| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.Certificates.SupportedContraction |
|
|
| 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 CB3_2_3I2PairValue (a : PairSlot) : ℝ := pairLaw (below (shape 3 2 3)) (shape 3 2 3) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) a |
| def CB3_2_3I2PairRaw (a : PairSlot) : Ball := pairLawBall (below (shape 3 2 3)) (shape 3 2 3) B3_2_3Law (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) a |
| lemma CB3_2_3I2PairRaw_sound (a : PairSlot) : |
| (CB3_2_3I2PairRaw a).Encloses (CB3_2_3I2PairValue a) := by |
| exact pairLawBall_sound_on (below (shape 3 2 3)) (shape 3 2 3) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) (fun u _ a => B3_2_3Little_sound (complement (shape 3 2 3) u) ((stageBPriority (shape 3 2 3)) 2) a) a |
| def CB3_2_3I2PairCertificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(657827693429655515259251577397 / 50000000000000000000000000000000), (3 / 50000000000000000000000000000000)⟩ ⟨(45583093825531771912031644789 / 800000000000000000000000000000), (2228806953 / 100000000000000000000000000000000)⟩ ⟨(-86616705029320451336803587500113 / 20000000000000000000000000000000), (1058791187 / 625000000000000000000000000000)⟩ ⟨-7, 657827693429655515259251577397, 390625000000000000000000000000⟩, |
| .log ⟨(2331743502850952336234925741329 / 5000000000000000000000000000000), (49 / 100000000000000000000000000000000)⟩ ⟨(17787044033619589124032271066687 / 50000000000000000000000000000000), (14812976831 / 50000000000000000000000000000000)⟩ ⟨(-9535270502454444362956674459109 / 12500000000000000000000000000000), (31763735577 / 50000000000000000000000000000000)⟩ ⟨-2, 2331743502850952336234925741329, 1250000000000000000000000000000⟩, |
| .log ⟨(1024737278060821122391491009313 / 50000000000000000000000000000000), (1 / 20000000000000000000000000000000)⟩ ⟨(3983755053946318443989142025409 / 50000000000000000000000000000000), (1518975927 / 50000000000000000000000000000000)⟩ ⟨(-97189668494471200819375168657627 / 25000000000000000000000000000000), (5929230641 / 4000000000000000000000000000000)⟩ ⟨-6, 1024737278060821122391491009313, 781250000000000000000000000000⟩] |
| lemma CB3_2_3I2PairCertificates_valid : |
| CB3_2_3I2PairCertificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2PairCertificateIndex (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 CB3_2_3I2PairP (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2PairCertificates (CB3_2_3I2PairCertificateIndex a)).input |
| lemma CB3_2_3I2PairP_check : ∀ a : PairSlot, contains (CB3_2_3I2PairRaw a) (CB3_2_3I2PairP a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2PairP_sound (a : PairSlot) : |
| (CB3_2_3I2PairP a).Encloses (CB3_2_3I2PairValue a) := |
| contains_sound (CB3_2_3I2PairRaw_sound a) (CB3_2_3I2PairP_check a) |
| def CB3_2_3I2PairTerms (a : PairSlot) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2PairCertificates (CB3_2_3I2PairCertificateIndex a)).output |
| lemma CB3_2_3I2PairTerms_sound (a : PairSlot) : |
| (CB3_2_3I2PairTerms a).Encloses (Foundation.entropyTerm (CB3_2_3I2PairValue a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2PairCertificates_valid |
| (CB3_2_3I2PairCertificateIndex a) (CB3_2_3I2PairP_sound a) |
| def CB3_2_3I2PairEntropy : Ball := ⟨(49239484903323286625046781782817 / 50000000000000000000000000000000), (34892712469 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2PairEntropy_sound : CB3_2_3I2PairEntropy.Encloses (Foundation.finiteEntropy CB3_2_3I2PairValue) := by |
| exact contains_sound (entropyPair_enclosed CB3_2_3I2PairValue CB3_2_3I2PairTerms CB3_2_3I2PairTerms_sound) (by decide +kernel) |
| def CB3_2_3I2PairMass : Ball := ⟨1, (3 / 2500000000000000000000000000000)⟩ |
| lemma CB3_2_3I2PairMass_sound : CB3_2_3I2PairMass.Encloses (∑ a, CB3_2_3I2PairValue a) := by |
| exact contains_sound (pairSumBall_sound CB3_2_3I2PairP CB3_2_3I2PairValue CB3_2_3I2PairP_sound) (by decide +kernel) |
| def CB3_2_3I2PairMassTermLogWitness : LogWitness := ⟨0, 1, 1⟩ |
| def CB3_2_3I2PairMassTermLog : Ball := ⟨0, (10587911901 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2PairMassTermLog_sound : CB3_2_3I2PairMassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2PairValue a))) := by |
| exact checkLog_sound logTwoBall_sound (CB3_2_3I2PairMass_sound) (w := CB3_2_3I2PairMassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2PairMassTerm : Ball := ⟨0, (21175823803 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2PairMassTerm_sound : CB3_2_3I2PairMassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2PairValue a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2PairMass_sound) CB3_2_3I2PairMassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2PairH : Ball := ⟨(49239484903323286625046781782817 / 50000000000000000000000000000000), (90961248741 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2PairH_sound : CB3_2_3I2PairH.Encloses (homogeneousEntropy CB3_2_3I2PairValue) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2PairValue CB3_2_3I2PairMassTerm_sound CB3_2_3I2PairEntropy_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 CB3_2_3I2R0Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 0 a |
| def CB3_2_3I2R0Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 0 a |
| lemma CB3_2_3I2R0Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R0Raw a).Encloses (CB3_2_3I2R0Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 0 a |
| def CB3_2_3I2R0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(657827693429655515259251577397 / 50000000000000000000000000000000), (3 / 50000000000000000000000000000000)⟩ ⟨(45583093825531771912031644789 / 800000000000000000000000000000), (2228806953 / 100000000000000000000000000000000)⟩ ⟨(-86616705029320451336803587500113 / 20000000000000000000000000000000), (1058791187 / 625000000000000000000000000000)⟩ ⟨-7, 657827693429655515259251577397, 390625000000000000000000000000⟩] |
| lemma CB3_2_3I2R0Certificates_valid : |
| CB3_2_3I2R0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R0CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | 0 => 1 |
| | _ => 0 |
| def CB3_2_3I2R0P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R0Certificates (CB3_2_3I2R0CertificateIndex a)).input |
| lemma CB3_2_3I2R0P_check : ∀ a : Fin 6, contains (CB3_2_3I2R0Raw a) (CB3_2_3I2R0P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R0P_sound (a : Fin 6) : |
| (CB3_2_3I2R0P a).Encloses (CB3_2_3I2R0Value a) := |
| contains_sound (CB3_2_3I2R0Raw_sound a) (CB3_2_3I2R0P_check a) |
| def CB3_2_3I2R0Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R0Certificates (CB3_2_3I2R0CertificateIndex a)).output |
| lemma CB3_2_3I2R0Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R0Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R0Certificates_valid |
| (CB3_2_3I2R0CertificateIndex a) (CB3_2_3I2R0P_sound a) |
| def CB3_2_3I2R0Entropy : Ball := ⟨(45583093825531771912031644789 / 800000000000000000000000000000), (2228806953 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R0Entropy_sound : CB3_2_3I2R0Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R0Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R0Value CB3_2_3I2R0Terms CB3_2_3I2R0Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R0Mass : Ball := ⟨(657827693429655515259251577397 / 50000000000000000000000000000000), (3 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R0Mass_sound : CB3_2_3I2R0Mass.Encloses (∑ a, CB3_2_3I2R0Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R0P CB3_2_3I2R0Value CB3_2_3I2R0P_sound) (by decide +kernel) |
| def CB3_2_3I2R0MassTermLogWitness : LogWitness := ⟨-7, 657827693429655515259251577397, 390625000000000000000000000000⟩ |
| def CB3_2_3I2R0MassTermLog : Ball := ⟨(-86616705029320451336803587500113 / 20000000000000000000000000000000), (1058791187 / 625000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R0MassTermLog_sound : CB3_2_3I2R0MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2R0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB3_2_3I2R0Mass_sound) (w := CB3_2_3I2R0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2R0MassTerm : Ball := ⟨(45583093825531771912031644789 / 800000000000000000000000000000), (2228806953 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R0MassTerm_sound : CB3_2_3I2R0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2R0Mass_sound) CB3_2_3I2R0MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2R0H : Ball := ⟨0, (2228806953 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R0H_sound : CB3_2_3I2R0H.Encloses (homogeneousEntropy CB3_2_3I2R0Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R0Value CB3_2_3I2R0MassTerm_sound CB3_2_3I2R0Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R1Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 1 a |
| def CB3_2_3I2R1Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 1 a |
| lemma CB3_2_3I2R1Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R1Raw a).Encloses (CB3_2_3I2R1Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 1 a |
| def CB3_2_3I2R1Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(47523174992684098213642460905101 / 100000000000000000000000000000000), (3 / 6250000000000000000000000000000)⟩ ⟨(35354994317325124691906992926299 / 100000000000000000000000000000000), (30190271319 / 100000000000000000000000000000000)⟩ ⟨(-74395269934653586537561574687477 / 100000000000000000000000000000000), (1270549423 / 2000000000000000000000000000000)⟩ ⟨-2, 47523174992684098213642460905101, 25000000000000000000000000000000⟩] |
| lemma CB3_2_3I2R1Certificates_valid : |
| CB3_2_3I2R1Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R1CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | 1 => 1 |
| | _ => 0 |
| def CB3_2_3I2R1P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R1Certificates (CB3_2_3I2R1CertificateIndex a)).input |
| lemma CB3_2_3I2R1P_check : ∀ a : Fin 6, contains (CB3_2_3I2R1Raw a) (CB3_2_3I2R1P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R1P_sound (a : Fin 6) : |
| (CB3_2_3I2R1P a).Encloses (CB3_2_3I2R1Value a) := |
| contains_sound (CB3_2_3I2R1Raw_sound a) (CB3_2_3I2R1P_check a) |
| def CB3_2_3I2R1Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R1Certificates (CB3_2_3I2R1CertificateIndex a)).output |
| lemma CB3_2_3I2R1Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R1Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R1Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R1Certificates_valid |
| (CB3_2_3I2R1CertificateIndex a) (CB3_2_3I2R1P_sound a) |
| def CB3_2_3I2R1Entropy : Ball := ⟨(35354994317325124691906992926299 / 100000000000000000000000000000000), (30190271319 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R1Entropy_sound : CB3_2_3I2R1Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R1Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R1Value CB3_2_3I2R1Terms CB3_2_3I2R1Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R1Mass : Ball := ⟨(47523174992684098213642460905101 / 100000000000000000000000000000000), (3 / 6250000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R1Mass_sound : CB3_2_3I2R1Mass.Encloses (∑ a, CB3_2_3I2R1Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R1P CB3_2_3I2R1Value CB3_2_3I2R1P_sound) (by decide +kernel) |
| def CB3_2_3I2R1MassTermLogWitness : LogWitness := ⟨-2, 47523174992684098213642460905101, 25000000000000000000000000000000⟩ |
| def CB3_2_3I2R1MassTermLog : Ball := ⟨(-74395269934653586537561574687477 / 100000000000000000000000000000000), (1270549423 / 2000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R1MassTermLog_sound : CB3_2_3I2R1MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2R1Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB3_2_3I2R1Mass_sound) (w := CB3_2_3I2R1MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2R1MassTerm : Ball := ⟨(35354994317325124691906992926299 / 100000000000000000000000000000000), (30190271319 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R1MassTerm_sound : CB3_2_3I2R1MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R1Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2R1Mass_sound) CB3_2_3I2R1MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2R1H : Ball := ⟨0, (30190271319 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R1H_sound : CB3_2_3I2R1H.Encloses (homogeneousEntropy CB3_2_3I2R1Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R1Value CB3_2_3I2R1MassTerm_sound CB3_2_3I2R1Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R2Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 2 a |
| def CB3_2_3I2R2Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 2 a |
| lemma CB3_2_3I2R2Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R2Raw a).Encloses (CB3_2_3I2R2Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 2 a |
| def CB3_2_3I2R2Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(31201979708678060382710687550019 / 100000000000000000000000000000000), (9 / 50000000000000000000000000000000)⟩ ⟨(36340591342924341329964561629037 / 100000000000000000000000000000000), (9910914333 / 50000000000000000000000000000000)⟩ ⟨(-116468864098444057946888340040549 / 100000000000000000000000000000000), (31763735553 / 50000000000000000000000000000000)⟩ ⟨-2, 31201979708678060382710687550019, 25000000000000000000000000000000⟩, |
| .log ⟨(37111064369939316642335233719 / 25000000000000000000000000000000), (1 / 100000000000000000000000000000000)⟩ ⟨(966775283033390482170794711793 / 100000000000000000000000000000000), (69155449 / 20000000000000000000000000000000)⟩ ⟨(-651271594770330307327486077108119 / 100000000000000000000000000000000), (116467030593 / 50000000000000000000000000000000)⟩ ⟨-10, 37111064369939316642335233719, 24414062500000000000000000000⟩] |
| lemma CB3_2_3I2R2Certificates_valid : |
| CB3_2_3I2R2Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R2CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | 2 => 1 |
| | 3 => 2 |
| | _ => 0 |
| def CB3_2_3I2R2P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R2Certificates (CB3_2_3I2R2CertificateIndex a)).input |
| lemma CB3_2_3I2R2P_check : ∀ a : Fin 6, contains (CB3_2_3I2R2Raw a) (CB3_2_3I2R2P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R2P_sound (a : Fin 6) : |
| (CB3_2_3I2R2P a).Encloses (CB3_2_3I2R2Value a) := |
| contains_sound (CB3_2_3I2R2Raw_sound a) (CB3_2_3I2R2P_check a) |
| def CB3_2_3I2R2Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R2Certificates (CB3_2_3I2R2CertificateIndex a)).output |
| lemma CB3_2_3I2R2Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R2Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R2Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R2Certificates_valid |
| (CB3_2_3I2R2CertificateIndex a) (CB3_2_3I2R2P_sound a) |
| def CB3_2_3I2R2Entropy : Ball := ⟨(3730736662595773181213535634083 / 10000000000000000000000000000000), (20167605911 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R2Entropy_sound : CB3_2_3I2R2Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R2Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R2Value CB3_2_3I2R2Terms CB3_2_3I2R2Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R2Mass : Ball := ⟨(6270084793231563529856005696979 / 20000000000000000000000000000000), (19 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R2Mass_sound : CB3_2_3I2R2Mass.Encloses (∑ a, CB3_2_3I2R2Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R2P CB3_2_3I2R2Value CB3_2_3I2R2P_sound) (by decide +kernel) |
| def CB3_2_3I2R2MassTermLogWitness : LogWitness := ⟨-2, 6270084793231563529856005696979, 5000000000000000000000000000000⟩ |
| def CB3_2_3I2R2MassTermLog : Ball := ⟨(-28998559883980189693420039678553 / 25000000000000000000000000000000), (63527471109 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R2MassTermLog_sound : CB3_2_3I2R2MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2R2Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB3_2_3I2R2Mass_sound) (w := CB3_2_3I2R2MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2R2MassTerm : Ball := ⟨(7272937174166361623897741548253 / 20000000000000000000000000000000), (19916131551 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R2MassTerm_sound : CB3_2_3I2R2MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R2Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2R2Mass_sound) CB3_2_3I2R2MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2R2H : Ball := ⟨(188536151025184738529329719913 / 20000000000000000000000000000000), (20041868731 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2R2H_sound : CB3_2_3I2R2H.Encloses (homogeneousEntropy CB3_2_3I2R2Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R2Value CB3_2_3I2R2MassTerm_sound CB3_2_3I2R2Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R3Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 3 a |
| def CB3_2_3I2R3Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 3 a |
| lemma CB3_2_3I2R3Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R3Raw a).Encloses (CB3_2_3I2R3Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 3 a |
| def CB3_2_3I2R3Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R3Certificates_valid : |
| CB3_2_3I2R3Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R3CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R3P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R3Certificates (CB3_2_3I2R3CertificateIndex a)).input |
| lemma CB3_2_3I2R3P_check : ∀ a : Fin 6, contains (CB3_2_3I2R3Raw a) (CB3_2_3I2R3P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R3P_sound (a : Fin 6) : |
| (CB3_2_3I2R3P a).Encloses (CB3_2_3I2R3Value a) := |
| contains_sound (CB3_2_3I2R3Raw_sound a) (CB3_2_3I2R3P_check a) |
| def CB3_2_3I2R3Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R3Certificates (CB3_2_3I2R3CertificateIndex a)).output |
| lemma CB3_2_3I2R3Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R3Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R3Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R3Certificates_valid |
| (CB3_2_3I2R3CertificateIndex a) (CB3_2_3I2R3P_sound a) |
| def CB3_2_3I2R3Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R3Entropy_sound : CB3_2_3I2R3Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R3Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R3Value CB3_2_3I2R3Terms CB3_2_3I2R3Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R3Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R3Mass_sound : CB3_2_3I2R3Mass.Encloses (∑ a, CB3_2_3I2R3Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R3P CB3_2_3I2R3Value CB3_2_3I2R3P_sound) (by decide +kernel) |
| def CB3_2_3I2R3MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R3MassTerm_sound : CB3_2_3I2R3MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R3Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R3Mass_sound) |
| def CB3_2_3I2R3H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R3H_sound : CB3_2_3I2R3H.Encloses (homogeneousEntropy CB3_2_3I2R3Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R3Value CB3_2_3I2R3MassTerm_sound CB3_2_3I2R3Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R4Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 4 a |
| def CB3_2_3I2R4Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 4 a |
| lemma CB3_2_3I2R4Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R4Raw a).Encloses (CB3_2_3I2R4Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 4 a |
| def CB3_2_3I2R4Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R4Certificates_valid : |
| CB3_2_3I2R4Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R4CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R4P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R4Certificates (CB3_2_3I2R4CertificateIndex a)).input |
| lemma CB3_2_3I2R4P_check : ∀ a : Fin 6, contains (CB3_2_3I2R4Raw a) (CB3_2_3I2R4P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R4P_sound (a : Fin 6) : |
| (CB3_2_3I2R4P a).Encloses (CB3_2_3I2R4Value a) := |
| contains_sound (CB3_2_3I2R4Raw_sound a) (CB3_2_3I2R4P_check a) |
| def CB3_2_3I2R4Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R4Certificates (CB3_2_3I2R4CertificateIndex a)).output |
| lemma CB3_2_3I2R4Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R4Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R4Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R4Certificates_valid |
| (CB3_2_3I2R4CertificateIndex a) (CB3_2_3I2R4P_sound a) |
| def CB3_2_3I2R4Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R4Entropy_sound : CB3_2_3I2R4Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R4Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R4Value CB3_2_3I2R4Terms CB3_2_3I2R4Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R4Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R4Mass_sound : CB3_2_3I2R4Mass.Encloses (∑ a, CB3_2_3I2R4Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R4P CB3_2_3I2R4Value CB3_2_3I2R4P_sound) (by decide +kernel) |
| def CB3_2_3I2R4MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R4MassTerm_sound : CB3_2_3I2R4MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R4Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R4Mass_sound) |
| def CB3_2_3I2R4H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R4H_sound : CB3_2_3I2R4H.Encloses (homogeneousEntropy CB3_2_3I2R4Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R4Value CB3_2_3I2R4MassTerm_sound CB3_2_3I2R4Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R5Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 5 a |
| def CB3_2_3I2R5Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 5 a |
| lemma CB3_2_3I2R5Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R5Raw a).Encloses (CB3_2_3I2R5Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 5 a |
| def CB3_2_3I2R5Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R5Certificates_valid : |
| CB3_2_3I2R5Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R5CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R5P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R5Certificates (CB3_2_3I2R5CertificateIndex a)).input |
| lemma CB3_2_3I2R5P_check : ∀ a : Fin 6, contains (CB3_2_3I2R5Raw a) (CB3_2_3I2R5P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R5P_sound (a : Fin 6) : |
| (CB3_2_3I2R5P a).Encloses (CB3_2_3I2R5Value a) := |
| contains_sound (CB3_2_3I2R5Raw_sound a) (CB3_2_3I2R5P_check a) |
| def CB3_2_3I2R5Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R5Certificates (CB3_2_3I2R5CertificateIndex a)).output |
| lemma CB3_2_3I2R5Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R5Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R5Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R5Certificates_valid |
| (CB3_2_3I2R5CertificateIndex a) (CB3_2_3I2R5P_sound a) |
| def CB3_2_3I2R5Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R5Entropy_sound : CB3_2_3I2R5Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R5Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R5Value CB3_2_3I2R5Terms CB3_2_3I2R5Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R5Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R5Mass_sound : CB3_2_3I2R5Mass.Encloses (∑ a, CB3_2_3I2R5Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R5P CB3_2_3I2R5Value CB3_2_3I2R5P_sound) (by decide +kernel) |
| def CB3_2_3I2R5MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R5MassTerm_sound : CB3_2_3I2R5MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R5Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R5Mass_sound) |
| def CB3_2_3I2R5H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R5H_sound : CB3_2_3I2R5H.Encloses (homogeneousEntropy CB3_2_3I2R5Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R5Value CB3_2_3I2R5MassTerm_sound CB3_2_3I2R5Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R6Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 6 a |
| def CB3_2_3I2R6Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 6 a |
| lemma CB3_2_3I2R6Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R6Raw a).Encloses (CB3_2_3I2R6Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 6 a |
| def CB3_2_3I2R6Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R6Certificates_valid : |
| CB3_2_3I2R6Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R6CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R6P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R6Certificates (CB3_2_3I2R6CertificateIndex a)).input |
| lemma CB3_2_3I2R6P_check : ∀ a : Fin 6, contains (CB3_2_3I2R6Raw a) (CB3_2_3I2R6P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R6P_sound (a : Fin 6) : |
| (CB3_2_3I2R6P a).Encloses (CB3_2_3I2R6Value a) := |
| contains_sound (CB3_2_3I2R6Raw_sound a) (CB3_2_3I2R6P_check a) |
| def CB3_2_3I2R6Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R6Certificates (CB3_2_3I2R6CertificateIndex a)).output |
| lemma CB3_2_3I2R6Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R6Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R6Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R6Certificates_valid |
| (CB3_2_3I2R6CertificateIndex a) (CB3_2_3I2R6P_sound a) |
| def CB3_2_3I2R6Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R6Entropy_sound : CB3_2_3I2R6Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R6Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R6Value CB3_2_3I2R6Terms CB3_2_3I2R6Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R6Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R6Mass_sound : CB3_2_3I2R6Mass.Encloses (∑ a, CB3_2_3I2R6Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R6P CB3_2_3I2R6Value CB3_2_3I2R6P_sound) (by decide +kernel) |
| def CB3_2_3I2R6MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R6MassTerm_sound : CB3_2_3I2R6MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R6Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R6Mass_sound) |
| def CB3_2_3I2R6H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R6H_sound : CB3_2_3I2R6H.Encloses (homogeneousEntropy CB3_2_3I2R6Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R6Value CB3_2_3I2R6MassTerm_sound CB3_2_3I2R6Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R7Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 7 a |
| def CB3_2_3I2R7Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 7 a |
| lemma CB3_2_3I2R7Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R7Raw a).Encloses (CB3_2_3I2R7Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 7 a |
| def CB3_2_3I2R7Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R7Certificates_valid : |
| CB3_2_3I2R7Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R7CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R7P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R7Certificates (CB3_2_3I2R7CertificateIndex a)).input |
| lemma CB3_2_3I2R7P_check : ∀ a : Fin 6, contains (CB3_2_3I2R7Raw a) (CB3_2_3I2R7P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R7P_sound (a : Fin 6) : |
| (CB3_2_3I2R7P a).Encloses (CB3_2_3I2R7Value a) := |
| contains_sound (CB3_2_3I2R7Raw_sound a) (CB3_2_3I2R7P_check a) |
| def CB3_2_3I2R7Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R7Certificates (CB3_2_3I2R7CertificateIndex a)).output |
| lemma CB3_2_3I2R7Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R7Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R7Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R7Certificates_valid |
| (CB3_2_3I2R7CertificateIndex a) (CB3_2_3I2R7P_sound a) |
| def CB3_2_3I2R7Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R7Entropy_sound : CB3_2_3I2R7Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R7Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R7Value CB3_2_3I2R7Terms CB3_2_3I2R7Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R7Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R7Mass_sound : CB3_2_3I2R7Mass.Encloses (∑ a, CB3_2_3I2R7Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R7P CB3_2_3I2R7Value CB3_2_3I2R7P_sound) (by decide +kernel) |
| def CB3_2_3I2R7MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R7MassTerm_sound : CB3_2_3I2R7MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R7Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R7Mass_sound) |
| def CB3_2_3I2R7H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R7H_sound : CB3_2_3I2R7H.Encloses (homogeneousEntropy CB3_2_3I2R7Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R7Value CB3_2_3I2R7MassTerm_sound CB3_2_3I2R7Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R8Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 8 a |
| def CB3_2_3I2R8Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 8 a |
| lemma CB3_2_3I2R8Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R8Raw a).Encloses (CB3_2_3I2R8Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 8 a |
| def CB3_2_3I2R8Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R8Certificates_valid : |
| CB3_2_3I2R8Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R8CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R8P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R8Certificates (CB3_2_3I2R8CertificateIndex a)).input |
| lemma CB3_2_3I2R8P_check : ∀ a : Fin 6, contains (CB3_2_3I2R8Raw a) (CB3_2_3I2R8P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R8P_sound (a : Fin 6) : |
| (CB3_2_3I2R8P a).Encloses (CB3_2_3I2R8Value a) := |
| contains_sound (CB3_2_3I2R8Raw_sound a) (CB3_2_3I2R8P_check a) |
| def CB3_2_3I2R8Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R8Certificates (CB3_2_3I2R8CertificateIndex a)).output |
| lemma CB3_2_3I2R8Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R8Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R8Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R8Certificates_valid |
| (CB3_2_3I2R8CertificateIndex a) (CB3_2_3I2R8P_sound a) |
| def CB3_2_3I2R8Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R8Entropy_sound : CB3_2_3I2R8Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R8Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R8Value CB3_2_3I2R8Terms CB3_2_3I2R8Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R8Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R8Mass_sound : CB3_2_3I2R8Mass.Encloses (∑ a, CB3_2_3I2R8Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R8P CB3_2_3I2R8Value CB3_2_3I2R8P_sound) (by decide +kernel) |
| def CB3_2_3I2R8MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R8MassTerm_sound : CB3_2_3I2R8MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R8Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R8Mass_sound) |
| def CB3_2_3I2R8H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R8H_sound : CB3_2_3I2R8H.Encloses (homogeneousEntropy CB3_2_3I2R8Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R8Value CB3_2_3I2R8MassTerm_sound CB3_2_3I2R8Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R9Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 9 a |
| def CB3_2_3I2R9Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 9 a |
| lemma CB3_2_3I2R9Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R9Raw a).Encloses (CB3_2_3I2R9Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 9 a |
| def CB3_2_3I2R9Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R9Certificates_valid : |
| CB3_2_3I2R9Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R9CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R9P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R9Certificates (CB3_2_3I2R9CertificateIndex a)).input |
| lemma CB3_2_3I2R9P_check : ∀ a : Fin 6, contains (CB3_2_3I2R9Raw a) (CB3_2_3I2R9P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R9P_sound (a : Fin 6) : |
| (CB3_2_3I2R9P a).Encloses (CB3_2_3I2R9Value a) := |
| contains_sound (CB3_2_3I2R9Raw_sound a) (CB3_2_3I2R9P_check a) |
| def CB3_2_3I2R9Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R9Certificates (CB3_2_3I2R9CertificateIndex a)).output |
| lemma CB3_2_3I2R9Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R9Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R9Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R9Certificates_valid |
| (CB3_2_3I2R9CertificateIndex a) (CB3_2_3I2R9P_sound a) |
| def CB3_2_3I2R9Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R9Entropy_sound : CB3_2_3I2R9Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R9Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R9Value CB3_2_3I2R9Terms CB3_2_3I2R9Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R9Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R9Mass_sound : CB3_2_3I2R9Mass.Encloses (∑ a, CB3_2_3I2R9Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R9P CB3_2_3I2R9Value CB3_2_3I2R9P_sound) (by decide +kernel) |
| def CB3_2_3I2R9MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R9MassTerm_sound : CB3_2_3I2R9MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R9Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R9Mass_sound) |
| def CB3_2_3I2R9H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R9H_sound : CB3_2_3I2R9H.Encloses (homogeneousEntropy CB3_2_3I2R9Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R9Value CB3_2_3I2R9MassTerm_sound CB3_2_3I2R9Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R10Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 10 a |
| def CB3_2_3I2R10Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 10 a |
| lemma CB3_2_3I2R10Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R10Raw a).Encloses (CB3_2_3I2R10Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 10 a |
| def CB3_2_3I2R10Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R10Certificates_valid : |
| CB3_2_3I2R10Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R10CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R10P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R10Certificates (CB3_2_3I2R10CertificateIndex a)).input |
| lemma CB3_2_3I2R10P_check : ∀ a : Fin 6, contains (CB3_2_3I2R10Raw a) (CB3_2_3I2R10P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R10P_sound (a : Fin 6) : |
| (CB3_2_3I2R10P a).Encloses (CB3_2_3I2R10Value a) := |
| contains_sound (CB3_2_3I2R10Raw_sound a) (CB3_2_3I2R10P_check a) |
| def CB3_2_3I2R10Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R10Certificates (CB3_2_3I2R10CertificateIndex a)).output |
| lemma CB3_2_3I2R10Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R10Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R10Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R10Certificates_valid |
| (CB3_2_3I2R10CertificateIndex a) (CB3_2_3I2R10P_sound a) |
| def CB3_2_3I2R10Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R10Entropy_sound : CB3_2_3I2R10Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R10Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R10Value CB3_2_3I2R10Terms CB3_2_3I2R10Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R10Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R10Mass_sound : CB3_2_3I2R10Mass.Encloses (∑ a, CB3_2_3I2R10Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R10P CB3_2_3I2R10Value CB3_2_3I2R10P_sound) (by decide +kernel) |
| def CB3_2_3I2R10MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R10MassTerm_sound : CB3_2_3I2R10MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R10Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R10Mass_sound) |
| def CB3_2_3I2R10H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R10H_sound : CB3_2_3I2R10H.Encloses (homogeneousEntropy CB3_2_3I2R10Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R10Value CB3_2_3I2R10MassTerm_sound CB3_2_3I2R10Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R11Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 11 a |
| def CB3_2_3I2R11Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 11 a |
| lemma CB3_2_3I2R11Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R11Raw a).Encloses (CB3_2_3I2R11Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 11 a |
| def CB3_2_3I2R11Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R11Certificates_valid : |
| CB3_2_3I2R11Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R11CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R11P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R11Certificates (CB3_2_3I2R11CertificateIndex a)).input |
| lemma CB3_2_3I2R11P_check : ∀ a : Fin 6, contains (CB3_2_3I2R11Raw a) (CB3_2_3I2R11P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R11P_sound (a : Fin 6) : |
| (CB3_2_3I2R11P a).Encloses (CB3_2_3I2R11Value a) := |
| contains_sound (CB3_2_3I2R11Raw_sound a) (CB3_2_3I2R11P_check a) |
| def CB3_2_3I2R11Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R11Certificates (CB3_2_3I2R11CertificateIndex a)).output |
| lemma CB3_2_3I2R11Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R11Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R11Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R11Certificates_valid |
| (CB3_2_3I2R11CertificateIndex a) (CB3_2_3I2R11P_sound a) |
| def CB3_2_3I2R11Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R11Entropy_sound : CB3_2_3I2R11Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R11Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R11Value CB3_2_3I2R11Terms CB3_2_3I2R11Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R11Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R11Mass_sound : CB3_2_3I2R11Mass.Encloses (∑ a, CB3_2_3I2R11Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R11P CB3_2_3I2R11Value CB3_2_3I2R11P_sound) (by decide +kernel) |
| def CB3_2_3I2R11MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R11MassTerm_sound : CB3_2_3I2R11MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R11Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R11Mass_sound) |
| def CB3_2_3I2R11H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R11H_sound : CB3_2_3I2R11H.Encloses (homogeneousEntropy CB3_2_3I2R11Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R11Value CB3_2_3I2R11MassTerm_sound CB3_2_3I2R11Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R12Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 12 a |
| def CB3_2_3I2R12Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 12 a |
| lemma CB3_2_3I2R12Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R12Raw a).Encloses (CB3_2_3I2R12Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 12 a |
| def CB3_2_3I2R12Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R12Certificates_valid : |
| CB3_2_3I2R12Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R12CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R12P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R12Certificates (CB3_2_3I2R12CertificateIndex a)).input |
| lemma CB3_2_3I2R12P_check : ∀ a : Fin 6, contains (CB3_2_3I2R12Raw a) (CB3_2_3I2R12P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R12P_sound (a : Fin 6) : |
| (CB3_2_3I2R12P a).Encloses (CB3_2_3I2R12Value a) := |
| contains_sound (CB3_2_3I2R12Raw_sound a) (CB3_2_3I2R12P_check a) |
| def CB3_2_3I2R12Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R12Certificates (CB3_2_3I2R12CertificateIndex a)).output |
| lemma CB3_2_3I2R12Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R12Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R12Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R12Certificates_valid |
| (CB3_2_3I2R12CertificateIndex a) (CB3_2_3I2R12P_sound a) |
| def CB3_2_3I2R12Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R12Entropy_sound : CB3_2_3I2R12Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R12Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R12Value CB3_2_3I2R12Terms CB3_2_3I2R12Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R12Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R12Mass_sound : CB3_2_3I2R12Mass.Encloses (∑ a, CB3_2_3I2R12Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R12P CB3_2_3I2R12Value CB3_2_3I2R12P_sound) (by decide +kernel) |
| def CB3_2_3I2R12MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R12MassTerm_sound : CB3_2_3I2R12MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R12Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R12Mass_sound) |
| def CB3_2_3I2R12H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R12H_sound : CB3_2_3I2R12H.Encloses (homogeneousEntropy CB3_2_3I2R12Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R12Value CB3_2_3I2R12MassTerm_sound CB3_2_3I2R12Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R13Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 13 a |
| def CB3_2_3I2R13Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 13 a |
| lemma CB3_2_3I2R13Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R13Raw a).Encloses (CB3_2_3I2R13Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 13 a |
| def CB3_2_3I2R13Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R13Certificates_valid : |
| CB3_2_3I2R13Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R13CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R13P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R13Certificates (CB3_2_3I2R13CertificateIndex a)).input |
| lemma CB3_2_3I2R13P_check : ∀ a : Fin 6, contains (CB3_2_3I2R13Raw a) (CB3_2_3I2R13P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R13P_sound (a : Fin 6) : |
| (CB3_2_3I2R13P a).Encloses (CB3_2_3I2R13Value a) := |
| contains_sound (CB3_2_3I2R13Raw_sound a) (CB3_2_3I2R13P_check a) |
| def CB3_2_3I2R13Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R13Certificates (CB3_2_3I2R13CertificateIndex a)).output |
| lemma CB3_2_3I2R13Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R13Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R13Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R13Certificates_valid |
| (CB3_2_3I2R13CertificateIndex a) (CB3_2_3I2R13P_sound a) |
| def CB3_2_3I2R13Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R13Entropy_sound : CB3_2_3I2R13Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R13Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R13Value CB3_2_3I2R13Terms CB3_2_3I2R13Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R13Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R13Mass_sound : CB3_2_3I2R13Mass.Encloses (∑ a, CB3_2_3I2R13Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R13P CB3_2_3I2R13Value CB3_2_3I2R13P_sound) (by decide +kernel) |
| def CB3_2_3I2R13MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R13MassTerm_sound : CB3_2_3I2R13MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R13Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R13Mass_sound) |
| def CB3_2_3I2R13H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R13H_sound : CB3_2_3I2R13H.Encloses (homogeneousEntropy CB3_2_3I2R13Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R13Value CB3_2_3I2R13MassTerm_sound CB3_2_3I2R13Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R14Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 14 a |
| def CB3_2_3I2R14Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 14 a |
| lemma CB3_2_3I2R14Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R14Raw a).Encloses (CB3_2_3I2R14Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 14 a |
| def CB3_2_3I2R14Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R14Certificates_valid : |
| CB3_2_3I2R14Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R14CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R14P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R14Certificates (CB3_2_3I2R14CertificateIndex a)).input |
| lemma CB3_2_3I2R14P_check : ∀ a : Fin 6, contains (CB3_2_3I2R14Raw a) (CB3_2_3I2R14P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R14P_sound (a : Fin 6) : |
| (CB3_2_3I2R14P a).Encloses (CB3_2_3I2R14Value a) := |
| contains_sound (CB3_2_3I2R14Raw_sound a) (CB3_2_3I2R14P_check a) |
| def CB3_2_3I2R14Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R14Certificates (CB3_2_3I2R14CertificateIndex a)).output |
| lemma CB3_2_3I2R14Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R14Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R14Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R14Certificates_valid |
| (CB3_2_3I2R14CertificateIndex a) (CB3_2_3I2R14P_sound a) |
| def CB3_2_3I2R14Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R14Entropy_sound : CB3_2_3I2R14Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R14Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R14Value CB3_2_3I2R14Terms CB3_2_3I2R14Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R14Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R14Mass_sound : CB3_2_3I2R14Mass.Encloses (∑ a, CB3_2_3I2R14Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R14P CB3_2_3I2R14Value CB3_2_3I2R14P_sound) (by decide +kernel) |
| def CB3_2_3I2R14MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R14MassTerm_sound : CB3_2_3I2R14MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R14Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R14Mass_sound) |
| def CB3_2_3I2R14H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R14H_sound : CB3_2_3I2R14H.Encloses (homogeneousEntropy CB3_2_3I2R14Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R14Value CB3_2_3I2R14MassTerm_sound CB3_2_3I2R14Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R15Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 15 a |
| def CB3_2_3I2R15Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 15 a |
| lemma CB3_2_3I2R15Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R15Raw a).Encloses (CB3_2_3I2R15Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 15 a |
| def CB3_2_3I2R15Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R15Certificates_valid : |
| CB3_2_3I2R15Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R15CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R15P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R15Certificates (CB3_2_3I2R15CertificateIndex a)).input |
| lemma CB3_2_3I2R15P_check : ∀ a : Fin 6, contains (CB3_2_3I2R15Raw a) (CB3_2_3I2R15P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R15P_sound (a : Fin 6) : |
| (CB3_2_3I2R15P a).Encloses (CB3_2_3I2R15Value a) := |
| contains_sound (CB3_2_3I2R15Raw_sound a) (CB3_2_3I2R15P_check a) |
| def CB3_2_3I2R15Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R15Certificates (CB3_2_3I2R15CertificateIndex a)).output |
| lemma CB3_2_3I2R15Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R15Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R15Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R15Certificates_valid |
| (CB3_2_3I2R15CertificateIndex a) (CB3_2_3I2R15P_sound a) |
| def CB3_2_3I2R15Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R15Entropy_sound : CB3_2_3I2R15Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R15Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R15Value CB3_2_3I2R15Terms CB3_2_3I2R15Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R15Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R15Mass_sound : CB3_2_3I2R15Mass.Encloses (∑ a, CB3_2_3I2R15Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R15P CB3_2_3I2R15Value CB3_2_3I2R15P_sound) (by decide +kernel) |
| def CB3_2_3I2R15MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R15MassTerm_sound : CB3_2_3I2R15MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R15Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R15Mass_sound) |
| def CB3_2_3I2R15H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R15H_sound : CB3_2_3I2R15H.Encloses (homogeneousEntropy CB3_2_3I2R15Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R15Value CB3_2_3I2R15MassTerm_sound CB3_2_3I2R15Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2R16Value (a : Fin 6) : ℝ := residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) 16 a |
| def CB3_2_3I2R16Raw (a : Fin 6) : Ball := residualBall (below (shape 3 2 3)) B3_2_3Law (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) 16 a |
| lemma CB3_2_3I2R16Raw_sound (a : Fin 6) : |
| (CB3_2_3I2R16Raw a).Encloses (CB3_2_3I2R16Value a) := by |
| exact residualBall_sound_on (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u => B3_2_3Little u ((stageBPriority (shape 3 2 3)) 2)) (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) (fun u _ a => B3_2_3Little_sound u ((stageBPriority (shape 3 2 3)) 2) a) 16 a |
| def CB3_2_3I2R16Certificates : List CompactCertificate.EntropyDatum := |
| [.zero] |
| lemma CB3_2_3I2R16Certificates_valid : |
| CB3_2_3I2R16Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I2R16CertificateIndex (a : Fin 6) : ℕ := |
| match a.val with |
| | _ => 0 |
| def CB3_2_3I2R16P (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R16Certificates (CB3_2_3I2R16CertificateIndex a)).input |
| lemma CB3_2_3I2R16P_check : ∀ a : Fin 6, contains (CB3_2_3I2R16Raw a) (CB3_2_3I2R16P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I2R16P_sound (a : Fin 6) : |
| (CB3_2_3I2R16P a).Encloses (CB3_2_3I2R16Value a) := |
| contains_sound (CB3_2_3I2R16Raw_sound a) (CB3_2_3I2R16P_check a) |
| def CB3_2_3I2R16Terms (a : Fin 6) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I2R16Certificates (CB3_2_3I2R16CertificateIndex a)).output |
| lemma CB3_2_3I2R16Terms_sound (a : Fin 6) : |
| (CB3_2_3I2R16Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2R16Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I2R16Certificates_valid |
| (CB3_2_3I2R16CertificateIndex a) (CB3_2_3I2R16P_sound a) |
| def CB3_2_3I2R16Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R16Entropy_sound : CB3_2_3I2R16Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2R16Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2R16Value CB3_2_3I2R16Terms CB3_2_3I2R16Terms_sound) (by decide +kernel) |
| def CB3_2_3I2R16Mass : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R16Mass_sound : CB3_2_3I2R16Mass.Encloses (∑ a, CB3_2_3I2R16Value a) := by |
| exact contains_sound (finSumBall_sound 6 CB3_2_3I2R16P CB3_2_3I2R16Value CB3_2_3I2R16P_sound) (by decide +kernel) |
| def CB3_2_3I2R16MassTerm : Ball := .exact 0 |
| lemma CB3_2_3I2R16MassTerm_sound : CB3_2_3I2R16MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2R16Value a))) := |
| entropyTerm_zero_ball (CB3_2_3I2R16Mass_sound) |
| def CB3_2_3I2R16H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2R16H_sound : CB3_2_3I2R16H.Encloses (homogeneousEntropy CB3_2_3I2R16Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2R16Value CB3_2_3I2R16MassTerm_sound CB3_2_3I2R16Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2ResidualEntropies (a : Fin 17) : Ball := |
| match a.val with |
| | 0 => CB3_2_3I2R0H |
| | 1 => CB3_2_3I2R1H |
| | 2 => CB3_2_3I2R2H |
| | 3 => CB3_2_3I2R3H |
| | 4 => CB3_2_3I2R4H |
| | 5 => CB3_2_3I2R5H |
| | 6 => CB3_2_3I2R6H |
| | 7 => CB3_2_3I2R7H |
| | 8 => CB3_2_3I2R8H |
| | 9 => CB3_2_3I2R9H |
| | 10 => CB3_2_3I2R10H |
| | 11 => CB3_2_3I2R11H |
| | 12 => CB3_2_3I2R12H |
| | 13 => CB3_2_3I2R13H |
| | 14 => CB3_2_3I2R14H |
| | 15 => CB3_2_3I2R15H |
| | 16 => CB3_2_3I2R16H |
| | _ => (.exact 0) |
| lemma CB3_2_3I2ResidualEntropies_sound (k : Fin 17) : |
| (CB3_2_3I2ResidualEntropies k).Encloses (homogeneousEntropy |
| (residualLaw (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) k)) := by |
| fin_cases k |
| · exact CB3_2_3I2R0H_sound |
| · exact CB3_2_3I2R1H_sound |
| · exact CB3_2_3I2R2H_sound |
| · exact CB3_2_3I2R3H_sound |
| · exact CB3_2_3I2R4H_sound |
| · exact CB3_2_3I2R5H_sound |
| · exact CB3_2_3I2R6H_sound |
| · exact CB3_2_3I2R7H_sound |
| · exact CB3_2_3I2R8H_sound |
| · exact CB3_2_3I2R9H_sound |
| · exact CB3_2_3I2R10H_sound |
| · exact CB3_2_3I2R11H_sound |
| · exact CB3_2_3I2R12H_sound |
| · exact CB3_2_3I2R13H_sound |
| · exact CB3_2_3I2R14H_sound |
| · exact CB3_2_3I2R15H_sound |
| · exact CB3_2_3I2R16H_sound |
| def CB3_2_3I2S0_1_3Value (a : Fin 6) : ℝ := (littleLaw (shape 3 2 3) (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2) a : ℝ) |
| def CB3_2_3I2S0_1_3E_4Log : Ball := .exact 0 |
| lemma CB3_2_3I2S0_1_3E_4Log_sound : CB3_2_3I2S0_1_3E_4Log.Encloses (Real.log (CB3_2_3I2S0_1_3Value (4 : Fin 6))) := by |
| exact log_exact_one_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6)) |
| def CB3_2_3I2S0_1_3E_4 : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S0_1_3E_4_sound : CB3_2_3I2S0_1_3E_4.Encloses (Foundation.entropyTerm (CB3_2_3I2S0_1_3Value (4 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6)) CB3_2_3I2S0_1_3E_4Log_sound) (by decide +kernel) |
| def CB3_2_3I2S0_1_3Terms (a : Fin 6) : Ball := |
| match a.val with |
| | 4 => ⟨0, 0⟩ |
| | _ => (.exact 0) |
| lemma CB3_2_3I2S0_1_3Terms_sound (a : Fin 6) : |
| (CB3_2_3I2S0_1_3Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2S0_1_3Value a)) := by |
| fin_cases a |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (0 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6))) |
| · exact CB3_2_3I2S0_1_3E_4_sound |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) (5 : Fin 6))) |
| def CB3_2_3I2S0_1_3Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S0_1_3Entropy_sound : CB3_2_3I2S0_1_3Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2S0_1_3Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2S0_1_3Value CB3_2_3I2S0_1_3Terms CB3_2_3I2S0_1_3Terms_sound) (by decide +kernel) |
| def CB3_2_3I2S0_1_3Mass : Ball := ⟨1, 0⟩ |
| lemma CB3_2_3I2S0_1_3Mass_sound : CB3_2_3I2S0_1_3Mass.Encloses (∑ a, CB3_2_3I2S0_1_3Value a) := by |
| exact contains_sound (finSumBall_sound 6 (B3_2_3Little (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2)) CB3_2_3I2S0_1_3Value (B3_2_3Little_sound (shape 0 1 3) ((stageBPriority (shape 3 2 3)) 2))) (by decide +kernel) |
| def CB3_2_3I2S0_1_3MassTermLog : Ball := .exact 0 |
| lemma CB3_2_3I2S0_1_3MassTermLog_sound : CB3_2_3I2S0_1_3MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2S0_1_3Value a))) := by |
| exact log_exact_one_ball (CB3_2_3I2S0_1_3Mass_sound) |
| def CB3_2_3I2S0_1_3MassTerm : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S0_1_3MassTerm_sound : CB3_2_3I2S0_1_3MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2S0_1_3Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2S0_1_3Mass_sound) CB3_2_3I2S0_1_3MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2S0_1_3H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S0_1_3H_sound : CB3_2_3I2S0_1_3H.Encloses (homogeneousEntropy CB3_2_3I2S0_1_3Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2S0_1_3Value CB3_2_3I2S0_1_3MassTerm_sound CB3_2_3I2S0_1_3Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2S0_2_2Value (a : Fin 6) : ℝ := (littleLaw (shape 3 2 3) (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2) a : ℝ) |
| def CB3_2_3I2S0_2_2E_2LogWitness : LogWitness := ⟨-1, 179163, 100000⟩ |
| def CB3_2_3I2S0_2_2E_2Log : Ball := ⟨(-11002136054002092463393093233409 / 100000000000000000000000000000000), (21175823683 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2E_2Log_sound : CB3_2_3I2S0_2_2E_2Log.Encloses (Real.log (CB3_2_3I2S0_2_2Value (2 : Fin 6))) := by |
| exact checkLog_sound logTwoBall_sound ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6)) (w := CB3_2_3I2S0_2_2E_2LogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2S0_2_2E_2 : Ball := ⟨(4927939254607942230047241907443 / 50000000000000000000000000000000), (18969620493 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2E_2_sound : CB3_2_3I2S0_2_2E_2.Encloses (Foundation.entropyTerm (CB3_2_3I2S0_2_2Value (2 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6)) CB3_2_3I2S0_2_2E_2Log_sound) (by decide +kernel) |
| def CB3_2_3I2S0_2_2E_3LogWitness : LogWitness := ⟨-4, 20837, 12500⟩ |
| def CB3_2_3I2S0_2_2E_3Log : Ball := ⟨(-226158711395997353564112106926423 / 100000000000000000000000000000000), (21175823683 / 20000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2E_3Log_sound : CB3_2_3I2S0_2_2E_3Log.Encloses (Real.log (CB3_2_3I2S0_2_2Value (3 : Fin 6))) := by |
| exact checkLog_sound logTwoBall_sound ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6)) (w := CB3_2_3I2S0_2_2E_3LogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2S0_2_2E_3 : Ball := ⟨(23562345346791984281077019860129 / 100000000000000000000000000000000), (11031015953 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2E_3_sound : CB3_2_3I2S0_2_2E_3.Encloses (Foundation.entropyTerm (CB3_2_3I2S0_2_2Value (3 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6)) CB3_2_3I2S0_2_2E_3Log_sound) (by decide +kernel) |
| def CB3_2_3I2S0_2_2Terms (a : Fin 6) : Ball := |
| match a.val with |
| | 2 => ⟨(4927939254607942230047241907443 / 50000000000000000000000000000000), (18969620493 / 50000000000000000000000000000000)⟩ |
| | 3 => ⟨(23562345346791984281077019860129 / 100000000000000000000000000000000), (11031015953 / 100000000000000000000000000000000)⟩ |
| | _ => (.exact 0) |
| lemma CB3_2_3I2S0_2_2Terms_sound (a : Fin 6) : |
| (CB3_2_3I2S0_2_2Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2S0_2_2Value a)) := by |
| fin_cases a |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (0 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6))) |
| · exact CB3_2_3I2S0_2_2E_2_sound |
| · exact CB3_2_3I2S0_2_2E_3_sound |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) (5 : Fin 6))) |
| def CB3_2_3I2S0_2_2Entropy : Ball := ⟨(6683644771201573748234300735003 / 20000000000000000000000000000000), (48970256939 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2Entropy_sound : CB3_2_3I2S0_2_2Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2S0_2_2Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2S0_2_2Value CB3_2_3I2S0_2_2Terms CB3_2_3I2S0_2_2Terms_sound) (by decide +kernel) |
| def CB3_2_3I2S0_2_2Mass : Ball := ⟨1, 0⟩ |
| lemma CB3_2_3I2S0_2_2Mass_sound : CB3_2_3I2S0_2_2Mass.Encloses (∑ a, CB3_2_3I2S0_2_2Value a) := by |
| exact contains_sound (finSumBall_sound 6 (B3_2_3Little (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2)) CB3_2_3I2S0_2_2Value (B3_2_3Little_sound (shape 0 2 2) ((stageBPriority (shape 3 2 3)) 2))) (by decide +kernel) |
| def CB3_2_3I2S0_2_2MassTermLog : Ball := .exact 0 |
| lemma CB3_2_3I2S0_2_2MassTermLog_sound : CB3_2_3I2S0_2_2MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2S0_2_2Value a))) := by |
| exact log_exact_one_ball (CB3_2_3I2S0_2_2Mass_sound) |
| def CB3_2_3I2S0_2_2MassTerm : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S0_2_2MassTerm_sound : CB3_2_3I2S0_2_2MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2S0_2_2Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2S0_2_2Mass_sound) CB3_2_3I2S0_2_2MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2S0_2_2H : Ball := ⟨(6683644771201573748234300735003 / 20000000000000000000000000000000), (48970256939 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S0_2_2H_sound : CB3_2_3I2S0_2_2H.Encloses (homogeneousEntropy CB3_2_3I2S0_2_2Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2S0_2_2Value CB3_2_3I2S0_2_2MassTerm_sound CB3_2_3I2S0_2_2Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2S1_0_3Value (a : Fin 6) : ℝ := (littleLaw (shape 3 2 3) (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2) a : ℝ) |
| def CB3_2_3I2S1_0_3E_4Log : Ball := .exact 0 |
| lemma CB3_2_3I2S1_0_3E_4Log_sound : CB3_2_3I2S1_0_3E_4Log.Encloses (Real.log (CB3_2_3I2S1_0_3Value (4 : Fin 6))) := by |
| exact log_exact_one_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6)) |
| def CB3_2_3I2S1_0_3E_4 : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S1_0_3E_4_sound : CB3_2_3I2S1_0_3E_4.Encloses (Foundation.entropyTerm (CB3_2_3I2S1_0_3Value (4 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6)) CB3_2_3I2S1_0_3E_4Log_sound) (by decide +kernel) |
| def CB3_2_3I2S1_0_3Terms (a : Fin 6) : Ball := |
| match a.val with |
| | 4 => ⟨0, 0⟩ |
| | _ => (.exact 0) |
| lemma CB3_2_3I2S1_0_3Terms_sound (a : Fin 6) : |
| (CB3_2_3I2S1_0_3Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2S1_0_3Value a)) := by |
| fin_cases a |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (0 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6))) |
| · exact CB3_2_3I2S1_0_3E_4_sound |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) (5 : Fin 6))) |
| def CB3_2_3I2S1_0_3Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S1_0_3Entropy_sound : CB3_2_3I2S1_0_3Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2S1_0_3Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2S1_0_3Value CB3_2_3I2S1_0_3Terms CB3_2_3I2S1_0_3Terms_sound) (by decide +kernel) |
| def CB3_2_3I2S1_0_3Mass : Ball := ⟨1, 0⟩ |
| lemma CB3_2_3I2S1_0_3Mass_sound : CB3_2_3I2S1_0_3Mass.Encloses (∑ a, CB3_2_3I2S1_0_3Value a) := by |
| exact contains_sound (finSumBall_sound 6 (B3_2_3Little (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2)) CB3_2_3I2S1_0_3Value (B3_2_3Little_sound (shape 1 0 3) ((stageBPriority (shape 3 2 3)) 2))) (by decide +kernel) |
| def CB3_2_3I2S1_0_3MassTermLog : Ball := .exact 0 |
| lemma CB3_2_3I2S1_0_3MassTermLog_sound : CB3_2_3I2S1_0_3MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2S1_0_3Value a))) := by |
| exact log_exact_one_ball (CB3_2_3I2S1_0_3Mass_sound) |
| def CB3_2_3I2S1_0_3MassTerm : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S1_0_3MassTerm_sound : CB3_2_3I2S1_0_3MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2S1_0_3Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2S1_0_3Mass_sound) CB3_2_3I2S1_0_3MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2S1_0_3H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S1_0_3H_sound : CB3_2_3I2S1_0_3H.Encloses (homogeneousEntropy CB3_2_3I2S1_0_3Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2S1_0_3Value CB3_2_3I2S1_0_3MassTerm_sound CB3_2_3I2S1_0_3Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2S2_0_2Value (a : Fin 6) : ℝ := (littleLaw (shape 3 2 3) (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2) a : ℝ) |
| def CB3_2_3I2S2_0_2E_2LogWitness : LogWitness := ⟨-1, 177987, 100000⟩ |
| def CB3_2_3I2S2_0_2E_2Log : Ball := ⟨(-11660685263090779968348502269377 / 100000000000000000000000000000000), (21175823683 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2E_2Log_sound : CB3_2_3I2S2_0_2E_2Log.Encloses (Real.log (CB3_2_3I2S2_0_2Value (2 : Fin 6))) := by |
| exact checkLog_sound logTwoBall_sound ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6)) (w := CB3_2_3I2S2_0_2E_2LogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2S2_0_2E_2 : Ball := ⟨(5188625969804346635566112183549 / 50000000000000000000000000000000), (37690213299 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2E_2_sound : CB3_2_3I2S2_0_2E_2.Encloses (Foundation.entropyTerm (CB3_2_3I2S2_0_2Value (2 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6)) CB3_2_3I2S2_0_2E_2Log_sound) (by decide +kernel) |
| def CB3_2_3I2S2_0_2E_3LogWitness : LogWitness := ⟨-4, 22013, 12500⟩ |
| def CB3_2_3I2S2_0_2E_3Log : Ball := ⟨(-27583552232710530620549709460953 / 12500000000000000000000000000000), (21175823683 / 20000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2E_3Log_sound : CB3_2_3I2S2_0_2E_3Log.Encloses (Real.log (CB3_2_3I2S2_0_2Value (3 : Fin 6))) := by |
| exact checkLog_sound logTwoBall_sound ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6)) (w := CB3_2_3I2S2_0_2E_3LogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I2S2_0_2E_3 : Ball := ⟨(12143934705973138211003215087279 / 50000000000000000000000000000000), (11653585169 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2E_3_sound : CB3_2_3I2S2_0_2E_3.Encloses (Foundation.entropyTerm (CB3_2_3I2S2_0_2Value (3 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6)) CB3_2_3I2S2_0_2E_3Log_sound) (by decide +kernel) |
| def CB3_2_3I2S2_0_2Terms (a : Fin 6) : Ball := |
| match a.val with |
| | 2 => ⟨(5188625969804346635566112183549 / 50000000000000000000000000000000), (37690213299 / 100000000000000000000000000000000)⟩ |
| | 3 => ⟨(12143934705973138211003215087279 / 50000000000000000000000000000000), (11653585169 / 100000000000000000000000000000000)⟩ |
| | _ => (.exact 0) |
| lemma CB3_2_3I2S2_0_2Terms_sound (a : Fin 6) : |
| (CB3_2_3I2S2_0_2Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2S2_0_2Value a)) := by |
| fin_cases a |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (0 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6))) |
| · exact CB3_2_3I2S2_0_2E_2_sound |
| · exact CB3_2_3I2S2_0_2E_3_sound |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) (5 : Fin 6))) |
| def CB3_2_3I2S2_0_2Entropy : Ball := ⟨(4333140168944371211642331817707 / 12500000000000000000000000000000), (12335949617 / 25000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2Entropy_sound : CB3_2_3I2S2_0_2Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2S2_0_2Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2S2_0_2Value CB3_2_3I2S2_0_2Terms CB3_2_3I2S2_0_2Terms_sound) (by decide +kernel) |
| def CB3_2_3I2S2_0_2Mass : Ball := ⟨1, 0⟩ |
| lemma CB3_2_3I2S2_0_2Mass_sound : CB3_2_3I2S2_0_2Mass.Encloses (∑ a, CB3_2_3I2S2_0_2Value a) := by |
| exact contains_sound (finSumBall_sound 6 (B3_2_3Little (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2)) CB3_2_3I2S2_0_2Value (B3_2_3Little_sound (shape 2 0 2) ((stageBPriority (shape 3 2 3)) 2))) (by decide +kernel) |
| def CB3_2_3I2S2_0_2MassTermLog : Ball := .exact 0 |
| lemma CB3_2_3I2S2_0_2MassTermLog_sound : CB3_2_3I2S2_0_2MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2S2_0_2Value a))) := by |
| exact log_exact_one_ball (CB3_2_3I2S2_0_2Mass_sound) |
| def CB3_2_3I2S2_0_2MassTerm : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S2_0_2MassTerm_sound : CB3_2_3I2S2_0_2MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2S2_0_2Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2S2_0_2Mass_sound) CB3_2_3I2S2_0_2MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2S2_0_2H : Ball := ⟨(4333140168944371211642331817707 / 12500000000000000000000000000000), (12335949617 / 25000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2S2_0_2H_sound : CB3_2_3I2S2_0_2H.Encloses (homogeneousEntropy CB3_2_3I2S2_0_2Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2S2_0_2Value CB3_2_3I2S2_0_2MassTerm_sound CB3_2_3I2S2_0_2Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2S3_0_1Value (a : Fin 6) : ℝ := (littleLaw (shape 3 2 3) (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2) a : ℝ) |
| def CB3_2_3I2S3_0_1E_1Log : Ball := .exact 0 |
| lemma CB3_2_3I2S3_0_1E_1Log_sound : CB3_2_3I2S3_0_1E_1Log.Encloses (Real.log (CB3_2_3I2S3_0_1Value (1 : Fin 6))) := by |
| exact log_exact_one_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6)) |
| def CB3_2_3I2S3_0_1E_1 : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S3_0_1E_1_sound : CB3_2_3I2S3_0_1E_1.Encloses (Foundation.entropyTerm (CB3_2_3I2S3_0_1Value (1 : Fin 6))) := by |
| exact contains_sound (entropyTerm_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (1 : Fin 6)) CB3_2_3I2S3_0_1E_1Log_sound) (by decide +kernel) |
| def CB3_2_3I2S3_0_1Terms (a : Fin 6) : Ball := |
| match a.val with |
| | 1 => ⟨0, 0⟩ |
| | _ => (.exact 0) |
| lemma CB3_2_3I2S3_0_1Terms_sound (a : Fin 6) : |
| (CB3_2_3I2S3_0_1Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I2S3_0_1Value a)) := by |
| fin_cases a |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (0 : Fin 6))) |
| · exact CB3_2_3I2S3_0_1E_1_sound |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (2 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (3 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (4 : Fin 6))) |
| · exact (entropyTerm_zero_ball ((B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) (5 : Fin 6))) |
| def CB3_2_3I2S3_0_1Entropy : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S3_0_1Entropy_sound : CB3_2_3I2S3_0_1Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I2S3_0_1Value) := by |
| exact contains_sound (entropyFin_enclosed 6 CB3_2_3I2S3_0_1Value CB3_2_3I2S3_0_1Terms CB3_2_3I2S3_0_1Terms_sound) (by decide +kernel) |
| def CB3_2_3I2S3_0_1Mass : Ball := ⟨1, 0⟩ |
| lemma CB3_2_3I2S3_0_1Mass_sound : CB3_2_3I2S3_0_1Mass.Encloses (∑ a, CB3_2_3I2S3_0_1Value a) := by |
| exact contains_sound (finSumBall_sound 6 (B3_2_3Little (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2)) CB3_2_3I2S3_0_1Value (B3_2_3Little_sound (shape 3 0 1) ((stageBPriority (shape 3 2 3)) 2))) (by decide +kernel) |
| def CB3_2_3I2S3_0_1MassTermLog : Ball := .exact 0 |
| lemma CB3_2_3I2S3_0_1MassTermLog_sound : CB3_2_3I2S3_0_1MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I2S3_0_1Value a))) := by |
| exact log_exact_one_ball (CB3_2_3I2S3_0_1Mass_sound) |
| def CB3_2_3I2S3_0_1MassTerm : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S3_0_1MassTerm_sound : CB3_2_3I2S3_0_1MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I2S3_0_1Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I2S3_0_1Mass_sound) CB3_2_3I2S3_0_1MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I2S3_0_1H : Ball := ⟨0, 0⟩ |
| lemma CB3_2_3I2S3_0_1H_sound : CB3_2_3I2S3_0_1H.Encloses (homogeneousEntropy CB3_2_3I2S3_0_1Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I2S3_0_1Value CB3_2_3I2S3_0_1MassTerm_sound CB3_2_3I2S3_0_1Entropy_sound) (by decide +kernel) |
| def CB3_2_3I2Singles (s : Shape) : Ball := |
| match s 0, s 1, s 2 with |
| | 0, 1, 3 => CB3_2_3I2S0_1_3H |
| | 0, 2, 2 => CB3_2_3I2S0_2_2H |
| | 1, 0, 3 => CB3_2_3I2S1_0_3H |
| | 2, 0, 2 => CB3_2_3I2S2_0_2H |
| | 3, 0, 1 => CB3_2_3I2S3_0_1H |
| | _, _, _ => (.exact 0) |
| lemma CB3_2_3I2Singles_sound (u : Shape) (hu : u ∈ below (shape 3 2 3)) |
| (hd : designated (stageBPriority (shape 3 2 3)) 2 u) : |
| (CB3_2_3I2Singles u).Encloses (homogeneousEntropy ((fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) u)) := by |
| rw [B3_2_3_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 |
| · exact CB3_2_3I2S0_1_3H_sound |
| · exact CB3_2_3I2S0_2_2H_sound |
| · exact CB3_2_3I2S1_0_3H_sound |
| · exact (show ¬ designated (stageBPriority (shape 3 2 3)) 2 (shape 1 1 2) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (stageBPriority (shape 3 2 3)) 2 (shape 1 2 1) by decide +kernel) hd |>.elim |
| · exact CB3_2_3I2S2_0_2H_sound |
| · exact (show ¬ designated (stageBPriority (shape 3 2 3)) 2 (shape 2 1 1) by decide +kernel) hd |>.elim |
| · exact (show ¬ designated (stageBPriority (shape 3 2 3)) 2 (shape 2 2 0) by decide +kernel) hd |>.elim |
| · exact CB3_2_3I2S3_0_1H_sound |
| · exact (show ¬ designated (stageBPriority (shape 3 2 3)) 2 (shape 3 1 0) by decide +kernel) hd |>.elim |
| def CB3_2_3I2Singleton : Ball := ⟨(2997173016171163830905521820877 / 50000000000000000000000000000000), (1068609679 / 12500000000000000000000000000000)⟩ |
| lemma CB3_2_3I2Singleton_sound : CB3_2_3I2Singleton.Encloses |
| (singletonEntropy (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ))) := by |
| exact contains_sound (singletonBall_sound (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 |
| CB3_2_3I2Singles (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ)) (fun u _ => B3_2_3Law_sound u) CB3_2_3I2Singles_sound) (by decide +kernel) |
| def CB3_2_3I2Group : Ball := ⟨(6937026787468251354457692241319 / 100000000000000000000000000000000), (56735385719 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2Group_sound : CB3_2_3I2Group.Encloses |
| (groupedEntropy (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (stageBPriority (shape 3 2 3)) 2 (fun u a => (littleLaw (shape 3 2 3) u ((stageBPriority (shape 3 2 3)) 2) a : ℝ))) := by |
| exact contains_sound (Ball.add_sound CB3_2_3I2Singleton_sound |
| (finSumBall_sound 17 CB3_2_3I2ResidualEntropies _ CB3_2_3I2ResidualEntropies_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 CB3_2_3I2H : Ball := ⟨(21151229057927517635294544770749 / 25000000000000000000000000000000), (317902791617 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I2_sound : CB3_2_3I2H.Encloses (stageBCapacity (shape 3 2 3) 2) := by |
| have hb := contains_sound (Ball.add_sound CB3_2_3I2PairH_sound |
| (Ball.neg_sound (Ball.mul_sound |
| (by simpa only [Rat.cast_ofNat] using Ball.exact_sound 2) CB3_2_3I2Group_sound))) |
| (show contains (.add CB3_2_3I2PairH (.neg (.mul (.exact 2) CB3_2_3I2Group))) CB3_2_3I2H = true by decide +kernel) |
| unfold CB3_2_3I2PairValue at hb |
| simpa only [stageBCapacity, nativeCapacity, |
| show (2 : Fin 3) ≠ 0 by decide, ite_false, sub_eq_add_neg] using hb |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
