Invertible Element of Monoid is Cancellable

Corollary to Invertible Element of Associative Structure is Cancellable

Let $\left({S, \circ}\right)$ be a monoid whose identity is $e_S$.

An element of $\left({S, \circ}\right)$ which is invertible is also cancellable.

Proof

By definition of monoid, $\left({S, \circ}\right)$ is an algebraic structure in which $\circ$ is associative.

The result follows from Invertible Element of Associative Structure is Cancellable.

$\blacksquare$