Corollary Sdom : forall A x (m : S.t A), Dom.In x (S.fold (fun x _ acc => Dom.add x acc) m Dom.empty) <-> S.In x m.

Lemma combine_OK : forall A B C (f : A -> B -> C) g₁ g₂ dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t B dom₂), OK (Dom.union dom₁ dom₂) (Scombine f g₁ g₂ (proj1_sig m₁) (proj1_sig m₂)).