Subset Product with Identity

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

Suppose that $\left({S,\circ}\right)$ has an identity element $e$.

Let $A \subseteq S$.

Then $e \circ S = S \circ e = S$, where $\circ$ is understood to be the subset product with singleton.

Proof
Thus:
 * $e \circ S = S$

A precisely similar argument shows that:
 * $S \circ e = S$