(* Proof of lem_x_inc_vide                                                 *)
unfold inc in H.
apply axs_extensionnalite; intros; unfold iff in |- *; split; intros.
exact (H v2 H0).
generalize (lem_vide_propertie v2 var_vide); intros.
unfold Vide in H0.
absurd (In v2 (vide var_vide)); auto with zfc.
Qed.
(* End of proof of lem_x_inc_vide                                          *)

Lemma lem_x_noteq_vide : forall x y : E, In y x -> x <> Vide.
intros.