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_l {U T} (s1 s2 : set U) (f : U -> set T) : bigcap s1 f \subset bigcap (s1 :&: s2) f.