Instance Included_proper (V: Type): Proper (Same_set ==> Same_set ==> iff) (@Included V).Instance complement_proper (V: Type): Proper (Same_set ==> Same_set) (Complement V).Instance Union_proper (V: Type): Proper (Same_set ==> Same_set ==> Same_set) (Union V).Instance Disjoint_proper (V: Type): Proper (Same_set ==> Same_set ==> iff) (Disjoint V).

Lemma Intersection_absort_left: forall U (A B: Ensemble U), Included B A -> Same_set (Intersection _ A B) B.