(* Proof of lem_rfull_dom                                                  *)
unfold rdom in |- *; intros; apply axs_extensionnalite; unfold iff in |- *;
split; intros.
elim
(axs_comprehension (fun x : E => exists y : E, In (couple x y) (rfull a)) a
v2); intros; generalize (H0 H); clear H H0 H1;
intros; elim H; clear H; intros; auto with zfc.
elim
(axs_comprehension (fun x : E => exists y : E, In (couple x y) (rfull a)) a
v2); intros; apply H1; clear H0 H1; split; [ auto with zfc | idtac ].
exists v2; unfold rfull in |- *.
elim
(axs_comprehension
(fun c : E => exists x : E, (exists y : E, c = couple x y))
(cartesien a a) (couple v2 v2)); intros; apply H1;
clear H0 H1; intros; split; [ idtac | exists v2; exists v2; reflexivity ].
elim (lem_cartesian_propertie a a (couple v2 v2)); intros; apply H1;
clear H0 H1; exists v2; exists v2; split;
[ auto with zfc | split; [ auto with zfc | reflexivity ] ].
Qed.
(* End of proof of lem_rfull_dom                                           *)

(* Specifications: *)
(***************************************************************************)
(* L'image de la relation pleine est a                                     *)
(***************************************************************************)
Lemma lem_rfull_Img :
forall a : E, rImg (rfull a) a a (lem_rfull_rel_sig a) = a.