Subset Relation is Compatible with Subset Product/Corollary 2

Theorem
Let $\left({S,\circ}\right)$ be a magma. Let $A,B \in \mathcal P \left({S}\right)$, the power set of $S$.

Let $A \subseteq B$.

Let $x \in S$.

Then:
 * $x \circ A \subseteq x \circ B$
 * $A \circ x \subseteq B \circ x$

Proof
This follows from Subset Relation is Compatible with Subset Product and the definition of the subset product with a singleton.