unfold proj in *.
spliter.
induction H1; induction H2; spliter; assert(Col A P P').
ColR.
eapply (l8_18_uniqueness A B T P P');
auto.
subst T.
contradiction.
contradiction.
subst P'.
ColR.
subst P'.
contradiction.
subst T.
subst P'.
Col.
subst T.
subst P'.
reflexivity.
Qed.

Lemma proj_col : forall T P A B, proj T A B P -> Col P A B.
intros.