proposition: Theorem zerop_elim_cb : forall (L : list (poly A0 eqA ltM)) (p q : poly A0 eqA ltM), zerop A A0 eqA n ltM p -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec q (p :: L) -> Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec q L.
proof: Proof. Proof using os minusA invA divA cs A1. intros L p q H' H'0. apply Cb_comp with (L1 := p :: L); auto. simpl in |- *; auto. intros p0 H'1; case H'1; [ intros H'2; rewrite <- H'2; clear H'1 | intros H'2; clear H'1 ]; auto. generalize H'; case p; simpl in |- *; auto. intros x; case x; simpl in |- *; auto. intros H'1 H'3; try assumption. change (CombLinear A A0 eqA plusA multA eqA_dec n ltM ltM_dec L (pO A n)) in |- *. apply CombLinear_0; auto. intros a l H'1 H'3; elim H'3; auto. apply Cb_id with (1 := cs); auto. Qed.
imports: Buchberger(Buch)