Reverse Triangle Inequality/Real and Complex Fields/Corollary 3

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

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

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

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

Let $z := -y$.

Then we have:

Hence the result.