(** 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_strict_col2_par_strict : forall A B C D E F,
E <> F -> Par_strict A B C D -> Col C D E -> Col C D F ->
Par_strict A B E F.