Set with Complement forms Partition

Theorem
Let $\varnothing \subset S \subset \mathbb U$.

Then $S$ and its complement $\complement \left({S}\right)$ form a partition of the universal set $\mathbb U$.

Proof
Follows directly from Relative Complement Partition: if $\varnothing \subset T \subset S$, then $\left\{{T, \complement_S \left({T}\right)}\right\}$ is a partition of $S$.