(* Proof of lem_inj_surj_is_bij                                            *)
unfold fun_surj, fun_inj, fun_bij in |- *; intros.
elim H; clear H; intros; clear H; elim H1; clear H1; intros; clear H.
elim H0; clear H0; intros; elim H0; clear H0; intros; elim H2; clear H2;
intros.
split;
[ auto with zfc
| split; [ auto with zfc | split; auto with zfc ] ].
Qed.
(* End of proof of lem_inj_surj_is_bij                                     *)
(***************************************************************************)
(***************************************************************************)
(* L'application Vide                                                      *)
(***************************************************************************)
(***************************************************************************)

(***************************************************************************)
(* Vide est une application                                                *)
(***************************************************************************)
Lemma lem_vide_application : fun_ Vide.
unfold fun_ in |- *; split;
[ exists Vide; exists Vide; exact (lem_vide_is_inc (cartesien Vide Vide))
| intros ].