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fix(Dusart): make corollary_5_3_a a strict inequality - #1708

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teorth merged 5 commits into
AlexKontorovich:mainfrom
Chessing234:fix/pi-star-and-dusart-statements
Aug 30, 2026
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fix(Dusart): make corollary_5_3_a a strict inequality#1708
teorth merged 5 commits into
AlexKontorovich:mainfrom
Chessing234:fix/pi-star-and-dusart-statements

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@Chessing234

@Chessing234 Chessing234 commented Jul 24, 2026

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Motivation

Dusart / Art01 use a strict lower bound for π(x) at x ≥ 5393. corollary_5_3_a was stubbed with non-strict , which disagreed with TMEEMT.pi_inequality and the cited paper.

Scope

Rebased onto current main. The π* / Buthe ψ index-from-1 fixes from the earlier tip are already on main, so this PR keeps only:

  • Dusart.corollary_5_3_a: docstring + statement use >
  • TMEEMT.pi_inequality comment aligned with the now-strict corollary

Test plan

  • CI Lean build

Chessing234 and others added 4 commits July 24, 2026 09:30
Co-authored-by: Cursor <cursoragent@cursor.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
@Chessing234

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awaiting-review

@Chessing234

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Superseded by #1713 (combine; drops Dusart 5.3(a) strictness).

@teorth teorth added ai Formalised using AI. cursor Formalized using Cursor labels Aug 3, 2026
@Chessing234 Chessing234 reopened this Aug 29, 2026
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reopening — the indexing fixes landed, but the strict 5.3(a) statement remains needed; branch needs rebase.

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reopening for the dusart 5.3(a) strictness that #1713 dropped; will rebase onto tip next.

Index fixes for π* / Buthe ψ already landed on main; keep the
strict Dusart corollary_5_3_a statement and align the TMEEMT note.
@Chessing234 Chessing234 changed the title fix: π* / Buthe ψ index from 1; Dusart 5.3(a) strict fix(Dusart): make corollary_5_3_a a strict inequality Aug 29, 2026
@teorth

teorth commented Aug 30, 2026

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Cross-PR coordination note: this PR tightens Dusart.corollary_5_3_a from to >. Meanwhile #1767 fills TMEEMT.pi_inequality using the current non-strict Dusart.corollary_5_3_a via a midpoint-of-Ico ⌊x⌋₊ (⌊x⌋₊+1) upgrade. The two PRs collide in two ways:

  1. Both touch the same comment inside TMEEMT.pi_inequality — text conflict on rebase.
  2. If this PR merges first, feat(TMEEMT): fill Dusart1999.pi_inequality from Dusart corollary 5.3(a) #1767's lt_of_lt_of_le hstrict hge type-mismatches because hge is now < rather than .

Suggested resolution: merge this one first (it fixes the API at the right layer of the paper's proof chain). #1767's proof can then collapse to

theorem pi_inequality (x : ℝ) (hx : x ≥ 5393) :
    _root_.pi x > x / (log x - 1) := Dusart.corollary_5_3_a hx

and the midpoint trick becomes unnecessary. Alternatively, @Chessing234 you could consolidate #1708 + #1767 into one PR.

@teorth
teorth merged commit a515467 into AlexKontorovich:main Aug 30, 2026
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2 participants