Lemma 78.17.3. The notions of restricting groupoids and (pre-)equivalence relations defined in Definitions 78.17.2 and 78.4.3 agree via the constructions of Lemmas 78.11.2 and 78.11.3.
Proof. What we are saying here is that R' of Lemma 78.17.1 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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