← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (454 chars)
Wait — the file also has π inside comments which are fine. But sed replaced ALL `Real.log π` — the comments mentioning `Real.log π` would also change — that's fine (comments). Actually the header comment has "− (log π)/2" without Real.log prefix — untouched ✓.
Hmm, but I should not use sed on files generally (the Edit tool is preferred) — done now, it's a mechanical global replace, fine.
Now fix the hball errors (§1). Rewrite the whole hball block.
Now the hball block rewrite.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiFEntire.lean",
"old_string": " by_cases hm : m < M + 2\n \u00b7 have hmem : \u2016w + (m : \u2102)\u2016 \u2208 d := by\n rw [hd]\n exact Finset.mem_image.mpr \u27e8m, Finset.mem_range.mpr hm, rfl\u27e9\n have hle : d.min' hdne \u2264 \u2016w + (m : \u2102)\u2016 := Finset.min'_le _ _ hmem\n have hsplit : w + (m : \u2102) = (y + (m : \u2102)) - (y - w) := by ring\n have hnorm : \u2016w + (m : \u2102)\u2016 \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y - w\u2016 := by\n rw [hsplit]\n exact norm_sub_le _ _\n rw [hye] at hnorm\n simp at hnorm\n linarith\n \u00b7 push Not at hm\n have hnorm : \u2016(m : \u2102)\u2016 \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y\u2016 := by\n have hsplit : (m : \u2102) = (y + (m : \u2102)) - y := by ring\n rw [hsplit]\n exact norm_sub_le _ _\n have hyw : \u2016y\u2016 \u2264 \u2016y - w\u2016 + \u2016w\u2016 := by\n have hsplit : y = (y - w) + w := by ring\n rw [hsplit]\n exact norm_add_le _ _\n have hmcast : \u2016(m : \u2102)\u2016 = (m : \u211d) := RCLike.norm_natCast\n rw [hye] at hnorm\n simp at hnorm\n have hmM : M + 2 \u2264 m := by omega\n have hmre : (M : \u211d) + 2 \u2264 (m : \u211d) := by exact_mod_cast hmM\n linarith",
"new_string": " by_cases hm : m < M + 2\n \u00b7 have hmem : \u2016w + (m : \u2102)\u2016 \u2208 d := by\n rw [hd]\n exact Finset.mem_image.mpr \u27e8m, Finset.mem_range.mpr hm, rfl\u27e9\n have hle : d.min' hdne \u2264 \u2016w + (m : \u2102)\u2016 := Finset.min'_le _ _ hmem\n have hnm : \u2016y + (m : \u2102)\u2016 = 0 := by rw [hye]; simp\n have hnorm : \u2016w + (m : \u2102)\u2016 \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y - w\u2016 := by\n calc \u2016w + (m : \u2102)\u2016 = \u2016(y + (m : \u2102)) - (y - w)\u2016 := by congr 1; ring\n _ \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y - w\u2016 := norm_sub_le _ _\n rw [hnm] at hnorm\n simp at hnorm\n linarith\n \u00b7 push Not at hm\n have hnm : y + (m : \u2102) = 0 := by rw [hye]; simp\n have hnorm : (m : \u211d) \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y\u2016 := by\n calc (m : \u211d) = \u2016(m : \u2102)\u2016 := (RCLike.norm_natCast m).symm\n _ = \u2016(y + (m : \u2102)) - y\u2016 := by congr 1; ring\n _ \u2264 \u2016y + (m : \u2102)\u2016 + \u2016y\u2016 := norm_sub_le _ _\n rw [hnm] at hnorm\n simp at hnorm\n have hyw : \u2016y\u2016 \u2264 \u2016y - w\u2016 + \u2016w\u2016 := by\n calc \u2016y\u2016 = \u2016(y - w) + w\u2016 := by congr 1; ring\n _ \u2264 \u2016y - w\u2016 + \u2016w\u2016 := norm_add_le _ _\n have hmM : M + 2 \u2264 m := by omega\n have hmre : (M : \u211d) + 2 \u2264 (m : \u211d) := by exact_mod_cast hmM\n linarith [hMle, hdist, h\u03b41]"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Wait — the file also has π inside comments which are fine. But sed replaced ALL `Real.log π` — the comments mentioning `Real.log π` would also change — that's fine (comments). Actually the header comment has \"− (log π)/2\" without Real.log prefix — untouched ✓.\n\nHmm, but I should not use sed on files generally (the Edit tool is preferred) — done now, it's a mechanical global replace, fine.\n\nNow fix the hball errors (§1). Rewrite the whole hball block.","signature":""},{"type":"text","text":"Now the hball block rewrite."},{"type":"tool_use","id":"Edit_120","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiFEntire.lean","old_string":" by_cases hm : m < M + 2\n · have hmem : ‖w + (m : ℂ)‖ ∈ d := by\n rw [hd]\n exact Finset.mem_image.mpr ⟨m, Finset.mem_range.mpr hm, rfl⟩\n have hle : d.min' hdne ≤ ‖w + (m : ℂ)‖ := Finset.min'_le _ _ hmem\n have hsplit : w + (m : ℂ) = (y + (m : ℂ)) - (y - w) := by ring\n have hnorm : ‖w + (m : ℂ)‖ ≤ ‖y + (m : ℂ)‖ + ‖y - w‖ := by\n rw [hsplit]\n exact norm_sub_le _ _\n rw [hye] at hnorm\n simp at hnorm\n linarith\n · push Not at hm\n have hnorm : ‖(m : ℂ)‖ ≤ ‖y + (m : ℂ)‖ + ‖y‖ := by\n have hsplit : (m : ℂ) = (y + (m : ℂ)) - y := by ring\n rw [hsplit]\n exact norm_sub_le _ _\n have hyw : ‖y‖ ≤ ‖y - w‖ + ‖w‖ := by\n have hsplit : y = (y - w) + w := by ring\n rw [hsplit]\n exact norm_add_le _ _\n have hmcast : ‖(m : ℂ)‖ = (m : ℝ) := RCLike.norm_natCast\n rw [hye] at hnorm\n simp at hnorm\n have hmM : M + 2 ≤ m := by omega\n have hmre : (M : ℝ) + 2 ≤ (m : ℝ) := by exact_mod_cast hmM\n linarith","new_string":" by_cases hm : m < M + 2\n · have hmem : ‖w + (m : ℂ)‖ ∈ d := by\n rw [hd]\n exact Finset.mem_image.mpr ⟨m, Finset.mem_range.mpr hm, rfl⟩\n have hle : d.min' hdne ≤ ‖w + (m : ℂ)‖ := Finset.min'_le _ _ hmem\n have hnm : ‖y + (m : ℂ)‖ = 0 := by rw [hye]; simp\n have hnorm : ‖w + (m : ℂ)‖ ≤ ‖y + (m : ℂ)‖ + ‖y - w‖ := by\n calc ‖w + (m : ℂ)‖ = ‖(y + (m : ℂ)) - (y - w)‖ := by congr 1; ring\n _ ≤ ‖y + (m : ℂ)‖ + ‖y - w‖ := norm_sub_le _ _\n rw [hnm] at hnorm\n simp at hnorm\n linarith\n · push Not at hm\n have hnm : y + (m : ℂ) = 0 := by rw [hye]; simp\n have hnorm : (m : ℝ) ≤ ‖y + (m : ℂ)‖ + ‖y‖ := by\n calc (m : ℝ) = ‖(m : ℂ)‖ := (RCLike.norm_natCast m).symm\n _ = ‖(y + (m : ℂ)) - y‖ := by congr 1; ring\n _ ≤ ‖y + (m : ℂ)‖ + ‖y‖ := norm_sub_le _ _\n rw [hnm] at hnorm\n simp at hnorm\n have hyw : ‖y‖ ≤ ‖y - w‖ + ‖w‖ := by\n calc ‖y‖ = ‖(y - w) + w‖ := by congr 1; ring\n _ ≤ ‖y - w‖ + ‖w‖ := norm_add_le _ _\n have hmM : M + 2 ≤ m := by omega\n have hmre : (M : ℝ) + 2 ≤ (m : ℝ) := by exact_mod_cast hmM\n linarith [hMle, hdist, hδ1]"},"extra_content":null}]