unfold le_h in |- *.
intros.
apply inclusion_trans with (synthesis g); trivial.
apply h_incl_syn.
Qed.

(* Specifications: *)
(** if g is included in S(h) then g <= h *)
Lemma incl_syn_impl_le_h :
forall g h : hedge, inclusion g (synthesis h) -> le_h g h.