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_bigcup' : forall (T U : Type) (A B : set T) (F G : T -> set U), A <--> B -> (forall x, F x <--> G x) -> \bigcup_(x in A) F x <--> \bigcup_(x in B) G x.