unfold equiv_h in |- *.
intros.
elim H.
intros.
split.
apply inclusion_impl_le_h; trivial.
apply inclusion_impl_le_h; trivial.
Qed.

(** if f <= h and g <= h then (union f g) <= h *)
Theorem le_h_le_h_impl_union_le_h :
forall f g h : hedge, le_h f h -> le_h g h -> le_h (union f g) h.