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_assoc {U} (s1 s2 s3 : set U) : (s1 :&: (s2 :&: s3)) <--> ((s1 :&: s2) :&: s3).