Require Export C10_Milieu.
Section MIDLINE.
Definition MidLineDef (A B : Point) : Figure :=
fun M : Point => Distance M A = Distance M B.

(* Specifications: *)
Lemma CollinearMidLine : forall A B C D M : Point,
A <> B ->
Distance C A = Distance C B ->
Clockwise A B C ->
Distance D A = Distance D B ->
Clockwise B A D ->
Collinear C D M ->
Distance M A = Distance M B.
Lemma MidLineNotClockwise : forall A B C D M : Point,
A <> B ->
Distance C A = Distance C B ->
Clockwise A B C ->
Distance D A = Distance D B ->
Clockwise B A D ->
Clockwise C D B ->
Distance M A = Distance M B ->
~Clockwise D C M.
Lemma ClockwiseDCA : forall A B C D : Point,
A <> B ->
Distance C A = Distance C B ->
Clockwise A B C ->
Distance D A = Distance D B ->
Clockwise B A D ->
Clockwise D C A.
Lemma ClockwiseCDB : forall A B C D : Point,
A <> B ->
Distance C A = Distance C B ->
Clockwise A B C ->
Distance D A = Distance D B ->
Clockwise B A D ->
Clockwise C D B.
Lemma MidLine : forall A B : Point,
A <> B ->
Line (MidLineDef A B).