unfold proj in H0.
spliter.
induction H1.
spliter.
repeat split.
induction (eq_dec_points A P).
treat_equalities.
apply l8_5.
apply perp_in_per.
eauto with perp.
induction (eq_dec_points B P).
treat_equalities.
apply l8_5.
apply perp_in_per.
apply perp_in_comm.
apply perp_perp_in.
apply perp_sym.
eapply perp_col.
assumption.
eauto with perp.
Col.
assumption.
spliter.
subst T.
repeat split.
Perp.
Perp.
assumption.
Qed.

(* Specifications: *)
Lemma proj_uniqueness : forall A B T P P', proj T A B P -> proj T A B P' -> P = P'.
intros.