(* Require Import VST.msl.alg_seplog. *)
Local Open Scope logic.
Hint Extern 0 (_ |-- _) => match goal with |- ?A |-- ?B => constr_eq A B; simple apply derives_refl end : core.
(* Hint Resolve @derives_refl.    too expensive sometimes when it fails . . . *)
Ltac solve_andp' :=
first [ apply derives_refl
| apply andp_left1; solve_andp'
| apply andp_left2; solve_andp'].
Ltac solve_andp := repeat apply andp_right; solve_andp'.
Hint Resolve @TT_right: norm.
Hint Resolve @FF_left : norm.
Ltac norm := auto with norm.
Proof with norm.
intros.
apply pred_ext.
apply andp_right. apply andp_left2... apply andp_left1...
apply andp_right. apply andp_left2... apply andp_left1...
Qed.
Class CCCviaNatDed (A: Type) (prod expo: A -> A -> A) {ND: NatDed A}: Prop :=
isCCC: CartesianClosedCat.CCC A derives eq prod expo.

Lemma CCC_expo_derives: forall A prod expo {ND: NatDed A} {CCC: CCCviaNatDed A prod expo},
forall P P' Q Q', P' |-- P -> Q |-- Q' -> expo P Q |-- expo P' Q'.