Left Regular Representation of Subset Product

Theorem
Let $\struct {S, \circ}$ be a magma.

Let $T \subseteq S$ be a subset of $S$.

Let $\lambda_a: S \to S$ be the left regular representation of $S$ with respect to $a$.

Then:
 * $\lambda_a \sqbrk T = \set a \circ T = a \circ T$

where $a \circ T$ denotes subset product with a singleton.