(** 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.

Theorem le_h_le_h_impl_le_h_union : forall g1 g2 h1 h2 : hedge, le_h g1 h1 -> le_h g2 h2 -> le_h (union g1 g2) (union h1 h2).