intros x c0 x0 c1; generalize c0 c1; case x; case x0; simpl in |- *; auto.
Qed.
Hint Resolve pO_irreducible.

Theorem reducetopO_pO :
forall Q : list (poly A0 eqA ltM),
reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
(pO A n) (pO A n).