Definition reducep (L : list (poly A0 eqA ltM)) (p q : poly A0 eqA ltM) :
  Prop :=
  reduce A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec L
    (s2p A A0 eqA n ltM p) (s2p A A0 eqA n ltM q).

Theorem zerop_nf_cb : forall (L : list (poly A0 eqA ltM)) (p : poly A0 eqA ltM), zerop A A0 eqA n ltM (nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec os p L) -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec p L.