(* Proof of lem_reunion_vide                                               *)
unfold iff in |- *; split; intros.
elim (axs_reunion Vide v2); intros.
elim H0; clear H0 H1; intros; [ idtac | auto with zfc ].
elim H0; clear H0; intros; unfold Vide in |- *; unfold Vide in H;
elim (lem_vide_propertie x var_vide); auto with zfc.
unfold Vide in H; elim (lem_vide_propertie v2 var_vide); auto with zfc.
Qed.
(* End of proof of lem_reunion_vide                                        *)

Lemma lem_union_vide : forall a : E, union a Vide = a.
intros; apply axs_extensionnalite; intros.