(* Proof of lem_rel_inv_is_rel_sig                                         *)
unfold rel_sig in |- *; unfold inc in |- *; unfold rel_inverse in |- *;
intros.
elim
(axs_comprehension
(fun c : E =>
exists x : E, (exists y : E, In (couple x y) r /\ c = couple y x))
(cartesien b a) v0); intros; generalize (H0 H);
clear H H0 H1; intros; elim H; clear H; intros; auto with zfc.
Qed.
(* End of proof of lem_rel_inv_is_rel_sig                                  *)

(***************************************************************************)
(* Le domaine de la relation inverse est l'image de la relation initiale   *)
(***************************************************************************)
Lemma lem_rel_inv_dom :
forall (r a b : E) (rRel : rel_sig r a b),
rdom (rel_inverse r a b rRel) b a (lem_rel_inv_is_rel_sig r a b rRel) =
rImg r a b rRel.