Module S := FMapList.Make(XOT).
(** The type of dependent maps **)
Definition key := X.t.
Definition OK {A} dom (map : S.t A) := ∀ x, S.In x map <-> Dom.In x dom.
Definition t := fun A dom => { map : S.t A | OK dom map}.
Instance OK_compat A : Proper (Dom.eq ==> @S.Equal A ==> iff) OK.
(** ***  Operations on maps **)

(** The empty map. **)
Lemma empty_OK : forall A, OK Dom.empty (S.empty A).