(** 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_col4__par_strict : forall A B C D E F G H, E <> F -> G <> H ->
Par_strict A B C D -> Col A B E -> Col A B F -> Col C D G -> Col C D H ->
Par_strict E F G H.