Lemma prod_x_axis_unit_change : forall O E E' A B C D U, Ar2_4 O E E' A B C D -> Col O E U -> U <> O -> ( exists X, Prod O E E' A B X /\ Prod O E E' C D X) -> ( exists Y, Prod O U E' A B Y /\ Prod O U E' C D Y).