intros a b p q H'; simple inversion H'; auto.
unfold pO in H0; inversion H0.
rewrite (pX_invl ma a p0 p); auto; rewrite (pX_invl mb b q0 q); auto.
Qed.

(* Specifications: *)
Theorem eqp_inv3r : forall a b p q, eqP (pX a p) (pX b q) -> eqP p q.
intros a b p q H'; simple inversion H'; auto.