| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.Certificates.Terminal4_2_2 |
|
|
| 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 CB4_2_2I0Value (a : Fin 17) : ℝ := marginal (below (shape 4 2 2)) (fun u => (stageBLaw (shape 4 2 2) u : ℝ)) ((stageBPriority (shape 4 2 2)) 0) a |
| def CB4_2_2I0Raw (a : Fin 17) : Ball := marginalBall (below (shape 4 2 2)) B4_2_2Law ((stageBPriority (shape 4 2 2)) 0) a |
| lemma CB4_2_2I0Raw_sound (a : Fin 17) : |
| (CB4_2_2I0Raw a).Encloses (CB4_2_2I0Value a) := by |
| exact marginalBall_sound (below (shape 4 2 2)) B4_2_2Law (fun u => (stageBLaw (shape 4 2 2) u : ℝ)) (fun u _ => B4_2_2Law_sound u) ((stageBPriority (shape 4 2 2)) 0) a |
| def CB4_2_2I0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(18443922190366941637623808000193 / 100000000000000000000000000000000), (69 / 100000000000000000000000000000000)⟩ ⟨(31178256963042688675819307809239 / 100000000000000000000000000000000), (15622609959 / 100000000000000000000000000000000)⟩ ⟨(-42260882258718742705346530515367 / 25000000000000000000000000000000), (42351647553 / 50000000000000000000000000000000)⟩ ⟨-3, 18443922190366941637623808000193, 12500000000000000000000000000000⟩, |
| .log ⟨(63112155619266116724752383999613 / 100000000000000000000000000000000), (93 / 100000000000000000000000000000000)⟩ ⟨(726194960879906850566047157421 / 2500000000000000000000000000000), (2672903773 / 10000000000000000000000000000000)⟩ ⟨(-23012839721742060809676949114857 / 50000000000000000000000000000000), (42351647513 / 100000000000000000000000000000000)⟩ ⟨-1, 63112155619266116724752383999613, 50000000000000000000000000000000⟩] |
| lemma CB4_2_2I0Certificates_valid : |
| CB4_2_2I0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB4_2_2I0CertificateIndex (a : Fin 17) : ℕ := |
| match a.val with |
| | 2 => 1 |
| | 1 => 2 |
| | 0 => 1 |
| | _ => 0 |
| def CB4_2_2I0P (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB4_2_2I0Certificates (CB4_2_2I0CertificateIndex a)).input |
| lemma CB4_2_2I0P_check : ∀ a : Fin 17, contains (CB4_2_2I0Raw a) (CB4_2_2I0P a) = true := by |
| decide +kernel |
| lemma CB4_2_2I0P_sound (a : Fin 17) : |
| (CB4_2_2I0P a).Encloses (CB4_2_2I0Value a) := |
| contains_sound (CB4_2_2I0Raw_sound a) (CB4_2_2I0P_check a) |
| def CB4_2_2I0Terms (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB4_2_2I0Certificates (CB4_2_2I0CertificateIndex a)).output |
| lemma CB4_2_2I0Terms_sound (a : Fin 17) : |
| (CB4_2_2I0Terms a).Encloses (Foundation.entropyTerm (CB4_2_2I0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB4_2_2I0Certificates_valid |
| (CB4_2_2I0CertificateIndex a) (CB4_2_2I0P_sound a) |
| def CB4_2_2I0Entropy : Ball := ⟨(45702156180640825687140250957659 / 50000000000000000000000000000000), (3623391103 / 6250000000000000000000000000000)⟩ |
| lemma CB4_2_2I0Entropy_sound : CB4_2_2I0Entropy.Encloses (Foundation.finiteEntropy CB4_2_2I0Value) := by |
| exact contains_sound (entropyFin_enclosed 17 CB4_2_2I0Value CB4_2_2I0Terms CB4_2_2I0Terms_sound) (by decide +kernel) |
| def CB4_2_2I0Mass : Ball := ⟨(99999999999999999999999999999999 / 100000000000000000000000000000000), (231 / 100000000000000000000000000000000)⟩ |
| lemma CB4_2_2I0Mass_sound : CB4_2_2I0Mass.Encloses (∑ a, CB4_2_2I0Value a) := by |
| exact contains_sound (finSumBall_sound 17 CB4_2_2I0P CB4_2_2I0Value CB4_2_2I0P_sound) (by decide +kernel) |
| def CB4_2_2I0MassTermLogWitness : LogWitness := ⟨-1, 99999999999999999999999999999999, 50000000000000000000000000000000⟩ |
| def CB4_2_2I0MassTermLog : Ball := ⟨0, (42351647597 / 100000000000000000000000000000000)⟩ |
| lemma CB4_2_2I0MassTermLog_sound : CB4_2_2I0MassTermLog.Encloses (Real.log ((∑ a, CB4_2_2I0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB4_2_2I0Mass_sound) (w := CB4_2_2I0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB4_2_2I0MassTerm : Ball := ⟨0, (21175823799 / 50000000000000000000000000000000)⟩ |
| lemma CB4_2_2I0MassTerm_sound : CB4_2_2I0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB4_2_2I0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB4_2_2I0Mass_sound) CB4_2_2I0MassTermLog_sound) (by decide +kernel) |
| def CB4_2_2I0H : Ball := ⟨(45702156180640825687140250957659 / 50000000000000000000000000000000), (50162952623 / 50000000000000000000000000000000)⟩ |
| lemma CB4_2_2I0H_sound : CB4_2_2I0H.Encloses (homogeneousEntropy CB4_2_2I0Value) := by |
| exact contains_sound (homogeneous_enclosed CB4_2_2I0Value CB4_2_2I0MassTerm_sound CB4_2_2I0Entropy_sound) (by decide +kernel) |
| lemma CB4_2_2I0_sound : CB4_2_2I0H.Encloses (stageBCapacity (shape 4 2 2) 0) := by |
| exact CB4_2_2I0H_sound |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
