Individual skill
lean4-theorem-proving
Use when working with Lean 4 (.lean files), writing mathematical proofs, seeing "failed to synthesize instance" errors, managing sorry/axiom elimination, or searching mathlib for lemmas - provides build-first workflow, haveI/letI patterns, compiler-guided repair, and LSP integration
tasks/lean4-proof/environment/skills/lean4-theorem-proving/SKILL.md
Source commit f860ecf02ef53412a030f8661c83d644b739ff01
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- Observed behavior
- Instructions only
- Last checked
- Nov 9, 2026
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Repository context
- Repository stars (not skill ratings)
- 1,915
- Repository last updated
- Nov 4, 2026
- License
- Apache-2.0
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- skillsbench Repository topic
- operations Derived category
- writing Derived category
Files and excerpt
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Browse files
SKILL.mdcore · 9,006 bytesreferences/axiom-elimination.mddoc · 6,011 bytesreferences/calc-patterns.mddoc · 8,865 bytesreferences/compilation-errors.mddoc · 20,585 bytesreferences/compiler-guided-repair.mddoc · 18,713 bytesreferences/domain-patterns.mddoc · 25,461 bytesreferences/instance-pollution.mddoc · 16,176 bytesreferences/lean-lsp-server.mddoc · 9,155 bytesreferences/lean-lsp-tools-api.mddoc · 25,937 bytesreferences/lean-phrasebook.mddoc · 17,026 bytesreferences/mathlib-guide.mddoc · 13,881 bytesreferences/mathlib-style.mddoc · 8,709 bytesreferences/measure-theory.mddoc · 28,139 bytesreferences/performance-optimization.mddoc · 16,706 bytesreferences/proof-golfing-patterns.mddoc · 11,462 bytesreferences/proof-golfing-safety.mddoc · 5,934 bytesreferences/proof-golfing.mddoc · 3,646 bytesreferences/proof-refactoring.mddoc · 28,903 bytesreferences/sorry-filling.mddoc · 4,875 bytesreferences/subagent-workflows.mddoc · 18,179 bytesreferences/tactics-reference.mddoc · 16,421 bytes
Read excerpt
# Lean 4 Theorem Proving
## Core Principle
**Build incrementally, structure before solving, trust the type checker.** Lean's type checker is your test suite.
**Success = `lake build` passes + zero sorries + zero custom axioms.** Theorems with sorries/axioms are scaffolding, not results.
## Quick Reference
| **Resource** | **What You Get** | **Where to Find** |
|--------------|------------------|-------------------|
| **Interactive Commands** | 10 slash commands for search, analysis, optimization, repair | Type `/lean` in Claude Code ([full guide](../../COMMANDS.md)) |
| **Automation Scripts** | 19 tools for search, verification, refactoring, repair | Plugin `scripts/` directory ([scripts/README.md](../../scripts/README.md)) |