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 join_unsquash : forall phi1 phi2 phi3,
join phi1 phi2 phi3 <->
join (unsquash phi1) (unsquash phi2) (unsquash phi3).