Section PARALLELOGRAMM.
Definition Parallelogramm := fun A B C D : Point =>
Clockwise A B C /\
Clockwise A C D /\
Distance A B = Distance C D /\
Distance A D = Distance B C.
Definition ParallelogrammCenter (A B C D : Point) (_ : Parallelogramm A B C D) :=
fun I : Point => Between A I C /\ Distance I A = Distance I C.

Lemma ParallelogrammDistinctAB : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B.