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 setI_set0 {U} (s1 s2 : set U) : (forall x, s1 x -> ~ s2 x) -> (s1 :&: s2) <--> set0.