Division Theorem/Positive Divisor/Uniqueness/Proof 1

Theorem
For every pair of integers $a, b$ where $b > 0$, the integers $q, r$ such that $a = q b + r$ and $0 \le r < b$ are unique:


 * $\forall a, b \in \Z, b > 0: \exists! q, r \in \Z: a = q b + r, 0 \le r < b$

Proof
It is given by Division Theorem: Positive Divisor: Existence that such $q$ and $r$ exist.