Subset Relation is Compatible with Subset Product/Corollary 2

Theorem
Let $\struct {S, \circ}$ be a magma. Let $A, B \in \powerset S$, 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.