Program Definition exactly {A} `{ageable A} (x: A) : pred A := necR x.

Lemma app_ext {A: Type} `{ageable A} : forall (F G: A -> Prop) p1 p2 w, (F w = G w) -> app_pred (exist (hereditary age) F p1) w = app_pred (exist (hereditary age) G p2) w.