(* Proof of lem_bij_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 | unfold inc in |- *; intros ] ].
rewrite <- H1; auto with zfc.
Qed.
(* End of proof of lem_bij_to_sig                                          *)

(***************************************************************************)
(* Une bijection est une injection                                         *)
(***************************************************************************)
Lemma lem_bij_is_inj : forall f a b : E, fun_bij f a b -> fun_inj f a b.
unfold fun_bij, fun_inj in |- *; intros.