unfold Projp.
split.
apply l8_14_2_1a in H.
apply perp_not_eq_1 in H.
assumption.
left.
split.
apply perp_in_col in H.
spliter.
assumption.
apply l8_14_2_1a in H.
assumption.
Qed.

Lemma proj_distinct : forall P P' A B, Projp P P' A B -> P' <> A \/ P' <> B.
intros.