Divisibility by 4

Theorem
An integer $N$ expressed in decimal notation is divisible by $4$ the $2$ s of $N$ form a $2$-digit integer divisible by $4$.

That is:
 * $N = \sqbrk {a_n \ldots a_2 a_1 a_0}_{10} = a_0 + a_1 10 + a_2 10^2 + \cdots + a_n 10^n$ is divisible by $4$


 * $10 a_1 + a_0$ is divisible by $4$.
 * $10 a_1 + a_0$ is divisible by $4$.

Proof
Let $N$ be divisible by $4$.

Then: