(* Proof of lem_Vide_dom                                                   *)
unfold rdom in H.
elim
(axs_comprehension (fun x : E => exists y : E, In (couple x y) Vide) a v0);
intros; generalize (H0 H); clear H H0 H1; intros;
elim H; clear H; intros; elim H0; clear H0; intros.
generalize (lem_vide_propertie (couple v0 x) var_vide); intros;
absurd (In (couple v0 x) Vide); auto with zfc.
Qed.
(* End of proof of lem_Vide_dom                                            *)

(***************************************************************************)
(* L'image de la relation vide est l'ensemble vide                         *)
(***************************************************************************)
Lemma lem_Vide_Img : forall a : E, rImg Vide a a (lem_Vide_rel_sig a) = Vide.
intros; apply (lem_x_inc_vide (rImg Vide a a (lem_Vide_rel_sig a)));
unfold inc in |- *; unfold rImg in |- *; intros.