intros.
induction  p as [| p Hrecp].
simpl in |- *.
trivial.
simpl in |- *.
apply stable_impl_ana_stable.
trivial.
Qed.

(** if the n-th analysis of h is stable under analysis then all the following analysis are equal to the n-th analysis *)
Lemma stable_ana_const :
forall (h : hedge) (n : nat),
stable_analysis (analysis_seq h n) ->
forall p : nat, equal (analysis_seq h n) (analysis_seq h (p + n)).