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lean-math-foundations

Guide Lean 4 formalization with universe management and Prop/Type distinctions.

2|Updated May 26, 2026
Search Tags:#lean4#formalization#foundations#category-theory#mathlib4#typeuniverses#prop-type
One-click install
npx skills add https://github.com/r-irbe/proof-skills --skill lean-math-foundations
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: lean-math-foundations
Source: https://github.com/r-irbe/proof-skills/tree/main/skills/lean-math-foundations
Command: npx skills add https://github.com/r-irbe/proof-skills --skill lean-math-foundations

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Provides foundational reasoning and patterns for Lean 4 formalization, including universe management, Prop/Type distinctions, and Mathlib's algebraic hierarchy, enabling robust foundational libraries.

Core Features & Use Cases

  • Foundation patterns for Lean type system design (Prop/Type, universes, classical vs constructive choices) across mathematical domains.
  • Guidance on using Mathlib's typeclass hierarchy (Group, Ring, Module, Category Theory basics) and domain conventions for scalable formalizations.
  • Real-world workflows: structure a new formalization with clean universe levels and a coherent hierarchy, then share reusable components across projects.

Quick Start

Start by reading the foundational routing notes and references, then open a small Lean project to explore universe levels and Prop/Type distinctions.

Frequently Asked Questions about lean-math-foundations

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

FAQPage Schema
How do I manage universe levels in Lean 4 formalization?▼

Managing universe levels in Lean 4 formalization requires distinguishing between Prop and Type universes to maintain coherent typeclass hierarchies. This Skill provides foundational reasoning patterns to automate and guide clean universe structuring across mathematical domains.

How do I use Mathlib's typeclass hierarchy for category theory proofs?▼

Using Mathlib's typeclass hierarchy for category theory proofs involves applying algebraic structures like Group, Ring, and Module correctly. This Skill provides guidance on navigating Mathlib's typeclass hierarchy and domain conventions to build scalable formalizations.

What is the difference between Prop and Type in Lean 4 and when does it matter?▼

The difference between Prop and Type in Lean 4 dictates classical versus constructive proof choices and impacts universe management. This Skill clarifies Prop/Type distinctions, ensuring robust foundational libraries and consistent discipline in proof development.

Can I structure a new Lean 4 formalization project with clean type universes?▼

Yes, you can structure a new Lean 4 formalization project with clean type universes and a coherent hierarchy. This Skill enables real-world workflows for structuring domain theory libraries and sharing reusable components across projects.

Does this approach support domain theory and categorically structured proofs in Lean 4?▼

Yes, this approach supports domain theory and categorically structured proofs in Lean 4. It is applicable to tasks where universes and classical versus constructive choices matter, satisfying routing and handoff guidance for consistent proof development.

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