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.

Lemma orp_derives {A} {NA: NatDed A}:
forall P Q P' Q': A, P |-- P' -> Q |-- Q' -> P || Q |-- P' || Q'.