Definition spO : poly A0 eqA ltM.Definition sp1 : poly A0 eqA ltM.Definition sgen : nat -> poly A0 eqA ltM.Definition sscal : A -> poly A0 eqA ltM -> poly A0 eqA ltM.

Theorem inP_reduce : forall P Q : list (poly A0 eqA ltM), (forall a : list (Term A n), inPolySet A A0 eqA n ltM a Q -> inPolySet A A0 eqA n ltM a P) -> forall a b : list (Term A n), reduce A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q a b -> reduce A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec P a b.