Lean Learnings

Community

scottnarmstrong

lean-learnings

Reusable Lean 4 and Mathlib lessons for analysis formalizations. Use when choosing an ambient carrier or repository layout, debugging elaboration and typeclass costs, preserving constant dependencies, or looking for recurring proof and API patterns.

Overview

Publisher	scottnarmstrong
Repository	`LeanAutoformalizationSkills`
Skill name	`lean-learnings`
Stars	66
Forks	7
Bundled files	6
License	CC-BY-4.0
Links	Skill source Repository

Markdown instructions
A SKILL.md file the model loads on demand, so it only costs tokens when a request actually matches.
Works with any LLM
AI skills are plain Markdown, not provider-specific code, so this works with GPT, Claude, Gemini, Grok, or a local model.
6 bundled files
Scripts, templates, and references the model can read while it works. Files are read-only and never executed.
Open source
Published by scottnarmstrong on GitHub. Read the source before you install it.

Installation

Install the Lean Learnings AI skill in TypingMind to use it with any LLM, or drop it into another agent that reads SKILL.md.

Install in TypingMind

TypingMind installs a skill straight from its GitHub folder — it reads SKILL.md, bundles the resource files, and stores the result locally.

Open the app and go to Plugins → Skills.
Choose "Install from GitHub".
Paste the skill folder URL below and confirm.
https://github.com/scottnarmstrong/LeanAutoformalizationSkills/tree/main/skills/lean-learnings
Enable the skill in any chat where you want it available.

Store

Installed

Skills

Add skills

Import one or more skills from a public GitHub folder or a local .skill or .zip archive, or SKILL.md file.

From GitHub URLFrom .skill, .zip, or SKILL.md

GitHub repo or folder

https://github.com/scottnarmstrong/LeanAutoformalizationSkills/tree/main/skills/lean-learnings

Points to a single skill folder, or any folder that contains multiple skills. Public repos only.

CancelContinue

Plugins → Skills → Add skill → From GitHub URL, then paste the folder URL and press Continue.

Install in another agent

Any agent that reads the Agent Skills format can use this skill — copy the folder into that agent's skills directory.

Claude Code — .claude/skills

git clone --depth 1 https://github.com/scottnarmstrong/LeanAutoformalizationSkills.git /tmp/LeanAutoformalizationSkills
mkdir -p .claude/skills
cp -r /tmp/LeanAutoformalizationSkills/skills/lean-learnings .claude/skills/lean-learnings

Restart Claude Code after copying so it picks up the new skill.

Use it in TypingMind

Enable Lean Learnings in any TypingMind chat and the model takes it from there. Its name and description sit in the system prompt, and the moment a request matches, the model loads the full instructions itself — you never invoke it by hand, and it costs no tokens until it is actually used.

The model loads Lean Learnings on its own as soon as a request matches it.

Works with any AI model

AI skills are plain Markdown instructions rather than provider-specific code, so Lean Learnings is not tied to the model it was written for. Install it once in TypingMind and use it with GPT-5, Claude, Gemini, Grok, DeepSeek, Mistral, Llama, or a local model you run yourself — all on your own API keys.

Loaded only when it is needed
The system prompt carries just the name and description. The instructions are fetched on the first matching request, so an idle skill costs nothing.
Switch models mid-chat
Because the skill is instructions rather than code, changing model does not break it — the next model reads the same SKILL.md.

Skill instructions

This is the SKILL.md content the model loads. Read it before installing — a skill is instructions your model will follow.

Lean Learnings

Use these empirical lessons as hypotheses to test, not as universal policy. Check the repository's own instructions, inspect the definitions and imports in the current version of Mathlib, profile before changing architecture, and A/B any performance intervention.

Reference map

Situation	Reference
Organizing modules, imports, and namespaces	references/repo_structure_policy.md
Diagnosing expensive carriers, instances, or large proofs	references/Lean4_EuclideanSpace_Elaboration_Guide.md
Planning an analysis, PDE, or probability development	references/dos_and_donts.md
Constant dependencies, quantifiers, Mathlib idioms, and proof shapes	references/lean_learnings.md
Variational PDE, multiscale, Besov, locality, concentration, and compiler-gate recipes	references/advanced_analysis_patterns.md

Working principles

Treat the dependency set and quantifier order of every public constant as part of the theorem. Audit types and instance arguments as well as named binders.
Keep source statements, source dependency topology, Lean declarations, and Lean proof status distinct. A source dependency graph records source topology; it does not certify a Lean proof.
Do not add axioms, placeholders, or proof-step hypotheses to make a theorem elaborate. Preserve the mathematical statement and change the proof or API.
Profile the dominant phase before restructuring. Narrow imports, helper extraction, explicit arguments, local instance caches, and carrier changes address different causes.
Treat EuclideanSpace, direct Pi types, bundled Lp, and bare functions as design choices with different APIs and elaboration costs. Change carriers only after checking the mathematics, downstream API, and measured cost.
Keep nonlinear and transcendental expressions opaque while proving small algebraic side lemmas. Prefer controlled rewriting and minimal automation.
Preserve dependency build artifacts according to the current repository's build policy. Never turn a project-specific cache rule into a general Lake command.
Record a reproducible lesson: Lean/Mathlib version, minimal trigger, measured symptom, intervention, and an A/B check.

Related skills

lean-workflow — router for choosing the appropriate Lean workflow
lean-project-architecture — declarations, module boundaries, and reusable APIs
lean-proof-patterns — stable translations from mathematics to Lean proofs
lean-search-discovery — finding existing Mathlib declarations
lean-elaboration — profiling and improving elaboration performance
lean-statement-audit — source, binder, semantics, consumption, and axiom checks
build-proof-dependency-graph — source-level dependency topology

Bundled files

The model reads these on demand while the skill is loaded. They are exposed as readable files and are never executed.

Frequently asked questions

What does the Lean Learnings AI skill do?

Why use Lean Learnings on TypingMind?

Because you install it once and use it with any model. Lean Learnings is plain Markdown rather than provider-specific code, so the same skill runs on GPT-5, Claude, Gemini, Grok, or a local model — and you can switch model mid-chat without it breaking. TypingMind runs on your own API keys, so you pay providers directly instead of a per-seat subscription, and your skills and chats stay in your own storage.

How do I install Lean Learnings in TypingMind?

Open Plugins → Skills → Install from GitHub in TypingMind and paste https://github.com/scottnarmstrong/LeanAutoformalizationSkills/tree/main/skills/lean-learnings. TypingMind reads its SKILL.md and bundles its files and installs it as a skill you can enable per chat.

Which AI models can use Lean Learnings?

Any model you connect in TypingMind. AI skills are plain Markdown instructions rather than provider-specific code, so GPT, Claude, Gemini, Grok, and local models can all load this skill when a request matches it.

How many AI models can I use with Lean Learnings?

As many as you like. As long as a model supports skills, you can use Lean Learnings with it — GPT, Claude, Gemini, Grok, DeepSeek, Mistral, Llama and more — all on TypingMind with your own API keys.

Is the Lean Learnings AI skill free?

Yes. It is published on GitHub by scottnarmstrong under the CC-BY-4.0 license. You only pay your own AI provider for the tokens you use.

What are AI skills?

An AI skill is a reusable instruction bundle that teaches an AI model how to do one specific task. It follows the open Agent Skills format: a SKILL.md file with a name and description, plus any scripts, templates or reference files the model may need. The model reads the instructions only when your request matches the skill, so an installed skill costs nothing until it is used.

How are AI skills different from plugins or MCP servers?

A plugin or MCP server gives a model new tools to call — code that runs somewhere and returns a result. An AI skill gives the model knowledge and process instead: how to approach a task, which steps to follow, what good output looks like. Skills are plain Markdown, so they need no server, no API key and no runtime, and they work with any model.

View all

Deslop

openclaw

OrganizationPopular

Diff-scoped AI-slop cleanup pass: strip comment slop, defensive-check slop, type-laundering, and style drift from the current branch diff before autoreview.

Discord Clawd

Use to talk to the Discord-backed OpenClaw agent/session; not for archive search.

Discrawl

Discord archive: search, sync freshness, DMs, summaries, TUI, repo/release work.

Gitcrawl

GitHub archive: issue/PR search, sync freshness, duplicate clusters, current GitHub handoff, and Gitcrawl repo work.

Overview

Installation

Install in TypingMind

Install in another agent

Use it in TypingMind

Works with any AI model

Skill instructions

Lean Learnings

Reference map

Working principles

Related skills

Bundled files

Frequently asked questions

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