openAI-math-dataset / lean /OAI /LinearAlgebra /MatrixMultiplication /FieldHistory /ProducedMasks.lean
| import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.ProducedMaskCore | |
| import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.MaskCore | |
| namespace OAI | |
| /-! Finite extraction histories, inherited masks and recovery bounds. -/ | |
| noncomputable section | |
| namespace MatrixMultiplication.AllFieldHistoryProducedMasks | |
| open MatrixMultiplication.Foundation AllFieldParameters AllFieldHistory | |
| open AllFieldHistoryChildLaws AllFieldHistoryMasks InheritedMasks | |
| open JointCanonicalization | |
| open scoped BigOperators | |
| attribute [local instance] Classical.propDecidable Classical.decEq | |
| variable {K tick : ℕ} | |
| theorem childWindows_of_produced_masks (allocation : Allocation) (dilation : ℕ) | |
| {ε : ℝ} (hε : 0 ≤ ε) (side : Fin 3) | |
| (x : ProducedWords (K := K) (tick := tick) allocation dilation) | |
| (hx : ∀ h : Produced K tick, residentMask allocation dilation ε h.val side (x h)) : | |
| AllFieldHistoryMasks.childWindows allocation dilation ε side | |
| (regroupWords allocation dilation x) := | |
| canonicalWindows_of_produced_masks allocation dilation hε side x hx | |
| end MatrixMultiplication.AllFieldHistoryProducedMasks | |
| end | |
| end OAI | |