Exercise 8.1.8.7. Show that Theorem 8.1.8.4 follows from Corollary 8.1.8.6. In other words, to prove Theorem 8.1.8.4, there is no loss of generality in assuming that $\operatorname{\mathcal{A}}$ has the form $\{ 0 < 1 < \cdots < n \} $ for some integer $n \geq 0$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$