(* Proof of lem_dom_vide                                                   *)
elim
(axs_comprehension
(fun v0 : E => fun_ Vide -> exists v1 : E, In (couple v0 v1) Vide)
(reunion (reunion Vide)) v2); intros; generalize (H0 H);
clear H H0 H1; intros.
generalize H; rewrite lem_reunion_vide; rewrite lem_reunion_vide; tauto.
elim (lem_vide_propertie v2 var_vide); auto with zfc.
Qed.
(* End of proof of  lem_dom_vide                                           *)

(* Specifications: *)
(***************************************************************************)
(* L'image de l'application Vide est Vide                                  *)
(***************************************************************************)
Lemma lem_img_vide : Img Vide = Vide.
apply axs_extensionnalite; intros; unfold iff in |- *; split; intros;
unfold Img in H.