Program Definition exactly {A} `{ageable A} (x: A) : pred A := necR x.
Next Obligation.
constructor 3 with a; auto.
constructor 1; auto.
Qed.

Lemma necR_level' {A} `{H : ageable A}: forall {w w': A}, necR w w' ->
@necR _ ag_nat (level w) (level w').