(** 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 inter_uniqueness_not_par : forall A B C D P,
~Col A B C -> Col A B P -> Col C D P -> ~Par A B C D.