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 setI_set_incl : forall (A : Type) (s1 s2 s3 : set A), s1 \subset s2 -> s1 \subset s3 -> s1 \subset s2 :&: s3.