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_r : forall (A B : Type) (l : A) (ls : seq A) (f : A -> set B) (s1 s2 : set B), s1 \subset f l -> s2 \subset \bigcup_(x in ls) f x -> s1 :|: s2 \subset \bigcup_(x in (l :: ls)) f x.