openAI-math-dataset / lean /OAI /Combinatorics /EditApproximation /Queries /QueryChargedTableWidth.lean
| import OAI.Combinatorics.EditApproximation.Queries.QueryChargedFamily | |
| import OAI.Combinatorics.EditApproximation.Queries.QueryWarmupWidth | |
| import OAI.Combinatorics.EditApproximation.Queries.QueryBoundedActiveCost | |
| namespace OAI | |
| namespace EditApproximation | |
| open BinaryFraction | |
| section Table | |
| variable {M J R passes copies T S : ℕ} [NeZero M] [NeZero R] | |
| (source target : List ℕ) (N P F exponent H Q eM eF B : ℕ) | |
| (hP : 0 < P) (hM : M = 2 ^ eM) (hF : F = 2 ^ eF) | |
| (A a : ℕ → BinaryFraction) (tau eta kappa delta : BinaryFraction) (multiplier : ℕ → ℕ) | |
| (occurrence : BinaryMemo PositionCounts) (symbolBits positionBits : ℕ) | |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S}) | |
| (oracle : ChargedFamilyQueryKey (R := R) target N P F exponent H Q (.inr parent) → BinaryFraction) | |
| theorem queryChargedFamilyTable_width | |
| (hB : 10 ≤ B) (hN : Nat.size N ≤ B) (hPb : Nat.size P ≤ B) | |
| (hFb : Nat.size F + 2 ≤ B) (hFpos : 1 ≤ F) | |
| (hs : Nat.size source.length + 2 ≤ B) (ht : Nat.size target.length + 2 ≤ B) | |
| (ht' : Nat.size (target.length + 1) + 2 ≤ B) | |
| (hinit : Nat.size ((32 * F + 1) * N) + 3 ≤ B) | |
| (hMb : Nat.size M ≤ B) (ha : (a parent.val.pass).width ≤ B) | |
| (hv : ∀ key, (oracle (Sum.inr key)).width ≤ B) | |
| (hactive : ∀ (hindex : T < parent.val.index) (hbelow : parent.val.node.1.val < J), | |
| ((queryFamilyBoundedActive (R := R) source target N P F exponent H Q eM eF hP hM hF | |
| tau (a parent.val.pass) eta kappa delta T S passes copies parent hindex hbelow).value | |
| (fun key => oracle (Sum.map id (fun child => | |
| ⟨Sum.inr child.val, ChargedPhysicalRequest.table_rank_lt parent child.val child.property⟩) key))).width ≤ | |
| preparedKernelWordBudget M B) : | |
| ((queryChargedFamilyTable (R := R) source target N P F exponent H Q eM eF hP hM hF A a tau eta kappa | |
| delta multiplier occurrence symbolBits positionBits parent).value oracle).width ≤ | |
| localWarmupWordBudget M B + preparedKernelWordBudget M B := by | |
| let tableOracle := fun key => oracle (Sum.inr key) | |
| have hw := queryChargedWarmup_width source target N P F B (A parent.val.pass) (a parent.val.pass) | |
| multiplier parent occurrence symbolBits positionBits tableOracle hB hP hN hPb hFb hFpos hs ht ht' | |
| hinit hMb ha hv | |
| have hi := queryPhysicalInitial_width source target N P F B (A parent.val.pass) (a parent.val.pass) | |
| multiplier parent occurrence symbolBits positionBits tableOracle parent.val.state hP ht' hinit | |
| have hsmall : B ≤ localWarmupWordBudget M B := by | |
| unfold localWarmupWordBudget physicalContinuationInputBudget | |
| dsimp only | |
| omega | |
| unfold queryChargedFamilyTable | |
| simp only [BitQuery.value] | |
| split | |
| · simp only [BitQuery.mapKeysWithWork_value] | |
| exact hw.trans (Nat.le_add_right _ _) | |
| · split | |
| · split | |
| · simp only [BitQuery.value, BitQuery.mapKeysWithWork_value] | |
| exact hi.trans (hsmall.trans (Nat.le_add_right _ _)) | |
| · rename_i hindex hbelow hlong | |
| simp only [BitQuery.value, BitQuery.mapKeysWithWork_value] | |
| exact (hactive _ _).trans (Nat.le_add_left _ _) | |
| · simp only [BitQuery.value, BitQuery.mapKeysWithWork_value] | |
| exact hi.trans (hsmall.trans (Nat.le_add_right _ _)) | |
| end Table | |
| end EditApproximation | |
| end OAI | |