intros l1 l2 a H' H'0.
apply order_plusP with (l1 := l1) (l2 := l2); auto.
apply canonical_pluspf; auto.
apply canonical_imp_canonical with (a := a); auto.
apply canonical_imp_canonical with (a := a); auto.
Qed.

Theorem pluspf_inv1_eqa :
forall a p q,
canonical A0 eqA ltM (pX a p) ->
canonical A0 eqA ltM (pX a q) -> pX a (pluspf p q) = pluspf (pX a p) q.