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cdec422 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | 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
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