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feat(TMEEMT): fill RS_prime.theorem_b from Dusart corollary 5.2(a) - #1765

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AlexKontorovich:mainfrom
Chessing234:feat/tmeemt-rs-theorem-b-from-dusart
Aug 30, 2026
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feat(TMEEMT): fill RS_prime.theorem_b from Dusart corollary 5.2(a)#1765
teorth merged 3 commits into
AlexKontorovich:mainfrom
Chessing234:feat/tmeemt-rs-theorem-b-from-dusart

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Fixes #1687.

Motivation

TMEEMT asks to fill sorrys that are already stated elsewhere. RS_prime.theorem_b is the wiki's strict form of Dusart 2018 corollary 5.2(a).

Scope

  • Uses Dusart.corollary_5_2_a (π(x) ≥ x / log x for x ≥ 17).
  • Upgrades to > because π is constant on each [n, n+1) while x / log x is strictly increasing for x > e: pick a point y in the same floor interval to the right of x.
  • No other declaration touched.

Test plan

  • lake build PrimeNumberTheoremAnd.IEANTN.TMEEMT — not run locally yet. CI covers it.
  • No new warnings other than declaration uses 'sorry'. The TMEEMT theorem_b sorry goes away; it still depends on the existing sorry in Dusart.corollary_5_2_a.

hyu previously fed floor_le into linarith and asked for the wrong
inequality. Also disambiguate _root_.pi from Filter.pi.
Avoid the empty-goal after field_simp; compare via mul_div_cancel₀ and nlinarith.
@teorth teorth added ai Formalised using AI. cursor Formalized using Cursor labels Aug 30, 2026
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teorth commented Aug 30, 2026

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Small housekeeping nudge: the auto-label workflow (added in #1743) reads the PR body for a disclosure phrase like Made with Cursor or the Co-Authored-By: Cursor footer, and then applies the ai + cursor labels automatically. Most of your recent PRs have the footer; this one doesn't, so I've applied the labels by hand. Keeping the footer in the body will let the workflow do it automatically going forward. Details in PULL_REQUEST_STYLE.md §13.1.

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teorth merged commit b66f961 into AlexKontorovich:main Aug 30, 2026
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[TMEEMT/RS]: Prove RS_prime.theorem_b (π(x) > x/log x for x ≥ 17)

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