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

Lemma exp_andp1 {A} `{ageable A}:
forall B (p: B -> pred A) q, (exp p && q)%pred = (exp (fun x => p x && q))%pred.