(* Notion of bijection: *)

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

Lemma not_pred_B_1:forall(m:fmap)(k:dim)(z:dart), inv_hmap m -> ~pred m k z -> B_1 m k z = m.