Let $\Omega$ be an open bounded subset of $\mathbb{R}^n$. For $h\in\mathbb{R}^n$ and $\delta>0$, define $$ \Omega^h:=\{x-h:x\in\Omega\},\quad\Omega_{\delta}:=\{x\in\Omega:d(x, \partial\Omega)>\delta\} $$ (where "$d$" denotes the distance). I don't understand why, if $|h|<\delta$, then $(\Omega_{\delta})^h\subset\Omega$. Some hints?
Thank You