Theorem elim_py_on_foot_left_right : forall B P U V Y : Point, on_foot Y P U V -> Py Y B Y = (Py P U V * Py P U V * Py V B V + Py P U V * Py P V U * Py V B U + Py P U V * Py P V U * Py U B V + Py P V U * Py P V U * Py U B U) / (Py U V U * Py U V U).