(* Proof of lem_Einter_vide                                                *)
intros.
apply lem_x_inc_vide; intros.
unfold inc in |- *; unfold Einter in |- *; intros.
elim
(axs_comprehension (fun v1 : E => forall v3 : E, In v3 x -> In v1 v3)
(reunion x) v0); intros; generalize (H1 H0); clear H0 H1 H2;
intros.
elim H0; clear H0; intros.
exact (H1 Vide H).
Qed.
(* End of proof of lem_Einter_vide                                         *)
(***************************************************************************)
(* Complementaire d'un ensemble                                            *)
(***************************************************************************)
Definition Comp (a b : E) := subset (fun y : E => ~ In y b) a.
Parameter OComp : E -> E -> E.

(* Specifications: *)
Axiom def_OComp : forall a b y : E, In y (OComp a b) <-> In y a /\ ~ In y b.
Lemma lem_Comp_eq_OComp : forall a b : E, OComp a b = Comp a b.
intros; apply axs_extensionnalite; unfold iff in |- *; split; intros.