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_bigcup_compat : forall (T U : Type) (A B : set T) (F G : T -> set U), A \subset B -> (forall x : T, F x \subset G x) -> \bigcup_(x in A) F x \subset \bigcup_(x in B) G x.