openAI-math-dataset / lean /OAI /Combinatorics /LowSpaceSubsetSum /Representation /RepresentationExtraDraw.lean
| import OAI.Combinatorics.LowSpaceSubsetSum.Counting.ScalarSamplerArrays | |
| namespace OAI | |
| /-! # The extra prime drawn at the stored fourth width -/ | |
| noncomputable section | |
| namespace LowSpaceSubsetSum.RepresentationExtraDraw | |
| variable {n : ℕ} | |
| def transport {ell ell' : ℕ} {h : 4 ≤ ell} {h' : 4 ≤ ell'} | |
| (he : ell = ell') (s : (primeCoupling h' n).Seed) : (primeCoupling h n).Seed := by | |
| subst ell' | |
| exact s | |
| def draw (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n) | |
| (ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) : | |
| Option ℕ × ℕ := | |
| ScalarSamplerArrays.extra (he.symm ▸ (R.extraPrimeParameter_range z hn).1) n | |
| (transport he s) | |
| theorem value (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n) | |
| (ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) : | |
| (draw R z hn ell he s).1 = ((R.extraPrimeCoupling z hn).bounded s).map Subtype.val := by | |
| subst ell | |
| exact ScalarSamplerArrays.extra_value _ _ s | |
| theorem work (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n) | |
| (ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) : | |
| (draw R z hn ell he s).2 ≤ n ^ 3 + SamplerExecution.primeTestBudget n + 1 := by | |
| subst ell | |
| exact ScalarSamplerArrays.extra_work _ (R.extraPrimeParameter_range z hn).2 s | |
| end LowSpaceSubsetSum.RepresentationExtraDraw | |
| end | |
| end OAI | |