← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
thinking (607 chars)
`Rectangle` comes from PrimeNumberTheoremAnd's Rectangle.lean — it's likely `Rectangle z w := [[z.re, w.re]] ×ℂ [[z.im, w.im]]` (from that project). The membership form: via the RectangleBorder proof pattern in LiSides:147: `obtain ⟨h1, h2⟩ := hmem; have h1' : z.re ≤ p.re ∧ p.re ≤ w.re := by simpa [Set.uIcc_of_le hre] using h1` — so membership gives two uIcc memberships (re and im) ✓. That's all I need (I don't need the exact def — the membership decomposes as ⟨re-uIcc, im-uIcc⟩).
Now write the LiContour additions. Append to LiContour.lean before the end. Let me check the file's end structure first.
Rectangle membership decomposes as re/im uIcc pairs — all I need. Appending the perimeter Props + wide pigeonhole to LiContour.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && tail -12 NguyenRH1/LiContour.lean && grep -n \"^import\\|^end\" NguyenRH1/LiContour.lean | head -8",
"description": "Check LiContour end + imports"
}
raw content_json (database row)
[{"type":"thinking","thinking":"`Rectangle` comes from PrimeNumberTheoremAnd's Rectangle.lean — it's likely `Rectangle z w := [[z.re, w.re]] ×ℂ [[z.im, w.im]]` (from that project). The membership form: via the RectangleBorder proof pattern in LiSides:147: `obtain ⟨h1, h2⟩ := hmem; have h1' : z.re ≤ p.re ∧ p.re ≤ w.re := by simpa [Set.uIcc_of_le hre] using h1` — so membership gives two uIcc memberships (re and im) ✓. That's all I need (I don't need the exact def — the membership decomposes as ⟨re-uIcc, im-uIcc⟩).\n\nNow write the LiContour additions. Append to LiContour.lean before the end. Let me check the file's end structure first.","signature":""},{"type":"text","text":"Rectangle membership decomposes as re/im uIcc pairs — all I need. Appending the perimeter Props + wide pigeonhole to LiContour."},{"type":"tool_use","id":"Bash_252","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && tail -12 NguyenRH1/LiContour.lean && grep -n \"^import\\|^end\" NguyenRH1/LiContour.lean | head -8","description":"Check LiContour end + imports"},"extra_content":null}]