Let $x_1, \dots, x_N \in \mathbb{R}$ and $y_1, \dots, y_N \in \mathbb{R}$ each be a D4685: Real sequence.

Then \begin{equation} x \leq y \quad \implies \quad \sum_{n = 1}^N x_n \leq \sum_{n = 1}^N y_n \end{equation}