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