Definition Dmult :
  forall (a : Term A n) (nZa : ~ zeroP (A:=A) A0 eqA (n:=n) a),
  list (Term A n) -> list (Term A n) -> list (Term A n).

Theorem spoly_Reducestar_pO : 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)) (Cpxb : canonical A0 eqA ltM (pX b q)) (Cpxa : canonical A0 eqA ltM (pX a p)), inPolySet A A0 eqA n ltM (pX b q) Q -> inPolySet A A0 eqA n ltM (pX a p) Q -> reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (spolyf A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec (pX a p) (pX b q) Cpxa Cpxb) (pO A n).