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

Lemma imp_derives {A} `{agA : ageable A}:
forall P P' Q Q',
P' |-- P ->
Q |-- Q' ->
P --> Q |-- P' --> Q'.