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Get Started Free →Search Mathlib for lemmas by type signature pattern using Loogle.
.claude/skills/loogle-search/SKILL.md| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-02 | ✗→✓ | ▲ Improved | 278% | 0% |
| case-04 | ✗→✓ | ▲ Improved | -51% | 0% |
| case-05 | ✗→✓ | ▲ Improved | -15% | 0% |
| case-08 | ✗→✓ | ▲ Improved | -40% | 0% |
| case-10 | ✗→✓ | ▲ Improved | -21% | 0% |
Search Mathlib for lemmas by type signature pattern.
Nontrivial ↔ _ lemmas)bash# Search by pattern (uses server if running, else direct) loogle-search "Nontrivial _ ↔ _" loogle-search "(?a → ?b) → List ?a → List ?b" loogle-search "IsCyclic, center" # JSON output loogle-search "List.map" --json # Start server for fast queries (keeps index in memory) loogle-server &
| Pattern | Meaning | |---------|---------| | _ | Any single type | | ?a, ?b | Type variables (same variable = same type) | | Foo, Bar | Must mention both Foo and Bar | | Foo.bar | Exact name match |
bash# Find lemmas relating Nontrivial and cardinality loogle-search "Nontrivial _ ↔ _ < Fintype.card _" # Find map-like functions loogle-search "(?a → ?b) → List ?a → List ?b" # → List.map, List.pmap, ... # Find everything about cyclic groups and center loogle-search "IsCyclic, center" # → commutative_of_cyclic_center_quotient, ... # Find Fintype.card lemmas loogle-search "Fintype.card"
Loogle must be built first:
bashcd ~/tools/loogle && lake build lake build LoogleMathlibCache # or use --write-index
When stuck in a Lean proof:
lean-- Goal: Nontrivial G from 1 < Fintype.card G -- Query: loogle-search "Nontrivial _ ↔ 1 < Fintype.card _" -- Found: Fintype.one_lt_card_iff_nontrivial exact Fintype.one_lt_card_iff_nontrivial.mpr h
| Case | Status | Duration (ms) | Turns | Tokens | Tool calls | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Without | With | Δ | Without | With | Δ | Without | With | Δ | Without | With | Δ | ||
case-01 | fail→fail | 8,650 | 5,284 | -39% | 1 | 1 | 0% | 1,745 | 817 | -53% | 0 | 0 | — |
case-02 | fail→pass | 5,525 | 3,996 | -28% | 1 | 1 | 0% | 297 | 1,123 | +278% | 0 | 0 | — |
case-03 | fail→fail | 10,220 | 4,689 | -54% | 1 | 1 | 0% | 2,104 | 799 | -62% | 0 | 0 | — |
case-04 | fail→pass | 10,801 | 1,966 | -82% | 1 | 1 | 0% | 1,823 | 887 | -51% | 0 | 0 | — |
case-05 | fail→pass | 9,774 | 4,684 | -52% | 1 | 1 | 0% | 1,700 | 1,448 | -15% | 0 | 0 | — |
case-06 | pass→pass | 8,252 | 7,312 | -11% | 1 | 1 | 0% | 1,388 | 1,077 | -22% | 0 | 0 | — |
case-07 | pass→pass | 10,818 | 1,919 | -82% | 1 | 1 | 0% | 1,781 | 874 | -51% | 0 | 0 | — |
case-08 | fail→pass | 10,242 | 3,337 | -67% | 1 | 1 | 0% | 1,740 | 1,052 | -40% | 0 | 0 | — |
case-09 | pass→pass | 5,108 | 2,187 | -57% | 1 | 1 | 0% | 897 | 970 | +8% | 0 | 0 | — |
case-10 | fail→pass | 6,996 | 2,220 | -68% | 1 | 1 | 0% | 1,291 | 1,016 | -21% | 0 | 0 | — |
case-11 | pass→pass | 6,247 | 1,700 | -73% | 1 | 1 | 0% | 1,032 | 886 | -14% | 0 | 0 | — |
case-12 | fail→fail | 10,627 | 7,604 | -28% | 1 | 1 | 0% | 1,884 | 1,735 | -8% | 0 | 0 | — |
case-13 | fail→fail | 7,988 | 5,216 | -35% | 1 | 1 | 0% | 1,777 | 1,818 | +2% | 0 | 0 | — |
case-14 | pass→pass | 8,812 | 7,108 | -19% | 1 | 1 | 0% | 1,590 | 1,837 | +16% | 0 | 0 | — |
case-15 | pass→pass | 13,035 | 2,795 | -79% | 1 | 1 | 0% | 1,985 | 1,058 | -47% | 0 | 0 | — |
case-16 | fail→pass | 14,120 | 7,480 | -47% | 1 | 1 | 0% | 2,273 | 1,903 | -16% | 0 | 0 | — |
case-17 | fail→pass | 6,789 | 1,608 | -76% | 1 | 1 | 0% | 1,314 | 869 | -34% | 0 | 0 | — |
case-18 | fail→pass | 6,838 | 4,763 | -30% | 1 | 1 | 0% | 1,093 | 1,374 | +26% | 0 | 0 | — |
case-19 | pass→pass | 2,528 | 2,662 | +5% | 1 | 1 | 0% | 389 | 948 | +144% | 0 | 0 | — |
case-20 | pass→pass | 8,788 | 7,304 | -17% | 1 | 1 | 0% | 1,515 | 1,688 | +11% | 0 | 0 | — |
case-21 | pass→pass | 3,825 | 3,496 | -9% | 1 | 1 | 0% | 724 | 1,188 | +64% | 0 | 0 | — |
case-22 | pass→pass | 8,594 | 4,534 | -47% | 1 | 1 | 0% | 1,445 | 1,319 | -9% | 0 | 0 | — |
DecimalAI ran this skill against gemini-3.6-flash twice over the same eval suite — once with the skill loaded and once without — and compared the two runs case by case. 22 cases were attempted, and 19 counted toward the lift figure. The other 3 produced results that are not comparable between the two arms, so they are excluded from the headline rather than averaged into it. The headline lift of +36 percentage points is the difference between those two pass rates over the 19 comparable cases.
Without the skill loaded, the model failed this case. With it loaded, the same prompt on the same model passed. This is one improved case from the latest verified run; every case, including any that regressed, is in the table above.
| Model | Method | Date | Lift |
|---|---|---|---|
| gemini-3.6-flash | verified | 7/30/2026 | +32% |
Other measured skills in the registry, with their headline benchmark lift.