Let $\mathbb{N}$ be the D225: Set of natural numbers such that

(i)	$x^+$ is a D589: Successor set of $x$ for any $x \in \mathbb{N}$

Let $+$ be the D637: Natural number addition operation.
A D554: Binary operation $\cdot : \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ is a natural number multiplication operation if and only if

(1)	\begin{equation} \forall \, n \in \mathbb{N} : n \cdot 0 = 0 \end{equation}
(2)	\begin{equation} \forall \, n, m \in \mathbb{N} : n \cdot m^+ = n \cdot m + n \end{equation}