intros.
induction  p as [| p Hrecp].
simpl in |- *.
apply equal_refl.
apply equal_trans with (analysis_seq h (p + n)).
trivial.
simpl in |- *.
apply stable_closed.
apply stable_ana_stable.
trivial.
Qed.
(** h could be an analysis of g iff g is included in h and h is stable under analysis *)
Definition analysis_cond (g h : hedge) := inclusion g h /\ stable_analysis h.

(* Specifications: *)
(** if h could be an analysis of g then h contains the n-th analysis of g for all n *)
Lemma analysis_seq_incl_analysis_cond :
forall g h : hedge,
analysis_cond g h -> forall n : nat, inclusion (analysis_seq g n) h.