Superset Relation is Compatible with Subset Product

Theorem
Let $\left({S,\circ}\right)$ be a magma.

Let $\circ_{\mathcal P}$ be the subset product on $\mathcal P \left({S}\right)$, the power set of $S$.

Then the superset relation $\supseteq$ is compatible with $\circ_{\mathcal P}$.

Proof
By Subset Relation is Compatible with Subset Product, the subset relation $\subseteq$ is compatible with $\circ_{\mathcal P}$.

From Inverse of Subset Relation is Superset, the inverse of $\subseteq$ is $\supseteq$.

The result follows from Inverse of Relation Compatible with Operation is Compatible.