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 unsquash_squash : forall n rm, (unsquash (squash (n,rm))) = (n,rmap_fmap (approx n) rm).
Instance Join_nat_rmap': Join (nat * rmap') := Join_prod _ (Join_equiv nat) _ _.