(* Proof of lem_inter_propertie_rl                                         *)
intros; elim (lem_inter_propertie a b x); intros; exact (H1 H).
Qed.
(* End of proof of lem_inter_propertie_rl                                  *)

Lemma lem_inter_unicite :
forall a b i : E,
(forall x : E, In x i <-> In x a /\ In x b) -> i = inter a b.