(i) | \begin{equation} X \neq \emptyset \end{equation} |

(ii) | $a, b \in X$ are each a D2218: Set element in $X$ |

(iii) | ${\prec}$ is the D5350: Partial ordering relation strictisation of ${\preceq}$ on $X$ |

**right-closed interval**in $P$ from $a$ to $b$ is the D11: Set \begin{equation} (a, b] : = \{ x \in X : a \prec x \preceq b \} \end{equation}