(* 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_1 : forall (m:fmap)(k:dim)(x:dart), inv_hmap m -> A_1 (B_1 m k x) k x = nil.