(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
(***************************************************************************)
Require Export advanced_parallel_lemmas.
Require Export geometry_tools.
(*********************************************************************)
(*  Elimination Theorems                                               *)
(*********************************************************************)
(* Area elimination *)
unfold on_line in |- *.

Theorem non_zero_denom_on_inter_parallel_parallel_area :
forall A B C D E G H : Point, on_inter_parallel_parallel A B C D E G H -> S4 C G D H <> 0.