Electric Flux out of Closed Surface surrounding Point Charge/Lemma

Theorem
Let $q$ be a point charge located at the origin of a system of spherical polar coordinates.

Let $S$ be a closed surface surrounding $q$.

Let $\delta \mathbf S$ be a vector area element of $S$ directed along the outward normal from $S$.

Let $\delta \Omega$ be the solid angle subtended by the projection of $\delta \mathbf S$ from $q$

The total electric flux through $\delta \Omega$ is given by:
 * $F = \dfrac q {4 \pi \varepsilon_0} \delta \Omega$