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 lift_subset_pres_r {A} (s1 : set (option A)) (s2 s3 : set A) : s1 \subset lift s3 -> s1 \subset lift (s2 :|: s3).