https://randylai.info/tags/lean/ Recent content in Lean on Randy Lai Hugo en-us Wed, 21 Oct 2026 00:00:00 +0000 https://randylai.info/post/2026/mse_of_sample_sd_lean/ Wed, 21 Oct 2026 00:00:00 +0000 https://randylai.info/post/2026/mse_of_sample_sd_lean/ <p>Back in 2023, I wrote a <a href="https://randylai.info/post/2023/mse_of_sample_sd_cont/">post</a> using SymPy to compute the second order expansion of the mean squared error (MSE) of the sample standard deviation up to $O(n^{-2})$. Earlier this year, I revisited the problem in <a href="https://randylai.info/post/2026/mse_of_sample_sd_gen_ai/">MSE of sample standard deviation (Gen AI)</a> and showed that a modern LLM can derive the entire second order expansion directly from a prompt.</p> <p>When an AI produces a long asymptotic derivation with dozens of polynomial moment terms, how can we trust that every coefficient is right and that no terms of order $n^{-2}$ were dropped? To check the derivation rigorously, I formalized and verified the entire proof in <a href="https://lean-lang.org/">Lean 4</a> with <a href="https://github.com/leanprover-community/mathlib4">Mathlib</a>.</p>