Exercise 3.6.6.7. Show that, for every pair of integers $0 \leq i \leq n$ with $n > 0$, there exists a homeomorphism of topological spaces
\[ h: [0,1] \times | \Delta ^{n-1} | \simeq | \Delta ^{n} | \]
which restricts to a homeomorphism of $\{ 0\} \times | \Delta ^{n-1} |$ with the horn $| \Lambda ^{n}_{i} | \subset | \Delta ^ n |$. Use this homeomorphism to give a more direct proof of Proposition 3.6.6.5.