unfold Perp_in.
intros;intuition.
Qed.

Lemma l8_13_2 : forall A B C D X,
A <> B -> C <> D -> Col X A B -> Col X C D ->
(exists U, exists V :Point, Col U A B /\ Col V C D /\ U<>X /\ V<>X /\ Per U X V) ->
Perp_in X A B C D.