← Session 31 — ii′-5f: tight R-bound 10.5/48 (piece 3 + pinch)
thinking (1994 chars)
No duplicates (4 = def farGLeftMaj + the three lemmas listed — wait, the grep counted 4 total matches of the pattern "def farGLeftMaj|lemma farGLeftMaj_combo_summable|lemma farGLeftMaj_shift_le|lemma tail14_inv_add_sq_summable" — 4 lines ✓ single copies).
So the isDefEq timeout at `hABC.mul_left _` is real. Let me think about what's REALLY happening: `hABC.mul_left _` — Summable.mul_left — checking its signature:
Maybe in this Mathlib `Summable.mul_left` is `Summable.mul_left {M : Type*} [Semiring M] [TopologicalSpace M] [IsTopologicalSemiring M] {f : ι → M} (r : M) (hf : Summable f) : Summable fun x => r * f x` — hABC.mul_left _ — the FIRST arg is r = ?m, second is hABC ✓. Type: Summable fun x => ?m * ((c0·A + c1·B) + c2·C) x — vs goal fun ℓ => 4.5 * (c0·A ℓ + c1·B ℓ + c2·C ℓ)... — the bodies: ?m * ((A+B)+C) vs 4.5 * (A+B+C) — the ASSOCIATION of the lambda bodies: hABC-body is `A ℓ + B ℓ + C ℓ` parsed as ((A+B)+C)... wait — no! Look at hABC's ascribed type: `fun ℓ => (0.433*0.1942+0.886*0.0736+2.9)·A ℓ + 0.433·B ℓ + 0.886·C ℓ` — hmm — that's also ((A+B)+C). And the goal: `4.5 * (A + B + C)` — the goal lambda from the LEMMA STATEMENT: `4.5 * ((0.433*0.1942+0.886*0.0736+2.9)·(1/..²) + 0.433·(log/..²) + 0.886·(loglog/..²))` — same association ✓.
OK let me stop guessing and bisect directly: comment out the farGLeftMaj section progressively. Actually — better idea: reproduce the timeout in a MINIMAL standalone file to see the real cause:
```lean
import Mathlib
open Complex Filter Topology MeasureTheory
noncomputable section
lemma test1 : Summable (fun ℓ : ℕ =>
4.5 * ((0.433 * 0.1942 + 0.886 * 0.0736 + 2.9) * (1 / (((ℓ : ℝ) + 14) + 10) ^ 2)
+ (0.433 * Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)
+ (0.886 * Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2))) := by
sorry
```
— elaborating the STATEMENT: if that alone hangs, it's the literal forms. Let me test quickly (with sorry to isolate elaboration of the statement).
Let me isolate the pathology with a minimal test file.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && cat > /tmp/test_lam.lean <<'EOF'\nimport Mathlib\nopen Complex Filter Topology MeasureTheory\nnoncomputable section\nnamespace TestNS\n\nlemma test1 : Summable (fun \u2113 : \u2115 =>\n 4.5 * ((0.433 * 0.1942 + 0.886 * 0.0736 + 2.9) * (1 / (((\u2113 : \u211d) + 14) + 10) ^ 2)\n + (0.433 * Real.log ((\u2113 : \u211d) + 14) / (((\u2113 : \u211d) + 14) + 10) ^ 2)\n + (0.886 * Real.log (Real.log ((\u2113 : \u211d) + 14)) / (((\u2113 : \u211d) + 14) + 10) ^ 2))) := by\n sorry\n\nend TestNS\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && time lake env lean /tmp/test_lam.lean 2>&1 | head -10",
"description": "Test statement elaboration in isolation",
"timeout": 300000
}
raw content_json (database row)
[{"type":"thinking","thinking":"No duplicates (4 = def farGLeftMaj + the three lemmas listed — wait, the grep counted 4 total matches of the pattern \"def farGLeftMaj|lemma farGLeftMaj_combo_summable|lemma farGLeftMaj_shift_le|lemma tail14_inv_add_sq_summable\" — 4 lines ✓ single copies).\n\nSo the isDefEq timeout at `hABC.mul_left _` is real. Let me think about what's REALLY happening: `hABC.mul_left _` — Summable.mul_left — checking its signature:\n\nMaybe in this Mathlib `Summable.mul_left` is `Summable.mul_left {M : Type*} [Semiring M] [TopologicalSpace M] [IsTopologicalSemiring M] {f : ι → M} (r : M) (hf : Summable f) : Summable fun x => r * f x` — hABC.mul_left _ — the FIRST arg is r = ?m, second is hABC ✓. Type: Summable fun x => ?m * ((c0·A + c1·B) + c2·C) x — vs goal fun ℓ => 4.5 * (c0·A ℓ + c1·B ℓ + c2·C ℓ)... — the bodies: ?m * ((A+B)+C) vs 4.5 * (A+B+C) — the ASSOCIATION of the lambda bodies: hABC-body is `A ℓ + B ℓ + C ℓ` parsed as ((A+B)+C)... wait — no! Look at hABC's ascribed type: `fun ℓ => (0.433*0.1942+0.886*0.0736+2.9)·A ℓ + 0.433·B ℓ + 0.886·C ℓ` — hmm — that's also ((A+B)+C). And the goal: `4.5 * (A + B + C)` — the goal lambda from the LEMMA STATEMENT: `4.5 * ((0.433*0.1942+0.886*0.0736+2.9)·(1/..²) + 0.433·(log/..²) + 0.886·(loglog/..²))` — same association ✓.\n\nOK let me stop guessing and bisect directly: comment out the farGLeftMaj section progressively. Actually — better idea: reproduce the timeout in a MINIMAL standalone file to see the real cause:\n\n```lean\nimport Mathlib\nopen Complex Filter Topology MeasureTheory\nnoncomputable section\nlemma test1 : Summable (fun ℓ : ℕ =>\n 4.5 * ((0.433 * 0.1942 + 0.886 * 0.0736 + 2.9) * (1 / (((ℓ : ℝ) + 14) + 10) ^ 2)\n + (0.433 * Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)\n + (0.886 * Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2))) := by\n sorry\n```\n— elaborating the STATEMENT: if that alone hangs, it's the literal forms. Let me test quickly (with sorry to isolate elaboration of the statement).","signature":""},{"type":"text","text":"Let me isolate the pathology with a minimal test file."},{"type":"tool_use","id":"Bash_204","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && cat > /tmp/test_lam.lean <<'EOF'\nimport Mathlib\nopen Complex Filter Topology MeasureTheory\nnoncomputable section\nnamespace TestNS\n\nlemma test1 : Summable (fun ℓ : ℕ =>\n 4.5 * ((0.433 * 0.1942 + 0.886 * 0.0736 + 2.9) * (1 / (((ℓ : ℝ) + 14) + 10) ^ 2)\n + (0.433 * Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)\n + (0.886 * Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2))) := by\n sorry\n\nend TestNS\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && time lake env lean /tmp/test_lam.lean 2>&1 | head -10","description":"Test statement elaboration in isolation","timeout":300000},"extra_content":null}]