(* Proof of lem_bij_is_inj                                                 *)
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_bij_is_inj                                          *)

(***************************************************************************)
(* Une injection surjective est une bijection                              *)
(***************************************************************************)
Lemma lem_inj_surj_is_bij :
forall f a b : E, fun_surj f a b -> fun_inj f a b -> fun_bij f a b.