Hint Resolve @sepcon_subp'.
Hint Resolve @subp_refl'.
Hint Resolve @andp_subp'.
Hint Resolve @allp_subp'.
Hint Resolve @derives_subp.
Hint Resolve @pred_eq_e1.
Hint Resolve @pred_eq_e2.

(* Specifications: *)
Lemma allp_imp2_later_e2 {B}{A}{agA: ageable A}:
forall (P Q: B -> pred A) (y: B) ,
(ALL x:B, |> P x <=> |> Q x) |-- |> Q y >=> |> P y.
Lemma allp_imp2_later_e1 {B}{A}{agA: ageable A}:
forall (P Q: B -> pred A) (y: B) ,
(ALL x:B, |> P x <=> |> Q x) |-- |> P y >=> |> Q y.