(* Proof of lem_inter_vide_prop                                            *)
elim (axs_comprehension (def_F_inter Vide) x v2); intros; generalize (H0 H);
clear H H0 H1; intros.
elim H; clear H; unfold def_F_inter in |- *; intros; auto with zfc.
elim (axs_comprehension (def_F_inter Vide) x v2); intros; apply H1;
clear H0 H1; intros.
unfold def_F_inter in |- *.
split; [ idtac | auto with zfc ].
generalize (lem_vide_propertie v2 var_vide); intros.
unfold Vide in H.
absurd (In v2 (vide var_vide)); auto with zfc.
Qed.
(* End of proof of lem_inter_vide_prop                                     *)

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(* L'ensemble de tous les ensembles ... n'existe pas !!!                   *)
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Theorem notEEexists : ~ (exists v0 : E, (forall v1 : E, In v1 v0)).
unfold not in |- *; intros; elim H; clear H; intros.