(* Proof of lem_x_noteq_vide                                               *)
unfold not in |- *; intros.
generalize H; clear H; rewrite H0; intros.
generalize (lem_vide_propertie y var_vide); intros; unfold Vide in H.
absurd (In y (vide var_vide)); auto with zfc.
Qed.
(* End of proof of lem_x_noteq_vide                                        *)

(* Specifications: *)
Lemma lem_paire_not_empty : forall a b : E, paire a b <> Vide.
intros.