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_setI_l {U T} (s1 s2 : set U) (f : U -> set T) : bigcap (s1 :|: s2) f <--> bigcap s1 f :&: bigcap s2 f.