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 setU_set0_r {A} (s1 s2 s3 : set A) : s1 <--> set0 -> s3 <--> s2 -> s3 <--> (s1 :|: s2).