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 set_eq_isSome_sound {A} (s : set (option A)) (s' : set A) : isSome :&: s <--> Some @: s' -> s \subset (Some @: s') :|: [set None].