name: openmath-lean-theorem description: Configures Lean environments, installs external proof skills, runs preflight checks, and guides the workflow for proving downloaded OpenMath Lean theorems locally. version: v1.2.0 requirements: commands: - lean - lake - elan side_effects:

• May install third-party Lean skills into a selected skills directory when preflight is run with --auto-install-skills

OpenMath Lean Theorem

Instructions

Set up the Lean proving environment, validate toolchains, and prove downloaded OpenMath theorems locally. Assumes the theorem workspace was already created by the openmath-open-theorem skill.

Workflow checklist

• Environment: Verify lean, lake, and elan are installed and match the workspace lean-toolchain.
• External skills: Install required Lean proof skills from leanprover/skills. Preferred manual install:

  npx leanprover-skills install lean-proof
  npx leanprover-skills install mathlib-build
  

  If you use preflight auto-install, pass an explicit target such as --install-dir .codex/skills or --install-dir .claude/skills so the write location is deliberate.
• Preflight: Run python3 scripts/check_theorem_env.py <workspace> (see references/preflight.md).
• Prove: Use lean-proof / mathlib-build skills to complete the proof. See references/proof_playbook.md for the OpenMath-specific proving loop.
• Verify: Confirm lake build -q --log-level=info passes and no sorry remains.
• Submit: Use the openmath-submit-theorem skill to hash and submit the proof.

Scripts

Notes

• Lean version: Scaffolds pin leanprover/lean4:v4.28.0 and mathlib4 v4.28.0 (set by openmath-open-theorem's download_theorem.py).
• External skills: Not bundled. Required: lean-proof, mathlib-build. Optional: lean-mwe, lean-bisect, nightly-testing, mathlib-review, lean-setup. Manual npx leanprover-skills install ... is preferred; preflight auto-install clones the upstream repo and copies the missing directories into the selected skills dir.
• Benchmarking: For agent evaluation, prompt comparison, or regression testing on the bundled Lean benchmark corpus, use the separate openmath-lean-benchmark skill.

References

Load when needed (one level from this file):

• references/preflight.md — Preflight command and Lean/Rocq checks.
• references/proof_playbook.md — Step-by-step workflow for proving a downloaded Lean theorem locally.
• references/languages.md — Lean version and standard library.