unfold le_h in |- *.
unfold inclusion in |- *.
unfold reduce in |- *.
intros g h H H0.
intros M N.
case M.
intros.
elim H1; auto.
case N; intros; elim H1; auto.
intros.
split; auto.
case H3.
intro; left; red in |- *; intro; apply H4; auto.
intro; right; red in |- *; intro; apply H4; auto.
case N; intros; elim H1; auto.
split; auto.
case H3.
intro; left; red in |- *; intro; apply H4; auto.
intro; right; red in |- *; intro; apply H4; auto.
case N; intros; elim H1; auto.
split; auto.
case H3; try tauto.
intros.
right; red in |- *; intro; apply H4; auto.
Qed.

Lemma equal_reduce_equal :
forall g h : hedge, equal g h -> equal (reduce g) (reduce h).