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The paper On Gödel's theorems on lengths of proofs I: Number of lines and speedup for arithmetics contains quite interesting results on proof length. But some of the details are still, to me, a bit fuzzy [I now find a lot of non-formalized mathematics a bit fuzzy, an occupational hazard it seems].

There is a somewhat related thread on here, but it doesn't link to machine-checked formalizations.

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    $\begingroup$ I don’t follow formalized mathematics, but it’s extremely unlikely. In this field, pretty much nothing at all has been formalized. $\endgroup$ – Emil Jeřábek Dec 14 '19 at 7:33

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