A D11: Set $\mathcal{S} \subseteq \mathcal{P}(X)$ is a proper set partition of $X$ if and only if
(1) | \begin{equation} X = \cup \mathcal{S} \end{equation} | D4984: Tight set cover |
(2) | \begin{equation} \forall \, E, F \in \mathcal{S} \left( E \neq F \quad \implies \quad E \cap F = \emptyset \right) \end{equation} | D1681: Disjoint set collection |
(3) | \begin{equation} \forall \, E \in \mathcal{S} : E \neq \emptyset \end{equation} |