Coercion seq_In T : seq T -> set T := fun s x => List.In x s.Coercion list_In T : list T -> set T := fun s x => List.In x s.

Lemma set_incl_setI_r {A} (s1 s2 s3 : set A) : s2 \subset s3 -> (s1 :&: s2) \subset s3.