intros a P; elim P; simpl in |- *; auto.
intros a0 l H'; elim H'; auto.
Qed.
Definition spolyp : poly A0 eqA ltM -> poly A0 eqA ltM -> poly A0 eqA ltM.
intros p q; case p; case q.
intros x Cpx x0 Cpx0;
exists
(spolyf A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec x x0 Cpx
Cpx0); auto.
apply spolyf_canonical with (1 := cs); auto.
Defined.

(* Specifications: *)
Theorem red_com :
forall (a b : poly A0 eqA ltM) (aL : list (poly A0 eqA ltM)),
red (spolyp a b) aL -> red (spolyp b a) aL.