Infimum_Plus_Constant

Let $T$ be a subset of the set of real numbers. Let $T$ be bounded below. Let $\xi \in \R$. Then $\displaystyle \map {\inf_{x \mathop \in T} } {x + \xi} = \xi + \map {\inf_{x \mathop \in T} } x$ where $\inf$ denotes infimum.