\begin{definition}[Definition:Infima Inheriting]
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 $L$ {{iff}}
:for all subsets $X$ of $T$ if $X$ admits an infimum of $L$, then
::$X$ admits an infimum of $R$ and $\inf_R X = \inf_L X$
\end{definition}