intros a p; case p; auto.
intros m l H'; try assumption.
change (plusP (pX a (pO A n)) (pX m l) (pX a (pX m l))) in |- *.
apply mainu1; auto.
apply (canonical_pX_order _ A0 eqA) with (l := l); auto.
Qed.

Theorem plusP_inv1 :
forall a b p q s,
plusP (pX a p) (pX b q) s -> ltT ltM b a -> s = pX a (pluspf p (pX b q)).