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_bigcapr (T U : Type) (A : set T) (F G : T -> set U) : (forall x : T, F x <--> G x) -> \bigcap_(x in A) F x <--> \bigcap_(x in A) G x.