fix(Dusart): make corollary_5_3_a a strict inequality - #1708
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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>
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awaiting-review |
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Superseded by #1713 (combine; drops Dusart 5.3(a) strictness). |
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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.
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Cross-PR coordination note: this PR tightens
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 hxand the midpoint trick becomes unnecessary. Alternatively, @Chessing234 you could consolidate #1708 + #1767 into one PR. |
Motivation
Dusart / Art01 use a strict lower bound for π(x) at x ≥ 5393.
corollary_5_3_awas stubbed with non-strict≥, which disagreed withTMEEMT.pi_inequalityand 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_inequalitycomment aligned with the now-strict corollaryTest plan