[{"type":"thinking","thinking":"BOTH fail now! test10a with simple coefficients (0.5/0.6) ALSO times out at 12:33 — col 33 is `0.6 * Real.log` — the goal's B-term. So the problem is the GOAL's two-summand form: `Summable (fun ℓ => 0.5·A ℓ + 0.6·B ℓ)` — the ascription elaboration — with testB being the log-form!\n\ntest7's #check (no goal) worked. test10a's goal with A+B times out. The difference: the GOAL `Summable (fun ℓ => 0.5·A ℓ + 0.6·B ℓ)` — the lambda body is `0.5·A ℓ + 0.6·B ℓ` — and the term's type: fun b => 0.5·A b + 0.6·B b — unification... — col 33 is the B-term in the GOAL — maybe the GOAL's elaboration is fine (test1 passed with the big 4.5·(A+B+C) goal!) — the failure is in the TERM-vs-GOAL unification: `fun b => 0.5·A b + 0.6·B b ≡ fun ℓ => 0.5·A ℓ + 0.6·B ℓ` — should be instant!!\n\nHmm — unless the GOAL's `0.6 * Real.log (↑ℓ + 14) / (↑ℓ + 14 + 10) ^ 2` — parses as `(0.6 * Real.log (↑ℓ+14)) / (...)` vs `0.6 * (Real.log (↑ℓ+14) / (...))` — DIVISION PRECEDENCE!! `a * b / c` parses as `(a·b)/c` — and testB.mul_left 0.6 : fun i => 0.6 * (B i) = 0.6·(Real.log X / D²) — while the goal has (0.6·Real.log X)/D² — DIFFERENT groupings — isDefEq must prove (0.6·log X)/D² = 0.6·(log X/D²) — NOT syntactically equal — isDefEq tries to prove it by unfolding division/multiplication — THAT's the explosion!! It tries to unfold HDiv/mul to prove them equal — possibly looping through semiring normalizations.\n\nYES — that's it: `0.433 * Real.log (↑ℓ + 14) / (↑ℓ + 14 + 10) ^ 2` parses as `(0.433 * Real.log (↑ℓ+14)) / ((↑ℓ+14+10)^2)` — but `testB.mul_left 0.433` gives `fun i => 0.433 * (Real.log (↑i+14) / ((↑i+14+10)^2))` — the goal's first summand group is `(0.433·log X)/D²` while the term's is `0.433·(log X/D²)` — isDefEq between these requires actual ring-normalization — and isDefEq is NOT supposed to do that (it's not ring) — it EXPLODES trying to unfold everything (HDiv.hDiv, Inv.inv, instHDiv instances, OfScientific literals with their massive binary representations).\n\nTHE FIX: make the goal's summands match the mul_left's grouping: write the goal as `0.433 * (Real.log (↑ℓ + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)` with EXPLICIT parens around the division: `0.433 * (Real.log X / D²)`. My test1 goal had the same `0.433 * Real.log X / D²` forms — and test1 PASSED (with just sorry)! Because test1's proof was sorry (no term-vs-goal unification needed). test6/test8/test10 all had the exact-vs-goal unification → explosion.\n\nLet me verify: change test10a's goal to `0.6 * (Real.log (↑ℓ+14) / (((ℓ:ℝ)+14)+10)^2)` (parens) and see if it passes.","signature":""},{"type":"text","text":"Found it — division precedence: `a * b / c` parses as `(a·b)/c`, but `mul_left c` gives `c·(b/c)` — isDefEq explodes proving them equal. Testing with explicit parens."},{"type":"tool_use","id":"Bash_221","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && cat > /tmp/test_lam11.lean <<'EOF'\nimport Mathlib\nopen Complex Filter Topology MeasureTheory\nnoncomputable section\nnamespace TestNS\n\nlemma testA : Summable (fun ℓ : ℕ => (1:ℝ) / (((ℓ:ℝ)+14)+10)^2) := by sorry\nlemma testB : Summable (fun ℓ : ℕ => Real.log ((ℓ:ℝ)+14) / (((ℓ:ℝ)+14)+10)^2) := by sorry\nlemma testC : Summable (fun ℓ : ℕ => Real.log (Real.log ((ℓ:ℝ)+14)) / (((ℓ:ℝ)+14)+10)^2) := by sorry\n\n-- goal with EXPLICIT parens matching mul_left's grouping\nlemma test11 : 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  have hAB : Summable (fun ℓ : ℕ =>\n      (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    (testA.mul_left (0.433*0.1942+0.886*0.0736+2.9)).add (testB.mul_left 0.433)\n  have hABC : Summable (fun ℓ : ℕ =>\n      (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)) :=\n    hAB.add (testC.mul_left 0.886)\n  exact hABC.mul_left 4.5\n\nend TestNS\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && time lake env lean /tmp/test_lam11.lean 2>&1 | head -10","description":"Test with parens matching mul_left grouping","timeout":300000},"extra_content":null}]