I recently set myself the exercise of using modern automated tools - in particular, a combination of the large language model and the dependent type matching tactic - to try to semi-automatically formalize in a one-page proof provided by a collaborator of the (Bruno Le Floch). With these tools, I was able to more or less blindly do the formalization in 33 minutes, withou any real high level conception of how the proof proceeded. It was a very different style to how I usually formalize results, but was workable for this type of technical, non-conceptual argument where the main issue is to get the details correct rather than the "big picture".

I recorded my attempt at youtube.com/watch?v=cyyR7j2ChC . See also additional discussion at leanprover.zulipchat.com/#narr . The final proof (which is far from optimized, but got the job done) can be found at github.com/teorth/estimate_too

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