| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.CapacityA.CapA2_7_7I2Pair |
|
|
| namespace OAI |
|
|
| namespace MatrixAllFields |
|
|
| open scoped BigOperators Topology Polynomial |
|
|
| section |
| noncomputable section |
| namespace MatrixMultiplication.NativeNumerics |
| open AllFieldParameters AllFieldHistory AllFieldCertificates AllFieldCertificates.Replay |
| open AllFieldInitialEntropyCertificate AllFieldNativeCapacity |
| open scoped BigOperators |
| def CA2_7_7I2R0Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 0 a |
| def CA2_7_7I2R0Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 0 a |
| lemma CA2_7_7I2R0Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R0Raw a).Encloses (CA2_7_7I2R0Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 0 a |
| def CA2_7_7I2R0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(502109287941468832085436601 / 100000000000000000000000000000000), (1 / 50000000000000000000000000000000)⟩ ⟨(3063334356907513434862083549 / 50000000000000000000000000000000), (2020217 / 100000000000000000000000000000000)⟩ ⟨(-244037258857845153364503487992193 / 20000000000000000000000000000000), (50292631037 / 12500000000000000000000000000000)⟩ ⟨-18, 502109287941468832085436601, 381469726562500000000000000⟩] |
| lemma CA2_7_7I2R0Certificates_valid : |
| CA2_7_7I2R0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R0CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 0, 0 => 1 |
| | _, _ => 0 |
| def CA2_7_7I2R0P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R0Certificates (CA2_7_7I2R0CertificateIndex a)).input |
| lemma CA2_7_7I2R0P_check : ∀ a : PairSlot, contains (CA2_7_7I2R0Raw a) (CA2_7_7I2R0P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R0P_sound (a : PairSlot) : |
| (CA2_7_7I2R0P a).Encloses (CA2_7_7I2R0Value a) := |
| contains_sound (CA2_7_7I2R0Raw_sound a) (CA2_7_7I2R0P_check a) |
| def CA2_7_7I2R0Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R0Certificates (CA2_7_7I2R0CertificateIndex a)).output |
| lemma CA2_7_7I2R0Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R0Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R0Certificates_valid |
| (CA2_7_7I2R0CertificateIndex a) (CA2_7_7I2R0P_sound a) |
| def CA2_7_7I2R0Entropy : Ball := ⟨(3063334356907513434862083549 / 50000000000000000000000000000000), (2020217 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R0Entropy_sound : CA2_7_7I2R0Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R0Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R0Value CA2_7_7I2R0Terms CA2_7_7I2R0Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R0Mass : Ball := ⟨(502109287941468832085436601 / 100000000000000000000000000000000), (1 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R0Mass_sound : CA2_7_7I2R0Mass.Encloses (∑ a, CA2_7_7I2R0Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R0P CA2_7_7I2R0Value CA2_7_7I2R0P_sound) (by decide +kernel) |
| def CA2_7_7I2R0MassTermLogWitness : LogWitness := ⟨-18, 502109287941468832085436601, 381469726562500000000000000⟩ |
| def CA2_7_7I2R0MassTermLog : Ball := ⟨(-244037258857845153364503487992193 / 20000000000000000000000000000000), (50292631037 / 12500000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R0MassTermLog_sound : CA2_7_7I2R0MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R0Mass_sound) (w := CA2_7_7I2R0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R0MassTerm : Ball := ⟨(3063334356907513434862083549 / 50000000000000000000000000000000), (2020217 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R0MassTerm_sound : CA2_7_7I2R0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R0Mass_sound) CA2_7_7I2R0MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R0H : Ball := ⟨0, (2020217 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R0H_sound : CA2_7_7I2R0H.Encloses (homogeneousEntropy CA2_7_7I2R0Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R0Value CA2_7_7I2R0MassTerm_sound CA2_7_7I2R0Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R1Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 1 a |
| def CA2_7_7I2R1Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 1 a |
| lemma CA2_7_7I2R1Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R1Raw a).Encloses (CA2_7_7I2R1Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 1 a |
| def CA2_7_7I2R1Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(61021004836896843510631497413 / 100000000000000000000000000000000), (1 / 50000000000000000000000000000000)⟩ ⟨(112914904520571858587520645573 / 25000000000000000000000000000000), (77530211 / 50000000000000000000000000000000)⟩ ⟨(-370085365924020147984039148650649 / 50000000000000000000000000000000), (254109887473 / 100000000000000000000000000000000)⟩ ⟨-11, 61021004836896843510631497413, 48828125000000000000000000000⟩] |
| lemma CA2_7_7I2R1Certificates_valid : |
| CA2_7_7I2R1Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R1CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 1, 0 => 1 |
| | 0, 1 => 1 |
| | _, _ => 0 |
| def CA2_7_7I2R1P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R1Certificates (CA2_7_7I2R1CertificateIndex a)).input |
| lemma CA2_7_7I2R1P_check : ∀ a : PairSlot, contains (CA2_7_7I2R1Raw a) (CA2_7_7I2R1P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R1P_sound (a : PairSlot) : |
| (CA2_7_7I2R1P a).Encloses (CA2_7_7I2R1Value a) := |
| contains_sound (CA2_7_7I2R1Raw_sound a) (CA2_7_7I2R1P_check a) |
| def CA2_7_7I2R1Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R1Certificates (CA2_7_7I2R1CertificateIndex a)).output |
| lemma CA2_7_7I2R1Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R1Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R1Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R1Certificates_valid |
| (CA2_7_7I2R1CertificateIndex a) (CA2_7_7I2R1P_sound a) |
| def CA2_7_7I2R1Entropy : Ball := ⟨(112914904520571858587520645573 / 12500000000000000000000000000000), (77530211 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R1Entropy_sound : CA2_7_7I2R1Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R1Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R1Value CA2_7_7I2R1Terms CA2_7_7I2R1Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R1Mass : Ball := ⟨(61021004836896843510631497413 / 50000000000000000000000000000000), (1 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R1Mass_sound : CA2_7_7I2R1Mass.Encloses (∑ a, CA2_7_7I2R1Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R1P CA2_7_7I2R1Value CA2_7_7I2R1P_sound) (by decide +kernel) |
| def CA2_7_7I2R1MassTermLogWitness : LogWitness := ⟨-10, 61021004836896843510631497413, 48828125000000000000000000000⟩ |
| def CA2_7_7I2R1MassTermLog : Ball := ⟨(-83857001724005720628294388031371 / 12500000000000000000000000000000), (23293406379 / 10000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R1MassTermLog_sound : CA2_7_7I2R1MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R1Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R1Mass_sound) (w := CA2_7_7I2R1MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R1MassTerm : Ball := ⟨(818726161249315203770880901103 / 100000000000000000000000000000000), (888367 / 312500000000000000000000000000)⟩ |
| lemma CA2_7_7I2R1MassTerm_sound : CA2_7_7I2R1MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R1Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R1Mass_sound) CA2_7_7I2R1MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R1H : Ball := ⟨(84593074915259664929284263481 / 100000000000000000000000000000000), (148599571 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R1H_sound : CA2_7_7I2R1H.Encloses (homogeneousEntropy CA2_7_7I2R1Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R1Value CA2_7_7I2R1MassTerm_sound CA2_7_7I2R1Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R2Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 2 a |
| def CA2_7_7I2R2Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 2 a |
| lemma CA2_7_7I2R2Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R2Raw a).Encloses (CA2_7_7I2R2Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 2 a |
| def CA2_7_7I2R2Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(461021550444907393413351550401 / 50000000000000000000000000000000), (7 / 100000000000000000000000000000000)⟩ ⟨(4321001467844565078070936299133 / 100000000000000000000000000000000), (1562001811 / 100000000000000000000000000000000)⟩ ⟨(-46863334953372529309297799122213 / 10000000000000000000000000000000), (84703295111 / 50000000000000000000000000000000)⟩ ⟨-7, 461021550444907393413351550401, 390625000000000000000000000000⟩, |
| .log ⟨(24386991200266839911037879939 / 25000000000000000000000000000000), (1 / 50000000000000000000000000000000)⟩ ⟨(169064798213358252125773084711 / 25000000000000000000000000000000), (247879037 / 100000000000000000000000000000000)⟩ ⟨(-346629063062745441837771588922581 / 50000000000000000000000000000000), (127054943123 / 50000000000000000000000000000000)⟩ ⟨-11, 24386991200266839911037879939, 12207031250000000000000000000⟩, |
| .log ⟨(3483774427281869882558098408561 / 100000000000000000000000000000000), (9 / 50000000000000000000000000000000)⟩ ⟨(5847609219356964929723995082299 / 50000000000000000000000000000000), (221315383 / 5000000000000000000000000000000)⟩ ⟨(-335705387442057754048834480698173 / 100000000000000000000000000000000), (63527471307 / 50000000000000000000000000000000)⟩ ⟨-5, 3483774427281869882558098408561, 3125000000000000000000000000000⟩] |
| lemma CA2_7_7I2R2Certificates_valid : |
| CA2_7_7I2R2Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R2CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 2, 0 => 1 |
| | 3, 0 => 2 |
| | 1, 1 => 3 |
| | 0, 2 => 1 |
| | 0, 3 => 2 |
| | _, _ => 0 |
| def CA2_7_7I2R2P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R2Certificates (CA2_7_7I2R2CertificateIndex a)).input |
| lemma CA2_7_7I2R2P_check : ∀ a : PairSlot, contains (CA2_7_7I2R2Raw a) (CA2_7_7I2R2P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R2P_sound (a : PairSlot) : |
| (CA2_7_7I2R2P a).Encloses (CA2_7_7I2R2Value a) := |
| contains_sound (CA2_7_7I2R2Raw_sound a) (CA2_7_7I2R2P_check a) |
| def CA2_7_7I2R2Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R2Certificates (CA2_7_7I2R2CertificateIndex a)).output |
| lemma CA2_7_7I2R2Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R2Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R2Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R2Certificates_valid |
| (CA2_7_7I2R2CertificateIndex a) (CA2_7_7I2R2P_sound a) |
| def CA2_7_7I2R2Entropy : Ball := ⟨(2711217470013740754074505930069 / 12500000000000000000000000000000), (2011517339 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R2Entropy_sound : CA2_7_7I2R2Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R2Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R2Value CA2_7_7I2R2Terms CA2_7_7I2R2Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R2Mass : Ball := ⟨(5522956558663634175499807649677 / 100000000000000000000000000000000), (9 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R2Mass_sound : CA2_7_7I2R2Mass.Encloses (∑ a, CA2_7_7I2R2Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R2P CA2_7_7I2R2Value CA2_7_7I2R2P_sound) (by decide +kernel) |
| def CA2_7_7I2R2MassTermLogWitness : LogWitness := ⟨-5, 5522956558663634175499807649677, 3125000000000000000000000000000⟩ |
| def CA2_7_7I2R2MassTermLog : Ball := ⟨(-1158502744253016410078641519441 / 400000000000000000000000000000), (127054942749 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R2MassTermLog_sound : CA2_7_7I2R2MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R2Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R2Mass_sound) (w := CA2_7_7I2R2MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R2MassTerm : Ball := ⟨(15995900824005039517055163864603 / 100000000000000000000000000000000), (3508594699 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R2MassTerm_sound : CA2_7_7I2R2MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R2Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R2Mass_sound) CA2_7_7I2R2MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R2H : Ball := ⟨(5693838936104886515540883575949 / 100000000000000000000000000000000), (7531629377 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R2H_sound : CA2_7_7I2R2H.Encloses (homogeneousEntropy CA2_7_7I2R2Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R2Value CA2_7_7I2R2MassTerm_sound CA2_7_7I2R2Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R3Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 3 a |
| def CA2_7_7I2R3Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 3 a |
| lemma CA2_7_7I2R3Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R3Raw a).Encloses (CA2_7_7I2R3Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 3 a |
| def CA2_7_7I2R3Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(131095704406984719407700239349 / 25000000000000000000000000000000), (1 / 25000000000000000000000000000000)⟩ ⟨(2753378685052309096502096580713 / 100000000000000000000000000000000), (499690727 / 50000000000000000000000000000000)⟩ ⟨(-21002813917567312255242342477773 / 4000000000000000000000000000000), (190582413909 / 100000000000000000000000000000000)⟩ ⟨-8, 131095704406984719407700239349, 97656250000000000000000000000⟩, |
| .log ⟨(2270939017850000493846381468481 / 12500000000000000000000000000000), (39 / 100000000000000000000000000000000)⟩ ⟨(30985332075472481453487574065897 / 100000000000000000000000000000000), (7694240731 / 50000000000000000000000000000000)⟩ ⟨(-170553523409931108265824846279181 / 100000000000000000000000000000000), (42351647473 / 50000000000000000000000000000000)⟩ ⟨-3, 2270939017850000493846381468481, 1562500000000000000000000000000⟩, |
| .log ⟨(1354896351343567252040316827981 / 100000000000000000000000000000000), (3 / 100000000000000000000000000000000)⟩ ⟨(1165602488999341910841382973429 / 20000000000000000000000000000000), (573820929 / 25000000000000000000000000000000)⟩ ⟨(-107536130701389604624485476198019 / 25000000000000000000000000000000), (33881317937 / 20000000000000000000000000000000)⟩ ⟨-7, 1354896351343567252040316827981, 781250000000000000000000000000⟩] |
| lemma CA2_7_7I2R3Certificates_valid : |
| CA2_7_7I2R3Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R3CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 4, 0 => 1 |
| | 2, 1 => 2 |
| | 3, 1 => 3 |
| | 1, 2 => 2 |
| | 1, 3 => 3 |
| | 0, 4 => 1 |
| | _, _ => 0 |
| def CA2_7_7I2R3P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R3Certificates (CA2_7_7I2R3CertificateIndex a)).input |
| lemma CA2_7_7I2R3P_check : ∀ a : PairSlot, contains (CA2_7_7I2R3Raw a) (CA2_7_7I2R3P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R3P_sound (a : PairSlot) : |
| (CA2_7_7I2R3P a).Encloses (CA2_7_7I2R3Value a) := |
| contains_sound (CA2_7_7I2R3Raw_sound a) (CA2_7_7I2R3P_check a) |
| def CA2_7_7I2R3Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R3Certificates (CA2_7_7I2R3CertificateIndex a)).output |
| lemma CA2_7_7I2R3Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R3Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R3Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R3Certificates_valid |
| (CA2_7_7I2R3CertificateIndex a) (CA2_7_7I2R3P_sound a) |
| def CA2_7_7I2R3Entropy : Ball := ⟨(7913344641104300020839317102751 / 10000000000000000000000000000000), (2335393329 / 6250000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R3Entropy_sound : CA2_7_7I2R3Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R3Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R3Value CA2_7_7I2R3Terms CA2_7_7I2R3Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R3Mass : Ball := ⟨(801871652470860403217686781329 / 2000000000000000000000000000000), (23 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R3Mass_sound : CA2_7_7I2R3Mass.Encloses (∑ a, CA2_7_7I2R3Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R3P CA2_7_7I2R3Value CA2_7_7I2R3P_sound) (by decide +kernel) |
| def CA2_7_7I2R3MassTermLogWitness : LogWitness := ⟨-2, 801871652470860403217686781329, 500000000000000000000000000000⟩ |
| def CA2_7_7I2R3MassTermLog : Ball := ⟨(-18279077976160747981294955766949 / 20000000000000000000000000000000), (31763735639 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R3MassTermLog_sound : CA2_7_7I2R3MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R3Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R3Mass_sound) (w := CA2_7_7I2R3MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R3MassTerm : Ball := ⟨(36643686155969324069048097794141 / 100000000000000000000000000000000), (2547043927 / 10000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R3MassTerm_sound : CA2_7_7I2R3MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R3Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R3Mass_sound) CA2_7_7I2R3MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R3H : Ball := ⟨(42489760255073676139345073233369 / 100000000000000000000000000000000), (31418366267 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R3H_sound : CA2_7_7I2R3H.Encloses (homogeneousEntropy CA2_7_7I2R3Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R3Value CA2_7_7I2R3MassTerm_sound CA2_7_7I2R3Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R4Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 4 a |
| def CA2_7_7I2R4Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 4 a |
| lemma CA2_7_7I2R4Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R4Raw a).Encloses (CA2_7_7I2R4Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 4 a |
| def CA2_7_7I2R4Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(5277967175821923079897539329 / 100000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(25992363903925895922513432917 / 50000000000000000000000000000000), (894123 / 5000000000000000000000000000000)⟩ ⟨(-246234611149113273170862319465459 / 25000000000000000000000000000000), (169406598937 / 50000000000000000000000000000000)⟩ ⟨-15, 5277967175821923079897539329, 3051757812500000000000000000⟩, |
| .log ⟨(2038260987631875115742940545529 / 100000000000000000000000000000000), (1 / 12500000000000000000000000000000)⟩ ⟨(7935099222952918042652310790589 / 100000000000000000000000000000000), (302132991 / 10000000000000000000000000000000)⟩ ⟨(-389307319872329085824439203688361 / 100000000000000000000000000000000), (148230766173 / 100000000000000000000000000000000)⟩ ⟨-6, 2038260987631875115742940545529, 1562500000000000000000000000000⟩, |
| .log ⟨(10796235779384559959949417266089 / 50000000000000000000000000000000), (21 / 50000000000000000000000000000000)⟩ ⟨(33097490387073889598235127180257 / 100000000000000000000000000000000), (18289534931 / 100000000000000000000000000000000)⟩ ⟨(-76641273549883082343996926940597 / 50000000000000000000000000000000), (42351647463 / 50000000000000000000000000000000)⟩ ⟨-3, 10796235779384559959949417266089, 6250000000000000000000000000000⟩, |
| .log ⟨(108499099170855725901779589871 / 10000000000000000000000000000000), (3 / 100000000000000000000000000000000)⟩ ⟨(613507953043183359593479737449 / 12500000000000000000000000000000), (459511563 / 25000000000000000000000000000000)⟩ ⟨(-226179925080144666452584544784981 / 50000000000000000000000000000000), (8470329487 / 5000000000000000000000000000000)⟩ ⟨-7, 108499099170855725901779589871, 78125000000000000000000000000⟩, |
| .log ⟨(15492620375214302470057270997 / 100000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(135909967504824284589811746589 / 100000000000000000000000000000000), (4592967 / 10000000000000000000000000000000)⟩ ⟨(-438628082962189999951851555532183 / 50000000000000000000000000000000), (9264423063 / 3125000000000000000000000000000)⟩ ⟨-13, 15492620375214302470057270997, 12207031250000000000000000000⟩] |
| lemma CA2_7_7I2R4Certificates_valid : |
| CA2_7_7I2R4Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R4CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 5, 0 => 1 |
| | 4, 1 => 2 |
| | 2, 2 => 3 |
| | 2, 3 => 4 |
| | 3, 2 => 4 |
| | 3, 3 => 5 |
| | 1, 4 => 2 |
| | 0, 5 => 1 |
| | _, _ => 0 |
| def CA2_7_7I2R4P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R4Certificates (CA2_7_7I2R4CertificateIndex a)).input |
| lemma CA2_7_7I2R4P_check : ∀ a : PairSlot, contains (CA2_7_7I2R4Raw a) (CA2_7_7I2R4P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R4P_sound (a : PairSlot) : |
| (CA2_7_7I2R4P a).Encloses (CA2_7_7I2R4Value a) := |
| contains_sound (CA2_7_7I2R4Raw_sound a) (CA2_7_7I2R4P_check a) |
| def CA2_7_7I2R4Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R4Certificates (CA2_7_7I2R4CertificateIndex a)).output |
| lemma CA2_7_7I2R4Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R4Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R4Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R4Certificates_valid |
| (CA2_7_7I2R4CertificateIndex a) (CA2_7_7I2R4P_sound a) |
| def CA2_7_7I2R4Entropy : Ball := ⟨(14755923876197796826328822509719 / 25000000000000000000000000000000), (5617996369 / 20000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R4Entropy_sound : CA2_7_7I2R4Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R4Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R4Value CA2_7_7I2R4Terms CA2_7_7I2R4Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R4Mass : Ball := ⟨(27865024072176842818050159770311 / 100000000000000000000000000000000), (67 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R4Mass_sound : CA2_7_7I2R4Mass.Encloses (∑ a, CA2_7_7I2R4Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R4P CA2_7_7I2R4Value CA2_7_7I2R4P_sound) (by decide +kernel) |
| def CA2_7_7I2R4MassTermLogWitness : LogWitness := ⟨-2, 27865024072176842818050159770311, 25000000000000000000000000000000⟩ |
| def CA2_7_7I2R4MassTermLog : Ball := ⟨(-25555958021623995984140828497229 / 20000000000000000000000000000000), (63527471289 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R4MassTermLog_sound : CA2_7_7I2R4MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R4Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R4Mass_sound) (w := CA2_7_7I2R4MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R4MassTerm : Ball := ⟨(178029346365023383066357772421 / 500000000000000000000000000000), (8850972627 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R4MassTerm_sound : CA2_7_7I2R4MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R4Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R4Mass_sound) CA2_7_7I2R4MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R4H : Ball := ⟨(5854456557946627673010933888669 / 25000000000000000000000000000000), (45791927099 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R4H_sound : CA2_7_7I2R4H.Encloses (homogeneousEntropy CA2_7_7I2R4Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R4Value CA2_7_7I2R4MassTerm_sound CA2_7_7I2R4Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R5Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 5 a |
| def CA2_7_7I2R5Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 5 a |
| lemma CA2_7_7I2R5Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R5Raw a).Encloses (CA2_7_7I2R5Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 5 a |
| def CA2_7_7I2R5Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(147261181015888131340596841 / 12500000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(3342543549552779568172383377 / 25000000000000000000000000000000), (1122619 / 25000000000000000000000000000000)⟩ ⟨(-283725786260683812153665541671581 / 25000000000000000000000000000000), (381164911177 / 100000000000000000000000000000000)⟩ ⟨-17, 147261181015888131340596841, 95367431640625000000000000⟩, |
| .log ⟨(192105488604869140798984184437 / 25000000000000000000000000000000), (1 / 20000000000000000000000000000000)⟩ ⟨(3741128725067483292783869146183 / 100000000000000000000000000000000), (732238567 / 50000000000000000000000000000000)⟩ ⟨(-97371729257626738127061474219161 / 20000000000000000000000000000000), (95291206899 / 50000000000000000000000000000000)⟩ ⟨-8, 192105488604869140798984184437, 97656250000000000000000000000⟩, |
| .log ⟨(28426185916905566073339232999 / 100000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(58029320434616063406177313117 / 25000000000000000000000000000000), (78253237 / 100000000000000000000000000000000)⟩ ⟨(-816561470529255613905471137791119 / 100000000000000000000000000000000), (68821427849 / 25000000000000000000000000000000)⟩ ⟨-12, 28426185916905566073339232999, 24414062500000000000000000000⟩] |
| lemma CA2_7_7I2R5Certificates_valid : |
| CA2_7_7I2R5Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R5CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 5, 1 => 1 |
| | 4, 2 => 2 |
| | 4, 3 => 3 |
| | 2, 4 => 2 |
| | 3, 4 => 3 |
| | 1, 5 => 1 |
| | _, _ => 0 |
| def CA2_7_7I2R5P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R5Certificates (CA2_7_7I2R5CertificateIndex a)).input |
| lemma CA2_7_7I2R5P_check : ∀ a : PairSlot, contains (CA2_7_7I2R5Raw a) (CA2_7_7I2R5P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R5P_sound (a : PairSlot) : |
| (CA2_7_7I2R5P a).Encloses (CA2_7_7I2R5Value a) := |
| contains_sound (CA2_7_7I2R5Raw_sound a) (CA2_7_7I2R5P_check a) |
| def CA2_7_7I2R5Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R5Certificates (CA2_7_7I2R5CertificateIndex a)).output |
| lemma CA2_7_7I2R5Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R5Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R5Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R5Certificates_valid |
| (CA2_7_7I2R5CertificateIndex a) (CA2_7_7I2R5P_sound a) |
| def CA2_7_7I2R5Entropy : Ball := ⟨(3986616181004158664681267932159 / 50000000000000000000000000000000), (1547220847 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R5Entropy_sound : CA2_7_7I2R5Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R5Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R5Value CA2_7_7I2R5Terms CA2_7_7I2R5Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R5Mass : Ball := ⟨(31921049191380369372800029819 / 2000000000000000000000000000000), (7 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R5Mass_sound : CA2_7_7I2R5Mass.Encloses (∑ a, CA2_7_7I2R5Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R5P CA2_7_7I2R5Value CA2_7_7I2R5P_sound) (by decide +kernel) |
| def CA2_7_7I2R5MassTermLogWitness : LogWitness := ⟨-6, 31921049191380369372800029819, 31250000000000000000000000000⟩ |
| def CA2_7_7I2R5MassTermLog : Ball := ⟨(-413763681809651446200549432929053 / 100000000000000000000000000000000), (148230766657 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R5MassTermLog_sound : CA2_7_7I2R5MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R5Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R5Mass_sound) (w := CA2_7_7I2R5MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R5MassTerm : Ball := ⟨(1650971355081567343108674590919 / 25000000000000000000000000000000), (295730107 / 12500000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R5MassTerm_sound : CA2_7_7I2R5MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R5Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R5Mass_sound) CA2_7_7I2R5MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R5H : Ball := ⟨(684673470841023978463918750321 / 50000000000000000000000000000000), (109205651 / 2000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R5H_sound : CA2_7_7I2R5H.Encloses (homogeneousEntropy CA2_7_7I2R5Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R5Value CA2_7_7I2R5MassTerm_sound CA2_7_7I2R5Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R6Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 6 a |
| def CA2_7_7I2R6Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 6 a |
| lemma CA2_7_7I2R6Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R6Raw a).Encloses (CA2_7_7I2R6Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 6 a |
| def CA2_7_7I2R6Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(158644053613467679879438893 / 100000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(529633875297408340945825551 / 25000000000000000000000000000000), (705493 / 100000000000000000000000000000000)⟩ ⟨(-1335401770778873824862002345811629 / 100000000000000000000000000000000), (111173231921 / 25000000000000000000000000000000)⟩ ⟨-20, 158644053613467679879438893, 95367431640625000000000000⟩, |
| .log ⟨(2498801268892056157639 / 25000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(4603057917178023187341 / 2000000000000000000000000000000), (99 / 100000000000000000000000000000000)⟩ ⟨(-2302633053737689631189372509690703 / 100000000000000000000000000000000), (751158626129 / 100000000000000000000000000000000)⟩ ⟨-34, 39980820302272898522224, 23283064365386962890625⟩, |
| .log ⟨(2079393777372476244711147537 / 12500000000000000000000000000000), (1 / 50000000000000000000000000000000)⟩ ⟨(2894984425979975586826580021 / 2000000000000000000000000000000), (49316841 / 100000000000000000000000000000000)⟩ ⟨(-870140752524420958626435392655381 / 100000000000000000000000000000000), (9264423237 / 3125000000000000000000000000000)⟩ ⟨-13, 2079393777372476244711147537, 1525878906250000000000000000⟩] |
| lemma CA2_7_7I2R6Certificates_valid : |
| CA2_7_7I2R6Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R6CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | 5, 2 => 1 |
| | 5, 3 => 2 |
| | 4, 4 => 3 |
| | 2, 5 => 1 |
| | 3, 5 => 2 |
| | _, _ => 0 |
| def CA2_7_7I2R6P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R6Certificates (CA2_7_7I2R6CertificateIndex a)).input |
| lemma CA2_7_7I2R6P_check : ∀ a : PairSlot, contains (CA2_7_7I2R6Raw a) (CA2_7_7I2R6P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R6P_sound (a : PairSlot) : |
| (CA2_7_7I2R6P a).Encloses (CA2_7_7I2R6Value a) := |
| contains_sound (CA2_7_7I2R6Raw_sound a) (CA2_7_7I2R6P_check a) |
| def CA2_7_7I2R6Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R6Certificates (CA2_7_7I2R6CertificateIndex a)).output |
| lemma CA2_7_7I2R6Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R6Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R6Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R6Certificates_valid |
| (CA2_7_7I2R6CertificateIndex a) (CA2_7_7I2R6P_sound a) |
| def CA2_7_7I2R6Entropy : Ball := ⟨(74493376303584881935607169779 / 50000000000000000000000000000000), (2029121 / 4000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R6Entropy_sound : CA2_7_7I2R6Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R6Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R6Value CA2_7_7I2R6Terms CA2_7_7I2R6Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R6Mass : Ball := ⟨(8476229158308448226948659597 / 50000000000000000000000000000000), (3 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R6Mass_sound : CA2_7_7I2R6Mass.Encloses (∑ a, CA2_7_7I2R6Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R6P CA2_7_7I2R6Value CA2_7_7I2R6P_sound) (by decide +kernel) |
| def CA2_7_7I2R6MassTermLogWitness : LogWitness := ⟨-13, 8476229158308448226948659597, 6103515625000000000000000000⟩ |
| def CA2_7_7I2R6MassTermLog : Ball := ⟨(-108531407602892182777984611149741 / 12500000000000000000000000000000), (148230783477 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R6MassTermLog_sound : CA2_7_7I2R6MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I2R6Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I2R6Mass_sound) (w := CA2_7_7I2R6MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I2R6MassTerm : Ball := ⟨(18398741634317878500727459383 / 12500000000000000000000000000000), (6282197 / 12500000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R6MassTerm_sound : CA2_7_7I2R6MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R6Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I2R6Mass_sound) CA2_7_7I2R6MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I2R6H : Ball := ⟨(898409766313367932697332247 / 50000000000000000000000000000000), (100985601 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2R6H_sound : CA2_7_7I2R6H.Encloses (homogeneousEntropy CA2_7_7I2R6Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R6Value CA2_7_7I2R6MassTerm_sound CA2_7_7I2R6Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R7Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 7 a |
| def CA2_7_7I2R7Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 7 a |
| lemma CA2_7_7I2R7Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R7Raw a).Encloses (CA2_7_7I2R7Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 7 a |
| def CA2_7_7I2R7Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R7Certificates_valid : |
| CA2_7_7I2R7Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R7CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R7P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R7Certificates (CA2_7_7I2R7CertificateIndex a)).input |
| lemma CA2_7_7I2R7P_check : ∀ a : PairSlot, contains (CA2_7_7I2R7Raw a) (CA2_7_7I2R7P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R7P_sound (a : PairSlot) : |
| (CA2_7_7I2R7P a).Encloses (CA2_7_7I2R7Value a) := |
| contains_sound (CA2_7_7I2R7Raw_sound a) (CA2_7_7I2R7P_check a) |
| def CA2_7_7I2R7Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R7Certificates (CA2_7_7I2R7CertificateIndex a)).output |
| lemma CA2_7_7I2R7Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R7Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R7Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R7Certificates_valid |
| (CA2_7_7I2R7CertificateIndex a) (CA2_7_7I2R7P_sound a) |
| def CA2_7_7I2R7Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R7Entropy_sound : CA2_7_7I2R7Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R7Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R7Value CA2_7_7I2R7Terms CA2_7_7I2R7Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R7Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R7Mass_sound : CA2_7_7I2R7Mass.Encloses (∑ a, CA2_7_7I2R7Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R7P CA2_7_7I2R7Value CA2_7_7I2R7P_sound) (by decide +kernel) |
| def CA2_7_7I2R7MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R7MassTerm_sound : CA2_7_7I2R7MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R7Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R7Mass_sound) |
| def CA2_7_7I2R7H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R7H_sound : CA2_7_7I2R7H.Encloses (homogeneousEntropy CA2_7_7I2R7Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R7Value CA2_7_7I2R7MassTerm_sound CA2_7_7I2R7Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R8Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 8 a |
| def CA2_7_7I2R8Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 8 a |
| lemma CA2_7_7I2R8Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R8Raw a).Encloses (CA2_7_7I2R8Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 8 a |
| def CA2_7_7I2R8Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R8Certificates_valid : |
| CA2_7_7I2R8Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R8CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R8P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R8Certificates (CA2_7_7I2R8CertificateIndex a)).input |
| lemma CA2_7_7I2R8P_check : ∀ a : PairSlot, contains (CA2_7_7I2R8Raw a) (CA2_7_7I2R8P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R8P_sound (a : PairSlot) : |
| (CA2_7_7I2R8P a).Encloses (CA2_7_7I2R8Value a) := |
| contains_sound (CA2_7_7I2R8Raw_sound a) (CA2_7_7I2R8P_check a) |
| def CA2_7_7I2R8Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R8Certificates (CA2_7_7I2R8CertificateIndex a)).output |
| lemma CA2_7_7I2R8Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R8Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R8Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R8Certificates_valid |
| (CA2_7_7I2R8CertificateIndex a) (CA2_7_7I2R8P_sound a) |
| def CA2_7_7I2R8Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R8Entropy_sound : CA2_7_7I2R8Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R8Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R8Value CA2_7_7I2R8Terms CA2_7_7I2R8Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R8Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R8Mass_sound : CA2_7_7I2R8Mass.Encloses (∑ a, CA2_7_7I2R8Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R8P CA2_7_7I2R8Value CA2_7_7I2R8P_sound) (by decide +kernel) |
| def CA2_7_7I2R8MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R8MassTerm_sound : CA2_7_7I2R8MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R8Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R8Mass_sound) |
| def CA2_7_7I2R8H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R8H_sound : CA2_7_7I2R8H.Encloses (homogeneousEntropy CA2_7_7I2R8Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R8Value CA2_7_7I2R8MassTerm_sound CA2_7_7I2R8Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R9Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 9 a |
| def CA2_7_7I2R9Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 9 a |
| lemma CA2_7_7I2R9Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R9Raw a).Encloses (CA2_7_7I2R9Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 9 a |
| def CA2_7_7I2R9Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R9Certificates_valid : |
| CA2_7_7I2R9Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R9CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R9P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R9Certificates (CA2_7_7I2R9CertificateIndex a)).input |
| lemma CA2_7_7I2R9P_check : ∀ a : PairSlot, contains (CA2_7_7I2R9Raw a) (CA2_7_7I2R9P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R9P_sound (a : PairSlot) : |
| (CA2_7_7I2R9P a).Encloses (CA2_7_7I2R9Value a) := |
| contains_sound (CA2_7_7I2R9Raw_sound a) (CA2_7_7I2R9P_check a) |
| def CA2_7_7I2R9Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R9Certificates (CA2_7_7I2R9CertificateIndex a)).output |
| lemma CA2_7_7I2R9Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R9Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R9Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R9Certificates_valid |
| (CA2_7_7I2R9CertificateIndex a) (CA2_7_7I2R9P_sound a) |
| def CA2_7_7I2R9Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R9Entropy_sound : CA2_7_7I2R9Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R9Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R9Value CA2_7_7I2R9Terms CA2_7_7I2R9Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R9Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R9Mass_sound : CA2_7_7I2R9Mass.Encloses (∑ a, CA2_7_7I2R9Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R9P CA2_7_7I2R9Value CA2_7_7I2R9P_sound) (by decide +kernel) |
| def CA2_7_7I2R9MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R9MassTerm_sound : CA2_7_7I2R9MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R9Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R9Mass_sound) |
| def CA2_7_7I2R9H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R9H_sound : CA2_7_7I2R9H.Encloses (homogeneousEntropy CA2_7_7I2R9Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R9Value CA2_7_7I2R9MassTerm_sound CA2_7_7I2R9Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R10Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 10 a |
| def CA2_7_7I2R10Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 10 a |
| lemma CA2_7_7I2R10Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R10Raw a).Encloses (CA2_7_7I2R10Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 10 a |
| def CA2_7_7I2R10Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R10Certificates_valid : |
| CA2_7_7I2R10Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R10CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R10P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R10Certificates (CA2_7_7I2R10CertificateIndex a)).input |
| lemma CA2_7_7I2R10P_check : ∀ a : PairSlot, contains (CA2_7_7I2R10Raw a) (CA2_7_7I2R10P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R10P_sound (a : PairSlot) : |
| (CA2_7_7I2R10P a).Encloses (CA2_7_7I2R10Value a) := |
| contains_sound (CA2_7_7I2R10Raw_sound a) (CA2_7_7I2R10P_check a) |
| def CA2_7_7I2R10Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R10Certificates (CA2_7_7I2R10CertificateIndex a)).output |
| lemma CA2_7_7I2R10Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R10Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R10Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R10Certificates_valid |
| (CA2_7_7I2R10CertificateIndex a) (CA2_7_7I2R10P_sound a) |
| def CA2_7_7I2R10Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R10Entropy_sound : CA2_7_7I2R10Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R10Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R10Value CA2_7_7I2R10Terms CA2_7_7I2R10Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R10Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R10Mass_sound : CA2_7_7I2R10Mass.Encloses (∑ a, CA2_7_7I2R10Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R10P CA2_7_7I2R10Value CA2_7_7I2R10P_sound) (by decide +kernel) |
| def CA2_7_7I2R10MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R10MassTerm_sound : CA2_7_7I2R10MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R10Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R10Mass_sound) |
| def CA2_7_7I2R10H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R10H_sound : CA2_7_7I2R10H.Encloses (homogeneousEntropy CA2_7_7I2R10Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R10Value CA2_7_7I2R10MassTerm_sound CA2_7_7I2R10Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R11Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 11 a |
| def CA2_7_7I2R11Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 11 a |
| lemma CA2_7_7I2R11Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R11Raw a).Encloses (CA2_7_7I2R11Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 11 a |
| def CA2_7_7I2R11Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R11Certificates_valid : |
| CA2_7_7I2R11Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R11CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R11P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R11Certificates (CA2_7_7I2R11CertificateIndex a)).input |
| lemma CA2_7_7I2R11P_check : ∀ a : PairSlot, contains (CA2_7_7I2R11Raw a) (CA2_7_7I2R11P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R11P_sound (a : PairSlot) : |
| (CA2_7_7I2R11P a).Encloses (CA2_7_7I2R11Value a) := |
| contains_sound (CA2_7_7I2R11Raw_sound a) (CA2_7_7I2R11P_check a) |
| def CA2_7_7I2R11Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R11Certificates (CA2_7_7I2R11CertificateIndex a)).output |
| lemma CA2_7_7I2R11Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R11Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R11Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R11Certificates_valid |
| (CA2_7_7I2R11CertificateIndex a) (CA2_7_7I2R11P_sound a) |
| def CA2_7_7I2R11Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R11Entropy_sound : CA2_7_7I2R11Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R11Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R11Value CA2_7_7I2R11Terms CA2_7_7I2R11Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R11Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R11Mass_sound : CA2_7_7I2R11Mass.Encloses (∑ a, CA2_7_7I2R11Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R11P CA2_7_7I2R11Value CA2_7_7I2R11P_sound) (by decide +kernel) |
| def CA2_7_7I2R11MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R11MassTerm_sound : CA2_7_7I2R11MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R11Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R11Mass_sound) |
| def CA2_7_7I2R11H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R11H_sound : CA2_7_7I2R11H.Encloses (homogeneousEntropy CA2_7_7I2R11Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R11Value CA2_7_7I2R11MassTerm_sound CA2_7_7I2R11Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R12Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 12 a |
| def CA2_7_7I2R12Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 12 a |
| lemma CA2_7_7I2R12Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R12Raw a).Encloses (CA2_7_7I2R12Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 12 a |
| def CA2_7_7I2R12Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R12Certificates_valid : |
| CA2_7_7I2R12Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R12CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R12P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R12Certificates (CA2_7_7I2R12CertificateIndex a)).input |
| lemma CA2_7_7I2R12P_check : ∀ a : PairSlot, contains (CA2_7_7I2R12Raw a) (CA2_7_7I2R12P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R12P_sound (a : PairSlot) : |
| (CA2_7_7I2R12P a).Encloses (CA2_7_7I2R12Value a) := |
| contains_sound (CA2_7_7I2R12Raw_sound a) (CA2_7_7I2R12P_check a) |
| def CA2_7_7I2R12Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R12Certificates (CA2_7_7I2R12CertificateIndex a)).output |
| lemma CA2_7_7I2R12Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R12Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R12Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R12Certificates_valid |
| (CA2_7_7I2R12CertificateIndex a) (CA2_7_7I2R12P_sound a) |
| def CA2_7_7I2R12Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R12Entropy_sound : CA2_7_7I2R12Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R12Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R12Value CA2_7_7I2R12Terms CA2_7_7I2R12Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R12Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R12Mass_sound : CA2_7_7I2R12Mass.Encloses (∑ a, CA2_7_7I2R12Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R12P CA2_7_7I2R12Value CA2_7_7I2R12P_sound) (by decide +kernel) |
| def CA2_7_7I2R12MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R12MassTerm_sound : CA2_7_7I2R12MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R12Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R12Mass_sound) |
| def CA2_7_7I2R12H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R12H_sound : CA2_7_7I2R12H.Encloses (homogeneousEntropy CA2_7_7I2R12Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R12Value CA2_7_7I2R12MassTerm_sound CA2_7_7I2R12Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R13Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 13 a |
| def CA2_7_7I2R13Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 13 a |
| lemma CA2_7_7I2R13Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R13Raw a).Encloses (CA2_7_7I2R13Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 13 a |
| def CA2_7_7I2R13Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R13Certificates_valid : |
| CA2_7_7I2R13Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R13CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R13P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R13Certificates (CA2_7_7I2R13CertificateIndex a)).input |
| lemma CA2_7_7I2R13P_check : ∀ a : PairSlot, contains (CA2_7_7I2R13Raw a) (CA2_7_7I2R13P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R13P_sound (a : PairSlot) : |
| (CA2_7_7I2R13P a).Encloses (CA2_7_7I2R13Value a) := |
| contains_sound (CA2_7_7I2R13Raw_sound a) (CA2_7_7I2R13P_check a) |
| def CA2_7_7I2R13Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R13Certificates (CA2_7_7I2R13CertificateIndex a)).output |
| lemma CA2_7_7I2R13Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R13Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R13Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R13Certificates_valid |
| (CA2_7_7I2R13CertificateIndex a) (CA2_7_7I2R13P_sound a) |
| def CA2_7_7I2R13Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R13Entropy_sound : CA2_7_7I2R13Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R13Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R13Value CA2_7_7I2R13Terms CA2_7_7I2R13Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R13Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R13Mass_sound : CA2_7_7I2R13Mass.Encloses (∑ a, CA2_7_7I2R13Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R13P CA2_7_7I2R13Value CA2_7_7I2R13P_sound) (by decide +kernel) |
| def CA2_7_7I2R13MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R13MassTerm_sound : CA2_7_7I2R13MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R13Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R13Mass_sound) |
| def CA2_7_7I2R13H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R13H_sound : CA2_7_7I2R13H.Encloses (homogeneousEntropy CA2_7_7I2R13Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R13Value CA2_7_7I2R13MassTerm_sound CA2_7_7I2R13Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R14Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 14 a |
| def CA2_7_7I2R14Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 14 a |
| lemma CA2_7_7I2R14Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R14Raw a).Encloses (CA2_7_7I2R14Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 14 a |
| def CA2_7_7I2R14Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R14Certificates_valid : |
| CA2_7_7I2R14Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R14CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R14P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R14Certificates (CA2_7_7I2R14CertificateIndex a)).input |
| lemma CA2_7_7I2R14P_check : ∀ a : PairSlot, contains (CA2_7_7I2R14Raw a) (CA2_7_7I2R14P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R14P_sound (a : PairSlot) : |
| (CA2_7_7I2R14P a).Encloses (CA2_7_7I2R14Value a) := |
| contains_sound (CA2_7_7I2R14Raw_sound a) (CA2_7_7I2R14P_check a) |
| def CA2_7_7I2R14Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R14Certificates (CA2_7_7I2R14CertificateIndex a)).output |
| lemma CA2_7_7I2R14Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R14Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R14Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R14Certificates_valid |
| (CA2_7_7I2R14CertificateIndex a) (CA2_7_7I2R14P_sound a) |
| def CA2_7_7I2R14Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R14Entropy_sound : CA2_7_7I2R14Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R14Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R14Value CA2_7_7I2R14Terms CA2_7_7I2R14Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R14Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R14Mass_sound : CA2_7_7I2R14Mass.Encloses (∑ a, CA2_7_7I2R14Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R14P CA2_7_7I2R14Value CA2_7_7I2R14P_sound) (by decide +kernel) |
| def CA2_7_7I2R14MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R14MassTerm_sound : CA2_7_7I2R14MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R14Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R14Mass_sound) |
| def CA2_7_7I2R14H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R14H_sound : CA2_7_7I2R14H.Encloses (homogeneousEntropy CA2_7_7I2R14Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R14Value CA2_7_7I2R14MassTerm_sound CA2_7_7I2R14Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R15Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 15 a |
| def CA2_7_7I2R15Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 15 a |
| lemma CA2_7_7I2R15Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R15Raw a).Encloses (CA2_7_7I2R15Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 15 a |
| def CA2_7_7I2R15Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R15Certificates_valid : |
| CA2_7_7I2R15Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R15CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R15P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R15Certificates (CA2_7_7I2R15CertificateIndex a)).input |
| lemma CA2_7_7I2R15P_check : ∀ a : PairSlot, contains (CA2_7_7I2R15Raw a) (CA2_7_7I2R15P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R15P_sound (a : PairSlot) : |
| (CA2_7_7I2R15P a).Encloses (CA2_7_7I2R15Value a) := |
| contains_sound (CA2_7_7I2R15Raw_sound a) (CA2_7_7I2R15P_check a) |
| def CA2_7_7I2R15Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R15Certificates (CA2_7_7I2R15CertificateIndex a)).output |
| lemma CA2_7_7I2R15Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R15Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R15Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R15Certificates_valid |
| (CA2_7_7I2R15CertificateIndex a) (CA2_7_7I2R15P_sound a) |
| def CA2_7_7I2R15Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R15Entropy_sound : CA2_7_7I2R15Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R15Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R15Value CA2_7_7I2R15Terms CA2_7_7I2R15Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R15Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R15Mass_sound : CA2_7_7I2R15Mass.Encloses (∑ a, CA2_7_7I2R15Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R15P CA2_7_7I2R15Value CA2_7_7I2R15P_sound) (by decide +kernel) |
| def CA2_7_7I2R15MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R15MassTerm_sound : CA2_7_7I2R15MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R15Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R15Mass_sound) |
| def CA2_7_7I2R15H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R15H_sound : CA2_7_7I2R15H.Encloses (homogeneousEntropy CA2_7_7I2R15Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R15Value CA2_7_7I2R15MassTerm_sound CA2_7_7I2R15Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2R16Value (a : PairSlot) : ℝ := residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) 16 a |
| def CA2_7_7I2R16Raw (a : PairSlot) : Ball := residualBall (below (shape 2 7 7)) A2_7_7Law (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) 16 a |
| lemma CA2_7_7I2R16Raw_sound (a : PairSlot) : |
| (CA2_7_7I2R16Raw a).Encloses (CA2_7_7I2R16Value a) := by |
| exact residualBall_sound_on (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u => halfTable u ((Equiv.refl (Fin 3)) 2)) (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) (fun u hu a => halfTable_sound u (stageA_children_size (shape 2 7 7) (show (shape 2 7 7) ∈ positiveInitial by decide +kernel) u hu) ((Equiv.refl (Fin 3)) 2) a) 16 a |
| def CA2_7_7I2R16Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CA2_7_7I2R16Certificates_valid : |
| CA2_7_7I2R16Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I2R16CertificateIndex (a : PairSlot) : ℕ := |
| match a.1.val, a.2.val with |
| | _, _ => 0 |
| def CA2_7_7I2R16P (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R16Certificates (CA2_7_7I2R16CertificateIndex a)).input |
| lemma CA2_7_7I2R16P_check : ∀ a : PairSlot, contains (CA2_7_7I2R16Raw a) (CA2_7_7I2R16P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I2R16P_sound (a : PairSlot) : |
| (CA2_7_7I2R16P a).Encloses (CA2_7_7I2R16Value a) := |
| contains_sound (CA2_7_7I2R16Raw_sound a) (CA2_7_7I2R16P_check a) |
| def CA2_7_7I2R16Terms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I2R16Certificates (CA2_7_7I2R16CertificateIndex a)).output |
| lemma CA2_7_7I2R16Terms_sound (a : PairSlot) : |
| (CA2_7_7I2R16Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I2R16Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I2R16Certificates_valid |
| (CA2_7_7I2R16CertificateIndex a) (CA2_7_7I2R16P_sound a) |
| def CA2_7_7I2R16Entropy : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R16Entropy_sound : CA2_7_7I2R16Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I2R16Value) := by |
| exact contains_sound (entropyPair_enclosed CA2_7_7I2R16Value CA2_7_7I2R16Terms CA2_7_7I2R16Terms_sound) (by decide +kernel) |
| def CA2_7_7I2R16Mass : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R16Mass_sound : CA2_7_7I2R16Mass.Encloses (∑ a, CA2_7_7I2R16Value a) := by |
| exact contains_sound (pairSumBall_sound CA2_7_7I2R16P CA2_7_7I2R16Value CA2_7_7I2R16P_sound) (by decide +kernel) |
| def CA2_7_7I2R16MassTerm : Ball := .exact 0 |
| lemma CA2_7_7I2R16MassTerm_sound : CA2_7_7I2R16MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I2R16Value a))) := |
| entropyTerm_zero_ball (CA2_7_7I2R16Mass_sound) |
| def CA2_7_7I2R16H : Ball := ⟨0, 0⟩ |
| lemma CA2_7_7I2R16H_sound : CA2_7_7I2R16H.Encloses (homogeneousEntropy CA2_7_7I2R16Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I2R16Value CA2_7_7I2R16MassTerm_sound CA2_7_7I2R16Entropy_sound) (by decide +kernel) |
| def CA2_7_7I2ResidualEntropies (a : Fin 17) : Ball := |
| match a.val with |
| | 0 => CA2_7_7I2R0H |
| | 1 => CA2_7_7I2R1H |
| | 2 => CA2_7_7I2R2H |
| | 3 => CA2_7_7I2R3H |
| | 4 => CA2_7_7I2R4H |
| | 5 => CA2_7_7I2R5H |
| | 6 => CA2_7_7I2R6H |
| | 7 => CA2_7_7I2R7H |
| | 8 => CA2_7_7I2R8H |
| | 9 => CA2_7_7I2R9H |
| | 10 => CA2_7_7I2R10H |
| | 11 => CA2_7_7I2R11H |
| | 12 => CA2_7_7I2R12H |
| | 13 => CA2_7_7I2R13H |
| | 14 => CA2_7_7I2R14H |
| | 15 => CA2_7_7I2R15H |
| | 16 => CA2_7_7I2R16H |
| | _ => (.exact 0) |
| lemma CA2_7_7I2ResidualEntropies_sound (k : Fin 17) : |
| (CA2_7_7I2ResidualEntropies k).Encloses (homogeneousEntropy |
| (residualLaw (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) k)) := by |
| fin_cases k |
| · exact CA2_7_7I2R0H_sound |
| · exact CA2_7_7I2R1H_sound |
| · exact CA2_7_7I2R2H_sound |
| · exact CA2_7_7I2R3H_sound |
| · exact CA2_7_7I2R4H_sound |
| · exact CA2_7_7I2R5H_sound |
| · exact CA2_7_7I2R6H_sound |
| · exact CA2_7_7I2R7H_sound |
| · exact CA2_7_7I2R8H_sound |
| · exact CA2_7_7I2R9H_sound |
| · exact CA2_7_7I2R10H_sound |
| · exact CA2_7_7I2R11H_sound |
| · exact CA2_7_7I2R12H_sound |
| · exact CA2_7_7I2R13H_sound |
| · exact CA2_7_7I2R14H_sound |
| · exact CA2_7_7I2R15H_sound |
| · exact CA2_7_7I2R16H_sound |
| def CA2_7_7I2Singles (s : Shape) : Ball := |
| match s 0, s 1, s 2 with |
| | 0, 1, 7 => Z0_1_7H2H |
| | 0, 2, 6 => Z0_2_6H2H |
| | 0, 3, 5 => Z0_3_5H2H |
| | 0, 4, 4 => Z0_4_4H2H |
| | 0, 5, 3 => Z0_5_3H2H |
| | 0, 6, 2 => Z0_6_2H2H |
| | 0, 7, 1 => Z0_7_1H2H |
| | 1, 0, 7 => Z1_0_7H2H |
| | 2, 0, 6 => Z2_0_6H2H |
| | _, _, _ => (.exact 0) |
| lemma CA2_7_7I2Singles_sound (u : Shape) (hu : u ∈ below (shape 2 7 7)) |
| (hd : designated (Equiv.refl (Fin 3)) 2 u) : |
| (CA2_7_7I2Singles u).Encloses (homogeneousEntropy ((fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) u)) := by |
| rw [A2_7_7_below] at hu |
| simp only [List.mem_cons, List.not_mem_nil, or_false] at hu |
| rcases hu with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl |
| · exact Z0_1_7H2H_sound |
| · exact Z0_2_6H2H_sound |
| · exact Z0_3_5H2H_sound |
| · exact Z0_4_4H2H_sound |
| · exact Z0_5_3H2H_sound |
| · exact Z0_6_2H2H_sound |
| · exact Z0_7_1H2H_sound |
| · exact Z1_0_7H2H_sound |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 1 6) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 2 5) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 3 4) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 4 3) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 5 2) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 6 1) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 1 7 0) by decide +kernel) hd |>.elim |
| · exact Z2_0_6H2H_sound |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 1 5) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 2 4) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 3 3) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 4 2) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 5 1) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (Equiv.refl (Fin 3)) 2 (shape 2 6 0) by decide +kernel) hd |>.elim |
| def CA2_7_7I2Singleton : Ball := ⟨(3735549344201020389155168425783 / 12500000000000000000000000000000), (3138425543 / 12500000000000000000000000000000)⟩ |
| lemma CA2_7_7I2Singleton_sound : CA2_7_7I2Singleton.Encloses |
| (singletonEntropy (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ))) := by |
| exact contains_sound (singletonBall_sound (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 |
| CA2_7_7I2Singles (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ)) (fun u _ => A2_7_7Law_sound u) CA2_7_7I2Singles_sound) (by decide +kernel) |
| def CA2_7_7I2Group : Ball := ⟨(823532456101625366543148449591 / 800000000000000000000000000000), (193698787 / 125000000000000000000000000000)⟩ |
| lemma CA2_7_7I2Group_sound : CA2_7_7I2Group.Encloses |
| (groupedEntropy (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (Equiv.refl (Fin 3)) 2 (fun u a => (halfLaw u ((Equiv.refl (Fin 3)) 2) a : ℝ))) := by |
| exact contains_sound (Ball.add_sound CA2_7_7I2Singleton_sound |
| (finSumBall_sound 17 CA2_7_7I2ResidualEntropies _ CA2_7_7I2ResidualEntropies_sound)) (by decide +kernel) |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| namespace MatrixAllFields |
|
|
| open scoped BigOperators Topology Polynomial |
|
|
| section |
| noncomputable section |
| namespace MatrixMultiplication.NativeNumerics |
| open AllFieldParameters AllFieldHistory AllFieldCertificates AllFieldCertificates.Replay |
| open AllFieldInitialEntropyCertificate AllFieldNativeCapacity |
| open scoped BigOperators |
| def CA2_7_7I2H : Ball := ⟨(53956368040931955078041468163973 / 50000000000000000000000000000000), (473949701211 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I2_sound : CA2_7_7I2H.Encloses (stageACapacity (shape 2 7 7) 2) := by |
| have hb := contains_sound (Ball.add_sound CA2_7_7I2PairH_sound |
| (Ball.neg_sound (Ball.mul_sound |
| (by simpa only [Rat.cast_ofNat] using Ball.exact_sound 2) CA2_7_7I2Group_sound))) |
| (show contains (.add CA2_7_7I2PairH (.neg (.mul (.exact 2) CA2_7_7I2Group))) CA2_7_7I2H = true by decide +kernel) |
| simp only [stageACapacity, nativeCapacity, |
| show (2 : Fin 3) ≠ 0 by decide, ite_false] |
| change CA2_7_7I2H.Encloses (homogeneousEntropy CA2_7_7I2PairValue - _) |
| simpa only [sub_eq_add_neg] using hb |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
