Integer Addition is Associative

Theorem
Integer addition is associative:

$$\left({\left[\left[{a, b}\right]\right]_\boxminus + \left[\left[{c, d}\right]\right]_\boxminus}\right) + \left[\left[{e, f}\right]\right]_\boxminus = \left[\left[{a, b}\right]\right]_\boxminus + \left({\left[\left[{c, d}\right]\right]_\boxminus + \left[\left[{e, f}\right]\right]_\boxminus}\right) $$

Proof
From Natural Numbers form Semiring, we take it for granted that addition is associative on the natural numbers $$\mathbb{N}$$.