intros.
induction  n as [| n Hrecn].
simpl in |- *.
unfold analysis_cond in H.
tauto.
simpl in |- *.
generalize (inclusion_analysis_inclusion (analysis_seq g n) h Hrecn).
intro.
apply inclusion_trans with (analysis h); trivial.
unfold analysis_cond in H.
unfold stable_analysis in H.
tauto.
Qed.
(** h is an analysis of g if h could be an analysis of g and if for all other candidates h' which could be an analysis of g, h is included in h' *)
Definition is_analysis (g h : hedge) :=
analysis_cond g h /\
(forall h' : hedge, analysis_cond g h' -> inclusion h h').

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