Definition assert := env -> pred rmap.Program Definition assert_safe
     (p: program) (vars: varset) (ctl: control) : assert :=
  fun s w => forall s' h, varcompat vars s' ->
                   locals2env s' = s -> cohere h w -> safeN p (s',h,ctl) (level w).

(* Specifications: *)
Lemma assert_safe0: forall p vars k s w, (forall w', age w w' -> app_pred (assert_safe p vars k s) w) -> app_pred (assert_safe p vars k s) w.