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

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