Definition Perp_in := fun X A B C D => 
   A<>B /\ C<>D /\ Col X A B /\ Col X C D /\
   (forall U V,  Col U A B -> Col V C D -> Per U X V).

Lemma l8_12 : forall A B C D X, Perp_in X A B C D -> Perp_in X C D A B.