openAI-math-dataset / lean /OAI /LinearAlgebra /MatrixMultiplication /FieldHistory /SourceAssignment.lean
| import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.Source | |
| import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.GroupedRecovery | |
| namespace OAI | |
| /-! Finite extraction histories, inherited masks and recovery bounds. -/ | |
| noncomputable section | |
| namespace MatrixMultiplication.AllFieldHistorySource | |
| open MatrixMultiplication.Foundation AllFieldHistory AllFieldFiniteFamily | |
| open scoped BigOperators Classical | |
| attribute [local instance] Classical.propDecidable Classical.decEq | |
| variable {K tick : ℕ} (allocation : Allocation) (m : ℕ) | |
| theorem groupedAssignment_coherent (F : Type*) [Field F] (ε : ℝ) | |
| (E : Placement → Type) | |
| (a : ∀ sigma, JointExtraction.Assignment | |
| (AllFieldHistoryGroupMasks.GroupRaw (K := K) (tick := tick) allocation m sigma) | |
| (AllFieldHistoryGroupMasks.GroupRaw (K := K) (tick := tick) allocation m sigma) | |
| (AllFieldHistoryGroupMasks.GroupRaw (K := K) (tick := tick) allocation m sigma) (E sigma)) | |
| (ha : ∀ sigma, JointExtraction.Coherent | |
| (AllFieldHistoryGroupMasks.groupPreparedSource F allocation m ε sigma) (a sigma)) : | |
| JointExtraction.Coherent (preparedSource (K := K) (tick := tick) allocation m F ε) | |
| (AllFieldHistoryGroupedRecovery.groupedAssignment allocation m E a) := by | |
| intro x y z i j k hT hx hy hz | |
| have hprod : CommonDimensions.familyProduct | |
| (fun sigma => AllFieldHistoryGroupMasks.groupPreparedSource F allocation m ε sigma) | |
| (fun sigma => AllFieldHistoryGroupMasks.projectRaw allocation m sigma x) | |
| (fun sigma => AllFieldHistoryGroupMasks.projectRaw allocation m sigma y) | |
| (fun sigma => AllFieldHistoryGroupMasks.projectRaw allocation m sigma z) ≠ 0 := by | |
| rw [preparedSource_eq_delete] at hT | |
| exact fun hzero => hT ((AllFieldHistoryGroupMasks.preparedSource_factor | |
| F allocation m ε x y z).trans hzero) | |
| exact GroupAssignment.product_coherent _ a ha _ _ _ i j k hprod hx hy hz | |
| end MatrixMultiplication.AllFieldHistorySource | |
| end | |
| end OAI | |