Let $n, m \in \mathbb{N}$ each be a D996: Natural number such that

(i)	\begin{equation} 1 \leq m \leq n \end{equation}

Using result R1831: Real arithmetic expression for binomial coefficient, we have \begin{equation} \begin{split} \frac{n + 1}{m + 1} \binom{n}{m} & = \frac{n + 1}{m + 1} \frac{n !}{(n - m) ! m !} \\ & = \frac{(n + 1) !}{(n - m) ! (m + 1) !} = \frac{(n + 1) !}{((n + 1) - (m + 1)) ! (m + 1) !} = \binom{n + 1}{m + 1} \end{split} \end{equation} $\square$