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.

(* Specifications: *)
Lemma andp_assoc {A} {NA: NatDed A} : forall P Q R : A,
(P && Q) && R = P && (Q && R).
Lemma andp_derives {A} {NA: NatDed A}:
forall P Q P' Q': A, P |-- P' -> Q |-- Q' -> P && Q |-- P' && Q'.
Lemma orp_derives {A} {NA: NatDed A}:
forall P Q P' Q': A, P |-- P' -> Q |-- Q' -> P || Q |-- P' || Q'.