(* Proof of lem_rfull_eq_cart                                              *)
elim
(axs_comprehension
(fun c : E => exists x : E, (exists y : E, c = couple x y))
(cartesien a a) v2); intros; generalize (H0 H);
clear H H0 H1; intros; elim H; clear H; intros; auto with zfc.
elim
(axs_comprehension
(fun c : E => exists x : E, (exists y : E, c = couple x y))
(cartesien a a) v2); intros; apply H1; clear H0 H1;
intros; split; [ auto with zfc | idtac ].
elim (lem_cartesian_propertie a a v2); intros; generalize (H0 H);
clear H H0 H1; intros; elim H; clear H; intros; elim H;
clear H; intros; elim H; clear H; intros; elim H0;
clear H0; intros.
exists x; exists x0; auto with zfc.
Qed.
(* End of proof of lem_rfull_eq_cart                                       *)

(***************************************************************************)
(* La propriete de la relation pleine                                      *)
(***************************************************************************)
Lemma lem_rfull_prop :
forall a x y : E, In x a -> In y a -> In (couple x y) (rfull a).