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

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.