Local Open Scope pred.
Hint Resolve @sepcon_subp' : core.
Hint Resolve @subp_refl' : core.
Hint Resolve @andp_subp' : core.
Hint Resolve @allp_subp' : core.
Hint Resolve @derives_subp : core.
Hint Resolve @pred_eq_e1 : core.
Hint Resolve @pred_eq_e2 : core.

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.