(* 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_on_perp_d_right :
forall A B P Q Y : Point, forall r: F,
on_perp_d Y P Q r ->
Py A B Y = Py A B P - (2+2) * r * S4 P A Q B.