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_set0_r (T U : Type) (s : set T) (F : T -> set U) : (forall x, F x <--> set0) -> \bigcup_(x in s) F x <--> set0.