(* Proof of lem_inter_vide                                                 *)
elim (lem_inter_propertie a Vide v2); intros.
unfold iff in |- *; split; intros.
elim H; clear H H0; intros; auto with zfc.
apply H0; clear H H0; unfold Vide in H1;
elim (lem_vide_propertie v2 var_vide); auto with zfc.
Qed.
(* End of proof of lem_inter_vide                                          *)

(* Specifications: *)
(***************************************************************************)
(* Proprietes de l'inclusion                                               *)
(***************************************************************************)
Lemma lem_vide_is_inc : forall a : E, inc Vide a.
unfold inc in |- *; intros.