(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                          Constructive Geometry                           *)
(*                             according to                                 *)
(*                            Jan von Plato                                 *)
(*                                                                          *)
(*                               Coq V5.10                                  *)
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(*			        Gilles Kahn 				    *)
(*				   INRIA                                    *)
(*		              Sophia-Antipolis		 	            *)
(*									    *)
(*                                                                          *)
(* Acknowledgments: This work started in Turin in May 95 with Yves Bertot.  *)
(* Thanks to the Newton Institute for providing an exceptional work         *)
(* environment in Summer 1995 so that I could complete this.                *)
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(*                             affinity.v                                   *)
(* little lemmas at the end to handle strict parallels                      *)
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Axiom
constructed_parallel :
forall (l : Line) (a : Point), {l' : Line | Par l' l /\ Incident a l'}.
Definition par : Line -> Point -> Line.
Hint Resolve Ax1_i Ax1_ii.
Hint Resolve thm7_1.

Theorem thm7_4 :
forall (l m n : Line) (a : Point),
Apart a l -> Incident a m -> Incident a n -> Par n l -> Par m l -> EqLn m n.