unfold is_analysis in |- *.
unfold analysis_cond in |- *.
intros.
elim H.
elim H0.
intros.
elim H1.
elim H3.
intros.
split.
split; trivial.
apply inclusion_trans with h; trivial.
intros.
apply inclusion_trans with h.
apply H2.
split; trivial.
apply inclusion_refl.
apply H4; tauto.
Qed.

(** if h is the analysis of g and h' is the analysis of h then h = h' *)
Lemma analysis_analysed :
forall g h h' : hedge, is_analysis g h -> is_analysis h h' -> equal h h'.