[{"type":"thinking","thinking":"More errors:\n\n1. Line 1774: one more `lt_of_not_le` (in hsub's hpowle — the pattern `lt_of_not_le hρF.2.1` — my replace only caught `lt_of_not_le hρ3`). Fix: `lt_of_not_ge hρF.2.1`.\n\n2. Line 1811 (hmax): `nlinarith [h3, h4]` failed on `max (2^j−1) (2^(j+1)) = 2^(j+1)` — nlinarith can't do max. Use `max_eq_right`: max_eq_right (h : a ≤ b) : max a b = b. Need 2^j−1 ≤ 2^{j+1}: linarith [h3, h4]: 2^{j+1} = 2·2^j ≥ 2·2 = 4 > 2^j−1 ✓. So `exact max_eq_right (by linarith [h3, h4])`. But careful — the goal's max is `max (2^j−1) (2^(j+1))` — after rw [h1, h2] — h1 : |2^{j+1}| = 2^{j+1}, h2 : |2^j−1| = 2^j−1: goal becomes max (2^j−1) (2^{j+1}) = 2^{j+1}: max_eq_right ✓.\n\n3. `Finset.eq_empty_iff_forall_not_mem` doesn't exist — use `Finset.eq_empty_iff_forall_notMem` (camelCase, like indicator_of_notMem) or `Finset.eq_empty_iff_forall_not_mem`... The banked gotcha says camelCase notMem in this Mathlib. Use `Finset.eq_empty_iff_forall_notMem`. Let me check: there's `Finset.eq_empty_iff_forall_notMem : s = ∅ ↔ ∀ x, x ∉ s`. Yes.\n\n4. Line 1817: \"No goals\" — after the failed eq_empty the subsequent tactics error. Will re-check after fixing 3.\n\n5. Line 1829: `mul_nonneg (by norm_num) A0count_pos.le (by positivity)` — mul_nonneg takes TWO args: mul_nonneg (ha : 0 ≤ a) (hb : 0 ≤ b). I passed three: `mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1` — wait the original: `exact mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1` — the INNER mul_nonneg got 3 args: (by norm_num) A0count_pos.le (by positivity) — the target 0 ≤ 3 * A0count * (2^j+3): = 3 * (A0count * (2^j+3)) or (3*A0count)*(2^j+3)? mul_nonneg a b : 0 ≤ a*b. For 3*A0count*(2^j+3) parsed as (3*A0count)*(2^j+3): mul_nonneg (h : 0 ≤ 3*A0count) (by positivity : 0 ≤ 2^j+3): inner = mul_nonneg (by norm_num : (0:ℝ) ≤ 3) A0count_pos.le. So: `mul_nonneg (mul_nonneg (by norm_num : (0:ℝ) ≤ 3) A0count_pos.le) (by positivity)`. My code had `mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1` — the inner has 3 args (error \"Function expected at mul_nonneg ?m A0count_pos.le\" — because mul_nonneg (by norm_num) A0count_pos.le is already complete, then (by positivity) is an extra arg). Fix to the 2-arg nesting. Wait — also the outer target: 0 ≤ 3 * A0count * (2^j + 3) * Real.log(...): the sum-empty goal is `0 ≤ 3 * A0count * (2 ^ j + 3) * Real.log (3 * 2 ^ (j + 1) + 5)`: = ((3*A0count)*(2^j+3))*log: mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le) (by positivity)) h1 — that's what I had: mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1 — the INNER is `mul_nonneg (by norm_num) A0count_pos.le (by positivity)` — 3 args again! The middle layer: 0 ≤ 3*A0count*(2^j+3) = (3*A0count)*(2^j+3): mul_nonneg (0 ≤ 3*A0count) (0 ≤ 2^j+3): = mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le) (by positivity). So full: mul_nonneg (mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le) (by positivity)) h1. My original text: `exact mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1` — inner mul_nonneg with 3 args (by norm_num), A0count_pos.le, (by positivity) — ERROR. Fix: add the paren layer.\n\nLet me apply these fixes.","signature":""},{"type":"text","text":"More fixes: another `lt_of_not_le`, `max_eq_right` for the max, `Finset.eq_empty_iff_forall_notMem` (camelCase), and the `mul_nonneg` arity."},{"type":"tool_use","id":"Bash_82","name":"Bash","input":{"command":"cd \"D:/Python/Quantum/research/lean/NguyenRH1\" && python - << 'EOF'\np = 'NguyenRH1/LiCircleBound.lean'\nsrc = open(p, encoding='utf-8').read()\nsrc = src.replace('lt_of_not_le hρF.2.1', 'lt_of_not_ge hρF.2.1')\nsrc = src.replace('''        rw [h1, h2]\n        have h3 : (2 : ℝ) ^ (j + 1) = 2 * (2 : ℝ) ^ j := by rw [pow_succ']\n        have h4 : (0 : ℝ) < (2 : ℝ) ^ j := by positivity\n        nlinarith [h3, h4]''', '''        rw [h1, h2]\n        have h3 : (2 : ℝ) ^ (j + 1) = 2 * (2 : ℝ) ^ j := by rw [pow_succ']\n        have h4 : (0 : ℝ) < (2 : ℝ) ^ j := by positivity\n        exact max_eq_right (by linarith [h3, h4])''')\nsrc = src.replace('Finset.eq_empty_iff_forall_not_mem.mpr', 'Finset.eq_empty_iff_forall_notMem.mpr')\nsrc = src.replace('exact mul_nonneg (mul_nonneg (by norm_num) A0count_pos.le (by positivity)) h1',\n  'exact mul_nonneg (mul_nonneg (mul_nonneg (by norm_num : (0 : ℝ) ≤ 3) A0count_pos.le) (by positivity)) h1')\nopen(p, 'w', encoding='utf-8').write(src)\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | head -40","description":"Apply second round of shell_inlo fixes","timeout":300000},"extra_content":null}]