intros a H' p; elim p; simpl in |- *; auto.
Qed.

Theorem spoly_Reduce :
forall (Q : list (poly A0 eqA ltM)) (a b : Term A n),
eqT (ppc (A:=A) A1 (n:=n) a b) (multTerm (A:=A) multA (n:=n) a b) ->
forall p q : list (Term A n),
inPolySet A A0 eqA n ltM (pX b q) Q ->
canonical A0 eqA ltM (pX a p) ->
reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
(minuspf A A0 A1 eqA invA minusA multA eqA_dec n ltM ltM_dec
(mults (A:=A) multA (n:=n) b p) (mults (A:=A) multA (n:=n) a q))
(mults (A:=A) multA (n:=n) (invTerm (A:=A) invA (n:=n) (T1 A1 n))
(multpf A A0 eqA plusA multA eqA_dec n ltM ltM_dec (pX a p) q)).