openAI-math-dataset / lean /OAI /LinearAlgebra /MatrixFields /Parameters /GroupStatisticComplement.lean
| 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 | |