unfold is_analysis in |- *.
unfold equal in |- *.
intros.
elim H.
elim H0.
intros.
split.
apply H4; trivial.
apply H2; trivial.
Qed.

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