Program Definition agedfrom {A} `{ageable A} (x:A) : pred A := necR x.
Next Obligation.
unfold hereditary; intros.
apply rt_trans with a; auto.
apply rt_step; auto.
Qed.

(* Specifications: *)
Lemma safe_approx : forall t t' p n r r' s s',
level p < n ->
termMeasure_incr t t' ->
store_incr r r' ->
stack_approx_rel n s s' ->
safe t  p r s ->
safe t' p r' s'.
Lemma ev_halts_approx : forall t t' p n r r' s s',
level p < n ->
termMeasure_incr t t' ->
store_incr r r' ->
stack_approx_rel n s s' ->
eventually_halts t  p r  s ->
eventually_halts t' p r' s'.