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+\subsection*{Exercise 04 (Gapry)}
+Let $S$ is an ordered set, $E \subset S$ 
+\begin{flushleft}
+$\exists\ \beta \in S \ni x \leq \beta \ \forall x \in E \cdots \text{(1)}$   \\
+$\exists\ \alpha \in S \ni x \geq \alpha \ \forall x \in E \cdots \text{(2)}$ \\
+$\text{(1)} \land \text{(2)} \implies \alpha \leq x \leq \beta \implies \alpha \leq \beta$
+\end{flushleft}