Existing Instance ag_nat. Hint Resolve ag_nat.
Program Definition fash {A: Type} `{NA: ageable A} (P: pred A): pred nat :=
fun n => forall y, n >= level y -> P y.
Next Obligation.
destruct P as [P HP].
simpl in *.
apply H0.
unfold age, age1, ag_nat,natAge1 in H.
destruct a; inv H.
omega.
Qed.
Notation "'#' e" := (fash e) (at level 30, right associativity): pred.

Lemma fash_and {A} `{H : ageable A}: forall (P Q:pred A),
# (P && Q) = # P && # Q.