Lemma 77.17.3. The notions of restricting groupoids and (pre-)equivalence relations defined in Definitions 77.17.2 and 77.4.3 agree via the constructions of Lemmas 77.11.2 and 77.11.3.

**Proof.**
What we are saying here is that $R'$ of Lemma 77.17.1 is also equal to

\[ R' = (U' \times _ B U')\times _{U \times _ B U} R \longrightarrow U' \times _ B U' \]

In fact this might have been a clearer way to state that lemma. $\square$

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