :
    CompactPair.expressionCheckPSD compact_full30_pair_35_base compact_full30_pair_35_hinges 0 compact_full30_pair_35_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_35_representation (x y:ℝ) :
    full30_pair_35 x y = CompactPair.expressionEval compact_full30_pair_35_base compact_full30_pair_35_hinges x y:=by rfl
theorem full30_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_35 x y:=by
  rw [compact_full30_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_35_check hy (by simpa using hx)
def compact_full30_pair_36_base:CompactPair.Quadratic:=⟨0,(7 / 0x7a120),0⟩
def compact_full30_pair_36_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_36_base compact_full30_pair_36_hinges x y
def compact_full30_pair_36_cuts:List ℚ:=[]
theorem compact_full30_pair_36_check :
    CompactPair.expressionCheckPSD compact_full30_pair_36_base compact_full30_pair_36_hinges 0 compact_full30_pair_36_cuts = true :=
  by decide +kernel
private def zz427:"s01ab"="s01ab":=by decide+kernel
theorem compact_full30_pair_36_representation (x y:ℝ) :
    full30_pair_36 x y = CompactPair.expressionEval compact_full30_pair_36_base compact_full30_pair_36_hinges x y:=by rfl
theorem full30_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_36 x y:=by
  rw [compact_full30_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_36_check hy (by simpa using hx)
def compact_full30_pair_37_base:CompactPair.Quadratic:=⟨0,(0x3e81 / 0x77359400),0⟩
def compact_full30_pair_37_hinges:List CompactPair.Hinge:=[]
noncomputable def full30_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_37_base compact_full30_pair_37_hinges x y
def compact_full30_pair_37_cuts:List ℚ:=[]
theorem compact_full30_pair_37_check :
    CompactPair.expressionCheckPSD compact_full30_pair_37_base compact_full30_pair_37_hinges 0 compact_full30_pair_37_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_37_representation (x y:ℝ) :
    full30_pair_37 x y = CompactPair.expressionEval compact_full30_pair_37_base compact_full30_pair_37_hinges x y:=by rfl
private def zz428:"s01ac"="s01ac":=by decide+kernel
theorem full30_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_37 x y:=by
  rw [compact_full30_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_37_check hy (by simpa using hx)
def compact_full30_pair_38_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x1323f / 0x186a0),(-49 / 50)⟩
def compact_full30_pair_38_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_38_base compact_full30_pair_38_hinges x y
def compact_full30_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_full30_pair_38_check :
    CompactPair.expressionCheckPSD compact_full30_pair_38_base compact_full30_pair_38_hinges 0 compact_full30_pair_38_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_38_representation (x y:ℝ) :
    full30_pair_38 x y = CompactPair.expressionEval compact_full30_pair_38_base compact_full30_pair_38_hinges x y:=by rfl
theorem full30_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_38 x y:=by
  rw [compact_full30_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_38_check hy (by simpa using hx)
def compact_full30_pair_39_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2fd9f / 0x3d090),(-49 / 50)⟩
def compact_full30_pair_39_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def full30_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_full30_pair_39_base compact_full30_pair_39_hinges x y
def compact_full30_pair_39_cuts:List ℚ:=[(1 / 3),3]
private def zz429:"s01ad"="s01ad":=by decide+kernel
theorem compact_full30_pair_39_check :
    CompactPair.expressionCheckPSD compact_full30_pair_39_base compact_full30_pair_39_hinges 0 compact_full30_pair_39_cuts = true :=
  by decide +kernel
theorem compact_full30_pair_39_representation (x y:ℝ) :
    full30_pair_39 x y = CompactPair.expressionEval compact_full30_pair_39_base compact_full30_pair_39_hinges x y:=by rfl
theorem full30_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ full30_pair_39 x y:=by
  rw [compact_full30_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_full30_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFull30Pairs
private def zz2143:"s085f"="s085f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x11a6f6d0c, -0xd5c8eff8, -0x140ad74f3,0xd7d4e54], ![-0xd5c8eff8, -0x39965e0fc,0x317a168,0x12f05dee5], ![-0x140ad74f3,0x317a168, -0x56b280d4c,0xd5c91ed8], ![0xd7d4e54,0x12f05dee5,0xd5c91ed8, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0xef7f8,l6),(0x175314c,l4),(-0x6d6dcc,l10),(0xd641ed08,l14),(-0x527a076,l17),(0x14d3e3310,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xd641ed08,l25),(0x65f9560e,l30),(0x6ae483b4,l33),(0x6d6dcc,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x175314c,l34),(-0x65f9560e,l43),(-0x14d3e3310,l41),(0x6ae483b4,l51),(0xef7f8,l60),(0x527a076,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6ae483b4,l27),(0x6ae483b4,l29),(0x6ae483b4,l33),(-0x6ae483b4,l35),(0x6ae483b4,l37),(0x6ae483b4,l51),(0xd641ed08,l14),(-0xd641ed08,l25),(0x65f9560e,l30),(-0x65f9560e,l43),(0x14d3e3310,l15),(-0x14d3e3310,l41),(-0x527a076,l17),(0x527a076,l62),(-0x6d6dcc,l10),(0x6d6dcc,l38),(0x175314c,l4),(-0x175314c,l34),(-0xef7f8,l6),(0xef7f8,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x17148a80a80100000000a8b0330040000000001819002000000000502480200000006c0026402000000000d80720080000000074029004000000000d034802000000098281a6010000000320013201000000000640390040000000036014802000000000f00a40100000002e00132010000000005c039004000000003201480200000002c00264020000000005807200818c118158079200a0000022084068c03000000098301c60100000000483033004000000341a0718040000000009038802000000048300c6010000000006805200800f81e04203c2008003c0841a0271004000000000480c401000000220a00c300c0000003a0a051804000002a0c4068c03000000000c81c40100000006c180e300800000000540290040000001505028c02000000000881c401002e07818c07a4010000000421e0398040000002215038c02000000001100a40100000003c28063008000000001a031004000000e05002cc03000000068480e6010000000281405300800000000028190020000000001c0c8010000005418026601800000028140b30080000000012049004000000098004c804000000001300e401000000461500a300c0000002612031805420a404200335006002905409007a802001582405809d401000b81403802ea0080000000098024803000000000700a4010000000442c06300800000000e00490060000000012014802,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case0" = "QuadFull30Case0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case0
private def zz2144:"s0860"="s0860":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x116742afb, -0xd5c8eff8, -0x140ad74f6,0xdf3098c], ![-0xd5c8eff8, -0x391657403,0x59edb2,0x13029db27], ![-0x140ad74f6,0x59edb2, -0x56b280d4c,0xd5c91ed8], ![0xdf3098c,0x13029db27,0xd5c91ed8, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0xef7f8,l6),(0x175314c,l4),(-0x6d6dcc,l10),(0xd9463334,l14),(-0x3d238b0,l17),(0x1418dac2c,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xd9463334,l25),(0x68eac4ab,l30),(0x6ae483b4,l33),(0x6d6dcc,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x175314c,l34),(-0x68eac4ab,l43),(-0x1418dac2c,l41),(-0xe799f8,l46),(0x6ae483b4,l51),(0xef7f8,l60),(0x3d238b0,l62),(0xe799f8,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6ae483b4,l27),(0x6ae483b4,l29),(0x6ae483b4,l33),(-0x6ae483b4,l35),(0x6ae483b4,l37),(0x6ae483b4,l51),(0xd9463334,l14),(-0xd9463334,l25),(0x68eac4ab,l30),(-0x68eac4ab,l43),(0x1418dac2c,l15),(-0x1418dac2c,l41),(-0x3d238b0,l17),(0x3d238b0,l62),(-0xe799f8,l46),(0xe799f8,l64),(-0x6d6dcc,l10),(0x6d6dcc,l38),(0x175314c,l4),(-0x175314c,l34),(-0xef7f8,l6),(0xef7f8,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case1" = "QuadFull30Case1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case1
private def zz2145:"s0861"="s0861":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7cb6d384c, -0x2cb416090, -0x196dc8fa4,0x2afef4], ![-0x2cb416090, -0x157f399118,0x6c67e1ba8, -0x1c2b46132], ![-0x196dc8fa4,0x6c67e1ba8, -0x14d5c876a3,0x4298f3199], ![0x2afef4, -0x1c2b46132,0x4298f3199, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x980af6c3,l6),(0x22af59e27,l4),(0x1f4ceb07,l10),(0xd9b40,l14),(-0x661b2126,l17),(0x3922eafd1,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x1cb750,l25),(0x4c57a55,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x30e392,l46),(0x165a0bc00,l51),(-0x105882330,l62),(0x1a3dc6,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x105882330,l62),(0x3922eafd1,l15),(-0x980af6c3,l6),(0x22af59e27,l4),(-0x661b2126,l17),(0x1f4ceb07,l10),(0x4c57a55,l30),(-0x30e392,l46),(-0x1cb750,l25),(0x1a3dc6,l64),(0xd9b40,l14)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x207167dd511c91a3eea629320615bc947489105ae0709e1807e93eb63c200a05307970660c2200848d0cf67ada48186fa524279218c11978c620300cd9b3ec405e770b0b4010400001f671200f50eccdc1270c230080000b8102509cc51e8000000304c76a7cd2fb068491c718a1471481080ca00800430200200d02401000088102309c0d55b27045cabcd5f7a9ba0911885abbd972d484dad6900e23964b0ede527bb49162a21842b5ed0b7645729e0d2bf84848167937d69330c3b027649040f483a50497cff33f33e860498ae513e525f6406bd541012407e79a65f0ab39f04996302902026810e38a619000034b338f80c819dbda27ab55881596d1362496002de048f842c0c0b8fd9f1c5925075dbfd3c84f0074f213c01089080c60c4003001000187226de3f06869948a0036bb0e8b5eb3d2e354676a064f40bca6b93c421074208953b073a53aeb2d2905711b4000c1cd5b9c11545c0a44f455b9c11545c0a44f3ddeccd5f953bc3ffeddeccd5f953bc3fff088a199d895d7c99b1383131162e2cf9622c5c59f41380127d647de948a5dcd6405ddcd650003e9c7c0640ceded13d5aac40a837d6e7380d62837d6e8000000034a2063842041020171e2f4dd1641749f4b8375e164a256e554909693ebd7d7e8e001dfd83312834f23e5bf04f87165cc3065c6d25c215629cc212e423543fa0abe258fb58545d13671284d8c50b84dca3132152742036a7a82027cf2cc22a499efe2b62e04211f425865a68003361c62b5e3bcd613d9588038fae4ec9bb4d30f6034087e856758b13000000000000000000231e208ff388c571500a758d4cb48a812ea3c88a101d76bafef8b0000000000000000008843021823002802008059de3684569f0ea257dd47b7312d96b12d21db8321a6175bfe7697ebbffd147455a606784a53827) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case2" = "QuadFull30Case2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case2
private def zz2146:"s0862"="s0862":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l44 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3af94f204, -0x2cb416090, -0x1b15b768a,0x14b236696], ![-0x2cb416090, -0xb8cf2e6ba,0x4c9098c0c, -0x1c80372f3], ![-0x1b15b768a,0x4c9098c0c, -0x14d5c876a3,0x4298f3199], ![0x14b236696, -0x1c80372f3,0x4298f3199, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x980af6c3,l6),(0x22af59e27,l4),(0x1f4ceb07,l10),(0xee34faec,l14),(0x64e6884d0,l12),(-0x6c8da953,l17),(0x3a4801a75,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x1e63e6a22,l25),(0xd3041e,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x2ffefe6d,l43),(-0x35696e78e,l41),(-0x1dabd196,l46),(-0x2483a83a,l44),(0x165a0bc00,l51),(-0xb20f1b1d,l62),(0x8d1f126c,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x1e63e6a22,l25),(0x64e6884d0,l12),(0xee34faec,l14),(0x3a4801a75,l15),(-0x35696e78e,l41),(-0xb20f1b1d,l62),(-0x980af6c3,l6),(0x8d1f126c,l64),(0x22af59e27,l4),(-0x6c8da953,l17),(-0x2ffefe6d,l43),(0x1f4ceb07,l10),(-0x1dabd196,l46),(-0x2483a83a,l44),(0xd3041e,l30)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x184510480884012461c418600b95006000000000140d20080000000001c0c801], #[]⟩
def dynamicCode : Nat := ((((((((((((((((0x1657ac1522bce2425a98e12481cfdcee5323042100861217df0bc4858c3204cf3c658b0259f5bac60606072d07e582282aac5086008ea16576c4c0848010000143370e742b6193476b34b2d05823f4b9986f2c1214b236696362b6ed12b2d05823f3d6b3502046c39506f89d5bf70de9b177d3414adba0f99641619008a098010015afe5ff1285ce4f5fadf0899dabbf721b57aa76f3cc89bb73abcfab82e990f558a45b47f05c90e855cc70763324dac084c4dd82506f2c11ce63d0003d120741308309e5bbad70180000000013133085062bb8564c321309649249241839431411801400a60400401a1040a00014336375949d08f5549063498c034e276ab000106ce48a5ae0e8f09db931f61575a6a1ee3705b467f6120a9173684f86e1430ffb984c72142b2f4b9baa38133023ef77a616df3ad6281c0c9c9d1e6bff10c01297b1b4c2bc01140b0ae3981ed5f7f3d294a2e77d0fe02b9c2d8aefcb464bade2e0268dc191dcf2de2442f7b336d5cfc02bb63808261a95309066aa84bc6c35d80d8097598559462487300009b07c88702b39d7815f6151602ac39506f96daeadfc490c09f3414adba0f91428e28e18408c00a00600a45e34670e046081370e820c9a372c08b04fcb5175b64580600d5d6fbe72aa37571c8c1b6800131902915e5bbad70180000000013133085062bb8564c321309229220c20e18c10e006000338cc5cec75ecf1c98b717f196676563d40a744cced48e74ce5c91bc50a0003d47c88702b39d7815f6151602af51ffcd355405d117752207b016c39506f96daeadfc490c09f3414adba0fa1220c20c1080860ae0158c95eb70dbf3718ee44250d92d94c0a2d771ec6cf95e99b33d8087005db9664c05a998bbc7dcb226518b325284084e453cc4fea7c9110a353c8c184a32951d1c6083ba126001015ae3a94e8301f3fcfb42015661c220080000a1900e210400a800128083f90e06493dfa224fd9389909731c28fe2c68cd085a4a9e55e0a10550c6ec442cdaddf337c409a0033a1555e2f01891781025e54483502ba3564182b1410c15ac3a5edbefc02c8c171c3223004636f8dda32557a70f482027b9804c06443a973db4dbfab3710926dd9428170306530510c00001bd9c09de6c6866d30e202778e340adf82860886cc32b029343002d67f280ae910a048b45543469cc20065192f6e3f1700023a252e90d921c9eb33fd44f42896fe7dc114b120e6d531a19020000094883f1681f4360f81b07b0503d00b852087e262af8304f27386afc304002d0a46b09f8380f4db7b9b4e0080007dfb5089a82f3bca4f8c492a0f2551fa42e1efecbc97402ff32a196f351414a0b00b123940597e10df070e6e49a425a683063df03bff4a224201759d17755081000ff4c1852c304514d17871f6300d4736296844542ee6c7dc5e10e1706dbb752408347242d030510d81d8) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case3" = "QuadFull30Case3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case3
private def zz2147:"s0863"="s0863":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x121a41275, -0xd5c8eff8, -0x140ad74f0,0xcdf4478], ![-0xd5c8eff8, -0x3a548f62e,0x4f72d7c,0x12f05dee5], ![-0x140ad74f0,0x4f72d7c, -0x56b606988,0xd5c91ed8], ![0xcdf4478,0x12f05dee5,0xd5c91ed8, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0x15be2a,l6),(0x1741bf6,l4),(-0x664b28,l10),(0xd550ec4c,l14),(-0x527a076,l17),(0x14d3e3310,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xd4d5070a,l25),(0x65f9560e,l30),(0x6ae483b4,l33),(0x7ae0f8,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x1b0f96f,l34),(-0x6601a546,l43),(-0x14df5ea9a,l41),(0x105576e,l46),(0x6ae483b4,l51),(0x15722e,l60),(0x5a4510c,l62),(-0x152ae7a,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6ae483b4,l27),(0x6ae483b4,l29),(0x6ae483b4,l33),(-0x6ae483b4,l35),(0x6ae483b4,l37),(0x6ae483b4,l51),(0xd550ec4c,l14),(-0xd4d5070a,l25),(-0x6601a546,l43),(0x65f9560e,l30),(-0x14df5ea9a,l41),(0x14d3e3310,l15),(0x5a4510c,l62),(-0x527a076,l17),(-0x152ae7a,l64),(0x105576e,l46),(0x7ae0f8,l38),(-0x1b0f96f,l34),(-0x664b28,l10),(0x1741bf6,l4),(-0x15be2a,l6),(0x15722e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x1c46108808840100000012024030c030000000c8340f3008000000000d01c80200000002600132010000000002601c80200000000044072008000000361301cc0200000000044062008000000002a0148020000000003409200800000000050188020000000443c0530080000138110058c04000094260900b400c000000007802480300000002a00132010000000002a01c8020001047431024400c0f208a0b40631005], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case4" = "QuadFull30Case4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case4
private def zz2148:"s0864"="s0864":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x10cf38a04, -0xd5c8eff8, -0x140ad74f0,0xd1bde62], ![-0xd5c8eff8, -0x389afefd7,0x1b35c9a,0x13029db27], ![-0x140ad74f0,0x1b35c9a, -0x56b606988,0xd5c91ed8], ![0xd1bde62,0x13029db27,0xd5c91ed8, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0x15be2a,l6),(0x1741bf6,l4),(-0x664b28,l10),(0xd98cde98,l14),(0x3ac8792,l12),(-0x3d238b0,l17),(0x1418dac2c,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xda91d5c6,l25),(0x68eac4ab,l30),(0x6ae483b4,l33),(0x7ae0f8,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x1b0f96f,l34),(-0x683418d5,l43),(-0x1454e2de0,l41),(-0x1db6a1e,l46),(0x6ae483b4,l51),(0x15722e,l60),(0x4d43674,l62),(0x16416e0,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x1ac14b2ac26053b64e00366b93401a37bcc42815ae9df1ab91dfef0d750665bad6ec4f637135fdfad219e714082403 s0
def s2:=qPath 0x1ab923db026053b64e00366b93401a37bcc42815ae9df1ab91dfef0d534c4bfadb3560477135fdfad219e71408240b s1
def s3:=qPath 0x1a8aa05c426053b64e00366b93401a37bcc42815ae9df1ab91dfef0d2e0cf7bad3d89b237135fdfad219e714082406 s0
def s4:=qPath 0x1ab0fc8b426053b64e00366b93401a37bcc42815ae9df1ab91dfef0d3ad65cbadb09e3f37135fdfad219e714082409 s3
def s5:=qPath 0x1adf800a026053b64e00366b93401a37bcc42815ae9df1ab91dfef0d6959db7addf21bdf7135fdfad219e71408240c s0
def s6:=qPath 0x1adf800a026053b64e00366b93401a37bcc42815ae9df1ab91dfef0d6959db7addf21bdf7135fdfad219e714082404 s5
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨8, #[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,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,0x24607011414220000301040c0010480000000a0210040500006030810001048000140c10400101e0000707100c00b0a8000100c20304101200000000c040020140000000a0814040d00009161c0c4050980000000c020804050000b02040400102901220042030420230000c020c0c00203800000010060004054058d01080c10909c0000000d020004050000c08100c0080980002c08203000c12]⟩
theorem v0:V s2:=(S (K 16 nt 0x10c1c510c901a412284302886480d2091002098661b86051920309e36f4f14cd8030df4c0468390050914626e1a3c3300c901a44050cc23240690006c61786e019203488021b886480d2000d8803f988a19906480cb8fefdb8634100c92b301120e4012e451c8f0cc632406108062602241c88546198607192030842313007a0e41a801d4807c102d6210e253823240610855dc4bbc8ef7cf0001c5b38962f98d8080fa7c602053fd1211201c6071096280da9eaeed0a68b586105d066081005f101b223e81902a0443c8090ea) (S (K 13 nt 0x1448e184033c85612203295398a0710a9c41989321a44941f0cb9a10892430060cbd803c92a410e5606a019203488181aa06480d2000d8d491806480d2000c49722050203120c90184210803be6b96bd255a0401486fb93000571019a25a8b14a7d122139fa1844a44a71eb62960e21538833164cfd2409044ce3d1d04c5e5cb763e0d6d5d7fb396a46a48c2c6033056c03ac95208721f448132ba1c8491121e55220c84080c4a32406108420012f1d4bd885e52d00295de5a6000b3202704a5032030f30c20490fe3f861624444812c97d791fc0b6851020cc142087095061920308420000d8f5658e42800a43e6080a830c901842108007d7353aff7a900290df4c0013e4051c8fa0644e808fcc3080fc444c3898fc498c4251a2710642ff8492240619f030f8f052283004cc01e092a0870c2049107b25033cb87c3243c8a4419081018a46480c21084003def38c7be84801486fa6000a42027047d0320540880a64812) (S (K 12 nt 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) (K 17 nt 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))))
theorem v1:V s1:=(P w269 (P w317 (S (K 20 nt 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) v0)))
private def zz439:"s01b7"="s01b7":=by decide+kernel
theorem v2:V s4:=(M w5 (S (K 17 nt 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) (M w22 (S (K 15 nt 0xb0337006480d22d0d1e019203489430a0014200ba5698735d6b8e50c29890b25a61ce7d87742fea4de838deebcd8f59cc201cf311ce092ffbd510f10321f20c1700c8680c430a5942ca50c2845082002a272c0600ac301de2ae821c887a86480d2207a86324069000624b910280ac38c90184210800ca77ffd6f9200522d30004a901332669812fa) (K 15 nt 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)))))
theorem v3:V s3:=(P w24 (S (K 20 nt 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) (S (S (K 18 nt 0x2e0c0a219203482441ce50c43340c901982521149a88d481b066819203301242293511a0067201c245189b868e0cc032406912b83310c901a4001b10e72a03120c90198252114988894880d8e32406602484526222400c44035c8a39c310d8c3240660248450822242a88545dc0a05cfc99f32d4842469ce7cdc80295e3badc41e5c794647559eac816680c40921142083d0aa0d402944076881b89087125c1192030842aee29def315ec8000e2d8b5657d6a40407d3e30102852e58c901842108001aeef0f5af985f4041777d3010200b42035052d0320548880d012) (K 18 nt 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)) v2)))
theorem v4:V s6:=(M w5 (M w40 (M w22 (S (S (K 14 nt 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) (K 14 nt 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)) (K 15 nt 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)))))
theorem v5:V s5:=(S (K 20 nt 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) (S (M w55 (S (K 17 nt 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) (K 17 nt 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))) v4))
private def zz440:"s01b8"="s01b8":=by decide+kernel
theorem v6:V s0:=(S v1 (S v3 (S v5 (K 15 nt 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))))
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v6
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case5
private def zz2149:"s0865"="s0865":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l44 l46 l51 l6 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7cacc944b, -0x2cb416090, -0x196c8a344,0x7860c], ![-0x2cb416090, -0x157f499bb2,0x6c6869b20, -0x1c2b46132], ![-0x196c8a344,0x6c6869b20, -0x14d5613676,0x42972b733], ![0x7860c, -0x1c2b46132,0x42972b733, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x9732454a,l6),(0x229af27f4,l4),(0x1f4da46c,l10),(0x19af50,l14),(-0x661b2126,l17),(0x3922eafd1,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x1c4696,l25),(0x4c57a55,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x44532c,l46),(0x528654,l44),(0x165a0bc00,l51),(-0x105630e9b,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x105630e9b,l62),(0x3922eafd1,l15),(-0x9732454a,l6),(0x229af27f4,l4),(-0x661b2126,l17),(0x1f4da46c,l10),(0x4c57a55,l30),(-0x44532c,l46),(-0x1c4696,l25),(0x19af50,l14),(0x528654,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x40e33b0641392348ce6dd6a40c218bf7851220aa773cf8300fd7dc71d84013b5edfe033041100420888e8925ca1038391b67de891843569849c40c158fa063424407521cde39200cae8bc5f08003e37142a4b3841280400005f081386c09827c7b66bb0faec718342b333d3285013de296a071433e8cb60320407a91ee00080c62ca6126e28009b7fa57b480099bd7a85610b0204c018025010000e7102409d221000014c066e0820240c30c48a488388308384180202e0700401a0001bc63f2becb6491a485d7504861bf4b83ddeb0223348b752b1802de048f842c0c0b32031831c01000c00400467e20b85f0b07bfd38ccc1c0aa69b162df8992b3cf21654c6c4c97a7613912f476208e1ba80013b9e170db0948f196a2998cbc9cf43b03361aaa23e0b064db0862a7e53b7908dbe27339de58ab80bb9e8743afc4ae578f97b1023d3a10527dd5e4bc1894ed3fd3df5142fce7123b017efbae0b3af59fefded39ba2bdc14e2a4b32853100e8ed3b4c59e1021c772b678f5f8999) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case6" = "QuadFull30Case6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case6
private def zz2150:"s0866"="s0866":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l41 l43 l44 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x331aa0d30, -0x2cb416090, -0x191a376e6,0x14af75348], ![-0x2cb416090, -0xb8b9a0a90,0x4c8b92caa, -0x1c80372f3], ![-0x191a376e6,0x4c8b92caa, -0x14d5613676,0x42972b733], ![0x14af75348, -0x1c80372f3,0x42972b733, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x9732454a,l6),(0x229af27f4,l4),(0x1f4da46c,l10),(0xee41865a,l14),(0x64e5cc20e,l12),(-0x6c8da953,l17),(0x3a4801a75,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x1e664d1c8,l25),(0xd3041e,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x2f2aba8f,l43),(-0x36607e6b4,l41),(-0x1a3c1aaa,l46),(-0x2b53b928,l44),(0x165a0bc00,l51),(-0xa2a55f73,l62),(0x8db2ab70,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x1e664d1c8,l25),(0x64e5cc20e,l12),(0xee41865a,l14),(0x3a4801a75,l15),(-0x36607e6b4,l41),(-0xa2a55f73,l62),(-0x9732454a,l6),(0x8db2ab70,l64),(0x229af27f4,l4),(-0x6c8da953,l17),(-0x2f2aba8f,l43),(0x1f4da46c,l10),(-0x1a3c1aaa,l46),(-0x2b53b928,l44),(0xd3041e,l30)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x6114412022100491871061802e540180000000005034802000000000070320040000000005018802], #[![8, 0, -63, -3],![-6, 0, -15, 11]]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case7" = "QuadFull30Case7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case7
private def zz2151:"s0867"="s0867":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz444:"s01bc"="s01bc":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case8
private def zz2152:"s0868"="s0868":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz445:"s01bd"="s01bd":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case9
private def zz2153:"s0869"="s0869":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case10
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l14 l17 l27 l29 l33 l34 l35 l37 l38 l41 l43 l46 l51 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x47393239c, -0x22dc31e1f, -0x430e21c90,0x39f780], ![-0x22dc31e1f, -0x132ea37c08,0x6cb2b4cb6,0x179bbd9ec], ![-0x430e21c90,0x6cb2b4cb6, -0x1229298c00,0x2cb418f70], ![0x39f780,0x179bbd9ec,0x2cb418f70, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0x44532c,l14),(-0x528654,l12),(0x105882330,l17),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x211c6206,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x223d12d3c,l34),(-0x536ac3d,l43),(-0x3922eafd1,l41),(-0x19af50,l46),(0x165a0bc00,l51),(0x9754cbdf,l60),(0x6627b4e7,l62),(0x1c4696,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x105882330,l17),(-0x3922eafd1,l41),(0x9754cbdf,l60),(-0x223d12d3c,l34),(0x6627b4e7,l62),(-0x211c6206,l38),(-0x536ac3d,l43),(0x44532c,l14),(0x1c4696,l64),(-0x19af50,l46),(-0x528654,l12)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x104911a9c1d6a65903e075a99640000000165841aaa160fcc2a1011429029020e11000e008020971401006c12446a7075a99640f81d6a65900000000596106aa8583f30a840458c48c48a3821820824808171001006d91ba717764de5102350dc09e22840bd2f782f66820000101d0050220f74a050858043d4217d28380228850a94400096cfa963f8962020a007184d6dcf51aa60a00167698181) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case10" = "QuadFull30Case10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case10
private def zz2154:"s086a"="s086a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l41 l44 l46 l51 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x54e7c4a39, -0x22dc31e1f, -0x42a4e6998,0x257aa6da], ![-0x22dc31e1f, -0xb26318d78,0x1655298fc,0x44b65bda2], ![-0x42a4e6998,0x1655298fc, -0x1229298c00,0x2cb418f70], ![0x257aa6da,0x44b65bda2,0x2cb418f70, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0x1e25cfef2,l14),(-0x6558d2156,l12),(0xb20f1b1d,l17),(0x35696e78e,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0xeb996c84,l25),(0x2ffefe6d,l30),(0x165a0bc00,l33),(-0x211c6206,l38),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x223d12d3c,l34),(-0x3a6b1aa75,l41),(-0x8bc3a680,l46),(0x1e7e0e52,l44),(0x165a0bc00,l51),(0x9754cbdf,l60),(0x6c1fe5eb,l62),(0x204b58e4,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0x1e25cfef2,l14),(-0x6558d2156,l12),(-0xeb996c84,l25),(-0x3a6b1aa75,l41),(0x35696e78e,l15),(0xb20f1b1d,l17),(0x9754cbdf,l60),(-0x8bc3a680,l46),(-0x223d12d3c,l34),(0x6c1fe5eb,l62),(0x2ffefe6d,l30),(-0x211c6206,l38),(0x204b58e4,l64),(0x1e7e0e52,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((0x6c6f1274000000047641d0f65cf9c9c0f89649249228c09601201000a0082381c01006d1235291e5240a0c9cf943e78121052e9c034f20219472ca7be28408f6eb4190704000005dc01604f5a31ec6e1c05c40e703c000488142701c586137136dc0294) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case11" = "QuadFull30Case11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case11
private def zz2155:"s086b"="s086b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz449:"s01c1"="s01c1":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case12
private def zz2156:"s086c"="s086c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case13
private def zz2157:"s086d"="s086d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l51 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x116d775c3, -0xd5c8eff8, -0x140ad74f0,0xee2f780], ![-0xd5c8eff8, -0x3919bb408,0x1398858,0x12e607258], ![-0x140ad74f0,0x1398858, -0x56abe11b7,0xd5c91edb], ![0xee2f780,0x12e607258,0xd5c91edb, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0x13ad57,l6),(0x1bd0497,l4),(-0x80a985,l10),(0xd74beca4,l14),(-0x5a4510c,l17),(0x14df5ea9a,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xd74beca4,l25),(0x6601a546,l30),(0x6ae483b4,l33),(0x80a985,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x1bd0497,l34),(-0x6601a546,l43),(-0x14df5ea9a,l41),(0x6ae483b4,l51),(0x13ad57,l60),(0x5a4510c,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x1ac084dc025cc0e4b00027310b001dc5ef002815ae9df1ab91dfef0d72b3785ad5a37e1b72337680f22daeeb862403 s0
def s2:=qPath 0x1ab923db625cc0e4b00027310b001dc5ef002815ae9df1ab91dfef0d5c90767ad57c236d72337680f22daeeb862402 s0
def s3:=qPath 0x1a818348825cc0e4b00027310b001dc5ef002815ae9df1ab91dfef0d24efe39ad2021a3f72337680f22daeeb862403 s2
def s4:=qPath 0x1ae9636d425cc0e4b00027310b001dc5ef002815ae9df1ab91dfef0d6ca5a71ade880ec772337680f22daeeb86240a s2
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨7, #[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,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]⟩
private def zz450:"s01c2"="s01c2":=by decide+kernel
theorem v0:V s1:=(P w269 (P w317 (S (K 17 nt 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) (S (K 14 nt 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) (K 16 nt 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)))))
theorem v1:V s3:=(P w24 (S (K 17 nt 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) (S (K 16 nt 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) (S (K 15 nt 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) (K 15 nt 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)))))
theorem v2:V s4:=(M w28 (S (K 15 nt 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) (S (K 14 nt 0x4900d243e087d51f43289418085ec20c901a4194007648b20e1930201920348b6b5dfab275a1fc6e6cff35aeeddbd4392d0434a1201df1a880f08e9c31169007c9b0306806480d223e543b90f112ea005cff4ce3ab94adedb353cded6106942403cca2039043044901881e8047080b298c317146480cc07a7ca3a0054245cad7106480cc07a1ca3a94a27b0c3240610084c0350c400b240314820190ee23a0232406109290be69c976403c23faead0b00cf83016501947192030842017b9587a11d00270f980022c80ad90c922089c2) (S (K 13 nt 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) (K 13 nt 0x594dc5b8a86dbcda81a575fbab10a0f1ce6c349ea120db30cf1f3bde81d4f73c8a14e645c96323a88bcf1679222c8a077f09c9130621b3b315d93370db5eed834b5b3b1fa1a2763588692bd381b5af2b0613a4681ce273d8b14a7c76af2a3a88bcf167920430b32e1850756183113d80e0960da354e2ed4fe273c5bd0288234bf15f938e61901218880326206480cc000d8924c1d4685808593a83b94327a46480d2207a4232406900062607206324069000624ba2ca072ca32406108401004e260005e2028671a9ce6b)))))
theorem v3:V s2:=(S v1 (S (S (K 17 nt 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) v2) (K 14 nt 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)))
private def zz451:"s01c3"="s01c3":=by decide+kernel
theorem v4:V s0:=(S v0 v3)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v4
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case14
private def zz2158:"s086e"="s086e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l34 l35 l37 l38 l4 l41 l43 l46 l51 l6 l60 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x11233bc38, -0xd5c8eff8, -0x140ad74f0,0xec0efd1], ![-0xd5c8eff8, -0x38c1cd71d,0x9bb4a0,0x12ec06013], ![-0x140ad74f0,0x9bb4a0, -0x56abe11b7,0xd5c91edb], ![0xec0efd1,0x12ec06013,0xd5c91edb, -0x6ae483b4]]
noncomputable def hinges:Hinges:=[(-0x13ad57,l6),(0x1bd0497,l4),(-0x80a985,l10),(0xd97995fe,l14),(-0x4d43674,l17),(0x1454e2de0,l15),(-0x6ae483b4,l27),(0x6ae483b4,l29),(-0xd97995fe,l25),(0x683418d5,l30),(0x6ae483b4,l33),(0x80a985,l38),(-0x6ae483b4,l35),(0x6ae483b4,l37),(-0x1bd0497,l34),(-0x683418d5,l43),(-0x1454e2de0,l41),(-0xafebf7,l46),(0x6ae483b4,l51),(0x13ad57,l60),(0x4d43674,l62),(0xafebf7,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x1ac084dc025d80c02600137694001d81dfa22815ae9df1ab91dfef0d72b3785ad5a37e1b71839ae392246778702403 s0
def s2:=qPath 0x1ab923db625d80c02600137694001d81dfa22815ae9df1ab91dfef0d5c90767ad57c236d71839ae392246778702402 s0
def s3:=qPath 0x1ab1c2da625d80c02600137694001d81dfa22815ae9df1ab91dfef0d3505143adb0e059971839ae392246778702413 s2
def s4:=qPath 0x1ab923db625d80c02600137694001d81dfa22815ae9df1ab91dfef0d5c90767ad57c236d71839ae392246778702402 s2
def s5:=qPath 0x1ae9636d425d80c02600137694001d81dfa22815ae9df1ab91dfef0d6ca5a71ade880ec771839ae392246778702411 s4
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨8, #[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,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,0x608140400f0c8000206060110142200006030404004048000140c20400041200004030410004078000181c303002c2a0000303040c00404800000003010008050000000242040103400020586030c142600000002c08201014000280810100040a3c48801080c10808c0002c0830300080e00000003c18001014f163004203042427]⟩
theorem v0:V s1:=(P w269 (P w317 (S (K 19 nt 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) (S (K 15 nt 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) (K 18 nt 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)))))
private def zz452:"s01c4"="s01c4":=by decide+kernel
theorem v1:V s3:=(S (S (K 16 nt 0x4317144324069040861ca1a062819203305042093d0fa46600e444d8938b9509c9018e8491c62506021706801920348be9b8e5f3cda4f9e6d27d371ca77b8749acd6c4d66b54ef70f169c0e3a1c78b4d8c911d3afc13a8914310a08057880d3984327806480d2250a0841000f90068230e7b467be6ef3e4207b467be6ef3dffe5b7b34df3ffdf7c5b7b34df3ffdf7a8b56d0b2276ecfe8ad7bc9a296ae2420c202a5507b3388a98310a08412721e428c07e089ba2d5b42c8ad7bc9a2b5ef268b56d0b043480a10225f867cc188504a68550f318745ab685910c52f9456bde4d11bf37c086101520d7e14c814e188504a494545badf3dfc85b8d67a86c75a7235efe63ad2fefea1e45ab685913b767f03f1488830a0f82e7493650a1885042093500ba185819006480d225c58b8896659167c2cfc1dd43cf883cbaf2a1f487e8430c203102284126a00f22027640f1cc52f2245de49d90031fe650dc39fdd737d2ffcacefc9ffb0a60d3eea3fc4e33de335106fd26912240760a32186101881142083d07247418806f4835690b7420ee44bc032406913b03170c901a4072474188015c8ea1c509d8919203084210019ed7f57bea7c80103aca4c038802bc80b9906454811212) (K 16 nt 0x2b0c12219203485d65ee3f8f83092e1be02e3f4aa0c0401824a3240690006c491805b92340ee13b0a32406108400004014898203b0a32406108420006968d6f6ef3b000523a79800290808f9064aa8d15c19b4032406917868e00c901a44a141000a1005d2b2c61ae35b728504b48552cb1872e7c3c443b80f9944314be83f86267e6a778804184095142083fd131d91f40621412c251528504209350015180315986480d2000d880d51576041055903b8fc4915fb10c7f1109250600714076186480c2108400653109763ba002924980025480889064aa95102241)) (M w148 (S (K 15 nt 0xb0327006480d22d0cde0192034896decd37cfff7de96decd37cfff7df1ed19ef9bbcf7ff9ed19ef9bbcf9082296ae248ad7bc9a276ecfe8b56d0b09ff153cf9b4f72c0c188604038e40840acb186b8d6dc9d2d0b7f17192dfe5c58b926139f4fc01c6169d3838ea11c6514b5712456bde4d10c52f944edda4081a40941077a6879730621811f2154b2c61ca1a060a1920330604b0945461a060a192033060420935002e135601ac55d816215640ee443803240691039431920348003123a87140559c6480c21084000f7f1f5f98de2800a51ab3000521014220c97d2f2) (K 15 nt 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))))
theorem v2:V s5:=(S (K 16 nt 0x24806921f043ea8fa1944a0c0441834a32406903e9198026113624ed1040324069113c601920330a237e6f88ad7bc9a218a5f28b56d0b0434a07fc225772459f386200358b6a012536862e00c901a444f0cc032406611f321dc0788973e01f9a9de21fc31344314be841a50900f32891e010c59340620040c882015720340461ca1986071920330674209392ca14600e444dcef0c0c3240660dc84126a5948ed71461834e32406008062600e46ac310038100fb2098a41dc474046480c2109292bda3ee46c0017b19d6b9e48087c1807140651c6480c210840016f54dfaf1c00290f980025480b8106454811212) (S (S (K 14 nt 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) (K 14 nt 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)) (K 15 nt 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)))
theorem v3:V s4:=(S (S (K 19 nt 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) (M w28 (S (K 17 nt 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) v2))) (K 14 nt 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))
theorem v4:V s2:=(S (P w24 (S (K 19 nt 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) (S (K 18 nt 0xb9e510c901a4102187286219206480cc1250824f43ea40d43240c9019808a1049e87d0033900e1226c49c3370640192034895c19086480d2000d88c395018906480cc1250824e498a4406a71920330114209392620062201ae44dce1886a619203301142093526214496a2e78562e7e4d483ceeb7a75a98a6004ffef88883cb8f28c8eca3d9104c901881142083d072464188050080e81036720ee24b42324061084318f7fecf376c000002072d300e2852d50c901842108002c62f595631ec20042b75d300e200b4202e241902a0448492900a) v1))) v3)
private def zz453:"s01c5"="s01c5":=by decide+kernel
theorem v5:V s0:=(S v0 v4)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v5
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case15
private def zz2159:"s086f"="s086f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l25 l27 l29 l30 l33 l35 l37 l4 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7ca7d0983, -0x2cb416090, -0x196c8a344,0x1522ce], ![-0x2cb416090, -0x15827ed2b3,0x6cac3e26a, -0x1c18686bd], ![-0x196c8a344,0x6cac3e26a, -0x14dd8e48bc,0x42973263c], ![0x1522ce, -0x1c18686bd,0x42973263c, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x975dd2f7,l6),(0x22448f01f,l4),(0x20d49ff4,l10),(0x1a3dc6,l14),(-0x6627b4e7,l17),(0x3922eafd1,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x30e392,l25),(0x536ac3d,l30),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x1cb750,l46),(0x165a0bc00,l51),(-0x105630e9b,l62),(0xd9b40,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x105630e9b,l62),(0x3922eafd1,l15),(-0x975dd2f7,l6),(0x22448f01f,l4),(-0x6627b4e7,l17),(0x20d49ff4,l10),(0x536ac3d,l30),(-0x30e392,l25),(-0x1cb750,l46),(0x1a3dc6,l14),(0xd9b40,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case16" = "QuadFull30Case16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case16
private def zz2160:"s0870"="s0870":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l25 l27 l29 l33 l35 l37 l4 l41 l43 l44 l46 l51 l6 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x342cece0c, -0x2cb416090, -0x191a376e6,0x14810a762], ![-0x2cb416090, -0xba9f572c8,0x4d555df36, -0x1c7fc70e4], ![-0x191a376e6,0x4d555df36, -0x14dd8e48bc,0x42973263c], ![0x14810a762, -0x1c7fc70e4,0x42973263c, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(-0x975dd2f7,l6),(0x22448f01f,l4),(0x20d49ff4,l10),(0xeb07ffb0,l14),(0x65889cfa2,l12),(-0x6c1fe5eb,l17),(0x3a6b1aa75,l15),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x1e342a174,l25),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(-0x2f2aba8f,l43),(-0x36607e6b4,l41),(-0x20400684,l46),(-0x1d0b02e4,l44),(0x165a0bc00,l51),(-0xa2a55f73,l62),(0x8adfd4da,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x1e342a174,l25),(0x65889cfa2,l12),(0xeb07ffb0,l14),(0x3a6b1aa75,l15),(-0x36607e6b4,l41),(-0xa2a55f73,l62),(-0x975dd2f7,l6),(0x8adfd4da,l64),(0x22448f01f,l4),(-0x6c1fe5eb,l17),(-0x2f2aba8f,l43),(0x20d49ff4,l10),(-0x20400684,l46),(-0x1d0b02e4,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x184510480884012461c418600b95006], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFull30Case17" = "QuadFull30Case17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFull30Case17
private def zz2161:"s0871"="s0871":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz457:"s01c9"="s01c9":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case18
private def zz2162:"s0872"="s0872":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFull30Case19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFull30Case19
private def zz2163:"s0873"="s0873":=by decide+kernel
end 
section 
namespace Green24Proof.Full30Rows
open QuadraticCertificates ExpressionCertificates FullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decode [0x101b203dceb9480718d963205faf8a039e8d2ae07e2779ae58003b38cefa606e203dceb948009e6858601e203dceb94800dd4c7abc66203dceb948004c4bdde07a22fd7c28001aad3c8ee01a203dceb94800da6d48e8a2209c4da8021f2fa07d201eeb5ca8007b8e9faf606d23bcdb2c0049a91b5de01d203dceb94801eb1f9d4a25201eeb5ca800ce1b1848207920ef3acd001d9da01923bcdb2c00eadea1217ebe18001e7a280f607c27a898006f9faa24203dceb94800dcb90da9a07823bcdb2c003acc1f6c20207b9d6a81af4ceb614]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107ea01eeb5ca800dcbe6abfe6a03dceb94800dcdb5f9de07aa17ebe18001ac9eafaa2a01eeb5ca8006dee8efb6763d84c002363d84c00207e65faf84800683e3ffca02e603dceb948021e491c0f201e601eeb5ca8007aeb2ecc26601eeb5ca8003dcb788aa07a62fd7c2801baa9e02a62fd7c2800b80b6265faf8480079fc7a3ea563d84c002163d84c00207f203dceb94800ef2868cda06f203dceb948021d0fbd6da01f217ebe18001c2c7aeca7203dceb948019c1f6f38e07b20bf5f0c002c8e214]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decode [0x12301eeb5ca8012afc39a03d303dceb948008d6ffa9da06d309c4da8001c6a29605d301eeb5ca8001818086c25301eeb5ca8031d2eab603930ef3acd001d9da05933bcdb2c00eadea1303dceb948058cfaa03c33bcdb2c001e7ccfe4301eeb5ca800efdbec6032fd7c28003ccb8b67e3d84c0023e3d84c00207fa3bcdb2c001eb83fff606fa5faf848006e2b5e8be01fa01eeb5ca800f8d85a1ba7a03dceb948019e3c7ea9207ba03e8a4806bbe01ba03dceb948001c3c7923a5faf8480079fabd9f614]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decode [0x102e7779ae5801cf19eee05e73bcdb2c0018dd9aaee67779ae58001dcd2b8c603a72fd7c2801baa9e06a72fd7c2800b80b62701eeb5ca80058282573d84c002173d84c00203f307b9d6a811bc9d9a06f303dceb948051a889c605f301eeb5ca80018196d8f27303dceb948063f8ef9e03b30bf5f0c002c8e205b303dceb9480718d963307b9d6a8019aca03e31de6d9a05982ee05e303dceb94800eedd49e6301eeb5ca8013abf2da07a303dceb94800acadcfa01a303dceb94800895aeee14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decode [0x15003dceb948006c7fbcd9607c0779ae58001daede602c0779ae58001f8e5e205c03bcdb2c00efbfe401ec2a0027f3d84c0023f3d84c00203fb01eeb5ca8004b4be92b606fb03dceb948061afc5be05fb03dceb948001edafa3967b03dceb948058e7889a03bb03e8a4806bbe05bb03dceb948001c3c7923b779ae58024fdb203eb03dceb94800affafee6b01eeb5ca8010f68ed22b01bede880ff0c2773d84c002373d84c00203e703dceb948001d1f0b5aa14]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decode [0x15801eeb5ca8003a498a9e207c83bcdb2c07af0be02c803dceb94800982ccca05c801eeb5ca8055e4ae481ec2a002741ec2a002641ec2a002541ec2a002441ec2a00203f0779ae5800183a99ffa02f003dceb948016ec97eaea05f003dceb948012f5eecbee7001eeb5ca8003a485e4e207e03bcdb2c066a5ca02e009c4da8013eca205e001eeb5ca8056fcaa601ec2a00203d02fd7c28034fd8dce02d0779ae58005dab68f8a05d003dceb948012f5a6afbe14]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1412fd7c28002fa03812fd7c28001a394a2b602811de6d9a06f8aaef6058101eeb5ca80299ec0f60103dceb94801dc67c1ec2a0026c1ec2a0025c1ec2a0024c1ec2a00203f817ebe1801985babe02f8779ae58005e29fb7fe05f801eeb5ca8009b9c98aca7803dceb948006c0fff7e607e85faf848001cdee8202e85faf848001edabf205e803dceb9480019db5ae681ec2a00203d803dceb948003f4e7ac8e02d803dceb9480178fe4a89a05d803dceb94801380d7db8614]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decode [0x105892fd7c28001a3afa6ee091ec2a00203f503dceb948005f2d5ea9e02f5779ae580098885a29e01f503dceb948014aaaafde67501eeb5ca800dfdfea8de01b503dceb948020d698bab635779ae58006f89185ca551ec2a002151ec2a00202e103dceb948026f984b8ce05e103dceb94800dc1ff97d6613bcdb2c004b1a1de03a103dceb948053b5b0fa02a103dceb9480268bd1eab605a103dceb94800ce2bdd3ce211ec2a00203c15faf848002cfde83de02c1779ae58003acdeb9b205c105faf8a061e99e14]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decode [0x103dd03dceb948005fff7f9da02dd01eeb5ca8011e6f3efda01dd03dceb948016a0f8ecba5d09c4da80449bd5a2019d05faf8a034a79bae1d779ae58006f883e1ba03e903dceb94800d83a0e3aa02e90ef3acd0369becca05e9779ae58013a8b6ba69779ae58007b203a901eeb5ca8006b086cac602a901eeb5ca8006fac7f1de05a9779ae58016c8d18629779ae58007b203c909c4da8021e1ce02c903dceb948026edaaf8ce05c903dceb94800dc8eda5a64903dceb948028a6f2fa038903dceb94804cabe9aa028903dceb9480268bd1eab614]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1089403e8a402010101000102010008921de6d9a001e1fbfdc2089001eeb5ca8066c28a088f010208882fd7c28042eeb6fa08871de6d9a001aad8baee088401eeb5ca80049dfecade08831de6d9a001aad8baee088003dceb948008c3f0f98a7d1ec2a0023d1ec2a0020b]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFull30Case0.base QuadFull30Case0.hinges QuadFull30Case0.normalizationDenominator
private def zz458:"s01ca"="s01ca":=by decide+kernel
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case0.base QuadFull30Case0.hinges QuadFull30Case0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFull30Case1.base QuadFull30Case1.hinges QuadFull30Case1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case1.base QuadFull30Case1.hinges QuadFull30Case1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFull30Case2.base QuadFull30Case2.hinges QuadFull30Case2.normalizationDenominator
private def zz459:"s01cb"="s01cb":=by decide+kernel
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case2.base QuadFull30Case2.hinges QuadFull30Case2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFull30Case3.base QuadFull30Case3.hinges QuadFull30Case3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case3.base QuadFull30Case3.hinges QuadFull30Case3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFull30Case4.base QuadFull30Case4.hinges QuadFull30Case4.normalizationDenominator
private def zz460:"s01cc"="s01cc":=by decide+kernel
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case4.base QuadFull30Case4.hinges QuadFull30Case4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFull30Case5.base QuadFull30Case5.hinges QuadFull30Case5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case5.base QuadFull30Case5.hinges QuadFull30Case5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFull30Case6.base QuadFull30Case6.hinges QuadFull30Case6.normalizationDenominator
private def zz461:"s01cd"="s01cd":=by decide+kernel
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case6.base QuadFull30Case6.hinges QuadFull30Case6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFull30Case7.base QuadFull30Case7.hinges QuadFull30Case7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case7.base QuadFull30Case7.hinges QuadFull30Case7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFull30Case8.base QuadFull30Case8.hinges QuadFull30Case8.normalizationDenominator
private def zz462:"s01ce"="s01ce":=by decide+kernel
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case8.base QuadFull30Case8.hinges QuadFull30Case8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFull30Case9.base QuadFull30Case9.hinges QuadFull30Case9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case9.base QuadFull30Case9.hinges QuadFull30Case9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r16,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFull30Case10.base QuadFull30Case10.hinges QuadFull30Case10.normalizationDenominator
private def zz463:"s01cf"="s01cf":=by decide+kernel
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case10.base QuadFull30Case10.hinges QuadFull30Case10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFull30Case11.base QuadFull30Case11.hinges QuadFull30Case11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case11.base QuadFull30Case11.hinges QuadFull30Case11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFull30Case12.base QuadFull30Case12.hinges QuadFull30Case12.normalizationDenominator
private def zz464:"s01d0"="s01d0":=by decide+kernel
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case12.base QuadFull30Case12.hinges QuadFull30Case12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFull30Case13.base QuadFull30Case13.hinges QuadFull30Case13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case13.base QuadFull30Case13.hinges QuadFull30Case13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFull30Case14.base QuadFull30Case14.hinges QuadFull30Case14.normalizationDenominator
private def zz465:"s01d1"="s01d1":=by decide+kernel
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case14.base QuadFull30Case14.hinges QuadFull30Case14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFull30Case15.base QuadFull30Case15.hinges QuadFull30Case15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case15.base QuadFull30Case15.hinges QuadFull30Case15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFull30Case16.base QuadFull30Case16.hinges QuadFull30Case16.normalizationDenominator
private def zz466:"s01d2"="s01d2":=by decide+kernel
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case16.base QuadFull30Case16.hinges QuadFull30Case16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFull30Case17.base QuadFull30Case17.hinges QuadFull30Case17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case17.base QuadFull30Case17.hinges QuadFull30Case17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFull30Case18.base QuadFull30Case18.hinges QuadFull30Case18.normalizationDenominator
private def zz467:"s01d3"="s01d3":=by decide+kernel
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case18.base QuadFull30Case18.hinges QuadFull30Case18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFull30Case19.base QuadFull30Case19.hinges QuadFull30Case19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFull30Case19.base QuadFull30Case19.hinges QuadFull30Case19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFull30Case19.nonnegative x hx
def pair20:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_20_base LocalFull30Pairs.compact_full30_pair_20_hinges
private def zz468:"s01d4"="s01d4":=by decide+kernel
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFull30Pairs.full30_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_20_base LocalFull30Pairs.compact_full30_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFull30Pairs.full30_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_21_base LocalFull30Pairs.compact_full30_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
private def zz469:"s01d5"="s01d5":=by decide+kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFull30Pairs.full30_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_21_base LocalFull30Pairs.compact_full30_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFull30Pairs.full30_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 1 false
def pair22Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_22_base LocalFull30Pairs.compact_full30_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFull30Pairs.full30_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_22_base LocalFull30Pairs.compact_full30_pair_22_hinges x
private def zz470:"s01d6"="s01d6":=by decide+kernel
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFull30Pairs.full30_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_23_base LocalFull30Pairs.compact_full30_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFull30Pairs.full30_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_23_base LocalFull30Pairs.compact_full30_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFull30Pairs.full30_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_24_base LocalFull30Pairs.compact_full30_pair_24_hinges
private def zz471:"s01d7"="s01d7":=by decide+kernel
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFull30Pairs.full30_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_24_base LocalFull30Pairs.compact_full30_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFull30Pairs.full30_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_25_base LocalFull30Pairs.compact_full30_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
private def zz472:"s01d8"="s01d8":=by decide+kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFull30Pairs.full30_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_25_base LocalFull30Pairs.compact_full30_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFull30Pairs.full30_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_26_base LocalFull30Pairs.compact_full30_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFull30Pairs.full30_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_26_base LocalFull30Pairs.compact_full30_pair_26_hinges x
private def zz473:"s01d9"="s01d9":=by decide+kernel
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFull30Pairs.full30_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (3) (1 / 0x186a0) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_27_base LocalFull30Pairs.compact_full30_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFull30Pairs.full30_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_27_base LocalFull30Pairs.compact_full30_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFull30Pairs.full30_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_28_base LocalFull30Pairs.compact_full30_pair_28_hinges
private def zz474:"s01da"="s01da":=by decide+kernel
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFull30Pairs.full30_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_28_base LocalFull30Pairs.compact_full30_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFull30Pairs.full30_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_29_base LocalFull30Pairs.compact_full30_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
private def zz475:"s01db"="s01db":=by decide+kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFull30Pairs.full30_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_29_base LocalFull30Pairs.compact_full30_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFull30Pairs.full30_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_30_base LocalFull30Pairs.compact_full30_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFull30Pairs.full30_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_30_base LocalFull30Pairs.compact_full30_pair_30_hinges x
private def zz476:"s01dc"="s01dc":=by decide+kernel
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFull30Pairs.full30_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_31_base LocalFull30Pairs.compact_full30_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFull30Pairs.full30_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_31_base LocalFull30Pairs.compact_full30_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFull30Pairs.full30_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_32_base LocalFull30Pairs.compact_full30_pair_32_hinges
private def zz477:"s01dd"="s01dd":=by decide+kernel
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFull30Pairs.full30_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_32_base LocalFull30Pairs.compact_full30_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFull30Pairs.full30_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (3) (1 / 0x186a0) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_33_base LocalFull30Pairs.compact_full30_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
private def zz478:"s01de"="s01de":=by decide+kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFull30Pairs.full30_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_33_base LocalFull30Pairs.compact_full30_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFull30Pairs.full30_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (3) (1 / 0x186a0) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_34_base LocalFull30Pairs.compact_full30_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFull30Pairs.full30_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_34_base LocalFull30Pairs.compact_full30_pair_34_hinges x
private def zz479:"s01df"="s01df":=by decide+kernel
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFull30Pairs.full30_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (3) (1 / 0x186a0) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_35_base LocalFull30Pairs.compact_full30_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFull30Pairs.full30_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_35_base LocalFull30Pairs.compact_full30_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFull30Pairs.full30_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (3) (1 / 0x186a0) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_36_base LocalFull30Pairs.compact_full30_pair_36_hinges
private def zz480:"s01e0"="s01e0":=by decide+kernel
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFull30Pairs.full30_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_36_base LocalFull30Pairs.compact_full30_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFull30Pairs.full30_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (3) (1 / 0x186a0) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_37_base LocalFull30Pairs.compact_full30_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
private def zz481:"s01e1"="s01e1":=by decide+kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFull30Pairs.full30_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_37_base LocalFull30Pairs.compact_full30_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFull30Pairs.full30_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (3) (1 / 0x186a0) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_38_base LocalFull30Pairs.compact_full30_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFull30Pairs.full30_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_38_base LocalFull30Pairs.compact_full30_pair_38_hinges x
private def zz482:"s01e2"="s01e2":=by decide+kernel
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFull30Pairs.full30_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (3) (1 / 0x186a0) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFull30Pairs.compact_full30_pair_39_base LocalFull30Pairs.compact_full30_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFull30Pairs.full30_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFull30Pairs.compact_full30_pair_39_base LocalFull30Pairs.compact_full30_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFull30Pairs.full30_pair_39_nonneg (hx 0) (hx 1)
private def zz483:"s01e3"="s01e3":=by decide+kernel
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (3) (1 / 0x186a0) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.Full30Rows
private def zz2164:"s0874"="s0874":=by decide+kernel
end 
section 
namespace Green24Proof.Full30Cyclic
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseSymmetry FullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack Full30Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact Full30Rows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse Full30Rows.rows p q same x]
    exact Full30Rows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 3 (1 / 0x186a0) Full30Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact Full30Rows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 3 (1 / 0x186a0) Full30Rows.rows p q same x]
    exact Full30Rows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
private def zz484:"s01e4"="s01e4":=by decide+kernel
theorem rows_admissible:rowsAdmissible Full30Rows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials Full30Rows.rows
theorem remaining_rows_count:remainingRows.length = 9:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
      weightedAggregate 3 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack Full30Rows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 3 (1 / 0x186a0) Full30Rows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 3 h4 h3 h5 g Full30Rows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
    weightedAggregate 3 h4 h3 g (stripPotentials Full30Rows.rows) + 4 * deficit g
  linarith
end Green24Proof.Full30Cyclic
private def zz2165:"s0875"="s0875":=by decide+kernel
end 
section 
namespace Green24Proof.Full30Mass
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows
theorem remainingRows_eq:Full30Cyclic.remainingRows = [
  ((0x443e1e45 / 0x3b9aca00), .balance 0 (1)),
  ((0xaab0eb7 / 0x3b9aca0), .balance 1 (-1)),
  ((0x21dfd2af / 0x1dcd6500), .balance 2 (1)),
  ((0xaab0eb7 / 0x3b9aca0), .balance 3 (-1)),
  ((0x42dcdbd / 0x5f5e100), .child 0),
  (1, .heightChild 1),
  ((0xcd085 / 0x1dcd6500), .ordered 0),
  ((0xe1f7f61 / 0x3b9aca0), .massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((1 / 0xf424), .normalization)]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff PackedPhaseRowsEquality.labelEq PackedPhaseRowsEquality.labelEq_iff _ _).mp
  decide +kernel
def oddDifference:Phase → ℚ:=fun p => (![0,1,0, -1]:Fin 4 → ℚ) p
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  ((0x443e1e45 / 0x3b9aca00:ℝ) * phaseTotal h4 g 0 +
    (0x21dfd2af / 0x1dcd6500:ℝ) * phaseTotal h4 g 2 -
    (0xaab0eb7 / 0x3b9aca0:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) *
  (phaseTotal h4 g 0 + phaseTotal h4 g 2 -
    (3:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
private def zz485:"s01e5"="s01e5":=by decide+kernel
theorem weighted_remaining_eq {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    weightedAggregate (3) h4 h3 g Full30Cyclic.remainingRows =
      balanceMass h4 g +
      (0x42dcdbd / 0x5f5e100:ℝ) * rowAggregate (3) h4 h3 g (.child 0) +
      rowAggregate (3) h4 h3 g (.heightChild 1) +
      (0xcd085 / 0x1dcd6500:ℝ) * rowAggregate (3) h4 h3 g (.ordered 0) +
      (0xe1f7f61 / 0x3b9aca0:ℝ) * rowAggregate (3) h4 h3 g (.massSquare false oddDifference) +
      (1 / 0xf424:ℝ) * mass g ^ 2:=by
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_balance,rowAggregate_normalization]
  norm_num
  unfold balanceMass oddDifference
  ring
noncomputable def meanBalance {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  ((0x87fdc3a3 / 0x77359400:ℝ) * (phaseTotal h4 g 0 + phaseTotal h4 g 2) -
    (0xaab0eb7 / 0x3b9aca0:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) *
  (phaseTotal h4 g 0 + phaseTotal h4 g 2 - 3 * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
theorem balanceMass_le_mean {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      3 * (phaseTotal h4 g 1 + phaseTotal h4 g 3)):balanceMass h4 g ≤ meanBalance h4 g:=by
  have hp:=mul_nonpos_of_nonneg_of_nonpos (sub_nonneg.mpr horder) (sub_nonpos.mpr hhigh)
  unfold balanceMass meanBalance
  nlinarith
noncomputable def massPolynomial (U V:ℝ):ℝ :=
  (-0x87fd0823 / 0x1dcd65000:ℝ) * U ^ 2 +
  (0x2ed5c98c9 / 0x1dcd65000:ℝ) * U * V - (0x20012649 / 0xee6b280:ℝ) * V ^ 2
theorem massPolynomial_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(0xfb / 0x64:ℝ) * V ≤ U) (hhigh:U ≤ 3 * V) :
    (0x885c3c01 / 0x48c273950000:ℝ) * V ^ 2 ≤ massPolynomial U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  unfold massPolynomial
  nlinarith
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (3:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate (3) h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate (3) h4 h3 g (.heightChild 1) ≤ 0) :
    weightedAggregate (3) h4 h3 g Full30Cyclic.remainingRows ≤ meanBalance h4 g + (1 / 0xf424:ℝ) * mass g ^ 2:=by
  rw [weighted_remaining_eq]
  have hb:=balanceMass_le_mean h4 g horder hhigh
  have ho:rowAggregate (3) h4 h3 g (.ordered 0) ≤ 0 :=
    rowAggregate_ordered_nonpos (3) h4 h3 g hg 0 (by simpa using horder)
  have hm:=rowAggregate_massSquare_nonpos (3) h4 h3 g oddDifference
  linarith
private def zz486:"s01e6"="s01e6":=by decide+kernel
theorem deficit_lower_bound_of_child_rows {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (horder:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hlow:(0xfb / 0x64:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤
      phaseTotal h4 g 0 + phaseTotal h4 g 2)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (3:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate (3) h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate (3) h4 h3 g (.heightChild 1) ≤ 0) :
    (0x885c3c01 / 0x48c273950000:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ^ 2 ≤ deficit g:=by
  have hc:=Full30Cyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg horder hhigh hchild hheight
  have hm:mass g = (phaseTotal h4 g 0 + phaseTotal h4 g 2) +
      (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    simpa only [add_assoc,add_comm,add_left_comm] using (phaseTotal_sum h4 g).symm
  have hp:massPolynomial (phaseTotal h4 g 0 + phaseTotal h4 g 2)
      (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ deficit g:=by
    rw [hm] at hc hr
    unfold meanBalance at hr
    unfold massPolynomial
    nlinarith
  exact (massPolynomial_lower_bound
    (add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)) hlow hhigh).trans hp
end Green24Proof.Full30Mass
private def zz2166:"s0876"="s0876":=by decide+kernel
end 
section 
namespace Green24Proof.Full30ProfileInterval
open FullPhaseRows FullPhaseAggregation PhaseMassRows ChildRows HeightChildRows
theorem interval_bound_of_height {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hh:(49 / 0xfa:ℝ) * energy v - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) v 0 - classMass (ZMod.castHom h2 (ZMod 2)) v 1) ^ 2 ≤ deficit v)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hlow:(0xfb / 0x64:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (3:ℝ) * mass v) :
    (0x885c3c01 / 0x48c273950000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    have ht:=phaseTotal_sum h4 (interleave u v)
    rw [mass_interleave] at ht
    linarith
  have hchild:rowAggregate (3) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have hheight:=rowAggregate_height_odd_nonpos (3) h4 h3 h2 u v hu hv hh
  have hc:=Full30Mass.deficit_lower_bound_of_child_rows h4 h3 h5 (interleave u v) hg horder
    (by rw [hU,hV]; exact hlow) (by rw [hU,hV]; exact hhigh) hchild hheight
  simpa only [hV] using hc
theorem interval_bound_ordered {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hlow:(0xfb / 0x64:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (3:ℝ) * mass v) :
    (0x885c3c01 / 0x48c273950000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  exact interval_bound_of_height h4 h3 h5 h2 u v hu hv ih
    (HeightStrong.strong_height_bound h2 h3m h5m v hv) horder hlow hhigh
theorem interval_bound {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(0xfb / 0x64:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (3:ℝ) * mass v) :
    (0x885c3c01 / 0x48c273950000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,horder⟩:=ProfileOrientation.orient_even_child h4 u v hu hv
  have hb:=interval_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih horder
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hU,hV,hd] using hb
end Green24Proof.Full30ProfileInterval
private def zz2167:"s0877"="s0877":=by decide+kernel
end 
section 
namespace Green24Proof.FullPhaseIntervals
private def zz487:"s01e7"="s01e7":=by decide+kernel
theorem interval_49_20_to_three {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(49 / 20:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ 3 * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (27 / 10:ℝ) * mass v
  · have hb:=Full27ProfileInterval.interval_bound h4 h3 h5 h2 u v hu hv ih hlow h
    exact (mul_nonneg (by norm_num) (sq_nonneg (mass u + mass v))).trans hb
  · have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
    have hl:(0xfb / 0x64:ℝ) * mass v ≤ mass u:=by linarith
    have hb:=Full30ProfileInterval.interval_bound h4 h3 h5 h2 u v hu hv ih hl hhigh
    exact (mul_nonneg (by norm_num) (sq_nonneg (mass v))).trans hb
end Green24Proof.FullPhaseIntervals
private def zz2168:"s0878"="s0878":=by decide+kernel
end 
section 
namespace Green24Proof.ParityCover
theorem low_coercivity {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (11 / 10:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (21 / 20:ℝ) * mass v
  · exact ParityNineteenTwentieths.coercivity h3 h5 u v hu hv hd hlow h
  · exact ParityNineTenths.coercivity h3 h5 u v hu hv hd (by linarith) hhigh
theorem interval_103_100_to_249_100 {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (0xf9 / 0x64:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (11 / 10:ℝ) * mass v
  · exact (mul_nonneg (by norm_num) (sq_nonneg _)).trans (low_coercivity h3 h5 u v hu hv hd hlow h)
  · by_cases htwo:mass u ≤ 2 * mass v
    · exact ParityIntervals.interval_eleven_tenths_to_two h3 h5 u v hu hv hd (by linarith) htwo
    · exact ParityTwoFifths.interval_nonneg h3 h5 u v hu hv hd (by linarith) hhigh
theorem coercivity_103_100_to_eleven_fifths {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (11 / 5:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ (11 / 10:ℝ) * mass v
  · exact low_coercivity h3 h5 u v hu hv hd hlow h
  · by_cases hmid:mass u ≤ (0x18d / 0xc8:ℝ) * mass v
    · exact ParityIntervals.coercivity_eleven_tenths_to_397_200 h3 h5 u v hu hv hd (by linarith) hmid
    · exact ParityTwoFifths.coercivity h3 h5 u v hu hv hd (by linarith) hhigh
private def zz488:"s01e8"="s01e8":=by decide+kernel
theorem near_balance_coercivity {U V du dg:ℝ} (hV:0 ≤ V) (horder:V ≤ U)
    (hratio:U ≤ (40 / 37:ℝ) * V) (hd:0 ≤ du) (hc:NearBalanceHypothesis U V du dg) :
    (1 / 0x12c:ℝ) * (U - V) ^ 2 ≤ dg:=by
  rcases hV.eq_or_lt with hz | hp
  · have hU:U = 0:=by linarith
    have h:=hc 0 (by norm_num) (by norm_num)
    simpa [hU, ← hz] using h
  · have h:=near_balance_descent hp horder hratio hc
    have hretained:0 ≤ (16 * (U - V) ^ 2 / (9 * U ^ 2)) * du:=by positivity
    nlinarith [sq_nonneg (U - V)]
theorem coercivity_to_eleven_fifths_of_near_balance {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ (11 / 5:ℝ) * mass v)
    (hc:NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v))) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v):=by
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  by_cases h:mass u ≤ (40 / 37:ℝ) * mass v
  · exact near_balance_coercivity hV horder h hd hc
  · exact coercivity_103_100_to_eleven_fifths h3 h5 u v hu hv hd (by linarith) hhigh
theorem interval_103_100_to_three {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(0x67 / 0x64:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ 3 * mass v) :
    0 ≤ deficit (interleave u v):=by
  have hm:0 < m:=NeZero.pos m
  have hd:0 ≤ deficit u:=ih m (by omega) (dvd_mul_left m 2) u hu
  by_cases h:mass u ≤ (0xf9 / 0x64:ℝ) * mass v
  · exact interval_103_100_to_249_100 h3 h5 u v hu hv hd hlow h
  · have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
    exact FullPhaseIntervals.interval_49_20_to_three h4 h3 h5 h2 u v hu hv ih (by linarith) hhigh
theorem interval_to_three_of_near_balance {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 3 * mass v)
    (hc:NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v))) :
    0 ≤ deficit (interleave u v):=by
  have hm:0 < m:=NeZero.pos m
  have hd:0 ≤ deficit u:=ih m (by omega) (dvd_mul_left m 2) u hu
  have hV:0 ≤ mass v:=Finset.sum_nonneg fun i _ => hv i
  by_cases h:mass u ≤ (40 / 37:ℝ) * mass v
  · exact near_balance_nonneg hV horder h hd hc
  · exact interval_103_100_to_three h4 h3 h5 h2 u v hu hv ih (by linarith) hhigh
end Green24Proof.ParityCover
private def zz2169:"s0879"="s0879":=by decide+kernel
end 
section 
namespace Green24Proof.NatBacksubRecoveredQuadraticCertificates
open IntegerQuadraticCertificates (Linear Quadratic Point linearEq linearEq_eq_true
  linearEval linearEval_zero linearEval_add linearEval_smul linearEval_neg product
  quadraticEval quadraticEval_zero quadraticEval_add quadraticEval_smul quadraticEval_product
  Hinges hingeEval positive_step negative_step)
abbrev Combination:=List (ℤ × ℕ)
def combine (C:ℕ → Linear) (w:Combination):Linear :=
  (w.map fun t => t.1 • C t.2).sum
def nonnegativeWeights (w:Combination):Bool :=
  w.all fun t => decide (0 ≤ t.1)
private def zz489:"s01e9"="s01e9":=by decide+kernel
theorem combine_nonneg (C:ℕ → Linear) (w:Combination) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:nonnegativeWeights w = true) :
    0 ≤ linearEval (combine C w) x:=by
  induction w with
  | nil => simp [combine,linearEval_zero]
  | cons t ts ih =>
    simp only [nonnegativeWeights,List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [combine,List.map_cons,List.sum_cons,linearEval_add,linearEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (hC t.2)) (ih hw.2)
inductive NonnegativeTerm where
  | square (a:Linear)
  | pair (i j:ℕ)
def termMatrix (C:ℕ → Linear):NonnegativeTerm → Quadratic
  | .square a => product a a
  | .pair i j => product (C i) (C j)
theorem termMatrix_nonneg (C:ℕ → Linear) (t:NonnegativeTerm)
    (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termMatrix C t) x:=by
  cases t with
  | square a => simpa only [termMatrix,quadraticEval_product, ← sq] using sq_nonneg (linearEval a x)
  | pair i j => simpa only [termMatrix,quadraticEval_product] using mul_nonneg (hC i) (hC j)
abbrev Decomposition:=List (ℤ × NonnegativeTerm)
def decompositionMatrix (C:ℕ → Linear) (d:Decomposition):Quadratic :=
  (d.map fun t => t.1 • termMatrix C t.2).sum
def decompositionCheck (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition):Bool :=
  decide (0 < s) && (d.all fun t => decide (0 ≤ t.1)) &&
    QuadraticCoefficientCheck.coefficientEq (decompositionMatrix C d) (s • Q)
theorem decomposition_nonneg (C:ℕ → Linear) (d:Decomposition) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun t => decide (0 ≤ t.1)) = true) :
    0 ≤ quadraticEval (decompositionMatrix C d) x:=by
  induction d with
  | nil => simp [decompositionMatrix,quadraticEval_zero]
  | cons t ts ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionMatrix,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using
      add_nonneg (mul_nonneg (by exact_mod_cast hw.1) (termMatrix_nonneg C t.2 x hC)) (ih hw.2)
theorem decompositionCheck_sound (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:decompositionCheck C Q s d = true):0 ≤ quadraticEval Q x:=by
  simp only [decompositionCheck,Bool.and_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d x hC h.1.2
  rw [QuadraticCoefficientCheck.coefficientEq_eval_eq _ _ h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
def combinationCheck (C:ℕ → Linear) (s:ℤ) (w:Combination)
    (a:Linear):Bool :=
  decide (0 < s) && nonnegativeWeights w && linearEq (combine C w) (s • a)
private def zz490:"s01ea"="s01ea":=by decide+kernel
theorem combinationCheck_sound (C:ℕ → Linear) (s:ℤ) (w:Combination)
    (a:Linear) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:combinationCheck C s w a = true):0 ≤ linearEval a x:=by
  simp only [combinationCheck,Bool.and_eq_true,linearEq_eq_true,decide_eq_true_eq] at h
  have ha:=combine_nonneg C w x hC h.1.2
  rw [h.2,linearEval_smul] at ha
  exact nonneg_of_mul_nonneg_right ha (by exact_mod_cast h.1.1:(0:ℝ) < s)
abbrev WeightFormula:=List (Nat × Int)
abbrev Plan:=List (Nat × Nat × WeightFormula)
def coefficient (Q:Quadratic):Nat → Int
  | 0 => Q 0 0
  | 1 => Q 1 1
  | 2 => Q 2 2
  | 3 => Q 3 3
  | 4 => Q 0 1 + Q 1 0
  | 5 => Q 0 2 + Q 2 0
  | 6 => Q 0 3 + Q 3 0
  | 7 => Q 1 2 + Q 2 1
  | 8 => Q 1 3 + Q 3 1
  | 9 => Q 2 3 + Q 3 2
  | _ => 0
def planDecomposition (Q:Quadratic) (rows:Plan):Decomposition :=
  rows.map fun (i,j,terms) =>
    ((terms.map fun (k,multiplier) => multiplier * coefficient Q k).sum, .pair i j)
def supportDecomposition (C:Nat → Linear) (Q:Quadratic)
    (pairs:List (Nat × Nat)):Int × Decomposition :=
  match BacksubIntegerElimination.solveScaled
      (pairs.toArray.map fun (i,j) =>
        PureIntegerSupportCertificateData.pairColumn (C i) (C j))
      (PureIntegerSupportCertificateData.matrixColumn Q) with
  | none => (0,[])
  | some (scale,weights) =>
      (scale,(weights.toList.zip pairs).map fun (weight,i,j) => (weight, .pair i j))
def cons (a:Linear) (C:ℕ → Linear):ℕ → Linear
  | 0 => a
  | i + 1 => C i
theorem cons_constraints (C:ℕ → Linear) (a:Linear) (x:Point)
    (hC:∀ i,0 ≤ linearEval (C i) x) (ha:0 ≤ linearEval a x) :
    ∀ i,0 ≤ linearEval (cons a C i) x:=by
  intro i
  cases i with
  | zero => exact ha
  | succ j => exact hC j
inductive Certificate:Type where
  | support (pairs:List (Nat × Nat)):Certificate
  | plan (scale:ℤ) (rows:Plan):Certificate
  | psd:Certificate
  | leaf (scale:ℤ) (d:Decomposition):Certificate
  | split (positive negative:Certificate):Certificate
  | cut (a:Linear) (positive negative:Certificate):Certificate
  | positive (scale:ℤ) (w:Combination) (next:Certificate):Certificate
  | negative (scale:ℤ) (w:Combination) (next:Certificate):Certificate
def check (cert:Certificate) (C:ℕ → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs => check p (cons a C) Q hs && check m (cons (-a) C) Q hs
  | .support pairs,[] =>
      let (scale,d):=supportDecomposition C Q pairs
      decompositionCheck C Q scale d
  | .plan scale rows,[] => decompositionCheck C Q scale (planDecomposition Q rows)
  | .psd,[] => IntegerPSDCheck.check 4 Q
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (cons a C) (Q + c • product a a) hs &&
      check m (cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (cons a C) (Q + c • product a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) &&
      check m (cons (-a) C) Q hs
  | _,_ => false
theorem check_sound (cert:Certificate) (C:ℕ → Linear)
    (Q:Quadratic) (hs:Hinges) (x:Point) (hC:∀ i,0 ≤ linearEval (C i) x)
    (h:check cert C Q hs = true):0 ≤ quadraticEval Q x + hingeEval hs x:=by
  induction cert generalizing C Q hs with
  | support pairs =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q (supportDecomposition C Q pairs).1
          (supportDecomposition C Q pairs).2 x hC h
    | cons t ts => simp [check] at h
  | plan scale rows =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q scale (planDecomposition Q rows) x hC h
    | cons t ts => simp [check] at h
  | psd =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero,
        quadraticEval,IntegerPSDCheck.eval] using
        IntegerPSDCheck.check_sound 4 Q h x
    | cons t ts => simp [check] at h
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q s d x hC h
    | cons t ts => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a ts x ha (hp (cons a C) (Q + c • product a a) ts
          (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a ts x (le_of_not_ge ha)
          (hm (cons (-a) C) Q ts (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a ts x ha (hp (cons a C) (Q + c • product a a) ts
        (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons t ts =>
      rcases t with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a ts x ha' (hm (cons (-a) C) Q ts
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.NatBacksubRecoveredQuadraticCertificates
private def zz2170:"s087a"="s087a":=by decide+kernel
end 
section 
namespace Green24Proof.PackedNaturalCertificateData
open IntegerQuadraticCertificates (Linear)
open NatBacksubRecoveredQuadraticCertificates
abbrev Reader (α:Type):=StateT (List Nat) Option α
def fail {α:Type}:Reader α:=fun _ => none
def readByte:Reader Nat
  | [] => none
  | n :: rest =>
    if n < 256 then readByte rest
    else some (n % 256,n / 256 :: rest)
def readPacked:Nat → Reader Nat
  | 0 => fail
  | fuel + 1 => do
    let b ← readByte
    if b < 128 then return b
    else return b % 128 + 128 * (← readPacked fuel)
def readNat:Reader Nat:=readPacked 128
def readInt:Reader Int:=do
  return PureCertificateData.unzig (← readNat)
def readLinear:Reader Linear:=do
  let a ← readInt
  let b ← readInt
  let c ← readInt
  let d ← readInt
  return ![a,b,c,d]
def readCombination:Nat → Reader Combination
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let i ← readNat
    return (w,i) :: (← readCombination count)
def readTerm:Reader NonnegativeTerm:=do
  match ← readNat with
  | 0 => return .square (← readLinear)
  | 1 => return .pair (← readNat) (← readNat)
  | _ => fail
def readDecomposition:Nat → Reader Decomposition
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let t ← readTerm
    return (w,t) :: (← readDecomposition count)
def readPairs:Nat → Reader (List (Nat × Nat))
  | 0 => pure []
  | count + 1 => do
    let i ← readNat
    let j ← readNat
    return (i,j) :: (← readPairs count)
def readTree:Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree fuel) (← readTree fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree fuel) (← readTree fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree fuel)
    | 5 => return .psd
    | 6 => return .support (← readPairs (← readNat))
    | _ => fail
def decode (fuel:Nat) (chunks:List Nat):Certificate :=
  match readTree fuel chunks with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.PackedNaturalCertificateData
private def zz2171:"s087b"="s087b":=by decide+kernel
end 
section 
namespace Green24Proof.NatParametricCertificates
open IntegerQuadraticCertificates (Linear Point linearEval linearEval_neg product)
open ParametricQuadraticCertificates (Coefficient Quadratic coefficientEval quadraticEval
  quadraticEval_zero quadraticEval_add quadraticEval_smul coefficientProduct coefficientProduct_eval
  Hinges hingeEval positive_step negative_step)
open NatBacksubRecoveredQuadraticCertificates (Combination combinationCheck
  combinationCheck_sound cons cons_constraints)
def polynomialEq (Q R:Quadratic):Bool :=
  (List.finRange 3).all fun d => QuadraticCoefficientCheck.coefficientEq (Q d) (R d)
theorem polynomialEq_eval_eq (Q R:Quadratic) (h:polynomialEq Q R = true)
    (t:ℝ) (x:Point):quadraticEval Q t x = quadraticEval R t x:=by
  have hd:∀ d,QuadraticCoefficientCheck.coefficientEq (Q d) (R d) = true:=by
    simpa only [polynomialEq,List.all_eq_true,List.mem_finRange,forall_true_left] using h
  simp only [quadraticEval,
    QuadraticCoefficientCheck.coefficientEq_eval_eq (Q 0) (R 0) (hd 0),
    QuadraticCoefficientCheck.coefficientEq_eval_eq (Q 1) (R 1) (hd 1),
    QuadraticCoefficientCheck.coefficientEq_eval_eq (Q 2) (R 2) (hd 2)]
inductive NonnegativeTerm where
  | square (a b:Linear)
  | middleSquare (a:Linear)
  | pair (degree:Fin 3) (i j:ℕ)
def termPolynomial (C:ℕ → Linear):NonnegativeTerm → Quadratic
  | .square a b => ![product a a,product a b + product b a,product b b]
  | .middleSquare a => ![0,product a a,(-1:ℤ) • product a a]
  | .pair d i j =>
      let A:=product (C i) (C j)
      if d = 0 then ![A,(-2:ℤ) • A,A]
      else if d = 1 then ![0,(2:ℤ) • A,(-2:ℤ) • A]
      else ![0,0,A]
private def zz491:"s01eb"="s01eb":=by decide+kernel
theorem termPolynomial_nonneg (C:ℕ → Linear) (v:NonnegativeTerm)
    (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) :
    0 ≤ quadraticEval (termPolynomial C v) t x:=by
  have h1:0 ≤ 1 - t:=sub_nonneg.mpr ht1
  cases v with
  | square a b =>
    change 0 ≤ IntegerQuadraticCertificates.quadraticEval (product a a) x +
      t * IntegerQuadraticCertificates.quadraticEval (product a b + product b a) x +
      t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product b b) x
    simp only [IntegerQuadraticCertificates.quadraticEval_add,
      IntegerQuadraticCertificates.quadraticEval_product]
    nlinarith only [sq_nonneg (linearEval a x + t * linearEval b x)]
  | middleSquare a =>
    change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
      t * IntegerQuadraticCertificates.quadraticEval (product a a) x +
      t ^ 2 * IntegerQuadraticCertificates.quadraticEval ((-1:ℤ) • product a a) x
    simp only [IntegerQuadraticCertificates.quadraticEval_zero,
      IntegerQuadraticCertificates.quadraticEval_smul,
      IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_one]
    nlinarith only [mul_nonneg (mul_nonneg ht0 h1) (sq_nonneg (linearEval a x))]
  | pair d i j =>
    have h:=mul_nonneg (hC i) (hC j)
    by_cases hd0:d = 0
    · simp only [termPolynomial,hd0, ↓reduceIte]
      change 0 ≤ IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x +
        t * IntegerQuadraticCertificates.quadraticEval ((-2:ℤ) • product (C i) (C j)) x +
        t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x
      simp only [IntegerQuadraticCertificates.quadraticEval_smul,
        IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_ofNat]
      nlinarith only [mul_nonneg (sq_nonneg (1 - t)) h]
    · by_cases hd1:d = 1
      · simp only [termPolynomial,hd1, ↓reduceIte]
        change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
          t * IntegerQuadraticCertificates.quadraticEval ((2:ℤ) • product (C i) (C j)) x +
          t ^ 2 * IntegerQuadraticCertificates.quadraticEval ((-2:ℤ) • product (C i) (C j)) x
        simp only [IntegerQuadraticCertificates.quadraticEval_zero,
          IntegerQuadraticCertificates.quadraticEval_smul,
          IntegerQuadraticCertificates.quadraticEval_product,Int.cast_neg,Int.cast_ofNat]
        nlinarith only [mul_nonneg (mul_nonneg ht0 h1) h]
      · simp only [termPolynomial,hd0,hd1, ↓reduceIte]
        change 0 ≤ IntegerQuadraticCertificates.quadraticEval 0 x +
          t * IntegerQuadraticCertificates.quadraticEval 0 x +
          t ^ 2 * IntegerQuadraticCertificates.quadraticEval (product (C i) (C j)) x
        simpa only [IntegerQuadraticCertificates.quadraticEval_zero,
          IntegerQuadraticCertificates.quadraticEval_product,mul_zero,zero_add]
          using mul_nonneg (sq_nonneg t) h
abbrev Decomposition:=List (ℤ × NonnegativeTerm)
def decompositionPolynomial (C:ℕ → Linear) (d:Decomposition):Quadratic :=
  (d.map fun v => v.1 • termPolynomial C v.2).sum
def decompositionCheck (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition):Bool :=
  decide (0 < s) && (d.all fun v => decide (0 ≤ v.1)) &&
    polynomialEq (decompositionPolynomial C d) (s • Q)
theorem decomposition_nonneg (C:ℕ → Linear) (d:Decomposition)
    (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (hw:(d.all fun v => decide (0 ≤ v.1)) = true) :
    0 ≤ quadraticEval (decompositionPolynomial C d) t x:=by
  induction d with
  | nil => simp [decompositionPolynomial,quadraticEval_zero]
  | cons v vs ih =>
    simp only [List.all_cons,Bool.and_eq_true,decide_eq_true_eq] at hw
    simpa only [decompositionPolynomial,List.map_cons,List.sum_cons,quadraticEval_add,
      quadraticEval_smul] using add_nonneg
      (mul_nonneg (by exact_mod_cast hw.1) (termPolynomial_nonneg C v.2 t x ht0 ht1 hC))
      (ih hw.2)
theorem decompositionCheck_sound (C:ℕ → Linear) (Q:Quadratic)
    (s:ℤ) (d:Decomposition) (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:decompositionCheck C Q s d = true) :
    0 ≤ quadraticEval Q t x:=by
  simp only [decompositionCheck,Bool.and_eq_true,decide_eq_true_eq] at h
  have hd:=decomposition_nonneg C d t x ht0 ht1 hC h.1.2
  rw [polynomialEq_eval_eq _ _ h.2,quadraticEval_smul] at hd
  exact nonneg_of_mul_nonneg_right hd (by exact_mod_cast h.1.1:(0:ℝ) < s)
abbrev Supports:=Fin 3 → List (Nat × Nat)
def bernsteinPart (Q:Quadratic) (d:Fin 3):IntegerQuadraticCertificates.Quadratic :=
  if d = 0 then (2:Int) • Q 0
  else if d = 1 then (2:Int) • Q 0 + Q 1
  else (2:Int) • (Q 0 + Q 1 + Q 2)
def supportCheck (C:Nat → Linear) (Q:Quadratic) (pairs:Supports):Bool :=
  (List.finRange 3).all fun d =>
    NatBacksubRecoveredQuadraticCertificates.check (.support (pairs d)) C (bernsteinPart Q d) []
theorem supportCheck_sound (C:Nat → Linear) (Q:Quadratic) (pairs:Supports)
    (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:supportCheck C Q pairs = true) :
    0 ≤ quadraticEval Q t x:=by
  have hd:∀ d,NatBacksubRecoveredQuadraticCertificates.check
      (.support (pairs d)) C (bernsteinPart Q d) [] = true:=by
    simpa only [supportCheck,List.all_eq_true,List.mem_finRange,forall_true_left] using h
  have hpart (d:Fin 3):0 ≤ IntegerQuadraticCertificates.quadraticEval (bernsteinPart Q d) x:=by
    simpa only [IntegerQuadraticCertificates.hingeEval,List.map_nil,List.sum_nil,add_zero] using
      NatBacksubRecoveredQuadraticCertificates.check_sound (.support (pairs d)) C
        (bernsteinPart Q d) [] x hC (hd d)
  have hmiddle:0 ≤ 2 * t * (1 - t) :=
    mul_nonneg (mul_nonneg (by norm_num) ht0) (sub_nonneg.mpr ht1)
  have hsum:=add_nonneg
    (add_nonneg (mul_nonneg (sq_nonneg (1-t)) (hpart 0))
      (mul_nonneg hmiddle (hpart 1)))
    (mul_nonneg (sq_nonneg t) (hpart 2))
  have hid:(1-t)^2 * IntegerQuadraticCertificates.quadraticEval (bernsteinPart Q 0) x +
      (2*t*(1-t)) * IntegerQuadraticCertificates.quadraticEval (bernsteinPart Q 1) x +
      t^2 * IntegerQuadraticCertificates.quadraticEval (bernsteinPart Q 2) x =
      2 * quadraticEval Q t x:=by
    simp only [bernsteinPart,show (0:Fin 3) = 0 from rfl,
      show (1:Fin 3) ≠ 0 from by decide,show (2:Fin 3) ≠ 0 from by decide,
      show (1:Fin 3) = 1 from rfl,show (2:Fin 3) ≠ 1 from by decide,
      if_true,if_false,IntegerQuadraticCertificates.quadraticEval_smul,
      IntegerQuadraticCertificates.quadraticEval_add,Int.cast_ofNat,quadraticEval]
    ring
  rw [hid] at hsum
  linarith
inductive Certificate:Type where
  | support (pairs:Supports):Certificate
  | leaf (scale:ℤ) (d:Decomposition):Certificate
  | split (positive negative:Certificate):Certificate
  | cut (a:Linear) (positive negative:Certificate):Certificate
  | positive (scale:ℤ) (w:Combination) (next:Certificate):Certificate
  | negative (scale:ℤ) (w:Combination) (next:Certificate):Certificate
def check (cert:Certificate) (C:ℕ → Linear) (Q:Quadratic) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs => check p (cons a C) Q hs && check m (cons (-a) C) Q hs
  | .support pairs,[] => supportCheck C Q pairs
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (cons a C) (Q + coefficientProduct c a a) hs &&
      check m (cons (-a) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      combinationCheck C s w a &&
      check p (cons a C) (Q + coefficientProduct c a a) hs
  | .negative s w m,(_,a) :: hs =>
      combinationCheck C s w (-a) && check m (cons (-a) C) Q hs
  | _,_ => false
private def zz492:"s01ec"="s01ec":=by decide+kernel
theorem check_sound (cert:Certificate) (C:ℕ → Linear)
    (Q:Quadratic) (hs:Hinges) (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hC:∀ i,0 ≤ linearEval (C i) x) (h:check cert C Q hs = true) :
    0 ≤ quadraticEval Q t x + hingeEval hs t x:=by
  induction cert generalizing C Q hs with
  | support pairs =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        supportCheck_sound C Q pairs t x ht0 ht1 hC h
    | cons v vs => simp [check] at h
  | leaf s d =>
    cases hs with
    | nil =>
      simpa only [hingeEval,List.map_nil,List.sum_nil,add_zero] using
        decompositionCheck_sound C Q s d t x ht0 ht1 hC h
    | cons v vs => simp [check] at h
  | split p m hp hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      by_cases ha:0 ≤ linearEval a x
      · exact positive_step Q c a vs t x ha (hp (cons a C)
          (Q + coefficientProduct c a a) vs (cons_constraints C a x hC ha) h.1)
      · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
        exact negative_step Q c a vs t x (le_of_not_ge ha)
          (hm (cons (-a) C) Q vs (cons_constraints C (-a) x hC ha') h.2)
  | cut a p m hp hm =>
    simp only [check,Bool.and_eq_true] at h
    by_cases ha:0 ≤ linearEval a x
    · exact hp (cons a C) Q hs (cons_constraints C a x hC ha) h.1
    · have ha':0 ≤ linearEval (-a) x:=by rw [linearEval_neg]; linarith
      exact hm (cons (-a) C) Q hs (cons_constraints C (-a) x hC ha') h.2
  | positive s w p hp =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w a x hC h.1
      exact positive_step Q c a vs t x ha (hp (cons a C)
        (Q + coefficientProduct c a a) vs (cons_constraints C a x hC ha) h.2)
  | negative s w m hm =>
    cases hs with
    | nil => simp [check] at h
    | cons v vs =>
      rcases v with ⟨c,a⟩
      simp only [check,Bool.and_eq_true] at h
      have ha:=combinationCheck_sound C s w (-a) x hC h.1
      have ha':linearEval a x ≤ 0:=by rw [linearEval_neg] at ha; linarith
      exact negative_step Q c a vs t x ha' (hm (cons (-a) C) Q vs
        (cons_constraints C (-a) x hC ha) h.2)
end Green24Proof.NatParametricCertificates
private def zz2172:"s087c"="s087c":=by decide+kernel
end 
section 
namespace Green24Proof.PackedParametricCertificateData
open IntegerQuadraticCertificates (Linear)
open NatParametricCertificates
open PackedNaturalCertificateData (Reader fail readNat readInt readLinear readCombination readPairs)
def readDegree:Reader (Fin 3):=do
  let d ← readNat
  if h:d < 3 then return ⟨d,h⟩ else fail
def readTerm:Reader NonnegativeTerm:=do
  match ← readNat with
  | 0 => return .square (← readLinear) (← readLinear)
  | 1 => return .middleSquare (← readLinear)
  | 2 => return .pair (← readDegree) (← readNat) (← readNat)
  | _ => fail
def readDecomposition:Nat → Reader Decomposition
  | 0 => pure []
  | count + 1 => do
    let w ← readInt
    let t ← readTerm
    return (w,t) :: (← readDecomposition count)
def readTree:Nat → Reader Certificate
  | 0 => fail
  | fuel + 1 => do
    match ← readNat with
    | 0 =>
      let scale ← readInt
      let count ← readNat
      return .leaf scale (← readDecomposition count)
    | 1 => return .split (← readTree fuel) (← readTree fuel)
    | 2 =>
      let a ← readLinear
      return .cut a (← readTree fuel) (← readTree fuel)
    | 3 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .positive scale w (← readTree fuel)
    | 4 =>
      let scale ← readInt
      let count ← readNat
      let w ← readCombination count
      return .negative scale w (← readTree fuel)
    | 6 =>
      let p0 ← readPairs (← readNat)
      let p1 ← readPairs (← readNat)
      let p2 ← readPairs (← readNat)
      return .support ![p0,p1,p2]
    | _ => fail
def decode (fuel:Nat) (chunks:List Nat):Certificate :=
  match readTree fuel chunks with
  | some (cert,_) => cert
  | none => .leaf 0 []
end Green24Proof.PackedParametricCertificateData
private def zz2173:"s087d"="s087d":=by decide+kernel
end 
section 
namespace Green24Proof.NatParametricCheckSteps
open IntegerQuadraticCertificates (Linear)
open ParametricQuadraticCertificates (Quadratic Coefficient Hinges coefficientProduct)
open NatBacksubRecoveredQuadraticCertificates (cons Combination combinationCheck)
open NatParametricCertificates
theorem split_valid (p m:Certificate) (C:Nat → Linear) (Q:Quadratic)
    (c:Coefficient) (a:Linear) (hs:Hinges)
    (hp:check p (cons a C) (Q + coefficientProduct c a a) hs = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.split p m) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hp hm
theorem cut_valid (a:Linear) (p m:Certificate) (C:Nat → Linear)
    (Q:Quadratic) (hs:Hinges)
    (hp:check p (cons a C) Q hs = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.cut a p m) C Q hs = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hp hm
theorem positive_valid (s:Int) (w:Combination) (p:Certificate)
    (C:Nat → Linear) (Q:Quadratic) (c:Coefficient) (a:Linear) (hs:Hinges)
    (hw:combinationCheck C s w a = true)
    (hp:check p (cons a C) (Q + coefficientProduct c a a) hs = true) :
    check (.positive s w p) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hw hp
private def zz493:"s01ed"="s01ed":=by decide+kernel
theorem negative_valid (s:Int) (w:Combination) (m:Certificate)
    (C:Nat → Linear) (Q:Quadratic) (c:Coefficient) (a:Linear) (hs:Hinges)
    (hw:combinationCheck C s w (-a) = true)
    (hm:check m (cons (-a) C) Q hs = true) :
    check (.negative s w m) C Q ((c,a) :: hs) = true:=by
  simpa only [check,Bool.and_eq_true] using And.intro hw hm
end Green24Proof.NatParametricCheckSteps
private def zz2174:"s087e"="s087e":=by decide+kernel
end 
section 
namespace Green24Proof.ParametricTupleCheck
open IntegerQuadraticCertificates (Linear)
open ParametricQuadraticCertificates (Coefficient Quadratic Hinges coefficientProduct)
open NatParametricCertificates (Certificate)
open EndToEndTupleCheck (Vec Mat vec mat ofVec ofMat context context_of mat_ofMat
  addM scaleM productM mat_add mat_scale mat_product vec_ofVec)
structure Poly where
  a:Mat
  b:Mat
  c:Mat
def poly (Q:Poly):Quadratic:=![mat Q.a,mat Q.b,mat Q.c]
def ofPoly (Q:Quadratic):Poly:=⟨ofMat (Q 0),ofMat (Q 1),ofMat (Q 2)⟩
def addP (Q R:Poly):Poly:=⟨addM Q.a R.a,addM Q.b R.b,addM Q.c R.c⟩
def zeroP:Poly:=⟨EndToEndTupleCheck.zeroM,EndToEndTupleCheck.zeroM,EndToEndTupleCheck.zeroM⟩
def scaleP (s:Int) (Q:Poly):Poly:=⟨scaleM s Q.a,scaleM s Q.b,scaleM s Q.c⟩
def productP (c:Coefficient) (a b:Linear):Poly :=
  let p:=productM (ofVec a) (ofVec b)
  ⟨scaleM (c 0) p,scaleM (c 1) p,scaleM (c 2) p⟩
theorem poly_of (Q:Quadratic):poly (ofPoly Q) = Q:=by
  funext d
  fin_cases d <;> exact mat_ofMat _
theorem poly_add (Q R:Poly):poly (addP Q R) = poly Q + poly R:=by
  funext d
  fin_cases d <;> exact mat_add _ _
theorem poly_zero:poly zeroP = 0:=by
  funext d
  fin_cases d <;> exact EndToEndTupleCheck.mat_zero
private def zz494:"s01ee"="s01ee":=by decide+kernel
theorem poly_scale (s:Int) (Q:Poly):poly (scaleP s Q) = s • poly Q:=by
  funext d
  fin_cases d <;> exact mat_scale _ _
theorem poly_product (c:Coefficient) (a b:Linear) :
    poly (productP c a b) = coefficientProduct c a b:=by
  funext d
  fin_cases d <;> simp [poly,productP,coefficientProduct,
    mat_scale,mat_product,vec_ofVec]
theorem context_cons (a:Linear) (C:Nat → Vec) :
    context (EndToEndTupleCheck.cons (ofVec a) C) =
      NatBacksubRecoveredQuadraticCertificates.cons a (context C):=by
  exact EndToEndTupleCheck.context_cons a C
theorem combination_eq (C:Nat → Vec) (s:Int)
    (w:NatBacksubRecoveredQuadraticCertificates.Combination) (a:Linear) :
    EndToEndTupleCheck.combinationCheck C s w a =
      NatBacksubRecoveredQuadraticCertificates.combinationCheck (context C) s w a:=by
  exact EndToEndTupleCheck.combinationCheck_eq C s w a
def termP (C:Nat → Vec):NatParametricCertificates.NonnegativeTerm → Poly
  | .square a b =>
      let a:=ofVec a
      let b:=ofVec b
      ⟨productM a a,addM (productM a b) (productM b a),productM b b⟩
  | .middleSquare a =>
      let p:=productM (ofVec a) (ofVec a)
      ⟨EndToEndTupleCheck.zeroM,p,scaleM (-1) p⟩
  | .pair d i j =>
      let p:=productM (C i) (C j)
      if d = 0 then ⟨p,scaleM (-2) p,p⟩
      else if d = 1 then ⟨EndToEndTupleCheck.zeroM,scaleM 2 p,scaleM (-2) p⟩
      else ⟨EndToEndTupleCheck.zeroM,EndToEndTupleCheck.zeroM,p⟩
private def zz495:"s01ef"="s01ef":=by decide+kernel
theorem poly_term (C:Nat → Vec) (v:NatParametricCertificates.NonnegativeTerm) :
    poly (termP C v) = NatParametricCertificates.termPolynomial (context C) v:=by
  cases v with
  | square a b =>
      funext d
      fin_cases d <;> simp [termP,poly,NatParametricCertificates.termPolynomial,
        mat_product,mat_add,vec_ofVec]
  | middleSquare a =>
      funext d
      fin_cases d <;> simp [termP,poly,NatParametricCertificates.termPolynomial,
        mat_product,mat_scale,vec_ofVec,EndToEndTupleCheck.mat_zero]
  | pair d i j =>
      fin_cases d <;> funext k <;> fin_cases k <;>
        simp [termP,poly,NatParametricCertificates.termPolynomial,
          mat_product,mat_scale,EndToEndTupleCheck.mat_zero,context]
def decomposeP (C:Nat → Vec):NatParametricCertificates.Decomposition → Poly
  | [] => zeroP
  | (s,v) :: ds => addP (scaleP s (termP C v)) (decomposeP C ds)
theorem poly_decompose (C:Nat → Vec) (d:NatParametricCertificates.Decomposition) :
    poly (decomposeP C d) = NatParametricCertificates.decompositionPolynomial (context C) d:=by
  induction d with
  | nil => exact poly_zero
  | cons v vs ih =>
      simp only [decomposeP,NatParametricCertificates.decompositionPolynomial,
        List.map_cons,List.sum_cons,poly_add,poly_scale,poly_term,ih]
def part (Q:Poly):Fin 3 → Mat:=![Q.a,Q.b,Q.c]
theorem mat_part (Q:Poly) (d:Fin 3):mat (part Q d) = poly Q d:=by
  fin_cases d <;> rfl
def polynomialEq (Q R:Poly):Bool :=
  (List.finRange 3).all fun d => EndToEndTupleCheck.coefficientEq (part Q d) (part R d)
theorem polynomialEq_eq (Q R:Poly) :
    polynomialEq Q R = NatParametricCertificates.polynomialEq (poly Q) (poly R):=by
  simp only [polynomialEq,NatParametricCertificates.polynomialEq,
    EndToEndTupleCheck.coefficientEq_eq,mat_part]
def decompositionCheck (C:Nat → Vec) (Q:Poly) (s:Int)
    (d:NatParametricCertificates.Decomposition):Bool :=
  decide (0 < s) && (d.all fun v => decide (0 ≤ v.1)) &&
    polynomialEq (decomposeP C d) (scaleP s Q)
private def zz496:"s01f0"="s01f0":=by decide+kernel
theorem decompositionCheck_eq (C:Nat → Vec) (Q:Poly) (s:Int)
    (d:NatParametricCertificates.Decomposition) :
    decompositionCheck C Q s d =
      NatParametricCertificates.decompositionCheck (context C) (poly Q) s d:=by
  simp only [decompositionCheck,NatParametricCertificates.decompositionCheck,
    polynomialEq_eq,poly_decompose,poly_scale]
def scalarTerm:NatBacksubRecoveredQuadraticCertificates.NonnegativeTerm →
    OrthantQuadraticCertificates.NonnegativeTerm
  | .square a => .square a
  | .pair i j => .pair i j
def scalarDecomposition (d:NatBacksubRecoveredQuadraticCertificates.Decomposition) :
    OrthantQuadraticCertificates.Decomposition:=d.map fun (s,v) => (s,scalarTerm v)
theorem scalar_matrix (C:Nat → Linear)
    (d:NatBacksubRecoveredQuadraticCertificates.Decomposition) :
    OrthantQuadraticCertificates.decompositionMatrix C (scalarDecomposition d) =
      NatBacksubRecoveredQuadraticCertificates.decompositionMatrix C d:=by
  simp only [scalarDecomposition,OrthantQuadraticCertificates.decompositionMatrix,
    NatBacksubRecoveredQuadraticCertificates.decompositionMatrix,List.map_map]
  congr 1
  apply List.map_congr_left
  intro v _
  rcases v with ⟨s,v⟩
  cases v <;> rfl
def scalarSupport (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)) :
    Int × OrthantQuadraticCertificates.Decomposition :=
  match BacksubIntegerElimination.solveScaled
      (pairs.toArray.map fun (i,j) => EndToEndTupleCheck.coefficients (productM (C i) (C j)))
      (EndToEndTupleCheck.coefficients Q) with
  | none => (0,[])
  | some (scale,weights) =>
      (scale,(weights.toList.zip pairs).map fun (weight,i,j) => (weight, .pair i j))
theorem scalar_support (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)) :
    scalarSupport C Q pairs =
      let d:=NatBacksubRecoveredQuadraticCertificates.supportDecomposition (context C) (mat Q) pairs
      (d.1,scalarDecomposition d.2):=by
  unfold scalarSupport NatBacksubRecoveredQuadraticCertificates.supportDecomposition
  simp only [EndToEndTupleCheck.pairColumn_eq]
  simp only [EndToEndTupleCheck.coefficients_eq,context]
  cases h:BacksubIntegerElimination.solveScaled
      (pairs.toArray.map fun (i,j) =>
        PureIntegerSupportCertificateData.pairColumn (context C i) (context C j))
      (PureIntegerSupportCertificateData.matrixColumn (mat Q)) with
  | none => simp_all [scalarDecomposition,context]
  | some result =>
      rcases result with ⟨s,weights⟩
      simp_all [scalarDecomposition,List.map_map,scalarTerm,context]
def scalarCheck (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)):Bool :=
  let d:=scalarSupport C Q pairs
  EndToEndTupleCheck.decompositionCheck C Q d.1 d.2
theorem scalarCheck_eq (C:Nat → Vec) (Q:Mat) (pairs:List (Nat × Nat)) :
    scalarCheck C Q pairs = NatBacksubRecoveredQuadraticCertificates.check
      (.support pairs) (context C) (mat Q) []:=by
  simp only [scalarCheck,NatBacksubRecoveredQuadraticCertificates.check,scalar_support,
    EndToEndTupleCheck.decompositionCheck_eq,OrthantQuadraticCertificates.decompositionCheck,
    NatBacksubRecoveredQuadraticCertificates.decompositionCheck]
  rw [scalar_matrix]
  simp only [scalarDecomposition,List.all_map,Function.comp_def]
def bernstein (Q:Poly) (d:Fin 3):Mat :=
  if d = 0 then scaleM 2 Q.a
  else if d = 1 then addM (scaleM 2 Q.a) Q.b
  else scaleM 2 (addM (addM Q.a Q.b) Q.c)
private def zz497:"s01f1"="s01f1":=by decide+kernel
theorem mat_bernstein (Q:Poly) (d:Fin 3) :
    mat (bernstein Q d) = NatParametricCertificates.bernsteinPart (poly Q) d:=by
  fin_cases d <;> simp [bernstein,NatParametricCertificates.bernsteinPart,poly,
    mat_scale,mat_add]
def supportCheck (C:Nat → Vec) (Q:Poly) (pairs:NatParametricCertificates.Supports):Bool :=
  (List.finRange 3).all fun d => scalarCheck C (bernstein Q d) (pairs d)
theorem supportCheck_eq (C:Nat → Vec) (Q:Poly) (pairs:NatParametricCertificates.Supports) :
    supportCheck C Q pairs = NatParametricCertificates.supportCheck (context C) (poly Q) pairs:=by
  simp only [supportCheck,NatParametricCertificates.supportCheck,scalarCheck_eq,mat_bernstein]
def check (cert:Certificate) (C:Nat → Vec) (Q:Poly) (hs:Hinges):Bool :=
  match cert,hs with
  | .cut a p m,hs =>
      check p (EndToEndTupleCheck.cons (ofVec a) C) Q hs &&
      check m (EndToEndTupleCheck.cons (ofVec (-a)) C) Q hs
  | .support pairs,[] => supportCheck C Q pairs
  | .leaf s d,[] => decompositionCheck C Q s d
  | .split p m,(c,a) :: hs =>
      check p (EndToEndTupleCheck.cons (ofVec a) C) (addP Q (productP c a a)) hs &&
      check m (EndToEndTupleCheck.cons (ofVec (-a)) C) Q hs
  | .positive s w p,(c,a) :: hs =>
      EndToEndTupleCheck.combinationCheck C s w a &&
      check p (EndToEndTupleCheck.cons (ofVec a) C) (addP Q (productP c a a)) hs
  | .negative s w m,(_,a) :: hs =>
      EndToEndTupleCheck.combinationCheck C s w (-a) &&
      check m (EndToEndTupleCheck.cons (ofVec (-a)) C) Q hs
  | _,_ => false
theorem check_eq (cert:Certificate) (C:Nat → Vec) (Q:Poly) (hs:Hinges) :
    check cert C Q hs = NatParametricCertificates.check cert (context C) (poly Q) hs:=by
  induction cert generalizing C Q hs <;> cases hs <;>
    simp only [check,NatParametricCertificates.check,combination_eq,
      context_cons,poly_add,poly_product,decompositionCheck_eq,supportCheck_eq, *]
theorem K {cert:Certificate} {C:Nat → Linear} {Q:Quadratic} {hs:Hinges}
    (h:check cert (fun i => ofVec (C i)) (ofPoly Q) hs = true:=by decide +kernel) :
    NatParametricCertificates.check cert C Q hs = true:=by
  rw [check_eq,context_of,poly_of] at h
  exact h
end Green24Proof.ParametricTupleCheck
private def zz2175:"s087f"="s087f":=by decide+kernel
namespace Green24Proof.QuadNearBalanceCase0
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x3797219f80b54, -0x221b262dd8000, -0x3328b944c4000,0x237342d5e5aa], ![-0x221b262dd8000, -0x126552ce068b54,0x41ff182e51a56,0x110d9316ec000], ![-0x3328b944c4000,0x41ff182e51a56, -0xde5bab6f61f20,0x2245f2ff317c8], ![0x237342d5e5aa,0x110d9316ec000,0x2245f2ff317c8, -0x110d9316ec000]], ![![0,0,0,0], ![0,0,0,0], ![0,0,0x1155bbf3a80, -0x4556efcea0], ![0,0, -0x4556efcea0,0]], ![![0x1202087f6040,0x57714333f70,0x831923eaa00, -0xd16a6e706c0], ![0x57714333f70,0x25a72fb42020, -0x68a5014e480,0x1a5329299a0], ![0x831923eaa00, -0x68a5014e480,0x2689cbe72c20, -0x6373d2bd250], ![-0xd16a6e706c0,0x1a5329299a0, -0x6373d2bd250,0x2ba7def3000]]]
def hinges:Hinges:=[(![0,0,0x1c3a90], ![0,0,1, -3]),(![-0x156668acbe4,0x22ab77e750,0x622c7c7930], ![0,0,1, -1]),(![0x156668acbe4, -0x22ab77e750, -0x622cd128e0], ![0,0,3, -1]),(![0x11b9a16af2d5,0, -0x22eca8eb020], ![0,1,0, -3]),(![0x3d90afd394f02,0,0], ![0,1,0, -1]),(![-0x110d9316ec000,0,0x2ba7def3000], ![0,3, -2, -1]),(![0x110d9316ec000,0, -0x2ba7def3000], ![0,3, -2,1]),(![0x11b9a16af2d5,0,0], ![0,3,0, -1]),(![0x110d9316ec000,0, -0x2ba7def3000], ![0,3,2, -1]),(![-0x156668acbe4,0x22ab77e750,0x622cd128e0], ![1, -3,0,0]),(![-0x110d9316ec000,0,0x2ba7def3000], ![1, -2, -3,0]),(![0x110d9316ec000,0, -0x2ba7def3000], ![1, -2,3,0]),(![0x156668acbe4, -0x22ab77e750, -0x622c7c7930], ![1, -1,0,0]),(![-0x11b9a16af2d5,0,0], ![1,0, -3,0]),(![-0x3d90afd394f02,0,0], ![1,0, -1,0]),(![0,0,0x45d951d6040], ![1,0,0, -3]),(![0x110d9316ec000,0, -0x2ba7def3000], ![1,2, -3,0]),(![0,0, -0x1c3a90], ![3, -1,0,0]),(![-0x11b9a16af2d5,0,0x22eca8eb020], ![3,0, -1,0]),(![0,0, -0x45d951d6040], ![3,0,0, -1])]
def normalizationDenominator:ℤ:=0x221b262dd8000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx2815:Nat → Linear:=constraintsNat
private def quad2815:Quadratic:=base
private def ctx729:Nat → Linear:=cons ![0,0,1, -3] ctx2815
private def quad729:Quadratic:=quad2815 + coefficientProduct ![0,0,0x1c3a90] ![0,0,1, -3] ![0,0,1, -3]
private def ctx342:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx729)))
private def quad342:Quadratic:=(((quad729 + coefficientProduct ![-0x156668acbe4,0x22ab77e750,0x622c7c7930] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0x11b9a16af2d5,0, -0x22eca8eb020] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx170:Nat → Linear:=cons (-![1, -3,0,0]) (cons ![0,3,2, -1] (cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] ctx342))))
private def quad170:Quadratic:=((((quad342 + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3,2, -1] ![0,3,2, -1])
private def ctx341:Nat → Linear:=cons (-![0,3, -2, -1]) ctx342
private def quad341:Quadratic:=quad342
private def ctx250:Nat → Linear:=cons ![0,3, -2,1] ctx341
private def quad250:Quadratic:=quad341 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx575:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx729)))
private def quad575:Quadratic:=(((quad729 + coefficientProduct ![-0x156668acbe4,0x22ab77e750,0x622c7c7930] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx574:Nat → Linear:=cons (-![0,3, -2, -1]) ctx575
private def quad574:Quadratic:=quad575
private def ctx490:Nat → Linear:=cons ![0,3, -2,1] ctx574
private def quad490:Quadratic:=quad574 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx725:Nat → Linear:=cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx729)))
private def quad725:Quadratic:=(((quad729 + coefficientProduct ![-0x156668acbe4,0x22ab77e750,0x622c7c7930] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx649:Nat → Linear:=cons ![0,3,0, -1] (cons (-![0,3, -2,1]) (cons (-![0,3, -2, -1]) ctx725))
private def quad649:Quadratic:=((quad725)) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1387:Nat → Linear:=cons ![0,0,1, -1] (cons (-![0,0,1, -3]) ctx2815)
private def quad1387:Quadratic:=(quad2815) + coefficientProduct ![-0x156668acbe4,0x22ab77e750,0x622c7c7930] ![0,0,1, -1] ![0,0,1, -1]
private def ctx865:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,0,3, -1] ctx1387)))))
private def quad865:Quadratic:=(((((quad1387 + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0x11b9a16af2d5,0, -0x22eca8eb020] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1385:Nat → Linear:=cons (-![0,1,0, -3]) (cons ![0,0,3, -1] ctx1387)
private def quad1385:Quadratic:=(quad1387 + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1])
private def ctx988:Nat → Linear:=cons ![0,3,2, -1] (cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1385))))
private def quad988:Quadratic:=((((quad1385 + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3,2, -1] ![0,3,2, -1]
private def ctx1142:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] ctx1385)
private def quad1142:Quadratic:=(quad1385 + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx1070:Nat → Linear:=cons ![0,3, -2,1] ctx1142
private def quad1070:Quadratic:=quad1142 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1384:Nat → Linear:=cons (-![0,1,0, -1]) ctx1385
private def quad1384:Quadratic:=quad1385
private def ctx1382:Nat → Linear:=cons (-![0,3, -2,1]) (cons (-![0,3, -2, -1]) ctx1384)
private def quad1382:Quadratic:=(quad1384)
private def ctx1304:Nat → Linear:=cons ![0,3,0, -1] ctx1382
private def quad1304:Quadratic:=quad1382 + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2813:Nat → Linear:=cons (-![0,0,1, -1]) (cons (-![0,0,1, -3]) ctx2815)
private def quad2813:Quadratic:=(quad2815)
private def ctx2067:Nat → Linear:=cons ![0,0,3, -1] ctx2813
private def quad2067:Quadratic:=quad2813 + coefficientProduct ![0x156668acbe4, -0x22ab77e750, -0x622cd128e0] ![0,0,3, -1] ![0,0,3, -1]
private def ctx1470:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] ctx2067))
private def quad1470:Quadratic:=((quad2067 + coefficientProduct ![0x11b9a16af2d5,0, -0x22eca8eb020] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx2066:Nat → Linear:=cons (-![0,1,0, -3]) ctx2067
private def quad2066:Quadratic:=quad2067
private def ctx1602:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx2066)))
private def quad1602:Quadratic:=(((quad2066 + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2065:Nat → Linear:=cons (-![0,1,0, -1]) ctx2066
private def quad2065:Quadratic:=quad2066
private def ctx1708:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] ctx2065)
private def quad1708:Quadratic:=(quad2065 + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1822:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) ctx2065))
private def quad1822:Quadratic:=((quad2065) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1983:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) ctx2065))
private def quad1983:Quadratic:=((quad2065) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1])
private def ctx2063:Nat → Linear:=cons (-![0,3, -2,1]) (cons (-![0,3, -2, -1]) ctx2065)
private def quad2063:Quadratic:=(quad2065)
private def ctx2148:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons (-![0,0,3, -1]) ctx2813)))
private def quad2148:Quadratic:=(((quad2813) + coefficientProduct ![0x11b9a16af2d5,0, -0x22eca8eb020] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx2811:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,0,3, -1]) ctx2813)
private def quad2811:Quadratic:=(quad2813)
private def ctx2241:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx2811)
private def quad2241:Quadratic:=(quad2811 + coefficientProduct ![0x3d90afd394f02,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx2359:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) ctx2811)))
private def quad2359:Quadratic:=(((quad2811) + coefficientProduct ![-0x110d9316ec000,0,0x2ba7def3000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2809:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx2811)
private def quad2809:Quadratic:=(quad2811)
private def ctx2489:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -2,1] ctx2809)
private def quad2489:Quadratic:=(quad2809 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x11b9a16af2d5,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2640:Nat → Linear:=cons ![0,3,2, -1] (cons (-![0,3,0, -1]) (cons ![0,3, -2,1] ctx2809))
private def quad2640:Quadratic:=((quad2809 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1])) + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3,2, -1] ![0,3,2, -1]
private def ctx2806:Nat → Linear:=cons (-![0,3,2, -1]) (cons (-![0,3,0, -1]) (cons ![0,3, -2,1] ctx2809))
private def quad2806:Quadratic:=((quad2809 + coefficientProduct ![0x110d9316ec000,0, -0x2ba7def3000] ![0,3, -2,1] ![0,3, -2,1]))
private def data27:List Nat:=[
  0x1131313110d0d100b0b0b0a0a10090b0908080a020a131313110d0d100b0b0b130910090b0908080a020a131313110d0d100b0b0b130910090b0908080a020a060a040306010c00080416030b020902011200300436030502040200020302030a040904060401020406030b0202020202030e04080207020404040803131313110d0d100b0a0a10090a0808080a0208020a131313110d0d0a0a10090e090b0908080a0208000a131313110d0d0a0a10090e090b0908080a0208000a060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030f040e0601020306030e040002020603010c0402020206030b04010800060306031313130b100b110a11090b09110417021701091313130b110a11090b09110417021701081313130b110a11090b0911041702170108060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030f040e0601020306030e0400020206030d08070606060212041a030c04010200020308030e060b020806010404060301]
private def node27:Certificate:=PackedParametricCertificateData.decode 11 data27
private def data37:List Nat:=[
  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,
  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,
  0x109aa8679c8a305cad0029e9f011ca186bbbcc5878fa4ac84e0d6c1f294f8d0de9485e850e906889f6dced735afd20107b1fdd09dd098b2ee9b90bfedb98c93f4a7b8c89080]
private def node37:Certificate:=PackedParametricCertificateData.decode 10 data37
private def data62:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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]
private def node62:Certificate:=PackedParametricCertificateData.decode 8 data62
private def data115:List Nat:=[
  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,
  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,
  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]
private def node115:Certificate:=PackedParametricCertificateData.decode 8 data115
private def node116:Certificate:=.split node62 node115
private def data168:List Nat:=[
  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,
  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,
  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]
private def node168:Certificate:=PackedParametricCertificateData.decode 9 data168
private def node169:Certificate:=.split node116 node168
private def node170:Certificate:=.split node37 node169
private def node171:Certificate:=.split node27 node170
private def node172:Certificate:=.positive 2 [(1,0),(1,1),(2,5)] node171
private def node173:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node172
private def node174:Certificate:=.positive 1 [(1,0),(2,9)] node173
private def data202:List Nat:=[
  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]
private def node202:Certificate:=PackedParametricCertificateData.decode 11 data202
private def data247:List Nat:=[
  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,
  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]
private def node247:Certificate:=PackedParametricCertificateData.decode 11 data247
private def node248:Certificate:=.split node202 node247
private def node249:Certificate:=.positive 2 [(1,0),(1,1),(2,5)] node248
private def node250:Certificate:=.positive 7 [(6,0),(3,3),(4,4)] node249
private def data290:List Nat:=[
  0x10804160301111007020206030a020902020201040406040f040b0605020306031010130c0d0c17080d0508050e010d01080103010a1010130c0d0c17080d0508050e010d01080103010a1010130c0d0c17080d0508050e010d01080103010a060a040306010c000804160315040a040312000c0412031104050202060304031010130c100c0d0b0d090e080808090604030a010a1010130c100c0d0b0d090e080808090604030a010a1010130c100c0d0b0d090e080808090604030a010a060a040306010c00080416030702010e0020032403050204020002030203010b0a050203020006040a03011010130c100c0d0b0e080808060610030d010a010a1010130c100c0d0b0d090e080808060604030a010a1010130c100c0d0b0d090e080808060604030a010a060a040306010c00080416030702010e00200324030502040200020302031304080402060306030f040e0601020306030e040002020603010c0402020206030b1c081205120102041e0310100e0e100c0b090e080b0417020e020b000910100e0e100c0b090e080b0417020e020b000910100e0e100c0b090e080b0417020e020b0009060a040306010c000804160315040904011e00480452030502040200020302031304080402060306030f040e0601020306030e0400020206031004050402060306030c0402020206030b1c081205120102041e0301,
  0x11010130c0c0917030c030a02080202020c01091010130c0c0617030c030a0202020c01081010130c0c0617030c030a0202020c0108060b0803060118031a031010130c110c090917080c030d010a01080102010a1010130c110c090917080c030d010a01080102010a1010130c110c090917080c030d010a01080102010a060a040306010c00]
private def node290:Certificate:=PackedParametricCertificateData.decode 11 data290
private def data337:List Nat:=[
  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,
  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]
private def node337:Certificate:=PackedParametricCertificateData.decode 11 data337
private def node338:Certificate:=.split node290 node337
private def node339:Certificate:=.positive 3 [(3,0),(2,5),(2,11)] node338
private def node340:Certificate:=.positive 3 [(1,3),(8,8)] node339
private def node341:Certificate:=.split node250 node340
private def node342:Certificate:=.split node174 node341
private def node343:Certificate:=.positive 3 [(1,0),(2,5)] node342
private def data371:List Nat:=[
  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]
private def node371:Certificate:=PackedParametricCertificateData.decode 11 data371
private def data411:List Nat:=[
  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,
  0x1131313110b0b0b090e030a02090202020a010d000a131313110b0b0b090e030a02090202020a010d000a131313110b0b0b090e030a02090202020a010d000a06131313110b0b0d040e030a02090202020a0100000a131313110b0b0d040e030a02090202020a0100000a131313110b0b0d040e030a02090202020a0100000a060111020e020002030204131313110b0b0a090e060d040e0302020a0100000a131313110b0b0e090a090d040e0302020a0100000a131313110b0b0e090a090d040e0302020a0100000a0612040d020b0401120412031313130b0a0a0a0709070d040e030b03020210010a1313130b0a0a0a070907]
private def node411:Certificate:=PackedParametricCertificateData.decode 11 data411
private def node412:Certificate:=.split node371 node411
private def node413:Certificate:=.positive 2 [(1,0),(1,1),(2,5)] node412
private def node414:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node413
private def node415:Certificate:=.positive 11 [(14,0),(9,2),(2,3)] node414
private def data447:List Nat:=[
  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]
private def node447:Certificate:=PackedParametricCertificateData.decode 11 data447
private def data487:List Nat:=[
  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,
  0x113130e0e0d0d130b0b0b0a0a130908080a0202020a13130e0e0d0d130b0b0b0a0a130908080a0202020a13130e0e0d0d130b0b0b0a0a130908080a0202020a0613130e0e0d0d130b0b0b0a0a130908080a0202020a13130e0e0d0d130b0b0b0a0a130908080a0202020a13130e0e0d0d130b0b0b0a0a130908080a0202020a060111020c060106001e04200413130e0e0d0d130b0a0a08080e0202020b010a010a13130e0e0d0d130b0a0a08080e0202020b010a010a13130e0e0d0d130b0a0a08080e0202020b010a010a0612040c020b02010c040c0313130e0e0d0d130b0a0a0e08090704040e0202020a13130e0e0d0d130b0a0a0e08090704040e0202020a13130e]
private def node487:Certificate:=PackedParametricCertificateData.decode 11 data487
private def node488:Certificate:=.split node447 node487
private def node489:Certificate:=.positive 2 [(1,0),(1,1),(2,5)] node488
private def node490:Certificate:=.positive 2 [(2,0),(1,4),(1,6)] node489
private def data530:List Nat:=[
  0x10c000804160301110404020202030a020902020201040406040a060502020203100e130c110c100808050c030e010d01080103010a100e130c110c100808050c030e010d01080103010a100e130c110c100808050c030e010d01080103010a060a040306010c00080416030e020a06031800100418031104050202060304031010100e130b0d0b0e08080809060e020d010a010a1010100e130b0d0b0d090e080808090610020a010a1010100e130b0d0b0d090e080808090610020a010a060a040306010c00080416030e020906012a0064047203050204020002030203010e020002020203011010100e130b0d0b09090e0808080e020d010a010a1010100e130b0d0b0e080808060610020e020a010a1010100e130b0d0b0e080808060610020e020a010a060a040306010c00080416030e020906012a00640472030502040200020302030c02080602080308030f040e0601020306030e040002020603010c0402020206030b1c081205120102041e03100e0e0e100a0b090b0410020e0211010b0009100e0e0e100a0b090b04110210020e020b0009100e0e0e100a0b090b04110210020e020b0009060a040306010c00080416030e020906012a00640472030502040200020302030c02080602080308030f040e0601020306030e0400020206030902050602080308030c0402020206030b1c081205120102041e0301,
  0x1100e100d130c110c10030c030d020a02020209100e100d130c110c10030c030a02020208100e100d130c110c10030c030a02020208060b0803060118031a03100e100d130c110c09090c0302020d010a0108010a100e100d130c110c090910080c0302020a0108010a100e100d130c110c090910080c0302020a0108010a060a04030601]
private def node530:Certificate:=PackedParametricCertificateData.decode 11 data530
private def data570:List Nat:=[
  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,
  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]
private def node570:Certificate:=PackedParametricCertificateData.decode 11 data570
private def node571:Certificate:=.split node530 node570
private def node572:Certificate:=.positive 12 [(13,0),(3,4),(8,5)] node571
private def node573:Certificate:=.positive 1 [(1,2),(2,8)] node572
private def node574:Certificate:=.split node490 node573
private def node575:Certificate:=.split node415 node574
private def data622:List Nat:=[
  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,
  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]
private def node622:Certificate:=PackedParametricCertificateData.decode 11 data622
private def data647:List Nat:=[
  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]
private def node647:Certificate:=PackedParametricCertificateData.decode 11 data647
private def node648:Certificate:=.split node622 node647
private def node649:Certificate:=.positive 12 [(13,0),(3,4),(8,5)] node648
private def data697:List Nat:=[
  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,
  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]
private def node697:Certificate:=PackedParametricCertificateData.decode 11 data697
private def data720:List Nat:=[
  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]
private def node720:Certificate:=PackedParametricCertificateData.decode 11 data720
private def node721:Certificate:=.split node697 node720
private def node722:Certificate:=.positive 8 [(5,5),(1,7),(24,9)] node721
private def node723:Certificate:=.split node649 node722
private def node724:Certificate:=.negative 2 [(1,0),(3,1),(2,5)] node723
private def node725:Certificate:=.negative 2 [(6,0),(1,2),(1,4)] node724
private def node726:Certificate:=.split node575 node725
private def node727:Certificate:=.split node343 node726
private def node728:Certificate:=.positive 3 [(1,1),(8,4)] node727
private def node729:Certificate:=.positive 3 [(1,0),(2,3)] node728
private def data750:List Nat:=[
  0x1131311110d0d0a0a10090a080808110413030a020a131311110d0d0a0a10090a080808110413030a020a131311110d0d0a0a10090a080808110413030a020a060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030c06090603020302030c0402020206030b100a120836012004300313131010130a110a0b0a13091109130211020913131010130a110a0b0a13091109130211020913131010130a110a0b0a130911091302110209060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030d08070606060212041a030c04010200020308030b100a120836012004300301]
private def node750:Certificate:=PackedParametricCertificateData.decode 11 data750
private def data760:List Nat:=[
  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,
  0x1038b900fdfb901a8f73b9410d4bc4c8ba702d8ba018bff000391e5d9e990d1c7e290c8c39c8bcb9ed4800bf1fa019dd69602cadb019cdc1cd0d64ed3cb10d109ae0001ba89acc197f8cffaf4a3c2a5a792b2b1a00686c404abb031bd9e1af0b303cf9544ed30cdca168a8f0003abedffc0b3c2b5a4d0fea7dfc0fceec013130202048bcde3d7b2bce7e5f8e7cce390e39693b4cc8cbd8080130d020230d2ffd3cd89a397db85d8bacafad6b48ad4dc88af800a0a02020493a1f1d9c0848b91a998efbaf7c2e4f0b2e1a5baa0130902020b86fd9dd3aba3edeebeeacd9d8a9ccbe3828c90c7c1ae1109020217e8eebffcddbeb9ccabc4a6c2cffbb5b8e4ded8cf99aa0a09020210dbfaecc08ba5a484ecfa938f8a88deef94908dc68012080202019cb6ee9899ac86b7bff3a2b2edd0a180c8c9cb99c3b81108020206c5f5fdf6bd8fabdcd1edc3d0a3de8780a6c5cb8fbbe81313010204aca6a1e3a380ddcfb08fc2d885b0aa9bd0b4c59bd8800a0a0102069595e7ee81e4d297e4a8e197ba9287aa93bde7e9e01309010208f2bffeb7fdd9f9cde7b19aadbf8e9ba2eaf7abe5adca1109010214eff1eee088f9c2b5c3]
private def node760:Certificate:=PackedParametricCertificateData.decode 10 data760
private def data811:List Nat:=[
  0x18b8089abac9492aa97a786a8dcc4be8fb2b5dfffbeba8db4df96a8fe8a9ac00606010202a2b3a5e299d4ee859dd280c3d49aa0e9e7d1d4e0b0899bc49acdefddd4f8f6d984ace99296da1313000208dcff8aa684c3a7eda2e3818b89cf9cfecedc8af996b69485e98bfacdce98f5c7c5a6d6d883b01212000270b6918ddef597edc4aca3d5a9e897d9d789d8f88382c2cf8fac88e9dff5aecde7c1a0a18e95b81210000215e7b2ec90bc94e396e5b8d1cdaf86b6bccb8196c0af9a8ef8b98186fcb3aeedc591ddd0c191f0120900026ae2b0f8fad1aadcc4acb5f7bc9a9bc5e1aa91b2ecb0a0fd9fcde2b3c7c4b48eb397dbaf9ab2e80909000214e3ba9082f9fe8c9bfbd0c7ace2beace3c0da93bbed90ead1a1b1baf9f589e4829be9a4e0f1fc1008000202f9debcc4babbcafee999e1e9fdb389acd9d6edd5a2e4e1edac83ffe3b1f0ba99d39a839598b01306000201a1e3b89188c1e1b484dbb4e4e084b884a3bd9c91f4848c86c9d7a5b9f590f1e59984bab2bbaad806060002028fc2c7ce9acc93c7c3dfa5ed8ee4afdfccdd87eabc84e096d086d7d88bcafe86a3e8a7d6b6e41e27f6f28dcac2dcd794d7d4cdd7b5e792e0eadad39ea8d89093a6f9ec83bbfdf9d8000a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030101,
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  0x1131311100b0909090d0410030e0302020a010d000a131311100b090d0410030e0302020e010a010d000a131311100b090d0410030e0302020e010a010d000a06131311100b090d0410030e0302020e010a0108000a131311100b090d0410030e0302020e010a0108000a131311100b090d0410030e0302020e010a0108000a060113131110110b090904040e030b030a02020208000a13131110110b090904040e030b030a02020208000a13131110110b090904040e030b030a02020208000a0610080f0c0706002a042c0301]
private def node811:Certificate:=PackedParametricCertificateData.decode 9 data811
private def data861:List Nat:=[
  0x1020201b69491d48dfeb2eca0dcef8efdcfd4cd8fe2fda0e00706020251a0f4a9bebdebe4b4dff5939f8080c4b980c9c01313010209eec390f9cdebeda1fdb6e89fda8cadabd0a981d6f21209010210fcfeacf68ec9939194979fffdffb98c7b5a7fc94b81109010202a59aa5cc84d884b597d4cfeb9ef5cab08d8da8cee813080102119d93a099848ad5dfbde5ab9a94fbd68ef4aafed8e41108010220c1dca8b1f1c488d69aaeccf4e7b7cfb181f8bca7c6070701020acc91daa3f1cb9caaaccee3bf93b2958ba8a49c921306010202b1ecd5e5e6c4acffe6edb5f7ffe8f3f389a59eb4de070601025bb7c5abadecf097a187beeefdc1bc9c8ba5e01313000209edcab1d1b4a6cec7ebbc92a8fbe9d9c8878bdd90a012090002109aadce9ea4c9c096c3a291f9bafe91b89f8ed689d81109000202cb8c93c5cbd7b3f6c5afc891fe83c3b99f82e986e813080002118abedcffc6a3b8f68df0b7a9bee1b595c5a2acf5861108000220b4c5ccf1d195dffdeaa0c1be9ecfd8bfbbbb8cddf2070700020b9daaf6b1d2ac86c0a3dec7d4fefde1eae5a8faa01306000202abeecbaf98a6be99bcb5e7c2d4bca4f0aef9fda6a01b3387ebe5c0d6e9e9aaefaff991a5b0000a040306010c00080416030b0209020112003004360311040402020203090c0208010600040412030b0202020202030e0400020206030102000402020301,
  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,
  0x1110e130d110c060201010d0003000913131110110e130d110c060201010d0003000913131110110e130d110b060201010d00030009060113131110110e130d0a0613031102060203010913131110110e130d0a0613031102060203010913131110110e130d0a0613031102060203010906110200020202030113131110090809070a0609050d041303080203020a131311100a0909080a0609050d041303080203020a13131110090809070a0609050d041303080203020a060f040a02010a0004040e030b0209020112003004360301100404020202030e02000202020413131110110e11080d0404041102060208000913131110110e11080d0404041102060208000913131110110e11080d04040411020602080009061102000202020312040302020203131311100a091108090810060a060d04080203020a131311101108090810060a0608060d04080203020a131311101108090810060a0608060d04080203020a060f040a02010a0004040e030b02090201120030043603010a0209020402010a0408031110110e130d11080e060404110206020800091110110e130d11080e060404110206020800091110110e130d11080e0604041102060208000906100803060018031a031204030202020313131110130d130809080a0608061303080203020a13131110130d130809080a0608061303080203020a13131110,
  0x113131110140e110e130d110c1102060201010913131110140e110e130d110a1102060201010913131110140e110e130d110b110206020101090613131110]
private def node861:Certificate:=PackedParametricCertificateData.decode 9 data861
private def node862:Certificate:=.split node811 node861
private def node863:Certificate:=.split node760 node862
private def node864:Certificate:=.split node750 node863
private def node865:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node864
private def node866:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node865
private def node867:Certificate:=.positive 4 [(4,0),(1,3),(3,5)] node866
private def node868:Certificate:=.positive 1 [(1,0),(2,1),(2,4)] node867
private def node869:Certificate:=.positive 3 [(1,0),(2,5)] node868
private def data897:List Nat:=[
  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]
private def node897:Certificate:=PackedParametricCertificateData.decode 11 data897
private def data931:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  0x1edbec19ff4f6b1e9ea86f4ef9ea3e0c4d4f2bc8ad3eceaa2fb8882b5bbafe41f8eae2385b42d96ee6faba943d18540b7cf1fffb701a4888e0072b4feed8af3eda680d7dc98fbf3d19688fadea1b7f3a3dd9caa8ab7bbb9dcb0bd9befc8c0a68bffb1a83cf8ce3cfa823d84903d9b9e05ee05b402c60de700019e97fcbacc93dbffe2e3f8a791aac18481a4e6f1d7b0eace84b8fcfd839dacdaefc6bccebaefa2e290120e020257d7ebef8ac2f4b79f91aca1d5d79adaba89c9fb9dc08eb2cb91ff95dfc886eb86add6b182eae2cebc9fa59abad4bec80e07020231e9fedab5ecbdacff9cf8ff9ac2edccaec6b6b2ddd6ecea83dfdfe09688989798ebe2ecfcd38fb6918bfa97d1fa91f80e05020209b6ae919597ef91fcb3a788d7eecad8f3feb1debb9bc8ed88a6b6cd82b7eabea1e79fc3d2ce81dacf959bfaaacbd7a00a05020208c58fd3ad8bcdc19a99fecdbad0fe869896deac9bb2f3f5a39e859ae18ef48e91cd82d2f5b8a5f89d8cc6d2e6e8100402020accecdfc195adcbe2e6cfcd9ba3a4cc9ba2eac2e892d6cac1868988dea9b18c8be3d986d1e5ad92a2f0e0d3c9f00a03020211dde8caa9f2a8ca9df7fb83ee8887d3b8c2b9fbc4baf5b8f8d5b7e9ccd6c3f3c681c3b9d78c8edef1efe9cc9c80121201020392f0a683e1c0c68a94be9fc7ce8f83d2b6d09fb9bacbfd8b819aa9d7c8b59bbd83f0f4ff8e8cf4,
  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,
  0x11212120f0e07]
private def node931:Certificate:=PackedParametricCertificateData.decode 8 data931
private def data963:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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]
private def node963:Certificate:=PackedParametricCertificateData.decode 8 data963
private def node964:Certificate:=.split node931 node963
private def data985:List Nat:=[
  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]
private def node985:Certificate:=PackedParametricCertificateData.decode 9 data985
private def node986:Certificate:=.split node964 node985
private def node987:Certificate:=.negative 1 [(1,0),(1,6),(3,8)] node986
private def node988:Certificate:=.split node897 node987
private def node989:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node988
private def node990:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node989
private def node991:Certificate:=.positive 4 [(4,0),(1,3),(3,5)] node990
private def data1023:List Nat:=[
  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]
private def node1023:Certificate:=PackedParametricCertificateData.decode 11 data1023
private def data1067:List Nat:=[
  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,
  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,
  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]
private def node1067:Certificate:=PackedParametricCertificateData.decode 11 data1067
private def node1068:Certificate:=.split node1023 node1067
private def node1069:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1068
private def node1070:Certificate:=.positive 5 [(3,0),(6,2),(2,4)] node1069
private def data1102:List Nat:=[
  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]
private def node1102:Certificate:=PackedParametricCertificateData.decode 11 data1102
private def data1138:List Nat:=[
  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,
  0x1130e130d110c0d0c0f0b0d0b0a0202020c0113000a130e130d110c0d0c0f0b0d0b0a0202020c0109130e130d110c0d0c0f0b0d0b0a0202020c010906130e130d110c120b0f0b0d0b02020c010a0108000a130e130d110c120b0f0b0d0b02020c010a0108000a130e130d110c120b0f0b0d0b02020c010a0108000a06010c020b0201060018041a04130e130d110c120b0f0b0d0b0e0202020a0108000a130e]
private def node1138:Certificate:=PackedParametricCertificateData.decode 11 data1138
private def node1139:Certificate:=.split node1102 node1138
private def node1140:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1139
private def node1141:Certificate:=.positive 1 [(1,2),(2,8)] node1140
private def node1142:Certificate:=.split node1070 node1141
private def node1143:Certificate:=.split node991 node1142
private def data1184:List Nat:=[
  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,
  0x1131312110c0b100a0a080d040a021100080003000a131312110c0b100a0a080d040a021100080003000a131312110c0b100a0a080d040a021100080003000a06110200020202030b020a02030c000c0410031104040202020311110d0d0e080a0813040d0404040d0303030a000a131311110d0d0e080a08080804040d0303030a000a131311110d0d0e080a08080804040d0303030a000a0611020002]
private def node1184:Certificate:=PackedParametricCertificateData.decode 11 data1184
private def data1219:List Nat:=[
  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,
  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,
  0x102021fa2e8d79498b8c2a88ba5e1a9eab39bebeb84020202021fac87c0b6ec82d186ad9acbf5d8e897c9b8e80b01020219cfe89593a7c3d68cafabaaebeba0b6b3cd9a0a0102020ad7af97e2f9d1a8f9d5f9cacdbb88a6efe4d20901020201dcdd97e2a7c5f781adc496b89a8dc7c0b3a80800020209ddd5e89dc38a91dbb48cec97d1dbe0c4f88e1211010217d7bdd4d5c7ceaeefe5e297b2eeeaaeeacb8c0e0e01020593a49bf8cec0bf89f2f0879ee3c1d3dea7c80d0d01021cc8fe8c8effd680f1f69281db8c90a8eb92d0120b01021d99a2e4a68cca9ef0e2a889c1ec90d6c889e00e0201027cd9b8f6abbdc39296cdcecfe8d2dfa186dc0202010220bad4e0cbd1d0a1dcacea8babecd5df878d840b01010217a2bbefdcf2b9b6a79df485f5c186dae9acde0a0101020fb089daa4cd98a392a9d6a5cae2c096cdc98a0800010205f8fea1de8bcedffcc0c4e5f9aff69580f7e6121100023587b48e8ede81def8fab8fbd9efeddebbd0f80e0e0002058beebfe4a08095eec5baa4de95d0b6c7e0f80d0d000215aee6cdb8d3abd5dcf498ab87eaf7bfa1bba80c0c000207a8c7deeff3e0ecccaa8ca1f7e086beb2c8980e020002018fc1a2b386a093a2e8aeedc1f8b0efaef2a80202000220b3d7acccecb4b5e6b4acd886f6e48ce8b0c00b01000216f4de92cee494a9d9dead9eaefe96eab1afec0a0100020ff4c58dc4,
  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,
  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]
private def node1219:Certificate:=PackedParametricCertificateData.decode 11 data1219
private def node1220:Certificate:=.split node1184 node1219
private def node1221:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1220
private def node1222:Certificate:=.positive 1 [(1,0),(2,5)] node1221
private def data1269:List Nat:=[
  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,
  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]
private def node1269:Certificate:=PackedParametricCertificateData.decode 11 data1269
private def data1302:List Nat:=[
  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,
  0x1130e130d110c0d0c110b0d0b0a0202020c0113000a130e130d110c0d0c110b0d0b0a0202020c0109130e130d110c0d0c110b0d0b0a0202020c0109060e0201020202040c020b0201060018041a04130e130d110c0d0c0d0b0e020d02080202020a010a130e130d110c0d0c0d0b0e020d02080202020a010a130e130d]
private def node1302:Certificate:=PackedParametricCertificateData.decode 11 data1302
private def node1303:Certificate:=.split node1269 node1302
private def node1304:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1303
private def data1354:List Nat:=[
  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,
  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]
private def node1354:Certificate:=PackedParametricCertificateData.decode 11 data1354
private def data1379:List Nat:=[
  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]
private def node1379:Certificate:=PackedParametricCertificateData.decode 11 data1379
private def node1380:Certificate:=.split node1354 node1379
private def node1381:Certificate:=.positive 2 [(1,5),(1,6),(6,9)] node1380
private def node1382:Certificate:=.split node1304 node1381
private def node1383:Certificate:=.split node1222 node1382
private def node1384:Certificate:=.negative 1 [(3,0),(2,3)] node1383
private def node1385:Certificate:=.split node1143 node1384
private def node1386:Certificate:=.split node869 node1385
private def node1387:Certificate:=.positive 1 [(1,0),(2,4)] node1386
private def data1398:List Nat:=[
  0x113131010130a110a0b0a13091109130211020913131010130a110a0b0a13091109130211020913131010130a110a0b0a130911091302110209060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030d08070606060212041a030c04010200020308030b100a1208360120043003080606020002030203]
private def node1398:Certificate:=PackedParametricCertificateData.decode 11 data1398
private def data1408:List Nat:=[
  0x11313100a130911090a09130811080808130212010a1313100a130911090a09130811080808130212010a1313100a130911090a09130811080808130212010a060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030d08070606060212041a030c04010200020308030a0608120008030803]
private def node1408:Certificate:=PackedParametricCertificateData.decode 10 data1408
private def data1465:List Nat:=[
  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,
  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,
  0x10302020203131311100a091108090810060a060d04080203020a131311101108090810060a0608060d04080203020a131311101108090810060a0608060d04080203020a060f040a02010a0004040e030b02090201120030043603010a0209020402010a0408030d060102020204011110110e11080d040404110210000e000800091110110e11080d040404110210000e000800091110110e11080d040404110210000e00080009061008050600060308031204030202020313131110110e0a09090911080d040802060213010a13131110110e0a09090911080d040802060213010a13131110110e0a09090911080d040802060213010a060f040a02010a0004040e030b02090201120030043603010a0209020202010404060313131110110e130d130811080404110202000913131110110e130d1108130211020713131110110e130d1308110811020706100803060018031a031204030202020313131110130d110a1308110811070907080206020a13131110130d110a1308110811070713131110130d110a13081108110707060a040306010c00080416030b0209020112003004360301090c020801060004041203010e0400020206030113131312111011091308110809080707120607060a13131312111011091308110807071202081313131211101109130811080707120108060a040306010c00080416030b,
  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]
private def node1465:Certificate:=PackedParametricCertificateData.decode 10 data1465
private def node1466:Certificate:=.split node1408 node1465
private def node1467:Certificate:=.split node1398 node1466
private def node1468:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1467
private def node1469:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node1468
private def node1470:Certificate:=.positive 4 [(4,0),(1,3),(3,5)] node1469
private def node1471:Certificate:=.positive 1 [(1,1),(2,3),(2,6)] node1470
private def node1472:Certificate:=.positive 3 [(1,0),(2,5)] node1471
private def data1493:List Nat:=[
  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]
private def node1493:Certificate:=PackedParametricCertificateData.decode 11 data1493
private def data1503:List Nat:=[
  0x113100e0a110910090b090a0911080808110410010a13100e0a110910090b090a0911080808110410010a13100e0a110910090b090a0911080808110410010a060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030c020a0404020302030e0400020206030d08070606060212041a030c04010200020308030b0408180708000a040e03]
private def node1503:Certificate:=PackedParametricCertificateData.decode 10 data1503
private def data1554:List Nat:=[
  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,
  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,
  0x10202030b020902011200300436030502040200020302030e040a0401060306030d0601020202040c020802010603060301b48b4ab13ebf0190ee08cbf028b79d43cf882387e10013dfb5b3f1fffc1010020202f1f3b0f8f2daf3c39ad8800a0a020233dc8b80c2a580e7b694c01306020204e6989ce6b4f2f7c888be801006020206abfc98e4c18cfbdb869280060602020f8cf98ffd95cdfdb589d880130402020397d9d185bcbea8f3cd9dc01004020201aeadfebd9de6c9e9f6eac00604020219f6b1a9aad084f898b3f8c0040402020b908da5f5eea6f1bbecc5901111010249d6e5ea9a99e5b4e3c5a80a0a010236ceb1b6adf1e1b8b4cda8080801025f9dabf8d2d184bc80ab961306010207bcf3dcb9f8d597eca8ca801006010207fbdb9c82fa8aaabf958088060601020db5e5fab5a7a2c8ff97eca21304010203dabbe38ddfe28a85a8ca881004010207d4f6acfaa5c4f9a3a7eaa00604010215a1f6f4a69ad98ce1b790a8040401020796c489e1cbbc81d5e2fcb01111000271bce6bac1d8a8dbb5ecf40a0a000231d5c3e1b1fb9bedcff7900808000241fce6d19cdc959c8e8a8c1306000208aa86c1e58cf8e2c489c7901006000206e6c29de9bea0fc87e58b90060600020d93f68e8aa6b9e7a8bb8bb41304000203a8b197bea4aec78ea3b0b81004000208f8afcbb0e0e782b69fc6800604000215a480c0fe,
  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,
  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,
  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]
private def node1554:Certificate:=PackedParametricCertificateData.decode 9 data1554
private def data1598:List Nat:=[
  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,
  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]
private def node1598:Certificate:=PackedParametricCertificateData.decode 9 data1598
private def node1599:Certificate:=.split node1554 node1598
private def node1600:Certificate:=.split node1503 node1599
private def node1601:Certificate:=.split node1493 node1600
private def node1602:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1601
private def node1603:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node1602
private def node1604:Certificate:=.positive 4 [(4,0),(1,3),(3,5)] node1603
private def node1605:Certificate:=.positive 1 [(3,0),(2,3)] node1604
private def data1636:List Nat:=[
  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]
private def node1636:Certificate:=PackedParametricCertificateData.decode 11 data1636
private def data1682:List Nat:=[
  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,
  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,
  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,
  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,
  0x113131111100e0e040d040e030b03020209010d000a13131111100e0e040d040e030b03020209010d000a13131111100e0e040d040e030b03020209010d000a0611020002020204131313121111100e0e040e030b03090202020d000a131313121111100e0e040e030b03090202020d000a131313121111100e0e040e030b03]
private def node1682:Certificate:=PackedParametricCertificateData.decode 9 data1682
private def data1703:List Nat:=[
  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]
private def node1703:Certificate:=PackedParametricCertificateData.decode 9 data1703
private def node1704:Certificate:=.split node1682 node1703
private def node1705:Certificate:=.negative 1 [(1,0),(1,5),(1,7)] node1704
private def node1706:Certificate:=.split node1636 node1705
private def node1707:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1706
private def node1708:Certificate:=.positive 3 [(1,0),(2,1),(2,4)] node1707
private def node1709:Certificate:=.positive 4 [(4,0),(1,3),(3,5)] node1708
private def data1751:List Nat:=[
  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,
  0x113121111130d0c090a080d040a021100080003000a131211110c0b0c090a080d040a021100080003000a131211110c0b0c090a080d040a021100080003000a0610020b06090600060408030b020a02030c000c0410031104040202020311110d0d0e080a0813040d0404040d0303030a000a131311110d0d0e080a08080804040d0303030a000a131311110d0d0e080a08080804040d0303030a000a0610020b06090600060408030b020902011200300436]
private def node1751:Certificate:=PackedParametricCertificateData.decode 11 data1751
private def data1809:List Nat:=[
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,
  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,
  0x12edae65fdad13bd0b001fbdb0101a1a08499e4dce1f1e784903c971e8436c6148c20a5dc42aecf2c888408d4bb0003b5c3ddaec4a8fbcbb18cd2e0131202020baa9dd8dcd5b3c2e58cdaa4e18bcdd3f0111102026888b3be8cf5bac8b2f596d59d94e68ea8120d02020193aa9aeba9ffa9aee7eec4ecc4f6b8fae80d0d020278cec68ccc93bad4ab8bf6de8ce4cbfff60c0c0202318f95d7afbcd2a1e6d1c5f385c297c3aa0c0b02020189c7c0c3b6f69493]
private def node1809:Certificate:=PackedParametricCertificateData.decode 9 data1809
private def data1818:List Nat:=[
  0x113130d0d0c0b100809080d0309020602060101010a13130d0d0c0b1008090813030d030902060201010a13130d0d0c0b1008090813030d030902060201010a060f0c0d0807120026042c040f040c0406060302040e020b0205040202040204100404020202030b0202020202040b040804020600020408040a0607060204000a040e04090606060104000e041204]
private def node1818:Certificate:=PackedParametricCertificateData.decode 9 data1818
private def node1819:Certificate:=.split node1809 node1818
private def node1820:Certificate:=.negative 11 [(11,0),(3,4),(2,6),(9,7)] node1819
private def node1821:Certificate:=.split node1751 node1820
private def node1822:Certificate:=.positive 4 [(4,0),(3,5),(1,7)] node1821
private def data1873:List Nat:=[
  0x10c0416030b02090201120030043603050204020002030203010806070601040304040111110d0d11080e080a0808080d06040403030a000a11110d0d0e080a0808080d06040403030a020a000a11110d0d0e080a0808080d06040403030a020a000a061008050600060308030b020902011200300436030502040200020302030902070202060306030d0d0e0808081306110408040d0303030c020a020a11110d0d0e08080813061104080403030c020a020a11110d0d0e08080813061104080403030c020a020a060a040306010c00080416030b02090201120030043603050204020002030203090c020801060004041203010e040002020603010c0402020206030b1c081205120102041e030d0d110a0b090e080a08080813040904040311000a0d0d110a0b090e080a08080813040904060411000a0d0d110a0b090e080a08080813040904060411000a0610060a0408060008040a030b020902011200300436030502040200020302030902070202060306030d0d0e0a10090b090e080b040d030e021100090d0d0e0a10090b090e080d0311020e021100090d0d0e0a10090b090e080d0311020e02110009060a040306010c00080416030b02090201120030043603050204020002030203090c020801060004041203010e0400020206030602040202060306030c04010200020308030b1c081205120102041e0301,
  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]
private def node1873:Certificate:=PackedParametricCertificateData.decode 11 data1873
private def data1910:List Nat:=[
  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,
  0x183cdb9c00c000002078fa6e7f5aa8b93ff91f0e2d0020000020185fc84e6caf6c7aaf1ef93f00100000203a8d790d8d9bc89bec0eac780000000020280bfb2e2b4e0caceeb978d881e1df7f7cd9cc0000101110404020202030d04080401060306040e02000202020405cd03cf29ab03a215928038a5d539edc816bee90009cdab92fba5abbe98a88bc1b1e4a83da8a40182c0f9539abe2cf2831c9fd53f9d982cb8a3169a8600058bf9a3b0d5839cebcacc89f1b00d0d020204f5f8c2d8d4ffbea5f68e8af4f1c387958b9fa2130c020204c1dadce1a4ebd1ee809bf5a0baf4a6c5eeedf20a0a020201b5af9fccc5948491a0afdbced995d288acade0100502020187f2a4f9a2f9c2c9c8e8efe7e8f086e3b5d5e00805020217ddade7f68883b2fda8cab1c0f099b99ea5c4a00c0202020490e9a8f39ccdf5b09accbabca3a0f599edc78a0c0102021dc7aeec859dcba488bd9b90f0f1a8b98596b6030002020d94979f9ecfe5aad19ae786fbdcbacebecf95e00000020259b5c6bcdfd2a09bb3d8b588e1ddaba1e3beb00d0d0102058fb1f5bdbad4b2a5c6b28af2c6f7f2ff8c9290130c010204d8ccb0b1cecbbda3a6c6dc81f38ea0888fbde00a0a010201b2a7fab0abb9c5bfd5c6ddb5d7b3d8dc89c49010050102018dcfa8beb7c4dd83ba8c97be9c87e697b5d1a00805010217b8abe68ce69ef7faf4d1f989b8e8e6e7,
  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,
  0x1b00a00020204aafebf9d8d99cbbed2809eced5afa4e4b9b5d1a2cfb8c00000020203d78081d3f189cfe0ecce86f0de85ddf1c391ada9b4fec011110102029cffcad3fcd6bf9dca97de8388bbefecb282bff6b2ef800d0d0102019d80b4adce93b0e5a4c3b4eaacd490c29ffe96fee3e4de0c0c01020882b7c48b8a9db2fae8b2d1e886c29296c8bdf3e8bcba820c07010226bc82dcd1c292dae6c3c5d7ec969dab9bd7d2c5e0a2dce00c02010201f789c1d7f8b9a6e4d3f3deaca2b9aeacd79499b9fa89a207020102428ffa89d2a4dd88b78fbbc7ced7d78fa6d9ef94b58bbb9a0c0101021cf5b69d92908ba4bcf4b0ffa180a9d5e4f39ad6ffaef5d8010101020c9490b9a5c0e4ce8abba2b1e0ac998eabe2bfb7c68ca3c80a0001020585ed8ea2ece199baf7eca4b9d891fdd6aac999ecd2a7be1111000201e6e984a6dd9fddd0c1eec298f88ca6d1e5849695eaeda00c0c000207b390b8dfdbe6df828ca7d0e6db98bfe992d9ecd5f9eec00a0a000202aedf9698b0d1f2cfe0ad8dc0cdd789a681c3a9b4dee5b00c0700021fe593a1b4b8c9b4baeba1d9a4c5b6d3f380fb85cde6ecf00c02000204eced91cee8c4c7e5cee5f1e28c9892c3a9f8868eeaf98c0702000244d2a29face5e3e9d4aea7b3eee7e0cbde9fc6ecdeb28f9c0c0100021b86ddc994a2eacde5d7e09abf98e5c086b7c3fbab8af0c0010100020baead,
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]
private def node1910:Certificate:=PackedParametricCertificateData.decode 11 data1910
private def node1911:Certificate:=.split node1873 node1910
private def data1957:List Nat:=[
  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,
  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]
private def node1957:Certificate:=PackedParametricCertificateData.decode 11 data1957
private def data1981:List Nat:=[
  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,
  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,
  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,
  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,
  0x1029ea005cacf79c8a409aa85011ca186bbbcc5878fa4ac84e0d6c1f294f8d0de9485e835afd26dced706889f50e90107b1fdd09dd098b2ee9b90bfedb98c93f4a7b8c8908048e101c29208db9408faff7ea002d8df4df79e14dcfd0008cbacdf81e0c0b3f5ce95a1acc99bcab6f3a4afcfd1a034c7e0]
private def node1981:Certificate:=PackedParametricCertificateData.decode 11 data1981
private def node1982:Certificate:=.split node1957 node1981
private def node1983:Certificate:=.split node1911 node1982
private def node1984:Certificate:=.split node1822 node1983
private def data2035:List Nat:=[
  0x1020c010a010a060c0a0a060206000e04100311020906012a0066047403050204020002030203010d06010202020401130d130c0d0b100a0d0908080c020a020d010a010a130d130c100c0d0b100a0d0908080c020d010a010a130d130c0d0b100a0d0908080c020a020d010a010a060c080a080506000e04100311020906012a006604740305020402000203020305020204020203130d130c100c0d0b0d0908080c020a020d010a010a130d130c100c0d0b100a0d0908080c020d010a010a130d130c0d0b100a0d0908080c020a020d010a010a060a040306010c000804160311020906012a006604740305020402000203020305020204020203010e040002020603010c0402020206030b1c081205120102041e03100e130d0b0908080a04090411020e0208020d010a100e130d0b0908080a04090411020e0208020d010a100e130d0b0908080a04090411020e0208020d010a060c080a080506000e04100311020906012a0066047403050204020002030203110402020202030b0a13090b090e0813040b04110210020e02090b0a13090b090e0813040b04110210020e02090b0a13090b090e0813040b04110210020e0209060a040306010c000804160311020906012a006604740305020402000203020311040202020203010e0400020206030e0402020202030c04010200020308030b1c081205120102041e0301,
  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]
private def node2035:Certificate:=PackedParametricCertificateData.decode 11 data2035
private def data2060:List Nat:=[
  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,
  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,
  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,
  0x102f3bf02f3c063abc446f0f501518cc5f5e7a7daebb8f785c03ab83a8f6ae705f29801fef501fef645a9a036e7990005bad9c9f5f79396ace7c7a4801212020263b4d0daf7c3bdedf4cda3cbd496bc801411020201b29689c6d4c29ae1c4e5fdecfed9b7d9c0140d02020be7d5da828dead7d8c1d7f9aed9b5af9ec0120c020222dbbef2ac83b29292a7ee9fe7ebe0800b0b02020b91adcbf4dfe5939bacb7d4bf9fc0800d0a02020cd6b5c8ff]
private def node2060:Certificate:=PackedParametricCertificateData.decode 11 data2060
private def node2061:Certificate:=.split node2035 node2060
private def node2062:Certificate:=.positive 1 [(1,1),(6,9)] node2061
private def node2063:Certificate:=.negative 1 [(1,0),(2,5)] node2062
private def node2064:Certificate:=.split node1984 node2063
private def node2065:Certificate:=.split node1709 node2064
private def node2066:Certificate:=.split node1605 node2065
private def node2067:Certificate:=.split node1472 node2066
private def data2078:List Nat:=[
  0x1131313111010110d160a130a0b0a1609160209131313111010110d160a130a0b0a1609160209131313111010110d160a130a0b0a1609160209060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030d08070606060212041a030c04010200020308030d2c0a02020601120412030712060404060016041603]
private def node2078:Certificate:=PackedParametricCertificateData.decode 11 data2078
private def data2088:List Nat:=[
  0x113131311110a100a160913090a091608080816020a13131311110a100a160913090a091608080816020a13131311110a100a160913090a091608080816020a060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030b0202020202030e0400020206030d08070606060212041a030c04010200020308030d0c0002020203]
private def node2088:Certificate:=PackedParametricCertificateData.decode 10 data2088
private def data2143:List Nat:=[
  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,
  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]
private def node2143:Certificate:=PackedParametricCertificateData.decode 10 data2143
private def node2144:Certificate:=.split node2088 node2143
private def node2145:Certificate:=.split node2078 node2144
private def node2146:Certificate:=.positive 1 [(1,0),(2,10)] node2145
private def node2147:Certificate:=.positive 5 [(4,0),(3,3),(8,9)] node2146
private def node2148:Certificate:=.positive 7 [(5,0),(4,5),(6,7)] node2147
private def node2149:Certificate:=.positive 9 [(5,1),(6,2),(22,6)] node2148
private def node2150:Certificate:=.positive 3 [(1,0),(2,5)] node2149
private def data2161:List Nat:=[
  0x1131113101010110d160a0b0a16091009160209131113101010110d160a0b0a16091009160209131113101010110d160a0b0a16091009160209060a040306010c00080416030b02090201120030043603050204020002030203090c0208010600040412030a0605020202030e0400020206030d08070606060212041a030c04010200020308030d24070202060110041003070205020002030203]
private def node2161:Certificate:=PackedParametricCertificateData.decode 11 data2161
private def data2176:List Nat:=[
  0x113130e0a0b090808110409040a030403080204010a13130e0a0b09080813041104090406040a0308020a13130e0a0b09080813041104090406040a0308020a060e0201020202030b020902011200300436030502040200020302030a020902020201040406031310110a10090a090908100608040a03160110010a1310110a10090a09090808040a030802160110010a1310110a10090a09090808040a030802160110010a060a040306010c00080416030b02090201120030043603050204020002030203090c020801060004041203010e0400020206030d08070606060212041a030c04010200020308030d0c0002020203]
private def node2176:Certificate:=PackedParametricCertificateData.decode 10 data2176
private def data2236:List Nat:=[
  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,
  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,
  0x113101110140d100d0b0b10080e060a06060201010a13101110140d100d0b0b10080e060a06060201010a13101110140d100d0b0b10080e060a06060201010a06100803060018031a0413131110100d0b0b10080e060a]
private def node2236:Certificate:=PackedParametricCertificateData.decode 10 data2236
private def node2237:Certificate:=.split node2176 node2236
private def node2238:Certificate:=.split node2161 node2237
private def node2239:Certificate:=.positive 1 [(1,0),(2,10)] node2238
private def node2240:Certificate:=.positive 1 [(1,1),(2,9)] node2239
private def node2241:Certificate:=.positive 7 [(5,0),(4,5),(6,7)] node2240
private def node2242:Certificate:=.positive 3 [(5,0),(2,2),(4,6)] node2241
private def data2268:List Nat:=[
  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]
private def node2268:Certificate:=PackedParametricCertificateData.decode 11 data2268
private def data2278:List Nat:=[
  0x10d0d0b09080811040e0409040a0304030b0108000a0d0d0b09080811040e0406040a0304030b0108000a0d0d0b09080811040e0406040a0304030b0108000a060b0a080607060106040a030b020902011200300436030502040200020302030a020902020201040406030a0605020202040e0400020206030d08070606060212041a030c04010200020308030d0c0002020203]
private def node2278:Certificate:=PackedParametricCertificateData.decode 10 data2278
private def data2312:List Nat:=[
  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,
  0x11111130e100e130d09091303110309020a0002000a1111130e100e130d09091303110309020a0002000a1111130e100e130d09091303110309020a0002000a060e0201020202040f040c040606030203130e100e130d0909130311030202]
private def node2312:Certificate:=PackedParametricCertificateData.decode 9 data2312
private def data2355:List Nat:=[
  0x1000a100e100d0f0d10080e06080610030802030209000a100e100d0f0d10080e06080610030802030209000a06100e100d0f0d10080e06080610031102080203020a100e100d0f0d10080e060a0608061003110208020a100e100d0f0d10080e060a0608061003110208020a06010b02090201120030043603010d040a08090401120412030b02020202020401100e100d0f0d160810080f0810030902080101000a100e100d0f0d160810080f0810030902080101000a100e100d0f0d160810080f0810030902080101000a060e020102020204120403020202030f0e100d0f0d0d09100809080f030802060203020a0f0e100d0f0d0d09100809080f030802060203020a0f0e100d0f0d0d09100809080f030802060203020a060f0e100d0f0d0d09100809080f030802060203020a0f0e100d0f0d0d09100809080f030802060203020a0f0e100d0f0d0d09100809080f030802060203020a06010b02090201120030043603010a020902020201040406030b0202020202040e04000202060301100e0f0e100d0d09100809080f030703080203020a100e100d0d09100809080e070f030703080203020a100e100d0f0d0e090d09100809080f03070308020a060b0206060202030b02090201120030043603110404020202030a020902020201040406030b020a06040203020404040e0400020206030102000402020301,
  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]
private def node2355:Certificate:=PackedParametricCertificateData.decode 9 data2355
private def node2356:Certificate:=.split node2312 node2355
private def node2357:Certificate:=.split node2278 node2356
private def node2358:Certificate:=.split node2268 node2357
private def node2359:Certificate:=.positive 1 [(1,0),(2,10)] node2358
private def node2360:Certificate:=.positive 1 [(1,1),(2,9)] node2359
private def node2361:Certificate:=.positive 7 [(5,0),(4,5),(6,7)] node2360
private def data2387:List Nat:=[
  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]
private def node2387:Certificate:=PackedParametricCertificateData.decode 11 data2387
private def data2397:List Nat:=[
  0x10d0d0d0a0b090e0809080808110409040a030e020a0e0e0d0d0d0a0b090e0809080808110409040a030a0e0e0d0d0d0a0b090e0809080808110409040a030a060b0a080607060106040a030b0209020112003004360305020402000203020309020802020401020406030c0c0b0c091205160416040e0400020206030d040606050602120416030c0401020002030803050602060004030403]
private def node2397:Certificate:=PackedParametricCertificateData.decode 10 data2397
private def data2442:List Nat:=[
  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,
  0x1131111110d0d0b09090908080a0202020b0109010a13110d0d0b09090908080b020a0202020b0109010a13110d0d0b09090908080b020a0202020b0109010a06100803060018031a04131111110d0d0b09090908080b020a02020210010a131111110d0d0b09090908080b020a02020210010a131111110d0d0b09090908080b020a02020210010a0610080d0c030601240426040113111111110d0d0d0a0a0808030302020b000a000a1311110d0d0d0a0a0e0808080e0202020b000a000a1311110d0d0d0a0a0e0808080e0202020b000a000a061002060402020302040f020a0200060306030113110e0e0d0d0b0b08080d0303030902020209010a13110e0e0d0d0b0b08080d0303030b02020209010a13110e0e0d0d0b0b08080d0303030b02020209010a06100803060018031a04131111110d0d0b0b08080d0303030b02090202020a131111110d0d0b0b08080d0303030b02090202020a131111110d0d0b0b08080d0303030b02090202020a0610080d0c0306]
private def node2442:Certificate:=PackedParametricCertificateData.decode 9 data2442
private def data2485:List Nat:=[
  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,
  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]
private def node2485:Certificate:=PackedParametricCertificateData.decode 9 data2485
private def node2486:Certificate:=.split node2442 node2485
private def node2487:Certificate:=.split node2397 node2486
private def node2488:Certificate:=.split node2387 node2487
private def node2489:Certificate:=.positive 1 [(2,0),(1,2)] node2488
private def data2526:List Nat:=[
  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,
  0x113130d0d0a0a0a0811040d040e020a02080003000a13130d0d0a0a0a0811040d040e020a02080003000a13130d0d0a0a0a0811040d040e020a02080003000a060a02090204040302030b0209]
private def node2526:Certificate:=PackedParametricCertificateData.decode 11 data2526
private def data2536:List Nat:=[
  0x10d0d0d0a0b090c0809080808110409040a030e020a0d0d0d0a0b090e0809080808110409040a030e020a0d0d0d0a0b090e0809080808110409040a030e020a060a1e081c07080112041e030b020902011200300436030504020600020304030902070202060306030b06070605080308040e0400020206030602040202060306030c0401020002030803050602060004030403]
private def node2536:Certificate:=PackedParametricCertificateData.decode 10 data2536
private def data2595:List Nat:=[
  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,
  0x1010a000a06100803060018031a0413111111110d0d0d0a0a08080c0202020b000a000a13111111110d0d0d0a0a08080c0202020b000a000a13111111110d0d0d0a0a08080c0202020b000a000a060b020606020204010113110e0e0d0d0b0b08080d0303030902020209010a13110e0e0d0d0b0b08080d0303030b02020209010a13110e0e0d0d0b0b08080d0303030b02020209010a06100803060018031a04131111110d0d080811030d0303030b02090202020a131111110d0d080811030d0303030b02090202020a131111110d0d080811030d0303030b02090202020a060b0803060118031a040113110d0d0a0a080811030d03030302020a0009000a13110d0d0a0a080811030d0303030c02020209000a13110d0d0a0a080811030d0303030c02020209000a060b0206060202040b0209020112003004360301010b02020202020413110e0e0d0d0a0a0e0808080d030d000a0009000a13110e0e0d0d0a0a0e0808080d030d000a0009000a13110e0e0d0d0a0a0e0808080d030d000a0009000a060b0206060202040b02090201120030043603050402060002030403030401060202030b020202020204010102000402020413111111110d0d0d0a0a08080c0202020b000a000a13111111110d0d0d0a0a08080c0202020b000a000a13111111110d0d0d0a0a08080c0202020b000a000a06100204060202040f0209,
  0x113111111130d110d0d0d08080a0202020b0109010a131111110d0d0b0908080d040b030a0202020b010a131111110d0d0b0908080d040b030a0202020b010a06100803060018031a0413111111130d110d0d0d08080b020a02020210010a13111111130d110d0d0d08080b020a02020210010a13111111130d110d0d0d08080b020a02020210010a060b0803060118031a040113111111110d0d0d0a0a08080e0202020b010a000a13111111110d0d0d0a0a08080e0202020b010a000a13111111110d0d0d0a0a08080e0202020b]
private def node2595:Certificate:=PackedParametricCertificateData.decode 9 data2595
private def data2637:List Nat:=[
  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,
  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]
private def node2637:Certificate:=PackedParametricCertificateData.decode 9 data2637
private def node2638:Certificate:=.split node2595 node2637
private def node2639:Certificate:=.split node2536 node2638
private def node2640:Certificate:=.split node2526 node2639
private def data2689:List Nat:=[
  0x10c000b000a000a0d0d10090b09080811030d0306020e000b000a000a06010702010e002003240311040402020203010e060c060108030804010b090808090411030d030403090003000100090b090808090413030d030403090003000100090b090808090413030d0304030900030001000906110d0d0d10090b090a08110304030e000c000a000a110d0d0d10090b090a08080811030e000c000a000a110d0d0d10090b090a08080811030e000b000a000a06010702010e0020032403110805020302030403110402020202030e040c02060404060406040e040002020603010c0402020206030b040108000603060315131511160b1609150908080d03090003000915131511160b160915090a080808090003000915131511160b150b1609150908080d030900090615131511160b150b160a16090e080d0304000915131511160b150b160a16090e080d030815131511160b150b160a16090e080d0308060113040106001003120311080502030203040311040202020203110d0d0d160b150b160a160915090b04160209110d0d0d160b150b160a160915090b04160209110d0d0d160b150b160a160915090c04160209060c0407060306000a040e030b060202010a0026042a03050402060002030403090c020801060004041203010e0400020206030e0402020202030c04010200020308030d120b02010403060301,
  0x115131511150b11090a0811020a02020201010915131511150b11090a0811020a02020201010915131511150b11090a0811020a02020201010906100803060018031a0415131511150b11090a080a020b01020101010915131511150b11090a080a020b01020101010915131511150b11090a080a020b010201010109061002040602020401111007020206030604020401060306040e0200020202041513150b0b090a090a080e05080515040503091513150b0b090a090a080e0515040504050309150b11090b090a090a080e051504050405030906110d0d0d10090b0908080d040e000c000a0003000a110d0d0d10090b0908080d040e000c000a0003000a110d0d0d10090b0908080d040e000b000a0003000a06011304030600040306031104050202060304030b090808090411030d030403090003000100090b0908080904130311030d03090003000100090b0908080904130311030d0309000300010009060d0d10090b09080811030d0306020c000b000a000a0d0d10090b09080811030d030602]
private def node2689:Certificate:=PackedParametricCertificateData.decode 11 data2689
private def data2700:List Nat:=[
  0x1110a0b0a0a090b081303020210010b010a0009110a0b0a0a090b081303020210010b010a0009110a0b0a0a090b0813030b02020210010a000906110d110a0a090b0809080202100110000c000b000a110d110a0a090b0809080202100110000c000b000a110d110a0a090b0809080202100110000e000b000a06010802010800160318031108050203020304030604020401060306030b06070605080308040e0400020206030d04030402060306030c04010200020308030d0c0002020203]
private def node2700:Certificate:=PackedParametricCertificateData.decode 10 data2700
private def data2761:List Nat:=[
  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,
  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,
  0x114131410110a0b0a0b090902020209010a000914131410110a0b0a0b09090202020a000814131410110a0b0a0b09090202020a0008060a040306010c0008041604110a0b0a0b090a040303090213010b010a0009130a110a0b0a0b090303090213010b010a0009130a110a0b0a0b090303090213010b010a0009060b0803060118031a0401130a110a0b0a1109130211020b020202010109130a110a0b0a1109130211020b020202010109130a110a0b0a1109130211020b02020201010906100803060018031a]
private def node2761:Certificate:=PackedParametricCertificateData.decode 9 data2761
private def data2803:List Nat:=[
  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,
  0x114130b09090413030d0303030601010109000914130b09090413030d0303030601010109000914130b09090413030d03030306010101090009060a040306010c0008041604100a0b09090413030303130111010301090009130a0b09090413030303130111010301090009130a0b09090413030303130111010301090009060b0803060118031a0401100a0b09090413030303130111010301090009130a0b09090413030303130111010301090009130a0b09090413030303130111010301090009060a1007180468030a042e040702010e002003240301100404020202030b020202020204130a11090b]
private def node2803:Certificate:=PackedParametricCertificateData.decode 9 data2803
private def node2804:Certificate:=.split node2761 node2803
private def node2805:Certificate:=.split node2700 node2804
private def node2806:Certificate:=.split node2689 node2805
private def node2807:Certificate:=.split node2640 node2806
private def node2808:Certificate:=.split node2489 node2807
private def node2809:Certificate:=.positive 8 [(5,3),(1,5),(24,7)] node2808
private def node2810:Certificate:=.split node2361 node2809
private def node2811:Certificate:=.split node2242 node2810
private def node2812:Certificate:=.split node2150 node2811
private def node2813:Certificate:=.split node2067 node2812
private def node2814:Certificate:=.split node1387 node2813
private def node2815:Certificate:=.split node729 node2814
private def zz498:"s01f2"="s01f2":=by decide+kernel
private theorem valid170:check node170 ctx170 quad170 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid250:check node250 ctx250 quad250 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid341:check node341 ctx341 quad341 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid250
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid342:check node342 ctx342 quad342 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid170
  · exact valid341
private def zz499:"s01f3"="s01f3":=by decide+kernel
private theorem valid490:check node490 ctx490 quad490 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid574:check node574 ctx574 quad574 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid490
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid575:check node575 ctx575 quad575 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid574
private theorem valid649:check node649 ctx649 quad649 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private def zz500:"s01f4"="s01f4":=by decide+kernel
private theorem valid725:check node725 ctx725 quad725 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · exact valid649
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid729:check node729 ctx729 quad729 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid342
      · apply NatParametricCheckSteps.split_valid
        · exact valid575
        · exact valid725
private theorem valid865:check node865 ctx865 quad865 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid988:check node988 ctx988 quad988 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private def zz501:"s01f5"="s01f5":=by decide+kernel
private theorem valid1070:check node1070 ctx1070 quad1070 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1142:check node1142 ctx1142 quad1142 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1070
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1304:check node1304 ctx1304 quad1304 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1382:check node1382 ctx1382 quad1382 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1304
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private def zz502:"s01f6"="s01f6":=by decide+kernel
private theorem valid1384:check node1384 ctx1384 quad1384 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid1382
private theorem valid1385:check node1385 ctx1385 quad1385 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid988
    · exact valid1142
  · exact valid1384
private theorem valid1387:check node1387 ctx1387 quad1387 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid865
    · exact valid1385
private theorem valid1470:check node1470 ctx1470 quad1470 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz503:"s01f7"="s01f7":=by decide+kernel
private theorem valid1602:check node1602 ctx1602 quad1602 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1708:check node1708 ctx1708 quad1708 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1822:check node1822 ctx1822 quad1822 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1983:check node1983 ctx1983 quad1983 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private def zz504:"s01f8"="s01f8":=by decide+kernel
private theorem valid2063:check node2063 ctx2063 quad2063 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2065:check node2065 ctx2065 quad2065 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid1708
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid1822
      · exact valid1983
    · exact valid2063
private theorem valid2066:check node2066 ctx2066 quad2066 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid1602
  · exact valid2065
private theorem valid2067:check node2067 ctx2067 quad2067 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1470
  · exact valid2066
private def zz505:"s01f9"="s01f9":=by decide+kernel
private theorem valid2148:check node2148 ctx2148 quad2148 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2241:check node2241 ctx2241 quad2241 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2359:check node2359 ctx2359 quad2359 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2489:check node2489 ctx2489 quad2489 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz506:"s01fa"="s01fa":=by decide+kernel
private theorem valid2640:check node2640 ctx2640 quad2640 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2806:check node2806 ctx2806 quad2806 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2809:check node2809 ctx2809 quad2809 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid2489
    · apply NatParametricCheckSteps.split_valid
      · exact valid2640
      · exact valid2806
private theorem valid2811:check node2811 ctx2811 quad2811 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid2241
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2359
    · exact valid2809
private def zz507:"s01fb"="s01fb":=by decide+kernel
private theorem valid2813:check node2813 ctx2813 quad2813 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2067
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2148
    · exact valid2811
private theorem valid2815:check node2815 ctx2815 quad2815 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid729
  · apply NatParametricCheckSteps.split_valid
    · exact valid1387
    · exact valid2813
theorem certificate_valid:check node2815 constraintsNat base hinges = true:=valid2815
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node2815 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase0
private def zz2176:"s0880"="s0880":=by decide+kernel
end 
section 
namespace Green24Proof.QuadNearBalanceCase1
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x12560049d02880, -0xaa87bee538000, -0xffcb9e57d4000,0x7bd1d6fd8b6c], ![-0xaa87bee538000, -0x5c2b42de1e43d8,0x149a3591f026f8,0x55da62ee47472], ![-0xffcb9e57d4000,0x149a3591f026f8, -0x457ca592ce9ba0,0xab5dbefbf76e8], ![0x7bd1d6fd8b6c,0x55da62ee47472,0xab5dbefbf76e8, -0x5543df729c000]], ![![-0x1119ea5fc70,0,0x88cf52fe38,0], ![0,0x99e93d5dff0,0, -0x2ac0c9ef718], ![0x88cf52fe38,0,0x56acabc2480, -0x15ab2af0920], ![0, -0x2ac0c9ef718, -0x15ab2af0920,0]], ![![-0x3bb390787c40,0x1b5365003d30,0x286f09137130, -0xa3d13b65800], ![0x1b5365003d30,0xd30257723da0, -0x2c3fcf26fa80, -0x3253dc8e7d0], ![0x286f09137130, -0x2c3fcf26fa80,0xc0b0fb83dca0, -0x1f1431db1b90], ![-0xa3d13b65800, -0x3253dc8e7d0, -0x1f1431db1b90,0xda475abf000]]]
def hinges:Hinges:=[(![0,0,0x8d24d0], ![0,0,1, -3]),(![-0x6b000b5fb74,0xad59578490,0x1eade6e5df0], ![0,0,1, -1]),(![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60], ![0,0,3, -1]),(![0,0,0x4c4b40], ![0,1, -3,0]),(![0x5b61255b6c84,0, -0x4f5f5c3d2b0], ![0,1,0, -3]),(![0x1327fce0a51aaf,0, -0x1cb26590e0f0], ![0,1,0, -1]),(![-0x5543df729c000,0,0xda475abf000], ![0,3, -2, -1]),(![0x5543df729c000,0, -0xda475abf000], ![0,3, -2,1]),(![0,0, -0x4c4b40], ![0,3, -1,0]),(![0x60154138c6bd, -0x1119ea5fc70,0], ![0,3,0, -1]),(![0x5543df729c000,0, -0xda475abf000], ![0,3,2, -1]),(![-0x6b000b5fb74,0xad59578490,0x1eae015cc60], ![1, -3,0,0]),(![-0x5543df729c000,0,0xda475abf000], ![1, -2, -3,0]),(![0x5543df729c000,0, -0xda475abf000], ![1, -2,3,0]),(![0x6b000b5fb74, -0xad59578490, -0x1eade6e5df0], ![1, -1,0,0]),(![-0x60154138c6bd,0x1119ea5fc70,0], ![1,0, -3,0]),(![-0x1327fce0a51aaf,0,0x1cb26590e0f0], ![1,0, -1,0]),(![0x1d7839dca6ce,0,0], ![1,0,0, -3]),(![0x5543df729c000,0, -0xda475abf000], ![1,2, -3,0]),(![0,0, -0x8d24d0], ![3, -1,0,0]),(![-0x5b61255b6c84,0,0x4f5f5c3d2b0], ![3,0, -1,0]),(![-0x1d7839dca6ce,0,0], ![3,0,0, -1])]
def normalizationDenominator:ℤ:=0xaa87bee538000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx3529:Nat → Linear:=constraintsNat
private def quad3529:Quadratic:=base
private def ctx920:Nat → Linear:=cons ![0,0,1, -1] (cons ![0,0,1, -3] ctx3529)
private def quad920:Quadratic:=(quad3529 + coefficientProduct ![0,0,0x8d24d0] ![0,0,1, -3] ![0,0,1, -3]) + coefficientProduct ![-0x6b000b5fb74,0xad59578490,0x1eade6e5df0] ![0,0,1, -1] ![0,0,1, -1]
private def ctx81:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -3,0] (cons ![0,0,3, -1] ctx920)))))
private def quad81:Quadratic:=(((((quad920 + coefficientProduct ![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0,0x4c4b40] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx918:Nat → Linear:=cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx920)
private def quad918:Quadratic:=(quad920 + coefficientProduct ![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60] ![0,0,3, -1] ![0,0,3, -1])
private def ctx467:Nat → Linear:=cons ![0,1,0, -3] ctx918
private def quad467:Quadratic:=quad918 + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx226:Nat → Linear:=cons ![0,3,2, -1] (cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx467)))))
private def quad226:Quadratic:=(((((quad467 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3,2, -1] ![0,3,2, -1]
private def ctx465:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] ctx467)
private def quad465:Quadratic:=(quad467 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx464:Nat → Linear:=cons (-![0,3, -2,1]) ctx465
private def quad464:Quadratic:=quad465
private def ctx387:Nat → Linear:=cons ![0,3, -1,0] ctx464
private def quad387:Quadratic:=quad464 + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]
private def ctx540:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx918))
private def quad540:Quadratic:=((quad918) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx764:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx918))
private def quad764:Quadratic:=((quad918) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx763:Nat → Linear:=cons (-![0,3, -2,1]) ctx764
private def quad763:Quadratic:=quad764
private def ctx687:Nat → Linear:=cons ![0,3, -1,0] ctx763
private def quad687:Quadratic:=quad763 + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]
private def ctx915:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx918))
private def quad915:Quadratic:=((quad918))
private def ctx839:Nat → Linear:=cons ![0,3,0, -1] (cons (-![0,3, -1,0]) (cons (-![0,3, -2,1]) ctx915))
private def quad839:Quadratic:=((quad915)) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1706:Nat → Linear:=cons ![0,0,1, -1] (cons (-![0,0,1, -3]) ctx3529)
private def quad1706:Quadratic:=(quad3529) + coefficientProduct ![-0x6b000b5fb74,0xad59578490,0x1eade6e5df0] ![0,0,1, -1] ![0,0,1, -1]
private def ctx1004:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -3,0] (cons ![0,0,3, -1] ctx1706)))))
private def quad1004:Quadratic:=(((((quad1706 + coefficientProduct ![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0,0x4c4b40] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1704:Nat → Linear:=cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx1706)
private def quad1704:Quadratic:=(quad1706 + coefficientProduct ![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60] ![0,0,3, -1] ![0,0,3, -1])
private def ctx1115:Nat → Linear:=cons ![0,1,0, -3] ctx1704
private def quad1115:Quadratic:=quad1704 + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx1111:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1115)))
private def quad1111:Quadratic:=(((quad1115 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]
private def ctx1392:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1704)
private def quad1392:Quadratic:=(quad1704) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1234:Nat → Linear:=cons ![0,3,2, -1] (cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] ctx1392))))
private def quad1234:Quadratic:=((((quad1392 + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3,2, -1] ![0,3,2, -1]
private def ctx1391:Nat → Linear:=cons (-![0,3, -2, -1]) ctx1392
private def quad1391:Quadratic:=quad1392
private def ctx1318:Nat → Linear:=cons ![0,3, -2,1] ctx1391
private def quad1318:Quadratic:=quad1391 + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1701:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1704))
private def quad1701:Quadratic:=((quad1704))
private def ctx1700:Nat → Linear:=cons (-![0,3, -2,1]) ctx1701
private def quad1700:Quadratic:=quad1701
private def ctx1699:Nat → Linear:=cons (-![0,3, -1,0]) ctx1700
private def quad1699:Quadratic:=quad1700
private def ctx1621:Nat → Linear:=cons ![0,3,0, -1] ctx1699
private def quad1621:Quadratic:=quad1699 + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx3527:Nat → Linear:=cons (-![0,0,1, -1]) (cons (-![0,0,1, -3]) ctx3529)
private def quad3527:Quadratic:=(quad3529)
private def ctx2513:Nat → Linear:=cons ![0,0,3, -1] ctx3527
private def quad2513:Quadratic:=quad3527 + coefficientProduct ![0x6b000b5fb74, -0xad59578490, -0x1eae015cc60] ![0,0,3, -1] ![0,0,3, -1]
private def ctx1792:Nat → Linear:=cons ![0,1,0, -3] (cons ![0,1, -3,0] ctx2513)
private def quad1792:Quadratic:=(quad2513 + coefficientProduct ![0,0,0x4c4b40] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx1789:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1792))
private def quad1789:Quadratic:=((quad1792 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1874:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) (cons ![0,1, -3,0] ctx2513))))
private def quad1874:Quadratic:=((((quad2513 + coefficientProduct ![0,0,0x4c4b40] ![0,1, -3,0] ![0,1, -3,0])) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2512:Nat → Linear:=cons (-![0,1, -3,0]) ctx2513
private def quad2512:Quadratic:=quad2513
private def ctx1976:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx2512))))
private def quad1976:Quadratic:=((((quad2512) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2510:Nat → Linear:=cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx2512)
private def quad2510:Quadratic:=(quad2512)
private def ctx2082:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] ctx2510))
private def quad2082:Quadratic:=((quad2510 + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2509:Nat → Linear:=cons (-![0,3, -2, -1]) ctx2510
private def quad2509:Quadratic:=quad2510
private def ctx2428:Nat → Linear:=cons ![0,3, -2,1] ctx2509
private def quad2428:Quadratic:=quad2509 + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2197:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] ctx2428)
private def quad2197:Quadratic:=(quad2428 + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2427:Nat → Linear:=cons (-![0,3, -1,0]) ctx2428
private def quad2427:Quadratic:=quad2428
private def ctx3016:Nat → Linear:=cons ![0,1, -3,0] (cons (-![0,0,3, -1]) ctx3527)
private def quad3016:Quadratic:=(quad3527) + coefficientProduct ![0,0,0x4c4b40] ![0,1, -3,0] ![0,1, -3,0]
private def ctx2594:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] ctx3016)))
private def quad2594:Quadratic:=(((quad3016 + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx3015:Nat → Linear:=cons (-![0,1,0, -3]) ctx3016
private def quad3015:Quadratic:=quad3016
private def ctx2688:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx3015))
private def quad2688:Quadratic:=((quad3015 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2772:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) ctx3015)
private def quad2772:Quadratic:=(quad3015) + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx3013:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx3015)
private def quad3013:Quadratic:=(quad3015)
private def ctx3010:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx3013))
private def quad3010:Quadratic:=((quad3013 + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0])
private def ctx3523:Nat → Linear:=cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) (cons (-![0,0,3, -1]) ctx3527)))
private def quad3523:Quadratic:=(((quad3527)))
private def ctx3104:Nat → Linear:=cons ![0,3, -2, -1] ctx3523
private def quad3104:Quadratic:=quad3523 + coefficientProduct ![-0x5543df729c000,0,0xda475abf000] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx3200:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) ctx3523)))
private def quad3200:Quadratic:=(((quad3523) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx3443:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) ctx3523)))
private def quad3443:Quadratic:=(((quad3523) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0,0, -0x4c4b40] ![0,3, -1,0] ![0,3, -1,0])
private def ctx3319:Nat → Linear:=cons ![0,3,2, -1] ctx3443
private def quad3319:Quadratic:=quad3443 + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3,2, -1] ![0,3,2, -1]
private def ctx3520:Nat → Linear:=cons (-![0,3, -1,0]) (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) ctx3523))
private def quad3520:Quadratic:=((quad3523) + coefficientProduct ![0x5543df729c000,0, -0xda475abf000] ![0,3, -2,1] ![0,3, -2,1])
private def data10:List Nat:=[
  0x11515150b110b130a13090b09130419021901091515150b130a13090b09130419021901081515150b130a13090b0913041902190108060a040306010c00080416030c020902011200300436030506030200040304030a02080202040102040603110410060102030603100400020206030f08080607060212041a030e04020202060310060d020a06010404060308020002020203]
private def node10:Certificate:=PackedParametricCertificateData.decode 11 data10
private def data20:List Nat:=[
  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,
  0x109859607bcef0197a93ab211e09e4fb1c903c2a201b3f90003cbe2f3d58d88efb5afbe9eb8fc4a8504939d0186f3ed429b821ff77cea1dcefa0df8a70078e4a7c5f5f49ab3c184fcc0151502020185d0b6b4cd8da687f19580828ab988b4ac90120a020201929b9297ff94b6ccc8a3fbc2bd86adde901909020205f9dc9a8fc5e3c8bf8f91e589e1b89b88c7f61309020207f5ec92cedab482d2ff9dccf0d4beaca08afe0a09020204cac091d8bccd8eedfac1a6928a8cff8db01908020202d795e4b1fdf0fe92888cabcfdeebb9f4efba130802022ed1d4a2f5e193d28380e6b282e5f998d1d21902020217edfadcf6d6b8c4ffafd89b858ba0b3a6c01515010201a0aa9b8bddedd5dbb7c0d3cc8881d481b1f8150a01020887faafaafcc48bdd]
private def node20:Certificate:=PackedParametricCertificateData.decode 10 data20
private def data76:List Nat:=[
  0x1d684bff4a7bfb1bfcc8dffbfbdeb89b2989adfe98af8dc0909000204928ba8a6d98cbbcba095cd9eaa9bcaa5e8b1cbd4aac9d68ec884b0d8c0c9d293b29a9feffef1cb9aadce8ab380b8c5ec19080002028bf38e88c09cdae0e08ceecbc8f8ef8de0bcb884f1c1f0f8e6ecf792ddbef19e81b0b1a7efcdfbdf9aec90afc698f091d409080002059f97c2a3d4eeb2d5a481abcc909edbf3a794d39fd4caba9189f1c2c696a6d9a381a0b39fc49faec2b6e894a9f5efdeda0808000206aff6ffaab3c5ba8d8de682f6eaa2df94dca789fad9c981fce1c79ba4f6aae4f78ad6d39fb1fb90d0cec9d4f5d1c9cea8060600026da1c8b1fab5d5b1979db3a1e1d08592c1e68eb5b0a6bc99f8d9f88b8d93abaea2f993bceeb985eccc8cd9d3ae869ff61904000203dbd4a0b4fba08cbad1dd88ab8f878a948aedcd8e9dc2f5caafc4a8ebaefdbfda9acce9bdd7e7bc96c0cd9be4a9eab1d0a00802000225ecede2839681a8d5d8e98de49399f4d09ebbc0f7e4d8e5e7d3e6ccb8e4becae7dcc8f288f8ffd7d282bdd78ad689981e1e97b2d287eaa6d2ab88fea6e2f89acba9f19ea7eacd86a58d8dc5f0c5d3aac596b9f887c3a9d3fdfba7be000a040306010c00080416030c020902011200300436030506030200040304030a02080202040102040603110410060102030603100400020206030b0200020202030a02000202020301,
  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,
  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,
  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,
  0x10306010c00080416030c02090201120030043603010a0208020204010204060311041006010203060310040002020603011db1c435bca901cb8b01cb8c01019691aadbd4c7a4eacde4c6c180038df80187ad38dc3989329e8244bce301fccf01fcd00006c9dc8ef7bef2f9c9c5e5f9a4e01515020202c2c5e4d1dabfbcdb86f8d39bc8fac993f3a0190a020202b49dc3b2fc83c8cd8ef18394e2d1a9eaf6801909020273d68db3cae0d096bdf1fde0d8a998c8ff901309020201ce81b7b6b7a1d9edede3fcb583e4ffdbb6b0090902020da2e9f3b4c0dcddeaa2dea492d4bb8fa0190802020daa95deb9989ac29290c0c0ddcde0deed9db0130802020f97f3f8d680d6d8d8838de3f8918683b595d00707020275d9b7e1dd88d9ebd687d285bcacf8b6800706020229cfb3fae2feecc8a5b0eaa7c89784ee801515010202dd95d1f9efcc9bb38ed4d2ef92e5e689d6a0190a010202bbbad4d3f880a8ad968cf2e5f2fd809cd180190901026dfedaf397cad5e8abca8dded6cda38099b01309010201bce0ea96fcaea3a7fbb6a2a2c5c2e5e5ba90190801020dc2c7cecea6828dec9d81a2b5bddaccb088b0130801020fb088cef2e5cda881bdbdd09e94eff48ba4b00707010202dad696f5dee5c989e589b1d9999bf2dc80070601020195a0a9b898d8f2cedcf6ebe8e1e5d2801515000203868ccfadcfb8c1cdc9a18c81edb0,
  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,
  0x115151311160f130f160e130b0e04060201010915151311160f130f160e130c0e04060201010915151311160f130f160e130c0e0406020101090615151311130f130b0e04060201010e0003000915151311130f130c0e04060201010e0003000915151311130f130c0e04060201010e00030009060115151311130f0f060a060e041302060203010915151311130f0f]
private def node76:Certificate:=PackedParametricCertificateData.decode 10 data76
private def node77:Certificate:=.split node20 node76
private def node78:Certificate:=.split node10 node77
private def node79:Certificate:=.positive 1 [(1,1),(1,7)] node78
private def node80:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node79
private def node81:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node80
private def node82:Certificate:=.positive 1 [(1,0),(2,10)] node81
private def node83:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node82
private def node84:Certificate:=.positive 3 [(1,0),(2,6)] node83
private def node85:Certificate:=.positive 3 [(1,0),(3,3),(2,5)] node84
private def data113:List Nat:=[
  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]
private def node113:Certificate:=PackedParametricCertificateData.decode 11 data113
private def data138:List Nat:=[
  0x1caa1daa8edbeabc2abdce4c88987c7a389b5b8a198cbcbf9afc0150801021d95e492ccddc3f2d8e7df859cb791ade4fbd8e486eaa7c4caa7880808010225c4ad9e8dbbdde4faecb083fd9cc1e1e8fbae9ed1d7b29db1eca0060601020affadf495948ec0d7d1f9a9d295d2efc6f88cbbd882cca4ebcd921204010208bc83e093978fd0e1cbe7e4d0acd98687a8c8f2cad996ce81f3b01515000274d3fe89d3bfa7e78fadefbe93f0baa7f1b2fdcd88ed8ea3e6e0a0151300020198d2e6de8fe6c3ac87e6e3b6c39babb3dfe5b5bb9fe3a7aa92fe801512000222cedbb497fbc1fd81d7b8eb97ebd2aac7eef4ba8b8788c38ca3e0120b000208bc8d8bb6e3f99ad2acc88ae8dcfd92b7f98e86b8acc3d8e595a0090900020bf3839581a9b493deb5e3dfc48fb3c5b8caacfd83a9adc8f685d0150800021ed6d6f1a9bbc9bba68db3d4ccc199f593a6d7858a8afee3f5acc00808000225dcfeaf9c8bd5d081cbc4ddeaef8dd8c395b3d5b8cfadf9bffb80060600020a83bbb19bbdbcebab8bb9f5b2e4badd88889bb4b9c2adbdd99c901204000206f3e0ae90a2c2d897d2ffabe8b1a582ba90a9fd87a281c6bad9801e018198f4fce6bacbfad5b0b2f39585b5efd9cdd9d0000a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406031104100601020306031004000202060301,
  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,
  0x11515010201a2d0f5bf95f5b89fdddce9918192d4ece8d4d1901513010201aa8cecc9ea96d5e7aeded9d19ba592a2e9b7f9900a0a01021ff6cba488a4979695ba9880ba96bebfb5d2aa801509010234e3d4e18aa2d9f1e9e3f8c2a980b0a0d1d6b2e0080801023db0a4cbc99b91b9f59dbffd9ba2cebcb6d5d9f8070701020885bececec0bbc7c2aaf398b0adc3d6d7c0b3e01506010219cbae90b3fde199a0f785eef4dfb087c8f180a00a0601022a96cfa4cadf91f88dabb38be0b281d29fcf98a0060601022aec8ee2bec5c989b7dbb3a5b6cea4dcaae6b5b01515000201a4eaa3d7def9fff8f2ccf48caebef7869a9fb2c81513000201a2a2a8deb8db97fbf7d99ba3d4d2a2f3abb2bfa80a0a00022092e789bdde8aaaebb8d6fe84f1c2a7a9aae4a01509000239dee6a390fd87fbeab4e9c9a78ed8eef2c3fa800808000234f2bf9ef0f5feadb38183c882d3998bcce4c4b80707000228bdf4b587c8cda19ac5dca2bfd5adadf5cdcda0150600021a968d9de1e7dacbe2a0f9d2d6edfddfdadbd2c00906000227f9b2eea6e9d1a59898fff7bc91e68bf482b2b0060600020df6bdc4e5b0afd18dba999199dbbaa0dbe4ffa01e01a8c4808cdebeb8879693a3f8c8000a040306010c00080416030c0209020112003004360305020402000203020301100200020202030104f393248fdd67c7a835af990141ebd291d0bfac,
  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]
private def node138:Certificate:=PackedParametricCertificateData.decode 8 data138
private def data191:List Nat:=[
  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,
  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,
  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]
private def node191:Certificate:=PackedParametricCertificateData.decode 8 data191
private def node192:Certificate:=.split node138 node191
private def data223:List Nat:=[
  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,
  0x11515131112110b0b0b09120812020602150101010a1515131112110b0b0b09120813021202060201010a1515131112110b0b0b09120813021202060201010a061515131112110b0b0b09120812020602150101010a1515131112110b0b0b09120813021202060201010a1515131112110b0b0b09120813021202060201010a0601151513111211120f0b09120811060602030101010a15]
private def node223:Certificate:=PackedParametricCertificateData.decode 9 data223
private def node224:Certificate:=.split node192 node223
private def node225:Certificate:=.negative 1 [(1,0),(1,8)] node224
private def node226:Certificate:=.split node113 node225
private def node227:Certificate:=.positive 1 [(1,1),(1,7)] node226
private def node228:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node227
private def node229:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node228
private def node230:Certificate:=.positive 1 [(1,0),(2,10)] node229
private def data258:List Nat:=[
  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]
private def node258:Certificate:=PackedParametricCertificateData.decode 11 data258
private def data303:List Nat:=[
  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,
  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]
private def node303:Certificate:=PackedParametricCertificateData.decode 11 data303
private def node304:Certificate:=.split node258 node303
private def node305:Certificate:=.positive 1 [(1,1),(1,7)] node304
private def node306:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node305
private def node307:Certificate:=.positive 14 [(13,0),(3,3),(4,5)] node306
private def data339:List Nat:=[
  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]
private def node339:Certificate:=PackedParametricCertificateData.decode 11 data339
private def data384:List Nat:=[
  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,
  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]
private def node384:Certificate:=PackedParametricCertificateData.decode 11 data384
private def node385:Certificate:=.split node339 node384
private def node386:Certificate:=.positive 1 [(1,1),(1,7)] node385
private def node387:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node386
private def data427:List Nat:=[
  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,
  0x11111150c0c0619030c030a02080202020c01091111150c0c0619030c030a02080202020c01091111150c0c0919030c030a0202020c0108060b0803060118031a031111150c130c090919080c030e010a01080102010a1111150c130c090919080c030e010a01080102010a1111150c130c090919080c030e010a01080102010a]
private def node427:Certificate:=PackedParametricCertificateData.decode 11 data427
private def data460:List Nat:=[
  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,
  0x11111150c16080c060f040c0302020c010a01091111150c0c0916080f040c0302020c010a01091111150c130c16080f040c0302020c010a0109061111150c0a060f0408040a0302020a010800091111150c0a060f]
private def node460:Certificate:=PackedParametricCertificateData.decode 11 data460
private def node461:Certificate:=.split node427 node460
private def node462:Certificate:=.positive 9 [(11,0),(6,6),(2,13)] node461
private def node463:Certificate:=.positive 3 [(1,4),(8,10)] node462
private def node464:Certificate:=.split node387 node463
private def node465:Certificate:=.split node307 node464
private def node466:Certificate:=.split node230 node465
private def node467:Certificate:=.positive 3 [(1,0),(2,6)] node466
private def data495:List Nat:=[
  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]
private def node495:Certificate:=PackedParametricCertificateData.decode 11 data495
private def data535:List Nat:=[
  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,
  0x1151515130b0b0b090f030a02090202020a010e000a151515130b0b0b090f030a02090202020a010e000a151515130b0b0b090f030a02090202020a010e000a06151515130b0b0e040f030a02090202020a0100000a151515130b0b0b090e040f030a02090202020a010a151515130b0b0b090e040f030a02090202020a010a060113020f020002030204151515130b0b0a090f060e040f0302020a0100000a151515130b0b0f090b090a090e040f0302020a010a151515130b0b0f090b090a090e040f0302020a010a0614040e020b0401120412031515150b0a0a0a0709070e040f030b03020211010a1515150b0a0a0a07]
private def node535:Certificate:=PackedParametricCertificateData.decode 11 data535
private def node536:Certificate:=.split node495 node535
private def node537:Certificate:=.positive 1 [(1,1),(1,7)] node536
private def node538:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node537
private def node539:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node538
private def node540:Certificate:=.positive 11 [(14,0),(9,2),(2,4)] node539
private def data572:List Nat:=[
  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]
private def node572:Certificate:=PackedParametricCertificateData.decode 11 data572
private def data612:List Nat:=[
  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,
  0x115150f0f0e0e150b0b0b0a0a150908080a0202020a15150f0f0e0e150b0b0b0a0a150908080a0202020a15150f0f0e0e150b0b0b0a0a150908080a0202020a0615150f0f0e0e150b0b0b0a0a150908080a0202020a15150f0f0e0e150b0b0b0a0a150908080a0202020a15150f0f0e0e150b0b0b0a0a150908080a0202020a060113020d060106001e04200415150f0f0e0e150b0a0a08080f0202020b010a010a15150f0f0e0e150b0a0a08080f0202020b010a010a15150f0f0e0e150b0a0a08080f0202020b010a010a0614040d020b02010c040c0315150f0f0e0e150b0a0a0f08090704040f0202020a15150f0f0e0e150b0a0a0f08090704040f0202020a15]
private def node612:Certificate:=PackedParametricCertificateData.decode 11 data612
private def node613:Certificate:=.split node572 node612
private def node614:Certificate:=.positive 1 [(1,1),(1,7)] node613
private def node615:Certificate:=.positive 4 [(4,0),(1,6),(1,8)] node614
private def node616:Certificate:=.positive 4 [(4,0),(1,5),(1,7)] node615
private def data648:List Nat:=[
  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]
private def node648:Certificate:=PackedParametricCertificateData.decode 11 data648
private def data684:List Nat:=[
  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,
  0x11111110f0e0d150c0b090d0302020d010c010a010a1111110f0e0d150c0b090d0302020d010c010a010a1111110f0e0d150c0b090d0302020d010c010a010a061111110f0e0d150c0b090d0302020d010c010a010a1111110f0e0d150c0b090d0302020d010c010a010a1111110f0e0d150c0b090d0302020d010c010a010a06010d020c0201060018041a041111110f0e0d150c0b090d030f02080202020a]
private def node684:Certificate:=PackedParametricCertificateData.decode 11 data684
private def node685:Certificate:=.split node648 node684
private def node686:Certificate:=.positive 1 [(1,1),(1,7)] node685
private def node687:Certificate:=.positive 4 [(4,0),(1,6),(1,8)] node686
private def data727:List Nat:=[
  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,
  0x1110f110e150c130c11030c030e020a02020209110f110e150c130c11030c030e020a02020209110f110e150c130c11030c030a02020208060b0803060118031a03110f110e150c130c09090c0302020e010a0108010a110f110e150c130c09090c0302020e010a0108010a110f110e150c130c09090c0302020e010a0108010a060a]
private def node727:Certificate:=PackedParametricCertificateData.decode 11 data727
private def data759:List Nat:=[
  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,
  0x1110f110e150c130c160811030c0302020a0109110f110e150c130c160811030c0302020a0109110f110e150c130c160811030c0302020a010906110f150c130c150a0c030a0302020a01080009110f150c]
private def node759:Certificate:=PackedParametricCertificateData.decode 11 data759
private def node760:Certificate:=.split node727 node759
private def node761:Certificate:=.positive 12 [(13,0),(3,5),(8,7)] node760
private def node762:Certificate:=.positive 1 [(1,3),(2,10)] node761
private def node763:Certificate:=.split node687 node762
private def node764:Certificate:=.split node616 node763
private def node765:Certificate:=.split node540 node764
private def data812:List Nat:=[
  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,
  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]
private def node812:Certificate:=PackedParametricCertificateData.decode 11 data812
private def data837:List Nat:=[
  0x1110e150c0e0c160811030c0302020a01000009110e150c0e0c160811030c0302020a01000009110e150c0e0c160811030c0302020a01000009060f0201020202040b0201060012031404150c150a0e0a0e040c030a0308020a01000009150c150a0e0a0e040c030a0308020a01000009150c150a0e0a0e040c030a0308020a0100000906150c150a0e0a0e040a0302020a010800000009150c150a0e0a0e040a0302020a010800000009150c150a0e0a0e040a0302020a01080000000906010b020506020204010a0c0208010600040412040c02020202020407020106000203080408060706020e0008041604150c150a0e0a0e040a0302020a010800000009150c150a0e0a0e040a0302020a010800000009150c150a0e0a0e040a0302020a010800000009060b020606020203150b150a0e0a0e040b030a03090302020e010d010a150b150a0e0a0e040b030a03090302020e010d010a150b150a0e0a0e040b030a03090302020e010d010a0614040a0201060008040e0301130404020202030a0c0208010600040412040b06050202020407020402020204060603020206030804010d1c091406060506041c0308020002020204]
private def node837:Certificate:=PackedParametricCertificateData.decode 11 data837
private def node838:Certificate:=.split node812 node837
private def node839:Certificate:=.positive 12 [(13,0),(3,5),(8,7)] node838
private def data887:List Nat:=[
  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,
  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]
private def node887:Certificate:=PackedParametricCertificateData.decode 11 data887
private def data910:List Nat:=[
  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]
private def node910:Certificate:=PackedParametricCertificateData.decode 11 data910
private def node911:Certificate:=.split node887 node910
private def node912:Certificate:=.positive 8 [(5,7),(1,9),(24,11)] node911
private def node913:Certificate:=.split node839 node912
private def node914:Certificate:=.negative 1 [(3,2),(1,7)] node913
private def node915:Certificate:=.negative 2 [(1,0),(3,1),(2,6)] node914
private def node916:Certificate:=.negative 2 [(5,0),(1,2),(1,5)] node915
private def node917:Certificate:=.split node765 node916
private def node918:Certificate:=.split node467 node917
private def node919:Certificate:=.split node85 node918
private def node920:Certificate:=.positive 3 [(1,1),(8,4)] node919
private def node921:Certificate:=.positive 3 [(1,0),(2,3)] node920
private def data932:List Nat:=[
  0x115151111150a130a0b0a15091309150213020915151111150a130a0b0a15091309150213020915151111150a130a0b0a150913091502130209060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060311040c0804020302040803100400020206030f08080607060212041a030e0402020206030d100c120a36012004300308020002020203]
private def node932:Certificate:=PackedParametricCertificateData.decode 11 data932
private def data942:List Nat:=[
  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,
  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]
private def node942:Certificate:=PackedParametricCertificateData.decode 10 data942
private def data999:List Nat:=[
  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,
  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,
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,
  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]
private def node999:Certificate:=PackedParametricCertificateData.decode 10 data999
private def node1000:Certificate:=.split node942 node999
private def node1001:Certificate:=.split node932 node1000
private def node1002:Certificate:=.positive 1 [(1,1),(1,7)] node1001
private def node1003:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node1002
private def node1004:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1003
private def node1005:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1004
private def node1006:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node1005
private def node1007:Certificate:=.positive 3 [(1,0),(2,6)] node1006
private def node1008:Certificate:=.positive 1 [(1,0),(3,2)] node1007
private def data1029:List Nat:=[
  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]
private def node1029:Certificate:=PackedParametricCertificateData.decode 11 data1029
private def data1080:List Nat:=[
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,
  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,
  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,
  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,
  0x1151513110b0909090e0411030f0302020a010e000a151513110b0909090e0411030f0302020a010e000a151513110b0909090e0411030f0302020a010e000a06151513110b090e0411030f0302020f010a0108000a151513110b090e0411030f0302020f010a0108000a151513110b090e0411030f0302020f010a0108000a060115151311130b090904040f]
private def node1080:Certificate:=PackedParametricCertificateData.decode 9 data1080
private def data1106:List Nat:=[
  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,
  0x115151311120f150e0b0b120815031202]
private def node1106:Certificate:=PackedParametricCertificateData.decode 9 data1106
private def node1107:Certificate:=.split node1080 node1106
private def node1108:Certificate:=.negative 1 [(1,0),(1,8)] node1107
private def node1109:Certificate:=.split node1029 node1108
private def node1110:Certificate:=.positive 1 [(1,1),(1,7)] node1109
private def node1111:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node1110
private def node1112:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1111
private def node1113:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1112
private def node1114:Certificate:=.positive 1 [(1,0),(2,1),(2,5)] node1113
private def node1115:Certificate:=.positive 3 [(1,0),(2,6)] node1114
private def data1143:List Nat:=[
  0x1151513130f0f0e0e0a080808130409040e030a020a151513130f0f0e0e0a080808130409040e030a020a151513130f0f0e0e0a080808130409040e030a020a060a040306010c00080416030c020902011200300436030702050800080306030b040a04060401020406030f040a0205020302030902080204020106040803151513130e0e0a0a0a0808081506130409040a020a151513130e0e0a0a0a0808081506130409040a020a151513130e0e0a0a0a0808081506130409040a020a060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030f06010202020310040002020603010e0402020206030d040906010203060315150e0e120a12090b0913040b04120211010915150e0e120a12090b0913040b04120211010915150e0e120a12090b0913040b041202110109060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030f1c0a020606040c040c03100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node1143:Certificate:=PackedParametricCertificateData.decode 11 data1143
private def data1177:List Nat:=[
  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,
  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,
  0x1e4ddafe084e9d8adbfddcfc5ef9dc6e9e787add6ced1b7c8f0901304010247aef2c7e78ae58e8e8ca6f4c9e6fcfee080e6a79ddeebaba6ac99a0d1f6d4ed8aadf00804010206e5cacee5c4af96ddcec0b7e8a6fbe0dea9efe8e6b7e5f1a3ecf0ff8a9eedd7b083c7f80404010213b3d1c1e8c9b58aceca8cace5a0a3e0d29de4fbaebab39caf9ed587c6f4cbaee8a89dfa0303010202b89eb2b7caeca28a95aeed82f4bdd4fce9e0d8a5a7f1f2d2a8b593c9ecbccfbec8eda004000102758380b6d0ad88aa81e8cf95d5c2d9a883d9d3b0a184c3f9dcf7b1c7e38ce0998a82ec0f0f00020384d0bce5de90a5ad82cfb79ef2eec7a2aea5e4abe79dd8fbae87a38af0a9edfbdec9800a0a000246eff1abd0e1e380b7e2d39086c6a9f6e486f683e8eda1f7aaafe081f4b8f3c7b7c3800808000202a3ddee8befc488ecbb96a7f38981a09de2dfaab989c58ed8b8bfd9f8b5eab89fe39b8007070002109ec8bc81ecbffc8f99a2bcf389a1868a84998599cdf6e989dfebd8e08ee29ae6a3e4800606000203f89b91aa9ab1ecd5c4d8c893f8a78dafa2a0d1d6ff9989a5ae95acdca3b5dabdd0af800804000201d0c282e7c2b3efc0ecb8bbfaa7cbf1f18feec1b1e3c0e882cee2aca8bfbaebfd96f4800404000215e3d28f88a6e1beacccd2c298b499de97d089c2c2b998b0e2d99381b3e6f3fff3fdcb800402000201fd9efca7,
  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,
  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,
  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,
  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,
  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]
private def node1177:Certificate:=PackedParametricCertificateData.decode 8 data1177
private def data1209:List Nat:=[
  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,
  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,
  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,
  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,
  0x102020901080000000a060f0201020202035de4853184943cec8169cbf401268d8deec089efd9c5aee8eea7acdf82f9bad9c6dcbdd89ab78c09d7c665cde842fabc01b29fe9014dccb4bd899af5bbefc58f8dadc5dd809293cee6a5afb4de89902cb8e617a9c719cdcc2edcdf08f6aa0fde85228ad41ba2f70009c8eb93e5e6c0f0c6b297b4cbceadf6d79a9ebdf3bbb7d7e2c026d88972de8d1dd69101b78bdc3b998e65cfe81197ec01b280e10003dcabe8c2d5a2abe79e92a8b3d1bad8cbcae79b82fda4a495c014140202149b9ff1beb0ece9eebac9afd9eec8aaeeaeaa86a1edbbb6ba91b699a489bf80140f020201c0f29cf1b3feadacfbe4a9cec3d29ba290bda8ebc599d3c490d8cea0a4ddc00707020213efe2efebcedbceade9c683c597c584f4f99698acda92c4f7b38db0da8dbec00704020223988492c1afdcedfdea95f6d9bef696edf5b4a7e8c6e0e3cda2bea1b6c00404020204c1df84fdd195ebdeb6deddfdcef2aedebfc58fc68ca7bdfca4b38fdcf00f03020202fc928fec98a79eab988f9787a19ff2f292a9cdf1dad4a9988be2edd4b29ac00703020201be9182de85bd9aebb0c988e0dfa5ccf9d3e0fab5d084ecf4f5d2d5db8ba0801400020223aa918fb2c796beafa99e9bbe97ce90aaab8191808ae1fc92cb9bc7e6800000020204c1aeb1a2f3d6f0b591b498c1d3d8c9def7f09f91f2f0e1f2fe,
  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]
private def node1209:Certificate:=PackedParametricCertificateData.decode 8 data1209
private def node1210:Certificate:=.split node1177 node1209
private def data1231:List Nat:=[
  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]
private def node1231:Certificate:=PackedParametricCertificateData.decode 9 data1231
private def node1232:Certificate:=.split node1210 node1231
private def node1233:Certificate:=.negative 1 [(1,0),(1,8)] node1232
private def node1234:Certificate:=.split node1143 node1233
private def node1235:Certificate:=.positive 1 [(1,1),(1,7)] node1234
private def node1236:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1235
private def node1237:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1236
private def node1238:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1237
private def data1270:List Nat:=[
  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]
private def node1270:Certificate:=PackedParametricCertificateData.decode 11 data1270
private def data1314:List Nat:=[
  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,
  0x1d799d089d0f4e0000f0201020202030c020a02030c000c0410031304050202060304034cb1a640ceb045f8b801d2f88d011897ead598f9ef9f9bd291e5ab82f985f6b021eacb07bd9e02a5bc188cee42c8c422cac002f7f2688af5000db398f9e59ba2c48cf8f9929bbdd8a88eb054aa8549aac94cf3f901ead1aa3bb2f238b1fa3ee28401b2c6ef000beccdeacdf2ccc59294cf878cd28ffdc88a141402021ccfd4908dfde6a4fcc1ac90f996e789bc8fcef6b2defea00f0f020206c287a7edf8a39fb89aa68fb3aac29daaaaaeacc280c5b81407020205cce480ca9cae98aac8bca2a687e6b7a9849fada2c088d00f07020209bce3ec85d0d1849ac4ddbcca8eb2d8a0a892e5d6ecb8d80707020204aea1beaac192b3ffef8193cba6a9b7d2c6e8c386c3c9f6040402020babc7f0acbdfcf0f09ac8d686fad0c0c0c989dfdcd00303020201e2d584c2d58ce8cce8bcc7c0b7cdd5e0fd87fdd9efc6b8140002022ab0a48fccc8b784a8a3859280f6a5c7a1c1e29dd6e0100002022eccdb86f7dbc2efeec4a882e4c3bbb190c28ae5b480141401021ec3c1a598c9d6f0c694e3beafc5c4f3d4c7a8c6c683a5c0140f0102048ea18085a7c48bd7caa3af9cffd7fcb5d9c7d5bd9f8aac0f0f01020886bea89ea2809b9bdaf0efb6a8c1de9adde4a78c9bb298140701020783cba9c2c2eac68cfdb585e5a7dbbed5fb819cdbd1fe,
  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,
  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,
  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,
  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]
private def node1314:Certificate:=PackedParametricCertificateData.decode 11 data1314
private def node1315:Certificate:=.split node1270 node1314
private def node1316:Certificate:=.positive 1 [(1,1),(1,7)] node1315
private def node1317:Certificate:=.positive 4 [(3,0),(3,3),(1,6)] node1316
private def node1318:Certificate:=.positive 5 [(4,0),(3,2),(1,5)] node1317
private def data1350:List Nat:=[
  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]
private def node1350:Certificate:=PackedParametricCertificateData.decode 11 data1350
private def data1386:List Nat:=[
  0x10b0f0202020a0108000a150f150e0e0d140b100b0e0b0f0202020c010a010a150f150e0e0d140b100b0e0b0f0202020c010a010a060f020102020203150f150e100b0e0b0a090b07090702020f010e010a150f150e100b0e0b0a090b07090702020f010e010a150f150e100b0e0b0a090b07090702020f010e010a060f02010202020301010a0c0208010600040412041002000202020409020802010c0002040e0408060706020e0008041604150f150e0e0b0a0a1009150207020e01070101010a150f150e0e0b0a0a1009150207020e01070101010a150f150e0e0b0a0a1009150207020e01070101010a060f0201020202030b020506020203130404020202030a0c02080106000404120410020002020204150f150e0e0d100b0e0b090508050f010e0108010a150f150e0e0d100b0e0b090508050f010e0108010a150f150e0e0d100b0e0b090508050f010e0108010a060f0201020202030b02030600060308031304050202060304030a060602020200020406041111150f0e0d0b0b0b040d030f010e01080103010a1111150f0e0d0b0b0b040d030f010e01080103010a1111150f0e0d0b0b0b040d030f010e01080103010a060a040306010c00080416030b020306000603080313040502020603040311060a12060a0202040c0401010806070603080206040e04010d1c091406060506041c0308020002020204,
  0x1150f150e0e0d140b100b0e0b02020d010c010a010a150f150e0e0d140b100b0e0b02020d010c010a010a150f0e0d130c140b100b0e0b0a0202020c010906150f150e0e0d140b100b0e0b02020c010a0108000a150f150e0e0d140b100b0e0b02020c010a0108000a150f150e0e0d140b100b0e0b02020c010a0108000a06010d020c0201060018041a04150f150e0e0d140b100b0e]
private def node1386:Certificate:=PackedParametricCertificateData.decode 11 data1386
private def node1387:Certificate:=.split node1350 node1386
private def node1388:Certificate:=.positive 1 [(1,1),(1,7)] node1387
private def node1389:Certificate:=.positive 4 [(3,0),(3,3),(1,6)] node1388
private def node1390:Certificate:=.positive 1 [(3,2),(1,7)] node1389
private def node1391:Certificate:=.split node1318 node1390
private def node1392:Certificate:=.split node1238 node1391
private def data1433:List Nat:=[
  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,
  0x115151413150e0c0b110a0a080e040a02080003000a15151413150e0c0b110a0a080e040a02080003000a15151413150e0c0b110a0a080e040a02080003000a06130200020202030c020a02030c000c04100313040502020603040313130e0e0f080a0815040e0404040e0303030a000a13130e0e0f080a0815040e0404040e0303030a000a13130e0e0f080a0815040e0404040e0303030a00]
private def node1433:Certificate:=PackedParametricCertificateData.decode 11 data1433
private def data1468:List Nat:=[
  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,
  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,
  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,
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,
  0x11515141313130f0f0e0e08080c020b020a0202020a1515141313130f0f0e0e08080c020b020a0202020a1515141313130f0f0e0e08080c020b020a0202020a060f02010202020412020d02000603060405e5cc2581dd63df823bc9bb011bbdecdaa7e8ea8faaacc783b78c8ae2e584c00ab313ce3db141ba0e96da20c681418af62cf0d30045848998fbbf828393a4dab7b39c9bd9f6e4dc80569ce256c3ce2bafa01bf9c406e7e506fa9f04949303b6cd0003b7c5b9f3eca99bd0bd84a4dcbbf2b59abd801413020262f3feded3aec9a1aae0eefed6e9ebcd94959ab9b2af85d4800f0f02020eaaf3e6caf1bf]
private def node1468:Certificate:=PackedParametricCertificateData.decode 11 data1468
private def node1469:Certificate:=.split node1433 node1468
private def node1470:Certificate:=.positive 1 [(1,1),(1,7)] node1469
private def node1471:Certificate:=.positive 1 [(1,0),(1,7)] node1470
private def node1472:Certificate:=.positive 1 [(1,0),(1,6)] node1471
private def data1513:List Nat:=[
  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,
  0x10e0d150a08050d030f010e01080103010e0008000a0e0d0e0c150a08050d030f010e010801030108000a0e0d150a08050d030f010e01080103010e0008000a060d020b0200040304030b02030600060308031304050202060304031313110f150e110e150a0e0908080e020a0100000a1313110f150e110e150a13090e0908080e020a010a1313110f110e]
private def node1513:Certificate:=PackedParametricCertificateData.decode 11 data1513
private def data1544:List Nat:=[
  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,
  0x1150f150e0e0d140b130b0e0b02020d010c010a010a150f150e0e0d140b130b0e0b02020d010c010a010a150f150e0e0d140b130b0e0b0a0202]
private def node1544:Certificate:=PackedParametricCertificateData.decode 11 data1544
private def node1545:Certificate:=.split node1513 node1544
private def node1546:Certificate:=.positive 1 [(1,1),(1,7)] node1545
private def node1547:Certificate:=.positive 1 [(1,0),(1,7)] node1546
private def data1594:List Nat:=[
  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,
  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]
private def node1594:Certificate:=PackedParametricCertificateData.decode 11 data1594
private def data1619:List Nat:=[
  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]
private def node1619:Certificate:=PackedParametricCertificateData.decode 11 data1619
private def node1620:Certificate:=.split node1594 node1619
private def node1621:Certificate:=.positive 4 [(4,0),(3,7),(1,9)] node1620
private def data1671:List Nat:=[
  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,
  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]
private def node1671:Certificate:=PackedParametricCertificateData.decode 11 data1671
private def data1696:List Nat:=[
  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]
private def node1696:Certificate:=PackedParametricCertificateData.decode 11 data1696
private def node1697:Certificate:=.split node1671 node1696
private def node1698:Certificate:=.positive 2 [(1,7),(1,8),(6,11)] node1697
private def node1699:Certificate:=.split node1621 node1698
private def node1700:Certificate:=.split node1547 node1699
private def node1701:Certificate:=.split node1472 node1700
private def node1702:Certificate:=.negative 1 [(3,0),(2,4)] node1701
private def node1703:Certificate:=.split node1392 node1702
private def node1704:Certificate:=.split node1115 node1703
private def node1705:Certificate:=.split node1008 node1704
private def node1706:Certificate:=.positive 1 [(1,0),(2,4)] node1705
private def data1717:List Nat:=[
  0x115151111150a130a0b0a15091309150213020915151111150a130a0b0a15091309150213020915151111150a130a0b0a150913091502130209060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060311040c0804020302040803100400020206030f08080607060212041a030e0402020206030d100c120a36012004300308020002020203]
private def node1717:Certificate:=PackedParametricCertificateData.decode 11 data1717
private def data1727:List Nat:=[
  0x11515120a150913090a09150813080808150214010a1515120a150913090a09150813080808150214010a1515120a150913090a09150813080808150214010a060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060311040c0804020302040803100400020206030f08080607060212041a030e04010200020308030c060a120008030803]
private def node1727:Certificate:=PackedParametricCertificateData.decode 10 data1727
private def data1784:List Nat:=[
  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,
  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,
  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,
  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]
private def node1784:Certificate:=PackedParametricCertificateData.decode 10 data1784
private def node1785:Certificate:=.split node1727 node1784
private def node1786:Certificate:=.split node1717 node1785
private def node1787:Certificate:=.positive 1 [(1,1),(1,7)] node1786
private def node1788:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node1787
private def node1789:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1788
private def node1790:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1789
private def node1791:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node1790
private def node1792:Certificate:=.positive 3 [(1,0),(2,6)] node1791
private def data1803:List Nat:=[
  0x111110f0f130a130911090b091304110213000911110f0f130a130911090b091304130211020911110f0f130a130911090b0913041102130009060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030e020b040402030203100400020206030f08080607060212041a030e0402020206030d080a120806010a04120308020002020203]
private def node1803:Certificate:=PackedParametricCertificateData.decode 11 data1803
private def data1813:List Nat:=[
  0x115151111120a13090b0913040a031102080213000a15151111120a13090b0913040a031102080213000a15151111120a13090b0913040a031102080213000a060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030e020b040402030203100400020206030f08080607060212041a030e04010200020308030d040a180808000a040e03]
private def node1813:Certificate:=PackedParametricCertificateData.decode 10 data1813
private def data1869:List Nat:=[
  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,
  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,
  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,
  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,
  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]
private def node1869:Certificate:=PackedParametricCertificateData.decode 10 data1869
private def node1870:Certificate:=.split node1813 node1869
private def node1871:Certificate:=.split node1803 node1870
private def node1872:Certificate:=.positive 1 [(1,1),(1,7)] node1871
private def node1873:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1872
private def node1874:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1873
private def node1875:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1874
private def node1876:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node1875
private def node1877:Certificate:=.positive 1 [(1,1),(1,2)] node1876
private def node1878:Certificate:=.split node1792 node1877
private def data1899:List Nat:=[
  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]
private def node1899:Certificate:=PackedParametricCertificateData.decode 11 data1899
private def data1950:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  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]
private def node1950:Certificate:=PackedParametricCertificateData.decode 9 data1950
private def data1971:List Nat:=[
  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]
private def node1971:Certificate:=PackedParametricCertificateData.decode 9 data1971
private def node1972:Certificate:=.split node1950 node1971
private def node1973:Certificate:=.negative 1 [(1,0),(1,8)] node1972
private def node1974:Certificate:=.split node1899 node1973
private def node1975:Certificate:=.positive 1 [(1,1),(1,7)] node1974
private def node1976:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1975
private def node1977:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1976
private def node1978:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1977
private def node1979:Certificate:=.positive 1 [(3,0),(2,4)] node1978
private def data2010:List Nat:=[
  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]
private def node2010:Certificate:=PackedParametricCertificateData.decode 11 data2010
private def data2056:List Nat:=[
  0x18dfe8daa86fbede8100e01026eaf82c8b989dadcfbd5cb8687d7d0bcbdd88ec00808010217a9afdd9fd5b1dcf6d5d8dfddb7a2ef848084ac150601020faedcecfdb1e2b8aaa0c7bcd7de8bede8b2d4941106010205eda1e5dbe4c195b6b4e6d9fafeaf88befa8de00f0401023de88eddadb1cfe8e8e1c0e5d594b6ebaeadc2f804040102048acdd6c59285aeb38097aac8fce4a8f3d3f7c80602010215c6aba6f1baaea2fda2a781cdb38fbe82fbfcf81001010204db98df86c7a6faf9e7afeeecf8c8cae8a7a8981313000206a28e8680f7b6cad7b2bcddead890eab8a3a0da100e00026eaaa5a585acf891b689f0acb2b8c693ebbfc8c00808000216f883adb78ffdc6d1a6b2c2a4be848b80b794c6150600020fe5facbb0ac8287bcbbe0d1a6fc9db2a880ecf41106000205abb8deb4d3f4ec868ec992e284dd9fdcc1b2c00f0400023dd9b1f686e88fa2fdaaa1b5a2e097bebdf7ad940404000204869c8eaca0e1a8ea97acd1e5ec81c7a8c28aea0602000215bcb4e6c8daa796b9d5c0c8de80c0fcade2afae1001000204f2a787a9a7dedf9d9b89adde9ce5a6c9c2e5fe0800000216fcfbd6f08eafc6a6f9f4c4eee4c893bce29e1e30e583cc9895f4b5aada94e0c00012100e06050c01120416030c020902011200300436030506030200040304030a020802020401020406030b060502020204100400020206030101,
  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,
  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,
  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,
  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,
  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,
  0x10a1313150f150e0e0e0909130815030901010102000a060f0201020202041313150f150e13080606150303030a00090002000a1313150f150e13080606150303030a00090002000a1313150f150e13080606150303030a00090002000a060f020102020204011313150f150e13081503030302020101090000000a1313150f150e13081503030302020101090000000a1313150f150e13081503030302020101090000000a0668e4f51197b93c9af501b697a6015aa3d491a091fec197f49bdc91bcadb0eedf9e9091b98805bde40afbbb2b860593ba1ec2974ff9d420928f11a5ab0001bfcfb68b9afbf8d2e1ba82e7e6e0a5b7d5dfd0f8eb87b608ed851b89b616991286df03d8d20597a839d7b842c7b10001b29be8c897ba98f1dbc7ccaffbe0fdc7968bbce2eb9ae0018ab8ba02caf82e95da01bb96e767acbf16eebf20b6a3019ed1a400348b97e7e283b089fc89e3d2c2b9cc909990bcb0c69cf0141402020fd0d6ff91f5f3cdc4f080d586fd84a8e289a9c59393f7e7b28b84b2d8110f020225e9bdd8daa28cbab48aafc6b587bfb2d098de8ec6a4b895baf0100f020211ffa0f48be8a3e6ea9be189d783d38f9fd9e4f9cad0cffcebf595b3a807070202149f9ee8acd4e484c7d1c8d7e3a88cefa0fc98af84a481fc87baa3faca070402024c86d584b8908bef90c3e1d8eb8f8ed9efa6eed8cd91d9fa869ac80504,
  0x115151313110f0f040e040f030902020209010e000a15151313110f0f040e040f030902020209010e000a15151313110f0f040e040f030902020209010e000a060f020102020204151515141313110f0f040f030b03090202020e000a151515141313110f0f040f030b03090202020e000a151515141313110f0f040f030b03090202020e000a060f02010202020401151515141313110f0f040f0302010a00090004000a151515141313110f0f040f0302010a00090004000a151515141313110f0f040f0302010a00090004000a061414110f100f14070707070514040f030a0300000a1414110f100f070705050f030a030703081414100f0707070505050f0306060112020d020006030603011313150f150e0e0e0909130815030901010102000a1313150f150e0e0e090913081503090101010200]
private def node2056:Certificate:=PackedParametricCertificateData.decode 9 data2056
private def data2077:List Nat:=[
  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]
private def node2077:Certificate:=PackedParametricCertificateData.decode 9 data2077
private def node2078:Certificate:=.split node2056 node2077
private def node2079:Certificate:=.negative 1 [(1,0),(1,8)] node2078
private def node2080:Certificate:=.split node2010 node2079
private def node2081:Certificate:=.positive 1 [(1,1),(1,7)] node2080
private def node2082:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node2081
private def node2083:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node2082
private def node2084:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node2083
private def data2126:List Nat:=[
  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,
  0x1151413130c0b0c090a080e040a021300080003000a151413130c0b0c090a080e040a021300080003000a151413130c0b0c090a080e040a021300080003000a060b08090601060308030c020a02030c000c04100313040502020603040313130e0e0f080a0815040e0404040e0303030a000a13130e0e0f080a0815040e0404040e0303030a000a13130e0e0f080a0815040e0404040e0303030a000a060b08090601060308030c02]
private def node2126:Certificate:=PackedParametricCertificateData.decode 11 data2126
private def data2184:List Nat:=[
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  0x12bebc65dddb540d1e803fb990104b0f7fcfad3c394fcaadc8ab1c06af905aa55da0488b22181ba42dbed2afb9e09e9970024e7daa9adbccca6a28eb6cba2c7e0151402020195f692a3c89db49797d8b5d8ea8ceafbfbb3e013130202088bb38ecbecb5f18edf8ac99290b9c1e1e2deb00e0e02020eeee6a9ef91949dfd838c82d2cde6e4d6f1a694130c020209db9bd4a9efc4f3b8e5bb90fae3dad08392c9b00c0c020209a9be88e8d4eca992f0c5eff3ef9c96bcace9e40c0b020201c684be96c4eabfc3db9fcd]
private def node2184:Certificate:=PackedParametricCertificateData.decode 9 data2184
private def data2193:List Nat:=[
  0x115150e0e0c0b110809080e0309020602060101010a15150e0e0c0b110809080e0309020602060101010a15150e0e0c0b110809080e0309020602060101010a06100c0e0807120026042c0411040d04060603020410020c020504020204020412040402020203100200020202040d020902020201020404040c0608060204000a040e040b0607060104000e041204]
private def node2193:Certificate:=PackedParametricCertificateData.decode 9 data2193
private def node2194:Certificate:=.split node2184 node2193
private def node2195:Certificate:=.negative 1 [(1,0),(1,8)] node2194
private def node2196:Certificate:=.split node2126 node2195
private def node2197:Certificate:=.positive 1 [(1,1),(1,7)] node2196
private def data2239:List Nat:=[
  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,
  0x1150e0b0b110a0a0811050e040a021300080003000a150e0b0b110a0a0811050e040a021300080003000a150e0b0b110a0a0811050e040a021300080003000a060a02090204040302030b020306000603080313040502020603040313130e0e13080f080a08080804040e030c000a000a13130e0e13080f080a08080804040e030c000a000a13130e0e13080f080a08080804040e030c000a000a061216090c02]
private def node2239:Certificate:=PackedParametricCertificateData.decode 11 data2239
private def data2274:List Nat:=[
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]
private def node2274:Certificate:=PackedParametricCertificateData.decode 11 data2274
private def node2275:Certificate:=.split node2239 node2274
private def node2276:Certificate:=.positive 1 [(1,1),(1,7)] node2275
private def node2277:Certificate:=.split node2197 node2276
private def data2328:List Nat:=[
  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,
  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]
private def node2328:Certificate:=PackedParametricCertificateData.decode 11 data2328
private def data2353:List Nat:=[
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private def node2353:Certificate:=PackedParametricCertificateData.decode 11 data2353
private def node2354:Certificate:=.split node2328 node2353
private def data2400:List Nat:=[
  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,
  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]
private def node2400:Certificate:=PackedParametricCertificateData.decode 11 data2400
private def data2424:List Nat:=[
  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,
  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,
  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,
  0x13ab10197aa07bcf009859501b3fa03c2a14fb1ca11e09d0003cbe2f3d58d88efb5afbe9eb8fc429b810186f3ee04939e4a860df8a81dcef97ce91ff80078e4a7c5f5f49ab3c184fcc01615020217edfadcf6d6b8c4ffafd89b858ba0b3a6c0160e020202d795e4b1fdf0fe92888cabcfdeebb9f4efba130d020201929b9297ff94b6ccc8a3fbc2bd86adde90160b020205f9dc9a8fc5e3c8bf8f91e589e1]
private def node2424:Certificate:=PackedParametricCertificateData.decode 11 data2424
private def node2425:Certificate:=.split node2400 node2424
private def node2426:Certificate:=.split node2354 node2425
private def node2427:Certificate:=.negative 1 [(1,0),(1,7)] node2426
private def node2428:Certificate:=.split node2277 node2427
private def data2479:List Nat:=[
  0x10809060c020e010c010a010a060d0a0a060206000e04100313020906012a0066047403070205080008030603010f06010202020401150e150d0e0b110a0e0908080d020a020e010a010a150e110c0e0b150a0e0908080a020e010d010a010a150e150c0e0b110a0e0908080c020a020e010a010a060d0a0a060206000e04100313020906012a006604740305060302000403040305020204020203150e150d110c0e0b0e0908080d020a020e010a010a150e110c0e0b0e0908080c020a020e010d010a010a150e150c110c0e0b0e0908080c020a020e010a010a060a040306010c000804160313020906012a0066047403050603020004030403050202040202030110040002020603010e0402020206030d0409060102030603110f150e0e0b0b090808090412020f0208020e010a110f150e0e0b0b090808090412020f0208020e010a110f150e0e0b0b090808090412020f0208020e010a060d0a0a060206000e04100313020906012a006604740305060302000403040313040202020203110e0e0b15090b090f080b0412020f020e0209110e0e0b15090b090f080b0412020f020e0209110e0e0b15090b090f080b0412020f020e0209060a040306010c000804160313020906012a0066047403050603020004030403130402020202030110040002020603100402020202030e0402020206030d040906010203060301,
  0x114141713170e170b0b0b140a0e020a02020214000a14141713170e150a140a0e020a0202020814141713170e150a140a0e020a020202080613020002020204140f170e150e130b0e0b150a0e010a01080102010a140f170e150e130b0e0b150a0e010a01080102010a140f170e140e130b0e0b150a0e010a01080102010a06140f170e150e130b0e0b150a0e010a01080102010a140f170e150e130b0e0b150a0e010a01080102010a140f170e140e130b0e0b150a0e010a01080102010a060101130404020202030a0208020204010204060410020002020204150f140f150e0e0b0b080f050b0305030e0108010a150f140f150e0e0b0b080f0508050e01080103010a150f140f150e0e0b0b080f0505030e01080103010a060d020a020406000204040313020906032a0012042003130405020206030403110e150d0e09080809060e020d020d010c010a010a150e150d110d0e09080809060e020d010c010a010a150e110e150c0e0908]
private def node2479:Certificate:=PackedParametricCertificateData.decode 11 data2479
private def data2504:List Nat:=[
  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,
  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,
  0x10e0a020203d2c4edaef0edf1c191b99ff498c8babb94900b0a020231b8d5f487d4e8fbe8d9a0e8e0ec9bede7f0020202024db4cce6c28b948ad0cdc9a6cabee3ca90a0141401025399e8c69ffd8dbaefb8a5b1e4daa4da80161301024bdaf296e3fdc986d3e8fbe4f0fdf2a48d80160e0102039faaed919fcdf195f0f7adbbe48fdafff080140c010223e985bfb2b5fbfecbcece9eecad9a80160b01021ab2f1a8f6d9be9cb2b4f0b7d7949198b8e00e0a010203d8ab8cc5b4afe6d0cbe6fdb7c5e79db6f9c00b0a01022da6cdb2e3df9ed8bdd28cfcb9a5efe5ff800202010253e6bedbfb82c38381dd83e6d6dbf8e7d6a0141400023fc6b79edcf1a3dffffcf1ca89a0f19e801613000251f4e7a88bcb90ac89a0fa96a9ebe3ade4c4160e000203a9c3ed8c96b4fe8892ffa09cac95c0ce89bc0e0a000203d1bcb3e890b380a6b6fc9fac9e95e4dae6a60b0a000233c4d0b3ef86cc9ea3e3e5ecd7fcc28dfbda1608000203e1c4aebdbcebd18a90939da2c889a1a9941502000201b1edcf9dd7d3f68a95df84e2d2b6f9fc80020200025dcfebeb88b88bc681a3fbced786ccab8cac1b019bd6c988a1c9d0c0bed9c0000b0803060118031a040c020a02010c002404280404eaf104eaf247fda662bcbc010190fabba0f5dffa93b7b4a8c8c89d9be0c035ac34ff01ba8e26db01f7d901f7da47b4ac2f99e1000e9be8ccbcaf,
  0x10396970396986af8d63ae383010981858fded6999fffc6849dc0398a38db0187ae038df701fccf01fcd044bce4329e810001ca81d494deb197e7d1fba3e7e0141402021c9fdadb89bce4cae795ef9ad6accd8e801613020249fceddc84c290a2c8ffb6f7aaa5e0a9ce80160e02020399bdccb3eebfd3bfebddf397f4cadad6aaf0140c020209feca8cb5b1a988bdc1e1b7828f87a680160b02021be1bc8793f78eceb5d882a7a3ce94f983d00b0b02020397dc84cd9eeacae7f6cda0e8d8cc9ca0]
private def node2504:Certificate:=PackedParametricCertificateData.decode 11 data2504
private def node2505:Certificate:=.split node2479 node2504
private def node2506:Certificate:=.positive 1 [(1,2),(6,11)] node2505
private def node2507:Certificate:=.negative 1 [(1,0),(1,7)] node2506
private def node2508:Certificate:=.negative 1 [(1,0),(1,6)] node2507
private def node2509:Certificate:=.split node2428 node2508
private def node2510:Certificate:=.split node2084 node2509
private def node2511:Certificate:=.split node1979 node2510
private def node2512:Certificate:=.negative 1 [(1,0),(3,2)] node2511
private def node2513:Certificate:=.split node1878 node2512
private def data2524:List Nat:=[
  0x1151515131111130e180a150a0b0a1809180209151515131111130e180a150a0b0a1809180209151515131111130e180a150a0b0a1809180209060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060311040c0804020302040803100400020206030f08080607060212041a030e0402020206030f2c0c020206011204120308020002020203]
private def node2524:Certificate:=PackedParametricCertificateData.decode 11 data2524
private def data2534:List Nat:=[
  0x115151513130a110a180915090a091808080818020a15151513130a110a180915090a091808080818020a15151513130a110a180915090a091808080818020a060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060311040c0804020302040803100400020206030f08080607060212041a030e04010200020308030f0c0002020203]
private def node2534:Certificate:=PackedParametricCertificateData.decode 10 data2534
private def data2589:List Nat:=[
  0x118080908150413040e040804130208020a1515180f18080908150413040e040804130208020a1515180f18080908150413040e040804130208020a0610040a02010a0004040e030c02090201120030043603010a0208020204010204060315151513180f1808040418021502130102000915151513180f18081802150213010715151513180f18081802130106061710030600100312031404030202020315151513180a18091808150709070404130207020a15151513180f180a1808150713020715151513180f180a18081507130207060a040306010c00080416030c02090201120030043603010a0208020204010204060301100400020206030115151513180a18090909180815081307070707040a15151513180a180815081307070713020815151513180a1808150813070707130208060a040306010c00080416030c02090201120030043603130404020202030a020802020401020406030c020202020203100400020206030b0200020202030115151513111113090a09090913080808080713020a15151513111113090a09090913080808080713020a15151513111113090a09090913080808080713020a060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030c0403020102030403100400020206030b0200020202030e040b0609020006040a0301,
  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]
private def node2589:Certificate:=PackedParametricCertificateData.decode 10 data2589
private def node2590:Certificate:=.split node2534 node2589
private def node2591:Certificate:=.split node2524 node2590
private def node2592:Certificate:=.positive 1 [(1,0),(2,12)] node2591
private def node2593:Certificate:=.positive 9 [(8,0),(3,4),(8,11)] node2592
private def node2594:Certificate:=.positive 4 [(1,0),(1,1),(6,9)] node2593
private def node2595:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2594
private def node2596:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node2595
private def node2597:Certificate:=.positive 3 [(1,0),(2,6)] node2596
private def data2608:List Nat:=[
  0x1151315111111130e180a0b0a18091109180209151315111111130e180a0b0a18091109180209151315111111130e180a0b0a18091109180209060a040306010c00080416030c020902011200300436030506030200040304030a020802020401020406030b060502020203100400020206030f08080607060212041a030e0402020206030f2408020206011004100308020002020203]
private def node2608:Certificate:=PackedParametricCertificateData.decode 11 data2608
private def data2623:List Nat:=[
  0x11515120a0f0a0b091504130409040a03040308020a1515120a0f0a0b09130409040a030403080204010a1515120a0f0a0b09130409040a030403080204010a060f0201020202030c020902011200300436030506030200040304030a0208020204010204060315111311130a120a11090a0909080804180111010a1511130a120a11090a09090808041103180111010a1511130a120a11090a09090808041103180111010a060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060301100400020206030f08080607060212041a030e04010200020308030f0c0002020203]
private def node2623:Certificate:=PackedParametricCertificateData.decode 10 data2623
private def data2683:List Nat:=[
  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,
  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,
  0x115111311160e110e0b0b11080f060a06060201010a15111311160e110e0b0b11080f060a06060201010a15111311160e110e0b0b11080f060a06060201010a06120803060018031a0415151311110e0b0b11080f]
private def node2683:Certificate:=PackedParametricCertificateData.decode 10 data2683
private def node2684:Certificate:=.split node2623 node2683
private def node2685:Certificate:=.split node2608 node2684
private def node2686:Certificate:=.positive 1 [(1,0),(2,12)] node2685
private def node2687:Certificate:=.positive 3 [(2,0),(3,3),(2,11)] node2686
private def node2688:Certificate:=.positive 4 [(1,0),(1,1),(6,9)] node2687
private def node2689:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2688
private def node2690:Certificate:=.positive 3 [(3,0),(2,2),(4,7)] node2689
private def data2706:List Nat:=[
  0x10e0e0b090a08080812040f040e0404030b0108000a0e0e0b090a08080812040f040e0404030b0108000a0e0e0b090a08080812040f040e0404030b0108000a060b08090601060308030c020902011200300436030506030200040304030a020802020401020406031211130e100d100c130b18090b0910031802091211130e100e100c130b18090b091802100009100f130e100e100c130b18090b091003180009060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060301100400020206030f08080607060212041a030e0402020206030f2408020206011004100308020002020203]
private def node2706:Certificate:=PackedParametricCertificateData.decode 11 data2706
private def data2767:List Nat:=[
  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,
  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,
  0x1110f160e110e100e1108100808061103060201010a110f160e110e100e1108100808061103060201010a]
private def node2767:Certificate:=PackedParametricCertificateData.decode 11 data2767
private def node2768:Certificate:=.split node2706 node2767
private def node2769:Certificate:=.positive 1 [(1,0),(2,12)] node2768
private def node2770:Certificate:=.positive 1 [(1,2),(2,11)] node2769
private def node2771:Certificate:=.positive 2 [(1,0),(1,1),(2,10)] node2770
private def node2772:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2771
private def data2788:List Nat:=[
  0x10e0e0f0a0b090f08080813041204090404030b010a0e0e0f0a0b090f08080813041204090404030b010a0e0e0f0a0b090f08080813041204090404030b010a060b08090601060308030c020902011200300436030506030200040304030a02080202040102040603120e0e0e0f0a11090b090b040f020f000b0009120e0e0e0f0a11090b090f040b040f020b0009120e0e0e0f0a11090b090f040b040f020b0009060a040306010c00080416030c020902011200300436030506030200040304030a0208020204010204060301100400020206030f04060c02120316030e0402020206030d0806120212011004180308020002020203]
private def node2788:Certificate:=PackedParametricCertificateData.decode 11 data2788
private def data2849:List Nat:=[
  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,
  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,
  0x113110e0e0c0b0b0809080e030602060101010f000a13110e0e0c0b0b0809080e030602060101010f000a13110e0e0c0b0b0809080e030602]
private def node2849:Certificate:=PackedParametricCertificateData.decode 11 data2849
private def node2850:Certificate:=.split node2788 node2849
private def node2851:Certificate:=.positive 1 [(2,0),(1,3)] node2850
private def data2867:List Nat:=[
  0x10e0e0f0a0b090f08080813041204090404030b010a0e0e0f0a0b090f08080813041204090404030b010a0e0e0f0a0b090f08080813041204090404030b010a060a060902080401040406030c0209020112003004360313040402020203090402040102030603120e0e0e0f0a11090b090b040f020f000b0009120e0e0e0f0a11090b090f040b040f020b0009120e0e0e0f0a11090b090f040b040f020b0009060a040306010c00080416030c020902011200300436030506030200040304030a0c02080106000404120301100400020206030f04060c02120316030e0402020206030d0806120212011004180308020002020203]
private def node2867:Certificate:=PackedParametricCertificateData.decode 11 data2867
private def data2928:List Nat:=[
  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,
  0x10306020f01060101010a13110e0e0c0c110809080e0306020f01060101010a060b0803060118031a041513131112110e0e090815030e030902030101010a1513131112110e0e090815030e030902030101010a1513131112110e0e090815030e030902030101010a060b0803060118031a04010f02020602020412100e0e090603100310020002020204131112110e0e090815030e0309021301080103010a131112110e0e090815030e0309021301080103010a131112110e0e090815030e0309021301080103010a060b0803060118031a0414040302020203151213110e0e0b0a15080b0809081302130112010a1513151213110e0e0b0a15080b080908130212010a1513151213110e0e0b0a15080b080908130212010a060b04070605060304040c02090201120030043603010e02090201040304030c040302010203040401151313110e0e11080908150615030902080103010a151313110e0e09081506150309021301080103010a151313110e0e09081506150309021301080103010a060b0803060118031a0414100402020603151313110e0e15080b08090815061106080212010a151313110e0e11080b08090815061106080212010a1513131112110e0e11080b0809081506080206010a060b0206060202040c02090201120030043603010904020401020306030c0202020202041004000202060301151313,
  0x113110e0e0c0c110809080e0306020f01060101010a13110e0e0c0c110809080e]
private def node2928:Certificate:=PackedParametricCertificateData.decode 11 data2928
private def node2929:Certificate:=.split node2867 node2928
private def data2946:List Nat:=[
  0x1150d130d180b0d0b18090d0908021200090009150d130d180b0d0b18090d0908021200090009150d130d180b0d0b18090d0908021200090009061811130d180b0d0b18090d090f0818020400091811130d180b0d0b18090d090f081802040009130d180b0d0b18090d090f081802180104000906010b02010600120314030502040200020302031204090c020e031203110f0f0f130d0d0b18090d090f081204180209110f0f0f130d0d0b18090d090f081204180209110f0f0f130d0d0b18090d090f081204180209060c180708031601380442030b020106001203140313140602050203080312040a0c020a000404120301100400020206030f04060c02120316030e0402020206030f120d02010403060308020002020203]
private def node2946:Certificate:=PackedParametricCertificateData.decode 11 data2946
private def data3008:List Nat:=[
  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,
  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,
  0x11615150d0b0915030e030303060101010900091615150d0b0915030e0303]
private def node3008:Certificate:=PackedParametricCertificateData.decode 11 data3008
private def node3009:Certificate:=.split node2946 node3008
private def node3010:Certificate:=.split node2929 node3009
private def node3011:Certificate:=.split node2851 node3010
private def node3012:Certificate:=.positive 3 [(1,4),(8,9)] node3011
private def node3013:Certificate:=.positive 9 [(5,3),(3,6),(22,8)] node3012
private def node3014:Certificate:=.split node2772 node3013
private def node3015:Certificate:=.split node2690 node3014
private def node3016:Certificate:=.split node2597 node3015
private def data3042:List Nat:=[
  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]
private def node3042:Certificate:=PackedParametricCertificateData.decode 11 data3042
private def data3099:List Nat:=[
  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,
  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,
  0x1120f110f110e120a11081103120206020901]
private def node3099:Certificate:=PackedParametricCertificateData.decode 11 data3099
private def node3100:Certificate:=.split node3042 node3099
private def node3101:Certificate:=.positive 4 [(4,0),(1,1),(3,6)] node3100
private def node3102:Certificate:=.positive 4 [(1,0),(4,2),(3,5)] node3101
private def node3103:Certificate:=.positive 7 [(4,0),(4,1),(3,4)] node3102
private def node3104:Certificate:=.positive 10 [(11,0),(3,3),(7,6)] node3103
private def data3130:List Nat:=[
  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]
private def node3130:Certificate:=PackedParametricCertificateData.decode 11 data3130
private def data3175:List Nat:=[
  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,
  0x1151313130e0e0b09090908080a0202020b0109010a15130e0e0b09090908080b020a0202020b0109010a15130e0e0b09090908080b020a0202020b0109010a06120803060018031a04151313130e0e0b09090908080b020a02020211010a151313130e0e0b09090908080b020a02020211010a151313130e0e0b09090908080b020a02020211010a0612080e0c03060124042604011513130e0e0e0a0a0f080808030302020b000a000a1513130e0e0e0a0a0f080808030302020b000a000a1513130e0e0e0a0a0f080808030302020b000a000a0612020604020203020411020a0200060306030115130f0f0e0e0b0b08080e0303030902020209010a15130f0f0e0e0b0b08080e0303030902020209010a15130f0f0e0e0b0b08080e0303030902020209010a06120803060018031a04151313130e0e0b0b08080e0303030b02090202020a151313130e0e0b0b08080e0303030b02090202020a151313130e0e0b0b08080e0303030b02090202020a0612080e0c0306]
private def node3175:Certificate:=PackedParametricCertificateData.decode 9 data3175
private def data3196:List Nat:=[
  0x113110e0e0c0b0b0809080e030602060101010f000a13110e0e0c0b0b0809080e030602060101010f000a13110e0e0c0b0b0809080e030602060101010f000a06120803060018031a0413110e0e0c0b150809080e0309020301010100000a13110e0e0c0b0b0809080e0309021501030101010a13110e0e0c0b0b0809080e0309021501030101010a0612080e0c030601240426040115130e0e0c0b150809080e0313010301010109000a15130e0e0c0b150809080e0313010301010109000a15130e0e0c0b150809080e0313010301010109000a060e100718042803020416040c0209020112003004360301120404020202031002000202020413110e0e0c0b15080b08130208020801030109000a13110e0e0c0b15080b08130208020801030109000a13110e0e0c0b15080b08130208020801030109000a0613110e0e0a0a15080b08040413020802080103010a13110e0e0b0a0a0a15080b0813020802080103010a13110e0e0b0a0a0a15080b0813020802080103010a06010c020902011200300436030f0202060202030a0208020404010e040a030c0403020102030404010b0200020202040a020002020204]
private def node3196:Certificate:=PackedParametricCertificateData.decode 9 data3196
private def node3197:Certificate:=.split node3175 node3196
private def node3198:Certificate:=.negative 1 [(1,0),(1,8)] node3197
private def node3199:Certificate:=.split node3130 node3198
private def node3200:Certificate:=.positive 12 [(15,0),(1,5),(8,6)] node3199
private def data3237:List Nat:=[
  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,
  0x115150e0e0a0a0a0813040e040f020a02080003000a15150e0e0a0a0a0813040e040f020a02080003000a15150e0e0a0a0a0813040e040f020a020800]
private def node3237:Certificate:=PackedParametricCertificateData.decode 11 data3237
private def data3296:List Nat:=[
  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,
  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,
  0x115131313150e130e0e0e08080a0202020b0109010a15131313150e130e0e0e08080a0202020b0109010a15131313150e130e0e0e08080a0202020b0109010a060b0803060118031a0415131313150e130e0e0e08080a02020211010d000a15131313150e130e0e0e08080a02020211010d000a15131313150e130e0e0e08080a02020211010d000a060b0803060118031a040115131313130e0e0e0a0a080802020b010d000a000a15131313130e0e0e0a0a080802020b010d000a000a15131313130e0e0e0a0a08]
private def node3296:Certificate:=PackedParametricCertificateData.decode 9 data3296
private def data3316:List Nat:=[
  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]
private def node3316:Certificate:=PackedParametricCertificateData.decode 9 data3316
private def node3317:Certificate:=.split node3296 node3316
private def node3318:Certificate:=.negative 1 [(1,0),(1,8)] node3317
private def node3319:Certificate:=.split node3237 node3318
private def data3360:List Nat:=[
  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,
  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]
private def node3360:Certificate:=PackedParametricCertificateData.decode 11 data3360
private def data3419:List Nat:=[
  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,
  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,
  0x11611150d130d0d0b0b090f08020209010d00091611150d130d0d0b0b090f08020209010d00091611130d0d0b0b090f080d04020209010d0009060a040306010c0008041604150d130d0d0b0b090808020211010a00090009150d130d0d0b0b090808020211010a00090009150d130d0d0b0b090808020211010a00090009060b0803060118031a0401150d130d0d]
private def node3419:Certificate:=PackedParametricCertificateData.decode 9 data3419
private def data3439:List Nat:=[
  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]
private def node3439:Certificate:=PackedParametricCertificateData.decode 9 data3439
private def node3440:Certificate:=.split node3419 node3439
private def node3441:Certificate:=.negative 1 [(1,0),(1,8)] node3440
private def node3442:Certificate:=.split node3360 node3441
private def node3443:Certificate:=.split node3319 node3442
private def node3444:Certificate:=.split node3200 node3443
private def data3493:List Nat:=[
  0x10a000a0e0e11090b09080813030e030f000d000b000a000a06010702010e00200324030502040200020302030110060e060108030804010b090d0808080904150313030b0109000300090b090d0808080904150313030b0109000300090b090d0808080904150313030b010900030009060e0e11090b09080813030e030f000d000b000a000a0e0e11090b09080813030e030f000d000b000a000a0e0e11090b09080813030e030f000d000b000a000a06010702010e00200324030502040200020302030502020402020310040e020604040604060410040002020603010e0402020206030d04090601020306031715170b120b120a12090e03030303010d00091715170b120b120a12090e03030303010d00091715170b120b120a12090e03030303010d0009061715170b120b120a170912090e03170104000917151711170b120b120a170912090e030400091715170b120b120a170912090e031701040009060115040106001003120305020402000203020313040202020203150e170b120b120a170912090d040b04120209150e170b120b120a170912090d040b04120209150e170b120b120a170912090d040b041202090611060d020306000e0410030c060202010a0026042a0313140602050203080312040a0c020a00040412030110040002020603100402020202030e0402020206030d040906010203060301,
  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]
private def node3493:Certificate:=PackedParametricCertificateData.decode 11 data3493
private def data3517:List Nat:=[
  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]
private def node3517:Certificate:=PackedParametricCertificateData.decode 11 data3517
private def node3518:Certificate:=.split node3493 node3517
private def node3519:Certificate:=.negative 1 [(1,1),(1,7)] node3518
private def node3520:Certificate:=.negative 13 [(12,0),(3,4),(4,6)] node3519
private def node3521:Certificate:=.split node3444 node3520
private def node3522:Certificate:=.positive 8 [(5,4),(1,6),(24,8)] node3521
private def node3523:Certificate:=.split node3104 node3522
private def node3524:Certificate:=.negative 1 [(1,1),(1,2)] node3523
private def node3525:Certificate:=.negative 4 [(4,0),(3,1),(3,3)] node3524
private def node3526:Certificate:=.split node3016 node3525
private def node3527:Certificate:=.split node2513 node3526
private def node3528:Certificate:=.split node1706 node3527
private def node3529:Certificate:=.split node921 node3528
private def zz508:"s01fc"="s01fc":=by decide+kernel
private theorem valid81:check node81 ctx81 quad81 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid226:check node226 ctx226 quad226 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid387:check node387 ctx387 quad387 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid464:check node464 ctx464 quad464 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid387
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz509:"s01fd"="s01fd":=by decide+kernel
private theorem valid465:check node465 ctx465 quad465 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid464
private theorem valid467:check node467 ctx467 quad467 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid226
    · exact valid465
private theorem valid540:check node540 ctx540 quad540 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid687:check node687 ctx687 quad687 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private def zz510:"s01fe"="s01fe":=by decide+kernel
private theorem valid763:check node763 ctx763 quad763 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid687
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid764:check node764 ctx764 quad764 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid763
private theorem valid839:check node839 ctx839 quad839 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid915:check node915 ctx915 quad915 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · exact valid839
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz511:"s01ff"="s01ff":=by decide+kernel
private theorem valid918:check node918 ctx918 quad918 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid467
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid540
      · exact valid764
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid915
private theorem valid920:check node920 ctx920 quad920 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid81
    · exact valid918
private theorem valid1004:check node1004 ctx1004 quad1004 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1111:check node1111 ctx1111 quad1111 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz512:"s0200"="s0200":=by decide+kernel
private theorem valid1115:check node1115 ctx1115 quad1115 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid1111
private theorem valid1234:check node1234 ctx1234 quad1234 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1318:check node1318 ctx1318 quad1318 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1391:check node1391 ctx1391 quad1391 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1318
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz513:"s0201"="s0201":=by decide+kernel
private theorem valid1392:check node1392 ctx1392 quad1392 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid1234
  · exact valid1391
private theorem valid1621:check node1621 ctx1621 quad1621 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1699:check node1699 ctx1699 quad1699 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1621
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1700:check node1700 ctx1700 quad1700 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1699
private def zz514:"s0202"="s0202":=by decide+kernel
private theorem valid1701:check node1701 ctx1701 quad1701 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1700
private theorem valid1704:check node1704 ctx1704 quad1704 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1115
  · apply NatParametricCheckSteps.split_valid
    · exact valid1392
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1701
private theorem valid1706:check node1706 ctx1706 quad1706 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid1004
    · exact valid1704
private theorem valid1789:check node1789 ctx1789 quad1789 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz515:"s0203"="s0203":=by decide+kernel
private theorem valid1792:check node1792 ctx1792 quad1792 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1789
private theorem valid1874:check node1874 ctx1874 quad1874 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1976:check node1976 ctx1976 quad1976 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2082:check node2082 ctx2082 quad2082 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz516:"s0204"="s0204":=by decide+kernel
private theorem valid2197:check node2197 ctx2197 quad2197 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2427:check node2427 ctx2427 quad2427 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2428:check node2428 ctx2428 quad2428 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid2197
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid2427
private theorem valid2509:check node2509 ctx2509 quad2509 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2428
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz517:"s0205"="s0205":=by decide+kernel
private theorem valid2510:check node2510 ctx2510 quad2510 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2082
  · exact valid2509
private theorem valid2512:check node2512 ctx2512 quad2512 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid1976
    · exact valid2510
private theorem valid2513:check node2513 ctx2513 quad2513 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid1792
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid1874
  · exact valid2512
private theorem valid2594:check node2594 ctx2594 quad2594 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz518:"s0206"="s0206":=by decide+kernel
private theorem valid2688:check node2688 ctx2688 quad2688 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2772:check node2772 ctx2772 quad2772 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3010:check node3010 ctx3010 quad3010 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3013:check node3013 ctx3013 quad3013 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid3010
private def zz519:"s0207"="s0207":=by decide+kernel
private theorem valid3015:check node3015 ctx3015 quad3015 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2688
  · apply NatParametricCheckSteps.split_valid
    · exact valid2772
    · exact valid3013
private theorem valid3016:check node3016 ctx3016 quad3016 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2594
  · exact valid3015
private theorem valid3104:check node3104 ctx3104 quad3104 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3200:check node3200 ctx3200 quad3200 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz520:"s0208"="s0208":=by decide+kernel
private theorem valid3319:check node3319 ctx3319 quad3319 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3443:check node3443 ctx3443 quad3443 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid3319
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3520:check node3520 ctx3520 quad3520 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3523:check node3523 ctx3523 quad3523 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid3104
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.split_valid
        · exact valid3200
        · exact valid3443
      · exact valid3520
private def zz521:"s0209"="s0209":=by decide+kernel
private theorem valid3527:check node3527 ctx3527 quad3527 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2513
  · apply NatParametricCheckSteps.split_valid
    · exact valid3016
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid3523
private theorem valid3529:check node3529 ctx3529 quad3529 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid920
  · apply NatParametricCheckSteps.split_valid
    · exact valid1706
    · exact valid3527
theorem certificate_valid:check node3529 constraintsNat base hinges = true:=valid3529
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node3529 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase1
private def zz2177:"s0881"="s0881":=by decide+kernel
end 
section 
namespace Green24Proof.QuadNearBalanceCase2
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x12038b4ed26ec6, -0xaa87bee538000, -0xffcb9e57d4000,0xb1404e2d7c52], ![-0xaa87bee538000, -0x5a0dab9f32163e,0x13fb66c17f4d8c,0x5543df729c000], ![-0xffcb9e57d4000,0x13fb66c17f4d8c, -0x460ff6eded75a8,0xadab046872d6a], ![0xb1404e2d7c52,0x5543df729c000,0xadab046872d6a, -0x5543df729c000]], ![![-0x69c0271f4cc0,0,0x19945ca262000, -0x6e9b12afd720], ![0, -0x30254342ffac0, -0x1ac58d12d0a0,0], ![0x19945ca262000, -0x1ac58d12d0a0, -0x282085272680,0xa082149c9a0], ![-0x6e9b12afd720,0,0xa082149c9a0,0]], ![![-0x10d8c266d720,0xa7a358200,0xa7a358200,0x1dd4cbf36c00], ![0xa7a358200,0x5540839ef2a0,0xa7a358200, -0x20b36426cfe0], ![0xa7a358200,0xa7a358200, -0x8862ab3bde40,0x222326abe800], ![0x1dd4cbf36c00, -0x20b36426cfe0,0x222326abe800,0]]]
def hinges:Hinges:=[(![0,0, -0x34edce0], ![0,0,1, -3]),(![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0], ![0,0,1, -1]),(![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490], ![0,0,3, -1]),(![0,0x16ada57d3700,0x1476b081e800], ![0,1, -1,0]),(![0x58a02716be29,0, -0xae9f4c970a0], ![0,1,0, -3]),(![0x133d36f21e8b0a,0,0], ![0,1,0, -1]),(![-0x5543df729c000,0,0], ![0,3, -2, -1]),(![0x5543df729c000,0,0], ![0,3, -2,1]),(![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00], ![0,3, -1,0]),(![0x58a02716be29,0,0], ![0,3,0, -1]),(![0x5543df729c000,0,0], ![0,3,2, -1]),(![-0x1b7e5fd92756,0x1b78ccf2f520,0], ![1, -3,0,0]),(![-0x5543df729c000,0,0], ![1, -2, -3,0]),(![0x5543df729c000,0,0], ![1, -2,3,0]),(![0x1b7e5fd92756, -0x1b78ccf2f520,0], ![1, -1,0,0]),(![-0x465418d301c3,0,0], ![1,0, -3,0]),(![-0x12c695003c6fa9,0,0x6eaa7278920], ![1,0, -1,0]),(![0,0x7d5efacaea0,0x9ee1b3f4e00], ![1,0,0, -3]),(![-0x36c599a8bcb6,0x61ea37729e20,0], ![1,0,0, -1]),(![0x5543df729c000,0,0], ![1,2, -3,0]),(![-0x7402f3eb1c84,0,0], ![3,0, -1,0])]
def normalizationDenominator:ℤ:=0xaa87bee538000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx2809:Nat → Linear:=constraintsNat
private def quad2809:Quadratic:=base
private def ctx748:Nat → Linear:=cons ![0,0,1, -3] ctx2809
private def quad748:Quadratic:=quad2809 + coefficientProduct ![0,0, -0x34edce0] ![0,0,1, -3] ![0,0,1, -3]
private def ctx115:Nat → Linear:=cons ![0,1, -1,0] (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx748))
private def quad115:Quadratic:=((quad748 + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0]
private def ctx109:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] ctx115)))))
private def quad109:Quadratic:=(((((quad115 + coefficientProduct ![0x58a02716be29,0, -0xae9f4c970a0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x58a02716be29,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx368:Nat → Linear:=cons ![0,1,0, -3] (cons (-![0,1, -1,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx748)))
private def quad368:Quadratic:=(((quad748 + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x58a02716be29,0, -0xae9f4c970a0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx744:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -1,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx748)))
private def quad744:Quadratic:=(((quad748 + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx618:Nat → Linear:=cons ![0,1,0, -1] ctx744
private def quad618:Quadratic:=quad744 + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx2808:Nat → Linear:=cons (-![0,0,1, -3]) ctx2809
private def quad2808:Quadratic:=quad2809
private def ctx1393:Nat → Linear:=cons ![0,0,1, -1] ctx2808
private def quad1393:Quadratic:=quad2808 + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]
private def ctx858:Nat → Linear:=cons ![0,1,0, -3] (cons ![0,1, -1,0] (cons ![0,0,3, -1] ctx1393))
private def quad858:Quadratic:=((quad1393 + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x58a02716be29,0, -0xae9f4c970a0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx853:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx858))))
private def quad853:Quadratic:=((((quad858 + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x58a02716be29,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx941:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) (cons ![0,1, -1,0] (cons ![0,0,3, -1] ctx1393)))
private def quad941:Quadratic:=(((quad1393 + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0])) + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1391:Nat → Linear:=cons (-![0,1, -1,0]) (cons ![0,0,3, -1] ctx1393)
private def quad1391:Quadratic:=(quad1393 + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1])
private def ctx1135:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1391)
private def quad1135:Quadratic:=(quad1391) + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1388:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1391))
private def quad1388:Quadratic:=((quad1391))
private def ctx1729:Nat → Linear:=cons ![0,1, -1,0] (cons ![0,0,3, -1] (cons (-![0,0,1, -1]) ctx2808))
private def quad1729:Quadratic:=((quad2808) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0]
private def ctx1463:Nat → Linear:=cons ![0,1,0, -3] ctx1729
private def quad1463:Quadratic:=quad1729 + coefficientProduct ![0x58a02716be29,0, -0xae9f4c970a0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx1570:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1729)
private def quad1570:Quadratic:=(quad1729) + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1566:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] ctx1570)))
private def quad1566:Quadratic:=(((quad1570 + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x58a02716be29,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1651:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1729))
private def quad1651:Quadratic:=((quad1729)) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1726:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1729))
private def quad1726:Quadratic:=((quad1729))
private def ctx2063:Nat → Linear:=cons (-![0,1, -1,0]) (cons ![0,0,3, -1] (cons (-![0,0,1, -1]) ctx2808))
private def quad2063:Quadratic:=((quad2808) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1])
private def ctx1993:Nat → Linear:=cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx2063)))
private def quad1993:Quadratic:=(((quad2063))) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1864:Nat → Linear:=cons ![0,3, -1,0] ctx1993
private def quad1864:Quadratic:=quad1993 + coefficientProduct ![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00] ![0,3, -1,0] ![0,3, -1,0]
private def ctx1796:Nat → Linear:=cons ![0,3,0, -1] ctx1864
private def quad1796:Quadratic:=quad1864 + coefficientProduct ![0x58a02716be29,0,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2806:Nat → Linear:=cons (-![0,0,3, -1]) (cons (-![0,0,1, -1]) ctx2808)
private def quad2806:Quadratic:=(quad2808)
private def ctx2134:Nat → Linear:=cons ![0,1,0, -3] (cons ![0,1, -1,0] ctx2806)
private def quad2134:Quadratic:=(quad2806 + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x58a02716be29,0, -0xae9f4c970a0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx2610:Nat → Linear:=cons (-![0,1,0, -3]) (cons ![0,1, -1,0] ctx2806)
private def quad2610:Quadratic:=(quad2806 + coefficientProduct ![0,0x16ada57d3700,0x1476b081e800] ![0,1, -1,0] ![0,1, -1,0])
private def ctx2211:Nat → Linear:=cons ![0,1,0, -1] ctx2610
private def quad2211:Quadratic:=quad2610 + coefficientProduct ![0x133d36f21e8b0a,0,0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx2311:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) ctx2610))
private def quad2311:Quadratic:=((quad2610) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2606:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx2610)))
private def quad2606:Quadratic:=(((quad2610)) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x36c599a8bcb6,0x531281a215c0, -0xa8895429a00] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2605:Nat → Linear:=cons (-![0,3,0, -1]) ctx2606
private def quad2605:Quadratic:=quad2606
private def ctx2509:Nat → Linear:=cons ![0,3,2, -1] ctx2605
private def quad2509:Quadratic:=quad2605 + coefficientProduct ![0x5543df729c000,0,0] ![0,3,2, -1] ![0,3,2, -1]
private def ctx2803:Nat → Linear:=cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -1,0]) ctx2806))
private def quad2803:Quadratic:=((quad2806))
private def data18:List Nat:=[
  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]
private def node18:Certificate:=PackedParametricCertificateData.decode 10 data18
private def data27:List Nat:=[
  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,
  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]
private def node27:Certificate:=PackedParametricCertificateData.decode 9 data27
private def data70:List Nat:=[
  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,
  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,
  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,
  0x1fddde0bbb494941412010204a1cdf5f68ef5dd8be7cacc8185a280ccbb87f3d40909010279f18cbff1d2e3b7ccf8e69ae1d0a9aedc80baa81408010201c3bba9d6ccf4e1dcd3e5dfabc1b09885868ee9f00707010201b7c8cce6d6dbcd8fcda79780f4cfe7dad49e9ce80606010202909a988bffa5b4b1d4feb0b9feffeaa59aed82c81405010246fcff8ae3f9a7b9c8eab3baa899dbe5d3eeeb900905010225d3d4f99cf7b694c096889bb282e7b5ff89c0c0080501027de6a689b7ccab86b0d2caf8a7befe9bf9def3d0141400020481f696968df8f38785b2a9a2c2b7a2abd9d7d7ac1412000203fea6ffedd0a6e9e9dada909dbdbfb0f9e9d3858c0909000261bacbf3acc9c58bac91b4dcffcf8e9ca8ff87881408000201a6afe9f5c2bfb78bd8f1c4c9fee4be808df5b9800707000276f58bed9fe58381d68dc2adcfa8a3a4b79a90ce070600020190b4bbde95e38ca8d6a3cf909be7c1c8c0f0eee8140500020199dab7e2f9f8afa396eef5c1ae93deb5b7a6ac8008050002019ae3ecdbb699e3e6afefdfb6b8ce92f4a39381a0050500023290a9dd90b7e483adf69ceabcedac96f481aa8a1e04aac8dff8d9bbf9c1b4c9c9c1a8000606050400080306030f04020202020312040002020603100200020202030c0201020202031ba8b3d73682cae014b2cdf502a0dda3038da2f8f003f5878a93028cc282c479ea88,
  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,
  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,
  0x11414141212100a0a0d030e010e000d00090000000a1414141212100a0a0d030e010e000d00090000000a1414141212100a0a0d030e010e000d00090000000a0613020106020204141414120d0d100a140808080707010108]
private def node70:Certificate:=PackedParametricCertificateData.decode 8 data70
private def data105:List Nat:=[
  0x1f4abe1b4c1dcee84a3a9e0e9f2d480080802026fb2d7c1c3cc88909ce8fba192a08080180702020187aa9fcaf2cd84f1d3cf85bec8dec1c680801207020268a8fb84f1f4e0c6eade90c89b8ae1d1ac800706020201d290b9d7febeb2c99798caf9c3e88080060502027fc8f094f29bbdfd98c9eb94bfc08080141401022083a2e5b69ca1f5b3eaba80f0c3a4febaea141201021595f8b59ebd82b99eada592ac9bf4f098c2180d010209b7c98ca0f4a9bbd28ccea4bad3919ec6801208010217e7fd9cd7bbc0cd86b3a3f4e8d89f90c3a81807010201848498e4ab8afbdbb6de97ffa08aeafeae801207010274f3a5a9b7cbc4e984c4bbaff89dc383bcd806060102018cdfd4cef99bd6dccf979cf9b3bd8cf1800605010201baeffee5f6969992d39de8a5a6e880801414000216c3ddc1e38db1969efe83d3b1a7b4eaa880180d000202fb8e98e581c5e7b0c3f895c9cfb99de8801809000218ceb9ecfde4c284e8bef3fcc9cccaf7c880120800020ceef08698b5f1b58de9d0b092f9f4b2b4801807000276c3fdcdffd5f081dcf4f6ede3feb685b880120700027ce8bb8fd4b48583f18ae2999baa8587cc800606000243fe9ffca68ce2d3f2d883b1fa98edc0801b2afe9befb7e1fcac89a08000140c050400020306030b06090203080004040c03120400020206030c020202020203100400020206030102000402020301,
  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,
  0x114141210120e150d12090d031200050000000914141210120e150d12090d031200050000000914141210120e150d12090d031200050000000906130201060202041304050202020314141210120e150d12090d031200050000000914141210120e150d12090d031200050000000914141210120e150d12090d0312000500000009061414121012070905070508040d030100000009141412101207]
private def node105:Certificate:=PackedParametricCertificateData.decode 8 data105
private def node106:Certificate:=.split node70 node105
private def node107:Certificate:=.split node27 node106
private def node108:Certificate:=.split node18 node107
private def node109:Certificate:=.positive 1 [(1,1),(1,7)] node108
private def node110:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node109
private def node111:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node110
private def node112:Certificate:=.positive 1 [(1,0),(2,10)] node111
private def node113:Certificate:=.positive 1 [(1,0),(2,2)] node112
private def node114:Certificate:=.positive 3 [(1,0),(2,6)] node113
private def node115:Certificate:=.positive 1 [(1,0),(1,3)] node114
private def data178:List Nat:=[
  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,
  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,
  0x11414141212100a0a0d030e010e000d00090000000a1414141212100a0a0d]
private def node178:Certificate:=PackedParametricCertificateData.decode 15 data178
private def data240:List Nat:=[
  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,
  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,
  0x114141010100a0d0909090e0707071000090000000a14141010100a0d0909090e0707071000090000000a14141010100a0d0909]
private def node240:Certificate:=PackedParametricCertificateData.decode 14 data240
private def data303:List Nat:=[
  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,
  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,
  0x11010140c140b0a0a1009150707070c010c0000000a1010140c140b0a0a140907070c010c00090000000a1010140c140b0a0a140907070c010c00090000000a060f0e0c02012c00040410040c020b0a030a00080412041010140c140b0a0a100915]
private def node303:Certificate:=PackedParametricCertificateData.decode 13 data303
private def data364:List Nat:=[
  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,
  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,
  0x11010140b]
private def node364:Certificate:=PackedParametricCertificateData.decode 13 data364
private def node365:Certificate:=.split node303 node364
private def node366:Certificate:=.split node240 node365
private def node367:Certificate:=.split node178 node366
private def node368:Certificate:=.positive 3 [(1,0),(2,6)] node367
private def data430:List Nat:=[
  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,
  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]
private def node430:Certificate:=PackedParametricCertificateData.decode 15 data430
private def data493:List Nat:=[
  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,
  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,
  0x110100e0e140a0d090909140807070d00090000000a10100e0e140a0d090909140807070d00090000000a10100e0e140a0d090909140807070d00090000000a06]
private def node493:Certificate:=PackedParametricCertificateData.decode 14 data493
private def data553:List Nat:=[
  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,
  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]
private def node553:Certificate:=PackedParametricCertificateData.decode 13 data553
private def data615:List Nat:=[
  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,
  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,
  0x11010100e140b120b0d091507100709000600091010100e140b120b0d091507100709000600091010100e140b120b0d0915071007]
private def node615:Certificate:=PackedParametricCertificateData.decode 13 data615
private def node616:Certificate:=.split node553 node615
private def node617:Certificate:=.split node493 node616
private def node618:Certificate:=.split node430 node617
private def data679:List Nat:=[
  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,
  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,
  0x1120b14090d0915070b070d0309000300020009140b120b14090d0915070d0309000300020009140b120b14090d]
private def node679:Certificate:=PackedParametricCertificateData.decode 12 data679
private def data739:List Nat:=[
  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,
  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]
private def node739:Certificate:=PackedParametricCertificateData.decode 12 data739
private def node740:Certificate:=.split node679 node739
private def node741:Certificate:=.negative 1 [(3,2),(1,7)] node740
private def node742:Certificate:=.negative 2 [(1,0),(3,1),(2,6)] node741
private def node743:Certificate:=.negative 1 [(1,0),(2,2)] node742
private def node744:Certificate:=.split node618 node743
private def node745:Certificate:=.split node368 node744
private def node746:Certificate:=.split node115 node745
private def node747:Certificate:=.positive 3 [(1,1),(8,4)] node746
private def node748:Certificate:=.positive 3 [(1,0),(2,3)] node747
private def data767:List Nat:=[
  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]
private def node767:Certificate:=PackedParametricCertificateData.decode 10 data767
private def data776:List Nat:=[
  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,
  0x104f7d502b0f86ff3ea3289c106cfc40bb2a16eb0f331c8ac002284d3b8be9fe2e0141402020a8983aedcebe2e8f184cb9992e0100902022cb1f4cbf5c6cad9bf90c4e01408020213c0fdda9bec8e9db3b3a9cfa2e01208020228de98edc286f4b9e3cea4cafac009080202509e]
private def node776:Certificate:=PackedParametricCertificateData.decode 9 data776
private def data815:List Nat:=[
  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,
  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,
  0x19ed88b83b2b1bdb61010010220be93b2bc8afcaab0abe8bcb7c1b6f1a3a9b3e5e8eea4aee0100901020b8aebdae88484c3c48a8486d3e9fa92ceb5d0cd989089ace00909010201d4bfb1e4b584edd688dab7cf8d89b5b0b0aaa6cce0e8bb981008010201c3d8cadbecad9ed182f4f19ac4dfe2fadaafdcb2c280b7a0060601020f97d1eeadd2c6aad39c86fed8c786b581e3ccf8cea6e5daa8100501022692e5ac9686e6b6ecd093c4e1f99a82e3e6b6eebeacc993e00905010204a89396a3d4e3aac2c1dfc7fbb799f9eebc8683dade9384800805010204efcce6b2d0fcf3c8f086a9efcec7cef6fcd5878dacdaccc0050501020aa191c88ee3c8ce9a99dee48faebbc59fcaf0a6c7caf4b280101000021f8283edbb938696d89fabd18dbedceddb8dcfe08eb9e080c0100900020abd86fbe0dffdd2bf87a1eba9ecfbbedaa3bcea9eccbbd480090900027bb6adecb2f38dd0d9e19cc6849cdc9481f0b5eac4c9b2a0070600026acaa6b08c99ecb2cda192ede6e8b9afefabe08be7b39ea00606000205f0ed9782b989f1d491c594b9a59cd18689d7eb80908cf3a01005000227fe8eafcaa3848cf5a2a88ce5d19996d8e68ae2c8e9cec0c00905000208a8c4cf8380f3c3ad8281eb95a1b0eeb5c5b0e0eeb586c4e00505000210978ac4ffe2b8c2fda0c1f7bd8debe08af6bfefa596fbf0801e2385ea8de0aab8ccfacbe485,
  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,
  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,
  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,
  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,
  0x114141210120a0a0a0d030e010e000d00090000000a14141210120a0a0a0d030e010e000d00090000000a14141210120a0a0a0d030e010e000d00090000000a0614140909100809060d0303030e010a01070000000a14140909100809060d0303030e010a01070000000a14140909100809060d0303030e010a01070000000a06011414121212100d0d100a100807070900080000000a1414121212100d0d100a100807070900080000000a141412121210]
private def node815:Certificate:=PackedParametricCertificateData.decode 8 data815
private def data849:List Nat:=[
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]
private def node849:Certificate:=PackedParametricCertificateData.decode 8 data849
private def node850:Certificate:=.split node815 node849
private def node851:Certificate:=.split node776 node850
private def node852:Certificate:=.split node767 node851
private def node853:Certificate:=.positive 1 [(1,1),(1,7)] node852
private def node854:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node853
private def node855:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node854
private def node856:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node855
private def node857:Certificate:=.positive 1 [(1,0),(2,2)] node856
private def node858:Certificate:=.positive 3 [(1,0),(2,6)] node857
private def data877:List Nat:=[
  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]
private def node877:Certificate:=PackedParametricCertificateData.decode 10 data877
private def data935:List Nat:=[
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private def node935:Certificate:=PackedParametricCertificateData.decode 10 data935
private def node936:Certificate:=.split node877 node935
private def node937:Certificate:=.positive 1 [(1,1),(1,7)] node936
private def node938:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node937
private def node939:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node938
private def node940:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node939
private def node941:Certificate:=.positive 1 [(1,0),(2,2)] node940
private def node942:Certificate:=.positive 1 [(1,1),(1,3)] node941
private def node943:Certificate:=.split node858 node942
private def data1007:List Nat:=[
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,
  0x102022899e8efd89888fed2928cb1ced6a8e5a0d8110002020f95e1bc95c09ae0dfd09f82cbe1c4f98eea90070002020fabfb90b7deb3ccb6baca88b7ece78195c20100020202fec4aeacb9a7ffb6bfe093b79adfc9cad013130102019987a3fcbfda82dce5bbd3a5b8f8b8cec3d9d0130f010216f7d0bfb6cdbbeea7f98acbf3b1f8ffda9aba120f01020287c3f1a2ead5949ecbf7e8c2f7c9e9e68fbe0e0501020bf3d4ecaaefcff5cd99aa95fec8efe2b5da0e04010204c2edd2f8d3b380f1bcfbb88fb087d6b8e48a020201020bd8cee6e6c3b7a5d3cafd9bbcf5a0f39e89e00e0101021895a9b1d1a8dba8fdc2e48bfe9ad1aaeecfec1100010204c49ef698bc8feedfabd698c4f6f693c3ef881313000201abc5ada3dcf0efbe9396caccc5f3a09bf9fcd8130e000209d6b998f5e69eac9f8880ce87c7ca9687f3d00606000201ceaa91b1bcf29bbbeafca49fa7d0c4b598c0020200020889a0b2a5d58de7f49cf2ecdbf2d5de87a7c00e0100021ad4ae91acc9f59cfe87c9b3c483e3c6f3c6c01913afd1e58ca0dbb9cdbdfbc800010f04020202020471d7b41fb3971fbea671e2c10112fffbac879ef191b9cfa7a8efa7c9d2ccec0281b003fcf602a7a502f6871dddec20e49b3c82cb3f88fc0004c2a9a29591ecaff1f3c8f5c5a2d4bcb4eeaa06aed502e9eb018b8808959c48a8de17a1ad11d9fa42e1a9000180a3,
  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]
private def node1007:Certificate:=PackedParametricCertificateData.decode 15 data1007
private def data1071:List Nat:=[
  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,
  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,
  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,
  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]
private def node1071:Certificate:=PackedParametricCertificateData.decode 13 data1071
private def node1072:Certificate:=.positive 5 [(4,0),(3,2),(1,5)] node1071
private def data1133:List Nat:=[
  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,
  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]
private def node1133:Certificate:=PackedParametricCertificateData.decode 14 data1133
private def node1134:Certificate:=.split node1072 node1133
private def node1135:Certificate:=.split node1007 node1134
private def data1199:List Nat:=[
  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,
  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,
  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,
  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,
  0x14de501dbb712865cff0fbdd82196a33fc7c22cbfcd003f9ea1efc5aacae1a01312020274f485f781a794a3f4de8aecd9a0150e020209cce4f6828f85cef3a794dd8c800e0e02020efae6ebadadc1998a92c6b4cf900d0d020220d9a2ac9caec894cbea8197cfd00b0b0202069fb194eac5e3c79ac49ebdb4b0130802020695f482cfce919bb7a6c1cfd6a00c000202189ad48efda2db8582c69496cae00b0002023af3a39fb49cf6f9dcaad0d7cba0000002023cd085f8e7aed3b8b8caf4b3d6c01312010274a692b4e4a4b8c6d28cb4efc3f80e0e0102]
private def node1199:Certificate:=PackedParametricCertificateData.decode 13 data1199
private def node1200:Certificate:=.positive 1 [(1,0),(1,6)] node1199
private def data1262:List Nat:=[
  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,
  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,
  0x1140e140d0d0c130a0d0a150707070c000b0000000a140e140d0d0c130a0d0a150707070c00]
private def node1262:Certificate:=PackedParametricCertificateData.decode 13 data1262
private def data1323:List Nat:=[
  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,
  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,
  0x1150d140d140c0d0a15070b010b000900060000000a150d140d140c0d0a15070b010b]
private def node1323:Certificate:=PackedParametricCertificateData.decode 12 data1323
private def data1385:List Nat:=[
  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,
  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,
  0x11512150d140d140b130a13090d091507090006000a1512150d13090d09150709000600071512150d13090d09]
private def node1385:Certificate:=PackedParametricCertificateData.decode 12 data1385
private def node1386:Certificate:=.split node1323 node1385
private def node1387:Certificate:=.split node1262 node1386
private def node1388:Certificate:=.split node1200 node1387
private def node1389:Certificate:=.negative 1 [(1,0),(2,2)] node1388
private def node1390:Certificate:=.split node1135 node1389
private def node1391:Certificate:=.negative 1 [(1,0),(1,3)] node1390
private def node1392:Certificate:=.split node943 node1391
private def node1393:Certificate:=.positive 1 [(1,0),(2,4)] node1392
private def data1457:List Nat:=[
  0x180e8a01007000203d9f982ceacb08ef2c8bcdebca2bbd2d3a9c9af97cc91bac007070002148b88d9a3e0ffb4e6acc38efd9f93daf2e8c997b5aaeeeaa0130500023afae2cadabdb38bc2eebbfaa0819f8ef4abaac2a784df8aa0100300020486fcb8b997a6e1929095fbf6b18ac1d88ed3aadcfcbfbcc01301000220e3cbb1dcdbb8eccecc9993f5cfccdfe0a8d7ad83d2f4d8e01e0198a596d79ef58fbae6d7f3cb95cdefaafaa0000608040200080306030b06090203080004040c03120400020206030c0403020102030403100400020206030d060a0200020302030c06090200020302030114141009140812080908140712070707140012000a14141009140812080908140712070707140012000a14141009140812080908140712070707140013000a060608040200080306030b06090203080004040c031204000202060311040c0804020302040803100400020206030f08080607060212041a030e04010200020308030c060a1200080308030114141010140912090a0914081208140012000914141010140912090a0914081208140012000914141010140912090a09140812081400120009060608040200080306030b06090203080004040c031204000202060311040c0804020302040803100400020206030f08080607060212041a030e0402020206030d100c120a3601200430030a060702000203020301,
  0x1fabdaba8939fcbf7d5acebebe4eab2a5f4dce0edb00908020205bfefe7d289e085aaa3fbbbebbf8faba3a8e1a1fbb1e8c2c8070702020e9ecdf8e9cca780adbef2e1e5a3eda7b3c4a1fe839980f28e0706020204b1c38a96a9edc3d7e1df81e5f69aeba993cbf6a5efb8a48c07030202519fa6c2d08f949ac792edb0f5db88bbe9cbc5efe682f3de1300020203cce3f6deebc38bcb99ccb1e8b59ad2ceafc2b7b6ec8b85fe1413010201dcb09fc59fb99bcea2fac9baf2bcfffceaf98bb7d6c0d5efc0121001022af3f4b69b8afec0fea9bdf4c1a8b68cfeec9feec7cce4a8b010100102048be5e884a1a2a5ef8399e1f4e9abd7eff4aa9895b1dab9e0130d010211fdebc9e6b7dacad1bf93d6edc9b1b4b3adee9ae7c6c4e0f00808010206bfb3fbcff49d95e4f996e4cedec6f9a381f9f1969e92f3a00707010213e0cde582fbcab4c5d289caceb7fb84b5f599a6d0c0d8d9f007030102028a95d7edb2ebcebb96b391d4b2aaba86afcde5a6f3e7c9b01301010224c8b68cf0cbf2bcf7bdbefb94d39c82b2cab0ebb8fc93acd0141300020295f9fcd6e8fabbabdfa3b6f4eec8a48dae9de287e7f38b9fe012100002279bd6a998bedcdb859f95a39d95aff0d19af5b48accb6bec0130d00021fb9b293e3d38cb9ecfbecabf2bac9b4def291f0d9f087f8c00808000205e6e2de8fe7b8c5faa9dcf283a7aacbea8ab5a2f5c9,
  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,
  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]
private def node1457:Certificate:=PackedParametricCertificateData.decode 11 data1457
private def node1458:Certificate:=.positive 1 [(1,1),(1,7)] node1457
private def node1459:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node1458
private def node1460:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1459
private def node1461:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1460
private def node1462:Certificate:=.positive 1 [(1,0),(2,2)] node1461
private def node1463:Certificate:=.positive 3 [(1,0),(2,6)] node1462
private def data1482:List Nat:=[
  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]
private def node1482:Certificate:=PackedParametricCertificateData.decode 10 data1482
private def data1491:List Nat:=[
  0x114100e09120810080a08090812070707120310000a14100e09120810080a08090812070707120310000a14100e09120810080a08090812070707120310000a060608040200080306030b06090203080004040c03120400020206030e020b040402030203100400020206030f08080607060212041a030e04010200020308030d040a180808000a040e03]
private def node1491:Certificate:=PackedParametricCertificateData.decode 9 data1491
private def data1528:List Nat:=[
  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,
  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,
  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,
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]
private def node1528:Certificate:=PackedParametricCertificateData.decode 8 data1528
private def data1562:List Nat:=[
  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,
  0x11414120e0f0a0e0a1007100112000800050000000a1414120e0f0a0e0a0a0a100710011200050000000a1414120e0f0a0e0a0b0a100710011200050000000a061310120f1207100708070a0408040700010000000a1310120f1207100708070a0408040700010000000a1310120f0f0a12]
private def node1562:Certificate:=PackedParametricCertificateData.decode 8 data1562
private def node1563:Certificate:=.split node1528 node1562
private def node1564:Certificate:=.split node1491 node1563
private def node1565:Certificate:=.split node1482 node1564
private def node1566:Certificate:=.positive 1 [(1,1),(1,7)] node1565
private def node1567:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1566
private def node1568:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1567
private def node1569:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1568
private def node1570:Certificate:=.positive 1 [(1,0),(2,2)] node1569
private def data1597:List Nat:=[
  0x1140e0a0912070907070714050d030702090000000a140e0a0912070907070714050d030702090000000a140e140d0a0912070907070714050d03090000000a060608040200080306030b06090203080004040c0308020602020203140e140d0a09120709071405070314010f0009000a140e140d0a09120709071405070314010f0009000a140e140d0a09120709071405070314010f0009000a060608040200080306030b06090203080004040c031204000202060301100400020206030d02080203020302030e0402020206030d080a120806010a0412030d0d0a08090707070e030d0308030702120007000a0d0d0a0807070e030d03080307021200070000000a0d0d0a0807070e030d03080307021200070000000a060608040200080306030b06090203080004040c030f02080205020302040403120912080a08120310031001120010000f0009120912080a08120310031001120010000f0009120912080a08120310031001120010000f0009060608040200080306030b06090203080004040c031204000202060301100400020206030f08080607060212041a030e0402020206030d080a120806010a04120301]
private def node1597:Certificate:=PackedParametricCertificateData.decode 10 data1597
private def data1646:List Nat:=[
  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,
  0x1899afdabd998b4ae9aec968a9ca2a1880f00020255c688e6b8c5dcc6aad2bd98b6bdd480b4a00f0e010201fcd88ce7bad6b9c087b6a3fbf2f6acc2bbd00606010252f9d3aad68b98ea8ab582f7aef6e99cc9ec1002010221efabf4abeac0a9b4efb2fafecef2fce5800f0201020698ace78ec7a58ba1f5e2e393f1f6df8d9eb80f01010202a688cc8fab86daf4bec1e6ecacaba8ece8e8060101020caee8cdb2c7eacc8a9e9facbea7dcf69cc80f0001022580acdbc2ae8fb1e1aca0c6fceea1b9c7c00f0e000201e493bd83c09da1f18ff79398fbcba8ccedc80604000202f7f1adaaa29c878f9bec8ededfa69baa95f2040400027c8af9bd9a8a889684f4e285c697b6b599e20f02000206bc8dd1b4ece79bbfebeca8c4f3d1bef0aa981301000232ef8af0da88a39cab9fa7dbac9f82cc84c20f01000202cce1dcc5d5ccb3cda8cfed95bac1cfbff3e61901fcf8ede6c7cfe0f296d0f40006060504000803060311040c040206030603010f0601020202040e020902010603060301b5f0038dc774ec01e6c11ac49238b9c534dcc415ddb70012a6feb5d7929ba6eea01212020201f0b0e9b3bff5a5f3c09ee3b292b80f0d02022a8cf099bbcdebb9bcc0a0e4d1a490070702020aacef9faccc8590d5e0f0f0cbc4ea1405020203dc8cde9981cbe4c0df99d18ad8981005020204bee5adf9dae3c2a3ccaaaebca0c80e0302,
  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,
  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,
  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,
  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,
  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,
  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,
  0x1030e010a010d00090000000a141414131212100e0e030e010a010d00090000000a141414131212100e0e030e010a010d00090000000a063090fb15a18d1ef6f764a982011dffa4bfc8cef5e8aebda598a493daef9dd0f0e6f5c4dc03a1880896be08a39b03f91defef33fc8c338fc31d83a8000fe9fc83a98bacc68f8987d29cabbcf3b796a3ca8beaa3f009a7ce03cfb50aa5d502879212d7c335a98c2cd89e4fa9e50007f5fa84d899fffcef83e8909ef3abe9fde0cff7daa1f18022d7f203b6ec2ae29b13e231d0a406fa900d95892bb5a90071909c9ccbc89ff6f99e85f0f18091a3ab99b19a8ad6801313020202d19cd68792a18694d8eafa98abab8bd8e8a78189a38ab19ff0bcffd0100e020210b79dc9c2dcfda5a4d8fea482f9f084db9bf8f2e89cb4c5b68d96800f0e02021a9fa88cf8aa82b2b6a9bce5dcd0b39c958bc6aca1e288ebbce0d5c1900e02020207fae4bbecf5b1f38791929ef6a48897f984eeb3fbe5c6acacefeb91e0120102027792f18f97f58de7d4c0efe18bbbcaa3b6a1cad2c9f9c4ffd4db8d800e010202228acda9afc7b6b9eb8fedfe92d5a69beaaee7cb80ce95c381b3c8f6e00101020204e3e3f6c6f9b4ccddf6f1d48ea8929fde8697bd9086af9499d4d7d9b00000020203c7f3c0e7939baab08ecafedfeb92c1e7daf0e9b0f7eca7eef2918013130102058cc3b2d7d184fbb1d89b84,
  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]
private def node1646:Certificate:=PackedParametricCertificateData.decode 10 data1646
private def node1647:Certificate:=.split node1597 node1646
private def node1648:Certificate:=.positive 1 [(1,1),(1,7)] node1647
private def node1649:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1648
private def node1650:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1649
private def node1651:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1650
private def data1678:List Nat:=[
  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]
private def node1678:Certificate:=PackedParametricCertificateData.decode 10 data1678
private def data1721:List Nat:=[
  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,
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  0x114140d0d0b0a14071007080714010d01050000000a14140d0d0b0a14071007080714010d01050000000a14140d0d0b0a14071007080714010d01050000000a0611040d040606030204130405020202030b040406010a0006041604100200020202040d020902020201020404040c0608060204000a040e040b0607060104000e04120414130e0e110d0d0d0b0b070711030b00090000000a14130e0e110d0d0d0b0b070711030b00090000000a14130e0e110d0d0d0b]
private def node1721:Certificate:=PackedParametricCertificateData.decode 10 data1721
private def node1722:Certificate:=.split node1678 node1721
private def node1723:Certificate:=.positive 1 [(1,1),(1,7)] node1722
private def node1724:Certificate:=.positive 1 [(3,5),(1,6)] node1723
private def node1725:Certificate:=.positive 2 [(1,0),(3,4),(1,5)] node1724
private def node1726:Certificate:=.positive 3 [(5,3),(1,6),(4,8)] node1725
private def node1727:Certificate:=.split node1651 node1726
private def node1728:Certificate:=.split node1570 node1727
private def node1729:Certificate:=.split node1463 node1728
private def data1764:List Nat:=[
  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,
  0x1141412120a0a09070d03080207020e00070001000a141412120a0a09070d03080207020e00070001000a141412120b0a0a0a09070d03080207020e0001000a061404030202020314141212140d0d0d1207]
private def node1764:Certificate:=PackedParametricCertificateData.decode 10 data1764
private def data1794:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  0x179d4028ff35d9701eadf17cc9833c8db39c2a01bf7c9006ed7b2d4e8ea9e80e7d1a698e588bb8cb8bc94a00596df05c68c02b79d069bd226f5b234dda524a2932becc40010c3adbbd9f0acc982e1d689c29fecb2a3e895b06095e368f0b2069fa260c9be30]
private def node1794:Certificate:=PackedParametricCertificateData.decode 10 data1794
private def node1795:Certificate:=.split node1764 node1794
private def node1796:Certificate:=.positive 1 [(1,1),(1,7)] node1795
private def data1836:List Nat:=[
  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,
  0x112120d0b120a090710040e040d030403120001000a12120d0b120a09070e040d0304030401120001000a12120d0b120a090710040e040d030403120001000a061404030202020312120d0d0b0a0e070907070703030d0101010b000a12120d0d0b0a0e070907070703030d0101010b000a12120d0d0b0a0e070907070703030d0101010b000a0608040616001c03120301141412120a0a09070d03080207020e00070001000a141412120a0a09070d03080207020e00070001000a1212140b0a0a0e0909070d03080207020e0001000a06140403020202031212]
private def node1836:Certificate:=PackedParametricCertificateData.decode 10 data1836
private def data1861:List Nat:=[
  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,
  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,
  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,
  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,
  0x10b0b020206a3e0aca089fe9fba95bbc4d1bce9ddbff2b6eef3a39f9ebc080602020293c2dab19abacfb5ecc4c2e5b1c39f89efcc98b2af9bb6e0060302020bd6a9ccc08dc3aea4f7a8d6c9b8f2b7a786d398edb58ce00b00020256f2eb95c2b2f1d3bcadca9494e0b698fff2b2f6dca6a7d9a0000002020e92a5fcf7c08398c9cfbafe90a1fdb1d8cfbec8e1948bf4d01313010207badba9dbd6e594b49d88dda7a18dd19db09fd690bbbf8ebe1212010203d0af96cbe79adacb9ba8aac4ea93c4e0d98ba78af7ebebe0130d0102028cdcc2aed4f1abe0e5f9d4dca8e28ea2a2adaac798a7edc40d0d010262c2d3b0f7c1fea1e992edb1a18586e7e1a0ebbce7c280fe140b010202f1d6d0d9e1a2d2f5afdb9afdb4ac84d6a7ffc59bbd90e9e00d06010218fbaead9dd2a7eea2efd99bb8d6a3d0a38c9789bcd288e3c60603010201a7f699f9b5fbdcc590b9a2cbacd58cca97ceda92c2bdbbfe0b00010251c6a2fd90b1bfe8c8c4dc9c8f8ae0b9ebcfc9c0f9db95bde00000010212c1dbedf5f2e8b5e6b6aeb8b9cc9af5c6d89bffdcf5b3cc821212000203c781e59df3a9e096e8dceacca2e4c589c8e9ead69d8494e8130d000205bbf1959099f6d3ce93daba80fcb4dfd08d99d7e7a6b8c4bc140b000202b2a9abac98ed98ddd397f7b6a1c4d4c299a5aed4ed88e5b40d0b0002038af8a4a6f3f284a680bcddbc85bde5d1,
  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,
  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,
  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]
private def node1861:Certificate:=PackedParametricCertificateData.decode 10 data1861
private def node1862:Certificate:=.split node1836 node1861
private def node1863:Certificate:=.positive 1 [(1,1),(1,7)] node1862
private def node1864:Certificate:=.split node1796 node1863
private def data1910:List Nat:=[
  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,
  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]
private def node1910:Certificate:=PackedParametricCertificateData.decode 10 data1910
private def data1928:List Nat:=[
  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,
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  0x101060002030804060602080002030a0433edd267aad121e7be13e48c0104b4cae8828a89808f838cf2bda0b3b8d0afd002829803edc902b7dd01e28b1ca79238ab8735e88413d8ab0002e6ea85d58ac9a58e8780d090ccdfc191f2efe806acd50bd1c40cd0830ef5e619909231efaf1fb9e333b1900001cdebc1f4cad1c5e087898e80c9c6838eaac3b8140d020209ecb3b69592fe9d9b9198e3df94f3b5a1d3adffbcacf8130d02023188dec4a4b9e18183b6c7b290b996b9e488acab8984eab80d0d020214b39d88adcaa7e8daf4ede0c6aada8bb9b7acb0c393ea900a0a02021295a6a5d48eaab3d3ecaa87b2afc1cd88cdf9a8fbc4edf81506020202f88dc1c8dba28590b5d5fe90f2c0eddd9af1a5b59490efe0100602020a90e383f8b8ea89f48ee8cbf2d1bbe2c98ebee7dddad0e00706020202d4ecb0f196d7879f9ae8d183e7e5a2d0c5e59da1b7fbdef80606020201d7d1adf7d3b6e3a6cec6caadb4d28ae8baf9d180ddfccac00900020271dae2adba98a6a98efbd7f8ec9be7b392e0d8fdc2ada1d8000002021cfdb795ccb6ada2ca9e93cb969f95e4ddcc90a989b7b0e80d0d01022dcc96f7e3949aeaffecadf8e3ddcfd6a081eccedde9a3e60a0a01020dc1f198a9d2ccb5cbf7e48f8cccf99d9e96c8b3dff6f28a1506010206d39fffbee4febbeab391c899d186bad69383ae8bd882d3e01206010201f296,
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,
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  0x1079ea0ee169495e313fb8dbb0bd8cce2018392d4da0299c8c5df03e1dac99002ebe9cccf00078fc299a181cec3c3caaeddf1b884d4cccdac8585d1d4f6b6e496e5e790d5bdf1fbecf4e8b6abd5f3e6dc96f881dccdef90fccda1efe88023e7aa13d5f7d230d6f28f16b989f101ff88b9ae03e9c28ad1319584910392e285bc0002d4829391b9a9a5baa9fc878bd48aeae9cfb8a9c59cfff7d2a2e2eddcb1e2bec589b68ec0aed783d598fb8df7b299bed2c0e5f9b795d8800299e5e2d503c8fbbb9206c0a5fad206ff]
private def node1928:Certificate:=PackedParametricCertificateData.decode 10 data1928
private def node1929:Certificate:=.split node1910 node1928
private def data1990:List Nat:=[
  0x10c0a08070714010a00090000000a061404030202020301120e0d0d120a0a0807070d030e020e000c0001000a120e0d0d120a0a0807070d030e020e000c0001000a120e0d0d120b0a08090707070d030e020e000c000a0614040302020203120e0d0d120c0a0807070d03140103010a0009000a120e140d0d0d120c0a0807070d0314010a0009000a120e140d0d0d120c0a08070714010a00090000000a0608040616001c031203010110120908061c041e041e0401120e0d0d120c0a08090707070d0303010a0009000a120e0d0d120c0a0807070d03140103010a0009000a120e0d0d120c0a0807070d03140103010a0009000a06060804020008030603060203040202030f02020202020310120908061c041e041e0410040002020603010e0402020206030d1c0a1206120102041e031414120a0d0a12090d08090707070803100003000a1414120a0d0a12090d08090707070803100003000a1414120c120a0d0a12090d0809070803100003000a06060804020008030603140403020202030f0202020202031414120c120a0d0a120912080d080c07100009120c120a0d0a120912080d080c071401100009120a0d0a120912080d080c0712031401100009060608040200080306030b0c030a01020006041203120400020206030110040002020603100402020202030e0402020206030d1c0a1206120102041e030101,
  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,
  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,
  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,
  0x101c2cc03a5d110d6a278efca0101dc9d81d0b4d4cea282bcba9a8fd89d93c7aad280a2c8fda001879602bac10ebbe106c9ff01fde004fbb158a3f818c09f000ffffcf5c391d0fab5b08fc891a0]
private def node1990:Certificate:=PackedParametricCertificateData.decode 11 data1990
private def node1991:Certificate:=.split node1929 node1990
private def node1992:Certificate:=.negative 1 [(1,0),(1,7)] node1991
private def node1993:Certificate:=.split node1864 node1992
private def data2057:List Nat:=[
  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,
  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,
  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,
  0x101ebcf01ebfc04c2ab04b78e03b2f903b2fa45c5f037f0c5006495fafaefd2909beab4898405c7cc05c7a148a68d47d2c0068dc5068dc64df7be13e8c80006e5bda7c7af8b9a9290dbd01313020201e9e9cab6afedacfba3eebcb8eb96c4b8150d020201eccff6fcef9f92b4e6a69e9ffbe9d6bd88130b020205c5fea5]
private def node2057:Certificate:=PackedParametricCertificateData.decode 12 data2057
private def node2058:Certificate:=.negative 1 [(1,0),(1,7)] node2057
private def node2059:Certificate:=.negative 1 [(1,0),(1,6)] node2058
private def node2060:Certificate:=.split node1993 node2059
private def node2061:Certificate:=.negative 1 [(1,0),(2,2)] node2060
private def node2062:Certificate:=.negative 1 [(1,1),(1,3)] node2061
private def node2063:Certificate:=.negative 1 [(1,0),(1,3)] node2062
private def node2064:Certificate:=.split node1729 node2063
private def data2128:List Nat:=[
  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,
  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]
private def node2128:Certificate:=PackedParametricCertificateData.decode 11 data2128
private def node2129:Certificate:=.positive 1 [(1,0),(2,12)] node2128
private def node2130:Certificate:=.positive 9 [(8,0),(3,4),(8,11)] node2129
private def node2131:Certificate:=.positive 4 [(1,0),(1,1),(6,9)] node2130
private def node2132:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2131
private def node2133:Certificate:=.positive 1 [(1,0),(2,2)] node2132
private def node2134:Certificate:=.positive 3 [(1,0),(2,6)] node2133
private def data2144:List Nat:=[
  0x114121410120d100d17090a0917081001170009141214101010120d17090a0917081008170009141214101010120d17090a0917081008170009060608040200080306030b06090203080004040c03120400020206030b060502020203100400020206030f08080607060212041a030e0402020206030f24080202060110041003090206020002030203]
private def node2144:Certificate:=PackedParametricCertificateData.decode 10 data2144
private def data2205:List Nat:=[
  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,
  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,
  0x114101210150d100d0a0a100709050705050000000a14101210150d100d0a0a10070905070505]
private def node2205:Certificate:=PackedParametricCertificateData.decode 10 data2205
private def node2206:Certificate:=.split node2144 node2205
private def node2207:Certificate:=.positive 1 [(1,0),(2,12)] node2206
private def node2208:Certificate:=.positive 3 [(2,0),(3,3),(2,11)] node2207
private def node2209:Certificate:=.positive 4 [(1,0),(1,1),(6,9)] node2208
private def node2210:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2209
private def node2211:Certificate:=.positive 1 [(1,0),(2,2)] node2210
private def data2234:List Nat:=[
  0x11412100e120d0a0907070e030d031001090000000a14121212100e120d07070e030d031001090000000a14121212100e120d07070e030d031001090000000a060608040200080306030b06090203080004040c03080206020202030e020b040402030204100400020206030f040c0608060306040a030e0402020206030802020601100006040a030a080907070712030e030503030117000a0007000a0d0d0a080907070712030e03080303010a0007000a0d0d0a080907070712030e03080303010a0007000a060608040200080306030b06090203080004040c03080206020202030f0e120d0f0d17090a091708170317000f00090f0e120d17090a09170817030f0317000f0009100e0f0e120d0a09170817030f0317000f0009060608040200080306030b06090203080004040c031204000202060301100400020206030f08080607060212041a030e0402020206030f2408020206011004100301]
private def node2234:Certificate:=PackedParametricCertificateData.decode 10 data2234
private def data2246:List Nat:=[
  0x10d0d0a08070712030e030503090103010a0007000a0d0d0a08070712030e030803090103010a0007000a0d0d0a08070712030e030803090103010a0007000a0606080402000803060313040b060906030e0412030d0d0a08070712030e030503090103010a0007000a0d0d0a08070712030e030803090103010a0007000a0d0d0a08070712030e030803090103010a0007000a060608040200080306030b06090203080004040c03010b060502020204100400020206030f08080607060212041a030e04010200020308030f0c0002020203]
private def node2246:Certificate:=PackedParametricCertificateData.decode 9 data2246
private def data2306:List Nat:=[
  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,
  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,
  0x1100e0f0e150d100d0f07090507051001050000000a100e0f0e150d100d0f07]
private def node2306:Certificate:=PackedParametricCertificateData.decode 9 data2306
private def node2307:Certificate:=.split node2246 node2306
private def node2308:Certificate:=.split node2234 node2307
private def node2309:Certificate:=.positive 1 [(1,0),(2,12)] node2308
private def node2310:Certificate:=.positive 1 [(1,2),(2,11)] node2309
private def node2311:Certificate:=.positive 2 [(1,0),(1,1),(2,10)] node2310
private def node2312:Certificate:=.positive 7 [(5,0),(4,6),(6,8)] node2311
private def data2335:List Nat:=[
  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]
private def node2335:Certificate:=PackedParametricCertificateData.decode 10 data2335
private def data2347:List Nat:=[
  0x10d0d0d090a080e07080707071203080309010e000a0e0e0d0d0d090a080e07080707071203080309010a0e0e0d0d0d090a080e07080707071203080309010a0606080402000803060313040b060906030e0412030e0e0d0d0d090a080e07080707071203080309010a0e0e0d0d0d090a080e07080707071203080309010a0e0e0d0d0d090a080e07080707071203080309010a060608040200080306030b06090203080004040c03010e0c0c0c0a120516041604100400020206030f04060c02120316030e0401020002030803060602060004030403]
private def node2347:Certificate:=PackedParametricCertificateData.decode 9 data2347
private def data2408:List Nat:=[
  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,
  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,
  0x112100d0d0b0a0a07080714010d010e00050000000a12100d0d0b0a0a07080714010d010e00050000000a12100d0d0b0a0a07080714010d010e00050000000a0614120909080814070d070a0703031200010000000a14120909080814070d070a0703031200010000000a14120909080814070d070a0703031200010000000a0601130405020202030b040406]
private def node2408:Certificate:=PackedParametricCertificateData.decode 9 data2408
private def node2409:Certificate:=.split node2347 node2408
private def node2410:Certificate:=.split node2335 node2409
private def node2411:Certificate:=.positive 1 [(2,0),(1,3)] node2410
private def data2440:List Nat:=[
  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]
private def node2440:Certificate:=PackedParametricCertificateData.decode 10 data2440
private def data2449:List Nat:=[
  0x10d0d0d090a080e07080707071203080309010e000a0d0d0d090a080b07080707071203080309010e000a0d0d0d090a080b07080707071203080309010e000a06140403020202030a0403040202030603080206020202040c0607060508030804100400020206030f04060c02120316030e0401020002030803060602060004030403]
private def node2449:Certificate:=PackedParametricCertificateData.decode 9 data2449
private def data2507:List Nat:=[
  0x106030b00070000000a120d0909120807071203090306030b00070000000a120d0909120807071203090306030b00070000000a060114120e0e0d0d0a0a07070d0101010800030000000a14120e0e0d0d0a0a07070d0101010800030000000a14120e0e0d0d0a0a07070d0101010800030000000a06120d100b09090b0707070906060301010b0000000a0e0e120d100b09090b070707060301010b0000000a120d100b0909070708040603030201010b0000000a060101080203060002030804100200020202040e0e120d0e0b0d0909090b07070712030d0100000a0e0e120d0e0b0d0909090b07070712030d0100000a0e0e120d0d0d0d0909090b07070712030d0100000a060602030200020302030f0402020202030802030600020308040c02020202020401010200040202040e0e120d0e0b0d0909090b07070712030d0100000a0e0e120d0e0b0d0909090b07070712030d0100000a0e0e120d0d0d0d0909090b07070712030d0100000a06140403020202030f0402020202030802060202020410060706050601020408040c020102020203120d0e0b0d0909090b0707070a0512030d0100000a120d0e0b0d0909090b0707070a0512030d0100000a0e0e120d0d0d0d0909090b07070712030d0100000a06140403020202030a0403040202030603080206020202040c060706050803080410040002020603010101,
  0x1000a12100d0d0c0a0a07080714010d010e00050000000a061412100b090914070d070a0703031200010000000a1412100b090914070d070a0703031200010000000a1412100b090914070d070a0703031200010000000a060113040502020203080404060112000a0422041002000202020412100d0d0908140710070a0703031200070001000a12100d0d0908140710070a0703031200070001000a12100d0d0908140710070a0703031200070001000a06140403020202030a040504020e030a030802030600020308040c040302010203040401141212100d0d10070a07080714051200070005000a141212100d0d10070a07080714051200070005000a12100d0d0a0910070a07080710051200070005000a06141004020206030a04030402020306030802030600020308040c0202020202041004000202060301141212100d0d10070a07080714051200070005000a141212100d0d10070a07080714051200070005000a12100d0d0a0910070a07080710051200070005000a06140c050400020306030a04030402020306030808050604060002040e040c0e0a060406030a04100410040002020603010200040202030115100d0d0d0c09090707120311030a00090000000a15100d0d0d0c09090707120311030a00090000000a15100d0d0d0c09090707120311030a00090000000a06120d09091208070712030903,
  0x112100d0d0c0a0a07080714010d010e00050000000a12100d0d0c0a0a07080714010d010e00050000]
private def node2507:Certificate:=PackedParametricCertificateData.decode 9 data2507
private def node2508:Certificate:=.split node2449 node2507
private def node2509:Certificate:=.split node2440 node2508
private def data2535:List Nat:=[
  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]
private def node2535:Certificate:=PackedParametricCertificateData.decode 10 data2535
private def data2544:List Nat:=[
  0x1120c0c0a12090a0909080a0708070707100009120c0c0a12090a0909080a0708070707100009120c12090a0909080a070807070710000a00090606060504000803060313040a0c030e031203080206020202040c0c0a0606060510041004100400020206030f04060c02120316030e04010200020308030f0c0002020203]
private def node2544:Certificate:=PackedParametricCertificateData.decode 9 data2544
private def data2602:List Nat:=[
  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,
  0x11514140c0a08080714010d01080005000000091514140c0a08080714010d01080005000000091514140c0a08080714010d010800050000000906140c0a081407080709030d010a000100000009140c0a081407080709030d010a000100000009140c0a081407080709030d010a00010000000906011304050202020307040406011a000e042e0410020002020204140c0a081407080709030d0112000a00070009140c0a081407080709030d0112000a00070009140c0a081407080709030d0112000a0007000906140403020202030a040504020e030a030706031202040008041e040c040302010203040401140c0a081407080709030d010a000700050009140c0a081407080709030d010a000700050009140c0a081407080709030d010a000700050009061410040202060313040a0c030e0312030802030600020308040c0202020202041004000202060301140c0a081407080709030d010a000700050009140c0a081407080709030d010a000700050009140c0a081407080709030d010a00070005000906140c0504000203060313040a0c030e0312030808050604060002040e040c0e0606040a03060410041004000202060301020004020203011510120c0c0a0a080e0707070c0309000000091510120c0c0a0a080e0707070c0309000000091510120c0c0a0a080e0707070c03]
private def node2602:Certificate:=PackedParametricCertificateData.decode 9 data2602
private def node2603:Certificate:=.split node2544 node2602
private def node2604:Certificate:=.split node2535 node2603
private def node2605:Certificate:=.split node2509 node2604
private def node2606:Certificate:=.split node2411 node2605
private def node2607:Certificate:=.positive 1 [(1,4),(2,9)] node2606
private def node2608:Certificate:=.positive 3 [(5,3),(1,6),(4,8)] node2607
private def node2609:Certificate:=.split node2312 node2608
private def node2610:Certificate:=.split node2211 node2609
private def node2611:Certificate:=.split node2134 node2610
private def data2671:List Nat:=[
  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,
  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,
  0x114121510120d0d0c070712030c]
private def node2671:Certificate:=PackedParametricCertificateData.decode 11 data2671
private def data2734:List Nat:=[
  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,
  0x10000091510120c0c0a0a080e0707070c030900000009060c0a12090a0807070c0309030a0007000000090c0a12090a0807070c0309030a0007000000090c0a12090a0807070c0309030a00070000000906010f0402020202040702030601040004040e04100200020202040c0201020202040b06020200020304040c0a12090a0807070c0309030a0007000000090c0a12090a0807070c0309030a0007000000090c0a12090a0807070c0309030a000700000009060b0205060202030f0402020202040f0201060002030804100200020202040c0a12090a080c0309030e000a0007000100090c0a12090a080c0309030e000a0007000100090c0a12090a080c0309030b000a0007000100090614040302020203140c120c0a0807070c0309030d010a00000009140c120c0a0807070c0309030d010a00000009140c120c0a0807070c0309030d010a0000000906060605040008030603010706060602040002040c04100c060605060108040e04010b060302020204010d0c09180002030a030e04080200020302040c0a0a08090707070c030e000a0009000100090c0a0a08090707070c030e000a0009000100090c0a0a08090707070c030e000b0009000100090614040302020203140c120c0a080e070907070708030a00000009140c120c0a080e070907070708030a00000009140c120c0a080e070907070708030a00,
  0x11510120c0c0a0a080e0707070c0309000000091510120c0c0a0a080e0707070c030900]
private def node2734:Certificate:=PackedParametricCertificateData.decode 11 data2734
private def node2735:Certificate:=.split node2671 node2734
private def node2736:Certificate:=.negative 1 [(3,5),(1,6)] node2735
private def data2800:List Nat:=[
  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,
  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,
  0x115141512150a12090a091208090309000000091514151212090a091208090309]
private def node2800:Certificate:=PackedParametricCertificateData.decode 13 data2800
private def node2801:Certificate:=.split node2736 node2800
private def node2802:Certificate:=.positive 8 [(5,4),(1,6),(24,8)] node2801
private def node2803:Certificate:=.negative 1 [(1,0),(2,2)] node2802
private def node2804:Certificate:=.negative 4 [(1,0),(3,1),(1,2)] node2803
private def node2805:Certificate:=.negative 1 [(1,0),(1,3)] node2804
private def node2806:Certificate:=.split node2611 node2805
private def node2807:Certificate:=.split node2064 node2806
private def node2808:Certificate:=.split node1393 node2807
private def node2809:Certificate:=.split node748 node2808
private def zz522:"s020a"="s020a":=by decide+kernel
private theorem valid109:check node109 ctx109 quad109 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid115:check node115 ctx115 quad115 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid109
private theorem valid368:check node368 ctx368 quad368 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid618:check node618 ctx618 quad618 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private def zz523:"s020b"="s020b":=by decide+kernel
private theorem valid744:check node744 ctx744 quad744 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid618
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid748:check node748 ctx748 quad748 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · exact valid115
      · apply NatParametricCheckSteps.split_valid
        · exact valid368
        · exact valid744
private theorem valid853:check node853 ctx853 quad853 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid858:check node858 ctx858 quad858 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid853
private def zz524:"s020c"="s020c":=by decide+kernel
private theorem valid941:check node941 ctx941 quad941 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1135:check node1135 ctx1135 quad1135 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1388:check node1388 ctx1388 quad1388 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1391:check node1391 ctx1391 quad1391 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid1135
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1388
private def zz525:"s020d"="s020d":=by decide+kernel
private theorem valid1393:check node1393 ctx1393 quad1393 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid858
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid941
    · exact valid1391
private theorem valid1463:check node1463 ctx1463 quad1463 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1566:check node1566 ctx1566 quad1566 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1570:check node1570 ctx1570 quad1570 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid1566
private def zz526:"s020e"="s020e":=by decide+kernel
private theorem valid1651:check node1651 ctx1651 quad1651 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1726:check node1726 ctx1726 quad1726 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1729:check node1729 ctx1729 quad1729 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1463
  · apply NatParametricCheckSteps.split_valid
    · exact valid1570
    · apply NatParametricCheckSteps.split_valid
      · exact valid1651
      · exact valid1726
private theorem valid1796:check node1796 ctx1796 quad1796 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private def zz527:"s020f"="s020f":=by decide+kernel
private theorem valid1864:check node1864 ctx1864 quad1864 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1796
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1993:check node1993 ctx1993 quad1993 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1864
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2063:check node2063 ctx2063 quad2063 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · exact valid1993
        · apply NatParametricCheckSteps.negative_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.negative_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2134:check node2134 ctx2134 quad2134 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private def zz528:"s0210"="s0210":=by decide+kernel
private theorem valid2211:check node2211 ctx2211 quad2211 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2311:check node2311 ctx2311 quad2311 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2509:check node2509 ctx2509 quad2509 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2605:check node2605 ctx2605 quad2605 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2509
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private def zz529:"s0211"="s0211":=by decide+kernel
private theorem valid2606:check node2606 ctx2606 quad2606 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid2605
private theorem valid2610:check node2610 ctx2610 quad2610 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2211
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2311
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2606
private theorem valid2803:check node2803 ctx2803 quad2803 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2806:check node2806 ctx2806 quad2806 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid2134
    · exact valid2610
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2803
private def zz530:"s0212"="s0212":=by decide+kernel
private theorem valid2808:check node2808 ctx2808 quad2808 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1393
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid1729
      · exact valid2063
    · exact valid2806
private theorem valid2809:check node2809 ctx2809 quad2809 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid748
  · exact valid2808
theorem certificate_valid:check node2809 constraintsNat base hinges = true:=valid2809
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node2809 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase2
private def zz2178:"s0882"="s0882":=by decide+kernel
end 
section 
namespace Green24Proof.QuadNearBalanceCase3
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x11bffdf5c3c49c, -0xaa87bee538000, -0xffcb9e57d4000,0xab14e5dd95c0], ![-0xaa87bee538000, -0x598a66949bfca4,0x13e83c05b2a3d0,0x55da62ee47472], ![-0xffcb9e57d4000,0x13e83c05b2a3d0, -0x460ff6eded75a8,0xadab046872d6a], ![0xab14e5dd95c0,0x55da62ee47472,0xadab046872d6a, -0x5543df729c000]], ![![-0x6f690f4db4c0,0,0x19945ca262000, -0x727f5ae944d0], ![0, -0x280966948cdd0, -0x30aa647ae830, -0x2ac0c9ef718], ![0x19945ca262000, -0x30aa647ae830, -0x282085272680,0xa082149c9a0], ![-0x727f5ae944d0, -0x2ac0c9ef718,0xa082149c9a0,0]], ![![-0x3abf21c93900,0xa7a358200,0xe0e1cc12130,0x162c0f166ce0], ![0xa7a358200,0xb87022d1740,0x28f7d1451a40, -0x2c129eccb7d0], ![0xe0e1cc12130,0x28f7d1451a40, -0x8862ab3bde40,0x222326abe800], ![0x162c0f166ce0, -0x2c129eccb7d0,0x222326abe800,0]]]
def hinges:Hinges:=[(![0,0, -0x34edce0], ![0,0,1, -3]),(![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0], ![0,0,1, -1]),(![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490], ![0,0,3, -1]),(![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0], ![0,1, -3,0]),(![0x83fc63,0x14904840,0x1e8480], ![0,1, -1,0]),(![0x5b61255b6c84,0, -0x4f5f5c3d2b0], ![0,1,0, -3]),(![0x1327fce0a51aaf,0, -0x1cb26590e0f0], ![0,1,0, -1]),(![-0x5543df729c000,0,0], ![0,3, -2, -1]),(![0x5543df729c000,0,0], ![0,3, -2,1]),(![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0], ![0,3, -1,0]),(![0x60154138c6bd, -0x1119ea5fc70,0], ![0,3,0, -1]),(![0x5543df729c000,0,0], ![0,3,2, -1]),(![-0x1b7e5fd92756,0x1b78ccf2f520,0], ![1, -3,0,0]),(![-0x5543df729c000,0,0], ![1, -2, -3,0]),(![0x5543df729c000,0,0], ![1, -2,3,0]),(![0x1b7e5fd92756, -0x1b78ccf2f520,0], ![1, -1,0,0]),(![-0x5653d9dc04a5,0,0], ![1,0, -3,0]),(![-0x131136072162ed,0,0x249d8ce84e20], ![1,0, -1,0]),(![0, -0xf10e91ec040,0], ![1,0,0, -3]),(![-0x72c9ab9f580,0x7e79f86c7500,0x162194e0eae0], ![1,0,0, -1]),(![0x5543df729c000,0,0], ![1,2, -3,0]),(![-0x61e2cbeeb816,0,0], ![3,0, -1,0]),(![-0x5d6b26ca1a4,0,0], ![3,0,0, -1])]
def normalizationDenominator:ℤ:=0xaa87bee538000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx3774:Nat → Linear:=constraintsNat
private def quad3774:Quadratic:=base
private def ctx956:Nat → Linear:=cons ![0,0,3, -1] (cons ![0,0,1, -1] (cons ![0,0,1, -3] ctx3774))
private def quad956:Quadratic:=((quad3774 + coefficientProduct ![0,0, -0x34edce0] ![0,0,1, -3] ![0,0,1, -3]) + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]
private def ctx79:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -1,0] (cons ![0,1, -3,0] ctx956)))))
private def quad79:Quadratic:=(((((quad956 + coefficientProduct ![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx955:Nat → Linear:=cons (-![0,1, -3,0]) ctx956
private def quad955:Quadratic:=quad956
private def ctx202:Nat → Linear:=cons ![0,1, -1,0] ctx955
private def quad202:Quadratic:=quad955 + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]
private def ctx197:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] ctx202))))
private def quad197:Quadratic:=((((quad202 + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx277:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons (-![0,1, -1,0]) ctx955)))
private def quad277:Quadratic:=(((quad955) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx502:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons (-![0,1, -1,0]) ctx955)))
private def quad502:Quadratic:=(((quad955) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx501:Nat → Linear:=cons (-![0,3, -2,1]) ctx502
private def quad501:Quadratic:=quad502
private def ctx427:Nat → Linear:=cons ![0,3, -1,0] ctx501
private def quad427:Quadratic:=quad501 + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx953:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -1,0]) ctx955)
private def quad953:Quadratic:=(quad955)
private def ctx577:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx953)
private def quad577:Quadratic:=(quad953 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx800:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] ctx953)
private def quad800:Quadratic:=(quad953 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx799:Nat → Linear:=cons (-![0,3, -2,1]) ctx800
private def quad799:Quadratic:=quad800
private def ctx723:Nat → Linear:=cons ![0,3, -1,0] ctx799
private def quad723:Quadratic:=quad799 + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx951:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx953)
private def quad951:Quadratic:=(quad953)
private def ctx875:Nat → Linear:=cons ![0,3,0, -1] (cons (-![0,3, -1,0]) (cons (-![0,3, -2,1]) ctx951))
private def quad875:Quadratic:=((quad951)) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx3773:Nat → Linear:=cons (-![0,0,1, -3]) ctx3774
private def quad3773:Quadratic:=quad3774
private def ctx1790:Nat → Linear:=cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx3773)
private def quad1790:Quadratic:=(quad3773 + coefficientProduct ![-0x191a2c19d6b5, -0x50410a4e4d0, -0x110c4aa72df0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]
private def ctx1038:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -1,0] (cons ![0,1, -3,0] ctx1790)))
private def quad1038:Quadratic:=(((quad1790 + coefficientProduct ![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1253:Nat → Linear:=cons ![0,1, -1,0] (cons (-![0,1, -3,0]) ctx1790)
private def quad1253:Quadratic:=(quad1790) + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]
private def ctx1149:Nat → Linear:=cons ![0,1,0, -3] ctx1253
private def quad1149:Quadratic:=quad1253 + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx1145:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1149)))
private def quad1145:Quadratic:=(((quad1149 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx1248:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1253))))
private def quad1248:Quadratic:=((((quad1253) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx1788:Nat → Linear:=cons (-![0,1, -1,0]) (cons (-![0,1, -3,0]) ctx1790)
private def quad1788:Quadratic:=(quad1790)
private def ctx1329:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1788))
private def quad1329:Quadratic:=((quad1788) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1480:Nat → Linear:=cons (-![0,3, -2, -1]) (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1788))
private def quad1480:Quadratic:=((quad1788) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1])
private def ctx1407:Nat → Linear:=cons ![0,3, -2,1] ctx1480
private def quad1407:Quadratic:=quad1480 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx1785:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1788))
private def quad1785:Quadratic:=((quad1788))
private def ctx1784:Nat → Linear:=cons (-![0,3, -2,1]) ctx1785
private def quad1784:Quadratic:=quad1785
private def ctx1783:Nat → Linear:=cons (-![0,3, -1,0]) ctx1784
private def quad1783:Quadratic:=quad1784
private def ctx1706:Nat → Linear:=cons ![0,3,0, -1] ctx1783
private def quad1706:Quadratic:=quad1783 + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx1960:Nat → Linear:=cons ![0,1, -3,0] (cons ![0,0,3, -1] (cons (-![0,0,1, -1]) ctx3773))
private def quad1960:Quadratic:=((quad3773) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1]) + coefficientProduct ![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0] ![0,1, -3,0] ![0,1, -3,0]
private def ctx1871:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -1,0] ctx1960))
private def quad1871:Quadratic:=((quad1960 + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1955:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] (cons (-![0,1,0, -3]) (cons ![0,1, -1,0] ctx1960))))
private def quad1955:Quadratic:=((((quad1960 + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0])) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2656:Nat → Linear:=cons (-![0,1, -3,0]) (cons ![0,0,3, -1] (cons (-![0,0,1, -1]) ctx3773))
private def quad2656:Quadratic:=((quad3773) + coefficientProduct ![0x191a2c19d6b5,0x50410a4e4d0,0x110c5493c490] ![0,0,3, -1] ![0,0,3, -1])
private def ctx2250:Nat → Linear:=cons (-![0,1,0, -3]) (cons ![0,1, -1,0] ctx2656)
private def quad2250:Quadratic:=(quad2656 + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0])
private def ctx2056:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx2250)))
private def quad2056:Quadratic:=(((quad2250 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2158:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) ctx2250)
private def quad2158:Quadratic:=(quad2250) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx2248:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx2250)
private def quad2248:Quadratic:=(quad2250)
private def ctx2652:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -1,0]) ctx2656)))
private def quad2652:Quadratic:=(((quad2656)))
private def ctx2571:Nat → Linear:=cons ![0,3, -2,1] ctx2652
private def quad2571:Quadratic:=quad2652 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2332:Nat → Linear:=cons ![0,3,0, -1] (cons ![0,3, -1,0] ctx2571)
private def quad2332:Quadratic:=(quad2571 + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]) + coefficientProduct ![0x60154138c6bd, -0x1119ea5fc70,0] ![0,3,0, -1] ![0,3,0, -1]
private def ctx2570:Nat → Linear:=cons (-![0,3, -1,0]) ctx2571
private def quad2570:Quadratic:=quad2571
private def ctx3771:Nat → Linear:=cons (-![0,0,3, -1]) (cons (-![0,0,1, -1]) ctx3773)
private def quad3771:Quadratic:=(quad3773)
private def ctx2738:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons ![0,1, -1,0] (cons ![0,1, -3,0] ctx3771)))
private def quad2738:Quadratic:=(((quad3771 + coefficientProduct ![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]) + coefficientProduct ![0x5b61255b6c84,0, -0x4f5f5c3d2b0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx3159:Nat → Linear:=cons (-![0,1,0, -3]) (cons ![0,1, -1,0] (cons ![0,1, -3,0] ctx3771))
private def quad3159:Quadratic:=((quad3771 + coefficientProduct ![0x4577d1e0e27b,0x2c0f7d034d60,0x1621b29f0da0] ![0,1, -3,0] ![0,1, -3,0]) + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0])
private def ctx2828:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx3159))
private def quad2828:Quadratic:=((quad3159 + coefficientProduct ![0x1327fce0a51aaf,0, -0x1cb26590e0f0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2917:Nat → Linear:=cons ![0,3, -2,1] (cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) ctx3159))
private def quad2917:Quadratic:=((quad3159) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx3157:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) ctx3159)
private def quad3157:Quadratic:=(quad3159)
private def ctx3154:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx3157))
private def quad3154:Quadratic:=((quad3157 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0])
private def ctx3770:Nat → Linear:=cons (-![0,1, -3,0]) ctx3771
private def quad3770:Quadratic:=quad3771
private def ctx3528:Nat → Linear:=cons ![0,1, -1,0] ctx3770
private def quad3528:Quadratic:=quad3770 + coefficientProduct ![0x83fc63,0x14904840,0x1e8480] ![0,1, -1,0] ![0,1, -1,0]
private def ctx3247:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx3528))
private def quad3247:Quadratic:=((quad3528)) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx3525:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx3528))
private def quad3525:Quadratic:=((quad3528))
private def ctx3522:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx3525))
private def quad3522:Quadratic:=((quad3525 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0])
private def ctx3766:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -1,0]) ctx3770)))
private def quad3766:Quadratic:=(((quad3770)))
private def ctx3684:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx3766)
private def quad3684:Quadratic:=(quad3766 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x527b1f8b7602,0x43597dba1f20, -0x9f437c0] ![0,3, -1,0] ![0,3, -1,0]
private def data10:List Nat:=[
  0x116111111160b140a14090b0914041a011400091611160b140a14090b0914041a011400081611160b140a14090b0914041a01140008060a08070c03120034043e03152c080400060312030c020b0a030a00080412031304000202060311020002020203110400020206031008080607060212041a030f04020202060311060e020b06010404060309020002020203]
private def node10:Certificate:=PackedParametricCertificateData.decode 11 data10
private def data20:List Nat:=[
  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,
  0x101d5bb129bf90b87a304c4e209b6984beddb0b9fce04ccef000197eae2ebc7a2f4e5a9d7dec6b0029ffe04a2f46ea5e432df8f0ed50af9856ea1ff32dddc000ae5cda8cbefa0e0c1afb69f941616020201e0c0ead08388fdf997d8ec8fd4f1aad4c180160a02020287dddcb7b7ff81dcd5e288e789d9d08ad0130a020208a29a85f3e2ebc9abeed4fb96b2dbc9c01a09020209fed8fcf2b4faf39f8cec85ceb0dac8e49da21409020207a6f7c7a6e487e5b58a8ec7aeace28adb97c20a0902020ea1f1f4a4a2b7d495a6f2f8a8dcac9f801a08020257d7e593e2f2e094a6c68592eec384c5e0961408020203b8a5dea1abf7a1e7edb9e4c88af4bae6dd9e080802020f8cedb8f486a8dadab6b4ebbdeedfefc01a0102027fafe78c]
private def node20:Certificate:=PackedParametricCertificateData.decode 10 data20
private def data74:List Nat:=[
  0x1d1d09fd1a4edb49c9cb6a4b4cef7a1c6ddab8cf5c5adc4b8e3d2edbfc888c3841607010201d0ceedc08587f2f3ba9ca9a395af859ce1fa87c89bd7c9b091e4d9df969ea8d8e4a99c8793cdbfdeab8e9c080701023a88dc9780dcd2d7b4f8e8c8d281e8f5fc8bd4cad69da3a7d98ffdb9f4a693acb091d3a6bbfebce29db6a8070701020dd4eb99dbededecaca0fabb8ec6f583cbed9fa6fe8eeefa93b8d598a5dabef6f4defcbadda0f7d9b4c5c61a1a000203cadca496e4f1eddcf89db1adb29cf6d1b99f90d5d492fc8ed6a3c190f7bbf48bc8ab89f8fcf9e2e6abfbc0161600020bb0a29098ee8a86d7cbbae9b1a0dbf2b2b6cfc7bbe0affdca88eb89b5c68f85fce8deecb9b5fad7e0801a130002219081b5fe8ebdd39bfd8da7b2aeabf5f79dc0b1bcb4a2c2aa9ed3c2feb4a6d9c6f3b79e8489aa9da1d180131300022ef8daeabfbda6be9cb4f2fdc9dda1aeb9aa9eb4ad818a8af4ecc8dfe9e5e1928688debec2a3c4c9c016080002168ad5f4e8929ebebb9086a18da4909dd9a8f08982baedada8ede2e2f390e8b7ebf1eeb2befca8c6e0801e1babe2d6e2a494b4eb91f5a5d0effff196c8e7a69da8f7edd1d1a3babff6b5d8fb8cdfd880000a08070c03120034043e03150c050400020306030c020b0a030a00080412031304000202060311020002020203110400020206030c0200020202030b02000202020301,
  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,
  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,
  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,
  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,
  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,
  0x116161411170f140f170e140a0e04060101010916161411140f170e140a0e041401060101010916161411140f170e140a0e041601060101010906161614110f060a060e04160106010101020009161614110f060a060e04140106010101020009161614110f060a060e04160106010101020009060114020106020204141c10140c060b06041c03161614110f060a060e04160106010101020009161614110f060a060e04140106010101020009161614110f060a060e041601060101010200]
private def node74:Certificate:=PackedParametricCertificateData.decode 10 data74
private def node75:Certificate:=.split node20 node74
private def node76:Certificate:=.split node10 node75
private def node77:Certificate:=.positive 2 [(1,0),(1,2),(2,8)] node76
private def node78:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node77
private def node79:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node78
private def node80:Certificate:=.positive 1 [(1,0),(2,11)] node79
private def node81:Certificate:=.positive 3 [(1,1),(6,2),(2,8)] node80
private def node82:Certificate:=.positive 3 [(1,0),(2,7)] node81
private def node83:Certificate:=.positive 3 [(1,1),(3,4),(2,6)] node82
private def node84:Certificate:=.positive 3 [(1,0),(2,5)] node83
private def data105:List Nat:=[
  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]
private def node105:Certificate:=PackedParametricCertificateData.decode 11 data105
private def data163:List Nat:=[
  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,
  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,
  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,
  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,
  0x1090b0911020f020f010a0100000a161614110b0b0b0911020f020f010a01010100000a161614110b0b0b0911020f020f010a01010100000a06161614110b0b0f090b0911020f020a01010108000a161614110b0b0f090b0911020f020a01010108000a161614110b0b0f090b0911020f020a01010108000a060114020106020204161616140e0e110b1609090908080202090101010a161616140e0e110b1609090908080202090101010a161616140e0e110b1609090908080202090101010a06161616140e0e110b1609090908080202090101010a161616140e0e110b1609090908080202090101010a161616140e0e110b1609090908080202090101010a06011402010602020401161614110b0b0b090a090f020a010101080000000a161614110b0b0f090b090a090f020a01010108000a161614110b0b0f090b0911020f020a01010108000a06160402020202031616160b0a0a0a070e0404040f020b02080101010a1616160b0a0a0a070e0404040f020b02080101010a1616160b0a0a0a070e0404040f020b02080101010a0615021302000803080301161616140e0e110b0909080802020901010100000a161616140e0e110b1609090908080202090101010a161616140e0e110b1609090908080202090101010a060702020201020302031616161408080a07070709050e040404020201010a1616161408080a,
  0x116161614141111]
private def node163:Certificate:=PackedParametricCertificateData.decode 9 data163
private def data192:List Nat:=[
  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,
  0x11616141113110b0b0b090a0913081106060101010a1616141113110b0b0b090a0913081106060101010a1616141113110b0b0b090a09130811060601]
private def node192:Certificate:=PackedParametricCertificateData.decode 9 data192
private def node193:Certificate:=.split node163 node192
private def node194:Certificate:=.negative 1 [(1,0),(1,9)] node193
private def node195:Certificate:=.split node105 node194
private def node196:Certificate:=.positive 8 [(9,0),(1,2),(6,7)] node195
private def node197:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node196
private def node198:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node197
private def node199:Certificate:=.positive 1 [(1,0),(2,11)] node198
private def node200:Certificate:=.positive 1 [(1,0),(2,2)] node199
private def node201:Certificate:=.positive 3 [(1,0),(2,7)] node200
private def node202:Certificate:=.positive 1 [(1,0),(1,4)] node201
private def data230:List Nat:=[
  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]
private def node230:Certificate:=PackedParametricCertificateData.decode 11 data230
private def data272:List Nat:=[
  0x10101010a06150213020008030803010f04020202020401161614110b0b0b090a0908040f020a01010108000a161614110f090b09080411020f020a01010108000a161614110b0b0f090b0911020f020a01010108000a06160402020202031616160b0a0a0a0708040f020b020801010104000a1616160b0a0a11090a0708040f020b02080101010a1616160b0a0a11090a0708040f020b02080101010a060a08070c03120034043e03010f04020202020413040002020603010c0201020202040c0200020202041616160b0a0a110908040f020b020801070102000a1616160b0a0a110908040f020b020801070102000a1616160b0a0a110908040f020b020801070102000a060a08070c03120034043e03150c0d020c02050c0408030f040202020204130400020206030c0202020202031616110b0a0a080404040f0208010701020102000a1616110b0a0a080404040f0208010701020102000a1616110b0a0a110908040f0208010701020102000a060a08070c03120034043e031504030202020316161614160b0a0a1609120808080606070112000a161616140a0a16091208080816060606070112000a161616140a0a16091208080816060606070112000a060a08070c03120034043e03150c05040002030603011304000202060311020002020203010b060302020204010e040a02090603040309020002020204,
  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]
private def node272:Certificate:=PackedParametricCertificateData.decode 11 data272
private def node273:Certificate:=.split node230 node272
private def node274:Certificate:=.positive 8 [(9,0),(1,2),(6,7)] node273
private def node275:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node274
private def node276:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node275
private def node277:Certificate:=.positive 1 [(1,0),(2,11)] node276
private def data305:List Nat:=[
  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]
private def node305:Certificate:=PackedParametricCertificateData.decode 11 data305
private def data347:List Nat:=[
  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,
  0x1161611110e0e110b0a0a0f080808110101010a000a16161111110b0a0a0f08080811010a0101010a000a16161111110b0a0a0f08080811010a0101010a000a06161611110f0f110b0a0a0f0808080a01010108000a161611110f0f110b0a0a0f0808080a01010108000a161611110f0f110b0a0a0f0808080a01010108000a06011402010602020413040c0c0304020e041204161611110f0f110b0a0a0f0808080a01010108000a161611110f0f110b0a0a0f0808080a01010108000a16161111110b0a0a0f08080811010a01010108000a061604020202020316161111160b110b0a0a0f080404090201010f000a16161111110b0a0a0f0809050404090201010f000a16161111110b0a0a0f0809070404090201010f000a061502130200080308030113040c0c0304020e041204]
private def node347:Certificate:=PackedParametricCertificateData.decode 11 data347
private def node348:Certificate:=.split node305 node347
private def node349:Certificate:=.positive 8 [(9,0),(1,2),(6,7)] node348
private def node350:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node349
private def node351:Certificate:=.positive 14 [(13,0),(3,3),(4,6)] node350
private def data382:List Nat:=[
  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]
private def node382:Certificate:=PackedParametricCertificateData.decode 11 data382
private def data424:List Nat:=[
  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,
  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]
private def node424:Certificate:=PackedParametricCertificateData.decode 11 data424
private def node425:Certificate:=.split node382 node424
private def node426:Certificate:=.positive 4 [(4,0),(1,1),(3,7)] node425
private def node427:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node426
private def data466:List Nat:=[
  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,
  0x11111160c1a080c061a020c020c0108000000091111160c0c091a081a020c020c0108000000091111160c0c091a080c061a020c0100000806161003020206031111160c0e0c0f0909091a080e010a01080101000a1111160c140c09091a080c020e010a]
private def node466:Certificate:=PackedParametricCertificateData.decode 11 data466
private def data497:List Nat:=[
  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,
  0x11111160c140c160a170808040c]
private def node497:Certificate:=PackedParametricCertificateData.decode 11 data497
private def node498:Certificate:=.split node466 node497
private def node499:Certificate:=.positive 9 [(11,0),(6,7),(2,14)] node498
private def node500:Certificate:=.positive 3 [(1,4),(8,11)] node499
private def node501:Certificate:=.split node427 node500
private def node502:Certificate:=.split node351 node501
private def node503:Certificate:=.split node277 node502
private def node504:Certificate:=.positive 3 [(1,0),(2,7)] node503
private def data532:List Nat:=[
  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]
private def node532:Certificate:=PackedParametricCertificateData.decode 11 data532
private def data572:List Nat:=[
  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,
  0x1161616140b0b0f090e040f020f010a01010100000a161616140b0b0f090e040f020f010a01010100000a161616140b0b0f090e040f020f010a01010100000a06161616140b0b0f090e040f020a010101080000000a161616140b0b0f090b090e040f020a01010108000a161616140b0b0f090b090e040f020a01010108000a0601140201060202040f040202020204161616140b0b0f090e040f020a010101080000000a161616140b0b0f090e040f020a010101080000000a161616140b0b0f090b090e040f020a01010108000a0616040202020203]
private def node572:Certificate:=PackedParametricCertificateData.decode 11 data572
private def node573:Certificate:=.split node532 node572
private def node574:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node573
private def node575:Certificate:=.positive 4 [(4,0),(1,7),(1,9)] node574
private def node576:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node575
private def node577:Certificate:=.positive 11 [(14,0),(9,2),(2,5)] node576
private def data608:List Nat:=[
  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]
private def node608:Certificate:=PackedParametricCertificateData.decode 11 data608
private def data648:List Nat:=[
  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,
  0x111110f0f0e0a0a0a1609080816010e000a0000000a11110f0f0e0a0a0a16090808160101010a0000000a11110f0f0e0a0a0a16090808160101010a0000000a0616160f0f0e0e160b0a0a160908080a01010108000a16160f0f0e0e160b0a0a160908080a01010108000a16160f0f0e0e160b0a0a160908080a01010108000a06011402010602020413040c0c0304020e04120416160f0f0e0e160b0a0a160908080a01010108000a16160f0f0e0e160b0a0a160908080a01010108000a16160f0f0e0e160b0a0a160908080a01010108000a061604020202020316160f0f0e0e160b0a0a0f080a0704040f0101010a16160f0f0e]
private def node648:Certificate:=PackedParametricCertificateData.decode 11 data648
private def node649:Certificate:=.split node608 node648
private def node650:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node649
private def node651:Certificate:=.positive 4 [(4,0),(1,7),(1,9)] node650
private def node652:Certificate:=.positive 4 [(4,0),(1,6),(1,8)] node651
private def data683:List Nat:=[
  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]
private def node683:Certificate:=PackedParametricCertificateData.decode 11 data683
private def data720:List Nat:=[
  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,
  0x11111110f0e0d160c140b0b0b160a0d010a0100000a1111110f0e0d160c140b0b0b160a0d010a0100000a1111110f0e0d160c140b0b0b160a0d010a0100000a061111110f0e0d160c0b0b160a0d020a01080000000a1111110f0e0d160c0b0b160a0d020a01080000000a1111110f0e0d160c0b0b160a0d020a01080000000a0601140201060202040c020b0a030a00080412041111110f0e0d160c0b0b16]
private def node720:Certificate:=PackedParametricCertificateData.decode 11 data720
private def node721:Certificate:=.split node683 node720
private def node722:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node721
private def node723:Certificate:=.positive 4 [(4,0),(1,7),(1,9)] node722
private def data762:List Nat:=[
  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,
  0x1110f110e160c11080c060c020c010800000009110f110e160c0c0911080c020c010800000009110f110e160c11080c060c020c010000080616100302020603110f110e160c0e0c090911080c020a01080101000a110f110e160c140c090911080c]
private def node762:Certificate:=PackedParametricCertificateData.decode 11 data762
private def data795:List Nat:=[
  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,
  0x1160c160a0c09170811080c020c010a01000009160c160a170811080c060c020c010a01000009160c160a170811080c060c020c010a01000009061111110f160c140c160a0a020a010800000009111111]
private def node795:Certificate:=PackedParametricCertificateData.decode 11 data795
private def node796:Certificate:=.split node762 node795
private def node797:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node796
private def node798:Certificate:=.positive 1 [(1,3),(2,11)] node797
private def node799:Certificate:=.split node723 node798
private def node800:Certificate:=.split node652 node799
private def node801:Certificate:=.split node577 node800
private def data847:List Nat:=[
  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,
  0x1110e160c0e0c0e040c0204020c010800000009160c0e0c0e040c0204020c010e000800000009110f160c0e0c0e040c0204020c0108000000090616040202020203160c0e0c160b140b0e040c020e010a01080100000a160c0e0c160b140b0e040c020a010801010000000a160c0e0c160b140b0e040c020a010801010101000a06150213020008030803010a040304020203060408020602020203110e160c0e0c110a11080c020c010800000009110e160c0e0c110a11080c020c010800000009110e160c0e0c110a11080c020c010000080616100302020603110e160c0e0c140b110a0c020a010801010101000a110e160c0e0c14]
private def node847:Certificate:=PackedParametricCertificateData.decode 11 data847
private def data873:List Nat:=[
  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]
private def node873:Certificate:=PackedParametricCertificateData.decode 11 data873
private def node874:Certificate:=.split node847 node873
private def node875:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node874
private def data926:List Nat:=[
  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,
  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]
private def node926:Certificate:=PackedParametricCertificateData.decode 11 data926
private def data946:List Nat:=[
  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]
private def node946:Certificate:=PackedParametricCertificateData.decode 11 data946
private def node947:Certificate:=.split node926 node946
private def node948:Certificate:=.positive 8 [(5,8),(1,10),(24,12)] node947
private def node949:Certificate:=.split node875 node948
private def node950:Certificate:=.negative 1 [(3,2),(1,8)] node949
private def node951:Certificate:=.negative 2 [(1,0),(3,1),(2,7)] node950
private def node952:Certificate:=.negative 1 [(1,0),(2,2)] node951
private def node953:Certificate:=.split node801 node952
private def node954:Certificate:=.split node504 node953
private def node955:Certificate:=.split node202 node954
private def node956:Certificate:=.split node84 node955
private def node957:Certificate:=.positive 3 [(1,1),(8,4)] node956
private def node958:Certificate:=.positive 3 [(1,0),(2,3)] node957
private def data969:List Nat:=[
  0x116161111160a140a0b0a16091409160114000916161111160a140a0b0a16091409160114000916161111160a140a0b0a160914091601140009060a08070c03120034043e03152c080400060312030c020b0a030a0008041203130400020206030c0a050203020006040a03110400020206031008080607060212041a030f0402020206030e100d120b36012004300309020002020203]
private def node969:Certificate:=PackedParametricCertificateData.decode 11 data969
private def data1032:List Nat:=[
  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,
  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,
  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,
  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,
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,
  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]
private def node1032:Certificate:=PackedParametricCertificateData.decode 11 data1032
private def node1033:Certificate:=.split node969 node1032
private def node1034:Certificate:=.positive 4 [(4,0),(3,8),(1,10)] node1033
private def node1035:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node1034
private def node1036:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1035
private def node1037:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1036
private def node1038:Certificate:=.positive 3 [(1,1),(6,2),(2,8)] node1037
private def node1039:Certificate:=.positive 3 [(1,0),(2,7)] node1038
private def node1040:Certificate:=.positive 1 [(1,1),(3,3)] node1039
private def node1041:Certificate:=.positive 3 [(1,0),(2,5)] node1040
private def data1062:List Nat:=[
  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]
private def node1062:Certificate:=PackedParametricCertificateData.decode 11 data1062
private def data1113:List Nat:=[
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,
  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,
  0x116161411140b11090b0911020f020f010a0100000a161614110b0b0b0911020f020f010a01010100000a161614]
private def node1113:Certificate:=PackedParametricCertificateData.decode 9 data1113
private def data1140:List Nat:=[
  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,
  0x116161411160e0b]
private def node1140:Certificate:=PackedParametricCertificateData.decode 9 data1140
private def node1141:Certificate:=.split node1113 node1140
private def node1142:Certificate:=.negative 1 [(1,0),(1,9)] node1141
private def node1143:Certificate:=.split node1062 node1142
private def node1144:Certificate:=.positive 13 [(16,0),(9,7),(1,10)] node1143
private def node1145:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node1144
private def node1146:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1145
private def node1147:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1146
private def node1148:Certificate:=.positive 3 [(1,1),(6,2),(2,8)] node1147
private def node1149:Certificate:=.positive 3 [(1,0),(2,7)] node1148
private def data1170:List Nat:=[
  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]
private def node1170:Certificate:=PackedParametricCertificateData.decode 11 data1170
private def data1221:List Nat:=[
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,
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]
private def node1221:Certificate:=PackedParametricCertificateData.decode 9 data1221
private def data1243:List Nat:=[
  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]
private def node1243:Certificate:=PackedParametricCertificateData.decode 9 data1243
private def node1244:Certificate:=.split node1221 node1243
private def node1245:Certificate:=.negative 1 [(1,0),(1,9)] node1244
private def node1246:Certificate:=.split node1170 node1245
private def node1247:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1246
private def node1248:Certificate:=.positive 2 [(1,0),(1,2),(1,7)] node1247
private def node1249:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1248
private def node1250:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1249
private def node1251:Certificate:=.positive 1 [(1,0),(2,2)] node1250
private def node1252:Certificate:=.positive 1 [(1,1),(1,4)] node1251
private def node1253:Certificate:=.split node1149 node1252
private def data1281:List Nat:=[
  0x1161614140e0e0a0a0a08080814040b0409040a010a161614140e0e0a0a0a08080814040b0409040a010a161614140e0e0a0a0a0808081404090406040a010a060a08070c03120034043e03152c080400060312030c040b04070402020406031304000202060310040a0205020302030902080204020106040803161614140e0e0a0a0a080808160614040b040a010a161614140e0e0a0a0a080808160614040b040a010a161614140e0e0a0a0a080808160614040b040a010a060a08070c03120034043e03152c080400060312030c020b0a030a00080412031304000202060310040a02050203020311040002020603010f0402020206030e040a06010203060316160e0e130a13090b0914040b04110113000916160e0e130a13090b0914040b04110113000916160e0e130a13090b0914040b041101130009060a08070c03120034043e03152c080400060312030c020b0a030a00080412031304000202060310040a020502030203110400020206031008080607060212041a030f0402020206030e040a06010203060301]
private def node1281:Certificate:=PackedParametricCertificateData.decode 11 data1281
private def data1324:List Nat:=[
  0x1e888898db7cbbeeca1fefba4080402021ac2a7a3c9cfa39b8cc2a2aa9dbdb21101020209d6c39bf8ccdbf6ddec9b82cedfaa0701020204fbdc8cdfcecddf9ab8d997bfa8ee1200020233a9ead1bea78894abc2c0c5af9ecc1616010216cefccebec1be87a8cbecc2d9eed00f0f010218fa99e191f9e4efaee0ecaf99a2900a0a010202adf6869995ca82b2ad90b7f6e8a80707010203e4fde38ac69b96dad2fde5f0bcc80606010215989aeedbcfc5a7ebf7fea5a48cd8090401020b96caa3e5adbf83d0f6b2bbd494a8080401021899c1a1adb6fda295a4f2d1d1f1e0160201020abdb5aeeba6c9abf59cadf8cfbd980701010208f4cbd3bd85e081a184f89db9b5b0120001023ca7979d8fc69dfe80cac8fdb1d2801616000216deac96cbc2f598edbee3ae86afb00f0f00021790fc8be8d2a0ebe1de9baed689f00a0a00027be6a0abf2c5f8ef80c4b789e1f00707000221d687dbd4defabaeb97888199aae00606000215a4b9fa8bbed697f6ead796e29bc0090400020b97eebe94fbddbaf5c8faaed5eea00804000216d2bafc87bd9b88adf78effa5cba0160200020bd9d1fc9e96d8dbfbf0fd8183f080120000023599f3b9c89e83ff8982fe9ddaeba01e198daaf2f4d8e5b0000a08070c03120034043e03150c05040002030603011304000202060301010b060302020204010e040a02090603040309020002020204,
  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,
  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,
  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,
  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,
  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,
  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]
private def node1324:Certificate:=PackedParametricCertificateData.decode 11 data1324
private def node1325:Certificate:=.split node1281 node1324
private def node1326:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1325
private def node1327:Certificate:=.positive 2 [(1,0),(1,2),(1,7)] node1326
private def node1328:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1327
private def node1329:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1328
private def data1360:List Nat:=[
  0x111110f0a0a0a0a0808080b040f010201080002000a11110f0a0a0a0a0808080b040f010201080002000a11110f0a0a0a0a0808080b040f010201080002000a060a08070c03120034043e0315040302020203161614140f0f0e0e0a0a0a0808080b0409040a010a161614140f0f0e0e0a0a0a0808080b0409040a010a161614140f0f0e0e0a0a0a0808080b0409040a010a060a08070c03120034043e03152c0804000603120301130400020206030b06050202020307020402020203161614140f0f0e0e0a0a0a08080816060b040a010a161614140f0f0e0e0a0a0a08080816060b040a010a161614140f0f0e0e0a0a0a08080816060b040a010a060a08070c03120034043e03152c080400060312030b020a0203040002040603130400020206030b06050202020311040002020603010f0402020206030e040a06010203060316160f0f0e0e130a0f0a0b090b04110113000916160f0f0e0e130a0f0a0b090b04110113000916160f0f0e0e130a0f0a0b090f080b04110109060a08070c03120034043e03152c080400060312030b020a0203040002040603130400020206030b060502020203110400020206031004060c02120316030f0402020206030e040a06010203060301]
private def node1360:Certificate:=PackedParametricCertificateData.decode 11 data1360
private def data1403:List Nat:=[
  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,
  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,
  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,
  0x1161615140f0f100b10090f0808080c0101010e000a16160f0f100b100908080c010b010a0101010e000a16160f0f100b10090808]
private def node1403:Certificate:=PackedParametricCertificateData.decode 11 data1403
private def node1404:Certificate:=.split node1360 node1403
private def node1405:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1404
private def node1406:Certificate:=.positive 4 [(3,0),(3,3),(1,7)] node1405
private def node1407:Certificate:=.positive 5 [(4,0),(3,2),(1,6)] node1406
private def data1438:List Nat:=[
  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]
private def node1438:Certificate:=PackedParametricCertificateData.decode 11 data1438
private def data1475:List Nat:=[
  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,
  0x1160f160e150b100b0e0b100908080d010c0100000a160f160e150b100b0e0b100908080d010c0100000a160f160e150b100b0e0b100908080c01010100000a06160f160e0e0d150b100b0e0b0c010a01010108000a160f160e0e0d150b100b0e0b0c010a01010108000a160f160e0e0d150b100b0e0b0c010a01010108000a0601160f110f160e100b0e0b0a0909070f010e0101010a160f110f160e100b0e0b]
private def node1475:Certificate:=PackedParametricCertificateData.decode 11 data1475
private def node1476:Certificate:=.split node1438 node1475
private def node1477:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1476
private def node1478:Certificate:=.positive 4 [(3,0),(3,3),(1,7)] node1477
private def node1479:Certificate:=.positive 1 [(3,2),(1,8)] node1478
private def node1480:Certificate:=.split node1407 node1479
private def node1481:Certificate:=.split node1329 node1480
private def data1520:List Nat:=[
  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,
  0x1161614140c0b0a080e0408030a011400080002000a161615140c0b0c090a080e0408030a01080002000a16161514110a0c090a080e0408030a01080002000a061302020600060308031504030202020314140e0e14080f080a08080804040e0202020a000a14140e0e14080f08]
private def node1520:Certificate:=PackedParametricCertificateData.decode 11 data1520
private def data1555:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  0x160a501a7bf0ee201e49b10c1e621b6af3efbb22cb9ab000ed198acbef4f4c4e0151402020e869cc7e6cedbc59aca95c5f0c0170f020202d7e6]
private def node1555:Certificate:=PackedParametricCertificateData.decode 11 data1555
private def node1556:Certificate:=.split node1520 node1555
private def node1557:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1556
private def node1558:Certificate:=.positive 1 [(1,0),(1,8)] node1557
private def node1559:Certificate:=.positive 1 [(1,0),(1,7)] node1558
private def data1598:List Nat:=[
  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,
  0x10e0d160a080509030d020f010e01080102010e000a0e0d0e0c160a080509030d020f010e01080102010a0e0d160a080509030d020f010e01080102010e000a06130202060006030803150403020202031414110f110e110a0e090e0808080e010a0100000a1414110f]
private def node1598:Certificate:=PackedParametricCertificateData.decode 11 data1598
private def data1630:List Nat:=[
  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,
  0x1160e0e0d140c150b0e0b170808080c01010100000a160e0e0d140c150b0e0b170808080c01010100000a160e0e0d140c150b0e0b170808080c010101]
private def node1630:Certificate:=PackedParametricCertificateData.decode 11 data1630
private def node1631:Certificate:=.split node1598 node1630
private def node1632:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1631
private def node1633:Certificate:=.positive 1 [(1,0),(1,8)] node1632
private def data1678:List Nat:=[
  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,
  0x1160e160d0e0c140b0e0b160a0b020a01080100000a160f160e160d0e0c140b160a0b020a01080100000a160f160e0e0c140b160a09090b020a01080100000a06130202060006030803140201060202030a04030402020306040802060202020311020002020204160e140c0e0c160a0c0808050c020e01080102010a160e140c0e0c160a0c0808050c020e01080102010a160e160d0e0c160a08050c020f010e01080102010a06130202060006030803150403020202031414160d110d0e0b110a14090e0908080e010a010a1414110d]
private def node1678:Certificate:=PackedParametricCertificateData.decode 11 data1678
private def data1704:List Nat:=[
  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]
private def node1704:Certificate:=PackedParametricCertificateData.decode 11 data1704
private def node1705:Certificate:=.split node1678 node1704
private def node1706:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node1705
private def data1758:List Nat:=[
  0x1060e010c010a010a160e110e160c110c0e09080809060e010c010a010a160e110e160c110c0e09080809060e010d010a010a06130202060006030803152c080400060312030111020102020203160f160e160d140b0e0b0b080f0505020e0108010a160f160e140b0e0b0b080f0505020e01080102010a160f160e140b0e0b0b080f0505020e01080102010a060a08070c03120034043e0315040302020203110e160d160c14090e09080809060e010c010a010a160e110e160c14090e09080809060e010c010a010a160e110e160c110c0e09080809060e010d010a010a060a08070c03120034043e03152c0804000603120301130400020206030101160e110c0e0b110a0e090f0808080b040e010a010a160e110c0e0b110a0e090f0808080b040e010a010a160e110e110c160a110a0e0908080e010d010a010a060a08070c03120034043e03152c0804000603120315040302020203130400020206031006010202020311040002020603010f0402020206030e040a060102030603110e0e0b16090b090f080b040e0113000f0009110e0e0b110a16090b090f080b0413000f0009110e0e0b110a16090b090f080b0413000f0009060a08070c03120034043e03152c0804000603120315040302020203130400020206031006010202020311040002020603110402020202030f0402020206030e040a06010203060301,
  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]
private def node1758:Certificate:=PackedParametricCertificateData.decode 11 data1758
private def data1780:List Nat:=[
  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]
private def node1780:Certificate:=PackedParametricCertificateData.decode 11 data1780
private def node1781:Certificate:=.split node1758 node1780
private def node1782:Certificate:=.positive 2 [(1,8),(1,9),(6,12)] node1781
private def node1783:Certificate:=.split node1706 node1782
private def node1784:Certificate:=.split node1633 node1783
private def node1785:Certificate:=.split node1559 node1784
private def node1786:Certificate:=.negative 1 [(1,0),(2,2)] node1785
private def node1787:Certificate:=.split node1481 node1786
private def node1788:Certificate:=.negative 1 [(1,0),(1,4)] node1787
private def node1789:Certificate:=.split node1253 node1788
private def node1790:Certificate:=.split node1041 node1789
private def node1791:Certificate:=.positive 1 [(1,0),(2,4)] node1790
private def data1802:List Nat:=[
  0x116161111160a140a0b0a16091409160114000916161111160a140a0b0a16091409160114000916161111160a140a0b0a160914091601140009060a08070c03120034043e03152c080400060312030c020b0a030a0008041203130400020206030c0a050203020006040a03110400020206031008080607060212041a030f0402020206030e100d120b36012004300309020002020203]
private def node1802:Certificate:=PackedParametricCertificateData.decode 11 data1802
private def data1865:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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,
  0x116161411170f140f160e140c140a06]
private def node1865:Certificate:=PackedParametricCertificateData.decode 11 data1865
private def node1866:Certificate:=.split node1802 node1865
private def node1867:Certificate:=.positive 4 [(4,0),(3,8),(1,10)] node1866
private def node1868:Certificate:=.positive 13 [(12,0),(3,4),(4,7)] node1867
private def node1869:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1868
private def node1870:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1869
private def node1871:Certificate:=.positive 3 [(1,1),(6,2),(2,8)] node1870
private def node1872:Certificate:=.positive 3 [(1,0),(2,7)] node1871
private def data1883:List Nat:=[
  0x111110f0f140a140911090b091404110114000911110f0f140a140911090b091404110114000911110f0f140a140911090b0914041101140009060a08070c03120034043e03152c080400060312030c020b0a030a0008041203130400020206030b060502020203110400020206031008080607060212041a030f0402020206030e080b120806010a04120309020002020203]
private def node1883:Certificate:=PackedParametricCertificateData.decode 11 data1883
private def data1893:List Nat:=[
  0x11111130a140911090b090a0908081404110114000a1111130a0f0a140911090b0908081404110114000a1111130a0f0a11090b09080814040b04110114000a060a08070c03120034043e03150c050400020306030c020b0a030a0008041203130400020206030f020b040402030203110400020206031008080607060212041a030f04010200020308030e040b180808000a040e03]
private def node1893:Certificate:=PackedParametricCertificateData.decode 10 data1893
private def data1950:List Nat:=[
  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,
  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,
  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,
  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,
  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]
private def node1950:Certificate:=PackedParametricCertificateData.decode 10 data1950
private def node1951:Certificate:=.split node1893 node1950
private def node1952:Certificate:=.split node1883 node1951
private def node1953:Certificate:=.positive 12 [(13,0),(3,5),(8,8)] node1952
private def node1954:Certificate:=.positive 2 [(1,0),(1,2),(1,7)] node1953
private def node1955:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node1954
private def node1956:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node1955
private def node1957:Certificate:=.positive 1 [(1,0),(2,2)] node1956
private def node1958:Certificate:=.positive 1 [(1,2),(1,3)] node1957
private def node1959:Certificate:=.split node1872 node1958
private def node1960:Certificate:=.positive 3 [(1,0),(2,5)] node1959
private def data1981:List Nat:=[
  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]
private def node1981:Certificate:=PackedParametricCertificateData.decode 11 data1981
private def data2029:List Nat:=[
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,
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,
  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]
private def node2029:Certificate:=PackedParametricCertificateData.decode 9 data2029
private def data2051:List Nat:=[
  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]
private def node2051:Certificate:=PackedParametricCertificateData.decode 9 data2051
private def node2052:Certificate:=.split node2029 node2051
private def node2053:Certificate:=.negative 1 [(1,0),(1,9)] node2052
private def node2054:Certificate:=.split node1981 node2053
private def node2055:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node2054
private def node2056:Certificate:=.positive 2 [(1,0),(1,2),(1,7)] node2055
private def node2057:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node2056
private def node2058:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node2057
private def node2059:Certificate:=.positive 1 [(1,0),(2,2)] node2058
private def data2090:List Nat:=[
  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]
private def node2090:Certificate:=PackedParametricCertificateData.decode 11 data2090
private def data2153:List Nat:=[
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  0x1130f110f110e09091308110811020901060101010a130f110f110e09091308110811020901060101010a130f110f110e09091308110811020901060101010a061004]
private def node2153:Certificate:=PackedParametricCertificateData.decode 11 data2153
private def node2154:Certificate:=.split node2090 node2153
private def node2155:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node2154
private def node2156:Certificate:=.positive 2 [(1,0),(1,2),(1,7)] node2155
private def node2157:Certificate:=.positive 3 [(2,0),(1,1),(1,6)] node2156
private def node2158:Certificate:=.positive 4 [(4,0),(1,5),(3,7)] node2157
private def data2189:List Nat:=[
  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]
private def node2189:Certificate:=PackedParametricCertificateData.decode 11 data2189
private def data2243:List Nat:=[
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]
private def node2243:Certificate:=PackedParametricCertificateData.decode 11 data2243
private def node2244:Certificate:=.split node2189 node2243
private def node2245:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node2244
private def node2246:Certificate:=.positive 1 [(3,5),(1,7)] node2245
private def node2247:Certificate:=.positive 2 [(1,0),(3,4),(1,6)] node2246
private def node2248:Certificate:=.positive 3 [(5,3),(1,7),(4,9)] node2247
private def node2249:Certificate:=.split node2158 node2248
private def node2250:Certificate:=.split node2059 node2249
private def node2251:Certificate:=.negative 1 [(1,1),(3,3)] node2250
private def data2292:List Nat:=[
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  0x1161614140c0b0a080e0408030a011400080002000a161514140c0b0c090a080e0408030a01080002000a161514140c0b0c090a080e0408030a01080002000a061302020600060308031504030202020314140e0e14080f080a08080804040e0202020a000a14140e0e14080f080a08080804040e0202020a000a161614140e0e0f080a0808]
private def node2292:Certificate:=PackedParametricCertificateData.decode 11 data2292
private def data2330:List Nat:=[
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,
  0x10188d91c940280f404c3fd17f9d033a5c138d5f01cc6e10001ffaefdd3f389c680d8fcd5cbfe87f48ebbc7eee001dfbe08ff9b029aea0cf3f41fe49a2ea4bd1ec2df2f96d8003aafbcf4ebd7c1f786a0e5cdf1ceb8b491c3e2e033d7dd75fb886cdbe722feee18b8d23cdca539c0920c97e900179799fcbcd780859ccba7c4d580ae9ca3c4a01515020207a6b399cdbedb8a82c8a4b2f0d89ccbd4cde78ff1dab4a8801414020202ddc8aec5d780e6ecc5c5dde3f9889c87d0cb94c5f8e385e0140c020216abaae1dfd5c6b5c19198fbe9eec38d8eb0dbbae2fdece0800c0c02023de096f2eeacd2cfa382f597a9a3ebb1bcedf5fae09d]
private def node2330:Certificate:=PackedParametricCertificateData.decode 11 data2330
private def node2331:Certificate:=.split node2292 node2330
private def node2332:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node2331
private def data2380:List Nat:=[
  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,
  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]
private def node2380:Certificate:=PackedParametricCertificateData.decode 11 data2380
private def data2411:List Nat:=[
  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,
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  0x12ba9ee16e5b55aa6d941fa8d0101d4cfe69fc3f1d2c595b98efcef8cc4e0ca868385dbdebfd6e589d0f0f462ff36d117de02d6fb108f8c22c38b3d8bb62e8dd70013c19ee4d580fec5dfe5cc948ba7b6ae97a3aeb9f1eecbf697ace3c986c19001a3cc1bed02e2e606dbfb20fad23fb6a509e4bb32a3ac000aa6b1ddb3c3fc9aba9d97c4e2dbadd698999bc197d69ce695f2a9b0ac8fb84bc4d4018f92d911afe439baf625add947808008b8a91cd1bb0002dbd6d283af9fa5eec5f6cac7c1c3aaceb0c0cccfa289c1ffd7efd099b029c1c4118f8b61b6cf43cef529d0c114819c588dc64683de000ce0b8f3f68cedd89fbbd6abcb819fda95dbc3f4abc795f597cae4cbf0a8171702022bc9d287d2a0b0e8be88dbb7bbbdadcef3f2dcea85b6d78ee79ffee4dcf6a787e2e590171602021baa93fbf1a8c2ebe081e9e68592f880fae4ebe89184e58abbd1cb88c8bbf8aaeceda01414020206b2dea2c8d1bb8dd5c0dbe2ee82ffa2ecaeefeeb2d1cdfb92f49b8891acc1a9fbd8d40c]
private def node2411:Certificate:=PackedParametricCertificateData.decode 11 data2411
private def node2412:Certificate:=.split node2380 node2411
private def node2413:Certificate:=.positive 1 [(1,1),(1,8)] node2412
private def node2414:Certificate:=.split node2332 node2413
private def data2471:List Nat:=[
  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,
  0x1160e0e0e140b0d0b170a160a0b0a0a08170701010a160e0e0e140b0b0b170a160a0b0a0a08170701010a160e0e0e140b0b0b170a160a0b0a0a08170701010a06140200020202041414160e0e0e0b0b110a0a0811010a0101010e000a1414160e0e0e0b0b110a0a0811010a0101010e000a14140e0e140b0b0b110a0a0811010a0101010e000a0616161414160e0e0e110a0a080a010101080000000a16161414160e0e0e110a0a080a010101080000000a16161414160e0e0e110a0a080a010101080000000a0601010a0403040202030604110201020202041102000202020414140b0b110a0a0811050e040a011400080002000a14140b0b110a0a0811050e040a011400080002000a14140b0b110a0a0811050e040a011400080002000a061302040602020315040302020203161614140e0e0d08080816020e0201010a0000000a161614140e0e0d08080816020e0201010a0000000a161614140e0e0d080a08080816020e020a0101010a061316090c0112000c041603152c08040006031203011414160c0b0b0a080e0408030c010a01080002000a1414160c0b0b110a0a080e0408030c01080002000a1414160c0b0b110a0a080e0408030c01080002000a0613020206000603080315040302020203161614140e0e0d08080816020e0201010a0000000a161614140e0e0d08080816020e020101]
private def node2471:Certificate:=PackedParametricCertificateData.decode 11 data2471
private def data2493:List Nat:=[
  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,
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,
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,
  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,
  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,
  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,
  0x101cbbe95e102d4fcfac804dd93f5e004ecfce98501058ff5ffcc8df6b3d38bd6e98ceab5abcdfdcdaaa89292a0a1c78be4d290a6a39fe8f790b1a1c4ba96b8e4e88fdedee5d3eac9f08aca88f589c7f7f598a3f3c0dec8b0018bf6c7df01dea2b7a004b6feadc205d0b8d2840145d8c195a9fcc9bdd2c6c9c0d9acf8addfe7eeaee785f884998ec4f1a9b3d1dda5979caca5e2c5c8a5ad93ebe39ad7d1e8d9d3e5f287fa9ea6e2adae95aeeec5b00581a38412e2d9f10fedfa8f05eabc9e7bb5d3b2028abcecfd03e6d2cfec02f09de6cb0022aaa29fc4f1d9b2d3999aea9ea88486bf8bbfe1e7dcc9bcf7adee9be5d1c1f4d6f8ece3b8b9aed5b99ed0c491a6f0c383eda5a298b48af6b4e2a5d7aef2dac0a3b8c0029c92d60fa9b7ea2cfea6a11cf5cb8d0283a2cdea03f2bacff32aa8abe103868ad79a000ee8edf0ddeca4cd80e0f38db29bfeeac6f9b7d2ebe3bb]
private def node2493:Certificate:=PackedParametricCertificateData.decode 11 data2493
private def node2494:Certificate:=.split node2471 node2493
private def data2546:List Nat:=[
  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,
  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]
private def node2546:Certificate:=PackedParametricCertificateData.decode 11 data2546
private def data2567:List Nat:=[
  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,
  0x1fabcae9d8984be90b2ae0e0e020202baeab885f2b2cae2a79582dcf2fdb3c3f981d2fae2a2cc80140d02024991f0c3a7a88183a68daf81c0e580ada7b7a08be6e69be8170b02022488e3febff0dda19ee0addbcaf7e9e29f93c193e6debca4fe140b020202a9b2b3aebeddf5bdeee694faafc5a289c7aec7b8e8f888b80b0a0202259ee6b3a1f3d8a2d0c7fdee8bf4a6c99690eb8bffa5ffb2800a0a020205ad97b0aab1efd88acbb493eba09ca7d59087e49cc9d8dd900a07020204fab7b1f7c6e0f8c0d0b5edaf80f4c5b38eb68ef8ed948ae00a0102020181cad0efecd4a6ece7f0cfc695d0adabf3a5f091e3fdd5e01716010202b9f4b588a4a6c7b3ffd2b692e7ff85dcbfb6aff8959786a00e0e010201a1aeb9d0b9abdac2bae9c49fd5b5e884e3bbf78ac082df80140d01022bbac8c488db80da90a1ebb4a8b3eaadb6c784b8d8b0a2e8170b010227cbece980c0afaad9abe4daaeae8e829f9fb9e5a192d6a1e0140b010201bb89a9a9bc8fc795a89bd09ba9fc83d8c8d1ddbfff8cc9b80e0a010257c1a6acd2abe1bd89a7f6b8e6fbf6e6ddfa8b82afd49fa00b0a010229bdc5e4aaffd9f9f7ee8bfbdfcb9f87f7a5e3f6afa2a7acb00a0a010209e2fae2a5868bca8280b1a8e7c2b4c792fd819ec29ea195e00701010275b6a2f0a3dd9ef092bdc7d4dbafc198deab9bee9892bf901716000201d6aad386fbdfa38f,
  0x101b0ea0396dd0c83e30297ef02828a058289579e8a1ac2d1000ebff48ee9c3e985b0c19dbfaeb781c49ec7b2f00386c207bc890de19c07bcf152a601c38114cafa54f2b60003dbabb6c8cef7afb4f298a880e593ba95c8d4c026a3fd48dd9204868e099f33ca8068d6d9088dad01abb10023eedfdf87aa8cc2b1fc9fcdf5a6cd848795e01711020231b0bdb7d4a89e96d29ea6f69ebdf9e89d968aba8cb2fb9c170f020203cea4c5dfbec5dacab58183f0a3f7]
private def node2567:Certificate:=PackedParametricCertificateData.decode 11 data2567
private def node2568:Certificate:=.split node2546 node2567
private def node2569:Certificate:=.split node2494 node2568
private def node2570:Certificate:=.negative 1 [(1,0),(1,8)] node2569
private def node2571:Certificate:=.split node2414 node2570
private def data2625:List Nat:=[
  0x1110c0e09080809060e010c010a010a110e160c110c14090e09080809060e010d010a010a06130202060006030803152c0804000603120301011006010202020401160e110c0e0b110a0e090a0908080e010a0100000a160e110c0e0b110a0e090a090f0808080e010a010a160e110e110c160a110a0e0908080e010d010a010a06130202060006030803152c08040006031203150403020202030a08070a0306020c041203160e110c0e0b110a0e090f0808080b040e010a010a160e110c0e0b110a0e090f0808080b040e010a010a160e110e110c160a110a0e0908080e010d010a010a060a08070c03120034043e03152c0804000603120315040302020203130400020206030111040002020603010f0402020206030e040a060102030603110f160e110c0b0908080904140113010e0108010a110f160e110e110a0b090808090413010e0108010a110f160e110e110a0b090808090413010e0108010a06130202060006030803152c08040006031203150403020202031004070605080302040a03110e0e0b16090b090f080b040e0113000f0009110e0e0b110a16090b090f080b0413000f0009110e0e0b110a16090b090f080b0413000f0009060a08070c03120034043e03152c0804000603120315040302020203130400020206030111040002020603110402020202030f0402020206030e040a06010203060301,
  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]
private def node2625:Certificate:=PackedParametricCertificateData.decode 11 data2625
private def data2647:List Nat:=[
  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,
  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]
private def node2647:Certificate:=PackedParametricCertificateData.decode 11 data2647
private def node2648:Certificate:=.split node2625 node2647
private def node2649:Certificate:=.positive 1 [(1,2),(6,12)] node2648
private def node2650:Certificate:=.negative 1 [(1,0),(1,8)] node2649
private def node2651:Certificate:=.negative 1 [(1,0),(1,7)] node2650
private def node2652:Certificate:=.split node2571 node2651
private def node2653:Certificate:=.negative 1 [(1,0),(2,2)] node2652
private def node2654:Certificate:=.negative 1 [(1,1),(1,4)] node2653
private def node2655:Certificate:=.negative 1 [(1,0),(1,4)] node2654
private def node2656:Certificate:=.split node2251 node2655
private def node2657:Certificate:=.split node1960 node2656
private def data2668:List Nat:=[
  0x1161616141111140e190a160a0b0a1909190009161616141111140e190a160a0b0a1909190009161616141111140e190a160a0b0a1909190009060a08070c03120034043e03152c080400060312030c020b0a030a0008041203130400020206030c0a050203020006040a03110400020206031008080607060212041a030f040202020603102c0d020206011204120309020002020203]
private def node2668:Certificate:=PackedParametricCertificateData.decode 11 data2668
private def data2732:List Nat:=[
  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,
  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,
  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,
  0x1c078db8c798a8f0b94ca02abfc79b2e379b2e40065bc92a3fce4a2f6dc9ed3a0fdb082e01616020201c0deaac99deae28bba8aa7cbc1c2c1c89df2c4d5f4a01614020209dbf9d3f6c1a3ab91db9e9acfd9d4f9a3ff88f9b4dee01111020202e082b6d8a180e7b3f8dfd3fd9a85a29e9bddbcc019090202088ba0dbbb99e3aad8e7c5fbaa8ac18b9a88d0a4cdebc01908020224dafaaf88eb9cac99deac8493ae8afce2bcdcd4c2c2c0140702020294b5a5a1ddb1a7bdbf8ee9dbc7a3dbc7d8a8e4ef801104020206d3f9b8fbfebfa9fbcad28c84cee2f6ac84b1ff80040402020397e591cde7f5e2ecfdc5f9c7989f9192f2d1b5c01616010203a5e9ddd09b8b97ce8ab6fda2fbf58e91f5e0d882dda416140102088289f2da8995e7f6a4f9d5f4e78ab6bf8a8682eafed4190f010250fbaaa1c1cddbf6faa6e19e9bdd9686d0dfc8bff3a0190a010208fafebbc381b49bc0a9b1fa87a4d1c3c698e1f88e99e0190801021aa2f1bfde95d484a0fdfbdbcbe3dfe4d68ee6e485b6a0160801024fa6f4f4b3cab3faaabfb8f9ffb1a784d4f691f1b4c01407010204a7f1d3939e98fe83808eb29999d5ffcec9d580eee1800707010210aeefcdf8cfe3c3d7e9ffca82d9f2e4ce8eafadf280070401021497c088c28d8bb0b9bfd7d0ffb589bff19fa7d5801616000203d887b2d09efbe79881badfd8ecf7e8829eb7e8baafb21614,
  0x10f060806130108010201040009161616140f060806130108010201040008061616161416080f060806130111000f000800091616161416080f0608061301080111000f00091616161416080f0608061301080111000f000906011504030202020310040c040b04020e040e031002020202020411060f0601080308040116161614190f1908040414010801090001000916161614190f1908040414010801090001000916161614190f190804041401010007061614190f1908160404040e031401030111000916161614190f190816040e041401030108000916161614190f19081604040414010706011510040202060314080c060b06030a0412031614190f190a190816040e040404140111000916161614190f1908160408040404140108000916161614190f1908160414010606180402060004030603150403020202030c020b0a030a00080412030116161614190a1908190716070404140107000916161614190a19081907160714010716161614190f190a190814010606181003060010031203150403020202030c020b0a030a00080412031304000202060301110400020206030173868e3ceadf03d8d603e09924a3a5168cb303e5cd03e5ce0027a7bf81d0daf5a79e8ea390dec2859b8039c3da3fffc808d7c908e092238cb406bfbe08ed9808ed97003de6cca8d48ef9f7a2d58df597c6999dc006ffc501d4,
  0x116161614170f160e11060f060a06060101010916161614170f160e11060f060a06060101010916161614170f11060f060a06060101010806130803060018031a041616161411060a0608061401020109000600091616161411060a0608061401020109000600091616161411060a06080614010201060008061302040602020401141c10140c060b06041c0310020106000203080411020002020204161616140f0608060804130108010201040009161616141608]
private def node2732:Certificate:=PackedParametricCertificateData.decode 11 data2732
private def node2733:Certificate:=.split node2668 node2732
private def node2734:Certificate:=.positive 1 [(1,0),(2,13)] node2733
private def node2735:Certificate:=.positive 9 [(8,0),(3,4),(8,12)] node2734
private def node2736:Certificate:=.positive 4 [(3,0),(3,2),(2,11)] node2735
private def node2737:Certificate:=.positive 7 [(5,0),(4,7),(6,9)] node2736
private def node2738:Certificate:=.positive 3 [(1,1),(6,2),(2,8)] node2737
private def node2739:Certificate:=.positive 3 [(1,0),(2,7)] node2738
private def data2750:List Nat:=[
  0x116141611140e110e190a0b0a19091102190009161416111111140e190a0b0a19091109190009161416111111140e190a0b0a19091109190009060a08070c03120034043e03152c080400060312030c020b0a030a0008041203130400020206030b060502020203110400020206031008080607060212041a030f040202020603102408020206011004100309020002020203]
private def node2750:Certificate:=PackedParametricCertificateData.decode 11 data2750
private def data2765:List Nat:=[
  0x11616130a0f0a0b091604140409040a02040108000a1616130a0f0a0b0916041404090406040a0208000a1616130a0f0a0b091404090406040a02040108000a060a0407060224001a042803150c050400020306030c020b0a030a00080412030c02030202020316111411140a190911090a0909080808190111010a1611140a130a11090a09090808041901110108000a1611140a130a11090a09090808041901110108000a060a08070c03120034043e03150c050400020306030c020b0a030a00080412031304000202060301110400020206031008080607060212041a030f0401020002030803100c0002020203]
private def node2765:Certificate:=PackedParametricCertificateData.decode 10 data2765
private def data2823:List Nat:=[
  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,
  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,
  0x116111411170e110e0b0b11080a0608]
private def node2823:Certificate:=PackedParametricCertificateData.decode 10 data2823
private def node2824:Certificate:=.split node2765 node2823
private def node2825:Certificate:=.split node2750 node2824
private def node2826:Certificate:=.positive 1 [(1,0),(2,13)] node2825
private def node2827:Certificate:=.positive 3 [(2,0),(3,3),(2,12)] node2826
private def node2828:Certificate:=.positive 4 [(3,0),(3,2),(2,11)] node2827
private def node2829:Certificate:=.positive 7 [(5,0),(4,7),(6,9)] node2828
private def node2830:Certificate:=.positive 1 [(1,0),(2,2)] node2829
private def data2846:List Nat:=[
  0x10b090a08080813040f040e04040219010b0108000a0e0e0b090a08080813040f040e0404020b0108000a0e0e0b090a08080813040f040e0404020b0108000a060a0407060224001a042803152c080400060312030c020b0a030a00080412030b0207020604030403140e100e100c190a0b0a190919041001190009100f140e100b0b0a19090b09100419001000091311140e140b100b19090b0910021900100009060a08070c03120034043e03152c080400060312030c020b0a030a00080412031304000202060301110400020206031008080607060212041a030f040202020603102408020206011004100309020002020203]
private def node2846:Certificate:=PackedParametricCertificateData.decode 11 data2846
private def data2860:List Nat:=[
  0x10e0e140a0b090808140413040a0204020b0108000a0e0e140a0b090808140413040a0204020b0108000a0e0e140a0b09080813040f040a0204020b0108000a060b0c0808070a0006040c03150c0504000203060314080c060b06030a0412030e0e140a0b090808140413040a0204020b0108000a0e0e140a0b090808140413040a0204020b0108000a0e0e140a0b09080813040f040a0204020b0108000a060a0407060224001a042803150c050400020306030c020b0a030a0008041203010b060502020204110400020206031008080607060212041a030f0401020002030803100c0002020203]
private def node2860:Certificate:=PackedParametricCertificateData.decode 10 data2860
private def data2912:List Nat:=[
  0x10919081108100811021002140008000a110f110e0a0919081108100811021002140008000a06011510040202060314080c060b06030a0412030c0203020202040c0202020202041104000202060301110f110e0a0911080908080711021002070214000a110f110e0a0911080908080711021002070214000a110f110e0a0911080908080711021002070214000a060b020606020203150c0504000203060314080c060b06030a041203110f110e100e0a091108090808071002070214000a110f110e0a0911080908080711021002070214000a110f110e0a0911080908080711021002070214000a0608020604020a0006040a03150c050400020306030c020b0a030a0008041203010c020b0604020302040404110400020206030c020002020203011614140e0a0a0f040e040e0314021401060108000a1614140e0a0a0f040e040e0314021401060108000a1614140e0a0a0f040e040e0314021401060108000a060e08070c05060002040803150c0504000203060314080c060b06030a0412031614140e090908080f040e040a041402100108000a1614140e090908080f040e040a041401100108000a1614140e090908080f040e040a041401100108000a060a0407060224001a042803150c050400020306030c020b0a030a0008041203010b060502020204110400020206030c0200020202030b02000202020301,
  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]
private def node2912:Certificate:=PackedParametricCertificateData.decode 10 data2912
private def node2913:Certificate:=.split node2860 node2912
private def node2914:Certificate:=.split node2846 node2913
private def node2915:Certificate:=.positive 1 [(1,0),(2,13)] node2914
private def node2916:Certificate:=.positive 1 [(1,2),(2,12)] node2915
private def node2917:Certificate:=.positive 2 [(1,0),(1,1),(2,11)] node2916
private def node2918:Certificate:=.positive 7 [(5,0),(4,7),(6,9)] node2917
private def data2934:List Nat:=[
  0x10e0e0f0a0b090f08080814041304090404020b010a0e0e0f0a0b090f08080814041304090406040b010a0e0e0f0a0b090f08080814041304090406040b010a060a0407060224001a042803152c080400060312030b020a020304000204060308020602020203130e0e0e0f0a11090b090f080b040f000b0009130e0e0e0f0a11090b090f080b040f000b0009130e0e0e0f0a11090b090f080b040f000b0009060a08070c03120034043e03152c080400060312030b020a02030400020406031304000202060301110400020206031004060c02120316030f0402020206030e0806120212011004180309020002020203]
private def node2934:Certificate:=PackedParametricCertificateData.decode 11 data2934
private def data2997:List Nat:=[
  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,
  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,
  0x1161414110e0e0c0c0c0b09080e020601010100000a14110e0e0c0b0b08090816020e02060101010f000a14110e0e0c0b0b08090816020e02060101010f000a0613080306]
private def node2997:Certificate:=PackedParametricCertificateData.decode 11 data2997
private def node2998:Certificate:=.split node2934 node2997
private def node2999:Certificate:=.positive 1 [(2,0),(1,3)] node2998
private def data3019:List Nat:=[
  0x1130e0e0e0f0a0b0908081404130409040b0103010a130e0e0e0f0a0b0908081404130409040b0103010a130e0e0e0f0a0b0908081404130409040b0103010a060a1a0912080c0010041a03150403020202030a04030402020306030e0e0f0a0b090f08080814041304090404020b010a0e0e0f0a0b090f08080814041304090406040b010a0e0e0f0a0b090f08080814041304090406040b010a060a0407060224001a042803152c080400060312030b020a020304000204060301130e0e0e0f0a11090b090f080b040f000b0009130e0e0e0f0a11090b090f080b040f000b0009130e0e0e0f0a11090b090f080b040f000b0009060a08070c03120034043e03152c080400060312030b020a02030400020406031304000202060301110400020206031004060c02120316030f0402020206030e0806120212011004180309020002020203]
private def node3019:Certificate:=PackedParametricCertificateData.decode 11 data3019
private def data3074:List Nat:=[
  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,
  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]
private def node3074:Certificate:=PackedParametricCertificateData.decode 11 data3074
private def node3075:Certificate:=.split node3019 node3074
private def data3096:List Nat:=[
  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]
private def node3096:Certificate:=PackedParametricCertificateData.decode 11 data3096
private def data3152:List Nat:=[
  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,
  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]
private def node3152:Certificate:=PackedParametricCertificateData.decode 11 data3152
private def node3153:Certificate:=.split node3096 node3152
private def node3154:Certificate:=.split node3075 node3153
private def node3155:Certificate:=.split node2999 node3154
private def node3156:Certificate:=.positive 3 [(1,5),(8,10)] node3155
private def node3157:Certificate:=.positive 9 [(5,4),(3,7),(22,9)] node3156
private def node3158:Certificate:=.split node2918 node3157
private def node3159:Certificate:=.split node2830 node3158
private def node3160:Certificate:=.split node2739 node3159
private def node3161:Certificate:=.positive 3 [(1,0),(2,5)] node3160
private def data3187:List Nat:=[
  0x116141414140e08080f040e0416020a00080000000a16141414140e08080f040e0416020a00080000000a16141414140e08080f040e0416020a00080000000a060a0407060224001a042803152c080400060312030c020b0a030a00080412030b02070206040304030f020b040402030204110400020206030d06080603040006040a030f0402020206030e040a0601020306030e0e0b090a08080814040f0409040402130008000a0e0e0b090a08080814040f0406040402130008000a0e0e0b090a08080814040f0406040402130008000a060a0407060224001a042803152c080400060312030c020b0a030a00080412030b0207020604030403160e140e0e0e140b0b09130411011300110009160e140e0e0e140b0b09130411011300110009160e140e0e0e140b0b09130411011300110009060a08070c03120034043e03152c080400060312030c020b0a030a00080412031304000202060301110400020206031008080607060212041a030f0402020206030e040a06010203060301]
private def node3187:Certificate:=PackedParametricCertificateData.decode 11 data3187
private def data3242:List Nat:=[
  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,
  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]
private def node3242:Certificate:=PackedParametricCertificateData.decode 11 data3242
private def node3243:Certificate:=.split node3187 node3242
private def node3244:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node3243
private def node3245:Certificate:=.positive 4 [(1,0),(4,2),(3,6)] node3244
private def node3246:Certificate:=.positive 7 [(4,0),(4,1),(3,5)] node3245
private def node3247:Certificate:=.positive 10 [(11,0),(3,4),(7,7)] node3246
private def data3273:List Nat:=[
  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]
private def node3273:Certificate:=PackedParametricCertificateData.decode 11 data3273
private def data3335:List Nat:=[
  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,
  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,
  0x114110e0e0c0b1308090816020e02060101010f000a14110e0e0c0b13080b08090816020e02060101010a14110e0e0c0b13080b08090816020e02060101010a06130803060018031a0416140e0e0c0b160809080e0214010201010109000a16140e0e0c0b160809080e0214010201010109000a16140e0e0c0b160809080e0214010201010109000a06]
private def node3335:Certificate:=PackedParametricCertificateData.decode 11 data3335
private def node3336:Certificate:=.split node3273 node3335
private def node3337:Certificate:=.positive 12 [(15,0),(1,5),(8,7)] node3336
private def data3371:List Nat:=[
  0x10a0808080e0202020a1614140e0e0e0a0a0f080a08080814020e0202020a060a04090405020002040403150403020202030a0403040202030603161414140f0f140e0e0e0a0a0a080808020203000a16140f0f140e0e0e0a0a0f080a0808080e0202020a1614140e0e0e0a0a0f080a08080814020e0202020a060a0407060224001a042803152c080400060312030b020a0203040002040603010f040c0207020404040404110400020206030b0603020202030f0402020206030e040a06010203060316160e0e130a0b090a08080814040904040213000a16160e0e130a0b090a08080814040904060413000a16160e0e130a0b090a08080814040904060413000a060a1a0912080c0010041a03150403020202030a04030402020306030e0e130a13090b090a08080816041404090413000a16160e0e130a0b090a08080814040904060413000a16160e0e130a0b090a08080814040904060413000a060a0407060224001a042803152c080400060312030b020a020304000204060301140e0e0e130a11090b090f080b040e02130009140e0e0e130a11090b090f080b040e02130009140e0e0e130a11090b090f080b040e02130009060a08070c03120034043e03152c080400060312030b020a02030400020406031304000202060301110400020206031004060c02120316030f0402020206030e040a06010203060301,
  0x1161414140f0f140e0e0e0a0a0f080a08080802020a16140f0f140e0e0e0a0a0f08]
private def node3371:Certificate:=PackedParametricCertificateData.decode 11 data3371
private def data3429:List Nat:=[
  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,
  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,
  0x114110e0e0d0b0b0b090816020e02060101010f000a14110e0e0d0b1308090816]
private def node3429:Certificate:=PackedParametricCertificateData.decode 11 data3429
private def node3430:Certificate:=.split node3371 node3429
private def data3462:List Nat:=[
  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,
  0x1160d140d0b090f080a0808080e020b01090009160d140d0b090f080a0808080e020b01090009160d140d]
private def node3462:Certificate:=PackedParametricCertificateData.decode 11 data3462
private def data3520:List Nat:=[
  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,
  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,
  0x11716160d]
private def node3520:Certificate:=PackedParametricCertificateData.decode 11 data3520
private def node3521:Certificate:=.split node3462 node3520
private def node3522:Certificate:=.split node3430 node3521
private def node3523:Certificate:=.split node3337 node3522
private def node3524:Certificate:=.positive 1 [(1,4),(2,10)] node3523
private def node3525:Certificate:=.positive 3 [(5,3),(1,7),(4,9)] node3524
private def node3526:Certificate:=.split node3247 node3525
private def node3527:Certificate:=.negative 1 [(1,2),(1,3)] node3526
private def node3528:Certificate:=.negative 4 [(4,1),(3,2),(3,4)] node3527
private def data3568:List Nat:=[
  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,
  0x1161616140e0e0a0a0a0814040e040f00080002000a161616140e0e0a0a0a0814040e040f00080002000a161616140a0a0a0814040e040f000a00080002000a060a020902040403020315040302020203161414140f0f140e0e0e0a0a0f080a08080802020a16140f0f140e0e0e0a0a0f080a0808080e0202020a1614140e0e0e0a0a]
private def node3568:Certificate:=PackedParametricCertificateData.decode 11 data3568
private def data3600:List Nat:=[
  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,
  0x116140e0d0d0a0a0a080814040b010a0101010d000a16140e0e0e0d0a0a080814040b010a0101010d000a16140e0e0e0d0a0a080814040b010a0101010d000a06130803060018031a041614140e0e0e0a0a0c0808081404]
private def node3600:Certificate:=PackedParametricCertificateData.decode 11 data3600
private def node3601:Certificate:=.split node3568 node3600
private def data3649:List Nat:=[
  0x1150403020202030a0403040202030603140e0e0e140d11090b090a0808080d040b000a000a140e0e0e160d140d0b0908080e0201010b000a000a140e0e0e160d140d0b0908080e0201010b000a000a06080207020212000c0412030606050400080306030b020a02030400020406030111040f020604040604060411040002020603010f0402020206030e040a060102030603160d130b0d0b130a13090d0913010401090009160d130b0d0b130a13090d0908081301040109160d130b0d0b130a13090d090808130104010906160d130b0d0b130a13090d0913010401030104000a160e160d130b0d0b130a13090d091301040111000a160e160d130b0d0b130a13090d090808130111000a0601150403020202030a0403040202030603160e160d130b0d0b130a13090d090404130100000a160e160d130b0d0b130a13090d090808130111000a160e160d130b0d0b130a13090d091301110009060c0407060218000e0418030606050400080306030b020a020304000204060301160e160d130b0d0b130a13090d091301110009160e160d130b0d0b130a13090d091301110009160e160d130b0d0b130a13090d0913011100090612060c0203060010041203152c080400060312030b020a02030400020406031304000202060301110400020206031004060c02120316030f04010200020308030e040a06010203060301,
  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]
private def node3649:Certificate:=PackedParametricCertificateData.decode 11 data3649
private def data3681:List Nat:=[
  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,
  0x11711140d0d0b0b090d04090101010d000a00091711140d0d0b0b090d04090101010d000a00091711140d0d0b0b090d04090101010d000a000906130803060018031a04]
private def node3681:Certificate:=PackedParametricCertificateData.decode 11 data3681
private def node3682:Certificate:=.split node3649 node3681
private def node3683:Certificate:=.split node3601 node3682
private def node3684:Certificate:=.negative 1 [(3,5),(1,7)] node3683
private def data3740:List Nat:=[
  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,
  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,
  0x1181618141714180b170a14090a081707010109181618141714180b170a1409]
private def node3740:Certificate:=PackedParametricCertificateData.decode 11 data3740
private def data3761:List Nat:=[
  0x117161714170b140a0b0a1409070101010a000917161714170b140a0b0a1409070101010a000917161714140a0b0a14090a01070101010a000906130803060018031a040b0205060202040a04030402020306040702030601040004040e0411020002020204070201060002030804060602080002030a0417161714170b140a0b0a1409160701010a000917161714170e140a0b0a1409160701010a00091714170e140a0b0a140916070a0101010a000906130803060018031a04160a140a0b0a0b09020216010b0101010a0009140a0b0a0b090a04020216010b0101010a0009140a0b0a0b090a0402021601140101010a00090613020406020204010a04030402020306041002010600020308041102000202020407020402020204060603020206030804010e100a0e040603100309020002020204]
private def node3761:Certificate:=PackedParametricCertificateData.decode 11 data3761
private def node3762:Certificate:=.split node3740 node3761
private def node3763:Certificate:=.negative 1 [(1,1),(1,8)] node3762
private def node3764:Certificate:=.negative 13 [(12,0),(3,4),(4,7)] node3763
private def node3765:Certificate:=.split node3684 node3764
private def node3766:Certificate:=.positive 8 [(5,5),(1,7),(24,9)] node3765
private def node3767:Certificate:=.negative 1 [(1,0),(2,2)] node3766
private def node3768:Certificate:=.negative 4 [(1,0),(3,1),(1,3)] node3767
private def node3769:Certificate:=.negative 1 [(1,0),(1,4)] node3768
private def node3770:Certificate:=.split node3528 node3769
private def node3771:Certificate:=.split node3161 node3770
private def node3772:Certificate:=.split node2657 node3771
private def node3773:Certificate:=.split node1791 node3772
private def node3774:Certificate:=.split node958 node3773
private def zz531:"s0213"="s0213":=by decide+kernel
private theorem valid79:check node79 ctx79 quad79 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid197:check node197 ctx197 quad197 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid202:check node202 ctx202 quad202 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid197
private theorem valid277:check node277 ctx277 quad277 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz532:"s0214"="s0214":=by decide+kernel
private theorem valid427:check node427 ctx427 quad427 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid501:check node501 ctx501 quad501 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid427
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid502:check node502 ctx502 quad502 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid501
private theorem valid577:check node577 ctx577 quad577 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz533:"s0215"="s0215":=by decide+kernel
private theorem valid723:check node723 ctx723 quad723 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid799:check node799 ctx799 quad799 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid723
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid800:check node800 ctx800 quad800 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid799
private theorem valid875:check node875 ctx875 quad875 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private def zz534:"s0216"="s0216":=by decide+kernel
private theorem valid951:check node951 ctx951 quad951 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · exact valid875
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid953:check node953 ctx953 quad953 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid577
    · exact valid800
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid951
private theorem valid955:check node955 ctx955 quad955 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid202
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · exact valid277
        · exact valid502
    · exact valid953
private theorem valid956:check node956 ctx956 quad956 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.positive_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · exact valid79
  · exact valid955
private def zz535:"s0217"="s0217":=by decide+kernel
private theorem valid1038:check node1038 ctx1038 quad1038 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1145:check node1145 ctx1145 quad1145 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1149:check node1149 ctx1149 quad1149 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid1145
private theorem valid1248:check node1248 ctx1248 quad1248 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz536:"s0218"="s0218":=by decide+kernel
private theorem valid1253:check node1253 ctx1253 quad1253 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1149
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid1248
private theorem valid1329:check node1329 ctx1329 quad1329 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1407:check node1407 ctx1407 quad1407 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1480:check node1480 ctx1480 quad1480 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1407
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz537:"s0219"="s0219":=by decide+kernel
private theorem valid1706:check node1706 ctx1706 quad1706 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1783:check node1783 ctx1783 quad1783 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid1706
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1784:check node1784 ctx1784 quad1784 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1783
private theorem valid1785:check node1785 ctx1785 quad1785 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1784
private def zz538:"s021a"="s021a":=by decide+kernel
private theorem valid1788:check node1788 ctx1788 quad1788 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid1329
      · exact valid1480
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1785
private theorem valid1790:check node1790 ctx1790 quad1790 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid1038
  · apply NatParametricCheckSteps.split_valid
    · exact valid1253
    · exact valid1788
private theorem valid1871:check node1871 ctx1871 quad1871 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1955:check node1955 ctx1955 quad1955 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz539:"s021b"="s021b":=by decide+kernel
private theorem valid1960:check node1960 ctx1960 quad1960 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid1871
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid1955
private theorem valid2056:check node2056 ctx2056 quad2056 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2158:check node2158 ctx2158 quad2158 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2248:check node2248 ctx2248 quad2248 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz540:"s021c"="s021c":=by decide+kernel
private theorem valid2250:check node2250 ctx2250 quad2250 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2056
  · apply NatParametricCheckSteps.split_valid
    · exact valid2158
    · exact valid2248
private theorem valid2332:check node2332 ctx2332 quad2332 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2570:check node2570 ctx2570 quad2570 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2571:check node2571 ctx2571 quad2571 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid2332
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid2570
private def zz541:"s021d"="s021d":=by decide+kernel
private theorem valid2652:check node2652 ctx2652 quad2652 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2571
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2656:check node2656 ctx2656 quad2656 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid2250
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2652
private theorem valid2738:check node2738 ctx2738 quad2738 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2828:check node2828 ctx2828 quad2828 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz542:"s021e"="s021e":=by decide+kernel
private theorem valid2917:check node2917 ctx2917 quad2917 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3154:check node3154 ctx3154 quad3154 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3157:check node3157 ctx3157 quad3157 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid3154
private theorem valid3159:check node3159 ctx3159 quad3159 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2828
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2917
    · exact valid3157
private def zz543:"s021f"="s021f":=by decide+kernel
private theorem valid3247:check node3247 ctx3247 quad3247 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3522:check node3522 ctx3522 quad3522 (hinges.drop 11) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3525:check node3525 ctx3525 quad3525 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid3522
private theorem valid3528:check node3528 ctx3528 quad3528 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · exact valid3247
      · exact valid3525
private def zz544:"s0220"="s0220":=by decide+kernel
private theorem valid3684:check node3684 ctx3684 quad3684 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3766:check node3766 ctx3766 quad3766 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid3684
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid3770:check node3770 ctx3770 quad3770 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid3528
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid3766
private theorem valid3771:check node3771 ctx3771 quad3771 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid2738
      · exact valid3159
  · exact valid3770
private def zz545:"s0221"="s0221":=by decide+kernel
private theorem valid3773:check node3773 ctx3773 quad3773 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid1790
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · exact valid1960
      · exact valid2656
    · exact valid3771
private theorem valid3774:check node3774 ctx3774 quad3774 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid956
  · exact valid3773
theorem certificate_valid:check node3774 constraintsNat base hinges = true:=valid3774
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node3774 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase3
private def zz2179:"s0883"="s0883":=by decide+kernel
end 
section 
namespace Green24Proof.QuadNearBalanceCase4
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x11ccc5b529b210, -0xaa87bee538000, -0xffcb9e57d4000,0xe805e7d63908], ![-0xaa87bee538000, -0x5c69c7ab6e2908,0x14c4b7477ffa38,0x4f8e040f98a7e], ![-0xffcb9e57d4000,0x14c4b7477ffa38, -0x460112777b9af0,0xad6f728eab6bc], ![0xe805e7d63908,0x4f8e040f98a7e,0xad6f728eab6bc, -0x5543df729c000]], ![![0x7b5287aa00,0,0x19945ca262000, -0xea29f388fd80], ![0,0, -0x24861a0c34280,0x19945ca262000], ![0x19945ca262000, -0x24861a0c34280,0x7b5287aa00, -0x3da943d500], ![-0xea29f388fd80,0x19945ca262000, -0x3da943d500,0]], ![![-0x6eaa7278920,0xac8e31c00,0xa7a358200,0x22d55c8b200], ![0xac8e31c00,0x6eaa7278920,0xbbcecf16440, -0x6e02cf20720], ![0xa7a358200,0xbbcecf16440,0,0xac8e31c00], ![0x22d55c8b200, -0x6e02cf20720,0xac8e31c00,0]]]
def hinges:Hinges:=[(![0,0x1ed4a1ea80,0], ![0,0,1, -3]),(![-0x173d9d4b9b5e, -0x9a27299480,0], ![0,0,1, -1]),(![0x173d9d4b9b5e,0,0], ![0,0,3, -1]),(![-0x2de2a95799a0,0,0], ![0,1, -3,0]),(![0x7402f3eb1c84,0,0], ![0,1,0, -3]),(![0x12c695003c6fa9,0, -0x6eaa7278920], ![0,1,0, -1]),(![-0x5543df729c000,0,0], ![0,3, -2, -1]),(![0x5543df729c000,0,0], ![0,3, -2,1]),(![0x2de2a95799a0,0,0], ![0,3, -1,0]),(![0x465418d301c3,0,0], ![0,3,0, -1]),(![0x5543df729c000,0,0], ![0,3,2, -1]),(![-0x173d9d4b9b5e,0,0], ![1, -3,0,0]),(![-0x5543df729c000,0,0], ![1, -2, -3,0]),(![0x5543df729c000,0,0], ![1, -2,3,0]),(![0x173d9d4b9b5e,0x9a27299480,0], ![1, -1,0,0]),(![-0x465418d301c3,0,0], ![1,0, -3,0]),(![-0x12c695003c6fa9,0,0x6eaa7278920], ![1,0, -1,0]),(![0x5543df729c000,0,0], ![1,2, -3,0]),(![0, -0x1ed4a1ea80,0], ![3, -1,0,0]),(![-0x7402f3eb1c84,0,0], ![3,0, -1,0])]
def normalizationDenominator:ℤ:=0xaa87bee538000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx2392:Nat → Linear:=constraintsNat
private def quad2392:Quadratic:=base
private def ctx619:Nat → Linear:=cons ![0,0,1, -3] ctx2392
private def quad619:Quadratic:=quad2392 + coefficientProduct ![0,0x1ed4a1ea80,0] ![0,0,1, -3] ![0,0,1, -3]
private def ctx301:Nat → Linear:=cons ![0,1,0, -3] (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx619)))
private def quad301:Quadratic:=(((quad619 + coefficientProduct ![-0x173d9d4b9b5e, -0x9a27299480,0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x173d9d4b9b5e,0,0] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x7402f3eb1c84,0,0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx142:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx301)
private def quad142:Quadratic:=(quad301 + coefficientProduct ![0x12c695003c6fa9,0, -0x6eaa7278920] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx615:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx619)))
private def quad615:Quadratic:=(((quad619 + coefficientProduct ![-0x173d9d4b9b5e, -0x9a27299480,0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x173d9d4b9b5e,0,0] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx511:Nat → Linear:=cons ![0,1,0, -1] ctx615
private def quad511:Quadratic:=quad615 + coefficientProduct ![0x12c695003c6fa9,0, -0x6eaa7278920] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1151:Nat → Linear:=cons ![0,0,1, -1] (cons (-![0,0,1, -3]) ctx2392)
private def quad1151:Quadratic:=(quad2392) + coefficientProduct ![-0x173d9d4b9b5e, -0x9a27299480,0] ![0,0,1, -1] ![0,0,1, -1]
private def ctx750:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx1151)))
private def quad750:Quadratic:=(((quad1151 + coefficientProduct ![0x173d9d4b9b5e,0,0] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x7402f3eb1c84,0,0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x12c695003c6fa9,0, -0x6eaa7278920] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1148:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx1151))
private def quad1148:Quadratic:=((quad1151 + coefficientProduct ![0x173d9d4b9b5e,0,0] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx833:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1148)
private def quad833:Quadratic:=(quad1148 + coefficientProduct ![0x12c695003c6fa9,0, -0x6eaa7278920] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1147:Nat → Linear:=cons (-![0,1,0, -1]) ctx1148
private def quad1147:Quadratic:=quad1148
private def ctx2390:Nat → Linear:=cons (-![0,0,1, -1]) (cons (-![0,0,1, -3]) ctx2392)
private def quad2390:Quadratic:=(quad2392)
private def ctx1694:Nat → Linear:=cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx2390)
private def quad1694:Quadratic:=(quad2390 + coefficientProduct ![0x173d9d4b9b5e,0,0] ![0,0,3, -1] ![0,0,3, -1])
private def ctx1340:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1694)
private def quad1340:Quadratic:=(quad1694) + coefficientProduct ![0x12c695003c6fa9,0, -0x6eaa7278920] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1409:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1694))
private def quad1409:Quadratic:=((quad1694)) + coefficientProduct ![-0x5543df729c000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1691:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1694))
private def quad1691:Quadratic:=((quad1694))
private def ctx1537:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx1691)
private def quad1537:Quadratic:=(quad1691 + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![0x2de2a95799a0,0,0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2389:Nat → Linear:=cons (-![0,0,3, -1]) ctx2390
private def quad2389:Quadratic:=quad2390
private def ctx2040:Nat → Linear:=cons ![0,1, -3,0] ctx2389
private def quad2040:Quadratic:=quad2389 + coefficientProduct ![-0x2de2a95799a0,0,0] ![0,1, -3,0] ![0,1, -3,0]
private def ctx2037:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx2040))
private def quad2037:Quadratic:=((quad2040))
private def ctx2384:Nat → Linear:=cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) ctx2389))))
private def quad2384:Quadratic:=((((quad2389)))) + coefficientProduct ![0x5543df729c000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2331:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] ctx2384)
private def quad2331:Quadratic:=(quad2384 + coefficientProduct ![0x2de2a95799a0,0,0] ![0,3, -1,0] ![0,3, -1,0])
private def data60:List Nat:=[
  0x18ce497b0adfdbde9cdf9dcfbfebad1b0d6801313000213faba8a90b9daabdbb6bff5dcabb5faeca0fef988e7d5801008000266e8aac2bdfb8ca7bf85c094cd97f6f7a0ebd3e4919c801707000275bce8dee8c9c7e29f9ba0fcbeeafcb6a5aeb78cde97fdc01107000269d6b4919bb789defbddfbd299c8d0bd97f5daf4acadaec008070002038defff9adc829fcaa7ecd7809c9d8b93f6c791efb4a8801706000207cad0e598ec8caadaff88a199ccf4d6c5f2acd6f9ffc8c011060002109aaa96908eb893ebe59ee5b9f1cfa8ddcfa595a0a68fc01701000206bfd9e1d2d6b49ddc8392b4fd97d0d18a95ec8a9fa5c6801e13ad9ad4eb83d480c8a58390e1c59b9ac0000b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e040102000203080310040a0400020302030113131311130911080908110709071101170009131313111309110809081107090711011700091313131113091108110709071101170008060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e04020202060310060d020a060104040603080200020202030107020102020203060804060018031a030502010200040306030a04000202020307080204000603060306040002020603050403060002030603,
  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,
  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,
  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,
  0x1c19097c4a1a59f8c959be5f3dcf3e5ab8bcaa0e9fdc19b92f58b9b98b2898ed3acef87c9b3a0130c02025a85e096c1e1dedd9f86fabed0e0f8eabc9fe180e4fc9ebce7adbceacdc2b9a886afd5ddcad8d6f3a6abbca7d7afa19b969ecfe5a80f0c020230a9b7ad8ad683a3b782cea1f59898b0b4f0e685cdbfa9e59ac9ba95afc9d4f7eca6b6f0e3c5c8fb9fab94f2838caea4f58eeea3ec090902022cca85a5f7acac9da1ef8db3aee5f4d4a6f5d5bedcf6be90ca84dc9ce08de8bd86fd828bd0d9e083cf8cc5aea6ccf9a6f4bfe0eccc13070202109f9c938dede6d29ff4f5e8c182e981dba78298e2948499e9dfa1ddbac1f7b2fb94a3b2a7bfcefb8dc2b7c4ddb9b998acdec2f3a6a01106020209f3d1bf8aeca484d3e3f7d99e91dcdcff91f4daa4d8b7fee6a5a19691f584b59d9d8de4dcb58deef994f1cd8ac08dbbb9b1ab83e490090602024df586d2c0a8a0a4c38fc796a3af83e8f9fcf5dfa481e0f8a5c3b7cce1cccbf5eaaac1c4b0d8af83b6d888d180eebaaac29b9999e0130102021fc0fd82a4a7e891adfad1f6ffa6e7ccb9c4a7c2fec0fde0dfb3b7e1c09aadafe3dfe084aaac97fad8eae5a9a2e2aa81a6e9a0e6d41101020201e0dfce83f0c9dbf7a5bda391dc88d280d2c3a585bfc3bbbcec8f9eb2e89b9abbe0928f9a9f849da682e6ad86d9d4eed0d5aed0dff4060102022beb8489ba8edf99a5e1ef,
  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,
  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,
  0x106041c031313110f170c0d04060404010f0006000100091313110f170c0d04060404010f000d000600091313110f170c0d04060404010f000d00060009061304020202020313131311170c0c0c07060d04060410010f0106010a13131311110f0c0c07060d04060410010f0106010a13131311110f0c0c07060d04060410010f0106010a060b02080201120030043603010d040a040904000e040e03011313110f110d170c1106110113000f000400091313110f110d170c1106110113000400081313110f110d170c11061101130007061310030202060313131311110f170c1106110507051301060105010a13131311170c1108110611050705130105010913131311110f170c11061105130107060b02080201120030043603011104080c010e031203100400020206030109f1b30e98f004c57d379ed44cc2ff0493fb0493fc007ceef4f0a1ed8486fee6a2d58001ef0d884aa5d04b8a8b3809ea339deb339dec0016f0fd9dc3c79a9897a9f1801313020247d0f491b285c9d1dff5a4ea9fe199889e8a1311020234bec6c3eda3c7abcef5a2fdab8da6e8f9e2170c020274c0a6d6f3c986d2d4ac9cdadbd8cdfbdc801107020224a4d2c0c0ed9f8da0a8e0f98ccd8ad786a80707020202c0c18a8989e794d4c0b3c182d797e8801706020202b2d8b8908bb3c4ab86d687b09382d6bb8e801106020202c4f08ad385b299,
  0x11313110f140d110d170c140c110904010000091313110f140d110d170c140c110904010000091313110f140d110d170c140c11090401000009061313110f170c0d04080404010d0002000000091313110f170c0d04080404010d0006000200091313110f170c0d040a0408040401060002000906010e020106020204111c0d140a0609]
private def node60:Certificate:=PackedParametricCertificateData.decode 17 data60
private def data82:List Nat:=[
  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]
private def node82:Certificate:=PackedParametricCertificateData.decode 9 data82
private def data137:List Nat:=[
  0x188afb1d499fb9fdca2c2faaaa0c01313010201b38b9dfdb48b8dbfa782d69ce0d290c1f4e8e0801311010201d7e7cfe38aa48796c382f0db90a8b88f94b9e080131001026cbed9fda886dcd7b4cdc9ca9a80aeedede2e0801110010204fb9282d69df5b2bcbbcaad81f484ddcda2dc80100901020addb4bee79dabe9c59c85b4c7bcc2a1c3dbb4800707010210f7bb9eb1b1ccf29ea9f1c9b0b3e6bec3a0ae801306010206af94c6fb9492d3f191d8e9f7fbeacddaf2e0800606010238919dcfa0e2c3b08382eb98b8d9aec5cb91d480040401020eb78ce6ca92bfedf88fb986b8bc8ddcfc9e9a801313000201b2bbb4f2b4fde2958badc5fdd18ec3f799f8fc801311000201d7958988bbddada39de4bbbdb5cdc6a4cfd6cc801310000267c0d69792ebaefbe881e2effeb3cd9e95b6b280111000022d998bf1c0b0c9eba0fafbd1dc82cf9fb983c6801009000205d6f9beb0b7a4ceaabb909e95f5e9eeaa8584801307000203c8ec9bb1bae489b79beec4a99088c2849fc080070700020d8fd5cbd980f6b7c8ffedc4ded1e3e2d5f7b680060600022ba6f6f3cbbdfc9289a89ee588dbb3e5b4f6d080040400020ad7c4e9deaee28aeea1f193b8b384c1dfa9c6801e01c48db0bec9c38fc4a2f7dff280000b020802011200300436030402030200020302031104080c010e0312031004000202060301010108020002020204,
  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,
  0x1000a1313110f130908080d02090213010501010102000a060c020b020406000604080312040302020203020400060202041313110f080813060f060d040d020501010102000a13131311110f080813060d0213010501010102000a1313110f130908080d02090213010501010102000a060c020b020206000c040e031204030202020303948c05a39f698c7ba307deec2eafb13faffa1d9f8d003cd6abe5a5b8f1bbf01313020237e48bd4f3fbd4e6d799d3fbc4c813110202388595edfbc9b094dd9495aef5e80808020209a9899c86ef8094e395c088b3e8130702020becfed785b4abfaa4e8e09988c0060602020cb9e8afb980d3cee6e2fbd0d0dc0605020206b1a491d3feddce8ee292e7fcc00f0402020e949dc6deaac2ac8ce2c5fdbd80070402020a828fea83a2f0f68a91e2e0eaa80404020208e7d4b1f9f6b5cff5e5b8e6f6e00501020204c1d2f9a2bba5e7bcb884fbfb8013130102398fc3a8acb9dadccfecc9f2fb881311010235d1e392f9b5c2ddb4c0a7fbf8a80808010209bedece92fddb9088bdd698a2f0130701020fc8a4a6f1dac99a819dc0d594b0060601020cf4c79b8ac1cbf7d6c3fa8ea1bc0505010211e18cbbe6abcca48f83d6ddfbe8130401020f9083ccb8919a94dc8cdb90c8b0080401023687b09bbdd396e4a0d9e1ce8007040102109ebfacf9dca0ef9fa996fbe2c80501010202b18ac3,
  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,
  0x11313110f100f0c0c0909100611011001040100000a1313110f100f0c0c090910060f041001040100000a1313110f100f09090907100610010401130000000a061313110f100f100d0909090710060401020000000a1313110f100f0909090710060f040401020000000a1313110f100f100d090710060f040401020000000a060113131311100f1006070607050f040804070302010a13131311100f1006070607050f040804070302010a1313110f100f1006070607050f040703060102010a060b02080201120030043603011104030202020313131311100f08071006070607050f04060102010a13131311100f08071006070607050f04060102010a1313110f100f08071006070607050f04060102010a060b020802011200300436030e0201060202030a0209020302000a040803010b0200020202040a02000202020413131311110f09070f060d02080101010c0008000a13131311110f09070f060d02080101010c0008000a13131311110f09070f060d02080101010c0008000a0613131311110f1109090707070d020c0108010101]
private def node137:Certificate:=PackedParametricCertificateData.decode 9 data137
private def node138:Certificate:=.split node82 node137
private def node139:Certificate:=.positive 1 [(1,1),(1,7)] node138
private def node140:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node139
private def node141:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node140
private def node142:Certificate:=.positive 1 [(1,0),(2,10)] node141
private def data193:List Nat:=[
  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,
  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]
private def node193:Certificate:=PackedParametricCertificateData.decode 13 data193
private def data246:List Nat:=[
  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,
  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]
private def node246:Certificate:=PackedParametricCertificateData.decode 12 data246
private def data297:List Nat:=[
  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,
  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]
private def node297:Certificate:=PackedParametricCertificateData.decode 12 data297
private def node298:Certificate:=.split node246 node297
private def node299:Certificate:=.split node193 node298
private def node300:Certificate:=.split node142 node299
private def node301:Certificate:=.positive 3 [(1,0),(2,6)] node300
private def data353:List Nat:=[
  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,
  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]
private def node353:Certificate:=PackedParametricCertificateData.decode 14 data353
private def data407:List Nat:=[
  0x10d0c0c130908080d0606060202130101010a060b0208020112003004360304020302000203020301010e060812030e0206041404010d300c020a1a06200430030802000202020413130f0f13090d080808080613010601020102000a13130f0f13090d080808080613010601020102000a13130f0f13090d080808080613010601020102000a0612020b06020c00120416031204030202020313130d0d0c0c130907070d0606060202130108010a13130d0d0c0c1309130707070d060606020208010a13130d0d0c0c1309130707070d060606020208010a060b02080201120030043603040203020002030203010f02080604040106040a0313130d0d0c0c130908080d0608060606130108010a13130d0d0c0c13090d08080813070d06060608010a13130d0d0c0c13090808130707070d06060608010a060b020802011200300436030402030200020302031104080c010e03120310040002020603010e0402020206030d040906010203060313130d0d0c0c130910080f070907100109000913130d0d0c0c130910080f070907100109000913130d0d0c0c130910080f0709071001090009060b020802011200300436030402030200020302031104080c010e031203100400020206030f04060c02120316030e0402020206030d0409060102030603010107020102020203080206020008030803070205020008030803,
  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]
private def node407:Certificate:=PackedParametricCertificateData.decode 13 data407
private def data457:List Nat:=[
  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,
  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]
private def node457:Certificate:=PackedParametricCertificateData.decode 12 data457
private def data508:List Nat:=[
  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,
  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]
private def node508:Certificate:=PackedParametricCertificateData.decode 12 data508
private def node509:Certificate:=.split node457 node508
private def node510:Certificate:=.split node407 node509
private def node511:Certificate:=.split node353 node510
private def data561:List Nat:=[
  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,
  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]
private def node561:Certificate:=PackedParametricCertificateData.decode 11 data561
private def data610:List Nat:=[
  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,
  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]
private def node610:Certificate:=PackedParametricCertificateData.decode 11 data610
private def node611:Certificate:=.split node561 node610
private def node612:Certificate:=.negative 1 [(3,2),(1,7)] node611
private def node613:Certificate:=.negative 2 [(1,0),(3,1),(2,6)] node612
private def node614:Certificate:=.negative 2 [(5,0),(1,2),(1,5)] node613
private def node615:Certificate:=.split node511 node614
private def node616:Certificate:=.split node301 node615
private def node617:Certificate:=.split node60 node616
private def node618:Certificate:=.positive 3 [(1,1),(8,4)] node617
private def node619:Certificate:=.positive 3 [(1,0),(2,3)] node618
private def data680:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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]
private def node680:Certificate:=PackedParametricCertificateData.decode 17 data680
private def data697:List Nat:=[
  0x113131111110f130c0c0c08080f070806060608010a13131111110f130c0c0c08080f070806060608010a13131111110f130c0c0c08080f070806060608010a060b020802011200300436030402030200020302031104080c010e031203100400020206030e060a0603020302030e0402020206030d04090601020306031313110f0c0c0f0910081307100709071001091313110f0c0c0f0910081307100709071001091313110f0c0c0f091008130710070907100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node697:Certificate:=PackedParametricCertificateData.decode 9 data697
private def data744:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  0x11313110f100d130c0909100613021001040100000a1313110f100d130c0909100613021001040100000a1313110f100d130c0909100613021001040100000a061313110f100d130c]
private def node744:Certificate:=PackedParametricCertificateData.decode 9 data744
private def node745:Certificate:=.split node697 node744
private def node746:Certificate:=.positive 1 [(1,1),(1,7)] node745
private def node747:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node746
private def node748:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node747
private def node749:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node748
private def node750:Certificate:=.positive 1 [(1,0),(2,1),(2,5)] node749
private def node751:Certificate:=.positive 3 [(1,0),(2,6)] node750
private def data773:List Nat:=[
  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]
private def node773:Certificate:=PackedParametricCertificateData.decode 9 data773
private def data828:List Nat:=[
  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,
  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,
  0x1aef49e84b6f00605020207cef49ea297bebbbfeee883d7adfd8780a2f8a2f5c5a2e3f880ba92caa9e38cf01102020228c7f5cadcfbb7cae29dfeefcec083ececef968194db98a4c88e8eb89dc7daa00601020210cdf1db9b908cd4cacbc4c3fa8bbaaa869dee8dc8bde9e485e6eec48cd8e080050102020195e6c2dae585b6decb93ebaeccbc8890d7c0cab2a5ffec95e18d8dbcf0c6c6f0010102021cbea69ec8a4d4d7c7d4c89ab4bdaec5d1d0d3f9d5c7b4b097fdf490b8d7a6901212010207f1ed95c1d0e490b3ce9589ac84b68ee4b3fbbc93c9ead0d7e8c1cfb8c9de86c21205010209f6c1b0e3b89b91aec5de8eda93a7b5b992f7f7d3fd85f0a087bef7b3df9ffedc1005010202eddfbfabf7b4a6cef3b9c4fa8ec6fbe9dc92d39cacf7e088c3e4c9e6fcafa2de060501020e8d99aac4f9acf7ce90a7b69b9ec292d193c1a880b1debaefafc4b9d68982f0a20d02010201b7a5d3c384c486cbb3c2ffecb4d9c983d1969bc3ece8c782d688f3b99ba796d80202010251bafaf0cb8398c3f0b6e3bcefb6b6bbb8cacda5c993cab4b0dcd8e2fa99aab01212000229fe89d4afc6aac3c78196d59fa1a38b98da9fdfa49dfedb938fea9b8f9fdac00d0d00020febf5d295ea988df28b9c9bc18fe595a58fdee8b8c1fda2e494dfd1eaf7a58012050002069aa6a5b69a89e682d5e4d0e5a3889eddaed2c88cfbb5bebceea1,
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private def node828:Certificate:=PackedParametricCertificateData.decode 9 data828
private def node829:Certificate:=.split node773 node828
private def node830:Certificate:=.positive 1 [(1,1),(1,7)] node829
private def node831:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node830
private def node832:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node831
private def node833:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node832
private def data887:List Nat:=[
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,
  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,
  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,
  0x1131312110d0d0c0c0e0912020c010b01080101010a131312110d0d0c0c0e0912020b010a01080101]
private def node887:Certificate:=PackedParametricCertificateData.decode 13 data887
private def data938:List Nat:=[
  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,
  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]
private def node938:Certificate:=PackedParametricCertificateData.decode 13 data938
private def node939:Certificate:=.split node887 node938
private def node940:Certificate:=.split node833 node939
private def data994:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  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]
private def node994:Certificate:=PackedParametricCertificateData.decode 13 data994
private def data1044:List Nat:=[
  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,
  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]
private def node1044:Certificate:=PackedParametricCertificateData.decode 12 data1044
private def data1093:List Nat:=[
  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,
  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]
private def node1093:Certificate:=PackedParametricCertificateData.decode 11 data1093
private def data1143:List Nat:=[
  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,
  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]
private def node1143:Certificate:=PackedParametricCertificateData.decode 11 data1143
private def node1144:Certificate:=.split node1093 node1143
private def node1145:Certificate:=.split node1044 node1144
private def node1146:Certificate:=.split node994 node1145
private def node1147:Certificate:=.negative 1 [(3,0),(2,4)] node1146
private def node1148:Certificate:=.split node940 node1147
private def node1149:Certificate:=.split node751 node1148
private def node1150:Certificate:=.split node680 node1149
private def node1151:Certificate:=.positive 1 [(1,0),(2,4)] node1150
private def data1211:List Nat:=[
  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,
  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,
  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,
  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,
  0x11313110f140d110d130c1109110104010000091313110f140d110d130c1108110104010000091313110f140d110d130c110811010401000009061313110f110d130c0d040804040102000000091313110f110d130c08041302110104010200091313110f110d130c080413021101040102000906010e020106020204111c0d140a060906041c031313110f110d130c11060804130104010600091313110f11]
private def node1211:Certificate:=PackedParametricCertificateData.decode 16 data1211
private def data1269:List Nat:=[
  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,
  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,
  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,
  0x11313100f110d0d090a090f0611010401040000000a1313100f110d0d090a090f0611010401040000000a1313100f110d0a0909090f061101]
private def node1269:Certificate:=PackedParametricCertificateData.decode 16 data1269
private def node1270:Certificate:=.split node1211 node1269
private def data1287:List Nat:=[
  0x113131111130c0c0c080613040f0411010e0108010a13131111130c0c0c080613040f0411010e0108010a131311110c0c080613040f0411010e01080101010a060b020802011200300436030402030200020302031104080c010e031203100400020206030d02080203020302030e0402020206030d04090601020306031313130c0c0c110810070f07090711011001091313130c0c0c110810070f07090711011001091313130c0c0c110810070f0709071101100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node1287:Certificate:=PackedParametricCertificateData.decode 9 data1287
private def data1334:List Nat:=[
  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,
  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,
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  0x11313110d11090e090a090f0611010701040100000a1313110d11090e090f06110107010401070000000a1313130f110d11090e090f0611010401070000000a061313110d11090e090a090f0611010701040100000a1313130f110d11090e090f0611010701040100000a1313130f110d11090e090f0611010701040100000a060113121111130f0f0f0f06070609030703060102010a13121111130f0f0f0f06070609031301060102010a13121111120f0f0f0f06070609031301060102010a060b0208020112003004360301110403020202031111130f120f10060f06070604040f02060102010a1111130f10060f06070604040f021301060102010a1111130f120f10060f06070604040f02060102010a060b020802011200300436030e]
private def node1334:Certificate:=PackedParametricCertificateData.decode 9 data1334
private def node1335:Certificate:=.split node1287 node1334
private def node1336:Certificate:=.positive 1 [(1,1),(1,7)] node1335
private def node1337:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1336
private def node1338:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1337
private def node1339:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1338
private def node1340:Certificate:=.positive 1 [(3,0),(2,4)] node1339
private def data1357:List Nat:=[
  0x111110f0d130c0f0c0908110608060f040f0208010a11110f0d130c0f0c0908110608060f0208010e000a11110f0d130c0f0c0908110608060f0208010e000a060b020802011200300436030402030200020302031104080c010e031203100400020206030d02080203020302030e0402020206030d040906010203060313130f0d130c110810070f07090711011001090f0d130c0f0c110810070f0709070f041001090f0d130c0f0c110810070f0709070f04100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node1357:Certificate:=PackedParametricCertificateData.decode 9 data1357
private def data1404:List Nat:=[
  0x10204bef9e1ddc5dbccfc85b6a8f2a40808020201c392a9f9f9bb80c68b848dc7b41106020212c5afd0b0a996c88e96def6e00606020201d0e7ac809ae4feb1a0d3a7a4841304020201a68484f7ffa4f1a8f3d8eac4e00f04020201c8cde7baa8a5ccb3b48babc69c0401020268bcd1adff83d0cefa8ae5ee940f0d010204b6b2c5ebcdeda28ad4fa958c0e0d010206c6f4cfc4e9f184f6d6ffc6a9c60e0c010205c6cfb6b8cd848e97d092cffdd00e09010212bcab94e184d4bafdd2afc6d41208010203cde6e9a8899bf2d888e6e7eca40808010201db849ca58a99a99bc7ebfe98f40606010201cee0a3a5c28eb7c28dbaa0f4fc1304010201bc9381f48eabc4f095cd8ed3fc0f04010201bfc3cba9bcc6edf8f4a2d09f880400010260d2f782b5bbed9d84e5aeaa9c0e0d000205ff82b7b1a78384dfd5fe9082de0e0c000205d0e5b097b4f4d298bba4b3aec80e0a000274e19edae686cfc3a5d5afdac81208000202d4ebb0f0aaaacd99b19bd0d8c40808000201f3a2e1ddd190f1b7e8b587b3940606000201c2ff96bcb09f9df2bab9f7c9fc1304000202f6acc9fee8f9ee9a93a88edcd80f0400021780a1dabdd5b2bacc9ae3e1d4040100025bf7f9aae8c0a4dcacd89484cc1e02f1fcee91bf82000b020802011200300436030402030200020302031104080c010e0312031004000202060301010108020002020204,
  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,
  0x13004360301010e0d0e0c060612050c050505060312020e0205020a1212120d0e0d0e0c050506030e0205020812120e0d12050d050505120206060b020802011200300436030404010600020304030f040a040006030603010b0200020202043edfae58a88c38a18a01cfa8c30138808d99deb19ddac0e9d7909f98fa909ad5d4c003e38902e2da0187bd0287f416d2a337a38438e8af1897d00010f8d0bff487ffbff289a38eeba7fed3c5fea68ac83cc3b34efbc734f1dd01c0b0c0499ef052e5ae30b18001ccb59d0019b4e4dbbc93fbf9c786f5fcdfa2f8f7c7f4b580121202020488f788d2d1e6abe6a7dff9a1c4e1ae8af79ed4d1a5def3cfba111102020dbef9e5dfa3a184a292d5f7abd5ddebd2cb8799be85cec4fe120d020201aa9cedeea08d8cddcabff4d9edf4a8e491fbcecdadf3cee6d40f0d02020981ababb9d1a3f49faac7fb98e49b82e7e0a4e8de85e2dbe80e0d02021ca9d9c0e6dbfd9accc1ebe4819ace84fe9cf4f5e298b4d3bae0120c020205a58c9bb999df85d3fff0cee2b0b8fec882f6c384d1b4a680cc06050202058182a29baccaf4fd9ea69ae8a1fe8d83a2bad096cdc9899fd0050502020f84bfcced95deaafef2e0b393efb99de383fce6efe7bce1c8f0120202021dd2a699acab839cc08bffe3f3a0e9c7e386b280e3cd81b1cd900e02020210aed2cdf4f7a2eccae9b1dabfe4e2fbfeff,
  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,
  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,
  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,
  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,
  0x1100d0f0d0f0c10060f060f02]
private def node1404:Certificate:=PackedParametricCertificateData.decode 9 data1404
private def node1405:Certificate:=.split node1357 node1404
private def node1406:Certificate:=.positive 1 [(1,1),(1,7)] node1405
private def node1407:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1406
private def node1408:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1407
private def node1409:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1408
private def data1434:List Nat:=[
  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]
private def node1434:Certificate:=PackedParametricCertificateData.decode 9 data1434
private def data1482:List Nat:=[
  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,
  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,
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private def node1482:Certificate:=PackedParametricCertificateData.decode 9 data1482
private def node1483:Certificate:=.split node1434 node1482
private def node1484:Certificate:=.positive 1 [(1,1),(1,7)] node1483
private def data1536:List Nat:=[
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private def node1536:Certificate:=PackedParametricCertificateData.decode 11 data1536
private def node1537:Certificate:=.split node1484 node1536
private def data1586:List Nat:=[
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,
  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,
  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]
private def node1586:Certificate:=PackedParametricCertificateData.decode 10 data1586
private def data1635:List Nat:=[
  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,
  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,
  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,
  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,
  0x115ed71c80289cd08d8c802829604fe9954cdbc18f3a10010c4a3aeeec8bbf190d2d39ce6fbf9adf3ac8007bffa10efd501a9d6900ea2de03b99307f4f256e0f911e2f70003aed2bd86b0b68ebdc18396e1bcdfecbbe98049f3c30195bdd411ad9614c82df2865d8f8b0acbf101d0810037c292cde690a594c2ecfda0d1b3be8abb8014130202068b82cdf1cefe95aa99b9b99c9aa0b2afbf9dfd87f1a8800c0c02027afbdaecf8a0e6cadfc981f0ad94d88c94e7e2be93a480110b020236949e88cfb397acca9ef98ccce9a29ac2a985bda1cd801409020222af8cd3f8a4dfe9e5b6c8fea184b88dd68f9dc8c1f9b0801109020201b3ddafeffd91bc8f9ff785bae0f38fe88390c9f084db800c08020209ac82bce2a7a989d7e58ccda4fc81ce9788859ccfe2a5a80908020238d3aba1aec3ddbe9bfebbc1a5eb9edfe189f781b0d6e2d8110102020591f4a5afbab18a99]
private def node1635:Certificate:=PackedParametricCertificateData.decode 10 data1635
private def node1636:Certificate:=.split node1586 node1635
private def node1637:Certificate:=.negative 1 [(1,0),(1,7)] node1636
private def node1638:Certificate:=.split node1537 node1637
private def data1690:List Nat:=[
  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,
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,
  0x17804cc0e94ef09f0b80493b70493b84cbb8e37a6d70007e3e2899acfb3d48e86a9d8cd80019694a00194cbf119d303e666b7eb66b7ec13cf018f002dc8d883caf9d1e6bd84e480121202020991a393bf889da287fda98192c3c0b2ea80140c0202138aadf89592f9a2c0d399ae9686f0fbc5e480]
private def node1690:Certificate:=PackedParametricCertificateData.decode 13 data1690
private def node1691:Certificate:=.split node1638 node1690
private def node1692:Certificate:=.split node1409 node1691
private def node1693:Certificate:=.split node1340 node1692
private def node1694:Certificate:=.negative 1 [(1,0),(3,2)] node1693
private def node1695:Certificate:=.split node1270 node1694
private def data1753:List Nat:=[
  0x1020df5c3d6f7cff6f2b9f980d2a8fc9f8ea9cabab1e6e8801b1fb68afcc9b38ef890b7d99194aca9e0000b02080201120030043603120403020202031104080c010e031203100400020206030b02000202020301131313110f0f11091107080706060605060111000a131313110f0f11091107080706060605110106010a131313110f0f110710070f0708070606060511010a060b020802011200300436030402030200020302031104080c010e031203100400020206030b0200020202030e040b0609020006040a03011313131111080f081607130708071606060616010a1313131111080f081607130708071606060616010a1313131111080f081607130708071606060616010a060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e04010200020308030f0c000202020301131313110f0f110c1608130809081607160109131313110f0f110c1608130809081607160109131313110f0f110c1608130809081607160109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030f2c0c020206011204120308020002020203010c0400020202030b1004060010031203090c01020002030803080c0608000a030e0307080204000603060306040002020603,
  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,
  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,
  0x113131311140d130c0f040d040a04040100000913131311140d130c0f040d040a04040100000913131311140d0f040d0408040401000008061313131113060d04080404010d000600020009131313111306]
private def node1753:Certificate:=PackedParametricCertificateData.decode 16 data1753
private def data1812:List Nat:=[
  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,
  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]
private def node1812:Certificate:=PackedParametricCertificateData.decode 15 data1812
private def data1870:List Nat:=[
  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,
  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]
private def node1870:Certificate:=PackedParametricCertificateData.decode 14 data1870
private def data1925:List Nat:=[
  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,
  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]
private def node1925:Certificate:=PackedParametricCertificateData.decode 11 data1925
private def data1979:List Nat:=[
  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,
  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]
private def node1979:Certificate:=PackedParametricCertificateData.decode 10 data1979
private def data2033:List Nat:=[
  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,
  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]
private def node2033:Certificate:=PackedParametricCertificateData.decode 10 data2033
private def node2034:Certificate:=.split node1979 node2033
private def node2035:Certificate:=.split node1925 node2034
private def node2036:Certificate:=.positive 3 [(1,4),(8,9)] node2035
private def node2037:Certificate:=.positive 9 [(5,3),(3,6),(22,8)] node2036
private def node2038:Certificate:=.split node1870 node2037
private def node2039:Certificate:=.split node1812 node2038
private def node2040:Certificate:=.split node1753 node2039
private def data2102:List Nat:=[
  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,
  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,
  0x1100d0f0d0f0c10060f060f0210010401070000000a100d0f0d0f0c10060f060f0210010401070000000a100d0f0d0f0c10080f060f0210010401070000000a0610]
private def node2102:Certificate:=PackedParametricCertificateData.decode 14 data2102
private def data2119:List Nat:=[
  0x111110d0d110c0c0c0808080606060c02020208010a131111110d0d110c0c0c080808060606110202020a131111110d0d110c0c0c0d06080606060c0208010a060b020802011200300436030402030200020302031104080c010e031203100400020206030c02050203020302030e0402020206030d04090601020306031311110c0c0c10080f0709070c021001090009131313110c0c10080f0709070c021001090009131313110c0c10080f0709070d060c02100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f04060c02120316030e0402020206030d040906010203060301]
private def node2119:Certificate:=PackedParametricCertificateData.decode 9 data2119
private def data2166:List Nat:=[
  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,
  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,
  0x1110f0c0c0a090f0607060c0204010d00]
private def node2166:Certificate:=PackedParametricCertificateData.decode 9 data2166
private def node2167:Certificate:=.split node2119 node2166
private def node2168:Certificate:=.positive 12 [(15,0),(1,5),(8,6)] node2167
private def data2193:List Nat:=[
  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]
private def node2193:Certificate:=PackedParametricCertificateData.decode 9 data2193
private def data2248:List Nat:=[
  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,
  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,
  0x1110f0c0c0a0a0f0607060c0204010d00040000000a110f0c0c0a0a0f0607060c0204010d00040000000a1313110f0c0c0a0a09060c0207010401040000000a06131313110c0c1107130607060c020701020000000a1311110f0c0c070613020c0207011300020000000a110f0c0c0a0a070613020c0207011300020000000a060113131308070713060c06090607041100020000000a13131308070713060c06090607041100020000000a13130f0f070713060c06090607041100020000000a060b0208020112003004360301110403020202031313110f0c0c08]
private def node2248:Certificate:=PackedParametricCertificateData.decode 9 data2248
private def node2249:Certificate:=.split node2193 node2248
private def data2274:List Nat:=[
  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]
private def node2274:Certificate:=PackedParametricCertificateData.decode 9 data2274
private def data2329:List Nat:=[
  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,
  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,
  0x11413130b090713020c020701070004000000091413130b090713020c020701070004000000091413130b090713020c0207010700040000000906130b0b09090713020202070111000200000009130b0b09090713020202070111000200000009130b0b090907130202020701110002]
private def node2329:Certificate:=PackedParametricCertificateData.decode 9 data2329
private def node2330:Certificate:=.split node2274 node2329
private def node2331:Certificate:=.split node2249 node2330
private def node2332:Certificate:=.split node2168 node2331
private def data2383:List Nat:=[
  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,
  0x1140f1308110809081107090708010701010109140f1308110809081107090708010701010109140f130811080908090708010701010108060a0201060012031404130811080908110709071301090101010000091308110809081107090713010901010100000913081108090811071301110109010101000009060a02040602020401080401040002030604070201060002030804060602080002030a04130811080908110709071301090101010000091308110809081107090713010901010100000913081108090811071301110109010101000009061308110809080907060601010f000a000900091308110809080907060601010f000a0009000913081108090809070606010113000f0009000906011204030202020308040104000203060407020402020204060603020206030804010d10090e04060310030802000202020415131511150911]
private def node2383:Certificate:=PackedParametricCertificateData.decode 12 data2383
private def node2384:Certificate:=.split node2332 node2383
private def node2385:Certificate:=.positive 8 [(5,4),(1,6),(24,8)] node2384
private def node2386:Certificate:=.split node2102 node2385
private def node2387:Certificate:=.negative 1 [(1,1),(1,2)] node2386
private def node2388:Certificate:=.negative 4 [(4,0),(3,1),(3,3)] node2387
private def node2389:Certificate:=.split node2040 node2388
private def node2390:Certificate:=.split node1695 node2389
private def node2391:Certificate:=.split node1151 node2390
private def node2392:Certificate:=.split node619 node2391
private def zz546:"s0222"="s0222":=by decide+kernel
private theorem valid142:check node142 ctx142 quad142 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid301:check node301 ctx301 quad301 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid142
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid511:check node511 ctx511 quad511 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid615:check node615 ctx615 quad615 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid511
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz547:"s0223"="s0223":=by decide+kernel
private theorem valid619:check node619 ctx619 quad619 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · exact valid301
        · exact valid615
private theorem valid750:check node750 ctx750 quad750 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid833:check node833 ctx833 quad833 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1147:check node1147 ctx1147 quad1147 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz548:"s0224"="s0224":=by decide+kernel
private theorem valid1148:check node1148 ctx1148 quad1148 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid833
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1147
private theorem valid1151:check node1151 ctx1151 quad1151 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid750
      · exact valid1148
private theorem valid1340:check node1340 ctx1340 quad1340 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1409:check node1409 ctx1409 quad1409 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz549:"s0225"="s0225":=by decide+kernel
private theorem valid1537:check node1537 ctx1537 quad1537 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1691:check node1691 ctx1691 quad1691 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid1537
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1694:check node1694 ctx1694 quad1694 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid1340
    · apply NatParametricCheckSteps.split_valid
      · exact valid1409
      · exact valid1691
private theorem valid2037:check node2037 ctx2037 quad2037 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz550:"s0226"="s0226":=by decide+kernel
private theorem valid2040:check node2040 ctx2040 quad2040 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2037
private theorem valid2331:check node2331 ctx2331 quad2331 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2384:check node2384 ctx2384 quad2384 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid2331
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2389:check node2389 ctx2389 quad2389 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2040
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid2384
private def zz551:"s0227"="s0227":=by decide+kernel
private theorem valid2390:check node2390 ctx2390 quad2390 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid1694
  · exact valid2389
private theorem valid2392:check node2392 ctx2392 quad2392 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid619
  · apply NatParametricCheckSteps.split_valid
    · exact valid1151
    · exact valid2390
theorem certificate_valid:check node2392 constraintsNat base hinges = true:=valid2392
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node2392 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase4
private def zz2180:"s0884"="s0884":=by decide+kernel
end 
section 
namespace Green24Proof.QuadNearBalanceCase5
open ParametricQuadraticCertificates hiding Certificate check check_sound
open NatParametricCertificates
open NatBacksubRecoveredQuadraticCertificates (cons)
open IntegerQuadraticCertificates (Linear Point linearEval combinationCheck)
def constraints:Fin 4 → Linear:=![![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1]]
def base:Quadratic:=![![![0x380da9dd80678, -0x221b262dd8000, -0x3328b944c4000,0x272784c5e33c], ![-0x221b262dd8000, -0x120fab7bccbbd0,0x40998df762514,0x10c399d674506], ![-0x3328b944c4000,0x40998df762514, -0xe0036e4b25230,0x22afe3b62248c], ![0x272784c5e33c,0x10c399d674506,0x22afe3b62248c, -0x110d9316ec000]], ![![0x18aa1b2200,0,0x51dac207a000, -0x2a96a9a4a280], ![0,0, -0x791eda6a9d80,0x51dac207a000], ![0x51dac207a000, -0x791eda6a9d80,0x18aa1b2200, -0xc550d9100], ![-0x2a96a9a4a280,0x51dac207a000, -0xc550d9100,0]], ![![-0x752b5c80fa0,0x2282d6c00,0x2cf9f59d370,0x37109fd8f40], ![0x2282d6c00,0x752b5c80fa0,0x21867f240, -0x483166e3c30], ![0x2cf9f59d370,0x21867f240,0,0x2282d6c00], ![0x37109fd8f40, -0x483166e3c30,0x2282d6c00,0]]]
def hinges:Hinges:=[(![0,0x62a86c880,0], ![0,0,1, -3]),(![-0x4a5ec425246, -0x1ed4a1ea80,0], ![0,0,1, -1]),(![0x4a5ec425246,0,0], ![0,0,3, -1]),(![0x95230bf7bd8,0,0], ![0,1, -3,0]),(![0x1393c262f19e,0,0], ![0,1,0, -3]),(![0x3d03e016d13c9,0, -0x752b5c80fa0], ![0,1,0, -1]),(![-0x110d9316ec000,0,0], ![0,3, -2, -1]),(![0x110d9316ec000,0,0], ![0,3, -2,1]),(![-0x95230bf7bd8,0,0], ![0,3, -1,0]),(![0x1143f85f3421,0,0], ![0,3,0, -1]),(![0x110d9316ec000,0,0], ![0,3,2, -1]),(![-0x4a5ec425246,0,0], ![1, -3,0,0]),(![-0x110d9316ec000,0,0], ![1, -2, -3,0]),(![0x110d9316ec000,0,0], ![1, -2,3,0]),(![0x4a5ec425246,0x1ed4a1ea80,0], ![1, -1,0,0]),(![-0x1143f85f3421,0,0], ![1,0, -3,0]),(![-0x3d03e016d13c9,0,0x752b5c80fa0], ![1,0, -1,0]),(![0x110d9316ec000,0,0], ![1,2, -3,0]),(![0, -0x62a86c880,0], ![3, -1,0,0]),(![-0x1393c262f19e,0,0], ![3,0, -1,0])]
def normalizationDenominator:ℤ:=0x221b262dd8000
noncomputable def slack (t:ℝ) (x:Point):ℝ :=
  (quadraticEval base t x + hingeEval hinges t x) / normalizationDenominator
def constraintsNat (i:Nat):Linear :=
  constraints ⟨i % 4,Nat.mod_lt _ (by decide)⟩
private def ctx2392:Nat → Linear:=constraintsNat
private def quad2392:Quadratic:=base
private def ctx619:Nat → Linear:=cons ![0,0,1, -3] ctx2392
private def quad619:Quadratic:=quad2392 + coefficientProduct ![0,0x62a86c880,0] ![0,0,1, -3] ![0,0,1, -3]
private def ctx301:Nat → Linear:=cons ![0,1,0, -3] (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx619)))
private def quad301:Quadratic:=(((quad619 + coefficientProduct ![-0x4a5ec425246, -0x1ed4a1ea80,0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x4a5ec425246,0,0] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x1393c262f19e,0,0] ![0,1,0, -3] ![0,1,0, -3]
private def ctx142:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx301)
private def quad142:Quadratic:=(quad301 + coefficientProduct ![0x3d03e016d13c9,0, -0x752b5c80fa0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx615:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] (cons ![0,0,1, -1] ctx619)))
private def quad615:Quadratic:=(((quad619 + coefficientProduct ![-0x4a5ec425246, -0x1ed4a1ea80,0] ![0,0,1, -1] ![0,0,1, -1]) + coefficientProduct ![0x4a5ec425246,0,0] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx511:Nat → Linear:=cons ![0,1,0, -1] ctx615
private def quad511:Quadratic:=quad615 + coefficientProduct ![0x3d03e016d13c9,0, -0x752b5c80fa0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1151:Nat → Linear:=cons ![0,0,1, -1] (cons (-![0,0,1, -3]) ctx2392)
private def quad1151:Quadratic:=(quad2392) + coefficientProduct ![-0x4a5ec425246, -0x1ed4a1ea80,0] ![0,0,1, -1] ![0,0,1, -1]
private def ctx750:Nat → Linear:=cons ![0,1,0, -1] (cons ![0,1,0, -3] (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx1151)))
private def quad750:Quadratic:=(((quad1151 + coefficientProduct ![0x4a5ec425246,0,0] ![0,0,3, -1] ![0,0,3, -1])) + coefficientProduct ![0x1393c262f19e,0,0] ![0,1,0, -3] ![0,1,0, -3]) + coefficientProduct ![0x3d03e016d13c9,0, -0x752b5c80fa0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1148:Nat → Linear:=cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx1151))
private def quad1148:Quadratic:=((quad1151 + coefficientProduct ![0x4a5ec425246,0,0] ![0,0,3, -1] ![0,0,3, -1]))
private def ctx833:Nat → Linear:=cons ![0,3, -2, -1] (cons ![0,1,0, -1] ctx1148)
private def quad833:Quadratic:=(quad1148 + coefficientProduct ![0x3d03e016d13c9,0, -0x752b5c80fa0] ![0,1,0, -1] ![0,1,0, -1]) + coefficientProduct ![-0x110d9316ec000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1147:Nat → Linear:=cons (-![0,1,0, -1]) ctx1148
private def quad1147:Quadratic:=quad1148
private def ctx2390:Nat → Linear:=cons (-![0,0,1, -1]) (cons (-![0,0,1, -3]) ctx2392)
private def quad2390:Quadratic:=(quad2392)
private def ctx1694:Nat → Linear:=cons (-![0,1, -3,0]) (cons ![0,0,3, -1] ctx2390)
private def quad1694:Quadratic:=(quad2390 + coefficientProduct ![0x4a5ec425246,0,0] ![0,0,3, -1] ![0,0,3, -1])
private def ctx1340:Nat → Linear:=cons ![0,1,0, -1] (cons (-![0,1,0, -3]) ctx1694)
private def quad1340:Quadratic:=(quad1694) + coefficientProduct ![0x3d03e016d13c9,0, -0x752b5c80fa0] ![0,1,0, -1] ![0,1,0, -1]
private def ctx1409:Nat → Linear:=cons ![0,3, -2, -1] (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1694))
private def quad1409:Quadratic:=((quad1694)) + coefficientProduct ![-0x110d9316ec000,0,0] ![0,3, -2, -1] ![0,3, -2, -1]
private def ctx1691:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx1694))
private def quad1691:Quadratic:=((quad1694))
private def ctx1537:Nat → Linear:=cons ![0,3, -1,0] (cons ![0,3, -2,1] ctx1691)
private def quad1537:Quadratic:=(quad1691 + coefficientProduct ![0x110d9316ec000,0,0] ![0,3, -2,1] ![0,3, -2,1]) + coefficientProduct ![-0x95230bf7bd8,0,0] ![0,3, -1,0] ![0,3, -1,0]
private def ctx2389:Nat → Linear:=cons (-![0,0,3, -1]) ctx2390
private def quad2389:Quadratic:=quad2390
private def ctx2040:Nat → Linear:=cons ![0,1, -3,0] ctx2389
private def quad2040:Quadratic:=quad2389 + coefficientProduct ![0x95230bf7bd8,0,0] ![0,1, -3,0] ![0,1, -3,0]
private def ctx2037:Nat → Linear:=cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) ctx2040))
private def quad2037:Quadratic:=((quad2040))
private def ctx2384:Nat → Linear:=cons ![0,3, -2,1] (cons (-![0,3, -2, -1]) (cons (-![0,1,0, -1]) (cons (-![0,1,0, -3]) (cons (-![0,1, -3,0]) ctx2389))))
private def quad2384:Quadratic:=((((quad2389)))) + coefficientProduct ![0x110d9316ec000,0,0] ![0,3, -2,1] ![0,3, -2,1]
private def ctx2331:Nat → Linear:=cons (-![0,3,0, -1]) (cons ![0,3, -1,0] ctx2384)
private def quad2331:Quadratic:=(quad2384 + coefficientProduct ![-0x95230bf7bd8,0,0] ![0,3, -1,0] ![0,3, -1,0])
private def data60:List Nat:=[
  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,
  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,
  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,
  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,
  0x1ada64cebe4800ac8f6f808b3dba102f79cf28043a99abd03f3ddd48f0286a7ffbe0008868cf98edec0ba979a85d5a29cc38385d28dd890e9efb1debd95c9e6c4a0a6be8acdfba8f807beb8dab5078f9a8ac001cefba6fa018ca188fd03bfc095da03e2dce88d5ccef3c3409ff6a80028eb8cec948da2c8ffebd6eaeda5d994f6b2c5e6bf86dcd98fa5e8cb93f6f898fa80cce2f019e99645b7ee018babb345f9860db2e322e4db46d2cc23cdf9000bb5c89eccd2d8d8c885a1998786b088e89ab5f1d1dbc58ee7e3939ff3e49d92fac9e6a4f9dc8cd03387e52397971494e50da3a24ad2ee49a1c4239cea14e2a900058dd6dcc1c5e9edc5ae91b0e3f4d4dcfe8f9cc18080d69993dcafa7a4a9af99edf19fbee5cab7901713020262efd3c6f8aef383c6fad78ad4e8ffaba697b7c5a5c388bbf0a6b2acd489ca81928a959395a8efc6b6a7f6b3ec170f020201e79ab2a8d99cbb9bc598ce8c978dcdf5ec95c6e5d59ce2dea895ccd8b2a691c3b9bc93b0a4e1cef7b3fac4c6cc110702021688f980e484d9f0d1a1fad7a8beded8a9daff86b5eec3ffbaede6d1f88ecc888a8ff9b5c0b887ee99fc9284b40907020203cacdc2e1ff85babbbbf0a494da88d8b19f84edfab792edb08edbdc8db6f6a1bf89d781d9eda497a3d3b59dc00706020209c5bbcce5e5cbdfcdc2ca87dddacf83b9ef8cf9f1858aa596ea9383daa9b982,
  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,
  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,
  0x11313110f140d110d170c140c110904010000091313110f140d110d170c140c110904010000091313110f140d110d170c140c11090401000009061313110f170c0d04080404010d0002000000091313110f170c0d04080404010d0006000200091313110f170c0d040a0408040401060002000906010e020106020204111c0d140a060906041c031313110f170c0d040604]
private def node60:Certificate:=PackedParametricCertificateData.decode 17 data60
private def data82:List Nat:=[
  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]
private def node82:Certificate:=PackedParametricCertificateData.decode 9 data82
private def data137:List Nat:=[
  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,
  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,
  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,
  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,
  0x11313110f100f0c0c0909100611011001040100000a1313110f100f0909090710060f041001040100000a1313110f100f09090907100610010401130000000a061313110f100f100d0909090710060401020000000a1313110f100f100d090710060f040401020000000a1313110f100f100d090710060f040401020000000a060113131311100f1006070607050f040804070302010a13131311100f1006070607050f040804070302010a1313110f100f1006070607050f040703060102010a060b02080201120030043603011104030202020313131311100f08071006070607050f04]
private def node137:Certificate:=PackedParametricCertificateData.decode 9 data137
private def node138:Certificate:=.split node82 node137
private def node139:Certificate:=.positive 1 [(1,1),(1,7)] node138
private def node140:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node139
private def node141:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node140
private def node142:Certificate:=.positive 1 [(1,0),(2,10)] node141
private def data193:List Nat:=[
  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,
  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]
private def node193:Certificate:=PackedParametricCertificateData.decode 13 data193
private def data246:List Nat:=[
  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,
  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]
private def node246:Certificate:=PackedParametricCertificateData.decode 12 data246
private def data297:List Nat:=[
  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,
  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]
private def node297:Certificate:=PackedParametricCertificateData.decode 12 data297
private def node298:Certificate:=.split node246 node297
private def node299:Certificate:=.split node193 node298
private def node300:Certificate:=.split node142 node299
private def node301:Certificate:=.positive 3 [(1,0),(2,6)] node300
private def data353:List Nat:=[
  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,
  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]
private def node353:Certificate:=PackedParametricCertificateData.decode 14 data353
private def data407:List Nat:=[
  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,
  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]
private def node407:Certificate:=PackedParametricCertificateData.decode 13 data407
private def data457:List Nat:=[
  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,
  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]
private def node457:Certificate:=PackedParametricCertificateData.decode 12 data457
private def data508:List Nat:=[
  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,
  0x10f0f0f0d130a110a14060f020a0201010800090f0d0f0c130a110a14060f020a0201010800090f0d0f0c130a110a0a0714060a020101080009060a02010600120314040f0f0f0d130a110a0a020802060101010800090f0d130a110a130808020d01060101010800090f0d130a110a130808020d0106010101080009060a0204060202040108040104000203060407020106000203080408060706020e00080416040f0f0f0d130a110a0a020802060101010800090f0d130a110a130808020d01060101010800090f0d130a110a130808020d0106010101080009060f0f0f0d130a08070707080201010d000c000b000a0f0f0f0d130a130807070804080201010b0001000a0f0f0f0d130a130808070707080201010b0001000a06011204030202020308040104000203060407020402020204060603020206030804010d1c091406060506041c03080200020202040f0d0f0c130a110a0f020a020c0108010101090f0d0f0c130a110a0f020a020c0108010101090f0d0f0c130a110a0f020a]
private def node508:Certificate:=PackedParametricCertificateData.decode 12 data508
private def node509:Certificate:=.split node457 node508
private def node510:Certificate:=.split node407 node509
private def node511:Certificate:=.split node353 node510
private def data561:List Nat:=[
  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,
  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]
private def node561:Certificate:=PackedParametricCertificateData.decode 11 data561
private def data610:List Nat:=[
  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,
  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]
private def node610:Certificate:=PackedParametricCertificateData.decode 11 data610
private def node611:Certificate:=.split node561 node610
private def node612:Certificate:=.negative 1 [(3,2),(1,7)] node611
private def node613:Certificate:=.negative 2 [(1,0),(3,1),(2,6)] node612
private def node614:Certificate:=.negative 2 [(5,0),(1,2),(1,5)] node613
private def node615:Certificate:=.split node511 node614
private def node616:Certificate:=.split node301 node615
private def node617:Certificate:=.split node60 node616
private def node618:Certificate:=.positive 3 [(1,1),(8,4)] node617
private def node619:Certificate:=.positive 3 [(1,0),(2,3)] node618
private def data680:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  0x11313110f140d110d130c1109110104010000091313110f140d110d130c1108110104010000091313110f140d110d130c110811010401000009061313110f110d130c0d040804040102000000091313110f110d130c08041302110104010200091313110f110d130c080413021101040102000906010e020106020204111c0d140a060906041c031313110f110d130c11060804130104010600091313110f110d130c110608041301]
private def node680:Certificate:=PackedParametricCertificateData.decode 17 data680
private def data697:List Nat:=[
  0x113131111110f130c0c0c08080f070806060608010a13131111110f130c0c0c08080f070806060608010a13131111110f130c0c0c08080f070806060608010a060b020802011200300436030402030200020302031104080c010e031203100400020206030e060a0603020302030e0402020206030d04090601020306031313110f0c0c0f0910081307100709071001091313110f0c0c0f0910081307100709071001091313110f0c0c0f091008130710070907100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node697:Certificate:=PackedParametricCertificateData.decode 9 data697
private def data744:List Nat:=[
  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,
  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,
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,
  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,
  0x11313110f100d130c0909100613021001040100000a1313110f100d130c0909100613021001040100000a1313110f100d130c0909100613021001040100000a061313110f100d130c0909090710060401020000000a1313110f100d130c0907]
private def node744:Certificate:=PackedParametricCertificateData.decode 9 data744
private def node745:Certificate:=.split node697 node744
private def node746:Certificate:=.positive 1 [(1,1),(1,7)] node745
private def node747:Certificate:=.positive 13 [(12,0),(3,4),(4,6)] node746
private def node748:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node747
private def node749:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node748
private def node750:Certificate:=.positive 1 [(1,0),(2,1),(2,5)] node749
private def node751:Certificate:=.positive 3 [(1,0),(2,6)] node750
private def data773:List Nat:=[
  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]
private def node773:Certificate:=PackedParametricCertificateData.decode 9 data773
private def data828:List Nat:=[
  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,
  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,
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private def node828:Certificate:=PackedParametricCertificateData.decode 9 data828
private def node829:Certificate:=.split node773 node828
private def node830:Certificate:=.positive 1 [(1,1),(1,7)] node829
private def node831:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node830
private def node832:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node831
private def node833:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node832
private def data887:List Nat:=[
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]
private def node887:Certificate:=PackedParametricCertificateData.decode 13 data887
private def data938:List Nat:=[
  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,
  0x1130d130c0c0b12090e090c0901010b000a0008000a130d0c0b110a11090e090c09080101010b000a000a130d130c0c0b12090e090c0901010b000a0008000a060c020b0201060018041a04130d0c0b12090e090c090d01060101010b0008000a130d0c0b11090e090c090d01060101010b0008000a130d130c0c0b12090e090c090d010601010108000a06130d130c0e090c0908070905070501010d000c000a130d130c0e090c0908070905070501010d000c000a130d130c0e090c0908070905070501010d000c000a0601010a0209020102000404060409020802010c0002040e0408060706020e0008041604130d130c0e090c0908080e0705010c00010000000a130d130c0c0908080e07130105010c00050000000a130d130c0c0908080e07130105010c00050000000a060a020406020203120403020202030a02090201020004040604130f130d0c0b0e090c09070306030d000c0006000a130f130d0c0b0e090c09070306030d00]
private def node938:Certificate:=PackedParametricCertificateData.decode 13 data938
private def node939:Certificate:=.split node887 node938
private def node940:Certificate:=.split node833 node939
private def data994:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  0x19aa5f48bc8e3ceb9bceba3e8090000026993bd9eb9898ecf8cdaa4f190b00000000207a8fdd38dd0b4ddf0e5dbbfb4901e05c5fed8f485aeb80007b9c310c4ec18c5b50fba8e0103c6bb8c90fba4d2def0c0f3f5e280c8e2ecafbd9bca83d9cfe8efb4c8e7eadea28caea2b28033f68c62a3ca32bbb601c8d58b011cbee6c68db6b089b6e09bf994ddc1e5fd95afdcabfbbd9398a08b8f81cd9be4e4fbe9f031ff01f58802c0910186b00aec9114cd841ee9cd1588dc0004d19ce7d791f7eed380d49aa1f7cab4e8eceef5b8808cedaabd8093b3bb9f9e98cceef48ba003ded005b2ab02f1ed622ac4d53bce9823c3b634ccf70052d59899f88797d3c78eeabee1cad391bdd7beabd58a8be0ee87b7f79cc6d882ede18ec6a823dbb957c2e00184ea8350d3be0ad4ac2bf6c953aaac32888d0010c5e0f7e7aee9b5a0afa7b4b9cef7faa6cec4f39fd79dffc3c1d4d1cadde389e1fa80a8f80cf28c0ba2f03089e513d8ba36d0a216d59a02b5824fdabd0058a0ce91b4bb8e89ffb4cdea9482d2baa4dfd8a8bfb2b0fae3f2d8cc9084feb3e9f9cde830c5e2018296e62ed0a801d6c0932bbcdb53fabb2bc29101aaf9aa000cdddbb0f7d2f998c5b3d880a692b4d8c0f0b8efef8dea9aa0a591ffbda3cb9dc1d5a6c0120e02026a81f6e1b3d9c5f6a8a0a3ded6eaa0a9b3a186decea183e8c4e18bdbc39cdac7a59da2f998b593,
  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,
  0x11211130c0c0c0d06060612020c010b01080101010a1313121111110d0d0c0c06060a010901080101010a1313121111110d0d0c0c06060a010901080101010a0611020c02000603]
private def node994:Certificate:=PackedParametricCertificateData.decode 13 data994
private def data1044:List Nat:=[
  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,
  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]
private def node1044:Certificate:=PackedParametricCertificateData.decode 12 data1044
private def data1093:List Nat:=[
  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,
  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]
private def node1093:Certificate:=PackedParametricCertificateData.decode 11 data1093
private def data1143:List Nat:=[
  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,
  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]
private def node1143:Certificate:=PackedParametricCertificateData.decode 11 data1143
private def node1144:Certificate:=.split node1093 node1143
private def node1145:Certificate:=.split node1044 node1144
private def node1146:Certificate:=.split node994 node1145
private def node1147:Certificate:=.negative 1 [(3,0),(2,4)] node1146
private def node1148:Certificate:=.split node940 node1147
private def node1149:Certificate:=.split node751 node1148
private def node1150:Certificate:=.split node680 node1149
private def node1151:Certificate:=.positive 1 [(1,0),(2,4)] node1150
private def data1211:List Nat:=[
  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,
  0x1c0070702024a8ba5d2f9d1e582a2d1a3a685bfaea999b9a3a78084d80f06020201e4b9f98e8787d4c6928cb1e0b88efd80c1be8bddd7ba90060602020596fa8beee2d7f6d4ce87c98da18286b5db8bd3b8fecba41204020205f4b1c0b0cbb2efc3a4bbc3b3c69d9da6cdbe8da1f3b3800404020238b68dfddff380fed9b2d1bed4d39ae5ffe5cfb3a8a5f412020202129ef2e7dbd7b5b4cababaa6c7dcdbcbcb90ed9bcadeeaf0131201026cf28fd29bd6f7b29c9dd2afa4e5d189e3fadbdeb8f18eb81310010202a1f0ef95bfa594f7e5d4fbbbc0cff790c4adf7e9bee7a8110f010209fee691b7b2aa808cddccabccf5f1daf6bdf996a7c2d6b80707010202a0dcf7a1e4a683f99ed5a694f79fcebcfeb7c1d4d596b80f06010201aadeeca9d4d3d6dea9b485f5b0b4b382a3c6d1b8d8c7f00606010207fdffda8aeadbbb9ff7c995f3bfba86c7f297f5ea8bb8f41204010217d8bea2c099c0f9a2c9c2ae9fc5dc90f3ddf1f3e4ac8aac0404010238ccf897f3f2a6f4b6a6bafcf0e8dcb6d0d4ad9db8ee841200010202bc9caff5e7babb8681e2f0bc9eb09aa7cbf584fd92b28c1312000269b5b1a5efcccbccc399faa3a88ff8eaebe28ec2d2b39fe01210000214bfa6dcf0c8c2b7c6f1edc5a48ce5a3d6a7b8948384a3a0110f0002059df7ccaaf191f283a2b4c396dce3f4f39bcd82fd90c3800f0f000201e4bda6c49a,
  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,
  0x1f7900a85c20a85c10020cc8dd4dee0e69484b4f2c99dd1818003e58a03b18c04d78203fec50edacb0be3a342a0f642a0f5000bd28d8cfae1ee9184d78484e7afb7c03fb236b80194f7d60195f8bd10840c8065d1cb65d1cc006198a1bac297d6f3a1c7aeccea82c0131302020cccc1e89adc9289e79cb9878ae6e1ede0e3ee86f480131202021df695becfa8e2c4c599bb9d8ceb858e9f9df4a98480110f02020ac89ad5bcf9faafb4a081cc8d9da89bf3bbfcb0f3c0110702020dcae3dbaee9b3f8d1d897e6a6f3f083dd80b68199c0130602021ddaaed7aad2e9c9a3e8f4fcb4cf84edcee7d39cc28811060202359faddee6a289ce9de3c8d7d18de583a3f6a3db9eb80706020204eeeabbc8bd9bdabef3a8fac2c7a8fda49791800601020218f7daa1e5b2fb9dec9beedffbf5e69ca891bc801200020207cfdcc88db2998d96eec4dbade7babed8edd5fde9e01313010211afcfb0ebbaefdae89da8b1b6add3caccc9d4f88ac21312010209a9b1ab81d9d387fba7bc81bba8d4d6a8dbd4e8ba9011110102238cf0f8b883a480aceafa9abfa8fe86fbc4cfe7a49e110f010206bb9ed1adb1e0ae93d0b0838ba8c69daadd9fa9fbe0130601021bf7f69fb0b5a295edcca3aee3dcae88f78982e1b6cc1106010248ab9ca7efe49ee1fabc88efca93d4d8efb3f1828dd40505010210ca8382f0cc9aa0d6cb87d89b83b08f999a,
  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]
private def node1211:Certificate:=PackedParametricCertificateData.decode 16 data1211
private def data1269:List Nat:=[
  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,
  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,
  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]
private def node1269:Certificate:=PackedParametricCertificateData.decode 16 data1269
private def node1270:Certificate:=.split node1211 node1269
private def data1287:List Nat:=[
  0x113131111130c0908080613040f0411010e0108010a13131111130c0c0c080613040f0411010e0108010a131311110c0c0d0908060f0411010e01080101010a060b020802011200300436030402030200020302031104080c010e031203100400020206030d02080203020302030e0402020206030d04090601020306031313130c0c0c110810070f07090711011001091313130c0c0c110810070f07090711011001091313130c0c0c110810070f0709071101100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node1287:Certificate:=PackedParametricCertificateData.decode 9 data1287
private def data1334:List Nat:=[
  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,
  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,
  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,
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  0x1a196dee8e0d4dcfddaa5a01212010203edcd95c396b0e089baf2ffeecae0c7fee4cbd4c6e2e4a4a4f394ff96a00d0301020786deecb988c0df80e897c9f3bbd5cd9bfccc96dfecffccc887edb9a00e0201026adaa5ffa2c2dbfd85ecf280e894c0d69e9ebdafbbcffce59b91c5efd80d02010201a2cd96eccce9d4e794fdb189c9d8de9bbab391abdcfdc3c4bbf2b9f5d8020001026fd9899585c28f95b8e6e6bd848a93aaf3a584aceaae8dd1f1a2a0c81212000202c080dee7eab88f91f1dacffcc6c0bf84fd99e5caa79faeb884b684b680120500023df0bcd0d4c9f3c4c4d58cb7b3cbb9b3a1befc9bbdab9ac88bd8addc900d03000201bde9bbc58585befce5dabcfa90b5decea4c5e1c7c7c2fadbaab094e80e02000201a2e6a5d5c3fea2f0a0968bf9cecfb3f4a982a9f88af3f7f0dae089d0f80d0200020195f3e5c2a49aacae8fdcbe9cb5b8b5c4859a8c9684fac7c9f7edd4d4b01905c8b5a5e9d4c39e8ba58ea5a98bd29fedd0cddeccb3f00011020c020006030603011313131211110e0913020c0213010801010107000a1313131211110e0913020c0213010101070000000a1313131211110e0913020c0213010101070000000a06131313121111060613020c0202021301070101010a1313131211110d0d0c02020213010801070101010a1313131211110d0d0e090c0202021301070101010a06011697e4,
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  0x11313110d11090e090a090f0611010701040100000a1313130f110d11090e090f0611010401070000000a1313130f110d11090e090f0611010401070000000a061313110d11090e090a090f0611010701040100000a1313130f110d11090e090f0611010701040100000a1313130f110d11090e090f0611010701040100000a060113121111130f0f0f0f06070609030703060102010a13121111120f0f0f0f06070609031301060102010a13121111120f0f0f0f06070609031301060102010a060b0208020112003004360301110403020202031111130f120f10060f06070604040f02060102010a1111130f10060f06070604040f030f02130106010a1111130f120f10060f06070604040f02060102010a060b020802011200300436030e0201060202030a0209020302000a040803010b0200020202040a0200020202041313131211110f0d0d040d0213010701010108000a1313131211110f0d0d070d0213010701010108000a1313131211110f0d0d040d0213010701010108000a061313131211110f0d0d040d0213010801070101010a1313131211110e090d070d0213010801070101010a1313131211110e090d040d0213010801070101010a06013eeecb3e8fe55499eb01d1989e0104a9dd89fc99eff4d4958189d4]
private def node1334:Certificate:=PackedParametricCertificateData.decode 9 data1334
private def node1335:Certificate:=.split node1287 node1334
private def node1336:Certificate:=.positive 1 [(1,1),(1,7)] node1335
private def node1337:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1336
private def node1338:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1337
private def node1339:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1338
private def node1340:Certificate:=.positive 1 [(3,0),(2,4)] node1339
private def data1357:List Nat:=[
  0x111110f0d130c0f0c0908110608060f040f0208010a11110f0d130c0f0c0908110608060f040f0208010a11110f0d130c0f0c0908110608060f0208010e000a060b020802011200300436030402030200020302031104080c010e031203100400020206030d02080203020302030e0402020206030d040906010203060313130f0d130c110810070f07090711011001090f0d130c0f0c110810070f0709070f041001090f0d130c0f0c110810070f0709070f04100109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030d040906010203060301]
private def node1357:Certificate:=PackedParametricCertificateData.decode 9 data1357
private def data1404:List Nat:=[
  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,
  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,
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,
  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,
  0x1ea9b8f4190c540c7e93cfe9301bed6c4001ab0a4b1e8fecdf6b4c3aee0a9cf88c1a5841312020206a6d4efd8e4fcb0e59ca8f7d8d4c7b1d2efedf196a2b5b0121202024dbfd7e5e9ddc5b7aaebcfb4de80f6f88dffe7a0df8ad7f00e0d02025d99cbc3c8acb8c4abd486ae8cb7df8d85b7adf2bbfefeb40e0c02024e82cff4cbc3c096ada2aaa0a68597fc9ac0d29c85afb81205020223f2f6fdb1f2ffc5d3f997d6a98bf7cb8bbade9a8fa1cee0050502020ed78796f3c788eaa8b8c199b2a3a6d5a6829bd29ba3ce980d0302020ec4b3a0e58af7ddc09daadeebffb2ecf9dda08de399f5fc0d0202020a9095cbff9d8b9cb38cfa92bee4cbb39f93bf80b8db83d4010102020bf8fa84f8cf9df5e6a984b2d0db9cf5dfc3e6aaffaaa81212010257cc81f1acb7edbfc88a88dbe0d6dcb29ec185c5f3daeba8130d010201d2befd9ca0b0a6b0f0bde0ebd19cf581d2e790f9c9bf92120d010219f49dd4f4b481cfaeb2cfa2d2ce8afcede3d3b883b1d5e20e0d01023c9380a5c2cfea95d2b49997d49deacfeda3cefd86a9dab20e0c0102058ef1bef388d6dcc5efe89cffd7c8c2d6ae96d7d88fd8d6120501021de09b82f6acd4c587e5c9d39b8feeebbb8ee59ae0a097f80d0201021988dfbcdab8a9c0abc2c2a9b3cec4a5f888d2a9a0f4fbc80200010258f5b19bbdeca7f3b6bcb9b3d195b487a399b7d5df88121200025b,
  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,
  0x1100d0f0d0f0c10060f060f0210010401070000000a]
private def node1404:Certificate:=PackedParametricCertificateData.decode 9 data1404
private def node1405:Certificate:=.split node1357 node1404
private def node1406:Certificate:=.positive 1 [(1,1),(1,7)] node1405
private def node1407:Certificate:=.positive 2 [(1,0),(1,2),(1,6)] node1406
private def node1408:Certificate:=.positive 3 [(2,0),(1,1),(1,5)] node1407
private def node1409:Certificate:=.positive 4 [(4,0),(1,4),(3,6)] node1408
private def data1434:List Nat:=[
  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]
private def node1434:Certificate:=PackedParametricCertificateData.decode 9 data1434
private def data1482:List Nat:=[
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,
  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]
private def node1482:Certificate:=PackedParametricCertificateData.decode 9 data1482
private def node1483:Certificate:=.split node1434 node1482
private def node1484:Certificate:=.positive 1 [(1,1),(1,7)] node1483
private def data1536:List Nat:=[
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,
  0x13ef536c40789c703e3f820d6b74498c625a08104d6bf0007f4b9ff8191c5efb080130c0202329fecb48b80ebafc0cf9fefd7800c0c020245a1ffbda6c6cfde83bdcbf7cca00a0a020220dbf099ca95dee0edc39efeaba009090202389fc2af8390dbd7d695a1cc93c00808020259a4a0f1d2be8994b0efa2e786c40b0702023d98e9b99e86e4f99d928a80df800c010202278bbaafe1e6ffb5d8b982d180800b01020203e7d8a5fea18b91a9d599d9e08b800801020207988393c6e3bdd9ac80ffa6b0d6a80101020206c7c6ca82c8dd9f95eca8d4edd4a4130c010225]
private def node1536:Certificate:=PackedParametricCertificateData.decode 11 data1536
private def node1537:Certificate:=.split node1484 node1536
private def data1586:List Nat:=[
  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,
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private def node1586:Certificate:=PackedParametricCertificateData.decode 10 data1586
private def data1635:List Nat:=[
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  0x1cae0140902026bb1cb91a8abefd3aa9686cfb0b4fef1fd80110902020381d8ddecebb5e091b2e191858acba4b3e00c080202138cadc3a7dc99ebcbdacb87abbcb1c5f2e80908020201858f8cd996f3a7a2b181fbb695ade9f4d3981101020206b98d84aef8f0efbb83f1fcdbdbb7d88d80080102020582b6d5c1bcfe83d3ad8cc6a3abb4c891f20101020216dbc09bfab6cef59cb8c0f4a486aba680da1413010208ff80c4ceabbcf7a3f3ccaf8ab99d93f5c0140c01020efcc1f3f9ce93b7caf3e4f5c1d0adc99e800c0c010201beb1c38396a5feafcde5abe89493fee280110b010279c5db94c0fab0e4b7b59efe90ec9da9a0140901026ac5cdb6daa6ec8ef2a7a49de6c0b2a5ecc0110901020398d1e8c3a7b2f1d0f9fdf38497c5e497c00c080102139698f59680f5cca9d4948deee7b1b5e780090801027fc7ac87eab49f92c1c0ad86f9a2c3c2d3e01101010204ff99b78abd86bfd5a8a0c4ea84bb94bfe00101010216cd9eecd5beebb7ebf1e7c5b6e29ce2f8801413000205deb293d3e9b0d2c097fbf5b2dbada3d680140c000229928ca6f7a4ce859bc3fdade78fa6b58a80110b000274f7dcca87ed8adfa9a0a680a38afec180140900026dba8bbcc88d98dad7ac90fbc09fa7a0a6801109000203ccb2b5a5ffcab9f5e2f5ee9f95d3e0a7800c08000212bad2f5c3de8994c99dfe99c4d9dce68b800908000279,
  0x147e901c4b403a8c40a82e20296a605a3c151a99e1bd2dd0034c5e3ecb9939a8cba93a0eca01483dd2ad4be03d3cd16a0ed2ed8965eeab102d8890ac5a2007be6ba96ef9cbae39bb8a6e0141302020aeafcfb9b9797eaef8cccb5938290b6c0800c0c020202b4b8f2ae989b8191a9aeac898991d586e0110b02027b9c958981c7dda5e6e3b98ec0e2f7]
private def node1635:Certificate:=PackedParametricCertificateData.decode 10 data1635
private def node1636:Certificate:=.split node1586 node1635
private def node1637:Certificate:=.negative 1 [(1,0),(1,7)] node1636
private def node1638:Certificate:=.split node1537 node1637
private def data1690:List Nat:=[
  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,
  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,
  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,
  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,
  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,
  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,
  0x15a04e40ceedd06dff8048f93048f944cd9ba34dc870005a6de99ccc2c19980c4f2e0800195e6c60194d8a53fd40d67cdf767cdf84af501b500268c9883fbad9daac49e80121202020592e4dbfff09cdf88b98785d5c3bdd2c0140c02020e8cac91d9ffbaa39ef7eded9af78baf8f80120a02020ee0a8d39b8aa9a3859c8894cf83c080090902020d88d1e9a4fdcde396f8f9ba99c5a0800c0802020cccf3da82a7849ba2c486c0e48c8396bec80908020201b29fec958d918e8581cbebc88c9dccb6b81406020203caaa989093fed0889199]
private def node1690:Certificate:=PackedParametricCertificateData.decode 13 data1690
private def node1691:Certificate:=.split node1638 node1690
private def node1692:Certificate:=.split node1409 node1691
private def node1693:Certificate:=.split node1340 node1692
private def node1694:Certificate:=.negative 1 [(1,0),(3,2)] node1693
private def node1695:Certificate:=.split node1270 node1694
private def data1753:List Nat:=[
  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,
  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,
  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]
private def node1753:Certificate:=PackedParametricCertificateData.decode 16 data1753
private def data1812:List Nat:=[
  0x10607060502110106010a130f110f0f0c080716060f0607060605050211010a130f110f0f0c080716060f0607060502110106010a060b02080201120030043603120403020202031104080c010e031203100400020206030b020002020203011311130f110c0f0c11090808080706060f0206010a1311130f110c11090808080706060f02060111000a1311130f110c11090808080706060f02060111000a060b020802011200300436030402030200020302031104080c010e031203100400020206030b0200020202030a02000202020301130f110f110810080f07080707060f02060116000a130f110f110810080f07080707060f04060116000a130f110f110810080f07080707060f02060116000a060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e04010200020308030f0c0002020203011311130f0f0f110c1608090816070f071601091311130f0f0f110c1608090816070f071601091311130f0f0f110c1608090816070f07160109060b020802011200300436030402030200020302031104080c010e031203100400020206030f08080607060212041a030e0402020206030f2408020206011004100308020002020203010c0400020202030b0403060004030603090c01020002030803080c0608000a030e03070802040006030603,
  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]
private def node1812:Certificate:=PackedParametricCertificateData.decode 15 data1812
private def data1870:List Nat:=[
  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,
  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]
private def node1870:Certificate:=PackedParametricCertificateData.decode 14 data1870
private def data1925:List Nat:=[
  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,
  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]
private def node1925:Certificate:=PackedParametricCertificateData.decode 11 data1925
private def data1979:List Nat:=[
  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,
  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]
private def node1979:Certificate:=PackedParametricCertificateData.decode 10 data1979
private def data2033:List Nat:=[
  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,
  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]
private def node2033:Certificate:=PackedParametricCertificateData.decode 10 data2033
private def node2034:Certificate:=.split node1979 node2033
private def node2035:Certificate:=.split node1925 node2034
private def node2036:Certificate:=.positive 3 [(1,4),(8,9)] node2035
private def node2037:Certificate:=.positive 9 [(5,3),(3,6),(22,8)] node2036
private def node2038:Certificate:=.split node1870 node2037
private def node2039:Certificate:=.split node1812 node2038
private def node2040:Certificate:=.split node1753 node2039
private def data2102:List Nat:=[
  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,
  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,
  0x1100d0f0d0f0c10060f060f0210010401070000000a100d0f0d0f0c10060f060f0210010401070000000a100d0f0d0f0c10080f060f0210010401070000000a0610]
private def node2102:Certificate:=PackedParametricCertificateData.decode 14 data2102
private def data2119:List Nat:=[
  0x111110d0d110c0c0c0808080606060c02020208010a131111110d0d110c0c0c080808060606110202020a131111110d0d110c0c0c0d06080606060c0208010a060b020802011200300436030402030200020302031104080c010e031203100400020206030c02050203020302030e0402020206030d04090601020306031311110c0c0c10080f0709070c021001090009131313110c0c10080f0709070c021001090009131313110c0c10080f0709070c021001090009060b020802011200300436030402030200020302031104080c010e031203100400020206030f04060c02120316030e0402020206030d040906010203060301]
private def node2119:Certificate:=PackedParametricCertificateData.decode 9 data2119
private def data2166:List Nat:=[
  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,
  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,
  0x1110f0c0c0a090f0607060c0204010d00]
private def node2166:Certificate:=PackedParametricCertificateData.decode 9 data2166
private def node2167:Certificate:=.split node2119 node2166
private def node2168:Certificate:=.positive 12 [(15,0),(1,5),(8,6)] node2167
private def data2193:List Nat:=[
  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]
private def node2193:Certificate:=PackedParametricCertificateData.decode 9 data2193
private def data2248:List Nat:=[
  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,
  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,
  0x1110f0c0c0f0607060c02100104010d00040000000a110f0c0c0a0a0f0607060c0204010d00040000000a110f0c0c0a0a09060c02100104010d00040000000a061311130c0c0c1109130607060c020701020000000a1311130c0c0c1306070613020c020701020000000a110f0c0c0a0a070613020c0207011300020000000a060113131308070713060c06090607041100020000000a13131308070713060c06090607041100020000000a13131308070713060c06090607041100020000000a060b0208020112003004360301110403020202031313110f0c0c08]
private def node2248:Certificate:=PackedParametricCertificateData.decode 9 data2248
private def node2249:Certificate:=.split node2193 node2248
private def data2274:List Nat:=[
  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]
private def node2274:Certificate:=PackedParametricCertificateData.decode 9 data2274
private def data2329:List Nat:=[
  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,
  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,
  0x11413130b090713020c020701070004000000091413130b090713020c020701070004000000091413130b090713020c0207010700040000000906130b0b09090713020202070111000200000009130b0b09090713020202070111000200000009130b0b090907130202020701110002]
private def node2329:Certificate:=PackedParametricCertificateData.decode 9 data2329
private def node2330:Certificate:=.split node2274 node2329
private def node2331:Certificate:=.split node2249 node2330
private def node2332:Certificate:=.split node2168 node2331
private def data2383:List Nat:=[
  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,
  0x1140f1308110809081107090708010701010109140f1308110809081107090708010701010109140f130811080908090708010701010108060a0201060012031404130811080908110709071301090101010000091308110809081107130111010901010100000913081108090811071301110109010101000009060a02040602020401080401040002030604070201060002030804060602080002030a041308110809081107090713010901010100000913081108090811071301110109010101000009130811080908110713011101090101010000090613081108090809070606010113000f0009000913081108090809070606010113000f0009000913081108090809070606010113000f0009000906011204030202020308040104000203060407020402020204060603020206030804010d10090e04060310030802000202020415131511150911]
private def node2383:Certificate:=PackedParametricCertificateData.decode 12 data2383
private def node2384:Certificate:=.split node2332 node2383
private def node2385:Certificate:=.positive 8 [(5,4),(1,6),(24,8)] node2384
private def node2386:Certificate:=.split node2102 node2385
private def node2387:Certificate:=.negative 1 [(1,1),(1,2)] node2386
private def node2388:Certificate:=.negative 4 [(4,0),(3,1),(3,3)] node2387
private def node2389:Certificate:=.split node2040 node2388
private def node2390:Certificate:=.split node1695 node2389
private def node2391:Certificate:=.split node1151 node2390
private def node2392:Certificate:=.split node619 node2391
private def zz552:"s0228"="s0228":=by decide+kernel
private theorem valid142:check node142 ctx142 quad142 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid301:check node301 ctx301 quad301 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid142
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid511:check node511 ctx511 quad511 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid615:check node615 ctx615 quad615 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid511
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.negative_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz553:"s0229"="s0229":=by decide+kernel
private theorem valid619:check node619 ctx619 quad619 (hinges.drop 1) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · exact valid301
        · exact valid615
private theorem valid750:check node750 ctx750 quad750 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid833:check node833 ctx833 quad833 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1147:check node1147 ctx1147 quad1147 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz554:"s022a"="s022a":=by decide+kernel
private theorem valid1148:check node1148 ctx1148 quad1148 (hinges.drop 5) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid833
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
  · exact valid1147
private theorem valid1151:check node1151 ctx1151 quad1151 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · exact valid750
      · exact valid1148
private theorem valid1340:check node1340 ctx1340 quad1340 (hinges.drop 6) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · apply NatParametricCheckSteps.split_valid
            · first | exact ParametricTupleCheck.K | decide+kernel
            · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1409:check node1409 ctx1409 quad1409 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.positive_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.split_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · first | exact ParametricTupleCheck.K | decide+kernel
private def zz555:"s022b"="s022b":=by decide+kernel
private theorem valid1537:check node1537 ctx1537 quad1537 (hinges.drop 9) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1691:check node1691 ctx1691 quad1691 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · exact valid1537
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid1694:check node1694 ctx1694 quad1694 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.negative_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · exact valid1340
    · apply NatParametricCheckSteps.split_valid
      · exact valid1409
      · exact valid1691
private theorem valid2037:check node2037 ctx2037 quad2037 (hinges.drop 7) = true:=by
  apply NatParametricCheckSteps.positive_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.positive_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
private def zz556:"s022c"="s022c":=by decide+kernel
private theorem valid2040:check node2040 ctx2040 quad2040 (hinges.drop 4) = true:=by
  apply NatParametricCheckSteps.split_valid
  · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · exact valid2037
private theorem valid2331:check node2331 ctx2331 quad2331 (hinges.drop 10) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
  · apply NatParametricCheckSteps.split_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2384:check node2384 ctx2384 quad2384 (hinges.drop 8) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.positive_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid2331
  · first | exact ParametricTupleCheck.K | decide+kernel
private theorem valid2389:check node2389 ctx2389 quad2389 (hinges.drop 3) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid2040
  · apply NatParametricCheckSteps.negative_valid
    · first | exact ParametricTupleCheck.K | decide+kernel
    · apply NatParametricCheckSteps.negative_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · apply NatParametricCheckSteps.split_valid
        · first | exact ParametricTupleCheck.K | decide+kernel
        · apply NatParametricCheckSteps.positive_valid
          · first | exact ParametricTupleCheck.K | decide+kernel
          · exact valid2384
private def zz557:"s022d"="s022d":=by decide+kernel
private theorem valid2390:check node2390 ctx2390 quad2390 (hinges.drop 2) = true:=by
  apply NatParametricCheckSteps.split_valid
  · apply NatParametricCheckSteps.split_valid
    · apply NatParametricCheckSteps.split_valid
      · first | exact ParametricTupleCheck.K | decide+kernel
      · first | exact ParametricTupleCheck.K | decide+kernel
    · exact valid1694
  · exact valid2389
private theorem valid2392:check node2392 ctx2392 quad2392 (hinges.drop 0) = true:=by
  apply NatParametricCheckSteps.split_valid
  · exact valid619
  · apply NatParametricCheckSteps.split_valid
    · exact valid1151
    · exact valid2390
theorem certificate_valid:check node2392 constraintsNat base hinges = true:=valid2392
theorem nonnegative (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (hx:∀ i,0 ≤ x i):0 ≤ slack t x:=by
  unfold slack
  apply div_nonneg
  · apply check_sound node2392 constraintsNat base hinges t x ht0 ht1 _ certificate_valid
    intro i
    have hC (j:Fin 4):0 ≤ linearEval (constraints j) x:=by
      fin_cases j <;> simpa [constraints,linearEval,Fin.sum_univ_succ] using hx _
    exact hC ⟨i % 4,Nat.mod_lt _ (by decide)⟩
  · norm_num [normalizationDenominator]
end Green24Proof.QuadNearBalanceCase5
private def zz2181:"s0885"="s0885":=by decide+kernel
end 
section 
namespace Green24Proof.NearBalanceVerified
open ExpressionCertificates
open ParametricQuadraticInterop
open NearBalanceParameterRows
open ParityPhaseRows (Phase)
open IntegerQuadraticCertificates (Point)
def quad0Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad0Degree0Target,NearBalanceCertificate.quad0Degree1Target,NearBalanceCertificate.quad0Degree2Target]
private def zz558:"s022e"="s022e":=by decide+kernel
theorem quad0_identity (d:Fin 3):normalEqual (quad0Normals d)
    (componentNormal QuadNearBalanceCase0.base QuadNearBalanceCase0.hinges QuadNearBalanceCase0.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
theorem quad0_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad0Polynomial t x = QuadNearBalanceCase0.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad0_identity 0)
  have h1:=normalEqual_sound _ _ x (quad0_identity 1)
  have h2:=normalEqual_sound _ _ x (quad0_identity 2)
  change normalEval NearBalanceCertificate.quad0Degree0Target x + t * normalEval NearBalanceCertificate.quad0Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad0Degree2Target x = _
  change normalEval NearBalanceCertificate.quad0Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad0Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad0Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase0.base QuadNearBalanceCase0.hinges QuadNearBalanceCase0.normalizationDenominator t x
theorem quad0_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 0 0 false) t x:=by
  rw [NearBalanceCertificate.quad0_eval,quad0_slack_eq]
  exact QuadNearBalanceCase0.nonnegative t x ht0 ht1 hx
def quad1Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad1Degree0Target,NearBalanceCertificate.quad1Degree1Target,NearBalanceCertificate.quad1Degree2Target]
theorem quad1_identity (d:Fin 3):normalEqual (quad1Normals d)
    (componentNormal QuadNearBalanceCase1.base QuadNearBalanceCase1.hinges QuadNearBalanceCase1.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
private def zz559:"s022f"="s022f":=by decide+kernel
theorem quad1_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad1Polynomial t x = QuadNearBalanceCase1.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad1_identity 0)
  have h1:=normalEqual_sound _ _ x (quad1_identity 1)
  have h2:=normalEqual_sound _ _ x (quad1_identity 2)
  change normalEval NearBalanceCertificate.quad1Degree0Target x + t * normalEval NearBalanceCertificate.quad1Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad1Degree2Target x = _
  change normalEval NearBalanceCertificate.quad1Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad1Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad1Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase1.base QuadNearBalanceCase1.hinges QuadNearBalanceCase1.normalizationDenominator t x
theorem quad1_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 0 0 true) t x:=by
  rw [NearBalanceCertificate.quad1_eval,quad1_slack_eq]
  exact QuadNearBalanceCase1.nonnegative t x ht0 ht1 hx
def quad2Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad2Degree0Target,NearBalanceCertificate.quad2Degree1Target,NearBalanceCertificate.quad2Degree2Target]
theorem quad2_identity (d:Fin 3):normalEqual (quad2Normals d)
    (componentNormal QuadNearBalanceCase2.base QuadNearBalanceCase2.hinges QuadNearBalanceCase2.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
theorem quad2_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad2Polynomial t x = QuadNearBalanceCase2.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad2_identity 0)
  have h1:=normalEqual_sound _ _ x (quad2_identity 1)
  have h2:=normalEqual_sound _ _ x (quad2_identity 2)
  change normalEval NearBalanceCertificate.quad2Degree0Target x + t * normalEval NearBalanceCertificate.quad2Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad2Degree2Target x = _
  change normalEval NearBalanceCertificate.quad2Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad2Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad2Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase2.base QuadNearBalanceCase2.hinges QuadNearBalanceCase2.normalizationDenominator t x
private def zz560:"s0230"="s0230":=by decide+kernel
theorem quad2_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 0 1 false) t x:=by
  rw [NearBalanceCertificate.quad2_eval,quad2_slack_eq]
  exact QuadNearBalanceCase2.nonnegative t x ht0 ht1 hx
def quad3Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad3Degree0Target,NearBalanceCertificate.quad3Degree1Target,NearBalanceCertificate.quad3Degree2Target]
theorem quad3_identity (d:Fin 3):normalEqual (quad3Normals d)
    (componentNormal QuadNearBalanceCase3.base QuadNearBalanceCase3.hinges QuadNearBalanceCase3.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
theorem quad3_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad3Polynomial t x = QuadNearBalanceCase3.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad3_identity 0)
  have h1:=normalEqual_sound _ _ x (quad3_identity 1)
  have h2:=normalEqual_sound _ _ x (quad3_identity 2)
  change normalEval NearBalanceCertificate.quad3Degree0Target x + t * normalEval NearBalanceCertificate.quad3Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad3Degree2Target x = _
  change normalEval NearBalanceCertificate.quad3Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad3Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad3Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase3.base QuadNearBalanceCase3.hinges QuadNearBalanceCase3.normalizationDenominator t x
theorem quad3_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 0 1 true) t x:=by
  rw [NearBalanceCertificate.quad3_eval,quad3_slack_eq]
  exact QuadNearBalanceCase3.nonnegative t x ht0 ht1 hx
def quad4Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad4Degree0Target,NearBalanceCertificate.quad4Degree1Target,NearBalanceCertificate.quad4Degree2Target]
private def zz561:"s0231"="s0231":=by decide+kernel
theorem quad4_identity (d:Fin 3):normalEqual (quad4Normals d)
    (componentNormal QuadNearBalanceCase4.base QuadNearBalanceCase4.hinges QuadNearBalanceCase4.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
theorem quad4_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad4Polynomial t x = QuadNearBalanceCase4.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad4_identity 0)
  have h1:=normalEqual_sound _ _ x (quad4_identity 1)
  have h2:=normalEqual_sound _ _ x (quad4_identity 2)
  change normalEval NearBalanceCertificate.quad4Degree0Target x + t * normalEval NearBalanceCertificate.quad4Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad4Degree2Target x = _
  change normalEval NearBalanceCertificate.quad4Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad4Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad4Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase4.base QuadNearBalanceCase4.hinges QuadNearBalanceCase4.normalizationDenominator t x
theorem quad4_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 1 1 false) t x:=by
  rw [NearBalanceCertificate.quad4_eval,quad4_slack_eq]
  exact QuadNearBalanceCase4.nonnegative t x ht0 ht1 hx
def quad5Normals:Fin 3 → NormalForm:=![NearBalanceCertificate.quad5Degree0Target,NearBalanceCertificate.quad5Degree1Target,NearBalanceCertificate.quad5Degree2Target]
theorem quad5_identity (d:Fin 3):normalEqual (quad5Normals d)
    (componentNormal QuadNearBalanceCase5.base QuadNearBalanceCase5.hinges QuadNearBalanceCase5.normalizationDenominator d) = true:=by
  fin_cases d <;> decide +kernel
private def zz562:"s0232"="s0232":=by decide+kernel
theorem quad5_slack_eq (t:ℝ) (x:Point) :
    NearBalanceCertificate.quad5Polynomial t x = QuadNearBalanceCase5.slack t x:=by
  have h0:=normalEqual_sound _ _ x (quad5_identity 0)
  have h1:=normalEqual_sound _ _ x (quad5_identity 1)
  have h2:=normalEqual_sound _ _ x (quad5_identity 2)
  change normalEval NearBalanceCertificate.quad5Degree0Target x + t * normalEval NearBalanceCertificate.quad5Degree1Target x + t ^ 2 * normalEval NearBalanceCertificate.quad5Degree2Target x = _
  change normalEval NearBalanceCertificate.quad5Degree0Target x = _ at h0
  change normalEval NearBalanceCertificate.quad5Degree1Target x = _ at h1
  change normalEval NearBalanceCertificate.quad5Degree2Target x = _ at h2
  rw [h0,h1,h2]
  exact componentNormal_eval QuadNearBalanceCase5.base QuadNearBalanceCase5.hinges QuadNearBalanceCase5.normalizationDenominator t x
theorem quad5_nonneg (t:ℝ) (x:Point) (ht0:0 ≤ t) (ht1:t ≤ 1) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d 1 1 true) t x:=by
  rw [NearBalanceCertificate.quad5_eval,quad5_slack_eq]
  exact QuadNearBalanceCase5.nonnegative t x ht0 ht1 hx
theorem quad_nonneg_sorted (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (t:ℝ) (ht0:0 ≤ t) (ht1:t ≤ 1) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d p q same) t x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg t x ht0 ht1 hx
  · exact quad1_nonneg t x ht0 ht1 hx
  · exact quad2_nonneg t x ht0 ht1 hx
  · exact quad3_nonneg t x ht0 ht1 hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad4_nonneg t x ht0 ht1 hx
  · exact quad5_nonneg t x ht0 ht1 hx
theorem quad_nonneg (p q:Phase) (same:Bool) (t:ℝ) (ht0:0 ≤ t) (ht1:t ≤ 1)
    (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ parameterEval (fun d => quadComponent NearBalanceCertificate.rows d p q same) t x:=by
  rcases le_total p.val q.val with h | h
  · exact quad_nonneg_sorted p q h same t ht0 ht1 x hx
  · rw [← parameterQuad_reverse NearBalanceCertificate.rows p q same t x]
    exact quad_nonneg_sorted q p h same t ht0 ht1 (FullPhaseSymmetry.reversePoint x)
      (FullPhaseSymmetry.reversePoint_nonneg x hx)
private def zz563:"s0233"="s0233":=by decide+kernel
theorem parameter_bound {m:ℕ} [NeZero m] (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    NearBalanceHypothesis (mass u) (mass v) (deficit u) (deficit (interleave u v)) :=
  NearBalanceCertificate.parameter_bound_of_quad_rows h3 h5 quad_nonneg u v hu hv
theorem coercivity_to_eleven_fifths {m:ℕ} [NeZero m]
    (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) (hd:0 ≤ deficit u)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ (11 / 5:ℝ) * mass v) :
    (1 / 0x12c:ℝ) * (mass u - mass v) ^ 2 ≤ deficit (interleave u v) :=
  ParityCover.coercivity_to_eleven_fifths_of_near_balance h3 h5 u v hu hv hd horder hhigh
    (parameter_bound h3 h5 u v hu hv)
theorem interval_to_three {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 3 * mass v) :
    0 ≤ deficit (interleave u v) :=
  ParityCover.interval_to_three_of_near_balance h4 h3 h5 h2 u v hu hv ih horder hhigh
    (parameter_bound h3 h5 u v hu hv)
end Green24Proof.NearBalanceVerified
private def zz2182:"s0886"="s0886":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullFourPairs
def compact_fullFour_pair_20_base:CompactPair.Quadratic:=⟨(-3 / 0x1dcd65000),(0xea71 / 0x165a0bc00),0⟩
def compact_fullFour_pair_20_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(1 / 0x1dcd65000),2, -1⟩]
noncomputable def fullFour_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_20_base compact_fullFour_pair_20_hinges x y
def compact_fullFour_pair_20_cuts:List ℚ:=[(1 / 2),2]
theorem compact_fullFour_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_20_base compact_fullFour_pair_20_hinges 0 compact_fullFour_pair_20_cuts = true :=
  by decide +kernel
private def zz564:"s0234"="s0234":=by decide+kernel
theorem compact_fullFour_pair_20_representation (x y:ℝ) :
    fullFour_pair_20 x y = CompactPair.expressionEval compact_fullFour_pair_20_base compact_fullFour_pair_20_hinges x y:=by rfl
theorem fullFour_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_20 x y:=by
  rw [compact_fullFour_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_20_check hy (by simpa using hx)
def compact_fullFour_pair_21_base:CompactPair.Quadratic:=⟨(-1 / 0x23c34600),(0x2eed / 0xb2d05e00),0⟩
def compact_fullFour_pair_21_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(-1 / 0xee6b2800),1, -2⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(-1 / 0x2cb417800),3, -2⟩,⟨(1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFour_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_21_base compact_fullFour_pair_21_hinges x y
def compact_fullFour_pair_21_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFour_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_21_base compact_fullFour_pair_21_hinges 0 compact_fullFour_pair_21_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_21_representation (x y:ℝ) :
    fullFour_pair_21 x y = CompactPair.expressionEval compact_fullFour_pair_21_base compact_fullFour_pair_21_hinges x y:=by rfl
private def zz565:"s0235"="s0235":=by decide+kernel
theorem fullFour_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_21 x y:=by
  rw [compact_fullFour_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_21_check hy (by simpa using hx)
def compact_fullFour_pair_22_base:CompactPair.Quadratic:=⟨0,(0x14821 / 0x165a0bc00),0⟩
def compact_fullFour_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullFour_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_22_base compact_fullFour_pair_22_hinges x y
def compact_fullFour_pair_22_cuts:List ℚ:=[]
theorem compact_fullFour_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_22_base compact_fullFour_pair_22_hinges 0 compact_fullFour_pair_22_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_22_representation (x y:ℝ) :
    fullFour_pair_22 x y = CompactPair.expressionEval compact_fullFour_pair_22_base compact_fullFour_pair_22_hinges x y:=by rfl
theorem fullFour_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_22 x y:=by
  rw [compact_fullFour_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_22_check hy (by simpa using hx)
def compact_fullFour_pair_23_base:CompactPair.Quadratic:=⟨(-0x234810eb / 0x5f5e1000),(0xee36595 / 0x47868c00),0⟩
def compact_fullFour_pair_23_hinges:List CompactPair.Hinge:=[⟨(1 / 0x77359400),1, -3⟩,⟨(-0x821a399 / 0x1dcd65000),1, -2⟩,⟨(0x149a3b1 / 0x77359400),2, -3⟩,⟨(0x37bacb6b / 0xee6b2800),2, -1⟩,⟨(-0x7d4a0d7 / 0x77359400),3, -2⟩]
noncomputable def fullFour_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_23_base compact_fullFour_pair_23_hinges x y
def compact_fullFour_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2,3]
private def zz566:"s0236"="s0236":=by decide+kernel
theorem compact_fullFour_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_23_base compact_fullFour_pair_23_hinges 0 compact_fullFour_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_23_representation (x y:ℝ) :
    fullFour_pair_23 x y = CompactPair.expressionEval compact_fullFour_pair_23_base compact_fullFour_pair_23_hinges x y:=by rfl
theorem fullFour_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_23 x y:=by
  rw [compact_fullFour_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_23_check hy (by simpa using hx)
def compact_fullFour_pair_24_base:CompactPair.Quadratic:=⟨(3 / 0x77359400),(0xea67 / 0x165a0bc00),0⟩
def compact_fullFour_pair_24_hinges:List CompactPair.Hinge:=[⟨(0x7373c6f / 0x165a0bc00),1, -3⟩,⟨(-0x4c90c73 / 0x2faf0800),1, -2⟩,⟨(0x3db23b / 0x8f0d180),2, -3⟩,⟨(-0x13335ed5 / 0x77359400),2, -1⟩,⟨(0x4882aff / 0x8f0d1800),3, -2⟩,⟨(0xd2c3611 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFour_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_24_base compact_fullFour_pair_24_hinges x y
def compact_fullFour_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFour_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_24_base compact_fullFour_pair_24_hinges 0 compact_fullFour_pair_24_cuts = true :=
  by decide +kernel
private def zz567:"s0237"="s0237":=by decide+kernel
theorem compact_fullFour_pair_24_representation (x y:ℝ) :
    fullFour_pair_24 x y = CompactPair.expressionEval compact_fullFour_pair_24_base compact_fullFour_pair_24_hinges x y:=by rfl
theorem fullFour_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_24 x y:=by
  rw [compact_fullFour_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_24_check hy (by simpa using hx)
def compact_fullFour_pair_25_base:CompactPair.Quadratic:=⟨(-11 / 0x11e1a3000),(0x2eeb / 0xb2d05e00),0⟩
def compact_fullFour_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0xb2d05e00),1, -3⟩,⟨(1 / 0xee6b2800),1, -2⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullFour_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_25_base compact_fullFour_pair_25_hinges x y
def compact_fullFour_pair_25_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFour_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_25_base compact_fullFour_pair_25_hinges 0 compact_fullFour_pair_25_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_25_representation (x y:ℝ) :
    fullFour_pair_25 x y = CompactPair.expressionEval compact_fullFour_pair_25_base compact_fullFour_pair_25_hinges x y:=by rfl
private def zz568:"s0238"="s0238":=by decide+kernel
theorem fullFour_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_25 x y:=by
  rw [compact_fullFour_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_25_check hy (by simpa using hx)
def compact_fullFour_pair_26_base:CompactPair.Quadratic:=⟨0,(0x1481f / 0x165a0bc00),0⟩
def compact_fullFour_pair_26_hinges:List CompactPair.Hinge:=[]
noncomputable def fullFour_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_26_base compact_fullFour_pair_26_hinges x y
def compact_fullFour_pair_26_cuts:List ℚ:=[]
theorem compact_fullFour_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_26_base compact_fullFour_pair_26_hinges 0 compact_fullFour_pair_26_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_26_representation (x y:ℝ) :
    fullFour_pair_26 x y = CompactPair.expressionEval compact_fullFour_pair_26_base compact_fullFour_pair_26_hinges x y:=by rfl
theorem fullFour_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_26 x y:=by
  rw [compact_fullFour_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_26_check hy (by simpa using hx)
def compact_fullFour_pair_27_base:CompactPair.Quadratic:=⟨(-0x4928d7369 / 0x2cb417800),(0xea1d05c1 / 0x165a0bc00),0⟩
def compact_fullFour_pair_27_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(-0x9c12dc2d / 0x1dcd65000),2, -1⟩,⟨(0x750e2523 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFour_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_27_base compact_fullFour_pair_27_hinges x y
def compact_fullFour_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),3]
private def zz569:"s0239"="s0239":=by decide+kernel
theorem compact_fullFour_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_27_base compact_fullFour_pair_27_hinges 0 compact_fullFour_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_27_representation (x y:ℝ) :
    fullFour_pair_27 x y = CompactPair.expressionEval compact_fullFour_pair_27_base compact_fullFour_pair_27_hinges x y:=by rfl
theorem fullFour_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_27 x y:=by
  rw [compact_fullFour_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_27_check hy (by simpa using hx)
def compact_fullFour_pair_28_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0xda9637b / 0x11e1a300),(-49 / 50)⟩
def compact_fullFour_pair_28_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_28_base compact_fullFour_pair_28_hinges x y
def compact_fullFour_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFour_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_28_base compact_fullFour_pair_28_hinges 0 compact_fullFour_pair_28_cuts = true :=
  by decide +kernel
private def zz570:"s023a"="s023a":=by decide+kernel
theorem compact_fullFour_pair_28_representation (x y:ℝ) :
    fullFour_pair_28 x y = CompactPair.expressionEval compact_fullFour_pair_28_base compact_fullFour_pair_28_hinges x y:=by rfl
theorem fullFour_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_28 x y:=by
  rw [compact_fullFour_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_28_check hy (by simpa using hx)
def compact_fullFour_pair_29_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x8c307d1f / 0xb2d05e00),(-49 / 50)⟩
def compact_fullFour_pair_29_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_29_base compact_fullFour_pair_29_hinges x y
def compact_fullFour_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFour_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_29_base compact_fullFour_pair_29_hinges 0 compact_fullFour_pair_29_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_29_representation (x y:ℝ) :
    fullFour_pair_29 x y = CompactPair.expressionEval compact_fullFour_pair_29_base compact_fullFour_pair_29_hinges x y:=by rfl
private def zz571:"s023b"="s023b":=by decide+kernel
theorem fullFour_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_29 x y:=by
  rw [compact_fullFour_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_29_check hy (by simpa using hx)
def compact_fullFour_pair_30_base:CompactPair.Quadratic:=⟨(-0xc691b7e1d / 0x165a0bc00),(0x6b9bf796f / 0x165a0bc00),0⟩
def compact_fullFour_pair_30_hinges:List CompactPair.Hinge:=[⟨(0x22e1c57 / 0x165a0bc00),1, -3⟩,⟨(-0x53b773 / 0x5f5e100),1, -1⟩,⟨(-0x51d02823 / 0x2cb417800),2, -3⟩,⟨(0x1752169 / 0x165a0bc),3, -1⟩]
noncomputable def fullFour_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_30_base compact_fullFour_pair_30_hinges x y
def compact_fullFour_pair_30_cuts:List ℚ:=[(1 / 3),1,(3 / 2),3]
theorem compact_fullFour_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_30_base compact_fullFour_pair_30_hinges 0 compact_fullFour_pair_30_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_30_representation (x y:ℝ) :
    fullFour_pair_30 x y = CompactPair.expressionEval compact_fullFour_pair_30_base compact_fullFour_pair_30_hinges x y:=by rfl
theorem fullFour_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_30 x y:=by
  rw [compact_fullFour_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_30_check hy (by simpa using hx)
def compact_fullFour_pair_31_base:CompactPair.Quadratic:=⟨(23 / 0x59682f000),(0x12bf / 0x23c34600),0⟩
def compact_fullFour_pair_31_hinges:List CompactPair.Hinge:=[⟨(-0x4eda2a8f / 0xb2d05e00),1, -3⟩,⟨(0xfb43983d / 0x1dcd65000),1, -2⟩,⟨(-0x3061ab61 / 0xee6b2800),1, -1⟩,⟨(0x3193213 / 0xee6b2800),3, -2⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def fullFour_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_31_base compact_fullFour_pair_31_hinges x y
def compact_fullFour_pair_31_cuts:List ℚ:=[(1 / 3),(2 / 3),1,2,3]
private def zz572:"s023c"="s023c":=by decide+kernel
theorem compact_fullFour_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_31_base compact_fullFour_pair_31_hinges 0 compact_fullFour_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_31_representation (x y:ℝ) :
    fullFour_pair_31 x y = CompactPair.expressionEval compact_fullFour_pair_31_base compact_fullFour_pair_31_hinges x y:=by rfl
theorem fullFour_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_31 x y:=by
  rw [compact_fullFour_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_31_check hy (by simpa using hx)
def compact_fullFour_pair_32_base:CompactPair.Quadratic:=⟨(-0x2e7e1303 / 0x165a0bc0),(-0x19e54973 / 0x2cb41780),(-49 / 50)⟩
def compact_fullFour_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0xc323391d / 0x165a0bc00),1, -3⟩,⟨(-0x11644055 / 0x7735940),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x7b19eb95 / 0x165a0bc00),3, -2⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_32_base compact_fullFour_pair_32_hinges x y
def compact_fullFour_pair_32_cuts:List ℚ:=[(1 / 3),(2 / 3),1,3]
theorem compact_fullFour_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_32_base compact_fullFour_pair_32_hinges 0 compact_fullFour_pair_32_cuts = true :=
  by decide +kernel
private def zz573:"s023d"="s023d":=by decide+kernel
theorem compact_fullFour_pair_32_representation (x y:ℝ) :
    fullFour_pair_32 x y = CompactPair.expressionEval compact_fullFour_pair_32_base compact_fullFour_pair_32_hinges x y:=by rfl
theorem fullFour_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_32 x y:=by
  rw [compact_fullFour_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_32_check hy (by simpa using hx)
def compact_fullFour_pair_33_base:CompactPair.Quadratic:=⟨(-0x2de53b7ab / 0x165a0bc00),(-0x1985536f / 0x2cb41780),(-49 / 50)⟩
def compact_fullFour_pair_33_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(-0xb47158a1 / 0x77359400),1, -2⟩,⟨(-0x1fe7487f / 0xee6b280),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x73ed691f / 0xb2d05e00),2, -3⟩,⟨(-0xaea521b / 0xee6b2800),2, -1⟩,⟨(0x61855d / 0x23c3460),3, -2⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_33_base compact_fullFour_pair_33_hinges x y
def compact_fullFour_pair_33_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullFour_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_33_base compact_fullFour_pair_33_hinges 0 compact_fullFour_pair_33_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_33_representation (x y:ℝ) :
    fullFour_pair_33 x y = CompactPair.expressionEval compact_fullFour_pair_33_base compact_fullFour_pair_33_hinges x y:=by rfl
private def zz574:"s023e"="s023e":=by decide+kernel
theorem fullFour_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_33 x y:=by
  rw [compact_fullFour_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_33_check hy (by simpa using hx)
def compact_fullFour_pair_34_base:CompactPair.Quadratic:=⟨(1 / 0x59682f00),(0xbb9 / 0x11e1a300),0⟩
def compact_fullFour_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x2876ef / 0x2cb41780),1, -3⟩,⟨(0x2876ef1 / 0x77359400),1, -2⟩,⟨(-0x2876ef1 / 0x165a0bc00),2, -3⟩,⟨(-0x2876ef1 / 0x77359400),2, -1⟩,⟨(0x2876ef1 / 0x165a0bc00),3, -2⟩,⟨(0x2876ef / 0x2cb41780),3, -1⟩]
noncomputable def fullFour_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_34_base compact_fullFour_pair_34_hinges x y
def compact_fullFour_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFour_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_34_base compact_fullFour_pair_34_hinges 0 compact_fullFour_pair_34_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_34_representation (x y:ℝ) :
    fullFour_pair_34 x y = CompactPair.expressionEval compact_fullFour_pair_34_base compact_fullFour_pair_34_hinges x y:=by rfl
theorem fullFour_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_34 x y:=by
  rw [compact_fullFour_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_34_check hy (by simpa using hx)
def compact_fullFour_pair_35_base:CompactPair.Quadratic:=⟨(-29 / 0x59682f000),(0x2ef3 / 0xb2d05e00),0⟩
def compact_fullFour_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0xee6b2800),1, -2⟩,⟨(1 / 0x59682f000),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullFour_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_35_base compact_fullFour_pair_35_hinges x y
def compact_fullFour_pair_35_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
private def zz575:"s023f"="s023f":=by decide+kernel
theorem compact_fullFour_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_35_base compact_fullFour_pair_35_hinges 0 compact_fullFour_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_35_representation (x y:ℝ) :
    fullFour_pair_35 x y = CompactPair.expressionEval compact_fullFour_pair_35_base compact_fullFour_pair_35_hinges x y:=by rfl
theorem fullFour_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_35 x y:=by
  rw [compact_fullFour_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_35_check hy (by simpa using hx)
def compact_fullFour_pair_36_base:CompactPair.Quadratic:=⟨0,(0x419f / 0x47868c00),0⟩
def compact_fullFour_pair_36_hinges:List CompactPair.Hinge:=[]
noncomputable def fullFour_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_36_base compact_fullFour_pair_36_hinges x y
def compact_fullFour_pair_36_cuts:List ℚ:=[]
theorem compact_fullFour_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_36_base compact_fullFour_pair_36_hinges 0 compact_fullFour_pair_36_cuts = true :=
  by decide +kernel
private def zz576:"s0240"="s0240":=by decide+kernel
theorem compact_fullFour_pair_36_representation (x y:ℝ) :
    fullFour_pair_36 x y = CompactPair.expressionEval compact_fullFour_pair_36_base compact_fullFour_pair_36_hinges x y:=by rfl
theorem fullFour_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_36 x y:=by
  rw [compact_fullFour_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_36_check hy (by simpa using hx)
def compact_fullFour_pair_37_base:CompactPair.Quadratic:=⟨(-0x19608d39 / 0x1c9c3800),(0x74de372b / 0x165a0bc00),0⟩
def compact_fullFour_pair_37_hinges:List CompactPair.Hinge:=[⟨(-0x6c68239 / 0x2cb417800),1, -3⟩,⟨(0x74bf6a3 / 0x5f5e1000),1, -2⟩,⟨(0x32486521 / 0x3b9aca00),1, -1⟩,⟨(-0x7696255d / 0x59682f000),2, -3⟩,⟨(-0xf6f98529 / 0x1dcd65000),2, -1⟩,⟨(-0x1ee46661 / 0x59682f000),3, -2⟩,⟨(0x33246aff / 0xb2d05e00),3, -1⟩]
noncomputable def fullFour_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_37_base compact_fullFour_pair_37_hinges x y
def compact_fullFour_pair_37_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullFour_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_37_base compact_fullFour_pair_37_hinges 0 compact_fullFour_pair_37_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_37_representation (x y:ℝ) :
    fullFour_pair_37 x y = CompactPair.expressionEval compact_fullFour_pair_37_base compact_fullFour_pair_37_hinges x y:=by rfl
private def zz577:"s0241"="s0241":=by decide+kernel
theorem fullFour_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_37 x y:=by
  rw [compact_fullFour_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_37_check hy (by simpa using hx)
def compact_fullFour_pair_38_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0xda9637b / 0x11e1a300),(-49 / 50)⟩
def compact_fullFour_pair_38_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_38_base compact_fullFour_pair_38_hinges x y
def compact_fullFour_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFour_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_38_base compact_fullFour_pair_38_hinges 0 compact_fullFour_pair_38_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_38_representation (x y:ℝ) :
    fullFour_pair_38 x y = CompactPair.expressionEval compact_fullFour_pair_38_base compact_fullFour_pair_38_hinges x y:=by rfl
theorem fullFour_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_38 x y:=by
  rw [compact_fullFour_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_38_check hy (by simpa using hx)
def compact_fullFour_pair_39_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x8c307d1f / 0xb2d05e00),(-49 / 50)⟩
def compact_fullFour_pair_39_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFour_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFour_pair_39_base compact_fullFour_pair_39_hinges x y
def compact_fullFour_pair_39_cuts:List ℚ:=[(1 / 3),3]
private def zz578:"s0242"="s0242":=by decide+kernel
theorem compact_fullFour_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullFour_pair_39_base compact_fullFour_pair_39_hinges 0 compact_fullFour_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullFour_pair_39_representation (x y:ℝ) :
    fullFour_pair_39 x y = CompactPair.expressionEval compact_fullFour_pair_39_base compact_fullFour_pair_39_hinges x y:=by rfl
theorem fullFour_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFour_pair_39 x y:=by
  rw [compact_fullFour_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFour_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullFourPairs
private def zz2183:"s0887"="s0887":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l17 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l36 l37 l38 l42 l43 l45 l51 l57 l58 l6 l60 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x19f49b4dd, -0xefee2004, -0x167e5534c,0x2e9e], ![-0xefee2004, -0x49a05fbf4,0x1d7333fc,0x14eb3ab72], ![-0x167e5534c,0x1d7333fc, -0x6178d2d86,0xefee84a2], ![0x2e9e,0x14eb3ab72,0xefee84a2, -0x77f72ae4]]
noncomputable def hinges:Hinges:=[(-0x241b7d8,l6),(0x3394304,l9),(-0xd8a0014,l8),(0x4d5da3a,l10),(0xd9d5cd1c,l14),(-0x8240658,l17),(0x332d374,l21),(0x1fd81aec,l23),(0xc7b59dc,l22),(-0x77f72ae4,l27),(-0x332d374,l28),(0x77f72ae4,l29),(-0xd9d5cd1c,l25),(0x217184a6,l31),(0x64c6e036,l30),(0x77f72ae4,l33),(-0x4d5da3a,l38),(-0x77f72ae4,l35),(0xd8a0014,l36),(0x77f72ae4,l37),(-0x64c6e036,l43),(-0xc7b59dc,l42),(0x18f6b3bb,l45),(0x77f72ae4,l51),(-0x217184a6,l57),(-0x18f6b3bb,l58),(-0x3394304,l61),(0x241b7d8,l60),(-0x1fd81aec,l63),(0x8240658,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x77f72ae4,l27),(0x77f72ae4,l29),(0x77f72ae4,l33),(-0x77f72ae4,l35),(0x77f72ae4,l37),(0x77f72ae4,l51),(0xd9d5cd1c,l14),(-0xd9d5cd1c,l25),(0x64c6e036,l30),(-0x64c6e036,l43),(0x217184a6,l31),(-0x217184a6,l57),(0x1fd81aec,l23),(-0x1fd81aec,l63),(0x18f6b3bb,l45),(-0x18f6b3bb,l58),(-0x8240658,l17),(0x8240658,l62),(-0xd8a0014,l8),(0xd8a0014,l36),(0xc7b59dc,l22),(-0xc7b59dc,l42),(0x3394304,l9),(-0x3394304,l61),(0x332d374,l21),(-0x332d374,l28),(0x4d5da3a,l10),(-0x4d5da3a,l38),(-0x241b7d8,l6),(0x241b7d8,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x1f0320040000000001881c4010000000001940288030000000000640290040000000f211034300c000001ae21012c602000000354440258c04000004c4310013180a0000000094380630080000013019002660200000000260e01cc0200000000004a0590040000000026001320100000000009e0264018000024c28c08c0c0500000418418118180a0000000000880d200800000000b8280e601000000158110124c0400000003a0c80e1806000000009c340d30080000000048381a601000000394420258c040000007088804b1808000000a80c4013301000000015c340266018000000981103e8c040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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase0" = "QuadFullFourCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase0
private def zz2184:"s0888"="s0888":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l21 l22 l23 l25 l27 l28 l29 l30 l33 l35 l36 l37 l38 l41 l42 l43 l45 l51 l58 l6 l60 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc1779cca, -0x77f71002, -0xb3f2a997,0x174c], ![-0x77f71002, -0x22059065e,0x72dc88d,0xa78d6538], ![-0xb3f2a997,0x72dc88d, -0x30bc696c3,0x77f74251], ![0x174c,0xa78d6538,0x77f74251, -0x3bfb9572]]
noncomputable def hinges:Hinges:=[(-0x120dbec,l6),(0x19ca182,l9),(-0x6c5000a,l8),(0x26aed1d,l10),(0x7042c55d,l14),(0xc4cf70cd,l15),(0x74ec3d1,l21),(-0x612542c,l23),(0x1157bbd5,l22),(-0x3bfb9572,l27),(-0x74ec3d1,l28),(0x3bfb9572,l29),(-0x7042c55d,l25),(0x32cfb520,l30),(0x3bfb9572,l33),(-0x26aed1d,l38),(-0x3bfb9572,l35),(0x6c5000a,l36),(0x3bfb9572,l37),(-0x32cfb520,l43),(-0x1157bbd5,l42),(-0xc4cf70cd,l41),(0xe60778f,l45),(0x3bfb9572,l51),(-0xe60778f,l58),(-0x19ca182,l61),(0x120dbec,l60),(0x612542c,l63)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3bfb9572,l27),(0x3bfb9572,l29),(0x3bfb9572,l33),(-0x3bfb9572,l35),(0x3bfb9572,l37),(0x3bfb9572,l51),(0x7042c55d,l14),(-0x7042c55d,l25),(0x32cfb520,l30),(-0x32cfb520,l43),(0xc4cf70cd,l15),(-0xc4cf70cd,l41),(0x74ec3d1,l21),(-0x74ec3d1,l28),(0x1157bbd5,l22),(-0x1157bbd5,l42),(-0x612542c,l23),(0x612542c,l63),(0xe60778f,l45),(-0xe60778f,l58),(-0x6c5000a,l8),(0x6c5000a,l36),(0x19ca182,l9),(-0x19ca182,l61),(0x26aed1d,l10),(-0x26aed1d,l38),(-0x120dbec,l6),(0x120dbec,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((0x1e53a952ac83c95e1e25f8aad2cdf4566cbbe127f7ecb4258aef82a90ef0c06c619bcf8efa8b4c2864e4d3d6ac2de8fb870322266bcdb851e8a3c3e0d5f0c2936eacfbb6c89a9284dcc4583945011c0125158f7e876ff11d8b6d1c5a59f2b2f21143100ad1050d8e4d5b7ee9b848181c5c4e6a0806ce9ad82f62809329854a37f897327d7ff50e3b1f2d3dba2b98458f494a0c40e6803f45e65418c8255d521ef7c01d0cc76dc74a9fefaea0e9e342c29834315bcbce5de2e38c24950d028a0be3058cfbe830e6bf8d90f092312060b0410753b4106e7aff708000056c5c981070021248002833904127473d8d08063a) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase1" = "QuadFullFourCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase1
private def zz2185:"s0889"="s0889":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l17 l22 l23 l27 l29 l33 l35 l37 l4 l41 l5 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xefbf5a5ea, -0x59682c120, -0x31e60e220,0x2ee0], ![-0x59682c120, -0x288420104a,0xfb8c479a8, -0x55b5f7084], ![-0x31e60e220,0xfb8c479a8, -0x2b973db529,0x90d0c73d6], ![0x2ee0, -0x55b5f7084,0x90d0c73d6, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xdc95de2d,l5),(0x4d5b4caa,l4),(0xc219ca96,l11),(0x1c9501b6,l10),(0x2b65e9d6,l13),(-0xceedf0bc,l17),(0xc22106ce,l23),(0x733438fe,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x685981fe0,l41),(0x2cb417800,l51),(-0x1402e1c3a,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x685981fe0,l41),(-0x1402e1c3a,l62),(0xc22106ce,l23),(0xc219ca96,l11),(-0xceedf0bc,l17),(-0xdc95de2d,l5),(0x733438fe,l22),(0x1c9501b6,l10),(0x2b65e9d6,l13),(0x4d5b4caa,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[![0, 1, -1, 0]]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase2" = "QuadFullFourCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase2
private def zz2186:"s088a"="s088a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l27 l29 l30 l31 l33 l35 l37 l4 l41 l42 l46 l5 l51 l56 l57 l59 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x7391a8561, -0x59682c120, -0x77ffdf030,0x3ff3c1674], ![-0x59682c120, -0x2643bfabcb,0xf2c3af21c, -0x55d7af032], ![-0x77ffdf030,0xf2c3af21c, -0x2b973db529,0x90d0c73d6], ![0x3ff3c1674, -0x55d7af032,0x90d0c73d6, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xdc95de2d,l5),(0x4d5b4caa,l4),(0xc219ca96,l11),(0x1c9501b6,l10),(0x1291f1c00,l14),(0xc7f4b76a,l13),(-0x4630ef1c,l17),(-0x6cb2202a,l16),(0x274f8bda8,l15),(0x267954798,l21),(-0x36e0314ce,l20),(-0x2cb417800,l27),(0x2cb417800,l29),(0x7bc32b1b,l31),(-0x3919233c,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x20bef651,l42),(-0x5fb5d97d0,l41),(-0x127fd674,l46),(0x2cb417800,l51),(-0x4ca58129,l57),(-0x43aa813c6,l56),(-0x1ed91038,l59),(0x1a3df7150,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x267954798,l21),(-0x43aa813c6,l56),(-0x36e0314ce,l20),(0x1a3df7150,l64),(-0x5fb5d97d0,l41),(0xc219ca96,l11),(0x1291f1c00,l14),(0x7bc32b1b,l31),(0x274f8bda8,l15),(-0xdc95de2d,l5),(-0x4ca58129,l57),(0xc7f4b76a,l13),(-0x4630ef1c,l17),(-0x6cb2202a,l16),(-0x3919233c,l30),(-0x1ed91038,l59),(0x1c9501b6,l10),(0x4d5b4caa,l4),(-0x127fd674,l46),(-0x20bef651,l42)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0xe11840693010000003a084028c0300000000e89033004000000310a014c02068cc104d01564014000001d864058c030000006611016300c000000006409c803000000000a40720080000000027018802030c43042011540140db14610407f500500000000007032004000000015002c80300000002600132010000000013c04c803000000340a01d300c00000c4110128c04000000980b013300c009108c190159004001484109002b40100000014884050c030000005219034300c0048084150091004001d0340840784010003c0841a0271004000002105003c30100000008828030c03000000000140620080000002e0d018c02000000b81900a300c000000000d0188020000d8260b014400c000010c13012cc04000004405009b3010000010411016cc0464852028c049f40180000000907028c02032850850015f401400001d11070390020000e46222024400c00001d19110390020000006219025300c0000184310254c04049828824016e40140004b218240ad00300000000e850330040000003211018c02000000c82100a300c00000000360148020000000d8940e30080000000019038802023030841024c401400000c42101b0c040000003211014300c0005d15824079003002ec530440364010000000017002c80303e061883021c40159b14306d01f750060000004219014300c0001021b40360c05000000044340f300800010a1c40360c05,0x51828824016e4014000002c944058c030000b894b0092301400002f4aa00a4c040000000b8a807300800002d0a100a4c04002f47204c055401000b41d81903e90040000008e3f026300c1332161b00a29005001cc360500c740101752922c8052900500000005c380e30080db1461a80d29005000006714c06a301000001b4570128c0400000691580253010000001b0b0074c030000006829015300c0001a62840628c050000068148095301000001484200e4c0400130350740c84010004f0841100e5004000000028180f30080000000f07028c0200000000a83033004000018811016cc0400000000094072008000000013002c80300000000013032004000000190d018c0260c57840c046040180000001f07028c02001042206006740111b0c306d01f750060000000006c062008000000001a014802000000000640620080000000f0a014c0200000a43c280540080000011064034c0300000a4241c05400800002a09070150020000000241c0530080000000032014802000000000c4062008000000088004c8040000000841c0b3008000000011c04c803000000880b013300c00001c811016cc040000000342c053008000002b82c02cc03000000aa0e013300c000000000440c8010000000008409200800000cc140248c040001047612032400c009213c3402690040018453058084401000000002e0c0cc010020c710c808440100000000006c0c801,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase3" = "QuadFullFourCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase3
private def zz2187:"s088b"="s088b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l36 l37 l38 l4 l41 l42 l43 l46 l5 l51 l55 l6 l60 l61 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x178f517a3, -0x11c0c8e78, -0x1aa12eece,0x1c2452c4], ![-0x11c0c8e78, -0x4fda37198,0x30bb26d8,0x10c86101a], ![-0x1aa12eece,0x30bb26d8, -0x73652d7a7,0x11c0cec3e], ![0x1c2452c4,0x10c86101a,0x11c0cec3e, -0x8e065eac]]
noncomputable def hinges:Hinges:=[(-0x1c76191c,l6),(-0x120c504f,l5),(0x61cd59a4,l4),(0x31ba0ab3,l9),(-0x15252f9c,l8),(-0x3b0fd808,l11),(0x28a8eb2e,l10),(0xd3923ab8,l14),(0x8f8f757a,l13),(-0x8240658,l17),(0x1fd81aec,l23),(0xc7b59dc,l22),(-0x8e065eac,l27),(-0x2d51adf6,l28),(0x8e065eac,l29),(-0xd257eb94,l25),(0x217184a6,l31),(0x64c6e036,l30),(0x8e065eac,l33),(-0x138f6a4a,l38),(-0x8e065eac,l35),(0x1504a7cf,l36),(0x8e065eac,l37),(-0x82fef52c,l43),(-0xf2c99a6,l42),(-0x13be4cca2,l41),(0xbfa3754,l46),(0x8e065eac,l51),(0x1349343c,l55),(-0x184a5000,l61),(0xf8e874a,l60),(-0x50edde2,l63),(-0x298d5ec,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8e065eac,l27),(0x8e065eac,l29),(0x8e065eac,l33),(-0x8e065eac,l35),(0x8e065eac,l37),(0x8e065eac,l51),(0xd3923ab8,l14),(-0xd257eb94,l25),(-0x82fef52c,l43),(0x64c6e036,l30),(-0x3b0fd808,l11),(0x8f8f757a,l13),(-0x13be4cca2,l41),(0x31ba0ab3,l9),(-0x2d51adf6,l28),(0x217184a6,l31),(0x1fd81aec,l23),(0x28a8eb2e,l10),(-0x184a5000,l61),(0x1349343c,l55),(-0x1c76191c,l6),(0x61cd59a4,l4),(-0x138f6a4a,l38),(0xf8e874a,l60),(0xbfa3754,l46),(-0x15252f9c,l8),(0x1504a7cf,l36),(-0x120c504f,l5),(-0xf2c99a6,l42),(-0x8240658,l17),(-0x50edde2,l63),(0xc7b59dc,l22),(-0x298d5ec,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 34 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase4" = "QuadFullFourCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 34 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase4
private def zz2188:"s088c"="s088c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l55 l56 l57 l58 l6 l60 l61 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x11bb7d84c, -0x11c0c8e78, -0x1aa12ee74,0x16164240], ![-0x11c0c8e78, -0x505a009c2,0x3acdcb8c,0x10ced2f18], ![-0x1aa12ee74,0x3acdcb8c, -0x73652d7a7,0x11c0cec3e], ![0x16164240,0x10ced2f18,0x11c0cec3e, -0x8e065eac]]
noncomputable def hinges:Hinges:=[(-0x1c76191c,l6),(-0x120c504f,l5),(0x61cd59a4,l4),(0x31ba0ab3,l9),(-0x15252f9c,l8),(-0x3b0fd808,l11),(0x28a8eb2e,l10),(0x38f28b54,l14),(0x1526ea9ac,l13),(0x1899ee19a,l15),(0x10adb62e,l21),(-0x6ef25414,l20),(-0xc24a858,l23),(0x22af77aa,l22),(-0x8e065eac,l27),(-0x287c9968,l28),(0x8e065eac,l29),(-0xb33970fc,l25),(0x659f6a40,l30),(0x8e065eac,l33),(-0x138f6a4a,l38),(-0x8e065eac,l35),(0x1504a7cf,l36),(0x8e065eac,l37),(-0xdb49d4e,l43),(-0x6671175f,l42),(-0x4eeb7af6,l41),(0x284e72d4,l45),(0x8e065eac,l51),(0x1349343c,l55),(-0x4a8e861c,l57),(0x1707c2b5,l56),(-0x43fe84b4,l58),(-0x184a5000,l61),(0xf8e874a,l60),(0x1702d994,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8e065eac,l27),(0x8e065eac,l29),(0x8e065eac,l33),(-0x8e065eac,l35),(0x8e065eac,l37),(0x8e065eac,l51),(0x1526ea9ac,l13),(-0xb33970fc,l25),(-0x4a8e861c,l57),(0x659f6a40,l30),(0x1899ee19a,l15),(-0x3b0fd808,l11),(0x31ba0ab3,l9),(-0x287c9968,l28),(-0x6ef25414,l20),(-0x6671175f,l42),(0x38f28b54,l14),(0x28a8eb2e,l10),(-0x43fe84b4,l58),(-0x184a5000,l61),(0x1349343c,l55),(-0x1c76191c,l6),(0x10adb62e,l21),(0x61cd59a4,l4),(0x1702d994,l64),(0x284e72d4,l45),(-0x4eeb7af6,l41),(-0x138f6a4a,l38),(0x22af77aa,l22),(-0xc24a858,l23),(0xf8e874a,l60),(-0xdb49d4e,l43),(0x1707c2b5,l56),(-0x15252f9c,l8),(0x1504a7cf,l36),(-0x120c504f,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 37 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase5" = "QuadFullFourCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 37 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase5
private def zz2189:"s088d"="s088d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l17 l22 l23 l27 l29 l33 l35 l37 l4 l44 l46 l5 l51 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x596cd8e06, -0x59682c120, -0x2625c134a,0x3452d690], ![-0x59682c120, -0x285eeeb0b4,0xfca656eb8, -0x55b5f7084], ![-0x2625c134a,0xfca656eb8, -0x29f2e8fc25,0x8ce090aee], ![0x3452d690, -0x55b5f7084,0x8ce090aee, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xf702f7a1,l5),(0x202126518,l4),(0x26a72f5fd,l8),(-0x90797c96,l10),(0x6348a40,l14),(-0xceedf0bc,l17),(0xc22106ce,l23),(0x733438fe,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x8b8715c,l46),(0x4e7bfbd0,l44),(0x2cb417800,l51),(-0xf633d72a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0xf633d72a,l63),(0x26a72f5fd,l8),(0xc22106ce,l23),(-0xceedf0bc,l17),(-0x90797c96,l10),(-0xf702f7a1,l5),(0x202126518,l4),(0x733438fe,l22),(0x4e7bfbd0,l44),(-0x8b8715c,l46),(0x6348a40,l14)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[0x44240a30080000c709900690c0600001505221016400c000551241600b9004003c82282d018c40140000000002601480200000005827013300c000000000b002480300000000036009200c0000000190901cc020000000640900c300c0000001b024030c030000068041002630140000001b84402cc0300000000001406200800000000016014802ed851c12102ff1401c0000001c8c40d8c03002903184301d2401400000008828030c030000150640b00b400c015418e09801250050002b46e0700494010000b11d04603590040000000000b40620080000000002f0188020000000be3900b300c0000002e8e804cc0300000008e2100b300c0000002288804cc03002542102200c9401400000000a0603cc02000000003c1c0a30080006214c42032d004062053042001e140180000022011004cc0400000000881407300800a211418803c50050000000044340a300a9510904180b95500700000000001c06200a9c10c04200275500700000000008406200800000000023018802046831810804ed40180000000002103880200000000003805200800000014864090c030000090220d027400f1c14c04200275500700000000009406200800000000027018802056841810804ed4018000000108640d8c0300000000007c062008000001b120901d0020000000002c00b200c0000000001901880200000000006c0620081440a1044006350060001702807005d4010000000000980248030000000001c009200c00000000012014802,0x8508c0940ddd0050038c510830178401400000138110058c0400000000443c0530080000000000f0148020000094260900b400c00000000078024803], #[![125, 323, -948, 0],![-7855, 2378, 16431, 0],![-7, -50, 63, 0]]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase6" = "QuadFullFourCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase6
private def zz2190:"s088e"="s088e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l15 l16 l17 l21 l25 l27 l29 l30 l31 l33 l35 l37 l4 l44 l45 l5 l51 l57 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xab029c09, -0x59682c120, -0x43484d85e,0x323ebc03c], ![-0x59682c120, -0x1f47481991,0xe1204b148, -0x55d7af032], ![-0x43484d85e,0xe1204b148, -0x29f2e8fc25,0x8ce090aee], ![0x323ebc03c, -0x55d7af032,0x8ce090aee, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xf702f7a1,l5),(0x202126518,l4),(0x26a72f5fd,l8),(-0x90797c96,l10),(0x5d1725f84,l13),(-0x4630ef1c,l17),(-0x6cb2202a,l16),(0x274f8bda8,l15),(0x10461ba6c,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x21d5794fc,l25),(0x7bc32b1b,l31),(-0x3919233c,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x5c092e30,l45),(0x3a381e48,l44),(0x2cb417800,l51),(-0x1cfb5a47c,l57),(-0xc68c3569,l63),(0x135ec9a80,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x5d1725f84,l13),(-0x1cfb5a47c,l57),(-0x21d5794fc,l25),(0x10461ba6c,l21),(0x26a72f5fd,l8),(-0xc68c3569,l63),(0x135ec9a80,l64),(0x7bc32b1b,l31),(0x274f8bda8,l15),(-0x90797c96,l10),(-0xf702f7a1,l5),(0x202126518,l4),(-0x4630ef1c,l17),(-0x6cb2202a,l16),(-0x3919233c,l30),(-0x5c092e30,l45),(0x3a381e48,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((0x16544e6d6e0f38901cf61292612412e70690b249e41219f1202e8aa3aab140406ee446a4c0846010b8122d8a0e588d03165a0b047d33109c1008c4c30b2cb28c20b14b08204104c01c82008034000498e9416998ff471452989f490dc512643e02a63163891b667e0058a4eb8c7ee7940837c73394858149edbb8a18400000023280e8042600c07f00800072480d84c0682603003c21878efbd1b0c0920ff0d61709480c1e04f82854e4f4a1dc1cecb06303c91cf518cc5d8368a145265635ef3a491494fb641987106019e4982dda2bc052b5040c1801e000086882a8ec15077647042e25eb192b2b57da0dac28867a6de47d058c7cd413407658dafa3bc32d1ebb58e86752bc8088455148534b12193de27910c10b3aa7793adc3379fde24752007c954d00ba6b1f0e603698626bca7bd8dbf4db9882a2862acc098474f8b2d13082d8763) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase7" = "QuadFullFourCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase7
private def zz2191:"s088f"="s088f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase8
private def zz2192:"s0890"="s0890":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz617:"s0269"="s0269":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase9
private def zz2193:"s0891"="s0891":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l15 l17 l21 l25 l27 l29 l33 l35 l36 l37 l43 l46 l51 l54 l55 l57 l61 l62 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2c029c831, -0x59682c120, -0x861c43920,0x2a2155f8], ![-0x59682c120,0x5d2182ece,0x26275c488,0x727c1926e], ![-0x861c43920,0x26275c488, -0x24524ccbaf,0x596831ee0], ![0x2a2155f8,0x727c1926e,0x596831ee0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xa13b,l9),(-0x97278,l8),(0x3c763,l11),(0x1402e1c3a,l17),(0x685981fe0,l15),(0xa3a05046,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x5d485a400,l25),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x264b5149,l36),(0x2cb417800,l37),(0x5569ef8c,l43),(-0x6348a40,l46),(0x2cb417800,l51),(-0xd258514c,l55),(0x95717e0e,l54),(-0xd568b93e,l57),(0x1f52835c,l61),(0x54d0a552,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x5d485a400,l25),(0x685981fe0,l15),(-0xd568b93e,l57),(-0xd258514c,l55),(0x1402e1c3a,l17),(0xa3a05046,l21),(0x5569ef8c,l43),(0x54d0a552,l62),(0x95717e0e,l54),(0x1f52835c,l61),(-0x264b5149,l36),(-0x6348a40,l46),(0x3c763,l11),(-0x97278,l8),(-0xa13b,l9)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[![-24, 69, 8, 0],![-21, -9, 17, 0],![4, -35, 0, -3],![4, -35, 0, 53],![4, -17, 0, -1],![4, -17, 0, 27],![27, -175, 0, 0],![3, -11, 0, 0],![17, -60, 0, 0]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 26 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase10" = "QuadFullFourCase10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 26 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase10
private def zz2194:"s0892"="s0892":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l14 l15 l16 l22 l25 l27 l28 l29 l31 l33 l35 l36 l37 l41 l42 l43 l46 l51 l54 l55 l56 l57 l58 l61 l62 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2bf425b0a, -0x59682c120, -0x861c4392c,0x2ee0], ![-0x59682c120, -0x112ae5f14f,0x27473eea8,0x8fe0ec2c4], ![-0x861c4392c,0x27473eea8, -0x24524ccbaf,0x596831ee0], ![0x2ee0,0x8fe0ec2c4,0x596831ee0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xa13b,l9),(-0x97278,l8),(0x3c763,l11),(0x276d15478,l14),(0x43aa813c6,l16),(0x5fb5d97d0,l15),(0x20bef651,l22),(-0x2cb417800,l27),(-0x258e48c34,l28),(0x2cb417800,l29),(-0x18bab9fa0,l25),(0x4ca58129,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x264b5149,l36),(0x2cb417800,l37),(0x898c41ec,l43),(-0x7e3c3e73,l42),(-0x1e244b732,l41),(-0x1b09e4794,l46),(0x2cb417800,l51),(-0xd258514c,l55),(0x95717e0e,l54),(-0x855e1724,l57),(0x5014e6b1,l56),(0x6c279522,l58),(0x1f52835c,l61),(0x4aad96a0,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x258e48c34,l28),(0x276d15478,l14),(0x43aa813c6,l16),(-0x1b09e4794,l46),(-0x18bab9fa0,l25),(0x5fb5d97d0,l15),(-0xd258514c,l55),(-0x855e1724,l57),(0x898c41ec,l43),(-0x1e244b732,l41),(0x4ca58129,l31),(0x95717e0e,l54),(0x4aad96a0,l62),(-0x7e3c3e73,l42),(0x6c279522,l58),(0x1f52835c,l61),(0x5014e6b1,l56),(-0x264b5149,l36),(0x20bef651,l22),(0x3c763,l11),(-0x97278,l8),(-0xa13b,l9)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0x168a62a02a400c00002e291501500200000b8ac580e40080000204410254c0400000000a8b033004000028c120248c04001c84304808740100093194210171004054c93089004f401400a9258440095004000000005500b200ea22461090023d00600015c962200d400c00a42584900bd00400284991180354010000018c23012cc0400264840d40274010009d23038019d00400270830c80574010130208194011d00500268860d00374010000019024026cc04000128881d017400c1222241b0049d005000006108405b301000912243603dd0040000005221014300c000000d82c090c030013c21044039401000480cc13011100400110350740c8401000430881201a500402602082100694014004c0cc13012100400118210440394010000000090503cc02000004c24140f400800440e4190321004000000028180f30080000000f07028c02000000000140920080000000907028c02000042824026b3014000000011c02c8030000000008407200800001dc330064c040000000743c073008000001e06c02cc0302984486600f740140a81181a008dd00502884186201574014000000000501880200000000038052008000000011002c80300208760cc05c401000511103303310040000004219022300c0063144410259004000000680b013300d8115b1120119d0060018453064056401000531042100a500402603082f019040140980c20fc0641005,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,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,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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase11" = "QuadFullFourCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase11
private def zz2195:"s0893"="s0893":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase12
private def zz2196:"s0894"="s0894":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz626:"s0272"="s0272":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase13
private def zz2197:"s0895"="s0895":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l22 l23 l25 l27 l29 l30 l33 l35 l36 l37 l38 l41 l42 l43 l5 l51 l54 l55 l6 l60 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x17067e776, -0x1165c4ec8, -0x1a18a8f46,0x1d7c7f08], ![-0x1165c4ec8, -0x4e0bc3852,0x1b91a2c8,0x160098378], ![-0x1a18a8f46,0x1b91a2c8, -0x7115930b9,0x1165cac82], ![0x1d7c7f08,0x160098378,0x1165cac82, -0x8b2e3ed4]]
noncomputable def hinges:Hinges:=[(-0x319f2e,l6),(-0x2fee8e02,l5),(0x1b692829,l9),(-0xa1d59c1,l8),(-0xd971541,l11),(0xb4013de,l10),(0x10b0cc838,l14),(0x13be4cca2,l15),(0x50edde2,l23),(0xf2c99a6,l22),(-0x8b2e3ed4,l27),(0x8b2e3ed4,l29),(-0x10b0cc838,l25),(0x82fef52c,l30),(0x8b2e3ed4,l33),(-0xb4013de,l38),(-0x8b2e3ed4,l35),(0xa1d59c1,l36),(0x8b2e3ed4,l37),(-0x82fef52c,l43),(-0xf2c99a6,l42),(-0x13be4cca2,l41),(0x8b2e3ed4,l51),(0xd971541,l55),(0x2fee8e02,l54),(-0x1b692829,l61),(0x319f2e,l60),(-0x50edde2,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8b2e3ed4,l27),(0x8b2e3ed4,l29),(0x8b2e3ed4,l33),(-0x8b2e3ed4,l35),(0x8b2e3ed4,l37),(0x8b2e3ed4,l51),(0x10b0cc838,l14),(-0x10b0cc838,l25),(0x82fef52c,l30),(-0x82fef52c,l43),(0x13be4cca2,l15),(-0x13be4cca2,l41),(0x1b692829,l9),(-0x1b692829,l61),(-0x2fee8e02,l5),(0x2fee8e02,l54),(-0xd971541,l11),(0xd971541,l55),(0xb4013de,l10),(-0xb4013de,l38),(0xf2c99a6,l22),(-0xf2c99a6,l42),(0x50edde2,l23),(-0x50edde2,l63),(-0xa1d59c1,l8),(0xa1d59c1,l36),(-0x319f2e,l6),(0x319f2e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x1c22b03080f9a00a08247185240a6b40181419210e1814b880300000000003103880290838904181b65200e0000000000c406200800968e615a07ac802800000000033018802000000342a1204a00400000000009c0620080000000001280c401020f1ca14f020ad006000000000278099006000000000098072009c1082410603cb28038249206189029ad006000000000024039004090c80860c072b4018000001e230812c6020000003504400e4c04000003305100f9980a000000d711c0393010000001aa2280d260200000003c8c4078c03000000418fa07d980800000000f46406300800000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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase14" = "QuadFullFourCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase14
private def zz2198:"s0896"="s0896":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l20 l21 l22 l25 l27 l28 l29 l30 l31 l33 l35 l36 l37 l38 l41 l42 l43 l46 l5 l51 l54 l55 l56 l57 l59 l6 l60 l61 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1aef31c71, -0x1165c4ec8, -0x1a18a8eec,0x9a29aec], ![-0x1165c4ec8, -0x5f0a2709d,0x77e4192a,0x134a891f0], ![-0x1a18a8eec,0x77e4192a, -0x7115930b9,0x1165cac82], ![0x9a29aec,0x134a891f0,0x1165cac82, -0x8b2e3ed4]]
noncomputable def hinges:Hinges:=[(-0x319f2e,l6),(-0x2fee8e02,l5),(0x1b692829,l9),(-0xa1d59c1,l8),(-0xd971541,l11),(0xb4013de,l10),(0x32a06f5e,l14),(0x16c6550f1,l13),(-0x1707c2b5,l16),(0x4eeb7af6,l15),(0xa1b215f,l21),(-0x16c6550f1,l20),(0x6671175f,l22),(-0x8b2e3ed4,l27),(-0xa1b215f,l28),(0x8b2e3ed4,l29),(-0x32a06f5e,l25),(0x4a8e861c,l31),(0xdb49d4e,l30),(0x8b2e3ed4,l33),(-0xb4013de,l38),(-0x8b2e3ed4,l35),(0xa1d59c1,l36),(0x8b2e3ed4,l37),(-0xdb49d4e,l43),(-0x6671175f,l42),(-0x4eeb7af6,l41),(0xb1de464,l46),(0x8b2e3ed4,l51),(0xd971541,l55),(0x2fee8e02,l54),(-0x4a8e861c,l57),(0x1707c2b5,l56),(0x1001329a,l59),(-0x1b692829,l61),(0x319f2e,l60),(-0x1001329a,l65),(-0xb1de464,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8b2e3ed4,l27),(0x8b2e3ed4,l29),(0x8b2e3ed4,l33),(-0x8b2e3ed4,l35),(0x8b2e3ed4,l37),(0x8b2e3ed4,l51),(0x16c6550f1,l13),(-0x16c6550f1,l20),(0x4a8e861c,l31),(-0x4a8e861c,l57),(0x6671175f,l22),(-0x6671175f,l42),(0x32a06f5e,l14),(-0x32a06f5e,l25),(0x1b692829,l9),(-0x1b692829,l61),(-0x2fee8e02,l5),(0x2fee8e02,l54),(0x1001329a,l59),(-0x1001329a,l65),(-0xd971541,l11),(0xd971541,l55),(0x4eeb7af6,l15),(-0x4eeb7af6,l41),(0xa1b215f,l21),(-0xa1b215f,l28),(0xdb49d4e,l30),(-0xdb49d4e,l43),(-0x1707c2b5,l16),(0x1707c2b5,l56),(0xb4013de,l10),(-0xb4013de,l38),(0xb1de464,l46),(-0xb1de464,l64),(-0xa1d59c1,l8),(0xa1d59c1,l36),(-0x319f2e,l6),(0x319f2e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,0x2a8099006000000000b8f03300400949061060160802800003b0c84c09900300000048902036180800000000006c06200800001011c204986028000001c86200e4c04000000001e120698040000005311c0a83010005188f05004a080280000000151103cc020000002888a034180800000000001c0620080000000642206c60180000000000901880200000214110039980a000010c542300e400c00000108e8680e80100000000170e02cc020000004986401498080000104721c026400c000008a05e01a6602800061144160331004000003045080c9180a0000000541c009300c000000aa1600766020000001642f006cc040000000291080a18060000053055010b3014000000a22280506020000001444101b0c0400000000001e031004004147284c00d240140000150842401a801801011c2160064900500000003d1a813180600000007231036300c00000000000606400800001c23040648c050000000410c807180600000728c5019230159c869828a01282803b120c604e0073050070000000320f00e98060000000681f00d300c0000000c45206c6018000001883b0214c04000000308ae03618080000000c242015300c0000319182a06a80180000492082c07900300292498518058200a0002183804407c40100000016649809060200000000000503880200000000004603100400000007631016300c000000000ba02640180000028c830120c0400000000003e0310040000000922a01d300ddc889838a0128280380000000000901c802,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,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,0x3b0520091808001942282201104014000198460b01108020000001945100a0c040000000311681918060000000622b022300c0000004208815060200000000001603480200000504908126180a000000922080393010000000124820286018012619218c02c100500000a621098132006000000003c140d300a490e303b005dc2803cb91d307d4069850070001625086c01ca00800584a087801924014000001a26080d86020000001d110d01d00200000000362c0598040000000054440a300800001b0843206c80180000000d0a0c0d0010019821032015da00a0030c40861019b401400660810c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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((0x81625c7189cd2e05cb1ce16180f8a52228201435f6e082ab00e9042a103e008d3040b237e1a5dd7c83223450d9d812a58641a90414a082fe884d020c73250ae0c00384309613840f8040000548c0b12dfafe469702c653d0b0c07cc11b14100a09718041b64ea4b054107c011a603590ff29a5b004b4b5161883294ea94104606c2d) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase15" = "QuadFullFourCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase15
private def zz2199:"s0897"="s0897":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase16
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l27 l29 l30 l31 l33 l35 l37 l5 l51 l58 l6 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x52ef97122, -0x59682c120, -0x2625c134a,0x56cc0268], ![-0x59682c120, -0x287d7789f0,0x1032fa8078, -0x55fffa046], ![-0x2625c134a,0x1032fa8078, -0x297f25eff7,0x89674e120], ![0x56cc0268, -0x55fffa046,0x89674e120, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x185faad0,l6),(-0x7805aa77,l5),(0x1f07b752c,l8),(0x56cb3e24,l11),(-0x9034c286,l10),(-0x54d0a552,l17),(-0x2cb417800,l27),(0x2cb417800,l29),(0xd568b93e,l31),(-0x5569ef8c,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x2b65e9d6,l58),(-0xf633d72a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0xf633d72a,l63),(0xd568b93e,l31),(0x1f07b752c,l8),(-0x9034c286,l10),(0x56cb3e24,l11),(-0x5569ef8c,l30),(-0x54d0a552,l17),(-0x7805aa77,l5),(0x2b65e9d6,l58),(-0x185faad0,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x38c7c6adb754a14616b83da102c89c7e8451c565a4f318228057abe6a4410019faa344224c2046010b24720bbb2e4926199f9b4b89207f8d59534a1d5a3b49b5891cd5464f4a8a0959fdce2f0700040fe9fd49c10900200540b926fdcc33a5c1241406e6ad2a2471feb169e3450a3206047578a10246227fd1141209e12d6293000000046500500c7b1e0af1c320209c0) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase16" = "QuadFullFourCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase16
private def zz2200:"s0898"="s0898":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l15 l16 l17 l21 l22 l25 l27 l29 l30 l31 l33 l35 l37 l45 l5 l51 l57 l58 l6 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x69017147, -0x59682c120, -0x43484d85e,0x33c0fdee4], ![-0x59682c120, -0x22601d6fab,0xf535560cc, -0x57fa9d142], ![-0x43484d85e,0xf535560cc, -0x297f25eff7,0x89674e120], ![0x33c0fdee4, -0x57fa9d142,0x89674e120, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x185faad0,l6),(-0x7805aa77,l5),(0x1f07b752c,l8),(0x56cb3e24,l11),(-0x9034c286,l10),(0x6d1e56e6a,l13),(0x14f6db430,l12),(-0x4aad96a0,l17),(-0x5014e6b1,l16),(0x1e244b732,l15),(0x7698090e,l21),(0x7e3c3e73,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x1aba32e6c,l25),(0x855e1724,l31),(-0x898c41ec,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x5f4dd622,l45),(0x2cb417800,l51),(-0x1cfb5a47c,l57),(0x3cadd8c4,l58),(-0xc68c3569,l63),(0x1291f1c0c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x6d1e56e6a,l13),(-0x1cfb5a47c,l57),(-0x1aba32e6c,l25),(-0xc68c3569,l63),(0x1291f1c0c,l64),(0x1f07b752c,l8),(0x855e1724,l31),(0x7698090e,l21),(-0x9034c286,l10),(-0x898c41ec,l30),(0x56cb3e24,l11),(0x1e244b732,l15),(0x14f6db430,l12),(-0x4aad96a0,l17),(0x7e3c3e73,l22),(-0x7805aa77,l5),(-0x5f4dd622,l45),(-0x5014e6b1,l16),(0x3cadd8c4,l58),(-0x185faad0,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((0x595319e98198e249ea15b96184a3653facd2c911ba3ce5a60e01370e95c900c150c33d2cc1046010e3243e391cd9858984dccbe34a68c225c4e6144e6697ff8c20ab49af029a0d98fb39d7280032415ef23000a4527d2a8002300809e00f0c6687ff63e0c2d0b4fe3e883490f9195d168d1473682229e3031256e9fff0d0547d61adaf3c0000005dc00d02308515b09220109804000036a4000df886702f0a3a8c2e24ab28938369c4aa33484eafdce15b2c8f53adc2dcb288234864c4612861c150f2ae33443752fb6ef01c04e535dae82419d020500380001ce2030230190981284ec99f71a0a48543084257449f6bd307aeab8801e33287a34c08627f82474b84c0229a82858e87c103ff824530f52facb0418066a985744084404db1040580580001fa20c6430611de90079a50a6582c8a3c51fab53162880cba603d0b0e739ec8d7906843af82d90553023ea6b96a7e14131ca70fa5fc1007ba0844ad80007231be823e451b523052038c282ed38b585631a42188d2f883ec2c8a44bd68f02c851052a1e0b67460c0892bf6ea0a7f0411467568ed6481c02ed27ec9383000ac10545ed37870f0e305e06800020420302b0190981284ec980f3b1ad1e0c202af9f0a6d13075fe82048f7ca1d2bf593767c24727f15c30430a1510cb9b67900412fd0e7c9148600b6fa4d9bf840404c88282a0200000f59000673342d2b8a4876392288eb0ebb5080e04b589ed014a8916b0f62830056712e327d48ad7a20ef31140084170e1cc1bddc2ed67b18600b5fcb85c74782bc2abfe5940bda1b2d95c72df79b16c528806a6b6a673ba0b625af2e680338ca04404c2c33d2de3c54352165525e45e2982c8700000dcce144bde5bb99af89f4b2551922353583cacc057aebb4d5c1843810c3bc776896d41f612305342ef1e11f0f9b770d90870429018c6484f5944f09938804e52c0d406a6dc62343970401d9f1a8c095ef4c56ee588a88013a25fcdd650b19be2e409d1f8ce89b37b9cd14c3200006ac68869ea99e525d368293901a05c7a234ab2b39a643070ecf92726c8bb1f030a18a57989ca6ba3d349c0805eef6f9a94f802c85a0a04cc1b27de8405a7a1000daa230d51759b42f12492bcc502fd64ccca52e1f7afaca708c1200002ca31d63e337b26a09f065fc758f8cdeb11b8cfbc7c13c94dfdea722a253c8069082b45724a4df473ee64c56a6a05c668c14469a1198818e10a1081040a0a0012faa6a2402be5d46c379f35d1eaf47f2ebfa8050d108588e66e3237cab0521e5ffd56d68eb0d905d19ccb0e75f2a11d692106b84627d19da53ab7c730b5252c992b496c42877913573fb5c993a48609229e6f17d400124cd05a18433cd228476d5246bb9396af6f280f36912f3b461f94de0000000000000000) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFourCase17" = "QuadFullFourCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFourCase17
private def zz2201:"s0899"="s0899":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase18
private def zz2202:"s089a"="s089a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFourCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz649:"s0289"="s0289":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFourCase19
private def zz2203:"s089b"="s089b":=by decide+kernel
end 
section 
namespace Green24Proof.FullFourRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decode [0x101e25faf8480018fb0c9e66203dceb94804eb3eec207a201eeb5ca8003a7929dae1fa25faf84804cc8b1e615a25faf848048c1abfe01a21389b48021d3eada2201eeb5ca8020beb19207d201eeb5ca04d29f8e1fd203dceb948004959bcfce1ed2779ae58009cf95a3e614d203dceb948012a5aee39a5203dceb948028bafcd0da1f9203dceb948073dd9bf21201eeb5ca8014fb96e9ce07c203dceb94800e849695ba1ec201eeb5ca8074f68fa24203dceb9480088a93caae078201eeb5ca8006e7abcd8e1e8217ebe18002c7c3f20201eeb5ca8003d48cc2d614]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107e601eeb5ca8009edd1aa9e15e609c4da806092a4aa01e60bf5f0c027c8cab26601eeb5ca8003a2fbfd8e1ea603dceb94800a9d81a0c601a601eeb5ca17a985d22601eeb5ca800396fccbb6563d84c002163d84c0021ff22fd7c280038d97e49e1ef201eeb5ca800891c3bab601f203dceb948010f5af94fe722fd7c28003e0a2b98e07b205faf8a027dbaa3201eeb5ca801586f792ba07e203dceb948001e3e58baa1fe201eeb5ca8003c39f8df21ee203dceb94800185b6ecae15e2779ae58050fcccda14e201eeb5ca800193f6f1ae14]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decode [0x11fc301eeb5ca804cd6ca8a4303dceb94804cd6d9ce1f8303dceb9480018591efd20303dceb948042c987ae7e3d84c0023e3d84c0021ffa5faf848007a392c1f61efa03dceb948007b4e0928e06fa779ae5806fe7cf8201fa03dceb94800daec6aeb67a03dceb948028ef8ea0a23a01eeb5ca8015ccd3c08a07ea5faf84805180acc61fea03dceb94800f97b8ebf61eea1389b48006bbf0ee6a3bcdb2c001b0eef3b207aa17ebe1806ae8fab62a779ae58002949ed4fa763d84c002363d84c00214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1573d84c002173d84c00203f303dceb94800dc2bcc7ca1cf35faf848039d7adbe733d84c00203b305faf8a027dbaa3301eeb5ca801c8b8eaa03e35faf848012b4abc21fe301eeb5ca805ad4ac9e14e301eeb5ca8035defbce6303dceb94800b9ec8b607a303dceb94800ab1d5f601a35faf848009cabea22303dceb94800fc203d303dceb948009a4be9c8617d32fd7c280109796fe1cd35faf848032ea8bbe5303dceb948007f781ea179303dceb948073dd9bf21303dceb94800fca14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decode [0x17f3d84c0023f3d84c00203fb17ebe18053fcdfa21dfb779ae5803dd9888e05fb5faf84800ee6aaf27b7a898001b7ca3b3d84c00207eb01eeb5ca802cbbe4b21eeb01eeb5ca80018084e59a6b03dceb948001b9acfd9e2b01eeb5ca8013d49596773d84c002373d84c00217e70bf5f0c00691afda06e701eeb5ca8026e8858605e70ef3acd026dee4ea675faf848001d6b0c08203a703dceb948022f0f1ae06a717ebe180059ddde627779ae58011b8bcc614]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decode [0x105f03bcdb2c018afeada701ec2a00203e003dceb948002c5a3d6ae1fe0779ae5801c98e59a1ee03bcdb2c0768fec8202e02fd7c2801a8aa88e15e003dceb9480069bd0aae61ce003dceb948060a0eb8a05e001eeb5ca8071ec998e601ec2a00217d003dceb948001cc9e978616d017ebe18001a8a3a9ee1dd0779ae5807da583ae1cd001eeb5ca80038ec1feda501ec2a00203c003dceb948026d7b4ba1fc0779ae5801286d5ae15c0779ae5800cf2c38205c0779ae58004c1dbf64001eeb5ca8011f614]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1681ec2a00203d81389b4800992dca616d801eeb5ca800c90e7959602d803dceb948001cea4b38e1cd803dceb94800998baa89e581ec2a00203c803dceb9480019cbdd4ca1fc803dceb9480708cb58a1ec8779ae5804d92b49e15c8779ae56194d005c803dceb94807cba8eca481ec2a002741ec2a002641ec2a002541ec2a002441ec2a00207f003dceb94800981d3858617f017ebe1800184b2cc8a16f0779ae58002db96be921cf003dceb948005808f8dfa14]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decode [0x10581779ae58010a48396011de6d9a001f27c1ec2a0021fec3bcdb2c003938a16ec03dceb94801e9dc61dec1389b48019e66c1ec2a0025c1ec2a0024c1ec2a00207f803dceb94800983e5f99617f85faf84800593d6f4e602f8779ae58002d6dbbbc21cf803dceb94800aa5b2ca96781ec2a00203e803dceb94805a80a7de1fe803dceb948035f8f7d61ee85faf84802bbec49a15e803dceb948003b6c9a0d21ce801eeb5ca807fe8ded605e803dceb948001c6beae14]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107e101eeb5ca8004a698c1f617e103dceb948005a1a0d3a216e1779ae5800495bc979202e103dceb94800a8686a4e61ce103dceb948003ab8d88f605e11de6d9a025abb2ea6101eeb5ca800fce07a101eeb5ca8002d5d3efc616a101eeb5ca800daba2f2be05a103dceb948005a6c2cad2211ec2a00203c102fdbc90058ab1aa17c101eeb5ca805cbfa58e02c15faf848001d1f795c61dc13bcdb2c018a4d4964103dceb94801eaa038103dceb948006a69bc0b61781779ae58010d29dfa168101eeb5ca80028bc689a61581779ae5807fb09af614]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decode [0x102a903dceb948006cab188b615a901eeb5ca8028bbbbe22903dceb94801e9207c901eeb5ca8001e4b2a39e16c903dceb94800fbc99acb602c9779ae58003a3a89fce1cc92fd7c28039fca6b605c92fd7c2803893c9b6491ec2a002178901eeb5ca8002b39afbaa158901eeb5ca800c91848dce058901eeb5ca8006bbdbf0de091ec2a00216f5779ae5800ebeeba4be15f503dceb948018e8e1d5d27503dceb948016a3aa8ab615b501eeb5ca800fb1cfaeaa355faf848006b2f193ea551ec2a002151ec2a00214]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decode [0x108835faf84800382a4a0da088003dceb94800585bcadde7d1ec2a0023d1ec2a00217dd03dceb948001aed2c8b616dd03dceb948009caac84d202dd3bcdb2c003febaa1fe14dd01eeb5ca8016c78ae2c25d02b196c00381a9ae029d1de6d9a00296a281aa019d03dceb94801481b8b8ba1d1de6d9a001e0c8a5ca03e903dceb94806dd2bace17e903dceb948004a2adc9ea16e9779ae58002aa9d868e02e903dceb948001d2b9fcd21ce95faf848018c8b3f6693bcdb2c003e603a901eeb5ca80048bfdf59617a901eeb5ca8028bbbbe214]
def rowsChunk11:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1089403e8a4020102010101010102089303dceb948013869ad60101010001020100089203dceb948016b3b097ae08911de6d9a010dfa8ca089009c4da80668ee6088c2fd7c28030c5aa088a01eeb5ca800edab3a6088f0102088803dceb948005fca7b38e088703dceb94800e85badef2088401eeb5ca8002aadf949a0b]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10 ++ rowsChunk11
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullFourCase0.base QuadFullFourCase0.hinges QuadFullFourCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
private def zz650:"s028a"="s028a":=by decide+kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase0.base QuadFullFourCase0.hinges QuadFullFourCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullFourCase1.base QuadFullFourCase1.hinges QuadFullFourCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase1.base QuadFullFourCase1.hinges QuadFullFourCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullFourCase2.base QuadFullFourCase2.hinges QuadFullFourCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
private def zz651:"s028b"="s028b":=by decide+kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase2.base QuadFullFourCase2.hinges QuadFullFourCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r67,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullFourCase3.base QuadFullFourCase3.hinges QuadFullFourCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase3.base QuadFullFourCase3.hinges QuadFullFourCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullFourCase4.base QuadFullFourCase4.hinges QuadFullFourCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
private def zz652:"s028c"="s028c":=by decide+kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase4.base QuadFullFourCase4.hinges QuadFullFourCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r80,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullFourCase5.base QuadFullFourCase5.hinges QuadFullFourCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase5.base QuadFullFourCase5.hinges QuadFullFourCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullFourCase6.base QuadFullFourCase6.hinges QuadFullFourCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
private def zz653:"s028d"="s028d":=by decide+kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase6.base QuadFullFourCase6.hinges QuadFullFourCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r30,RewriteAtoms.r32,RewriteAtoms.r77,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullFourCase7.base QuadFullFourCase7.hinges QuadFullFourCase7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase7.base QuadFullFourCase7.hinges QuadFullFourCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullFourCase8.base QuadFullFourCase8.hinges QuadFullFourCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
private def zz654:"s028e"="s028e":=by decide+kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase8.base QuadFullFourCase8.hinges QuadFullFourCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullFourCase9.base QuadFullFourCase9.hinges QuadFullFourCase9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase9.base QuadFullFourCase9.hinges QuadFullFourCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r16,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r4,RewriteAtoms.r63,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullFourCase10.base QuadFullFourCase10.hinges QuadFullFourCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
private def zz655:"s028f"="s028f":=by decide+kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase10.base QuadFullFourCase10.hinges QuadFullFourCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r20,RewriteAtoms.r81,RewriteAtoms.r16,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullFourCase11.base QuadFullFourCase11.hinges QuadFullFourCase11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase11.base QuadFullFourCase11.hinges QuadFullFourCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullFourCase12.base QuadFullFourCase12.hinges QuadFullFourCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
private def zz656:"s0290"="s0290":=by decide+kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase12.base QuadFullFourCase12.hinges QuadFullFourCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullFourCase13.base QuadFullFourCase13.hinges QuadFullFourCase13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase13.base QuadFullFourCase13.hinges QuadFullFourCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullFourCase14.base QuadFullFourCase14.hinges QuadFullFourCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
private def zz657:"s0291"="s0291":=by decide+kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase14.base QuadFullFourCase14.hinges QuadFullFourCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullFourCase15.base QuadFullFourCase15.hinges QuadFullFourCase15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase15.base QuadFullFourCase15.hinges QuadFullFourCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r68,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullFourCase16.base QuadFullFourCase16.hinges QuadFullFourCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
private def zz658:"s0292"="s0292":=by decide+kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase16.base QuadFullFourCase16.hinges QuadFullFourCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r80,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullFourCase17.base QuadFullFourCase17.hinges QuadFullFourCase17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase17.base QuadFullFourCase17.hinges QuadFullFourCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullFourCase18.base QuadFullFourCase18.hinges QuadFullFourCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
private def zz659:"s0293"="s0293":=by decide+kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase18.base QuadFullFourCase18.hinges QuadFullFourCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullFourCase19.base QuadFullFourCase19.hinges QuadFullFourCase19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFourCase19.base QuadFullFourCase19.hinges QuadFullFourCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFourCase19.nonnegative x hx
def pair20:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_20_base LocalFullFourPairs.compact_fullFour_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
private def zz660:"s0294"="s0294":=by decide+kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullFourPairs.fullFour_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_20_base LocalFullFourPairs.compact_fullFour_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullFourPairs.fullFour_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_21_base LocalFullFourPairs.compact_fullFour_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullFourPairs.fullFour_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_21_base LocalFullFourPairs.compact_fullFour_pair_21_hinges x
private def zz661:"s0295"="s0295":=by decide+kernel
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullFourPairs.fullFour_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 1 false
def pair22Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r53]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_22_base LocalFullFourPairs.compact_fullFour_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullFourPairs.fullFour_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_22_base LocalFullFourPairs.compact_fullFour_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullFourPairs.fullFour_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_23_base LocalFullFourPairs.compact_fullFour_pair_23_hinges
private def zz662:"s0296"="s0296":=by decide+kernel
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullFourPairs.fullFour_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_23_base LocalFullFourPairs.compact_fullFour_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullFourPairs.fullFour_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r69]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_24_base LocalFullFourPairs.compact_fullFour_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
private def zz663:"s0297"="s0297":=by decide+kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullFourPairs.fullFour_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_24_base LocalFullFourPairs.compact_fullFour_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullFourPairs.fullFour_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_25_base LocalFullFourPairs.compact_fullFour_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullFourPairs.fullFour_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_25_base LocalFullFourPairs.compact_fullFour_pair_25_hinges x
private def zz664:"s0298"="s0298":=by decide+kernel
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullFourPairs.fullFour_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r2]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_26_base LocalFullFourPairs.compact_fullFour_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullFourPairs.fullFour_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_26_base LocalFullFourPairs.compact_fullFour_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullFourPairs.fullFour_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (4) (1 / 0x186a0) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_27_base LocalFullFourPairs.compact_fullFour_pair_27_hinges
private def zz665:"s0299"="s0299":=by decide+kernel
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullFourPairs.fullFour_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_27_base LocalFullFourPairs.compact_fullFour_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullFourPairs.fullFour_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_28_base LocalFullFourPairs.compact_fullFour_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
private def zz666:"s029a"="s029a":=by decide+kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullFourPairs.fullFour_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_28_base LocalFullFourPairs.compact_fullFour_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullFourPairs.fullFour_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_29_base LocalFullFourPairs.compact_fullFour_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullFourPairs.fullFour_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_29_base LocalFullFourPairs.compact_fullFour_pair_29_hinges x
private def zz667:"s029b"="s029b":=by decide+kernel
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullFourPairs.fullFour_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r0,RewriteAtoms.r2]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_30_base LocalFullFourPairs.compact_fullFour_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullFourPairs.fullFour_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_30_base LocalFullFourPairs.compact_fullFour_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullFourPairs.fullFour_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_31_base LocalFullFourPairs.compact_fullFour_pair_31_hinges
private def zz668:"s029c"="s029c":=by decide+kernel
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullFourPairs.fullFour_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_31_base LocalFullFourPairs.compact_fullFour_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullFourPairs.fullFour_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_32_base LocalFullFourPairs.compact_fullFour_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
private def zz669:"s029d"="s029d":=by decide+kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullFourPairs.fullFour_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_32_base LocalFullFourPairs.compact_fullFour_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullFourPairs.fullFour_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (4) (1 / 0x186a0) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_33_base LocalFullFourPairs.compact_fullFour_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullFourPairs.fullFour_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_33_base LocalFullFourPairs.compact_fullFour_pair_33_hinges x
private def zz670:"s029e"="s029e":=by decide+kernel
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullFourPairs.fullFour_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (4) (1 / 0x186a0) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_34_base LocalFullFourPairs.compact_fullFour_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullFourPairs.fullFour_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_34_base LocalFullFourPairs.compact_fullFour_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullFourPairs.fullFour_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (4) (1 / 0x186a0) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_35_base LocalFullFourPairs.compact_fullFour_pair_35_hinges
private def zz671:"s029f"="s029f":=by decide+kernel
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullFourPairs.fullFour_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_35_base LocalFullFourPairs.compact_fullFour_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullFourPairs.fullFour_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (4) (1 / 0x186a0) rows 2 3 false
def pair36Rewrites:Rewrites:=[]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_36_base LocalFullFourPairs.compact_fullFour_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
private def zz672:"s02a0"="s02a0":=by decide+kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullFourPairs.fullFour_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_36_base LocalFullFourPairs.compact_fullFour_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullFourPairs.fullFour_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (4) (1 / 0x186a0) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r69]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_37_base LocalFullFourPairs.compact_fullFour_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullFourPairs.fullFour_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_37_base LocalFullFourPairs.compact_fullFour_pair_37_hinges x
private def zz673:"s02a1"="s02a1":=by decide+kernel
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullFourPairs.fullFour_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (4) (1 / 0x186a0) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_38_base LocalFullFourPairs.compact_fullFour_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullFourPairs.fullFour_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_38_base LocalFullFourPairs.compact_fullFour_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullFourPairs.fullFour_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (4) (1 / 0x186a0) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullFourPairs.compact_fullFour_pair_39_base LocalFullFourPairs.compact_fullFour_pair_39_hinges
private def zz674:"s02a2"="s02a2":=by decide+kernel
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullFourPairs.fullFour_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFourPairs.compact_fullFour_pair_39_base LocalFullFourPairs.compact_fullFour_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullFourPairs.fullFour_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
private def zz675:"s02a3"="s02a3":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (4) (1 / 0x186a0) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullFourRows
private def zz2204:"s089c"="s089c":=by decide+kernel
end 
section 
namespace Green24Proof.FullFourCyclic
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseSymmetry FullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullFourRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullFourRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullFourRows.rows p q same x]
    exact FullFourRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 4 (1 / 0x186a0) FullFourRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullFourRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 4 (1 / 0x186a0) FullFourRows.rows p q same x]
    exact FullFourRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullFourRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullFourRows.rows
private def zz676:"s02a4"="s02a4":=by decide+kernel
theorem remaining_rows_count:remainingRows.length = 13:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
      weightedAggregate 4 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullFourRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 4 (1 / 0x186a0) FullFourRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 4 h4 h3 h5 g FullFourRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
    weightedAggregate 4 h4 h3 g (stripPotentials FullFourRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullFourCyclic
private def zz2205:"s089d"="s089d":=by decide+kernel
end 
section 
namespace Green24Proof.PhaseColourRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows
theorem rowAggregate_colouredMassSquare_nonpos {q:ℕ} [NeZero q]
    (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (v:Phase → ℚ) :
    rowAggregate S h4 h3 g (.massSquare true v) ≤ 0:=by
  let χ:=ZMod.castHom h3 (ZMod 3)
  let f (i:ZMod q):ℝ:=(v (ZMod.castHom h4 (ZMod 4) i):ℝ) * g i
  have hp (j k:ZMod q):rowValue S h4 h3 g (.massSquare true v) j k =
      colourVarianceRow χ f j k:=by
    simp only [rowValue,rowQuad,rowPair,if_true]
    rw [pairProduct_eval]
    simp only [expressionEval,List.map_nil,List.sum_nil,zero_add,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
    dsimp only [χ,f,colourVarianceRow,sameColour]
    by_cases h:ZMod.castHom h3 (ZMod 3) j = ZMod.castHom h3 (ZMod 3) k
    · simp only [h,decide_true,if_true]
      norm_num
      ring
    · simp only [h,decide_false,Bool.false_eq_true,if_false]
      norm_num
      ring
  unfold rowAggregate
  simp_rw [hp]
  exact colourVarianceRow_sum_nonpos χ f
end Green24Proof.PhaseColourRows
private def zz2206:"s089e"="s089e":=by decide+kernel
end 
section 
namespace Green24Proof.FullFourMass
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows PhaseColourRows
theorem remainingRows_eq:FullFourCyclic.remainingRows = [
  ((0x28578b6f / 0x3b9aca00), .balance 0 (1)),
  ((0x1824882d / 0xbebc200), .balance 1 (-1)),
  ((0x12abe50d / 0x1dcd6500), .balance 2 (1)),
  ((0x705757b9 / 0x3b9aca00), .balance 3 (-1)),
  ((0x2fc4ecc7 / 0x3b9aca00), .child 0),
  (1, .heightChild 1),
  ((0xeb4cd3 / 0x1dcd6500), .grandchild 0),
  ((0x61155 / 0x5f5e100), .grandchild 2),
  ((0xcc3b3 / 0x1312d00), .ordered 0),
  ((0x10bea25 / 0x3b9aca0), .ordered 1),
  ((0xb33605d7 / 0x3b9aca00), .massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((0x130c6ab / 0x3b9aca00), .massSquare true (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)),
  ((1 / 0xf424), .normalization)]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff PackedPhaseRowsEquality.labelEq PackedPhaseRowsEquality.labelEq_iff _ _).mp
  decide +kernel
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0x28578b6f / 0x3b9aca00):ℝ) * phaseTotal h4 g 0 + ((-0x1824882d / 0xbebc200):ℝ) * phaseTotal h4 g 1 + ((0x12abe50d / 0x1dcd6500):ℝ) * phaseTotal h4 g 2 + ((-0x705757b9 / 0x3b9aca00):ℝ) * phaseTotal h4 g 3) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - (4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
noncomputable def meanBalance {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0x4daf5589 / 0x77359400):ℝ) * (phaseTotal h4 g 0 + phaseTotal h4 g 2) + ((-0x7487004d / 0x3b9aca00):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - (4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
private def zz677:"s02a5"="s02a5":=by decide+kernel
theorem weighted_remaining_eq {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    weightedAggregate 4 h4 h3 g FullFourCyclic.remainingRows =
      balanceMass h4 g +
      ((0x2fc4ecc7 / 0x3b9aca00):ℝ) * rowAggregate 4 h4 h3 g (.child 0) +
      (1:ℝ) * rowAggregate 4 h4 h3 g (.heightChild 1) +
      ((0xeb4cd3 / 0x1dcd6500):ℝ) * rowAggregate 4 h4 h3 g (.grandchild 0) +
      ((0x61155 / 0x5f5e100):ℝ) * rowAggregate 4 h4 h3 g (.grandchild 2) +
      ((0xcc3b3 / 0x1312d00):ℝ) * rowAggregate 4 h4 h3 g (.ordered 0) +
      ((0x10bea25 / 0x3b9aca0):ℝ) * rowAggregate 4 h4 h3 g (.ordered 1) +
      ((0xb33605d7 / 0x3b9aca00):ℝ) * rowAggregate 4 h4 h3 g (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)) +
      ((0x130c6ab / 0x3b9aca00):ℝ) * rowAggregate 4 h4 h3 g (.massSquare true (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)) +
      ((1 / 0xf424):ℝ) * mass g ^ 2:=by
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_balance,rowAggregate_normalization]
  norm_num
  unfold balanceMass
  ring
theorem balanceMass_le_mean {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hU:0 ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2))
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) :
    balanceMass h4 g + ((0x10bea25 / 0x3b9aca0):ℝ) * rowAggregate 4 h4 h3 g (.ordered 1) ≤ meanBalance h4 g:=by
  have hp:=mul_nonpos_of_nonneg_of_nonpos (sub_nonneg.mpr heven) (sub_nonpos.mpr hhigh)
  have ho:=mul_nonpos_of_nonneg_of_nonpos hU (sub_nonpos.mpr hodd)
  rw [rowAggregate_ordered]
  norm_num
  unfold balanceMass meanBalance
  nlinarith
noncomputable def massPolynomial (U V:ℝ):ℝ :=
  ((-0x4dae9a09 / 0x1dcd65000):ℝ) * U ^ 2 + ((0x10fe666df / 0xee6b2800):ℝ) * U * V + ((-0x7486e8dd / 0x3b9aca00):ℝ) * V ^ 2
theorem massPolynomial_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(3:ℝ) * V ≤ U) (hhigh:U ≤ (4:ℝ) * V) :
    ((0xbb801 / 0x1dcd65000):ℝ) * V ^ 2 ≤ massPolynomial U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  have hh:=mul_nonneg hV (sub_nonneg.mpr hhigh)
  unfold massPolynomial
  nlinarith
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate 4 h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate 4 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:rowAggregate 4 h4 h3 g (.grandchild 0) ≤ 0)
    (hg2:rowAggregate 4 h4 h3 g (.grandchild 2) ≤ 0) :
    weightedAggregate 4 h4 h3 g FullFourCyclic.remainingRows ≤
      meanBalance h4 g + ((1 / 0xf424):ℝ) * mass g ^ 2:=by
  rw [weighted_remaining_eq]
  have hb:=balanceMass_le_mean h4 h3 g
    (add_nonneg (phaseTotal_nonneg h4 g hg 0) (phaseTotal_nonneg h4 g hg 2)) heven hodd hhigh
  have ho:rowAggregate 4 h4 h3 g (.ordered 0) ≤ 0 :=
    rowAggregate_ordered_nonpos 4 h4 h3 g hg 0 (by simpa using heven)
  have hm6:=rowAggregate_massSquare_nonpos 4 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hm7:=rowAggregate_colouredMassSquare_nonpos 4 h4 h3 g (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)
  linarith
private def zz678:"s02a6"="s02a6":=by decide+kernel
theorem deficit_lower_bound_of_child_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hlow:(3:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2))
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate 4 h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate 4 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:rowAggregate 4 h4 h3 g (.grandchild 0) ≤ 0)
    (hg2:rowAggregate 4 h4 h3 g (.grandchild 2) ≤ 0) :
    ((0xbb801 / 0x1dcd65000):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ^ 2 ≤ deficit g:=by
  have hc:=FullFourCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg heven hodd hhigh hchild hheight hg0 hg2
  have hm:mass g = (phaseTotal h4 g 0 + phaseTotal h4 g 2) + (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    simpa only [add_assoc,add_comm,add_left_comm] using (phaseTotal_sum h4 g).symm
  have hp:massPolynomial (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ deficit g:=by
    rw [hm] at hc hr
    unfold meanBalance at hr
    unfold massPolynomial
    nlinarith
  exact (massPolynomial_lower_bound
    (add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)) hlow hhigh).trans hp
end Green24Proof.FullFourMass
private def zz2207:"s089f"="s089f":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileDoubleOrientation
open FullPhaseRows (Phase)
open PhaseMassRows ProfileOrientation
theorem phaseTotal_reflect {q:ℕ} [NeZero q] (h4:4 ∣ q)
    (g:ZMod q → ℝ) (r:Phase) :
    phaseTotal h4 (fun i => g (-i)) r = phaseTotal h4 g (-r):=by
  unfold phaseTotal colourTotal
  have h:=Equiv.sum_comp (Equiv.neg (ZMod q))
    (fun i => if ZMod.castHom h4 (ZMod 4) i = -r then g i else 0)
  simpa only [Equiv.neg_apply,map_neg,neg_inj] using h
theorem parityEquiv_neg_even {m:ℕ} [NeZero m] (i:ZMod m) :
    -parityEquiv m (0,i) = parityEquiv m (0, -i):=by
  simp [parityEquiv_apply]
theorem parityEquiv_neg_odd {m:ℕ} [NeZero m] (i:ZMod m) :
    -parityEquiv m (1,i) = parityEquiv m (1, -i - 1):=by
  simp only [parityEquiv_apply,map_sub,map_neg]
  have h:doubleResidue m 1 = 2:=by simpa using doubleResidue_natCast m 1
  rw [h]
  simp only [show (1:ZMod 2).val = 1 from rfl,Nat.cast_one]
  ring
private def zz679:"s02a7"="s02a7":=by decide+kernel
theorem interleave_reflect {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    interleave (fun i => u (-i)) (fun i => v (-i - 1)) =
      fun i => interleave u v (-i):=by
  funext x
  obtain ⟨⟨r,i⟩,rfl⟩:=(parityEquiv m).surjective x
  rcases zmod_two_eq_zero_or_one r with rfl | rfl
  · rw [parityEquiv_neg_even,interleave_even,interleave_even]
  · rw [parityEquiv_neg_odd,interleave_odd,interleave_odd]
theorem odd_mass_reflect {m:ℕ} [NeZero m] (v:ZMod m → ℝ) :
    mass (fun i => v (-i - 1)) = mass v:=by
  have h:=mass_reflect (fun i => v (i - 1))
  have ht:=mass_translate v (-1)
  simp only [sub_eq_add_neg] at h
  simpa only [sub_eq_add_neg] using h.trans ht
theorem orient_both_children {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    ∃ u' v':ZMod m → ℝ,(∀ i,0 ≤ u' i) ∧ (∀ i,0 ≤ v' i) ∧
      mass u' = mass u ∧ mass v' = mass v ∧ deficit (interleave u' v') = deficit (interleave u v) ∧
      phaseTotal h4 (interleave u' v') 2 ≤ phaseTotal h4 (interleave u' v') 0 ∧
      phaseTotal h4 (interleave u' v') 3 ≤ phaseTotal h4 (interleave u' v') 1:=by
  obtain ⟨a,b,ha,hb,hA,hB,hd,ho⟩:=orient_even_child h4 u v hu hv
  rcases le_total (phaseTotal h4 (interleave a b) 3) (phaseTotal h4 (interleave a b) 1) with h | h
  · exact ⟨a,b,ha,hb,hA,hB,hd,ho,h⟩
  · refine ⟨(fun i => a (-i)),(fun i => b (-i - 1)),(fun i => ha _),(fun i => hb _),
      (mass_reflect a).trans hA,(odd_mass_reflect b).trans hB, ?_, ?_, ?_⟩
    · rw [interleave_reflect,deficit_reflect]
      exact hd
    · rw [interleave_reflect,phaseTotal_reflect,phaseTotal_reflect]
      simpa only [show (-2:Phase) = 2 from rfl,neg_zero] using ho
    · rw [interleave_reflect,phaseTotal_reflect,phaseTotal_reflect]
      simpa only [show (-3:Phase) = 1 from rfl,show (-1:Phase) = 3 from rfl] using h
end Green24Proof.ProfileDoubleOrientation
private def zz2208:"s08a0"="s08a0":=by decide+kernel
end 
section 
namespace Green24Proof.FullFourProfileInterval
open FullPhaseRows FullPhaseAggregation PhaseMassRows ChildRows HeightChildRows
theorem interval_bound_of_height {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hh:(49 / 0xfa:ℝ) * energy v - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) v 0 - classMass (ZMod.castHom h2 (ZMod 2)) v 1) ^ 2 ≤ deficit v)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(3:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (4:ℝ) * mass v) :
    (0xbb801 / 0x1dcd65000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    have ht:=phaseTotal_sum h4 (interleave u v)
    rw [mass_interleave] at ht
    linarith
  have hchild:rowAggregate (4) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have hheight:=rowAggregate_height_odd_nonpos (4) h4 h3 h2 u v hu hv hh
  have hg0:=Full27ProfileInterval.grandchild_nonpos_of_induction 4 h4 h3 (interleave u v) hg 0 ih
  have hg2:=Full27ProfileInterval.grandchild_nonpos_of_induction 4 h4 h3 (interleave u v) hg 2 ih
  have hc:=FullFourMass.deficit_lower_bound_of_child_rows h4 h3 h5 (interleave u v) hg horder hodd
    (by rw [hU,hV]; exact hlow) (by rw [hU,hV]; exact hhigh) hchild hheight hg0 hg2
  simpa only [hV] using hc
private def zz680:"s02a8"="s02a8":=by decide+kernel
theorem interval_bound_ordered {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(3:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (4:ℝ) * mass v) :
    (0xbb801 / 0x1dcd65000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  exact interval_bound_of_height h4 h3 h5 h2 u v hu hv ih
    (HeightStrong.strong_height_bound h2 h3m h5m v hv) horder hodd hlow hhigh
theorem interval_bound {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(3:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (4:ℝ) * mass v) :
    (0xbb801 / 0x1dcd65000:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,horder,hodd⟩:=ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have hb:=interval_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih horder hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hU,hV,hd] using hb
end Green24Proof.FullFourProfileInterval
private def zz2209:"s08a1"="s08a1":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCover
theorem interval_to_four {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 4 * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases h:mass u ≤ 3 * mass v
  · exact NearBalanceVerified.interval_to_three h4 h3 h5 h2 u v hu hv ih horder h
  · have hb:=FullFourProfileInterval.interval_bound h4 h3 h5 h2 u v hu hv ih
      (le_of_lt (lt_of_not_ge h)) hhigh
    exact (mul_nonneg (by norm_num) (sq_nonneg (mass v))).trans hb
end Green24Proof.RatioCover
private def zz2210:"s08a2"="s08a2":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullFivePairs
def compact_fullFive_pair_20_base:CompactPair.Quadratic:=⟨(1 / 0x5f5e1000),(0x4e1d / 0x77359400),0⟩
def compact_fullFive_pair_20_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(-0x13f9f18b / 0x1dcd65000),1, -2⟩,⟨(0x11fa8c95 / 0x2cb417800),2, -3⟩,⟨(0x13f9f18b / 0x1dcd65000),2, -1⟩,⟨(-0x11fa8c95 / 0x2cb417800),3, -2⟩,⟨(-1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFive_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_20_base compact_fullFive_pair_20_hinges x y
def compact_fullFive_pair_20_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFive_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_20_base compact_fullFive_pair_20_hinges 0 compact_fullFive_pair_20_cuts = true :=
  by decide +kernel
private def zz681:"s02a9"="s02a9":=by decide+kernel
theorem compact_fullFive_pair_20_representation (x y:ℝ) :
    fullFive_pair_20 x y = CompactPair.expressionEval compact_fullFive_pair_20_base compact_fullFive_pair_20_hinges x y:=by rfl
theorem fullFive_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_20 x y:=by
  rw [compact_fullFive_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_20_check hy (by simpa using hx)
def compact_fullFive_pair_21_base:CompactPair.Quadratic:=⟨(-13 / 0x1dcd65000),(0x1f41 / 0x77359400),0⟩
def compact_fullFive_pair_21_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0xee6b2800),1, -2⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullFive_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_21_base compact_fullFive_pair_21_hinges x y
def compact_fullFive_pair_21_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFive_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_21_base compact_fullFive_pair_21_hinges 0 compact_fullFive_pair_21_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_21_representation (x y:ℝ) :
    fullFive_pair_21 x y = CompactPair.expressionEval compact_fullFive_pair_21_base compact_fullFive_pair_21_hinges x y:=by rfl
private def zz682:"s02aa"="s02aa":=by decide+kernel
theorem fullFive_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_21 x y:=by
  rw [compact_fullFive_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_21_check hy (by simpa using hx)
def compact_fullFive_pair_22_base:CompactPair.Quadratic:=⟨0,(0x36b1 / 0x3b9aca00),0⟩
def compact_fullFive_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullFive_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_22_base compact_fullFive_pair_22_hinges x y
def compact_fullFive_pair_22_cuts:List ℚ:=[]
theorem compact_fullFive_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_22_base compact_fullFive_pair_22_hinges 0 compact_fullFive_pair_22_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_22_representation (x y:ℝ) :
    fullFive_pair_22 x y = CompactPair.expressionEval compact_fullFive_pair_22_base compact_fullFive_pair_22_hinges x y:=by rfl
theorem fullFive_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_22 x y:=by
  rw [compact_fullFive_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_22_check hy (by simpa using hx)
def compact_fullFive_pair_23_base:CompactPair.Quadratic:=⟨(-0x2c29b0d7 / 0xb2d05e00),(0x835b29 / 0x3b9aca0),0⟩
def compact_fullFive_pair_23_hinges:List CompactPair.Hinge:=[⟨(1 / 0xb2d05e00),1, -3⟩,⟨(-0x4bb9cc7 / 0xee6b2800),1, -2⟩,⟨(0x8f1dec1 / 0x2cb417800),2, -3⟩,⟨(0x4f6581d7 / 0x1dcd65000),2, -1⟩,⟨(-0x23b36f99 / 0x2cb417800),3, -2⟩]
noncomputable def fullFive_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_23_base compact_fullFive_pair_23_hinges x y
def compact_fullFive_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2,3]
private def zz683:"s02ab"="s02ab":=by decide+kernel
theorem compact_fullFive_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_23_base compact_fullFive_pair_23_hinges 0 compact_fullFive_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_23_representation (x y:ℝ) :
    fullFive_pair_23 x y = CompactPair.expressionEval compact_fullFive_pair_23_base compact_fullFive_pair_23_hinges x y:=by rfl
theorem fullFive_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_23 x y:=by
  rw [compact_fullFive_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_23_check hy (by simpa using hx)
def compact_fullFive_pair_24_base:CompactPair.Quadratic:=⟨(1 / 0xee6b2800),(1 / 0x186a0),0⟩
def compact_fullFive_pair_24_hinges:List CompactPair.Hinge:=[⟨(0xb5c9c5 / 0x77359400),1, -3⟩,⟨(-0x1244d2b1 / 0x77359400),1, -2⟩,⟨(0x10c12325 / 0xee6b2800),2, -3⟩,⟨(-0x4e1d4ab5 / 0xee6b2800),2, -1⟩,⟨(0x1eff6d55 / 0x2cb417800),3, -2⟩,⟨(0x7d0af01 / 0x59682f00),3, -1⟩]
noncomputable def fullFive_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_24_base compact_fullFive_pair_24_hinges x y
def compact_fullFive_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFive_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_24_base compact_fullFive_pair_24_hinges 0 compact_fullFive_pair_24_cuts = true :=
  by decide +kernel
private def zz684:"s02ac"="s02ac":=by decide+kernel
theorem compact_fullFive_pair_24_representation (x y:ℝ) :
    fullFive_pair_24 x y = CompactPair.expressionEval compact_fullFive_pair_24_base compact_fullFive_pair_24_hinges x y:=by rfl
theorem fullFive_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_24 x y:=by
  rw [compact_fullFive_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_24_check hy (by simpa using hx)
def compact_fullFive_pair_25_base:CompactPair.Quadratic:=⟨(-67 / 0x59682f000),(0xfa3 / 0x3b9aca00),0⟩
def compact_fullFive_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0xb2d05e00),1, -3⟩,⟨(-3 / 0x1dcd65000),1, -2⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(1 / 0x2cb417800),3, -2⟩,⟨(1 / 0xee6b2800),3, -1⟩]
noncomputable def fullFive_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_25_base compact_fullFive_pair_25_hinges x y
def compact_fullFive_pair_25_cuts:List ℚ:=[(1 / 3),(2 / 3),(3 / 2),2,3]
theorem compact_fullFive_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_25_base compact_fullFive_pair_25_hinges 0 compact_fullFive_pair_25_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_25_representation (x y:ℝ) :
    fullFive_pair_25 x y = CompactPair.expressionEval compact_fullFive_pair_25_base compact_fullFive_pair_25_hinges x y:=by rfl
private def zz685:"s02ad"="s02ad":=by decide+kernel
theorem fullFive_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_25 x y:=by
  rw [compact_fullFive_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_25_check hy (by simpa using hx)
def compact_fullFive_pair_26_base:CompactPair.Quadratic:=⟨0,(0x36b1 / 0x3b9aca00),0⟩
def compact_fullFive_pair_26_hinges:List CompactPair.Hinge:=[]
noncomputable def fullFive_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_26_base compact_fullFive_pair_26_hinges x y
def compact_fullFive_pair_26_cuts:List ℚ:=[]
theorem compact_fullFive_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_26_base compact_fullFive_pair_26_hinges 0 compact_fullFive_pair_26_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_26_representation (x y:ℝ) :
    fullFive_pair_26 x y = CompactPair.expressionEval compact_fullFive_pair_26_base compact_fullFive_pair_26_hinges x y:=by rfl
theorem fullFive_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_26 x y:=by
  rw [compact_fullFive_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_26_check hy (by simpa using hx)
def compact_fullFive_pair_27_base:CompactPair.Quadratic:=⟨(-0x9d5f45463 / 0x59682f000),(0x15015811 / 0x1dcd6500),0⟩
def compact_fullFive_pair_27_hinges:List CompactPair.Hinge:=[⟨(-0x619f06f / 0x5f5e1000),1, -2⟩,⟨(-0x17a2820d / 0x77359400),1, -1⟩,⟨(0x22989f77 / 0x2cb417800),2, -3⟩,⟨(-0x9e3df607 / 0x1dcd65000),2, -1⟩,⟨(0x29cec285 / 0x77359400),3, -1⟩]
noncomputable def fullFive_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_27_base compact_fullFive_pair_27_hinges x y
def compact_fullFive_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2),2]
private def zz686:"s02ae"="s02ae":=by decide+kernel
theorem compact_fullFive_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_27_base compact_fullFive_pair_27_hinges 0 compact_fullFive_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_27_representation (x y:ℝ) :
    fullFive_pair_27 x y = CompactPair.expressionEval compact_fullFive_pair_27_base compact_fullFive_pair_27_hinges x y:=by rfl
theorem fullFive_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_27 x y:=by
  rw [compact_fullFive_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_27_check hy (by simpa using hx)
def compact_fullFive_pair_28_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2ebabcef / 0x3b9aca00),(-49 / 50)⟩
def compact_fullFive_pair_28_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_28_base compact_fullFive_pair_28_hinges x y
def compact_fullFive_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFive_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_28_base compact_fullFive_pair_28_hinges 0 compact_fullFive_pair_28_cuts = true :=
  by decide +kernel
private def zz687:"s02af"="s02af":=by decide+kernel
theorem compact_fullFive_pair_28_representation (x y:ℝ) :
    fullFive_pair_28 x y = CompactPair.expressionEval compact_fullFive_pair_28_base compact_fullFive_pair_28_hinges x y:=by rfl
theorem fullFive_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_28 x y:=by
  rw [compact_fullFive_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_28_check hy (by simpa using hx)
def compact_fullFive_pair_29_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2ebad45f / 0x3b9aca00),(-49 / 50)⟩
def compact_fullFive_pair_29_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_29_base compact_fullFive_pair_29_hinges x y
def compact_fullFive_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFive_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_29_base compact_fullFive_pair_29_hinges 0 compact_fullFive_pair_29_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_29_representation (x y:ℝ) :
    fullFive_pair_29 x y = CompactPair.expressionEval compact_fullFive_pair_29_base compact_fullFive_pair_29_hinges x y:=by rfl
private def zz688:"s02b0"="s02b0":=by decide+kernel
theorem fullFive_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_29 x y:=by
  rw [compact_fullFive_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_29_check hy (by simpa using hx)
def compact_fullFive_pair_30_base:CompactPair.Quadratic:=⟨(-0xdab608961 / 0x165a0bc00),(0x3f9c0571 / 0xbebc200),0⟩
def compact_fullFive_pair_30_hinges:List CompactPair.Hinge:=[⟨(-0x376de9 / 0x3b9aca00),1, -1⟩,⟨(-0x5a9f7a89 / 0x2cb417800),2, -3⟩,⟨(0x1991a3ae1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFive_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_30_base compact_fullFive_pair_30_hinges x y
def compact_fullFive_pair_30_cuts:List ℚ:=[(1 / 3),1,(3 / 2)]
theorem compact_fullFive_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_30_base compact_fullFive_pair_30_hinges 0 compact_fullFive_pair_30_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_30_representation (x y:ℝ) :
    fullFive_pair_30 x y = CompactPair.expressionEval compact_fullFive_pair_30_base compact_fullFive_pair_30_hinges x y:=by rfl
theorem fullFive_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_30 x y:=by
  rw [compact_fullFive_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_30_check hy (by simpa using hx)
def compact_fullFive_pair_31_base:CompactPair.Quadratic:=⟨(-1 / 0x11e1a3000),(0xf9f / 0x1dcd6500),0⟩
def compact_fullFive_pair_31_hinges:List CompactPair.Hinge:=[⟨(-0x50810291 / 0xb2d05e00),1, -3⟩,⟨(0x2ae6db85 / 0x5f5e1000),1, -2⟩,⟨(-0x26fadb81 / 0xee6b2800),1, -1⟩,⟨(0xfe547b / 0x2faf0800),2, -3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(0x665ee65 / 0x2cb417800),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullFive_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_31_base compact_fullFive_pair_31_hinges x y
def compact_fullFive_pair_31_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz689:"s02b1"="s02b1":=by decide+kernel
theorem compact_fullFive_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_31_base compact_fullFive_pair_31_hinges 0 compact_fullFive_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_31_representation (x y:ℝ) :
    fullFive_pair_31 x y = CompactPair.expressionEval compact_fullFive_pair_31_base compact_fullFive_pair_31_hinges x y:=by rfl
theorem fullFive_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_31 x y:=by
  rw [compact_fullFive_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_31_check hy (by simpa using hx)
def compact_fullFive_pair_32_base:CompactPair.Quadratic:=⟨(-0xe9a673ff / 0xee6b2800),(-0x46182eef / 0x3b9aca00),(-49 / 50)⟩
def compact_fullFive_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x1293207 / 0x17d7840),1, -3⟩,⟨(-0xec3a7475 / 0x77359400),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x954e63c3 / 0x2cb417800),3, -2⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_32_base compact_fullFive_pair_32_hinges x y
def compact_fullFive_pair_32_cuts:List ℚ:=[(1 / 3),(2 / 3),1,3]
theorem compact_fullFive_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_32_base compact_fullFive_pair_32_hinges 0 compact_fullFive_pair_32_cuts = true :=
  by decide +kernel
private def zz690:"s02b2"="s02b2":=by decide+kernel
theorem compact_fullFive_pair_32_representation (x y:ℝ) :
    fullFive_pair_32 x y = CompactPair.expressionEval compact_fullFive_pair_32_base compact_fullFive_pair_32_hinges x y:=by rfl
theorem fullFive_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_32 x y:=by
  rw [compact_fullFive_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_32_check hy (by simpa using hx)
def compact_fullFive_pair_33_base:CompactPair.Quadratic:=⟨(-0x493185df / 0x2cb41780),(-0x21c065 / 0x2625a0),(-49 / 50)⟩
def compact_fullFive_pair_33_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(-0x6adb6f71 / 0xee6b2800),1, -2⟩,⟨(-0x38d9e97 / 0x17d7840),1, -1⟩,⟨(49 / 0x1f4),1,3⟩,⟨(0x14acdd2ab / 0x2cb417800),2, -3⟩,⟨(0x4407dabf / 0x2cb417800),3, -2⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_33_base compact_fullFive_pair_33_hinges x y
def compact_fullFive_pair_33_cuts:List ℚ:=[(1 / 3),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullFive_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_33_base compact_fullFive_pair_33_hinges 0 compact_fullFive_pair_33_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_33_representation (x y:ℝ) :
    fullFive_pair_33 x y = CompactPair.expressionEval compact_fullFive_pair_33_base compact_fullFive_pair_33_hinges x y:=by rfl
private def zz691:"s02b3"="s02b3":=by decide+kernel
theorem fullFive_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_33 x y:=by
  rw [compact_fullFive_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_33_check hy (by simpa using hx)
def compact_fullFive_pair_34_base:CompactPair.Quadratic:=⟨(1 / 0x59682f00),(0x4e27 / 0x77359400),0⟩
def compact_fullFive_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x115e967 / 0x2cb417800),1, -3⟩,⟨(0x22bd2d / 0xee6b280),1, -2⟩,⟨(-0x22bd2d / 0x2cb41780),2, -3⟩,⟨(-0x22bd2d / 0xee6b280),2, -1⟩,⟨(0x22bd2d / 0x2cb41780),3, -2⟩,⟨(0x115e967 / 0x2cb417800),3, -1⟩]
noncomputable def fullFive_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_34_base compact_fullFive_pair_34_hinges x y
def compact_fullFive_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullFive_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_34_base compact_fullFive_pair_34_hinges 0 compact_fullFive_pair_34_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_34_representation (x y:ℝ) :
    fullFive_pair_34 x y = CompactPair.expressionEval compact_fullFive_pair_34_base compact_fullFive_pair_34_hinges x y:=by rfl
theorem fullFive_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_34 x y:=by
  rw [compact_fullFive_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_34_check hy (by simpa using hx)
def compact_fullFive_pair_35_base:CompactPair.Quadratic:=⟨(-1 / 0x8f0d1800),(0x1f49 / 0x77359400),0⟩
def compact_fullFive_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),2, -3⟩,⟨(1 / 0x2cb417800),3, -2⟩]
noncomputable def fullFive_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_35_base compact_fullFive_pair_35_hinges x y
def compact_fullFive_pair_35_cuts:List ℚ:=[(2 / 3),(3 / 2)]
private def zz692:"s02b4"="s02b4":=by decide+kernel
theorem compact_fullFive_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_35_base compact_fullFive_pair_35_hinges 0 compact_fullFive_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_35_representation (x y:ℝ) :
    fullFive_pair_35 x y = CompactPair.expressionEval compact_fullFive_pair_35_base compact_fullFive_pair_35_hinges x y:=by rfl
theorem fullFive_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_35 x y:=by
  rw [compact_fullFive_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_35_check hy (by simpa using hx)
def compact_fullFive_pair_36_base:CompactPair.Quadratic:=⟨(-0x55d13c9 / 0x77359400),(0x2dca65 / 0x5f5e100),0⟩
def compact_fullFive_pair_36_hinges:List CompactPair.Hinge:=[⟨(0x1c9b143 / 0x165a0bc00),3, -1⟩]
noncomputable def fullFive_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_36_base compact_fullFive_pair_36_hinges x y
def compact_fullFive_pair_36_cuts:List ℚ:=[(1 / 3)]
theorem compact_fullFive_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_36_base compact_fullFive_pair_36_hinges 0 compact_fullFive_pair_36_cuts = true :=
  by decide +kernel
private def zz693:"s02b5"="s02b5":=by decide+kernel
theorem compact_fullFive_pair_36_representation (x y:ℝ) :
    fullFive_pair_36 x y = CompactPair.expressionEval compact_fullFive_pair_36_base compact_fullFive_pair_36_hinges x y:=by rfl
theorem fullFive_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_36 x y:=by
  rw [compact_fullFive_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_36_check hy (by simpa using hx)
def compact_fullFive_pair_37_base:CompactPair.Quadratic:=⟨(-0x4be31e1a3 / 0x59682f000),(0x3ca7b41 / 0xbebc200),0⟩
def compact_fullFive_pair_37_hinges:List CompactPair.Hinge:=[⟨(-3 / 0x17d78400),1, -3⟩,⟨(0x3a9 / 0x1dcd65000),1, -2⟩,⟨(0x309717f1 / 0x77359400),1, -1⟩,⟨(-0x4dcd499 / 0xb2d05e00),2, -3⟩,⟨(-0x18077035 / 0x3b9aca00),2, -1⟩,⟨(0x157b90a9 / 0x59682f00),3, -1⟩]
noncomputable def fullFive_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_37_base compact_fullFive_pair_37_hinges x y
def compact_fullFive_pair_37_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2),2,3]
theorem compact_fullFive_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_37_base compact_fullFive_pair_37_hinges 0 compact_fullFive_pair_37_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_37_representation (x y:ℝ) :
    fullFive_pair_37 x y = CompactPair.expressionEval compact_fullFive_pair_37_base compact_fullFive_pair_37_hinges x y:=by rfl
private def zz694:"s02b6"="s02b6":=by decide+kernel
theorem fullFive_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_37 x y:=by
  rw [compact_fullFive_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_37_check hy (by simpa using hx)
def compact_fullFive_pair_38_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2ebabcef / 0x3b9aca00),(-49 / 50)⟩
def compact_fullFive_pair_38_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_38_base compact_fullFive_pair_38_hinges x y
def compact_fullFive_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullFive_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_38_base compact_fullFive_pair_38_hinges 0 compact_fullFive_pair_38_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_38_representation (x y:ℝ) :
    fullFive_pair_38 x y = CompactPair.expressionEval compact_fullFive_pair_38_base compact_fullFive_pair_38_hinges x y:=by rfl
theorem fullFive_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_38 x y:=by
  rw [compact_fullFive_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_38_check hy (by simpa using hx)
def compact_fullFive_pair_39_base:CompactPair.Quadratic:=⟨(-0x1b9 / 0xfa),(-0x2ebad45f / 0x3b9aca00),(-49 / 50)⟩
def compact_fullFive_pair_39_hinges:List CompactPair.Hinge:=[⟨(-49 / 0x1f4),1, -3⟩,⟨(49 / 0x1f4),1,3⟩,⟨(49 / 0x1f4),3, -1⟩,⟨(49 / 0x1f4),3,1⟩]
noncomputable def fullFive_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullFive_pair_39_base compact_fullFive_pair_39_hinges x y
def compact_fullFive_pair_39_cuts:List ℚ:=[(1 / 3),3]
private def zz695:"s02b7"="s02b7":=by decide+kernel
theorem compact_fullFive_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullFive_pair_39_base compact_fullFive_pair_39_hinges 0 compact_fullFive_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullFive_pair_39_representation (x y:ℝ) :
    fullFive_pair_39 x y = CompactPair.expressionEval compact_fullFive_pair_39_base compact_fullFive_pair_39_hinges x y:=by rfl
theorem fullFive_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullFive_pair_39 x y:=by
  rw [compact_fullFive_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullFive_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullFivePairs
private def zz2211:"s08a3"="s08a3":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l42 l43 l45 l5 l51 l54 l55 l57 l58 l6 l60 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1133b2dff, -0x113ff180a, -0x19dfec09e,0x1d2753aa], ![-0x113ff180a, -0x3b229d19e,0x3fadad44,0x102cfd6f8], ![-0x19dfec09e,0x3fadad44, -0x701fb6089,0x113ff78ca], ![0x1d2753aa,0x102cfd6f8,0x113ff78ca, -0x89ffa4f8]]
noncomputable def hinges:Hinges:=[(-0xfd827e,l6),(-0x13997a45,l5),(0x90f4d4f6,l4),(0x19c3403,l9),(-0x652c6bf3,l8),(-0x77231c,l11),(0x1ee5b22a,l10),(0x11e5dbf00,l14),(-0x307d43a4,l17),(0x22197abf,l23),(0x890413b,l22),(-0x89ffa4f8,l27),(0x89ffa4f8,l29),(-0x11e5dbf00,l25),(0x34140754,l31),(0x5eb19bde,l30),(0x89ffa4f8,l33),(-0x1ee5b22a,l38),(-0x89ffa4f8,l35),(0x652c6bf3,l36),(0x89ffa4f8,l37),(-0x90f4d4f6,l34),(-0x5eb19bde,l43),(-0x890413b,l42),(0x4d0e5717,l45),(0x89ffa4f8,l51),(0x77231c,l55),(0x13997a45,l54),(-0x34140754,l57),(-0x4d0e5717,l58),(-0x19c3403,l61),(0xfd827e,l60),(-0x22197abf,l63),(0x307d43a4,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x89ffa4f8,l27),(0x89ffa4f8,l29),(0x89ffa4f8,l33),(-0x89ffa4f8,l35),(0x89ffa4f8,l37),(0x89ffa4f8,l51),(0x11e5dbf00,l14),(-0x11e5dbf00,l25),(0x5eb19bde,l30),(-0x5eb19bde,l43),(0x34140754,l31),(-0x34140754,l57),(-0x652c6bf3,l8),(0x652c6bf3,l36),(0x22197abf,l23),(-0x22197abf,l63),(-0x307d43a4,l17),(0x307d43a4,l62),(0x4d0e5717,l45),(-0x4d0e5717,l58),(0x90f4d4f6,l4),(-0x90f4d4f6,l34),(0x1ee5b22a,l10),(-0x1ee5b22a,l38),(-0x13997a45,l5),(0x13997a45,l54),(0x890413b,l22),(-0x890413b,l42),(0x19c3403,l9),(-0x19c3403,l61),(-0xfd827e,l6),(0xfd827e,l60),(-0x77231c,l11),(0x77231c,l55)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((0x102c055226016385af6ab1145313ae6185851faab75ca0041f1a360001c71eeae) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase0" = "QuadFullFiveCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase0
private def zz2212:"s08a4"="s08a4":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l55 l58 l6 l60 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x12e346660, -0x113ff180a, -0x19dfec086,0x12663afe], ![-0x113ff180a, -0x38d87911b,0x3c0ec4e4,0x109ffd2da], ![-0x19dfec086,0x3c0ec4e4, -0x701fb6089,0x113ff78ca], ![0x12663afe,0x109ffd2da,0x113ff78ca, -0x89ffa4f8]]
noncomputable def hinges:Hinges:=[(-0xfd827e,l6),(-0x13997a45,l5),(0x90f4d4f6,l4),(0x19c3403,l9),(-0x652c6bf3,l8),(-0x77231c,l11),(0x1ee5b22a,l10),(0x10a8481fe,l14),(0x21e69e9b,l13),(-0x1fe4ea90,l17),(0x14b0ee904,l15),(0x1884620e,l21),(-0x21e69e9b,l20),(-0xf5f33b5,l23),(0xbc2004fa,l22),(-0x89ffa4f8,l27),(-0x1884620e,l28),(0x89ffa4f8,l29),(-0x10a8481fe,l25),(0x35888772,l30),(0x89ffa4f8,l33),(-0x1ee5b22a,l38),(-0x89ffa4f8,l35),(0x652c6bf3,l36),(0x89ffa4f8,l37),(-0x90f4d4f6,l34),(-0x35888772,l43),(-0xbc2004fa,l42),(-0x14b0ee904,l41),(0x61a09655,l45),(0x89ffa4f8,l51),(0x77231c,l55),(0x13997a45,l54),(-0x61a09655,l58),(-0x19c3403,l61),(0xfd827e,l60),(0xf5f33b5,l63),(0x1fe4ea90,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x89ffa4f8,l27),(0x89ffa4f8,l29),(0x89ffa4f8,l33),(-0x89ffa4f8,l35),(0x89ffa4f8,l37),(0x89ffa4f8,l51),(0x10a8481fe,l14),(-0x10a8481fe,l25),(0xbc2004fa,l22),(-0xbc2004fa,l42),(0x14b0ee904,l15),(-0x14b0ee904,l41),(-0x652c6bf3,l8),(0x652c6bf3,l36),(0x61a09655,l45),(-0x61a09655,l58),(0x35888772,l30),(-0x35888772,l43),(0x1884620e,l21),(-0x1884620e,l28),(0x90f4d4f6,l4),(-0x90f4d4f6,l34),(-0x1fe4ea90,l17),(0x1fe4ea90,l62),(0x1ee5b22a,l10),(-0x1ee5b22a,l38),(-0xf5f33b5,l23),(0xf5f33b5,l63),(0x21e69e9b,l13),(-0x21e69e9b,l20),(-0x13997a45,l5),(0x13997a45,l54),(0x19c3403,l9),(-0x19c3403,l61),(-0xfd827e,l6),(0xfd827e,l60),(-0x77231c,l11),(0x77231c,l55)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase1" = "QuadFullFiveCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase1
private def zz2213:"s08a5"="s08a5":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l22 l23 l27 l29 l33 l35 l37 l4 l41 l5 l51 l62 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x13de6e72de, -0x59682c120, -0x31d0e6d10,0x2ee0], ![-0x59682c120, -0x290a690656,0x10822d75a0, -0x5b2719238], ![-0x31d0e6d10,0x10822d75a0, -0x2d6c316797,0x988bfb34c], ![0x2ee0, -0x5b2719238,0x988bfb34c, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xd6824999,l5),(0x4df5b702,l4),(0x12a224681,l8),(0x71776e84,l11),(0x1c136ed6,l10),(-0x7cf47ebe,l17),(0x62eabb26,l23),(0xea57e01f,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x5895ebabe,l41),(0x2cb417800,l51),(-0x1e7257720,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x1e7257720,l62),(-0x5895ebabe,l41),(0x71776e84,l11),(0x12a224681,l8),(0x62eabb26,l23),(0xea57e01f,l22),(-0x7cf47ebe,l17),(-0xd6824999,l5),(0x1c136ed6,l10),(0x4df5b702,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase2" = "QuadFullFiveCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase2
private def zz2214:"s08a6"="s08a6":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l16 l17 l20 l21 l22 l23 l27 l29 l30 l31 l33 l35 l37 l4 l41 l44 l46 l5 l51 l56 l57 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x58ceff14, -0x59682c120, -0x228a33860,0x2cb550a48], ![-0x59682c120, -0x27a59fa636,0x101fa99b34, -0x5adbf7344], ![-0x228a33860,0x101fa99b34, -0x2d6c316797,0x988bfb34c], ![0x2cb550a48, -0x5adbf7344,0x988bfb34c, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xd6824999,l5),(0x4df5b702,l4),(0x12a224681,l8),(0x71776e84,l11),(0x1c136ed6,l10),(0xfd01fb24,l14),(0x494e71f60,l13),(-0x381818d2,l17),(-0x813bec8,l16),(0x143e12cde,l21),(-0x300afcb12,l20),(-0xc54e32d,l23),(0x5483b764,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x9793a778,l31),(-0x2aae7e38,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x6a9895b20,l41),(-0x74b1ec8,l46),(-0x120ff3a68,l44),(0x2cb417800,l51),(-0x6779ef9c,l57),(-0x140924e53,l56),(0x155492220,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x494e71f60,l13),(0x143e12cde,l21),(-0x300afcb12,l20),(-0x6a9895b20,l41),(0x155492220,l64),(0xfd01fb24,l14),(0x9793a778,l31),(-0x140924e53,l56),(0x71776e84,l11),(0x12a224681,l8),(-0x6779ef9c,l57),(-0xd6824999,l5),(-0x120ff3a68,l44),(-0x381818d2,l17),(0x5483b764,l22),(-0x2aae7e38,l30),(0x1c136ed6,l10),(0x4df5b702,l4),(-0xc54e32d,l23),(-0x74b1ec8,l46),(-0x813bec8,l16)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[0x9032004000000c8440d8c03049436032008340140004a0d83802d003000000360e009300c00970d819008d004000000000980720080004d0d83802d00300244360700234010000490d8380250030000036064021301000531043a00e50040001884609014400c00b41983901d9004000000b81b00e300c000000000f01880200000ba0cc01630100000002d0f01cc020000000b83c063008000003a044028c0300000000024062008000029250e029002000000000380d2008000000000140c801000000000c4072008000000032140cc01000000006400b200c000000017002c8030000005c683034004000000017404c80300000b704c01930100000002d0701cc02000000005f00b200c0002e008c00a4c0500000b50580293010000002e02c02cc03000000000e8052008000000022140cc010000000844805300800003b2109019002000007118406c30100000001d1903cc020000061104048301000051118240cd0030000002609022300c0000000009024802000000822102c300c000000000901c8020000000cc84053008000000002501c802000000004c00b200c000000002102c802001e4510cc024401000000188440b0c03029828826012d40140a20ae08801b50050013423048032401000520a81200f5004001702807005d40100000000098024803000000000380520080000001109018c02000000001c009200c0000000012014802,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,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,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,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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 28 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase3" = "QuadFullFiveCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 28 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase3
private def zz2215:"s08a7"="s08a7":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l36 l37 l38 l41 l42 l43 l46 l5 l51 l54 l55 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xdd9c15bf, -0x11fdd2876, -0x1b3030144,0x234698dc], ![-0x11fdd2876, -0x460776f3c,0x558c64f8,0xedcb9694], ![-0x1b3030144,0x558c64f8, -0x75d0dd74e,0x122024e68], ![0x234698dc,0xedcb9694,0x122024e68, -0x91010fc4]]
noncomputable def hinges:Hinges:=[(-0x10149be,l6),(-0x93f0812a,l5),(0x53576114,l9),(-0x60283098,l8),(-0x1934df02,l11),(0x2f73a844,l10),(0xccdf100c,l14),(0xdb39e04c,l13),(-0x307d43a4,l17),(0x22197abf,l23),(0x890413b,l22),(-0x91010fc4,l27),(-0x3dfedaaa,l28),(0x91010fc4,l29),(-0xe66d1d3c,l25),(0x34140754,l31),(0x5eb19bde,l30),(0x91010fc4,l33),(-0x27c982c0,l38),(-0x91010fc4,l35),(0x6015d3aa,l36),(0x91010fc4,l37),(-0x7568385e,l43),(-0x19d1f1bc,l42),(-0x1593d9728,l41),(0xe51ef04,l46),(0x91010fc4,l51),(0xa1febf6,l55),(0x2a234b97,l54),(-0x2bcf6841,l61),(0xfb953e8,l60),(-0x22bd2d0,l63),(0x1b7fa332,l62),(-0xec6ae14,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x91010fc4,l27),(0x91010fc4,l29),(0x91010fc4,l33),(-0x91010fc4,l35),(0x91010fc4,l37),(0x91010fc4,l51),(-0xe66d1d3c,l25),(0xccdf100c,l14),(0x53576114,l9),(0xdb39e04c,l13),(-0x7568385e,l43),(-0x3dfedaaa,l28),(0x5eb19bde,l30),(-0x1593d9728,l41),(-0x93f0812a,l5),(0x34140754,l31),(-0x2bcf6841,l61),(-0x60283098,l8),(0x6015d3aa,l36),(0x22197abf,l23),(-0x307d43a4,l17),(0x2f73a844,l10),(-0x27c982c0,l38),(-0x1934df02,l11),(0x1b7fa332,l62),(0x2a234b97,l54),(0xa1febf6,l55),(0xfb953e8,l60),(-0xec6ae14,l64),(-0x19d1f1bc,l42),(0xe51ef04,l46),(0x890413b,l22),(-0x22bd2d0,l63),(-0x10149be,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase4" = "QuadFullFiveCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase4
private def zz2216:"s08a8"="s08a8":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l35 l36 l37 l38 l41 l42 l43 l45 l5 l51 l54 l55 l56 l57 l58 l59 l6 l60 l61 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xffd563f0, -0x11fdd2876, -0x1b3030108,0x1962a9ec], ![-0x11fdd2876, -0x4e4d3b318,0x5be517d4,0xf4fb9276], ![-0x1b3030108,0x5be517d4, -0x75d0dd74e,0x122024e68], ![0x1962a9ec,0xf4fb9276,0x122024e68, -0x91010fc4]]
noncomputable def hinges:Hinges:=[(-0x10149be,l6),(-0x93f0812a,l5),(0x53576114,l9),(-0x60283098,l8),(-0x1934df02,l11),(0x2f73a844,l10),(0x4be76898,l14),(0x147253854,l13),(-0x1fe4ea90,l17),(0x14b0ee904,l15),(0x202a1bf2,l21),(-0x10548136e,l20),(-0xf5f33b5,l23),(0xbc2004fa,l22),(-0x91010fc4,l27),(-0x1cccf962,l28),(0x91010fc4,l29),(-0x93f40370,l25),(0x35888772,l30),(0x91010fc4,l33),(-0x27c982c0,l38),(-0x91010fc4,l35),(0x6015d3aa,l36),(0x91010fc4,l37),(-0x17e823dc,l43),(-0x704e897b,l42),(-0x7304ee6,l41),(0x5525f9d6,l45),(0x91010fc4,l51),(0xa1febf6,l55),(0x2a234b97,l54),(-0x5246a3ef,l57),(0x641a4419,l56),(0xbd9183c,l59),(-0x8b166424,l58),(-0x2bcf6841,l61),(0xfb953e8,l60),(-0xcb1cba8,l63),(-0x80f6a92,l65),(0x1debbdf8,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x91010fc4,l27),(0x91010fc4,l29),(0x91010fc4,l33),(-0x91010fc4,l35),(0x91010fc4,l37),(0x91010fc4,l51),(0x147253854,l13),(-0x93f40370,l25),(-0x10548136e,l20),(0x53576114,l9),(-0x5246a3ef,l57),(0xbc2004fa,l22),(-0x93f0812a,l5),(0x14b0ee904,l15),(-0x8b166424,l58),(0x4be76898,l14),(-0x2bcf6841,l61),(-0x704e897b,l42),(0x641a4419,l56),(-0x60283098,l8),(0x6015d3aa,l36),(0x35888772,l30),(0x202a1bf2,l21),(0x5525f9d6,l45),(0x2f73a844,l10),(-0x1cccf962,l28),(-0x27c982c0,l38),(-0x1934df02,l11),(-0x1fe4ea90,l17),(0x1debbdf8,l64),(-0xf5f33b5,l23),(-0x17e823dc,l43),(0x2a234b97,l54),(-0xcb1cba8,l63),(0xbd9183c,l59),(0xa1febf6,l55),(0xfb953e8,l60),(-0x80f6a92,l65),(-0x7304ee6,l41),(-0x10149be,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase5" = "QuadFullFiveCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase5
private def zz2217:"s08a9"="s08a9":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l17 l20 l22 l23 l27 l29 l33 l35 l37 l4 l44 l46 l5 l51 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x26fe18bc7, -0x59682c120,0x225b5926,0x3770d6c], ![-0x59682c120, -0x28fca821a6,0x107b4d0354, -0x5b2719238], ![0x225b5926,0x107b4d0354, -0x2c209b88f8,0x961b9d51e], ![0x3770d6c, -0x5b2719238,0x961b9d51e, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xe5473384,l5),(0x122b1733c,l4),(0x2e42e666f,l8),(-0x71c30b9c,l10),(-0x7cf47ebe,l17),(-0x370392c,l20),(0x62eabb26,l23),(0xea57e01f,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x93cfc4,l46),(0x5324dd8,l44),(0x2cb417800,l51),(-0x954e63c3,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x2e42e666f,l8),(-0x954e63c3,l63),(0x62eabb26,l23),(0xea57e01f,l22),(-0xe5473384,l5),(-0x7cf47ebe,l17),(-0x71c30b9c,l10),(0x122b1733c,l4),(-0x370392c,l20),(0x5324dd8,l44),(-0x93cfc4,l46)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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,0xa50cc1140ddd005], #[![-9, 66, -71, 0]]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    0xee79bf993b7c215ea189b5df1cbf06521e68e5aeffa82c26c40868587f59000c67fea4b89231a5b62ff8935149016d89c6486951c4d05ff851f9747790ef0caf00202ba11be0d47d5001eafed80cc9de980a8361f4aadf910cbe80fb5a78c1b85abaf6bf3bdc6758fabc1598d4b2e633796f8787c45166ded250a1f9cd6f92fbd665b80909e1b0c8edcdf25e48848b0c3c01bb944870ca14a3d4ee35b83017b1994821ca00019348004169001a633c78ae8e74eb00e2801b1b66600710007d70f1b62840000005dc01c123d5ab1ca80000001f40241328c14806007c1601a0b01e01f8ab99fcbd7d8b64730fa7e1fe14772cf117f78972d5d5f25e8314000000000000000000240c004438a2884023823022802054f168d8d24ff8ae368d8fafc3c078d408280ed47ea06f9891a049a0004d44074140380201b010002311001fd12008240646c98cb24a58024438bf2e3738a1c40f6a430ee3e1c3444cd8d848014209de49ecd00082222ff9e6fc01810555248b5001010648f0a06c110030788b30a3d2404821601628a2482461451c41c31420821010c134080200d00009a20340b816e6bea0a7cb22040630365b1bf060c72e6801a8c11820090b84c92b0404264cd04501b04118466f570efc800a3817a5b239128f3f48e1960000028c9682a717082e03000c8080008d880c08c05c4723789846f66489987ba81b0e217f7af15c1842b687e878808821a6510300549b64dd8801eb65e2d81000b310e320501044010914c065b07d12277cfe9b6c1c401a515e16184023f5e2dc4042cd426d2840819e86d9b240be73d689613841180400005b880b06c05417641c4a66418454b1dc7ec72ec9be58d6c4e8fe0fa12c386e214f83c78a10000142e92a82087a05da85b98202002434bce0024000a264009e0040000005b8d801fa12085a058dd9a02fc9bb3405f8dcece3dce80000000008c4b20b1cb18b0c508408208600400c820080340004a8f93af58c7689e84f693600a89659439430c31429028818e0040064200401a0001e46c839087bffa6163b97247822a4b1ade7145932a48c00000b89202c387f6fd9212181000005c49004040048f60f844800147559f08002458720b5fa010a4071641c38d046a9058ee62cd800dc983000002e0ddc58d701caa09ee923000002e248060600000005a9161c41ab310a4c20200000f5f9d080000000f61807e48215010000083cd0e62e43ade1e50c855478882650b0986f35d7a5048867a7d17e58206816ae81e40200000f61804800680e07a9e30000003d8600354041400c000072480030390140100055b1000e1920262b00a0de0c66d8470107050c9180bac6066443a62604040000119403005e94dc1c82010b453391c00118a6cbe5500f965ce881542730094d6dc9090020000394404805c31a7e384c383547d861756530add0fae5e1846b7dfcde04e62316c8cd2b7cce07d4d0050286fe478670bcb9a08bb5dd795ac86eda080263e414f348a558a61d4e462712d993c50c00873cc396eff285d9e9b1850de52cf1d000a821c1d83ac7d926c21205f830e78c7e0885b701ca7d259e2fcf6229cffd1a36649c610274da77346577336847a994a20c61122fe510d6c0001546f512a0848608001135d9c76aca00b7bb8490324402cec3c7373bd352b918687b30e6f1ae5eafaf574542dbd0dbb80400000000000000000000000000000000000000000000000000006735e0d014eec42be48140b52c72462060804dff2b6835b40a77b0fc09214f3a15dbcb781ce225dd561b18e635ef85c718145f8e6ca66256ed90afaaebb165ffc31c25004a09df4895298e209be2a3ec9dce289a6dfdf600e740d2742ed08127a9b6238221fdb7ef2808ebd458e0c018c73b4dd4a0610802000036480882f8a39274cf18e4feaf7c869071ce800b0068388392792df06a66fc6345535f9ff05067bc2093dc0b662d2819310e736078d27b17c8102808697800a928e15c82662c63a1ccb185ee200866a74a510bc680cee05f82531afb4ebc247160d8163123bad85c906c8597cf7ff40000d0fb93c36bf5bd9452b531fc318e152045399073b4db44ea4a3905286420c800402401e0200048a200154040385601a1b914cc7226428808a78572aa041d28e9feb000020be3ffb10524182300850c8a4fb73318538db32650a155ceb39581007e85ac8c82c82842010dda035744635f72cb41608f597aa8f882264daee6b450fab76731720542840332051c41041c208214011e04acfc78fe8a4b78a5333803b740f4eb7bad7ec9f51cb3b7abf946fb998520c65a0004b64000d5480608802c24000906400401c800a431ec3c7373bd352b918687b30e6f1ae5eafaf574542dbd0dbb80400000000000000000000000000000000000000000000000000006711c71c51c41441c3101100fa025dc303802bc7b6264297da071412059ea94d203000000ea60070cde499b3113183000000ea60040401f4700b1f1c00b7e744d6185a3861500a000068c80502f0d23e6be488c186d3aae806100bcf9467ccd00414d918e1000000423472c97f91001821efce679a1a86843d23a28400000108d1cb25fe44006001bcd666a6ae427eb0140800000eb460330c3f900ad322409370c189e14800909004008000ba080388c01827432e76b71eca060411826442dd14186068079e9840400000b8920140bb54097cc58300118258b9bd1012d12eb73380bac5dc1de941857b8853abf6202a0180000fb10050500200800c040013064008b40020200001001a1f9))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase6" = "QuadFullFiveCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase6
private def zz2218:"s08aa"="s08aa":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l16 l17 l21 l22 l23 l25 l27 l29 l30 l31 l33 l35 l37 l4 l5 l51 l57 l59 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x8f685dcd, -0x59682c120, -0x192f04434,0x271e41580], ![-0x59682c120, -0x1f2db9ede2,0xe893b654c, -0x5adbf7344], ![-0x192f04434,0xe893b654c, -0x2c209b88f8,0x961b9d51e], ![0x271e41580, -0x5adbf7344,0x961b9d51e, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xe5473384,l5),(0x122b1733c,l4),(0x2e42e666f,l8),(-0x71c30b9c,l10),(0x8b0487178,l13),(-0x381818d2,l17),(-0x813bec8,l16),(0x2e334f30,l21),(-0xc54e32d,l23),(0x5483b764,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x223cfa418,l25),(0x9793a778,l31),(-0x2aae7e38,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x14acdd2ab,l57),(-0x1dcde66a,l59),(-0xab81ca5b,l63),(0x10c3d19b4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x8b0487178,l13),(-0x223cfa418,l25),(-0x14acdd2ab,l57),(0x2e42e666f,l8),(0x10c3d19b4,l64),(-0xab81ca5b,l63),(0x9793a778,l31),(-0xe5473384,l5),(-0x71c30b9c,l10),(0x122b1733c,l4),(0x2e334f30,l21),(-0x381818d2,l17),(0x5483b764,l22),(-0x1dcde66a,l59),(-0x2aae7e38,l30),(-0xc54e32d,l23),(-0x813bec8,l16)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((0xa26bbae45351641135c676c288219952af84020d77366f48009c616f908a03ccca3ecb098208c0216591bf2bd98b20514329e4db7e761449018045b55725101158acdc69a96380f3c833fd9050405c905d4779040800003920a60082157e6f086461605459db0fd7209804841701400008dce120408541719649908b9b51c4926b38b4e991241c549bfc3a50c2bb590b9c9419318861530600000008ca0140545d09f4aa08009482b468082600c05a0080007c485988c1084608013a222f09dd620c6163a462f4b6b4d52c62b0c1ca1835648c6ec6706230a0818e11cfef512c12204b8676cf1902040913fab8f41828065bb29554180005a4440e1781a00008488220ac2c80744c89852b76590dffc21d8944375f1723458cfa3149880c192b055abe4801fc402811002f13b913c233881100430a84aeb7b09f05103535e964984b1c123ac54717962296098823d330307d11e128345065386520c5acd001f448ecfad1605c861db410211f68102b0200000f39021158100ac07c2764dec406601ad406108982646331499839d657a1dd4dda50e7d4f468758c41239f3d9dc75c0c050a1a48b7760e280411495fbb0dcf10300709d2392e4300002dc644101902000008bcd10f4c07aa0c6f8170664056a6b8c8c3a271918b901f81563ca52d965ee6bcea5970055f690515e579c78f82ae1c1542c62462441c01800108b90fae4aa508f961870bdad1294b08abbef8e3d16b82c99de44db2879f4ae64876a16d96a62d87f42fa6a496a4c500033720012906a6b8c8c3a271918b901f81563ca52d965ee6bcea5970055f690515e579c78f82ae1c1532441c418214010008001011ce486b6ee66aa27a42e100267e023e0ea33a71eaa70498453f3353d57c22d97024c3bb62c9a1f28001599c794a5b2cbdcd79d4b2e00ac8572d438bb017bb3405f9376680bf1d) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase7" = "QuadFullFiveCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase7
private def zz2219:"s08ab"="s08ab":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase8
private def zz2220:"s08ac"="s08ac":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz771:"s0303"="s0303":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase9
private def zz2221:"s08ad"="s08ad":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l17 l21 l25 l27 l29 l33 l35 l36 l37 l43 l51 l54 l55 l57 l58 l61 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2a9d47622, -0x596827038, -0x861c43920,0x6e0a12c], ![-0x596827038,0xaef4959ba,0x1cc2e2608,0x821c0b30e], ![-0x861c43920,0x1cc2e2608, -0x2452531800,0x596831ee0], ![0x6e0a12c,0x821c0b30e,0x596831ee0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x93cfc4,l14),(0x1e7257720,l17),(0x5895ebabe,l15),(0xb53ef512,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x66468eb84,l25),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x17170ff50,l36),(0x2cb417800,l37),(0xadee510,l43),(0x2cb417800,l51),(-0x71ec4e20,l55),(0xb0d5172f,l54),(-0x952e2495,l57),(0x370392c,l58),(0xd1703e2,l61),(0x3bda0e18,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x66468eb84,l25),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1e7257720,l17),(0x5895ebabe,l15),(0xb53ef512,l21),(-0x952e2495,l57),(-0x17170ff50,l36),(-0x71ec4e20,l55),(0xb0d5172f,l54),(0x3bda0e18,l62),(0xd1703e2,l61),(0xadee510,l43),(0x370392c,l58),(0x93cfc4,l14)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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,0x230a018c02000000000088052008000000000230188020000000000840e2008000001ec220058c040000000000680720080000000007802480300001706229026400c0000166218011cc050000059082006730140000017443005cc040000005b12403730100000001689805cc03000000551180973010000000000b0024803], #[![6, -21, -2, 0],![6, -103, 0, 0],![2, -17, 0, 0],![6, -25, 0, 0]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 23 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase10" = "QuadFullFiveCase10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 23 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase10
private def zz2222:"s08ae"="s08ae":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l16 l20 l25 l27 l28 l29 l31 l33 l35 l36 l37 l42 l43 l44 l46 l51 l54 l55 l56 l57 l58 l61 l62 l63)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2ce858bbe, -0x596827038, -0x861c43920,0xd374a8], ![-0x596827038, -0xb9b2ef179,0x26f9a1704,0x96ee65d0e], ![-0x861c43920,0x26f9a1704, -0x2452531800,0x596831ee0], ![0xd374a8,0x96ee65d0e,0x596831ee0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x284081488,l14),(0x140924e53,l16),(0x6a9895b20,l15),(-0x37e66d380,l20),(-0x2cb417800,l27),(-0x161322856,l28),(0x2cb417800,l29),(-0x160776638,l25),(0x6779ef9c,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x17170ff50,l36),(0x2cb417800,l37),(0x7fddbdc0,l43),(-0x1321166f1,l42),(-0x15bb8498c,l46),(0x11b9e189c,l44),(0x2cb417800,l51),(-0x71ec4e20,l55),(0xb0d5172f,l54),(-0x6f4e4af9,l57),(0xaeb4afe,l56),(0x10d73ccc,l58),(0xd1703e2,l61),(0x8f254e5,l63),(0x37784d30,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x284081488,l14),(-0x161322856,l28),(-0x37e66d380,l20),(0x6a9895b20,l15),(-0x160776638,l25),(-0x15bb8498c,l46),(-0x17170ff50,l36),(0x140924e53,l16),(-0x71ec4e20,l55),(-0x6f4e4af9,l57),(-0x1321166f1,l42),(0x6779ef9c,l31),(0x7fddbdc0,l43),(0xb0d5172f,l54),(0x11b9e189c,l44),(0x37784d30,l62),(0xd1703e2,l61),(0x8f254e5,l63),(0x10d73ccc,l58),(0xaeb4afe,l56)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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,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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((0x4762f9f3a0000000014d225d76e8ec5f3e781209238e19211400c00200002aa365b044f4322c08e4f75d3f19e219795ca1418b10d3b7246311a89402c13c171d8be7ce8000000005348975dba3b17cf9e048279e79628a78478270270060180001006f9fd12f267863cb0277bb1851e106df985f4d10400000bb807823f24e04ea381000002ee04c004a010000147227e0b13e01c0c02097743900e0440f22a082030e4ea79004a5586330340001c9a6bc200037e8c9126042200840c0fef6ff9a01c8ebc8f8020808911d48802ac993b9324042100800006c1c2064d125150eeed77) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase11" = "QuadFullFiveCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase11
private def zz2223:"s08af"="s08af":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz776:"s0308"="s0308":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase12
private def zz2224:"s08b0"="s08b0":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz777:"s0309"="s0309":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase13
private def zz2225:"s08b1"="s08b1":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l58 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x13778b4d7, -0x1102bbc10, -0x19841b260,0xbd4dd3c], ![-0x1102bbc10, -0x3ded28ddc,0x38bd8b2a,0x10f6078a4], ![-0x19841b260,0x38bd8b2a, -0x6e91d770f,0x1102c19ca], ![0xbd4dd3c,0x10f6078a4,0x1102c19ca, -0x8815f578]]
noncomputable def hinges:Hinges:=[(-0x1129f5e,l6),(-0x3aea12b3,l5),(0x1724fc46,l4),(0x1f70c960,l9),(-0x5ba6d1b3,l8),(0x1edaa61e,l10),(0x11b153d56,l14),(-0x1b7fa332,l17),(0x1593d9728,l15),(0x22bd2d0,l23),(0x19d1f1bc,l22),(-0x8815f578,l27),(0x8815f578,l29),(-0x11b153d56,l25),(0x7568385e,l30),(0x8815f578,l33),(-0x1edaa61e,l38),(-0x8815f578,l35),(0x5ba6d1b3,l36),(0x8815f578,l37),(-0x1724fc46,l34),(-0x7568385e,l43),(-0x19d1f1bc,l42),(-0x1593d9728,l41),(0x8e64c98,l46),(0x269cf298,l45),(0x8815f578,l51),(0x3aea12b3,l54),(-0x269cf298,l58),(-0x1f70c960,l61),(0x1129f5e,l60),(-0x22bd2d0,l63),(0x1b7fa332,l62),(-0x8e64c98,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8815f578,l27),(0x8815f578,l29),(0x8815f578,l33),(-0x8815f578,l35),(0x8815f578,l37),(0x8815f578,l51),(0x11b153d56,l14),(-0x11b153d56,l25),(0x7568385e,l30),(-0x7568385e,l43),(0x1593d9728,l15),(-0x1593d9728,l41),(-0x5ba6d1b3,l8),(0x5ba6d1b3,l36),(0x1f70c960,l9),(-0x1f70c960,l61),(-0x3aea12b3,l5),(0x3aea12b3,l54),(0x1edaa61e,l10),(-0x1edaa61e,l38),(-0x1b7fa332,l17),(0x1b7fa332,l62),(0x269cf298,l45),(-0x269cf298,l58),(0x19d1f1bc,l22),(-0x19d1f1bc,l42),(0x8e64c98,l46),(-0x8e64c98,l64),(0x1724fc46,l4),(-0x1724fc46,l34),(0x22bd2d0,l23),(-0x22bd2d0,l63),(-0x1129f5e,l6),(0x1129f5e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase14" = "QuadFullFiveCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase14
private def zz2226:"s08b2"="s08b2":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l16 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l56 l57 l58 l59 l6 l60 l61 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x15283d87b, -0x1102bbc10, -0x19841b224,0x176ef76a], ![-0x1102bbc10, -0x42b53840b,0x3a20008a,0x108e230a4], ![-0x19841b224,0x3a20008a, -0x6e91d770f,0x1102c19ca], ![0x176ef76a,0x108e230a4,0x1102c19ca, -0x8815f578]]
noncomputable def hinges:Hinges:=[(-0x1129f5e,l6),(-0x3aea12b3,l5),(0x1724fc46,l4),(0x1f70c960,l9),(-0x5ba6d1b3,l8),(0x1edaa61e,l10),(0x8f98182c,l14),(0x11fff03fd,l13),(-0x641a4419,l16),(0x7304ee6,l15),(0xa5b4f0a,l21),(-0x11fff03fd,l20),(0xcb1cba8,l23),(0x704e897b,l22),(-0x8815f578,l27),(-0xa5b4f0a,l28),(0x8815f578,l29),(-0x8f98182c,l25),(0x5246a3ef,l31),(0x17e823dc,l30),(0x8815f578,l33),(-0x1edaa61e,l38),(-0x8815f578,l35),(0x5ba6d1b3,l36),(0x8815f578,l37),(-0x1724fc46,l34),(-0x17e823dc,l43),(-0x704e897b,l42),(-0x7304ee6,l41),(0x269c5a2b,l45),(0x8815f578,l51),(0x3aea12b3,l54),(-0x5246a3ef,l57),(0x641a4419,l56),(0x227c0566,l59),(-0x269c5a2b,l58),(-0x1f70c960,l61),(0x1129f5e,l60),(-0xcb1cba8,l63),(-0x227c0566,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8815f578,l27),(0x8815f578,l29),(0x8815f578,l33),(-0x8815f578,l35),(0x8815f578,l37),(0x8815f578,l51),(0x11fff03fd,l13),(-0x11fff03fd,l20),(0x8f98182c,l14),(-0x8f98182c,l25),(0x5246a3ef,l31),(-0x5246a3ef,l57),(0x704e897b,l22),(-0x704e897b,l42),(-0x641a4419,l16),(0x641a4419,l56),(0x227c0566,l59),(-0x227c0566,l65),(-0x5ba6d1b3,l8),(0x5ba6d1b3,l36),(0x1f70c960,l9),(-0x1f70c960,l61),(-0x3aea12b3,l5),(0x3aea12b3,l54),(0x1edaa61e,l10),(-0x1edaa61e,l38),(0x17e823dc,l30),(-0x17e823dc,l43),(0x269c5a2b,l45),(-0x269c5a2b,l58),(0xcb1cba8,l23),(-0xcb1cba8,l63),(0xa5b4f0a,l21),(-0xa5b4f0a,l28),(0x1724fc46,l4),(-0x1724fc46,l34),(0x7304ee6,l15),(-0x7304ee6,l41),(-0x1129f5e,l6),(0x1129f5e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase15" = "QuadFullFiveCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase15
private def zz2227:"s08b3"="s08b3":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase16
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l25 l27 l29 l30 l31 l33 l35 l37 l5 l51 l6 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2748009db, -0x59682c120,0x225b5926,0x2ee0], ![-0x59682c120, -0x28b2e55829,0x10a2bf6bb8, -0x5b6da371a], ![0x225b5926,0x10a2bf6bb8, -0x2c0d06a5f3,0x9500b3a28], ![0x2ee0, -0x5b6da371a,0x9500b3a28, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xf5f81f4,l6),(-0x98a0e1c3,l5),(0x2c6ebc8fd,l8),(0x2676da0a,l11),(-0x73e81884,l10),(-0x3bda0e18,l17),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x726c50c,l25),(0x952e2495,l31),(-0xadee510,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x954e63c3,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x2c6ebc8fd,l8),(-0x954e63c3,l63),(0x952e2495,l31),(-0x73e81884,l10),(-0x98a0e1c3,l5),(0x2676da0a,l11),(-0x3bda0e18,l17),(-0xf5f81f4,l6),(-0xadee510,l30),(-0x726c50c,l25)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[![-3, 42, -47, 0]]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase16" = "QuadFullFiveCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase16
private def zz2228:"s08b4"="s08b4":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l16 l17 l20 l21 l22 l23 l25 l27 l29 l30 l31 l33 l35 l37 l5 l51 l57 l58 l59 l6 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x8dbe6995, -0x59682c120, -0x192f04434,0x27e9814a8], ![-0x59682c120, -0x2353d4b00d,0xfd26642cc, -0x5d3525d92], ![-0x192f04434,0xfd26642cc, -0x2c0d06a5f3,0x9500b3a28], ![0x27e9814a8, -0x5d3525d92,0x9500b3a28, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xf5f81f4,l6),(-0x98a0e1c3,l5),(0x2c6ebc8fd,l8),(0x2676da0a,l11),(-0x73e81884,l10),(0x8ac8b2852,l13),(-0x37784d30,l17),(-0xaeb4afe,l16),(0x26e6a4c8,l21),(-0x6f231594,l20),(-0x8f254e5,l23),(0x1321166f1,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x15f042958,l25),(0x6f4e4af9,l31),(-0x7fddbdc0,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x14acdd2ab,l57),(-0x2021d38c,l59),(0x242e74c6,l58),(-0xab81ca5b,l63),(0xfd01fb2c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x8ac8b2852,l13),(-0x14acdd2ab,l57),(0x2c6ebc8fd,l8),(-0x15f042958,l25),(-0xab81ca5b,l63),(0xfd01fb2c,l64),(0x6f4e4af9,l31),(0x1321166f1,l22),(-0x7fddbdc0,l30),(-0x73e81884,l10),(-0x98a0e1c3,l5),(-0x6f231594,l20),(0x26e6a4c8,l21),(0x2676da0a,l11),(-0x37784d30,l17),(-0x2021d38c,l59),(0x242e74c6,l58),(-0xf5f81f4,l6),(-0x8f254e5,l23),(-0xaeb4afe,l16)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,0xc0cb0890c0a5c4018000632912c0b9003000000005f013200c0000014884058c030000004a0900b300c000000110f014c020000000003c0520080000120110058c04000094260900b400c000000007802480300000250740c63010000000003c034803000000000901d200c000000005003c803000000001c00b200c000000007003c803000000000c00f200c00000000190388020000000006c06200800000d42701b0c04000000003500a200c000001609c04cc030000000584405300800000000b00248030000000036009200c00001a8210058c04], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullFiveCase17" = "QuadFullFiveCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullFiveCase17
private def zz2229:"s08b5"="s08b5":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz815:"s032f"="s032f":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase18
private def zz2230:"s08b6"="s08b6":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullFiveCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1e8480
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz816:"s0330"="s0330":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullFiveCase19
private def zz2231:"s08b7"="s08b7":=by decide+kernel
end 
section 
namespace Green24Proof.FullFiveRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decode [0x114e203dceb948005b8e08cfa01e2779ae5800193fa80ee6203e8a4807dbbe607a21389b48020e3e1f61fa201eeb5ca8002a4a6cae215a203dceb948003effbb5aa01a203dceb94800799da9d9e2201eeb5ca80398490ea07d203dceb948007f483fb921fd21ec2a001c896ba1ed203dceb9480149f84d9de14d203dceb94801081eab2865203dceb94802affc6b3de123bcdb2c005c0aeba9e07c203dceb948010d49283fe1fc203dceb948001b4e6fe921ec201eeb5ca8001c491c48e4201eeb5ca8005ccabf8de07825faf8403ca97e60203dceb948009ceafa3b614]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decode [0x115e603dceb94801689c8d0d614e601bede8807ba83d201e601eeb5ca8005c0f7b38e6603dceb948006bfbc87d607a65faf84803b8ffa1ea603dceb94800ba9fbea9201a603dceb94803391d1ebc22601eeb5ca8002b2e4dbd6563d84c002163d84c0021ff2779ae5800bcaedbdca1ef23bcdb2c02e99d3e601f201eeb5ca8008c7cfd2867203dceb948026e1d2a1e214b201eeb5ca8004cae8b23203dceb94802bf9de818e07e201eeb5ca800197e7b4a61fe201eeb5ca8003b498e88e1ee203dceb94800281a8b7f215e203dceb948001e6b3f2e214]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decode [0x11f8303dceb9480039afbc9ba0301eeb5ca807a96d5d27e3d84c0023e3d84c0021ffa03dceb94802ea1b9c5c61efa779ae5804de6d2b214fa2fd7c2801dd1bd9601fa01eeb5ca8005be8494d67a03dceb94802a98c496a201ba03dceb94801ccdc5863a2fd7c28004b7ead0b207ea01eeb5ca8004beb098961fea03dceb94800bfffdaffe1eea2fd7c28010c986826a03dceb94800bdedc8eb607aa03dceb948011d8d4fad62a03dceb948009b7fe96b2763d84c002363d84c00207e601eeb5ca800a88888aa214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decode [0x11cf32fd7c28004beeaba732fd7c2800e8cb61cb301eeb5ca8004cae8b2335faf848001eae08a03e301eeb5ca803bebdefe1fe301eeb5ca8001b9b9cc861ee31389b48002ca92e215e301eeb5ca802fb2989e14e31389b480098ac7c26303dceb94801bd9bbc607a303dceb94803b8dae8a01a303dceb948039a3ef822303dceb948030edf28203d303dceb948007f483fb9617d303dceb948060bdf8c21dd301eeb5ca800180c3d3c6533d84c002133d84c0021fc303dceb94800488d6f38e4301eeb5ca80018eb7e6ce14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decode [0x17b01eeb5ca8001c8df8e3b3d84c0021feb03dceb948001cdf6a2f21eeb2fd7c2803796b5ae6b5faf848052828dce07ab779ae58011e6a6a61fab3bcdb2c019defde22b03dceb9480019aabe2de773d84c002373d84c00216e75faf84802fd7f5e205e703dceb948008b0fa99da670ef3acd01a8a8af203a75faf84803b8ffa06a701eeb5ca8003bbb7d22703dceb948004cfaf92573d84c002173d84c00203f303dceb94800aeef0c9c606f303dceb948002fa94889a14]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decode [0x105e05faf848001cdeaa66003dceb94800f9ca217d01de6d9a07b92eace16d00ef3acd038fb89e21dd02fd7c28014f8e7fa1cd003dceb948007af8dc9ca50779ae58015a603c003dceb948001f796e4aa1fc05faf84806bf5c7ba1ec0779ae58001eea38e02c003dceb94800382c6b8d215c003dceb948019e1d0861cc003dceb948068c3f8ae05c003dceb948007f684fe4003dceb948021a27f3d84c0023f3d84c00203fb0bf5f0c02290baba06fb2fd7c28026c49bc605fb01eeb5ca800ecb8fb214]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decode [0x11ec801eeb5ca8050ffd7f615c803dceb948005bcfba1821cc803dceb948001e0de8fba05c817ebe18006a588b24803dceb948005dbfa86741ec2a002641ec2a002541ec2a002441ec2a00207f001eeb5ca8003cfd098c217f003dceb94801dcfca8bfe16f001eeb5ca8002b3dbb48a1cf003dceb948006ae82ad8205f001eeb5ca803dbf81fa701ec2a00203e001eeb5ca8001bde7a8a21fe03bcdb2c0408db2e21ee001eeb5ca8001c9d3be8215e0779ae58002cdaee18a1ce001eeb5ca80038ac0d68e14]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107f809c4da801299ebfe17f803dceb94801eebd188ca02f801eeb5ca800383cbd18a1cf8779ae58002b1da9196781ec2a00203e803dceb948001f6eacc9e1fe85faf848061e1c0ba02e803dceb94803ddbfdc215e802fdbc900392b89e1ce803dceb948002ba9aeea205e803dceb948008cabede681ec2a00203d803dceb948001e0cdddd617d803dceb94800cb68688d616d8779ae58003c5eeeec202d803dceb948001cff2a4d61cd85faf848001e4e7cfae581ec2a00203c80ef3acd009f998961fc801eeb5ca8002809d8d8e14]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decode [0x107a13bcdb2c00aefb9a216a15faf848003ddb09da205a104e2ad8004e4f0f6211ec2a00203c103dceb948003aca28ef217c101eeb5ca8003f5d5adfe02c101eeb5ca8003b9b4cdd61dc103dceb948001f5f9ceea05c13bcdb2c01ff2bad24103dceb94801ef6038103dceb948005f5c6b7de178103dceb94802dd681d21681779ae58001d0a887aa158103dceb948004a1cbeafe058101eeb5ca8001c1fac3d2011389b480019e7c1ec2a0026c1ec2a0025c1ec2a0024c1ec2a00214]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decode [0x105c903dceb948003c0e0b1d2491ec2a002178903dceb948009e1eaaaea158901eeb5ca800697aaf6a6058903dceb948007e7d1fdbe091ec2a00216f503dceb948029aceecad615f503dceb948015b88ea9b67501eeb5ca801293e2e1a215b503dceb948012d4f38f863503dceb94802db5d580e2551ec2a002151ec2a00207e10ef3acd01ffbdbee17e103dceb94800ce0aeb3f616e103dceb94800df4f2abf21de103dceb9480018f92d3ca1ce101eeb5ca801d8f87aa05e10bf5f0c00b8c83ee611ec2a00214]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1019d05faf8a030dbbcca1d3bcdb2c003c1c8ffca03e901f4928061f68617e95faf848077e5cfaa16e903dceb94800aa4b58fde02e903dceb94801395dfa215e902b196c00181fefa1ce903dceb94800495f0dae66901eeb5ca800fb603a903dceb948007aba0f0de17a9779ae58022b6d0ca02a9779ae58001e694c3ee15a91de6d9a00295f4da05a903dceb948001dbfec6b229779ae58007d607c9779ae58055aebf8e17c9779ae58070d7e7e616c90bf5f0c03cd0ddc61dc903dceb948001c5a78cda1cc93bcdb2c005b19fe614]
def rowsChunk11:List (ℚ × Label):=PackedPhaseRowsData.decode [0x1089403e8a4020101010001020100089203dceb94801dc2fbdbbe089001eeb5ca8008e2ade2088c5faf848002b0b4fa088a03dceb948009abcea2088f0102088803dceb948005f8aaf88a088702fdbc900ab9888208843bcdb2c036ab9fb6088302fdbc900ab98882088001eeb5ca8001e7e182a67d1ec2a0023d1ec2a00216dd779ae580039df3efce02dd05faf8a038ecfaae14dd03dceb94800daddbbde25d1de6d9a00289c2e1fe029d03dceb94801dc3d3d1ea12]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10 ++ rowsChunk11
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullFiveCase0.base QuadFullFiveCase0.hinges QuadFullFiveCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase0.base QuadFullFiveCase0.hinges QuadFullFiveCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullFiveCase1.base QuadFullFiveCase1.hinges QuadFullFiveCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz817:"s0331"="s0331":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase1.base QuadFullFiveCase1.hinges QuadFullFiveCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullFiveCase2.base QuadFullFiveCase2.hinges QuadFullFiveCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase2.base QuadFullFiveCase2.hinges QuadFullFiveCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullFiveCase3.base QuadFullFiveCase3.hinges QuadFullFiveCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz818:"s0332"="s0332":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase3.base QuadFullFiveCase3.hinges QuadFullFiveCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullFiveCase4.base QuadFullFiveCase4.hinges QuadFullFiveCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase4.base QuadFullFiveCase4.hinges QuadFullFiveCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullFiveCase5.base QuadFullFiveCase5.hinges QuadFullFiveCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz819:"s0333"="s0333":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase5.base QuadFullFiveCase5.hinges QuadFullFiveCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullFiveCase6.base QuadFullFiveCase6.hinges QuadFullFiveCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase6.base QuadFullFiveCase6.hinges QuadFullFiveCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r30,RewriteAtoms.r61,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullFiveCase7.base QuadFullFiveCase7.hinges QuadFullFiveCase7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
private def zz820:"s0334"="s0334":=by decide+kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase7.base QuadFullFiveCase7.hinges QuadFullFiveCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullFiveCase8.base QuadFullFiveCase8.hinges QuadFullFiveCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase8.base QuadFullFiveCase8.hinges QuadFullFiveCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullFiveCase9.base QuadFullFiveCase9.hinges QuadFullFiveCase9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
private def zz821:"s0335"="s0335":=by decide+kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase9.base QuadFullFiveCase9.hinges QuadFullFiveCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r20,RewriteAtoms.r81,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r4,RewriteAtoms.r63,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullFiveCase10.base QuadFullFiveCase10.hinges QuadFullFiveCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase10.base QuadFullFiveCase10.hinges QuadFullFiveCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r20,RewriteAtoms.r81,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullFiveCase11.base QuadFullFiveCase11.hinges QuadFullFiveCase11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
private def zz822:"s0336"="s0336":=by decide+kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase11.base QuadFullFiveCase11.hinges QuadFullFiveCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullFiveCase12.base QuadFullFiveCase12.hinges QuadFullFiveCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase12.base QuadFullFiveCase12.hinges QuadFullFiveCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullFiveCase13.base QuadFullFiveCase13.hinges QuadFullFiveCase13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
private def zz823:"s0337"="s0337":=by decide+kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase13.base QuadFullFiveCase13.hinges QuadFullFiveCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullFiveCase14.base QuadFullFiveCase14.hinges QuadFullFiveCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase14.base QuadFullFiveCase14.hinges QuadFullFiveCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullFiveCase15.base QuadFullFiveCase15.hinges QuadFullFiveCase15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
private def zz824:"s0338"="s0338":=by decide+kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase15.base QuadFullFiveCase15.hinges QuadFullFiveCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullFiveCase16.base QuadFullFiveCase16.hinges QuadFullFiveCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase16.base QuadFullFiveCase16.hinges QuadFullFiveCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r67,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullFiveCase17.base QuadFullFiveCase17.hinges QuadFullFiveCase17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
private def zz825:"s0339"="s0339":=by decide+kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase17.base QuadFullFiveCase17.hinges QuadFullFiveCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullFiveCase18.base QuadFullFiveCase18.hinges QuadFullFiveCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase18.base QuadFullFiveCase18.hinges QuadFullFiveCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullFiveCase19.base QuadFullFiveCase19.hinges QuadFullFiveCase19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
private def zz826:"s033a"="s033a":=by decide+kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullFiveCase19.base QuadFullFiveCase19.hinges QuadFullFiveCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullFiveCase19.nonnegative x hx
def pair20:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_20_base LocalFullFivePairs.compact_fullFive_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullFivePairs.fullFive_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_20_base LocalFullFivePairs.compact_fullFive_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullFivePairs.fullFive_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_21_base LocalFullFivePairs.compact_fullFive_pair_21_hinges
private def zz827:"s033b"="s033b":=by decide+kernel
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullFivePairs.fullFive_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_21_base LocalFullFivePairs.compact_fullFive_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullFivePairs.fullFive_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_22_base LocalFullFivePairs.compact_fullFive_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
private def zz828:"s033c"="s033c":=by decide+kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullFivePairs.fullFive_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_22_base LocalFullFivePairs.compact_fullFive_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullFivePairs.fullFive_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_23_base LocalFullFivePairs.compact_fullFive_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullFivePairs.fullFive_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_23_base LocalFullFivePairs.compact_fullFive_pair_23_hinges x
private def zz829:"s033d"="s033d":=by decide+kernel
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullFivePairs.fullFive_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r69]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_24_base LocalFullFivePairs.compact_fullFive_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullFivePairs.fullFive_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_24_base LocalFullFivePairs.compact_fullFive_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullFivePairs.fullFive_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_25_base LocalFullFivePairs.compact_fullFive_pair_25_hinges
private def zz830:"s033e"="s033e":=by decide+kernel
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullFivePairs.fullFive_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_25_base LocalFullFivePairs.compact_fullFive_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullFivePairs.fullFive_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r47]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_26_base LocalFullFivePairs.compact_fullFive_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
private def zz831:"s033f"="s033f":=by decide+kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullFivePairs.fullFive_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_26_base LocalFullFivePairs.compact_fullFive_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullFivePairs.fullFive_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (5) (1 / 0x186a0) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_27_base LocalFullFivePairs.compact_fullFive_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullFivePairs.fullFive_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_27_base LocalFullFivePairs.compact_fullFive_pair_27_hinges x
private def zz832:"s0340"="s0340":=by decide+kernel
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullFivePairs.fullFive_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_28_base LocalFullFivePairs.compact_fullFive_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullFivePairs.fullFive_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_28_base LocalFullFivePairs.compact_fullFive_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullFivePairs.fullFive_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_29_base LocalFullFivePairs.compact_fullFive_pair_29_hinges
private def zz833:"s0341"="s0341":=by decide+kernel
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullFivePairs.fullFive_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_29_base LocalFullFivePairs.compact_fullFive_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullFivePairs.fullFive_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_30_base LocalFullFivePairs.compact_fullFive_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
private def zz834:"s0342"="s0342":=by decide+kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullFivePairs.fullFive_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_30_base LocalFullFivePairs.compact_fullFive_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullFivePairs.fullFive_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_31_base LocalFullFivePairs.compact_fullFive_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullFivePairs.fullFive_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_31_base LocalFullFivePairs.compact_fullFive_pair_31_hinges x
private def zz835:"s0343"="s0343":=by decide+kernel
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullFivePairs.fullFive_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_32_base LocalFullFivePairs.compact_fullFive_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullFivePairs.fullFive_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_32_base LocalFullFivePairs.compact_fullFive_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullFivePairs.fullFive_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (5) (1 / 0x186a0) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_33_base LocalFullFivePairs.compact_fullFive_pair_33_hinges
private def zz836:"s0344"="s0344":=by decide+kernel
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullFivePairs.fullFive_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_33_base LocalFullFivePairs.compact_fullFive_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullFivePairs.fullFive_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (5) (1 / 0x186a0) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_34_base LocalFullFivePairs.compact_fullFive_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
private def zz837:"s0345"="s0345":=by decide+kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullFivePairs.fullFive_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_34_base LocalFullFivePairs.compact_fullFive_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullFivePairs.fullFive_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (5) (1 / 0x186a0) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_35_base LocalFullFivePairs.compact_fullFive_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullFivePairs.fullFive_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_35_base LocalFullFivePairs.compact_fullFive_pair_35_hinges x
private def zz838:"s0346"="s0346":=by decide+kernel
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullFivePairs.fullFive_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (5) (1 / 0x186a0) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r18]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_36_base LocalFullFivePairs.compact_fullFive_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullFivePairs.fullFive_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_36_base LocalFullFivePairs.compact_fullFive_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullFivePairs.fullFive_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (5) (1 / 0x186a0) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_37_base LocalFullFivePairs.compact_fullFive_pair_37_hinges
private def zz839:"s0347"="s0347":=by decide+kernel
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullFivePairs.fullFive_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_37_base LocalFullFivePairs.compact_fullFive_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullFivePairs.fullFive_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (5) (1 / 0x186a0) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_38_base LocalFullFivePairs.compact_fullFive_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
private def zz840:"s0348"="s0348":=by decide+kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullFivePairs.fullFive_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_38_base LocalFullFivePairs.compact_fullFive_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullFivePairs.fullFive_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (5) (1 / 0x186a0) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullFivePairs.compact_fullFive_pair_39_base LocalFullFivePairs.compact_fullFive_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullFivePairs.fullFive_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullFivePairs.compact_fullFive_pair_39_base LocalFullFivePairs.compact_fullFive_pair_39_hinges x
private def zz841:"s0349"="s0349":=by decide+kernel
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullFivePairs.fullFive_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (5) (1 / 0x186a0) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullFiveRows
private def zz2232:"s08b8"="s08b8":=by decide+kernel
end 
section 
namespace Green24Proof.FullFiveCyclic
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseSymmetry FullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullFiveRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullFiveRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullFiveRows.rows p q same x]
    exact FullFiveRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz842:"s034a"="s034a":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 5 (1 / 0x186a0) FullFiveRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullFiveRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 5 (1 / 0x186a0) FullFiveRows.rows p q same x]
    exact FullFiveRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullFiveRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullFiveRows.rows
theorem remaining_rows_count:remainingRows.length = 11:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
      weightedAggregate 5 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullFiveRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 5 (1 / 0x186a0) FullFiveRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 5 h4 h3 h5 g FullFiveRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x61a8:ℝ) * mass g ^ 2 ≤
    weightedAggregate 5 h4 h3 g (stripPotentials FullFiveRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullFiveCyclic
private def zz2233:"s08b9"="s08b9":=by decide+kernel
end 
section 
namespace Green24Proof.FullFiveMass
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation PhaseMassRows PhaseColourRows
private def zz843:"s034b"="s034b":=by decide+kernel
theorem remainingRows_eq:FullFiveCyclic.remainingRows = [
  ((0xe7c2093 / 0x1dcd6500), .balance 0 (1)),
  ((0xa72201 / 0x5f5e10), .balance 1 (-1)),
  ((0x36567db / 0x7735940), .balance 2 (1)),
  ((0xa72201 / 0x5f5e10), .balance 3 (-1)),
  ((0x2f855e05 / 0x3b9aca00), .child 0),
  (1, .heightChild 1),
  ((0x957391 / 0x3b9aca00), .grandchild 0),
  ((0x260d3d / 0xbebc200), .grandchild 2),
  ((0x8c4b71 / 0x1dcd6500), .ordered 0),
  ((0xec2f76df / 0x3b9aca00), .massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((1 / 0xf424), .normalization)]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff PackedPhaseRowsEquality.labelEq PackedPhaseRowsEquality.labelEq_iff _ _).mp
  decide +kernel
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0xe7c2093 / 0x1dcd6500):ℝ) * phaseTotal h4 g 0 + ((-0xa72201 / 0x5f5e10):ℝ) * phaseTotal h4 g 1 + ((0x36567db / 0x7735940):ℝ) * phaseTotal h4 g 2 + ((-0xa72201 / 0x5f5e10):ℝ) * phaseTotal h4 g 3) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - (5:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
noncomputable def meanBalance {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0x1c11bfff / 0x3b9aca00):ℝ) * (phaseTotal h4 g 0 + phaseTotal h4 g 2) + ((-0xa72201 / 0x5f5e10):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - (5:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
theorem weighted_remaining_eq {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    weightedAggregate 5 h4 h3 g FullFiveCyclic.remainingRows =
      balanceMass h4 g +
      ((0x2f855e05 / 0x3b9aca00):ℝ) * rowAggregate 5 h4 h3 g (.child 0) +
      (1:ℝ) * rowAggregate 5 h4 h3 g (.heightChild 1) +
      ((0x957391 / 0x3b9aca00):ℝ) * rowAggregate 5 h4 h3 g (.grandchild 0) +
      ((0x260d3d / 0xbebc200):ℝ) * rowAggregate 5 h4 h3 g (.grandchild 2) +
      ((0x8c4b71 / 0x1dcd6500):ℝ) * rowAggregate 5 h4 h3 g (.ordered 0) +
      ((0xec2f76df / 0x3b9aca00):ℝ) * rowAggregate 5 h4 h3 g (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)) +
      ((1 / 0xf424):ℝ) * mass g ^ 2:=by
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_balance,rowAggregate_normalization]
  norm_num
  unfold balanceMass
  ring
theorem balanceMass_le_mean {q:ℕ} [NeZero q] (h4:4 ∣ q) (_h3:3 ∣ q)
    (g:ZMod q → ℝ) (_hU:0 ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2))
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (_hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (5:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3)) :
    balanceMass h4 g ≤ meanBalance h4 g:=by
  have hp:=mul_nonpos_of_nonneg_of_nonpos (sub_nonneg.mpr heven) (sub_nonpos.mpr hhigh)
  unfold balanceMass meanBalance
  nlinarith
noncomputable def massPolynomial (U V:ℝ):ℝ :=
  ((-0x1c11623f / 0xee6b2800):ℝ) * U ^ 2 + ((0x9cad453 / 0x9896800):ℝ) * U * V + ((-0xa721e3 / 0x4c4b40):ℝ) * V ^ 2
theorem massPolynomial_lower_bound {U V:ℝ} (hV:0 ≤ V)
    (hlow:(4:ℝ) * V ≤ U) (hhigh:U ≤ (5:ℝ) * V) :
    ((27 / 0x1e848):ℝ) * V ^ 2 ≤ massPolynomial U V:=by
  have hp:=mul_nonneg (sub_nonneg.mpr hlow) (sub_nonneg.mpr hhigh)
  have hl:=mul_nonneg hV (sub_nonneg.mpr hlow)
  have hh:=mul_nonneg hV (sub_nonneg.mpr hhigh)
  unfold massPolynomial
  nlinarith
private def zz844:"s034c"="s034c":=by decide+kernel
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (5:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate 5 h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate 5 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:rowAggregate 5 h4 h3 g (.grandchild 0) ≤ 0)
    (hg2:rowAggregate 5 h4 h3 g (.grandchild 2) ≤ 0) :
    weightedAggregate 5 h4 h3 g FullFiveCyclic.remainingRows ≤
      meanBalance h4 g + ((1 / 0xf424):ℝ) * mass g ^ 2:=by
  rw [weighted_remaining_eq]
  have hb:=balanceMass_le_mean h4 h3 g
    (add_nonneg (phaseTotal_nonneg h4 g hg 0) (phaseTotal_nonneg h4 g hg 2)) heven hodd hhigh
  have ho:rowAggregate 5 h4 h3 g (.ordered 0) ≤ 0 :=
    rowAggregate_ordered_nonpos 5 h4 h3 g hg 0 (by simpa using heven)
  have hm5:=rowAggregate_massSquare_nonpos 5 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  linarith
theorem deficit_lower_bound_of_child_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hlow:(4:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2))
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (5:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hchild:rowAggregate 5 h4 h3 g (.child 0) ≤ 0)
    (hheight:rowAggregate 5 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:rowAggregate 5 h4 h3 g (.grandchild 0) ≤ 0)
    (hg2:rowAggregate 5 h4 h3 g (.grandchild 2) ≤ 0) :
    ((27 / 0x1e848):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ^ 2 ≤ deficit g:=by
  have hc:=FullFiveCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg heven hodd hhigh hchild hheight hg0 hg2
  have hm:mass g = (phaseTotal h4 g 0 + phaseTotal h4 g 2) + (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    simpa only [add_assoc,add_comm,add_left_comm] using (phaseTotal_sum h4 g).symm
  have hp:massPolynomial (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ deficit g:=by
    rw [hm] at hc hr
    unfold meanBalance at hr
    unfold massPolynomial
    nlinarith
  exact (massPolynomial_lower_bound
    (add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)) hlow hhigh).trans hp
end Green24Proof.FullFiveMass
private def zz2234:"s08ba"="s08ba":=by decide+kernel
end 
section 
namespace Green24Proof.FullFiveProfileInterval
open FullPhaseRows FullPhaseAggregation PhaseMassRows ChildRows HeightChildRows
theorem interval_bound_of_height {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hh:(49 / 0xfa:ℝ) * energy v - (6 / 5:ℝ) *
      (classMass (ZMod.castHom h2 (ZMod 2)) v 0 - classMass (ZMod.castHom h2 (ZMod 2)) v 1) ^ 2 ≤ deficit v)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(4:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (5:ℝ) * mass v) :
    (27 / 0x1e848:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    have ht:=phaseTotal_sum h4 (interleave u v)
    rw [mass_interleave] at ht
    linarith
  have hchild:rowAggregate (5) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have hheight:=rowAggregate_height_odd_nonpos (5) h4 h3 h2 u v hu hv hh
  have hg0:=Full27ProfileInterval.grandchild_nonpos_of_induction 5 h4 h3 (interleave u v) hg 0 ih
  have hg2:=Full27ProfileInterval.grandchild_nonpos_of_induction 5 h4 h3 (interleave u v) hg 2 ih
  have hc:=FullFiveMass.deficit_lower_bound_of_child_rows h4 h3 h5 (interleave u v) hg horder hodd
    (by rw [hU,hV]; exact hlow) (by rw [hU,hV]; exact hhigh) hchild hheight hg0 hg2
  simpa only [hV] using hc
theorem interval_bound_ordered {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(4:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (5:ℝ) * mass v) :
    (27 / 0x1e848:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  exact interval_bound_of_height h4 h3 h5 h2 u v hu hv ih
    (HeightStrong.strong_height_bound h2 h3m h5m v hv) horder hodd hlow hhigh
private def zz845:"s034d"="s034d":=by decide+kernel
theorem interval_bound {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m)
    (h5:¬5 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(4:ℝ) * mass v ≤ mass u)
    (hhigh:mass u ≤ (5:ℝ) * mass v) :
    (27 / 0x1e848:ℝ) * mass v ^ 2 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,horder,hodd⟩:=ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have hb:=interval_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih horder hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hU,hV,hd] using hb
end Green24Proof.FullFiveProfileInterval
private def zz2235:"s08bb"="s08bb":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullSixPairs
def compact_fullSix_pair_20_base:CompactPair.Quadratic:=⟨(-37 / 0x59682f000),(0x1f7 / 0x1dcd6500),0⟩
def compact_fullSix_pair_20_hinges:List CompactPair.Hinge:=[⟨(0xd1 / 0xee6b2800),1, -3⟩,⟨(-0x1a07bbb / 0x1dcd65000),1, -2⟩,⟨(0x176d1d3 / 0x2cb417800),2, -3⟩,⟨(0x1a07bbb / 0x1dcd65000),2, -1⟩,⟨(-0x176d1d3 / 0x2cb417800),3, -2⟩,⟨(-0xd1 / 0xee6b2800),3, -1⟩]
noncomputable def fullSix_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_20_base compact_fullSix_pair_20_hinges x y
def compact_fullSix_pair_20_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullSix_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_20_base compact_fullSix_pair_20_hinges 0 compact_fullSix_pair_20_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_20_representation (x y:ℝ) :
    fullSix_pair_20 x y = CompactPair.expressionEval compact_fullSix_pair_20_base compact_fullSix_pair_20_hinges x y:=by rfl
theorem fullSix_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_20 x y:=by
  rw [compact_fullSix_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_20_check hy (by simpa using hx)
def compact_fullSix_pair_21_base:CompactPair.Quadratic:=⟨(11 / 0x165a0bc00),(0x333 / 0x77359400),0⟩
def compact_fullSix_pair_21_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -3⟩,⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(1 / 0x59682f000),2, -3⟩,⟨(1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(-1 / 0xee6b2800),3, -1⟩]
noncomputable def fullSix_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_21_base compact_fullSix_pair_21_hinges x y
def compact_fullSix_pair_21_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
private def zz846:"s034e"="s034e":=by decide+kernel
theorem compact_fullSix_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_21_base compact_fullSix_pair_21_hinges 0 compact_fullSix_pair_21_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_21_representation (x y:ℝ) :
    fullSix_pair_21 x y = CompactPair.expressionEval compact_fullSix_pair_21_base compact_fullSix_pair_21_hinges x y:=by rfl
theorem fullSix_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_21 x y:=by
  rw [compact_fullSix_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_21_check hy (by simpa using hx)
def compact_fullSix_pair_22_base:CompactPair.Quadratic:=⟨0,(0x20bf / 0x165a0bc00),0⟩
def compact_fullSix_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullSix_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_22_base compact_fullSix_pair_22_hinges x y
def compact_fullSix_pair_22_cuts:List ℚ:=[]
theorem compact_fullSix_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_22_base compact_fullSix_pair_22_hinges 0 compact_fullSix_pair_22_cuts = true :=
  by decide +kernel
private def zz847:"s034f"="s034f":=by decide+kernel
theorem compact_fullSix_pair_22_representation (x y:ℝ) :
    fullSix_pair_22 x y = CompactPair.expressionEval compact_fullSix_pair_22_base compact_fullSix_pair_22_hinges x y:=by rfl
theorem fullSix_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_22 x y:=by
  rw [compact_fullSix_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_22_check hy (by simpa using hx)
def compact_fullSix_pair_23_base:CompactPair.Quadratic:=⟨(-0x21c63d84d / 0x2cb417800),(0x9412b0d3 / 0x165a0bc00),0⟩
def compact_fullSix_pair_23_hinges:List CompactPair.Hinge:=[⟨(-0x168bea1 / 0x9896800),1, -2⟩,⟨(-0x863fc5f / 0x77359400),1, -1⟩,⟨(0x88492573 / 0x59682f000),2, -3⟩,⟨(0x233442c9 / 0x3b9aca00),2, -1⟩,⟨(-0xbb8c53b / 0x3b9aca00),3, -2⟩]
noncomputable def fullSix_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_23_base compact_fullSix_pair_23_hinges x y
def compact_fullSix_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),2]
theorem compact_fullSix_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_23_base compact_fullSix_pair_23_hinges 0 compact_fullSix_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_23_representation (x y:ℝ) :
    fullSix_pair_23 x y = CompactPair.expressionEval compact_fullSix_pair_23_base compact_fullSix_pair_23_hinges x y:=by rfl
private def zz848:"s0350"="s0350":=by decide+kernel
theorem fullSix_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_23 x y:=by
  rw [compact_fullSix_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_23_check hy (by simpa using hx)
def compact_fullSix_pair_24_base:CompactPair.Quadratic:=⟨(-1 / 0x8f0d1800),(0xd55 / 0xcaa7e200),0⟩
def compact_fullSix_pair_24_hinges:List CompactPair.Hinge:=[⟨(0x258b579 / 0x47868c00),1, -3⟩,⟨(-0x24a2455 / 0x7735940),1, -2⟩,⟨(0x1bd2c72d / 0xee6b2800),2, -3⟩,⟨(-0x845447af / 0xee6b2800),2, -1⟩,⟨(0x3ba1d2f3 / 0x2cb417800),3, -2⟩,⟨(0x43aed35 / 0x1dcd6500),3, -1⟩]
noncomputable def fullSix_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_24_base compact_fullSix_pair_24_hinges x y
def compact_fullSix_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullSix_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_24_base compact_fullSix_pair_24_hinges 0 compact_fullSix_pair_24_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_24_representation (x y:ℝ) :
    fullSix_pair_24 x y = CompactPair.expressionEval compact_fullSix_pair_24_base compact_fullSix_pair_24_hinges x y:=by rfl
theorem fullSix_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_24 x y:=by
  rw [compact_fullSix_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_24_check hy (by simpa using hx)
def compact_fullSix_pair_25_base:CompactPair.Quadratic:=⟨(-17 / 0x59682f000),(0x363b / 0x7ea8ed400),0⟩
def compact_fullSix_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(1 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullSix_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_25_base compact_fullSix_pair_25_hinges x y
def compact_fullSix_pair_25_cuts:List ℚ:=[(1 / 3),(2 / 3),1,3]
private def zz849:"s0351"="s0351":=by decide+kernel
theorem compact_fullSix_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_25_base compact_fullSix_pair_25_hinges 0 compact_fullSix_pair_25_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_25_representation (x y:ℝ) :
    fullSix_pair_25 x y = CompactPair.expressionEval compact_fullSix_pair_25_base compact_fullSix_pair_25_hinges x y:=by rfl
theorem fullSix_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_25 x y:=by
  rw [compact_fullSix_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_25_check hy (by simpa using hx)
def compact_fullSix_pair_26_base:CompactPair.Quadratic:=⟨0,(0x20c3 / 0x165a0bc00),0⟩
def compact_fullSix_pair_26_hinges:List CompactPair.Hinge:=[]
noncomputable def fullSix_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_26_base compact_fullSix_pair_26_hinges x y
def compact_fullSix_pair_26_cuts:List ℚ:=[]
theorem compact_fullSix_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_26_base compact_fullSix_pair_26_hinges 0 compact_fullSix_pair_26_cuts = true :=
  by decide +kernel
private def zz850:"s0352"="s0352":=by decide+kernel
theorem compact_fullSix_pair_26_representation (x y:ℝ) :
    fullSix_pair_26 x y = CompactPair.expressionEval compact_fullSix_pair_26_base compact_fullSix_pair_26_hinges x y:=by rfl
theorem fullSix_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_26 x y:=by
  rw [compact_fullSix_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_26_check hy (by simpa using hx)
def compact_fullSix_pair_27_base:CompactPair.Quadratic:=⟨(-0x6193d4f65 / 0x2cb417800),(0x1383f890f / 0x165a0bc00),0⟩
def compact_fullSix_pair_27_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-0xd02a4edb / 0x1dcd65000),2, -1⟩,⟨(0x7ce62f5 / 0x11e1a300),3, -1⟩]
noncomputable def fullSix_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_27_base compact_fullSix_pair_27_hinges x y
def compact_fullSix_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),3]
theorem compact_fullSix_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_27_base compact_fullSix_pair_27_hinges 0 compact_fullSix_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_27_representation (x y:ℝ) :
    fullSix_pair_27 x y = CompactPair.expressionEval compact_fullSix_pair_27_base compact_fullSix_pair_27_hinges x y:=by rfl
private def zz851:"s0353"="s0353":=by decide+kernel
theorem fullSix_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_27 x y:=by
  rw [compact_fullSix_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_27_check hy (by simpa using hx)
def compact_fullSix_pair_28_base:CompactPair.Quadratic:=⟨(-0x1e57a29c15 / 0xe8d4a5100),(-0x32ce5a87 / 0x574fbde6),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_28_hinges:List CompactPair.Hinge:=[⟨(-0x837f36a97 / 0x3a35294400),1, -3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(0x837f36a97 / 0x3a35294400),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_28_base compact_fullSix_pair_28_hinges x y
def compact_fullSix_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSix_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_28_base compact_fullSix_pair_28_hinges 0 compact_fullSix_pair_28_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_28_representation (x y:ℝ) :
    fullSix_pair_28 x y = CompactPair.expressionEval compact_fullSix_pair_28_base compact_fullSix_pair_28_hinges x y:=by rfl
theorem fullSix_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_28 x y:=by
  rw [compact_fullSix_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_28_check hy (by simpa using hx)
def compact_fullSix_pair_29_base:CompactPair.Quadratic:=⟨(-0x19078532d3 / 0xe8d4a5100),(-0x215f5b15e9 / 0x2ba7def300),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_29_hinges:List CompactPair.Hinge:=[⟨(-0x2c7f25afb / 0x1d1a94a200),1, -3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_29_base compact_fullSix_pair_29_hinges x y
def compact_fullSix_pair_29_cuts:List ℚ:=[(1 / 3),3]
private def zz852:"s0354"="s0354":=by decide+kernel
theorem compact_fullSix_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_29_base compact_fullSix_pair_29_hinges 0 compact_fullSix_pair_29_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_29_representation (x y:ℝ) :
    fullSix_pair_29 x y = CompactPair.expressionEval compact_fullSix_pair_29_base compact_fullSix_pair_29_hinges x y:=by rfl
theorem fullSix_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_29 x y:=by
  rw [compact_fullSix_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_29_check hy (by simpa using hx)
def compact_fullSix_pair_30_base:CompactPair.Quadratic:=⟨(-0xa95f0445 / 0xee6b280),(0x1bb71d08f / 0x47868c00),0⟩
def compact_fullSix_pair_30_hinges:List CompactPair.Hinge:=[⟨(-0x1198d539 / 0x77359400),2, -3⟩,⟨(0x76c79f41 / 0x59682f00),3, -1⟩]
noncomputable def fullSix_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_30_base compact_fullSix_pair_30_hinges x y
def compact_fullSix_pair_30_cuts:List ℚ:=[(1 / 3),(3 / 2)]
theorem compact_fullSix_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_30_base compact_fullSix_pair_30_hinges 0 compact_fullSix_pair_30_cuts = true :=
  by decide +kernel
private def zz853:"s0355"="s0355":=by decide+kernel
theorem compact_fullSix_pair_30_representation (x y:ℝ) :
    fullSix_pair_30 x y = CompactPair.expressionEval compact_fullSix_pair_30_base compact_fullSix_pair_30_hinges x y:=by rfl
theorem fullSix_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_30 x y:=by
  rw [compact_fullSix_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_30_check hy (by simpa using hx)
def compact_fullSix_pair_31_base:CompactPair.Quadratic:=⟨(7 / 0x59682f000),(0x4af / 0x59682f00),0⟩
def compact_fullSix_pair_31_hinges:List CompactPair.Hinge:=[⟨(-0x8a9c07 / 0x59682f00),1, -3⟩,⟨(-0x36a732b / 0x3b9aca00),1, -1⟩,⟨(0x6c8a9d / 0x2faf0800),2, -3⟩,⟨(0x46b1055 / 0x59682f000),3, -2⟩,⟨(-1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullSix_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_31_base compact_fullSix_pair_31_hinges x y
def compact_fullSix_pair_31_cuts:List ℚ:=[(1 / 3),(2 / 3),1,(3 / 2),3]
theorem compact_fullSix_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_31_base compact_fullSix_pair_31_hinges 0 compact_fullSix_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_31_representation (x y:ℝ) :
    fullSix_pair_31 x y = CompactPair.expressionEval compact_fullSix_pair_31_base compact_fullSix_pair_31_hinges x y:=by rfl
private def zz854:"s0356"="s0356":=by decide+kernel
theorem fullSix_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_31 x y:=by
  rw [compact_fullSix_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_31_check hy (by simpa using hx)
def compact_fullSix_pair_32_base:CompactPair.Quadratic:=⟨(-0x1e11f064b1 / 0x3a35294400),(-0x641e0efed5 / 0x574fbde600),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x4b9c091c91 / 0x3a35294400),1, -3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_32_base compact_fullSix_pair_32_hinges x y
def compact_fullSix_pair_32_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSix_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_32_base compact_fullSix_pair_32_hinges 0 compact_fullSix_pair_32_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_32_representation (x y:ℝ) :
    fullSix_pair_32 x y = CompactPair.expressionEval compact_fullSix_pair_32_base compact_fullSix_pair_32_hinges x y:=by rfl
theorem fullSix_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_32 x y:=by
  rw [compact_fullSix_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_32_check hy (by simpa using hx)
def compact_fullSix_pair_33_base:CompactPair.Quadratic:=⟨(-0x1bcf778fc9 / 0x1d1a94a200),(-0x641e1267e1 / 0x574fbde600),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0x2c7f25afb / 0x1d1a94a200),1, -3⟩,⟨(-0x44b6d347 / 0xee6b2800),1, -2⟩,⟨(-0x35a9dc27 / 0x77359400),1, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(0x1adfb41b / 0x77359400),2, -3⟩,⟨(-0x40e3d801 / 0xee6b2800),2, -1⟩,⟨(0xcc8b7bf / 0x2cb417800),3, -2⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_33_base compact_fullSix_pair_33_hinges x y
def compact_fullSix_pair_33_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz855:"s0357"="s0357":=by decide+kernel
theorem compact_fullSix_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_33_base compact_fullSix_pair_33_hinges 0 compact_fullSix_pair_33_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_33_representation (x y:ℝ) :
    fullSix_pair_33 x y = CompactPair.expressionEval compact_fullSix_pair_33_base compact_fullSix_pair_33_hinges x y:=by rfl
theorem fullSix_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_33 x y:=by
  rw [compact_fullSix_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_33_check hy (by simpa using hx)
def compact_fullSix_pair_34_base:CompactPair.Quadratic:=⟨(1 / 0x59682f00),(0x2159 / 0x1faa3b500),0⟩
def compact_fullSix_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x10030445 / 0x165a0bc00),1, -3⟩,⟨(0x6679b4f / 0x17d78400),1, -2⟩,⟨(-0x6679b4f / 0x47868c00),2, -3⟩,⟨(-0x6679b4f / 0x17d78400),2, -1⟩,⟨(0x6679b4f / 0x47868c00),3, -2⟩,⟨(0x10030445 / 0x165a0bc00),3, -1⟩]
noncomputable def fullSix_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_34_base compact_fullSix_pair_34_hinges x y
def compact_fullSix_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullSix_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_34_base compact_fullSix_pair_34_hinges 0 compact_fullSix_pair_34_cuts = true :=
  by decide +kernel
private def zz856:"s0358"="s0358":=by decide+kernel
theorem compact_fullSix_pair_34_representation (x y:ℝ) :
    fullSix_pair_34 x y = CompactPair.expressionEval compact_fullSix_pair_34_base compact_fullSix_pair_34_hinges x y:=by rfl
theorem fullSix_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_34 x y:=by
  rw [compact_fullSix_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_34_check hy (by simpa using hx)
def compact_fullSix_pair_35_base:CompactPair.Quadratic:=⟨(-1 / 0x1c9c3800),(0x1b51 / 0x3f5476a00),0⟩
def compact_fullSix_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(-1 / 0xee6b2800),1, -2⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullSix_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_35_base compact_fullSix_pair_35_hinges x y
def compact_fullSix_pair_35_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
theorem compact_fullSix_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_35_base compact_fullSix_pair_35_hinges 0 compact_fullSix_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_35_representation (x y:ℝ) :
    fullSix_pair_35 x y = CompactPair.expressionEval compact_fullSix_pair_35_base compact_fullSix_pair_35_hinges x y:=by rfl
private def zz857:"s0359"="s0359":=by decide+kernel
theorem fullSix_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_35 x y:=by
  rw [compact_fullSix_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_35_check hy (by simpa using hx)
def compact_fullSix_pair_36_base:CompactPair.Quadratic:=⟨(-0x61997 / 0x8f0d180),(0x1a26927 / 0x165a0bc00),0⟩
def compact_fullSix_pair_36_hinges:List CompactPair.Hinge:=[⟨(-0x1a2487 / 0x1dcd6500),1, -2⟩,⟨(0x8b6d7b / 0x165a0bc00),2, -3⟩]
noncomputable def fullSix_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_36_base compact_fullSix_pair_36_hinges x y
def compact_fullSix_pair_36_cuts:List ℚ:=[(3 / 2),2]
theorem compact_fullSix_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_36_base compact_fullSix_pair_36_hinges 0 compact_fullSix_pair_36_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_36_representation (x y:ℝ) :
    fullSix_pair_36 x y = CompactPair.expressionEval compact_fullSix_pair_36_base compact_fullSix_pair_36_hinges x y:=by rfl
theorem fullSix_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_36 x y:=by
  rw [compact_fullSix_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_36_check hy (by simpa using hx)
def compact_fullSix_pair_37_base:CompactPair.Quadratic:=⟨(1 / 0x77359400),(0x95f / 0xb2d05e00),0⟩
def compact_fullSix_pair_37_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -2⟩,⟨(-3 / 0xee6b2800),1, -1⟩]
noncomputable def fullSix_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_37_base compact_fullSix_pair_37_hinges x y
def compact_fullSix_pair_37_cuts:List ℚ:=[1,2]
private def zz858:"s035a"="s035a":=by decide+kernel
theorem compact_fullSix_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_37_base compact_fullSix_pair_37_hinges 0 compact_fullSix_pair_37_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_37_representation (x y:ℝ) :
    fullSix_pair_37 x y = CompactPair.expressionEval compact_fullSix_pair_37_base compact_fullSix_pair_37_hinges x y:=by rfl
theorem fullSix_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_37 x y:=by
  rw [compact_fullSix_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_37_check hy (by simpa using hx)
def compact_fullSix_pair_38_base:CompactPair.Quadratic:=⟨(-0x9dabbba7f9 / 0x574fbde600),(-0xdf48d0ad3 / 0x15d3ef7980),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_38_hinges:List CompactPair.Hinge:=[⟨(-0x2c7f25afb / 0x1d1a94a200),1, -3⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(-0x311dcf7 / 0xb2d05e00),2, -3⟩,⟨(0x311dcf7 / 0xb2d05e00),3, -2⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_38_base compact_fullSix_pair_38_hinges x y
def compact_fullSix_pair_38_cuts:List ℚ:=[(1 / 3),(2 / 3),(3 / 2),3]
theorem compact_fullSix_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_38_base compact_fullSix_pair_38_hinges 0 compact_fullSix_pair_38_cuts = true :=
  by decide +kernel
private def zz859:"s035b"="s035b":=by decide+kernel
theorem compact_fullSix_pair_38_representation (x y:ℝ) :
    fullSix_pair_38 x y = CompactPair.expressionEval compact_fullSix_pair_38_base compact_fullSix_pair_38_hinges x y:=by rfl
theorem fullSix_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_38 x y:=by
  rw [compact_fullSix_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_38_check hy (by simpa using hx)
def compact_fullSix_pair_39_base:CompactPair.Quadratic:=⟨(-0x19070fbc6b9 / 0xe8d4a51000),(-0x42c08c0689 / 0x574fbde600),(-0x2c7f25afb / 0x2e90edd00)⟩
def compact_fullSix_pair_39_hinges:List CompactPair.Hinge:=[⟨(-0x2c7f25afb / 0x1d1a94a200),1, -3⟩,⟨(0x50301 / 0x1dcd65000),1, -2⟩,⟨(0x2c7f25afb / 0x1d1a94a200),1,3⟩,⟨(-0x50301 / 0x1dcd65000),2, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3, -1⟩,⟨(0x2c7f25afb / 0x1d1a94a200),3,1⟩]
noncomputable def fullSix_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSix_pair_39_base compact_fullSix_pair_39_hinges x y
def compact_fullSix_pair_39_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
theorem compact_fullSix_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullSix_pair_39_base compact_fullSix_pair_39_hinges 0 compact_fullSix_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullSix_pair_39_representation (x y:ℝ) :
    fullSix_pair_39 x y = CompactPair.expressionEval compact_fullSix_pair_39_base compact_fullSix_pair_39_hinges x y:=by rfl
private def zz860:"s035c"="s035c":=by decide+kernel
theorem fullSix_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSix_pair_39 x y:=by
  rw [compact_fullSix_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSix_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullSixPairs
private def zz2236:"s08bc"="s08bc":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l42 l43 l45 l5 l51 l54 l57 l58 l6 l60 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x16b910163, -0x1aafadbc8, -0x280784c82,0x27f0a81e], ![-0x1aafadbc8, -0x640647708,0x378a0746,0x20c6dd884], ![-0x280784c82,0x378a0746, -0xadad9eba4,0x1ab9076ee], ![0x27f0a81e,0x20c6dd884,0x1ab9076ee, -0xd57d703c]]
noncomputable def hinges:Hinges:=[(-0x5f3d0,l6),(-0x1492017c,l5),(0x1ec69684,l4),(0x8dff121,l9),(-0x2a3e9d18,l8),(0xe16245c,l10),(0x1acc80a02,l14),(-0x4aa010cc,l17),(0x4e69ff51,l23),(0x9dcc85a,l22),(-0xd57d703c,l27),(0xd57d703c,l29),(-0x1acc80a02,l25),(0x4fe0d124,l31),(0x8bc3f6a8,l30),(0xd57d703c,l33),(-0xe16245c,l38),(-0xd57d703c,l35),(0x2a3e9d18,l36),(0xd57d703c,l37),(-0x1ec69684,l34),(-0x8bc3f6a8,l43),(-0x9dcc85a,l42),(0x189b03e5,l45),(0xd57d703c,l51),(0x1492017c,l54),(-0x4fe0d124,l57),(-0x189b03e5,l58),(-0x8dff121,l61),(0x5f3d0,l60),(-0x4e69ff51,l63),(0x4aa010cc,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xd57d703c,l27),(0xd57d703c,l29),(0xd57d703c,l33),(-0xd57d703c,l35),(0xd57d703c,l37),(0xd57d703c,l51),(0x1acc80a02,l14),(-0x1acc80a02,l25),(0x8bc3f6a8,l30),(-0x8bc3f6a8,l43),(0x4fe0d124,l31),(-0x4fe0d124,l57),(0x4e69ff51,l23),(-0x4e69ff51,l63),(-0x4aa010cc,l17),(0x4aa010cc,l62),(-0x2a3e9d18,l8),(0x2a3e9d18,l36),(0xe16245c,l10),(-0xe16245c,l38),(0x8dff121,l9),(-0x8dff121,l61),(0x189b03e5,l45),(-0x189b03e5,l58),(-0x1492017c,l5),(0x1492017c,l54),(0x1ec69684,l4),(-0x1ec69684,l34),(0x9dcc85a,l22),(-0x9dcc85a,l42),(-0x5f3d0,l6),(0x5f3d0,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase0" = "QuadFullSixCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase0
private def zz2237:"s08bd"="s08bd":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l58 l6 l60 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2616c8d47, -0x1874d83e8, -0x24af44894,0x4a4], ![-0x1874d83e8, -0x6c1ca0593,0x2381fb44,0x20d05afea], ![-0x24af44894,0x2381fb44, -0x9f2f33074,0x187e31f0e], ![0x4a4,0x20d05afea,0x187e31f0e, -0xc3a6c44c]]
noncomputable def hinges:Hinges:=[(-0x5f3d0,l6),(-0x1492017c,l5),(0x1ec69684,l4),(0x8dff121,l9),(-0x2a3e9d18,l8),(0xe16245c,l10),(0x166ef2f52,l14),(0x10fe4e5d,l13),(0x29bc89dbc,l15),(0x1ccc87b0,l21),(-0x10fe4e5d,l20),(-0x1bb62d8a,l23),(0x43c708e0,l22),(-0xc3a6c44c,l27),(-0x1ccc87b0,l28),(0xc3a6c44c,l29),(-0x166ef2f52,l25),(0x9e4d736a,l30),(0xc3a6c44c,l33),(-0xe16245c,l38),(-0xc3a6c44c,l35),(0x2a3e9d18,l36),(0xc3a6c44c,l37),(-0x1ec69684,l34),(-0x9e4d736a,l43),(-0x43c708e0,l42),(-0x29bc89dbc,l41),(0x3589f092,l45),(0xc3a6c44c,l51),(0x1492017c,l54),(-0x3589f092,l58),(-0x8dff121,l61),(0x5f3d0,l60),(0x1bb62d8a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xc3a6c44c,l27),(0xc3a6c44c,l29),(0xc3a6c44c,l33),(-0xc3a6c44c,l35),(0xc3a6c44c,l37),(0xc3a6c44c,l51),(0x166ef2f52,l14),(-0x166ef2f52,l25),(0x29bc89dbc,l15),(-0x29bc89dbc,l41),(0x9e4d736a,l30),(-0x9e4d736a,l43),(0x1ccc87b0,l21),(-0x1ccc87b0,l28),(-0x1bb62d8a,l23),(0x1bb62d8a,l63),(0x43c708e0,l22),(-0x43c708e0,l42),(0x3589f092,l45),(-0x3589f092,l58),(-0x2a3e9d18,l8),(0x2a3e9d18,l36),(0xe16245c,l10),(-0xe16245c,l38),(0x8dff121,l9),(-0x8dff121,l61),(-0x1492017c,l5),(0x1492017c,l54),(0x10fe4e5d,l13),(-0x10fe4e5d,l20),(0x1ec69684,l4),(-0x1ec69684,l34),(-0x5f3d0,l6),(0x5f3d0,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,0x2c0290040000a4c90407a4301800002610c3403480180000000230e038c020000000000420710040000000000740620080000001042401860180000026230e0390020000004a461c06a0040000000821202c300c00002510c340548018000001841201e0c040000004a441c04a0040000000861201c300c0000000c414038601800000000221c0cc010028240461012da00a0000000004850330040000000000901a40100000000000e01c80200000001a0700598060000000000240d20080000000000680c40100000000000502480200000000002c0690040000000540901c300c0000000148901c601000000001205038c02000000005a22079804000000b110406930100000016220807260200000000290e018c020000000510e00f18060000000000ac0620080000000000360640080000003384402cc030000000062120398040000000c81100b300c000000194240266018000000001b402880300000000006a0310040000000000dc0620080000000001b00a401589284020c047c5007b3651804481e78a00f624a1008302771401c0000000001d80c4010000000000390188020000005092201418080000000000210320041e4964943012c680303c32c32820188d006000000000048061006000000000019032004000290861900f480200000001c86409cc030018c118158079200a0000003108c06830100002c066148050802000000022084068c0300000000260c0718040000000088440e30080000000108881a601000000221306019002,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,0xe0290040000000320a00c300c0000000641405860180000001c8c4088c0300000001b0500e180600000000000f032004000000e21b805060200000000190d028c020000000491580b180600000000a41409300800000162398112602000000020844070c03000004845180af980a00000000078703300412090883200c248030000001cc2b0338c04000000488a604498080000000001c00f200c0000000003a03e4018000000002a2c0cc010000000000520590040000003505404c3010000000a82280726020000000dc170230c04000000001c0c0398040001d8250740cc401000668a511801b08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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase1" = "QuadFullSixCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase1
private def zz2238:"s08be"="s08be":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l22 l23 l27 l29 l33 l35 l37 l4 l51 l6 l62 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1b63d29ace, -0x59682eb50, -0x296e3b47a,0xd124838], ![-0x59682eb50, -0x2a99a09cc4,0xfa6b9c96c, -0x58ca8bc78], ![-0x296e3b47a,0xfa6b9c96c, -0x2f231e6d23,0xa1f622db6], ![0xd124838, -0x58ca8bc78,0xa1f622db6, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x4f26bcc0,l6),(0x1b539958,l4),(0x8f990117,l11),(0xa9cdefdc,l10),(-0x414382bc,l17),(0x15276ad3,l23),(0x18cfcd70d,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x35cbe29ca,l62),(0x22db5ec,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x35cbe29ca,l62),(0x8f990117,l11),(0x18cfcd70d,l22),(0xa9cdefdc,l10),(-0x4f26bcc0,l6),(-0x414382bc,l17),(0x15276ad3,l23),(0x1b539958,l4),(0x22db5ec,l65)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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], #[]⟩
def dynamicCode : Nat := (((((((0x22db6b406e7b48be8ee6b2737d7f0e41cd048008b6dad03dc95cd04773593cdf41f62b7341238aa42e8d7d8162748dc0ed1a05a1231220e20a008001b286a18d199cd4fa85f5bb736453a953f86432a80c9ce48a42d725698e062cd263c4077ca3ad7847f785462cc96b43c7867982424701e38131a484d74a2f524702604ce57604017a54eaa1000df3914fb44c08460108b6dad01b9ed22fa3b9ac9cdf5fc3907341209249241439239429420408209401904010068000929822d469e1c350b1c000000360081c235e1f97c4818222468d28491025abd11c9890c07570b66b09083e10eefb48b04017dff9ba090045141f33d074841400600007e881402c09c17c7bf01eb06ff981c60564074a931b2850d82a3a4449820500593e4aaa281c50cefe3ad72e12010aff2e3a5658080029f86b14b620400a04a9d69d8e1001e2bf0306f4b2a40a18016000090c80038d1beca860278c05a0cdd4c3ea4953a541d7591cda5099b35312db2672f627bca0000000000000000082e2a90ba35f60599018c18c108006002001ec9cc3070d3bf7a26143e64d656deca5178c07911318696f848dbef0de1963b4db2cd2345ab797b) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase2" = "QuadFullSixCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase2
private def zz2239:"s08bf"="s08bf":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l27 l29 l31 l33 l35 l37 l4 l41 l42 l44 l46 l51 l56 l57 l6 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x6a3f403b, -0x572d59370,0x2777efaee,0x11bc088ac], ![-0x572d59370, -0x24bbf0404e,0xdf60a36b8, -0x584ab26f8], ![0x2777efaee,0xdf60a36b8, -0x2e3b37b1f3,0x9fbb4d5d6], ![0x11bc088ac, -0x584ab26f8,0x9fbb4d5d6, -0x2b96acc10]]
noncomputable def hinges:Hinges:=[(-0x4f26bcc0,l6),(0x1b539958,l4),(0x8f990117,l11),(0xa9cdefdc,l10),(0x9cb281c4,l14),(0x787f1811c,l13),(-0x37c40fc6,l17),(-0x3d9933e,l15),(0x358b55fa,l21),(-0x34ce642d8,l20),(-0x13938381,l23),(0x7f5ca4e2,l22),(-0x2b96acc10,l27),(0x2b96acc10,l29),(0x744ebe66,l31),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(-0xc2ab8803,l42),(-0x141fb28ea,l41),(-0x538eadc,l46),(-0x4d7885d8,l44),(0x2b96acc10,l51),(-0x4a7b3886,l57),(-0xce2479d5,l56),(0x7da14378,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2b96acc10,l27),(0x2b96acc10,l29),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(0x2b96acc10,l51),(0x787f1811c,l13),(-0x34ce642d8,l20),(0x8f990117,l11),(0x744ebe66,l31),(0xa9cdefdc,l10),(0x9cb281c4,l14),(0x7da14378,l64),(-0x4a7b3886,l57),(-0xce2479d5,l56),(-0xc2ab8803,l42),(0x358b55fa,l21),(-0x141fb28ea,l41),(-0x4f26bcc0,l6),(0x7f5ca4e2,l22),(-0x37c40fc6,l17),(-0x13938381,l23),(-0x4d7885d8,l44),(0x1b539958,l4),(-0x538eadc,l46),(-0x3d9933e,l15)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase3" = "QuadFullSixCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase3
private def zz2240:"s08c0"="s08c0":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l46 l51 l6 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2e97cb946, -0x1fde7e608, -0x2fcdbdbca,0x4d0aae78], ![-0x1fde7e608, -0xa36763542,0xd25feef0,0x1900a4924], ![-0x2fcdbdbca,0xd25feef0, -0xcf26389be,0x1fde7ef6e], ![0x4d0aae78,0x1900a4924,0x1fde7ef6e, -0xfef3f55c]]
noncomputable def hinges:Hinges:=[(-0x4cac40da,l6),(0x52e606de,l4),(0x5644e7cf,l9),(-0xafe62dcc,l8),(-0x34b44c7c,l11),(0x5bd91eee,l10),(0x5398d804,l14),(0x1b79b3fc0,l13),(-0x4aa010cc,l17),(0x4e69ff51,l23),(0x9dcc85a,l22),(-0xfef3f55c,l27),(-0x7743a5e6,l28),(0xfef3f55c,l29),(-0x10b399f04,l25),(0x4fe0d124,l31),(0x8bc3f6a8,l30),(0xfef3f55c,l33),(-0xfef3f55c,l35),(0xfef3f55c,l37),(-0x5cbc9986,l43),(-0xc0243342,l42),(-0xcebc5036,l41),(0xdb446a4,l46),(0xfef3f55c,l51),(-0x400c1116,l63),(0x5fcf90e,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xfef3f55c,l27),(0xfef3f55c,l29),(0xfef3f55c,l33),(-0xfef3f55c,l35),(0xfef3f55c,l37),(0xfef3f55c,l51),(-0x10b399f04,l25),(0x1b79b3fc0,l13),(-0x7743a5e6,l28),(0x8bc3f6a8,l30),(0x5644e7cf,l9),(0x4fe0d124,l31),(0x4e69ff51,l23),(-0xc0243342,l42),(-0x400c1116,l63),(-0xafe62dcc,l8),(-0x5cbc9986,l43),(0x5bd91eee,l10),(0x5398d804,l14),(-0x34b44c7c,l11),(-0x4cac40da,l6),(-0x4aa010cc,l17),(-0xcebc5036,l41),(0x52e606de,l4),(0xdb446a4,l46),(0x5fcf90e,l65),(0x9dcc85a,l22)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,0x5f013200dc318210300fad00673c62843c082b4018000000002502c80200000002600132010000000013c04c80300000000013032004000000000a01c802728654428092b4019c9186109029ad006708678408086b40180000018850074c030000000067013200c000000017c02c803000000005d013200c000000033021c804000000006f013200c0000204710138c040000007621037300c00631303302ad004000005110404e30118a1550ca024ad0066245183240a6b40198215e0c2021ad006000006114404e3010000000015c02c80300000000a85033004000000015404c8030000000582c07300800001c4610138c0400204510cc0bb4010000000000601c802028c3b043028b40140000138110058c040000000443c053008000000000f01480200000480440163010000250982402d003000000001e009200c0000211e190290020000000002c092008000000903405cc030000034090039301000009e0ec0438c05000002107408e30100000ca1140348c05000000078380d3008000001982809cc03000000421c015300c0001121d40428c05000104760a032400c0000000029018802000000000a80520080e518e0980919005000005111c06c301000000148840d8c0381c744278090c40180000000015018802], #[![-5, 8, 0, -9],![-7, 13, 0, 0]]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((0x148e6c122fcdbdbc93fbcfcc0f4752595f023000000b40000005baa7dfe07f64033cec084d3153aed4ac0b33072832431832821c207f46f0d4eb518f477cf51718e516f1a2720bfb7b39aee54577f348dba6fbf4ec331048ea79afd4610a623ada10030473553eff03f51ef84d5042698a9d76a56058f33b185537a4b964663982a660e4863843044003800e68380c51dfba4bd8fc202b7341b82d9b808eb5970d6fc9df6a687f5d8308fcb15f6b1842587da000524405447635a4526895b3f9f19a40ff8f6d985488ea7aee1101fcf4b47b37e3af7f346f71c1f274b6de8565e39011c7317f95782358edc565078bf4dff38068ae794051bf7bf58239b14cbc2e88f4aa9bba91a1c9eb88056d58f2b52ffc1c964f6d6c5a15919b94acdcd80a18e0a52c6fe7c8990fe31ac3d556b0e105ddc41b1351534fc238f92928b570500bebcff0c43b7dadc4cd3376eaad89428f551ca855946260790000a1043c037455539e3a79c7d4aff334290c46b9e471fe48d2203bb677f0b251fd7f17bd3ddb4f0637ecc906b4ce7e8aa830ac957b3925899ace57bde789dd0cd4347399c2e1968644a22c8c0f9a042847b39aa132ce6505d51d1a2ad83ba5daa2c339296fc10848543f49e32deebab8ab03a6014d9b23aaa3e186ec6d4487b3de1c959fc65dc74d6d8f30718a1264077bbff2045c93634d9aac29ce8ed9c5118432d00b10e1a06ec9b1cc7468c0cb307ad7c00c20cb3003ebfc020815dacfcf8d4d017c2c2c20a841000c7637bc69e000065909bab1c6ee92005a070d367555e901a50d2c4f13298416cd1c333a67cd724a1c00b19cf2458d0c536091d30183080dd1d10c4c870029e77a7d2f8300208793e6e780001b978929013f648016016000088800669207715a6452430c7de0b74c4f868aa390e63d9aa58207d35e386dc3027354299abd2580029bcb42cc0300e1d7c895376080603da76dc4400102c25f3b159a9520058060000223365f019a59f0712057f0a081629f65807b428a26e283941810b187dab4602106c0a1e1c000b5d9e205802acf232a1000000002dd9002200407c80800074c80045190e105c8f5f0dc907619a2c31ad0c0e925cc1d46cf95439a810187c1b1837102685cf0c2006c741439d834f3c9fe83800d6d705d2aa368d8b883044a8a19ad4831fa2fcc4bfba9525a966b10c29229a2544462882585a0000a74c0d212a5c1d7be4a45b92aea1b8e6c2020d4592b1063e0bb56d96a2f156c1400eaedc79552dcd8c671680c9bb5050058541939a147f69941c89fb5a782004862d0369cabfddd92ae42543044473815ddde921a20b7e31aef1d01066262044e953cb649d093b1d9d6cbcbd9a4bae3bac6f2428a3689a0000eb487c0883dc2400281043d8961ea2b0f40587982f07143078208283c02c2f2fe884e90c4d4c90680cb59a1b38173895b77e7a13b83c7b396e4cf15b7fd8d83844aea4d4470188004d959f2c4119e21a79b6597effcc85f1487009771be23e3a3f485cbee65fabe3b88c9f9b7eeabbfd66972506fab2964b8ebd9d96e1764cffb9e09e3aa9f8350845c1385db89ca5763eda5417d6733e931afbd4fe5185a823a2a125ae27392b15e2356436bcf9d2944feeab6bffb944a904a3a502d08018239aa9f7f81fa8f7c26a82142e0875238702c0000000051a92227a8aa17821ec842d42033071830c31c21c014025603de2317e0eb3d254139c3374fe816928eb486ee73d398cc1de6e6dde4c40fbf994dbf45d4b3cadcc11664a50002ee202a13b4200608e6aa7dfe07ea3df09aa084c2040422c62062421420821811004c5703dda97a8e1b7c374ed315622b94109562b58e0463883308f40006f88790ac3c4261e0130ef0187700e01802008e3b9e93d13c538d01a11e5ec8e24380c26ddc2087a5d0ec520e188c3a477362032771fccd003084515102d82012ed6bf1050104932830dab9240098061c70f74b25f651c68ec0b1a1751041168d233d50c345470581210610cdc20656c060858c6b1032020a9b45e6d52080148b5e5570020267925c655e44801401000007ecd9006594489f6061aa70337e6961020ba40b2922c1c208326d2718a1841e5b8e23068d04150c6dde980c09e8352a0bdc08109fecf797c2082c8b7eeba55b33480158162c80321aa6d168061a5c84bdd482420413d728dee4807081c2abbab9190c20d8aef5df528d04126ae022c5018135cf871cd0c0204220d49fb31904157a) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase4" = "QuadFullSixCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase4
private def zz2241:"s08c1"="s08c1":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l15 l20 l22 l23 l25 l27 l29 l30 l33 l35 l37 l4 l41 l42 l43 l45 l51 l56 l57 l58 l6 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2b69be299, -0x1da3a8e28, -0x2b8329d5a,0x3671dcf0], ![-0x1da3a8e28, -0x909573430,0x721e1ac4,0x190a2208a], ![-0x2b8329d5a,0x721e1ac4, -0xc0a7cce8e,0x1da3a978e], ![0x3671dcf0,0x190a2208a,0x1da3a978e, -0xed1d496c]]
noncomputable def hinges:Hinges:=[(-0x4cac40da,l6),(0x52e606de,l4),(0x5644e7cf,l9),(-0xafe62dcc,l8),(-0x34b44c7c,l11),(0x5bd91eee,l10),(0x29677396e,l13),(0x29bc89dbc,l15),(-0x1938dc09e,l20),(-0x1bb62d8a,l23),(0x43c708e0,l22),(-0xed1d496c,l27),(0xed1d496c,l29),(-0xe604c290,l25),(0x9e4d736a,l30),(0xed1d496c,l33),(-0xed1d496c,l35),(0xed1d496c,l37),(-0xa1f592,l43),(-0xa0cc5fc6,l42),(-0x1495a3f9a,l41),(0x385a74ec,l45),(0xed1d496c,l51),(-0x5d0c6f70,l57),(0x333cb202,l56),(-0x2b879b00,l58),(-0x18f9e29b,l63),(-0x1f2caac,l62),(0x9996178,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xed1d496c,l27),(0xed1d496c,l29),(0xed1d496c,l33),(-0xed1d496c,l35),(0xed1d496c,l37),(0xed1d496c,l51),(0x29677396e,l13),(-0xe604c290,l25),(-0x1938dc09e,l20),(0x29bc89dbc,l15),(0x9e4d736a,l30),(-0x5d0c6f70,l57),(0x5644e7cf,l9),(-0xafe62dcc,l8),(0x5bd91eee,l10),(-0xa0cc5fc6,l42),(-0x34b44c7c,l11),(-0x1495a3f9a,l41),(-0x4cac40da,l6),(-0x1bb62d8a,l23),(-0x18f9e29b,l63),(0x43c708e0,l22),(0x385a74ec,l45),(0x333cb202,l56),(-0x2b879b00,l58),(0x52e606de,l4),(0x9996178,l64),(-0x1f2caac,l62),(-0xa1f592,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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,0x90c80860c03eb401a4f20a18f020ad0069248186240a6b4018000000000601c8020000000005406200800731704302ad004030842862017040140000000003c0c801000000000140d200800032118680b100360843430808d04018000000001e014802000000000240d20080000014884058c03001c44108c0bb4011c214d1020234100600000004c140d30080000000011024802028c3b043028b4014000000000d0248020000000443c053008000000000f01480200000480440163010000250982402d003], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 30 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase5" = "QuadFullSixCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 30 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase5
private def zz2242:"s08c2"="s08c2":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l1 l10 l17 l20 l22 l23 l27 l29 l33 l35 l37 l4 l51 l6 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l1, ![-0x59682eb50, -0x2a80f773f4,0xfd8d1e8d8, -0x58ca8bc78], ![0x388290d20,0xfd8d1e8d8, -0x2de762faca,0x9f0297cfc], ![0x4b0, -0x58ca8bc78,0x9f0297cfc, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x338df320,l6),(0x1a0131fe,l4),(0x270287679,l8),(-0x2009438,l10),(-0x414382bc,l17),(-0x62a4a34,l20),(0x15276ad3,l23),(0x18cfcd70d,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x270287679,l8),(0x18cfcd70d,l22),(-0x414382bc,l17),(-0x338df320,l6),(0x15276ad3,l23),(0x1a0131fe,l4),(-0x62a4a34,l20),(-0x2009438,l10)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 14 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase6" = "QuadFullSixCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 14 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase6
private def zz2243:"s08c3"="s08c3":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l13 l15 l17 l22 l23 l25 l27 l29 l31 l33 l35 l37 l4 l51 l57 l59 l6 l63 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x13c852d67, -0x572d59370,0x302b19b7a,0x1056134c4], ![-0x572d59370, -0x1b6754f840,0xc97a57640, -0x584ab26f8], ![0x302b19b7a,0xc97a57640, -0x2cff7c3f9a,0x9cc7c251c], ![0x1056134c4, -0x584ab26f8,0x9cc7c251c, -0x2b96acc10]]
noncomputable def hinges:Hinges:=[(-0x338df320,l6),(0x1a0131fe,l4),(0x270287679,l8),(-0x2009438,l10),(0x8f641fede,l13),(-0x8f2ea674,l12),(-0x37c40fc6,l17),(-0x3d9933e,l15),(-0x13938381,l23),(0x7f5ca4e2,l22),(-0x2b96acc10,l27),(0x2b96acc10,l29),(-0x2707eec90,l25),(0x744ebe66,l31),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(0x2b96acc10,l51),(-0xa13e38a2,l57),(-0xcb83e66,l59),(-0x5743f045,l63),(-0xdb90724,l65),(0x87fba8e8,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2b96acc10,l27),(0x2b96acc10,l29),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(0x2b96acc10,l51),(0x8f641fede,l13),(-0x2707eec90,l25),(0x270287679,l8),(-0xa13e38a2,l57),(0x744ebe66,l31),(-0x5743f045,l63),(0x87fba8e8,l64),(0x7f5ca4e2,l22),(-0x37c40fc6,l17),(-0x338df320,l6),(-0x8f2ea674,l12),(-0x13938381,l23),(-0xdb90724,l65),(-0xcb83e66,l59),(0x1a0131fe,l4),(-0x2009438,l10),(-0x3d9933e,l15)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((0x30b96563feda6143ef683d68c214c41d6ed1408631c0a5f28040ec4a88a38061766a52a600230087188d0c5e26030b2610da12998507f4068340d2419a1f) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase7" = "QuadFullSixCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase7
private def zz2244:"s08c4"="s08c4":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2dfdb4f5, -0x5f23888, -0x8eb5530,0xc8], ![-0x5f23888, -0x2c17367d,0x308ccf4,0x766f0af], ![-0x8eb5530,0x308ccf4, -0x26a67488,0x5f23a18], ![0xc8,0x766f0af,0x5f23a18, -0x2f91ca8]]
noncomputable def hinges:Hinges:=[(0x570c1f5,l17),(-0x2f91ca8,l27),(0x2f91ca8,l29),(0x2f91ca8,l33),(-0x2f91ca8,l35),(0x2f91ca8,l37),(0x2f91ca8,l51),(-0x570c1f5,l62)]
def normalizationDenominator:ℤ:=0xee6b2800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2f91ca8,l27),(0x2f91ca8,l29),(0x2f91ca8,l33),(-0x2f91ca8,l35),(0x2f91ca8,l37),(0x2f91ca8,l51),(0x570c1f5,l17),(-0x570c1f5,l62)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000029090009980800000000b0024803000000006c01240180006804100263014000000001c029005420a404200335006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 9 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase8" = "QuadFullSixCase8" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 9 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase8
private def zz2245:"s08c5"="s08c5":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixCase9
private def zz2246:"s08c6"="s08c6":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l21 l25 l27 l29 l33 l35 l36 l37 l4 l5 l51 l55 l57 l58 l61 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2abdbf63e, -0x59682eb50, -0x861c46350,0x1e2e7b14], ![-0x59682eb50,0x17d4905816,0x187a5236c,0x77f56c8e4], ![-0x861c46350,0x187a5236c, -0x245275dc0d,0x5969a220e], ![0x1e2e7b14,0x77f56c8e4,0x5969a220e, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xb96af,l5),(0x2e5abc,l4),(0x35cbe29ca,l17),(0xd329feac,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x76c79f410,l25),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x23c309a42,l36),(0x2cb417800,l37),(0x2cb417800,l51),(-0x40574ba9,l55),(-0x65a143d3,l57),(0x62a4a34,l58),(0x5c2c32c4,l61),(0x26f0b5dc,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x76c79f410,l25),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x35cbe29ca,l17),(0xd329feac,l21),(-0x23c309a42,l36),(-0x65a143d3,l57),(0x5c2c32c4,l61),(-0x40574ba9,l55),(0x26f0b5dc,l62),(0x62a4a34,l58),(0x2e5abc,l4),(-0xb96af,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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], #[![2, -7, 0, 0]]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase10" = "QuadFullSixCase10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase10
private def zz2247:"s08c7"="s08c7":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l16 l22 l25 l27 l28 l29 l31 l33 l35 l36 l37 l4 l41 l42 l43 l44 l46 l5 l51 l55 l56 l57 l58 l61 l63)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2bc920528, -0x572d59370, -0x82c405f80,0xcd8900], ![-0x572d59370, -0x697b666a3,0x3a537c3b0,0x899fd7aac], ![-0x82c405f80,0x3a537c3b0, -0x236a8f20dd,0x572ecca2e], ![0xcd8900,0x899fd7aac,0x572ecca2e, -0x2b96acc10]]
noncomputable def hinges:Hinges:=[(-0xb96af,l5),(0x2e5abc,l4),(0xf61df6b0,l14),(0xce2479d5,l16),(0x141fb28ea,l15),(0xc2ab8803,l22),(-0x2b96acc10,l27),(-0x1a57d0c76,l28),(0x2b96acc10,l29),(-0x285657878,l25),(0x4a7b3886,l31),(0x2b96acc10,l33),(-0x2b96acc10,l35),(-0x23c309a42,l36),(0x2b96acc10,l37),(0xc6566ee6,l43),(-0x268d8aee9,l42),(0x80329d88,l41),(-0xb868f5c8,l46),(0x8f2ea674,l44),(0x2b96acc10,l51),(-0x40574ba9,l55),(-0x3b7aef39,l57),(0x669775e3,l56),(0xb18621a,l58),(0x5c2c32c4,l61),(0xd189d51,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2b96acc10,l27),(0x2b96acc10,l29),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(0x2b96acc10,l51),(-0x1a57d0c76,l28),(-0x285657878,l25),(-0x268d8aee9,l42),(-0x23c309a42,l36),(0xf61df6b0,l14),(0xc6566ee6,l43),(-0xb868f5c8,l46),(0x5c2c32c4,l61),(0x4a7b3886,l31),(0xce2479d5,l16),(0xc2ab8803,l22),(-0x40574ba9,l55),(-0x3b7aef39,l57),(0x141fb28ea,l15),(0x669775e3,l56),(0x8f2ea674,l44),(0x80329d88,l41),(0xd189d51,l63),(0xb18621a,l58),(0x2e5abc,l4),(-0xb96af,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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,0x7c1c053008000000001a0c0cc0100000000746c0a30080000000000340c801002b832857034e401400000001d1a02cc020000007119408630100000001e8dc098c0300000007233022300c000000c42d0238c04000000000687033004000711a45c02a9004000000b10440393010000be1584901690040002d05612405a4010000002043201fcc040000124461901d400c00002021880444c050030c3102400f540140000000015402c8030000000000a807200800000000a0501cc020000000008830330040000001584809cc03000208661240bb401000e614e1c005d90050000000b213026300c0000000110901cc020051c6204d023d401400000000024030803000000a124406c30100000000002e01c80200000000642409300800000920d40428c050000000220c015300c0000009c1d0128c040000020833018a301400000088180254c040000025833018a301400000ce11c0348c05000000210640ca3010000a12644601fd0040002a496110025401000000204410124c040000000044140b30080000002882c098c0300000000342407300800c60d410403d5005003183884801d540140000002686804cc030000000094340730080000002606402cc030000000000070320040000000002601480200000004219036300c000001043701b0c04000000b128406c30100000000190d02cc020001c4610d808c40100000000000501c80200000007a35016300c00000001d1901cc0200020c5604404c40100000000170602cc02,0x3f00b200c0000000000440c80100000000000f0320040000001609c04cc030000000058480730080000001509402cc03000000005844053008000001a44100c8c04000000006c480530080000000001b01480200000005821013300c000000000b002480300000000036009200c0000001b024030c030000000640900c300c0000001a044038c03000000006424073008000001a8210058c0400000000682406300801422060b40ced005000000b83c180b4008000000002e2c0cc0100000000088703300424520518f0216d00600484808c3019b401401242083300aed0050000044827022d301400000110160274c040001c46808c053401000000000007c0c80100604b0923019b401400000000361c0cc010000184a60901e400c000003041100e4c0400584a0903019b4014000000000150188020000000ca13014300c0000003084c050c030000000b20b026300c000b12581900b10040000000038240730080000000026140cc010000000000280d20080000000290a038c020000000000a40e20080000000002a0148020001c8560e40bb401000c610e14005d900500000084442406400800000001e0f034c0200000000009406200800000000027018802000000007438093008000010c11c082cc050000104761c022400c00000002512038c020000004209809b301000c508a0a404c1005000000008c180e300800000020828070c0300000008a0a01c300c00000000021038802000000000088052008000000c4170120c04,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,0x820bc055cc05000002282600973014000002842100e4c04000000a40900393010000014a21005ccc050000000001500c200c000008608403dcc05000002602400b730140000000c848094c0300000000001b032004000000000240b080300000000fcc40930080000000000502480200000007419025300c01622860b409d5005], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 28 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase11" = "QuadFullSixCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 28 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase11
private def zz2248:"s08c8"="s08c8":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l63)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2e563366, -0x11d6a998, -0x105a13eb,0x258], ![-0x11d6a998, -0x8445a377,0xc8b7b50,0x1634d20d], ![-0x105a13eb,0xc8b7b50, -0x73f35d98,0x11d6ae48], ![0x258,0x1634d20d,0x11d6ae48, -0x8eb55f8]]
noncomputable def hinges:Hinges:=[(0x105245df,l17),(-0x8eb55f8,l27),(0x8eb55f8,l29),(0x8eb55f8,l33),(-0x8eb55f8,l35),(0x8eb55f8,l37),(0x8eb55f8,l51),(-0x623b9ee,l63)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x8eb55f8,l27),(0x8eb55f8,l29),(0x8eb55f8,l33),(-0x8eb55f8,l35),(0x8eb55f8,l37),(0x8eb55f8,l51),(0x105245df,l17),(-0x623b9ee,l63)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000002c13809980600000000b0024803000000006c01240180006804100263014000000001c029005440a104400635006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[![0, 0, -3, 5]]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 10 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase12" = "QuadFullSixCase12" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 10 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase12
private def zz2249:"s08c9"="s08c9":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixCase13
private def zz2250:"s08ca"="s08ca":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l46 l5 l51 l54 l61 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x40516b400, -0x1fde7e608, -0x2fcdbdbca,0xe852d6c], ![-0x1fde7e608, -0xe10590e98,0x20791fb9c,0x1e8a70e06], ![-0x2fcdbdbca,0x20791fb9c, -0xcf26375ed,0x1fde7ef62], ![0xe852d6c,0x1e8a70e06,0x1fde7ef62, -0xfef3f55c]]
noncomputable def hinges:Hinges:=[(-0x3b1d09a7,l5),(-0xab333b58,l4),(0x2be58046,l9),(0xbb55166,l8),(0xe08e10,l10),(0xde8525cc,l14),(0xcebc5036,l15),(0x400c1116,l23),(0xc0243342,l22),(-0xfef3f55c,l27),(0xfef3f55c,l29),(-0xde8525cc,l25),(0x5cbc9986,l30),(0xfef3f55c,l33),(-0xe08e10,l38),(-0xfef3f55c,l35),(-0xbb55166,l36),(0xfef3f55c,l37),(0xab333b58,l34),(-0x5cbc9986,l43),(-0xc0243342,l42),(-0xcebc5036,l41),(0x1b001e54,l46),(0xfef3f55c,l51),(0x3b1d09a7,l54),(-0x2be58046,l61),(-0x400c1116,l63),(-0x1b001e54,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xfef3f55c,l27),(0xfef3f55c,l29),(0xfef3f55c,l33),(-0xfef3f55c,l35),(0xfef3f55c,l37),(0xfef3f55c,l51),(0xde8525cc,l14),(-0xde8525cc,l25),(0xc0243342,l22),(-0xc0243342,l42),(0x400c1116,l23),(-0x400c1116,l63),(0x5cbc9986,l30),(-0x5cbc9986,l43),(0x2be58046,l9),(-0x2be58046,l61),(0xcebc5036,l15),(-0xcebc5036,l41),(-0xab333b58,l4),(0xab333b58,l34),(-0x3b1d09a7,l5),(0x3b1d09a7,l54),(0x1b001e54,l46),(-0x1b001e54,l64),(0xbb55166,l8),(-0xbb55166,l36),(0xe08e10,l10),(-0xe08e10,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,0xce01640180000000019002c8030000032140481ba0060000000000c407200a4c0e90232067de80382832421c301cad006050648438601f5a00c000000000074062008000000a220809c602000000184510138c04000102330a2047a0080030444061017340140000000050380a601000000002506038c0200000000000c0690040000000000340920080000000088780a60100000000000f014802], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase14" = "QuadFullSixCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase14
private def zz2251:"s08cb"="s08cb":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l15 l16 l17 l20 l22 l23 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l5 l51 l54 l56 l57 l59 l61 l62 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2ad8354ed, -0x1da3a8e28, -0x2b8329d5a,0x498], ![-0x1da3a8e28, -0xbdf2c0b1f,0x11fbc2a7a,0x2382b2ac4], ![-0x2b8329d5a,0x11fbc2a7a, -0xc0a7cbabd,0x1da3a9782], ![0x498,0x2382b2ac4,0x1da3a9782, -0xed1d496c]]
noncomputable def hinges:Hinges:=[(-0x3b1d09a7,l5),(-0xab333b58,l4),(0x2be58046,l9),(0xbb55166,l8),(0xe08e10,l10),(0x27c8934bd,l13),(0x1f2caac,l17),(-0x333cb202,l16),(0x1495a3f9a,l15),(-0x27c8934bd,l20),(0x18f9e29b,l23),(0xa0cc5fc6,l22),(-0xed1d496c,l27),(0xed1d496c,l29),(0x5d0c6f70,l31),(0xa1f592,l30),(0xed1d496c,l33),(-0xe08e10,l38),(-0xed1d496c,l35),(-0xbb55166,l36),(0xed1d496c,l37),(0xab333b58,l34),(-0xa1f592,l43),(-0xa0cc5fc6,l42),(-0x1495a3f9a,l41),(0xed1d496c,l51),(0x3b1d09a7,l54),(-0x5d0c6f70,l57),(0x333cb202,l56),(0x47498d8,l59),(-0x2be58046,l61),(-0x18f9e29b,l63),(-0x1f2caac,l62),(-0x47498d8,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0xed1d496c,l27),(0xed1d496c,l29),(0xed1d496c,l33),(-0xed1d496c,l35),(0xed1d496c,l37),(0xed1d496c,l51),(0x27c8934bd,l13),(-0x27c8934bd,l20),(0x5d0c6f70,l31),(-0x5d0c6f70,l57),(0xa0cc5fc6,l22),(-0xa0cc5fc6,l42),(0x1495a3f9a,l15),(-0x1495a3f9a,l41),(0x2be58046,l9),(-0x2be58046,l61),(-0xab333b58,l4),(0xab333b58,l34),(0x18f9e29b,l23),(-0x18f9e29b,l63),(-0x3b1d09a7,l5),(0x3b1d09a7,l54),(-0x333cb202,l16),(0x333cb202,l56),(0x47498d8,l59),(-0x47498d8,l65),(0xbb55166,l8),(-0xbb55166,l36),(0x1f2caac,l17),(-0x1f2caac,l62),(0xe08e10,l10),(-0xe08e10,l38),(0xa1f592,l30),(-0xa1f592,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase15" = "QuadFullSixCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase15
private def zz2252:"s08cc"="s08cc":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l1 l10 l13 l17 l27 l29 l31 l33 l35 l37 l5 l51 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l1, ![-0x59682eb50, -0x27c2f49ddf,0x12868be0dc, -0x674ceedf2], ![0x388290d20,0x12868be0dc, -0x2d4fa35c4d,0x95c6651a0], ![0x4b0, -0x674ceedf2,0x95c6651a0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xcc77837d,l5),(0x2fcc0aa4a,l8),(-0x3d7851ee,l10),(0x4e6d950,l13),(-0x26f0b5dc,l17),(-0x2cb417800,l27),(0x2cb417800,l29),(0x65a143d3,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x2fcc0aa4a,l8),(0x65a143d3,l31),(-0xcc77837d,l5),(-0x3d7851ee,l10),(-0x26f0b5dc,l17),(0x4e6d950,l13)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[0x11c02c803000120110058c0400000110f014c0200000000f01480200250982402d0030000000780248030000000b00248030000000d8024803001a01040098c0500001b024030c03000001a09018c02000000005018802000000016014802d510e19c0f6d005cc10218406490058408608c07490050000841400f0c0400002b8c402cc0300000002b01880200000000340c801000000f07028c0200000001f01880200000000e01480200000002301880200000000502c80200000001b01880205c0a01c0175004000000098024803000000070024803000000012014802], #[![-4, 23, -18, 0],![-17, -20, 57, 0],![31, 190, -177, 0],![5, 26, -39, 0],![-7, 18, 0, 0]]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase16" = "QuadFullSixCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase16
private def zz2253:"s08cd"="s08cd":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l16 l22 l23 l25 l27 l29 l30 l31 l33 l35 l37 l44 l5 l51 l57 l59 l63 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x210b0f99d, -0x572d59370,0x302b19b7a,0x1416be8cc], ![-0x572d59370, -0x293a2ddad6,0x12010094dc, -0x5e4a5ec3e], ![0x302b19b7a,0x12010094dc, -0x2c67bca11d,0x938b8f9c0], ![0x1416be8cc, -0x5e4a5ec3e,0x938b8f9c0, -0x2b96acc10]]
noncomputable def hinges:Hinges:=[(-0xcc77837d,l5),(0x2fcc0aa4a,l8),(-0x3d7851ee,l10),(0x779f86d0,l14),(0x7509c2772,l13),(-0x669775e3,l16),(-0x80329d88,l15),(-0xd189d51,l23),(0x268d8aee9,l22),(-0x2b96acc10,l27),(0x2b96acc10,l29),(-0x9fe2c43c,l25),(0x3b7aef39,l31),(-0xc6566ee6,l30),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(-0x64afd474,l44),(0x2b96acc10,l51),(-0xa13e38a2,l57),(-0x4cde53c,l59),(-0x5743f045,l63),(-0x331678e,l65),(0x9cb281c4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2b96acc10,l27),(0x2b96acc10,l29),(0x2b96acc10,l33),(-0x2b96acc10,l35),(0x2b96acc10,l37),(0x2b96acc10,l51),(0x7509c2772,l13),(0x2fcc0aa4a,l8),(0x268d8aee9,l22),(-0xa13e38a2,l57),(-0xc6566ee6,l30),(-0x9fe2c43c,l25),(0x9cb281c4,l64),(-0x5743f045,l63),(0x779f86d0,l14),(-0xcc77837d,l5),(0x3b7aef39,l31),(-0x3d7851ee,l10),(-0x669775e3,l16),(-0x80329d88,l15),(-0x64afd474,l44),(-0xd189d51,l23),(-0x4cde53c,l59),(-0x331678e,l65)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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], #[![-21, 22, 34, -16],![-21, -5, 52, -7]]⟩
def dynamicCode : Nat := (((((((((((((((((((0x164b5eec0d2c24911a8a3b88490b08839674a1ee32b91c41239045c043e283152910fd36002300459319cd937b342490bdd10cc161240d332cdf214c1c0033dd53e048e079986bfd52851a26e6b71b14193d972bf9f8c0007f4981ac0500fd094ba8d492400a406000040440f4160b40b0590586f00ec6420f13fd6ac91933d895b0b52060ad60a1737030cdd110d486a242a63d58be998b04a5a0f123ec2807fe8901721880028dd0b47a454646050a80800003c243740723d496669de050c074e3af750e322669e2c7050a8d2884d86102ff3b4f321838a2994372f00e1a6dcf1cdac5042676101ad88017bcd3a2e8008ec8e1300800007ccc027d11a84e669de171ae8fc706e09118b8f5d8b601b5a00000000000000007ae82ccc0f03205b190742f54ee3812eb6ac18a84574dc83e6488388304280200100aaddf91261ed61dde3ad878e6afe9a6bc1f882b0311315cf738551a8a37ed24847577654f2b12c2a892f6b327c7249460335adff82901d08c3620ea33e8001f810dc1d86d8cc124661b433e29f0836c83b040840f31fbb550a207d44432b5640685e17675f40c1cc3a0172eac28614803fb6008a0b5b62ffaef0100846a5af5f30000045249be53c88ce41a150100000868e1a2682dbbc0e1821aef1691033b56216b838516a005858508f29d334c8811e70ae064081178bc81dc0002a8139c118040000614c027d11a84e669de171ae8fc706e09118b8f5d8b601b5a00000000000000007a22863022021823002802000005e856d2d8f0e251b60163a16d45cd994714d56e7282324d3e3dc0af631a67e5486dd97f9fa1dcf2787fa0005644364a41b0430d70906b04c354141a802e13c5e361a0060923cd3bf902840f9d5a1941802d07b2df00a01545c8f5380002146d2740a8062eaf0a382b29156690c6c4883f628c484a0180aa01595fc84b77200a440e80d38780e65830c81499e21a26c306025efe0e0a246040bfc3467f33058410054c5dd9803840d615a1d817e48227685b639fb43802fff622069b35842400c00f1654efba8f706916d9777c49844726f36e440e32664098162dd60ca9244840bbc689092087d243492400636106ddd00044010000191343941daf92dc0c91c2c597fb75d040f2028f853c7d28634a90fe7f100c33f2992fec420708a7aad2783f0502ebca058e0101415da3533806a04085ba857d46c28812005a068b29524db8281a41a019f36b3081495c301e40e3db93ebe4b165c779ec516188dc827f6242056287b7e400347916b72800230080000cc90003e1219e139207d28a58da58ce0c40f24230511526ce390c2c0698baa2090e7162e2d683842e7034c63241b117d111782013edcb2b185a4061280a00006c8d13f421adfa64c1c65d7bf5566fb1a28098b191c1289140d8ce52287e28a7e0cd27869c2041603c45432d90184c572ba6028204704a8d2cc581000d5c8e8e7f0bf49002d03048c960f9328220838d9f0aff9459fa48af6cd03d1292628a71cb7323149040859f23c89e9b83843af11a21f7e81029ab65c7afb0048151996b45a4dc200d4466a414c99e1812006008000024b36342eddc7c0286a77b657bc30a051f4d2acc0c1f189fce121b5429ae1b1c217c2bb5b4cc084601000013d21a6130100980030a10d211c91bb2a12dd10287175fa1630ae534bcb39020df0f3d60208f47650a10e180ea490ac184faf01bd10a01769fd10c10058b0ad1f5200440100cf0186880c34007242bd1ee90a58c8678bb3a9828affdb73230ae65f0ad4921d518dd398184870dbdb3920927d3bcfa0801cbc6fa10340611004000065ce1518618b39aff930425181b60c4840811f0c7aa041c4d1041247171ed19c08087705fad70d8e0c29874ac57f56b080457fa623a5d7c1815e5ed2ddb86f01008e923693ff20f01048019022033c07243e8023e3c50d086d7703182846040c6e30acfb774ed98191bb) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase17" = "QuadFullSixCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase17
private def zz2254:"s08ce"="s08ce":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l23 l27 l29 l33 l34 l35 l36 l37 l4 l51 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x5cac66cf, -0x23ad5330, -0x20b427d6,0x4b0], ![-0x23ad5330, -0x119048aa0,0x188c95a4,0x28f88f52], ![-0x20b427d6,0x188c95a4, -0xe7f5c436,0x23b25f94], ![0x4b0,0x28f88f52,0x23b25f94, -0x11d6abf0]]
noncomputable def hinges:Hinges:=[(-0x502fe,l4),(0x50301,l8),(0xc4773dc,l23),(-0x11d6abf0,l27),(0x11d6abf0,l29),(0x11d6abf0,l33),(-0x11d6abf0,l35),(-0x50301,l36),(0x11d6abf0,l37),(0x502fe,l34),(0x11d6abf0,l51),(-0xc4773dc,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x11d6abf0,l27),(0x11d6abf0,l29),(0x11d6abf0,l33),(-0x11d6abf0,l35),(0x11d6abf0,l37),(0x11d6abf0,l51),(0xc4773dc,l23),(-0xc4773dc,l63),(0x50301,l8),(-0x50301,l36),(-0x502fe,l4),(0x502fe,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 13 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase18" = "QuadFullSixCase18" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 13 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase18
private def zz2255:"s08cf"="s08cf":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l34 l36 l4 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![1,0x190,0x190,0x190], ![0x190,0,0x190,0x190], ![0x190,0x190, -0x50302,0x1ad3c], ![0x190,0x190,0x1ad3c,0]]
noncomputable def hinges:Hinges:=[(-0x1abaa,l4),(0x1abab,l8),(-0x1abab,l36),(0x1abaa,l34)]
def normalizationDenominator:ℤ:=0x1dcd65000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x1abab,l8),(-0x1abab,l36),(-0x1abaa,l4),(0x1abaa,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨29, #[0x11018802], #[]⟩
def dynamicCode : Nat := 0xa21b1ee2860190081806402840190081006401040191080d030201905382090042886c7b8a18064020601900a10064020401900610064420340c08606aeacd0082401000011220000ba2e4450f2020790142c808164020b2390b215820240114500c88a18064040c0320284019010200c806100644303575680642b840880200003fc8000e69
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 4 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixCase19" = "QuadFullSixCase19" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 4 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixCase19
private def zz2256:"s08d0"="s08d0":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixRows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x114e20003dceb948008b492ab8a01e200779ae58001e682b0d2620003dceb948001989488f607a2001389b4800db088d21fa2000ef3acd024d191aa15a20003dceb948007ba8ecbe601a20003dceb948008acf39f822200779ae580468ffeca07d20003dceb948004f2e581e21fd2002fd7c28004828f91921ed20003dceb948003acadabfa14d200779ae58004b3a28b92520001eeb5ca8012ced8deba12005faf848008acbaf3ea07c20003dceb948016b7bcded21fc20003dceb94805ad0e8be1ec2001de6d9a01ce6a1f6420003dceb94800ddee4f1ae0782005faf848005ae86b79a02005faf848002e5eaf9fa14]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x107aa0001eeb5ca8006fa8aa5e62a0007b9d6a818ddd79e760004e2ad800236003bcdb2c004979fce07e600779ae58001f68efdd615e60003dceb94801aabf498f601e60001eeb5ca800a8ae5bc9e6600779ae58002b789a5d21ea60001eeb5ca8006ccd3fed601a600779ae5800eecbcfd82260003dceb9480048a98e192560004e2ad8002160001eeb5ca800c91ccfa1ff2005faf848009c7cdaac202f20003dceb948001bef4b7be01f20017ebe1807cf38bea720005faf8a035dd8eae14b20001eeb5ca80089c98de320001eeb5ca801590c5fc921fe20003dceb94800de6c9d0fa14]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x103d30003dceb948004f2e581e21ed30003dceb948019c5cf8e06d30003dceb948001869ff1be1dd30001eeb5ca80139be59e530004e2ad8002130004e2ad80021fc30001eeb5ca80018ee2cb8643002fd7c2800ea3baee1f830003dceb948001839dafee030001eeb5ca803bb7c7fe7e0004e2ad80023e0003dceb948020dddcc607fa0017ebe18017f6ad921ffa0003dceb94802781d09aa601fa0003dceb948004ffc5c49e7a0003dceb94803081ab86fa1fba003bcdb2c001d1928e3a005faf848009f0d6f5b21fea0003dceb94801ac2edf0fe6a0003dceb948010a189dbfe14]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x116e7005faf848014acffae15e70001eeb5ca8036f2879205e70001eeb5ca80028ffbd4ba670003dceb948002dcc0e6f6270004e2ad8002570004e2ad8002170004e2ad800203f30001eeb5ca8002f0e8faf206f30003dceb948001bef4b7be1cf30003dceb94801dcb96de730007b9d6a80292861cb30001eeb5ca80089c98de330003dceb9480289efeae03e30001eeb5ca801399b0de1fe30003dceb94748a9214e30001eeb5ca804b91d1d2630004e2ad800216a3005faf848009cab0b601a30003dceb948036e8c6d223002fd7c2801214]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11fc0000bf5f0c005d0fcda02c0002fd7c280089abd9e15c0005faf84801cb38dda1cc000779ae5801bb6d5ea05c0003bcdb2c002fcfa400002b196c0027f0004e2ad80023f0004e2ad800203fb0001eeb5ca8001fba1a1de06fb0001eeb5ca8033d2ebd205fb005faf84800496e2967b0004e2ad800216bb0001eeb5ca8008dbb5f63b0004e2ad80021eeb003bcdb2c008f4ccb66b0001eeb5ca8011e999ce07ab0001eeb5ca806c809eaa2b0001eeb5ca803fd796de770004e2ad8002370004e2ad800214]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1740002b196c002640002b196c002540002b196c002440002b196c00207f0005faf848062ad879617f0002fd7c2800397ef8e961cf00003dceb948008c2bed9fe70003bcdb2c009f4abbe03e00003dceb948005dee4bdee1fe000779ae58001eac48fa21ee000779ae58001d2e8ccbe02e00003e8a48001e2af9215e00003dceb94800ae4a79f9e05e0005faf84807ad6cd92600003dceb94803ad0929617d0002fd7c28002b195bf9e16d0001389b4802996e8a21dd000779ae58002f0d8b2e2500002b196c00203c00001eeb5ca8038aca4ae14]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x16c0002b196c0025c0002b196c0024c0002b196c00207f800779ae5800480ca8e17f80003dceb94801a80ebf3a602f8001389b48002e386ba05f8001de6d9a019e3beb2780001eeb5ca8001ae03e8003bcdb2c070a3c217e8002fd7c280069fa4ba06e800779ae580729189f215e8002fd7c280469e808e1ce80003dceb948002bba2e29a680002b196c00203d80001eeb5ca8005a79befee16d8001389b4805bf3c2de02d800779ae580129beef205d8000ef3acd013e4ebe6580007b9d6a806480002b196c00214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1610002b196c00216a1001389b4804185c39605a10001eeb5ca80019be1b5ee210002b196c00203c10003dceb948009f2b5e6ea17c1000ef3acd00ba5f5da02c10001eeb5ca8006fab0b4ca1dc10001eeb5ca8001ddd8db8a41003bcdb2c02e038100779ae5800297c3fbaa17810001eeb5ca801aa6b09e168100779ae58002bfc1d19215810003dceb948009e6cffda205810001eeb5ca8002aac090e6010003dceb948002e617fc0003dceb94800daed606fc0003dceb948006d7aa7c0002b196c00202ec0001eeb5ca801ef3ca1cec0003dceb94801ef3ca14]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11dc90003dceb948002b99c8e8205c90003dceb948003be909fc6490003dceb948029d38de217890003dceb948010c5a29ede15890003dceb948002d2bbaba60589002fd7c280349b80c6090002b196c00216f50001eeb5ca800a89f8f1a215f50003dceb94800af49fc18a750003dceb94803bd2c2d58e35000198cba014aacdb6550002b196c0020195005faf8480349d9ea6150002b196c00207e10003dceb94800cb2d9dde617e10003dceb948019d9ecbec616e10003dceb948007b7d7bcf206e100779ae58055bbc4f61de1005faf848029f497ba1ce10003dceb948004a393f2c214]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x114dd0003dceb948008cbb6cd8e5d0003dceb948038dfa9ea8a019d0003dceb948035e5f8d3ca1d0003dceb94801ef2abcd8203e90003dceb94800587eb9217e90001eeb5ca8003ace5eac216e9001de6d9a05d869bee02e90003dceb948006eea2ffde15e90003dceb9480038fcf8ab61ce90001eeb5ca800188d0f6d601e90001eeb5ca8007e5cad6690003dceb948028b1d4ce03a90003dceb948005e5f2b38617a9002fd7c28066bced9e02a90003dceb948004a7a5e09215a9002fd7c28066bced9e290003dceb948002ee17c90001eeb5ca8002d3d0edf616c90001eeb5ca8007a2bafce606c90003dceb94800aa28cea14]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [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]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullSixCase0.base QuadFullSixCase0.hinges QuadFullSixCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
private def zz919:"s0397"="s0397":=by decide+kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase0.base QuadFullSixCase0.hinges QuadFullSixCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullSixCase1.base QuadFullSixCase1.hinges QuadFullSixCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase1.base QuadFullSixCase1.hinges QuadFullSixCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r62,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullSixCase2.base QuadFullSixCase2.hinges QuadFullSixCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
private def zz920:"s0398"="s0398":=by decide+kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase2.base QuadFullSixCase2.hinges QuadFullSixCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullSixCase3.base QuadFullSixCase3.hinges QuadFullSixCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase3.base QuadFullSixCase3.hinges QuadFullSixCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r62,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullSixCase4.base QuadFullSixCase4.hinges QuadFullSixCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
private def zz921:"s0399"="s0399":=by decide+kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase4.base QuadFullSixCase4.hinges QuadFullSixCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r45,RewriteAtoms.r80,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullSixCase5.base QuadFullSixCase5.hinges QuadFullSixCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase5.base QuadFullSixCase5.hinges QuadFullSixCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullSixCase6.base QuadFullSixCase6.hinges QuadFullSixCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
private def zz922:"s039a"="s039a":=by decide+kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase6.base QuadFullSixCase6.hinges QuadFullSixCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r30,RewriteAtoms.r82,RewriteAtoms.r61,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullSixCase7.base QuadFullSixCase7.hinges QuadFullSixCase7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase7.base QuadFullSixCase7.hinges QuadFullSixCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullSixCase8.base QuadFullSixCase8.hinges QuadFullSixCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
private def zz923:"s039b"="s039b":=by decide+kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase8.base QuadFullSixCase8.hinges QuadFullSixCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullSixCase9.base QuadFullSixCase9.hinges QuadFullSixCase9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase9.base QuadFullSixCase9.hinges QuadFullSixCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r81,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r4,RewriteAtoms.r63,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullSixCase10.base QuadFullSixCase10.hinges QuadFullSixCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
private def zz924:"s039c"="s039c":=by decide+kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase10.base QuadFullSixCase10.hinges QuadFullSixCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r20,RewriteAtoms.r81,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullSixCase11.base QuadFullSixCase11.hinges QuadFullSixCase11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase11.base QuadFullSixCase11.hinges QuadFullSixCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullSixCase12.base QuadFullSixCase12.hinges QuadFullSixCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
private def zz925:"s039d"="s039d":=by decide+kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase12.base QuadFullSixCase12.hinges QuadFullSixCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullSixCase13.base QuadFullSixCase13.hinges QuadFullSixCase13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase13.base QuadFullSixCase13.hinges QuadFullSixCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullSixCase14.base QuadFullSixCase14.hinges QuadFullSixCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
private def zz926:"s039e"="s039e":=by decide+kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase14.base QuadFullSixCase14.hinges QuadFullSixCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullSixCase15.base QuadFullSixCase15.hinges QuadFullSixCase15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase15.base QuadFullSixCase15.hinges QuadFullSixCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r64,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullSixCase16.base QuadFullSixCase16.hinges QuadFullSixCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
private def zz927:"s039f"="s039f":=by decide+kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase16.base QuadFullSixCase16.hinges QuadFullSixCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullSixCase17.base QuadFullSixCase17.hinges QuadFullSixCase17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase17.base QuadFullSixCase17.hinges QuadFullSixCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullSixCase18.base QuadFullSixCase18.hinges QuadFullSixCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
private def zz928:"s03a0"="s03a0":=by decide+kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase18.base QuadFullSixCase18.hinges QuadFullSixCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullSixCase19.base QuadFullSixCase19.hinges QuadFullSixCase19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixCase19.base QuadFullSixCase19.hinges QuadFullSixCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixCase19.nonnegative x hx
def pair20:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_20_base LocalFullSixPairs.compact_fullSix_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
private def zz929:"s03a1"="s03a1":=by decide+kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullSixPairs.fullSix_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_20_base LocalFullSixPairs.compact_fullSix_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullSixPairs.fullSix_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_21_base LocalFullSixPairs.compact_fullSix_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullSixPairs.fullSix_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_21_base LocalFullSixPairs.compact_fullSix_pair_21_hinges x
private def zz930:"s03a2"="s03a2":=by decide+kernel
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullSixPairs.fullSix_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_22_base LocalFullSixPairs.compact_fullSix_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullSixPairs.fullSix_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_22_base LocalFullSixPairs.compact_fullSix_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullSixPairs.fullSix_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_23_base LocalFullSixPairs.compact_fullSix_pair_23_hinges
private def zz931:"s03a3"="s03a3":=by decide+kernel
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullSixPairs.fullSix_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_23_base LocalFullSixPairs.compact_fullSix_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullSixPairs.fullSix_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r69]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_24_base LocalFullSixPairs.compact_fullSix_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
private def zz932:"s03a4"="s03a4":=by decide+kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullSixPairs.fullSix_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_24_base LocalFullSixPairs.compact_fullSix_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullSixPairs.fullSix_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_25_base LocalFullSixPairs.compact_fullSix_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullSixPairs.fullSix_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_25_base LocalFullSixPairs.compact_fullSix_pair_25_hinges x
private def zz933:"s03a5"="s03a5":=by decide+kernel
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullSixPairs.fullSix_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r47]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_26_base LocalFullSixPairs.compact_fullSix_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullSixPairs.fullSix_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_26_base LocalFullSixPairs.compact_fullSix_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullSixPairs.fullSix_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_27_base LocalFullSixPairs.compact_fullSix_pair_27_hinges
private def zz934:"s03a6"="s03a6":=by decide+kernel
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullSixPairs.fullSix_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_27_base LocalFullSixPairs.compact_fullSix_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullSixPairs.fullSix_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_28_base LocalFullSixPairs.compact_fullSix_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
private def zz935:"s03a7"="s03a7":=by decide+kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullSixPairs.fullSix_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_28_base LocalFullSixPairs.compact_fullSix_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullSixPairs.fullSix_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_29_base LocalFullSixPairs.compact_fullSix_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullSixPairs.fullSix_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_29_base LocalFullSixPairs.compact_fullSix_pair_29_hinges x
private def zz936:"s03a8"="s03a8":=by decide+kernel
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullSixPairs.fullSix_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_30_base LocalFullSixPairs.compact_fullSix_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullSixPairs.fullSix_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_30_base LocalFullSixPairs.compact_fullSix_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullSixPairs.fullSix_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_31_base LocalFullSixPairs.compact_fullSix_pair_31_hinges
private def zz937:"s03a9"="s03a9":=by decide+kernel
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullSixPairs.fullSix_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_31_base LocalFullSixPairs.compact_fullSix_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullSixPairs.fullSix_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_32_base LocalFullSixPairs.compact_fullSix_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
private def zz938:"s03aa"="s03aa":=by decide+kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullSixPairs.fullSix_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_32_base LocalFullSixPairs.compact_fullSix_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullSixPairs.fullSix_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_33_base LocalFullSixPairs.compact_fullSix_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullSixPairs.fullSix_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_33_base LocalFullSixPairs.compact_fullSix_pair_33_hinges x
private def zz939:"s03ab"="s03ab":=by decide+kernel
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullSixPairs.fullSix_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_34_base LocalFullSixPairs.compact_fullSix_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullSixPairs.fullSix_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_34_base LocalFullSixPairs.compact_fullSix_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullSixPairs.fullSix_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_35_base LocalFullSixPairs.compact_fullSix_pair_35_hinges
private def zz940:"s03ac"="s03ac":=by decide+kernel
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullSixPairs.fullSix_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_35_base LocalFullSixPairs.compact_fullSix_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullSixPairs.fullSix_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r51]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_36_base LocalFullSixPairs.compact_fullSix_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
private def zz941:"s03ad"="s03ad":=by decide+kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullSixPairs.fullSix_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_36_base LocalFullSixPairs.compact_fullSix_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullSixPairs.fullSix_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r27]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_37_base LocalFullSixPairs.compact_fullSix_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullSixPairs.fullSix_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_37_base LocalFullSixPairs.compact_fullSix_pair_37_hinges x
private def zz942:"s03ae"="s03ae":=by decide+kernel
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullSixPairs.fullSix_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_38_base LocalFullSixPairs.compact_fullSix_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullSixPairs.fullSix_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_38_base LocalFullSixPairs.compact_fullSix_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullSixPairs.fullSix_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (6) ((1 / 0xf4240)) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullSixPairs.compact_fullSix_pair_39_base LocalFullSixPairs.compact_fullSix_pair_39_hinges
private def zz943:"s03af"="s03af":=by decide+kernel
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullSixPairs.fullSix_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixPairs.compact_fullSix_pair_39_base LocalFullSixPairs.compact_fullSix_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullSixPairs.fullSix_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
private def zz944:"s03b0"="s03b0":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (6) ((1 / 0xf4240)) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullSixRows
private def zz2257:"s08d1"="s08d1":=by decide+kernel
end 
section 
namespace Green24Proof.ExtendedFullPhaseAggregation
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase Potential scale expressionEval_append expressionEval_scale area pairProduct)
open FullPhaseAggregation (area_sum pairProduct_sum)
noncomputable def rowValue {q:ℕ} (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Label) (j k:ZMod q):ℝ :=
  expressionEval (rowQuad l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (quadPoint g j k) +
  expressionEval (rowPair S l (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
      (sameColour h3 j k)) (pairPoint g j k)
noncomputable def rowAggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:Label):ℝ:=∑ j, ∑ k,rowValue S h4 h3 g l j k
noncomputable def weightedAggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)):ℝ :=
  (rows.map fun t => (t.1:ℝ) * rowAggregate S h4 h3 g t.2).sum
theorem potential_aggregate {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (h5:¬5 ∣ q) (g:ZMod q → ℝ) (l:Potential) (hl:admissible l = true) :
    rowAggregate S h4 h3 g (.base (.potential l)) = 0 :=
  potentialRow_sum h4 h3 h5 g l hl
theorem weightedRows_sum {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (weightedQuad rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (weightedPair S rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate S h4 h3 g rows:=by
  induction rows with
  | nil => simp [weightedQuad,weightedPair,expressionEval,weightedAggregate]
  | cons t ts ih =>
    simp only [weightedQuad,weightedPair,List.flatMap_cons,expressionEval_append,
      expressionEval_scale] at *
    have hdistrib (j k:ZMod q) :
        (t.1:ℝ) * expressionEval (rowQuad t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (rowQuad t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)))) (quadPoint g j k) +
        ((t.1:ℝ) * expressionEval (rowPair S t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k) +
        expressionEval ((ts.flatMap fun t => scale t.1 (rowPair S t.2 (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)))) (pairPoint g j k)) =
        (t.1:ℝ) * rowValue S h4 h3 g t.2 j k +
        (expressionEval (weightedQuad ts (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
        expressionEval (weightedPair S ts (ZMod.castHom h4 (ZMod 4) j)
          (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k)):=by
      unfold rowValue weightedQuad weightedPair
      ring
    simp_rw [hdistrib]
    simp only [Finset.sum_add_distrib] at ih
    simp only [Finset.sum_add_distrib, ← Finset.mul_sum,weightedQuad,weightedPair]
    rw [ih]
    rfl
theorem local_slacks_sum {q:ℕ} [NeZero q] (S margin:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (rows:List (ℚ × Label)) :
    (∑ j:ZMod q, ∑ k:ZMod q,(
      expressionEval (quadSlack rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack S margin rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate S h4 h3 g rows + 4 * deficit g - 4 * (margin:ℝ) * mass g ^ 2:=by
  have hw:=weightedRows_sum S h4 h3 g rows
  simp only [Finset.sum_add_distrib] at hw
  simp only [quadSlack,pairSlack,expressionEval_append,expressionEval_scale,Rat.cast_neg,Rat.cast_one]
  simp_rw [show ∀ a b c d:ℝ,a + -1 * b + (c + d) = (a + c) - b + d by intros; ring]
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib,
    area_sum,pairProduct_sum]
  rw [← hw]
  push_cast
  unfold deficit
  ring
def labelAdmissible:Label → Bool
  | .base l => FullPhaseAggregation.labelAdmissible l
  | _ => true
def rowsAdmissible (rows:List (ℚ × Label)):Bool:=rows.all fun t => labelAdmissible t.2
def stripPotentials:List (ℚ × Label) → List (ℚ × Label)
  | [] => []
  | (_, .base (.potential _)) :: ts => stripPotentials ts
  | t :: ts => t :: stripPotentials ts
private def zz945:"s03b1"="s03b1":=by decide+kernel
theorem weightedAggregate_cons {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (t:ℚ × Label) (ts:List (ℚ × Label)) :
    weightedAggregate S h4 h3 g (t :: ts) =
      (t.1:ℝ) * rowAggregate S h4 h3 g t.2 + weightedAggregate S h4 h3 g ts:=rfl
theorem stripPotentials_sound {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (h5:¬5 ∣ q) (g:ZMod q → ℝ) (rows:List (ℚ × Label))
    (hrows:rowsAdmissible rows = true) :
    weightedAggregate S h4 h3 g rows = weightedAggregate S h4 h3 g (stripPotentials rows):=by
  induction rows with
  | nil => rfl
  | cons t ts ih =>
    simp only [rowsAdmissible,List.all_cons,Bool.and_eq_true] at hrows
    rcases t with ⟨w,l⟩
    cases l with
    | base l =>
      cases l with
      | potential l =>
        have hl:admissible l = true:=hrows.1
        simp only [stripPotentials,weightedAggregate_cons,potential_aggregate S h4 h3 h5 g l hl,
          mul_zero,zero_add]
        exact ih hrows.2
      | balance r s | child r | grandchild r | heightChild r | ordered r | massSquare c v | normalization =>
        simp only [stripPotentials,weightedAggregate_cons]
        rw [ih hrows.2]
    | colourChild scope | massProduct a b | massCorrection r a c | massCoercivity c =>
      simp only [stripPotentials,weightedAggregate_cons]
      rw [ih hrows.2]
theorem rowAggregate_base {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (l:FullPhaseRows.Label) :
    rowAggregate S h4 h3 g (.base l) = FullPhaseAggregation.rowAggregate S h4 h3 g l:=rfl
end Green24Proof.ExtendedFullPhaseAggregation
private def zz2258:"s08d2"="s08d2":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixCyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullSixRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullSixRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullSixRows.rows p q same x]
    exact FullSixRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz946:"s03b2"="s03b2":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 6 (1 / 0xf4240) FullSixRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullSixRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 6 (1 / 0xf4240) FullSixRows.rows p q same x]
    exact FullSixRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullSixRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullSixRows.rows
theorem remaining_rows_count:remainingRows.length = 14:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
      weightedAggregate 6 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullSixRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 6 (1 / 0xf4240) FullSixRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 6 h4 h3 h5 g FullSixRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
    weightedAggregate 6 h4 h3 g (stripPotentials FullSixRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullSixCyclic
private def zz2259:"s08d3"="s08d3":=by decide+kernel
end 
section 
namespace Green24Proof.ExtendedMassRows
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open FullPhaseRows (Phase pairProduct)
open FullPhaseSemantics (pairPoint pairProduct_eval)
open PhaseMassRows
private def zz947:"s03b3"="s03b3":=by decide+kernel
theorem rowAggregate_massProduct {q:ℕ} [NeZero q] (S:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (a b:Phase → ℚ) :
    rowAggregate S h4 h3 g (.massProduct a b) =
      -massWeighted h4 g (fun p => (a p:ℝ)) * massWeighted h4 g (fun p => (b p:ℝ)):=by
  let f (i:ZMod q):ℝ:=(a (ZMod.castHom h4 (ZMod 4) i):ℝ) * g i
  let f' (i:ZMod q):ℝ:=(b (ZMod.castHom h4 (ZMod 4) i):ℝ) * g i
  have hp (j k:ZMod q):rowValue S h4 h3 g (.massProduct a b) j k =
      -(f j * f' k + f' j * f k) / 2:=by
    simp only [rowValue,rowQuad,rowPair,expressionEval_nil,zero_add,pairProduct_eval,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one]
    dsimp only [f,f']
    push_cast
    ring
  unfold rowAggregate
  simp_rw [hp]
  exact negative_symmetric_product_sum f f'
theorem rowAggregate_massProduct_nonpos {q:ℕ} [NeZero q] (S:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (a b:Phase → ℚ)
    (ha:0 ≤ massWeighted h4 g (fun p => (a p:ℝ)))
    (hb:0 ≤ massWeighted h4 g (fun p => (b p:ℝ))) :
    rowAggregate S h4 h3 g (.massProduct a b) ≤ 0:=by
  rw [rowAggregate_massProduct]
  exact mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr ha) hb
theorem weighted_phase_pair_sum {q:ℕ} [NeZero q] (h4:4 ∣ q)
    (g:ZMod q → ℝ) (w:Phase → Phase → ℝ) :
    (∑ j:ZMod q, ∑ k:ZMod q,
      w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g j * g k) =
      ∑ p:Phase, ∑ r:Phase,w p r * phaseTotal h4 g p * phaseTotal h4 g r:=by
  have hi (j:ZMod q) :
      (∑ k:ZMod q,w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g j * g k) =
      ∑ r:Phase,w (ZMod.castHom h4 (ZMod 4) j) r * g j * phaseTotal h4 g r:=by
    have he (k:ZMod q):w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g j * g k =
        g j * (w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g k):=by ring
    simp_rw [he]
    rw [← Finset.mul_sum,weighted_colourTotal]
    simp only [Finset.mul_sum,phaseTotal]
    congr 1
    funext r
    ring
  simp_rw [hi]
  rw [Finset.sum_comm]
  conv_rhs => rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro r _
  rw [← Finset.sum_mul, ← Finset.sum_mul]
  congr 1
  exact weighted_colourTotal (ZMod.castHom h4 (ZMod 4)) g (fun p => w p r)
theorem rowAggregate_massCoercivity {q:ℕ} [NeZero q] (S c:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    rowAggregate S h4 h3 g (.massCoercivity c) =
      FullPhaseAggregation.rowAggregate S h4 h3 g (.child 0) +
        4 * (c:ℝ) * (phaseTotal h4 g 0 - phaseTotal h4 g 2) ^ 2:=by
  let w (p r:Phase):ℝ:=if FullPhaseRows.parity p = 0 ∧ FullPhaseRows.parity r = 0
    then 4 * (c:ℝ) * (-1:ℝ) ^ (p.val / 2 + r.val / 2) else 0
  have hp (j k:ZMod q):rowValue S h4 h3 g (.massCoercivity c) j k =
      FullPhaseAggregation.rowValue S h4 h3 g (.child 0) j k +
        w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g j * g k:=by
    simp only [rowValue,rowQuad,rowPair,FullPhaseAggregation.rowValue,
      FullPhaseRows.rowQuad,FullPhaseRows.rowPair,w]
    split_ifs <;> simp only [pairProduct_eval,expressionEval_nil,
      pairPoint,Matrix.cons_val_zero,Matrix.cons_val_one] <;> push_cast <;> ring
  unfold rowAggregate
  simp_rw [hp]
  simp only [Finset.sum_add_distrib]
  rw [weighted_phase_pair_sum]
  change FullPhaseAggregation.rowAggregate S h4 h3 g (.child 0) + _ = _
  congr 1
  simp only [sum_phase]
  norm_num [w,FullPhaseRows.parity,ZMod.val_ofNat,ZMod.val_one_eq_one_mod]
  ring
private def zz948:"s03b4"="s03b4":=by decide+kernel
theorem rowAggregate_massCorrection_odd {q:ℕ} [NeZero q] (S:ℚ) (c:Correction)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) :
    rowAggregate S h4 h3 g (.massCorrection 1 1 c) =
      FullPhaseAggregation.rowAggregate S h4 h3 g (.child 1) -
        (c.retained:ℝ) * FullPhaseAggregation.rowAggregate S h4 h3 g (.grandchild 1) +
        4 * ((c.even:ℝ) * phaseTotal h4 g 1 ^ 2 +
          (c.mixed:ℝ) * phaseTotal h4 g 1 * phaseTotal h4 g 3 +
          (c.odd:ℝ) * phaseTotal h4 g 3 ^ 2):=by
  let w (p r:Phase):ℝ:=if FullPhaseRows.parity p = 1 ∧ FullPhaseRows.parity r = 1
    then 4 * (correctionCoefficient c 1 p r:ℝ) else 0
  have hv (p r:Phase) (same:Bool) (x y:Point) :
      expressionEval (rowQuad (.massCorrection 1 1 c) p r same) x +
        expressionEval (rowPair S (.massCorrection 1 1 c) p r same) y =
      expressionEval (FullPhaseRows.rowQuad (.child 1) p r same) x +
        expressionEval (FullPhaseRows.rowPair S (.child 1) p r same) y -
        (c.retained:ℝ) * (expressionEval (FullPhaseRows.rowQuad (.grandchild 1) p r same) x +
          expressionEval (FullPhaseRows.rowPair S (.grandchild 1) p r same) y) +
        w p r * y 0 * y 1:=by
    have hc (p:Phase):p = 0 ∨ p = 1 ∨ p = 2 ∨ p = 3:=by
      revert p
      decide +kernel
    rcases hc p with rfl | rfl | rfl | rfl
    all_goals rcases hc r with rfl | rfl | rfl | rfl
    all_goals
      simp +decide [rowQuad,rowPair,FullPhaseRows.rowQuad,FullPhaseRows.rowPair,
        FullPhaseRows.parity,expressionEval_nil,FullPhaseRows.expressionEval_scale,
        pairProduct_eval,w,correctionCoefficient] <;> ring
  have hp (j k:ZMod q):rowValue S h4 h3 g (.massCorrection 1 1 c) j k =
      FullPhaseAggregation.rowValue S h4 h3 g (.child 1) j k -
        (c.retained:ℝ) * FullPhaseAggregation.rowValue S h4 h3 g (.grandchild 1) j k +
        w (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k) * g j * g k :=
    hv _ _ _ _ _
  unfold rowAggregate
  simp_rw [hp]
  simp only [Finset.sum_add_distrib,Finset.sum_sub_distrib, ← Finset.mul_sum]
  rw [weighted_phase_pair_sum]
  change FullPhaseAggregation.rowAggregate S h4 h3 g (.child 1) -
    (c.retained:ℝ) * FullPhaseAggregation.rowAggregate S h4 h3 g (.grandchild 1) + _ = _
  congr 1
  simp only [sum_phase]
  simp +decide [w,correctionCoefficient,FullPhaseRows.parity]
  ring
end Green24Proof.ExtendedMassRows
private def zz2260:"s08d4"="s08d4":=by decide+kernel
end 
section 
namespace Green24Proof
theorem negative_parent_mass_constraint {a b c d du dv dg:ℝ}
    (hdu:0 ≤ du) (hdv:0 ≤ dv) (hdg:dg < 0)
    (hexpansion:du + dv + 4 * (a + b) * (c + d) - 12 * b * (c + d) - 12 * c * d ≤ dg) :
    (a - 2 * b) * (c + d) < 3 * c * d:=by nlinarith
theorem negative_parent_ratio_cap {a b c d L:ℝ}
    (hV:0 < c + d) (hL:3 / 4 < L)
    (hconstraint:(a - 2 * b) * (c + d) < 3 * c * d)
    (hlower:L * (c + d) ≤ a + b) :
    a < ((8 * L + 3) / (4 * L - 3)) * b:=by
  have hlinear:4 * a - 8 * b < 3 * (c + d):=by
    apply (mul_lt_mul_iff_right₀ hV).mp
    nlinarith [sq_nonneg (c - d)]
  have hscaled:=mul_lt_mul_of_pos_left hlinear (by linarith:0 < L)
  have hden:0 < 4 * L - 3:=by linarith
  apply (mul_lt_mul_iff_right₀ hden).mp
  have hcancel:((8 * L + 3) / (4 * L - 3)) * (4 * L - 3) = 8 * L + 3 :=
    div_mul_cancel₀ _ (ne_of_gt hden)
  have hb:=congrArg (fun x:ℝ => x * b) hcancel
  nlinarith
theorem weighted_mass_mean {c d t:ℝ} (hV:0 < c + d) (ht:0 ≤ t) :
    c * d / (c + d) ≤ (t ^ 2 * c + d) / (1 + t) ^ 2:=by
  apply (div_le_div_iff₀ hV (by positivity:0 < (1 + t) ^ 2)).mpr
  nlinarith [sq_nonneg (t * c - d)]
private def zz949:"s03b5"="s03b5":=by decide+kernel
theorem conditional_mass_form_pos {a b c d t:ℝ} (hV:0 < c + d) (ht:0 ≤ t)
    (hconstraint:(a - 2 * b) * (c + d) < 3 * c * d) :
    0 < 2 * b - a + 3 * (t ^ 2 * c + d) / (1 + t) ^ 2:=by
  have hratio:a - 2 * b < 3 * (c * d / (c + d)):=by
    apply (mul_lt_mul_iff_right₀ hV).mp
    have hcancel:c * d / (c + d) * (c + d) = c * d:=div_mul_cancel₀ _ (ne_of_gt hV)
    nlinarith
  have hmean:=weighted_mass_mean hV ht
  rw [mul_div_assoc]
  linarith
theorem conditional_mass_product_nonpos {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    -(x * y) ≤ 0:=neg_nonpos.mpr (mul_nonneg hx hy)
theorem ratio_twelve_child_cap {a b c d:ℝ} (hV:0 < c + d)
    (hconstraint:(a - 2 * b) * (c + d) < 3 * c * d)
    (hlower:12 * (c + d) ≤ a + b):a < (11 / 5) * b:=by
  have h:=negative_parent_ratio_cap hV (by norm_num:(3 / 4:ℝ) < 12) hconstraint hlower
  norm_num at h
  exact h
theorem coercivity_three_thousandths {a b du:ℝ}
    (hc:(1 / 0x12c) * (a - b) ^ 2 ≤ du):(3 / 0x3e8) * (a - b) ^ 2 ≤ du:=by
  nlinarith [sq_nonneg (a - b)]
end Green24Proof
end 
section 
namespace Green24Proof
private def zz950:"s03b6"="s03b6":=by decide+kernel
theorem mixedFunctional_le_twelve_parity_product {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    mixedFunctional v u 1 ≤
      12 * classMass (ZMod.castHom h2 (ZMod 2)) v 0 *
        classMass (ZMod.castHom h2 (ZMod 2)) v 1:=by
  have hcorr:=odd_shift_correlation_le_parity h2 v hv
  unfold mixedFunctional
  calc
    _ ≤ ∑ j, ∑ k,3 * (v (3 * k - 2 * j + 1) * v k):=by
      apply Finset.sum_le_sum
      intro j _
      apply Finset.sum_le_sum
      intro k _
      have h:=kernel_le_product (hv (3 * k - 2 * j + 1))
        (mul_nonneg (by norm_num:(0:ℝ) ≤ 3) (hv k))
        (mul_nonneg (by norm_num:(0:ℝ) ≤ 2) (hu j))
      rw [kernel_swap23] at h
      nlinarith
    _ = 3 * (∑ k, ∑ j,v (3 * k - 2 * j + 1) * v k):=by
      simp only [← Finset.mul_sum]
      rw [Finset.sum_comm]
    _ ≤ _:=by nlinarith
theorem deficit_interleave_parity_expansion {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    deficit u + deficit v + 4 * mass u * mass v -
      12 * classMass (ZMod.castHom h2 (ZMod 2)) u 1 * mass v -
      12 * classMass (ZMod.castHom h2 (ZMod 2)) v 0 *
        classMass (ZMod.castHom h2 (ZMod 2)) v 1 ≤ deficit (interleave u v):=by
  have hm₁:=mixedFunctional_le_overlap u v hu hv
    (fun j => cyclic_overlap_le_six_classMass h2 u hu j 1)
  have hm₂:=mixedFunctional_le_twelve_parity_product h2 u v hu hv
  unfold deficit
  rw [mass_interleave,profileFunctional_interleave]
  nlinarith
theorem negative_parent_profile_constraint {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hdg:deficit (interleave u v) < 0) :
    (classMass (ZMod.castHom h2 (ZMod 2)) u 0 -
      2 * classMass (ZMod.castHom h2 (ZMod 2)) u 1) * mass v <
      3 * classMass (ZMod.castHom h2 (ZMod 2)) v 0 *
        classMass (ZMod.castHom h2 (ZMod 2)) v 1:=by
  have h:=deficit_interleave_parity_expansion h2 u v hu hv
  have hmu:=classMass_sum (ZMod.castHom h2 (ZMod 2)) u
  rw [← hmu] at h
  nlinarith
theorem negative_parent_profile_child_cap {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hdg:deficit (interleave u v) < 0) (hV:0 < mass v)
    (hlower:12 * mass v ≤ mass u) :
    classMass (ZMod.castHom h2 (ZMod 2)) u 0 <
      (11 / 5) * classMass (ZMod.castHom h2 (ZMod 2)) u 1:=by
  have h:=negative_parent_profile_constraint h2 u v hu hv hdu hdv hdg
  have hmu:=classMass_sum (ZMod.castHom h2 (ZMod 2)) u
  have hmv:=classMass_sum (ZMod.castHom h2 (ZMod 2)) v
  apply ratio_twelve_child_cap (c:=classMass (ZMod.castHom h2 (ZMod 2)) v 0)
    (d:=classMass (ZMod.castHom h2 (ZMod 2)) v 1)
  · rwa [hmv]
  · rwa [hmv]
  · rwa [hmu,hmv]
end Green24Proof
end 
section 
namespace Green24Proof.ConditionalMassRows
open FullPhaseRows (Phase)
open PhaseMassRows
def domainForm (L H:ℚ) (i:Fin 14) (p:Phase):ℚ :=
  let forms:Fin 14 → Fin 4 → ℚ:=![
  ![1,0,0,0], ![0,1,0,0], ![0,0,1,0], ![0,0,0,1],
  ![1,0, -1,0], ![0,1,0, -1], ![-1,0,(8 * L + 3) / (4 * L - 3),0],
  ![1, -L,1, -L], ![-1,H, -1,H],
  ![-1,0,2,3], ![-1,3 / 25,2,48 / 25], ![-1,1 / 3,2,4 / 3],
  ![-1,27 / 49,2,48 / 49], ![-1,3 / 4,2,3 / 4]]
  forms i ⟨p.val,p.val_lt⟩
private def zz951:"s03b7"="s03b7":=by decide+kernel
theorem domainForm_nonneg {q:ℕ} [NeZero q] (h4:4 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) (L H:ℚ)
    (hL:(3 / 4:ℝ) < (L:ℝ))
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hodd:phaseTotal h4 g 3 ≤ phaseTotal h4 g 1)
    (hV:0 < phaseTotal h4 g 1 + phaseTotal h4 g 3)
    (hlow:(L:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤
      phaseTotal h4 g 0 + phaseTotal h4 g 2)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      (H:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hconstraint:(phaseTotal h4 g 0 - 2 * phaseTotal h4 g 2) *
      (phaseTotal h4 g 1 + phaseTotal h4 g 3) <
        3 * phaseTotal h4 g 1 * phaseTotal h4 g 3)
    (i:Fin 14) :
    0 ≤ massWeighted h4 g (fun p => (domainForm L H i p:ℝ)):=by
  have ha:=phaseTotal_nonneg h4 g hg 0
  have hc:=phaseTotal_nonneg h4 g hg 1
  have hb:=phaseTotal_nonneg h4 g hg 2
  have hd:=phaseTotal_nonneg h4 g hg 3
  have hcap:=negative_parent_ratio_cap hV hL hconstraint hlow
  have ht0:=conditional_mass_form_pos hV (by norm_num:(0:ℝ) ≤ 0) hconstraint
  have ht1:=conditional_mass_form_pos hV (by norm_num:(0:ℝ) ≤ 1 / 4) hconstraint
  have ht2:=conditional_mass_form_pos hV (by norm_num:(0:ℝ) ≤ 1 / 2) hconstraint
  have ht3:=conditional_mass_form_pos hV (by norm_num:(0:ℝ) ≤ 3 / 4) hconstraint
  have ht4:=conditional_mass_form_pos hV (by norm_num:(0:ℝ) ≤ 1) hconstraint
  norm_num at ht0 ht1 ht2 ht3 ht4
  rw [massWeighted_phaseTotal,sum_phase]
  fin_cases i <;> norm_num [domainForm,ZMod.val_ofNat,ZMod.val_one_eq_one_mod,
    Rat.cast_div,Rat.cast_mul,Rat.cast_add,Rat.cast_sub] <;> linarith
theorem domainProduct_nonpos {q:ℕ} [NeZero q] (S L H:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ)
    (hs:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm L H i p:ℝ)))
    (i j:Fin 14) :
    ExtendedFullPhaseAggregation.rowAggregate S h4 h3 g
      (.massProduct (domainForm L H i) (domainForm L H j)) ≤ 0 :=
  ExtendedMassRows.rowAggregate_massProduct_nonpos S h4 h3 g _ _ (hs i) (hs j)
end Green24Proof.ConditionalMassRows
private def zz2261:"s08d5"="s08d5":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixMass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open FullPhaseRows (Phase)
open PhaseMassRows PhaseColourRows ConditionalMassRows
theorem remainingRows_eq:FullSixCyclic.remainingRows = [
  ((0x265bcae3 / 0x3b9aca00), .base (.child 0)),
  ((0xe878eeb / 0xee6b280), .base (.heightChild 1)),
  ((0x6e9163 / 0x7735940), .base (.grandchild 0)),
  ((0x5f2395 / 0xee6b280), .colourChild .whole),
  ((0xd2fe5 / 0x2faf080), .massProduct (fun p => (![1,0,0,0]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)),
  ((0xcb1a63 / 0x7735940), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((0x5c7f1fb / 0xbebc200), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,0,(43 / 17),0]:Fin 4 → ℚ) p)),
  ((0x4dfffeb / 0x1dcd6500), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)),
  ((0xc7b1b1 / 0x2625a00), .massProduct (fun p => (![1, -5,1, -5]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)),
  ((0x936d9649 / 0x1dcd6500), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x40cc6f / 0xbebc200), .base (.massSquare true (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p))),
  ((0x41409c9 / 0xee6b280), .base (.massSquare true (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x839617 / 0x3b9aca00), .base (.massSquare true (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p))),
  ((1 / 0x98968), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ)
    (_heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (_hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (6:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 5 6 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 6 h4 h3 g (.colourChild .whole) ≤ 0) :
    weightedAggregate 6 h4 h3 g FullSixCyclic.remainingRows ≤
      ((1 / 0x98968):ℝ) * mass g ^ 2:=by
  have hp4:rowAggregate 6 h4 h3 g (.massProduct (fun p => (![1,0,0,0]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 6 5 6 h4 h3 g hforms 0 8
  have hp5:rowAggregate 6 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 6 5 6 h4 h3 g hforms 4 5
  have hp6:rowAggregate 6 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,0,(43 / 17),0]:Fin 4 → ℚ) p)) ≤ 0:=by
    have h:=domainProduct_nonpos 6 5 6 h4 h3 g hforms 4 6
    have he:domainForm 5 6 6 =
        (fun p:Phase => (![-1,0,(43 / 17),0]:Fin 4 → ℚ) p):=by
      funext p
      norm_num [domainForm]
      rfl
    rw [he] at h
    exact h
  have hp7:rowAggregate 6 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 6 5 6 h4 h3 g hforms 4 8
  have hp8:rowAggregate 6 h4 h3 g (.massProduct (fun p => (![1, -5,1, -5]:Fin 4 → ℚ) p) (fun p => (![-1,6, -1,6]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 6 5 6 h4 h3 g hforms 7 8
  have hs9:=rowAggregate_massSquare_nonpos 6 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hs10:=rowAggregate_colouredMassSquare_nonpos 6 h4 h3 g (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p)
  have hs11:=rowAggregate_colouredMassSquare_nonpos 6 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hs12:=rowAggregate_colouredMassSquare_nonpos 6 h4 h3 g (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_normalization]
  norm_num
  linarith
private def zz952:"s03b8"="s03b8":=by decide+kernel
theorem deficit_nonneg_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (6:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 5 6 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 6 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 6 h4 h3 g (.colourChild .whole) ≤ 0) :
    0 ≤ deficit g:=by
  have hc:=FullSixCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g heven hhigh hforms hchild hheight hgrand hcolour
  nlinarith [sq_nonneg (mass g)]
end Green24Proof.FullSixMass
private def zz2262:"s08d6"="s08d6":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileChildren
open FullPhaseRows (Phase)
open PhaseMassRows HeightChildRows GrandchildRows
noncomputable def child {m:ℕ} [NeZero m] (g:ZMod (2 * m) → ℝ)
    (r:ZMod 2):ZMod m → ℝ:=fun i => g (parityEquiv m (r,i))
theorem child_nonneg {m:ℕ} [NeZero m] (g:ZMod (2 * m) → ℝ)
    (hg:∀ i,0 ≤ g i) (r:ZMod 2):∀ i,0 ≤ child g r i:=fun i => hg (parityEquiv m (r,i))
theorem interleave_children {m:ℕ} [NeZero m] (g:ZMod (2 * m) → ℝ) :
    interleave (child g 0) (child g 1) = g:=by
  funext x
  obtain ⟨⟨r,i⟩,rfl⟩:=(parityEquiv m).surjective x
  rcases zmod_two_eq_zero_or_one r with rfl | rfl
  · exact interleave_even _ _ i
  · exact interleave_odd _ _ i
theorem child_mass {m:ℕ} [NeZero m] (g:ZMod (2 * m) → ℝ) (r:ZMod 2) :
    mass (child g r) = classMass (ZMod.castHom (dvd_mul_right 2 m) (ZMod 2)) g r:=by
  rcases zmod_two_eq_zero_or_one r with rfl | rfl
  · rw [← interleave_children g,classMass_interleave_even]
    rw [interleave_children]
  · rw [← interleave_children g,classMass_interleave_odd]
    rw [interleave_children]
private def zz953:"s03b9"="s03b9":=by decide+kernel
theorem phaseTotal_interleave_zero {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) :
    phaseTotal h4 (interleave u v) 0 = classMass (ZMod.castHom h2 (ZMod 2)) u 0:=by
  unfold phaseTotal colourTotal
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [cast_four_even h4 h2,cast_four_odd h4 h2,interleave_even,interleave_odd]
  have he (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) = (0:ZMod 4) then u i else 0) =
        if ZMod.castHom h2 (ZMod 2) i = 0 then u i else 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; simp
    · rw [h,doubleResidue_two_one]; simp +decide
  have ho (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) + 1 = (0:ZMod 4) then v i else 0) = 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; simp +decide
    · rw [h,doubleResidue_two_one]; simp +decide
  simp only [he,ho,Finset.sum_const_zero,add_zero]
  rfl
theorem phaseTotal_interleave_two {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) :
    phaseTotal h4 (interleave u v) 2 = classMass (ZMod.castHom h2 (ZMod 2)) u 1:=by
  unfold phaseTotal colourTotal
  rw [← (parityEquiv m).sum_comp,Fintype.sum_prod_type,sum_zmod_two]
  simp only [cast_four_even h4 h2,cast_four_odd h4 h2,interleave_even,interleave_odd]
  have he (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) = (2:ZMod 4) then u i else 0) =
        if ZMod.castHom h2 (ZMod 2) i = 1 then u i else 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; simp +decide
    · rw [h,doubleResidue_two_one]; simp
  have ho (i:ZMod m) :
      (if doubleResidue 2 (ZMod.castHom h2 (ZMod 2) i) + 1 = (2:ZMod 4) then v i else 0) = 0:=by
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; simp +decide
    · rw [h,doubleResidue_two_one]; simp +decide
  simp only [he,ho,Finset.sum_const_zero,add_zero]
  rfl
end Green24Proof.ProfileChildren
private def zz2263:"s08d7"="s08d7":=by decide+kernel
end 
section 
namespace Green24Proof.ConditionalProfileRows
open FullPhaseRows (Phase)
open PhaseMassRows ProfileChildren HeightChildRows ConditionalMassRows
theorem odd_mass_pos_of_negative_parent {m:ℕ} [NeZero m] (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hneg:deficit (interleave u v) < 0):0 < mass v:=by
  have he:=deficit_interleave_parity_expansion h2 u v hu hv
  have hm:=classMass_sum (ZMod.castHom h2 (ZMod 2)) v
  have hc:0 ≤ classMass (ZMod.castHom h2 (ZMod 2)) v 0 :=
    Finset.sum_nonneg fun i _ => by split_ifs <;> first | exact hv i | rfl
  have hd:0 ≤ classMass (ZMod.castHom h2 (ZMod 2)) v 1 :=
    Finset.sum_nonneg fun i _ => by split_ifs <;> first | exact hv i | rfl
  by_contra! h
  have hV:mass v = 0:=le_antisymm h (Finset.sum_nonneg fun i _ => hv i)
  have hc0:classMass (ZMod.castHom h2 (ZMod 2)) v 0 = 0:=by linarith
  rw [hV,hc0] at he
  nlinarith
theorem phase_constraint {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hneg:deficit (interleave u v) < 0) :
    (phaseTotal h4 (interleave u v) 0 - 2 * phaseTotal h4 (interleave u v) 2) *
      (phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3) <
        3 * phaseTotal h4 (interleave u v) 1 * phaseTotal h4 (interleave u v) 3:=by
  rw [phaseTotal_interleave_zero h4 h2,phaseTotal_interleave_two h4 h2,
    phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  exact negative_parent_profile_constraint h2 u v hu hv hdu hdv hneg
private def zz954:"s03ba"="s03ba":=by decide+kernel
theorem domainForms_nonneg {m:ℕ} [NeZero m] (L H:ℚ)
    (h4:4 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (hdu:0 ≤ deficit u) (hdv:0 ≤ deficit v)
    (hneg:deficit (interleave u v) < 0)
    (hL:(3 / 4:ℝ) < (L:ℝ))
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(L:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (H:ℝ) * mass v)
    (i:Fin 14) :
    0 ≤ massWeighted h4 (interleave u v) (fun p => (domainForm L H i p:ℝ)):=by
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    rw [phaseTotal_interleave_zero h4 h2,phaseTotal_interleave_two h4 h2,classMass_sum]
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  apply domainForm_nonneg h4 (interleave u v) (interleave_nonneg u v hu hv) L H hL heven hodd
  · rw [hV]; exact odd_mass_pos_of_negative_parent h2 u v hu hv hdu hdv hneg
  · rwa [hU,hV]
  · rwa [hU,hV]
  · exact phase_constraint h4 h2 u v hu hv hdu hdv hneg
end Green24Proof.ConditionalProfileRows
private def zz2264:"s08d8"="s08d8":=by decide+kernel
end 
section 
namespace Green24Proof.ResidueProfiles
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics FullPhaseAggregation
noncomputable def embed (d m:ℕ):ZMod m →+ ZMod (d * m) :=
  ZMod.lift m ⟨
    { toFun:=fun z:ℤ => (d:ZMod (d * m)) * (z:ZMod (d * m))
      map_zero':=by simp
      map_add':=by intros; simp [mul_add] },by
      change (d:ZMod (d * m)) * ((m:ℤ):ZMod (d * m)) = 0
      simpa only [Int.cast_natCast,Nat.cast_mul] using (ZMod.natCast_self (d * m))⟩
theorem embed_natCast (d m n:ℕ):embed d m (n:ZMod m) = d * (n:ZMod (d * m)):=by
  unfold embed
  rw [← Int.cast_natCast n,ZMod.lift_coe]
  simp only [Int.cast_natCast,AddMonoidHom.coe_mk,ZeroHom.coe_mk]
theorem embed_val {d m:ℕ} [NeZero m] (x:ZMod m) :
    embed d m x = d * (x.val:ZMod (d * m)):=by
  conv_lhs => rw [← ZMod.natCast_zmod_val x]
  exact embed_natCast d m x.val
theorem embed_mul_nat (d m n:ℕ) (x:ZMod m):embed d m (n * x) = n * embed d m x:=by
  simpa only [nsmul_eq_mul] using (embed d m).map_nsmul n x
noncomputable def residueEquiv (d m:ℕ) [NeZero d] [NeZero m] :
    (ZMod d × ZMod m) ≃ ZMod (d * m) where
  toFun p:=((d * p.2.val + p.1.val:ℕ):ZMod (d * m))
  invFun x:=(((x.val % d:ℕ):ZMod d),((x.val / d:ℕ):ZMod m))
  left_inv:=by
    rintro ⟨r,i⟩
    have hd:0 < d:=NeZero.pos d
    have hr:=r.val_lt
    have hi:=i.val_lt
    have hlt:d * i.val + r.val < d * m:=calc
      _ < d * i.val + d:=Nat.add_lt_add_left hr _
      _ = d * (i.val + 1):=by ring
      _ ≤ d * m:=Nat.mul_le_mul_left d (Nat.succ_le_of_lt hi)
    simp only [ZMod.val_natCast_of_lt hlt]
    apply Prod.ext
    · have hmod:(d * i.val + r.val) % d = r.val:=by
        rw [Nat.mul_add_mod_self_left,Nat.mod_eq_of_lt hr]
      simp only [hmod,ZMod.natCast_zmod_val]
    · have hdiv:(d * i.val + r.val) / d = i.val:=by
        rw [Nat.add_comm,Nat.add_mul_div_left _ _ hd,Nat.div_eq_of_lt hr,Nat.zero_add]
      simp only [hdiv,ZMod.natCast_zmod_val]
  right_inv:=by
    intro x
    have hd:0 < d:=NeZero.pos d
    have hx:=x.val_lt
    have hmod:x.val % d < d:=Nat.mod_lt _ hd
    have hdiv:x.val / d < m:=(Nat.div_lt_iff_lt_mul hd).mpr (by simpa [Nat.mul_comm] using hx)
    simp only [ZMod.val_natCast_of_lt hmod,ZMod.val_natCast_of_lt hdiv]
    rw [show d * (x.val / d) + x.val % d = x.val from Nat.div_add_mod _ _]
    exact ZMod.natCast_zmod_val x
private def zz955:"s03bb"="s03bb":=by decide+kernel
theorem residueEquiv_apply {d m:ℕ} [NeZero d] [NeZero m] (r:ZMod d) (i:ZMod m) :
    residueEquiv d m (r,i) = embed d m i + (r.val:ZMod (d * m)):=by
  change ((d * i.val + r.val:ℕ):ZMod (d * m)) = _
  rw [Nat.cast_add,Nat.cast_mul,embed_val]
theorem residueCast_apply {d m:ℕ} [NeZero d] [NeZero m] (r:ZMod d) (i:ZMod m) :
    ZMod.castHom (dvd_mul_right d m) (ZMod d) (residueEquiv d m (r,i)) = r:=by
  rw [residueEquiv_apply,embed_val]
  simp only [map_add,map_mul,map_natCast,ZMod.natCast_self,
    zero_mul,zero_add,ZMod.natCast_zmod_val]
theorem residueEquiv_affine_same {d m:ℕ} [NeZero d] [NeZero m]
    (r:ZMod d) (j k:ZMod m) :
    3 * residueEquiv d m (r,k) - 2 * residueEquiv d m (r,j) =
      residueEquiv d m (r,3 * k - 2 * j):=by
  rw [residueEquiv_apply,residueEquiv_apply,residueEquiv_apply]
  have h3:embed d m (3 * k) = 3 * embed d m k:=by
    simpa only [Nat.cast_ofNat] using embed_mul_nat d m 3 k
  have h2:embed d m (2 * j) = 2 * embed d m j:=by
    simpa only [Nat.cast_ofNat] using embed_mul_nat d m 2 j
  rw [map_sub,h3,h2]
  ring
noncomputable def profile {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (r:ZMod d):ZMod m → ℝ:=fun i => g (residueEquiv d m (r,i))
theorem profile_nonneg {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (hg:∀ i,0 ≤ g i) (r:ZMod d) :
    ∀ i,0 ≤ profile g r i:=fun _ => hg _
noncomputable def selectedValue {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (w:ZMod d → ℝ) (j k:ZMod (d * m)):ℝ :=
  if ZMod.castHom (dvd_mul_right d m) (ZMod d) j =
      ZMod.castHom (dvd_mul_right d m) (ZMod d) k then
    w (ZMod.castHom (dvd_mul_right d m) (ZMod d) j) *
      (expressionEval area (quadPoint g j k) + expressionEval (pairProduct (-8)) (pairPoint g j k))
  else 0
private def zz956:"s03bc"="s03bc":=by decide+kernel
theorem selectedValue_residue {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (w:ZMod d → ℝ) (a b:ZMod d) (j k:ZMod m) :
    selectedValue g w (residueEquiv d m (a,j)) (residueEquiv d m (b,k)) =
      if a = b then w a * (expressionEval area (quadPoint (profile g a) j k) +
        expressionEval (pairProduct (-8)) (pairPoint (profile g a) j k)) else 0:=by
  by_cases h:a = b
  · subst b
    simp only [selectedValue,residueCast_apply,if_true]
    rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
    simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,
      residueEquiv_affine_same,profile]
  · simp only [selectedValue,residueCast_apply,if_neg h]
theorem selectedValue_sum {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (w:ZMod d → ℝ) :
    (∑ j, ∑ k,selectedValue g w j k) = ∑ r,w r * (-4 * deficit (profile g r)):=by
  have hk (a:ZMod d) (j:ZMod m) :
      (∑ k,selectedValue g w (residueEquiv d m (a,j)) k) =
      ∑ b:ZMod d, ∑ k:ZMod m,
        selectedValue g w (residueEquiv d m (a,j)) (residueEquiv d m (b,k)):=by
    rw [← (residueEquiv d m).sum_comp,Fintype.sum_prod_type]
  rw [← (residueEquiv d m).sum_comp,Fintype.sum_prod_type]
  simp_rw [hk,selectedValue_residue]
  simp only [Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq,
    Finset.mem_univ,if_true]
  apply Finset.sum_congr rfl
  intro r _
  simp only [mul_add,Finset.sum_add_distrib, ← Finset.mul_sum]
  rw [area_sum,pairProduct_sum]
  unfold deficit
  norm_num
  ring
theorem selectedValue_sum_nonpos {d m:ℕ} [NeZero d] [NeZero m]
    (g:ZMod (d * m) → ℝ) (w:ZMod d → ℝ) (hw:∀ r,0 ≤ w r)
    (hd:∀ r,0 ≤ deficit (profile g r)):(∑ j, ∑ k,selectedValue g w j k) ≤ 0:=by
  rw [selectedValue_sum]
  exact Finset.sum_nonpos fun r _ => mul_nonpos_of_nonneg_of_nonpos (hw r) (by linarith [hd r])
end Green24Proof.ResidueProfiles
private def zz2265:"s08d9"="s08d9":=by decide+kernel
end 
section 
namespace Green24Proof.ColourChildRows
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open FullPhaseRows (Phase area pairProduct)
open FullPhaseSemantics (quadPoint pairPoint sameColour)
theorem eval_ite (P:Prop) [Decidable P] (e:Expression) (x:Point) :
    expressionEval (if P then e else []) x = if P then expressionEval e x else 0:=by
  split_ifs <;> rfl
private def zz957:"s03bd"="s03bd":=by decide+kernel
theorem selected_sum (P Q:Prop) [Decidable P] [Decidable Q] (a b:ℝ) :
    (if P ∧ Q then a else 0) + (if P ∧ Q then b else 0) =
      if P then (if Q then 1 else 0) * (a + b) else 0:=by
  by_cases hp:P <;> by_cases hq:Q <;> simp [hp,hq]
theorem whole_value {m:ℕ} [NeZero m] (S:ℚ) (h4:4 ∣ 3 * m)
    (g:ZMod (3 * m) → ℝ) (j k:ZMod (3 * m)) :
    rowValue S h4 (dvd_mul_right 3 m) g (.colourChild .whole) j k =
      ResidueProfiles.selectedValue g (fun _ => 1) j k:=by
  simp only [rowValue,rowQuad,rowPair,scopeActive,Bool.true_and,sameColour,
    decide_eq_true_eq,ResidueProfiles.selectedValue]
  split_ifs <;> simp only [expressionEval_nil,one_mul,zero_add]
theorem whole_nonpos_of_induction {q:ℕ} [NeZero q] (S:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (ih:∀ (n:ℕ) [NeZero n],n < q → n ∣ q →
      ∀ u:ZMod n → ℝ,(∀ i,0 ≤ u i) → 0 ≤ deficit u) :
    rowAggregate S h4 h3 g (.colourChild .whole) ≤ 0:=by
  rcases h3 with ⟨m,rfl⟩
  have hm:0 < m:=by have hp:=NeZero.pos (3 * m); omega
  let:NeZero m:=⟨by omega⟩
  unfold rowAggregate
  simp_rw [whole_value]
  apply ResidueProfiles.selectedValue_sum_nonpos g (fun _ => 1) (by intro r; norm_num)
  intro r
  exact ih m (by omega) (dvd_mul_left m 3) (ResidueProfiles.profile g r)
    (ResidueProfiles.profile_nonneg g hg r)
theorem phase_colour_equiv (a b:ZMod 12) (r:Phase) :
    ((ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) a = r ∧
      ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) b = r) ∧
      ZMod.castHom (by decide:3 ∣ 12) (ZMod 3) a =
        ZMod.castHom (by decide:3 ∣ 12) (ZMod 3) b) ↔
    (a = b ∧ ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) a = r):=by
  revert a b r
  decide +kernel
private def zz958:"s03be"="s03be":=by decide+kernel
theorem phase_value {m:ℕ} [NeZero m] (S:ℚ) (r:Phase)
    (h4:4 ∣ 12 * m) (h3:3 ∣ 12 * m)
    (g:ZMod (12 * m) → ℝ) (j k:ZMod (12 * m)) :
    rowValue S h4 h3 g (.colourChild (.phase r)) j k =
      ResidueProfiles.selectedValue g
        (fun a => if ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) a = r then 1 else 0) j k:=by
  let χ:=ZMod.castHom (dvd_mul_right 12 m) (ZMod 12)
  have hcast4 (i:ZMod (12 * m)):ZMod.castHom h4 (ZMod 4) i =
      ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) (χ i) :=
    (congrArg (fun f:ZMod (12 * m) →+* ZMod 4 => f i)
      (ZMod.castHom_comp (by decide:4 ∣ 12) (dvd_mul_right 12 m))).symm
  have hcast3 (i:ZMod (12 * m)):ZMod.castHom h3 (ZMod 3) i =
      ZMod.castHom (by decide:3 ∣ 12) (ZMod 3) (χ i) :=
    (congrArg (fun f:ZMod (12 * m) →+* ZMod 3 => f i)
      (ZMod.castHom_comp (by decide:3 ∣ 12) (dvd_mul_right 12 m))).symm
  have ha:((scopeActive (.phase r) (ZMod.castHom h4 (ZMod 4) j)
      (ZMod.castHom h4 (ZMod 4) k) && sameColour h3 j k) = true) ↔
      χ j = χ k ∧ ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) (χ j) = r:=by
    simp only [scopeActive,sameColour,Bool.and_eq_true,decide_eq_true_eq,hcast4,hcast3]
    exact phase_colour_equiv (χ j) (χ k) r
  simp only [rowValue,rowQuad,rowPair,ha,ResidueProfiles.selectedValue]
  change expressionEval (if χ j = χ k ∧ ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) (χ j) = r then area else []) (quadPoint g j k) +
      expressionEval (if χ j = χ k ∧ ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) (χ j) = r then pairProduct (-8) else []) (pairPoint g j k) =
      if χ j = χ k then
        (if ZMod.castHom (by decide:4 ∣ 12) (ZMod 4) (χ j) = r then 1 else 0) *
          (expressionEval area (quadPoint g j k) + expressionEval (pairProduct (-8)) (pairPoint g j k))
      else 0
  simp only [eval_ite]
  exact selected_sum _ _ _ _
theorem phase_nonpos_of_induction {q:ℕ} [NeZero q] (S:ℚ) (r:Phase)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (ih:∀ (n:ℕ) [NeZero n],n < q → n ∣ q →
      ∀ u:ZMod n → ℝ,(∀ i,0 ≤ u i) → 0 ≤ deficit u) :
    rowAggregate S h4 h3 g (.colourChild (.phase r)) ≤ 0:=by
  have h12:12 ∣ q :=
    Nat.Coprime.mul_dvd_of_dvd_of_dvd (by decide:Nat.Coprime 4 3) h4 h3
  rcases h12 with ⟨m,rfl⟩
  have hm:0 < m:=by have hp:=NeZero.pos (12 * m); omega
  let:NeZero m:=⟨by omega⟩
  unfold rowAggregate
  simp_rw [phase_value]
  apply ResidueProfiles.selectedValue_sum_nonpos
  · intro a; split_ifs <;> norm_num
  · intro a
    exact ih m (by omega) (dvd_mul_left m 12) (ResidueProfiles.profile g a)
      (ResidueProfiles.profile_nonneg g hg a)
end Green24Proof.ColourChildRows
private def zz2266:"s08da"="s08da":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixProfileInterval
open FullPhaseRows (Phase)
open PhaseMassRows ChildRows HeightChildRows
theorem interval_nonneg_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(5:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (6:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_contra! hneg
  have hm:m < 2 * m:=by have hp:=NeZero.pos m; omega
  have hdu:=ih m hm (dvd_mul_left m 2) u hu
  have hdv:=ih m hm (dvd_mul_left m 2) v hv
  have hg:=interleave_nonneg u v hu hv
  have hforms:=ConditionalProfileRows.domainForms_nonneg 5 6 h4 h2 u v hu hv hdu hdv hneg
    (by norm_num) heven hodd hlow hhigh
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hchild:FullPhaseAggregation.rowAggregate 6 h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]; linarith
  have hheight:=rowAggregate_height_odd_nonpos 6 h4 h3 h2 u v hu hv
    (HeightStrong.strong_height_bound h2 h3m h5m v hv)
  have hgrand:=Full27ProfileInterval.grandchild_nonpos_of_induction 6 h4 h3 (interleave u v) hg 0 ih
  have hcolour:=ColourChildRows.whole_nonpos_of_induction 6 h4 h3 (interleave u v) hg ih
  have hhigh':phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 ≤
      (6:ℝ) * (phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3):=by
    rw [ProfileChildren.phaseTotal_interleave_zero h4 h2,
      ProfileChildren.phaseTotal_interleave_two h4 h2,phaseTotal_interleave_one h4 h2,
      phaseTotal_interleave_three h4 h2,classMass_sum,classMass_sum]
    exact hhigh
  have h:=FullSixMass.deficit_nonneg_of_rows h4 h3 h5 (interleave u v) hg
    heven hhigh' hforms hchild hheight hgrand hcolour
  linarith
theorem interval_nonneg {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(5:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (6:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,heven,hodd⟩ :=
    ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have h:=interval_nonneg_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hd] using h
end Green24Proof.FullSixProfileInterval
private def zz2267:"s08db"="s08db":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCoverSix
private def zz959:"s03bf"="s03bf":=by decide+kernel
theorem interval_to_six {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 6 * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases hfour:mass u ≤ 4 * mass v
  · exact RatioCover.interval_to_four h4 h3 h5 h2 u v hu hv ih horder hfour
  · by_cases hfive:mass u ≤ 5 * mass v
    · have h:=FullFiveProfileInterval.interval_bound h4 h3 h5 h2 u v hu hv ih
        (le_of_lt (lt_of_not_ge hfour)) hfive
      exact (mul_nonneg (by norm_num) (sq_nonneg (mass v))).trans h
    · exact FullSixProfileInterval.interval_nonneg h4 h3 h5 h2 u v hu hv ih
        (le_of_lt (lt_of_not_ge hfive)) hhigh
end Green24Proof.RatioCoverSix
private def zz2268:"s08dc"="s08dc":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileEnergyOrientation
open FullPhaseRows (Phase)
open PhaseMassRows ProfileOrientation
theorem energy_comp_equiv {ι κ:Type*} [Fintype ι] [Fintype κ]
    (e:ι ≃ κ) (g:κ → ℝ):energy (fun i => g (e i)) = energy g:=by
  unfold energy
  have hi (i:ι):(∑ j:ι,rho (g (e i)) (g (e j))) =
      ∑ j:κ,rho (g (e i)) (g j):=e.sum_comp (fun j:κ => rho (g (e i)) (g j))
  simp_rw [hi]
  rw [e.sum_comp (fun i:κ => ∑ j:κ,rho (g i) (g j))]
theorem energy_translate {m:ℕ} [NeZero m] (g:ZMod m → ℝ) (t:ZMod m) :
    energy (fun i => g (i + t)) = energy g:=energy_comp_equiv (Equiv.addRight t) g
theorem orient_even_child {m:ℕ} [NeZero m] (h4:4 ∣ 2 * m) (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    ∃ u' v':ZMod m → ℝ,(∀ i,0 ≤ u' i) ∧ (∀ i,0 ≤ v' i) ∧
      mass u' = mass u ∧ mass v' = mass v ∧ deficit (interleave u' v') = deficit (interleave u v) ∧
      energy (interleave u' v') = energy (interleave u v) ∧
      phaseTotal h4 (interleave u' v') 2 ≤ phaseTotal h4 (interleave u' v') 0:=by
  rcases le_total (phaseTotal h4 (interleave u v) 2) (phaseTotal h4 (interleave u v) 0) with h | h
  · exact ⟨u,v,hu,hv,rfl,rfl,rfl,rfl,h⟩
  · refine ⟨(fun i => u (i + 1)),(fun i => v (i + 1)),(fun i => hu _),(fun i => hv _),
      mass_translate u 1,mass_translate v 1, ?_, ?_, ?_⟩
    · rw [interleave_translate,deficit_translate]
    · rw [interleave_translate,energy_translate]
    · rw [phaseTotal_shift_children,phaseTotal_shift_children]
      simpa only [zero_add,show (2 + 2:Phase) = 0 from rfl] using h
end Green24Proof.ProfileEnergyOrientation
private def zz2269:"s08dd"="s08dd":=by decide+kernel
end 
section 
namespace Green24Proof.ParentParityOrientation
open ProfileEnergyOrientation
private def zz960:"s03c0"="s03c0":=by decide+kernel
theorem parityEquiv_even_add_one {m:ℕ} [NeZero m] (i:ZMod m) :
    parityEquiv m (0,i) + 1 = parityEquiv m (1,i):=by
  simp only [parityEquiv_apply,ZMod.val_zero,ZMod.val_one,Nat.cast_zero,
    Nat.cast_one,add_zero]
theorem parityEquiv_odd_add_one {m:ℕ} [NeZero m] (i:ZMod m) :
    parityEquiv m (1,i) + 1 = parityEquiv m (0,i + 1):=by
  have h:doubleResidue m 1 = 2:=by simpa using doubleResidue_natCast m 1
  simp only [parityEquiv_apply,ZMod.val_zero,ZMod.val_one,Nat.cast_zero,
    Nat.cast_one,map_add,h,add_zero]
  ring
theorem interleave_swap_translate {m:ℕ} [NeZero m] (u v:ZMod m → ℝ) :
    interleave v (fun i => u (i + 1)) = fun i => interleave u v (i + 1):=by
  funext x
  obtain ⟨⟨r,i⟩,rfl⟩:=(parityEquiv m).surjective x
  rcases zmod_two_eq_zero_or_one r with rfl | rfl
  · rw [parityEquiv_even_add_one,interleave_even,interleave_odd]
  · rw [parityEquiv_odd_add_one,interleave_odd,interleave_even]
theorem orient_parent {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    ∃ u' v':ZMod m → ℝ,(∀ i,0 ≤ u' i) ∧ (∀ i,0 ≤ v' i) ∧
      mass (interleave u' v') = mass (interleave u v) ∧
      deficit (interleave u' v') = deficit (interleave u v) ∧
      energy (interleave u' v') = energy (interleave u v) ∧
      mass v' ≤ mass u':=by
  rcases le_total (mass v) (mass u) with h | h
  · exact ⟨u,v,hu,hv,rfl,rfl,rfl,h⟩
  · refine ⟨v,(fun i => u (i + 1)),hv,(fun i => hu _), ?_, ?_, ?_, ?_⟩
    · rw [interleave_swap_translate,mass_translate]
    · rw [interleave_swap_translate,deficit_translate]
    · rw [interleave_swap_translate,energy_translate]
    · simpa only [mass_translate] using h
private def zz961:"s03c1"="s03c1":=by decide+kernel
theorem orient_parent_with_child_masses {m:ℕ} [NeZero m] (u v:ZMod m → ℝ)
    (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i) :
    ∃ u' v':ZMod m → ℝ,(∀ i,0 ≤ u' i) ∧ (∀ i,0 ≤ v' i) ∧
      mass (interleave u' v') = mass (interleave u v) ∧
      deficit (interleave u' v') = deficit (interleave u v) ∧
      energy (interleave u' v') = energy (interleave u v) ∧
      mass v' ≤ mass u' ∧
      ((mass u' = mass u ∧ mass v' = mass v) ∨
        (mass u' = mass v ∧ mass v' = mass u)):=by
  rcases le_total (mass v) (mass u) with h | h
  · exact ⟨u,v,hu,hv,rfl,rfl,rfl,h,Or.inl ⟨rfl,rfl⟩⟩
  · refine ⟨v,(fun i => u (i + 1)),hv,(fun i => hu _), ?_, ?_, ?_, ?_, ?_⟩
    · rw [interleave_swap_translate,mass_translate]
    · rw [interleave_swap_translate,deficit_translate]
    · rw [interleave_swap_translate,energy_translate]
    · simpa only [mass_translate] using h
    · exact Or.inr ⟨rfl,mass_translate u 1⟩
end Green24Proof.ParentParityOrientation
private def zz2270:"s08de"="s08de":=by decide+kernel
end 
section 
namespace Green24Proof.ProfileInduction
def ProperDivisorNonneg (q:ℕ):Prop :=
  ∀ (n:ℕ) [NeZero n],n < q → n ∣ q →
    ∀ (g:ZMod n → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g
theorem deficit_nonneg_of_ordered_parity_step
    (step:∀ (m:ℕ) [NeZero m],
      4 ∣ 2 * m → 3 ∣ 2 * m → 2 ∣ m → ¬5 ∣ 2 * m →
      ∀ (u v:ZMod m → ℝ),(∀ i,0 ≤ u i) → (∀ i,0 ≤ v i) →
      ProperDivisorNonneg (2 * m) → mass v ≤ mass u →
      0 ≤ deficit (interleave u v)) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g:=by
  intro q
  induction q using Nat.strong_induction_on with
  | h q ih =>
    intro hq h5 g hg
    by_cases h12:12 ∣ q
    · have h2:2 ∣ q:=dvd_trans (by decide:2 ∣ 12) h12
      obtain ⟨m,rfl⟩:=h2
      have hm:m ≠ 0:=by
        intro hm
        exact NeZero.ne (2 * m) (by rw [hm,mul_zero])
      have:NeZero m:=⟨hm⟩
      have h4:4 ∣ 2 * m:=dvd_trans (by decide:4 ∣ 12) h12
      have h3:3 ∣ 2 * m:=dvd_trans (by decide:3 ∣ 12) h12
      have h2m:2 ∣ m:=by
        obtain ⟨k,hk⟩:=h4
        exact ⟨k,by omega⟩
      have hproper:ProperDivisorNonneg (2 * m):=by
        intro n hn hnlt hndvd f hf
        exact ih n hnlt (fun h5n => h5 (dvd_trans h5n hndvd)) f hf
      let u:=ProfileChildren.child g 0
      let v:=ProfileChildren.child g 1
      have hu:∀ i,0 ≤ u i:=ProfileChildren.child_nonneg g hg 0
      have hv:∀ i,0 ≤ v i:=ProfileChildren.child_nonneg g hg 1
      obtain ⟨u',v',hu',hv',_,hd,_,horder⟩ :=
        ParentParityOrientation.orient_parent u v hu hv
      have hs:=step m h4 h3 h2m h5 u' v' hu' hv' hproper horder
      rw [hd] at hs
      simpa only [u,v,ProfileChildren.interleave_children] using hs
    · exact deficit_nonneg_of_twelve_not_dvd h12 g hg
end Green24Proof.ProfileInduction
private def zz2271:"s08df"="s08df":=by decide+kernel
end 
section 
namespace Green24Proof.PeriodicLiftMasses
theorem periodicLift_nonneg {q:ℕ} [NeZero q] (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i):∀ i,0 ≤ periodicLift g i:=by
  intro i
  exact mul_nonneg (by norm_num) (hg _)
theorem classMass_periodicLift {q:ℕ} [NeZero q] (h2:2 ∣ q)
    (g:ZMod q → ℝ) (r:ZMod 2) :
    classMass (ZMod.castHom (dvd_mul_right 2 q) (ZMod 2)) (periodicLift g) r =
      classMass (ZMod.castHom h2 (ZMod 2)) g r:=by
  let π:=ZMod.castHom (dvd_mul_left q 2) (ZMod q)
  have he (i:ZMod (2 * q)) :
      ZMod.castHom (dvd_mul_right 2 q) (ZMod 2) i = ZMod.castHom h2 (ZMod 2) (π i) :=
    (congrArg (fun f:ZMod (2 * q) →+* ZMod 2 => f i)
      (ZMod.castHom_comp h2 (dvd_mul_left q 2))).symm
  unfold classMass periodicLift
  simp only [he]
  change (∑ i:ZMod (2 * q),if ZMod.castHom h2 (ZMod 2) (π i) = r then
    (1 / 2:ℝ) * g (π i) else 0) = _
  have hp (i:ZMod (2 * q)) :
      (if ZMod.castHom h2 (ZMod 2) (π i) = r then (1 / 2:ℝ) * g (π i) else 0) =
        (1 / 2:ℝ) * (if ZMod.castHom h2 (ZMod 2) (π i) = r then g (π i) else 0):=by
    split_ifs <;> ring
  simp_rw [hp]
  rw [← Finset.mul_sum,sum_comp_eq_card π 2 double_quotient_fibers
    (fun i:ZMod q => if ZMod.castHom h2 (ZMod 2) i = r then g i else 0)]
  norm_num
  ring
private def zz962:"s03c2"="s03c2":=by decide+kernel
theorem child_mass_periodicLift {q:ℕ} [NeZero q] (h2:2 ∣ q)
    (g:ZMod q → ℝ) (r:ZMod 2) :
    mass (ProfileChildren.child (periodicLift g) r) =
      classMass (ZMod.castHom h2 (ZMod 2)) g r:=by
  rw [ProfileChildren.child_mass,classMass_periodicLift h2]
end Green24Proof.PeriodicLiftMasses
private def zz2272:"s08e0"="s08e0":=by decide+kernel
end 
section 
namespace Green24Proof.LiftedHeightBounds
open ProfileChildren PeriodicLiftMasses
theorem of_interleave_bound {q:ℕ} [NeZero q] (h2:2 ∣ q)
    (c:ℝ) (Q:ℝ → ℝ → ℝ) (u:ZMod q → ℝ) (hu:∀ i,0 ≤ u i)
    (hAB:classMass (ZMod.castHom h2 (ZMod 2)) u 1 ≤
      classMass (ZMod.castHom h2 (ZMod 2)) u 0)
    (hbound:∀ a b:ZMod q → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      mass b ≤ mass a →
      c * energy (interleave a b) + Q (mass a) (mass b) ≤ deficit (interleave a b)) :
    c * energy u + Q (classMass (ZMod.castHom h2 (ZMod 2)) u 0)
      (classMass (ZMod.castHom h2 (ZMod 2)) u 1) ≤ deficit u:=by
  have hnonneg:=periodicLift_nonneg u hu
  have h:=hbound (child (periodicLift u) 0) (child (periodicLift u) 1)
    (child_nonneg _ hnonneg 0) (child_nonneg _ hnonneg 1)
    (by simpa only [child_mass_periodicLift h2] using hAB)
  simpa only [interleave_children,child_mass_periodicLift h2,
    energy_periodicLift u hu,deficit_periodicLift] using h
theorem of_interleave_certificate {q:ℕ} [NeZero q]
    (h2:2 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ 2 * q)
    (c:ℝ) (Q:ℝ → ℝ → ℝ) (u:ZMod q → ℝ) (hu:∀ i,0 ≤ u i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * q → n ∣ 2 * q →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hAB:classMass (ZMod.castHom h2 (ZMod 2)) u 1 ≤
      classMass (ZMod.castHom h2 (ZMod 2)) u 0)
    (hcertificate:(4 ∣ 2 * q) → (3 ∣ 2 * q) → (¬5 ∣ 2 * q) → (2 ∣ q) →
      ∀ a b:ZMod q → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      (∀ (n:ℕ) [NeZero n],n < 2 * q → n ∣ 2 * q →
        ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w) →
      mass b ≤ mass a →
      c * energy (interleave a b) + Q (mass a) (mass b) ≤ deficit (interleave a b)) :
    c * energy u + Q (classMass (ZMod.castHom h2 (ZMod 2)) u 0)
      (classMass (ZMod.castHom h2 (ZMod 2)) u 1) ≤ deficit u:=by
  have h4:4 ∣ 2 * q:=by
    rcases h2 with ⟨k,hk⟩
    exact ⟨k,by omega⟩
  apply of_interleave_bound h2 c Q u hu hAB
  intro a b ha hb hmass
  exact hcertificate h4 (dvd_mul_of_dvd_right h3 2) h5 h2 a b ha hb ih hmass
end Green24Proof.LiftedHeightBounds
private def zz2273:"s08e1"="s08e1":=by decide+kernel
end 
section 
namespace Green24Proof.OrientedOverlapBounds
open ParentParityOrientation ProfileChildren
theorem interleave_overlap_bound {n:ℕ} [NeZero n]
    (w z:ZMod n → ℝ) (hw:∀ i,0 ≤ w i) (hz:∀ i,0 ≤ z i) (R:ℝ)
    (hd:0 ≤ deficit (interleave w z))
    (hsharp:R ≤ mass (interleave w z) + Real.sqrt (8 * energy (interleave w z)))
    (hparity0:R ≤ 6 * mass w) (hparity1:R ≤ 6 * mass z)
    (h12:∀ a b:ZMod n → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      mass b ≤ mass a →
      (2 / 5) * energy (interleave a b) + Q12 (mass a) (mass b) ≤ deficit (interleave a b))
    (h18:∀ a b:ZMod n → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      mass b ≤ mass a →
      (2 / 5) * energy (interleave a b) + Q18 (mass a) (mass b) ≤ deficit (interleave a b)) :
    mass (interleave w z) * R ≤
      (61 / 32) * mass (interleave w z) ^ 2 + 8 * deficit (interleave w z):=by
  obtain ⟨a,b,ha,hb,hM,hd',hE,horder,hpair⟩ :=
    orient_parent_with_child_masses w z hw hz
  have hR:R ≤ 6 * mass b:=by
    rcases hpair with ⟨_,hB⟩ | ⟨_,hB⟩
    · simpa only [hB] using hparity1
    · simpa only [hB] using hparity0
  have hsharp':R ≤ mass a + mass b + Real.sqrt (8 * energy (interleave a b)):=by
    rw [← mass_interleave,hM,hE]
    exact hsharp
  have h:=overlap_bound (mass_nonneg hb) horder
    (energy_nonneg (interleave_nonneg a b ha hb))
    (by simpa only [hd'] using hd) hsharp' hR
    (h12 a b ha hb horder) (h18 a b ha hb horder)
  simpa only [← mass_interleave,hM,hd'] using h
private def zz963:"s03c3"="s03c3":=by decide+kernel
theorem profile_overlap_bound {n:ℕ} [NeZero n]
    (u:ZMod (2 * n) → ℝ) (hu:∀ i,0 ≤ u i) (R:ℝ) (hd:0 ≤ deficit u)
    (hsharp:R ≤ mass u + Real.sqrt (8 * energy u))
    (hparity0:R ≤ 6 * mass (child u 0)) (hparity1:R ≤ 6 * mass (child u 1))
    (h12:∀ a b:ZMod n → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      mass b ≤ mass a →
      (2 / 5) * energy (interleave a b) + Q12 (mass a) (mass b) ≤ deficit (interleave a b))
    (h18:∀ a b:ZMod n → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
      mass b ≤ mass a →
      (2 / 5) * energy (interleave a b) + Q18 (mass a) (mass b) ≤ deficit (interleave a b)) :
    mass u * R ≤ (61 / 32) * mass u ^ 2 + 8 * deficit u:=by
  have h:=interleave_overlap_bound (child u 0) (child u 1)
    (child_nonneg u hu 0) (child_nonneg u hu 1) R
    (by simpa only [interleave_children] using hd)
    (by simpa only [interleave_children] using hsharp) hparity0 hparity1 h12 h18
  simpa only [interleave_children] using h
end Green24Proof.OrientedOverlapBounds
private def zz2274:"s08e2"="s08e2":=by decide+kernel
end 
section 
namespace Green24Proof.BoundaryFromHeightCertificates
open ProfileChildren
def HeightCertificate (m:ℕ) [NeZero m] (Q:ℝ → ℝ → ℝ):Prop :=
  (4 ∣ 2 * m) → (3 ∣ 2 * m) → (¬5 ∣ 2 * m) → (2 ∣ m) →
  ∀ a b:ZMod m → ℝ,(∀ i,0 ≤ a i) → (∀ i,0 ≤ b i) →
    (∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w) →
    mass b ≤ mass a →
    (2 / 5) * energy (interleave a b) + Q (mass a) (mass b) ≤ deficit (interleave a b)
theorem overlap_bound_of_certificates {m:ℕ} [NeZero m]
    (h2:2 ∣ m) (h3:3 ∣ m) (h5:¬5 ∣ 2 * m)
    (u:ZMod m → ℝ) (hu:∀ i,0 ≤ u i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hcertificate12:HeightCertificate m Q12)
    (hcertificate18:HeightCertificate m Q18) :
    mass u * overlapMaximum u ≤ (61 / 32) * mass u ^ 2 + 8 * deficit u:=by
  have hdu:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
  have h12w (w:ZMod m → ℝ) (hw:∀ i,0 ≤ w i)
      (hAB:classMass (ZMod.castHom h2 (ZMod 2)) w 1 ≤
        classMass (ZMod.castHom h2 (ZMod 2)) w 0) :
      (2 / 5) * energy w + Q12 (classMass (ZMod.castHom h2 (ZMod 2)) w 0)
        (classMass (ZMod.castHom h2 (ZMod 2)) w 1) ≤ deficit w :=
    LiftedHeightBounds.of_interleave_certificate h2 h3 h5 (2 / 5) Q12 w hw ih hAB hcertificate12
  have h18w (w:ZMod m → ℝ) (hw:∀ i,0 ≤ w i)
      (hAB:classMass (ZMod.castHom h2 (ZMod 2)) w 1 ≤
        classMass (ZMod.castHom h2 (ZMod 2)) w 0) :
      (2 / 5) * energy w + Q18 (classMass (ZMod.castHom h2 (ZMod 2)) w 0)
        (classMass (ZMod.castHom h2 (ZMod 2)) w 1) ≤ deficit w :=
    LiftedHeightBounds.of_interleave_certificate h2 h3 h5 (2 / 5) Q18 w hw ih hAB hcertificate18
  rcases h2 with ⟨n,rfl⟩
  have hn:0 < n:=by have hp:=NeZero.pos (2 * n); omega
  let:NeZero n:=⟨Nat.ne_of_gt hn⟩
  have hparity0:overlapMaximum u ≤ 6 * mass (child u 0):=by
    rw [child_mass]
    exact overlapMaximum_parity (dvd_mul_right 2 n) u hu 0
  have hparity1:overlapMaximum u ≤ 6 * mass (child u 1):=by
    rw [child_mass]
    exact overlapMaximum_parity (dvd_mul_right 2 n) u hu 1
  apply OrientedOverlapBounds.profile_overlap_bound u hu (overlapMaximum u) hdu
    (overlapMaximum_sharp u hu) hparity0 hparity1
  · intro a b ha hb hAB
    have h:=h12w (interleave a b) (interleave_nonneg a b ha hb)
      (by simpa only [classMass_interleave_even,classMass_interleave_odd] using hAB)
    simpa only [classMass_interleave_even,classMass_interleave_odd] using h
  · intro a b ha hb hAB
    have h:=h18w (interleave a b) (interleave_nonneg a b ha hb)
      (by simpa only [classMass_interleave_even,classMass_interleave_odd] using hAB)
    simpa only [classMass_interleave_even,classMass_interleave_odd] using h
theorem boundary_nonneg_of_certificates {m:ℕ} [NeZero m]
    (h2:2 ∣ m) (h3:3 ∣ m) (h5:¬5 ∣ 2 * m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hU:0 < mass u) (hratio:16 * mass v ≤ mass u)
    (hcertificate12:HeightCertificate m Q12)
    (hcertificate18:HeightCertificate m Q18) :
    0 ≤ deficit (interleave u v):=by
  have hm:m < 2 * m:=by have hp:=NeZero.pos m; omega
  exact boundary_nonneg hU (mass_nonneg hv) hratio
    (ih m hm (dvd_mul_left m 2) u hu) (ih m hm (dvd_mul_left m 2) v hv)
    (overlap_bound_of_certificates h2 h3 h5 u hu ih hcertificate12 hcertificate18)
    (deficit_interleave_expansion u v hu hv (overlap_le_maximum u))
end Green24Proof.BoundaryFromHeightCertificates
private def zz2275:"s08e3"="s08e3":=by decide+kernel
end 
section 
namespace Green24Proof.ConditionalProfileEndpoint
open ProfileInduction BoundaryFromHeightCertificates
def RatioToSixteen:Prop :=
  ∀ (m:ℕ) [NeZero m],
    4 ∣ 2 * m → 3 ∣ 2 * m → ¬5 ∣ 2 * m → 2 ∣ m →
    ∀ u v:ZMod m → ℝ,(∀ i,0 ≤ u i) → (∀ i,0 ≤ v i) →
      ProperDivisorNonneg (2 * m) → mass v ≤ mass u → mass u ≤ 16 * mass v →
      0 ≤ deficit (interleave u v)
theorem deficit_nonneg_of_certificates
    (hratio:RatioToSixteen)
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g:=by
  apply deficit_nonneg_of_ordered_parity_step
  intro m _ h4 h3 h2 h5 u v hu hv ih horder
  by_cases hhigh:mass u ≤ 16 * mass v
  · exact hratio m h4 h3 h5 h2 u v hu hv ih horder hhigh
  · have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
    have hU:0 < mass u:=by linarith [mass_nonneg hv]
    exact boundary_nonneg_of_certificates h2 h3m h5 u v hu hv ih hU
      (le_of_lt (lt_of_not_ge hhigh)) (hcertificate12 m) (hcertificate18 m)
private def zz964:"s03c4"="s03c4":=by decide+kernel
theorem profileFunctional_le_of_certificates
    (hratio:RatioToSixteen)
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18)
    (q:ℕ) [NeZero q] (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    profileFunctional g ≤ 2 * mass g ^ 2:=by
  exact sub_nonneg.mp (deficit_nonneg_of_certificates hratio hcertificate12 hcertificate18 q h5 g hg)
end Green24Proof.ConditionalProfileEndpoint
private def zz2276:"s08e4"="s08e4":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCoverSixteenFromRemaining
open ProfileInduction BoundaryFromHeightCertificates ConditionalProfileEndpoint
def IntervalCertificate (L H:ℝ):Prop :=
  ∀ (m:ℕ) [NeZero m],
    4 ∣ 2 * m → 3 ∣ 2 * m → ¬5 ∣ 2 * m → 2 ∣ m →
    ∀ u v:ZMod m → ℝ,(∀ i,0 ≤ u i) → (∀ i,0 ≤ v i) →
      ProperDivisorNonneg (2 * m) → L * mass v ≤ mass u → mass u ≤ H * mass v →
      0 ≤ deficit (interleave u v)
theorem ratio_to_sixteen_of_remaining
    (h68:IntervalCertificate 6 8)
    (h812:IntervalCertificate 8 12)
    (h1216:IntervalCertificate 12 16):RatioToSixteen:=by
  intro m _ h4 h3 h5 h2 u v hu hv ih horder hhigh
  by_cases hsix:mass u ≤ 6 * mass v
  · exact RatioCoverSix.interval_to_six h4 h3 h5 h2 u v hu hv ih horder hsix
  · by_cases height:mass u ≤ 8 * mass v
    · exact h68 m h4 h3 h5 h2 u v hu hv ih (le_of_lt (lt_of_not_ge hsix)) height
    · by_cases htwelve:mass u ≤ 12 * mass v
      · exact h812 m h4 h3 h5 h2 u v hu hv ih (le_of_lt (lt_of_not_ge height)) htwelve
      · exact h1216 m h4 h3 h5 h2 u v hu hv ih (le_of_lt (lt_of_not_ge htwelve)) hhigh
theorem deficit_nonneg_of_remaining
    (h68:IntervalCertificate 6 8)
    (h812:IntervalCertificate 8 12)
    (h1216:IntervalCertificate 12 16)
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g :=
  deficit_nonneg_of_certificates (ratio_to_sixteen_of_remaining h68 h812 h1216)
    hcertificate12 hcertificate18
end Green24Proof.RatioCoverSixteenFromRemaining
private def zz2277:"s08e5"="s08e5":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullEightPairs
def compact_fullEight_pair_20_base:CompactPair.Quadratic:=⟨(-17 / 0x2cb417800),(0x7cf / 0x77359400),0⟩
def compact_fullEight_pair_20_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-0x2b81fed / 0x3b9aca00),1, -2⟩,⟨(0x686b305 / 0xee6b2800),2, -3⟩,⟨(0x2b81fed / 0x3b9aca00),2, -1⟩,⟨(-0x686b305 / 0xee6b2800),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩]
noncomputable def fullEight_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_20_base compact_fullEight_pair_20_hinges x y
def compact_fullEight_pair_20_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullEight_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_20_base compact_fullEight_pair_20_hinges 0 compact_fullEight_pair_20_cuts = true :=
  by decide +kernel
private def zz965:"s03c5"="s03c5":=by decide+kernel
theorem compact_fullEight_pair_20_representation (x y:ℝ) :
    fullEight_pair_20 x y = CompactPair.expressionEval compact_fullEight_pair_20_base compact_fullEight_pair_20_hinges x y:=by rfl
theorem fullEight_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_20 x y:=by
  rw [compact_fullEight_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_20_check hy (by simpa using hx)
def compact_fullEight_pair_21_base:CompactPair.Quadratic:=⟨(1 / 0x59682f000),(0x18d / 0x3b9aca00),0⟩
def compact_fullEight_pair_21_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x2cb417800),3, -2⟩]
noncomputable def fullEight_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_21_base compact_fullEight_pair_21_hinges x y
def compact_fullEight_pair_21_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2]
theorem compact_fullEight_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_21_base compact_fullEight_pair_21_hinges 0 compact_fullEight_pair_21_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_21_representation (x y:ℝ) :
    fullEight_pair_21 x y = CompactPair.expressionEval compact_fullEight_pair_21_base compact_fullEight_pair_21_hinges x y:=by rfl
private def zz966:"s03c6"="s03c6":=by decide+kernel
theorem fullEight_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_21 x y:=by
  rw [compact_fullEight_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_21_check hy (by simpa using hx)
def compact_fullEight_pair_22_base:CompactPair.Quadratic:=⟨0,(0x15f / 0xee6b280),0⟩
def compact_fullEight_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullEight_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_22_base compact_fullEight_pair_22_hinges x y
def compact_fullEight_pair_22_cuts:List ℚ:=[]
theorem compact_fullEight_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_22_base compact_fullEight_pair_22_hinges 0 compact_fullEight_pair_22_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_22_representation (x y:ℝ) :
    fullEight_pair_22 x y = CompactPair.expressionEval compact_fullEight_pair_22_base compact_fullEight_pair_22_hinges x y:=by rfl
theorem fullEight_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_22 x y:=by
  rw [compact_fullEight_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_22_check hy (by simpa using hx)
def compact_fullEight_pair_23_base:CompactPair.Quadratic:=⟨(-0x6a19ce1e1 / 0x59682f000),(0x280088ab / 0x3b9aca00),0⟩
def compact_fullEight_pair_23_hinges:List CompactPair.Hinge:=[⟨(-0x4d574fb / 0x2faf0800),1, -3⟩,⟨(0x2f1fa253 / 0x5f5e1000),1, -2⟩,⟨(-0x15e4af / 0x5f5e100),1, -1⟩,⟨(-0x860bd6f / 0x47868c00),2, -3⟩,⟨(0xac9d0e9b / 0xee6b2800),2, -1⟩,⟨(-0x2ae479d7 / 0xee6b2800),3, -2⟩]
noncomputable def fullEight_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_23_base compact_fullEight_pair_23_hinges x y
def compact_fullEight_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz967:"s03c7"="s03c7":=by decide+kernel
theorem compact_fullEight_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_23_base compact_fullEight_pair_23_hinges 0 compact_fullEight_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_23_representation (x y:ℝ) :
    fullEight_pair_23 x y = CompactPair.expressionEval compact_fullEight_pair_23_base compact_fullEight_pair_23_hinges x y:=by rfl
theorem fullEight_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_23 x y:=by
  rw [compact_fullEight_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_23_check hy (by simpa using hx)
def compact_fullEight_pair_24_base:CompactPair.Quadratic:=⟨(-0x33965db9 / 0x165a0bc00),(0x149862b / 0x1a13b860),0⟩
def compact_fullEight_pair_24_hinges:List CompactPair.Hinge:=[⟨(0x2505965 / 0x59682f00),1, -3⟩,⟨(-0x1966e893 / 0x77359400),1, -2⟩,⟨(0x45f3ee7 / 0x3b9aca00),2, -3⟩,⟨(-0x225f50b7 / 0x3b9aca00),2, -1⟩,⟨(0x60eaa13 / 0x3b9aca00),3, -2⟩,⟨(0xe34fc5f / 0x59682f00),3, -1⟩]
noncomputable def fullEight_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_24_base compact_fullEight_pair_24_hinges x y
def compact_fullEight_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullEight_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_24_base compact_fullEight_pair_24_hinges 0 compact_fullEight_pair_24_cuts = true :=
  by decide +kernel
private def zz968:"s03c8"="s03c8":=by decide+kernel
theorem compact_fullEight_pair_24_representation (x y:ℝ) :
    fullEight_pair_24 x y = CompactPair.expressionEval compact_fullEight_pair_24_base compact_fullEight_pair_24_hinges x y:=by rfl
theorem fullEight_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_24 x y:=by
  rw [compact_fullEight_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_24_check hy (by simpa using hx)
def compact_fullEight_pair_25_base:CompactPair.Quadratic:=⟨(23 / 0x59682f000),(0x15c3 / 0x342770c00),0⟩
def compact_fullEight_pair_25_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(1 / 0x59682f000),2, -3⟩,⟨(-1 / 0x2cb417800),3, -2⟩]
noncomputable def fullEight_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_25_base compact_fullEight_pair_25_hinges x y
def compact_fullEight_pair_25_cuts:List ℚ:=[(2 / 3),1,(3 / 2),2]
theorem compact_fullEight_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_25_base compact_fullEight_pair_25_hinges 0 compact_fullEight_pair_25_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_25_representation (x y:ℝ) :
    fullEight_pair_25 x y = CompactPair.expressionEval compact_fullEight_pair_25_base compact_fullEight_pair_25_hinges x y:=by rfl
private def zz969:"s03c9"="s03c9":=by decide+kernel
theorem fullEight_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_25 x y:=by
  rw [compact_fullEight_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_25_check hy (by simpa using hx)
def compact_fullEight_pair_26_base:CompactPair.Quadratic:=⟨(-1 / 0xb2d05e00),(0x15f / 0xee6b280),0⟩
def compact_fullEight_pair_26_hinges:List CompactPair.Hinge:=[⟨(-0x1af9a1 / 0x77359400),1, -3⟩,⟨(-0x88baf / 0x17d78400),1, -1⟩,⟨(0xa9997 / 0x59682f00),2, -3⟩,⟨(0x695c9 / 0xee6b2800),2, -1⟩]
noncomputable def fullEight_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_26_base compact_fullEight_pair_26_hinges x y
def compact_fullEight_pair_26_cuts:List ℚ:=[(1 / 2),1,(3 / 2),3]
theorem compact_fullEight_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_26_base compact_fullEight_pair_26_hinges 0 compact_fullEight_pair_26_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_26_representation (x y:ℝ) :
    fullEight_pair_26 x y = CompactPair.expressionEval compact_fullEight_pair_26_base compact_fullEight_pair_26_hinges x y:=by rfl
theorem fullEight_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_26 x y:=by
  rw [compact_fullEight_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_26_check hy (by simpa using hx)
def compact_fullEight_pair_27_base:CompactPair.Quadratic:=⟨(-0xf3ef33aa9 / 0x59682f000),(0x821932e5 / 0x77359400),0⟩
def compact_fullEight_pair_27_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-0x10432593f / 0x1dcd65000),2, -1⟩,⟨(0x27078d63 / 0x47868c00),3, -1⟩]
noncomputable def fullEight_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_27_base compact_fullEight_pair_27_hinges x y
def compact_fullEight_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
private def zz970:"s03ca"="s03ca":=by decide+kernel
theorem compact_fullEight_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_27_base compact_fullEight_pair_27_hinges 0 compact_fullEight_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_27_representation (x y:ℝ) :
    fullEight_pair_27 x y = CompactPair.expressionEval compact_fullEight_pair_27_base compact_fullEight_pair_27_hinges x y:=by rfl
theorem fullEight_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_27 x y:=by
  rw [compact_fullEight_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_27_check hy (by simpa using hx)
def compact_fullEight_pair_28_base:CompactPair.Quadratic:=⟨(-0x14756e72529 / 0xae9f7bcc00),(-0x1f304269b7 / 0x2ba7def300),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_28_hinges:List CompactPair.Hinge:=[⟨(-0x276b6979dd / 0x15d3ef79800),1, -3⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(0x276b6979dd / 0x15d3ef79800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_28_base compact_fullEight_pair_28_hinges x y
def compact_fullEight_pair_28_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullEight_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_28_base compact_fullEight_pair_28_hinges 0 compact_fullEight_pair_28_cuts = true :=
  by decide +kernel
private def zz971:"s03cb"="s03cb":=by decide+kernel
theorem compact_fullEight_pair_28_representation (x y:ℝ) :
    fullEight_pair_28 x y = CompactPair.expressionEval compact_fullEight_pair_28_base compact_fullEight_pair_28_hinges x y:=by rfl
theorem fullEight_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_28 x y:=by
  rw [compact_fullEight_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_28_check hy (by simpa using hx)
def compact_fullEight_pair_29_base:CompactPair.Quadratic:=⟨(-0x65cbf3f1d3 / 0x3a35294400),(-0x43dd4b15c5 / 0x574fbde600),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_29_hinges:List CompactPair.Hinge:=[⟨(-0xb4f8ce1fb / 0x746a528800),1, -3⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(0xb4f8ce1fb / 0x746a528800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_29_base compact_fullEight_pair_29_hinges x y
def compact_fullEight_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullEight_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_29_base compact_fullEight_pair_29_hinges 0 compact_fullEight_pair_29_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_29_representation (x y:ℝ) :
    fullEight_pair_29 x y = CompactPair.expressionEval compact_fullEight_pair_29_base compact_fullEight_pair_29_hinges x y:=by rfl
private def zz972:"s03cc"="s03cc":=by decide+kernel
theorem fullEight_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_29 x y:=by
  rw [compact_fullEight_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_29_check hy (by simpa using hx)
def compact_fullEight_pair_30_base:CompactPair.Quadratic:=⟨(-0xd218b3d / 0x1312d00),(0x17116df7b / 0x3b9aca00),0⟩
def compact_fullEight_pair_30_hinges:List CompactPair.Hinge:=[⟨(-0x1d67b0cd / 0xee6b2800),2, -3⟩,⟨(0xe4a6f63d / 0xb2d05e00),3, -1⟩]
noncomputable def fullEight_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_30_base compact_fullEight_pair_30_hinges x y
def compact_fullEight_pair_30_cuts:List ℚ:=[(1 / 3),(3 / 2)]
theorem compact_fullEight_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_30_base compact_fullEight_pair_30_hinges 0 compact_fullEight_pair_30_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_30_representation (x y:ℝ) :
    fullEight_pair_30 x y = CompactPair.expressionEval compact_fullEight_pair_30_base compact_fullEight_pair_30_hinges x y:=by rfl
theorem fullEight_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_30 x y:=by
  rw [compact_fullEight_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_30_check hy (by simpa using hx)
def compact_fullEight_pair_31_base:CompactPair.Quadratic:=⟨(13 / 0x1dcd65000),(0x31f / 0x3b9aca00),0⟩
def compact_fullEight_pair_31_hinges:List CompactPair.Hinge:=[⟨(-0x7ee33 / 0xe4e1c00),1, -3⟩,⟨(-0x31c28d / 0x9896800),1, -1⟩,⟨(0x48791 / 0x59682f0),2, -3⟩,⟨(0x192160f / 0x59682f000),3, -2⟩,⟨(-1 / 0x165a0bc00),3, -1⟩]
noncomputable def fullEight_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_31_base compact_fullEight_pair_31_hinges x y
def compact_fullEight_pair_31_cuts:List ℚ:=[(1 / 3),(2 / 3),1,(3 / 2),3]
private def zz973:"s03cd"="s03cd":=by decide+kernel
theorem compact_fullEight_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_31_base compact_fullEight_pair_31_hinges 0 compact_fullEight_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_31_representation (x y:ℝ) :
    fullEight_pair_31 x y = CompactPair.expressionEval compact_fullEight_pair_31_base compact_fullEight_pair_31_hinges x y:=by rfl
theorem fullEight_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_31 x y:=by
  rw [compact_fullEight_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_31_check hy (by simpa using hx)
def compact_fullEight_pair_32_base:CompactPair.Quadratic:=⟨(-0x4c80aa0b75 / 0xae9f7bcc00),(0x13b5b4e5c7 / 0xae9f7bcc0),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x1ebb50a39f9 / 0x15d3ef79800),1, -3⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(0xb4f8ce1fb / 0x746a528800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_32_base compact_fullEight_pair_32_hinges x y
def compact_fullEight_pair_32_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullEight_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_32_base compact_fullEight_pair_32_hinges 0 compact_fullEight_pair_32_cuts = true :=
  by decide +kernel
private def zz974:"s03ce"="s03ce":=by decide+kernel
theorem compact_fullEight_pair_32_representation (x y:ℝ) :
    fullEight_pair_32 x y = CompactPair.expressionEval compact_fullEight_pair_32_base compact_fullEight_pair_32_hinges x y:=by rfl
theorem fullEight_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_32 x y:=by
  rw [compact_fullEight_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_32_check hy (by simpa using hx)
def compact_fullEight_pair_33_base:CompactPair.Quadratic:=⟨(-0x7bece2ebe7 / 0x574fbde600),(-0x5673ba4fe1 / 0x574fbde600),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0xb4f8ce1fb / 0x746a528800),1, -3⟩,⟨(-0x331c99 / 0x7735940),1, -2⟩,⟨(-0x3845939 / 0x1dcd6500),1, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(0x20818355 / 0x2cb417800),2, -3⟩,⟨(-0x1f4a0e77 / 0xee6b2800),2, -1⟩,⟨(0x21951ef / 0x77359400),3, -2⟩,⟨(0xb4f8ce1fb / 0x746a528800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_33_base compact_fullEight_pair_33_hinges x y
def compact_fullEight_pair_33_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullEight_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_33_base compact_fullEight_pair_33_hinges 0 compact_fullEight_pair_33_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_33_representation (x y:ℝ) :
    fullEight_pair_33 x y = CompactPair.expressionEval compact_fullEight_pair_33_base compact_fullEight_pair_33_hinges x y:=by rfl
private def zz975:"s03cf"="s03cf":=by decide+kernel
theorem fullEight_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_33 x y:=by
  rw [compact_fullEight_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_33_check hy (by simpa using hx)
def compact_fullEight_pair_34_base:CompactPair.Quadratic:=⟨(1 / 0x59682f00),(0x1b4b / 0x1a13b8600),0⟩
def compact_fullEight_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x4cdefc1 / 0xb2d05e00),1, -3⟩,⟨(0x3d7f301 / 0x17d78400),1, -2⟩,⟨(-0x147fbab / 0x17d78400),2, -3⟩,⟨(-0x3d7f301 / 0x17d78400),2, -1⟩,⟨(0x147fbab / 0x17d78400),3, -2⟩,⟨(0x4cdefc1 / 0xb2d05e00),3, -1⟩]
noncomputable def fullEight_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_34_base compact_fullEight_pair_34_hinges x y
def compact_fullEight_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullEight_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_34_base compact_fullEight_pair_34_hinges 0 compact_fullEight_pair_34_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_34_representation (x y:ℝ) :
    fullEight_pair_34 x y = CompactPair.expressionEval compact_fullEight_pair_34_base compact_fullEight_pair_34_hinges x y:=by rfl
theorem fullEight_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_34 x y:=by
  rw [compact_fullEight_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_34_check hy (by simpa using hx)
def compact_fullEight_pair_35_base:CompactPair.Quadratic:=⟨0,(0x15cd / 0x342770c00),0⟩
def compact_fullEight_pair_35_hinges:List CompactPair.Hinge:=[]
noncomputable def fullEight_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_35_base compact_fullEight_pair_35_hinges x y
def compact_fullEight_pair_35_cuts:List ℚ:=[]
private def zz976:"s03d0"="s03d0":=by decide+kernel
theorem compact_fullEight_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_35_base compact_fullEight_pair_35_hinges 0 compact_fullEight_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_35_representation (x y:ℝ) :
    fullEight_pair_35 x y = CompactPair.expressionEval compact_fullEight_pair_35_base compact_fullEight_pair_35_hinges x y:=by rfl
theorem fullEight_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_35 x y:=by
  rw [compact_fullEight_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_35_check hy (by simpa using hx)
def compact_fullEight_pair_36_base:CompactPair.Quadratic:=⟨(-0x1b3f025 / 0x1dcd6500),(0xa37a657 / 0x3b9aca00),0⟩
def compact_fullEight_pair_36_hinges:List CompactPair.Hinge:=[⟨(0x1b3f025 / 0x77359400),2, -3⟩]
noncomputable def fullEight_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_36_base compact_fullEight_pair_36_hinges x y
def compact_fullEight_pair_36_cuts:List ℚ:=[(3 / 2)]
theorem compact_fullEight_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_36_base compact_fullEight_pair_36_hinges 0 compact_fullEight_pair_36_cuts = true :=
  by decide +kernel
private def zz977:"s03d1"="s03d1":=by decide+kernel
theorem compact_fullEight_pair_36_representation (x y:ℝ) :
    fullEight_pair_36 x y = CompactPair.expressionEval compact_fullEight_pair_36_base compact_fullEight_pair_36_hinges x y:=by rfl
theorem fullEight_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_36 x y:=by
  rw [compact_fullEight_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_36_check hy (by simpa using hx)
def compact_fullEight_pair_37_base:CompactPair.Quadratic:=⟨(1 / 0x59682f000),(0x641 / 0x77359400),0⟩
def compact_fullEight_pair_37_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩]
noncomputable def fullEight_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_37_base compact_fullEight_pair_37_hinges x y
def compact_fullEight_pair_37_cuts:List ℚ:=[2,3]
theorem compact_fullEight_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_37_base compact_fullEight_pair_37_hinges 0 compact_fullEight_pair_37_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_37_representation (x y:ℝ) :
    fullEight_pair_37 x y = CompactPair.expressionEval compact_fullEight_pair_37_base compact_fullEight_pair_37_hinges x y:=by rfl
private def zz978:"s03d2"="s03d2":=by decide+kernel
theorem fullEight_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_37 x y:=by
  rw [compact_fullEight_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_37_check hy (by simpa using hx)
def compact_fullEight_pair_38_base:CompactPair.Quadratic:=⟨(-0x1369579306d / 0xae9f7bcc00),(-0x4010bd1029 / 0x574fbde600),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_38_hinges:List CompactPair.Hinge:=[⟨(-0xb4f8ce1fb / 0x746a528800),1, -3⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(-0x88270d / 0x59682f00),2, -3⟩,⟨(0x88270d / 0x59682f00),3, -2⟩,⟨(0xb4f8ce1fb / 0x746a528800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_38_base compact_fullEight_pair_38_hinges x y
def compact_fullEight_pair_38_cuts:List ℚ:=[(1 / 3),(2 / 3),(3 / 2),3]
theorem compact_fullEight_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_38_base compact_fullEight_pair_38_hinges 0 compact_fullEight_pair_38_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_38_representation (x y:ℝ) :
    fullEight_pair_38 x y = CompactPair.expressionEval compact_fullEight_pair_38_base compact_fullEight_pair_38_hinges x y:=by rfl
theorem fullEight_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_38 x y:=by
  rw [compact_fullEight_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_38_check hy (by simpa using hx)
def compact_fullEight_pair_39_base:CompactPair.Quadratic:=⟨(-0xcb976830bb / 0x746a528800),(-0x87bb15de75 / 0xae9f7bcc00),(-0xb4f8ce1fb / 0xba43b7400)⟩
def compact_fullEight_pair_39_hinges:List CompactPair.Hinge:=[⟨(-0xb4f8ce1fb / 0x746a528800),1, -3⟩,⟨(0x572d / 0xee6b2800),1, -2⟩,⟨(0xb4f8ce1fb / 0x746a528800),1,3⟩,⟨(-0x572d / 0xee6b2800),2, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3, -1⟩,⟨(0xb4f8ce1fb / 0x746a528800),3,1⟩]
noncomputable def fullEight_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullEight_pair_39_base compact_fullEight_pair_39_hinges x y
def compact_fullEight_pair_39_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
private def zz979:"s03d3"="s03d3":=by decide+kernel
theorem compact_fullEight_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullEight_pair_39_base compact_fullEight_pair_39_hinges 0 compact_fullEight_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullEight_pair_39_representation (x y:ℝ) :
    fullEight_pair_39 x y = CompactPair.expressionEval compact_fullEight_pair_39_base compact_fullEight_pair_39_hinges x y:=by rfl
theorem fullEight_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullEight_pair_39 x y:=by
  rw [compact_fullEight_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullEight_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullEightPairs
private def zz2278:"s08e6"="s08e6":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l42 l43 l45 l5 l51 l54 l55 l57 l58 l6 l60 l62 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x185d58c29, -0x2390c4a68, -0x355927260,0x4369a01c], ![-0x2390c4a68, -0x7adb31bea,0x95218c4a,0x24026ff16], ![-0x355927260,0x95218c4a, -0xe72d00244,0x2390c53c8], ![0x4369a01c,0x24026ff16,0x2390c53c8, -0x11c86278c]]
noncomputable def hinges:Hinges:=[(-0x6080b4,l6),(-0x1b3672fc,l5),(0xdb9ca96e,l4),(-0x7e23ac7b,l8),(-0x55185f2,l11),(0x280b6918,l10),(0x239db7946,l14),(-0x7a8613a4,l17),(0x61b58d2d,l23),(0xa0cbe79,l22),(-0x11c86278c,l27),(0x11c86278c,l29),(-0x239db7946,l25),(0x7549a63c,l31),(0xa267a8fe,l30),(0x11c86278c,l33),(-0x280b6918,l38),(-0x11c86278c,l35),(0x7e23ac7b,l36),(0x11c86278c,l37),(-0xdb9ca96e,l34),(-0xa267a8fe,l43),(-0xa0cbe79,l42),(0x555c7b2a,l45),(0x11c86278c,l51),(0x55185f2,l55),(0x1b3672fc,l54),(-0x7549a63c,l57),(-0x555c7b2a,l58),(0x6080b4,l60),(-0x61b58d2d,l63),(0x7a8613a4,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x11c86278c,l27),(0x11c86278c,l29),(0x11c86278c,l33),(-0x11c86278c,l35),(0x11c86278c,l37),(0x11c86278c,l51),(0x239db7946,l14),(-0x239db7946,l25),(0x7549a63c,l31),(-0x7549a63c,l57),(0xa267a8fe,l30),(-0xa267a8fe,l43),(0x61b58d2d,l23),(-0x61b58d2d,l63),(-0x7a8613a4,l17),(0x7a8613a4,l62),(-0x7e23ac7b,l8),(0x7e23ac7b,l36),(0xdb9ca96e,l4),(-0xdb9ca96e,l34),(0x555c7b2a,l45),(-0x555c7b2a,l58),(0x280b6918,l10),(-0x280b6918,l38),(-0x1b3672fc,l5),(0x1b3672fc,l54),(-0x55185f2,l11),(0x55185f2,l55),(0xa0cbe79,l22),(-0xa0cbe79,l42),(-0x6080b4,l6),(0x6080b4,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase0" = "QuadFullEightCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase0
private def zz2279:"s08e7"="s08e7":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l55 l58 l6 l60 l62 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x224a246d8, -0x22cc3e870, -0x34325df4e,0x2b8f38b2], ![-0x22cc3e870, -0x7c32aa016,0x67d40d62,0x25c96c134], ![-0x34325df4e,0x67d40d62, -0xe22f98578,0x22cc3f1d0], ![0x2b8f38b2,0x25c96c134,0x22cc3f1d0, -0x11661f690]]
noncomputable def hinges:Hinges:=[(-0x6080b4,l6),(-0x1b3672fc,l5),(0xdb9ca96e,l4),(-0x7e23ac7b,l8),(-0x55185f2,l11),(0x280b6918,l10),(0x20bed7a26,l14),(0x600e5bd8,l13),(-0x3751d142,l17),(0x2fa7be40c,l15),(0x169223e6,l21),(-0x600e5bd8,l20),(-0x13435adf,l23),(0x110ec745a,l22),(-0x11661f690,l27),(-0x169223e6,l28),(0x11661f690,l29),(-0x20bed7a26,l25),(0x89a5cd96,l30),(0x11661f690,l33),(-0x280b6918,l38),(-0x11661f690,l35),(0x7e23ac7b,l36),(0x11661f690,l37),(-0xdb9ca96e,l34),(-0x89a5cd96,l43),(-0x110ec745a,l42),(-0x2fa7be40c,l41),(-0x10ba7f12,l46),(0x9902e062,l45),(0x11661f690,l51),(0x55185f2,l55),(0x1b3672fc,l54),(-0x9902e062,l58),(0x6080b4,l60),(0x13435adf,l63),(0x3751d142,l62),(0x10ba7f12,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x11661f690,l27),(0x11661f690,l29),(0x11661f690,l33),(-0x11661f690,l35),(0x11661f690,l37),(0x11661f690,l51),(0x20bed7a26,l14),(-0x20bed7a26,l25),(0x2fa7be40c,l15),(-0x2fa7be40c,l41),(0x110ec745a,l22),(-0x110ec745a,l42),(0x89a5cd96,l30),(-0x89a5cd96,l43),(0x9902e062,l45),(-0x9902e062,l58),(-0x7e23ac7b,l8),(0x7e23ac7b,l36),(-0x3751d142,l17),(0x3751d142,l62),(0xdb9ca96e,l4),(-0xdb9ca96e,l34),(0x600e5bd8,l13),(-0x600e5bd8,l20),(0x280b6918,l10),(-0x280b6918,l38),(0x169223e6,l21),(-0x169223e6,l28),(-0x13435adf,l23),(0x13435adf,l63),(-0x10ba7f12,l46),(0x10ba7f12,l64),(-0x1b3672fc,l5),(0x1b3672fc,l54),(-0x55185f2,l11),(0x55185f2,l55),(-0x6080b4,l6),(0x6080b4,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((0xe28afc071f08235a17a1c382b4e526de4842eba780cd0036646d30002444d164098207c021c50ad16c283870f289bd070582b23614d080225cb3000070736da094207c0200001f840a427a48328823c3471c6e59d21861c278200d070a7d2bb812060f80403a4040001d04a28461ce0b03b05c460592153c9110073b5df54421fa82593d1023f1c142264042200851419244a343042099fc70082b68ff6cb1e0041a2c2149010840200001ac4a241734cf131c8dd24200007245f483f002f9e7a9842873db4192082b8e796b240c7296c75508000000a286ce08460109a21e6b23dcb251400001c445480e0413b30a8a38fabc0438334482000002bf20382309b26b7ce4800ab9c0594038022f7267a2a0001cca35ef3d2d20050040a2800002ed12b280e034c4a0c8ed1c7a53f8b03187a010398afc9b5089040000048c8d038229ee664f54b4400b07a9c8a87820007b515fc4780005b63249aeb7f0f2005a06000022c2000886648021749bd861b24128118984b87a88aa441000c9b66980857e430d41051034f368100000059f39c008402124800006c8b8c3677a8ae1a0c2866b4f0f32008250c44c19a081646cf990209e8b14caea400590e36b7900000000a8c0c00b317d9b7cc8012008000074c944028000d808004a310290994380e27ea711428a29e42406221c41966b9e13b0a9c992020e0040a18173441a07267e38ffaea10804c4515862ac1a20b25b96e54095943196460203c1de1298008402134411d98e7ec0071e8b8dba70c01414322b5d4a0e1311554bcaed73cd1066ee3374f04c0411d98a370c160000000927c0140063122e34363e84001601600007accd103d1f9decc1c0d11cc591c782f183819310e15e3e5350227940c6d4d0418ef960f980088021b5450d4000000034f0808992df7a580f8a689838e3a82a621a0ac028060000401a00021040009648002d518870a2cac9a60803d470010) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase1" = "QuadFullEightCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase1
private def zz2280:"s08e8"="s08e8":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l22 l27 l29 l33 l35 l37 l4 l51 l6 l62 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1d728a784c, -0x59682eb50, -0x319ae899c,0x7a9b8f18], ![-0x59682eb50, -0x2a965dceb0,0xfaf31fd60, -0x5b2521508], ![-0x319ae899c,0xfaf31fd60, -0x303c9f346d,0xa6967d720], ![0x7a9b8f18, -0x5b2521508,0xa6967d720, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x2bcf2460,l6),(0x9b7ff8a,l4),(0x6d7dbe67,l11),(0xe937f384,l10),(-0x2dd46ba0,l17),(0x19c77c894,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x3a985eaa8,l62),(0x146f41bc,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x3a985eaa8,l62),(0xe937f384,l10),(0x19c77c894,l22),(0x6d7dbe67,l11),(-0x2dd46ba0,l17),(-0x2bcf2460,l6),(0x146f41bc,l65),(0x9b7ff8a,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase2" = "QuadFullEightCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase2
private def zz2281:"s08e9"="s08e9":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l20 l21 l22 l23 l27 l29 l31 l33 l35 l37 l4 l41 l42 l44 l46 l51 l56 l6 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2ec79d8cf, -0x58a3a8958,0x731c6130c,0x4ac85f00], ![-0x58a3a8958, -0x2407b8cb96,0xd9e0a332c, -0x596316726], ![0x731c6130c,0xd9e0a332c, -0x2fecc8b7a1,0xa5d1f7528], ![0x4ac85f00, -0x596316726,0xa5d1f7528, -0x2c51d4704]]
noncomputable def hinges:Hinges:=[(-0x2bcf2460,l6),(0x9b7ff8a,l4),(0x6d7dbe67,l11),(0xe937f384,l10),(0xad62205c,l14),(0x6417f29a0,l13),(-0x639f7332,l16),(-0xba7a412,l15),(0xa78eccac,l21),(-0x40bae57a2,l20),(-0xd5c7c16,l23),(0x1813e4f92,l22),(-0x2c51d4704,l27),(0x2c51d4704,l29),(0x2449df82,l31),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(-0x5dde2b65,l42),(-0x54685d58,l41),(-0x4d3698,l46),(-0x21c59e2c,l44),(0x2c51d4704,l51),(-0x132ab960,l56),(0x247c896c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c51d4704,l27),(0x2c51d4704,l29),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(0x2c51d4704,l51),(0x6417f29a0,l13),(-0x40bae57a2,l20),(0xa78eccac,l21),(0xe937f384,l10),(0x1813e4f92,l22),(0xad62205c,l14),(0x6d7dbe67,l11),(0x2449df82,l31),(-0x639f7332,l16),(-0x5dde2b65,l42),(-0x2bcf2460,l6),(0x247c896c,l64),(-0x54685d58,l41),(-0xd5c7c16,l23),(-0x132ab960,l56),(-0x21c59e2c,l44),(-0xba7a412,l15),(0x9b7ff8a,l4),(-0x4d3698,l46)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,0x4e0440163010000000110f014c020000004a0900b300c0000120110058c04000094260900b400c0000000078024803000000044240a300800000148940d8c0300000009484073008000000d854050c030000003213014300c000000211d028c02000000000e807200a011d1058036490060384688b200d2401400000188b40d8c0303c82282d018c4014000000003002c803000000783400b300c0000001d1901cc02], #[![0, -11, -25, 22]]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase3" = "QuadFullEightCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase3
private def zz2282:"s08ea"="s08ea":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l46 l51 l56 l6 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x372dcd0c5, -0x289368078, -0x3cdd1c38a,0x9b2e5dd8], ![-0x289368078, -0xf55cf8e74,0x1f235c0ac,0x1c7e7adfe], ![-0x3cdd1c38a,0x1f235c0ac, -0x107be27545,0x2893689d8], ![0x9b2e5dd8,0x1c7e7adfe,0x2893689d8, -0x1449b4294]]
noncomputable def hinges:Hinges:=[(-0x3b28bd2c,l6),(0x635bcd9a,l4),(0x38846002,l9),(-0xfa12c9ef,l8),(-0x8e852b9,l11),(0x5a774948,l10),(0x4cc77fe4,l14),(0x22add17ae,l13),(-0x7a8613a4,l17),(0x61b58d2d,l23),(0xa0cbe79,l22),(-0x1449b4294,l27),(-0x915ff1c8,l28),(0x1449b4294,l29),(-0x10f744fd8,l25),(0x7549a63c,l31),(0xa267a8fe,l30),(0x1449b4294,l33),(-0x1449b4294,l35),(0x1449b4294,l37),(-0x7596cad8,l43),(-0xab3d9ec3,l42),(-0x24a8cb24a,l41),(0x1b488c10,l46),(0x1449b4294,l51),(-0x1edcc986,l56),(-0x266f7e0a,l63),(0xc38c8fe,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1449b4294,l27),(0x1449b4294,l29),(0x1449b4294,l33),(-0x1449b4294,l35),(0x1449b4294,l37),(0x1449b4294,l51),(0x22add17ae,l13),(-0x10f744fd8,l25),(-0x915ff1c8,l28),(0x7549a63c,l31),(0xa267a8fe,l30),(0x61b58d2d,l23),(-0x24a8cb24a,l41),(-0xfa12c9ef,l8),(-0x7a8613a4,l17),(-0x7596cad8,l43),(-0xab3d9ec3,l42),(0x5a774948,l10),(0x38846002,l9),(0x4cc77fe4,l14),(-0x266f7e0a,l63),(-0x3b28bd2c,l6),(0x1b488c10,l46),(0x635bcd9a,l4),(0xc38c8fe,l65),(-0x1edcc986,l56),(-0x8e852b9,l11),(0xa0cbe79,l22)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0x3d45388703db4015cf1451050216d00600000530880923010000000002d02480200084c70407a4301800001842201fcc0461843c33c03a240180000018848054c03000004109c04830100000001b0a038c020000063088092301015621217008e9005000000b21902c300c1612581a408b100500000005c4c0a300800000000050188020001186229036400c000000000440c8010454638a703db40160f1851450216d0060000008239036300c000000211d03cc02000000074640a3008000001c8c4088c0300094c80407a4301a981cd18d024a9006002eca615c02940101732982a00525005002907118406e401000bd2b05e01250040548708c10375401400b22985700a5004000007108807f3010000000000f0188020000007212015300c0000000f07028c0200000000007032004000010421025cc0400000210540c6301000000088280ccc03000000000140920080000000004c0c80100000000098052008000001182c088c03000000000240e2008000000000d0188020020c610840ba40100000001909028c020000000c4240f30080000002d0e024c02000000000ec062008000002a85808cc03000000000740620080000000003c0c801000000000740920080a210618803c50056145604140a614018006214c42032d004000f02105003c40100000008828030c03000f02106809c401000740d02101e10040000000002406200800000841400f0c04,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase4" = "QuadFullEightCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase4
private def zz2283:"s08eb"="s08eb":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l15 l17 l20 l22 l23 l25 l27 l29 l30 l33 l35 l37 l4 l41 l42 l43 l44 l45 l46 l51 l56 l57 l58 l59 l6 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3858a53be, -0x27cee1e80, -0x3bb653018,0x928499ac], ![-0x27cee1e80, -0xeb3d3c3ca,0x19158bdf0,0x1e457701c], ![-0x3bb653018,0x19158bdf0, -0x102c0bf879,0x27cee27e0], ![0x928499ac,0x1e457701c,0x27cee27e0, -0x13e771198]]
noncomputable def hinges:Hinges:=[(-0x3b28bd2c,l6),(0x635bcd9a,l4),(0x38846002,l9),(-0xfa12c9ef,l8),(-0x8e852b9,l11),(0x5a774948,l10),(0x386267022,l13),(-0x3751d142,l17),(0x2fa7be40c,l15),(-0x29c36e5d2,l20),(-0x13435adf,l23),(0x110ec745a,l22),(-0x13e771198,l27),(0x13e771198,l29),(-0xae042fa4,l25),(0x89a5cd96,l30),(0x13e771198,l33),(-0x13e771198,l35),(0x13e771198,l37),(-0x568507c,l43),(-0xd36eed51,l42),(-0x1cf2c2754,l41),(0x37607e0,l46),(0x6645b952,l45),(-0xf017040,l44),(0x13e771198,l51),(-0x7fe575d7,l57),(0x5ca03ed6,l56),(0x5c02134,l59),(-0x3b9e0ffe,l58),(-0x20532145,l63),(-0x894c8aa,l62),(0xa71470c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x13e771198,l27),(0x13e771198,l29),(0x13e771198,l33),(-0x13e771198,l35),(0x13e771198,l37),(0x13e771198,l51),(0x386267022,l13),(-0x29c36e5d2,l20),(-0x7fe575d7,l57),(0x2fa7be40c,l15),(-0xae042fa4,l25),(0x110ec745a,l22),(-0xfa12c9ef,l8),(0x89a5cd96,l30),(-0xd36eed51,l42),(-0x1cf2c2754,l41),(0x5a774948,l10),(0x38846002,l9),(-0x3b28bd2c,l6),(0x6645b952,l45),(-0x3751d142,l17),(0x5ca03ed6,l56),(-0x20532145,l63),(-0x3b9e0ffe,l58),(-0x13435adf,l23),(0x635bcd9a,l4),(-0x8e852b9,l11),(0xa71470c,l64),(0x5c02134,l59),(-0x894c8aa,l62),(-0x568507c,l43),(-0xf017040,l44),(0x37607e0,l46)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 34 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase5" = "QuadFullEightCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 34 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase5
private def zz2284:"s08ec"="s08ec":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l17 l20 l22 l27 l29 l33 l35 l37 l4 l51 l59 l6 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2bcdf4244, -0x59682eb50,0x3bf179b3c,0x4b0], ![-0x59682eb50, -0x2a9defbb28,0xfa6dedd54, -0x5b2521508], ![0x3bf179b3c,0xfa6dedd54, -0x2f39d08e10,0xa5266835c], ![0x4b0, -0x5b2521508,0xa5266835c, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x135d25e0,l6),(0xb41df64,l4),(0x1e8495529,l8),(0x5e0cd2a8,l10),(0x62f3a4c,l14),(0x200bd04,l12),(-0x2dd46ba0,l17),(-0x2782b6,l20),(0x19c77c894,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0xc0df7e,l59),(-0x1eedb14,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1e8495529,l8),(0x19c77c894,l22),(0x5e0cd2a8,l10),(-0x2dd46ba0,l17),(-0x135d25e0,l6),(0x62f3a4c,l14),(0xb41df64,l4),(-0x1eedb14,l64),(0xc0df7e,l59),(0x200bd04,l12),(-0x2782b6,l20)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    0x8a13ee2adc247956dea052a68dbb5a5b6c2fb7aefce1f9226fb4902764901b65ba2980f6cfc12c6d14b4c8f8473fa6b472e7e42736cf65d4412ab19ccd719699a26007005c5022e9e5344880f4b1fc5490e362fdfab02082aaaa4d60c0140d2f9fc04a1846010910a342dacc243f08ff5d18c08614d2fed0c208312f4d89023f0dd0500650c22008000086980c2c472b2d9014982447fe0810eb7fe7a22804a609dbe8001a206e17400ca204601000011420361b0160980a84c050274469e14367a408089612ae90176cae17b8403301f1c7400920a110040068060320380b694ed985821081f964f19f7a1bea3650900809f3046b526c6ddfde366c320c2693591403d4dc68786cdc2cefc6880a679e174daa000a5aa80c50843416592ebf36b2eda3c9f000016fbce2110bb1d994327f70055b05a85381bd944c2d8e5eba32db641f20e418c40000d3880c02800122c80b8ae01802008e30802eeaa240603a49c2ca01007601c467815bc6b49d9202110042008020080000223008010040000111000154301001004000011180a008020000088c0600401000004440583602a1301409e082a5b741c82081e1a9caa24006576c564180172938d640026603f3c3000284a504601000011f2000782400314ce1bbeee2ec806042827e184030446d9342147000051d5da0603083701970200000000640501406c6048008013010000b61001442200690278925f9fcfeba081008537984808722fcb5db33351797aa8c0e13026074c8014e5dc2014ca14239f5d4fe7781cf1eb758de2820eddea76486dcde09c4344400ea36f185a472cba2a3f9984015abfbdc5fc666db5fe573042de88d89315803bf110e845aa40d43b29a18e28ae1b0c30875d610aa8757d10295f26b3c14905ee90210091ccb8be26c6141e504b5124fcf36d0c188142604adac5be8a09b1dfdfa731e8f188089a148adc8480c60a05118663971b30d88600fed47193699df2064843324841e0382c646ee66eb32c4a79c4aaeb2430000008661420000010cc082003a45de2241000000a832c01933a2c9c270424008610221a8536060f03c54cb6a60aa2593b5ee386000d363a63820002437b02020042d950c0800011393753801200430812ccd4d643078166064393054fb295fff1c300216195e340001a4660220000002824a0c0000c750819c00900200002e24000bf480024598200be8833aa050fb75b70b8af20700000052d01431a0ed2b97c080800004aeeb0582000001f0e02813e168f9fc19402042a6aed400000000174091aa400a407002403b1d0eb6847ee58d323af530d2c479ad318a212180398e8bc0c08000004b005847d1a9788018100000025806080051babd0100003037949a4009403163aa9b9de5b13060000015f9058d800617447cc140245a45e11624b6f532224243004cbd85705849c5708eda02000000023287a0009c0500003784000ec88088080017e8c865508a617924071944e26676306000000fd20304255c46c1dc40316790ec6b220030367bd5b60802d8414cbc200515dca9908172fc96815b3881400c00007a48007c290101180786f07b4594a31f060810422aefc8e0c7f39f789c181cfada1ccee202000001fa405003427200330404838adb89c00515dca9902025a55d482876720270180000f3900e2500680b8633613cf55e56a830713f7ec82c95d302840afc07c345d0141845a6abba087766e202c63e3b2b5837622816491aecc2508ac200eece386a266ac618002b0767abcc4c200a8a2669229805fa111ca28a0a0e017122a27f8975c51087edb25e2810a3518a608013adea5f80920a1080420753c6b5823877a6d38b48051ab99ee8604b9e44cd090207c021c3b8265b9f183bd34244f1c038b9bbd1040040eeae549020800200001a870cc9ba506a2055a1266de8a2fb509d908609af971c86580051dddc0180351544f60a02c5e048fd19c30840200002c26864cb0be978a0959838f3c404acbf7ef83802f6b1a3014017b49ca28204f6567d9d166102100800009b900048e20183200b1180506e04075cfd86003882913102ffc40c17230632f86182f91da7d814208ad2d8f7a2802b2c36de443003f5f27c4f0004d955790a05054a4101380a0024040003c24001f0c80053f9d25526f35e0b7e0513f5387ce110f0d05b56c7a05e9879368000000000000000000000000000000000000000000000000006311861841831c21821420c07b366c92b880b0076078e0174c25cda5b782168fae9a1749cbb2f5424e7cbeb30f80000000000000000086248e50a48a40a308208386380e0100401b658f022402a1c51077762f7586943658dc08d2d648c4f10511e068c2014d89d33ee584031ce4d4ac100007fe8df32a30025825088d5644001501028aa1c45861d458c000a3ac7c0a1894efd0905123000000096008200412ecc740820006d27d00a00168ef7d1bce004e01000018620006f060897856e0d541103034ccdbf8b84910000ffbd81c04083e9a281608f1c40000000ea601200003ff553e0080019f9088737cb91c20b4070000372608cbcea99a5840e305904399c7146738b313d901c5693702151c3bd2eb40ddc306000001e780409723126a570a04547f7f8e5405065021c46a0309c0500003d240024208040a801c4600c1ba2d8d86e125a1830017044170286716eee8140506866003e660808000002a30140b6e368e02ea0037a863ec803231caadc000000384219620270100000ec90051d00200800c04001b864008d4002020000100170b9))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 18 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase6" = "QuadFullEightCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 18 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase6
private def zz2285:"s08ed"="s08ed":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l13 l14 l15 l16 l22 l23 l25 l27 l29 l31 l33 l35 l37 l4 l51 l57 l59 l6 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2a332dc3e, -0x58a3a8958,0x7551237ae,0x3673af58], ![-0x58a3a8958, -0x17bb713090,0xb709b65b0, -0x596316726], ![0x7551237ae,0xb709b65b0, -0x2ee9fa1144,0xa461e2164], ![0x3673af58, -0x596316726,0xa461e2164, -0x2c51d4704]]
noncomputable def hinges:Hinges:=[(-0x135d25e0,l6),(0xb41df64,l4),(0x1e8495529,l8),(0x5e0cd2a8,l10),(0x19a681c8,l14),(0x8907433b6,l13),(-0x26afc8c4,l12),(-0x639f7332,l16),(-0xba7a412,l15),(-0xd5c7c16,l23),(0x1813e4f92,l22),(-0x2c51d4704,l27),(0x2c51d4704,l29),(-0x30c970bbc,l25),(0x2449df82,l31),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(0x2c51d4704,l51),(-0x20818355,l57),(-0x4879100,l59),(-0xc97eb9a,l63),(0x19490538,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c51d4704,l27),(0x2c51d4704,l29),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(0x2c51d4704,l51),(0x8907433b6,l13),(-0x30c970bbc,l25),(0x1e8495529,l8),(0x1813e4f92,l22),(0x5e0cd2a8,l10),(0x2449df82,l31),(-0x639f7332,l16),(-0x20818355,l57),(0x19a681c8,l14),(0x19490538,l64),(-0xd5c7c16,l23),(-0xc97eb9a,l63),(-0x135d25e0,l6),(-0x26afc8c4,l12),(-0x4879100,l59),(-0xba7a412,l15),(0xb41df64,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,0x5f013200c0000004e320298040000011024038c03000009c08802c6020000000443c053008000000001e0290040000120110058c040001284c12016801800000001e009200c00001283a06318080000000028034803000000000c80c401000003509c06c301000000001a8051006000001609c04cc030000000b0880a601000000002c009200c00000001b00490060000019024030c03000000d02201c601800006a0440143010000003708805980600001a8210058c040000000d0480c6010000000642407300800000003c28198020a60820c40919005000000a432048601e945042d807a6401800029c408124180a005611c3301a9004], #[]⟩
def dynamicCode : Nat := (((((((((((((0x1856df3676f928900821cd9a50db29d17df880439391a3f1002f63381b694008c021853d5f4cd6a4a2433045429e58e0d1d2d2e3286163fc96e0920809dd075b0b0238c74b9305005c57121509c00940200002f07c51dc2100) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 24 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase7" = "QuadFullEightCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 24 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase7
private def zz2286:"s08ee"="s08ee":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l62 l66)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x17c01750, -0x3121752, -0x49b2391,0x12c], ![-0x3121752, -0x16c4dc0a,0x1912713,0x3d292f4], ![-0x49b2391,0x1912713, -0x13f59f33,0x31219aa],l66]
noncomputable def hinges:Hinges:=[(0x2cf3cd7,l17),(-0x1890c3f,l27),(0x1890c3f,l29),(0x1890c3f,l33),(-0x1890c3f,l35),(0x1890c3f,l37),(0x1890c3f,l51),(-0x2cf3cd7,l62)]
def normalizationDenominator:ℤ:=0x165a0bc00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1890c3f,l27),(0x1890c3f,l29),(0x1890c3f,l33),(-0x1890c3f,l35),(0x1890c3f,l37),(0x1890c3f,l51),(0x2cf3cd7,l17),(-0x2cf3cd7,l62)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000029090009980800000000b0024803000000006c01240180006804100263014000000001c029005420a404200335006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 9 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase8" = "QuadFullEightCase8" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 9 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase8
private def zz2287:"s08ef"="s08ef":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz1021:"s03fd"="s03fd":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullEightCase9
private def zz2288:"s08f0"="s08f0":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase10
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l21 l25 l27 l29 l33 l35 l36 l37 l38 l42 l43 l46 l51 l57 l59 l61 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2c398fd28, -0x59682eb50, -0x861c46350,0x85324bc], ![-0x59682eb50,0x158301758c,0x25ddb1f0c,0x7e2e3365c], ![-0x861c46350,0x25ddb1f0c, -0x2452531800,0x59682f4b0], ![0x85324bc,0x7e2e3365c,0x59682f4b0, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x3a985eaa8,l17),(0xafad4550,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x72348d6d4,l25),(0x2cb417800,l33),(-0xdd8ae6,l38),(-0x2cb417800,l35),(-0x30173397f,l36),(0x2cb417800,l37),(-0xb121f7a,l43),(-0x7d051865,l42),(-0x4eb86c0,l46),(0x2cb417800,l51),(-0x2e5a8e55,l57),(-0xa99970,l59),(0x55973244,l61),(0x23b68afc,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
def s1:=qPath 0x59682f4b006335d133709776c7c3000429925e0861c4634f8b2d05d69f78a9cf1fa1229298bffd92c876034058731fa4f2703 s0
def s2:=qPath 0x59682f4b00fc5c66cb809776c7c3000429925e0861c4634f8b2d05d69f0b2d05dfff229298bffd58301758c058731fa4f2708 s0
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨7, #[0x8031c0c1010180002404701080c0e2418201041800209c0001804401080c0e0000d022018207098000200460104100e240c601041800106cd072c1c20900546f0000000140400101460114281030030330000903140c1020180000c3020700201e0000000141c201034000101820104080e2c488010c0c20808c0000000704080405000060204040010280001008202000c0e0000000401c9020340003008b0314040e5008b02080c00305c000241430b00404a000000038082010140000000b02080405000060c10043020380000000e01080c090000c0a0c0c0121389011c0c30208040f1410403040c00808cc01242410c00083b00008020804102038000280850608242e00005080c04003068b042804201000c130000c012c08301028a03142c10300343700008011c044020280001c10401001c1a00000002404701014000101c31a0090560000206041c0070a80000000f01080405000000038043010140000000d012c040500004010c080010280002c0820104040a3414b050c240181bc00000006010404052418509087c00d21c00010042060004122c18301080800306c0000000a030004050000000200410101400000001010008052804901200810606cb0b140420400182f00000002c04002034a041c0c60308243700000002c0c001014000000080104080d000071a100c008098000182030300242a000000018080010140000c1010100080e,0xf0724040070590072c5421e0070c34004b030c1800a0cc00000006060404050000c0e080c015178b0528109010c100b0000b0d241410c0688081c24601100c0f0000306041c012078b03240c20400101b2c0c9030c1820204cb0c202c60700484b0000907082c0070c80002c0c90310100a2c04801180840202c00000010021c04050000b03280c001018b03203c70e002023]⟩
theorem v0:V s1:=(S (K 17 nt 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) (S (K 16 nt 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) (S (K 15 nt 0x5493846480d20caa16900c90184200000613044d59c6480c2100082604486a006329199401c651b950b00c9018420000061304a08a2087a349121080114cd9a0fff0ca0bb05101122bf86142220c822e90c4114410f4692142107401d44ca08a6535632406108058972d59eb30b1032e69810a1083a408ca088033081509308fa) (K 15 nt 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))))
theorem v1:V s2:=(S (S (K 14 nt 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) (K 14 nt 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)) (S (K 14 nt 0x910500c9018420000010852260952618c9018421000200a04c065003696ce75a0032406108005cc3fe8f6c132a0c16948219203309a88298932bcded0a3617f610920488fe1a402624c30a24310951052d1a4018e6460603192030844c0410f499498ae03bc42bd35ab88af33b503137b428d85fc8861c5c911d49059ea98a0310951043d1a4024c406708171199818346480c211301043d1a4853f41d0040932822992d50c90184215daf8def30f10fe6042a520e9023282200b8209d264a) (K 22 nt 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)))
theorem v2:V s0:=(S v0 (S (K 13 nt 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) (S (K 16 nt 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) v1)))
private def zz1022:"s03fe"="s03fe":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v2
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullEightCase10
private def zz2289:"s08f1"="s08f1":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l16 l22 l25 l27 l28 l29 l33 l35 l36 l37 l38 l41 l42 l43 l44 l46 l51 l61 l63)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2c51d47e6, -0x58a3a8958, -0x84f57d05c,0x4ec], ![-0x58a3a8958, -0x151311f68,0x4caa97d64,0x8684039ee], ![-0x84f57d05c,0x4caa97d64, -0x24027c9b34,0x58a3a92b8], ![0x4ec,0x8684039ee,0x58a3a92b8, -0x2c51d4704]]
noncomputable def hinges:Hinges:=[(0x8686790c,l14),(0x132ab960,l16),(0x54685d58,l15),(0x5dde2b65,l22),(-0x2c51d4704,l27),(-0x14a0b5144,l28),(0x2c51d4704,l29),(-0x2d4f0dfc0,l25),(0x2c51d4704,l33),(-0xdd8ae6,l38),(-0x2c51d4704,l35),(-0x30173397f,l36),(0x2c51d4704,l37),(0x8ceb9172,l43),(-0x2f45efbc3,l42),(0x9930a05c,l41),(-0x26afc7e8,l46),(0x26afc8c4,l44),(0x2c51d4704,l51),(0x55973244,l61),(0x335cc11c,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c51d4704,l27),(0x2c51d4704,l29),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(0x2c51d4704,l51),(-0x2d4f0dfc0,l25),(-0x14a0b5144,l28),(-0x30173397f,l36),(-0x2f45efbc3,l42),(0x8ceb9172,l43),(0x8686790c,l14),(0x55973244,l61),(0x335cc11c,l63),(0x5dde2b65,l22),(-0x26afc7e8,l46),(0x9930a05c,l41),(0x54685d58,l15),(0x132ab960,l16),(0x26afc8c4,l44),(-0xdd8ae6,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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], #[![4, -15, -3, 0],![4, -21, -1, 0],![5, -16, -5, 0]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 25 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase11" = "QuadFullEightCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 25 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase11
private def zz2290:"s08f2"="s08f2":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l63 l66)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x809b2ab, -0x3121752, -0x2dc9e6d,0x12c], ![-0x3121752, -0x16c4dc0a,0x22be019,0x3d292f4], ![-0x2dc9e6d,0x22be019, -0x13f59f33,0x31219aa],l66]
noncomputable def hinges:Hinges:=[(0x2cf3cd7,l17),(-0x1890c3f,l27),(0x1890c3f,l29),(0x1890c3f,l33),(-0x1890c3f,l35),(0x1890c3f,l37),(0x1890c3f,l51),(-0x1104e1a,l63)]
def normalizationDenominator:ℤ:=0x165a0bc00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1890c3f,l27),(0x1890c3f,l29),(0x1890c3f,l33),(-0x1890c3f,l35),(0x1890c3f,l37),(0x1890c3f,l51),(0x2cf3cd7,l17),(-0x1104e1a,l63)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000002c13809980600000000b0024803000000006c01240180006804100263014000000001c029005440a104400635006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := 0x5fe00000769a56ab2bc1511861851c41841c31010411c0c00008036069578085048a0790b77c614a07cfd192201e42ddf1c421b6da143087da12594800bbcb6ec0a0059886c710003a0804324800f80c00006a0cbaf68000011ffdbb954005446189146147103041047001030000200d81a055be80448a11059cd71851f65b8418e20e5bb6844610e3b5b78008358991c662002837c64d0a005580f05c40008b5cfd1f2400840700003764000ae4e42535dc20c0fefcc3a9381a000032258ceca8303e2d06082a0696262d300d497606a5d800155d0615ca61d02d06187084083042068b226b67377af1de6f7228e2db487b40b912a9889e9f1e220478214560ecb21496e6a21404b4843713b8508b127680018c1a10d2893bfc0c209d8ee04410412cdaad8060412cdaad80a09b42b43dc0c109d8aebc42819179c91c8400ec545626108eebfa18761018460480001c820160a00a0140da84a6bea11c275df498110c1166b1758745089d2a33c0c4004e94bc90e1c00ffd0a1358a009d2a71f5c981b2721f0aeacd87629f4e104a058e3e56b69b1bf74943d120581c9b9e3c0574c9a84096b70faa2b55ee79a07100001b11bcb6168240e10aaecb6f3268a93762000b6cfda6998805bd828000002b4f94568a6a0000000059d325525321c9eacd607f20010c2914413c2911492056fb4707f64093d0c9cf4840c00007b0c0c000000c4e00c000404c41c1000fe892b001003c6cbb3549a0008c0900003407880001a04f001437c53e9ada7881ce3126101b420ae5a20fba3030235d61cae051418ffa00a4e5880b6e879640b03006817d58648000fcf5dbac00853848014822286c5c04d07ea7cca095620706c7300265ec5f97fa104e066e943e9dce20900282d7223f3df296e45086202f56486db188f5dc3ca1820174e29b83f41294202000000925a9dcf1fa401b51c4b605e81c01202f000053240013008004aa9c2515978d8c180004b00a1329088e0a0d44b17b0e000000c80c030ac42684000000644e00380100090100400801c040002ee401837559d494286005ecf02b771fdfe47ad5554f210fd35abc0a703c000000000000000000000000000000000000009641824003802801011d31d61954c872626a67efb25ad363fc89112d8c3f8d4125868933d0ce2501712694a37d081475dc63068da5b3675f22518964fcb3db2397a4ec4ac9b98ce3f4fede015ae1b0d7ffc5dd72b23f91bcc349eb7967da61f355037e54044ce14a65412866395f6c8df426910452b9858b1833911e30c169faa2c5053ab814281f3e985100f3d573800c804366aaf0f8da8166ec88dd90f5d3dceab360a11630c30c210110096008002060000401a00022a600002008c20645af0809588c0208350dfaa100127f9104008beb62a00320080000d8200022a6054a82f8413466501410bff987007acdd0a040b00200002b0800225996faeb47c8598a84b9685336aa683d919f603170000000000000003600001d8a428044d55319e3e84d5a2151fc3fed6000000000000000d5db3000531030c1180140040a118b56ec00279f06e58337120cf9f0a969260d659d1404d8de35c2d8923edb3f514bab1bf3f6fcd39d6a4fa7d85d93e8743900a21aa5f50003d82001a6040068c4f16f75346386ec3ea2181a7d0c9080922afa42043ec4f8200133eb70c091136813820c8043a311237690000027af81398c060163a92991d1fbf69a629c8a97b77f73efc4396f8000000000000000000000000000000000000004c31c71c51831821811012c080200d00021e200a028200c9ca860cc0fd12384a9db1d14201e1d70e097e9f385065b09722805a2bd39c006402123caeabd848a0319630c152a684a2829ce75b8601d356981000ce82602003769253800d00400004ace0db5228070addaa04508687ba0500d5c2ca4001800849346ec08828800b0aa2384021e8fa3046116bb6180206478c1000009a973000e00400004448000ee18122c8821434ce51644f3f986ad4ec48c724521106c0104db51e55cff9556e705e757681f78ec7e639888158180d5708c3a702ef0016f7d9bd2b840161009f9f02380a04eb6b96022bd26a74e0e651dd62ccc2f63f2455130401cf22bd6887fc25bb0e9a9b52ddc8e3e04929741a4294d95261c79880239f26be950486e5bac5ac2787b325b3bd96a69eb157174fa38e575e9ef734504a523870a7fddd22162a59f62a108c03b727046738c04545381626afca74263d75cef4d08c4f0c96bc85a19e583fa268464f1797bf282bbaf25b9e18a8d2234a0642100b249d71c8f638749b3a8c560620681c857eedf5fc61ed93fc4f7a48c6f279922e2e141565508ac7bb2b319983f7c7cb15cf9ac1da40042dda2c63515c387a501055453000021010009042001afe68b550a6c98d0ba0a1869f13c35d2ac2826183644e1e55080800005f5e1000200150dd2cb3e208600000017d784001000534c1ca2a647a1201c00c8151430001500181000012c14182045ec101000012c00000003fba800e002000039c80202800c040040200032620020200001000a3c1
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 9 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase12" = "QuadFullEightCase12" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 9 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase12
private def zz2291:"s08f3"="s08f3":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullEightCase13
private def zz2292:"s08f4"="s08f4":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l16 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l56 l58 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x492929074, -0x289368078, -0x3cdd1c38a,0x16c802e8], ![-0x289368078, -0x11c164d460,0x2aedd2a98,0x258511416], ![-0x3cdd1c38a,0x2aedd2a98, -0x107be26242,0x2893689d8], ![0x16c802e8,0x258511416,0x2893689d8, -0x1449b4294]]
noncomputable def hinges:Hinges:=[(-0x565cf224,l5),(-0xf4475256,l4),(0x3fb6e30c,l9),(0xe2f79fd,l8),(0x21da574,l10),(0x1119d13b8,l14),(0x1edcc986,l16),(0x24a8cb24a,l15),(0x266f7e0a,l23),(0xab3d9ec3,l22),(-0x1449b4294,l27),(0x1449b4294,l29),(-0x1119d13b8,l25),(0x7596cad8,l30),(0x1449b4294,l33),(-0x21da574,l38),(-0x1449b4294,l35),(-0xe2f79fd,l36),(0x1449b4294,l37),(0xf4475256,l34),(-0x7596cad8,l43),(-0xab3d9ec3,l42),(-0x24a8cb24a,l41),(0x3224b63e,l45),(0x1449b4294,l51),(0x565cf224,l54),(-0x1edcc986,l56),(-0x3224b63e,l58),(-0x3fb6e30c,l61),(-0x266f7e0a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1449b4294,l27),(0x1449b4294,l29),(0x1449b4294,l33),(-0x1449b4294,l35),(0x1449b4294,l37),(0x1449b4294,l51),(0x1119d13b8,l14),(-0x1119d13b8,l25),(0x24a8cb24a,l15),(-0x24a8cb24a,l41),(0x7596cad8,l30),(-0x7596cad8,l43),(0x3fb6e30c,l9),(-0x3fb6e30c,l61),(0xab3d9ec3,l22),(-0xab3d9ec3,l42),(-0xf4475256,l4),(0xf4475256,l34),(0x266f7e0a,l23),(-0x266f7e0a,l63),(-0x565cf224,l5),(0x565cf224,l54),(0x3224b63e,l45),(-0x3224b63e,l58),(0x1edcc986,l16),(-0x1edcc986,l56),(0xe2f79fd,l8),(-0xe2f79fd,l36),(0x21da574,l10),(-0x21da574,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase14" = "QuadFullEightCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase14
private def zz2293:"s08f5"="s08f5":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l15 l16 l17 l20 l22 l23 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l56 l57 l58 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3e3f37d1f, -0x27cee1e80, -0x3bb653018,0x444], ![-0x27cee1e80, -0xff9d10744,0x190a099d6,0x2ecaf2a4c], ![-0x3bb653018,0x190a099d6, -0x102c0be576,0x27cee27e0], ![0x444,0x2ecaf2a4c,0x27cee27e0, -0x13e771198]]
noncomputable def hinges:Hinges:=[(-0x565cf224,l5),(-0xf4475256,l4),(0x3fb6e30c,l9),(0xe2f79fd,l8),(0x21da574,l10),(0x3640a95f5,l13),(0x894c8aa,l17),(-0x5ca03ed6,l16),(0x1cf2c2754,l15),(-0x3640a95f5,l20),(0x20532145,l23),(0xd36eed51,l22),(-0x13e771198,l27),(0x13e771198,l29),(0x7fe575d7,l31),(0x568507c,l30),(0x13e771198,l33),(-0x21da574,l38),(-0x13e771198,l35),(-0xe2f79fd,l36),(0x13e771198,l37),(0xf4475256,l34),(-0x568507c,l43),(-0xd36eed51,l42),(-0x1cf2c2754,l41),(0x29b906bc,l45),(0x13e771198,l51),(0x565cf224,l54),(-0x7fe575d7,l57),(0x5ca03ed6,l56),(-0x29b906bc,l58),(-0x3fb6e30c,l61),(-0x20532145,l63),(-0x894c8aa,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x13e771198,l27),(0x13e771198,l29),(0x13e771198,l33),(-0x13e771198,l35),(0x13e771198,l37),(0x13e771198,l51),(0x3640a95f5,l13),(-0x3640a95f5,l20),(0x7fe575d7,l31),(-0x7fe575d7,l57),(0xd36eed51,l22),(-0xd36eed51,l42),(0x1cf2c2754,l15),(-0x1cf2c2754,l41),(0x3fb6e30c,l9),(-0x3fb6e30c,l61),(-0xf4475256,l4),(0xf4475256,l34),(-0x5ca03ed6,l16),(0x5ca03ed6,l56),(0x20532145,l23),(-0x20532145,l63),(-0x565cf224,l5),(0x565cf224,l54),(0x29b906bc,l45),(-0x29b906bc,l58),(0x894c8aa,l17),(-0x894c8aa,l62),(0xe2f79fd,l8),(-0xe2f79fd,l36),(0x568507c,l30),(-0x568507c,l43),(0x21da574,l10),(-0x21da574,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase15" = "QuadFullEightCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase15
private def zz2294:"s08f6"="s08f6":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l17 l22 l27 l29 l30 l31 l33 l35 l37 l5 l51 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb417800, -0x59682eb50,0x3bf179b3c,0x4b0], ![-0x59682eb50, -0x2827830adf,0x133051ccbc, -0x69b881f0e], ![0x3bf179b3c,0x133051ccbc, -0x2e924a86a7,0x98c571fd8], ![0x4b0, -0x69b881f0e,0x98c571fd8, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x10432593f,l5),(0x2dad16693,l8),(-0x4586cb6,l10),(-0x23b68afc,l17),(0x7d051865,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2e5a8e55,l31),(0xb121f7a,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x2dad16693,l8),(-0x10432593f,l5),(0x2e5a8e55,l31),(0x7d051865,l22),(-0x23b68afc,l17),(0xb121f7a,l30),(-0x4586cb6,l10)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[0x110f014c0200000000f01480200250982402d0030000000780248030000000d8024803000000009018802001a01040098c0500000190901cc02000001a09018c0200001b024030c030000000050188020000000160148020731043103250048408608c074900500002b8c402cc0300000000340c80100000002b018802000000f07028c02a210618803c500500000001f018802000104210120c0400000002301880200000001d02c80200000001b01880205c0a01c017500400000009802480300000000e014802000000070024803000000012014802], #[![-11, 22, -6, 0],![-29, 346, -249, 0],![31, 190, -177, 0],![1, 16, -24, 0]]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase16" = "QuadFullEightCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase16
private def zz2295:"s08f7"="s08f7":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l22 l23 l25 l27 l29 l30 l33 l35 l37 l44 l5 l51 l57 l59 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2a2d8987e, -0x58a3a8958,0x7551237ae,0x354b65ec], ![-0x58a3a8958, -0x2e6301df5a,0x1379cbd370, -0x5dab9b430], ![0x7551237ae,0x1379cbd370, -0x2e427409db,0x9800ebde0], ![0x354b65ec, -0x5dab9b430,0x9800ebde0, -0x2c51d4704]]
noncomputable def hinges:Hinges:=[(-0x10432593f,l5),(0x2dad16693,l8),(-0x4586cb6,l10),(0x13ea30168,l14),(0x5b8dbff78,l13),(-0x9930a05c,l15),(-0x335cc11c,l23),(0x2f45efbc3,l22),(-0x2c51d4704,l27),(0x2c51d4704,l29),(-0x3a64a838,l25),(-0x8ceb9172,l30),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(-0x14866410,l44),(0x2c51d4704,l51),(-0x20818355,l57),(-0x95443e,l59),(-0xc97eb9a,l63),(0x19c5ca40,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c51d4704,l27),(0x2c51d4704,l29),(0x2c51d4704,l33),(-0x2c51d4704,l35),(0x2c51d4704,l37),(0x2c51d4704,l51),(0x5b8dbff78,l13),(0x2f45efbc3,l22),(0x2dad16693,l8),(0x13ea30168,l14),(-0x10432593f,l5),(-0x8ceb9172,l30),(-0x335cc11c,l23),(-0x3a64a838,l25),(-0x20818355,l57),(-0x9930a05c,l15),(0x19c5ca40,l64),(-0xc97eb9a,l63),(-0x14866410,l44),(-0x4586cb6,l10),(-0x95443e,l59)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    0x20d4c16388007c021222352dcc43860e53f9e081e129914240005512c10a0001cc640200b061b91060084eba553800f004000051c8000ec106409e33da259edf2949270708055c41f5cbe8100b68a6b3bf206fa04a408e718423a418ab2181bddb8c689ea00000000000000000fcca187084084000027cfa53e2112e0103c0978ea7512f0c23a30cc6e3e3aa17da5b77169cac508656f252d96753c5866185b5c6ac21f95a70d3a8c96135c6b552995dd54e4fbd5351d5ef08c781462bf50cc62b280021c10630981a84c18817018037d2ab3b60c18110aa204fc8c101b9149684b0416f95ffbdf8016002ab6a2bca40e004bc4c0278c0109d2dc678116e9830b00b100001004412343a471e8a0010aa89f9100001382dd130023004000056106101f1006f28f650818da0d0a310c39182a675c60002962f1bc400380d705284a104601000010f20004507a30f568320147abb4e77bb702f87541118e5f7e810d3de6232b7b6baf5728000000000000000020aa4006de5bd61008a05a0e10a1020840020164a66570a3b1190e4841f09981108d8650031fe9725c253c17714acb0d70104e78ad8ae1f94752d1b3495a64b2885f1454000d508300ac17c06000f104178860ba3b05c1582d888168460b21b0580982b80b0800052f9449c0dcda53586b5289bed836cd1ff19155aaa7105e02901e110f0627844351b41085bfda679545efcf1f80e77f58e11377de405e12351f6ccdc81db151c2caf896fec7027c740cabab62e899dd404003dd3ff3011437ac2fea1347f9457a0016f25c8b262d53ff22ac28a01e153d75ebf3c5f0cbac6e541e21a34e718c6f971e016d57cefc853d6383f6b7221905bda3c54ce44cbc1bf47e422bab8908348b1164c13c7157649161d9ab69922353e46b62487d282497d2aa483044010c24183991be12450b4385a32437181e5bf2280013e79c3d552418230080000749056190000ff10551182a04c14c178cf68967b7ca5249c1c201568a6b3bf206fa04a408e718423a418ab2181bddb8c689ea00000000000000000fdb032a965becd64804cb641532c72032c22020410802a320bfef72860690145cee4bc84565f40c005a825dcd7b799463b5d6e483bc025260e00e5ae60646772df851e854890724feeb948694610e432282900c144060a00304f01d130521bb288a12173d7cc18e189d8ee6160c3768a1e6c85000149650a55465182300869416ab37a9ca181904b76314265da02e2a180085d9a5502a320c1180400003a4e33da259edf29492707080546b0036c0caa596fb35920132d90559ae653a93af1f069447bb89bb35cca74c2142c924424330014055190c41d100c50832e6c9cef172ed64b5423d32d3ddd45e2f4ad61a4aa0fc148129dd089a5c8959f51ca723e800182100053b209c4204d0d02604800272c81084c07c07419792977f7ada98d1b062b7ed34356958e8b66ab2ec0fef302570541973e68c446642400ff1beac3080ad8a79aaa4afc5966384c53c3fbc3b0a72687e2b483bb9559ae65b2c801e5c66b26a0179ee75fc28881909a7957d9a950ed2d0daf1ca3fd8134b9dd1b938ed3d8ef9c016c1a2558e704ddd03d85000118d80f57681c312812d3dc2b2d31225137555372ccc43cd4711d1b01534506a8cd34b6ca443a768d880000802204e3398d786196d35e4c5002e9fef99800e8020000270c93318feca8e1c7ae5bf192394ba44e61c1066e08952000f80430d0de360b47061ab053c2102056bfcd88800bbb4abc50002704a6b2801000400003f08000f21f14474615bc28b690a1e7820101cb415084610420100000ac20961b04a09d88dd27911a743040ef2c95ae78c5a4d85373bb5bee12c3b42540eb92b5b695c06609ec1fd367184905a4f3e1fa3c93f4a066422e2e674588fa77be1bb83692fb5e82efa335cfafb72b7c024f18e0037a7b95701aa1c6d9c8e0379c6e288577ec3a6455c2364bc3652ec1364c9c1f6ea750ff6c910020381ed411374e99021b7c353721f493df4c84c8cf89428d1120981c3dfc75f686131a5b94c137e31387e2f9ef1539b94ec66f752cfe923ba5ab69c59e97c2b7377efcd1d828c54a5090000bf440c0040013e6604089f50f51dcc9d0ba674fda818dcb3b4820ea1a7da53a22085d6a1c42cb93498e62245a7602001df6eca52b92195ef68ef71d54dbeab68216fc02cf9ea6e7015ae1f013adb6bf86fa697a1600156871cb79ca5ebe34f9debedbdc908d24b73bc829444183bac55955db9c8a9eab52b6070480a81d9c865c453debf01ae0558ace8fce036acc5c775e2253181dfed4d1cc9cefcf8bb029f094140ff916da23a5647b6208a29f56266af35b14def6a38f0dcb9556733561bb171b8c84a1070000bf24124460901304705e86051abe54c50c2fb12c968e1043e8b66c082ef437752c500071740c0d1094508c021003fb36cbe39b18ec5f16e33cff650104235801b796f584022816651250628638410430089a8d3905a73f82b887c7c02ddfd355fc64f773601a8602545cc6c28e42c5000215208c0b0450182200f00bf1a7e8286f52ac51d44abb5dfec96008c0801fd9b65f1cd8c762f8b719e7fb2808217107d72fa0402cf5769cef76e05f0ea82231cbefd021a7bcc4656f6d75eae50000000000000000041424804118010000047b7ca9cd6b1969ca4d12aafc1a9a9f49c2ab24791bf254f4f004669034ae4567aa111ba4b70ebb3c2bc7c734aa730323bb2fb670f79c533155ca49d868d00049220861a0420900042e101b09f083dfa71fc08246)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase17" = "QuadFullEightCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase17
private def zz2296:"s08f8"="s08f8":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l23 l27 l29 l33 l34 l35 l36 l37 l4 l51 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x10136556, -0x6242ea4, -0x5b93cda,0x258], ![-0x6242ea4, -0x306daf36,0x4480bd8,0x70a6c5e], ![-0x5b93cda,0x4480bd8, -0x27ec43ed,0x6248a81], ![0x258,0x70a6c5e,0x6248a81, -0x312187e]]
noncomputable def hinges:Hinges:=[(-0x572d,l4),(0x572d,l8),(0x2209c34,l23),(-0x312187e,l27),(0x312187e,l29),(0x312187e,l33),(-0x312187e,l35),(-0x572d,l36),(0x312187e,l37),(0x572d,l34),(0x312187e,l51),(-0x2209c34,l63)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x312187e,l27),(0x312187e,l29),(0x312187e,l33),(-0x312187e,l35),(0x312187e,l37),(0x312187e,l51),(0x2209c34,l23),(-0x2209c34,l63),(0x572d,l8),(-0x572d,l36),(-0x572d,l4),(0x572d,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1470cc08700bb5006000000000780a401000094260900b400c00000000f004900600000000210188020000630560338602800003506406e3010000188118079180a0000001b11018c02000000000d80a4010000005827013300c000000016004900600000000d8024803000000c8120186018000006e1100b300c000388218079180b99147046012d9006002104609807680200000000014062008000000001c029004004c0c4170121004000000441202c6018000642409016400c0000228520371809070d9052006d90060000a208601e460280000004c240630080000000026029005440a104400635006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 13 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase18" = "QuadFullEightCase18" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 13 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase18
private def zz2297:"s08f9"="s08f9":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullEightCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l34 l36 l4 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0,0xc8,0xc8,0xc8], ![0xc8,0,0xc8,0xc8], ![0xc8,0xc8, -0x572d,0x1dd7], ![0xc8,0xc8,0x1dd7,0]]
noncomputable def hinges:Hinges:=[(-0x1d0f,l4),(0x1d0f,l8),(-0x1d0f,l36),(0x1d0f,l34)]
def normalizationDenominator:ℤ:=0xee6b2800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x1d0f,l8),(-0x1d0f,l36),(-0x1d0f,l4),(0x1d0f,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨29, #[0x11018802], #[]⟩
def dynamicCode : Nat := 0x28880bc50c190081832014206402040c80208190080d72d064147040f00c5110178a1832010306402840c804081900610320101ae5a181d0f190081e0180000fb20000ba2e40a1e4081e40a164081640416464591582020011450640a1832040c1902840c81020640610320303a1e8322b8406802000037c8000d29
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 4 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullEightCase19" = "QuadFullEightCase19" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 4 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullEightCase19
private def zz2298:"s08fa"="s08fa":=by decide+kernel
end 
section 
namespace Green24Proof.FullEightRows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x114e20003dceb94800df5f3eec601e20003dceb948005b888afd26200779ae5800185e48fea07a2005faf84803db699ca1fa20003dceb94800bc7d1baba15a200779ae58002a2dff8f201a20001eeb5ca80049ef4a7f622001389b4801ac98ec207d2005faf8480018adab9d61fd2001de6d9a0028af5a1de1ed2002fd7c280018685f5de14d20003dceb948015c9e8bab6520003dceb948024a886e6b212003bcdb2c0059d99bff207c2005faf848006c6a4b0ee1fc2003bcdb2c04084e4d21ec20001eeb5ca8001b4c8c7e6420001eeb5ca800ab7b7acbe07820003dceb948023ceedf2c6020003dceb948013aea2d2da14]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1360003dceb94800bcaaae607e60003dceb9480049a8cf98615e6002fd7c280028884c3ba01e6001de6d9a001b59e8dfe660003e8a4800d8ae6de1ea6003bcdb2c001afd6d1aa01a6005faf84800bb5e9f7e2260003dceb948006a7e7b582560004e2ad8002160003dceb948008addee207f20009c4da800286d4c21ff20003dceb94802dd6c5cd9202f20003dceb948033cac2f601f2005faf848004f0bcb5c6720017ebe18001c39ee3ea07b20003dceb948018debaa606b2005faf848044aede14b20003dceb948034d792320003dceb948029debf9f8e1fe20003dceb948012e5ddf5b614]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11dd30003dceb948004d588be530004e2ad8002130004e2ad800203c30003dceb94800185e9fe921fc30001eeb5ca80039883eaf643001de6d9a018f9c7f61f830001eeb5ca8001e3d0d28e0300779ae5804fb0b79a7e0004e2ad80023e00779ae58002edacd207fa0001eeb5ca8004fda380da1ffa00779ae58007d0c9aaca01fa0001eeb5ca8074e4d48e7a00779ae5800cfdf7a6fa3a005faf84800a9df9ebc21fea0003dceb94802495c6f2ce6a001de6d9a001b287c9ba07aa00779ae58004a39d89ee2a0005faf8a01990b7f2760004e2ad800214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1570004e2ad8002170004e2ad800203f30001eeb5ca804dafe3fa06f30003dceb948033cac2f673005faf84802a03b30005faf8a01fbebe16b3003bcdb2c054e6ae33005faf8480029c93c203e30003dceb948029e2c7861fe30003dceb9480019efdb5aa06e3001de6d9a001a087d615e30001eeb5ca801780a19a14e30003dceb94800290dcfbc601e3003bcdb2c001ddc0fe63002fd7c2800e16a30003dceb948061e391fe01a30017ebe18005baba9a230003dceb9480019e03d3001de6d9a006b8dcd206d30017ebe18001af92de14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x17f0004e2ad80023f0004e2ad800203fb005faf84801d989bbe06fb0003dceb94802d83dfb205fb0001eeb5ca804d9ba67b0004e2ad800216bb0001eeb5ca8051dec1de3b0004e2ad80021feb0017ebe1800b9091c26b0003dceb94806fa1b0ca1fab0001f492800188f6b22b0003dceb948001a48bcfe6770004e2ad8002370004e2ad800216e70003dceb94249ea205e70001eeb5ca8032c982ce670001eeb5ca8024a6c7f21ea70003dceb94800683befe01a70003dceb948007dddb8a270004e2ad800214]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11cf00003dceb94800aebdbccaa700003dceb948001e4a9e7c603e000779ae58001b4f7a4d21fe00003dceb94800ab5dce2ca1ee00003dceb9480018ec2caf202e00003dceb94800288fab3de15e00001eeb5ca8003c491c08205e00001eeb5ca8001ecd1bd96600003dceb948038c7e4ce03d00003dceb948006f695e617d00003dceb94802087ddf7aa1dd000779ae58002d6aeb2a2500002b196c00203c00017ebe1801082a48e1fc00003dceb948005a0df90d21ec00001eeb5ca802ac68bf202c00003dceb948004c9d0f0fa1cc000779ae58024a4a6aa05c00001eeb5ca8001c180da400002b196c00214]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x105f8001de6d9a009d7a4de780003dceb9480029a03e80001eeb5ca8008bba5ba17e8005faf84800f90e4e606e80003dceb9480058bb4b6f215e800779ae58001feede3861ce800779ae5807393a686680002b196c00203d80001eeb5ca8007a4eff3c216d80003dceb94800dd7edf9ce02d8001389b4800184d8de05d8001de6d9a015f3e4c6580002fdbc9002480002b196c002740002b196c002640002b196c002540002b196c002440002b196c00207f00003dceb948022e1d9b617f00003dceb94801eb9d988e214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x117c10001eeb5ca8005d7e5f89e02c10009c4da8028d59cd21dc10003dceb948002b49aebbe05c10003dceb948003bac7a2c2410003dceb948002f603810003dceb94800a939ed1fe17810003dceb948035ccd3a6168100779ae58003d593a69e15810003dceb94800c9bacb4da05810001eeb5ca8003ea8c93d2010001eeb5ca8001b617fc0001eeb5ca80749e06fc0003dceb9480749e7c0002b196c0026c0002b196c0025c0002b196c0024c0002b196c00203f800779ae58001bc8ce9aa17f80003dceb948014ac98f1c602f80001eeb5ca800f819fe614]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10589001de6d9a016f58dba090002b196c00216f50003dceb948004888c8daa15f50001eeb5ca8064dfd79a750003dceb948053b6b888be350001eeb5ca8020abe8818a550002b196c00201950001eeb5ca802cf9f3ae150002b196c00207e10003dceb948008e7aea2f217e10003dceb94801fc1fda58206e10001eeb5ca8001cca0b5ba1de100779ae58001cdb9c18e610002b196c00203a10003dceb948058c8befa17a1001389b4801ad5f09e16a10003dceb948005e5d4b9aa05a10001eeb5ca80018eed8afe210002b196c00203c10003dceb948008cd979b9614]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x117e90003dceb948008e7d2bcb616e90003dceb94800ffeabd7ae02e9002fd7c2807bc1cfb615e90003dceb9480048599858a1ce90001eeb5ca8001f780a9f201e90003dceb948044d391aa690002b196c00203a90004e2ad8009b48ea617a9001389b48024c481d202a90003dceb94800c9c90f6ee15a9002fd7c2803dbfcc8214a9002fd7c28010baf09a290003dceb948002e617c90001eeb5ca800883a8b58616c90001eeb5ca8002a2a7bf8206c9005faf8480069bd1ce1dc90001eeb5ca806af1f8961cc90001eeb5ca800289d4cce6490002b196c002178900779ae58004a5fac2ee14]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [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]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullEightCase0.base QuadFullEightCase0.hinges QuadFullEightCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase0.base QuadFullEightCase0.hinges QuadFullEightCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullEightCase1.base QuadFullEightCase1.hinges QuadFullEightCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz1045:"s0415"="s0415":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase1.base QuadFullEightCase1.hinges QuadFullEightCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r62,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullEightCase2.base QuadFullEightCase2.hinges QuadFullEightCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase2.base QuadFullEightCase2.hinges QuadFullEightCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullEightCase3.base QuadFullEightCase3.hinges QuadFullEightCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz1046:"s0416"="s0416":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase3.base QuadFullEightCase3.hinges QuadFullEightCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r62,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullEightCase4.base QuadFullEightCase4.hinges QuadFullEightCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase4.base QuadFullEightCase4.hinges QuadFullEightCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r45,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullEightCase5.base QuadFullEightCase5.hinges QuadFullEightCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz1047:"s0417"="s0417":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase5.base QuadFullEightCase5.hinges QuadFullEightCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r61,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullEightCase6.base QuadFullEightCase6.hinges QuadFullEightCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase6.base QuadFullEightCase6.hinges QuadFullEightCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r61,RewriteAtoms.r19,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullEightCase7.base QuadFullEightCase7.hinges QuadFullEightCase7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
private def zz1048:"s0418"="s0418":=by decide+kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase7.base QuadFullEightCase7.hinges QuadFullEightCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullEightCase8.base QuadFullEightCase8.hinges QuadFullEightCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase8.base QuadFullEightCase8.hinges QuadFullEightCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullEightCase9.base QuadFullEightCase9.hinges QuadFullEightCase9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
private def zz1049:"s0419"="s0419":=by decide+kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase9.base QuadFullEightCase9.hinges QuadFullEightCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r61,RewriteAtoms.r16,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullEightCase10.base QuadFullEightCase10.hinges QuadFullEightCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase10.base QuadFullEightCase10.hinges QuadFullEightCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r20,RewriteAtoms.r32,RewriteAtoms.r16,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullEightCase11.base QuadFullEightCase11.hinges QuadFullEightCase11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
private def zz1050:"s041a"="s041a":=by decide+kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase11.base QuadFullEightCase11.hinges QuadFullEightCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullEightCase12.base QuadFullEightCase12.hinges QuadFullEightCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase12.base QuadFullEightCase12.hinges QuadFullEightCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullEightCase13.base QuadFullEightCase13.hinges QuadFullEightCase13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
private def zz1051:"s041b"="s041b":=by decide+kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase13.base QuadFullEightCase13.hinges QuadFullEightCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullEightCase14.base QuadFullEightCase14.hinges QuadFullEightCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase14.base QuadFullEightCase14.hinges QuadFullEightCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullEightCase15.base QuadFullEightCase15.hinges QuadFullEightCase15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
private def zz1052:"s041c"="s041c":=by decide+kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase15.base QuadFullEightCase15.hinges QuadFullEightCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullEightCase16.base QuadFullEightCase16.hinges QuadFullEightCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase16.base QuadFullEightCase16.hinges QuadFullEightCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullEightCase17.base QuadFullEightCase17.hinges QuadFullEightCase17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
private def zz1053:"s041d"="s041d":=by decide+kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase17.base QuadFullEightCase17.hinges QuadFullEightCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullEightCase18.base QuadFullEightCase18.hinges QuadFullEightCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase18.base QuadFullEightCase18.hinges QuadFullEightCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullEightCase19.base QuadFullEightCase19.hinges QuadFullEightCase19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
private def zz1054:"s041e"="s041e":=by decide+kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullEightCase19.base QuadFullEightCase19.hinges QuadFullEightCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullEightCase19.nonnegative x hx
def pair20:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_20_base LocalFullEightPairs.compact_fullEight_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullEightPairs.fullEight_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_20_base LocalFullEightPairs.compact_fullEight_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullEightPairs.fullEight_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_21_base LocalFullEightPairs.compact_fullEight_pair_21_hinges
private def zz1055:"s041f"="s041f":=by decide+kernel
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullEightPairs.fullEight_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_21_base LocalFullEightPairs.compact_fullEight_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullEightPairs.fullEight_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_22_base LocalFullEightPairs.compact_fullEight_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
private def zz1056:"s0420"="s0420":=by decide+kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullEightPairs.fullEight_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_22_base LocalFullEightPairs.compact_fullEight_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullEightPairs.fullEight_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_23_base LocalFullEightPairs.compact_fullEight_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullEightPairs.fullEight_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_23_base LocalFullEightPairs.compact_fullEight_pair_23_hinges x
private def zz1057:"s0421"="s0421":=by decide+kernel
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullEightPairs.fullEight_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r69]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_24_base LocalFullEightPairs.compact_fullEight_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullEightPairs.fullEight_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_24_base LocalFullEightPairs.compact_fullEight_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullEightPairs.fullEight_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_25_base LocalFullEightPairs.compact_fullEight_pair_25_hinges
private def zz1058:"s0422"="s0422":=by decide+kernel
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullEightPairs.fullEight_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_25_base LocalFullEightPairs.compact_fullEight_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullEightPairs.fullEight_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r51,RewriteAtoms.r2]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_26_base LocalFullEightPairs.compact_fullEight_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
private def zz1059:"s0423"="s0423":=by decide+kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullEightPairs.fullEight_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_26_base LocalFullEightPairs.compact_fullEight_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullEightPairs.fullEight_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_27_base LocalFullEightPairs.compact_fullEight_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullEightPairs.fullEight_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_27_base LocalFullEightPairs.compact_fullEight_pair_27_hinges x
private def zz1060:"s0424"="s0424":=by decide+kernel
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullEightPairs.fullEight_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_28_base LocalFullEightPairs.compact_fullEight_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullEightPairs.fullEight_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_28_base LocalFullEightPairs.compact_fullEight_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullEightPairs.fullEight_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_29_base LocalFullEightPairs.compact_fullEight_pair_29_hinges
private def zz1061:"s0425"="s0425":=by decide+kernel
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullEightPairs.fullEight_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_29_base LocalFullEightPairs.compact_fullEight_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullEightPairs.fullEight_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r18,RewriteAtoms.r51]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_30_base LocalFullEightPairs.compact_fullEight_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
private def zz1062:"s0426"="s0426":=by decide+kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullEightPairs.fullEight_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_30_base LocalFullEightPairs.compact_fullEight_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullEightPairs.fullEight_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r26,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_31_base LocalFullEightPairs.compact_fullEight_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullEightPairs.fullEight_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_31_base LocalFullEightPairs.compact_fullEight_pair_31_hinges x
private def zz1063:"s0427"="s0427":=by decide+kernel
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullEightPairs.fullEight_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_32_base LocalFullEightPairs.compact_fullEight_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullEightPairs.fullEight_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_32_base LocalFullEightPairs.compact_fullEight_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullEightPairs.fullEight_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r70,RewriteAtoms.r27,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_33_base LocalFullEightPairs.compact_fullEight_pair_33_hinges
private def zz1064:"s0428"="s0428":=by decide+kernel
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullEightPairs.fullEight_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_33_base LocalFullEightPairs.compact_fullEight_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullEightPairs.fullEight_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_34_base LocalFullEightPairs.compact_fullEight_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
private def zz1065:"s0429"="s0429":=by decide+kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullEightPairs.fullEight_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_34_base LocalFullEightPairs.compact_fullEight_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullEightPairs.fullEight_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_35_base LocalFullEightPairs.compact_fullEight_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullEightPairs.fullEight_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_35_base LocalFullEightPairs.compact_fullEight_pair_35_hinges x
private def zz1066:"s042a"="s042a":=by decide+kernel
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullEightPairs.fullEight_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r51]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_36_base LocalFullEightPairs.compact_fullEight_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullEightPairs.fullEight_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_36_base LocalFullEightPairs.compact_fullEight_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullEightPairs.fullEight_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_37_base LocalFullEightPairs.compact_fullEight_pair_37_hinges
private def zz1067:"s042b"="s042b":=by decide+kernel
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullEightPairs.fullEight_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_37_base LocalFullEightPairs.compact_fullEight_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullEightPairs.fullEight_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_38_base LocalFullEightPairs.compact_fullEight_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
private def zz1068:"s042c"="s042c":=by decide+kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullEightPairs.fullEight_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_38_base LocalFullEightPairs.compact_fullEight_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullEightPairs.fullEight_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (8) ((1 / 0xf4240)) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullEightPairs.compact_fullEight_pair_39_base LocalFullEightPairs.compact_fullEight_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullEightPairs.fullEight_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullEightPairs.compact_fullEight_pair_39_base LocalFullEightPairs.compact_fullEight_pair_39_hinges x
private def zz1069:"s042d"="s042d":=by decide+kernel
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullEightPairs.fullEight_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (8) ((1 / 0xf4240)) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullEightRows
private def zz2299:"s08fb"="s08fb":=by decide+kernel
end 
section 
namespace Green24Proof.FullEightCyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullEightRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullEightRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullEightRows.rows p q same x]
    exact FullEightRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz1070:"s042e"="s042e":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 8 (1 / 0xf4240) FullEightRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullEightRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 8 (1 / 0xf4240) FullEightRows.rows p q same x]
    exact FullEightRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullEightRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullEightRows.rows
theorem remaining_rows_count:remainingRows.length = 10:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
      weightedAggregate 8 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullEightRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 8 (1 / 0xf4240) FullEightRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 8 h4 h3 h5 g FullEightRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
    weightedAggregate 8 h4 h3 g (stripPotentials FullEightRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullEightCyclic
private def zz2300:"s08fc"="s08fc":=by decide+kernel
end 
section 
namespace Green24Proof.FullEightMass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open FullPhaseRows (Phase)
open PhaseMassRows PhaseColourRows ConditionalMassRows
private def zz1071:"s042f"="s042f":=by decide+kernel
theorem remainingRows_eq:FullEightCyclic.remainingRows = [
  ((0x208dd9c9 / 0x3b9aca00), .base (.child 0)),
  ((0x3b17c5eb / 0x3b9aca00), .base (.heightChild 1)),
  ((0x1ab8bcb / 0x1dcd6500), .base (.grandchild 0)),
  ((0x830415 / 0x3b9aca00), .colourChild .whole),
  ((0x42d85e1 / 0x5f5e100), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,0,(17 / 7),0]:Fin 4 → ℚ) p)),
  ((0x21fdb63 / 0xbebc200), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,8, -1,8]:Fin 4 → ℚ) p)),
  ((0x38ffc79 / 0xee6b280), .massProduct (fun p => (![1, -6,1, -6]:Fin 4 → ℚ) p) (fun p => (![-1,8, -1,8]:Fin 4 → ℚ) p)),
  ((0x18c7b48d5 / 0x3b9aca00), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x172c307 / 0xee6b280), .base (.massSquare true (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((1 / 0x98968), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ)
    (_heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (_hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (8:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 6 8 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 8 h4 h3 g (.colourChild .whole) ≤ 0) :
    weightedAggregate 8 h4 h3 g FullEightCyclic.remainingRows ≤
      ((1 / 0x98968):ℝ) * mass g ^ 2:=by
  have hp4:rowAggregate 8 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,0,(17 / 7),0]:Fin 4 → ℚ) p)) ≤ 0:=by
    have h:=domainProduct_nonpos 8 6 8 h4 h3 g hforms 4 6
    have he:domainForm 6 8 6 =
        (fun p:Phase => (![-1,0,(17 / 7),0]:Fin 4 → ℚ) p):=by
      funext p
      norm_num [domainForm]
      rfl
    rw [he] at h
    exact h
  have hp5:rowAggregate 8 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,8, -1,8]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 8 6 8 h4 h3 g hforms 4 8
  have hp6:rowAggregate 8 h4 h3 g (.massProduct (fun p => (![1, -6,1, -6]:Fin 4 → ℚ) p) (fun p => (![-1,8, -1,8]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 8 6 8 h4 h3 g hforms 7 8
  have hs7:=rowAggregate_massSquare_nonpos 8 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hs8:=rowAggregate_colouredMassSquare_nonpos 8 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_normalization]
  norm_num
  linarith
theorem deficit_nonneg_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (8:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 6 8 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 8 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 8 h4 h3 g (.colourChild .whole) ≤ 0) :
    0 ≤ deficit g:=by
  have hc:=FullEightCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g heven hhigh hforms hchild hheight hgrand hcolour
  nlinarith [sq_nonneg (mass g)]
end Green24Proof.FullEightMass
private def zz2301:"s08fd"="s08fd":=by decide+kernel
end 
section 
namespace Green24Proof.FullEightProfileInterval
open FullPhaseRows (Phase)
open PhaseMassRows ChildRows HeightChildRows
theorem interval_nonneg_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(6:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (8:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_contra! hneg
  have hm:m < 2 * m:=by have hp:=NeZero.pos m; omega
  have hdu:=ih m hm (dvd_mul_left m 2) u hu
  have hdv:=ih m hm (dvd_mul_left m 2) v hv
  have hg:=interleave_nonneg u v hu hv
  have hforms:=ConditionalProfileRows.domainForms_nonneg 6 8 h4 h2 u v hu hv hdu hdv hneg
    (by norm_num) heven hodd hlow hhigh
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hchild:FullPhaseAggregation.rowAggregate 8 h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]; linarith
  have hheight:=rowAggregate_height_odd_nonpos 8 h4 h3 h2 u v hu hv
    (HeightStrong.strong_height_bound h2 h3m h5m v hv)
  have hgrand:=Full27ProfileInterval.grandchild_nonpos_of_induction 8 h4 h3 (interleave u v) hg 0 ih
  have hcolour:=ColourChildRows.whole_nonpos_of_induction 8 h4 h3 (interleave u v) hg ih
  have hhigh':phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 ≤
      (8:ℝ) * (phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3):=by
    rw [ProfileChildren.phaseTotal_interleave_zero h4 h2,
      ProfileChildren.phaseTotal_interleave_two h4 h2,phaseTotal_interleave_one h4 h2,
      phaseTotal_interleave_three h4 h2,classMass_sum,classMass_sum]
    exact hhigh
  have h:=FullEightMass.deficit_nonneg_of_rows h4 h3 h5 (interleave u v) hg
    heven hhigh' hforms hchild hheight hgrand hcolour
  linarith
private def zz1072:"s0430"="s0430":=by decide+kernel
theorem interval_nonneg {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(6:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (8:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,heven,hodd⟩ :=
    ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have h:=interval_nonneg_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hd] using h
end Green24Proof.FullEightProfileInterval
private def zz2302:"s08fe"="s08fe":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCoverEight
open ProfileInduction BoundaryFromHeightCertificates ConditionalProfileEndpoint
open RatioCoverSixteenFromRemaining (IntervalCertificate)
theorem interval_to_eight {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:ProperDivisorNonneg (2 * m))
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 8 * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases hsix:mass u ≤ 6 * mass v
  · exact RatioCoverSix.interval_to_six h4 h3 h5 h2 u v hu hv ih horder hsix
  · exact FullEightProfileInterval.interval_nonneg h4 h3 h5 h2 u v hu hv ih
      (le_of_lt (lt_of_not_ge hsix)) hhigh
theorem ratio_to_sixteen_of_remaining
    (h812:IntervalCertificate 8 12)
    (h1216:IntervalCertificate 12 16):RatioToSixteen:=by
  apply RatioCoverSixteenFromRemaining.ratio_to_sixteen_of_remaining _ h812 h1216
  intro m _
  exact FullEightProfileInterval.interval_nonneg
theorem deficit_nonneg_of_remaining
    (h812:IntervalCertificate 8 12)
    (h1216:IntervalCertificate 12 16)
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g :=
  deficit_nonneg_of_certificates (ratio_to_sixteen_of_remaining h812 h1216)
    hcertificate12 hcertificate18
end Green24Proof.RatioCoverEight
private def zz2303:"s08ff"="s08ff":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullTwelvePairs
def compact_fullTwelve_pair_20_base:CompactPair.Quadratic:=⟨(-1 / 0xb2d05e00),(0xc9 / 0xbebc200),0⟩
def compact_fullTwelve_pair_20_hinges:List CompactPair.Hinge:=[⟨(-0x910904f / 0x77359400),1, -2⟩,⟨(0x105103c1 / 0x165a0bc00),2, -3⟩,⟨(0x910904f / 0x77359400),2, -1⟩,⟨(-0x105103c1 / 0x165a0bc00),3, -2⟩]
noncomputable def fullTwelve_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_20_base compact_fullTwelve_pair_20_hinges x y
def compact_fullTwelve_pair_20_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2]
private def zz1073:"s0431"="s0431":=by decide+kernel
theorem compact_fullTwelve_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_20_base compact_fullTwelve_pair_20_hinges 0 compact_fullTwelve_pair_20_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_20_representation (x y:ℝ) :
    fullTwelve_pair_20 x y = CompactPair.expressionEval compact_fullTwelve_pair_20_base compact_fullTwelve_pair_20_hinges x y:=by rfl
theorem fullTwelve_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_20 x y:=by
  rw [compact_fullTwelve_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_20_check hy (by simpa using hx)
def compact_fullTwelve_pair_21_base:CompactPair.Quadratic:=⟨(7 / 0x11e1a3000),(0x329 / 0x77359400),0⟩
def compact_fullTwelve_pair_21_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x2cb417800),3, -2⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def fullTwelve_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_21_base compact_fullTwelve_pair_21_hinges x y
def compact_fullTwelve_pair_21_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullTwelve_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_21_base compact_fullTwelve_pair_21_hinges 0 compact_fullTwelve_pair_21_cuts = true :=
  by decide +kernel
private def zz1074:"s0432"="s0432":=by decide+kernel
theorem compact_fullTwelve_pair_21_representation (x y:ℝ) :
    fullTwelve_pair_21 x y = CompactPair.expressionEval compact_fullTwelve_pair_21_base compact_fullTwelve_pair_21_hinges x y:=by rfl
theorem fullTwelve_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_21 x y:=by
  rw [compact_fullTwelve_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_21_check hy (by simpa using hx)
def compact_fullTwelve_pair_22_base:CompactPair.Quadratic:=⟨0,(0x10b4f / 0xb68a0aa00),0⟩
def compact_fullTwelve_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullTwelve_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_22_base compact_fullTwelve_pair_22_hinges x y
def compact_fullTwelve_pair_22_cuts:List ℚ:=[]
theorem compact_fullTwelve_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_22_base compact_fullTwelve_pair_22_hinges 0 compact_fullTwelve_pair_22_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_22_representation (x y:ℝ) :
    fullTwelve_pair_22 x y = CompactPair.expressionEval compact_fullTwelve_pair_22_base compact_fullTwelve_pair_22_hinges x y:=by rfl
private def zz1075:"s0433"="s0433":=by decide+kernel
theorem fullTwelve_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_22 x y:=by
  rw [compact_fullTwelve_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_22_check hy (by simpa using hx)
def compact_fullTwelve_pair_23_base:CompactPair.Quadratic:=⟨(-0x29262a7 / 0x1e84800),(0xb5755677 / 0xe9a67400),0⟩
def compact_fullTwelve_pair_23_hinges:List CompactPair.Hinge:=[⟨(-0x29e0fa4d / 0x165a0bc00),1, -3⟩,⟨(0x12d044c15 / 0x1dcd65000),1, -2⟩,⟨(-0x3e8d8af3 / 0x165a0bc00),2, -3⟩,⟨(0xb16563b3 / 0xee6b2800),2, -1⟩,⟨(-0x4c6b6e33 / 0x1dcd65000),3, -2⟩]
noncomputable def fullTwelve_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_23_base compact_fullTwelve_pair_23_hinges x y
def compact_fullTwelve_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullTwelve_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_23_base compact_fullTwelve_pair_23_hinges 0 compact_fullTwelve_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_23_representation (x y:ℝ) :
    fullTwelve_pair_23 x y = CompactPair.expressionEval compact_fullTwelve_pair_23_base compact_fullTwelve_pair_23_hinges x y:=by rfl
theorem fullTwelve_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_23 x y:=by
  rw [compact_fullTwelve_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_23_check hy (by simpa using hx)
def compact_fullTwelve_pair_24_base:CompactPair.Quadratic:=⟨(-0x413f095 / 0x77359400),(0x15f9093 / 0x77359400),0⟩
def compact_fullTwelve_pair_24_hinges:List CompactPair.Hinge:=[⟨(0x41a3f1 / 0x23c34600),1, -3⟩,⟨(-0x87d571 / 0xbebc200),1, -2⟩,⟨(-0x2ed0f68f / 0x77359400),1, -1⟩,⟨(0x10d43a33 / 0x2cb417800),2, -3⟩,⟨(-0x19f24b59 / 0x2faf0800),2, -1⟩,⟨(0x21a0eaed / 0xb2d05e00),3, -2⟩,⟨(0x10f84997 / 0xb2d05e00),3, -1⟩]
noncomputable def fullTwelve_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_24_base compact_fullTwelve_pair_24_hinges x y
def compact_fullTwelve_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz1076:"s0434"="s0434":=by decide+kernel
theorem compact_fullTwelve_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_24_base compact_fullTwelve_pair_24_hinges 0 compact_fullTwelve_pair_24_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_24_representation (x y:ℝ) :
    fullTwelve_pair_24 x y = CompactPair.expressionEval compact_fullTwelve_pair_24_base compact_fullTwelve_pair_24_hinges x y:=by rfl
theorem fullTwelve_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_24 x y:=by
  rw [compact_fullTwelve_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_24_check hy (by simpa using hx)
def compact_fullTwelve_pair_25_base:CompactPair.Quadratic:=⟨(3 / 0x1dcd65000),(0x323 / 0x77359400),0⟩
def compact_fullTwelve_pair_25_hinges:List CompactPair.Hinge:=[⟨(-1 / 0xee6b2800),1, -2⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(1 / 0x59682f000),3, -2⟩]
noncomputable def fullTwelve_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_25_base compact_fullTwelve_pair_25_hinges x y
def compact_fullTwelve_pair_25_cuts:List ℚ:=[(1 / 2),(2 / 3),2]
theorem compact_fullTwelve_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_25_base compact_fullTwelve_pair_25_hinges 0 compact_fullTwelve_pair_25_cuts = true :=
  by decide +kernel
private def zz1077:"s0435"="s0435":=by decide+kernel
theorem compact_fullTwelve_pair_25_representation (x y:ℝ) :
    fullTwelve_pair_25 x y = CompactPair.expressionEval compact_fullTwelve_pair_25_base compact_fullTwelve_pair_25_hinges x y:=by rfl
theorem fullTwelve_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_25 x y:=by
  rw [compact_fullTwelve_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_25_check hy (by simpa using hx)
def compact_fullTwelve_pair_26_base:CompactPair.Quadratic:=⟨(0x5b5d93 / 0x47868c00),(0x6aeb / 0x490404400),0⟩
def compact_fullTwelve_pair_26_hinges:List CompactPair.Hinge:=[⟨(-0x7d24bbb / 0x165a0bc00),1, -3⟩,⟨(-0x11e13f9 / 0x17d78400),1, -1⟩,⟨(0xbd9ec5 / 0x3b9aca00),2, -3⟩,⟨(0x158cf3 / 0x7735940),2, -1⟩,⟨(-0xcace5 / 0xe4e1c00),3, -1⟩]
noncomputable def fullTwelve_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_26_base compact_fullTwelve_pair_26_hinges x y
def compact_fullTwelve_pair_26_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2),3]
theorem compact_fullTwelve_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_26_base compact_fullTwelve_pair_26_hinges 0 compact_fullTwelve_pair_26_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_26_representation (x y:ℝ) :
    fullTwelve_pair_26 x y = CompactPair.expressionEval compact_fullTwelve_pair_26_base compact_fullTwelve_pair_26_hinges x y:=by rfl
private def zz1078:"s0436"="s0436":=by decide+kernel
theorem fullTwelve_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_26 x y:=by
  rw [compact_fullTwelve_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_26_check hy (by simpa using hx)
def compact_fullTwelve_pair_27_base:CompactPair.Quadratic:=⟨(-0x52697dd39 / 0x1dcd65000),(0xc9e8e435f / 0xb68a0aa00),0⟩
def compact_fullTwelve_pair_27_hinges:List CompactPair.Hinge:=[⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-0x107b7f90d / 0x1dcd65000),2, -1⟩,⟨(0x41edfe43 / 0x77359400),3, -1⟩]
noncomputable def fullTwelve_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_27_base compact_fullTwelve_pair_27_hinges x y
def compact_fullTwelve_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),2]
theorem compact_fullTwelve_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_27_base compact_fullTwelve_pair_27_hinges 0 compact_fullTwelve_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_27_representation (x y:ℝ) :
    fullTwelve_pair_27 x y = CompactPair.expressionEval compact_fullTwelve_pair_27_base compact_fullTwelve_pair_27_hinges x y:=by rfl
theorem fullTwelve_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_27 x y:=by
  rw [compact_fullTwelve_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_27_check hy (by simpa using hx)
def compact_fullTwelve_pair_28_base:CompactPair.Quadratic:=⟨(-0x13c6059933d / 0xae9f7bcc00),(-0xaf89f5a69 / 0xe8d4a5100),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_28_hinges:List CompactPair.Hinge:=[⟨(-0x24785e4863 / 0x15d3ef79800),1, -3⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(0x24785e4863 / 0x15d3ef79800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_28_base compact_fullTwelve_pair_28_hinges x y
def compact_fullTwelve_pair_28_cuts:List ℚ:=[(1 / 3),3]
private def zz1079:"s0437"="s0437":=by decide+kernel
theorem compact_fullTwelve_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_28_base compact_fullTwelve_pair_28_hinges 0 compact_fullTwelve_pair_28_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_28_representation (x y:ℝ) :
    fullTwelve_pair_28 x y = CompactPair.expressionEval compact_fullTwelve_pair_28_base compact_fullTwelve_pair_28_hinges x y:=by rfl
theorem fullTwelve_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_28 x y:=by
  rw [compact_fullTwelve_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_28_check hy (by simpa using hx)
def compact_fullTwelve_pair_29_base:CompactPair.Quadratic:=⟨(-0x664c204437 / 0x3a35294400),(-0x16bb94952b / 0x1d1a94a200),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_29_hinges:List CompactPair.Hinge:=[⟨(-0xb5dcab23f / 0x746a528800),1, -3⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(0xb5dcab23f / 0x746a528800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_29_base compact_fullTwelve_pair_29_hinges x y
def compact_fullTwelve_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullTwelve_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_29_base compact_fullTwelve_pair_29_hinges 0 compact_fullTwelve_pair_29_cuts = true :=
  by decide +kernel
private def zz1080:"s0438"="s0438":=by decide+kernel
theorem compact_fullTwelve_pair_29_representation (x y:ℝ) :
    fullTwelve_pair_29 x y = CompactPair.expressionEval compact_fullTwelve_pair_29_base compact_fullTwelve_pair_29_hinges x y:=by rfl
theorem fullTwelve_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_29 x y:=by
  rw [compact_fullTwelve_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_29_check hy (by simpa using hx)
def compact_fullTwelve_pair_30_base:CompactPair.Quadratic:=⟨(-0xea68f9f7 / 0x17d78400),(0x3f909d9925 / 0xb68a0aa00),0⟩
def compact_fullTwelve_pair_30_hinges:List CompactPair.Hinge:=[⟨(-0x191c1609 / 0xee6b2800),2, -3⟩,⟨(0x1976c59f7 / 0x165a0bc00),3, -1⟩]
noncomputable def fullTwelve_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_30_base compact_fullTwelve_pair_30_hinges x y
def compact_fullTwelve_pair_30_cuts:List ℚ:=[(1 / 3),(3 / 2)]
theorem compact_fullTwelve_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_30_base compact_fullTwelve_pair_30_hinges 0 compact_fullTwelve_pair_30_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_30_representation (x y:ℝ) :
    fullTwelve_pair_30 x y = CompactPair.expressionEval compact_fullTwelve_pair_30_base compact_fullTwelve_pair_30_hinges x y:=by rfl
private def zz1081:"s0439"="s0439":=by decide+kernel
theorem fullTwelve_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_30 x y:=by
  rw [compact_fullTwelve_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_30_check hy (by simpa using hx)
def compact_fullTwelve_pair_31_base:CompactPair.Quadratic:=⟨(7 / 0x59682f000),(0x2635 / 0x2da282a80),0⟩
def compact_fullTwelve_pair_31_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x59682f000),3, -2⟩]
noncomputable def fullTwelve_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_31_base compact_fullTwelve_pair_31_hinges x y
def compact_fullTwelve_pair_31_cuts:List ℚ:=[(2 / 3),3]
theorem compact_fullTwelve_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_31_base compact_fullTwelve_pair_31_hinges 0 compact_fullTwelve_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_31_representation (x y:ℝ) :
    fullTwelve_pair_31 x y = CompactPair.expressionEval compact_fullTwelve_pair_31_base compact_fullTwelve_pair_31_hinges x y:=by rfl
theorem fullTwelve_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_31 x y:=by
  rw [compact_fullTwelve_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_31_check hy (by simpa using hx)
def compact_fullTwelve_pair_32_base:CompactPair.Quadratic:=⟨(-0x4f444248d / 0x15d3ef7980),(0x5cfde7dab1 / 0x1d1a94a200),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x2389ddf6737 / 0x15d3ef79800),1, -3⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(0xb5dcab23f / 0x746a528800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_32_base compact_fullTwelve_pair_32_hinges x y
def compact_fullTwelve_pair_32_cuts:List ℚ:=[(1 / 3),3]
private def zz1082:"s043a"="s043a":=by decide+kernel
theorem compact_fullTwelve_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_32_base compact_fullTwelve_pair_32_hinges 0 compact_fullTwelve_pair_32_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_32_representation (x y:ℝ) :
    fullTwelve_pair_32 x y = CompactPair.expressionEval compact_fullTwelve_pair_32_base compact_fullTwelve_pair_32_hinges x y:=by rfl
theorem fullTwelve_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_32 x y:=by
  rw [compact_fullTwelve_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_32_check hy (by simpa using hx)
def compact_fullTwelve_pair_33_base:CompactPair.Quadratic:=⟨(-0x132e465740d / 0xae9f7bcc00),(-0x16bb93d465 / 0x1d1a94a200),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0xb5dcab23f / 0x746a528800),1, -3⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(61 / 0x23c34600),2, -3⟩,⟨(0xb5dcab23f / 0x746a528800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_33_base compact_fullTwelve_pair_33_hinges x y
def compact_fullTwelve_pair_33_cuts:List ℚ:=[(1 / 3),(3 / 2),3]
theorem compact_fullTwelve_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_33_base compact_fullTwelve_pair_33_hinges 0 compact_fullTwelve_pair_33_cuts = true :=
  by decide +kernel
private def zz1083:"s043b"="s043b":=by decide+kernel
theorem compact_fullTwelve_pair_33_representation (x y:ℝ) :
    fullTwelve_pair_33 x y = CompactPair.expressionEval compact_fullTwelve_pair_33_base compact_fullTwelve_pair_33_hinges x y:=by rfl
theorem fullTwelve_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_33 x y:=by
  rw [compact_fullTwelve_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_33_check hy (by simpa using hx)
def compact_fullTwelve_pair_34_base:CompactPair.Quadratic:=⟨(-1 / 0x39387000),(1 / 0xf4240),0⟩
def compact_fullTwelve_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x2235db91 / 0x2cb417800),1, -3⟩,⟨(0x88d76e3f / 0x1dcd65000),1, -2⟩,⟨(-0x247db7 / 0x17d7840),2, -3⟩,⟨(-0x88d76e3f / 0x1dcd65000),2, -1⟩,⟨(0x247db7 / 0x17d7840),3, -2⟩,⟨(0x2235db91 / 0x2cb417800),3, -1⟩]
noncomputable def fullTwelve_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_34_base compact_fullTwelve_pair_34_hinges x y
def compact_fullTwelve_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullTwelve_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_34_base compact_fullTwelve_pair_34_hinges 0 compact_fullTwelve_pair_34_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_34_representation (x y:ℝ) :
    fullTwelve_pair_34 x y = CompactPair.expressionEval compact_fullTwelve_pair_34_base compact_fullTwelve_pair_34_hinges x y:=by rfl
private def zz1084:"s043c"="s043c":=by decide+kernel
theorem fullTwelve_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_34 x y:=by
  rw [compact_fullTwelve_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_34_check hy (by simpa using hx)
def compact_fullTwelve_pair_35_base:CompactPair.Quadratic:=⟨0,(0x193 / 0x3b9aca00),0⟩
def compact_fullTwelve_pair_35_hinges:List CompactPair.Hinge:=[]
noncomputable def fullTwelve_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_35_base compact_fullTwelve_pair_35_hinges x y
def compact_fullTwelve_pair_35_cuts:List ℚ:=[]
theorem compact_fullTwelve_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_35_base compact_fullTwelve_pair_35_hinges 0 compact_fullTwelve_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_35_representation (x y:ℝ) :
    fullTwelve_pair_35 x y = CompactPair.expressionEval compact_fullTwelve_pair_35_base compact_fullTwelve_pair_35_hinges x y:=by rfl
theorem fullTwelve_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_35 x y:=by
  rw [compact_fullTwelve_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_35_check hy (by simpa using hx)
def compact_fullTwelve_pair_36_base:CompactPair.Quadratic:=⟨(-0x8e41f81 / 0x3b9aca00),(0x8515c96e1 / 0x16d1415400),0⟩
def compact_fullTwelve_pair_36_hinges:List CompactPair.Hinge:=[⟨(-0x32a399 / 0x2625a00),1, -2⟩,⟨(0x6eb0cb9 / 0x77359400),2, -3⟩]
noncomputable def fullTwelve_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_36_base compact_fullTwelve_pair_36_hinges x y
def compact_fullTwelve_pair_36_cuts:List ℚ:=[(3 / 2),2]
private def zz1085:"s043d"="s043d":=by decide+kernel
theorem compact_fullTwelve_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_36_base compact_fullTwelve_pair_36_hinges 0 compact_fullTwelve_pair_36_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_36_representation (x y:ℝ) :
    fullTwelve_pair_36 x y = CompactPair.expressionEval compact_fullTwelve_pair_36_base compact_fullTwelve_pair_36_hinges x y:=by rfl
theorem fullTwelve_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_36 x y:=by
  rw [compact_fullTwelve_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_36_check hy (by simpa using hx)
def compact_fullTwelve_pair_37_base:CompactPair.Quadratic:=⟨(-0x92b1927 / 0x2cb417800),(0x88edf13 / 0x490404400),0⟩
def compact_fullTwelve_pair_37_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(-0xc1 / 0x77359400),1, -1⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(0x1bf0fe7 / 0xee6b2800),2, -1⟩,⟨(-0x6fc399 / 0xee6b2800),3, -2⟩]
noncomputable def fullTwelve_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_37_base compact_fullTwelve_pair_37_hinges x y
def compact_fullTwelve_pair_37_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),3]
theorem compact_fullTwelve_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_37_base compact_fullTwelve_pair_37_hinges 0 compact_fullTwelve_pair_37_cuts = true :=
  by decide +kernel
private def zz1086:"s043e"="s043e":=by decide+kernel
theorem compact_fullTwelve_pair_37_representation (x y:ℝ) :
    fullTwelve_pair_37 x y = CompactPair.expressionEval compact_fullTwelve_pair_37_base compact_fullTwelve_pair_37_hinges x y:=by rfl
theorem fullTwelve_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_37 x y:=by
  rw [compact_fullTwelve_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_37_check hy (by simpa using hx)
def compact_fullTwelve_pair_38_base:CompactPair.Quadratic:=⟨(-0x9a9166b109 / 0x574fbde600),(-0x162f885e2d / 0x1d1a94a200),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_38_hinges:List CompactPair.Hinge:=[⟨(-0xb5dcab23f / 0x746a528800),1, -3⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(-0xeb48bd / 0x165a0bc00),2, -3⟩,⟨(0xeb48bd / 0x165a0bc00),3, -2⟩,⟨(0xb5dcab23f / 0x746a528800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_38_base compact_fullTwelve_pair_38_hinges x y
def compact_fullTwelve_pair_38_cuts:List ℚ:=[(1 / 3),(2 / 3),(3 / 2),3]
theorem compact_fullTwelve_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_38_base compact_fullTwelve_pair_38_hinges 0 compact_fullTwelve_pair_38_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_38_representation (x y:ℝ) :
    fullTwelve_pair_38 x y = CompactPair.expressionEval compact_fullTwelve_pair_38_base compact_fullTwelve_pair_38_hinges x y:=by rfl
private def zz1087:"s043f"="s043f":=by decide+kernel
theorem fullTwelve_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_38 x y:=by
  rw [compact_fullTwelve_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_38_check hy (by simpa using hx)
def compact_fullTwelve_pair_39_base:CompactPair.Quadratic:=⟨(-0x199303965b1 / 0xe8d4a51000),(-0x2d7735178f / 0x3a35294400),(-0xb5dcab23f / 0xba43b7400)⟩
def compact_fullTwelve_pair_39_hinges:List CompactPair.Hinge:=[⟨(-0xb5dcab23f / 0x746a528800),1, -3⟩,⟨(0x1f5 / 0x1312d000),1, -2⟩,⟨(0xb5dcab23f / 0x746a528800),1,3⟩,⟨(-0x1f5 / 0x1312d000),2, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3, -1⟩,⟨(0xb5dcab23f / 0x746a528800),3,1⟩]
noncomputable def fullTwelve_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullTwelve_pair_39_base compact_fullTwelve_pair_39_hinges x y
def compact_fullTwelve_pair_39_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
theorem compact_fullTwelve_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullTwelve_pair_39_base compact_fullTwelve_pair_39_hinges 0 compact_fullTwelve_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullTwelve_pair_39_representation (x y:ℝ) :
    fullTwelve_pair_39 x y = CompactPair.expressionEval compact_fullTwelve_pair_39_base compact_fullTwelve_pair_39_hinges x y:=by rfl
theorem fullTwelve_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullTwelve_pair_39 x y:=by
  rw [compact_fullTwelve_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullTwelve_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullTwelvePairs
private def zz2304:"s0900"="s0900":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l42 l43 l45 l5 l51 l54 l55 l57 l58 l6 l60 l62 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1d5109629, -0x2b4041b78, -0x40e062c04,0x52df6604], ![-0x2b4041b78, -0x912e80310,0xab06a2d8,0x2b30c06da], ![-0x40e062c04,0xab06a2d8, -0x11921ad149,0x2b40424d8], ![0x52df6604,0x2b30c06da,0x2b40424d8, -0x15a021014]]
noncomputable def hinges:Hinges:=[(-0x10fa62e,l6),(-0x22d212bf,l5),(0x127276ec6,l4),(-0xa5868d88,l8),(-0x884b066,l11),(0x3546f792,l10),(0x2bfcc4c00,l14),(-0x97808a8a,l17),(0x72e31d7a,l23),(0x3f8b8ab,l22),(-0x15a021014,l27),(0x15a021014,l29),(-0x2bfcc4c00,l25),(0x938524fc,l31),(0xc8659b76,l30),(0x15a021014,l33),(-0x3546f792,l38),(-0x15a021014,l35),(0xa5868d88,l36),(0x15a021014,l37),(-0x127276ec6,l34),(-0xc8659b76,l43),(-0x3f8b8ab,l42),(0x74b8350a,l45),(0x15a021014,l51),(0x884b066,l55),(0x22d212bf,l54),(-0x938524fc,l57),(-0x74b8350a,l58),(0x10fa62e,l60),(-0x72e31d7a,l63),(0x97808a8a,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x15a021014,l27),(0x15a021014,l29),(0x15a021014,l33),(-0x15a021014,l35),(0x15a021014,l37),(0x15a021014,l51),(0x2bfcc4c00,l14),(-0x2bfcc4c00,l25),(0x938524fc,l31),(-0x938524fc,l57),(0xc8659b76,l30),(-0xc8659b76,l43),(0x72e31d7a,l23),(-0x72e31d7a,l63),(-0x97808a8a,l17),(0x97808a8a,l62),(-0xa5868d88,l8),(0xa5868d88,l36),(0x127276ec6,l4),(-0x127276ec6,l34),(0x74b8350a,l45),(-0x74b8350a,l58),(0x3546f792,l10),(-0x3546f792,l38),(-0x22d212bf,l5),(0x22d212bf,l54),(-0x884b066,l11),(0x884b066,l55),(0x3f8b8ab,l22),(-0x3f8b8ab,l42),(-0x10fa62e,l6),(0x10fa62e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase0" = "QuadFullTwelveCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase0
private def zz2305:"s0901"="s0901":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l55 l58 l6 l60 l62 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x237543275, -0x2aeb56de0, -0x406102776,0x4397dc0c], ![-0x2aeb56de0, -0x8ff9ef492,0x878b8666,0x2c9c6031c], ![-0x406102776,0x878b8666, -0x116f9b68ed,0x2aeb57740], ![0x4397dc0c,0x2c9c6031c,0x2aeb57740, -0x1575ab948]]
noncomputable def hinges:Hinges:=[(-0x10fa62e,l6),(-0x22d212bf,l5),(0x127276ec6,l4),(-0xa5868d88,l8),(-0x884b066,l11),(0x3546f792,l10),(0x2a8ab1aaa,l14),(0x1f4a1bfc,l13),(-0x4b9cffbe,l17),(0x4002f231c,l15),(0x2bf8ffba,l21),(-0x1f4a1bfc,l20),(-0x22c38877,l23),(0x151d2fd10,l22),(-0x1575ab948,l27),(-0x2bf8ffba,l28),(0x1575ab948,l29),(-0x2a8ab1aaa,l25),(0x9fcf151e,l30),(0x1575ab948,l33),(-0x3546f792,l38),(-0x1575ab948,l35),(0xa5868d88,l36),(0x1575ab948,l37),(-0x127276ec6,l34),(-0x9fcf151e,l43),(-0x151d2fd10,l42),(-0x4002f231c,l41),(-0x2ecf17b4,l46),(0xfc3e6dc6,l45),(0x1575ab948,l51),(0x884b066,l55),(0x22d212bf,l54),(-0xfc3e6dc6,l58),(0x10fa62e,l60),(0x22c38877,l63),(0x4b9cffbe,l62),(0x2ecf17b4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1575ab948,l27),(0x1575ab948,l29),(0x1575ab948,l33),(-0x1575ab948,l35),(0x1575ab948,l37),(0x1575ab948,l51),(0x2a8ab1aaa,l14),(-0x2a8ab1aaa,l25),(0x4002f231c,l15),(-0x4002f231c,l41),(0x151d2fd10,l22),(-0x151d2fd10,l42),(0x9fcf151e,l30),(-0x9fcf151e,l43),(0xfc3e6dc6,l45),(-0xfc3e6dc6,l58),(-0xa5868d88,l8),(0xa5868d88,l36),(-0x4b9cffbe,l17),(0x4b9cffbe,l62),(0x127276ec6,l4),(-0x127276ec6,l34),(0x2bf8ffba,l21),(-0x2bf8ffba,l28),(-0x22c38877,l23),(0x22c38877,l63),(0x3546f792,l10),(-0x3546f792,l38),(-0x2ecf17b4,l46),(0x2ecf17b4,l64),(-0x22d212bf,l5),(0x22d212bf,l54),(0x1f4a1bfc,l13),(-0x1f4a1bfc,l20),(-0x884b066,l11),(0x884b066,l55),(-0x10fa62e,l6),(0x10fa62e,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase1" = "QuadFullTwelveCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase1
private def zz2306:"s0902"="s0902":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l16 l22 l27 l29 l33 l35 l37 l51 l6 l62 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x20c5cf7b86, -0x59682eb50, -0x62ae81e3e,0x1f21b98b8], ![-0x59682eb50, -0x29b1953b42,0x10414b2c34, -0x63ba9ef5e], ![-0x62ae81e3e,0x10414b2c34, -0x30b51ae2a5,0xa94348484], ![0x1f21b98b8, -0x63ba9ef5e,0xa94348484, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x1c163d9e,l6),(0x628e17bf,l11),(0x100dfe92c,l10),(-0x5baf140e,l16),(0x16ebc4dd4,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x446b12582,l62),(0x530498ac,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x446b12582,l62),(0x100dfe92c,l10),(0x16ebc4dd4,l22),(0x628e17bf,l11),(0x530498ac,l65),(-0x5baf140e,l16),(-0x1c163d9e,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 14 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase2" = "QuadFullTwelveCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 14 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase2
private def zz2307:"s0903"="s0903":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l22 l23 l27 l29 l31 l33 l35 l37 l44 l51 l6 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2c89a682c, -0x591343db8,0x859ce38e8,0x1650], ![-0x591343db8, -0x2232849eca,0xdd7c53be0, -0x61f1ed124], ![0x859ce38e8,0xdd7c53be0, -0x30929b7a49,0xa8ee5d6ec], ![0x1650, -0x61f1ed124,0xa8ee5d6ec, -0x2c89a2134]]
noncomputable def hinges:Hinges:=[(-0x1c163d9e,l6),(0x628e17bf,l11),(0x100dfe92c,l10),(0x31bdb6434,l14),(0x19b533256,l13),(0x22c,l17),(-0x15caa9ee,l16),(0xcb8de20,l15),(0xfa362b44,l21),(-0x428605632,l20),(-0x2148ccee,l23),(0x1e07ed1d0,l22),(-0x2c89a2134,l27),(0x2c89a2134,l29),(-0x1a9f7982,l31),(0x2c89a2134,l33),(-0x2c89a2134,l35),(0x2c89a2134,l37),(-0x90c,l44),(0x2c89a2134,l51),(0x8e4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c89a2134,l27),(0x2c89a2134,l29),(0x2c89a2134,l33),(-0x2c89a2134,l35),(0x2c89a2134,l37),(0x2c89a2134,l51),(0x31bdb6434,l14),(-0x428605632,l20),(0xfa362b44,l21),(0x1e07ed1d0,l22),(0x100dfe92c,l10),(0x19b533256,l13),(0x628e17bf,l11),(-0x2148ccee,l23),(-0x1a9f7982,l31),(-0x1c163d9e,l6),(-0x15caa9ee,l16),(0xcb8de20,l15),(0x8e4,l64),(-0x90c,l44),(0x22c,l17)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x1340288030000000009c0620080000120110058c040000000443c053008000001282402cc03000004e0440163010000250982402d003], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase3" = "QuadFullTwelveCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase3
private def zz2308:"s0904"="s0904":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l17 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l46 l5 l51 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3c120f4d7, -0x3183ffb58, -0x4a45ffbf8,0x112f37184], ![-0x3183ffb58, -0x180efff124,0x3c3cd6e9c,0x21cb2370a], ![-0x4a45ffbf8,0x3c3cd6e9c, -0x1426c172cb,0x319c7a1f8], ![0x112f37184,0x21cb2370a,0x319c7a1f8, -0x18c200004]]
noncomputable def hinges:Hinges:=[(-0x3d10e71,l5),(0x18fd7d738,l4),(-0x18a5ca13,l9),(-0x8fce70ac,l8),(-0x10f0c930,l11),(0x30d2129c,l10),(0xfcf67134,l14),(0x19438cb78,l13),(0x231cb8eb4,l12),(-0x97808a8a,l17),(0x72e31d7a,l23),(0x3f8b8ab,l22),(-0x18c200004,l27),(-0x10d075768,l28),(0x18c200004,l29),(-0x8a2b9834,l25),(0x938524fc,l31),(0xc8659b76,l30),(0x18c200004,l33),(-0x18c200004,l35),(0x18c200004,l37),(-0x9871fefc,l43),(-0xd7f02c0b,l42),(-0x2bc57027e,l41),(0x18559134,l46),(0x18c200004,l51),(-0x446bb720,l63),(0x21a87466,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x18c200004,l27),(0x18c200004,l29),(0x18c200004,l33),(-0x18c200004,l35),(0x18c200004,l37),(0x18c200004,l51),(-0x10d075768,l28),(0xfcf67134,l14),(0x938524fc,l31),(0x19438cb78,l13),(0xc8659b76,l30),(0x72e31d7a,l23),(-0x2bc57027e,l41),(-0x9871fefc,l43),(-0x97808a8a,l17),(0x231cb8eb4,l12),(-0x8a2b9834,l25),(-0xd7f02c0b,l42),(-0x446bb720,l63),(0x18fd7d738,l4),(-0x8fce70ac,l8),(0x21a87466,l65),(0x30d2129c,l10),(-0x18a5ca13,l9),(-0x10f0c930,l11),(0x18559134,l46),(0x3f8b8ab,l22),(-0x3d10e71,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0xc304409130100000000031034802000000000b40920080000024844054c03002b49c138049401000002582100bcc04002889611c02940100000184210124c04000000860b025300c000000000440c801000000064240730080000021028034c030000005221014300c00000000e140cc01001c8631480cb401000000000210248020000003a1100d300c00000000050248020000000481409300800020629006c8c05000000064140a30080002062a809c8c0500000000054072008000000190503cc020000003a11022300c10318408806c9005040c62825027240140000018824058c030000000000303200400000000390388020000004a19022300c0000000006c0c801000000000d4092008000000001d02480202884186200f14014000001c86409cc030000c4321100d400d8115210101c85006001704109c0c84010006214c42032d004000f02105003c4010003c0841a0271004001d03408407840100000000009018802000002105003c30100000008828030c03000000098540530080000000002c0c8010000000945406300800000248ac038c03000000004f00b200c000000013404c8030000000058303300400000000150348020000000542c0d30080000001511028c02000000000a40d20081431c42540621005000000863902f300c0000001106014c020000000645c0d3008000000000d02480200000007c480e30080000000005018802,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((0x9202243c1683070462d2d14a1ea1c9d73c24709f90d8bc910cb7d158828301efef41c700a31cfade4270c2200800d00c1b8076508d) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase4" = "QuadFullTwelveCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase4
private def zz2309:"s0905"="s0905":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l15 l17 l20 l22 l23 l27 l28 l29 l30 l33 l35 l37 l4 l41 l42 l44 l45 l5 l51 l56 l57 l59 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3c06a31b4, -0x312f14dc0, -0x49c69f6f8,0x10a06abc4], ![-0x312f14dc0, -0x1806b7f5f8,0x38da5b994,0x2336c334c], ![-0x49c69f6f8,0x38da5b994, -0x1404420a6f,0x31478f460], ![0x10a06abc4,0x2336c334c,0x31478f460, -0x18978a938]]
noncomputable def hinges:Hinges:=[(-0x3d10e71,l5),(0x18fd7d738,l4),(-0x18a5ca13,l9),(-0x8fce70ac,l8),(-0x10f0c930,l11),(0x30d2129c,l10),(0x417166d46,l13),(-0x4b9cffbe,l17),(0x4002f231c,l15),(-0x3712d634c,l20),(-0x22c38877,l23),(0x151d2fd10,l22),(-0x18978a938,l27),(-0x98acd16,l28),(0x18978a938,l29),(0x9fcf151e,l30),(0x18978a938,l33),(-0x18978a938,l35),(0x18978a938,l37),(-0x1278c4fa4,l42),(-0x28d1645ba,l41),(0x5b436ba4,l45),(-0x1f437270,l44),(0x18978a938,l51),(-0x73c0ebd9,l57),(0x4e01f2b7,l56),(0x192efafa,l59),(-0x31bed88e,l63),(-0xfbf3e4c,l65),(0x13619d48,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x18978a938,l27),(0x18978a938,l29),(0x18978a938,l33),(-0x18978a938,l35),(0x18978a938,l37),(0x18978a938,l51),(0x417166d46,l13),(-0x3712d634c,l20),(0x4002f231c,l15),(0x151d2fd10,l22),(-0x73c0ebd9,l57),(-0x1278c4fa4,l42),(-0x28d1645ba,l41),(0x9fcf151e,l30),(0x18fd7d738,l4),(-0x8fce70ac,l8),(-0x31bed88e,l63),(-0x4b9cffbe,l17),(-0x22c38877,l23),(0x5b436ba4,l45),(0x30d2129c,l10),(0x4e01f2b7,l56),(0x192efafa,l59),(-0x18a5ca13,l9),(-0x10f0c930,l11),(-0xfbf3e4c,l65),(0x13619d48,l64),(-0x98acd16,l28),(-0x1f437270,l44),(-0x3d10e71,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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,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,0x39024802000000000340d2008000000390d038c020000000002903200400001c43602bcc04000000000f407200800000001fc02c803000000007d013200c000001d0680b4c03000000520902d300c0000000035018802000000006d00a200c000000003601480200000560440fa30100000000035038802058c91103028b4014000000008c0b080300000610d80af301000000190680b4c03000000420902d300c00001181103e8c040028c8c1cc0ab4010000000004403480300000000044092008000000000940c801], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase5" = "QuadFullTwelveCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase5
private def zz2310:"s0906"="s0906":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase6
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l16 l20 l22 l27 l29 l33 l35 l37 l5 l51 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x1655c90ee, -0x2cb4175a8,0x2331bb5f0,0x258], ![-0x2cb4175a8, -0x14e9a21fc5,0x80e032414, -0x31dd4f7af], ![0x2331bb5f0,0x80e032414, -0x18160875f6,0x54b6b0599], ![0x258, -0x31dd4f7af,0x54b6b0599, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0x1bf0fe7,l5),(0xc5713425,l8),(0x50985663,l10),(0xfa49776,l14),(0x2186572e,l12),(-0x2dd78a07,l16),(-0x814db20,l20),(0xb75e26ea,l22),(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x79302,l64)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(0xc5713425,l8),(0xb75e26ea,l22),(0x50985663,l10),(-0x2dd78a07,l16),(0xfa49776,l14),(0x2186572e,l12),(-0x814db20,l20),(0x1bf0fe7,l5),(-0x79302,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase6" = "QuadFullTwelveCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase6
private def zz2311:"s0907"="s0907":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l16 l17 l22 l23 l25 l27 l29 l31 l33 l35 l37 l5 l51 l57 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x1644d0712, -0x2c89a1edc,0x42ce727e4,0x258], ![-0x2c89a1edc, -0xae667fc7d,0x5c53d5e66, -0x30f8f6892], ![0x42ce727e4,0x5c53d5e66, -0x1804c8c1c8,0x548c3aecd], ![0x258, -0x30f8f6892,0x548c3aecd, -0x1644d109a]]
noncomputable def hinges:Hinges:=[(0x1bf0fe7,l5),(0xc5713425,l8),(0x50985663,l10),(0x11aff2796,l14),(0x2999d1d0d,l13),(0x116,l17),(-0xae554f7,l16),(0x65c6f10,l15),(-0x10a46677,l23),(0xf03f68e8,l22),(-0x1644d109a,l27),(0x1644d109a,l29),(-0x18b93f592,l25),(-0xd4fbcc1,l31),(0x1644d109a,l33),(-0x1644d109a,l35),(0x1644d109a,l37),(0x1644d109a,l51),(-0x262,l57)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1644d109a,l27),(0x1644d109a,l29),(0x1644d109a,l33),(-0x1644d109a,l35),(0x1644d109a,l37),(0x1644d109a,l51),(-0x18b93f592,l25),(0x2999d1d0d,l13),(0x11aff2796,l14),(0xf03f68e8,l22),(0xc5713425,l8),(0x50985663,l10),(-0x10a46677,l23),(-0xd4fbcc1,l31),(-0xae554f7,l16),(0x65c6f10,l15),(0x1bf0fe7,l5),(-0x262,l57),(0x116,l17)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((0x91f14b6da8907147c7899cc08100c741617c80c15d06ba8070c28d38eda46000259716c450037b7c6b449c109002123ca9299c2930a18000000834038c2a56af66c91c5152b5771c49020e6ed4c9228a04135f7cda840822af9c6da1c2004af9b99c593c4021480c000073c83004c17c0600c030200180f80e068e1eb109d0122884f9407f946140c22bcdc3048816ab8d03b31841a1da4786412086aa81c0b803005c53d5e6600001dcaed3) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 20 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase7" = "QuadFullTwelveCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 20 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase7
private def zz2312:"s0908"="s0908":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l62 l68)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x148660a1, -0x2a75474, -0x3faffda,0x258], ![-0x2a75474, -0x13ad43bd,0x15aadc6,0x34daed3], ![-0x3faffda,0x15aadc6, -0x113fb42e,0x2a75924],l68]
noncomputable def hinges:Hinges:=[(0x26d8f8f,l17),(-0x153ab66,l27),(0x153ab66,l29),(0x153ab66,l33),(-0x153ab66,l35),(0x153ab66,l37),(0x153ab66,l51),(-0x26d8f8f,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x153ab66,l27),(0x153ab66,l29),(0x153ab66,l33),(-0x153ab66,l35),(0x153ab66,l37),(0x153ab66,l51),(0x26d8f8f,l17),(-0x26d8f8f,l62)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000029090009980800000000b0024803000000006c01240180006804100263014000000001c029005420a404200335006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := 0x18696ba29c61400012c1c42b55d1c604004b0d1010000190104000036b000d0022450a4715b2440fb46cc1c4982a12e18472d9ca4182fea81e0200fe6953414035775610800e7c5c5a4000e00a0000590c0c00020d1f1869631140a3b74048a009f5f9f2f0b5442d7f9b1ee38882d7ff04266c77bd40327d7a3840dc57cac6331589e9bef5db81820023303c5d13409b28cff6bc083d6beb9b85909c048342f71c7c01a88e276abbc477180180471c42251d33eccf6662e9a1840a96b70390e42fd4521822599a78871f70555290c100bdb60bbf35f257050419648e1c54d2baa6d282002025b0acddb2c60d6d14005317b2d6e8a2ff5550800f7a6b1b8eadf5ba81f98206a1fa0a001202e00005d840017d4e1bc7be2b157f9598fc0c985dd47cefd2c070851685f96d104dcb5704d2bdcf1dd4558408f2526c2c5ae202e2a03dd2b8e6d3f1443041ae93b4967863a33f3a93fb21c72b9bc204a32c192f9535ed120e68ac501a98b280772f8f2339be06d6f2fa501689433296224d8b631aa4873fab4297388eca11003480003c73421ba4892fb861046eb59b3c20821da488e03020876922381413507bbc43860846e73b03c502de2b215e82006a5ef735a3f9327f1443c22030940b00003b8402c140140281a4c9663e49028adea0e121c273d4f417c304323751774508437d147c100134e1b4da140086faff0839a78c28a1c924e849449c208c091c7929f3fd88144f805272042665738c71000012c0200001fa37450000004b000000002aa27001e00840ad15c7fc4880000c8040900cfc183820e54cce30000003201001571e6a08014ecda93800e00400004e4c8e9e4dbe5af2a6388c5de0eed353e4060003b830fc8038770d41555147018403b3614161d220003b44f4da0f203387f623b3565912cc08600b00001cf200090870d49d8a938c1800012c02823a45ada8c00e91652a1800000064040000003216001e0040048080200400e0200015a200c1b815688e7fbf5422dbeb003040a8f08661d60f2e750803d59c62ea0e35b10b587002d7e550feefe18809c500eea9a20d1d784f7dec201b914b5e622ee70becb4735605bf6c7b4fb0267c228ad69492b8d1a9f7fa4922f9b731b5dab1a373ccbf0a60c480c0596470b1b5396296318406220820a5000b0086d20fd8c66a05f25eca3dd200000171dd828458c30c3084044022001000818000100680008a1800008022461026be4808053a37041f65d5d840042846808026a105e5001a00800006f900011c3028fc7ce8822fea4b020d0ce930e01009fb84810300100000b5200079475d12e14c48c146afe104759c5accae99bd000000000000000d4ecd4ceea813e00e4e6259152200000000022b0008c40c30460050010324b5c2ba727252aad9eae781dcc03206cc17cafb86bb0d8ff0b04e59639ed64535b088794b6d35ce6b3821f4308cc6a886295d4000d3080053890012703c3bedf40041000cd886059a360c20232b5f008109c24f0a0230d6c8301827bda4e0832010e3c2a05b038a0002580c2800433430405fb4e0c0a9d4cba20200012c13020d004000041880280a0507b6788a2052612c7050afba82833d314d90006402123b87e35460974929c3823439931418ffe6e0602c251c82012344220801ae6779c006402000024870d5655605098d81dc4002e010a20034ed0e10fbb8e8c17f11628604c70d184052c89aca00300100000d420002aa6043c9077d3ac0cc3ff09af59513eb037082bcfa9db2ab44f2744dde107ad16a1c180e72ab8ac235e30f13c53fdb14d91a31409bf7fab149817806cb043398f23553100826623aa0938c0498b6f3381c7e1042b01a00535afdc712ab6120fae919ebaa288c02b1e889cc3041e15ca08f0308e18f91ffac2088ec8ee0cfbf2ecd44769aaa59b5dc1b65b514260f69c944e1f7ae12bb46250a1ee9e55be72ef0862553d4748370fa75078c04ce641c11819ed3c8ddd070d8c9b0afa1a14d6df6e3725322e210de229933de37edc9e54b1025b95a0000c288003599000a323458de2033850c2bcdd9d1412f5211b440400006401000d2aa910300000019008001e087ba7001e0086197ff6400c516653125e461000002ee060c00002ee050c000110f450491acc37040400002ee2b8010006000055480202800c04004020002f5200202000010007f11
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 9 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase8" = "QuadFullTwelveCase8" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 9 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase8
private def zz2313:"s0909"="s0909":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz1128:"s0468"="s0468":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullTwelveCase9
private def zz2314:"s090a"="s090a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l17 l21 l25 l27 l29 l33 l35 l36 l37 l38 l42 l43 l51 l56 l59 l6 l61 l62 l64 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2d8ea1ddc, -0x588e87e56, -0x861c46350,0x498], ![-0x588e87e56,0xe570e023e,0x5ec285b84,0x6a92b5248], ![-0x861c46350,0x5ec285b84, -0x2458a17658,0x5996c0c64], ![0x498,0x6a92b5248,0x5996c0c64, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(26,l6),(-0x6358a1,l9),(0xdf8732,l11),(0x446b12582,l17),(0x96a88436,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x65da241d8,l25),(0x2cb417800,l33),(-0xd1727da0,l38),(-0x2cb417800,l35),(-0x1b6200787,l36),(0x2cb417800,l37),(-0x839c076e,l43),(-0x4e974b32,l42),(0x2cb417800,l51),(0x16761c63,l56),(-0x11c6e278,l59),(0x4c6b6e33,l61),(0xd5f6e58,l62),(0x4f38974,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x65da241d8,l25),(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x446b12582,l17),(-0x1b6200787,l36),(0x96a88436,l21),(-0xd1727da0,l38),(-0x839c076e,l43),(0x4c6b6e33,l61),(-0x4e974b32,l42),(-0x11c6e278,l59),(0xd5f6e58,l62),(0x16761c63,l56),(0x4f38974,l64),(0xdf8732,l11),(-0x6358a1,l9),(26,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, #[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,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,0x882c0d30081f01950b303ad5006063041c1640a6d401800051114140265004000150450440694010000018819405ccc0500000650630253301401021c60c40929005], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase10" = "QuadFullTwelveCase10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase10
private def zz2315:"s090b"="s090b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l14 l25 l27 l28 l29 l33 l35 l36 l37 l38 l41 l42 l43 l51 l6 l61 l63 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2f0ce7bd7, -0x58399d0be, -0x859ce5eec,0x4b0], ![-0x58399d0be,0xf883b044,0x66efa1314,0x859ce38e8], ![-0x859ce5eec,0x66efa1314, -0x2436220dfc,0x5941d5ecc], ![0x4b0,0x859ce38e8,0x5941d5ecc, -0x2c89a2134]]
noncomputable def hinges:Hinges:=[(26,l6),(-0x6358a1,l9),(0xdf8732,l11),(0x5442b8d8,l14),(-0x2c89a2134,l27),(-0x127aa473c,l28),(0x2c89a2134,l29),(-0x3029fbb84,l25),(0x2c89a2134,l33),(-0xd1727da0,l38),(-0x2c89a2134,l35),(-0x1b6200787,l36),(0x2c89a2134,l37),(0x52ebe862,l43),(-0x2cd7635b4,l42),(0x23b692b7c,l41),(0x2c89a2134,l51),(0x4c6b6e33,l61),(0x703ae6d,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c89a2134,l27),(0x2c89a2134,l29),(0x2c89a2134,l33),(-0x2c89a2134,l35),(0x2c89a2134,l37),(0x2c89a2134,l51),(-0x3029fbb84,l25),(-0x127aa473c,l28),(-0x2cd7635b4,l42),(-0x1b6200787,l36),(-0xd1727da0,l38),(0x23b692b7c,l41),(0x4c6b6e33,l61),(0x5442b8d8,l14),(0x52ebe862,l43),(0x703ae6d,l63),(0xdf8732,l11),(-0x6358a1,l9),(26,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0xc848094c0300000001d03880200000002502480200000000a03480200000001e01480200371488404d003000000019018802000001511028c0200019151102d002a30ec10c0a2d0050490c822019500404b0cc23011500400220c84407500300210d84c09500300000120e01cc026e0920a4066900503908c13013500400001206404cc03000000090024803000138110058c0400250982402d003000000078024803000000001c0c801], #[![-1, -5, 2, 0],![5, -16, -5, 0]]⟩
def dynamicCode : Nat := ((((((((((0x3a38e5e8ee33e49efe7950966f28cbf60844c24a18a08a04904b00700600cb31b2fc3e53b7) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 22 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase11" = "QuadFullTwelveCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 22 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase11
private def zz2316:"s090c"="s090c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l17 l27 l29 l33 l35 l37 l51 l63 l68)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x6f1e33f, -0x2a75474, -0x278d7cb,0x258], ![-0x2a75474, -0x13ad43bd,0x1e051ae,0x34daed3], ![-0x278d7cb,0x1e051ae, -0x113fb42e,0x2a75924],l68]
noncomputable def hinges:Hinges:=[(0x26d8f8f,l17),(-0x153ab66,l27),(0x153ab66,l29),(0x153ab66,l33),(-0x153ab66,l35),(0x153ab66,l37),(0x153ab66,l51),(-0xeb48bd,l63)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x153ab66,l27),(0x153ab66,l29),(0x153ab66,l33),(-0x153ab66,l35),(0x153ab66,l37),(0x153ab66,l51),(0x26d8f8f,l17),(-0xeb48bd,l63)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x1284c12016801800000001e009200c000002c13809980600000000b0024803000000006c01240180006804100263014000000001c029005440a104400635006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 9 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase12" = "QuadFullTwelveCase12" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 9 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase12
private def zz2317:"s090d"="s090d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullTwelveCase13
private def zz2318:"s090e"="s090e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l15 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l4 l41 l42 l43 l45 l5 l51 l54 l58 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x54870c5a0, -0x3183ffb58, -0x4a45ffbf8,0x256f0806], ![-0x3183ffb58, -0x14fceadd6a,0x2e13afa4a,0x32bb3a650], ![-0x4a45ffbf8,0x2e13afa4a, -0x141d79c7d3,0x3184004b2], ![0x256f0806,0x32bb3a650,0x3184004b2, -0x18c200004]]
noncomputable def hinges:Hinges:=[(-0x3ab94065,l5),(-0xafb9180c,l4),(0x2c016232,l9),(0xe91a5d2,l8),(0x1754fb51a,l14),(0x2bc57027e,l15),(0x446bb720,l23),(0xd7f02c0b,l22),(-0x18c200004,l27),(0x18c200004,l29),(-0x1754fb51a,l25),(0x9871fefc,l30),(0x18c200004,l33),(-0x18c200004,l35),(-0xe91a5d2,l36),(0x18c200004,l37),(0xafb9180c,l34),(-0x9871fefc,l43),(-0xd7f02c0b,l42),(-0x2bc57027e,l41),(0x155a0d59,l45),(0x18c200004,l51),(0x3ab94065,l54),(-0x155a0d59,l58),(-0x2c016232,l61),(-0x446bb720,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x18c200004,l27),(0x18c200004,l29),(0x18c200004,l33),(-0x18c200004,l35),(0x18c200004,l37),(0x18c200004,l51),(0x1754fb51a,l14),(-0x1754fb51a,l25),(0x2bc57027e,l15),(-0x2bc57027e,l41),(0x9871fefc,l30),(-0x9871fefc,l43),(0xd7f02c0b,l22),(-0xd7f02c0b,l42),(0x446bb720,l23),(-0x446bb720,l63),(0x2c016232,l9),(-0x2c016232,l61),(-0xafb9180c,l4),(0xafb9180c,l34),(-0x3ab94065,l5),(0x3ab94065,l54),(0x155a0d59,l45),(-0x155a0d59,l58),(0xe91a5d2,l8),(-0xe91a5d2,l36)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,0x6400b200c003304504a026a80280000000003101c80200000000005a03100523072409f0236f401c1419210e180e5680302832421c300fad00600000000003203100400308428620170401400000000001e0640080000000001e014802000000005a1c07180400000004219014300c0c1086861011a08030000610c41302ed00400000000000381900200000000003c0520080000009c08802c60200000250982402d0030000000000f004900600000006229022300c0003b04a0e819880200000000068004c804], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase14" = "QuadFullTwelveCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase14
private def zz2319:"s090f"="s090f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l13 l15 l16 l20 l22 l23 l27 l29 l31 l33 l34 l35 l36 l37 l4 l41 l42 l45 l5 l51 l54 l56 l57 l58 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x48da69949, -0x312f14dc0, -0x49c69f6f8,0x4aa], ![-0x312f14dc0, -0x1467fd5bdc,0x24f435558,0x384bfa306], ![-0x49c69f6f8,0x24f435558, -0x13fafa5f77,0x312f1571a], ![0x4aa,0x384bfa306,0x312f1571a, -0x18978a938]]
noncomputable def hinges:Hinges:=[(-0x3ab94065,l5),(-0xafb9180c,l4),(0x2c016232,l9),(0xe91a5d2,l8),(0x3c30ed378,l13),(-0x4e01f2b7,l16),(0x28d1645ba,l15),(-0x3c30ed378,l20),(0x31bed88e,l23),(0x1278c4fa4,l22),(-0x18978a938,l27),(0x18978a938,l29),(0x73c0ebd9,l31),(0x18978a938,l33),(-0x18978a938,l35),(-0xe91a5d2,l36),(0x18978a938,l37),(0xafb9180c,l34),(-0x1278c4fa4,l42),(-0x28d1645ba,l41),(0x3ee63e3,l45),(0x18978a938,l51),(0x3ab94065,l54),(-0x73c0ebd9,l57),(0x4e01f2b7,l56),(-0x3ee63e3,l58),(-0x2c016232,l61),(-0x31bed88e,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x18978a938,l27),(0x18978a938,l29),(0x18978a938,l33),(-0x18978a938,l35),(0x18978a938,l37),(0x18978a938,l51),(0x3c30ed378,l13),(-0x3c30ed378,l20),(0x73c0ebd9,l31),(-0x73c0ebd9,l57),(0x1278c4fa4,l22),(-0x1278c4fa4,l42),(0x28d1645ba,l15),(-0x28d1645ba,l41),(0x31bed88e,l23),(-0x31bed88e,l63),(0x2c016232,l9),(-0x2c016232,l61),(-0xafb9180c,l4),(0xafb9180c,l34),(-0x4e01f2b7,l16),(0x4e01f2b7,l56),(-0x3ab94065,l5),(0x3ab94065,l54),(0xe91a5d2,l8),(-0xe91a5d2,l36),(0x3ee63e3,l45),(-0x3ee63e3,l58)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x3304208813e8020000000001b002c8030028830825809f200a0000000000d40720080000008c08815e60202c328220301cad0060000000000620310040b0ca0880c03eb401800808c814202e680280000000013002c803], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase15" = "QuadFullTwelveCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase15
private def zz2320:"s0910"="s0910":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l16 l17 l22 l27 l29 l30 l33 l35 l37 l5 l51 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb417800, -0x59682eb50,0x466376be0,0x4b0], ![-0x59682eb50, -0x2a80066b83,0x149dd1a498, -0x68ecc3a70], ![0x466376be0,0x149dd1a498, -0x30db8e59f3,0x9ab9b1bbe], ![0x4b0, -0x68ecc3a70,0x9ab9b1bbe, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x107b7f90d,l5),(0x1bbbe135f,l8),(0xbcaa1a64,l10),(0x76af6e98,l13),(-0xd5f6e58,l17),(-0x16761c63,l16),(0x4e974b32,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0x839c076e,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1bbbe135f,l8),(0xbcaa1a64,l10),(-0x107b7f90d,l5),(0x839c076e,l30),(0x76af6e98,l13),(0x4e974b32,l22),(-0xd5f6e58,l17),(-0x16761c63,l16)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x9008802c6020000000443c053008000000001e029004000250982402d003000000003c012401800000002c009200c00000001b004900600001a8210058c040000d0082004c602800000064240730080000000012031004000001b024030c03000000000280c4010000000005805200b9820218203d2200c007310431032500404204304603a4802800002105003c30100000054188059806000002b8c402cc03000000001580c40100000003c1c0a300800000000480e9006000000001f018802000000001180c401000000004d00a200c0000000036031004005c0a01c0175004000000004c0124018000000003805200800000000e00490060000000012014802], #[![-11, 97, -117, 0],![-29, -50, 129, 0],![5, 62, -93, 0],![35, 164, -183, 0],![5, 26, -39, 0]]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase16" = "QuadFullTwelveCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase16
private def zz2321:"s0911"="s0911":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l21 l22 l23 l27 l29 l30 l33 l35 l37 l5 l51 l57 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2c89a1c7c, -0x591343db8,0x859ce4fc8,0x7e0], ![-0x591343db8, -0x30accae52c,0x157f5b29c8, -0x61d24eeb4], ![0x859ce4fc8,0x157f5b29c8, -0x30b90ef197,0x9a64c6e26], ![0x7e0, -0x61d24eeb4,0x9a64c6e26, -0x2c89a2134]]
noncomputable def hinges:Hinges:=[(-0x107b7f90d,l5),(0x1bbbe135f,l8),(0xbcaa1a64,l10),(0x1e3920eec,l14),(0x4a0a738de,l13),(-0x23b692b7c,l15),(0x12a09e4,l21),(-0x703ae6d,l23),(0x2cd7635b4,l22),(-0x2c89a2134,l27),(0x2c89a2134,l29),(-0x52ebe862,l30),(0x2c89a2134,l33),(-0x2c89a2134,l35),(0x2c89a2134,l37),(0x2c89a2134,l51),(-0x4c4,l57),(-0x88,l65),(0x220,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c89a2134,l27),(0x2c89a2134,l29),(0x2c89a2134,l33),(-0x2c89a2134,l35),(0x2c89a2134,l37),(0x2c89a2134,l51),(0x4a0a738de,l13),(0x1e3920eec,l14),(0x2cd7635b4,l22),(0x1bbbe135f,l8),(0xbcaa1a64,l10),(-0x107b7f90d,l5),(-0x23b692b7c,l15),(-0x52ebe862,l30),(-0x703ae6d,l23),(0x12a09e4,l21),(-0x4c4,l57),(0x220,l64),(-0x88,l65)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0x2201480200001282402cc0300000110f014c0200000000f014802000138110058c04000120110058c0400250982402d0030000000780248030000c4110320c040001544701b0c040000000d802480300001b84402cc0300000000901880200001a044038c0300001b024030c0300000190901cc02000130150358c04000000002c0c801a812a1a40429005002a12064055003002b1307007500305c124310329004000000016014802a40c610c07490050000001a2c0cc010000188a4050c0300018c5701a0c04000002d1d01cc020000148840d8c03000000905028c02000000005018802000008828030c03], #[![0, -5, -16, 5]]⟩
def dynamicCode : Nat := (((((((0xd61b845688a4326d2bdba2deb5ef819c62ac12210310aa8afcd5730ecae82a440c30a388308386304000161c055c580509e83873b08c42fa733e8fc91bcbd7556d9df59cb8e388380cd6069639689c0c1850c8c7bdf791840c8c7b5ab91c3060e1c253e1c23443e3482c18200000072c02400594a3df281c0530247ad22040578703b12c810280100000f9905f0980702f8b665677ff8e04083485828b9fa4061b2df70159230676cb1313d3c2864117961c418402001c3eafe8428200000117b401004133d60fbdc08018bd113ac057540e160100000880f0d99b1) <<< 16000) +
    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)) <<< 16000) +
    0x180a00aa42e08700200c7ce83c0f808991038500400001d42000c0c646000001ad9228042e93586100000264230000000c46140d0a143e000ca20420100260181280c0900604603a2f5ccafe77a8ff5e6c27cef5ea1000000000001384ad3e3357e4f3e895a7c68000000003c14e013ac0f358cecf63050feafbb418150b000000000000000000000000000000000000239faeaa74c0001689a8545f6bf1ebc2036db920000002a0fa9239230c21201bc6f76ec406535480b0ad8479d35bba4a898e21c7a8143d269c07220808a0424acf865652c04a0c67c346e526203556c3fdbc4dde85f4dbf62a17b7aa1204bbbcef92ca4db8cd8ea4b9db58fb26e31e63f0a2850353949a04403c281a5b456f995db40cfc7ee08a811bdacc201a670cc789ebe80a61b038fd88a24a0a2000000466384d29d4786a84ba2bb78ecc0789804014bd17f2abd0056ded29bc450804000002fad075bc2c2bb5dc95a04bbc8a00000064a98c0d403de860b9c8c519fa40000002840dcd553e76a2acd3c893d78c00424af3db6ed96ed87c09831f05a1865449012352a799a500000016e36001850000000659fa01440000000895440180944a774ca18761a0000000089544018001d842b78df050000000177fa011d4c1c30d00f000045040019b8cb0ed9ed2d4eda638529d4a4f4142b796dc957f18b94e4ea18000000000000000000000000000000000000000000000000018c4a20818b0ca08800600000000bd90d9cba83bc50ad3b0d9c7fa81947f8bd524073181c1a058421c643d60ed2246ae66fb06c856f6c8e2dc39f986fb48a08b3224956f22aec57809385473181dcb497d4c0a18deb7c7772bc803762717b0a7318b400127481082e4723710baaaf5dc9148dc41db9b4371c5000000b2872009047da4e07338691c05b459a2e8ebc05016d16702a86f0000dfb96310e95280000007a3140214d8c258c845588985838e1902200009508009ea900154e2003d0a40688400402c127a3e68b3fdfddac622f23880ea8cd952e19be82911841c31830c21011401000c0007998011cbd4ef8991bb801d8dcac900256ba752ce019610928b60c1b850b44115b2e7e03035e34a8f18504273d15918024630460100200580482e45015ea4410668a208573e658ee060d31c7442d290302c9731d9df391410216dda4a760c0249b516e91604007d78488e6d2001cb80ee79f420154fa10405a058000202203e0201e01c8c0c6b8606c614094286d608257bd0702c18110b7e0e243007dc8eb084065102300800c00c074060380301b01c0e08bd8404246112568af121a071e587c30ad1159738048184201001a01e042ce727e4591343db6591347218230f648d0d54a5102ed428a0554fd797c0000a32463042432401c0180028e17bd2e3465734a585afc8c324ce536fa269d6b02a85a0cfbe598203621e57a718424076a00050c4064260240bc0859ce4fc8b22687b6cb2268e430461ec91a1aa94a205da85140aa9faf2f800014640c38c4043002800000327b3afff854319528c48fbd72d415dfc08f7244303bc69e64fe0a10b4bcfbf612b0e480e14000a1880032e1a180178f1518a28024f9248104b10c07d60380022c0d658600cf3e36c98ca10460100180180b80c0580602a038020080200500764810933a4cb201922493448810d58a6e241be1b0b27900e34049ba01000027987930010804349f57cbdf50d23d5f3bff7241763495b28805d8d1456a38000000a8b49002afb084a2000abed852a700220080000b19013050001611c0859ce4fc8b22687b6cb2268e430461d2d3f353306cbf8000000a91648e39230e10e00c00000463bd4d82decb6926a30e435448506fb01faf5d9689f39fd2e45c31b05fa000446404817810b39c9f91644d0f6d9644d1c8608c3a5a7e6a660d97f0000001522881862051812801400000035c5ce481bb1d2125bc027e2de521782a00c0598ee0f6b035f51737446f9518c9582d5ff888e53edf68835016148319280015d100083c202232010190004f2900f1d0008fa10015392002eb6686f2cd35968830454874510641845212539270302521254abb028287a981fae820293ac5e8b3018189e358294020e789e00374076808b91471e7202801461156e7c0ed9870c1fbe4ef58450c7dadbc319470800000396c0608789879fdc050ba8abf50748706935a6dc140105a927930fb8403a8abf17089503191828018714ed92e9eec3879faa25082183000000e1002084c0b4f0106004a31354b228000000096010006b110550b3821280400380601a0300c0180580f07000000bb801c1686293b627041c5f7cdf0001c014e08403fb040259761cc2200008e74b1caaa3001400a2cb99d3e8a4762c90067dad1d930700000009602c720ff5ece1f28700000009600c0000ab908b69800a00200002b200100280765f1f6f4a21c2c72167399ff86020000003844b042c537392212080000017701c000000012c00800000010686e004e008b2fad79bc5cb16480ec681dcf307000000177058e3f1cd2c8b4208000002a309800000000e102c004b38a25da48000000009630004e0080001b820006b06569f19abf279f44ad3e34000000001e128a2892492852452051811c00c0400803400042080482e08b13048444489180000002ee0206082f71e2d7c81086465894791c40000000bb80800608549cc1700000008ca0805f7d472a28a6102a0100000e1900097a20016c4402074001b2c401c9400c4a0052500200800c040020124008a400202000010024d19))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase17" = "QuadFullTwelveCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase17
private def zz2322:"s0912"="s0912":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l23 l27 l29 l33 l35 l36 l37 l5 l51 l54 l63 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xde3bba7, -0x54ea624, -0x4f1af96,0x4b0], ![-0x54ea624, -0x29d9ae44,0x3b2e0e4,0x615b946], ![-0x4f1af96,0x3b2e0e4, -0x227ff04c,0x54ee716], ![0x4b0,0x615b946,0x54ee716, -0x2a756cc]]
noncomputable def hinges:Hinges:=[(-0xbf4,l5),(0x24f9,l8),(0x1d6917a,l23),(-0x2a756cc,l27),(0x2a756cc,l29),(0x2a756cc,l33),(-0x2a756cc,l35),(-0x24f9,l36),(0x2a756cc,l37),(0x2a756cc,l51),(0xbf4,l54),(-0x1d6917a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2a756cc,l27),(0x2a756cc,l29),(0x2a756cc,l33),(-0x2a756cc,l35),(0x2a756cc,l37),(0x2a756cc,l51),(0x1d6917a,l23),(-0x1d6917a,l63),(0x24f9,l8),(-0x24f9,l36),(-0xbf4,l5),(0xbf4,l54)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0xa21b042047a008000000000f0148020001284c12016801800000001e009200c0000108260341808000000d02c038c030000000d8980c6010000000006c052008000002c13809980600000000b0024803000000006c0124018000006c0900c300c0000037088059806004208c1300ed004000000000280c4010000000003805200a822241820390a00c004c0c41701210040000c8481202c80180000004c2c0630080000000026029005440a104400635006002e0500e00ba8020000000026009200c00000000e00490060000000012014802], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 13 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase18" = "QuadFullTwelveCase18" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 13 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase18
private def zz2323:"s0913"="s0913":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullTwelveCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l36 l5 l54 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x39d,0x27c,0x190,0x190], ![0x27c,0,0x198,0x190], ![0x190,0x198, -0x2d50,0x132a], ![0x190,0x190,0x132a,0]]
noncomputable def hinges:Hinges:=[(-0x3fc,l5),(0xc53,l8),(-0xc53,l36),(0x3fc,l54)]
def normalizationDenominator:ℤ:=0x1dcd65000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0xc53,l8),(-0xc53,l36),(-0x3fc,l5),(0x3fc,l54)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨29, #[0x13018802], #[]⟩
def dynamicCode : Nat := 0xa23eb02863200818cc02843200810c8018415b080daa01ced1c1038031447d61431901031981421901021900c26d7101b540c0c537008180080000e120000ba22b6143c8020798050b200816400c256ce7673b46080b00c5102b6143190040c66014219004086400c26d7030314c439da3840700600003a48000e49
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 4 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullTwelveCase19" = "QuadFullTwelveCase19" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 4 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullTwelveCase19
private def zz2324:"s0914"="s0914":=by decide+kernel
end 
section 
namespace Green24Proof.FullTwelveRows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x114e20001eeb5ca800996f3cbe2620003dceb948009bceebdee07a20003dceb948007f3ecf19a1fa200779ae580028dbdccca06a20003dceb948005ed87da9e15a200779ae580049a87abda01a2005faf84806ec4d1d2220003dceb94800a8588fa9a07d20003dceb948018efb6e49a1fd2001389b4802beffac21ed2002fd7c28001c895d5ba14d20003dceb94801696ab8ee652003bcdb2c004ced0b7ea120003dceb94802bacb28ede07c20003dceb94802ac5acb5aa1fc200779ae58029dc89aa1ec20001eeb5ca8002dfe3ffba420001eeb5ca800d85a7d7ba078200779ae50affcca6020001eeb5ca800bf1cec19214]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x136005faf848001808af207e6002fd7c28021da92be15e60001eeb5ca80099ed4c79e01e60003dceb9480188abfbbc266005faf848003b798e7d61ea60003dceb948009b5a288b601a60001eeb5ca8019bba2a0f6260003dceb94800fe5c5c996560004e2ad8002160003dceb948003ce9ec207f20003dceb948011d7fccf961ff20003dceb94801bddf8a6de01f20003dceb948018dccfeb92720003dceb94801ee3a794a207b20003dceb94807d92aef606b2005faf848011f0cff214b2000ef3acd001acb3e6320001eeb5ca8015bdace1ae1fe20003dceb948015e89df3c215e20003dceb94804cab9a9614]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1530004e2ad8002130004e2ad800203c30001eeb5ca8001bb9e97da1fc30001eeb5ca8005a0d39ec2430003dceb948004bfc4faea1f830001eeb5ca8002b7a0a3ae030001eeb5ca8001d2eff8827e0001eeb5ca80663e0003dceb948004f7a0a607fa0003dceb94800f8ea48ef61ffa0003dceb948018d789d0ca1efa002fd7c280779bca7a002fd7c28005dde3f8ee1fba0004e2ad8003958eb23a0001eeb5ca801bbec5f0e21fea003bcdb2c0058284f8ca6a0001eeb5ca800d8ea0aa8607aa0003dceb948017aabeea9a2a0001eeb5ca8009d68e84a2760004e2ad800214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1670004e2ad800201a70003dceb94801ea682270004e2ad8002570004e2ad8002170004e2ad8002730004e2ad800216b300779ae58023c6f19e05b3001389b48065b3ca330001eeb5ca806203e3002fd7c28007e0a9aa1ee30001eeb5ca803efebea606e300779ae5800ab5f49a15e30003dceb948001c9bbf5fa14e30001eeb5ca8079d7cec6630007b9d6a80216a30003dceb9480028da1e8e601a30003dceb948061ab919a23001389b4800603d3003bcdb2c0221ed300779ae5802214]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x103c00003dceb948003aa9bef921fc0003bcdb2c06eacecf61ec00001eeb5ca804492e0e602c00003dceb9480069389f4c21cc00003dceb948001b9daeeaa05c00003dceb948008beccae400002b196c0027f0004e2ad80023f0004e2ad800203fb0003dceb948008f206fb0003dceb948003827b0004e2ad800216bb0001eeb5ca8002cc8998d63b0004e2ad80021feb0003dceb948014fbdac26b00779ae58002cfbbda1fab0003dceb948071f091e62b0001eeb5ca8035b6b0ba770004e2ad8002370004e2ad800214]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1480002b196c002740002b196c002640002b196c002540002b196c002440002b196c00203f00001eeb5ca8005f2d49ab217f00003dceb948012bed099ea1cf00003dceb94800afebff6de700003dceb948002bdbceffa03e00001eeb5ca8001c3a492ce1fe000779ae58001bfdefaf21ee0000198cba056de9602e00017ebe18035a7fed21de0005faf84804eefd4ee1ce00003dceb948014adbdf6600002b196c00203d0001de6d9a068dccfda17d00003dceb948012a0d5b4da1dd00003dceb948009c6dbb8e650001389b48001b9ddbe14]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x17c0001eeb5ca8002be16ec0001eeb5ca8006fe8eb21dec0003dceb9480069ae2c201ec0003dceb94801a6c0002b196c0025c0002b196c0024c0002b196c00203f80003dceb94800a89c2d9c617f80001eeb5ca80089d839aee14f80001eeb5ca8009a8959a780002b196c00217e80001eeb5ca8026eceec606e80001eeb5ca8001eaa6888215e80001eeb5ca8002e085c4b21ce80003dceb948002b998d5ee680002b196c00203d80001eeb5ca800883bfe99616d80003dceb94800ca8f0defe05d80003dceb948001e0d8fb9e58001de6d9a01214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1610002b196c00203a10003dceb9480089cf08eee17a10001eeb5ca8001d1c9dce61ca10003dceb948077e5d0c205a100779ae5801adfb796210002b196c00203c10003dceb948009febcaa9e17c1001de6d9a070cdeab602c10001eeb5ca800ad5ca8bda1dc10003dceb948004ac9ca1ee05c10003dceb948004dcf3ffbe410003dceb948002f603810003dceb94800cc396b6f617810003dceb94801597a0f2168100779ae58004ce8aa4fe15810001eeb5ca8007978cbafa0581005faf848001f2b3d182010017ebe1801217fc005faf848009ee1cfc0017ebe1806614]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x117c9001de6d9a001a09591be1ec90001eeb5ca8001d4fdf38202c90005faf8a036a3fe1dc90001eeb5ca80028aa399ee1cc9002fd7c2800bcfd2b201c90001eeb5ca800296490002b196c002178900779ae58003e8fdc4ce1c89002fd7c28030f2fa92090003dceb948003b216f50017ebe1807a75002fd7c28008f494f2ae35001de6d9a004a1aaa8ea550002b196c00201950003dceb948026ecbe9e150002b196c00207e10003dceb94800597afd0e217e100779ae58007bccee79e06e10001eeb5ca8005f9f0e3ea1de10003dceb9480709db9da14]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x108880003dceb948003a9c0fdaa08850003dceb948055e78eaa08800003dceb948055e78eaa7d0002b196c00215bd0001eeb5ca800edaa2fa3d0003dceb94800885e39a5d0001eeb5ca802cc4e8b496019d0003dceb948044b5c4cb821d0003dceb94800be7d0b19617e900779ae580038a889ac616e90003dceb94800ebc87afb202e9005faf848002dca889a615e90001eeb5ca80038dfbb18e1ce90003dceb948003a08598fa690002b196c00203a90001eeb5ca8004e1e3fefe17a9005faf848001e6aae18a02a9005faf848002f5c1efa215a90002fdbc9006ebe4ca290001eeb5ca8001ae14]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10894002692e802010101000102010008930003dceb94802886c7f201010100010201000892005faf84800ad2edc0fe0118010101180101010f0102010f01020403dceb948076e29796011801010118010101010100010201000401eeb5ca8012316001043136010101000101010001020403dceb9480089e88b9fe010101000102010001000101010001020403dceb948001b096f7c20103dceb948003c4f2a2088a00779ae58010daa9aa088f0003dceb948007b691b5de0a]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullTwelveCase0.base QuadFullTwelveCase0.hinges QuadFullTwelveCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase0.base QuadFullTwelveCase0.hinges QuadFullTwelveCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullTwelveCase1.base QuadFullTwelveCase1.hinges QuadFullTwelveCase1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz1147:"s047b"="s047b":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase1.base QuadFullTwelveCase1.hinges QuadFullTwelveCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r62,RewriteAtoms.r19,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullTwelveCase2.base QuadFullTwelveCase2.hinges QuadFullTwelveCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase2.base QuadFullTwelveCase2.hinges QuadFullTwelveCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullTwelveCase3.base QuadFullTwelveCase3.hinges QuadFullTwelveCase3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz1148:"s047c"="s047c":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase3.base QuadFullTwelveCase3.hinges QuadFullTwelveCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r62,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullTwelveCase4.base QuadFullTwelveCase4.hinges QuadFullTwelveCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase4.base QuadFullTwelveCase4.hinges QuadFullTwelveCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullTwelveCase5.base QuadFullTwelveCase5.hinges QuadFullTwelveCase5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz1149:"s047d"="s047d":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase5.base QuadFullTwelveCase5.hinges QuadFullTwelveCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullTwelveCase6.base QuadFullTwelveCase6.hinges QuadFullTwelveCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase6.base QuadFullTwelveCase6.hinges QuadFullTwelveCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r63,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullTwelveCase7.base QuadFullTwelveCase7.hinges QuadFullTwelveCase7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
private def zz1150:"s047e"="s047e":=by decide+kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase7.base QuadFullTwelveCase7.hinges QuadFullTwelveCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullTwelveCase8.base QuadFullTwelveCase8.hinges QuadFullTwelveCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase8.base QuadFullTwelveCase8.hinges QuadFullTwelveCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullTwelveCase9.base QuadFullTwelveCase9.hinges QuadFullTwelveCase9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
private def zz1151:"s047f"="s047f":=by decide+kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase9.base QuadFullTwelveCase9.hinges QuadFullTwelveCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r30,RewriteAtoms.r61,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullTwelveCase10.base QuadFullTwelveCase10.hinges QuadFullTwelveCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase10.base QuadFullTwelveCase10.hinges QuadFullTwelveCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r20,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullTwelveCase11.base QuadFullTwelveCase11.hinges QuadFullTwelveCase11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
private def zz1152:"s0480"="s0480":=by decide+kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase11.base QuadFullTwelveCase11.hinges QuadFullTwelveCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullTwelveCase12.base QuadFullTwelveCase12.hinges QuadFullTwelveCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase12.base QuadFullTwelveCase12.hinges QuadFullTwelveCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullTwelveCase13.base QuadFullTwelveCase13.hinges QuadFullTwelveCase13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
private def zz1153:"s0481"="s0481":=by decide+kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase13.base QuadFullTwelveCase13.hinges QuadFullTwelveCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullTwelveCase14.base QuadFullTwelveCase14.hinges QuadFullTwelveCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase14.base QuadFullTwelveCase14.hinges QuadFullTwelveCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullTwelveCase15.base QuadFullTwelveCase15.hinges QuadFullTwelveCase15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
private def zz1154:"s0482"="s0482":=by decide+kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase15.base QuadFullTwelveCase15.hinges QuadFullTwelveCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullTwelveCase16.base QuadFullTwelveCase16.hinges QuadFullTwelveCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase16.base QuadFullTwelveCase16.hinges QuadFullTwelveCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r62,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullTwelveCase17.base QuadFullTwelveCase17.hinges QuadFullTwelveCase17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
private def zz1155:"s0483"="s0483":=by decide+kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase17.base QuadFullTwelveCase17.hinges QuadFullTwelveCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullTwelveCase18.base QuadFullTwelveCase18.hinges QuadFullTwelveCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase18.base QuadFullTwelveCase18.hinges QuadFullTwelveCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullTwelveCase19.base QuadFullTwelveCase19.hinges QuadFullTwelveCase19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
private def zz1156:"s0484"="s0484":=by decide+kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullTwelveCase19.base QuadFullTwelveCase19.hinges QuadFullTwelveCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullTwelveCase19.nonnegative x hx
def pair20:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_20_base LocalFullTwelvePairs.compact_fullTwelve_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullTwelvePairs.fullTwelve_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_20_base LocalFullTwelvePairs.compact_fullTwelve_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_21_base LocalFullTwelvePairs.compact_fullTwelve_pair_21_hinges
private def zz1157:"s0485"="s0485":=by decide+kernel
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullTwelvePairs.fullTwelve_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_21_base LocalFullTwelvePairs.compact_fullTwelve_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_22_base LocalFullTwelvePairs.compact_fullTwelve_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
private def zz1158:"s0486"="s0486":=by decide+kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullTwelvePairs.fullTwelve_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_22_base LocalFullTwelvePairs.compact_fullTwelve_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_23_base LocalFullTwelvePairs.compact_fullTwelve_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullTwelvePairs.fullTwelve_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_23_base LocalFullTwelvePairs.compact_fullTwelve_pair_23_hinges x
private def zz1159:"s0487"="s0487":=by decide+kernel
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r69]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_24_base LocalFullTwelvePairs.compact_fullTwelve_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullTwelvePairs.fullTwelve_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_24_base LocalFullTwelvePairs.compact_fullTwelve_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_25_base LocalFullTwelvePairs.compact_fullTwelve_pair_25_hinges
private def zz1160:"s0488"="s0488":=by decide+kernel
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullTwelvePairs.fullTwelve_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_25_base LocalFullTwelvePairs.compact_fullTwelve_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_26_base LocalFullTwelvePairs.compact_fullTwelve_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
private def zz1161:"s0489"="s0489":=by decide+kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullTwelvePairs.fullTwelve_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_26_base LocalFullTwelvePairs.compact_fullTwelve_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_27_base LocalFullTwelvePairs.compact_fullTwelve_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullTwelvePairs.fullTwelve_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_27_base LocalFullTwelvePairs.compact_fullTwelve_pair_27_hinges x
private def zz1162:"s048a"="s048a":=by decide+kernel
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_28_base LocalFullTwelvePairs.compact_fullTwelve_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullTwelvePairs.fullTwelve_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_28_base LocalFullTwelvePairs.compact_fullTwelve_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_29_base LocalFullTwelvePairs.compact_fullTwelve_pair_29_hinges
private def zz1163:"s048b"="s048b":=by decide+kernel
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullTwelvePairs.fullTwelve_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_29_base LocalFullTwelvePairs.compact_fullTwelve_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r18]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_30_base LocalFullTwelvePairs.compact_fullTwelve_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
private def zz1164:"s048c"="s048c":=by decide+kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullTwelvePairs.fullTwelve_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_30_base LocalFullTwelvePairs.compact_fullTwelve_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r71,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_31_base LocalFullTwelvePairs.compact_fullTwelve_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullTwelvePairs.fullTwelve_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_31_base LocalFullTwelvePairs.compact_fullTwelve_pair_31_hinges x
private def zz1165:"s048d"="s048d":=by decide+kernel
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_32_base LocalFullTwelvePairs.compact_fullTwelve_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullTwelvePairs.fullTwelve_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_32_base LocalFullTwelvePairs.compact_fullTwelve_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_33_base LocalFullTwelvePairs.compact_fullTwelve_pair_33_hinges
private def zz1166:"s048e"="s048e":=by decide+kernel
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullTwelvePairs.fullTwelve_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_33_base LocalFullTwelvePairs.compact_fullTwelve_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_34_base LocalFullTwelvePairs.compact_fullTwelve_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
private def zz1167:"s048f"="s048f":=by decide+kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullTwelvePairs.fullTwelve_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_34_base LocalFullTwelvePairs.compact_fullTwelve_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_35_base LocalFullTwelvePairs.compact_fullTwelve_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullTwelvePairs.fullTwelve_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_35_base LocalFullTwelvePairs.compact_fullTwelve_pair_35_hinges x
private def zz1168:"s0490"="s0490":=by decide+kernel
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r51]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_36_base LocalFullTwelvePairs.compact_fullTwelve_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullTwelvePairs.fullTwelve_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_36_base LocalFullTwelvePairs.compact_fullTwelve_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r71]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_37_base LocalFullTwelvePairs.compact_fullTwelve_pair_37_hinges
private def zz1169:"s0491"="s0491":=by decide+kernel
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullTwelvePairs.fullTwelve_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_37_base LocalFullTwelvePairs.compact_fullTwelve_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_38_base LocalFullTwelvePairs.compact_fullTwelve_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
private def zz1170:"s0492"="s0492":=by decide+kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullTwelvePairs.fullTwelve_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_38_base LocalFullTwelvePairs.compact_fullTwelve_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (12) ((1 / 0xf4240)) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullTwelvePairs.compact_fullTwelve_pair_39_base LocalFullTwelvePairs.compact_fullTwelve_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullTwelvePairs.fullTwelve_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullTwelvePairs.compact_fullTwelve_pair_39_base LocalFullTwelvePairs.compact_fullTwelve_pair_39_hinges x
private def zz1171:"s0493"="s0493":=by decide+kernel
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullTwelvePairs.fullTwelve_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (12) ((1 / 0xf4240)) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullTwelveRows
private def zz2325:"s0915"="s0915":=by decide+kernel
end 
section 
namespace Green24Proof.FullTwelveCyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullTwelveRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullTwelveRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullTwelveRows.rows p q same x]
    exact FullTwelveRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz1172:"s0494"="s0494":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 12 (1 / 0xf4240) FullTwelveRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullTwelveRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 12 (1 / 0xf4240) FullTwelveRows.rows p q same x]
    exact FullTwelveRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullTwelveRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullTwelveRows.rows
theorem remaining_rows_count:remainingRows.length = 13:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
      weightedAggregate 12 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullTwelveRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 12 (1 / 0xf4240) FullTwelveRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 12 h4 h3 h5 g FullTwelveRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
    weightedAggregate 12 h4 h3 g (stripPotentials FullTwelveRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullTwelveCyclic
private def zz2326:"s0916"="s0916":=by decide+kernel
end 
section 
namespace Green24Proof.FullTwelveMass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open FullPhaseRows (Phase)
open PhaseMassRows PhaseColourRows ConditionalMassRows
private def zz1173:"s0495"="s0495":=by decide+kernel
theorem remainingRows_eq:FullTwelveCyclic.remainingRows = [
  ((0x55ce395 / 0x3b9aca00), .base (.balance 0 (1))),
  ((0x55ce395 / 0x3b9aca00), .base (.balance 2 (-1))),
  ((0x1a981f55 / 0x3b9aca00), .base (.child 0)),
  ((0x3b622d6f / 0x3b9aca00), .base (.heightChild 1)),
  ((0x10b4a55 / 0xee6b280), .base (.grandchild 0)),
  ((0x389c91 / 0x3b9aca00), .colourChild .whole),
  ((0xb02dde1 / 0x3b9aca00), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)),
  ((0x41e10e7f / 0x3b9aca00), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,(27 / 49),2,(48 / 49)]:Fin 4 → ℚ) p)),
  ((9 / 0x1dcd6500), .massProduct (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p) (fun p => (![-1,12, -1,12]:Fin 4 → ℚ) p)),
  ((0x76c45cb / 0x3b9aca00), .massProduct (fun p => (![1, -8,1, -8]:Fin 4 → ℚ) p) (fun p => (![-1,12, -1,12]:Fin 4 → ℚ) p)),
  ((0x552db03f / 0xbebc200), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x280d1f9 / 0x3b9aca00), .base (.massSquare true (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((1 / 0x98968), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
theorem weighted_remaining_le {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (12:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 8 12 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 12 h4 h3 g (.colourChild .whole) ≤ 0) :
    weightedAggregate 12 h4 h3 g FullTwelveCyclic.remainingRows ≤
      ((1 / 0x98968):ℝ) * mass g ^ 2:=by
  have hbal:=mul_nonpos_of_nonneg_of_nonpos (sub_nonneg.mpr heven) (sub_nonpos.mpr hhigh)
  have hp6:rowAggregate 12 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 12 8 12 h4 h3 g hforms 4 5
  have hp7:rowAggregate 12 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,(27 / 49),2,(48 / 49)]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 12 8 12 h4 h3 g hforms 4 12
  have hp8:rowAggregate 12 h4 h3 g (.massProduct (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p) (fun p => (![-1,12, -1,12]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 12 8 12 h4 h3 g hforms 5 8
  have hp9:rowAggregate 12 h4 h3 g (.massProduct (fun p => (![1, -8,1, -8]:Fin 4 → ℚ) p) (fun p => (![-1,12, -1,12]:Fin 4 → ℚ) p)) ≤ 0:=by
    exact domainProduct_nonpos 12 8 12 h4 h3 g hforms 7 8
  have hs10:=rowAggregate_massSquare_nonpos 12 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hs11:=rowAggregate_colouredMassSquare_nonpos 12 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_balance,rowAggregate_normalization]
  norm_num
  linarith
theorem deficit_nonneg_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0) (hhigh:(phaseTotal h4 g 0 + phaseTotal h4 g 2) ≤ (12:ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 8 12 i p:ℝ)))
    (hchild:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.child 0) ≤ 0)
    (hheight:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.heightChild 1) ≤ 0)
    (hgrand:FullPhaseAggregation.rowAggregate 12 h4 h3 g (.grandchild 0) ≤ 0)
    (hcolour:rowAggregate 12 h4 h3 g (.colourChild .whole) ≤ 0) :
    0 ≤ deficit g:=by
  have hc:=FullTwelveCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g heven hhigh hforms hchild hheight hgrand hcolour
  nlinarith [sq_nonneg (mass g)]
end Green24Proof.FullTwelveMass
private def zz2327:"s0917"="s0917":=by decide+kernel
end 
section 
namespace Green24Proof.FullTwelveProfileInterval
open FullPhaseRows (Phase)
open PhaseMassRows ChildRows HeightChildRows
theorem interval_nonneg_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(8:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (12:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_contra! hneg
  have hm:m < 2 * m:=by have hp:=NeZero.pos m; omega
  have hdu:=ih m hm (dvd_mul_left m 2) u hu
  have hdv:=ih m hm (dvd_mul_left m 2) v hv
  have hg:=interleave_nonneg u v hu hv
  have hforms:=ConditionalProfileRows.domainForms_nonneg 8 12 h4 h2 u v hu hv hdu hdv hneg
    (by norm_num) heven hodd hlow hhigh
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hchild:FullPhaseAggregation.rowAggregate 12 h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]; linarith
  have hheight:=rowAggregate_height_odd_nonpos 12 h4 h3 h2 u v hu hv
    (HeightStrong.strong_height_bound h2 h3m h5m v hv)
  have hgrand:=Full27ProfileInterval.grandchild_nonpos_of_induction 12 h4 h3 (interleave u v) hg 0 ih
  have hcolour:=ColourChildRows.whole_nonpos_of_induction 12 h4 h3 (interleave u v) hg ih
  have hhigh':phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 ≤
      (12:ℝ) * (phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3):=by
    rw [ProfileChildren.phaseTotal_interleave_zero h4 h2,
      ProfileChildren.phaseTotal_interleave_two h4 h2,phaseTotal_interleave_one h4 h2,
      phaseTotal_interleave_three h4 h2,classMass_sum,classMass_sum]
    exact hhigh
  have h:=FullTwelveMass.deficit_nonneg_of_rows h4 h3 h5 (interleave u v) hg
    heven hhigh' hforms hchild hheight hgrand hcolour
  linarith
private def zz1174:"s0496"="s0496":=by decide+kernel
theorem interval_nonneg {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(8:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (12:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,heven,hodd⟩ :=
    ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have h:=interval_nonneg_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hd] using h
end Green24Proof.FullTwelveProfileInterval
private def zz2328:"s0918"="s0918":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCoverTwelve
open ProfileInduction BoundaryFromHeightCertificates ConditionalProfileEndpoint
open RatioCoverSixteenFromRemaining (IntervalCertificate)
theorem interval_to_twelve {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:ProperDivisorNonneg (2 * m))
    (horder:mass v ≤ mass u) (hhigh:mass u ≤ 12 * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_cases height:mass u ≤ 8 * mass v
  · exact RatioCoverEight.interval_to_eight h4 h3 h5 h2 u v hu hv ih horder height
  · exact FullTwelveProfileInterval.interval_nonneg h4 h3 h5 h2 u v hu hv ih
      (le_of_lt (lt_of_not_ge height)) hhigh
theorem ratio_to_sixteen_of_remaining
    (h1216:IntervalCertificate 12 16):RatioToSixteen:=by
  apply RatioCoverEight.ratio_to_sixteen_of_remaining _ h1216
  intro m _
  exact FullTwelveProfileInterval.interval_nonneg
theorem deficit_nonneg_of_remaining
    (h1216:IntervalCertificate 12 16)
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g :=
  deficit_nonneg_of_certificates (ratio_to_sixteen_of_remaining h1216)
    hcertificate12 hcertificate18
end Green24Proof.RatioCoverTwelve
private def zz2329:"s0919"="s0919":=by decide+kernel
end 
section 
namespace Green24Proof.LocalFullSixteenPairs
def compact_fullSixteen_pair_20_base:CompactPair.Quadratic:=⟨0,(0x1367 / 0x12a05f200),0⟩
def compact_fullSixteen_pair_20_hinges:List CompactPair.Hinge:=[]
noncomputable def fullSixteen_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_20_base compact_fullSixteen_pair_20_hinges x y
def compact_fullSixteen_pair_20_cuts:List ℚ:=[]
private def zz1175:"s0497"="s0497":=by decide+kernel
theorem compact_fullSixteen_pair_20_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_20_base compact_fullSixteen_pair_20_hinges 0 compact_fullSixteen_pair_20_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_20_representation (x y:ℝ) :
    fullSixteen_pair_20 x y = CompactPair.expressionEval compact_fullSixteen_pair_20_base compact_fullSixteen_pair_20_hinges x y:=by rfl
theorem fullSixteen_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_20 x y:=by
  rw [compact_fullSixteen_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_20_check hy (by simpa using hx)
def compact_fullSixteen_pair_21_base:CompactPair.Quadratic:=⟨(13 / 0x59682f000),(0xf6d / 0x2540be400),0⟩
def compact_fullSixteen_pair_21_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -2⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(-1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x59682f000),3, -2⟩]
noncomputable def fullSixteen_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_21_base compact_fullSixteen_pair_21_hinges x y
def compact_fullSixteen_pair_21_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2]
theorem compact_fullSixteen_pair_21_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_21_base compact_fullSixteen_pair_21_hinges 0 compact_fullSixteen_pair_21_cuts = true :=
  by decide +kernel
private def zz1176:"s0498"="s0498":=by decide+kernel
theorem compact_fullSixteen_pair_21_representation (x y:ℝ) :
    fullSixteen_pair_21 x y = CompactPair.expressionEval compact_fullSixteen_pair_21_base compact_fullSixteen_pair_21_hinges x y:=by rfl
theorem fullSixteen_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_21 x y:=by
  rw [compact_fullSixteen_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_21_check hy (by simpa using hx)
def compact_fullSixteen_pair_22_base:CompactPair.Quadratic:=⟨0,(0x2beb / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_22_hinges:List CompactPair.Hinge:=[]
noncomputable def fullSixteen_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_22_base compact_fullSixteen_pair_22_hinges x y
def compact_fullSixteen_pair_22_cuts:List ℚ:=[]
theorem compact_fullSixteen_pair_22_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_22_base compact_fullSixteen_pair_22_hinges 0 compact_fullSixteen_pair_22_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_22_representation (x y:ℝ) :
    fullSixteen_pair_22 x y = CompactPair.expressionEval compact_fullSixteen_pair_22_base compact_fullSixteen_pair_22_hinges x y:=by rfl
private def zz1177:"s0499"="s0499":=by decide+kernel
theorem fullSixteen_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_22 x y:=by
  rw [compact_fullSixteen_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_22_check hy (by simpa using hx)
def compact_fullSixteen_pair_23_base:CompactPair.Quadratic:=⟨(-0x282f4bde3 / 0x1dcd65000),(0x170f9bfc3 / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_23_hinges:List CompactPair.Hinge:=[⟨(-0x14aefedb / 0x8f0d1800),1, -3⟩,⟨(0x5bc9345 / 0x7735940),1, -2⟩,⟨(-73 / 0x3b9aca00),1, -1⟩,⟨(-0x1df8de85 / 0x8f0d1800),2, -3⟩,⟨(0x8fde035 / 0xbebc200),2, -1⟩,⟨(-0xf6db7af / 0x5f5e1000),3, -2⟩]
noncomputable def fullSixteen_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_23_base compact_fullSixteen_pair_23_hinges x y
def compact_fullSixteen_pair_23_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullSixteen_pair_23_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_23_base compact_fullSixteen_pair_23_hinges 0 compact_fullSixteen_pair_23_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_23_representation (x y:ℝ) :
    fullSixteen_pair_23 x y = CompactPair.expressionEval compact_fullSixteen_pair_23_base compact_fullSixteen_pair_23_hinges x y:=by rfl
theorem fullSixteen_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_23 x y:=by
  rw [compact_fullSixteen_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_23_check hy (by simpa using hx)
def compact_fullSixteen_pair_24_base:CompactPair.Quadratic:=⟨(-19 / 0x3b9aca00),(0x26e9 / 0x2540be400),0⟩
def compact_fullSixteen_pair_24_hinges:List CompactPair.Hinge:=[⟨(0x14f96bd / 0xb2d05e00),1, -3⟩,⟨(-0x9c3323f / 0xee6b2800),1, -2⟩,⟨(-0x9b1e251 / 0x1dcd6500),1, -1⟩,⟨(0x71dc71f / 0x165a0bc00),2, -3⟩,⟨(-0x6999dd61 / 0xee6b2800),2, -1⟩,⟨(0x25313859 / 0xee6b2800),3, -2⟩,⟨(0x8921161 / 0x77359400),3, -1⟩]
noncomputable def fullSixteen_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_24_base compact_fullSixteen_pair_24_hinges x y
def compact_fullSixteen_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz1178:"s049a"="s049a":=by decide+kernel
theorem compact_fullSixteen_pair_24_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_24_base compact_fullSixteen_pair_24_hinges 0 compact_fullSixteen_pair_24_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_24_representation (x y:ℝ) :
    fullSixteen_pair_24 x y = CompactPair.expressionEval compact_fullSixteen_pair_24_base compact_fullSixteen_pair_24_hinges x y:=by rfl
theorem fullSixteen_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_24 x y:=by
  rw [compact_fullSixteen_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_24_check hy (by simpa using hx)
def compact_fullSixteen_pair_25_base:CompactPair.Quadratic:=⟨(29 / 0x59682f000),(0xf65 / 0x2540be400),0⟩
def compact_fullSixteen_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(-3 / 0x1dcd65000),1, -2⟩,⟨(1 / 0xee6b2800),1, -1⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x2cb417800),3, -1⟩]
noncomputable def fullSixteen_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_25_base compact_fullSixteen_pair_25_hinges x y
def compact_fullSixteen_pair_25_cuts:List ℚ:=[(1 / 3),(1 / 2),1,2,3]
theorem compact_fullSixteen_pair_25_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_25_base compact_fullSixteen_pair_25_hinges 0 compact_fullSixteen_pair_25_cuts = true :=
  by decide +kernel
private def zz1179:"s049b"="s049b":=by decide+kernel
theorem compact_fullSixteen_pair_25_representation (x y:ℝ) :
    fullSixteen_pair_25 x y = CompactPair.expressionEval compact_fullSixteen_pair_25_base compact_fullSixteen_pair_25_hinges x y:=by rfl
theorem fullSixteen_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_25 x y:=by
  rw [compact_fullSixteen_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_25_check hy (by simpa using hx)
def compact_fullSixteen_pair_26_base:CompactPair.Quadratic:=⟨(0x861f4d / 0xb2d05e00),(0x2beb / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_26_hinges:List CompactPair.Hinge:=[⟨(-0x13edab87 / 0x165a0bc00),1, -3⟩,⟨(-0x375ac5f / 0x77359400),1, -1⟩,⟨(0x11a91a1 / 0x3b9aca00),2, -3⟩,⟨(0x18b252f / 0xee6b2800),2, -1⟩,⟨(-0x7b1df / 0xee6b280),3, -1⟩]
noncomputable def fullSixteen_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_26_base compact_fullSixteen_pair_26_hinges x y
def compact_fullSixteen_pair_26_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2),3]
theorem compact_fullSixteen_pair_26_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_26_base compact_fullSixteen_pair_26_hinges 0 compact_fullSixteen_pair_26_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_26_representation (x y:ℝ) :
    fullSixteen_pair_26 x y = CompactPair.expressionEval compact_fullSixteen_pair_26_base compact_fullSixteen_pair_26_hinges x y:=by rfl
private def zz1180:"s049c"="s049c":=by decide+kernel
theorem fullSixteen_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_26 x y:=by
  rw [compact_fullSixteen_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_26_check hy (by simpa using hx)
def compact_fullSixteen_pair_27_base:CompactPair.Quadratic:=⟨(-0x5fcfdf83f / 0x1dcd65000),(0x265327c77 / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_27_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(-0x3d51d6bb / 0x5f5e1000),2, -1⟩,⟨(0xe5f2e53d / 0x165a0bc00),3, -1⟩]
noncomputable def fullSixteen_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_27_base compact_fullSixteen_pair_27_hinges x y
def compact_fullSixteen_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),2]
theorem compact_fullSixteen_pair_27_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_27_base compact_fullSixteen_pair_27_hinges 0 compact_fullSixteen_pair_27_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_27_representation (x y:ℝ) :
    fullSixteen_pair_27 x y = CompactPair.expressionEval compact_fullSixteen_pair_27_base compact_fullSixteen_pair_27_hinges x y:=by rfl
theorem fullSixteen_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_27 x y:=by
  rw [compact_fullSixteen_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_27_check hy (by simpa using hx)
def compact_fullSixteen_pair_28_base:CompactPair.Quadratic:=⟨(-0x1987ff863f / 0xe8d4a5100),(-0xdda0062c7a99 / 0x11c37937e0800),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_28_hinges:List CompactPair.Hinge:=[⟨(-0x2d638d607 / 0x1d1a94a200),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_28_base compact_fullSixteen_pair_28_hinges x y
def compact_fullSixteen_pair_28_cuts:List ℚ:=[(1 / 3),3]
private def zz1181:"s049d"="s049d":=by decide+kernel
theorem compact_fullSixteen_pair_28_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_28_base compact_fullSixteen_pair_28_hinges 0 compact_fullSixteen_pair_28_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_28_representation (x y:ℝ) :
    fullSixteen_pair_28 x y = CompactPair.expressionEval compact_fullSixteen_pair_28_base compact_fullSixteen_pair_28_hinges x y:=by rfl
theorem fullSixteen_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_28 x y:=by
  rw [compact_fullSixteen_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_28_check hy (by simpa using hx)
def compact_fullSixteen_pair_29_base:CompactPair.Quadratic:=⟨(-0x1987ff863f / 0xe8d4a5100),(-0xdda011598079 / 0x11c37937e0800),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_29_hinges:List CompactPair.Hinge:=[⟨(-0x2d638d607 / 0x1d1a94a200),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_29_base compact_fullSixteen_pair_29_hinges x y
def compact_fullSixteen_pair_29_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSixteen_pair_29_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_29_base compact_fullSixteen_pair_29_hinges 0 compact_fullSixteen_pair_29_cuts = true :=
  by decide +kernel
private def zz1182:"s049e"="s049e":=by decide+kernel
theorem compact_fullSixteen_pair_29_representation (x y:ℝ) :
    fullSixteen_pair_29 x y = CompactPair.expressionEval compact_fullSixteen_pair_29_base compact_fullSixteen_pair_29_hinges x y:=by rfl
theorem fullSixteen_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_29 x y:=by
  rw [compact_fullSixteen_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_29_check hy (by simpa using hx)
def compact_fullSixteen_pair_30_base:CompactPair.Quadratic:=⟨(-0x54bcd7679 / 0xb2d05e00),(0x88c7b152d / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_30_hinges:List CompactPair.Hinge:=[⟨(-0x72163cd / 0x8f0d1800),2, -3⟩,⟨(0x4d4d9415 / 0x59682f00),3, -1⟩]
noncomputable def fullSixteen_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_30_base compact_fullSixteen_pair_30_hinges x y
def compact_fullSixteen_pair_30_cuts:List ℚ:=[(1 / 3),(3 / 2)]
theorem compact_fullSixteen_pair_30_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_30_base compact_fullSixteen_pair_30_hinges 0 compact_fullSixteen_pair_30_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_30_representation (x y:ℝ) :
    fullSixteen_pair_30 x y = CompactPair.expressionEval compact_fullSixteen_pair_30_base compact_fullSixteen_pair_30_hinges x y:=by rfl
private def zz1183:"s049f"="s049f":=by decide+kernel
theorem fullSixteen_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_30 x y:=by
  rw [compact_fullSixteen_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_30_check hy (by simpa using hx)
def compact_fullSixteen_pair_31_base:CompactPair.Quadratic:=⟨(9 / 0x1dcd65000),(0x191d / 0x1dcd65000),0⟩
def compact_fullSixteen_pair_31_hinges:List CompactPair.Hinge:=[⟨(-0x214b / 0xee6b2800),1, -1⟩,⟨(0xd5 / 0x3b9aca00),2, -3⟩,⟨(0xd4f / 0x59682f000),3, -2⟩]
noncomputable def fullSixteen_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_31_base compact_fullSixteen_pair_31_hinges x y
def compact_fullSixteen_pair_31_cuts:List ℚ:=[(2 / 3),1,(3 / 2)]
theorem compact_fullSixteen_pair_31_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_31_base compact_fullSixteen_pair_31_hinges 0 compact_fullSixteen_pair_31_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_31_representation (x y:ℝ) :
    fullSixteen_pair_31 x y = CompactPair.expressionEval compact_fullSixteen_pair_31_base compact_fullSixteen_pair_31_hinges x y:=by rfl
theorem fullSixteen_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_31 x y:=by
  rw [compact_fullSixteen_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_31_check hy (by simpa using hx)
def compact_fullSixteen_pair_32_base:CompactPair.Quadratic:=⟨(-0xa816013b1 / 0x2ba7def300),(0x61c9933743b5f / 0x2386f26fc1000),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_32_hinges:List CompactPair.Hinge:=[⟨(-0x8cafe7802d / 0x574fbde600),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_32_base compact_fullSixteen_pair_32_hinges x y
def compact_fullSixteen_pair_32_cuts:List ℚ:=[(1 / 3),3]
private def zz1184:"s04a0"="s04a0":=by decide+kernel
theorem compact_fullSixteen_pair_32_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_32_base compact_fullSixteen_pair_32_hinges 0 compact_fullSixteen_pair_32_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_32_representation (x y:ℝ) :
    fullSixteen_pair_32 x y = CompactPair.expressionEval compact_fullSixteen_pair_32_base compact_fullSixteen_pair_32_hinges x y:=by rfl
theorem fullSixteen_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_32 x y:=by
  rw [compact_fullSixteen_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_32_check hy (by simpa using hx)
def compact_fullSixteen_pair_33_base:CompactPair.Quadratic:=⟨(-0x1987ff863f / 0xe8d4a5100),(-0x1bb40233486d1 / 0x2386f26fc1000),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_33_hinges:List CompactPair.Hinge:=[⟨(-0x2d638d607 / 0x1d1a94a200),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_33_base compact_fullSixteen_pair_33_hinges x y
def compact_fullSixteen_pair_33_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSixteen_pair_33_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_33_base compact_fullSixteen_pair_33_hinges 0 compact_fullSixteen_pair_33_cuts = true :=
  by decide +kernel
private def zz1185:"s04a1"="s04a1":=by decide+kernel
theorem compact_fullSixteen_pair_33_representation (x y:ℝ) :
    fullSixteen_pair_33 x y = CompactPair.expressionEval compact_fullSixteen_pair_33_base compact_fullSixteen_pair_33_hinges x y:=by rfl
theorem fullSixteen_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_33 x y:=by
  rw [compact_fullSixteen_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_33_check hy (by simpa using hx)
def compact_fullSixteen_pair_34_base:CompactPair.Quadratic:=⟨(1 / 0x39387000),(0x26dd / 0x2540be400),0⟩
def compact_fullSixteen_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0xa30d2f / 0x11e1a300),1, -3⟩,⟨(0x1461a5e1 / 0x5f5e1000),1, -2⟩,⟨(-0x197a0f59 / 0x165a0bc00),2, -3⟩,⟨(-0x1461a5e1 / 0x5f5e1000),2, -1⟩,⟨(0x197a0f59 / 0x165a0bc00),3, -2⟩,⟨(0xa30d2f / 0x11e1a300),3, -1⟩]
noncomputable def fullSixteen_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_34_base compact_fullSixteen_pair_34_hinges x y
def compact_fullSixteen_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_fullSixteen_pair_34_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_34_base compact_fullSixteen_pair_34_hinges 0 compact_fullSixteen_pair_34_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_34_representation (x y:ℝ) :
    fullSixteen_pair_34 x y = CompactPair.expressionEval compact_fullSixteen_pair_34_base compact_fullSixteen_pair_34_hinges x y:=by rfl
private def zz1186:"s04a2"="s04a2":=by decide+kernel
theorem fullSixteen_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_34 x y:=by
  rw [compact_fullSixteen_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_34_check hy (by simpa using hx)
def compact_fullSixteen_pair_35_base:CompactPair.Quadratic:=⟨(-1 / 0x11e1a3000),(0xf6d / 0x2540be400),0⟩
def compact_fullSixteen_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x59682f000),2, -3⟩,⟨(1 / 0x59682f000),3, -2⟩]
noncomputable def fullSixteen_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_35_base compact_fullSixteen_pair_35_hinges x y
def compact_fullSixteen_pair_35_cuts:List ℚ:=[(2 / 3),(3 / 2)]
theorem compact_fullSixteen_pair_35_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_35_base compact_fullSixteen_pair_35_hinges 0 compact_fullSixteen_pair_35_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_35_representation (x y:ℝ) :
    fullSixteen_pair_35 x y = CompactPair.expressionEval compact_fullSixteen_pair_35_base compact_fullSixteen_pair_35_hinges x y:=by rfl
theorem fullSixteen_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_35 x y:=by
  rw [compact_fullSixteen_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_35_check hy (by simpa using hx)
def compact_fullSixteen_pair_36_base:CompactPair.Quadratic:=⟨(-0x5fc8831 / 0x165a0bc0),(0xf5349ed / 0x1312d000),0⟩
def compact_fullSixteen_pair_36_hinges:List CompactPair.Hinge:=[⟨(0x5fc8831 / 0x59682f00),2, -3⟩]
noncomputable def fullSixteen_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_36_base compact_fullSixteen_pair_36_hinges x y
def compact_fullSixteen_pair_36_cuts:List ℚ:=[(3 / 2)]
private def zz1187:"s04a3"="s04a3":=by decide+kernel
theorem compact_fullSixteen_pair_36_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_36_base compact_fullSixteen_pair_36_hinges 0 compact_fullSixteen_pair_36_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_36_representation (x y:ℝ) :
    fullSixteen_pair_36 x y = CompactPair.expressionEval compact_fullSixteen_pair_36_base compact_fullSixteen_pair_36_hinges x y:=by rfl
theorem fullSixteen_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_36 x y:=by
  rw [compact_fullSixteen_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_36_check hy (by simpa using hx)
def compact_fullSixteen_pair_37_base:CompactPair.Quadratic:=⟨(-0x1392c07d7 / 0x1dcd65000),(0x31152ecd / 0x5f5e1000),0⟩
def compact_fullSixteen_pair_37_hinges:List CompactPair.Hinge:=[⟨(0xbd / 0xee6b2800),1, -3⟩,⟨(-0x17a75f4f / 0x1dcd65000),1, -2⟩,⟨(-1 / 0x77359400),1, -1⟩,⟨(0x28fe60b / 0x1dcd65000),2, -3⟩,⟨(0x5e9d6ff7 / 0x1dcd65000),2, -1⟩,⟨(-0xb878b3 / 0x3b9aca00),3, -2⟩]
noncomputable def fullSixteen_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_37_base compact_fullSixteen_pair_37_hinges x y
def compact_fullSixteen_pair_37_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_fullSixteen_pair_37_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_37_base compact_fullSixteen_pair_37_hinges 0 compact_fullSixteen_pair_37_cuts = true :=
  by decide +kernel
private def zz1188:"s04a4"="s04a4":=by decide+kernel
theorem compact_fullSixteen_pair_37_representation (x y:ℝ) :
    fullSixteen_pair_37 x y = CompactPair.expressionEval compact_fullSixteen_pair_37_base compact_fullSixteen_pair_37_hinges x y:=by rfl
theorem fullSixteen_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_37 x y:=by
  rw [compact_fullSixteen_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_37_check hy (by simpa using hx)
def compact_fullSixteen_pair_38_base:CompactPair.Quadratic:=⟨(-0x1987ff863f / 0xe8d4a5100),(-0x37680183a0ad5 / 0x470de4df82000),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_38_hinges:List CompactPair.Hinge:=[⟨(-0x2d638d607 / 0x1d1a94a200),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_38_base compact_fullSixteen_pair_38_hinges x y
def compact_fullSixteen_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSixteen_pair_38_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_38_base compact_fullSixteen_pair_38_hinges 0 compact_fullSixteen_pair_38_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_38_representation (x y:ℝ) :
    fullSixteen_pair_38 x y = CompactPair.expressionEval compact_fullSixteen_pair_38_base compact_fullSixteen_pair_38_hinges x y:=by rfl
private def zz1189:"s04a5"="s04a5":=by decide+kernel
theorem fullSixteen_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_38 x y:=by
  rw [compact_fullSixteen_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_38_check hy (by simpa using hx)
def compact_fullSixteen_pair_39_base:CompactPair.Quadratic:=⟨(-0x1987ff863f / 0xe8d4a5100),(-0x3768044ee2255 / 0x470de4df82000),(-0x2d638d607 / 0x2e90edd00)⟩
def compact_fullSixteen_pair_39_hinges:List CompactPair.Hinge:=[⟨(-0x2d638d607 / 0x1d1a94a200),1, -3⟩,⟨(0x2d638d607 / 0x1d1a94a200),1,3⟩,⟨(0x2d638d607 / 0x1d1a94a200),3, -1⟩,⟨(0x2d638d607 / 0x1d1a94a200),3,1⟩]
noncomputable def fullSixteen_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_fullSixteen_pair_39_base compact_fullSixteen_pair_39_hinges x y
def compact_fullSixteen_pair_39_cuts:List ℚ:=[(1 / 3),3]
theorem compact_fullSixteen_pair_39_check :
    CompactPair.expressionCheckPSD compact_fullSixteen_pair_39_base compact_fullSixteen_pair_39_hinges 0 compact_fullSixteen_pair_39_cuts = true :=
  by decide +kernel
theorem compact_fullSixteen_pair_39_representation (x y:ℝ) :
    fullSixteen_pair_39 x y = CompactPair.expressionEval compact_fullSixteen_pair_39_base compact_fullSixteen_pair_39_hinges x y:=by rfl
theorem fullSixteen_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ fullSixteen_pair_39 x y:=by
  rw [compact_fullSixteen_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_fullSixteen_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalFullSixteenPairs
private def zz2330:"s091a"="s091a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l42 l43 l45 l46 l5 l51 l54 l55 l57 l58 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1f99c6240, -0x337cede60, -0x4d3b6502a,0x5ffdf04e], ![-0x337cede60, -0x97ac49f7c,0xbf6f2c86,0x3308b39ec], ![-0x4d3b6502a,0xbf6f2c86, -0x14eac0c434,0x337cee7c0], ![0x5ffdf04e,0x3308b39ec,0x337cee7c0, -0x19be77188]]
noncomputable def hinges:Hinges:=[(-0xeb1ec0,l6),(-0x101e0a7c,l5),(0x19011f2ac,l4),(-0x126713fb,l9),(-0xd9bb09c4,l8),(-0x21f81c6,l11),(0x408306de,l10),(0x36f46b566,l14),(-0xfb8f8da0,l17),(0xb081d748,l23),(0x1ae9683,l22),(-0x19be77188,l27),(0x19be77188,l29),(-0x36f46b566,l25),(0xb081d748,l31),(0xe47efa30,l30),(0x19be77188,l33),(-0x408306de,l38),(-0x19be77188,l35),(0xd9bb09c4,l36),(0x19be77188,l37),(-0x19011f2ac,l34),(-0xe47efa30,l43),(-0x1ae9683,l42),(0x50d65a3a,l46),(0x35d2d06,l45),(0x19be77188,l51),(0x21f81c6,l55),(0x101e0a7c,l54),(-0xb081d748,l57),(-0x35d2d06,l58),(0x126713fb,l61),(0xeb1ec0,l60),(-0xb081d748,l63),(0xfb8f8da0,l62),(-0x50d65a3a,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x19be77188,l27),(0x19be77188,l29),(0x19be77188,l33),(-0x19be77188,l35),(0x19be77188,l37),(0x19be77188,l51),(0x36f46b566,l14),(-0x36f46b566,l25),(0xb081d748,l23),(0xb081d748,l31),(-0xb081d748,l57),(-0xb081d748,l63),(-0xfb8f8da0,l17),(0xfb8f8da0,l62),(0xe47efa30,l30),(-0xe47efa30,l43),(-0xd9bb09c4,l8),(0xd9bb09c4,l36),(0x19011f2ac,l4),(-0x19011f2ac,l34),(0x50d65a3a,l46),(-0x50d65a3a,l64),(0x408306de,l10),(-0x408306de,l38),(-0x126713fb,l9),(0x126713fb,l61),(-0x101e0a7c,l5),(0x101e0a7c,l54),(-0x21f81c6,l11),(0x21f81c6,l55),(0x35d2d06,l45),(-0x35d2d06,l58),(0x1ae9683,l22),(-0x1ae9683,l42),(-0xeb1ec0,l6),(0xeb1ec0,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨76, 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#[![4, 0, 21, -6],![8, 0, -21, 2],![-1, 0, 1, 0],![-1, 0, -25, 4],![30, 0, -29, 3],![39, 0, -25, 4]]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((0x3070551430d98180f3de844c0532bae11c302002d453914102837daf9e0446a4b8000098508402183810452e71c2001a633f16201759755181877022a3980cfdc73df98005a66bd0120130d2da520ce20400100fa010000b9121d1590e0ac86c264200b02805f8ac297f3f20088b00c507825ee9f048a001592fac081621c8c0a92860f0040868264180b88880df82aa886aee9f86e8847496ac56883687d7376b204100040864174513297cfdf8992000075f5f5050858f3ba928104d8fad85130817fd3165e9831c6dd8cbe080000002010338212804288013fd42bc0249000006dc20411ea7cb62d4d5144d9150e3828282406356402040d4a0ceade208055a3e1cece040000025801008840425b20c24009c06124800001cf0a7089004ef253e9541044156588db00e2080a8c678ea709c0800000278d004021ea0332c984240014e498c6458280007279a63ba02000f353222ba19512005c0600002352000882668819a9666bbc38f910d8d7372a83029fff3170280a00b142a77aa811c508108b2c6020bb4720fee0208b6051d00341000001a91757e0e000a809104000003372f101c1528d60f5038fbfe709b08d0c30c9f661195a2083e530f8798404024ce64044980111b74d79c3400000008ca00e00d12c32adb2d2400a408000040848601400081a40027fcc4f1373c60028bcaf57bf070cc42c1c82810052e9c944291b8f54c78232dc91981060a220164e003e01021701c9001c8b55696030d2115175999d314220bffb2482210005a092c782c202dcc020c881041b9d1c45a853049a8e40c000020000029c9460902000ac0a1c700000525181e3029163e085061aa95dc760da80408d363277834200c7e50ce60410806c62260d50000000546009801ed44c64301800d69801b0c4848014810000080c80020010a50910b0280016a480086492151181308c85007c15c7968b23040797f8da0084c59a2208042e8e6c248103c01021301d16825b07ac1846a8fed3348110ffc0f6a20955a0937c24082100871f83760322506230eaa1f53144979d1ec485036cb2700c14300d4f505023772bb1b2600220084d30d1e65fdb134039da6f7e820800000db84141ccb0225ce14070676c6bda070639bba2fd950038cbc323c0d00000004b001c017ff7c13830900260180000f41e3f03394920a0c4bd3e0dc2628ea244f6a90a06c5b7a918284bae27baa0468d4a7b798080aca65481000000caa25000440109a6a75efef932038f854a92ee20800003529fa8196fb84968498645d09c020180a744771232083e26c506662600ba794efb66800000048a85d9002601c0000f490003942000dcc4001f6490906e230748efb3346062316ec30618e4a8d46067bcb1d1212060f804084407d3c231db4c4541fb1d39a7cb235c47c799913866e28d8bbb7198ffabd99d9858f4886290e70a28a306784384304a02080864300401bc28804c8d650a2b1025fe9a0c1f84baef501e101b47efe51a1007d21cff8e1032465f788c1017493e622800804cb26124017acfbac6019218480200001d92000740400129087e8c83ec341f412000de9241a3200205f23e84b09b0d83a84effef827000000237398936b04deb03723d824382ca19362b02c8e0ca0cd04c04104d00b01861a934074ecf64b389ff2ae38e049a24275ae0aac8c3cd745c61a852a4200b0280190780e43803d679c8445168c7d83680a00b2ae7f4b14149eff058a2d64ce82fa4440e45ad50810000b055e412708230084900013069dc60c052c3de34b18024575310c34d4ed83064850b142ca2298211708317d2040f32201693821180426880de5a87e347051c1f21a38f33bb2f0394186eab39d6a80870a0079f04000004a49730011804269ba9639430e921c6cf249b6dc20800001914d5243362f5840f7061f378625c5693083246664fca98000e6ae03c214000000112380600cf029544e2bf2005204800020620006ba4001394c4f0c1a1d13d1146af16133145dadd1d6e11100e4d24d42c107556f86470001d62500498208802124018a1bf99186c9cdb2a212141cce36d0302038c7d29130437319ce94810bab8c7e89810880213440e3a1aca4c72fbe9f640d1c026d692f1c7fbbf80c814194cf581f9343097ce0db8100000464ca9c008802134cb07348fd934800000d7b943c9bf6069d131fca2f9088c410000052518d0c8ffd2f40070fedfe0b2b1408c4c91a4205000000070825200480280001d520006a8400129c8002fe10bb0d85d06e4387f9f2a8f405021b7276450a1419104bc5160173f1cd14100a697eb71c206ed1eb3e84c184601090e63b92c5234050a3c698ea685830a54b5a4796dc28bd1fbbce6fd83840c243f165d830419149d9be5e70200369c320d62021fbccd7c0a618002060b51644041d4861601800008a890704e2350c2e6c8884885640fb1630a21cd97992b24822159dfa238c08000009f782820457b38af9200a313d3bd020094f1244ca800000dde9006d0284c0300001e62000b3a60835e37e68d1068e00000249f00f12ebca6162b01c200000229b603832d9c4c48f2838425f51411944309c0398424cc0415df564407fe0003e840e1581600007c09068a800522085) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 40 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase0" = "QuadFullSixteenCase0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 40 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase0
private def zz2331:"s091b"="s091b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l17 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l55 l58 l59 l6 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1f165d25d, -0x337cede60, -0x4d3b65024,0x60354768], ![-0x337cede60, -0x97707be90,0xbf791836,0x3306a9878], ![-0x4d3b65024,0xbf791836, -0x14eac0c434,0x337cee7c0], ![0x60354768,0x3306a9878,0x337cee7c0, -0x19be77188]]
noncomputable def hinges:Hinges:=[(-0xeb1ec0,l6),(-0x101e0a7c,l5),(0x19011f2ac,l4),(-0x126713fb,l9),(-0xd9bb09c4,l8),(-0x21f81c6,l11),(0x408306de,l10),(0x378fd832e,l14),(-0x9d0b1866,l17),(0x56e67c004,l15),(0x898a750,l21),(-0x8b32e1b,l23),(0x1094514e7,l22),(-0x19be77188,l27),(-0x898a750,l28),(0x19be77188,l29),(-0x378fd832e,l25),(0xda2bc98a,l30),(0x19be77188,l33),(-0x408306de,l38),(-0x19be77188,l35),(0xd9bb09c4,l36),(0x19be77188,l37),(-0x19011f2ac,l34),(-0xda2bc98a,l43),(-0x1094514e7,l42),(-0x56e67c004,l41),(0x39bab18c,l46),(-0x4a4cd410,l45),(0x19be77188,l51),(0x21f81c6,l55),(0x101e0a7c,l54),(0x39a46b86,l59),(0x4a4cd410,l58),(0x126713fb,l61),(0xeb1ec0,l60),(0x8b32e1b,l63),(0x9d0b1866,l62),(-0x39a46b86,l65),(-0x39bab18c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x19be77188,l27),(0x19be77188,l29),(0x19be77188,l33),(-0x19be77188,l35),(0x19be77188,l37),(0x19be77188,l51),(0x378fd832e,l14),(-0x378fd832e,l25),(0x56e67c004,l15),(-0x56e67c004,l41),(0xda2bc98a,l30),(-0xda2bc98a,l43),(-0x9d0b1866,l17),(0x9d0b1866,l62),(0x1094514e7,l22),(-0x1094514e7,l42),(-0xd9bb09c4,l8),(0xd9bb09c4,l36),(0x19011f2ac,l4),(-0x19011f2ac,l34),(0x39a46b86,l59),(-0x39a46b86,l65),(0x408306de,l10),(-0x408306de,l38),(0x39bab18c,l46),(-0x39bab18c,l64),(-0x4a4cd410,l45),(0x4a4cd410,l58),(-0x126713fb,l9),(0x126713fb,l61),(-0x8b32e1b,l23),(0x8b32e1b,l63),(0x898a750,l21),(-0x898a750,l28),(-0x101e0a7c,l5),(0x101e0a7c,l54),(-0x21f81c6,l11),(0x21f81c6,l55),(-0xeb1ec0,l6),(0xeb1ec0,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((0x286084ed73394201868d918a053a2218942820871c4be3409a443e5e000081e6210800985084021420a26f13a9a18bc6bc9692180bcfc2e) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase1" = "QuadFullSixteenCase1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase1
private def zz2332:"s091c"="s091c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase2
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l16 l22 l27 l29 l30 l31 l33 l35 l37 l4 l51 l62 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1fe7d1d350, -0x59682eb50, -0x61794a440,0x23eb31710], ![-0x59682eb50, -0x2826c8cb56,0x1001a03600, -0x69ba78030], ![-0x61794a440,0x1001a03600, -0x3118968bc7,0xacc2b7da4], ![0x23eb31710, -0x69ba78030,0xacc2b7da4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x7b421d22,l4),(0x35cca889,l11),(0x127de2834,l10),(-0x58d496e7,l16),(0x1613e760a,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0xd3c74f3,l31),(-0x336c6846,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x43acaa7e0,l62),(0x5fc88310,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x43acaa7e0,l62),(0x127de2834,l10),(0x1613e760a,l22),(0x5fc88310,l65),(0x35cca889,l11),(-0x336c6846,l30),(-0x58d496e7,l16),(0x7b421d22,l4),(0xd3c74f3,l31)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase2" = "QuadFullSixteenCase2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase2
private def zz2333:"s091d"="s091d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l22 l23 l27 l29 l30 l31 l33 l35 l37 l4 l44 l51 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb41783c, -0x59682eb50,0x861c46c5c,0x4bc], ![-0x59682eb50, -0x1f657bc0f4,0xda268f588, -0x6b63d669c], ![0x861c46c5c,0xda268f588, -0x3118968bc7,0xacc2b7da4], ![0x4bc, -0x6b63d669c,0xacc2b7da4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x7b421d22,l4),(0x35cca889,l11),(0x127de2834,l10),(0x23ce17048,l14),(0x1c93e9ffc,l13),(-0x15390468,l17),(0x46cd4cea,l16),(-0xd19e31ee,l15),(0x12bb8b132,l21),(-0x4370118d8,l20),(-0x2f743d5c,l23),(0x326f97baf,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x208b4f34,l31),(-0xc3713aa4,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-12,l44),(0x2cb417800,l51),(8,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x4370118d8,l20),(0x23ce17048,l14),(0x12bb8b132,l21),(0x326f97baf,l22),(0x127de2834,l10),(0x1c93e9ffc,l13),(-0xc3713aa4,l30),(0x35cca889,l11),(-0x2f743d5c,l23),(-0xd19e31ee,l15),(-0x208b4f34,l31),(0x46cd4cea,l16),(0x7b421d22,l4),(-0x15390468,l17),(8,l64),(-12,l44)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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], #[![0, 31, 63, -83],![0, -17, -21, 41],![0, -4, -47, 6],![0, -8, -45, 12],![0, -16, -41, 24]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 26 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase3" = "QuadFullSixteenCase3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 26 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase3
private def zz2334:"s091e"="s091e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l22 l23 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l44 l45 l5 l51 l6 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x46eaf41dc, -0x3c55cf710, -0x5a80b75aa,0x197e3dd30], ![-0x3c55cf710, -0x22e68dc296,0x61075ade4,0x25c3614e4], ![-0x5a80b75aa,0x61075ade4, -0x191fba0e43,0x3e1f7eb34], ![0x197e3dd30,0x25c3614e4,0x3e1f7eb34, -0x1e2ae7de0]]
noncomputable def hinges:Hinges:=[(-0xf5e2e6,l6),(0x829f9ad,l5),(0xd104d842,l4),(-0x104e6c2e,l9),(-0x637a4921,l8),(-0xa8da7d6,l11),(0x376af0bc,l10),(0x1a1c38bbc,l14),(0x17e566792,l13),(-0xfb8f8da0,l17),(0xb081d748,l23),(0x1ae9683,l22),(-0x1e2ae7de0,l27),(-0xf9a03bfc,l28),(0x1e2ae7de0,l29),(0xb081d748,l31),(0xe47efa30,l30),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(-0xf18980b0,l43),(-0xb4d76fb8,l42),(-0x44fd0b9b8,l41),(0x48e1bbce,l45),(0x75d4f244,l44),(0x1e2ae7de0,l51),(-0x32f41eb2,l63),(0x1c771c7c,l65),(-0x8d51388,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(0x1e2ae7de0,l51),(0x1a1c38bbc,l14),(-0xf9a03bfc,l28),(-0x44fd0b9b8,l41),(0xb081d748,l23),(0xb081d748,l31),(-0xfb8f8da0,l17),(-0xf18980b0,l43),(0xe47efa30,l30),(0x17e566792,l13),(-0xb4d76fb8,l42),(-0x32f41eb2,l63),(-0x637a4921,l8),(0x376af0bc,l10),(0xd104d842,l4),(0x1c771c7c,l65),(0x48e1bbce,l45),(0x75d4f244,l44),(-0x104e6c2e,l9),(-0xa8da7d6,l11),(-0x8d51388,l64),(0x829f9ad,l5),(-0xf5e2e6,l6),(0x1ae9683,l22)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x106360a6055a0080000000000640620080e18a6881805c68030000000000270188020000000110480a180600000000443c0530080000000000780a401000000120110058c040000002702200b18080000094260900b400c0000000003c012401800000001d19028c0200000000001602900400001686229024400c000590c629818880200006114c1203110040000901b8220242008002403482f028840140000000a44602860180000000211d028c020001023a88c079a00800001047a26036400c0000000001c80e401000000010864098c03000001a42a8085180a00000003214015300c000388c60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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 30 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase4" = "QuadFullSixteenCase4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 30 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase4
private def zz2335:"s091f"="s091f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l22 l23 l25 l27 l29 l30 l33 l35 l37 l4 l41 l42 l43 l44 l45 l46 l5 l51 l57 l58 l59 l6 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2bb7c0183, -0x3c55cf710, -0x5a80b7610,0x1d47faa9c], ![-0x3c55cf710, -0x2585744fd4,0x645a17ba0,0x25c157370], ![-0x5a80b7610,0x645a17ba0, -0x191fba0e43,0x3e1f7eb34], ![0x1d47faa9c,0x25c157370,0x3e1f7eb34, -0x1e2ae7de0]]
noncomputable def hinges:Hinges:=[(-0xf5e2e6,l6),(0x829f9ad,l5),(0xd104d842,l4),(-0x104e6c2e,l9),(-0x637a4921,l8),(-0xa8da7d6,l11),(0x376af0bc,l10),(0x1d9ab73a8,l14),(0x27cd34e44,l13),(-0x9d0b1866,l17),(0x56e67c004,l15),(-0x57713b518,l20),(-0x8b32e1b,l23),(0x1094514e7,l22),(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(0x18f3f4b40,l25),(0xda2bc98a,l30),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(-0xdd32799c,l43),(-0xd3bf5ad8,l42),(-0x4ae1148a2,l41),(0xb3e7ea8,l46),(0xbe615536,l45),(-0x5850150,l44),(0x1e2ae7de0,l51),(-0x34e018bc,l57),(-0x102b59de,l59),(-0xc56727c,l58),(-0x21bbb865,l63),(0x25947aba,l62),(0x3c67d680,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(0x1e2ae7de0,l51),(-0x57713b518,l20),(0x1d9ab73a8,l14),(0x18f3f4b40,l25),(0x27cd34e44,l13),(0x56e67c004,l15),(-0x4ae1148a2,l41),(-0xdd32799c,l43),(0xda2bc98a,l30),(-0x9d0b1866,l17),(0x1094514e7,l22),(-0xd3bf5ad8,l42),(0xbe615536,l45),(-0x34e018bc,l57),(0x3c67d680,l64),(-0x637a4921,l8),(0x376af0bc,l10),(-0x21bbb865,l63),(0xd104d842,l4),(0x25947aba,l62),(-0x104e6c2e,l9),(-0x102b59de,l59),(-0xa8da7d6,l11),(-0x8b32e1b,l23),(0xb3e7ea8,l46),(-0xc56727c,l58),(0x829f9ad,l5),(-0x5850150,l44),(-0xf5e2e6,l6)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((0x30b05d73802a794021a6609cd2abad9f0a69a4016a9f53f3053ac85bd4a688049a895fcc0cc17bb94494004e236dea40a0408c02039a0be2ed8ef8b109c382e6f39b1) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase5" = "QuadFullSixteenCase5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase5
private def zz2336:"s0920"="s0920":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase6
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l16 l2 l20 l22 l27 l29 l30 l31 l33 l35 l37 l5 l51 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l2, ![-0x59682eb50, -0x282033c8e6,0xfff4ea9f8, -0x69ba78030], ![0x53b8290e8,0xfff4ea9f8, -0x31084d13f9,0xac9237abe], ![0x4b0, -0x69ba78030,0xac9237abe, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x5e9d6ff7,l5),(0x846a332f,l8),(0x124306a96,l10),(0x4fb6ae1c,l14),(0x29841474,l12),(-0x58d496e7,l16),(-0x1ff3f140,l20),(0x1613e760a,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0xd3c74f3,l31),(-0x336c6846,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x124306a96,l10),(0x1613e760a,l22),(0x4fb6ae1c,l14),(0x846a332f,l8),(0x5e9d6ff7,l5),(-0x336c6846,l30),(-0x58d496e7,l16),(0xd3c74f3,l31),(-0x1ff3f140,l20),(0x29841474,l12)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[]⟩
def dynamicCode : Nat := ((((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) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 17 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase6" = "QuadFullSixteenCase6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 17 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase6
private def zz2337:"s0921"="s0921":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l16 l17 l22 l23 l25 l27 l29 l30 l31 l33 l35 l37 l5 l51 l59 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb41dcd4, -0x59682eb50,0x861c42090,0x18c0], ![-0x59682eb50, -0xed36f20de,0xa74e6ccb8, -0x6b63d669c], ![0x861c42090,0xa74e6ccb8, -0x31084d13f9,0xac9237abe], ![0x18c0, -0x6b63d669c,0xac9237abe, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x5e9d6ff7,l5),(0x846a332f,l8),(0x124306a96,l10),(0x12c305748,l14),(0x670e9b6e2,l13),(-0x15390468,l17),(0x46cd4cea,l16),(-0xd19e31ee,l15),(-0x2f743d5c,l23),(0x326f97baf,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x397cb94f4,l25),(-0x208b4f34,l31),(-0xc3713aa4,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x13f8,l59),(0x1414,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x670e9b6e2,l13),(-0x397cb94f4,l25),(0x326f97baf,l22),(0x12c305748,l14),(0x124306a96,l10),(-0xc3713aa4,l30),(0x846a332f,l8),(-0x2f743d5c,l23),(0x5e9d6ff7,l5),(-0xd19e31ee,l15),(-0x208b4f34,l31),(0x46cd4cea,l16),(-0x15390468,l17),(-0x13f8,l59),(0x1414,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x4d00a200c00000000270188020000000003c052008000000110f014c02000004e04401630100000120110058c04000094260900b400c0000000078024803], #[![0, -19, -45, 23],![0, -8, -45, 12],![0, -16, -41, 24]]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    0xa6cdc38e60b01e500019f210a2a0841104188c208261020a08001710658b25d66451000001bd80070b936e77a61c609e0f7e19080504000005aea0600000018a08050000003308a027ff95377080ec5de73f4290e285003806401491be47aa757b048835ec613c75a209c01c3611f2848715fab2b8ebe30621f12a9c0083046257b6abe6020461b23fec45810459080f4be302839c56651e1a914920058060c14a95aedbc1841dc34428890c4cc945e718337fb722b45060fc5ed0320015be420f830123b4a9f99c00880200002c66cb1962f62fcf7bf8590c95b8e0651395061870c61f27bd4c5142af0d54a08888b714313a74ce786768640549d2f00b0ed39450870280d3e28e998a005683b0a8735c23d09010086e0a800024e3c6475adab44f8912fd71c321d6204388e6505ba0a0c5a41e0f14a1031f8a20b244c70ad053c268de281069a51acf50706d053ffda0e1410aa5e88e4349c48215012003c0600044841581605003915841459e8af10e280540ce1dbfa145d72bb68d86bc4087df5ff3e33189084c9f95b3c340a10102bf0e29c008247d71d5bdb203031c98b8580e5c600496f21bc885f4712005e070c24e74d5197d7ccd164236ac5e135fcb3208000004c5caab9c58817c87f31836dcc4100365c929298810e1c0daf5caa61efe1420518ad8fb4e4f4583419ce768dd39c3d09010006e0a800024c3c784ce7bab8614d1f2ec3f20140ca6f95840481927a0c18014a2e02d8100729020b026042200800009b1920ff8f220a1d61c504f8c2b5f0c86157a74cf347ef30406fa18a18500810b2727b6048f104a8ac838ea9a080416d0f0d387c1400fe480562e10100113c2e31f20bd04801701a2c8a1544a176490350363818b1a1884dc919430b7491f1818519f2569764841f84e78a08001f6a8022ce004601000016a20fe030003d020480b814561aacd49708c2a7691ef6ab6b2044d7aad66ea30209a53abf8a240860c4f2825a696e0619cdf471550ae1010b1f0010d9402801cf1fd2977103004634e630f0e59712005e070b23789e4d3e16351eaad0c928650375797630a00000482c7086aa9848104113dbb015810100000e7613801180400005a8c0a64561e6249f0614b6942f732d79022879f9f17aba104b1c8b05346e038604f6b01fc5a060c427f61ce4708e091ee15cc6db4140068c71d3d104180049adf07ceaa4609002f038591c8089c9c9470c681871c016d1b0bc08c6cab16325e6c4a3369d993692862fbef8922b28ee3be30a0111c9c4207132bb470460f1db668750d2dc0c00016d0d058096ee4fb2d071f83802184200009a4800262107e0583e8080023388009709001b6f20f8339240000170b650162d8216e581bc2244c9ac0badee3040889fb3b18fb5c5100efefdedc6d08193ac6a746995282bd2182304fba280000005fb68003005b4c5291db17bc480178182c984fb76330962c65a7e691e64b28508fc0388cdf10332c5b16900328211e16b7f2ba0410000000a5c42c01388393bb8010002feaa0a658c88002c0200000f39b2000000a4d90511f827876267287703eb793c71426445d15afe4910000001fa40186955c5c14401c21c18370e43120c0aff1282a8b0000000ca2f0ed2085203000020434380000209c7c123d8759f7b2eb8a2870fe73b7da122157b2c4e5321218f443d51cc49018000001d010120baa7f54ce1d0c083dbaac5a6e020003d89fd07826348416010000088cc1000000c1aac0b0d54c1ea3648901dfdef8bd9cf1c31b05b47690e2070e4dc09aac46086b2642582c881400d40b91aa0810991cb77fea20000000648c020920056048a2212370694050b00b85e0a124443d5625b70a1806b3b47d030cfcaf4c0ec304034c4ad370410000000d40600b4e39e7a6800250080000d49a1c00000f438123afa8ff11f32468cf1baf294488b2777045f890e780aea574901e84e2784f21c2d09c4e4e642822c88bacfc0a00000012b8834904270140000f89038018002fe107b05c1000000a5eba40918bf0750d658b9229181f1724b53244bf7f31aab9f440464929d630ed870920b8e3607da08110be3c085696100000002b1220018047d0fc5dddeb7b2400bc0c14443e1bf6d5943b3673a3c9142dd4c6ff5f12242c799f410c1929fad6028e10e29c63ac8208000000d40401642865785000480100001a134380000186c048e5f8089b2812371fb6adb064885a7df7f56921c74e2fea80406e6b8496e80a11ab8701640382e6b848428140000001df40c48213008000079cc90639329fef0208000003b9701438bee94c403ca16d12c5c2502508455712f7e0244326a0fb1b8041448e793aa00400000007bc0010042cd1ff3a0a2400a406143c3a7280999c32e48a3a41bbf8734401424f39cae0da7136488000015442786006119a5d9ae2512f61041fc80abbe0f050808000000946eca0500594b2c66b562b8200000000a552f2117122400d81300005086474bd639a34e923405c9d67bf8718000004f5f04082b6b9ac3202436552faf9239018000068ade0209613b7f46a048028c4b1c25618000000185643a9042901400010190006bf20f40b0790100068010780103b80800703883b0ec1d4760e83b0731d8390ec1c4760e03b06f1d8370af0648a591163040000ff9218248a760ce480d290817230198acffec08198adda80004c2840010a28f3f025321820000029c43020000162ec100000079328005907f68f40025142300800008a906d158360ac1ac560d42b069158340ac19c560cc2b0650503)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 25 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase7" = "QuadFullSixteenCase7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 25 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase7
private def zz2338:"s0922"="s0922":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase8
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz1249:"s04e1"="s04e1":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase8
private def zz2339:"s0923"="s0923":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase9
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase9
private def zz2340:"s0924"="s0924":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l17 l21 l25 l27 l29 l33 l35 l36 l37 l38 l41 l42 l43 l51 l58 l59 l61 l64 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x30abde5ec, -0x58497fea0, -0x861c46350,0x208e480], ![-0x58497fea0,0x1d14df3e8,0xa3b0e4264,0x698cb5360], ![-0x861c46350,0xa3b0e4264, -0x247bf5722c,0x5a9ba31fe], ![0x208e480,0x698cb5360,0x5a9ba31fe, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x28fe60b,l9),(0x5c3c598,l11),(0x43acaa7e0,l17),(0x474de602,l21),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x4d4d94150,l25),(0x2cb417800,l33),(-0x7a03d21a,l38),(-0x2cb417800,l35),(-0x2078f0694,l36),(0x2cb417800,l37),(-0xda8aaa96,l43),(-0x490d0625,l42),(0x12397b0ba,l41),(0x2cb417800,l51),(-0x1a7da718,l59),(0x16b11226,l58),(0x4d24966b,l61),(0x2e2b3a0,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x4d4d94150,l25),(0x43acaa7e0,l17),(-0x2078f0694,l36),(-0xda8aaa96,l43),(-0x7a03d21a,l38),(0x4d24966b,l61),(0x474de602,l21),(0x12397b0ba,l41),(-0x1a7da718,l59),(-0x490d0625,l42),(0x16b11226,l58),(0x5c3c598,l11),(-0x28fe60b,l9),(0x2e2b3a0,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0x1086c058c0300000c848094c0300000000440c801000144470130c04000304510258c0400000000601480200411c8300d90030002b251d025002000002b1d024c020000188a4050c03003b15050069003003915050069003001e20880098c050001ec120058c04000001f06018c0200000001e014802cd1181b4055500500001483809cc0300015013025cc0400000130a018c020032118680b9003a30ec10c0a2d0059c09809406b10059009809406b10050000b0150350c0400220c84407500304b0cc23011500400210d84c09500300000009002480300001282402cc03], #[]⟩
def dynamicCode : Nat := ((((((((((0x5921fa71a54cc227485f55c98270d9edce220400145f68870603610c01cc0cd146019116183dbf864124003d3133583404118042c9000000384061078d98af8f49140000004b01824a548d149b30313bfe685a058601cb0d5ae85040000004ad1800ab5d651930010475c29190104e0200001e6344041b38e4d0e0b1cead381ad750408000307a2f74144040289625d8161c5162e17634c70c36130b1ef005840c173d0493f2820162ad481e00e00202c86f54601c62430b40a0000460686544677b565038607cd092cbf0a0a0f671622cc8c10299ad966d0281190fc49702a48200ed0ae5100c0002c880f6a80c0014cd6d5c28040003b57be2108bb12205604000021e3648b3e7c6d7861162c4c4f4d982618db34a924081af0758cd0824639b5ad9048604394f0210c183abe21ee2480098fb005bad202098051abc248f048e5f0df64f45bb5e92397c37e08c4d24d14914514a10710d04200001c820080374967d67b565e14300000000090718000000e07068b295e11538d245036250fdef8a2aacb8c226e8a10013dda32003880586c83a5f34015a0a601fc322410a407000040a4000d1cd8f26ac1a41ed04080078f5cdcb0288152fae100d85878f166164d7438644ff8d7c6d818715c22d5d2ea4040c5e2e2b884380162198f055800002a9bc96b1a0f7f21858050000227343455a784ca0e1835fa8946141527a9b2030c108a58ba56041347dbd37690080b2be80b080826e86b0a180005a02eb00c00268c40c72af220480100001d920012a04174260b80b05b01d92840265eb9847c3f19f406074caf65461018bb97ce5a1865941ad5f1608a57a0e884800f0287822ce1044010b2474c5b8f289308e0db0321b989140000015f90303cee886f348c80c4dd92337e60c37e819da0318e040000041c0d2c11a4878e578cc0191a2e5a2604e1484150120000848d10468c308f5c963b696b6d10084080008a163998a204a7ec800ec48617367db38296150a3e3f36f038463e3b07bd604100235763a2c38012b0f3eb1e231a90c2a02400010a1a19b05c57436c91483f42f1ddc70c25b0ecf1c08081922ca18c0a06316b2f5970604cacf1d3ddc10467c097c160c0007031d06c06001b0c89e8c15644881400e000080882d02c03807850030092cd1a482e2f1e719a1ea2ffac010a08056bc7a79400193eca43880002ee41f0020003986bac0ce1048010f3e60bc22309485a6679600d96076cf5aa2d18600083faa1073cd71e2950a80b00d54dea8f0814732882e3d4966302000001ae74f51fc041000eacd20ffbe031c00005d6f12c2fb3ec100000005addeece536f3f532007a0c0f2c4c9652600f174ed54af38f082ba4dd13060400007b23c1040063b70c2500240080000889d04cd100000016f8d894d04cd2036279e79630c78a88278270270180001006f9f71a9da5a56dc7960cc15b07827678a66e2677601da882000000249f00782095a232068a2702000000249f01f41800c00b00003244000a9880035a9d242d6e6b350d0e67f089620d042f36cf64030409864805410407dbf8f68a000122d6b0830014a4324319c1090021a099a20000002df1b129a099a406c4d34d24410d0c304204d02595c102401a0001f04164240005366cbb985f29a38b1c1cbc3332a1440000000c8040800d2ff0520820000004b08b04f12d2ee6a2810000002580d0005728a7692c0042458cda916910260080000f5905405e1208f05b6224285ccd3f492081aca4de08c108402125d72de0199e8bff0ec3621e03e7d7720867baca6d1ba078ecd87b681509917887463cd5ec06d1105437dd2a2f6ade9dd1c56841543082452422401c0f9b44e0617daf308ed39da95dde69f4f9bd07b7361455b50e957c8e574f00ff556fc40900f2bdeff6d5cf59d2676c5dd2a09965b500038920b013c2018063a2b12280bfbf5b824200001568e7020de760138c043296aeaa180489ff93cb66042300802b80a72929b37ae0a201b80e415128628320320218220128014008072080200da1974071b7792830df22280ec80d13745f1c9202228fa9deb460810827fef3201982ceb9dac704d897fd8003c000b00e2e15c8804260200000dc90002c2200085e4158440aa120008d72002c10413814003c846860000004b02044faaa3c961c30294a85252010d70b431b0418409a0084200535bad2f41000ebafa2810400474b0a9800043f69279c545291c2400858e000000960122978e51ddae4080b1a69069921068ae19cd010508c92200c0e086af08fe404806544103c20a00d4e73d60600000e4d28902c4841300828aa4ccdd33f0c200000004b02860b3905b36ca0c0d15c339a0c32119244018c080d5e11fc80410000004b08a00c0b583e3724000000025829002600802a00f4c05a8898f734903dac1e1e2c71470aa83710482bc547362c030e68358f04000001214d980090021a501a38dcd0104eb66b16b83021d1b9d81c6002d27dd364800460100000dd200047240011308288681403409e1204e0500035210491d0268e8002320f14e8c4b0c5fb923) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase10" = "QuadFullSixteenCase10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase10
private def zz2341:"s0925"="s0925":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l12 l25 l27 l28 l29 l33 l35 l36 l37 l38 l41 l42 l43 l51 l56 l57 l61 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2fff7e910, -0x58497fea0, -0x861c46350,0x4b0], ![-0x58497fea0,0x20077a80e,0x76cccf170,0x861c46c5c], ![-0x861c46350,0x76cccf170, -0x247bf5722c,0x5a9ba31fe], ![0x4b0,0x861c46c5c,0x5a9ba31fe, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x28fe60b,l9),(0x5c3c598,l11),(-0x171c58fa4,l12),(-0x2cb417800,l27),(-0xa16606ea,l28),(0x2cb417800,l29),(-0x3779a8cb0,l25),(0x2cb417800,l33),(-0x7a03d21a,l38),(-0x2cb417800,l35),(-0x2078f0694,l36),(0x2cb417800,l37),(-0x66486114,l43),(-0x220999af7,l42),(0x20862f5a6,l41),(0x2cb417800,l51),(0x1f9fc19b,l57),(-3,l56),(0x4d24966b,l61)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x3779a8cb0,l25),(-0x220999af7,l42),(-0x2078f0694,l36),(-0xa16606ea,l28),(0x20862f5a6,l41),(-0x7a03d21a,l38),(0x4d24966b,l61),(-0x66486114,l43),(-0x171c58fa4,l12),(0x1f9fc19b,l57),(0x5c3c598,l11),(-0x28fe60b,l9),(-3,l56)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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,0x10a19005ccc0500000001d03880200000c848094c030000001b404c80300000000440c801000001d0a038c0200000001e01480200000001903880200371488404d00300000001901880200019151102d00200015013025cc0400001483809cc03000001511028c02a30ec10c0a2d00500270c8440750030410cc23025500404b0cc23011500400220c84407500300210d84c095003000000090024803], #[![6, -19, -12, 0],![4, -7, -6, 0]]⟩
def dynamicCode : Nat := ((((((((((0x309000000d6c2864e5eca90c245003c60f16282c8ea200d9281192717ef62410122a69e82c0013373a031c00000001686804240086140000003b80c2400000257c18300000012b82863b66678b8048a0000004b00a0a5daa71ccf940898) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 21 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase11" = "QuadFullSixteenCase11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 21 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase11
private def zz2342:"s0926"="s0926":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase12
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz1254:"s04e6"="s04e6":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase12
private def zz2343:"s0927"="s0927":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase13
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
private def zz1255:"s04e7"="s04e7":=by decide+kernel
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase13
private def zz2344:"s0928"="s0928":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l5 l51 l54 l55 l58 l6 l60 l61 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x687cd87e8, -0x3c55cf710, -0x5a80b75aa,0x7b6ddb2], ![-0x3c55cf710, -0x183f77dd70,0x31a05af58,0x417c95dba], ![-0x5a80b75aa,0x31a05af58, -0x1882c9dee7,0x3c55d0070], ![0x7b6ddb2,0x417c95dba,0x3c55d0070, -0x1e2ae7de0]]
noncomputable def hinges:Hinges:=[(0x1b33ee2,l6),(-0x191fcd12,l5),(-0x4ba6e480,l4),(0x106df07a,l9),(0x2f7fed,l8),(0x3ab0595,l11),(-0xd5612,l10),(0x216072010,l14),(0x44fd0b9b8,l15),(0x32f41eb2,l23),(0xb4d76fb8,l22),(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(-0x216072010,l25),(0xf18980b0,l30),(0x1e2ae7de0,l33),(0xd5612,l38),(-0x1e2ae7de0,l35),(-0x2f7fed,l36),(0x1e2ae7de0,l37),(0x4ba6e480,l34),(-0xf18980b0,l43),(-0xb4d76fb8,l42),(-0x44fd0b9b8,l41),(0x37f62741,l45),(0x1e2ae7de0,l51),(-0x3ab0595,l55),(0x191fcd12,l54),(-0x37f62741,l58),(-0x106df07a,l61),(-0x1b33ee2,l60),(-0x32f41eb2,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(0x1e2ae7de0,l51),(0x216072010,l14),(-0x216072010,l25),(0x44fd0b9b8,l15),(-0x44fd0b9b8,l41),(0xf18980b0,l30),(-0xf18980b0,l43),(0xb4d76fb8,l22),(-0xb4d76fb8,l42),(0x32f41eb2,l23),(-0x32f41eb2,l63),(0x37f62741,l45),(-0x37f62741,l58),(0x106df07a,l9),(-0x106df07a,l61),(-0x4ba6e480,l4),(0x4ba6e480,l34),(-0x191fcd12,l5),(0x191fcd12,l54),(0x3ab0595,l11),(-0x3ab0595,l55),(0x1b33ee2,l6),(-0x1b33ee2,l60),(0x2f7fed,l8),(-0x2f7fed,l36),(-0xd5612,l10),(0xd5612,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[0x609620631808004b0828c5039840140096101182053080280000000261103cc02000000005414039804000000000e890330040000288441605680180000000000240c801000005049080c9180a00000d0260a01e400c0000000000480c401000000001d0901cc020000000006488198020000000006850330040000000000a80c401000000000222c0cc0100000000241a0718040000000000440e20080000000088301c601000000010864088c030000000000018190020000003c24180a40080000158843203c801800000000001c0c80100000000140a029804000000002c140a300800000000000a0640080000000a824088c030000001582e043180800000025044086301000000000004812401000000000a0502cc02000000000062071004000000000017032004000000000168164010000000000260148020000000000098190020000000000940920080000000000220640080000000002102c80200000000000a8190020000000004700b200c0000000008801640180000000011404c803000000000042039004000000006c2409300800000000d0680c6010000000000130148020000000230a80518060000004908403230100000000098580c601000000001309018c020000000026140298040001342104803240100a20508220031a80300005409c1401b50040000ac1202c04ea0080001482a04803d40100002e0500e00ba80200000000009802480300000000001c02900400000000442c06300800000000038012401800000000012014802,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,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,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,0x521403180400000a8842002630140000000000281c401000000002b0a018c020021c3d410818fa00a000000ab088016301000810e305207be80280000002a848038c03041039808a037f200c000000a80880133012060e4812e0577c80380000000130501cc020000002302202498080000000c81900a300c0000000190680c60100000000000d01880200000000064381980200020c6c14c0ab40100000000000c80c4010000032118680b1003001842143100b8200a00000000000f0320040000000000f00a401000000010864050c0300000000000a069004060843430808d040180003086209817680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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase14" = "QuadFullSixteenCase14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase14
private def zz2345:"s0929"="s0929":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l5 l51 l54 l55 l57 l6 l60 l61 l62 l63 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x52f08fecc, -0x3c55cf710, -0x5a80b7610,0x4b0], ![-0x3c55cf710, -0x14a7457fcd,0x199446d3e,0x4dc056bae], ![-0x5a80b7610,0x199446d3e, -0x1882c9dee7,0x3c55d0070], ![0x4b0,0x4dc056bae,0x3c55d0070, -0x1e2ae7de0]]
noncomputable def hinges:Hinges:=[(0x1b33ee2,l6),(-0x191fcd12,l5),(-0x4ba6e480,l4),(0x106df07a,l9),(0x2f7fed,l8),(0x3ab0595,l11),(-0xd5612,l10),(0x2004c29d0,l14),(0x1f36c9cad,l13),(-0x25947aba,l17),(0x4ae1148a2,l15),(-0x1f36c9cad,l20),(0x21bbb865,l23),(0xd3bf5ad8,l22),(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(-0x2004c29d0,l25),(0x34e018bc,l31),(0xdd32799c,l30),(0x1e2ae7de0,l33),(0xd5612,l38),(-0x1e2ae7de0,l35),(-0x2f7fed,l36),(0x1e2ae7de0,l37),(0x4ba6e480,l34),(-0xdd32799c,l43),(-0xd3bf5ad8,l42),(-0x4ae1148a2,l41),(0x1e2ae7de0,l51),(-0x3ab0595,l55),(0x191fcd12,l54),(-0x34e018bc,l57),(-0x106df07a,l61),(-0x1b33ee2,l60),(-0x21bbb865,l63),(0x25947aba,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x1e2ae7de0,l27),(0x1e2ae7de0,l29),(0x1e2ae7de0,l33),(-0x1e2ae7de0,l35),(0x1e2ae7de0,l37),(0x1e2ae7de0,l51),(0x2004c29d0,l14),(-0x2004c29d0,l25),(0x4ae1148a2,l15),(-0x4ae1148a2,l41),(0x1f36c9cad,l13),(-0x1f36c9cad,l20),(0xdd32799c,l30),(-0xdd32799c,l43),(0xd3bf5ad8,l22),(-0xd3bf5ad8,l42),(0x34e018bc,l31),(-0x34e018bc,l57),(0x21bbb865,l23),(-0x21bbb865,l63),(-0x25947aba,l17),(0x25947aba,l62),(0x106df07a,l9),(-0x106df07a,l61),(-0x4ba6e480,l4),(0x4ba6e480,l34),(-0x191fcd12,l5),(0x191fcd12,l54),(0x3ab0595,l11),(-0x3ab0595,l55),(0x1b33ee2,l6),(-0x1b33ee2,l60),(0x2f7fed,l8),(-0x2f7fed,l36),(-0xd5612,l10),(0xd5612,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[![0, -9, 11, -19]]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((0x4ad36be1522929f4d643b055ab584ab9ae5106b800000016245144e44d40d444104041040c0000803628eddd15df11399838d1d671c00003f6644d0032a30d2223cbf01688e10000000f8208c761244d3c00000008a6000840100003127cd0ca5ba808333ca284e16da83d4051b151b6f9e54017879dd9baa030107c62f75d88041cdb418f45264002f4e09836f93000000fcf34393e84021601600007b0c10a6890b1d14cf8c81a96eec0a69d8004d3400005dc45db10a01aa667a412d4abe303004ae3f06577b81869b4d06836c6598a04054409898674b0e08000006eeb66a8bd4d7e000dc161e6af1f5bc966062583bb331208f0e388f838214c591b9820e12aba3d0800381480d49800000976f538011004000058c8ea028000f84f320b309c5546e227dac60a89a59c31c19611408c08209c0040064200401a3b00a00010723a6231d2118e886c74017e6195c505a238c0074c46ee404004bc9504208a1c1fc101e0486d1a9a02c0004c9a5800130811804348443081ace9d66c9c340ab56b095735ca20d700000002c489c81c804104102082300000180801006c4ecc19436ea0700015b60d11804bf2c2a2089f7d1c684003e366d808006925cc1b826082100800009a181a4aadf6b78f3400117364a028390b7718041eb14199e08000da6b4898c000000686300000760c7d80270c230080000b8900042232c01c2f5b275edf7f41362e4872e302439905984e2aa37113ed630548d2) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 38 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase15" = "QuadFullSixteenCase15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 38 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase15
private def zz2346:"s092a"="s092a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase16
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l15 l2 l22 l27 l29 l30 l33 l35 l37 l5 l51 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l2, ![-0x59682eb50, -0x2c01cf7f20,0x14cecae1b8, -0x663a207fe], ![0x53b8290e8,0x14cecae1b8, -0x2f3ad7e005,0x94fa91a9e], ![0x4b0, -0x663a207fe,0x94fa91a9e, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x1329931a7,l5),(0x225a33cf5,l8),(0x64101d18,l10),(-0x12397b0ba,l15),(0x490d0625,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(0xda8aaa96,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x225a33cf5,l8),(0xda8aaa96,l30),(-0x1329931a7,l5),(0x64101d18,l10),(-0x12397b0ba,l15),(0x490d0625,l22)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨60, #[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], #[![35, 164, -183, 0],![1, 82, -123, 0]]⟩
def dynamicCode : Nat := 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
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 15 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase16" = "QuadFullSixteenCase16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 15 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase16
private def zz2347:"s092b"="s092b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l13 l14 l15 l16 l22 l27 l29 l30 l31 l33 l35 l37 l44 l5 l51 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb41a1f4, -0x59682eb50,0x861c42090,0xea0], ![-0x59682eb50, -0x32890a1c50,0x1563b982e4, -0x5b3d98968], ![0x861c42090,0x1563b982e4, -0x2f3ad7e005,0x94fa91a9e], ![0xea0, -0x5b3d98968,0x94fa91a9e, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x1329931a7,l5),(0x225a33cf5,l8),(0x64101d18,l10),(0x36c913b5c,l14),(0x1d434b77a,l13),(3,l16),(-0x20862f5a6,l15),(0x220999af7,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x1f9fc19b,l31),(0x66486114,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x6d8,l44),(0x2cb417800,l51),(0x56c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x36c913b5c,l14),(0x225a33cf5,l8),(0x220999af7,l22),(0x1d434b77a,l13),(-0x1329931a7,l5),(-0x20862f5a6,l15),(0x66486114,l30),(0x64101d18,l10),(-0x1f9fc19b,l31),(0x56c,l64),(-0x6d8,l44),(3,l16)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadFullSixteenCase17" = "QuadFullSixteenCase17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadFullSixteenCase17
private def zz2348:"s092c"="s092c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase18
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
private def zz1271:"s04f7"="s04f7":=by decide+kernel
theorem v0:V s0:=(K 1 nt 0x1004431920330)
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase18
private def zz2349:"s092d"="s092d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadFullSixteenCase19
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l19 l48 l49 l50)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l19,l48,l49,l50]
noncomputable def hinges:Hinges:=[]
def normalizationDenominator:ℤ:=0x1312d00
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat
def s0:State:=initial constraintsNat base hinges
open BranchWitnessAtoms
def nt:IndexedNatTreeCheck.Table:=⟨1, #[]⟩
theorem v0:V s0:=(K 1 nt 0x1004431920330)
private def zz1272:"s04f8"="s04f8":=by decide+kernel
theorem certificate_valid:∃ p,check p constraintsNat base hinges = true:=root v0
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  obtain ⟨p,hp⟩:=certificate_valid
  exact ScalarRowDefaults.nonnegative p base hinges normalizationDenominator hp
    (by decide +kernel) x hx
end
end Green24Proof.QuadFullSixteenCase19
private def zz2350:"s092e"="s092e":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixteenRows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x107e20001eeb5ca8007b3abb9ea1fe20001eeb5ca8006d18cefb614e200779ae58007a4dbf3c205e2001de6d9a063e7f4da62003bcdb2c0028bcdbabe07a20003dceb94800d87878bde1fa20003dceb948007fbc8c58615a20009c4da8027f8abae22005faf8480039dfecfee07d20001eeb5ca8008f9e1b8921fd20009c4da8018b1baba1ed2005faf848003dfc6fa8a14d20017ebe180018fef80ea52002fd7c28003d1b1d4fe120003dceb942ad7c09207c20003dceb948037c7f686ae1ec2001de6d9a008cca9ea42003bcdb2c003e580bb9e07820003dceb948036fa9aeae6020001eeb5ca800ede96b7ba14]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x12a0001eeb5ca800cbdb3d7f6760004e2ad8002360004e2ad800202e60003dceb948003ed83dac615e60003dceb94800a8b988dea01e600779ae58006f7cda3966600779ae58004f9cce9ba1ea6005faf8480728b8f9a01a600779ae58009d4ecd0aa260003dceb94801ba489c0e6560004e2ad8002160004e2ad800207f20001eeb5ca8004d8b0abd21ff20003dceb948022ad8cf9f601f20003dceb94801cdf9794fa720001eeb5ca800df8ccf7ba07b20003dceb948002beedae8e06b20003dceb948037adb1be14b2000ef3acd002d4eaae32002fd7c28004a2859fa214]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x106d30001eeb5ca800192530003dceb948001de130004e2ad800207c3002fd7c2802e97bd8e17c3001de6d9a018e291d61ec30001eeb5ca8003cd91d786430017ebe1801f8e89be07830003dceb94800586d9b4ba1f830001eeb5ca8008fc9e82030001eeb5ca8001e693e4967e0004e2ad80023e0004e2ad800207fa0003dceb94801bb2a2bbae1ffa005faf848001f9daede67a0003dceb94803984fbd6a63a0001eeb5ca801bdf98fafa07ea003bcdb2c00480a68aba1fea0003dceb948014e7cca69e6a0001eeb5ca800fababb0d607aa003bcdb2c0049683c88214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1570004e2ad8002170004e2ad8002730004e2ad800216b300779ae58034fdd3c61cb3005faf84800c8d8afa05b3003bcdb2c001b8d6ba33000ef3acd00aed8603e30002fdbc9001c1a6921fe30001eeb5ca8010b9d0ea06e300779ae58001ebc08e1de3005faf848019efbdc614e30003dceb948003fbd78e9201e30001eeb5ca8016bebfaa630003dceb94805e07a30001eeb5ca8011d589e216a30001eeb5ca8071ee9cbe02a30003dceb9480019d8dfbb614a3005faf848026efb2d2230007b9d6a80203d30003dceb948005b614]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11dc00003dceb948002a6b8cff61cc00017ebe18004a691e205c0000ef3acd01db1f6400002b196c0027f0004e2ad80023f0004e2ad800203fb0001eeb5ca800206fb0003dceb9480027b0004e2ad800216bb003bcdb2c05fe4a0e23b0004e2ad80026b0004e2ad80021fab005faf84803bd8cede2b0003dceb9480019fc28ede770004e2ad8002370004e2ad800216e700779ae58009fe05e7005faf8480048267001de6d9a042270004e2ad800214]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x103f000779ae58001c8908ec617f00003dceb948016f3b3a6ce1cf0005faf848002c784f3d270005faf84805980bba603e00001eeb5ca8001ddd5f0de1fe00003dceb94800492c68c961ee00001eeb5ca8054b6cfd602e0001389b48016a5e7861de00001eeb5ca800182b9d8ae14e00003dceb94802bc5a29e05e00003dceb948007d7c5e6600002b196c00203d00003dceb948007d08fa49a17d000779ae58005b4dfacee1dd0005faf848001f6eddede50001de6d9a002fe9fb203c00003dceb948004848c8dde1fc000779ae58002a2a7adf61ec0002fd7c28003b2e78e02c00001eeb5ca800495b6d0f214]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x117f80003dceb948005c29b99ca14f80003dceb948003f8cebffa780002b196c00207e80003dceb948035ac9217e80003dceb94807ed59e16e80003dceb94803ad896aa06e80007b9d6a80393bd8615e80001eeb5ca800183b7e0fa1ce80001eeb5ca8042ffde8601e80003dceb94800dccfde2680002b196c00203d80001eeb5ca80099fbca89a16d80003dceb948006dce5a29202d80003dceb948002c8d893b6580002b196c002480002b196c002740002b196c002640002b196c002540002b196c002440002b196c00214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1210002b196c00203c1005faf848002dd89b78217c1001389b48038cbd1aa02c10001eeb5ca800ebdefead61dc1001389b48005c8d9a605c10003dceb948009e8acb0e641002fd7c280260381003bcdb2c001e4bfbec617810003dceb948008fc9e821681003bcdb2c002e181ebd21581003bcdb2c002e181ebd205810005faf8a01993fd92010003dceb948002fa7c0002b196c00216ec003bcdb2c00bc3e2e61dec0003dceb948028ff98966c0002b196c0025c0002b196c0024c0002b196c00203f80003dceb948012a1c1d59614]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x105c900779ae5802ab9829a490001eeb5ca800fb7e3c607890003dceb9480039bb1d0c617890001eeb5ca8007adfdf9ae16890003dceb948001d3e3d3e61c890003dceb948003d9e1c99a090003dceb94802fc38e75003bcdb2c00b96c1b68635007a898012cba496550002b196c002150002b196c00203e10001eeb5ca80039990e18a17e10003dceb948016d8c4a3fa1ee10003dceb948003f9fe86b606e10003dceb94800aebd9a3e214e10003dceb948002610002b196c00203a10003dceb94800dd4aad59617a10003dceb94800385cdb2ee06a10003dceb94800689caa0be14]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1019d0005faf8a06ca3dde61d0002fdbc9009e2c48203e90001eeb5ca8006f4e4f9ce17e9003bcdb2c0018d958f9216e900779ae58001d3c098de02e90003dceb948018faecb0b615e9005faf84806bf993c205e90003dceb948002acd1f5ba69003bcdb2c02603a9003bcdb2c001f1c4e09617a9000bf5f0c0188eaeb202a90017ebe180019396b9b215a90001eeb5ca800397d0bdb2290003dceb948002d207c90009c4da801fa2d4a217c90003dceb948021cfeecfca1ec900779ae580018296cf9a06c90003dceb948004aefdcbfa1dc900779ae58001bde8bdae14c9002fd7c28025e1b4f614]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10894002692e802010101000102010008920003dceb948035d4e2f182012001010120010101170102011701020403dceb94803bcdcdea01200101012001010101010001020100042fd7c28004ec92040601040406010101000101010001020403dceb94800a8d8ef19e07e8060602b196c001c6bba609c4da801ad3a1b90793c3c01ed4e3ba15bacac022d6f3c90902010105779ae58001a4bb92088b00779ae58012a382088a0001eeb5ca802f97d7b2088f00779ae58001ed918eee08850003dceb948049d0b1ce08800003dceb948069eae09a7d0002b196c0023d0002b196c0025d0001eeb5ca802cda85f1ba0f]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadFullSixteenCase0.base QuadFullSixteenCase0.hinges QuadFullSixteenCase0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase0.base QuadFullSixteenCase0.hinges QuadFullSixteenCase0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadFullSixteenCase1.base QuadFullSixteenCase1.hinges QuadFullSixteenCase1.normalizationDenominator
private def zz1273:"s04f9"="s04f9":=by decide+kernel
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase1.base QuadFullSixteenCase1.hinges QuadFullSixteenCase1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r62,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadFullSixteenCase2.base QuadFullSixteenCase2.hinges QuadFullSixteenCase2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase2.base QuadFullSixteenCase2.hinges QuadFullSixteenCase2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadFullSixteenCase3.base QuadFullSixteenCase3.hinges QuadFullSixteenCase3.normalizationDenominator
private def zz1274:"s04fa"="s04fa":=by decide+kernel
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase3.base QuadFullSixteenCase3.hinges QuadFullSixteenCase3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r66,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r80,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadFullSixteenCase4.base QuadFullSixteenCase4.hinges QuadFullSixteenCase4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase4.base QuadFullSixteenCase4.hinges QuadFullSixteenCase4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadFullSixteenCase5.base QuadFullSixteenCase5.hinges QuadFullSixteenCase5.normalizationDenominator
private def zz1275:"s04fb"="s04fb":=by decide+kernel
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase5.base QuadFullSixteenCase5.hinges QuadFullSixteenCase5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadFullSixteenCase6.base QuadFullSixteenCase6.hinges QuadFullSixteenCase6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase6.base QuadFullSixteenCase6.hinges QuadFullSixteenCase6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r61,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadFullSixteenCase7.base QuadFullSixteenCase7.hinges QuadFullSixteenCase7.normalizationDenominator
private def zz1276:"s04fc"="s04fc":=by decide+kernel
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase7.base QuadFullSixteenCase7.hinges QuadFullSixteenCase7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadFullSixteenCase8.base QuadFullSixteenCase8.hinges QuadFullSixteenCase8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase8.base QuadFullSixteenCase8.hinges QuadFullSixteenCase8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadFullSixteenCase9.base QuadFullSixteenCase9.hinges QuadFullSixteenCase9.normalizationDenominator
private def zz1277:"s04fd"="s04fd":=by decide+kernel
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase9.base QuadFullSixteenCase9.hinges QuadFullSixteenCase9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r59,RewriteAtoms.r30,RewriteAtoms.r81,RewriteAtoms.r61,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadFullSixteenCase10.base QuadFullSixteenCase10.hinges QuadFullSixteenCase10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase10.base QuadFullSixteenCase10.hinges QuadFullSixteenCase10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r50,RewriteAtoms.r52,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadFullSixteenCase11.base QuadFullSixteenCase11.hinges QuadFullSixteenCase11.normalizationDenominator
private def zz1278:"s04fe"="s04fe":=by decide+kernel
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase11.base QuadFullSixteenCase11.hinges QuadFullSixteenCase11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadFullSixteenCase12.base QuadFullSixteenCase12.hinges QuadFullSixteenCase12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase12.base QuadFullSixteenCase12.hinges QuadFullSixteenCase12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadFullSixteenCase13.base QuadFullSixteenCase13.hinges QuadFullSixteenCase13.normalizationDenominator
private def zz1279:"s04ff"="s04ff":=by decide+kernel
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase13.base QuadFullSixteenCase13.hinges QuadFullSixteenCase13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadFullSixteenCase14.base QuadFullSixteenCase14.hinges QuadFullSixteenCase14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase14.base QuadFullSixteenCase14.hinges QuadFullSixteenCase14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadFullSixteenCase15.base QuadFullSixteenCase15.hinges QuadFullSixteenCase15.normalizationDenominator
private def zz1280:"s0500"="s0500":=by decide+kernel
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase15.base QuadFullSixteenCase15.hinges QuadFullSixteenCase15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadFullSixteenCase16.base QuadFullSixteenCase16.hinges QuadFullSixteenCase16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase16.base QuadFullSixteenCase16.hinges QuadFullSixteenCase16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadFullSixteenCase17.base QuadFullSixteenCase17.hinges QuadFullSixteenCase17.normalizationDenominator
private def zz1281:"s0501"="s0501":=by decide+kernel
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase17.base QuadFullSixteenCase17.hinges QuadFullSixteenCase17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadFullSixteenCase18.base QuadFullSixteenCase18.hinges QuadFullSixteenCase18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase18.base QuadFullSixteenCase18.hinges QuadFullSixteenCase18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadFullSixteenCase19.base QuadFullSixteenCase19.hinges QuadFullSixteenCase19.normalizationDenominator
private def zz1282:"s0502"="s0502":=by decide+kernel
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadFullSixteenCase19.base QuadFullSixteenCase19.hinges QuadFullSixteenCase19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadFullSixteenCase19.nonnegative x hx
def pair20:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair20Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_20_base LocalFullSixteenPairs.compact_fullSixteen_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalFullSixteenPairs.fullSixteen_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_20_base LocalFullSixteenPairs.compact_fullSixteen_pair_20_hinges x
private def zz1283:"s0503"="s0503":=by decide+kernel
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair21Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_21_base LocalFullSixteenPairs.compact_fullSixteen_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalFullSixteenPairs.fullSixteen_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_21_base LocalFullSixteenPairs.compact_fullSixteen_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 1 false
def pair22Rewrites:Rewrites:=[]
def pair22Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_22_base LocalFullSixteenPairs.compact_fullSixteen_pair_22_hinges
private def zz1284:"s0504"="s0504":=by decide+kernel
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalFullSixteenPairs.fullSixteen_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_22_base LocalFullSixteenPairs.compact_fullSixteen_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2]
def pair23Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_23_base LocalFullSixteenPairs.compact_fullSixteen_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
private def zz1285:"s0505"="s0505":=by decide+kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalFullSixteenPairs.fullSixteen_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_23_base LocalFullSixteenPairs.compact_fullSixteen_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28]
def pair24Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_24_base LocalFullSixteenPairs.compact_fullSixteen_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalFullSixteenPairs.fullSixteen_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_24_base LocalFullSixteenPairs.compact_fullSixteen_pair_24_hinges x
private def zz1286:"s0506"="s0506":=by decide+kernel
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28]
def pair25Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_25_base LocalFullSixteenPairs.compact_fullSixteen_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalFullSixteenPairs.fullSixteen_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_25_base LocalFullSixteenPairs.compact_fullSixteen_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51]
def pair26Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_26_base LocalFullSixteenPairs.compact_fullSixteen_pair_26_hinges
private def zz1287:"s0507"="s0507":=by decide+kernel
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalFullSixteenPairs.fullSixteen_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_26_base LocalFullSixteenPairs.compact_fullSixteen_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2]
def pair27Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_27_base LocalFullSixteenPairs.compact_fullSixteen_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
private def zz1288:"s0508"="s0508":=by decide+kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalFullSixteenPairs.fullSixteen_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_27_base LocalFullSixteenPairs.compact_fullSixteen_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_28_base LocalFullSixteenPairs.compact_fullSixteen_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalFullSixteenPairs.fullSixteen_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_28_base LocalFullSixteenPairs.compact_fullSixteen_pair_28_hinges x
private def zz1289:"s0509"="s0509":=by decide+kernel
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_29_base LocalFullSixteenPairs.compact_fullSixteen_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalFullSixteenPairs.fullSixteen_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_29_base LocalFullSixteenPairs.compact_fullSixteen_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r51]
def pair30Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_30_base LocalFullSixteenPairs.compact_fullSixteen_pair_30_hinges
private def zz1290:"s050a"="s050a":=by decide+kernel
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalFullSixteenPairs.fullSixteen_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_30_base LocalFullSixteenPairs.compact_fullSixteen_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28]
def pair31Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_31_base LocalFullSixteenPairs.compact_fullSixteen_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
private def zz1291:"s050b"="s050b":=by decide+kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalFullSixteenPairs.fullSixteen_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_31_base LocalFullSixteenPairs.compact_fullSixteen_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_32_base LocalFullSixteenPairs.compact_fullSixteen_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalFullSixteenPairs.fullSixteen_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_32_base LocalFullSixteenPairs.compact_fullSixteen_pair_32_hinges x
private def zz1292:"s050c"="s050c":=by decide+kernel
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_33_base LocalFullSixteenPairs.compact_fullSixteen_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalFullSixteenPairs.fullSixteen_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_33_base LocalFullSixteenPairs.compact_fullSixteen_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair34Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_34_base LocalFullSixteenPairs.compact_fullSixteen_pair_34_hinges
private def zz1293:"s050d"="s050d":=by decide+kernel
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalFullSixteenPairs.fullSixteen_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_34_base LocalFullSixteenPairs.compact_fullSixteen_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28]
def pair35Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_35_base LocalFullSixteenPairs.compact_fullSixteen_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
private def zz1294:"s050e"="s050e":=by decide+kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalFullSixteenPairs.fullSixteen_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_35_base LocalFullSixteenPairs.compact_fullSixteen_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r51]
def pair36Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_36_base LocalFullSixteenPairs.compact_fullSixteen_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalFullSixteenPairs.fullSixteen_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_36_base LocalFullSixteenPairs.compact_fullSixteen_pair_36_hinges x
private def zz1295:"s050f"="s050f":=by decide+kernel
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r72,RewriteAtoms.r71]
def pair37Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_37_base LocalFullSixteenPairs.compact_fullSixteen_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalFullSixteenPairs.fullSixteen_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_37_base LocalFullSixteenPairs.compact_fullSixteen_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_38_base LocalFullSixteenPairs.compact_fullSixteen_pair_38_hinges
private def zz1296:"s0510"="s0510":=by decide+kernel
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalFullSixteenPairs.fullSixteen_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_38_base LocalFullSixteenPairs.compact_fullSixteen_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=pairSlack (16) ((1 / 0xf4240)) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalFullSixteenPairs.compact_fullSixteen_pair_39_base LocalFullSixteenPairs.compact_fullSixteen_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
private def zz1297:"s0511"="s0511":=by decide+kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalFullSixteenPairs.fullSixteen_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalFullSixteenPairs.compact_fullSixteen_pair_39_base LocalFullSixteenPairs.compact_fullSixteen_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalFullSixteenPairs.fullSixteen_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (pairSlack (16) ((1 / 0xf4240)) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.FullSixteenRows
private def zz2351:"s092f"="s092f":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixteenCyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
private def zz1298:"s0512"="s0512":=by decide+kernel
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack FullSixteenRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullSixteenRows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse FullSixteenRows.rows p q same x]
    exact FullSixteenRows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (pairSlack 16 (1 / 0xf4240) FullSixteenRows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact FullSixteenRows.pair_nonneg p q h same x hx
  · rw [← pairSlack_swap 16 (1 / 0xf4240) FullSixteenRows.rows p q same x]
    exact FullSixteenRows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible FullSixteenRows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials FullSixteenRows.rows
theorem remaining_rows_count:remainingRows.length = 12:=by decide +kernel
private def zz1299:"s0513"="s0513":=by decide+kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
      weightedAggregate 16 h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack FullSixteenRows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (pairSlack 16 (1 / 0xf4240) FullSixteenRows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [local_slacks_sum,stripPotentials_sound 16 h4 h3 h5 g FullSixteenRows.rows rows_admissible] at hs
  norm_num at hs
  change (1 / 0x3d090:ℝ) * mass g ^ 2 ≤
    weightedAggregate 16 h4 h3 g (stripPotentials FullSixteenRows.rows) + 4 * deficit g
  linarith
end Green24Proof.FullSixteenCyclic
private def zz2352:"s0930"="s0930":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixteenMass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open PhaseMassRows ConditionalMassRows
theorem remainingRows_eq:FullSixteenCyclic.remainingRows = [
  ((0x69d580d / 0x3b9aca00), .base (.balance 0 (1))),
  ((0x49a0c67 / 0x3b9aca00), .base (.balance 2 (-1))),
  ((0xed223b7 / 0xee6b280), .base (.heightChild 1)),
  ((0x2f2f5d9 / 0x1dcd6500), .base (.grandchild 0)),
  ((0x248c1 / 0xee6b280), .base (.grandchild 1)),
  ((0x148ec9 / 0xee6b280), .massCorrection 1 1 ⟨(1 / 9),(-0x22adce5 / 0x2aea540),(0x1ea98dd / 0xe4e1c0),(-0x1aa685d / 0x1312d00)⟩),
  ((0x18ced3 / 0x4c4b40), .massCoercivity (3 / 0x3e8)),
  ((0x50d1dc4f / 0x3b9aca00), .massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,(3 / 4),2,(3 / 4)]:Fin 4 → ℚ) p)),
  ((0x9b09 / 0x5f5e100), .massProduct (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p) (fun p => (![-1,16, -1,16]:Fin 4 → ℚ) p)),
  ((0x3b9b375 / 0x3b9aca00), .massProduct (fun p => (![1, -12,1, -12]:Fin 4 → ℚ) p) (fun p => (![-1,16, -1,16]:Fin 4 → ℚ) p)),
  ((0x1ad4c5c41 / 0x3b9aca00), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((1 / 0x98968), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
theorem weighted_remaining_le {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      16 * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 12 16 i p:ℝ)))
    (hheight:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.grandchild 0) ≤ 0)
    (hg1:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.grandchild 1) ≤ 0)
    (hcorr:rowAggregate 16 h4 h3 g (.massCorrection 1 1 ⟨(1 / 9),(-0x22adce5 / 0x2aea540),(0x1ea98dd / 0xe4e1c0),(-0x1aa685d / 0x1312d00)⟩) ≤ 0)
    (hcoerc:rowAggregate 16 h4 h3 g (.massCoercivity (3 / 0x3e8)) ≤ 0) :
    weightedAggregate 16 h4 h3 g FullSixteenCyclic.remainingRows ≤ (1 / 0x98968:ℝ) * mass g ^ 2:=by
  have hw:0 ≤ ((0x69d580d / 0x3b9aca00):ℝ) * phaseTotal h4 g 0 - ((0x49a0c67 / 0x3b9aca00):ℝ) * phaseTotal h4 g 2:=by
    have hb:=phaseTotal_nonneg h4 g hg 2
    linarith
  have hbal:=mul_nonpos_of_nonneg_of_nonpos hw (sub_nonpos.mpr hhigh)
  have hp7:rowAggregate 16 h4 h3 g (.massProduct (fun p => (![1,0, -1,0]:Fin 4 → ℚ) p) (fun p => (![-1,(3 / 4),2,(3 / 4)]:Fin 4 → ℚ) p)) ≤ 0 :=
    domainProduct_nonpos 16 12 16 h4 h3 g hforms 4 13
  have hp8:rowAggregate 16 h4 h3 g (.massProduct (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p) (fun p => (![-1,16, -1,16]:Fin 4 → ℚ) p)) ≤ 0 :=
    domainProduct_nonpos 16 12 16 h4 h3 g hforms 5 8
  have hp9:rowAggregate 16 h4 h3 g (.massProduct (fun p => (![1, -12,1, -12]:Fin 4 → ℚ) p) (fun p => (![-1,16, -1,16]:Fin 4 → ℚ) p)) ≤ 0 :=
    domainProduct_nonpos 16 12 16 h4 h3 g hforms 7 8
  have hs10:=rowAggregate_massSquare_nonpos 16 h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_balance,rowAggregate_normalization]
  norm_num
  linarith
theorem deficit_nonneg_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hhigh:phaseTotal h4 g 0 + phaseTotal h4 g 2 ≤
      16 * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
    (hforms:∀ i:Fin 14,0 ≤ massWeighted h4 g (fun p => (domainForm 12 16 i p:ℝ)))
    (hheight:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.heightChild 1) ≤ 0)
    (hg0:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.grandchild 0) ≤ 0)
    (hg1:FullPhaseAggregation.rowAggregate 16 h4 h3 g (.grandchild 1) ≤ 0)
    (hcorr:rowAggregate 16 h4 h3 g (.massCorrection 1 1 ⟨(1 / 9),(-0x22adce5 / 0x2aea540),(0x1ea98dd / 0xe4e1c0),(-0x1aa685d / 0x1312d00)⟩) ≤ 0)
    (hcoerc:rowAggregate 16 h4 h3 g (.massCoercivity (3 / 0x3e8)) ≤ 0) (h5:¬5 ∣ q):0 ≤ deficit g:=by
  have hc:=FullSixteenCyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg heven hhigh hforms hheight hg0 hg1 hcorr hcoerc
  nlinarith [sq_nonneg (mass g)]
end Green24Proof.FullSixteenMass
private def zz2353:"s0931"="s0931":=by decide+kernel
end 
section 
namespace Green24Proof.NestedChildRows
open QuadraticCertificates ExpressionCertificates FullPhaseRows FullPhaseSemantics
open FullPhaseAggregation ChildRows HeightChildRows ProfileChildren PhaseMassRows
noncomputable def selectedEven {m:ℕ} (h2:2 ∣ m) (v:ZMod m → ℝ)
    (j k:ZMod m):ℝ :=
  if ZMod.castHom h2 (ZMod 2) j = 0 ∧ ZMod.castHom h2 (ZMod 2) k = 0
  then expressionEval area (quadPoint v j k) + expressionEval (pairProduct (-8)) (pairPoint v j k)
  else 0
private def zz1300:"s0514"="s0514":=by decide+kernel
theorem grandchild_off {q:ℕ} (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) (r:Phase) (j k:ZMod q)
    (h:¬(ZMod.castHom h4 (ZMod 4) j = r ∧ ZMod.castHom h4 (ZMod 4) k = r)) :
    rowValue S h4 h3 g (.grandchild r) j k = 0:=by
  simp only [rowValue,rowQuad,rowPair,if_neg h,
    ExtendedFullPhaseRows.expressionEval_nil,add_zero]
theorem grandchild_one_sum {m:ℕ} [NeZero m] (S:ℚ)
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h2:2 ∣ m) (u v:ZMod m → ℝ) :
    rowAggregate S h4 h3 (interleave u v) (.grandchild 1) =
      ∑ j, ∑ k,selectedEven h2 v j k:=by
  have he (i:ZMod m):ZMod.castHom h4 (ZMod 4) (parityEquiv m (0,i)) ≠ 1:=by
    rw [cast_four_even h4 h2]
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; decide
    · rw [h,doubleResidue_two_one]; decide
  have ho (i:ZMod m):ZMod.castHom h4 (ZMod 4) (parityEquiv m (1,i)) = 1 ↔
      ZMod.castHom h2 (ZMod 2) i = 0:=by
    rw [cast_four_odd h4 h2]
    rcases zmod_two_eq_zero_or_one (ZMod.castHom h2 (ZMod 2) i) with h | h
    · rw [h,map_zero]; decide
    · rw [h,doubleResidue_two_one]; decide
  have hodd (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.grandchild 1)
      (parityEquiv m (1,j)) (parityEquiv m (1,k)) = selectedEven h2 v j k:=by
    simp only [rowValue,rowQuad,rowPair,ho,selectedEven]
    split_ifs
    · rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
      simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,
        parityEquiv_affine,interleave_odd]
    · simp only [ExtendedFullPhaseRows.expressionEval_nil,add_zero]
  have h00 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.grandchild 1)
      (parityEquiv m (0,j)) (parityEquiv m (0,k)) = 0 :=
    grandchild_off S h4 h3 _ 1 _ _ (fun h => he j h.1)
  have h01 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.grandchild 1)
      (parityEquiv m (0,j)) (parityEquiv m (1,k)) = 0 :=
    grandchild_off S h4 h3 _ 1 _ _ (fun h => he j h.1)
  have h10 (j k:ZMod m):rowValue S h4 h3 (interleave u v) (.grandchild 1)
      (parityEquiv m (1,j)) (parityEquiv m (0,k)) = 0 :=
    grandchild_off S h4 h3 _ 1 _ _ (fun h => he k h.2)
  unfold rowAggregate
  rw [sum_parity_pairs]
  simp only [h00,h01,h10,hodd,Finset.sum_const_zero,zero_add]
theorem selectedEven_sum {n:ℕ} [NeZero n] (w z:ZMod n → ℝ) :
    (∑ j, ∑ k,selectedEven (dvd_mul_right 2 n) (interleave w z) j k) = -4 * deficit w:=by
  rw [sum_parity_pairs]
  simp only [selectedEven,parityCast_apply]
  norm_num
  have hp (j k:ZMod n) :
      expressionEval area (quadPoint (interleave w z) (parityEquiv n (0,j)) (parityEquiv n (0,k))) +
        expressionEval (pairProduct (-8)) (pairPoint (interleave w z) (parityEquiv n (0,j)) (parityEquiv n (0,k))) =
      expressionEval area (quadPoint w j k) + expressionEval (pairProduct (-8)) (pairPoint w j k):=by
    rw [area_eval,area_eval,pairProduct_eval,pairProduct_eval]
    simp [quadPoint,pairPoint,Matrix.cons_val_two,Matrix.cons_val_three,
      parityEquiv_affine,interleave_even]
  simp_rw [hp]
  simp only [Finset.sum_add_distrib,area_sum,pairProduct_sum]
  unfold deficit
  norm_num
  ring
theorem grandchild_one_child {n:ℕ} [NeZero n] (S:ℚ)
    (h4:4 ∣ 2 * (2 * n)) (h3:3 ∣ 2 * (2 * n)) (u v:ZMod (2 * n) → ℝ) :
    rowAggregate S h4 h3 (interleave u v) (.grandchild 1) = -4 * deficit (child v 0):=by
  rw [grandchild_one_sum S h4 h3 (dvd_mul_right 2 n)]
  have h:=selectedEven_sum (child v 0) (child v 1)
  simpa only [interleave_children] using h
def twoThirdsCorrection:ExtendedFullPhaseRows.Correction where
  retained:=1 / 9
  even:=(2 / 3) * (-0x22ad5dd / 0x1c9c380) - 1 / 0x61a8
  mixed:=(2 / 3) * (0x1aa653d / 0x1312d00) + 0x22ad5dd / 0x1c9c380 - 2 / 0x61a8
  odd:=-0x1aa653d / 0x1312d00 - 1 / 0x61a8
private def zz1301:"s0515"="s0515":=by decide+kernel
theorem odd_correction_nonpos {m:ℕ} [NeZero m] (S:ℚ)
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hv:∀ i,0 ≤ v i) :
    ExtendedFullPhaseAggregation.rowAggregate S h4 h3 (interleave u v)
      (.massCorrection 1 1 twoThirdsCorrection) ≤ 0:=by
  rcases h2 with ⟨n,rfl⟩
  have hn:0 < n:=by have hp:=NeZero.pos (2 * n); omega
  let:NeZero n:=⟨by omega⟩
  have h3v:3 ∣ 2 * n:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5v:¬5 ∣ 2 * n:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hc:=ParityTwoThirds.correction h3v h5v (child v 0) (child v 1)
    (child_nonneg v hv 0) (child_nonneg v hv 1)
  rw [interleave_children] at hc
  rw [ExtendedMassRows.rowAggregate_massCorrection_odd,rowAggregate_child_odd,
    grandchild_one_child,phaseTotal_interleave_one h4 (dvd_mul_right 2 n),
    phaseTotal_interleave_three h4 (dvd_mul_right 2 n), ← child_mass, ← child_mass]
  norm_num [twoThirdsCorrection]
  unfold ParityTwoThirds.massCorrection at hc
  nlinarith only [hc]
end Green24Proof.NestedChildRows
private def zz2354:"s0932"="s0932":=by decide+kernel
end 
section 
namespace Green24Proof.ChildCoercivityRows
open PhaseMassRows ProfileChildren HeightChildRows
theorem even_nonpos_of_negative_parent {m:ℕ} [NeZero m] (S:ℚ)
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hneg:deficit (interleave u v) < 0)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hlow:12 * mass v ≤ mass u) :
    ExtendedFullPhaseAggregation.rowAggregate S h4 h3 (interleave u v)
      (.massCoercivity (3 / 0x3e8)) ≤ 0:=by
  rcases h2 with ⟨n,rfl⟩
  have hn:0 < n:=by have hp:=NeZero.pos (2 * n); omega
  let:NeZero n:=⟨by omega⟩
  have hm:2 * n < 2 * (2 * n):=by omega
  have hdu:=ih (2 * n) hm (dvd_mul_left (2 * n) 2) u hu
  have hdv:=ih (2 * n) hm (dvd_mul_left (2 * n) 2) v hv
  have hV:=ConditionalProfileRows.odd_mass_pos_of_negative_parent
    (dvd_mul_right 2 n) u v hu hv hdu hdv hneg
  have hcap:=negative_parent_profile_child_cap (dvd_mul_right 2 n) u v hu hv hdu hdv hneg hV hlow
  have h3u:3 ∣ 2 * n:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5u:¬5 ∣ 2 * n:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hsmall:=ih n (by omega) (dvd_mul_of_dvd_right (dvd_mul_left n 2) 2)
    (child u 0) (child_nonneg u hu 0)
  rw [phaseTotal_interleave_zero h4 (dvd_mul_right 2 n),
    phaseTotal_interleave_two h4 (dvd_mul_right 2 n)] at heven
  rw [← child_mass, ← child_mass] at heven hcap
  have hc:=NearBalanceVerified.coercivity_to_eleven_fifths h3u h5u
    (child u 0) (child u 1) (child_nonneg u hu 0) (child_nonneg u hu 1)
    hsmall heven (le_of_lt hcap)
  rw [interleave_children] at hc
  rw [ExtendedMassRows.rowAggregate_massCoercivity,ChildRows.rowAggregate_child_even,
    phaseTotal_interleave_zero h4 (dvd_mul_right 2 n),
    phaseTotal_interleave_two h4 (dvd_mul_right 2 n), ← child_mass, ← child_mass]
  norm_num
  nlinarith [sq_nonneg (mass (child u 0) - mass (child u 1))]
end Green24Proof.ChildCoercivityRows
private def zz2355:"s0933"="s0933":=by decide+kernel
end 
section 
namespace Green24Proof.FullSixteenProfileInterval
open FullPhaseRows (Phase)
open PhaseMassRows ChildRows HeightChildRows
theorem interval_nonneg_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hodd:phaseTotal h4 (interleave u v) 3 ≤ phaseTotal h4 (interleave u v) 1)
    (hlow:(12:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (16:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  by_contra! hneg
  have hm:m < 2 * m:=by have hp:=NeZero.pos m; omega
  have hdu:=ih m hm (dvd_mul_left m 2) u hu
  have hdv:=ih m hm (dvd_mul_left m 2) v hv
  have hg:=interleave_nonneg u v hu hv
  have hforms:=ConditionalProfileRows.domainForms_nonneg 12 16 h4 h2 u v hu hv hdu hdv hneg
    (by norm_num) heven hodd hlow hhigh
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hheight:=rowAggregate_height_odd_nonpos 16 h4 h3 h2 u v hu hv
    (HeightStrong.strong_height_bound h2 h3m h5m v hv)
  have hg0:=Full27ProfileInterval.grandchild_nonpos_of_induction 16 h4 h3 (interleave u v) hg 0 ih
  have hg1:=Full27ProfileInterval.grandchild_nonpos_of_induction 16 h4 h3 (interleave u v) hg 1 ih
  have hcoerc:=ChildCoercivityRows.even_nonpos_of_negative_parent 16 h4 h3 h5 h2 u v hu hv ih hneg heven hlow
  have hcorr:ExtendedFullPhaseAggregation.rowAggregate 16 h4 h3 (interleave u v)
      (.massCorrection 1 1 ⟨(1 / 9),(-0x22adce5 / 0x2aea540),(0x1ea98dd / 0xe4e1c0),(-0x1aa685d / 0x1312d00)⟩) ≤ 0:=by
    have h:=NestedChildRows.odd_correction_nonpos 16 h4 h3 h5 h2 u v hv
    norm_num [NestedChildRows.twoThirdsCorrection] at h ⊢
    exact h
  have hhigh':phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 ≤
      (16:ℝ) * (phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3):=by
    rw [ProfileChildren.phaseTotal_interleave_zero h4 h2,
      ProfileChildren.phaseTotal_interleave_two h4 h2,phaseTotal_interleave_one h4 h2,
      phaseTotal_interleave_three h4 h2,classMass_sum,classMass_sum]
    exact hhigh
  have h:=FullSixteenMass.deficit_nonneg_of_rows h4 h3 (interleave u v) hg
    heven hhigh' hforms hheight hg0 hg1 hcorr hcoerc h5
  linarith
theorem interval_nonneg {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (hlow:(12:ℝ) * mass v ≤ mass u) (hhigh:mass u ≤ (16:ℝ) * mass v) :
    0 ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,heven,hodd⟩ :=
    ProfileDoubleOrientation.orient_both_children h4 u v hu hv
  have h:=interval_nonneg_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven hodd
    (by simpa only [hU,hV] using hlow) (by simpa only [hU,hV] using hhigh)
  simpa only [hd] using h
end Green24Proof.FullSixteenProfileInterval
private def zz2356:"s0934"="s0934":=by decide+kernel
end 
section 
namespace Green24Proof.RatioCoverSixteen
open BoundaryFromHeightCertificates ConditionalProfileEndpoint
private def zz1302:"s0516"="s0516":=by decide+kernel
theorem ratio_to_sixteen:RatioToSixteen:=by
  apply RatioCoverTwelve.ratio_to_sixteen_of_remaining
  intro m _
  exact FullSixteenProfileInterval.interval_nonneg
theorem deficit_nonneg_of_remaining
    (hcertificate12:∀ (m:ℕ) [NeZero m],HeightCertificate m Q12)
    (hcertificate18:∀ (m:ℕ) [NeZero m],HeightCertificate m Q18) :
    ∀ (q:ℕ) [NeZero q], ¬5 ∣ q →
      ∀ (g:ZMod q → ℝ),(∀ i,0 ≤ g i) → 0 ≤ deficit g :=
  deficit_nonneg_of_certificates ratio_to_sixteen hcertificate12 hcertificate18
end Green24Proof.RatioCoverSixteen
private def zz2357:"s0935"="s0935":=by decide+kernel
end 
section 
namespace Green24Proof.HeightFullPhaseRows
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
open FullPhaseRows (Phase scale rhoExpression expressionEval_append expressionEval_scale)
open FullPhaseSemantics (quadPoint pairPoint sameColour)
open ExtendedFullPhaseAggregation
def pairSlack (S margin lam:ℚ) (rows:List (ℚ × Label))
    (p q:Phase) (same:Bool):Expression :=
  ExtendedFullPhaseRows.pairSlack S margin rows p q same ++ scale (-2 * lam) rhoExpression
theorem pairSlack_swap (S margin lam:ℚ) (rows:List (ℚ × Label))
    (p q:Phase) (same:Bool) (x:Point) :
    expressionEval (pairSlack S margin lam rows q p same) (FullPhaseSymmetry.swapPair x) =
      expressionEval (pairSlack S margin lam rows p q same) x:=by
  simp only [pairSlack,expressionEval_append,expressionEval_scale,
    ExtendedFullPhaseRows.pairSlack_swap,FullPhaseSymmetry.rhoExpression_swap]
theorem local_slacks_sum {q:ℕ} [NeZero q] (S margin lam:ℚ)
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (rows:List (ℚ × Label)) :
    (∑ j:ZMod q, ∑ k:ZMod q,
      (expressionEval (quadSlack rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
       expressionEval (pairSlack S margin lam rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (pairPoint g j k))) =
      weightedAggregate S h4 h3 g rows + 4 * deficit g - 4 * (margin:ℝ) * mass g ^ 2 -
        4 * (lam:ℝ) * energy g:=by
  simp only [pairSlack,expressionEval_append,expressionEval_scale, ← add_assoc]
  simp only [Finset.sum_add_distrib, ← Finset.mul_sum]
  have hs:=ExtendedFullPhaseAggregation.local_slacks_sum S margin h4 h3 g rows
  simp only [Finset.sum_add_distrib] at hs
  rw [hs,ParityPhaseAggregation.rho_sum g hg]
  push_cast
  ring
end Green24Proof.HeightFullPhaseRows
private def zz2358:"s0936"="s0936":=by decide+kernel
end 
section 
namespace Green24Proof.LocalPairs
def compact_height12_pair_20_base:CompactPair.Quadratic:=⟨(0xb2d05e00d / 0x59682f000),(0x39b28201 / 0x17d78400),2⟩
def compact_height12_pair_20_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(-1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x59682f000),3, -2⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_20_base compact_height12_pair_20_hinges x y
def compact_height12_pair_20_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2]
private def zz1303:"s0517"="s0517":=by decide+kernel
theorem compact_height12_pair_20_check :
    CompactPair.expressionCheckPSD compact_height12_pair_20_base compact_height12_pair_20_hinges 0 compact_height12_pair_20_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_20_representation (x y:ℝ) :
    height12_pair_20 x y = CompactPair.expressionEval compact_height12_pair_20_base compact_height12_pair_20_hinges x y:=by rfl
theorem height12_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_20 x y:=by
  rw [compact_height12_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_20_check hy (by simpa using hx)
def compact_height12_pair_21_base:CompactPair.Quadratic:=⟨(0x3b9aca017 / 0x1dcd65000),(0x47c39501 / 0x1dcd6500),2⟩
def compact_height12_pair_21_hinges:List CompactPair.Hinge:=[⟨(11 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0xee6b2800),2, -3⟩,⟨(-11 / 0x1dcd65000),2, -1⟩,⟨(1 / 0xee6b2800),3, -2⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_21_base compact_height12_pair_21_hinges x y
def compact_height12_pair_21_cuts:List ℚ:=[(1 / 2),(2 / 3),(3 / 2),2]
theorem compact_height12_pair_21_check :
    CompactPair.expressionCheckPSD compact_height12_pair_21_base compact_height12_pair_21_hinges 0 compact_height12_pair_21_cuts = true :=
  by decide +kernel
private def zz1304:"s0518"="s0518":=by decide+kernel
theorem compact_height12_pair_21_representation (x y:ℝ) :
    height12_pair_21 x y = CompactPair.expressionEval compact_height12_pair_21_base compact_height12_pair_21_hinges x y:=by rfl
theorem height12_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_21 x y:=by
  rw [compact_height12_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_21_check hy (by simpa using hx)
def compact_height12_pair_22_base:CompactPair.Quadratic:=⟨2,(0xb4e66cbf / 0x4a817c80),2⟩
def compact_height12_pair_22_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_22_base compact_height12_pair_22_hinges x y
def compact_height12_pair_22_cuts:List ℚ:=[]
theorem compact_height12_pair_22_check :
    CompactPair.expressionCheckPSD compact_height12_pair_22_base compact_height12_pair_22_hinges 0 compact_height12_pair_22_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_22_representation (x y:ℝ) :
    height12_pair_22 x y = CompactPair.expressionEval compact_height12_pair_22_base compact_height12_pair_22_hinges x y:=by rfl
private def zz1305:"s0519"="s0519":=by decide+kernel
theorem height12_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_22 x y:=by
  rw [compact_height12_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_22_check hy (by simpa using hx)
def compact_height12_pair_23_base:CompactPair.Quadratic:=⟨(0x59682f01 / 0x2cb41780),(0x5a00c57f3 / 0x2540be400),2⟩
def compact_height12_pair_23_hinges:List CompactPair.Hinge:=[⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x2cb417800),2, -3⟩,⟨(-1 / 0x2cb417800),3, -2⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_23_base compact_height12_pair_23_hinges x y
def compact_height12_pair_23_cuts:List ℚ:=[(2 / 3),1,(3 / 2)]
theorem compact_height12_pair_23_check :
    CompactPair.expressionCheckPSD compact_height12_pair_23_base compact_height12_pair_23_hinges 0 compact_height12_pair_23_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_23_representation (x y:ℝ) :
    height12_pair_23 x y = CompactPair.expressionEval compact_height12_pair_23_base compact_height12_pair_23_hinges x y:=by rfl
theorem height12_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_23 x y:=by
  rw [compact_height12_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_23_check hy (by simpa using hx)
def compact_height12_pair_24_base:CompactPair.Quadratic:=⟨(0x8f0d1801 / 0x47868c00),(0x39b28201 / 0x17d78400),2⟩
def compact_height12_pair_24_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(1 / 0x77359400),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(-1 / 0x165a0bc00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_24_base compact_height12_pair_24_hinges x y
def compact_height12_pair_24_cuts:List ℚ:=[(1 / 3),1,(3 / 2),3]
private def zz1306:"s051a"="s051a":=by decide+kernel
theorem compact_height12_pair_24_check :
    CompactPair.expressionCheckPSD compact_height12_pair_24_base compact_height12_pair_24_hinges 0 compact_height12_pair_24_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_24_representation (x y:ℝ) :
    height12_pair_24 x y = CompactPair.expressionEval compact_height12_pair_24_base compact_height12_pair_24_hinges x y:=by rfl
theorem height12_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_24 x y:=by
  rw [compact_height12_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_24_check hy (by simpa using hx)
def compact_height12_pair_25_base:CompactPair.Quadratic:=⟨(0x3b9ac9ff3 / 0x1dcd65000),(0x1cb4a201 / 0xbebc200),2⟩
def compact_height12_pair_25_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(1 / 0xee6b2800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_25_base compact_height12_pair_25_hinges x y
def compact_height12_pair_25_cuts:List ℚ:=[(1 / 3),(1 / 2),1,(3 / 2),2,3]
theorem compact_height12_pair_25_check :
    CompactPair.expressionCheckPSD compact_height12_pair_25_base compact_height12_pair_25_hinges 0 compact_height12_pair_25_cuts = true :=
  by decide +kernel
private def zz1307:"s051b"="s051b":=by decide+kernel
theorem compact_height12_pair_25_representation (x y:ℝ) :
    height12_pair_25 x y = CompactPair.expressionEval compact_height12_pair_25_base compact_height12_pair_25_hinges x y:=by rfl
theorem height12_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_25 x y:=by
  rw [compact_height12_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_25_check hy (by simpa using hx)
def compact_height12_pair_26_base:CompactPair.Quadratic:=⟨2,(0x5a73365fd / 0x2540be400),2⟩
def compact_height12_pair_26_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_26_base compact_height12_pair_26_hinges x y
def compact_height12_pair_26_cuts:List ℚ:=[]
theorem compact_height12_pair_26_check :
    CompactPair.expressionCheckPSD compact_height12_pair_26_base compact_height12_pair_26_hinges 0 compact_height12_pair_26_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_26_representation (x y:ℝ) :
    height12_pair_26 x y = CompactPair.expressionEval compact_height12_pair_26_base compact_height12_pair_26_hinges x y:=by rfl
private def zz1308:"s051c"="s051c":=by decide+kernel
theorem height12_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_26 x y:=by
  rw [compact_height12_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_26_check hy (by simpa using hx)
def compact_height12_pair_27_base:CompactPair.Quadratic:=⟨(0xb2d05e00b / 0x59682f000),(0x5a00c5807 / 0x2540be400),2⟩
def compact_height12_pair_27_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_27_base compact_height12_pair_27_hinges x y
def compact_height12_pair_27_cuts:List ℚ:=[1,(3 / 2),2,3]
theorem compact_height12_pair_27_check :
    CompactPair.expressionCheckPSD compact_height12_pair_27_base compact_height12_pair_27_hinges 0 compact_height12_pair_27_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_27_representation (x y:ℝ) :
    height12_pair_27 x y = CompactPair.expressionEval compact_height12_pair_27_base compact_height12_pair_27_hinges x y:=by rfl
theorem height12_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_27 x y:=by
  rw [compact_height12_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_27_check hy (by simpa using hx)
def compact_height12_pair_28_base:CompactPair.Quadratic:=⟨(0x7270dfff / 0x39387000),(0x2d137590b / 0x12a05f200),2⟩
def compact_height12_pair_28_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(1 / 0x1dcd65000),2, -1⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_28_base compact_height12_pair_28_hinges x y
def compact_height12_pair_28_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
private def zz1309:"s051d"="s051d":=by decide+kernel
theorem compact_height12_pair_28_check :
    CompactPair.expressionCheckPSD compact_height12_pair_28_base compact_height12_pair_28_hinges 0 compact_height12_pair_28_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_28_representation (x y:ℝ) :
    height12_pair_28 x y = CompactPair.expressionEval compact_height12_pair_28_base compact_height12_pair_28_hinges x y:=by rfl
theorem height12_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_28 x y:=by
  rw [compact_height12_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_28_check hy (by simpa using hx)
def compact_height12_pair_29_base:CompactPair.Quadratic:=⟨(0x3b9aca003 / 0x1dcd65000),(0x2cda3d20b / 0x12a05f200),2⟩
def compact_height12_pair_29_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x5f5e1000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x165a0bc00),2, -3⟩,⟨(-1 / 0x5f5e1000),2, -1⟩,⟨(1 / 0x165a0bc00),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_29_base compact_height12_pair_29_hinges x y
def compact_height12_pair_29_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height12_pair_29_check :
    CompactPair.expressionCheckPSD compact_height12_pair_29_base compact_height12_pair_29_hinges 0 compact_height12_pair_29_cuts = true :=
  by decide +kernel
private def zz1310:"s051e"="s051e":=by decide+kernel
theorem compact_height12_pair_29_representation (x y:ℝ) :
    height12_pair_29 x y = CompactPair.expressionEval compact_height12_pair_29_base compact_height12_pair_29_hinges x y:=by rfl
theorem height12_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_29 x y:=by
  rw [compact_height12_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_29_check hy (by simpa using hx)
def compact_height12_pair_30_base:CompactPair.Quadratic:=⟨2,(0x2d399b2ff / 0x12a05f200),2⟩
def compact_height12_pair_30_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_30_base compact_height12_pair_30_hinges x y
def compact_height12_pair_30_cuts:List ℚ:=[]
theorem compact_height12_pair_30_check :
    CompactPair.expressionCheckPSD compact_height12_pair_30_base compact_height12_pair_30_hinges 0 compact_height12_pair_30_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_30_representation (x y:ℝ) :
    height12_pair_30 x y = CompactPair.expressionEval compact_height12_pair_30_base compact_height12_pair_30_hinges x y:=by rfl
private def zz1311:"s051f"="s051f":=by decide+kernel
theorem height12_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_30 x y:=by
  rw [compact_height12_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_30_check hy (by simpa using hx)
def compact_height12_pair_31_base:CompactPair.Quadratic:=⟨(0x3b9aca003 / 0x1dcd65000),(0x5a00c57f9 / 0x2540be400),2⟩
def compact_height12_pair_31_hinges:List CompactPair.Hinge:=[⟨(1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0xee6b2800),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_31_base compact_height12_pair_31_hinges x y
def compact_height12_pair_31_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1]
theorem compact_height12_pair_31_check :
    CompactPair.expressionCheckPSD compact_height12_pair_31_base compact_height12_pair_31_hinges 0 compact_height12_pair_31_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_31_representation (x y:ℝ) :
    height12_pair_31 x y = CompactPair.expressionEval compact_height12_pair_31_base compact_height12_pair_31_hinges x y:=by rfl
theorem height12_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_31 x y:=by
  rw [compact_height12_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_31_check hy (by simpa using hx)
def compact_height12_pair_32_base:CompactPair.Quadratic:=⟨(0x2faf07ff / 0x17d78400),(0x903e44ff / 0x3b9aca00),2⟩
def compact_height12_pair_32_hinges:List CompactPair.Hinge:=[⟨(1 / 0x165a0bc00),1, -3⟩,⟨(-1 / 0x77359400),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x165a0bc00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_32_base compact_height12_pair_32_hinges x y
def compact_height12_pair_32_cuts:List ℚ:=[(1 / 3),(1 / 2),(3 / 2),2,3]
private def zz1312:"s0520"="s0520":=by decide+kernel
theorem compact_height12_pair_32_check :
    CompactPair.expressionCheckPSD compact_height12_pair_32_base compact_height12_pair_32_hinges 0 compact_height12_pair_32_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_32_representation (x y:ℝ) :
    height12_pair_32 x y = CompactPair.expressionEval compact_height12_pair_32_base compact_height12_pair_32_hinges x y:=by rfl
theorem height12_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_32 x y:=by
  rw [compact_height12_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_32_check hy (by simpa using hx)
def compact_height12_pair_33_base:CompactPair.Quadratic:=⟨(0x2cb4177f9 / 0x165a0bc00),(0x8f8729ff / 0x3b9aca00),2⟩
def compact_height12_pair_33_hinges:List CompactPair.Hinge:=[⟨(1 / 0x77359400),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x2cb417800),2, -3⟩,⟨(1 / 0xee6b2800),2, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_33_base compact_height12_pair_33_hinges x y
def compact_height12_pair_33_cuts:List ℚ:=[(1 / 2),1,(3 / 2)]
theorem compact_height12_pair_33_check :
    CompactPair.expressionCheckPSD compact_height12_pair_33_base compact_height12_pair_33_hinges 0 compact_height12_pair_33_cuts = true :=
  by decide +kernel
private def zz1313:"s0521"="s0521":=by decide+kernel
theorem compact_height12_pair_33_representation (x y:ℝ) :
    height12_pair_33 x y = CompactPair.expressionEval compact_height12_pair_33_base compact_height12_pair_33_hinges x y:=by rfl
theorem height12_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_33 x y:=by
  rw [compact_height12_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_33_check hy (by simpa using hx)
def compact_height12_pair_34_base:CompactPair.Quadratic:=⟨(0x8f0d17ff / 0x47868c00),(0x39b28201 / 0x17d78400),2⟩
def compact_height12_pair_34_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(1 / 0x59682f000),2, -3⟩,⟨(1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_34_base compact_height12_pair_34_hinges x y
def compact_height12_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height12_pair_34_check :
    CompactPair.expressionCheckPSD compact_height12_pair_34_base compact_height12_pair_34_hinges 0 compact_height12_pair_34_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_34_representation (x y:ℝ) :
    height12_pair_34 x y = CompactPair.expressionEval compact_height12_pair_34_base compact_height12_pair_34_hinges x y:=by rfl
private def zz1314:"s0522"="s0522":=by decide+kernel
theorem height12_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_34 x y:=by
  rw [compact_height12_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_34_check hy (by simpa using hx)
def compact_height12_pair_35_base:CompactPair.Quadratic:=⟨(0xb2d05dfef / 0x59682f000),(0x8f872a03 / 0x3b9aca00),2⟩
def compact_height12_pair_35_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x2cb417800),2, -3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(1 / 0x2cb417800),3, -2⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_35_base compact_height12_pair_35_hinges x y
def compact_height12_pair_35_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height12_pair_35_check :
    CompactPair.expressionCheckPSD compact_height12_pair_35_base compact_height12_pair_35_hinges 0 compact_height12_pair_35_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_35_representation (x y:ℝ) :
    height12_pair_35 x y = CompactPair.expressionEval compact_height12_pair_35_base compact_height12_pair_35_hinges x y:=by rfl
theorem height12_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_35 x y:=by
  rw [compact_height12_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_35_check hy (by simpa using hx)
def compact_height12_pair_36_base:CompactPair.Quadratic:=⟨2,(0x5a73365f9 / 0x2540be400),2⟩
def compact_height12_pair_36_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_36_base compact_height12_pair_36_hinges x y
def compact_height12_pair_36_cuts:List ℚ:=[]
private def zz1315:"s0523"="s0523":=by decide+kernel
theorem compact_height12_pair_36_check :
    CompactPair.expressionCheckPSD compact_height12_pair_36_base compact_height12_pair_36_hinges 0 compact_height12_pair_36_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_36_representation (x y:ℝ) :
    height12_pair_36 x y = CompactPair.expressionEval compact_height12_pair_36_base compact_height12_pair_36_hinges x y:=by rfl
theorem height12_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_36 x y:=by
  rw [compact_height12_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_36_check hy (by simpa using hx)
def compact_height12_pair_37_base:CompactPair.Quadratic:=⟨(0xbebc2001 / 0x5f5e1000),(0x5a00c57f9 / 0x2540be400),2⟩
def compact_height12_pair_37_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x59682f000),2, -3⟩,⟨(-1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x59682f000),3, -2⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_37_base compact_height12_pair_37_hinges x y
def compact_height12_pair_37_cuts:List ℚ:=[(1 / 2),(2 / 3),1,(3 / 2),3]
theorem compact_height12_pair_37_check :
    CompactPair.expressionCheckPSD compact_height12_pair_37_base compact_height12_pair_37_hinges 0 compact_height12_pair_37_cuts = true :=
  by decide +kernel
private def zz1316:"s0524"="s0524":=by decide+kernel
theorem compact_height12_pair_37_representation (x y:ℝ) :
    height12_pair_37 x y = CompactPair.expressionEval compact_height12_pair_37_base compact_height12_pair_37_hinges x y:=by rfl
theorem height12_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_37 x y:=by
  rw [compact_height12_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_37_check hy (by simpa using hx)
def compact_height12_pair_38_base:CompactPair.Quadratic:=⟨(0xb2d05dff9 / 0x59682f000),(0x1689bac87 / 0x9502f900),2⟩
def compact_height12_pair_38_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x2cb417800),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_38_base compact_height12_pair_38_hinges x y
def compact_height12_pair_38_cuts:List ℚ:=[(1 / 3),(1 / 2),2,3]
theorem compact_height12_pair_38_check :
    CompactPair.expressionCheckPSD compact_height12_pair_38_base compact_height12_pair_38_hinges 0 compact_height12_pair_38_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_38_representation (x y:ℝ) :
    height12_pair_38 x y = CompactPair.expressionEval compact_height12_pair_38_base compact_height12_pair_38_hinges x y:=by rfl
private def zz1317:"s0525"="s0525":=by decide+kernel
theorem height12_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_38 x y:=by
  rw [compact_height12_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_38_check hy (by simpa using hx)
def compact_height12_pair_39_base:CompactPair.Quadratic:=⟨(0xee6b2803 / 0x77359400),(0x2cda3d1ff / 0x12a05f200),2⟩
def compact_height12_pair_39_hinges:List CompactPair.Hinge:=[⟨(1 / 0x47868c00),1, -3⟩,⟨(-21 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(13 / 0x59682f000),2, -3⟩,⟨(21 / 0x1dcd65000),2, -1⟩,⟨(-13 / 0x59682f000),3, -2⟩,⟨(-1 / 0x47868c00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height12_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height12_pair_39_base compact_height12_pair_39_hinges x y
def compact_height12_pair_39_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height12_pair_39_check :
    CompactPair.expressionCheckPSD compact_height12_pair_39_base compact_height12_pair_39_hinges 0 compact_height12_pair_39_cuts = true :=
  by decide +kernel
theorem compact_height12_pair_39_representation (x y:ℝ) :
    height12_pair_39 x y = CompactPair.expressionEval compact_height12_pair_39_base compact_height12_pair_39_hinges x y:=by rfl
theorem height12_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height12_pair_39 x y:=by
  rw [compact_height12_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height12_pair_39_check hy (by simpa using hx)
def compact_height18_pair_20_base:CompactPair.Quadratic:=⟨(0xb2d05dff5 / 0x59682f000),(0x903e44fd / 0x3b9aca00),2⟩
def compact_height18_pair_20_hinges:List CompactPair.Hinge:=[⟨(-0x1cab4109 / 0xee6b2800),1, -3⟩,⟨(0x554d56f3 / 0xee6b2800),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-0x1fdd957d / 0x59682f000),2, -3⟩,⟨(-0x554d56f3 / 0xee6b2800),2, -1⟩,⟨(0x1fdd957d / 0x59682f000),3, -2⟩,⟨(0x1cab4109 / 0xee6b2800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_20 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_20_base compact_height18_pair_20_hinges x y
def compact_height18_pair_20_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
private def zz1318:"s0526"="s0526":=by decide+kernel
theorem compact_height18_pair_20_check :
    CompactPair.expressionCheckPSD compact_height18_pair_20_base compact_height18_pair_20_hinges 0 compact_height18_pair_20_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_20_representation (x y:ℝ) :
    height18_pair_20 x y = CompactPair.expressionEval compact_height18_pair_20_base compact_height18_pair_20_hinges x y:=by rfl
theorem height18_pair_20_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_20 x y:=by
  rw [compact_height18_pair_20_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_20_check hy (by simpa using hx)
def compact_height18_pair_21_base:CompactPair.Quadratic:=⟨(0x3b9ac9fff / 0x1dcd65000),(0x12d / 0x7d),2⟩
def compact_height18_pair_21_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x165a0bc00),1, -3⟩,⟨(3 / 0xee6b2800),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x11e1a3000),2, -3⟩,⟨(-3 / 0xee6b2800),2, -1⟩,⟨(1 / 0x11e1a3000),3, -2⟩,⟨(1 / 0x165a0bc00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_21 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_21_base compact_height18_pair_21_hinges x y
def compact_height18_pair_21_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height18_pair_21_check :
    CompactPair.expressionCheckPSD compact_height18_pair_21_base compact_height18_pair_21_hinges 0 compact_height18_pair_21_cuts = true :=
  by decide +kernel
private def zz1319:"s0527"="s0527":=by decide+kernel
theorem compact_height18_pair_21_representation (x y:ℝ) :
    height18_pair_21 x y = CompactPair.expressionEval compact_height18_pair_21_base compact_height18_pair_21_hinges x y:=by rfl
theorem height18_pair_21_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_21 x y:=by
  rw [compact_height18_pair_21_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_21_check hy (by simpa using hx)
def compact_height18_pair_22_base:CompactPair.Quadratic:=⟨2,(0x5a7336603 / 0x2540be400),2⟩
def compact_height18_pair_22_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_22 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_22_base compact_height18_pair_22_hinges x y
def compact_height18_pair_22_cuts:List ℚ:=[]
theorem compact_height18_pair_22_check :
    CompactPair.expressionCheckPSD compact_height18_pair_22_base compact_height18_pair_22_hinges 0 compact_height18_pair_22_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_22_representation (x y:ℝ) :
    height18_pair_22 x y = CompactPair.expressionEval compact_height18_pair_22_base compact_height18_pair_22_hinges x y:=by rfl
private def zz1320:"s0528"="s0528":=by decide+kernel
theorem height18_pair_22_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_22 x y:=by
  rw [compact_height18_pair_22_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_22_check hy (by simpa using hx)
def compact_height18_pair_23_base:CompactPair.Quadratic:=⟨(0x2cb417807 / 0x165a0bc00),(0x5a00c57f9 / 0x2540be400),2⟩
def compact_height18_pair_23_hinges:List CompactPair.Hinge:=[⟨(-0x199bd3 / 0x1dcd6500),1, -3⟩,⟨(0x19704b5 / 0x3b9aca00),1, -2⟩,⟨(0x48766e9d / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-0x121d8847 / 0x2cb417800),2, -3⟩,⟨(0x6620a3 / 0x5f5e100),2, -1⟩,⟨(-0xd13d9cf / 0xee6b2800),3, -2⟩,⟨(-1 / 0x59682f00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_23 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_23_base compact_height18_pair_23_hinges x y
def compact_height18_pair_23_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_height18_pair_23_check :
    CompactPair.expressionCheckPSD compact_height18_pair_23_base compact_height18_pair_23_hinges 0 compact_height18_pair_23_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_23_representation (x y:ℝ) :
    height18_pair_23 x y = CompactPair.expressionEval compact_height18_pair_23_base compact_height18_pair_23_hinges x y:=by rfl
theorem height18_pair_23_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_23 x y:=by
  rw [compact_height18_pair_23_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_23_check hy (by simpa using hx)
def compact_height18_pair_24_base:CompactPair.Quadratic:=⟨(0x2cb417801 / 0x165a0bc00),(0x1207c89fd / 0x77359400),2⟩
def compact_height18_pair_24_hinges:List CompactPair.Hinge:=[⟨(-0x334cb1d / 0x11e1a300),1, -3⟩,⟨(0x123bcea9 / 0xee6b280),1, -2⟩,⟨(0x53e892f7 / 0x1dcd6500),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-0x10c29219 / 0x1dcd6500),2, -3⟩,⟨(0x2d40514d / 0x77359400),2, -1⟩,⟨(-0x1fcbd36f / 0x59682f00),3, -2⟩,⟨(0x927703 / 0x47868c00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_24 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_24_base compact_height18_pair_24_hinges x y
def compact_height18_pair_24_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
private def zz1321:"s0529"="s0529":=by decide+kernel
theorem compact_height18_pair_24_check :
    CompactPair.expressionCheckPSD compact_height18_pair_24_base compact_height18_pair_24_hinges 0 compact_height18_pair_24_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_24_representation (x y:ℝ) :
    height18_pair_24 x y = CompactPair.expressionEval compact_height18_pair_24_base compact_height18_pair_24_hinges x y:=by rfl
theorem height18_pair_24_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_24 x y:=by
  rw [compact_height18_pair_24_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_24_check hy (by simpa using hx)
def compact_height18_pair_25_base:CompactPair.Quadratic:=⟨(0xbc8a70af / 0x59682f00),(0x1cb4a1fd / 0xbebc200),2⟩
def compact_height18_pair_25_hinges:List CompactPair.Hinge:=[⟨(-0x95 / 0x2cb417800),1, -3⟩,⟨(0xb1 / 0x5f5e1000),1, -2⟩,⟨(0x3bd / 0x77359400),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-0x7b / 0x77359400),2, -3⟩,⟨(0x33e06807 / 0xee6b2800),2, -1⟩,⟨(-0x33e06f69 / 0x59682f000),3, -2⟩,⟨(-0x2980511 / 0x23c34600),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_25 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_25_base compact_height18_pair_25_hinges x y
def compact_height18_pair_25_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_height18_pair_25_check :
    CompactPair.expressionCheckPSD compact_height18_pair_25_base compact_height18_pair_25_hinges 0 compact_height18_pair_25_cuts = true :=
  by decide +kernel
private def zz1322:"s052a"="s052a":=by decide+kernel
theorem compact_height18_pair_25_representation (x y:ℝ) :
    height18_pair_25 x y = CompactPair.expressionEval compact_height18_pair_25_base compact_height18_pair_25_hinges x y:=by rfl
theorem height18_pair_25_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_25 x y:=by
  rw [compact_height18_pair_25_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_25_check hy (by simpa using hx)
def compact_height18_pair_26_base:CompactPair.Quadratic:=⟨2,(0x5a7336603 / 0x2540be400),2⟩
def compact_height18_pair_26_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_26 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_26_base compact_height18_pair_26_hinges x y
def compact_height18_pair_26_cuts:List ℚ:=[]
theorem compact_height18_pair_26_check :
    CompactPair.expressionCheckPSD compact_height18_pair_26_base compact_height18_pair_26_hinges 0 compact_height18_pair_26_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_26_representation (x y:ℝ) :
    height18_pair_26 x y = CompactPair.expressionEval compact_height18_pair_26_base compact_height18_pair_26_hinges x y:=by rfl
private def zz1323:"s052b"="s052b":=by decide+kernel
theorem height18_pair_26_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_26 x y:=by
  rw [compact_height18_pair_26_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_26_check hy (by simpa using hx)
def compact_height18_pair_27_base:CompactPair.Quadratic:=⟨(0x59682f00d / 0x2cb417800),(0x5a00c5803 / 0x2540be400),2⟩
def compact_height18_pair_27_hinges:List CompactPair.Hinge:=[⟨(-0x1d40a3b / 0x3b9aca00),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x2cb417800),2, -3⟩,⟨(-0x1d40a3ad / 0x1dcd65000),2, -1⟩,⟨(0x2ecdd2b / 0x8f0d1800),3, -2⟩,⟨(0x3a81475 / 0x165a0bc00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_27 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_27_base compact_height18_pair_27_hinges x y
def compact_height18_pair_27_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2)]
theorem compact_height18_pair_27_check :
    CompactPair.expressionCheckPSD compact_height18_pair_27_base compact_height18_pair_27_hinges 0 compact_height18_pair_27_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_27_representation (x y:ℝ) :
    height18_pair_27 x y = CompactPair.expressionEval compact_height18_pair_27_base compact_height18_pair_27_hinges x y:=by rfl
theorem height18_pair_27_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_27 x y:=by
  rw [compact_height18_pair_27_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_27_check hy (by simpa using hx)
def compact_height18_pair_28_base:CompactPair.Quadratic:=⟨(0x996319793 / 0x6fc23ac00),(0x18f8d93d3 / 0x12a05f200),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_28_hinges:List CompactPair.Hinge:=[⟨(0x2f775001 / 0x6fc23ac00),1, -3⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(0x16b8721 / 0x77359400),2, -3⟩,⟨(-0x16b8721 / 0x77359400),3, -2⟩,⟨(-0x2f775001 / 0x6fc23ac00),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_28 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_28_base compact_height18_pair_28_hinges x y
def compact_height18_pair_28_cuts:List ℚ:=[(1 / 3),(2 / 3),(3 / 2),3]
private def zz1324:"s052c"="s052c":=by decide+kernel
theorem compact_height18_pair_28_check :
    CompactPair.expressionCheckPSD compact_height18_pair_28_base compact_height18_pair_28_hinges 0 compact_height18_pair_28_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_28_representation (x y:ℝ) :
    height18_pair_28 x y = CompactPair.expressionEval compact_height18_pair_28_base compact_height18_pair_28_hinges x y:=by rfl
theorem height18_pair_28_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_28 x y:=by
  rw [compact_height18_pair_28_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_28_check hy (by simpa using hx)
def compact_height18_pair_29_base:CompactPair.Quadratic:=⟨(0x7d000085d / 0x6fc23ac00),(0x18bfa0d4b / 0x12a05f200),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_29_hinges:List CompactPair.Hinge:=[⟨(0x2ab75ec3 / 0xdf8475800),1, -3⟩,⟨(-0x111625d7 / 0x1dcd65000),1, -2⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(0x2d9064d / 0x1dcd65000),2, -3⟩,⟨(0x111625d7 / 0x1dcd65000),2, -1⟩,⟨(-0x2d9064d / 0x1dcd65000),3, -2⟩,⟨(-0x2ab75ec3 / 0xdf8475800),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_29 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_29_base compact_height18_pair_29_hinges x y
def compact_height18_pair_29_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height18_pair_29_check :
    CompactPair.expressionCheckPSD compact_height18_pair_29_base compact_height18_pair_29_hinges 0 compact_height18_pair_29_cuts = true :=
  by decide +kernel
private def zz1325:"s052d"="s052d":=by decide+kernel
theorem compact_height18_pair_29_representation (x y:ℝ) :
    height18_pair_29 x y = CompactPair.expressionEval compact_height18_pair_29_base compact_height18_pair_29_hinges x y:=by rfl
theorem height18_pair_29_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_29 x y:=by
  rw [compact_height18_pair_29_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_29_check hy (by simpa using hx)
def compact_height18_pair_30_base:CompactPair.Quadratic:=⟨2,(0x169ccd981 / 0x9502f900),2⟩
def compact_height18_pair_30_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_30 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_30_base compact_height18_pair_30_hinges x y
def compact_height18_pair_30_cuts:List ℚ:=[]
theorem compact_height18_pair_30_check :
    CompactPair.expressionCheckPSD compact_height18_pair_30_base compact_height18_pair_30_hinges 0 compact_height18_pair_30_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_30_representation (x y:ℝ) :
    height18_pair_30 x y = CompactPair.expressionEval compact_height18_pair_30_base compact_height18_pair_30_hinges x y:=by rfl
private def zz1326:"s052e"="s052e":=by decide+kernel
theorem height18_pair_30_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_30 x y:=by
  rw [compact_height18_pair_30_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_30_check hy (by simpa using hx)
def compact_height18_pair_31_base:CompactPair.Quadratic:=⟨(0xb2d05dff5 / 0x59682f000),(0x2d0062c07 / 0x12a05f200),2⟩
def compact_height18_pair_31_hinges:List CompactPair.Hinge:=[⟨(-1 / 0x1dcd65000),1, -2⟩,⟨(1 / 0xee6b2800),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(1 / 0x2cb417800),2, -3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_31 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_31_base compact_height18_pair_31_hinges x y
def compact_height18_pair_31_cuts:List ℚ:=[1,(3 / 2),2]
theorem compact_height18_pair_31_check :
    CompactPair.expressionCheckPSD compact_height18_pair_31_base compact_height18_pair_31_hinges 0 compact_height18_pair_31_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_31_representation (x y:ℝ) :
    height18_pair_31 x y = CompactPair.expressionEval compact_height18_pair_31_base compact_height18_pair_31_hinges x y:=by rfl
theorem height18_pair_31_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_31 x y:=by
  rw [compact_height18_pair_31_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_31_check hy (by simpa using hx)
def compact_height18_pair_32_base:CompactPair.Quadratic:=⟨(0x5eb344823 / 0x4a817c800),(0x6e566a39 / 0x4a817c80),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_32_hinges:List CompactPair.Hinge:=[⟨(0x28eeee29 / 0x12a05f200),1, -3⟩,⟨(-0x777ec91b / 0xee6b2800),1, -2⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(-0xebe9f / 0x77359400),2, -1⟩,⟨(0x3ed393b / 0x1dcd6500),3, -2⟩,⟨(-0x4199489 / 0x2540be40),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_32 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_32_base compact_height18_pair_32_hinges x y
def compact_height18_pair_32_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),2,3]
private def zz1327:"s052f"="s052f":=by decide+kernel
theorem compact_height18_pair_32_check :
    CompactPair.expressionCheckPSD compact_height18_pair_32_base compact_height18_pair_32_hinges 0 compact_height18_pair_32_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_32_representation (x y:ℝ) :
    height18_pair_32 x y = CompactPair.expressionEval compact_height18_pair_32_base compact_height18_pair_32_hinges x y:=by rfl
theorem height18_pair_32_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_32 x y:=by
  rw [compact_height18_pair_32_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_32_check hy (by simpa using hx)
def compact_height18_pair_33_base:CompactPair.Quadratic:=⟨(0x1b0351dbef / 0x1bf08eb000),(0x19a175e77 / 0x12a05f200),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_33_hinges:List CompactPair.Hinge:=[⟨(0x81dfbded / 0x4a817c800),1, -3⟩,⟨(-0x2771acef / 0x77359400),1, -2⟩,⟨(-0x1bff669 / 0xee6b280),1, -1⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(0x291e4d9f / 0x2cb417800),2, -3⟩,⟨(-0xf3c422d / 0x3b9aca00),2, -1⟩,⟨(0x69200b37 / 0x59682f000),3, -2⟩,⟨(0x780a81a9 / 0x6fc23ac00),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_33 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_33_base compact_height18_pair_33_hinges x y
def compact_height18_pair_33_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_height18_pair_33_check :
    CompactPair.expressionCheckPSD compact_height18_pair_33_base compact_height18_pair_33_hinges 0 compact_height18_pair_33_cuts = true :=
  by decide +kernel
private def zz1328:"s0530"="s0530":=by decide+kernel
theorem compact_height18_pair_33_representation (x y:ℝ) :
    height18_pair_33 x y = CompactPair.expressionEval compact_height18_pair_33_base compact_height18_pair_33_hinges x y:=by rfl
theorem height18_pair_33_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_33 x y:=by
  rw [compact_height18_pair_33_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_33_check hy (by simpa using hx)
def compact_height18_pair_34_base:CompactPair.Quadratic:=⟨(0x59682ef09 / 0x2cb417800),(0x1207c89fd / 0x77359400),2⟩
def compact_height18_pair_34_hinges:List CompactPair.Hinge:=[⟨(-0x817d174b / 0x2cb417800),1, -3⟩,⟨(0x205f45bd7 / 0x1dcd65000),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-0x205f45b29 / 0x59682f000),2, -3⟩,⟨(-0x205f45bd7 / 0x1dcd65000),2, -1⟩,⟨(0x205f45b29 / 0x59682f000),3, -2⟩,⟨(0x817d174b / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_34 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_34_base compact_height18_pair_34_hinges x y
def compact_height18_pair_34_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height18_pair_34_check :
    CompactPair.expressionCheckPSD compact_height18_pair_34_base compact_height18_pair_34_hinges 0 compact_height18_pair_34_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_34_representation (x y:ℝ) :
    height18_pair_34 x y = CompactPair.expressionEval compact_height18_pair_34_base compact_height18_pair_34_hinges x y:=by rfl
private def zz1329:"s0531"="s0531":=by decide+kernel
theorem height18_pair_34_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_34 x y:=by
  rw [compact_height18_pair_34_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_34_check hy (by simpa using hx)
def compact_height18_pair_35_base:CompactPair.Quadratic:=⟨(0x77359401 / 0x3b9aca00),(0x11f0e53f9 / 0x77359400),2⟩
def compact_height18_pair_35_hinges:List CompactPair.Hinge:=[⟨(1 / 0x2cb417800),1, -3⟩,⟨(1 / 0xee6b2800),1, -2⟩,⟨(-1 / 5),1,3⟩,⟨(-1 / 0x2cb417800),2, -3⟩,⟨(-1 / 0xee6b2800),2, -1⟩,⟨(1 / 0x2cb417800),3, -2⟩,⟨(-1 / 0x2cb417800),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_35 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_35_base compact_height18_pair_35_hinges x y
def compact_height18_pair_35_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height18_pair_35_check :
    CompactPair.expressionCheckPSD compact_height18_pair_35_base compact_height18_pair_35_hinges 0 compact_height18_pair_35_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_35_representation (x y:ℝ) :
    height18_pair_35 x y = CompactPair.expressionEval compact_height18_pair_35_base compact_height18_pair_35_hinges x y:=by rfl
theorem height18_pair_35_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_35 x y:=by
  rw [compact_height18_pair_35_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_35_check hy (by simpa using hx)
def compact_height18_pair_36_base:CompactPair.Quadratic:=⟨2,(0x169ccd981 / 0x9502f900),2⟩
def compact_height18_pair_36_hinges:List CompactPair.Hinge:=[⟨(-1 / 5),1,3⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_36 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_36_base compact_height18_pair_36_hinges x y
def compact_height18_pair_36_cuts:List ℚ:=[]
private def zz1330:"s0532"="s0532":=by decide+kernel
theorem compact_height18_pair_36_check :
    CompactPair.expressionCheckPSD compact_height18_pair_36_base compact_height18_pair_36_hinges 0 compact_height18_pair_36_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_36_representation (x y:ℝ) :
    height18_pair_36 x y = CompactPair.expressionEval compact_height18_pair_36_base compact_height18_pair_36_hinges x y:=by rfl
theorem height18_pair_36_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_36 x y:=by
  rw [compact_height18_pair_36_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_36_check hy (by simpa using hx)
def compact_height18_pair_37_base:CompactPair.Quadratic:=⟨(0x59682ede3 / 0x2cb417800),(0x168031601 / 0x9502f900),2⟩
def compact_height18_pair_37_hinges:List CompactPair.Hinge:=[⟨(0x193a4e37 / 0xee6b2800),1, -3⟩,⟨(-0x25d7c183 / 0x77359400),1, -2⟩,⟨(-0x407337 / 0x1dcd6500),1, -1⟩,⟨(-1 / 5),1,3⟩,⟨(0x25d918dd / 0x2cb417800),2, -3⟩,⟨(-0x7fd525 / 0x1dcd6500),2, -1⟩,⟨(0x66651d / 0x47868c00),3, -2⟩,⟨(0x7fbbe3 / 0xb2d05e00),3, -1⟩,⟨(-1 / 5),3,1⟩]
noncomputable def height18_pair_37 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_37_base compact_height18_pair_37_hinges x y
def compact_height18_pair_37_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),1,(3 / 2),2,3]
theorem compact_height18_pair_37_check :
    CompactPair.expressionCheckPSD compact_height18_pair_37_base compact_height18_pair_37_hinges 0 compact_height18_pair_37_cuts = true :=
  by decide +kernel
private def zz1331:"s0533"="s0533":=by decide+kernel
theorem compact_height18_pair_37_representation (x y:ℝ) :
    height18_pair_37 x y = CompactPair.expressionEval compact_height18_pair_37_base compact_height18_pair_37_hinges x y:=by rfl
theorem height18_pair_37_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_37 x y:=by
  rw [compact_height18_pair_37_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_37_check hy (by simpa using hx)
def compact_height18_pair_38_base:CompactPair.Quadratic:=⟨(0x7aff680f / 0x6fc23ac0),(0x18f8d945b / 0x12a05f200),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_38_hinges:List CompactPair.Hinge:=[⟨(1 / 0x37e11d600),1, -3⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(-1 / 0x37e11d600),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_38 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_38_base compact_height18_pair_38_hinges x y
def compact_height18_pair_38_cuts:List ℚ:=[(1 / 3),3]
theorem compact_height18_pair_38_check :
    CompactPair.expressionCheckPSD compact_height18_pair_38_base compact_height18_pair_38_hinges 0 compact_height18_pair_38_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_38_representation (x y:ℝ) :
    height18_pair_38 x y = CompactPair.expressionEval compact_height18_pair_38_base compact_height18_pair_38_hinges x y:=by rfl
private def zz1332:"s0534"="s0534":=by decide+kernel
theorem height18_pair_38_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_38 x y:=by
  rw [compact_height18_pair_38_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_38_check hy (by simpa using hx)
def compact_height18_pair_39_base:CompactPair.Quadratic:=⟨(0x51ff9ab21 / 0x4a817c800),(0x18bfa0d5b / 0x12a05f200),(0x4199489 / 0x3b9aca0)⟩
def compact_height18_pair_39_hinges:List CompactPair.Hinge:=[⟨(-1 / 0xdf847580),1, -3⟩,⟨(1 / 0x1dcd65000),1, -2⟩,⟨(-0x4199489 / 0x2540be40),1,3⟩,⟨(1 / 0x59682f000),2, -3⟩,⟨(-1 / 0x1dcd65000),2, -1⟩,⟨(-1 / 0x59682f000),3, -2⟩,⟨(1 / 0xdf847580),3, -1⟩,⟨(-0x4199489 / 0x2540be40),3,1⟩]
noncomputable def height18_pair_39 (x y:ℝ):ℝ :=
  CompactPair.expressionEval compact_height18_pair_39_base compact_height18_pair_39_hinges x y
def compact_height18_pair_39_cuts:List ℚ:=[(1 / 3),(1 / 2),(2 / 3),(3 / 2),2,3]
theorem compact_height18_pair_39_check :
    CompactPair.expressionCheckPSD compact_height18_pair_39_base compact_height18_pair_39_hinges 0 compact_height18_pair_39_cuts = true :=
  by decide +kernel
theorem compact_height18_pair_39_representation (x y:ℝ) :
    height18_pair_39 x y = CompactPair.expressionEval compact_height18_pair_39_base compact_height18_pair_39_hinges x y:=by rfl
theorem height18_pair_39_nonneg {x y:ℝ} (hx:0 ≤ x) (hy:0 ≤ y) :
    0 ≤ height18_pair_39 x y:=by
  rw [compact_height18_pair_39_representation]
  exact CompactPair.expressionCheckPSD_sound compact_height18_pair_39_check hy (by simpa using hx)
end Green24Proof.LocalPairs
private def zz2359:"s0937"="s0937":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l55 l56 l58 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x51bb1798e, -0x547044420, -0x7eb3d8322,0x3b560eb4], ![-0x547044420, -0xf68381486,0x1a17b4332,0x5eccff5c0], ![-0x7eb3d8322,0x1a17b4332, -0x2256e81a2b,0x549e0b026], ![0x3b560eb4,0x5eccff5c0,0x549e0b026, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-0x2387916,l6),(0x10179ca8,l5),(-0x7c240992,l4),(-0x92dafd0,l9),(-0x174095cd6,l8),(0x7592ae97,l11),(0x401ba984,l10),(0x89320e280,l14),(-0x709096ffe,l13),(-0x169bdb3c8,l17),(0x24416a153,l16),(0x78ee6b9d2,l15),(-0xa56e7109,l21),(0x709096ffe,l20),(0x52b73885,l23),(-0x1bb201919,l22),(-0x2a4393d10,l27),(0xa56e7109,l28),(0x2a4393d10,l29),(-0x89320e280,l25),(0x281627cf2,l30),(0x2a4393d10,l33),(-0x401ba984,l38),(-0x2a4393d10,l35),(0x174095cd6,l36),(0x2a4393d10,l37),(0x7c240992,l34),(-0x281627cf2,l43),(0x1bb201919,l42),(-0x78ee6b9d2,l41),(0x6139aef4,l46),(-0xf56404e0,l45),(0x2a4393d10,l51),(-0x7592ae97,l55),(-0x10179ca8,l54),(-0x24416a153,l56),(0xf56404e0,l58),(0x92dafd0,l61),(0x2387916,l60),(-0x52b73885,l63),(0x169bdb3c8,l62),(-0x6139aef4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x89320e280,l14),(-0x89320e280,l25),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(-0x709096ffe,l13),(0x709096ffe,l20),(0x281627cf2,l30),(-0x281627cf2,l43),(0x78ee6b9d2,l15),(-0x78ee6b9d2,l41),(-0x169bdb3c8,l17),(0x169bdb3c8,l62),(0x24416a153,l16),(-0x24416a153,l56),(-0xa56e7109,l21),(0xa56e7109,l28),(-0x1bb201919,l22),(0x1bb201919,l42),(-0x174095cd6,l8),(0x174095cd6,l36),(0x7592ae97,l11),(-0x7592ae97,l55),(-0xf56404e0,l45),(0xf56404e0,l58),(0x52b73885,l23),(-0x52b73885,l63),(0x6139aef4,l46),(-0x6139aef4,l64),(0x401ba984,l10),(-0x401ba984,l38),(-0x7c240992,l4),(0x7c240992,l34),(-0x92dafd0,l9),(0x92dafd0,l61),(0x10179ca8,l5),(-0x10179ca8,l54),(-0x2387916,l6),(0x2387916,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 43 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case0" = "QuadHeightCover12Case0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 43 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case0
private def zz2360:"s0938"="s0938":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l5 l51 l54 l55 l56 l57 l58 l59 l6 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x5b90174e4, -0x547044420, -0x7eb3d824a,0x3cbb0e6c], ![-0x547044420, -0x103ecdeef4,0x1a517e41e,0x5ea4f2490], ![-0x7eb3d824a,0x1a517e41e, -0x2256e81a2b,0x549e0b026], ![0x3cbb0e6c,0x5ea4f2490,0x549e0b026, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-0x2387916,l6),(0x10179ca8,l5),(-0x7c240992,l4),(-0x92dafd0,l9),(-0x174095cd6,l8),(0x7592ae97,l11),(0x401ba984,l10),(0x93341d44e,l14),(-0xd9583f1c6,l13),(-0x1b3034372,l17),(0x39b084952,l16),(0x8267e5d68,l15),(0x2054f19b2,l21),(0xd9583f1c6,l20),(-0x1814cf86,l23),(-0x152da0f2c,l22),(-0x2a4393d10,l27),(-0x2054f19b2,l28),(0x2a4393d10,l29),(-0x93341d44e,l25),(-0x39cc07c,l31),(0x249f6ffd8,l30),(0x2a4393d10,l33),(-0x401ba984,l38),(-0x2a4393d10,l35),(0x174095cd6,l36),(0x2a4393d10,l37),(0x7c240992,l34),(-0x249f6ffd8,l43),(0x152da0f2c,l42),(-0x8267e5d68,l41),(0xabc94a14,l46),(-0xd2a3abd1,l45),(0x2a4393d10,l51),(-0x7592ae97,l55),(-0x10179ca8,l54),(0x39cc07c,l57),(-0x39b084952,l56),(-0x601de063,l59),(0xd2a3abd1,l58),(0x92dafd0,l61),(0x2387916,l60),(0x1814cf86,l63),(0x1b3034372,l62),(0x601de063,l65),(-0xabc94a14,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x93341d44e,l14),(-0x93341d44e,l25),(-0xd9583f1c6,l13),(0xd9583f1c6,l20),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(0x2054f19b2,l21),(-0x2054f19b2,l28),(0x249f6ffd8,l30),(-0x249f6ffd8,l43),(0x8267e5d68,l15),(-0x8267e5d68,l41),(0x39b084952,l16),(-0x39b084952,l56),(-0x1b3034372,l17),(0x1b3034372,l62),(-0x174095cd6,l8),(0x174095cd6,l36),(-0x152da0f2c,l22),(0x152da0f2c,l42),(0x7592ae97,l11),(-0x7592ae97,l55),(0xabc94a14,l46),(-0xabc94a14,l64),(-0x601de063,l59),(0x601de063,l65),(-0xd2a3abd1,l45),(0xd2a3abd1,l58),(0x401ba984,l10),(-0x401ba984,l38),(-0x1814cf86,l23),(0x1814cf86,l63),(-0x7c240992,l4),(0x7c240992,l34),(-0x92dafd0,l9),(0x92dafd0,l61),(0x10179ca8,l5),(-0x10179ca8,l54),(-0x39cc07c,l31),(0x39cc07c,l57),(-0x2387916,l6),(0x2387916,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 47 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case1" = "QuadHeightCover12Case1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 47 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case1
private def zz2361:"s0939"="s0939":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l29 l30 l33 l35 l37 l4 l41 l42 l44 l45 l46 l51 l57 l62 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x44eedac25, -0x59514ba00, -0x54e07e3ac,0x1e065ec08], ![-0x59514ba00, -0x32d9814472,0x64b38a6d8,0x532499a0c], ![-0x54e07e3ac,0x64b38a6d8, -0x2439b7b835,0x597f125ee], ![0x1e065ec08,0x532499a0c,0x597f125ee, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(6,l4),(0x3136beee,l8),(-0x833ca7b,l11),(-0x10679506,l10),(0x11e1a3000,l14),(0x1027c90f8,l13),(-0x119adeeb8,l12),(-0x19c96f90a,l17),(0x42aef26ee,l16),(0x47d50557e,l15),(-0x3da566c,l21),(0x150480fc,l20),(-0xe12048e,l23),(0x8d4d5ef6,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x122e548f8,l25),(0x19a57d068,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x94a537e2,l42),(-0x16946bf0e,l41),(0x79c3b2c,l46),(0xf906fba,l45),(-0x14f123fdc,l44),(0x2cb417800,l51),(-0xb4d51ce8,l57),(-0x58030c33,l63),(-0xc3af6ee4,l62),(0xfd5c21b0,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x42aef26ee,l16),(-0x19c96f90a,l17),(0x19a57d068,l30),(-0x122e548f8,l25),(0x47d50557e,l15),(0x11e1a3000,l14),(-0xb4d51ce8,l57),(0xfd5c21b0,l64),(-0xc3af6ee4,l62),(0x1027c90f8,l13),(-0x58030c33,l63),(-0x16946bf0e,l41),(-0x14f123fdc,l44),(-0x94a537e2,l42),(0x8d4d5ef6,l22),(-0x119adeeb8,l12),(0x3136beee,l8),(-0xe12048e,l23),(-0x10679506,l10),(-0x833ca7b,l11),(0x150480fc,l20),(0xf906fba,l45),(0x79c3b2c,l46),(-0x3da566c,l21),(6,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,0xc806900600000004219022300c000318881a00f480200006110c330269004000000003a1c0318040028c3084103d540140000000128d00c60100000000251a038c0200000000523c039804000000000a8b03300400b20c914c042680280000024c290090c04000000002a140298040000124541900d400c000000e20900fe6020012120230c066d005048a40a31e042da00c0049c838d503db40140000000001081c4010000046148840d900300000000003a031004004185088102464014000418a421012c8020000831444102590040000000000420310040000000861a02a300c00000000110e0660080000025220e0250020000086291080f200600000098843405400800002610c340548018000043150880790030000000000320310040000050881024c30140000000078381460100005210c3201e90040204186104048ba00c0000051821015230140000001245204e60181020c30820215d0060010c1a423007ba00a0020831842015740140000188642201a801819c1430ed010b100600000000320e05180400000ac240c00a400c000000b850301c8010000000158480a8c030000000002c281980200000003211022300c00020868118198802000980c20fc06410050284206184048ba00c0000000000140620080001e0420d013880200003c0841400f10040000e81a04203c20080000002105003c30100000000441401860180000000000d034802000000005a36051804000000000013032004000298841a0112802000003b0f04c051003,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,0xb8004c8040000000002e80590060000000000b80720080000258c41201a801800000002719014c02001c430c190115200a00000004219016300c0000000a44401c6018000000188a4058c030000c626066055a0080029433845017d401400588720a2053a8028000000000190388020000000000360310040000000003500a200c0000000941201660180000000110f014c0200000000001e0290040000000440900e300c0000009008802c602000000138110058c04000004a1304805a0060000000001e009200c0000000842202c6018000b218c530121004], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 32 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case2" = "QuadHeightCover12Case2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 32 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case2
private def zz2362:"s093a"="s093a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l44 l45 l46 l51 l57 l58 l59 l62 l63 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3ddc75a11, -0x59514ba00, -0x579816a74,0x251f195b8], ![-0x59514ba00, -0x326d249175,0x64b38a6cc,0x52ba3aea4], ![-0x579816a74,0x64b38a6cc, -0x2439b7b835,0x597f125ee], ![0x251f195b8,0x52ba3aea4,0x597f125ee, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(6,l4),(0x3136beee,l8),(-0x833ca7b,l11),(-0x10679506,l10),(0x1be8020bc,l14),(0x16baf13ac,l13),(-0x2f95233f0,l12),(-0x171ce0498,l17),(0x390f54c21,l16),(0x4666492f8,l15),(0x18fae1d4,l21),(0x252a8c816,l20),(0x15e89e2b,l23),(0x1691da09e,l22),(-0x2cb417800,l27),(-0x81fa8932,l28),(0x2cb417800,l29),(-0x19528b424,l25),(-0x2aa4f7fe,l31),(0x1566bdf84,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x171a36ddc,l42),(0x875155ec,l41),(-0x518af684,l46),(0x1d72a9372,l45),(-0x2b7a382b0,l44),(0x2cb417800,l51),(-0xb376592b,l57),(-0x70938c02,l59),(0x106bf60c6,l58),(-0x9873b777,l63),(-0xa5bee440,l62),(0x2cffa2f0,l65),(0x9cce715c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x390f54c21,l16),(0x1be8020bc,l14),(-0x19528b424,l25),(-0x171ce0498,l17),(0x1566bdf84,l30),(0x252a8c816,l20),(0x4666492f8,l15),(-0xb376592b,l57),(0x1d72a9372,l45),(-0x9873b777,l63),(-0x171a36ddc,l42),(0x16baf13ac,l13),(0x1691da09e,l22),(-0x81fa8932,l28),(-0x2f95233f0,l12),(-0x70938c02,l59),(-0x2b7a382b0,l44),(-0xa5bee440,l62),(0x9cce715c,l64),(0x106bf60c6,l58),(-0x518af684,l46),(0x2cffa2f0,l65),(-0x2aa4f7fe,l31),(0x18fae1d4,l21),(0x15e89e2b,l23),(0x875155ec,l41),(0x3136beee,l8),(-0x10679506,l10),(-0x833ca7b,l11),(6,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 37 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case3" = "QuadHeightCover12Case3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 37 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case3
private def zz2363:"s093b"="s093b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l43 l45 l46 l5 l51 l54 l55 l56 l58 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x43086edf1, -0x547044420, -0x7eb3d82c8,0x85bd2cc0], ![-0x547044420, -0x1459b4589f,0x1f5530e74,0x5eccff5c0], ![-0x7eb3d82c8,0x1f5530e74, -0x2256e819f5,0x549e0b020], ![0x85bd2cc0,0x5eccff5c0,0x549e0b020, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-3,l5),(-0x6abab546,l4),(4,l9),(-0xd5756a7d,l8),(0x47272378,l11),(0x239391ca,l10),(0x6857558b8,l14),(-0x455e23f90,l13),(-0x110170404,l12),(-0x169bdb3c8,l17),(0x24416a153,l16),(0x78ee6b9d2,l15),(0x59e04e7fa,l20),(0x52b73885,l23),(-0x1bb201919,l22),(-0x2a4393d10,l27),(0x2a4393d10,l29),(-0x6fd6d1c6c,l25),(0x281627cf2,l30),(0x2a4393d10,l33),(-0x23c1eada,l38),(-0x2a4393d10,l35),(0xd68b9d30,l36),(0x2a4393d10,l37),(0x6b468a24,l34),(-0x1d6b31eb2,l43),(-0x5138e1ac6,l41),(0x4ecbe794,l46),(-0x10442c886,l45),(0x2a4393d10,l51),(-0x4783f056,l55),(0x2c76,l54),(-0x4d096212b,l56),(0x3fffc0e4c,l58),(-0x1c2d,l61),(-0x5ee,l60),(-0x111aa17c,l63),(0x23ccd800e,l62),(-0x8f8a4e34,l65),(-0x128e4faf0,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6fd6d1c6c,l25),(0x6857558b8,l14),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(0x59e04e7fa,l20),(-0x4d096212b,l56),(0x281627cf2,l30),(-0x455e23f90,l13),(0x3fffc0e4c,l58),(0x23ccd800e,l62),(0x78ee6b9d2,l15),(-0x1d6b31eb2,l43),(-0x169bdb3c8,l17),(0x24416a153,l16),(-0x5138e1ac6,l41),(-0x128e4faf0,l64),(-0x1bb201919,l22),(-0x8f8a4e34,l65),(-0x10442c886,l45),(0x52b73885,l23),(0xd68b9d30,l36),(-0xd5756a7d,l8),(-0x4783f056,l55),(0x47272378,l11),(0x4ecbe794,l46),(-0x110170404,l12),(-0x23c1eada,l38),(0x239391ca,l10),(0x6b468a24,l34),(-0x111aa17c,l63),(-0x6abab546,l4),(-0x1c2d,l61),(0x2c76,l54),(-0x5ee,l60),(4,l9),(-3,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case4" = "QuadHeightCover12Case4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case4
private def zz2364:"s093c"="s093c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l43 l44 l45 l46 l5 l51 l54 l55 l56 l57 l58 l59 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x359ab213e, -0x547044420, -0x7eb3d8214,0xa3676424], ![-0x547044420, -0x149c3c6952,0x1e9e83b00,0x5ea4f2490], ![-0x7eb3d8214,0x1e9e83b00, -0x2256e819f5,0x549e0b020], ![0xa3676424,0x5ea4f2490,0x549e0b020, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-3,l5),(-0x6abab546,l4),(4,l9),(-0xd5756a7d,l8),(0x47272378,l11),(0x239391ca,l10),(0x6978abd74,l14),(-0x64b98aa1a,l13),(-0xbc4cc1ec,l12),(-0x1b3034372,l17),(0x39b084952,l16),(0x8267e5d68,l15),(0xec7d73c0,l21),(0x7030bb034,l20),(-0x1814cf86,l23),(-0x152da0f2c,l22),(-0x2a4393d10,l27),(-0xddc67d40,l28),(0x2a4393d10,l29),(-0x6e6454178,l25),(-0x39cc07c,l31),(0x249f6ffd8,l30),(0x2a4393d10,l33),(-0x23c1eada,l38),(-0x2a4393d10,l35),(0xd68b9d30,l36),(0x2a4393d10,l37),(0x6b468a24,l34),(-0x1dde8eef8,l43),(-0x83646dd46,l41),(0x4f863150,l46),(-0x5f878ba2,l45),(0xb23a5c5c,l44),(0x2a4393d10,l51),(-0x4783f056,l55),(0x2c76,l54),(0x3accaed3,l57),(-0x57b02cd73,l56),(-0x6f1a510a,l59),(0x1d0ff12c4,l58),(-0x1c2d,l61),(-0x5ee,l60),(0x6f9a51bf,l63),(0x2494375f4,l62),(0x113a884,l65),(-0x9f9256b8,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6e6454178,l25),(0x6978abd74,l14),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(0x7030bb034,l20),(-0x64b98aa1a,l13),(-0x57b02cd73,l56),(0x249f6ffd8,l30),(0x2494375f4,l62),(-0x83646dd46,l41),(0x8267e5d68,l15),(0x39b084952,l16),(-0x1dde8eef8,l43),(-0x1b3034372,l17),(0xec7d73c0,l21),(-0xddc67d40,l28),(0x1d0ff12c4,l58),(-0x152da0f2c,l22),(0x6f9a51bf,l63),(-0x6f1a510a,l59),(-0x9f9256b8,l64),(0xd68b9d30,l36),(-0xd5756a7d,l8),(-0x4783f056,l55),(0x47272378,l11),(0x3accaed3,l57),(0x4f863150,l46),(-0x5f878ba2,l45),(-0xbc4cc1ec,l12),(0xb23a5c5c,l44),(-0x1814cf86,l23),(-0x23c1eada,l38),(0x239391ca,l10),(0x6b468a24,l34),(-0x6abab546,l4),(-0x39cc07c,l31),(0x113a884,l65),(-0x1c2d,l61),(0x2c76,l54),(-0x5ee,l60),(4,l9),(-3,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((0x1e50633592b30af178c8ee60c36cf2c30d1465334769803c9517942805afb20000016181f0041bf02f8c91a6367d9e580e6bb434c0004ae44aa00462842010921219e0230499e25073b4ec99a085d61e) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 47 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case5" = "QuadHeightCover12Case5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 47 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case5
private def zz2365:"s093d"="s093d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case6
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l44 l45 l46 l5 l51 l54 l55 l57 l58 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4de723a7d, -0x5859e065e, -0x48f3bd1c8,0x101ea77b0], ![-0x5859e065e, -0x32f4fda45a,0x64e1c296c,0x532499a0c], ![-0x48f3bd1c8,0x64e1c296c, -0x2444b96de5,0x597f125f4], ![0x101ea77b0,0x532499a0c,0x597f125f4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xd4f082,l5),(-0x879f552,l4),(0xc1eab3,l9),(0x141fb580,l8),(-0x1cb1bbd,l11),(-0x7f6cf7e,l10),(0x1bae89c88,l14),(0x4f8e9898,l13),(-0x1357953c0,l12),(-0x19c96f90a,l17),(0x42aef26ee,l16),(0x47d50557e,l15),(0x17647a7c,l20),(-0xe12048e,l23),(0x8d4d5ef6,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x11d102aa0,l25),(0x19a57d068,l30),(0x2cb417800,l33),(0xb0,l38),(-0x2cb417800,l35),(-0x26f4c,l36),(0x2cb417800,l37),(-0x445cce,l34),(-0x34a256e6,l43),(-0xaf52441d,l42),(-0x15782a20a,l41),(-0x86f432c,l46),(0x20d56064,l45),(-0x130aaf8d0,l44),(0x2cb417800,l51),(0x2e0da,l55),(-0x113eb735,l54),(-0x9fc0cfa7,l57),(0xe2f0534e,l58),(0x5cc350,l61),(0xfffd620,l60),(-0x82a7b8b4,l63),(-0x3582b1c6,l62),(0x164ddedc,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x42aef26ee,l16),(0x1bae89c88,l14),(-0x19c96f90a,l17),(0x19a57d068,l30),(0x47d50557e,l15),(-0x11d102aa0,l25),(-0x9fc0cfa7,l57),(-0x82a7b8b4,l63),(0xe2f0534e,l58),(-0xaf52441d,l42),(-0x15782a20a,l41),(0x8d4d5ef6,l22),(-0x1357953c0,l12),(-0x130aaf8d0,l44),(-0x3582b1c6,l62),(-0x34a256e6,l43),(0x4f8e9898,l13),(0x164ddedc,l64),(-0xe12048e,l23),(0x20d56064,l45),(0xfffd620,l60),(0x17647a7c,l20),(0x141fb580,l8),(-0x113eb735,l54),(-0x86f432c,l46),(-0x7f6cf7e,l10),(-0x1cb1bbd,l11),(-0x879f552,l4),(0xc1eab3,l9),(0x5cc350,l61),(-0xd4f082,l5),(-0x445cce,l34),(0x2e0da,l55),(-0x26f4c,l36),(0xb0,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 42 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case6" = "QuadHeightCover12Case6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 42 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case6
private def zz2366:"s093e"="s093e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l44 l45 l46 l5 l51 l54 l55 l56 l57 l58 l59 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x42ac16a4e, -0x5859e065e, -0x5ea5cd9b2,0x29eea55d0], ![-0x5859e065e, -0x329205e0f1,0x64e1c2984,0x52ba3aea4], ![-0x5ea5cd9b2,0x64e1c2984, -0x2444b96de5,0x597f125f4], ![0x29eea55d0,0x52ba3aea4,0x597f125f4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xd4f082,l5),(-0x879f552,l4),(0xc1eab3,l9),(0x141fb580,l8),(-0x1cb1bbd,l11),(-0x7f6cf7e,l10),(0x1ac9c4704,l14),(0xc071c376,l13),(-0x2e11570d8,l12),(-0x171ce0498,l17),(0x390f54c21,l16),(0x4666492f8,l15),(0x581f88b0,l21),(0x213ec9196,l20),(0x15e89e2b,l23),(0x1691da09e,l22),(-0x2cb417800,l27),(-0x86f0b48c,l28),(0x2cb417800,l29),(-0x179f5a678,l25),(-0x2aa4f7fe,l31),(0x1566bdf84,l30),(0x2cb417800,l33),(0xb0,l38),(-0x2cb417800,l35),(-0x26f4c,l36),(0x2cb417800,l37),(-0x445cce,l34),(-0x1e9309be,l43),(-0xcccdfcf2,l42),(0x161cc55de,l41),(-0x905234d0,l46),(0x2c46b178c,l45),(-0x37cfb093c,l44),(0x2cb417800,l51),(0x2e0da,l55),(-0x113eb735,l54),(-0xeb8331b2,l57),(0x18d35fbb8,l56),(-0x93db850a,l59),(0x8136744,l58),(0x5cc350,l61),(0xfffd620,l60),(-0xe993b890,l63),(-0x157d32b22,l62),(0x62d2693c,l65),(0x11d8d2590,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x390f54c21,l16),(0x1ac9c4704,l14),(0x2c46b178c,l45),(-0x179f5a678,l25),(-0x171ce0498,l17),(-0xeb8331b2,l57),(-0xe993b890,l63),(-0x157d32b22,l62),(0x1566bdf84,l30),(0x213ec9196,l20),(0x11d8d2590,l64),(0x4666492f8,l15),(-0x93db850a,l59),(0x18d35fbb8,l56),(-0x37cfb093c,l44),(-0x86f0b48c,l28),(0x1691da09e,l22),(-0x2e11570d8,l12),(0x62d2693c,l65),(-0x905234d0,l46),(0x581f88b0,l21),(-0xcccdfcf2,l42),(0xc071c376,l13),(0x161cc55de,l41),(-0x2aa4f7fe,l31),(0x15e89e2b,l23),(-0x1e9309be,l43),(0xfffd620,l60),(0x141fb580,l8),(-0x113eb735,l54),(-0x7f6cf7e,l10),(0x8136744,l58),(-0x1cb1bbd,l11),(-0x879f552,l4),(0xc1eab3,l9),(0x5cc350,l61),(-0xd4f082,l5),(-0x445cce,l34),(0x2e0da,l55),(-0x26f4c,l36),(0xb0,l38)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 48 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case7" = "QuadHeightCover12Case7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 48 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case7
private def zz2367:"s093f"="s093f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case8
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l16 l17 l21 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l43 l45 l51 l55 l56 l57 l58 l59 l61 l62 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xb67a92d48, -0x586f71828, -0x84b29c1b8,0x889a126a], ![-0x586f71828, -0x25d7962d37,0x4b1c9ecf6,0x565a87328], ![-0x84b29c1b8,0x4b1c9ecf6, -0x23f6927c03,0x589d38428], ![0x889a126a,0x565a87328,0x589d38428, -0x2c432a714]]
noncomputable def hinges:Hinges:=[(-0x411d818c,l4),(2,l9),(-0x823b02c7,l8),(0x2b6900f3,l11),(0x15b48074,l10),(0x1c7974226,l14),(0xb27f96f2,l17),(0x398d5a5d,l16),(0x6693842f4,l15),(0x971ff14c,l21),(-0x2c432a714,l27),(-0x971ff14c,l28),(0x2c432a714,l29),(-0x1c7974226,l25),(0x468baeb8,l31),(0x1073e2004,l30),(0x2c432a714,l33),(-0x15b48074,l38),(-0x2c432a714,l35),(0x823b02c7,l36),(0x2c432a714,l37),(0x411d818c,l34),(-0x1073e2004,l43),(-0x6693842f4,l41),(-0x731ab4b7,l45),(0x2c432a714,l51),(-0x2b6900f3,l55),(-0x468baeb8,l57),(-0x398d5a5d,l56),(-0xa0893dc,l59),(0x731ab4b7,l58),(-2,l61),(-0xb27f96f2,l62),(0xa0893dc,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c432a714,l27),(0x2c432a714,l29),(0x2c432a714,l33),(-0x2c432a714,l35),(0x2c432a714,l37),(0x2c432a714,l51),(0x1c7974226,l14),(-0x1c7974226,l25),(0x6693842f4,l15),(-0x6693842f4,l41),(0x1073e2004,l30),(-0x1073e2004,l43),(0x971ff14c,l21),(-0x971ff14c,l28),(0xb27f96f2,l17),(-0xb27f96f2,l62),(0x468baeb8,l31),(-0x468baeb8,l57),(-0x823b02c7,l8),(0x823b02c7,l36),(0x2b6900f3,l11),(-0x2b6900f3,l55),(-0x731ab4b7,l45),(0x731ab4b7,l58),(0x398d5a5d,l16),(-0x398d5a5d,l56),(0x15b48074,l10),(-0x15b48074,l38),(-0x411d818c,l4),(0x411d818c,l34),(-0xa0893dc,l59),(0xa0893dc,l65),(2,l9),(-2,l61)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case8" = "QuadHeightCover12Case8" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case8
private def zz2368:"s0940"="s0940":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case9
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l51 l55 l56 l58 l59 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xbe4926ca2, -0x586f71828, -0x84b29c11c,0x8a7f9092], ![-0x586f71828, -0x238c209e6e,0x3b9beddfa,0x5dec7b4ea], ![-0x84b29c11c,0x3b9beddfa, -0x23f6927c03,0x589d38428], ![0x8a7f9092,0x5dec7b4ea,0x589d38428, -0x2c432a714]]
noncomputable def hinges:Hinges:=[(-0x411d818c,l4),(2,l9),(-0x823b02c7,l8),(0x2b6900f3,l11),(0x15b48074,l10),(0x2e5140962,l14),(-0x1aad26333,l13),(0xad18366a,l17),(0x3dc486fe,l16),(0x7453df244,l15),(0xcd05692f,l21),(0x1aad26333,l20),(-0x59c928e,l23),(-0xd411362,l22),(-0x2c432a714,l27),(-0xcd05692f,l28),(0x2c432a714,l29),(-0x2e5140962,l25),(0x18a0522e0,l30),(0x2c432a714,l33),(-0x15b48074,l38),(-0x2c432a714,l35),(0x823b02c7,l36),(0x2c432a714,l37),(0x411d818c,l34),(-0x18a0522e0,l43),(0xd411362,l42),(-0x7453df244,l41),(0x33fd80e8,l46),(-0x71e9d9f1,l45),(0x2c432a714,l51),(-0x2b6900f3,l55),(-0x3dc486fe,l56),(-0x3f91413c,l59),(0x71e9d9f1,l58),(-2,l61),(0x59c928e,l63),(-0xad18366a,l62),(0x3f91413c,l65),(-0x33fd80e8,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c432a714,l27),(0x2c432a714,l29),(0x2c432a714,l33),(-0x2c432a714,l35),(0x2c432a714,l37),(0x2c432a714,l51),(0x2e5140962,l14),(-0x2e5140962,l25),(0x7453df244,l15),(-0x7453df244,l41),(0x18a0522e0,l30),(-0x18a0522e0,l43),(0xcd05692f,l21),(-0xcd05692f,l28),(-0x1aad26333,l13),(0x1aad26333,l20),(0xad18366a,l17),(-0xad18366a,l62),(-0x3f91413c,l59),(0x3f91413c,l65),(-0x823b02c7,l8),(0x823b02c7,l36),(0x2b6900f3,l11),(-0x2b6900f3,l55),(-0x71e9d9f1,l45),(0x71e9d9f1,l58),(0x33fd80e8,l46),(-0x33fd80e8,l64),(0x3dc486fe,l16),(-0x3dc486fe,l56),(0x15b48074,l10),(-0x15b48074,l38),(-0x411d818c,l4),(0x411d818c,l34),(-0x59c928e,l23),(0x59c928e,l63),(-0xd411362,l22),(0xd411362,l42),(2,l9),(-2,l61)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
    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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 41 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case9" = "QuadHeightCover12Case9" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 41 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case9
private def zz2369:"s0941"="s0941":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case10
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l13 l14 l15 l17 l20 l22 l23 l25 l27 l29 l31 l33 l35 l36 l37 l41 l43 l44 l45 l46 l51 l55 l56 l57 l58 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x5f179409b, -0x59514ba00, -0x860563200,0x16e3600], ![-0x59514ba00, -0x24605d9312,0x541d26308,0x5dca88e74], ![-0x860563200,0x541d26308, -0x2452531800,0x597f12600], ![0x16e3600,0x5dca88e74,0x597f12600, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x12689732c,l14),(-0x20d56064,l13),(0x130aaf8d0,l12),(0xc3af6ee4,l17),(0x16946bf0e,l15),(-0xe2f0534e,l20),(0x58030c33,l23),(0x94a537e2,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x134680edc,l25),(0xb4d51ce8,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x1314612f,l36),(0x2cb417800,l37),(-0x1ab8918c8,l43),(-0x3f544d382,l41),(-0x9cce6c88,l46),(-0x4f8e9898,l45),(0x1357953c0,l44),(0x2cb417800,l51),(0x4c5184c,l55),(-0x39b3228d,l57),(-0x3de713736,l56),(-0x17647a7c,l58),(0x17cb7999a,l62),(-0x10a0560,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x3de713736,l56),(-0x1ab8918c8,l43),(0x17cb7999a,l62),(-0x134680edc,l25),(0x12689732c,l14),(0xb4d51ce8,l31),(-0x3f544d382,l41),(0xc3af6ee4,l17),(-0x9cce6c88,l46),(0x58030c33,l23),(-0xe2f0534e,l20),(0x16946bf0e,l15),(-0x39b3228d,l57),(0x94a537e2,l22),(0x1357953c0,l44),(0x130aaf8d0,l12),(-0x4f8e9898,l45),(-0x20d56064,l13),(-0x17647a7c,l58),(-0x1314612f,l36),(0x4c5184c,l55),(-0x10a0560,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case10" = "QuadHeightCover12Case10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case10
private def zz2370:"s0942"="s0942":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l31 l33 l35 l36 l37 l41 l42 l43 l44 l45 l46 l51 l55 l56 l57 l58 l59 l62 l63 l64 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x5eb8a701b, -0x59514ba00, -0x860563314,0x16e35dc], ![-0x59514ba00, -0x2035ed95f9,0x3a4d28524,0x69b2d2be4], ![-0x860563314,0x3a4d28524, -0x2452531800,0x597f12600], ![0x16e35dc,0x69b2d2be4,0x597f12600, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x1ae6c64d0,l14),(-0x2c46b178c,l13),(0x37cfb0924,l12),(0xa5bee440,l17),(-0x875155ec,l15),(0x93db850a,l21),(-0x9bb7a408,l20),(0x9873b777,l23),(0x171a36ddc,l22),(-0x2cb417800,l27),(-0x4a3709ca,l28),(0x2cb417800,l29),(-0x20a709680,l25),(0xb376592b,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(-0x1314612f,l36),(0x2cb417800,l37),(-0x165561bb6,l43),(-0xc2d94abe,l42),(-0x3ae4f4484,l41),(-0xa8116ed8,l46),(-0x73c3bc3c,l45),(0x2e11570f0,l44),(0x2cb417800,l51),(0x4c5184c,l55),(-0x20e2f8d8,l57),(-0x3d895d2c4,l56),(-0x64e7348c,l59),(-0x213ec9196,l58),(-0x94ada62,l63),(0x17fc9e196,l62),(0x86f0b48c,l65),(0x5bdb7678,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x3d895d2c4,l56),(-0x20a709680,l25),(0x1ae6c64d0,l14),(-0x2c46b178c,l13),(0x17fc9e196,l62),(-0x165561bb6,l43),(-0x213ec9196,l58),(0xb376592b,l31),(0x9873b777,l23),(-0x3ae4f4484,l41),(0x93db850a,l21),(0x37cfb0924,l12),(0x86f0b48c,l65),(0x171a36ddc,l22),(0x2e11570f0,l44),(-0xa8116ed8,l46),(0xa5bee440,l17),(-0x64e7348c,l59),(-0x4a3709ca,l28),(-0xc2d94abe,l42),(0x5bdb7678,l64),(-0x9bb7a408,l20),(-0x73c3bc3c,l45),(-0x20e2f8d8,l57),(-0x875155ec,l15),(-0x94ada62,l63),(-0x1314612f,l36),(0x4c5184c,l55)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨72, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case11" = "QuadHeightCover12Case11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case11
private def zz2371:"s0943"="s0943":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case12
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l13 l15 l16 l17 l20 l21 l25 l27 l28 l29 l30 l31 l33 l35 l37 l41 l42 l43 l45 l46 l51 l56 l58 l59 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa3ec2f8f0, -0x59514ba00, -0x86056346a,0xb31a7520], ![-0x59514ba00, -0x2c58dbdb49,0x6211f5d38,0x5507c0064], ![-0x86056346a,0x6211f5d38, -0x2452531800,0x597f12600], ![0xb31a7520,0x5507c0064,0x597f12600, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x21213f636,l13),(-0x23883a08,l12),(0xb27f96f2,l17),(0x398d5a5d,l16),(0x6693842f4,l15),(0x8f7b86e6,l21),(-0x1916f6f88,l20),(-0x2cb417800,l27),(-0x86fa17fc,l28),(0x2cb417800,l29),(-0x776b5460,l25),(0x468baeb8,l31),(0x1073e2004,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x40b4d536,l43),(-0x1e6f839fa,l42),(-0x612cab702,l41),(0x3ba97818,l46),(-0x6824ffbe,l45),(0x2cb417800,l51),(-0xc917a0c0,l56),(-0x229f4f94,l59),(0xb36f6df0,l58),(-0x6ae21f48,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x6693842f4,l15),(-0x612cab702,l41),(0x21213f636,l13),(-0x1e6f839fa,l42),(0x1073e2004,l30),(-0x1916f6f88,l20),(0x8f7b86e6,l21),(-0x86fa17fc,l28),(0xb27f96f2,l17),(-0x776b5460,l25),(-0xc917a0c0,l56),(0x468baeb8,l31),(-0x6ae21f48,l62),(0xb36f6df0,l58),(-0x40b4d536,l43),(0x3ba97818,l46),(-0x6824ffbe,l45),(-0x229f4f94,l59),(0x398d5a5d,l16),(-0x23883a08,l12)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x3211014300c0000000019024802000000440900e300c000001282402cc0300000480440163010000250982402d003000000001e009200c00000941d0318c04001d8250740cc40100f208a0b4063100500000000014072008000000002408c803000000000c00b200c0000000024034803000000863b014300c00000228f4050c030000007633014300c000001e8d4050c03], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case12" = "QuadHeightCover12Case12" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case12
private def zz2372:"s0944"="s0944":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case13
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l13 l14 l15 l16 l17 l20 l22 l23 l25 l27 l28 l29 l30 l33 l35 l37 l41 l42 l43 l44 l45 l46 l51 l58 l59 l62 l63 l64 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x727cffa6e, -0x59514ba00, -0x860563578,0x1e387240c], ![-0x59514ba00, -0x2d441405d2,0x508706874,0x5c99b4226], ![-0x860563578,0x508706874, -0x2452531800,0x597f12600], ![0x1e387240c,0x5c99b4226,0x597f12600, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x190c2ec8,l14),(0x50b99b9b4,l13),(-0x7c4ac0a8,l12),(0xad18366a,l17),(0x3dc486fe,l16),(0x7453df244,l15),(-0x70252fb36,l20),(-0x59c928e,l23),(-0xd411362,l22),(-0x2cb417800,l27),(0x6cf6f56a,l28),(0x2cb417800,l29),(0xc579e6e0,l25),(0x18a0522e0,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x1da696b70,l43),(0x85f736f1,l42),(-0x77ddbc37e,l41),(-0xcc123f64,l46),(-0x104a02808,l45),(0x138ab3f48,l44),(0x2cb417800,l51),(0xbc36a0,l59),(0x371fdbfd0,l58),(0x6fe94cd,l63),(-0xcf94fb76,l62),(-0xa61ef478,l65),(-0x28cea9c4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x70252fb36,l20),(0x50b99b9b4,l13),(0x371fdbfd0,l58),(-0x77ddbc37e,l41),(-0x1da696b70,l43),(0x7453df244,l15),(0x18a0522e0,l30),(-0xa61ef478,l65),(-0xcf94fb76,l62),(-0xcc123f64,l46),(0xc579e6e0,l25),(0xad18366a,l17),(0x6cf6f56a,l28),(-0x104a02808,l45),(0x138ab3f48,l44),(0x85f736f1,l42),(-0x28cea9c4,l64),(0x3dc486fe,l16),(-0x7c4ac0a8,l12),(-0x190c2ec8,l14),(0x6fe94cd,l63),(-0x59c928e,l23),(-0xd411362,l22),(0xbc36a0,l59)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 30 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case13" = "QuadHeightCover12Case13" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 30 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case13
private def zz2373:"s0945"="s0945":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l43 l46 l5 l51 l54 l55 l56 l59 l6 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4dcd35075, -0x547044420, -0x7eb3d82c8,0x3b632d52], ![-0x547044420, -0xf1265bc2e,0x18dd21664,0x5fdcd7f28], ![-0x7eb3d82c8,0x18dd21664, -0x2256e819cf,0x549e0b020], ![0x3b632d52,0x5fdcd7f28,0x549e0b020, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-0x329a300,l6),(0x166f3b9f,l5),(-0x665f5f98,l4),(-0xbc48827,l9),(-0x159085c17,l8),(0x6c1389b6,l11),(0x3bbc2aba,l10),(0x914028f56,l14),(-0x9a12c4253,l13),(-0x23ccd800e,l17),(0x4d096212b,l16),(0x5138e1ac6,l15),(0x9a12c4253,l20),(0x111aa17c,l23),(-0x2a4393d10,l27),(0x2a4393d10,l29),(-0x914028f56,l25),(0x1d6b31eb2,l30),(0x2a4393d10,l33),(-0x3bbc2aba,l38),(-0x2a4393d10,l35),(0x159085c17,l36),(0x2a4393d10,l37),(0x665f5f98,l34),(-0x1d6b31eb2,l43),(-0x5138e1ac6,l41),(0x3118de2c,l46),(0x2a4393d10,l51),(-0x6c1389b6,l55),(-0x166f3b9f,l54),(-0x4d096212b,l56),(-0x223542f9,l59),(0xbc48827,l61),(0x329a300,l60),(-0x111aa17c,l63),(0x23ccd800e,l62),(0x223542f9,l65),(-0x3118de2c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x914028f56,l14),(-0x914028f56,l25),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(-0x9a12c4253,l13),(0x9a12c4253,l20),(0x4d096212b,l16),(-0x4d096212b,l56),(-0x23ccd800e,l17),(0x23ccd800e,l62),(0x1d6b31eb2,l30),(-0x1d6b31eb2,l43),(0x5138e1ac6,l15),(-0x5138e1ac6,l41),(-0x159085c17,l8),(0x159085c17,l36),(0x6c1389b6,l11),(-0x6c1389b6,l55),(0x3bbc2aba,l10),(-0x3bbc2aba,l38),(-0x223542f9,l59),(0x223542f9,l65),(0x3118de2c,l46),(-0x3118de2c,l64),(0x111aa17c,l23),(-0x111aa17c,l63),(-0x665f5f98,l4),(0x665f5f98,l34),(-0xbc48827,l9),(0xbc48827,l61),(0x166f3b9f,l5),(-0x166f3b9f,l54),(-0x329a300,l6),(0x329a300,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨70, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((0x2cb355c5) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case14" = "QuadHeightCover12Case14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case14
private def zz2374:"s0946"="s0946":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l21 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l43 l45 l46 l5 l51 l54 l55 l56 l57 l58 l59 l6 l60 l61 l62 l63 l64 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x4fac889f7, -0x547044420, -0x7eb3d8214,0x3dea0296], ![-0x547044420, -0xf34b97326,0x185bb8292,0x600955db8], ![-0x7eb3d8214,0x185bb8292, -0x2256e819cf,0x549e0b020], ![0x3dea0296,0x600955db8,0x549e0b020, -0x2a4393d10]]
noncomputable def hinges:Hinges:=[(-0x329a300,l6),(0x166f3b9f,l5),(-0x665f5f98,l4),(-0xbc48827,l9),(-0x159085c17,l8),(0x6c1389b6,l11),(0x3bbc2aba,l10),(0x97e924ed2,l14),(-0xe86f5f2d3,l13),(-0x2494375f4,l17),(0x57b02cd73,l16),(0x83646dd46,l15),(0x23b383e55,l21),(0xe86f5f2d3,l20),(-0x6f9a51bf,l23),(-0x2a4393d10,l27),(-0x23b383e55,l28),(0x2a4393d10,l29),(-0x97e924ed2,l25),(-0x3accaed3,l31),(0x1dde8eef8,l30),(0x2a4393d10,l33),(-0x3bbc2aba,l38),(-0x2a4393d10,l35),(0x159085c17,l36),(0x2a4393d10,l37),(0x665f5f98,l34),(-0x1dde8eef8,l43),(-0x83646dd46,l41),(0xaa921436,l46),(-0xbd766f38,l45),(0x2a4393d10,l51),(-0x6c1389b6,l55),(-0x166f3b9f,l54),(0x3accaed3,l57),(-0x57b02cd73,l56),(-0x6a14c2e4,l59),(0xbd766f38,l58),(0xbc48827,l61),(0x329a300,l60),(0x6f9a51bf,l63),(0x2494375f4,l62),(0x6a14c2e4,l65),(-0xaa921436,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(0x97e924ed2,l14),(-0x97e924ed2,l25),(-0xe86f5f2d3,l13),(0xe86f5f2d3,l20),(-0x2a4393d10,l27),(0x2a4393d10,l29),(0x2a4393d10,l33),(-0x2a4393d10,l35),(0x2a4393d10,l37),(0x2a4393d10,l51),(0x23b383e55,l21),(-0x23b383e55,l28),(0x57b02cd73,l16),(-0x57b02cd73,l56),(-0x2494375f4,l17),(0x2494375f4,l62),(0x83646dd46,l15),(-0x83646dd46,l41),(0x1dde8eef8,l30),(-0x1dde8eef8,l43),(-0x159085c17,l8),(0x159085c17,l36),(-0x6f9a51bf,l23),(0x6f9a51bf,l63),(0xaa921436,l46),(-0xaa921436,l64),(0x6c1389b6,l11),(-0x6c1389b6,l55),(-0x6a14c2e4,l59),(0x6a14c2e4,l65),(-0xbd766f38,l45),(0xbd766f38,l58),(-0x3accaed3,l31),(0x3accaed3,l57),(0x3bbc2aba,l10),(-0x3bbc2aba,l38),(-0x665f5f98,l4),(0x665f5f98,l34),(-0xbc48827,l9),(0xbc48827,l61),(0x166f3b9f,l5),(-0x166f3b9f,l54),(-0x329a300,l6),(0x329a300,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 45 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case15" = "QuadHeightCover12Case15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 45 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case15
private def zz2375:"s0947"="s0947":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case16
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l14 l15 l16 l17 l20 l25 l27 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l44 l45 l46 l51 l57 l58 l62 l63 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x58ae60e93, -0x59514ba00, -0x48f3bd1c8,0xf14319c0], ![-0x59514ba00, -0x32f8a7d463,0x645c7587c,0x538785cc6], ![-0x48f3bd1c8,0x645c7587c, -0x24458b6bed,0x597f125f4], ![0xf14319c0,0x538785cc6,0x597f125f4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(6,l4),(0x198f57bd,l8),(-0x4428e9f,l11),(-0x8851d46,l10),(0x21b7651b0,l14),(-0x14f123fdc,l12),(-0x17cb7999a,l17),(0x3de713736,l16),(0x3f544d382,l15),(0xf906fba,l20),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x1167df4d4,l25),(0x39b3228d,l31),(0x1ab8918c8,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x34a256e6,l43),(-0xaf52441d,l42),(-0x15782a20a,l41),(-0x4cb18f8,l46),(0x150480fc,l45),(-0x119adeeb8,l44),(0x2cb417800,l51),(-0x9fc0cfa7,l57),(0x1027c90f8,l58),(-0x82a7b8b4,l63),(-0x3582b1c6,l62),(-0x3da566c,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x3de713736,l16),(0x21b7651b0,l14),(0x1ab8918c8,l30),(-0x17cb7999a,l17),(-0x1167df4d4,l25),(0x3f544d382,l15),(-0x9fc0cfa7,l57),(-0x82a7b8b4,l63),(0x1027c90f8,l58),(-0xaf52441d,l42),(0x39b3228d,l31),(-0x15782a20a,l41),(-0x14f123fdc,l12),(-0x119adeeb8,l44),(-0x3582b1c6,l62),(-0x34a256e6,l43),(0x198f57bd,l8),(0x150480fc,l45),(0xf906fba,l20),(-0x8851d46,l10),(-0x4428e9f,l11),(-0x3da566c,l65),(-0x4cb18f8,l46),(6,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((0xb295f1ffe19) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case16" = "QuadHeightCover12Case16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case16
private def zz2376:"s0948"="s0948":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l14 l15 l16 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l44 l45 l46 l51 l56 l57 l58 l59 l62 l63 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x6c4f12fa0, -0x59514ba00, -0x5ea5cd9b2,0x23fd16674], ![-0x59514ba00, -0x327aafad80,0x645c7587c,0x5328eee30], ![-0x5ea5cd9b2,0x645c7587c, -0x24458b6bed,0x597f125f4], ![0x23fd16674,0x5328eee30,0x597f125f4, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(6,l4),(0x198f57bd,l8),(-0x4428e9f,l11),(-0x8851d46,l10),(0x1a30432e4,l14),(0x1431e8146,l13),(-0x2d11162ac,l12),(-0x17fc9e196,l17),(0x3d895d2c4,l16),(0x3ae4f4484,l15),(0x279e4fba,l21),(0x1d4abc1f2,l20),(0x94ada62,l23),(0xc2d94abe,l22),(-0x2cb417800,l27),(-0x6e4dcbea,l28),(0x2cb417800,l29),(-0x16fa52684,l25),(0x20e2f8d8,l31),(0x165561bb6,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x1e9309be,l43),(-0xcccdfcf2,l42),(0x161cc55de,l41),(-0x770e8634,l46),(0x252b015fa,l45),(-0x2f8851d8c,l44),(0x2cb417800,l51),(-0xeb8331b2,l57),(0x18d35fbb8,l56),(-0x82032bc2,l59),(0x1662e15be,l58),(-0xe993b890,l63),(-0x157d32b22,l62),(0x2633e0c6,l65),(0x70666e5c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x3d895d2c4,l16),(0x1a30432e4,l14),(-0x17fc9e196,l17),(-0xeb8331b2,l57),(-0x16fa52684,l25),(-0xe993b890,l63),(0x165561bb6,l30),(-0x157d32b22,l62),(0x252b015fa,l45),(0x1d4abc1f2,l20),(0x3ae4f4484,l15),(0x18d35fbb8,l56),(-0x82032bc2,l59),(0x1662e15be,l58),(-0x2f8851d8c,l44),(0x1431e8146,l13),(-0x2d11162ac,l12),(-0x6e4dcbea,l28),(-0x770e8634,l46),(-0xcccdfcf2,l42),(0x70666e5c,l64),(0xc2d94abe,l22),(0x161cc55de,l41),(0x279e4fba,l21),(0x2633e0c6,l65),(0x20e2f8d8,l31),(-0x1e9309be,l43),(0x94ada62,l23),(0x198f57bd,l8),(-0x8851d46,l10),(-0x4428e9f,l11),(6,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((((((((0x79cbd546bd8523402d5731d206d7e74632f3cd0d6e4a90a80e0a9ef7b74f1861d04a7b1a000a5cb10127042300840f56b9f5a0a89d6077e371902c0413868222402906c7794072cb0fcd8688211b215ce8e0006ce6308ce004601099e002255101a079d98daaba899c0022550fea274231a4fda081610a513298224040fc3bd4080e4040f569e2200a07ded5e190004c0200001b420006746268011e1a300071a6a3189c29b1e6497fe8defdc7181120b008a11248296ac4913478c13a14bcc41222803dc62e63e70a0424e8f785e44001501000140446a0200020224680b16c01f9a33f96171bc4454b15014966a234c1634fc277008557dfcc80d1652058012c5ea2e773f98cf7a676800e2e824571da66199d5c63538e6e26963b11e9a72bb2a9cf2643491e738702b605e4f9222bdca7935649107f25fa95d18583fd1b52325beb47e4fcb90202a4973043288608cc2446412231050001d81c30ae21247054861671ca2b9aa363ca03ee31441071a5444c55497d38d2026c18117d8860e12172c00bc23c027b3612cfe8920006bf83538f303400168160430044600222f011170088b4044580200027024561bd2cc6958bed73f491e74519d2cb90b285c1ce99eb56240e5543187b5f4e2400a8f53ba2313c5f4b4da2a800c26dbee917deabfc5b94775af0fc0b2463e79a741ee7d4378af457848cc1405f2ceeb912d22400cf1e510e00150283a31bc57e002c6a268aaec3867140890be4a79811a04604540a2290511402889c1444c02225010fa00800106885902f41a2cf581cb4aa47365452e7fec486dad904678fe4bea595353d5aca9a9eae4beebe6010a16b48f6e808877b5c424e1a382216b48f6e848669059050650248040002a3afe87c52f9d7c54bb5cd1f5e6df6d4f23aa4976f2b09c46ad2378b2e2c15e3f3ef241135fd0270e89370a2ff4a4b8297479a850db146f97f4000f708a812c53c9629c4314d09c85c72bf0000000064d97b219c7d0863040160111449641441a1900880840800a205cc00401b70822f5b92ace3265c208bd6e4ab38c96ed0e3c77ea79dab4bb438f1dfa9e76ad421216b48f6e808877b5c424e1a382216b48f6e848469059051068610248040000a8ffc8b85b9f48ebaa4138bcf951a76bdf02f317e6b89351a4b6c816b23065a36656cc24687f24041f1862851b83ddd6d7c3d4067d448e61c46150003e121a86a224350002aa11a22dd8cced04ac55c48d6711c4104c40db9946aa42430a2ba1ffc4c05820ac19df3183809209db80d4200331ee333100002d3c09ce4015302c886a9b28062db9df3797e7442801c000116122311dc208bd6e4ab38c9970822f5b92ace325bb438f1dfa9e76ad2ed0e3c77ea79dab5084d068b3d6072d2a91cd9514b9ffb121b6b6411b1004660e50e48e3841020028ace132b6f025cbbdefec2c05) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 39 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case17" = "QuadHeightCover12Case17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 39 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case17
private def zz2377:"s0949"="s0949":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case18
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l22 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l51 l55 l56 l58 l62 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xa8e021078, -0x585b03a48, -0x8493f74d6,0x829bcaa4], ![-0x585b03a48, -0x2646ce274d,0x52150b828,0x52c6fd51a], ![-0x8493f74d6,0x52150b828, -0x23ee45e00a,0x5888ca648], ![0x829bcaa4,0x52c6fd51a,0x5888ca648, -0x2c38f3824]]
noncomputable def hinges:Hinges:=[(-0x3ed72bb8,l4),(-0x7dae63ca,l8),(0x29e4c9de,l11),(0x14f26808,l10),(0xef9749f6,l14),(0x2713f6ae5,l13),(0x6ae21f48,l17),(0xc917a0c0,l16),(0x612cab702,l15),(-0x2713f6ae5,l20),(0x1e6f839fa,l22),(-0x2c38f3824,l27),(0x2c38f3824,l29),(-0xef9749f6,l25),(0x40b4d536,l30),(0x2c38f3824,l33),(-0x14f26808,l38),(-0x2c38f3824,l35),(0x7dae63ca,l36),(0x2c38f3824,l37),(0x3ed72bb8,l34),(-0x40b4d536,l43),(-0x1e6f839fa,l42),(-0x612cab702,l41),(-0x25d7ae18,l46),(-0x357e3874,l45),(0x2c38f3824,l51),(-0x29e4c9de,l55),(-0xc917a0c0,l56),(0x357e3874,l58),(-0x6ae21f48,l62),(0x25d7ae18,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c38f3824,l27),(0x2c38f3824,l29),(0x2c38f3824,l33),(-0x2c38f3824,l35),(0x2c38f3824,l37),(0x2c38f3824,l51),(0x612cab702,l15),(-0x612cab702,l41),(0x2713f6ae5,l13),(-0x2713f6ae5,l20),(0x1e6f839fa,l22),(-0x1e6f839fa,l42),(0xef9749f6,l14),(-0xef9749f6,l25),(0xc917a0c0,l16),(-0xc917a0c0,l56),(0x6ae21f48,l17),(-0x6ae21f48,l62),(-0x7dae63ca,l8),(0x7dae63ca,l36),(0x29e4c9de,l11),(-0x29e4c9de,l55),(0x40b4d536,l30),(-0x40b4d536,l43),(-0x25d7ae18,l46),(0x25d7ae18,l64),(-0x357e3874,l45),(0x357e3874,l58),(0x14f26808,l10),(-0x14f26808,l38),(-0x3ed72bb8,l4),(0x3ed72bb8,l34)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case18" = "QuadHeightCover12Case18" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case18
private def zz2378:"s094a"="s094a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover12Case19
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l17 l20 l21 l22 l23 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l45 l46 l51 l55 l58 l59 l62 l63 l64 l65 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc0d219b4d, -0x57f0ff7c8, -0x83f4f1224,0x8a095442], ![-0x57f0ff7c8, -0x22b80c8645,0x35af795ae,0x606a1fb5c], ![-0x83f4f1224,0x35af795ae, -0x23c3342fca,0x581ec63c8], ![0x8a095442,0x606a1fb5c,0x581ec63c8, -0x2c03f16e4]]
noncomputable def hinges:Hinges:=[(-0x3ed72bb8,l4),(-0x7dae63ca,l8),(0x29e4c9de,l11),(0x14f26808,l10),(0x33eb5bcec,l14),(-0x1d4382a97,l13),(0xcf94fb76,l17),(0x77ddbc37e,l15),(0xab7cea20,l21),(0x1d4382a97,l20),(-0x6fe94cd,l23),(-0x85f736f1,l22),(-0x2c03f16e4,l27),(-0xab7cea20,l28),(0x2c03f16e4,l29),(-0x33eb5bcec,l25),(0x1da696b70,l30),(0x2c03f16e4,l33),(-0x14f26808,l38),(-0x2c03f16e4,l35),(0x7dae63ca,l36),(0x2c03f16e4,l37),(0x3ed72bb8,l34),(-0x1da696b70,l43),(0x85f736f1,l42),(-0x77ddbc37e,l41),(0x33e48b0c,l46),(-0xb0c16e6a,l45),(0x2c03f16e4,l51),(-0x29e4c9de,l55),(-0x1fd162f9,l59),(0xb0c16e6a,l58),(0x6fe94cd,l63),(-0xcf94fb76,l62),(0x1fd162f9,l65),(-0x33e48b0c,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2c03f16e4,l27),(0x2c03f16e4,l29),(0x2c03f16e4,l33),(-0x2c03f16e4,l35),(0x2c03f16e4,l37),(0x2c03f16e4,l51),(0x33eb5bcec,l14),(-0x33eb5bcec,l25),(0x77ddbc37e,l15),(-0x77ddbc37e,l41),(0x1da696b70,l30),(-0x1da696b70,l43),(0xab7cea20,l21),(-0xab7cea20,l28),(-0x1d4382a97,l13),(0x1d4382a97,l20),(0xcf94fb76,l17),(-0xcf94fb76,l62),(-0xb0c16e6a,l45),(0xb0c16e6a,l58),(-0x85f736f1,l22),(0x85f736f1,l42),(-0x7dae63ca,l8),(0x7dae63ca,l36),(0x29e4c9de,l11),(-0x29e4c9de,l55),(0x33e48b0c,l46),(-0x33e48b0c,l64),(-0x1fd162f9,l59),(0x1fd162f9,l65),(0x14f26808,l10),(-0x14f26808,l38),(-0x3ed72bb8,l4),(0x3ed72bb8,l34),(-0x6fe94cd,l23),(0x6fe94cd,l63)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,0x324760440684010000260d04c075003b0c908134092640180000003113014c0200000948838094008000000230e038c02000000000840e200800049218680a5003000130861a02a400c000020c2202d0c04000000821202c300c00001841201e0c04000128861a02a400c000026210d015002000000000740620080000020848030c03000000861201c300c0000018828070c03000000008870330040000000f07028c02000000024140d3008000000000d0188020000000241c0a3008000000000502480200000005448063008000000002d01c802000000361300d300c0000000035018802000000000d40e2008000000003901c802000000000c4072008000001186c034c03000000000190320040000000025038802000000004d00a200c000000002701880200208731880bc4010005210c3201e90040000007219027300c0c608c0ac03c900502844082602524015a41410f701c810060000000582c063008000000002102480200000004c180e30080000000011038802000104460a029400c00044118280a900300000844c180940080000221306019002000108460a02a400c0000000022014802000000004830330041011c2118094900580c70823407a040180000002515024c02002585610409a4011c318204d01e810067c060447c061c40180000001b0e018c020000000006409200800000000090388020000000241806300800019088300c9003,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,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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 37 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover12Case19" = "QuadHeightCover12Case19" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 37 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover12Case19
private def zz2379:"s094b"="s094b":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover12Rows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x102d200779ae58001fde384aa15d20003dceb9480088fea92b21cd20003dceb94800cb1e185b201d20003dceb94800cd4d1b492520003dceb948010e4a5e2a2079200050c1f9200779ae58001aca9c2ea1692002fd7c280038ac4be02920001eeb5ca8001bbe4d2ba1c920009c4da80018fbdba01920001eeb5ca8004c5e5a4be120001eeb5ca8008b292f19207c2005faf84801db8b4d4f617c20001eeb5ca8048b9aff6c21ec20001eeb5ca8020aabcb3b2420001eeb5ca8012f7e5aece07820007b9d6a80292b2878a1782002fd7c28007c0c6e4a216820003dceb948014d6f3c49202000ef3acd064abe18614]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11cb20001eeb5ca801f98a8ea01b2003bcdb2c0018ec485aa320003dceb948010e892e39207e2005faf84800ac684a5f217e20003dceb948021c9cbc6de1ee2000ef3acd03b8fd79e02e20003dceb948001fb88c0d215e2000ef3acd037b8e7ea1ce20001eeb5ca8012d9b2bade01e20009c4da80018da6ce8e620001bede880285a4aa07a20001eeb5ca801a8af5acae17a2003bcdb2c002f1fb85a602a20003dceb948002eae4d6d61ca20003dceb94801dfadbeffe01a20003dceb948037f5da9cb6220003dceb9480059cb7afbe07d20003dceb94800dfa80a0de1fd20001eeb5ca8003e4f4dbf21ed20001eeb5ca8063f5e1ea14]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x101a60003dceb948009d1d08eee260001eeb5ca8007819bbb9607d60003dceb94802ea8d092e217d60003dceb948011e4b184a21ed60003dceb948019d0aba4de560003dceb94802581f9e3ce0796001389b4800191e580961e9600779ae58004dcbff1a61600779ae5800986b7f2a207f20003dceb94800db2b8c7821ff20003dceb9480048197d7d21ef2003bcdb2c0588fe29602f20001eeb5ca8003ebb1e89215f20001eeb5ca80049be1b4c61cf20003dceb94800b8abbb6b201f20001eeb5ca8005f3f5d39e72005faf848003aeb6fa9e07b20001eeb5ca8006f5e8cea21fb20017ebe1800acde2fa02b20005faf8a005949b8214]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x176005faf848002d7cadca61fb60003dceb94800b85c5a4921eb6001389b4802df585d602b60001eeb5ca8017d889d615b60001eeb5ca80049bf497fe14b600779ae580028bcfe7f601b6003bcdb2c03bdaeac6360001eeb5ca8008968aba9a07e600779ae58003aeb6999a17e60001eeb5ca8007b0c7b2c21ee60003dceb9480099eee8a8a06e60003dceb948009a6d2838615e6005faf848076df9dc214e60017ebe18014e1c9de01e6000ef3acd041a784da660003dceb948009dbe1d78607a6005faf848001ebd0ca9e17a60001eeb5ca802be3cae606a60017ebe18014a7eac614a60003dceb948004dd95e29a14]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x101fa0003dceb94800bbecaa6c27a0003dceb948010dd84f2ea07ba00779ae580049bbb94b602ba0003dceb948003bee1bffa1cba0003dceb948029c0cabe01ba0003dceb948008d9fbf4ea3a0003dceb948010dd84f2ea07ea0003dceb94800197f4c99dd217ea0003dceb9480019afabac3e21eea0003dceb948047b3c1f9aa6a003bcdb2c004e3e7aad207aa0003e8a4800194dea58e17aa0003dceb948066dbcbade22a001de6d9a001cba5b1aa03f60001eeb5ca80328c97b21ff60001eeb5ca800dba91939e02f60001eeb5ca8052eea08e1df6005faf848001aeabfbe214f60003dceb948025b0eed29205f6003bcdb2c062debcee14]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x107c30001eeb5ca8005af92ca8a17c30003dceb948008e3b4bab616c30003dceb94800c81ef81c604c30003dceb948004b2c2b9e207830001eeb5ca800384f3aefa1783000ef3acd028f3809a048300779ae5802ecbbec207fe002fd7c2800598c8d8fe17fe0003dceb948013c195e3ba1efe000ef3acd055df9da27e005faf84800796a587de07be0003dceb94800efcdd93f61fbe0003dceb94801a86d3e3ee3e005faf848006ebadc2f607fa0003dceb94800d8c88b2f21ffa0003dceb948006ddd3abc21efa0003dceb948002bcf99fba02fa0003dceb948007c1b6a0f215fa0003dceb948006f2b797ea1cfa0003dceb948009e1e581a614]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x107a300779ae58002a8f2bede17a30009c4da8036ceb3b21ea30001eeb5ca8004be94ce9a1ca3005faf8480018ae7929a01a3005faf84803f84e1c223000ef3acd00589df9603d30003dceb948003c1cceeae17d3001389b480269aacfa16d30003dceb948002b1cfc1c606d30003dceb948007f683b4c21dd3005faf848001d082c4da14d30003dceb94800cb1eae3fe05d30003dceb948003dc9d869a530003f402179300779ae58001aca9c2ea1e93002fd7c280038ac4be06930001eeb5ca8001bbe4d2ba14930009c4da80018fbdba05930001eeb5ca8009cb8cbe130003f40214]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x116f30001eeb5ca800393ceb4c606f30017ebe1803191e4821df30001eeb5ca80049be1b4c614f30003dceb94800b8abbb6b205f30001eeb5ca8001b7dbbb9e730003dceb948001f491fa03b30001eeb5ca8002b9ceb6a217b30017ebe1800acde2fa06b30005faf8a005949b8214b30001eeb5ca801f98a8ea01b3003bcdb2c042c0d6330003f40207e30009c4da800ce281de17e30001eeb5ca8004ebffb0f616e3002fd7c2806ea1da02e3005faf84802fc3c1f21de30003dceb948006f8e9a28a1ce30003dceb948001fedfb2b601e300779ae5804fc38caa63000bf5f0c004f19ed214]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x102e70003dceb948009a6d2838a1de70001eeb5ca80038ba4e99e1ce70001eeb5ca800ae2a2b605e700779ae580029dc6c9b26700779ae58001dfd1dcbe03a7005faf848006dfda9e1fa70001eeb5ca802be3cae602a70017ebe18014a7eac61ca70003dceb948004dd95e29a05a70003dceb9480599bdeee2700779ae58055fcb4d207d700779ae58067fdc0ba17d70003dceb948004dfc4f7f616d700779ae58001fea2c19e04d700779ae568f5ee17970003dceb948004e5f1f0fa16970004e2ad8001cdbe9e04970003dceb948001cd89efb203f30001eeb5ca8002d091b7b617f30001eeb5ca80019aad948a14]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x104eb00779ae5800193a1c48607ab0001eeb5ca8001c4b1de9616ab0003dceb948004a3aa8bf22b0003f40207f70003dceb948001a39da9e217f7003bcdb2c002a5ffcffe1ef70017ebe18042b9b28602f70001eeb5ca8001d0b98ac615f7001de6d9a02f86ea1cf700779ae58001ade086d605f7005faf848001a3a0f38a770003dceb948006e9b7f6ca17b7003bcdb2c03be7f3ea1db7002fd7c2801bd9a9c21cb7005faf848037c5cce201b70001eeb5ca8077a9bc8637005faf84800fa2e7aa03e700779ae5800190a98d9a1fe70001eeb5ca8007b0c7b2c216e70003dceb9480099eee8a8a14]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x104ff005faf848042edaebe03bf0004e2ad800383c0f617bf00779ae58047a9bdbe04bf0003dceb948077efe5c203fb0003dceb948004f39cf1ae17fb0003dceb948005bcd4c0c216fb003bcdb2c02cffe8de06fb00779ae58001e7f0caf21dfb0003dceb94800784ce988214fb0003dceb948009e8b8e2a605fb0003dceb948002c695f6c27b0003dceb948001f491fa03bb00779ae58001fdae88b606bb0003dceb948003bee1bffa14bb0003dceb948029c0cabe01bb0003dceb94801eb8bb963b0003dceb948001f491fa07eb001389b48036cac9a617eb003bcdb2c07ea7bd9a16eb00779ae58003a8a9c2f214]
def rowsChunk11:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11fe00003dceb948008f2b98dfe16e0000bf5f0c01cbb83c606e00003dceb9480029ccea3c215e000779ae580021ce00003dceb948002600001fa0217d00003dceb948065e181ca1ed000779ae580138a98a6500001fa0203c00001eeb5ca800280b7a9c21fc00001eeb5ca8007e08cbdf216c00003dceb94800ed995baae06c0005faf8480429ad6ce1dc0001de6d9a00996ebfa14c0003bcdb2c00add9a8e05c00003dceb948011e1f296400001fa0207ff002fd7c28029c1e8ce17ff002fd7c2805ea2c1f616ff0003dceb948003fd8b8bf214]
def rowsChunk12:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x103d40009c4da8003bcc2ca1fd4005faf8480018af4e79216d40003dceb948005b6c883e606d40001eeb5ca8056e980c215d40001eeb5ca8002540001fa0207c4003bcdb2c01617c400779ae58001cfe21ec40001eeb5ca800bc1da02c40003dceb94805b939a1dc4001de6d9a02eb0ea14c4005faf848012b2c1f605c4001de6d9a007fffae2440003dceb94802d86c6b607f0005faf84800dd0f28e17f00003dceb94800188a8f4fe1ef00003dceb94804494babe02f00003dceb948002700001fa0203e00003dceb9480029ccea3ca14]
def rowsChunk13:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x106e800779ae580449fe5a21de80003dceb948001bca4a0ce14e80003dceb948077d3a4ea05e80003dceb9419a6c6680001fa0207d80003dceb948001839eaa8617d80001eeb5ca8001839ea9fa1ed80003dceb948001839ea9f602d80003dceb948002580001fa0203c8005faf8480399b91921fc8001de6d9a047c1f7e216c80001eeb5ca8004bc8fe0d606c80001eeb5ca80018f84ae8615c80003dceb948070da1cc80001eeb5ca801dd201c80003dceb94800bee480001fa02740001fa02640001fa0214]
def rowsChunk14:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1058100779ae58005d3bdd9f2010003dceb948003e8a2da03fc00779ae58029f2b4821ffc002fd7c2804383eb9616fc0001eeb5ca8002cf9393de06fc00779ae58029f2b1fa7c0001fa026c0001fa025c0001fa024c0001fa0207f80003dceb94803fdb9efe17f8001389b404a5c21ef80061d48005f09a06f80003dceb948016cda3c615f80003dceb94800c8faae61cf80001eeb5ca80029bf5d6780001fa0203e8001389b480138edfca1fe80003dceb94800eb096a5ba16e80001eeb5ca8006e0ce93b614]
def rowsChunk15:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1610001eeb5ca8001f491d203a100779ae58006d7898cb216a10003dceb9480079b998a9a02a10003dceb9480158e86b7d614a10001eeb5ca8014d196fa9205a1005faf848004e192f0d2210001fa0203c100779ae5800993f6fff61fc10017ebe1805aae928a1ec10017ebe18002f1f3a602c100779ae5800aeeffba9e1dc1002fd7c28026c3ecce14c10001eeb5ca80139db5dbc605c10003dceb94801b988d86f2410003dceb948003e8a3a20381005faf848008829bcbca1f81005faf848003d8d5b1ae02810003dceb948028a7dea6c615810003dceb94800aabb9e28a14810003dceb94801895e781e214]
def rowsChunk16:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x103d5001de6d9a001c581a4ae1fd5002fd7c2800788e8fe02d50001eeb5ca8013b1d3fbb61dd50001eeb5ca802cf2a58e14d5002fd7c28020f8d6a201d50003dceb94800ae8e0ecea550005faf8a0068d9e03950001eeb5ca80089cfca0821695003bcdb2c0018d8bd7ae02950001eeb5ca80118ca5c0fe14950003dceb948002b2f8f8be01950003dceb94800b93feadf2150001eeb5ca8001f4919603e10003dceb948016aad8b7b617e10009c4da8014e4aafa16e1003bcdb2c041e2fcb602e10001eeb5ca8009e8b4ec9615e10001eeb5ca804aabb4e214e100779ae5800aa0e3f0f605e10003dceb948017fea7c39614]
def rowsChunk17:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10289001389b4807acbfbba1d890001eeb5ca8070c8898e14890001eeb5ca80169d9499fa05890003dceb948019e4dbf28a090001fa0203f50003dceb948001f4cc93be17f50001eeb5ca8004a292d3a616f50001eeb5ca800edc8ce3b206f50003dceb948007afbb8eca15f5001de6d9a001e9c9ee921cf50002b196c00acbe88a01f50003dceb948015beccd6a2750003dceb94800d93dfb49a03b5005faf8480549bbcae17b50003dceb948007a78685be16b5005faf848003ff9af2f602b50061d48001bbcd8e15b500779ae580048acfb8da01b50003dceb948003ac8ae3c6350004e2ad801a8c87ea14]
def rowsChunk18:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11de90003dceb94800df9d2c6fe14e9005faf84800bd8c5e1ba05e90001eeb5ca8012a586f5fa690001eeb5ca8001f491da03a90003dceb94801db5ccbdb202a9001389b480018acfa19215a900779ae58044b5a1be14a90003dceb948033ade5d6f205a90003dceb948023e6b6808e2900779ae5807a88de03c90001eeb5ca800ad9d7dfc217c90001eeb5ca8007c2fceb8a1ec90001eeb5ca8002d593effe02c90017ebe180019697e2e215c90003dceb948002dec4f8d614c90003dceb948026858e909605c900779ae58005e3ce82a649002fd7c28030e9f2038900779ae58006b4d7e89a17890001eeb5ca8002f8e794d214]
def rowsChunk19:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x117bd0001eeb5ca800a92cafbfe02bd0003dceb948020b28ea4d614bd0007b9d6a810e0fe8201bd0017ebe1802ae0b6aa3d0003dceb948003e8a2b217dd00779ae58003ececf9fa16dd0003dceb948016b7b2e4d606dd0001eeb5ca8001b4b69cd215dd0003dceb948013879dddee01dd000ef3acd029b7eea25d0001eeb5ca8007e0acd4c2179d0001eeb5ca80038cb1cff6169d003bcdb2c002e9d58eba029d0003dceb948007c3b3d4da159d0003dceb94800b8098b0e6019d0001eeb5ca80068edeeef21d0001eeb5ca80089aa8ac8e03e90017ebe18001bf94fea61ee90003dceb948007ace5bba602e90003dceb94802be68993c214]
def rowsChunk20:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10894007d0801010100010201000893002fd7c28042cd9a01020101010101020892001de6d9a001c6f601010100010201000892005faf848002c9d0c5b6030305faf8a00788d6088d0003dceb94800aa1bffa088b0003e8a48009d1ba08880004e2ad8042ceda08870003dceb94802784ccd5aa08840003dceb94801cdbe0f7a6088300779ae58009e3a2c4c2088000779ae580079293888603fd003bcdb2c003dab4daee1ffd005faf8480018ef2e3fe02fd0003dceb948027faa582aa1dfd0003dceb94806ff4d39a01fd0003dceb94800cfcd3f6f67d00779ae5807a88b603bd0003dceb94800485d3aab613]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10 ++ rowsChunk11 ++ rowsChunk12 ++ rowsChunk13 ++ rowsChunk14 ++ rowsChunk15 ++ rowsChunk16 ++ rowsChunk17 ++ rowsChunk18 ++ rowsChunk19 ++ rowsChunk20
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadHeightCover12Case0.base QuadHeightCover12Case0.hinges QuadHeightCover12Case0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case0.base QuadHeightCover12Case0.hinges QuadHeightCover12Case0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadHeightCover12Case1.base QuadHeightCover12Case1.hinges QuadHeightCover12Case1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
private def zz1670:"s0686"="s0686":=by decide+kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case1.base QuadHeightCover12Case1.hinges QuadHeightCover12Case1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r23,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadHeightCover12Case2.base QuadHeightCover12Case2.hinges QuadHeightCover12Case2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case2.base QuadHeightCover12Case2.hinges QuadHeightCover12Case2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadHeightCover12Case3.base QuadHeightCover12Case3.hinges QuadHeightCover12Case3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
private def zz1671:"s0687"="s0687":=by decide+kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case3.base QuadHeightCover12Case3.hinges QuadHeightCover12Case3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadHeightCover12Case4.base QuadHeightCover12Case4.hinges QuadHeightCover12Case4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case4.base QuadHeightCover12Case4.hinges QuadHeightCover12Case4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadHeightCover12Case5.base QuadHeightCover12Case5.hinges QuadHeightCover12Case5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
private def zz1672:"s0688"="s0688":=by decide+kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case5.base QuadHeightCover12Case5.hinges QuadHeightCover12Case5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r81,RewriteAtoms.r32,RewriteAtoms.r77,RewriteAtoms.r16,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadHeightCover12Case6.base QuadHeightCover12Case6.hinges QuadHeightCover12Case6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case6.base QuadHeightCover12Case6.hinges QuadHeightCover12Case6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r81,RewriteAtoms.r82,RewriteAtoms.r32,RewriteAtoms.r61,RewriteAtoms.r77,RewriteAtoms.r16,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadHeightCover12Case7.base QuadHeightCover12Case7.hinges QuadHeightCover12Case7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
private def zz1673:"s0689"="s0689":=by decide+kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case7.base QuadHeightCover12Case7.hinges QuadHeightCover12Case7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadHeightCover12Case8.base QuadHeightCover12Case8.hinges QuadHeightCover12Case8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case8.base QuadHeightCover12Case8.hinges QuadHeightCover12Case8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadHeightCover12Case9.base QuadHeightCover12Case9.hinges QuadHeightCover12Case9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
private def zz1674:"s068a"="s068a":=by decide+kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case9.base QuadHeightCover12Case9.hinges QuadHeightCover12Case9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r81,RewriteAtoms.r32,RewriteAtoms.r77,RewriteAtoms.r16,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadHeightCover12Case10.base QuadHeightCover12Case10.hinges QuadHeightCover12Case10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case10.base QuadHeightCover12Case10.hinges QuadHeightCover12Case10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r81,RewriteAtoms.r82,RewriteAtoms.r32,RewriteAtoms.r61,RewriteAtoms.r77,RewriteAtoms.r16,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadHeightCover12Case11.base QuadHeightCover12Case11.hinges QuadHeightCover12Case11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
private def zz1675:"s068b"="s068b":=by decide+kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case11.base QuadHeightCover12Case11.hinges QuadHeightCover12Case11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r68,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadHeightCover12Case12.base QuadHeightCover12Case12.hinges QuadHeightCover12Case12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case12.base QuadHeightCover12Case12.hinges QuadHeightCover12Case12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadHeightCover12Case13.base QuadHeightCover12Case13.hinges QuadHeightCover12Case13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
private def zz1676:"s068c"="s068c":=by decide+kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case13.base QuadHeightCover12Case13.hinges QuadHeightCover12Case13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadHeightCover12Case14.base QuadHeightCover12Case14.hinges QuadHeightCover12Case14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case14.base QuadHeightCover12Case14.hinges QuadHeightCover12Case14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadHeightCover12Case15.base QuadHeightCover12Case15.hinges QuadHeightCover12Case15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
private def zz1677:"s068d"="s068d":=by decide+kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case15.base QuadHeightCover12Case15.hinges QuadHeightCover12Case15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadHeightCover12Case16.base QuadHeightCover12Case16.hinges QuadHeightCover12Case16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case16.base QuadHeightCover12Case16.hinges QuadHeightCover12Case16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r80,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadHeightCover12Case17.base QuadHeightCover12Case17.hinges QuadHeightCover12Case17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
private def zz1678:"s068e"="s068e":=by decide+kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case17.base QuadHeightCover12Case17.hinges QuadHeightCover12Case17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadHeightCover12Case18.base QuadHeightCover12Case18.hinges QuadHeightCover12Case18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case18.base QuadHeightCover12Case18.hinges QuadHeightCover12Case18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r77,RewriteAtoms.r68,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadHeightCover12Case19.base QuadHeightCover12Case19.hinges QuadHeightCover12Case19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
private def zz1679:"s068f"="s068f":=by decide+kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover12Case19.base QuadHeightCover12Case19.hinges QuadHeightCover12Case19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover12Case19.nonnegative x hx
def pair20:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair20Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_20_base LocalPairs.compact_height12_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalPairs.height12_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_20_base LocalPairs.compact_height12_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalPairs.height12_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair21Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_21_base LocalPairs.compact_height12_pair_21_hinges
private def zz1680:"s0690"="s0690":=by decide+kernel
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalPairs.height12_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_21_base LocalPairs.compact_height12_pair_21_hinges x
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalPairs.height12_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 1 false
def pair22Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair22Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_22_base LocalPairs.compact_height12_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
private def zz1681:"s0691"="s0691":=by decide+kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalPairs.height12_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_22_base LocalPairs.compact_height12_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalPairs.height12_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair23Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_23_base LocalPairs.compact_height12_pair_23_hinges
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalPairs.height12_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_23_base LocalPairs.compact_height12_pair_23_hinges x
private def zz1682:"s0692"="s0692":=by decide+kernel
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalPairs.height12_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair24Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_24_base LocalPairs.compact_height12_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalPairs.height12_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_24_base LocalPairs.compact_height12_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalPairs.height12_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair25Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_25_base LocalPairs.compact_height12_pair_25_hinges
private def zz1683:"s0693"="s0693":=by decide+kernel
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalPairs.height12_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_25_base LocalPairs.compact_height12_pair_25_hinges x
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalPairs.height12_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair26Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_26_base LocalPairs.compact_height12_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
private def zz1684:"s0694"="s0694":=by decide+kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalPairs.height12_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_26_base LocalPairs.compact_height12_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalPairs.height12_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair27Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_27_base LocalPairs.compact_height12_pair_27_hinges
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalPairs.height12_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_27_base LocalPairs.compact_height12_pair_27_hinges x
private def zz1685:"s0695"="s0695":=by decide+kernel
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalPairs.height12_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_28_base LocalPairs.compact_height12_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalPairs.height12_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_28_base LocalPairs.compact_height12_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalPairs.height12_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_29_base LocalPairs.compact_height12_pair_29_hinges
private def zz1686:"s0696"="s0696":=by decide+kernel
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalPairs.height12_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_29_base LocalPairs.compact_height12_pair_29_hinges x
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalPairs.height12_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair30Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_30_base LocalPairs.compact_height12_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
private def zz1687:"s0697"="s0697":=by decide+kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalPairs.height12_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_30_base LocalPairs.compact_height12_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalPairs.height12_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair31Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_31_base LocalPairs.compact_height12_pair_31_hinges
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalPairs.height12_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_31_base LocalPairs.compact_height12_pair_31_hinges x
private def zz1688:"s0698"="s0698":=by decide+kernel
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalPairs.height12_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_32_base LocalPairs.compact_height12_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalPairs.height12_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_32_base LocalPairs.compact_height12_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalPairs.height12_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_33_base LocalPairs.compact_height12_pair_33_hinges
private def zz1689:"s0699"="s0699":=by decide+kernel
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalPairs.height12_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_33_base LocalPairs.compact_height12_pair_33_hinges x
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalPairs.height12_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair34Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_34_base LocalPairs.compact_height12_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
private def zz1690:"s069a"="s069a":=by decide+kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalPairs.height12_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_34_base LocalPairs.compact_height12_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalPairs.height12_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair35Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_35_base LocalPairs.compact_height12_pair_35_hinges
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalPairs.height12_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_35_base LocalPairs.compact_height12_pair_35_hinges x
private def zz1691:"s069b"="s069b":=by decide+kernel
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalPairs.height12_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair36Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_36_base LocalPairs.compact_height12_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalPairs.height12_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_36_base LocalPairs.compact_height12_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalPairs.height12_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair37Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_37_base LocalPairs.compact_height12_pair_37_hinges
private def zz1692:"s069c"="s069c":=by decide+kernel
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalPairs.height12_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_37_base LocalPairs.compact_height12_pair_37_hinges x
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalPairs.height12_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_38_base LocalPairs.compact_height12_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
private def zz1693:"s069d"="s069d":=by decide+kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalPairs.height12_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_38_base LocalPairs.compact_height12_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalPairs.height12_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height12_pair_39_base LocalPairs.compact_height12_pair_39_hinges
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalPairs.height12_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height12_pair_39_base LocalPairs.compact_height12_pair_39_hinges x
private def zz1694:"s069e"="s069e":=by decide+kernel
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalPairs.height12_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.HeightCover12Rows
private def zz2380:"s094c"="s094c":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover12Cyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack HeightCover12Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightCover12Rows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse HeightCover12Rows.rows p q same x]
    exact HeightCover12Rows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
private def zz1695:"s069f"="s069f":=by decide+kernel
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) HeightCover12Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightCover12Rows.pair_nonneg p q h same x hx
  · rw [← HeightFullPhaseRows.pairSlack_swap ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) HeightCover12Rows.rows p q same x]
    exact HeightCover12Rows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible HeightCover12Rows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials HeightCover12Rows.rows
theorem remaining_rows_count:remainingRows.length = 12:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    ((0x5f0eef / 0xee6b280):ℝ) * mass g ^ 2 + (8 / 5:ℝ) * energy g ≤
      weightedAggregate ((6 / 5)) h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack HeightCover12Rows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (HeightFullPhaseRows.pairSlack ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) HeightCover12Rows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [HeightFullPhaseRows.local_slacks_sum ((6 / 5)) ((0x5f0eef / 0x3b9aca00)) (2 / 5) h4 h3 g hg,stripPotentials_sound ((6 / 5)) h4 h3 h5 g HeightCover12Rows.rows rows_admissible] at hs
  norm_num at hs
  change ((0x5f0eef / 0xee6b280):ℝ) * mass g ^ 2 + (8 / 5:ℝ) * energy g ≤
    weightedAggregate ((6 / 5)) h4 h3 g (stripPotentials HeightCover12Rows.rows) + 4 * deficit g
  linarith
end Green24Proof.HeightCover12Cyclic
private def zz2381:"s094d"="s094d":=by decide+kernel
end 
section 
namespace Green24Proof.PhaseWeightedVectors
open FullPhaseRows (Phase)
open PhaseMassRows
private def zz1696:"s06a0"="s06a0":=by decide+kernel
theorem massWeighted_vector {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ)
    (a c b d:ℚ) :
    massWeighted h4 g (fun p => ((![a,c,b,d]:Fin 4 → ℚ) p:ℝ)) =
      (a:ℝ) * phaseTotal h4 g 0 + (c:ℝ) * phaseTotal h4 g 1 +
      (b:ℝ) * phaseTotal h4 g 2 + (d:ℝ) * phaseTotal h4 g 3:=by
  rw [massWeighted_phaseTotal,sum_phase]
  rfl
theorem odd_massSquare {q:ℕ} [NeZero q] (S:ℚ) (h4:4 ∣ q) (h3:3 ∣ q)
    (g:ZMod q → ℝ) :
    FullPhaseAggregation.rowAggregate S h4 h3 g
      (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)) =
      -(phaseTotal h4 g 1 - phaseTotal h4 g 3) ^ 2:=by
  rw [rowAggregate_massSquare,massWeighted_vector]
  norm_num
  ring
end Green24Proof.PhaseWeightedVectors
private def zz2382:"s094e"="s094e":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover12Mass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open PhaseMassRows PhaseWeightedVectors PhaseColourRows
theorem remainingRows_eq:HeightCover12Cyclic.remainingRows = [
  ((0x39226203 / 0xee6b280), .base (.balance 0 (1))),
  ((0x4e345121 / 0xee6b280), .base (.balance 1 (-1))),
  ((0xe5bc1dd3 / 0x3b9aca00), .base (.balance 2 (1))),
  ((0x138499555 / 0x3b9aca00), .base (.balance 3 (-1))),
  ((0x853ad / 0x989680), .base (.child 0)),
  ((0x1345d / 0x7a1200), .base (.grandchild 1)),
  ((0xa42ffd / 0x3b9aca00), .base (.grandchild 3)),
  ((0xe22b / 0xbebc20), .colourChild (.phase 3)),
  ((0x149a115b / 0xbebc200), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x31bb / 0x3b9aca0), .base (.massSquare false (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p))),
  ((0x8534d / 0x5f5e100), .base (.massSquare true (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((4 / 0x7d), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0x39226203 / 0xee6b280):ℝ) * phaseTotal h4 g 0 + ((-0x4e345121 / 0xee6b280):ℝ) * phaseTotal h4 g 1 + ((0xe5bc1dd3 / 0x3b9aca00):ℝ) * phaseTotal h4 g 2 + ((-0x138499555 / 0x3b9aca00):ℝ) * phaseTotal h4 g 3) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - ((6 / 5):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
theorem weighted_remaining_le {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (_hg:∀ i,0 ≤ g i)
    (_heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((6 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 1)) ≤ 0)
    (hrow2:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 3)) ≤ 0)
    (hrow3:rowAggregate ((6 / 5)) h4 h3 g (.colourChild (.phase 3)) ≤ 0) :
    weightedAggregate ((6 / 5)) h4 h3 g HeightCover12Cyclic.remainingRows ≤
      balanceMass h4 g - ((0x149a115b / 0xbebc200):ℝ) * (phaseTotal h4 g 1 - phaseTotal h4 g 3) ^ 2 + ((4 / 0x7d):ℝ) * mass g ^ 2:=by
  have hs9:=rowAggregate_massSquare_nonpos ((6 / 5)) h4 h3 g (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)
  have hs10:=rowAggregate_colouredMassSquare_nonpos ((6 / 5)) h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_balance,rowAggregate_normalization,odd_massSquare]
  simp only [rowAggregate_base] at hrow0 hrow1 hrow2 hrow3
  norm_num
  unfold balanceMass
  linarith
private def zz1697:"s06a1"="s06a1":=by decide+kernel
theorem aggregate_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((6 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 1)) ≤ 0)
    (hrow2:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 3)) ≤ 0)
    (hrow3:rowAggregate ((6 / 5)) h4 h3 g (.colourChild (.phase 3)) ≤ 0) (h5:¬5 ∣ q) :
    height12.Aggregate (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) (phaseTotal h4 g 0 - phaseTotal h4 g 2) (phaseTotal h4 g 1 - phaseTotal h4 g 3) (energy g) (deficit g):=by
  have hc:=HeightCover12Cyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg heven hrow0 hrow1 hrow2 hrow3
  have hm:mass g = (phaseTotal h4 g 0 + phaseTotal h4 g 2) + (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    have ht:=phaseTotal_sum h4 g
    linarith
  rw [hm] at hc hr
  unfold HeightCoefficients.Aggregate height12
  unfold balanceMass at hr
  norm_num
  nlinarith only [hc,hr]
theorem height_bound_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((6 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 1)) ≤ 0)
    (hrow2:rowAggregate ((6 / 5)) h4 h3 g (.base (.grandchild 3)) ≤ 0)
    (hrow3:rowAggregate ((6 / 5)) h4 h3 g (.colourChild (.phase 3)) ≤ 0) (h5:¬5 ∣ q) (hAB:(phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2)) :
    (2 / 5:ℝ) * energy g + Q12 (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ deficit g:=by
  apply height12_of_aggregate
  · exact add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)
  · exact hAB
  · exact sub_nonneg.mpr heven
  · have hb:=phaseTotal_nonneg h4 g hg 2
    linarith
  · exact aggregate_of_rows h4 h3 g hg heven hrow0 hrow1 hrow2 hrow3 h5
end Green24Proof.HeightCover12Mass
private def zz2383:"s094f"="s094f":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover12Profile
open PhaseMassRows ChildRows HeightChildRows ProfileChildren
theorem height_bound_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hAB:mass v ≤ mass u) :
    (2 / 5:ℝ) * energy (interleave u v) + Q12 (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hrow0:FullPhaseAggregation.rowAggregate ((6 / 5)) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have hrow1:=Full27ProfileInterval.grandchild_nonpos_of_induction ((6 / 5)) h4 h3 (interleave u v) hg 1 ih
  have hrow2:=Full27ProfileInterval.grandchild_nonpos_of_induction ((6 / 5)) h4 h3 (interleave u v) hg 3 ih
  have hrow3:=ColourChildRows.phase_nonpos_of_induction ((6 / 5)) 3 h4 h3 (interleave u v) hg ih
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    rw [phaseTotal_interleave_zero h4 h2,phaseTotal_interleave_two h4 h2,classMass_sum]
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have h:=HeightCover12Mass.height_bound_of_rows h4 h3 (interleave u v) hg heven hrow0 hrow1 hrow2 hrow3 h5
    (by rwa [hU,hV])
  simpa only [hU,hV] using h
theorem height_bound {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w) (hAB:mass v ≤ mass u) :
    (2 / 5:ℝ) * energy (interleave u v) + Q12 (mass u) (mass v) ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,hE,heven⟩ :=
    ProfileEnergyOrientation.orient_even_child h4 u v hu hv
  have h:=height_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven
    (by simpa only [hU,hV] using hAB)
  simpa only [hU,hV,hd,hE] using h
end Green24Proof.HeightCover12Profile
private def zz2384:"s0950"="s0950":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case0
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l17 l21 l22 l25 l27 l28 l29 l30 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l5 l51 l54 l55 l6 l60 l62 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x2286f2260, -0x540e2cab8, -0x7e20b4b6e,0x126cb93ac], ![-0x540e2cab8, -0xced2df439,0x14eb65fdc,0x3e6a95b02], ![-0x7e20b4b6e,0x14eb65fdc, -0x20df0b8210,0x543bf3580], ![0x126cb93ac,0x3e6a95b02,0x543bf3580, -0x2a1288050]]
noncomputable def hinges:Hinges:=[(-0x2175f44,l6),(-0x579f12ff,l5),(0x29e08155a,l4),(-0x579f12f9,l8),(-0x298d6887,l11),(-0x1551bdd4,l10),(0x54a749fee,l14),(-0xa61c4490,l17),(0x86d0bd98a,l15),(0x1fdd957d,l21),(0xffe804d9,l22),(-0x2a1288050,l27),(-0x1fdd957d,l28),(0x2a1288050,l29),(-0x54a749fee,l25),(0x11a0f304c,l30),(0x2a1288050,l33),(0x1551bdd4,l38),(-0x2a1288050,l35),(0x579f12f9,l36),(0x2a1288050,l37),(-0x29e08155a,l34),(-0x11a0f304c,l43),(-0xffe804d9,l42),(-0x86d0bd98a,l41),(0x2a1288050,l51),(0x298d6887,l55),(0x579f12ff,l54),(0x2175f44,l60),(0xa61c4490,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2a1288050,l27),(0x2a1288050,l29),(0x2a1288050,l33),(-0x2a1288050,l35),(0x2a1288050,l37),(0x2a1288050,l51),(0x54a749fee,l14),(-0x54a749fee,l25),(0x86d0bd98a,l15),(-0x86d0bd98a,l41),(0x11a0f304c,l30),(-0x11a0f304c,l43),(0x29e08155a,l4),(-0x29e08155a,l34),(-0xa61c4490,l17),(0xa61c4490,l62),(0xffe804d9,l22),(-0xffe804d9,l42),(-0x298d6887,l11),(0x298d6887,l55),(0x1fdd957d,l21),(-0x1fdd957d,l28),(-0x579f12ff,l5),(0x579f12ff,l54),(-0x579f12f9,l8),(0x579f12f9,l36),(-0x1551bdd4,l10),(0x1551bdd4,l38),(-0x2175f44,l6),(0x2175f44,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,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,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,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,0x2c328220302971006000000000d40e2008000000002d0248020000008211032300c0000000037018802000000000d406200800033128300d1003048c710c3028b4014000000320603cc020000000c4140f300800000308240ccc030000000f444063008000003c884078c03000006c281c0e40080002461240d70c05000090843025c301400831b05302ad0040000000006406200800032118680b1003030842862017040140000003516038c0200000000589033006071c718302591006], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case0" = "QuadHeightCover18Case0" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case0
private def zz2385:"s0951"="s0951":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case1
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l17 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l43 l46 l5 l51 l54 l55 l57 l6 l60 l62 l63 l64 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x263d210a6, -0x540e2cab8, -0x7e20b4b32,0x11a4f25c4], ![-0x540e2cab8, -0xcdeb8365d,0x143b7f844,0x3f24e161e], ![-0x7e20b4b32,0x143b7f844, -0x20df0b8210,0x543bf3580], ![0x11a4f25c4,0x3f24e161e,0x543bf3580, -0x2a1288050]]
noncomputable def hinges:Hinges:=[(-0x2175f44,l6),(-0x579f12ff,l5),(0x29e08155a,l4),(-0x579f12f9,l8),(-0x298d6887,l11),(-0x1551bdd4,l10),(0x591c1777c,l14),(-0x148a6aa40,l17),(0x378e0d030,l15),(0x94f3045d,l23),(-0x2a1288050,l27),(0x2a1288050,l29),(-0x591c1777c,l25),(0xd3472125,l31),(0x1415a8f9c,l30),(0x2a1288050,l33),(0x1551bdd4,l38),(-0x2a1288050,l35),(0x579f12f9,l36),(0x2a1288050,l37),(-0x29e08155a,l34),(-0x1415a8f9c,l43),(-0x378e0d030,l41),(0x66ac1090,l46),(0x2a1288050,l51),(0x298d6887,l55),(0x579f12ff,l54),(-0xd3472125,l57),(0x2175f44,l60),(-0x94f3045d,l63),(0x148a6aa40,l62),(-0x66ac1090,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2a1288050,l27),(0x2a1288050,l29),(0x2a1288050,l33),(-0x2a1288050,l35),(0x2a1288050,l37),(0x2a1288050,l51),(0x591c1777c,l14),(-0x591c1777c,l25),(0xd3472125,l31),(-0xd3472125,l57),(-0x148a6aa40,l17),(0x148a6aa40,l62),(0x1415a8f9c,l30),(-0x1415a8f9c,l43),(0x94f3045d,l23),(-0x94f3045d,l63),(0x378e0d030,l15),(-0x378e0d030,l41),(0x29e08155a,l4),(-0x29e08155a,l34),(0x66ac1090,l46),(-0x66ac1090,l64),(-0x298d6887,l11),(0x298d6887,l55),(-0x579f12ff,l5),(0x579f12ff,l54),(-0x579f12f9,l8),(0x579f12f9,l36),(-0x1551bdd4,l10),(0x1551bdd4,l38),(-0x2175f44,l6),(0x2175f44,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x690481998060000000de2101b300c000498f831815680200000003b82404cc030024440c308125200a0000000084140730080000218481602c801800000002f21014c020000000036240718040001ec6304409a401000000000e8300c60100000000001d01880200000000663207180400000008629037300c0e68c602781f7480300000000110701cc0200000000002203900400000cc4c1b027400c0c1886861805c68030000711844303710040000000391881318060000000006870330040000000058380c601000000000260c0cc0100000000004a0390040000000004d013200c00040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#[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case1" = "QuadHeightCover18Case1" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case1
private def zz2386:"s0952"="s0952":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case2
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l31 l33 l35 l37 l4 l5 l51 l56 l57 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x930213bc0, -0x59514ba00, -0x3123b4b28,0x16e3600], ![-0x59514ba00, -0x3075b6cf5e,0x7d5e33594,0x39c4098fc], ![-0x3123b4b28,0x7d5e33594, -0x23ace41e45,0x597f12570], ![0x16e3600,0x39c4098fc,0x597f12570, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xbc91b7,l5),(0x68fa92be,l4),(-0xf07fdc4,l9),(0x12d80f8a,l11),(-0x2a209e2c,l10),(0x11e1a3000,l14),(-0xe3bfa20e,l17),(0x8b9356cf,l23),(0x2b61501be,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x11e1a3000,l25),(0xfe5e9b78,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x9ce0bbf2,l57),(-0x261f7f0fe,l56)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0xfe5e9b78,l31),(0x2b61501be,l22),(-0x261f7f0fe,l56),(0x11e1a3000,l14),(-0x11e1a3000,l25),(-0x9ce0bbf2,l57),(-0xe3bfa20e,l17),(0x8b9356cf,l23),(-0x2a209e2c,l10),(0x12d80f8a,l11),(0x68fa92be,l4),(-0xf07fdc4,l9),(-0xbc91b7,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨66, #[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,0x65013200c000000003101c802000000000d40920080000011068074c03030444061017340140c712419c0a4d005000000341201d300c0000000001c0c80150c33420c02e340180002b0f04c09d003000000000840b2008000000110f014c02000004e0440163010000250982402d003000000001e009200c000000d028074c0300000005844053008000001509402cc03000000002c009200c00000000d80248030000006c0900c300c000001a024028c03000000640900c300c000001902c070c030000006e1100b300c0001a01040098c05000000064240730080000001a09018c02000000541a01d300c0000000d09028c02], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
    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)) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 20 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case2" = "QuadHeightCover18Case2" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 20 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case2
private def zz2387:"s0953"="s0953":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case3
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l14 l17 l20 l21 l23 l25 l27 l29 l30 l31 l33 l35 l37 l4 l41 l42 l43 l44 l5 l51 l56 l57 l58 l59 l63 l65 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x90963589e, -0x59514ba00, -0x36948e6b8,0x2ce73dc0], ![-0x59514ba00, -0x317f9f5091,0x7d595a1ac,0x3b17aa8b8], ![-0x36948e6b8,0x7d595a1ac, -0x23ace41e45,0x597f12570], ![0x2ce73dc0,0x3b17aa8b8,0x597f12570, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0xbc91b7,l5),(0x68fa92be,l4),(-0xf07fdc4,l9),(0x12d80f8a,l11),(-0x2a209e2c,l10),(0x85f4aa44,l14),(0x133a565d8,l12),(-0x20271c034,l17),(0x38b70b06,l21),(-0x5fbe98d0,l20),(0x1602bf4c5,l23),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x11e1a2ff0,l25),(0x13635038d,l31),(0xdba01878,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x4ce92620,l43),(-0x9e191b4b,l42),(-0x560eda8a,l41),(-0x638a4d58,l44),(0x2cb417800,l51),(-0x4e8db9d7,l57),(-0x13f337d8a,l56),(0x7ffe644,l59),(0x480d1c52,l58),(-0x8c6620b9,l63),(-0x82e6184,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1602bf4c5,l23),(-0x20271c034,l17),(0x13635038d,l31),(-0x11e1a2ff0,l25),(0xdba01878,l30),(-0x8c6620b9,l63),(-0x13f337d8a,l56),(0x85f4aa44,l14),(-0x4e8db9d7,l57),(-0x9e191b4b,l42),(0x38b70b06,l21),(0x133a565d8,l12),(-0x4ce92620,l43),(-0x5fbe98d0,l20),(-0x2a209e2c,l10),(0x480d1c52,l58),(0x12d80f8a,l11),(0x68fa92be,l4),(-0x638a4d58,l44),(-0xf07fdc4,l9),(-0x560eda8a,l41),(-0x82e6184,l65),(0x7ffe644,l59),(-0xbc91b7,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[0x320490040000000005830330040000208c45c04c80180000000001501c80200000842a09806200600000000543406300800000000000e0640080000491c8d8099003000000000032039004000000911c404c301000001d888120388018008c0c20840a610050000000190481218060000000058140f30080000000000900e401000000204610130c0400000000342403980400000007231014300c000000e23080d8602000000001e0903cc020000000410901b98060000000000580720080000014628805860200006a12829013d0040000000000880690060000000064440730080000188a43404c80180000000160d024c02001641b817808aa00a0000000520a017300c00000e30a602a4602800ac0ce08c0555005000000000012039004000000000054092008000000e610803260200000001d844098c03000000031108121806000000540440873010000000aa09814e602011208e04801b85006020c1020940130a00c050444c24807b6401800000a110203246028000000d4150230c040000000310900e180600000000006c062008000000b868280a801000000170e0501d0020000000001280990060000004d04803130100002905409007a80200004d0841200c90040000ac1202c04ea0080001502705006d4010005305104c025a802800a20ae08801b5005028814208800c6a00c0001702807005d40100000000004c012401800000001109018c0200000000001c02900400000000442c06300800000000038012401800000000012014802,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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case3" = "QuadHeightCover18Case3" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case3
private def zz2388:"s0954"="s0954":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case4
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l14 l15 l17 l20 l21 l22 l25 l27 l29 l30 l33 l34 l35 l36 l37 l4 l42 l43 l51 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3b91092db, -0x540e2caa0, -0x7e20b4c3a,0xb13f5250], ![-0x540e2caa0, -0x9fad486f2,0x142e6c2d0,0x3e6a95b02], ![-0x7e20b4c3a,0x142e6c2d0, -0x20efaed99e,0x543bf358c], ![0xb13f5250,0x3e6a95b02,0x543bf358c, -0x2a1288050]]
noncomputable def hinges:Hinges:=[(-0x152463f0,l6),(0x2a63d4e8c,l4),(-0x1c3ca3b7,l9),(-0xec537127,l8),(0x916319a,l10),(0x3c94bcadc,l14),(-0xa61c4490,l17),(0x86d0bd98a,l15),(0x20d54b712,l21),(-0x78b2dd318,l20),(0xffe804d9,l22),(-0x2a1288050,l27),(0x2a1288050,l29),(-0x3145bbe8c,l25),(0x11a0f304c,l30),(0x2a1288050,l33),(-0x2a1288050,l35),(0xfd58bd4c,l36),(0x2a1288050,l37),(-0x35eada578,l34),(-0x2dbff60,l43),(-0x3ca47a6a1,l42),(0x2a1288050,l51),(0x32f54a3c,l61),(0x10becf90,l60),(-0xfb65b4be,l63),(0xcfa23cb4,l62),(-0x1ccd2250,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2a1288050,l27),(0x2a1288050,l29),(0x2a1288050,l33),(-0x2a1288050,l35),(0x2a1288050,l37),(0x2a1288050,l51),(-0x78b2dd318,l20),(0x3c94bcadc,l14),(0x20d54b712,l21),(-0x3145bbe8c,l25),(-0x3ca47a6a1,l42),(0x86d0bd98a,l15),(-0xfb65b4be,l63),(0x11a0f304c,l30),(-0x35eada578,l34),(0xcfa23cb4,l62),(0x2a63d4e8c,l4),(-0xa61c4490,l17),(0xffe804d9,l22),(0xfd58bd4c,l36),(-0xec537127,l8),(0x32f54a3c,l61),(-0x1c3ca3b7,l9),(-0x1ccd2250,l64),(-0x152463f0,l6),(0x10becf90,l60),(0x916319a,l10),(-0x2dbff60,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,0x1f00a40100000000003d024802071268c5920535a00da30b36089036f1401c00000000003a064008000000248240c8c03079270c6120535a00c000000000108052008000000000208124010000033118480c900300000000000a069004000000000084062008000408e23181968020000000208e4058c0300000000000981900200408628a2017040140000000001300a401000000000009034802040431a2840468200c0002045108c0bb4010000000000088124010000001442102e0c04], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 29 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case4" = "QuadHeightCover18Case4" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 29 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case4
private def zz2389:"s0955"="s0955":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case5
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l12 l14 l15 l17 l20 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l4 l41 l42 l43 l46 l51 l57 l58 l6 l60 l61 l62 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x424e48590, -0x540e2caa0, -0x7e20b4b8c,0xfaf8099c], ![-0x540e2caa0, -0xd26a3b375,0x139eec124,0x3f24e161e], ![-0x7e20b4b8c,0x139eec124, -0x20efaed99e,0x543bf358c], ![0xfaf8099c,0x3f24e161e,0x543bf358c, -0x2a1288050]]
noncomputable def hinges:Hinges:=[(-0x152463f0,l6),(0x2a63d4e8c,l4),(-0x1c3ca3b7,l9),(-0xec537127,l8),(0x916319a,l10),(0x5707cb510,l14),(-0x2295131a0,l12),(-0x148a6aa40,l17),(0x378e0d030,l15),(0x1c0c7c7ba,l20),(0x94f3045d,l23),(-0x2a1288050,l27),(0x2a1288050,l29),(-0x6100be020,l25),(0xd3472125,l31),(0x1415a8f9c,l30),(0x2a1288050,l33),(-0x2a1288050,l35),(0xfd58bd4c,l36),(0x2a1288050,l37),(-0x35eada578,l34),(-0x37614d88,l43),(-0x2e4f166e4,l42),(-0x1ab46c910,l41),(0x840100c0,l46),(0x2a1288050,l51),(-0x48a183fc,l57),(-0x9f6ad92e,l58),(0x32f54a3c,l61),(0x10becf90,l60),(-0xa73dfa46,l63),(0xd06b2ebc,l62),(-0x96d8c12,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x6100be020,l25),(-0x2a1288050,l27),(0x2a1288050,l29),(0x2a1288050,l33),(-0x2a1288050,l35),(0x2a1288050,l37),(0x2a1288050,l51),(0x5707cb510,l14),(-0x2e4f166e4,l42),(0xd3472125,l31),(-0x148a6aa40,l17),(0x1415a8f9c,l30),(-0xa73dfa46,l63),(0x1c0c7c7ba,l20),(0x94f3045d,l23),(0x378e0d030,l15),(-0x35eada578,l34),(0xd06b2ebc,l62),(0x2a63d4e8c,l4),(0xfd58bd4c,l36),(-0x2295131a0,l12),(-0xec537127,l8),(0x840100c0,l46),(-0x48a183fc,l57),(-0x1ab46c910,l41),(-0x9f6ad92e,l58),(0x32f54a3c,l61),(-0x37614d88,l43),(-0x1c3ca3b7,l9),(-0x152463f0,l6),(0x10becf90,l60),(-0x96d8c12,l65),(0x916319a,l10)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((0x8100e8e32ae4011aedc45f08820840201380b09b05c0100401034403d0c9be70a384112d74642341f4eef2920800425064090107c021c7626a8bc341e683f3b3b261c2598eafdd28410a13084602000016e35fa1c00fc21bb6208003dcd05c213821200400005cc80012e980000802068407a190ae13d48414b688b9d1a0b7e05a8c02000a5e047c80040010bcd5caa9cf54277400000000000000009340d74cbbb83bfbb205b25123f1990f841138e3842c21c2082381400380c0000803400064880013f10600900017290005af231e2b1a0058c702c11c1633e039141b573bce5840b79748414204cd1c2212045ca042092408210080cd02c6641633c0b19d05f0a06470d9260bc1e205641055f49399088008219ac320010004067007a31621b3533c4032706d01872b0eb12cf056fce2fa82003551f29a800f8022081d980040e79f20dfe77210401e581bf848c3f198fc02020e68b418e78800b71ab2061f0de8f36090000b71afd20018d5240bb900220040000df90002d1386117f95fea4388365b192a38612e9cef1bd11c10e83bbd73808133b4a0e66008318b31f7d610000365c1ca99e00d13c7db2434035d38c18889b4841380c00007cc8cb06c650076ec43ca11e905a62bdd6b3556edd6b355702362e6c907be9307399e74405690d0accad002ec34a6e781533c63462c32430c31c0d20da81defb34360143b7190af8fda9a750dd3ebc628c0dcff379912863b5aeb6048d1c6d765463aa000000000cf5b6ad1f150b395008c4f3cf1901090c30d000f03d08ff570417006800094119b09f14f0bf11bd43c375b9886d80808c886fb31f1425066e46ae420b6a146b71e4401d1e6be0e90000112a80b002b3414f3e0044aa158230e184c0280001d33a58016e356438a1a293ac3038843ca6491c61106188f4c020c05accb080000d827a13c0001e847fa2610230080000b310007852001b546c70c8285c9881a65711814b0a17b7bc6028009edcfb6900084021638225c8630e20fd3e8be1617dc072fba0019c18e1e040540cd7c04a00400100000fd3f5f013389bf4d5b3c444128efd1c78ed30118270062d5bd05a46ece211af7ce0a80f4ff95aaebf548c2ec0706ab9d832446844850a502482300001512cc983794770634c2aaa41ffafc56fd49512499e57984e4d1ac83222722296479d875033566f302ac166ce8ef76c8504cd2ba8001bb1045098cd04c664263300b80000802065c07002de8672c2b285798ce4652e6) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 34 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case5" = "QuadHeightCover18Case5" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 34 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case5
private def zz2390:"s0956"="s0956":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case6
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l17 l22 l23 l25 l27 l29 l31 l33 l35 l37 l4 l42 l43 l5 l51 l63 l67)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l67, ![-0x59514ba00, -0x3075b6cf5e,0x7da287718,0x39c4098fc], ![-0x2a9670cb0,0x7da287718, -0x23a9aee220,0x597f1256a], ![0x16e3600,0x39c4098fc,0x597f1256a, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x10f3ece4,l5),(0xe30d6c,l4),(0x1bf5866a,l11),(-0x2ce97392,l10),(0x11e1a3000,l14),(-0xe3bfa20e,l17),(0x8b9356cf,l23),(0x2b61501be,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x11e1a3000,l25),(0xfe5e9b78,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x12239f36,l43),(-0xfb7b95ad,l42),(0x2cb417800,l51),(-0xfb1e197a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0xfe5e9b78,l31),(-0xfb1e197a,l63),(0x2b61501be,l22),(0x11e1a3000,l14),(-0x11e1a3000,l25),(-0xe3bfa20e,l17),(0x8b9356cf,l23),(-0xfb7b95ad,l42),(-0x2ce97392,l10),(0x1bf5866a,l11),(-0x12239f36,l43),(-0x10f3ece4,l5),(0xe30d6c,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0xe115020405cd0050738b210e0526802800000341200f300e8619a1060171a00c0002b0f04c09d003000000001081640100000000014062008000000221e0298040000138110058c040001284c12016801800000001e009200c000001a0500798060000019024030c03], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 20 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case6" = "QuadHeightCover18Case6" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 20 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case6
private def zz2391:"s0957"="s0957":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case7
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l14 l17 l21 l23 l25 l27 l28 l29 l30 l31 l33 l35 l37 l4 l41 l42 l5 l51 l57 l62 l63)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc323f830c, -0x59514ba00, -0x3c2106ffc,0x16e3600], ![-0x59514ba00, -0x31803da713,0x7d9f714c4,0x3b17aa8b8], ![-0x3c2106ffc,0x7d9f714c4, -0x23a9aee220,0x597f1256a], ![0x16e3600,0x3b17aa8b8,0x597f1256a, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x10f3ece4,l5),(0xe30d6c,l4),(0x1bf5866a,l11),(-0x2ce97392,l10),(0xa437d108,l14),(0x10545dfa4,l12),(-0x20271c034,l17),(0x3f3dd80a,l21),(0x1602bf4c5,l23),(-0x2cb417800,l27),(-0x1cab95aa,l28),(0x2cb417800,l29),(-0x12d06ec34,l25),(0x13635038d,l31),(0xdba01878,l30),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x3b3ad6d1,l42),(-0x11ad30bc,l41),(0x2cb417800,l51),(-0xafc7a05e,l57),(-0x842e5ead,l63),(-0xcf89e6e2,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1602bf4c5,l23),(-0x20271c034,l17),(0x13635038d,l31),(-0x12d06ec34,l25),(-0xafc7a05e,l57),(0xdba01878,l30),(-0xcf89e6e2,l62),(-0x842e5ead,l63),(0xa437d108,l14),(0x3f3dd80a,l21),(0x10545dfa4,l12),(-0x2ce97392,l10),(-0x1cab95aa,l28),(0x1bf5866a,l11),(-0x3b3ad6d1,l42),(-0x10f3ece4,l5),(-0x11ad30bc,l41),(0xe30d6c,l4)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 25 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case7" = "QuadHeightCover18Case7" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 25 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case7
private def zz2392:"s0958"="s0958":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case8
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l17 l27 l29 l31 l33 l34 l35 l36 l37 l4 l5 l51 l54 l55 l57 l62 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x200de8612, -0x742b8d00, -0xaef86e80,0x16e3600], ![-0x742b8d00, -0x384d15ebc,0x934b79e0,0x3758d0f6], ![-0xaef86e80,0x934b79e0, -0x2bfc2b2a1,0x7707f8d0], ![0x16e3600,0x3758d0f6,0x7707f8d0, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0x14d7122f,l5),(0x80cb59de,l4),(-0x25ed3806,l8),(-0x1e07646,l11),(0x3bbb6a46,l17),(-0x3acce180,l27),(0x3acce180,l29),(0x8852ac6,l31),(0x3acce180,l33),(-0x3acce180,l35),(0x25ed3806,l36),(0x3acce180,l37),(-0x80cb59de,l34),(0x3acce180,l51),(0x1e07646,l55),(0x14d7122f,l54),(-0x8852ac6,l57),(-0x3bbb6a46,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(0x3bbb6a46,l17),(-0x3bbb6a46,l62),(0x80cb59de,l4),(-0x80cb59de,l34),(-0x25ed3806,l8),(0x25ed3806,l36),(0x8852ac6,l31),(-0x8852ac6,l57),(-0x14d7122f,l5),(0x14d7122f,l54),(-0x1e07646,l11),(0x1e07646,l55)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x84240f3008000003114811180600000000250248020718a2106051680280003384700d0301400000291081318060ad0d81340555005000148682204e8018000000037013200e901921100175200c000000000f0148020001284c12016801800000001e009200c0002042181a9180a0000000001c0c801], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case8" = "QuadHeightCover18Case8" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case8
private def zz2393:"s0959"="s0959":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case9
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l11 l14 l15 l17 l21 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l4 l41 l43 l5 l51 l54 l55 l57 l62 l8)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1683ad960, -0x742b8d00, -0xaef86eb0,0x16e3600], ![-0x742b8d00, -0x1dcb35a1a,0x4d22de3c,0x2d896f8e], ![-0xaef86eb0,0x4d22de3c, -0x2bfc2b2a1,0x7707f8d0], ![0x16e3600,0x2d896f8e,0x7707f8d0, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0x14d7122f,l5),(0x80cb59de,l4),(-0x25ed3806,l8),(-0x1e07646,l11),(0x3218d44e,l14),(0x1ca60728,l17),(0xa5059892,l15),(-0x7d94e93,l21),(-0x3acce180,l27),(0x7d94e93,l28),(0x3acce180,l29),(-0x3218d44e,l25),(0x3299393,l31),(-0x107a6c6a,l30),(0x3acce180,l33),(-0x3acce180,l35),(0x25ed3806,l36),(0x3acce180,l37),(-0x80cb59de,l34),(0x107a6c6a,l43),(-0xa5059892,l41),(0x3acce180,l51),(0x1e07646,l55),(0x14d7122f,l54),(-0x3299393,l57),(-0x1ca60728,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(0x3218d44e,l14),(-0x3218d44e,l25),(0xa5059892,l15),(-0xa5059892,l41),(0x80cb59de,l4),(-0x80cb59de,l34),(0x1ca60728,l17),(-0x1ca60728,l62),(-0x25ed3806,l8),(0x25ed3806,l36),(-0x107a6c6a,l30),(0x107a6c6a,l43),(-0x7d94e93,l21),(0x7d94e93,l28),(-0x14d7122f,l5),(0x14d7122f,l54),(0x3299393,l31),(-0x3299393,l57),(-0x1e07646,l11),(0x1e07646,l55)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[0x2206400800000000940920080000000009819002000000001a0148020510830c404548028000000000703200400000044220718040000221306019002000000001100a40100000004c180e30080000000241819802000000190701cc02000000128a8126010000004211034300c012c2b08204d20080000000906018c0200000044120446018010c31084096401000621202606620080000000005018802000000000480c401000000220a00c300c0000004c2a0718040000000026014802000000000a81c4010000000a46409300800002884407c18080000014848070c0300530cc28813480200000004418063008000000001a0710040000000005c0c801000000000681a4010000071144084301000000391481218060000184510318c04000000c45206c601800000000440e200800000002438198020000000009034802002988218812c8020000002609022300c000000160a051804000000c824090c0300000000048124010000002a0c013300c00000000028190020000000a0502cc02000000cc2605e6018000049084032301014c144130096a00a000000130b018c02002b0480b013a8020000000004c05200a841480840066a00c0000001309018c02002905409007a802001702807005d40100000000130049006000000000240c801000000000700a4010000000442c06300800000000e00490060000000012014802,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,0x68580c6010000000004c06200800000000520490040000000011034802000000000d80c401040c610a3028b401400064230d0162006000000001d024802000000000f00a4010308428620170401400000411c813180600014218c09a8c0500000a21981346020000004219034300c182184118165a00a0a30ec10c0a2d005], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 27 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case9" = "QuadHeightCover18Case9" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 27 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case9
private def zz2394:"s095a"="s095a":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case10
open EndToEndTupleState (State qPath initial)
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l14 l16 l25 l27 l29 l31 l33 l34 l35 l36 l37 l38 l41 l42 l51 l55 l61 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x11730dcb, -0x2ca8a5d00, -0x4302b1900,0xb71b00], ![-0x2ca8a5d00, -0x11a3b01240,0x3e253d206,0x2af7c7f40], ![-0x4302b1900,0x3e253d206, -0x1229298c00,0x2cbf89300], ![0xb71b00,0x2af7c7f40,0x2cbf89300, -0x165a0bc00]]
noncomputable def hinges:Hinges:=[(0x8f0d1800,l14),(0x130fbf87f,l16),(-0x165a0bc00,l27),(0x165a0bc00,l29),(-0x8f0d1800,l25),(0x4e705df9,l31),(0x165a0bc00,l33),(0x1a2874e2,l38),(-0x165a0bc00,l35),(-0x60c4515,l36),(0x165a0bc00,l37),(-0x7bbcaa41,l34),(-0x1b59b5fd8,l42),(-0x3eee6e394,l41),(0x165a0bc00,l51),(-0x3848b74,l55),(0xd13d9cf,l61),(0x7ab41094,l62)]
def normalizationDenominator:ℤ:=0x2cb417800
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x165a0bc00,l27),(0x165a0bc00,l29),(0x165a0bc00,l33),(-0x165a0bc00,l35),(0x165a0bc00,l37),(0x165a0bc00,l51),(-0x3eee6e394,l41),(-0x1b59b5fd8,l42),(0x130fbf87f,l16),(0x8f0d1800,l14),(-0x8f0d1800,l25),(0x7ab41094,l62),(0x4e705df9,l31),(-0x7bbcaa41,l34),(0x1a2874e2,l38),(0xd13d9cf,l61),(-0x3848b74,l55),(-0x60c4515,l36)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x110480a18060000010864088c0300016884320468018000a84219026400c00002702200b1808000250982402d003000000003c012401800000000a409200800020c17017c180a000000000501c802000000000d80a4010000069104032301000000036240298040000001b11018c02], #[]⟩
def dynamicCode : Nat := (((((((0x289002dc6c00d20005b8d802c85fd018f00b1c2d1cf1072c516f1471c4104002dc6c02c0eae9af55820000b71b000004ef1265400322044008c261c6a112740b242163dbf8c0e0c0112a88000c0cd58a6a660020412d73efc6080001b659ca546003c920212840015a771e4750304041400e309bbdee4200592005b8d800c18e216f3d49c1802dc6c0030340e663cde100019bfcc001006315a4c88003c46025be090104601800019e208c0a000398324aaf20fbb4848e00501bd001426f2e3e11f41862b08d86a698122011ba060602109267923140b1579c73fa3001953c513480006665e73de0072450980500003e06c613634a18923558c1ef18914075cbf7e300587e2c5b00012ec59b80284a304201000010e36306135da4848cf1e003149030be41c37c487292cfa60860a85f2ca5a4802fb64b850a004dac0754004e2844010b182f02fb4248da2d2973c20647d40c878e08506e28746047f32a9ea182826a2f2220015a5358f00138a10804000059881b06c000c0cc10499ef665a040c0022551000487361ca2137848467a4a3829428402af389b9e1048fc8a06d005820eb82d18a058001a7d0ad1448036b522dbee00612285003091838c76092921c475ce9d524238cb2c5f840408c394ddc20977df282516084c92690620010c7c0d0a30007006e94c00a0508c02000034678a6149700faefa93d66084a2013ac0a374b092aae02cf1f08080222ccbb17e05b8e9566c1063ea04ce79bad953e65c5c280507de40af2b6bd65b46e808009a31dbd47c21f0dc44100004bcef159beedfc937519ab4feb363683249861543400005f240b424000dd44134073eb401282bcb86d5a48340a8a554d122f8816430c30a488388308282202050d67fa3fa5bf85f6658bf44474ea4c8fc52f907b8a2e081644108894910e237dd95984610c0a2bac2403ae8d7f9514168473b07880a5e40a38880046fd07a21801bf3c0a80030284200800019220982a04b15025088078340007687853518cefa405e3dfc3e71e30ab4d30205ec842d3d5793d079a854231178588102a2512ac492f0cff55940d19ec70fa281594f69b7143ebdf2837063735aea20800e8b18eef9debe5d5a4cddca79e3400179b4af89d359cdeea4738803fbe7483a06186faf8e8ff804ea894e9e41a45bfbcfda0538b1a53c48694b1d05500007e2704143c5b860586103a0c9ebb54104032a56d44e0c0857461bc0b21822c2ca8edd50c007819f3d400281c615d2ac6a0802c1b1b573100a0818b7886eea50c120c0a80900004324124560900a0470140dcda22876e0c709e4146bf07c0c1276c73c08ad1422872187c3504005093027fea07012e4d6d788a8a00c8a6f58d01041047b96d3d30d445d43865b2ae33961581230cc5c372330aa6a3b1ae27651408e02dd8d713b28a04701840134b34a2c82c72871c520004000c080080378c20b556cad86127fbb6ccbacd2000cdfe600184739e93b9d12c837f6f984903060044aa2000b04b002b8a060c0801406f40024037c379ec90124841380c309ca474f4a918) <<< 16000) +
    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)) <<< 16000) +
    0x0982849adf9978f7beaa5f8cab03b91fcd11d78e0ff3327ed0196ace674458cbd6e4a599512867d9bb77c97b242d4c4da06f5927435720e362a4a1806413a23e88000000000000000000000000000000000000000000000005e12082021c21420c10410406b60a4aa0a39b8f77396e57fa89e339ee0651ab6bf03a23fd381f70c76162800167902c1181588c0a84605203914a0fc450f24345297b6c880eb8b1b15218343dd94d68500ab803b9c0c0021ff4d40598308802143019b2e958a10b32ed40638898187f6f0811043102088051d8f9931941084021346d64040f25a23b444d5a3f8c6fb413150b9e5407c00000000000000000000000000000000000000000002b09431421220e20e18a10408e01804010068000f510240500018f10281181386e451cfb1fe6d53a2613a2ab203ac4627c576bce866e1cb1830f3ba67e18a316490e1514015bb676088ca9f1c36f80c015fa8120945e138bcfcc08024257b5e7aeb1c6b4a8e12236b693126eb3453ec391313974b96c1833e559baa4836859d7130a2805e2885886ab190912268270ea1c41add804d8a0d8e651f3e1002a59efba8100b27095df1260c2200858ed8c6e4f414384b94fe4258a0eb7efc8142ccc86306c5880f6f0ac81020022550fa5014360fb1e8007a12014e084401002605d8ee0028c79943802343d7030c03a751c416282fa82b8050b57bec56c8a00edfcd2c84c0844010025010000a6100030320480a00046e2000f524000340018ee408c960443b0210148c267bd24c0c287dfeeb704059729b1368c106cfad5e0302bd8b2c491002c1f88c660cc1844010c20307f93d060c87c74a263049a9511fa181969cc8d00000246b51e8250821008010008000468cd1b590103c9688ed113568fe31bed04c542e79501f00000000000000000000000000000000000000000000ad97e32026000000000320fb51e6641f6a3ca1190c29010c10808609000a069d65ab96eaaa70978a35bf2192e633e196bddfe082c319fba805c1ba2a252d43f1bcf32e7b554b4042a50cb222363cfa3dbab902b9c708fc104aeca8adf7eae120c785b09801b551fd6800584c00daa8feb3ffed62e69a3438a10d9dcfecdd86730491b4212d6c2298d9e017346d64040f25a23b444d5a3f8c6fb413150b9e5407c00000000000000000000000000000000000000000002b47c21f17246816838e3063042021825161d08457a68b0d46c47d92a966c46293c17f6c25260e74b7170e11602a9dbff2f85f4065ce25349f1d62656d48a8cee1f11f8915f4a522d18bdaaa3136113bb03deb28880387e36ead6b52081415bb0591c99934a4284b229540017c880d028002a3480c8ac060576130036aa3fad000b09801b551fd67ffdac5cd346871421b3b9fd9bb0ce6092368427d175db401e02e8ede67185117b3df399576a1b50a312b6c41d0d6739fc5ba20000000000000000000000000000000000000000000000000063438b3f0737702e5d8e1f09be120c8f3bac14520414110104008d56e8789ad19e95417d715ccbd037bf277585fae44fb12d2cfcee6a1b53ac7d26b1c7400ab0399e17ad9c60c8178efa6d2a98a3f82ec31384c654c82c0e1859b865d932de572c1418f0470328bec79a62ee827e2a8beb917bd55a4ede36431d1435f0ddf9bb882b48c4d01f0500f028001c8c80e8ac070260360ba1a1e5698ad8ead300e8436f0eb8894aac43ff88204f7000f6eaaf8a93cbae21961b5293cc510242092271b57052e12cf1519815451f1cc73ec0284afc5a2e0c6ccaa47201e31a423f70c1f334850057009cb60c3d080d973a502add0e04b9e89843c1b55ec4681ea4edd1ecac3a0913d51d7a8627d2ceb9c285d241812038754ca111e378a0c023f6ba3086a79d6d5a9eb061c9812491214b008f9547034282b65834ebbcfe6470693dcba3041a8739987bf9e2b28c2927460447c064d6a691304fa7e7b4060c3225d3ea40191df26d5f5508149e2269b8c2a2551167a3400db7c70b2df2d6b7817343cbd2526e680d96217085b0e80001c49824003abbe202683d40d0700eec22ef80045185c381a040f8020068140001c6406446030230170d80b06c0541602803b1d433c206420b087b0548905522f6d807078a6923fc901293237048016733d8f80261020008611dfcc2c342073e0d72d8e05a5dd3ca0230c1f008610e363c2a880b4011940840a2a9216808c207c020026020000bb20002fc640e9fb39b71802ddc2cdb0220c2000840200401002402000037201e020000e620221b01005d0c73371dd028300ad7aee140fc41098b05044c5d25ac3008df188f70800e45b0988024c3042010b0cd6cb17b228607a3d3b62c2ba2bbcc10c1002f69ed030001a463f010035b0715b0098408402165eb3dc7284b0dba18cd300121021004000041100f050000f4900e150001aa100d0d0003bc90010dc2004b6c68b249c9b224a143074c886d958a099ef5687dd4404002aea45782000193b7d9eb0c0000393870004002a7a99c8594a3861480a38a26cfe5a578e2001c9c380030883cea72650e18539c08a22305ca635c5a10a11dd20ddb3020076d5c6c6e347042601440b0fc8dcbe0e2a4f34b53c4061a0e99d88e1ff2c9e65818065ce473c020074db887d30011004205002dc6c0038ab2991028c810b6ae14a40e1addf9dbda20102c6044e43818b44bf24c60000b71aa34e004601000016a20005744030140008da402c44014220091100406801c2400c020050100200800c04000dc240087400202000010021191))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case10" = "QuadHeightCover18Case10" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case10
private def zz2395:"s095b"="s095b":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case11
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l12 l13 l14 l15 l16 l21 l22 l23 l25 l27 l28 l29 l30 l31 l33 l34 l35 l36 l37 l38 l42 l46 l51 l55 l57 l59 l61 l62 l63 l64 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![-0x2cb417812, -0x59514ba00, -0x860563200,0x16e3600], ![-0x59514ba00, -0x29083bacf9,0x7c476435c,0x6afd1b73c], ![-0x860563200,0x7c476435c, -0x2452531800,0x597f12600], ![0x16e3600,0x6afd1b73c,0x597f12600, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(0x11e1a3000,l14),(0x235b528,l13),(-0x13aefb840,l12),(0x13f337d8a,l16),(0x560eda8a,l15),(0x2d17f94a,l21),(0x8c6620b9,l23),(0x9e191b4b,l22),(-0x2cb417800,l27),(-0x38882e9e,l28),(0x2cb417800,l29),(-0x9fb8557c,l25),(0x4e8db9d7,l31),(0x4ce92620,l30),(0x2cb417800,l33),(0x3450e9c4,l38),(-0x2cb417800,l35),(-0xc188a2a,l36),(0x2cb417800,l37),(-0xf7795482,l34),(-0x1b2329b81,l42),(-0x24c18190,l46),(0x2cb417800,l51),(-0x70916e8,l55),(-0x11872c892,l57),(0x9d3d09a,l59),(0x1a27b39e,l61),(-0x1469fc16b,l63),(0x1f3830f64,l62),(-0x950e04,l65),(0x4c6a60,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(-0x1469fc16b,l63),(0x1f3830f64,l62),(-0x11872c892,l57),(0x11e1a3000,l14),(-0x1b2329b81,l42),(0x8c6620b9,l23),(0x13f337d8a,l16),(-0x9fb8557c,l25),(0x4e8db9d7,l31),(0x9e191b4b,l22),(-0x38882e9e,l28),(-0x13aefb840,l12),(0x4ce92620,l30),(0x2d17f94a,l21),(-0xf7795482,l34),(0x3450e9c4,l38),(0x1a27b39e,l61),(-0x24c18190,l46),(0x560eda8a,l15),(0x9d3d09a,l59),(-0x70916e8,l55),(-0xc188a2a,l36),(0x235b528,l13),(-0x950e04,l65),(0x4c6a60,l64)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨75, #[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,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,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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((((((((0x1e50022551001a550288394c1a3ca4130cdf9a33d747d71c18302d2f08a10208044aa2001a07209b122092000da1778b08000b71b004868202400c40b003c14dc0038b7c866fadc834b0ffc8b72883882823d31d62387c766e8322934709bd8843810811128f3be882800dbf7c7adb0004b78ad4201a903050038f3e12eb7a20079868320a3103cb09e13010ca240016e3) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 32 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case11" = "QuadHeightCover18Case11" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 32 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case11
private def zz2396:"s095c"="s095c":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case12
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l27 l29 l31 l33 l35 l37 l4 l45 l51 l55 l61 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x270ff4d69, -0x74010ec4, -0xaef86e80,0x857907c], ![-0x74010ec4, -0x384d15ebc,0xcbd31efc,0x3758d0f6], ![-0xaef86e80,0xcbd31efc, -0x2f1ff1767,0x7707f8f4], ![0x857907c,0x3758d0f6,0x7707f8f4, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0xa685bec,l4),(0x3781ea5,l11),(-0x3781eaa,l10),(0x3bbb6a46,l17),(-0x3acce180,l27),(0x3acce180,l29),(0x8852ac6,l31),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(-0xb0ef74,l45),(0x3acce180,l51),(-0xae4d69,l55),(0x5b1557,l61),(-0x4eb7f0ac,l62),(0x2c3bdcc,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(-0x4eb7f0ac,l62),(0x3bbb6a46,l17),(0x8852ac6,l31),(0x3781ea5,l11),(-0x3781eaa,l10),(0x2c3bdcc,l64),(-0xa685bec,l4),(-0xae4d69,l55),(0x5b1557,l61),(-0xb0ef74,l45)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((0xb2002b6dd0944000ee5032082816b66448d323be4889142937fdf0c01a898a310400043a23a804e283e010b1f6b5003d09004d37d5c7c82f26381f130a28a2c82c62c22821c20820c01c84008036cb84f5dba6c) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 16 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case12" = "QuadHeightCover18Case12" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 16 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case12
private def zz2397:"s095d"="s095d":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case13
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l15 l17 l20 l27 l29 l30 l31 l33 l35 l37 l4 l41 l43 l46 l51 l55 l56 l57 l59 l61 l62 l64)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xd1d739e5, -0x74010ec4, -0xaef86ec8,0x136b05c4], ![-0x74010ec4, -0x3dd6e37f5,0xe1e97240,0x2d896f8e], ![-0xaef86ec8,0xe1e97240, -0x2f1ff1767,0x7707f8f4], ![0x136b05c4,0x2d896f8e,0x7707f8f4, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0xa685bec,l4),(0x3781ea5,l11),(-0x3781eaa,l10),(-0x2e9d323e,l13),(0x1ca60728,l17),(0xa5059892,l15),(0x3173fda2,l20),(-0x3acce180,l27),(0x3acce180,l29),(0x3299393,l31),(-0x107a6c6a,l30),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x8db83c6,l43),(-0x8e2b5de2,l41),(-0x7c93870,l46),(0x3acce180,l51),(-0xae4d69,l55),(-0x387a028,l57),(-0x2c1ed2fa,l56),(-0x16563a,l59),(0x5b1557,l61),(-0x1d3d128,l62),(0x8d1c4f4,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(0xa5059892,l15),(-0x8e2b5de2,l41),(0x1ca60728,l17),(0x3173fda2,l20),(-0x2e9d323e,l13),(-0x2c1ed2fa,l56),(-0x107a6c6a,l30),(0x8db83c6,l43),(0x8d1c4f4,l64),(-0x7c93870,l46),(-0x387a028,l57),(0x3781ea5,l11),(0x3299393,l31),(-0x3781eaa,l10),(-0xa685bec,l4),(-0x1d3d128,l62),(-0xae4d69,l55),(0x5b1557,l61),(-0x16563a,l59)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := (((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 25 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case13" = "QuadHeightCover18Case13" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 25 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case13
private def zz2398:"s095e"="s095e":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case14
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l17 l20 l22 l23 l25 l27 l29 l30 l33 l34 l35 l36 l37 l38 l4 l42 l43 l51 l55 l59 l6 l60 l61 l62 l63 l65 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x35b282b95, -0x48de0a050, -0x6d5880cc2,0xb53b47d6], ![-0x48de0a050, -0xd4bb23909,0xda4b2ec0,0x43d16c4f8], ![-0x6d5880cc2,0xda4b2ec0, -0x1da3807115,0x490bd0c56], ![0xb53b47d6,0x43d16c4f8,0x490bd0c56, -0x247a76b28]]
noncomputable def hinges:Hinges:=[(-0xedf00aa,l6),(0x1cdab22fc,l4),(-0x10b3535b,l9),(-0x1edf64496,l8),(0x2e5fa62b,l11),(0x82f17d1c,l10),(0x3c610d6be,l14),(0x182b239bd,l13),(-0xcfa23cb4,l17),(-0x182b239bd,l20),(0xfb65b4be,l23),(0x3ca47a6a1,l22),(-0x247a76b28,l27),(0x247a76b28,l29),(-0x3c610d6be,l25),(0x2dbff60,l30),(0x247a76b28,l33),(-0x82f17d1c,l38),(-0x247a76b28,l35),(0x1edf64496,l36),(0x247a76b28,l37),(-0x1cdab22fc,l34),(-0x2dbff60,l43),(-0x3ca47a6a1,l42),(0x247a76b28,l51),(-0x2e5fa62b,l55),(0xf28f1ad,l59),(0x10b3535b,l61),(0xedf00aa,l60),(-0xfb65b4be,l63),(0xcfa23cb4,l62),(-0xf28f1ad,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x247a76b28,l27),(0x247a76b28,l29),(0x247a76b28,l33),(-0x247a76b28,l35),(0x247a76b28,l37),(0x247a76b28,l51),(0x3c610d6be,l14),(-0x3c610d6be,l25),(0x3ca47a6a1,l22),(-0x3ca47a6a1,l42),(0xfb65b4be,l23),(-0xfb65b4be,l63),(-0x1edf64496,l8),(0x1edf64496,l36),(0x182b239bd,l13),(-0x182b239bd,l20),(-0xcfa23cb4,l17),(0xcfa23cb4,l62),(0x82f17d1c,l10),(-0x82f17d1c,l38),(0x1cdab22fc,l4),(-0x1cdab22fc,l34),(0x2e5fa62b,l11),(-0x2e5fa62b,l55),(-0x10b3535b,l9),(0x10b3535b,l61),(0xf28f1ad,l59),(-0xf28f1ad,l65),(-0xedf00aa,l6),(0xedf00aa,l60),(0x2dbff60,l30),(-0x2dbff60,l43)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, #[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,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,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,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,0x68190020d24c18a240a6b401800000000003e0640080000003c8cc0c8c03071268c5920535a00c0d0cb481240f7e4018000000000188124010016324440c0a2d005000122408c606e2008000000004c1c0530080000249045406c801800000002207014c02], #[]⟩
def dynamicCode : Nat := ((((((((((((((((((((((((((((0x1a602ec858c0d1cd4513e3058e5701be1d104514607ee16149581f9a810575ed1c7850018a0995b09c2084021e348bf919e50564321ae90cafada9f664111070062757102223ea94d1d576e0a879e5157f47cf6d1079e5157f47cf6d0e4870f94d56fb07b64870f94d56fb07a880881658e806584285d56218e075e50cd5df06fec1e5b214512fa49ca0b585a63d338df705340b0232191fc8d1c25037c5a2dbaa758e9e82cf8241707257f8d0c711c808a847b9bf400111c80e02e0581c6928ee0f59858e1f6461948e77b8825393f465f75f505848ac09007380d114101652bea0560f66021c766ee7c6ae90e099f7b2324d8b305000ab2743edee1a9e84808043605458e486dc008208e7a90eec5857e05ccb848401b02cee682da3f7dac602372fbe524c084001000012b214412105090001db910b1581288c204460481bd2d9f600d2104c6cced20e04e4bfa9b281204ad94009030780202140bc350bc8d523c4b4ae977e28682603c90f0a17169df820968737b6094207c02113c0a67a0c1061e7014e5d699442490134fd9024030d1581891cf5d00801285c746002083903eecac148000337f980008002cfd0bd7ab03001e7f79b3ea0482420ac09000043870dd3b08380f12f1bee478e18edba20a3c2725d514a083b5e76ee0d000532bd593020f80424901e0a6e0380c3684334e431d01038cfe577e0782053601bd3a38101eeba65400208888b9be65520001406f40008003bfe3f32b00c00b4842d7b01c2410a407000040a4424140006b24001a9888404c07007c604e06e2d145a9473e90604b2ceccb4600047fc8112020f804041c060f40380b72c0ed2501390c55661a1833a4f374026086d6d8700021f022020001e74da93020f8042081e2a2cf7228a02255100438f7c63dfe091145fd93edd2021073040733c4002dc696c5085a4216bd9300016e36002200f7c049322904230080000e599245edf68a74030d926ea199ea3c31845c3cb1d121c8a8058998070818be5eefbc8023027cfdb66440086f23d79c1e006171b3b17c722020a40800003a640013e8f0641043541817761d25a44083c0101060183d00e2298eac4fb405bd65e360809d7fbcae51081d30d00a011fec7e1308003529f7e4c083e01082003cb6f73c38f0abab02dc88a4a5555ade808735fcafd8786002dc696c5063390fe5f898000b71b00088023e2e93aa48042400c0000d29c180b149fe4838c01b7eb31f1869af0bf67e1e185d5c5036890e73feb6efc8023dcd6b4d64400385924b31e00dbb54c19c0286d2f22590104a0200001d420009aa4001644851088414240017c84410140027c66455af8df141045fa6612810666e75f79a00f180e3a24098306f9815081f00404082c09017004010046923fb19898a2dedf29b470106f655f93041e0040000501c209e75b1618761206d14006a6175214005a6608028103a0080000c83042a63bd3e0c3aa6879ae3011b8ae38908c2080021841b589c1430cde193f88012b2771109840e802000027c8000b1100033d220622102118808684001404c0a0004e621fe3b01505f8d22fe467941590c86ba432beb6a7d99044260c50c606586186680600500480264300401a09a0b0fd05e081774a1584412f09d32411c081e7e8fae3410a248f) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 33 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case14" = "QuadHeightCover18Case14" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 33 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case14
private def zz2399:"s095f"="s095f":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case15
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l17 l22 l23 l25 l27 l29 l30 l31 l33 l34 l35 l36 l37 l38 l4 l41 l42 l43 l46 l51 l55 l57 l6 l60 l61 l62 l63 l64 l8 l9)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x3e14c82cf, -0x48de0a050, -0x6d5880c14,0x5a313812], ![-0x48de0a050, -0xbc7791798,0xc7cfab62,0x473c0dcb4], ![-0x6d5880c14,0xc7cfab62, -0x1da3807115,0x490bd0c56], ![0x5a313812,0x473c0dcb4,0x490bd0c56, -0x247a76b28]]
noncomputable def hinges:Hinges:=[(-0xedf00aa,l6),(0x1cdab22fc,l4),(-0x10b3535b,l9),(-0x1edf64496,l8),(0x2e5fa62b,l11),(0x82f17d1c,l10),(0x4acf73ac2,l14),(-0xd06b2ebc,l17),(0x1ab46c910,l15),(0xa73dfa46,l23),(0x2e4f166e4,l22),(-0x247a76b28,l27),(0x247a76b28,l29),(-0x4acf73ac2,l25),(0x48a183fc,l31),(0x37614d88,l30),(0x247a76b28,l33),(-0x82f17d1c,l38),(-0x247a76b28,l35),(0x1edf64496,l36),(0x247a76b28,l37),(-0x1cdab22fc,l34),(-0x37614d88,l43),(-0x2e4f166e4,l42),(-0x1ab46c910,l41),(0x362d6716,l46),(0x247a76b28,l51),(-0x2e5fa62b,l55),(-0x48a183fc,l57),(0x10b3535b,l61),(0xedf00aa,l60),(-0xa73dfa46,l63),(0xd06b2ebc,l62),(-0x362d6716,l64)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x247a76b28,l27),(0x247a76b28,l29),(0x247a76b28,l33),(-0x247a76b28,l35),(0x247a76b28,l37),(0x247a76b28,l51),(0x4acf73ac2,l14),(-0x4acf73ac2,l25),(0x2e4f166e4,l22),(-0x2e4f166e4,l42),(-0x1edf64496,l8),(0x1edf64496,l36),(0xa73dfa46,l23),(-0xa73dfa46,l63),(-0xd06b2ebc,l17),(0xd06b2ebc,l62),(0x82f17d1c,l10),(-0x82f17d1c,l38),(0x1cdab22fc,l4),(-0x1cdab22fc,l34),(0x48a183fc,l31),(-0x48a183fc,l57),(0x1ab46c910,l15),(-0x1ab46c910,l41),(0x2e5fa62b,l11),(-0x2e5fa62b,l55),(0x37614d88,l30),(-0x37614d88,l43),(0x362d6716,l46),(-0x362d6716,l64),(-0x10b3535b,l9),(0x10b3535b,l61),(-0xedf00aa,l6),(0xedf00aa,l60)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨71, 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#[]⟩
def dynamicCode : Nat := (((((((((((((((((((((((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 35 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case15" = "QuadHeightCover18Case15" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 35 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case15
private def zz2400:"s0960"="s0960":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case16
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l14 l15 l17 l22 l25 l27 l29 l33 l35 l37 l4 l42 l43 l5 l51 l63 l67)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![l67, ![-0x59514ba00, -0x2ff6c23cc0,0x7c8ab0d20,0x373acb110], ![-0x2a9670cb0,0x7c8ab0d20, -0x237cd2c555,0x599664816], ![0x16e3600,0x373acb110,0x599664816, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x1d40a3ad,l5),(0x4876f8b4,l4),(0x185b3836,l11),(-0x34e14ad8,l10),(0x11e1a3000,l14),(-0xf5682128,l17),(0x7ddcdc728,l15),(0x36b36bfb0,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x11e1a3000,l25),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x12239f36,l43),(-0xfb7b95ad,l42),(0x2cb417800,l51),(-0xfb1e197a,l63)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x7ddcdc728,l15),(0x36b36bfb0,l22),(-0xfb1e197a,l63),(0x11e1a3000,l14),(-0x11e1a3000,l25),(-0xf5682128,l17),(-0xfb7b95ad,l42),(-0x34e14ad8,l10),(0x185b3836,l11),(-0x12239f36,l43),(0x4876f8b4,l4),(-0x1d40a3ad,l5)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,0x1106803cc030608880c202e6802831c4906702934014000000001a0710040a20ca10805c10050001506c240588018000000000d032004000000000a031004000000110f014c02], #[]⟩
def dynamicCode : Nat := (((((((0x2c90c8276796249ddf0b56f424824746e69a3070169dd1052874dc154f682473532bf8f61c007ca5394949c2090021a3cf0d0689adbcfab6f38157e4c1d0188a28a24b20a20b18b0cb04801c020080368aed28527439a480044aa200a246c93b03d069000112a8802c82e91bc93014414bfba1c40a1039f374e50586161f931982c0478cfcfb81c8212804000077080017f18234c1d5a58103ac6edd1af2c61f631fff048cec4748878600c06e8b028200a8ed84b74260c230080000a0904805f18a3d54ccf006e28d050a3b56a2ebaa11ab04205a986a273a7ce04ba0e19e56eef57c8ab5d1c6003f7f2b8bf7fe64ac2800043b68b4369268e0c0090fcd1ffce2866881c5e7ec2fe5230925455a35740a9f427895b61ef027144107c00017218231686682e10b1c12edabbe8c81c4de444c20c91846db097b3881896ea518274b0c75d2e234f450849787da06890414) <<< 16000) +
    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)) <<< 16000) +
    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))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case16" = "QuadHeightCover18Case16" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case16
private def zz2401:"s0961"="s0961":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case17
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l12 l13 l17 l20 l22 l23 l25 l27 l29 l31 l33 l35 l37 l4 l41 l42 l5 l51 l57 l58 l62 l63 l65)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0xc305dd564, -0x59514ba00, -0x3c2106ffc,0x1ef13bc], ![-0x59514ba00, -0x2f39196658,0x7c8dc6f80,0x363f512c4], ![-0x3c2106ffc,0x7c8dc6f80, -0x237cd2c555,0x599664816], ![0x1ef13bc,0x363f512c4,0x599664816, -0x2cb417800]]
noncomputable def hinges:Hinges:=[(-0x1d40a3ad,l5),(0x4876f8b4,l4),(0x185b3836,l11),(-0x34e14ad8,l10),(0x20e2a2e76,l13),(-0x54cb8ac4,l12),(-0x1f3830f64,l17),(-0x1ae3cfbc,l20),(0x1469fc16b,l23),(0x1b2329b81,l22),(-0x2cb417800,l27),(0x2cb417800,l29),(-0x122180f18,l25),(0x11872c892,l31),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(-0x3b3ad6d1,l42),(-0x11ad30bc,l41),(0x2cb417800,l51),(-0xafc7a05e,l57),(0x1ded27a,l58),(-0x842e5ead,l63),(-0xcf89e6e2,l62),(-0x9f4a40,l65)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x2cb417800,l27),(0x2cb417800,l29),(0x2cb417800,l33),(-0x2cb417800,l35),(0x2cb417800,l37),(0x2cb417800,l51),(0x1469fc16b,l23),(-0x1f3830f64,l17),(0x11872c892,l31),(0x20e2a2e76,l13),(-0x122180f18,l25),(-0xafc7a05e,l57),(0x1b2329b81,l22),(-0xcf89e6e2,l62),(-0x842e5ead,l63),(-0x34e14ad8,l10),(0x185b3836,l11),(-0x3b3ad6d1,l42),(-0x54cb8ac4,l12),(0x4876f8b4,l4),(-0x1d40a3ad,l5),(-0x1ae3cfbc,l20),(-0x11ad30bc,l41),(0x1ded27a,l58),(-0x9f4a40,l65)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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], #[]⟩
def dynamicCode : Nat := ((((((((((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) <<< 16000) +
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)) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 26 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case17" = "QuadHeightCover18Case17" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 26 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case17
private def zz2402:"s0962"="s0962":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case18
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l17 l27 l29 l33 l34 l35 l37 l38 l4 l5 l51 l54 l55 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x289aa86d8, -0x742b8d00, -0xaef86e80,0x16e3600], ![-0x742b8d00, -0x34b1f642c,0x78b5206c,0x3d2f6384], ![-0xaef86e80,0x78b5206c, -0x2a8cda35c,0x7707f8b8], ![0x16e3600,0x3d2f6384,0x7707f8b8, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0x54a4c10,l6),(-0x13417e3,l5),(0x4c8f3414,l4),(-0x25a6ac5,l11),(-0xeb88a98,l10),(0x4eb7f0ac,l17),(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(0xeb88a98,l38),(-0x3acce180,l35),(0x3acce180,l37),(-0x4c8f3414,l34),(0x3acce180,l51),(0x25a6ac5,l55),(0x13417e3,l54),(0x54a4c10,l60),(-0x4eb7f0ac,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(0x4eb7f0ac,l17),(-0x4eb7f0ac,l62),(0x4c8f3414,l4),(-0x4c8f3414,l34),(-0xeb88a98,l10),(0xeb88a98,l38),(-0x54a4c10,l6),(0x54a4c10,l60),(-0x25a6ac5,l11),(0x25a6ac5,l55),(-0x13417e3,l5),(0x13417e3,l54)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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], #[]⟩
def dynamicCode : Nat := (((((((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) <<< 16000) +
    0x0c271a0614330d1df9020701e990200656307d013840f80400005488188680c024000be0400204480051010018f23233b472ed30102bffbcfbc08c2807b7edf8101cc13a0c7f9212969be746081049a688960e0f2d7bf0060400a59c172e02067c3d8c045b2004803091c67dede5209180337f98007180337f8de081402fb8348c71001d4b3cd080c003c75954705acddffea080216919209260009004000034668863d2ab43f01866bb11662e8384d8c946e2dc3040aee498b7c38254cb0219f83032eec0f7a0028054053b4d98200479d4a7aec0800c59619a58cd6410a00900003fa40bc2405c1202d090160080ac04054020290100031f10282581390c0987604a230240dc0a7e1cac622008023f9e9d34df0e02e5176cc44d140423ec9c4dc2100ac8f8c484f911077e009e6010ea071e38e48072accd3de951382b1ebd809d5a07c692d5e605342b03441108eb08b7befa12df123de70a65634aae70cf34663445ff561f061848000600866ea3aae5497966fa0eafeb3eba4c5ae496c7b833c51be478700362fa248b6afbb66ce4b58075bfa42dd16866a1c5d35d86c887c0f04000bce128102e49509ae02a16e6996d196b9e47c3c0b8cb8ec979d5b00034b72dd214530d69b340e94d57895c3cb051cb95af90934aabf5d340007ca54934f79cb48f2e5fdfec46ac957eb7668878a3275b66b897f54a16ab1ce879b1077cdbf544ff23e7dbc3dfbfdcd7f168c8a520db2f801186e01802008a2b01b099010434d0e7b008234fec760282161abf104045486cf78c003bd1ab40400015698404e183e0100001542044130210901000c07c0403c030001fa38666261080a296f3f07f9a83918c2f23991da8e98b90cb6db41f80376416ea7eceb82d5e4261f79c628aec12535b13bd0880800101e1e7d497b5a7f412e1726430f3c4cc89e2e884726d47ed68e93b6f32e7b2f093f2d1fbe5f6f76c633f601b62cb6720201c7b887305afe4092000bcbdf9dab3684c422d805b24f7cad70aea03ac45086cd241eb2d2077b5527c60b7d43b6967803008000954fe1dcdf56a917e1850dcfe9c320d9da946f53204427f920ea0e59f0d5b0dbed9299412db2e98ff07cf57444defc40010d7964d4989c68e3c0e180491110b49ea20e1bdb8e333917eaf4db92adfd766927bb9e552ec15c9b97d373c355a005164ec5efb925bde1182fc7fe574ae20e40d3f9f77ae71cace43ed904be9878c18d96cdd1b3f82078d14ad5d6c3f1c44214c2ad0000258cdb8d803d2f6385d0ae33fbaccd3cc0f283e306a8968d4fdab55c5c3d9ceb73a105e552ba9c8c000000000000000007be4799d91ec5432d62a9fd48291a3fdb424af846fb0000000000000000000000000000000000000000002998a28e08e008000020205661c8a7f647974884d6a7e720281c5b8c6263072c440a1958cbdb3fd84aaf346b66fa371403f9b37eb65cac47c494ac1dd704ff41c3142bf87e541236c787896811cd824929149c33d417ce1d75b130992fcc492f813097f30445bde1fe0ecb4d82db46e05b3599006a232fe6bfad40f0acc71781f6636fd13e8cf4815963ce5e2846c1abfa96b629d4001db4d044208c9a46dfa8341ed3a3a108cdc87c6d7931322ca3fe995ff15976005bc7ec553a651826a66f9b07536fb683d997cb68750449b0502c9d124216269cd994d14083c0b83d480e113f691f920d4565e8e706a18d7b7d8ec1d12edb160ccdfdabe577a894b13994cde1b7f831423c37841fd779e5c249ac63f18e0229c771833030e20040b27fea8d9e5cca58ed5b736ff8d87fb4636bcf0df6f364d712c3640ce721c4edec9127bcd175581ab5b50793c4c2c30aa5963e2e72f54b4f8d0707a977d0c644a49fa9ae2206a623ba231cc54bdb3e48f12327c0d812315fee608a083af9c8c6106349be16b77f0a95409ac94df0c3b1296dcd343a5bf82a035c12dd1d11bde80019eb07c6310d4742f42702019c85dfe4ac5706d97e0b27fc6ec2fab531b6ed806d09c056b468f11cc00f583aec6cf5b8528807474e67b14e2e4c5dfaf589d5285b13a3c1ff0f45f5833da6ec17ba865eec8717376981fc8efd34896c08d109aab4d3d15d0f78ba0b4fb379c96f5286cddd6ef8cd4eadf51422c68ff9472320179400061c10025cb3d67bf65976e326d528297138cf93dd18dc7335beff9e0000000000000000f016111ce23c66017756159bcb3e5562e6d02f0ce1170000000000000003944ebc6d6cfb0b7491c94589e8af4c8e0f75aa4f7ba000000000000000000000000000000000000000000150c40c60050010111ecb8bc629cae3aa25ebd2fe272d16196e6f42a95887142cdcef49c7059b90db45d592e73e10c3ce76729b99521bd747f3aead448a81fbeba290f4e204d6e14e7fc95959233d2e036aee218ed90c87ea6fa1820d6a514e9e1cd33661ae846a21977b219237ba94820dbc85c0dc81237bd72a1abbceb499948b8d95b42834b6a743c9f85ebd46a3b1fdb7123c6ccaf040c0881652a1e71320b1abe1fa87342c3d00087920061544014a00f81b8a22ccfd229d79bfdd41834f14963b0003f3400000000000000000000000000000000000000000a25c9c83fab060590410c08808a0080060203d0be85bc356a635eff162d23b6918d0d1aa5903d121ab1c1fcb8434af23e1cb389e27e9e72a2df68126c42bffab8e2895b08f1533841c4c0984f6a139e275ae24861ba23573b094a5fe1d95abb146996d7c8f33b23d8a865ac553fa9052347fb68495f08df60000000000000000000000000)) <<< 16000) +
    0x000000000000000005312082062051c41c21420c0000040170480200da2a3317b2bcc4880c58df1a81c40066ff300041000b714260a05e8540f0da4822c53368891c10134fd9000a080337f9800900e16c06090004a45094051455b008b670b192fa091038fdd5dbf495f4e3880535eb737dadf1d281628f4a777d7bf320e0810e18ad2e8247c04002e25ef41463323c080011d9d2f20d20700013f8f3de90c5ef004728d62bb9f58e88e02cc938a1e83a0000afc80e8ac07027631d404b20048c0337f980082002dc509858511388fdb18082aecd21050202dc6c00020dcb8a487058024ab440b0600089544001321044020d20860cd3923445e0485338c0c02dc6c0018202c0c5970e0648e9310d2c10112a8800304b979d48b3400f82e7618900034aea3c00004a487dc350011006348311e47c1a52a618600f71e84deae03444a18627faad81144092f73a676243381a738cb2b8cc0d2c10508b4fbcd2230c140d6d0ea4508e20005192d5974066180040d9814e40a9f42404801a02a00009d0e9057a9fedb4688adf3d5c88706080c676306060269fb2001871629ed9503040631bc93c6802e5b5214848001da23c1c2800269fb2000000a7231af1ba0024014791e67647b150cb58aa7f520a468ff6d092be11bec000000000000000000000000000000000000000000a65c9c83fab060591a40c31a20a20c18619000c060000401a00042440010c48004649c30304a6c520c280cdfe6000b18b066b1cb091804d3f640041001129e390b0991288f2d01060dfbf4000b003998ae9603000337f9800dc821200a34d1576690834b066ff3003074e5230563039523f9c0082e9c5500014105818b2e3002bbfcb5020001a5751e1000225510000009490fb8e8008002183f829732c68a21c41f40a280c65cdc606f93b7580819e24496638048b2f438a00721fe6f3800f004000051c80019d901b050002a0901a09f91e67647b150cb58aa7f520a468ff6d092be11bec000000000000000000000000000000000000000000a65c9c83fab060591451220e214108088004001498e674d1086ff061c6074bce2760a769163db05a5a5223abb27b97f1576b8a420d54000bf480c868060140026b84006188800d3590171580b00adc6c0000b71b001f818c7eb7c723a3a045e06e288b33f48a75e6ff75060d3c5258ec000fcd0000000000000000000000000000000000000000028976720feac1816630c40a286284282000aa296be772e61e48d36a84ff82a64a7d57c2ce2694dc49ad0f38b2a3a936daab42977e931ee1f3fa55a5e854eb9235fcc7d3358fef40a7b9c314847aad85df29ab9168546f0d9d7d71728dc972bf908f8c457106c50596bc18164711abd0e648e16a421878591d0bf2098b907101ca4c78ca86084c75eebc1450840282295f470485acd0369c5069553548f9c300b51254dc602023692c2c1380003e8410140160000768db8d801e97b1c2840a712ed4d300b81ff23ccec8f62a196b154fea4148d1feda1257c237d80000000000000000000000000000000000000000014c882040c504404500000002cb891ec6188431f1772cc0d8370debf2bf1d685e6c692388b5707a862c82ecaadac85f7241ae2cadf8c37bd6a0a2f82a424c1a86152cefd2cb6431ee7a52b1257123400110480a88c05045803c998ca840299696cd40400222c1e008492b13fac911fe84afa201447a83148e8fea741392b0361705cafc8accfd9660bf7bcd514208197abe33aab2ca20d54e3aa240866f6ac7874414b72f3065e83ca4db0e26264a74283020000ee7912d880b578cfb868ad2d129692b201ae1479e5c7aec65ecaf5d33ed4b0f8f2a000ffd741ce535ed6f0181f2b12ede1560b5a056c689ba8c78f0861f00391113ee2b06fba000061d7284c9b843406f3a184ed7979246ef4265ad0a54447161740a4999345199e75b1d2bb3f2d77f5ef84eaf6c3e1bbcc021abf5337f1370e138de02162e95bd46c8bbb15888970aa5dbe1c9c131b91d25f5692efeaba9859d6e07241e6ed0e7bf873574c2f50a45cf91456e88f0e384104df84169001090d788a02013242000469bf093c896181001a093916002da08e1c900023c67584000047169c0942084021008010040000111d37a5af6cdc38600af78fe2c00501633a120006c8eec480000ada6644a084201080200802000008880982800055880904c04407014010040080480000dc807888038140006b440010ac8006161000cd120031da683de087b9c08100b71ae50a02f1ffde284002c1fded6180016e35ee080143468f22a84c30420109264ee99218c48c00862064420602654dacb10206fd49114c90a4daeed2f22800b56f20bf10012278802c02003140290c690004a028926e8b31b2a78918047868c000818ae89717dd0718047867df0081008b2b2946c90ad86389d4688022f38b4fa4721c00a008000032640341724d27d418104082d690cab9212c3f04b783840104408f0a0022caf31c2001ee173e5040023e99f504e084401092604c57ef73c48c011e1a3000206127b7a43900e30047867df008102c5dc85c2e484889089256a2003f3baec6f4990e085204000019c200063840303601613814388a6748e29b7d9e871c37bb47a3e18254ea23b840071cef09060482f8673098207c0210408201ee6881405b8d80038a5da4bc07185016e35b80e18eefd044c702839025dc13041080400004cc8050480240400053e40026288040e801c6400c2a0050900202800c0400402000b72200202000010021e81))
theorem certificate_valid : DynamicPackedCheck.check dynamicTables 19 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case18" = "QuadHeightCover18Case18" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 19 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case18
private def zz2403:"s0963"="s0963":=by decide+kernel
end 
section 
namespace Green24Proof.QuadHeightCover18Case19
open EndToEndTupleState (State qPath initial)
open BranchWitnessAtoms
open ExistentialState (V S P M root)
open IndexedNatTreeCheck (K)
open NumericLinearAtoms (l10 l11 l13 l14 l15 l16 l17 l20 l25 l27 l29 l30 l31 l33 l34 l35 l37 l38 l4 l41 l43 l5 l51 l54 l55 l56 l57 l6 l60 l62)
noncomputable section
open IntegerQuadraticCertificates hiding Certificate check check_sound
open OrthantQuadraticCertificates
open StateCompactData (qs)
open DictionaryOrthantPackedData (LinearWitness)
open FiveBitDenseData (decodeTable)
abbrev constraints:=ScalarRowDefaults.constraints
noncomputable def base:Quadratic:=![![0x1198f11d8, -0x742b8d00, -0xaef86ec8,0x16e3600], ![-0x742b8d00, -0x12842b080,0x2a3e0e50,0x37873e24], ![-0xaef86ec8,0x2a3e0e50, -0x2a8cda35c,0x7707f8b8], ![0x16e3600,0x37873e24,0x7707f8b8, -0x3acce180]]
noncomputable def hinges:Hinges:=[(-0x54a4c10,l6),(-0x13417e3,l5),(0x4c8f3414,l4),(-0x25a6ac5,l11),(-0xeb88a98,l10),(0x6bc67bec,l14),(-0x54a15e4e,l13),(0x1d3d128,l17),(0x2c1ed2fa,l16),(0x8e2b5de2,l15),(0x54a15e4e,l20),(-0x3acce180,l27),(0x3acce180,l29),(-0x6bc67bec,l25),(0x387a028,l31),(-0x8db83c6,l30),(0x3acce180,l33),(0xeb88a98,l38),(-0x3acce180,l35),(0x3acce180,l37),(-0x4c8f3414,l34),(0x8db83c6,l43),(-0x8e2b5de2,l41),(0x3acce180,l51),(0x25a6ac5,l55),(0x13417e3,l54),(-0x387a028,l57),(-0x2c1ed2fa,l56),(0x54a4c10,l60),(-0x1d3d128,l62)]
def normalizationDenominator:ℤ:=0x59682f000
noncomputable def slack (x:Point):ℝ :=
  (quadraticEval base x + hingeEval hinges x) / normalizationDenominator
abbrev constraintsNat:=ScalarRowDefaults.constraintsNat

noncomputable def reordered : Hinges := [(-0x3acce180,l27),(0x3acce180,l29),(0x3acce180,l33),(-0x3acce180,l35),(0x3acce180,l37),(0x3acce180,l51),(0x6bc67bec,l14),(-0x6bc67bec,l25),(-0x54a15e4e,l13),(0x54a15e4e,l20),(0x8e2b5de2,l15),(-0x8e2b5de2,l41),(0x2c1ed2fa,l16),(-0x2c1ed2fa,l56),(0x4c8f3414,l4),(-0x4c8f3414,l34),(-0xeb88a98,l10),(0xeb88a98,l38),(-0x8db83c6,l30),(0x8db83c6,l43),(0x387a028,l31),(-0x387a028,l57),(-0x54a4c10,l6),(0x54a4c10,l60),(-0x25a6ac5,l11),(0x25a6ac5,l55),(0x1d3d128,l17),(-0x1d3d128,l62),(-0x13417e3,l5),(0x13417e3,l54)]
def dynamicTables : DynamicPackedCheck.Tables := ⟨65, #[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,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,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], #[]⟩
def dynamicCode : Nat := ((((((((((((((((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) <<< 16000) +
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theorem certificate_valid : DynamicPackedCheck.check dynamicTables 31 dynamicCode
    (fun i => EndToEndTupleCheck.ofVec (constraintsNat i)) (EndToEndTupleCheck.ofMat base) reordered = true := by
  decide +kernel
private def dynamicSync : "QuadHeightCover18Case19" = "QuadHeightCover18Case19" := by decide +kernel
theorem reordered_perm : reordered.Perm hinges := by decide +kernel
theorem expression_eq (x : Point) : hingeEval reordered x = hingeEval hinges x := by
  exact (reordered_perm.map (fun t => (t.1 : ℝ) * (max (linearEval t.2 x) 0)^2)).sum_eq
theorem nonnegative (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ slack x:=by
  have h := DynamicPackedCheck.scalar_nonnegative dynamicTables 31 dynamicCode base reordered
    normalizationDenominator certificate_valid (by decide +kernel) x hx
  simpa only [slack, expression_eq] using h
end
end Green24Proof.QuadHeightCover18Case19
private def zz2404:"s0964"="s0964":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover18Rows
open FullPhaseRows (Phase)
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows
def rowsChunk0:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x162005faf848053dbc8ce07a20003dceb94801ea597caee1ea2005faf848006c8c3e2ea14a200779ae5800a87b9f8c201a20003dceb948018d1b7bec62200779ae5806bd1909e07d2001389b48015b7b4f21ed20003dceb948003c5dc968606d20001eeb5ca8001cd8cbbd214d2000bf5f0c006b182c601d200779ae580029e8d8bfe520003dceb948014f28eb5f2079200050c019200050c120003dceb948014f2c291ee07c20001eeb5ca802cc782f7be42002fd7c28004e5bbbef207820003dceb948054d3d2bfee1e820003dceb948003fdecd5fa020003dceb94802fe783eaee14]
def rowsChunk1:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x107a600050c01a600050c260003dceb948014dbc58c8207d60003dceb94800390e3a8ce16d60003dceb94807dcabaa6560003dceb948001f0b9819e16003bcdb2c018c6a58a07f20001eeb5ca8002c8b7e8c21ef2005faf84806597f08206f20003dceb948002dcaecac615f20003dceb948001e5aeabaa01f2001389b480309584aa720003dceb948014f7fa86f607b200050c01b200050c320001eeb5ca800abc8dbec207e200779ae5800af0beada202e2003bcdb2c05c9c8cde1ce20003dceb948009acdfdabe01e2003bcdb2c0068882fc8214]
def rowsChunk2:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x17a000ef3acd05384cbea07ba00050c01ba00050c3a003bcdb2c002cc8ea0c607ea005faf84800efb92cada6a002fd7c28003f9b6e0f607aa0003dceb94803cb0c3adbe1faa005faf8480039cbcf5e62a0003dceb948028c2c1b7be17f6001389b48004fcb7fa1cf60003dceb94800183effeb676001de6d9a012e9dd86360003dceb9480028fe28aaa07e600050c1fe600779ae58001bcc8ee1ee60003dceb948002e8dff2ca02e6001de6d9a01a9fa99615e60003dceb948003c4a0dd9e01e60003dceb948004fef0d5be66001389b4806a86c8ca14]
def rowsChunk3:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11ee30003dceb94804bb6989201e30005faf8a006cce9ce63005faf84803db6f7ce07a300779ae5801ce6c8ca23001de6d9a015fca3ee17d3005faf84807fd7e61ed3000ef3acd013f4d2530001eeb5ca8001a4b286130003f40207c3003bcdb2c066d68492430003dceb948006938cf2be030003dceb9480038987dbf207fe0001eeb5ca8003af8cfbf617fe0001eeb5ca8001e1d7949a7e0001eeb5ca800182efcbca3e0003dceb948001a0f8e0921ffa0003dceb94800afb8dc9d202fa0003dceb94807187d8f614fa0001eeb5ca8023ed9aca01fa0001eeb5ca8004c49887c614]
def rowsChunk4:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11eab0003dceb948001f2c7c6da2b0003dceb948002eaf5fba603f70003dceb948023a3c4fa1df70003dceb948059acba05f700779ae58007e4ce8e77001389b48072fc9e03b7005faf8480029b8cae1cb70001eeb5ca8075fabe370003f402670003f402270003f402570003f402170003f40203f300779ae58024e0e0b21ef30003dceb94804ecfa19a15f30001eeb5ca8002aa8e8205f3003bcdb2c0138da6730003f402330003f4021fe30003dceb948003a98ebbba14]
def rowsChunk5:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x102d00003dceb94800593f78dd61dd00001eeb5ca8001d19ee79e500001fa0207c00001eeb5ca8055a3bdea1fc00003dceb948003d3a899a61ec00003dceb94800598eba28e02c00003dceb94800dfae08e9e1cc00003dceb948003d3a899aa05c00001eeb5ca8008aedfa24000779ae5807a88fe7f0003f4023f0003f40217fb005faf848026b6d98e1efb0001eeb5ca8020dce1c206fb0001eeb5ca8042ae8cf215fb002fd7c28006b394ba7b0003dceb948001f491fe3b0003f40207eb0003dceb948003b1b5ce966b005faf848043b2a9b614]
def rowsChunk6:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11fd40001eeb5ca806591d0821ed40001eeb5ca800f81ecc602d40003dceb948002d7b9e6ca1cd4005faf8480169dafc2540001fa02440001fa0207f000779ae58069e1a5b616f00009c4da8007e5d1a602f00001eeb5ca8060cfa89e1cf00003dceb9480019c81da9e700001fa0203e00003dceb948048d8e39a1fe00003dceb948009ecb3ec9a02e00001eeb5ca800788a8efc21de00003dceb948003c3e58eee05e0003bcdb2c0159298fe600003dceb948003e8a3fe07d00001eeb5ca8001d1a1e9e217d00001eeb5ca8020a0dc8e16d00002b196c04885ca14]
def rowsChunk7:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x102e80001eeb5ca8004e7c7b6aa1de80003dceb9480028b9acdb605e80003dceb948076fc81aa680001fa0207d80001eeb5ca8001a8c19e9616d80001eeb5ca800196e09f8a02d8005faf848037fec6e21dd800779ae5803c8ffde21cd80003dceb948003f6ecfa580001fa021fc800779ae58002d1e5e9e202c80017ebe180738385c21dc800779ae58001cbeaca9e05c8003bcdb2c010dfb3f2480001fa0207f40003dceb94801be0bdaa16f40003dceb948037c0faca06f40001eeb5ca800df09ed2740001fa02640001fa0214]
def rowsChunk8:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1010003dceb948003e8a3d607fc00779ae5801db8c5a61efc005faf848007c3ef8202fc0001eeb5ca80668a91ae1cfc0003dceb948006b5cac205fc003bcdb2c005a593827c0001fa026c0001fa0216dc0003dceb94800af2b5d21ddc0003dceb948005d8d5ae5c0001eeb5ca800290bc8a4c0001fa0207f80003dceb948002e7a5e79216f80001eeb5ca8001dfd68cea02f80001eeb5ca800197af921cf800779ae58016cda4a6780001fa0203e80001eeb5ca80048be2fd8e1fe80001eeb5ca800aa59dd8b216e8005faf84800194b2d1de14]
def rowsChunk9:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x1150001fa0217e10003dceb9480128bdca4d616e1002fd7c28003c0dbe9ea15e1005faf84800895999ade05e1002fd7c280038fce838a610001fa0217a1001de6d9a002a3debad202a100779ae5800abec4cbee05a100779ae58003eae890ca210001fa0203c1002fd7c28002818acff616c10003dceb94801ab4b984ca02c1003bcdb2c002a8a5bc8215c10003dceb948012cf9891ba05c1000ef3acd05294ead2410003dceb948003e8a3ea03810001eeb5ca8008e89eb0a617810003dceb94800ad4eadbe602810003dceb94802cf88fe6ae0581003bcdb2c001a68e919214]
def rowsChunk10:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x115890003dceb948011b99adb9e05890003dceb94800e9dfec48e090001fa0217f5001389b4800cd1afa616f50001eeb5ca800afe9ec0de02f50001eeb5ca8017c8e5ca15f5005faf848003a6fdb29201f50061d48002d48482750001eeb5ca800caaa2d2d603b50003dceb948001918ebeb617b50003dceb94800abd9ef29e15b50001eeb5ca800fd8f8b2fa35003bcdb2c003e88fc7ce07d50003dceb94800183e9d8ea16d50003dceb948032cccea602d50003dceb948003b887bb8601d500779ae58039a683ca55003bcdb2c03d84be16950001eeb5ca804494d5c601950003dceb948003ddedd4c614]
def rowsChunk11:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x11d0017ebe18001b5a2deea03e90017ebe1801693bafa17e900779ae58007dbf6a2a616e900779ae58002a2c383fe02e9003bcdb2c0018eb6bbb615e90001eeb5ca800ab9f7f4c605e90001eeb5ca8006c1d6aede690001eeb5ca8001f491e603a9001de6d9a001b6fff617a90003dceb948028b6e9de9615a90001eeb5ca800fdb96e9be05a90001eeb5ca8006bec4bcda29005faf848061d3ea03c900779ae58003b7a08c9e16c90003dceb948026e3a88e9a15c90003dceb94802c82dfd38a05c90001eeb5ca801089e3c09a490001fa0217890001eeb5ca800ebaf1abea1689003bcdb2c003fcdecdde14]
def rowsChunk12:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x108840003dceb948013e9cf82aa08830003dceb94801ec0a0a99608800001eeb5ca8009e7f9b3ae07fd0003dceb948046ee87c616fd003bcdb2c00787d08a02fd0003dceb948002fb8f93f614fd0001eeb5ca8075d3e1fe01fd00779ae58003d3e8ca7d00779ae5807a88fa01bd0001eeb5ca8002baeff0d63d0001fa0203dd001de6d9a026baa4e217dd005faf848001a8d1d48a16dd0003dceb948009e8ede7ae02dd0003dceb948001e5bebcae15dd0003dceb948011c6b182f214dd0001eeb5ca8006d399feae5d00779ae58006d0a995c6169d0001eeb5ca8009e782f7f2149d002fd7c28002c5a8c2a214]
def rowsChunk13:List (ℚ × Label):=PackedPhaseRowsData.decodeExtended [0x10894007d08010201010101010208930003dceb948020f68e0101010001020100089300779ae5801deeaaaa01010100010201000892000bf5f0c0398ceefa08900001eeb5ca802299998a088c0001eeb5ca803bd5d8ee088f004ca5d0018c85ce088800779ae5800e8494d208870003dceb94801eb59ac5d209]
def rows:List (ℚ × Label) :=
  rowsChunk0 ++ rowsChunk1 ++ rowsChunk2 ++ rowsChunk3 ++ rowsChunk4 ++ rowsChunk5 ++ rowsChunk6 ++ rowsChunk7 ++ rowsChunk8 ++ rowsChunk9 ++ rowsChunk10 ++ rowsChunk11 ++ rowsChunk12 ++ rowsChunk13
def quad0:Expression:=quadSlack rows 0 0 false
def quad0Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad0Target:NormalForm:=rationalNormal QuadHeightCover18Case0.base QuadHeightCover18Case0.hinges QuadHeightCover18Case0.normalizationDenominator
theorem quad0_identity:identityCheck quad0 quad0Rewrites quad0Target = true:=by decide +kernel
private def zz1772:"s06ec"="s06ec":=by decide+kernel
theorem quad0_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad0 x:=by
  rw [identityCheck_sound _ _ _ x quad0_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case0.base QuadHeightCover18Case0.hinges QuadHeightCover18Case0.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case0.nonnegative x hx
def quad1:Expression:=quadSlack rows 0 0 true
def quad1Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad1Target:NormalForm:=rationalNormal QuadHeightCover18Case1.base QuadHeightCover18Case1.hinges QuadHeightCover18Case1.normalizationDenominator
theorem quad1_identity:identityCheck quad1 quad1Rewrites quad1Target = true:=by decide +kernel
theorem quad1_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad1 x:=by
  rw [identityCheck_sound _ _ _ x quad1_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case1.base QuadHeightCover18Case1.hinges QuadHeightCover18Case1.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case1.nonnegative x hx
def quad2:Expression:=quadSlack rows 0 1 false
def quad2Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r55,RewriteAtoms.r63,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad2Target:NormalForm:=rationalNormal QuadHeightCover18Case2.base QuadHeightCover18Case2.hinges QuadHeightCover18Case2.normalizationDenominator
theorem quad2_identity:identityCheck quad2 quad2Rewrites quad2Target = true:=by decide +kernel
private def zz1773:"s06ed"="s06ed":=by decide+kernel
theorem quad2_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad2 x:=by
  rw [identityCheck_sound _ _ _ x quad2_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case2.base QuadHeightCover18Case2.hinges QuadHeightCover18Case2.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case2.nonnegative x hx
def quad3:Expression:=quadSlack rows 0 1 true
def quad3Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r20,RewriteAtoms.r67,RewriteAtoms.r23,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r48,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r55,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad3Target:NormalForm:=rationalNormal QuadHeightCover18Case3.base QuadHeightCover18Case3.hinges QuadHeightCover18Case3.normalizationDenominator
theorem quad3_identity:identityCheck quad3 quad3Rewrites quad3Target = true:=by decide +kernel
theorem quad3_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad3 x:=by
  rw [identityCheck_sound _ _ _ x quad3_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case3.base QuadHeightCover18Case3.hinges QuadHeightCover18Case3.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case3.nonnegative x hx
def quad4:Expression:=quadSlack rows 0 2 false
def quad4Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r59,RewriteAtoms.r20,RewriteAtoms.r17,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad4Target:NormalForm:=rationalNormal QuadHeightCover18Case4.base QuadHeightCover18Case4.hinges QuadHeightCover18Case4.normalizationDenominator
theorem quad4_identity:identityCheck quad4 quad4Rewrites quad4Target = true:=by decide +kernel
private def zz1774:"s06ee"="s06ee":=by decide+kernel
theorem quad4_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad4 x:=by
  rw [identityCheck_sound _ _ _ x quad4_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case4.base QuadHeightCover18Case4.hinges QuadHeightCover18Case4.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case4.nonnegative x hx
def quad5:Expression:=quadSlack rows 0 2 true
def quad5Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r20,RewriteAtoms.r25,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r19,RewriteAtoms.r50,RewriteAtoms.r1,RewriteAtoms.r54,RewriteAtoms.r3,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad5Target:NormalForm:=rationalNormal QuadHeightCover18Case5.base QuadHeightCover18Case5.hinges QuadHeightCover18Case5.normalizationDenominator
theorem quad5_identity:identityCheck quad5 quad5Rewrites quad5Target = true:=by decide +kernel
theorem quad5_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad5 x:=by
  rw [identityCheck_sound _ _ _ x quad5_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case5.base QuadHeightCover18Case5.hinges QuadHeightCover18Case5.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case5.nonnegative x hx
def quad6:Expression:=quadSlack rows 0 3 false
def quad6Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r78,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad6Target:NormalForm:=rationalNormal QuadHeightCover18Case6.base QuadHeightCover18Case6.hinges QuadHeightCover18Case6.normalizationDenominator
theorem quad6_identity:identityCheck quad6 quad6Rewrites quad6Target = true:=by decide +kernel
private def zz1775:"s06ef"="s06ef":=by decide+kernel
theorem quad6_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad6 x:=by
  rw [identityCheck_sound _ _ _ x quad6_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case6.base QuadHeightCover18Case6.hinges QuadHeightCover18Case6.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case6.nonnegative x hx
def quad7:Expression:=quadSlack rows 0 3 true
def quad7Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad7Target:NormalForm:=rationalNormal QuadHeightCover18Case7.base QuadHeightCover18Case7.hinges QuadHeightCover18Case7.normalizationDenominator
theorem quad7_identity:identityCheck quad7 quad7Rewrites quad7Target = true:=by decide +kernel
theorem quad7_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad7 x:=by
  rw [identityCheck_sound _ _ _ x quad7_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case7.base QuadHeightCover18Case7.hinges QuadHeightCover18Case7.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case7.nonnegative x hx
def quad8:Expression:=quadSlack rows 1 1 false
def quad8Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad8Target:NormalForm:=rationalNormal QuadHeightCover18Case8.base QuadHeightCover18Case8.hinges QuadHeightCover18Case8.normalizationDenominator
theorem quad8_identity:identityCheck quad8 quad8Rewrites quad8Target = true:=by decide +kernel
private def zz1776:"s06f0"="s06f0":=by decide+kernel
theorem quad8_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad8 x:=by
  rw [identityCheck_sound _ _ _ x quad8_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case8.base QuadHeightCover18Case8.hinges QuadHeightCover18Case8.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case8.nonnegative x hx
def quad9:Expression:=quadSlack rows 1 1 true
def quad9Rewrites:Rewrites:=[RewriteAtoms.r59,RewriteAtoms.r60,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad9Target:NormalForm:=rationalNormal QuadHeightCover18Case9.base QuadHeightCover18Case9.hinges QuadHeightCover18Case9.normalizationDenominator
theorem quad9_identity:identityCheck quad9 quad9Rewrites quad9Target = true:=by decide +kernel
theorem quad9_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad9 x:=by
  rw [identityCheck_sound _ _ _ x quad9_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case9.base QuadHeightCover18Case9.hinges QuadHeightCover18Case9.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case9.nonnegative x hx
def quad10:Expression:=quadSlack rows 1 2 false
def quad10Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r6,RewriteAtoms.r57,RewriteAtoms.r56,RewriteAtoms.r64,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad10Target:NormalForm:=rationalNormal QuadHeightCover18Case10.base QuadHeightCover18Case10.hinges QuadHeightCover18Case10.normalizationDenominator
theorem quad10_identity:identityCheck quad10 quad10Rewrites quad10Target = true:=by decide +kernel
private def zz1777:"s06f1"="s06f1":=by decide+kernel
theorem quad10_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad10 x:=by
  rw [identityCheck_sound _ _ _ x quad10_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case10.base QuadHeightCover18Case10.hinges QuadHeightCover18Case10.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case10.nonnegative x hx
def quad11:Expression:=quadSlack rows 1 2 true
def quad11Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r66,RewriteAtoms.r24,RewriteAtoms.r59,RewriteAtoms.r45,RewriteAtoms.r20,RewriteAtoms.r30,RewriteAtoms.r82,RewriteAtoms.r61,RewriteAtoms.r16,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r56,RewriteAtoms.r79,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad11Target:NormalForm:=rationalNormal QuadHeightCover18Case11.base QuadHeightCover18Case11.hinges QuadHeightCover18Case11.normalizationDenominator
theorem quad11_identity:identityCheck quad11 quad11Rewrites quad11Target = true:=by decide +kernel
theorem quad11_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad11 x:=by
  rw [identityCheck_sound _ _ _ x quad11_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case11.base QuadHeightCover18Case11.hinges QuadHeightCover18Case11.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case11.nonnegative x hx
def quad12:Expression:=quadSlack rows 1 3 false
def quad12Rewrites:Rewrites:=[RewriteAtoms.r80,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r5,RewriteAtoms.r64,RewriteAtoms.r4,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad12Target:NormalForm:=rationalNormal QuadHeightCover18Case12.base QuadHeightCover18Case12.hinges QuadHeightCover18Case12.normalizationDenominator
theorem quad12_identity:identityCheck quad12 quad12Rewrites quad12Target = true:=by decide +kernel
private def zz1778:"s06f2"="s06f2":=by decide+kernel
theorem quad12_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad12 x:=by
  rw [identityCheck_sound _ _ _ x quad12_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case12.base QuadHeightCover18Case12.hinges QuadHeightCover18Case12.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case12.nonnegative x hx
def quad13:Expression:=quadSlack rows 1 3 true
def quad13Rewrites:Rewrites:=[RewriteAtoms.r65,RewriteAtoms.r45,RewriteAtoms.r25,RewriteAtoms.r67,RewriteAtoms.r17,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r64,RewriteAtoms.r9,RewriteAtoms.r4,RewriteAtoms.r55,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad13Target:NormalForm:=rationalNormal QuadHeightCover18Case13.base QuadHeightCover18Case13.hinges QuadHeightCover18Case13.normalizationDenominator
theorem quad13_identity:identityCheck quad13 quad13Rewrites quad13Target = true:=by decide +kernel
theorem quad13_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad13 x:=by
  rw [identityCheck_sound _ _ _ x quad13_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case13.base QuadHeightCover18Case13.hinges QuadHeightCover18Case13.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case13.nonnegative x hx
def quad14:Expression:=quadSlack rows 2 2 false
def quad14Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r61,RewriteAtoms.r62,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad14Target:NormalForm:=rationalNormal QuadHeightCover18Case14.base QuadHeightCover18Case14.hinges QuadHeightCover18Case14.normalizationDenominator
theorem quad14_identity:identityCheck quad14 quad14Rewrites quad14Target = true:=by decide +kernel
private def zz1779:"s06f3"="s06f3":=by decide+kernel
theorem quad14_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad14 x:=by
  rw [identityCheck_sound _ _ _ x quad14_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case14.base QuadHeightCover18Case14.hinges QuadHeightCover18Case14.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case14.nonnegative x hx
def quad15:Expression:=quadSlack rows 2 2 true
def quad15Rewrites:Rewrites:=[RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r16,RewriteAtoms.r17,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r49,RewriteAtoms.r50,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r53,RewriteAtoms.r54,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r78,RewriteAtoms.r79,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r57,RewriteAtoms.r58,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad15Target:NormalForm:=rationalNormal QuadHeightCover18Case15.base QuadHeightCover18Case15.hinges QuadHeightCover18Case15.normalizationDenominator
theorem quad15_identity:identityCheck quad15 quad15Rewrites quad15Target = true:=by decide +kernel
theorem quad15_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad15 x:=by
  rw [identityCheck_sound _ _ _ x quad15_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case15.base QuadHeightCover18Case15.hinges QuadHeightCover18Case15.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case15.nonnegative x hx
def quad16:Expression:=quadSlack rows 2 3 false
def quad16Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r20,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r7,RewriteAtoms.r58,RewriteAtoms.r78,RewriteAtoms.r57,RewriteAtoms.r8,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad16Target:NormalForm:=rationalNormal QuadHeightCover18Case16.base QuadHeightCover18Case16.hinges QuadHeightCover18Case16.normalizationDenominator
theorem quad16_identity:identityCheck quad16 quad16Rewrites quad16Target = true:=by decide +kernel
private def zz1780:"s06f4"="s06f4":=by decide+kernel
theorem quad16_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad16 x:=by
  rw [identityCheck_sound _ _ _ x quad16_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case16.base QuadHeightCover18Case16.hinges QuadHeightCover18Case16.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case16.nonnegative x hx
def quad17:Expression:=quadSlack rows 2 3 true
def quad17Rewrites:Rewrites:=[RewriteAtoms.r22,RewriteAtoms.r65,RewriteAtoms.r24,RewriteAtoms.r45,RewriteAtoms.r62,RewriteAtoms.r68,RewriteAtoms.r48,RewriteAtoms.r1,RewriteAtoms.r52,RewriteAtoms.r3,RewriteAtoms.r5,RewriteAtoms.r79,RewriteAtoms.r64,RewriteAtoms.r58,RewriteAtoms.r4,RewriteAtoms.r78,RewriteAtoms.r6,RewriteAtoms.r63,RewriteAtoms.r57,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad17Target:NormalForm:=rationalNormal QuadHeightCover18Case17.base QuadHeightCover18Case17.hinges QuadHeightCover18Case17.normalizationDenominator
theorem quad17_identity:identityCheck quad17 quad17Rewrites quad17Target = true:=by decide +kernel
theorem quad17_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad17 x:=by
  rw [identityCheck_sound _ _ _ x quad17_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case17.base QuadHeightCover18Case17.hinges QuadHeightCover18Case17.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case17.nonnegative x hx
def quad18:Expression:=quadSlack rows 3 3 false
def quad18Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad18Target:NormalForm:=rationalNormal QuadHeightCover18Case18.base QuadHeightCover18Case18.hinges QuadHeightCover18Case18.normalizationDenominator
theorem quad18_identity:identityCheck quad18 quad18Rewrites quad18Target = true:=by decide +kernel
private def zz1781:"s06f5"="s06f5":=by decide+kernel
theorem quad18_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad18 x:=by
  rw [identityCheck_sound _ _ _ x quad18_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case18.base QuadHeightCover18Case18.hinges QuadHeightCover18Case18.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case18.nonnegative x hx
def quad19:Expression:=quadSlack rows 3 3 true
def quad19Rewrites:Rewrites:=[RewriteAtoms.r45,RewriteAtoms.r46,RewriteAtoms.r20,RewriteAtoms.r21,RewriteAtoms.r18,RewriteAtoms.r19,RewriteAtoms.r47,RewriteAtoms.r48,RewriteAtoms.r0,RewriteAtoms.r1,RewriteAtoms.r51,RewriteAtoms.r52,RewriteAtoms.r2,RewriteAtoms.r3,RewriteAtoms.r4,RewriteAtoms.r5,RewriteAtoms.r55,RewriteAtoms.r56,RewriteAtoms.r6,RewriteAtoms.r7,RewriteAtoms.r63,RewriteAtoms.r64,RewriteAtoms.r8,RewriteAtoms.r9,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15,RewriteAtoms.r10,RewriteAtoms.r11,RewriteAtoms.r12,RewriteAtoms.r13,RewriteAtoms.r14,RewriteAtoms.r15]
def quad19Target:NormalForm:=rationalNormal QuadHeightCover18Case19.base QuadHeightCover18Case19.hinges QuadHeightCover18Case19.normalizationDenominator
theorem quad19_identity:identityCheck quad19 quad19Rewrites quad19Target = true:=by decide +kernel
theorem quad19_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval quad19 x:=by
  rw [identityCheck_sound _ _ _ x quad19_identity]
  change 0 ≤ normalEval (rationalNormal QuadHeightCover18Case19.base QuadHeightCover18Case19.hinges QuadHeightCover18Case19.normalizationDenominator) x
  rw [rationalNormal_eval]
  exact QuadHeightCover18Case19.nonnegative x hx
def pair20:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 0 false
def pair20Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair20Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_20_base LocalPairs.compact_height18_pair_20_hinges
theorem pair20_identity:identityCheck pair20 pair20Rewrites pair20Target = true:=by decide +kernel
private def zz1782:"s06f6"="s06f6":=by decide+kernel
theorem pair20_target_eval (x:Point):normalEval pair20Target x = LocalPairs.height18_pair_20 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_20_base LocalPairs.compact_height18_pair_20_hinges x
theorem pair20_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair20 x:=by
  rw [identityCheck_sound _ _ _ x pair20_identity,pair20_target_eval]
  exact LocalPairs.height18_pair_20_nonneg (hx 0) (hx 1)
def pair21:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 0 true
def pair21Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair21Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_21_base LocalPairs.compact_height18_pair_21_hinges
theorem pair21_identity:identityCheck pair21 pair21Rewrites pair21Target = true:=by decide +kernel
theorem pair21_target_eval (x:Point):normalEval pair21Target x = LocalPairs.height18_pair_21 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_21_base LocalPairs.compact_height18_pair_21_hinges x
private def zz1783:"s06f7"="s06f7":=by decide+kernel
theorem pair21_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair21 x:=by
  rw [identityCheck_sound _ _ _ x pair21_identity,pair21_target_eval]
  exact LocalPairs.height18_pair_21_nonneg (hx 0) (hx 1)
def pair22:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 1 false
def pair22Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair22Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_22_base LocalPairs.compact_height18_pair_22_hinges
theorem pair22_identity:identityCheck pair22 pair22Rewrites pair22Target = true:=by decide +kernel
theorem pair22_target_eval (x:Point):normalEval pair22Target x = LocalPairs.height18_pair_22 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_22_base LocalPairs.compact_height18_pair_22_hinges x
theorem pair22_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair22 x:=by
  rw [identityCheck_sound _ _ _ x pair22_identity,pair22_target_eval]
  exact LocalPairs.height18_pair_22_nonneg (hx 0) (hx 1)
def pair23:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 1 true
def pair23Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair23Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_23_base LocalPairs.compact_height18_pair_23_hinges
private def zz1784:"s06f8"="s06f8":=by decide+kernel
theorem pair23_identity:identityCheck pair23 pair23Rewrites pair23Target = true:=by decide +kernel
theorem pair23_target_eval (x:Point):normalEval pair23Target x = LocalPairs.height18_pair_23 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_23_base LocalPairs.compact_height18_pair_23_hinges x
theorem pair23_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair23 x:=by
  rw [identityCheck_sound _ _ _ x pair23_identity,pair23_target_eval]
  exact LocalPairs.height18_pair_23_nonneg (hx 0) (hx 1)
def pair24:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 2 false
def pair24Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair24Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_24_base LocalPairs.compact_height18_pair_24_hinges
theorem pair24_identity:identityCheck pair24 pair24Rewrites pair24Target = true:=by decide +kernel
private def zz1785:"s06f9"="s06f9":=by decide+kernel
theorem pair24_target_eval (x:Point):normalEval pair24Target x = LocalPairs.height18_pair_24 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_24_base LocalPairs.compact_height18_pair_24_hinges x
theorem pair24_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair24 x:=by
  rw [identityCheck_sound _ _ _ x pair24_identity,pair24_target_eval]
  exact LocalPairs.height18_pair_24_nonneg (hx 0) (hx 1)
def pair25:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 2 true
def pair25Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r26,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair25Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_25_base LocalPairs.compact_height18_pair_25_hinges
theorem pair25_identity:identityCheck pair25 pair25Rewrites pair25Target = true:=by decide +kernel
theorem pair25_target_eval (x:Point):normalEval pair25Target x = LocalPairs.height18_pair_25 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_25_base LocalPairs.compact_height18_pair_25_hinges x
private def zz1786:"s06fa"="s06fa":=by decide+kernel
theorem pair25_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair25 x:=by
  rw [identityCheck_sound _ _ _ x pair25_identity,pair25_target_eval]
  exact LocalPairs.height18_pair_25_nonneg (hx 0) (hx 1)
def pair26:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 3 false
def pair26Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair26Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_26_base LocalPairs.compact_height18_pair_26_hinges
theorem pair26_identity:identityCheck pair26 pair26Rewrites pair26Target = true:=by decide +kernel
theorem pair26_target_eval (x:Point):normalEval pair26Target x = LocalPairs.height18_pair_26 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_26_base LocalPairs.compact_height18_pair_26_hinges x
theorem pair26_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair26 x:=by
  rw [identityCheck_sound _ _ _ x pair26_identity,pair26_target_eval]
  exact LocalPairs.height18_pair_26_nonneg (hx 0) (hx 1)
def pair27:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 0 3 true
def pair27Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair27Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_27_base LocalPairs.compact_height18_pair_27_hinges
private def zz1787:"s06fb"="s06fb":=by decide+kernel
theorem pair27_identity:identityCheck pair27 pair27Rewrites pair27Target = true:=by decide +kernel
theorem pair27_target_eval (x:Point):normalEval pair27Target x = LocalPairs.height18_pair_27 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_27_base LocalPairs.compact_height18_pair_27_hinges x
theorem pair27_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair27 x:=by
  rw [identityCheck_sound _ _ _ x pair27_identity,pair27_target_eval]
  exact LocalPairs.height18_pair_27_nonneg (hx 0) (hx 1)
def pair28:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 1 false
def pair28Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair28Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_28_base LocalPairs.compact_height18_pair_28_hinges
theorem pair28_identity:identityCheck pair28 pair28Rewrites pair28Target = true:=by decide +kernel
private def zz1788:"s06fc"="s06fc":=by decide+kernel
theorem pair28_target_eval (x:Point):normalEval pair28Target x = LocalPairs.height18_pair_28 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_28_base LocalPairs.compact_height18_pair_28_hinges x
theorem pair28_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair28 x:=by
  rw [identityCheck_sound _ _ _ x pair28_identity,pair28_target_eval]
  exact LocalPairs.height18_pair_28_nonneg (hx 0) (hx 1)
def pair29:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 1 true
def pair29Rewrites:Rewrites:=[RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair29Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_29_base LocalPairs.compact_height18_pair_29_hinges
theorem pair29_identity:identityCheck pair29 pair29Rewrites pair29Target = true:=by decide +kernel
theorem pair29_target_eval (x:Point):normalEval pair29Target x = LocalPairs.height18_pair_29 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_29_base LocalPairs.compact_height18_pair_29_hinges x
private def zz1789:"s06fd"="s06fd":=by decide+kernel
theorem pair29_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair29 x:=by
  rw [identityCheck_sound _ _ _ x pair29_identity,pair29_target_eval]
  exact LocalPairs.height18_pair_29_nonneg (hx 0) (hx 1)
def pair30:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 2 false
def pair30Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair30Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_30_base LocalPairs.compact_height18_pair_30_hinges
theorem pair30_identity:identityCheck pair30 pair30Rewrites pair30Target = true:=by decide +kernel
theorem pair30_target_eval (x:Point):normalEval pair30Target x = LocalPairs.height18_pair_30 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_30_base LocalPairs.compact_height18_pair_30_hinges x
theorem pair30_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair30 x:=by
  rw [identityCheck_sound _ _ _ x pair30_identity,pair30_target_eval]
  exact LocalPairs.height18_pair_30_nonneg (hx 0) (hx 1)
def pair31:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 2 true
def pair31Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair31Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_31_base LocalPairs.compact_height18_pair_31_hinges
private def zz1790:"s06fe"="s06fe":=by decide+kernel
theorem pair31_identity:identityCheck pair31 pair31Rewrites pair31Target = true:=by decide +kernel
theorem pair31_target_eval (x:Point):normalEval pair31Target x = LocalPairs.height18_pair_31 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_31_base LocalPairs.compact_height18_pair_31_hinges x
theorem pair31_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair31 x:=by
  rw [identityCheck_sound _ _ _ x pair31_identity,pair31_target_eval]
  exact LocalPairs.height18_pair_31_nonneg (hx 0) (hx 1)
def pair32:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 3 false
def pair32Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r2,RewriteAtoms.r49,RewriteAtoms.r53,RewriteAtoms.r2,RewriteAtoms.r70,RewriteAtoms.r71,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair32Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_32_base LocalPairs.compact_height18_pair_32_hinges
theorem pair32_identity:identityCheck pair32 pair32Rewrites pair32Target = true:=by decide +kernel
private def zz1791:"s06ff"="s06ff":=by decide+kernel
theorem pair32_target_eval (x:Point):normalEval pair32Target x = LocalPairs.height18_pair_32 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_32_base LocalPairs.compact_height18_pair_32_hinges x
theorem pair32_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair32 x:=by
  rw [identityCheck_sound _ _ _ x pair32_identity,pair32_target_eval]
  exact LocalPairs.height18_pair_32_nonneg (hx 0) (hx 1)
def pair33:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 1 3 true
def pair33Rewrites:Rewrites:=[RewriteAtoms.r47,RewriteAtoms.r53,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r2,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r72,RewriteAtoms.r71,RewriteAtoms.r18,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r70,RewriteAtoms.r72,RewriteAtoms.r27,RewriteAtoms.r71,RewriteAtoms.r69,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair33Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_33_base LocalPairs.compact_height18_pair_33_hinges
theorem pair33_identity:identityCheck pair33 pair33Rewrites pair33Target = true:=by decide +kernel
theorem pair33_target_eval (x:Point):normalEval pair33Target x = LocalPairs.height18_pair_33 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_33_base LocalPairs.compact_height18_pair_33_hinges x
private def zz1792:"s0700"="s0700":=by decide+kernel
theorem pair33_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair33 x:=by
  rw [identityCheck_sound _ _ _ x pair33_identity,pair33_target_eval]
  exact LocalPairs.height18_pair_33_nonneg (hx 0) (hx 1)
def pair34:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 2 2 false
def pair34Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair34Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_34_base LocalPairs.compact_height18_pair_34_hinges
theorem pair34_identity:identityCheck pair34 pair34Rewrites pair34Target = true:=by decide +kernel
theorem pair34_target_eval (x:Point):normalEval pair34Target x = LocalPairs.height18_pair_34 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_34_base LocalPairs.compact_height18_pair_34_hinges x
theorem pair34_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair34 x:=by
  rw [identityCheck_sound _ _ _ x pair34_identity,pair34_target_eval]
  exact LocalPairs.height18_pair_34_nonneg (hx 0) (hx 1)
def pair35:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 2 2 true
def pair35Rewrites:Rewrites:=[RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r49,RewriteAtoms.r72,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair35Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_35_base LocalPairs.compact_height18_pair_35_hinges
private def zz1793:"s0701"="s0701":=by decide+kernel
theorem pair35_identity:identityCheck pair35 pair35Rewrites pair35Target = true:=by decide +kernel
theorem pair35_target_eval (x:Point):normalEval pair35Target x = LocalPairs.height18_pair_35 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_35_base LocalPairs.compact_height18_pair_35_hinges x
theorem pair35_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair35 x:=by
  rw [identityCheck_sound _ _ _ x pair35_identity,pair35_target_eval]
  exact LocalPairs.height18_pair_35_nonneg (hx 0) (hx 1)
def pair36:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 2 3 false
def pair36Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair36Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_36_base LocalPairs.compact_height18_pair_36_hinges
theorem pair36_identity:identityCheck pair36 pair36Rewrites pair36Target = true:=by decide +kernel
private def zz1794:"s0702"="s0702":=by decide+kernel
theorem pair36_target_eval (x:Point):normalEval pair36Target x = LocalPairs.height18_pair_36 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_36_base LocalPairs.compact_height18_pair_36_hinges x
theorem pair36_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair36 x:=by
  rw [identityCheck_sound _ _ _ x pair36_identity,pair36_target_eval]
  exact LocalPairs.height18_pair_36_nonneg (hx 0) (hx 1)
def pair37:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 2 3 true
def pair37Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r53,RewriteAtoms.r49,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r53,RewriteAtoms.r47,RewriteAtoms.r0,RewriteAtoms.r51,RewriteAtoms.r2,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair37Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_37_base LocalPairs.compact_height18_pair_37_hinges
theorem pair37_identity:identityCheck pair37 pair37Rewrites pair37Target = true:=by decide +kernel
theorem pair37_target_eval (x:Point):normalEval pair37Target x = LocalPairs.height18_pair_37 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_37_base LocalPairs.compact_height18_pair_37_hinges x
private def zz1795:"s0703"="s0703":=by decide+kernel
theorem pair37_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair37 x:=by
  rw [identityCheck_sound _ _ _ x pair37_identity,pair37_target_eval]
  exact LocalPairs.height18_pair_37_nonneg (hx 0) (hx 1)
def pair38:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 3 3 false
def pair38Rewrites:Rewrites:=[RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair38Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_38_base LocalPairs.compact_height18_pair_38_hinges
theorem pair38_identity:identityCheck pair38 pair38Rewrites pair38Target = true:=by decide +kernel
theorem pair38_target_eval (x:Point):normalEval pair38Target x = LocalPairs.height18_pair_38 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_38_base LocalPairs.compact_height18_pair_38_hinges x
theorem pair38_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair38 x:=by
  rw [identityCheck_sound _ _ _ x pair38_identity,pair38_target_eval]
  exact LocalPairs.height18_pair_38_nonneg (hx 0) (hx 1)
def pair39:Expression:=HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows 3 3 true
def pair39Rewrites:Rewrites:=[RewriteAtoms.r53,RewriteAtoms.r69,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r18,RewriteAtoms.r26,RewriteAtoms.r47,RewriteAtoms.r70,RewriteAtoms.r0,RewriteAtoms.r27,RewriteAtoms.r51,RewriteAtoms.r71,RewriteAtoms.r2,RewriteAtoms.r28,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76,RewriteAtoms.r73,RewriteAtoms.r2,RewriteAtoms.r74,RewriteAtoms.r75,RewriteAtoms.r28,RewriteAtoms.r76]
def pair39Target:NormalForm:=CompactPair.toNormal LocalPairs.compact_height18_pair_39_base LocalPairs.compact_height18_pair_39_hinges
private def zz1796:"s0704"="s0704":=by decide+kernel
theorem pair39_identity:identityCheck pair39 pair39Rewrites pair39Target = true:=by decide +kernel
theorem pair39_target_eval (x:Point):normalEval pair39Target x = LocalPairs.height18_pair_39 (x 0) (x 1):=by
  exact CompactPair.toNormal_eval LocalPairs.compact_height18_pair_39_base LocalPairs.compact_height18_pair_39_hinges x
theorem pair39_nonneg (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval pair39 x:=by
  rw [identityCheck_sound _ _ _ x pair39_identity,pair39_target_eval]
  exact LocalPairs.height18_pair_39_nonneg (hx 0) (hx 1)
theorem quad_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (quadSlack rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact quad0_nonneg x hx
  · exact quad1_nonneg x hx
  · exact quad2_nonneg x hx
  · exact quad3_nonneg x hx
  · exact quad4_nonneg x hx
  · exact quad5_nonneg x hx
  · exact quad6_nonneg x hx
  · exact quad7_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact quad8_nonneg x hx
  · exact quad9_nonneg x hx
  · exact quad10_nonneg x hx
  · exact quad11_nonneg x hx
  · exact quad12_nonneg x hx
  · exact quad13_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact quad14_nonneg x hx
  · exact quad15_nonneg x hx
  · exact quad16_nonneg x hx
  · exact quad17_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact quad18_nonneg x hx
  · exact quad19_nonneg x hx
private def zz1797:"s0705"="s0705":=by decide+kernel
theorem pair_nonneg (p q:Phase) (hpq:p.val ≤ q.val) (same:Bool)
    (x:Point) (hx:∀ i,0 ≤ x i):0 ≤ expressionEval (HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) rows p q same) x:=by
  fin_cases p <;> fin_cases q <;> cases same
  · exact pair20_nonneg x hx
  · exact pair21_nonneg x hx
  · exact pair22_nonneg x hx
  · exact pair23_nonneg x hx
  · exact pair24_nonneg x hx
  · exact pair25_nonneg x hx
  · exact pair26_nonneg x hx
  · exact pair27_nonneg x hx
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (1:ℕ) ≤ 0) hpq)
  · exact pair28_nonneg x hx
  · exact pair29_nonneg x hx
  · exact pair30_nonneg x hx
  · exact pair31_nonneg x hx
  · exact pair32_nonneg x hx
  · exact pair33_nonneg x hx
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (2:ℕ) ≤ 1) hpq)
  · exact pair34_nonneg x hx
  · exact pair35_nonneg x hx
  · exact pair36_nonneg x hx
  · exact pair37_nonneg x hx
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 0) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 1) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact False.elim ((by decide:¬ (3:ℕ) ≤ 2) hpq)
  · exact pair38_nonneg x hx
  · exact pair39_nonneg x hx
end Green24Proof.HeightCover18Rows
private def zz2405:"s0965"="s0965":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover18Cyclic
open QuadraticCertificates ExpressionCertificates ExtendedFullPhaseRows FullPhaseSemantics
open FullPhaseRows (Phase)
open FullPhaseAggregation (quadPoint_nonneg pairPoint_nonneg)
open FullPhaseSymmetry (reversePoint swapPair reversePoint_nonneg swapPair_nonneg)
open ExtendedFullPhaseAggregation
theorem quad_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (quadSlack HeightCover18Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightCover18Rows.quad_nonneg p q h same x hx
  · rw [← quadSlack_reverse HeightCover18Rows.rows p q same x]
    exact HeightCover18Rows.quad_nonneg q p h same (reversePoint x) (reversePoint_nonneg x hx)
theorem pair_nonneg (p q:Phase) (same:Bool) (x:Point) (hx:∀ i,0 ≤ x i) :
    0 ≤ expressionEval (HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) HeightCover18Rows.rows p q same) x:=by
  rcases le_total p.val q.val with h | h
  · exact HeightCover18Rows.pair_nonneg p q h same x hx
  · rw [← HeightFullPhaseRows.pairSlack_swap ((9 / 5)) ((-1 / 0xc8)) (2 / 5) HeightCover18Rows.rows p q same x]
    exact HeightCover18Rows.pair_nonneg q p h same (swapPair x) (swapPair_nonneg x hx)
theorem rows_admissible:rowsAdmissible HeightCover18Rows.rows = true:=by decide +kernel
def remainingRows:List (ℚ × Label):=stripPotentials HeightCover18Rows.rows
private def zz1798:"s0706"="s0706":=by decide+kernel
theorem remaining_rows_count:remainingRows.length = 12:=by decide +kernel
theorem certificate_sum {q:ℕ} [NeZero q] (h4:4 ∣ q) (h3:3 ∣ q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    ((-1 / 50):ℝ) * mass g ^ 2 + (8 / 5:ℝ) * energy g ≤
      weightedAggregate ((9 / 5)) h4 h3 g remainingRows + 4 * deficit g:=by
  have hl (j k:ZMod q):0 ≤
      expressionEval (quadSlack HeightCover18Rows.rows (ZMod.castHom h4 (ZMod 4) j)
        (ZMod.castHom h4 (ZMod 4) k) (sameColour h3 j k)) (quadPoint g j k) +
      expressionEval (HeightFullPhaseRows.pairSlack ((9 / 5)) ((-1 / 0xc8)) (2 / 5) HeightCover18Rows.rows
        (ZMod.castHom h4 (ZMod 4) j) (ZMod.castHom h4 (ZMod 4) k)
        (sameColour h3 j k)) (pairPoint g j k) :=
    add_nonneg (quad_nonneg _ _ _ _ (quadPoint_nonneg g hg j k))
      (pair_nonneg _ _ _ _ (pairPoint_nonneg g hg j k))
  have hs:=Finset.sum_nonneg (s:=Finset.univ) fun j _ =>
    Finset.sum_nonneg (s:=Finset.univ) fun k _ => hl j k
  rw [HeightFullPhaseRows.local_slacks_sum ((9 / 5)) ((-1 / 0xc8)) (2 / 5) h4 h3 g hg,stripPotentials_sound ((9 / 5)) h4 h3 h5 g HeightCover18Rows.rows rows_admissible] at hs
  norm_num at hs
  change ((-1 / 50):ℝ) * mass g ^ 2 + (8 / 5:ℝ) * energy g ≤
    weightedAggregate ((9 / 5)) h4 h3 g (stripPotentials HeightCover18Rows.rows) + 4 * deficit g
  linarith
end Green24Proof.HeightCover18Cyclic
private def zz2406:"s0966"="s0966":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover18Mass
open ExtendedFullPhaseRows ExtendedFullPhaseAggregation
open PhaseMassRows PhaseWeightedVectors PhaseColourRows
theorem remainingRows_eq:HeightCover18Cyclic.remainingRows = [
  ((0x4e7f2cd7 / 0x1dcd6500), .base (.balance 0 (1))),
  ((0xf4040a4b / 0x3b9aca00), .base (.balance 1 (-1))),
  ((0x9e99e095 / 0x3b9aca00), .base (.balance 2 (1))),
  ((0xf3535169 / 0x3b9aca00), .base (.balance 3 (-1))),
  ((0xe08529 / 0xee6b280), .base (.child 0)),
  ((0x118167 / 0x1312d0), .base (.heightChild 1)),
  ((0x3bab637 / 0x1dcd6500), .base (.grandchild 2)),
  ((0x2232645 / 0x1dcd6500), .base (.ordered 0)),
  ((0x3919bbd / 0x17d7840), .base (.massSquare false (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x1ddca95 / 0xee6b280), .base (.massSquare true (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p))),
  ((0x41d87 / 0x3b9aca00), .base (.massSquare true (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p))),
  ((4 / 0x7d), .base (.normalization))]:=by
  apply (CombinedPolicyPackedRowsEquality.rowsEqWith_iff CombinedPolicyPackedRowsEquality.extendedEq CombinedPolicyPackedRowsEquality.extendedEq_iff _ _).mp
  decide +kernel
noncomputable def balanceMass {q:ℕ} [NeZero q] (h4:4 ∣ q) (g:ZMod q → ℝ):ℝ :=
  (((0x4e7f2cd7 / 0x1dcd6500):ℝ) * phaseTotal h4 g 0 + ((-0xf4040a4b / 0x3b9aca00):ℝ) * phaseTotal h4 g 1 + ((0x9e99e095 / 0x3b9aca00):ℝ) * phaseTotal h4 g 2 + ((-0xf3535169 / 0x3b9aca00):ℝ) * phaseTotal h4 g 3) * ((phaseTotal h4 g 0 + phaseTotal h4 g 2) - ((9 / 5):ℝ) * (phaseTotal h4 g 1 + phaseTotal h4 g 3))
theorem weighted_remaining_le {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((9 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((9 / 5)) h4 h3 g (.base (.heightChild 1)) ≤ 0)
    (hrow2:rowAggregate ((9 / 5)) h4 h3 g (.base (.grandchild 2)) ≤ 0) :
    weightedAggregate ((9 / 5)) h4 h3 g HeightCover18Cyclic.remainingRows ≤
      balanceMass h4 g - ((0x3919bbd / 0x17d7840):ℝ) * (phaseTotal h4 g 1 - phaseTotal h4 g 3) ^ 2 + ((4 / 0x7d):ℝ) * mass g ^ 2:=by
  have ho:=rowAggregate_ordered_nonpos ((9 / 5)) h4 h3 g hg 0 (by simpa using heven)
  have hs9:=rowAggregate_colouredMassSquare_nonpos ((9 / 5)) h4 h3 g (fun p => (![0,1,0, -1]:Fin 4 → ℚ) p)
  have hs10:=rowAggregate_colouredMassSquare_nonpos ((9 / 5)) h4 h3 g (fun p => (![1, -1, -1,1]:Fin 4 → ℚ) p)
  rw [remainingRows_eq]
  simp only [weightedAggregate,List.map_cons,List.map_nil,List.sum_cons,List.sum_nil,
    rowAggregate_base,rowAggregate_balance,rowAggregate_normalization,odd_massSquare]
  simp only [rowAggregate_base] at hrow0 hrow1 hrow2
  norm_num
  unfold balanceMass
  linarith
private def zz1799:"s0707"="s0707":=by decide+kernel
theorem aggregate_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((9 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((9 / 5)) h4 h3 g (.base (.heightChild 1)) ≤ 0)
    (hrow2:rowAggregate ((9 / 5)) h4 h3 g (.base (.grandchild 2)) ≤ 0) (h5:¬5 ∣ q) :
    height18.Aggregate (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) (phaseTotal h4 g 0 - phaseTotal h4 g 2) (phaseTotal h4 g 1 - phaseTotal h4 g 3) (energy g) (deficit g):=by
  have hc:=HeightCover18Cyclic.certificate_sum h4 h3 h5 g hg
  have hr:=weighted_remaining_le h4 h3 g hg heven hrow0 hrow1 hrow2
  have hm:mass g = (phaseTotal h4 g 0 + phaseTotal h4 g 2) + (phaseTotal h4 g 1 + phaseTotal h4 g 3):=by
    have ht:=phaseTotal_sum h4 g
    linarith
  rw [hm] at hc hr
  unfold HeightCoefficients.Aggregate height18
  unfold balanceMass at hr
  norm_num
  nlinarith only [hc,hr]
theorem height_bound_of_rows {q:ℕ} [NeZero q]
    (h4:4 ∣ q) (h3:3 ∣ q) (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i)
    (heven:phaseTotal h4 g 2 ≤ phaseTotal h4 g 0)
    (hrow0:rowAggregate ((9 / 5)) h4 h3 g (.base (.child 0)) ≤ 0)
    (hrow1:rowAggregate ((9 / 5)) h4 h3 g (.base (.heightChild 1)) ≤ 0)
    (hrow2:rowAggregate ((9 / 5)) h4 h3 g (.base (.grandchild 2)) ≤ 0) (h5:¬5 ∣ q) (hAB:(phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ (phaseTotal h4 g 0 + phaseTotal h4 g 2)) :
    (2 / 5:ℝ) * energy g + Q18 (phaseTotal h4 g 0 + phaseTotal h4 g 2) (phaseTotal h4 g 1 + phaseTotal h4 g 3) ≤ deficit g:=by
  apply height18_of_aggregate
  · exact add_nonneg (phaseTotal_nonneg h4 g hg 1) (phaseTotal_nonneg h4 g hg 3)
  · exact hAB
  · exact sub_nonneg.mpr heven
  · have hb:=phaseTotal_nonneg h4 g hg 2
    linarith
  · exact aggregate_of_rows h4 h3 g hg heven hrow0 hrow1 hrow2 h5
end Green24Proof.HeightCover18Mass
private def zz2407:"s0967"="s0967":=by decide+kernel
end 
section 
namespace Green24Proof.HeightCover18Profile
open PhaseMassRows ChildRows HeightChildRows ProfileChildren
theorem height_bound_ordered {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w)
    (heven:phaseTotal h4 (interleave u v) 2 ≤ phaseTotal h4 (interleave u v) 0)
    (hAB:mass v ≤ mass u) :
    (2 / 5:ℝ) * energy (interleave u v) + Q18 (mass u) (mass v) ≤ deficit (interleave u v):=by
  have hg:=interleave_nonneg u v hu hv
  have hrow0:FullPhaseAggregation.rowAggregate ((9 / 5)) h4 h3 (interleave u v) (.child 0) ≤ 0:=by
    rw [rowAggregate_child_even]
    have hd:=ih m (by have hp:=NeZero.pos m; omega) (dvd_mul_left m 2) u hu
    linarith
  have h3m:3 ∣ m:=((Nat.prime_three.dvd_mul).mp h3).resolve_left (by decide)
  have h5m:¬5 ∣ m:=fun h => h5 (dvd_mul_of_dvd_right h 2)
  have hrow1:=rowAggregate_height_odd_nonpos ((9 / 5)) h4 h3 h2 u v hu hv
    (HeightStrong.strong_height_bound h2 h3m h5m v hv)
  have hrow2:=Full27ProfileInterval.grandchild_nonpos_of_induction ((9 / 5)) h4 h3 (interleave u v) hg 2 ih
  have hU:phaseTotal h4 (interleave u v) 0 + phaseTotal h4 (interleave u v) 2 = mass u:=by
    rw [phaseTotal_interleave_zero h4 h2,phaseTotal_interleave_two h4 h2,classMass_sum]
  have hV:phaseTotal h4 (interleave u v) 1 + phaseTotal h4 (interleave u v) 3 = mass v:=by
    rw [phaseTotal_interleave_one h4 h2,phaseTotal_interleave_three h4 h2,classMass_sum]
  have h:=HeightCover18Mass.height_bound_of_rows h4 h3 (interleave u v) hg heven hrow0 hrow1 hrow2 h5
    (by rwa [hU,hV])
  simpa only [hU,hV] using h
theorem height_bound {m:ℕ} [NeZero m]
    (h4:4 ∣ 2 * m) (h3:3 ∣ 2 * m) (h5:¬5 ∣ 2 * m) (h2:2 ∣ m)
    (u v:ZMod m → ℝ) (hu:∀ i,0 ≤ u i) (hv:∀ i,0 ≤ v i)
    (ih:∀ (n:ℕ) [NeZero n],n < 2 * m → n ∣ 2 * m →
      ∀ w:ZMod n → ℝ,(∀ i,0 ≤ w i) → 0 ≤ deficit w) (hAB:mass v ≤ mass u) :
    (2 / 5:ℝ) * energy (interleave u v) + Q18 (mass u) (mass v) ≤ deficit (interleave u v):=by
  obtain ⟨u',v',hu',hv',hU,hV,hd,hE,heven⟩ :=
    ProfileEnergyOrientation.orient_even_child h4 u v hu hv
  have h:=height_bound_ordered h4 h3 h5 h2 u' v' hu' hv' ih heven
    (by simpa only [hU,hV] using hAB)
  simpa only [hU,hV,hd,hE] using h
end Green24Proof.HeightCover18Profile
private def zz2408:"s0968"="s0968":=by decide+kernel
end 
section 
namespace Green24Proof.VerifiedProfileEndpoint
open BoundaryFromHeightCertificates
private def zz1800:"s0708"="s0708":=by decide+kernel
private theorem height_certificate_12 (m:ℕ) [NeZero m]:HeightCertificate m Q12 :=
  HeightCover12Profile.height_bound
private theorem height_certificate_18 (m:ℕ) [NeZero m]:HeightCertificate m Q18 :=
  HeightCover18Profile.height_bound
theorem deficit_nonneg (q:ℕ) [NeZero q] (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i):0 ≤ deficit g :=
  RatioCoverSixteen.deficit_nonneg_of_remaining
    height_certificate_12 height_certificate_18 q h5 g hg
theorem profileFunctional_le (q:ℕ) [NeZero q] (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    profileFunctional g ≤ 2 * mass g ^ 2 :=
  sub_nonneg.mp (deficit_nonneg q h5 g hg)
private def zz1801:"s0709"="s0709":=by decide+kernel
theorem deficit_nonneg_of_pos (q:ℕ) (hq:0 < q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    letI:NeZero q:=⟨Nat.ne_of_gt hq⟩
    0 ≤ deficit g:=by
  let:NeZero q:=⟨Nat.ne_of_gt hq⟩
  exact deficit_nonneg q h5 g hg
theorem profileFunctional_le_of_pos (q:ℕ) (hq:0 < q) (h5:¬5 ∣ q)
    (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    letI:NeZero q:=⟨Nat.ne_of_gt hq⟩
    profileFunctional g ≤ 2 * mass g ^ 2:=by
  let:NeZero q:=⟨Nat.ne_of_gt hq⟩
  exact profileFunctional_le q h5 g hg
end Green24Proof.VerifiedProfileEndpoint
private def zz2409:"s0969"="s0969":=by decide+kernel
end 
section 
namespace Green24Proof.AllModuliProfileEndpoint
theorem profileFunctional_le (q:ℕ) [NeZero q] (g:ZMod q → ℝ)
    (hg:∀ i,0 ≤ g i):profileFunctional g ≤ 2 * mass g ^ 2:=by
  obtain ⟨a,m,hm,hq⟩:=Nat.exists_eq_pow_mul_and_not_dvd (NeZero.ne q) 5 (by norm_num)
  have hm0:m ≠ 0:=by
    intro hz
    apply NeZero.ne q
    rw [hq,hz,mul_zero]
  let:NeZero m:=⟨hm0⟩
  let:NeZero (5 ^ a):=⟨pow_ne_zero _ (by norm_num)⟩
  have hmn:Nat.Coprime m (5 ^ a):=Nat.prime_five.coprime_pow_of_not_dvd hm
  have hq':q = m * 5 ^ a:=hq.trans (Nat.mul_comm _ _)
  let e:ZMod q ≃+* ZMod m × ZMod (5 ^ a) :=
    (ZMod.ringEquivCongr hq').trans (ZMod.chineseRemainder hmn)
  exact ProfileCoprimeCollapse.bound_of_equiv e
    ((by norm_num:Nat.Coprime 2 5).pow_right a)
    ((by norm_num:Nat.Coprime 3 5).pow_right a)
    (fun f hf => VerifiedProfileEndpoint.profileFunctional_le m hm f hf) g hg
theorem deficit_nonneg (q:ℕ) [NeZero q] (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    0 ≤ deficit g:=sub_nonneg.mpr (profileFunctional_le q g hg)
end Green24Proof.AllModuliProfileEndpoint
private def zz2410:"s096a"="s096a":=by decide+kernel
end 
section 
namespace Green24Proof.FinitePartitionAverage
open Finset
open scoped BigOperators
variable {α β:Type*} [Fintype α] [DecidableEq β]
def fiber (π:α → β) (b:β):Finset α :=
  Finset.univ.filter (fun x => π x = b)
private def zz1802:"s070a"="s070a":=by decide+kernel
theorem mem_fiber (π:α → β) (b:β) (x:α) :
    x ∈ fiber π b ↔ π x = b:=by
  simp [fiber]
noncomputable def fiberMean (π:α → β) (f:α → ℝ) (b:β):ℝ :=
  (∑ x ∈ fiber π b,f x) / (fiber π b).card
noncomputable def average (π:α → β) (f:α → ℝ) (x:α):ℝ :=
  fiberMean π f (π x)
theorem average_eq_on_fiber (π:α → β) (f:α → ℝ) {b:β} {x:α}
    (hx:x ∈ fiber π b):average π f x = fiberMean π f b:=by
  simp only [average,(mem_fiber π b x).mp hx]
theorem sum_fibers [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ b, ∑ x ∈ fiber π b,f x) = ∑ x,f x:=by
  simp only [fiber,Finset.sum_filter]
  rw [Finset.sum_comm]
  simp
theorem fiberMean_nonneg (π:α → β) (f:α → ℝ) (hf:∀ x,0 ≤ f x) (b:β) :
    0 ≤ fiberMean π f b :=
  div_nonneg (Finset.sum_nonneg (fun x _ => hf x)) (Nat.cast_nonneg _)
private def zz1803:"s070b"="s070b":=by decide+kernel
theorem fiberMean_le_one (π:α → β) (f:α → ℝ) (hf:∀ x,f x ≤ 1) (b:β) :
    fiberMean π f b ≤ 1:=by
  by_cases hempty:fiber π b = ∅
  · simp [fiberMean,hempty]
  · have hcard:(0:ℝ) < (fiber π b).card :=
      Nat.cast_pos.mpr (Finset.card_pos.mpr (Finset.nonempty_iff_ne_empty.mpr hempty))
    rw [fiberMean,div_le_one hcard]
    calc
      (∑ x ∈ fiber π b,f x) ≤ ∑ _x ∈ fiber π b,(1:ℝ) :=
        Finset.sum_le_sum (fun x _ => hf x)
      _ = _:=by simp
theorem average_mem_Icc (π:α → β) (f:α → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1)
    (x:α):average π f x ∈ Set.Icc 0 1 :=
  ⟨fiberMean_nonneg π f (fun x => (hf x).1) (π x),
    fiberMean_le_one π f (fun x => (hf x).2) (π x)⟩
theorem residual_mem_Icc (π:α → β) (f:α → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1)
    (x:α):f x - average π f x ∈ Set.Icc (-1) 1:=by
  have hx:=hf x
  have ha:=average_mem_Icc π f hf x
  constructor <;> linarith [hx.1,hx.2,ha.1,ha.2]
theorem sum_fiber_average (π:α → β) (f:α → ℝ) (b:β) :
    (∑ x ∈ fiber π b,average π f x) = ∑ x ∈ fiber π b,f x:=by
  calc
    (∑ x ∈ fiber π b,average π f x) =
        ∑ _x ∈ fiber π b,fiberMean π f b:=by
      apply Finset.sum_congr rfl
      intro x hx
      exact average_eq_on_fiber π f hx
    _ = _:=by
      by_cases hempty:fiber π b = ∅
      · simp [fiberMean,hempty]
      · have hcard:((fiber π b).card:ℝ) ≠ 0:=by
          exact_mod_cast (Finset.card_ne_zero.mpr
            (Finset.nonempty_iff_ne_empty.mpr hempty))
        simp only [Finset.sum_const,nsmul_eq_mul,fiberMean]
        exact mul_div_cancel₀ _ hcard
private def zz1804:"s070c"="s070c":=by decide+kernel
theorem sum_average [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ x,average π f x) = ∑ x,f x:=by
  rw [← sum_fibers π (average π f)]
  simp_rw [sum_fiber_average]
  exact sum_fibers π f
theorem mean_average [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ x,average π f x) / Fintype.card α = (∑ x,f x) / Fintype.card α:=by
  rw [sum_average]
theorem average_idempotent (π:α → β) (f:α → ℝ) :
    average π (average π f) = average π f:=by
  funext x
  change fiberMean π (average π f) (π x) = fiberMean π f (π x)
  unfold fiberMean
  rw [sum_fiber_average]
theorem sum_fiber_residual (π:α → β) (f:α → ℝ) (b:β) :
    (∑ x ∈ fiber π b,(f x - average π f x)) = 0:=by
  rw [Finset.sum_sub_distrib,sum_fiber_average,sub_self]
private def zz1805:"s070d"="s070d":=by decide+kernel
theorem residual_orthogonal [Fintype β] (π:α → β) (f:α → ℝ) (g:β → ℝ) :
    (∑ x,(f x - average π f x) * g (π x)) = 0:=by
  rw [← sum_fibers π]
  apply Finset.sum_eq_zero
  intro b _
  calc
    (∑ x ∈ fiber π b,(f x - average π f x) * g (π x)) =
        ∑ x ∈ fiber π b,(f x - average π f x) * g b:=by
      apply Finset.sum_congr rfl
      intro x hx
      rw [(mem_fiber π b x).mp hx]
    _ = (∑ x ∈ fiber π b,(f x - average π f x)) * g b :=
      (Finset.sum_mul _ _ _).symm
    _ = 0:=by rw [sum_fiber_residual,zero_mul]
theorem residual_orthogonal_average [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ x,(f x - average π f x) * average π f x) = 0 :=
  residual_orthogonal π f (fiberMean π f)
theorem energy_split [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ x,f x ^ 2) = (∑ x,average π f x ^ 2) +
      ∑ x,(f x - average π f x) ^ 2:=by
  calc
    (∑ x,f x ^ 2) = ∑ x,(average π f x ^ 2 + (f x - average π f x) ^ 2 +
        2 * ((f x - average π f x) * average π f x)):=by
      apply Finset.sum_congr rfl
      intro x _
      ring
    _ = _:=by
      rw [Finset.sum_add_distrib,Finset.sum_add_distrib, ← Finset.mul_sum,
        residual_orthogonal_average,mul_zero,add_zero]
theorem average_energy_le [Fintype β] (π:α → β) (f:α → ℝ) :
    (∑ x,average π f x ^ 2) ≤ ∑ x,f x ^ 2:=by
  have he:=energy_split π f
  have hn:0 ≤ ∑ x,(f x - average π f x) ^ 2 :=
    Finset.sum_nonneg (fun _ _ => sq_nonneg _)
  linarith
private def zz1806:"s070e"="s070e":=by decide+kernel
theorem average_energy_le_card [Fintype β] (π:α → β) (f:α → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) :
    (∑ x,average π f x ^ 2) ≤ (Fintype.card α:ℝ):=by
  calc
    (∑ x,average π f x ^ 2) ≤ ∑ x,f x ^ 2:=average_energy_le π f
    _ ≤ ∑ _x:α,(1:ℝ):=by
      apply Finset.sum_le_sum
      intro x _
      have hx:=hf x
      nlinarith [hx.1,hx.2]
    _ = _:=by simp
end Green24Proof.FinitePartitionAverage
private def zz2411:"s096b"="s096b":=by decide+kernel
end 
section 
namespace Green24Proof.FinitePartitionRefinement
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
variable {α β γ:Type*} [Fintype α] [Fintype β] [Fintype γ]
  [DecidableEq β] [DecidableEq γ]
noncomputable def energy (π:α → β) (f:α → ℝ):ℝ :=
  ∑ x,average π f x ^ 2
omit [Fintype γ] in
theorem refined_residual_orthogonal_coarse (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) :
    (∑ x,(f x - average π f x) * average ρ f x) = 0:=by
  have h:=residual_orthogonal π f (fun b => fiberMean ρ f (φ b))
  simpa only [average,href] using h
theorem average_difference_orthogonal_coarse (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) :
    (∑ x,(average π f x - average ρ f x) * average ρ f x) = 0:=by
  calc
    (∑ x,(average π f x - average ρ f x) * average ρ f x) =
        (∑ x,(f x - average ρ f x) * average ρ f x) -
          ∑ x,(f x - average π f x) * average ρ f x:=by
      rw [← Finset.sum_sub_distrib]
      apply Finset.sum_congr rfl
      intro x _
      ring
    _ = 0:=by
      rw [residual_orthogonal_average,
        refined_residual_orthogonal_coarse π ρ φ href f,sub_self]
theorem refinement_energy_identity (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) :
    energy π f = energy ρ f + ∑ x,(average π f x - average ρ f x) ^ 2:=by
  unfold energy
  calc
    (∑ x,average π f x ^ 2) =
        ∑ x,(average ρ f x ^ 2 + (average π f x - average ρ f x) ^ 2 +
          2 * ((average π f x - average ρ f x) * average ρ f x)):=by
      apply Finset.sum_congr rfl
      intro x _
      ring
    _ = _:=by
      rw [Finset.sum_add_distrib,Finset.sum_add_distrib, ← Finset.mul_sum,
        average_difference_orthogonal_coarse π ρ φ href f,mul_zero,add_zero]
private def zz1807:"s070f"="s070f":=by decide+kernel
theorem refinement_energy_mono (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) :
    energy ρ f ≤ energy π f:=by
  have he:=refinement_energy_identity π ρ φ href f
  have hn:0 ≤ ∑ x,(average π f x - average ρ f x) ^ 2 :=
    Finset.sum_nonneg (fun _ _ => sq_nonneg _)
  linarith
omit [Fintype γ] in
theorem correlation_eq_average_difference (π:α → β) (ρ:α → γ)
    (f:α → ℝ) (g:β → ℝ) :
    (∑ x,(f x - average ρ f x) * g (π x)) =
      ∑ x,(average π f x - average ρ f x) * g (π x):=by
  calc
    (∑ x,(f x - average ρ f x) * g (π x)) =
        (∑ x,(average π f x - average ρ f x) * g (π x)) +
          ∑ x,(f x - average π f x) * g (π x):=by
      rw [← Finset.sum_add_distrib]
      apply Finset.sum_congr rfl
      intro x _
      ring
    _ = _:=by rw [residual_orthogonal,add_zero]
theorem correlation_sq_le_energy_difference (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) (g:β → ℝ) :
    (∑ x,(f x - average ρ f x) * g (π x)) ^ 2 ≤
      (energy π f - energy ρ f) * ∑ x,g (π x) ^ 2:=by
  rw [correlation_eq_average_difference]
  have hcs:=Finset.sum_mul_sq_le_sq_mul_sq Finset.univ
    (fun x => average π f x - average ρ f x) (fun x => g (π x))
  have he:(∑ x,(average π f x - average ρ f x) ^ 2) =
      energy π f - energy ρ f:=by
    have h:=refinement_energy_identity π ρ φ href f
    linarith
  rw [he] at hcs
  exact hcs
theorem energy_increment_of_correlation (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) (g:β → ℝ)
    {B t:ℝ} (hB:0 < B) (ht:0 ≤ t)
    (hg:(∑ x,g (π x) ^ 2) ≤ B)
    (hc:t ≤ |∑ x,(f x - average ρ f x) * g (π x)|) :
    energy ρ f + t ^ 2 / B ≤ energy π f:=by
  have hΔ:0 ≤ energy π f - energy ρ f :=
    sub_nonneg.mpr (refinement_energy_mono π ρ φ href f)
  have hsq:t ^ 2 ≤ (∑ x,(f x - average ρ f x) * g (π x)) ^ 2:=by
    nlinarith [sq_abs (∑ x,(f x - average ρ f x) * g (π x)),
      abs_nonneg (∑ x,(f x - average ρ f x) * g (π x))]
  have hbound:t ^ 2 ≤ (energy π f - energy ρ f) * B :=
    hsq.trans ((correlation_sq_le_energy_difference π ρ φ href f g).trans
      (mul_le_mul_of_nonneg_left hg hΔ))
  have hd:t ^ 2 / B ≤ energy π f - energy ρ f :=
    (div_le_iff₀ hB).mpr hbound
  linarith
private def zz1808:"s0710"="s0710":=by decide+kernel
theorem energy_increment_of_bounded_correlation [Nonempty α]
    (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) (g:β → ℝ)
    {η:ℝ} (hη:0 ≤ η) (hg:∀ x, |g (π x)| ≤ 1)
    (hc:η * Fintype.card α ≤ |∑ x,(f x - average ρ f x) * g (π x)|) :
    energy ρ f + η ^ 2 * Fintype.card α ≤ energy π f:=by
  have hn:(0:ℝ) < Fintype.card α:=Nat.cast_pos.mpr Fintype.card_pos
  have hge:(∑ x,g (π x) ^ 2) ≤ (Fintype.card α:ℝ):=by
    calc
      (∑ x,g (π x) ^ 2) ≤ ∑ _x:α,(1:ℝ):=by
        apply Finset.sum_le_sum
        intro x _
        have hx:=hg x
        nlinarith [sq_abs (g (π x)),abs_nonneg (g (π x))]
      _ = _:=by simp
  have h:=energy_increment_of_correlation π ρ φ href f g hn
    (mul_nonneg hη hn.le) hge hc
  have hscale:(η * Fintype.card α) ^ 2 / Fintype.card α = η ^ 2 * Fintype.card α:=by
    apply (div_eq_iff hn.ne').mpr
    ring
  rwa [hscale] at h
theorem normalized_energy_increment [Nonempty α]
    (π:α → β) (ρ:α → γ) (φ:β → γ)
    (href:∀ x,ρ x = φ (π x)) (f:α → ℝ) (g:β → ℝ)
    {η:ℝ} (hη:0 ≤ η) (hg:∀ x, |g (π x)| ≤ 1)
    (hc:η * Fintype.card α ≤ |∑ x,(f x - average ρ f x) * g (π x)|) :
    energy ρ f / Fintype.card α + η ^ 2 ≤ energy π f / Fintype.card α:=by
  have hn:(0:ℝ) < Fintype.card α:=Nat.cast_pos.mpr Fintype.card_pos
  apply (le_div_iff₀ hn).mpr
  calc
    (energy ρ f / Fintype.card α + η ^ 2) * Fintype.card α =
        energy ρ f + η ^ 2 * Fintype.card α:=by
      rw [add_mul,div_mul_cancel₀ _ hn.ne']
    _ ≤ _:=energy_increment_of_bounded_correlation π ρ φ href f g hη hg hc
end Green24Proof.FinitePartitionRefinement
private def zz2412:"s096c"="s096c":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteScalarQuantization
open Finset
open scoped BigOperators
noncomputable def quantize (m:ℕ) (t:ℝ):Fin (2 * m + 1) :=
  ⟨min ⌊(m:ℝ) * (t + 1)⌋₊ (2 * m),Nat.lt_succ_of_le (min_le_right _ _)⟩
noncomputable def gridValue (m:ℕ) (k:Fin (2 * m + 1)):ℝ :=
  (k.val:ℝ) / m - 1
theorem gridValue_mem_Icc {m:ℕ} (hm:0 < m) (k:Fin (2 * m + 1)) :
    gridValue m k ∈ Set.Icc (-1) 1:=by
  have hmR:(0:ℝ) < m:=Nat.cast_pos.mpr hm
  have hk:(k.val:ℝ) ≤ 2 * (m:ℝ):=by
    exact_mod_cast (Nat.le_of_lt_succ k.isLt)
  have h0:0 ≤ (k.val:ℝ) / m:=div_nonneg (Nat.cast_nonneg _) hmR.le
  have h2:(k.val:ℝ) / m ≤ 2:=(div_le_iff₀ hmR).mpr (by linarith)
  unfold gridValue
  constructor <;> linarith
theorem quantize_val {m:ℕ} {t:ℝ} (ht:t ∈ Set.Icc (-1) 1) :
    (quantize m t).val = ⌊(m:ℝ) * (t + 1)⌋₊:=by
  have hbound:(m:ℝ) * (t + 1) ≤ (2 * m:ℕ):=by
    push_cast
    nlinarith [(Nat.cast_nonneg m:(0:ℝ) ≤ m),ht.2]
  have hfloor:⌊(m:ℝ) * (t + 1)⌋₊ ≤ 2 * m:=by
    exact (Nat.floor_le_floor hbound).trans_eq (Nat.floor_natCast _)
  exact min_eq_left hfloor
private def zz1809:"s0711"="s0711":=by decide+kernel
theorem quantization_error {m:ℕ} (hm:0 < m) {t:ℝ}
    (ht:t ∈ Set.Icc (-1) 1) :
    0 ≤ t - gridValue m (quantize m t) ∧
      t - gridValue m (quantize m t) < 1 / m:=by
  have hmR:(0:ℝ) < m:=Nat.cast_pos.mpr hm
  have hnonneg:0 ≤ (m:ℝ) * (t + 1) :=
    mul_nonneg hmR.le (by linarith [ht.1])
  have hlo:=Nat.floor_le hnonneg
  have hhi:=Nat.lt_floor_add_one ((m:ℝ) * (t + 1))
  unfold gridValue
  rw [quantize_val ht]
  have hdiv:(⌊(m:ℝ) * (t + 1)⌋₊:ℝ) / m ≤ t + 1 :=
    (div_le_iff₀ hmR).mpr (by nlinarith)
  have hdiv':t + 1 < (⌊(m:ℝ) * (t + 1)⌋₊:ℝ) / m + 1 / m:=by
    have h:t + 1 < ((⌊(m:ℝ) * (t + 1)⌋₊:ℝ) + 1) / m :=
      (lt_div_iff₀ hmR).mpr (by nlinarith)
    simpa only [add_div] using h
  constructor <;> linarith
theorem quantization_abs_error {m:ℕ} (hm:0 < m) {t:ℝ}
    (ht:t ∈ Set.Icc (-1) 1):|t - gridValue m (quantize m t)| ≤ 1 / m:=by
  have h:=quantization_error hm ht
  rw [abs_of_nonneg h.1]
  exact h.2.le
variable {α:Type*} [Fintype α]
theorem correlation_error {m:ℕ} (hm:0 < m) (r g:α → ℝ)
    (hr:∀ x, |r x| ≤ 1) (hg:∀ x,g x ∈ Set.Icc (-1) 1) :
    |(∑ x,r x * g x) - ∑ x,r x * gridValue m (quantize m (g x))| ≤
      (Fintype.card α:ℝ) / m:=by
  rw [← Finset.sum_sub_distrib]
  calc
    |∑ x,(r x * g x - r x * gridValue m (quantize m (g x)))| ≤
        ∑ x, |r x * g x - r x * gridValue m (quantize m (g x))| :=
      Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _x:α,(1:ℝ) / m:=by
      apply Finset.sum_le_sum
      intro x _
      rw [← mul_sub,abs_mul]
      calc
        |r x| * |g x - gridValue m (quantize m (g x))| ≤
            1 * (1 / m) :=
          mul_le_mul (hr x) (quantization_abs_error hm (hg x)) (abs_nonneg _) (by norm_num)
        _ = _:=one_mul _
    _ = _:=by simp [div_eq_mul_inv]
theorem correlation_transfer {m:ℕ} (hm:0 < m) (r g:α → ℝ)
    (hr:∀ x, |r x| ≤ 1) (hg:∀ x,g x ∈ Set.Icc (-1) 1) :
    |∑ x,r x * g x| - (Fintype.card α:ℝ) / m ≤
      |∑ x,r x * gridValue m (quantize m (g x))|:=by
  have he:=correlation_error hm r g hr hg
  have ht:=abs_add_le
    ((∑ x,r x * g x) - ∑ x,r x * gridValue m (quantize m (g x)))
    (∑ x,r x * gridValue m (quantize m (g x)))
  rw [sub_add_cancel] at ht
  linarith
noncomputable def resolution (η:ℝ):ℕ:=⌈4 / η⌉₊ + 1
private def zz1810:"s0712"="s0712":=by decide+kernel
theorem resolution_pos (η:ℝ):0 < resolution η:=Nat.succ_pos _
theorem resolution_precision {η:ℝ} (hη:0 < η) :
    1 / (resolution η:ℝ) ≤ η / 4:=by
  have hm:(0:ℝ) < resolution η:=Nat.cast_pos.mpr (resolution_pos η)
  have hceil:=Nat.le_ceil (4 / η)
  have hres:(4 / η) ≤ (resolution η:ℝ):=by
    unfold resolution
    push_cast
    linarith
  have hmul:=(div_le_iff₀ hη).mp hres
  apply (div_le_iff₀ hm).mpr
  nlinarith
end Green24Proof.FiniteScalarQuantization
private def zz2413:"s096d"="s096d":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFourierCounting
open Finset
open scoped BigOperators
variable {q:ℕ} [NeZero q]
noncomputable def trilinear (f g h:ZMod q → ℂ):ℂ :=
  ∑ y, ∑ z,f (3 * z - 2 * y) * g y * h z
theorem inversion_sum (f:ZMod q → ℂ) (x:ZMod q) :
    (∑ r,ZMod.stdAddChar (r * x) * ZMod.dft f r) = (q:ℂ) * f x:=by
  have h:=congrFun (ZMod.dft_dft f) (-x)
  simpa only [ZMod.dft_apply,mul_neg,neg_neg,smul_eq_mul] using h
theorem character_factor (r y z:ZMod q) :
    ZMod.stdAddChar (r * (3 * z - 2 * y)) =
      ZMod.stdAddChar (-(y * (2 * r))) * ZMod.stdAddChar (-(z * (-3 * r))):=by
  rw [← AddChar.map_add_eq_mul]
  congr 1
  ring
private def zz1811:"s0713"="s0713":=by decide+kernel
theorem trilinear_fourier (f g h:ZMod q → ℂ) :
    (q:ℂ) * trilinear f g h =
      ∑ r,ZMod.dft f r * ZMod.dft g (2 * r) * ZMod.dft h (-3 * r):=by
  symm
  calc
    (∑ r,ZMod.dft f r * ZMod.dft g (2 * r) * ZMod.dft h (-3 * r)) =
        ∑ r, ∑ y, ∑ z,ZMod.dft f r *
          (ZMod.stdAddChar (-(y * (2 * r))) * g y) *
          (ZMod.stdAddChar (-(z * (-3 * r))) * h z):=by
      simp only [ZMod.dft_apply g,ZMod.dft_apply h,smul_eq_mul,
        Finset.mul_sum,Finset.sum_mul]
      apply Finset.sum_congr rfl
      intro r _
      exact Finset.sum_comm
    _ = ∑ y, ∑ z,(∑ r,ZMod.stdAddChar (r * (3 * z - 2 * y)) *
        ZMod.dft f r) * g y * h z:=by
      rw [Finset.sum_comm]
      apply Finset.sum_congr rfl
      intro y _
      rw [Finset.sum_comm]
      apply Finset.sum_congr rfl
      intro z _
      simp only [Finset.sum_mul]
      apply Finset.sum_congr rfl
      intro r _
      rw [character_factor]
      ring
    _ = (q:ℂ) * trilinear f g h:=by
      simp_rw [inversion_sum]
      simp only [trilinear,Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro y _
      apply Finset.sum_congr rfl
      intro z _
      ring
theorem sum_dft_mul_neg (f g:ZMod q → ℂ) :
    (∑ r,ZMod.dft f r * ZMod.dft g (-r)) =
      (q:ℂ) * ∑ x,f x * g x:=by
  calc
    (∑ r,ZMod.dft f r * ZMod.dft g (-r)) =
        ∑ r, ∑ x,ZMod.dft f r * (ZMod.stdAddChar (x * r) * g x):=by
      simp only [ZMod.dft_apply g,smul_eq_mul,mul_neg,neg_neg,Finset.mul_sum]
    _ = ∑ x,(∑ r,ZMod.stdAddChar (r * x) * ZMod.dft f r) * g x:=by
      rw [Finset.sum_comm]
      apply Finset.sum_congr rfl
      intro x _
      rw [Finset.sum_mul]
      apply Finset.sum_congr rfl
      intro r _
      rw [mul_comm r x]
      ring
    _ = (q:ℂ) * ∑ x,f x * g x:=by
      simp_rw [inversion_sum]
      rw [Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro x _
      ring
theorem conj_stdAddChar (x:ZMod q) :
    (starRingEnd ℂ) (ZMod.stdAddChar x) = ZMod.stdAddChar (-x):=by
  rw [AddChar.map_neg_eq_inv]
  exact (Complex.inv_eq_conj (by simp only [ZMod.stdAddChar_apply,Circle.norm_coe])).symm
theorem dft_conj_neg (f:ZMod q → ℂ) (r:ZMod q) :
    ZMod.dft (fun x => (starRingEnd ℂ) (f x)) (-r) =
      (starRingEnd ℂ) (ZMod.dft f r):=by
  simp only [ZMod.dft_apply,smul_eq_mul,map_sum,map_mul,
    conj_stdAddChar,mul_neg,neg_neg]
private def zz1812:"s0714"="s0714":=by decide+kernel
theorem parseval (f:ZMod q → ℂ) :
    (∑ r, ‖ZMod.dft f r‖ ^ 2) = (q:ℝ) * ∑ x, ‖f x‖ ^ 2:=by
  have h:=sum_dft_mul_neg f (fun x => (starRingEnd ℂ) (f x))
  simp only [dft_conj_neg,Complex.mul_conj'] at h
  exact_mod_cast h
theorem trilinear_norm_le (f g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {M:ℝ} (hM:∀ r, ‖ZMod.dft f r‖ ≤ M) :
    ‖trilinear f g h‖ ≤
      M * Real.sqrt (∑ x, ‖g x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2):=by
  have hM0:0 ≤ M:=(norm_nonneg (ZMod.dft f 0)).trans (hM 0)
  have hq0:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  have hb2:=IsUnit.isUnit_iff_mulLeft_bijective.mp h2
  have hb3:=IsUnit.isUnit_iff_mulLeft_bijective.mp h3.neg
  have hg:(∑ r:ZMod q, ‖ZMod.dft g (2 * r)‖ ^ 2) =
      (q:ℝ) * ∑ x, ‖g x‖ ^ 2 :=
    (hb2.sum_comp (fun r:ZMod q => ‖ZMod.dft g r‖ ^ 2)).trans (parseval g)
  have hh:(∑ r:ZMod q, ‖ZMod.dft h (-3 * r)‖ ^ 2) =
      (q:ℝ) * ∑ x, ‖h x‖ ^ 2 :=
    (hb3.sum_comp (fun r:ZMod q => ‖ZMod.dft h r‖ ^ 2)).trans (parseval h)
  have hcs:=Real.sum_mul_le_sqrt_mul_sqrt Finset.univ
    (fun r:ZMod q => ‖ZMod.dft g (2 * r)‖)
    (fun r:ZMod q => ‖ZMod.dft h (-3 * r)‖)
  rw [hg,hh] at hcs
  have hnorm:(q:ℝ) * ‖trilinear f g h‖ =
      ‖∑ r,ZMod.dft f r * ZMod.dft g (2 * r) * ZMod.dft h (-3 * r)‖:=by
    have hn:=congrArg (fun z:ℂ => ‖z‖) (trilinear_fourier f g h)
    simpa only [norm_mul,Complex.norm_natCast] using hn
  refine le_of_mul_le_mul_left (a:=(q:ℝ)) ?_ hq0
  calc
    (q:ℝ) * ‖trilinear f g h‖ =
        ‖∑ r,ZMod.dft f r * ZMod.dft g (2 * r) * ZMod.dft h (-3 * r)‖:=hnorm
    _ ≤ ∑ r, ‖ZMod.dft f r * ZMod.dft g (2 * r) * ZMod.dft h (-3 * r)‖ :=
      norm_sum_le _ _
    _ ≤ ∑ r,M * (‖ZMod.dft g (2 * r)‖ * ‖ZMod.dft h (-3 * r)‖):=by
      apply Finset.sum_le_sum
      intro r _
      simpa only [norm_mul,mul_assoc] using mul_le_mul_of_nonneg_right (hM r)
        (mul_nonneg (norm_nonneg _) (norm_nonneg _))
    _ = M * ∑ r, ‖ZMod.dft g (2 * r)‖ * ‖ZMod.dft h (-3 * r)‖ :=
      (Finset.mul_sum _ _ _).symm
    _ ≤ M * (Real.sqrt ((q:ℝ) * ∑ x, ‖g x‖ ^ 2) *
        Real.sqrt ((q:ℝ) * ∑ x, ‖h x‖ ^ 2)):=mul_le_mul_of_nonneg_left hcs hM0
    _ = (q:ℝ) * (M * Real.sqrt (∑ x, ‖g x‖ ^ 2) *
        Real.sqrt (∑ x, ‖h x‖ ^ 2)):=by
      rw [Real.sqrt_mul hq0.le,Real.sqrt_mul hq0.le]
      calc
        M * (Real.sqrt q * Real.sqrt (∑ x, ‖g x‖ ^ 2) *
            (Real.sqrt q * Real.sqrt (∑ x, ‖h x‖ ^ 2))) =
            (Real.sqrt q * Real.sqrt q) *
              (M * Real.sqrt (∑ x, ‖g x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2)):=by ring
        _ = _:=by rw [Real.mul_self_sqrt hq0.le]
theorem trilinear_norm_le_of_prime (f g h:ZMod q → ℂ)
    (hq:q.Prime) (hq3:3 < q) {M:ℝ}
    (hM:∀ r, ‖ZMod.dft f r‖ ≤ M) :
    ‖trilinear f g h‖ ≤
      M * Real.sqrt (∑ x, ‖g x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2):=by
  apply trilinear_norm_le f g h ?_ ?_ hM
  · apply ZMod.isUnit_prime_of_not_dvd Nat.prime_two
    intro hd
    have he:=(Nat.dvd_prime hq).mp hd
    omega
  · apply ZMod.isUnit_prime_of_not_dvd Nat.prime_three
    intro hd
    have he:=(Nat.dvd_prime hq).mp hd
    omega
noncomputable def indicator (A:Finset (ZMod q)) (x:ZMod q):ℂ :=
  if x ∈ A then 1 else 0
theorem trilinear_indicators (A B C:Finset (ZMod q)) :
    trilinear (indicator A) (indicator B) (indicator C) =
      (((B ×ˢ C).filter (fun p => 3 * p.2 - 2 * p.1 ∈ A)).card:ℂ):=by
  calc
    trilinear (indicator A) (indicator B) (indicator C) =
        ∑ y,if y ∈ B then
          ∑ z,if z ∈ C then (if 3 * z - 2 * y ∈ A then (1:ℂ) else 0) else 0
          else 0:=by
      unfold trilinear indicator
      apply Finset.sum_congr rfl
      intro y _
      by_cases hy:y ∈ B
      · simp only [hy,if_true,mul_one]
        apply Finset.sum_congr rfl
        intro z _
        by_cases hz:z ∈ C <;> simp [hz]
      · simp [hy]
    _ = _:=by
      simp only [Finset.sum_ite_mem_eq,Finset.natCast_card_filter,Finset.sum_product]
private def zz1813:"s0715"="s0715":=by decide+kernel
theorem trilinear_sub_left (f₁ f₂ g h:ZMod q → ℂ) :
    trilinear (fun x => f₁ x - f₂ x) g h =
      trilinear f₁ g h - trilinear f₂ g h:=by
  simp only [trilinear,sub_mul,Finset.sum_sub_distrib]
theorem trilinear_difference_norm_le (f₁ f₂ g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {M:ℝ} (hM:∀ r, ‖ZMod.dft (fun x => f₁ x - f₂ x) r‖ ≤ M) :
    ‖trilinear f₁ g h - trilinear f₂ g h‖ ≤
      M * Real.sqrt (∑ x, ‖g x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2):=by
  rw [← trilinear_sub_left]
  exact trilinear_norm_le _ g h h2 h3 hM
theorem trilinear_norm_le_fourier_max (f g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q)) :
    ‖trilinear f g h‖ ≤
      ‖ZMod.dft f‖ * Real.sqrt (∑ x, ‖g x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2) :=
  trilinear_norm_le f g h h2 h3 (fun r => norm_le_pi_norm (ZMod.dft f) r)
theorem trilinear_norm_le_of_bounded (f g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {η:ℝ} (hη:0 ≤ η) (hf:∀ r, ‖ZMod.dft f r‖ ≤ η * q)
    (hg:∀ x, ‖g x‖ ≤ 1) (hh:∀ x, ‖h x‖ ≤ 1) :
    ‖trilinear f g h‖ ≤ η * (q:ℝ) ^ 2:=by
  have hgsum:(∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ):=by
    calc
      (∑ x, ‖g x‖ ^ 2) ≤ ∑ _x:ZMod q,(1:ℝ):=by
        apply Finset.sum_le_sum
        intro x _
        nlinarith [norm_nonneg (g x),hg x]
      _ = _:=by simp
  have hhsum:(∑ x, ‖h x‖ ^ 2) ≤ (q:ℝ):=by
    calc
      (∑ x, ‖h x‖ ^ 2) ≤ ∑ _x:ZMod q,(1:ℝ):=by
        apply Finset.sum_le_sum
        intro x _
        nlinarith [norm_nonneg (h x),hh x]
      _ = _:=by simp
  calc
    ‖trilinear f g h‖ ≤ (η * q) * Real.sqrt (∑ x, ‖g x‖ ^ 2) *
        Real.sqrt (∑ x, ‖h x‖ ^ 2):=trilinear_norm_le f g h h2 h3 hf
    _ ≤ (η * q) * Real.sqrt q * Real.sqrt q:=by
      gcongr
    _ = η * (q:ℝ) ^ 2:=by
      rw [mul_assoc,Real.mul_self_sqrt (Nat.cast_nonneg q)]
      ring
end Green24Proof.CyclicFourierCounting
private def zz2414:"s096e"="s096e":=by decide+kernel
end 
section 
namespace Green24Proof.FourierPartitionIncrement
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization
variable {q:ℕ} [NeZero q]
private def zz1814:"s0716"="s0716":=by decide+kernel
theorem dft_real_re (r:ZMod q → ℝ) (k:ZMod q) :
    (ZMod.dft (fun x => (r x:ℂ)) k).re =
      ∑ x,r x * (ZMod.stdAddChar (-(x * k))).re:=by
  rw [ZMod.dft_apply]
  change Complex.reAddGroupHom
    (∑ x,ZMod.stdAddChar (-(x * k)) * (r x:ℂ)) = _
  rw [map_sum]
  simp [Complex.coe_reAddGroupHom,Complex.mul_re,mul_comm]
theorem dft_real_im (r:ZMod q → ℝ) (k:ZMod q) :
    (ZMod.dft (fun x => (r x:ℂ)) k).im =
      ∑ x,r x * (ZMod.stdAddChar (-(x * k))).im:=by
  rw [ZMod.dft_apply]
  change Complex.imAddGroupHom
    (∑ x,ZMod.stdAddChar (-(x * k)) * (r x:ℂ)) = _
  rw [map_sum]
  simp [Complex.coe_imAddGroupHom,Complex.mul_im,mul_comm]
theorem exists_real_character_test (r:ZMod q → ℝ) (k:ZMod q) {η:ℝ}
    (hlarge:η * q ≤ ‖ZMod.dft (fun x => (r x:ℂ)) k‖) :
    ∃ g:ZMod q → ℝ,(∀ x,g x ∈ Set.Icc (-1) 1) ∧
      η * q / 2 ≤ |∑ x,r x * g x|:=by
  have hn (x:ZMod q):‖ZMod.stdAddChar (-(x * k))‖ = 1:=by
    simp only [ZMod.stdAddChar_apply,Circle.norm_coe]
  by_cases hre:η * q / 2 ≤ |(ZMod.dft (fun x => (r x:ℂ)) k).re|
  · refine ⟨fun x => (ZMod.stdAddChar (-(x * k))).re, ?_, ?_⟩
    · intro x
      exact abs_le.mp ((Complex.abs_re_le_norm _).trans_eq (hn x))
    · rwa [dft_real_re] at hre
  · refine ⟨fun x => (ZMod.stdAddChar (-(x * k))).im, ?_, ?_⟩
    · intro x
      exact abs_le.mp ((Complex.abs_im_le_norm _).trans_eq (hn x))
    · have hab:=Complex.norm_le_abs_re_add_abs_im
        (ZMod.dft (fun x => (r x:ℂ)) k)
      have hi:η * q / 2 ≤ |(ZMod.dft (fun x => (r x:ℂ)) k).im|:=by
        linarith
      rwa [dft_real_im] at hi
theorem exists_quantized_correlating_test (r:ZMod q → ℝ) (k:ZMod q)
    (hr:∀ x, |r x| ≤ 1) {η:ℝ}
    (hlarge:η * q ≤ ‖ZMod.dft (fun x => (r x:ℂ)) k‖)
    {m:ℕ} (hm:0 < m) (hprecision:1 / (m:ℝ) ≤ η / 4) :
    ∃ s:ZMod q → Fin (2 * m + 1),
      (η / 4) * q ≤ |∑ x,r x * gridValue m (s x)|:=by
  obtain ⟨g,hg,hc⟩:=exists_real_character_test r k hlarge
  refine ⟨fun x => quantize m (g x), ?_⟩
  have he:=correlation_transfer hm r g hr hg
  simp only [ZMod.card] at he
  have hp:=mul_le_mul_of_nonneg_left hprecision (Nat.cast_nonneg q)
  rw [mul_one_div] at hp
  nlinarith
variable {β:Type*} [Fintype β] [DecidableEq β]
private def zz1815:"s0717"="s0717":=by decide+kernel
theorem exists_refinement_of_large_dft (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (k:ZMod q) {η:ℝ} (hη:0 < η)
    (hlarge:η * q ≤
      ‖ZMod.dft (fun x => ((f x - average ρ f x:ℝ):ℂ)) k‖)
    {m:ℕ} (hm:0 < m) (hprecision:1 / (m:ℝ) ≤ η / 4) :
    ∃ π:ZMod q → β × Fin (2 * m + 1),
      (∀ x,ρ x = (π x).1) ∧
      Green24Proof.FinitePartitionRefinement.energy ρ f / q + η ^ 2 / 16 ≤ Green24Proof.FinitePartitionRefinement.energy π f / q:=by
  have hr:∀ x, |f x - average ρ f x| ≤ 1 :=
    fun x => abs_le.mpr (residual_mem_Icc ρ f hf x)
  obtain ⟨s,hs⟩:=exists_quantized_correlating_test
    (fun x => f x - average ρ f x) k hr hlarge hm hprecision
  let π:ZMod q → β × Fin (2 * m + 1):=fun x => (ρ x,s x)
  let g:β × Fin (2 * m + 1) → ℝ:=fun b => gridValue m b.2
  have hg:∀ x, |g (π x)| ≤ 1 :=
    fun x => abs_le.mpr (gridValue_mem_Icc hm (s x))
  have hc:(η / 4) * Fintype.card (ZMod q) ≤
      |∑ x,(f x - average ρ f x) * g (π x)|:=by
    simpa only [ZMod.card] using hs
  have hi:=normalized_energy_increment π ρ Prod.fst (fun _ => rfl) f g
    (show 0 ≤ η / 4 by positivity) hg hc
  refine ⟨π,fun _ => rfl, ?_⟩
  norm_num only [ZMod.card,div_pow] at hi
  exact hi
theorem exists_bounded_refinement_of_large_dft (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (k:ZMod q) {η:ℝ} (hη:0 < η)
    (hlarge:η * q ≤
      ‖ZMod.dft (fun x => ((f x - average ρ f x:ℝ):ℂ)) k‖) :
    ∃ π:ZMod q → β × Fin (2 * resolution η + 1),
      (∀ x,ρ x = (π x).1) ∧
      Green24Proof.FinitePartitionRefinement.energy ρ f / q + η ^ 2 / 16 ≤ Green24Proof.FinitePartitionRefinement.energy π f / q :=
  exists_refinement_of_large_dft ρ f hf k hη hlarge
    (resolution_pos η) (resolution_precision hη)
omit [DecidableEq β] in
theorem refinement_alphabet_card (m:ℕ) :
    Fintype.card (β × Fin (2 * m + 1)) = Fintype.card β * (2 * m + 1):=by
  simp
end Green24Proof.FourierPartitionIncrement
private def zz2415:"s096f"="s096f":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicWeakRegularity
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization
open Green24Proof.FourierPartitionIncrement
section Relabel
variable {α β γ:Type*} [Fintype α] [DecidableEq β] [DecidableEq γ]
theorem average_comp_injective (π:α → β) (e:β → γ) (he:Function.Injective e)
    (f:α → ℝ):average (fun x => e (π x)) f = average π f:=by
  funext x
  have hfiber:fiber (fun y => e (π y)) (e (π x)) = fiber π (π x):=by
    ext y
    simp only [mem_fiber,he.eq_iff]
  simp only [average,fiberMean]
  rw [hfiber]
private def zz1816:"s0718"="s0718":=by decide+kernel
theorem energy_comp_injective (π:α → β) (e:β → γ) (he:Function.Injective e)
    (f:α → ℝ):Green24Proof.FinitePartitionRefinement.energy (fun x => e (π x)) f = Green24Proof.FinitePartitionRefinement.energy π f:=by
  simp only [Green24Proof.FinitePartitionRefinement.energy,average_comp_injective π e he f]
end Relabel
variable {q:ℕ} [NeZero q]
abbrev Alphabet (η:ℝ) (n:ℕ):=Fin n → Fin (2 * resolution η + 1)
def successorEquiv (η:ℝ) (n:ℕ) :
    Alphabet η n × Fin (2 * resolution η + 1) ≃ Alphabet η (n + 1) :=
  (Equiv.prodComm _ _).trans (Fin.consEquiv (fun _ => Fin (2 * resolution η + 1)))
theorem alphabet_card (η:ℝ) (n:ℕ) :
    Fintype.card (Alphabet η n) = (2 * resolution η + 1) ^ n:=by
  simp [Alphabet]
def FourierUniform {β:Type*} [DecidableEq β] (π:ZMod q → β)
    (f:ZMod q → ℝ) (η:ℝ):Prop :=
  ∀ k, ‖ZMod.dft (fun x => ((f x - average π f x:ℝ):ℂ)) k‖ ≤ η * q
theorem normalized_energy_nonneg {β:Type*} [DecidableEq β]
    (π:ZMod q → β) (f:ZMod q → ℝ):0 ≤ Green24Proof.FinitePartitionRefinement.energy π f / q :=
  div_nonneg (Finset.sum_nonneg (fun _ _ => sq_nonneg _)) (Nat.cast_nonneg q)
theorem normalized_energy_le_one {β:Type*} [Fintype β] [DecidableEq β]
    (π:ZMod q → β) (f:ZMod q → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1) :
    Green24Proof.FinitePartitionRefinement.energy π f / q ≤ 1:=by
  apply (div_le_one (Nat.cast_pos.mpr (NeZero.pos q))).mpr
  simpa only [Green24Proof.FinitePartitionRefinement.energy,ZMod.card] using average_energy_le_card π f hf
private def zz1817:"s0719"="s0719":=by decide+kernel
theorem exists_uniform_or_large_energy (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (n:ℕ) :
    (∃ j ≤ n, ∃ π:ZMod q → Alphabet η j,FourierUniform π f η) ∨
      ∃ π:ZMod q → Alphabet η n,(n:ℝ) * (η ^ 2 / 16) ≤ Green24Proof.FinitePartitionRefinement.energy π f / q:=by
  classical
  induction n with
  | zero =>
      right
      let ρ:ZMod q → Alphabet η 0:=fun _ i => Fin.elim0 i
      refine ⟨ρ, ?_⟩
      simpa only [Nat.cast_zero,zero_mul] using
        normalized_energy_nonneg ρ f
  | succ n ih =>
      rcases ih with ⟨j,hj,π,hπ⟩ | ⟨ρ,hρ⟩
      · exact Or.inl ⟨j,hj.trans (Nat.le_succ n),π,hπ⟩
      · by_cases hu:FourierUniform ρ f η
        · exact Or.inl ⟨n,Nat.le_succ n,ρ,hu⟩
        · change ¬ ∀ k, ‖ZMod.dft
              (fun x => ((f x - average ρ f x:ℝ):ℂ)) k‖ ≤ η * q at hu
          obtain ⟨k,hk⟩:=not_forall.mp hu
          obtain ⟨σ,_hσ,hinc⟩:=exists_bounded_refinement_of_large_dft
            ρ f hf k hη (lt_of_not_ge hk).le
          let π:ZMod q → Alphabet η (n + 1):=fun x => successorEquiv η n (σ x)
          have he:Green24Proof.FinitePartitionRefinement.energy π f = Green24Proof.FinitePartitionRefinement.energy σ f :=
            energy_comp_injective σ (successorEquiv η n)
              (successorEquiv η n).injective f
          right
          refine ⟨π, ?_⟩
          rw [he,Nat.cast_add,Nat.cast_one]
          nlinarith
noncomputable def stepBound (η:ℝ):ℕ:=⌈16 / η ^ 2⌉₊ + 1
theorem stepBound_exceeds_energy {η:ℝ} (hη:0 < η) :
    1 < (stepBound η:ℝ) * (η ^ 2 / 16):=by
  have hc:=Nat.le_ceil (16 / η ^ 2)
  have hb:16 / η ^ 2 < (stepBound η:ℝ):=by
    unfold stepBound
    push_cast
    linarith
  have hp:=(div_lt_iff₀ (sq_pos_of_pos hη)).mp hb
  nlinarith
theorem exists_fourier_uniform_partition (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) :
    ∃ n ≤ stepBound η, ∃ π:ZMod q → Alphabet η n,FourierUniform π f η:=by
  rcases exists_uniform_or_large_energy f hf hη (stepBound η) with h | ⟨π,hπ⟩
  · exact h
  · have hu:=normalized_energy_le_one π f hf
    have hl:=stepBound_exceeds_energy hη
    exfalso
    linarith
theorem alphabet_card_le_bound {η:ℝ} {n:ℕ} (hn:n ≤ stepBound η) :
    Fintype.card (Alphabet η n) ≤ (2 * resolution η + 1) ^ stepBound η:=by
  rw [alphabet_card]
  exact Nat.pow_le_pow_right (Nat.succ_pos _) hn
private def zz1818:"s071a"="s071a":=by decide+kernel
theorem exists_range_preserving_fourier_approximation (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) :
    ∃ n ≤ stepBound η, ∃ π:ZMod q → Alphabet η n,
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 1) ^ stepBound η ∧
      (∀ x,average π f x ∈ Set.Icc 0 1) ∧
      (∑ x,average π f x) = (∑ x,f x) ∧
      (∀ x,f x - average π f x ∈ Set.Icc (-1) 1) ∧
      FourierUniform π f η:=by
  obtain ⟨n,hn,π,hπ⟩:=exists_fourier_uniform_partition f hf hη
  exact ⟨n,hn,π,alphabet_card_le_bound hn,average_mem_Icc π f hf,
    sum_average π f,residual_mem_Icc π f hf,hπ⟩
end Green24Proof.CyclicWeakRegularity
private def zz2416:"s0970"="s0970":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicCharacterFactor
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization
open Green24Proof.FourierPartitionIncrement
open Green24Proof.CyclicWeakRegularity
variable {q:ℕ} [NeZero q]
noncomputable def characterTest (k:ZMod q) (imaginary:Bool) (x:ZMod q):ℝ :=
  if imaginary then (ZMod.stdAddChar (-(x * k))).im
  else (ZMod.stdAddChar (-(x * k))).re
theorem characterTest_mem_Icc (k:ZMod q) (b:Bool) (x:ZMod q) :
    characterTest k b x ∈ Set.Icc (-1) 1:=by
  have hn:‖ZMod.stdAddChar (-(x * k))‖ = 1:=by
    simp only [ZMod.stdAddChar_apply,Circle.norm_coe]
  cases b
  · exact abs_le.mp ((Complex.abs_re_le_norm _).trans_eq hn)
  · exact abs_le.mp ((Complex.abs_im_le_norm _).trans_eq hn)
theorem exists_correlating_component (r:ZMod q → ℝ) (k:ZMod q) {η:ℝ}
    (hlarge:η * q ≤ ‖ZMod.dft (fun x => (r x:ℂ)) k‖) :
    ∃ b:Bool,η * q / 2 ≤ |∑ x,r x * characterTest k b x|:=by
  by_cases hre:η * q / 2 ≤ |(ZMod.dft (fun x => (r x:ℂ)) k).re|
  · refine ⟨false, ?_⟩
    change η * q / 2 ≤ |∑ x,r x * (ZMod.stdAddChar (-(x * k))).re|
    rwa [dft_real_re] at hre
  · refine ⟨true, ?_⟩
    have hab:=Complex.norm_le_abs_re_add_abs_im
      (ZMod.dft (fun x => (r x:ℂ)) k)
    have hi:η * q / 2 ≤ |(ZMod.dft (fun x => (r x:ℂ)) k).im|:=by
      linarith
    change η * q / 2 ≤ |∑ x,r x * (ZMod.stdAddChar (-(x * k))).im|
    rwa [dft_real_im] at hi
noncomputable def quantizedCharacter (η:ℝ) (k:ZMod q) (b:Bool) (x:ZMod q) :
    Fin (2 * resolution η + 1) :=
  quantize (resolution η) (characterTest k b x)
theorem exists_quantized_correlating_component (r:ZMod q → ℝ) (k:ZMod q)
    (hr:∀ x, |r x| ≤ 1) {η:ℝ} (hη:0 < η)
    (hlarge:η * q ≤ ‖ZMod.dft (fun x => (r x:ℂ)) k‖) :
    ∃ b:Bool,(η / 4) * q ≤
      |∑ x,r x * gridValue (resolution η) (quantizedCharacter η k b x)|:=by
  obtain ⟨b,hb⟩:=exists_correlating_component r k hlarge
  refine ⟨b, ?_⟩
  have he:=correlation_transfer (resolution_pos η) r (characterTest k b) hr
    (characterTest_mem_Icc k b)
  simp only [ZMod.card] at he
  have hp:=mul_le_mul_of_nonneg_left (resolution_precision hη) (Nat.cast_nonneg q)
  rw [mul_one_div] at hp
  change (η / 4) * q ≤
    |∑ x,r x * gridValue (resolution η) (quantize (resolution η) (characterTest k b x))|
  nlinarith
noncomputable def phaseFactor {n:ℕ} (η:ℝ) (frequencies:Fin n → ZMod q)
    (components:Fin n → Bool) (x:ZMod q):Alphabet η n :=
  fun i => quantizedCharacter η (frequencies i) (components i) x
private def zz1819:"s071b"="s071b":=by decide+kernel
theorem phaseFactor_cons {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q) (bs:Fin n → Bool)
    (k:ZMod q) (b:Bool) (x:ZMod q) :
    phaseFactor η (Fin.cons k ks) (Fin.cons b bs) x =
      Fin.cons (quantizedCharacter η k b x) (phaseFactor η ks bs x):=by
  funext i
  refine Fin.cases ?_ (fun j => ?_) i <;> simp [phaseFactor]
theorem phaseFactor_cons_tail {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (k:ZMod q) (b:Bool) (x:ZMod q) :
    phaseFactor η ks bs x = Fin.tail (phaseFactor η (Fin.cons k ks) (Fin.cons b bs) x):=by
  rw [phaseFactor_cons,Fin.tail_cons]
theorem exists_phase_extension {n:ℕ} (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (k:ZMod q)
    (hlarge:η * q ≤ ‖ZMod.dft
      (fun x => ((f x - average (phaseFactor η ks bs) f x:ℝ):ℂ)) k‖) :
    ∃ b:Bool,Green24Proof.FinitePartitionRefinement.energy (phaseFactor η ks bs) f / q + η ^ 2 / 16 ≤
      Green24Proof.FinitePartitionRefinement.energy (phaseFactor η (Fin.cons k ks) (Fin.cons b bs)) f / q:=by
  let ρ:=phaseFactor η ks bs
  have hr:∀ x, |f x - average ρ f x| ≤ 1 :=
    fun x => abs_le.mpr (residual_mem_Icc ρ f hf x)
  obtain ⟨b,hc⟩:=exists_quantized_correlating_component
    (fun x => f x - average ρ f x) k hr hη hlarge
  let π:=phaseFactor η (Fin.cons k ks) (Fin.cons b bs)
  let g:Alphabet η (n + 1) → ℝ:=fun v => gridValue (resolution η) (v 0)
  have hg:∀ x, |g (π x)| ≤ 1 :=
    fun x => abs_le.mpr (gridValue_mem_Icc (resolution_pos η) (π x 0))
  have href:∀ x,ρ x = Fin.tail (π x):=phaseFactor_cons_tail η ks bs k b
  have hcorr:(η / 4) * Fintype.card (ZMod q) ≤
      |∑ x,(f x - average ρ f x) * g (π x)|:=by
    simpa only [ZMod.card,g,π,phaseFactor_cons,Fin.cons_zero] using hc
  have hi:=normalized_energy_increment π ρ Fin.tail href f g
    (show 0 ≤ η / 4 by positivity) hg hcorr
  refine ⟨b, ?_⟩
  norm_num only [ZMod.card,div_pow] at hi
  exact hi
theorem exists_uniform_character_factor_or_large_energy (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (n:ℕ) :
    (∃ j ≤ n, ∃ (ks:Fin j → ZMod q) (bs:Fin j → Bool),
      FourierUniform (phaseFactor η ks bs) f η) ∨
    ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool),
      (n:ℝ) * (η ^ 2 / 16) ≤ Green24Proof.FinitePartitionRefinement.energy (phaseFactor η ks bs) f / q:=by
  classical
  induction n with
  | zero =>
      right
      let ks:Fin 0 → ZMod q:=Fin.elim0
      let bs:Fin 0 → Bool:=Fin.elim0
      refine ⟨ks,bs, ?_⟩
      simpa only [Nat.cast_zero,zero_mul] using
        normalized_energy_nonneg (phaseFactor η ks bs) f
  | succ n ih =>
      rcases ih with ⟨j,hj,ks,bs,hu⟩ | ⟨ks,bs,he⟩
      · exact Or.inl ⟨j,hj.trans (Nat.le_succ n),ks,bs,hu⟩
      · by_cases hu:FourierUniform (phaseFactor η ks bs) f η
        · exact Or.inl ⟨n,Nat.le_succ n,ks,bs,hu⟩
        · change ¬ ∀ k, ‖ZMod.dft
              (fun x => ((f x - average (phaseFactor η ks bs) f x:ℝ):ℂ)) k‖ ≤ η * q at hu
          obtain ⟨k,hk⟩:=not_forall.mp hu
          obtain ⟨b,hb⟩:=exists_phase_extension f hf hη ks bs k (lt_of_not_ge hk).le
          right
          refine ⟨Fin.cons k ks,Fin.cons b bs, ?_⟩
          rw [Nat.cast_add,Nat.cast_one]
          nlinarith
private def zz1820:"s071c"="s071c":=by decide+kernel
theorem exists_uniform_character_factor (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool),
      FourierUniform (phaseFactor η ks bs) f η:=by
  rcases exists_uniform_character_factor_or_large_energy f hf hη (stepBound η) with
    h | ⟨ks,bs,he⟩
  · exact h
  · have hu:=normalized_energy_le_one (phaseFactor η ks bs) f hf
    have hl:=stepBound_exceeds_energy hη
    exfalso
    linarith
theorem exists_character_factor_approximation (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool)
      (F:Alphabet η n → ℝ),
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 1) ^ stepBound η ∧
      (∀ a,F a ∈ Set.Icc 0 1) ∧
      (∀ x,average (phaseFactor η ks bs) f x = F (phaseFactor η ks bs x)) ∧
      (∑ x,F (phaseFactor η ks bs x)) = (∑ x,f x) ∧
      (∀ k, ‖ZMod.dft (fun x =>
        ((f x - F (phaseFactor η ks bs x):ℝ):ℂ)) k‖ ≤ η * q):=by
  obtain ⟨n,hn,ks,bs,hu⟩:=exists_uniform_character_factor f hf hη
  refine ⟨n,hn,ks,bs,fiberMean (phaseFactor η ks bs) f,
    alphabet_card_le_bound hn, ?_,fun _ => rfl, ?_,hu⟩
  · intro a
    exact ⟨fiberMean_nonneg _ f (fun x => (hf x).1) a,
      fiberMean_le_one _ f (fun x => (hf x).2) a⟩
  · exact sum_average (phaseFactor η ks bs) f
end Green24Proof.CyclicCharacterFactor
private def zz2417:"s0971"="s0971":=by decide+kernel
end 
section 
namespace Green24Proof.GridLipschitzSmoothing
open scoped NNReal
section SeparatedLabels
variable {X B:Type*} [PseudoMetricSpace X]
theorem exists_bounded_extension (label:X → B) (F:B → ℝ)
    (hF:∀ b,F b ∈ Set.Icc 0 1) (good:Set X) (K:ℝ≥0)
    (hsep:∀ x ∈ good, ∀ y ∈ good,label x ≠ label y → 1 ≤ (K:ℝ) * dist x y) :
    ∃ G:X → ℝ,LipschitzWith K G ∧ (∀ x,G x ∈ Set.Icc 0 1) ∧
      ∀ x ∈ good,G x = F (label x):=by
  have hl:LipschitzOnWith K (fun x => F (label x)) good:=by
    apply LipschitzOnWith.of_dist_le_mul
    intro x hx y hy
    by_cases he:label x = label y
    · rw [he,dist_self]
      exact mul_nonneg K.coe_nonneg dist_nonneg
    · rw [Real.dist_eq]
      have hFx:=hF (label x)
      have hFy:=hF (label y)
      have hv:|F (label x) - F (label y)| ≤ 1:=by
        apply abs_le.mpr
        constructor <;> linarith [hFx.1,hFx.2,hFy.1,hFy.2]
      exact hv.trans (hsep x hx y hy he)
  obtain ⟨g,hg,heq⟩:=hl.extend_real
  refine ⟨fun x => max 0 (min 1 (g x)),(hg.const_min 1).const_max 0, ?_, ?_⟩
  · intro x
    exact ⟨le_max_left _ _,max_le (by norm_num) (min_le_left _ _)⟩
  · intro x hx
    change max 0 (min 1 (g x)) = F (label x)
    rw [← heq hx,min_eq_right (hF (label x)).2,max_eq_right (hF (label x)).1]
end SeparatedLabels
noncomputable def cellIndex (h o x:ℝ):ℤ:=⌊(x - o) / h⌋
def GridGood (h δ o:ℝ):Set ℝ :=
  {x | ∀ j:ℤ,δ ≤ |x - (o + (j:ℝ) * h)|}
theorem gap_of_cellIndex_lt {h δ o x y:ℝ} (hh:0 < h)
    (hx:x ∈ GridGood h δ o) (hy:y ∈ GridGood h δ o)
    (hxy:cellIndex h o x < cellIndex h o y):2 * δ ≤ y - x:=by
  let i:=cellIndex h o x
  let j:=cellIndex h o y
  have hxi:(x - o) / h < (i:ℝ) + 1:=Int.lt_floor_add_one _
  have hyj:(j:ℝ) ≤ (y - o) / h:=Int.floor_le _
  have hij:(i:ℝ) + 1 ≤ (j:ℝ):=by
    have hijZ:i + 1 ≤ j:=by omega
    exact_mod_cast hijZ
  have hxb:x < o + ((i:ℝ) + 1) * h:=by
    have ht:=(div_lt_iff₀ hh).mp hxi
    linarith
  have hby:o + ((i:ℝ) + 1) * h ≤ y:=by
    have ht:=(le_div_iff₀ hh).mp hyj
    have hm:=mul_le_mul_of_nonneg_right hij hh.le
    linarith
  have hxg:=hx (i + 1)
  have hyg:=hy (i + 1)
  push_cast at hxg hyg
  rw [abs_of_nonpos (by linarith)] at hxg
  rw [abs_of_nonneg (by linarith)] at hyg
  linarith
private def zz1821:"s071d"="s071d":=by decide+kernel
theorem grid_core_separation {h δ o x y:ℝ} (hh:0 < h)
    (hx:x ∈ GridGood h δ o) (hy:y ∈ GridGood h δ o)
    (hne:cellIndex h o x ≠ cellIndex h o y):2 * δ ≤ dist x y:=by
  rcases lt_or_gt_of_ne hne with hxy | hyx
  · have hg:=gap_of_cellIndex_lt hh hx hy hxy
    exact hg.trans (by rw [Real.dist_eq,abs_sub_comm]; exact le_abs_self _)
  · have hg:=gap_of_cellIndex_lt hh hy hx hyx
    exact hg.trans (by rw [Real.dist_eq]; exact le_abs_self _)
theorem exists_scalar_grid_smoothing (h δ o:ℝ) (hh:0 < h) (hδ:0 < δ)
    (F:ℤ → ℝ) (hF:∀ j,F j ∈ Set.Icc 0 1) :
    ∃ G:ℝ → ℝ,
      LipschitzWith ⟨1 / (2 * δ),by positivity⟩ G ∧
      (∀ x,G x ∈ Set.Icc 0 1) ∧
      ∀ x ∈ GridGood h δ o,G x = F (cellIndex h o x):=by
  apply exists_bounded_extension (cellIndex h o) F hF (GridGood h δ o) _
  intro x hx y hy hne
  change (1:ℝ) ≤ (1 / (2 * δ)) * dist x y
  have hs:=grid_core_separation hh hx hy hne
  have hd:(0:ℝ) < 2 * δ:=by positivity
  have hb:(1:ℝ) ≤ dist x y / (2 * δ):=(le_div_iff₀ hd).mpr (by simpa using hs)
  simpa only [div_eq_mul_inv,one_mul,mul_comm] using hb
section VectorGrid
variable {ι:Type*} [Fintype ι]
noncomputable def vectorCellIndex (h:ℝ) (o x:ι → ℝ):ι → ℤ :=
  fun i => cellIndex h (o i) (x i)
def VectorGridGood (h δ:ℝ) (o:ι → ℝ):Set (ι → ℝ) :=
  {x | ∀ i,x i ∈ GridGood h δ (o i)}
theorem vector_grid_core_separation {h δ:ℝ} {o x y:ι → ℝ} (hh:0 < h)
    (hx:x ∈ VectorGridGood h δ o) (hy:y ∈ VectorGridGood h δ o)
    (hne:vectorCellIndex h o x ≠ vectorCellIndex h o y):2 * δ ≤ dist x y:=by
  obtain ⟨i,hi⟩:=Function.ne_iff.mp hne
  exact (grid_core_separation hh (hx i) (hy i) hi).trans (dist_le_pi_dist x y i)
theorem exists_vector_grid_smoothing (h δ:ℝ) (o:ι → ℝ)
    (hh:0 < h) (hδ:0 < δ) (F:(ι → ℤ) → ℝ)
    (hF:∀ j,F j ∈ Set.Icc 0 1) :
    ∃ G:(ι → ℝ) → ℝ,
      LipschitzWith ⟨1 / (2 * δ),by positivity⟩ G ∧
      (∀ x,G x ∈ Set.Icc 0 1) ∧
      ∀ x ∈ VectorGridGood h δ o,G x = F (vectorCellIndex h o x):=by
  apply exists_bounded_extension (vectorCellIndex h o) F hF (VectorGridGood h δ o) _
  intro x hx y hy hne
  change (1:ℝ) ≤ (1 / (2 * δ)) * dist x y
  have hs:=vector_grid_core_separation hh hx hy hne
  have hd:(0:ℝ) < 2 * δ:=by positivity
  have hb:(1:ℝ) ≤ dist x y / (2 * δ):=(le_div_iff₀ hd).mpr (by simpa using hs)
  simpa only [div_eq_mul_inv,one_mul,mul_comm] using hb
end VectorGrid
end Green24Proof.GridLipschitzSmoothing
private def zz2418:"s0972"="s0972":=by decide+kernel
end 
section 
namespace Green24Proof.ShiftedScalarQuantization
open Finset
open scoped BigOperators
noncomputable def coordinate (m:ℕ) (t:ℝ):ℝ:=(m:ℝ) * (t + 1) + 1
noncomputable def quantize (m:ℕ) (o t:ℝ):Fin (2 * m + 2) :=
  ⟨min ⌊coordinate m t - o⌋₊ (2 * m + 1),by omega⟩
noncomputable def rawValue (m:ℕ) (o:ℝ) (k:Fin (2 * m + 2)):ℝ :=
  ((k.val:ℝ) + o - 1) / m - 1
noncomputable def gridValue (m:ℕ) (o:ℝ) (k:Fin (2 * m + 2)):ℝ :=
  max (-1) (min 1 (rawValue m o k))
private def zz1822:"s071e"="s071e":=by decide+kernel
theorem gridValue_mem_Icc (m:ℕ) (o:ℝ) (k:Fin (2 * m + 2)) :
    gridValue m o k ∈ Set.Icc (-1) 1:=by
  exact ⟨le_max_left _ _,max_le (by norm_num) (min_le_left _ _)⟩
theorem coordinate_bounds {m:ℕ} {t:ℝ} (ht:t ∈ Set.Icc (-1) 1) :
    1 ≤ coordinate m t ∧ coordinate m t ≤ 2 * m + 1:=by
  unfold coordinate
  constructor <;> nlinarith [ht.1,ht.2,(Nat.cast_nonneg m:(0:ℝ) ≤ m)]
theorem quantize_val {m:ℕ} {o t:ℝ} (ho:o ∈ Set.Icc 0 1)
    (ht:t ∈ Set.Icc (-1) 1) :
    (quantize m o t).val = ⌊coordinate m t - o⌋₊:=by
  have hb:coordinate m t - o ≤ (2 * m + 1:ℕ):=by
    push_cast
    linarith [(coordinate_bounds (m:=m) ht).2,ho.1]
  have hf:⌊coordinate m t - o⌋₊ ≤ 2 * m + 1 :=
    (Nat.floor_le_floor hb).trans_eq (Nat.floor_natCast _)
  exact min_eq_left hf
theorem raw_quantization_error {m:ℕ} (hm:0 < m) {o t:ℝ}
    (ho:o ∈ Set.Icc 0 1) (ht:t ∈ Set.Icc (-1) 1) :
    0 ≤ t - rawValue m o (quantize m o t) ∧
      t - rawValue m o (quantize m o t) < 1 / m:=by
  have hmR:(0:ℝ) < m:=Nat.cast_pos.mpr hm
  have hnonneg:0 ≤ coordinate m t - o:=by linarith [(coordinate_bounds (m:=m) ht).1,ho.2]
  have hlo:=Nat.floor_le hnonneg
  have hhi:=Nat.lt_floor_add_one (coordinate m t - o)
  unfold rawValue
  rw [quantize_val ho ht]
  have hdiv:((⌊coordinate m t - o⌋₊:ℝ) + o - 1) / m ≤ t + 1:=by
    apply (div_le_iff₀ hmR).mpr
    dsimp [coordinate] at hlo ⊢
    nlinarith
  have hdiv':t + 1 < ((⌊coordinate m t - o⌋₊:ℝ) + o - 1) / m + 1 / m:=by
    rw [← add_div]
    apply (lt_div_iff₀ hmR).mpr
    dsimp [coordinate] at hhi ⊢
    nlinarith
  constructor <;> linarith
private def zz1823:"s071f"="s071f":=by decide+kernel
theorem quantization_error {m:ℕ} (hm:0 < m) {o t:ℝ}
    (ho:o ∈ Set.Icc 0 1) (ht:t ∈ Set.Icc (-1) 1) :
    0 ≤ t - gridValue m o (quantize m o t) ∧
      t - gridValue m o (quantize m o t) < 1 / m:=by
  have he:=raw_quantization_error hm ho ht
  have hr:rawValue m o (quantize m o t) ≤ 1:=by linarith [ht.2]
  unfold gridValue
  rw [min_eq_right hr]
  have hmax:max (-1) (rawValue m o (quantize m o t)) ≤ t :=
    max_le ht.1 (by linarith)
  have hraw:=le_max_right (-1) (rawValue m o (quantize m o t))
  constructor <;> linarith
theorem quantization_abs_error {m:ℕ} (hm:0 < m) {o t:ℝ}
    (ho:o ∈ Set.Icc 0 1) (ht:t ∈ Set.Icc (-1) 1) :
    |t - gridValue m o (quantize m o t)| ≤ 1 / m:=by
  have he:=quantization_error hm ho ht
  rw [abs_of_nonneg he.1]
  exact he.2.le
noncomputable def encodeCell (m:ℕ) (j:ℤ):Fin (2 * m + 2) :=
  ⟨min j.toNat (2 * m + 1),by omega⟩
theorem quantize_eq_encodeCell (m:ℕ) (o t:ℝ) :
    quantize m o t = encodeCell m
      (Green24Proof.GridLipschitzSmoothing.cellIndex 1 o (coordinate m t)):=by
  apply Fin.ext
  simp only [quantize,encodeCell,Green24Proof.GridLipschitzSmoothing.cellIndex,
    div_one,Int.floor_toNat]
variable {α:Type*} [Fintype α]
theorem correlation_error {m:ℕ} (hm:0 < m) {o:ℝ}
    (ho:o ∈ Set.Icc 0 1) (r g:α → ℝ)
    (hr:∀ x, |r x| ≤ 1) (hg:∀ x,g x ∈ Set.Icc (-1) 1) :
    |(∑ x,r x * g x) - ∑ x,r x * gridValue m o (quantize m o (g x))| ≤
      (Fintype.card α:ℝ) / m:=by
  rw [← Finset.sum_sub_distrib]
  calc
    |∑ x,(r x * g x - r x * gridValue m o (quantize m o (g x)))| ≤
        ∑ x, |r x * g x - r x * gridValue m o (quantize m o (g x))| :=
      Finset.abs_sum_le_sum_abs _ _
    _ ≤ ∑ _x:α,(1:ℝ) / m:=by
      apply Finset.sum_le_sum
      intro x _
      rw [← mul_sub,abs_mul]
      exact (mul_le_mul (hr x) (quantization_abs_error hm ho (hg x))
        (abs_nonneg _) (by norm_num)).trans_eq (one_mul _)
    _ = _:=by simp [div_eq_mul_inv]
private def zz1824:"s0720"="s0720":=by decide+kernel
theorem correlation_transfer {m:ℕ} (hm:0 < m) {o:ℝ}
    (ho:o ∈ Set.Icc 0 1) (r g:α → ℝ)
    (hr:∀ x, |r x| ≤ 1) (hg:∀ x,g x ∈ Set.Icc (-1) 1) :
    |∑ x,r x * g x| - (Fintype.card α:ℝ) / m ≤
      |∑ x,r x * gridValue m o (quantize m o (g x))|:=by
  have he:=correlation_error hm ho r g hr hg
  have ht:=abs_add_le
    ((∑ x,r x * g x) - ∑ x,r x * gridValue m o (quantize m o (g x)))
    (∑ x,r x * gridValue m o (quantize m o (g x)))
  rw [sub_add_cancel] at ht
  linarith
end Green24Proof.ShiftedScalarQuantization
private def zz2419:"s0973"="s0973":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteGridBoundaryAvoidance
open Finset
open scoped BigOperators
def BoundaryBad {M:ℕ} (a:Fin M) (t:ℝ):Prop :=
  ∃ j:ℤ, |(M:ℝ) * t - (((M:ℤ) * j + (a.val:ℤ):ℤ):ℝ)| < 1 / 2
theorem boundaryBad_unique {M:ℕ} {a b:Fin M} {t:ℝ}
    (ha:BoundaryBad a t) (hb:BoundaryBad b t):a = b:=by
  obtain ⟨j,hj⟩:=ha
  obtain ⟨k,hk⟩:=hb
  let u:ℤ:=(M:ℤ) * j + a.val
  let v:ℤ:=(M:ℤ) * k + b.val
  have huvR:|((u - v:ℤ):ℝ)| < 1:=by
    rw [Int.cast_sub,abs_lt]
    have hj':=abs_lt.mp hj
    have hk':=abs_lt.mp hk
    change -(1:ℝ) < (u:ℝ) - v ∧ (u:ℝ) - v < 1
    constructor <;> dsimp [u,v] at * <;> linarith [hj'.1,hj'.2,hk'.1,hk'.2]
  have huvZ:|u - v| < 1:=by exact_mod_cast huvR
  have huv:u = v:=sub_eq_zero.mp (Int.abs_lt_one_iff.mp huvZ)
  have hmod:=congrArg (fun z:ℤ => z % (M:ℤ)) huv
  dsimp [u,v] at hmod
  have haM:(a.val:ℤ) % M = a.val :=
    Int.emod_eq_of_lt (Int.natCast_nonneg _) (by exact_mod_cast a.isLt)
  have hbM:(b.val:ℤ) % M = b.val :=
    Int.emod_eq_of_lt (Int.natCast_nonneg _) (by exact_mod_cast b.isLt)
  rw [add_comm ((M:ℤ) * j),add_comm ((M:ℤ) * k),
    Int.add_mul_emod_self_left,Int.add_mul_emod_self_left,haM,hbM] at hmod
  apply Fin.ext
  exact_mod_cast hmod
theorem boundaryBad_iff_near_grid {M:ℕ} (hM:0 < M) (a:Fin M) (t:ℝ) :
    BoundaryBad a t ↔
      ∃ j:ℤ, |t - ((j:ℝ) + (a.val:ℝ) / M)| < 1 / (2 * M):=by
  have hMR:(0:ℝ) < M:=Nat.cast_pos.mpr hM
  unfold BoundaryBad
  apply exists_congr
  intro j
  have he:(M:ℝ) * (t - ((j:ℝ) + (a.val:ℝ) / M)) =
      (M:ℝ) * t - (((M:ℤ) * j + (a.val:ℤ):ℤ):ℝ):=by
    push_cast
    rw [mul_sub,mul_add,mul_div_cancel₀ _ hMR.ne']
  rw [← he,abs_mul,abs_of_pos hMR, ← div_div,lt_div_iff₀ hMR,mul_comm]
theorem boundaryBad_iff_near_scaled_grid {M:ℕ} (hM:0 < M) {s:ℝ} (hs:0 < s)
    (a:Fin M) (t:ℝ) :
    BoundaryBad a (s * t) ↔
      ∃ j:ℤ, |t - ((j:ℝ) + (a.val:ℝ) / M) / s| < 1 / (2 * M * s):=by
  rw [boundaryBad_iff_near_grid hM]
  apply exists_congr
  intro j
  have he:s * (t - ((j:ℝ) + (a.val:ℝ) / M) / s) =
      s * t - ((j:ℝ) + (a.val:ℝ) / M):=by
    rw [mul_sub,mul_div_cancel₀ _ hs.ne']
  rw [← he,abs_mul,abs_of_pos hs, ← div_div (1:ℝ) (2 * M) s,
    lt_div_iff₀ hs,mul_comm]
noncomputable def badOffsets (M:ℕ) (t:ℝ):Finset (Fin M):=by
  classical
  exact Finset.univ.filter (fun a => BoundaryBad a t)
private def zz1825:"s0721"="s0721":=by decide+kernel
theorem badOffsets_card_le_one (M:ℕ) (t:ℝ):(badOffsets M t).card ≤ 1:=by
  classical
  apply Finset.card_le_one.mpr
  intro a ha b hb
  exact boundaryBad_unique (Finset.mem_filter.mp ha).2 (Finset.mem_filter.mp hb).2
variable {α:Type*} [Fintype α]
noncomputable def badSamples {M:ℕ} (a:Fin M) (samples:α → ℝ):Finset α:=by
  classical
  exact Finset.univ.filter (fun x => BoundaryBad a (samples x))
theorem sum_badSamples_card (M:ℕ) (samples:α → ℝ) :
    (∑ a:Fin M,(badSamples a samples).card) =
      ∑ x,(badOffsets M (samples x)).card:=by
  classical
  simp only [badSamples,badOffsets,Finset.card_eq_sum_ones,Finset.sum_filter]
  exact Finset.sum_comm
theorem sum_badSamples_card_le (M:ℕ) (samples:α → ℝ) :
    (∑ a:Fin M,(badSamples a samples).card) ≤ Fintype.card α:=by
  rw [sum_badSamples_card]
  calc
    (∑ x,(badOffsets M (samples x)).card) ≤ ∑ _x:α,1 :=
      Finset.sum_le_sum (fun x _ => badOffsets_card_le_one M (samples x))
    _ = _:=by simp
theorem exists_offset_card_bound {M:ℕ} (hM:0 < M) (samples:α → ℝ) :
    ∃ a:Fin M,M * (badSamples a samples).card ≤ Fintype.card α:=by
  have hs:(Finset.univ:Finset (Fin M)).Nonempty:=⟨⟨0,hM⟩,Finset.mem_univ _⟩
  have hsum:(∑ a:Fin M,M * (badSamples a samples).card) ≤
      ∑ _a:Fin M,Fintype.card α:=by
    calc
      (∑ a:Fin M,M * (badSamples a samples).card) =
          M * ∑ a:Fin M,(badSamples a samples).card:=(Finset.mul_sum _ _ _).symm
      _ ≤ M * Fintype.card α:=Nat.mul_le_mul_left M (sum_badSamples_card_le M samples)
      _ = _:=by simp
  obtain ⟨a,_,ha⟩:=Finset.exists_le_of_sum_le hs hsum
  exact ⟨a,ha⟩
private def zz1826:"s0722"="s0722":=by decide+kernel
theorem exists_offset_fraction_bound {M:ℕ} (hM:0 < M) (samples:α → ℝ) :
    ∃ a:Fin M,((badSamples a samples).card:ℝ) ≤ (Fintype.card α:ℝ) / M:=by
  obtain ⟨a,ha⟩:=exists_offset_card_bound hM samples
  refine ⟨a,(le_div_iff₀ (Nat.cast_pos.mpr hM)).mpr ?_⟩
  have h:(M:ℝ) * (badSamples a samples).card ≤ Fintype.card α:=by exact_mod_cast ha
  simpa only [mul_comm] using h
variable {ι:Type*} [Fintype ι]
noncomputable def badCoordinateSamples {M:ℕ} (offsets:ι → Fin M)
    (samples:α → ι → ℝ):Finset α:=by
  classical
  exact Finset.univ.filter (fun x => ∃ i,BoundaryBad (offsets i) (samples x i))
theorem exists_coordinate_offsets_card_bound {M:ℕ} (hM:0 < M)
    (samples:α → ι → ℝ) :
    ∃ offsets:ι → Fin M,
      M * (badCoordinateSamples offsets samples).card ≤ Fintype.card ι * Fintype.card α:=by
  classical
  choose offsets hoff using fun i => exists_offset_card_bound hM (fun x => samples x i)
  refine ⟨offsets, ?_⟩
  have hsets:badCoordinateSamples offsets samples =
      Finset.univ.biUnion (fun i => badSamples (offsets i) (fun x => samples x i)):=by
    ext x
    simp [badCoordinateSamples,badSamples]
  rw [hsets]
  calc
    M * (Finset.univ.biUnion (fun i => badSamples (offsets i) (fun x => samples x i))).card ≤
        M * ∑ i,(badSamples (offsets i) (fun x => samples x i)).card :=
      Nat.mul_le_mul_left M Finset.card_biUnion_le
    _ = ∑ i,M * (badSamples (offsets i) (fun x => samples x i)).card :=
      Finset.mul_sum _ _ _
    _ ≤ ∑ _i:ι,Fintype.card α:=Finset.sum_le_sum (fun i _ => hoff i)
    _ = _:=by simp
theorem exists_coordinate_offsets_fraction_bound {M:ℕ} (hM:0 < M)
    (samples:α → ι → ℝ) :
    ∃ offsets:ι → Fin M,
      ((badCoordinateSamples offsets samples).card:ℝ) ≤
        (Fintype.card ι:ℝ) * Fintype.card α / M:=by
  obtain ⟨offsets,ho⟩:=exists_coordinate_offsets_card_bound hM samples
  refine ⟨offsets,(le_div_iff₀ (Nat.cast_pos.mpr hM)).mpr ?_⟩
  have h:(M:ℝ) * (badCoordinateSamples offsets samples).card ≤
      (Fintype.card ι:ℝ) * Fintype.card α:=by exact_mod_cast ho
  simpa only [mul_comm] using h
end Green24Proof.FiniteGridBoundaryAvoidance
private def zz2420:"s0974"="s0974":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicShiftedCharacterFactor
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization (resolution resolution_pos resolution_precision)
open Green24Proof.CyclicWeakRegularity (FourierUniform stepBound stepBound_exceeds_energy
  normalized_energy_nonneg normalized_energy_le_one)
open Green24Proof.CyclicCharacterFactor (characterTest characterTest_mem_Icc
  exists_correlating_component)
open Green24Proof.ShiftedScalarQuantization
open Green24Proof.FiniteGridBoundaryAvoidance
variable {q M:ℕ} [NeZero q]
noncomputable def offset (a:Fin M):ℝ:=(a.val:ℝ) / M
theorem offset_mem_Icc (hM:0 < M) (a:Fin M):offset a ∈ Set.Icc 0 1:=by
  have hMR:(0:ℝ) < M:=Nat.cast_pos.mpr hM
  refine ⟨div_nonneg (Nat.cast_nonneg _) hMR.le, ?_⟩
  exact (div_le_one hMR).mpr (by exact_mod_cast a.isLt.le)
noncomputable def characterCoordinate (η:ℝ) (k:ZMod q) (b:Bool)
    (x:ZMod q):ℝ:=coordinate (resolution η) (characterTest k b x)
noncomputable def quantizedCharacter (η:ℝ) (a:Fin M) (k:ZMod q)
    (b:Bool) (x:ZMod q):Fin (2 * resolution η + 2) :=
  quantize (resolution η) (offset a) (characterTest k b x)
abbrev Alphabet (η:ℝ) (n:ℕ):=Fin n → Fin (2 * resolution η + 2)
noncomputable def phaseFactor {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (as:Fin n → Fin M) (x:ZMod q):Alphabet η n :=
  fun i => quantizedCharacter η (as i) (ks i) (bs i) x
def BoundaryControlled {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (as:Fin n → Fin M):Prop :=
  ∀ i,M * (badSamples (as i) (characterCoordinate η (ks i) (bs i))).card ≤ q
private def zz1827:"s0723"="s0723":=by decide+kernel
theorem phaseFactor_cons {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (as:Fin n → Fin M) (k:ZMod q) (b:Bool)
    (a:Fin M) (x:ZMod q) :
    phaseFactor η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as) x =
      Fin.cons (quantizedCharacter η a k b x) (phaseFactor η ks bs as x):=by
  funext i
  refine Fin.cases ?_ (fun j => ?_) i <;> simp [phaseFactor]
theorem phaseFactor_cons_tail {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (as:Fin n → Fin M) (k:ZMod q) (b:Bool)
    (a:Fin M) (x:ZMod q) :
    phaseFactor η ks bs as x = Fin.tail
      (phaseFactor η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as) x):=by
  rw [phaseFactor_cons,Fin.tail_cons]
theorem boundaryControlled_cons {n:ℕ} {η:ℝ} {ks:Fin n → ZMod q}
    {bs:Fin n → Bool} {as:Fin n → Fin M} {k:ZMod q} {b:Bool} {a:Fin M}
    (hold:BoundaryControlled η ks bs as)
    (hnew:M * (badSamples a (characterCoordinate η k b)).card ≤ q) :
    BoundaryControlled η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as):=by
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · simpa only [Fin.cons_zero] using hnew
  · simpa only [Fin.cons_succ] using hold j
theorem exists_shifted_correlating_component (r:ZMod q → ℝ) (k:ZMod q)
    (hr:∀ x, |r x| ≤ 1) {η:ℝ} (hη:0 < η) (hM:0 < M)
    (hlarge:η * q ≤ ‖ZMod.dft (fun x => (r x:ℂ)) k‖) :
    ∃ (b:Bool) (a:Fin M),
      M * (badSamples a (characterCoordinate η k b)).card ≤ q ∧
      (η / 4) * q ≤ |∑ x,r x *
        gridValue (resolution η) (offset a) (quantizedCharacter η a k b x)|:=by
  obtain ⟨b,hb⟩:=exists_correlating_component r k hlarge
  obtain ⟨a,ha⟩:=exists_offset_card_bound hM (characterCoordinate η k b)
  refine ⟨b,a,by simpa only [ZMod.card] using ha, ?_⟩
  have he:=correlation_transfer (resolution_pos η) (offset_mem_Icc hM a) r
    (characterTest k b) hr (characterTest_mem_Icc k b)
  simp only [ZMod.card] at he
  have hp:=mul_le_mul_of_nonneg_left (resolution_precision hη) (Nat.cast_nonneg q)
  rw [mul_one_div] at hp
  change (η / 4) * q ≤ |∑ x,r x *
    gridValue (resolution η) (offset a) (quantize (resolution η) (offset a) (characterTest k b x))|
  nlinarith
private def zz1828:"s0724"="s0724":=by decide+kernel
theorem exists_phase_extension {n:ℕ} (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M) (k:ZMod q)
    (hlarge:η * q ≤ ‖ZMod.dft
      (fun x => ((f x - average (phaseFactor η ks bs as) f x:ℝ):ℂ)) k‖) :
    ∃ (b:Bool) (a:Fin M),
      M * (badSamples a (characterCoordinate η k b)).card ≤ q ∧
      Green24Proof.FinitePartitionRefinement.energy (phaseFactor η ks bs as) f / q + η ^ 2 / 16 ≤
        Green24Proof.FinitePartitionRefinement.energy (phaseFactor η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as)) f / q:=by
  let ρ:=phaseFactor η ks bs as
  have hr:∀ x, |f x - average ρ f x| ≤ 1 :=
    fun x => abs_le.mpr (residual_mem_Icc ρ f hf x)
  obtain ⟨b,a,ha,hc⟩:=exists_shifted_correlating_component
    (fun x => f x - average ρ f x) k hr hη hM hlarge
  let π:=phaseFactor η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as)
  let g:Alphabet η (n + 1) → ℝ:=fun v => gridValue (resolution η) (offset a) (v 0)
  have hg:∀ x, |g (π x)| ≤ 1 :=
    fun x => abs_le.mpr (gridValue_mem_Icc (resolution η) (offset a) (π x 0))
  have href:∀ x,ρ x = Fin.tail (π x):=phaseFactor_cons_tail η ks bs as k b a
  have hcorr:(η / 4) * Fintype.card (ZMod q) ≤
      |∑ x,(f x - average ρ f x) * g (π x)|:=by
    simpa only [ZMod.card,g,π,phaseFactor_cons,Fin.cons_zero] using hc
  have hi:=normalized_energy_increment π ρ Fin.tail href f g
    (show 0 ≤ η / 4 by positivity) hg hcorr
  refine ⟨b,a,ha, ?_⟩
  norm_num only [ZMod.card,div_pow] at hi
  exact hi
theorem exists_uniform_or_large_energy (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) (n:ℕ) :
    (∃ j ≤ n, ∃ (ks:Fin j → ZMod q) (bs:Fin j → Bool) (as:Fin j → Fin M),
      BoundaryControlled η ks bs as ∧ FourierUniform (phaseFactor η ks bs as) f η) ∨
    ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M),
      BoundaryControlled η ks bs as ∧
      (n:ℝ) * (η ^ 2 / 16) ≤ Green24Proof.FinitePartitionRefinement.energy (phaseFactor η ks bs as) f / q:=by
  classical
  induction n with
  | zero =>
      right
      let ks:Fin 0 → ZMod q:=Fin.elim0
      let bs:Fin 0 → Bool:=Fin.elim0
      let as:Fin 0 → Fin M:=Fin.elim0
      refine ⟨ks,bs,as,fun i => Fin.elim0 i, ?_⟩
      simpa only [Nat.cast_zero,zero_mul] using
        normalized_energy_nonneg (phaseFactor η ks bs as) f
  | succ n ih =>
      rcases ih with ⟨j,hj,ks,bs,as,hc,hu⟩ | ⟨ks,bs,as,hc,he⟩
      · exact Or.inl ⟨j,hj.trans (Nat.le_succ n),ks,bs,as,hc,hu⟩
      · by_cases hu:FourierUniform (phaseFactor η ks bs as) f η
        · exact Or.inl ⟨n,Nat.le_succ n,ks,bs,as,hc,hu⟩
        · change ¬ ∀ k, ‖ZMod.dft
              (fun x => ((f x - average (phaseFactor η ks bs as) f x:ℝ):ℂ)) k‖ ≤ η * q at hu
          obtain ⟨k,hk⟩:=not_forall.mp hu
          obtain ⟨b,a,ha,hi⟩:=exists_phase_extension f hf hη hM ks bs as k (lt_of_not_ge hk).le
          right
          refine ⟨Fin.cons k ks,Fin.cons b bs,Fin.cons a as,
            boundaryControlled_cons hc ha, ?_⟩
          rw [Nat.cast_add,Nat.cast_one]
          nlinarith
theorem exists_uniform_character_factor (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M),
      BoundaryControlled η ks bs as ∧ FourierUniform (phaseFactor η ks bs as) f η:=by
  rcases exists_uniform_or_large_energy f hf hη hM (stepBound η) with
    h | ⟨ks,bs,as,_hc,he⟩
  · exact h
  · have hu:=normalized_energy_le_one (phaseFactor η ks bs as) f hf
    have hl:=stepBound_exceeds_energy hη
    exfalso
    linarith
theorem boundary_union_card_bound {n:ℕ} {η:ℝ} {ks:Fin n → ZMod q}
    {bs:Fin n → Bool} {as:Fin n → Fin M} (hc:BoundaryControlled η ks bs as) :
    M * (badCoordinateSamples as (fun x i => characterCoordinate η (ks i) (bs i) x)).card ≤ n * q:=by
  classical
  have hsets:badCoordinateSamples as (fun x i => characterCoordinate η (ks i) (bs i) x) =
      Finset.univ.biUnion (fun i => badSamples (as i) (characterCoordinate η (ks i) (bs i))):=by
    ext x
    simp [badCoordinateSamples,badSamples]
  rw [hsets]
  calc
    M * (Finset.univ.biUnion (fun i => badSamples (as i) (characterCoordinate η (ks i) (bs i)))).card ≤
        M * ∑ i,(badSamples (as i) (characterCoordinate η (ks i) (bs i))).card :=
      Nat.mul_le_mul_left M Finset.card_biUnion_le
    _ = ∑ i,M * (badSamples (as i) (characterCoordinate η (ks i) (bs i))).card:=Finset.mul_sum _ _ _
    _ ≤ ∑ _i:Fin n,q:=Finset.sum_le_sum (fun i _ => hc i)
    _ = _:=by simp
private def zz1829:"s0725"="s0725":=by decide+kernel
theorem exists_character_factor_approximation (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M)
      (F:Alphabet η n → ℝ),
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 2) ^ stepBound η ∧
      BoundaryControlled η ks bs as ∧
      M * (badCoordinateSamples as (fun x i => characterCoordinate η (ks i) (bs i) x)).card ≤ n * q ∧
      (∀ a,F a ∈ Set.Icc 0 1) ∧
      (∀ x,average (phaseFactor η ks bs as) f x = F (phaseFactor η ks bs as x)) ∧
      (∑ x,F (phaseFactor η ks bs as x)) = (∑ x,f x) ∧
      (∀ k, ‖ZMod.dft (fun x =>
        ((f x - F (phaseFactor η ks bs as x):ℝ):ℂ)) k‖ ≤ η * q):=by
  obtain ⟨n,hn,ks,bs,as,hc,hu⟩:=exists_uniform_character_factor f hf hη hM
  refine ⟨n,hn,ks,bs,as,fiberMean (phaseFactor η ks bs as) f,
    ?_,hc,boundary_union_card_bound hc, ?_,fun _ => rfl, ?_,hu⟩
  · simp only [Alphabet,Fintype.card_fun,Fintype.card_fin]
    exact Nat.pow_le_pow_right (by omega) hn
  · intro a
    exact ⟨fiberMean_nonneg _ f (fun x => (hf x).1) a,
      fiberMean_le_one _ f (fun x => (hf x).2) a⟩
  · exact sum_average (phaseFactor η ks bs as) f
end Green24Proof.CyclicShiftedCharacterFactor
private def zz2421:"s0975"="s0975":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteGridSmoothingSamples
open Finset
open scoped BigOperators NNReal
open Green24Proof.GridLipschitzSmoothing
open Green24Proof.FiniteGridBoundaryAvoidance
theorem not_boundaryBad_iff_gridGood {M:ℕ} (hM:0 < M) (a:Fin M) (t:ℝ) :
    ¬ BoundaryBad a t ↔ t ∈ GridGood 1 (1 / (2 * M)) ((a.val:ℝ) / M):=by
  rw [boundaryBad_iff_near_grid hM]
  simp only [not_exists,not_lt,GridGood,Set.mem_ofPred_eq,mul_one,add_comm]
variable {α ι:Type*} [Fintype α] [Fintype ι]
theorem sq_error_sum_le_bad (bad:Finset α) (u v:α → ℝ)
    (hu:∀ x,u x ∈ Set.Icc 0 1) (hv:∀ x,v x ∈ Set.Icc 0 1)
    (heq:∀ x,x ∉ bad → u x = v x) :
    (∑ x,(u x - v x) ^ 2) ≤ (bad.card:ℝ):=by
  classical
  calc
    (∑ x,(u x - v x) ^ 2) ≤ ∑ x,if x ∈ bad then (1:ℝ) else 0:=by
      apply Finset.sum_le_sum
      intro x _
      by_cases hx:x ∈ bad
      · rw [if_pos hx]
        have hux:=hu x
        have hvx:=hv x
        nlinarith [hux.1,hux.2,hvx.1,hvx.2]
      · rw [if_neg hx,heq x hx,sub_self,zero_pow (by decide:2 ≠ 0)]
    _ = _:=by simp only [Finset.sum_ite_mem_eq,Finset.sum_const,nsmul_eq_mul,mul_one]
theorem sample_good_of_not_bad {M:ℕ} (hM:0 < M)
    (offsets:ι → Fin M) (samples:α → ι → ℝ) (x:α)
    (hx:x ∉ badCoordinateSamples offsets samples) :
    samples x ∈ VectorGridGood 1 (1 / (2 * M)) (fun i => (offsets i).val / (M:ℝ)):=by
  classical
  have hn:¬ ∃ i,BoundaryBad (offsets i) (samples x i):=by
    simpa only [badCoordinateSamples,Finset.mem_filter,Finset.mem_univ,true_and] using hx
  intro i
  apply (not_boundaryBad_iff_gridGood hM (offsets i) (samples x i)).mp
  exact fun hi => hn ⟨i,hi⟩
private def zz1830:"s0726"="s0726":=by decide+kernel
theorem exists_grid_smoothing_with_sample_error {M:ℕ} (hM:0 < M)
    (samples:α → ι → ℝ) :
    ∃ offsets:ι → Fin M, ∀ F:(ι → ℤ) → ℝ,
      (∀ j,F j ∈ Set.Icc 0 1) →
      ∃ G:(ι → ℝ) → ℝ,LipschitzWith (M:ℝ≥0) G ∧
        (∀ z,G z ∈ Set.Icc 0 1) ∧
        (∀ z ∈ VectorGridGood 1 (1 / (2 * M))
          (fun i => (offsets i).val / (M:ℝ)),
          G z = F (vectorCellIndex 1 (fun i => (offsets i).val / (M:ℝ)) z)) ∧
        (∑ x,(G (samples x) - F (vectorCellIndex 1
          (fun i => (offsets i).val / (M:ℝ)) (samples x))) ^ 2) ≤
          (Fintype.card ι:ℝ) * Fintype.card α / M:=by
  classical
  obtain ⟨offsets,hoff⟩:=exists_coordinate_offsets_fraction_bound hM samples
  refine ⟨offsets, ?_⟩
  intro F hF
  have hMR:(0:ℝ) < M:=Nat.cast_pos.mpr hM
  have hδ:(0:ℝ) < 1 / (2 * M):=by positivity
  obtain ⟨G,hG,hGrange,hGeq⟩:=exists_vector_grid_smoothing
    1 (1 / (2 * M)) (fun i => (offsets i).val / (M:ℝ)) (by norm_num) hδ F hF
  have hK:(⟨1 / (2 * (1 / (2 * M))),by positivity⟩:ℝ≥0) = (M:ℝ≥0):=by
    apply NNReal.eq
    change (1:ℝ) / (2 * (1 / (2 * M))) = M
    field_simp
  rw [hK] at hG
  refine ⟨G,hG,hGrange,hGeq, ?_⟩
  apply le_trans ?_ hoff
  apply sq_error_sum_le_bad (badCoordinateSamples offsets samples)
  · exact fun x => hGrange (samples x)
  · exact fun x => hF _
  · intro x hx
    exact hGeq (samples x) (sample_good_of_not_bad hM offsets samples x hx)
end Green24Proof.FiniteGridSmoothingSamples
private def zz2422:"s0976"="s0976":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicSmoothedCharacterFactor
open Finset
open scoped BigOperators NNReal
open Green24Proof.FinitePartitionAverage
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.CyclicWeakRegularity (stepBound FourierUniform)
open Green24Proof.CyclicShiftedCharacterFactor
open Green24Proof.GridLipschitzSmoothing
open Green24Proof.FiniteGridBoundaryAvoidance
open Green24Proof.FiniteGridSmoothingSamples
variable {q M:ℕ} [NeZero q]
noncomputable def characterSamples {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (x:ZMod q):Fin n → ℝ :=
  fun i => characterCoordinate η (ks i) (bs i) x
noncomputable def encodedCell {n:ℕ} (η:ℝ) (j:Fin n → ℤ):Alphabet η n :=
  fun i => Green24Proof.ShiftedScalarQuantization.encodeCell (resolution η) (j i)
theorem phaseFactor_eq_encoded_grid {n:ℕ} (η:ℝ) (ks:Fin n → ZMod q)
    (bs:Fin n → Bool) (as:Fin n → Fin M) (x:ZMod q) :
    phaseFactor η ks bs as x = encodedCell η
      (vectorCellIndex 1 (fun i => offset (as i)) (characterSamples η ks bs x)):=by
  funext i
  exact Green24Proof.ShiftedScalarQuantization.quantize_eq_encodeCell
    (resolution η) (offset (as i)) (Green24Proof.CyclicCharacterFactor.characterTest (ks i) (bs i) x)
theorem exists_smoothing_of_boundaryControlled {n:ℕ} {η:ℝ} (hM:0 < M)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M)
    (hc:BoundaryControlled η ks bs as) (F:Alphabet η n → ℝ)
    (hF:∀ a,F a ∈ Set.Icc 0 1) :
    ∃ G:(Fin n → ℝ) → ℝ,LipschitzWith (M:ℝ≥0) G ∧
      (∀ z,G z ∈ Set.Icc 0 1) ∧
      (∀ z ∈ VectorGridGood 1 (1 / (2 * M)) (fun i => offset (as i)),
        G z = F (encodedCell η (vectorCellIndex 1 (fun i => offset (as i)) z))) ∧
      (∑ x,(G (characterSamples η ks bs x) - F (phaseFactor η ks bs as x)) ^ 2) ≤
        (n:ℝ) * q / M:=by
  classical
  have hMR:(0:ℝ) < M:=Nat.cast_pos.mpr hM
  have hδ:(0:ℝ) < 1 / (2 * M):=by positivity
  obtain ⟨G,hG,hGrange,hGeq⟩:=exists_vector_grid_smoothing
    1 (1 / (2 * M)) (fun i => offset (as i)) (by norm_num) hδ
    (fun j => F (encodedCell η j)) (fun j => hF _)
  have hK:(⟨1 / (2 * (1 / (2 * M))),by positivity⟩:ℝ≥0) = (M:ℝ≥0):=by
    apply NNReal.eq
    change (1:ℝ) / (2 * (1 / (2 * M))) = M
    field_simp
  rw [hK] at hG
  refine ⟨G,hG,hGrange,hGeq, ?_⟩
  have hbad:((badCoordinateSamples as (characterSamples η ks bs)).card:ℝ) ≤
      (n:ℝ) * q / M:=by
    apply (le_div_iff₀ hMR).mpr
    have hb:=boundary_union_card_bound hc
    have hbR:(M:ℝ) * (badCoordinateSamples as (characterSamples η ks bs)).card ≤
        (n:ℝ) * q:=by exact_mod_cast hb
    simpa only [mul_comm] using hbR
  apply le_trans ?_ hbad
  apply sq_error_sum_le_bad (badCoordinateSamples as (characterSamples η ks bs))
  · exact fun x => hGrange _
  · exact fun x => hF _
  · intro x hx
    rw [phaseFactor_eq_encoded_grid]
    exact hGeq _ (sample_good_of_not_bad hM as (characterSamples η ks bs) x hx)
theorem exists_smoothed_character_factor (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool)
      (as:Fin n → Fin M) (F:Alphabet η n → ℝ) (G:(Fin n → ℝ) → ℝ),
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 2) ^ stepBound η ∧
      BoundaryControlled η ks bs as ∧
      (∀ a,F a ∈ Set.Icc 0 1) ∧
      LipschitzWith (M:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
      (∀ x,average (phaseFactor η ks bs as) f x = F (phaseFactor η ks bs as x)) ∧
      (∑ x,F (phaseFactor η ks bs as x)) = (∑ x,f x) ∧
      (∀ k, ‖ZMod.dft (fun x =>
        ((f x - F (phaseFactor η ks bs as x):ℝ):ℂ)) k‖ ≤ η * q) ∧
      (∑ x,(G (characterSamples η ks bs x) - F (phaseFactor η ks bs as x)) ^ 2) ≤
        (n:ℝ) * q / M:=by
  obtain ⟨n,hn,ks,bs,as,F,hcard,hc,_hb,hF,havg,hmass,hu⟩ :=
    exists_character_factor_approximation f hf hη hM
  obtain ⟨G,hG,hGrange,_hGeq,herr⟩:=exists_smoothing_of_boundaryControlled hM ks bs as hc F hF
  exact ⟨n,hn,ks,bs,as,F,G,hcard,hc,hF,hG,hGrange,havg,hmass,hu,herr⟩
end Green24Proof.CyclicSmoothedCharacterFactor
private def zz2423:"s0977"="s0977":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusSmoothing
open Finset
open scoped BigOperators NNReal
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.CyclicWeakRegularity (stepBound)
open Green24Proof.CyclicShiftedCharacterFactor
open Green24Proof.CyclicSmoothedCharacterFactor
open Green24Proof.FinitePartitionAverage
noncomputable def component (b:Bool) (z:Circle):ℝ :=
  if b then (z:ℂ).im else (z:ℂ).re
private def zz1831:"s0727"="s0727":=by decide+kernel
theorem component_dist_le (b:Bool) (z w:Circle) :
    dist (component b z) (component b w) ≤ dist z w:=by
  cases b
  · change dist (z:ℂ).re (w:ℂ).re ≤ dist (z:ℂ) (w:ℂ)
    simpa only [Real.dist_eq,Complex.dist_eq,Complex.sub_re] using
      Complex.abs_re_le_norm ((z:ℂ) - (w:ℂ))
  · change dist (z:ℂ).im (w:ℂ).im ≤ dist (z:ℂ) (w:ℂ)
    simpa only [Real.dist_eq,Complex.dist_eq,Complex.sub_im] using
      Complex.abs_im_le_norm ((z:ℂ) - (w:ℂ))
noncomputable def torusCoordinates {n:ℕ} (η:ℝ) (bs:Fin n → Bool)
    (z:Fin n → Circle):Fin n → ℝ :=
  fun i => Green24Proof.ShiftedScalarQuantization.coordinate (resolution η)
    (component (bs i) (z i))
theorem torusCoordinates_lipschitz {n:ℕ} (η:ℝ) (bs:Fin n → Bool) :
    LipschitzWith (resolution η:ℝ≥0) (torusCoordinates η bs):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  apply (dist_pi_le_iff (mul_nonneg (by positivity) dist_nonneg)).mpr
  intro i
  have hc:=(component_dist_le (bs i) (z i) (w i)).trans (dist_le_pi_dist z w i)
  change |(resolution η:ℝ) * (component (bs i) (z i) + 1) + 1 -
    ((resolution η:ℝ) * (component (bs i) (w i) + 1) + 1)| ≤ _
  rw [show (resolution η:ℝ) * (component (bs i) (z i) + 1) + 1 -
      ((resolution η:ℝ) * (component (bs i) (w i) + 1) + 1) =
      (resolution η:ℝ) * (component (bs i) (z i) - component (bs i) (w i)) by ring,
    abs_mul,abs_of_nonneg (Nat.cast_nonneg _)]
  exact mul_le_mul_of_nonneg_left hc (Nat.cast_nonneg _)
variable {q M:ℕ} [NeZero q]
noncomputable def characterOrbit {n:ℕ} (ks:Fin n → ZMod q)
    (x:ZMod q):Fin n → Circle:=fun i => ZMod.toCircle (-(x * ks i))
theorem characterOrbit_add {n:ℕ} (ks:Fin n → ZMod q) (x y:ZMod q) :
    characterOrbit ks (x + y) = characterOrbit ks x * characterOrbit ks y:=by
  funext i
  change ZMod.toCircle (-((x + y) * ks i)) =
    ZMod.toCircle (-(x * ks i)) * ZMod.toCircle (-(y * ks i))
  rw [add_mul,neg_add_rev,AddChar.map_add_eq_mul,mul_comm]
theorem characterOrbit_zero {n:ℕ} (ks:Fin n → ZMod q) :
    characterOrbit ks 0 = 1:=by
  funext i
  simp [characterOrbit]
private def zz1832:"s0728"="s0728":=by decide+kernel
theorem characterOrbit_intCast {n:ℕ} (ks:Fin n → ZMod q) (a:ℤ) :
    characterOrbit ks (a:ZMod q) = characterOrbit ks 1 ^ a:=by
  funext i
  change ZMod.toCircle (-((a:ZMod q) * ks i)) =
    ZMod.toCircle (-(1 * ks i)) ^ a
  rw [one_mul, ← mul_neg, ← zsmul_eq_mul,AddChar.map_zsmul_eq_zpow]
theorem torusCoordinates_characterOrbit {n:ℕ} (η:ℝ)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (x:ZMod q) :
    torusCoordinates η bs (characterOrbit ks x) = characterSamples η ks bs x:=by
  funext i
  rfl
theorem exists_torus_smoothed_character_factor (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool)
      (as:Fin n → Fin M) (F:Alphabet η n → ℝ) (H:(Fin n → Circle) → ℝ),
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 2) ^ stepBound η ∧
      BoundaryControlled η ks bs as ∧
      (∀ a,F a ∈ Set.Icc 0 1) ∧
      LipschitzWith ((M:ℝ≥0) * resolution η) H ∧ (∀ z,H z ∈ Set.Icc 0 1) ∧
      (∀ x,average (phaseFactor η ks bs as) f x = F (phaseFactor η ks bs as x)) ∧
      (∑ x,F (phaseFactor η ks bs as x)) = (∑ x,f x) ∧
      (∀ k, ‖ZMod.dft (fun x =>
        ((f x - F (phaseFactor η ks bs as x):ℝ):ℂ)) k‖ ≤ η * q) ∧
      (∑ x,(H (characterOrbit ks x) - F (phaseFactor η ks bs as x)) ^ 2) ≤
        (n:ℝ) * q / M:=by
  obtain ⟨n,hn,ks,bs,as,F,G,hcard,hc,hF,hG,hGrange,havg,hmass,hu,herr⟩ :=
    exists_smoothed_character_factor f hf hη hM
  refine ⟨n,hn,ks,bs,as,F,G ∘ torusCoordinates η bs,hcard,hc,hF,
    hG.comp (torusCoordinates_lipschitz η bs),fun z => hGrange _,havg,hmass,hu, ?_⟩
  simpa only [Function.comp_apply,torusCoordinates_characterOrbit] using herr
end Green24Proof.CyclicTorusSmoothing
private def zz2424:"s0978"="s0978":=by decide+kernel
end 
section 
namespace Green24Proof.ModularRectification
open scoped Pointwise
theorem exists_common_good_difference {G:Type*} [AddCommGroup G] [DecidableEq G]
    (A S:Finset G) (hsmall:2 * ((A - A) \ S).card < A.card)
    {a b:G} (ha:a ∈ A) (hb:b ∈ A) :
    ∃ c ∈ A,c - a ∈ S ∧ c - b ∈ S:=by
  classical
  have hbad (x:G) (hx:x ∈ A) :
      (A.filter (fun c => c - x ∉ S)).card ≤ ((A - A) \ S).card:=by
    calc
      _ = ((A.filter (fun c => c - x ∉ S)).image (fun c => c - x)).card :=
        (Finset.card_image_of_injective _ (fun _ _ he => sub_left_inj.mp he)).symm
      _ ≤ _:=Finset.card_le_card (by
        intro y hy
        obtain ⟨c,hc,rfl⟩:=Finset.mem_image.mp hy
        obtain ⟨hcA,hcS⟩:=Finset.mem_filter.mp hc
        exact Finset.mem_sdiff.mpr ⟨Finset.sub_mem_sub hcA hx,hcS⟩)
  by_contra h
  have hcover:A ⊆ A.filter (fun c => c - a ∉ S) ∪
      A.filter (fun c => c - b ∉ S):=by
    intro c hc
    by_cases hca:c - a ∈ S
    · have hcb:c - b ∉ S:=fun hcb => h ⟨c,hc,hca,hcb⟩
      exact Finset.mem_union_right _ (Finset.mem_filter.mpr ⟨hc,hcb⟩)
    · exact Finset.mem_union_left _ (Finset.mem_filter.mpr ⟨hc,hca⟩)
  have hcard:=(Finset.card_le_card hcover).trans (Finset.card_union_le _ _)
  have hba:=hbad a ha
  have hbb:=hbad b hb
  omega
private def zz1833:"s0729"="s0729":=by decide+kernel
theorem sub_subset_sub_of_few_exceptions {G:Type*} [AddCommGroup G] [DecidableEq G]
    (A S:Finset G) (hsmall:2 * ((A - A) \ S).card < A.card) :
    A - A ⊆ S - S:=by
  intro x hx
  obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hx
  obtain ⟨c,_,hca,hcb⟩:=exists_common_good_difference A S hsmall ha hb
  convert Finset.sub_mem_sub hcb hca using 1
  abel
noncomputable def arc (q:ℕ) (b:ZMod q) (L:ℤ):Finset (ZMod q) :=
  (Finset.Icc 0 L).image (fun t:ℤ => b + (t:ZMod q))
theorem difference_has_small_representative {q:ℕ} (A:Finset (ZMod q))
    (b:ZMod q) (L:ℤ)
    (hsmall:2 * ((A - A) \ arc q b L).card < A.card)
    {x y:ZMod q} (hx:x ∈ A) (hy:y ∈ A) :
    ∃ t:ℤ, -L ≤ t ∧ t ≤ L ∧ (t:ZMod q) = x - y:=by
  have h:=sub_subset_sub_of_few_exceptions A (arc q b L) hsmall
    (Finset.sub_mem_sub hx hy)
  obtain ⟨u,hu,v,hv,he⟩:=Finset.mem_sub.mp h
  obtain ⟨i,hi,rfl⟩:=Finset.mem_image.mp hu
  obtain ⟨j,hj,rfl⟩:=Finset.mem_image.mp hv
  obtain ⟨hi0,hiL⟩:=Finset.mem_Icc.mp hi
  obtain ⟨hj0,hjL⟩:=Finset.mem_Icc.mp hj
  refine ⟨i - j,by omega,by omega, ?_⟩
  push_cast
  linear_combination he
theorem int_eq_of_cast_eq_of_abs_sub_lt {q:ℕ} {a b:ℤ}
    (hcast:(a:ZMod q) = (b:ZMod q)) (hbound:|a - b| < (q:ℤ)):a = b:=by
  have hd:(q:ℤ) ∣ a - b :=
    (ZMod.intCast_zmod_eq_zero_iff_dvd (a - b) q).mp (by simpa using sub_eq_zero.mpr hcast)
  exact sub_eq_zero.mp (Int.eq_zero_of_abs_lt_dvd hd hbound)
theorem freiman_three_of_short_lift {q:ℕ} (A:Finset (ZMod q))
    (f:ZMod q → ℤ) (a:ZMod q) (L:ℤ) (hL:3 * L < (q:ℤ))
    (hf:∀ x ∈ A,0 ≤ f x ∧ f x ≤ L ∧ (f x:ZMod q) = x - a) :
    IsAddFreimanIso 3 (A:Set (ZMod q)) (A.image f:Set ℤ) f:=by
  classical
  have hinj:Set.InjOn f (A:Set (ZMod q)):=by
    intro x hx y hy he
    have hc:=congrArg (fun z:ℤ => (z:ZMod q)) he
    rw [(hf x hx).2.2,(hf y hy).2.2] at hc
    exact sub_left_inj.mp hc
  refine ⟨by simpa only [Finset.coe_image] using hinj.bijOn_image, ?_⟩
  intro s t hsA htA hs ht
  have hsum (u:Multiset (ZMod q)) (huA:∀ x ∈ u,x ∈ A) (hu:u.card = 3) :
      (((u.map f).sum:ℤ):ZMod q) = u.sum - 3 • a:=by
    rw [Int.cast_multiset_sum,Multiset.map_map]
    calc
      _ = (u.map (fun x => x - a)).sum:=by
        congr 1
        exact Multiset.map_congr rfl (fun x hx => (hf x (huA x hx)).2.2)
      _ = _:=by
        simp [Multiset.sum_map_sub,hu,nsmul_eq_mul]
        ring
  have hbound (u:Multiset (ZMod q)) (huA:∀ x ∈ u,x ∈ A) (hu:u.card = 3) :
      0 ≤ (u.map f).sum ∧ (u.map f).sum ≤ 3 * L:=by
    constructor
    · exact Multiset.sum_nonneg (by
        intro z hz
        obtain ⟨x,hx,rfl⟩:=Multiset.mem_map.mp hz
        exact (hf x (huA x hx)).1)
    · have h:=Multiset.sum_le_card_nsmul (u.map f) L (by
        intro z hz
        obtain ⟨x,hx,rfl⟩:=Multiset.mem_map.mp hz
        exact (hf x (huA x hx)).2.1)
      simpa [hu] using h
  constructor
  · intro he
    have hc:=congrArg (fun z:ℤ => (z:ZMod q)) he
    rw [hsum s (fun _ hx => hsA hx) hs,hsum t (fun _ hx => htA hx) ht] at hc
    exact sub_left_inj.mp hc
  · intro he
    apply int_eq_of_cast_eq_of_abs_sub_lt
    · rw [hsum s (fun _ hx => hsA hx) hs,hsum t (fun _ hx => htA hx) ht,he]
    · have hb1:=hbound s (fun _ hx => hsA hx) hs
      have hb2:=hbound t (fun _ hx => htA hx) ht
      exact abs_lt.mpr (by omega)
private def zz1834:"s072a"="s072a":=by decide+kernel
theorem exists_freiman_three_model_of_few_arc_exceptions {q:ℕ}
    (A:Finset (ZMod q)) (b:ZMod q) (L:ℤ)
    (hLq:3 * L < (q:ℤ))
    (hsmall:2 * ((A - A) \ arc q b L).card < A.card) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 L ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f ∧
      ∃ a:ZMod q, ∀ x ∈ A,(f x:ZMod q) = x - a:=by
  classical
  have hA:A.Nonempty:=Finset.card_pos.mp (by omega)
  obtain ⟨a₀,ha₀⟩:=hA
  have hex:∀ x:ZMod q, ∃ t:ℤ,
      x ∈ A → -L ≤ t ∧ t ≤ L ∧ (t:ZMod q) = x - a₀:=by
    intro x
    by_cases hx:x ∈ A
    · obtain ⟨t,ht⟩:=difference_has_small_representative A b L hsmall hx ha₀
      exact ⟨t,fun _ => ht⟩
    · exact ⟨0,fun hx' => False.elim (hx hx')⟩
  choose f hf using hex
  have hspan (x:ZMod q) (hx:x ∈ A) (y:ZMod q) (hy:y ∈ A) :
      -L ≤ f x - f y ∧ f x - f y ≤ L:=by
    obtain ⟨t,ht0,htL,htc⟩:=difference_has_small_representative A b L hsmall hx hy
    have he:f x - f y = t:=by
      apply int_eq_of_cast_eq_of_abs_sub_lt
      · push_cast
        rw [(hf x hx).2.2,(hf y hy).2.2,htc]
        abel
      · have hfx:=hf x hx
        have hfy:=hf y hy
        exact abs_lt.mpr (by omega)
    simpa [he] using And.intro ht0 htL
  obtain ⟨a,ha,hmin⟩:=A.exists_min_image f ⟨a₀,ha₀⟩
  let g:ZMod q → ℤ:=fun x => f x - f a
  have hg:∀ x ∈ A,0 ≤ g x ∧ g x ≤ L ∧ (g x:ZMod q) = x - a:=by
    intro x hx
    refine ⟨sub_nonneg.mpr (hmin x hx),(hspan x hx a ha).2, ?_⟩
    change ((f x - f a:ℤ):ZMod q) = x - a
    push_cast
    rw [(hf x hx).2.2,(hf a ha).2.2]
    abel
  have hiso:=freiman_three_of_short_lift A g a L hLq hg
  refine ⟨A.image g,g, ?_, ?_,hiso,a,fun x hx => (hg x hx).2.2⟩
  · intro z hz
    obtain ⟨x,hx,rfl⟩:=Finset.mem_image.mp hz
    exact Finset.mem_Icc.mpr ⟨(hg x hx).1,(hg x hx).2.1⟩
  · exact Finset.card_image_of_injOn hiso.bijOn.injOn
theorem exists_arc_cover_of_few_arc_exceptions {q:ℕ}
    (A:Finset (ZMod q)) (b:ZMod q) (L:ℤ)
    (hLq:3 * L < (q:ℤ))
    (hsmall:2 * ((A - A) \ arc q b L).card < A.card) :
    ∃ a:ZMod q,A ⊆ arc q a L:=by
  obtain ⟨B,f,hB,_,hiso,a,hcast⟩ :=
    exists_freiman_three_model_of_few_arc_exceptions A b L hLq hsmall
  refine ⟨a,fun x hx => ?_⟩
  apply Finset.mem_image.mpr
  refine ⟨f x,hB (hiso.bijOn.mapsTo hx), ?_⟩
  rw [hcast x hx]
  abel
end Green24Proof.ModularRectification
private def zz2425:"s0979"="s0979":=by decide+kernel
end 
section 
namespace Green24Proof.FourierArcConcentration
open scoped BigOperators Pointwise
open Green24Proof.ModularRectification
open Green24Proof.CyclicFourierCounting
variable {q:ℕ} [NeZero q]
theorem re_stdAddChar (x:ZMod q) :
    (ZMod.stdAddChar x).re = Real.cos (2 * Real.pi * (x.val:ℝ) / q):=by
  rw [ZMod.stdAddChar_apply,ZMod.toCircle_apply]
  have he:2 * (Real.pi:ℂ) * Complex.I * (x.val:ℂ) / q =
      ((2 * Real.pi * (x.val:ℝ) / q:ℝ):ℂ) * Complex.I:=by
    push_cast
    ring
  rw [he,Complex.exp_ofReal_mul_I_re]
theorem character_defect_nonneg (x:ZMod q) :
    0 ≤ 1 - (ZMod.stdAddChar x).re:=by
  rw [re_stdAddChar]
  exact sub_nonneg.mpr (Real.cos_le_one _)
private def zz1835:"s072b"="s072b":=by decide+kernel
theorem sum_character_defect (B:Finset (ZMod q)) :
    (∑ b ∈ B, ∑ x ∈ B,(1 - (ZMod.stdAddChar (x - b)).re)) =
      (B.card:ℝ) ^ 2 - ‖∑ x ∈ B,ZMod.stdAddChar x‖ ^ 2:=by
  have hchar (x b:ZMod q) :
      ZMod.stdAddChar (x - b) =
        ZMod.stdAddChar x * (starRingEnd ℂ) (ZMod.stdAddChar b):=by
    rw [sub_eq_add_neg,AddChar.map_add_eq_mul,conj_stdAddChar]
  simp_rw [hchar,Finset.sum_sub_distrib]
  simp only [Finset.sum_const,nsmul_eq_mul]
  simp_rw [← Complex.re_sum]
  congr 1
  · ring
  calc
    (∑ b ∈ B, ∑ x ∈ B,
        ZMod.stdAddChar x * (starRingEnd ℂ) (ZMod.stdAddChar b)).re =
        ((∑ x ∈ B,ZMod.stdAddChar x) *
          (starRingEnd ℂ) (∑ x ∈ B,ZMod.stdAddChar x)).re:=by
      congr 1
      simp only [map_sum,Finset.sum_mul,Finset.mul_sum]
    _ = _:=by rw [Complex.mul_conj,Complex.ofReal_re,Complex.normSq_eq_norm_sq]
theorem mem_centered_arc_of_val {b x:ZMod q} {R:ℤ} (hR:0 ≤ R)
    (hval:((x - b).val:ℤ) ≤ R ∨ (q:ℤ) - R ≤ ((x - b).val:ℤ)) :
    x ∈ arc q (b - (R:ZMod q)) (2 * R):=by
  have hv0:0 ≤ ((x - b).val:ℤ):=by positivity
  have hvq:((x - b).val:ℤ) < q:=by exact_mod_cast (ZMod.val_lt (x - b))
  rcases hval with hval | hval
  · apply Finset.mem_image.mpr
    refine ⟨((x - b).val:ℤ) + R,Finset.mem_Icc.mpr ⟨by omega,by omega⟩, ?_⟩
    push_cast
    rw [ZMod.natCast_zmod_val]
    abel
  · apply Finset.mem_image.mpr
    refine ⟨((x - b).val:ℤ) - q + R,
      Finset.mem_Icc.mpr ⟨by omega,by omega⟩, ?_⟩
    push_cast
    rw [ZMod.natCast_zmod_val]
    simp
theorem cos_le_cos_of_circular_separation {θ t:ℝ}
    (hθ:0 ≤ θ) (hlo:θ ≤ t) (hhi:t ≤ 2 * Real.pi - θ) :
    Real.cos t ≤ Real.cos θ:=by
  by_cases ht:t ≤ Real.pi
  · exact Real.cos_le_cos_of_nonneg_of_le_pi hθ ht hlo
  · rw [← Real.cos_two_pi_sub t]
    exact Real.cos_le_cos_of_nonneg_of_le_pi hθ (by linarith) (by linarith)
theorem character_defect_ge_of_not_mem_arc {b x:ZMod q} {R:ℤ}
    (hR:0 ≤ R) (hx:x ∉ arc q (b - (R:ZMod q)) (2 * R)) :
    1 - Real.cos (2 * Real.pi * (R:ℝ) / q) ≤
      1 - (ZMod.stdAddChar (x - b)).re:=by
  have hq:(0:ℝ) < q:=by exact_mod_cast (NeZero.pos q)
  have hv:R < ((x - b).val:ℤ) ∧ ((x - b).val:ℤ) < (q:ℤ) - R:=by
    by_contra hv
    push Not at hv
    apply hx
    apply mem_centered_arc_of_val hR
    omega
  have hRr:(0:ℝ) ≤ R:=by exact_mod_cast hR
  have hlo:(R:ℝ) ≤ (x - b).val:=by exact_mod_cast hv.1.le
  have hhi:((x - b).val:ℝ) ≤ (q:ℝ) - R:=by exact_mod_cast hv.2.le
  rw [re_stdAddChar]
  apply sub_le_sub_left
  apply cos_le_cos_of_circular_separation (by positivity)
  · gcongr
  · calc
      2 * Real.pi * ((x - b).val:ℝ) / q ≤
          2 * Real.pi * ((q:ℝ) - R) / q:=by gcongr
      _ = 2 * Real.pi - 2 * Real.pi * (R:ℝ) / q:=by
        field_simp
private def zz1836:"s072c"="s072c":=by decide+kernel
theorem boundary_defect_pos {R:ℤ} (hR:0 < R) (hRq:2 * R ≤ (q:ℤ)) :
    0 < 1 - Real.cos (2 * Real.pi * (R:ℝ) / q):=by
  have hq:(0:ℝ) < q:=by exact_mod_cast (NeZero.pos q)
  have hRr:(0:ℝ) < R:=by exact_mod_cast hR
  have hRqr:2 * (R:ℝ) ≤ q:=by exact_mod_cast hRq
  have hθ0:0 < 2 * Real.pi * (R:ℝ) / q:=by positivity
  have hθπ:2 * Real.pi * (R:ℝ) / q ≤ Real.pi:=by
    apply (div_le_iff₀ hq).mpr
    nlinarith [Real.pi_pos]
  have hc:=Real.cos_lt_cos_of_nonneg_of_le_pi (show (0:ℝ) ≤ 0 by rfl) hθπ hθ0
  simpa using sub_pos.mpr hc
theorem arc_exception_bound (B:Finset (ZMod q)) (b:ZMod q) {R:ℤ}
    (hR:0 ≤ R) :
    ((B \ arc q (b - (R:ZMod q)) (2 * R)).card:ℝ) *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q)) ≤
      ∑ x ∈ B,(1 - (ZMod.stdAddChar (x - b)).re):=by
  calc
    _ = ∑ x ∈ B \ arc q (b - (R:ZMod q)) (2 * R),
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q)):=by
      simp
      ring
    _ ≤ ∑ x ∈ B \ arc q (b - (R:ZMod q)) (2 * R),
        (1 - (ZMod.stdAddChar (x - b)).re):=by
      apply Finset.sum_le_sum
      intro x hx
      exact character_defect_ge_of_not_mem_arc hR (Finset.mem_sdiff.mp hx).2
    _ ≤ _:=Finset.sum_le_sum_of_subset_of_nonneg Finset.sdiff_subset
      (fun x _ _ => character_defect_nonneg (x - b))
theorem exists_arc_few_exceptions (B:Finset (ZMod q)) {R:ℤ}
    (hR:0 < R) (hRq:2 * R ≤ (q:ℤ)) (δ:ℝ)
    (hlarge:(B.card:ℝ) ^ 2 - ‖∑ x ∈ B,ZMod.stdAddChar x‖ ^ 2 <
      δ * B.card * (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ b ∈ B,((B \ arc q (b - (R:ZMod q)) (2 * R)).card:ℝ) < δ:=by
  have hc:=boundary_defect_pos hR hRq
  have hsum:(∑ b ∈ B, ∑ x ∈ B,(1 - (ZMod.stdAddChar (x - b)).re)) <
      ∑ _b ∈ B,δ * (1 - Real.cos (2 * Real.pi * (R:ℝ) / q)):=by
    rw [sum_character_defect]
    simpa [mul_assoc,mul_comm,mul_left_comm] using hlarge
  obtain ⟨b,hb,hdefect⟩:=Finset.exists_lt_of_sum_lt hsum
  refine ⟨b,hb, ?_⟩
  have hbound:=arc_exception_bound B b hR.le
  nlinarith
theorem exists_freiman_three_model_of_large_difference_character
    (A:Finset (ZMod q)) {R:ℤ} (hR:0 < R) (hRq:6 * R < (q:ℤ))
    (hlarge:((A - A).card:ℝ) ^ 2 -
        ‖∑ x ∈ A - A,ZMod.stdAddChar x‖ ^ 2 <
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 (2 * R) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f ∧
      ∃ a:ZMod q, ∀ x ∈ A,(f x:ZMod q) = x - a:=by
  obtain ⟨b,_,hb⟩:=exists_arc_few_exceptions (A - A) hR (by omega)
    ((A.card:ℝ) / 2) hlarge
  have hn:(2:ℝ) * (((A - A) \ arc q (b - (R:ZMod q)) (2 * R)).card:ℝ) <
      (A.card:ℝ):=by linarith
  have hsmall:2 * ((A - A) \ arc q (b - (R:ZMod q)) (2 * R)).card < A.card:=by
    exact_mod_cast hn
  exact exists_freiman_three_model_of_few_arc_exceptions A (b - (R:ZMod q))
    (2 * R) (by omega) hsmall
private def zz1837:"s072d"="s072d":=by decide+kernel
omit [NeZero q] in
theorem freimanIso_dilate (A:Finset (ZMod q)) (r:ZMod q) (hr:IsUnit r) (k:ℕ) :
    IsAddFreimanIso k (A:Set (ZMod q))
      (A.image (fun x => r * x):Set (ZMod q)) (fun x => r * x) where
  bijOn:=by
    simpa only [Finset.coe_image] using hr.mul_right_injective.bijOn_image (s:=(A:Set (ZMod q)))
  map_sum_eq_map_sum s t _ _ _ _:=by
    have hsum (u:Multiset (ZMod q)):(u.map (fun x => r * x)).sum = r * u.sum:=by
      simpa using
        (Multiset.sum_map_mul_left (s:=u) (a:=r) (f:=id))
    rw [hsum,hsum]
    exact hr.mul_right_inj
omit [NeZero q] in
theorem image_dilate_sub (A:Finset (ZMod q)) (r:ZMod q) :
    A.image (fun x => r * x) - A.image (fun x => r * x) =
      (A - A).image (fun x => r * x):=by
  ext x
  constructor
  · intro hx
    obtain ⟨y,hy,z,hz,rfl⟩:=Finset.mem_sub.mp hx
    obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hy
    obtain ⟨b,hb,rfl⟩:=Finset.mem_image.mp hz
    exact Finset.mem_image.mpr ⟨a - b,Finset.sub_mem_sub ha hb,mul_sub r a b⟩
  · intro hx
    obtain ⟨y,hy,rfl⟩:=Finset.mem_image.mp hx
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hy
    exact Finset.mem_sub.mpr ⟨r * a,Finset.mem_image.mpr ⟨a,ha,rfl⟩,
      r * b,Finset.mem_image.mpr ⟨b,hb,rfl⟩,(mul_sub r a b).symm⟩
theorem exists_freiman_three_model_of_large_character
    (A:Finset (ZMod q)) (r:ZMod q) (hr:IsUnit r)
    {R:ℤ} (hR:0 < R) (hRq:6 * R < (q:ℤ))
    (hlarge:((A - A).card:ℝ) ^ 2 -
        ‖∑ x ∈ A - A,ZMod.stdAddChar (r * x)‖ ^ 2 <
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 (2 * R) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f ∧
      ∃ a:ZMod q, ∀ x ∈ A,(f x:ZMod q) = r * x - a:=by
  let A':=A.image (fun x => r * x)
  have hcard:A'.card = A.card:=Finset.card_image_of_injective _ hr.mul_right_injective
  have hdiff:A' - A' = (A - A).image (fun x => r * x):=image_dilate_sub A r
  have hdiffcard:(A' - A').card = (A - A).card:=by
    rw [hdiff]
    exact Finset.card_image_of_injective _ hr.mul_right_injective
  have hsum:(∑ x ∈ A' - A',ZMod.stdAddChar x) =
      ∑ x ∈ A - A,ZMod.stdAddChar (r * x):=by
    rw [hdiff]
    exact Finset.sum_image (fun _ _ _ _ he => hr.mul_right_injective he)
  have hlarge':((A' - A').card:ℝ) ^ 2 -
        ‖∑ x ∈ A' - A',ZMod.stdAddChar x‖ ^ 2 <
      (A'.card:ℝ) / 2 * (A' - A').card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q)):=by
    simpa only [hcard,hdiffcard,hsum] using hlarge
  obtain ⟨B,f,hB,hBA',hf,a,hcast⟩ :=
    exists_freiman_three_model_of_large_difference_character A' hR hRq hlarge'
  refine ⟨B,fun x => f (r * x),hB,hBA'.trans hcard,
    hf.comp (freimanIso_dilate A r hr 3),a, ?_⟩
  intro x hx
  exact hcast (r * x) (Finset.mem_image.mpr ⟨x,hx,rfl⟩)
theorem exists_freiman_three_model_of_large_nonzero_character
    [Fact q.Prime] (A:Finset (ZMod q)) (r:ZMod q) (hr:r ≠ 0)
    {R:ℤ} (hR:0 < R) (hRq:6 * R < (q:ℤ))
    (hlarge:((A - A).card:ℝ) ^ 2 -
        ‖∑ x ∈ A - A,ZMod.stdAddChar (r * x)‖ ^ 2 <
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 (2 * R) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f ∧
      ∃ a:ZMod q, ∀ x ∈ A,(f x:ZMod q) = r * x - a :=
  exists_freiman_three_model_of_large_character A r (isUnit_iff_ne_zero.mpr hr) hR hRq hlarge
end Green24Proof.FourierArcConcentration
private def zz2426:"s097a"="s097a":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFourierMoments
open scoped BigOperators Pointwise
open Green24Proof.CyclicFourierCounting
variable {q:ℕ} [NeZero q]
noncomputable def coefficient (B:Finset (ZMod q)) (r:ZMod q):ℂ :=
  ∑ x ∈ B,ZMod.stdAddChar (-(x * r))
def tupleSum (B:Finset (ZMod q)) (k:ℕ) (v:Fin k → B):ZMod q :=
  ∑ i,(v i:ZMod q)
def iteratedSumset (B:Finset (ZMod q)) (k:ℕ):Finset (ZMod q) :=
  Finset.univ.image (tupleSum B k)
def representations (B:Finset (ZMod q)) (k:ℕ) (x:ZMod q):ℕ :=
  (Finset.univ.filter (fun v:Fin k → B => tupleSum B k v = x)).card
private def zz1838:"s072e"="s072e":=by decide+kernel
omit [NeZero q] in
theorem iteratedSumset_eq_nsmul (B:Finset (ZMod q)) (k:ℕ) :
    iteratedSumset B k = k • B:=by
  ext x
  simp [iteratedSumset,tupleSum,Finset.mem_nsmul,List.sum_ofFn]
omit [NeZero q] in
theorem representations_cast (B:Finset (ZMod q)) (k:ℕ) (x:ZMod q) :
    (representations B k x:ℂ) =
      ∑ v:Fin k → B,if tupleSum B k v = x then (1:ℂ) else 0:=by
  simp [representations]
omit [NeZero q] in
theorem representations_zero_off_sumset (B:Finset (ZMod q)) (k:ℕ)
    {x:ZMod q} (hx:x ∉ iteratedSumset B k):representations B k x = 0:=by
  apply Finset.card_eq_zero.mpr
  apply Finset.filter_eq_empty_iff.mpr
  intro v _ hv
  exact hx (Finset.mem_image.mpr ⟨v,Finset.mem_univ _,hv⟩)
omit [NeZero q] in
theorem sum_representations (B:Finset (ZMod q)) (k:ℕ) :
    (∑ x ∈ iteratedSumset B k,representations B k x) = B.card ^ k:=by
  have h:=Finset.card_eq_sum_card_fiberwise
    (s:=(Finset.univ:Finset (Fin k → B)))
    (t:=iteratedSumset B k) (f:=tupleSum B k)
    (fun v hv => Finset.mem_image.mpr ⟨v,hv,rfl⟩)
  simpa [representations] using h.symm
private def zz1839:"s072f"="s072f":=by decide+kernel
theorem stdAddChar_sum {ι:Type*} (s:Finset ι) (f:ι → ZMod q) :
    ZMod.stdAddChar (∑ i ∈ s,f i) = ∏ i ∈ s,ZMod.stdAddChar (f i):=by
  classical
  induction s using Finset.induction_on with
  | empty => simp
  | @insert i s hi ih => simp [Finset.sum_insert,Finset.prod_insert,hi,
      AddChar.map_add_eq_mul,ih]
theorem dft_representations (B:Finset (ZMod q)) (k:ℕ) (r:ZMod q) :
    ZMod.dft (fun x => (representations B k x:ℂ)) r = coefficient B r ^ k:=by
  rw [ZMod.dft_apply]
  simp only [representations_cast,smul_eq_mul,Finset.mul_sum,mul_ite,mul_one,mul_zero]
  rw [Finset.sum_comm]
  simp only [Finset.sum_ite_eq,Finset.mem_univ,if_true]
  have hchar (v:Fin k → B) :
      ZMod.stdAddChar (-(tupleSum B k v * r)) =
        ∏ i,ZMod.stdAddChar (-((v i:ZMod q) * r)):=by
    rw [tupleSum,Finset.sum_mul, ← Finset.sum_neg_distrib,stdAddChar_sum]
  simp_rw [hchar]
  rw [← Fintype.sum_pow (fun x:B => ZMod.stdAddChar (-((x:ZMod q) * r))) k]
  congr 1
  exact Finset.sum_coe_sort B (fun x => ZMod.stdAddChar (-(x * r)))
theorem coefficient_zero (B:Finset (ZMod q)):coefficient B 0 = B.card:=by
  simp [coefficient]
theorem moment_identity (B:Finset (ZMod q)) (k:ℕ) :
    (∑ r:ZMod q, ‖coefficient B r‖ ^ (2 * k)) =
      (q:ℝ) * ∑ x:ZMod q,(representations B k x:ℝ) ^ 2:=by
  have h:=parseval (fun x => (representations B k x:ℂ))
  simp only [dft_representations,norm_pow,Complex.norm_natCast, ← pow_mul] at h
  simpa only [Nat.mul_comm k 2] using h
private def zz1840:"s0730"="s0730":=by decide+kernel
theorem sumset_moment_lower_bound (B:Finset (ZMod q)) (k:ℕ) :
    (q:ℝ) * (B.card:ℝ) ^ (2 * k) ≤
      ((iteratedSumset B k).card:ℝ) *
        ∑ r:ZMod q, ‖coefficient B r‖ ^ (2 * k):=by
  have hcs:=Finset.sum_mul_sq_le_sq_mul_sq (iteratedSumset B k)
    (fun _:ZMod q => (1:ℝ)) (fun x => (representations B k x:ℝ))
  have hmass:(∑ x ∈ iteratedSumset B k,(representations B k x:ℝ)) =
      (B.card:ℝ) ^ k:=by exact_mod_cast sum_representations B k
  simp only [one_mul,one_pow,Finset.sum_const,nsmul_eq_mul,mul_one,hmass] at hcs
  have henergy:(∑ x ∈ iteratedSumset B k,(representations B k x:ℝ) ^ 2) =
      ∑ x:ZMod q,(representations B k x:ℝ) ^ 2:=by
    apply Finset.sum_subset (Finset.subset_univ _)
    intro x _ hx
    simp [representations_zero_off_sumset B k hx]
  rw [henergy] at hcs
  rw [moment_identity]
  have h:=mul_le_mul_of_nonneg_left hcs (show (0:ℝ) ≤ q by positivity)
  simpa [← pow_mul,mul_assoc,mul_left_comm,mul_comm] using h
theorem dft_indicator (B:Finset (ZMod q)) (r:ZMod q) :
    ZMod.dft (fun x => if x ∈ B then (1:ℂ) else 0) r = coefficient B r:=by
  simp [ZMod.dft_apply,smul_eq_mul,coefficient]
theorem second_moment (B:Finset (ZMod q)) :
    (∑ r:ZMod q, ‖coefficient B r‖ ^ 2) = (q:ℝ) * B.card:=by
  have h:=parseval (fun x:ZMod q => if x ∈ B then (1:ℂ) else 0)
  simp only [dft_indicator] at h
  simp_rw [apply_ite (fun z:ℂ => ‖z‖ ^ 2)] at h
  simpa using h
theorem second_moment_nonzero (B:Finset (ZMod q)) :
    (∑ r ∈ Finset.univ.erase (0:ZMod q), ‖coefficient B r‖ ^ 2) =
      (q:ℝ) * B.card - (B.card:ℝ) ^ 2:=by
  have h:=Finset.sum_erase_add (s:=Finset.univ)
    (f:=fun r:ZMod q => ‖coefficient B r‖ ^ 2) (Finset.mem_univ (0:ZMod q))
  rw [coefficient_zero,Complex.norm_natCast,second_moment] at h
  linarith
private def zz1841:"s0731"="s0731":=by decide+kernel
theorem moment_upper_of_nonzero_bound (B:Finset (ZMod q)) (m:ℕ) {M:ℝ}
    (hcoeff:∀ r:ZMod q,r ≠ 0 → ‖coefficient B r‖ ≤ M) :
    (∑ r:ZMod q, ‖coefficient B r‖ ^ (2 * (m + 1))) ≤
      (B.card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2):=by
  have hsplit:=Finset.sum_erase_add (s:=Finset.univ)
    (f:=fun r:ZMod q => ‖coefficient B r‖ ^ (2 * (m + 1)))
    (Finset.mem_univ (0:ZMod q))
  rw [coefficient_zero,Complex.norm_natCast] at hsplit
  rw [← hsplit,add_comm]
  apply add_le_add_right
  rw [← second_moment_nonzero,Finset.mul_sum]
  apply Finset.sum_le_sum
  intro r hr
  rw [show 2 * (m + 1) = 2 * m + 2 by omega,pow_add]
  have hb:=hcoeff r (Finset.ne_of_mem_erase hr)
  gcongr
theorem exists_large_nonzero_coefficient (B:Finset (ZMod q)) (m:ℕ) {M:ℝ}
    (hgrowth:((iteratedSumset B (m + 1)).card:ℝ) *
      ((B.card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2)) <
      (q:ℝ) * (B.card:ℝ) ^ (2 * (m + 1))) :
    ∃ r:ZMod q,r ≠ 0 ∧ M < ‖coefficient B r‖:=by
  by_contra h
  have hcoeff:∀ r:ZMod q,r ≠ 0 → ‖coefficient B r‖ ≤ M:=by
    intro r hr
    exact le_of_not_gt (fun hc => h ⟨r,hr,hc⟩)
  have hlower:=sumset_moment_lower_bound B (m + 1)
  have hupper:=mul_le_mul_of_nonneg_left (moment_upper_of_nonzero_bound B m hcoeff)
    (show (0:ℝ) ≤ (iteratedSumset B (m + 1)).card by positivity)
  linarith
theorem coefficient_eq_positive (B:Finset (ZMod q)) (r:ZMod q) :
    coefficient B r = ∑ x ∈ B,ZMod.stdAddChar ((-r) * x):=by
  apply Finset.sum_congr rfl
  intro x _
  congr 1
  ring
theorem exists_freiman_three_model_of_moment_growth [Fact q.Prime]
    (A:Finset (ZMod q)) (m:ℕ) {M:ℝ} (hM:0 ≤ M)
    {R:ℤ} (hR:0 < R) (hRq:6 * R < (q:ℤ))
    (hgrowth:((iteratedSumset (A - A) (m + 1)).card:ℝ) *
      (((A - A).card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * (A - A).card - ((A - A).card:ℝ) ^ 2)) <
      (q:ℝ) * ((A - A).card:ℝ) ^ (2 * (m + 1)))
    (hbudget:((A - A).card:ℝ) ^ 2 - M ^ 2 ≤
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 (2 * R) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f:=by
  obtain ⟨r,hr,hcoeff⟩:=exists_large_nonzero_coefficient (A - A) m hgrowth
  have hlarge:((A - A).card:ℝ) ^ 2 -
      ‖∑ x ∈ A - A,ZMod.stdAddChar ((-r) * x)‖ ^ 2 <
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q)):=by
    rw [coefficient_eq_positive] at hcoeff
    nlinarith [norm_nonneg (∑ x ∈ A - A,ZMod.stdAddChar ((-r) * x))]
  obtain ⟨B,f,hB,hcard,hf,_⟩ :=
    Green24Proof.FourierArcConcentration.exists_freiman_three_model_of_large_nonzero_character
      A (-r) (neg_ne_zero.mpr hr) hR hRq hlarge
  exact ⟨B,f,hB,hcard,hf⟩
end Green24Proof.CyclicFourierMoments
private def zz2427:"s097b"="s097b":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusLaurent
open Finset
open scoped BigOperators
variable {ι:Type*} [Fintype ι]
noncomputable def monomial (m:ι → ℤ) (z:ι → Circle):ℂ :=
  ∏ i,(z i:ℂ) ^ m i
private def zz1842:"s0732"="s0732":=by decide+kernel
theorem monomial_zero (z:ι → Circle):monomial (0:ι → ℤ) z = 1:=by
  simp [monomial]
theorem monomial_mul (m:ι → ℤ) (z w:ι → Circle) :
    monomial m (z * w) = monomial m z * monomial m w:=by
  simp only [monomial,Pi.mul_apply,Circle.coe_mul,mul_zpow,Finset.prod_mul_distrib]
variable {q:ℕ} [NeZero q]
noncomputable def weightedFrequency (ks:ι → ZMod q) (m:ι → ℤ):ZMod q :=
  ∑ i,(m i:ZMod q) * ks i
omit [NeZero q] in
theorem weightedFrequency_zero (ks:ι → ZMod q):weightedFrequency ks 0 = 0:=by
  simp [weightedFrequency]
theorem monomial_character_values (ks:ι → ZMod q) (m:ι → ℤ) (x:ZMod q) :
    monomial m (fun i => ZMod.toCircle (-(x * ks i))) =
      ZMod.stdAddChar (-(x * weightedFrequency ks m)):=by
  change (∏ i,ZMod.stdAddChar (-(x * ks i)) ^ m i) = _
  rw [weightedFrequency,Finset.mul_sum, ← Finset.sum_neg_distrib,
    Green24Proof.CyclicFourierMoments.stdAddChar_sum]
  apply Finset.prod_congr rfl
  intro i _
  rw [← AddChar.map_zsmul_eq_zpow,zsmul_eq_mul]
  congr 1
  ring
private def zz1843:"s0733"="s0733":=by decide+kernel
theorem monomial_characterOrbit {n:ℕ} (ks:Fin n → ZMod q)
    (m:Fin n → ℤ) (x:ZMod q) :
    monomial m (Green24Proof.CyclicTorusSmoothing.characterOrbit ks x) =
      ZMod.stdAddChar (-(x * weightedFrequency ks m)) :=
  monomial_character_values ks m x
theorem sum_monomial_character_values (ks:ι → ZMod q) (m:ι → ℤ) :
    (∑ x:ZMod q,monomial m (fun i => ZMod.toCircle (-(x * ks i)))) =
      if weightedFrequency ks m = 0 then (q:ℂ) else 0:=by
  classical
  simp_rw [monomial_character_values]
  by_cases hw:weightedFrequency ks m = 0
  · simp [hw,ZMod.card]
  · rw [if_neg hw]
    have h:(∑ x:ZMod q,ZMod.stdAddChar ((-weightedFrequency ks m) * x)) = 0 :=
      AddChar.sum_eq_zero_of_ne_one (ZMod.isPrimitive_stdAddChar q (neg_ne_zero.mpr hw))
    simpa only [neg_mul,mul_neg,mul_comm] using h
noncomputable def polynomial (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ)
    (z:ι → Circle):ℂ:=∑ m ∈ S,c m * monomial m z
noncomputable def resonantCoefficient (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ):ℂ:=∑ m ∈ S,if weightedFrequency ks m = 0 then c m else 0
noncomputable def constantCoefficient (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ):ℂ :=
  ∑ m ∈ S,if m = 0 then c m else 0
def Nonresonant (ks:ι → ZMod q) (S:Finset (ι → ℤ)):Prop :=
  ∀ m ∈ S,m ≠ 0 → weightedFrequency ks m ≠ 0
theorem sum_polynomial_character_values (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ) :
    (∑ x:ZMod q,polynomial S c (fun i => ZMod.toCircle (-(x * ks i)))) =
      (q:ℂ) * resonantCoefficient ks S c:=by
  classical
  simp only [polynomial]
  rw [Finset.sum_comm]
  simp only [← Finset.mul_sum,sum_monomial_character_values]
  unfold resonantCoefficient
  rw [Finset.mul_sum]
  apply Finset.sum_congr rfl
  intro m _
  split_ifs <;> ring
omit [NeZero q] in
theorem resonantCoefficient_eq_constant (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ) (hn:Nonresonant ks S) :
    resonantCoefficient ks S c = constantCoefficient S c:=by
  classical
  apply Finset.sum_congr rfl
  intro m hm
  by_cases hzero:m = 0
  · simp [hzero,weightedFrequency_zero]
  · simp [hzero,hn m hm hzero]
noncomputable def orbitMean (ks:ι → ZMod q) (F:(ι → Circle) → ℂ):ℂ :=
  (q:ℂ)⁻¹ * ∑ x:ZMod q,F (fun i => ZMod.toCircle (-(x * ks i)))
private def zz1844:"s0734"="s0734":=by decide+kernel
theorem orbitMean_polynomial (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ) :
    orbitMean ks (polynomial S c) = resonantCoefficient ks S c:=by
  rw [orbitMean,sum_polynomial_character_values, ← mul_assoc,
    inv_mul_cancel₀ (by exact_mod_cast NeZero.ne q),one_mul]
theorem orbitMean_polynomial_of_nonresonant (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ) (hn:Nonresonant ks S) :
    orbitMean ks (polynomial S c) = constantCoefficient S c:=by
  rw [orbitMean_polynomial,resonantCoefficient_eq_constant ks S c hn]
omit [Fintype ι] in
theorem orbitMean_error_le (ks:ι → ZMod q) (F P:(ι → Circle) → ℂ)
    {ε:ℝ} (herr:∀ z, ‖F z - P z‖ ≤ ε) :
    ‖orbitMean ks F - orbitMean ks P‖ ≤ ε:=by
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  have hs:‖∑ x:ZMod q,(F (fun i => ZMod.toCircle (-(x * ks i))) -
      P (fun i => ZMod.toCircle (-(x * ks i))))‖ ≤ (q:ℝ) * ε:=by
    calc
      _ ≤ ∑ x:ZMod q, ‖F (fun i => ZMod.toCircle (-(x * ks i))) -
          P (fun i => ZMod.toCircle (-(x * ks i)))‖:=norm_sum_le _ _
      _ ≤ ∑ _x:ZMod q,ε:=Finset.sum_le_sum (fun _ _ => herr _)
      _ = _:=by simp [ZMod.card]
  rw [orbitMean,orbitMean, ← mul_sub, ← Finset.sum_sub_distrib,norm_mul,
    norm_inv,Complex.norm_natCast]
  calc
    (q:ℝ)⁻¹ * _ ≤ (q:ℝ)⁻¹ * ((q:ℝ) * ε) :=
      mul_le_mul_of_nonneg_left hs (inv_nonneg.mpr hq.le)
    _ = ε:=by field_simp
theorem orbitMean_discrepancy_from_constant (ks:ι → ZMod q)
    (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) (F:(ι → Circle) → ℂ)
    (hn:Nonresonant ks S) {ε:ℝ}
    (herr:∀ z, ‖F z - polynomial S c z‖ ≤ ε) :
    ‖orbitMean ks F - constantCoefficient S c‖ ≤ ε:=by
  rw [← orbitMean_polynomial_of_nonresonant ks S c hn]
  exact orbitMean_error_le ks F (polynomial S c) herr
end Green24Proof.CyclicTorusLaurent
private def zz2428:"s097c"="s097c":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusHaarDiscrepancy
open Finset MeasureTheory TopologicalSpace
open scoped BigOperators
open Green24Proof.CyclicTorusLaurent
noncomputable def circleMeasurableSpace:MeasurableSpace Circle:=borel Circle
def circleBorelSpace:@BorelSpace Circle inferInstance circleMeasurableSpace:=by
  letI:=circleMeasurableSpace
  exact ⟨rfl⟩
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable (ι:Type*) [Fintype ι]
noncomputable def torusHaar:Measure (ι → Circle) :=
  Measure.haarMeasure (⟨⟨Set.univ,isCompact_univ⟩,by simp⟩:PositiveCompacts (ι → Circle))
private def zz1845:"s0735"="s0735":=by decide+kernel
theorem torusHaar_isProbabilityMeasure:IsProbabilityMeasure (torusHaar ι):=by
  constructor
  exact Measure.haarMeasure_self
theorem torusHaar_isHaarMeasure:Measure.IsHaarMeasure (torusHaar ι):=by
  unfold torusHaar
  infer_instance
variable {ι}
theorem monomial_continuous (m:ι → ℤ):Continuous (monomial m):=by
  change Continuous (fun z:ι → Circle => ∏ i,((z i ^ m i:Circle):ℂ))
  fun_prop (disch:=simp)
theorem monomial_integrable (m:ι → ℤ):Integrable (monomial m) (torusHaar ι):=by
  letI:=torusHaar_isHaarMeasure ι
  exact (monomial_continuous m).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
private def zz1846:"s0736"="s0736":=by decide+kernel
theorem monomial_single [DecidableEq ι] (m:ι → ℤ) (i:ι) (w:Circle) :
    monomial m (fun j => if j = i then w else 1) = (w:ℂ) ^ m i:=by
  unfold monomial
  rw [Finset.prod_eq_single i]
  · simp
  · intro j _ hji
    simp [hji]
  · simp
theorem exists_monomial_ne_one {m:ι → ℤ} (hm:m ≠ 0) :
    ∃ z:ι → Circle,monomial m z ≠ 1:=by
  classical
  obtain ⟨i,hi⟩:=Function.ne_iff.mp hm
  change m i ≠ 0 at hi
  have hiR:(m i:ℝ) ≠ 0:=by exact_mod_cast hi
  let w:Circle:=Circle.exp (Real.pi / m i)
  have hw:w ^ m i = Circle.exp Real.pi:=by
    dsimp [w]
    rw [← Circle.exp_intCast_mul]
    congr 1
    field_simp
  refine ⟨fun j => if j = i then w else 1, ?_⟩
  rw [monomial_single, ← Circle.coe_zpow,hw]
  norm_num [Circle.coe_exp,Complex.exp_pi_mul_I]
theorem integral_monomial (m:ι → ℤ) :
    (∫ z,monomial m z ∂torusHaar ι) = if m = 0 then 1 else 0:=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isHaarMeasure ι
  classical
  by_cases hm:m = 0
  · simp [hm,monomial_zero]
  · rw [if_neg hm]
    obtain ⟨w,hw⟩:=exists_monomial_ne_one hm
    have htrans:=integral_mul_left_eq_self (μ:=torusHaar ι) (monomial m) w
    simp_rw [monomial_mul] at htrans
    rw [integral_const_mul] at htrans
    have hz:(monomial m w - 1) * (∫ z,monomial m z ∂torusHaar ι) = 0:=by
      linear_combination htrans
    exact (mul_eq_zero.mp hz).resolve_left (sub_ne_zero.mpr hw)
theorem polynomial_integrable (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) :
    Integrable (polynomial S c) (torusHaar ι):=by
  apply integrable_finsetSum
  intro m _
  exact (monomial_integrable m).const_mul (c m)
private def zz1847:"s0737"="s0737":=by decide+kernel
theorem integral_polynomial (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) :
    (∫ z,polynomial S c z ∂torusHaar ι) = constantCoefficient S c:=by
  classical
  change (∫ z, ∑ m ∈ S,c m * monomial m z ∂torusHaar ι) = _
  rw [integral_finsetSum]
  · simp only [integral_const_mul,integral_monomial,mul_ite,mul_one,mul_zero,
      constantCoefficient]
  · intro m _
    exact (monomial_integrable m).const_mul (c m)
variable {q:ℕ} [NeZero q]
theorem orbitMean_polynomial_eq_haar_integral (ks:ι → ZMod q)
    (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) (hn:Nonresonant ks S) :
    orbitMean ks (polynomial S c) = ∫ z,polynomial S c z ∂torusHaar ι:=by
  rw [orbitMean_polynomial_of_nonresonant ks S c hn,integral_polynomial]
theorem orbitMean_haar_discrepancy_le (ks:ι → ZMod q) (S:Finset (ι → ℤ))
    (c:(ι → ℤ) → ℂ) (F:(ι → Circle) → ℂ) (hF:Integrable F (torusHaar ι))
    (hn:Nonresonant ks S) {ε:ℝ}
    (herr:∀ z, ‖F z - polynomial S c z‖ ≤ ε) :
    ‖orbitMean ks F - ∫ z,F z ∂torusHaar ι‖ ≤ 2 * ε:=by
  letI:=torusHaar_isProbabilityMeasure ι
  have ho:=orbitMean_error_le ks F (polynomial S c) herr
  have hi:‖(∫ z,F z ∂torusHaar ι) - ∫ z,polynomial S c z ∂torusHaar ι‖ ≤ ε:=by
    rw [← integral_sub hF (polynomial_integrable S c)]
    simpa only [probReal_univ,mul_one] using
      norm_integral_le_of_norm_le_const (μ:=torusHaar ι) (Filter.Eventually.of_forall herr)
  have he:=orbitMean_polynomial_eq_haar_integral ks S c hn
  calc
    ‖orbitMean ks F - ∫ z,F z ∂torusHaar ι‖ =
        ‖(orbitMean ks F - orbitMean ks (polynomial S c)) +
          ((∫ z,polynomial S c z ∂torusHaar ι) - ∫ z,F z ∂torusHaar ι)‖:=by
      rw [← he,sub_add_sub_cancel]
    _ ≤ ‖orbitMean ks F - orbitMean ks (polynomial S c)‖ +
        ‖(∫ z,polynomial S c z ∂torusHaar ι) - ∫ z,F z ∂torusHaar ι‖:=norm_add_le _ _
    _ ≤ ε + ε:=add_le_add ho (by simpa only [norm_sub_rev] using hi)
    _ = 2 * ε:=by ring
theorem orbitMean_haar_discrepancy_of_continuous (ks:ι → ZMod q)
    (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) (F:(ι → Circle) → ℂ)
    (hF:Continuous F) (hn:Nonresonant ks S) {ε:ℝ}
    (herr:∀ z, ‖F z - polynomial S c z‖ ≤ ε) :
    ‖orbitMean ks F - ∫ z,F z ∂torusHaar ι‖ ≤ 2 * ε:=by
  letI:=torusHaar_isHaarMeasure ι
  exact orbitMean_haar_discrepancy_le ks S c F
    (hF.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) hn herr
end Green24Proof.CyclicTorusHaarDiscrepancy
private def zz2429:"s097d"="s097d":=by decide+kernel
end 
section 
namespace Green24Proof.RealTorusDilation
open MeasureTheory Set
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
abbrev Space (ι:Type*):=ℝ × (ι → Circle)
noncomputable def measure (ι:Type*) [Fintype ι]:Measure (Space ι) :=
  volume.prod (torusHaar ι)
private def zz1848:"s0738"="s0738":=by decide+kernel
theorem measure_sigmaFinite:SigmaFinite (measure ι):=by
  letI:=torusHaar_isProbabilityMeasure ι
  unfold measure
  infer_instance
theorem measure_isLocallyFinite:IsLocallyFiniteMeasure (measure ι):=by
  letI:=torusHaar_isHaarMeasure ι
  unfold measure
  infer_instance
omit [Fintype ι] in
theorem power_surjective {n:ℕ} (hn:n ≠ 0) :
    Function.Surjective (fun z:ι → Circle => z ^ n):=by
  intro z
  have hn':(n:ℤ) ≠ 0:=by exact_mod_cast hn
  have hz:Function.Surjective (fun u:Circle => u ^ (n:ℤ)):=by
    intro y
    obtain ⟨t,rfl⟩:=Circle.exp_surjective y
    refine ⟨Circle.exp (t / n), ?_⟩
    change Circle.exp (t / n) ^ (n:ℤ) = Circle.exp t
    rw [← Circle.exp_intCast_mul]
    congr 1
    have hnR:(n:ℝ) ≠ 0:=by exact_mod_cast hn
    push_cast
    field_simp
  choose u hu using fun i => hz (z i)
  refine ⟨u, ?_⟩
  funext i
  simpa only [Pi.pow_apply,zpow_natCast] using hu i
theorem power_measurePreserving {n:ℕ} (hn:n ≠ 0) :
    MeasurePreserving (fun z:ι → Circle => z ^ n) (torusHaar ι) (torusHaar ι):=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isHaarMeasure ι
  exact MonoidHom.measurePreserving (f:=powMonoidHom (α:=ι → Circle) n)
    (show Continuous (fun z:ι → Circle => z ^ n) by fun_prop)
    (power_surjective hn) (by simp)
noncomputable def dilationMap (a:ℝ) (n:ℕ) (v:Space ι):Space ι:=(v.1 / a,v.2 ^ n)
private def zz1849:"s0739"="s0739":=by decide+kernel
omit [Fintype ι] in
theorem dilationMap_continuous (a:ℝ) (n:ℕ) :
    Continuous (dilationMap (ι:=ι) a n):=by
  unfold dilationMap
  fun_prop
omit [Fintype ι] in
theorem dilationMap_isProper {a:ℝ} (ha:a ≠ 0) (n:ℕ) :
    IsProperMap (dilationMap (ι:=ι) a n):=by
  have hreal:IsProperMap (fun t:ℝ => t / a):=by
    simpa only [Homeomorph.coe_mulRight₀,div_eq_mul_inv] using
      (Homeomorph.mulRight₀ a⁻¹ (inv_ne_zero ha)).isProperMap
  have htorus:IsProperMap (fun z:ι → Circle => z ^ n) :=
    (by fun_prop:Continuous (fun z:ι → Circle => z ^ n)).isProperMap
  exact hreal.prodMap htorus
theorem map_dilationMap {a:ℝ} (ha:a ≠ 0) {n:ℕ} (hn:n ≠ 0) :
    Measure.map (dilationMap (ι:=ι) a n) (measure ι) =
      ENNReal.ofReal |a| • measure ι:=by
  letI:=torusHaar_isProbabilityMeasure ι
  have hreal:Measure.map (fun t:ℝ => t / a) volume =
      ENNReal.ofReal |a| • volume:=by
    simpa only [div_eq_mul_inv,inv_inv] using Real.map_volume_mul_right (inv_ne_zero ha)
  change Measure.map (Prod.map (fun t:ℝ => t / a) (fun z:ι → Circle => z ^ n))
    (volume.prod (torusHaar ι)) = _
  rw [← Measure.map_prod_map _ _ (by fun_prop) (by fun_prop),hreal,
    (power_measurePreserving (ι:=ι) hn).map_eq,Measure.prod_smul_left]
  rfl
noncomputable def pullback (a:ℝ) (n:ℕ) (F:Space ι → ℝ):Space ι → ℝ :=
  F ∘ dilationMap a n
omit [Fintype ι] in
theorem pullback_continuous (a:ℝ) (n:ℕ) (F:Space ι → ℝ) (hF:Continuous F) :
    Continuous (pullback a n F):=hF.comp (dilationMap_continuous a n)
private def zz1850:"s073a"="s073a":=by decide+kernel
omit [Fintype ι] in
theorem pullback_range (a:ℝ) (n:ℕ) (F:Space ι → ℝ)
    (hF:∀ z,F z ∈ Icc 0 1) (z:Space ι):pullback a n F z ∈ Icc 0 1:=hF _
omit [Fintype ι] in
theorem pullback_compactSupport {a:ℝ} (ha:a ≠ 0) (n:ℕ) (F:Space ι → ℝ)
    (hF:HasCompactSupport F):HasCompactSupport (pullback a n F):=by
  apply HasCompactSupport.intro ((dilationMap_isProper (ι:=ι) ha n).isCompact_preimage hF)
  intro v hv
  change F (dilationMap a n v) = 0
  exact image_eq_zero_of_notMem_tsupport hv
theorem integral_pullback {a:ℝ} (ha:a ≠ 0) {n:ℕ} (hn:n ≠ 0)
    (F:Space ι → ℝ) (hF:Continuous F) :
    (∫ v,pullback a n F v ∂measure ι) = |a| * ∫ v,F v ∂measure ι:=by
  have h:=integral_map (μ:=measure ι)
    (dilationMap_continuous (ι:=ι) a n).measurable.aemeasurable hF.aestronglyMeasurable
  rw [map_dilationMap ha hn,integral_smul_measure,ENNReal.toReal_ofReal (abs_nonneg a),
    smul_eq_mul] at h
  exact h.symm
theorem map_pair_dilation {a b:ℝ} (ha:a ≠ 0) (hb:b ≠ 0)
    {n m:ℕ} (hn:n ≠ 0) (hm:m ≠ 0) :
    Measure.map (Prod.map (dilationMap (ι:=ι) a n) (dilationMap b m))
      ((measure ι).prod (measure ι)) =
      ENNReal.ofReal (|a| * |b|) • ((measure ι).prod (measure ι)):=by
  letI:=measure_sigmaFinite (ι:=ι)
  rw [← Measure.map_prod_map _ _ (dilationMap_continuous a n).measurable
    (dilationMap_continuous b m).measurable,map_dilationMap ha hn,map_dilationMap hb hm,
    Measure.prod_smul_left,Measure.prod_smul_right,smul_smul,
    ← ENNReal.ofReal_mul (abs_nonneg a)]
private def zz1851:"s073b"="s073b":=by decide+kernel
theorem integral_pair_dilation {a b:ℝ} (ha:a ≠ 0) (hb:b ≠ 0)
    {n m:ℕ} (hn:n ≠ 0) (hm:m ≠ 0)
    (K:Space ι × Space ι → ℝ) (hK:Continuous K) :
    (∫ yz,K (dilationMap a n yz.1,dilationMap b m yz.2)
      ∂(measure ι).prod (measure ι)) =
      (|a| * |b|) * ∫ yz,K yz ∂(measure ι).prod (measure ι):=by
  have h:=integral_map (μ:=(measure ι).prod (measure ι))
    ((dilationMap_continuous a n).prodMap
      (dilationMap_continuous b m)).measurable.aemeasurable hK.aestronglyMeasurable
  rw [map_pair_dilation ha hb hn hm,integral_smul_measure,
    ENNReal.toReal_ofReal (mul_nonneg (abs_nonneg a) (abs_nonneg b)),smul_eq_mul] at h
  exact h.symm
end Green24Proof.RealTorusDilation
private def zz2430:"s097e"="s097e":=by decide+kernel
end 
section 
namespace Green24Proof.CircleProbabilityHaar
open MeasureTheory Set TopologicalSpace
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
noncomputable def circleHaar:Measure Circle :=
  Measure.haarMeasure (⟨⟨Set.univ,isCompact_univ⟩,by simp⟩:PositiveCompacts Circle)
theorem circleHaar_isProbabilityMeasure:IsProbabilityMeasure circleHaar :=
  ⟨Measure.haarMeasure_self⟩
theorem circleHaar_isHaarMeasure:Measure.IsHaarMeasure circleHaar:=by
  unfold circleHaar
  infer_instance
def one_pos:Fact (0 < (1:ℝ)):=⟨by norm_num⟩
section UnitCircle
variable [Fact (0 < (1:ℝ))]
theorem addCircleOne_probability:IsProbabilityMeasure (volume:Measure (AddCircle (1:ℝ))) :=
  ⟨by simp⟩
private def zz1852:"s073c"="s073c":=by decide+kernel
theorem map_toCircle_volume :
    Measure.map (@AddCircle.toCircle 1) (volume:Measure (AddCircle (1:ℝ))) = circleHaar:=by
  letI:=addCircleOne_probability
  letI:=circleHaar_isProbabilityMeasure
  letI:=circleHaar_isHaarMeasure
  let f:=@AddCircle.toCircle 1
  have hf:Continuous f:=AddCircle.continuous_toCircle
  have hs:Function.Surjective f:=by
    intro z
    obtain ⟨x,hx⟩:=(AddCircle.homeomorphCircle (T:=1) one_ne_zero).surjective z
    exact ⟨x,by simpa only [f,AddCircle.homeomorphCircle_apply] using hx⟩
  let μ:=Measure.map f (volume:Measure (AddCircle (1:ℝ)))
  have:IsProbabilityMeasure μ:=Measure.isProbabilityMeasure_map hf.measurable.aemeasurable
  have:Measure.IsMulLeftInvariant μ:=by
    constructor
    intro z
    obtain ⟨a,rfl⟩:=hs z
    change Measure.map (f a * ·) (Measure.map f volume) = Measure.map f volume
    rw [Measure.map_map (measurable_const_mul _) hf.measurable]
    have heq:(fun z => f a * z) ∘ f = f ∘ (a + ·):=by
      funext b
      exact (AddCircle.toCircle_add a b).symm
    rw [heq, ← Measure.map_map hf.measurable (measurable_const_add _),
      Measure.IsAddLeftInvariant.map_add_left_eq_self]
  have:Measure.IsHaarMeasure μ :=
    Measure.isHaarMeasure_of_isCompact_nonempty_interior μ univ isCompact_univ
      (by simp) (by simp) (by simp)
  exact Measure.isHaarMeasure_eq_of_isProbabilityMeasure μ circleHaar
end UnitCircle
theorem measurePreserving_unit_exp (a:ℝ) :
    MeasurePreserving (fun x:ℝ => Circle.exp (2 * Real.pi * x))
      (volume.restrict (Ioc a (a + 1))) circleHaar:=by
  letI:=one_pos
  letI:=addCircleOne_probability
  have hp:MeasurePreserving (@AddCircle.toCircle 1)
      (volume:Measure (AddCircle (1:ℝ))) circleHaar :=
    ⟨AddCircle.continuous_toCircle.measurable,map_toCircle_volume⟩
  have h:=hp.comp (AddCircle.measurePreserving_mk 1 a)
  simpa only [Function.comp_def,AddCircle.toCircle_apply_mk,div_one] using h
theorem integral_unit_exp (F:Circle → ℝ) (hF:Continuous F) (a:ℝ) :
    (∫ z,F z ∂circleHaar) = ∫ x in a..a + 1,F (Circle.exp (2 * Real.pi * x)):=by
  have hp:=measurePreserving_unit_exp a
  have h:=integral_map (μ:=volume.restrict (Ioc a (a + 1)))
    hp.measurable.aemeasurable hF.aestronglyMeasurable
  rw [hp.map_eq] at h
  rw [intervalIntegral.integral_of_le (by linarith)]
  exact h
theorem integral_exp (F:Circle → ℝ) (hF:Continuous F) (a:ℝ) :
    (∫ z,F z ∂circleHaar) =
      (2 * Real.pi)⁻¹ * ∫ t in a..a + 2 * Real.pi,F (Circle.exp t):=by
  have hpi:(2:ℝ) * Real.pi ≠ 0:=by positivity
  rw [integral_unit_exp F hF (a / (2 * Real.pi)),
    intervalIntegral.integral_comp_mul_left (fun t => F (Circle.exp t)) hpi]
  have h0:2 * Real.pi * (a / (2 * Real.pi)) = a:=by field_simp
  have h1:2 * Real.pi * (a / (2 * Real.pi) + 1) = a + 2 * Real.pi:=by
    rw [mul_add,h0,mul_one]
  rw [h0,h1,smul_eq_mul]
end Green24Proof.CircleProbabilityHaar
private def zz2431:"s097f"="s097f":=by decide+kernel
end 
section 
namespace Green24Proof.PolicyHaarTorusMarginal
open MeasureTheory Set
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {X:Type*} [TopologicalSpace X] [FirstCountableTopology X]
  [LocallyCompactSpace X]
private def zz1853:"s073d"="s073d":=by decide+kernel
theorem torus_marginal_continuous {ι:Type*} [Fintype ι]
    (K:X × (ι → Circle) → ℝ) (hK:Continuous K) :
    Continuous (fun x => ∫ u,K (x,u) ∂torusHaar ι):=by
  letI:=torusHaar_isProbabilityMeasure ι
  have h:=continuous_parametric_integral_of_continuous
    (μ:=torusHaar ι) (f:=fun x u => K (x,u)) hK
    (s:=Set.univ) isCompact_univ
  simpa only [Measure.restrict_univ] using h
end Green24Proof.PolicyHaarTorusMarginal
private def zz2432:"s0980"="s0980":=by decide+kernel
end 
section 
namespace Green24Proof.CompactCircleLift
open MeasureTheory Set
open Green24Proof.RealTorusDilation Green24Proof.CircleProbabilityHaar
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.PolicyHaarTorusMarginal
variable {ι:Type*}
theorem two_pi_pos:Fact (0 < 2 * Real.pi):=⟨by positivity⟩
def SmallSupport (F:Space ι → ℝ):Prop :=
  ∀ (t:ℝ) (u:ι → Circle),Real.pi / 4 ≤ |t| → F (t,u) = 0
noncomputable def circleLift (F:Space ι → ℝ)
    (zu:Circle × (ι → Circle)):ℝ :=
  letI:=two_pi_pos
  AddCircle.liftIoc (2 * Real.pi) (-Real.pi) (fun t => F (t,zu.2))
    (AddCircle.homeomorphCircle'.symm zu.1)
theorem circleLift_exp (F:Space ι → ℝ) {t:ℝ}
    (ht:t ∈ Ioc (-Real.pi) Real.pi) (u:ι → Circle) :
    circleLift F (Circle.exp t,u) = F (t,u):=by
  letI:=two_pi_pos
  unfold circleLift
  rw [← AddCircle.homeomorphCircle'_apply_mk,
    AddCircle.homeomorphCircle'.symm_apply_apply]
  apply AddCircle.liftIoc_coe_apply
  constructor
  · exact ht.1
  · linarith [ht.2]
theorem circleLift_eq_arg (F:Space ι → ℝ) (z:Circle) (u:ι → Circle) :
    circleLift F (z,u) = F (Complex.arg (z:ℂ),u):=by
  have h:=circleLift_exp F
    (t:=Complex.arg (z:ℂ)) ⟨Complex.neg_pi_lt_arg _,Complex.arg_le_pi _⟩ u
  simpa only [Circle.exp_arg] using h
private def zz1854:"s073e"="s073e":=by decide+kernel
theorem circleLift_range (F:Space ι → ℝ) (hF:∀ v,F v ∈ Icc 0 1)
    (zu:Circle × (ι → Circle)):circleLift F zu ∈ Icc 0 1:=by
  rw [show zu = (zu.1,zu.2) from rfl,circleLift_eq_arg]
  exact hF _
theorem circleLift_zero_outside (F:Space ι → ℝ) (hs:SmallSupport F)
    (z:Circle) (u:ι → Circle) (hz:Real.pi / 4 ≤ |Complex.arg (z:ℂ)|) :
    circleLift F (z,u) = 0:=by
  rw [circleLift_eq_arg]
  exact hs _ _ hz
theorem smallSupport_compactSupport (F:Space ι → ℝ) (hs:SmallSupport F) :
    HasCompactSupport F:=by
  apply HasCompactSupport.intro
    (isCompact_Icc.prod (isCompact_univ:IsCompact (univ:Set (ι → Circle))))
  intro v hv
  apply hs
  have hv':v.1 ∉ Icc (-Real.pi / 4) (Real.pi / 4):=by simpa using hv
  by_contra h
  have ha:|v.1| < Real.pi / 4:=lt_of_not_ge h
  exact hv' ⟨by linarith [(abs_lt.mp ha).1],(abs_lt.mp ha).2.le⟩
theorem circleLift_continuous (F:Space ι → ℝ) (hF:Continuous F)
    (hs:SmallSupport F):Continuous (circleLift F):=by
  letI:=two_pi_pos
  let Fc:C(ℝ × (ι → Circle),ℝ):=⟨F,hF⟩
  let fc:C(ℝ,C(ι → Circle,ℝ)):=Fc.curry
  have he:fc (-Real.pi) = fc (-Real.pi + 2 * Real.pi):=by
    ext u
    change F (-Real.pi,u) = F (-Real.pi + 2 * Real.pi,u)
    rw [hs _ _ (by rw [abs_neg,abs_of_pos Real.pi_pos]; linarith [Real.pi_pos]),
      hs _ _ (by rw [show -Real.pi + 2 * Real.pi = Real.pi by ring,
        abs_of_pos Real.pi_pos]; linarith [Real.pi_pos])]
  let L:C(AddCircle (2 * Real.pi),C(ι → Circle,ℝ)) :=
    ⟨AddCircle.liftIoc (2 * Real.pi) (-Real.pi) fc,
      AddCircle.liftIoc_continuous he fc.continuous.continuousOn⟩
  let LC:C(Circle,C(ι → Circle,ℝ)) :=
    L.comp ⟨AddCircle.homeomorphCircle'.symm,
      AddCircle.homeomorphCircle'.symm.continuous⟩
  exact LC.uncurry.continuous
private def zz1855:"s073f"="s073f":=by decide+kernel
theorem difference_product_exp (F G H:Space ι → ℝ)
    (hsG:SmallSupport G) (hsH:SmallSupport H)
    {s t:ℝ} (hs:s ∈ Ioc (-Real.pi) Real.pi)
    (ht:t ∈ Ioc (-Real.pi) Real.pi) (u v:ι → Circle) :
    circleLift F (Circle.exp t / Circle.exp s,v / u) *
        circleLift G (Circle.exp s,u) * circleLift H (Circle.exp t,v) =
      F (t - s,v / u) * G (s,u) * H (t,v):=by
  rw [circleLift_exp G hs,circleLift_exp H ht]
  by_cases hG:G (s,u) = 0
  · simp only [hG,mul_zero,zero_mul]
  by_cases hH:H (t,v) = 0
  · simp only [hH,mul_zero]
  have hs':|s| < Real.pi / 4:=lt_of_not_ge (fun h => hG (hsG s u h))
  have ht':|t| < Real.pi / 4:=lt_of_not_ge (fun h => hH (hsH t v h))
  have hts:t - s ∈ Ioc (-Real.pi) Real.pi:=by
    obtain ⟨hs1,hs2⟩:=abs_lt.mp hs'
    obtain ⟨ht1,ht2⟩:=abs_lt.mp ht'
    exact ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
  rw [← Circle.exp_sub,circleLift_exp F hts]
variable [Fintype ι] [MeasurableSpace Circle] [BorelSpace Circle]
theorem integral_eq_principal (F:Space ι → ℝ) (hF:Continuous F)
    (hs:SmallSupport F) :
    (∫ v,F v ∂measure ι) =
      ∫ t in -Real.pi..Real.pi, ∫ u,F (t,u) ∂torusHaar ι:=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=circleHaar_isProbabilityMeasure
  unfold RealTorusDilation.measure
  rw [integral_prod _ (hF.integrable_of_hasCompactSupport (smallSupport_compactSupport F hs))]
  symm
  apply intervalIntegral.integral_eq_integral_of_support_subset
  intro t ht
  by_contra hn
  have ha:Real.pi / 4 ≤ |t|:=by
    by_contra h
    obtain ⟨h1,h2⟩:=abs_lt.mp (lt_of_not_ge h)
    exact hn ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
  apply ht
  simp_rw [hs t _ ha]
  exact integral_zero _ _
theorem integral_circleLift (F:Space ι → ℝ) (hF:Continuous F)
    (hs:SmallSupport F) :
    (∫ zu,circleLift F zu ∂circleHaar.prod (torusHaar ι)) =
      (2 * Real.pi)⁻¹ * ∫ v,F v ∂measure ι:=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=circleHaar_isProbabilityMeasure
  have hc:=circleLift_continuous F hF hs
  rw [integral_prod _ (hc.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)),
    integral_exp _ (torus_marginal_continuous _ hc) (-Real.pi),
    show -Real.pi + 2 * Real.pi = Real.pi by ring,integral_eq_principal F hF hs]
  congr 1
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht
  apply integral_congr_ae
  filter_upwards [] with u
  exact circleLift_exp F ⟨ht.1,ht.2.le⟩ u
end Green24Proof.CompactCircleLift
private def zz2433:"s0981"="s0981":=by decide+kernel
end 
section 
namespace Green24Proof.RealTorusCoefficientNormalization
open MeasureTheory Set
open Green24Proof.RealTorusDilation
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
noncomputable def coefficientIntegrand (F G H:Space ι → ℝ) (yz:Space ι × Space ι):ℝ :=
  F (3 * yz.2.1 - 2 * yz.1.1,yz.2.2 ^ 3 * yz.1.2 ^ (-2:ℤ)) * G yz.1 * H yz.2
noncomputable def differenceIntegrand (F G H:Space ι → ℝ) (yz:Space ι × Space ι):ℝ :=
  F (yz.2.1 - yz.1.1,yz.2.2 / yz.1.2) * G yz.1 * H yz.2
noncomputable def coefficientCount (F G H:Space ι → ℝ):ℝ :=
  ∫ yz,coefficientIntegrand F G H yz ∂(measure ι).prod (measure ι)
noncomputable def differenceCount (F G H:Space ι → ℝ):ℝ :=
  ∫ yz,differenceIntegrand F G H yz ∂(measure ι).prod (measure ι)
omit [Fintype ι] in
theorem coefficientIntegrand_continuous (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H) :
    Continuous (coefficientIntegrand F G H):=by
  unfold coefficientIntegrand
  fun_prop
private def zz1856:"s0740"="s0740":=by decide+kernel
omit [Fintype ι] in
theorem differenceIntegrand_continuous (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H) :
    Continuous (differenceIntegrand F G H):=by
  unfold differenceIntegrand
  fun_prop
omit [Fintype ι] in
theorem product_weight_compactSupport (L:Space ι × Space ι → ℝ) (G H:Space ι → ℝ)
    (hG:HasCompactSupport G) (hH:HasCompactSupport H) :
    HasCompactSupport (fun yz:Space ι × Space ι => L yz * G yz.1 * H yz.2):=by
  apply HasCompactSupport.intro (hG.prod hH)
  intro yz hyz
  by_cases hy:yz.1 ∈ tsupport G
  · have hz:yz.2 ∉ tsupport H:=fun hz => hyz ⟨hy,hz⟩
    rw [image_eq_zero_of_notMem_tsupport hz,mul_zero]
  · rw [image_eq_zero_of_notMem_tsupport hy,mul_zero,zero_mul]
theorem coefficientIntegrand_integrable (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsG:HasCompactSupport G) (hsH:HasCompactSupport H) :
    Integrable (coefficientIntegrand F G H) ((measure ι).prod (measure ι)):=by
  letI:=measure_isLocallyFinite (ι:=ι)
  exact (coefficientIntegrand_continuous F G H hF hG hH).integrable_of_hasCompactSupport
    (product_weight_compactSupport _ G H hsG hsH)
theorem differenceIntegrand_integrable (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsG:HasCompactSupport G) (hsH:HasCompactSupport H) :
    Integrable (differenceIntegrand F G H) ((measure ι).prod (measure ι)):=by
  letI:=measure_isLocallyFinite (ι:=ι)
  exact (differenceIntegrand_continuous F G H hF hG hH).integrable_of_hasCompactSupport
    (product_weight_compactSupport _ G H hsG hsH)
private def zz1857:"s0741"="s0741":=by decide+kernel
omit [Fintype ι] in
theorem coefficient_pullback_identity (F G H:Space ι → ℝ) (yz:Space ι × Space ι) :
    coefficientIntegrand F G H (dilationMap 2 3 yz.1,dilationMap 3 2 yz.2) =
      differenceIntegrand (pullback 1 6 F) (pullback 2 3 G) (pullback 3 2 H) yz:=by
  have hpow:(yz.2.2 ^ 2) ^ 3 * (yz.1.2 ^ 3) ^ (-2:ℤ) = (yz.2.2 / yz.1.2) ^ 6:=by
    simp [zpow_neg, ← pow_mul,div_eq_mul_inv,mul_pow]
  unfold coefficientIntegrand differenceIntegrand pullback dilationMap
  simp only [Function.comp_apply,div_one,hpow]
  rw [show 3 * (yz.2.1 / 3) - 2 * (yz.1.1 / 2) = yz.2.1 - yz.1.1 by ring]
theorem count_normalization (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H) :
    differenceCount (pullback 1 6 F) (pullback 2 3 G) (pullback 3 2 H) =
      6 * coefficientCount F G H:=by
  have h:=integral_pair_dilation (ι:=ι)
    (by norm_num:(2:ℝ) ≠ 0) (by norm_num:(3:ℝ) ≠ 0)
    (by norm_num:(3:ℕ) ≠ 0) (by norm_num:(2:ℕ) ≠ 0)
    (coefficientIntegrand F G H) (coefficientIntegrand_continuous F G H hF hG hH)
  simp_rw [coefficient_pullback_identity] at h
  norm_num only [abs_of_pos (by norm_num:(0:ℝ) < 2),
    abs_of_pos (by norm_num:(0:ℝ) < 3),show (2:ℝ) * 3 = 6 by norm_num] at h
  exact h
def RearrangementBound (ι:Type*) [Fintype ι]:Prop :=
  ∀ F G H:Space ι → ℝ,
    Continuous F → Continuous G → Continuous H →
    HasCompactSupport F → HasCompactSupport G → HasCompactSupport H →
    (∀ z,F z ∈ Icc 0 1) → (∀ z,G z ∈ Icc 0 1) → (∀ z,H z ∈ Icc 0 1) →
    differenceCount F G H ≤ kernel (∫ z,F z ∂measure ι)
      (∫ z,G z ∂measure ι) (∫ z,H z ∂measure ι)
theorem coefficient_bound_of_rearrangement (hR:RearrangementBound ι)
    (F G H:Space ι → ℝ) (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:HasCompactSupport F) (hsG:HasCompactSupport G) (hsH:HasCompactSupport H)
    (hrF:∀ z,F z ∈ Icc 0 1) (hrG:∀ z,G z ∈ Icc 0 1) (hrH:∀ z,H z ∈ Icc 0 1) :
    coefficientCount F G H ≤ kernel (∫ z,F z ∂measure ι)
      (2 * ∫ z,G z ∂measure ι) (3 * ∫ z,H z ∂measure ι) / 6:=by
  have h:=hR (pullback 1 6 F) (pullback 2 3 G) (pullback 3 2 H)
    (pullback_continuous 1 6 F hF) (pullback_continuous 2 3 G hG)
    (pullback_continuous 3 2 H hH)
    (pullback_compactSupport (by norm_num) 6 F hsF)
    (pullback_compactSupport (by norm_num) 3 G hsG)
    (pullback_compactSupport (by norm_num) 2 H hsH)
    (pullback_range 1 6 F hrF) (pullback_range 2 3 G hrG) (pullback_range 3 2 H hrH)
  rw [count_normalization F G H hF hG hH,
    integral_pullback (by norm_num:(1:ℝ) ≠ 0) (by norm_num:(6:ℕ) ≠ 0) F hF,
    integral_pullback (by norm_num:(2:ℝ) ≠ 0) (by norm_num:(3:ℕ) ≠ 0) G hG,
    integral_pullback (by norm_num:(3:ℝ) ≠ 0) (by norm_num:(2:ℕ) ≠ 0) H hH] at h
  norm_num only [abs_one,one_mul,abs_of_pos (by norm_num:(0:ℝ) < 2),
    abs_of_pos (by norm_num:(0:ℝ) < 3)] at h
  linarith
end Green24Proof.RealTorusCoefficientNormalization
private def zz2434:"s0982"="s0982":=by decide+kernel
end 
section 
namespace Green24Proof.CircleLiftCounting
open MeasureTheory Set
open Green24Proof.CompactCircleLift Green24Proof.RealTorusDilation
open Green24Proof.RealTorusCoefficientNormalization Green24Proof.CircleProbabilityHaar
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.PolicyHaarTorusMarginal
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
abbrev CircleSpace (ι:Type*):=Circle × (ι → Circle)
noncomputable def circleMeasure (ι:Type*) [Fintype ι]:Measure (CircleSpace ι) :=
  circleHaar.prod (torusHaar ι)
theorem circleMeasure_probability:IsProbabilityMeasure (circleMeasure ι):=by
  letI:=circleHaar_isProbabilityMeasure
  letI:=torusHaar_isProbabilityMeasure ι
  unfold circleMeasure
  infer_instance
private def zz1858:"s0742"="s0742":=by decide+kernel
theorem integral_angular (L:CircleSpace ι → ℝ) (hL:Continuous L) :
    (∫ z,L z ∂circleMeasure ι) =
      (2 * Real.pi)⁻¹ * ∫ t in -Real.pi..Real.pi, ∫ u,
        L (Circle.exp t,u) ∂torusHaar ι:=by
  letI:=circleHaar_isProbabilityMeasure
  letI:=torusHaar_isProbabilityMeasure ι
  unfold circleMeasure
  rw [integral_prod _ (hL.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)),
    integral_exp _ (torus_marginal_continuous L hL) (-Real.pi),
    show -Real.pi + 2 * Real.pi = Real.pi by ring]
theorem circle_marginal_continuous {X:Type*} [TopologicalSpace X]
    [FirstCountableTopology X] [LocallyCompactSpace X]
    (K:X × CircleSpace ι → ℝ) (hK:Continuous K) :
    Continuous (fun x => ∫ z,K (x,z) ∂circleMeasure ι):=by
  letI:=circleMeasure_probability (ι:=ι)
  have h:=continuous_parametric_integral_of_continuous
    (μ:=circleMeasure ι) (f:=fun x z => K (x,z)) hK
    (s:=Set.univ) isCompact_univ
  simpa only [Measure.restrict_univ] using h
theorem integral_pair_angular (K:CircleSpace ι × CircleSpace ι → ℝ)
    (hK:Continuous K) :
    (∫ yz,K yz ∂(circleMeasure ι).prod (circleMeasure ι)) =
      ((2 * Real.pi)⁻¹) ^ 2 * ∫ s in -Real.pi..Real.pi, ∫ u,
        (∫ t in -Real.pi..Real.pi, ∫ v,
          K ((Circle.exp s,u),(Circle.exp t,v)) ∂torusHaar ι) ∂torusHaar ι:=by
  letI:=circleMeasure_probability (ι:=ι)
  have hinner (y:CircleSpace ι):=integral_angular (fun z => K (y,z))
    (hK.comp (continuous_const.prodMk continuous_id))
  rw [integral_prod _ (hK.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)),
    integral_angular _ (circle_marginal_continuous K hK)]
  simp_rw [hinner,integral_const_mul,intervalIntegral.integral_const_mul]
  ring
theorem integral_real_principal (f:ℝ → ℝ)
    (hf:∀ t,Real.pi / 4 ≤ |t| → f t = 0) :
    (∫ t,f t) = ∫ t in -Real.pi..Real.pi,f t:=by
  symm
  apply intervalIntegral.integral_eq_integral_of_support_subset
  intro t ht
  by_contra hn
  apply ht
  apply hf
  by_contra ha
  obtain ⟨h1,h2⟩:=abs_lt.mp (lt_of_not_ge ha)
  exact hn ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
private def zz1859:"s0743"="s0743":=by decide+kernel
theorem differenceCount_eq_principal (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsG:SmallSupport G) (hsH:SmallSupport H) :
    differenceCount F G H = ∫ s in -Real.pi..Real.pi, ∫ u,
      (∫ t in -Real.pi..Real.pi, ∫ v,
        F (t - s,v / u) * G (s,u) * H (t,v) ∂torusHaar ι) ∂torusHaar ι:=by
  letI:=measure_sigmaFinite (ι:=ι)
  letI:=torusHaar_isProbabilityMeasure ι
  let K:=differenceIntegrand F G H
  have hc:=differenceIntegrand_continuous F G H hF hG hH
  have hi:=differenceIntegrand_integrable F G H hF hG hH
    (smallSupport_compactSupport G hsG) (smallSupport_compactSupport H hsH)
  have hinner (y:Space ι) :
      (∫ z,K (y,z) ∂measure ι) =
        ∫ t in -Real.pi..Real.pi, ∫ v,K (y,(t,v)) ∂torusHaar ι:=by
    apply integral_eq_principal (fun z => K (y,z))
      (hc.comp (continuous_const.prodMk continuous_id))
    intro t v ht
    change F (t - y.1,v / y.2) * G y * H (t,v) = 0
    rw [hsH t v ht,mul_zero]
  unfold differenceCount
  rw [integral_prod _ hi]
  change (∫ y,(∫ z,K (y,z) ∂measure ι) ∂volume.prod (torusHaar ι)) = _
  rw [integral_prod _ hi.integral_prod_left]
  change (∫ s, ∫ u, ∫ z,K ((s,u),z) ∂measure ι ∂torusHaar ι) = _
  simp_rw [hinner]
  change (∫ s, ∫ u,(∫ t in -Real.pi..Real.pi, ∫ v,
    F (t - s,v / u) * G (s,u) * H (t,v) ∂torusHaar ι) ∂torusHaar ι) = _
  apply integral_real_principal
  intro s hs
  simp_rw [hsG s _ hs,mul_zero,zero_mul]
  simp
noncomputable def liftedDifferenceIntegrand (F G H:Space ι → ℝ)
    (yz:CircleSpace ι × CircleSpace ι):ℝ :=
  circleLift F (yz.2 / yz.1) * circleLift G yz.1 * circleLift H yz.2
omit [Fintype ι] in
theorem liftedDifferenceIntegrand_continuous (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H) :
    Continuous (liftedDifferenceIntegrand F G H):=by
  unfold liftedDifferenceIntegrand
  exact (((circleLift_continuous F hF hsF).comp (by fun_prop)).mul
    ((circleLift_continuous G hG hsG).comp continuous_fst)).mul
      ((circleLift_continuous H hH hsH).comp continuous_snd)
theorem integrated_count_identity (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H) :
    (∫ yz,liftedDifferenceIntegrand F G H yz
      ∂(circleMeasure ι).prod (circleMeasure ι)) =
      ((2 * Real.pi)⁻¹) ^ 2 * differenceCount F G H:=by
  rw [integral_pair_angular _
    (liftedDifferenceIntegrand_continuous F G H hF hG hH hsF hsG hsH),
    differenceCount_eq_principal F G H hF hG hH hsG hsH]
  congr 1
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro s hs
  apply integral_congr_ae
  filter_upwards [] with u
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht
  apply integral_congr_ae
  filter_upwards [] with v
  exact difference_product_exp F G H hsG hsH ⟨hs.1,hs.2.le⟩ ⟨ht.1,ht.2.le⟩ u v
end Green24Proof.CircleLiftCounting
private def zz2435:"s0983"="s0983":=by decide+kernel
end 
section 
namespace Green24Proof.CircleLaurentApproximation
open Set Algebra Submodule Finset
open scoped BigOperators ComplexConjugate
open Green24Proof.CyclicTorusLaurent
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
noncomputable def monomialMap (m:ι → ℤ):C(ι → Circle,ℂ) :=
  ⟨monomial m,monomial_continuous m⟩
theorem monomialMap_zero:monomialMap (0:ι → ℤ) = 1:=by
  ext z
  exact monomial_zero z
private def zz1860:"s0744"="s0744":=by decide+kernel
theorem monomialMap_add (m n:ι → ℤ) :
    monomialMap (m + n) = monomialMap m * monomialMap n:=by
  ext z
  change (∏ i,(z i:ℂ) ^ (m i + n i)) = (∏ i,(z i:ℂ) ^ m i) * ∏ i,(z i:ℂ) ^ n i
  simp only [zpow_add₀ (Circle.coe_ne_zero _),Finset.prod_mul_distrib]
theorem monomialMap_neg (m:ι → ℤ):monomialMap (-m) = star (monomialMap m):=by
  ext z
  change (∏ i,(z i:ℂ) ^ (-m i)) = (starRingEnd ℂ) (∏ i,(z i:ℂ) ^ m i)
  rw [map_prod]
  apply Finset.prod_congr rfl
  intro i _
  rw [← Circle.coe_zpow, ← Circle.coe_zpow,zpow_neg,Circle.coe_inv_eq_conj]
theorem monomialMap_single [DecidableEq ι] (i:ι) (z:ι → Circle) :
    monomialMap (Pi.single i (1:ℤ)) z = (z i:ℂ):=by
  change (∏ j,(z j:ℂ) ^ ((Pi.single i (1:ℤ):ι → ℤ) j)) = _
  rw [Finset.prod_eq_single i]
  · simp
  · intro j _ hji
    simp [Pi.single_eq_of_ne hji]
  · simp
noncomputable def laurentAlgebra (ι:Type*) [Fintype ι]:StarSubalgebra ℂ C(ι → Circle,ℂ) where
  toSubalgebra:=Algebra.adjoin ℂ (Set.range monomialMap)
  star_mem':=by
    change Algebra.adjoin ℂ (Set.range monomialMap) ≤ star (Algebra.adjoin ℂ (Set.range monomialMap))
    refine adjoin_le ?_
    rintro _ ⟨m,rfl⟩
    refine subset_adjoin ⟨-m, ?_⟩
    exact monomialMap_neg m
theorem laurentAlgebra_eq_span :
    (laurentAlgebra ι).toSubalgebra.toSubmodule = Submodule.span ℂ (Set.range monomialMap):=by
  apply adjoin_eq_span_of_subset
  refine .trans (fun x => Submonoid.closure_induction (fun _ => id) ⟨0, ?_⟩ ?_) subset_span
  · exact monomialMap_zero
  · rintro _ _ _ _ ⟨m,rfl⟩ ⟨n,rfl⟩
    exact ⟨m + n,monomialMap_add m n⟩
private def zz1861:"s0745"="s0745":=by decide+kernel
theorem laurentAlgebra_separatesPoints:(laurentAlgebra ι).SeparatesPoints:=by
  classical
  change (Algebra.adjoin ℂ (Set.range (monomialMap (ι:=ι)))).SeparatesPoints
  intro x y hxy
  obtain ⟨i,hi⟩:=Function.ne_iff.mp hxy
  refine ⟨(monomialMap (Pi.single i (1:ℤ)):(ι → Circle) → ℂ), ?_, ?_⟩
  · refine ⟨monomialMap (Pi.single i (1:ℤ)), ?_,rfl⟩
    change monomialMap (Pi.single i (1:ℤ)) ∈
      Algebra.adjoin ℂ (Set.range (monomialMap (ι:=ι)))
    exact Algebra.subset_adjoin ⟨Pi.single i (1:ℤ),rfl⟩
  · change monomialMap (Pi.single i (1:ℤ)) x ≠ monomialMap (Pi.single i (1:ℤ)) y
    rw [monomialMap_single,monomialMap_single]
    exact fun h => hi (Subtype.ext h)
theorem laurent_span_closure_eq_top :
    (Submodule.span ℂ (Set.range (monomialMap (ι:=ι)))).topologicalClosure = ⊤:=by
  rw [← laurentAlgebra_eq_span]
  exact congrArg (Subalgebra.toSubmodule ∘ StarSubalgebra.toSubalgebra)
    (ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints
      (laurentAlgebra ι) laurentAlgebra_separatesPoints)
theorem exists_finite_laurent_approximation (F:C(ι → Circle,ℂ))
    {ε:ℝ} (hε:0 < ε) :
    ∃ (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ),
      ∀ z, ‖F z - polynomial S c z‖ < ε:=by
  classical
  have hcl:F ∈ closure (Submodule.span ℂ (Set.range (monomialMap (ι:=ι))):Set C(ι → Circle,ℂ)):=by
    change F ∈ (Submodule.span ℂ (Set.range (monomialMap (ι:=ι)))).topologicalClosure
    rw [laurent_span_closure_eq_top]
    trivial
  obtain ⟨P,hP,hdist⟩:=Metric.mem_closure_iff.mp hcl ε hε
  obtain ⟨c,hc⟩:=Finsupp.mem_span_range_iff_exists_finsupp.mp hP
  refine ⟨c.support,c, ?_⟩
  intro z
  have heval:P z = polynomial c.support c z:=by
    rw [← hc]
    simp only [Finsupp.sum,ContinuousMap.sum_apply,ContinuousMap.smul_apply,
      smul_eq_mul,monomialMap,ContinuousMap.coe_mk,polynomial]
  rw [← heval, ← dist_eq_norm]
  exact (ContinuousMap.dist_apply_le_dist (f:=F) (g:=P) z).trans_lt hdist
end Green24Proof.CircleLaurentApproximation
private def zz2436:"s0984"="s0984":=by decide+kernel
end 
section 
namespace Green24Proof.IntegerMomentCurve
open scoped BigOperators
def frequency {d:ℕ} (w m:Fin d → ℤ):ℤ:=∑ i,m i * w i
def weights (d:ℕ) (a:ℤ) (i:Fin d):ℤ:=a ^ i.val
theorem weights_zero (d:ℕ) (a:ℤ):weights (d + 1) a 0 = 1:=by
  simp [weights]
private def zz1862:"s0746"="s0746":=by decide+kernel
theorem frequency_eq_eval {d:ℕ} (m:Fin d → ℤ) (a:ℤ) :
    frequency (weights d a) m = (Polynomial.ofFn d m).eval a:=by
  rw [Polynomial.ofFn_eq_sum_monomial]
  simp only [Polynomial.eval_finsetSum,Polynomial.eval_monomial,frequency,weights]
theorem exists_avoiding_weights {d:ℕ} (S:Finset (Fin d → ℤ)) :
    ∃ a:ℤ, ∀ m ∈ S,m ≠ 0 → frequency (weights d a) m ≠ 0:=by
  classical
  let P:Polynomial ℤ:=∏ m ∈ S.erase 0,Polynomial.ofFn d m
  have hP:P ≠ 0:=by
    apply Finset.prod_ne_zero_iff.mpr
    intro m hm hzero
    apply (Finset.mem_erase.mp hm).1
    apply Polynomial.injective_ofFn d
    simpa only [map_zero] using hzero
  obtain ⟨a,ha⟩:∃ a:ℤ,P.eval a ≠ 0:=by
    by_contra h
    push Not at h
    exact hP (Polynomial.zero_of_eval_zero P h)
  refine ⟨a, ?_⟩
  intro m hm hm0
  rw [frequency_eq_eval]
  have heval:(∏ v ∈ S.erase 0,(Polynomial.ofFn d v).eval a) ≠ 0:=by
    simpa only [P,Polynomial.eval_prod] using ha
  exact Finset.prod_ne_zero_iff.mp heval m (Finset.mem_erase.mpr ⟨hm0,hm⟩)
theorem exists_weights_first_one (d:ℕ) (S:Finset (Fin (d + 1) → ℤ)) :
    ∃ w:Fin (d + 1) → ℤ,w 0 = 1 ∧ ∀ m ∈ S,m ≠ 0 → frequency w m ≠ 0:=by
  obtain ⟨a,ha⟩:=exists_avoiding_weights S
  exact ⟨weights (d + 1) a,weights_zero d a,ha⟩
end Green24Proof.IntegerMomentCurve
private def zz2437:"s0985"="s0985":=by decide+kernel
end 
section 
namespace Green24Proof.CircleTorusOrbit
open MeasureTheory Finset
open scoped BigOperators
open Green24Proof.CircleProbabilityHaar Green24Proof.CyclicTorusLaurent
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CircleLaurentApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
noncomputable def orbit (w:ι → ℤ) (z:Circle):ι → Circle:=fun i => z ^ w i
omit [Fintype ι] in
theorem orbit_continuous (w:ι → ℤ):Continuous (orbit w):=by
  unfold orbit
  fun_prop
private def zz1863:"s0747"="s0747":=by decide+kernel
omit [Fintype ι] in
theorem orbit_div (w:ι → ℤ) (y z:Circle):orbit w (z / y) = orbit w z / orbit w y:=by
  funext i
  exact div_zpow _ _ _
def Nonresonant (w:ι → ℤ) (S:Finset (ι → ℤ)):Prop :=
  ∀ m ∈ S,m ≠ 0 → ∑ i,m i * w i ≠ 0
theorem integral_circle_zpow (n:ℤ) :
    (∫ z:Circle,(z:ℂ) ^ n ∂circleHaar) = if n = 0 then 1 else 0:=by
  letI:=circleHaar_isProbabilityMeasure
  letI:=circleHaar_isHaarMeasure
  classical
  by_cases hn:n = 0
  · simp [hn]
  · rw [if_neg hn]
    have hm:(fun _:Fin 1 => n) ≠ 0:=fun h => hn (congrFun h 0)
    obtain ⟨w,hw⟩:=exists_monomial_ne_one hm
    have hw':(w 0:ℂ) ^ n ≠ 1:=by
      simpa only [monomial,Fin.prod_univ_one] using hw
    have htrans:=integral_mul_left_eq_self (μ:=circleHaar) (fun z:Circle => (z:ℂ) ^ n) (w 0)
    simp only [Circle.coe_mul,mul_zpow] at htrans
    rw [integral_const_mul] at htrans
    have hzero:((w 0:ℂ) ^ n - 1) * (∫ z:Circle,(z:ℂ) ^ n ∂circleHaar) = 0:=by
      linear_combination htrans
    exact (mul_eq_zero.mp hzero).resolve_left (sub_ne_zero.mpr hw')
theorem monomial_orbit (w m:ι → ℤ) (z:Circle) :
    monomial m (orbit w z) = (z:ℂ) ^ (∑ i,m i * w i):=by
  classical
  have hp (S:Finset ι) :
      (∏ i ∈ S,(z:ℂ) ^ (w i * m i)) = (z:ℂ) ^ (∑ i ∈ S,w i * m i):=by
    induction S using Finset.induction_on with
    | empty => simp
    | @insert a S ha ih =>
      rw [Finset.prod_insert ha,Finset.sum_insert ha,ih,zpow_add₀ (Circle.coe_ne_zero z)]
  simp only [monomial,orbit,Circle.coe_zpow, ← zpow_mul]
  rw [hp]
  congr 1
  apply Finset.sum_congr rfl
  intro i _
  exact mul_comm _ _
theorem integral_monomial_orbit (w m:ι → ℤ) :
    (∫ z,monomial m (orbit w z) ∂circleHaar) =
      if (∑ i,m i * w i) = 0 then 1 else 0:=by
  simp_rw [monomial_orbit]
  exact integral_circle_zpow _
private def zz1864:"s0748"="s0748":=by decide+kernel
theorem polynomial_continuous (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ) :
    Continuous (polynomial S c):=by
  unfold polynomial
  exact continuous_finsetSum _ (fun m _ => continuous_const.mul (monomial_continuous m))
theorem integral_polynomial_orbit (w:ι → ℤ) (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ)
    (hw:Nonresonant w S) :
    (∫ z,polynomial S c (orbit w z) ∂circleHaar) = ∫ z,polynomial S c z ∂torusHaar ι:=by
  letI:=circleHaar_isProbabilityMeasure
  classical
  rw [integral_polynomial]
  change (∫ z, ∑ m ∈ S,c m * monomial m (orbit w z) ∂circleHaar) = _
  rw [integral_finsetSum]
  · unfold constantCoefficient
    apply Finset.sum_congr rfl
    intro m hm
    rw [integral_const_mul,integral_monomial_orbit]
    by_cases hm0:m = 0
    · subst m
      simp
    · simp only [if_neg hm0,if_neg (hw m hm hm0),mul_zero]
  · intro m _
    exact (continuous_const.mul ((monomial_continuous m).comp
      (orbit_continuous w))).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
omit [Fintype ι] in
theorem integral_orbit_error (w:ι → ℤ) (F P:(ι → Circle) → ℂ)
    (hF:Continuous F) (hP:Continuous P) {ε:ℝ}
    (herr:∀ z, ‖F z - P z‖ ≤ ε) :
    ‖(∫ z,F (orbit w z) ∂circleHaar) - ∫ z,P (orbit w z) ∂circleHaar‖ ≤ ε:=by
  letI:=circleHaar_isProbabilityMeasure
  have hFi:Integrable (fun z => F (orbit w z)) circleHaar :=
    (hF.comp (orbit_continuous w)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
  have hPi:Integrable (fun z => P (orbit w z)) circleHaar :=
    (hP.comp (orbit_continuous w)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
  rw [← integral_sub hFi hPi]
  simpa only [probReal_univ,mul_one] using
    norm_integral_le_of_norm_le_const (μ:=circleHaar) (Filter.Eventually.of_forall (fun z => herr _))
theorem integral_orbit_discrepancy (w:ι → ℤ) (S:Finset (ι → ℤ)) (c:(ι → ℤ) → ℂ)
    (F:(ι → Circle) → ℂ) (hF:Continuous F) (hw:Nonresonant w S) {ε:ℝ}
    (herr:∀ z, ‖F z - polynomial S c z‖ ≤ ε) :
    ‖(∫ z,F (orbit w z) ∂circleHaar) - ∫ z,F z ∂torusHaar ι‖ ≤ 2 * ε:=by
  letI:=torusHaar_isProbabilityMeasure ι
  have ho:=integral_orbit_error w F (polynomial S c) hF (polynomial_continuous S c) herr
  have hi:‖(∫ z,polynomial S c z ∂torusHaar ι) - ∫ z,F z ∂torusHaar ι‖ ≤ ε:=by
    rw [norm_sub_rev, ← integral_sub
      (hF.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))
      (polynomial_integrable S c)]
    simpa only [probReal_univ,mul_one] using
      norm_integral_le_of_norm_le_const (μ:=torusHaar ι) (Filter.Eventually.of_forall herr)
  have hp:=integral_polynomial_orbit w S c hw
  calc
    _ = ‖((∫ z,F (orbit w z) ∂circleHaar) - ∫ z,polynomial S c (orbit w z) ∂circleHaar) +
        ((∫ z,polynomial S c z ∂torusHaar ι) - ∫ z,F z ∂torusHaar ι)‖:=by
      rw [hp,sub_add_sub_cancel]
    _ ≤ _ + _:=norm_add_le _ _
    _ ≤ ε + ε:=add_le_add ho hi
    _ = 2 * ε:=by ring
private def zz1865:"s0749"="s0749":=by decide+kernel
theorem exists_approximation_support (F:(ι → Circle) → ℂ) (hF:Continuous F)
    {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (ι → ℤ), ∀ w:ι → ℤ,Nonresonant w S →
      ‖(∫ z,F (orbit w z) ∂circleHaar) - ∫ z,F z ∂torusHaar ι‖ ≤ 2 * ε:=by
  obtain ⟨S,c,hc⟩:=exists_finite_laurent_approximation ⟨F,hF⟩ hε
  exact ⟨S,fun w hw => integral_orbit_discrepancy w S c F hF hw (fun z => (hc z).le)⟩
theorem exists_approximation_first_one (d:ℕ) (F:(Fin (d + 1) → Circle) → ℂ)
    (hF:Continuous F) {ε:ℝ} (hε:0 < ε) :
    ∃ w:Fin (d + 1) → ℤ,w 0 = 1 ∧
      ‖(∫ z,F (orbit w z) ∂circleHaar) - ∫ z,F z ∂torusHaar (Fin (d + 1))‖ ≤ 2 * ε:=by
  obtain ⟨S,hS⟩:=exists_approximation_support F hF hε
  obtain ⟨w,hw,hnon⟩:=IntegerMomentCurve.exists_weights_first_one d S
  exact ⟨w,hw,hS w hnon⟩
end Green24Proof.CircleTorusOrbit
private def zz2438:"s0986"="s0986":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusPairDiscrepancy
open Finset MeasureTheory
open scoped BigOperators
open Green24Proof.CyclicTorusLaurent
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι κ:Type*} [Fintype ι] [Fintype κ]
abbrev PairTorus (ι κ:Type*):=(ι → Circle) × (κ → Circle)
abbrev PairExponent (ι κ:Type*):=(ι → ℤ) × (κ → ℤ)
noncomputable def pairMonomial (m:PairExponent ι κ) (z:PairTorus ι κ):ℂ :=
  monomial m.1 z.1 * monomial m.2 z.2
noncomputable def pairPolynomial (S:Finset (PairExponent ι κ))
    (c:PairExponent ι κ → ℂ) (z:PairTorus ι κ):ℂ :=
  ∑ m ∈ S,c m * pairMonomial m z
noncomputable def pairHaar:Measure (PairTorus ι κ):=(torusHaar ι).prod (torusHaar κ)
theorem pairHaar_isProbabilityMeasure:IsProbabilityMeasure (pairHaar (ι:=ι) (κ:=κ)):=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isProbabilityMeasure κ
  unfold pairHaar
  infer_instance
theorem pairMonomial_continuous (m:PairExponent ι κ):Continuous (pairMonomial m) :=
  ((monomial_continuous m.1).comp continuous_fst).mul
    ((monomial_continuous m.2).comp continuous_snd)
private def zz1866:"s074a"="s074a":=by decide+kernel
theorem pairMonomial_integrable (m:PairExponent ι κ) :
    Integrable (pairMonomial m) pairHaar:=by
  letI:=pairHaar_isProbabilityMeasure (ι:=ι) (κ:=κ)
  exact (pairMonomial_continuous m).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
theorem integral_pairMonomial (m:PairExponent ι κ) :
    (∫ z,pairMonomial m z ∂pairHaar) =
      (if m.1 = 0 then 1 else 0) * (if m.2 = 0 then 1 else 0):=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isProbabilityMeasure κ
  classical
  change (∫ z,monomial m.1 z.1 * monomial m.2 z.2
    ∂(torusHaar ι).prod (torusHaar κ)) = _
  rw [integral_prod_mul,integral_monomial,integral_monomial]
theorem pairPolynomial_integrable (S:Finset (PairExponent ι κ))
    (c:PairExponent ι κ → ℂ):Integrable (pairPolynomial S c) pairHaar:=by
  apply integrable_finsetSum
  intro m _
  exact (pairMonomial_integrable m).const_mul (c m)
theorem integral_pairPolynomial (S:Finset (PairExponent ι κ))
    (c:PairExponent ι κ → ℂ) :
    (∫ z,pairPolynomial S c z ∂pairHaar) =
      ∑ m ∈ S,c m * ∫ z,pairMonomial m z ∂pairHaar:=by
  unfold pairPolynomial
  rw [integral_finsetSum]
  · simp only [integral_const_mul]
  · intro m _
    exact (pairMonomial_integrable m).const_mul (c m)
variable {q:ℕ} [NeZero q]
noncomputable def pairOrbitMean (ks:ι → ZMod q) (ls:κ → ZMod q)
    (F:PairTorus ι κ → ℂ):ℂ :=
  ((q:ℂ) ^ 2)⁻¹ * ∑ p:ZMod q × ZMod q,
    F (fun i => ZMod.toCircle (-(p.1 * ks i)),fun j => ZMod.toCircle (-(p.2 * ls j)))
private def zz1867:"s074b"="s074b":=by decide+kernel
theorem pairOrbitMean_monomial (ks:ι → ZMod q) (ls:κ → ZMod q)
    (m:PairExponent ι κ) :
    pairOrbitMean ks ls (pairMonomial m) =
      (if weightedFrequency ks m.1 = 0 then 1 else 0) *
      (if weightedFrequency ls m.2 = 0 then 1 else 0):=by
  classical
  unfold pairOrbitMean pairMonomial
  rw [Fintype.sum_prod_type]
  have hfactor:(∑ x:ZMod q, ∑ y:ZMod q,
      monomial m.1 (fun i => ZMod.toCircle (-(x * ks i))) *
      monomial m.2 (fun j => ZMod.toCircle (-(y * ls j)))) =
      (∑ x:ZMod q,monomial m.1 (fun i => ZMod.toCircle (-(x * ks i)))) *
      (∑ y:ZMod q,monomial m.2 (fun j => ZMod.toCircle (-(y * ls j)))):=by
    rw [Finset.sum_mul]
    apply Finset.sum_congr rfl
    intro x _
    rw [Finset.mul_sum]
  rw [hfactor,sum_monomial_character_values,sum_monomial_character_values]
  have hq:(q:ℂ) ≠ 0:=by exact_mod_cast NeZero.ne q
  split_ifs <;> simp [pow_two]
  field_simp
theorem pairOrbitMean_polynomial (ks:ι → ZMod q) (ls:κ → ZMod q)
    (S:Finset (PairExponent ι κ)) (c:PairExponent ι κ → ℂ) :
    pairOrbitMean ks ls (pairPolynomial S c) =
      ∑ m ∈ S,c m * pairOrbitMean ks ls (pairMonomial m):=by
  unfold pairOrbitMean pairPolynomial
  rw [Finset.sum_comm,Finset.mul_sum]
  apply Finset.sum_congr rfl
  intro m _
  rw [← Finset.mul_sum]
  ring
theorem pairOrbitMean_polynomial_eq_haar_integral
    [DecidableEq (ι → ℤ)] [DecidableEq (κ → ℤ)]
    (ks:ι → ZMod q) (ls:κ → ZMod q)
    (S:Finset (PairExponent ι κ)) (c:PairExponent ι κ → ℂ)
    (hk:Nonresonant ks (S.image Prod.fst)) (hl:Nonresonant ls (S.image Prod.snd)) :
    pairOrbitMean ks ls (pairPolynomial S c) = ∫ z,pairPolynomial S c z ∂pairHaar:=by
  classical
  rw [pairOrbitMean_polynomial,integral_pairPolynomial]
  apply Finset.sum_congr rfl
  intro m hm
  have hk':weightedFrequency ks m.1 = 0 ↔ m.1 = 0:=by
    constructor
    · intro h
      by_contra hn
      exact hk m.1 (Finset.mem_image.mpr ⟨m,hm,rfl⟩) hn h
    · rintro h
      rw [h,weightedFrequency_zero]
  have hl':weightedFrequency ls m.2 = 0 ↔ m.2 = 0:=by
    constructor
    · intro h
      by_contra hn
      exact hl m.2 (Finset.mem_image.mpr ⟨m,hm,rfl⟩) hn h
    · rintro h
      rw [h,weightedFrequency_zero]
  simp only [pairOrbitMean_monomial,integral_pairMonomial,hk',hl']
  split_ifs <;> rfl
omit [Fintype ι] [Fintype κ] in
theorem pairOrbitMean_error_le (ks:ι → ZMod q) (ls:κ → ZMod q)
    (F P:PairTorus ι κ → ℂ) {ε:ℝ} (herr:∀ z, ‖F z - P z‖ ≤ ε) :
    ‖pairOrbitMean ks ls F - pairOrbitMean ks ls P‖ ≤ ε:=by
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  have hs:‖∑ p:ZMod q × ZMod q,
      (F (fun i => ZMod.toCircle (-(p.1 * ks i)),fun j => ZMod.toCircle (-(p.2 * ls j))) -
       P (fun i => ZMod.toCircle (-(p.1 * ks i)),fun j => ZMod.toCircle (-(p.2 * ls j))))‖ ≤
      (q:ℝ) ^ 2 * ε:=by
    calc
      _ ≤ ∑ p:ZMod q × ZMod q, ‖F
          (fun i => ZMod.toCircle (-(p.1 * ks i)),fun j => ZMod.toCircle (-(p.2 * ls j))) -
          P (fun i => ZMod.toCircle (-(p.1 * ks i)),fun j => ZMod.toCircle (-(p.2 * ls j)))‖:=norm_sum_le _ _
      _ ≤ ∑ _p:ZMod q × ZMod q,ε:=Finset.sum_le_sum (fun _ _ => herr _)
      _ = _:=by simp [Fintype.card_prod,ZMod.card,pow_two]
  rw [pairOrbitMean,pairOrbitMean, ← mul_sub, ← Finset.sum_sub_distrib,norm_mul,
    norm_inv,norm_pow,Complex.norm_natCast]
  calc
    ((q:ℝ) ^ 2)⁻¹ * _ ≤ ((q:ℝ) ^ 2)⁻¹ * ((q:ℝ) ^ 2 * ε) :=
      mul_le_mul_of_nonneg_left hs (inv_nonneg.mpr (sq_nonneg _))
    _ = ε:=by field_simp
private def zz1868:"s074c"="s074c":=by decide+kernel
theorem pairOrbitMean_haar_discrepancy_of_continuous
    [DecidableEq (ι → ℤ)] [DecidableEq (κ → ℤ)]
    (ks:ι → ZMod q) (ls:κ → ZMod q)
    (S:Finset (PairExponent ι κ)) (c:PairExponent ι κ → ℂ)
    (F:PairTorus ι κ → ℂ) (hF:Continuous F)
    (hk:Nonresonant ks (S.image Prod.fst)) (hl:Nonresonant ls (S.image Prod.snd))
    {ε:ℝ} (herr:∀ z, ‖F z - pairPolynomial S c z‖ ≤ ε) :
    ‖pairOrbitMean ks ls F - ∫ z,F z ∂pairHaar‖ ≤ 2 * ε:=by
  letI:=pairHaar_isProbabilityMeasure (ι:=ι) (κ:=κ)
  have hFi:Integrable F pairHaar :=
    hF.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
  have ho:=pairOrbitMean_error_le ks ls F (pairPolynomial S c) herr
  have hi:‖(∫ z,F z ∂pairHaar) - ∫ z,pairPolynomial S c z ∂pairHaar‖ ≤ ε:=by
    rw [← integral_sub hFi (pairPolynomial_integrable S c)]
    simpa only [probReal_univ,mul_one] using
      norm_integral_le_of_norm_le_const (μ:=pairHaar) (Filter.Eventually.of_forall herr)
  have hp:=pairOrbitMean_polynomial_eq_haar_integral ks ls S c hk hl
  calc
    ‖pairOrbitMean ks ls F - ∫ z,F z ∂pairHaar‖ =
        ‖(pairOrbitMean ks ls F - pairOrbitMean ks ls (pairPolynomial S c)) +
          ((∫ z,pairPolynomial S c z ∂pairHaar) - ∫ z,F z ∂pairHaar)‖:=by
      rw [← hp,sub_add_sub_cancel]
    _ ≤ ‖pairOrbitMean ks ls F - pairOrbitMean ks ls (pairPolynomial S c)‖ +
        ‖(∫ z,pairPolynomial S c z ∂pairHaar) - ∫ z,F z ∂pairHaar‖:=norm_add_le _ _
    _ ≤ ε + ε:=add_le_add ho (by simpa only [norm_sub_rev] using hi)
    _ = 2 * ε:=by ring
end Green24Proof.CyclicTorusPairDiscrepancy
private def zz2439:"s0987"="s0987":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusPairApproximation
open Finset MeasureTheory
open scoped BigOperators
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusPairDiscrepancy
open Green24Proof.CircleLaurentApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι κ:Type*} [Fintype ι] [Fintype κ]
def joinTorus (p:PairTorus ι κ):(ι ⊕ κ) → Circle:=Sum.elim p.1 p.2
def splitTorus (z:(ι ⊕ κ) → Circle):PairTorus ι κ :=
  (fun i => z (Sum.inl i),fun j => z (Sum.inr j))
def exponentEquiv:((ι ⊕ κ) → ℤ) ≃ PairExponent ι κ where
  toFun m:=(fun i => m (Sum.inl i),fun j => m (Sum.inr j))
  invFun m:=Sum.elim m.1 m.2
  left_inv m:=by funext i; cases i <;> rfl
  right_inv m:=by rcases m with ⟨m,n⟩; rfl
omit [Fintype ι] [Fintype κ] in
theorem splitTorus_joinTorus (p:PairTorus ι κ):splitTorus (joinTorus p) = p:=by
  rcases p with ⟨z,w⟩
  rfl
omit [Fintype ι] [Fintype κ] in
theorem splitTorus_continuous:Continuous (splitTorus (ι:=ι) (κ:=κ)):=by
  unfold splitTorus
  fun_prop
theorem monomial_joinTorus (m:(ι ⊕ κ) → ℤ) (p:PairTorus ι κ) :
    monomial m (joinTorus p) = pairMonomial (exponentEquiv m) p:=by
  simp only [monomial,Fintype.prod_sum_type,joinTorus,Sum.elim_inl,Sum.elim_inr,
    pairMonomial,exponentEquiv,Equiv.coe_fn_mk]
private def zz1869:"s074d"="s074d":=by decide+kernel
theorem pairPolynomial_map (S:Finset ((ι ⊕ κ) → ℤ))
    (c:((ι ⊕ κ) → ℤ) → ℂ) (p:PairTorus ι κ) :
    pairPolynomial (S.map exponentEquiv.toEmbedding) (fun m => c (exponentEquiv.symm m)) p =
      polynomial S c (joinTorus p):=by
  simp only [pairPolynomial,Finset.sum_map,Equiv.coe_toEmbedding,Equiv.symm_apply_apply,
    polynomial,monomial_joinTorus]
theorem exists_finite_pair_laurent_approximation (F:PairTorus ι κ → ℂ)
    (hF:Continuous F) {ε:ℝ} (hε:0 < ε) :
    ∃ (S:Finset (PairExponent ι κ)) (c:PairExponent ι κ → ℂ),
      ∀ z, ‖F z - pairPolynomial S c z‖ < ε:=by
  let F':C((ι ⊕ κ) → Circle,ℂ):=⟨fun z => F (splitTorus z),hF.comp splitTorus_continuous⟩
  obtain ⟨S,c,herr⟩:=exists_finite_laurent_approximation F' hε
  refine ⟨S.map exponentEquiv.toEmbedding,fun m => c (exponentEquiv.symm m), ?_⟩
  intro p
  rw [pairPolynomial_map]
  simpa only [F',ContinuousMap.coe_mk,splitTorus_joinTorus] using herr (joinTorus p)
variable {q:ℕ} [NeZero q]
theorem exists_pair_discrepancy_support (F:PairTorus ι κ → ℂ)
    (hF:Continuous F) {ε:ℝ} (hε:0 < ε) :
    ∃ (S:Finset (PairExponent ι κ)) (c:PairExponent ι κ → ℂ),
      (∀ z, ‖F z - pairPolynomial S c z‖ < ε) ∧
      ∀ (ks:ι → ZMod q) (ls:κ → ZMod q),
        Nonresonant ks (S.image Prod.fst) → Nonresonant ls (S.image Prod.snd) →
        ‖pairOrbitMean ks ls F - ∫ z,F z ∂pairHaar‖ ≤ 2 * ε:=by
  classical
  obtain ⟨S,c,herr⟩:=exists_finite_pair_laurent_approximation F hF hε
  exact ⟨S,c,herr,fun ks ls hk hl =>
    pairOrbitMean_haar_discrepancy_of_continuous ks ls S c F hF hk hl (fun z => (herr z).le)⟩
end Green24Proof.CyclicTorusPairApproximation
private def zz2440:"s0988"="s0988":=by decide+kernel
end 
section 
namespace Green24Proof.CircleTorusPairOrbit
open MeasureTheory Finset
open scoped BigOperators
open Green24Proof.CircleProbabilityHaar Green24Proof.CircleTorusOrbit
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairDiscrepancy
open Green24Proof.CyclicTorusPairApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
noncomputable def pairOrbit (w:ι → ℤ) (yz:Circle × Circle):PairTorus ι ι :=
  (orbit w yz.1,orbit w yz.2)
omit [Fintype ι] in
theorem pairOrbit_continuous (w:ι → ℤ):Continuous (pairOrbit w) :=
  ((orbit_continuous w).comp continuous_fst).prodMk ((orbit_continuous w).comp continuous_snd)
private def zz1870:"s074e"="s074e":=by decide+kernel
theorem integral_pairMonomial_orbit (w:ι → ℤ) (m:PairExponent ι ι) :
    (∫ yz,pairMonomial m (pairOrbit w yz) ∂circleHaar.prod circleHaar) =
      (if (∑ i,m.1 i * w i) = 0 then 1 else 0) *
      (if (∑ i,m.2 i * w i) = 0 then 1 else 0):=by
  letI:=circleHaar_isProbabilityMeasure
  change (∫ yz,CyclicTorusLaurent.monomial m.1 (orbit w yz.1) *
    CyclicTorusLaurent.monomial m.2 (orbit w yz.2) ∂circleHaar.prod circleHaar) = _
  rw [integral_prod_mul (fun z:Circle => CyclicTorusLaurent.monomial m.1 (orbit w z))
    (fun z:Circle => CyclicTorusLaurent.monomial m.2 (orbit w z)),
    integral_monomial_orbit,integral_monomial_orbit]
theorem pairPolynomial_continuous (S:Finset (PairExponent ι ι)) (c:PairExponent ι ι → ℂ) :
    Continuous (pairPolynomial S c):=by
  unfold pairPolynomial
  exact continuous_finsetSum _ (fun m _ => continuous_const.mul (pairMonomial_continuous m))
theorem integral_pairPolynomial_orbit (w:ι → ℤ) (S:Finset (PairExponent ι ι))
    (c:PairExponent ι ι → ℂ)
    (h1:CircleTorusOrbit.Nonresonant w (S.image Prod.fst))
    (h2:CircleTorusOrbit.Nonresonant w (S.image Prod.snd)) :
    (∫ yz,pairPolynomial S c (pairOrbit w yz) ∂circleHaar.prod circleHaar) =
      ∫ yz,pairPolynomial S c yz ∂pairHaar:=by
  letI:=circleHaar_isProbabilityMeasure
  classical
  rw [integral_pairPolynomial]
  change (∫ yz, ∑ m ∈ S,c m * pairMonomial m (pairOrbit w yz)
    ∂circleHaar.prod circleHaar) = _
  rw [integral_finsetSum]
  · apply Finset.sum_congr rfl
    intro m hm
    rw [integral_const_mul,integral_pairMonomial_orbit,integral_pairMonomial]
    have hf:((∑ i,m.1 i * w i) = 0) ↔ m.1 = 0:=by
      constructor
      · intro hz
        by_contra hn
        exact h1 _ (Finset.mem_image.mpr ⟨m,hm,rfl⟩) hn hz
      · intro hz
        simp [hz]
    have hs:((∑ i,m.2 i * w i) = 0) ↔ m.2 = 0:=by
      constructor
      · intro hz
        by_contra hn
        exact h2 _ (Finset.mem_image.mpr ⟨m,hm,rfl⟩) hn hz
      · intro hz
        simp [hz]
    simp only [hf,hs]
  · intro m _
    exact (continuous_const.mul ((pairMonomial_continuous m).comp
      (pairOrbit_continuous w))).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
omit [Fintype ι] in
theorem integral_pairOrbit_error (w:ι → ℤ) (F P:PairTorus ι ι → ℂ)
    (hF:Continuous F) (hP:Continuous P) {ε:ℝ}
    (herr:∀ z, ‖F z - P z‖ ≤ ε) :
    ‖(∫ yz,F (pairOrbit w yz) ∂circleHaar.prod circleHaar) -
      ∫ yz,P (pairOrbit w yz) ∂circleHaar.prod circleHaar‖ ≤ ε:=by
  letI:=circleHaar_isProbabilityMeasure
  have hFi:Integrable (fun z => F (pairOrbit w z)) (circleHaar.prod circleHaar) :=
    (hF.comp (pairOrbit_continuous w)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
  have hPi:Integrable (fun z => P (pairOrbit w z)) (circleHaar.prod circleHaar) :=
    (hP.comp (pairOrbit_continuous w)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
  rw [← integral_sub hFi hPi]
  simpa only [probReal_univ,mul_one] using norm_integral_le_of_norm_le_const
    (μ:=circleHaar.prod circleHaar) (Filter.Eventually.of_forall (fun z => herr _))
private def zz1871:"s074f"="s074f":=by decide+kernel
theorem integral_pairOrbit_discrepancy (w:ι → ℤ) (S:Finset (PairExponent ι ι))
    (c:PairExponent ι ι → ℂ) (F:PairTorus ι ι → ℂ) (hF:Continuous F)
    (h1:CircleTorusOrbit.Nonresonant w (S.image Prod.fst))
    (h2:CircleTorusOrbit.Nonresonant w (S.image Prod.snd)) {ε:ℝ}
    (herr:∀ z, ‖F z - pairPolynomial S c z‖ ≤ ε) :
    ‖(∫ yz,F (pairOrbit w yz) ∂circleHaar.prod circleHaar) -
      ∫ yz,F yz ∂pairHaar‖ ≤ 2 * ε:=by
  letI:=pairHaar_isProbabilityMeasure (ι:=ι) (κ:=ι)
  have ho:=integral_pairOrbit_error w F (pairPolynomial S c) hF
    (pairPolynomial_continuous S c) herr
  have hi:‖(∫ z,pairPolynomial S c z ∂pairHaar) - ∫ z,F z ∂pairHaar‖ ≤ ε:=by
    rw [norm_sub_rev, ← integral_sub
      (hF.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))
      (pairPolynomial_integrable S c)]
    simpa only [probReal_univ,mul_one] using
      norm_integral_le_of_norm_le_const (μ:=pairHaar) (Filter.Eventually.of_forall herr)
  have hp:=integral_pairPolynomial_orbit w S c h1 h2
  calc
    _ = ‖((∫ z,F (pairOrbit w z) ∂circleHaar.prod circleHaar) -
        ∫ z,pairPolynomial S c (pairOrbit w z) ∂circleHaar.prod circleHaar) +
        ((∫ z,pairPolynomial S c z ∂pairHaar) - ∫ z,F z ∂pairHaar)‖:=by
      rw [hp,sub_add_sub_cancel]
    _ ≤ _ + _:=norm_add_le _ _
    _ ≤ ε + ε:=add_le_add ho hi
    _ = 2 * ε:=by ring
theorem exists_pair_approximation_support (F:PairTorus ι ι → ℂ) (hF:Continuous F)
    {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (PairExponent ι ι), ∀ w:ι → ℤ,
      CircleTorusOrbit.Nonresonant w (S.image Prod.fst) →
      CircleTorusOrbit.Nonresonant w (S.image Prod.snd) →
      ‖(∫ yz,F (pairOrbit w yz) ∂circleHaar.prod circleHaar) -
        ∫ yz,F yz ∂pairHaar‖ ≤ 2 * ε:=by
  obtain ⟨S,c,hc⟩:=exists_finite_pair_laurent_approximation F hF hε
  exact ⟨S,fun w h1 h2 => integral_pairOrbit_discrepancy w S c F hF h1 h2 (fun z => (hc z).le)⟩
theorem exists_joint_approximation_first_one (d r:ℕ)
    (F:Fin r → (Fin (d + 1) → Circle) → ℂ) (hF:∀ i,Continuous (F i))
    (K:PairTorus (Fin (d + 1)) (Fin (d + 1)) → ℂ) (hK:Continuous K)
    {ε:ℝ} (hε:0 < ε) :
    ∃ w:Fin (d + 1) → ℤ,w 0 = 1 ∧
      (∀ i, ‖(∫ z,F i (orbit w z) ∂circleHaar) - ∫ z,F i z ∂torusHaar (Fin (d + 1))‖ ≤ 2 * ε) ∧
      ‖(∫ yz,K (pairOrbit w yz) ∂circleHaar.prod circleHaar) -
        ∫ yz,K yz ∂pairHaar‖ ≤ 2 * ε:=by
  classical
  choose S hS using fun i => exists_approximation_support (F i) (hF i) hε
  obtain ⟨T,hT⟩:=exists_pair_approximation_support K hK hε
  let U:=(Finset.univ.biUnion S) ∪ (T.image Prod.fst ∪ T.image Prod.snd)
  obtain ⟨w,hw,hn⟩:=IntegerMomentCurve.exists_weights_first_one d U
  have hrestrict (V:Finset (Fin (d + 1) → ℤ)) (hV:V ⊆ U) :
      CircleTorusOrbit.Nonresonant w V:=fun m hm hm0 => hn m (hV hm) hm0
  refine ⟨w,hw, ?_, ?_⟩
  · intro i
    apply hS i w
    apply hrestrict
    exact (Finset.subset_biUnion_of_mem S (Finset.mem_univ i)).trans Finset.subset_union_left
  · apply hT w
    · apply hrestrict
      exact Finset.subset_union_left.trans Finset.subset_union_right
    · apply hrestrict
      exact Finset.subset_union_right.trans Finset.subset_union_right
end Green24Proof.CircleTorusPairOrbit
private def zz2441:"s0989"="s0989":=by decide+kernel
end 
section 
namespace Green24Proof.CircleProductOrbit
open MeasureTheory Set
open scoped BigOperators
open Green24Proof.CircleLiftCounting Green24Proof.CircleTorusOrbit
open Green24Proof.CircleTorusPairOrbit Green24Proof.CircleProbabilityHaar
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
theorem exists_weights_pivot_one {κ:Type*} [Fintype κ] (p:κ)
    (S:Finset (κ → ℤ)) :
    ∃ w:κ → ℤ,w p = 1 ∧ ∀ m ∈ S,m ≠ 0 → (∑ i,m i * w i) ≠ 0:=by
  classical
  have hcard:0 < Fintype.card κ:=Fintype.card_pos_iff.mpr ⟨p⟩
  let d:=Fintype.card κ - 1
  have hd:Fintype.card κ = d + 1:=by omega
  let e₀:κ ≃ Fin (d + 1):=Fintype.equivFinOfCardEq hd
  let e:κ ≃ Fin (d + 1):=e₀.trans (Equiv.swap (e₀ p) 0)
  have hep:e p = 0:=by simp [e]
  let U:Finset (Fin (d + 1) → ℤ):=S.image (fun m => m ∘ e.symm)
  obtain ⟨w,hw,hn⟩:=IntegerMomentCurve.exists_weights_first_one d U
  refine ⟨fun i => w (e i),by change w (e p) = 1; rw [hep,hw], ?_⟩
  intro m hm hm0
  have hm':m ∘ e.symm ≠ 0:=by
    intro hz
    apply hm0
    funext i
    have h:=congrFun hz (e i)
    simpa only [Function.comp_apply,Equiv.symm_apply_apply,Pi.zero_apply] using h
  have h:=hn (m ∘ e.symm) (Finset.mem_image.mpr ⟨m,hm,rfl⟩) hm'
  have heq:(∑ i,m i * w (e i)) = ∑ j,m (e.symm j) * w j:=by
    simpa only [Equiv.symm_apply_apply] using
      e.sum_comp (fun j => m (e.symm j) * w j)
  rwa [heq]
private def zz1872:"s0750"="s0750":=by decide+kernel
theorem exists_joint_approximation_pivot_one {κ:Type*} [Fintype κ] (p:κ) (r:ℕ)
    (F:Fin r → (κ → Circle) → ℂ) (hF:∀ i,Continuous (F i))
    (K:PairTorus κ κ → ℂ) (hK:Continuous K) {ε:ℝ} (hε:0 < ε) :
    ∃ w:κ → ℤ,w p = 1 ∧
      (∀ i, ‖(∫ z,F i (orbit w z) ∂circleHaar) - ∫ z,F i z ∂torusHaar κ‖ ≤ 2 * ε) ∧
      ‖(∫ yz,K (pairOrbit w yz) ∂circleHaar.prod circleHaar) -
        ∫ yz,K yz ∂pairHaar‖ ≤ 2 * ε:=by
  classical
  choose S hS using fun i => exists_approximation_support (F i) (hF i) hε
  obtain ⟨T,hT⟩:=exists_pair_approximation_support K hK hε
  let U:=(Finset.univ.biUnion S) ∪ (T.image Prod.fst ∪ T.image Prod.snd)
  obtain ⟨w,hw,hn⟩:=exists_weights_pivot_one p U
  have hrestrict (V:Finset (κ → ℤ)) (hV:V ⊆ U) :
      CircleTorusOrbit.Nonresonant w V:=fun m hm hm0 => hn m (hV hm) hm0
  refine ⟨w,hw, ?_, ?_⟩
  · intro i
    apply hS i w
    apply hrestrict
    exact (Finset.subset_biUnion_of_mem S (Finset.mem_univ i)).trans Finset.subset_union_left
  · apply hT w
    · apply hrestrict
      exact Finset.subset_union_left.trans Finset.subset_union_right
    · apply hrestrict
      exact Finset.subset_union_right.trans Finset.subset_union_right
variable {ι:Type*} [Fintype ι]
def splitOption:(Option ι → Circle) →* CircleSpace ι where
  toFun z:=(z none,fun i => z (some i))
  map_one':=rfl
  map_mul' _ _:=rfl
omit [Fintype ι] in
theorem splitOption_continuous:Continuous (splitOption (ι:=ι)):=by
  change Continuous (fun z:Option ι → Circle => (z none,fun i => z (some i)))
  fun_prop
omit [Fintype ι] in
theorem splitOption_surjective:Function.Surjective (splitOption (ι:=ι)):=by
  intro v
  exact ⟨fun o => o.elim v.1 v.2,rfl⟩
theorem circleMeasure_haar:Measure.IsHaarMeasure (circleMeasure ι):=by
  letI:=circleHaar_isHaarMeasure
  letI:=torusHaar_isHaarMeasure ι
  unfold circleMeasure
  infer_instance
private def zz1873:"s0751"="s0751":=by decide+kernel
theorem splitOption_measurePreserving :
    MeasurePreserving (splitOption (ι:=ι)) (torusHaar (Option ι)) (circleMeasure ι):=by
  letI:=torusHaar_isHaarMeasure (Option ι)
  letI:=torusHaar_isProbabilityMeasure (Option ι)
  letI:=circleMeasure_haar (ι:=ι)
  letI:=circleMeasure_probability (ι:=ι)
  exact MonoidHom.measurePreserving splitOption_continuous splitOption_surjective (by simp)
theorem integral_splitOption (L:CircleSpace ι → ℂ) (hL:Continuous L) :
    (∫ z,L (splitOption z) ∂torusHaar (Option ι)) = ∫ z,L z ∂circleMeasure ι:=by
  have h:=integral_map (μ:=torusHaar (Option ι))
    splitOption_continuous.measurable.aemeasurable hL.aestronglyMeasurable
  rw [splitOption_measurePreserving.map_eq] at h
  exact h.symm
theorem integral_pair_splitOption (K:CircleSpace ι × CircleSpace ι → ℂ)
    (hK:Continuous K) :
    (∫ yz,K (splitOption yz.1,splitOption yz.2) ∂pairHaar) =
      ∫ yz,K yz ∂(circleMeasure ι).prod (circleMeasure ι):=by
  letI:=torusHaar_isProbabilityMeasure (Option ι)
  letI:=circleMeasure_probability (ι:=ι)
  have hp:=(splitOption_measurePreserving (ι:=ι)).prod
    (splitOption_measurePreserving (ι:=ι))
  have h:=integral_map (μ:=(torusHaar (Option ι)).prod (torusHaar (Option ι)))
    hp.measurable.aemeasurable hK.aestronglyMeasurable
  rw [hp.map_eq] at h
  exact h.symm
noncomputable def productOrbit (w:ι → ℤ) (z:Circle):CircleSpace ι:=(z,orbit w z)
omit [Fintype ι] in
theorem productOrbit_continuous (w:ι → ℤ):Continuous (productOrbit w) :=
  continuous_id.prodMk (orbit_continuous w)
private def zz1874:"s0752"="s0752":=by decide+kernel
omit [Fintype ι] in
theorem productOrbit_div (w:ι → ℤ) (z y:Circle) :
    productOrbit w (z / y) = productOrbit w z / productOrbit w y:=by
  change (z / y,orbit w (z / y)) = (z / y,orbit w z / orbit w y)
  rw [orbit_div]
theorem exists_joint_approximation_complex (r:ℕ)
    (F:Fin r → CircleSpace ι → ℂ) (hF:∀ i,Continuous (F i))
    (K:CircleSpace ι × CircleSpace ι → ℂ) (hK:Continuous K)
    {ε:ℝ} (hε:0 < ε) :
    ∃ w:ι → ℤ,
      (∀ i, ‖(∫ z,F i (productOrbit w z) ∂circleHaar) -
        ∫ z,F i z ∂circleMeasure ι‖ ≤ 2 * ε) ∧
      ‖(∫ yz,K (productOrbit w yz.1,productOrbit w yz.2) ∂circleHaar.prod circleHaar) -
        ∫ yz,K yz ∂(circleMeasure ι).prod (circleMeasure ι)‖ ≤ 2 * ε:=by
  obtain ⟨w,hw,hmass,hcount⟩:=exists_joint_approximation_pivot_one
    (none:Option ι) r (fun i z => F i (splitOption z))
    (fun i => (hF i).comp splitOption_continuous)
    (fun yz => K (splitOption yz.1,splitOption yz.2))
    (hK.comp (splitOption_continuous.prodMap splitOption_continuous)) hε
  have ho (z:Circle):splitOption (orbit w z) = productOrbit (fun i => w (some i)) z:=by
    apply Prod.ext
    · change z ^ w none = z
      rw [hw,zpow_one]
    · rfl
  refine ⟨fun i => w (some i), ?_, ?_⟩
  · intro i
    simpa only [ho,integral_splitOption (F i) (hF i)] using hmass i
  · simpa only [pairOrbit,ho,integral_pair_splitOption K hK] using hcount
theorem exists_joint_approximation (r:ℕ)
    (F:Fin r → CircleSpace ι → ℝ) (hF:∀ i,Continuous (F i))
    (K:CircleSpace ι × CircleSpace ι → ℝ) (hK:Continuous K)
    {ε:ℝ} (hε:0 < ε) :
    ∃ w:ι → ℤ,
      (∀ i, |(∫ z,F i (productOrbit w z) ∂circleHaar) -
        ∫ z,F i z ∂circleMeasure ι| ≤ 2 * ε) ∧
      |(∫ yz,K (productOrbit w yz.1,productOrbit w yz.2) ∂circleHaar.prod circleHaar) -
        ∫ yz,K yz ∂(circleMeasure ι).prod (circleMeasure ι)| ≤ 2 * ε:=by
  obtain ⟨w,hm,hc⟩:=exists_joint_approximation_complex r
    (fun i z => (F i z:ℂ)) (fun i => Complex.continuous_ofReal.comp (hF i))
    (fun yz => (K yz:ℂ)) (Complex.continuous_ofReal.comp hK) hε
  refine ⟨w, ?_, ?_⟩
  · intro i
    simpa only [integral_complex_ofReal, ← Complex.ofReal_sub,Complex.norm_real,Real.norm_eq_abs]
      using hm i
  · simpa only [integral_complex_ofReal, ← Complex.ofReal_sub,Complex.norm_real,Real.norm_eq_abs]
      using hc
end Green24Proof.CircleProductOrbit
private def zz2442:"s098a"="s098a":=by decide+kernel
end 
section 
namespace Green24Proof.RealLatticeRiemannSums
open MeasureTheory Set Filter
open scoped BigOperators Topology Pointwise
noncomputable def lineGrid (n M:ℕ):Finset ℝ:=by
  classical
  exact (Finset.Icc (-(M * n:ℤ)) (M * n)).image (fun k:ℤ => (k:ℝ) / n)
theorem mem_lineGrid {n M:ℕ} (hn:0 < n) {x:ℝ} :
    x ∈ lineGrid n M ↔ x ∈ Icc (-(M:ℝ)) M ∧
      (n:ℝ) * x ∈ Set.range (algebraMap ℤ ℝ):=by
  classical
  have hn':(0:ℝ) < n:=by exact_mod_cast hn
  constructor
  · intro hx
    obtain ⟨k,hk,rfl⟩:=Finset.mem_image.mp hx
    have hlo':-((M:ℝ) * n) ≤ k:=by exact_mod_cast (Finset.mem_Icc.mp hk).1
    have hlo:-(M:ℝ) * n ≤ k:=by simpa only [neg_mul] using hlo'
    have hhi:(k:ℝ) ≤ M * n:=by exact_mod_cast (Finset.mem_Icc.mp hk).2
    refine ⟨⟨(le_div_iff₀ hn').mpr hlo,(div_le_iff₀ hn').mpr hhi⟩,k, ?_⟩
    simp only [eq_intCast]
    field_simp
  · rintro ⟨hx,k,hk⟩
    have hk':(k:ℝ) = n * x:=by simpa only [eq_intCast] using hk
    apply Finset.mem_image.mpr
    refine ⟨k,Finset.mem_Icc.mpr ⟨?_, ?_⟩, ?_⟩
    · have h:-((M:ℝ) * n) ≤ k:=by rw [hk']; nlinarith [hx.1]
      exact_mod_cast h
    · have h:(k:ℝ) ≤ M * n:=by rw [hk']; nlinarith [hx.2]
      exact_mod_cast h
    · rw [hk']
      field_simp
private def zz1875:"s0753"="s0753":=by decide+kernel
theorem sub_mem_lineGrid {n M:ℕ} (hn:0 < n) {y z:ℝ}
    (hy:y ∈ lineGrid n M) (hz:z ∈ lineGrid n M):z - y ∈ lineGrid n (2 * M):=by
  obtain ⟨hyb,a,ha⟩:=(mem_lineGrid hn).mp hy
  obtain ⟨hzb,b,hb⟩:=(mem_lineGrid hn).mp hz
  apply (mem_lineGrid hn).mpr
  refine ⟨⟨?_, ?_⟩,b - a, ?_⟩
  · push_cast
    linarith [hyb.2,hzb.1]
  · push_cast
    linarith [hyb.1,hzb.2]
  · simp only [map_sub,ha,hb]
    ring
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def piGrid (n M:ℕ):Finset (ι → ℝ) :=
  Fintype.piFinset (fun _ => lineGrid n M)
def cube (M:ℕ):Set (ι → ℝ):=Icc (fun _ => -(M:ℝ)) (fun _ => (M:ℝ))
theorem piGrid_eq_lattice {n:ℕ} (hn:0 < n) (M:ℕ) :
    (piGrid (ι:=ι) n M:Set (ι → ℝ)) = cube M ∩
      (n:ℝ)⁻¹ • (Submodule.span ℤ (Set.range (Pi.basisFun ℝ ι)):Set (ι → ℝ)):=by
  let:NeZero n:=⟨Nat.ne_of_gt hn⟩
  ext v
  have hlat:v ∈ (n:ℝ)⁻¹ •
      (Submodule.span ℤ (Set.range (Pi.basisFun ℝ ι)):Set (ι → ℝ)) ↔
      ∀ i,(n:ℝ) * v i ∈ Set.range (algebraMap ℤ ℝ):=by
    rw [← Submodule.coe_pointwise_smul]
    exact BoxIntegral.unitPartition.mem_smul_span_iff
  rw [Finset.mem_coe,piGrid,Fintype.mem_piFinset,mem_inter_iff,hlat]
  simp only [mem_lineGrid hn,cube,mem_Icc,Pi.le_def]
  aesop
theorem lattice_sum_eq_piGrid {n:ℕ} (hn:0 < n) (M:ℕ) (F:(ι → ℝ) → ℝ) :
    (∑' v:↑(cube (ι:=ι) M ∩
      (n:ℝ)⁻¹ • (Submodule.span ℤ (Set.range (Pi.basisFun ℝ ι)):Set (ι → ℝ))),F v) =
      ∑ v ∈ piGrid n M,F v:=by
  classical
  rw [← piGrid_eq_lattice hn M]
  rw [tsum_fintype,Finset.sum_set_coe]
  congr 1
  ext v
  simp
theorem tendsto_piGrid_sum (M:ℕ) (F:(ι → ℝ) → ℝ) (hF:Continuous F) :
    Tendsto (fun n:ℕ => (∑ v ∈ piGrid n M,F v) / (n:ℝ) ^ Fintype.card ι)
      atTop (𝓝 (∫ v in cube M,F v)):=by
  have h:=tendsto_tsum_div_pow_atTop_integral (cube (ι:=ι) M) F hF
    (isCompact_Icc.isBounded) measurableSet_Icc ((convex_Icc _ _).addHaar_frontier volume)
  apply h.congr'
  filter_upwards [eventually_gt_atTop (0:ℕ)] with n hn
  rw [lattice_sum_eq_piGrid hn M]
end Green24Proof.RealLatticeRiemannSums
private def zz2443:"s098b"="s098b":=by decide+kernel
end 
section 
namespace Green24Proof.RealGridIntegralLimits
open MeasureTheory Set Filter
open scoped BigOperators Topology
open Green24Proof.RealLatticeRiemannSums
private def zz1876:"s0754"="s0754":=by decide+kernel
theorem mem_cube_one (M:ℕ) (v:Fin 1 → ℝ) :
    v ∈ cube M ↔ v 0 ∈ Icc (-(M:ℝ)) M:=by
  simp only [cube,mem_Icc,Pi.le_def,Fin.forall_fin_one]
theorem mem_cube_two (M:ℕ) (v:Fin 2 → ℝ) :
    v ∈ cube M ↔ (v 0,v 1) ∈ Icc (-(M:ℝ)) M ×ˢ Icc (-(M:ℝ)) M:=by
  simp only [cube,mem_Icc,Pi.le_def,Fin.forall_fin_two,mem_prod]
  tauto
theorem piGrid_sum_one (n M:ℕ) (f:ℝ → ℝ) :
    (∑ v ∈ piGrid (ι:=Fin 1) n M,f (v 0)) = ∑ x ∈ lineGrid n M,f x:=by
  classical
  refine Finset.sum_bij (fun v _ => v 0) ?_ ?_ ?_ ?_
  · intro v hv
    exact Fintype.mem_piFinset.mp hv 0
  · intro v _ w _ hvw
    funext i
    have hi:i = 0:=Subsingleton.elim _ _
    simpa only [hi] using hvw
  · intro x hx
    refine ⟨fun _ => x,Fintype.mem_piFinset.mpr (fun _ => hx),rfl⟩
  · intro v _
    rfl
theorem piGrid_sum_two (n M:ℕ) (K:ℝ × ℝ → ℝ) :
    (∑ v ∈ piGrid (ι:=Fin 2) n M,K (v 0,v 1)) =
      ∑ y ∈ lineGrid n M, ∑ z ∈ lineGrid n M,K (y,z):=by
  classical
  rw [← Finset.sum_product]
  refine Finset.sum_bij (fun v _ => (v 0,v 1)) ?_ ?_ ?_ ?_
  · intro v hv
    exact Finset.mem_product.mpr ⟨Fintype.mem_piFinset.mp hv 0,Fintype.mem_piFinset.mp hv 1⟩
  · intro v _ w _ hvw
    funext i
    fin_cases i
    · exact congrArg Prod.fst hvw
    · exact congrArg Prod.snd hvw
  · intro yz hyz
    refine ⟨![yz.1,yz.2], ?_,rfl⟩
    apply Fintype.mem_piFinset.mpr
    intro i
    fin_cases i
    · exact (Finset.mem_product.mp hyz).1
    · exact (Finset.mem_product.mp hyz).2
  · intro v _
    rfl
private def zz1877:"s0755"="s0755":=by decide+kernel
theorem integral_pi_one (f:ℝ → ℝ):(∫ v:Fin 1 → ℝ,f (v 0)) = ∫ x,f x:=by
  exact (volume_preserving_piUnique (fun _:Fin 1 => ℝ)).integral_comp
    (MeasurableEquiv.piUnique (fun _:Fin 1 => ℝ)).measurableEmbedding f
theorem integral_pi_two (K:ℝ × ℝ → ℝ) :
    (∫ v:Fin 2 → ℝ,K (v 0,v 1)) = ∫ yz,K yz:=by
  exact (volume_preserving_piFinTwo (fun _ => ℝ)).integral_comp
    (MeasurableEquiv.piFinTwo (fun _ => ℝ)).measurableEmbedding K
theorem tendsto_piGrid_sum_full {ι:Type*} [Fintype ι] [DecidableEq ι]
    (M:ℕ) (F:(ι → ℝ) → ℝ) (hF:Continuous F)
    (hs:∀ v,v ∉ cube M → F v = 0) :
    Tendsto (fun n:ℕ => (∑ v ∈ piGrid n M,F v) / (n:ℝ) ^ Fintype.card ι)
      atTop (𝓝 (∫ v,F v)):=by
  have h:=tendsto_piGrid_sum M F hF
  rwa [setIntegral_eq_integral_of_forall_compl_eq_zero hs] at h
theorem tendsto_lineGrid_sum (M:ℕ) (f:ℝ → ℝ) (hf:Continuous f)
    (hs:∀ x,x ∉ Icc (-(M:ℝ)) M → f x = 0) :
    Tendsto (fun n:ℕ => (∑ x ∈ lineGrid n M,f x) / (n:ℝ))
      atTop (𝓝 (∫ x,f x)):=by
  have h:=tendsto_piGrid_sum_full M (fun v:Fin 1 → ℝ => f (v 0))
    (hf.comp (continuous_apply 0)) (fun v hv => hs (v 0) (by simpa only [mem_cube_one] using hv))
  simpa only [piGrid_sum_one,Fintype.card_fin,pow_one,integral_pi_one] using h
private def zz1878:"s0756"="s0756":=by decide+kernel
theorem tendsto_pairGrid_sum (M:ℕ) (K:ℝ × ℝ → ℝ) (hK:Continuous K)
    (hs:∀ yz,yz ∉ Icc (-(M:ℝ)) M ×ˢ Icc (-(M:ℝ)) M → K yz = 0) :
    Tendsto (fun n:ℕ =>
      (∑ y ∈ lineGrid n M, ∑ z ∈ lineGrid n M,K (y,z)) / (n:ℝ) ^ 2)
      atTop (𝓝 (∫ yz,K yz)):=by
  have h:=tendsto_piGrid_sum_full M (fun v:Fin 2 → ℝ => K (v 0,v 1))
    (hK.comp ((continuous_apply 0).prodMk (continuous_apply 1)))
    (fun v hv => hs (v 0,v 1) (by simpa only [mem_cube_two] using hv))
  simpa only [piGrid_sum_two,Fintype.card_fin,integral_pi_two] using h
end Green24Proof.RealGridIntegralLimits
private def zz2444:"s098c"="s098c":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteThreeSetChains
open Finset
open scoped BigOperators
def chainIndex {a b:ℕ} (p:Fin a × Fin b):ℕ :=
  min p.1.val (b - 1 - p.2.val)
theorem chainIndex_lt {a b:ℕ} (p:Fin a × Fin b) :
    chainIndex p < min a b:=by
  dsimp [chainIndex]
  have:=p.1.isLt
  have:=p.2.isLt
  omega
theorem chain_comparable {a b:ℕ} {p q:Fin a × Fin b}
    (h:chainIndex p = chainIndex q) (hpq:p.1 < q.1):p.2 ≤ q.2:=by
  have hp:=p.2.isLt
  have hq:=q.2.isLt
  change p.1.val < q.1.val at hpq
  change p.2.val ≤ q.2.val
  dsimp [chainIndex] at h
  omega
theorem addition_injective_on_chain {a b:ℕ}
    (f:Fin a ↪o ℝ) (g:Fin b ↪o ℝ) (i:ℕ) :
    Set.InjOn (fun p:Fin a × Fin b => f p.1 + g p.2)
      {p | chainIndex p = i}:=by
  intro p hp q hq heq
  have hidx:chainIndex p = chainIndex q:=hp.trans hq.symm
  rcases lt_trichotomy p.1 q.1 with h | h | h
  · have h1:=f.strictMono h
    have h2:=g.monotone (chain_comparable hidx h)
    linarith
  · have h2:p.2 = q.2:=g.injective (by simpa [h] using heq)
    exact Prod.ext h h2
  · have h1:=f.strictMono h
    have h2:=g.monotone (chain_comparable hidx.symm h)
    linarith
private def zz1879:"s0757"="s0757":=by decide+kernel
theorem chain_card_le {a b:ℕ} (i:ℕ) :
    (univ.filter (fun p:Fin a × Fin b => chainIndex p = i)).card ≤
      a + b - 2 * i - 1:=by
  classical
  let S:=univ.filter (fun p:Fin a × Fin b => chainIndex p = i)
  have h:=card_le_card_of_injOn (s:=S) (t:=range (a + b - 2 * i - 1))
    (fun p => p.1.val + p.2.val - i) ?_ ?_
  · simpa using h
  · intro p hp
    have hpi:chainIndex p = i:=(mem_filter.mp hp).2
    have hp1:=p.1.isLt
    have hp2:=p.2.isLt
    change p.1.val + p.2.val - i ∈ range (a + b - 2 * i - 1)
    apply mem_range.mpr
    dsimp [chainIndex] at hpi
    omega
  · intro p hp q hq heq
    have hpi:chainIndex p = i:=(mem_filter.mp hp).2
    have hqi:chainIndex q = i:=(mem_filter.mp hq).2
    have hp1:=p.1.isLt
    have hp2:=p.2.isLt
    have hq1:=q.1.isLt
    have hq2:=q.2.isLt
    dsimp [chainIndex] at hpi hqi
    apply Prod.ext <;> apply Fin.ext <;> dsimp at * <;> omega
theorem ordered_three_set_bound {a b:ℕ}
    (f:Fin a ↪o ℝ) (g:Fin b ↪o ℝ) (C:Finset ℝ) :
    (univ.filter (fun p:Fin a × Fin b => f p.1 + g p.2 ∈ C)).card ≤
      ∑ i ∈ range (min a b),min C.card (a + b - 2 * i - 1):=by
  classical
  let S:=univ.filter (fun p:Fin a × Fin b => f p.1 + g p.2 ∈ C)
  have hpartition:S.card = ∑ i ∈ range (min a b),
      (S.filter (fun p => chainIndex p = i)).card:=by
    exact card_eq_sum_card_fiberwise (fun p _ => mem_range.mpr (chainIndex_lt p))
  rw [show (univ.filter (fun p:Fin a × Fin b => f p.1 + g p.2 ∈ C)).card =
    S.card from rfl,hpartition]
  apply sum_le_sum
  intro i _hi
  apply le_min
  · apply card_le_card_of_injOn (fun p => f p.1 + g p.2)
    · intro p hp
      exact (mem_filter.mp (mem_filter.mp hp).1).2
    · intro p hp q hq heq
      exact addition_injective_on_chain f g i (mem_filter.mp hp).2
        (mem_filter.mp hq).2 heq
  · exact (card_le_card (show S.filter (fun p => chainIndex p = i) ⊆
        univ.filter (fun p => chainIndex p = i) from
      fun p hp => mem_filter.mpr ⟨mem_univ _,(mem_filter.mp hp).2⟩)).trans
        (chain_card_le i)
theorem three_set_chain_bound (A B C:Finset ℝ) :
    ((A ×ˢ B).filter (fun p => p.1 + p.2 ∈ C)).card ≤
      ∑ i ∈ range (min A.card B.card),min C.card (A.card + B.card - 2 * i - 1):=by
  classical
  let f:=A.orderEmbOfFin rfl
  let g:=B.orderEmbOfFin rfl
  have heq:(univ.filter (fun p:Fin A.card × Fin B.card =>
      f p.1 + g p.2 ∈ C)).card = ((A ×ˢ B).filter (fun p => p.1 + p.2 ∈ C)).card:=by
    apply card_bij (fun p _ => (f p.1,g p.2))
    · intro p hp
      exact mem_filter.mpr ⟨mem_product.mpr ⟨A.orderEmbOfFin_mem rfl _,
        B.orderEmbOfFin_mem rfl _⟩,(mem_filter.mp hp).2⟩
    · intro p _ q _ hpq
      exact Prod.ext (f.injective (congrArg Prod.fst hpq))
        (g.injective (congrArg Prod.snd hpq))
    · intro p hp
      obtain ⟨hpAB,hpC⟩:=mem_filter.mp hp
      obtain ⟨hpA,hpB⟩:=mem_product.mp hpAB
      obtain ⟨i,hi⟩:∃ i,f i = p.1:=by
        have h:=A.range_orderEmbOfFin rfl
        change p.1 ∈ (A:Set ℝ) at hpA
        rw [← h] at hpA
        exact hpA
      obtain ⟨j,hj⟩:∃ j,g j = p.2:=by
        have h:=B.range_orderEmbOfFin rfl
        change p.2 ∈ (B:Set ℝ) at hpB
        rw [← h] at hpB
        exact hpB
      exact ⟨(i,j),mem_filter.mpr ⟨mem_univ _,by simpa [hi,hj] using hpC⟩,
        by simp [hi,hj]⟩
  rw [← heq]
  exact ordered_three_set_bound f g C
end Green24Proof.FiniteThreeSetChains
private def zz2445:"s098d"="s098d":=by decide+kernel
end 
section 
namespace Green24Proof.ThreeSetChainArithmetic
open Finset
open scoped BigOperators
theorem sum_linear (n:ℕ) (x:ℝ) :
    (∑ i ∈ range n,(x - 2 * i - 1)) = n * (x - n):=by
  induction n with
  | zero => simp
  | succ n ih =>
    rw [sum_range_succ,ih]
    push_cast
    ring
private def zz1880:"s0758"="s0758":=by decide+kernel
theorem capped_sum_le_quadratic (n k:ℕ) (hk:k ≤ n) (x c:ℝ) :
    (∑ i ∈ range n,min c (x - 2 * i - 1)) ≤
      n * (x - n) - k * (x - c - k):=by
  have hsplit:=sum_range_add (fun i:ℕ => min c (x - 2 * i - 1)) k (n - k)
  rw [Nat.add_sub_of_le hk] at hsplit
  rw [hsplit]
  calc
    _ ≤ (∑ _i ∈ range k,c) +
        ∑ i ∈ range (n - k),(x - 2 * (k + i:ℕ) - 1):=by
      exact add_le_add (sum_le_sum (fun _ _ => min_le_left _ _))
        (sum_le_sum (fun _ _ => min_le_right _ _))
    _ = (k:ℝ) * c + (n - k:ℕ) * (x - 2 * k - (n - k:ℕ)):=by
      simp only [sum_const,card_range,nsmul_eq_mul]
      congr 1
      convert sum_linear (n - k) (x - 2 * k) using 1
      apply sum_congr rfl
      intro i _
      push_cast
      ring
    _ = _:=by rw [Nat.cast_sub hk]; ring
theorem chain_sum_le_kernel (a b c:ℕ) :
    (∑ i ∈ range (min a b),(min c (a + b - 2 * i - 1):ℕ):ℝ) ≤
      kernel a b c + 1 / 4:=by
  have hcast :
      (∑ i ∈ range (min a b),(min c (a + b - 2 * i - 1):ℕ):ℝ) =
      ∑ i ∈ range (min a b),min (c:ℝ) ((a:ℝ) + b - 2 * i - 1):=by
    apply sum_congr rfl
    intro i hi
    have hi':=mem_range.mp hi
    rw [Nat.cast_min,Nat.cast_sub (by omega),Nat.cast_sub (by omega)]
    push_cast
    rfl
  rw [hcast]
  have hbase:((min a b:ℕ):ℝ) * ((a:ℝ) + b - (min a b:ℕ)) =
      (a:ℝ) * b:=by
    rcases le_total a b with h | h
    · rw [min_eq_left h]
      ring
    · rw [min_eq_right h]
      ring
  have hquad (k:ℕ) (hk:k ≤ min a b) :
      (∑ i ∈ range (min a b),min (c:ℝ) ((a:ℝ) + b - 2 * i - 1)) ≤
      (a:ℝ) * b - k * ((a:ℝ) + b - c - k):=by
    simpa only [hbase] using capped_sum_le_quadratic (min a b) k hk ((a:ℝ) + b) c
  by_cases hc:a + b ≤ c
  · have hc':(a:ℝ) + b ≤ c:=by exact_mod_cast hc
    rw [kernel_eq_product (Nat.cast_nonneg _) (Nat.cast_nonneg _) hc']
    have h:=hquad 0 (Nat.zero_le _)
    norm_num at h
    linarith
  by_cases ha:b + c ≤ a
  · have hab:b ≤ a:=by omega
    have ha':(b:ℝ) + c ≤ a:=by exact_mod_cast ha
    rw [kernel_cycle,kernel_eq_product (Nat.cast_nonneg _) (Nat.cast_nonneg _) ha']
    have h:=hquad b (by omega)
    nlinarith
  by_cases hb:a + c ≤ b
  · have hab:a ≤ b:=by omega
    have hb':(a:ℝ) + c ≤ b:=by exact_mod_cast hb
    rw [kernel_swap23,kernel_eq_product (Nat.cast_nonneg _) (Nat.cast_nonneg _) hb']
    have h:=hquad a (by omega)
    nlinarith
  have hat:(a:ℝ) ≤ b + c:=by exact_mod_cast (show a ≤ b + c by omega)
  have hbt:(b:ℝ) ≤ a + c:=by exact_mod_cast (show b ≤ a + c by omega)
  have hct:(c:ℝ) ≤ a + b:=by exact_mod_cast (show c ≤ a + b by omega)
  rw [kernel_eq_triangle hat hbt hct]
  let k:=(a + b - c) / 2
  have hk:k ≤ min a b:=by dsimp [k]; omega
  have h:=hquad k hk
  have hklo:2 * k ≤ a + b - c:=by dsimp [k]; omega
  have hkhi:a + b - c ≤ 2 * k + 1:=by dsimp [k]; omega
  have hlo:0 ≤ (a:ℝ) + b - c - 2 * k:=by
    have h':2 * k + c ≤ a + b:=by omega
    exact_mod_cast (show (0:ℤ) ≤ (a:ℤ) + b - c - 2 * k by omega)
  have hhi:(a:ℝ) + b - c - 2 * k ≤ 1:=by
    have h':a + b ≤ 2 * k + 1 + c:=by omega
    exact_mod_cast (show (a:ℤ) + b - c - 2 * k ≤ 1 by omega)
  nlinarith [mul_nonneg hlo (sub_nonneg.mpr hhi)]
end Green24Proof.ThreeSetChainArithmetic
private def zz2446:"s098e"="s098e":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteThreeSetRearrangement
open Finset
open scoped BigOperators
theorem three_set_bound (A B C:Finset ℝ) :
    (((A ×ˢ B).filter (fun p => p.1 + p.2 ∈ C)).card:ℝ) ≤
      kernel A.card B.card C.card + 1 / 4:=by
  have h:=FiniteThreeSetChains.three_set_chain_bound A B C
  have h':(((A ×ˢ B).filter (fun p => p.1 + p.2 ∈ C)).card:ℝ) ≤
      ∑ i ∈ range (min A.card B.card),
        ((min C.card (A.card + B.card - 2 * i - 1):ℕ):ℝ):=by exact_mod_cast h
  exact h'.trans (ThreeSetChainArithmetic.chain_sum_le_kernel A.card B.card C.card)
theorem three_set_sum_bound (A B C:Finset ℝ) :
    (∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,if x + y = z then (1:ℝ) else 0) ≤
      kernel A.card B.card C.card + 1 / 4:=by
  classical
  have h:(∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,if x + y = z then (1:ℝ) else 0) =
      (((A ×ˢ B).filter (fun p => p.1 + p.2 ∈ C)).card:ℝ):=by
    simp only [sum_ite_eq]
    rw [← sum_product A B (fun p:ℝ × ℝ => if p.1 + p.2 ∈ C then (1:ℝ) else 0)]
    simp only [← sum_filter,sum_const,nsmul_eq_mul,mul_one]
  rw [h]
  exact three_set_bound A B C
end Green24Proof.FiniteThreeSetRearrangement
private def zz2447:"s098f"="s098f":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteWeightRounding
open Finset
open scoped BigOperators
private def zz1881:"s0759"="s0759":=by decide+kernel
theorem exists_top_subset {ι:Type*} [DecidableEq ι]
    (S:Finset ι) (v:ι → ℝ) (k:ℕ) (hk:k ≤ S.card) :
    ∃ T ⊆ S,T.card = k ∧ ∀ i ∈ T, ∀ j ∈ S \ T,v j ≤ v i:=by
  induction k generalizing S with
  | zero => exact ⟨∅,empty_subset _,rfl,by simp⟩
  | succ k ih =>
    have hS:S.Nonempty:=card_pos.mp (by omega)
    obtain ⟨x,hx,hmax⟩:=S.exists_max_image v hS
    obtain ⟨T,hT,hcard,htop⟩:=ih (S.erase x) (by rw [card_erase_of_mem hx]; omega)
    have hxT:x ∉ T:=fun h => (mem_erase.mp (hT h)).1 rfl
    refine ⟨insert x T,insert_subset hx (hT.trans (erase_subset _ _)),
      by rw [card_insert_of_notMem hxT,hcard], ?_⟩
    intro i hi j hj
    obtain ⟨hjS,hjout⟩:=mem_sdiff.mp hj
    rcases mem_insert.mp hi with rfl | hiT
    · exact hmax j hjS
    · apply htop i hiT j
      exact mem_sdiff.mpr ⟨mem_erase.mpr ⟨by
        intro heq
        subst j
        exact hjout (mem_insert_self _ _),hjS⟩,
        fun hjT => hjout (mem_insert_of_mem hjT)⟩
theorem exists_rounding_of_mass_le {ι:Type*} [DecidableEq ι]
    (S:Finset ι) (w v:ι → ℝ) (k:ℕ)
    (hw:∀ i ∈ S,w i ∈ Set.Icc 0 1) (hv:∀ i ∈ S,0 ≤ v i)
    (hmass:∑ i ∈ S,w i ≤ k) :
    ∃ T ⊆ S,T.card ≤ k ∧ (∑ i ∈ S,w i * v i) ≤ ∑ i ∈ T,v i:=by
  by_cases hSk:S.card ≤ k
  · refine ⟨S,Subset.refl _,hSk,sum_le_sum ?_⟩
    intro i hi
    exact mul_le_of_le_one_left (hv i hi) (hw i hi).2
  have hkS:k ≤ S.card:=by omega
  by_cases hk0:k = 0
  · have hw0 (i:ι) (hi:i ∈ S):w i = 0:=by
      have h:=single_le_sum (fun j hj => (hw j hj).1) hi
      simp only [hk0,Nat.cast_zero] at hmass
      linarith [(hw i hi).1]
    refine ⟨∅,empty_subset _,by simp, ?_⟩
    simp only [sum_empty]
    apply sum_nonpos
    intro i hi
    rw [hw0 i hi,zero_mul]
  obtain ⟨T,hTS,hcard,htop⟩:=exists_top_subset S v k hkS
  obtain ⟨i₀,hi₀,hmin⟩:=T.exists_min_image v (card_pos.mp (by omega))
  have hm0:0 ≤ v i₀:=hv i₀ (hTS hi₀)
  have hin:(∑ i ∈ T,w i * v i) ≤
      (∑ i ∈ T,v i) + v i₀ * ((∑ i ∈ T,w i) - k):=by
    calc
      _ ≤ ∑ i ∈ T,(v i + v i₀ * (w i - 1)):=by
        apply sum_le_sum
        intro i hi
        have hwi:=hw i (hTS hi)
        have hvi:=hmin i hi
        nlinarith [mul_nonneg (sub_nonneg.mpr hwi.2) (sub_nonneg.mpr hvi)]
      _ = _:=by simp [sum_add_distrib, ← mul_sum,sum_sub_distrib,hcard]
  have hout:(∑ i ∈ S \ T,w i * v i) ≤ v i₀ * ∑ i ∈ S \ T,w i:=by
    calc
      _ ≤ ∑ i ∈ S \ T,w i * v i₀:=by
        apply sum_le_sum
        intro i hi
        exact mul_le_mul_of_nonneg_left (htop i₀ hi₀ i hi)
          (hw i (mem_sdiff.mp hi).1).1
      _ = _:=by rw [← sum_mul]; ring
  refine ⟨T,hTS,hcard.le, ?_⟩
  have hsumw:=sum_sdiff hTS (f:=w)
  have hsumwv:=sum_sdiff hTS (f:=fun i => w i * v i)
  nlinarith [mul_nonneg hm0 (sub_nonneg.mpr hmass)]
theorem exists_rounding {ι:Type*} [DecidableEq ι]
    (S:Finset ι) (w v:ι → ℝ)
    (hw:∀ i ∈ S,w i ∈ Set.Icc 0 1) (hv:∀ i ∈ S,0 ≤ v i) :
    ∃ T ⊆ S,(T.card:ℝ) ≤ (∑ i ∈ S,w i) + 1 ∧
      (∑ i ∈ S,w i * v i) ≤ ∑ i ∈ T,v i:=by
  obtain ⟨T,hTS,hcard,hval⟩:=exists_rounding_of_mass_le S w v
    ⌈∑ i ∈ S,w i⌉₊ hw hv (Nat.le_ceil _)
  refine ⟨T,hTS, ?_,hval⟩
  have h:=Nat.ceil_lt_add_one (sum_nonneg (fun i hi => (hw i hi).1))
  exact (Nat.cast_le.mpr hcard).trans h.le
end Green24Proof.FiniteWeightRounding
private def zz2448:"s0990"="s0990":=by decide+kernel
end 
section 
namespace Green24Proof.TrilinearWeightRounding
open Finset
open scoped BigOperators
open Green24Proof.FiniteWeightRounding
theorem exists_trilinear_rounding {α β γ:Type*}
    [DecidableEq α] [DecidableEq β] [DecidableEq γ]
    (A:Finset α) (B:Finset β) (C:Finset γ)
    (f:α → ℝ) (g:β → ℝ) (h:γ → ℝ) (K:α → β → γ → ℝ)
    (hf:∀ x ∈ A,f x ∈ Set.Icc 0 1)
    (hg:∀ y ∈ B,g y ∈ Set.Icc 0 1)
    (hh:∀ z ∈ C,h z ∈ Set.Icc 0 1)
    (hK:∀ x ∈ A, ∀ y ∈ B, ∀ z ∈ C,0 ≤ K x y z) :
    ∃ A' ⊆ A, ∃ B' ⊆ B, ∃ C' ⊆ C,
      (A'.card:ℝ) ≤ (∑ x ∈ A,f x) + 1 ∧
      (B'.card:ℝ) ≤ (∑ y ∈ B,g y) + 1 ∧
      (C'.card:ℝ) ≤ (∑ z ∈ C,h z) + 1 ∧
      (∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,f x * g y * h z * K x y z) ≤
        ∑ x ∈ A', ∑ y ∈ B', ∑ z ∈ C',K x y z:=by
  obtain ⟨A',hA',hAm,hAv⟩:=exists_rounding A f
    (fun x => ∑ y ∈ B, ∑ z ∈ C,g y * h z * K x y z) hf (by
      intro x hx
      exact sum_nonneg (fun y hy => sum_nonneg (fun z hz =>
        mul_nonneg (mul_nonneg (hg y hy).1 (hh z hz).1) (hK x hx y hy z hz))))
  obtain ⟨B',hB',hBm,hBv⟩:=exists_rounding B g
    (fun y => ∑ x ∈ A', ∑ z ∈ C,h z * K x y z) hg (by
      intro y hy
      exact sum_nonneg (fun x hx => sum_nonneg (fun z hz =>
        mul_nonneg (hh z hz).1 (hK x (hA' hx) y hy z hz))))
  obtain ⟨C',hC',hCm,hCv⟩:=exists_rounding C h
    (fun z => ∑ x ∈ A', ∑ y ∈ B',K x y z) hh (by
      intro z hz
      exact sum_nonneg (fun x hx => sum_nonneg (fun y hy =>
        hK x (hA' hx) y (hB' hy) z hz)))
  refine ⟨A',hA',B',hB',C',hC',hAm,hBm,hCm, ?_⟩
  calc
    _ = ∑ x ∈ A,f x * (∑ y ∈ B, ∑ z ∈ C,g y * h z * K x y z):=by
      simp only [mul_sum,mul_assoc]
    _ ≤ ∑ x ∈ A', ∑ y ∈ B, ∑ z ∈ C,g y * h z * K x y z:=hAv
    _ = ∑ y ∈ B,g y * (∑ x ∈ A', ∑ z ∈ C,h z * K x y z):=by
      rw [sum_comm]
      simp only [mul_sum,mul_assoc]
    _ ≤ ∑ y ∈ B', ∑ x ∈ A', ∑ z ∈ C,h z * K x y z:=hBv
    _ = ∑ z ∈ C,h z * (∑ x ∈ A', ∑ y ∈ B',K x y z):=by
      rw [sum_comm]
      simp_rw [sum_comm (s:=B') (t:=C)]
      rw [sum_comm]
      simp only [mul_sum]
    _ ≤ ∑ z ∈ C', ∑ x ∈ A', ∑ y ∈ B',K x y z:=hCv
    _ = _:=by
      rw [sum_comm]
      apply sum_congr rfl
      intro x _
      rw [sum_comm]
end Green24Proof.TrilinearWeightRounding
private def zz2449:"s0991"="s0991":=by decide+kernel
end 
section 
namespace Green24Proof.KernelMonotonicity
private def zz1882:"s075a"="s075a":=by decide+kernel
theorem mono_first {a a' b c:ℝ} (ha:0 ≤ a) (haa:a ≤ a')
    (hb:0 ≤ b) (hc:0 ≤ c):kernel a b c ≤ kernel a' b c:=by
  have h:0 ≤ ∫ t in a..a',kernelSlope t b c:=by
    apply intervalIntegral.integral_nonneg_of_forall haa
    intro t
    exact le_min hb (le_min hc (le_max_right _ _))
  rw [kernel_integral_slope ha haa hb hc] at h
  linarith
theorem mono_second {a b b' c:ℝ} (ha:0 ≤ a) (hb:0 ≤ b)
    (hbb:b ≤ b') (hc:0 ≤ c):kernel a b c ≤ kernel a b' c:=by
  rw [kernel_swap12 a b c,kernel_swap12 a b' c]
  exact mono_first hb hbb ha hc
theorem mono_third {a b c c':ℝ} (ha:0 ≤ a) (hb:0 ≤ b)
    (hc:0 ≤ c) (hcc:c ≤ c'):kernel a b c ≤ kernel a b c':=by
  rw [kernel_swap23 a b c,kernel_swap23 a b c']
  exact mono_second ha hc hcc hb
theorem mono {a b c a' b' c':ℝ} (ha:0 ≤ a) (hb:0 ≤ b) (hc:0 ≤ c)
    (haa:a ≤ a') (hbb:b ≤ b') (hcc:c ≤ c') :
    kernel a b c ≤ kernel a' b' c' :=
  (mono_first ha haa hb hc).trans
    ((mono_second (ha.trans haa) hb hbb hc).trans
      (mono_third (ha.trans haa) (hb.trans hbb) hc hcc))
end Green24Proof.KernelMonotonicity
private def zz2450:"s0992"="s0992":=by decide+kernel
end 
section 
namespace Green24Proof.WeightedThreeSetRearrangement
open Finset Filter
open scoped BigOperators Topology
private def zz1883:"s075b"="s075b":=by decide+kernel
theorem weighted_three_set_bound (A B C:Finset ℝ) (f g h:ℝ → ℝ)
    (hf:∀ x ∈ A,f x ∈ Set.Icc 0 1)
    (hg:∀ y ∈ B,g y ∈ Set.Icc 0 1)
    (hh:∀ z ∈ C,h z ∈ Set.Icc 0 1) :
    (∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,if x + y = z then f x * g y * h z else 0) ≤
      kernel ((∑ x ∈ A,f x) + 1) ((∑ y ∈ B,g y) + 1)
        ((∑ z ∈ C,h z) + 1) + 1 / 4:=by
  classical
  obtain ⟨A',hA',B',hB',C',hC',hAm,hBm,hCm,hval⟩ :=
    TrilinearWeightRounding.exists_trilinear_rounding A B C f g h
      (fun x y z => if x + y = z then 1 else 0) hf hg hh (by
        intro x _ y _ z _
        split_ifs <;> norm_num)
  simp only [mul_ite,mul_one,mul_zero] at hval
  exact hval.trans ((FiniteThreeSetRearrangement.three_set_sum_bound A' B' C').trans
    (add_le_add (KernelMonotonicity.mono (Nat.cast_nonneg _) (Nat.cast_nonneg _)
      (Nat.cast_nonneg _) hAm hBm hCm) le_rfl))
theorem normalized_weighted_three_set_bound (A B C:Finset ℝ) (f g h:ℝ → ℝ)
    (hf:∀ x ∈ A,f x ∈ Set.Icc 0 1)
    (hg:∀ y ∈ B,g y ∈ Set.Icc 0 1)
    (hh:∀ z ∈ C,h z ∈ Set.Icc 0 1) {η:ℝ} (hη:0 ≤ η) :
    η ^ 2 * (∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,
      if x + y = z then f x * g y * h z else 0) ≤
      kernel (η * (∑ x ∈ A,f x) + η) (η * (∑ y ∈ B,g y) + η)
        (η * (∑ z ∈ C,h z) + η) + η ^ 2 / 4:=by
  have hv:=mul_le_mul_of_nonneg_left (weighted_three_set_bound A B C f g h hf hg hh)
    (sq_nonneg η)
  calc
    _ ≤ η ^ 2 * (kernel ((∑ x ∈ A,f x) + 1) ((∑ y ∈ B,g y) + 1)
        ((∑ z ∈ C,h z) + 1) + 1 / 4):=hv
    _ = _:=by rw [mul_add, ← kernel_scale _ _ _ hη]; simp only [mul_add,mul_one]; ring
theorem bound_of_limits {a b c t η:ℕ → ℝ} {A B C T:ℝ}
    (ha:Tendsto a atTop (𝓝 A)) (hb:Tendsto b atTop (𝓝 B))
    (hc:Tendsto c atTop (𝓝 C)) (ht:Tendsto t atTop (𝓝 T))
    (hη:Tendsto η atTop (𝓝 0))
    (hbound:∀ n,t n ≤ kernel (a n + η n) (b n + η n) (c n + η n) + η n ^ 2 / 4) :
    T ≤ kernel A B C:=by
  have harg:Tendsto (fun n => (a n + η n,b n + η n,c n + η n)) atTop
      (𝓝 (A,B,C)):=by
    simpa only [add_zero] using (ha.add hη).prodMk_nhds ((hb.add hη).prodMk_nhds (hc.add hη))
  have hkernel:=kernel_continuous.continuousAt.tendsto.comp harg
  have hlim:Tendsto (fun n => kernel (a n + η n) (b n + η n) (c n + η n) + η n ^ 2 / 4)
      atTop (𝓝 (kernel A B C)):=by
    simpa only [Function.comp_apply,zero_pow (by norm_num:2 ≠ 0),zero_div,add_zero]
      using hkernel.add ((hη.pow 2).div_const 4)
  exact le_of_tendsto_of_tendsto ht hlim (Eventually.of_forall hbound)
end Green24Proof.WeightedThreeSetRearrangement
private def zz2451:"s0993"="s0993":=by decide+kernel
end 
section 
namespace Green24Proof.RealContinuousRearrangement
open MeasureTheory Set Filter
open scoped BigOperators Topology
open Green24Proof.RealLatticeRiemannSums Green24Proof.RealGridIntegralLimits
open Green24Proof.WeightedThreeSetRearrangement
theorem finite_difference_sum (A B C:Finset ℝ) (f g h:ℝ → ℝ)
    (hA:∀ y ∈ B, ∀ z ∈ C,z - y ∈ A) :
    (∑ x ∈ A, ∑ y ∈ B, ∑ z ∈ C,if x + y = z then f x * g y * h z else 0) =
      ∑ y ∈ B, ∑ z ∈ C,f (z - y) * g y * h z:=by
  classical
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro y hy
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro z hz
  rw [Finset.sum_eq_single (z - y)]
  · simp only [sub_add_cancel,if_true]
  · intro x _ hxy
    apply if_neg
    intro heq
    exact hxy (by linarith)
  · intro hnot
    exact False.elim (hnot (hA y hy z hz))
private def zz1884:"s075c"="s075c":=by decide+kernel
theorem normalized_grid_bound {n:ℕ} (hn:0 < n) (M:ℕ) (f g h:ℝ → ℝ)
    (hf:∀ x,f x ∈ Icc 0 1) (hg:∀ x,g x ∈ Icc 0 1) (hh:∀ x,h x ∈ Icc 0 1) :
    ((n:ℝ)⁻¹) ^ 2 *
      (∑ y ∈ lineGrid n M, ∑ z ∈ lineGrid n M,f (z - y) * g y * h z) ≤
      kernel ((n:ℝ)⁻¹ * (∑ x ∈ lineGrid n (2 * M),f x) + (n:ℝ)⁻¹)
        ((n:ℝ)⁻¹ * (∑ y ∈ lineGrid n M,g y) + (n:ℝ)⁻¹)
        ((n:ℝ)⁻¹ * (∑ z ∈ lineGrid n M,h z) + (n:ℝ)⁻¹) + ((n:ℝ)⁻¹) ^ 2 / 4:=by
  have hb:=normalized_weighted_three_set_bound
    (lineGrid n (2 * M)) (lineGrid n M) (lineGrid n M) f g h
    (fun x _ => hf x) (fun y _ => hg y) (fun z _ => hh z)
    (η:=(n:ℝ)⁻¹) (by positivity)
  rwa [finite_difference_sum _ _ _ f g h
    (fun _ hy _ hz => sub_mem_lineGrid hn hy hz)] at hb
theorem bound_of_support (M:ℕ) (f g h:ℝ → ℝ)
    (hf:Continuous f) (hg:Continuous g) (hh:Continuous h)
    (hsf:∀ x,x ∉ Icc (-(2 * M:ℕ):ℝ) (2 * M:ℕ) → f x = 0)
    (hsg:∀ x,x ∉ Icc (-(M:ℝ)) M → g x = 0)
    (hsh:∀ x,x ∉ Icc (-(M:ℝ)) M → h x = 0)
    (hrf:∀ x,f x ∈ Icc 0 1) (hrg:∀ x,g x ∈ Icc 0 1) (hrh:∀ x,h x ∈ Icc 0 1) :
    (∫ yz:ℝ × ℝ,f (yz.2 - yz.1) * g yz.1 * h yz.2) ≤
      kernel (∫ x,f x) (∫ y,g y) (∫ z,h z):=by
  have hf':=tendsto_lineGrid_sum (2 * M) f hf hsf
  have hg':=tendsto_lineGrid_sum M g hg hsg
  have hh':=tendsto_lineGrid_sum M h hh hsh
  have ht:=tendsto_pairGrid_sum M
    (fun yz:ℝ × ℝ => f (yz.2 - yz.1) * g yz.1 * h yz.2)
    (by fun_prop) (by
      intro yz hyz
      by_cases hy:yz.1 ∈ Icc (-(M:ℝ)) M
      · have hz:yz.2 ∉ Icc (-(M:ℝ)) M:=fun hz => hyz ⟨hy,hz⟩
        rw [hsh _ hz,mul_zero]
      · rw [hsg _ hy,mul_zero,zero_mul])
  have hη:Tendsto (fun n:ℕ => (n:ℝ)⁻¹) atTop (𝓝 0):=by
    simpa only [one_div] using
      ((tendsto_const_nhds (x:=(1:ℝ))).div_atTop tendsto_natCast_atTop_atTop)
  simp only [div_eq_inv_mul, ← inv_pow] at hf' hg' hh' ht
  apply bound_of_limits hf' hg' hh' ht hη
  intro n
  by_cases hn:n = 0
  · subst n
    simp [kernel]
  · exact normalized_grid_bound (Nat.pos_of_ne_zero hn) M f g h hrf hrg hrh
theorem exists_common_support_interval (f g h:ℝ → ℝ)
    (hf:HasCompactSupport f) (hg:HasCompactSupport g) (hh:HasCompactSupport h) :
    ∃ M:ℕ,
      (∀ x,x ∉ Icc (-(M:ℝ)) M → f x = 0) ∧
      (∀ x,x ∉ Icc (-(M:ℝ)) M → g x = 0) ∧
      (∀ x,x ∉ Icc (-(M:ℝ)) M → h x = 0):=by
  let S:=(tsupport f ∪ tsupport g) ∪ tsupport h
  have hS:IsCompact S:=(hf.union hg).union hh
  obtain ⟨R,hR⟩:=hS.exists_bound_of_continuousOn (continuous_id.continuousOn)
  let M:ℕ:=⌈R⌉₊
  have hM:R ≤ (M:ℝ):=Nat.le_ceil R
  have hzero (F:ℝ → ℝ) (hF:tsupport F ⊆ S) :
      ∀ x,x ∉ Icc (-(M:ℝ)) M → F x = 0:=by
    intro x hx
    apply image_eq_zero_of_notMem_tsupport
    intro hxs
    apply hx
    apply abs_le.mp
    exact (hR x (hF hxs)).trans hM
  exact ⟨M,hzero f (fun _ hx => Or.inl (Or.inl hx)),
    hzero g (fun _ hx => Or.inl (Or.inr hx)),hzero h (fun _ hx => Or.inr hx)⟩
theorem three_function_bound (f g h:ℝ → ℝ)
    (hf:Continuous f) (hg:Continuous g) (hh:Continuous h)
    (hsf:HasCompactSupport f) (hsg:HasCompactSupport g) (hsh:HasCompactSupport h)
    (hrf:∀ x,f x ∈ Icc 0 1) (hrg:∀ x,g x ∈ Icc 0 1) (hrh:∀ x,h x ∈ Icc 0 1) :
    (∫ yz:ℝ × ℝ,f (yz.2 - yz.1) * g yz.1 * h yz.2) ≤
      kernel (∫ x,f x) (∫ y,g y) (∫ z,h z):=by
  obtain ⟨M,hMf,hMg,hMh⟩:=exists_common_support_interval f g h hsf hsg hsh
  apply bound_of_support M f g h hf hg hh _ hMg hMh hrf hrg hrh
  intro x hx
  apply hMf x
  intro hsmall
  apply hx
  constructor <;> push_cast <;> linarith [hsmall.1,hsmall.2,Nat.cast_nonneg (α:=ℝ) M]
end Green24Proof.RealContinuousRearrangement
private def zz2452:"s0994"="s0994":=by decide+kernel
end 
section 
namespace Green24Proof.RealLineOrbitIntegrals
open MeasureTheory Set
open Green24Proof.CompactCircleLift Green24Proof.RealTorusDilation
open Green24Proof.CircleLiftCounting Green24Proof.CircleProductOrbit
open Green24Proof.CircleTorusOrbit Green24Proof.CircleProbabilityHaar
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*}
noncomputable def lineFunction (w:ι → ℤ) (F:Space ι → ℝ) (t:ℝ):ℝ :=
  F (t,orbit w (Circle.exp t))
private def zz1885:"s075d"="s075d":=by decide+kernel
theorem lineFunction_continuous (w:ι → ℤ) (F:Space ι → ℝ) (hF:Continuous F) :
    Continuous (lineFunction w F) :=
  hF.comp (continuous_id.prodMk ((orbit_continuous w).comp Circle.exp.continuous))
theorem lineFunction_zero (w:ι → ℤ) (F:Space ι → ℝ) (hs:SmallSupport F)
    {t:ℝ} (ht:Real.pi / 4 ≤ |t|):lineFunction w F t = 0:=hs t _ ht
theorem lineFunction_compactSupport (w:ι → ℤ) (F:Space ι → ℝ)
    (hs:SmallSupport F):HasCompactSupport (lineFunction w F):=by
  apply HasCompactSupport.intro (isCompact_Icc:IsCompact (Icc (-Real.pi / 4) (Real.pi / 4)))
  intro t ht
  apply lineFunction_zero w F hs
  by_contra hn
  obtain ⟨h1,h2⟩:=abs_lt.mp (lt_of_not_ge hn)
  exact ht ⟨by linarith,h2.le⟩
theorem lineFunction_range (w:ι → ℤ) (F:Space ι → ℝ)
    (hr:∀ z,F z ∈ Icc 0 1) (t:ℝ):lineFunction w F t ∈ Icc 0 1:=hr _
private def zz1886:"s075e"="s075e":=by decide+kernel
theorem integral_orbit_mass (w:ι → ℤ) (F:Space ι → ℝ) (hF:Continuous F)
    (hs:SmallSupport F) :
    (∫ z,circleLift F (productOrbit w z) ∂circleHaar) =
      (2 * Real.pi)⁻¹ * ∫ t,lineFunction w F t:=by
  rw [integral_exp (fun z => circleLift F (productOrbit w z))
    ((circleLift_continuous F hF hs).comp (productOrbit_continuous w))
    (-Real.pi),show -Real.pi + 2 * Real.pi = Real.pi by ring,
    integral_real_principal (lineFunction w F) (fun _ ht => lineFunction_zero w F hs ht)]
  congr 1
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht
  exact circleLift_exp F ⟨ht.1,ht.2.le⟩ _
theorem integral_circle_pair_exp (K:Circle × Circle → ℝ) (hK:Continuous K) :
    (∫ yz,K yz ∂circleHaar.prod circleHaar) =
      ((2 * Real.pi)⁻¹) ^ 2 * ∫ s in -Real.pi..Real.pi,
        ∫ t in -Real.pi..Real.pi,K (Circle.exp s,Circle.exp t):=by
  letI:=circleHaar_isProbabilityMeasure
  have hcont:Continuous (fun y => ∫ z,K (y,z) ∂circleHaar):=by
    have h:=continuous_parametric_integral_of_continuous
      (μ:=circleHaar) (f:=fun y z => K (y,z)) hK (s:=Set.univ) isCompact_univ
    simpa only [Measure.restrict_univ] using h
  have hinner (y:Circle):(∫ z,K (y,z) ∂circleHaar) =
      (2 * Real.pi)⁻¹ * ∫ t in -Real.pi..Real.pi,K (y,Circle.exp t):=by
    rw [integral_exp (fun z => K (y,z))
      (hK.comp (continuous_const.prodMk continuous_id)) (-Real.pi),
      show -Real.pi + 2 * Real.pi = Real.pi by ring]
  rw [integral_prod _ (hK.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)),
    integral_exp _ hcont (-Real.pi),show -Real.pi + 2 * Real.pi = Real.pi by ring]
  simp_rw [hinner,intervalIntegral.integral_const_mul]
  ring
theorem real_count_eq_principal (f g h:ℝ → ℝ)
    (hf:Continuous f) (hg:Continuous g) (hh:Continuous h)
    (hsg:∀ t,Real.pi / 4 ≤ |t| → g t = 0)
    (hsh:∀ t,Real.pi / 4 ≤ |t| → h t = 0) :
    (∫ yz:ℝ × ℝ,f (yz.2 - yz.1) * g yz.1 * h yz.2) =
      ∫ s in -Real.pi..Real.pi, ∫ t in -Real.pi..Real.pi,f (t - s) * g s * h t:=by
  let K:=fun yz:ℝ × ℝ => f (yz.2 - yz.1) * g yz.1 * h yz.2
  have hzero (F:ℝ → ℝ) (hF:∀ t,Real.pi / 4 ≤ |t| → F t = 0)
      (t:ℝ) (ht:t ∉ Icc (-Real.pi / 4) (Real.pi / 4)):F t = 0:=by
    apply hF
    by_contra hn
    obtain ⟨h1,h2⟩:=abs_lt.mp (lt_of_not_ge hn)
    exact ht ⟨by linarith,h2.le⟩
  have hsK:HasCompactSupport K:=by
    apply HasCompactSupport.intro (isCompact_Icc.prod isCompact_Icc)
    intro yz hyz
    by_cases hy:yz.1 ∈ Icc (-Real.pi / 4) (Real.pi / 4)
    · have hz:yz.2 ∉ Icc (-Real.pi / 4) (Real.pi / 4):=fun hz => hyz ⟨hy,hz⟩
      simp only [K,hzero h hsh _ hz,mul_zero]
    · simp only [K,hzero g hsg _ hy,mul_zero,zero_mul]
  have hi:Integrable K:=(by fun_prop:Continuous K).integrable_of_hasCompactSupport hsK
  have hinner (s:ℝ):(∫ t,f (t - s) * g s * h t) =
      ∫ t in -Real.pi..Real.pi,f (t - s) * g s * h t:=by
    apply integral_real_principal
    intro t ht
    rw [hsh t ht,mul_zero]
  change (∫ yz,K yz ∂volume.prod volume) = _
  rw [integral_prod K hi]
  change (∫ s, ∫ t,f (t - s) * g s * h t) = _
  simp_rw [hinner]
  apply integral_real_principal
  intro s hs
  simp_rw [hsg s hs,mul_zero,zero_mul]
  simp
theorem orbit_count_pointwise (w:ι → ℤ) (F G H:Space ι → ℝ)
    (hsG:SmallSupport G) (hsH:SmallSupport H)
    {s t:ℝ} (hs:s ∈ Ioc (-Real.pi) Real.pi) (ht:t ∈ Ioc (-Real.pi) Real.pi) :
    liftedDifferenceIntegrand F G H (productOrbit w (Circle.exp s),productOrbit w (Circle.exp t)) =
      lineFunction w F (t - s) * lineFunction w G s * lineFunction w H t:=by
  change circleLift F (Circle.exp t / Circle.exp s,orbit w (Circle.exp t) / orbit w (Circle.exp s)) *
    circleLift G (Circle.exp s,orbit w (Circle.exp s)) *
      circleLift H (Circle.exp t,orbit w (Circle.exp t)) = _
  rw [difference_product_exp F G H hsG hsH hs ht,
    ← orbit_div, ← Circle.exp_sub]
  rfl
private def zz1887:"s075f"="s075f":=by decide+kernel
theorem integral_orbit_count (w:ι → ℤ) (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H) :
    (∫ yz,liftedDifferenceIntegrand F G H (productOrbit w yz.1,productOrbit w yz.2)
      ∂circleHaar.prod circleHaar) = ((2 * Real.pi)⁻¹) ^ 2 *
      ∫ yz:ℝ × ℝ,lineFunction w F (yz.2 - yz.1) * lineFunction w G yz.1 * lineFunction w H yz.2:=by
  rw [integral_circle_pair_exp
    (fun yz => liftedDifferenceIntegrand F G H (productOrbit w yz.1,productOrbit w yz.2))
    ((liftedDifferenceIntegrand_continuous F G H hF hG hH hsF hsG hsH).comp
      ((productOrbit_continuous w).prodMap (productOrbit_continuous w))),
    real_count_eq_principal _ _ _ (lineFunction_continuous w F hF)
      (lineFunction_continuous w G hG) (lineFunction_continuous w H hH)
      (fun _ ht => lineFunction_zero w G hsG ht) (fun _ ht => lineFunction_zero w H hsH ht)]
  congr 1
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro s hs
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht
  exact orbit_count_pointwise w F G H hsG hsH ⟨hs.1,hs.2.le⟩ ⟨ht.1,ht.2.le⟩
theorem orbit_rearrangement_bound (w:ι → ℤ) (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H)
    (hrF:∀ z,F z ∈ Icc 0 1) (hrG:∀ z,G z ∈ Icc 0 1) (hrH:∀ z,H z ∈ Icc 0 1) :
    (∫ yz,liftedDifferenceIntegrand F G H (productOrbit w yz.1,productOrbit w yz.2)
      ∂circleHaar.prod circleHaar) ≤
      kernel (∫ z,circleLift F (productOrbit w z) ∂circleHaar)
        (∫ z,circleLift G (productOrbit w z) ∂circleHaar)
        (∫ z,circleLift H (productOrbit w z) ∂circleHaar):=by
  rw [integral_orbit_count w F G H hF hG hH hsF hsG hsH,
    integral_orbit_mass w F hF hsF,integral_orbit_mass w G hG hsG,
    integral_orbit_mass w H hH hsH,kernel_scale _ _ _ (by positivity:0 ≤ (2 * Real.pi)⁻¹)]
  apply mul_le_mul_of_nonneg_left _ (sq_nonneg _)
  exact RealContinuousRearrangement.three_function_bound _ _ _
    (lineFunction_continuous w F hF) (lineFunction_continuous w G hG)
    (lineFunction_continuous w H hH) (lineFunction_compactSupport w F hsF)
    (lineFunction_compactSupport w G hsG) (lineFunction_compactSupport w H hsH)
    (lineFunction_range w F hrF) (lineFunction_range w G hrG) (lineFunction_range w H hrH)
end Green24Proof.RealLineOrbitIntegrals
private def zz2453:"s0995"="s0995":=by decide+kernel
end 
section 
namespace Green24Proof.SmallSupportRearrangement
open MeasureTheory Set Filter
open scoped Topology
open Green24Proof.CompactCircleLift Green24Proof.RealTorusDilation
open Green24Proof.RealTorusCoefficientNormalization Green24Proof.CircleLiftCounting
open Green24Proof.CircleProductOrbit Green24Proof.RealLineOrbitIntegrals
open Green24Proof.CircleProbabilityHaar
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
theorem tendsto_of_absolute_error {f e:ℕ → ℝ} {a:ℝ}
    (he:Tendsto e atTop (𝓝 0)) (hf:∀ n, |f n - a| ≤ e n) :
    Tendsto f atTop (𝓝 a):=by
  apply tendsto_iff_dist_tendsto_zero.mpr
  simp only [Real.dist_eq]
  exact squeeze_zero (fun n => abs_nonneg (f n - a)) hf he
theorem lifted_rearrangement_bound (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H)
    (hrF:∀ z,F z ∈ Icc 0 1) (hrG:∀ z,G z ∈ Icc 0 1) (hrH:∀ z,H z ∈ Icc 0 1) :
    (∫ yz,liftedDifferenceIntegrand F G H yz ∂(circleMeasure ι).prod (circleMeasure ι)) ≤
      kernel (∫ z,circleLift F z ∂circleMeasure ι)
        (∫ z,circleLift G z ∂circleMeasure ι) (∫ z,circleLift H z ∂circleMeasure ι):=by
  let L:Fin 3 → CircleSpace ι → ℝ:=![circleLift F,circleLift G,circleLift H]
  have hL (i:Fin 3):Continuous (L i):=by
    fin_cases i
    · exact circleLift_continuous F hF hsF
    · exact circleLift_continuous G hG hsG
    · exact circleLift_continuous H hH hsH
  let K:=liftedDifferenceIntegrand F G H
  have hK:Continuous K:=liftedDifferenceIntegrand_continuous F G H hF hG hH hsF hsG hsH
  let ε:ℕ → ℝ:=fun n => 1 / ((n:ℝ) + 1)
  have hε (n:ℕ):0 < ε n:=by dsimp [ε]; positivity
  choose w hm hc using fun n => exists_joint_approximation 3 L hL K hK (hε n)
  have he:Tendsto (fun n => 2 * ε n) atTop (𝓝 0):=by
    have h:=tendsto_one_div_add_atTop_nhds_zero_nat (𝕜:=ℝ)
    simpa only [mul_zero] using h.const_mul 2
  have hmass (i:Fin 3) :
      Tendsto (fun n => ∫ z,L i (productOrbit (w n) z) ∂circleHaar) atTop
        (𝓝 (∫ z,L i z ∂circleMeasure ι)) :=
    tendsto_of_absolute_error he (fun n => hm n i)
  have hcount:=tendsto_of_absolute_error he hc
  have hargs:=(hmass 0).prodMk_nhds ((hmass 1).prodMk_nhds (hmass 2))
  have hk:=kernel_continuous.continuousAt.tendsto.comp hargs
  exact le_of_tendsto_of_tendsto hcount hk
    (Eventually.of_forall (fun n => orbit_rearrangement_bound (w n) F G H
      hF hG hH hsF hsG hsH hrF hrG hrH))
private def zz1888:"s0760"="s0760":=by decide+kernel
theorem three_function_bound (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:SmallSupport F) (hsG:SmallSupport G) (hsH:SmallSupport H)
    (hrF:∀ z,F z ∈ Icc 0 1) (hrG:∀ z,G z ∈ Icc 0 1) (hrH:∀ z,H z ∈ Icc 0 1) :
    differenceCount F G H ≤ kernel (∫ z,F z ∂measure ι)
      (∫ z,G z ∂measure ι) (∫ z,H z ∂measure ι):=by
  have h:=lifted_rearrangement_bound F G H hF hG hH hsF hsG hsH hrF hrG hrH
  rw [integrated_count_identity F G H hF hG hH hsF hsG hsH] at h
  change ((2 * Real.pi)⁻¹) ^ 2 * differenceCount F G H ≤
    kernel (∫ z,circleLift F z ∂circleHaar.prod _)
      (∫ z,circleLift G z ∂circleHaar.prod _) (∫ z,circleLift H z ∂circleHaar.prod _) at h
  rw [integral_circleLift F hF hsF,integral_circleLift G hG hsG,
    integral_circleLift H hH hsH,kernel_scale _ _ _ (by positivity:0 ≤ (2 * Real.pi)⁻¹)] at h
  exact le_of_mul_le_mul_left h (by positivity:0 < ((2 * Real.pi)⁻¹) ^ 2)
end Green24Proof.SmallSupportRearrangement
private def zz2454:"s0996"="s0996":=by decide+kernel
end 
section 
namespace Green24Proof.RealTorusRearrangement
open MeasureTheory Set
open Green24Proof.RealTorusDilation Green24Proof.RealTorusCoefficientNormalization
open Green24Proof.CompactCircleLift
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
omit [Fintype ι] in
theorem common_small_dilation (F G H:Space ι → ℝ)
    (hsF:HasCompactSupport F) (hsG:HasCompactSupport G) (hsH:HasCompactSupport H) :
    ∃ a:ℝ,0 < a ∧ SmallSupport (pullback a 1 F) ∧
      SmallSupport (pullback a 1 G) ∧ SmallSupport (pullback a 1 H):=by
  let S:=(tsupport F ∪ tsupport G) ∪ tsupport H
  have hS:IsCompact S:=(hsF.union hsG).union hsH
  obtain ⟨R,hR⟩:=hS.exists_bound_of_continuousOn (f:=fun v:Space ι => v.1)
    continuous_fst.continuousOn
  let a:=Real.pi / (4 * (|R| + 1))
  have ha:0 < a:=by dsimp [a]; positivity
  have haR:a * (|R| + 1) = Real.pi / 4:=by
    dsimp [a]
    have hn:|R| + 1 ≠ 0:=by positivity
    field_simp
  have hsmall (J:Space ι → ℝ) (hJ:tsupport J ⊆ S):SmallSupport (pullback a 1 J):=by
    intro t u ht
    change J (t / a,u ^ 1) = 0
    rw [pow_one]
    by_contra hj
    have hm:(t / a,u) ∈ tsupport J:=subset_tsupport _ hj
    have hb:=hR (t / a,u) (hJ hm)
    change |t / a| ≤ R at hb
    rw [abs_div,abs_of_pos ha] at hb
    have htR:|t| ≤ a * R:=by
      have hb':=(div_le_iff₀ ha).mp hb
      linarith
    have hRa:a * R < a * (|R| + 1) :=
      mul_lt_mul_of_pos_left (by linarith [le_abs_self R]) ha
    linarith
  exact ⟨a,ha,hsmall F (fun _ h => Or.inl (Or.inl h)),
    hsmall G (fun _ h => Or.inl (Or.inr h)),hsmall H (fun _ h => Or.inr h)⟩
omit [Fintype ι] in
theorem difference_dilation_identity (a:ℝ) (F G H:Space ι → ℝ)
    (yz:Space ι × Space ι) :
    differenceIntegrand F G H (dilationMap a 1 yz.1,dilationMap a 1 yz.2) =
      differenceIntegrand (pullback a 1 F) (pullback a 1 G) (pullback a 1 H) yz:=by
  simp only [differenceIntegrand,dilationMap,pullback,Function.comp_apply,pow_one,sub_div]
theorem differenceCount_dilation {a:ℝ} (ha:a ≠ 0) (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H) :
    differenceCount (pullback a 1 F) (pullback a 1 G) (pullback a 1 H) =
      a ^ 2 * differenceCount F G H:=by
  have h:=integral_pair_dilation (ι:=ι) ha ha (n:=1) (m:=1) one_ne_zero one_ne_zero
    (differenceIntegrand F G H) (differenceIntegrand_continuous F G H hF hG hH)
  simp_rw [difference_dilation_identity] at h
  simpa only [differenceCount, ← pow_two,sq_abs] using h
private def zz1889:"s0761"="s0761":=by decide+kernel
theorem three_function_bound (F G H:Space ι → ℝ)
    (hF:Continuous F) (hG:Continuous G) (hH:Continuous H)
    (hsF:HasCompactSupport F) (hsG:HasCompactSupport G) (hsH:HasCompactSupport H)
    (hrF:∀ z,F z ∈ Icc 0 1) (hrG:∀ z,G z ∈ Icc 0 1) (hrH:∀ z,H z ∈ Icc 0 1) :
    differenceCount F G H ≤ kernel (∫ z,F z ∂measure ι)
      (∫ z,G z ∂measure ι) (∫ z,H z ∂measure ι):=by
  obtain ⟨a,ha,hsF',hsG',hsH'⟩:=common_small_dilation F G H hsF hsG hsH
  have h:=SmallSupportRearrangement.three_function_bound
    (pullback a 1 F) (pullback a 1 G) (pullback a 1 H)
    (pullback_continuous a 1 F hF) (pullback_continuous a 1 G hG) (pullback_continuous a 1 H hH)
    hsF' hsG' hsH' (pullback_range a 1 F hrF) (pullback_range a 1 G hrG) (pullback_range a 1 H hrH)
  rw [differenceCount_dilation ha.ne' F G H hF hG hH,
    integral_pullback ha.ne' (n:=1) one_ne_zero F hF,
    integral_pullback ha.ne' (n:=1) one_ne_zero G hG,
    integral_pullback ha.ne' (n:=1) one_ne_zero H hH,
    abs_of_pos ha,kernel_scale _ _ _ ha.le] at h
  exact le_of_mul_le_mul_left h (sq_pos_of_pos ha)
theorem rearrangementBound (ι:Type*) [Fintype ι]:RearrangementBound ι :=
  three_function_bound
end Green24Proof.RealTorusRearrangement
private def zz2455:"s0997"="s0997":=by decide+kernel
end 
section 
namespace Green24Proof.TorusCoordinateHaar
open MeasureTheory
open Green24Proof.CircleProbabilityHaar Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def splitEquiv (p:ι):(ι → Circle) ≃* Circle × ({j:ι // j ≠ p} → Circle) where
  toEquiv:=(Homeomorph.funSplitAt Circle p).toEquiv
  map_mul':=by intro z w; rfl
noncomputable def join (p:ι):Circle × ({j:ι // j ≠ p} → Circle) → (ι → Circle) :=
  (splitEquiv p).symm
omit [Fintype ι] in
theorem join_continuous (p:ι):Continuous (join p) :=
  (Homeomorph.funSplitAt Circle p).continuous_invFun
theorem split_measurePreserving (p:ι) :
    MeasurePreserving (splitEquiv p) (torusHaar ι)
      (circleHaar.prod (torusHaar {j:ι // j ≠ p})):=by
  letI:=circleHaar_isProbabilityMeasure
  letI:=circleHaar_isHaarMeasure
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isHaarMeasure ι
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  letI:=torusHaar_isHaarMeasure {j:ι // j ≠ p}
  apply MonoidHom.measurePreserving (f:=(splitEquiv p).toMonoidHom)
  · exact (Homeomorph.funSplitAt Circle p).continuous
  · exact (splitEquiv p).surjective
  · simp
private def zz1890:"s0762"="s0762":=by decide+kernel
theorem integral_split (p:ι) (F:(ι → Circle) → ℝ) :
    (∫ z,F z ∂torusHaar ι) =
      ∫ v,F (join p v) ∂circleHaar.prod (torusHaar {j:ι // j ≠ p}):=by
  have h:=(split_measurePreserving p).integral_comp
    (Homeomorph.funSplitAt Circle p).measurableEmbedding (fun v => F (join p v))
  simpa only [join,MulEquiv.symm_apply_apply] using h
theorem integral_split_iterated (p:ι) (F:(ι → Circle) → ℝ) (hF:Continuous F) :
    (∫ z,F z ∂torusHaar ι) =
      ∫ s, ∫ u,F (join p (s,u)) ∂torusHaar {j:ι // j ≠ p} ∂circleHaar:=by
  letI:=circleHaar_isProbabilityMeasure
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  rw [integral_split p F]
  apply integral_prod
  exact (hF.comp (join_continuous p)).integrable_of_hasCompactSupport
    (HasCompactSupport.of_compactSpace _)
omit [Fintype ι] in
theorem join_equation (p:ι) (y z:Circle × ({j:ι // j ≠ p} → Circle)) :
    join p (z ^ 3 * y ^ (-2:ℤ)) = (join p z) ^ 3 * (join p y) ^ (-2:ℤ):=by
  exact map_mul ((splitEquiv p).symm) _ _ |>.trans (by rw [map_pow,map_zpow]; rfl)
omit [Fintype ι] in
theorem join_pivot (p:ι) (v:Circle × ({j:ι // j ≠ p} → Circle)) :
    join p v p = v.1:=by
  have h:=(splitEquiv p).apply_symm_apply v
  exact congrArg Prod.fst h
end Green24Proof.TorusCoordinateHaar
private def zz2456:"s0998"="s0998":=by decide+kernel
end 
section 
namespace Green24Proof.SpatialCircleCutoff
open scoped NNReal
open Green24Proof.CyclicTorusSmoothing
noncomputable def cutoff (z:Circle):ℝ:=max 0 (min 1 (10 * (z:ℂ).re - 8))
def window:Set Circle:={z | (4 / 5:ℝ) < (z:ℂ).re}
private def zz1891:"s0763"="s0763":=by decide+kernel
theorem cutoff_range (z:Circle):cutoff z ∈ Set.Icc 0 1:=by
  exact ⟨le_max_left _ _,max_le (by norm_num) (min_le_left _ _)⟩
theorem cutoff_eq_one {z:Circle} (hz:(9 / 10:ℝ) ≤ (z:ℂ).re):cutoff z = 1:=by
  unfold cutoff
  rw [min_eq_left (by linarith)]
  norm_num
theorem cutoff_zero_outside (z:Circle) (hz:z ∉ window):cutoff z = 0:=by
  have hr:(z:ℂ).re ≤ (4 / 5:ℝ):=le_of_not_gt hz
  apply max_eq_left
  exact (min_le_right _ _).trans (by linarith)
theorem cutoff_lipschitz:LipschitzWith 10 cutoff:=by
  have hlin:LipschitzWith 10 (fun z:Circle => 10 * (z:ℂ).re - 8):=by
    apply LipschitzWith.of_dist_le_mul
    intro z w
    have h:=component_dist_le false z w
    simp only [component,Bool.false_eq_true,if_false,Real.dist_eq] at h
    change |10 * (z:ℂ).re - 8 - (10 * (w:ℂ).re - 8)| ≤ (10:ℝ) * dist z w
    rw [show 10 * (z:ℂ).re - 8 - (10 * (w:ℂ).re - 8) =
      10 * ((z:ℂ).re - (w:ℂ).re) by ring,abs_mul,abs_of_pos (by norm_num:(0:ℝ) < 10)]
    exact mul_le_mul_of_nonneg_left h (by norm_num)
  exact (hlin.const_min 1).const_max 0
private def zz1892:"s0764"="s0764":=by decide+kernel
theorem cutoff_exp_eq_one {θ:ℝ} (hθ:|θ| ≤ 1 / 4):cutoff (Circle.exp θ) = 1:=by
  apply cutoff_eq_one
  rw [Circle.coe_exp,Complex.exp_ofReal_mul_I_re]
  have hs:θ ^ 2 ≤ (1 / 4:ℝ)^2:=by
    simpa only [sq_abs] using (sq_le_sq₀ (abs_nonneg θ) (by norm_num:(0:ℝ) ≤ 1 / 4)).mpr hθ
  nlinarith [Real.one_sub_sq_div_two_le_cos (x:=θ)]
theorem toCircle_neg_intCast {q:ℕ} [NeZero q] (x:ℤ) :
    ZMod.toCircle (-(x:ZMod q)) = Circle.exp (-2 * Real.pi * (x:ℝ) / q):=by
  apply Circle.coe_injective
  rw [← Int.cast_neg,ZMod.toCircle_intCast,Circle.coe_exp]
  push_cast
  congr 1
  ring
theorem cutoff_integer_plateau {q:ℕ} [NeZero q] (x:ℤ)
    (hx:(32:ℝ) * |(x:ℝ)| ≤ q):cutoff (ZMod.toCircle (-(x:ZMod q))) = 1:=by
  rw [toCircle_neg_intCast]
  apply cutoff_exp_eq_one
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  rw [abs_div,abs_mul,abs_mul,abs_of_pos hq,abs_of_pos Real.pi_pos]
  norm_num only [abs_neg,abs_of_nonneg (by norm_num:(0:ℝ) ≤ 2)]
  apply (div_le_iff₀ hq).mpr
  nlinarith [Real.pi_lt_four,abs_nonneg (x:ℝ)]
end Green24Proof.SpatialCircleCutoff
private def zz2457:"s0999"="s0999":=by decide+kernel
end 
section 
namespace Green24Proof.WindowArcGeometry
open Green24Proof.SpatialCircleCutoff
theorem window_inv_iff (z:Circle):z⁻¹ ∈ window ↔ z ∈ window:=by
  simp only [window,Set.mem_ofPred_eq,Circle.coe_inv_eq_conj,Complex.conj_re]
private def zz1893:"s0765"="s0765":=by decide+kernel
theorem window_zpow_natAbs_iff (z:Circle) (n:ℤ) :
    z ^ n ∈ window ↔ z ^ n.natAbs ∈ window:=by
  cases n with
  | ofNat n => simp
  | negSucc n =>
    simpa only [Int.negSucc_eq, ← Int.natCast_add_one,zpow_neg,zpow_natCast,
      Int.natAbs_neg,Int.natAbs_natCast] using window_inv_iff (z ^ (n + 1))
theorem window_arg_bound {z:Circle} (hz:z ∈ window) :
    |Complex.arg (z:ℂ)| < Real.pi / 4:=by
  have hcos:Real.cos (Complex.arg (z:ℂ)) = (z:ℂ).re:=by
    simpa only [z.norm_coe,div_one] using Complex.cos_arg (Circle.coe_ne_zero z)
  have hconst:Real.cos (Real.pi / 4) < (4 / 5:ℝ):=by
    rw [Real.cos_pi_div_four]
    have hsq:=Real.sq_sqrt (by norm_num:(0:ℝ) ≤ 2)
    have hpos:=Real.sqrt_nonneg (2:ℝ)
    nlinarith
  by_contra h
  have hle:=Real.cos_le_cos_of_nonneg_of_le_pi
    (by positivity:0 ≤ Real.pi / 4) (Complex.abs_arg_le_pi (z:ℂ)) (le_of_not_gt h)
  rw [Real.cos_abs,hcos] at hle
  change (4 / 5:ℝ) < (z:ℂ).re at hz
  linarith
theorem exp_eq_one_no_wrap {t:ℝ} (ht:|t| < 2 * Real.pi)
    (hexp:Circle.exp t = 1):t = 0:=by
  obtain ⟨k,hk⟩:=Circle.exp_eq_one.mp hexp
  have hkp:(0:ℝ) < 2 * Real.pi:=by positivity
  have hkr:|(k:ℝ)| < 1:=by
    rw [hk,abs_mul,abs_of_pos hkp] at ht
    nlinarith
  have hki:|k| < 1:=by exact_mod_cast hkr
  have hk0:k = 0:=by have:=neg_abs_le k; have:=le_abs_self k; omega
  simp [hk,hk0]
theorem linear_form_no_wrap {x y z:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) (hz:|z| < Real.pi / 4) :
    |x + 2 * y - 3 * z| < 2 * Real.pi:=by
  have h1:|x + 2 * y - 3 * z| ≤ |x + 2 * y| + 3 * |z|:=by
    calc
      _ = |(x + 2 * y) + -(3 * z)|:=by rw [sub_eq_add_neg]
      _ ≤ |x + 2 * y| + |-(3 * z)|:=abs_add_le _ _
      _ = _:=by rw [abs_neg,abs_mul]; norm_num
  have h2:=abs_add_le x (2 * y)
  rw [abs_mul,abs_of_pos (by norm_num:(0:ℝ) < 2)] at h2
  nlinarith [Real.pi_pos]
private def zz1894:"s0766"="s0766":=by decide+kernel
theorem exp_equation_iff {x y z:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) (hz:|z| < Real.pi / 4) :
    Circle.exp x * Circle.exp y ^ 2 = Circle.exp z ^ 3 ↔ x + 2 * y = 3 * z:=by
  have heq:Circle.exp (x + 2 * y - 3 * z) =
      Circle.exp x * Circle.exp y ^ 2 / Circle.exp z ^ 3:=by
    rw [Circle.exp_sub,Circle.exp_add]
    congr 2
    · simpa using Circle.exp_natCast_mul y 2
    · simpa using Circle.exp_natCast_mul z 3
  constructor
  · intro h
    have h0:=exp_eq_one_no_wrap (linear_form_no_wrap hx hy hz)
      (by rw [heq,h]; simp)
    linarith
  · intro h
    have h0:Circle.exp (x + 2 * y - 3 * z) = 1:=by rw [h,sub_self,Circle.exp_zero]
    rw [heq,div_eq_one] at h0
    exact h0
end Green24Proof.WindowArcGeometry
private def zz2458:"s099a"="s099a":=by decide+kernel
end 
section 
namespace Green24Proof.CircleArcResidues
open Green24Proof.WindowArcGeometry Green24Proof.SpatialCircleCutoff
noncomputable def arcLift (n r:ℤ) (t:ℝ):Circle :=
  Circle.exp ((t + 2 * Real.pi * r) / n)
theorem arcLift_zpow {n:ℤ} (hn:n ≠ 0) (r:ℤ) (t:ℝ) :
    arcLift n r t ^ n = Circle.exp t:=by
  have hnR:(n:ℝ) ≠ 0:=by exact_mod_cast hn
  unfold arcLift
  rw [← Circle.exp_intCast_mul]
  have h:(n:ℝ) * ((t + 2 * Real.pi * r) / n) = t + 2 * Real.pi * r:=by field_simp
  rw [h,Circle.exp_add,Circle.exp_two_pi_mul_int,mul_one]
theorem exists_arcLift {n:ℤ} (hn:n ≠ 0) (z:Circle) (hz:z ^ n ∈ window) :
    ∃ (r:ℤ) (t:ℝ), |t| < Real.pi / 4 ∧ z = arcLift n r t:=by
  have heq:Circle.exp ((n:ℝ) * Complex.arg (z:ℂ)) =
      Circle.exp (Complex.arg (z ^ n:Circle)):=by
    rw [Circle.exp_intCast_mul,Circle.exp_arg,Circle.exp_arg]
  obtain ⟨r,hr⟩:=Circle.exp_eq_exp.mp heq
  refine ⟨r,Complex.arg (z ^ n:Circle),window_arg_bound hz, ?_⟩
  have hnR:(n:ℝ) ≠ 0:=by exact_mod_cast hn
  calc
    z = Circle.exp (Complex.arg (z:ℂ)):=(Circle.exp_arg z).symm
    _ = arcLift n r (Complex.arg (z ^ n:Circle)):=by
      unfold arcLift
      congr 1
      apply (eq_div_iff hnR).mpr
      linarith
theorem arcLift_equation_expression (n r s t:ℤ) (x y z:ℝ) :
    arcLift n r x * arcLift n s y ^ 2 / arcLift n t z ^ 3 =
      Circle.exp ((x + 2 * y - 3 * z + 2 * Real.pi * (r + 2 * s - 3 * t:ℤ)) / n):=by
  unfold arcLift
  rw [← Circle.exp_natCast_mul, ← Circle.exp_natCast_mul, ← Circle.exp_add, ← Circle.exp_sub]
  congr 1
  push_cast
  ring
private def zz1895:"s0767"="s0767":=by decide+kernel
theorem arcLift_equation_iff {n:ℤ} (hn:n ≠ 0) (r s t:ℤ) {x y z:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) (hz:|z| < Real.pi / 4) :
    arcLift n r x * arcLift n s y ^ 2 = arcLift n t z ^ 3 ↔
      x + 2 * y = 3 * z ∧ n ∣ r + 2 * s - 3 * t:=by
  have hnR:(n:ℝ) ≠ 0:=by exact_mod_cast hn
  have hpi:(2:ℝ) * Real.pi ≠ 0:=by positivity
  constructor
  · intro h
    have hpower:=congrArg (zpowGroupHom n) h
    simp only [map_mul,map_pow,zpowGroupHom_apply,arcLift_zpow hn] at hpower
    have hreal:=(exp_equation_iff hx hy hz).mp hpower
    refine ⟨hreal, ?_⟩
    have he:Circle.exp ((2 * Real.pi * (r + 2 * s - 3 * t:ℤ)) / n) = 1:=by
      have h':=arcLift_equation_expression n r s t x y z
      rw [h,div_self',hreal,sub_self,zero_add] at h'
      exact h'.symm
    obtain ⟨k,hk⟩:=Circle.exp_eq_one.mp he
    have hfrac:((r + 2 * s - 3 * t:ℤ):ℝ) / n = (k:ℝ):=by
      apply mul_left_cancel₀ hpi
      simpa only [mul_div_assoc,mul_comm (k:ℝ) (2 * Real.pi)] using hk
    refine ⟨k, ?_⟩
    have hR:=(div_eq_iff hnR).mp hfrac
    have:((r + 2 * s - 3 * t:ℤ):ℝ) = ((n * k:ℤ):ℝ):=by
      push_cast
      simpa only [Int.cast_add,Int.cast_sub,Int.cast_mul,Int.cast_ofNat,mul_comm] using hR
    exact_mod_cast this
  · rintro ⟨hreal,k,hk⟩
    apply div_eq_one.mp
    rw [arcLift_equation_expression,hreal,sub_self,zero_add,hk]
    have he:(2 * Real.pi * ((n * k:ℤ):ℝ)) / n = (k:ℝ) * (2 * Real.pi):=by
      push_cast
      field_simp
    rw [he,Circle.exp_int_mul_two_pi]
theorem phase_divisibility {n:ℤ} (hn:n ≠ 0) (r:ℤ) :
    Circle.exp ((2 * Real.pi * r) / n) = 1 ↔ n ∣ r:=by
  have hnR:(n:ℝ) ≠ 0:=by exact_mod_cast hn
  have hpi:(2:ℝ) * Real.pi ≠ 0:=by positivity
  rw [Circle.exp_eq_one]
  constructor
  · rintro ⟨k,hk⟩
    have hfrac:(r:ℝ) / n = (k:ℝ):=by
      apply mul_left_cancel₀ hpi
      simpa only [mul_div_assoc,mul_comm (k:ℝ) (2 * Real.pi)] using hk
    refine ⟨k, ?_⟩
    have hR:=(div_eq_iff hnR).mp hfrac
    have h':(r:ℝ) = ((n * k:ℤ):ℝ):=by
      push_cast
      simpa only [mul_comm] using hR
    exact_mod_cast h'
  · rintro ⟨k,rfl⟩
    refine ⟨k, ?_⟩
    push_cast
    field_simp
theorem arcLift_eq_iff {n:ℤ} (hn:n ≠ 0) (r s:ℤ) {x y:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) :
    arcLift n r x = arcLift n s y ↔ x = y ∧ n ∣ r - s:=by
  have hdiv:arcLift n r x / arcLift n s y =
      Circle.exp ((x - y + 2 * Real.pi * (r - s:ℤ)) / n):=by
    unfold arcLift
    rw [← Circle.exp_sub]
    congr 1
    push_cast
    ring
  constructor
  · intro h
    have hpower:=congrArg (fun u:Circle => u ^ n) h
    change arcLift n r x ^ n = arcLift n s y ^ n at hpower
    rw [arcLift_zpow hn,arcLift_zpow hn] at hpower
    have hxy:x = y:=Circle.exp_injOn_Icc
      (a:=-(Real.pi / 4)) (b:=Real.pi / 4) (by linarith [Real.pi_pos])
      (by obtain ⟨h1,h2⟩:=abs_lt.mp hx; exact ⟨h1.le,h2.le⟩)
      (by obtain ⟨h1,h2⟩:=abs_lt.mp hy; exact ⟨h1.le,h2.le⟩) hpower
    refine ⟨hxy,(phase_divisibility hn _).mp ?_⟩
    rw [h,div_self',hxy,sub_self,zero_add] at hdiv
    exact hdiv.symm
  · rintro ⟨hxy,hrs⟩
    apply div_eq_one.mp
    rw [hdiv,hxy,sub_self,zero_add]
    exact (phase_divisibility hn _).mpr hrs
theorem arcLift_eq_iff_zmod {q:ℕ} [NeZero q] (r s:ZMod q) {x y:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) :
    arcLift q r.val x = arcLift q s.val y ↔ x = y ∧ r = s:=by
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  rw [arcLift_eq_iff hq _ _ hx hy]
  have hres:(q:ℤ) ∣ (r.val:ℤ) - (s.val:ℤ) ↔ r = s:=by
    rw [← ZMod.intCast_zmod_eq_zero_iff_dvd ((r.val:ℤ) - (s.val:ℤ)) q]
    simp only [Int.cast_sub,ZMod.natCast_val,ZMod.intCast_cast,ZMod.cast_id,sub_eq_zero]
  rw [hres]
private def zz1896:"s0768"="s0768":=by decide+kernel
theorem exists_residue_arcLift {q:ℕ} [NeZero q] (z:Circle) (hz:z ^ (q:ℤ) ∈ window) :
    ∃ (r:ZMod q) (t:ℝ), |t| < Real.pi / 4 ∧ z = arcLift q r.val t:=by
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  obtain ⟨r,t,ht,hr⟩:=exists_arcLift hq z hz
  refine ⟨(r:ZMod q),t,ht,hr.trans ?_⟩
  apply (arcLift_eq_iff hq _ _ ht ht).mpr
  refine ⟨rfl, ?_⟩
  rw [← ZMod.intCast_zmod_eq_zero_iff_dvd]
  simp
theorem arcLift_equation_iff_zmod {q:ℕ} [NeZero q] (r s t:ZMod q) {x y z:ℝ}
    (hx:|x| < Real.pi / 4) (hy:|y| < Real.pi / 4) (hz:|z| < Real.pi / 4) :
    arcLift q r.val x * arcLift q s.val y ^ 2 = arcLift q t.val z ^ 3 ↔
      x + 2 * y = 3 * z ∧ r + 2 * s = 3 * t:=by
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  rw [arcLift_equation_iff hq _ _ _ hx hy hz]
  have hres:(q:ℤ) ∣ (r.val:ℤ) + 2 * s.val - 3 * t.val ↔ r + 2 * s = 3 * t:=by
    rw [← ZMod.intCast_zmod_eq_zero_iff_dvd ((r.val:ℤ) + 2 * s.val - 3 * t.val) q]
    simp only [Int.cast_sub,Int.cast_add,Int.cast_mul,Int.cast_ofNat,
      ZMod.natCast_val,ZMod.intCast_cast,ZMod.cast_id,sub_eq_zero]
  rw [hres]
end Green24Proof.CircleArcResidues
private def zz2459:"s099b"="s099b":=by decide+kernel
end 
section 
namespace Green24Proof.CircleArcHaar
open MeasureTheory Finset
open scoped BigOperators
open Green24Proof.CircleProbabilityHaar Green24Proof.CircleArcResidues
variable [MeasurableSpace Circle] [BorelSpace Circle]
theorem integral_arcLift (F:Circle → ℝ) {q:ℕ} (hq:0 < q) (r:ℕ) :
    (∫ t in -Real.pi..Real.pi,F (arcLift q r t)) =
      (q:ℝ) * ∫ t in (-Real.pi + 2 * Real.pi * r) / q..
        (Real.pi + 2 * Real.pi * r) / q,F (Circle.exp t):=by
  have hqR:(q:ℝ) ≠ 0:=by exact_mod_cast (Nat.ne_zero_of_lt hq)
  simp only [arcLift,Int.cast_natCast]
  rw [intervalIntegral.integral_comp_add_right (fun t => F (Circle.exp (t / q))),
    intervalIntegral.integral_comp_div (fun t => F (Circle.exp t)) hqR,smul_eq_mul]
theorem integral_sum_arcs_range (F:Circle → ℝ) (hF:Continuous F) {q:ℕ} (hq:0 < q) :
    (∫ z,F z ∂circleHaar) =
      (2 * Real.pi * q)⁻¹ * ∑ r ∈ range q, ∫ t in -Real.pi..Real.pi,F (arcLift q r t):=by
  have hqR:(q:ℝ) ≠ 0:=by exact_mod_cast (Nat.ne_zero_of_lt hq)
  have hpi:(2:ℝ) * Real.pi ≠ 0:=by positivity
  let a:ℕ → ℝ:=fun r => (-Real.pi + 2 * Real.pi * r) / q
  have ha0:a 0 = -Real.pi / q:=by simp [a]
  have haq:a q = -Real.pi / q + 2 * Real.pi:=by dsimp [a]; field_simp
  have hstep (r:ℕ):(Real.pi + 2 * Real.pi * r) / (q:ℝ) = a (r + 1):=by
    dsimp [a]
    push_cast
    ring
  have hs:(∑ r ∈ range q, ∫ t in -Real.pi..Real.pi,F (arcLift q r t)) =
      (q:ℝ) * ∫ t in a 0..a q,F (Circle.exp t):=by
    simp_rw [integral_arcLift F hq,hstep]
    rw [← mul_sum]
    congr 1
    exact intervalIntegral.sum_integral_adjacent_intervals
      (fun _ _ => (hF.comp Circle.exp.continuous).intervalIntegrable _ _)
  rw [hs,ha0,haq,integral_exp F hF (-Real.pi / q)]
  field_simp
private def zz1897:"s0769"="s0769":=by decide+kernel
theorem sum_residue_vals {q:ℕ} [NeZero q] (f:ℕ → ℝ) :
    (∑ r ∈ range q,f r) = ∑ r:ZMod q,f r.val:=by
  apply sum_bij (fun (r:ℕ) _ => (r:ZMod q))
  · intro r _
    exact mem_univ _
  · intro r hr s hs hrs
    have h:=congrArg ZMod.val hrs
    simpa only [ZMod.val_natCast_of_lt (mem_range.mp hr),
      ZMod.val_natCast_of_lt (mem_range.mp hs)] using h
  · intro r _
    exact ⟨r.val,mem_range.mpr (ZMod.val_lt r),by simp⟩
  · intro r hr
    rw [ZMod.val_natCast_of_lt (mem_range.mp hr)]
theorem integral_sum_arcs (F:Circle → ℝ) (hF:Continuous F) {q:ℕ} [NeZero q] :
    (∫ z,F z ∂circleHaar) =
      (2 * Real.pi * q)⁻¹ * ∑ r:ZMod q, ∫ t in -Real.pi..Real.pi,F (arcLift q r.val t):=by
  rw [integral_sum_arcs_range F hF (NeZero.pos q),sum_residue_vals]
end Green24Proof.CircleArcHaar
private def zz2460:"s099c"="s099c":=by decide+kernel
end 
section 
namespace Green24Proof.TorusArcMass
open MeasureTheory
open scoped BigOperators
open Green24Proof.CircleProbabilityHaar Green24Proof.CircleArcResidues
open Green24Proof.CircleArcHaar Green24Proof.TorusCoordinateHaar
open Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def sliceMass (p:ι) (F:(ι → Circle) → ℝ) (s:Circle):ℝ :=
  ∫ u,F (join p (s,u)) ∂torusHaar {j:ι // j ≠ p}
theorem sliceMass_continuous (p:ι) (F:(ι → Circle) → ℝ) (hF:Continuous F) :
    Continuous (sliceMass p F):=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  have h:=continuous_parametric_integral_of_continuous
    (μ:=torusHaar {j:ι // j ≠ p}) (f:=fun s u => F (join p (s,u)))
    (hF.comp (join_continuous p)) (s:=Set.univ) isCompact_univ
  unfold sliceMass
  simpa only [Measure.restrict_univ] using h
noncomputable def angularPullback (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (r:ZMod q) (v:ℝ × ({j:ι // j ≠ p} → Circle)):ℝ :=
  F (join p (arcLift q r.val v.1,v.2))
omit [Fintype ι] in
theorem angularPullback_continuous (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (r:ZMod q):Continuous (angularPullback p q F r):=by
  unfold angularPullback arcLift
  apply hF.comp
  apply (join_continuous p).comp
  fun_prop
private def zz1898:"s076a"="s076a":=by decide+kernel
omit [Fintype ι] in
theorem angularPullback_range (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (hF:∀ z,F z ∈ Set.Icc 0 1) (r:ZMod q) (v:ℝ × ({j:ι // j ≠ p} → Circle)) :
    angularPullback p q F r v ∈ Set.Icc 0 1:=hF _
theorem integral_sum_residue_arcs (p:ι) {q:ℕ} [NeZero q]
    (F:(ι → Circle) → ℝ) (hF:Continuous F) :
    (∫ z,F z ∂torusHaar ι) =
      (2 * Real.pi * q)⁻¹ * ∑ r:ZMod q,
        ∫ t in -Real.pi..Real.pi, ∫ u,
          angularPullback p q F r (t,u) ∂torusHaar {j:ι // j ≠ p}:=by
  rw [integral_split_iterated p F hF]
  exact integral_sum_arcs (sliceMass p F) (sliceMass_continuous p F hF)
end Green24Proof.TorusArcMass
private def zz2461:"s099d"="s099d":=by decide+kernel
end 
section 
namespace Green24Proof.TorusArcPairIntegral
open MeasureTheory Set
open scoped BigOperators
open Green24Proof.TorusArcMass Green24Proof.TorusCoordinateHaar
open Green24Proof.CircleArcResidues Green24Proof.CyclicTorusHaarDiscrepancy
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {X:Type*} [TopologicalSpace X] [FirstCountableTopology X]
  [LocallyCompactSpace X]
theorem torus_marginal_continuous {ι:Type*} [Fintype ι]
    (K:X × (ι → Circle) → ℝ) (hK:Continuous K) :
    Continuous (fun x => ∫ u,K (x,u) ∂torusHaar ι):=by
  letI:=torusHaar_isProbabilityMeasure ι
  have h:=continuous_parametric_integral_of_continuous
    (μ:=torusHaar ι) (f:=fun x u => K (x,u)) hK
    (s:=Set.univ) isCompact_univ
  simpa only [Measure.restrict_univ] using h
theorem interval_marginal_continuous (K:X × ℝ → ℝ) (hK:Continuous K)
    {a b:ℝ} (hab:a ≤ b) :
    Continuous (fun x => ∫ t in a..b,K (x,t)):=by
  have h:=continuous_parametric_integral_of_continuous
    (μ:=volume) (f:=fun x t => K (x,t)) hK
    (s:=Icc a b) isCompact_Icc
  simpa only [integral_Icc_eq_integral_Ioc,intervalIntegral.integral_of_le hab] using h
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def arcMarginal (p:ι) (q:ℕ) (k:ZMod q)
    (K:X × (ι → Circle) → ℝ) (x:X):ℝ :=
  ∫ t in -Real.pi..Real.pi, ∫ v,
    K (x,join p (arcLift q k.val t,v)) ∂torusHaar {j:ι // j ≠ p}
private def zz1899:"s076b"="s076b":=by decide+kernel
theorem arcMarginal_continuous (p:ι) (q:ℕ) (k:ZMod q)
    (K:X × (ι → Circle) → ℝ) (hK:Continuous K) :
    Continuous (arcMarginal p q k K):=by
  unfold arcMarginal
  apply interval_marginal_continuous
    (fun xt:X × ℝ => ∫ v,K (xt.1,join p (arcLift q k.val xt.2,v))
      ∂torusHaar {j:ι // j ≠ p})
  · apply torus_marginal_continuous
      (fun xtv:(X × ℝ) × ({j:ι // j ≠ p} → Circle) =>
        K (xtv.1.1,join p (arcLift q k.val xtv.1.2,xtv.2)))
    apply hK.comp
    apply Continuous.prodMk continuous_fst.fst
    apply (join_continuous p).comp
    unfold arcLift
    fun_prop
  · linarith [Real.pi_pos]
theorem integral_pair_sum_residue_arcs (p:ι) {q:ℕ} [NeZero q]
    (K:(ι → Circle) × (ι → Circle) → ℝ) (hK:Continuous K) :
    (∫ yz,K yz ∂(torusHaar ι).prod (torusHaar ι)) =
      ((2 * Real.pi * q)⁻¹) ^ 2 * ∑ j:ZMod q, ∑ k:ZMod q,
        ∫ s in -Real.pi..Real.pi, ∫ u,
          (∫ t in -Real.pi..Real.pi, ∫ v,
            K (join p (arcLift q j.val s,u),join p (arcLift q k.val t,v))
              ∂torusHaar {i:ι // i ≠ p}) ∂torusHaar {i:ι // i ≠ p}:=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  classical
  have hinner (y:ι → Circle) :
      (∫ z,K (y,z) ∂torusHaar ι) =
        (2 * Real.pi * q)⁻¹ * ∑ k:ZMod q,arcMarginal p q k K y:=by
    exact integral_sum_residue_arcs p (q:=q) (fun z => K (y,z))
      (hK.comp (continuous_const.prodMk continuous_id))
  have hcont (k:ZMod q):=arcMarginal_continuous p q k K hK
  rw [integral_prod _ (hK.integrable_of_hasCompactSupport
    (HasCompactSupport.of_compactSpace _))]
  simp_rw [hinner]
  rw [integral_const_mul,integral_finsetSum]
  · simp_rw [integral_sum_residue_arcs p (q:=q) _ (hcont _)]
    rw [← Finset.mul_sum,Finset.sum_comm]
    simp only [angularPullback,arcMarginal]
    ring
  · intro k _
    exact (hcont k).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)
end Green24Proof.TorusArcPairIntegral
private def zz2462:"s099e"="s099e":=by decide+kernel
end 
section 
namespace Green24Proof.CompactTorusArcModel
open MeasureTheory Set
open scoped BigOperators
open Green24Proof.TorusArcMass Green24Proof.TorusCoordinateHaar
open Green24Proof.CircleArcResidues Green24Proof.WindowArcGeometry
open Green24Proof.SpatialCircleCutoff Green24Proof.CyclicTorusHaarDiscrepancy
noncomputable def realCutoff (t:ℝ):ℝ:=max 0 (min 1 (2 - 4 * |t| / Real.pi))
theorem realCutoff_continuous:Continuous realCutoff:=by unfold realCutoff; fun_prop
theorem realCutoff_range (t:ℝ):realCutoff t ∈ Icc 0 1 :=
  ⟨le_max_left _ _,max_le (by norm_num) (min_le_left _ _)⟩
private def zz1900:"s076c"="s076c":=by decide+kernel
theorem realCutoff_one {t:ℝ} (ht:|t| ≤ Real.pi / 4):realCutoff t = 1:=by
  have h:4 * |t| / Real.pi ≤ 1:=(div_le_iff₀ Real.pi_pos).mpr (by linarith)
  unfold realCutoff
  rw [min_eq_left (by linarith)]
  norm_num
theorem realCutoff_zero {t:ℝ} (ht:Real.pi / 2 ≤ |t|):realCutoff t = 0:=by
  have h:2 ≤ 4 * |t| / Real.pi:=(le_div_iff₀ Real.pi_pos).mpr (by linarith)
  unfold realCutoff
  apply max_eq_left
  exact (min_le_right _ _).trans (by linarith)
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def model (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (r:ZMod q) (v:ℝ × ({j:ι // j ≠ p} → Circle)):ℝ :=
  realCutoff v.1 * angularPullback p q F r v
omit [Fintype ι] in
theorem model_continuous (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ) (hF:Continuous F)
    (r:ZMod q):Continuous (model p q F r) :=
  (realCutoff_continuous.comp continuous_fst).mul (angularPullback_continuous p q F hF r)
omit [Fintype ι] in
theorem model_range (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ) (hF:∀ z,F z ∈ Icc 0 1)
    (r:ZMod q) (v:ℝ × ({j:ι // j ≠ p} → Circle)):model p q F r v ∈ Icc 0 1:=by
  have h1:=realCutoff_range v.1
  have h2:=angularPullback_range p q F hF r v
  exact ⟨mul_nonneg h1.1 h2.1,mul_le_one₀ h1.2 h2.1 h2.2⟩
private def zz1901:"s076d"="s076d":=by decide+kernel
omit [Fintype ι] in
theorem model_zero_outside (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (r:ZMod q) (v:ℝ × ({j:ι // j ≠ p} → Circle))
    (hv:Real.pi / 2 ≤ |v.1|):model p q F r v = 0:=by
  rw [model,realCutoff_zero hv,zero_mul]
omit [Fintype ι] in
theorem model_compactSupport (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ) (r:ZMod q) :
    HasCompactSupport (model p q F r):=by
  apply HasCompactSupport.intro
    (isCompact_Icc.prod (isCompact_univ:IsCompact (univ:Set ({j:ι // j ≠ p} → Circle))))
  intro v hv
  apply model_zero_outside
  have h:v.1 ∉ Icc (-(Real.pi / 2)) (Real.pi / 2):=fun h => hv ⟨h,trivial⟩
  have hn:¬ |v.1| ≤ Real.pi / 2:=fun h' => h (abs_le.mp h')
  exact (lt_of_not_ge hn).le
omit [Fintype ι] in
theorem angular_nonzero_small (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) (r:ZMod q)
    {t:ℝ} (ht:t ∈ Ioo (-Real.pi) Real.pi) (u:{j:ι // j ≠ p} → Circle)
    (hval:angularPullback p q F r (t,u) ≠ 0):|t| < Real.pi / 4:=by
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  have hpow:arcLift q r.val t ^ q = Circle.exp t:=by
    simpa only [zpow_natCast] using arcLift_zpow hq r.val t
  have hw:Circle.exp t ∈ window:=by
    by_contra h
    apply hval
    apply hs
    simpa only [join_pivot,hpow] using h
  have h:=window_arg_bound hw
  rwa [Circle.arg_exp ht.1 ht.2.le] at h
omit [Fintype ι] in
theorem model_agrees_on_principal (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) (r:ZMod q)
    {t:ℝ} (ht:t ∈ Ioo (-Real.pi) Real.pi) (u:{j:ι // j ≠ p} → Circle) :
    model p q F r (t,u) = angularPullback p q F r (t,u):=by
  by_cases h:angularPullback p q F r (t,u) = 0
  · simp only [model,h,mul_zero]
  · rw [model,realCutoff_one (angular_nonzero_small p F hs r ht u h).le,one_mul]
private def zz1902:"s076e"="s076e":=by decide+kernel
omit [Fintype ι] in
theorem model_nonzero_small (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) (r:ZMod q)
    (v:ℝ × ({j:ι // j ≠ p} → Circle)) (hv:model p q F r v ≠ 0) :
    |v.1| < Real.pi / 4:=by
  have hsmall:|v.1| < Real.pi / 2:=by
    by_contra h
    exact hv (model_zero_outside p q F r v (le_of_not_gt h))
  have hprincipal:v.1 ∈ Ioo (-Real.pi) Real.pi:=by
    obtain ⟨h1,h2⟩:=abs_lt.mp hsmall
    exact ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
  have hval:angularPullback p q F r (v.1,v.2) ≠ 0:=by
    intro h
    apply hv
    rw [model,h,mul_zero]
  exact angular_nonzero_small p F hs r hprincipal v.2 hval
theorem model_integrable (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ) (hF:Continuous F)
    (r:ZMod q):Integrable (model p q F r)
      (volume.prod (torusHaar {j:ι // j ≠ p})):=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  exact (model_continuous p q F hF r).integrable_of_hasCompactSupport (model_compactSupport p q F r)
theorem integral_model_eq_arc (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hs:∀ z,z p ^ q ∉ window → F z = 0) (r:ZMod q) :
    (∫ v,model p q F r v ∂volume.prod (torusHaar {j:ι // j ≠ p})) =
      ∫ t in -Real.pi..Real.pi, ∫ u,angularPullback p q F r (t,u)
        ∂torusHaar {j:ι // j ≠ p}:=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  rw [integral_prod _ (model_integrable p q F hF r)]
  have hsupport:Function.support (fun t => ∫ u,model p q F r (t,u)
      ∂torusHaar {j:ι // j ≠ p}) ⊆ Ioc (-Real.pi) Real.pi:=by
    intro t ht
    by_contra h
    have habs:Real.pi / 2 ≤ |t|:=by
      by_contra h'
      have ha:=abs_lt.mp (lt_of_not_ge h')
      exact h ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
    have hzero:(∫ u,model p q F r (t,u) ∂torusHaar {j:ι // j ≠ p}) = 0:=by
      simp_rw [show ∀ u,model p q F r (t,u) = 0 from
        fun u => model_zero_outside p q F r (t,u) habs]
      exact integral_zero _ _
    exact ht hzero
  rw [← intervalIntegral.integral_eq_integral_of_support_subset hsupport]
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht
  apply integral_congr_ae
  filter_upwards [] with u
  exact model_agrees_on_principal p F hs r ht u
theorem mass_identity (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hs:∀ z,z p ^ q ∉ window → F z = 0) :
    (∫ z,F z ∂torusHaar ι) =
      (2 * Real.pi * q)⁻¹ * ∑ r:ZMod q,
        ∫ v,model p q F r v ∂volume.prod (torusHaar {j:ι // j ≠ p}):=by
  rw [integral_sum_residue_arcs p (q:=q) F hF]
  congr 1
  apply Finset.sum_congr rfl
  intro r _
  exact (integral_model_eq_arc p F hF hs r).symm
end Green24Proof.CompactTorusArcModel
private def zz2463:"s099f"="s099f":=by decide+kernel
end 
section 
namespace Green24Proof.ArcLiftAlgebra
open Green24Proof.CircleArcResidues
private def zz1903:"s076f"="s076f":=by decide+kernel
theorem arcLift_mul (n r s:ℤ) (x y:ℝ) :
    arcLift n (r + s) (x + y) = arcLift n r x * arcLift n s y:=by
  unfold arcLift
  rw [← Circle.exp_add]
  congr 1
  push_cast
  ring
theorem arcLift_zpow_linear (n r k:ℤ) (x:ℝ) :
    arcLift n (k * r) ((k:ℝ) * x) = arcLift n r x ^ k:=by
  unfold arcLift
  rw [← Circle.exp_intCast_mul]
  congr 1
  push_cast
  ring
theorem arcLift_change_label {n:ℤ} (hn:n ≠ 0) (r s:ℤ) (t:ℝ)
    (h:n ∣ r - s):arcLift n r t = arcLift n s t:=by
  apply div_eq_one.mp
  have heq:arcLift n r t / arcLift n s t =
      Circle.exp ((2 * Real.pi * (r - s:ℤ)) / n):=by
    unfold arcLift
    rw [← Circle.exp_sub]
    congr 1
    push_cast
    ring
  rw [heq]
  exact (phase_divisibility hn _).mpr h
theorem arcLift_affine {q:ℕ} [NeZero q] (j k:ZMod q) (s t:ℝ) :
    arcLift q k.val t ^ 3 * arcLift q j.val s ^ (-2:ℤ) =
      arcLift q (3 * k - 2 * j).val (3 * t - 2 * s):=by
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  let R:ℤ:=3 * k.val - 2 * j.val
  have halg:arcLift q k.val t ^ 3 * arcLift q j.val s ^ (-2:ℤ) =
      arcLift q R (3 * t - 2 * s):=by
    change arcLift q k.val t ^ (3:ℤ) * arcLift q j.val s ^ (-2:ℤ) = _
    rw [← arcLift_zpow_linear, ← arcLift_zpow_linear, ← arcLift_mul]
    congr 1
    simp
    ring
  rw [halg]
  apply arcLift_change_label hq
  rw [← ZMod.intCast_zmod_eq_zero_iff_dvd (R - ((3 * k - 2 * j).val:ℤ)) q]
  simp [R]
end Green24Proof.ArcLiftAlgebra
private def zz2464:"s09a0"="s09a0":=by decide+kernel
end 
section 
namespace Green24Proof.WindowExpUnwrapping
open Green24Proof.WindowArcGeometry Green24Proof.SpatialCircleCutoff
private def zz1904:"s0770"="s0770":=by decide+kernel
theorem small_of_exp_mem_window {t:ℝ} (ht:|t| < 7 * Real.pi / 4)
    (hw:Circle.exp t ∈ window):|t| < Real.pi / 4:=by
  let a:=Complex.arg (Circle.exp t:ℂ)
  have ha:|a| < Real.pi / 4:=window_arg_bound hw
  have he:Circle.exp (t - a) = 1:=by
    rw [Circle.exp_sub]
    have h:Circle.exp a = Circle.exp t:=Circle.exp_arg _
    rw [h]
    simp
  have hdiff:|t - a| < 2 * Real.pi:=by
    have h:=abs_add_le t (-a)
    rw [abs_neg, ← sub_eq_add_neg] at h
    linarith
  have hzero:=exp_eq_one_no_wrap hdiff he
  have hta:t = a:=sub_eq_zero.mp hzero
  rwa [hta]
end Green24Proof.WindowExpUnwrapping
private def zz2465:"s09a1"="s09a1":=by decide+kernel
end 
section 
namespace Green24Proof.CompactTorusArcCounting
open Set
open Green24Proof.CompactTorusArcModel Green24Proof.TorusArcMass
open Green24Proof.TorusCoordinateHaar Green24Proof.CircleArcResidues
open Green24Proof.SpatialCircleCutoff Green24Proof.WindowExpUnwrapping
open Green24Proof.ArcLiftAlgebra
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [DecidableEq ι]
theorem model_agrees_on_wide (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) (r:ZMod q) {t:ℝ}
    (ht:|t| < 7 * Real.pi / 4) (u:{j:ι // j ≠ p} → Circle) :
    model p q F r (t,u) = angularPullback p q F r (t,u):=by
  by_cases hval:angularPullback p q F r (t,u) = 0
  · simp only [model,hval,mul_zero]
  have hq:(q:ℤ) ≠ 0:=by exact_mod_cast (NeZero.ne q)
  have hpow:arcLift q r.val t ^ q = Circle.exp t:=by
    simpa only [zpow_natCast] using arcLift_zpow hq r.val t
  have hw:Circle.exp t ∈ window:=by
    by_contra h
    apply hval
    apply hs
    simpa only [join_pivot,hpow] using h
  rw [model,realCutoff_one (small_of_exp_mem_window ht hw).le,one_mul]
theorem counting_integrand_identity (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) (j k:ZMod q) {s t:ℝ}
    (hs':s ∈ Ioo (-Real.pi) Real.pi) (ht':t ∈ Ioo (-Real.pi) Real.pi)
    (u v:{j:ι // j ≠ p} → Circle) :
    F ((join p (arcLift q k.val t,v)) ^ 3 *
        (join p (arcLift q j.val s,u)) ^ (-2:ℤ)) *
      F (join p (arcLift q j.val s,u)) * F (join p (arcLift q k.val t,v)) =
    model p q F (3 * k - 2 * j) (3 * t - 2 * s,v ^ 3 * u ^ (-2:ℤ)) *
      model p q F j (s,u) * model p q F k (t,v):=by
  have hpoint:(join p (arcLift q k.val t,v)) ^ 3 *
      (join p (arcLift q j.val s,u)) ^ (-2:ℤ) =
      join p (arcLift q (3 * k - 2 * j).val (3 * t - 2 * s),v ^ 3 * u ^ (-2:ℤ)):=by
    rw [← join_equation]
    congr 1
    apply Prod.ext
    · exact arcLift_affine j k s t
    · rfl
  rw [hpoint]
  change angularPullback p q F (3 * k - 2 * j) (3 * t - 2 * s,v ^ 3 * u ^ (-2:ℤ)) *
      angularPullback p q F j (s,u) * angularPullback p q F k (t,v) = _
  rw [← model_agrees_on_principal p F hs j hs' u,
    ← model_agrees_on_principal p F hs k ht' v]
  by_cases hj:model p q F j (s,u) = 0
  · simp only [hj,mul_zero,zero_mul]
  by_cases hk:model p q F k (t,v) = 0
  · simp only [hk,mul_zero]
  have hs0:=model_nonzero_small p F hs j (s,u) hj
  have ht0:=model_nonzero_small p F hs k (t,v) hk
  have hwide:|3 * t - 2 * s| < 7 * Real.pi / 4:=by
    have h:=abs_add_le (3 * t) (-(2 * s))
    rw [← sub_eq_add_neg,abs_neg,abs_mul,abs_mul] at h
    norm_num at h
    change |s| < Real.pi / 4 at hs0
    change |t| < Real.pi / 4 at ht0
    nlinarith [Real.pi_pos]
  rw [model_agrees_on_wide p F hs (3 * k - 2 * j) hwide]
end Green24Proof.CompactTorusArcCounting
private def zz2466:"s09a2"="s09a2":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicCharacterRefinement
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.CyclicWeakRegularity (FourierUniform stepBound stepBound_exceeds_energy
  normalized_energy_nonneg normalized_energy_le_one energy_comp_injective)
open Green24Proof.CyclicShiftedCharacterFactor
open Green24Proof.ShiftedScalarQuantization (gridValue gridValue_mem_Icc)
open Green24Proof.FiniteGridBoundaryAvoidance
variable {q M:ℕ} [NeZero q]
variable {β:Type*} [Fintype β] [DecidableEq β]
noncomputable def combinedFactor {n:ℕ} (ρ:ZMod q → β) (η:ℝ)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M)
    (x:ZMod q):β × Alphabet η n:=(ρ x,phaseFactor η ks bs as x)
omit [Fintype β] [DecidableEq β] in
theorem combinedFactor_refines {n:ℕ} (ρ:ZMod q → β) (η:ℝ)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M) (x:ZMod q) :
    ρ x = (combinedFactor ρ η ks bs as x).1:=rfl
private def zz1905:"s0771"="s0771":=by decide+kernel
omit [Fintype β] in
theorem combinedFactor_zero_energy (ρ:ZMod q → β) (f:ZMod q → ℝ) (η:ℝ)
    (ks:Fin 0 → ZMod q) (bs:Fin 0 → Bool) (as:Fin 0 → Fin M) :
    Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η ks bs as) f = Green24Proof.FinitePartitionRefinement.energy ρ f:=by
  let e:β → β × Alphabet η 0:=fun b => (b,Fin.elim0)
  have he:Function.Injective e:=fun _ _ h => congrArg Prod.fst h
  have hp:combinedFactor ρ η ks bs as = fun x => e (ρ x):=by
    funext x
    apply Prod.ext
    · rfl
    · exact Subsingleton.elim _ _
  rw [hp,energy_comp_injective ρ e he f]
theorem exists_combined_extension {n:ℕ} (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M)
    (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M) (k:ZMod q)
    (hlarge:η * q ≤ ‖ZMod.dft
      (fun x => ((f x - average (combinedFactor ρ η ks bs as) f x:ℝ):ℂ)) k‖) :
    ∃ (b:Bool) (a:Fin M),
      M * (badSamples a (characterCoordinate η k b)).card ≤ q ∧
      Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η ks bs as) f / q + η ^ 2 / 16 ≤
        Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as)) f / q:=by
  let σ:=combinedFactor ρ η ks bs as
  have hr:∀ x, |f x - average σ f x| ≤ 1 :=
    fun x => abs_le.mpr (residual_mem_Icc σ f hf x)
  obtain ⟨b,a,ha,hc⟩:=exists_shifted_correlating_component
    (fun x => f x - average σ f x) k hr hη hM hlarge
  let π:=combinedFactor ρ η (Fin.cons k ks) (Fin.cons b bs) (Fin.cons a as)
  let φ:β × Alphabet η (n + 1) → β × Alphabet η n:=fun v => (v.1,Fin.tail v.2)
  let g:β × Alphabet η (n + 1) → ℝ:=fun v => gridValue (resolution η) (offset a) (v.2 0)
  have hg:∀ x, |g (π x)| ≤ 1 :=
    fun x => abs_le.mpr (gridValue_mem_Icc (resolution η) (offset a) ((π x).2 0))
  have href:∀ x,σ x = φ (π x):=by
    intro x
    apply Prod.ext rfl
    exact phaseFactor_cons_tail η ks bs as k b a x
  have hcorr:(η / 4) * Fintype.card (ZMod q) ≤
      |∑ x,(f x - average σ f x) * g (π x)|:=by
    simpa only [ZMod.card,g,π,combinedFactor,phaseFactor_cons,Fin.cons_zero] using hc
  have hi:=normalized_energy_increment π σ φ href f g
    (show 0 ≤ η / 4 by positivity) hg hcorr
  refine ⟨b,a,ha, ?_⟩
  norm_num only [ZMod.card,div_pow] at hi
  exact hi
theorem exists_uniform_refinement_or_large_energy (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) (n:ℕ) :
    (∃ j ≤ n, ∃ (ks:Fin j → ZMod q) (bs:Fin j → Bool) (as:Fin j → Fin M),
      BoundaryControlled η ks bs as ∧ FourierUniform (combinedFactor ρ η ks bs as) f η) ∨
    ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M),
      BoundaryControlled η ks bs as ∧
      Green24Proof.FinitePartitionRefinement.energy ρ f / q + (n:ℝ) * (η ^ 2 / 16) ≤ Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η ks bs as) f / q:=by
  classical
  induction n with
  | zero =>
      right
      let ks:Fin 0 → ZMod q:=Fin.elim0
      let bs:Fin 0 → Bool:=Fin.elim0
      let as:Fin 0 → Fin M:=Fin.elim0
      refine ⟨ks,bs,as,fun i => Fin.elim0 i, ?_⟩
      simp only [Nat.cast_zero,zero_mul,add_zero,combinedFactor_zero_energy,le_refl]
  | succ n ih =>
      rcases ih with ⟨j,hj,ks,bs,as,hc,hu⟩ | ⟨ks,bs,as,hc,he⟩
      · exact Or.inl ⟨j,hj.trans (Nat.le_succ n),ks,bs,as,hc,hu⟩
      · by_cases hu:FourierUniform (combinedFactor ρ η ks bs as) f η
        · exact Or.inl ⟨n,Nat.le_succ n,ks,bs,as,hc,hu⟩
        · change ¬ ∀ k, ‖ZMod.dft
              (fun x => ((f x - average (combinedFactor ρ η ks bs as) f x:ℝ):ℂ)) k‖ ≤ η * q at hu
          obtain ⟨k,hk⟩:=not_forall.mp hu
          obtain ⟨b,a,ha,hi⟩:=exists_combined_extension ρ f hf hη hM ks bs as k (lt_of_not_ge hk).le
          right
          refine ⟨Fin.cons k ks,Fin.cons b bs,Fin.cons a as,
            boundaryControlled_cons hc ha, ?_⟩
          rw [Nat.cast_add,Nat.cast_one]
          nlinarith
theorem exists_uniform_character_refinement (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M),
      BoundaryControlled η ks bs as ∧ FourierUniform (combinedFactor ρ η ks bs as) f η:=by
  rcases exists_uniform_refinement_or_large_energy ρ f hf hη hM (stepBound η) with
    h | ⟨ks,bs,as,_hc,he⟩
  · exact h
  · have hu:=normalized_energy_le_one (combinedFactor ρ η ks bs as) f hf
    have hl:=stepBound_exceeds_energy hη
    have h0:=normalized_energy_nonneg ρ f
    exfalso
    linarith
private def zz1906:"s0772"="s0772":=by decide+kernel
theorem combinedFactor_energy_identity {n:ℕ} (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (η:ℝ) (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M) :
    Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η ks bs as) f = Green24Proof.FinitePartitionRefinement.energy ρ f +
      ∑ x,(average (combinedFactor ρ η ks bs as) f x - average ρ f x) ^ 2 :=
  refinement_energy_identity _ ρ Prod.fst (fun _ => rfl) f
theorem exists_bounded_character_refinement (ρ:ZMod q → β) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) (hM:0 < M) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool) (as:Fin n → Fin M),
      Fintype.card (β × Alphabet η n) ≤
        Fintype.card β * (2 * resolution η + 2) ^ stepBound η ∧
      BoundaryControlled η ks bs as ∧
      (∀ x,ρ x = (combinedFactor ρ η ks bs as x).1) ∧
      FourierUniform (combinedFactor ρ η ks bs as) f η ∧
      Green24Proof.FinitePartitionRefinement.energy (combinedFactor ρ η ks bs as) f = Green24Proof.FinitePartitionRefinement.energy ρ f +
        ∑ x,(average (combinedFactor ρ η ks bs as) f x - average ρ f x) ^ 2:=by
  obtain ⟨n,hn,ks,bs,as,hc,hu⟩:=exists_uniform_character_refinement ρ f hf hη hM
  refine ⟨n,hn,ks,bs,as, ?_,hc,fun _ => rfl,hu,
    combinedFactor_energy_identity ρ f η ks bs as⟩
  simp only [Fintype.card_prod,Alphabet,Fintype.card_fun,Fintype.card_fin]
  exact Nat.mul_le_mul_left _ (Nat.pow_le_pow_right (by omega) hn)
end Green24Proof.CyclicCharacterRefinement
private def zz2467:"s09a3"="s09a3":=by decide+kernel
end 
section 
namespace Green24Proof.FinitePartitionEnergyPigeonhole
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.CyclicWeakRegularity
theorem exists_small_step (E:ℕ → ℝ) {N:ℕ} {ε:ℝ}
    (h0:0 ≤ E 0) (hN:E N ≤ 1) (hsteps:1 < (N:ℝ) * ε) :
    ∃ i < N,E (i + 1) - E i ≤ ε:=by
  by_contra hn
  push Not at hn
  have hs:(N:ℝ) * ε ≤ ∑ i ∈ Finset.range N,(E (i + 1) - E i):=by
    calc
      (N:ℝ) * ε = ∑ _i ∈ Finset.range N,ε:=by simp
      _ ≤ _:=Finset.sum_le_sum (fun i hi => (hn i (Finset.mem_range.mp hi)).le)
  rw [Finset.sum_range_sub] at hs
  linarith
noncomputable def outerSteps (ε:ℝ):ℕ:=⌈1 / ε⌉₊ + 1
theorem outerSteps_exceeds {ε:ℝ} (hε:0 < ε) :
    1 < (outerSteps ε:ℝ) * ε:=by
  have hc:=Nat.le_ceil (1 / ε)
  have hb:1 / ε < (outerSteps ε:ℝ):=by
    unfold outerSteps
    push_cast
    linarith
  exact (div_lt_iff₀ hε).mp hb
variable {q:ℕ} [NeZero q]
variable {β:ℕ → Type*} [∀ i,Fintype (β i)] [∀ i,DecidableEq (β i)]
private def zz1907:"s0773"="s0773":=by decide+kernel
theorem exists_small_average_gap (ρ:(i:ℕ) → ZMod q → β i)
    (φ:(i:ℕ) → β (i + 1) → β i)
    (href:∀ i x,ρ i x = φ i (ρ (i + 1) x))
    (f:ZMod q → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1)
    {N:ℕ} {ε:ℝ} (hsteps:1 < (N:ℝ) * ε) :
    ∃ i < N,(∑ x,(average (ρ (i + 1)) f x - average (ρ i) f x) ^ 2) ≤ ε * q:=by
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  obtain ⟨i,hi,he⟩:=exists_small_step (fun i => Green24Proof.FinitePartitionRefinement.energy (ρ i) f / q)
    (normalized_energy_nonneg (ρ 0) f) (normalized_energy_le_one (ρ N) f hf) hsteps
  refine ⟨i,hi, ?_⟩
  have hident:=refinement_energy_identity (ρ (i + 1)) (ρ i) (φ i) (href i) f
  have hd:(∑ x,(average (ρ (i + 1)) f x - average (ρ i) f x) ^ 2) / q ≤ ε:=by
    rw [hident,add_div] at he
    linarith
  exact (div_le_iff₀ hq).mp hd
theorem exists_small_gap_with_uniform_fine (ρ:(i:ℕ) → ZMod q → β i)
    (φ:(i:ℕ) → β (i + 1) → β i)
    (href:∀ i x,ρ i x = φ i (ρ (i + 1) x))
    (f:ZMod q → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1) (τ:ℕ → ℝ)
    (hU:∀ i,FourierUniform (ρ (i + 1)) f (τ i))
    {ε:ℝ} (hε:0 < ε) :
    ∃ i < outerSteps ε,
      (∑ x,(average (ρ (i + 1)) f x - average (ρ i) f x) ^ 2) ≤ ε * q ∧
      FourierUniform (ρ (i + 1)) f (τ i):=by
  obtain ⟨i,hi,hg⟩:=exists_small_average_gap ρ φ href f hf (outerSteps_exceeds hε)
  exact ⟨i,hi,hg,hU i⟩
end Green24Proof.FinitePartitionEnergyPigeonhole
private def zz2468:"s09a4"="s09a4":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicCharacterBlockChain
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionRefinement
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.CyclicWeakRegularity (FourierUniform stepBound normalized_energy_nonneg
  normalized_energy_le_one)
open Green24Proof.CyclicShiftedCharacterFactor (Alphabet phaseFactor BoundaryControlled)
open Green24Proof.CyclicCharacterRefinement
open Green24Proof.FinitePartitionEnergyPigeonhole
variable (q:ℕ) [NeZero q]
structure Block where
  tolerance:ℝ
  denominator:ℕ
  length:ℕ
  frequencies:Fin length → ZMod q
  components:Fin length → Bool
  offsets:Fin length → Fin denominator
variable {q}
def Labels:List (Block q) → Type
  | [] => Unit
  | b :: bs => Labels bs × Alphabet b.tolerance b.length
noncomputable def labelsFintype:(bs:List (Block q)) → Fintype (Labels bs)
  | [] => inferInstanceAs (Fintype Unit)
  | b :: bs => by
      letI:=labelsFintype bs
      exact inferInstanceAs (Fintype (Labels bs × Alphabet b.tolerance b.length))
noncomputable def labelsDecidableEq:(bs:List (Block q)) → DecidableEq (Labels bs)
  | [] => inferInstanceAs (DecidableEq Unit)
  | b :: bs => by
      letI:=labelsDecidableEq bs
      exact inferInstanceAs (DecidableEq (Labels bs × Alphabet b.tolerance b.length))
noncomputable def factor:(bs:List (Block q)) → ZMod q → Labels bs
  | [] => fun _ => ()
  | b :: bs => fun x => (factor bs x,
      phaseFactor b.tolerance b.frequencies b.components b.offsets x)
noncomputable def blockCost (b:Block q):ℕ :=
  b.length + resolution b.tolerance * b.denominator
noncomputable def complexity:List (Block q) → ℕ
  | [] => 1
  | b :: bs => complexity bs + blockCost b
def coordinateCount:List (Block q) → ℕ
  | [] => 0
  | b :: bs => coordinateCount bs + b.length
omit [NeZero q] in
theorem coordinateCount_le_complexity (bs:List (Block q)) :
    coordinateCount bs ≤ complexity bs:=by
  induction bs with
  | nil => simp [coordinateCount,complexity]
  | cons b bs ih => simp only [coordinateCount,complexity,blockCost]; omega
omit [NeZero q] in
theorem block_scale_le_complexity {b:Block q} {bs:List (Block q)} (hb:b ∈ bs) :
    resolution b.tolerance * b.denominator ≤ complexity bs:=by
  induction bs with
  | nil => simp at hb
  | cons c bs ih =>
      simp only [List.mem_cons] at hb
      rcases hb with rfl | hb
      · simp only [complexity,blockCost]; omega
      · have hi:=ih hb
        simp only [complexity]; omega
private def zz1908:"s0774"="s0774":=by decide+kernel
theorem exists_extension_block (bs:List (Block q)) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η)
    {M:ℕ} (hM:0 < M) :
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq;
    ∃ b:Block q,b.tolerance = η ∧ b.denominator = M ∧ b.length ≤ stepBound η ∧
      BoundaryControlled b.tolerance b.frequencies b.components b.offsets ∧
      FourierUniform (factor (b :: bs)) f η:=by
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq
  letI:(bs:List (Block q)) → Fintype (Labels bs):=labelsFintype
  obtain ⟨n,hn,ks,cs,offsets,hc,hu⟩ :=
    exists_uniform_character_refinement (factor bs) f hf hη hM
  exact ⟨⟨η,M,n,ks,cs,offsets⟩,rfl,rfl,hn,hc,hu⟩
noncomputable def extensionBlock (bs:List (Block q)) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η)
    {M:ℕ} (hM:0 < M):Block q :=
  Classical.choose (exists_extension_block bs f hf hη hM)
theorem extensionBlock_spec (bs:List (Block q)) (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η)
    {M:ℕ} (hM:0 < M) :
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq;
    let b:=extensionBlock bs f hf hη hM
    b.tolerance = η ∧ b.denominator = M ∧ b.length ≤ stepBound η ∧
      BoundaryControlled b.tolerance b.frequencies b.components b.offsets ∧
      FourierUniform (factor (b :: bs)) f η :=
  Classical.choose_spec (exists_extension_block bs f hf hη hM)
noncomputable def budget (τ:ℕ → ℝ) (D:ℕ → ℕ):ℕ → ℕ
  | 0 => 1
  | i + 1 => budget τ D i + stepBound (τ (budget τ D i)) +
      resolution (τ (budget τ D i)) * D (budget τ D i)
theorem budget_mono (τ:ℕ → ℝ) (D:ℕ → ℕ):Monotone (budget τ D):=by
  apply monotone_nat_of_le_succ
  intro i
  simp only [budget]
  omega
variable (f:ZMod q → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1)
  (τ:ℕ → ℝ) (hτ:∀ C,0 < τ C) (D:ℕ → ℕ) (hD:∀ C,0 < D C)
noncomputable def chain:ℕ → List (Block q)
  | 0 => []
  | i + 1 => extensionBlock (chain i) f hf (hτ (budget τ D i)) (hD (budget τ D i)) :: chain i
theorem chain_complexity_le (i:ℕ) :
    complexity (chain f hf τ hτ D hD i) ≤ budget τ D i:=by
  induction i with
  | zero => rfl
  | succ i ih =>
      have hs:=extensionBlock_spec (chain f hf τ hτ D hD i) f hf
        (hτ (budget τ D i)) (hD (budget τ D i))
      simp only [chain,complexity,blockCost]
      rw [hs.1,hs.2.1]
      have hn:=hs.2.2.1
      simp only [budget]
      omega
private def zz1909:"s0775"="s0775":=by decide+kernel
theorem chain_blocks_controlled (i:ℕ) (b:Block q)
    (hb:b ∈ chain f hf τ hτ D hD i) :
    0 < b.tolerance ∧ 0 < b.denominator ∧
      BoundaryControlled b.tolerance b.frequencies b.components b.offsets:=by
  induction i with
  | zero => simp [chain] at hb
  | succ i ih =>
      simp only [chain,List.mem_cons] at hb
      rcases hb with rfl | hb
      · have hs:=extensionBlock_spec (chain f hf τ hτ D hD i) f hf
          (hτ (budget τ D i)) (hD (budget τ D i))
        refine ⟨?_, ?_,hs.2.2.2.1⟩
        · rw [hs.1]
          exact hτ _
        · rw [hs.2.1]
          exact hD _
      · exact ih hb
theorem chain_uniform (i:ℕ) :
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq;
    FourierUniform (factor (chain f hf τ hτ D hD (i + 1))) f (τ (budget τ D i)):=by
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq
  letI:(bs:List (Block q)) → Fintype (Labels bs):=labelsFintype
  exact (extensionBlock_spec (chain f hf τ hτ D hD i) f hf
    (hτ (budget τ D i)) (hD (budget τ D i))).2.2.2.2
noncomputable def chainProjection (i:ℕ) :
    Labels (chain f hf τ hτ D hD (i + 1)) → Labels (chain f hf τ hτ D hD i):=Prod.fst
theorem chain_refines (i:ℕ) (x:ZMod q) :
    factor (chain f hf τ hτ D hD i) x =
      chainProjection f hf τ hτ D hD i (factor (chain f hf τ hτ D hD (i + 1)) x):=rfl
theorem exists_small_gap_with_complexity_tolerance {ε:ℝ} (hε:0 < ε) :
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq;
    ∃ i < outerSteps ε,
      complexity (chain f hf τ hτ D hD i) ≤ budget τ D i ∧
      complexity (chain f hf τ hτ D hD (i + 1)) ≤ budget τ D (outerSteps ε) ∧
      (∑ x,(average (factor (chain f hf τ hτ D hD (i + 1))) f x -
        average (factor (chain f hf τ hτ D hD i)) f x) ^ 2) ≤ ε * q ∧
      FourierUniform (factor (chain f hf τ hτ D hD (i + 1))) f (τ (budget τ D i)):=by
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq
  letI:(bs:List (Block q)) → Fintype (Labels bs):=labelsFintype
  obtain ⟨i,hi,hg,hu⟩:=exists_small_gap_with_uniform_fine
    (fun i => factor (chain f hf τ hτ D hD i))
    (chainProjection f hf τ hτ D hD) (chain_refines f hf τ hτ D hD)
    f hf (fun i => τ (budget τ D i)) (chain_uniform f hf τ hτ D hD) hε
  exact ⟨i,hi,chain_complexity_le f hf τ hτ D hD i,
    (chain_complexity_le f hf τ hτ D hD (i + 1)).trans
      (budget_mono τ D (by omega)),hg,hu⟩
end Green24Proof.CyclicCharacterBlockChain
private def zz2469:"s09a5"="s09a5":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicCharacterChainBoundary
open Finset
open scoped BigOperators
open Green24Proof.FinitePartitionAverage
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.CyclicWeakRegularity (FourierUniform stepBound)
open Green24Proof.CyclicShiftedCharacterFactor
open Green24Proof.CyclicCharacterBlockChain
open Green24Proof.FiniteGridBoundaryAvoidance
open Green24Proof.FinitePartitionEnergyPigeonhole
variable {q:ℕ} [NeZero q]
noncomputable def blockBad (b:Block q):Finset (ZMod q) :=
  badCoordinateSamples b.offsets
    (fun x i => characterCoordinate b.tolerance (b.frequencies i) (b.components i) x)
noncomputable def allBad:List (Block q) → Finset (ZMod q)
  | [] => ∅
  | b :: bs => blockBad b ∪ allBad bs
noncomputable def boundaryMass:List (Block q) → ℝ
  | [] => 0
  | b :: bs => boundaryMass bs + (b.length:ℝ) / b.denominator
private def zz1910:"s0776"="s0776":=by decide+kernel
theorem blockBad_card_le (b:Block q) (hM:0 < b.denominator)
    (hc:BoundaryControlled b.tolerance b.frequencies b.components b.offsets) :
    ((blockBad b).card:ℝ) ≤ (b.length:ℝ) / b.denominator * q:=by
  have hb:=boundary_union_card_bound hc
  have hMR:(0:ℝ) < b.denominator:=Nat.cast_pos.mpr hM
  calc
    ((blockBad b).card:ℝ) ≤ (b.length:ℝ) * q / b.denominator:=by
      apply (le_div_iff₀ hMR).mpr
      have h:(b.denominator:ℝ) * (blockBad b).card ≤ (b.length:ℝ) * q:=by
        exact_mod_cast hb
      simpa only [mul_comm] using h
    _ = _:=by ring
theorem allBad_card_le (bs:List (Block q))
    (hc:∀ b ∈ bs,0 < b.denominator ∧
      BoundaryControlled b.tolerance b.frequencies b.components b.offsets) :
    ((allBad bs).card:ℝ) ≤ boundaryMass bs * q:=by
  induction bs with
  | nil => simp [allBad,boundaryMass]
  | cons b bs ih =>
      have hb:=hc b (List.mem_cons_self ..)
      have ht:=ih (fun c h => hc c (List.mem_cons_of_mem _ h))
      have hblock:=blockBad_card_le b hb.1 hb.2
      have hu:(((blockBad b ∪ allBad bs).card:ℕ):ℝ) ≤
          (blockBad b).card + (allBad bs).card:=by
        exact_mod_cast Finset.card_union_le (blockBad b) (allBad bs)
      change ((blockBad b ∪ allBad bs).card:ℝ) ≤
        (boundaryMass bs + (b.length:ℝ) / b.denominator) * q
      nlinarith
noncomputable def denominator (τ:ℕ → ℝ) (δ:ℝ) (C:ℕ):ℕ :=
  ⌈(stepBound (τ C):ℝ) / δ⌉₊ + 1
theorem denominator_pos (τ:ℕ → ℝ) (δ:ℝ) (C:ℕ):0 < denominator τ δ C :=
  Nat.succ_pos _
theorem denominator_precision (τ:ℕ → ℝ) {δ:ℝ} (hδ:0 < δ) (C:ℕ) :
    (stepBound (τ C):ℝ) / denominator τ δ C ≤ δ:=by
  have hD:(0:ℝ) < denominator τ δ C:=Nat.cast_pos.mpr (denominator_pos τ δ C)
  have hc:=Nat.le_ceil ((stepBound (τ C):ℝ) / δ)
  have hb:(stepBound (τ C):ℝ) / δ ≤ denominator τ δ C:=by
    unfold denominator
    push_cast
    linarith
  have hm:=(div_le_iff₀ hδ).mp hb
  apply (div_le_iff₀ hD).mpr
  nlinarith
variable (f:ZMod q → ℝ) (hf:∀ x,f x ∈ Set.Icc 0 1)
  (τ:ℕ → ℝ) (hτ:∀ C,0 < τ C) (D:ℕ → ℕ) (hD:∀ C,0 < D C)
private def zz1911:"s0777"="s0777":=by decide+kernel
theorem chain_boundaryMass_le {δ:ℝ}
    (hprecision:∀ C,(stepBound (τ C):ℝ) / D C ≤ δ) (i:ℕ) :
    boundaryMass (chain f hf τ hτ D hD i) ≤ (i:ℝ) * δ:=by
  induction i with
  | zero => simp [chain,boundaryMass]
  | succ i ih =>
      have hs:=extensionBlock_spec (chain f hf τ hτ D hD i) f hf
        (hτ (budget τ D i)) (hD (budget τ D i))
      have hl:((extensionBlock (chain f hf τ hτ D hD i) f hf
          (hτ (budget τ D i)) (hD (budget τ D i))).length:ℝ) ≤
          stepBound (τ (budget τ D i)):=by exact_mod_cast hs.2.2.1
      have hp:=(div_le_div_of_nonneg_right hl
        (Nat.cast_nonneg (D (budget τ D i)))).trans (hprecision (budget τ D i))
      simp only [chain,boundaryMass,Nat.cast_add,Nat.cast_one]
      rw [hs.2.1]
      linarith
theorem chain_allBad_card_le {δ:ℝ}
    (hprecision:∀ C,(stepBound (τ C):ℝ) / D C ≤ δ) (i:ℕ) :
    ((allBad (chain f hf τ hτ D hD i)).card:ℝ) ≤ (i:ℝ) * δ * q:=by
  have hc:=allBad_card_le (chain f hf τ hτ D hD i)
    (fun b hb => (chain_blocks_controlled f hf τ hτ D hD i b hb).2)
  exact hc.trans (mul_le_mul_of_nonneg_right
    (chain_boundaryMass_le f hf τ hτ D hD hprecision i) (Nat.cast_nonneg q))
omit D hD in
theorem exists_small_gap_and_small_boundaries {ε κ:ℝ} (hε:0 < ε) (hκ:0 < κ) :
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq;
    let N:=outerSteps ε
    let δ:=κ / N
    let Ds:=denominator τ δ
    let hDs:=denominator_pos τ δ
    ∃ i < N,
      complexity (chain f hf τ hτ Ds hDs i) ≤ budget τ Ds i ∧
      complexity (chain f hf τ hτ Ds hDs (i + 1)) ≤ budget τ Ds N ∧
      (∑ x,(average (factor (chain f hf τ hτ Ds hDs (i + 1))) f x -
        average (factor (chain f hf τ hτ Ds hDs i)) f x) ^ 2) ≤ ε * q ∧
      FourierUniform (factor (chain f hf τ hτ Ds hDs (i + 1))) f (τ (budget τ Ds i)) ∧
      ((allBad (chain f hf τ hτ Ds hDs i)).card:ℝ) ≤ κ * q ∧
      ((allBad (chain f hf τ hτ Ds hDs (i + 1))).card:ℝ) ≤ κ * q:=by
  letI:(bs:List (Block q)) → DecidableEq (Labels bs):=labelsDecidableEq
  letI:(bs:List (Block q)) → Fintype (Labels bs):=labelsFintype
  let N:=outerSteps ε
  have hN:(0:ℝ) < N:=by
    exact Nat.cast_pos.mpr (Nat.succ_pos _)
  let δ:=κ / N
  have hδ:0 < δ:=div_pos hκ hN
  let Ds:=denominator τ δ
  let hDs:=denominator_pos τ δ
  obtain ⟨i,hi,hcoarse,hfine,hgap,hunif⟩ :=
    exists_small_gap_with_complexity_tolerance f hf τ hτ Ds hDs hε
  have hbound (j:ℕ) (hj:j ≤ N) :
      ((allBad (chain f hf τ hτ Ds hDs j)).card:ℝ) ≤ κ * q:=by
    have hb:=chain_allBad_card_le f hf τ hτ Ds hDs
      (denominator_precision τ hδ) j
    have hjR:(j:ℝ) ≤ N:=by exact_mod_cast hj
    have hmul:(j:ℝ) * δ ≤ κ:=by
      calc
        (j:ℝ) * δ ≤ (N:ℝ) * δ:=mul_le_mul_of_nonneg_right hjR hδ.le
        _ = κ:=by dsimp [δ]; field_simp
    exact hb.trans (mul_le_mul_of_nonneg_right hmul (Nat.cast_nonneg q))
  refine ⟨i,hi,hcoarse,hfine,hgap,hunif, ?_, ?_⟩
  · exact hbound i (Nat.le_of_lt hi)
  · exact hbound (i + 1) (by omega)
end Green24Proof.CyclicCharacterChainBoundary
private def zz2470:"s09a6"="s09a6":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicBlockTorusSmoothing
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicCharacterBlockChain
open Green24Proof.CyclicCharacterChainBoundary
open Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicSmoothedCharacterFactor
open Green24Proof.CyclicShiftedCharacterFactor
open Green24Proof.FiniteScalarQuantization (resolution)
open Green24Proof.GridLipschitzSmoothing
open Green24Proof.FiniteGridSmoothingSamples
variable {q:ℕ} [NeZero q]
def Coordinates:List (Block q) → Type
  | [] => Empty
  | b :: bs => Coordinates bs ⊕ Fin b.length
def coordinatesFintype:(bs:List (Block q)) → Fintype (Coordinates bs)
  | [] => inferInstanceAs (Fintype Empty)
  | b :: bs => by
      letI:=coordinatesFintype bs
      exact inferInstanceAs (Fintype (Coordinates bs ⊕ Fin b.length))
def coordinatesDecidableEq:(bs:List (Block q)) → DecidableEq (Coordinates bs)
  | [] => inferInstanceAs (DecidableEq Empty)
  | b :: bs => by
      letI:=coordinatesDecidableEq bs
      exact inferInstanceAs (DecidableEq (Coordinates bs ⊕ Fin b.length))
omit [NeZero q] in
theorem coordinates_card (bs:List (Block q)) :
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype;
    Fintype.card (Coordinates bs) = coordinateCount bs:=by
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype
  induction bs with
  | nil => rfl
  | cons b bs ih =>
      change Fintype.card (Coordinates bs ⊕ Fin b.length) = _
      simp [Fintype.card_sum,ih,coordinateCount]
abbrev Torus (bs:List (Block q)):=Coordinates bs → Circle
noncomputable def frequencies:(bs:List (Block q)) → Coordinates bs → ZMod q
  | [] => Empty.elim
  | b :: bs => Sum.elim (frequencies bs) b.frequencies
noncomputable def orbit (bs:List (Block q)) (x:ZMod q):Torus bs :=
  fun i => ZMod.toCircle (-(x * frequencies bs i))
noncomputable def torusLabel:(bs:List (Block q)) → Torus bs → Labels bs
  | [] => fun _ => ()
  | b :: bs => fun z => (torusLabel bs (z ∘ Sum.inl),encodedCell b.tolerance
      (vectorCellIndex 1 (fun i => offset (b.offsets i))
        (torusCoordinates b.tolerance b.components (z ∘ Sum.inr))))
noncomputable def Good:(bs:List (Block q)) → Set (Torus bs)
  | [] => Set.univ
  | b :: bs => {z | z ∘ Sum.inl ∈ Good bs ∧
      torusCoordinates b.tolerance b.components (z ∘ Sum.inr) ∈
        VectorGridGood 1 (1 / (2 * b.denominator)) (fun i => offset (b.offsets i))}
private def zz1912:"s0778"="s0778":=by decide+kernel
private theorem dist_reindex_le {ι κ:Type*} [Fintype ι] [Fintype κ]
    (r:ι → κ) (z w:κ → Circle):dist (z ∘ r) (w ∘ r) ≤ dist z w:=by
  exact (dist_pi_le_iff dist_nonneg).mpr (fun i => dist_le_pi_dist z w (r i))
omit [NeZero q] in
theorem label_separation (bs:List (Block q))
    (hM:∀ b ∈ bs,0 < b.denominator) (z w:Torus bs)
    (hz:z ∈ Good bs) (hw:w ∈ Good bs) (hne:torusLabel bs z ≠ torusLabel bs w) :
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype;
    1 ≤ (complexity bs:ℝ) * dist z w:=by
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype
  induction bs with
  | nil => exact False.elim (hne rfl)
  | cons b bs ih =>
      have hMt:=fun c hc => hM c (List.mem_cons_of_mem _ hc)
      have hMb:=hM b (List.mem_cons_self ..)
      have hz':z ∘ Sum.inl ∈ Good bs ∧ _:=hz
      have hw':w ∘ Sum.inl ∈ Good bs ∧ _:=hw
      by_cases ht:torusLabel bs (z ∘ Sum.inl) = torusLabel bs (w ∘ Sum.inl)
      · have hb:vectorCellIndex 1 (fun i => offset (b.offsets i))
              (torusCoordinates b.tolerance b.components (z ∘ Sum.inr)) ≠
            vectorCellIndex 1 (fun i => offset (b.offsets i))
              (torusCoordinates b.tolerance b.components (w ∘ Sum.inr)):=by
          intro he
          apply hne
          simp only [torusLabel,ht,he]
          rfl
        have hsep:=vector_grid_core_separation (by norm_num:(0:ℝ) < 1)
          hz'.2 hw'.2 hb
        have hscale:=(torusCoordinates_lipschitz b.tolerance b.components).dist_le_mul
          (z ∘ Sum.inr) (w ∘ Sum.inr)
        have hd:=dist_reindex_le Sum.inr z w
        have hres:(0:ℝ) ≤ resolution b.tolerance:=Nat.cast_nonneg _
        have hMR:(0:ℝ) < b.denominator:=Nat.cast_pos.mpr hMb
        have hs:(1:ℝ) / b.denominator ≤
            (resolution b.tolerance:ℝ) * dist z w:=by
          have he:(2:ℝ) * (1 / (2 * b.denominator)) = 1 / b.denominator:=by
            field_simp
          rw [he] at hsep
          exact hsep.trans (hscale.trans (mul_le_mul_of_nonneg_left hd hres))
        have hs':(1:ℝ) ≤ (resolution b.tolerance * b.denominator:ℕ) * dist z w:=by
          have hm:=(div_le_iff₀ hMR).mp hs
          push_cast
          nlinarith
        have hc:((resolution b.tolerance * b.denominator:ℕ):ℝ) ≤
            complexity (b :: bs):=by
          exact_mod_cast block_scale_le_complexity (show b ∈ b :: bs from List.mem_cons_self)
        exact hs'.trans (mul_le_mul_of_nonneg_right hc dist_nonneg)
      · have hs:=ih hMt (z ∘ Sum.inl) (w ∘ Sum.inl) hz'.1 hw'.1 ht
        have hd:=dist_reindex_le Sum.inl z w
        have hc:(complexity bs:ℝ) ≤ complexity (b :: bs):=by
          simp only [complexity,Nat.cast_add]
          exact le_add_of_nonneg_right (Nat.cast_nonneg _)
        exact hs.trans ((mul_le_mul_of_nonneg_left hd (Nat.cast_nonneg _)).trans
          (mul_le_mul_of_nonneg_right hc dist_nonneg))
theorem torusLabel_orbit (bs:List (Block q)) (x:ZMod q) :
    torusLabel bs (orbit bs x) = factor bs x:=by
  induction bs with
  | nil => rfl
  | cons b bs ih =>
      change (torusLabel bs (orbit bs x),_) = (factor bs x,_)
      rw [ih]
      congr 1
      exact (phaseFactor_eq_encoded_grid b.tolerance b.frequencies b.components b.offsets x).symm
theorem orbit_good_of_not_bad (bs:List (Block q))
    (hM:∀ b ∈ bs,0 < b.denominator) (x:ZMod q) (hx:x ∉ allBad bs) :
    orbit bs x ∈ Good bs:=by
  induction bs with
  | nil => trivial
  | cons b bs ih =>
      have hx':x ∉ blockBad b ∧ x ∉ allBad bs:=by
        simpa only [allBad,Finset.mem_union,not_or] using hx
      constructor
      · exact ih (fun c hc => hM c (List.mem_cons_of_mem _ hc)) hx'.2
      · exact sample_good_of_not_bad (hM b (List.mem_cons_self ..))
          b.offsets (characterSamples b.tolerance b.frequencies b.components) x hx'.1
private def zz1913:"s0779"="s0779":=by decide+kernel
theorem exists_torus_realization (bs:List (Block q))
    (hM:∀ b ∈ bs,0 < b.denominator) (F:Labels bs → ℝ)
    (hF:∀ a,F a ∈ Set.Icc 0 1) :
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype;
    ∃ H:Torus bs → ℝ,LipschitzWith (complexity bs:ℝ≥0) H ∧
      (∀ z,H z ∈ Set.Icc 0 1) ∧
      (∀ x,x ∉ allBad bs → H (orbit bs x) = F (factor bs x)) ∧
      (∑ x,(H (orbit bs x) - F (factor bs x)) ^ 2) ≤ ((allBad bs).card:ℝ):=by
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype
  obtain ⟨H,hH,hHr,hHe⟩:=exists_bounded_extension (torusLabel bs) F hF (Good bs)
    (complexity bs:ℝ≥0) (fun z hz w hw => label_separation bs hM z w hz hw)
  have he:∀ x,x ∉ allBad bs → H (orbit bs x) = F (factor bs x):=by
    intro x hx
    rw [hHe _ (orbit_good_of_not_bad bs hM x hx),torusLabel_orbit]
  exact ⟨H,hH,hHr,he,sq_error_sum_le_bad (allBad bs)
    (fun x => H (orbit bs x)) (fun x => F (factor bs x)) (fun x => hHr _) (fun x => hF _) he⟩
theorem exists_fin_torus_realization (bs:List (Block q))
    (hM:∀ b ∈ bs,0 < b.denominator) (F:Labels bs → ℝ)
    (hF:∀ a,F a ∈ Set.Icc 0 1) :
    ∃ n ≤ complexity bs, ∃ (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ),
      LipschitzWith (complexity bs:ℝ≥0) H ∧
      (∀ z,H z ∈ Set.Icc 0 1) ∧
      (∀ x,x ∉ allBad bs → H (characterOrbit ks x) = F (factor bs x)) ∧
      (∑ x,(H (characterOrbit ks x) - F (factor bs x)) ^ 2) ≤
        ((allBad bs).card:ℝ):=by
  letI:(bs:List (Block q)) → Fintype (Coordinates bs):=coordinatesFintype
  classical
  obtain ⟨H,hH,hHr,hHe,hHerr⟩:=exists_torus_realization bs hM F hF
  let e:=Fintype.equivFin (Coordinates bs)
  let ks:Fin (Fintype.card (Coordinates bs)) → ZMod q:=fun i => frequencies bs (e.symm i)
  let H':(Fin (Fintype.card (Coordinates bs)) → Circle) → ℝ:=fun z => H (z ∘ e)
  have ho (x:ZMod q):characterOrbit ks x ∘ e = orbit bs x:=by
    funext i
    simp [characterOrbit,orbit,ks]
  have hl:LipschitzWith (complexity bs:ℝ≥0) H':=by
    apply LipschitzWith.of_dist_le_mul
    intro z w
    exact (hH.dist_le_mul (z ∘ e) (w ∘ e)).trans
      (mul_le_mul_of_nonneg_left (dist_reindex_le e z w) (Nat.cast_nonneg _))
  refine ⟨_, ?_,ks,H',hl,(fun z => hHr _), ?_, ?_⟩
  · rw [coordinates_card]
    exact coordinateCount_le_complexity bs
  · intro x hx
    simpa only [H',ho] using hHe x hx
  · simpa only [H',ho] using hHerr
end Green24Proof.CyclicBlockTorusSmoothing
private def zz2471:"s09a7"="s09a7":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicGrowthDecomposition
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicCharacterBlockChain
open Green24Proof.CyclicCharacterChainBoundary
open Green24Proof.CyclicBlockTorusSmoothing
open Green24Proof.CyclicTorusSmoothing
open Green24Proof.FinitePartitionAverage
open Green24Proof.FinitePartitionEnergyPigeonhole
noncomputable def complexityBound (τ:ℕ → ℝ) (ε:ℝ):ℕ :=
  let η:=ε ^ 2 / 4
  let N:=outerSteps η
  budget τ (denominator τ (η / N)) N
variable {q:ℕ} [NeZero q]
theorem exists_growth_decomposition (f:ZMod q → ℝ)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (τ:ℕ → ℝ) (hτ:∀ C,0 < τ C)
    {ε:ℝ} (hε:0 < ε) :
    ∃ M ≤ complexityBound τ ε, ∃ n ≤ M,
      ∃ (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ)
        (small uniform:ZMod q → ℝ),
      LipschitzWith (M:ℝ≥0) H ∧
      (∀ z,H z ∈ Set.Icc 0 1) ∧
      (∀ x,f x = H (characterOrbit ks x) + small x + uniform x) ∧
      (∀ x,H (characterOrbit ks x) + small x ∈ Set.Icc 0 1) ∧
      (∀ x,small x ∈ Set.Icc (-1) 1) ∧
      (∀ x,uniform x ∈ Set.Icc (-1) 1) ∧
      (∑ x,small x ^ 2) ≤ ε ^ 2 * q ∧
      (∑ x,uniform x) = 0 ∧
      (∀ k, ‖ZMod.dft (fun x => (uniform x:ℂ)) k‖ ≤ τ M * q):=by
  letI:=(labelsFintype:(bs:List (Block q)) → Fintype (Labels bs))
  letI:=(labelsDecidableEq:(bs:List (Block q)) → DecidableEq (Labels bs))
  classical
  let η:=ε ^ 2 / 4
  have hη:0 < η:=by dsimp [η]; positivity
  let N:=outerSteps η
  let Ds:=denominator τ (η / N)
  let hDs:=denominator_pos τ (η / N)
  obtain ⟨i,hi,hc,_hfin,hgap,hu,hb,_hbf⟩ :=
    exists_small_gap_and_small_boundaries f hf τ hτ hη hη
  let coarse:=chain f hf τ hτ Ds hDs i
  let fine:=chain f hf τ hτ Ds hDs (i + 1)
  let M:=budget τ Ds i
  have hc':complexity coarse ≤ M:=hc
  have hM:M ≤ complexityBound τ ε:=budget_mono τ Ds (Nat.le_of_lt hi)
  let F:=fiberMean (factor coarse) f
  have hF:∀ a,F a ∈ Set.Icc 0 1:=fun a =>
    ⟨fiberMean_nonneg _ f (fun x => (hf x).1) a,
      fiberMean_le_one _ f (fun x => (hf x).2) a⟩
  obtain ⟨n,hn,ks,H,hH,hHr,_hHe,hHerr⟩ :=
    exists_fin_torus_realization coarse
      (fun b hb => (chain_blocks_controlled f hf τ hτ Ds hDs i b hb).2.1) F hF
  let A:=average (factor fine) f
  let B:=average (factor coarse) f
  let small:=fun x => A x - H (characterOrbit ks x)
  let uniform:=fun x => f x - A x
  have hA:∀ x,A x ∈ Set.Icc 0 1:=average_mem_Icc _ f hf
  have hL:LipschitzWith (M:ℝ≥0) H:=hH.weaken (by exact_mod_cast hc')
  have he:(∑ x,(H (characterOrbit ks x) - B x) ^ 2) ≤ η * q :=
    hHerr.trans hb
  have hg:(∑ x,(A x - B x) ^ 2) ≤ η * q:=hgap
  have hs:(∑ x,small x ^ 2) ≤ ε ^ 2 * q:=by
    calc
      (∑ x,small x ^ 2) ≤
          ∑ x,(2 * (A x - B x) ^ 2 + 2 * (H (characterOrbit ks x) - B x) ^ 2):=by
        apply Finset.sum_le_sum
        intro x _
        dsimp only [small]
        nlinarith [sq_nonneg (A x + H (characterOrbit ks x) - 2 * B x)]
      _ = 2 * (∑ x,(A x - B x) ^ 2) +
          2 * (∑ x,(H (characterOrbit ks x) - B x) ^ 2):=by
        rw [Finset.sum_add_distrib, ← Finset.mul_sum, ← Finset.mul_sum]
      _ ≤ ε ^ 2 * q:=by dsimp [η] at hg he; linarith
  refine ⟨M,hM,n,hn.trans hc',ks,H,small,uniform,hL,hHr, ?_, ?_, ?_, ?_,hs, ?_,hu⟩
  · intro x
    dsimp [small,uniform]
    ring
  · intro x
    simpa only [small,add_sub_cancel] using hA x
  · intro x
    have ha:=hA x
    have hh:=hHr (characterOrbit ks x)
    change A x - H (characterOrbit ks x) ∈ Set.Icc (-1) 1
    constructor <;> linarith [ha.1,ha.2,hh.1,hh.2]
  · exact residual_mem_Icc _ f hf
  · change (∑ x,(f x - average (factor fine) f x)) = 0
    rw [Finset.sum_sub_distrib,sum_average,sub_self]
end Green24Proof.CyclicGrowthDecomposition
private def zz2472:"s09a8"="s09a8":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFourierReplacement
open Finset CyclicFourierCounting
open scoped BigOperators
variable {q:ℕ} [NeZero q]
theorem norm_le_of_fourier_sum (a b c:ZMod q → ℂ) (t:ℂ) (F G M:ℝ)
    (hid:(q:ℂ) * t = ∑ r,a r * b r * c r)
    (ha:∀ r, ‖a r‖ ≤ M)
    (hb:(∑ r, ‖b r‖ ^ 2) = (q:ℝ) * F)
    (hc:(∑ r, ‖c r‖ ^ 2) = (q:ℝ) * G) :
    ‖t‖ ≤ M * Real.sqrt F * Real.sqrt G:=by
  have hM:0 ≤ M:=(norm_nonneg (a 0)).trans (ha 0)
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  have hcs:=Real.sum_mul_le_sqrt_mul_sqrt Finset.univ
    (fun r => ‖b r‖) (fun r => ‖c r‖)
  rw [hb,hc] at hcs
  have hn:=congrArg (fun z:ℂ => ‖z‖) hid
  simp only [norm_mul,Complex.norm_natCast] at hn
  refine le_of_mul_le_mul_left (a:=(q:ℝ)) ?_ hq
  calc
    (q:ℝ) * ‖t‖ = ‖∑ r,a r * b r * c r‖:=hn
    _ ≤ ∑ r, ‖a r * b r * c r‖:=norm_sum_le _ _
    _ ≤ ∑ r,M * (‖b r‖ * ‖c r‖):=by
      apply Finset.sum_le_sum
      intro r _
      simpa only [norm_mul,mul_assoc] using mul_le_mul_of_nonneg_right (ha r)
        (mul_nonneg (norm_nonneg _) (norm_nonneg _))
    _ = M * ∑ r, ‖b r‖ * ‖c r‖:=(Finset.mul_sum _ _ _).symm
    _ ≤ M * (Real.sqrt ((q:ℝ) * F) * Real.sqrt ((q:ℝ) * G)) :=
      mul_le_mul_of_nonneg_left hcs hM
    _ = (q:ℝ) * (M * Real.sqrt F * Real.sqrt G):=by
      rw [Real.sqrt_mul hq.le,Real.sqrt_mul hq.le]
      calc
        M * (Real.sqrt q * Real.sqrt F * (Real.sqrt q * Real.sqrt G)) =
          (Real.sqrt q * Real.sqrt q) * (M * Real.sqrt F * Real.sqrt G):=by ring
        _ = _:=by rw [Real.mul_self_sqrt hq.le]
private def zz1914:"s077a"="s077a":=by decide+kernel
theorem trilinear_norm_le_middle (f g h:ZMod q → ℂ)
    (h3:IsUnit (3:ZMod q)) {M:ℝ}
    (hg:∀ r, ‖ZMod.dft g r‖ ≤ M) :
    ‖trilinear f g h‖ ≤
      M * Real.sqrt (∑ x, ‖f x‖ ^ 2) * Real.sqrt (∑ x, ‖h x‖ ^ 2):=by
  apply norm_le_of_fourier_sum (fun r => ZMod.dft g (2 * r))
    (ZMod.dft f) (fun r => ZMod.dft h (-3 * r))
  · rw [trilinear_fourier]
    apply Finset.sum_congr rfl
    intro r _
    ring
  · exact fun r => hg (2 * r)
  · exact parseval f
  · exact ((IsUnit.isUnit_iff_mulLeft_bijective.mp h3.neg).sum_comp
      (fun r:ZMod q => ‖ZMod.dft h r‖ ^ 2)).trans (parseval h)
theorem trilinear_norm_le_right (f g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) {M:ℝ}
    (hh:∀ r, ‖ZMod.dft h r‖ ≤ M) :
    ‖trilinear f g h‖ ≤
      M * Real.sqrt (∑ x, ‖f x‖ ^ 2) * Real.sqrt (∑ x, ‖g x‖ ^ 2):=by
  apply norm_le_of_fourier_sum (fun r => ZMod.dft h (-3 * r))
    (ZMod.dft f) (fun r => ZMod.dft g (2 * r))
  · rw [trilinear_fourier]
    apply Finset.sum_congr rfl
    intro r _
    ring
  · exact fun r => hh (-3 * r)
  · exact parseval f
  · exact ((IsUnit.isUnit_iff_mulLeft_bijective.mp h2).sum_comp
      (fun r:ZMod q => ‖ZMod.dft g r‖ ^ 2)).trans (parseval g)
theorem l2_sq_le_card (f:ZMod q → ℂ) (hf:∀ x, ‖f x‖ ≤ 1) :
    (∑ x, ‖f x‖ ^ 2) ≤ (q:ℝ):=by
  calc
    (∑ x, ‖f x‖ ^ 2) ≤ ∑ _x:ZMod q,(1:ℝ):=by
      apply Finset.sum_le_sum
      intro x _
      nlinarith [norm_nonneg (f x),hf x]
    _ = _:=by simp
theorem sqrt_product_le_card (f g:ZMod q → ℂ)
    (hf:∀ x, ‖f x‖ ≤ 1) (hg:∀ x, ‖g x‖ ≤ 1) :
    Real.sqrt (∑ x, ‖f x‖ ^ 2) * Real.sqrt (∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ):=by
  calc
    _ ≤ Real.sqrt q * Real.sqrt q:=by
      gcongr
      · exact l2_sq_le_card f hf
      · exact l2_sq_le_card g hg
    _ = _:=Real.mul_self_sqrt (Nat.cast_nonneg q)
private def zz1915:"s077b"="s077b":=by decide+kernel
theorem trilinear_norm_le_middle_of_bounded (f g h:ZMod q → ℂ)
    (h3:IsUnit (3:ZMod q)) {η:ℝ} (hη:0 ≤ η)
    (hg:∀ r, ‖ZMod.dft g r‖ ≤ η * q)
    (hf:∀ x, ‖f x‖ ≤ 1) (hh:∀ x, ‖h x‖ ≤ 1) :
    ‖trilinear f g h‖ ≤ η * (q:ℝ) ^ 2:=by
  have hp:=mul_le_mul_of_nonneg_left (sqrt_product_le_card f h hf hh)
    (mul_nonneg hη (Nat.cast_nonneg q))
  have he:=trilinear_norm_le_middle f g h h3 hg
  nlinarith
theorem trilinear_norm_le_right_of_bounded (f g h:ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) {η:ℝ} (hη:0 ≤ η)
    (hh:∀ r, ‖ZMod.dft h r‖ ≤ η * q)
    (hf:∀ x, ‖f x‖ ≤ 1) (hg:∀ x, ‖g x‖ ≤ 1) :
    ‖trilinear f g h‖ ≤ η * (q:ℝ) ^ 2:=by
  have hp:=mul_le_mul_of_nonneg_left (sqrt_product_le_card f g hf hg)
    (mul_nonneg hη (Nat.cast_nonneg q))
  have he:=trilinear_norm_le_right f g h h2 hh
  nlinarith
theorem trilinear_sub_middle (f g₁ g₂ h:ZMod q → ℂ) :
    trilinear f (fun x => g₁ x - g₂ x) h =
      trilinear f g₁ h - trilinear f g₂ h:=by
  simp only [trilinear,mul_sub,sub_mul,Finset.sum_sub_distrib]
theorem trilinear_sub_right (f g h₁ h₂:ZMod q → ℂ) :
    trilinear f g (fun x => h₁ x - h₂ x) =
      trilinear f g h₁ - trilinear f g h₂:=by
  simp only [trilinear,mul_sub,Finset.sum_sub_distrib]
private def zz1916:"s077c"="s077c":=by decide+kernel
theorem sqrt_product_le_card_of_energy (f g:ZMod q → ℂ)
    (hf:(∑ x, ‖f x‖ ^ 2) ≤ (q:ℝ))
    (hg:(∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ)) :
    Real.sqrt (∑ x, ‖f x‖ ^ 2) * Real.sqrt (∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ):=by
  calc
    _ ≤ Real.sqrt q * Real.sqrt q:=by gcongr
    _ = _:=Real.mul_self_sqrt (Nat.cast_nonneg q)
theorem count_bound_of_energy (t:ℂ) (f g:ZMod q → ℂ)
    {η:ℝ} (hη:0 ≤ η)
    (hf:(∑ x, ‖f x‖ ^ 2) ≤ (q:ℝ))
    (hg:(∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ))
    (ht:‖t‖ ≤ (η * q) * Real.sqrt (∑ x, ‖f x‖ ^ 2) *
      Real.sqrt (∑ x, ‖g x‖ ^ 2)):‖t‖ ≤ η * (q:ℝ) ^ 2:=by
  have hp:=mul_le_mul_of_nonneg_left (sqrt_product_le_card_of_energy f g hf hg)
    (mul_nonneg hη (Nat.cast_nonneg q))
  nlinarith
theorem trilinear_replacement_bound_of_energy (f f' g g' h h':ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {η:ℝ} (hη:0 ≤ η)
    (hF:∀ r, ‖ZMod.dft (fun x => f x - f' x) r‖ ≤ η * q)
    (hG:∀ r, ‖ZMod.dft (fun x => g x - g' x) r‖ ≤ η * q)
    (hH:∀ r, ‖ZMod.dft (fun x => h x - h' x) r‖ ≤ η * q)
    (hf':(∑ x, ‖f' x‖ ^ 2) ≤ (q:ℝ))
    (hg:(∑ x, ‖g x‖ ^ 2) ≤ (q:ℝ))
    (hg':(∑ x, ‖g' x‖ ^ 2) ≤ (q:ℝ))
    (hh:(∑ x, ‖h x‖ ^ 2) ≤ (q:ℝ)) :
    ‖trilinear f g h - trilinear f' g' h'‖ ≤ 3 * η * (q:ℝ) ^ 2:=by
  have h₁:=count_bound_of_energy _ g h hη hg hh
    (trilinear_norm_le (fun x => f x - f' x) g h h2 h3 hF)
  have h₂:=count_bound_of_energy _ f' h hη hf' hh
    (trilinear_norm_le_middle f' (fun x => g x - g' x) h h3 hG)
  have h₃:=count_bound_of_energy _ f' g' hη hf' hg'
    (trilinear_norm_le_right f' g' (fun x => h x - h' x) h2 hH)
  rw [trilinear_sub_left] at h₁
  rw [trilinear_sub_middle] at h₂
  rw [trilinear_sub_right] at h₃
  have hid:trilinear f g h - trilinear f' g' h' =
      (trilinear f g h - trilinear f' g h) +
      (trilinear f' g h - trilinear f' g' h) +
      (trilinear f' g' h - trilinear f' g' h'):=by ring
  rw [hid]
  calc
    _ ≤ ‖(trilinear f g h - trilinear f' g h) +
        (trilinear f' g h - trilinear f' g' h)‖ +
        ‖trilinear f' g' h - trilinear f' g' h'‖:=norm_add_le _ _
    _ ≤ (‖trilinear f g h - trilinear f' g h‖ +
        ‖trilinear f' g h - trilinear f' g' h‖) +
        ‖trilinear f' g' h - trilinear f' g' h'‖ :=
      add_le_add (norm_add_le _ _) le_rfl
    _ ≤ 3 * η * (q:ℝ) ^ 2:=by linarith
theorem trilinear_replacement_bound (f f' g g' h h':ZMod q → ℂ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {η:ℝ} (hη:0 ≤ η)
    (hF:∀ r, ‖ZMod.dft (fun x => f x - f' x) r‖ ≤ η * q)
    (hG:∀ r, ‖ZMod.dft (fun x => g x - g' x) r‖ ≤ η * q)
    (hH:∀ r, ‖ZMod.dft (fun x => h x - h' x) r‖ ≤ η * q)
    (hf':∀ x, ‖f' x‖ ≤ 1) (hg:∀ x, ‖g x‖ ≤ 1)
    (hg':∀ x, ‖g' x‖ ≤ 1) (hh:∀ x, ‖h x‖ ≤ 1) :
    ‖trilinear f g h - trilinear f' g' h'‖ ≤ 3 * η * (q:ℝ) ^ 2 :=
  trilinear_replacement_bound_of_energy f f' g g' h h' h2 h3 hη hF hG hH
    (l2_sq_le_card f' hf') (l2_sq_le_card g hg) (l2_sq_le_card g' hg')
    (l2_sq_le_card h hh)
end Green24Proof.CyclicFourierReplacement
private def zz2473:"s09a9"="s09a9":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicCharacterCounting
open scoped BigOperators
open CyclicFourierCounting CyclicFourierReplacement CyclicCharacterFactor
open CyclicWeakRegularity FourierPartitionIncrement FiniteScalarQuantization
variable {q:ℕ} [NeZero q]
private def zz1917:"s077d"="s077d":=by decide+kernel
theorem self_count_replacement (f g:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {η:ℝ} (hη:0 ≤ η)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (hg:∀ x,g x ∈ Set.Icc 0 1)
    (hu:∀ k, ‖ZMod.dft (fun x => ((f x - g x:ℝ):ℂ)) k‖ ≤ η * q) :
    ‖trilinear (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) -
      trilinear (fun x => (g x:ℂ)) (fun x => (g x:ℂ)) (fun x => (g x:ℂ))‖ ≤
        3 * η * (q:ℝ) ^ 2:=by
  have hf':∀ x, ‖(f x:ℂ)‖ ≤ 1:=by
    intro x
    simpa only [Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg (hf x).1] using
      (hf x).2
  have hg':∀ x, ‖(g x:ℂ)‖ ≤ 1:=by
    intro x
    simpa only [Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg (hg x).1] using
      (hg x).2
  have hu':∀ k, ‖ZMod.dft (fun x => (f x:ℂ) - (g x:ℂ)) k‖ ≤ η * q:=by
    simpa only [Complex.ofReal_sub] using hu
  exact trilinear_replacement_bound _ _ _ _ _ _ h2 h3 hη hu' hu' hu'
    hg' hf' hg' hf'
theorem exists_character_factor_count_approximation (f:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    (hf:∀ x,f x ∈ Set.Icc 0 1) {η:ℝ} (hη:0 < η) :
    ∃ n ≤ stepBound η, ∃ (ks:Fin n → ZMod q) (bs:Fin n → Bool)
      (F:Alphabet η n → ℝ),
      Fintype.card (Alphabet η n) ≤ (2 * resolution η + 1) ^ stepBound η ∧
      (∀ a,F a ∈ Set.Icc 0 1) ∧
      (∑ x,F (phaseFactor η ks bs x)) = (∑ x,f x) ∧
      (∀ k, ‖ZMod.dft (fun x =>
        ((f x - F (phaseFactor η ks bs x):ℝ):ℂ)) k‖ ≤ η * q) ∧
      ‖trilinear (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) -
        trilinear (fun x => (F (phaseFactor η ks bs x):ℂ))
          (fun x => (F (phaseFactor η ks bs x):ℂ))
          (fun x => (F (phaseFactor η ks bs x):ℂ))‖ ≤ 3 * η * (q:ℝ) ^ 2:=by
  obtain ⟨n,hn,ks,bs,F,hc,hF,_,hm,hu⟩ :=
    exists_character_factor_approximation f hf hη
  exact ⟨n,hn,ks,bs,F,hc,hF,hm,hu,
    self_count_replacement f (fun x => F (phaseFactor η ks bs x))
      h2 h3 hη.le hf (fun x => hF _) hu⟩
end Green24Proof.CyclicCharacterCounting
private def zz2474:"s09aa"="s09aa":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicL2Replacement
open Finset
open scoped BigOperators
open Green24Proof.CyclicFourierCounting
open Green24Proof.CyclicCharacterCounting
theorem sum_abs_le_of_sum_sq_le {α:Type*} [Fintype α] (u:α → ℝ)
    {ε:ℝ} (hε:0 ≤ ε) (hu:(∑ x,u x ^ 2) ≤ ε ^ 2 * Fintype.card α) :
    (∑ x, |u x|) ≤ ε * Fintype.card α:=by
  have hcs:=Real.sum_mul_le_sqrt_mul_sqrt Finset.univ (fun x => |u x|)
    (fun _ => (1:ℝ))
  simp only [mul_one,sq_abs,one_pow,Finset.sum_const,Finset.card_univ,
    nsmul_eq_mul,mul_one] at hcs
  calc
    (∑ x, |u x|) ≤ Real.sqrt (∑ x,u x ^ 2) * Real.sqrt (Fintype.card α):=hcs
    _ ≤ Real.sqrt (ε ^ 2 * Fintype.card α) * Real.sqrt (Fintype.card α):=by gcongr
    _ = ε * Fintype.card α:=by
      rw [Real.sqrt_mul (sq_nonneg ε),Real.sqrt_sq_eq_abs,abs_of_nonneg hε,
        mul_assoc,Real.mul_self_sqrt (Nat.cast_nonneg _)]
theorem abs_sum_le_of_sum_sq_le {α:Type*} [Fintype α] (u:α → ℝ)
    {ε:ℝ} (hε:0 ≤ ε) (hu:(∑ x,u x ^ 2) ≤ ε ^ 2 * Fintype.card α) :
    |∑ x,u x| ≤ ε * Fintype.card α :=
  (Finset.abs_sum_le_sum_abs _ _).trans (sum_abs_le_of_sum_sq_le u hε hu)
variable {q:ℕ} [NeZero q]
private def zz1918:"s077e"="s077e":=by decide+kernel
theorem dft_norm_le_sum_abs (u:ZMod q → ℝ) (k:ZMod q) :
    ‖ZMod.dft (fun x => (u x:ℂ)) k‖ ≤ ∑ x, |u x|:=by
  calc
    ‖ZMod.dft (fun x => (u x:ℂ)) k‖ ≤
        ∑ x, ‖ZMod.stdAddChar (-(x * k)) * (u x:ℂ)‖:=norm_sum_le _ _
    _ = _:=by
      simp only [norm_mul,ZMod.stdAddChar_apply,Circle.norm_coe,one_mul,
        Complex.norm_real,Real.norm_eq_abs]
theorem dft_norm_le_of_sum_sq_le (u:ZMod q → ℝ)
    {ε:ℝ} (hε:0 ≤ ε) (hu:(∑ x,u x ^ 2) ≤ ε ^ 2 * q) (k:ZMod q) :
    ‖ZMod.dft (fun x => (u x:ℂ)) k‖ ≤ ε * q:=by
  have h:=sum_abs_le_of_sum_sq_le u hε (by simpa only [ZMod.card] using hu)
  simpa only [ZMod.card] using (dft_norm_le_sum_abs u k).trans h
theorem self_count_l2_replacement (f g:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {ε:ℝ} (hε:0 ≤ ε)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (hg:∀ x,g x ∈ Set.Icc 0 1)
    (he:(∑ x,(f x - g x) ^ 2) ≤ ε ^ 2 * q) :
    ‖trilinear (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) -
      trilinear (fun x => (g x:ℂ)) (fun x => (g x:ℂ)) (fun x => (g x:ℂ))‖ ≤
        3 * ε * (q:ℝ) ^ 2 :=
  self_count_replacement f g h2 h3 hε hf hg
    (dft_norm_le_of_sum_sq_le (fun x => f x - g x) hε he)
end Green24Proof.CyclicL2Replacement
private def zz2475:"s09ab"="s09ab":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicGrowthCounting
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicFourierCounting
open Green24Proof.CyclicCharacterCounting
open Green24Proof.CyclicL2Replacement
open Green24Proof.CyclicGrowthDecomposition
open Green24Proof.CyclicTorusSmoothing
variable {q:ℕ} [NeZero q]
noncomputable def weightedCount (f:ZMod q → ℝ):ℝ :=
  ∑ y, ∑ z,f (3 * z - 2 * y) * f y * f z
theorem weightedCount_ofReal (f:ZMod q → ℝ) :
    (weightedCount f:ℂ) =
      trilinear (fun x => (f x:ℂ)) (fun x => (f x:ℂ)) (fun x => (f x:ℂ)):=by
  simp only [weightedCount,trilinear,Complex.ofReal_sum,Complex.ofReal_mul]
private def zz1919:"s077f"="s077f":=by decide+kernel
theorem mass_count_of_decomposition (f structured small uniform:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {ε η:ℝ} (hε:0 ≤ ε) (hη:0 ≤ η)
    (hf:∀ x,f x ∈ Set.Icc 0 1) (hs:∀ x,structured x ∈ Set.Icc 0 1)
    (hd:∀ x,f x = structured x + small x + uniform x)
    (hb:∀ x,structured x + small x ∈ Set.Icc 0 1)
    (he:(∑ x,small x ^ 2) ≤ ε ^ 2 * q)
    (hm:(∑ x,uniform x) = 0)
    (hu:∀ k, ‖ZMod.dft (fun x => (uniform x:ℂ)) k‖ ≤ η * q) :
    |(∑ x,f x) - ∑ x,structured x| ≤ ε * q ∧
      |weightedCount f - weightedCount structured| ≤ 3 * (ε + η) * (q:ℝ) ^ 2:=by
  have hmass:(∑ x,f x) - ∑ x,structured x = ∑ x,small x:=by
    simp_rw [hd]
    rw [Finset.sum_add_distrib,Finset.sum_add_distrib,hm]
    ring
  have hsmall:|∑ x,small x| ≤ ε * q:=by
    simpa only [ZMod.card] using abs_sum_le_of_sum_sq_le small hε
      (by simpa only [ZMod.card] using he)
  let fine:=fun x => structured x + small x
  have hdiff:(fun x => f x - fine x) = uniform:=by
    funext x
    rw [hd]
    dsimp only [fine]
    ring
  have hUF:=self_count_replacement f fine h2 h3 hη hf hb
    (by simpa only [congrFun hdiff] using hu)
  have hLS:=self_count_l2_replacement fine structured h2 h3 hε hb hs
    (by simpa only [fine,add_sub_cancel_left] using he)
  rw [← weightedCount_ofReal, ← weightedCount_ofReal, ← Complex.ofReal_sub,
    Complex.norm_real,Real.norm_eq_abs] at hUF hLS
  have htri:=abs_add_le (weightedCount f - weightedCount fine)
    (weightedCount fine - weightedCount structured)
  have hid:weightedCount f - weightedCount fine +
      (weightedCount fine - weightedCount structured) =
      weightedCount f - weightedCount structured:=by ring
  rw [hid] at htri
  refine ⟨by rwa [hmass], ?_⟩
  nlinarith
theorem exists_growth_count_approximation (f:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    (hf:∀ x,f x ∈ Set.Icc 0 1) (τ:ℕ → ℝ) (hτ:∀ C,0 < τ C)
    {ε:ℝ} (hε:0 < ε) :
    ∃ M ≤ complexityBound τ ε, ∃ n ≤ M,
      ∃ (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ),
      LipschitzWith (M:ℝ≥0) H ∧
      (∀ z,H z ∈ Set.Icc 0 1) ∧
      |(∑ x,f x) - ∑ x,H (characterOrbit ks x)| ≤ ε * q ∧
      |weightedCount f - weightedCount (fun x => H (characterOrbit ks x))| ≤
        3 * (ε + τ M) * (q:ℝ) ^ 2:=by
  obtain ⟨M,hM,n,hn,ks,H,small,uniform,hL,hH,hd,hb,_hs,_hu,
    he,hm,hU⟩:=exists_growth_decomposition f hf τ hτ hε
  obtain ⟨hmass,hcount⟩:=mass_count_of_decomposition f
    (fun x => H (characterOrbit ks x)) small uniform h2 h3 hε.le (hτ M).le
    hf (fun x => hH _) hd hb he hm hU
  exact ⟨M,hM,n,hn,ks,H,hL,hH,hmass,hcount⟩
end Green24Proof.CyclicGrowthCounting
private def zz2476:"s09ac"="s09ac":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicTorusPairCounting
open Finset MeasureTheory
open scoped BigOperators
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusPairDiscrepancy
open Green24Proof.CyclicTorusPairApproximation Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicGrowthCounting
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι]
noncomputable def realCountingIntegrand (H:(ι → Circle) → ℝ) (p:PairTorus ι ι):ℝ :=
  H (p.2 ^ 3 * p.1 ^ (-2:ℤ)) * H p.1 * H p.2
noncomputable def countingIntegrand (H:(ι → Circle) → ℝ) (p:PairTorus ι ι):ℂ :=
  (realCountingIntegrand H p:ℂ)
noncomputable def haarWeightedCount (H:(ι → Circle) → ℝ):ℝ :=
  ∫ p,realCountingIntegrand H p ∂pairHaar
omit [Fintype ι] in
theorem countingIntegrand_continuous (H:(ι → Circle) → ℝ) (hH:Continuous H) :
    Continuous (countingIntegrand H):=by
  unfold countingIntegrand realCountingIntegrand
  fun_prop
theorem integral_countingIntegrand (H:(ι → Circle) → ℝ) :
    (∫ p,countingIntegrand H p ∂pairHaar) = (haarWeightedCount H:ℂ):=by
  exact integral_ofReal
variable {q n:ℕ} [NeZero q]
private def zz1920:"s0780"="s0780":=by decide+kernel
theorem characterOrbit_equation (ks:Fin n → ZMod q) (y z:ZMod q) :
    characterOrbit ks (3 * z - 2 * y) =
      characterOrbit ks z ^ 3 * characterOrbit ks y ^ (-2:ℤ):=by
  funext i
  change ZMod.toCircle (-((3 * z - 2 * y) * ks i)) =
    ZMod.toCircle (-(z * ks i)) ^ 3 * ZMod.toCircle (-(y * ks i)) ^ (-2:ℤ)
  rw [← AddChar.map_nsmul_eq_pow, ← AddChar.map_zsmul_eq_zpow, ← AddChar.map_add_eq_mul]
  congr 1
  simp only [nsmul_eq_mul,zsmul_eq_mul]
  ring
theorem pairOrbitMean_countingIntegrand (ks:Fin n → ZMod q)
    (H:(Fin n → Circle) → ℝ) :
    pairOrbitMean ks ks (countingIntegrand H) =
      ((weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ) ^ 2:ℝ):ℂ):=by
  have heval (y z:ZMod q) :
      countingIntegrand H (characterOrbit ks y,characterOrbit ks z) =
        ((H (characterOrbit ks (3 * z - 2 * y)) *
          H (characterOrbit ks y) * H (characterOrbit ks z):ℝ):ℂ):=by
    unfold countingIntegrand realCountingIntegrand
    rw [characterOrbit_equation]
  rw [pairOrbitMean,Fintype.sum_prod_type]
  change ((q:ℂ) ^ 2)⁻¹ *
    (∑ y:ZMod q, ∑ z:ZMod q,
      countingIntegrand H (characterOrbit ks y,characterOrbit ks z)) = _
  simp_rw [heval]
  simp only [weightedCount,Complex.ofReal_div,Complex.ofReal_pow,Complex.ofReal_natCast,
    Complex.ofReal_sum]
  ring
theorem weightedCount_haar_discrepancy_of_approximation (ks:Fin n → ZMod q)
    (H:(Fin n → Circle) → ℝ) (hH:Continuous H)
    (S:Finset (PairExponent (Fin n) (Fin n))) (c:PairExponent (Fin n) (Fin n) → ℂ)
    (hk:Nonresonant ks (S.image Prod.fst)) (hl:Nonresonant ks (S.image Prod.snd))
    {ε:ℝ} (herr:∀ z, ‖countingIntegrand H z - pairPolynomial S c z‖ ≤ ε) :
    |weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ) ^ 2 -
      haarWeightedCount H| ≤ 2 * ε:=by
  have h:=pairOrbitMean_haar_discrepancy_of_continuous ks ks S c (countingIntegrand H)
    (countingIntegrand_continuous H hH) hk hl herr
  rw [pairOrbitMean_countingIntegrand,integral_countingIntegrand, ← Complex.ofReal_sub,
    Complex.norm_real,Real.norm_eq_abs] at h
  exact h
theorem exists_weightedCount_discrepancy_support
    (H:(Fin n → Circle) → ℝ) (hH:Continuous H) {ε:ℝ} (hε:0 < ε) :
    ∃ (S:Finset (PairExponent (Fin n) (Fin n))) (c:PairExponent (Fin n) (Fin n) → ℂ),
      (∀ z, ‖countingIntegrand H z - pairPolynomial S c z‖ < ε) ∧
      ∀ ks:Fin n → ZMod q,
        Nonresonant ks (S.image Prod.fst) → Nonresonant ks (S.image Prod.snd) →
        |weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ) ^ 2 -
          haarWeightedCount H| ≤ 2 * ε:=by
  obtain ⟨S,c,herr⟩:=exists_finite_pair_laurent_approximation
    (countingIntegrand H) (countingIntegrand_continuous H hH) hε
  exact ⟨S,c,herr,fun ks hk hl => weightedCount_haar_discrepancy_of_approximation
    ks H hH S c hk hl (fun z => (herr z).le)⟩
end Green24Proof.CyclicTorusPairCounting
private def zz2477:"s09ad"="s09ad":=by decide+kernel
end 
section 
namespace Green24Proof.CompactTorusIntegratedCounting
open MeasureTheory Set
open scoped BigOperators
open Green24Proof.CompactTorusArcModel Green24Proof.CompactTorusArcCounting
open Green24Proof.TorusArcPairIntegral Green24Proof.TorusCoordinateHaar
open Green24Proof.CircleArcResidues Green24Proof.CyclicTorusHaarDiscrepancy
open Green24Proof.CyclicTorusPairCounting Green24Proof.CyclicTorusPairDiscrepancy
open Green24Proof.SpatialCircleCutoff
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
abbrev ArcSpace (p:ι):=ℝ × ({j:ι // j ≠ p} → Circle)
noncomputable def arcMeasure (p:ι):Measure (ArcSpace p) :=
  volume.prod (torusHaar {j:ι // j ≠ p})
private def zz1921:"s0781"="s0781":=by decide+kernel
theorem arcMeasure_sigmaFinite (p:ι):SigmaFinite (arcMeasure p):=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  unfold arcMeasure
  infer_instance
noncomputable def compactCountingIntegrand (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (j k:ZMod q) (yz:ArcSpace p × ArcSpace p):ℝ :=
  model p q F (3 * k - 2 * j) (3 * yz.2.1 - 2 * yz.1.1,yz.2.2 ^ 3 * yz.1.2 ^ (-2:ℤ)) *
    model p q F j yz.1 * model p q F k yz.2
omit [Fintype ι] in
theorem compactCountingIntegrand_continuous (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (hF:Continuous F) (j k:ZMod q) :
    Continuous (compactCountingIntegrand p q F j k):=by
  unfold compactCountingIntegrand
  exact (((model_continuous p q F hF _).comp (by fun_prop)).mul
    ((model_continuous p q F hF j).comp continuous_fst)).mul
      ((model_continuous p q F hF k).comp continuous_snd)
omit [Fintype ι] in
theorem compactCountingIntegrand_zero_left (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (j k:ZMod q) (yz:ArcSpace p × ArcSpace p)
    (hy:Real.pi / 2 ≤ |yz.1.1|):compactCountingIntegrand p q F j k yz = 0:=by
  simp only [compactCountingIntegrand,model_zero_outside p q F j yz.1 hy,
    mul_zero,zero_mul]
omit [Fintype ι] in
theorem compactCountingIntegrand_zero_right (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (j k:ZMod q) (yz:ArcSpace p × ArcSpace p)
    (hz:Real.pi / 2 ≤ |yz.2.1|):compactCountingIntegrand p q F j k yz = 0:=by
  simp only [compactCountingIntegrand,model_zero_outside p q F k yz.2 hz,mul_zero]
private def zz1922:"s0782"="s0782":=by decide+kernel
omit [Fintype ι] in
theorem compactCountingIntegrand_compactSupport (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (j k:ZMod q) :
    HasCompactSupport (compactCountingIntegrand p q F j k):=by
  let S:Set (ArcSpace p):=Icc (-(Real.pi / 2)) (Real.pi / 2) ×ˢ univ
  have hS:IsCompact S:=isCompact_Icc.prod isCompact_univ
  apply HasCompactSupport.intro (hS.prod hS)
  intro yz hyz
  by_cases hy:yz.1 ∈ S
  · apply compactCountingIntegrand_zero_right
    have hz:yz.2 ∉ S:=fun hz => hyz ⟨hy,hz⟩
    have hn:¬ |yz.2.1| ≤ Real.pi / 2:=fun ha => hz ⟨abs_le.mp ha,trivial⟩
    exact (lt_of_not_ge hn).le
  · apply compactCountingIntegrand_zero_left
    have hn:¬ |yz.1.1| ≤ Real.pi / 2:=fun ha => hy ⟨abs_le.mp ha,trivial⟩
    exact (lt_of_not_ge hn).le
theorem compactCountingIntegrand_integrable (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (hF:Continuous F) (j k:ZMod q) :
    Integrable (compactCountingIntegrand p q F j k) ((arcMeasure p).prod (arcMeasure p)):=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  unfold arcMeasure
  exact (compactCountingIntegrand_continuous p q F hF j k).integrable_of_hasCompactSupport
    (compactCountingIntegrand_compactSupport p q F j k)
theorem compactCountingIntegrand_slice_integrable (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (hF:Continuous F) (j k:ZMod q) (y:ArcSpace p) :
    Integrable (fun z => compactCountingIntegrand p q F j k (y,z)) (arcMeasure p):=by
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  unfold arcMeasure
  apply ((compactCountingIntegrand_continuous p q F hF j k).comp
    (continuous_const.prodMk continuous_id)).integrable_of_hasCompactSupport
  exact (model_compactSupport p q F k).mul_left
theorem integral_eq_principal_of_zero_outside (f:ℝ → ℝ)
    (hf:∀ t,Real.pi / 2 ≤ |t| → f t = 0) :
    (∫ t,f t) = ∫ t in -Real.pi..Real.pi,f t:=by
  symm
  apply intervalIntegral.integral_eq_integral_of_support_subset
  intro t ht
  by_contra h
  apply ht
  apply hf
  by_contra h'
  have ha:=abs_lt.mp (lt_of_not_ge h')
  exact h ⟨by linarith [Real.pi_pos],by linarith [Real.pi_pos]⟩
private def zz1923:"s0783"="s0783":=by decide+kernel
theorem integral_compact_count_eq_arc (p:ι) (q:ℕ)
    (F:(ι → Circle) → ℝ) (hF:Continuous F) (j k:ZMod q) :
    (∫ yz,compactCountingIntegrand p q F j k yz ∂(arcMeasure p).prod (arcMeasure p)) =
      ∫ s in -Real.pi..Real.pi, ∫ u,
        (∫ t in -Real.pi..Real.pi, ∫ v,
          compactCountingIntegrand p q F j k ((s,u),(t,v))
            ∂torusHaar {i:ι // i ≠ p}) ∂torusHaar {i:ι // i ≠ p}:=by
  letI:=arcMeasure_sigmaFinite p
  letI:=torusHaar_isProbabilityMeasure {j:ι // j ≠ p}
  let L:=compactCountingIntegrand p q F j k
  have hint:=compactCountingIntegrand_integrable p q F hF j k
  have hinner (y:ArcSpace p) :
      (∫ z,L (y,z) ∂arcMeasure p) =
        ∫ t in -Real.pi..Real.pi, ∫ v,L (y,(t,v)) ∂torusHaar {i:ι // i ≠ p}:=by
    rw [show arcMeasure p = volume.prod (torusHaar {i:ι // i ≠ p}) from rfl,
      integral_prod _ (compactCountingIntegrand_slice_integrable p q F hF j k y)]
    apply integral_eq_principal_of_zero_outside
    intro t ht
    change (∫ v,L (y,(t,v)) ∂torusHaar {i:ι // i ≠ p}) = 0
    have hz (v:{i:ι // i ≠ p} → Circle):L (y,(t,v)) = 0 :=
      compactCountingIntegrand_zero_right p q F j k _ ht
    simp_rw [hz]
    exact integral_zero _ _
  rw [integral_prod _ hint]
  change (∫ y,(∫ z,L (y,z) ∂arcMeasure p)
    ∂volume.prod (torusHaar {i:ι // i ≠ p})) = _
  rw [integral_prod _ hint.integral_prod_left]
  change (∫ s, ∫ u, ∫ z,L ((s,u),z) ∂arcMeasure p
    ∂torusHaar {i:ι // i ≠ p}) = _
  simp_rw [hinner]
  apply integral_eq_principal_of_zero_outside
  intro s hs
  have hz (u:{i:ι // i ≠ p} → Circle) (t:ℝ)
      (v:{i:ι // i ≠ p} → Circle):L ((s,u),(t,v)) = 0 :=
    compactCountingIntegrand_zero_left p q F j k _ hs
  simp_rw [hz]
  simp
theorem integrated_count_identity (p:ι) {q:ℕ} [NeZero q]
    (F:(ι → Circle) → ℝ) (hF:Continuous F)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) :
    haarWeightedCount F = ((2 * Real.pi * q)⁻¹) ^ 2 *
      ∑ j:ZMod q, ∑ k:ZMod q,
        ∫ yz,compactCountingIntegrand p q F j k yz
          ∂(arcMeasure p).prod (arcMeasure p):=by
  have hcont:Continuous (realCountingIntegrand F):=by
    unfold realCountingIntegrand
    fun_prop
  unfold haarWeightedCount pairHaar
  rw [integral_pair_sum_residue_arcs p (q:=q) _ hcont]
  congr 1
  apply Finset.sum_congr rfl
  intro j _
  apply Finset.sum_congr rfl
  intro k _
  rw [integral_compact_count_eq_arc p q F hF j k]
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro s hs'
  apply integral_congr_ae
  filter_upwards [] with u
  apply intervalIntegral.integral_congr_Ioo_of_le (by linarith [Real.pi_pos])
  intro t ht'
  apply integral_congr_ae
  filter_upwards [] with v
  exact counting_integrand_identity p F hs j k hs' ht' u v
end Green24Proof.CompactTorusIntegratedCounting
private def zz2478:"s09ae"="s09ae":=by decide+kernel
end 
section 
namespace Green24Proof.CompactTorusProfileComparison
open MeasureTheory Set
open scoped BigOperators
open Green24Proof.CompactTorusArcModel Green24Proof.CompactTorusIntegratedCounting
open Green24Proof.RealTorusDilation Green24Proof.RealTorusCoefficientNormalization
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairCounting
open Green24Proof.SpatialCircleCutoff
variable [MeasurableSpace Circle] [BorelSpace Circle]
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
noncomputable def profileMass (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ) (r:ZMod q):ℝ :=
  ∫ z,model p q F r z ∂arcMeasure p
theorem profileMass_nonneg (p:ι) (q:ℕ) (F:(ι → Circle) → ℝ)
    (hr:∀ z,F z ∈ Icc 0 1) (r:ZMod q):0 ≤ profileMass p q F r :=
  integral_nonneg (fun z => (model_range p q F hr r z).1)
theorem integral_eq_profile_mass (p:ι) {q:ℕ} [NeZero q] (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hs:∀ z,z p ^ q ∉ window → F z = 0) :
    (∫ z,F z ∂torusHaar ι) = (2 * Real.pi * q)⁻¹ * mass (profileMass p q F) :=
  mass_identity p F hF hs
private def zz1924:"s0784"="s0784":=by decide+kernel
theorem model_count_le_kernel (p:ι) {q:ℕ} [NeZero q]
    (hR:RearrangementBound {i:ι // i ≠ p}) (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hr:∀ z,F z ∈ Icc 0 1) (j k:ZMod q) :
    (∫ yz,compactCountingIntegrand p q F j k yz ∂(arcMeasure p).prod (arcMeasure p)) ≤
      kernel (profileMass p q F (3 * k - 2 * j))
        (2 * profileMass p q F j) (3 * profileMass p q F k) / 6:=by
  exact coefficient_bound_of_rearrangement hR
    (model p q F (3 * k - 2 * j)) (model p q F j) (model p q F k)
    (model_continuous p q F hF _) (model_continuous p q F hF _) (model_continuous p q F hF _)
    (model_compactSupport p q F _) (model_compactSupport p q F _) (model_compactSupport p q F _)
    (model_range p q F hr _) (model_range p q F hr _) (model_range p q F hr _)
theorem count_le_profile (p:ι) {q:ℕ} [NeZero q]
    (hR:RearrangementBound {i:ι // i ≠ p}) (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hr:∀ z,F z ∈ Icc 0 1)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) :
    haarWeightedCount F ≤ ((2 * Real.pi * q)⁻¹) ^ 2 *
      (profileFunctional (profileMass p q F) / 6):=by
  rw [integrated_count_identity p F hF hs]
  apply mul_le_mul_of_nonneg_left _ (sq_nonneg _)
  unfold profileFunctional
  rw [Finset.sum_div]
  apply Finset.sum_le_sum
  intro j _
  rw [Finset.sum_div]
  apply Finset.sum_le_sum
  intro k _
  exact model_count_le_kernel p hR F hF hr j k
theorem upper_bound_of_profile (p:ι) {q:ℕ} [NeZero q]
    (hR:RearrangementBound {i:ι // i ≠ p}) (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hr:∀ z,F z ∈ Icc 0 1)
    (hs:∀ z,z p ^ q ∉ window → F z = 0)
    (hP:profileFunctional (profileMass p q F) ≤ 2 * mass (profileMass p q F) ^ 2) :
    haarWeightedCount F ≤ (1 / 3:ℝ) * (∫ z,F z ∂torusHaar ι) ^ 2:=by
  rw [integral_eq_profile_mass p F hF hs]
  calc
    _ ≤ ((2 * Real.pi * q)⁻¹) ^ 2 *
        (profileFunctional (profileMass p q F) / 6):=count_le_profile p hR F hF hr hs
    _ ≤ ((2 * Real.pi * q)⁻¹) ^ 2 * (2 * mass (profileMass p q F) ^ 2 / 6) :=
      mul_le_mul_of_nonneg_left (div_le_div_of_nonneg_right hP (by norm_num)) (sq_nonneg _)
    _ = _:=by ring
theorem upper_bound_not_five (p:ι) {q:ℕ} [NeZero q] (h5:¬5 ∣ q)
    (hR:RearrangementBound {i:ι // i ≠ p}) (F:(ι → Circle) → ℝ)
    (hF:Continuous F) (hr:∀ z,F z ∈ Icc 0 1)
    (hs:∀ z,z p ^ q ∉ window → F z = 0) :
    haarWeightedCount F ≤ (1 / 3:ℝ) * (∫ z,F z ∂torusHaar ι) ^ 2 :=
  upper_bound_of_profile p hR F hF hr hs
    (VerifiedProfileEndpoint.profileFunctional_le q h5 _ (profileMass_nonneg p q F hr))
end Green24Proof.CompactTorusProfileComparison
private def zz2479:"s09af"="s09af":=by decide+kernel
end 
section 
namespace Green24Proof.UniformCircleLaurentApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset Set Metric BoundedContinuousFunction
open scoped BigOperators NNReal
open Green24Proof.CyclicTorusLaurent
open Green24Proof.CircleLaurentApproximation
variable {ι:Type*} [Fintype ι]
private def zz1925:"s0785"="s0785":=by decide+kernel
theorem polynomial_extend_support (S T:Finset (ι → ℤ)) (hST:S ⊆ T)
    (c:(ι → ℤ) → ℂ) (z:ι → Circle) :
    polynomial T (fun m => if m ∈ S then c m else 0) z = polynomial S c z:=by
  classical
  unfold polynomial
  calc
    (∑ m ∈ T,(if m ∈ S then c m else 0) * monomial m z) =
        ∑ m ∈ S,(if m ∈ S then c m else 0) * monomial m z:=by
      symm
      apply Finset.sum_subset hST
      intro m _ hm
      simp [hm]
    _ = _:=Finset.sum_congr rfl (fun m hm => by rw [if_pos hm])
theorem exists_common_support_of_isCompact (A:Set ((ι → Circle) →ᵇ ℂ))
    (hA:IsCompact A) {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (ι → ℤ), ∀ F ∈ A, ∃ c:(ι → ℤ) → ℂ,
      ∀ z, ‖F z - polynomial S c z‖ < ε:=by
  classical
  have hhalf:0 < ε / 2:=half_pos hε
  choose supports coeffs happrox using
    fun F:(ι → Circle) →ᵇ ℂ => exists_finite_laurent_approximation F.toContinuousMap hhalf
  obtain ⟨t,_htA,htfinite,hcover⟩:=finite_cover_balls_of_compact hA hhalf
  let S:=htfinite.toFinset.biUnion supports
  refine ⟨S, ?_⟩
  intro F hF
  obtain ⟨G,hGt,hFG⟩:=Set.mem_iUnion₂.mp (hcover hF)
  have hsub:supports G ⊆ S :=
    Finset.subset_biUnion_of_mem supports (htfinite.mem_toFinset.mpr hGt)
  refine ⟨fun m => if m ∈ supports G then coeffs G m else 0, ?_⟩
  intro z
  rw [polynomial_extend_support (supports G) S hsub]
  have hpoint:‖F z - G z‖ < ε / 2:=by
    rw [← dist_eq_norm]
    exact (BoundedContinuousFunction.dist_coe_le_dist z).trans_lt hFG
  have happ:=happrox G z
  change ‖G z - polynomial (supports G) (coeffs G) z‖ < ε / 2 at happ
  have ht:=norm_add_le (F z - G z) (G z - polynomial (supports G) (coeffs G) z)
  rw [sub_add_sub_cancel] at ht
  linarith
def boundedLipschitzClass (K:ℝ≥0):Set ((ι → Circle) →ᵇ ℂ) :=
  {F | LipschitzWith K F ∧ ∀ z, ‖F z‖ ≤ 1}
theorem isCompact_closure_boundedLipschitzClass (K:ℝ≥0) :
    IsCompact (closure (boundedLipschitzClass (ι:=ι) K)):=by
  apply BoundedContinuousFunction.arzela_ascoli (Metric.closedBall (0:ℂ) 1)
    (isCompact_closedBall _ _)
  · intro F z hF
    simpa only [Metric.mem_closedBall,dist_zero_right] using hF.2 z
  · exact (LipschitzWith.uniformEquicontinuous
      (fun F:boundedLipschitzClass (ι:=ι) K => (F.val:(ι → Circle) → ℂ)) K
      (fun F => F.property.1)).equicontinuous
theorem exists_uniform_support_boundedLipschitz (K:ℝ≥0) {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (ι → ℤ), ∀ F:(ι → Circle) → ℂ,
      LipschitzWith K F → (∀ z, ‖F z‖ ≤ 1) →
      ∃ c:(ι → ℤ) → ℂ, ∀ z, ‖F z - polynomial S c z‖ < ε:=by
  obtain ⟨S,hS⟩:=exists_common_support_of_isCompact
    (closure (boundedLipschitzClass (ι:=ι) K)) (isCompact_closure_boundedLipschitzClass K) hε
  refine ⟨S, ?_⟩
  intro F hF hnorm
  let Fb:(ι → Circle) →ᵇ ℂ:=BoundedContinuousFunction.mkOfCompact ⟨F,hF.continuous⟩
  exact hS Fb (subset_closure (show Fb ∈ boundedLipschitzClass K from ⟨hF,hnorm⟩))
private def zz1926:"s0786"="s0786":=by decide+kernel
theorem exists_uniform_support_unit_interval (K:ℝ≥0) {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (ι → ℤ), ∀ F:(ι → Circle) → ℝ,
      LipschitzWith K F → (∀ z,F z ∈ Set.Icc 0 1) →
      ∃ c:(ι → ℤ) → ℂ, ∀ z, ‖(F z:ℂ) - polynomial S c z‖ < ε:=by
  obtain ⟨S,hS⟩:=exists_uniform_support_boundedLipschitz (ι:=ι) K hε
  refine ⟨S, ?_⟩
  intro F hF hrange
  have hcomplex:LipschitzWith K (fun z => (F z:ℂ)):=by
    simpa only [one_mul,Function.comp_def] using Complex.isometry_ofReal.lipschitz.comp hF
  apply hS _ hcomplex
  intro z
  simpa only [Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg (hrange z).1] using (hrange z).2
end Green24Proof.UniformCircleLaurentApproximation
private def zz2480:"s09b0"="s09b0":=by decide+kernel
end 
section 
namespace Green24Proof.UniformTorusCountingApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped NNReal BigOperators
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusPairDiscrepancy
open Green24Proof.CyclicTorusPairApproximation Green24Proof.CyclicTorusPairCounting
open Green24Proof.UniformCircleLaurentApproximation
open Green24Proof.CyclicTorusSmoothing Green24Proof.CyclicGrowthCounting
theorem circle_dist_mul_le (a b c d:Circle) :
    dist (a * b) (c * d) ≤ dist a c + dist b d:=by
  change dist ((a:ℂ) * b) ((c:ℂ) * d) ≤ dist (a:ℂ) c + dist (b:ℂ) d
  simp only [dist_eq_norm]
  calc
    _ = ‖((a:ℂ) - c) * b + (c:ℂ) * ((b:ℂ) - d)‖:=by congr 1; ring
    _ ≤ ‖((a:ℂ) - c) * b‖ + ‖(c:ℂ) * ((b:ℂ) - d)‖:=norm_add_le _ _
    _ = _:=by rw [norm_mul,norm_mul,Circle.norm_coe,Circle.norm_coe,mul_one,one_mul]
theorem circle_dist_inv (a b:Circle):dist a⁻¹ b⁻¹ = dist a b:=by
  change dist ((a⁻¹:Circle):ℂ) ((b⁻¹:Circle):ℂ) = dist (a:ℂ) b
  simp only [dist_eq_norm]
  rw [Circle.coe_inv_eq_conj,Circle.coe_inv_eq_conj, ← map_sub]
  exact Complex.norm_conj _
theorem circle_dist_pow_le (a b:Circle) (m:ℕ) :
    dist (a ^ m) (b ^ m) ≤ m * dist a b:=by
  induction m with
  | zero => simp
  | succ m ih =>
    rw [pow_succ,pow_succ]
    have h:=(circle_dist_mul_le (a ^ m) a (b ^ m) b).trans (add_le_add ih le_rfl)
    simpa [Nat.cast_add,Nat.cast_one,add_mul] using h
variable {ι κ:Type*} [Fintype ι] [Fintype κ]
private def zz1927:"s0787"="s0787":=by decide+kernel
theorem splitTorus_lipschitz :
    LipschitzWith 1 (splitTorus (ι:=ι) (κ:=κ)):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  rw [NNReal.coe_one,one_mul,Prod.dist_eq]
  apply max_le
  · exact (dist_pi_le_iff dist_nonneg).mpr (fun i => dist_le_pi_dist z w (Sum.inl i))
  · exact (dist_pi_le_iff dist_nonneg).mpr (fun i => dist_le_pi_dist z w (Sum.inr i))
theorem equationMap_lipschitz :
    LipschitzWith 5 (fun p:PairTorus ι ι => p.2 ^ 3 * p.1 ^ (-2:ℤ)):=by
  apply LipschitzWith.of_dist_le_mul
  intro p r
  apply (dist_pi_le_iff (mul_nonneg (by norm_num) dist_nonneg)).mpr
  intro i
  change dist (p.2 i ^ 3 * p.1 i ^ (-2:ℤ)) (r.2 i ^ 3 * r.1 i ^ (-2:ℤ)) ≤ _
  have hfst:=(dist_le_pi_dist p.1 r.1 i).trans (show dist p.1 r.1 ≤ dist p r from le_max_left _ _)
  have hsnd:=(dist_le_pi_dist p.2 r.2 i).trans (show dist p.2 r.2 ≤ dist p r from le_max_right _ _)
  have hthree:=circle_dist_pow_le (p.2 i) (r.2 i) 3
  have htwo:=circle_dist_pow_le (p.1 i) (r.1 i) 2
  have hmul:=circle_dist_mul_le (p.2 i ^ 3) (p.1 i ^ (-2:ℤ))
    (r.2 i ^ 3) (r.1 i ^ (-2:ℤ))
  simp only [zpow_neg,zpow_ofNat,circle_dist_inv] at hmul ⊢
  norm_num only [Nat.cast_ofNat,NNReal.coe_ofNat] at *
  linarith
theorem real_mul_dist_le {a b c d:ℝ}
    (hb:b ∈ Set.Icc 0 1) (hc:c ∈ Set.Icc 0 1) :
    dist (a * b) (c * d) ≤ dist a c + dist b d:=by
  simp only [Real.dist_eq]
  calc
    |a * b - c * d| = |(a - c) * b + c * (b - d)|:=by congr 1; ring
    _ ≤ |(a - c) * b| + |c * (b - d)|:=abs_add_le _ _
    _ = |a - c| * b + c * |b - d|:=by
      rw [abs_mul,abs_mul,abs_of_nonneg hb.1,abs_of_nonneg hc.1]
    _ ≤ |a - c| + |b - d|:=by
      nlinarith [hb.2,hc.2,abs_nonneg (a-c),abs_nonneg (b-d)]
theorem countingIntegrand_lipschitz (H:(ι → Circle) → ℝ) {K:ℝ≥0}
    (hH:LipschitzWith K H) (hr:∀ z,H z ∈ Set.Icc 0 1) :
    LipschitzWith (7 * K) (countingIntegrand H):=by
  apply LipschitzWith.of_dist_le_mul
  intro p r
  have h1:=hH.dist_le_mul_of_le (equationMap_lipschitz.dist_le_mul p r)
  have h2:=hH.dist_le_mul_of_le (show dist p.1 r.1 ≤ dist p r from le_max_left _ _)
  have h3:=hH.dist_le_mul_of_le (show dist p.2 r.2 ≤ dist p r from le_max_right _ _)
  have hmul:=real_mul_dist_le (hr p.1) (hr (r.2 ^ 3 * r.1 ^ (-2:ℤ)))
    (a:=H (p.2 ^ 3 * p.1 ^ (-2:ℤ))) (d:=H r.1)
  have hrprod:H (r.2 ^ 3 * r.1 ^ (-2:ℤ)) * H r.1 ∈ Set.Icc 0 1 :=
    ⟨mul_nonneg (hr _).1 (hr _).1,
      (mul_le_mul (hr _).2 (hr _).2 (hr _).1 (by norm_num)).trans (by norm_num)⟩
  have hmul':=real_mul_dist_le (hr p.2) hrprod
    (a:=H (p.2 ^ 3 * p.1 ^ (-2:ℤ)) * H p.1) (d:=H r.2)
  change dist ((realCountingIntegrand H p:ℝ):ℂ) ((realCountingIntegrand H r:ℝ):ℂ) ≤ _
  rw [Complex.isometry_ofReal.dist_eq]
  unfold realCountingIntegrand
  norm_num only [NNReal.coe_mul,NNReal.coe_ofNat] at *
  nlinarith
private def zz1928:"s0788"="s0788":=by decide+kernel
omit [Fintype ι] in
theorem countingIntegrand_norm_le (H:(ι → Circle) → ℝ)
    (hr:∀ z,H z ∈ Set.Icc 0 1) (p:PairTorus ι ι) :
    ‖countingIntegrand H p‖ ≤ 1:=by
  unfold countingIntegrand realCountingIntegrand
  rw [Complex.norm_real,Real.norm_eq_abs,
    abs_of_nonneg (mul_nonneg (mul_nonneg (hr _).1 (hr _).1) (hr _).1)]
  calc
    _ ≤ 1 * 1 * 1:=mul_le_mul
      (mul_le_mul (hr _).2 (hr _).2 (hr _).1 (by norm_num))
      (hr _).2 (hr _).1 (by norm_num)
    _ = 1:=by norm_num
theorem exists_uniform_counting_support (K:ℝ≥0) {ε:ℝ} (hε:0 < ε) :
    ∃ S:Finset (PairExponent ι ι), ∀ H:(ι → Circle) → ℝ,
      LipschitzWith K H → (∀ z,H z ∈ Set.Icc 0 1) →
      ∃ c:PairExponent ι ι → ℂ,
        ∀ p, ‖countingIntegrand H p - pairPolynomial S c p‖ < ε:=by
  obtain ⟨S,hS⟩:=exists_uniform_support_boundedLipschitz (ι:=ι ⊕ ι) (7 * K) hε
  refine ⟨S.map exponentEquiv.toEmbedding, ?_⟩
  intro H hH hr
  have hlip:LipschitzWith (7 * K) (countingIntegrand H ∘ splitTorus):=by
    simpa only [mul_one] using (countingIntegrand_lipschitz H hH hr).comp splitTorus_lipschitz
  obtain ⟨c,hc⟩:=hS _ hlip (fun z => countingIntegrand_norm_le H hr _)
  refine ⟨fun m => c (exponentEquiv.symm m), ?_⟩
  intro p
  rw [pairPolynomial_map]
  simpa only [Function.comp_apply,splitTorus_joinTorus] using hc (joinTorus p)
theorem nonresonant_of_subset {q:ℕ} [NeZero q] (ks:ι → ZMod q)
    {S T:Finset (ι → ℤ)} (hST:S ⊆ T) (hk:Nonresonant ks T) :
    Nonresonant ks S:=fun m hm hne => hk m (hST hm) hne
theorem orbitMean_ofReal {q n:ℕ} [NeZero q] (ks:Fin n → ZMod q)
    (H:(Fin n → Circle) → ℝ) :
    orbitMean ks (fun z => (H z:ℂ)) =
      (((∑ x:ZMod q,H (characterOrbit ks x)) / q:ℝ):ℂ):=by
  simp only [orbitMean,Complex.ofReal_div,Complex.ofReal_sum,Complex.ofReal_natCast]
  unfold characterOrbit
  ring
private def zz1929:"s0789"="s0789":=by decide+kernel
theorem exists_uniform_mass_count_discrepancy_support (n:ℕ) (K:ℝ≥0)
    {ε:ℝ} (hε:0 < ε) :
    ∃ T:Finset (Fin n → ℤ), ∀ (q:ℕ) [NeZero q]
      (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ),
      LipschitzWith K H → (∀ z,H z ∈ Set.Icc 0 1) → Nonresonant ks T →
      |(∑ x:ZMod q,H (characterOrbit ks x)) / q -
          ∫ z,H z ∂Green24Proof.CyclicTorusHaarDiscrepancy.torusHaar (Fin n)| ≤ 2 * ε ∧
      |weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ) ^ 2 -
          haarWeightedCount H| ≤ 2 * ε:=by
  classical
  obtain ⟨S,hS⟩:=exists_uniform_support_unit_interval (ι:=Fin n) K hε
  obtain ⟨U,hU⟩:=exists_uniform_counting_support (ι:=Fin n) K hε
  refine ⟨S ∪ (U.image Prod.fst ∪ U.image Prod.snd), ?_⟩
  intro q _ ks H hH hr hk
  have hs:Nonresonant ks S:=nonresonant_of_subset ks Finset.subset_union_left hk
  have hu:Nonresonant ks (U.image Prod.fst ∪ U.image Prod.snd) :=
    nonresonant_of_subset ks Finset.subset_union_right hk
  obtain ⟨c,hc⟩:=hS H hH hr
  obtain ⟨d,hd⟩:=hU H hH hr
  constructor
  · have hcont:Continuous (fun z => (H z:ℂ)):=Complex.continuous_ofReal.comp hH.continuous
    have h:=Green24Proof.CyclicTorusHaarDiscrepancy.orbitMean_haar_discrepancy_of_continuous
      ks S c _ hcont hs (fun z => (hc z).le)
    have hint:(∫ z,(H z:ℂ) ∂Green24Proof.CyclicTorusHaarDiscrepancy.torusHaar (Fin n)) =
        Complex.ofReal (∫ z,H z ∂Green24Proof.CyclicTorusHaarDiscrepancy.torusHaar (Fin n)):=by
      exact integral_ofReal (𝕜:=ℂ)
    rw [orbitMean_ofReal,hint, ← Complex.ofReal_sub,
      Complex.norm_real,Real.norm_eq_abs] at h
    exact h
  · exact weightedCount_haar_discrepancy_of_approximation ks H hH.continuous U d
      (nonresonant_of_subset ks Finset.subset_union_left hu)
      (nonresonant_of_subset ks Finset.subset_union_right hu) (fun z => (hd z).le)
end Green24Proof.UniformTorusCountingApproximation
private def zz2481:"s09b1"="s09b1":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFrequencyElimination
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
open Green24Proof.UniformTorusCountingApproximation
variable {q n:ℕ} [NeZero q]
def reducedFrequencies (u:(ZMod q)ˣ) (ks:Fin (n + 1) → ZMod q):Fin n → ZMod q :=
  fun i => (u⁻¹:(ZMod q)ˣ) * ks i.succ
noncomputable def monomialLift (m:Fin (n + 1) → ℤ) (z:Fin n → Circle):Fin (n + 1) → Circle :=
  Fin.cases (∏ i,z i ^ (-m i.succ)) (fun i => z i ^ m 0)
omit [NeZero q] in
theorem reduced_relation (u:(ZMod q)ˣ) (ks:Fin (n + 1) → ZMod q)
    (m:Fin (n + 1) → ℤ) (hu:(u:ZMod q) = m 0)
    (hm:weightedFrequency ks m = 0) :
    weightedFrequency (reducedFrequencies u ks) (fun i => -m i.succ) = ks 0:=by
  have hs:(∑ i:Fin n,(m i.succ:ZMod q) * ks i.succ) = -(u:ZMod q) * ks 0:=by
    unfold weightedFrequency at hm
    rw [Fin.sum_univ_succ, ← hu] at hm
    linear_combination hm
  unfold weightedFrequency reducedFrequencies
  calc
    (∑ i:Fin n,((-m i.succ:ℤ):ZMod q) * ((u⁻¹:(ZMod q)ˣ) * ks i.succ)) =
        -(u⁻¹:(ZMod q)ˣ) * ∑ i:Fin n,(m i.succ:ZMod q) * ks i.succ:=by
      rw [Finset.mul_sum]
      apply Finset.sum_congr rfl
      intro i _
      simp only [Int.cast_neg]
      ring
    _ = ks 0:=by rw [hs]; simp [← mul_assoc]
theorem monomialLift_characterOrbit (u:(ZMod q)ˣ) (ks:Fin (n + 1) → ZMod q)
    (m:Fin (n + 1) → ℤ) (hu:(u:ZMod q) = m 0)
    (hm:weightedFrequency ks m = 0) (x:ZMod q) :
    monomialLift m (characterOrbit (reducedFrequencies u ks) x) = characterOrbit ks x:=by
  funext i
  refine Fin.cases ?_ (fun j => ?_) i
  · apply Circle.coe_injective
    change Circle.coeHom (∏ j:Fin n,characterOrbit (reducedFrequencies u ks) x j ^ (-m j.succ)) = _
    rw [map_prod]
    have h:=monomial_characterOrbit (reducedFrequencies u ks) (fun j => -m j.succ) x
    rw [reduced_relation u ks m hu hm] at h
    simp only [map_zpow]
    exact h
  · change ZMod.toCircle (-(x * reducedFrequencies u ks j)) ^ m 0 =
      ZMod.toCircle (-(x * ks j.succ))
    rw [← AddChar.map_zsmul_eq_zpow]
    congr 1
    rw [zsmul_eq_mul, ← hu]
    unfold reducedFrequencies
    calc
      (u:ZMod q) * -(x * ((u⁻¹:(ZMod q)ˣ) * ks j.succ)) =
          -(x * (((u:ZMod q) * (u⁻¹:(ZMod q)ˣ)) * ks j.succ)):=by ring
      _ = _:=by simp
omit [NeZero q] in
theorem monomialLift_continuous (m:Fin (n + 1) → ℤ):Continuous (monomialLift m):=by
  apply continuous_pi
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · change Continuous (fun z:Fin n → Circle => ∏ j,z j ^ (-m j.succ))
    fun_prop
  · change Continuous (fun z:Fin n → Circle => z j ^ m 0)
    fun_prop
private def zz1930:"s078a"="s078a":=by decide+kernel
theorem circle_dist_zpow_le (a b:Circle) (m:ℤ) :
    dist (a ^ m) (b ^ m) ≤ m.natAbs * dist a b:=by
  cases m with
  | ofNat m =>
    change dist (a ^ (m:ℤ)) (b ^ (m:ℤ)) ≤ (m:ℝ) * dist a b
    simpa only [zpow_natCast] using circle_dist_pow_le a b m
  | negSucc m =>
    simpa only [zpow_negSucc,circle_dist_inv,Int.natAbs_negSucc] using
      circle_dist_pow_le a b (m + 1)
theorem circle_dist_prod_le {α:Type*} (s:Finset α) (a b:α → Circle) :
    dist (∏ i ∈ s,a i) (∏ i ∈ s,b i) ≤ ∑ i ∈ s,dist (a i) (b i):=by
  classical
  induction s using Finset.induction_on with
  | empty => simp
  | @insert i s hi ih =>
    simp only [Finset.prod_insert hi,Finset.sum_insert hi]
    exact (circle_dist_mul_le _ _ _ _).trans (add_le_add le_rfl ih)
theorem monomialLift_lipschitz (m:Fin (n + 1) → ℤ) :
    LipschitzWith ((m 0).natAbs + ∑ i:Fin n,(m i.succ).natAbs:ℝ≥0)
      (monomialLift m):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  apply (dist_pi_le_iff (mul_nonneg (by positivity) dist_nonneg)).mpr
  intro i
  refine Fin.cases ?_ (fun j => ?_) i
  · change dist (∏ j:Fin n,z j ^ (-m j.succ)) (∏ j:Fin n,w j ^ (-m j.succ)) ≤ _
    have hp:=circle_dist_prod_le Finset.univ
      (fun j:Fin n => z j ^ (-m j.succ)) (fun j => w j ^ (-m j.succ))
    have hb:(∑ j:Fin n,dist (z j ^ (-m j.succ)) (w j ^ (-m j.succ))) ≤
        (∑ j:Fin n,((m j.succ).natAbs:ℝ)) * dist z w:=by
      rw [Finset.sum_mul]
      apply Finset.sum_le_sum
      intro j _
      have h:=circle_dist_zpow_le (z j) (w j) (-m j.succ)
      simp only [Int.natAbs_neg] at h
      exact h.trans (mul_le_mul_of_nonneg_left (dist_le_pi_dist z w j) (by positivity))
    have htotal:=hp.trans hb
    simp only [NNReal.coe_add,NNReal.coe_natCast,Nat.cast_sum,NNReal.coe_sum]
    nlinarith [mul_nonneg (Nat.cast_nonneg (m 0).natAbs) (dist_nonneg (x:=z) (y:=w))]
  · change dist (z j ^ m 0) (w j ^ m 0) ≤ _
    have h:=(circle_dist_zpow_le (z j) (w j) (m 0)).trans
      (mul_le_mul_of_nonneg_left (dist_le_pi_dist z w j) (by positivity))
    simp only [NNReal.coe_add,NNReal.coe_natCast,Nat.cast_sum,NNReal.coe_sum]
    have hs:0 ≤ ∑ i:Fin n,((m i.succ).natAbs:ℝ):=Finset.sum_nonneg (fun i _ => by positivity)
    nlinarith [mul_nonneg hs (dist_nonneg (x:=z) (y:=w))]
theorem model_factorization (u:(ZMod q)ˣ) (ks:Fin (n + 1) → ZMod q)
    (m:Fin (n + 1) → ℤ) (hu:(u:ZMod q) = m 0)
    (hm:weightedFrequency ks m = 0) (H:(Fin (n + 1) → Circle) → ℝ) :
    ∀ x,(H ∘ monomialLift m) (characterOrbit (reducedFrequencies u ks) x) =
      H (characterOrbit ks x):=by
  intro x
  rw [Function.comp_apply,monomialLift_characterOrbit u ks m hu hm]
end Green24Proof.CyclicFrequencyElimination
private def zz2482:"s09b2"="s09b2":=by decide+kernel
end 
section 
namespace Green24Proof.TorusIntegerMatrix
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicFrequencyElimination Green24Proof.CyclicTorusLaurent
variable {ι κ ν:Type*} [Fintype ι] [Fintype κ] [Fintype ν]
noncomputable def torusMap (A:ι → κ → ℤ) (z:κ → Circle):ι → Circle :=
  fun i => ∏ j,z j ^ A i j
def matrixComp (A:ι → κ → ℤ) (B:κ → ν → ℤ):ι → ν → ℤ :=
  fun i k => ∑ j,A i j * B j k
noncomputable def matrixId:ι → ι → ℤ:=by
  classical
  exact fun i j => if i = j then 1 else 0
def rowSize (A:ι → κ → ℤ) (i:ι):ℕ:=∑ j,(A i j).natAbs
private def zz1931:"s078b"="s078b":=by decide+kernel
theorem torusMap_id (z:ι → Circle):torusMap matrixId z = z:=by
  classical
  funext i
  simp [torusMap,matrixId]
theorem circle_zpow_sum {α:Type*} (a:Circle) (s:Finset α) (f:α → ℤ) :
    a ^ (∑ j ∈ s,f j) = ∏ j ∈ s,a ^ f j:=by
  classical
  induction s using Finset.induction_on with
  | empty => simp
  | @insert i s hi ih => simp [hi,zpow_add,ih]
omit [Fintype ι] in
theorem torusMap_comp (A:ι → κ → ℤ) (B:κ → ν → ℤ) (z:ν → Circle) :
    torusMap (matrixComp A B) z = torusMap A (torusMap B z):=by
  funext i
  simp only [torusMap,matrixComp,circle_zpow_sum, ← Finset.prod_zpow, ← zpow_mul]
  rw [Finset.prod_comm]
  apply Finset.prod_congr rfl
  intro j _
  apply Finset.prod_congr rfl
  intro k _
  rw [mul_comm]
omit [Fintype ι] in
theorem torusMap_continuous (A:ι → κ → ℤ):Continuous (torusMap A):=by
  unfold torusMap
  fun_prop
private def zz1932:"s078c"="s078c":=by decide+kernel
theorem rowSize_id (i:ι):rowSize (matrixId:ι → ι → ℤ) i = 1:=by
  classical
  simp [rowSize,matrixId,apply_ite]
omit [Fintype ι] in
theorem rowSize_comp_le (A:ι → κ → ℤ) (B:κ → ν → ℤ) (i:ι)
    {D:ℕ} (hB:∀ j,rowSize B j ≤ D) :
    rowSize (matrixComp A B) i ≤ rowSize A i * D:=by
  unfold rowSize matrixComp
  calc
    (∑ k,(∑ j,A i j * B j k).natAbs) ≤ ∑ k, ∑ j,(A i j * B j k).natAbs :=
      Finset.sum_le_sum (fun k _ => Int.natAbs_sum_le _ _)
    _ = ∑ j,(A i j).natAbs * ∑ k,(B j k).natAbs:=by
      simp only [Int.natAbs_mul,Finset.mul_sum]
      rw [Finset.sum_comm]
    _ ≤ ∑ j,(A i j).natAbs * D:=by
      apply Finset.sum_le_sum
      intro j _
      exact Nat.mul_le_mul_left _ (hB j)
    _ = _:=by rw [Finset.sum_mul]
theorem torusMap_lipschitz (A:ι → κ → ℤ) {D:ℕ}
    (hA:∀ i,rowSize A i ≤ D):LipschitzWith (D:ℝ≥0) (torusMap A):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  apply (dist_pi_le_iff (mul_nonneg (by positivity) dist_nonneg)).mpr
  intro i
  change dist (∏ j,z j ^ A i j) (∏ j,w j ^ A i j) ≤ _
  calc
    _ ≤ ∑ j,dist (z j ^ A i j) (w j ^ A i j):=circle_dist_prod_le _ _ _
    _ ≤ ∑ j,((A i j).natAbs:ℝ) * dist z w:=by
      apply Finset.sum_le_sum
      intro j _
      exact (circle_dist_zpow_le _ _ _).trans
        (mul_le_mul_of_nonneg_left (dist_le_pi_dist z w j) (by positivity))
    _ = (rowSize A i:ℝ) * dist z w:=by simp [rowSize,Finset.sum_mul]
    _ ≤ _:=mul_le_mul_of_nonneg_right (by exact_mod_cast hA i) dist_nonneg
noncomputable def frequencyMap {q:ℕ} (A:ι → κ → ℤ) (ks:κ → ZMod q):ι → ZMod q :=
  fun i => weightedFrequency ks (A i)
theorem frequencyMap_id {q:ℕ} (ks:ι → ZMod q):frequencyMap matrixId ks = ks:=by
  classical
  funext i
  simp [frequencyMap,weightedFrequency,matrixId]
private def zz1933:"s078d"="s078d":=by decide+kernel
omit [Fintype ι] in
theorem frequencyMap_comp {q:ℕ} (A:ι → κ → ℤ) (B:κ → ν → ℤ)
    (ks:ν → ZMod q) :
    frequencyMap (matrixComp A B) ks = frequencyMap A (frequencyMap B ks):=by
  funext i
  simp only [frequencyMap,weightedFrequency,matrixComp,Int.cast_sum,Int.cast_mul,
    Finset.sum_mul,Finset.mul_sum]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro j _
  apply Finset.sum_congr rfl
  intro k _
  ring
omit [Fintype ι] in
theorem torusMap_character_values {q:ℕ} [NeZero q]
    (A:ι → κ → ℤ) (ks:κ → ZMod q) (x:ZMod q) :
    torusMap A (fun j => ZMod.toCircle (-(x * ks j))) =
      fun i => ZMod.toCircle (-(x * frequencyMap A ks i)):=by
  funext i
  apply Circle.coe_injective
  change Circle.coeHom (∏ j,ZMod.toCircle (-(x * ks j)) ^ A i j) = _
  rw [map_prod]
  simp only [map_zpow]
  exact monomial_character_values ks (A i) x
omit [Fintype ι] in
theorem row_ne_zero_of_frequency_ne_zero {q:ℕ}
    (A:ι → κ → ℤ) (ks:κ → ZMod q) (i:ι)
    (hi:frequencyMap A ks i ≠ 0):A i ≠ 0:=by
  intro hz
  apply hi
  simp [frequencyMap,hz,weightedFrequency_zero]
end Green24Proof.TorusIntegerMatrix
private def zz2483:"s09b3"="s09b3":=by decide+kernel
end 
section 
namespace Green24Proof.TorusMatrixHaarInvariance
variable [MeasurableSpace Circle] [BorelSpace Circle]
open MeasureTheory
open scoped BigOperators
open Green24Proof.TorusIntegerMatrix Green24Proof.CyclicTorusHaarDiscrepancy
open Green24Proof.CyclicTorusPairDiscrepancy Green24Proof.CyclicTorusPairCounting
variable {ι κ:Type*} [Fintype ι] [Fintype κ]
noncomputable def torusHom (A:ι → κ → ℤ):(κ → Circle) →* (ι → Circle) where
  toFun:=Green24Proof.TorusIntegerMatrix.torusMap A
  map_one':=by funext i; simp [Green24Proof.TorusIntegerMatrix.torusMap]
  map_mul':=by
    intro z w
    funext i
    simp [Green24Proof.TorusIntegerMatrix.torusMap,mul_zpow,Finset.prod_mul_distrib]
theorem torusMap_surjective_of_right_inverse (A:ι → κ → ℤ) (B:κ → ι → ℤ)
    (hAB:matrixComp A B = matrixId):Function.Surjective (Green24Proof.TorusIntegerMatrix.torusMap A):=by
  intro z
  refine ⟨torusMap B z, ?_⟩
  rw [← torusMap_comp,hAB,torusMap_id]
private def zz1934:"s078e"="s078e":=by decide+kernel
theorem torusMap_measurePreserving (A:ι → κ → ℤ)
    (hA:Function.Surjective (Green24Proof.TorusIntegerMatrix.torusMap A)) :
    MeasurePreserving (Green24Proof.TorusIntegerMatrix.torusMap A) (torusHaar κ) (torusHaar ι):=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isHaarMeasure ι
  letI:=torusHaar_isProbabilityMeasure κ
  letI:=torusHaar_isHaarMeasure κ
  exact MonoidHom.measurePreserving (f:=torusHom A) (torusMap_continuous A) hA (by simp)
theorem integral_comp_torusMap (A:ι → κ → ℤ)
    (hA:Function.Surjective (Green24Proof.TorusIntegerMatrix.torusMap A)) (F:(ι → Circle) → ℝ) (hF:Continuous F) :
    (∫ z,F (Green24Proof.TorusIntegerMatrix.torusMap A z) ∂torusHaar κ) = ∫ z,F z ∂torusHaar ι:=by
  have hp:=torusMap_measurePreserving A hA
  have hi:=integral_map (μ:=torusHaar κ) hp.measurable.aemeasurable hF.aestronglyMeasurable
  rw [hp.map_eq] at hi
  exact hi.symm
omit [Fintype ι] in
theorem torusMap_equation (A:ι → κ → ℤ) (y z:κ → Circle) :
    Green24Proof.TorusIntegerMatrix.torusMap A (z ^ 3 * y ^ (-2:ℤ)) =
      (Green24Proof.TorusIntegerMatrix.torusMap A z) ^ 3 * (Green24Proof.TorusIntegerMatrix.torusMap A y) ^ (-2:ℤ):=by
  change torusHom A (z ^ 3 * y ^ (-2:ℤ)) =
    (torusHom A z) ^ 3 * (torusHom A y) ^ (-2:ℤ)
  rw [map_mul,map_pow,map_zpow]
theorem haarWeightedCount_comp_torusMap (A:ι → κ → ℤ)
    (hA:Function.Surjective (Green24Proof.TorusIntegerMatrix.torusMap A)) (F:(ι → Circle) → ℝ) (hF:Continuous F) :
    haarWeightedCount (F ∘ Green24Proof.TorusIntegerMatrix.torusMap A) = haarWeightedCount F:=by
  letI:=torusHaar_isProbabilityMeasure ι
  letI:=torusHaar_isProbabilityMeasure κ
  have hp:MeasurePreserving (Prod.map (Green24Proof.TorusIntegerMatrix.torusMap A) (Green24Proof.TorusIntegerMatrix.torusMap A))
      (pairHaar (ι:=κ) (κ:=κ)) (pairHaar (ι:=ι) (κ:=ι)) :=
    (torusMap_measurePreserving A hA).prod (torusMap_measurePreserving A hA)
  have hcont:Continuous (realCountingIntegrand F):=by
    unfold realCountingIntegrand
    fun_prop
  have hi:=integral_map (μ:=pairHaar (ι:=κ) (κ:=κ))
    hp.measurable.aemeasurable hcont.aestronglyMeasurable
  rw [hp.map_eq] at hi
  change (∫ p,realCountingIntegrand (F ∘ Green24Proof.TorusIntegerMatrix.torusMap A) p ∂pairHaar) =
    ∫ p,realCountingIntegrand F p ∂pairHaar
  rw [hi]
  apply integral_congr_ae
  filter_upwards [] with p
  change F (Green24Proof.TorusIntegerMatrix.torusMap A (p.2 ^ 3 * p.1 ^ (-2:ℤ))) * F (Green24Proof.TorusIntegerMatrix.torusMap A p.1) * F (Green24Proof.TorusIntegerMatrix.torusMap A p.2) =
    F ((Green24Proof.TorusIntegerMatrix.torusMap A p.2) ^ 3 * (Green24Proof.TorusIntegerMatrix.torusMap A p.1) ^ (-2:ℤ)) * F (Green24Proof.TorusIntegerMatrix.torusMap A p.1) * F (Green24Proof.TorusIntegerMatrix.torusMap A p.2)
  rw [torusMap_equation]
end Green24Proof.TorusMatrixHaarInvariance
private def zz2484:"s09b4"="s09b4":=by decide+kernel
end 
section 
namespace Green24Proof.TorusCharacterCover
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset MeasureTheory
open scoped BigOperators
open Green24Proof.TorusIntegerMatrix Green24Proof.TorusMatrixHaarInvariance
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairCounting
variable {ι:Type*} [Fintype ι] [DecidableEq ι]
def coverMatrix (w:ι → ℤ) (p:ι):ι → ι → ℤ :=
  fun i j => if i = p then (if j = p then 1 else -w j)
    else (if i = j then w p else 0)
private def zz1935:"s078f"="s078f":=by decide+kernel
theorem cover_apply_pivot (w:ι → ℤ) (p:ι) (z:ι → Circle) :
    Green24Proof.TorusIntegerMatrix.torusMap (coverMatrix w p) z p = z p * ∏ j ∈ univ.erase p,z j ^ (-w j):=by
  unfold Green24Proof.TorusIntegerMatrix.torusMap
  rw [← prod_erase_mul _ _ (mem_univ p)]
  simp only [coverMatrix,ite_true,zpow_one]
  have h:(∏ j ∈ univ.erase p,z j ^ (if j = p then (1:ℤ) else -w j)) =
      ∏ j ∈ univ.erase p,z j ^ (-w j):=by
    apply prod_congr rfl
    intro j hj
    rw [if_neg (mem_erase.mp hj).1]
  rw [h,mul_comm]
theorem cover_apply_other (w:ι → ℤ) (p:ι) (z:ι → Circle) {i:ι} (hi:i ≠ p) :
    Green24Proof.TorusIntegerMatrix.torusMap (coverMatrix w p) z i = z i ^ w p:=by
  simp [Green24Proof.TorusIntegerMatrix.torusMap,coverMatrix,hi]
theorem circle_zpow_surjective {n:ℤ} (hn:n ≠ 0) :
    Function.Surjective (fun z:Circle => z ^ n):=by
  intro z
  obtain ⟨t,rfl⟩:=Circle.exp_surjective z
  refine ⟨Circle.exp (t / n), ?_⟩
  change Circle.exp (t / n) ^ n = Circle.exp t
  rw [← Circle.exp_intCast_mul]
  congr 1
  have hn':(n:ℝ) ≠ 0:=by exact_mod_cast hn
  field_simp
theorem cover_surjective (w:ι → ℤ) (p:ι) (hp:w p ≠ 0) :
    Function.Surjective (Green24Proof.TorusIntegerMatrix.torusMap (coverMatrix w p)):=by
  intro y
  choose r hr using fun i => circle_zpow_surjective hp (y i)
  let P:=∏ j ∈ univ.erase p,r j ^ (-w j)
  let z:=Function.update r p (y p * P⁻¹)
  refine ⟨z, ?_⟩
  funext i
  by_cases hi:i = p
  · subst i
    rw [cover_apply_pivot]
    have heq:(∏ j ∈ univ.erase p,z j ^ (-w j)) = P:=by
      apply prod_congr rfl
      intro j hj
      simp only [z,Function.update_of_ne (mem_erase.mp hj).1]
    rw [heq]
    simp [z]
  · rw [cover_apply_other w p z hi]
    simpa only [z,Function.update_of_ne hi] using hr i
private def zz1936:"s0790"="s0790":=by decide+kernel
theorem cover_character (w:ι → ℤ) (p:ι) (z:ι → Circle) :
    (∏ i,(Green24Proof.TorusIntegerMatrix.torusMap (coverMatrix w p) z i) ^ w i) = z p ^ w p:=by
  rw [← prod_erase_mul _ _ (mem_univ p),cover_apply_pivot]
  have hother:(∏ i ∈ univ.erase p,(Green24Proof.TorusIntegerMatrix.torusMap (coverMatrix w p) z i) ^ w i) =
      ∏ i ∈ univ.erase p,(z i ^ w p) ^ w i:=by
    apply prod_congr rfl
    intro i hi
    rw [cover_apply_other w p z (mem_erase.mp hi).1]
  rw [hother,mul_zpow,mul_left_comm, ← Finset.prod_zpow,
    ← Finset.prod_mul_distrib]
  have hcancel:(∏ i ∈ univ.erase p,(z i ^ w p) ^ w i * (z i ^ (-w i)) ^ w p) = 1:=by
    apply prod_eq_one
    intro i _
    rw [← zpow_mul, ← zpow_mul, ← zpow_add]
    have:w p * w i + -w i * w p = 0:=by ring
    rw [this,zpow_zero]
  rw [hcancel,mul_one]
theorem exists_single_coordinate_model (G:(ι → Circle) → ℝ) (w:ι → ℤ)
    (hG:Continuous G) (hGr:∀ z,G z ∈ Set.Icc 0 1) (hw:w ≠ 0)
    (W:Set Circle) (hGs:∀ z,(∏ j,z j ^ w j) ∉ W → G z = 0) :
    ∃ (p:ι) (n:ℤ) (H:(ι → Circle) → ℝ),
      n ≠ 0 ∧ Continuous H ∧ (∀ z,H z ∈ Set.Icc 0 1) ∧
      (∀ z,z p ^ n ∉ W → H z = 0) ∧
      (∫ z,H z ∂torusHaar ι) = (∫ z,G z ∂torusHaar ι) ∧
      haarWeightedCount H = haarWeightedCount G:=by
  obtain ⟨p,hp⟩:=Function.ne_iff.mp hw
  change w p ≠ 0 at hp
  let A:=coverMatrix w p
  refine ⟨p,w p,G ∘ Green24Proof.TorusIntegerMatrix.torusMap A,hp,hG.comp (torusMap_continuous A),
    fun z => hGr _, ?_, ?_, ?_⟩
  · intro z hz
    apply hGs (Green24Proof.TorusIntegerMatrix.torusMap A z)
    simpa only [A,cover_character] using hz
  · exact integral_comp_torusMap A (cover_surjective w p hp) G hG
  · exact haarWeightedCount_comp_torusMap A (cover_surjective w p hp) G hG
end Green24Proof.TorusCharacterCover
private def zz2485:"s09b5"="s09b5":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFourierCutoff
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
open Green24Proof.CircleLaurentApproximation
variable {q n:ℕ} [NeZero q]
theorem dft_norm_le_sum_norm (u:ZMod q → ℂ) (r:ZMod q) :
    ‖ZMod.dft u r‖ ≤ ∑ x, ‖u x‖:=by
  calc
    _ ≤ ∑ x, ‖ZMod.stdAddChar (-(x * r)) * u x‖:=norm_sum_le _ _
    _ = _:=by simp only [norm_mul,ZMod.stdAddChar_apply,Circle.norm_coe,one_mul]
theorem dft_norm_le_of_pointwise (u:ZMod q → ℂ) {ε:ℝ}
    (hu:∀ x, ‖u x‖ ≤ ε) (r:ZMod q):‖ZMod.dft u r‖ ≤ ε * q:=by
  calc
    _ ≤ ∑ x, ‖u x‖:=dft_norm_le_sum_norm u r
    _ ≤ ∑ _x:ZMod q,ε:=Finset.sum_le_sum (fun x _ => hu x)
    _ = _:=by simp [ZMod.card,mul_comm]
private def zz1937:"s0791"="s0791":=by decide+kernel
theorem dft_character_mul (t:ZMod q) (u:ZMod q → ℂ) (r:ZMod q) :
    ZMod.dft (fun x => ZMod.stdAddChar (-(x * t)) * u x) r = ZMod.dft u (r + t):=by
  simp only [ZMod.dft_apply,smul_eq_mul]
  apply Finset.sum_congr rfl
  intro x _
  rw [← mul_assoc, ← AddChar.map_add_eq_mul]
  congr 2
  ring
theorem dft_polynomial_mul (ks:Fin n → ZMod q) (S:Finset (Fin n → ℤ))
    (c:(Fin n → ℤ) → ℂ) (u:ZMod q → ℂ) (r:ZMod q) :
    ZMod.dft (fun x => polynomial S c (characterOrbit ks x) * u x) r =
      ∑ m ∈ S,c m * ZMod.dft u (r + weightedFrequency ks m):=by
  have hfun:(fun x => polynomial S c (characterOrbit ks x) * u x) =
      ∑ m ∈ S,(fun x => c m * (ZMod.stdAddChar (-(x * weightedFrequency ks m)) * u x)):=by
    funext x
    simp only [polynomial,Finset.sum_apply,Finset.sum_mul,monomial_characterOrbit]
    apply Finset.sum_congr rfl
    intro m _
    ring
  rw [hfun,map_sum]
  simp only [Finset.sum_apply,ZMod.dft_const_mul,dft_character_mul]
theorem dft_polynomial_mul_norm_le (ks:Fin n → ZMod q) (S:Finset (Fin n → ℤ))
    (c:(Fin n → ℤ) → ℂ) (u:ZMod q → ℂ) {η:ℝ}
    (hu:∀ r, ‖ZMod.dft u r‖ ≤ η * q) (r:ZMod q) :
    ‖ZMod.dft (fun x => polynomial S c (characterOrbit ks x) * u x) r‖ ≤
      ((∑ m ∈ S, ‖c m‖) * η) * q:=by
  rw [dft_polynomial_mul]
  calc
    _ ≤ ∑ m ∈ S, ‖c m * ZMod.dft u (r + weightedFrequency ks m)‖:=norm_sum_le _ _
    _ ≤ ∑ m ∈ S, ‖c m‖ * (η * q):=by
      apply Finset.sum_le_sum
      intro m _
      rw [norm_mul]
      exact mul_le_mul_of_nonneg_left (hu _) (norm_nonneg _)
    _ = _:=by rw [← Finset.sum_mul]; ring
theorem dft_cutoff_mul_norm_le (ks:Fin n → ZMod q) (F:(Fin n → Circle) → ℂ)
    (S:Finset (Fin n → ℤ)) (c:(Fin n → ℤ) → ℂ) (u:ZMod q → ℂ)
    {η δ:ℝ} (hδ:0 ≤ δ) (hu:∀ x, ‖u x‖ ≤ 1)
    (hdf:∀ r, ‖ZMod.dft u r‖ ≤ η * q)
    (herr:∀ z, ‖F z - polynomial S c z‖ ≤ δ) (r:ZMod q) :
    ‖ZMod.dft (fun x => F (characterOrbit ks x) * u x) r‖ ≤
      ((∑ m ∈ S, ‖c m‖) * η + δ) * q:=by
  let a:=fun x => F (characterOrbit ks x) * u x
  let b:=fun x => polynomial S c (characterOrbit ks x) * u x
  have he:‖ZMod.dft (a - b) r‖ ≤ δ * q:=dft_norm_le_of_pointwise _ (fun x => by
    change ‖F (characterOrbit ks x) * u x - polynomial S c (characterOrbit ks x) * u x‖ ≤ δ
    rw [← sub_mul,norm_mul]
    exact (mul_le_mul (herr _) (hu x) (norm_nonneg _) hδ).trans (by rw [mul_one])) r
  rw [map_sub,Pi.sub_apply] at he
  have hb:=dft_polynomial_mul_norm_le ks S c u hdf r
  change ‖ZMod.dft a r‖ ≤ _
  have ht:=norm_add_le (ZMod.dft a r - ZMod.dft b r) (ZMod.dft b r)
  rw [sub_add_cancel] at ht
  change ‖ZMod.dft b r‖ ≤ _ at hb
  nlinarith
private def zz1938:"s0792"="s0792":=by decide+kernel
theorem exists_uniform_cutoff_multiplier (F:(Fin n → Circle) → ℂ) (hF:Continuous F)
    {δ:ℝ} (hδ:0 < δ) :
    ∃ C:ℝ,0 ≤ C ∧ ∀ (q:ℕ) [NeZero q] (ks:Fin n → ZMod q)
      (u:ZMod q → ℂ) (η:ℝ),
      (∀ x, ‖u x‖ ≤ 1) → (∀ r, ‖ZMod.dft u r‖ ≤ η * q) →
      ∀ r, ‖ZMod.dft (fun x => F (characterOrbit ks x) * u x) r‖ ≤ (C * η + δ) * q:=by
  obtain ⟨S,c,herr⟩:=exists_finite_laurent_approximation ⟨F,hF⟩ hδ
  refine ⟨∑ m ∈ S, ‖c m‖,Finset.sum_nonneg (fun m _ => norm_nonneg _), ?_⟩
  intro q _ ks u η hu hdf r
  exact dft_cutoff_mul_norm_le ks F S c u hδ.le hu hdf (fun z => (herr z).le) r
end Green24Proof.CyclicFourierCutoff
private def zz2486:"s09b6"="s09b6":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicMaskedRegularity
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicFourierCutoff Green24Proof.CyclicGrowthDecomposition
open Green24Proof.CyclicTorusSmoothing Green24Proof.CyclicL2Replacement
open Green24Proof.UniformTorusCountingApproximation
theorem exists_uniform_orbit_fourier_approximation {η:ℝ} (hη:0 < η) :
    ∃ C:ℕ, ∀ (q:ℕ) [NeZero q] (f:ZMod q → ℝ),
      (∀ x,f x ∈ Set.Icc 0 1) →
      ∃ n ≤ C, ∃ (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ),
        LipschitzWith (C:ℝ≥0) H ∧ (∀ z,H z ∈ Set.Icc 0 1) ∧
        ∀ r, ‖ZMod.dft (fun x => ((f x - H (characterOrbit ks x):ℝ):ℂ)) r‖ ≤ η * q:=by
  refine ⟨complexityBound (fun _ => η / 2) (η / 2), ?_⟩
  intro q _ f hf
  obtain ⟨M,hM,n,hn,ks,H,small,uniform,hL,hH,hd,_,_,_,hs,_,hu⟩ :=
    exists_growth_decomposition f hf (fun _ => η / 2) (fun _ => half_pos hη) (half_pos hη)
  refine ⟨n,hn.trans hM,ks,H,hL.weaken (by exact_mod_cast hM),hH, ?_⟩
  intro r
  have he:(fun x => ((f x - H (characterOrbit ks x):ℝ):ℂ)) =
      (fun x => (small x:ℂ)) + (fun x => (uniform x:ℂ)):=by
    funext x
    simp only [Pi.add_apply,hd,Complex.ofReal_sub,Complex.ofReal_add]
    ring
  rw [he,map_add,Pi.add_apply]
  have hsmall:=dft_norm_le_of_sum_sq_le small (half_pos hη).le hs r
  have htri:=norm_add_le (ZMod.dft (fun x => (small x:ℂ)) r)
    (ZMod.dft (fun x => (uniform x:ℂ)) r)
  have hunif:=hu r
  linarith
noncomputable def maskedModel {n:ℕ} (χ:Circle → ℝ) (H:(Fin n → Circle) → ℝ)
    (z:Fin (n + 1) → Circle):ℝ:=χ (z 0) * H (fun i => z i.succ)
theorem maskedModel_lipschitz {n:ℕ} (χ:Circle → ℝ) (H:(Fin n → Circle) → ℝ)
    {L K:ℝ≥0} (hχ:LipschitzWith L χ) (hH:LipschitzWith K H)
    (hχr:∀ z,χ z ∈ Set.Icc 0 1) (hHr:∀ z,H z ∈ Set.Icc 0 1) :
    LipschitzWith (L + K) (maskedModel χ H):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  have hd:dist (fun i:Fin n => z i.succ) (fun i => w i.succ) ≤ dist z w :=
    (dist_pi_le_iff dist_nonneg).mpr (fun i => dist_le_pi_dist z w i.succ)
  have h1:=hχ.dist_le_mul_of_le (dist_le_pi_dist z w 0)
  have h2:=hH.dist_le_mul_of_le hd
  have h:=real_mul_dist_le (hHr (fun i => z i.succ)) (hχr (w 0))
    (a:=χ (z 0)) (d:=H (fun i => w i.succ))
  change dist (χ (z 0) * H (fun i => z i.succ)) (χ (w 0) * H (fun i => w i.succ)) ≤ _
  simp only [NNReal.coe_add]
  nlinarith
theorem maskedModel_range {n:ℕ} (χ:Circle → ℝ) (H:(Fin n → Circle) → ℝ)
    (hχr:∀ z,χ z ∈ Set.Icc 0 1) (hHr:∀ z,H z ∈ Set.Icc 0 1)
    (z:Fin (n + 1) → Circle):maskedModel χ H z ∈ Set.Icc 0 1:=by
  exact ⟨mul_nonneg (hχr _).1 (hHr _).1,
    (mul_le_mul (hχr _).2 (hHr _).2 (hHr _).1 (by norm_num)).trans (by norm_num)⟩
private def zz1939:"s0793"="s0793":=by decide+kernel
theorem exists_masked_approximation (χ:Circle → ℝ) {L:ℝ≥0}
    (hχ:LipschitzWith L χ) (hχr:∀ z,χ z ∈ Set.Icc 0 1)
    {δ:ℝ} (hδ:0 < δ) :
    ∃ C:ℕ, ∀ (q:ℕ) [NeZero q] (f:ZMod q → ℝ),
      (∀ x,f x ∈ Set.Icc 0 1) →
      (∀ x,χ (ZMod.toCircle (-x)) * f x = f x) →
      ∃ n,n + 1 ≤ C ∧ ∃ (ks:Fin (n + 1) → ZMod q) (G:(Fin (n + 1) → Circle) → ℝ),
        ks 0 = 1 ∧ LipschitzWith (C:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
        (∀ z,χ (z 0) = 0 → G z = 0) ∧
        ∀ r, ‖ZMod.dft (fun x => ((f x - G (characterOrbit ks x):ℝ):ℂ)) r‖ ≤ δ * q:=by
  let F:(Fin 1 → Circle) → ℂ:=fun z => (χ (z 0):ℂ)
  have hF:Continuous F:=Complex.continuous_ofReal.comp (hχ.continuous.comp (continuous_apply 0))
  obtain ⟨D,hD,hmult⟩:=exists_uniform_cutoff_multiplier F hF (half_pos hδ)
  let η:=δ / (2 * (D + 1))
  have hη:0 < η:=by dsimp [η]; positivity
  obtain ⟨B,hB⟩:=exists_uniform_orbit_fourier_approximation hη
  let C:=B + ⌈L⌉₊ + 1
  refine ⟨C, ?_⟩
  intro q _ f hf hmask
  obtain ⟨n,hn,ks,H,hH,hHr,hdf⟩:=hB q f hf
  let ls:Fin (n + 1) → ZMod q:=Fin.cases 1 ks
  let G:=maskedModel χ H
  have hLip:LipschitzWith (C:ℝ≥0) G:=(maskedModel_lipschitz χ H hχ hH hχr hHr).weaken (by
    dsimp [C]
    have hceil:L ≤ (⌈L⌉₊:ℝ≥0):=Nat.le_ceil L
    push_cast
    linarith)
  refine ⟨n,by dsimp [C]; omega,ls,G,rfl,hLip,maskedModel_range χ H hχr hHr, ?_, ?_⟩
  · intro z hz
    change χ (z 0) * H (fun i => z i.succ) = 0
    rw [hz,zero_mul]
  · intro r
    let u:=fun x => ((f x - H (characterOrbit ks x):ℝ):ℂ)
    have hu:∀ x, ‖u x‖ ≤ 1:=by
      intro x
      change ‖((f x - H (characterOrbit ks x):ℝ):ℂ)‖ ≤ 1
      rw [Complex.norm_real,Real.norm_eq_abs]
      exact abs_le.mpr ⟨by linarith [(hf x).1,(hHr (characterOrbit ks x)).2],
        by linarith [(hf x).2,(hHr (characterOrbit ks x)).1]⟩
    have hm:=hmult q (fun _:Fin 1 => 1) u η hu hdf r
    have hdif:(fun x => ((f x - G (characterOrbit ls x):ℝ):ℂ)) =
        fun x => F (characterOrbit (fun _:Fin 1 => (1:ZMod q)) x) * u x:=by
      funext x
      have he:f x - G (characterOrbit ls x) =
          χ (ZMod.toCircle (-x)) * (f x - H (characterOrbit ks x)):=by
        simp only [G,maskedModel,characterOrbit,ls,Fin.cases_zero,Fin.cases_succ,mul_one]
        change f x - χ (ZMod.toCircle (-x)) * H (characterOrbit ks x) =
          χ (ZMod.toCircle (-x)) * (f x - H (characterOrbit ks x))
        linear_combination -(hmask x)
      simpa only [F,characterOrbit,mul_one,u,Complex.ofReal_mul] using congrArg Complex.ofReal he
    rw [hdif]
    apply hm.trans
    apply mul_le_mul_of_nonneg_right _ (Nat.cast_nonneg q)
    have hid:η * (D + 1) = δ / 2:=by dsimp [η]; field_simp
    nlinarith [hη.le]
end Green24Proof.CyclicMaskedRegularity
private def zz2487:"s09b7"="s09b7":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFrequencyPivot
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicFrequencyElimination
variable {ι:Type*} [Fintype ι]
theorem permute_lipschitz (e:ι ≃ ι) :
    LipschitzWith 1 (fun z:ι → Circle => z ∘ e):=by
  apply LipschitzWith.of_dist_le_mul
  intro z w
  simp only [NNReal.coe_one,one_mul]
  exact (dist_pi_le_iff dist_nonneg).mpr (fun i => dist_le_pi_dist z w (e i))
theorem weightedFrequency_permute {q:ℕ} (e:ι ≃ ι)
    (ks:ι → ZMod q) (m:ι → ℤ) :
    weightedFrequency (ks ∘ e) (m ∘ e) = weightedFrequency ks m:=by
  exact e.sum_comp (fun i => (m i:ZMod q) * ks i)
theorem natAbs_sum_permute (e:ι ≃ ι) (m:ι → ℤ) :
    (∑ i,(m (e i)).natAbs) = ∑ i,(m i).natAbs :=
  e.sum_comp (fun i => (m i).natAbs)
private def zz1940:"s0794"="s0794":=by decide+kernel
theorem intCast_ne_zero_of_natAbs_lt {q:ℕ} {m:ℤ}
    (hm:m ≠ 0) (hsize:m.natAbs < q):(m:ZMod q) ≠ 0:=by
  intro hz
  have hd:=Int.natCast_dvd.mp ((ZMod.intCast_zmod_eq_zero_iff_dvd m q).mp hz)
  have hp:0 < m.natAbs:=Int.natAbs_pos.mpr hm
  exact (not_le_of_gt hsize) (Nat.le_of_dvd hp hd)
variable {q n:ℕ} [NeZero q]
theorem characterOrbit_permute (e:Fin n ≃ Fin n) (ks:Fin n → ZMod q) (x:ZMod q) :
    characterOrbit (ks ∘ e) x = characterOrbit ks x ∘ e:=rfl
theorem exists_dimension_reduction [Fact q.Prime] (ks:Fin (n + 1) → ZMod q)
    (m:Fin (n + 1) → ℤ) (hm:m ≠ 0) (hrel:weightedFrequency ks m = 0)
    (hsize:(∑ i,(m i).natAbs) < q) :
    ∃ (ls:Fin n → ZMod q) (Φ:(Fin n → Circle) → (Fin (n + 1) → Circle)),
      LipschitzWith (∑ i,((m i).natAbs:ℝ≥0)) Φ ∧
      ∀ x,Φ (characterOrbit ls x) = characterOrbit ks x:=by
  classical
  obtain ⟨j,hj⟩:∃ j,m j ≠ 0:=by
    by_contra h
    push Not at h
    exact hm (funext h)
  have hjbound:(m j).natAbs < q :=
    lt_of_le_of_lt (Finset.single_le_sum (fun i _ => Nat.zero_le (m i).natAbs) (Finset.mem_univ j)) hsize
  have hjunit:IsUnit (m j:ZMod q) :=
    isUnit_iff_ne_zero.mpr (intCast_ne_zero_of_natAbs_lt hj hjbound)
  obtain ⟨u,hu⟩:=hjunit
  let e:Fin (n + 1) ≃ Fin (n + 1):=Equiv.swap 0 j
  have he0:e 0 = j:=Equiv.swap_apply_left _ _
  have hu':(u:ZMod q) = (m ∘ e) 0:=by simpa only [Function.comp_apply,he0] using hu
  have hrel':weightedFrequency (ks ∘ e) (m ∘ e) = 0 :=
    (weightedFrequency_permute e ks m).trans hrel
  let Φ:=fun z:Fin n → Circle => monomialLift (m ∘ e) z ∘ e.symm
  refine ⟨reducedFrequencies u (ks ∘ e),Φ, ?_, ?_⟩
  · have hb:=(permute_lipschitz e.symm).comp (monomialLift_lipschitz (m ∘ e))
    have hsum:((m (e 0)).natAbs + ∑ i:Fin n,(m (e i.succ)).natAbs:ℝ≥0) =
        ∑ i:Fin (n + 1),((m i).natAbs:ℝ≥0):=by
      have hnat:(m (e 0)).natAbs + (∑ i:Fin n,(m (e i.succ)).natAbs) =
          ∑ i:Fin (n + 1),(m i).natAbs:=by
        exact (Fin.sum_univ_succ (fun i => (m (e i)).natAbs)).symm.trans
          (natAbs_sum_permute e m)
      exact_mod_cast hnat
    simpa only [one_mul,Function.comp_def,hsum,Φ] using hb
  · intro x
    change monomialLift (m ∘ e) (characterOrbit (reducedFrequencies u (ks ∘ e)) x) ∘ e.symm = _
    rw [monomialLift_characterOrbit u (ks ∘ e) (m ∘ e) hu' hrel',characterOrbit_permute]
    funext i
    simp only [Function.comp_apply,Equiv.apply_symm_apply]
end Green24Proof.CyclicFrequencyPivot
private def zz2488:"s09b8"="s09b8":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicFrequencyMatrix
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.TorusIntegerMatrix Green24Proof.CyclicFrequencyElimination
open Green24Proof.CyclicFrequencyPivot Green24Proof.CyclicTorusLaurent
variable {n:ℕ}
def stepMatrix (m:Fin (n + 1) → ℤ):Fin (n + 1) → Fin n → ℤ :=
  Fin.cases (fun j => -m j.succ) (fun i j => if j = i then m 0 else 0)
theorem torusMap_stepMatrix (m:Fin (n + 1) → ℤ):torusMap (stepMatrix m) = monomialLift m:=by
  classical
  funext z i
  refine Fin.cases (by rfl) (fun k => ?_) i
  change (∏ j:Fin n,z j ^ (if j = k then m 0 else 0)) = z k ^ m 0
  simp only [apply_ite,zpow_zero]
  simp
private def zz1941:"s0795"="s0795":=by decide+kernel
theorem rowSize_stepMatrix_le (m:Fin (n + 1) → ℤ) (i:Fin (n + 1)) :
    rowSize (stepMatrix m) i ≤ ∑ j,(m j).natAbs:=by
  classical
  refine Fin.cases ?_ (fun k => ?_) i
  · simp only [rowSize,stepMatrix,Fin.cases_zero,Int.natAbs_neg,Fin.sum_univ_succ]
    omega
  · simp only [rowSize,stepMatrix,Fin.cases_succ,apply_ite,Int.natAbs_zero]
    simp only [Finset.sum_ite_eq',Finset.mem_univ,if_true]
    exact Finset.single_le_sum (fun j _ => Nat.zero_le (m j).natAbs)
      (Finset.mem_univ (0:Fin (n + 1)))
theorem frequencyMap_stepMatrix {q:ℕ} (u:(ZMod q)ˣ) (ks:Fin (n + 1) → ZMod q)
    (m:Fin (n + 1) → ℤ) (hu:(u:ZMod q) = m 0)
    (hm:weightedFrequency ks m = 0) :
    frequencyMap (stepMatrix m) (reducedFrequencies u ks) = ks:=by
  classical
  funext i
  refine Fin.cases (reduced_relation u ks m hu hm) (fun k => ?_) i
  change (∑ j:Fin n,((if j = k then m 0 else 0:ℤ):ZMod q) * reducedFrequencies u ks j) = _
  simp only [ite_mul,Int.cast_ite,Int.cast_zero,zero_mul]
  simp only [Finset.sum_ite_eq',Finset.mem_univ,if_true]
  rw [← hu]
  simp [reducedFrequencies, ← mul_assoc]
theorem exists_matrix_reduction {q:ℕ} [NeZero q] [Fact q.Prime]
    (ks:Fin (n + 1) → ZMod q) (m:Fin (n + 1) → ℤ)
    (hm:m ≠ 0) (hrel:weightedFrequency ks m = 0)
    (hsize:(∑ i,(m i).natAbs) < q) :
    ∃ (ls:Fin n → ZMod q) (A:Fin (n + 1) → Fin n → ℤ),
      (∀ i,rowSize A i ≤ ∑ j,(m j).natAbs) ∧ frequencyMap A ls = ks:=by
  classical
  obtain ⟨j,hj⟩:∃ j,m j ≠ 0:=by
    by_contra h
    push Not at h
    exact hm (funext h)
  have hjbound:(m j).natAbs < q :=
    lt_of_le_of_lt (Finset.single_le_sum (fun i _ => Nat.zero_le (m i).natAbs) (Finset.mem_univ j)) hsize
  obtain ⟨u,hu⟩:=isUnit_iff_ne_zero.mpr (intCast_ne_zero_of_natAbs_lt hj hjbound)
  let e:Fin (n + 1) ≃ Fin (n + 1):=Equiv.swap 0 j
  have he0:e 0 = j:=Equiv.swap_apply_left _ _
  have hu':(u:ZMod q) = (m ∘ e) 0:=by simpa only [Function.comp_apply,he0] using hu
  have hrel':weightedFrequency (ks ∘ e) (m ∘ e) = 0 :=
    (weightedFrequency_permute e ks m).trans hrel
  let A:=fun i k => stepMatrix (m ∘ e) (e.symm i) k
  refine ⟨reducedFrequencies u (ks ∘ e),A, ?_, ?_⟩
  · intro i
    have h:=rowSize_stepMatrix_le (m ∘ e) (e.symm i)
    rw [show (∑ j,((m ∘ e) j).natAbs) = ∑ j,(m j).natAbs from natAbs_sum_permute e m] at h
    exact h
  · funext i
    have h:=congrFun (frequencyMap_stepMatrix u (ks ∘ e) (m ∘ e) hu' hrel') (e.symm i)
    simpa only [frequencyMap,A,Function.comp_apply,Equiv.apply_symm_apply] using h
end Green24Proof.CyclicFrequencyMatrix
private def zz2489:"s09b9"="s09b9":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicNonresonantFactorization
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicFrequencyPivot
variable (S:∀ n:ℕ,ℕ → Finset (Fin n → ℤ))
def relationRadius (n M:ℕ):ℕ:=max 1 ((S n M).sup (fun m => ∑ i,(m i).natAbs))
def primeThreshold:ℕ → ℕ → ℕ
  | 0,_ => 0
  | n + 1,M => max (relationRadius S (n + 1) M)
      (primeThreshold n (M * relationRadius S (n + 1) M))
def finalBudget:ℕ → ℕ → ℕ
  | 0,M => M
  | n + 1,M => max M (finalBudget n (M * relationRadius S (n + 1) M))
theorem le_finalBudget (n M:ℕ):M ≤ finalBudget S n M:=by
  cases n with
  | zero => exact le_rfl
  | succ n => exact le_max_left _ _
private def zz1942:"s0796"="s0796":=by decide+kernel
theorem relationSize_le {n M:ℕ} {m:Fin n → ℤ} (hm:m ∈ S n M) :
    (∑ i,(m i).natAbs) ≤ relationRadius S n M :=
  (Finset.le_sup (f:=fun v:Fin n → ℤ => ∑ i,(v i).natAbs) hm).trans (le_max_right _ _)
theorem exists_factorization (n M:ℕ) {q:ℕ} [NeZero q] [Fact q.Prime]
    (hq:primeThreshold S n M < q) (ks:Fin n → ZMod q)
    (H:(Fin n → Circle) → ℝ) (hH:LipschitzWith (M:ℝ≥0) H)
    (hr:∀ z,H z ∈ Set.Icc 0 1) :
    ∃ d ≤ n, ∃ B ≤ finalBudget S n M,
      ∃ (ls:Fin d → ZMod q) (G:(Fin d → Circle) → ℝ),
        LipschitzWith (B:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
        Nonresonant ls (S d B) ∧
        ∀ x,G (characterOrbit ls x) = H (characterOrbit ks x):=by
  classical
  induction n generalizing M with
  | zero =>
    refine ⟨0,le_rfl,M,le_rfl,ks,H,hH,hr, ?_,fun _ => rfl⟩
    intro m _ hm
    exact False.elim (hm (Subsingleton.elim _ _))
  | succ n ih =>
    by_cases hn:Nonresonant ks (S (n + 1) M)
    · exact ⟨n + 1,le_rfl,M,le_finalBudget S _ _,ks,H,hH,hr,hn,fun _ => rfl⟩
    · unfold Nonresonant at hn
      push Not at hn
      obtain ⟨m,hmS,hm,hrel⟩:=hn
      have hrad:relationRadius S (n + 1) M < q :=
        lt_of_le_of_lt (le_max_left _ _) hq
      have hsize:=(relationSize_le S hmS).trans_lt hrad
      obtain ⟨ls,Φ,hΦ,hsample⟩:=exists_dimension_reduction ks m hm hrel hsize
      have hΦ':LipschitzWith (relationRadius S (n + 1) M:ℝ≥0) Φ :=
        hΦ.weaken (by exact_mod_cast relationSize_le S hmS)
      have hG:LipschitzWith ((M * relationRadius S (n + 1) M:ℕ):ℝ≥0) (H ∘ Φ):=by
        simpa only [Nat.cast_mul] using hH.comp hΦ'
      have hnext:primeThreshold S n (M * relationRadius S (n + 1) M) < q :=
        lt_of_le_of_lt (le_max_right _ _) hq
      obtain ⟨d,hd,B,hB,ls',G,hGl,hGr,hGn,hGe⟩ :=
        ih (M * relationRadius S (n + 1) M) hnext ls (H ∘ Φ) hG (fun z => hr _)
      refine ⟨d,hd.trans (Nat.le_succ n),B,hB.trans (le_max_right _ _),ls',G,
        hGl,hGr,hGn, ?_⟩
      intro x
      rw [hGe,Function.comp_apply,hsample]
end Green24Proof.CyclicNonresonantFactorization
private def zz2490:"s09ba"="s09ba":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicMatrixFactorization
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.TorusIntegerMatrix Green24Proof.CyclicFrequencyMatrix
open Green24Proof.CyclicNonresonantFactorization
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
variable (S:∀ n:ℕ,ℕ → Finset (Fin n → ℤ))
def matrixBudget:ℕ → ℕ → ℕ
  | 0,_ => 1
  | n + 1,M => max 1 (relationRadius S (n + 1) M *
      matrixBudget n (M * relationRadius S (n + 1) M))
theorem one_le_matrixBudget (n M:ℕ):1 ≤ matrixBudget S n M:=by
  cases n with
  | zero => exact le_rfl
  | succ n => exact le_max_left _ _
theorem exists_matrix_factorization (n M:ℕ) {q:ℕ} [NeZero q] [Fact q.Prime]
    (hq:primeThreshold S n M < q) (ks:Fin n → ZMod q)
    (H:(Fin n → Circle) → ℝ) (hH:LipschitzWith (M:ℝ≥0) H) :
    ∃ d ≤ n, ∃ B ≤ finalBudget S n M,
      ∃ (ls:Fin d → ZMod q) (A:Fin n → Fin d → ℤ),
        (∀ i,rowSize A i ≤ matrixBudget S n M) ∧ frequencyMap A ls = ks ∧
        LipschitzWith (B:ℝ≥0) (H ∘ torusMap A) ∧ Nonresonant ls (S d B):=by
  classical
  induction n generalizing M with
  | zero =>
    refine ⟨0,le_rfl,M,le_rfl,ks,matrixId, ?_,frequencyMap_id ks, ?_, ?_⟩
    · intro i
      exact (rowSize_id i).le
    · simpa only [Function.comp_def,torusMap_id] using hH
    · intro m _ hm
      exact False.elim (hm (Subsingleton.elim _ _))
  | succ n ih =>
    by_cases hn:Nonresonant ks (S (n + 1) M)
    · refine ⟨n + 1,le_rfl,M,le_finalBudget S _ _,ks,matrixId, ?_,frequencyMap_id ks, ?_,hn⟩
      · intro i
        rw [rowSize_id]
        exact one_le_matrixBudget S _ _
      · simpa only [Function.comp_def,torusMap_id] using hH
    · unfold Nonresonant at hn
      push Not at hn
      obtain ⟨m,hmS,hm,hrel⟩:=hn
      have hrad:relationRadius S (n + 1) M < q :=
        lt_of_le_of_lt (le_max_left _ _) hq
      obtain ⟨ls,A,hA,hfreq⟩:=exists_matrix_reduction ks m hm hrel
        ((relationSize_le S hmS).trans_lt hrad)
      have hAr:∀ i,rowSize A i ≤ relationRadius S (n + 1) M :=
        fun i => (hA i).trans (relationSize_le S hmS)
      have hG:LipschitzWith ((M * relationRadius S (n + 1) M:ℕ):ℝ≥0) (H ∘ torusMap A):=by
        simpa only [Nat.cast_mul] using hH.comp (torusMap_lipschitz A hAr)
      have hnext:primeThreshold S n (M * relationRadius S (n + 1) M) < q :=
        lt_of_le_of_lt (le_max_right _ _) hq
      obtain ⟨d,hd,B,hB,ls',D,hD,hDfreq,hGl,hGn⟩ :=
        ih (M * relationRadius S (n + 1) M) hnext ls (H ∘ torusMap A) hG
      refine ⟨d,hd.trans (Nat.le_succ n),B,hB.trans (le_max_right _ _),ls',matrixComp A D,
        ?_, ?_, ?_,hGn⟩
      · intro i
        exact ((rowSize_comp_le A D i hD).trans
          (Nat.mul_le_mul_right _ (hAr i))).trans (le_max_right _ _)
      · rw [frequencyMap_comp,hDfreq,hfreq]
      · simpa only [Function.comp_def,torusMap_comp] using hGl
private def zz1943:"s0797"="s0797":=by decide+kernel
theorem orbit_identity {q n d:ℕ} [NeZero q]
    (A:Fin n → Fin d → ℤ) (ls:Fin d → ZMod q) (ks:Fin n → ZMod q)
    (hfreq:frequencyMap A ls = ks) (x:ZMod q) :
    torusMap A (characterOrbit ls x) = characterOrbit ks x:=by
  have h:=torusMap_character_values A ls x
  rw [hfreq] at h
  exact h
theorem support_pullback {n d:ℕ} (A:Fin n → Fin d → ℤ)
    (H:(Fin n → Circle) → ℝ) (i:Fin n) (W:Set Circle)
    (hH:∀ z,z i ∉ W → H z = 0) :
    ∀ z,(∏ j,z j ^ A i j) ∉ W → (H ∘ torusMap A) z = 0 :=
  fun z hz => hH (torusMap A z) hz
end Green24Proof.CyclicMatrixFactorization
private def zz2491:"s09bb"="s09bb":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicSpatialHaarModel
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.TorusIntegerMatrix Green24Proof.CyclicMatrixFactorization
open Green24Proof.CyclicNonresonantFactorization
open Green24Proof.UniformTorusCountingApproximation
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicGrowthCounting Green24Proof.CyclicTorusPairCounting
open Green24Proof.CyclicTorusHaarDiscrepancy
theorem exists_uniform_spatial_haar_model (n M:ℕ) {ε:ℝ} (hε:0 < ε) :
    ∃ C Q R:ℕ, ∀ (q:ℕ) [NeZero q] [Fact q.Prime],Q < q →
      ∀ (ks:Fin n → ZMod q) (H:(Fin n → Circle) → ℝ)
        (i:Fin n) (W:Set Circle),
        LipschitzWith (M:ℝ≥0) H → (∀ z,H z ∈ Set.Icc 0 1) →
        ks i = 1 → (∀ z,z i ∉ W → H z = 0) →
        ∃ d ≤ n, ∃ B ≤ C, ∃ (ls:Fin d → ZMod q) (G:(Fin d → Circle) → ℝ)
          (w:Fin d → ℤ),
          w ≠ 0 ∧ (∑ j,(w j).natAbs) ≤ R ∧ weightedFrequency ls w = 1 ∧
          LipschitzWith (B:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
          (∀ z,(∏ j,z j ^ w j) ∉ W → G z = 0) ∧
          (∀ x,G (characterOrbit ls x) = H (characterOrbit ks x)) ∧
          |(∑ x:ZMod q,H (characterOrbit ks x)) / q - ∫ z,G z ∂torusHaar (Fin d)| ≤ 2 * ε ∧
          |weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ) ^ 2 -
              haarWeightedCount G| ≤ 2 * ε:=by
  classical
  choose S hS using fun d B:ℕ =>
    exists_uniform_mass_count_discrepancy_support d (B:ℝ≥0) hε
  refine ⟨finalBudget S n M,primeThreshold S n M,matrixBudget S n M, ?_⟩
  intro q _ _ hq ks H i W hH hr hi hsupp
  obtain ⟨d,hd,B,hB,ls,A,hA,hfreq,hGl,hGn⟩ :=
    exists_matrix_factorization S n M hq ks H hH
  let G:=H ∘ torusMap A
  have hGr:∀ z,G z ∈ Set.Icc 0 1:=fun z => hr _
  have he:∀ x,G (characterOrbit ls x) = H (characterOrbit ks x):=by
    intro x
    rw [show G (characterOrbit ls x) = H (torusMap A (characterOrbit ls x)) from rfl,
      orbit_identity A ls ks hfreq]
  have hwi:weightedFrequency ls (A i) = 1:=by
    change frequencyMap A ls i = 1
    rw [hfreq,hi]
  have hw:A i ≠ 0:=row_ne_zero_of_frequency_ne_zero A ls i (by
    change weightedFrequency ls (A i) ≠ 0
    rw [hwi]
    exact one_ne_zero)
  have hc:=hS d B q ls G hGl hGr hGn
  simp_rw [he] at hc
  exact ⟨d,hd,B,hB,ls,G,A i,hw,hA i,hwi,hGl,hGr,
    support_pullback A H i W hsupp,he,hc⟩
end Green24Proof.CyclicSpatialHaarModel
private def zz2492:"s09bc"="s09bc":=by decide+kernel
end 
section 
namespace Green24Proof.CyclicLocalizedHaarApproximation
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.CyclicMaskedRegularity Green24Proof.CyclicSpatialHaarModel
open Green24Proof.CyclicFrequencyPivot Green24Proof.CyclicTorusSmoothing
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicGrowthCounting
open Green24Proof.CyclicTorusPairCounting Green24Proof.CyclicTorusHaarDiscrepancy
open Green24Proof.CyclicCharacterCounting
theorem normalized_mass_count_error {q:ℕ} [NeZero q] (f g:ZMod q → ℝ)
    (h2:IsUnit (2:ZMod q)) (h3:IsUnit (3:ZMod q))
    {δ:ℝ} (hδ:0 ≤ δ) (hf:∀ x,f x ∈ Set.Icc 0 1) (hg:∀ x,g x ∈ Set.Icc 0 1)
    (he:∀ r, ‖ZMod.dft (fun x => ((f x - g x:ℝ):ℂ)) r‖ ≤ δ * q) :
    |(∑ x,f x) / q - (∑ x,g x) / q| ≤ δ ∧
      |weightedCount f / (q:ℝ)^2 - weightedCount g / (q:ℝ)^2| ≤ 3 * δ:=by
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr (NeZero.pos q)
  have hm:=he 0
  rw [ZMod.dft_apply_zero, ← Complex.ofReal_sum,Complex.norm_real,Real.norm_eq_abs,
    Finset.sum_sub_distrib] at hm
  have hc:=self_count_replacement f g h2 h3 hδ hf hg he
  rw [← weightedCount_ofReal, ← weightedCount_ofReal, ← Complex.ofReal_sub,
    Complex.norm_real,Real.norm_eq_abs] at hc
  constructor
  · rw [← sub_div,abs_div,abs_of_pos hq]
    exact (div_le_iff₀ hq).mpr hm
  · rw [← sub_div,abs_div,abs_of_pos (sq_pos_of_pos hq)]
    exact (div_le_iff₀ (sq_pos_of_pos hq)).mpr hc
private def zz1944:"s0798"="s0798":=by decide+kernel
theorem exists_localized_haar_approximation (χ:Circle → ℝ) {L:ℝ≥0}
    (hχ:LipschitzWith L χ) (hχr:∀ z,χ z ∈ Set.Icc 0 1)
    (W:Set Circle) (hχW:∀ z,z ∉ W → χ z = 0)
    {ε:ℝ} (hε:0 < ε) :
    ∃ C Q R:ℕ, ∀ (q:ℕ) [NeZero q] [Fact q.Prime],Q < q →
      ∀ f:ZMod q → ℝ,(∀ x,f x ∈ Set.Icc 0 1) →
        (∀ x,χ (ZMod.toCircle (-x)) * f x = f x) →
        ∃ d ≤ C, ∃ (ls:Fin d → ZMod q) (G:(Fin d → Circle) → ℝ) (w:Fin d → ℤ),
          w ≠ 0 ∧ (∑ j,(w j).natAbs) ≤ R ∧ weightedFrequency ls w = 1 ∧
          LipschitzWith (C:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
          (∀ z,(∏ j,z j ^ w j) ∉ W → G z = 0) ∧
          |(∑ x,f x) / q - ∫ z,G z ∂torusHaar (Fin d)| ≤ 3 * ε ∧
          |weightedCount f / (q:ℝ)^2 - haarWeightedCount G| ≤ 5 * ε:=by
  classical
  obtain ⟨M,hM⟩:=exists_masked_approximation χ hχ hχr hε
  choose Cs Qs Rs hmodel using fun n:ℕ => exists_uniform_spatial_haar_model n M hε
  let I:=Finset.range (M + 1)
  let C:=max M (I.sup Cs)
  let Q:=max 3 (I.sup Qs)
  let R:=I.sup Rs
  refine ⟨C,Q,R, ?_⟩
  intro q _ _ hq f hf hmask
  have h3q:3 < q:=lt_of_le_of_lt (le_max_left _ _) hq
  have h2:IsUnit (2:ZMod q):=isUnit_iff_ne_zero.mpr (by
    have h:=intCast_ne_zero_of_natAbs_lt (q:=q) (m:=2) (by norm_num) (by norm_num; omega)
    simpa using h)
  have h3:IsUnit (3:ZMod q):=isUnit_iff_ne_zero.mpr (by
    have h:=intCast_ne_zero_of_natAbs_lt (q:=q) (m:=3) (by norm_num) (by simpa using h3q)
    simpa using h)
  obtain ⟨n,hn,ks,H,hk,hH,hHr,hHz,hdf⟩:=hM q f hf hmask
  have hnI:n + 1 ∈ I:=Finset.mem_range.mpr (Nat.lt_succ_of_le hn)
  have hQn:Qs (n + 1) < q :=
    lt_of_le_of_lt ((Finset.le_sup (f:=Qs) hnI).trans (le_max_right _ _)) hq
  obtain ⟨d,hd,B,hB,ls,G,w,hw,hwsize,hwfreq,hGl,hGr,hGs,hGe,hGm,hGc⟩ :=
    hmodel (n + 1) q hQn ks H 0 W hH hHr hk (fun z hz => hHz z (hχW _ hz))
  have hBC:B ≤ C:=hB.trans ((Finset.le_sup (f:=Cs) hnI).trans (le_max_right _ _))
  have he:=normalized_mass_count_error f (fun x => H (characterOrbit ks x)) h2 h3 hε.le hf
    (fun x => hHr _) hdf
  refine ⟨d,(hd.trans hn).trans (le_max_left _ _),ls,G,w,hw,
    hwsize.trans (Finset.le_sup (f:=Rs) hnI),hwfreq,
    hGl.weaken (by exact_mod_cast hBC),hGr,hGs, ?_, ?_⟩
  · have ht:=abs_sub_le ((∑ x,f x) / q) ((∑ x,H (characterOrbit ks x)) / q)
      (∫ z,G z ∂torusHaar (Fin d))
    linarith [he.1]
  · have ht:=abs_sub_le (weightedCount f / (q:ℝ)^2)
      (weightedCount (fun x => H (characterOrbit ks x)) / (q:ℝ)^2) (haarWeightedCount G)
    linarith [he.2]
end Green24Proof.CyclicLocalizedHaarApproximation
private def zz2493:"s09bd"="s09bd":=by decide+kernel
end 
section 
namespace Contribution.Green24VariantsConjecture
open Finset
def pairCount (A:Finset ℤ):ℕ :=
  ((A ×ˢ A).filter (fun (x,y) ↦ x ≠ y ∧ x + 3 * (y - x) ∈ A)).card
lemma bddAbove_pairCounts (n:ℕ) :
    BddAbove { k | ∃ A:Finset ℤ,A.card = n ∧
      k = ((A ×ˢ A).filter (fun (x,y) ↦ x ≠ y ∧ x + 3 * (y - x) ∈ A)).card }:=by
  refine ⟨n ^ 2, ?_⟩
  rintro k ⟨A,hA,rfl⟩
  calc ((A ×ˢ A).filter (fun (x,y) ↦ x ≠ y ∧ x + 3 * (y - x) ∈ A)).card
      ≤ (A ×ˢ A).card:=Finset.card_filter_le _ _
    _ = n ^ 2:=by rw [Finset.card_product,hA,sq]
lemma pairCount_le_max {A:Finset ℤ} {n:ℕ} (hA:A.card = n) :
    pairCount A ≤ Green24.max013AffineTranslates n:=by
  unfold Green24.max013AffineTranslates pairCount
  exact le_csSup (bddAbove_pairCounts n) ⟨A,hA,rfl⟩
def interval (n:ℕ):Finset ℤ:=(Finset.range n).image (Nat.cast:ℕ → ℤ)
lemma card_interval (n:ℕ):(interval n).card = n:=by
  rw [interval,Finset.card_image_of_injective _ Nat.cast_injective,Finset.card_range]
private def zz1945:"s0799"="s0799":=by decide+kernel
lemma mem_interval {n:ℕ} {z:ℤ}:z ∈ interval n ↔ 0 ≤ z ∧ z < n:=by
  unfold interval
  constructor
  · rintro hz
    obtain ⟨m,hm,rfl⟩:=Finset.mem_image.1 hz
    exact ⟨Int.natCast_nonneg m,by exact_mod_cast Finset.mem_range.1 hm⟩
  · rintro ⟨h0,hn⟩
    refine Finset.mem_image.2 ⟨z.toNat,Finset.mem_range.2 ?_,Int.toNat_of_nonneg h0⟩
    have:(z.toNat:ℤ) < n:=by rw [Int.toNat_of_nonneg h0]; exact hn
    exact_mod_cast this
lemma natCast_mem_interval {n m:ℕ} (h:m < n):(m:ℤ) ∈ interval n :=
  Finset.mem_image.2 ⟨m,Finset.mem_range.2 h,rfl⟩
def intervalPairs (n:ℕ):Finset (ℤ × ℤ) :=
  (interval n ×ˢ interval n).filter (fun (x,y) ↦ x ≠ y ∧ x + 3 * (y - x) ∈ interval n)
lemma pairCount_interval_eq (n:ℕ):pairCount (interval n) = (intervalPairs n).card:=rfl
def copyIndex (n:ℕ):Finset ((_:ℕ) × ℕ) :=
  (Finset.range ((n - 1) / 3)).sigma fun i => Finset.range (n - 3 * (i + 1))
lemma mem_copyIndex {n:ℕ} {p:(_:ℕ) × ℕ} :
    p ∈ copyIndex n ↔ p.1 < (n - 1) / 3 ∧ p.2 + 3 * (p.1 + 1) < n:=by
  rcases p with ⟨i,x⟩
  simp only [copyIndex,Finset.mem_sigma,Finset.mem_range]
  omega
private def zz1946:"s079a"="s079a":=by decide+kernel
lemma card_copyIndex (n:ℕ) :
    (copyIndex n).card = ∑ i ∈ Finset.range ((n - 1) / 3),(n - 3 * (i + 1)):=by
  simp [copyIndex,Finset.card_sigma,Finset.card_range]
lemma two_mul_sum_copies (n:ℕ):∀ m:ℕ,3 * m ≤ n →
    2 * (∑ i ∈ Finset.range m,(n - 3 * (i + 1))) + 3 * m * (m + 1) = 2 * m * n:=by
  intro m
  induction m with
  | zero => intro _; simp
  | succ m ih =>
    intro h3
    have ih':=ih (by omega)
    rw [Finset.sum_range_succ]
    generalize hS:∑ i ∈ Finset.range m,(n - 3 * (i + 1)) = S at ih' ⊢
    zify [h3] at ih' ⊢
    linear_combination ih'
def upPair (p:(_:ℕ) × ℕ):ℤ × ℤ:=((p.2:ℤ),((p.2 + (p.1 + 1):ℕ):ℤ))
def downPair (p:(_:ℕ) × ℕ):ℤ × ℤ :=
  (((p.2 + 3 * (p.1 + 1):ℕ):ℤ),((p.2 + 2 * (p.1 + 1):ℕ):ℤ))
lemma upPair_mem {n:ℕ} {p:(_:ℕ) × ℕ} (hp:p ∈ copyIndex n) :
    upPair p ∈ intervalPairs n:=by
  obtain ⟨hi,hx⟩:=mem_copyIndex.1 hp
  refine Finset.mem_filter.2 ⟨Finset.mem_product.2 ⟨mem_interval.2 ⟨?_, ?_⟩,
    mem_interval.2 ⟨?_, ?_⟩⟩, ?_,mem_interval.2 ⟨?_, ?_⟩⟩ <;>
  (try simp only [upPair]) <;> (try push_cast) <;> omega
lemma downPair_mem {n:ℕ} {p:(_:ℕ) × ℕ} (hp:p ∈ copyIndex n) :
    downPair p ∈ intervalPairs n:=by
  obtain ⟨hi,hx⟩:=mem_copyIndex.1 hp
  refine Finset.mem_filter.2 ⟨Finset.mem_product.2 ⟨mem_interval.2 ⟨?_, ?_⟩,
    mem_interval.2 ⟨?_, ?_⟩⟩, ?_,mem_interval.2 ⟨?_, ?_⟩⟩ <;>
  (try simp only [downPair]) <;> (try push_cast) <;> omega
private def zz1947:"s079b"="s079b":=by decide+kernel
lemma upPair_injOn (n:ℕ):Set.InjOn upPair (copyIndex n:Set ((_:ℕ) × ℕ)):=by
  rintro ⟨i,x⟩ - ⟨j,y⟩ - h
  simp only [upPair,Prod.mk.injEq,Nat.cast_inj] at h
  obtain ⟨rfl,h2⟩:=h
  obtain rfl:i = j:=by omega
  rfl
lemma downPair_injOn (n:ℕ):Set.InjOn downPair (copyIndex n:Set ((_:ℕ) × ℕ)):=by
  rintro ⟨i,x⟩ - ⟨j,y⟩ - h
  simp only [downPair,Prod.mk.injEq,Nat.cast_inj] at h
  obtain ⟨h1,h2⟩:=h
  obtain rfl:i = j:=by omega
  obtain rfl:x = y:=by omega
  rfl
lemma disjoint_upPair_downPair (n:ℕ) :
    Disjoint ((copyIndex n).image upPair) ((copyIndex n).image downPair):=by
  rw [Finset.disjoint_left]
  rintro a ha hb
  obtain ⟨p, -,rfl⟩:=Finset.mem_image.1 ha
  obtain ⟨q, -,hq⟩:=Finset.mem_image.1 hb
  simp only [upPair,downPair,Prod.mk.injEq] at hq
  push_cast at hq
  omega
lemma two_mul_card_copyIndex_le (n:ℕ):2 * (copyIndex n).card ≤ pairCount (interval n):=by
  have hsub:(copyIndex n).image upPair ∪ (copyIndex n).image downPair ⊆ intervalPairs n:=by
    intro a ha
    rcases Finset.mem_union.1 ha with h | h
    · obtain ⟨p,hp,rfl⟩:=Finset.mem_image.1 h
      exact upPair_mem hp
    · obtain ⟨p,hp,rfl⟩:=Finset.mem_image.1 h
      exact downPair_mem hp
  calc 2 * (copyIndex n).card
      = ((copyIndex n).image upPair).card + ((copyIndex n).image downPair).card:=by
        rw [Finset.card_image_of_injOn (upPair_injOn n),
          Finset.card_image_of_injOn (downPair_injOn n)]
        ring
    _ = ((copyIndex n).image upPair ∪ (copyIndex n).image downPair).card :=
        (Finset.card_union_of_disjoint (disjoint_upPair_downPair n)).symm
    _ ≤ (intervalPairs n).card:=Finset.card_le_card hsub
    _ = pairCount (interval n):=(pairCount_interval_eq n).symm
private def zz1948:"s079c"="s079c":=by decide+kernel
lemma pairCount_interval_ge (n:ℕ) :
    n ^ 2 ≤ 3 * pairCount (interval n) + 5 * n:=by
  have hcard:=two_mul_card_copyIndex_le n
  rw [card_copyIndex] at hcard
  set m:=(n - 1) / 3 with hm
  have hmn:3 * m ≤ n:=by omega
  have hsum:=two_mul_sum_copies n m hmn
  generalize hS:∑ i ∈ Finset.range m,(n - 3 * (i + 1)) = S at hcard hsum
  rcases Nat.eq_zero_or_pos n with rfl | hn
  · positivity
  · have h1:3 * m + 1 ≤ n:=by omega
    have h2:n ≤ 3 * m + 3:=by omega
    zify at hcard hsum h1 h2 ⊢
    nlinarith [hcard,hsum,
      mul_nonneg (by linarith:(0:ℤ) ≤ (n:ℤ) - 3 * m - 1)
        (by linarith:(0:ℤ) ≤ 3 * m + 3 - (n:ℤ))]
lemma max_ge (n:ℕ) :
    n ^ 2 ≤ 3 * Green24.max013AffineTranslates n + 5 * n:=by
  have h1:=pairCount_interval_ge n
  have h2:=pairCount_le_max (card_interval n)
  omega
open Filter Topology
lemma ratio_le_one (n:ℕ):(Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2 ≤ 1:=by
  rcases Nat.eq_zero_or_pos n with rfl | hn
  · simp
  · have hp:(0:ℝ) < (n:ℝ) ^ 2:=by positivity
    rw [div_le_one hp]
    exact_mod_cast Green24.variants.upper_trivial (n:=n)
lemma ratio_isBoundedUnder :
    IsBoundedUnder (· ≤ ·) atTop
      (fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2) :=
  isBoundedUnder_of ⟨1,fun n => ratio_le_one n⟩
private def zz1949:"s079d"="s079d":=by decide+kernel
theorem gamma_ge_of_eventually {c C:ℝ}
    (h:∀ᶠ n:ℕ in atTop,
      c * (n:ℝ) ^ 2 - C * n ≤ Green24.max013AffineTranslates n) :
    c ≤ Green24.variants.gamma:=by
  unfold Green24.variants.gamma
  have hlim:Tendsto (fun n:ℕ => c - C / (n:ℝ)) atTop (𝓝 c):=by
    have h0:=(tendsto_const_nhds (x:=c)).sub
      ((tendsto_const_nhds (x:=C)).div_atTop tendsto_natCast_atTop_atTop)
    simpa using h0
  have hle:(fun n:ℕ => c - C / (n:ℝ)) ≤ᶠ[atTop]
      fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2:=by
    filter_upwards [h,eventually_gt_atTop 0] with n hn hn0
    have hnr:(0:ℝ) < n:=by exact_mod_cast hn0
    rw [le_div_iff₀ (by positivity)]
    have hexp:(c - C / (n:ℝ)) * (n:ℝ) ^ 2 = c * (n:ℝ) ^ 2 - C * n:=by
      field_simp
    linarith [hexp]
  have hcob:IsCoboundedUnder (· ≤ ·) atTop (fun n:ℕ => c - C / (n:ℝ)):=by
    refine isCoboundedUnder_le_of_eventually_le atTop (x:=c - |C|) ?_
    filter_upwards [eventually_ge_atTop 1] with n hn
    have hn1:(1:ℝ) ≤ n:=by exact_mod_cast hn
    have hCn:C / (n:ℝ) ≤ |C|:=by
      calc C / (n:ℝ) ≤ |C| / (n:ℝ):=by gcongr; exact le_abs_self C
        _ ≤ |C|:=div_le_self (abs_nonneg C) hn1
    linarith
  calc c = limsup (fun n:ℕ => c - C / (n:ℝ)) atTop:=hlim.limsup_eq.symm
    _ ≤ limsup (fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2) atTop :=
        limsup_le_limsup hle hcob ratio_isBoundedUnder
theorem gamma_ge_one_third :
    Green24.variants.gamma ≥ 1 / 3:=by
  rw [ge_iff_le]
  refine gamma_ge_of_eventually (C:=(5 / 3:ℝ)) (Filter.Eventually.of_forall fun n => ?_)
  have h:(n:ℝ) ^ 2 ≤ 3 * (Green24.max013AffineTranslates n:ℝ) + 5 * (n:ℝ):=by
    exact_mod_cast max_ge n
  linarith
lemma ratio_nonneg (n:ℕ):0 ≤ (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2:=by
  positivity
theorem gamma_le_of_eventually {c C:ℝ}
    (h:∀ᶠ n:ℕ in atTop,
      (Green24.max013AffineTranslates n:ℝ) ≤ c * (n:ℝ) ^ 2 + C * n) :
    Green24.variants.gamma ≤ c:=by
  unfold Green24.variants.gamma
  have hlim:Tendsto (fun n:ℕ => c + C / (n:ℝ)) atTop (𝓝 c):=by
    have h0:=(tendsto_const_nhds (x:=c)).add
      ((tendsto_const_nhds (x:=C)).div_atTop tendsto_natCast_atTop_atTop)
    simpa using h0
  have hle:(fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2) ≤ᶠ[atTop]
      fun n:ℕ => c + C / (n:ℝ):=by
    filter_upwards [h,eventually_gt_atTop 0] with n hn hn0
    have hnr:(0:ℝ) < n:=by exact_mod_cast hn0
    rw [div_le_iff₀ (by positivity)]
    have hexp:(c + C / (n:ℝ)) * (n:ℝ) ^ 2 = c * (n:ℝ) ^ 2 + C * n:=by
      field_simp
    linarith [hexp]
  have hcob:IsCoboundedUnder (· ≤ ·) atTop
      (fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2) :=
    isCoboundedUnder_le_of_le atTop fun n => ratio_nonneg n
  have hbdd:IsBoundedUnder (· ≤ ·) atTop (fun n:ℕ => c + C / (n:ℝ)):=by
    refine ⟨c + |C|, ?_⟩
    rw [eventually_map]
    filter_upwards [eventually_ge_atTop 1] with n hn
    have hn1:(1:ℝ) ≤ n:=by exact_mod_cast hn
    have hCn:C / (n:ℝ) ≤ |C|:=by
      calc C / (n:ℝ) ≤ |C| / (n:ℝ):=by gcongr; exact le_abs_self C
        _ ≤ |C|:=div_le_self (abs_nonneg C) hn1
    linarith
  calc limsup (fun n:ℕ => (Green24.max013AffineTranslates n:ℝ) / (n:ℝ) ^ 2) atTop
      ≤ limsup (fun n:ℕ => c + C / (n:ℝ)) atTop:=limsup_le_limsup hle hcob hbdd
    _ = c:=hlim.limsup_eq
private def zz1950:"s079e"="s079e":=by decide+kernel
theorem conjecture_of_upper_bound {C:ℝ}
    (h:∀ᶠ n:ℕ in atTop,
      (Green24.max013AffineTranslates n:ℝ) ≤ (n:ℝ) ^ 2 / 3 + C * n) :
    Green24.variants.gamma = 1 / 3:=by
  refine le_antisymm (gamma_le_of_eventually (C:=C) ?_) gamma_ge_one_third
  filter_upwards [h] with n hn
  linarith [hn]
end Contribution.Green24VariantsConjecture
end 
section 
namespace Green24Proof
open Contribution.Green24VariantsConjecture Filter
def integerSolutionPairs (A:Finset ℤ):Finset (ℤ × ℤ) :=
  (A ×ˢ A).filter (fun p => 3 * p.2 - 2 * p.1 ∈ A)
def integerSolutionTriples (A:Finset ℤ):Finset (ℤ × ℤ × ℤ) :=
  (A ×ˢ (A ×ˢ A)).filter (fun p => p.1 + 2 * p.2.1 = 3 * p.2.2)
def integerSolutionCount (A:Finset ℤ):ℕ:=(integerSolutionPairs A).card
theorem integerSolutionTriples_eq_image (A:Finset ℤ) :
    integerSolutionTriples A = (integerSolutionPairs A).image
      (fun p => (3 * p.2 - 2 * p.1,p.1,p.2)):=by
  ext ⟨x,y,z⟩
  simp only [integerSolutionTriples,integerSolutionPairs,Finset.mem_filter,
    Finset.mem_product,Finset.mem_image,Prod.exists,Prod.mk.injEq]
  constructor
  · rintro ⟨⟨hx,hy,hz⟩,heq⟩
    refine ⟨y,z,⟨⟨hy,hz⟩, ?_⟩, ?_,rfl,rfl⟩
    · have h:3 * z - 2 * y = x:=by omega
      simpa only [h] using hx
    · omega
  · rintro ⟨a,b,⟨⟨ha,hb⟩,hc⟩,hx,rfl,rfl⟩
    refine ⟨⟨?_,ha,hb⟩, ?_⟩
    · simpa only [hx] using hc
    · omega
theorem integerSolutionTriples_card (A:Finset ℤ) :
    (integerSolutionTriples A).card = integerSolutionCount A:=by
  rw [integerSolutionTriples_eq_image,Finset.card_image_of_injective]
  · rfl
  · intro p q h
    exact congrArg Prod.snd h
theorem integerSolutionCount_eq_pairCount_add_card (A:Finset ℤ) :
    integerSolutionCount A = pairCount A + A.card:=by
  have hdiag:(integerSolutionPairs A).filter (fun p => p.1 = p.2) = A.diag:=by
    ext ⟨y,z⟩
    simp only [integerSolutionPairs,Finset.mem_filter,Finset.mem_product,Finset.mem_diag]
    constructor
    · exact fun h => ⟨h.1.1.1,h.2⟩
    · rintro ⟨hy,rfl⟩
      refine ⟨⟨⟨hy,hy⟩, ?_⟩,rfl⟩
      simpa only [show 3 * y - 2 * y = y by ring] using hy
  have hoff:((integerSolutionPairs A).filter (fun p => ¬p.1 = p.2)).card = pairCount A:=by
    unfold pairCount
    congr 1
    ext ⟨y,z⟩
    simp only [integerSolutionPairs,Finset.mem_filter,Finset.mem_product]
    rw [show y + 3 * (z - y) = 3 * z - 2 * y by ring]
    tauto
  have h:=(integerSolutionPairs A).card_filter_add_card_filter_not (fun p => p.1 = p.2)
  rw [hdiag,Finset.diag_card,hoff] at h
  unfold integerSolutionCount
  omega
private def zz1951:"s079f"="s079f":=by decide+kernel
theorem max013_attained (n:ℕ) :
    ∃ A:Finset ℤ,A.card = n ∧ pairCount A = Green24.max013AffineTranslates n:=by
  let S:Set ℕ:={k | ∃ A:Finset ℤ,A.card = n ∧ k = pairCount A}
  have hne:S.Nonempty:=⟨pairCount (interval n),interval n,card_interval n,rfl⟩
  have hbd:BddAbove S:=bddAbove_pairCounts n
  have hfin:S.Finite:=Set.finite_iff_bddAbove.mpr hbd
  obtain ⟨A,hA,heq⟩:=hne.csSup_mem hfin
  exact ⟨A,hA,heq.symm⟩
theorem max013_le_of_solution_bound {n:ℕ} {B:ℝ}
    (h:∀ A:Finset ℤ,A.card = n → (integerSolutionCount A:ℝ) ≤ B) :
    (Green24.max013AffineTranslates n:ℝ) + n ≤ B:=by
  obtain ⟨A,hA,hmax⟩:=max013_attained n
  have hb:=h A hA
  rw [integerSolutionCount_eq_pairCount_add_card,Nat.cast_add,hmax,hA] at hb
  exact hb
theorem gamma_le_of_solution_asymptotic {c:ℝ}
    (h:∀ ε:ℝ,0 < ε → ∀ᶠ n:ℕ in atTop, ∀ A:Finset ℤ,A.card = n →
      (integerSolutionCount A:ℝ) ≤ (c + ε) * (n:ℝ) ^ 2) :
    Green24.variants.gamma ≤ c:=by
  apply le_of_forall_pos_le_add
  intro ε hε
  apply gamma_le_of_eventually (C:=0)
  filter_upwards [h ε hε] with n hn
  have hmax:=max013_le_of_solution_bound hn
  have hn0:(0:ℝ) ≤ n:=Nat.cast_nonneg n
  linarith
theorem conjecture_of_solution_asymptotic
    (h:∀ ε:ℝ,0 < ε → ∀ᶠ n:ℕ in atTop, ∀ A:Finset ℤ,A.card = n →
      (integerSolutionCount A:ℝ) ≤ (1 / 3 + ε) * (n:ℝ) ^ 2) :
    Green24.variants.gamma = 1 / 3 :=
  le_antisymm (gamma_le_of_solution_asymptotic h) gamma_ge_one_third
end Green24Proof
end 
section 
namespace Green24Proof.IntegerCyclicEmbedding
private def zz1952:"s07a0"="s07a0":=by decide+kernel
theorem intCast_injOn_interval {L q:ℕ} (hq:L < q) :
    Set.InjOn (fun x:ℤ => (x:ZMod q)) (Set.Icc 0 (L:ℤ)):=by
  apply (CharP.intCast_injOn_Ico (ZMod q) q).mono
  intro x hx
  exact ⟨hx.1,lt_of_le_of_lt hx.2 (by exact_mod_cast hq)⟩
theorem equation_iff {L q:ℕ} (hq:3 * L < q) {x y z:ℤ}
    (hx:0 ≤ x ∧ x ≤ L) (hy:0 ≤ y ∧ y ≤ L) (hz:0 ≤ z ∧ z ≤ L) :
    (x:ZMod q) + 2 * (y:ZMod q) = 3 * (z:ZMod q) ↔
      x + 2 * y = 3 * z:=by
  constructor
  · intro h
    have hcast:((x + 2 * y:ℤ):ZMod q) = ((3 * z:ℤ):ZMod q):=by
      push_cast
      exact h
    apply intCast_injOn_interval hq ?_ ?_ hcast
    · constructor <;> push_cast <;> omega
    · constructor <;> push_cast <;> omega
  · intro h
    have hc:=congrArg (fun t:ℤ => (t:ZMod q)) h
    push_cast at hc
    exact hc
def cyclicImage (q:ℕ) (A:Finset ℤ):Finset (ZMod q) :=
  A.image (fun x:ℤ => (x:ZMod q))
theorem intCast_injOn_set {L q:ℕ} (hq:L < q) (A:Finset ℤ)
    (hA:∀ x ∈ A,0 ≤ x ∧ x ≤ (L:ℤ)) :
    Set.InjOn (fun x:ℤ => (x:ZMod q)) (A:Set ℤ) :=
  (intCast_injOn_interval hq).mono (fun x hx => hA x hx)
theorem cyclicImage_card {L q:ℕ} (hq:L < q) (A:Finset ℤ)
    (hA:∀ x ∈ A,0 ≤ x ∧ x ≤ (L:ℤ)) :
    (cyclicImage q A).card = A.card :=
  Finset.card_image_of_injOn (intCast_injOn_set hq A hA)
def cyclicSolutionTriples {q:ℕ} (B:Finset (ZMod q)) :
    Finset (ZMod q × ZMod q × ZMod q) :=
  (B ×ˢ (B ×ˢ B)).filter (fun p => p.1 + 2 * p.2.1 = 3 * p.2.2)
def cyclicSolutionCount {q:ℕ} (B:Finset (ZMod q)):ℕ :=
  (cyclicSolutionTriples B).card
private def zz1953:"s07a1"="s07a1":=by decide+kernel
theorem cyclicSolutionCount_eq_integerSolutionCount {L q:ℕ}
    (hq:3 * L < q) (A:Finset ℤ)
    (hA:∀ x ∈ A,0 ≤ x ∧ x ≤ (L:ℤ)) :
    cyclicSolutionCount (cyclicImage q A) = integerSolutionCount A:=by
  rw [← integerSolutionTriples_card A]
  symm
  unfold cyclicSolutionCount
  have hinj:=intCast_injOn_set (show L < q by omega) A hA
  refine Finset.card_bij
    (fun p _ => ((p.1:ZMod q),(p.2.1:ZMod q),(p.2.2:ZMod q))) ?_ ?_ ?_
  · rintro ⟨x,y,z⟩ hp
    simp only [integerSolutionTriples,cyclicSolutionTriples,Finset.mem_filter,
      Finset.mem_product] at hp ⊢
    refine ⟨⟨?_, ?_, ?_⟩, ?_⟩
    · exact Finset.mem_image.mpr ⟨x,hp.1.1,rfl⟩
    · exact Finset.mem_image.mpr ⟨y,hp.1.2.1,rfl⟩
    · exact Finset.mem_image.mpr ⟨z,hp.1.2.2,rfl⟩
    · exact (equation_iff hq (hA x hp.1.1) (hA y hp.1.2.1) (hA z hp.1.2.2)).mpr hp.2
  · rintro ⟨x,y,z⟩ hp ⟨x',y',z'⟩ hp' he
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product] at hp hp'
    have hx:=hinj hp.1.1 hp'.1.1 (congrArg Prod.fst he)
    have hy:=hinj hp.1.2.1 hp'.1.2.1 (congrArg (fun p => p.2.1) he)
    have hz:=hinj hp.1.2.2 hp'.1.2.2 (congrArg (fun p => p.2.2) he)
    exact Prod.ext hx (Prod.ext hy hz)
  · rintro ⟨x,y,z⟩ hp
    simp only [cyclicSolutionTriples,Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hp.1.1
    obtain ⟨b,hb,rfl⟩:=Finset.mem_image.mp hp.1.2.1
    obtain ⟨c,hc,rfl⟩:=Finset.mem_image.mp hp.1.2.2
    refine ⟨(a,b,c), ?_,rfl⟩
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product]
    exact ⟨⟨ha,hb,hc⟩,(equation_iff hq (hA a ha) (hA b hb) (hA c hc)).mp hp.2⟩
end Green24Proof.IntegerCyclicEmbedding
private def zz2494:"s09be"="s09be":=by decide+kernel
end 
section 
namespace Green24Proof.IntegerLocalizedHaarTransfer
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset
open scoped BigOperators NNReal
open Green24Proof.IntegerCyclicEmbedding Green24Proof.CyclicGrowthCounting
open Green24Proof.CyclicTorusLaurent Green24Proof.CyclicTorusPairCounting
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.SpatialCircleCutoff
open Green24Proof.CyclicLocalizedHaarApproximation
variable {q:ℕ} [NeZero q]
noncomputable def weight (B:Finset (ZMod q)) (x:ZMod q):ℝ:=if x ∈ B then 1 else 0
omit [NeZero q] in
theorem weight_range (B:Finset (ZMod q)) (x:ZMod q):weight B x ∈ Set.Icc 0 1:=by
  unfold weight
  split_ifs <;> norm_num
theorem sum_weight (B:Finset (ZMod q)):(∑ x,weight B x) = B.card:=by
  classical
  simp [weight]
theorem weightedCount_weight (B:Finset (ZMod q)) :
    weightedCount (weight B) = cyclicSolutionCount B:=by
  classical
  have he (x y z:ZMod q):x + 2 * y = 3 * z ↔ x = 3 * z - 2 * y:=by
    constructor <;> intro h <;> linear_combination h
  have hc:(cyclicSolutionCount B:ℝ) =
      ∑ x ∈ B, ∑ y ∈ B, ∑ z ∈ B,if x = 3 * z - 2 * y then (1:ℝ) else 0:=by
    simp only [cyclicSolutionCount,cyclicSolutionTriples,Finset.card_filter,
      Nat.cast_sum,Nat.cast_ite,Nat.cast_one,Nat.cast_zero,Finset.sum_product,he]
  rw [hc,weightedCount]
  simp only [weight,mul_ite,mul_zero,mul_one,Finset.sum_ite_mem_eq]
  symm
  calc
    (∑ x ∈ B, ∑ y ∈ B, ∑ z ∈ B,if x = 3 * z - 2 * y then (1:ℝ) else 0) =
        ∑ y ∈ B, ∑ z ∈ B, ∑ x ∈ B,if x = 3 * z - 2 * y then (1:ℝ) else 0:=by
      rw [Finset.sum_comm]
      apply Finset.sum_congr rfl
      intro y _
      rw [Finset.sum_comm]
    _ = _:=by simp
private def zz1954:"s07a2"="s07a2":=by decide+kernel
theorem weight_cutoff_interval {L:ℕ} (hq:32 * L ≤ q) (A:Finset ℤ)
    (hA:∀ x ∈ A,0 ≤ x ∧ x ≤ (L:ℤ)) :
    ∀ x:ZMod q,cutoff (ZMod.toCircle (-x)) * weight (cyclicImage q A) x =
      weight (cyclicImage q A) x:=by
  classical
  intro x
  by_cases hx:x ∈ cyclicImage q A
  · obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hx
    have hb:(32:ℝ) * |(a:ℝ)| ≤ q:=by
      rw [abs_of_nonneg (by exact_mod_cast (hA a ha).1)]
      have hL:(a:ℝ) ≤ L:=by exact_mod_cast (hA a ha).2
      have hp:(32:ℝ) * L ≤ q:=by exact_mod_cast hq
      linarith
    rw [cutoff_integer_plateau a hb,one_mul]
  · simp [weight,hx]
theorem exists_integer_haar_model {ε:ℝ} (hε:0 < ε) :
    ∃ C Q R:ℕ, ∀ (q:ℕ) [NeZero q] [Fact q.Prime],Q < q →
      ∀ (L:ℕ),32 * L < q → ∀ A:Finset ℤ,
        (∀ x ∈ A,0 ≤ x ∧ x ≤ (L:ℤ)) →
        ∃ d ≤ C, ∃ (ls:Fin d → ZMod q) (G:(Fin d → Circle) → ℝ) (w:Fin d → ℤ),
          w ≠ 0 ∧ (∑ j,(w j).natAbs) ≤ R ∧ weightedFrequency ls w = 1 ∧
          LipschitzWith (C:ℝ≥0) G ∧ (∀ z,G z ∈ Set.Icc 0 1) ∧
          (∀ z,(∏ j,z j ^ w j) ∉ window → G z = 0) ∧
          |(A.card:ℝ) / q - ∫ z,G z ∂torusHaar (Fin d)| ≤ 3 * ε ∧
          |(Green24Proof.integerSolutionCount A:ℝ) / (q:ℝ)^2 - haarWeightedCount G| ≤ 5 * ε:=by
  obtain ⟨C,Q,R,hmodel⟩:=exists_localized_haar_approximation cutoff cutoff_lipschitz
    cutoff_range window cutoff_zero_outside hε
  refine ⟨C,Q,R, ?_⟩
  intro q _ _ hq L hL A hA
  have h:=hmodel q hq (weight (cyclicImage q A)) (weight_range _)
    (weight_cutoff_interval hL.le A hA)
  rw [sum_weight,cyclicImage_card (by omega:L < q) A hA,weightedCount_weight,
    cyclicSolutionCount_eq_integerSolutionCount (by omega:3 * L < q) A hA] at h
  exact h
end Green24Proof.IntegerLocalizedHaarTransfer
private def zz2495:"s09bf"="s09bf":=by decide+kernel
end 
section 
namespace Green24Proof.PopularSums
open scoped BigOperators Pointwise
theorem weighted_threshold_energy_bound {ι:Type*} (T:Finset ι) (w:ι → ℝ)
    (M t:ℝ) (ht:0 ≤ t) (hw:∀ i ∈ T,0 ≤ w i ∧ w i ≤ M) :
    (∑ i ∈ T,w i ^ 2) ≤
      t * (∑ i ∈ T,w i) + M * (∑ i ∈ T.filter (fun i => t ≤ w i),w i):=by
  classical
  rw [Finset.sum_filter]
  calc
    (∑ i ∈ T,w i ^ 2) ≤
        ∑ i ∈ T,(t * w i + M * (if t ≤ w i then w i else 0)):=by
      apply Finset.sum_le_sum
      intro i hi
      rcases hw i hi with ⟨h0,hM⟩
      by_cases h:t ≤ w i
      · simp only [if_pos h]
        nlinarith [mul_nonneg (sub_nonneg.mpr hM) h0,mul_nonneg ht h0]
      · simp only [if_neg h,mul_zero,add_zero]
        have hi':w i ≤ t:=le_of_lt (lt_of_not_ge h)
        nlinarith [mul_nonneg (sub_nonneg.mpr hi') h0]
    _ = _:=by rw [Finset.sum_add_distrib,Finset.mul_sum,Finset.mul_sum]
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
theorem sum_addConvolution (A:Finset G) :
    (∑ s ∈ A + A,A.addConvolution A s) = A.card ^ 2:=by
  change (∑ s ∈ A + A,((A ×ˢ A).filter (fun p => p.1 + p.2 = s)).card) = _
  rw [Finset.sum_card_fiberwise_eq_card_filter]
  rw [Finset.filter_eq_self.mpr (by
    intro p hp
    exact Finset.add_mem_add (Finset.mem_product.mp hp).1 (Finset.mem_product.mp hp).2)]
  simp [pow_two]
noncomputable def sums (A:Finset G) (η:ℝ):Finset G:=by
  classical
  exact (A + A).filter (fun s => η * (A.card:ℝ) / 2 ≤ (A.addConvolution A s:ℝ))
private def zz1955:"s07a3"="s07a3":=by decide+kernel
theorem popular_sum_selection (A:Finset G) (hA:A.Nonempty) (η:ℝ) (hη:0 < η)
    (hE:η * (A.card:ℝ) ^ 3 ≤ (A.addEnergy A:ℝ)) :
    sums A η ⊆ A + A ∧
    ((sums A η).card:ℝ) ≤ 2 * (A.card:ℝ) / η ∧
    η * (A.card:ℝ) ^ 2 / 2 ≤
      (((A ×ˢ A).filter (fun p => p.1 + p.2 ∈ sums A η)).card:ℝ) ∧
    ∀ s ∈ sums A η,η * (A.card:ℝ) / 2 ≤ (A.addConvolution A s:ℝ):=by
  classical
  let N:ℝ:=A.card
  let r:G → ℝ:=fun s => A.addConvolution A s
  let S:=sums A η
  have hN:0 < N:=by
    dsimp [N]
    exact_mod_cast hA.card_pos
  have ht:0 ≤ η * N / 2:=by positivity
  have hS:S ⊆ A + A:=Finset.filter_subset _ _
  have hpopular (s:G) (hs:s ∈ S):η * N / 2 ≤ r s :=
    (Finset.mem_filter.mp hs).2
  have hweights (s:G) (_hs:s ∈ A + A):0 ≤ r s ∧ r s ≤ N:=by
    constructor
    · positivity
    · dsimp [N,r]
      exact_mod_cast (Finset.addConvolution_le_card_left (A:=A) (B:=A) (x:=s))
  have htotal:(∑ s ∈ A + A,r s) = N ^ 2:=by
    dsimp [N,r]
    exact_mod_cast sum_addConvolution A
  have henergy:(A.addEnergy A:ℝ) = ∑ s ∈ A + A,r s ^ 2:=by
    dsimp [r,Finset.addConvolution]
    exact_mod_cast Finset.addEnergy_eq_sum_sq' A A
  have hpair:(∑ s ∈ S,r s) =
      (((A ×ˢ A).filter (fun p => p.1 + p.2 ∈ S)).card:ℝ):=by
    dsimp [r,Finset.addConvolution]
    exact_mod_cast Finset.sum_card_fiberwise_eq_card_filter (A ×ˢ A) S
      (fun p:G × G => p.1 + p.2)
  have hmass_upper:(∑ s ∈ S,r s) ≤ N ^ 2:=by
    rw [← htotal]
    exact Finset.sum_le_sum_of_subset_of_nonneg hS (fun _ _ _ => by positivity)
  have hcard_mass:η * N / 2 * (S.card:ℝ) ≤ ∑ s ∈ S,r s:=by
    calc
      _ = ∑ _s ∈ S,η * N / 2:=by simp [mul_comm]
      _ ≤ _:=Finset.sum_le_sum hpopular
  have hcard:(S.card:ℝ) ≤ 2 * N / η:=by
    apply (le_div_iff₀ hη).2
    apply (mul_le_mul_iff_right₀ hN).mp
    nlinarith [hcard_mass.trans hmass_upper]
  have hbound:(A.addEnergy A:ℝ) ≤
      η * N / 2 * N ^ 2 + N * (∑ s ∈ S,r s):=by
    rw [henergy]
    simpa only [htotal,S,sums,N,r] using
      weighted_threshold_energy_bound (A + A) r N (η * N / 2) ht hweights
  have hmass_lower:η * N ^ 2 / 2 ≤ ∑ s ∈ S,r s:=by
    apply (mul_le_mul_iff_right₀ hN).mp
    have hE':η * N ^ 3 ≤ (A.addEnergy A:ℝ):=hE
    nlinarith [hE'.trans hbound]
  exact ⟨hS,hcard,by simpa only [hpair] using hmass_lower,hpopular⟩
theorem exists_popular_sums (A:Finset G) (hA:A.Nonempty) (η:ℝ) (hη:0 < η)
    (hE:η * (A.card:ℝ) ^ 3 ≤ (A.addEnergy A:ℝ)) :
    ∃ S:Finset G,S ⊆ A + A ∧
      (S.card:ℝ) ≤ 2 * (A.card:ℝ) / η ∧
      η * (A.card:ℝ) ^ 2 / 2 ≤
        (((A ×ˢ A).filter (fun p => p.1 + p.2 ∈ S)).card:ℝ) ∧
      ∀ s ∈ S,η * (A.card:ℝ) / 2 ≤ (A.addConvolution A s:ℝ) :=
  ⟨sums A η,popular_sum_selection A hA η hη hE⟩
end Green24Proof.PopularSums
private def zz2496:"s09c0"="s09c0":=by decide+kernel
end 
section 
namespace Green24Proof.DenseGraphCommonNeighbors
open scoped BigOperators
variable {α β:Type*}
def leftNeighbors (U:Finset α) (R:α → β → Prop) [DecidableRel R] (b:β):Finset α :=
  U.filter (fun a => R a b)
def commonNeighbors (V:Finset β) (R:α → β → Prop) [DecidableRel R]
    (a a':α):Finset β:=V.filter (fun b => R a b ∧ R a' b)
noncomputable def badPairs (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (t:ℝ):Finset (α × α):=by
  classical
  exact (U ×ˢ U).filter (fun p => ((commonNeighbors V R p.1 p.2).card:ℝ) < t)
theorem edge_count_eq_sum_degrees (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] :
    ((U ×ˢ V).filter (fun p => R p.1 p.2)).card =
      ∑ b ∈ V,(leftNeighbors U R b).card:=by
  simp only [Finset.card_filter,Finset.sum_product,leftNeighbors]
  rw [Finset.sum_comm]
theorem sum_badPairs_neighborhoods (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (t:ℝ) :
    (∑ b ∈ V,(badPairs (leftNeighbors U R b) V R t).card) =
      ∑ p ∈ badPairs U V R t,(commonNeighbors V R p.1 p.2).card:=by
  classical
  have hfilter (b:β):badPairs (leftNeighbors U R b) V R t =
      (badPairs U V R t).filter (fun p => R p.1 b ∧ R p.2 b):=by
    ext p
    simp only [badPairs,leftNeighbors,Finset.mem_filter,Finset.mem_product]
    tauto
  simp_rw [hfilter,Finset.card_filter]
  rw [Finset.sum_comm]
  apply Finset.sum_congr rfl
  intro p hp
  simp only [commonNeighbors,Finset.card_filter]
private def zz1956:"s07a4"="s07a4":=by decide+kernel
theorem sum_badPairs_neighborhoods_le (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] {t:ℝ} (ht:0 ≤ t) :
    (∑ b ∈ V,((badPairs (leftNeighbors U R b) V R t).card:ℝ)) ≤
      t * (U.card:ℝ) ^ 2:=by
  classical
  have hcount:(∑ b ∈ V,((badPairs (leftNeighbors U R b) V R t).card:ℝ)) =
      ∑ p ∈ badPairs U V R t,((commonNeighbors V R p.1 p.2).card:ℝ):=by
    exact_mod_cast sum_badPairs_neighborhoods U V R t
  rw [hcount]
  calc
    _ ≤ ∑ _p ∈ badPairs U V R t,t:=by
      apply Finset.sum_le_sum
      intro p hp
      exact (Finset.mem_filter.mp hp).2.le
    _ = ((badPairs U V R t).card:ℝ) * t:=by simp
    _ ≤ ((U ×ˢ U).card:ℝ) * t:=by
      gcongr
      exact (show badPairs U V R t ⊆ U ×ˢ U from Finset.filter_subset _ _)
    _ = _:=by simp [pow_two]; ring
theorem exists_good_neighborhood (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (hU:U.Nonempty) (hV:V.Nonempty)
    {a ε:ℝ} (ha:0 < a) (hε:0 < ε)
    (hdense:a * U.card * V.card ≤
      (((U ×ˢ V).filter (fun p => R p.1 p.2)).card:ℝ)) :
    ∃ b ∈ V,a * U.card / 2 ≤ ((leftNeighbors U R b).card:ℝ) ∧
      ((badPairs (leftNeighbors U R b) V R (ε * a ^ 2 * V.card / 4)).card:ℝ) ≤
        ε * ((leftNeighbors U R b).card:ℝ) ^ 2:=by
  classical
  let N:ℝ:=U.card
  let M:ℝ:=V.card
  let c:ℝ:=ε * a * N / 2
  let t:ℝ:=ε * a ^ 2 * M / 4
  let d:β → ℝ:=fun b => (leftNeighbors U R b).card
  let bad:β → ℝ:=fun b => (badPairs (leftNeighbors U R b) V R t).card
  let score:β → ℝ:=fun b => c * d b - bad b
  have hN:0 < N:=by dsimp [N]; exact_mod_cast hU.card_pos
  have hM:0 < M:=by dsimp [M]; exact_mod_cast hV.card_pos
  have hc:0 < c:=by dsimp [c]; positivity
  have ht:0 ≤ t:=by dsimp [t]; positivity
  have hd:a * N * M ≤ ∑ b ∈ V,d b:=by
    rw [edge_count_eq_sum_degrees] at hdense
    simpa only [Nat.cast_sum] using hdense
  have hbad:(∑ b ∈ V,bad b) ≤ t * N ^ 2 :=
    sum_badPairs_neighborhoods_le U V R ht
  have hscore:M * (c * (a * N / 2)) ≤ ∑ b ∈ V,score b:=by
    have hmul:=mul_le_mul_of_nonneg_left hd hc.le
    simp only [score,Finset.sum_sub_distrib, ← Finset.mul_sum]
    dsimp [c,t] at hmul hbad ⊢
    nlinarith
  obtain ⟨b,hb,hmax⟩:=V.exists_max_image score hV
  have hmaxsum:(∑ w ∈ V,score w) ≤ M * score b:=by
    calc
      _ ≤ ∑ _w ∈ V,score b:=Finset.sum_le_sum (fun w hw => hmax w hw)
      _ = _:=by simp [M]
  have hscoreb:c * (a * N / 2) ≤ score b :=
    le_of_mul_le_mul_left (hscore.trans hmaxsum) hM
  have hbad0:0 ≤ bad b:=Nat.cast_nonneg _
  have hd0:0 ≤ d b:=Nat.cast_nonneg _
  have hsize:a * N / 2 ≤ d b:=by
    apply le_of_mul_le_mul_left (a:=c) _ hc
    dsimp [score] at hscoreb
    linarith
  have hnonneg:0 ≤ c * (a * N / 2):=by positivity
  have hbadb:bad b ≤ c * d b:=by dsimp [score] at hscoreb; linarith
  have hcle:c ≤ ε * d b:=by
    have h:=mul_le_mul_of_nonneg_left hsize hε.le
    dsimp [c]
    nlinarith
  refine ⟨b,hb,hsize, ?_⟩
  change bad b ≤ ε * d b ^ 2
  calc
    _ ≤ c * d b:=hbadb
    _ ≤ (ε * d b) * d b:=mul_le_mul_of_nonneg_right hcle hd0
    _ = _:=by ring
end Green24Proof.DenseGraphCommonNeighbors
private def zz2497:"s09c1"="s09c1":=by decide+kernel
end 
section 
namespace Green24Proof.DenseGraphFourWalks
open scoped BigOperators
open Green24Proof.DenseGraphCommonNeighbors
variable {α β:Type*}
theorem exists_pruned_subset (S:Finset α) (Bad:α → α → Prop) [DecidableRel Bad]
    (hS:S.Nonempty)
    (hbad:(((S ×ˢ S).filter (fun p => Bad p.1 p.2)).card:ℝ) ≤
      (S.card:ℝ) ^ 2 / 8) :
    ∃ T ⊆ S,(S.card:ℝ) / 2 ≤ (T.card:ℝ) ∧
      ∀ x ∈ T,((S.filter (Bad x)).card:ℝ) ≤ (S.card:ℝ) / 4:=by
  classical
  let d:α → ℝ:=fun x => (S.filter (Bad x)).card
  let T:=S.filter (fun x => d x ≤ (S.card:ℝ) / 4)
  have hTS:T ⊆ S:=Finset.filter_subset _ _
  have hsum:(∑ x ∈ S,d x) ≤ (S.card:ℝ) ^ 2 / 8:=by
    convert hbad using 1
    simp only [d,Finset.card_filter,Finset.sum_product,Nat.cast_sum,Nat.cast_ite,
      Nat.cast_one,Nat.cast_zero]
  have hremoved:(S.card:ℝ) / 4 * ((S \ T).card:ℝ) ≤ ∑ x ∈ S,d x:=by
    calc
      _ = ∑ _x ∈ S \ T,(S.card:ℝ) / 4:=by simp [mul_comm]
      _ ≤ ∑ x ∈ S \ T,d x:=by
        apply Finset.sum_le_sum
        intro x hx
        have hxS:=(Finset.mem_sdiff.mp hx).1
        have hxT:=(Finset.mem_sdiff.mp hx).2
        have hd:¬ d x ≤ (S.card:ℝ) / 4:=by
          intro hd
          exact hxT (Finset.mem_filter.mpr ⟨hxS,hd⟩)
        exact (lt_of_not_ge hd).le
      _ ≤ _:=Finset.sum_le_sum_of_subset_of_nonneg Finset.sdiff_subset
        (fun x _ _ => Nat.cast_nonneg _)
  have hpos:(0:ℝ) < S.card:=by exact_mod_cast hS.card_pos
  have hr:((S \ T).card:ℝ) ≤ (S.card:ℝ) / 2:=by
    apply le_of_mul_le_mul_left (a:=(S.card:ℝ)) _ hpos
    nlinarith [hremoved.trans hsum]
  have hcards:((S \ T).card:ℝ) + (T.card:ℝ) = S.card:=by
    exact_mod_cast Finset.card_sdiff_add_card_eq_card hTS
  refine ⟨T,hTS,by linarith, ?_⟩
  intro x hx
  exact (Finset.mem_filter.mp hx).2
def walksFour (U:Finset α) (V:Finset β) (R:α → β → Prop) [DecidableRel R]
    (x y:α):Finset (α × β × β) :=
  (U ×ˢ (V ×ˢ V)).filter (fun p =>
    R x p.2.1 ∧ R p.1 p.2.1 ∧ R y p.2.2 ∧ R p.1 p.2.2)
theorem walksFour_card (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (x y:α) :
    (walksFour U V R x y).card =
      ∑ z ∈ U,(commonNeighbors V R x z).card * (commonNeighbors V R y z).card:=by
  simp only [walksFour,Finset.card_filter,Finset.sum_product,commonNeighbors]
  apply Finset.sum_congr rfl
  intro z hz
  rw [Finset.sum_mul_sum]
  apply Finset.sum_congr rfl
  intro b hb
  apply Finset.sum_congr rfl
  intro c hc
  by_cases h₁:R x b <;> by_cases h₂:R z b <;>
    by_cases h₃:R y c <;> by_cases h₄:R z c <;> simp [h₁,h₂,h₃,h₄]
private def zz1957:"s07a5"="s07a5":=by decide+kernel
theorem many_good_middle_vertices (S:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (t:ℝ) (x y:α)
    (hx:((S.filter (fun z => ((commonNeighbors V R x z).card:ℝ) < t)).card:ℝ) ≤
      (S.card:ℝ) / 4)
    (hy:((S.filter (fun z => ((commonNeighbors V R y z).card:ℝ) < t)).card:ℝ) ≤
      (S.card:ℝ) / 4) :
    (S.card:ℝ) / 2 ≤ ((S.filter (fun z =>
      t ≤ ((commonNeighbors V R x z).card:ℝ) ∧
      t ≤ ((commonNeighbors V R y z).card:ℝ))).card:ℝ):=by
  classical
  let X:=S.filter (fun z => ((commonNeighbors V R x z).card:ℝ) < t)
  let Y:=S.filter (fun z => ((commonNeighbors V R y z).card:ℝ) < t)
  have hsub:X ∪ Y ⊆ S:=Finset.union_subset (Finset.filter_subset _ _) (Finset.filter_subset _ _)
  have heq:S.filter (fun z => t ≤ ((commonNeighbors V R x z).card:ℝ) ∧
      t ≤ ((commonNeighbors V R y z).card:ℝ)) = S \ (X ∪ Y):=by
    ext z
    simp only [X,Y,Finset.mem_filter,Finset.mem_sdiff,Finset.mem_union, ← not_lt]
    tauto
  rw [heq]
  have hcard:((S \ (X ∪ Y)).card:ℝ) + ((X ∪ Y).card:ℝ) = S.card:=by
    exact_mod_cast Finset.card_sdiff_add_card_eq_card hsub
  have hu:((X ∪ Y).card:ℝ) ≤ (X.card:ℝ) + Y.card:=by
    exact_mod_cast Finset.card_union_le X Y
  change (X.card:ℝ) ≤ (S.card:ℝ) / 4 at hx
  change (Y.card:ℝ) ≤ (S.card:ℝ) / 4 at hy
  linarith
theorem walksFour_card_lower (U S:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (hSU:S ⊆ U) {t:ℝ} (ht:0 ≤ t)
    (x y:α)
    (hx:((S.filter (fun z => ((commonNeighbors V R x z).card:ℝ) < t)).card:ℝ) ≤
      (S.card:ℝ) / 4)
    (hy:((S.filter (fun z => ((commonNeighbors V R y z).card:ℝ) < t)).card:ℝ) ≤
      (S.card:ℝ) / 4) :
    (S.card:ℝ) / 2 * t ^ 2 ≤ (walksFour U V R x y).card:=by
  classical
  let Z:=S.filter (fun z => t ≤ ((commonNeighbors V R x z).card:ℝ) ∧
    t ≤ ((commonNeighbors V R y z).card:ℝ))
  have hZ:=many_good_middle_vertices S V R t x y hx hy
  have hZU:Z ⊆ U:=(Finset.filter_subset _ _).trans hSU
  calc
    _ ≤ (Z.card:ℝ) * t ^ 2:=mul_le_mul_of_nonneg_right hZ (sq_nonneg _)
    _ = ∑ _z ∈ Z,t ^ 2:=by simp
    _ ≤ ∑ z ∈ Z,((commonNeighbors V R x z).card:ℝ) * (commonNeighbors V R y z).card:=by
      apply Finset.sum_le_sum
      intro z hz
      have hgood:=(Finset.mem_filter.mp hz).2
      simpa only [pow_two] using mul_le_mul hgood.1 hgood.2 ht (Nat.cast_nonneg _)
    _ ≤ ∑ z ∈ U,((commonNeighbors V R x z).card:ℝ) * (commonNeighbors V R y z).card :=
      Finset.sum_le_sum_of_subset_of_nonneg hZU (fun z _ _ => by positivity)
    _ = _:=by rw [walksFour_card]; push_cast; rfl
theorem exists_many_four_walks (U:Finset α) (V:Finset β)
    (R:α → β → Prop) [DecidableRel R] (hU:U.Nonempty) (hV:V.Nonempty)
    {a:ℝ} (ha:0 < a)
    (hdense:a * U.card * V.card ≤
      (((U ×ˢ V).filter (fun p => R p.1 p.2)).card:ℝ)) :
    ∃ T ⊆ U,a * U.card / 4 ≤ (T.card:ℝ) ∧
      ∀ x ∈ T, ∀ y ∈ T,
        a ^ 5 * U.card * (V.card:ℝ) ^ 2 / 0x1000 ≤ (walksFour U V R x y).card:=by
  classical
  obtain ⟨b,_,hsize,hbad⟩:=exists_good_neighborhood U V R hU hV ha
    (by norm_num:(0:ℝ) < 1 / 8) hdense
  let S:=leftNeighbors U R b
  let t:ℝ:=(1 / 8) * a ^ 2 * V.card / 4
  have hS:S.Nonempty:=by
    apply Finset.card_pos.mp
    have hUpos:(0:ℝ) < U.card:=by exact_mod_cast hU.card_pos
    have hpos:(0:ℝ) < S.card:=lt_of_lt_of_le (by positivity) hsize
    exact_mod_cast hpos
  obtain ⟨T,hTS,hTsize,hTgood⟩:=exists_pruned_subset S
    (fun x z => ((commonNeighbors V R x z).card:ℝ) < t) hS (by
      simpa only [badPairs,S,t,one_div_mul_eq_div] using hbad)
  refine ⟨T,hTS.trans (Finset.filter_subset _ _),by linarith, ?_⟩
  intro x hx y hy
  have hpaths:=walksFour_card_lower U S V R (Finset.filter_subset _ _) (by dsimp [t]; positivity)
    x y (hTgood x hx) (hTgood y hy)
  calc
    _ = (a * U.card / 2) / 2 * t ^ 2:=by dsimp [t]; ring
    _ ≤ (S.card:ℝ) / 2 * t ^ 2:=by gcongr
    _ ≤ _:=hpaths
end Green24Proof.DenseGraphFourWalks
private def zz2498:"s09c2"="s09c2":=by decide+kernel
end 
section 
namespace Green24Proof.RestrictedSumDifferenceBound
open scoped BigOperators Pointwise
open Green24Proof.DenseGraphFourWalks
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
def quadruples (S:Finset G):Finset (G × G × G × G):=S ×ˢ (S ×ˢ (S ×ˢ S))
def alternatingSum (p:G × G × G × G):G:=p.1 - p.2.1 + p.2.2.1 - p.2.2.2
def representations (S:Finset G) (d:G):Finset (G × G × G × G) :=
  (quadruples S).filter (fun p => alternatingSum p = d)
theorem walks_card_le_representations (U V S:Finset G) (x y:G) :
    (walksFour U V (fun a b => a + b ∈ S) x y).card ≤ (representations S (x - y)).card:=by
  refine Finset.card_le_card_of_injOn
    (fun p:G × G × G => (x + p.2.1,p.1 + p.2.1,p.1 + p.2.2,y + p.2.2)) ?_ ?_
  · rintro ⟨z,b,c⟩ hp
    change (z,b,c) ∈ walksFour U V (fun a b => a + b ∈ S) x y at hp
    change (x + b,z + b,z + c,y + c) ∈ representations S (x - y)
    simp only [walksFour,Finset.mem_filter,Finset.mem_product] at hp
    apply Finset.mem_filter.mpr
    constructor
    · exact Finset.mem_product.mpr ⟨hp.2.1,Finset.mem_product.mpr
        ⟨hp.2.2.1,Finset.mem_product.mpr ⟨hp.2.2.2.2,hp.2.2.2.1⟩⟩⟩
    · change (x + b) - (z + b) + (z + c) - (y + c) = x - y
      abel
  · rintro ⟨z,b,c⟩ _ ⟨z',b',c'⟩ _ heq
    simp only [Prod.mk.injEq] at heq
    have hb:b = b':=add_left_cancel heq.1
    have hz:z = z':=add_right_cancel (hb ▸ heq.2.1)
    have hc:c = c':=add_left_cancel (hz ▸ heq.2.2.1)
    exact Prod.ext hz (Prod.ext hb hc)
private def zz1958:"s07a6"="s07a6":=by decide+kernel
theorem sum_representations_le (S D:Finset G) :
    (∑ d ∈ D,(representations S d).card) ≤ S.card ^ 4:=by
  unfold representations
  rw [Finset.sum_card_fiberwise_eq_card_filter]
  calc
    _ ≤ (quadruples S).card:=Finset.card_filter_le _ _
    _ = _:=by simp [quadruples]; ring
theorem difference_card_mul_le (U V S T:Finset G) (P:ℝ)
    (hwalks:∀ x ∈ T, ∀ y ∈ T,
      P ≤ ((walksFour U V (fun a b => a + b ∈ S) x y).card:ℝ)) :
    ((T - T).card:ℝ) * P ≤ (S.card:ℝ) ^ 4:=by
  have hfiber:∀ d ∈ T - T,P ≤ ((representations S d).card:ℝ):=by
    intro d hd
    obtain ⟨x,hx,y,hy,rfl⟩:=Finset.mem_sub.mp hd
    exact (hwalks x hx y hy).trans (by exact_mod_cast walks_card_le_representations U V S x y)
  calc
    _ = ∑ _d ∈ T - T,P:=by simp
    _ ≤ ∑ d ∈ T - T,((representations S d).card:ℝ):=Finset.sum_le_sum hfiber
    _ ≤ _:=by exact_mod_cast sum_representations_le S (T - T)
theorem exists_subset_small_difference (U V S:Finset G) (hU:U.Nonempty) (hV:V.Nonempty)
    {a:ℝ} (ha:0 < a)
    (hdense:a * U.card * V.card ≤
      (((U ×ˢ V).filter (fun p => p.1 + p.2 ∈ S)).card:ℝ)) :
    ∃ T ⊆ U,a * U.card / 4 ≤ (T.card:ℝ) ∧
      ((T - T).card:ℝ) * (a ^ 5 * U.card * (V.card:ℝ) ^ 2 / 0x1000) ≤
        (S.card:ℝ) ^ 4:=by
  obtain ⟨T,hTU,hTcard,hwalks⟩ :=
    exists_many_four_walks U V (fun a b => a + b ∈ S) hU hV ha hdense
  exact ⟨T,hTU,hTcard,difference_card_mul_le U V S T _ hwalks⟩
end Green24Proof.RestrictedSumDifferenceBound
private def zz2499:"s09c3"="s09c3":=by decide+kernel
end 
section 
namespace Green24Proof.SelfEnergyBSG
open scoped Pointwise
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
theorem exists_large_subset_difference_bound (A:Finset G) (hA:A.Nonempty)
    {η:ℝ} (hη:0 < η)
    (hE:η * (A.card:ℝ) ^ 3 ≤ (A.addEnergy A:ℝ)) :
    ∃ T ⊆ A,η * A.card / 8 ≤ (T.card:ℝ) ∧
      ((T - T).card:ℝ) ≤ 0x200000 * A.card / η ^ 9:=by
  obtain ⟨S,_hSA,hScard,hdense,_hpopular⟩ :=
    Green24Proof.PopularSums.exists_popular_sums A hA η hη hE
  have hdense':(η / 2) * A.card * A.card ≤
      (((A ×ˢ A).filter (fun p => p.1 + p.2 ∈ S)).card:ℝ):=by
    convert hdense using 1
    ring
  obtain ⟨T,hTA,hTcard,hTdiff⟩ :=
    Green24Proof.RestrictedSumDifferenceBound.exists_subset_small_difference
      A A S hA hA (by positivity:0 < η / 2) hdense'
  have hN:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  have hp:0 < (η / 2) ^ 5 * A.card * (A.card:ℝ) ^ 2 / 0x1000:=by positivity
  have hS4:(S.card:ℝ) ^ 4 ≤ (2 * A.card / η) ^ 4:=by
    gcongr
  refine ⟨T,hTA, ?_, ?_⟩
  · convert hTcard using 1
    ring
  · calc
      ((T - T).card:ℝ) ≤
          (2 * A.card / η) ^ 4 /
            ((η / 2) ^ 5 * A.card * (A.card:ℝ) ^ 2 / 0x1000) :=
        (le_div_iff₀ hp).2 (hTdiff.trans hS4)
      _ = 0x200000 * A.card / η ^ 9:=by
        field_simp
        ring
private def zz1959:"s07a7"="s07a7":=by decide+kernel
theorem exists_large_subset_small_difference (A:Finset G) (hA:A.Nonempty)
    {η:ℝ} (hη:0 < η)
    (hE:η * (A.card:ℝ) ^ 3 ≤ (A.addEnergy A:ℝ)) :
    ∃ T ⊆ A,T.Nonempty ∧ η * A.card / 8 ≤ (T.card:ℝ) ∧
      ((T - T).card:ℝ) ≤ (0x1000000 / η ^ 10) * T.card:=by
  obtain ⟨T,hTA,hTcard,hTdiff⟩ :=
    exists_large_subset_difference_bound A hA hη hE
  have hN:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  have hTpos:(0:ℝ) < T.card:=lt_of_lt_of_le (by positivity) hTcard
  have hT:T.Nonempty:=Finset.card_pos.mp (by exact_mod_cast hTpos)
  have hNbound:(A.card:ℝ) ≤ 8 * T.card / η:=by
    apply (le_div_iff₀ hη).2
    linarith
  refine ⟨T,hTA,hT,hTcard,hTdiff.trans ?_⟩
  calc
    0x200000 * A.card / η ^ 9 ≤ 0x200000 * (8 * T.card / η) / η ^ 9:=by
      gcongr
    _ = (0x1000000 / η ^ 10) * T.card:=by
      field_simp
      ring
theorem exists_uniform_constants {η:ℝ} (hη:0 < η) :
    ∃ c K:ℝ,0 < c ∧ 0 < K ∧
      ∀ A:Finset G,A.Nonempty →
        η * (A.card:ℝ) ^ 3 ≤ (A.addEnergy A:ℝ) →
        ∃ T ⊆ A,T.Nonempty ∧ c * A.card ≤ (T.card:ℝ) ∧
          ((T - T).card:ℝ) ≤ K * T.card:=by
  refine ⟨η / 8,0x1000000 / η ^ 10,by positivity,by positivity, ?_⟩
  intro A hA hE
  obtain ⟨T,hTA,hT,hTcard,hTdiff⟩ :=
    exists_large_subset_small_difference A hA hη hE
  refine ⟨T,hTA,hT, ?_,hTdiff⟩
  convert hTcard using 1
  ring
end Green24Proof.SelfEnergyBSG
private def zz2500:"s09c4"="s09c4":=by decide+kernel
end 
section 
namespace Green24Proof.FiniteEnergyPeeling
open scoped BigOperators Pointwise
section Finite
variable {α:Type*} [DecidableEq α]
theorem exists_disjoint_peeling (A:Finset α) (Bad Good:Finset α → Prop) (μ:ℝ)
    (hextract:∀ Q ⊆ A,Bad Q →
      ∃ B ⊆ Q,B.Nonempty ∧ μ ≤ (B.card:ℝ) ∧ Good B) :
    ∃ (P:List (Finset α)) (R:Finset α),
      R ⊆ A ∧ ¬ Bad R ∧
      (∀ B ∈ P,B ⊆ A ∧ B.Nonempty ∧ μ ≤ (B.card:ℝ) ∧ Good B) ∧
      P.Pairwise Disjoint ∧ (∀ B ∈ P,Disjoint B R) ∧
      P.foldr (fun B C => B ∪ C) R = A ∧
      (P.map Finset.card).sum + R.card = A.card:=by
  classical
  have aux (Q:Finset α):Q ⊆ A →
      ∃ (P:List (Finset α)) (R:Finset α),
        R ⊆ Q ∧ ¬ Bad R ∧
        (∀ B ∈ P,B ⊆ Q ∧ B.Nonempty ∧ μ ≤ (B.card:ℝ) ∧ Good B) ∧
        P.Pairwise Disjoint ∧ (∀ B ∈ P,Disjoint B R) ∧
        P.foldr (fun B C => B ∪ C) R = Q ∧
        (P.map Finset.card).sum + R.card = Q.card:=by
    refine Finset.strongInductionOn Q ?_
    intro Q ih hQA
    by_cases hbad:Bad Q
    · obtain ⟨B,hBQ,hB,hμB,hgoodB⟩:=hextract Q hQA hbad
      have hproper:Q \ B ⊂ Q:=by
        refine Finset.ssubset_iff_subset_ne.mpr ⟨Finset.sdiff_subset, ?_⟩
        intro heq
        obtain ⟨b,hb⟩:=hB
        have hmem:b ∈ Q \ B:=heq.symm ▸ hBQ hb
        exact (Finset.mem_sdiff.mp hmem).2 hb
      obtain ⟨P,R,hRQ,hnot,hpieces,hpair,hdisj,hcover,hmass⟩ :=
        ih (Q \ B) hproper (Finset.sdiff_subset.trans hQA)
      have hBdisj (C:Finset α) (hC:C ⊆ Q \ B):Disjoint B C:=by
        apply Finset.disjoint_left.mpr
        intro x hxB hxC
        exact (Finset.mem_sdiff.mp (hC hxC)).2 hxB
      refine ⟨B :: P,R,hRQ.trans Finset.sdiff_subset,hnot, ?_, ?_, ?_, ?_, ?_⟩
      · intro C hC
        rcases List.mem_cons.mp hC with rfl | hC
        · exact ⟨hBQ,hB,hμB,hgoodB⟩
        · obtain ⟨hCQ,hCne,hμC,hgoodC⟩:=hpieces C hC
          exact ⟨hCQ.trans Finset.sdiff_subset,hCne,hμC,hgoodC⟩
      · exact List.pairwise_cons.mpr ⟨fun C hC => hBdisj C (hpieces C hC).1,hpair⟩
      · intro C hC
        rcases List.mem_cons.mp hC with rfl | hC
        · exact hBdisj R hRQ
        · exact hdisj C hC
      · change B ∪ P.foldr (fun B C => B ∪ C) R = Q
        rw [hcover]
        exact Finset.union_sdiff_of_subset hBQ
      · simp only [List.map_cons,List.sum_cons]
        have hcard:=Finset.card_sdiff_add_card_eq_card hBQ
        omega
    · exact ⟨[],Q,Finset.Subset.refl Q,hbad,by simp,by simp,
        by simp,rfl,by simp⟩
  exact aux A (Finset.Subset.refl A)
omit [DecidableEq α] in
theorem length_mul_le_card_sum (P:List (Finset α)) (μ:ℝ)
    (hμ:∀ B ∈ P,μ ≤ (B.card:ℝ)) :
    (P.length:ℝ) * μ ≤ ((P.map Finset.card).sum:ℝ):=by
  induction P with
  | nil => simp
  | cons B P ih =>
    have hB:=hμ B (by simp)
    have hP:=ih (fun C hC => hμ C (by simp [hC]))
    simp only [List.length_cons,Nat.cast_add,Nat.cast_one,List.map_cons,List.sum_cons]
    nlinarith
end Finite
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
private def zz1960:"s07a8"="s07a8":=by decide+kernel
theorem self_energy_le_card_cube (A:Finset G) :
    (A.addEnergy A:ℝ) ≤ (A.card:ℝ) ^ 3:=by
  have henergy:(A.addEnergy A:ℝ) =
      ∑ s ∈ A + A,(A.addConvolution A s:ℝ) ^ 2:=by
    dsimp [Finset.addConvolution]
    exact_mod_cast Finset.addEnergy_eq_sum_sq' A A
  rw [henergy]
  calc
    _ ≤ ∑ s ∈ A + A,(A.card:ℝ) * A.addConvolution A s:=by
      apply Finset.sum_le_sum
      intro s _hs
      have h:(A.addConvolution A s:ℝ) ≤ A.card:=by
        exact_mod_cast (Finset.addConvolution_le_card_left (A:=A) (B:=A) (x:=s))
      nlinarith [mul_nonneg (sub_nonneg.mpr h)
        (show (0:ℝ) ≤ A.addConvolution A s by positivity)]
    _ = (A.card:ℝ) ^ 3:=by
      rw [← Finset.mul_sum]
      have hsum:(∑ s ∈ A + A,(A.addConvolution A s:ℝ)) = (A.card:ℝ) ^ 2:=by
        exact_mod_cast Green24Proof.PopularSums.sum_addConvolution A
      rw [hsum]
      ring
theorem exists_energy_partition (A:Finset G) (hA:A.Nonempty)
    {δ:ℝ} (hδ:0 < δ) :
    ∃ (P:List (Finset G)) (R:Finset G),
      R ⊆ A ∧ (R.addEnergy R:ℝ) < δ * (A.card:ℝ) ^ 3 ∧
      (∀ B ∈ P,B ⊆ A ∧ B.Nonempty ∧
        δ ^ 2 * A.card / 8 ≤ (B.card:ℝ) ∧
        ((B - B).card:ℝ) ≤ (0x1000000 / δ ^ 10) * B.card) ∧
      P.Pairwise Disjoint ∧ (∀ B ∈ P,Disjoint B R) ∧
      P.foldr (fun B C => B ∪ C) R = A ∧
      (P.length:ℝ) ≤ 8 / δ ^ 2:=by
  have hN:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  let Bad:Finset G → Prop:=fun Q => δ * (A.card:ℝ) ^ 3 ≤ (Q.addEnergy Q:ℝ)
  let Good:Finset G → Prop:=fun B =>
    ((B - B).card:ℝ) ≤ (0x1000000 / δ ^ 10) * B.card
  let μ:ℝ:=δ ^ 2 * A.card / 8
  have hextract:∀ Q ⊆ A,Bad Q →
      ∃ B ⊆ Q,B.Nonempty ∧ μ ≤ (B.card:ℝ) ∧ Good B:=by
    intro Q hQA hbad
    have hQcard:(Q.card:ℝ) ≤ A.card:=by exact_mod_cast Finset.card_le_card hQA
    have hQupper:(Q.addEnergy Q:ℝ) ≤ (Q.card:ℝ) * (A.card:ℝ) ^ 2:=by
      calc
        _ ≤ (Q.card:ℝ) ^ 3:=self_energy_le_card_cube Q
        _ = (Q.card:ℝ) * (Q.card:ℝ) ^ 2:=by ring
        _ ≤ _:=by gcongr
    have hQlower:δ * A.card ≤ (Q.card:ℝ):=by
      apply (mul_le_mul_iff_right₀ (sq_pos_of_pos hN)).mp
      calc
        (A.card:ℝ) ^ 2 * (δ * A.card) = δ * (A.card:ℝ) ^ 3:=by ring
        _ ≤ (Q.card:ℝ) * (A.card:ℝ) ^ 2:=hbad.trans hQupper
        _ = (A.card:ℝ) ^ 2 * Q.card:=by ring
    have hQpos:(0:ℝ) < Q.card:=lt_of_lt_of_le (by positivity) hQlower
    have hQ:Q.Nonempty:=Finset.card_pos.mp (by exact_mod_cast hQpos)
    have hrelative:δ * (Q.card:ℝ) ^ 3 ≤ (Q.addEnergy Q:ℝ):=by
      calc
        _ ≤ δ * (A.card:ℝ) ^ 3:=by gcongr
        _ ≤ _:=hbad
    obtain ⟨B,hBQ,hB,hBsize,hBdiff⟩ :=
      Green24Proof.SelfEnergyBSG.exists_large_subset_small_difference Q hQ hδ hrelative
    refine ⟨B,hBQ,hB, ?_,hBdiff⟩
    calc
      μ = δ * (δ * A.card) / 8:=by dsimp [μ]; ring
      _ ≤ δ * Q.card / 8:=by gcongr
      _ ≤ _:=hBsize
  obtain ⟨P,R,hRA,hnot,hpieces,hpair,hdisj,hcover,hmass⟩ :=
    exists_disjoint_peeling A Bad Good μ hextract
  refine ⟨P,R,hRA,lt_of_not_ge hnot,hpieces,hpair,hdisj,hcover, ?_⟩
  have hmass_bound:((P.map Finset.card).sum:ℝ) ≤ A.card:=by
    exact_mod_cast (show (P.map Finset.card).sum ≤ A.card by omega)
  have hlength:=(length_mul_le_card_sum P μ (fun B hB => (hpieces B hB).2.2.1)).trans
    hmass_bound
  apply (le_div_iff₀ (sq_pos_of_pos hδ)).2
  apply (mul_le_mul_iff_right₀ hN).mp
  dsimp [μ] at hlength
  nlinarith
end Green24Proof.FiniteEnergyPeeling
private def zz2501:"s09c5"="s09c5":=by decide+kernel
end 
section 
namespace Green24Proof.EnergyOverlapMerge
open scoped BigOperators Pointwise
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
def differenceFiber (A B:Finset G) (x:G):Finset (G × G) :=
  (A ×ˢ B).filter (fun p => p.1 - p.2 = x)
theorem energy_eq_difference_count (A B:Finset G) :
    Finset.addEnergy A B =
      (((A ×ˢ B) ×ˢ (A ×ˢ B)).filter
        (fun p => p.1.1 - p.1.2 = p.2.1 - p.2.2)).card:=by
  unfold Finset.addEnergy
  refine Finset.card_bij (fun p _ => ((p.1.1,p.2.2),(p.1.2,p.2.1))) ?_ ?_ ?_
  · rintro ⟨⟨a,c⟩,b,d⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    exact ⟨⟨⟨hp.1.1.1,hp.1.2.2⟩,hp.1.1.2,hp.1.2.1⟩,
      sub_eq_sub_iff_add_eq_add.mpr hp.2⟩
  · rintro ⟨⟨a,c⟩,b,d⟩ _ ⟨⟨a',c'⟩,b',d'⟩ _ heq
    simp only [Prod.mk.injEq] at heq ⊢
    exact ⟨⟨heq.1.1,heq.2.1⟩,heq.2.2,heq.1.2⟩
  · rintro ⟨⟨a,d⟩,c,b⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    refine ⟨((a,c),b,d), ?_,rfl⟩
    simp only [Finset.mem_filter,Finset.mem_product]
    exact ⟨⟨⟨hp.1.1.1,hp.1.2.1⟩,hp.1.2.2,hp.1.1.2⟩,
      sub_eq_sub_iff_add_eq_add.mp hp.2⟩
theorem energy_eq_sum_differenceFiber (A B:Finset G) :
    Finset.addEnergy A B = ∑ p ∈ A ×ˢ B,(differenceFiber A B (p.1 - p.2)).card:=by
  rw [energy_eq_difference_count]
  simp only [Finset.card_filter,Finset.sum_product,differenceFiber]
  simp only [eq_comm]
private def zz1961:"s07a9"="s07a9":=by decide+kernel
theorem differenceFiber_card (A B:Finset G) (x:G) :
    (differenceFiber A B x).card = (A ∩ (B + {x})).card:=by
  refine Finset.card_bij (fun p _ => p.1) ?_ ?_ ?_
  · rintro ⟨a,b⟩ hp
    simp only [differenceFiber,Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨⟨ha,hb⟩,hab⟩:=hp
    refine Finset.mem_inter.mpr ⟨ha,Finset.mem_add.mpr ⟨b,hb,x,by simp, ?_⟩⟩
    dsimp at hab ⊢
    rw [← hab]
    abel
  · rintro ⟨a,b⟩ hp ⟨a',b'⟩ hp' heq
    obtain ⟨_,hab⟩:=Finset.mem_filter.mp hp
    obtain ⟨_,hab'⟩:=Finset.mem_filter.mp hp'
    dsimp at hab hab' heq
    have hb:b = b':=sub_right_inj.mp (heq ▸ hab.trans hab'.symm)
    exact Prod.ext heq hb
  · intro a ha
    obtain ⟨haA,haB⟩:=Finset.mem_inter.mp ha
    obtain ⟨b,hb,y,hy,hby⟩:=Finset.mem_add.mp haB
    have hyx:y = x:=Finset.mem_singleton.mp hy
    subst y
    refine ⟨(a,b),Finset.mem_filter.mpr ⟨Finset.mem_product.mpr ⟨haA,hb⟩, ?_⟩,rfl⟩
    dsimp
    rw [← hby]
    abel
theorem exists_large_overlap (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty) :
    ∃ x:G,Finset.addEnergy A B ≤ A.card * B.card * (A ∩ (B + {x})).card:=by
  obtain ⟨x,hx,hmax⟩:=(A - B).exists_max_image
    (fun y => (differenceFiber A B y).card) (hA.sub hB)
  refine ⟨x, ?_⟩
  rw [energy_eq_sum_differenceFiber, ← differenceFiber_card]
  calc
    _ ≤ ∑ _p ∈ A ×ˢ B,(differenceFiber A B x).card:=by
      apply Finset.sum_le_sum
      intro p hp
      exact hmax _ (Finset.sub_mem_sub (Finset.mem_product.mp hp).1 (Finset.mem_product.mp hp).2)
    _ = _:=by simp
theorem sub_translate_right (A B:Finset G) (x:G) :
    A - (B + {x}) = (A - B).image (fun y => y - x):=by
  ext y
  constructor
  · intro hy
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hy
    obtain ⟨c,hc,z,hz,rfl⟩:=Finset.mem_add.mp hb
    have hzx:z = x:=Finset.mem_singleton.mp hz
    subst z
    exact Finset.mem_image.mpr ⟨a - c,Finset.sub_mem_sub ha hc,by abel⟩
  · intro hy
    obtain ⟨z,hz,rfl⟩:=Finset.mem_image.mp hy
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hz
    exact Finset.mem_sub.mpr ⟨a,ha,b + x,Finset.add_mem_add hb (by simp),by abel⟩
theorem cross_difference_mul_energy_le (A B:Finset G)
    (hA:A.Nonempty) (hB:B.Nonempty) :
    (A - B).card * Finset.addEnergy A B ≤
      (A - A).card * (B - B).card * (A.card * B.card):=by
  obtain ⟨x,hx⟩:=exists_large_overlap A B hA hB
  let S:=A ∩ (B + {x})
  have htriangle:=Finset.ruzsa_triangle_inequality_sub_sub_sub A S B
  have hAS:(A - S).card ≤ (A - A).card :=
    Finset.card_le_card (Finset.sub_subset_sub (fun _ h => h) Finset.inter_subset_left)
  have hBS:(B - S).card ≤ (B - B).card:=by
    have hsub:(B - S).card ≤ (B - (B + {x})).card :=
      Finset.card_le_card (Finset.sub_subset_sub (fun _ h => h) Finset.inter_subset_right)
    rw [sub_translate_right,Finset.card_image_of_injective _ (fun a b h => sub_left_inj.mp h)] at hsub
    exact hsub
  have htriangle':(A - B).card * S.card ≤ (A - A).card * (B - B).card :=
    htriangle.trans (Nat.mul_le_mul hAS hBS)
  calc
    _ ≤ (A - B).card * (A.card * B.card * S.card):=Nat.mul_le_mul_left _ hx
    _ = ((A - B).card * S.card) * (A.card * B.card):=by ac_rfl
    _ ≤ _:=Nat.mul_le_mul_right _ htriangle'
private def zz1962:"s07aa"="s07aa":=by decide+kernel
theorem card_sub_comm (A B:Finset G):(A - B).card = (B - A).card:=by
  refine Finset.card_bij (fun x _ => -x) ?_ ?_ ?_
  · intro x hx
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hx
    exact Finset.mem_sub.mpr ⟨b,hb,a,ha,by abel⟩
  · exact fun _ _ _ _ h => neg_injective h
  · intro x hx
    obtain ⟨b,hb,a,ha,rfl⟩:=Finset.mem_sub.mp hx
    exact ⟨a - b,Finset.sub_mem_sub ha hb,by abel⟩
theorem union_difference_card_le (A B:Finset G) :
    ((A ∪ B) - (A ∪ B)).card ≤
      (A - A).card + (B - B).card + 2 * (A - B).card:=by
  rw [Finset.union_sub,Finset.sub_union,Finset.sub_union]
  have h₁:=Finset.card_union_le (A - A ∪ (A - B)) (B - A ∪ (B - B))
  have h₂:=Finset.card_union_le (A - A) (A - B)
  have h₃:=Finset.card_union_le (B - A) (B - B)
  rw [← card_sub_comm A B] at h₃
  omega
theorem union_difference_mul_energy_le (A B:Finset G)
    (hA:A.Nonempty) (hB:B.Nonempty) :
    ((A ∪ B) - (A ∪ B)).card * Finset.addEnergy A B ≤
      ((A - A).card + (B - B).card) * Finset.addEnergy A B +
        2 * ((A - A).card * (B - B).card * (A.card * B.card)):=by
  have h₁:=Nat.mul_le_mul_right (Finset.addEnergy A B) (union_difference_card_le A B)
  have h₂:=Nat.mul_le_mul_left 2 (cross_difference_mul_energy_le A B hA hB)
  calc
    _ ≤ ((A - A).card + (B - B).card + 2 * (A - B).card) *
        Finset.addEnergy A B:=h₁
    _ = ((A - A).card + (B - B).card) * Finset.addEnergy A B +
        2 * ((A - B).card * Finset.addEnergy A B):=by
      simp only [add_mul,mul_assoc]
    _ ≤ _:=Nat.add_le_add_left h₂ _
theorem union_small_difference_of_high_energy (A B:Finset G)
    (hA:A.Nonempty) (hB:B.Nonempty) {K η:ℝ} (hK:0 ≤ K) (hη:0 < η)
    (hDA:((A - A).card:ℝ) ≤ K * A.card)
    (hDB:((B - B).card:ℝ) ≤ K * B.card)
    (hE:η * ((A ∪ B).card:ℝ) ^ 3 ≤ Finset.addEnergy A B) :
    (((A ∪ B) - (A ∪ B)).card:ℝ) ≤
      (2 * K + 2 * K ^ 2 / η) * (A ∪ B).card:=by
  let N:ℝ:=(A ∪ B).card
  have hN:0 < N:=by
    dsimp [N]
    exact_mod_cast (hA.mono (Finset.subset_union_left:A ⊆ A ∪ B)).card_pos
  have ha:(A.card:ℝ) ≤ N:=by
    dsimp [N]
    exact_mod_cast Finset.card_le_card (Finset.subset_union_left:A ⊆ A ∪ B)
  have hb:(B.card:ℝ) ≤ N:=by
    dsimp [N]
    exact_mod_cast Finset.card_le_card (Finset.subset_union_right:B ⊆ A ∪ B)
  have hDA':((A - A).card:ℝ) ≤ K * N:=hDA.trans (mul_le_mul_of_nonneg_left ha hK)
  have hDB':((B - B).card:ℝ) ≤ K * N:=hDB.trans (mul_le_mul_of_nonneg_left hb hK)
  have hcross:((A - B).card:ℝ) * Finset.addEnergy A B ≤
      ((A - A).card:ℝ) * (B - B).card * (A.card * (B.card:ℝ)):=by
    exact_mod_cast cross_difference_mul_energy_le A B hA hB
  have hprod:((A - A).card:ℝ) * (B - B).card * (A.card * (B.card:ℝ)) ≤
      (K * N) * (K * N) * (N * N):=by
    gcongr
  have hcross':((A - B).card:ℝ) * η ≤ K ^ 2 * N:=by
    apply le_of_mul_le_mul_right (a:=N ^ 3) _ (pow_pos hN 3)
    calc
      _ = ((A - B).card:ℝ) * (η * N ^ 3):=by ring
      _ ≤ ((A - B).card:ℝ) * Finset.addEnergy A B :=
        mul_le_mul_of_nonneg_left hE (Nat.cast_nonneg _)
      _ ≤ (K * N) * (K * N) * (N * N):=hcross.trans hprod
      _ = _:=by ring
  have hcross'':((A - B).card:ℝ) ≤ K ^ 2 * N / η :=
    (le_div_iff₀ hη).mpr hcross'
  have hu:(((A ∪ B) - (A ∪ B)).card:ℝ) ≤
      ((A - A).card:ℝ) + (B - B).card + 2 * (A - B).card:=by
    exact_mod_cast union_difference_card_le A B
  calc
    _ ≤ K * N + K * N + 2 * (K ^ 2 * N / η):=by linarith
    _ = _:=by ring
end Green24Proof.EnergyOverlapMerge
private def zz2502:"s09c6"="s09c6":=by decide+kernel
end 
section 
namespace Green24Proof.EnergyAgglomeration
open scoped Pointwise
noncomputable def growthStep (θ K:ℝ):ℝ:=2 * K + 2 * K ^ 2 / θ
noncomputable def growthBound (θ:ℝ):ℕ → ℝ → ℝ
  | 0,K => K
  | n + 1,K => growthBound θ n (growthStep θ K)
private def zz1963:"s07ab"="s07ab":=by decide+kernel
theorem growthStep_ge {θ K:ℝ} (hθ:0 < θ) (hK:0 ≤ K):K ≤ growthStep θ K:=by
  dsimp [growthStep]
  have h:0 ≤ 2 * K ^ 2 / θ:=by positivity
  linarith
theorem growthBound_ge {θ K:ℝ} (hθ:0 < θ) (hK:0 ≤ K) (n:ℕ) :
    K ≤ growthBound θ n K:=by
  induction n generalizing K with
  | zero => exact le_rfl
  | succ n ih =>
    exact (growthStep_ge hθ hK).trans (ih (hK.trans (growthStep_ge hθ hK)))
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
def ControlledFamily (A R:Finset G) (μ K:ℝ) (P:Finset (Finset G)):Prop :=
  (∀ B ∈ P,B ⊆ A ∧ B.Nonempty ∧ μ ≤ (B.card:ℝ) ∧
    ((B - B).card:ℝ) ≤ K * B.card ∧ Disjoint B R) ∧
  (P:Set (Finset G)).Pairwise Disjoint ∧ P.biUnion id ∪ R = A
def mergeFamily (P:Finset (Finset G)) (B C:Finset G):Finset (Finset G) :=
  insert (B ∪ C) ((P.erase B).erase C)
theorem controlledFamily_mono {A R:Finset G} {μ K L:ℝ} {P:Finset (Finset G)}
    (h:ControlledFamily A R μ K P) (hKL:K ≤ L):ControlledFamily A R μ L P:=by
  refine ⟨?_,h.2⟩
  intro B hB
  obtain ⟨hBA,hBne,hμB,hDB,hBR⟩:=h.1 B hB
  exact ⟨hBA,hBne,hμB,hDB.trans (mul_le_mul_of_nonneg_right hKL (Nat.cast_nonneg _)),hBR⟩
omit [AddCommGroup G] in
theorem mergeFamily_union (P:Finset (Finset G)) (B C:Finset G)
    (hB:B ∈ P) (hC:C ∈ P) :
    (mergeFamily P B C).biUnion id = P.biUnion id:=by
  ext x
  simp only [mergeFamily,Finset.biUnion_insert,id_eq,Finset.mem_union,
    Finset.mem_biUnion,Finset.mem_erase]
  constructor
  · rintro ((hxB | hxC) | ⟨D,⟨_hDC,_hDB,hD⟩,hxD⟩)
    · exact ⟨B,hB,hxB⟩
    · exact ⟨C,hC,hxC⟩
    · exact ⟨D,hD,hxD⟩
  · rintro ⟨D,hD,hxD⟩
    by_cases hDB:D = B
    · exact Or.inl (Or.inl (hDB ▸ hxD))
    by_cases hDC:D = C
    · exact Or.inl (Or.inr (hDC ▸ hxD))
    · exact Or.inr ⟨D,⟨hDC,hDB,hD⟩,hxD⟩
private def zz1964:"s07ac"="s07ac":=by decide+kernel
omit [AddCommGroup G] in
theorem mergeFamily_card_lt (P:Finset (Finset G)) (B C:Finset G)
    (hB:B ∈ P) (hC:C ∈ P) (hBC:B ≠ C) (hBne:B.Nonempty)
    (hpair:(P:Set (Finset G)).Pairwise Disjoint) :
    (mergeFamily P B C).card < P.card:=by
  have hC':C ∈ P.erase B:=Finset.mem_erase.mpr ⟨hBC.symm,hC⟩
  have hnew:B ∪ C ∉ (P.erase B).erase C:=by
    intro hmem
    obtain ⟨_,hmem⟩:=Finset.mem_erase.mp hmem
    obtain ⟨hne,hmem⟩:=Finset.mem_erase.mp hmem
    have hd:=hpair hB hmem hne.symm
    obtain ⟨b,hb⟩:=hBne
    exact Finset.disjoint_left.mp hd hb (Finset.mem_union_left C hb)
  dsimp [mergeFamily]
  rw [Finset.card_insert_of_notMem hnew]
  have hcardB:=Finset.card_erase_add_one hB
  have hcardC:=Finset.card_erase_add_one hC'
  omega
theorem merge_controlledFamily {A R:Finset G} {μ K θ:ℝ} {P:Finset (Finset G)}
    (h:ControlledFamily A R μ K P) (hK:0 ≤ K) (hθ:0 < θ)
    (B C:Finset G) (hB:B ∈ P) (hC:C ∈ P) (_hBC:B ≠ C)
    (hE:θ * (A.card:ℝ) ^ 3 ≤ (B.addEnergy C:ℝ)) :
    ControlledFamily A R μ (growthStep θ K) (mergeFamily P B C):=by
  obtain ⟨hBA,hBne,hμB,hDB,hBR⟩:=h.1 B hB
  obtain ⟨hCA,hCne,_hμC,hDC,hCR⟩:=h.1 C hC
  have hUA:B ∪ C ⊆ A:=Finset.union_subset hBA hCA
  have hUcard:((B ∪ C).card:ℝ) ≤ A.card:=by
    exact_mod_cast Finset.card_le_card hUA
  have hEU:θ * ((B ∪ C).card:ℝ) ^ 3 ≤ (B.addEnergy C:ℝ):=by
    calc
      _ ≤ θ * (A.card:ℝ) ^ 3:=by gcongr
      _ ≤ _:=hE
  have hDU:=Green24Proof.EnergyOverlapMerge.union_small_difference_of_high_energy
    B C hBne hCne hK hθ hDB hDC hEU
  have hrest (D:Finset G) (hD:D ∈ (P.erase B).erase C):D ∈ P ∧ D ≠ B ∧ D ≠ C:=by
    obtain ⟨hDC,hDB,hDP⟩:=by simpa only [Finset.mem_erase] using hD
    exact ⟨hDP,hDB,hDC⟩
  have hUd (D:Finset G) (hD:D ∈ (P.erase B).erase C):Disjoint (B ∪ C) D:=by
    obtain ⟨hDP,hDB,hDC⟩:=hrest D hD
    exact Finset.disjoint_union_left.mpr ⟨h.2.1 hB hDP hDB.symm,h.2.1 hC hDP hDC.symm⟩
  refine ⟨?_, ?_, ?_⟩
  · intro D hD
    rcases Finset.mem_insert.mp hD with rfl | hD
    · refine ⟨hUA,hBne.mono Finset.subset_union_left, ?_,hDU, ?_⟩
      · exact hμB.trans (by exact_mod_cast Finset.card_le_card (Finset.subset_union_left:B ⊆ B ∪ C))
      · exact Finset.disjoint_union_left.mpr ⟨hBR,hCR⟩
    · exact (controlledFamily_mono h (growthStep_ge hθ hK)).1 D (hrest D hD).1
  · intro D hD E hE hDE
    rcases Finset.mem_insert.mp hD with rfl | hD
    · rcases Finset.mem_insert.mp hE with rfl | hE
      · exact (hDE rfl).elim
      · exact hUd E hE
    · rcases Finset.mem_insert.mp hE with rfl | hE
      · exact (hUd D hD).symm
      · exact h.2.1 (hrest D hD).1 (hrest E hE).1 hDE
  · rw [mergeFamily_union P B C hB hC]
    exact h.2.2
theorem exists_separated_family (n:ℕ) (A R:Finset G) (μ K θ:ℝ)
    (hK:0 ≤ K) (hθ:0 < θ) (P:Finset (Finset G)) (hn:P.card ≤ n)
    (h:ControlledFamily A R μ K P) :
    ∃ Q:Finset (Finset G),Q.card ≤ P.card ∧
      ControlledFamily A R μ (growthBound θ n K) Q ∧
      (Q:Set (Finset G)).Pairwise (fun B C => (B.addEnergy C:ℝ) < θ * (A.card:ℝ) ^ 3):=by
  induction n generalizing P K with
  | zero =>
    have hP:P = ∅:=Finset.card_eq_zero.mp (by omega)
    refine ⟨P,le_rfl,h, ?_⟩
    simp [hP]
  | succ n ih =>
    by_cases hsep:(P:Set (Finset G)).Pairwise (fun B C => (B.addEnergy C:ℝ) < θ * (A.card:ℝ) ^ 3)
    · exact ⟨P,le_rfl,controlledFamily_mono h (growthBound_ge hθ hK (n + 1)),hsep⟩
    · simp only [Set.Pairwise] at hsep
      push Not at hsep
      obtain ⟨B,hB,C,hC,hBC,hE⟩:=hsep
      have hlt:=mergeFamily_card_lt P B C hB hC hBC (h.1 B hB).2.1 h.2.1
      have hmerge:=merge_controlledFamily h hK hθ B C hB hC hBC hE
      obtain ⟨Q,hQcard,hQ,hsepQ⟩ :=
        ih (growthStep θ K) (hK.trans (growthStep_ge hθ hK)) (mergeFamily P B C)
          (by omega) hmerge
      exact ⟨Q,hQcard.trans hlt.le,hQ,hsepQ⟩
end Green24Proof.EnergyAgglomeration
private def zz2503:"s09c7"="s09c7":=by decide+kernel
end 
section 
namespace Green24Proof.AdaptiveEnergyPartition
open scoped Pointwise
open Green24Proof.EnergyAgglomeration
noncomputable def adaptiveBound (ψ:ℝ → ℝ):ℕ → ℝ → ℝ
  | 0,K => K
  | n + 1,K => adaptiveBound ψ n (growthStep (ψ K) K)
theorem adaptiveBound_ge (ψ:ℝ → ℝ) (hψ:∀ K,0 ≤ K → 0 < ψ K)
    {K:ℝ} (hK:0 ≤ K) (n:ℕ):K ≤ adaptiveBound ψ n K:=by
  induction n generalizing K with
  | zero => exact le_rfl
  | succ n ih =>
    have hstep:=growthStep_ge (hψ K hK) hK
    exact hstep.trans (ih (hK.trans hstep))
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
private def zz1965:"s07ad"="s07ad":=by decide+kernel
theorem exists_adaptively_separated_family (n:ℕ) (A R:Finset G) (μ K:ℝ)
    (hK:0 ≤ K) (ψ:ℝ → ℝ) (hψ:∀ L,0 ≤ L → 0 < ψ L)
    (P:Finset (Finset G)) (hn:P.card ≤ n) (h:ControlledFamily A R μ K P) :
    ∃ (L:ℝ) (Q:Finset (Finset G)),K ≤ L ∧ L ≤ adaptiveBound ψ n K ∧
      Q.card ≤ P.card ∧ ControlledFamily A R μ L Q ∧
      (Q:Set (Finset G)).Pairwise
        (fun B C => (B.addEnergy C:ℝ) < ψ L * (A.card:ℝ) ^ 3):=by
  induction n generalizing P K with
  | zero =>
    have hP:P = ∅:=Finset.card_eq_zero.mp (by omega)
    refine ⟨K,P,le_rfl,le_rfl,le_rfl,h, ?_⟩
    simp [hP]
  | succ n ih =>
    by_cases hsep:(P:Set (Finset G)).Pairwise
        (fun B C => (B.addEnergy C:ℝ) < ψ K * (A.card:ℝ) ^ 3)
    · exact ⟨K,P,le_rfl,adaptiveBound_ge ψ hψ hK (n + 1),le_rfl,h,hsep⟩
    · simp only [Set.Pairwise] at hsep
      push Not at hsep
      obtain ⟨B,hB,C,hC,hBC,hE⟩:=hsep
      have hlt:=mergeFamily_card_lt P B C hB hC hBC (h.1 B hB).2.1 h.2.1
      have hstep:=growthStep_ge (hψ K hK) hK
      have hmerge:=merge_controlledFamily h hK (hψ K hK) B C hB hC hBC hE
      obtain ⟨L,Q,hKL,hLbound,hQcard,hQ,hsepQ⟩ :=
        ih (growthStep (ψ K) K) (hK.trans hstep) (mergeFamily P B C) (by omega) hmerge
      exact ⟨L,Q,hstep.trans hKL,hLbound,hQcard.trans hlt.le,hQ,hsepQ⟩
omit [AddCommGroup G] in
theorem list_toFinset_union (P:List (Finset G)) (R:Finset G) :
    P.toFinset.biUnion id ∪ R = P.foldr (fun B C => B ∪ C) R:=by
  induction P with
  | nil => simp
  | cons B P ih => simp only [List.toFinset_cons,Finset.biUnion_insert,
      id_eq,List.foldr_cons,Finset.union_assoc,ih]
theorem exists_adaptive_energy_partition (A:Finset G) (hA:A.Nonempty)
    {δ:ℝ} (hδ:0 < δ) (ψ:ℝ → ℝ) (hψ:∀ K,0 ≤ K → 0 < ψ K) :
    ∃ (L:ℝ) (P:Finset (Finset G)) (R:Finset G),
      0x1000000 / δ ^ 10 ≤ L ∧
      L ≤ adaptiveBound ψ ⌈8 / δ ^ 2⌉₊ (0x1000000 / δ ^ 10) ∧
      P.card ≤ ⌈8 / δ ^ 2⌉₊ ∧ R ⊆ A ∧
      (R.addEnergy R:ℝ) < δ * (A.card:ℝ) ^ 3 ∧
      ControlledFamily A R (δ ^ 2 * A.card / 8) L P ∧
      (P:Set (Finset G)).Pairwise
        (fun B C => (B.addEnergy C:ℝ) < ψ L * (A.card:ℝ) ^ 3):=by
  obtain ⟨P,R,hRA,hRE,hpieces,hpair,hdisj,hcover,hcount⟩ :=
    Green24Proof.FiniteEnergyPeeling.exists_energy_partition A hA hδ
  have hcontrolled:ControlledFamily A R (δ ^ 2 * A.card / 8)
      (0x1000000 / δ ^ 10) P.toFinset:=by
    refine ⟨?_, ?_, ?_⟩
    · intro B hB
      have hBP:B ∈ P:=List.mem_toFinset.mp hB
      obtain ⟨hBA,hBne,hBsize,hBdiff⟩:=hpieces B hBP
      exact ⟨hBA,hBne,hBsize,hBdiff,hdisj B hBP⟩
    · intro B hB C hC hBC
      exact hpair.forall (List.mem_toFinset.mp hB) (List.mem_toFinset.mp hC) hBC
    · exact (list_toFinset_union P R).trans hcover
  have hn:P.toFinset.card ≤ ⌈8 / δ ^ 2⌉₊:=by
    have hp:(P.toFinset.card:ℝ) ≤ P.length:=by exact_mod_cast P.toFinset_card_le
    have hb:=hp.trans (hcount.trans (Nat.le_ceil (8 / δ ^ 2)))
    exact_mod_cast hb
  obtain ⟨L,Q,hKL,hLbound,hQcard,hQ,hsepQ⟩ :=
    exists_adaptively_separated_family ⌈8 / δ ^ 2⌉₊ A R (δ ^ 2 * A.card / 8)
      (0x1000000 / δ ^ 10) (by positivity) ψ hψ P.toFinset hn hcontrolled
  exact ⟨L,Q,R,hKL,hLbound,hQcard.trans hn,hRA,hRE,hQ,hsepQ⟩
end Green24Proof.AdaptiveEnergyPartition
private def zz2504:"s09c8"="s09c8":=by decide+kernel
end 
section 
namespace Green24Proof.DilationEnergyTransfer
open scoped BigOperators Pointwise
open Green24Proof.EnergyOverlapMerge
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
def dilate (ℓ:ℕ) (A:Finset G):Finset G:=A.image (fun x => ℓ • x)
theorem exists_overlap_preimage (ℓ:ℕ) (hℓ:Function.Injective (fun x:G => ℓ • x))
    (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty) :
    ∃ (S:Finset G) (x:G),S ⊆ A ∧ dilate ℓ S ⊆ B + {x} ∧
      Finset.addEnergy (dilate ℓ A) B ≤ A.card * B.card * S.card:=by
  obtain ⟨x,hx⟩:=exists_large_overlap (dilate ℓ A) B (hA.image _) hB
  let S:=A.filter (fun a => ℓ • a ∈ B + {x})
  have himage:dilate ℓ S = dilate ℓ A ∩ (B + {x}):=by
    ext y
    simp only [dilate,S,Finset.mem_image,Finset.mem_filter,Finset.mem_inter]
    constructor
    · rintro ⟨a,⟨ha,hax⟩,rfl⟩
      exact ⟨⟨a,ha,rfl⟩,hax⟩
    · rintro ⟨⟨a,ha,rfl⟩,hax⟩
      exact ⟨a,⟨ha,hax⟩,rfl⟩
  refine ⟨S,x,Finset.filter_subset _ _, ?_, ?_⟩
  · rw [himage]
    exact Finset.inter_subset_right
  · have hcardS:(dilate ℓ S).card = S.card:=Finset.card_image_of_injective _ hℓ
    have hcardA:(dilate ℓ A).card = A.card:=Finset.card_image_of_injective _ hℓ
    rw [← himage,hcardS,hcardA] at hx
    exact hx
private def zz1966:"s07ae"="s07ae":=by decide+kernel
theorem card_add_le_higher_sumset_of_dilate_subset (ℓ:ℕ)
    (hℓ:Function.Injective (fun x:G => ℓ • x))
    (S B:Finset G) (x:G) (hS:dilate ℓ S ⊆ B + {x}) :
    (S + B).card ≤ ((ℓ + 1) • B).card:=by
  have hsub:dilate ℓ (S + B) ⊆ ((ℓ + 1) • B) + {x}:=by
    intro y hy
    obtain ⟨z,hz,rfl⟩:=Finset.mem_image.mp hy
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_add.mp hz
    have hax:=hS (Finset.mem_image.mpr ⟨a,ha,rfl⟩)
    obtain ⟨c,hc,d,hd,hcd⟩:=Finset.mem_add.mp hax
    have hdx:d = x:=Finset.mem_singleton.mp hd
    subst d
    refine Finset.mem_add.mpr ⟨ℓ • b + c, ?_,x,by simp, ?_⟩
    · rw [add_nsmul,one_nsmul]
      exact Finset.add_mem_add (Finset.nsmul_mem_nsmul hb) hc
    · rw [nsmul_add, ← hcd]
      abel
  have hcard:=Finset.card_le_card hsub
  rw [Finset.card_add_singleton] at hcard
  rw [dilate,Finset.card_image_of_injective _ hℓ] at hcard
  exact hcard
theorem dilated_energy_sq_le (ℓ:ℕ)
    (hℓ:Function.Injective (fun x:G => ℓ • x))
    (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty) :
    Finset.addEnergy (dilate ℓ A) B ^ 2 ≤
      A.card ^ 2 * ((ℓ + 1) • B).card * Finset.addEnergy A B:=by
  obtain ⟨S,x,hSA,hS,henergy⟩:=exists_overlap_preimage ℓ hℓ A B hA hB
  have hcard:=card_add_le_higher_sumset_of_dilate_subset ℓ hℓ S B x hS
  have hCS:=Finset.le_card_add_mul_addEnergy S B
  have hmono:Finset.addEnergy S B ≤ Finset.addEnergy A B :=
    Finset.addEnergy_mono_left hSA
  have hbound:S.card ^ 2 * B.card ^ 2 ≤ ((ℓ + 1) • B).card * Finset.addEnergy A B :=
    hCS.trans (Nat.mul_le_mul hcard hmono)
  calc
    _ ≤ (A.card * B.card * S.card) ^ 2:=Nat.pow_le_pow_left henergy 2
    _ = A.card ^ 2 * (S.card ^ 2 * B.card ^ 2):=by ring
    _ ≤ A.card ^ 2 * (((ℓ + 1) • B).card * Finset.addEnergy A B) :=
      Nat.mul_le_mul_left _ hbound
    _ = _:=by ring
theorem higher_sumset_card_le {K:ℝ} (B:Finset G) (hB:B.Nonempty)
    (_hK:0 ≤ K) (hdoubling:((B + B).card:ℝ) ≤ K * B.card) (m:ℕ) :
    ((m • B).card:ℝ) ≤ K ^ m * B.card:=by
  have hp:=Finset.pluennecke_ruzsa_inequality_nsmul_add hB B m
  have hp':((m • B).card:ℝ) ≤
      (((B + B).card:ℝ) / B.card) ^ m * B.card:=by
    have hc:=NNRat.cast_mono (K:=ℝ) hp
    change (NNRat.castHom ℝ) ((m • B).card:ℚ≥0) ≤
      (NNRat.castHom ℝ) ((((B + B).card:ℚ≥0) / B.card) ^ m * B.card) at hc
    rw [map_mul,map_pow] at hc
    simpa only [NNRat.coe_castHom,NNRat.cast_div,NNRat.cast_natCast] using hc
  have hbpos:(0:ℝ) < B.card:=by exact_mod_cast hB.card_pos
  apply hp'.trans
  gcongr
  exact (div_le_iff₀ hbpos).mpr hdoubling
theorem dilated_energy_sq_le_of_small_doubling (ℓ:ℕ)
    (hℓ:Function.Injective (fun x:G => ℓ • x))
    (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty)
    {K:ℝ} (hK:0 ≤ K) (hdoubling:((B + B).card:ℝ) ≤ K * B.card) :
    (Finset.addEnergy (dilate ℓ A) B:ℝ) ^ 2 ≤
      K ^ (ℓ + 1) * (A.card:ℝ) ^ 2 * B.card * Finset.addEnergy A B:=by
  have hcore:(Finset.addEnergy (dilate ℓ A) B:ℝ) ^ 2 ≤
      (A.card:ℝ) ^ 2 * ((ℓ + 1) • B).card * Finset.addEnergy A B:=by
    exact_mod_cast dilated_energy_sq_le ℓ hℓ A B hA hB
  calc
    _ ≤ (A.card:ℝ) ^ 2 * (K ^ (ℓ + 1) * B.card) * Finset.addEnergy A B:=by
      apply hcore.trans
      gcongr
      exact higher_sumset_card_le B hB hK hdoubling (ℓ + 1)
    _ = _:=by ring
private def zz1967:"s07af"="s07af":=by decide+kernel
theorem dilated_energy_le_of_budget (ℓ:ℕ)
    (hℓ:Function.Injective (fun x:G => ℓ • x))
    (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty)
    {K η N:ℝ} (hK:0 ≤ K) (hη:0 ≤ η) (hN:0 ≤ N)
    (hdoubling:((B + B).card:ℝ) ≤ K * B.card)
    (hAN:(A.card:ℝ) ≤ N) (hBN:(B.card:ℝ) ≤ N)
    (hbudget:K ^ (ℓ + 1) * Finset.addEnergy A B ≤ η ^ 2 * N ^ 3) :
    (Finset.addEnergy (dilate ℓ A) B:ℝ) ≤ η * N ^ 3:=by
  have hcore:=dilated_energy_sq_le_of_small_doubling ℓ hℓ A B hA hB hK hdoubling
  have hsize:(A.card:ℝ) ^ 2 * B.card ≤ N ^ 3:=by
    calc
      _ ≤ N ^ 2 * N:=by gcongr
      _ = _:=by ring
  have hsquare:(Finset.addEnergy (dilate ℓ A) B:ℝ) ^ 2 ≤ (η * N ^ 3) ^ 2:=by
    calc
      _ ≤ ((A.card:ℝ) ^ 2 * B.card) * (K ^ (ℓ + 1) * Finset.addEnergy A B):=by
        convert hcore using 1
        ring
      _ ≤ (N ^ 3) * (η ^ 2 * N ^ 3):=by gcongr
      _ = _:=by ring
  exact (sq_le_sq₀ (Nat.cast_nonneg _) (by positivity)).mp hsquare
theorem energy_neg_left (A B:Finset G) :
    Finset.addEnergy (A.image (fun a => -a)) B = Finset.addEnergy A B:=by
  symm
  unfold Finset.addEnergy
  refine Finset.card_bij (fun p _ => ((-p.1.1, -p.1.2),p.2.2,p.2.1)) ?_ ?_ ?_
  · rintro ⟨⟨a,c⟩,b,d⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    refine ⟨⟨⟨Finset.mem_image.mpr ⟨a,hp.1.1.1,rfl⟩,
      Finset.mem_image.mpr ⟨c,hp.1.1.2,rfl⟩⟩,hp.1.2.2,hp.1.2.1⟩, ?_⟩
    rw [neg_add_eq_sub,neg_add_eq_sub]
    apply sub_eq_sub_iff_add_eq_add.mpr
    simpa only [add_comm] using hp.2.symm
  · rintro ⟨⟨a,c⟩,b,d⟩ _ ⟨⟨a',c'⟩,b',d'⟩ _ heq
    simp only [Prod.mk.injEq,neg_inj] at heq ⊢
    exact ⟨heq.1,heq.2.2,heq.2.1⟩
  · rintro ⟨⟨a,c⟩,d,b⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨a',ha',rfl⟩:=Finset.mem_image.mp hp.1.1.1
    obtain ⟨c',hc',rfl⟩:=Finset.mem_image.mp hp.1.1.2
    refine ⟨((a',c'),b,d), ?_,rfl⟩
    simp only [Finset.mem_filter,Finset.mem_product]
    refine ⟨⟨⟨ha',hc'⟩,hp.1.2.2,hp.1.2.1⟩, ?_⟩
    have heq:=hp.2
    rw [neg_add_eq_sub,neg_add_eq_sub] at heq
    have heq':=sub_eq_sub_iff_add_eq_add.mp heq
    simpa only [add_comm] using heq'.symm
theorem energy_neg_right (A B:Finset G) :
    Finset.addEnergy A (B.image (fun b => -b)) = Finset.addEnergy A B:=by
  rw [Finset.addEnergy_comm,energy_neg_left,Finset.addEnergy_comm]
theorem dilate_add (ℓ:ℕ) (A B:Finset G) :
    dilate ℓ (A + B) = dilate ℓ A + dilate ℓ B:=by
  ext x
  constructor
  · intro hx
    obtain ⟨y,hy,rfl⟩:=Finset.mem_image.mp hx
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_add.mp hy
    exact Finset.mem_add.mpr ⟨ℓ • a,Finset.mem_image.mpr ⟨a,ha,rfl⟩,
      ℓ • b,Finset.mem_image.mpr ⟨b,hb,rfl⟩,(nsmul_add _ _ _).symm⟩
  · intro hx
    obtain ⟨y,hy,z,hz,rfl⟩:=Finset.mem_add.mp hx
    obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hy
    obtain ⟨b,hb,rfl⟩:=Finset.mem_image.mp hz
    exact Finset.mem_image.mpr ⟨a + b,Finset.add_mem_add ha hb,nsmul_add _ _ _⟩
private def zz1968:"s07b0"="s07b0":=by decide+kernel
theorem both_dilated_energy_le_of_budget (ℓ m:ℕ)
    (hℓ:Function.Injective (fun x:G => ℓ • x))
    (hm:Function.Injective (fun x:G => m • x))
    (A B:Finset G) (hA:A.Nonempty) (hB:B.Nonempty)
    {KA KB δ η N:ℝ} (hKA:0 ≤ KA) (hKB:0 ≤ KB)
    (hδ:0 ≤ δ) (hη:0 ≤ η) (hN:0 ≤ N)
    (hdoubleA:((A + A).card:ℝ) ≤ KA * A.card)
    (hdoubleB:((B + B).card:ℝ) ≤ KB * B.card)
    (hAN:(A.card:ℝ) ≤ N) (hBN:(B.card:ℝ) ≤ N)
    (hfirst:KB ^ (ℓ + 1) * Finset.addEnergy A B ≤ δ ^ 2 * N ^ 3)
    (hsecond:KA ^ (m + 1) * δ ≤ η ^ 2) :
    (Finset.addEnergy (dilate ℓ A) (dilate m B):ℝ) ≤ η * N ^ 3:=by
  have hfirst':=dilated_energy_le_of_budget ℓ hℓ A B hA hB hKB hδ hN
    hdoubleB hAN hBN hfirst
  have hcard:(dilate ℓ A).card = A.card:=Finset.card_image_of_injective _ hℓ
  have hdoubling:((dilate ℓ A + dilate ℓ A).card:ℝ) ≤ KA * (dilate ℓ A).card:=by
    rw [← dilate_add,hcard]
    have hc:(dilate ℓ (A + A)).card = (A + A).card:=Finset.card_image_of_injective _ hℓ
    rw [hc]
    exact hdoubleA
  have hbudget:KA ^ (m + 1) * Finset.addEnergy B (dilate ℓ A) ≤ η ^ 2 * N ^ 3:=by
    rw [Finset.addEnergy_comm]
    calc
      _ ≤ KA ^ (m + 1) * (δ * N ^ 3):=by gcongr
      _ = (KA ^ (m + 1) * δ) * N ^ 3:=by ring
      _ ≤ _:=mul_le_mul_of_nonneg_right hsecond (by positivity)
  have h:=dilated_energy_le_of_budget m hm B (dilate ℓ A) hB (hA.image _)
    hKA hη hN hdoubling hBN (by simpa only [hcard] using hAN) hbudget
  rwa [Finset.addEnergy_comm] at h
theorem integer_dilated_energy_sq_le (ℓ:ℕ) (hℓ:ℓ ≠ 0)
    (A B:Finset ℤ) (hA:A.Nonempty) (hB:B.Nonempty) :
    Finset.addEnergy (A.image (fun a => (ℓ:ℤ) * a)) B ^ 2 ≤
      A.card ^ 2 * ((ℓ + 1) • B).card * Finset.addEnergy A B:=by
  have hinj:Function.Injective (fun a:ℤ => ℓ • a):=by
    intro a b heq
    simp only [nsmul_eq_mul] at heq
    exact mul_left_cancel₀ (by exact_mod_cast hℓ:(ℓ:ℤ) ≠ 0) heq
  simpa only [dilate,nsmul_eq_mul] using dilated_energy_sq_le ℓ hinj A B hA hB
theorem integer_signed_energy_sq_le (k:ℤ) (hk:k ≠ 0)
    (A B:Finset ℤ) (hA:A.Nonempty) (hB:B.Nonempty) :
    Finset.addEnergy (A.image (fun a => k * a)) B ^ 2 ≤
      A.card ^ 2 * ((k.natAbs + 1) • B).card * Finset.addEnergy A B:=by
  cases k with
  | ofNat ℓ =>
    have hℓ:ℓ ≠ 0:=by
      intro hzero
      subst ℓ
      exact hk rfl
    simpa using integer_dilated_energy_sq_le ℓ hℓ A B hA hB
  | negSucc ℓ =>
    have h:=integer_dilated_energy_sq_le (ℓ + 1) (by omega) A B hA hB
    have he:A.image (fun a => Int.negSucc ℓ * a) =
        (A.image (fun a => ((ℓ + 1:ℕ):ℤ) * a)).image (fun a => -a):=by
      rw [Finset.image_image]
      congr 1
      funext a
      simp only [Int.negSucc_eq,Nat.cast_add,Nat.cast_one]
      dsimp only [Function.comp_apply]
      ring
    rw [he,energy_neg_left]
    simpa using h
theorem integer_energy_abs_left (k:ℤ) (A B:Finset ℤ) :
    Finset.addEnergy (A.image (fun a => k * a)) B =
      Finset.addEnergy (dilate k.natAbs A) B:=by
  cases k with
  | ofNat ℓ =>
    simp only [dilate,nsmul_eq_mul]
    rfl
  | negSucc ℓ =>
    have he:A.image (fun a => Int.negSucc ℓ * a) =
        (dilate (ℓ + 1) A).image (fun a => -a):=by
      rw [dilate,Finset.image_image]
      congr 1
      funext a
      simp only [Int.negSucc_eq,nsmul_eq_mul,Nat.cast_add,Nat.cast_one]
      dsimp only [Function.comp_apply]
      ring
    rw [he,energy_neg_left]
    rfl
private def zz1969:"s07b1"="s07b1":=by decide+kernel
theorem integer_energy_abs_coefficients (k l:ℤ) (A B:Finset ℤ) :
    Finset.addEnergy (A.image (fun a => k * a)) (B.image (fun b => l * b)) =
      Finset.addEnergy (dilate k.natAbs A) (dilate l.natAbs B):=by
  rw [integer_energy_abs_left,Finset.addEnergy_comm,integer_energy_abs_left,
    Finset.addEnergy_comm]
theorem integer_signed_energy_le_of_budget (k l:ℤ) (hk:k ≠ 0) (hl:l ≠ 0)
    (A B:Finset ℤ) (hA:A.Nonempty) (hB:B.Nonempty)
    {KA KB δ η N:ℝ} (hKA:0 ≤ KA) (hKB:0 ≤ KB)
    (hδ:0 ≤ δ) (hη:0 ≤ η) (hN:0 ≤ N)
    (hdoubleA:((A + A).card:ℝ) ≤ KA * A.card)
    (hdoubleB:((B + B).card:ℝ) ≤ KB * B.card)
    (hAN:(A.card:ℝ) ≤ N) (hBN:(B.card:ℝ) ≤ N)
    (hfirst:KB ^ (k.natAbs + 1) * Finset.addEnergy A B ≤ δ ^ 2 * N ^ 3)
    (hsecond:KA ^ (l.natAbs + 1) * δ ≤ η ^ 2) :
    (Finset.addEnergy (A.image (fun a => k * a)) (B.image (fun b => l * b)):ℝ) ≤
      η * N ^ 3:=by
  rw [integer_energy_abs_coefficients]
  have hinj (n:ℤ) (hn:n ≠ 0):Function.Injective (fun a:ℤ => n.natAbs • a):=by
    intro a b heq
    simp only [nsmul_eq_mul] at heq
    apply mul_left_cancel₀ _ heq
    exact_mod_cast (Int.natAbs_ne_zero.mpr hn)
  exact both_dilated_energy_le_of_budget k.natAbs l.natAbs (hinj k hk) (hinj l hl)
    A B hA hB hKA hKB hδ hη hN hdoubleA hdoubleB hAN hBN hfirst hsecond
end Green24Proof.DilationEnergyTransfer
private def zz2505:"s09c9"="s09c9":=by decide+kernel
end 
section 
namespace Green24Proof.IteratedCoveringGrowth
open scoped BigOperators Pointwise
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
theorem bounded_coefficients_of_mem_nsmul_sub (T:Finset G) (m:ℕ)
    {x:G} (hx:x ∈ m • (T - T)) :
    ∃ z:T → ℤ,(∀ t, -(m:ℤ) ≤ z t ∧ z t ≤ m) ∧
      x = ∑ t:T,z t • (t:G):=by
  induction m generalizing x with
  | zero =>
    have hx0:x = 0:=by simpa using hx
    exact ⟨fun _ => 0,by simp,by simp [hx0]⟩
  | succ m ih =>
    rw [succ_nsmul] at hx
    obtain ⟨y,hy,a,ha,rfl⟩:=Finset.mem_add.mp hx
    obtain ⟨u,hu,v,hv,rfl⟩:=Finset.mem_sub.mp ha
    obtain ⟨z,hz,hyz⟩:=ih hy
    let u':T:=⟨u,hu⟩
    let v':T:=⟨v,hv⟩
    let w:T → ℤ:=fun t => z t + (if t = u' then 1 else 0) - (if t = v' then 1 else 0)
    refine ⟨w, ?_, ?_⟩
    · intro t
      have ht:=hz t
      dsimp [w]
      split_ifs <;> omega
    · simp only [w,sub_smul,add_smul,Finset.sum_sub_distrib,Finset.sum_add_distrib,
        ite_smul,one_smul,zero_smul]
      simp only [Finset.sum_ite_eq',Finset.mem_univ,if_true]
      change y + (u - v) = (∑ t:T,z t • (t:G)) + u - v
      rw [hyz]
      abel
def coefficientBoxImage (T:Finset G) (m:ℕ):Finset G :=
  Finset.univ.image (fun c:T → Fin (2 * m + 1) =>
    ∑ t:T,(((c t:ℕ):ℤ) - (m:ℤ)) • (t:G))
theorem nsmul_sub_subset_coefficientBoxImage (T:Finset G) (m:ℕ) :
    m • (T - T) ⊆ coefficientBoxImage T m:=by
  intro x hx
  obtain ⟨z,hz,hrepr⟩:=bounded_coefficients_of_mem_nsmul_sub T m hx
  let c:T → Fin (2 * m + 1):=fun t =>
    ⟨(z t + (m:ℤ)).toNat,by have ht:=hz t; omega⟩
  have hc (t:T):(((c t:ℕ):ℤ) - (m:ℤ)) = z t:=by
    have ht:=hz t
    dsimp [c]
    omega
  apply Finset.mem_image.mpr
  refine ⟨c,Finset.mem_univ _, ?_⟩
  simpa only [hc] using hrepr.symm
private def zz1970:"s07b2"="s07b2":=by decide+kernel
theorem card_nsmul_sub_le (T:Finset G) (m:ℕ) :
    (m • (T - T)).card ≤ (2 * m + 1) ^ T.card:=by
  calc
    (m • (T - T)).card ≤ (coefficientBoxImage T m).card :=
      Finset.card_le_card (nsmul_sub_subset_coefficientBoxImage T m)
    _ ≤ (Finset.univ:Finset (T → Fin (2 * m + 1))).card:=Finset.card_image_le
    _ = _:=by simp
theorem iterated_cover (B T:Finset G) (hcover:B + B ⊆ B + (T - T)) (m:ℕ) :
    (m + 1) • B ⊆ B + m • (T - T):=by
  induction m with
  | zero => simp
  | succ m ih =>
    calc
      (m + 1 + 1) • B = (m + 1) • B + B:=by rw [add_nsmul,one_nsmul]
      _ ⊆ (B + m • (T - T)) + B:=Finset.add_subset_add ih (fun _ hx => hx)
      _ = (B + B) + m • (T - T):=by ac_rfl
      _ ⊆ (B + (T - T)) + m • (T - T):=Finset.add_subset_add hcover (fun _ hx => hx)
      _ = B + (m + 1) • (T - T):=by rw [add_nsmul,one_nsmul]; ac_rfl
theorem polynomial_growth_of_cover (B T:Finset G)
    (hcover:B + B ⊆ B + (T - T)) (m:ℕ) :
    ((m + 1) • B).card ≤ B.card * (2 * m + 1) ^ T.card:=by
  calc
    ((m + 1) • B).card ≤ (B + m • (T - T)).card :=
      Finset.card_le_card (iterated_cover B T hcover m)
    _ ≤ B.card * (m • (T - T)).card:=Finset.card_add_le
    _ ≤ _:=Nat.mul_le_mul_left _ (card_nsmul_sub_le T m)
open Green24Proof.CyclicFourierMoments
variable {q:ℕ} [NeZero q]
theorem moment_bracket_nonneg (B:Finset (ZMod q)) (m:ℕ) (M:ℝ) :
    0 ≤ (B.card:ℝ) ^ (2 * (m + 1)) +
      M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2):=by
  have henergy:0 ≤ (q:ℝ) * B.card - (B.card:ℝ) ^ 2:=by
    rw [← second_moment_nonzero]
    exact Finset.sum_nonneg (fun _ _ => sq_nonneg _)
  have hpow:0 ≤ M ^ (2 * m):=by
    rw [pow_mul]
    exact pow_nonneg (sq_nonneg M) m
  positivity
private def zz1971:"s07b3"="s07b3":=by decide+kernel
theorem moment_criterion_of_cover (B T:Finset (ZMod q))
    (hcover:B + B ⊆ B + (T - T)) (m:ℕ) (M:ℝ)
    (hnum:(B.card:ℝ) * (2 * (m:ℝ) + 1) ^ T.card *
      ((B.card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2)) <
      (q:ℝ) * (B.card:ℝ) ^ (2 * (m + 1))) :
    ((iteratedSumset B (m + 1)).card:ℝ) *
      ((B.card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2)) <
      (q:ℝ) * (B.card:ℝ) ^ (2 * (m + 1)):=by
  have hgrowth:((iteratedSumset B (m + 1)).card:ℝ) ≤
      (B.card:ℝ) * (2 * (m:ℝ) + 1) ^ T.card:=by
    rw [iteratedSumset_eq_nsmul]
    exact_mod_cast polynomial_growth_of_cover B T hcover m
  exact lt_of_le_of_lt
    (mul_le_mul_of_nonneg_right hgrowth (moment_bracket_nonneg B m M)) hnum
theorem exists_large_nonzero_coefficient_of_cover (B T:Finset (ZMod q))
    (hcover:B + B ⊆ B + (T - T)) (m:ℕ) (M:ℝ)
    (hnum:(B.card:ℝ) * (2 * (m:ℝ) + 1) ^ T.card *
      ((B.card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * B.card - (B.card:ℝ) ^ 2)) <
      (q:ℝ) * (B.card:ℝ) ^ (2 * (m + 1))) :
    ∃ r:ZMod q,r ≠ 0 ∧ M < ‖coefficient B r‖ :=
  exists_large_nonzero_coefficient B m (moment_criterion_of_cover B T hcover m M hnum)
theorem exists_freiman_three_model_of_cover [Fact q.Prime]
    (A T:Finset (ZMod q)) (hcover:(A - A) + (A - A) ⊆ (A - A) + (T - T))
    (m:ℕ) {M:ℝ} (hM:0 ≤ M) {R:ℤ} (hR:0 < R) (hRq:6 * R < (q:ℤ))
    (hnum:((A - A).card:ℝ) * (2 * (m:ℝ) + 1) ^ T.card *
      (((A - A).card:ℝ) ^ (2 * (m + 1)) +
        M ^ (2 * m) * ((q:ℝ) * (A - A).card - ((A - A).card:ℝ) ^ 2)) <
      (q:ℝ) * ((A - A).card:ℝ) ^ (2 * (m + 1)))
    (hbudget:((A - A).card:ℝ) ^ 2 - M ^ 2 ≤
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * (R:ℝ) / q))) :
    ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
      B ⊆ Finset.Icc 0 (2 * R) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f :=
  exists_freiman_three_model_of_moment_growth A m hM hR hRq
    (moment_criterion_of_cover (A - A) T hcover m M hnum) hbudget
end Green24Proof.IteratedCoveringGrowth
private def zz2506:"s09ca"="s09ca":=by decide+kernel
end 
section 
namespace Green24Proof.SmallDoublingCover
open scoped BigOperators Pointwise
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
omit [AddCommGroup G] [DecidableEq G] in
theorem exists_max_potential_max_card (U:Finset G) (F:Finset G → ℤ) :
    ∃ T ⊆ U,(∀ S ⊆ U,F S ≤ F T) ∧
      (∀ S ⊆ U,F S = F T → S.card ≤ T.card):=by
  classical
  obtain ⟨T₀,hT₀,hmax⟩:=U.powerset.exists_max_image F ⟨∅,by simp⟩
  let C:=U.powerset.filter (fun S => F S = F T₀)
  have hC:C.Nonempty:=⟨T₀,Finset.mem_filter.mpr ⟨hT₀,rfl⟩⟩
  obtain ⟨T,hT,hcard⟩:=C.exists_max_image Finset.card hC
  obtain ⟨hTU,hFT⟩:=Finset.mem_filter.mp hT
  refine ⟨T,Finset.mem_powerset.mp hTU, ?_, ?_⟩
  · intro S hS
    rw [hFT]
    exact hmax S (Finset.mem_powerset.mpr hS)
  · intro S hS hFS
    exact hcard S (Finset.mem_filter.mpr ⟨Finset.mem_powerset.mpr hS,hFS.trans hFT⟩)
private def zz1972:"s07b4"="s07b4":=by decide+kernel
theorem exists_half_cover (X U:Finset G) (hX:X.Nonempty) (hU:U.Nonempty) :
    ∃ T ⊆ U,
      (T.card + 1) * X.card ≤ 2 * (X + U).card ∧
      ∀ u ∈ U,2 * ((X + {u}) \ (X + T)).card < X.card:=by
  classical
  let F:Finset G → ℤ:=fun T => 2 * ((X + T).card:ℤ) - (X.card:ℤ) * T.card
  obtain ⟨T,hTU,hmax,hmaxcard⟩:=exists_max_potential_max_card U F
  refine ⟨T,hTU, ?_, ?_⟩
  · obtain ⟨u,hu⟩:=hU
    have h:=hmax {u} (Finset.singleton_subset_iff.mpr hu)
    have hsub:(X + T).card ≤ (X + U).card :=
      Finset.card_le_card (Finset.add_subset_add (fun _ hx => hx) hTU)
    have hF:F {u} = X.card:=by simp [F]; ring
    rw [hF] at h
    dsimp [F] at h
    have hsubi:((X + T).card:ℤ) ≤ (X + U).card:=by exact_mod_cast hsub
    have hi:((T.card:ℤ) + 1) * X.card ≤ 2 * (X + U).card:=by nlinarith
    exact_mod_cast hi
  · intro u hu
    by_cases hut:u ∈ T
    · have hsub:X + {u} ⊆ X + T :=
        Finset.add_subset_add (fun _ hx => hx) (Finset.singleton_subset_iff.mpr hut)
      rw [Finset.sdiff_eq_empty_iff_subset.mpr hsub]
      simpa using hX.card_pos
    · have hinsert:insert u T ⊆ U:=Finset.insert_subset hu hTU
      have hle:=hmax (insert u T) hinsert
      have hlt:F (insert u T) < F T:=by
        apply lt_of_le_of_ne hle
        intro he
        have hc:=hmaxcard (insert u T) hinsert he
        rw [Finset.card_insert_of_notMem hut] at hc
        omega
      have hset:X + insert u T = (X + {u}) ∪ (X + T):=by
        rw [Finset.insert_eq,Finset.add_union]
      have hc:=Finset.card_sdiff_add_card (X + {u}) (X + T)
      rw [← hset] at hc
      dsimp [F] at hlt
      rw [Finset.card_insert_of_notMem hut] at hlt
      push_cast at hlt
      have hlt':(2:ℤ) * ((X + {u}) \ (X + T)).card < X.card:=by
        have hci:(((X + {u}) \ (X + T)).card:ℤ) + (X + T).card =
            (X + insert u T).card:=by exact_mod_cast hc
        nlinarith
      exact_mod_cast hlt'
theorem card_bad_translate (X T:Finset G) (u:G) :
    (X.filter (fun x => x + u ∉ X + T)).card = ((X + {u}) \ (X + T)).card:=by
  classical
  symm
  apply Finset.card_bij (fun x _ => x - u)
  · intro x hx
    obtain ⟨hxu,hxT⟩:=Finset.mem_sdiff.mp hx
    obtain ⟨y,hy,z,hz,hxyz⟩:=Finset.mem_add.mp hxu
    have hz':z = u:=Finset.mem_singleton.mp hz
    subst z
    subst x
    simpa using And.intro hy hxT
  · intro x _ y _ he
    exact sub_left_inj.mp he
  · intro x hx
    obtain ⟨hxX,hxT⟩:=Finset.mem_filter.mp hx
    refine ⟨x + u,Finset.mem_sdiff.mpr ⟨Finset.add_mem_add hxX (by simp),hxT⟩,by simp⟩
theorem difference_cover_of_half_cover (X U T:Finset G)
    (hhalf:∀ u ∈ U,2 * ((X + {u}) \ (X + T)).card < X.card) :
    U - U ⊆ (X - X) + (T - T):=by
  classical
  intro z hz
  obtain ⟨u,hu,v,hv,rfl⟩:=Finset.mem_sub.mp hz
  have hgood:∃ x ∈ X,x + u ∈ X + T ∧ x + v ∈ X + T:=by
    by_contra hn
    have hsub:X ⊆ (X.filter (fun x => x + u ∉ X + T)) ∪
        (X.filter (fun x => x + v ∉ X + T)):=by
      intro x hx
      by_cases hxu:x + u ∈ X + T
      · exact Finset.mem_union_right _ (Finset.mem_filter.mpr
          ⟨hx,fun hxv => hn ⟨x,hx,hxu,hxv⟩⟩)
      · exact Finset.mem_union_left _ (Finset.mem_filter.mpr ⟨hx,hxu⟩)
    have hcard:=(Finset.card_le_card hsub).trans (Finset.card_union_le _ _)
    rw [card_bad_translate,card_bad_translate] at hcard
    have hu':=hhalf u hu
    have hv':=hhalf v hv
    omega
  obtain ⟨x,_,hxu,hxv⟩:=hgood
  obtain ⟨a,ha,t,ht,hat⟩:=Finset.mem_add.mp hxu
  obtain ⟨b,hb,s,hs,hbs⟩:=Finset.mem_add.mp hxv
  refine Finset.mem_add.mpr ⟨a - b,Finset.sub_mem_sub ha hb,
    t - s,Finset.sub_mem_sub ht hs, ?_⟩
  have he:=congrArg₂ (fun i j:G => i - j) hat hbs
  abel_nf at he ⊢
  exact he
theorem exists_difference_cover (X U:Finset G) (hX:X.Nonempty) (hU:U.Nonempty) :
    ∃ T ⊆ U,(T.card + 1) * X.card ≤ 2 * (X + U).card ∧
      U - U ⊆ (X - X) + (T - T):=by
  obtain ⟨T,hTU,hcard,hhalf⟩:=exists_half_cover X U hX hU
  exact ⟨T,hTU,hcard,difference_cover_of_half_cover X U T hhalf⟩
private def zz1973:"s07b5"="s07b5":=by decide+kernel
theorem exists_subset_second_sum_bound (A:Finset G) (hA:A.Nonempty)
    {K:ℝ} (hK:0 ≤ K) (hdoubling:((A + A).card:ℝ) ≤ K * A.card) :
    ∃ C ⊆ A,C.Nonempty ∧ ((C + (A + A)).card:ℝ) ≤ K ^ 2 * C.card:=by
  classical
  let F:Finset G → ℝ:=fun C => ((C + A).card:ℝ) / C.card
  have hmem:A ∈ A.powerset.erase ∅ :=
    Finset.mem_erase.mpr ⟨hA.ne_empty,Finset.mem_powerset_self _⟩
  obtain ⟨C,hC,hmin⟩:=(A.powerset.erase ∅).exists_min_image F ⟨A,hmem⟩
  obtain ⟨hC0,hCA⟩:=Finset.mem_erase.mp hC
  have hCne:C.Nonempty:=Finset.nonempty_iff_ne_empty.mpr hC0
  have hCA':C ⊆ A:=Finset.mem_powerset.mp hCA
  have hcpos:(0:ℝ) < C.card:=by exact_mod_cast hCne.card_pos
  have hapos:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  have hminimal:∀ D ⊆ C,(C + A).card * D.card ≤ (D + A).card * C.card:=by
    intro D hDC
    obtain rfl | hD:=D.eq_empty_or_nonempty
    · simp
    have hdpos:(0:ℝ) < D.card:=by exact_mod_cast hD.card_pos
    have hDm:D ∈ A.powerset.erase ∅:=Finset.mem_erase.mpr
      ⟨hD.ne_empty,Finset.mem_powerset.mpr (hDC.trans hCA')⟩
    have hrat:=hmin D hDm
    dsimp [F] at hrat
    exact_mod_cast (div_le_div_iff₀ hcpos hdpos).mp hrat
  have hP:=Finset.pluennecke_petridis_inequality_add (A:=C) (B:=A) A hminimal
  have hP':((C + (A + A)).card:ℝ) * C.card ≤ ((C + A).card:ℝ) ^ 2:=by
    have he₁:A + C + A = C + (A + A):=by ac_rfl
    have he₂:A + C = C + A:=add_comm _ _
    rw [he₁,he₂] at hP
    have hPnat:(C + (A + A)).card * C.card ≤ (C + A).card ^ 2:=by
      simpa only [pow_two] using hP
    exact_mod_cast hPnat
  have hratio:F C ≤ K:=by
    apply (hmin A hmem).trans
    exact (div_le_iff₀ hapos).mpr hdoubling
  have hfirst:((C + A).card:ℝ) ≤ K * C.card :=
    (div_le_iff₀ hcpos).mp hratio
  have hsquare:((C + A).card:ℝ) ^ 2 ≤ (K * C.card) ^ 2 :=
    (sq_le_sq₀ (Nat.cast_nonneg _) (mul_nonneg hK hcpos.le)).mpr hfirst
  refine ⟨C,hCA',hCne, ?_⟩
  apply le_of_mul_le_mul_right (a:=(C.card:ℝ)) _ hcpos
  nlinarith
theorem exists_cover_of_small_doubling (A:Finset G) (hA:A.Nonempty)
    {K:ℝ} (hK:0 ≤ K) (hdoubling:((A + A).card:ℝ) ≤ K * A.card) :
    ∃ T ⊆ A + A,(T.card:ℝ) ≤ 2 * K ^ 2 - 1 ∧
      (A - A) + (A - A) ⊆ (A - A) + (T - T):=by
  obtain ⟨C,hCA,hC,hsecond⟩:=exists_subset_second_sum_bound A hA hK hdoubling
  obtain ⟨T,hTU,hcard,hcover⟩:=exists_difference_cover C (A + A) hC (hA.add hA)
  have hcpos:(0:ℝ) < C.card:=by exact_mod_cast hC.card_pos
  have hcard':((T.card:ℝ) + 1) * C.card ≤ 2 * ((C + (A + A)).card:ℝ):=by
    exact_mod_cast hcard
  have hT:(T.card:ℝ) ≤ 2 * K ^ 2 - 1:=by
    have hmul:((T.card:ℝ) + 1) * C.card ≤ (2 * K ^ 2) * C.card:=by nlinarith
    have hle:=le_of_mul_le_mul_right hmul hcpos
    linarith
  refine ⟨T,hTU,hT, ?_⟩
  intro x hx
  obtain ⟨u,hu,v,hv,rfl⟩:=Finset.mem_add.mp hx
  obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_sub.mp hu
  obtain ⟨c,hc,d,hd,rfl⟩:=Finset.mem_sub.mp hv
  have hdiff:(a - b) + (c - d) ∈ (A + A) - (A + A):=by
    convert Finset.sub_mem_sub (Finset.add_mem_add ha hc) (Finset.add_mem_add hb hd) using 1
    abel
  obtain ⟨y,hy,z,hz,he⟩:=Finset.mem_add.mp (hcover hdiff)
  obtain ⟨e,heC,f,hfC,rfl⟩:=Finset.mem_sub.mp hy
  exact Finset.mem_add.mpr ⟨e - f,Finset.sub_mem_sub (hCA heC) (hCA hfC),z,hz,he⟩
theorem exists_polynomial_growth_of_small_doubling (A:Finset G) (hA:A.Nonempty)
    {K:ℝ} (hK:0 ≤ K) (hdoubling:((A + A).card:ℝ) ≤ K * A.card) :
    ∃ T ⊆ A + A,(T.card:ℝ) ≤ 2 * K ^ 2 - 1 ∧
      ∀ m:ℕ,((m + 1) • (A - A)).card ≤
        (A - A).card * (2 * m + 1) ^ T.card:=by
  obtain ⟨T,hT,hcard,hcover⟩:=exists_cover_of_small_doubling A hA hK hdoubling
  exact ⟨T,hT,hcard,fun m =>
    Green24Proof.IteratedCoveringGrowth.polynomial_growth_of_cover (A - A) T hcover m⟩
end Green24Proof.SmallDoublingCover
private def zz2507:"s09cb"="s09cb":=by decide+kernel
end 
section 
namespace Green24Proof.UniformFourierParameters
open scoped BigOperators Pointwise Topology
open Filter
open Green24Proof.CyclicFourierMoments
open Green24Proof.IteratedCoveringGrowth
open Green24Proof.SmallDoublingCover
theorem exists_polynomial_decay_index (k:ℕ) {ρ:ℝ} (hρ0:0 ≤ ρ) (hρ1:ρ < 1) :
    ∃ m:ℕ,1 ≤ m ∧ (2 * (m:ℝ) + 1) ^ k * ρ ^ (2 * m) < 1 / 4:=by
  have hρsq:ρ ^ 2 < 1:=by nlinarith
  have hlim:=(tendsto_pow_const_mul_const_pow_of_lt_one k (sq_nonneg ρ) hρsq).const_mul
    ((3:ℝ) ^ k)
  have hevent:∀ᶠ m:ℕ in atTop,
      (3:ℝ) ^ k * ((m:ℝ) ^ k * (ρ ^ 2) ^ m) < 1 / 4 :=
    hlim.eventually (gt_mem_nhds (by norm_num))
  obtain ⟨N,hN⟩:=eventually_atTop.mp hevent
  let m:=max N 1
  have hm:1 ≤ m:=le_max_right _ _
  have hmr:(1:ℝ) ≤ m:=by exact_mod_cast hm
  refine ⟨m,hm,lt_of_le_of_lt ?_ (hN m (le_max_left _ _))⟩
  calc
    (2 * (m:ℝ) + 1) ^ k * ρ ^ (2 * m) ≤
        (3 * (m:ℝ)) ^ k * (ρ ^ 2) ^ m:=by
      rw [pow_mul]
      gcongr
      linarith
    _ = _:=by rw [mul_pow]; ring
private def zz1974:"s07b6"="s07b6":=by decide+kernel
theorem moment_numerical_of_density_decay {n q P ρ:ℝ} (m:ℕ)
    (hn:0 < n) (hq:0 < q) (hP:0 ≤ P) (hρ:0 ≤ ρ)
    (hdensity:n * P < q / 4) (hdecay:P * ρ ^ (2 * m) < 1 / 4) :
    n * P * (n ^ (2 * (m + 1)) + (ρ * n) ^ (2 * m) * (q * n - n ^ 2)) <
      q * n ^ (2 * (m + 1)):=by
  have hdecayq:=mul_lt_mul_of_pos_right hdecay hq
  have hnonneg:0 ≤ P * ρ ^ (2 * m) * n:=by positivity
  have hfactor:n * P + P * ρ ^ (2 * m) * (q - n) < q:=by nlinarith
  have heq:n * P * (n ^ (2 * (m + 1)) + (ρ * n) ^ (2 * m) * (q * n - n ^ 2)) =
      (n * P + P * ρ ^ (2 * m) * (q - n)) * n ^ (2 * (m + 1)):=by
    rw [show 2 * (m + 1) = 2 * m + 2 by omega,pow_add,mul_pow]
    ring
  rw [heq]
  exact mul_lt_mul_of_pos_right hfactor (pow_pos hn _)
theorem exists_density_threshold_for_cover (k:ℕ) {ρ:ℝ}
    (hρ0:0 ≤ ρ) (hρ1:ρ < 1) :
    ∃ δ:ℝ,0 < δ ∧ ∀ (q:ℕ) [NeZero q] (B T:Finset (ZMod q)),
      B.Nonempty → T.card ≤ k → B + B ⊆ B + (T - T) →
      (B.card:ℝ) < δ * q →
      ∃ r:ZMod q,r ≠ 0 ∧ ρ * B.card < ‖coefficient B r‖:=by
  obtain ⟨m,_,hdecay⟩:=exists_polynomial_decay_index k hρ0 hρ1
  let P:ℝ:=(2 * (m:ℝ) + 1) ^ k
  have hP:0 < P:=by dsimp [P]; positivity
  refine ⟨1 / (4 * P),by positivity, ?_⟩
  intro q hq B T hB hTk hcover hdensity
  have hn:(0:ℝ) < B.card:=by exact_mod_cast hB.card_pos
  have hqpos:(0:ℝ) < q:=by exact_mod_cast (NeZero.pos q)
  have hdensity':(B.card:ℝ) * P < (q:ℝ) / 4:=by
    have h:=mul_lt_mul_of_pos_right hdensity (show 0 < 4 * P by positivity)
    field_simp at h
    nlinarith
  have hnum:=moment_numerical_of_density_decay m hn hqpos hP.le hρ0 hdensity' hdecay
  apply exists_large_nonzero_coefficient_of_cover B T hcover m (ρ * B.card)
  have hbase:(1:ℝ) ≤ 2 * (m:ℝ) + 1:=by
    have hm:(0:ℝ) ≤ m:=by positivity
    linarith
  have hpow:(2 * (m:ℝ) + 1) ^ T.card ≤ P:=by
    exact pow_le_pow_right₀ hbase hTk
  have hscale:(B.card:ℝ) * (2 * (m:ℝ) + 1) ^ T.card ≤ B.card * P :=
    mul_le_mul_of_nonneg_left hpow hn.le
  exact lt_of_le_of_lt (mul_le_mul_of_nonneg_right hscale
    (moment_bracket_nonneg B m (ρ * B.card))) hnum
theorem exists_density_threshold_for_difference_set {K ρ:ℝ}
    (hK:0 ≤ K) (hρ0:0 ≤ ρ) (hρ1:ρ < 1) :
    ∃ δ:ℝ,0 < δ ∧ ∀ (q:ℕ) [NeZero q] (A:Finset (ZMod q)),
      A.Nonempty → ((A + A).card:ℝ) ≤ K * A.card →
      ((A - A).card:ℝ) < δ * q →
      ∃ r:ZMod q,r ≠ 0 ∧ ρ * (A - A).card < ‖coefficient (A - A) r‖:=by
  obtain ⟨δ,hδ,hcoeff⟩:=exists_density_threshold_for_cover ⌈2 * K ^ 2⌉₊ hρ0 hρ1
  refine ⟨δ,hδ, ?_⟩
  intro q hq A hA hdoubling hdensity
  obtain ⟨T,_,hTcard,hcover⟩:=exists_cover_of_small_doubling A hA hK hdoubling
  have hTk:T.card ≤ ⌈2 * K ^ 2⌉₊:=by
    have hceil:=Nat.le_ceil (2 * K ^ 2)
    have hreal:(T.card:ℝ) ≤ (⌈2 * K ^ 2⌉₊:ℝ):=by linarith
    exact_mod_cast hreal
  exact hcoeff q (A - A) T (hA.sub hA) hTk hcover hdensity
theorem difference_card_le_of_small_doubling {G:Type*} [AddCommGroup G] [DecidableEq G]
    (A:Finset G) (hA:A.Nonempty) {K:ℝ} (hK:0 ≤ K)
    (hdoubling:((A + A).card:ℝ) ≤ K * A.card) :
    ((A - A).card:ℝ) ≤ K ^ 2 * A.card:=by
  have h:=Finset.ruzsa_triangle_inequality_sub_add_add A A A
  have hpos:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  have hcast:((A - A).card:ℝ) * A.card ≤ ((A + A).card:ℝ) ^ 2:=by
    have hn:(A - A).card * A.card ≤ (A + A).card ^ 2:=by
      simpa only [pow_two] using h
    exact_mod_cast hn
  have hsquare:((A + A).card:ℝ) ^ 2 ≤ (K * A.card) ^ 2 :=
    (sq_le_sq₀ (Nat.cast_nonneg _) (mul_nonneg hK hpos.le)).mpr hdoubling
  apply le_of_mul_le_mul_right (a:=(A.card:ℝ)) _ hpos
  nlinarith
private def zz1975:"s07b7"="s07b7":=by decide+kernel
theorem exists_density_threshold_for_small_doubling {K ρ:ℝ}
    (hK:1 ≤ K) (hρ0:0 ≤ ρ) (hρ1:ρ < 1) :
    ∃ δ:ℝ,0 < δ ∧ ∀ (q:ℕ) [NeZero q] (A:Finset (ZMod q)),
      A.Nonempty → ((A + A).card:ℝ) ≤ K * A.card →
      (A.card:ℝ) < δ * q →
      ∃ r:ZMod q,r ≠ 0 ∧ ρ * (A - A).card < ‖coefficient (A - A) r‖:=by
  have hK0:0 < K:=by linarith
  obtain ⟨δ,hδ,hcoeff⟩:=exists_density_threshold_for_difference_set hK0.le hρ0 hρ1
  refine ⟨δ / K ^ 2,by positivity, ?_⟩
  intro q hq A hA hdoubling hdensity
  apply hcoeff q A hA hdoubling
  have hdiff:=difference_card_le_of_small_doubling A hA hK0.le hdoubling
  have hden:K ^ 2 * (A.card:ℝ) < δ * q:=by
    have hm:=mul_lt_mul_of_pos_right hdensity (pow_pos hK0 2)
    field_simp at hm
    nlinarith
  exact lt_of_le_of_lt hdiff hden
end Green24Proof.UniformFourierParameters
private def zz2508:"s09cc"="s09cc":=by decide+kernel
end 
section 
namespace Green24Proof.UniformRectification
open scoped BigOperators Pointwise
open Green24Proof.CyclicFourierMoments
open Green24Proof.UniformFourierParameters
open Green24Proof.FourierArcConcentration
theorem boundary_defect_uniform {q:ℕ} (hq:48 ≤ q) :
    0 < (q / 24:ℕ) ∧ 6 * (q / 24:ℕ) < q ∧
    1 - Real.cos (Real.pi / 24) ≤
      1 - Real.cos (2 * Real.pi * (q / 24:ℕ) / q):=by
  have hR:0 < q / 24:=by omega
  have hsmall:6 * (q / 24) < q:=by omega
  refine ⟨hR,hsmall, ?_⟩
  have hqpos:(0:ℝ) < q:=by exact_mod_cast (by omega:0 < q)
  have hlo:(q:ℝ) ≤ 48 * (q / 24:ℕ):=by
    exact_mod_cast (by omega:q ≤ 48 * (q / 24))
  have hhi:2 * (q / 24:ℕ) ≤ q:=by omega
  have hhir:2 * ((q / 24:ℕ):ℝ) ≤ q:=by exact_mod_cast hhi
  have hθlo:Real.pi / 24 ≤ 2 * Real.pi * (q / 24:ℕ) / q:=by
    apply (le_div_iff₀ hqpos).mpr
    nlinarith [Real.pi_pos]
  have hθhi:2 * Real.pi * (q / 24:ℕ) / q ≤ Real.pi:=by
    apply (div_le_iff₀ hqpos).mpr
    nlinarith [Real.pi_pos]
  have hc:=Real.cos_le_cos_of_nonneg_of_le_pi (by positivity:0 ≤ Real.pi / 24)
    hθhi hθlo
  linarith
theorem exists_ratio_for_defect {K κ:ℝ} (hK:1 ≤ K)
    (hκ:0 < κ) (hκ2:κ ≤ 2) :
    ∃ ρ:ℝ,0 ≤ ρ ∧ ρ < 1 ∧ (1 - ρ ^ 2) * K ^ 2 ≤ κ / 2:=by
  have hKsq:1 ≤ K ^ 2:=by nlinarith
  let e:ℝ:=κ / (4 * K ^ 2)
  have hepos:0 < e:=by dsimp [e]; positivity
  have heq:e * (4 * K ^ 2) = κ:=by dsimp [e]; field_simp
  have hehalf:e ≤ 1 / 2:=by nlinarith
  refine ⟨1 - e,by linarith,by linarith, ?_⟩
  have hnonneg:0 ≤ e ^ 2 * K ^ 2:=by positivity
  nlinarith
theorem relative_coefficient_budget {K ρ κ₀ κ n d:ℝ}
    (hρ0:0 ≤ ρ) (hρ1:ρ ≤ 1) (hn:0 ≤ n) (hd:0 ≤ d)
    (hdiff:d ≤ K ^ 2 * n) (hκ:κ₀ ≤ κ)
    (hbudget:(1 - ρ ^ 2) * K ^ 2 ≤ κ₀ / 2) :
    d ^ 2 - (ρ * d) ^ 2 ≤ n / 2 * d * κ:=by
  have hρ:0 ≤ 1 - ρ ^ 2:=by nlinarith
  calc
    d ^ 2 - (ρ * d) ^ 2 = (1 - ρ ^ 2) * d * d:=by ring
    _ ≤ (1 - ρ ^ 2) * (K ^ 2 * n) * d:=by gcongr
    _ = ((1 - ρ ^ 2) * K ^ 2) * n * d:=by ring
    _ ≤ (κ₀ / 2) * n * d:=by gcongr
    _ ≤ (κ / 2) * n * d:=by gcongr
    _ = n / 2 * d * κ:=by ring
private def zz1976:"s07b8"="s07b8":=by decide+kernel
theorem exists_uniform_prime_rectification {K:ℝ} (hK:1 ≤ K) :
    ∃ δ:ℝ,0 < δ ∧ ∀ (q:ℕ) [NeZero q] [Fact q.Prime]
      (A:Finset (ZMod q)),48 ≤ q → A.Nonempty →
      ((A + A).card:ℝ) ≤ K * A.card → (A.card:ℝ) < δ * q →
      ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
        B ⊆ Finset.Icc 0 (2 * ((q / 24:ℕ):ℤ)) ∧ B.card = A.card ∧
        IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f:=by
  let κ₀:ℝ:=1 - Real.cos (Real.pi / 24)
  have hκ₀:0 < κ₀:=by
    have hc:=Real.cos_lt_cos_of_nonneg_of_le_pi (by norm_num:(0:ℝ) ≤ 0)
      (by linarith [Real.pi_pos]:Real.pi / 24 ≤ Real.pi)
      (by positivity:(0:ℝ) < Real.pi / 24)
    dsimp [κ₀]
    simpa using sub_pos.mpr hc
  have hκ₂:κ₀ ≤ 2:=by dsimp [κ₀]; linarith [Real.neg_one_le_cos (Real.pi / 24)]
  obtain ⟨ρ,hρ0,hρ1,hρbudget⟩:=exists_ratio_for_defect hK hκ₀ hκ₂
  obtain ⟨δ,hδ,hcoeff⟩:=exists_density_threshold_for_small_doubling hK hρ0 hρ1
  refine ⟨δ,hδ, ?_⟩
  intro q hq hprime A hq48 hA hdoubling hdensity
  obtain ⟨r,hr,hlarge⟩:=hcoeff q A hA hdoubling hdensity
  obtain ⟨hR,hRq,hboundary⟩:=boundary_defect_uniform hq48
  have hdiff:=difference_card_le_of_small_doubling A hA (by linarith:0 ≤ K) hdoubling
  have hbudget:=relative_coefficient_budget hρ0 hρ1.le (Nat.cast_nonneg A.card)
    (Nat.cast_nonneg (A - A).card) hdiff hboundary hρbudget
  have hρd:0 ≤ ρ * ((A - A).card:ℝ):=by positivity
  have hsq:(ρ * ((A - A).card:ℝ)) ^ 2 < ‖coefficient (A - A) r‖ ^ 2 :=
    (sq_lt_sq₀ hρd (norm_nonneg _)).mpr hlarge
  have hlarge':((A - A).card:ℝ) ^ 2 -
      ‖∑ x ∈ A - A,ZMod.stdAddChar ((-r) * x)‖ ^ 2 <
      (A.card:ℝ) / 2 * (A - A).card *
        (1 - Real.cos (2 * Real.pi * ((q / 24:ℕ):ℤ) / q)):=by
    rw [coefficient_eq_positive] at hsq
    simp only [Int.cast_natCast]
    linarith
  obtain ⟨B,f,hB,hcard,hf,_⟩ :=
    exists_freiman_three_model_of_large_nonzero_character A (-r) (neg_ne_zero.mpr hr)
      (by exact_mod_cast hR) (by exact_mod_cast hRq) hlarge'
  exact ⟨B,f,hB,hcard,hf⟩
theorem exists_uniform_prime_rectification_of_low_density {K:ℝ} (hK:1 ≤ K) :
    ∃ δ:ℝ,0 < δ ∧ ∀ (q:ℕ) [NeZero q] [Fact q.Prime]
      (A:Finset (ZMod q)),A.Nonempty →
      ((A + A).card:ℝ) ≤ K * A.card → (A.card:ℝ) < δ * q →
      ∃ (B:Finset ℤ) (f:ZMod q → ℤ),
        B ⊆ Finset.Icc 0 (2 * ((q / 24:ℕ):ℤ)) ∧ B.card = A.card ∧
        IsAddFreimanIso 3 (A:Set (ZMod q)) (B:Set ℤ) f:=by
  obtain ⟨δ,hδ,hmodel⟩:=exists_uniform_prime_rectification hK
  refine ⟨min δ (1 / 48),lt_min hδ (by norm_num), ?_⟩
  intro q hq hprime A hA hdoubling hdensity
  have hqpos:(0:ℝ) ≤ q:=by positivity
  have hdensity':(A.card:ℝ) < δ * q :=
    lt_of_lt_of_le hdensity (mul_le_mul_of_nonneg_right (min_le_left _ _) hqpos)
  have hlargeq:(A.card:ℝ) < (1 / 48) * q :=
    lt_of_lt_of_le hdensity (mul_le_mul_of_nonneg_right (min_le_right _ _) hqpos)
  have hcard:(1:ℝ) ≤ A.card:=by exact_mod_cast hA.card_pos
  have hq48r:(48:ℝ) ≤ q:=by linarith
  exact hmodel q A (by exact_mod_cast hq48r) hA hdoubling hdensity'
end Green24Proof.UniformRectification
private def zz2509:"s09cd"="s09cd":=by decide+kernel
end 
section 
namespace Green24Proof.FreimanSumsetCardinality
open Finset
open scoped Pointwise
variable {G H:Type*} [AddCommGroup G] [AddCommGroup H]
  [DecidableEq G] [DecidableEq H]
omit [DecidableEq G] [DecidableEq H] in
theorem isAddFreimanIso_two_of_three {A:Set G} {B:Set H} {f:G → H}
    (hf:IsAddFreimanIso 3 A B f):IsAddFreimanIso 2 A B f :=
  hf.mono (hmn:=by decide)
omit [DecidableEq G] [DecidableEq H] in
theorem card_eq {n:ℕ} {A:Finset G} {B:Finset H} {f:G → H}
    (hf:IsAddFreimanIso n (A:Set G) (B:Set H) f):A.card = B.card:=by
  exact Finset.card_bij (fun a _ => f a)
    (fun a ha => hf.bijOn.mapsTo ha)
    (fun a ha b hb he => hf.bijOn.injOn ha hb he)
    (fun b hb => by
      obtain ⟨a,ha,he⟩:=hf.bijOn.surjOn hb
      exact ⟨a,ha,he⟩)
private def zz1977:"s07b9"="s07b9":=by decide+kernel
theorem add_card_eq_of_two {A:Finset G} {B:Finset H} {f:G → H}
    (hf:IsAddFreimanIso 2 (A:Set G) (B:Set H) f) :
    (A + A).card = (B + B).card:=by
  classical
  have hreps:∀ s ∈ A + A, ∃ a ∈ A, ∃ b ∈ A,a + b = s:=by
    intro s hs
    exact Finset.mem_add.mp hs
  choose a ha b hb hab using hreps
  refine Finset.card_bij (fun s hs => f (a s hs) + f (b s hs)) ?_ ?_ ?_
  · intro s hs
    exact Finset.add_mem_add (hf.bijOn.mapsTo (ha s hs)) (hf.bijOn.mapsTo (hb s hs))
  · intro s hs t ht he
    have h:=(hf.add_eq_add (ha s hs) (hb s hs) (ha t ht) (hb t ht)).mp he
    rwa [hab s hs,hab t ht] at h
  · intro t ht
    obtain ⟨u,hu,v,hv,huv⟩:=Finset.mem_add.mp ht
    obtain ⟨x,hx,hfx⟩:=hf.bijOn.surjOn hu
    obtain ⟨y,hy,hfy⟩:=hf.bijOn.surjOn hv
    have hxy:x + y ∈ A + A:=Finset.add_mem_add hx hy
    refine ⟨x + y,hxy, ?_⟩
    have he:=(hf.add_eq_add (ha (x + y) hxy) (hb (x + y) hxy) hx hy).mpr
      (hab (x + y) hxy)
    rw [he,hfx,hfy]
    exact huv
theorem add_card_eq_of_order {n:ℕ} (hn:2 ≤ n)
    {A:Finset G} {B:Finset H} {f:G → H}
    (hf:IsAddFreimanIso n (A:Set G) (B:Set H) f) :
    (A + A).card = (B + B).card :=
  add_card_eq_of_two (hf.mono (hmn:=hn))
theorem add_card_eq {A:Finset G} {B:Finset H} {f:G → H}
    (hf:IsAddFreimanIso 3 (A:Set G) (B:Set H) f) :
    (A + A).card = (B + B).card :=
  add_card_eq_of_two (isAddFreimanIso_two_of_three hf)
theorem add_card_eq_image {A:Finset G} {f:G → H}
    (hf:IsAddFreimanIso 3 (A:Set G) (A.image f:Set H) f) :
    (A + A).card = (A.image f + A.image f).card :=
  add_card_eq hf
private def zz1978:"s07ba"="s07ba":=by decide+kernel
theorem doubling_iff {A:Finset G} {B:Finset H} {f:G → H}
    (hf:IsAddFreimanIso 3 (A:Set G) (B:Set H) f) (K:ℝ) :
    ((A + A).card:ℝ) ≤ K * A.card ↔ ((B + B).card:ℝ) ≤ K * B.card:=by
  rw [add_card_eq hf,card_eq hf]
end Green24Proof.FreimanSumsetCardinality
private def zz2510:"s09ce"="s09ce":=by decide+kernel
end 
section 
namespace Green24Proof.SmallDoublingIntegerModel
open scoped BigOperators Pointwise
open Green24Proof.ModularRectification
open Green24Proof.UniformRectification
theorem freiman_three_intCast {q L:ℕ} (A:Finset ℤ)
    (hA:A ⊆ Finset.Icc 0 (L:ℤ)) (hLq:3 * L < q) :
    IsAddFreimanIso 3 (A:Set ℤ)
      (A.image (fun x:ℤ => (x:ZMod q)):Set (ZMod q))
      (fun x:ℤ => (x:ZMod q)):=by
  have hinj:Set.InjOn (fun x:ℤ => (x:ZMod q)) (A:Set ℤ):=by
    intro x hx y hy heq
    have hx':=Finset.mem_Icc.mp (hA hx)
    have hy':=Finset.mem_Icc.mp (hA hy)
    apply int_eq_of_cast_eq_of_abs_sub_lt heq
    have hLq':3 * (L:ℤ) < q:=by exact_mod_cast hLq
    exact abs_lt.mpr (by omega)
  refine ⟨by simpa only [Finset.coe_image] using hinj.bijOn_image, ?_⟩
  intro s t hsA htA hs ht
  have hbound (u:Multiset ℤ) (huA:∀ x ∈ u,x ∈ A) (hu:u.card = 3) :
      0 ≤ u.sum ∧ u.sum ≤ 3 * (L:ℤ):=by
    constructor
    · exact Multiset.sum_nonneg (fun x hx => (Finset.mem_Icc.mp (hA (huA x hx))).1)
    · have h:=Multiset.sum_le_card_nsmul u (L:ℤ)
        (fun x hx => (Finset.mem_Icc.mp (hA (huA x hx))).2)
      simpa [hu] using h
  rw [← Int.cast_multiset_sum, ← Int.cast_multiset_sum]
  constructor
  · intro heq
    apply int_eq_of_cast_eq_of_abs_sub_lt heq
    have hsbound:=hbound s (fun _ hx => hsA hx) hs
    have htbound:=hbound t (fun _ hx => htA hx) ht
    have hLq':3 * (L:ℤ) < q:=by exact_mod_cast hLq
    exact abs_lt.mpr (by omega)
  · exact congrArg (fun z:ℤ => (z:ZMod q))
theorem freimanIso_translate (A:Finset ℤ) (t:ℤ) (n:ℕ) :
    IsAddFreimanIso n (A:Set ℤ) (A.image (fun x => x + t):Set ℤ)
      (fun x => x + t) where
  bijOn:=by
    simpa only [Finset.coe_image,Equiv.coe_addRight] using
      (Equiv.addRight t).injective.bijOn_image (s:=(A:Set ℤ))
  map_sum_eq_map_sum s r _ _ hs hr:=by
    simp [Multiset.sum_map_add,hs,hr]
theorem exists_interval_model (A:Finset ℤ) (hA:A.Nonempty) :
    ∃ (L:ℕ) (B:Finset ℤ) (f:ℤ → ℤ),
      B ⊆ Finset.Icc 0 (L:ℤ) ∧ B.card = A.card ∧
      IsAddFreimanIso 3 (A:Set ℤ) (B:Set ℤ) f:=by
  let a:=A.min' hA
  let b:=A.max' hA
  let B:=A.image (fun x => x + -a)
  refine ⟨(b - a).natAbs,B,(fun x => x + -a), ?_, ?_,freimanIso_translate A (-a) 3⟩
  · intro x hx
    obtain ⟨y,hy,rfl⟩:=Finset.mem_image.mp hx
    have hlo:a ≤ y:=Finset.min'_le A y hy
    have hhi:y ≤ b:=Finset.le_max' A y hy
    have hab:b - a ≤ ((b - a).natAbs:ℤ):=Int.le_natAbs
    exact Finset.mem_Icc.mpr ⟨by omega,by omega⟩
  · exact Finset.card_image_of_injective _ (Equiv.addRight (-a)).injective
private def zz1979:"s07bb"="s07bb":=by decide+kernel
theorem exists_bounded_integer_model {K:ℝ} (hK:1 ≤ K) :
    ∃ C:ℝ,0 < C ∧ ∀ (A:Finset ℤ),A.Nonempty →
      ((A + A).card:ℝ) ≤ K * A.card →
      ∃ (L:ℕ) (B:Finset ℤ) (f:ℤ → ℤ),
        (L:ℝ) ≤ C * A.card ∧ B ⊆ Finset.Icc 0 (L:ℤ) ∧ B.card = A.card ∧
        IsAddFreimanIso 3 (A:Set ℤ) (B:Set ℤ) f:=by
  classical
  obtain ⟨δ,hδ,hrectify⟩:=exists_uniform_prime_rectification_of_low_density hK
  refine ⟨1 / δ,by positivity, ?_⟩
  intro A hA hdoubling
  let P:ℕ → Prop:=fun L => ∃ (B:Finset ℤ) (f:ℤ → ℤ),
    B ⊆ Finset.Icc 0 (L:ℤ) ∧ B.card = A.card ∧
    IsAddFreimanIso 3 (A:Set ℤ) (B:Set ℤ) f
  have hex:∃ L,P L:=exists_interval_model A hA
  let L:=Nat.find hex
  obtain ⟨B,f,hB,hcard,hf⟩:=Nat.find_spec hex
  refine ⟨L,B,f, ?_,hB,hcard,hf⟩
  by_contra hbound
  have hwide:(1 / δ) * A.card < (L:ℝ):=lt_of_not_ge hbound
  have hLpos:0 < L:=by
    have hnonneg:(0:ℝ) ≤ (1 / δ) * A.card:=by positivity
    have hpos:(0:ℝ) < L:=lt_of_le_of_lt hnonneg hwide
    exact_mod_cast hpos
  obtain ⟨q,hprime,hLq,hqL⟩:=Nat.exists_prime_lt_and_le_two_mul (3 * L) (by omega)
  have:Fact q.Prime:=⟨hprime⟩
  have:NeZero q:=⟨hprime.ne_zero⟩
  let S:=B.image (fun x:ℤ => (x:ZMod q))
  have hcast:=freiman_three_intCast B hB hLq
  have hScard:S.card = B.card:=(FreimanSumsetCardinality.card_eq hcast).symm
  have hBnonempty:B.Nonempty:=by
    rw [← Finset.card_pos,hcard]
    exact hA.card_pos
  have hSnonempty:S.Nonempty:=hBnonempty.image _
  have hdoubleB:((B + B).card:ℝ) ≤ K * B.card :=
    (FreimanSumsetCardinality.doubling_iff hf K).mp hdoubling
  have hdoubleS:((S + S).card:ℝ) ≤ K * S.card :=
    (FreimanSumsetCardinality.doubling_iff hcast K).mp hdoubleB
  have hdensity:(S.card:ℝ) < δ * q:=by
    rw [hScard,hcard]
    have hmul:=mul_lt_mul_of_pos_left hwide hδ
    field_simp at hmul
    have hLqr:(L:ℝ) < q:=by exact_mod_cast (by omega:L < q)
    exact lt_trans (by nlinarith:(A.card:ℝ) < δ * L)
      (mul_lt_mul_of_pos_left hLqr hδ)
  obtain ⟨D,g,hD,hDcard,hg⟩:=hrectify q S hSnonempty hdoubleS hdensity
  have hnew:P (2 * (q / 24)):=by
    refine ⟨D,g ∘ (fun x:ℤ => (x:ZMod q)) ∘ f, ?_, ?_, ?_⟩
    · simpa only [Nat.cast_mul,Nat.cast_ofNat] using hD
    · exact hDcard.trans (hScard.trans hcard)
    · exact hg.comp (hcast.comp hf)
  have hminimal:L ≤ 2 * (q / 24):=Nat.find_min' hex hnew
  omega
end Green24Proof.SmallDoublingIntegerModel
private def zz2511:"s09cf"="s09cf":=by decide+kernel
end 
section 
namespace Green24Proof.SmallDifferenceIntegerModel
open scoped Pointwise
variable {G:Type*} [AddCommGroup G] [DecidableEq G]
theorem higher_sumset_card_le {K:ℝ} (A:Finset G) (hA:A.Nonempty)
    (hdiff:((A - A).card:ℝ) ≤ K * A.card) (m:ℕ) :
    ((m • A).card:ℝ) ≤ K ^ m * A.card:=by
  have hp:=Finset.pluennecke_ruzsa_inequality_nsmul_sub hA A m
  have hp':((m • A).card:ℝ) ≤
      (((A - A).card:ℝ) / A.card) ^ m * A.card:=by
    have hc:=NNRat.cast_mono (K:=ℝ) hp
    change (NNRat.castHom ℝ) ((m • A).card:ℚ≥0) ≤
      (NNRat.castHom ℝ) ((((A - A).card:ℚ≥0) / A.card) ^ m * A.card) at hc
    rw [map_mul,map_pow] at hc
    simpa only [NNRat.coe_castHom,NNRat.cast_div,NNRat.cast_natCast] using hc
  have hpos:(0:ℝ) < A.card:=by exact_mod_cast hA.card_pos
  apply hp'.trans
  gcongr
  exact (div_le_iff₀ hpos).mpr hdiff
theorem doubling_card_le {K:ℝ} (A:Finset G) (hA:A.Nonempty)
    (hdiff:((A - A).card:ℝ) ≤ K * A.card) :
    ((A + A).card:ℝ) ≤ K ^ 2 * A.card:=by
  simpa only [two_nsmul] using higher_sumset_card_le A hA hdiff 2
theorem exists_bounded_integer_model {K:ℝ} (hK:1 ≤ K) :
    ∃ C:ℝ,0 < C ∧ ∀ (A:Finset ℤ),A.Nonempty →
      ((A - A).card:ℝ) ≤ K * A.card →
      ∃ (L:ℕ) (B:Finset ℤ) (f:ℤ → ℤ),
        (L:ℝ) ≤ C * A.card ∧ B ⊆ Finset.Icc 0 (L:ℤ) ∧ B.card = A.card ∧
        IsAddFreimanIso 3 (A:Set ℤ) (B:Set ℤ) f:=by
  have hKsq:1 ≤ K ^ 2:=by nlinarith
  obtain ⟨C,hC,hm⟩ :=
    Green24Proof.SmallDoublingIntegerModel.exists_bounded_integer_model hKsq
  exact ⟨C,hC,fun A hA hdiff => hm A hA (doubling_card_le A hA hdiff)⟩
end Green24Proof.SmallDifferenceIntegerModel
private def zz2512:"s09d0"="s09d0":=by decide+kernel
end 
section 
namespace Green24Proof.DilatedEnergyPartition
open scoped Pointwise
open Green24Proof.EnergyAgglomeration Green24Proof.AdaptiveEnergyPartition
noncomputable def dilationThreshold (ε L:ℝ):ℝ:=ε ^ 8 / ((1 + L) ^ 2) ^ 12
private def zz1980:"s07bc"="s07bc":=by decide+kernel
theorem dilationThreshold_pos {ε L:ℝ} (hε:0 < ε) (hL:0 ≤ L) :
    0 < dilationThreshold ε L:=by
  dsimp [dilationThreshold]
  positivity
theorem dilated_energy_le_of_threshold (A B:Finset ℤ) (hA:A.Nonempty) (hB:B.Nonempty)
    {L ε N:ℝ} (hL:0 ≤ L) (hN:0 ≤ N)
    (hDA:((A - A).card:ℝ) ≤ L * A.card)
    (hDB:((B - B).card:ℝ) ≤ L * B.card)
    (hAN:(A.card:ℝ) ≤ N) (hBN:(B.card:ℝ) ≤ N)
    (hE:(A.addEnergy B:ℝ) ≤ dilationThreshold ε L * N ^ 3)
    (k l:ℤ) (hk:k ≠ 0) (hl:l ≠ 0) (hk3:k.natAbs ≤ 3) (hl3:l.natAbs ≤ 3) :
    ((A.image (fun a => k * a)).addEnergy (B.image (fun b => l * b)):ℝ) ≤ ε ^ 2 * N ^ 3:=by
  let D:ℝ:=(1 + L) ^ 2
  have hD:1 ≤ D:=by dsimp [D]; nlinarith
  have hDpos:0 < D:=lt_of_lt_of_le zero_lt_one hD
  have hLD:L ^ 2 ≤ D:=by dsimp [D]; nlinarith
  have hp (n:ℕ) (hn:n ≤ 3):(L ^ 2) ^ (n + 1) ≤ D ^ 4:=by
    calc
      _ ≤ D ^ (n + 1):=by gcongr
      _ ≤ D ^ 4:=pow_le_pow_right₀ hD (by omega)
  have hfirst:(L ^ 2) ^ (k.natAbs + 1) * (A.addEnergy B:ℝ) ≤
      (ε ^ 4 / D ^ 4) ^ 2 * N ^ 3:=by
    calc
      _ ≤ D ^ 4 * (dilationThreshold ε L * N ^ 3) :=
        mul_le_mul (hp k.natAbs hk3) hE (Nat.cast_nonneg _) (by positivity)
      _ = (ε ^ 4 / D ^ 4) ^ 2 * N ^ 3:=by
        change D ^ 4 * (ε ^ 8 / D ^ 12 * N ^ 3) = _
        field_simp
  have hsecond:(L ^ 2) ^ (l.natAbs + 1) * (ε ^ 4 / D ^ 4) ≤ (ε ^ 2) ^ 2:=by
    calc
      _ ≤ D ^ 4 * (ε ^ 4 / D ^ 4) :=
        mul_le_mul_of_nonneg_right (hp l.natAbs hl3) (by positivity)
      _ = (ε ^ 2) ^ 2:=by field_simp
  exact Green24Proof.DilationEnergyTransfer.integer_signed_energy_le_of_budget k l hk hl
    A B hA hB (sq_nonneg L) (sq_nonneg L) (by positivity) (sq_nonneg ε) hN
    (Green24Proof.SmallDifferenceIntegerModel.doubling_card_le A hA hDA)
    (Green24Proof.SmallDifferenceIntegerModel.doubling_card_le B hB hDB)
    hAN hBN hfirst hsecond
theorem exists_dilated_energy_partition (A:Finset ℤ) (hA:A.Nonempty)
    {δ ε:ℝ} (hδ:0 < δ) (hε:0 < ε) :
    ∃ (L:ℝ) (P:Finset (Finset ℤ)) (R:Finset ℤ),
      0x1000000 / δ ^ 10 ≤ L ∧
      L ≤ adaptiveBound (dilationThreshold ε) ⌈8 / δ ^ 2⌉₊ (0x1000000 / δ ^ 10) ∧
      P.card ≤ ⌈8 / δ ^ 2⌉₊ ∧ R ⊆ A ∧
      (R.addEnergy R:ℝ) < δ * (A.card:ℝ) ^ 3 ∧
      ControlledFamily A R (δ ^ 2 * A.card / 8) L P ∧
      ∀ B ∈ P, ∀ C ∈ P,B ≠ C →
        ∀ k l:ℤ,k ≠ 0 → l ≠ 0 → k.natAbs ≤ 3 → l.natAbs ≤ 3 →
          ((B.image (fun b => k * b)).addEnergy (C.image (fun c => l * c)):ℝ) ≤
            ε ^ 2 * (A.card:ℝ) ^ 3:=by
  obtain ⟨L,P,R,hKL,hLbound,hPcard,hRA,hRE,hcontrolled,hsep⟩ :=
    exists_adaptive_energy_partition A hA hδ (dilationThreshold ε)
      (fun _ hL => dilationThreshold_pos hε hL)
  have hL:0 ≤ L:=(by positivity:0 ≤ 0x1000000 / δ ^ 10).trans hKL
  refine ⟨L,P,R,hKL,hLbound,hPcard,hRA,hRE,hcontrolled, ?_⟩
  intro B hB C hC hBC k l hk hl hk3 hl3
  obtain ⟨hBA,hBne,_hBsize,hDB,_hBR⟩:=hcontrolled.1 B hB
  obtain ⟨hCA,hCne,_hCsize,hDC,_hCR⟩:=hcontrolled.1 C hC
  exact dilated_energy_le_of_threshold B C hBne hCne hL (Nat.cast_nonneg _)
    hDB hDC (by exact_mod_cast Finset.card_le_card hBA)
    (by exact_mod_cast Finset.card_le_card hCA) (hsep hB hC hBC).le k l hk hl hk3 hl3
theorem equation_energy_budgets {A:Finset ℤ} {P:Finset (Finset ℤ)} {ε:ℝ}
    (henergy:∀ B ∈ P, ∀ C ∈ P,B ≠ C →
      ∀ k l:ℤ,k ≠ 0 → l ≠ 0 → k.natAbs ≤ 3 → l.natAbs ≤ 3 →
        ((B.image (fun b => k * b)).addEnergy (C.image (fun c => l * c)):ℝ) ≤
          ε ^ 2 * (A.card:ℝ) ^ 3)
    (B C:Finset ℤ) (hB:B ∈ P) (hC:C ∈ P) (hBC:B ≠ C) :
    (B.addEnergy (C.image (fun c => 2 * c)):ℝ) ≤ ε ^ 2 * (A.card:ℝ) ^ 3 ∧
      ((C.image (fun c => 3 * c)).addEnergy (B.image (fun b => -2 * b)):ℝ) ≤
        ε ^ 2 * (A.card:ℝ) ^ 3:=by
  constructor
  · simpa using henergy B hB C hC hBC 1 2 (by norm_num) (by norm_num) (by norm_num) (by norm_num)
  · exact henergy C hC B hB hBC.symm 3 (-2) (by norm_num) (by norm_num) (by norm_num) (by norm_num)
end Green24Proof.DilatedEnergyPartition
private def zz2513:"s09d1"="s09d1":=by decide+kernel
end 
section 
namespace Green24Proof.EnergyCauchy
open Finset
open scoped BigOperators Pointwise
open Green24Proof.EnergyOverlapMerge (differenceFiber)
variable {G H:Type*} [AddCommGroup G] [DecidableEq G]
  [AddCommGroup H] [DecidableEq H]
private def zz1981:"s07bd"="s07bd":=by decide+kernel
theorem energy_eq_self_difference_count (A B:Finset G) :
    A.addEnergy B = (((A ×ˢ A) ×ˢ (B ×ˢ B)).filter
      (fun p => p.1.1 - p.1.2 = p.2.1 - p.2.2)).card:=by
  unfold Finset.addEnergy
  refine Finset.card_bij (fun p _ => (p.1,p.2.2,p.2.1)) ?_ ?_ ?_
  · rintro ⟨⟨a,c⟩,b,d⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    refine ⟨⟨hp.1.1,hp.1.2.2,hp.1.2.1⟩, ?_⟩
    simpa only [sub_eq_sub_iff_add_eq_add,add_comm d c] using hp.2
  · rintro ⟨⟨a,c⟩,b,d⟩ _ ⟨⟨a',c'⟩,b',d'⟩ _ he
    simpa only [Prod.mk.injEq,and_comm,and_left_comm,and_assoc] using he
  · rintro ⟨⟨a,c⟩,d,b⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    refine ⟨((a,c),b,d), ?_,rfl⟩
    simp only [Finset.mem_filter,Finset.mem_product]
    refine ⟨⟨hp.1.1,hp.1.2.2,hp.1.2.1⟩, ?_⟩
    simpa only [sub_eq_sub_iff_add_eq_add,add_comm d c] using hp.2
theorem energy_eq_sum_self_difference (A B U:Finset G) (hAU:A - A ⊆ U) :
    A.addEnergy B = ∑ t ∈ U,
      (differenceFiber A A t).card * (differenceFiber B B t).card:=by
  have hmap:∀ p ∈ A ×ˢ A,p.1 - p.2 ∈ U:=by
    intro p hp
    exact hAU (Finset.sub_mem_sub (Finset.mem_product.mp hp).1 (Finset.mem_product.mp hp).2)
  have hfiber:=Finset.sum_fiberwise_of_maps_to' hmap
    (fun t => (differenceFiber B B t).card)
  have hsum:A.addEnergy B = ∑ p ∈ A ×ˢ A,(differenceFiber B B (p.1 - p.2)).card:=by
    rw [energy_eq_self_difference_count]
    simp only [Finset.card_filter,Finset.sum_product,differenceFiber]
    simp only [eq_comm]
  rw [hsum, ← hfiber]
  apply Finset.sum_congr rfl
  intro t _
  simp [differenceFiber]
theorem mixed_energy_sq_le (A B:Finset G) :
    A.addEnergy B ^ 2 ≤ A.addEnergy A * B.addEnergy B:=by
  let U:=(A - A) ∪ (B - B)
  have ha:A - A ⊆ U:=Finset.subset_union_left
  have hb:B - B ⊆ U:=Finset.subset_union_right
  rw [energy_eq_sum_self_difference A B U ha,
    energy_eq_sum_self_difference A A U ha,
    energy_eq_sum_self_difference B B U hb]
  simpa only [← pow_two] using Finset.sum_mul_sq_le_sq_mul_sq (R:=ℕ) U
    (fun t => (differenceFiber A A t).card) (fun t => (differenceFiber B B t).card)
theorem energy_image (f:G →+ H) (hf:Function.Injective f) (A B:Finset G) :
    (A.image f).addEnergy (B.image f) = A.addEnergy B:=by
  symm
  unfold Finset.addEnergy
  refine Finset.card_bij (fun p _ => ((f p.1.1,f p.1.2),f p.2.1,f p.2.2)) ?_ ?_ ?_
  · rintro ⟨⟨a,c⟩,b,d⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    refine ⟨⟨⟨Finset.mem_image.mpr ⟨a,hp.1.1.1,rfl⟩,
      Finset.mem_image.mpr ⟨c,hp.1.1.2,rfl⟩⟩,
      Finset.mem_image.mpr ⟨b,hp.1.2.1,rfl⟩,
      Finset.mem_image.mpr ⟨d,hp.1.2.2,rfl⟩⟩, ?_⟩
    simpa only [map_add] using congrArg f hp.2
  · rintro ⟨⟨a,c⟩,b,d⟩ _ ⟨⟨a',c'⟩,b',d'⟩ _ he
    simp only [Prod.mk.injEq] at he ⊢
    exact ⟨⟨hf he.1.1,hf he.1.2⟩,hf he.2.1,hf he.2.2⟩
  · rintro ⟨⟨a,c⟩,b,d⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hp.1.1.1
    obtain ⟨c,hc,rfl⟩:=Finset.mem_image.mp hp.1.1.2
    obtain ⟨b,hb,rfl⟩:=Finset.mem_image.mp hp.1.2.1
    obtain ⟨d,hd,rfl⟩:=Finset.mem_image.mp hp.1.2.2
    refine ⟨((a,c),b,d), ?_,rfl⟩
    simp only [Finset.mem_filter,Finset.mem_product]
    exact ⟨⟨⟨ha,hc⟩,hb,hd⟩,hf (by simpa only [map_add] using hp.2)⟩
private def zz1982:"s07be"="s07be":=by decide+kernel
theorem integer_energy_dilate (k:ℤ) (hk:k ≠ 0) (A B:Finset ℤ) :
    (A.image (fun x => k * x)).addEnergy (B.image (fun x => k * x)) =
      A.addEnergy B:=by
  exact energy_image (AddMonoidHom.mulLeft k) (fun _ _ h => mul_left_cancel₀ hk h) A B
theorem mixed_energy_le_of_self_budget (A B:Finset G) {δ N:ℝ} (hN:0 ≤ N)
    (hA:(A.addEnergy A:ℝ) ≤ δ ^ 4 * N ^ 3)
    (hB:(B.addEnergy B:ℝ) ≤ N ^ 3) :
    (A.addEnergy B:ℝ) ≤ δ ^ 2 * N ^ 3:=by
  have hs:(A.addEnergy B:ℝ) ^ 2 ≤ (A.addEnergy A:ℝ) * B.addEnergy B:=by
    exact_mod_cast mixed_energy_sq_le A B
  have hsq:(A.addEnergy B:ℝ) ^ 2 ≤ (δ ^ 2 * N ^ 3) ^ 2:=by
    calc
      _ ≤ (A.addEnergy A:ℝ) * B.addEnergy B:=hs
      _ ≤ (δ ^ 4 * N ^ 3) * N ^ 3 :=
        mul_le_mul hA hB (Nat.cast_nonneg _) (by positivity)
      _ = _:=by ring
  exact (sq_le_sq₀ (Nat.cast_nonneg _) (by positivity)).mp hsq
end Green24Proof.EnergyCauchy
private def zz2514:"s09d2"="s09d2":=by decide+kernel
end 
section 
namespace Green24Proof.IntegerStructuralCounting
open scoped Pointwise
theorem equation_iff_of_freiman_three {A B:Set ℤ} {f:ℤ → ℤ}
    (hf:IsAddFreimanIso 3 A B f) {x y z:ℤ}
    (hx:x ∈ A) (hy:y ∈ A) (hz:z ∈ A) :
    f x + 2 * f y = 3 * f z ↔ x + 2 * y = 3 * z:=by
  have h:=hf.map_sum_eq_map_sum
    (s:=x ::ₘ y ::ₘ y ::ₘ 0) (t:=z ::ₘ z ::ₘ z ::ₘ 0)
    (by simpa using (show ∀ a,a = x ∨ a = y → a ∈ A from by aesop))
    (by simpa using hz) (by simp) (by simp)
  simp only [Multiset.map_cons,Multiset.map_zero,Multiset.sum_cons,
    Multiset.sum_zero,add_zero] at h
  ring_nf at h ⊢
  exact h
theorem integerSolutionCount_eq_of_freiman_three {A B:Finset ℤ} {f:ℤ → ℤ}
    (hf:IsAddFreimanIso 3 (A:Set ℤ) (B:Set ℤ) f) :
    integerSolutionCount A = integerSolutionCount B:=by
  rw [← integerSolutionTriples_card A, ← integerSolutionTriples_card B]
  refine Finset.card_bij (fun p _ => (f p.1,f p.2.1,f p.2.2)) ?_ ?_ ?_
  · rintro ⟨x,y,z⟩ hp
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product] at hp ⊢
    exact ⟨⟨hf.bijOn.mapsTo hp.1.1,hf.bijOn.mapsTo hp.1.2.1,
      hf.bijOn.mapsTo hp.1.2.2⟩,
      (equation_iff_of_freiman_three hf hp.1.1 hp.1.2.1 hp.1.2.2).mpr hp.2⟩
  · rintro ⟨x,y,z⟩ hp ⟨x',y',z'⟩ hp' he
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product] at hp hp'
    have hx:=hf.bijOn.injOn hp.1.1 hp'.1.1 (congrArg Prod.fst he)
    have hy:=hf.bijOn.injOn hp.1.2.1 hp'.1.2.1 (congrArg (fun p => p.2.1) he)
    have hz:=hf.bijOn.injOn hp.1.2.2 hp'.1.2.2 (congrArg (fun p => p.2.2) he)
    exact Prod.ext hx (Prod.ext hy hz)
  · rintro ⟨x,y,z⟩ hp
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨a,ha,rfl⟩:=hf.bijOn.surjOn hp.1.1
    obtain ⟨b,hb,rfl⟩:=hf.bijOn.surjOn hp.1.2.1
    obtain ⟨c,hc,rfl⟩:=hf.bijOn.surjOn hp.1.2.2
    refine ⟨(a,b,c), ?_,rfl⟩
    simp only [integerSolutionTriples,Finset.mem_filter,Finset.mem_product]
    exact ⟨⟨ha,hb,hc⟩,(equation_iff_of_freiman_three hf ha hb hc).mp hp.2⟩
private def zz1983:"s07bf"="s07bf":=by decide+kernel
theorem freimanIso_translate (A:Finset ℤ) (t:ℤ) (n:ℕ) :
    IsAddFreimanIso n (A:Set ℤ) (A.image (fun x => x + t):Set ℤ)
      (fun x => x + t) where
  bijOn:=by
    simpa only [Finset.coe_image,Equiv.coe_addRight] using
      (Equiv.addRight t).injective.bijOn_image (s:=(A:Set ℤ))
  map_sum_eq_map_sum s r _ _ hs hr:=by
    simp [Multiset.sum_map_add,hs,hr]
theorem integerSolutionCount_translate (A:Finset ℤ) (t:ℤ) :
    integerSolutionCount (A.image (fun x => x + t)) = integerSolutionCount A :=
  (integerSolutionCount_eq_of_freiman_three (freimanIso_translate A t 3)).symm
theorem double_sum_translate (A:Finset ℤ) (t:ℤ) :
    A.image (fun x => x + t) + A.image (fun x => x + t) =
      (A + A).image (fun x => x + 2 * t):=by
  ext z
  constructor
  · intro hz
    obtain ⟨u,hu,v,hv,rfl⟩:=Finset.mem_add.mp hz
    obtain ⟨a,ha,rfl⟩:=Finset.mem_image.mp hu
    obtain ⟨b,hb,rfl⟩:=Finset.mem_image.mp hv
    exact Finset.mem_image.mpr ⟨a + b,Finset.add_mem_add ha hb,by ring⟩
  · intro hz
    obtain ⟨u,hu,rfl⟩:=Finset.mem_image.mp hz
    obtain ⟨a,ha,b,hb,rfl⟩:=Finset.mem_add.mp hu
    exact Finset.mem_add.mpr ⟨a + t,Finset.mem_image.mpr ⟨a,ha,rfl⟩,
      b + t,Finset.mem_image.mpr ⟨b,hb,rfl⟩,by ring⟩
theorem exists_zero_normalized (A:Finset ℤ) (hA:A.Nonempty) :
    ∃ B:Finset ℤ,0 ∈ B ∧ B.card = A.card ∧
      (B + B).card = (A + A).card ∧ integerSolutionCount B = integerSolutionCount A:=by
  obtain ⟨a,ha⟩:=hA
  refine ⟨A.image (fun x => x + -a), ?_, ?_, ?_,integerSolutionCount_translate A (-a)⟩
  · exact Finset.mem_image.mpr ⟨a,ha,by omega⟩
  · exact Finset.card_image_of_injective _ (fun _ _ h => add_right_cancel h)
  · rw [double_sum_translate]
    exact Finset.card_image_of_injective _ (fun _ _ h => add_right_cancel h)
def mixedSolutionCount (A B C:Finset ℤ):ℕ :=
  ((A ×ˢ (B ×ˢ C)).filter (fun p => p.1 + 2 * p.2.1 = 3 * p.2.2)).card
private def zz1984:"s07c0"="s07c0":=by decide+kernel
theorem mixedSolutionCount_self (A:Finset ℤ) :
    mixedSolutionCount A A A = integerSolutionCount A :=
  integerSolutionTriples_card A
theorem mixedSolutionCount_eq_pair_count (A B C:Finset ℤ) :
    mixedSolutionCount A B C =
      (((A ×ˢ B.image (fun y => 2 * y))).filter
        (fun p => p.1 + p.2 ∈ C.image (fun z => 3 * z))).card:=by
  unfold mixedSolutionCount
  refine Finset.card_bij (fun p _ => (p.1,2 * p.2.1)) ?_ ?_ ?_
  · rintro ⟨x,y,z⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    exact ⟨⟨hp.1.1,Finset.mem_image.mpr ⟨y,hp.1.2.1,rfl⟩⟩,
      Finset.mem_image.mpr ⟨z,hp.1.2.2,hp.2.symm⟩⟩
  · rintro ⟨x,y,z⟩ hp ⟨x',y',z'⟩ hp' he
    simp only [Finset.mem_filter,Finset.mem_product] at hp hp'
    have hx:=congrArg Prod.fst he
    have hy:=congrArg Prod.snd he
    dsimp at hx hy
    have hyy:y = y':=by omega
    have hzz:z = z':=by omega
    exact Prod.ext hx (Prod.ext hyy hzz)
  · rintro ⟨x,v⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨y,hy,rfl⟩:=Finset.mem_image.mp hp.1.2
    obtain ⟨z,hz,he⟩:=Finset.mem_image.mp hp.2
    refine ⟨(x,y,z), ?_,rfl⟩
    exact Finset.mem_filter.mpr ⟨Finset.mem_product.mpr
      ⟨hp.1.1,Finset.mem_product.mpr ⟨hy,hz⟩⟩,he.symm⟩
theorem mixedSolutionCount_sq_le_energy (A B C:Finset ℤ) :
    mixedSolutionCount A B C ^ 2 ≤
      C.card * Finset.addEnergy A (B.image (fun y => 2 * y)):=by
  rw [mixedSolutionCount_eq_pair_count]
  have h:=Finset.card_sq_le_card_mul_addEnergy A
    (B.image (fun y => 2 * y)) (C.image (fun z => 3 * z))
  rw [Finset.card_image_of_injective C (fun a b h => by omega)] at h
  exact h
theorem mixedSolutionCount_le_of_energy {A B C:Finset ℤ} {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hC:(C.card:ℝ) ≤ N)
    (hE:(Finset.addEnergy A (B.image (fun y => 2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3) :
    (mixedSolutionCount A B C:ℝ) ≤ δ * N ^ 2:=by
  have hs:(mixedSolutionCount A B C:ℝ) ^ 2 ≤
      (C.card:ℝ) * (Finset.addEnergy A (B.image (fun y => 2 * y)):ℝ):=by
    exact_mod_cast mixedSolutionCount_sq_le_energy A B C
  have hprod:=mul_le_mul hC hE (Nat.cast_nonneg _) hN
  have hsq:(mixedSolutionCount A B C:ℝ) ^ 2 ≤ (δ * N ^ 2) ^ 2:=by
    nlinarith [hs.trans hprod]
  exact (sq_le_sq₀ (Nat.cast_nonneg _) (mul_nonneg hδ (sq_nonneg N))).mp hsq
end Green24Proof.IntegerStructuralCounting
private def zz2515:"s09d3"="s09d3":=by decide+kernel
end 
section 
namespace Green24Proof.RemainderSolutionCounting
open Finset
open scoped Pointwise
open Green24Proof.IntegerStructuralCounting
open Green24Proof.EnergyCauchy
private def zz1985:"s07c1"="s07c1":=by decide+kernel
theorem self_energy_le_of_card (A:Finset ℤ) {N:ℝ} (hA:(A.card:ℝ) ≤ N) :
    (A.addEnergy A:ℝ) ≤ N ^ 3:=by
  have h:(A.addEnergy A:ℝ) ≤ (A.card:ℝ) ^ 3:=by
    exact_mod_cast Green24Proof.FiniteEnergyPeeling.self_energy_le_card_cube A
  exact h.trans (by gcongr)
theorem mixed_count_left (A B C:Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hB:(B.card:ℝ) ≤ N) (hC:(C.card:ℝ) ≤ N)
    (hEA:(A.addEnergy A:ℝ) ≤ δ ^ 4 * N ^ 3) :
    (mixedSolutionCount A B C:ℝ) ≤ δ * N ^ 2:=by
  apply mixedSolutionCount_le_of_energy hδ hN hC
  apply mixed_energy_le_of_self_budget _ _ hN hEA
  rw [integer_energy_dilate 2 (by norm_num)]
  exact self_energy_le_of_card B hB
theorem mixed_count_middle (A B C:Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hA:(A.card:ℝ) ≤ N) (hC:(C.card:ℝ) ≤ N)
    (hEB:(B.addEnergy B:ℝ) ≤ δ ^ 4 * N ^ 3) :
    (mixedSolutionCount A B C:ℝ) ≤ δ * N ^ 2:=by
  apply mixedSolutionCount_le_of_energy hδ hN hC
  rw [Finset.addEnergy_comm]
  apply mixed_energy_le_of_self_budget _ _ hN
  · rwa [integer_energy_dilate 2 (by norm_num)]
  · exact self_energy_le_of_card A hA
theorem mixed_count_eq_reversed_pair_count (A B C:Finset ℤ) :
    mixedSolutionCount A B C =
      (((C.image (fun z => 3 * z)) ×ˢ (B.image (fun y => -2 * y))).filter
        (fun p => p.1 + p.2 ∈ A)).card:=by
  unfold mixedSolutionCount
  refine Finset.card_bij (fun p _ => (3 * p.2.2, -2 * p.2.1)) ?_ ?_ ?_
  · rintro ⟨x,y,z⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp ⊢
    refine ⟨⟨Finset.mem_image.mpr ⟨z,hp.1.2.2,rfl⟩,
      Finset.mem_image.mpr ⟨y,hp.1.2.1,rfl⟩⟩, ?_⟩
    have heq:3 * z + -2 * y = x:=by omega
    rw [heq]
    exact hp.1.1
  · rintro ⟨x,y,z⟩ hp ⟨x',y',z'⟩ hp' he
    simp only [Finset.mem_filter,Finset.mem_product] at hp hp'
    have hz:=congrArg Prod.fst he
    have hy:=congrArg Prod.snd he
    dsimp at hz hy
    have hyy:y = y':=by omega
    have hzz:z = z':=by omega
    have hxx:x = x':=by omega
    exact Prod.ext hxx (Prod.ext hyy hzz)
  · rintro ⟨u,v⟩ hp
    simp only [Finset.mem_filter,Finset.mem_product] at hp
    obtain ⟨z,hz,rfl⟩:=Finset.mem_image.mp hp.1.1
    obtain ⟨y,hy,rfl⟩:=Finset.mem_image.mp hp.1.2
    refine ⟨(3 * z + -2 * y,y,z), ?_,rfl⟩
    simp only [Finset.mem_filter,Finset.mem_product]
    exact ⟨⟨hp.2,hy,hz⟩,by omega⟩
private def zz1986:"s07c2"="s07c2":=by decide+kernel
theorem mixed_count_sq_le_reversed_energy (A B C:Finset ℤ) :
    mixedSolutionCount A B C ^ 2 ≤ A.card *
      (C.image (fun z => 3 * z)).addEnergy (B.image (fun y => -2 * y)):=by
  rw [mixed_count_eq_reversed_pair_count]
  exact Finset.card_sq_le_card_mul_addEnergy _ _ _
theorem mixed_count_right (A B C:Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hA:(A.card:ℝ) ≤ N) (hB:(B.card:ℝ) ≤ N)
    (hEC:(C.addEnergy C:ℝ) ≤ δ ^ 4 * N ^ 3) :
    (mixedSolutionCount A B C:ℝ) ≤ δ * N ^ 2:=by
  have hE:((C.image (fun z => 3 * z)).addEnergy
      (B.image (fun y => -2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3:=by
    apply mixed_energy_le_of_self_budget _ _ hN
    · rwa [integer_energy_dilate 3 (by norm_num)]
    · rw [integer_energy_dilate (-2) (by norm_num)]
      exact self_energy_le_of_card B hB
  have hs:(mixedSolutionCount A B C:ℝ) ^ 2 ≤ (A.card:ℝ) *
      (C.image (fun z => 3 * z)).addEnergy (B.image (fun y => -2 * y)):=by
    exact_mod_cast mixed_count_sq_le_reversed_energy A B C
  have hsq:(mixedSolutionCount A B C:ℝ) ^ 2 ≤ (δ * N ^ 2) ^ 2:=by
    calc
      _ ≤ (A.card:ℝ) *
          (C.image (fun z => 3 * z)).addEnergy (B.image (fun y => -2 * y)):=hs
      _ ≤ N * (δ ^ 2 * N ^ 3):=mul_le_mul hA hE (Nat.cast_nonneg _) hN
      _ = _:=by ring
  exact (sq_le_sq₀ (Nat.cast_nonneg _) (by positivity)).mp hsq
theorem count_le_after_removing (A R:Finset ℤ) :
    integerSolutionCount A ≤ integerSolutionCount (A \ R) +
      mixedSolutionCount R A A + mixedSolutionCount A R A + mixedSolutionCount A A R:=by
  let T (X Y Z:Finset ℤ):=(X ×ˢ (Y ×ˢ Z)).filter
    (fun p => p.1 + 2 * p.2.1 = 3 * p.2.2)
  let S:=A \ R
  have hcover:T A A A ⊆ ((T S S S ∪ T R A A) ∪ T A R A) ∪ T A A R:=by
    rintro ⟨x,y,z⟩ hp
    simp only [T,S,Finset.mem_union,Finset.mem_filter,
      Finset.mem_product,Finset.mem_sdiff] at hp ⊢
    by_cases hx:x ∈ R <;> by_cases hy:y ∈ R <;> by_cases hz:z ∈ R <;> tauto
  have hcard:=Finset.card_le_card hcover
  have h₁:=Finset.card_union_le (T S S S) (T R A A)
  have h₂:=Finset.card_union_le (T S S S ∪ T R A A) (T A R A)
  have h₃:=Finset.card_union_le ((T S S S ∪ T R A A) ∪ T A R A) (T A A R)
  have h:(T A A A).card ≤
      (T S S S).card + (T R A A).card + (T A R A).card + (T A A R).card:=by omega
  change mixedSolutionCount A A A ≤ mixedSolutionCount S S S +
    mixedSolutionCount R A A + mixedSolutionCount A R A + mixedSolutionCount A A R at h
  simpa only [mixedSolutionCount_self] using h
theorem count_le_remainder_error (A R:Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hA:(A.card:ℝ) ≤ N)
    (hR:(R.addEnergy R:ℝ) ≤ δ ^ 4 * N ^ 3) :
    (integerSolutionCount A:ℝ) ≤ integerSolutionCount (A \ R) + 3 * δ * N ^ 2:=by
  have hcover:(integerSolutionCount A:ℝ) ≤ integerSolutionCount (A \ R) +
      mixedSolutionCount R A A + mixedSolutionCount A R A + mixedSolutionCount A A R:=by
    exact_mod_cast count_le_after_removing A R
  have h₁:=mixed_count_left R A A hδ hN hA hA hR
  have h₂:=mixed_count_middle A R A hδ hN hA hA hR
  have h₃:=mixed_count_right A A R hδ hN hA hA hR
  linarith
end Green24Proof.RemainderSolutionCounting
private def zz2516:"s09d4"="s09d4":=by decide+kernel
end 
section 
namespace Green24Proof.UnionSolutionCounting
open Finset
open scoped BigOperators Pointwise
open Green24Proof.IntegerStructuralCounting
open Green24Proof.RemainderSolutionCounting
variable {ι:Type*}
def triples (A B C:Finset ℤ):Finset (ℤ × ℤ × ℤ) :=
  (A ×ˢ (B ×ˢ C)).filter (fun p => p.1 + 2 * p.2.1 = 3 * p.2.2)
private def zz1987:"s07c3"="s07c3":=by decide+kernel
theorem mixed_count_union_left (I:Finset ι) (F:ι → Finset ℤ) (B C:Finset ℤ) :
    mixedSolutionCount (I.biUnion F) B C ≤ ∑ i ∈ I,mixedSolutionCount (F i) B C:=by
  have heq:triples (I.biUnion F) B C = I.biUnion (fun i => triples (F i) B C):=by
    ext p
    simp only [triples,Finset.mem_filter,Finset.mem_product,Finset.mem_biUnion]
    aesop
  change (triples (I.biUnion F) B C).card ≤ ∑ i ∈ I,(triples (F i) B C).card
  rw [heq]
  exact Finset.card_biUnion_le
theorem mixed_count_union_middle (I:Finset ι) (F:ι → Finset ℤ) (A C:Finset ℤ) :
    mixedSolutionCount A (I.biUnion F) C ≤ ∑ i ∈ I,mixedSolutionCount A (F i) C:=by
  have heq:triples A (I.biUnion F) C = I.biUnion (fun i => triples A (F i) C):=by
    ext p
    simp only [triples,Finset.mem_filter,Finset.mem_product,Finset.mem_biUnion]
    aesop
  change (triples A (I.biUnion F) C).card ≤ ∑ i ∈ I,(triples A (F i) C).card
  rw [heq]
  exact Finset.card_biUnion_le
theorem mixed_count_union_right (I:Finset ι) (F:ι → Finset ℤ) (A B:Finset ℤ) :
    mixedSolutionCount A B (I.biUnion F) ≤ ∑ i ∈ I,mixedSolutionCount A B (F i):=by
  have heq:triples A B (I.biUnion F) = I.biUnion (fun i => triples A B (F i)):=by
    ext p
    simp only [triples,Finset.mem_filter,Finset.mem_product,Finset.mem_biUnion]
    aesop
  change (triples A B (I.biUnion F)).card ≤ ∑ i ∈ I,(triples A B (F i)).card
  rw [heq]
  exact Finset.card_biUnion_le
theorem count_union_le_triple_sum (I:Finset ι) (F:ι → Finset ℤ) :
    integerSolutionCount (I.biUnion F) ≤
      ∑ i ∈ I, ∑ j ∈ I, ∑ k ∈ I,mixedSolutionCount (F i) (F j) (F k):=by
  rw [← mixedSolutionCount_self]
  apply (mixed_count_union_left I F _ _).trans
  apply Finset.sum_le_sum
  intro i _
  apply (mixed_count_union_middle I F _ _).trans
  apply Finset.sum_le_sum
  intro j _
  exact mixed_count_union_right I F _ _
private def zz1988:"s07c4"="s07c4":=by decide+kernel
theorem mixed_count_le_of_reversed_energy (A B C:Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hA:(A.card:ℝ) ≤ N)
    (hE:((C.image (fun z => 3 * z)).addEnergy
      (B.image (fun y => -2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3) :
    (mixedSolutionCount A B C:ℝ) ≤ δ * N ^ 2:=by
  have hs:(mixedSolutionCount A B C:ℝ) ^ 2 ≤ (A.card:ℝ) *
      (C.image (fun z => 3 * z)).addEnergy (B.image (fun y => -2 * y)):=by
    exact_mod_cast mixed_count_sq_le_reversed_energy A B C
  have hsq:(mixedSolutionCount A B C:ℝ) ^ 2 ≤ (δ * N ^ 2) ^ 2:=by
    calc
      _ ≤ (A.card:ℝ) *
          (C.image (fun z => 3 * z)).addEnergy (B.image (fun y => -2 * y)):=hs
      _ ≤ N * (δ ^ 2 * N ^ 3):=mul_le_mul hA hE (Nat.cast_nonneg _) hN
      _ = _:=by ring
  exact (sq_le_sq₀ (Nat.cast_nonneg _) (by positivity)).mp hsq
theorem mixed_count_of_distinct_indices (I:Finset ι) (F:ι → Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hcard:∀ i ∈ I,((F i).card:ℝ) ≤ N)
    (h12:∀ i ∈ I, ∀ j ∈ I,i ≠ j →
      ((F i).addEnergy ((F j).image (fun y => 2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3)
    (h32:∀ j ∈ I, ∀ k ∈ I,j ≠ k →
      (((F k).image (fun z => 3 * z)).addEnergy
        ((F j).image (fun y => -2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3)
    {i j k:ι} (hi:i ∈ I) (hj:j ∈ I) (hk:k ∈ I) (hne:¬(i = j ∧ j = k)) :
    (mixedSolutionCount (F i) (F j) (F k):ℝ) ≤ δ * N ^ 2:=by
  by_cases hij:i = j
  · have hjk:j ≠ k:=fun h => hne ⟨hij,h⟩
    exact mixed_count_le_of_reversed_energy _ _ _ hδ hN (hcard i hi) (h32 j hj k hk hjk)
  · exact mixedSolutionCount_le_of_energy hδ hN (hcard k hk) (h12 i hi j hj hij)
theorem count_union_le_self_counts (I:Finset ι) (F:ι → Finset ℤ) {e:ℝ}
    (he:0 ≤ e)
    (hmixed:∀ i ∈ I, ∀ j ∈ I, ∀ k ∈ I, ¬(i = j ∧ j = k) →
      (mixedSolutionCount (F i) (F j) (F k):ℝ) ≤ e) :
    (integerSolutionCount (I.biUnion F):ℝ) ≤
      (∑ i ∈ I,(integerSolutionCount (F i):ℝ)) + (I.card:ℝ) ^ 3 * e:=by
  classical
  have hfirst:(integerSolutionCount (I.biUnion F):ℝ) ≤
      ∑ i ∈ I, ∑ j ∈ I, ∑ k ∈ I,(mixedSolutionCount (F i) (F j) (F k):ℝ):=by
    exact_mod_cast count_union_le_triple_sum I F
  apply hfirst.trans
  calc
    _ ≤ ∑ i ∈ I, ∑ j ∈ I, ∑ k ∈ I,
        ((if i = j ∧ j = k then (integerSolutionCount (F i):ℝ) else 0) + e):=by
      apply Finset.sum_le_sum
      intro i hi
      apply Finset.sum_le_sum
      intro j hj
      apply Finset.sum_le_sum
      intro k hk
      by_cases h:i = j ∧ j = k
      · rcases h with ⟨rfl,rfl⟩
        simp only [and_self,ite_true,mixedSolutionCount_self]
        linarith
      · simpa only [if_neg h,zero_add] using hmixed i hi j hj k hk h
    _ = _:=by
      simp only [Finset.sum_add_distrib]
      have hdiag:(∑ i ∈ I, ∑ j ∈ I, ∑ k ∈ I,
          if i = j ∧ j = k then (integerSolutionCount (F i):ℝ) else 0) =
          ∑ i ∈ I,(integerSolutionCount (F i):ℝ):=by
        apply Finset.sum_congr rfl
        intro i hi
        rw [Finset.sum_eq_single i]
        · simp [hi]
        · intro j _ hji
          have hij:i ≠ j:=Ne.symm hji
          simp [hij]
        · exact fun h => (h hi).elim
      rw [hdiag]
      simp
      ring
theorem count_union_le_of_dilated_energy (I:Finset ι) (F:ι → Finset ℤ) {δ N:ℝ}
    (hδ:0 ≤ δ) (hN:0 ≤ N) (hcard:∀ i ∈ I,((F i).card:ℝ) ≤ N)
    (h12:∀ i ∈ I, ∀ j ∈ I,i ≠ j →
      ((F i).addEnergy ((F j).image (fun y => 2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3)
    (h32:∀ j ∈ I, ∀ k ∈ I,j ≠ k →
      (((F k).image (fun z => 3 * z)).addEnergy
        ((F j).image (fun y => -2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3) :
    (integerSolutionCount (I.biUnion F):ℝ) ≤
      (∑ i ∈ I,(integerSolutionCount (F i):ℝ)) + (I.card:ℝ) ^ 3 * (δ * N ^ 2) :=
  count_union_le_self_counts I F (by positivity)
    (fun _ hi _ hj _ hk hne => mixed_count_of_distinct_indices I F hδ hN hcard h12 h32 hi hj hk hne)
private def zz1989:"s07c5"="s07c5":=by decide+kernel
theorem count_union_le_quadratic (I:Finset ι) (F:ι → Finset ℤ) {c δ N:ℝ}
    (hc:0 ≤ c) (hδ:0 ≤ δ) (hsum:(∑ i ∈ I,((F i).card:ℝ)) ≤ N)
    (hself:∀ i ∈ I,(integerSolutionCount (F i):ℝ) ≤ c * ((F i).card:ℝ) ^ 2)
    (h12:∀ i ∈ I, ∀ j ∈ I,i ≠ j →
      ((F i).addEnergy ((F j).image (fun y => 2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3)
    (h32:∀ j ∈ I, ∀ k ∈ I,j ≠ k →
      (((F k).image (fun z => 3 * z)).addEnergy
        ((F j).image (fun y => -2 * y)):ℝ) ≤ δ ^ 2 * N ^ 3) :
    (integerSolutionCount (I.biUnion F):ℝ) ≤ (c + (I.card:ℝ) ^ 3 * δ) * N ^ 2:=by
  have hN:0 ≤ N:=(Finset.sum_nonneg (fun _ _ => Nat.cast_nonneg _)).trans hsum
  have hcard:∀ i ∈ I,((F i).card:ℝ) ≤ N:=by
    intro i hi
    exact (Finset.single_le_sum (fun j _ => Nat.cast_nonneg (F j).card) hi).trans hsum
  have hsq:(∑ i ∈ I,((F i).card:ℝ) ^ 2) ≤ N ^ 2:=by
    apply (Finset.sum_sq_le_sq_sum_of_nonneg (fun _ _ => Nat.cast_nonneg _)).trans
    gcongr
  have hlocal:(∑ i ∈ I,(integerSolutionCount (F i):ℝ)) ≤ c * N ^ 2:=by
    calc
      _ ≤ ∑ i ∈ I,c * ((F i).card:ℝ) ^ 2:=Finset.sum_le_sum hself
      _ = c * ∑ i ∈ I,((F i).card:ℝ) ^ 2:=by rw [Finset.mul_sum]
      _ ≤ c * N ^ 2:=mul_le_mul_of_nonneg_left hsq hc
  calc
    _ ≤ (∑ i ∈ I,(integerSolutionCount (F i):ℝ)) +
        (I.card:ℝ) ^ 3 * (δ * N ^ 2):=count_union_le_of_dilated_energy I F hδ hN hcard h12 h32
    _ ≤ c * N ^ 2 + (I.card:ℝ) ^ 3 * (δ * N ^ 2):=add_le_add hlocal le_rfl
    _ = _:=by ring
end Green24Proof.UnionSolutionCounting
private def zz2517:"s09d5"="s09d5":=by decide+kernel
end 
section 
namespace Green24Proof.SparseCountingReduction
open scoped BigOperators Pointwise
open Green24Proof.EnergyAgglomeration Green24Proof.AdaptiveEnergyPartition
open Green24Proof.DilatedEnergyPartition
theorem pieces_union_eq_sdiff {A R:Finset ℤ} {μ K:ℝ} {P:Finset (Finset ℤ)}
    (h:ControlledFamily A R μ K P):P.biUnion id = A \ R:=by
  have hdisj:Disjoint (P.biUnion id) R :=
    (Finset.disjoint_biUnion_left _ _ _).mpr (fun B hB => (h.1 B hB).2.2.2.2)
  ext x
  constructor
  · intro hx
    apply Finset.mem_sdiff.mpr
    constructor
    · rw [← h.2.2]
      exact Finset.mem_union_left R hx
    · exact fun hxR => Finset.disjoint_left.mp hdisj hx hxR
  · intro hx
    obtain ⟨hxA,hxR⟩:=Finset.mem_sdiff.mp hx
    rw [← h.2.2] at hxA
    exact (Finset.mem_union.mp hxA).resolve_right hxR
theorem pieces_card_sum_le {A R:Finset ℤ} {μ K:ℝ} {P:Finset (Finset ℤ)}
    (h:ControlledFamily A R μ K P) :
    (∑ B ∈ P,(B.card:ℝ)) ≤ A.card:=by
  have hcard:(P.biUnion id).card = ∑ B ∈ P,B.card:=Finset.card_biUnion h.2.1
  have hsub:P.biUnion id ⊆ A:=by
    rw [← h.2.2]
    exact Finset.subset_union_left
  have hle:=Finset.card_le_card hsub
  rw [hcard] at hle
  exact_mod_cast hle
theorem exists_sparse_counting_reduction {ε:ℝ} (hε:0 < ε) :
    ∃ (m:ℕ) (K μ:ℝ),0 < m ∧ 1 ≤ K ∧ 0 < μ ∧
      ∀ (A:Finset ℤ),A.Nonempty →
        ∃ P:Finset (Finset ℤ),P.card ≤ m ∧
          (∀ B ∈ P,B ⊆ A ∧ B.Nonempty ∧ μ * A.card ≤ (B.card:ℝ) ∧
            ((B - B).card:ℝ) ≤ K * B.card) ∧
          (P:Set (Finset ℤ)).Pairwise Disjoint ∧
          (∑ B ∈ P,(B.card:ℝ)) ≤ A.card ∧
          (integerSolutionCount A:ℝ) ≤
            (∑ B ∈ P,(integerSolutionCount B:ℝ)) + ε * (A.card:ℝ) ^ 2:=by
  let d:ℝ:=ε / 6
  let δ:ℝ:=d ^ 4
  let m:ℕ:=⌈8 / δ ^ 2⌉₊
  let e:ℝ:=ε / (2 * (m:ℝ) ^ 3)
  let K₀:ℝ:=0x1000000 / δ ^ 10
  let K:ℝ:=max 1 (adaptiveBound (dilationThreshold e) m K₀)
  let μ:ℝ:=δ ^ 2 / 8
  have hd:0 < d:=by dsimp [d]; positivity
  have hδ:0 < δ:=by dsimp [δ]; positivity
  have hm:0 < m:=by
    dsimp [m]
    exact Nat.ceil_pos.mpr (by positivity)
  have hmreal:(0:ℝ) < m:=by exact_mod_cast hm
  have he:0 < e:=by dsimp [e]; positivity
  have hμ:0 < μ:=by dsimp [μ]; positivity
  refine ⟨m,K,μ,hm,le_max_left _ _,hμ, ?_⟩
  intro A hA
  obtain ⟨L,P,R,_hKL,hLbound,hPcard,_hRA,hRE,hcontrolled,henergy⟩ :=
    exists_dilated_energy_partition A hA hδ he
  have hLK:L ≤ K:=hLbound.trans (le_max_right _ _)
  have hN:(0:ℝ) ≤ A.card:=Nat.cast_nonneg _
  have hcard:∀ B ∈ P,(B.card:ℝ) ≤ A.card:=by
    intro B hB
    exact_mod_cast Finset.card_le_card (hcontrolled.1 B hB).1
  have hunion:(integerSolutionCount (P.biUnion id):ℝ) ≤
      (∑ B ∈ P,(integerSolutionCount B:ℝ)) +
        (P.card:ℝ) ^ 3 * (e * (A.card:ℝ) ^ 2):=by
    apply Green24Proof.UnionSolutionCounting.count_union_le_of_dilated_energy P id he.le hN hcard
    · intro B hB C hC hBC
      exact (equation_energy_budgets henergy B C hB hC hBC).1
    · intro B hB C hC hBC
      exact (equation_energy_budgets henergy B C hB hC hBC).2
  have hrem:(integerSolutionCount A:ℝ) ≤
      integerSolutionCount (P.biUnion id) + 3 * d * (A.card:ℝ) ^ 2:=by
    rw [pieces_union_eq_sdiff hcontrolled]
    exact Green24Proof.RemainderSolutionCounting.count_le_remainder_error A R hd.le hN
      le_rfl hRE.le
  have hcoeff:(P.card:ℝ) ^ 3 * e ≤ ε / 2:=by
    have hP:(P.card:ℝ) ≤ m:=by exact_mod_cast hPcard
    calc
      _ ≤ (m:ℝ) ^ 3 * e:=by gcongr
      _ = ε / 2:=by dsimp [e]; field_simp
  refine ⟨P,hPcard, ?_,hcontrolled.2.1,pieces_card_sum_le hcontrolled, ?_⟩
  · intro B hB
    obtain ⟨hBA,hBne,hBsize,hBdiff,_hBR⟩:=hcontrolled.1 B hB
    refine ⟨hBA,hBne, ?_,hBdiff.trans (mul_le_mul_of_nonneg_right hLK (Nat.cast_nonneg _))⟩
    convert hBsize using 1
    dsimp [μ]
    ring
  · calc
      _ ≤ (∑ B ∈ P,(integerSolutionCount B:ℝ)) +
          (P.card:ℝ) ^ 3 * (e * (A.card:ℝ) ^ 2) +
          3 * d * (A.card:ℝ) ^ 2:=by linarith
      _ ≤ (∑ B ∈ P,(integerSolutionCount B:ℝ)) +
          (ε / 2) * (A.card:ℝ) ^ 2 + 3 * d * (A.card:ℝ) ^ 2:=by
        have hmul:=mul_le_mul_of_nonneg_right hcoeff (sq_nonneg (A.card:ℝ))
        nlinarith
      _ = _:=by dsimp [d]; ring
end Green24Proof.SparseCountingReduction
private def zz2518:"s09d6"="s09d6":=by decide+kernel
end 
section 
namespace Green24Proof.DenseIntervalReduction
open scoped BigOperators Pointwise
open Filter
def DenseIntervalUpperBound (c:ℝ):Prop :=
  ∀ C:ℝ,0 < C → ∀ ε:ℝ,0 < ε → ∃ M:ℕ,
    ∀ (L:ℕ) (A:Finset ℤ),M ≤ A.card →
      A ⊆ Finset.Icc 0 (L:ℤ) → (L:ℝ) ≤ C * A.card →
      (integerSolutionCount A:ℝ) ≤ (c + ε) * (A.card:ℝ) ^ 2
private def zz1990:"s07c6"="s07c6":=by decide+kernel
theorem solution_asymptotic_of_dense_interval {c:ℝ} (hc:0 ≤ c)
    (hdense:DenseIntervalUpperBound c) :
    ∀ ε:ℝ,0 < ε → ∀ᶠ n:ℕ in atTop, ∀ A:Finset ℤ,A.card = n →
      (integerSolutionCount A:ℝ) ≤ (c + ε) * (n:ℝ) ^ 2:=by
  intro ε hε
  have hhalf:0 < ε / 2:=by positivity
  obtain ⟨m,K,μ,_hm,hK,hμ,hsparse⟩ :=
    Green24Proof.SparseCountingReduction.exists_sparse_counting_reduction hhalf
  obtain ⟨C,hC,hmodel⟩ :=
    Green24Proof.SmallDifferenceIntegerModel.exists_bounded_integer_model hK
  obtain ⟨M,hdenseM⟩:=hdense C hC (ε / 2) hhalf
  refine Filter.eventually_atTop.mpr ⟨⌈(M:ℝ) / μ⌉₊ + 1, ?_⟩
  intro n hn A hAn
  have hnpos:0 < n:=by omega
  have hA:A.Nonempty:=Finset.card_pos.mp (hAn.symm ▸ hnpos)
  have hMdiv:(M:ℝ) / μ ≤ n:=by
    apply (Nat.le_ceil ((M:ℝ) / μ)).trans
    exact_mod_cast (show ⌈(M:ℝ) / μ⌉₊ ≤ n by omega)
  have hMn:(M:ℝ) ≤ μ * n:=by
    have h:=(div_le_iff₀ hμ).mp hMdiv
    nlinarith
  obtain ⟨P,_hPcard,hpieces,_hpair,hmass,hcount⟩:=hsparse A hA
  have hself:∀ B ∈ P,
      (integerSolutionCount B:ℝ) ≤ (c + ε / 2) * (B.card:ℝ) ^ 2:=by
    intro B hB
    obtain ⟨_hBA,hBne,hBsize,hBdiff⟩:=hpieces B hB
    have hMB:M ≤ B.card:=by
      rw [hAn] at hBsize
      exact_mod_cast hMn.trans hBsize
    obtain ⟨L,D,f,hL,hDI,hDcard,hf⟩:=hmodel B hBne hBdiff
    have hcount_eq :=
      Green24Proof.IntegerStructuralCounting.integerSolutionCount_eq_of_freiman_three hf
    have hMD:M ≤ D.card:=by rwa [hDcard]
    have hLD:(L:ℝ) ≤ C * D.card:=by rwa [hDcard]
    have hbound:=hdenseM L D hMD hDI hLD
    rw [hDcard, ← hcount_eq] at hbound
    exact hbound
  have hcoef:0 ≤ c + ε / 2:=by positivity
  have hsq:(∑ B ∈ P,(B.card:ℝ) ^ 2) ≤ (A.card:ℝ) ^ 2:=by
    apply (Finset.sum_sq_le_sq_sum_of_nonneg (fun _ _ => Nat.cast_nonneg _)).trans
    gcongr
  have hlocal:(∑ B ∈ P,(integerSolutionCount B:ℝ)) ≤
      (c + ε / 2) * (A.card:ℝ) ^ 2:=by
    calc
      _ ≤ ∑ B ∈ P,(c + ε / 2) * (B.card:ℝ) ^ 2:=Finset.sum_le_sum hself
      _ = (c + ε / 2) * ∑ B ∈ P,(B.card:ℝ) ^ 2:=by rw [Finset.mul_sum]
      _ ≤ _:=mul_le_mul_of_nonneg_left hsq hcoef
  rw [hAn] at hcount hlocal
  nlinarith
theorem conjecture_of_dense_interval_upper_bound
    (hdense:DenseIntervalUpperBound (1 / 3)):Green24.variants.gamma = 1 / 3 :=
  Green24Proof.conjecture_of_solution_asymptotic
    (solution_asymptotic_of_dense_interval (by norm_num) hdense)
end Green24Proof.DenseIntervalReduction
private def zz2519:"s09d7"="s09d7":=by decide+kernel
end 
section 
namespace Green24Proof.LocalizedHaarReduction
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Finset MeasureTheory
open scoped BigOperators
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairCounting
open Green24Proof.SpatialCircleCutoff Green24Proof.IntegerLocalizedHaarTransfer
open Green24Proof.DenseIntervalReduction
def LocalizedHaarUpperBound:Prop :=
  ∀ (d:ℕ) (G:(Fin d → Circle) → ℝ) (w:Fin d → ℤ),
    Continuous G → (∀ z,G z ∈ Set.Icc 0 1) → w ≠ 0 →
    (∀ z,(∏ j,z j ^ w j) ∉ window → G z = 0) →
    haarWeightedCount G ≤ (1 / 3:ℝ) * (∫ z,G z ∂torusHaar (Fin d)) ^ 2
theorem dense_interval_of_localized_haar (hgeo:LocalizedHaarUpperBound) :
    DenseIntervalUpperBound (1 / 3):=by
  intro C hC ε hε
  let D:=10 * (64 * C) ^ 2
  have hD:0 < D:=by dsimp [D]; positivity
  let δ:=min 1 (ε / D)
  have hδ:0 < δ:=lt_min (by norm_num) (div_pos hε hD)
  have hδ1:δ ≤ 1:=min_le_left _ _
  have hδD:δ * D ≤ ε:=(le_div_iff₀ hD).mp (min_le_right _ _)
  obtain ⟨C0,Q,R,hmodel⟩:=exists_integer_haar_model hδ
  refine ⟨Q + 2, ?_⟩
  intro L A hsize hA hLC
  have hcard:A.card ≤ L + 1:=by
    have h:=Finset.card_le_card hA
    have hc:(Finset.Icc (0:ℤ) L).card = L + 1:=by rw [Int.card_Icc]; omega
    rwa [hc] at h
  have hL:0 < L:=by omega
  obtain ⟨q,hprime,hqL,hqhi⟩:=Nat.exists_prime_lt_and_le_two_mul (32 * L) (by omega)
  let:Fact q.Prime:=⟨hprime⟩
  let:NeZero q:=⟨hprime.ne_zero⟩
  have hqQ:Q < q:=by omega
  have hq:(0:ℝ) < q:=Nat.cast_pos.mpr hprime.pos
  obtain ⟨d,_,ls,G,w,hw,_,_,hGl,hGr,hGs,hm,hc⟩ :=
    hmodel q hqQ L hqL A (fun x hx => Finset.mem_Icc.mp (hA hx))
  let a:ℝ:=A.card
  let mass:ℝ:=∫ z,G z ∂torusHaar (Fin d)
  have hm0:0 ≤ mass:=integral_nonneg (fun z => (hGr z).1)
  have ha0:0 ≤ a / q:=div_nonneg (Nat.cast_nonneg _) hq.le
  have ha1:a / q ≤ 1:=by
    apply (div_le_iff₀ hq).mpr
    have hNq:A.card ≤ q:=by omega
    simpa only [one_mul] using (show a ≤ (q:ℝ) by dsimp [a]; exact_mod_cast hNq)
  have hmub:mass ≤ a / q + 3 * δ:=by
    change |a / q - mass| ≤ 3 * δ at hm
    have h:=(abs_le.mp hm).1
    linarith
  have hsharp:=hgeo d G w hGl.continuous hGr hw hGs
  have hmasssq:mass ^ 2 ≤ (a / q + 3 * δ) ^ 2:=by
    exact sq_le_sq₀ hm0 (by positivity) |>.mpr hmub
  have hcount:(integerSolutionCount A:ℝ) / (q:ℝ)^2 ≤
      (1 / 3:ℝ) * (a / q)^2 + 10 * δ:=by
    have hu:=(abs_le.mp hc).2
    change haarWeightedCount G ≤ (1 / 3:ℝ) * mass ^ 2 at hsharp
    nlinarith [sq_nonneg δ,mul_nonneg hδ.le (sub_nonneg.mpr ha1),
      mul_nonneg hδ.le (sub_nonneg.mpr hδ1)]
  have hcount':(integerSolutionCount A:ℝ) ≤ (1 / 3:ℝ) * a^2 + 10 * δ * (q:ℝ)^2:=by
    have h:=(div_le_iff₀ (sq_pos_of_pos hq)).mp hcount
    calc
      _ ≤ ((1 / 3:ℝ) * (a / q)^2 + 10 * δ) * (q:ℝ)^2:=h
      _ = _:=by field_simp
  have hqbound:(q:ℝ) ≤ (64 * C) * a:=by
    have hqL':(q:ℝ) ≤ 64 * (L:ℝ):=by exact_mod_cast (show q ≤ 64 * L by omega)
    change (L:ℝ) ≤ C * a at hLC
    linarith
  have hqsq:(q:ℝ)^2 ≤ (64 * C)^2 * a^2:=by
    have h:=(sq_le_sq₀ hq.le (by positivity:0 ≤ (64 * C) * a)).mpr hqbound
    nlinarith
  have herr:10 * δ * (q:ℝ)^2 ≤ ε * a^2:=by
    calc
      _ ≤ 10 * δ * ((64 * C)^2 * a^2):=mul_le_mul_of_nonneg_left hqsq (by positivity)
      _ = (δ * D) * a^2:=by dsimp [D]; ring
      _ ≤ ε * a^2:=mul_le_mul_of_nonneg_right hδD (sq_nonneg a)
  change (integerSolutionCount A:ℝ) ≤ (1 / 3 + ε) * a^2
  nlinarith
theorem conjecture_of_localized_haar (hgeo:LocalizedHaarUpperBound) :
    Green24.variants.gamma = 1 / 3 :=
  conjecture_of_dense_interval_upper_bound (dense_interval_of_localized_haar hgeo)
end Green24Proof.LocalizedHaarReduction
private def zz2520:"s09d8"="s09d8":=by decide+kernel
end 
section 
namespace Green24Proof.SingleCoordinateHaarReduction
variable [MeasurableSpace Circle] [BorelSpace Circle]
open MeasureTheory
open Green24Proof.CyclicTorusHaarDiscrepancy Green24Proof.CyclicTorusPairCounting
open Green24Proof.SpatialCircleCutoff Green24Proof.LocalizedHaarReduction
def SingleCoordinateHaarUpperBound:Prop :=
  ∀ (d:ℕ) (p:Fin d) (q:ℕ) (H:(Fin d → Circle) → ℝ),
    0 < q → Continuous H → (∀ z,H z ∈ Set.Icc 0 1) →
    (∀ z,z p ^ q ∉ window → H z = 0) →
    haarWeightedCount H ≤ (1 / 3:ℝ) * (∫ z,H z ∂torusHaar (Fin d)) ^ 2
private def zz1991:"s07c7"="s07c7":=by decide+kernel
theorem localized_of_single_coordinate (hgeo:SingleCoordinateHaarUpperBound) :
    LocalizedHaarUpperBound:=by
  intro d G w hG hGr hw hGs
  obtain ⟨p,n,H,hn,hH,hHr,hHs,hm,hc⟩ :=
    TorusCharacterCover.exists_single_coordinate_model G w hG hGr hw window hGs
  have hpos:0 < n.natAbs:=Int.natAbs_pos.mpr hn
  have hs:∀ z,z p ^ n.natAbs ∉ window → H z = 0:=by
    intro z hz
    apply hHs z
    exact fun h => hz ((WindowArcGeometry.window_zpow_natAbs_iff (z p) n).mp h)
  have h:=hgeo d p n.natAbs H hpos hH hHr hs
  rwa [hm,hc] at h
theorem conjecture_of_single_coordinate (hgeo:SingleCoordinateHaarUpperBound) :
    Green24.variants.gamma = 1 / 3 :=
  conjecture_of_localized_haar (localized_of_single_coordinate hgeo)
end Green24Proof.SingleCoordinateHaarReduction
private def zz2521:"s09d9"="s09d9":=by decide+kernel
end 
section 
namespace Green24Proof.GeometricEndpointReduction
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Green24Proof.RealTorusCoefficientNormalization Green24Proof.CompactTorusProfileComparison
open Green24Proof.SingleCoordinateHaarReduction
def ContinuousRearrangementInput:Prop :=
  ∀ (d:ℕ) (p:Fin d),RearrangementBound {i:Fin d // i ≠ p}
def FiveDivisibleProfileInput:Prop :=
  ∀ (q:ℕ) [NeZero q],5 ∣ q → ∀ g:ZMod q → ℝ,
    (∀ i,0 ≤ g i) → profileFunctional g ≤ 2 * mass g ^ 2
theorem profile_bound_all_moduli (h5:FiveDivisibleProfileInput)
    (q:ℕ) [NeZero q] (g:ZMod q → ℝ) (hg:∀ i,0 ≤ g i) :
    profileFunctional g ≤ 2 * mass g ^ 2:=by
  by_cases hq:5 ∣ q
  · exact h5 q hq g hg
  · exact VerifiedProfileEndpoint.profileFunctional_le q hq g hg
theorem single_coordinate_of_rearrangement_and_five
    (hR:ContinuousRearrangementInput) (h5:FiveDivisibleProfileInput) :
    SingleCoordinateHaarUpperBound:=by
  intro d p q F hq hF hr hs
  let:NeZero q:=⟨Nat.ne_of_gt hq⟩
  exact upper_bound_of_profile p (hR d p) F hF hr hs
    (profile_bound_all_moduli h5 q _ (profileMass_nonneg p q F hr))
private def zz1992:"s07c8"="s07c8":=by decide+kernel
theorem conjecture_of_rearrangement_and_five
    (hR:ContinuousRearrangementInput) (h5:FiveDivisibleProfileInput) :
    Green24.variants.gamma = 1 / 3 :=
  conjecture_of_single_coordinate (single_coordinate_of_rearrangement_and_five hR h5)
end Green24Proof.GeometricEndpointReduction
private def zz2522:"s09da"="s09da":=by decide+kernel
end 
section 
namespace Green24Proof.GeometricEndpointFromProfile
variable [MeasurableSpace Circle] [BorelSpace Circle]
open Green24Proof.GeometricEndpointReduction Green24Proof.SingleCoordinateHaarReduction
theorem continuous_rearrangement_input:ContinuousRearrangementInput :=
  fun _ _ => RealTorusRearrangement.rearrangementBound _
theorem single_coordinate_of_five (h5:FiveDivisibleProfileInput) :
    SingleCoordinateHaarUpperBound :=
  single_coordinate_of_rearrangement_and_five continuous_rearrangement_input h5
theorem conjecture_of_five (h5:FiveDivisibleProfileInput):Green24.variants.gamma = 1 / 3 :=
  conjecture_of_rearrangement_and_five continuous_rearrangement_input h5
end Green24Proof.GeometricEndpointFromProfile
private def zz2523:"s09db"="s09db":=by decide+kernel
end 
section 
namespace Green24Proof.CompleteEndpoint
private def zz1993:"s07c9"="s07c9":=by decide+kernel
theorem five_divisible_profile_input:GeometricEndpointReduction.FiveDivisibleProfileInput:=by
  intro q _ _ g hg
  exact AllModuliProfileEndpoint.profileFunctional_le q g hg
theorem gamma_eq_one_third:Green24.variants.gamma = 1 / 3:=by
  letI:=CyclicTorusHaarDiscrepancy.circleMeasurableSpace
  letI:=CyclicTorusHaarDiscrepancy.circleBorelSpace
  exact GeometricEndpointFromProfile.conjecture_of_five five_divisible_profile_input
end Green24Proof.CompleteEndpoint
private def zz2524:"s09dc"="s09dc":=by decide+kernel
end 
section 
namespace Bounty
theorem target:fcTypeOfName% "Green24.variants.conjecture":=by
  exact Green24Proof.CompleteEndpoint.gamma_eq_one_third
end Bounty
end
end
namespace Bounty