(* 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.
Instance andp_imp_CCC: forall A {ND : NatDed A}, CCCviaNatDed A andp imp.
Instance sepcon_wand_CCC: forall A {ND : NatDed A} {SL: SepLog A}, CCCviaNatDed A sepcon wand.
Hint Rewrite @FF_sepcon @sepcon_FF : norm.
Hint Rewrite @FF_andp @andp_FF : norm.

Lemma allp_depended_uncurry': forall {A} `{NatDed A} {S: Type} {T: S -> Type} (P: forall s: S, T s -> A),
ALL s: S, (ALL t: T s, P s t) = ALL st: sigT T, P (projT1 st) (projT2 st).