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 l12_18 :
forall A B C D P,
Cong A B C D -> Cong B C D A -> ~Col A B C ->
B <> D -> Col A P C -> Col B P D ->
Par A B C D /\ Par B C D A /\ TS B D A C /\ TS A C B D.