Guide · Agent skill
How to use the Proof Writer agent skill
Updated · written with AI from the project's own documentation and checked against our catalogue data
Proof Writer is an agent skill that makes an AI agent draft mathematical proofs for theorems, lemmas, propositions and corollaries, mainly in ML and AI theory. It is aimed at researchers drafting appendix proofs, students checking whether a proof sketch works, and reviewers testing whether a claim is correctly scoped. After this guide you will know what the skill does, how to install it, how to trigger it with plain requests, and what to check in its output.
Proof Writerwanshuiyin/Auto-claude-code-research-in-sleep · MIT Download the skill Quick start
- 1Download the ZIP. Download the proof-writer ZIP from this page.
- 2Unzip into a skills folder. Unzip into ~/.claude/skills/ for personal use, or into the project's .claude/skills/ for a single project.
- 3Or upload in the Claude apps. In the Claude apps, go to Settings → Capabilities → Skills and upload the ZIP.
- 4State the claim and assumptions. Write the exact theorem, lemma or proposition and list its assumptions in your request.
- 5Make the request in plain language. Ask the agent to prove, check or formalize the claim; the skill loads from its description.
- 6Review PROOF_PACKAGE.md. Open the proof document, check the Status line, and read the Corrections and Open Risks sections.
What an agent skill is and what Proof Writer does
An agent skill is a folder containing a SKILL.md file that gives an AI agent specific instructions for one kind of task. When the skill is installed, the agent can load these instructions when a request matches the skill's description.
Proof Writer is designed to write a mathematically honest proof package rather than a polished but possibly invalid proof. Before proving anything, it checks whether the conclusion really follows from the stated assumptions. If it cannot justify the claim, it may report that the claim is only provable after weakening it, or that it is not currently justified.
- Restates the exact claim and separates assumptions from conclusions.
- Classifies the claim as PROVABLE AS STATED, PROVABLE AFTER WEAKENING / EXTRA ASSUMPTION, or NOT CURRENTLY JUSTIFIED.
- Builds a dependency map and numbered proof steps, with justification for each nontrivial implication.
- Writes results to a proof document, by default PROOF_PACKAGE.md in the project root.
- Can optionally call the separate lean-formalize skill for machine-checked verification.
Install Proof Writer
Download the proof-writer ZIP from this page and unzip it. The skill's files go into a skills folder that the agent reads. You can install it for yourself across all projects, or for a single project.
For a personal install, unzip into ~/.claude/skills/. For a project-only install, unzip into the project's .claude/skills/ folder. Alternatively, you can upload the ZIP in the Claude apps under Settings → Capabilities → Skills.
- Personal: ~/.claude/skills/
- Project only: the project's .claude/skills/ folder
- Claude apps: Settings → Capabilities → Skills, then upload the ZIP
Trigger the skill with natural requests
You do not need a special command. The skill's description tells the agent when to use it, so ask in plain language. The description covers requests to prove a theorem, lemma, proposition or corollary, to fill in missing proof steps, to formalize a proof sketch, or to determine whether a claimed proof can be completed under the stated assumptions. It also lists the Chinese phrases 补全证明, 写证明 and 证明某个命题.
State the exact statement and its assumptions in your request. The skill's argument hint is a theorem statement plus assumptions, so including both gives it what it needs.
- Prove this lemma: [statement], under assumptions [list].
- Fill in the missing steps in my proof sketch for Proposition 3 in appendix A.
- Can this corollary actually be proved under the assumptions I listed? Check the scope.
- Formalize this proof sketch in Lean, using the lean-formalize skill.
What you need before running it
Proof Writer needs access to the project files it reads and writes. The source lists the tools Read, Write, Edit, Grep and Glob. Lean formalization is optional and only needed if you ask for it.
If you request Lean formalization, you also need the separate lean-formalize skill and a Lean setup. The source does not describe how to install either, so check those separately.
- Access to project files through Read, Write, Edit, Grep and Glob.
- Only for Lean: the separate lean-formalize skill and a Lean setup.
Safety notes: scripts and network
According to the skill's listing, Proof Writer runs no scripts and uses no network. Its work consists of reading and writing files in your project. The only file it is documented to write by default is PROOF_PACKAGE.md in the project root.
The skill instructs the agent not to write directly into paper sections or appendix .tex files unless you explicitly ask for that target. Review the output file before copying anything into a manuscript.
- Runs scripts: no.
- Uses network: no.
- Writes to PROOF_PACKAGE.md by default, not to paper or .tex files unless you ask.
Read and use the output
Every run should end with a proof document that has a Claim, Status, Assumptions, Notation, Proof Strategy, Dependency Map, numbered Proof steps, Corrections or Missing Assumptions, and Open Risks. The chat reply is brief and reports the status, whether the original claim survived unchanged, and which file was updated.
Treat the proof as a draft. The skill itself says the output can contain errors or gaps it does not catch, so check each step before relying on it.
- Check the Status line first.
- If the status is not PROVABLE AS STATED, read the corrected claim and the blocker.
- Read the Open Risks section for fragile points.
What people use it for
- Drafting an appendix proof for an ML theory paper from a stated theorem and assumptions.
- Checking whether a proof sketch actually works under its listed assumptions.
- Filling in missing steps in a partial proof, with each nontrivial step justified.
- Testing whether a claimed theorem is scoped correctly before submitting it to reviewers.
- Producing a corrected, weaker claim with a proof when the original is too strong.
Frequently asked questions
How do I install the proof-writer skill?
Download the proof-writer ZIP from this page and unzip it into ~/.claude/skills/ for personal use, or into a project's .claude/skills/ folder for one project. You can also upload the ZIP in the Claude apps under Settings → Capabilities → Skills.
Is the proof-writer skill free?
The source lists the skill under the MIT licence. It does not describe pricing for the Claude apps or any other service, so check those separately.
What does Proof Writer need to run?
It needs access to your project files through the Read, Write, Edit, Grep and Glob tools. Lean formalization additionally requires the separate lean-formalize skill and a Lean setup, but only if you request it.
Does Proof Writer run scripts or use the internet?
According to its listing, it runs no scripts and uses no network. It reads and writes files in your project.
Will Proof Writer always produce a proof?
No. It first checks whether the conclusion follows from the stated assumptions. If the claim is not provable as stated, it may report a weaker corrected claim or say the claim is not currently justified, rather than fabricating a proof.
How does Proof Writer compare with Lean formalization?
Proof Writer drafts a structured written proof and can optionally call the lean-formalize skill for machine-checked verification. Ordinary proof drafting does not require Lean, so use Lean when you need formal checking.
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Our verdict
Proof Writer suits ML or AI theory researchers drafting appendix proofs, students checking whether a sketch holds under its assumptions, and reviewers testing claim scope. It is not a substitute for expert review, and it does not handle non-mathematical writing or general coding tasks, so choose another tool for those.
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