[{"type":"thinking","thinking":"Two errors:\n\n1. Line 3797 (h2c): after `rw [h3]`, the goal became `1 * C0hat (...) ≤ A0count * (1 * C0hat (...))` — rw [h3] rewrote Ĉ₀ to 1·Ĉ₀ EVERYWHERE (both sides). Fix: don't rw — use calc:\n```\nhave h2c : C0hat (4 * (k : ℝ) + 9 / 2) ≤ A0count * C0hat (4 * (k : ℝ) + 9 / 2) :=\n  calc C0hat (4 * (k : ℝ) + 9 / 2)\n      = 1 * C0hat (4 * (k : ℝ) + 9 / 2) := by ring\n    _ ≤ A0count * C0hat (4 * (k : ℝ) + 9 / 2) :=\n        mul_le_mul_of_nonneg_right A0count_ge_one hĈpos.le\n```\nSame for the Fexpr h2c (the earlier one I already fixed — check if it has the same bug: yes — same pattern: `rw [h3]; exact mul_le_mul_of_nonneg_right A0count_ge_one hĈR2pos.le` — same rw-everywhere issue: fix with calc too).\n\n2. Line 3861 (hchain's final step): the last `apply add_le_add_right` then `exact norm_sub_le _ _` — the goal at that point: `‖logDeriv ζ s − seriesFun s‖ + ‖1/s‖ + ‖1/(s−1)‖ + ‖logπ/2‖ + ‖ψ/2‖ ≤ ‖logDeriv ζ s‖ + ‖seriesFun s‖ + ‖1/s‖ + ...` — this needs add_le_add on the FIRST component (‖X−Y‖ ≤ ‖X‖+‖Y‖), NOT add_le_add_right (which adds on the LEFT of each side?? add_le_add_right (h : b ≤ c) (a) : a + b ≤ a + c — adds a on the LEFT ✓ — the goal: (‖X−Y‖ + ‖1/s‖ + ‖1/(s−1)‖ + ‖logπ/2‖) + ‖ψ/2‖ ≤ ... — my nested `apply add_le_add_right` four times then norm_sub_le: each add_le_add_right strips one trailing +term... the mismatch: the LAST apply add_le_add_right's expected form `?a + ?b ≤ ?a + ?c` vs the goal `‖X−Y‖ + ‖1/s‖ + ‖1/(s−1)‖ + ‖logπ/2‖ + ‖ψ/2‖ ≤ ‖X‖ + ‖Y‖ + ‖1/s‖ + ...` — with ?a := ‖X−Y‖ + ‖1/s‖ + ‖1/(s−1)‖ + ‖logπ/2‖ + ‖ψ/2‖... hmm — after three add_le_add_right applications, the goal should be `‖X−Y‖ + ‖1/s‖ ≤ ‖X‖ + ‖Y‖ + ‖1/s‖`?? Let me re-think the chain structure. The expression tree: ((((X−S) + A) + B) − C) + D where X = logDeriv, S = seriesFun, A = 1/s, B = 1/(s−1), C = logπ/2, D = ψ/2.\nGoal: ‖((((X−S)+A)+B)−C)+D‖ ≤ ‖X‖+‖S‖+A'+B'+C'+D' (with A' = ‖1/s‖ etc).\nStep 1: ≤ ‖(((X−S)+A)+B)−C‖ + D' (norm_add_le) — that's what I did.\nStep 2: ≤ ‖((X−S)+A)+B‖ + C' + D' (norm_sub_le on the first part: ‖P−C‖ ≤ ‖P‖+‖C‖): add_le_add_right (norm_sub_le) _ ✓.\nStep 3: ‖((X−S)+A)+B‖ ≤ ‖(X−S)+A‖ + B' (norm_add_le) ✓.\nStep 4: ‖(X−S)+A‖ ≤ ‖X−S‖ + A' (norm_add_le) ✓.\nStep 5: ‖X−S‖ ≤ ‖X‖ + ‖S‖ (norm_sub_le) — the final goal after 4 add_le_add_right: `‖X−S‖ + A' + B' + C' + D' ≤ ‖X‖ + ‖S‖ + A' + B' + C' + D'` — need add_le_add_right (norm_sub_le _ _) (A'+B'+C'+D')?? — the goal after 4 strips: hmm — each `add_le_add_right h _` adds a on the LEFT: add_le_add_right (h : b ≤ c) (a) : a + b ≤ a + c. The calc step form: `_ ≤ LHS4 + D' := add_le_add_right (norm_add_le _ _) _` — wait — my calc steps used add_le_add_right to transform: e.g. step: `_ ≤ ‖(X−S)+A‖ + B' + C' + D' := add_le_add_right (add_le_add_right (norm_add_le _ _) _) _` — these transform the RIGHTMOST sum: ‖((X−S)+A)+B‖ + (C'+D')?? — the associativity: the stated step forms in my calc: `_ ≤ ‖logDeriv riemannZeta s - seriesFun s‖ + ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖ + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖` — flat left-assoc sums ✓ — the transformations: each step peels one level: from ‖((((X−S)+A)+B)−C)+D‖ ≤ [step1] ‖(((X−S)+A)+B)−C‖+‖D‖ ≤ [step2: norm_sub_le on the first] (‖((X−S)+A)+B‖+‖C‖)+‖D‖ — hmm — step2's add_le_add_right (norm_sub_le _ _) _ : (‖P−C‖ ≤ ‖P‖+‖C‖) with a := ‖D‖: ‖P−C‖+‖D‖ ≤ (‖P‖+‖C‖)+‖D‖ ✓. Step3: goal-form: ‖((X−S)+A)+B‖+‖C‖+‖D‖ ≤ (‖(X−S)+A‖+‖B‖)+‖C‖+‖D‖: add_le_add_right (add_le_add_right (norm_add_le _ _) _) _: inner: ‖Q+B‖+‖C‖ ≤ (‖Q‖+‖B‖)+‖C‖ ✓ then outer +‖D‖ ✓. Step4: ‖(X−S)+A‖+‖B‖+‖C‖+‖D‖ ≤ (‖X−S‖+‖A‖)+‖B‖+‖C‖+‖D‖ ✓ add_le_add_right³. Step5 (LAST): goal: ‖X−S‖+‖A‖+‖B‖+‖C‖+‖D‖ ≤ (‖X‖+‖S‖)+‖A‖+‖B‖+‖C‖+‖D‖ — my final stated form: `‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ + ‖(1 : ℂ) / s‖ + ...` — flat: ‖X‖+‖S‖+A'+B'+C'+D' left-assoc ✓ the step needs: add_le_add_right (add_le_add_right (add_le_add_right (add_le_add_right (norm_sub_le _ _) _) _) _) _?? — the norm_sub_le transforms ‖X−S‖ → ‖X‖+‖S‖ at the HEAD of the sum: (‖X−S‖)+A'+B'+C'+D' → (‖X‖+‖S‖)+A'+B'+C'+D': the head replacement with four trailing terms: add_le_add_right (norm_sub_le _ _) (‖A‖+‖B‖+‖C‖+‖D‖)?? — add_le_add_right h a : a + b ≤ a + c with b := ‖X−S‖, c := ‖X‖+‖S‖, a := the REST — but the rest is on the RIGHT of the head: ‖X−S‖+A'+B'+C'+D' = ‖X−S‖ + (A'+B'+C'+D')?? NO — left-assoc: ((((‖X−S‖+A')+B')+C')+D') — the head ‖X−S‖ is the LEFTMOST; transforming it needs add_le_add on the LEFT factor of the INNERMOST sum: (((‖X−S‖+A')+B')+C')+D' — to replace ‖X−S‖ with ‖X‖+‖S‖: apply add_le_add_right 4 times with h := norm_sub_le: \nadd_le_add_right (h : b ≤ c) (a) : a + b ≤ a + c — with b := ‖X−S‖?? no: the innermost sum is ‖X−S‖+A': transform to (‖X‖+‖S‖)+A' — that's add_le_add (norm_sub_le) (le_refl A') hmm — add_le_add_right h a gives a+b ≤ a+c — the a is on the LEFT. For ‖X−S‖+A' ≤ (‖X‖+‖S‖)+A': need b := ‖X−S‖ → c := ‖X‖+‖S‖ with a := A' on the LEFT: A' + ‖X−S‖ — WRONG SIDE. add_le_add_right is for modifying the RIGHT addend. To modify the LEFT addend: add_le_add_left h a : b + a ≤ c + a ✓ — the session-025 gotcha: \"add_le_add_left/right are swapped vs classic\"! In THIS Mathlib: add_le_add_left (h : b ≤ c) (a) : b + a ≤ c + a?? or a+b ≤ a+c? From the earlier error in 3a: `add_le_add_left (mul_le_mul_of_nonneg_left hΔle ...) ?m` produced `0.532*Δ1 + ?m ≤ 0.532*Δ2 + ?m` — i.e., add_le_add_left h a : b + a ≤ c + a in this Mathlib (modifies the LEFT addend b→c with a on the RIGHT). And add_le_add_right h a : a + b ≤ a + c (modifies RIGHT). So the step: ‖X−S‖ + A' ≤ (‖X‖+‖S‖) + A' = add_le_add_left (norm_sub_le _ _) A' ✓!! So my LAST step should be add_le_add_LEFT (norm_sub_le _ _) applied 4 times (one per trailing term):\n```\n_ ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ + ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖\n      + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ := by\n    apply add_le_add_right\n    apply add_le_add_right\n    apply add_le_add_right\n    apply add_le_add_right\n    exact norm_sub_le _ _\n```\nWith add_le_add_right h a : a + b ≤ a + c — peeling: the goal at the last apply: `?a + ?b ≤ ?a + ?c` vs `‖X−S‖+‖A‖+‖B‖+‖C‖+‖D‖ ≤ ‖X‖+‖S‖+‖A‖+‖B‖+‖C‖+‖D‖` — hmm — add_le_add_right unifies a + b with LHS: a := ‖X−S‖+‖A‖+‖B‖+‖C‖, b := ‖D‖: then c should satisfy ‖D‖ = c: the RHS must be a + c = same-a + c: RHS: ‖X‖+‖S‖+‖A‖+‖B‖+‖C‖+‖D‖ — a ≠ that prefix (prefix differs: ‖X−S‖ vs ‖X‖+‖S‖) — FAILS. So peeling with add_le_add_right can't change the LEFTMOST factor. Correct final step: transform the head with add_le_add_LEFT four times?? — add_le_add_left h a : b + a ≤ c + a (this Mathlib): goal: ‖X−S‖+A'+B'+C'+D' ≤ (‖X‖+‖S‖)+A'+B'+C'+D': the head ‖X−S‖ is inside the nesting: ((((h+A')+B')+C')+D'): to change h → h': apply add_le_add_right (a := D'): changes the RIGHTMOST: (((h+A')+B')+C')+D' ≤ ?+D' with ? := ((h+A')+B')+C' — hmm — add_le_add_right h' a : a + b ≤ a + c: unifies a+b with ((((h+A')+B')+C')+D'): a := (((h+A')+B')+C'), b := D' — no, we want to change the HEAD not D'. So: the right approach: each `apply add_le_add_right` peels the RHS structure: goal := X₁ + t ≤ Y₁ + t where t is the last term and X₁ ≤ Y₁ is the sub-goal: with the FINAL sub-goal ‖X−S‖ + A' ≤ (‖X‖+‖S‖) + A' — then the LAST tactic must be add_le_add_LEFT (norm_sub_le _ _) A' — modifying the left addend. Wait — which one is \"left\" in this Mathlib: add_le_add_left h a : b + a ≤ c + a (per the 3a evidence: produced `0.532*Δ1 + ?m ≤ 0.532*Δ2 + ?m` — the changed part is the FIRST addend, a is appended on the RIGHT). So final step: `exact add_le_add_left (norm_sub_le _ _) _` with the trailing-term argument — after 4 `apply add_le_add_right` peels, the goal is ‖X−S‖ + A' ≤ (‖X‖+‖S‖) + A' — `exact add_le_add_left (norm_sub_le _ _) _` ✓ (a := ‖(1:ℂ)/s‖ inferred).\n\nHmm wait — but then steps 2-4 of my calc (the add_le_add_right (norm_...) _ steps) — are THOSE right? Step: `_ ≤ ‖(X−S)+A‖ + ‖B‖ + ‖C‖ + ‖D‖` from `‖((X−S)+A)+B‖ + ‖C‖ + ‖D‖`: transform ((X−S)+A)+B → (X−S)+A+B: peeling: the stated RHS form is flat left-assoc ✓: the transformations needed: at each step the change is in the LEFT-addend of the current innermost sum — SAME ISSUE at every step!! E.g. step from `‖P−C‖ + ‖D‖` to `(‖P‖+‖C‖) + ‖D‖` — that's add_le_add_LEFT (norm_sub_le) ‖D‖ (the changed part is the left addend ‖P−C‖ → ‖P‖+‖C‖)!! So ALL my steps 2-5 should use add_le_add_left (this-Mathlib-swapped sense) not add_le_add_right!!\n\nHold on — but steps 2-4 compiled?? The error was only at the LAST apply (3861). Let me recheck the error: \"could not unify the conclusion of @add_le_add_right ?a + ?b ≤ ?a + ?c with the goal ‖X−S‖+A'+B'+C'+D' ≤ ‖X‖+‖S‖+A'+B'+C'+D'\" — the failure is at the step transforming ‖X−S‖... — hmm but wait: my calc's earlier steps used add_le_add_right with norm_sub_le/norm_add_le — let me recheck step 2's stated forms: `_ ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)‖ + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ := add_le_add_right (norm_sub_le _ _) _` — the PREVIOUS step's RHS: `‖logDeriv ζ s − seriesFun s + 1/s + 1/(s−1) − logπ/2‖ + ‖ψ/2‖` — and this step's RHS: `‖logDeriv ζ s − seriesFun s + 1/s + 1/(s−1)‖ + ‖logπ/2‖ + ‖ψ/2‖` — the change: ‖P−C‖ → ‖P‖+‖C‖ in the LEFT addend ✓ add_le_add_right h a : a+b ≤ a+c — unify a+b with (‖P−C‖+‖ψ/2‖): a := ‖P−C‖, b := ‖ψ/2‖; a+c with (‖P‖+‖C‖+‖ψ/2‖): c := ‖ψ/2‖ — so h : ‖ψ/2‖ ≤ ‖ψ/2‖?! That's le_refl not norm_sub_le!! But the error wasn't raised at step 2... hmm — because `add_le_add_right (norm_sub_le _ _) _` unified b := ‖P−C‖-with-... — add_le_add_right (h : b ≤ c) (a) : a + b ≤ a + c — with h := norm_sub_le _ _ : ‖?x − ?y‖ ≤ ‖?x‖+‖?y‖: unify a + (‖?x‖+‖?y‖)... wait h gives the RELATION b ≤ c with b := ‖?x−?y‖?? no — norm_sub_le : ‖x−y‖ ≤ ‖x‖+‖y‖: so b := ‖?x−?y‖, c := ‖?x‖+‖?y‖: the conclusion a+b ≤ a+c: a + ‖?x−?y‖ ≤ a + (‖?x‖+‖?y‖): unify with LHS ‖P−C‖+‖ψ/2‖: a + ‖?x−?y‖ = ‖P−C‖+‖ψ/2‖ — so a := ‖P−C‖ and ‖?x−?y‖ := ‖ψ/2‖ — MISMATCH (?x−?y can't unify with a norm). UNLESS the elaborator tried a := ‖ψ/2‖... a + ‖?x−?y‖ = ‖P−C‖+‖ψ/2‖: first-addend must match: a := ‖P−C‖ ✓ then ‖?x−?y‖ = ‖ψ/2‖ ✗. Hmm — so how did steps 2-4 elaborate at all? Maybe they DIDN'T and the errors are all at those positions but only the FIRST is shown (3861 — which is... the last apply in the final step's `apply add_le_add_right × 4; exact norm_sub_le _ _` sequence). Since Lean elaborates tactic blocks and reports errors per-tactic, earlier steps may have elaborated OK by luck: let me recheck step 2: the PREVIOUS step's RHS (step 1's): `‖logDeriv ζ s − seriesFun s + 1/s + 1/(s−1) − logπ/2‖ + ‖ψ/2‖` and step 2's RHS: `‖logDeriv ζ s − seriesFun s + 1/s + 1/(s−1)‖ + ‖logπ/2‖ + ‖ψ/2‖` — change: inside the first factor, ‖P−C‖ → ‖P‖+‖C‖ — but the first factor is itself `‖...−logπ/2‖` — as an addend: `‖P−C‖ + ‖D‖` where the OUTER expression is ‖P−C‖+‖D‖: to transform the FIRST addend: add_le_add_left (norm_sub_le _ _) ‖D‖ — modifies LEFT addend ✓. So step 2 should be add_le_add_left. But the error was only at 3861?? — the elaborator processes ALL tactics; with multiple errors it shows several — the head -40 cut off everything below. Likely ALL four steps have the same issue but only the first-position error got displayed... Actually errors ARE reported per tactic position — the head -40 showed only the 3861 one (plus 3797). Maybe steps 2-4 unified by luck of metavariable assignment?? — e.g. step 2: add_le_add_right (norm_sub_le _ _) _: a + ‖?x−?y‖ ≤ a + (‖?x‖+‖?y‖) against `‖logDeriv...− logπ/2‖ + ‖ψ/2‖ ≤ ‖logDeriv...‖ + ‖logπ/2‖ + ‖ψ/2‖`: hmm the RHS's associativity: (‖...‖ + ‖logπ/2‖) + ‖ψ/2‖: a + c := (‖...‖+‖logπ/2‖) + ‖ψ/2‖: a := ‖...‖+‖logπ/2‖?? and LHS a + ‖?x−?y‖ := ‖...−logπ/2‖+‖ψ/2‖: a must equal both: ‖...−logπ/2‖ vs ‖...‖+‖logπ/2‖ — no. So it can't have worked — the errors at steps 2-4 must exist but got cut by head -40. Let me restructure the whole hchain to avoid the left/right confusion: use a single `calc` with explicit steps each proved by a dedicated have, or better — use gcongr! `gcongr` handles monotone-add chains: the whole chain: ‖((((X−S)+A)+B)−C)+D‖ ≤ ‖X‖+‖S‖+A'+B'+C'+D': gcongr should decompose: ‖?‖ ≤ ‖?‖ with norm_sub_le/norm_add_le as its lemmas?? — gcongr uses tagged lemmas; norm_add_le/norm_sub_le aren't gcongr-tagged by default. Alternative robust: prove the 6-term bound by repeated have + linarith:\n```\nhave hc1 : ‖Fexpr s‖ ≤ ‖logDeriv riemannZeta s - seriesFun s + 1/s + 1/(s-1) - (logπ)/2‖ + ‖Complex.digamma (s/2)/2‖ := by\n  rw [Fexpr]; exact norm_add_le _ _\nhave hc2 : ‖logDeriv riemannZeta s - seriesFun s + 1/s + 1/(s-1) - (Real.log Real.pi : ℂ)/2‖\n    ≤ ‖logDeriv riemannZeta s - seriesFun s + 1/s + 1/(s-1)‖ + ‖(Real.log Real.pi : ℂ)/2‖ :=\n  norm_sub_le _ _\nhave hc3 : ... ≤ ‖logDeriv ζ s - seriesFun s + 1/s‖ + ‖(1:ℂ)/(s-1)‖ := norm_add_le _ _\nhave hc4 : ... ≤ ‖logDeriv ζ s - seriesFun s‖ + ‖(1:ℂ)/s‖ := norm_add_le _ _\nhave hc5 : ‖logDeriv riemannZeta s - seriesFun s‖ ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ :=\n  norm_sub_le _ _\n-- then combine by linarith\nlinarith [hc1, hc2, hc3, hc4, hc5, hser2?, ...]\n```\nwith each norm_ lemma applied directly to the expression — no add_le_add_* at all, and linarith does the sum bookkeeping (norm terms as atoms ✓ same atoms everywhere since the sub-expressions are textual). MUCH more robust. The hchain's goal: ‖Fexpr‖ ≤ [6 atoms] — from hc1..hc5 by linarith ✓. Let me rewrite hchain that way.","signature":""},{"type":"text","text":"The add_le_add_left/right swap strikes the whole chain. Restructuring hchain to per-step `norm_add_le/norm_sub_le` haves + linarith (no add_le_add at all)."},{"type":"tool_use","id":"Bash_236","name":"Bash","input":{"command":"cd \"D:/Python/Quantum/research/lean/NguyenRH1\" && python - << 'PYEOF'\np = 'NguyenRH1/LiCircleBound.lean'\nsrc = open(p, encoding='utf-8').read()\n# fix h2c with calc (no rw-everywhere)\nsrc = src.replace('''        have h2c : C0hat (4 * (k : ℝ) + 9 / 2)\n            ≤ A0count * C0hat (4 * (k : ℝ) + 9 / 2) := by\n          have h3 : C0hat (4 * (k : ℝ) + 9 / 2)\n              = 1 * C0hat (4 * (k : ℝ) + 9 / 2) := by ring\n          rw [h3]\n          exact mul_le_mul_of_nonneg_right A0count_ge_one hĈpos.le\n        linarith [hĈ2, h2c]''', '''        have h2c : C0hat (4 * (k : ℝ) + 9 / 2)\n            ≤ A0count * C0hat (4 * (k : ℝ) + 9 / 2) :=\n          calc C0hat (4 * (k : ℝ) + 9 / 2)\n              = 1 * C0hat (4 * (k : ℝ) + 9 / 2) := by ring\n            _ ≤ A0count * C0hat (4 * (k : ℝ) + 9 / 2) :=\n                mul_le_mul_of_nonneg_right A0count_ge_one hĈpos.le\n        linarith [hĈ2, h2c]''')\nsrc = src.replace('''        have h2c : C0hat (R + 2) ≤ A0count * C0hat (R + 2) := by\n          have h3 : C0hat (R + 2) = 1 * C0hat (R + 2) := by ring\n          rw [h3]\n          exact mul_le_mul_of_nonneg_right A0count_ge_one hĈR2pos.le\n        linarith [hĈ2, hĈR2, h2c]''', '''        have h2c : C0hat (R + 2) ≤ A0count * C0hat (R + 2) :=\n          calc C0hat (R + 2) = 1 * C0hat (R + 2) := by ring\n            _ ≤ A0count * C0hat (R + 2) :=\n                mul_le_mul_of_nonneg_right A0count_ge_one hĈR2pos.le\n        linarith [hĈ2, hĈR2, h2c]''')\n# rewrite hchain with per-step haves + linarith\nold_chain = '''  have hchain : ‖Fexpr s‖ ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ +\n      ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖ + ‖(Real.log Real.pi : ℂ) / 2‖ +\n      ‖Complex.digamma (s / 2) / 2‖ := by\n    rw [Fexpr]\n    calc ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)\n          - (Real.log Real.pi : ℂ) / 2 + Complex.digamma (s / 2) / 2‖\n        ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)\n            - (Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ :=\n          norm_add_le _ _\n      _ ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)‖\n            + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ :=\n          add_le_add_right (norm_sub_le _ _) _\n      _ ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s‖ + ‖(1 : ℂ) / (s - 1)‖\n            + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ :=\n          add_le_add_right (add_le_add_right (norm_add_le _ _) _) _\n      _ ≤ ‖logDeriv riemannZeta s - seriesFun s‖ + ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖\n            + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ :=\n          add_le_add_right (add_le_add_right (add_le_add_right (norm_add_le _ _) _) _) _\n      _ ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ + ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖\n            + ‖(Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ := by\n          apply add_le_add_right\n          apply add_le_add_right\n          apply add_le_add_right\n          apply add_le_add_right\n          exact norm_sub_le _ _\n'''\nnew_chain = '''  have hchain : ‖Fexpr s‖ ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ +\n      ‖(1 : ℂ) / s‖ + ‖(1 : ℂ) / (s - 1)‖ + ‖(Real.log Real.pi : ℂ) / 2‖ +\n      ‖Complex.digamma (s / 2) / 2‖ := by\n    have hc1 : ‖Fexpr s‖ ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)\n          - (Real.log Real.pi : ℂ) / 2‖ + ‖Complex.digamma (s / 2) / 2‖ := by\n      rw [Fexpr]\n      exact norm_add_le _ _\n    have hc2 : ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)\n          - (Real.log Real.pi : ℂ) / 2‖\n        ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)‖\n          + ‖(Real.log Real.pi : ℂ) / 2‖ :=\n        norm_sub_le _ _\n    have hc3 : ‖logDeriv riemannZeta s - seriesFun s + 1 / s + 1 / (s - 1)‖\n        ≤ ‖logDeriv riemannZeta s - seriesFun s + 1 / s‖ + ‖(1 : ℂ) / (s - 1)‖ :=\n        norm_add_le _ _\n    have hc4 : ‖logDeriv riemannZeta s - seriesFun s + 1 / s‖\n        ≤ ‖logDeriv riemannZeta s - seriesFun s‖ + ‖(1 : ℂ) / s‖ :=\n        norm_add_le _ _\n    have hc5 : ‖logDeriv riemannZeta s - seriesFun s‖\n        ≤ ‖logDeriv riemannZeta s‖ + ‖seriesFun s‖ :=\n        norm_sub_le _ _\n    linarith [hc1, hc2, hc3, hc4, hc5]\n'''\nassert old_chain in src, \"chain not found\"\nsrc = src.replace(old_chain, new_chain)\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"done\")\nPYEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | head -30","description":"Fix h2c calc + hchain restructure; recompile","timeout":300000},"extra_content":null}]