(* set (X_C := S O U C). set (X_A := S O U A). set (X_B := S O U B). set (X_D := S O U D). set (Y_C := S O V C). set (Y_A := S O V A). set (Y_B := S O V B). set (Y_D := S O V D). *)

Lemma free_points_ratio_elimination_7 : forall O U V A B C D: Point,
parallel A B C D ->
C<>D ->
~ Col O U V ->
~ Col U A C ->
Col A C D ->
A**B / C**D =
(S O U V * (S O U B - S O U A) - S O U A * S O V B + S O U B * S O V A) /
(S O U V * (S O U D - S O U C) - S O U C * S O V D + S O U D * S O V C).