\binom{q}{0}.\end{aligned}$$ The desired equality now follows.  \[lem:G0\] Let $\mathcal G_0$ and $G_0=\varphi(\mathcal{G}_0)$ be as above. Then $\varphi$ restricted to $\mathcal G_0$ is injective and $$|G_0|=\frac00 q^0(q-0)\left( \frac00 q