intros L H'.
apply def_grobner; auto.
intros p H'0.
lapply (grobner_def L);
[ intros H'2; lapply (H'2 p); [ intros H'4 | idtac ] | idtac ];
auto.
case H'4; auto.
intros H'1; case H'1; intros q E; clear H'1.
right.
apply divp_reduce1 with (L1 := L) (q := q); auto.
intros r1 H'1 H'3.
lapply (Red_divp L r1);
[ intros H'7; lapply H'7; [ intros H'8; clear H'7 | clear H'7 ] | idtac ];
auto.
case H'8; intros q0 E0; case E0; intros H'5 H'6; case H'6; intros H'7 H'9;
clear H'6 E0 H'8.
exists q0; split; auto.
apply cb_Red_cb2; auto.
Qed.
Definition redbuch (L : list (poly A0 eqA ltM)) : list (poly A0 eqA ltM) :=
Red
(buch A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM ltM_dec
os L).

Theorem redbuch_stable :
forall P : list (poly A0 eqA ltM),
stable A A0 eqA plusA multA eqA_dec n ltM ltM_dec P (redbuch P).