(** We show that the diagonals of a parallelogram intersect in the midpoint *)

(* Specifications: *)
Theorem parallelogram_midpoint :
forall A B C D I : Point,
on_parallel_d D C A B (0-1) ->
inter_ll  I A C B D ->
A<>C ->
A<>I ->
parallel A I A C ->
A ** I / A**C = 1 / 2.
Theorem Prop51Hartsshornebis :
forall A B C D E : Point,
~ Col D A C ->
~ Col A B C ->
is_midpoint D A B ->
is_midpoint E A C ->
parallel D E B C ->
B <> C ->
D ** E / B ** C = 1 / 2.