← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (644 chars)
Now the mismatch is only the tail: `3^{−(2√↑n−2)} * 1` vs `3^{−(2√↑n−2)}` — the expected form has NO ·1, the proved form has ·1. The h3 statement's RHS is `3^{−(2√↑n−2)}` (bare), and add_le_add_right gives `3^{−(2√↑n−2)}·1` — mul_one mismatch: close with `by rw [mul_one]` after, or use `simpa using`:
```
exact add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)
(Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))
```
→ then `by rw [mul_one]` or wrap in `by simpa using ...`. Use: `by simpa using add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn) (Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))` — simpa normalizes the ·1 ✓.
Just a `mul_one` mismatch — wrapping with `simpa`.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiDogLeg.lean",
"old_string": " refine h2.trans ?_\n exact add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)\n (Real.log 2 * (2 : \u211d) ^ (-(2 * Real.sqrt (n : \u211d))))",
"new_string": " refine h2.trans ?_\n simpa using add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)\n (Real.log 2 * (2 : \u211d) ^ (-(2 * Real.sqrt (n : \u211d))))"
}
tool: Bash ok
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && export PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiDogLeg.lean 2>&1 | grep -E \"^NguyenRH1.*error\" | head -6; echo DONE",
"description": "Recompile LiDogLeg after the simpa wrap",
"timeout": 300000
}
result 2026-08-26 10:16:39Z → 2026-08-26 10:17:09Z
DONE
raw content_json (database row)
[{"type":"thinking","thinking":"Now the mismatch is only the tail: `3^{−(2√↑n−2)} * 1` vs `3^{−(2√↑n−2)}` — the expected form has NO ·1, the proved form has ·1. The h3 statement's RHS is `3^{−(2√↑n−2)}` (bare), and add_le_add_right gives `3^{−(2√↑n−2)}·1` — mul_one mismatch: close with `by rw [mul_one]` after, or use `simpa using`:\n```\n exact add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)\n (Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))\n```\n→ then `by rw [mul_one]` or wrap in `by simpa using ...`. Use: `by simpa using add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn) (Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))` — simpa normalizes the ·1 ✓.","signature":""},{"type":"text","text":"Just a `mul_one` mismatch — wrapping with `simpa`."},{"type":"tool_use","id":"Edit_491","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiDogLeg.lean","old_string":" refine h2.trans ?_\n exact add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)\n (Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))","new_string":" refine h2.trans ?_\n simpa using add_le_add_right (mul_le_mul_of_nonneg_left hC2 hnn)\n (Real.log 2 * (2 : ℝ) ^ (-(2 * Real.sqrt (n : ℝ))))"},"extra_content":null},{"type":"tool_use","id":"Bash_492","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && export PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiDogLeg.lean 2>&1 | grep -E \"^NguyenRH1.*error\" | head -6; echo DONE","description":"Recompile LiDogLeg after the simpa wrap","timeout":300000},"extra_content":null}]