Forward Difference of Falling Factorial

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

Let $\Delta$ denote the forward difference operator.

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

Then:
 * $\map \Delta {x^{\underline m} } = m x^{\underline {m - 1} }$

Proof
From the definitions: