(* Proof of lem_inj_to_sig                                                 *)
elim H; clear H; intros; elim H0; clear H0; intros; elim H1; clear H1; intros.
split; [ auto with zfc | split; auto with zfc ].
Qed.
(* End of proof of lem_inj_to_sig                                          *)

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