> you need to review only the lines that correspond to the theorem that you want to prove and their types

This is (unfortunately) not actually the case—just a few weeks ago, someone "proved" the Collatz conjecture via a Lean proof 1) whose theorem statement was correct, 2) typechecked, and 3) was even verified by external tools with their own implementations of the kernel.[0]

The problem was (AFAIK) that the Lean kernel has a lot of fancy features that aren't yet perfectly understood from a type-theoretic perspective (I don't think Lean is unique in this regard; pretty sure Rocq and Agda are in a similar situation). And so when the kernel implements some feature whose soundness isn't guaranteed, the independent verification tools (or at least some of them) follow suit, and now any issues in the former affect the latter as well.

[0] See e.g. https://x.com/gro_tsen/status/2082483878480977959 for more detail