feat: add Szemerédi's theorem eval problem#285
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This PR adds Szemerédi's theorem (§37 of Knill's "Some Fundamental Theorems in Mathematics", the section's first additional statement generalizing Roth's theorem from 3-APs to k-APs) as a new eval problem: every subset of ℕ of positive upper density contains arbitrarily long arithmetic progressions. Mathlib has Roth's theorem (the k=3 case) but not the full Szemerédi theorem, which has not yet been formalized in any major proof assistant. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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May 22, 2026
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| Filter.limsup | ||
| (fun n : ℕ => | ||
| (∑ k ∈ Finset.range (n + 1), A.indicator (fun _ => (1 : ℝ)) k) / (n + 1)) | ||
| Filter.atTop |
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This is a roundabout way to define it. How about
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| Filter.limsup | |
| (fun n : ℕ => | |
| (∑ k ∈ Finset.range (n + 1), A.indicator (fun _ => (1 : ℝ)) k) / (n + 1)) | |
| Filter.atTop | |
| Filter.atTop.limsup fun n : ℕ ↦ (A ∩ .Iio n).ncard / n |
and you can then remove open scoped BigOperators
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This PR adds Szemerédi's theorem as a new lean-eval challenge problem — §37 of Oliver Knill's Some Fundamental Theorems in Mathematics, the section's first additional statement (generalizing Roth's theorem from 3-APs to
k-APs).Every subset of
ℕof positive upper density contains arbitrarily long arithmetic progressions.mathlib has Roth's theorem (
roth_3ap_theorem_nat, thek = 3case) but not the full Szemerédi theorem. As of 2026 it has not been formalized in any major proof assistant — a well-known open formalization target.🤖 Prepared with Claude Code