(** 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 all_one_side_par_strict : forall A B C D,
C <> D -> (forall P, Col C D P -> OS A B C P) ->
Par_strict A B C D.