Forward Difference of Falling Factorial

Theorem
Let $f: \R \to \R$ be a real function.

Let $\Delta$ be the forward difference operator.

Let $x^{\underline m}$ be the $m$th falling factorial of $x$

Then:
 * $\Delta \left({x^{\underline m}}\right) = m x^{\underline{m-1}}$

Proof
From the definitions: