Hint Rewrite @andp_dup : normalize.

(* Specifications: *)
Lemma andp_emp_sepcon_TT {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}:
forall (Q: pred A),
(forall w1 w2, core w1 = core w2 -> Q w1 -> Q w2) ->
(Q && emp * TT = Q).
Lemma sepcon_TT {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}:
forall (P: pred A), P |-- (P * TT).