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

(***************************************************************************)
(* Pour tout ensemble a, Vide est une application de Vide vers a           *)
(***************************************************************************)
Lemma lem_fun_vide_sig : forall a : E, fun_sig Vide Vide a.
unfold fun_sig in |- *; intros.