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

Theorem elim_ratio_on_foot_a :
forall Y P U V A C D : Point,
on_foot Y P U V ->
Col A U V ->
parallel A Y C D ->
C <> D ->
A <> Y ->
A**Y / C**D = Py4 P C A D / Py C D C.