intros p L H'; elim H'; auto.
intros a p0 H'0 H'1; exists a; exists p0; auto.
Qed.
Inductive reduce (Q : list (poly A0 eqA ltM)) :
list (Term A n) -> list (Term A n) -> Prop :=
| reducetop :
forall (a b : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b)
(p q r : list (Term A n)),
inPolySet (pX b q) Q ->
divP A A0 eqA multA divA n a b ->
eqP A eqA n
(spminusf A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec a
b nZb p q) r -> reduce Q (pX a p) r
| reduceskip :
forall (a b : Term A n) (p q : list (Term A n)),
reduce Q p q ->
eqTerm (A:=A) eqA (n:=n) a b -> reduce Q (pX a p) (pX b q).
Hint Resolve reduceskip.

(* Specifications: *)
Lemma pO_reduce :
forall (Q : list (poly A0 eqA ltM)) (p : list (Term A n)),
~ reduce Q (pO A n) p.