(* Proof of lem_union_propertie_lr                                         *)
intros; elim (lem_union_propertie a b v0); intros; exact (H0 H).
Qed.
(* End of proof of lem_union_propertie_lr                                  *)

Lemma lem_union_propertie_rl :
forall a b v0 : E, In v0 a \/ In v0 b -> In v0 (union a b).