Definition:Finite Suprema Set

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

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

Then finite suprema set of $X$, denoted $\map {\mathrm {finsups} } X$, is defined by:

$\leftset {\sup A: A \in \map {\mathit {Fin} } X \land A}$ admits a supremum$\rightset{}$

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