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by svara 120 days ago
Can you give some examples of this? Maybe have something online? I would love to learn more about how to do proof driven AI assisted development.
2 comments
Gehinnn 120 days ago
Here is a session that I just had with AI: https://gist.github.com/hediet/e3569a7c6b4b7c4f7d4a7db410104... (summarized by AI).

And here are some examples of the different philosophies of AI proofs and human proofs: https://gist.github.com/hediet/e3569a7c6b4b7c4f7d4a7db410104...

I use VS Code in a beefy Codespace, with GitHub Copilot (Opus 4.5). I have a single instruction file telling the AI to always run "lake build ./lean-file.lean" to get feedback.

(disclaimer: I work on VS Code)

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nwyin 120 days ago
it's a bit dated, but Terence Tao has a video of formalizing a proof with LLMs from 9 months ago which should be illuminating

https://youtu.be/zZr54G7ec7A?si=-l3jIZZzfghoqJtq

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Gehinnn 120 days ago
This is very similar to how I worked with Lean a year ago (of course in a much simpler domain) - mostly manual editing, sometimes accepting an inline completion or next edit suggestion. However, with agentic AI that can run lean via CLI my workflow changed completely and I rarely write full proofs anymore (only intermediate lemma statements or very high level calc statements).
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pvillano 120 days ago
Do lean poofs need to be manually reviewed?

Or is it as long as you formalize your theorem correctly, a valid lean program is an academically useful proof?

Are there any minimal examples of programs which claim to prove the thing without actually proving the thing in a meaningful way?

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Gehinnn 120 days ago
There have been bugs in Lean that allowed people to prove False, from which you can prove anything (they have been fixed).

Otherwise, if you check that no custom axiom has been used (via print axioms), the proof is valid.

It's easy to construct such an example: Prove that for all a, b, c and n between 3 and 10^5, a^n=b^n+c^n has no solution. The unmeaningful proof would enumerate all ~10^20 cases and proof them individually. The meaningful (and probably even shorter) proof would derive this from Fermat's theorem after proving that one.

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