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← Session 25 — ii′-5 R-bound: design + level-2 EM disc bound

#1340 assistant 2026-08-22 22:27:25.836 UTC · 1672→1075 tok open ⤢
thinking (2432 chars)
Good progress — the logDeriv chain compiled (hlogB, hlogF, hlogP, hlogcomp all fine!). Four errors: 1. **Line 1153**: `differentiableAt_id'` unknown — use `differentiableAt_id` (the id-form). The deriv_const_mul's hd : DifferentiableAt 𝕜 f x where f := id... then the rewrite pattern has id... Let me look at what's there — `deriv_const_mul (5 / 2 : ℂ) differentiableAt_id'` — differentiableAt_id' doesn't exist in this Mathlib? Then check the name: maybe `differentiableAt_id` is stated with (fun x => x) directly in this version. Let me check. 2. **Line 1193**: `Cf_collZeros_ne_zero ht` — signature mismatch: my lemma is `{w : ℂ} (hw : w ∈ Metric.closedBall 0 (rC ht)) → ... ≠ 0` — i.e. explicit arg version. LogOfAnalyticFunction wants `∀ z ∈ closedBall 0 R, B z ≠ 0` — that's `∀ z, z ∈ ball → ...` — which IS the same as my lemma's form modulo the implicit w. My lemma: Cf_collZeros_ne_zero {t} (ht) {w} (hw) : ... — the w is IMPLICIT. The target ∀ z ∈ ..., ... has z explicit-bounded. So `Cf_collZeros_ne_zero ht` doesn't syntactically match ∀ z ∈ ... — because my lemma's w is implicit. Fix: `fun z hz => Cf_collZeros_ne_zero ht hz`. ✓ 3. **Line 1204** (hMpos): `rw [le_div_iff₀ hδM0, one_mul]` — the goal is `1 < X/δ^M` (Real.log_pos wants 1 < x, not 1 ≤!). I used Real.log_pos : 1 < x → 0 < log x. So the goal is 1 < X/δ^M not ≤. Fix: use lt_div_iff₀ : a < b/c ↔ a*c < b: `rw [lt_div_iff₀ hδM0, one_mul]` then need δ^M < X: have: δ^M ≤ 1 ≤ X with at least one strict: X ≥ 225 > 1 ≥ δ^M: δ^M ≤ 1 < X: (hδM.trans_lt (by nlinarith [hX1]: (1:ℝ) < (9/4)|t|^2)) — hX1 : 1 ≤ X; need 1 < X: X ≥ 225: nlinarith [hsq]. Let me restructure: ```lean have hX1' : (1:ℝ) < (9 / 4) * |t| ^ 2 := by have hsq : (10:ℝ) ^ 2 ≤ |t| ^ 2 := (sq_le_sq₀ (by norm_num) (abs_nonneg t)).mpr ht nlinarith rw [lt_div_iff₀ hδM0, one_mul] exact hδM.trans_lt hX1' ``` ✓ (drop hX1, keep hX1'). 4. **Line 1237**: `hB_eq.deriv` — EventuallyEq.deriv : f =ᶠ[𝓝 x] g → deriv f =ᶠ[𝓝 x] deriv g — it's the EVENTUALLY version! I need the pointwise: `Filter.EventuallyEq.deriv_eq`? or `EventuallyEq.deriv (h)` gives =ᶠ... For pointwise deriv f x = deriv g x from f =ᶠ[𝓝 x] g: the lemma is `Filter.EventuallyEq.deriv : f₁ =ᶠ[𝓝 x] f₂ → deriv f₁ x = deriv f₂ x`?? — the error shows hB_eq.deriv has type deriv f =ᶠ[𝓝] deriv g — so .deriv is the eventually version in this Mathlib. The pointwise one: `Filter.EventuallyEq.deriv_eq`? Let me check.
Fixing four errors. Checking `differentiableAt_id'` and the pointwise EventuallyEq-deriv name.
tool: Bash
input
{
  "command": "cd \"D:/Python/Quantum/zeta-23-lean/.lake/packages/mathlib\" && grep -rn \"theorem differentiableAt_id\\|lemma differentiableAt_id\" Mathlib/Analysis/Calculus/Deriv/Basic.lean Mathlib/Analysis/Calculus/FDeriv/Basic.lean 2>/dev/null | head -4; echo ---; grep -rn \"EventuallyEq.deriv_eq\\|theorem EventuallyEq.deriv\" Mathlib/Analysis/Calculus/*.lean Mathlib/Analysis/Calculus/**/*.lean 2>/dev/null | head -6",
  "description": "Find differentiableAt_id and EventuallyEq.deriv variants"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Good progress — the logDeriv chain compiled (hlogB, hlogF, hlogP, hlogcomp all fine!). Four errors:\n\n1. **Line 1153**: `differentiableAt_id'` unknown — use `differentiableAt_id` (the id-form). The deriv_const_mul's hd : DifferentiableAt 𝕜 f x where f := id... then the rewrite pattern has id... Let me look at what's there — `deriv_const_mul (5 / 2 : ℂ) differentiableAt_id'` — differentiableAt_id' doesn't exist in this Mathlib? Then check the name: maybe `differentiableAt_id` is stated with (fun x => x) directly in this version. Let me check.\n\n2. **Line 1193**: `Cf_collZeros_ne_zero ht` — signature mismatch: my lemma is `{w : ℂ} (hw : w ∈ Metric.closedBall 0 (rC ht)) → ... ≠ 0` — i.e. explicit arg version. LogOfAnalyticFunction wants `∀ z ∈ closedBall 0 R, B z ≠ 0` — that's `∀ z, z ∈ ball → ...` — which IS the same as my lemma's form modulo the implicit w. My lemma: Cf_collZeros_ne_zero {t} (ht) {w} (hw) : ... — the w is IMPLICIT. The target ∀ z ∈ ..., ... has z explicit-bounded. So `Cf_collZeros_ne_zero ht` doesn't syntactically match ∀ z ∈ ... — because my lemma's w is implicit. Fix: `fun z hz => Cf_collZeros_ne_zero ht hz`. ✓\n\n3. **Line 1204** (hMpos): `rw [le_div_iff₀ hδM0, one_mul]` — the goal is `1 < X/δ^M` (Real.log_pos wants 1 < x, not 1 ≤!). I used Real.log_pos : 1 < x → 0 < log x. So the goal is 1 < X/δ^M not ≤. Fix: use lt_div_iff₀ : a < b/c ↔ a*c < b: `rw [lt_div_iff₀ hδM0, one_mul]` then need δ^M < X: have: δ^M ≤ 1 ≤ X with at least one strict: X ≥ 225 > 1 ≥ δ^M: δ^M ≤ 1 < X: (hδM.trans_lt (by nlinarith [hX1]: (1:ℝ) < (9/4)|t|^2)) — hX1 : 1 ≤ X; need 1 < X: X ≥ 225: nlinarith [hsq]. Let me restructure:\n```lean\n    have hX1' : (1:ℝ) < (9 / 4) * |t| ^ 2 := by\n      have hsq : (10:ℝ) ^ 2 ≤ |t| ^ 2 := (sq_le_sq₀ (by norm_num) (abs_nonneg t)).mpr ht\n      nlinarith\n    rw [lt_div_iff₀ hδM0, one_mul]\n    exact hδM.trans_lt hX1'\n```\n✓ (drop hX1, keep hX1').\n\n4. **Line 1237**: `hB_eq.deriv` — EventuallyEq.deriv : f =ᶠ[𝓝 x] g → deriv f =ᶠ[𝓝 x] deriv g — it's the EVENTUALLY version! I need the pointwise: `Filter.EventuallyEq.deriv_eq`? or `EventuallyEq.deriv (h)` gives =ᶠ... For pointwise deriv f x = deriv g x from f =ᶠ[𝓝 x] g: the lemma is `Filter.EventuallyEq.deriv : f₁ =ᶠ[𝓝 x] f₂ → deriv f₁ x = deriv f₂ x`?? — the error shows hB_eq.deriv has type deriv f =ᶠ[𝓝] deriv g — so .deriv is the eventually version in this Mathlib. The pointwise one: `Filter.EventuallyEq.deriv_eq`? Let me check.","signature":""},{"type":"text","text":"Fixing four errors. Checking `differentiableAt_id'` and the pointwise EventuallyEq-deriv name."},{"type":"tool_use","id":"Bash_100","name":"Bash","input":{"command":"cd \"D:/Python/Quantum/zeta-23-lean/.lake/packages/mathlib\" && grep -rn \"theorem differentiableAt_id\\|lemma differentiableAt_id\" Mathlib/Analysis/Calculus/Deriv/Basic.lean Mathlib/Analysis/Calculus/FDeriv/Basic.lean 2>/dev/null | head -4; echo ---; grep -rn \"EventuallyEq.deriv_eq\\|theorem EventuallyEq.deriv\" Mathlib/Analysis/Calculus/*.lean Mathlib/Analysis/Calculus/**/*.lean 2>/dev/null | head -6","description":"Find differentiableAt_id and EventuallyEq.deriv variants"},"extra_content":null}]