Difference between Terms of Wythoff Pair

Theorem
Let $\left({\left\lfloor {k \phi}\right\rfloor, \left\lfloor {k \phi^2}\right\rfloor}\right)$ be a Wythoff pair.

The difference between the coordinates of this Wythoff pair is $k$.

That is:
 * $\left\lfloor {k \phi^2}\right\rfloor - \left\lfloor {k \phi}\right\rfloor = k$