(* Proof of lem_rel_sig_is_rel                                             *)
unfold rel in |- *; intros.
generalize (H c H0); clear H H0; intros.
elim (lem_cartesian_propertie a b c); 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_rel_sig_is_rel                                      *)

Lemma lem_rel_to_rel_sig :
forall r : E, rel r -> exists a : E, (exists b : E, rel_sig r a b).