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by 4ad 731 days ago
Lean (and Coq, and Agda, etc) do not use ZFC, they use variants of MLTT/CiC. Even Isabelle does not use ZFC.
1 comments

Isabelle is generic and supports many object logics, listed in [1]. Isabelle/HOL is most popular, but Isabelle/ZF is also shipped in the distribution bundle for people who prefer set theory (like myself).

[1] https://isabelle.in.tum.de/doc/logics.pdf