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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 *)

Theorem parallellogram_construction_2 :
forall A B C D I : Point,
is_midpoint I A C ->
on_line_d D I B (-(1)) ->
parallel C D A B /\ parallel A D B C.