unfold eq_o in H.
spliter.
unfold eqo.
repeat split; auto.
intros.
eapply H1.
apply H2.
apply per_proj.
apply perp_not_eq_2 in H2.
auto.
assumption.
apply l8_5.
Col.
apply H4.
apply per_proj.
apply perp_not_eq_2 in H4.
auto.
assumption.
apply l8_5.
Col.
apply H6.
assumption.
apply H8.
apply H9.
assumption.
assumption.
Qed.

Lemma eq_o_one_side : forall A B X Y, eq_o A B X A B Y -> OS A B X Y.
intros.