intros.
apply SynInc.
trivial.
Qed.
(** g <= h if S(g) is included in S(h) *)
Definition le_h (g h : hedge) := inclusion (synthesis g) (synthesis h).
(** g ~ h if g <= h and h <= g *)
Definition equiv_h (g h : hedge) := le_h g h /\ le_h h g.

(** <= is reflexive, ... *)
Lemma le_h_refl : forall h : hedge, le_h h h.
unfold le_h in |- *.