assert(A <> B).
apply perp_not_eq_1 in H4.
assumption.
assert(P <> Q).
apply perp_not_eq_2 in H4.
assumption.
induction (eq_dec_points C C').
subst C'.
apply one_side_reflexivity.
intro.
apply H1.
Col.
assert(Perp C C' C' P).
eapply per_perp_in in H5.
eapply perp_in_perp_bis in H5.
induction H5.
apply perp_not_eq_1 in H5.
tauto.
assumption.
auto.
auto.
assert(Perp C C' P Q).
apply perp_sym.
eapply perp_col.
assumption.
apply perp_sym.
apply perp_right_comm.
apply H9.
Col.
assert(Par C C' A B).
eapply l12_9_2D.
apply H10.
assumption.
assert(Par_strict C C' A B).
induction H11.
assumption.
spliter.
apply False_ind.
apply H1.
Col.
eapply l12_6.
apply par_strict_symmetry.
assumption.
Qed.

Lemma one_side_eqo : forall A B X Y, OS A B X Y -> eqo A B X A B Y.
intros.