Proof with norm.
intros.
apply pred_ext. apply andp_left2...
apply andp_right... apply prop_right...
Qed.

(* Specifications: *)
Lemma prop_true_andp' (P: Prop) {A} {NA: NatDed A}:
forall (Q: A),  P -> (!! P && Q = Q).
Lemma TT_andp_right {A}{NA: NatDed A}:
forall P Q, TT |-- P -> TT |-- Q -> TT |-- P && Q.