(* Proof of lem_inter_propertie_lr                                         *)
intros; elim (lem_inter_propertie a b x); intros; exact (H0 H).
Qed.
(* End of proof of lem_inter_propertie_lr                                  *)

Lemma lem_inter_propertie_rl :
forall a b x : E, In x a /\ In x b -> In x (inter a b).