(* Proof of lem_surj_to_sig                                                *)
elim H; clear H; intros; elim H0; clear H0; intros.
split;
[ auto with zfc
| split; [ auto with zfc | unfold inc in |- *; intros ] ].
generalize H2; rewrite H1; tauto.
Qed.
(* End of proof of lem_surj_to_sig                                         *)

Lemma lem_inj_to_sig : forall f a b : E, fun_inj f a b -> fun_sig f a b.
unfold fun_inj in |- *; unfold fun_sig in |- *; intros.