(***********************************************************************)
(** *** Challenge exercise [machine_is_scoped]  Show that if the abstract machine is scoped, then any resulting configurations are also scoped. *)

(* Specifications: *)
Lemma machine_is_scoped: forall D h e s conf',
machine_step (dom h \u D) (h,e,s) = TakeStep _ conf' ->
scoped_conf D (h,e,s) ->
scoped_conf D conf'.