mod(a+b) is greater than or equal to mod(mod(a)+mod(b))
i dont get it
$|a+b| \le |a| + |b|$ is known as the Triangle Inequality. It is fairly simple to prove for real numbers. In this case, Plato used the Triangle Inequality to show that
$|(x+y)+(-y)| \le |x+y|+|-y| = |x+y|+|y|$.
Then, Plato goes on to show that both
$|x|-|y| \le |x+y|$
and
$|y|-|x| \le |x+y|$
so
$\left\lvert \lvert x \rvert - \lvert y \rvert \right\rvert \le |x+y|$