Remark 4.7.1.13 (Transitivity). Let $(R, \leq )$, $(S, \leq )$, and $(T, \leq )$ be linearly ordered sets. Suppose that $f: R \hookrightarrow S$ and $g: S \hookrightarrow T$ are initial segment embeddings. Then the composition $(g \circ f): R \hookrightarrow T$ is also an initial segment embedding.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$