Definition DistLn := fun A B C D => 
(exists X, Col X A B /\ ~Col X C D) \/ (exists X, ~ Col X A B /\ Col X C D).

(* Specifications: *)
Lemma l8_14_1 : forall A B, ~ Perp A B A B.
Lemma l8_14_2_1a : forall X A B C D, Perp_in X A B C D -> Perp A B C D.
Lemma l8_14_2_1b : forall X A B C D Y, Perp_in X A B C D -> Col Y A B -> Col Y C D -> X=Y.
Lemma l8_14_2_1b_bis : forall A B C D X, Perp A B C D -> Col X A B -> Col X C D -> Perp_in X A B C D.
Lemma l8_14_2_2 : forall X A B C D, Perp A B C D -> (forall Y, Col Y A B -> Col Y C D -> X=Y) -> Perp_in X A B C D.
Lemma l8_14_3 : forall A B C D X Y, Perp_in X A B C D -> Perp_in Y A B C D -> X=Y.
Lemma l8_15_1 : forall A B C X, A<>B -> Col A B X -> Perp A B C X -> Perp_in X A B C X.
Lemma l8_15_2 : forall A B C X, A<>B -> Col A B X -> Perp_in X A B C X -> Perp A B C X.
Lemma l8_16_1 : forall A B C U X, A<>B -> Col A B X -> Col A B U -> U<>X -> Perp A B C X -> ~ Col A B C /\ Per C X U.
Lemma l8_16_2 : forall A B C U X, A<>B -> Col A B X -> Col A B U -> U<>X -> ~ Col A B C -> Per C X U ->Perp A B C X.
Lemma l8_18_unicity : forall A B C X Y, ~ Col A B C -> Col A B X -> Perp A B C X -> Col A B Y -> Perp A B C Y -> X=Y.