Definition:Finite Infima Set

Definition
Let $P = \struct{S, \preceq}$ be an ordered set.

Let $X$ be a subset of $S$.

Then finite infima set of $X$, denoted $\map {\operatorname{fininfs}} X$, is defined by
 * $\leftset {\inf A: A \in \map {\mathit{Fin}} X \land A}$ admits an infimum$\rightset{}$

where $\map {\mathit{Fin}} X$ denotes the set of all finite subsets of $X$.