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