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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 | import Mathlib
import OAI.LinearAlgebra.MatrixFields.Histories.GroupOrbitTransport
namespace OAI
namespace MatrixAllFields
open scoped BigOperators Topology Polynomial
noncomputable section
namespace MatrixMultiplication.AllFieldGroupStatisticComplement
open AllFieldHistory AllFieldHistoryChildLaws
theorem statistic_wordComplement {K tick : ℕ} {sigma : Placement}
(h : ActiveOrder K tick sigma) (w : Fin (activeHalfLength h.val) → Fin 7) :
statistic h.val (CWCompatibilityTransfer.wordComplement w) =
AllFieldGroupOrbitData.complement h (statistic h.val w) := by
rcases h with ⟨⟨⟨work, phi⟩, ht⟩, ho⟩
cases work with
| stageA a => exact CWCompleteStatistics.four_complement w
| stageB b => exact CWCompleteStatistics.two_complement w
| stageC c => rfl
end MatrixMultiplication.AllFieldGroupStatisticComplement
end
end MatrixAllFields
end OAI
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