(***************************************************************************)
(* 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 geometry_tools.
Proof with try solve [ ring | congruence ].
intros.
assert (- -a=-0).
rewrite H...
assert (- -a=a)...
assert (-0=0)...
Qed.
Hint Resolve field_prop1 : Geom.
(** Some propositions about Col *)
Proof with uniformize_signed_areas;Geometry.
unfold Col in |- *.
intros...
Qed.
Proof with uniformize_signed_areas;Geometry.
unfold Col in |- *.
intros...
Qed.
Proof with uniformize_signed_areas;Geometry.
unfold Col in |- *.
intros...
Qed.
Proof with uniformize_signed_areas;Geometry.
unfold Col in |- *.
intros...
Qed.

Theorem col_5 : forall A B C : Point, Col A B C -> Col C A B.