Reverse Triangle Inequality/Real and Complex Fields/Corollary 1/Proof 1

Proof
From the Reverse Triangle Inequality:
 * $\cmod {x - y} \ge \cmod {\cmod x - \cmod y}$

By the definition of both absolute value and complex modulus:
 * $\cmod {\cmod x - \cmod y} \ge 0$

As:
 * $\cmod x - \cmod y = \pm \cmod {\cmod x - \cmod y}$

it follows that:
 * $\cmod {\cmod x - \cmod y} \ge \cmod x - \cmod y$

Hence the result.