unfold eq_o.
repeat split; auto.
intros.
unfold Midpoint in H8.
apply l7_3 in H6.
subst M.
spliter.
assert(proj P A C C1).
eapply proj_col_proj.
apply H3.
apply perp_not_eq_2 in H0.
auto.
eapply perp2__col.
apply perp_comm.
apply perp_sym.
apply H2.
apply perp_comm.
Perp.
assert(C=C1).
eapply proj_uniqueness.
apply H1.
assumption.
subst C1.
left.
assumption.
Qed.

Lemma eqo_refl : forall A B P, ~Col A B P -> eqo A B P A B P.
intros.