unfold Projp in H.
spliter.
induction H0.
spliter.
induction(eq_dec_points P' A).
subst P'.
right.
apply perp_not_eq_1 in H1.
assumption.
left.
assumption.
spliter.
subst P'.
induction(eq_dec_points P A).
subst P.
right.
assumption.
left.
assumption.
Qed.

Lemma projp_id : forall P P' Q' A B, Projp P P' A B -> Projp P Q' A B -> P' = Q'.
intros.