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

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'.