Lemma 88.10.2. Let $\mathcal{F}$ be a category cofibered in groupoids over $\mathcal C_\Lambda $. Then $\mathcal{F}$ satisfies (S1) if the condition of (S1) is assumed to hold only when $A_2 \to A$ is a small extension.

**Proof.**
Proof omitted. Hints: apply Lemma 88.3.3 and use induction similar to the proof of Lemma 88.8.2.
$\square$

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