(* elimination of area for euclidean constructions *)

Theorem elim_py_on_perp_d_left_right :
forall B U V Y : Point, forall r: F,
on_perp_d Y U V r ->
Py Y B Y = Py U B U - (2 + 2) * r * S U V B -
(2 + 2) * r * (0 - r / (2 + 2) * Py U V U + S U V B).