Let $\mathsf{LB} = \mathsf{LB}_P(E)$ be the D553: Set of lower bounds of $E \subseteq X$ with respect to $P$.

A D2218: Set element $x_0 \in X$ is an

**infimum**of $E$ with respect to $P$ if and only if

(1) | $x_0 \in \mathsf{LB}$ |

(2) | $\forall \, x \in \mathsf{LB} : x \preceq x_0$ |