Section T12_2'.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** 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. *)

(** In the proof given by Tarski on page 125 the distinction of cases is explicit. This is a good example on the significance of decidability. *)
Lemma l12_17 : forall A B C D P,
A <> B -> Midpoint P A C -> Midpoint P B D -> Par A B C D.