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. *)

Lemma not_par_inter_uniqueness : forall A B C D X Y,
A <> B -> C <> D -> ~Par A B C D -> Col A B X -> Col C D X -> Col A B Y -> Col C D Y ->
X = Y.