(* Proof of lem_vide_propertie                                             *)
elim (axs_comprehension def_F_vide v1 v0); unfold def_F_vide in |- *;
unfold not in |- *; intros.
elim H0; clear H0; intros.
clear H; clear H1; clear H0; apply H2; clear H2; reflexivity.
apply H1; clear H1.
split.
elim (axs_comprehension def_F_vide v1 v0); unfold def_F_vide in |- *;
unfold not in |- *; intros.
elim H0; clear H0; intros; assumption.
elim (axs_comprehension def_F_vide v1 v0); unfold def_F_vide in |- *;
unfold not in |- *; intros.
elim H0; clear H0; intros.
apply H3; reflexivity.
assumption.
Qed.
(* End of proof of lem_vide_existence                                      *)

Lemma lem_vide_unicite : forall v0 v1 : E, vide v0 = vide v1.
intros; apply axs_extensionnalite; unfold iff in |- *; split; intros.