(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
(***************************************************************************)
(** Transitivity of the parallel predicate expressed constructively *)

Theorem parallel_transitivity :
forall A B C D E F : Point,
A <> B ->
on_parallel C D A B ->
on_parallel E F C D ->
parallel A B E F.