Theorem elim_py_on_parallel_d_left_right : forall (B W U V Y : Point) (r : F), on_parallel_d Y W U V r -> Py Y B Y = Py W B W + r * r * Py V B V - 2 * r * r * Py V B U + r * r * Py U B U + 2 * r * Py V B W - 2 * r * Py U B W.