The Deletion Index Map

In the setting of Routine Facts Used Without Citation: Arithmetic, Maps, Predicativity and Indices, let $n\in\mathbb{N}$ with $2\le n$ and let $i\in[n]$, with $[n]$ and $[n-1]$ as in Intervals of Natural Numbers §segment and the difference $n-1\in\mathbb{N}$ as in The Index Map Skipping One Element of [n] §difference.

¶ The deletion index map $s_{i}:[n-1]\to[n]$ is the map $s$ of The Index Map Skipping One Element of [n] §map, so that $s_{i}(k)=k$ for every $k\in[n-1]$ with $k<i$ and $s_{i}(k)=k+1$ for every $k\in[n-1]$ with $i\le k$.