Exercise 7.4.5.14. Let $\overline{U}: \overline{\operatorname{\mathcal{E}}} \rightarrow \operatorname{\mathcal{C}}^{\triangleright }$ and $\overline{U}': \overline{\operatorname{\mathcal{E}}}' \rightarrow \operatorname{\mathcal{C}}^{\triangleright }$ be cocartesian fibrations of simplicial sets which are equivalent as inner fibrations over $\operatorname{\mathcal{C}}^{\triangleright }$ (in the sense of Definition 5.1.7.1). Show that $\overline{U}$ satisfies condition $(\ast )$ of Theorem 7.4.5.11 if and only if $\overline{U}'$ satisfies condition $(\ast )$ of Theorem 7.4.5.11.
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