intros a b p q H'; rewrite (plusP_inv1 a b p q (pluspf (pX a p) (pX b q)));
auto.
Qed.

Theorem pluspf_inv2_eq :
forall a b p q,
ltT ltM a b -> pX b (pluspf (pX a p) q) = pluspf (pX a p) (pX b q).