intros.
apply pred_ext; intros w ?; hnf in *; simpl; intros; intuition.
Qed.

(* Specifications: *)
Lemma distrib_orp_andp {A}{agA: ageable A}:
forall P Q R, (P||Q)&&R = (P&&R)||(Q&&R).
Lemma allp_right {B A: Type}{agA: ageable A}:
forall (P: pred A) (Q: B -> pred A),
(forall v, P |-- Q v) ->
P |-- allp Q.
Lemma allp_left {B}{A}{agA: ageable A}:
forall (P: B -> pred A) x Q, P x |-- Q -> allp P |-- Q.
Lemma later_imp2 {A}{agA: ageable A}: forall P Q: pred A,
|> (P <--> Q) = |> P <--> |> Q.