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_subset_compat : forall (T : Type) (s1 s2 s1' s2' : set T), s1 \subset s1' -> s2 \subset s2' -> s1 :|: s2 \subset s1' :|: s2'.