(* 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
| split;
[ unfold inc in |- *; intros; rewrite <- H1; auto with zfc
| auto with zfc ] ] ].
Qed.
(* End of proof of lem_bij_is_inj                                          *)

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