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).