Infimum_of_Subset

Let $\struct {U, \preceq}$ be an ordered set. Let $S \subseteq U$. Let $T \subseteq S$. Let $\struct {S, \preceq}$ admit an infimum in $U$. If $T$ also admits an infimum in $U$, then $\map \inf S \preceq \map \inf T$.