(** 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 parallel_existence : forall A B P, A <> B ->
exists C, exists D, C<>D /\ Par A B C D /\ Col P C D.