Require Export C5_Droite_Prop.
Section EQUIDIRECTED_PROPERTIES.

(* Specifications: *)
Lemma EquiDirectedRefl : forall A B : Point,
EquiDirected A B A B.
Lemma EquiDirectedSym : forall A B C D : Point,
EquiDirected A B C D ->
EquiDirected C D A B.
Lemma EquiDirectedPermut : forall A B C D : Point,
EquiDirected A B C D ->
EquiDirected B A C D.
Lemma EquiDirectedPermutCD: forall A B C D : Point,
EquiDirected A B C D ->
EquiDirected A B D C.
Lemma  ParallelNotClockwiseABC : forall A B C D,
EquiOriented A B C D ->
~Clockwise A B C.
Lemma  ParallelNotClockwiseABD : forall A B C D,
EquiOriented A B C D ->
~Clockwise A B D.
Lemma  ParallelCollinearABD : forall A B C D,
EquiOriented A B C D ->
Collinear A B C ->
Collinear A B D.
Lemma  ParallelCollinearABC : forall A B C D,
EquiOriented A B C D ->
Collinear A B D ->
Collinear A B C.
Lemma  ParallelCollinearCDB : forall A B C D,
EquiOriented A B C D ->
Collinear C D A ->
Collinear C D B.
Lemma  ParallelCollinearCDA : forall A B C D,
EquiOriented A B C D ->
Collinear C D B ->
Collinear C D A.