(* This file is copied from RamifyCoq project. *)
Require Coq.Setoids.Setoid.
Require Export Coq.Classes.Equivalence.
Require Export Coq.Sets.Ensembles.
intros.
split; intros [].
Qed.

Lemma Union_iff: forall U A B x, Ensembles.In U (Union U A B) x <-> Ensembles.In U A x \/ Ensembles.In U B x.