Isomorphism_to_Closed_Interval

Let $m, n \in \N$ such that $m < n$. Then $\left|{\left[{m + 1 \,.\,.\, n}\right]}\right| = n - m$ Let $h: \N_{n - m} \to \left[{m + 1 \,.\,.\, n}\right]$ be the mapping defined as $\forall x \in \N_{n - m}: h \left({x}\right) = x + m + 1$ Let the orderings on $\left[{m + 1 \,.\,.\, n}\right]$ and $\N_{n - m}$ be those induced by the ordering of $\N$. Then $h$ a unique order isomorphism.