openAI-math-dataset / lean /OAI /Combinatorics /EditApproximation /Queries /QueryBufferedSharedCost.lean
| import OAI.Combinatorics.EditApproximation.Queries.QueryScopedSourceCost | |
| import OAI.Combinatorics.EditApproximation.Queries.QuerySharedInputCost | |
| namespace OAI | |
| /-! Shared-state generation using the actual gathered scalar buffer. | |
| The lookup bound is instantiated at visited keys, including discarded cells. -/ | |
| namespace EditApproximation.BinaryFraction | |
| def queryBufferedGroupReadBudget (M F exponent eM eF B V : ℕ) : ℕ := | |
| queryGroupBufferReadBudget (queryGroupSourceKeysLength M F exponent eM eF B) B V | |
| theorem querySharedInputsWithWork_buffered_bounds {nx ny M N F Q : ℕ} [NeZero M] | |
| (exponent eM eF B V : ℕ) (hMdef : M = 2 ^ eM) (hFdef : F = 2 ^ eF) | |
| (parent : TargetInterval nx) (a value : BinaryFraction) (q : TargetInterval ny) | |
| (words : List BinaryFraction) | |
| (hB : 7 ≤ B) (hN : Nat.size N ≤ B) (hF : Nat.size F + 2 ≤ B) | |
| (hM : Nat.size M + 2 ≤ B) (hQ : Nat.size Q + 2 ≤ B) (hes : eM + eF + 7 ≤ B) | |
| (he : exponent + 1 ≤ B) (hnx : Nat.size nx ≤ B) (hny : Nat.size ny ≤ B) | |
| (ha : a.width ≤ B) (hv : value.width ≤ B) (hw : 0 ≤ value.value) | |
| (hV : 2 ≤ V) (hwords : ∀ v ∈ words, v.width ≤ V) : | |
| let keys := (queryGroupSourceKeysWithWork M N F Q exponent eM eF hMdef hFdef a value q).1 | |
| let result := querySharedInputsWithWork M N F Q exponent eM eF hMdef hFdef parent a value q | |
| (queryGroupDrawReadWithWork keys words) | |
| result.1.length ≤ querySharedInputsLength M F exponent eM eF B ∧ | |
| result.2 ≤ querySharedInputsBitBudget M F exponent eM eF B | |
| (queryBufferedGroupReadBudget M F exponent eM eF B V) := by | |
| have hk := (queryGroupSourceKeysWithWork_bounds M N F Q exponent eM eF B hMdef hFdef a value q | |
| hB hN hF hM hQ hes he hny ha hv hw).1 | |
| apply querySharedInputsWithWork_bounds_on M N F Q exponent eM eF B | |
| (queryBufferedGroupReadBudget M F exponent eM eF B V) hMdef hFdef parent a value q | |
| (queryGroupDrawReadWithWork _ words) hB hN hF hM hQ hes he hnx hny ha hv hw | |
| intro eb heb cell hcell scale sample | |
| have hguard : (refinementScaleGuardWithWork F (2 ^ eb) a value).1 = true := by | |
| have h := heb | |
| simp only [queryExponentsWithWork, filterWithWork_value, List.mem_filter] at h | |
| exact h.2 | |
| have hrange : eb ∈ List.range (max 1 N.bits.length) := by | |
| have h := heb | |
| simp only [queryExponentsWithWork, filterWithWork_value, List.mem_filter] at h | |
| exact h.1 | |
| have hc := queryGroupDrawReadWithWork_scoped_cost exponent eM eF B V hMdef hFdef a value q words | |
| hB hN hF (by omega) (by omega) he hny ha hv hw hV hwords eb hrange hguard cell hcell scale sample | |
| apply hc.trans | |
| unfold queryBufferedGroupReadBudget queryGroupBufferReadBudget | |
| gcongr | |
| end EditApproximation.BinaryFraction | |
| end OAI | |