Section BuchRed.
Load "hCoefStructure".
Load "hOrderStructure".
Load "hBuch".
intros L p q H; apply Cb_incl with (1 := cs) (P := addEnd A A0 eqA n ltM p L);
auto.
elim L; simpl in |- *; auto.
intros a l H0 a0 H1; elim H1; clear H1; intros H1; auto.
case (H0 a0); auto.
Qed.
intros L p q H; apply Cb_incl with (1 := cs) (P := p :: L); auto.
elim L; simpl in |- *; auto.
intros a l H0 a0 H1; elim H1; clear H1; intros H1; auto.
case H1; auto.
Qed.
intros L p q H H0.
apply Cb_trans with (1 := cs) (b := p); auto.
apply Cb_cons_addEnd; auto.
Qed.

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