Right Regular Representation of Subset Product

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

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

Let $\rho_a: S \to S$ be the right regular representation of $S$ with respect to $a$.

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

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

Also see

 * Left Regular Representation of Subset Product