(* Lemmas about aging and the later operator *)
(* Lemma nec_useless {A} `{ageable A} : forall P, []P = P. intros. apply pred_ext; intros. hnf; intros; apply H0. simpl; apply necM_refl. hnf; intros. hnf; intros. apply pred_nec_hereditary with a; auto. Qed. *)

(* Specifications: *)
Lemma later_age {A} `{ageable A} : forall P,
|>P = box ageM P.
Lemma now_later {A} `{ageable A} : forall P,
P |-- |>P.
Lemma now_later2 {A} `{ageable A} : forall G P,
G |-- P ->
G |-- |>P.