The Segments [n]: Each Is a Set, and 1 Lies in [n] for n ∈ ℕ

This helper adopts the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, with $\mathbb{N}$, $\mathbb{N}_{0}$ and $1$ as in The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion §sets, and $[n]$ as in Intervals of Natural Numbers §segment.

¶ For every $n\in\mathbb{N}_{0}$, $[n]$ is a set, and $[n]\subseteq\mathbb{N}_{0}$.

¶ For every $n\in\mathbb{N}$, $1\in[n]$.