Section Buch.
Load "hCoefStructure".
Load "hOrderStructure".
Load "hWfRO".
Inductive stable :
list (poly A0 eqA ltM) -> list (poly A0 eqA ltM) -> Prop :=
stable0 :
forall P Q : list (poly A0 eqA ltM),
(forall a : poly A0 eqA ltM,
Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a P ->
Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a Q) ->
(forall a : poly A0 eqA ltM,
Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a Q ->
Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a P) ->
stable P Q.
Hint Resolve stable0.
auto.
Qed.
intros Q y R H' H'0; inversion H'; inversion H'0; auto.
Qed.
intros Q R H'; elim H'; auto.
Qed.
Hint Resolve (Cb_in _ _ _ _ _ _ _ _ _ cs eqA_dec _ _ ltM_dec os).

Theorem Cb_stable :
forall (a : poly A0 eqA ltM) (Q : list (poly A0 eqA ltM)),
Cb A A0 eqA plusA multA eqA_dec n ltM ltM_dec a Q ->
stable Q (addEnd A A0 eqA n ltM a Q).