proposition: 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.
proof: Proof. intros P Q H' a b H'0; elim H'0; auto. intros a0 b0 nZb p q r H'1 H'2 H'3; auto. apply reducetop with (b := b0) (nZb := nZb) (q := q); auto. Qed.
imports: Buchberger(moreCoefStructure)