Orca CLI
stablyai/orca
Operate Orca-managed worktrees, folder contexts, terminals, repos, automations, artifacts, skill sharing, worktree comments, and Orca's embedded browser…
A skill your agent uses when working with Lean 4 (.lean files), writing mathematical proofs, seeing "failed to synthesize instance" errors, managing sorry/axiom elimination, or searching mathlib for…
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-proving --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .claude/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .claude/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .claude/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-provingType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-proving --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .agents/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .agents/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .agents/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-proving --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .cursor/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .cursor/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/benchflow-ai/skillsbench.git --path tasks/lean4-proof/environment/skills/lean4-theorem-proving--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-proving --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .gemini/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .gemini/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-provingInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .github/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .github/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .github/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install benchflow-ai/skillsbench lean4-theorem-proving --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/benchflow-ai/skillsbench.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/tasks/lean4-proof/environment/skills/lean4-theorem-proving .opencode/skills/lean4-theorem-proving && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "lean4-theorem-proving" agent skill from https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lean4-proof/environment/skills/lean4-theorem-proving into .opencode/skills/lean4-theorem-proving/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean4-theorem-proving", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
lean4-theorem-provingA skill your agent uses when working with Lean 4 (.lean files), writing mathematical proofs, seeing "failed to synthesize instance" errors, managing sorry/axiom elimination, or searching mathlib for…
Lean4 Theorem Proving is an agent skill from benchflow-ai/skillsbench. 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
Its SKILL.md is about 2.2k tokens, which your agent loads only when the skill is triggered. The skill folder holds 21 other files, including reference files (for example `references/axiom-elimination.md`, `references/calc-patterns.md` and `references/compilation-errors.md`).
It sits in Agent Workflows. The repository describes itself as: SkillsBench evaluates how well skills work and how effective agents are at using them. The licence is Apache-2.0.
4 steps, taken from the first numbered list in SKILL.md.
Read from SKILL.md and the folder at commit 9a1f4dd. It shows what the files ask for, not the result of running them.
Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.
From allowed-tools in the SKILL.md frontmatter.
No scripts in the folder and no shell commands in SKILL.md.
From the folder's file list and the shell code blocks in SKILL.md.
Links to these hosts (documentation or services it may open):
arxiv.orgFrom URLs in SKILL.md, links to its own repository left out.
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Lean4 Theorem Proving loads about 2.2k tokens when it runs, and up to ~78k if it reads all its reference files. Until then it costs about 76 tokens; SKILL.md has 849 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
The automated check found no risky patterns in SKILL.md.
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
The full file from benchflow-ai/skillsbench at commit 9a1f4dd, republished under its Apache-2.0 licence (© benchflow-ai). 849 words, ~2,245 tokens.
.claude/skills/lean4-theorem-proving/SKILL.md (or your agent's skills folder). This skill also uses 20 other files; get the full folder from GitHub.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.
| Resource | What You Get | Where to Find |
|---|---|---|
| Interactive Commands | 10 slash commands for search, analysis, optimization, repair | Type /lean in Claude Code (full guide) |
| Automation Scripts | 19 tools for search, verification, refactoring, repair | Plugin scripts/ directory (scripts/README.md) |
| Subagents | 4 specialized agents for batch tasks (optional) | subagent-workflows.md |
| LSP Server | 30x faster feedback with instant proof state (optional) | lean-lsp-server.md |
| Reference Files | 18 detailed guides (phrasebook, tactics, patterns, errors, repair, performance) | List below |
Use for ANY Lean 4 development: pure/applied math, program verification, mathlib contributions.
Critical for: Type class synthesis errors, sorry/axiom management, mathlib search, measure theory/probability work.
7 slash commands for search, analysis, and optimization - type /lean in Claude Code. See COMMANDS.md for full guide with examples and workflows.
16 automation scripts for search, verification, and refactoring. See scripts/README.md for complete documentation.
Lean LSP Server (optional) provides 30x faster feedback with instant proof state and parallel tactic testing. See lean-lsp-server.md for setup and workflows.
Subagent delegation (optional, Claude Code users) enables batch automation. See subagent-workflows.md for patterns.
ALWAYS compile before committing. Run lake build to verify. "Compiles" ≠ "Complete" - files can compile with sorries/axioms but aren't done until those are eliminated.
have statements and documented sorries before writing tacticshaveI/letI when synthesis fails, respect binder order for sub-structuresPhilosophy: Search before prove. Mathlib has 100,000+ theorems.
Use /search-mathlib slash command, LSP server search tools, or automation scripts. See mathlib-guide.md for detailed search techniques, naming conventions, and import organization.
Key tactics: simp only, rw, apply, exact, refine, by_cases, rcases, ext/funext. See tactics-reference.md for comprehensive guide with examples and decision trees.
Analysis & Topology: Integrability, continuity, compactness patterns. Tactics: continuity, fun_prop.
Algebra: Instance building, quotient constructions. Tactics: ring, field_simp, group.
Measure Theory & Probability (emphasis in this skill): Conditional expectation, sub-σ-algebras, a.e. properties. Tactics: measurability, positivity. See measure-theory.md for detailed patterns.
Complete domain guide: domain-patterns.md
Standard mathlib axioms (acceptable): Classical.choice, propext, quot.sound. Check with #print axioms theorem_name or /check-axioms.
CRITICAL: Sorries/axioms are NOT complete work. A theorem that compiles with sorries is scaffolding, not a result. Document every sorry with concrete strategy and dependencies. Search mathlib exhaustively before adding custom axioms.
When sorries are acceptable: (1) Active work in progress with documented plan, (2) User explicitly approves temporary axioms with elimination strategy.
Not acceptable: "Should be in mathlib", "infrastructure lemma", "will prove later" without concrete plan.
When proofs fail to compile, use iterative compiler-guided repair instead of blind resampling.
Quick repair: /lean4-theorem-proving:repair-file FILE.lean
How it works:
rfl → simp → ring → linarith → nlinarith → omega → exact? → apply? → aesoplean4-proof-repair agent:Key benefits:
Expected outcomes: Success improves over time as structured logging enables learning from attempts. Cost optimized through solver cascade (free) and multi-stage escalation.
Commands:
/repair-file FILE.lean - Full file repair/repair-goal FILE.lean LINE - Specific goal repair/repair-interactive FILE.lean - Interactive with confirmationsDetailed guide: compiler-guided-repair.md
Inspired by: APOLLO (https://arxiv.org/abs/2505.05758) - compiler-guided repair with multi-stage models and low sampling budgets.
| Error | Fix |
|---|---|
| "failed to synthesize instance" | Add haveI : Instance := ... |
| "maximum recursion depth" | Provide manually: letI := ... |
| "type mismatch" | Use coercion: (x : ℝ) or ↑x |
| "unknown identifier" | Add import |
See compilation-errors.md for detailed debugging workflows.
private or in dedicated sectionsexample for educational code, not lemma/theoremBefore commit:
lake build succeeds on full projectDoing it right: Sorries/axioms decrease over time, each commit completes one lemma, proofs build on mathlib.
Red flags: Sorries multiply, claiming "complete" with sorries/axioms, fighting type checker for hours, monolithic proofs (>100 lines), long have blocks (>30 lines should be extracted as lemmas - see proof-refactoring.md).
Core references: lean-phrasebook.md, mathlib-guide.md, tactics-reference.md, compilation-errors.md
Domain-specific: domain-patterns.md, measure-theory.md, instance-pollution.md, calc-patterns.md
Incomplete proofs: sorry-filling.md, axiom-elimination.md
Optimization & refactoring: performance-optimization.md, proof-golfing.md, proof-refactoring.md, mathlib-style.md
Automation: compiler-guided-repair.md, lean-lsp-server.md, lean-lsp-tools-api.md, subagent-workflows.md
© benchflow-ai, Apache-2.0. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
SKILL.md and 20 other files (references) in tasks/lean4-proof/environment/skills/lean4-theorem-proving of benchflow-ai/skillsbench.
Open the folder on GitHubat commit 9a1f4dd
Lean4 Theorem Proving next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Lean4 Theorem Proving this skillbenchflow-ai/skillsbench | 1.8k | — | ~2.2k | Automated safety check: Pass | Apache-2.0 | |
| Orca CLIstablyai/orca | 88k | 2 repos | ~593 | Automated safety check: Pass | MIT | |
| OpenSpec Guided OnboardingFission-AI/OpenSpec | 71k | 1 repos | ~4.5k | Automated safety check: Pass | MIT | |
| Claude Code Plugin Structureanthropics/claude-plugins-official | 38k | 10 repos | ~3.4k | Automated safety check: Pass | Apache-2.0 | |
| Neat-Freak Knowledge CloseoutKKKKhazix/khazix-skills | 21k | — | ~1.9k | Automated safety check: Pass | MIT | |
| O2 Review Loopopenobserve/openobserve | 22k | — | ~3.7k | Automated safety check: Pass | AGPL-3.0 |
stablyai/orca
Operate Orca-managed worktrees, folder contexts, terminals, repos, automations, artifacts, skill sharing, worktree comments, and Orca's embedded browser…
Fission-AI/OpenSpec
Walks you through a complete OpenSpec workflow cycle with narration while doing real work in your codebase.
anthropics/claude-plugins-official
Explains the directory layout, plugin.json manifest and component organization of a Claude Code plugin, including auto-discovery and portable paths.
KKKKhazix/khazix-skills
Brings project docs, agent rule files, authorized memory and leftover workspace files back in line with what the code and runtime actually do at the end of a work session.
openobserve/openobserve
Splits a change into planner, coder and independent reviewer roles: you confirm a spec, a subagent implements it, and a separate reviewer checks each round's local WIP commit.
uditgoenka/autoresearch
Runs an autonomous modify, verify, keep-or-discard loop against any metric, with subcommands for planning, debugging, fixing, security audits, shipping and more.
benchflow-ai/skillsbench
This skill should be used when working on Lean 4 formalization projects to maintain persistent memory of successful proof patterns, failed approaches, project conventions, and user preferences…
benchflow-ai/skillsbench
World-class data engineering skill for building scalable data pipelines, ETL/ELT systems, real-time streaming, and data infrastructure.
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Categories
A skill your agent uses when working with Lean 4 (.lean files), writing mathematical proofs, seeing "failed to synthesize instance" errors, managing sorry/axiom elimination, or searching mathlib for…. Lean4 Theorem Proving is an agent skill from benchflow-ai/skillsbench.
Lean4 Theorem Proving fits situations like: working with Lean 4 (.lean files); writing mathematical proofs; seeing failed to synthesize instance errors; managing sorry/axiom elimination.
Run `npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a claude-code`. Or copy the skill folder (tasks/lean4-proof/environment/skills/lean4-theorem-proving in benchflow-ai/skillsbench) into .claude/skills/lean4-theorem-proving in your project. Claude Code loads it when a task matches its description.
Run `npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a codex`. Or copy the skill folder (tasks/lean4-proof/environment/skills/lean4-theorem-proving in benchflow-ai/skillsbench) into .agents/skills/lean4-theorem-proving in your project. Codex loads it when a task matches its description.
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add benchflow-ai/skillsbench --skill lean4-theorem-proving -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/lean4-theorem-proving, .gemini/skills/lean4-theorem-proving, .github/skills/lean4-theorem-proving and .opencode/skills/lean4-theorem-proving in your project.
SKILL.md names no scripts, command-line tools or credentials: Lean4 Theorem Proving is instructions for the agent only.
SKILL.md names 1 domain. As links in the text: arxiv.org. This is read from the text; nothing was executed.
Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.
Lean4 Theorem Proving is published under the Apache-2.0 licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
About 2.2k tokens (SKILL.md is roughly 9k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full. Its references folder adds about 76k tokens, read only when the agent opens those files.
Skills that share tags, products or a category with Lean4 Theorem Proving: Orca CLI (stablyai/orca, 88k stars), OpenSpec Guided Onboarding (Fission-AI/OpenSpec, 71k stars), Claude Code Plugin Structure (anthropics/claude-plugins-official, 38k stars) and Neat-Freak Knowledge Closeout (KKKKhazix/khazix-skills, 21k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
benchflow-ai (a GitHub organization) maintains it in benchflow-ai/skillsbench, which has 1,834 GitHub stars. The repository holds 189 skills in this directory. The repository was last updated on July 23, 2026.
Source: benchflow-ai/skillsbench on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.