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

Lemma conjoin_hyp0  {A} `{H : ageable A}:
forall (P Q: pred A) w,  P w -> (P --> Q) w -> (TT --> Q) w.