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Conversion of proofs between HoTT and ZFC

HoTT provides a foundation of math that remains mysterious for many mathematicians including me. Hence this question. There are several implementations of math based on ZFC, an example being MetaMath. ...
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Proof formalization

I read some time ago some papers about proof formalization. Typically, I began whith this one, from Lamport. Are there more recent works in this field ?