Next Obligation.
split; intros.
apply EqSet2.union_1 in H. destruct H; rewrite eqs_same in H.
apply EqSet.union_2; auto. apply EqSet.union_3; auto.
apply EqSet.union_1 in H. destruct H; rewrite <- eqs_same in H.
apply EqSet2.union_2; auto. apply EqSet2.union_3; auto.
Qed.

(* Specifications: *)
Lemma ge_lub_left: forall x y, ge (lub x y) x.
Lemma ge_lub_right: forall x y, ge (lub x y) y.
End LEq.