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.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.

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).