intro.
split.
apply h_le_h_red.
apply inclusion_impl_le_h.
apply red_incl_h.
Qed.

(** if g is included in h and h <= g then (reduce g) is included in (reduce h) *)
Lemma inclusion_le_h_reduce_inclusion :
forall g h : hedge,
inclusion g h -> le_h h g -> inclusion (reduce g) (reduce h).