unfold Projp in *.
spliter.
induction H1; induction H2.
spliter.
apply (l8_18_uniqueness A B P); Col.
apply perp_not_col2 in H4.
induction H4.
assumption.
contradiction.
spliter.
subst P'.
apply perp_not_col2 in H3.
induction H3; contradiction.
spliter.
subst Q'.
apply perp_not_col2 in H4.
induction H4; contradiction.
spliter.
subst P'.
subst Q'.
auto.
Qed.

Lemma col_par_projp2_eq : forall L11 L12 L21 L22 P P' P'',
Col L11 L12 P ->
Par L11 L12 L21 L22 ->
Projp P P' L21 L22 -> Projp P' P'' L11 L12 ->
P = P''.