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.

(* Specifications: *)
Lemma ExistsParallelogrammCenter : forall A B C D : Point,
forall H : Parallelogramm A B C D,
{I : Point | ParallelogrammCenter A B C D H I}.
Lemma ParallelogrammDistinctAB : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B.
Lemma ParallelogrammDistinctAC : forall A B C D : Point,
Parallelogramm A B C D ->
A <> C.
Lemma ParallelogrammDistinctCD : forall A B C D : Point,
Parallelogramm A B C D ->
C <> D.