openAI-math-dataset / lean /OAI /Combinatorics /LowSpaceSubsetSum /Word /WordSeedBucketExecution.lean
| import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedHistoryExecution | |
| import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedSeparatorPreparation | |
| import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSamplingBounds | |
| namespace OAI | |
| /-! # Executed separator families complete the representation history -/ | |
| noncomputable section | |
| namespace LowSpaceSubsetSum.WordSeedMeasured | |
| variable {n : ℕ} | |
| private theorem clog_le (k w : ℕ) (h : k ≤ w) : Nat.clog 2 k ≤ w := | |
| (Nat.clog_le_of_le_pow Nat.lt_two_pow_self.le).trans h | |
| def separatorDraws (R : RepresentationSetup n) (h : R.PrimeHistory) | |
| (hn : 2200 ≤ n) (w : ℕ) | |
| (hw : Nat.clog 2 (2*RepresentationSetup.blockHalf n 0) ≤ w) : | |
| Execution (WordSeedRealization.separatorDraws R h hn w hw) := by | |
| unfold WordSeedRealization.separatorDraws RepresentationSetup.separatorParameters | |
| exact familiesPrepared _ _ _ _ _ _ w n hw | |
| def bucketHistory (I : Instance n) (hn : 10000 ≤ n) (w : ℕ) (hw : 3*n+1 ≤ w) : | |
| Execution (WordSeedRealization.bucketHistory (canonicalRepresentationData I).zeroSetup hn w hw) := | |
| bind (extraHistory I (by omega) w hw) | |
| (fun h => (canonicalRepresentationData I).zeroSetup.SeparatorDraws h.1.1 (by omega)) | |
| (fun h => (canonicalRepresentationData I).zeroSetup.separatorCoupling h.1.1 (by omega)) | |
| (fun h => WordSeedRealization.separatorDraws _ h.1.1 (by omega) w | |
| (clog_le _ _ (by | |
| have hg := WordSamplingBounds.family_width n | |
| omega))) | |
| (fun h => separatorDraws _ h.1.1 (by omega) w | |
| (clog_le _ _ (by | |
| have hg := WordSamplingBounds.family_width n | |
| omega))) | |
| end LowSpaceSubsetSum.WordSeedMeasured | |
| end | |
| end OAI | |