(* Notion of bijection: *)

Definition bij_dart(Df:dart->Prop)(f:dart->dart):Prop:=              inj_dart Df f /\ surj_dart Df f.

Lemma A_1_B_bis : forall (m:fmap)(k:dim)(x y:dart), inv_hmap m -> y <> A m k x -> A_1 (B m k x) k y = A_1 m k y.