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 Union_Empty_left {A: Type}: forall P, Same_set (Union _ (Empty_set A) P) P.