(* Proof of lem_fun_sig_is_fun                                             *)
elim H; clear H; intros; auto with zfc.
Qed.
(* End of proof of lem_fun_sig_is_fun                                      *)

Lemma lem_fun_sig_dom : forall f a b : E, fun_sig f a b -> dom f = a.
intros; elim H; clear H; intros; elim H0; clear H0; intros; auto with zfc.