Let $x, y : \mathbb{N} \to \mathbb{R}$ each be a D4685: Real sequence such that

(i)	\begin{equation} \forall \, n \in \mathbb{N} : x_n \leq y_n \end{equation}
(ii)	\begin{equation} \lim_{N \to \infty} \sum_{n = 0}^N x_n \neq \emptyset \neq \lim_{N \to \infty} \sum_{n = 0}^N y_n \end{equation}

Then \begin{equation} \lim_{N \to \infty} \sum_{n = 0}^N x_n \leq \lim_{N \to \infty} \sum_{n = 0}^N y_n \end{equation}