Definition PPO_rule (r: rule) : Prop :=
  match r with
    | rule_intro f lp t => PPO t (fapply f (map (@term_from_pattern _ _ _) lp))
  end.Definition PPO_prog : Prop :=
  forall r, In r prog -> PPO_rule r.

Lemma value_PPO_function (v: value) (f: function) (lt: list term) : PPO (@term_from_value _ _ _ v) (fapply f lt).