Section MIDPOINT.
Definition Middle (A B : Point) : Figure :=
fun I : Point => Collinear A B I /\ Distance I A = Distance I B.

Lemma MidPointBetweenCD : forall (A B C D : Point) (H : A <> B),
Distance C A = Distance C B ->
Distance D A = Distance D B ->
Clockwise A B C ->
Clockwise B A D ->
Between C (MidPoint A B H) D.