Prove-It
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Only unary/binary functions in the core
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I'm not sure how well this would work or if it would be desirable, but what if n-ary functions were implemented as definitions outside of the core? This would simplify proof-checking, but proofs would be longer. This may (or may not) be a desirable trade. Alternatively, we could keep the core as is but translate proofs from into something that can be checked by a simpler proof-checker. It's worth exploring the possibilities before deciding.