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

Theorem elim_ratio_on_foot_spec_b :
forall Y P U V A C : Point,
on_foot Y P U V ->
~ Col A U V ->
parallel A Y C Y ->
C <> Y ->
A**Y / C**Y = S A U V / S C U V.