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 incl_bigcapl T U A B (F : T -> set U) : B \subset A -> \bigcap_(x in A) F x \subset \bigcap_(x in B) F x.