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 col_cop_perp2__pars : forall P Q A B C D, ~ Col A B P ->
Col C D P -> Coplanar A B C D -> Perp A B P Q -> Perp C D P Q -> Par_strict A B C D.