Theorem elim_py_inter_ll_middle : forall A B P Q U V Y : Point, inter_ll Y P Q U V -> Py A Y B = - (S P V U / S4 P U Q V) * Py A Q B + - (S Q U V / S4 P U Q V) * Py A P B - - (S P V U / S4 P U Q V) * - (S Q U V / S4 P U Q V) * Py P Q P.