(* 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_6_non_zero_denom: forall O U V A B C D: Point,
parallel A B C D ->
C<>D ->
~ Col O U V ->
~ Col O A C ->
Col A C D ->
S O U C * S O V D - S O V C * S O U D <> 0.