[{"type":"thinking","thinking":"Errors:\n\n1. `lt_of_not_ge hreg1` — hreg1 was PUSHED: `push Not at hreg1` converted ¬(2 ≤ s.re) to (s.re < 2)! So hreg1 is already s.re < 2 — no lt_of_not_ge needed: just use hreg1 directly (s.re < 2) and hreg1.le. Fix both spots: h1's pair: ⟨hreg2, hreg1.le⟩ — but hreg1 is now < : .le works? For h : s.re < 2, h.le : s.re ≤ 2 ✓. And the 7/2 bound: (by linarith [hreg1] : s.re ≤ 7/2) ✓ (linarith handles <).\n\nWait — I did `push Not at hreg1` after the first by_cases? Let me check: after `by_cases hreg1 : 2 ≤ s.re · ... · push Not at hreg1; by_cases hreg2...`. Yes — hreg1 pushed: type s.re < 2. Fix: revert to hreg1 directly.\n\n2. h1's rw [h3] at h2 — h2's form is `32 * C0hat(...) * (3 * A0count) * Real.log(...) ≤ 32 * C0hat(...) * (3 * A0count) * (2 * Real.log R)` — h3 : 32·Ĉ·(3·A₀·(2L)) = 192·A₀·Ĉ·L — pattern mismatch: the goal has (3 * A0count) * Real.log(...) NOT (3 * A0count * (2 * Real.log R)): mul_le_mul_of_nonneg_left hlogmax gave the bound with `(3 * A0count) * (2 * Real.log R)`?? — no: hlogmax : Real.log(3·max+5) ≤ 2·Real.log R: mul_le_mul_of_nonneg_left hlogmax (0 ≤ 32·Ĉ·(3·A₀)): gives (32·Ĉ·(3·A₀))·Real.log(...) ≤ (32·Ĉ·(3·A₀))·(2·Real.log R) — the error shows the goal form is `32 * C0hat(...) * (3 * A0count) * Real.log(...)` — associativity: `32 * C0hat(...) * (3 * A0count) * X` = ((32·Ĉ)·(3·A₀))·X — hmm that IS the form (32·Ĉ·(3·A₀))·X by left-assoc. So h2 : ... ≤ 32·Ĉ·(3·A₀)·(2L) — and h3 : 32·Ĉ·(3·A₀·(2L)) = ... — DIFFERENT: (3·A₀)·(2L) vs (3·(A₀·(2L)))? `3 * A0count * (2 * Real.log R)` = (3·A₀)·(2L) left-assoc ✓ same as the goal's RHS?? The goal RHS: `32 * C0hat(...) * (3 * A0count) * (2 * Real.log R)` = ((32·Ĉ)·(3·A₀))·(2L) ✓ and h3's LHS: `32 * C0hat(...) * (3 * A0count * (2 * Real.log R))` = (32·Ĉ)·((3·A₀)·(2L)) ✓ same ✓ — so h3 SHOULD rewrite... the error says pattern not found: h3's LHS as I wrote it: `32 * C0hat (4 * ↑k + 9 / 2) * (3 * A0count * (2 * Real.log R))` — vs goal's `32 * C0hat (...) * (3 * A0count) * (2 * Real.log R)` — the difference: (3 * A0count * (2L)) vs ((3 * A0count) * (2L)) — these ARE the same term by left-assoc: 3 * A0count * (2 * Real.log R) parses as (3 * A0count) * (2 * Real.log R) — identical! Hmm — but the error shows h3 wasn't found in the goal `32 * C0hat (...) * (3 * A0count) * Real.log (3 * max ...) ≤ 32 * C0hat (...) * (3 * A0count) * (2 * Real.log R)` — the LHS of the iff... rw [h3] at h2: h2's RHS is `32·Ĉ·(3·A₀)·(2·L)` and h3 : `32·Ĉ·(3·A₀·(2·L))` — the forms: h2's RHS: (32·Ĉ·(3·A₀))·(2·Real.log R); h3's LHS: (32·Ĉ)·((3·A₀)·(2·Real.log R)) — SAME term? (32 * C0hat(...) * (3 * A0count)) * (2 * Real.log R) vs (32 * C0hat(...)) * ((3 * A0count) * (2 * Real.log R)) — associativity of *: (a*b)*c = a*(b*c) — SAME term in Lean? NO — HMul.hMul (HMul.hMul a b) c vs HMul.hMul a (HMul.hMul b c) — DIFFERENT terms (rw is syntactic). So rewrite h3's form to match: h3 : 32 * C0hat(...) * (3 * A0count) * (2 * Real.log R) = 192·A₀·Ĉ·L — as written: `32 * C0hat (4 * (k:ℝ)+9/2) * (3 * A0count) * (2 * Real.log R)` — the parse of that is ((32·Ĉ)·(3·A₀))·(2L) ✓ matches h2's RHS. My h3 was written with explicit parens (3 * A0count * (2 * Real.log R)) — hmm that's ((3·A₀)·(2L)) — and the goal has the same... WAIT the error's goal RHS: `32 * C0hat (4 * ↑k + 9 / 2) * (3 * A0count) * (2 * Real.log R)` — YES and h3's LHS: `32 * C0hat (4 * ↑k + 9 / 2) * (3 * A0count * (2 * Real.log R))` — hmm the goal text shows (3 * A0count) * (2 * Real.log R) — with the OUTER product ((32·Ĉ)·(3·A₀))·(2L)?? The display `32 * C0hat (...) * (3 * A0count) * (2 * Real.log R)` — all left-assoc ✓ and h3's LHS `32 * C0hat (...) * (3 * A0count * (2 * Real.log R))` — the parenthesization (3 * A0count * (2 * Real.log R)) is ((3·A₀)·(2L)) — so h3's LHS = (32·Ĉ)·((3·A₀)·(2L)) — DIFFERENT from ((32·Ĉ)·(3·A₀))·(2L). So the mismatch IS associativity. Fix: restate h3 as `32 * C0hat (...) * (3 * A0count) * (2 * Real.log R) = ...` — wait that's what I need to match: ((32·Ĉ)·(3·A₀))·(2L) — write h3's LHS exactly as the goal's RHS. Change h3 to:\n```\nhave h3 : 32 * C0hat (4 * (k : ℝ) + 9 / 2) * (3 * A0count) * (2 * Real.log R)\n    = 192 * A0count * C0hat (4 * (k : ℝ) + 9 / 2) * Real.log R := by ring\n```\nWait — that parses as ((32·Ĉ)·(3·A₀))·(2L) ✓. ring proves ✓.\n\nHmm — but wait, h2 was built as mul_le_mul_of_nonneg_left hlogmax (0 ≤ 32·Ĉ·(3·A₀)) — its RHS form: (32·Ĉ·(3·A₀))·(2·L)?? mul_le_mul_of_nonneg_left (h : b ≤ a) (hc : 0 ≤ c) : c * b ≤ c * a — with c := 32·Ĉ·(3·A₀): c·Real.log(...) ≤ c·(2·L) — the display showed `32 * C0hat (...) * (3 * A0count) * (2 * Real.log R)` — consistent with c := (32·Ĉ·(3·A₀)) hmm — the c I passed: `mul_nonneg (mul_nonneg (by norm_num : (0:ℝ) ≤ 32) hĈpos.le) (mul_nonneg (by norm_num : (0:ℝ) ≤ 3) hA0)` : 0 ≤ (32·Ĉ)·(3·A₀) ✓ so h2 : ((32·Ĉ)·(3·A₀))·log(...) ≤ ((32·Ĉ)·(3·A₀))·(2L) ✓ then h3 must match ((32·Ĉ)·(3·A₀))·(2L) — as the goal shows: `32 * C0hat (...) * (3 * A0count) * (2 * Real.log R)` ✓ parse ((32·Ĉ)·(3·A₀))·(2L) ✓. So restate h3 in THAT form (without the inner parens around (2 * Real.log R)).","signature":""},{"type":"text","text":"Two fixes: `hreg1` was already pushed (use it directly), and h3's associativity must match the goal."},{"type":"tool_use","id":"Bash_208","name":"Bash","input":{"command":"cd \"D:/Python/Quantum/research/lean/NguyenRH1\" && python - << 'PYEOF'\np = 'NguyenRH1/LiCircleBound.lean'\nsrc = open(p, encoding='utf-8').read()\nsrc = src.replace(\"have h1 : -5 / 2 ≤ s.re ∧ s.re ≤ 2 := ⟨hreg2, (lt_of_not_ge hreg1).le⟩\",\n  \"have h1 : -5 / 2 ≤ s.re ∧ s.re ≤ 2 := ⟨hreg2, hreg1.le⟩\")\nsrc = src.replace(\"\"\"        · exact logDeriv_riemannZeta_sub_nearZeros_le (t := s.im) ht10 rfl hhalf\n            (by linarith [lt_of_not_ge hreg1] : s.re ≤ 7 / 2) hζs\"\"\",\n  \"\"\"        · exact logDeriv_riemannZeta_sub_nearZeros_le (t := s.im) ht10 rfl hhalf\n            (by linarith [hreg1] : s.re ≤ 7 / 2) hζs\"\"\")\nsrc = src.replace(\"\"\"              have h3 : 32 * C0hat (4 * (k : ℝ) + 9 / 2) * (3 * A0count * (2 * Real.log R))\n                  = 192 * A0count * C0hat (4 * (k : ℝ) + 9 / 2) * Real.log R := by ring\"\"\",\n  \"\"\"              have h3 : 32 * C0hat (4 * (k : ℝ) + 9 / 2) * (3 * A0count) * (2 * Real.log R)\n                  = 192 * A0count * C0hat (4 * (k : ℝ) + 9 / 2) * Real.log R := by ring\"\"\")\nopen(p, 'w', encoding='utf-8').write(src)\nPYEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | head -40","description":"Fix hreg1 + h3 associativity; recompile","timeout":300000},"extra_content":null}]