Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that

(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 $X$

The left-closed interval in $P$ from $a$ to $b$ is the D11: Set \begin{equation} [a, b) : = \{ x \in X : a \preceq x \prec b \} \end{equation}