unfold equal in |- *.
intro.
split; try apply red_incl_h.
apply inclusion_le_h_impl_inclusion_red.
apply inclusion_refl.
apply le_h_refl.
Qed.

(** if (reduce g) ~ h then (reduce g) is included in h *)
Lemma red_equiv_impl_red_incl :
forall g h : hedge, equiv_h (reduce g) h -> inclusion (reduce g) h.