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