(* 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.
Arguments Included {U} B C.
Arguments Same_set {U} B C.
Instance Included_proper (V: Type): Proper (Same_set ==> Same_set ==> iff) (@Included V).
Instance Intersection_proper {A}: Proper (Same_set ==> Same_set ==> Same_set) (Intersection A).

Lemma Union_left_Disjoint: forall A P Q R,
Disjoint A (Union A P Q) R <-> Disjoint A P R /\ Disjoint A Q R.