intros a p; case p; auto.
intros a0 l H'.
apply ltP_trans with (y := pX a (pO A n)); auto.
change (ltP (A:=A) (n:=n) ltM (pX a0 l) (pX a (pO A n))) in |- *.
apply ltP_hd; auto.
apply (canonical_pX_order A A0) with (eqA := eqA) (l := l); auto.
apply ltP_tl; auto.
change (ltP (A:=A) (n:=n) ltM (pO A n) (pX a0 l)) in |- *; apply ltPO.
Qed.

Theorem eqp_eqTerm :
forall a b p q, eqP (pX a p) (pX b q) -> eqTerm (A:=A) eqA (n:=n) a b.