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_cons_subset {A B} l (ls : seq A) (f : A -> set B) s : f l \subset s -> \bigcup_(x in ls) (f x) \subset s -> \bigcup_(x in l :: ls) (f x) \subset s.