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.

Theorem stable_trans :
forall Q y R : list (poly A0 eqA ltM),
stable Q y -> stable y R -> stable Q R.