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4 changes: 3 additions & 1 deletion Coxeter/StrongExchange.lean
Original file line number Diff line number Diff line change
Expand Up @@ -115,7 +115,9 @@ local notation "S'" => CoxeterMatrix.SimpleRefl (toMatrix S)
def invmap (S:Set G) [CoxeterSystem G S] : G →* CoxeterMatrix.toGroup (toMatrix S) := monoidLift.mapLift (CoxeterMatrix.of_relation (toMatrix S))

lemma invmap.of_eq {S:Set G} [CoxeterSystem G S] {s :S} : invmap S s = s := by
sorry
simp [CoxeterSystem.Presentation.invmap]
unfold CoxeterSystem.toMatrix
apply CoxeterSystem.monoidLift.mapLift.of

def invmap_map_eq_id : MonoidHom.comp (invmap S) (map S) = MonoidHom.id G':= by
ext x
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