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 bigcup_pointwise_incl A B (s : set A) (t : A -> set B) (u : set B) : (forall x, x \in s -> t x \subset u) -> \bigcup_(x in s) t x \subset u.