induction (col_dec B A A').
left.
assumption.
induction(eq_dec_points B B').
subst B'.
right.
apply one_side_reflexivity.
assumption.
assert(Par A A' B B').
unfold proj in *.
spliter.
induction H5; induction H4;spliter.
eapply l12_9_2D.
apply perp_sym.
apply H8.
Perp.
subst B'.
tauto.
subst A'.
tauto.
subst B'.
tauto.
assert(Par_strict A A' B B').
induction H4.
assumption.
spliter.
apply False_ind.
apply H2.
ColR.
right.
eapply l12_6.
assumption.
Qed.

Lemma proj_eq_col : forall A B P Q C, proj A P Q C -> proj B P Q C -> Col A B C.
intros.