(** We show here that from the axioms of neutral geometry we can deduce the existence of a parallel line. This is important because it shows that axioms of neutral geometry are inconsistent with those of elliptic geometry as elliptic geometry assumes that no parallel lines exist. *)
(** This corresponds to l12_10 in Tarski's book. *)

Lemma col_not_col_not_par :
forall A B C D,
(exists P, Col A B P /\ Col C D P) ->
(exists Q, Col C D Q /\ ~Col A B Q) -> ~Par A B C D.