(* elimination of ratios for euclidean constructions *)
(* the condition A<>Y is required *)

Theorem elim_ratio_on_perp_d_b_aux :
forall Y P Q A C D : Point, forall r: F,
on_perp_d Y P Q r->
~ Col A P Y  ->
parallel A Y C D ->
C<>D -> C**D <>A**Y ->
A**Y / C**D = Py A P Q / Py4 C P D Q.