Hint Resolve @boxy_allp.

(* Specifications: *)
Lemma later_allp {A} `{agA : ageable A}:
forall B P, |> (allp P) = allp (fun x:B => |> (P x)).
Lemma later_prop {A} `{agA : ageable A}:
forall P: Prop, |> (prop P) |-- prop P || |> FF.
Lemma box_derives {A} `{ageable A} : forall M (P Q:pred A),
P |-- Q ->  box M P |-- box M Q.
Lemma forall_pred_ext  {A} `{agA : ageable A}: forall B (P Q: B -> pred A),
(ALL x : B, (P x <--> Q x)) |-- (ALL x : B, P x) <--> (ALL x: B, Q x) .
Lemma exists_pred_ext  {A} `{agA : ageable A}: forall B (P Q: B -> pred A),
(ALL x : B, (P x <--> Q x)) |-- (EX x : B, P x) <--> (EX x: B, Q x) .
Lemma imp_pred_ext  {A} `{agA : ageable A}: forall B B' P Q,
(B <--> B') && (B --> (P <--> Q))
|-- (B --> P) <-->  (B' --> Q).
Lemma derives_refl {A: Type} `{ageable A}:
forall (P: pred A), (P |-- P).