Proposition 3.1.6.10. Let $f: X_{} \rightarrow S_{}$ be a trivial Kan fibration of simplicial sets. Then $f$ is a homotopy equivalence.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. By virtue of Corollary 1.5.5.5, the morphism $f$ admits a section $s: S \rightarrow X$ such that $s \circ f$ is homotopic to the identity map $\operatorname{id}_{X}$. $\square$