← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (407 chars)
The parse is `HMul.hMul (Neg.neg (2^(j+1))) X` — so the abs argument is `(−2^{j+1}) · X` — a product whose first factor is negated. The probe's second example (rw [neg_mul, abs_neg, abs_of_nonneg h]) didn't error this time (no error shown for the example)! So `rw [neg_mul, abs_neg, abs_of_nonneg h]` works: neg_mul : (−a)·b = −(a·b) → then abs_neg → abs_of_nonneg ✓. Let me apply that form in hlog2's hmax.
The parse is `(−2^(j+1))·X` — needs `neg_mul` first. Fixing the two abs-neg sites and the hdisj lower bound.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiCircleBound.lean",
"old_string": " have hdisj : Disjoint hW1.toFinset hW2.toFinset := by\n rw [Finset.disjoint_left]\n intro z hz1 hz2\n rw [Set.Finite.mem_toFinset] at hz1 hz2\n have h1 : (2 : \u211d) ^ j * X - 1 < z.im := hz1.2.1\n have h2 : z.im \u2264 -((2 : \u211d) ^ j * X) := hz2.2.2\n linarith",
"new_string": " have hdisj : Disjoint hW1.toFinset hW2.toFinset := by\n rw [Finset.disjoint_left]\n intro z hz1 hz2\n rw [Set.Finite.mem_toFinset] at hz1 hz2\n have h1 : (2 : \u211d) ^ j * X - 1 < z.im := hz1.2.1\n have h2 : z.im \u2264 -((2 : \u211d) ^ j * X) := hz2.2.2\n have hge : (1 : \u211d) \u2264 (2 : \u211d) ^ j * X := by\n have h1le : (1 : \u211d) \u2264 (2 : \u211d) ^ j := by exact_mod_cast Nat.one_le_two_pow\n nlinarith [h1le, hX]\n linarith"
}
raw content_json (database row)
[{"type":"thinking","thinking":"The parse is `HMul.hMul (Neg.neg (2^(j+1))) X` — so the abs argument is `(−2^{j+1}) · X` — a product whose first factor is negated. The probe's second example (rw [neg_mul, abs_neg, abs_of_nonneg h]) didn't error this time (no error shown for the example)! So `rw [neg_mul, abs_neg, abs_of_nonneg h]` works: neg_mul : (−a)·b = −(a·b) → then abs_neg → abs_of_nonneg ✓. Let me apply that form in hlog2's hmax.","signature":""},{"type":"text","text":"The parse is `(−2^(j+1))·X` — needs `neg_mul` first. Fixing the two abs-neg sites and the hdisj lower bound."},{"type":"tool_use","id":"Edit_396","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiCircleBound.lean","old_string":" have hdisj : Disjoint hW1.toFinset hW2.toFinset := by\n rw [Finset.disjoint_left]\n intro z hz1 hz2\n rw [Set.Finite.mem_toFinset] at hz1 hz2\n have h1 : (2 : ℝ) ^ j * X - 1 < z.im := hz1.2.1\n have h2 : z.im ≤ -((2 : ℝ) ^ j * X) := hz2.2.2\n linarith","new_string":" have hdisj : Disjoint hW1.toFinset hW2.toFinset := by\n rw [Finset.disjoint_left]\n intro z hz1 hz2\n rw [Set.Finite.mem_toFinset] at hz1 hz2\n have h1 : (2 : ℝ) ^ j * X - 1 < z.im := hz1.2.1\n have h2 : z.im ≤ -((2 : ℝ) ^ j * X) := hz2.2.2\n have hge : (1 : ℝ) ≤ (2 : ℝ) ^ j * X := by\n have h1le : (1 : ℝ) ≤ (2 : ℝ) ^ j := by exact_mod_cast Nat.one_le_two_pow\n nlinarith [h1le, hX]\n linarith"},"extra_content":null}]