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_setU_r: forall (U T : Type) (s : set U) (f g : U -> set T), \bigcup_(i in s) (f i :|: g i) <--> \bigcup_(i in s) f i :|: \bigcup_(i in s) g i.