Definition:Infima Inheriting

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Definition

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

Let $R = \struct {T, \preceq'}$ be an ordered subset of $L$.


Then $R$ inherits infima of $L$ if and only if

for all subsets $X$ of $T$ if $X$ admits an infimum of $L$, then
$X$ admits an infimum of $R$ and $\inf_R X = \inf_L X$


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