intros a p; red in |- *; intros H'; try exact H'.
absurd (ltT a a); auto.
apply canonical_pX_order with (l := p); auto.
Qed.

(* Specifications: *)
Theorem canonical_imp_in_nzero :
forall p : list (Term A n),
canonical p -> forall a : Term A n, In a p -> ~ zeroP (A:=A) A0 eqA (n:=n) a.