Divisibility by 12

Theorem
Let $N \in \N$ be expressed as:


 * $N = a_0 + a_1 10 + a_2 10^2 + \cdots + a_n 10^n$

Then $N$ is divisible by $12$ $a_0 - 2 a_1 + 4 \paren {\displaystyle \sum_{r \mathop = 2}^n a_r}$ is  divisible by $12$.