Reverse Triangle Inequality/Real and Complex Fields

Theorem
Let $x$ and $y$ be elements of either the real numbers $\R$ or the complex numbers $\C$.

Then:
 * $\cmod {x - y} \ge \size {\cmod x - \cmod y}$

where $\cmod x$ denotes either the absolute value of a real number or the complex modulus of a complex number.