unfold proj in *.
spliter.
induction H2; repeat split; auto; spliter.
left.
repeat split.
intro.
apply H2.
ColR.
eapply (perp_col _ B); auto.
ColR.
subst T.
right.
split; auto.
ColR.
Qed.

Lemma per_proj : forall A B T P, A <> B -> Per T P A -> Per T P B -> Col A B P -> proj T A B P.
intros.