intros a p; elim p; simpl in |- *; auto.
intros a0 l H' H'0 H'1.
apply canonical_pluspf; auto.
apply canonicalp1; auto.
cut (~ zeroP (A:=A) A0 eqA (n:=n) a0); auto.
apply (canonical_nzeroP A A0 eqA n ltM) with (p := l); auto.
apply H'; auto.
apply canonical_imp_canonical with (a := a0); auto.
Qed.
Hint Resolve divpf_canonical.

Theorem divPp_divpf :
forall (a : Term A n) (nZa : ~ zeroP (A:=A) A0 eqA (n:=n) a)
(p : list (Term A n)),
canonical A0 eqA ltM p ->
divPp a p -> eqP A eqA n p (mults (A:=A) multA (n:=n) a (divpf a nZa p)).