openAI-math-dataset / lean /OAI /LinearAlgebra /MatrixMultiplication /FieldGroups /StatisticComplement.lean
| import OAI.LinearAlgebra.MatrixMultiplication.FieldGroups.OrbitData | |
| import OAI.LinearAlgebra.MatrixMultiplication.CoppersmithWinograd.CWCompatibilityTransfer | |
| namespace OAI | |
| /-! Group assignments, orbit counts and extraction capacities. -/ | |
| 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 OAI | |