proposition: Theorem reduceplus_divp : forall (a b : poly A0 eqA ltM) (Q : list (poly A0 eqA ltM)), reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (s2p A A0 eqA n ltM a) (s2p A A0 eqA n ltM b) -> ~ zerop A A0 eqA n ltM a -> exists r : poly A0 eqA ltM, In r (b :: Q) /\ divp A A0 eqA multA divA n ltM a r /\ ~ zerop A A0 eqA n ltM r.
proof: Proof. Proof using plusA os cs. intros a b Q H' H'0. apply reduceplus_divp_lem with (a := s2p A A0 eqA n ltM a) (b := s2p A A0 eqA n ltM b); auto. apply canonical_s2p; auto. Qed.
imports: Buchberger(Buch)