intros.
assert (S O V U <> 0).
intro; assert (Col O U V) by auto with Geom;intuition.
rewrite (free_points_ratio_elimination_3 O V U A B C D) by auto.
reflexivity.
Qed.

(* Specifications: *)
Lemma free_points_ratio_elimination_5 : forall O U V A B C D: Point,
parallel A B C D ->
C<>D ->
~ Col O U V ->
~ Col A C D ->
A**B / C**D = (S O U C * S O V A - S O U C * S O V B - S O V A * S O U B +
S O V B * S O U A - S O V C * S O U A + S O V C * S O U B) /
(S O U C * S O V A - S O U C * S O V D - S O V A * S O U D -
S O V C * S O U A + S O V C * S O U D + S O U A * S O V D) .