proof-writer

Generate formal ML/AI theory proofs with explicit assumptions and notation.

Updated Mar 17, 2026

Search Tags:#mathematics #formal-verification #proof #theorem #proof-writing #ml-theory

Ready to run

npx skills add https://github.com/loujc/Auto-claude-code-research-in-sleep-manual --skill proof-writer-loujc

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: proof-writer
Source: https://github.com/loujc/Auto-claude-code-research-in-sleep-manual/tree/main/skills/proof-writer
Command: npx skills add https://github.com/loujc/Auto-claude-code-research-in-sleep-manual --skill proof-writer-loujc

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Writes mathematically rigorous proofs for ML/AI theory on demand, including completing missing steps and formalizing proof sketches across theorem, lemma, proposition, or corollary statements.

Core Features & Use Cases

Proof construction: generate complete proofs or corrected claims from user input.
Proof normalization & documentation: clarify statements, assumptions, and notation, and produce a reusable proof package.
Use Case: researchers request a formal PROOF_PACKAGE.md for a new lemma in optimization or learning theory.

Quick Start

Prove or critique the provided theorem draft and return a complete PROOF_PACKAGE.md

Frequently Asked Questions about proof-writer

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I write rigorous mathematical proofs for machine learning theory?▼

To write rigorous mathematical proofs for ML theory, you need a process that delineates exact claims, assumptions, and notation. This generates a formal proof package by completing missing steps and formalizing proof sketches into verified theorem statements.

Can I formalize a proof sketch into a complete theorem proof?▼

Yes, formalizing a proof sketch into a complete theorem proof involves taking an incomplete mathematical argument and applying rigorous normalization. This clarifies statements and assumptions to produce a reusable proof package with all missing steps justified.

What is the best way to document assumptions and notation for optimization lemmas?▼

Documenting assumptions and notation for optimization lemmas requires proof normalization, which explicitly delineates exact claims and available proof sketches. This process produces a formal package that clarifies all mathematical statements for learning theory research.

How do I critique and correct a drafted ML theorem statement?▼

To critique and correct a drafted ML theorem statement, you evaluate the provided assumptions and notation against the exact claim. This generates a justified critique or a corrected formal proof package identifying logical gaps or missing mathematical steps.

Does formal verification work for generating proofs across different mathematical statement types?▼

Formal verification applies to generating proofs across theorem, lemma, proposition, and corollary statements. It takes user input drafts and produces a complete, rigorous mathematical proof package with explicit notation and assumptions for machine learning theory.