Translation of Integer Interval is Bijection

Theorem
Let $a,b,c\in\Z$ be integers.

Let $\left[{a \,.\,.\, b}\right]$ denote the integer interval between $a$ and $b$.

Then the mapping $T : \left[{a \,.\,.\, b}\right] \to \left[{a+c \,.\,.\, b+c}\right]$ defined as:
 * $T(k) = T(k+c)$

is a bijection.