eapply l12_9_2D.
unfold proj in *.
spliter.
induction H4; induction H3; spliter.
apply perp_sym.
apply H7.
Perp.
subst A'.
tauto.
subst B'.
tauto.
unfold proj in *.
spliter.
induction H4; induction H3; spliter.
apply perp_sym.
apply H5.
subst B'.
tauto.
subst A'.
tauto.
subst A'.
tauto.
Qed.

Lemma proj_not_col : forall A A' P Q, A <> A' -> proj A P Q A' -> ~Col P Q A.
intros.