(** 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 par_one_or_two_sides :
forall A B C D,
Par_strict A B C D ->
TS A C B D /\ TS B D A C \/ OS A C B D /\ OS B D A C.