(* Proof of lem_Comp_eq_OComp                                              *)
elim (def_OComp a b v2); intros; generalize (H0 H); clear H H0 H1; intros.
elim H; clear H; intros.
unfold Comp in |- *.
elim (axs_comprehension (fun y : E => ~ In y b) a v2); intros; apply H2;
clear H1 H2; intros.
split; auto with zfc.
unfold Comp in H.
elim (axs_comprehension (fun y : E => ~ In y b) a v2); intros;
generalize (H0 H); clear H H0 H1; intros.
elim (def_OComp a b v2); intros; apply H1; clear H0 H1; intros;
auto with zfc.
Qed.
(* End of proof of lem_Comp_eq_OComp                                       *)
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(* Difference symetrique de deux ensembles                                 *)
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Definition Delta (a b : E) := union (Comp a b) (Comp b a).

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(* Quelques proprietes agreables                                           *)
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Lemma lem_inter_commut : forall a b : E, inter a b = inter b a.
intros; apply axs_extensionnalite; intros.