(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                                                                          *)
(*                          Constructive Geometry                           *)
(*                             according to                                 *)
(*                            Jan von Plato                                 *)
(*                                                                          *)
(*                               Coq V5.10                                  *)
(*									    *)
(*			        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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(*                                part2.v                                   *)
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(* Specifications: *)
Theorem thm4_1a :
forall (x : Segment) (l : Line),
DiLn l (ln x) -> Apart (origin x) l \/ Apart (extremity x) l.
Theorem thm4_1b :
forall (x : Segment) (l : Line),
Apart (origin x) l \/ Apart (extremity x) l -> DiLn l (ln x).