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(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
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(** Transitivity of the parallel predicate expressed constructively *)
(** Pseudo-transitivity of the parallel predicate expressed constructively *)
(** If AB and CD are two parallel and congruent segments then AC is parallel to BD *)
(** The construction of a parallelogram using the fact that the diagonals intersect in the midpoint *)
(** An example where a complex sequence of constructions is compiled into higher level constructions to ease the elimination process *)
(** We show that the diagonals of a parallelogram intersect in the midpoint *)

Theorem parallelogram_midpoint :
forall A B C D I : Point,
on_parallel_d D C A B (0-1) ->
inter_ll  I A C B D ->
A<>C ->
A<>I ->
parallel A I A C ->
A ** I / A**C = 1 / 2.