$\forall$$g$:IMonoid, $e$:$\mid$$g$$\mid$, $a$, $b$:$\mathbb{N}$. (($a$+$b$) $\cdot$ $e$) = (($a$ $\cdot$ $e$) $\ast$ ($b$ $\cdot$ $e$)) $\in$ $\mid$$g$$\mid$