Definition:Infima Inheriting

Definition
Let $L = \left({S, \preceq}\right)$ be an ordered set.

Let $R = \left({T, \preceq'}\right)$ be an ordered subset of $L$.

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