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 isSome_subset {A : Type} (s1 s2 s1' s2' : set (option A)) : isSome :&: s1 \subset isSome :&: s2 -> isSome :&: (s1 :|: ([set None] :&: s1')) \subset isSome :&: (s2 :|: ([set None] :&: s2')).