(* Proof of lem_Einter_propertie                                           *)
unfold Einter in |- *; intros.
elim
(axs_comprehension (fun v1 : E => forall v3 : E, In v3 a -> In v1 v3)
(reunion a) v0); intros; generalize (H1 H); clear H H1 H2;
intros.
elim H; clear H; intros.
exact (H1 v3 H0).
Qed.
(* End of proof of lem_Einter_propertie                                    *)

(* Specifications: *)
Lemma lem_Einter_sing :
forall a : E, Einter (singleton a) (lem_paire_not_empty a a) = a.