Program Definition approx (n:nat) (p: (pred rmap)) : (pred rmap) :=
fun w => level w < n /\ p w.
Next Obligation.
destruct H0.
split.
apply age_level in H.
simpl in *. omega.
apply pred_hereditary with a; auto.
Qed.

Lemma fmap_p2p'_inj:
forall p q,
@fmap SM.preds f_preds K.predicate (@pred rmap ag_rmap) p2p' p =
@fmap SM.preds f_preds K.predicate (@pred rmap ag_rmap) p2p' q ->
p=q.