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