(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
(***************************************************************************)
(** 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 *)

Lemma example_construction_simplification:
forall A B C D E F G Line_3_b Line_6_b,
on_line C A B ->
on_parallel Line_3_b C A D ->
inter_ll E C Line_3_b B D ->
on_parallel Line_6_b C F A ->
inter_ll G C Line_6_b F B  ->
parallel E G D F.