(* 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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(*                               part1.v                                    *)
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(* Congruence lemmas near the end slightly more explicit than in von Plato  *)
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Hint Resolve Convergent_imp_distinct.
Hint Resolve sym_SPar.
Definition reverse : Segment -> Segment.
Hint Resolve rev_defines_sameln.
Definition flip : Twolines -> Twolines.
Hint Resolve rev_defines_sameln flip_defines_samept.
Definition colinear (x y : Segment) : Prop := EqLn (ln x) (ln y).

Theorem Colinearity_is_equivalence : Equivalence Segment colinear.