intros.
apply incl_syn_impl_le_h.
apply union_intro; apply le_h_impl_incl_syn; trivial.
Qed.

(** if g1 <= h1 and g2 <= h2 then (union g1 g2) <= (union h1 h2) *)
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).