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_set_eq_compat {T} (s1 s2 s1' s2' : set T) : s1 <--> s1' -> s2 <--> s2' -> s1 :|: s2 <--> s1' :|: s2'.