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_set_eq_r {A : Type} (s1 s2 s2' : set A) : s2 <--> s2' -> (s1 :&: s2) <--> (s1 :&: s2').