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_hyp1 {A} `{agA : ageable A}: forall (P Q R: pred A)  w,
P w -> (P&&Q --> R) w -> (Q --> R) w.