(** 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.

Lemma incl_syn_impl_le_h : forall g h : hedge, inclusion g (synthesis h) -> le_h g h.