unfold equal in |- *.
split.
unfold inclusion in |- *.
intros.
apply SynInc; trivial.
generalize (incl_syn_impl_le_h (synthesis h) h).
unfold le_h in |- *.
intros.
apply H.
apply inclusion_refl.
Qed.

(** if h is stable under analysis then so is S(h) *)
Lemma stable_ana_impl_stable_syn_ana :
forall h : hedge, stable_analysis h -> stable_analysis (synthesis h).