Supremum_Plus_Constant

Let $S$ be a subset of the set of real numbers $\R$. Let $S$ be bounded above. Let $\xi \in \R$. Then $\displaystyle \map {\sup_{x \mathop \in S} } {x + \xi} = \xi + \map {\sup_{x \mathop \in S} } x$ where $\sup$ denotes supremum.