(* shows that we need A<>B in elim_py_on_line_d_middle Lemma essai : forall A P Q Y : Point, forall r:F, r<> 0 -> on_line_d Y P Q r -> False. *)

Theorem elim_py_inter_ll_right :
forall A B P Q U V Y : Point,
inter_ll Y P Q U V ->
Py A B Y = 1 / S4 P U Q V * (S P U V * Py A B Q + S Q V U * Py A B P).