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 bigcap_setU_distr: forall (U T : Type) (s1 s2 : set U) (f : U -> set T), \bigcap_(i in s1) f i :&: \bigcap_(i in s2) f i <--> \bigcap_(i in s1 :|: s2) f i.